LMFDB - Embedded newform 9.12.c.a.7.1

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			7.1
Root			$-44.9985i$ of defining polynomial
Character	$\chi$	$=$	9.7
Dual form			9.12.c.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-40.4699 + 70.0959i) q^{2} +(-411.436 + 88.6985i) q^{3} +(-2251.62 - 3899.92i) q^{4} +(-156.497 - 271.061i) q^{5} +(10433.4 - 32429.6i) q^{6} +(-40821.5 + 70704.9i) q^{7} +198726. q^{8} +(161412. - 72987.5i) q^{9} +O(q^{10})$	\(q+(-40.4699 + 70.0959i) q^{2} +(-411.436 + 88.6985i) q^{3} +(-2251.62 - 3899.92i) q^{4} +(-156.497 - 271.061i) q^{5} +(10433.4 - 32429.6i) q^{6} +(-40821.5 + 70704.9i) q^{7} +198726. q^{8} +(161412. - 72987.5i) q^{9} +25333.7 q^{10} +(163450. - 283104. i) q^{11} +(1.27231e6 + 1.40485e6i) q^{12} +(-258027. - 446915. i) q^{13} +(-3.30408e6 - 5.72284e6i) q^{14} +(88431.3 + 97643.2i) q^{15} +(-3.43111e6 + 5.94286e6i) q^{16} +6.16340e6 q^{17} +(-1.41621e6 + 1.42681e7i) q^{18} -9.85977e6 q^{19} +(-704744. + 1.22065e6i) q^{20} +(1.05240e7 - 3.27114e7i) q^{21} +(1.32296e7 + 2.29144e7i) q^{22} +(-1.51672e7 - 2.62703e7i) q^{23} +(-8.17632e7 + 1.76267e7i) q^{24} +(2.43651e7 - 4.22016e7i) q^{25} +4.17692e7 q^{26} +(-5.99369e7 + 4.43467e7i) q^{27} +3.67658e8 q^{28} +(-1.70781e7 + 2.95801e7i) q^{29} +(-1.04232e7 + 2.24706e6i) q^{30} +(-3.19589e7 - 5.53544e7i) q^{31} +(-7.42175e7 - 1.28548e8i) q^{32} +(-4.21384e7 + 1.30977e8i) q^{33} +(-2.49432e8 + 4.32029e8i) q^{34} +2.55538e7 q^{35} +(-6.48084e8 - 4.65154e8i) q^{36} -3.37469e8 q^{37} +(3.99023e8 - 6.91129e8i) q^{38} +(1.45802e8 + 1.60990e8i) q^{39} +(-3.11001e7 - 5.38670e7i) q^{40} +(-1.73517e8 - 3.00541e8i) q^{41} +(1.86703e9 + 2.06151e9i) q^{42} +(-4.07707e8 + 7.06170e8i) q^{43} -1.47211e9 q^{44} +(-4.50446e7 - 3.23302e7i) q^{45} +2.45526e9 q^{46} +(5.62782e8 - 9.74766e8i) q^{47} +(8.84560e8 - 2.74944e9i) q^{48} +(-2.34413e9 - 4.06015e9i) q^{49} +(1.97210e9 + 3.41578e9i) q^{50} +(-2.53584e9 + 5.46684e8i) q^{51} +(-1.16196e9 + 2.01257e9i) q^{52} +4.18100e9 q^{53} +(-6.82882e8 - 5.99603e9i) q^{54} -1.02318e8 q^{55} +(-8.11231e9 + 1.40509e10i) q^{56} +(4.05666e9 - 8.74546e8i) q^{57} +(-1.38229e9 - 2.39420e9i) q^{58} +(-2.15438e9 - 3.73150e9i) q^{59} +(1.81687e8 - 5.64730e8i) q^{60} +(1.80749e9 - 3.13066e9i) q^{61} +5.17349e9 q^{62} +(-1.42851e9 + 1.43921e10i) q^{63} -2.03955e9 q^{64} +(-8.07609e7 + 1.39882e8i) q^{65} +(-7.47561e9 - 8.25435e9i) q^{66} +(1.29801e9 + 2.24823e9i) q^{67} +(-1.38776e10 - 2.40368e10i) q^{68} +(8.57047e9 + 9.46326e9i) q^{69} +(-1.03416e9 + 1.79122e9i) q^{70} +1.08045e10 q^{71} +(3.20769e10 - 1.45045e10i) q^{72} -2.52190e10 q^{73} +(1.36573e10 - 2.36552e10i) q^{74} +(-6.28146e9 + 1.95244e10i) q^{75} +(2.22004e10 + 3.84523e10i) q^{76} +(1.33446e10 + 2.31135e10i) q^{77} +(-1.71854e10 + 3.70487e9i) q^{78} +(4.75604e9 - 8.23771e9i) q^{79} +2.14784e9 q^{80} +(2.07267e10 - 2.35621e10i) q^{81} +2.80889e10 q^{82} +(2.27734e9 - 3.94447e9i) q^{83} +(-1.51268e11 + 3.26107e10i) q^{84} +(-9.64555e8 - 1.67066e9i) q^{85} +(-3.29997e10 - 5.71572e10i) q^{86} +(4.40282e9 - 1.36851e10i) q^{87} +(3.24819e10 - 5.62602e10i) q^{88} -7.34546e10 q^{89} +(4.08916e9 - 1.84904e9i) q^{90} +4.21322e10 q^{91} +(-6.83015e10 + 1.18302e11i) q^{92} +(1.80589e10 + 1.99401e10i) q^{93} +(4.55514e10 + 7.88973e10i) q^{94} +(1.54303e9 + 2.67260e9i) q^{95} +(4.19378e10 + 4.63065e10i) q^{96} +(4.91645e10 - 8.51555e10i) q^{97} +3.79466e11 q^{98} +(5.71979e9 - 5.76263e10i) 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 $

$2$	−40.4699	+	70.0959i	−0.894266	+	1.54891i	−0.0595558	+	0.998225i	$0.518968\pi$
$2$	−40.4699	+	70.0959i	−0.894266	+	1.54891i	−0.834710	+	0.550689i	$0.814365\pi$
$3$	−411.436	+	88.6985i	−0.977542	+	0.210741i
$3$	−411.436	+	88.6985i	−0.977542	+	0.210741i
$4$	−2251.62	−	3899.92i	−1.09942	−	1.90426i
$5$	−156.497	−	271.061i	−0.0223961	−	0.0387911i	0.854610	−	0.519270i	$-0.173796\pi$
$5$	−156.497	−	271.061i	−0.0223961	−	0.0387911i	−0.877006	+	0.480479i	$0.840463\pi$
$6$	10433.4	−	32429.6i	0.547763	−	1.70259i
$7$	−40821.5	+	70704.9i	−0.918015	+	1.59005i	−0.115590	+	0.993297i	$0.536876\pi$
$7$	−40821.5	+	70704.9i	−0.918015	+	1.59005i	−0.802426	+	0.596752i	$0.796458\pi$
$8$	198726.			2.14418
$9$	161412.	−	72987.5i	0.911176	−	0.412017i
$10$	25333.7			0.0801121
$11$	163450.	−	283104.i	0.306003	−	0.530013i	−0.671481	−	0.741022i	$-0.734342\pi$
$11$	163450.	−	283104.i	0.306003	−	0.530013i	0.977484	+	0.211009i	$0.0676749\pi$
$12$	1.27231e6	+	1.40485e6i	1.47604	+	1.62980i
$13$	−258027.	−	446915.i	−0.192742	−	0.333839i	0.753416	−	0.657544i	$-0.228405\pi$
$13$	−258027.	−	446915.i	−0.192742	−	0.333839i	−0.946158	+	0.323705i	$0.895071\pi$
$14$	−3.30408e6	−	5.72284e6i	−1.64190	−	2.84385i
$15$	88431.3	+	97643.2i	0.0300680	+	0.0332002i
$16$	−3.43111e6	+	5.94286e6i	−0.818041	+	1.41689i
$17$	6.16340e6			1.05281			0.526407	−	0.850233i	$-0.323539\pi$
$17$	6.16340e6			1.05281			0.526407	+	0.850233i	$0.323539\pi$
$18$	−1.41621e6	+	1.42681e7i	−0.176656	+	1.77979i
$19$	−9.85977e6			−0.913528			−0.456764	−	0.889588i	$-0.650992\pi$
$19$	−9.85977e6			−0.913528			−0.456764	+	0.889588i	$0.650992\pi$
$20$	−704744.	+	1.22065e6i	−0.0492455	+	0.0852957i
$21$	1.05240e7	−	3.27114e7i	0.562310	−	1.74780i
$22$	1.32296e7	+	2.29144e7i	0.547296	+	0.947945i
$23$	−1.51672e7	−	2.62703e7i	−0.491363	−	0.851065i	0.508588	−	0.861010i	$-0.330168\pi$
$23$	−1.51672e7	−	2.62703e7i	−0.491363	−	0.851065i	−0.999951	+	0.00994502i	$0.996834\pi$
$24$	−8.17632e7	+	1.76267e7i	−2.09602	+	0.451866i
$25$	2.43651e7	−	4.22016e7i	0.498997	−	0.864288i
$26$	4.17692e7			0.689450
$27$	−5.99369e7	+	4.43467e7i	−0.803884	+	0.594786i
$28$	3.67658e8			4.03715
$29$	−1.70781e7	+	2.95801e7i	−0.154614	+	0.267800i	−0.932919	−	0.360087i	$-0.882747\pi$
$29$	−1.70781e7	+	2.95801e7i	−0.154614	+	0.267800i	0.778304	+	0.627887i	$0.216080\pi$
$30$	−1.04232e7	+	2.24706e6i	−0.0783130	+	0.0168829i
$31$	−3.19589e7	−	5.53544e7i	−0.200495	−	0.347267i	0.748193	−	0.663481i	$-0.230922\pi$
$31$	−3.19589e7	−	5.53544e7i	−0.200495	−	0.347267i	−0.948688	+	0.316214i	$0.897588\pi$
$32$	−7.42175e7	−	1.28548e8i	−0.391004	−	0.677239i
$33$	−4.21384e7	+	1.30977e8i	−0.187435	+	0.582597i
$34$	−2.49432e8	+	4.32029e8i	−0.941495	+	1.63072i
$35$	2.55538e7			0.0822397
$36$	−6.48084e8	−	4.65154e8i	−1.78635	−	1.28213i
$37$	−3.37469e8			−0.800064			−0.400032	−	0.916501i	$-0.631001\pi$
$37$	−3.37469e8			−0.800064			−0.400032	+	0.916501i	$0.631001\pi$
$38$	3.99023e8	−	6.91129e8i	0.816937	−	1.41498i
$39$	1.45802e8	+	1.60990e8i	0.258767	+	0.285723i
$40$	−3.11001e7	−	5.38670e7i	−0.0480211	−	0.0831750i
$41$	−1.73517e8	−	3.00541e8i	−0.233901	−	0.405128i	0.725052	−	0.688694i	$-0.241816\pi$
$41$	−1.73517e8	−	3.00541e8i	−0.233901	−	0.405128i	−0.958953	+	0.283566i	$0.908482\pi$
$42$	1.86703e9	+	2.06151e9i	2.20434	+	2.43397i
$43$	−4.07707e8	+	7.06170e8i	−0.422933	+	0.732542i	−0.996225	−	0.0868093i	$-0.972333\pi$
$43$	−4.07707e8	+	7.06170e8i	−0.422933	+	0.732542i	0.573292	+	0.819351i	$0.305666\pi$
$44$	−1.47211e9			−1.34571
$45$	−4.50446e7	−	3.23302e7i	−0.0363893	−	0.0261180i
$46$	2.45526e9			1.75764
$47$	5.62782e8	−	9.74766e8i	0.357933	−	0.619958i	−0.629682	−	0.776853i	$-0.716815\pi$
$47$	5.62782e8	−	9.74766e8i	0.357933	−	0.619958i	0.987615	+	0.156895i	$0.0501483\pi$
$48$	8.84560e8	−	2.74944e9i	0.501073	−	1.55746i
$49$	−2.34413e9	−	4.06015e9i	−1.18550	−	2.05335i
$50$	1.97210e9	+	3.41578e9i	0.892472	+	1.54581i
$51$	−2.53584e9	+	5.46684e8i	−1.02917	+	0.221871i
$52$	−1.16196e9	+	2.01257e9i	−0.423810	+	0.734060i
$53$	4.18100e9			1.37329			0.686646	−	0.726992i	$-0.259082\pi$
$53$	4.18100e9			1.37329			0.686646	+	0.726992i	$0.259082\pi$
$54$	−6.82882e8	−	5.99603e9i	−0.202386	−	1.77704i
$55$	−1.02318e8			−0.0274130
$56$	−8.11231e9	+	1.40509e10i	−1.96839	+	3.40935i
$57$	4.05666e9	−	8.74546e8i	0.893012	−	0.192518i
$58$	−1.38229e9	−	2.39420e9i	−0.276533	−	0.478969i
$59$	−2.15438e9	−	3.73150e9i	−0.392316	−	0.679512i	0.600438	−	0.799671i	$-0.294993\pi$
$59$	−2.15438e9	−	3.73150e9i	−0.392316	−	0.679512i	−0.992755	+	0.120159i	$0.961660\pi$
$60$	1.81687e8	−	5.64730e8i	0.0301642	−	0.0937582i
$61$	1.80749e9	−	3.13066e9i	0.274007	−	0.474594i	−0.695877	−	0.718161i	$-0.744984\pi$
$61$	1.80749e9	−	3.13066e9i	0.274007	−	0.474594i	0.969884	+	0.243567i	$0.0783176\pi$
$62$	5.17349e9			0.717182
$63$	−1.42851e9	+	1.43921e10i	−0.181347	+	1.82705i
$64$	−2.03955e9			−0.237435
$65$	−8.07609e7	+	1.39882e8i	−0.00863331	+	0.0149533i
$66$	−7.47561e9	−	8.25435e9i	−0.734776	−	0.811318i
$67$	1.29801e9	+	2.24823e9i	0.117454	+	0.203436i	0.918758	−	0.394821i	$-0.129193\pi$
$67$	1.29801e9	+	2.24823e9i	0.117454	+	0.203436i	−0.801304	+	0.598257i	$0.795860\pi$
$68$	−1.38776e10	−	2.40368e10i	−1.15749	−	2.00483i
$69$	8.57047e9	+	9.46326e9i	0.659682	+	0.728401i
$70$	−1.03416e9	+	1.79122e9i	−0.0735442	+	0.127382i
$71$	1.08045e10			0.710693			0.355346	−	0.934735i	$-0.384363\pi$
$71$	1.08045e10			0.710693			0.355346	+	0.934735i	$0.384363\pi$
$72$	3.20769e10	−	1.45045e10i	1.95372	−	0.883436i
$73$	−2.52190e10			−1.42381			−0.711905	−	0.702275i	$-0.752168\pi$
$73$	−2.52190e10			−1.42381			−0.711905	+	0.702275i	$0.752168\pi$
$74$	1.36573e10	−	2.36552e10i	0.715470	−	1.23923i
$75$	−6.28146e9	+	1.95244e10i	−0.305649	+	0.950037i
$76$	2.22004e10	+	3.84523e10i	1.00435	+	1.73959i
$77$	1.33446e10	+	2.31135e10i	0.561831	+	0.973120i
$78$	−1.71854e10	+	3.70487e9i	−0.673966	+	0.145295i
$79$	4.75604e9	−	8.23771e9i	0.173899	−	0.301202i	−0.765881	−	0.642983i	$-0.777697\pi$
$79$	4.75604e9	−	8.23771e9i	0.173899	−	0.301202i	0.939780	+	0.341781i	$0.111030\pi$
$80$	2.14784e9			0.0732836
$81$	2.07267e10	−	2.35621e10i	0.660485	−	0.750840i
$82$	2.80889e10			0.836678
$83$	2.27734e9	−	3.94447e9i	0.0634597	−	0.109915i	−0.832550	−	0.553950i	$-0.813120\pi$
$83$	2.27734e9	−	3.94447e9i	0.0634597	−	0.109915i	0.896010	+	0.444034i	$0.146453\pi$
$84$	−1.51268e11	+	3.26107e10i	−3.94648	+	0.850794i
$85$	−9.64555e8	−	1.67066e9i	−0.0235789	−	0.0408398i
$86$	−3.29997e10	−	5.71572e10i	−0.756430	−	1.31018i
$87$	4.40282e9	−	1.36851e10i	0.0947056	−	0.294369i
$88$	3.24819e10	−	5.62602e10i	0.656125	−	1.13644i
$89$	−7.34546e10			−1.39436			−0.697178	−	0.716898i	$-0.745561\pi$
$89$	−7.34546e10			−1.39436			−0.697178	+	0.716898i	$0.745561\pi$
$90$	4.08916e9	−	1.84904e9i	0.0729963	−	0.0330075i
$91$	4.21322e10			0.707760
$92$	−6.83015e10	+	1.18302e11i	−1.08043	+	1.87136i
$93$	1.80589e10	+	1.99401e10i	0.269175	+	0.297215i
$94$	4.55514e10	+	7.88973e10i	0.640175	+	1.10881i
$95$	1.54303e9	+	2.67260e9i	0.0204594	+	0.0354368i
$96$	4.19378e10	+	4.63065e10i	0.524945	+	0.579629i
$97$	4.91645e10	−	8.51555e10i	0.581310	−	1.00686i	−0.414015	−	0.910270i	$-0.635874\pi$
$97$	4.91645e10	−	8.51555e10i	0.581310	−	1.00686i	0.995324	−	0.0965876i	$-0.0307928\pi$
$98$	3.79466e11			4.24063
$99$	5.71979e9	−	5.76263e10i	0.0604487	−	0.609013i
$100$	−2.19444e11			−2.19444
$101$	−1.96506e10	+	3.40359e10i	−0.186041	+	0.322233i	−0.943927	−	0.330155i	$-0.892899\pi$
$101$	−1.96506e10	+	3.40359e10i	−0.186041	+	0.322233i	0.757886	+	0.652387i	$0.226232\pi$
$102$	6.43050e10	−	1.99876e11i	0.576692	−	1.79251i
$103$	−2.13692e10	−	3.70126e10i	−0.181629	−	0.314590i	0.760807	−	0.648979i	$-0.224804\pi$
$103$	−2.13692e10	−	3.70126e10i	−0.181629	−	0.314590i	−0.942435	+	0.334389i	$0.891470\pi$
$104$	−5.12767e10	−	8.88138e10i	−0.413273	−	0.715809i
$105$	−1.05138e10	+	2.26658e9i	−0.0803927	+	0.0173313i
$106$	−1.69204e11	+	2.93071e11i	−1.22809	+	2.12711i
$107$	−2.36816e11			−1.63230			−0.816149	−	0.577841i	$-0.803895\pi$
$107$	−2.36816e11			−1.63230			−0.816149	+	0.577841i	$0.803895\pi$
$108$	3.07904e11	+	1.33897e11i	2.01643	+	0.876881i
$109$	3.99569e10			0.248740			0.124370	−	0.992236i	$-0.460309\pi$
$109$	3.99569e10			0.248740			0.124370	+	0.992236i	$0.460309\pi$
$110$	4.14080e9	−	7.17207e9i	0.0245146	−	0.0424605i
$111$	1.38847e11	−	2.99330e10i	0.782096	−	0.168606i
$112$	−2.80126e11	−	4.85193e11i	−1.50195	−	2.60145i
$113$	−9.21288e10	−	1.59572e11i	−0.470397	−	0.814751i	0.529030	−	0.848603i	$-0.322556\pi$
$113$	−9.21288e10	−	1.59572e11i	−0.470397	−	0.814751i	−0.999427	+	0.0338521i	$0.989222\pi$
$114$	−1.02871e11	+	3.19748e11i	−0.500396	+	1.55536i
$115$	−4.74725e9	+	8.22247e9i	−0.0220092	+	0.0381210i
$116$	1.53813e11			0.679947
$117$	−7.42679e10	−	5.33048e10i	−0.313169	−	0.224773i
$118$	3.48750e11			1.40334
$119$	−2.51599e11	+	4.35783e11i	−0.966499	+	1.67402i
$120$	1.75736e10	+	1.94043e10i	0.0644710	+	0.0711870i
$121$	8.92239e10	+	1.54540e11i	0.312724	+	0.541654i
$122$	1.46298e11	+	2.53395e11i	0.490070	+	0.848826i
$123$	9.80488e10	+	1.08263e11i	0.314025	+	0.346737i
$124$	−1.43919e11	+	2.49274e11i	−0.440857	+	0.763587i
$125$	−3.05352e10			−0.0894944
$126$	−9.51015e11	−	6.82579e11i	−2.66778	−	1.91476i
$127$	−2.05291e11			−0.551378			−0.275689	−	0.961247i	$-0.588906\pi$
$127$	−2.05291e11			−0.551378			−0.275689	+	0.961247i	$0.588906\pi$
$128$	2.34538e11	−	4.06231e11i	0.603334	−	1.04501i
$129$	1.05109e11	−	3.26707e11i	0.259058	−	0.805220i
$130$	−6.53676e9	−	1.13220e10i	−0.0154410	−	0.0267445i
$131$	2.54710e11	+	4.41171e11i	0.576838	+	0.999113i	0.995839	+	0.0911275i	$0.0290471\pi$
$131$	2.54710e11	+	4.41171e11i	0.576838	+	0.999113i	−0.419001	+	0.907986i	$0.637620\pi$
$132$	6.05679e11	−	1.30574e11i	1.31549	−	0.283596i
$133$	4.02491e11	−	6.97134e11i	0.838633	−	1.45255i
$134$	−2.10122e11			−0.420141
$135$	2.14006e10	+	9.30643e9i	0.0410762	+	0.0178627i
$136$	1.22483e12			2.25742
$137$	6.85754e10	−	1.18776e11i	0.121396	−	0.210265i	−0.798922	−	0.601434i	$-0.794596\pi$
$137$	6.85754e10	−	1.18776e11i	0.121396	−	0.210265i	0.920319	+	0.391170i	$0.127929\pi$
$138$	−1.01018e12	+	2.17778e11i	−1.71816	+	0.370406i
$139$	−1.97775e10	−	3.42556e10i	−0.0323288	−	0.0559951i	0.849408	−	0.527736i	$-0.176959\pi$
$139$	−1.97775e10	−	3.42556e10i	−0.0323288	−	0.0559951i	−0.881737	+	0.471741i	$0.843626\pi$
$140$	−5.75375e10	−	9.96578e10i	−0.0904163	−	0.156606i
$141$	−1.45088e11	+	4.50972e11i	−0.219244	+	0.681466i
$142$	−4.37255e11	+	7.57348e11i	−0.635548	+	1.10080i
$143$	−1.68698e11			−0.235918
$144$	−1.20069e11	+	1.20968e12i	−0.161598	+	1.62808i
$145$	1.06907e10			0.0138510
$146$	1.02061e12	−	1.76775e12i	1.27327	−	2.20536i
$147$	1.32459e12	+	1.46257e12i	1.59161	+	1.75741i
$148$	7.59853e11	+	1.31610e12i	0.879610	+	1.52353i
$149$	−6.94024e11	−	1.20209e12i	−0.774195	−	1.34094i	−0.935246	−	0.353999i	$-0.884822\pi$
$149$	−6.94024e11	−	1.20209e12i	−0.774195	−	1.34094i	0.161051	−	0.986946i	$-0.448512\pi$
$150$	−1.11437e12	−	1.23045e12i	−1.19819	−	1.32301i
$151$	4.91648e10	−	8.51559e10i	0.0509660	−	0.0882758i	−0.839417	−	0.543488i	$-0.817103\pi$
$151$	4.91648e10	−	8.51559e10i	0.0509660	−	0.0882758i	0.890383	+	0.455212i	$0.150437\pi$
$152$	−1.95940e12			−1.95877
$153$	9.94848e11	−	4.49851e11i	0.959298	−	0.433776i
$154$	−2.16021e12			−2.00971
$155$	−1.00030e10	+	1.73256e10i	−0.00898057	+	0.0155548i
$156$	2.99559e11	−	9.31106e11i	0.259595	−	0.806889i
$157$	−4.79441e11	−	8.30417e11i	−0.401132	−	0.694781i	0.592731	−	0.805401i	$-0.298050\pi$
$157$	−4.79441e11	−	8.30417e11i	−0.401132	−	0.694781i	−0.993863	+	0.110619i	$0.964717\pi$
$158$	3.84953e11	+	6.66758e11i	0.311024	+	0.538709i
$159$	−1.72021e12	+	3.70848e11i	−1.34245	+	0.289409i
$160$	−2.32297e10	+	4.02349e10i	−0.0175139	+	0.0303350i
$161$	2.47659e12			1.80431
$162$	8.12801e11	+	2.40641e12i	0.572337	+	1.69448i
$163$	−2.10222e12			−1.43102			−0.715511	−	0.698602i	$-0.753806\pi$
$163$	−2.10222e12			−1.43102			−0.715511	+	0.698602i	$0.753806\pi$
$164$	−7.81390e11	+	1.35341e12i	−0.514312	+	0.890814i
$165$	4.20973e10	−	9.07545e9i	0.0267974	−	0.00577706i
$166$	1.84327e11	+	3.19264e11i	0.113500	+	0.196587i
$167$	7.63182e11	+	1.32187e12i	0.454661	+	0.787495i	0.998669	−	0.0515846i	$-0.0164272\pi$
$167$	7.63182e11	+	1.32187e12i	0.454661	+	0.787495i	−0.544008	+	0.839080i	$0.683094\pi$
$168$	2.09140e12	−	6.50061e12i	1.20569	−	3.74760i
$169$	7.62925e11	−	1.32142e12i	0.425701	−	0.737336i
$170$	1.56142e11			0.0843431
$171$	−1.59149e12	+	7.19640e11i	−0.832385	+	0.376389i
$172$	3.67201e12			1.85993
$173$	−3.27600e11	+	5.67420e11i	−0.160728	+	0.278388i	−0.935130	−	0.354305i	$-0.884717\pi$
$173$	−3.27600e11	+	5.67420e11i	−0.160728	+	0.278388i	0.774402	+	0.632694i	$0.218051\pi$
$174$	7.81088e11	+	8.62454e11i	0.371261	+	0.409935i
$175$	1.98924e12	+	3.44546e12i	0.916174	+	1.58686i
$176$	1.12163e12	+	1.94272e12i	0.500646	+	0.867144i
$177$	1.21737e12	+	1.34418e12i	0.526707	+	0.581574i
$178$	2.97270e12	−	5.14886e12i	1.24693	−	2.15974i
$179$	−1.81401e12			−0.737816			−0.368908	−	0.929466i	$-0.620268\pi$
$179$	−1.81401e12			−0.737816			−0.368908	+	0.929466i	$0.620268\pi$
$180$	−2.46619e10	+	2.48466e11i	−0.00972809	+	0.0980094i
$181$	−4.42869e12			−1.69450			−0.847252	−	0.531191i	$-0.821745\pi$
$181$	−4.42869e12			−1.69450			−0.847252	+	0.531191i	$0.821745\pi$
$182$	−1.70508e12	+	2.95329e12i	−0.632926	+	1.09626i
$183$	−4.65981e11	+	1.44839e12i	−0.167837	+	0.521680i
$184$	−3.01412e12	−	5.22061e12i	−1.05357	−	1.82483i
$185$	5.28130e10	+	9.14748e10i	0.0179183	+	0.0310354i
$186$	−2.12856e12	+	4.58881e11i	−0.701075	+	0.151140i
$187$	1.00741e12	−	1.74488e12i	0.322164	−	0.558004i
$188$	−5.06868e12			−1.57408
$189$	−6.88816e11	−	6.04813e12i	−0.207761	−	1.82424i
$190$	−2.49784e11			−0.0731847
$191$	3.13694e12	−	5.43335e12i	0.892942	−	1.54662i	0.0566111	−	0.998396i	$-0.481971\pi$
$191$	3.13694e12	−	5.43335e12i	0.892942	−	1.54662i	0.836331	−	0.548225i	$-0.184696\pi$
$192$	8.39145e11	−	1.80905e11i	0.232103	−	0.0500373i
$193$	−3.22204e10	−	5.58073e10i	−0.00866095	−	0.0150012i	0.861662	−	0.507482i	$-0.169424\pi$
$193$	−3.22204e10	−	5.58073e10i	−0.00866095	−	0.0150012i	−0.870323	+	0.492481i	$0.836090\pi$
$194$	3.97936e12	+	6.89246e12i	1.03969	+	1.80080i
$195$	2.08206e10	−	6.47158e10i	0.00528814	−	0.0164369i
$196$	−1.05562e13	+	1.82838e13i	−2.60674	+	4.51501i
$197$	−1.16291e12			−0.279244			−0.139622	−	0.990205i	$-0.544589\pi$
$197$	−1.16291e12			−0.279244			−0.139622	+	0.990205i	$0.544589\pi$
$198$	3.80788e12	+	2.73306e12i	0.889252	+	0.638250i
$199$	2.64496e12			0.600797			0.300399	−	0.953814i	$-0.402880\pi$
$199$	2.64496e12			0.600797			0.300399	+	0.953814i	$0.402880\pi$
$200$	4.84198e12	−	8.38656e12i	1.06994	−	1.85319i
$201$	−7.33464e11	−	8.09870e11i	−0.157689	−	0.174115i
$202$	−1.59052e12	−	2.75486e12i	−0.332740	−	0.576323i
$203$	−1.39431e12	−	2.41501e12i	−0.283877	−	0.491689i
$204$	7.84178e12	+	8.65867e12i	1.55399	+	1.71587i
$205$	−5.43099e10	+	9.40676e10i	−0.0104769	+	0.0181465i
$206$	3.45924e12			0.649697
$207$	−4.36558e12	−	3.13334e12i	−0.798371	−	0.573021i
$208$	3.54127e12			0.630683
$209$	−1.61158e12	+	2.79134e12i	−0.279542	+	0.484182i
$210$	2.66612e11	−	8.28699e11i	0.0450478	−	0.140020i
$211$	1.40254e12	+	2.42927e12i	0.230867	+	0.399874i	0.958064	−	0.286556i	$-0.0925103\pi$
$211$	1.40254e12	+	2.42927e12i	0.230867	+	0.399874i	−0.727196	+	0.686430i	$0.759177\pi$
$212$	−9.41401e12	−	1.63056e13i	−1.50983	−	2.61510i
$213$	−4.44534e12	+	9.58339e11i	−0.694732	+	0.149772i
$214$	9.58390e12	−	1.65998e13i	1.45971	−	2.52829i
$215$	2.55220e11			0.0378882
$216$	−1.19110e13	+	8.81286e12i	−1.72367	+	1.27533i
$217$	5.21844e12			0.736228
$218$	−1.61705e12	+	2.80081e12i	−0.222440	+	0.385277i
$219$	1.03760e13	−	2.23689e12i	1.39183	−	0.300055i
$220$	2.30381e11	+	3.99032e11i	0.0301385	+	0.0522015i
$221$	−1.59032e12	−	2.75452e12i	−0.202921	−	0.351470i
$222$	−3.52094e12	+	1.09440e13i	−0.438245	+	1.36218i
$223$	−4.79394e12	+	8.30335e12i	−0.582124	+	1.00827i	0.413103	+	0.910684i	$0.364445\pi$
$223$	−4.79394e12	+	8.30335e12i	−0.582124	+	1.00827i	−0.995227	+	0.0975848i	$0.968888\pi$
$224$	1.21187e13			1.43579
$225$	8.52634e11	−	8.59019e12i	0.0985732	−	0.993114i
$226$	1.49138e13			1.68264
$227$	−6.52031e12	+	1.12935e13i	−0.718002	+	1.24362i	0.243788	+	0.969829i	$0.421610\pi$
$227$	−6.52031e12	+	1.12935e13i	−0.718002	+	1.24362i	−0.961790	+	0.273788i	$0.911723\pi$
$228$	−1.25447e13	−	1.38515e13i	−1.34840	−	1.48887i
$229$	8.69786e12	+	1.50651e13i	0.912677	+	1.58080i	0.810266	+	0.586062i	$0.199322\pi$
$229$	8.69786e12	+	1.50651e13i	0.912677	+	1.58080i	0.102411	+	0.994742i	$0.467344\pi$
$230$	−3.84241e11	−	6.65525e11i	−0.0393641	−	0.0681806i
$231$	−7.54057e12	−	8.32607e12i	−0.754290	−	0.832864i
$232$	−3.39386e12	+	5.87834e12i	−0.331521	+	0.574210i
$233$	1.87559e13			1.78929			0.894646	−	0.446776i	$-0.147428\pi$
$233$	1.87559e13			1.78929			0.894646	+	0.446776i	$0.147428\pi$
$234$	6.74206e12	−	3.04863e12i	0.628211	−	0.284065i
$235$	−3.52295e11			−0.0320651
$236$	−9.70170e12	+	1.68038e13i	−0.862644	+	1.49414i
$237$	−1.22613e12	+	3.81114e12i	−0.106518	+	0.331085i
$238$	−2.03644e13	−	3.52721e13i	−1.72861	−	2.99405i
$239$	6.61406e12	+	1.14559e13i	0.548630	+	0.950255i	0.998369	+	0.0570950i	$0.0181838\pi$
$239$	6.61406e12	+	1.14559e13i	0.548630	+	0.950255i	−0.449739	+	0.893160i	$0.648483\pi$
$240$	−8.83698e11	+	1.90510e11i	−0.0716378	+	0.0154439i
$241$	−1.16556e12	+	2.01881e12i	−0.0923511	+	0.159957i	−0.908500	−	0.417885i	$-0.862772\pi$
$241$	−1.16556e12	+	2.01881e12i	−0.0923511	+	0.159957i	0.816149	+	0.577842i	$0.196105\pi$
$242$	−1.44435e13			−1.11863
$243$	−6.43779e12	+	1.15327e13i	−0.487419	+	0.873168i
$244$	−1.62791e13			−1.20500
$245$	−7.33699e11	+	1.27080e12i	−0.0531013	+	0.0919741i
$246$	−1.15568e13	+	2.49144e12i	−0.817888	+	0.176322i
$247$	2.54408e12	+	4.40648e12i	0.176075	+	0.304971i
$248$	−6.35108e12	−	1.10004e13i	−0.429896	−	0.744601i
$249$	−5.87111e11	+	1.82489e12i	−0.0388708	+	0.120821i
$250$	1.23576e12	−	2.14039e12i	0.0800318	−	0.138619i
$251$	−9.00009e12			−0.570219			−0.285109	−	0.958495i	$-0.592030\pi$
$251$	−9.00009e12			−0.570219			−0.285109	+	0.958495i	$0.592030\pi$
$252$	5.93445e13	−	2.68344e13i	3.67856	−	1.66337i
$253$	−9.91632e12			−0.601434
$254$	8.30811e12	−	1.43901e13i	0.493079	−	0.854038i
$255$	5.45037e11	+	6.01814e11i	0.0316559	+	0.0349536i
$256$	1.68949e13	+	2.92629e13i	0.960365	+	1.66340i
$257$	−1.27481e13	−	2.20804e13i	−0.709274	−	1.22850i	−0.965127	−	0.261783i	$-0.915690\pi$
$257$	−1.27481e13	−	2.20804e13i	−0.709274	−	1.22850i	0.255853	−	0.966716i	$-0.417644\pi$
$258$	1.86470e13	+	2.05895e13i	1.01555	+	1.12134i
$259$	1.37760e13	−	2.38608e13i	0.734471	−	1.27214i
$260$	7.27371e11			0.0379667
$261$	−5.97632e11	+	6.02107e12i	−0.0305429	+	0.307717i
$262$	−4.12323e13			−2.06339
$263$	1.52170e13	−	2.63567e13i	0.745716	−	1.29162i	−0.204144	−	0.978941i	$-0.565441\pi$
$263$	1.52170e13	−	2.63567e13i	0.745716	−	1.29162i	0.949860	−	0.312676i	$-0.101226\pi$
$264$	−8.37401e12	+	2.60286e13i	−0.401894	+	1.24919i
$265$	−6.54314e11	−	1.13331e12i	−0.0307563	−	0.0532715i
$266$	3.25775e13	+	5.64259e13i	1.49992	+	2.59794i
$267$	3.02219e13	−	6.51531e12i	1.36304	−	0.293848i
$268$	5.84527e12	−	1.01243e13i	0.258264	−	0.447326i
$269$	1.11521e13			0.482744			0.241372	−	0.970433i	$-0.422403\pi$
$269$	1.11521e13			0.482744			0.241372	+	0.970433i	$0.422403\pi$
$270$	−1.51842e12	+	1.12347e12i	−0.0644009	+	0.0476496i
$271$	−1.21063e13			−0.503131			−0.251565	−	0.967840i	$-0.580945\pi$
$271$	−1.21063e13			−0.503131			−0.251565	+	0.967840i	$0.580945\pi$
$272$	−2.11473e13	+	3.66282e13i	−0.861244	+	1.49172i
$273$	−1.73347e13	+	3.73706e12i	−0.691865	+	0.149154i
$274$	5.55048e12	+	9.61371e12i	0.217121	+	0.376065i
$275$	−7.96495e12	−	1.37957e13i	−0.305389	−	0.528949i
$276$	1.76085e13	−	5.47318e13i	0.661794	−	2.05703i
$277$	−9.35867e12	+	1.62097e13i	−0.344806	+	0.597222i	−0.985319	−	0.170726i	$-0.945389\pi$
$277$	−9.35867e12	+	1.62097e13i	−0.344806	+	0.597222i	0.640512	+	0.767948i	$0.278722\pi$
$278$	3.20157e12			0.115642
$279$	−9.19874e12	−	6.60228e12i	−0.325766	−	0.233814i
$280$	5.07822e12			0.176336
$281$	−1.00164e13	+	1.73490e13i	−0.341058	+	0.590731i	−0.984630	−	0.174656i	$-0.944119\pi$
$281$	−1.00164e13	+	1.73490e13i	−0.341058	+	0.590731i	0.643571	+	0.765386i	$0.277452\pi$
$282$	−2.57396e13	−	2.84209e13i	−0.859470	−	0.949002i
$283$	−2.74133e13	−	4.74812e13i	−0.897710	−	1.55488i	−0.830415	−	0.557146i	$-0.811896\pi$
$283$	−2.74133e13	−	4.74812e13i	−0.897710	−	1.55488i	−0.0672952	−	0.997733i	$-0.521437\pi$
$284$	−2.43275e13	−	4.21365e13i	−0.781352	−	1.35334i
$285$	−8.71912e11	−	9.62740e11i	−0.0274679	−	0.0303293i
$286$	6.82719e12	−	1.18250e13i	0.210974	−	0.365417i
$287$	2.83330e13			0.858898
$288$	−2.13620e13	−	1.53323e13i	−0.635307	−	0.455984i
$289$	3.71561e12			0.108416
$290$	−4.32650e11	+	7.49372e11i	−0.0123865	+	0.0214540i
$291$	−1.26749e13	+	3.93969e13i	−0.356068	+	1.10675i
$292$	5.67836e13	+	9.83521e13i	1.56537	+	2.71130i
$293$	2.16864e13	+	3.75619e13i	0.586698	+	1.01619i	0.994661	+	0.103192i	$0.0329058\pi$
$293$	2.16864e13	+	3.75619e13i	0.586698	+	1.01619i	−0.407963	+	0.912998i	$0.633761\pi$
$294$	−1.56126e14	+	3.36581e13i	−4.14539	+	0.893674i
$295$	−6.74309e11	+	1.16794e12i	−0.0175727	+	0.0304368i
$296$	−6.70641e13			−1.71548
$297$	2.75803e12	+	2.42169e13i	0.0692531	+	0.608075i
$298$	1.12348e14			2.76934
$299$	−7.82708e12	+	1.35569e13i	−0.189412	+	0.328072i
$300$	9.02870e13	−	1.94643e13i	2.14515	−	0.462458i
$301$	−3.32865e13	−	5.76538e13i	−0.776519	−	1.34497i
$302$	3.97938e12	+	6.89249e12i	0.0911544	+	0.157884i
$303$	5.06604e12	−	1.57466e13i	0.113955	−	0.354202i
$304$	3.38300e13	−	5.85952e13i	0.747303	−	1.29437i
$305$	−1.13147e12			−0.0245467
$306$	−8.72865e12	+	8.79401e13i	−0.185986	+	1.87378i
$307$	3.77434e13			0.789915			0.394957	−	0.918699i	$-0.370759\pi$
$307$	3.77434e13			0.789915			0.394957	+	0.918699i	$0.370759\pi$
$308$	6.00938e13	−	1.04086e14i	1.23538	−	2.13974i
$309$	1.20750e13	+	1.33329e13i	0.243847	+	0.269248i
$310$	−8.09637e11	−	1.40233e12i	−0.0160620	−	0.0278203i
$311$	−4.71140e13	−	8.16038e13i	−0.918264	−	1.59048i	−0.802051	−	0.597256i	$-0.796258\pi$
$311$	−4.71140e13	−	8.16038e13i	−0.918264	−	1.59048i	−0.116213	−	0.993224i	$-0.537076\pi$
$312$	2.89747e13	+	3.19930e13i	0.554842	+	0.612640i
$313$	−4.17359e13	+	7.22887e13i	−0.785265	+	1.36012i	0.143576	+	0.989639i	$0.454140\pi$
$313$	−4.17359e13	+	7.22887e13i	−0.785265	+	1.36012i	−0.928841	+	0.370479i	$0.879193\pi$
$314$	7.76117e13			1.43488
$315$	4.12470e12	−	1.86511e12i	0.0749349	−	0.0338841i
$316$	−4.28352e13			−0.764754
$317$	−2.44968e13	+	4.24298e13i	−0.429817	+	0.744466i	−0.996857	−	0.0792252i	$-0.974755\pi$
$317$	−2.44968e13	+	4.24298e13i	−0.429817	+	0.744466i	0.567039	+	0.823691i	$0.308089\pi$
$318$	4.36219e13	−	1.35588e14i	0.752237	−	2.33815i
$319$	5.58283e12	+	9.66974e12i	0.0946249	+	0.163895i
$320$	3.19184e11	+	5.52843e11i	0.00531761	+	0.00921036i
$321$	9.74345e13	−	2.10052e13i	1.59564	−	0.343992i
$322$	−1.00227e14	+	1.73599e14i	−1.61354	+	2.79473i
$323$	−6.07697e13			−0.961774
$324$	−1.38559e14	−	2.77795e13i	−2.15594	−	0.432242i
$325$	−2.51474e13			−0.384710
$326$	8.50765e13	−	1.47357e14i	1.27971	−	2.21653i
$327$	−1.64397e13	+	3.54411e12i	−0.243154	+	0.0524198i
$328$	−3.44825e13	−	5.97254e13i	−0.501524	−	0.868666i
$329$	4.59472e13	+	7.95829e13i	0.657176	+	1.13826i
$330$	−1.06752e12	+	3.31813e12i	−0.0150158	+	0.0466731i
$331$	5.13882e13	−	8.90069e13i	0.710901	−	1.23132i	−0.253618	−	0.967304i	$-0.581621\pi$
$331$	5.13882e13	−	8.90069e13i	0.710901	−	1.23132i	0.964519	−	0.264012i	$-0.0850459\pi$
$332$	−2.05108e13			−0.279076
$333$	−5.44717e13	+	2.46311e13i	−0.729000	+	0.329640i
$334$	−1.23543e14			−1.62635
$335$	4.06271e11	−	7.03682e11i	0.00526102	−	0.00911235i
$336$	1.58290e14	+	1.74779e14i	2.01645	+	2.22650i
$337$	−1.04790e13	−	1.81502e13i	−0.131328	−	0.227466i	0.792861	−	0.609403i	$-0.208591\pi$
$337$	−1.04790e13	−	1.81502e13i	−0.131328	−	0.227466i	−0.924189	+	0.381936i	$0.875257\pi$
$338$	6.17509e13	+	1.06956e14i	0.761380	+	1.31875i
$339$	5.20589e13	+	5.74819e13i	0.631534	+	0.697321i
$340$	−4.34362e12	+	7.52337e12i	−0.0518463	+	0.0898005i
$341$	−2.08948e13			−0.245408
$342$	1.39635e13	−	1.40680e14i	0.161380	−	1.62588i
$343$	2.21329e14			2.51721
$344$	−8.10222e13	+	1.40335e14i	−0.906844	+	1.57070i
$345$	1.22387e12	−	3.80409e12i	0.0134812	−	0.0419031i
$346$	−2.65158e13	−	4.59268e13i	−0.287466	−	0.497906i
$347$	−6.31236e13	−	1.09333e14i	−0.673565	−	1.16665i	−0.976886	−	0.213761i	$-0.931429\pi$
$347$	−6.31236e13	−	1.09333e14i	−0.673565	−	1.16665i	0.303321	−	0.952889i	$-0.401905\pi$
$348$	−6.32843e13	+	1.36430e13i	−0.664676	+	0.143293i
$349$	7.83077e12	−	1.35633e13i	0.0809589	−	0.140225i	−0.822703	−	0.568471i	$-0.807535\pi$
$349$	7.83077e12	−	1.35633e13i	0.0809589	−	0.140225i	0.903662	+	0.428246i	$0.140868\pi$
$350$	−3.22017e14			−3.27721
$351$	3.52845e13	+	1.53441e13i	0.353505	+	0.153728i
$352$	−4.85235e13			−0.478594
$353$	−5.44257e13	+	9.42681e13i	−0.528498	+	0.915385i	0.470950	+	0.882160i	$0.343911\pi$
$353$	−5.44257e13	+	9.42681e13i	−0.528498	+	0.915385i	−0.999448	+	0.0332250i	$0.989422\pi$
$354$	−1.43488e14	+	3.09336e13i	−1.37182	+	0.295742i
$355$	−1.69087e12	−	2.92867e12i	−0.0159167	−	0.0275686i
$356$	1.65392e14	+	2.86467e14i	1.53299	+	2.65521i
$357$	6.48638e13	−	2.01613e14i	0.592007	−	1.84011i
$358$	7.34128e13	−	1.27155e14i	0.659804	−	1.14281i
$359$	1.11505e14			0.986908			0.493454	−	0.869772i	$-0.335734\pi$
$359$	1.11505e14			0.986908			0.493454	+	0.869772i	$0.335734\pi$
$360$	−8.95155e12	−	6.42487e12i	−0.0780252	−	0.0560016i
$361$	−1.92752e13			−0.165467
$362$	1.79228e14	−	3.10432e14i	1.51534	−	2.62464i
$363$	−5.04174e13	−	5.56694e13i	−0.419850	−	0.463586i
$364$	−9.48656e13	−	1.64312e14i	−0.778128	−	1.34776i
$365$	3.94670e12	+	6.83589e12i	0.0318877	+	0.0552312i
$366$	−8.26678e13	−	9.12794e13i	−0.657946	−	0.726485i
$367$	−7.41634e13	+	1.28455e14i	−0.581468	+	1.00713i	0.413837	+	0.910351i	$0.364188\pi$
$367$	−7.41634e13	+	1.28455e14i	−0.581468	+	1.00713i	−0.995306	+	0.0967818i	$0.969145\pi$
$368$	2.08161e14			1.60782
$369$	−4.99435e13	−	3.58463e13i	−0.380044	−	0.272772i
$370$	−8.54934e12			−0.0640949
$371$	−1.70675e14	+	2.95617e14i	−1.26070	+	2.18360i
$372$	3.71030e13	−	1.15326e14i	0.270037	−	0.839345i
$373$	7.55273e13	+	1.30817e14i	0.541633	+	0.938136i	0.998810	+	0.0487606i	$0.0155271\pi$
$373$	7.55273e13	+	1.30817e14i	0.541633	+	0.938136i	−0.457177	+	0.889376i	$0.651140\pi$
$374$	8.15394e13	+	1.41230e14i	0.576201	+	0.998009i
$375$	1.25633e13	−	2.70843e12i	0.0874845	−	0.0188601i
$376$	1.11840e14	−	1.93712e14i	0.767471	−	1.32930i
$377$	1.76264e13			0.119203
$378$	4.51825e14	+	1.96484e14i	3.01138	+	1.30955i
$379$	−6.82843e13			−0.448544			−0.224272	−	0.974527i	$-0.572000\pi$
$379$	−6.82843e13			−0.448544			−0.224272	+	0.974527i	$0.572000\pi$
$380$	6.94861e12	−	1.20354e13i	0.0449871	−	0.0779200i
$381$	8.44642e13	−	1.82090e13i	0.538996	−	0.116198i
$382$	2.53903e14	+	4.39774e14i	1.59706	+	2.76618i
$383$	−5.38251e13	−	9.32277e13i	−0.333727	−	0.578032i	0.649513	−	0.760351i	$-0.274973\pi$
$383$	−5.38251e13	−	9.32277e13i	−0.333727	−	0.578032i	−0.983239	+	0.182319i	$0.941640\pi$
$384$	−6.04652e13	+	1.87941e14i	−0.369559	+	1.14868i
$385$	4.17678e12	−	7.23439e12i	0.0251656	−	0.0435881i
$386$	5.21582e12			0.0309808
$387$	−1.42673e13	+	1.43742e14i	−0.0835474	+	0.841731i
$388$	−4.42799e14			−2.55642
$389$	1.39127e14	−	2.40975e14i	0.791933	−	1.37167i	−0.132835	−	0.991138i	$-0.542408\pi$
$389$	1.39127e14	−	2.40975e14i	0.791933	−	1.37167i	0.924768	−	0.380531i	$-0.124259\pi$
$390$	3.69370e12	+	4.07848e12i	0.0207304	+	0.0228899i
$391$	−9.34815e13	−	1.61915e14i	−0.517313	−	0.896013i
$392$	−4.65840e14	−	8.06859e14i	−2.54193	−	4.40275i
$393$	−1.43928e14	−	1.58921e14i	−0.774438	−	0.855112i
$394$	4.70630e13	−	8.15154e13i	0.249718	−	0.432524i
$395$	−2.97723e12			−0.0155786
$396$	−2.37617e14	+	1.07446e14i	−1.22618	+	0.554454i
$397$	2.42124e13			0.123222			0.0616112	−	0.998100i	$-0.480376\pi$
$397$	2.42124e13			0.123222			0.0616112	+	0.998100i	$0.480376\pi$
$398$	−1.07041e14	+	1.85401e14i	−0.537272	+	0.930583i
$399$	−1.03764e14	+	3.22526e14i	−0.513686	+	1.59667i
$400$	1.67199e14	+	2.89597e14i	0.816400	+	1.41405i
$401$	−7.66045e13	−	1.32683e14i	−0.368944	−	0.639030i	0.620457	−	0.784241i	$-0.286947\pi$
$401$	−7.66045e13	−	1.32683e14i	−0.368944	−	0.639030i	−0.989401	+	0.145211i	$0.953614\pi$
$402$	8.64517e13	−	1.86375e13i	0.410705	−	0.0885409i
$403$	−1.64925e13	+	2.85658e13i	−0.0772874	+	0.133866i
$404$	1.76983e14			0.818152
$405$	−9.63045e12	−	1.93080e12i	−0.0439181	−	0.00880509i
$406$	2.25709e14			1.01545
$407$	−5.51594e13	+	9.55390e13i	−0.244822	+	0.424044i
$408$	−5.03939e14	+	1.08641e14i	−2.20672	+	0.475731i
$409$	−7.60653e13	−	1.31749e14i	−0.328631	−	0.569205i	0.653610	−	0.756832i	$-0.273254\pi$
$409$	−7.60653e13	−	1.31749e14i	−0.328631	−	0.569205i	−0.982240	+	0.187627i	$0.939921\pi$
$410$	−4.39583e12	−	7.61380e12i	−0.0187383	−	0.0324557i
$411$	−1.76791e13	+	5.49513e13i	−0.0743586	+	0.231126i
$412$	−9.62308e13	+	1.66677e14i	−0.399374	+	0.691736i
$413$	3.51781e14			1.44061
$414$	3.96308e14	−	1.79203e14i	1.60152	−	0.724175i
$415$	−1.42559e12			−0.00568499
$416$	−3.83002e13	+	6.63378e13i	−0.150726	+	0.261065i
$417$	1.11756e13	+	1.23397e13i	0.0434032	+	0.0479245i
$418$	−1.30441e14	−	2.25930e14i	−0.499970	−	0.865974i
$419$	−2.40507e13	−	4.16571e13i	−0.0909811	−	0.157584i	0.816943	−	0.576718i	$-0.195667\pi$
$419$	−2.40507e13	−	4.16571e13i	−0.0909811	−	0.157584i	−0.907924	+	0.419134i	$0.862334\pi$
$420$	3.25125e13	+	3.58993e13i	0.121389	+	0.134034i
$421$	−5.19807e13	+	9.00333e13i	−0.191554	+	0.331781i	−0.945765	−	0.324851i	$-0.894686\pi$
$421$	−5.19807e13	+	9.00333e13i	−0.191554	+	0.331781i	0.754211	+	0.656632i	$0.228019\pi$
$422$	−2.27043e14			−0.825827
$423$	1.96940e13	−	1.98415e14i	0.0707070	−	0.712365i
$424$	8.30874e14			2.94458
$425$	1.50172e14	−	2.60105e14i	0.525350	−	0.909934i
$426$	1.12727e14	−	3.50384e14i	0.389291	−	1.21002i
$427$	1.47569e14	+	2.55597e14i	0.503085	+	0.871369i
$428$	5.33219e14	+	9.23562e14i	1.79459	+	3.10832i
$429$	6.94084e13	−	1.49633e13i	0.230620	−	0.0497177i
$430$	−1.03287e13	+	1.78899e13i	−0.0338821	+	0.0586855i
$431$	−1.67647e14			−0.542965			−0.271482	−	0.962443i	$-0.587514\pi$
$431$	−1.67647e14			−0.542965			−0.271482	+	0.962443i	$0.587514\pi$
$432$	−5.78961e13	−	5.08355e14i	−0.185135	−	1.62557i
$433$	−5.11703e14			−1.61560			−0.807801	−	0.589455i	$-0.799343\pi$
$433$	−5.11703e14			−1.61560			−0.807801	+	0.589455i	$0.799343\pi$
$434$	−2.11190e14	+	3.65791e14i	−0.658384	+	1.14035i
$435$	−4.39853e12	+	9.48247e11i	−0.0135399	+	0.00291898i
$436$	−8.99677e13	−	1.55829e14i	−0.273471	−	0.473665i
$437$	1.49545e14	+	2.59020e14i	0.448874	+	0.777472i
$438$	−2.63119e14	+	8.17842e14i	−0.779910	+	2.42416i
$439$	2.73465e14	−	4.73656e14i	0.800474	−	1.38646i	−0.118830	−	0.992915i	$-0.537914\pi$
$439$	2.73465e14	−	4.73656e14i	0.800474	−	1.38646i	0.919304	−	0.393547i	$-0.128752\pi$
$440$	−2.03333e13			−0.0587784
$441$	−6.74711e14	−	4.84266e14i	−1.92622	−	1.38252i
$442$	2.57440e14			0.725862
$443$	2.67729e14	−	4.63721e14i	0.745548	−	1.29133i	−0.204391	−	0.978889i	$-0.565521\pi$
$443$	2.67729e14	−	4.63721e14i	0.745548	−	1.29133i	0.949938	−	0.312437i	$-0.101145\pi$
$444$	−4.29367e14	−	4.74095e14i	−1.18093	−	1.30394i
$445$	1.14954e13	+	1.99107e13i	0.0312281	+	0.0540886i
$446$	−3.88020e14	−	6.72071e14i	−1.04115	−	1.80332i
$447$	3.92170e14	+	4.33022e14i	1.03940	+	1.14767i
$448$	8.32576e13	−	1.44206e14i	0.217969	−	0.377533i
$449$	5.95142e14			1.53910			0.769548	−	0.638589i	$-0.220481\pi$
$449$	5.95142e14			1.53910			0.769548	+	0.638589i	$0.220481\pi$
$450$	5.67631e14	+	4.07410e14i	1.45010	+	1.04079i
$451$	−1.13446e14			−0.286297
$452$	−4.14878e14	+	7.18590e14i	−1.03433	+	1.79151i
$453$	−1.26750e13	+	3.93970e13i	−0.0312181	+	0.0970339i
$454$	−5.27752e14	−	9.14093e14i	−1.28417	−	2.22425i
$455$	−6.59356e12	−	1.14204e13i	−0.0158510	−	0.0274548i
$456$	8.06166e14	−	1.73795e14i	1.91478	−	0.412792i
$457$	−1.63920e14	+	2.83918e14i	−0.384674	+	0.666275i	−0.991724	−	0.128389i	$-0.959019\pi$
$457$	−1.63920e14	+	2.83918e14i	−0.384674	+	0.666275i	0.607050	+	0.794664i	$0.292353\pi$
$458$	−1.40801e15			−3.26471
$459$	−3.69415e14	+	2.73326e14i	−0.846340	+	0.626198i
$460$	4.27560e13			0.0967896
$461$	−4.61807e13	+	7.99873e13i	−0.103301	+	0.178923i	−0.913043	−	0.407864i	$-0.866274\pi$
$461$	−4.61807e13	+	7.99873e13i	−0.103301	+	0.178923i	0.809742	+	0.586787i	$0.199607\pi$
$462$	8.88789e14	−	1.91608e14i	1.96457	−	0.423528i
$463$	1.92367e14	+	3.33189e14i	0.420179	+	0.727771i	0.995957	−	0.0898349i	$-0.0286339\pi$
$463$	1.92367e14	+	3.33189e14i	0.420179	+	0.727771i	−0.575778	+	0.817606i	$0.695301\pi$
$464$	−1.17194e14	−	2.02985e14i	−0.252962	−	0.438143i
$465$	2.57882e12	−	8.01564e12i	0.00550085	−	0.0170981i
$466$	−7.59050e14	+	1.31471e15i	−1.60010	+	2.77146i
$467$	6.68124e13			0.139192			0.0695960	−	0.997575i	$-0.477829\pi$
$467$	6.68124e13			0.139192			0.0695960	+	0.997575i	$0.477829\pi$
$468$	−4.06616e13	+	4.09661e14i	−0.0837206	+	0.843475i
$469$	−2.11948e14			−0.431299
$470$	1.42573e13	−	2.46944e13i	0.0286748	−	0.0496662i
$471$	2.70916e14	+	2.99138e14i	0.538543	+	0.594643i
$472$	−4.28132e14	−	7.41547e14i	−0.841196	−	1.45699i
$473$	1.33280e14	+	2.30847e14i	0.258838	+	0.448320i
$474$	−2.17524e14	−	2.40183e14i	−0.417567	−	0.461065i
$475$	−2.40234e14	+	4.16098e14i	−0.455848	+	0.789551i
$476$	2.26602e15			4.25037
$477$	6.74864e14	−	3.05161e14i	1.25131	−	0.565819i
$478$	−1.07068e15			−1.96249
$479$	−1.88019e14	+	3.25659e14i	−0.340688	+	0.590089i	−0.984561	−	0.175044i	$-0.943993\pi$
$479$	−1.88019e14	+	3.25659e14i	−0.340688	+	0.590089i	0.643873	+	0.765133i	$0.277327\pi$
$480$	5.98874e12	−	1.86145e13i	0.0107277	−	0.0333446i
$481$	8.70761e13	+	1.50820e14i	0.154206	+	0.267092i
$482$	−9.43403e13	−	1.63402e14i	−0.165173	−	0.286088i
$483$	−1.01896e15	+	2.19670e14i	−1.76379	+	0.380243i
$484$	4.01797e14	−	6.95932e14i	0.687633	−	1.19102i
$485$	−3.07765e13			−0.0520762
$486$	−5.47861e14	−	9.17991e14i	−0.916581	−	1.53581i
$487$	7.76080e14			1.28380			0.641900	−	0.766789i	$-0.278147\pi$
$487$	7.76080e14			1.28380			0.641900	+	0.766789i	$0.278147\pi$
$488$	3.59196e14	−	6.22145e14i	0.587519	−	1.01761i
$489$	8.64928e14	−	1.86464e14i	1.39888	−	0.301575i
$490$	−5.93854e13	−	1.02859e14i	−0.0949733	−	0.164499i
$491$	−4.65165e14	−	8.05690e14i	−0.735630	−	1.27415i	−0.954447	−	0.298382i	$-0.903553\pi$
$491$	−4.65165e14	−	8.05690e14i	−0.735630	−	1.27415i	0.218817	−	0.975766i	$-0.429780\pi$
$492$	2.01447e14	−	6.26148e14i	0.315030	−	0.979195i
$493$	−1.05259e14	+	1.82314e14i	−0.162780	+	0.281943i
$494$	−4.11835e14			−0.629832
$495$	−1.65154e13	+	7.46793e12i	−0.0249781	+	0.0112946i
$496$	4.38618e14			0.656051
$497$	−4.41054e14	+	7.63928e14i	−0.652427	+	1.13004i
$498$	−1.04157e14	−	1.15007e14i	−0.152380	−	0.168253i
$499$	4.03812e14	+	6.99423e14i	0.584287	+	1.01202i	0.994964	+	0.100234i	$0.0319592\pi$
$499$	4.03812e14	+	6.99423e14i	0.584287	+	1.01202i	−0.410677	+	0.911781i	$0.634708\pi$
$500$	6.87536e13	+	1.19085e14i	0.0983922	+	0.170420i
$501$	−4.31248e14	−	4.76172e14i	−0.610408	−	0.673994i
$502$	3.64233e14	−	6.30869e14i	0.509927	−	0.883220i
$503$	−4.43662e14			−0.614367			−0.307184	−	0.951650i	$-0.599387\pi$
$503$	−4.43662e14			−0.614367			−0.307184	+	0.951650i	$0.599387\pi$
$504$	−2.83883e14	+	2.86009e15i	−0.388841	+	3.91752i
$505$	1.23011e13			0.0166663
$506$	4.01312e14	−	6.95093e14i	0.537842	−	0.931569i
$507$	−1.96686e14	+	6.11352e14i	−0.260754	+	0.810490i
$508$	4.62238e14	+	8.00619e14i	0.606198	+	1.04997i
$509$	2.14586e14	+	3.71673e14i	0.278389	+	0.482184i	0.970985	−	0.239142i	$-0.0768661\pi$
$509$	2.14586e14	+	3.71673e14i	0.278389	+	0.482184i	−0.692595	+	0.721326i	$0.743533\pi$
$510$	−6.42423e13	+	1.38495e13i	−0.0824489	+	0.0177746i
$511$	1.02948e15	−	1.78311e15i	1.30708	−	2.26393i
$512$	−1.77427e15			−2.22862
$513$	5.90964e14	−	4.37248e14i	0.734371	−	0.543353i
$514$	2.06366e15			2.53712
$515$	−6.68845e12	+	1.15847e13i	−0.00813553	+	0.0140912i
$516$	−1.51080e15	+	3.25701e14i	−1.81816	+	0.391964i
$517$	−1.83974e14	−	3.18651e14i	−0.219057	−	0.379418i
$518$	1.11503e15	+	1.93128e15i	1.31363	+	2.27527i
$519$	8.44571e13	−	2.62514e14i	0.0984500	−	0.306008i
$520$	−1.60493e13	+	2.77982e13i	−0.0185114	+	0.0320626i
$521$	1.70248e14			0.194300			0.0971502	−	0.995270i	$-0.469027\pi$
$521$	1.70248e14			0.194300			0.0971502	+	0.995270i	$0.469027\pi$
$522$	−3.97866e14	−	2.85563e14i	−0.449313	−	0.322489i
$523$	−2.88242e13			−0.0322105			−0.0161052	−	0.999870i	$-0.505127\pi$
$523$	−2.88242e13			−0.0322105			−0.0161052	+	0.999870i	$0.505127\pi$
$524$	1.14702e15	−	1.98670e15i	1.26838	−	2.19690i
$525$	−1.12405e15	−	1.24115e15i	−1.23001	−	1.35815i
$526$	1.23166e15	+	2.13330e15i	1.33374	+	2.31010i
$527$	−1.96976e14	−	3.41172e14i	−0.211083	−	0.365607i
$528$	−6.33796e14	−	6.99819e14i	−0.672145	−	0.742163i
$529$	1.63174e13	−	2.82625e13i	0.0171255	−	0.0296623i
$530$	1.05920e14			0.110017
$531$	−6.20096e14	−	4.45066e14i	−0.637440	−	0.457514i
$532$	−3.62502e15			−3.68805
$533$	−8.95441e13	+	1.55095e14i	−0.0901649	+	0.156170i
$534$	−7.66378e14	+	2.38210e15i	−0.763776	+	2.37401i
$535$	3.70610e13	+	6.41915e13i	0.0365570	+	0.0633187i
$536$	2.57950e14	+	4.46782e14i	0.251842	+	0.436204i
$537$	7.46349e14	−	1.60900e14i	0.721246	−	0.155488i
$538$	−4.51322e14	+	7.81713e14i	−0.431702	+	0.747730i
$539$	−1.53259e15			−1.45107
$540$	−1.18917e13	−	1.04415e14i	−0.0111450	−	0.0978584i
$541$	−1.98320e15			−1.83985			−0.919924	−	0.392097i	$-0.871750\pi$
$541$	−1.98320e15			−1.83985			−0.919924	+	0.392097i	$0.871750\pi$
$542$	4.89941e14	−	8.48603e14i	0.449933	−	0.779307i
$543$	1.82212e15	−	3.92818e14i	1.65645	−	0.357102i
$544$	−4.57432e14	−	7.92296e14i	−0.411654	−	0.713006i
$545$	−6.25314e12	−	1.08308e13i	−0.00557080	−	0.00964890i
$546$	4.39580e14	−	1.36633e15i	0.387684	−	1.20502i
$547$	1.73726e13	−	3.00903e13i	0.0151683	−	0.0262722i	−0.858342	−	0.513079i	$-0.828505\pi$
$547$	1.73726e13	−	3.00903e13i	0.0151683	−	0.0262722i	0.873510	+	0.486806i	$0.161838\pi$
$548$	−6.17623e14			−0.533864
$549$	6.32514e13	−	6.37251e14i	0.0541280	−	0.545334i
$550$	1.28936e15			1.09240
$551$	1.68386e14	−	2.91653e14i	0.141245	−	0.244643i
$552$	1.70318e15	+	1.88060e15i	1.41447	+	1.56182i
$553$	3.88298e14	+	6.72551e14i	0.319284	+	0.553015i
$554$	−7.57488e14	−	1.31201e15i	−0.616698	−	1.06815i
$555$	−2.98429e13	−	3.29516e13i	−0.0240563	−	0.0265623i
$556$	−8.90627e13	+	1.54261e14i	−0.0710860	+	0.123125i
$557$	1.68133e14			0.132877			0.0664386	−	0.997791i	$-0.478836\pi$
$557$	1.68133e14			0.132877			0.0664386	+	0.997791i	$0.478836\pi$
$558$	8.35064e14	−	3.77600e14i	0.653479	−	0.295491i
$559$	4.20797e14			0.326068
$560$	−8.76780e13	+	1.51863e14i	−0.0672754	+	0.116524i
$561$	−2.59716e14	+	8.07264e14i	−0.197334	+	0.613366i
$562$	−8.10728e14	−	1.40422e15i	−0.609994	−	1.05654i
$563$	1.10321e14	+	1.91081e14i	0.0821979	+	0.142371i	0.904194	−	0.427123i	$-0.140473\pi$
$563$	1.10321e14	+	1.91081e14i	0.0821979	+	0.142371i	−0.821996	+	0.569493i	$0.807139\pi$
$564$	2.08544e15	−	4.49584e14i	1.53873	−	0.331723i
$565$	−2.88358e13	+	4.99451e13i	−0.0210701	+	0.0364944i
$566$	4.43765e15			3.21117
$567$	8.19864e14	+	2.42732e15i	0.587537	+	1.73949i
$568$	2.14713e15			1.52385
$569$	−1.97064e14	+	3.41326e14i	−0.138513	+	0.239912i	−0.926934	−	0.375224i	$-0.877566\pi$
$569$	−1.97064e14	+	3.41326e14i	−0.138513	+	0.239912i	0.788421	+	0.615136i	$0.210899\pi$
$570$	1.02770e14	−	2.21555e13i	0.0715411	−	0.0154230i
$571$	−1.00004e15	−	1.73212e15i	−0.689475	−	1.19421i	−0.972008	−	0.234948i	$-0.924508\pi$
$571$	−1.00004e15	−	1.73212e15i	−0.689475	−	1.19421i	0.282533	−	0.959258i	$-0.408825\pi$
$572$	3.79844e14	+	6.57909e14i	0.259374	+	0.449249i
$573$	−8.08722e14	+	2.51372e15i	−0.546952	+	1.70007i
$574$	−1.14663e15	+	1.98602e15i	−0.768083	+	1.33036i
$575$	−1.47820e15			−0.980754
$576$	−3.29208e14	+	1.48862e14i	−0.216345	+	0.0978271i
$577$	9.85091e14			0.641224			0.320612	−	0.947211i	$-0.396111\pi$
$577$	9.85091e14			0.641224			0.320612	+	0.947211i	$0.396111\pi$
$578$	−1.50370e14	+	2.60449e14i	−0.0969524	+	0.167926i
$579$	1.82067e13	+	2.01033e13i	0.0116278	+	0.0128391i
$580$	−2.40713e13	−	4.16928e13i	−0.0152281	−	0.0263759i
$581$	1.85929e14	+	3.22038e14i	0.116514	+	0.201808i
$582$	−2.24860e15	−	2.48284e15i	−1.39584	−	1.54125i
$583$	6.83385e14	−	1.18366e15i	0.420231	−	0.727862i
$584$	−5.01168e15			−3.05290
$585$	−2.82615e12	+	2.84732e13i	−0.00170545	+	0.0171822i
$586$	−3.51057e15			−2.09866
$587$	−1.04279e14	+	1.80616e14i	−0.0617571	+	0.106966i	−0.895251	−	0.445562i	$-0.853004\pi$
$587$	−1.04279e14	+	1.80616e14i	−0.0617571	+	0.106966i	0.833494	+	0.552529i	$0.186337\pi$
$588$	2.72144e15	−	8.45894e15i	1.59670	−	4.96296i
$589$	3.15107e14	+	5.45782e14i	0.183157	+	0.317238i
$590$	−5.45784e13	−	9.45326e13i	−0.0314293	−	0.0544372i
$591$	4.78465e14	−	1.03149e14i	0.272972	−	0.0588481i
$592$	1.15790e15	−	2.00553e15i	0.654485	−	1.13360i
$593$	1.89399e15			1.06066			0.530332	−	0.847790i	$-0.322067\pi$
$593$	1.89399e15			1.06066			0.530332	+	0.847790i	$0.322067\pi$
$594$	−1.80912e15	−	7.86726e14i	−1.00379	−	0.436514i
$595$	1.57498e14			0.0865830
$596$	−3.12536e15	+	5.41328e15i	−1.70234	+	2.94853i
$597$	−1.08823e15	+	2.34604e14i	−0.587304	+	0.126613i
$598$	−6.33522e14	−	1.09729e15i	−0.338770	−	0.586767i
$599$	5.81342e14	+	1.00691e15i	0.308024	+	0.533513i	0.977930	−	0.208933i	$-0.0669990\pi$
$599$	5.81342e14	+	1.00691e15i	0.308024	+	0.533513i	−0.669906	+	0.742446i	$0.733666\pi$
$600$	−1.24829e15	+	3.88001e15i	−0.655366	+	2.03705i
$601$	−7.53946e14	+	1.30587e15i	−0.392221	+	0.679346i	−0.992742	−	0.120263i	$-0.961626\pi$
$601$	−7.53946e14	+	1.30587e15i	−0.392221	+	0.679346i	0.600521	+	0.799609i	$0.294960\pi$
$602$	5.38839e15			2.77766
$603$	3.73608e14	+	2.68152e14i	0.190841	+	0.136973i
$604$	−4.42802e14			−0.224133
$605$	2.79266e13	−	4.83703e13i	0.0140076	−	0.0242618i
$606$	8.98747e14	+	9.92370e14i	0.446723	+	0.493258i
$607$	−1.52863e15	−	2.64766e15i	−0.752946	−	1.30414i	−0.946389	−	0.323029i	$-0.895299\pi$
$607$	−1.52863e15	−	2.64766e15i	−0.752946	−	1.30414i	0.193443	−	0.981111i	$-0.438035\pi$
$608$	7.31767e14	+	1.26746e15i	0.357193	+	0.618677i
$609$	7.87875e14	+	8.69949e14i	0.381120	+	0.420822i
$610$	4.57903e13	−	7.93112e13i	0.0219513	−	0.0380207i
$611$	−5.80850e14			−0.275955
$612$	−3.99440e15	−	2.86693e15i	−1.88070	−	1.34985i
$613$	1.94474e14			0.0907465			0.0453732	−	0.998970i	$-0.485552\pi$
$613$	1.94474e14			0.0907465			0.0453732	+	0.998970i	$0.485552\pi$
$614$	−1.52747e15	+	2.64566e15i	−0.706394	+	1.22351i
$615$	1.40014e13	−	4.35200e13i	0.00641739	−	0.0199469i
$616$	2.65192e15	+	4.59326e15i	1.20466	+	2.08654i
$617$	7.01467e14	+	1.21498e15i	0.315819	+	0.547015i	0.979611	−	0.200902i	$-0.0643873\pi$
$617$	7.01467e14	+	1.21498e15i	0.315819	+	0.547015i	−0.663792	+	0.747917i	$0.731054\pi$
$618$	−1.42326e15	+	3.06829e14i	−0.635106	+	0.136918i
$619$	−5.05763e14	+	8.76007e14i	−0.223691	+	0.387444i	−0.955926	−	0.293608i	$-0.905144\pi$
$619$	−5.05763e14	+	8.76007e14i	−0.223691	+	0.387444i	0.732235	+	0.681052i	$0.238477\pi$
$620$	9.00914e13			0.0394938
$621$	2.07408e15	+	9.01948e14i	0.901200	+	0.391902i
$622$	7.62678e15			3.28469
$623$	2.99853e15	−	5.19360e15i	1.28004	−	2.21710i
$624$	−1.45701e15	+	3.14106e14i	−0.616519	+	0.132911i
$625$	−1.18492e15	−	2.05235e15i	−0.496993	−	0.860816i
$626$	−3.37809e15	−	5.85103e15i	−1.40447	−	2.43262i
$627$	4.15475e14	−	1.29140e15i	0.171227	−	0.532219i
$628$	−2.15904e15	+	3.73957e15i	−0.882028	+	1.52772i
$629$	−2.07996e15			−0.842318
$630$	−3.61895e13	+	3.64605e14i	−0.0145281	+	0.146369i
$631$	2.20849e15			0.878890			0.439445	−	0.898270i	$-0.355175\pi$
$631$	2.20849e15			0.878890			0.439445	+	0.898270i	$0.355175\pi$
$632$	9.45151e14	−	1.63705e15i	0.372870	−	0.645830i
$633$	−7.92529e14	−	8.75088e14i	−0.309952	−	0.342240i
$634$	−1.98277e15	−	3.43425e15i	−0.768742	−	1.33150i
$635$	3.21275e13	+	5.56464e13i	0.0123487	+	0.0213886i
$636$	5.31954e15	+	5.87368e15i	2.02703	+	2.23819i
$637$	−1.20970e15	+	2.09525e15i	−0.456993	+	0.791535i
$638$	−9.03745e14			−0.338479
$639$	1.74397e15	−	7.88590e14i	0.647566	−	0.292817i
$640$	−1.46818e14			−0.0540492
$641$	4.17337e14	−	7.22850e14i	0.152324	−	0.263833i	−0.779757	−	0.626082i	$-0.784658\pi$
$641$	4.17337e14	−	7.22850e14i	0.152324	−	0.263833i	0.932081	+	0.362249i	$0.117991\pi$
$642$	−2.47078e15	+	7.67983e15i	−0.894112	+	2.77913i
$643$	−9.46408e14	−	1.63923e15i	−0.339561	−	0.588137i	0.644789	−	0.764360i	$-0.276945\pi$
$643$	−9.46408e14	−	1.63923e15i	−0.339561	−	0.588137i	−0.984350	+	0.176224i	$0.943612\pi$
$644$	−5.57634e15	−	9.65851e15i	−1.98371	−	3.43588i
$645$	−1.05007e14	+	2.26376e13i	−0.0370373	+	0.00798459i
$646$	2.45934e15	−	4.25970e15i	0.860082	−	1.48971i
$647$	2.42422e15			0.840617			0.420308	−	0.907381i	$-0.361922\pi$
$647$	2.42422e15			0.840617			0.420308	+	0.907381i	$0.361922\pi$
$648$	4.11894e15	−	4.68242e15i	1.41620	−	1.60993i
$649$	−1.40854e15			−0.480200
$650$	1.01771e15	−	1.76273e15i	0.344033	−	0.595883i
$651$	−2.14706e15	+	4.62868e14i	−0.719694	+	0.155154i
$652$	4.73340e15	+	8.19848e15i	1.57330	+	2.72503i
$653$	1.58214e15	+	2.74035e15i	0.521462	+	0.903199i	0.999688	+	0.0249621i	$0.00794651\pi$
$653$	1.58214e15	+	2.74035e15i	0.521462	+	0.903199i	−0.478226	+	0.878237i	$0.658720\pi$
$654$	4.16885e14	−	1.29578e15i	0.136251	−	0.423502i
$655$	7.97228e13	−	1.38084e14i	0.0258378	−	0.0447524i
$656$	2.38143e15			0.765361
$657$	−4.07065e15	+	1.84067e15i	−1.29734	+	0.586634i
$658$	−7.43791e15			−2.35076
$659$	−1.49138e15	+	2.58315e15i	−0.467433	+	0.809618i	−0.999308	−	0.0372053i	$-0.988154\pi$
$659$	−1.49138e15	+	2.58315e15i	−0.467433	+	0.809618i	0.531875	+	0.846823i	$0.321488\pi$
$660$	−1.30181e14	−	1.43742e14i	−0.0404627	−	0.0446777i
$661$	8.68756e14	+	1.50473e15i	0.267787	+	0.463821i	0.968290	−	0.249829i	$-0.0803743\pi$
$661$	8.68756e14	+	1.50473e15i	0.267787	+	0.463821i	−0.700503	+	0.713649i	$0.747041\pi$
$662$	4.15934e15	+	7.20419e15i	1.27147	+	2.20225i
$663$	8.98637e14	+	9.92248e14i	0.272433	+	0.300813i
$664$	4.52567e14	−	7.83870e14i	0.136069	−	0.235678i
$665$	−2.51955e14			−0.0751283
$666$	4.77926e14	−	4.81505e15i	0.141336	−	1.42394i
$667$	1.03611e15			0.303887
$668$	3.43679e15	−	5.95270e15i	0.999730	−	1.73158i
$669$	1.23591e15	−	3.84151e15i	0.356567	−	1.10830i
$670$	3.28835e13	+	5.69559e13i	0.00940950	+	0.0162977i
$671$	−5.90869e14	−	1.02341e15i	−0.167694	−	0.290454i
$672$	−4.98606e15	+	1.07491e15i	−1.40355	+	0.302580i
$673$	−6.07465e14	+	1.05216e15i	−0.169605	+	0.293764i	−0.938281	−	0.345874i	$-0.887583\pi$
$673$	−6.07465e14	+	1.05216e15i	−0.169605	+	0.293764i	0.768676	+	0.639638i	$0.220916\pi$
$674$	1.69634e15			0.469768
$675$	4.11133e14	+	3.60994e15i	0.112930	+	0.991584i
$676$	−6.87127e15			−1.87210
$677$	4.32434e14	−	7.48998e14i	0.116865	−	0.202415i	−0.801659	−	0.597782i	$-0.796049\pi$
$677$	4.32434e14	−	7.48998e14i	0.116865	−	0.202415i	0.918524	+	0.395366i	$0.129382\pi$
$678$	−6.13606e15	+	1.32283e15i	−1.64485	+	0.354601i
$679$	4.01394e15	+	6.95235e15i	1.06730	+	1.84862i
$680$	−1.91683e14	−	3.32004e14i	−0.0505573	−	0.0875677i
$681$	1.68097e15	−	5.22490e15i	0.439796	−	1.36700i
$682$	8.45608e14	−	1.46464e15i	0.219460	−	0.380116i
$683$	−5.50473e15			−1.41717			−0.708585	−	0.705626i	$-0.750666\pi$
$683$	−5.50473e15			−1.41717			−0.708585	+	0.705626i	$0.750666\pi$
$684$	6.38996e15	+	4.58631e15i	1.63188	+	1.17127i
$685$	−4.29274e13			−0.0108752
$686$	−8.95715e15	+	1.55142e16i	−2.25106	+	3.89895i
$687$	−4.91487e15	−	5.42685e15i	−1.22532	−	1.35296i
$688$	−2.79778e15	−	4.84590e15i	−0.691954	−	1.19850i
$689$	−1.07881e15	−	1.86855e15i	−0.264691	−	0.458458i
$690$	2.17122e14	+	2.39739e14i	0.0528485	+	0.0583538i
$691$	−4.37658e14	+	7.58046e14i	−0.105683	+	0.183049i	−0.914017	−	0.405676i	$-0.867036\pi$
$691$	−4.37658e14	+	7.58046e14i	−0.105683	+	0.183049i	0.808334	+	0.588724i	$0.200370\pi$
$692$	2.95052e15			0.706830
$693$	3.84097e15	+	2.75681e15i	0.912869	+	0.655200i
$694$	1.02184e16			2.40939
$695$	−6.19024e12	+	1.07218e13i	−0.00144807	+	0.00250814i
$696$	8.74957e14	−	2.71959e15i	0.203065	−	0.631180i
$697$	−1.06946e15	−	1.85235e15i	−0.246254	−	0.426524i
$698$	6.33820e14	+	1.09781e15i	0.144798	+	0.250797i
$699$	−7.71687e15	+	1.66362e15i	−1.74911	+	0.377077i
$700$	8.95802e15	−	1.55157e16i	2.01453	−	3.48926i
$701$	−2.56400e15			−0.572095			−0.286048	−	0.958215i	$-0.592342\pi$
$701$	−2.56400e15			−0.572095			−0.286048	+	0.958215i	$0.592342\pi$
$702$	−2.50352e15	+	1.85233e15i	−0.554238	+	0.410075i
$703$	3.32737e15			0.730881
$704$	−3.33365e14	+	5.77405e14i	−0.0726558	+	0.125844i
$705$	1.44947e14	−	3.12480e13i	0.0313450	−	0.00675744i
$706$	−4.40520e15	−	7.63003e15i	−0.945235	−	1.63720i
$707$	−1.60434e15	−	2.77879e15i	−0.341577	−	0.591629i
$708$	2.50115e15	−	7.77423e15i	0.528393	−	1.64238i
$709$	1.94293e15	−	3.36526e15i	0.407289	−	0.705446i	−0.587296	−	0.809373i	$-0.699807\pi$
$709$	1.94293e15	−	3.36526e15i	0.407289	−	0.705446i	0.994585	+	0.103927i	$0.0331407\pi$
$710$	2.73717e14			0.0569351
$711$	1.66433e14	−	1.67680e15i	0.0343524	−	0.346097i
$712$	−1.45974e16			−2.98975
$713$	−9.69454e14	+	1.67914e15i	−0.197031	+	0.341268i
$714$	1.15072e16	+	1.27059e16i	2.32076	+	2.56252i
$715$	2.64008e13	+	4.57275e13i	0.00528364	+	0.00915153i
$716$	4.08446e15	+	7.07449e15i	0.811172	+	1.40499i
$717$	−3.73738e15	−	4.12671e15i	−0.736567	−	0.813295i
$718$	−4.51261e15	+	7.81607e15i	−0.882559	+	1.52864i
$719$	7.99862e15			1.55241			0.776204	−	0.630481i	$-0.217142\pi$
$719$	7.99862e15			1.55241			0.776204	+	0.630481i	$0.217142\pi$
$720$	3.46687e14	−	1.56765e14i	0.0667743	−	0.0301940i
$721$	3.48930e15			0.666952
$722$	7.80067e14	−	1.35111e15i	0.147971	−	0.256294i
$723$	3.00489e14	−	9.33996e14i	0.0565676	−	0.175827i
$724$	9.97171e15	+	1.72715e16i	1.86298	+	3.22677i
$725$	8.32217e14	+	1.44144e15i	0.154304	+	0.267263i
$726$	5.94258e15	−	1.28112e15i	1.09351	−	0.235742i
$727$	−4.77528e15	+	8.27102e15i	−0.872086	+	1.51050i	−0.0122507	+	0.999925i	$0.503900\pi$
$727$	−4.77528e15	+	8.27102e15i	−0.872086	+	1.51050i	−0.859835	+	0.510572i	$0.829434\pi$
$728$	8.37277e15			1.51756
$729$	1.62580e15	−	5.31601e15i	0.292460	−	0.956278i
$730$	−6.38890e14			−0.114065
$731$	−2.51286e15	+	4.35241e15i	−0.445270	+	0.771230i
$732$	6.69781e15	−	1.44393e15i	1.17794	−	0.253943i
$733$	−3.16460e14	−	5.48125e14i	−0.0552392	−	0.0956771i	0.837084	−	0.547075i	$-0.184259\pi$
$733$	−3.16460e14	−	5.48125e14i	−0.0552392	−	0.0956771i	−0.892323	+	0.451398i	$0.850925\pi$
$734$	−6.00276e15	−	1.03971e16i	−1.03997	−	1.80129i
$735$	1.89152e14	−	5.87933e14i	0.0325260	−	0.101099i
$736$	−2.25134e15	+	3.89944e15i	−0.384250	+	0.665540i
$737$	8.48643e14			0.143765
$738$	4.53389e15	−	2.05014e15i	0.762361	−	0.344725i
$739$	−6.39843e15			−1.06790			−0.533948	−	0.845517i	$-0.679292\pi$
$739$	−6.39843e15			−1.06790			−0.533948	+	0.845517i	$0.679292\pi$
$740$	2.37830e14	−	4.11933e14i	0.0393996	−	0.0682421i
$741$	−1.43758e15	−	1.58733e15i	−0.236391	−	0.261016i
$742$	−1.38144e16	−	2.39272e16i	−2.25481	−	3.90544i
$743$	2.36624e15	+	4.09845e15i	0.383372	+	0.664020i	0.991542	−	0.129787i	$-0.0414293\pi$
$743$	2.36624e15	+	4.09845e15i	0.383372	+	0.664020i	−0.608170	+	0.793807i	$0.708096\pi$
$744$	3.58878e15	+	3.96263e15i	0.577159	+	0.637282i
$745$	−2.17226e14	+	3.76246e14i	−0.0346778	+	0.0600637i
$746$	−1.22263e16			−1.93746
$747$	7.96934e13	−	8.02902e14i	0.0125360	−	0.126299i
$748$	−9.07321e15			−1.41678
$749$	9.66717e15	−	1.67440e16i	1.49848	−	2.59544i
$750$	−3.18585e14	+	9.90243e14i	−0.0490217	+	0.152372i
$751$	1.60299e15	+	2.77646e15i	0.244856	+	0.424103i	0.962091	−	0.272728i	$-0.0879260\pi$
$751$	1.60299e15	+	2.77646e15i	0.244856	+	0.424103i	−0.717235	+	0.696831i	$0.754593\pi$
$752$	3.86193e15	+	6.68907e15i	0.585608	+	1.01430i
$753$	3.70296e15	−	7.98295e14i	0.557413	−	0.120169i
$754$	−7.13337e14	+	1.23554e15i	−0.106599	+	0.184635i
$755$	−3.07766e13			−0.00456575
$756$	−2.20363e16	+	1.63044e16i	−3.24540	+	2.40124i
$757$	9.37198e15			1.37026			0.685132	−	0.728419i	$-0.259745\pi$
$757$	9.37198e15			1.37026			0.685132	+	0.728419i	$0.259745\pi$
$758$	2.76346e15	−	4.78645e15i	0.401118	−	0.694756i
$759$	4.07993e15	−	8.79563e14i	0.587927	−	0.126747i
$760$	3.06640e14	+	5.31116e14i	0.0438686	+	0.0759827i
$761$	8.97676e13	+	1.55482e14i	0.0127498	+	0.0220833i	0.872330	−	0.488918i	$-0.162608\pi$
$761$	8.97676e13	+	1.55482e14i	0.0127498	+	0.0220833i	−0.859580	+	0.511001i	$0.829275\pi$
$762$	−2.14188e15	+	6.65751e15i	−0.302025	+	0.938770i
$763$	−1.63110e15	+	2.82515e15i	−0.228347	+	0.395509i
$764$	−2.82528e16			−3.92689
$765$	−2.77628e14	−	1.99264e14i	−0.0383112	−	0.0274974i
$766$	8.71317e15			1.19376
$767$	−1.11178e15	+	1.92565e15i	−0.151232	+	0.261941i
$768$	−9.54675e15	−	1.05412e16i	−1.28934	−	1.42366i
$769$	−9.00442e14	−	1.55961e15i	−0.120743	−	0.209133i	0.799318	−	0.600908i	$-0.205194\pi$
$769$	−9.00442e14	−	1.55961e15i	−0.120743	−	0.209133i	−0.920061	+	0.391776i	$0.871861\pi$
$770$	3.38067e14	+	5.85549e14i	0.0450095	+	0.0779587i
$771$	7.20353e15	+	7.95393e15i	0.952240	+	1.05144i
$772$	−1.45096e14	+	2.51314e14i	−0.0190441	+	0.0329854i
$773$	−1.37573e16			−1.79286			−0.896428	−	0.443189i	$-0.853847\pi$
$773$	−1.37573e16			−1.79286			−0.896428	+	0.443189i	$0.853847\pi$
$774$	−9.49832e15	−	6.81730e15i	−1.22905	−	0.882139i
$775$	−3.11473e15			−0.400185
$776$	9.77029e15	−	1.69226e16i	1.24643	−	2.15888i
$777$	−3.55154e15	+	1.10391e16i	−0.449884	+	1.39836i
$778$	1.12609e16	+	1.95045e16i	1.41640	+	2.45327i
$779$	1.71084e15	+	2.96326e15i	0.213675	+	0.370096i
$780$	−2.99267e14	+	6.45167e13i	−0.0371140	+	0.00800114i
$781$	1.76599e15	−	3.05878e15i	0.217474	−	0.376676i
$782$	1.51327e16			1.85046
$783$	−2.88173e14	−	2.53029e15i	−0.0349915	−	0.307243i
$784$	3.21719e16			3.87917
$785$	−1.50063e14	+	2.59916e14i	−0.0179676	+	0.0311207i
$786$	1.69645e16	−	3.65725e15i	2.01705	−	0.434841i
$787$	−1.36641e15	−	2.36669e15i	−0.161332	−	0.279435i	0.774015	−	0.633168i	$-0.218246\pi$
$787$	−1.36641e15	−	2.36669e15i	−0.161332	−	0.279435i	−0.935347	+	0.353733i	$0.884912\pi$
$788$	2.61844e15	+	4.53527e15i	0.307007	+	0.531752i
$789$	−3.92304e15	+	1.21938e16i	−0.456771	+	1.41976i
$790$	1.20488e14	−	2.08691e14i	0.0139314	−	0.0241299i
$791$	1.50434e16			1.72733
$792$	1.13667e15	−	1.14519e16i	0.129613	−	1.30583i
$793$	−1.86552e15			−0.211250
$794$	−9.79871e14	+	1.69719e15i	−0.110194	+	0.190861i
$795$	3.69731e14	+	4.08246e14i	0.0412921	+	0.0455935i
$796$	−5.95545e15	−	1.03151e16i	−0.660530	−	1.14407i
$797$	5.59100e15	+	9.68390e15i	0.615841	+	1.06667i	0.990236	+	0.139399i	$0.0445171\pi$
$797$	5.59100e15	+	9.68390e15i	0.615841	+	1.06667i	−0.374395	+	0.927269i	$0.622150\pi$
$798$	−1.84084e16	−	2.03261e16i	−2.01373	−	2.22350i
$799$	3.46865e15	−	6.00787e15i	0.376836	−	0.652700i
$800$	−7.23326e15			−0.780439
$801$	−1.18565e16	+	5.36126e15i	−1.27050	+	0.574498i
$802$	1.24007e16			1.31974
$803$	−4.12205e15	+	7.13960e15i	−0.435690	+	0.754638i
$804$	−1.50694e15	+	4.68397e15i	−0.158194	+	0.491706i
$805$	−3.87580e14	−	6.71308e14i	−0.0404095	−	0.0699913i
$806$	−1.33490e15	−	2.31211e15i	−0.138231	−	0.239423i
$807$	−4.58836e15	+	9.89170e14i	−0.471903	+	0.101734i
$808$	−3.90510e15	+	6.76383e15i	−0.398905	+	0.690924i
$809$	−1.79374e15			−0.181988			−0.0909939	−	0.995851i	$-0.529004\pi$
$809$	−1.79374e15			−0.181988			−0.0909939	+	0.995851i	$0.529004\pi$
$810$	5.25084e14	−	5.96916e14i	0.0529128	−	0.0601514i
$811$	−1.28101e16			−1.28215			−0.641073	−	0.767480i	$-0.721510\pi$
$811$	−1.28101e16			−1.28215			−0.641073	+	0.767480i	$0.721510\pi$
$812$	−6.27889e15	+	1.08754e16i	−0.624202	+	1.08115i
$813$	4.98097e15	−	1.07381e15i	0.491831	−	0.106030i
$814$	−4.46459e15	−	7.73290e15i	−0.437872	−	0.758417i
$815$	3.28991e14	+	5.69830e14i	0.0320492	+	0.0555109i
$816$	5.45190e15	−	1.69459e16i	0.527536	−	1.63972i
$817$	4.01990e15	−	6.96267e15i	0.386361	−	0.669198i
$818$	1.23134e16			1.17553
$819$	6.80064e15	−	3.07512e15i	0.644894	−	0.291609i
$820$	4.89141e14			0.0460742
$821$	5.84251e15	−	1.01195e16i	0.546653	−	0.946831i	−0.451848	−	0.892095i	$-0.649235\pi$
$821$	5.84251e15	−	1.01195e16i	0.546653	−	0.946831i	0.998501	−	0.0547358i	$-0.0174317\pi$
$822$	−3.13639e15	−	3.46311e15i	−0.291497	−	0.321863i
$823$	−5.62912e14	−	9.74992e14i	−0.0519686	−	0.0900123i	0.838871	−	0.544331i	$-0.183216\pi$
$823$	−5.62912e14	−	9.74992e14i	−0.0519686	−	0.0900123i	−0.890839	+	0.454318i	$0.849883\pi$
$824$	−4.24663e15	−	7.35538e15i	−0.389444	−	0.674537i
$825$	4.50073e15	+	4.96957e15i	0.410002	+	0.452712i
$826$	−1.42365e16	+	2.46584e16i	−1.28829	+	2.23138i
$827$	−2.09168e15			−0.188025			−0.0940126	−	0.995571i	$-0.529969\pi$
$827$	−2.09168e15			−0.188025			−0.0940126	+	0.995571i	$0.529969\pi$
$828$	−2.39015e15	+	2.40805e16i	−0.213431	+	2.15030i
$829$	−6.68122e15			−0.592660			−0.296330	−	0.955086i	$-0.595763\pi$
$829$	−6.68122e15			−0.592660			−0.296330	+	0.955086i	$0.595763\pi$
$830$	5.76934e13	−	9.99279e13i	0.00508389	−	0.00880556i
$831$	2.41272e15	−	7.49935e15i	0.211203	−	0.656475i
$832$	5.26258e14	+	9.11506e14i	0.0457636	+	0.0792650i
$833$	−1.44478e16	−	2.50243e16i	−1.24811	−	2.16180i
$834$	−1.31724e15	+	2.83974e14i	−0.113045	+	0.0243705i
$835$	2.38872e14	−	4.13738e14i	0.0203652	−	0.0352736i
$836$	1.45147e16			1.22934
$837$	4.37030e15	+	1.90050e15i	0.367724	+	0.159911i
$838$	3.89332e15			0.325445
$839$	−4.63339e14	+	8.02526e14i	−0.0384776	+	0.0666451i	−0.884623	−	0.466307i	$-0.845584\pi$
$839$	−4.63339e14	+	8.02526e14i	−0.0384776	+	0.0666451i	0.846145	+	0.532952i	$0.178917\pi$
$840$	−2.08936e15	+	4.50430e14i	−0.172376	+	0.0371613i
$841$	5.51693e15	+	9.55561e15i	0.452189	+	0.783214i
$842$	−4.20731e15	−	7.28727e15i	−0.342600	−	0.593401i
$843$	2.58230e15	−	8.02644e15i	0.208908	−	0.649339i
$844$	6.31598e15	−	1.09396e16i	0.507642	−	0.879262i
$845$	−4.77582e14			−0.0381361
$846$	1.31111e16	+	9.41030e15i	1.04016	+	0.746563i
$847$	−1.45690e16			−1.14834
$848$	−1.43455e16	+	2.48471e16i	−1.12341	+	1.94580i
$849$	1.54903e16	+	1.71040e16i	1.20523	+	1.33077i
$850$	1.21549e16	+	2.10528e16i	0.939606	+	1.62745i
$851$	5.11846e15	+	8.86544e15i	0.393122	+	0.680907i
$852$	1.37467e16	+	1.51787e16i	1.04901	+	1.15829i
$853$	8.07496e15	−	1.39862e16i	0.612239	−	1.06043i	−0.378624	−	0.925551i	$-0.623602\pi$
$853$	8.07496e15	−	1.39862e16i	0.612239	−	1.06043i	0.990862	−	0.134878i	$-0.0430642\pi$
$854$	−2.38884e16			−1.79957
$855$	4.44129e14	+	3.18768e14i	0.0332427	+	0.0238595i
$856$	−4.70615e16			−3.49994
$857$	−8.88411e15	+	1.53877e16i	−0.656477	+	1.13705i	0.325045	+	0.945699i	$0.394621\pi$
$857$	−8.88411e15	+	1.53877e16i	−0.656477	+	1.13705i	−0.981521	+	0.191352i	$0.938713\pi$
$858$	−1.76009e15	+	5.47080e15i	−0.129227	+	0.401672i
$859$	−5.75163e15	−	9.96212e15i	−0.419593	−	0.726757i	0.576305	−	0.817235i	$-0.304494\pi$
$859$	−5.75163e15	−	9.96212e15i	−0.419593	−	0.726757i	−0.995898	+	0.0904776i	$0.971161\pi$
$860$	−5.74659e14	−	9.95338e14i	−0.0416551	−	0.0721488i
$861$	−1.16572e16	+	2.51309e15i	−0.839609	+	0.181005i
$862$	6.78467e15	−	1.17514e16i	0.485555	−	0.841006i
$863$	8.44929e15			0.600843			0.300422	−	0.953807i	$-0.402873\pi$
$863$	8.44929e15			0.600843			0.300422	+	0.953807i	$0.402873\pi$
$864$	1.01491e16	+	4.41349e15i	0.717134	+	0.311858i
$865$	2.05074e14			0.0143986
$866$	2.07085e16	−	3.58683e16i	1.44478	−	2.50243i
$867$	−1.52874e15	+	3.29569e14i	−0.105981	+	0.0228476i
$868$	−1.17500e16	−	2.03515e16i	−0.809427	−	1.40197i
$869$	−1.55475e15	−	2.69291e15i	−0.106427	−	0.184337i
$870$	1.11540e14	−	3.46694e14i	0.00758706	−	0.0235825i
$871$	6.69845e14	−	1.16020e15i	0.0452766	−	0.0784214i
$872$	7.94049e15			0.533343
$873$	1.72047e15	−	1.73335e16i	0.114833	−	1.15693i
$874$	−2.42083e16			−1.60565
$875$	1.24649e15	−	2.15899e15i	0.0821572	−	0.142300i
$876$	−3.20865e16	−	3.54290e16i	−2.10160	−	2.32052i
$877$	−3.64690e14	−	6.31662e14i	−0.0237370	−	0.0411137i	0.853913	−	0.520416i	$-0.174223\pi$
$877$	−3.64690e14	−	6.31662e14i	−0.0237370	−	0.0411137i	−0.877650	+	0.479302i	$0.840890\pi$
$878$	2.21342e16	+	3.83376e16i	1.43167	+	2.47973i
$879$	−1.22542e16	−	1.35308e16i	−0.787675	−	0.869728i
$880$	3.51065e14	−	6.08062e14i	0.0224250	−	0.0388412i
$881$	−6.07342e15			−0.385537			−0.192768	−	0.981244i	$-0.561747\pi$
$881$	−6.07342e15			−0.385537			−0.192768	+	0.981244i	$0.561747\pi$
$882$	6.12505e16	−	2.76963e16i	3.86396	−	1.74721i
$883$	−4.64230e15			−0.291038			−0.145519	−	0.989355i	$-0.546485\pi$
$883$	−4.64230e15			−0.291038			−0.145519	+	0.989355i	$0.546485\pi$
$884$	−7.16160e15	+	1.24042e16i	−0.446193	+	0.772828i
$885$	1.73841e14	−	5.40342e14i	0.0107638	−	0.0334565i
$886$	2.16699e16	+	3.75334e16i	1.33344	+	2.30958i
$887$	−8.18800e15	−	1.41820e16i	−0.500723	−	0.867278i	−1.00000		0.000835565i	$-0.999734\pi$
$887$	−8.18800e15	−	1.41820e16i	−0.500723	−	0.867278i	0.499276	−	0.866443i	$-0.333599\pi$
$888$	2.75926e16	−	5.94848e15i	1.67695	−	0.361522i
$889$	8.38030e15	−	1.45151e16i	0.506174	−	0.876719i
$890$	−1.86087e15			−0.111705
$891$	−3.28275e15	−	9.71905e15i	−0.195844	−	0.579824i
$892$	4.31765e16			2.56001
$893$	−5.54890e15	+	9.61097e15i	−0.326982	+	0.566349i
$894$	−4.62241e16	+	9.96512e15i	−2.70715	+	0.583615i
$895$	2.83888e14	+	4.91708e14i	0.0165242	+	0.0286207i
$896$	1.91484e16	+	3.31660e16i	1.10774	+	1.91866i
$897$	2.01787e15	−	6.27205e15i	0.116020	−	0.360621i
$898$	−2.40853e16	+	4.17170e16i	−1.37636	+	2.38393i
$899$	2.18319e15			0.123997
$900$	−3.54209e16	+	1.60166e16i	−1.99952	+	0.904144i
$901$	2.57692e16			1.44582
$902$	4.59113e15	−	7.95208e15i	0.256026	−	0.443450i
$903$	1.88091e16	+	2.07684e16i	1.04252	+	1.15112i
$904$	−1.83084e16	−	3.17111e16i	−1.00861	−	1.74697i
$905$	6.93077e14	+	1.20044e15i	0.0379502	+	0.0657317i
$906$	−2.24862e15	−	2.48286e15i	−0.122380	−	0.135128i
$907$	6.58776e14	−	1.14103e15i	0.0356367	−	0.0617246i	−0.847657	−	0.530545i	$-0.821987\pi$
$907$	6.58776e14	−	1.14103e15i	0.0356367	−	0.0617246i	0.883294	+	0.468820i	$0.155321\pi$
$908$	5.87250e16			3.15756
$909$	−6.87656e14	+	6.92806e15i	−0.0367511	+	0.370263i
$910$	1.06736e15			0.0567002
$911$	−1.04032e16	+	1.80188e16i	−0.549306	+	0.951425i	0.449017	+	0.893523i	$0.351774\pi$
$911$	−1.04032e16	+	1.80188e16i	−0.549306	+	0.951425i	−0.998322	+	0.0579020i	$0.981559\pi$
$912$	−8.72156e15	+	2.71089e16i	−0.457744	+	1.42279i
$913$	−7.44463e14	−	1.28945e15i	−0.0388377	−	0.0672689i
$914$	−1.32676e16	−	2.29802e16i	−0.688002	−	1.19165i
$915$	4.65526e14	−	1.00359e14i	0.0239954	−	0.00517300i
$916$	3.91686e16	−	6.78419e16i	2.00684	−	3.47595i
$917$	−4.15906e16			−2.11819
$918$	−4.20888e15	−	3.69559e16i	−0.213074	−	1.87090i
$919$	2.62352e16			1.32023			0.660115	−	0.751165i	$-0.270508\pi$
$919$	2.62352e16			1.32023			0.660115	+	0.751165i	$0.270508\pi$
$920$	−9.43403e14	+	1.63402e15i	−0.0471916	+	0.0817382i
$921$	−1.55290e16	+	3.34778e15i	−0.772175	+	0.166468i
$922$	−3.73785e15	−	6.47415e15i	−0.184758	−	0.320009i
$923$	−2.78784e15	−	4.82867e15i	−0.136980	−	0.237257i
$924$	−1.54925e16	+	4.81548e16i	−0.756705	+	2.35203i
$925$	−8.22247e15	+	1.42417e16i	−0.399230	+	0.691486i
$926$	−3.11402e16			−1.50301
$927$	−6.15071e15	−	4.41460e15i	−0.295112	−	0.211813i
$928$	5.06997e15			0.241819
$929$	−1.59549e16	+	2.76347e16i	−0.756498	+	1.31029i	0.188128	+	0.982144i	$0.439758\pi$
$929$	−1.59549e16	+	2.76347e16i	−0.756498	+	1.31029i	−0.944626	+	0.328148i	$0.893575\pi$
$930$	4.57498e14	+	5.05156e14i	0.0215642	+	0.0238106i
$931$	2.31126e16	+	4.00322e16i	1.08299	+	1.87580i
$932$	−4.22312e16	−	7.31466e16i	−1.96719	−	3.40727i
$933$	2.66225e16	+	2.93958e16i	1.23282	+	1.36124i
$934$	−2.70389e15	+	4.68327e15i	−0.124475	+	0.215597i
$935$	−6.30627e14			−0.0288608
$936$	−1.47590e16	−	1.05931e16i	−0.671489	−	0.481953i
$937$	−2.86567e16			−1.29616			−0.648079	−	0.761573i	$-0.724427\pi$
$937$	−2.86567e16			−1.29616			−0.648079	+	0.761573i	$0.724427\pi$
$938$	8.57749e15	−	1.48567e16i	0.385696	−	0.668045i
$939$	1.07598e16	−	3.34441e16i	0.480996	−	1.49506i
$940$	7.93234e14	+	1.37392e15i	0.0352532	+	0.0610603i
$941$	8.18753e15	+	1.41812e16i	0.361751	+	0.626572i	0.988249	−	0.152852i	$-0.0488456\pi$
$941$	8.18753e15	+	1.41812e16i	0.361751	+	0.626572i	−0.626498	+	0.779423i	$0.715512\pi$
$942$	−3.19323e16	+	6.88404e15i	−1.40265	+	0.302387i
$943$	−5.26354e15	+	9.11672e15i	−0.229860	+	0.398129i
$944$	2.95677e16			1.28372
$945$	−1.53162e15	+	1.13323e15i	−0.0661112	+	0.0489150i
$946$	−2.15752e16			−0.925879
$947$	1.10330e16	−	1.91097e16i	0.470726	−	0.815321i	−0.528714	−	0.848800i	$-0.677326\pi$
$947$	1.10330e16	−	1.91097e16i	0.470726	−	0.815321i	0.999439	+	0.0334796i	$0.0106589\pi$
$948$	1.76239e16	−	3.79942e15i	0.747579	−	0.161165i
$949$	6.50718e15	+	1.12708e16i	0.274428	+	0.475323i
$950$	−1.94445e16	−	3.36788e16i	−0.815298	−	1.41214i
$951$	6.31542e15	−	1.96300e16i	0.263275	−	0.818326i
$952$	−4.99994e16	+	8.66016e16i	−2.07234	+	3.58941i
$953$	3.84441e16			1.58423			0.792116	−	0.610371i	$-0.208980\pi$
$953$	3.84441e16			1.58423			0.792116	+	0.610371i	$0.208980\pi$
$954$	−5.92115e15	+	5.96550e16i	−0.242600	+	2.44416i
$955$	−1.96369e15			−0.0799935
$956$	2.97847e16	−	5.15886e16i	1.20635	−	2.08947i
$957$	−3.15467e15	−	3.48329e15i	−0.127039	−	0.140273i
$958$	−1.52182e16	−	2.63587e16i	−0.609331	−	1.05539i
$959$	5.59871e15	+	9.69724e15i	0.222887	+	0.386052i
$960$	−1.80360e14	−	1.99148e14i	−0.00713919	−	0.00788288i
$961$	1.06615e16	−	1.84663e16i	0.419604	−	0.726775i
$962$	−1.40958e16			−0.551604
$963$	−3.82249e16	+	1.72846e16i	−1.48731	+	0.672534i
$964$	1.04976e16			0.406132
$965$	−1.00848e13	+	1.74674e13i	−0.000387942	+	0.000671936i
$966$	2.58392e16	−	8.03148e16i	0.988336	−	3.07200i
$967$	−1.40713e16	−	2.43723e16i	−0.535168	−	0.926938i	−0.999155	−	0.0410962i	$-0.986915\pi$
$967$	−1.40713e16	−	2.43723e16i	−0.535168	−	0.926938i	0.463987	−	0.885842i	$-0.346418\pi$
$968$	1.77311e16	+	3.07112e16i	0.670536	+	1.16140i
$969$	2.50028e16	−	5.39018e15i	0.940175	−	0.202685i
$970$	1.24552e15	−	2.15730e15i	0.0465699	−	0.0806615i
$971$	3.57443e16			1.32893			0.664464	−	0.747320i	$-0.268660\pi$
$971$	3.57443e16			1.32893			0.664464	+	0.747320i	$0.268660\pi$
$972$	5.94722e16	−	8.60488e14i	2.19862	−	0.0318112i
$973$	3.22939e15			0.118713
$974$	−3.14079e16	+	5.44000e16i	−1.14806	+	1.98850i
$975$	1.03465e16	−	2.23053e15i	0.376070	−	0.0810743i
$976$	1.24034e16	+	2.14833e16i	0.448298	+	0.776474i
$977$	−8.29391e15	−	1.43655e16i	−0.298085	−	0.516298i	0.677613	−	0.735419i	$-0.263014\pi$
$977$	−8.29391e15	−	1.43655e16i	−0.298085	−	0.516298i	−0.975698	+	0.219121i	$0.929681\pi$
$978$	−2.19332e16	+	6.81741e16i	−0.783860	+	2.43644i
$979$	−1.20062e16	+	2.07953e16i	−0.426677	+	0.739027i
$980$	6.60805e15			0.233523
$981$	6.44953e15	−	2.91635e15i	0.226646	−	0.102485i
$982$	7.53007e16			2.63139
$983$	2.30379e15	−	3.99028e15i	0.0800569	−	0.138663i	−0.823217	−	0.567726i	$-0.807823\pi$
$983$	2.30379e15	−	3.99028e15i	0.0800569	−	0.138663i	0.903274	+	0.429064i	$0.141156\pi$
$984$	1.94849e16	+	2.15146e16i	0.673325	+	0.743465i
$985$	1.81993e14	+	3.15221e14i	0.00625396	+	0.0108322i
$986$	−8.51963e15	−	1.47564e16i	−0.291137	−	0.504265i
$987$	−2.59632e16	−	2.86678e16i	−0.882296	−	0.974205i
$988$	1.14566e16	−	1.98434e16i	0.387162	−	0.670585i
$989$	2.47351e16			0.831255
$990$	1.44903e14	−	1.45989e15i	0.00484267	−	0.0487894i
$991$	−1.24460e16			−0.413641			−0.206821	−	0.978379i	$-0.566312\pi$
$991$	−1.24460e16			−0.413641			−0.206821	+	0.978379i	$0.566312\pi$
$992$	−4.74382e15	+	8.21654e15i	−0.156788	+	0.271565i
$993$	−1.32482e16	+	4.11787e16i	−0.435446	+	1.35348i
$994$	−3.56988e16	−	6.18322e16i	−1.16689	−	2.02111i
$995$	−4.13929e14	−	7.16947e14i	−0.0134555	−	0.0233056i
$996$	8.43888e15	−	1.81928e15i	0.272809	−	0.0588129i
$997$	−1.27720e16	+	2.21218e16i	−0.410616	+	0.711208i	−0.994957	−	0.100300i	$-0.968020\pi$
$997$	−1.27720e16	+	2.21218e16i	−0.410616	+	0.711208i	0.584341	+	0.811508i	$0.301353\pi$
$998$	−6.53689e16			−2.09003
$999$	2.02269e16	−	1.49657e16i	0.643159	−	0.475867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.12.c.a.7.1	yes	20
3.2	odd	2		27.12.c.a.19.10		20
9.2	odd	6		81.12.a.c.1.1		10
9.4	even	3	inner	9.12.c.a.4.1	✓	20
9.5	odd	6		27.12.c.a.10.10		20
9.7	even	3		81.12.a.e.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.12.c.a.4.1	✓	20	9.4	even	3	inner
9.12.c.a.7.1	yes	20	1.1	even	1	trivial
27.12.c.a.10.10		20	9.5	odd	6
27.12.c.a.19.10		20	3.2	odd	2
81.12.a.c.1.1		10	9.2	odd	6
81.12.a.e.1.10		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)

\(f(q)\)	\(=\)	\(q+(-40.4699 + 70.0959i) q^{2} +(-411.436 + 88.6985i) q^{3} +(-2251.62 - 3899.92i) q^{4} +(-156.497 - 271.061i) q^{5} +(10433.4 - 32429.6i) q^{6} +(-40821.5 + 70704.9i) q^{7} +198726. q^{8} +(161412. - 72987.5i) q^{9} +O(q^{10})\)	\(q+(-40.4699 + 70.0959i) q^{2} +(-411.436 + 88.6985i) q^{3} +(-2251.62 - 3899.92i) q^{4} +(-156.497 - 271.061i) q^{5} +(10433.4 - 32429.6i) q^{6} +(-40821.5 + 70704.9i) q^{7} +198726. q^{8} +(161412. - 72987.5i) q^{9} +25333.7 q^{10} +(163450. - 283104. i) q^{11} +(1.27231e6 + 1.40485e6i) q^{12} +(-258027. - 446915. i) q^{13} +(-3.30408e6 - 5.72284e6i) q^{14} +(88431.3 + 97643.2i) q^{15} +(-3.43111e6 + 5.94286e6i) q^{16} +6.16340e6 q^{17} +(-1.41621e6 + 1.42681e7i) q^{18} -9.85977e6 q^{19} +(-704744. + 1.22065e6i) q^{20} +(1.05240e7 - 3.27114e7i) q^{21} +(1.32296e7 + 2.29144e7i) q^{22} +(-1.51672e7 - 2.62703e7i) q^{23} +(-8.17632e7 + 1.76267e7i) q^{24} +(2.43651e7 - 4.22016e7i) q^{25} +4.17692e7 q^{26} +(-5.99369e7 + 4.43467e7i) q^{27} +3.67658e8 q^{28} +(-1.70781e7 + 2.95801e7i) q^{29} +(-1.04232e7 + 2.24706e6i) q^{30} +(-3.19589e7 - 5.53544e7i) q^{31} +(-7.42175e7 - 1.28548e8i) q^{32} +(-4.21384e7 + 1.30977e8i) q^{33} +(-2.49432e8 + 4.32029e8i) q^{34} +2.55538e7 q^{35} +(-6.48084e8 - 4.65154e8i) q^{36} -3.37469e8 q^{37} +(3.99023e8 - 6.91129e8i) q^{38} +(1.45802e8 + 1.60990e8i) q^{39} +(-3.11001e7 - 5.38670e7i) q^{40} +(-1.73517e8 - 3.00541e8i) q^{41} +(1.86703e9 + 2.06151e9i) q^{42} +(-4.07707e8 + 7.06170e8i) q^{43} -1.47211e9 q^{44} +(-4.50446e7 - 3.23302e7i) q^{45} +2.45526e9 q^{46} +(5.62782e8 - 9.74766e8i) q^{47} +(8.84560e8 - 2.74944e9i) q^{48} +(-2.34413e9 - 4.06015e9i) q^{49} +(1.97210e9 + 3.41578e9i) q^{50} +(-2.53584e9 + 5.46684e8i) q^{51} +(-1.16196e9 + 2.01257e9i) q^{52} +4.18100e9 q^{53} +(-6.82882e8 - 5.99603e9i) q^{54} -1.02318e8 q^{55} +(-8.11231e9 + 1.40509e10i) q^{56} +(4.05666e9 - 8.74546e8i) q^{57} +(-1.38229e9 - 2.39420e9i) q^{58} +(-2.15438e9 - 3.73150e9i) q^{59} +(1.81687e8 - 5.64730e8i) q^{60} +(1.80749e9 - 3.13066e9i) q^{61} +5.17349e9 q^{62} +(-1.42851e9 + 1.43921e10i) q^{63} -2.03955e9 q^{64} +(-8.07609e7 + 1.39882e8i) q^{65} +(-7.47561e9 - 8.25435e9i) q^{66} +(1.29801e9 + 2.24823e9i) q^{67} +(-1.38776e10 - 2.40368e10i) q^{68} +(8.57047e9 + 9.46326e9i) q^{69} +(-1.03416e9 + 1.79122e9i) q^{70} +1.08045e10 q^{71} +(3.20769e10 - 1.45045e10i) q^{72} -2.52190e10 q^{73} +(1.36573e10 - 2.36552e10i) q^{74} +(-6.28146e9 + 1.95244e10i) q^{75} +(2.22004e10 + 3.84523e10i) q^{76} +(1.33446e10 + 2.31135e10i) q^{77} +(-1.71854e10 + 3.70487e9i) q^{78} +(4.75604e9 - 8.23771e9i) q^{79} +2.14784e9 q^{80} +(2.07267e10 - 2.35621e10i) q^{81} +2.80889e10 q^{82} +(2.27734e9 - 3.94447e9i) q^{83} +(-1.51268e11 + 3.26107e10i) q^{84} +(-9.64555e8 - 1.67066e9i) q^{85} +(-3.29997e10 - 5.71572e10i) q^{86} +(4.40282e9 - 1.36851e10i) q^{87} +(3.24819e10 - 5.62602e10i) q^{88} -7.34546e10 q^{89} +(4.08916e9 - 1.84904e9i) q^{90} +4.21322e10 q^{91} +(-6.83015e10 + 1.18302e11i) q^{92} +(1.80589e10 + 1.99401e10i) q^{93} +(4.55514e10 + 7.88973e10i) q^{94} +(1.54303e9 + 2.67260e9i) q^{95} +(4.19378e10 + 4.63065e10i) q^{96} +(4.91645e10 - 8.51555e10i) q^{97} +3.79466e11 q^{98} +(5.71979e9 - 5.76263e10i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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