LMFDB - Embedded newform 9.12.c.a.7.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,12,Mod(4,9)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9.4");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	9.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.91508862504$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 9863 x^{18} + 40416552 x^{16} + 89424581388 x^{14} + 116167273852206 x^{12} + \cdots + 59\!\cdots\!24 $ x^20 + 9863x^18 + 40416552x^16 + 89424581388x^14 + 116167273852206x^12 + 90155066123992770x^10 + 40615438428348034476x^8 + 9750032167348768665084x^6 + 1016547159346572680888121x^4 + 22772285013675084656406191*x^2 + 59348899944549565171293124
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{45} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.6
Root			$1.73070i$ of defining polynomial
Character	$\chi$	$=$	9.7
Dual form			9.12.c.a.4.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.00116679 + 0.00202094i) q^{2} +(35.8201 + 419.361i) q^{3} +(1024.00 + 1773.62i) q^{4} +(-5478.49 - 9489.02i) q^{5} +(-0.889299 - 0.416917i) q^{6} +(-31655.6 + 54829.1i) q^{7} -9.55835 q^{8} +(-174581. + 30043.1i) q^{9} +O(q^{10})$	\(q+(-0.00116679 + 0.00202094i) q^{2} +(35.8201 + 419.361i) q^{3} +(1024.00 + 1773.62i) q^{4} +(-5478.49 - 9489.02i) q^{5} +(-0.889299 - 0.416917i) q^{6} +(-31655.6 + 54829.1i) q^{7} -9.55835 q^{8} +(-174581. + 30043.1i) q^{9} +25.5690 q^{10} +(-210274. + 364206. i) q^{11} +(-707108. + 492957. i) q^{12} +(-411718. - 713117. i) q^{13} +(-73.8710 - 127.948i) q^{14} +(3.78309e6 - 2.63736e6i) q^{15} +(-2.09715e6 + 3.63237e6i) q^{16} +2.83043e6 q^{17} +(142.984 - 387.872i) q^{18} +9.56151e6 q^{19} +(1.12199e7 - 1.94335e7i) q^{20} +(-2.41271e7 - 1.13112e7i) q^{21} +(-490.693 - 849.905i) q^{22} +(2.24591e7 + 3.89002e7i) q^{23} +(-342.381 - 4008.40i) q^{24} +(-3.56136e7 + 6.16846e7i) q^{25} +1921.56 q^{26} +(-1.88524e7 - 7.21363e7i) q^{27} -1.29661e8 q^{28} +(2.76388e7 - 4.78719e7i) q^{29} +(915.884 + 10722.7i) q^{30} +(1.13073e8 + 1.95847e8i) q^{31} +(-14681.6 - 25429.3i) q^{32} +(-1.60266e8 - 7.51351e7i) q^{33} +(-3302.52 + 5720.14i) q^{34} +6.93700e8 q^{35} +(-2.32056e8 - 2.78876e8i) q^{36} +2.57577e7 q^{37} +(-11156.3 + 19323.3i) q^{38} +(2.84306e8 - 1.98203e8i) q^{39} +(52365.3 + 90699.4i) q^{40} +(-1.99518e8 - 3.45576e8i) q^{41} +(51010.5 - 35561.7i) q^{42} +(-2.26306e8 + 3.91974e8i) q^{43} -8.61284e8 q^{44} +(1.24152e9 + 1.49201e9i) q^{45} -104820. q^{46} +(-7.54076e8 + 1.30610e9i) q^{47} +(-1.59840e9 - 7.49352e8i) q^{48} +(-1.01549e9 - 1.75888e9i) q^{49} +(-83107.3 - 143946. i) q^{50} +(1.01386e8 + 1.18697e9i) q^{51} +(8.43199e8 - 1.46046e9i) q^{52} -1.27376e9 q^{53} +(167780. + 46068.4i) q^{54} +4.60794e9 q^{55} +(302575. - 524076. i) q^{56} +(3.42494e8 + 4.00973e9i) q^{57} +(64497.5 + 111713. i) q^{58} +(-3.21846e9 - 5.57453e9i) q^{59} +(8.55156e9 + 4.00910e9i) q^{60} +(3.21169e9 - 5.56280e9i) q^{61} -527728. q^{62} +(3.87922e9 - 1.05231e10i) q^{63} -8.58993e9 q^{64} +(-4.51119e9 + 7.81361e9i) q^{65} +(338840. - 236221. i) q^{66} +(6.99828e8 + 1.21214e9i) q^{67} +(2.89836e9 + 5.02011e9i) q^{68} +(-1.55088e10 + 1.08119e10i) q^{69} +(-809402. + 1.40193e6i) q^{70} +9.59171e9 q^{71} +(1.66871e6 - 287163. i) q^{72} -2.26608e9 q^{73} +(-30053.9 + 52054.8i) q^{74} +(-2.71438e10 - 1.27254e10i) q^{75} +(9.79099e9 + 1.69585e10i) q^{76} +(-1.33127e10 - 2.30583e10i) q^{77} +(68830.3 + 805827. i) q^{78} +(-2.30878e10 + 3.99892e10i) q^{79} +4.59569e10 q^{80} +(2.95759e10 - 1.04899e10i) q^{81} +931184. q^{82} +(-2.03528e9 + 3.52521e9i) q^{83} +(-4.64448e9 - 5.43750e10i) q^{84} +(-1.55065e10 - 2.68580e10i) q^{85} +(-528104. - 914703. i) q^{86} +(2.10656e10 + 9.87589e9i) q^{87} +(2.00988e6 - 3.48121e6i) q^{88} +8.43049e10 q^{89} +(-4.46386e6 + 768173. i) q^{90} +5.21328e10 q^{91} +(-4.59962e10 + 7.96677e10i) q^{92} +(-7.80806e10 + 5.44335e10i) q^{93} +(-1.75970e6 - 3.04789e6i) q^{94} +(-5.23826e10 - 9.07294e10i) q^{95} +(1.01382e7 - 7.06779e6i) q^{96} +(1.93390e10 - 3.34962e10i) q^{97} +4.73946e6 q^{98} +(2.57680e10 - 6.99007e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 33 q^{2} - 12 q^{3} - 9217 q^{4} - 7230 q^{5} + 20583 q^{6} + 8512 q^{7} - 29118 q^{8} + 135504 q^{9}+O(q^{10}) $ 20 * q - 33 * q^2 - 12 * q^3 - 9217 * q^4 - 7230 * q^5 + 20583 * q^6 + 8512 * q^7 - 29118 * q^8 + 135504 * q^9	\( 20 q - 33 q^{2} - 12 q^{3} - 9217 q^{4} - 7230 q^{5} + 20583 q^{6} + 8512 q^{7} - 29118 q^{8} + 135504 q^{9} + 4092 q^{10} - 112776 q^{11} + 1027860 q^{12} + 279706 q^{13} - 3901584 q^{14} - 6358608 q^{15} - 7342081 q^{16} + 27765792 q^{17} + 8682876 q^{18} + 7029400 q^{19} - 34163508 q^{20} + 55012206 q^{21} + 2274591 q^{22} - 69371616 q^{23} - 211100355 q^{24} - 45286204 q^{25} + 481929144 q^{26} - 83699352 q^{27} - 61345796 q^{28} - 25437246 q^{29} - 23582592 q^{30} + 114575368 q^{31} + 80396559 q^{32} + 31338342 q^{33} - 243855063 q^{34} - 178147464 q^{35} - 19984653 q^{36} - 134218328 q^{37} + 489799995 q^{38} - 1999064976 q^{39} + 107425416 q^{40} + 331873026 q^{41} + 4171968882 q^{42} - 1118847584 q^{43} + 278477274 q^{44} + 1749349170 q^{45} + 2882537592 q^{46} - 1469650704 q^{47} - 9335236125 q^{48} - 3553434720 q^{49} - 6643771701 q^{50} + 1736777052 q^{51} + 3632448874 q^{52} + 14914261944 q^{53} + 18127857753 q^{54} + 4981449984 q^{55} - 27669139026 q^{56} - 7855424196 q^{57} - 1387480560 q^{58} - 26505032592 q^{59} - 10283356116 q^{60} + 990409066 q^{61} + 91044996180 q^{62} + 51565206888 q^{63} - 7516709566 q^{64} - 39045315390 q^{65} - 93201828246 q^{66} + 6557215720 q^{67} - 77299152993 q^{68} + 6907292550 q^{69} - 785437278 q^{70} + 122053719744 q^{71} + 161899013547 q^{72} - 12612893936 q^{73} - 109519086216 q^{74} - 218383044348 q^{75} + 14574055597 q^{76} - 88616208018 q^{77} + 150319870614 q^{78} - 7621233248 q^{79} + 399166683072 q^{80} + 222307104312 q^{81} - 59168477334 q^{82} - 99007044180 q^{83} - 711968015814 q^{84} + 12911595156 q^{85} - 214357830519 q^{86} + 99715491216 q^{87} - 54423523605 q^{88} + 476597704824 q^{89} + 620021743884 q^{90} + 138211652216 q^{91} - 461776423998 q^{92} - 572981484354 q^{93} + 13393667064 q^{94} - 418952909328 q^{95} + 118587589272 q^{96} + 123483551938 q^{97} + 1310123604078 q^{98} + 621154334268 q^{99}+O(q^{100}) \) 20 * q - 33 * q^2 - 12 * q^3 - 9217 * q^4 - 7230 * q^5 + 20583 * q^6 + 8512 * q^7 - 29118 * q^8 + 135504 * q^9 + 4092 * q^10 - 112776 * q^11 + 1027860 * q^12 + 279706 * q^13 - 3901584 * q^14 - 6358608 * q^15 - 7342081 * q^16 + 27765792 * q^17 + 8682876 * q^18 + 7029400 * q^19 - 34163508 * q^20 + 55012206 * q^21 + 2274591 * q^22 - 69371616 * q^23 - 211100355 * q^24 - 45286204 * q^25 + 481929144 * q^26 - 83699352 * q^27 - 61345796 * q^28 - 25437246 * q^29 - 23582592 * q^30 + 114575368 * q^31 + 80396559 * q^32 + 31338342 * q^33 - 243855063 * q^34 - 178147464 * q^35 - 19984653 * q^36 - 134218328 * q^37 + 489799995 * q^38 - 1999064976 * q^39 + 107425416 * q^40 + 331873026 * q^41 + 4171968882 * q^42 - 1118847584 * q^43 + 278477274 * q^44 + 1749349170 * q^45 + 2882537592 * q^46 - 1469650704 * q^47 - 9335236125 * q^48 - 3553434720 * q^49 - 6643771701 * q^50 + 1736777052 * q^51 + 3632448874 * q^52 + 14914261944 * q^53 + 18127857753 * q^54 + 4981449984 * q^55 - 27669139026 * q^56 - 7855424196 * q^57 - 1387480560 * q^58 - 26505032592 * q^59 - 10283356116 * q^60 + 990409066 * q^61 + 91044996180 * q^62 + 51565206888 * q^63 - 7516709566 * q^64 - 39045315390 * q^65 - 93201828246 * q^66 + 6557215720 * q^67 - 77299152993 * q^68 + 6907292550 * q^69 - 785437278 * q^70 + 122053719744 * q^71 + 161899013547 * q^72 - 12612893936 * q^73 - 109519086216 * q^74 - 218383044348 * q^75 + 14574055597 * q^76 - 88616208018 * q^77 + 150319870614 * q^78 - 7621233248 * q^79 + 399166683072 * q^80 + 222307104312 * q^81 - 59168477334 * q^82 - 99007044180 * q^83 - 711968015814 * q^84 + 12911595156 * q^85 - 214357830519 * q^86 + 99715491216 * q^87 - 54423523605 * q^88 + 476597704824 * q^89 + 620021743884 * q^90 + 138211652216 * q^91 - 461776423998 * q^92 - 572981484354 * q^93 + 13393667064 * q^94 - 418952909328 * q^95 + 118587589272 * q^96 + 123483551938 * q^97 + 1310123604078 * q^98 + 621154334268 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.00116679	+	0.00202094i	−2.57827e−5	+	4.46569e-5i	−0.866038	−	0.499978i	$-0.833342\pi$
$2$	−0.00116679	+	0.00202094i	−2.57827e−5	+	4.46569e-5i	0.866013	+	0.500022i	$0.166675\pi$
$3$	35.8201	+	419.361i	0.0851059	+	0.996372i
$3$	35.8201	+	419.361i	0.0851059	+	0.996372i
$4$	1024.00	+	1773.62i	0.500000	+	0.866025i
$5$	−5478.49	−	9489.02i	−0.784018	−	1.35796i	−0.929584	−	0.368610i	$-0.879834\pi$
$5$	−5478.49	−	9489.02i	−0.784018	−	1.35796i	0.145567	−	0.989348i	$-0.453499\pi$
$6$	−0.889299	−	0.416917i	−4.66892e−5	−	2.18886e-5i
$7$	−31655.6	+	54829.1i	−0.711888	+	1.23303i	0.252260	+	0.967659i	$0.418826\pi$
$7$	−31655.6	+	54829.1i	−0.711888	+	1.23303i	−0.964148	+	0.265366i	$0.914507\pi$
$8$	−9.55835			−0.000103131
$9$	−174581.	+	30043.1i	−0.985514	+	0.169594i
$10$	25.5690			8.08563e−5
$11$	−210274.	+	364206.i	−0.393665	+	0.681848i	−0.992930	−	0.118703i	$-0.962126\pi$
$11$	−210274.	+	364206.i	−0.393665	+	0.681848i	0.599265	+	0.800551i	$0.295460\pi$
$12$	−707108.	+	492957.i	−0.820330	+	0.571890i
$13$	−411718.	−	713117.i	−0.307547	−	0.532687i	0.670278	−	0.742110i	$-0.266175\pi$
$13$	−411718.	−	713117.i	−0.307547	−	0.532687i	−0.977825	+	0.209423i	$0.932842\pi$
$14$	−73.8710	−	127.948i	−3.67087e−5	−	6.35814e-5i
$15$	3.78309e6	−	2.63736e6i	1.28631	−	0.896743i
$16$	−2.09715e6	+	3.63237e6i	−0.500000	+	0.866025i
$17$	2.83043e6			0.483486			0.241743	−	0.970340i	$-0.422281\pi$
$17$	2.83043e6			0.483486			0.241743	+	0.970340i	$0.422281\pi$
$18$	142.984	−	387.872i	1.78356e−5	−	4.83826e-5i
$19$	9.56151e6			0.885894			0.442947	−	0.896548i	$-0.353933\pi$
$19$	9.56151e6			0.885894			0.442947	+	0.896548i	$0.353933\pi$
$20$	1.12199e7	−	1.94335e7i	0.784018	−	1.35796i
$21$	−2.41271e7	−	1.13112e7i	−1.28914	−	0.604367i
$22$	−490.693	−	849.905i	−2.02995e−5	−	3.51597e-5i
$23$	2.24591e7	+	3.89002e7i	0.727593	+	1.26023i	0.957898	+	0.287110i	$0.0926944\pi$
$23$	2.24591e7	+	3.89002e7i	0.727593	+	1.26023i	−0.230305	+	0.973119i	$0.573972\pi$
$24$	−342.381	−	4008.40i	−8.77704e−6	−	0.000102757i
$25$	−3.56136e7	+	6.16846e7i	−0.729367	+	1.26330i
$26$	1921.56			3.17176e−5
$27$	−1.88524e7	−	7.21363e7i	−0.252852	−	0.967505i
$28$	−1.29661e8			−1.42378
$29$	2.76388e7	−	4.78719e7i	0.250225	−	0.433403i	−0.713363	−	0.700795i	$-0.752829\pi$
$29$	2.76388e7	−	4.78719e7i	0.250225	−	0.433403i	0.963588	+	0.267393i	$0.0861620\pi$
$30$	915.884	+	10722.7i	6.88135e−6	+	8.05630e-5i
$31$	1.13073e8	+	1.95847e8i	0.709362	+	1.22865i	0.965094	+	0.261903i	$0.0843501\pi$
$31$	1.13073e8	+	1.95847e8i	0.709362	+	1.22865i	−0.255732	+	0.966748i	$0.582317\pi$
$32$	−14681.6	−	25429.3i	−7.73481e−5	−	0.000133971i
$33$	−1.60266e8	−	7.51351e7i	−0.712877	−	0.334207i
$34$	−3302.52	+	5720.14i	−1.24656e−5	+	2.15910e-5i
$35$	6.93700e8			2.23253
$36$	−2.32056e8	−	2.78876e8i	−0.639630	−	0.768683i
$37$	2.57577e7			0.0610657			0.0305329	−	0.999534i	$-0.490280\pi$
$37$	2.57577e7			0.0610657			0.0305329	+	0.999534i	$0.490280\pi$
$38$	−11156.3	+	19323.3i	−2.28407e−5	+	3.95613e-5i
$39$	2.84306e8	−	1.98203e8i	0.504581	−	0.351766i
$40$	52365.3	+	90699.4i	8.08563e−5	+	0.000140047i
$41$	−1.99518e8	−	3.45576e8i	−0.268950	−	0.465835i	0.699641	−	0.714494i	$-0.253343\pi$
$41$	−1.99518e8	−	3.45576e8i	−0.268950	−	0.465835i	−0.968591	+	0.248660i	$0.920010\pi$
$42$	51010.5	−	35561.7i	6.02266e−5	−	4.19867e-5i
$43$	−2.26306e8	+	3.91974e8i	−0.234758	+	0.406612i	−0.959202	−	0.282721i	$-0.908763\pi$
$43$	−2.26306e8	+	3.91974e8i	−0.234758	+	0.406612i	0.724444	+	0.689333i	$0.242096\pi$
$44$	−8.61284e8			−0.787330
$45$	1.24152e9	+	1.49201e9i	1.00296	+	1.20532i
$46$	−104820.			−7.50372e−5
$47$	−7.54076e8	+	1.30610e9i	−0.479597	+	0.830687i	−0.999726	−	0.0234009i	$-0.992551\pi$
$47$	−7.54076e8	+	1.30610e9i	−0.479597	+	0.830687i	0.520129	+	0.854088i	$0.325884\pi$
$48$	−1.59840e9	−	7.49352e8i	−0.905436	−	0.424482i
$49$	−1.01549e9	−	1.75888e9i	−0.513568	−	0.889525i
$50$	−83107.3	−	143946.i	−3.76101e−5	−	6.51426e-5i
$51$	1.01386e8	+	1.18697e9i	0.0411475	+	0.481732i
$52$	8.43199e8	−	1.46046e9i	0.307547	−	0.532687i
$53$	−1.27376e9			−0.418381			−0.209190	−	0.977875i	$-0.567083\pi$
$53$	−1.27376e9			−0.418381			−0.209190	+	0.977875i	$0.567083\pi$
$54$	167780.	+	46068.4i	4.97250e−5	+	1.36533e-5i
$55$	4.60794e9			1.23456
$56$	302575.	−	524076.i	7.34175e−5	−	0.000127163i
$57$	3.42494e8	+	4.00973e9i	0.0753948	+	0.882680i
$58$	64497.5	+	111713.i	1.29030e−5	+	2.23486e-5i
$59$	−3.21846e9	−	5.57453e9i	−0.586087	−	1.01513i	−0.994739	−	0.102442i	$-0.967334\pi$
$59$	−3.21846e9	−	5.57453e9i	−0.586087	−	1.01513i	0.408652	−	0.912690i	$-0.365999\pi$
$60$	8.55156e9	+	4.00910e9i	1.41976	+	0.665603i
$61$	3.21169e9	−	5.56280e9i	0.486877	−	0.843295i	−0.513009	−	0.858383i	$-0.671469\pi$
$61$	3.21169e9	−	5.56280e9i	0.486877	−	0.843295i	0.999886	+	0.0150876i	$0.00480272\pi$
$62$	−527728.			−7.31570e−5
$63$	3.87922e9	−	1.05231e10i	0.492461	−	1.33590i
$64$	−8.58993e9			−1.00000
$65$	−4.51119e9	+	7.81361e9i	−0.482245	+	0.835272i
$66$	338840.	−	236221.i	3.33046e−5	−	2.32181e-5i
$67$	6.99828e8	+	1.21214e9i	0.0633257	+	0.109683i	0.895950	−	0.444155i	$-0.146496\pi$
$67$	6.99828e8	+	1.21214e9i	0.0633257	+	0.109683i	−0.832624	+	0.553838i	$0.813163\pi$
$68$	2.89836e9	+	5.02011e9i	0.241743	+	0.418711i
$69$	−1.55088e10	+	1.08119e10i	−1.19373	+	0.832206i
$70$	−809402.	+	1.40193e6i	−5.75606e−5	+	9.96979e-5i
$71$	9.59171e9			0.630922			0.315461	−	0.948939i	$-0.397841\pi$
$71$	9.59171e9			0.630922			0.315461	+	0.948939i	$0.397841\pi$
$72$	1.66871e6	−	287163.i	0.000101637	−	1.74904e-5i
$73$	−2.26608e9			−0.127938			−0.0639690	−	0.997952i	$-0.520376\pi$
$73$	−2.26608e9			−0.127938			−0.0639690	+	0.997952i	$0.520376\pi$
$74$	−30053.9	+	52054.8i	−1.57444e−6	+	2.72701e-6i
$75$	−2.71438e10	−	1.27254e10i	−1.32079	−	0.619206i
$76$	9.79099e9	+	1.69585e10i	0.442947	+	0.767207i
$77$	−1.33127e10	−	2.30583e10i	−0.560490	−	0.970798i
$78$	68830.3	+	805827.i	2.69935e−6	+	3.16025e-5i
$79$	−2.30878e10	+	3.99892e10i	−0.844176	+	1.46216i	0.0421580	+	0.999111i	$0.486577\pi$
$79$	−2.30878e10	+	3.99892e10i	−0.844176	+	1.46216i	−0.886334	+	0.463046i	$0.846757\pi$
$80$	4.59569e10			1.56804
$81$	2.95759e10	−	1.04899e10i	0.942476	−	0.334275i
$82$	931184.			2.77370e−5
$83$	−2.03528e9	+	3.52521e9i	−0.0567145	+	0.0982324i	−0.892989	−	0.450079i	$-0.851396\pi$
$83$	−2.03528e9	+	3.52521e9i	−0.0567145	+	0.0982324i	0.836274	+	0.548311i	$0.184729\pi$
$84$	−4.64448e9	−	5.43750e10i	−0.121172	−	1.41861i
$85$	−1.55065e10	−	2.68580e10i	−0.379061	−	0.656554i
$86$	−528104.	−	914703.i	−1.21054e−5	−	2.09671e-5i
$87$	2.10656e10	+	9.87589e9i	0.453126	+	0.212432i
$88$	2.00988e6	−	3.48121e6i	4.05989e−5	−	7.03194e-5i
$89$	8.43049e10			1.60032			0.800162	−	0.599784i	$-0.204747\pi$
$89$	8.43049e10			1.60032			0.800162	+	0.599784i	$0.204747\pi$
$90$	−4.46386e6	+	768173.i	−7.96850e−5	+	1.37128e-5i
$91$	5.21328e10			0.875756
$92$	−4.59962e10	+	7.96677e10i	−0.727593	+	1.26023i
$93$	−7.80806e10	+	5.44335e10i	−1.16382	+	0.811354i
$94$	−1.75970e6	−	3.04789e6i	−2.47306e−5	−	4.28347e-5i
$95$	−5.23826e10	−	9.07294e10i	−0.694557	−	1.20301i
$96$	1.01382e7	−	7.06779e6i	0.000126902	−	8.84691e-5i
$97$	1.93390e10	−	3.34962e10i	0.228660	−	0.396050i	−0.728751	−	0.684778i	$-0.759899\pi$
$97$	1.93390e10	−	3.34962e10i	0.228660	−	0.396050i	0.957411	+	0.288728i	$0.0932323\pi$
$98$	4.73946e6			5.29646e−5
$99$	2.57680e10	−	6.99007e10i	0.272325	−	0.738734i
$100$	−1.45873e11			−1.45873
$101$	−1.15786e10	+	2.00547e10i	−0.109620	+	0.189867i	−0.915616	−	0.402053i	$-0.868297\pi$
$101$	−1.15786e10	+	2.00547e10i	−0.109620	+	0.189867i	0.805996	+	0.591920i	$0.201630\pi$
$102$	−2.51710e6	−	1.18005e6i	−2.25735e−5	−	1.05828e-5i
$103$	5.58245e10	+	9.66908e10i	0.474482	+	0.821827i	0.999573	−	0.0292188i	$-0.00930197\pi$
$103$	5.58245e10	+	9.66908e10i	0.474482	+	0.821827i	−0.525091	+	0.851046i	$0.675969\pi$
$104$	3.93535e6	+	6.81622e6i	3.17176e−5	+	5.49364e-5i
$105$	2.48484e10	+	2.90911e11i	0.190001	+	2.22443i
$106$	1.48622e6	−	2.57420e6i	1.07870e−5	−	1.86836e-5i
$107$	−2.39870e11			−1.65335			−0.826675	−	0.562680i	$-0.809770\pi$
$107$	−2.39870e11			−1.65335			−0.826675	+	0.562680i	$0.809770\pi$
$108$	1.08638e11	−	1.07305e11i	0.711458	−	0.702729i
$109$	1.58154e11			0.984544			0.492272	−	0.870441i	$-0.336166\pi$
$109$	1.58154e11			0.984544			0.492272	+	0.870441i	$0.336166\pi$
$110$	−5.37651e6	+	9.31239e6i	−3.18303e−5	+	5.51317e-5i
$111$	9.22643e8	+	1.08018e10i	0.00519706	+	0.0608442i
$112$	−1.32773e11	−	2.29970e11i	−0.711888	−	1.23303i
$113$	−2.91890e9	−	5.05568e9i	−0.0149035	−	0.0258136i	0.858477	−	0.512851i	$-0.171411\pi$
$113$	−2.91890e9	−	5.05568e9i	−0.0149035	−	0.0258136i	−0.873381	+	0.487038i	$0.838077\pi$
$114$	−8.50305e6	−	3.98636e6i	−4.13617e−5	−	1.93910e-5i
$115$	2.46083e11	−	4.26229e11i	1.14089	−	1.97608i
$116$	1.13209e11			0.500450
$117$	9.33024e10	+	1.12127e11i	0.393433	+	0.472813i
$118$	1.50211e7			6.04436e−5
$119$	−8.95990e10	+	1.55190e11i	−0.344187	+	0.596150i
$120$	−3.61601e7	+	2.52089e7i	−0.000132658	+	9.24818e-5i
$121$	5.42252e10	+	9.39208e10i	0.190056	+	0.329187i
$122$	7.49474e6	+	1.29813e7i	2.51060e−5	+	4.34848e-5i
$123$	1.37774e11	−	9.60487e10i	0.441255	−	0.307619i
$124$	−2.31573e11	+	4.01096e11i	−0.709362	+	1.22865i
$125$	2.45427e11			0.719311
$126$	1.67404e7	+	2.01180e7i	4.69600e−5	+	5.64348e-5i
$127$	7.57587e10			0.203476			0.101738	−	0.994811i	$-0.467560\pi$
$127$	7.57587e10			0.203476			0.101738	+	0.994811i	$0.467560\pi$
$128$	4.00906e7	−	6.94390e7i	0.000103131	−	0.000178628i
$129$	−1.72485e11	−	8.08635e10i	−0.425116	−	0.199301i
$130$	−1.05272e7	−	1.82337e7i	−2.48671e−5	−	4.30711e-5i
$131$	−3.72884e11	−	6.45854e11i	−0.844465	−	1.46266i	−0.886085	−	0.463523i	$-0.846585\pi$
$131$	−3.72884e11	−	6.45854e11i	−0.844465	−	1.46266i	0.0416198	−	0.999134i	$-0.486748\pi$
$132$	−3.08513e10	−	3.61189e11i	−0.0670064	−	0.784473i
$133$	−3.02675e11	+	5.24249e11i	−0.630657	+	1.09233i
$134$	−3.26621e6			−6.53082e−6
$135$	−5.81220e11	+	5.74089e11i	−1.11559	+	1.10190i
$136$	−2.70543e7			−4.98622e−5
$137$	1.02957e11	−	1.78327e11i	0.182261	−	0.315685i	−0.760389	−	0.649468i	$-0.774992\pi$
$137$	1.02957e11	−	1.78327e11i	0.182261	−	0.315685i	0.942650	+	0.333783i	$0.108325\pi$
$138$	−3.75467e6	−	4.39575e7i	−6.38611e−6	−	7.47650e-5i
$139$	2.93119e10	+	5.07697e10i	0.0479140	+	0.0829895i	0.888988	−	0.457931i	$-0.151409\pi$
$139$	2.93119e10	+	5.07697e10i	0.0479140	+	0.0829895i	−0.841074	+	0.540921i	$0.818076\pi$
$140$	7.10348e11	+	1.23036e12i	1.11626	+	1.93343i
$141$	−5.74738e11	−	2.69446e11i	−0.868490	−	0.407161i
$142$	−1.11915e7	+	1.93843e7i	−1.62669e−5	+	2.81750e-5i
$143$	3.46295e11			0.484282
$144$	2.56995e11	−	6.97148e11i	0.345884	−	0.938277i
$145$	−6.05676e11			−0.784724
$146$	2.64404e6	−	4.57961e6i	3.29858e−6	−	5.71332e-6i
$147$	7.01232e11	−	4.88861e11i	0.842590	−	0.587408i
$148$	2.63759e10	+	4.56844e10i	0.0305329	+	0.0528845i
$149$	1.65587e11	+	2.86805e11i	0.184715	+	0.319935i	0.943480	−	0.331429i	$-0.107531\pi$
$149$	1.65587e11	+	2.86805e11i	0.184715	+	0.319935i	−0.758766	+	0.651364i	$0.774197\pi$
$150$	5.73885e7	−	4.00082e7i	6.17054e−5	−	4.30176e-5i
$151$	2.15126e11	−	3.72610e11i	0.223008	−	0.386261i	−0.732712	−	0.680539i	$-0.761746\pi$
$151$	2.15126e11	−	3.72610e11i	0.223008	−	0.386261i	0.955720	+	0.294278i	$0.0950790\pi$
$152$	−9.13923e7			−9.13629e−5
$153$	−4.94139e11	+	8.50350e10i	−0.476482	+	0.0819964i
$154$	6.21327e7			5.78038e−5
$155$	1.23893e12	−	2.14590e12i	1.11230	−	1.92657i
$156$	6.42665e11	+	3.01291e11i	0.556929	+	0.261097i
$157$	6.81979e11	+	1.18122e12i	0.570589	+	0.988289i	0.996506	+	0.0835263i	$0.0266183\pi$
$157$	6.81979e11	+	1.18122e12i	0.570589	+	0.988289i	−0.425917	+	0.904762i	$0.640048\pi$
$158$	−5.38772e7	−	9.33181e7i	−4.35303e−5	−	7.53966e-5i
$159$	−4.56263e10	−	5.34167e11i	−0.0356067	−	0.416863i
$160$	−1.60866e8	+	2.78629e8i	−0.000121284	+	0.000210071i
$161$	−2.84382e12			−2.07186
$162$	−1.33094e7	+	7.20107e7i	−9.37185e−6	+	5.07066e-5i
$163$	3.45319e11			0.235065			0.117533	−	0.993069i	$-0.462502\pi$
$163$	3.45319e11			0.235065			0.117533	+	0.993069i	$0.462502\pi$
$164$	4.08613e11	−	7.07739e11i	0.268950	−	0.465835i
$165$	1.65057e11	+	1.93239e12i	0.105068	+	1.23008i
$166$	−4.74949e6	−	8.22636e6i	−2.92451e−6	−	5.06539e-6i
$167$	1.10593e12	+	1.91553e12i	0.658853	+	1.14117i	0.980913	+	0.194447i	$0.0622914\pi$
$167$	1.10593e12	+	1.91553e12i	0.658853	+	1.14117i	−0.322060	+	0.946719i	$0.604375\pi$
$168$	2.30615e8	+	1.08116e8i	0.000132950	+	6.23288e-5i
$169$	5.57056e11	−	9.64850e11i	0.310829	−	0.538372i
$170$	7.23714e7			3.90929e−5
$171$	−1.66926e12	+	2.87258e11i	−0.873061	+	0.150243i
$172$	−9.26950e11			−0.469516
$173$	−1.82759e12	+	3.16548e12i	−0.896655	+	1.55305i	−0.0649116	+	0.997891i	$0.520677\pi$
$173$	−1.82759e12	+	3.16548e12i	−0.896655	+	1.55305i	−0.831743	+	0.555161i	$0.812657\pi$
$174$	−4.45378e7	+	3.10493e7i	−2.11694e−5	+	1.47581e-5i
$175$	−2.25474e12	−	3.90533e12i	−1.03845	−	1.79866i
$176$	−8.81955e11	−	1.52759e12i	−0.393665	−	0.681848i
$177$	2.22246e12	−	1.54938e12i	0.961569	−	0.670354i
$178$	−9.83662e7	+	1.70375e8i	−4.12606e−5	+	7.14655e-5i
$179$	−2.01499e12			−0.819562			−0.409781	−	0.912184i	$-0.634395\pi$
$179$	−2.01499e12			−0.819562			−0.409781	+	0.912184i	$0.634395\pi$
$180$	−1.37494e12	+	3.72980e12i	−0.542358	+	1.47125i
$181$	3.82616e12			1.46397			0.731983	−	0.681323i	$-0.238595\pi$
$181$	3.82616e12			1.46397			0.731983	+	0.681323i	$0.238595\pi$
$182$	−6.08280e7	+	1.05357e8i	−2.25793e−5	+	3.91086e-5i
$183$	2.44787e12	+	1.14760e12i	0.881672	+	0.413341i
$184$	−2.14672e8	−	3.71822e8i	−7.50372e−5	−	0.000129968i
$185$	−1.41113e11	−	2.44415e11i	−0.0478766	−	0.0829247i
$186$	−1.89033e7	−	2.21309e8i	−6.22610e−6	−	7.28916e-5i
$187$	−5.95167e11	+	1.03086e12i	−0.190331	+	0.329664i
$188$	−3.08869e12			−0.959195
$189$	4.55195e12	+	1.24986e12i	1.37296	+	0.376982i
$190$	2.44478e8			7.16301e−5
$191$	2.35104e12	−	4.07212e12i	0.669231	−	1.15914i	−0.308888	−	0.951098i	$-0.599957\pi$
$191$	2.35104e12	−	4.07212e12i	0.669231	−	1.15914i	0.978119	−	0.208044i	$-0.0667099\pi$
$192$	−3.07692e11	−	3.60229e12i	−0.0851059	−	0.996372i
$193$	1.53133e12	+	2.65235e12i	0.411628	+	0.712960i	0.995068	−	0.0991962i	$-0.0316271\pi$
$193$	1.53133e12	+	2.65235e12i	0.411628	+	0.712960i	−0.583440	+	0.812156i	$0.698294\pi$
$194$	4.51292e7	+	7.81660e7i	1.17909e−5	+	2.04225e-5i
$195$	−3.43832e12	−	1.61193e12i	−0.873284	−	0.409408i
$196$	2.07973e12	−	3.60219e12i	0.513568	−	0.889525i
$197$	6.23027e12			1.49604			0.748019	−	0.663677i	$-0.231005\pi$
$197$	6.23027e12			1.49604			0.748019	+	0.663677i	$0.231005\pi$
$198$	1.11199e8	+	1.33635e8i	2.59683e−5	+	3.12077e-5i
$199$	−3.20062e12			−0.727012			−0.363506	−	0.931592i	$-0.618420\pi$
$199$	−3.20062e12			−0.727012			−0.363506	+	0.931592i	$0.618420\pi$
$200$	3.40408e8	−	5.89603e8i	7.52202e−5	−	0.000130285i
$201$	−4.83256e11	+	3.36900e11i	−0.103896	+	0.0724306i
$202$	−2.70196e7	−	4.67994e7i	−5.65258e−6	−	9.79056e-6i
$203$	1.74985e12	+	3.03083e12i	0.356264	+	0.617068i
$204$	−2.00142e12	+	1.39528e12i	−0.396618	+	0.276501i
$205$	−2.18612e12	+	3.78646e12i	−0.421723	+	0.730445i
$206$	−2.60542e8			−4.89337e−5
$207$	−5.08961e12	−	6.11650e12i	−0.930781	−	1.11858i
$208$	3.45374e12			0.615094
$209$	−2.01054e12	+	3.48236e12i	−0.348745	+	0.604045i
$210$	−6.16906e8	−	2.89215e8i	−0.000104235	−	4.88669e-5i
$211$	3.53237e11	+	6.11825e11i	0.0581451	+	0.100710i	0.893633	−	0.448799i	$-0.148148\pi$
$211$	3.53237e11	+	6.11825e11i	0.0581451	+	0.100710i	−0.835488	+	0.549509i	$0.814815\pi$
$212$	−1.30433e12	−	2.25917e12i	−0.209190	−	0.362328i
$213$	3.43576e11	+	4.02239e12i	0.0536952	+	0.628632i
$214$	2.79878e8	−	4.84763e8i	4.26278e−5	−	7.38335e-5i
$215$	4.95927e12			0.736217
$216$	1.80198e8	+	6.89504e8i	2.60768e−5	+	9.97795e-5i
$217$	−1.43175e13			−2.01994
$218$	−1.84533e8	+	3.19621e8i	−2.53842e−5	+	4.39667e-5i
$219$	−8.11712e10	−	9.50306e11i	−0.0108883	−	0.127474i
$220$	4.71854e12	+	8.17274e12i	0.617280	+	1.06916i
$221$	−1.16534e12	−	2.01843e12i	−0.148695	−	0.257547i
$222$	−2.29063e7	−	1.07388e7i	−2.85111e−6	−	1.33664e-6i
$223$	−4.50921e12	+	7.81017e12i	−0.547549	+	0.948383i	0.450892	+	0.892578i	$0.351106\pi$
$223$	−4.50921e12	+	7.81017e12i	−0.547549	+	0.948383i	−0.998442	+	0.0558051i	$0.982227\pi$
$224$	1.85902e9			0.000220252
$225$	4.36426e12	−	1.18389e13i	0.504553	−	1.36870i
$226$	1.36230e7			1.53701e−6
$227$	−1.67817e12	+	2.90668e12i	−0.184797	+	0.320077i	−0.943508	−	0.331350i	$-0.892496\pi$
$227$	−1.67817e12	+	2.90668e12i	−0.184797	+	0.320077i	0.758711	+	0.651427i	$0.225829\pi$
$228$	−6.76102e12	+	4.71342e12i	−0.726726	+	0.506634i
$229$	−3.49641e12	−	6.05595e12i	−0.366882	−	0.635459i	0.622194	−	0.782863i	$-0.286241\pi$
$229$	−3.49641e12	−	6.05595e12i	−0.366882	−	0.635459i	−0.989076	+	0.147404i	$0.952908\pi$
$230$	5.74256e8	+	9.94641e8i	5.88305e−5	+	0.000101897i
$231$	9.19290e12	−	6.40879e12i	0.919574	−	0.641077i
$232$	−2.64182e8	+	4.57576e8i	−2.58059e−5	+	4.46971e-5i
$233$	1.27289e13			1.21432			0.607160	−	0.794580i	$-0.292309\pi$
$233$	1.27289e13			1.21432			0.607160	+	0.794580i	$0.292309\pi$
$234$	−3.35467e8	+	5.77296e7i	−3.12581e−5	+	5.37912e-6i
$235$	1.65248e13			1.50405
$236$	6.59140e12	−	1.14166e13i	0.586087	−	1.01513i
$237$	−1.75969e13	−	8.24971e12i	−1.52870	−	0.716676i
$238$	−2.09087e8	−	3.62149e8i	−1.77482e−5	−	3.07407e-5i
$239$	−2.47171e12	−	4.28113e12i	−0.205026	−	0.355116i	0.745115	−	0.666936i	$-0.232395\pi$
$239$	−2.47171e12	−	4.28113e12i	−0.205026	−	0.355116i	−0.950141	+	0.311820i	$0.899061\pi$
$240$	1.64618e12	+	1.92725e13i	0.133449	+	1.56235i
$241$	6.27109e12	−	1.08618e13i	0.496877	−	0.860617i	−0.503116	−	0.864219i	$-0.667813\pi$
$241$	6.27109e12	−	1.08618e13i	0.496877	−	0.860617i	0.999994	+	0.00360181i	$0.00114649\pi$
$242$	−2.53078e8			−1.96006e−5
$243$	5.45847e12	+	1.20272e13i	0.413273	+	0.910607i
$244$	1.31551e13			0.973754
$245$	−1.11267e13	+	1.92720e13i	−0.805292	+	1.39481i
$246$	3.33551e7	+	3.90503e8i	2.36058e−6	+	2.76364e-5i
$247$	−3.93665e12	−	6.81848e12i	−0.272454	−	0.471905i
$248$	−1.08079e9	−	1.87198e9i	−7.31570e−5	−	0.000126712i
$249$	−1.55124e12	−	7.27244e11i	−0.102703	−	0.0481486i
$250$	−2.86362e8	+	4.95993e8i	−1.85458e−5	+	3.21222e-5i
$251$	−1.07007e13			−0.677963			−0.338981	−	0.940793i	$-0.610082\pi$
$251$	−1.07007e13			−0.677963			−0.338981	+	0.940793i	$0.610082\pi$
$252$	2.26364e13	−	3.89543e12i	1.40315	−	0.241464i
$253$	−1.88903e13			−1.14571
$254$	−8.83946e7	+	1.53104e8i	−5.24615e−6	+	9.08659e-6i
$255$	1.07078e13	−	7.46488e12i	0.621911	−	0.433563i
$256$	−8.79609e12	−	1.52353e13i	−0.500000	−	0.866025i
$257$	−1.17626e13	−	2.03735e13i	−0.654444	−	1.13353i	−0.982033	−	0.188710i	$-0.939569\pi$
$257$	−1.17626e13	−	2.03735e13i	−0.654444	−	1.13353i	0.327589	−	0.944820i	$-0.393764\pi$
$258$	3.64674e8	−	2.54231e8i	1.98608e−5	−	1.38459e-5i
$259$	−8.15375e11	+	1.41227e12i	−0.0434719	+	0.0752956i
$260$	−1.84778e13			−0.964490
$261$	−3.38699e12	+	9.18787e12i	−0.173098	+	0.469561i
$262$	1.74031e9			8.70903e−5
$263$	−1.85023e13	+	3.20469e13i	−0.906712	+	1.57047i	−0.0881085	+	0.996111i	$0.528082\pi$
$263$	−1.85023e13	+	3.20469e13i	−0.906712	+	1.57047i	−0.818603	+	0.574360i	$0.805251\pi$
$264$	1.53188e9	+	7.18167e8i	7.35195e−5	+	3.44671e-5i
$265$	6.97830e12	+	1.20868e13i	0.328018	+	0.568143i
$266$	−7.06318e8	−	1.22338e9i	−3.25201e−5	−	5.63264e-5i
$267$	3.01981e12	+	3.53542e13i	0.136197	+	1.59452i
$268$	−1.43325e12	+	2.48246e12i	−0.0633257	+	0.109683i
$269$	3.04610e13			1.31858			0.659291	−	0.751888i	$-0.270857\pi$
$269$	3.04610e13			1.31858			0.659291	+	0.751888i	$0.270857\pi$
$270$	−4.82038e8	−	1.84445e9i	−2.04447e−5	−	7.82289e-5i
$271$	6.39110e12			0.265610			0.132805	−	0.991142i	$-0.457602\pi$
$271$	6.39110e12			0.265610			0.132805	+	0.991142i	$0.457602\pi$
$272$	−5.93585e12	+	1.02812e13i	−0.241743	+	0.418711i
$273$	1.86740e12	+	2.18625e13i	0.0745320	+	0.872579i
$274$	2.40259e8	+	4.16140e8i	9.39834e−6	+	1.62784e-5i
$275$	−1.49773e13	−	2.59414e13i	−0.574252	−	0.994634i
$276$	−3.50571e13	−	1.64353e13i	−1.31758	−	0.617700i
$277$	2.54374e13	−	4.40588e13i	0.937203	−	1.62328i	0.166544	−	0.986034i	$-0.446739\pi$
$277$	2.54374e13	−	4.40588e13i	0.937203	−	1.62328i	0.770658	−	0.637249i	$-0.219928\pi$
$278$	−1.36804e8			−4.94141e−6
$279$	−2.56242e13	−	3.07942e13i	−0.907458	−	1.09055i
$280$	−6.63062e9			−0.000230242
$281$	1.93488e13	−	3.35130e13i	0.658822	−	1.14111i	−0.322099	−	0.946706i	$-0.604388\pi$
$281$	1.93488e13	−	3.35130e13i	0.658822	−	1.14111i	0.980921	−	0.194408i	$-0.0622784\pi$
$282$	1.21513e9	−	8.47125e8i	4.05745e−5	−	2.82864e-5i
$283$	1.68221e13	+	2.91367e13i	0.550877	+	0.954148i	0.998212	+	0.0597808i	$0.0190402\pi$
$283$	1.68221e13	+	2.91367e13i	0.550877	+	0.954148i	−0.447334	+	0.894367i	$0.647626\pi$
$284$	9.82192e12	+	1.70121e13i	0.315461	+	0.546394i
$285$	3.61721e13	−	2.52172e13i	1.13953	−	0.794420i
$286$	−4.04054e8	+	6.99843e8i	−1.24861e−5	+	2.16265e-5i
$287$	2.52635e13			0.765848
$288$	3.32711e9	+	3.99839e9i	9.89483e−5	+	0.000118912i
$289$	−2.62605e13			−0.766241
$290$	7.06698e8	−	1.22404e9i	2.02323e−5	−	3.50433e-5i
$291$	1.47397e13	+	6.91020e12i	0.414074	+	0.194124i
$292$	−2.32047e12	−	4.01916e12i	−0.0639690	−	0.110798i
$293$	2.26867e13	+	3.92945e13i	0.613761	+	1.06306i	0.990601	+	0.136786i	$0.0436774\pi$
$293$	2.26867e13	+	3.92945e13i	0.613761	+	1.06306i	−0.376840	+	0.926278i	$0.622989\pi$
$294$	1.69768e8	+	1.98755e9i	4.50760e−6	+	5.27725e-5i
$295$	−3.52646e13	+	6.10800e13i	−0.919004	+	1.59176i
$296$	−2.46201e8			−6.29775e−6
$297$	3.02367e13	+	8.30225e12i	0.759230	+	0.208466i
$298$	−7.72821e8			−1.90497e−5
$299$	1.84936e13	−	3.20319e13i	0.447538	−	0.775159i
$300$	−5.22520e12	−	6.11737e13i	−0.124147	−	1.45344i
$301$	−1.43277e13	−	2.48163e13i	−0.334242	−	0.578925i
$302$	5.02015e8	+	8.69516e8i	1.14995e−5	+	1.99177e-5i
$303$	−8.82493e12	−	4.13726e12i	−0.198507	−	0.0930633i
$304$	−2.00519e13	+	3.47310e13i	−0.442947	+	0.767207i
$305$	−7.03808e13			−1.52688
$306$	4.04706e8	−	1.09784e9i	8.62328e−6	−	2.33923e-5i
$307$	6.36068e13			1.33120			0.665599	−	0.746310i	$-0.268176\pi$
$307$	6.36068e13			1.33120			0.665599	+	0.746310i	$0.268176\pi$
$308$	2.72645e13	−	4.72234e13i	0.560490	−	0.970798i
$309$	−3.85488e13	+	2.68741e13i	−0.778464	+	0.542703i
$310$	2.89115e9	+	5.00762e9i	5.73564e−5	+	9.93442e-5i
$311$	2.35237e13	+	4.07443e13i	0.458484	+	0.794118i	0.998881	−	0.0472923i	$-0.0150592\pi$
$311$	2.35237e13	+	4.07443e13i	0.458484	+	0.794118i	−0.540397	+	0.841410i	$0.681726\pi$
$312$	−2.71750e9	+	1.89449e9i	−5.20378e−5	+	3.62779e-5i
$313$	−2.84546e12	+	4.92849e12i	−0.0535376	+	0.0927299i	−0.891552	−	0.452918i	$-0.850383\pi$
$313$	−2.84546e12	+	4.92849e12i	−0.0535376	+	0.0927299i	0.838015	+	0.545648i	$0.183716\pi$
$314$	−3.18291e9			−5.88452e−5
$315$	−1.21107e14	+	2.08409e13i	−2.20019	+	0.378624i
$316$	−9.45676e13			−1.68835
$317$	6.51732e11	−	1.12883e12i	0.0114352	−	0.0198063i	−0.860251	−	0.509870i	$-0.829693\pi$
$317$	6.51732e11	−	1.12883e12i	0.0114352	−	0.0198063i	0.871686	+	0.490064i	$0.163027\pi$
$318$	1.13276e9	+	5.31053e8i	1.95338e−5	+	9.15776e-6i
$319$	1.16235e13	+	2.01325e13i	0.197010	+	0.341231i
$320$	4.70599e13	+	8.15101e13i	0.784018	+	1.35796i
$321$	−8.59216e12	−	1.00592e14i	−0.140710	−	1.64735i
$322$	3.31815e9	−	5.74720e9i	5.34181e−5	−	9.25228e-5i
$323$	2.70632e13			0.428317
$324$	4.88908e13	+	4.17147e13i	0.760729	+	0.649070i
$325$	5.86511e13			0.897259
$326$	−4.02915e8	+	6.97869e8i	−6.06061e−6	+	1.04973e-5i
$327$	5.66510e12	+	6.63238e13i	0.0837906	+	0.980972i
$328$	1.90706e9	+	3.30313e9i	2.77370e−5	+	4.80419e-5i
$329$	−4.77414e13	−	8.26906e13i	−0.682839	−	1.18271i
$330$	−4.09784e9	−	1.92113e9i	−5.76406e−5	−	2.70228e-5i
$331$	1.59281e12	−	2.75882e12i	0.0220348	−	0.0381654i	−0.854798	−	0.518961i	$-0.826319\pi$
$331$	1.59281e12	−	2.75882e12i	0.0220348	−	0.0381654i	0.876833	+	0.480796i	$0.159652\pi$
$332$	−8.33650e12			−0.113429
$333$	−4.49680e12	+	7.73842e11i	−0.0601811	+	0.0103564i
$334$	−5.16157e9			−6.79480e−5
$335$	7.66800e12	−	1.32814e13i	0.0992969	−	0.171987i
$336$	9.16846e13	−	6.39175e13i	1.16797	−	0.814242i
$337$	4.95233e11	+	8.57768e11i	0.00620647	+	0.0107499i	0.869112	−	0.494615i	$-0.164691\pi$
$337$	4.95233e11	+	8.57768e11i	0.00620647	+	0.0107499i	−0.862905	+	0.505365i	$0.831358\pi$
$338$	1.29994e9	+	2.25156e9i	1.60280e−5	+	2.77614e-5i
$339$	2.01560e12	−	1.40517e12i	0.0244516	−	0.0170463i
$340$	3.17573e13	−	5.50053e13i	0.379061	−	0.656554i
$341$	−9.51051e13			−1.11700
$342$	1.36714e9	−	3.70864e9i	1.58005e−5	−	4.28619e-5i
$343$	3.39700e12			0.0386347
$344$	2.16311e9	−	3.74662e9i	2.42107e−5	−	4.19342e-5i
$345$	1.87559e14	+	8.79303e13i	2.06601	+	0.968576i
$346$	−4.26483e9	−	7.38691e9i	−4.62363e−5	−	8.00837e-5i
$347$	−6.21122e13	−	1.07581e14i	−0.662773	−	1.14796i	−0.979884	−	0.199568i	$-0.936046\pi$
$347$	−6.21122e13	−	1.07581e14i	−0.662773	−	1.14796i	0.317111	−	0.948388i	$-0.397287\pi$
$348$	4.05515e12	+	4.74754e13i	0.0425913	+	0.498635i
$349$	8.56322e13	−	1.48319e14i	0.885314	−	1.53341i	0.0399613	−	0.999201i	$-0.487277\pi$
$349$	8.56322e13	−	1.48319e14i	0.885314	−	1.53341i	0.845353	−	0.534208i	$-0.179390\pi$
$350$	1.05233e10			0.000107097
$351$	−4.36797e13	+	4.31438e13i	−0.437614	+	0.432244i
$352$	1.23487e10			0.000121797
$353$	−5.77929e13	+	1.00100e14i	−0.561194	+	0.972017i	0.436198	+	0.899851i	$0.356325\pi$
$353$	−5.77929e13	+	1.00100e14i	−0.561194	+	0.972017i	−0.997393	+	0.0721666i	$0.977009\pi$
$354$	5.38056e8	+	6.29926e9i	5.14410e−6	+	6.02243e-5i
$355$	−5.25481e13	−	9.10160e13i	−0.494654	−	0.856765i
$356$	8.63282e13	+	1.49525e14i	0.800162	+	1.38592i
$357$	−6.82902e13	−	3.20155e13i	−0.623280	−	0.292203i
$358$	2.35108e9	−	4.07218e9i	2.11305e−5	−	3.65991e-5i
$359$	1.40290e13			0.124167			0.0620836	−	0.998071i	$-0.480225\pi$
$359$	1.40290e13			0.124167			0.0620836	+	0.998071i	$0.480225\pi$
$360$	−1.18669e10	−	1.42612e10i	−0.000103436	−	0.000124306i
$361$	−2.50677e13			−0.215192
$362$	−4.46433e9	+	7.73245e9i	−3.77450e−5	+	6.53762e-5i
$363$	−3.74444e13	+	2.61042e13i	−0.311817	+	0.217382i
$364$	5.33840e13	+	9.24637e13i	0.437878	+	0.758427i
$365$	1.24147e13	+	2.15029e13i	0.100306	+	0.173734i
$366$	−5.17538e9	+	3.60799e9i	−4.11904e−5	+	2.87157e-5i
$367$	−2.61139e13	+	4.52306e13i	−0.204743	+	0.354625i	−0.950051	−	0.312096i	$-0.898969\pi$
$367$	−2.61139e13	+	4.52306e13i	−0.204743	+	0.354625i	0.745308	+	0.666720i	$0.232302\pi$
$368$	−1.88400e14			−1.45519
$369$	4.52142e13	+	5.43367e13i	0.344057	+	0.413474i
$370$	6.58599e8			4.93755e−6
$371$	4.03218e13	−	6.98393e13i	0.297840	−	0.515874i
$372$	−1.76499e14	−	8.27453e13i	−1.28456	−	0.602223i
$373$	−3.18814e13	−	5.52202e13i	−0.228633	−	0.396004i	0.728770	−	0.684758i	$-0.240092\pi$
$373$	−3.18814e13	−	5.52202e13i	−0.228633	−	0.396004i	−0.957403	+	0.288755i	$0.906759\pi$
$374$	−1.38887e9	−	2.40560e9i	−9.81451e−6	−	1.69992e-5i
$375$	8.79121e12	+	1.02922e14i	0.0612176	+	0.716702i
$376$	7.20772e9	−	1.24841e10i	4.94612e−5	−	8.56693e-5i
$377$	−4.55177e13			−0.307824
$378$	−7.83707e9	+	7.74091e9i	−5.22334e−5	+	5.15926e-5i
$379$	4.14208e13			0.272084			0.136042	−	0.990703i	$-0.456562\pi$
$379$	4.14208e13			0.272084			0.136042	+	0.990703i	$0.456562\pi$
$380$	1.07280e14	−	1.85814e14i	0.694557	−	1.20301i
$381$	2.71368e12	+	3.17703e13i	0.0173170	+	0.202737i
$382$	5.48634e9	+	9.50263e9i	3.45092e−5	+	5.97716e-5i
$383$	−5.35649e13	−	9.27771e13i	−0.332114	−	0.575238i	0.650812	−	0.759239i	$-0.274428\pi$
$383$	−5.35649e13	−	9.27771e13i	−0.332114	−	0.575238i	−0.982926	+	0.184001i	$0.941095\pi$
$384$	3.05561e10	+	1.43252e10i	0.000186757	+	8.75543e-5i
$385$	−1.45867e14	+	2.52650e14i	−0.878868	+	1.52224i
$386$	−7.14698e9			−4.24515e−5
$387$	2.77326e13	−	7.52301e13i	0.162398	−	0.440536i
$388$	7.92126e13			0.457320
$389$	−1.05341e14	+	1.82455e14i	−0.599616	+	1.03857i	0.393262	+	0.919427i	$0.371347\pi$
$389$	−1.05341e14	+	1.82455e14i	−0.599616	+	1.03857i	−0.992878	+	0.119139i	$0.961987\pi$
$390$	7.26942e9	−	5.06785e9i	4.07985e−5	−	2.84425e-5i
$391$	6.35689e13	+	1.10104e14i	0.351781	+	0.609302i
$392$	9.70642e9	+	1.68120e10i	5.29646e−5	+	9.17374e-5i
$393$	2.57490e14	−	1.79508e14i	1.38548	−	0.965882i
$394$	−7.26942e9	+	1.25910e10i	−3.85719e−5	+	6.68084e-5i
$395$	5.05945e14			2.64740
$396$	1.50364e14	−	2.58757e13i	0.775924	−	0.133527i
$397$	−9.86416e13			−0.502010			−0.251005	−	0.967986i	$-0.580761\pi$
$397$	−9.86416e13			−0.502010			−0.251005	+	0.967986i	$0.580761\pi$
$398$	3.73445e9	−	6.46826e9i	1.87443e−5	−	3.24661e-5i
$399$	−2.30692e14	−	1.08152e14i	−1.14204	−	0.535405i
$400$	−1.49374e14	−	2.58724e14i	−0.729367	−	1.26330i
$401$	8.82693e13	+	1.52887e14i	0.425124	+	0.736336i	0.996432	−	0.0843996i	$-0.0268972\pi$
$401$	8.82693e13	+	1.52887e14i	0.425124	+	0.736336i	−0.571308	+	0.820736i	$0.693564\pi$
$402$	−1.16996e8	−	1.36972e9i	−5.55812e−7	−	6.50713e-6i
$403$	9.31081e13	−	1.61268e14i	0.436325	−	0.755736i
$404$	−4.74260e13			−0.219240
$405$	−2.61570e14	−	2.23177e14i	−1.19285	−	1.01776i
$406$	−8.16683e9			−3.67418e−5
$407$	−5.41618e12	+	9.38111e12i	−0.0240394	+	0.0416375i
$408$	−9.69086e8	−	1.13455e10i	−4.24357e−6	−	4.96813e-5i
$409$	1.10075e14	+	1.90656e14i	0.475567	+	0.823706i	0.999608	−	0.0279871i	$-0.00890973\pi$
$409$	1.10075e14	+	1.90656e14i	0.475567	+	0.823706i	−0.524042	+	0.851693i	$0.675576\pi$
$410$	−5.10148e9	−	8.83602e9i	−2.17463e−5	−	3.76657e-5i
$411$	7.84713e13	+	3.67885e13i	0.330051	+	0.154733i
$412$	−1.14329e14	+	1.98023e14i	−0.474482	+	0.821827i
$413$	4.07529e14			1.66891
$414$	1.82996e10	−	3.14912e9i	7.39502e−5	−	1.27259e-5i
$415$	4.46010e13			0.177861
$416$	−1.20894e10	+	2.09394e10i	−4.75763e−5	+	8.24047e-5i
$417$	−2.02409e13	+	1.41109e13i	−0.0786107	+	0.0548031i
$418$	−4.69176e9	−	8.12637e9i	−1.79832e−5	−	3.11478e-5i
$419$	−1.70481e14	−	2.95282e14i	−0.644910	−	1.11702i	−0.984322	−	0.176379i	$-0.943562\pi$
$419$	−1.70481e14	−	2.95282e14i	−0.644910	−	1.11702i	0.339413	−	0.940638i	$-0.389772\pi$
$420$	−4.90520e14	+	3.41964e14i	−1.83141	+	1.27676i
$421$	−3.11565e12	+	5.39646e12i	−0.0114814	+	0.0198865i	−0.871709	−	0.490024i	$-0.836988\pi$
$421$	−3.11565e12	+	5.39646e12i	−0.0114814	+	0.0198865i	0.860228	+	0.509910i	$0.170321\pi$
$422$	−1.64862e9			−5.99655e−6
$423$	9.24079e13	−	2.50674e14i	0.331770	−	0.899990i
$424$	1.21751e10			4.31479e−5
$425$	−1.00802e14	+	1.74594e14i	−0.352639	+	0.610788i
$426$	−8.52990e9	−	3.99895e9i	−2.94572e−5	−	1.38100e-5i
$427$	2.03336e14	+	3.52188e14i	0.693203	+	1.20066i
$428$	−2.45627e14	−	4.25438e14i	−0.826675	−	1.43184i
$429$	1.24043e13	+	1.45223e14i	0.0412153	+	0.482525i
$430$	−5.78643e9	+	1.00224e10i	−1.89816e−5	+	3.28772e-5i
$431$	−2.17000e14			−0.702804			−0.351402	−	0.936225i	$-0.614295\pi$
$431$	−2.17000e14			−0.702804			−0.351402	+	0.936225i	$0.614295\pi$
$432$	3.01562e14	+	8.28017e13i	0.964310	+	0.264776i
$433$	−5.40006e14			−1.70496			−0.852482	−	0.522756i	$-0.824904\pi$
$433$	−5.40006e14			−1.70496			−0.852482	+	0.522756i	$0.824904\pi$
$434$	1.67056e10	−	2.89349e10i	5.20796e−5	−	9.02045e-5i
$435$	−2.16954e13	−	2.53997e14i	−0.0667846	−	0.781877i
$436$	1.61950e14	+	2.80506e14i	0.492272	+	0.852640i
$437$	2.14743e14	+	3.71945e14i	0.644570	+	1.11643i
$438$	2.01522e9	+	9.44767e8i	5.97332e−6	+	2.80038e-6i
$439$	−1.95307e13	+	3.38281e13i	−0.0571692	+	0.0990200i	−0.893194	−	0.449672i	$-0.851541\pi$
$439$	−1.95307e13	+	3.38281e13i	−0.0571692	+	0.0990200i	0.836024	+	0.548692i	$0.184874\pi$
$440$	−4.40444e10			−0.000127321
$441$	2.30128e14	+	2.76559e14i	0.656987	+	0.789541i
$442$	5.43884e9			1.53350e−5
$443$	−2.22365e14	+	3.85147e14i	−0.619221	+	1.07252i	0.370407	+	0.928869i	$0.379218\pi$
$443$	−2.22365e14	+	3.85147e14i	−0.619221	+	1.07252i	−0.989628	+	0.143653i	$0.954115\pi$
$444$	−1.82135e13	+	1.26974e13i	−0.0500941	+	0.0349229i
$445$	−4.61864e14	−	7.99971e14i	−1.25468	−	2.17317i
$446$	−1.05226e10	−	1.82257e10i	−2.82346e−5	−	4.89037e-5i
$447$	−1.14343e14	+	7.97140e13i	−0.303054	+	0.211273i
$448$	2.71920e14	−	4.70978e14i	0.711888	−	1.23303i
$449$	2.32197e13			0.0600483			0.0300242	−	0.999549i	$-0.490442\pi$
$449$	2.32197e13			0.0600483			0.0300242	+	0.999549i	$0.490442\pi$
$450$	1.88335e10	+	2.26334e10i	4.81131e−5	+	5.78205e-5i
$451$	1.67814e14			0.423504
$452$	5.97791e12	−	1.03540e13i	0.0149035	−	0.0258136i
$453$	1.63964e14	+	7.68688e13i	0.403839	+	0.189326i
$454$	−3.91615e9	−	6.78297e9i	−9.52910e−6	−	1.65049e-5i
$455$	−2.85609e14	−	4.94689e14i	−0.686608	−	1.18924i
$456$	−3.27368e9	−	3.83264e10i	−7.77553e−6	−	9.10314e-5i
$457$	2.09485e14	−	3.62839e14i	0.491602	−	0.851480i	−0.508351	−	0.861150i	$-0.669745\pi$
$457$	2.09485e14	−	3.62839e14i	0.491602	−	0.851480i	0.999953	+	0.00966968i	$0.00307800\pi$
$458$	1.63183e10			3.78368e−5
$459$	−5.33605e13	−	2.04177e14i	−0.122250	−	0.467775i
$460$	1.00796e15			2.28178
$461$	−1.86463e14	+	3.22963e14i	−0.417097	+	0.722433i	−0.995646	−	0.0932143i	$-0.970286\pi$
$461$	−1.86463e14	+	3.22963e14i	−0.417097	+	0.722433i	0.578549	+	0.815648i	$0.303619\pi$
$462$	2.22560e9	+	2.60560e10i	4.91944e−6	+	5.75941e-5i
$463$	−1.22043e14	−	2.11385e14i	−0.266574	−	0.461720i	0.701401	−	0.712767i	$-0.252558\pi$
$463$	−1.22043e14	−	2.11385e14i	−0.266574	−	0.461720i	−0.967975	+	0.251047i	$0.919225\pi$
$464$	1.15926e14	+	2.00789e14i	0.250225	+	0.433403i
$465$	9.44284e14	+	4.42695e14i	2.01424	+	0.944307i
$466$	−1.48520e10	+	2.57244e10i	−3.13084e−5	+	5.42278e-5i
$467$	7.92205e13			0.165042			0.0825211	−	0.996589i	$-0.473703\pi$
$467$	7.92205e13			0.165042			0.0825211	+	0.996589i	$0.473703\pi$
$468$	−1.03330e14	+	2.80301e14i	−0.212751	+	0.577129i
$469$	−8.86139e13			−0.180323
$470$	−1.92810e10	+	3.33956e10i	−3.87785e−5	+	6.71663e-5i
$471$	−4.70931e14	+	3.28307e14i	−0.936143	+	0.652628i
$472$	3.07632e10	+	5.32834e10i	6.04436e−5	+	0.000104691i
$473$	−9.51728e13	−	1.64844e14i	−0.184832	−	0.320138i
$474$	3.72041e10	−	2.59367e10i	7.14184e−5	−	4.97890e-5i
$475$	−3.40520e14	+	5.89798e14i	−0.646142	+	1.11915i
$476$	−3.66998e14			−0.688375
$477$	2.22375e14	−	3.82678e13i	0.412320	−	0.0709550i
$478$	1.15359e10			2.11445e−5
$479$	4.79469e14	−	8.30465e14i	0.868791	−	1.50479i	0.00555842	−	0.999985i	$-0.498231\pi$
$479$	4.79469e14	−	8.30465e14i	0.868791	−	1.50479i	0.863233	−	0.504806i	$-0.168436\pi$
$480$	−1.22608e11	−	5.74806e10i	−0.000219631	−	0.000102966i
$481$	−1.06049e13	−	1.83683e13i	−0.0187806	−	0.0325289i
$482$	1.46341e10	+	2.53470e10i	2.56217e−5	+	4.43780e-5i
$483$	−1.01866e14	−	1.19259e15i	−0.176327	−	2.06434i
$484$	−1.11053e14	+	1.92350e14i	−0.190056	+	0.329187i
$485$	−4.23794e14			−0.717093
$486$	−3.06752e10	−	3.00201e9i	−5.13202e−5	−	5.02242e-6i
$487$	−9.46756e13			−0.156613			−0.0783067	−	0.996929i	$-0.524951\pi$
$487$	−9.46756e13			−0.156613			−0.0783067	+	0.996929i	$0.524951\pi$
$488$	−3.06984e10	+	5.31713e10i	−5.02120e−5	+	8.69697e-5i
$489$	1.23693e13	+	1.44813e14i	0.0200054	+	0.234212i
$490$	−2.59651e10	−	4.49729e10i	−4.15252e−5	−	7.19237e-5i
$491$	7.86165e13	+	1.36168e14i	0.124327	+	0.215341i	0.921470	−	0.388450i	$-0.126990\pi$
$491$	7.86165e13	+	1.36168e14i	0.124327	+	0.215341i	−0.797143	+	0.603791i	$0.793656\pi$
$492$	3.11435e14	+	1.46005e14i	0.487034	+	0.228329i
$493$	7.82299e13	−	1.35498e14i	0.120980	−	0.209544i
$494$	1.83730e10			2.80984e−5
$495$	−8.04459e14	+	1.38437e14i	−1.21668	+	0.209374i
$496$	−9.48521e14			−1.41872
$497$	−3.03632e14	+	5.25905e14i	−0.449145	+	0.777942i
$498$	3.27969e9	−	2.28642e9i	4.79812e−6	−	3.34499e-6i
$499$	3.46034e14	+	5.99349e14i	0.500687	+	0.867215i	1.00000		0.000793410i	$0.000252550\pi$
$499$	3.46034e14	+	5.99349e14i	0.500687	+	0.867215i	−0.499313	+	0.866422i	$0.666414\pi$
$500$	2.51317e14	+	4.35294e14i	0.359656	+	0.622942i
$501$	−7.63686e14	+	5.32400e14i	−1.08095	+	0.753583i
$502$	1.24855e10	−	2.16254e10i	1.74797e−5	−	3.02757e-5i
$503$	2.17927e14			0.301778			0.150889	−	0.988551i	$-0.451786\pi$
$503$	2.17927e14			0.301778			0.150889	+	0.988551i	$0.451786\pi$
$504$	−3.70790e10	+	1.00584e11i	−5.07879e−5	+	0.000137772i
$505$	2.53733e14			0.343775
$506$	2.20410e10	−	3.81761e10i	2.95395e−5	−	5.11639e-5i
$507$	4.24574e14	+	1.99047e14i	0.562873	+	0.263883i
$508$	7.75769e13	+	1.34367e14i	0.101738	+	0.176215i
$509$	5.50998e14	+	9.54357e14i	0.714830	+	1.23812i	0.963025	+	0.269411i	$0.0868291\pi$
$509$	5.50998e14	+	9.54357e14i	0.714830	+	1.23812i	−0.248196	+	0.968710i	$0.579838\pi$
$510$	2.59235e9	+	3.03497e10i	3.32704e−6	+	3.89510e-5i
$511$	7.17341e13	−	1.24247e14i	0.0910774	−	0.157751i
$512$	2.05264e11			0.000257827
$513$	−1.80258e14	−	6.89732e14i	−0.224000	−	0.857107i
$514$	5.48982e10			6.74933e−5
$515$	6.11668e14	−	1.05944e15i	0.744005	−	1.28865i
$516$	−3.32034e13	−	3.88727e14i	−0.0399586	−	0.467812i
$517$	−3.17126e14	−	5.49278e14i	−0.377601	−	0.654024i
$518$	−1.90275e9	−	3.29565e9i	−2.24165e−6	−	3.88264e-6i
$519$	−1.39294e15	−	6.53033e14i	−1.62373	−	0.761228i
$520$	4.31195e10	−	7.46852e10i	4.97343e−5	−	8.61423e-5i
$521$	−1.23237e14			−0.140648			−0.0703238	−	0.997524i	$-0.522403\pi$
$521$	−1.23237e14			−0.140648			−0.0703238	+	0.997524i	$0.522403\pi$
$522$	−1.46162e10	−	1.75652e10i	−1.65062e−5	−	1.98366e-5i
$523$	−1.97663e14			−0.220885			−0.110443	−	0.993882i	$-0.535227\pi$
$523$	−1.97663e14			−0.220885			−0.110443	+	0.993882i	$0.535227\pi$
$524$	7.63667e14	−	1.32271e15i	0.844465	−	1.46266i
$525$	1.55698e15	−	1.08544e15i	1.70375	−	1.18776i
$526$	−4.31766e10	−	7.47841e10i	−4.67549e−5	−	8.09819e-5i
$527$	3.20044e14	+	5.54333e14i	0.342966	+	0.594035i
$528$	6.09021e14	−	4.24576e14i	0.645871	−	0.450266i
$529$	−5.32414e14	+	9.22169e14i	−0.558783	+	0.967841i
$530$	−3.25689e10			−3.38287e−5
$531$	7.29358e14	+	8.76514e14i	0.749757	+	0.901030i
$532$	−1.23976e15			−1.26131
$533$	−1.64291e14	+	2.84560e14i	−0.165429	+	0.286532i
$534$	−7.49723e10	−	3.51481e10i	−7.47178e−5	−	3.50288e-5i
$535$	1.31412e15	+	2.27613e15i	1.29626	+	2.24518i
$536$	−6.68920e9	−	1.15860e10i	−6.53082e−6	−	1.13117e-5i
$537$	−7.21772e13	−	8.45010e14i	−0.0697496	−	0.816588i
$538$	−3.55417e10	+	6.15600e10i	−3.39966e−5	+	5.88838e-5i
$539$	8.54127e14			0.808694
$540$	−1.61339e15	−	4.42997e14i	−1.51207	−	0.415178i
$541$	1.61751e15			1.50059			0.750297	−	0.661101i	$-0.229911\pi$
$541$	1.61751e15			1.50059			0.750297	+	0.661101i	$0.229911\pi$
$542$	−7.45708e9	+	1.29160e10i	−6.84814e−6	+	1.18613e-5i
$543$	1.37053e14	+	1.60454e15i	0.124592	+	1.45865i
$544$	−4.15554e10	−	7.19760e10i	−3.73967e−5	−	6.47730e-5i
$545$	−8.66447e14	−	1.50073e15i	−0.771900	−	1.33697i
$546$	−4.63616e10	−	2.17350e10i	−4.08883e−5	−	1.91690e-5i
$547$	4.01838e14	−	6.96005e14i	0.350850	−	0.607690i	−0.635549	−	0.772061i	$-0.719226\pi$
$547$	4.01838e14	−	6.96005e14i	0.350850	−	0.607690i	0.986399	+	0.164371i	$0.0525594\pi$
$548$	4.21712e14			0.364521
$549$	−3.93575e14	+	1.06765e15i	−0.336806	+	0.913651i
$550$	6.99014e10			5.92231e−5
$551$	2.64269e14	−	4.57728e14i	0.221673	−	0.383949i
$552$	1.48238e11	−	1.03344e11i	0.000123111	−	8.58260e-5i
$553$	−1.46172e15	−	2.53177e15i	−1.20192	−	2.08178i
$554$	5.93602e10	+	1.02815e11i	4.83272e−5	+	8.37052e-5i
$555$	9.74436e13	−	6.79324e13i	0.0785493	−	0.0547603i
$556$	−6.00308e13	+	1.03976e14i	−0.0479140	+	0.0829895i
$557$	−1.41700e15			−1.11986			−0.559932	−	0.828539i	$-0.689173\pi$
$557$	−1.41700e15			−1.11986			−0.559932	+	0.828539i	$0.689173\pi$
$558$	9.21312e10	−	1.58546e10i	7.20973e−5	−	1.24070e-5i
$559$	3.72698e14			0.288796
$560$	−1.45479e15	+	2.51978e15i	−1.11626	+	1.93343i
$561$	−4.53622e14	−	2.12665e14i	−0.344666	−	0.161585i
$562$	4.51519e10	+	7.82054e10i	3.39724e−5	+	5.88420e-5i
$563$	7.03466e14	+	1.21844e15i	0.524140	+	0.907837i	0.999605	+	0.0281023i	$0.00894642\pi$
$563$	7.03466e14	+	1.21844e15i	0.524140	+	0.907837i	−0.475465	+	0.879735i	$0.657720\pi$
$564$	−1.10637e14	−	1.29528e15i	−0.0816331	−	0.955715i
$565$	−3.19823e13	+	5.53950e13i	−0.0233692	+	0.0404766i
$566$	−7.85115e10			−5.68124e−5
$567$	−3.61090e14	+	1.95368e15i	−0.258767	+	1.40006i
$568$	−9.16810e10			−6.50674e−5
$569$	3.31228e13	−	5.73704e13i	0.0232814	−	0.0403246i	−0.854150	−	0.520027i	$-0.825922\pi$
$569$	3.31228e13	−	5.73704e13i	0.0232814	−	0.0403246i	0.877431	+	0.479702i	$0.159255\pi$
$570$	8.75724e9	+	1.02525e11i	6.09615e−6	+	7.13703e-5i
$571$	−4.81407e14	−	8.33821e14i	−0.331905	−	0.574876i	0.650980	−	0.759094i	$-0.274358\pi$
$571$	−4.81407e14	−	8.33821e14i	−0.331905	−	0.574876i	−0.982885	+	0.184218i	$0.941025\pi$
$572$	3.54606e14	+	6.14196e14i	0.242141	+	0.419401i
$573$	1.79190e15	+	8.40071e14i	1.21189	+	0.568153i
$574$	−2.94772e10	+	5.10560e10i	−1.97456e−5	+	3.42004e-5i
$575$	−3.19939e15			−2.12273
$576$	1.49964e15	−	2.58068e14i	0.985514	−	0.169594i
$577$	−3.50147e14			−0.227920			−0.113960	−	0.993485i	$-0.536354\pi$
$577$	−3.50147e14			−0.227920			−0.113960	+	0.993485i	$0.536354\pi$
$578$	3.06406e10	−	5.30710e10i	1.97558e−5	−	3.42180e-5i
$579$	−1.05744e15	+	7.37189e14i	−0.675341	+	0.470811i
$580$	−6.20213e14	−	1.07424e15i	−0.392362	−	0.679591i
$581$	−1.28856e14	−	2.23185e14i	−0.0807487	−	0.139861i
$582$	−3.11633e10	+	2.17253e10i	−1.93449e−5	+	1.34862e-5i
$583$	2.67840e14	−	4.63912e14i	0.164702	−	0.285272i
$584$	2.16600e10			1.31943e−5
$585$	5.52822e14	−	1.49964e15i	0.333601	−	0.904959i
$586$	−1.05882e11			−6.32976e−5
$587$	1.44704e15	−	2.50634e15i	0.856980	−	1.48433i	−0.0178162	−	0.999841i	$-0.505671\pi$
$587$	1.44704e15	−	2.50634e15i	0.856980	−	1.48433i	0.874796	−	0.484491i	$-0.160995\pi$
$588$	1.58512e15	+	7.43126e14i	0.930006	+	0.436001i
$589$	1.08114e15	+	1.87260e15i	0.628420	+	1.08845i
$590$	−8.22928e10	−	1.42535e11i	−4.73888e−5	−	8.20798e-5i
$591$	2.23169e14	+	2.61273e15i	0.127322	+	1.49061i
$592$	−5.40178e13	+	9.35616e13i	−0.0305329	+	0.0528845i
$593$	−8.84310e14			−0.495226			−0.247613	−	0.968859i	$-0.579646\pi$
$593$	−8.84310e14			−0.495226			−0.247613	+	0.968859i	$0.579646\pi$
$594$	−5.20582e10	+	5.14195e10i	−2.88844e−5	+	2.85301e-5i
$595$	1.96347e15			1.07940
$596$	−3.39122e14	+	5.87376e14i	−0.184715	+	0.319935i
$597$	−1.14646e14	−	1.34221e15i	−0.0618730	−	0.724374i
$598$	4.31564e10	+	7.47490e10i	2.30775e−5	+	3.99714e-5i
$599$	−9.80674e14	−	1.69858e15i	−0.519610	−	0.899990i	−0.999740	−	0.0227933i	$-0.992744\pi$
$599$	−9.80674e14	−	1.69858e15i	−0.519610	−	0.899990i	0.480131	−	0.877197i	$-0.340589\pi$
$600$	2.59450e11	+	1.21634e11i	0.000136214	+	6.38592e-5i
$601$	1.11515e15	−	1.93150e15i	0.580128	−	1.00481i	−0.415335	−	0.909668i	$-0.636336\pi$
$601$	1.11515e15	−	1.93150e15i	0.580128	−	1.00481i	0.995464	−	0.0951432i	$-0.0303309\pi$
$602$	6.68698e10			3.44707e−5
$603$	−1.58593e14	−	1.90591e14i	−0.0810100	−	0.0973547i
$604$	8.81158e14			0.446016
$605$	5.94144e14	−	1.02909e15i	0.298014	−	0.516176i
$606$	1.86580e10	−	1.30074e10i	9.27397e−6	−	6.46531e-6i
$607$	2.17207e14	+	3.76214e14i	0.106988	+	0.185309i	0.914549	−	0.404475i	$-0.132546\pi$
$607$	2.17207e14	+	3.76214e14i	0.106988	+	0.185309i	−0.807560	+	0.589785i	$0.799213\pi$
$608$	−1.40379e11	−	2.43143e11i	−6.85222e−5	−	0.000118684i
$609$	−1.20833e15	+	8.42383e14i	−0.584509	+	0.407488i
$610$	8.21197e10	−	1.42235e11i	3.93671e−5	−	6.81858e-5i
$611$	1.24187e15			0.589995
$612$	−6.56818e14	−	7.89339e14i	−0.309252	−	0.371647i
$613$	−2.29850e15			−1.07253			−0.536267	−	0.844048i	$-0.680166\pi$
$613$	−2.29850e15			−1.07253			−0.536267	+	0.844048i	$0.680166\pi$
$614$	−7.42159e10	+	1.28546e11i	−3.43219e−5	+	5.94472e-5i
$615$	−1.66620e15	−	7.81141e14i	−0.763686	−	0.358027i
$616$	1.27248e11	+	2.20400e11i	5.78038e−5	+	0.000100119i
$617$	7.90592e14	+	1.36934e15i	0.355946	+	0.616516i	0.987279	−	0.158995i	$-0.0508255\pi$
$617$	7.90592e14	+	1.36934e15i	0.355946	+	0.616516i	−0.631334	+	0.775511i	$0.717492\pi$
$618$	−9.33264e9	−	1.09261e11i	−4.16455e−6	−	4.87562e-5i
$619$	1.05337e15	−	1.82449e15i	0.465888	−	0.806942i	−0.533353	−	0.845893i	$-0.679068\pi$
$619$	1.05337e15	−	1.82449e15i	0.465888	−	0.806942i	0.999241	+	0.0389507i	$0.0124015\pi$
$620$	5.07467e15			2.22461
$621$	2.38271e15	−	2.35348e15i	1.03530	−	1.02260i
$622$	−1.09789e11			−4.72838e−5
$623$	−2.66872e15	+	4.62236e15i	−1.13925	+	1.97324i
$624$	1.23713e14	+	1.44837e15i	0.0523482	+	0.612863i
$625$	3.94379e14	+	6.83084e14i	0.165414	+	0.286506i
$626$	−6.64012e9	−	1.15010e10i	−2.76069e−6	−	4.78165e-6i
$627$	−1.53239e15	−	7.18405e14i	−0.631534	−	0.296072i
$628$	−1.39669e15	+	2.41914e15i	−0.570589	+	0.988289i
$629$	7.29054e13			0.0295244
$630$	9.91879e10	−	2.69066e11i	3.98186e−5	−	0.000108016i
$631$	−4.57498e15			−1.82066			−0.910328	−	0.413888i	$-0.864170\pi$
$631$	−4.57498e15			−1.82066			−0.910328	+	0.413888i	$0.864170\pi$
$632$	2.20681e11	−	3.82231e11i	8.70605e−5	−	0.000150793i
$633$	−2.43923e14	+	1.70050e14i	−0.0953964	+	0.0665052i
$634$	1.52087e9	+	2.63423e9i	5.89660e−7	+	1.02132e-6i
$635$	−4.15043e14	−	7.18876e14i	−0.159528	−	0.276311i
$636$	9.00688e14	−	6.27911e14i	0.343210	−	0.239268i
$637$	−8.36193e14	+	1.44833e15i	−0.315893	+	0.547142i
$638$	−5.42487e10			−2.03178e−5
$639$	−1.67453e15	+	2.88165e14i	−0.621782	+	0.107001i
$640$	−8.78544e11			−0.000323425
$641$	−6.49830e14	+	1.12554e15i	−0.237181	+	0.410810i	−0.959904	−	0.280328i	$-0.909557\pi$
$641$	−6.49830e14	+	1.12554e15i	−0.237181	+	0.410810i	0.722723	+	0.691138i	$0.242890\pi$
$642$	2.13316e11	+	1.00006e11i	7.71935e−5	+	3.61895e-5i
$643$	9.04586e14	+	1.56679e15i	0.324556	+	0.562147i	0.981422	−	0.191860i	$-0.0614519\pi$
$643$	9.04586e14	+	1.56679e15i	0.324556	+	0.562147i	−0.656867	+	0.754007i	$0.728119\pi$
$644$	−2.91207e15	−	5.04386e15i	−1.03593	−	1.79428i
$645$	1.77641e14	+	2.07972e15i	0.0626564	+	0.733546i
$646$	−3.15771e10	+	5.46932e10i	−1.10432e−5	+	1.91273e-5i
$647$	1.26070e15			0.437158			0.218579	−	0.975819i	$-0.429858\pi$
$647$	1.26070e15			0.437158			0.218579	+	0.975819i	$0.429858\pi$
$648$	−2.82697e11	+	1.00266e11i	−9.71982e−5	+	3.44740e-5i
$649$	2.70704e15			0.922887
$650$	−6.84336e10	+	1.18530e11i	−2.31337e−5	+	4.00688e-5i
$651$	−5.12855e14	−	6.00421e15i	−0.171909	−	2.01262i
$652$	3.53606e14	+	6.12464e14i	0.117533	+	0.203572i
$653$	−1.08593e14	−	1.88089e14i	−0.0357915	−	0.0619927i	0.847575	−	0.530676i	$-0.178062\pi$
$653$	−1.08593e14	−	1.88089e14i	−0.0357915	−	0.0619927i	−0.883366	+	0.468683i	$0.844729\pi$
$654$	−1.40646e11	−	6.59372e10i	−4.59675e−5	−	2.15503e-5i
$655$	−4.08568e15	+	7.07661e15i	−1.32415	+	2.29350i
$656$	1.67368e15			0.537900
$657$	3.95614e14	−	6.80801e13i	0.126085	−	0.0216976i
$658$	2.22817e11			7.04217e−5
$659$	1.32465e15	−	2.29435e15i	0.415174	−	0.719102i	−0.580273	−	0.814422i	$-0.697054\pi$
$659$	1.32465e15	−	2.29435e15i	0.415174	−	0.719102i	0.995447	+	0.0953198i	$0.0303874\pi$
$660$	−3.25831e15	+	2.27152e15i	−1.01275	+	0.706033i
$661$	−1.94856e15	−	3.37500e15i	−0.600628	−	1.04032i	−0.992726	−	0.120394i	$-0.961584\pi$
$661$	−1.94856e15	−	3.37500e15i	−0.600628	−	1.04032i	0.392098	−	0.919923i	$-0.371749\pi$
$662$	3.71695e9	+	6.43794e9i	1.13623e−6	+	1.96801e-6i
$663$	8.04709e14	−	5.60999e14i	0.243958	−	0.170074i
$664$	1.94539e10	−	3.36952e10i	5.84901e−6	−	1.01308e-5i
$665$	6.63282e15			1.97778
$666$	3.68294e9	−	9.99068e9i	1.08915e−6	−	2.95452e-6i
$667$	2.48297e15			0.728248
$668$	−2.26495e15	+	3.92301e15i	−0.658853	+	1.14117i
$669$	−3.43681e15	−	1.61123e15i	−0.991542	−	0.464850i
$670$	1.78939e10	+	3.09932e10i	5.12028e−6	+	8.86859e-6i
$671$	1.35067e15	+	2.33943e15i	0.383333	+	0.663952i
$672$	6.65904e10	+	7.79603e11i	1.87448e−5	+	0.000219453i
$673$	2.95086e15	−	5.11105e15i	0.823885	−	1.42701i	−0.0788841	−	0.996884i	$-0.525136\pi$
$673$	2.95086e15	−	5.11105e15i	0.823885	−	1.42701i	0.902769	−	0.430126i	$-0.141531\pi$
$674$	−2.31133e9			−6.40078e−7
$675$	5.12110e15	+	1.40613e15i	1.40667	+	0.386238i
$676$	2.28170e15			0.621659
$677$	1.74255e15	−	3.01819e15i	0.470921	−	0.815658i	−0.528526	−	0.848917i	$-0.677255\pi$
$677$	1.74255e15	−	3.01819e15i	0.470921	−	0.815658i	0.999447	+	0.0332586i	$0.0105885\pi$
$678$	4.87977e8	+	5.71295e9i	1.30808e−7	+	1.53143e-6i
$679$	1.22438e15	+	2.12068e15i	0.325560	+	0.563887i
$680$	1.48217e11	+	2.56719e11i	3.90929e−5	+	6.77108e-5i
$681$	−1.27906e15	−	5.99642e14i	−0.334643	−	0.156886i
$682$	1.10968e11	−	1.92202e11i	2.87994e−5	−	4.98819e-5i
$683$	6.64535e14			0.171082			0.0855410	−	0.996335i	$-0.472738\pi$
$683$	6.64535e14			0.171082			0.0855410	+	0.996335i	$0.472738\pi$
$684$	−2.21881e15	−	2.66648e15i	−0.566644	−	0.680972i
$685$	−2.25620e15			−0.571582
$686$	−3.96359e9	+	6.86514e9i	−9.96107e−7	+	1.72531e-6i
$687$	2.41439e15	−	1.68318e15i	0.601929	−	0.419632i
$688$	−9.49197e14	−	1.64406e15i	−0.234758	−	0.406612i
$689$	5.24432e14	+	9.08343e14i	0.128672	+	0.222866i
$690$	−3.96544e11	+	2.76449e11i	−9.65209e−5	+	6.72891e-5i
$691$	2.83349e14	−	4.90775e14i	0.0684214	−	0.118509i	−0.829785	−	0.558083i	$-0.811537\pi$
$691$	2.83349e14	−	4.90775e14i	0.0684214	−	0.118509i	0.898207	+	0.439574i	$0.144870\pi$
$692$	−7.48581e15			−1.79331
$693$	3.01689e15	+	3.62558e15i	0.717013	+	0.861679i
$694$	2.89888e11			6.83522e−5
$695$	3.21170e14	−	5.56283e14i	0.0751309	−	0.130131i
$696$	−2.01353e11	−	9.43972e10i	−4.67312e−5	−	2.19083e-5i
$697$	−5.64723e14	−	9.78128e14i	−0.130033	−	0.225224i
$698$	1.99830e11	+	3.46116e11i	4.56516e−5	+	7.90708e-5i
$699$	4.55950e14	+	5.33801e15i	0.103346	+	1.20991i
$700$	4.61771e15	−	7.99811e15i	1.03845	−	1.79866i
$701$	−8.08219e15			−1.80335			−0.901675	−	0.432415i	$-0.857662\pi$
$701$	−8.08219e15			−1.80335			−0.901675	+	0.432415i	$0.857662\pi$
$702$	−3.62260e10	−	1.38614e11i	−8.01985e−6	−	3.06869e-5i
$703$	2.46283e14			0.0540978
$704$	1.80624e15	−	3.12851e15i	0.393665	−	0.681848i
$705$	5.91919e14	+	6.92985e15i	0.128004	+	1.49859i
$706$	−1.34864e11	−	2.33592e11i	−2.89382e−5	−	5.01224e-5i
$707$	−7.33056e14	−	1.26969e15i	−0.156074	−	0.270328i
$708$	5.02380e15	+	2.35523e15i	1.06133	+	0.497567i
$709$	−4.30078e15	+	7.44916e15i	−0.901556	+	1.56154i	−0.0760812	+	0.997102i	$0.524241\pi$
$709$	−4.30078e15	+	7.44916e15i	−0.901556	+	1.56154i	−0.825475	+	0.564439i	$0.809093\pi$
$710$	2.45251e11			5.10140e−5
$711$	2.82928e15	−	7.67498e15i	0.583974	−	1.58414i
$712$	−8.05816e11			−0.000165043
$713$	−5.07901e15	+	8.79710e15i	−1.03225	+	1.78792i
$714$	1.44382e11	−	1.00655e11i	2.91187e−5	−	2.03000e-5i
$715$	−1.89718e15	−	3.28600e15i	−0.379686	−	0.657635i
$716$	−2.06335e15	−	3.57383e15i	−0.409781	−	0.709761i
$717$	1.70681e15	−	1.18989e15i	0.336379	−	0.234505i
$718$	−1.63689e10	+	2.83518e10i	−3.20136e−6	+	5.54493e-6i
$719$	1.24659e14			0.0241944			0.0120972	−	0.999927i	$-0.496149\pi$
$719$	1.24659e14			0.0241944			0.0120972	+	0.999927i	$0.496149\pi$
$720$	−8.02319e15	+	1.38069e15i	−1.54532	+	0.265930i
$721$	−7.06863e15			−1.35111
$722$	2.92488e10	−	5.06604e10i	5.54821e−6	−	9.60979e-6i
$723$	4.77967e15	+	2.24078e15i	0.899782	+	0.421831i
$724$	3.91799e15	+	6.78615e15i	0.731983	+	1.26783i
$725$	1.96864e15	+	3.40978e15i	0.365012	+	0.632219i
$726$	−9.06527e9	−	1.06131e11i	−1.66813e−6	−	1.95295e-5i
$727$	4.38219e15	−	7.59018e15i	0.800299	−	1.38616i	−0.119121	−	0.992880i	$-0.538008\pi$
$727$	4.38219e15	−	7.59018e15i	0.800299	−	1.38616i	0.919419	−	0.393278i	$-0.128659\pi$
$728$	−4.98303e11			−9.03174e−5
$729$	−4.84823e15	+	2.71989e15i	−0.872132	+	0.489271i
$730$	−5.79414e10			−1.03446e−5
$731$	−6.40544e14	+	1.10946e15i	−0.113502	+	0.196591i
$732$	4.71216e14	+	5.51673e15i	0.0828722	+	0.970221i
$733$	−6.41473e14	−	1.11106e15i	−0.111971	−	0.193940i	0.804594	−	0.593826i	$-0.202383\pi$
$733$	−6.41473e14	−	1.11106e15i	−0.111971	−	0.193940i	−0.916565	+	0.399886i	$0.869050\pi$
$734$	−6.09389e10	−	1.05549e11i	−1.05576e−5	−	1.82864e-5i
$735$	−8.48051e15	−	3.97579e15i	−1.45828	−	0.683664i
$736$	6.59471e11	−	1.14224e12i	0.000112556	−	0.000194952i
$737$	−5.88624e14			−0.0997164
$738$	−1.62567e11	+	2.79757e10i	−2.73352e−5	+	4.70404e-6i
$739$	8.28107e15			1.38211			0.691054	−	0.722803i	$-0.257147\pi$
$739$	8.28107e15			1.38211			0.691054	+	0.722803i	$0.257147\pi$
$740$	2.89000e14	−	5.00563e14i	0.0478766	−	0.0829247i
$741$	2.71839e15	−	1.89512e15i	0.447005	−	0.311628i
$742$	9.40941e10	+	1.62976e11i	1.53582e−5	+	2.66012e-5i
$743$	1.58808e15	+	2.75063e15i	0.257296	+	0.445650i	0.965517	−	0.260341i	$-0.0838351\pi$
$743$	1.58808e15	+	2.75063e15i	0.257296	+	0.445650i	−0.708220	+	0.705991i	$0.750502\pi$
$744$	7.46322e11	−	5.20295e11i	0.000120026	−	8.36755e-5i
$745$	1.81433e15	−	3.14251e15i	0.289639	−	0.501669i
$746$	1.48796e11			2.35791e−5
$747$	2.49412e14	−	6.76579e14i	0.0392333	−	0.106428i
$748$	−2.43781e15			−0.380663
$749$	7.59322e15	−	1.31518e16i	1.17700	−	2.03862i
$750$	−2.18258e11	−	1.02323e11i	−3.35840e−5	−	1.57447e-5i
$751$	−3.41648e15	−	5.91752e15i	−0.521867	−	0.903900i	−0.999676	−	0.0254365i	$-0.991902\pi$
$751$	−3.41648e15	−	5.91752e15i	−0.521867	−	0.903900i	0.477810	−	0.878463i	$-0.341431\pi$
$752$	−3.16282e15	−	5.47817e15i	−0.479597	−	0.830687i
$753$	−3.83299e14	−	4.48745e15i	−0.0576986	−	0.675503i
$754$	5.31096e10	−	9.19886e10i	7.93653e−6	−	1.37465e-5i
$755$	−4.71427e15			−0.699369
$756$	2.44443e15	+	9.35329e15i	0.360004	+	1.37751i
$757$	8.31963e15			1.21640			0.608201	−	0.793783i	$-0.291892\pi$
$757$	8.31963e15			1.21640			0.608201	+	0.793783i	$0.291892\pi$
$758$	−4.83294e10	+	8.37089e10i	−7.01505e−6	+	1.21504e-5i
$759$	−6.76651e14	−	7.92185e15i	−0.0975068	−	1.14155i
$760$	5.00692e11	+	8.67224e11i	7.16301e−5	+	0.000124067i
$761$	6.00066e15	+	1.03934e16i	0.852282	+	1.47620i	0.879144	+	0.476557i	$0.158115\pi$
$761$	6.00066e15	+	1.03934e16i	0.852282	+	1.47620i	−0.0268615	+	0.999639i	$0.508551\pi$
$762$	−6.73722e10	−	3.15851e10i	−9.50010e−6	−	4.45379e-6i
$763$	−5.00647e15	+	8.67146e15i	−0.700885	+	1.21397i
$764$	9.62986e15			1.33846
$765$	3.51404e15	+	4.22303e15i	0.484918	+	0.582756i
$766$	2.49996e11			3.42511e−5
$767$	−2.65020e15	+	4.59027e15i	−0.360499	+	0.624402i
$768$	6.07401e15	−	4.23447e15i	0.820330	−	0.571890i
$769$	5.24201e15	+	9.07942e15i	0.702915	+	1.21748i	0.967439	+	0.253105i	$0.0814518\pi$
$769$	5.24201e15	+	9.07942e15i	0.702915	+	1.21748i	−0.264524	+	0.964379i	$0.585215\pi$
$770$	−3.40393e11	−	5.89578e11i	−4.53192e−5	−	7.84951e-5i
$771$	8.12251e15	−	5.66258e15i	1.07372	−	0.748540i
$772$	−3.13617e15	+	5.43201e15i	−0.411628	+	0.712960i
$773$	−4.56013e15			−0.594278			−0.297139	−	0.954834i	$-0.596032\pi$
$773$	−4.56013e15			−0.594278			−0.297139	+	0.954834i	$0.596032\pi$
$774$	1.19677e11	+	1.43824e11i	1.54859e−5	+	1.86104e-5i
$775$	−1.61077e16			−2.06954
$776$	−1.84849e11	+	3.20168e11i	−2.35818e−5	+	4.08450e-5i
$777$	−6.21459e14	−	2.91349e14i	−0.0787221	−	0.0369061i
$778$	−2.45821e11	−	4.25775e11i	−3.09194e−5	−	5.35540e-5i
$779$	−1.90770e15	−	3.30423e15i	−0.238261	−	0.412680i
$780$	−6.61878e14	−	7.74889e15i	−0.0820838	−	0.960990i
$781$	−2.01689e15	+	3.49336e15i	−0.248372	+	0.430192i
$782$	−2.96686e11			−3.62794e−5
$783$	−3.97436e15	−	1.09126e15i	−0.482589	−	0.132507i
$784$	8.51856e15			1.02714
$785$	7.47243e15	−	1.29426e16i	0.894703	−	1.54967i
$786$	6.23381e10	+	7.29819e11i	7.41190e−6	+	8.67743e-5i
$787$	−6.85195e15	−	1.18679e16i	−0.809009	−	1.40124i	−0.913551	−	0.406724i	$-0.866671\pi$
$787$	−6.85195e15	−	1.18679e16i	−0.809009	−	1.40124i	0.104542	−	0.994521i	$-0.466662\pi$
$788$	6.37980e15	+	1.10501e16i	0.748019	+	1.29561i
$789$	−1.41020e16	−	6.61123e15i	−1.64194	−	0.769766i
$790$	−5.90332e11	+	1.02248e12i	−6.82570e−5	+	0.000118225i
$791$	3.69598e14			0.0424384
$792$	−2.46300e11	+	6.68135e11i	−2.80851e−5	+	7.61861e-5i
$793$	−5.28924e15			−0.598950
$794$	1.15094e11	−	1.99349e11i	1.29432e−5	−	2.24182e-5i
$795$	−4.81876e15	+	3.35938e15i	−0.538166	+	0.375180i
$796$	−3.27743e15	−	5.67668e15i	−0.363506	−	0.629611i
$797$	1.92656e15	+	3.33690e15i	0.212208	+	0.367555i	0.952405	−	0.304835i	$-0.0986012\pi$
$797$	1.92656e15	+	3.33690e15i	0.212208	+	0.367555i	−0.740197	+	0.672390i	$0.765268\pi$
$798$	4.87737e11	−	3.40024e11i	5.33544e−5	−	3.71958e-5i
$799$	−2.13436e15	+	3.69682e15i	−0.231878	+	0.401625i
$800$	2.09146e12			0.000225660
$801$	−1.47180e16	+	2.53278e15i	−1.57714	+	0.271406i
$802$	−4.11967e11			−4.38433e−5
$803$	4.76499e14	−	8.25320e14i	0.0503647	−	0.0872342i
$804$	−1.09239e15	−	5.12127e14i	−0.114675	−	0.0537612i
$805$	1.55798e16	+	2.69851e16i	1.62437	+	2.81350i
$806$	2.17275e11	+	3.76332e11i	2.24992e−5	+	3.89698e-5i
$807$	1.09112e15	+	1.27742e16i	0.112219	+	1.31380i
$808$	1.10672e11	−	1.91690e11i	1.13052e−5	−	1.95811e-5i
$809$	−9.14884e14			−0.0928216			−0.0464108	−	0.998922i	$-0.514778\pi$
$809$	−9.14884e14			−0.0928216			−0.0464108	+	0.998922i	$0.514778\pi$
$810$	7.56226e11	−	2.68217e11i	7.62051e−5	−	2.70283e-5i
$811$	1.50297e16			1.50431			0.752154	−	0.658988i	$-0.229015\pi$
$811$	1.50297e16			1.50431			0.752154	+	0.658988i	$0.229015\pi$
$812$	−3.58369e15	+	6.20713e15i	−0.356264	+	0.617068i
$813$	2.28930e14	+	2.68018e15i	0.0226050	+	0.264646i
$814$	−1.26391e10	−	2.18916e10i	−1.23960e−6	−	2.14705e-6i
$815$	−1.89182e15	−	3.27674e15i	−0.184295	−	0.319209i
$816$	−4.52416e15	−	2.12099e15i	−0.437766	−	0.205231i
$817$	−2.16383e15	+	3.74786e15i	−0.207971	+	0.360216i
$818$	−5.13739e11			−4.90455e−5
$819$	−9.10138e15	+	1.56623e15i	−0.863070	+	0.148523i
$820$	−8.95433e15			−0.843445
$821$	3.28720e15	−	5.69359e15i	0.307566	−	0.532720i	−0.670263	−	0.742123i	$-0.733819\pi$
$821$	3.28720e15	−	5.69359e15i	0.307566	−	0.532720i	0.977829	+	0.209403i	$0.0671522\pi$
$822$	−1.65907e11	+	1.15661e11i	−1.54195e−5	+	1.07496e-5i
$823$	−1.03015e16	−	1.78427e16i	−0.951044	−	1.64726i	−0.743171	−	0.669102i	$-0.766679\pi$
$823$	−1.03015e16	−	1.78427e16i	−0.951044	−	1.64726i	−0.207874	−	0.978156i	$-0.566654\pi$
$824$	−5.33590e11	−	9.24205e11i	−4.89337e−5	−	8.47557e-5i
$825$	1.03423e16	−	7.21011e15i	0.942153	−	0.656818i
$826$	−4.75501e11	+	8.23592e11i	−4.30290e−5	+	7.45284e-5i
$827$	7.46785e15			0.671298			0.335649	−	0.941987i	$-0.391044\pi$
$827$	7.46785e15			0.671298			0.335649	+	0.941987i	$0.391044\pi$
$828$	5.63658e15	−	1.52903e16i	0.503326	−	1.36537i
$829$	−1.28603e16			−1.14078			−0.570390	−	0.821374i	$-0.693208\pi$
$829$	−1.28603e16			−1.14078			−0.570390	+	0.821374i	$0.693208\pi$
$830$	−5.20401e10	+	9.01360e10i	−4.58573e−6	+	7.94271e-6i
$831$	1.93877e16	+	9.08926e15i	1.69715	+	0.795651i
$832$	3.53663e15	+	6.12563e15i	0.307547	+	0.532687i
$833$	−2.87428e15	−	4.97840e15i	−0.248303	−	0.430073i
$834$	−4.90031e9	−	5.73701e10i	−4.20543e−7	−	4.92348e-6i
$835$	1.21177e16	−	2.09885e16i	1.03310	−	1.78939i
$836$	−8.23518e15			−0.697491
$837$	1.19960e16	−	1.18488e16i	1.00936	−	0.996978i
$838$	7.95663e11			6.65100e−5
$839$	−1.78981e15	+	3.10004e15i	−0.148633	+	0.257441i	−0.930723	−	0.365726i	$-0.880821\pi$
$839$	−1.78981e15	+	3.10004e15i	−0.148633	+	0.257441i	0.782089	+	0.623167i	$0.214154\pi$
$840$	−2.37510e11	−	2.78063e12i	−1.95950e−5	−	0.000229407i
$841$	4.57244e15	+	7.91970e15i	0.374775	+	0.649129i
$842$	−7.27062e9	−	1.25931e10i	−5.92045e−7	−	1.02545e-6i
$843$	1.47471e16	+	6.91368e15i	1.19304	+	0.559317i
$844$	−7.23430e14	+	1.25302e15i	−0.0581451	+	0.100710i
$845$	−1.22073e16			−0.974783
$846$	3.98777e11	+	4.79236e11i	3.16369e−5	+	3.80200e-5i
$847$	−6.86612e15			−0.541194
$848$	2.67128e15	−	4.62679e15i	0.209190	−	0.362328i
$849$	−1.16163e16	+	8.09822e15i	−0.903803	+	0.630082i
$850$	−2.35230e11	−	4.07430e11i	−1.81839e−5	−	3.14955e-5i
$851$	5.78494e14	+	1.00198e15i	0.0444310	+	0.0769568i
$852$	−6.78238e15	+	4.72831e15i	−0.517564	+	0.360818i
$853$	1.02046e16	−	1.76749e16i	0.773705	−	1.34010i	−0.161814	−	0.986821i	$-0.551735\pi$
$853$	1.02046e16	−	1.76749e16i	0.773705	−	1.34010i	0.935519	−	0.353275i	$-0.114932\pi$
$854$	−9.49001e11			−7.14905e−5
$855$	1.18708e16	+	1.42659e16i	0.888518	+	1.06779i
$856$	2.29276e12			0.000170511
$857$	−5.07901e15	+	8.79710e15i	−0.375305	+	0.650048i	−0.990373	−	0.138427i	$-0.955795\pi$
$857$	−5.07901e15	+	8.79710e15i	−0.375305	+	0.650048i	0.615068	+	0.788474i	$0.289129\pi$
$858$	−3.07960e11	−	1.44376e11i	−2.26107e−5	−	1.06002e-5i
$859$	1.60369e15	+	2.77767e15i	0.116992	+	0.202637i	0.918574	−	0.395248i	$-0.129341\pi$
$859$	1.60369e15	+	2.77767e15i	0.116992	+	0.202637i	−0.801582	+	0.597885i	$0.796008\pi$
$860$	5.07829e15	+	8.79585e15i	0.368108	+	0.637583i
$861$	9.04940e14	+	1.05945e16i	0.0651782	+	0.763069i
$862$	2.53193e11	−	4.38544e11i	1.81202e−5	−	3.13850e-5i
$863$	−5.14985e15			−0.366214			−0.183107	−	0.983093i	$-0.558616\pi$
$863$	−5.14985e15			−0.366214			−0.183107	+	0.983093i	$0.558616\pi$
$864$	−1.55759e12	+	1.53848e12i	−0.000110060	+	0.000108709i
$865$	4.00497e16			2.81197
$866$	6.30075e11	−	1.09132e12i	4.39586e−5	−	7.61385e-5i
$867$	−9.40655e14	−	1.10127e16i	−0.0652117	−	0.763462i
$868$	−1.46611e16	−	2.53938e16i	−1.00997	−	1.74932i
$869$	−9.70954e15	−	1.68174e16i	−0.664645	−	1.15120i
$870$	5.38628e11	+	2.52517e11i	3.66381e−5	+	1.71765e-5i
$871$	5.76264e14	−	9.98118e14i	0.0389513	−	0.0674656i
$872$	−1.51169e12			−0.000101537
$873$	−2.36989e15	+	6.42879e15i	−0.158180	+	0.429093i
$874$	−1.00224e12			−6.64750e−5
$875$	−7.76913e15	+	1.34565e16i	−0.512069	+	0.886929i
$876$	1.60236e15	−	1.11708e15i	0.104951	−	0.0731664i
$877$	−5.67231e15	−	9.82472e15i	−0.369200	−	0.639473i	0.620241	−	0.784412i	$-0.287035\pi$
$877$	−5.67231e15	−	9.82472e15i	−0.369200	−	0.639473i	−0.989441	+	0.144938i	$0.953702\pi$
$878$	−4.55764e10	−	7.89407e10i	−2.94795e−6	−	5.10600e-6i
$879$	−1.56659e16	+	1.09214e16i	−1.00697	+	0.702007i
$880$	−9.66356e15	+	1.67378e16i	−0.617280	+	1.06916i
$881$	5.58681e15			0.354647			0.177323	−	0.984153i	$-0.443256\pi$
$881$	5.58681e15			0.354647			0.177323	+	0.984153i	$0.443256\pi$
$882$	−8.27420e11	+	1.42388e11i	−5.21974e−5	+	8.98250e-6i
$883$	−1.38862e15			−0.0870563			−0.0435282	−	0.999052i	$-0.513860\pi$
$883$	−1.38862e15			−0.0870563			−0.0435282	+	0.999052i	$0.513860\pi$
$884$	2.38662e15	−	4.13374e15i	0.148695	−	0.257547i
$885$	−2.68778e16	−	1.26007e16i	−1.66420	−	0.780202i
$886$	−5.18907e11	−	8.98773e11i	−3.19304e−5	−	5.53050e-5i
$887$	−1.39137e15	−	2.40993e15i	−0.0850871	−	0.147375i	0.820341	−	0.571874i	$-0.193784\pi$
$887$	−1.39137e15	−	2.40993e15i	−0.0850871	−	0.147375i	−0.905428	+	0.424499i	$0.860450\pi$
$888$	−8.81895e9	−	1.03247e11i	−5.35976e−7	−	6.27490e-6i
$889$	−2.39819e15	+	4.15378e15i	−0.144852	+	0.250890i
$890$	2.15559e12			0.000129396
$891$	−2.39856e15	+	1.29775e16i	−0.143095	+	0.774217i
$892$	−1.84697e16			−1.09510
$893$	−7.21010e15	+	1.24883e16i	−0.424872	+	0.735901i
$894$	−2.76825e10	−	3.24091e11i	−1.62125e−6	−	1.89806e-5i
$895$	1.10391e16	+	1.91203e16i	0.642551	+	1.11293i
$896$	2.53819e12	+	4.39627e12i	0.000146835	+	0.000254326i
$897$	1.40954e16	+	6.60812e15i	0.810435	+	0.379944i
$898$	−2.70925e10	+	4.69256e10i	−1.54821e−6	+	2.68157e-6i
$899$	1.25008e16			0.710001
$900$	2.54667e16	−	4.38249e15i	1.43760	−	0.247393i
$901$	−3.60530e15			−0.202281
$902$	−1.95804e11	+	3.39143e11i	−1.09191e−5	+	1.89124e-5i
$903$	9.89379e15	−	6.89742e15i	0.548378	−	0.382300i
$904$	2.78999e10	+	4.83240e10i	1.53701e−6	+	2.66218e-6i
$905$	−2.09616e16	−	3.63065e16i	−1.14777	−	1.98800i
$906$	−3.46659e11	+	2.41672e11i	−1.88668e−5	+	1.31529e-5i
$907$	−1.12465e16	+	1.94795e16i	−0.608384	+	1.05375i	0.383123	+	0.923697i	$0.374849\pi$
$907$	−1.12465e16	+	1.94795e16i	−0.608384	+	1.05375i	−0.991507	+	0.130055i	$0.958485\pi$
$908$	−6.87378e15			−0.369593
$909$	1.41890e15	−	3.84903e15i	0.0758315	−	0.205707i
$910$	1.33298e12			7.08104e−5
$911$	−1.61554e16	+	2.79819e16i	−0.853034	+	1.47750i	0.0254236	+	0.999677i	$0.491907\pi$
$911$	−1.61554e16	+	2.79819e16i	−0.853034	+	1.47750i	−0.878457	+	0.477821i	$0.841427\pi$
$912$	−1.52831e16	−	7.16494e15i	−0.802121	−	0.376046i
$913$	−8.55934e14	−	1.48252e15i	−0.0446530	−	0.0773413i
$914$	4.88851e11	+	8.46714e11i	2.53497e−5	+	4.39069e-5i
$915$	−2.52105e15	−	2.95150e16i	−0.129947	−	1.52134i
$916$	7.16064e15	−	1.24026e16i	0.366882	−	0.635459i
$917$	4.72155e16			2.40466
$918$	4.74890e11	+	1.30393e11i	2.40413e−5	+	6.60117e-6i
$919$	1.36671e16			0.687768			0.343884	−	0.939012i	$-0.388257\pi$
$919$	1.36671e16			0.687768			0.343884	+	0.939012i	$0.388257\pi$
$920$	−2.35215e12	+	4.07405e12i	−0.000117661	+	0.000203795i
$921$	2.27840e15	+	2.66742e16i	0.113293	+	1.32637i
$922$	−4.35126e11	−	7.53661e11i	−2.15078e−5	−	3.72525e-5i
$923$	−3.94908e15	−	6.84001e15i	−0.194038	−	0.336084i
$924$	2.07803e16	+	9.74211e15i	1.01498	+	0.475836i
$925$	−9.17325e14	+	1.58885e15i	−0.0445393	+	0.0771444i
$926$	5.69596e11			2.74920e−5
$927$	−1.26508e16	−	1.52032e16i	−0.606986	−	0.729453i
$928$	−1.62313e12			−7.74177e−5
$929$	1.31196e16	−	2.27237e16i	0.622061	−	1.07744i	−0.367041	−	0.930205i	$-0.619629\pi$
$929$	1.31196e16	−	2.27237e16i	0.622061	−	1.07744i	0.989101	−	0.147236i	$-0.0470376\pi$
$930$	−1.99644e12	+	1.39181e12i	−9.41024e−5	+	6.56031e-5i
$931$	−9.70963e15	−	1.68176e16i	−0.454967	−	0.788025i
$932$	1.30344e16	+	2.25762e16i	0.607160	+	1.05163i
$933$	−1.62440e16	+	1.13244e16i	−0.752217	+	0.524405i
$934$	−9.24338e10	+	1.60100e11i	−4.25523e−6	+	7.37027e-6i
$935$	1.30425e16			0.596893
$936$	−8.91817e11	−	1.07175e12i	−4.05750e−5	−	4.87615e-5i
$937$	−5.23726e15			−0.236884			−0.118442	−	0.992961i	$-0.537790\pi$
$937$	−5.23726e15			−0.236884			−0.118442	+	0.992961i	$0.537790\pi$
$938$	1.03394e11	−	1.79084e11i	4.64921e−6	−	8.05267e-6i
$939$	−2.16874e15	−	1.01674e15i	−0.0969498	−	0.0454515i
$940$	1.69214e16	+	2.93087e16i	0.752025	+	1.30255i
$941$	3.82099e15	+	6.61815e15i	0.168824	+	0.292411i	0.938007	−	0.346618i	$-0.112670\pi$
$941$	3.82099e15	+	6.61815e15i	0.168824	+	0.292411i	−0.769183	+	0.639029i	$0.779336\pi$
$942$	−1.14012e11	−	1.33479e12i	−5.00808e−6	−	5.86317e-5i
$943$	8.96198e15	−	1.55226e16i	0.391372	−	0.677876i
$944$	2.69984e16			1.17217
$945$	−1.30779e16	−	5.00409e16i	−0.564500	−	2.15998i
$946$	4.44187e11			1.90618e−5
$947$	−5.15519e15	+	8.92905e15i	−0.219948	+	0.380961i	−0.954792	−	0.297275i	$-0.903922\pi$
$947$	−5.15519e15	+	8.92905e15i	−0.219948	+	0.380961i	0.734844	+	0.678236i	$0.237255\pi$
$948$	−3.38742e15	−	3.96580e16i	−0.143689	−	1.68223i
$949$	9.32986e14	+	1.61598e15i	0.0393470	+	0.0681509i
$950$	−7.94632e11	−	1.37634e12i	−3.33186e−5	−	5.77094e-5i
$951$	4.96734e14	+	2.32876e14i	0.0207077	+	0.00970807i
$952$	8.56419e11	−	1.48336e12i	3.54963e−5	−	6.14814e-5i
$953$	−2.15508e15			−0.0888079			−0.0444039	−	0.999014i	$-0.514139\pi$
$953$	−2.15508e15			−0.0888079			−0.0444039	+	0.999014i	$0.514139\pi$
$954$	−1.82128e11	+	4.94057e11i	−7.46209e−6	+	2.02424e-5i
$955$	−5.15206e16			−2.09876
$956$	5.06207e15	−	8.76776e15i	0.205026	−	0.355116i
$957$	−8.02642e15	+	5.59559e15i	−0.323226	+	0.225336i
$958$	1.11888e12	+	1.93796e12i	4.47995e−5	+	7.75951e-5i
$959$	6.51834e15	+	1.12901e16i	0.259498	+	0.449464i
$960$	−3.24965e16	+	2.26548e16i	−1.28631	+	0.896743i
$961$	−1.28666e16	+	2.22855e16i	−0.506389	+	0.877091i
$962$	4.94949e10			1.93686e−6
$963$	4.18767e16	−	7.20644e15i	1.62940	−	0.280399i
$964$	2.56864e16			0.993755
$965$	1.67788e16	−	2.90617e16i	0.645446	−	1.11795i
$966$	2.52901e12	+	1.18564e12i	9.67333e−5	+	4.53500e-5i
$967$	2.11121e16	+	3.65673e16i	0.802946	+	1.39074i	0.917669	+	0.397346i	$0.130069\pi$
$967$	2.11121e16	+	3.65673e16i	0.802946	+	1.39074i	−0.114722	+	0.993398i	$0.536598\pi$
$968$	−5.18303e11	−	8.97728e11i	−1.96006e−5	−	3.39493e-5i
$969$	9.69407e14	+	1.13493e16i	0.0364523	+	0.426763i
$970$	4.94479e11	−	8.56463e11i	1.84886e−5	−	3.20232e-5i
$971$	−1.77215e16			−0.658864			−0.329432	−	0.944179i	$-0.606857\pi$
$971$	−1.77215e16			−0.658864			−0.329432	+	0.944179i	$0.606857\pi$
$972$	−1.57423e16	+	2.19971e16i	−0.581973	+	0.813208i
$973$	−3.71155e15			−0.136438
$974$	1.10467e11	−	1.91334e11i	4.03791e−6	−	6.99387e-6i
$975$	2.10089e15	+	2.45960e16i	0.0763621	+	0.894004i
$976$	1.34708e16	+	2.33321e16i	0.486877	+	0.843295i
$977$	−1.03742e16	−	1.79686e16i	−0.372849	−	0.645794i	0.617153	−	0.786843i	$-0.288286\pi$
$977$	−1.03742e16	−	1.79686e16i	−0.372849	−	0.645794i	−0.990003	+	0.141049i	$0.954952\pi$
$978$	−3.07092e11	−	1.43969e11i	−1.09750e−5	−	5.14524e-6i
$979$	−1.77272e16	+	3.07044e16i	−0.629991	+	1.09118i
$980$	−4.55750e16			−1.61058
$981$	−2.76107e16	+	4.75145e15i	−0.970282	+	0.166973i
$982$	−3.66916e11			−1.28219e−5
$983$	6.30460e14	−	1.09199e15i	0.0219085	−	0.0379467i	−0.854863	−	0.518853i	$-0.826359\pi$
$983$	6.30460e14	−	1.09199e15i	0.0219085	−	0.0379467i	0.876772	+	0.480907i	$0.159692\pi$
$984$	−1.31690e12	+	9.18068e11i	−4.55070e−5	+	3.17250e-5i
$985$	−3.41325e16	−	5.91192e16i	−1.17292	−	2.03156i
$986$	1.82556e11	+	3.16196e11i	6.23839e−6	+	1.08052e-5i
$987$	3.29671e16	−	2.29829e16i	1.12031	−	0.781017i
$988$	8.06226e15	−	1.39642e16i	0.272454	−	0.471905i
$989$	−2.03305e16			−0.683233
$990$	6.58862e11	−	1.78729e12i	2.20192e−5	−	5.97313e-5i
$991$	1.21567e15			0.0404029			0.0202014	−	0.999796i	$-0.493569\pi$
$991$	1.21567e15			0.0404029			0.0202014	+	0.999796i	$0.493569\pi$
$992$	3.32018e12	−	5.75072e12i	0.000109736	−	0.000190068i
$993$	1.21400e15	+	5.69141e14i	0.0399023	+	0.0187068i
$994$	−7.08549e11	−	1.22724e12i	−2.31603e−5	−	4.01149e-5i
$995$	1.75345e16	+	3.03707e16i	0.569990	+	0.987252i
$996$	−2.98614e14	−	3.49601e15i	−0.00965348	−	0.113018i
$997$	9.85852e15	−	1.70755e16i	0.316948	−	0.548970i	−0.662902	−	0.748707i	$-0.730675\pi$
$997$	9.85852e15	−	1.70755e16i	0.316948	−	0.548970i	0.979850	+	0.199736i	$0.0640086\pi$
$998$	−1.61500e12			−5.16362e−5
$999$	−4.85595e14	−	1.85807e15i	−0.0154406	−	0.0590814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.12.c.a.7.6	yes	20
3.2	odd	2		27.12.c.a.19.5		20
9.2	odd	6		81.12.a.c.1.6		10
9.4	even	3	inner	9.12.c.a.4.6	✓	20
9.5	odd	6		27.12.c.a.10.5		20
9.7	even	3		81.12.a.e.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.12.c.a.4.6	✓	20	9.4	even	3	inner
9.12.c.a.7.6	yes	20	1.1	even	1	trivial
27.12.c.a.10.5		20	9.5	odd	6
27.12.c.a.19.5		20	3.2	odd	2
81.12.a.c.1.6		10	9.2	odd	6
81.12.a.e.1.5		10	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	9.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.00116679 + 0.00202094i) q^{2} +(35.8201 + 419.361i) q^{3} +(1024.00 + 1773.62i) q^{4} +(-5478.49 - 9489.02i) q^{5} +(-0.889299 - 0.416917i) q^{6} +(-31655.6 + 54829.1i) q^{7} -9.55835 q^{8} +(-174581. + 30043.1i) q^{9} +O(q^{10})\)	\(q+(-0.00116679 + 0.00202094i) q^{2} +(35.8201 + 419.361i) q^{3} +(1024.00 + 1773.62i) q^{4} +(-5478.49 - 9489.02i) q^{5} +(-0.889299 - 0.416917i) q^{6} +(-31655.6 + 54829.1i) q^{7} -9.55835 q^{8} +(-174581. + 30043.1i) q^{9} +25.5690 q^{10} +(-210274. + 364206. i) q^{11} +(-707108. + 492957. i) q^{12} +(-411718. - 713117. i) q^{13} +(-73.8710 - 127.948i) q^{14} +(3.78309e6 - 2.63736e6i) q^{15} +(-2.09715e6 + 3.63237e6i) q^{16} +2.83043e6 q^{17} +(142.984 - 387.872i) q^{18} +9.56151e6 q^{19} +(1.12199e7 - 1.94335e7i) q^{20} +(-2.41271e7 - 1.13112e7i) q^{21} +(-490.693 - 849.905i) q^{22} +(2.24591e7 + 3.89002e7i) q^{23} +(-342.381 - 4008.40i) q^{24} +(-3.56136e7 + 6.16846e7i) q^{25} +1921.56 q^{26} +(-1.88524e7 - 7.21363e7i) q^{27} -1.29661e8 q^{28} +(2.76388e7 - 4.78719e7i) q^{29} +(915.884 + 10722.7i) q^{30} +(1.13073e8 + 1.95847e8i) q^{31} +(-14681.6 - 25429.3i) q^{32} +(-1.60266e8 - 7.51351e7i) q^{33} +(-3302.52 + 5720.14i) q^{34} +6.93700e8 q^{35} +(-2.32056e8 - 2.78876e8i) q^{36} +2.57577e7 q^{37} +(-11156.3 + 19323.3i) q^{38} +(2.84306e8 - 1.98203e8i) q^{39} +(52365.3 + 90699.4i) q^{40} +(-1.99518e8 - 3.45576e8i) q^{41} +(51010.5 - 35561.7i) q^{42} +(-2.26306e8 + 3.91974e8i) q^{43} -8.61284e8 q^{44} +(1.24152e9 + 1.49201e9i) q^{45} -104820. q^{46} +(-7.54076e8 + 1.30610e9i) q^{47} +(-1.59840e9 - 7.49352e8i) q^{48} +(-1.01549e9 - 1.75888e9i) q^{49} +(-83107.3 - 143946. i) q^{50} +(1.01386e8 + 1.18697e9i) q^{51} +(8.43199e8 - 1.46046e9i) q^{52} -1.27376e9 q^{53} +(167780. + 46068.4i) q^{54} +4.60794e9 q^{55} +(302575. - 524076. i) q^{56} +(3.42494e8 + 4.00973e9i) q^{57} +(64497.5 + 111713. i) q^{58} +(-3.21846e9 - 5.57453e9i) q^{59} +(8.55156e9 + 4.00910e9i) q^{60} +(3.21169e9 - 5.56280e9i) q^{61} -527728. q^{62} +(3.87922e9 - 1.05231e10i) q^{63} -8.58993e9 q^{64} +(-4.51119e9 + 7.81361e9i) q^{65} +(338840. - 236221. i) q^{66} +(6.99828e8 + 1.21214e9i) q^{67} +(2.89836e9 + 5.02011e9i) q^{68} +(-1.55088e10 + 1.08119e10i) q^{69} +(-809402. + 1.40193e6i) q^{70} +9.59171e9 q^{71} +(1.66871e6 - 287163. i) q^{72} -2.26608e9 q^{73} +(-30053.9 + 52054.8i) q^{74} +(-2.71438e10 - 1.27254e10i) q^{75} +(9.79099e9 + 1.69585e10i) q^{76} +(-1.33127e10 - 2.30583e10i) q^{77} +(68830.3 + 805827. i) q^{78} +(-2.30878e10 + 3.99892e10i) q^{79} +4.59569e10 q^{80} +(2.95759e10 - 1.04899e10i) q^{81} +931184. q^{82} +(-2.03528e9 + 3.52521e9i) q^{83} +(-4.64448e9 - 5.43750e10i) q^{84} +(-1.55065e10 - 2.68580e10i) q^{85} +(-528104. - 914703. i) q^{86} +(2.10656e10 + 9.87589e9i) q^{87} +(2.00988e6 - 3.48121e6i) q^{88} +8.43049e10 q^{89} +(-4.46386e6 + 768173. i) q^{90} +5.21328e10 q^{91} +(-4.59962e10 + 7.96677e10i) q^{92} +(-7.80806e10 + 5.44335e10i) q^{93} +(-1.75970e6 - 3.04789e6i) q^{94} +(-5.23826e10 - 9.07294e10i) q^{95} +(1.01382e7 - 7.06779e6i) q^{96} +(1.93390e10 - 3.34962e10i) q^{97} +4.73946e6 q^{98} +(2.57680e10 - 6.99007e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 33 q^{2} - 12 q^{3} - 9217 q^{4} - 7230 q^{5} + 20583 q^{6} + 8512 q^{7} - 29118 q^{8} + 135504 q^{9}+O(q^{10}) \) 20 * q - 33 * q^2 - 12 * q^3 - 9217 * q^4 - 7230 * q^5 + 20583 * q^6 + 8512 * q^7 - 29118 * q^8 + 135504 * q^9	\( 20 q - 33 q^{2} - 12 q^{3} - 9217 q^{4} - 7230 q^{5} + 20583 q^{6} + 8512 q^{7} - 29118 q^{8} + 135504 q^{9} + 4092 q^{10} - 112776 q^{11} + 1027860 q^{12} + 279706 q^{13} - 3901584 q^{14} - 6358608 q^{15} - 7342081 q^{16} + 27765792 q^{17} + 8682876 q^{18} + 7029400 q^{19} - 34163508 q^{20} + 55012206 q^{21} + 2274591 q^{22} - 69371616 q^{23} - 211100355 q^{24} - 45286204 q^{25} + 481929144 q^{26} - 83699352 q^{27} - 61345796 q^{28} - 25437246 q^{29} - 23582592 q^{30} + 114575368 q^{31} + 80396559 q^{32} + 31338342 q^{33} - 243855063 q^{34} - 178147464 q^{35} - 19984653 q^{36} - 134218328 q^{37} + 489799995 q^{38} - 1999064976 q^{39} + 107425416 q^{40} + 331873026 q^{41} + 4171968882 q^{42} - 1118847584 q^{43} + 278477274 q^{44} + 1749349170 q^{45} + 2882537592 q^{46} - 1469650704 q^{47} - 9335236125 q^{48} - 3553434720 q^{49} - 6643771701 q^{50} + 1736777052 q^{51} + 3632448874 q^{52} + 14914261944 q^{53} + 18127857753 q^{54} + 4981449984 q^{55} - 27669139026 q^{56} - 7855424196 q^{57} - 1387480560 q^{58} - 26505032592 q^{59} - 10283356116 q^{60} + 990409066 q^{61} + 91044996180 q^{62} + 51565206888 q^{63} - 7516709566 q^{64} - 39045315390 q^{65} - 93201828246 q^{66} + 6557215720 q^{67} - 77299152993 q^{68} + 6907292550 q^{69} - 785437278 q^{70} + 122053719744 q^{71} + 161899013547 q^{72} - 12612893936 q^{73} - 109519086216 q^{74} - 218383044348 q^{75} + 14574055597 q^{76} - 88616208018 q^{77} + 150319870614 q^{78} - 7621233248 q^{79} + 399166683072 q^{80} + 222307104312 q^{81} - 59168477334 q^{82} - 99007044180 q^{83} - 711968015814 q^{84} + 12911595156 q^{85} - 214357830519 q^{86} + 99715491216 q^{87} - 54423523605 q^{88} + 476597704824 q^{89} + 620021743884 q^{90} + 138211652216 q^{91} - 461776423998 q^{92} - 572981484354 q^{93} + 13393667064 q^{94} - 418952909328 q^{95} + 118587589272 q^{96} + 123483551938 q^{97} + 1310123604078 q^{98} + 621154334268 q^{99}+O(q^{100}) \) 20 * q - 33 * q^2 - 12 * q^3 - 9217 * q^4 - 7230 * q^5 + 20583 * q^6 + 8512 * q^7 - 29118 * q^8 + 135504 * q^9 + 4092 * q^10 - 112776 * q^11 + 1027860 * q^12 + 279706 * q^13 - 3901584 * q^14 - 6358608 * q^15 - 7342081 * q^16 + 27765792 * q^17 + 8682876 * q^18 + 7029400 * q^19 - 34163508 * q^20 + 55012206 * q^21 + 2274591 * q^22 - 69371616 * q^23 - 211100355 * q^24 - 45286204 * q^25 + 481929144 * q^26 - 83699352 * q^27 - 61345796 * q^28 - 25437246 * q^29 - 23582592 * q^30 + 114575368 * q^31 + 80396559 * q^32 + 31338342 * q^33 - 243855063 * q^34 - 178147464 * q^35 - 19984653 * q^36 - 134218328 * q^37 + 489799995 * q^38 - 1999064976 * q^39 + 107425416 * q^40 + 331873026 * q^41 + 4171968882 * q^42 - 1118847584 * q^43 + 278477274 * q^44 + 1749349170 * q^45 + 2882537592 * q^46 - 1469650704 * q^47 - 9335236125 * q^48 - 3553434720 * q^49 - 6643771701 * q^50 + 1736777052 * q^51 + 3632448874 * q^52 + 14914261944 * q^53 + 18127857753 * q^54 + 4981449984 * q^55 - 27669139026 * q^56 - 7855424196 * q^57 - 1387480560 * q^58 - 26505032592 * q^59 - 10283356116 * q^60 + 990409066 * q^61 + 91044996180 * q^62 + 51565206888 * q^63 - 7516709566 * q^64 - 39045315390 * q^65 - 93201828246 * q^66 + 6557215720 * q^67 - 77299152993 * q^68 + 6907292550 * q^69 - 785437278 * q^70 + 122053719744 * q^71 + 161899013547 * q^72 - 12612893936 * q^73 - 109519086216 * q^74 - 218383044348 * q^75 + 14574055597 * q^76 - 88616208018 * q^77 + 150319870614 * q^78 - 7621233248 * q^79 + 399166683072 * q^80 + 222307104312 * q^81 - 59168477334 * q^82 - 99007044180 * q^83 - 711968015814 * q^84 + 12911595156 * q^85 - 214357830519 * q^86 + 99715491216 * q^87 - 54423523605 * q^88 + 476597704824 * q^89 + 620021743884 * q^90 + 138211652216 * q^91 - 461776423998 * q^92 - 572981484354 * q^93 + 13393667064 * q^94 - 418952909328 * q^95 + 118587589272 * q^96 + 123483551938 * q^97 + 1310123604078 * q^98 + 621154334268 * q^99

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