LMFDB - Embedded newform 9.10.c.a.7.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,10,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, 10, names="a")

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

chi := DirichletCharacter("9.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 10 $
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:	$4.63532252547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1984 x^{14} - 13748 x^{13} + 1552498 x^{12} - 9136628 x^{11} + 609566956 x^{10} + \cdots + 13\!\cdots\!25 $ x^16 - 8x^15 + 1984x^14 - 13748x^13 + 1552498x^12 - 9136628x^11 + 609566956x^10 - 2964409064x^9 + 126210674407x^8 - 487156186164x^7 + 13162328064828x^6 - 37794288146040x^5 + 578928267028062x^4 - 1095428523832956x^3 + 5807598664427172x^2 - 5266103139591300*x + 1336504689748125
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{28}\cdot 17^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.8
Root			$0.500000 + 22.2094i$ of defining polynomial
Character	$\chi$	$=$	9.7
Dual form			9.10.c.a.4.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(19.9839 - 34.6131i) q^{2} +(92.3087 - 105.651i) q^{3} +(-542.712 - 940.005i) q^{4} +(1103.58 + 1911.45i) q^{5} +(-1812.22 - 5306.41i) q^{6} +(-2172.76 + 3763.33i) q^{7} -22918.5 q^{8} +(-2641.20 - 19505.0i) q^{9} +O(q^{10})$	\(q+(19.9839 - 34.6131i) q^{2} +(92.3087 - 105.651i) q^{3} +(-542.712 - 940.005i) q^{4} +(1103.58 + 1911.45i) q^{5} +(-1812.22 - 5306.41i) q^{6} +(-2172.76 + 3763.33i) q^{7} -22918.5 q^{8} +(-2641.20 - 19505.0i) q^{9} +88215.0 q^{10} +(4138.79 - 7168.59i) q^{11} +(-149409. - 29432.6i) q^{12} +(34563.2 + 59865.3i) q^{13} +(86840.4 + 150412. i) q^{14} +(303816. + 59849.7i) q^{15} +(-180132. + 311998. i) q^{16} -41893.6 q^{17} +(-727910. - 298365. i) q^{18} +12629.9 q^{19} +(1.19785e6 - 2.07473e6i) q^{20} +(197034. + 576942. i) q^{21} +(-165418. - 286513. i) q^{22} +(-609041. - 1.05489e6i) q^{23} +(-2.11558e6 + 2.42136e6i) q^{24} +(-1.45920e6 + 2.52740e6i) q^{25} +2.76283e6 q^{26} +(-2.30452e6 - 1.52144e6i) q^{27} +4.71673e6 q^{28} +(-3.21809e6 + 5.57389e6i) q^{29} +(8.14301e6 - 9.31999e6i) q^{30} +(369878. + 640648. i) q^{31} +(1.33234e6 + 2.30769e6i) q^{32} +(-375322. - 1.09899e6i) q^{33} +(-837198. + 1.45007e6i) q^{34} -9.59122e6 q^{35} +(-1.69014e7 + 1.30683e7i) q^{36} +1.64142e7 q^{37} +(252394. - 437160. i) q^{38} +(9.51531e6 + 1.87445e6i) q^{39} +(-2.52923e7 - 4.38075e7i) q^{40} +(-1.18987e6 - 2.06092e6i) q^{41} +(2.39073e7 + 4.70958e6i) q^{42} +(-1.10625e7 + 1.91609e7i) q^{43} -8.98468e6 q^{44} +(3.43680e7 - 2.65738e7i) q^{45} -4.86841e7 q^{46} +(1.70843e7 - 2.95908e7i) q^{47} +(1.63351e7 + 4.78312e7i) q^{48} +(1.07350e7 + 1.85936e7i) q^{49} +(5.83209e7 + 1.01015e8i) q^{50} +(-3.86715e6 + 4.42610e6i) q^{51} +(3.75158e7 - 6.49792e7i) q^{52} -1.05262e8 q^{53} +(-9.87150e7 + 4.93626e7i) q^{54} +1.82699e7 q^{55} +(4.97964e7 - 8.62498e7i) q^{56} +(1.16585e6 - 1.33436e6i) q^{57} +(1.28620e8 + 2.22776e8i) q^{58} +(-4.43759e7 - 7.68614e7i) q^{59} +(-1.08626e8 - 3.18070e8i) q^{60} +(5.94329e7 - 1.02941e8i) q^{61} +2.95664e7 q^{62} +(7.91424e7 + 3.24399e7i) q^{63} -7.79534e7 q^{64} +(-7.62863e7 + 1.32132e8i) q^{65} +(-4.55399e7 - 8.97105e6i) q^{66} +(-4.90722e7 - 8.49956e7i) q^{67} +(2.27362e7 + 3.93802e7i) q^{68} +(-1.67670e8 - 3.30299e7i) q^{69} +(-1.91670e8 + 3.31982e8i) q^{70} +3.15854e8 q^{71} +(6.05323e7 + 4.47025e8i) q^{72} +4.17458e6 q^{73} +(3.28020e8 - 5.68147e8i) q^{74} +(1.32326e8 + 3.87467e8i) q^{75} +(-6.85439e6 - 1.18722e7i) q^{76} +(1.79852e7 + 3.11513e7i) q^{77} +(2.55034e8 - 2.91896e8i) q^{78} +(2.33429e8 - 4.04312e8i) q^{79} -7.95157e8 q^{80} +(-3.73469e8 + 1.03033e8i) q^{81} -9.51133e7 q^{82} +(-5.59890e6 + 9.69757e6i) q^{83} +(4.35395e8 - 4.98327e8i) q^{84} +(-4.62328e7 - 8.00776e7i) q^{85} +(4.42145e8 + 7.65817e8i) q^{86} +(2.91829e8 + 8.54512e8i) q^{87} +(-9.48548e7 + 1.64293e8i) q^{88} -7.22061e8 q^{89} +(-2.32994e8 - 1.72063e9i) q^{90} -3.00391e8 q^{91} +(-6.61068e8 + 1.14500e9i) q^{92} +(1.01828e8 + 2.00594e7i) q^{93} +(-6.82820e8 - 1.18268e9i) q^{94} +(1.39380e7 + 2.41414e7i) q^{95} +(3.66796e8 + 7.22564e7i) q^{96} +(3.48673e8 - 6.03920e8i) q^{97} +8.58111e8 q^{98} +(-1.50755e8 - 6.17933e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9}+O(q^{10}) $ 16 * q + 15 * q^2 - 3 * q^3 - 1793 * q^4 + 453 * q^5 + 2439 * q^6 - 343 * q^7 - 14478 * q^8 - 15669 * q^9	\( 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9} + 1020 q^{10} + 99150 q^{11} - 241212 q^{12} + 32435 q^{13} + 394824 q^{14} + 723843 q^{15} - 328193 q^{16} - 831078 q^{17} - 1039500 q^{18} - 170554 q^{19} + 1855164 q^{20} - 503475 q^{21} + 529359 q^{22} + 1064559 q^{23} - 2686059 q^{24} - 2293229 q^{25} + 2436312 q^{26} - 6176520 q^{27} + 1225724 q^{28} - 1309053 q^{29} + 30713544 q^{30} - 2359819 q^{31} + 5760063 q^{32} - 19931472 q^{33} + 981801 q^{34} - 31066554 q^{35} - 48894093 q^{36} + 16391516 q^{37} + 39490203 q^{38} + 74528535 q^{39} - 16760496 q^{40} + 54747318 q^{41} + 25242354 q^{42} + 15249608 q^{43} - 332509926 q^{44} - 139865967 q^{45} + 2390520 q^{46} + 156295545 q^{47} + 312045027 q^{48} + 15239583 q^{49} + 315590163 q^{50} + 3098385 q^{51} - 19773358 q^{52} - 525516228 q^{53} - 591710103 q^{54} - 7579770 q^{55} + 470339790 q^{56} + 581271465 q^{57} + 55408560 q^{58} + 307774074 q^{59} - 430082172 q^{60} + 69192125 q^{61} - 914436924 q^{62} - 693544725 q^{63} - 403588478 q^{64} + 482470359 q^{65} + 1912534074 q^{66} + 14328044 q^{67} + 915409575 q^{68} - 724756329 q^{69} - 229271934 q^{70} - 1239601392 q^{71} - 1729340037 q^{72} + 598613198 q^{73} + 1022736000 q^{74} + 1477690413 q^{75} + 119954093 q^{76} + 717995541 q^{77} + 243023958 q^{78} + 30257531 q^{79} - 2927826528 q^{80} - 1055378241 q^{81} - 202376022 q^{82} + 1176168291 q^{83} + 1383634866 q^{84} + 4818366 q^{85} + 1426944009 q^{86} + 617958567 q^{87} + 911312427 q^{88} - 3317041296 q^{89} - 981417492 q^{90} - 739230122 q^{91} - 76813998 q^{92} - 552731577 q^{93} - 1954316784 q^{94} - 391400652 q^{95} + 1854064512 q^{96} - 267311278 q^{97} + 4827300318 q^{98} + 1672014609 q^{99}+O(q^{100}) \) 16 * q + 15 * q^2 - 3 * q^3 - 1793 * q^4 + 453 * q^5 + 2439 * q^6 - 343 * q^7 - 14478 * q^8 - 15669 * q^9 + 1020 * q^10 + 99150 * q^11 - 241212 * q^12 + 32435 * q^13 + 394824 * q^14 + 723843 * q^15 - 328193 * q^16 - 831078 * q^17 - 1039500 * q^18 - 170554 * q^19 + 1855164 * q^20 - 503475 * q^21 + 529359 * q^22 + 1064559 * q^23 - 2686059 * q^24 - 2293229 * q^25 + 2436312 * q^26 - 6176520 * q^27 + 1225724 * q^28 - 1309053 * q^29 + 30713544 * q^30 - 2359819 * q^31 + 5760063 * q^32 - 19931472 * q^33 + 981801 * q^34 - 31066554 * q^35 - 48894093 * q^36 + 16391516 * q^37 + 39490203 * q^38 + 74528535 * q^39 - 16760496 * q^40 + 54747318 * q^41 + 25242354 * q^42 + 15249608 * q^43 - 332509926 * q^44 - 139865967 * q^45 + 2390520 * q^46 + 156295545 * q^47 + 312045027 * q^48 + 15239583 * q^49 + 315590163 * q^50 + 3098385 * q^51 - 19773358 * q^52 - 525516228 * q^53 - 591710103 * q^54 - 7579770 * q^55 + 470339790 * q^56 + 581271465 * q^57 + 55408560 * q^58 + 307774074 * q^59 - 430082172 * q^60 + 69192125 * q^61 - 914436924 * q^62 - 693544725 * q^63 - 403588478 * q^64 + 482470359 * q^65 + 1912534074 * q^66 + 14328044 * q^67 + 915409575 * q^68 - 724756329 * q^69 - 229271934 * q^70 - 1239601392 * q^71 - 1729340037 * q^72 + 598613198 * q^73 + 1022736000 * q^74 + 1477690413 * q^75 + 119954093 * q^76 + 717995541 * q^77 + 243023958 * q^78 + 30257531 * q^79 - 2927826528 * q^80 - 1055378241 * q^81 - 202376022 * q^82 + 1176168291 * q^83 + 1383634866 * q^84 + 4818366 * q^85 + 1426944009 * q^86 + 617958567 * q^87 + 911312427 * q^88 - 3317041296 * q^89 - 981417492 * q^90 - 739230122 * q^91 - 76813998 * q^92 - 552731577 * q^93 - 1954316784 * q^94 - 391400652 * q^95 + 1854064512 * q^96 - 267311278 * q^97 + 4827300318 * q^98 + 1672014609 * 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 $

$2$	19.9839	−	34.6131i	0.883172	−	1.52970i	0.0353766	−	0.999374i	$-0.488737\pi$
$2$	19.9839	−	34.6131i	0.883172	−	1.52970i	0.847795	−	0.530324i	$-0.177930\pi$
$3$	92.3087	−	105.651i	0.657956	−	0.753056i
$3$	92.3087	−	105.651i	0.657956	−	0.753056i
$4$	−542.712	−	940.005i	−1.05998	−	1.83595i
$5$	1103.58	+	1911.45i	0.789655	+	1.36772i	0.926179	+	0.377085i	$0.123074\pi$
$5$	1103.58	+	1911.45i	0.789655	+	1.36772i	−0.136524	+	0.990637i	$0.543593\pi$
$6$	−1812.22	−	5306.41i	−0.570860	−	1.67155i
$7$	−2172.76	+	3763.33i	−0.342035	+	0.592422i	−0.984811	−	0.173633i	$-0.944449\pi$
$7$	−2172.76	+	3763.33i	−0.342035	+	0.592422i	0.642775	+	0.766055i	$0.277783\pi$
$8$	−22918.5			−1.97825
$9$	−2641.20	−	19505.0i	−0.134187	−	0.990956i
$10$	88215.0			2.78960
$11$	4138.79	−	7168.59i	0.0852327	−	0.147627i	−0.820258	−	0.571994i	$-0.806170\pi$
$11$	4138.79	−	7168.59i	0.0852327	−	0.147627i	0.905490	+	0.424367i	$0.139503\pi$
$12$	−149409.	−	29432.6i	−2.07999	−	0.409745i
$13$	34563.2	+	59865.3i	0.335637	+	0.581340i	0.983607	−	0.180326i	$-0.0577152\pi$
$13$	34563.2	+	59865.3i	0.335637	+	0.581340i	−0.647970	+	0.761666i	$0.724382\pi$
$14$	86840.4	+	150412.i	0.604151	+	1.04642i
$15$	303816.	+	59849.7i	1.54953	+	0.305247i
$16$	−180132.	+	311998.i	−0.687149	+	1.19018i
$17$	−41893.6			−0.121654			−0.0608272	−	0.998148i	$-0.519374\pi$
$17$	−41893.6			−0.121654			−0.0608272	+	0.998148i	$0.519374\pi$
$18$	−727910.	−	298365.i	−1.63437	−	0.669919i
$19$	12629.9			0.0222335			0.0111168	−	0.999938i	$-0.496461\pi$
$19$	12629.9			0.0222335			0.0111168	+	0.999938i	$0.496461\pi$
$20$	1.19785e6	−	2.07473e6i	1.67404	−	2.89953i
$21$	197034.	+	576942.i	0.221083	+	0.647359i
$22$	−165418.	−	286513.i	−0.150550	−	0.260761i
$23$	−609041.	−	1.05489e6i	−0.453807	−	0.786017i	0.544811	−	0.838559i	$-0.316601\pi$
$23$	−609041.	−	1.05489e6i	−0.453807	−	0.786017i	−0.998619	+	0.0525412i	$0.983268\pi$
$24$	−2.11558e6	+	2.42136e6i	−1.30160	+	1.48973i
$25$	−1.45920e6	+	2.52740e6i	−0.747109	+	1.29403i
$26$	2.76283e6			1.18570
$27$	−2.30452e6	−	1.52144e6i	−0.834535	−	0.550955i
$28$	4.71673e6			1.45021
$29$	−3.21809e6	+	5.57389e6i	−0.844903	+	1.46341i	0.0408032	+	0.999167i	$0.487008\pi$
$29$	−3.21809e6	+	5.57389e6i	−0.844903	+	1.46341i	−0.885706	+	0.464247i	$0.846325\pi$
$30$	8.14301e6	−	9.31999e6i	1.83544	−	2.10073i
$31$	369878.	+	640648.i	0.0719335	+	0.124592i	0.899749	−	0.436408i	$-0.143750\pi$
$31$	369878.	+	640648.i	0.0719335	+	0.124592i	−0.827815	+	0.561001i	$0.810416\pi$
$32$	1.33234e6	+	2.30769e6i	0.224616	+	0.389047i
$33$	−375322.	−	1.09899e6i	−0.0550923	−	0.161317i
$34$	−837198.	+	1.45007e6i	−0.107442	+	0.186095i
$35$	−9.59122e6			−1.08036
$36$	−1.69014e7	+	1.30683e7i	−1.67711	+	1.29676i
$37$	1.64142e7			1.43983			0.719916	−	0.694061i	$-0.244180\pi$
$37$	1.64142e7			1.43983			0.719916	+	0.694061i	$0.244180\pi$
$38$	252394.	−	437160.i	0.0196360	−	0.0340106i
$39$	9.51531e6	+	1.87445e6i	0.658616	+	0.129743i
$40$	−2.52923e7	−	4.38075e7i	−1.56213	−	2.70569i
$41$	−1.18987e6	−	2.06092e6i	−0.0657618	−	0.113903i	0.831270	−	0.555869i	$-0.187614\pi$
$41$	−1.18987e6	−	2.06092e6i	−0.0657618	−	0.113903i	−0.897032	+	0.441966i	$0.854281\pi$
$42$	2.39073e7	+	4.70958e6i	1.18552	+	0.233539i
$43$	−1.10625e7	+	1.91609e7i	−0.493453	+	0.854686i	−0.999972	−	0.00754294i	$-0.997599\pi$
$43$	−1.10625e7	+	1.91609e7i	−0.493453	+	0.854686i	0.506518	+	0.862229i	$0.330932\pi$
$44$	−8.98468e6			−0.361381
$45$	3.43680e7	−	2.65738e7i	1.24939	−	0.966044i
$46$	−4.86841e7			−1.60316
$47$	1.70843e7	−	2.95908e7i	0.510688	−	0.884538i	−0.489235	−	0.872152i	$-0.662724\pi$
$47$	1.70843e7	−	2.95908e7i	0.510688	−	0.884538i	0.999923	−	0.0123862i	$-0.00394274\pi$
$48$	1.63351e7	+	4.78312e7i	0.444156	+	1.30055i
$49$	1.07350e7	+	1.85936e7i	0.266024	+	0.460767i
$50$	5.83209e7	+	1.01015e8i	1.31965	+	2.28570i
$51$	−3.86715e6	+	4.42610e6i	−0.0800433	+	0.0916126i
$52$	3.75158e7	−	6.49792e7i	0.711539	−	1.23242i
$53$	−1.05262e8			−1.83245			−0.916223	−	0.400668i	$-0.868778\pi$
$53$	−1.05262e8			−1.83245			−0.916223	+	0.400668i	$0.868778\pi$
$54$	−9.87150e7	+	4.93626e7i	−1.57983	+	0.789998i
$55$	1.82699e7			0.269218
$56$	4.97964e7	−	8.62498e7i	0.676630	−	1.17196i
$57$	1.16585e6	−	1.33436e6i	0.0146287	−	0.0167431i
$58$	1.28620e8	+	2.22776e8i	1.49239	+	2.58489i
$59$	−4.43759e7	−	7.68614e7i	−0.476775	−	0.825799i	0.522871	−	0.852412i	$-0.324861\pi$
$59$	−4.43759e7	−	7.68614e7i	−0.476775	−	0.825799i	−0.999646	+	0.0266134i	$0.991528\pi$
$60$	−1.08626e8	−	3.18070e8i	−1.08206	−	3.16841i
$61$	5.94329e7	−	1.02941e8i	0.549595	−	0.951926i	−0.448707	−	0.893679i	$-0.648115\pi$
$61$	5.94329e7	−	1.02941e8i	0.549595	−	0.951926i	0.998302	−	0.0582475i	$-0.0185513\pi$
$62$	2.95664e7			0.254118
$63$	7.91424e7	+	3.24399e7i	0.632961	+	0.259446i
$64$	−7.79534e7			−0.580798
$65$	−7.62863e7	+	1.32132e8i	−0.530074	+	0.918116i
$66$	−4.55399e7	−	8.97105e6i	−0.295423	−	0.0581963i
$67$	−4.90722e7	−	8.49956e7i	−0.297508	−	0.515299i	0.678057	−	0.735009i	$-0.262822\pi$
$67$	−4.90722e7	−	8.49956e7i	−0.297508	−	0.515299i	−0.975565	+	0.219710i	$0.929489\pi$
$68$	2.27362e7	+	3.93802e7i	0.128952	+	0.223351i
$69$	−1.67670e8	−	3.30299e7i	−0.890501	−	0.175423i
$70$	−1.91670e8	+	3.31982e8i	−0.954142	+	1.65262i
$71$	3.15854e8			1.47511			0.737554	−	0.675288i	$-0.235981\pi$
$71$	3.15854e8			1.47511			0.737554	+	0.675288i	$0.235981\pi$
$72$	6.05323e7	+	4.47025e8i	0.265455	+	1.96036i
$73$	4.17458e6			0.0172052			0.00860260	−	0.999963i	$-0.497262\pi$
$73$	4.17458e6			0.0172052			0.00860260	+	0.999963i	$0.497262\pi$
$74$	3.28020e8	−	5.68147e8i	1.27162	−	2.20251i
$75$	1.32326e8	+	3.87467e8i	0.482913	+	1.41403i
$76$	−6.85439e6	−	1.18722e7i	−0.0235672	−	0.0408196i
$77$	1.79852e7	+	3.11513e7i	0.0583051	+	0.100987i
$78$	2.55034e8	−	2.91896e8i	0.780138	−	0.892898i
$79$	2.33429e8	−	4.04312e8i	0.674270	−	1.16787i	−0.302412	−	0.953177i	$-0.597792\pi$
$79$	2.33429e8	−	4.04312e8i	0.674270	−	1.16787i	0.976682	−	0.214692i	$-0.0688748\pi$
$80$	−7.95157e8			−2.17044
$81$	−3.73469e8	+	1.03033e8i	−0.963988	+	0.265947i
$82$	−9.51133e7			−0.232316
$83$	−5.59890e6	+	9.69757e6i	−0.0129494	+	0.0224291i	−0.872428	−	0.488744i	$-0.837455\pi$
$83$	−5.59890e6	+	9.69757e6i	−0.0129494	+	0.0224291i	0.859478	+	0.511173i	$0.170789\pi$
$84$	4.35395e8	−	4.98327e8i	0.954173	−	1.09209i
$85$	−4.62328e7	−	8.00776e7i	−0.0960650	−	0.166389i
$86$	4.42145e8	+	7.65817e8i	0.871608	+	1.50967i
$87$	2.91829e8	+	8.54512e8i	0.546124	+	1.59912i
$88$	−9.48548e7	+	1.64293e8i	−0.168611	+	0.292044i
$89$	−7.22061e8			−1.21988			−0.609942	−	0.792446i	$-0.708807\pi$
$89$	−7.22061e8			−1.21988			−0.609942	+	0.792446i	$0.708807\pi$
$90$	−2.32994e8	−	1.72063e9i	−0.374328	−	2.76437i
$91$	−3.00391e8			−0.459198
$92$	−6.61068e8	+	1.14500e9i	−0.962057	+	1.66633i
$93$	1.01828e8	+	2.00594e7i	0.141154	+	0.0278064i
$94$	−6.82820e8	−	1.18268e9i	−0.902051	−	1.56240i
$95$	1.39380e7	+	2.41414e7i	0.0175568	+	0.0304093i
$96$	3.66796e8	+	7.22564e7i	0.440762	+	0.0868272i
$97$	3.48673e8	−	6.03920e8i	0.399895	−	0.692638i	−0.593818	−	0.804600i	$-0.702380\pi$
$97$	3.48673e8	−	6.03920e8i	0.399895	−	0.692638i	0.993713	+	0.111962i	$0.0357133\pi$
$98$	8.58111e8			0.939779
$99$	−1.50755e8	−	6.17933e7i	−0.157729	−	0.0646522i
$100$	3.16770e9			3.16770
$101$	1.55558e8	−	2.69434e8i	0.148746	−	0.257636i	−0.782018	−	0.623256i	$-0.785810\pi$
$101$	1.55558e8	−	2.69434e8i	0.148746	−	0.257636i	0.930764	+	0.365620i	$0.119143\pi$
$102$	7.59204e7	+	2.22305e8i	0.0694477	+	0.203352i
$103$	3.89849e8	+	6.75238e8i	0.341294	+	0.591139i	0.984673	−	0.174409i	$-0.0558014\pi$
$103$	3.89849e8	+	6.75238e8i	0.341294	+	0.591139i	−0.643379	+	0.765548i	$0.722468\pi$
$104$	−7.92137e8	−	1.37202e9i	−0.663973	−	1.15003i
$105$	−8.85354e8	+	1.01332e9i	−0.710829	+	0.813571i
$106$	−2.10355e9	+	3.64346e9i	−1.61836	+	2.80309i
$107$	−4.21203e8			−0.310645			−0.155322	−	0.987864i	$-0.549642\pi$
$107$	−4.21203e8			−0.310645			−0.155322	+	0.987864i	$0.549642\pi$
$108$	−1.79463e8	+	2.99196e9i	−0.126931	+	2.11617i
$109$	−1.81817e9			−1.23371			−0.616857	−	0.787076i	$-0.711594\pi$
$109$	−1.81817e9			−1.23371			−0.616857	+	0.787076i	$0.711594\pi$
$110$	3.65103e8	−	6.32377e8i	0.237765	−	0.411822i
$111$	1.51517e9	−	1.73417e9i	0.947347	−	1.08427i
$112$	−7.82767e8	−	1.35579e9i	−0.470058	−	0.814164i
$113$	−1.11921e8	−	1.93852e8i	−0.0645739	−	0.111845i	0.831931	−	0.554879i	$-0.187236\pi$
$113$	−1.11921e8	−	1.93852e8i	−0.0645739	−	0.111845i	−0.896505	+	0.443034i	$0.853902\pi$
$114$	−2.28881e7	−	6.70193e7i	−0.0126922	−	0.0371645i
$115$	1.34425e9	−	2.32830e9i	0.716702	−	1.24136i
$116$	6.98597e9			3.58233
$117$	1.07638e9	−	8.32272e8i	0.531044	−	0.410609i
$118$	−3.54722e9			−1.68430
$119$	9.10248e7	−	1.57660e8i	0.0416101	−	0.0720708i
$120$	−6.96300e9	−	1.37166e9i	−3.06536	−	0.603855i
$121$	1.14471e9	+	1.98270e9i	0.485471	+	0.840860i
$122$	−2.37540e9	−	4.11432e9i	−0.970773	−	1.68143i
$123$	−3.27574e8	−	6.45299e7i	−0.129044	−	0.0254207i
$124$	4.01475e8	−	6.95374e8i	0.152497	−	0.264132i
$125$	−2.13050e9			−0.780524
$126$	2.70442e9	−	2.09109e9i	0.955888	−	0.739103i
$127$	4.30949e9			1.46997			0.734986	−	0.678082i	$-0.237189\pi$
$127$	4.30949e9			1.46997			0.734986	+	0.678082i	$0.237189\pi$
$128$	−2.23997e9	+	3.87975e9i	−0.737561	+	1.27749i
$129$	1.00319e9	+	2.93748e9i	0.318956	+	0.933944i
$130$	3.04900e9	+	5.28102e9i	0.936293	+	1.62171i
$131$	−1.36090e8	−	2.35714e8i	−0.0403742	−	0.0699303i	0.845132	−	0.534557i	$-0.179522\pi$
$131$	−1.36090e8	−	2.35714e8i	−0.0403742	−	0.0699303i	−0.885506	+	0.464627i	$0.846188\pi$
$132$	−8.29364e8	+	9.49239e8i	−0.237773	+	0.272140i
$133$	−2.74417e7	+	4.75305e7i	−0.00760465	+	0.0131716i
$134$	−3.92261e9			−1.05100
$135$	3.64929e8	−	6.08400e9i	0.0945598	−	1.57648i
$136$	9.60139e8			0.240663
$137$	9.94174e7	−	1.72196e8i	0.0241113	−	0.0417619i	−0.853718	−	0.520736i	$-0.825658\pi$
$137$	9.94174e7	−	1.72196e8i	0.0241113	−	0.0417619i	0.877829	+	0.478974i	$0.158991\pi$
$138$	−4.49396e9	+	5.14351e9i	−1.05481	+	1.20727i
$139$	2.80165e9	+	4.85260e9i	0.636572	+	1.10257i	0.986180	+	0.165678i	$0.0529814\pi$
$139$	2.80165e9	+	4.85260e9i	0.636572	+	1.10257i	−0.349608	+	0.936896i	$0.613685\pi$
$140$	5.20527e9	+	9.01580e9i	1.14516	+	1.98348i
$141$	−1.54927e9	−	4.53646e9i	−0.330096	−	0.966565i
$142$	6.31199e9	−	1.09327e10i	1.30277	−	2.25647i
$143$	5.72200e8			0.114429
$144$	6.56128e9	+	2.68942e9i	1.27162	+	0.521228i
$145$	−1.42056e10			−2.66873
$146$	8.34243e7	−	1.44495e8i	0.0151951	−	0.0263188i
$147$	2.95537e9	+	5.82188e8i	0.522016	+	0.102834i
$148$	−8.90818e9	−	1.54294e10i	−1.52620	−	2.64346i
$149$	−5.23469e8	−	9.06676e8i	−0.0870068	−	0.150700i	0.819238	−	0.573454i	$-0.194397\pi$
$149$	−5.23469e8	−	9.06676e8i	−0.0870068	−	0.150700i	−0.906245	+	0.422754i	$0.861064\pi$
$150$	1.60558e10	+	3.16289e9i	2.58954	+	0.510121i
$151$	−4.14232e9	+	7.17471e9i	−0.648406	+	1.12307i	0.335097	+	0.942184i	$0.391231\pi$
$151$	−4.14232e9	+	7.17471e9i	−0.648406	+	1.12307i	−0.983504	+	0.180889i	$0.942103\pi$
$152$	−2.89458e8			−0.0439834
$153$	1.10650e8	+	8.17135e8i	0.0163244	+	0.120554i
$154$	1.43766e9			0.205974
$155$	−8.16377e8	+	1.41401e9i	−0.113605	+	0.196770i
$156$	−3.40208e9	−	9.96172e9i	−0.459921	−	1.34671i
$157$	−2.01799e8	−	3.49526e8i	−0.0265076	−	0.0459125i	0.852467	−	0.522781i	$-0.175105\pi$
$157$	−2.01799e8	−	3.49526e8i	−0.0265076	−	0.0459125i	−0.878975	+	0.476868i	$0.841772\pi$
$158$	−9.32966e9	−	1.61594e10i	−1.19099	−	2.06286i
$159$	−9.71663e9	+	1.11210e10i	−1.20567	+	1.37994i
$160$	−2.94069e9	+	5.09342e9i	−0.354739	+	0.614426i
$161$	5.29320e9			0.620872
$162$	−3.89706e9	+	1.49859e10i	−0.444548	+	1.70949i
$163$	4.57840e9			0.508007			0.254004	−	0.967203i	$-0.418253\pi$
$163$	4.57840e9			0.508007			0.254004	+	0.967203i	$0.418253\pi$
$164$	−1.29152e9	+	2.23697e9i	−0.139413	+	0.241470i
$165$	1.68647e9	−	1.93023e9i	0.177133	−	0.202736i
$166$	2.23775e8	+	3.87590e8i	0.0228732	+	0.0396175i
$167$	4.24681e9	+	7.35569e9i	0.422511	+	0.731811i	0.996184	−	0.0872731i	$-0.0278153\pi$
$167$	4.24681e9	+	7.35569e9i	0.422511	+	0.731811i	−0.573673	+	0.819084i	$0.694482\pi$
$168$	−4.51573e9	−	1.32226e10i	−0.437357	−	1.28064i
$169$	2.91301e9	−	5.04549e9i	0.274696	−	0.475787i
$170$	−3.69565e9			−0.339368
$171$	−3.33581e7	−	2.46346e8i	−0.00298345	−	0.0220324i
$172$	2.40151e10			2.09221
$173$	3.53574e9	−	6.12409e9i	0.300105	−	0.519797i	−0.676054	−	0.736852i	$-0.736312\pi$
$173$	3.53574e9	−	6.12409e9i	0.300105	−	0.519797i	0.976160	+	0.217054i	$0.0696449\pi$
$174$	3.54092e10	+	6.97538e9i	2.92849	+	0.576894i
$175$	−6.34097e9	−	1.09829e10i	−0.511075	−	0.885208i
$176$	1.49106e9	+	2.58259e9i	0.117135	+	0.202884i
$177$	−1.22168e10	−	2.40662e9i	−0.935570	−	0.184301i
$178$	−1.44296e10	+	2.49928e10i	−1.07737	+	1.86606i
$179$	1.24682e10			0.907749			0.453874	−	0.891066i	$-0.350042\pi$
$179$	1.24682e10			0.907749			0.453874	+	0.891066i	$0.350042\pi$
$180$	−4.36314e10	−	1.78842e10i	−3.09794	−	1.26982i
$181$	5.38680e9			0.373059			0.186530	−	0.982449i	$-0.440276\pi$
$181$	5.38680e9			0.373059			0.186530	+	0.982449i	$0.440276\pi$
$182$	−6.00297e9	+	1.03975e10i	−0.405551	+	0.702435i
$183$	−5.38961e9	−	1.57815e10i	−0.355244	−	1.04020i
$184$	1.39583e10	+	2.41765e10i	0.897744	+	1.55494i
$185$	1.81143e10	+	3.13749e10i	1.13697	+	1.96929i
$186$	2.72924e9	−	3.12372e9i	0.167199	−	0.191365i
$187$	−1.73389e8	+	3.00318e8i	−0.0103689	+	0.0179595i
$188$	−3.70873e10			−2.16529
$189$	1.07328e10	−	5.36697e9i	0.611838	−	0.305951i
$190$	1.11415e9			0.0620227
$191$	1.35610e10	−	2.34884e10i	0.737296	−	1.27703i	−0.216413	−	0.976302i	$-0.569436\pi$
$191$	1.35610e10	−	2.34884e10i	0.737296	−	1.27703i	0.953709	−	0.300732i	$-0.0972310\pi$
$192$	−7.19578e9	+	8.23585e9i	−0.382140	+	0.437374i
$193$	3.76358e9	+	6.51871e9i	0.195251	+	0.338185i	0.946983	−	0.321284i	$-0.104115\pi$
$193$	3.76358e9	+	6.51871e9i	0.195251	+	0.338185i	−0.751732	+	0.659469i	$0.770781\pi$
$194$	−1.39357e10	−	2.41373e10i	−0.706351	−	1.22344i
$195$	6.91794e9	+	2.02566e10i	0.342627	+	1.00326i
$196$	1.16521e10	−	2.01820e10i	0.563963	−	0.976812i
$197$	−7.91081e9			−0.374217			−0.187108	−	0.982339i	$-0.559912\pi$
$197$	−7.91081e9			−0.374217			−0.187108	+	0.982339i	$0.559912\pi$
$198$	−5.15153e9	+	3.98322e9i	−0.238200	+	0.184179i
$199$	−1.98001e10			−0.895010			−0.447505	−	0.894282i	$-0.647687\pi$
$199$	−1.98001e10			−0.895010			−0.447505	+	0.894282i	$0.647687\pi$
$200$	3.34426e10	−	5.79243e10i	1.47797	−	2.55992i
$201$	−1.35096e10	−	2.66131e9i	−0.583797	−	0.115004i
$202$	−6.21730e9	−	1.07687e10i	−0.262737	−	0.455074i
$203$	−1.39843e10	−	2.42214e10i	−0.577973	−	1.00108i
$204$	6.25930e9	+	1.23304e9i	0.253040	+	0.0498473i
$205$	2.62623e9	−	4.54877e9i	0.103858	−	0.179888i
$206$	3.11628e10			1.20569
$207$	−1.89670e10	+	1.46655e10i	−0.718014	+	0.555176i
$208$	−2.49038e10			−0.922530
$209$	5.22725e7	−	9.05386e7i	0.00189502	−	0.00328228i
$210$	1.73814e10	+	5.08949e10i	0.616734	+	1.80588i
$211$	−1.38998e10	−	2.40751e10i	−0.482766	−	0.836176i	0.517038	−	0.855963i	$-0.327035\pi$
$211$	−1.38998e10	−	2.40751e10i	−0.482766	−	0.836176i	−0.999804	+	0.0197866i	$0.993701\pi$
$212$	5.71271e10	+	9.89470e10i	1.94236	+	3.36427i
$213$	2.91561e10	−	3.33702e10i	0.970556	−	1.11084i
$214$	−8.41727e9	+	1.45791e10i	−0.274353	+	0.475193i
$215$	−4.88333e10			−1.55863
$216$	5.28162e10	+	3.48690e10i	1.65092	+	1.08993i
$217$	−3.21463e9			−0.0984151
$218$	−3.63340e10	+	6.29324e10i	−1.08958	+	1.88721i
$219$	3.85350e8	−	4.41048e8i	0.0113203	−	0.0129565i
$220$	−9.91528e9	−	1.71738e10i	−0.285366	−	0.494269i
$221$	−1.44798e9	−	2.50798e9i	−0.0408317	−	0.0707226i
$222$	−2.97461e10	−	8.71004e10i	−0.821943	−	2.40675i
$223$	−1.53014e10	+	2.65028e10i	−0.414343	+	0.717662i	−0.995359	−	0.0962293i	$-0.969322\pi$
$223$	−1.53014e10	+	2.65028e10i	−0.414343	+	0.717662i	0.581017	+	0.813892i	$0.302655\pi$
$224$	−1.15795e10			−0.307307
$225$	5.31510e10	+	2.17862e10i	1.38258	+	0.566710i
$226$	−8.94644e9			−0.228119
$227$	−5.88893e9	+	1.01999e10i	−0.147204	+	0.254965i	−0.930193	−	0.367071i	$-0.880361\pi$
$227$	−5.88893e9	+	1.01999e10i	−0.147204	+	0.254965i	0.782989	+	0.622036i	$0.213694\pi$
$228$	−1.88702e9	−	3.71731e8i	−0.0462456	−	0.00911008i
$229$	3.97514e10	+	6.88514e10i	0.955196	+	1.65445i	0.733920	+	0.679236i	$0.237689\pi$
$229$	3.97514e10	+	6.88514e10i	0.955196	+	1.65445i	0.221276	+	0.975211i	$0.428978\pi$
$230$	−5.37266e10	−	9.30572e10i	−1.26594	−	2.19268i
$231$	4.95135e9	+	9.75383e8i	0.114411	+	0.0225383i
$232$	7.37536e10	−	1.27745e11i	1.67143	−	2.89500i
$233$	2.44585e10			0.543661			0.271831	−	0.962345i	$-0.412371\pi$
$233$	2.44585e10			0.543661			0.271831	+	0.962345i	$0.412371\pi$
$234$	−7.29720e9	−	5.38890e10i	−0.159105	−	1.17498i
$235$	7.54151e10			1.61307
$236$	−4.81667e10	+	8.34272e10i	−1.01075	+	1.75067i
$237$	−2.11683e10	−	6.19835e10i	−0.435831	−	1.27617i
$238$	−3.63806e9	−	6.30131e9i	−0.0734977	−	0.127302i
$239$	−1.03475e10	−	1.79225e10i	−0.205138	−	0.355310i	0.745039	−	0.667021i	$-0.232431\pi$
$239$	−1.03475e10	−	1.79225e10i	−0.205138	−	0.355310i	−0.950177	+	0.311712i	$0.899098\pi$
$240$	−7.33999e10	+	8.40090e10i	−1.42806	+	1.63446i
$241$	2.56371e10	−	4.44048e10i	0.489545	−	0.847917i	−0.510383	−	0.859947i	$-0.670496\pi$
$241$	2.56371e10	−	4.44048e10i	0.489545	−	0.847917i	0.999928	+	0.0120307i	$0.00382958\pi$
$242$	9.15034e10			1.71502
$243$	−2.35889e10	+	4.89681e10i	−0.433989	+	0.900918i
$244$	−1.29020e11			−2.33025
$245$	−2.36938e10	+	4.10389e10i	−0.420134	+	0.727694i
$246$	−8.77979e9	+	1.00488e10i	−0.152854	+	0.174947i
$247$	4.36530e8	+	7.56092e8i	0.00746239	+	0.0129252i
$248$	−8.47705e9	−	1.46827e10i	−0.142302	−	0.246475i
$249$	5.07730e8	+	1.48670e9i	0.00837019	+	0.0245090i
$250$	−4.25757e10	+	7.37432e10i	−0.689337	+	1.19397i
$251$	−1.02820e11			−1.63510			−0.817552	−	0.575855i	$-0.804669\pi$
$251$	−1.02820e11			−1.63510			−0.817552	+	0.575855i	$0.804669\pi$
$252$	−1.24578e10	−	9.19998e10i	−0.194599	−	1.43709i
$253$	−1.00828e10			−0.154717
$254$	8.61204e10	−	1.49165e11i	1.29824	−	2.24861i
$255$	−1.27280e10	−	2.50732e9i	−0.188507	−	0.0371347i
$256$	6.95707e10	+	1.20500e11i	1.01239	+	1.75351i
$257$	2.90942e10	+	5.03927e10i	0.416014	+	0.720557i	0.995534	−	0.0944005i	$-0.0300934\pi$
$257$	2.90942e10	+	5.03927e10i	0.416014	+	0.720557i	−0.579520	+	0.814958i	$0.696760\pi$
$258$	1.21723e11	+	2.39786e10i	1.71035	+	0.336927i
$259$	−3.56641e10	+	6.17721e10i	−0.492473	+	0.852988i
$260$	1.65606e11			2.24748
$261$	1.17218e11	+	4.80470e10i	1.56355	+	0.640890i
$262$	−1.08784e10			−0.142630
$263$	2.83424e10	−	4.90905e10i	0.365289	−	0.632699i	−0.623534	−	0.781796i	$-0.714304\pi$
$263$	2.83424e10	−	4.90905e10i	0.365289	−	0.632699i	0.988822	+	0.149098i	$0.0476370\pi$
$264$	8.60180e9	+	2.51872e10i	0.108986	+	0.319126i
$265$	−1.16165e11	−	2.01204e11i	−1.44700	−	2.50628i
$266$	1.09678e9	+	1.89969e9i	0.0134324	+	0.0232656i
$267$	−6.66525e10	+	7.62864e10i	−0.802631	+	0.918642i
$268$	−5.32641e10	+	9.22562e10i	−0.630708	+	1.09242i
$269$	−1.24479e11			−1.44947			−0.724737	−	0.689026i	$-0.758039\pi$
$269$	−1.24479e11			−1.44947			−0.724737	+	0.689026i	$0.758039\pi$
$270$	−2.03294e11	−	1.34213e11i	−2.32802	−	1.53695i
$271$	1.72085e11			1.93812			0.969062	−	0.246816i	$-0.0793842\pi$
$271$	1.72085e11			1.93812			0.969062	+	0.246816i	$0.0793842\pi$
$272$	7.54638e9	−	1.30707e10i	0.0835947	−	0.144790i
$273$	−2.77287e10	+	3.17365e10i	−0.302132	+	0.345802i
$274$	−3.97349e9	−	6.88229e9i	−0.0425888	−	0.0737659i
$275$	1.20786e10	+	2.09208e10i	0.127356	+	0.220588i
$276$	5.99482e10	+	1.75536e11i	0.621850	+	1.82086i
$277$	−6.70133e10	+	1.16070e11i	−0.683915	+	1.18458i	0.289862	+	0.957068i	$0.406391\pi$
$277$	−6.70133e10	+	1.16070e11i	−0.683915	+	1.18458i	−0.973777	+	0.227507i	$0.926943\pi$
$278$	2.23951e11			2.24881
$279$	1.15189e10	−	8.90655e9i	0.113813	−	0.0880016i
$280$	2.19816e11			2.13722
$281$	6.28091e10	−	1.08789e11i	0.600958	−	1.04089i	−0.391718	−	0.920085i	$-0.628119\pi$
$281$	6.28091e10	−	1.08789e11i	0.600958	−	1.04089i	0.992676	−	0.120805i	$-0.0385474\pi$
$282$	−1.87981e11	−	3.70311e10i	−1.77008	−	0.348695i
$283$	6.31516e9	+	1.09382e10i	0.0585256	+	0.101369i	0.893804	−	0.448458i	$-0.148027\pi$
$283$	6.31516e9	+	1.09382e10i	0.0585256	+	0.101369i	−0.835278	+	0.549828i	$0.814693\pi$
$284$	−1.71418e11	−	2.96904e11i	−1.56359	−	2.70822i
$285$	3.83716e9	+	7.55896e8i	0.0344515	+	0.00678672i
$286$	1.14348e10	−	1.98056e10i	0.101060	−	0.175042i
$287$	1.03412e10			0.0899714
$288$	4.14924e10	−	3.20824e10i	0.355388	−	0.274790i
$289$	−1.16833e11			−0.985200
$290$	−2.83883e11	+	4.91700e11i	−2.35694	+	4.08234i
$291$	−3.16190e10	−	9.25847e10i	−0.258482	−	0.756869i
$292$	−2.26559e9	−	3.92412e9i	−0.0182372	−	0.0315878i
$293$	4.11968e10	+	7.13550e10i	0.326557	+	0.565614i	0.981826	−	0.189782i	$-0.0607781\pi$
$293$	4.11968e10	+	7.13550e10i	0.326557	+	0.565614i	−0.655269	+	0.755396i	$0.727445\pi$
$294$	7.92111e10	−	9.06601e10i	0.618334	−	0.707707i
$295$	9.79444e10	−	1.69645e11i	0.752975	−	1.30419i
$296$	−3.76188e11			−2.84835
$297$	−2.04445e10	+	1.02233e10i	−0.152466	+	0.0762407i
$298$	−4.18438e10			−0.307368
$299$	4.21009e10	−	7.29209e10i	0.304629	−	0.527633i
$300$	2.92406e11	−	3.34670e11i	2.08421	−	2.38545i
$301$	−4.80724e10	−	8.32639e10i	−0.337557	−	0.584665i
$302$	1.65559e11	+	2.86757e11i	1.14531	+	1.98373i
$303$	−1.41066e10	−	4.13059e10i	−0.0961458	−	0.281527i
$304$	−2.27505e9	+	3.94050e9i	−0.0152777	+	0.0264618i
$305$	2.62355e11			1.73596
$306$	3.04948e10	+	1.24996e10i	0.198829	+	0.0814986i
$307$	1.60599e11			1.03186			0.515931	−	0.856630i	$-0.327446\pi$
$307$	1.60599e11			1.03186			0.515931	+	0.856630i	$0.327446\pi$
$308$	1.95216e10	−	3.38123e10i	0.123605	−	0.214090i
$309$	1.07326e11	+	2.11425e10i	0.669718	+	0.131930i
$310$	3.26288e10	+	5.65147e10i	0.200666	+	0.347563i
$311$	−5.20453e10	−	9.01450e10i	−0.315471	−	0.546412i	0.664067	−	0.747674i	$-0.268829\pi$
$311$	−5.20453e10	−	9.01450e10i	−0.315471	−	0.546412i	−0.979538	+	0.201262i	$0.935496\pi$
$312$	−2.18076e11	−	4.29596e10i	−1.30291	−	0.256664i
$313$	1.73815e10	−	3.01056e10i	0.102362	−	0.177296i	−0.810296	−	0.586021i	$-0.800693\pi$
$313$	1.73815e10	−	3.01056e10i	0.102362	−	0.177296i	0.912657	+	0.408726i	$0.134027\pi$
$314$	−1.61309e10			−0.0936431
$315$	2.53324e10	+	1.87077e11i	0.144970	+	1.07059i
$316$	−5.06740e11			−2.85886
$317$	−8.40884e10	+	1.45645e11i	−0.467702	+	0.810084i	−0.999319	−	0.0369011i	$-0.988251\pi$
$317$	−8.40884e10	+	1.45645e11i	−0.467702	+	0.810084i	0.531617	+	0.846985i	$0.321585\pi$
$318$	1.90758e11	+	5.58565e11i	1.04607	+	3.06303i
$319$	2.66380e10	+	4.61383e10i	0.144027	+	0.249462i
$320$	−8.60276e10	−	1.49004e11i	−0.458630	−	0.794371i
$321$	−3.88807e10	+	4.45004e10i	−0.204391	+	0.233933i
$322$	1.05779e11	−	1.83214e11i	0.548337	−	0.949747i
$323$	−5.29112e8			−0.00270481
$324$	2.99538e11	+	2.95145e11i	1.51008	+	1.48793i
$325$	−2.01738e11			−1.00303
$326$	9.14943e10	−	1.58473e11i	0.448657	−	0.777097i
$327$	−1.67833e11	+	1.92091e11i	−0.811729	+	0.929055i
$328$	2.72701e10	+	4.72332e10i	0.130093	+	0.225328i
$329$	7.42400e10	+	1.28588e11i	0.349347	+	0.605086i
$330$	−3.31090e10	−	9.69474e10i	−0.153686	−	0.450011i
$331$	4.45717e10	−	7.72005e10i	0.204096	−	0.353504i	−0.745749	−	0.666227i	$-0.767908\pi$
$331$	4.45717e10	−	7.72005e10i	0.204096	−	0.353504i	0.949844	+	0.312723i	$0.101241\pi$
$332$	1.21543e10			0.0549048
$333$	−4.33532e10	−	3.20159e11i	−0.193207	−	1.42681i
$334$	3.39471e11			1.49260
$335$	1.08310e11	−	1.87598e11i	0.469858	−	0.813817i
$336$	−2.15497e11	−	4.24514e10i	−0.922389	−	0.181705i
$337$	1.01221e10	+	1.75320e10i	0.0427500	+	0.0740451i	0.886609	−	0.462520i	$-0.153055\pi$
$337$	1.01221e10	+	1.75320e10i	0.0427500	+	0.0740451i	−0.843859	+	0.536565i	$0.819721\pi$
$338$	−1.16427e11	−	2.01657e11i	−0.485207	−	0.840404i
$339$	−3.08119e10	−	6.06974e9i	−0.126713	−	0.0249616i
$340$	−5.01822e10	+	8.69181e10i	−0.203655	+	0.352740i
$341$	6.12339e9			0.0245243
$342$	−9.19342e9	−	3.76832e9i	−0.0363379	−	0.0148947i
$343$	−2.68656e11			−1.04803
$344$	2.53536e11	−	4.39138e11i	0.976174	−	1.69078i
$345$	−1.21902e11	−	3.56944e11i	−0.463259	−	1.35648i
$346$	−1.41316e11	−	2.44766e11i	−0.530089	−	0.918140i
$347$	1.30566e11	+	2.26148e11i	0.483447	+	0.837354i	0.999819	−	0.0190098i	$-0.00605137\pi$
$347$	1.30566e11	+	2.26148e11i	0.483447	+	0.837354i	−0.516373	+	0.856364i	$0.672718\pi$
$348$	6.44866e11	−	7.38074e11i	2.35702	−	2.69770i
$349$	−1.81998e11	+	3.15230e11i	−0.656678	+	1.13740i	0.324793	+	0.945785i	$0.394705\pi$
$349$	−1.81998e11	+	3.15230e11i	−0.656678	+	1.13740i	−0.981470	+	0.191614i	$0.938628\pi$
$350$	−5.06869e11			−1.80547
$351$	1.14293e10	−	1.90547e11i	0.0401919	−	0.670069i
$352$	2.20572e10			0.0765787
$353$	−1.43068e11	+	2.47801e11i	−0.490406	+	0.849408i	−0.999939	−	0.0110432i	$-0.996485\pi$
$353$	−1.43068e11	+	2.47801e11i	−0.490406	+	0.849408i	0.509533	+	0.860451i	$0.329818\pi$
$354$	−3.27439e11	+	3.74766e11i	−1.10819	+	1.26837i
$355$	3.48569e11	+	6.03739e11i	1.16483	+	2.01754i
$356$	3.91871e11	+	6.78741e11i	1.29306	+	2.23964i
$357$	−8.25449e9	−	2.41702e10i	−0.0268957	−	0.0787542i
$358$	2.49163e11	−	4.31564e11i	0.801698	−	1.38858i
$359$	−3.55452e11			−1.12942			−0.564710	−	0.825290i	$-0.691012\pi$
$359$	−3.55452e11			−1.12942			−0.564710	+	0.825290i	$0.691012\pi$
$360$	−7.87663e11	+	6.09030e11i	−2.47161	+	1.91107i
$361$	−3.22528e11			−0.999506
$362$	1.07649e11	−	1.86454e11i	0.329475	−	0.570668i
$363$	3.15141e11	+	6.20808e10i	0.952633	+	0.187662i
$364$	1.63026e11	+	2.82369e11i	0.486743	+	0.843063i
$365$	4.60696e9	+	7.97950e9i	0.0135862	+	0.0235319i
$366$	−6.53951e11	−	1.28824e11i	−1.90494	−	0.375260i
$367$	9.17091e10	−	1.58845e11i	0.263885	−	0.457063i	−0.703386	−	0.710808i	$-0.748329\pi$
$367$	9.17091e10	−	1.58845e11i	0.263885	−	0.457063i	0.967271	+	0.253746i	$0.0816626\pi$
$368$	4.38831e11			1.24733
$369$	−3.70556e10	+	2.86518e10i	−0.104048	+	0.0804513i
$370$	1.44798e12			4.01656
$371$	2.28710e11	−	3.96137e11i	0.626761	−	1.08558i
$372$	−3.64073e10	−	1.06605e11i	−0.0985701	−	0.288626i
$373$	1.83383e11	+	3.17628e11i	0.490533	+	0.849628i	0.999941	−	0.0108971i	$-0.00346872\pi$
$373$	1.83383e11	+	3.17628e11i	0.490533	+	0.849628i	−0.509407	+	0.860525i	$0.670135\pi$
$374$	6.92997e9	+	1.20031e10i	0.0183151	+	0.0317227i
$375$	−1.96664e11	+	2.25089e11i	−0.513551	+	0.587778i
$376$	−3.91545e11	+	6.78177e11i	−1.01027	+	1.74984i
$377$	−4.44910e11			−1.13432
$378$	2.87163e10	−	4.78750e11i	0.0723461	−	1.20613i
$379$	9.56611e10			0.238154			0.119077	−	0.992885i	$-0.462006\pi$
$379$	9.56611e10			0.238154			0.119077	+	0.992885i	$0.462006\pi$
$380$	1.51287e10	−	2.62037e10i	0.0372199	−	0.0644667i
$381$	3.97803e11	−	4.55301e11i	0.967177	−	1.10697i
$382$	−5.42003e11	−	9.38778e11i	−1.30232	−	2.25568i
$383$	−3.57222e11	−	6.18726e11i	−0.848288	−	1.46928i	−0.882735	−	0.469872i	$-0.844300\pi$
$383$	−3.57222e11	−	6.18726e11i	−0.848288	−	1.46928i	0.0344462	−	0.999407i	$-0.489033\pi$
$384$	2.03130e11	+	5.94790e11i	0.476741	+	1.39596i
$385$	−3.96961e10	+	6.87556e10i	−0.0920819	+	0.159490i
$386$	3.00844e11			0.689761
$387$	4.02951e11	+	1.65167e11i	0.913172	+	0.374303i
$388$	−7.56916e11			−1.69553
$389$	−1.95115e11	+	3.37949e11i	−0.432034	+	0.748305i	−0.997048	−	0.0767763i	$-0.975537\pi$
$389$	−1.95115e11	+	3.37949e11i	−0.432034	+	0.748305i	0.565014	+	0.825081i	$0.308871\pi$
$390$	8.39393e11	+	1.65355e11i	1.83728	+	0.361931i
$391$	2.55150e10	+	4.41932e10i	0.0552077	+	0.0956225i
$392$	−2.46031e11	−	4.26137e11i	−0.526262	−	0.911512i
$393$	−3.74657e10	−	7.38049e9i	−0.0792259	−	0.0156070i
$394$	−1.58089e11	+	2.73818e11i	−0.330498	+	0.572439i
$395$	1.03043e12			2.12976
$396$	2.37304e10	+	1.75246e11i	0.0484927	+	0.358113i
$397$	−3.19066e10			−0.0644649			−0.0322325	−	0.999480i	$-0.510262\pi$
$397$	−3.19066e10			−0.0644649			−0.0322325	+	0.999480i	$0.510262\pi$
$398$	−3.95682e11	+	6.85342e11i	−0.790447	+	1.36909i
$399$	2.48852e9	+	7.28672e9i	0.00491545	+	0.0143931i
$400$	−5.25696e11	−	9.10533e11i	−1.02675	−	1.77838i
$401$	2.91662e11	+	5.05173e11i	0.563287	+	0.975642i	0.997207	+	0.0746901i	$0.0237968\pi$
$401$	2.91662e11	+	5.05173e11i	0.563287	+	0.975642i	−0.433920	+	0.900951i	$0.642870\pi$
$402$	−3.62092e11	+	4.14428e11i	−0.691514	+	0.791464i
$403$	−2.55684e10	+	4.42857e10i	−0.0482870	+	0.0836356i
$404$	−3.37692e11			−0.630674
$405$	−6.09094e11	−	6.00161e11i	−1.12496	−	1.10846i
$406$	−1.11784e12			−2.04180
$407$	6.79349e10	−	1.17667e11i	0.122721	−	0.212559i
$408$	8.86292e10	−	1.01439e11i	0.158346	−	0.181233i
$409$	−2.98447e11	−	5.16926e11i	−0.527367	−	0.913426i	−0.999491	−	0.0318943i	$-0.989846\pi$
$409$	−2.98447e11	−	5.16926e11i	−0.527367	−	0.913426i	0.472124	−	0.881532i	$-0.343487\pi$
$410$	−1.04965e11	−	1.81804e11i	−0.183449	−	0.317744i
$411$	−9.01556e9	−	2.63987e10i	−0.0155849	−	0.0456346i
$412$	4.23151e11	−	7.32920e11i	0.723533	−	1.25320i
$413$	3.85673e11			0.652295
$414$	1.28584e11	+	9.49582e11i	0.215123	+	1.58866i
$415$	−2.47152e10			−0.0409023
$416$	−9.21003e10	+	1.59522e11i	−0.150779	+	0.261157i
$417$	7.71298e11	+	1.51941e11i	1.24914	+	0.246072i
$418$	−2.08921e9	−	3.61863e9i	−0.00334726	−	0.00579763i
$419$	−1.56398e11	−	2.70889e11i	−0.247895	−	0.429366i	0.715047	−	0.699076i	$-0.246405\pi$
$419$	−1.56398e11	−	2.70889e11i	−0.247895	−	0.429366i	−0.962941	+	0.269711i	$0.913072\pi$
$420$	1.43302e12	+	2.82295e11i	2.24714	+	0.442672i
$421$	3.03250e11	−	5.25245e11i	0.470470	−	0.814878i	−0.528960	−	0.848647i	$-0.677418\pi$
$421$	3.03250e11	−	5.25245e11i	0.470470	−	0.814878i	0.999430	+	0.0337688i	$0.0107510\pi$
$422$	−1.11109e12			−1.70546
$423$	−6.22292e11	−	2.55073e11i	−0.945066	−	0.387376i
$424$	2.41245e12			3.62504
$425$	6.11311e10	−	1.05882e11i	0.0908891	−	0.157425i
$426$	−5.72396e11	−	1.67605e12i	−0.842080	−	2.46572i
$427$	2.58267e11	+	4.47331e11i	0.375961	+	0.651184i
$428$	2.28592e11	+	3.95933e11i	0.329279	+	0.570327i
$429$	5.28191e10	−	6.04534e10i	0.0752892	−	0.0861714i
$430$	−9.75880e11	+	1.69027e12i	−1.37654	+	2.38424i
$431$	−4.53090e11			−0.632466			−0.316233	−	0.948682i	$-0.602418\pi$
$431$	−4.53090e11			−0.632466			−0.316233	+	0.948682i	$0.602418\pi$
$432$	8.89803e11	−	4.44947e11i	1.22918	−	0.614655i
$433$	1.62218e11			0.221771			0.110885	−	0.993833i	$-0.464631\pi$
$433$	1.62218e11			0.221771			0.110885	+	0.993833i	$0.464631\pi$
$434$	−6.42407e10	+	1.11268e11i	−0.0869174	+	0.150545i
$435$	−1.31130e12	+	1.50083e12i	−1.75590	+	2.00970i
$436$	9.86740e11	+	1.70908e12i	1.30772	+	2.26503i
$437$	−7.69213e9	−	1.33232e10i	−0.0100897	−	0.0174759i
$438$	−7.56524e9	−	2.21520e10i	−0.00982176	−	0.0287594i
$439$	5.71922e11	−	9.90598e11i	0.734931	−	1.27294i	−0.219823	−	0.975540i	$-0.570548\pi$
$439$	5.71922e11	−	9.90598e11i	0.734931	−	1.27294i	0.954754	−	0.297398i	$-0.0961187\pi$
$440$	−4.18718e11			−0.532579
$441$	3.34315e11	−	2.58496e11i	0.420903	−	0.325447i
$442$	−1.15745e11			−0.144246
$443$	−6.63980e11	+	1.15005e12i	−0.819103	+	1.41873i	0.0872411	+	0.996187i	$0.472195\pi$
$443$	−6.63980e11	+	1.15005e12i	−0.819103	+	1.41873i	−0.906344	+	0.422541i	$0.861138\pi$
$444$	−2.45243e12	−	4.83113e11i	−2.99484	−	0.589964i
$445$	−7.96849e11	−	1.38018e12i	−0.963288	−	1.66846i
$446$	6.11563e11	+	1.05926e12i	0.731871	+	1.26764i
$447$	−1.44112e11	−	2.83891e10i	−0.170732	−	0.0336331i
$448$	1.69374e11	−	2.93365e11i	0.198653	−	0.344078i
$449$	5.29567e11			0.614911			0.307456	−	0.951562i	$-0.400522\pi$
$449$	5.29567e11			0.614911			0.307456	+	0.951562i	$0.400522\pi$
$450$	1.81625e12	−	1.40435e12i	2.08795	−	1.61443i
$451$	−1.96986e10			−0.0224202
$452$	−1.21481e11	+	2.10412e11i	−0.136895	+	0.237109i
$453$	3.75642e11	+	1.09993e12i	0.419114	+	1.22722i
$454$	2.35367e11	+	4.07668e11i	0.260013	+	0.450356i
$455$	−3.31504e11	−	5.74182e11i	−0.362608	−	0.628055i
$456$	−2.67195e10	+	3.05815e10i	−0.0289392	+	0.0331220i
$457$	−5.32572e11	+	9.22441e11i	−0.571157	+	0.989272i	0.425291	+	0.905057i	$0.360172\pi$
$457$	−5.32572e11	+	9.22441e11i	−0.571157	+	0.989272i	−0.996448	+	0.0842156i	$0.973162\pi$
$458$	3.17755e12			3.37441
$459$	9.65449e10	+	6.37385e10i	0.101525	+	0.0670262i
$460$	−2.91816e12			−3.03877
$461$	4.10593e11	−	7.11169e11i	0.423407	−	0.733362i	−0.572863	−	0.819651i	$-0.694167\pi$
$461$	4.10593e11	−	7.11169e11i	0.423407	−	0.733362i	0.996270	+	0.0862888i	$0.0275008\pi$
$462$	1.32708e11	−	1.51890e11i	0.135522	−	0.155110i
$463$	−1.91618e11	−	3.31892e11i	−0.193786	−	0.335647i	0.752716	−	0.658345i	$-0.228743\pi$
$463$	−1.91618e11	−	3.31892e11i	−0.193786	−	0.335647i	−0.946502	+	0.322699i	$0.895410\pi$
$464$	−1.15936e12	−	2.00807e12i	−1.16115	−	2.01117i
$465$	7.40323e10	+	2.16776e11i	0.0734316	+	0.215017i
$466$	4.88776e11	−	8.46586e11i	0.480146	−	0.831638i
$467$	−9.49206e11			−0.923495			−0.461748	−	0.887011i	$-0.652777\pi$
$467$	−9.49206e11			−0.923495			−0.461748	+	0.887011i	$0.652777\pi$
$468$	−1.36651e12	−	5.60121e11i	−1.31676	−	0.539729i
$469$	4.26489e11			0.407033
$470$	1.50709e12	−	2.61035e12i	1.42462	−	2.46751i
$471$	−5.55556e10	−	1.09441e10i	−0.0520156	−	0.0102467i
$472$	1.01703e12	+	1.76155e12i	0.943180	+	1.63363i
$473$	9.15709e10	+	1.58605e11i	0.0841167	+	0.145694i
$474$	−2.56847e12	−	5.05971e11i	−2.33707	−	0.460387i
$475$	−1.84295e10	+	3.19208e10i	−0.0166109	+	0.0287709i
$476$	−1.97601e11			−0.176424
$477$	2.78019e11	+	2.05314e12i	0.245890	+	1.81587i
$478$	−8.27136e11			−0.724689
$479$	2.45674e11	−	4.25521e11i	0.213231	−	0.369327i	−0.739493	−	0.673164i	$-0.764935\pi$
$479$	2.45674e11	−	4.25521e11i	0.213231	−	0.369327i	0.952724	+	0.303838i	$0.0982680\pi$
$480$	2.66673e11	+	7.80853e11i	0.229294	+	0.671403i
$481$	5.67328e11	+	9.82641e11i	0.483261	+	0.837032i
$482$	−1.02466e12	−	1.77476e12i	−0.864704	−	1.49771i
$483$	4.88609e11	−	5.59231e11i	0.408507	−	0.467552i
$484$	1.24250e12	−	2.15207e12i	1.02918	−	1.78260i
$485$	1.53915e12			1.26312
$486$	1.22354e12	+	1.79506e12i	0.994846	+	1.45954i
$487$	−4.36740e11			−0.351838			−0.175919	−	0.984405i	$-0.556290\pi$
$487$	−4.36740e11			−0.351838			−0.175919	+	0.984405i	$0.556290\pi$
$488$	−1.36211e12	+	2.35925e12i	−1.08724	+	1.88315i
$489$	4.22626e11	−	4.83712e11i	0.334246	−	0.382558i
$490$	9.46990e11	+	1.64024e12i	0.742101	+	1.28536i
$491$	9.21516e9	+	1.59611e10i	0.00715544	+	0.0123936i	0.869581	−	0.493790i	$-0.164389\pi$
$491$	9.21516e9	+	1.59611e10i	0.00715544	+	0.0123936i	−0.862426	+	0.506184i	$0.831056\pi$
$492$	1.17120e11	+	3.42942e11i	0.0901131	+	0.263863i
$493$	1.34817e11	−	2.33510e11i	0.102786	−	0.178031i
$494$	3.48943e10			0.0263623
$495$	−4.82544e10	−	3.56354e11i	−0.0361255	−	0.266783i
$496$	−2.66507e11			−0.197716
$497$	−6.86275e11	+	1.18866e12i	−0.504538	+	0.873886i
$498$	6.16057e10	+	1.21359e10i	0.0448837	+	0.00884179i
$499$	−8.42550e10	−	1.45934e11i	−0.0608336	−	0.105367i	0.834005	−	0.551757i	$-0.186043\pi$
$499$	−8.42550e10	−	1.45934e11i	−0.0608336	−	0.105367i	−0.894838	+	0.446391i	$0.852709\pi$
$500$	1.15625e12	+	2.00268e12i	0.827343	+	1.43300i
$501$	1.16915e12	+	2.30315e11i	0.829089	+	0.163325i
$502$	−2.05474e12	+	3.55892e12i	−1.44408	+	2.50122i
$503$	−1.21652e12			−0.847348			−0.423674	−	0.905815i	$-0.639260\pi$
$503$	−1.21652e12			−0.847348			−0.423674	+	0.905815i	$0.639260\pi$
$504$	−1.81382e12	−	7.43474e11i	−1.25215	−	0.513249i
$505$	6.86680e11			0.469833
$506$	−2.01493e11	+	3.48996e11i	−0.136642	+	0.236670i
$507$	−2.64163e11	−	7.73505e11i	−0.177557	−	0.519909i
$508$	−2.33881e12	−	4.05094e12i	−1.55815	−	2.69879i
$509$	−4.37914e11	−	7.58490e11i	−0.289174	−	0.500864i	0.684439	−	0.729070i	$-0.260047\pi$
$509$	−4.37914e11	−	7.58490e11i	−0.289174	−	0.500864i	−0.973613	+	0.228206i	$0.926714\pi$
$510$	−3.41140e11	+	3.90448e11i	−0.223289	+	0.255563i
$511$	−9.07036e9	+	1.57103e10i	−0.00588478	+	0.0101927i
$512$	3.26744e12			2.10132
$513$	−2.91059e10	−	1.92156e10i	−0.0185546	−	0.0122497i
$514$	2.32566e12			1.46965
$515$	−8.60456e11	+	1.49035e12i	−0.539009	+	0.933591i
$516$	2.21680e12	−	2.53721e12i	1.37658	−	1.57555i
$517$	−1.41416e11	−	2.44940e11i	−0.0870547	−	0.150783i
$518$	1.42542e12	+	2.46889e12i	0.869877	+	1.50667i
$519$	−3.20635e11	−	9.38861e11i	−0.193980	−	0.568000i
$520$	1.74837e12	−	3.02826e12i	1.04862	−	1.81626i
$521$	−1.84603e12			−1.09766			−0.548830	−	0.835934i	$-0.684927\pi$
$521$	−1.84603e12			−1.09766			−0.548830	+	0.835934i	$0.684927\pi$
$522$	4.00553e12	−	3.09712e12i	2.36126	−	1.82575i
$523$	2.49101e12			1.45585			0.727926	−	0.685656i	$-0.240484\pi$
$523$	2.49101e12			1.45585			0.727926	+	0.685656i	$0.240484\pi$
$524$	−1.47715e11	+	2.55850e11i	−0.0855921	+	0.148250i
$525$	−1.74568e12	−	3.43887e11i	−1.00288	−	0.197560i
$526$	−1.13278e12	−	1.96204e12i	−0.645225	−	1.11756i
$527$	−1.54955e10	−	2.68391e10i	−0.00875103	−	0.0151572i
$528$	4.10490e11	+	8.08638e10i	0.229853	+	0.0452795i
$529$	1.58714e11	−	2.74900e11i	0.0881177	−	0.152624i
$530$	−9.28571e12			−5.11180
$531$	−1.38197e12	+	1.06856e12i	−0.754353	+	0.583274i
$532$	5.95718e10			0.0322432
$533$	8.22518e10	−	1.42464e11i	0.0441442	−	0.0764599i
$534$	1.30853e12	+	3.83155e12i	0.696384	+	2.03910i
$535$	−4.64829e11	−	8.05108e11i	−0.245302	−	0.424876i
$536$	1.12466e12	+	1.94797e12i	0.588545	+	1.01939i
$537$	1.15092e12	−	1.31728e12i	0.597259	−	0.683586i
$538$	−2.48757e12	+	4.30860e12i	−1.28013	+	2.21726i
$539$	1.77720e11			0.0906958
$540$	−5.91704e12	+	2.95883e12i	−2.99456	+	1.49743i
$541$	−3.86244e10			−0.0193854			−0.00969269	−	0.999953i	$-0.503085\pi$
$541$	−3.86244e10			−0.0193854			−0.00969269	+	0.999953i	$0.503085\pi$
$542$	3.43893e12	−	5.95641e12i	1.71170	−	2.96475i
$543$	4.97249e11	−	5.69120e11i	0.245457	−	0.280934i
$544$	−5.58167e10	−	9.66774e10i	−0.0273256	−	0.0473293i
$545$	−2.00648e12	−	3.47533e12i	−0.974208	−	1.68738i
$546$	5.44373e11	+	1.59400e12i	0.262138	+	0.767574i
$547$	−2.07167e12	+	3.58823e12i	−0.989411	+	1.71371i	−0.369010	+	0.929425i	$0.620303\pi$
$547$	−2.07167e12	+	3.58823e12i	−0.989411	+	1.71371i	−0.620401	+	0.784285i	$0.713030\pi$
$548$	−2.15820e11			−0.102230
$549$	−2.16483e12	−	8.87351e11i	−1.01707	−	0.416888i
$550$	9.65512e11			0.449910
$551$	−4.06441e10	+	7.03976e10i	−0.0187852	+	0.0325369i
$552$	3.84274e12	+	7.56994e11i	1.76163	+	0.347030i
$553$	1.01437e12	+	1.75694e12i	0.461248	+	0.798905i
$554$	2.67837e12	+	4.63908e12i	1.20803	+	2.09237i
$555$	4.98690e12	+	9.82385e11i	2.23106	+	0.439505i
$556$	3.04098e12	−	5.26713e12i	1.34951	−	2.33742i
$557$	3.76741e12			1.65842			0.829210	−	0.558937i	$-0.188791\pi$
$557$	3.76741e12			1.65842			0.829210	+	0.558937i	$0.188791\pi$
$558$	−7.80909e10	−	5.76693e11i	−0.0340994	−	0.251820i
$559$	−1.52943e12			−0.662484
$560$	1.72769e12	−	2.99244e12i	0.742367	−	1.28582i
$561$	1.57236e10	+	4.60407e10i	0.00670222	+	0.0196250i
$562$	−2.51034e12	−	4.34804e12i	−1.06150	−	1.83857i
$563$	6.56959e11	+	1.13789e12i	0.275582	+	0.477322i	0.970282	−	0.241978i	$-0.0777962\pi$
$563$	6.56959e11	+	1.13789e12i	0.275582	+	0.477322i	−0.694700	+	0.719300i	$0.744463\pi$
$564$	−3.42348e12	+	3.91831e12i	−1.42466	+	1.63058i
$565$	2.47026e11	−	4.27861e11i	0.101982	−	0.176638i
$566$	5.04806e11			0.206753
$567$	4.23710e11	−	1.62935e12i	0.172165	−	0.662051i
$568$	−7.23889e12			−2.91813
$569$	−1.80021e11	+	3.11806e11i	−0.0719978	+	0.124704i	−0.899777	−	0.436351i	$-0.856271\pi$
$569$	−1.80021e11	+	3.11806e11i	−0.0719978	+	0.124704i	0.827779	+	0.561054i	$0.189604\pi$
$570$	1.02845e11	−	1.17710e11i	0.0408082	−	0.0467066i
$571$	−1.06470e12	−	1.84412e12i	−0.419147	−	0.725984i	0.576707	−	0.816951i	$-0.304337\pi$
$571$	−1.06470e12	−	1.84412e12i	−0.419147	−	0.725984i	−0.995854	+	0.0909672i	$0.971004\pi$
$572$	−3.10540e11	−	5.37871e11i	−0.121293	−	0.210085i
$573$	−1.22977e12	−	3.60091e12i	−0.476570	−	1.39546i
$574$	2.06658e11	−	3.57943e11i	0.0794602	−	0.137629i
$575$	3.55485e12			1.35617
$576$	2.05891e11	+	1.52048e12i	0.0779356	+	0.575546i
$577$	9.24466e11			0.347216			0.173608	−	0.984815i	$-0.444457\pi$
$577$	9.24466e11			0.347216			0.173608	+	0.984815i	$0.444457\pi$
$578$	−2.33477e12	+	4.04395e12i	−0.870101	+	1.50706i
$579$	1.03612e12	+	2.04109e11i	0.383139	+	0.0754758i
$580$	7.70955e12	+	1.33533e13i	2.82881	+	4.89964i
$581$	−2.43301e10	−	4.21410e10i	−0.00885832	−	0.0153431i
$582$	−3.83652e12	−	7.55768e11i	−1.38606	−	0.273046i
$583$	−4.35658e11	+	7.54583e11i	−0.156184	+	0.270519i
$584$	−9.56750e10			−0.0340362
$585$	2.77872e12	+	1.13898e12i	0.980941	+	0.402081i
$586$	3.29309e12			1.15362
$587$	1.67810e12	−	2.90655e12i	0.583373	−	1.01043i	−0.411704	−	0.911318i	$-0.635066\pi$
$587$	1.67810e12	−	2.90655e12i	0.583373	−	1.01043i	0.995076	−	0.0991132i	$-0.0316006\pi$
$588$	−1.05665e12	−	3.09402e12i	−0.364531	−	1.06739i
$589$	4.67152e9	+	8.09131e9i	0.00159934	+	0.00277013i
$590$	−3.91462e12	−	6.78032e12i	−1.33001	−	2.30365i
$591$	−7.30237e11	+	8.35784e11i	−0.246218	+	0.281806i
$592$	−2.95672e12	+	5.12119e12i	−0.989379	+	1.71365i
$593$	−2.23226e12			−0.741308			−0.370654	−	0.928771i	$-0.620866\pi$
$593$	−2.23226e12			−0.741308			−0.370654	+	0.928771i	$0.620866\pi$
$594$	−5.47003e10	+	9.11949e11i	−0.0180281	+	0.300560i
$595$	4.01811e11			0.131430
$596$	−5.68186e11	+	9.84127e11i	−0.184452	+	0.319480i
$597$	−1.82772e12	+	2.09189e12i	−0.588877	+	0.673992i
$598$	−1.68268e12	−	2.91449e12i	−0.538079	−	0.931980i
$599$	9.21454e11	+	1.59601e12i	0.292451	+	0.506540i	0.974389	−	0.224870i	$-0.0721959\pi$
$599$	9.21454e11	+	1.59601e12i	0.292451	+	0.506540i	−0.681938	+	0.731410i	$0.738863\pi$
$600$	−3.03271e12	−	8.88015e12i	−0.955322	−	2.79731i
$601$	1.67573e11	−	2.90245e11i	0.0523925	−	0.0907464i	−0.838640	−	0.544687i	$-0.816649\pi$
$601$	1.67573e11	−	2.90245e11i	0.0523925	−	0.0907464i	0.891032	+	0.453940i	$0.149982\pi$
$602$	−3.84270e12			−1.19248
$603$	−1.52823e12	+	1.18164e12i	−0.470717	+	0.363964i
$604$	8.99234e12			2.74920
$605$	−2.52656e12	+	4.37613e12i	−0.766709	+	1.32798i
$606$	−1.71163e12	−	3.37180e11i	−0.515565	−	0.101563i
$607$	−1.50886e10	−	2.61342e10i	−0.00451128	−	0.00781376i	0.863761	−	0.503902i	$-0.168103\pi$
$607$	−1.50886e10	−	2.61342e10i	−0.00451128	−	0.00781376i	−0.868272	+	0.496088i	$0.834769\pi$
$608$	1.68274e10	+	2.91458e10i	0.00499401	+	0.00864989i
$609$	−3.84989e12	−	7.58402e11i	−1.13415	−	0.223420i
$610$	5.24287e12	−	9.08092e12i	1.53315	−	2.65550i
$611$	2.36195e12			0.685623
$612$	7.08060e11	−	5.47480e11i	0.204027	−	0.157756i
$613$	−6.97355e11			−0.199472			−0.0997360	−	0.995014i	$-0.531800\pi$
$613$	−6.97355e11			−0.199472			−0.0997360	+	0.995014i	$0.531800\pi$
$614$	3.20940e12	−	5.55885e12i	0.911310	−	1.57844i
$615$	−2.38157e11	−	6.97355e11i	−0.0671314	−	0.196569i
$616$	−4.12193e11	−	7.13940e11i	−0.115342	−	0.199778i
$617$	5.30375e11	+	9.18636e11i	0.147333	+	0.255188i	0.930241	−	0.366949i	$-0.119598\pi$
$617$	5.30375e11	+	9.18636e11i	0.147333	+	0.255188i	−0.782908	+	0.622138i	$0.786264\pi$
$618$	2.87660e12	−	3.29238e12i	0.793288	−	0.907949i
$619$	−3.84166e10	+	6.65395e10i	−0.0105175	+	0.0182168i	−0.871236	−	0.490864i	$-0.836681\pi$
$619$	−3.84166e10	+	6.65395e10i	−0.0105175	+	0.0182168i	0.860719	+	0.509081i	$0.170015\pi$
$620$	1.77223e12			0.481679
$621$	−2.01397e11	+	3.35764e12i	−0.0543426	+	0.905986i
$622$	−4.16027e12			−1.11446
$623$	1.56887e12	−	2.71735e12i	0.417243	−	0.722687i
$624$	−2.29884e12	+	2.63111e12i	−0.606984	+	0.694717i
$625$	4.98828e11	+	8.63996e11i	0.130765	+	0.226491i
$626$	−6.94699e11	−	1.20325e12i	−0.180806	−	0.313165i
$627$	−4.74027e9	−	1.38801e10i	−0.00122490	−	0.00358665i
$628$	−2.19038e11	+	3.79384e11i	−0.0561953	+	0.0973331i
$629$	−6.87650e11			−0.175162
$630$	6.98155e12	+	2.86169e12i	1.76571	+	0.723752i
$631$	−7.39558e12			−1.85712			−0.928560	−	0.371183i	$-0.878952\pi$
$631$	−7.39558e12			−1.85712			−0.928560	+	0.371183i	$0.878952\pi$
$632$	−5.34985e12	+	9.26621e12i	−1.33387	+	2.31034i
$633$	−3.82663e12	−	7.53821e11i	−0.947327	−	0.186617i
$634$	3.36083e12	+	5.82112e12i	0.826123	+	1.43089i
$635$	4.75585e12	+	8.23737e12i	1.16077	+	2.01051i
$636$	1.57272e13	+	3.09815e12i	3.81148	+	0.750836i
$637$	−7.42075e11	+	1.28531e12i	−0.178575	+	0.309301i
$638$	2.12932e12			0.508801
$639$	−8.34234e11	−	6.16073e12i	−0.197940	−	1.46177i
$640$	−9.88792e12			−2.32967
$641$	1.18942e12	−	2.06014e12i	0.278275	−	0.481987i	−0.692681	−	0.721244i	$-0.743571\pi$
$641$	1.18942e12	−	2.06014e12i	0.278275	−	0.481987i	0.970956	+	0.239257i	$0.0769040\pi$
$642$	7.63311e11	+	2.23507e12i	0.177335	+	0.519259i
$643$	−3.16832e12	−	5.48768e12i	−0.730936	−	1.26602i	−0.956484	−	0.291785i	$-0.905751\pi$
$643$	−3.16832e12	−	5.48768e12i	−0.730936	−	1.26602i	0.225548	−	0.974232i	$-0.427583\pi$
$644$	−2.87268e12	−	4.97564e12i	−0.658115	−	1.13989i
$645$	−4.50774e12	+	5.15928e12i	−1.02551	+	1.17374i
$646$	−1.05737e10	+	1.83142e10i	−0.00238881	+	0.00413754i
$647$	1.61691e11			0.0362759			0.0181379	−	0.999835i	$-0.494226\pi$
$647$	1.61691e11			0.0362759			0.0181379	+	0.999835i	$0.494226\pi$
$648$	8.55933e12	−	2.36136e12i	1.90701	−	0.526109i
$649$	−7.34651e11			−0.162547
$650$	−4.03152e12	+	6.98280e12i	−0.885847	+	1.53433i
$651$	−2.96738e11	+	3.39628e11i	−0.0647528	+	0.0741121i
$652$	−2.48475e12	−	4.30372e12i	−0.538479	−	0.932674i
$653$	−1.08212e12	−	1.87428e12i	−0.232897	−	0.403390i	0.725762	−	0.687946i	$-0.241487\pi$
$653$	−1.08212e12	−	1.87428e12i	−0.232897	−	0.403390i	−0.958660	+	0.284556i	$0.908154\pi$
$654$	3.29491e12	+	9.64793e12i	0.704278	+	2.06222i
$655$	3.00371e11	−	5.20257e11i	0.0637634	−	0.110442i
$656$	8.57338e11			0.180753
$657$	−1.10259e10	−	8.14251e10i	−0.00230871	−	0.0170496i
$658$	5.93442e12			1.23413
$659$	1.01477e12	−	1.75764e12i	0.209597	−	0.363032i	−0.741991	−	0.670410i	$-0.766118\pi$
$659$	1.01477e12	−	1.75764e12i	0.209597	−	0.363032i	0.951588	+	0.307378i	$0.0994515\pi$
$660$	−2.72969e12	−	5.37731e11i	−0.559971	−	0.110311i
$661$	2.20704e12	+	3.82270e12i	0.449680	+	0.778868i	0.998365	−	0.0571607i	$-0.0182047\pi$
$661$	2.20704e12	+	3.82270e12i	0.449680	+	0.778868i	−0.548685	+	0.836029i	$0.684871\pi$
$662$	−1.78143e12	−	3.08553e12i	−0.360503	−	0.624409i
$663$	−3.98631e11	−	7.85277e10i	−0.0801235	−	0.0157838i
$664$	1.28318e11	−	2.22254e11i	0.0256172	−	0.0443703i
$665$	−1.21136e11			−0.0240202
$666$	−1.19481e13	−	4.89743e12i	−2.35322	−	0.964571i
$667$	7.83979e12			1.53369
$668$	4.60959e12	−	7.98404e12i	0.895711	−	1.55142i
$669$	1.38759e12	+	4.06305e12i	0.267821	+	0.784214i
$670$	−4.32890e12	−	7.49788e12i	−0.829930	−	1.43748i
$671$	−4.91961e11	−	8.52101e11i	−0.0936869	−	0.162271i
$672$	−1.06888e12	+	1.22338e12i	−0.202194	+	0.231419i
$673$	3.63786e12	−	6.30096e12i	0.683563	−	1.18397i	−0.290323	−	0.956929i	$-0.593763\pi$
$673$	3.63786e12	−	6.30096e12i	0.683563	−	1.18397i	0.973886	−	0.227037i	$-0.0729039\pi$
$674$	8.09115e11			0.151022
$675$	7.20804e12	−	3.60439e12i	1.33644	−	0.668290i
$676$	−6.32371e12			−1.16469
$677$	2.66342e12	−	4.61318e12i	0.487294	−	0.844018i	−0.512599	−	0.858628i	$-0.671317\pi$
$677$	2.66342e12	−	4.61318e12i	0.487294	−	0.844018i	0.999893	+	0.0146098i	$0.00465061\pi$
$678$	−8.25835e11	+	9.45199e11i	−0.150093	+	0.171787i
$679$	1.51517e12	+	2.62434e12i	0.273556	+	0.473813i
$680$	1.05959e12	+	1.83526e12i	0.190040	+	0.329160i
$681$	5.34031e11	+	1.56371e12i	0.0951490	+	0.278609i
$682$	1.22369e11	−	2.11950e11i	0.0216592	−	0.0375148i
$683$	−4.26484e12			−0.749910			−0.374955	−	0.927043i	$-0.622342\pi$
$683$	−4.26484e12			−0.749910			−0.374955	+	0.927043i	$0.622342\pi$
$684$	−2.13462e11	+	1.65052e11i	−0.0372880	+	0.0288315i
$685$	4.38859e11			0.0761583
$686$	−5.36879e12	+	9.29902e12i	−0.925589	+	1.60317i
$687$	1.09436e13	+	2.15582e12i	1.87437	+	0.369238i
$688$	−3.98543e12	−	6.90296e12i	−0.678152	−	1.17459i
$689$	−3.63821e12	−	6.30156e12i	−0.615036	−	1.06527i
$690$	−1.47910e13	−	2.91373e12i	−2.48414	−	0.489360i
$691$	−3.04089e12	+	5.26698e12i	−0.507400	+	0.878842i	0.492564	+	0.870276i	$0.336060\pi$
$691$	−3.04089e12	+	5.26698e12i	−0.507400	+	0.878842i	−0.999963	+	0.00856561i	$0.997273\pi$
$692$	−7.67556e12			−1.27243
$693$	5.60103e11	−	4.33078e11i	0.0922504	−	0.0713290i
$694$	1.04369e13			1.70787
$695$	−6.18367e12	+	1.07104e13i	−1.00534	+	1.74131i
$696$	−6.68827e12	−	1.95841e13i	−1.08037	−	3.16346i
$697$	4.98482e10	+	8.63396e10i	0.00800022	+	0.0138568i
$698$	7.27406e12	+	1.25990e13i	1.15992	+	2.00904i
$699$	2.25773e12	−	2.58406e12i	0.357705	−	0.409408i
$700$	−6.88264e12	+	1.19211e13i	−1.08346	+	1.87661i
$701$	1.02189e12			0.159835			0.0799174	−	0.996801i	$-0.474534\pi$
$701$	1.02189e12			0.159835			0.0799174	+	0.996801i	$0.474534\pi$
$702$	−6.36702e12	−	4.20347e12i	−0.989507	−	0.653268i
$703$	2.07310e11			0.0320126
$704$	−3.22633e11	+	5.58817e11i	−0.0495030	+	0.0857417i
$705$	6.96148e12	−	7.96767e12i	1.06133	−	1.21473i
$706$	5.71810e12	+	9.90404e12i	0.866225	+	1.50035i
$707$	6.75980e11	+	1.17083e12i	0.101753	+	0.176241i
$708$	4.36794e12	+	1.27899e13i	0.653322	+	1.91301i
$709$	9.54547e11	−	1.65332e12i	0.141870	−	0.245725i	−0.786331	−	0.617805i	$-0.788022\pi$
$709$	9.54547e11	−	1.65332e12i	0.141870	−	0.245725i	0.928201	+	0.372080i	$0.121355\pi$
$710$	2.78630e13			4.11496
$711$	−8.50263e12	−	3.48517e12i	−1.24779	−	0.511459i
$712$	1.65485e13			2.41324
$713$	4.50542e11	−	7.80362e11i	0.0652879	−	0.113082i
$714$	−1.00156e12	−	1.97301e11i	−0.144224	−	0.0284111i
$715$	6.31466e11	+	1.09373e12i	0.0903593	+	0.156507i
$716$	−6.76665e12	−	1.17202e13i	−0.962199	−	1.66658i
$717$	−2.84869e12	−	5.61173e11i	−0.402540	−	0.0792977i
$718$	−7.10330e12	+	1.23033e13i	−0.997471	+	1.72767i
$719$	−4.88529e12			−0.681726			−0.340863	−	0.940113i	$-0.610719\pi$
$719$	−4.88529e12			−0.681726			−0.340863	+	0.940113i	$0.610719\pi$
$720$	2.10017e12	+	1.55095e13i	0.291245	+	2.15081i
$721$	−3.38819e12			−0.466938
$722$	−6.44537e12	+	1.11637e13i	−0.882735	+	1.52894i
$723$	−2.32487e12	−	6.80753e12i	−0.316430	−	0.926547i
$724$	−2.92348e12	−	5.06362e12i	−0.395437	−	0.684917i
$725$	−9.39165e12	−	1.62668e13i	−1.26247	−	2.18666i
$726$	8.44656e12	−	9.66741e12i	1.12841	−	1.29150i
$727$	5.08696e12	−	8.81087e12i	0.675388	−	1.16981i	−0.300967	−	0.953635i	$-0.597309\pi$
$727$	5.08696e12	−	8.81087e12i	0.675388	−	1.16981i	0.976355	−	0.216172i	$-0.0693573\pi$
$728$	6.88450e12			0.908408
$729$	2.99607e12	+	7.01237e12i	0.392896	+	0.919583i
$730$	3.68260e11			0.0479957
$731$	4.63449e11	−	8.02718e11i	0.0600308	−	0.103976i
$732$	−1.19097e13	+	1.36310e13i	−1.53320	+	1.75481i
$733$	6.27206e12	+	1.08635e13i	0.802495	+	1.38996i	0.917969	+	0.396651i	$0.129828\pi$
$733$	6.27206e12	+	1.08635e13i	0.802495	+	1.38996i	−0.115475	+	0.993310i	$0.536839\pi$
$734$	−3.66541e12	−	6.34868e12i	−0.466112	−	0.807330i
$735$	2.14865e12	+	6.29153e12i	0.271564	+	0.795175i
$736$	1.62291e12	−	2.81095e12i	0.203865	−	0.353105i
$737$	−8.12398e11			−0.101430
$738$	2.51213e11	+	1.85518e12i	0.0311738	+	0.230215i
$739$	−9.22997e12			−1.13841			−0.569207	−	0.822194i	$-0.692750\pi$
$739$	−9.22997e12			−1.13841			−0.569207	+	0.822194i	$0.692750\pi$
$740$	1.96617e13	−	3.40551e13i	2.41034	−	4.17483i
$741$	1.20177e11	+	2.36741e10i	0.0146434	+	0.00288464i
$742$	−9.14102e12	−	1.58327e13i	−1.10708	−	1.91751i
$743$	5.91953e12	+	1.02529e13i	0.712587	+	1.23424i	0.963883	+	0.266326i	$0.0858099\pi$
$743$	5.91953e12	+	1.02529e13i	0.712587	+	1.23424i	−0.251296	+	0.967910i	$0.580857\pi$
$744$	−2.33374e12	−	4.59732e11i	−0.279238	−	0.0550081i
$745$	1.15538e12	−	2.00117e12i	0.137411	−	0.238002i
$746$	1.46588e13			1.73290
$747$	2.03939e11	+	8.35931e10i	0.0239639	+	0.00982263i
$748$	3.76401e11			0.0439636
$749$	9.15173e11	−	1.58513e12i	0.106251	−	0.184033i
$750$	3.86093e12	+	1.13053e13i	0.445570	+	1.30469i
$751$	3.65219e12	+	6.32577e12i	0.418960	+	0.725661i	0.995835	−	0.0911718i	$-0.0290612\pi$
$751$	3.65219e12	+	6.32577e12i	0.418960	+	0.725661i	−0.576875	+	0.816833i	$0.695728\pi$
$752$	6.15484e12	+	1.06605e13i	0.701838	+	1.21562i
$753$	−9.49117e12	+	1.08630e13i	−1.07583	+	1.23133i
$754$	−8.89103e12	+	1.53997e13i	−1.00180	+	1.73517i
$755$	−1.82855e13			−2.04807
$756$	−1.08698e13	−	7.17620e12i	−1.21025	−	0.799000i
$757$	4.96772e12			0.549827			0.274913	−	0.961469i	$-0.411351\pi$
$757$	4.96772e12			0.549827			0.274913	+	0.961469i	$0.411351\pi$
$758$	1.91168e12	−	3.31113e12i	0.210331	−	0.364304i
$759$	−9.30728e11	+	1.06525e12i	−0.101797	+	0.116511i
$760$	−3.19439e11	−	5.53284e11i	−0.0347317	−	0.0601571i
$761$	7.26962e12	+	1.25914e13i	0.785744	+	1.36095i	0.928554	+	0.371198i	$0.121053\pi$
$761$	7.26962e12	+	1.25914e13i	0.785744	+	1.36095i	−0.142810	+	0.989750i	$0.545614\pi$
$762$	−7.80973e12	−	2.28679e13i	−0.839148	−	2.45714i
$763$	3.95044e12	−	6.84236e12i	0.421973	−	0.730879i
$764$	−2.94389e13			−3.12609
$765$	−1.43980e12	+	1.11327e12i	−0.151994	+	0.117523i
$766$	−2.85547e13			−2.99674
$767$	3.06755e12	−	5.31316e12i	0.320046	−	0.554337i
$768$	1.91529e13	+	3.77300e12i	1.98659	+	0.391346i
$769$	−6.05017e12	−	1.04792e13i	−0.623877	−	1.08059i	−0.988757	−	0.149532i	$-0.952223\pi$
$769$	−6.05017e12	−	1.04792e13i	−0.623877	−	1.08059i	0.364880	−	0.931054i	$-0.381110\pi$
$770$	1.58656e12	+	2.74801e12i	0.162648	+	0.281715i
$771$	8.00968e12	+	1.57785e12i	0.816339	+	0.160813i
$772$	4.08508e12	−	7.07557e12i	0.413926	−	0.716941i
$773$	−7.51240e12			−0.756782			−0.378391	−	0.925646i	$-0.623523\pi$
$773$	−7.51240e12			−0.756782			−0.378391	+	0.925646i	$0.623523\pi$
$774$	1.37695e13	−	1.06467e13i	1.37906	−	1.06630i
$775$	−2.15890e12			−0.214969
$776$	−7.99106e12	+	1.38409e13i	−0.791091	+	1.37021i
$777$	3.23416e12	+	9.47004e12i	0.318322	+	0.932089i
$778$	7.79832e12	+	1.35071e13i	0.763120	+	1.32176i
$779$	−1.50280e10	−	2.60292e10i	−0.00146212	−	0.00253246i
$780$	1.52869e13	−	1.74964e13i	1.47874	−	1.69248i
$781$	1.30725e12	−	2.26423e12i	0.125727	−	0.217766i
$782$	2.03955e12			0.195031
$783$	1.58965e13	−	7.94905e12i	1.51138	−	0.755766i
$784$	−7.73489e12			−0.731192
$785$	4.45401e11	−	7.71458e11i	0.0418637	−	0.0725101i
$786$	−1.00417e12	+	1.14931e12i	−0.0938440	+	0.107408i
$787$	−3.04156e12	−	5.26813e12i	−0.282624	−	0.489520i	0.689406	−	0.724375i	$-0.257872\pi$
$787$	−3.04156e12	−	5.26813e12i	−0.282624	−	0.489520i	−0.972030	+	0.234856i	$0.924538\pi$
$788$	4.29329e12	+	7.43620e12i	0.396664	+	0.687042i
$789$	−2.57020e12	−	7.52588e12i	−0.236113	−	0.691371i
$790$	2.05920e13	−	3.56663e13i	1.88094	−	3.25789i
$791$	9.72707e11			0.0883462
$792$	3.45507e12	+	1.41621e12i	0.312028	+	0.127898i
$793$	8.21678e12			0.737857
$794$	−6.37618e11	+	1.10439e12i	−0.0569336	+	0.0986118i
$795$	−3.19804e13	−	6.29992e12i	−2.83943	−	0.559349i
$796$	1.07457e13	+	1.86122e13i	0.948696	+	1.64319i
$797$	3.72388e12	+	6.44995e12i	0.326914	+	0.566231i	0.981898	−	0.189412i	$-0.0606581\pi$
$797$	3.72388e12	+	6.44995e12i	0.326914	+	0.566231i	−0.654984	+	0.755643i	$0.727325\pi$
$798$	3.01946e11	+	5.94814e10i	0.0263583	+	0.00519240i
$799$	−7.15722e11	+	1.23967e12i	−0.0621275	+	0.107608i
$800$	−7.77661e12			−0.671252
$801$	1.90711e12	+	1.40838e13i	0.163693	+	1.20885i
$802$	2.33141e13			1.98992
$803$	1.72777e10	−	2.99259e10i	0.00146645	−	0.00253996i
$804$	4.83020e12	+	1.41435e13i	0.407674	+	1.19372i
$805$	5.84145e12	+	1.01177e13i	0.490275	+	0.849181i
$806$	1.02191e12	+	1.77000e12i	0.0852915	+	0.147729i
$807$	−1.14905e13	+	1.31513e13i	−0.953690	+	1.09154i
$808$	−3.56515e12	+	6.17502e12i	−0.294257	+	0.509668i
$809$	7.32627e12			0.601333			0.300666	−	0.953729i	$-0.402791\pi$
$809$	7.32627e12			0.601333			0.300666	+	0.953729i	$0.402791\pi$
$810$	−3.29455e13	+	9.08907e12i	−2.68914	+	0.741886i
$811$	−1.94054e13			−1.57517			−0.787586	−	0.616205i	$-0.788669\pi$
$811$	−1.94054e13			−1.57517			−0.787586	+	0.616205i	$0.788669\pi$
$812$	−1.51788e13	+	2.62905e13i	−1.22528	+	2.12225i
$813$	1.58850e13	−	1.81809e13i	1.27520	−	1.45952i
$814$	−2.71521e12	−	4.70288e12i	−0.216767	−	0.375452i
$815$	5.05262e12	+	8.75139e12i	0.401150	+	0.694812i
$816$	−6.84336e11	−	2.00382e12i	−0.0540335	−	0.158217i
$817$	−1.39718e11	+	2.41999e11i	−0.0109712	+	0.0190027i
$818$	−2.38566e13			−1.86302
$819$	7.93392e11	+	5.85912e12i	0.0616184	+	0.455045i
$820$	−5.70115e12			−0.440352
$821$	2.58219e12	−	4.47249e12i	0.198356	−	0.343562i	−0.749640	−	0.661846i	$-0.769773\pi$
$821$	2.58219e12	−	4.47249e12i	0.198356	−	0.343562i	0.947995	+	0.318284i	$0.103107\pi$
$822$	−1.09391e12	−	2.15493e11i	−0.0835714	−	0.0164630i
$823$	1.05680e12	+	1.83043e12i	0.0802957	+	0.139076i	0.903377	−	0.428847i	$-0.141080\pi$
$823$	1.05680e12	+	1.83043e12i	0.0802957	+	0.139076i	−0.823081	+	0.567924i	$0.807747\pi$
$824$	−8.93475e12	−	1.54754e13i	−0.675165	−	1.16942i
$825$	3.32526e12	+	6.55055e11i	0.249910	+	0.0492305i
$826$	7.70725e12	−	1.33493e13i	0.576089	−	0.997815i
$827$	1.74289e13			1.29567			0.647835	−	0.761781i	$-0.275675\pi$
$827$	1.74289e13			1.29567			0.647835	+	0.761781i	$0.275675\pi$
$828$	2.40793e13	+	9.86994e12i	1.78036	+	0.729756i
$829$	1.70846e13			1.25635			0.628173	−	0.778074i	$-0.283803\pi$
$829$	1.70846e13			1.25635			0.628173	+	0.778074i	$0.283803\pi$
$830$	−4.93906e11	+	8.55471e11i	−0.0361238	+	0.0625682i
$831$	6.07703e12	+	1.77943e13i	0.442065	+	1.29442i
$832$	−2.69432e12	−	4.66671e12i	−0.194937	−	0.337641i
$833$	−4.49729e11	−	7.78954e11i	−0.0323630	−	0.0560544i
$834$	2.06727e13	−	2.36607e13i	1.47962	−	1.69348i
$835$	−9.37335e12	+	1.62351e13i	−0.667276	+	1.15576i
$836$	−1.13476e11			−0.00803478
$837$	1.22311e11	−	2.03913e12i	0.00861391	−	0.143609i
$838$	−1.25017e13			−0.875734
$839$	1.15781e13	−	2.00539e13i	0.806696	−	1.39724i	−0.108444	−	0.994103i	$-0.534587\pi$
$839$	1.15781e13	−	2.00539e13i	0.806696	−	1.39724i	0.915140	−	0.403136i	$-0.132080\pi$
$840$	2.02910e13	−	2.32238e13i	1.40620	−	1.60944i
$841$	−1.34586e13	−	2.33109e13i	−0.927721	−	1.60686i
$842$	−1.21203e13	−	2.09929e13i	−0.831012	−	1.43935i
$843$	−5.69577e12	−	1.66780e13i	−0.388444	−	1.13742i
$844$	−1.50872e13	+	2.61317e13i	−1.02345	+	1.77267i
$845$	1.28589e13			0.867660
$846$	−2.12647e13	+	1.64421e13i	−1.42722	+	1.10355i
$847$	−9.94876e12			−0.664192
$848$	1.89611e13	−	3.28416e13i	1.25916	−	2.18094i
$849$	1.73857e12	+	3.42487e11i	0.114844	+	0.0226235i
$850$	−2.44327e12	−	4.23188e12i	−0.160541	−	0.278066i
$851$	−9.99693e12	−	1.73152e13i	−0.653406	−	1.13173i
$852$	−4.71915e13	−	9.29642e12i	−3.06821	−	0.604418i
$853$	−3.95259e12	+	6.84609e12i	−0.255630	+	0.442764i	−0.965066	−	0.262006i	$-0.915616\pi$
$853$	−3.95259e12	+	6.84609e12i	−0.255630	+	0.442764i	0.709437	+	0.704769i	$0.248949\pi$
$854$	2.06447e13			1.32815
$855$	4.34065e11	−	3.35624e11i	0.0277784	−	0.0214786i
$856$	9.65333e12			0.614533
$857$	−1.35356e13	+	2.34444e13i	−0.857164	+	1.48465i	0.0174588	+	0.999848i	$0.494442\pi$
$857$	−1.35356e13	+	2.34444e13i	−0.857164	+	1.48465i	−0.874623	+	0.484804i	$0.838891\pi$
$858$	−1.03695e12	−	3.03633e12i	−0.0653229	−	0.191274i
$859$	−1.35523e13	−	2.34733e13i	−0.849268	−	1.47098i	−0.881863	−	0.471506i	$-0.843710\pi$
$859$	−1.35523e13	−	2.34733e13i	−0.849268	−	1.47098i	0.0325947	−	0.999469i	$-0.489623\pi$
$860$	2.65024e13	+	4.59036e13i	1.65212	+	2.86156i
$861$	9.54587e11	−	1.09256e12i	0.0591972	−	0.0677535i
$862$	−9.05451e12	+	1.56829e13i	−0.558576	+	0.967482i
$863$	−1.94364e13			−1.19280			−0.596399	−	0.802688i	$-0.703402\pi$
$863$	−1.94364e13			−1.19280			−0.596399	+	0.802688i	$0.703402\pi$
$864$	4.40578e11	−	7.34520e12i	0.0268974	−	0.448427i
$865$	1.56079e13			0.947918
$866$	3.24175e12	−	5.61487e12i	0.195861	−	0.339242i
$867$	−1.07847e13	+	1.23435e13i	−0.648219	+	0.741911i
$868$	1.74462e12	+	3.02176e12i	0.104318	+	0.180685i
$869$	−1.93223e12	−	3.34672e12i	−0.114940	−	0.199081i
$870$	2.57437e13	+	7.53808e13i	1.52347	+	4.46091i
$871$	3.39219e12	−	5.87545e12i	0.199709	−	0.345907i
$872$	4.16696e13			2.44059
$873$	−1.27004e13	−	5.20579e12i	−0.740034	−	0.303335i
$874$	−6.14874e11			−0.0356439
$875$	4.62906e12	−	8.01777e12i	0.266967	−	0.462400i
$876$	−6.23721e11	−	1.22869e11i	−0.0357867	−	0.00704975i
$877$	−2.86815e12	−	4.96778e12i	−0.163721	−	0.283572i	0.772480	−	0.635040i	$-0.219016\pi$
$877$	−2.86815e12	−	4.96778e12i	−0.163721	−	0.283572i	−0.936200	+	0.351467i	$0.885683\pi$
$878$	−2.28585e13	−	3.95920e13i	−1.29814	−	2.24844i
$879$	1.13415e13	+	2.23421e12i	0.640799	+	0.126233i
$880$	−3.29099e12	+	5.70016e12i	−0.184993	+	0.320417i
$881$	1.87555e13			1.04891			0.524453	−	0.851439i	$-0.324270\pi$
$881$	1.87555e13			1.04891			0.524453	+	0.851439i	$0.324270\pi$
$882$	−2.26644e12	−	1.67374e13i	−0.126106	−	0.931280i
$883$	1.44505e13			0.799947			0.399973	−	0.916527i	$-0.369019\pi$
$883$	1.44505e13			0.799947			0.399973	+	0.916527i	$0.369019\pi$
$884$	−1.57167e12	+	2.72222e12i	−0.0865619	+	0.149930i
$885$	−8.88199e12	−	2.60076e13i	−0.486704	−	1.42513i
$886$	2.65378e13	+	4.59649e13i	1.44682	+	2.50596i
$887$	8.24167e12	+	1.42750e13i	0.447053	+	0.774318i	0.998193	−	0.0600948i	$-0.0191403\pi$
$887$	8.24167e12	+	1.42750e13i	0.447053	+	0.774318i	−0.551140	+	0.834413i	$0.685807\pi$
$888$	−3.47255e13	+	3.97446e13i	−1.87409	+	2.14496i
$889$	−9.36349e12	+	1.62180e13i	−0.502782	+	0.870844i
$890$	−6.36966e13			−3.40299
$891$	−8.07105e11	+	3.10368e12i	−0.0429023	+	0.164978i
$892$	3.32170e13			1.75679
$893$	2.15772e11	−	3.73729e11i	0.0113544	−	0.0196664i
$894$	−3.86255e12	+	4.42084e12i	−0.202235	+	0.231465i
$895$	1.37596e13	+	2.38324e13i	0.716808	+	1.24155i
$896$	−9.73385e12	−	1.68595e13i	−0.504543	−	0.873895i
$897$	−3.81787e12	−	1.11792e13i	−0.196904	−	0.576562i
$898$	1.05828e13	−	1.83300e13i	0.543072	−	0.940629i
$899$	−4.76120e12			−0.243107
$900$	−8.36652e12	−	6.17859e13i	−0.425063	−	3.13905i
$901$	4.40982e12			0.222925
$902$	−3.93654e11	+	6.81829e11i	−0.0198009	+	0.0342962i
$903$	−1.32344e13	−	2.60709e12i	−0.662383	−	0.130485i
$904$	2.56505e12	+	4.44280e12i	0.127743	+	0.221258i
$905$	5.94475e12	+	1.02966e13i	0.294588	+	0.510241i
$906$	4.55787e13	+	8.97870e12i	2.24742	+	0.442728i
$907$	−4.83281e11	+	8.37067e11i	−0.0237119	+	0.0410702i	−0.877638	−	0.479324i	$-0.840882\pi$
$907$	−4.83281e11	+	8.37067e11i	−0.0237119	+	0.0410702i	0.853926	+	0.520395i	$0.174215\pi$
$908$	1.27840e13			0.624136
$909$	−5.66617e12	−	2.32252e12i	−0.275266	−	0.112830i
$910$	−2.64990e13			−1.28098
$911$	−8.89072e8	+	1.53992e9i	−4.27666e−5	+	7.40739e-5i	−0.866047	−	0.499963i	$-0.833347\pi$
$911$	−8.89072e8	+	1.53992e9i	−4.27666e−5	+	7.40739e-5i	0.866004	+	0.500037i	$0.166680\pi$
$912$	2.06310e11	+	6.04103e11i	0.00987515	+	0.0289157i
$913$	4.63453e10	+	8.02724e10i	0.00220743	+	0.00382338i
$914$	2.12857e13	+	3.68679e13i	1.00886	+	1.74739i
$915$	2.42176e13	−	2.77180e13i	1.14219	−	1.30728i
$916$	4.31471e13	−	7.47329e13i	2.02498	−	3.50738i
$917$	1.18276e12			0.0552376
$918$	4.13553e12	−	2.06798e12i	0.192194	−	0.0961067i
$919$	1.23275e13			0.570105			0.285052	−	0.958512i	$-0.407989\pi$
$919$	1.23275e13			0.570105			0.285052	+	0.958512i	$0.407989\pi$
$920$	−3.08081e13	+	5.33612e13i	−1.41782	+	2.45573i
$921$	1.48247e13	−	1.69675e13i	0.678920	−	0.777049i
$922$	−1.64105e13	−	2.84238e13i	−0.747882	−	1.29537i
$923$	1.09169e13	+	1.89087e13i	0.495100	+	0.857539i
$924$	−1.77029e12	−	5.18364e12i	−0.0798952	−	0.233944i
$925$	−2.39516e13	+	4.14853e13i	−1.07571	+	1.86319i
$926$	−1.53171e13			−0.684584
$927$	1.21408e13	−	9.38744e12i	0.539996	−	0.417531i
$928$	−1.71504e13			−0.759116
$929$	−9.55300e12	+	1.65463e13i	−0.420794	+	0.728836i	−0.996017	−	0.0891604i	$-0.971582\pi$
$929$	−9.55300e12	+	1.65463e13i	−0.420794	+	0.728836i	0.575224	+	0.817996i	$0.304915\pi$
$930$	8.98275e12	+	1.76954e12i	0.393764	+	0.0775689i
$931$	1.35582e11	+	2.34835e11i	0.00591465	+	0.0102445i
$932$	−1.32739e13	−	2.29911e13i	−0.576272	−	0.998133i
$933$	−1.43281e13	−	2.82255e12i	−0.619045	−	0.121948i
$934$	−1.89688e13	+	3.28550e13i	−0.815605	+	1.41267i
$935$	−7.65392e11			−0.0327515
$936$	−2.46691e13	+	1.90744e13i	−1.05054	+	0.812288i
$937$	−4.13512e13			−1.75251			−0.876253	−	0.481851i	$-0.839965\pi$
$937$	−4.13512e13			−1.75251			−0.876253	+	0.481851i	$0.839965\pi$
$938$	8.52290e12	−	1.47621e13i	0.359480	−	0.622638i
$939$	−1.57622e12	−	4.61538e12i	−0.0661640	−	0.193737i
$940$	−4.09287e13	−	7.08906e13i	−1.70983	−	2.96151i
$941$	−2.10949e13	−	3.65375e13i	−0.877051	−	1.51910i	−0.854562	−	0.519349i	$-0.826174\pi$
$941$	−2.10949e13	−	3.65375e13i	−0.877051	−	1.51910i	−0.0224885	−	0.999747i	$-0.507159\pi$
$942$	−1.48902e12	+	1.70425e12i	−0.0616131	+	0.0705185i
$943$	−1.44937e12	+	2.51037e12i	−0.0596864	+	0.103380i
$944$	3.19741e13			1.31046
$945$	2.21032e13	+	1.45924e13i	0.901597	+	0.595229i
$946$	7.31977e12			0.297158
$947$	1.80301e13	−	3.12290e13i	0.728489	−	1.26178i	−0.229033	−	0.973419i	$-0.573556\pi$
$947$	1.80301e13	−	3.12290e13i	0.728489	−	1.26178i	0.957522	−	0.288361i	$-0.0931104\pi$
$948$	−4.67765e13	+	5.35375e13i	−1.88101	+	2.15288i
$949$	1.44287e11	+	2.49912e11i	0.00577470	+	0.0100021i
$950$	7.36587e11	+	1.27581e12i	0.0293405	+	0.0508192i
$951$	7.62546e12	+	2.23283e13i	0.302311	+	0.885206i
$952$	−2.08615e12	+	3.61332e12i	−0.0823151	+	0.142574i
$953$	−1.37784e13			−0.541104			−0.270552	−	0.962705i	$-0.587206\pi$
$953$	−1.37784e13			−0.541104			−0.270552	+	0.962705i	$0.587206\pi$
$954$	7.66215e13	+	3.14066e13i	2.99490	+	1.22759i
$955$	5.98624e13			2.32884
$956$	−1.12315e13	+	1.94535e13i	−0.434886	+	0.753245i
$957$	7.33347e12	+	1.44464e12i	0.282622	+	0.0556746i
$958$	−9.81906e12	−	1.70071e13i	−0.376639	−	0.652358i
$959$	4.32020e11	+	7.48281e11i	0.0164938	+	0.0285681i
$960$	−2.36835e13	−	4.66549e12i	−0.899964	−	0.177287i
$961$	1.29462e13	−	2.24235e13i	0.489651	−	0.848101i
$962$	4.53497e13			1.70721
$963$	1.11248e12	+	8.21555e12i	0.0416845	+	0.307835i
$964$	−5.56543e13			−2.07564
$965$	−8.30679e12	+	1.43878e13i	−0.308362	+	0.534098i
$966$	−9.59244e12	−	2.80879e13i	−0.354431	−	1.03782i
$967$	2.30760e13	+	3.99688e13i	0.848674	+	1.46995i	0.882392	+	0.470516i	$0.155932\pi$
$967$	2.30760e13	+	3.99688e13i	0.848674	+	1.46995i	−0.0337170	+	0.999431i	$0.510734\pi$
$968$	−2.62351e13	−	4.54406e13i	−0.960382	−	1.66343i
$969$	−4.88417e10	+	5.59011e10i	−0.00177965	+	0.00203687i
$970$	3.07582e13	−	5.32748e13i	1.11555	−	1.93218i
$971$	−2.79369e13			−1.00854			−0.504268	−	0.863547i	$-0.668237\pi$
$971$	−2.79369e13			−1.00854			−0.504268	+	0.863547i	$0.668237\pi$
$972$	5.88322e13	−	4.40195e12i	2.11406	−	0.158178i
$973$	−2.43493e13			−0.870919
$974$	−8.72776e12	+	1.51169e13i	−0.310733	+	0.538205i
$975$	−1.86222e13	+	2.13138e13i	−0.659949	+	0.755337i
$976$	2.14115e13	+	3.70859e13i	0.755307	+	1.30823i
$977$	−3.24140e12	−	5.61427e12i	−0.113817	−	0.197137i	0.803489	−	0.595319i	$-0.202974\pi$
$977$	−3.24140e12	−	5.61427e12i	−0.113817	−	0.197137i	−0.917306	+	0.398182i	$0.869641\pi$
$978$	−8.29706e12	−	2.42949e13i	−0.290001	−	0.849160i
$979$	−2.98846e12	+	5.17616e12i	−0.103974	+	0.180088i
$980$	5.14357e13			1.78134
$981$	4.80214e12	+	3.54633e13i	0.165548	+	1.22256i
$982$	7.36619e11			0.0252779
$983$	−1.05088e13	+	1.82018e13i	−0.358974	+	0.621761i	−0.987790	−	0.155793i	$-0.950207\pi$
$983$	−1.05088e13	+	1.82018e13i	−0.358974	+	0.621761i	0.628816	+	0.777554i	$0.283540\pi$
$984$	7.50750e12	+	1.47893e12i	0.255280	+	0.0502885i
$985$	−8.73019e12	−	1.51211e13i	−0.295502	−	0.511824i
$986$	−5.38835e12	−	9.33290e12i	−0.181556	−	0.314464i
$987$	2.04384e13	+	4.02623e12i	0.685519	+	0.135043i
$988$	4.73820e11	−	8.20681e11i	0.0158200	−	0.0274011i
$989$	2.69501e13			0.895731
$990$	−1.32988e13	−	5.45110e12i	−0.440002	−	0.180354i
$991$	−3.89754e13			−1.28369			−0.641844	−	0.766835i	$-0.721830\pi$
$991$	−3.89754e13			−1.28369			−0.641844	+	0.766835i	$0.721830\pi$
$992$	−9.85610e11	+	1.70713e12i	−0.0323149	+	0.0559710i
$993$	−4.04194e12	−	1.18353e13i	−0.131922	−	0.386286i
$994$	2.74289e13	+	4.75082e13i	0.891188	+	1.54358i
$995$	−2.18509e13	−	3.78468e13i	−0.706749	−	1.22412i
$996$	1.12195e12	−	1.28412e12i	0.0361250	−	0.0413464i
$997$	−1.31809e13	+	2.28300e13i	−0.422490	+	0.731774i	−0.996182	−	0.0872966i	$-0.972177\pi$
$997$	−1.31809e13	+	2.28300e13i	−0.422490	+	0.731774i	0.573692	+	0.819071i	$0.305511\pi$
$998$	−6.73497e12			−0.214906
$999$	−3.78269e13	−	2.49731e13i	−1.20159	−	0.793283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.10.c.a.7.8	yes	16
3.2	odd	2		27.10.c.a.19.1		16
9.2	odd	6		81.10.a.d.1.8		8
9.4	even	3	inner	9.10.c.a.4.8	✓	16
9.5	odd	6		27.10.c.a.10.1		16
9.7	even	3		81.10.a.c.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.10.c.a.4.8	✓	16	9.4	even	3	inner
9.10.c.a.7.8	yes	16	1.1	even	1	trivial
27.10.c.a.10.1		16	9.5	odd	6
27.10.c.a.19.1		16	3.2	odd	2
81.10.a.c.1.1		8	9.7	even	3
81.10.a.d.1.8		8	9.2	odd	6

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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	9.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(19.9839 - 34.6131i) q^{2} +(92.3087 - 105.651i) q^{3} +(-542.712 - 940.005i) q^{4} +(1103.58 + 1911.45i) q^{5} +(-1812.22 - 5306.41i) q^{6} +(-2172.76 + 3763.33i) q^{7} -22918.5 q^{8} +(-2641.20 - 19505.0i) q^{9} +O(q^{10})\)	\(q+(19.9839 - 34.6131i) q^{2} +(92.3087 - 105.651i) q^{3} +(-542.712 - 940.005i) q^{4} +(1103.58 + 1911.45i) q^{5} +(-1812.22 - 5306.41i) q^{6} +(-2172.76 + 3763.33i) q^{7} -22918.5 q^{8} +(-2641.20 - 19505.0i) q^{9} +88215.0 q^{10} +(4138.79 - 7168.59i) q^{11} +(-149409. - 29432.6i) q^{12} +(34563.2 + 59865.3i) q^{13} +(86840.4 + 150412. i) q^{14} +(303816. + 59849.7i) q^{15} +(-180132. + 311998. i) q^{16} -41893.6 q^{17} +(-727910. - 298365. i) q^{18} +12629.9 q^{19} +(1.19785e6 - 2.07473e6i) q^{20} +(197034. + 576942. i) q^{21} +(-165418. - 286513. i) q^{22} +(-609041. - 1.05489e6i) q^{23} +(-2.11558e6 + 2.42136e6i) q^{24} +(-1.45920e6 + 2.52740e6i) q^{25} +2.76283e6 q^{26} +(-2.30452e6 - 1.52144e6i) q^{27} +4.71673e6 q^{28} +(-3.21809e6 + 5.57389e6i) q^{29} +(8.14301e6 - 9.31999e6i) q^{30} +(369878. + 640648. i) q^{31} +(1.33234e6 + 2.30769e6i) q^{32} +(-375322. - 1.09899e6i) q^{33} +(-837198. + 1.45007e6i) q^{34} -9.59122e6 q^{35} +(-1.69014e7 + 1.30683e7i) q^{36} +1.64142e7 q^{37} +(252394. - 437160. i) q^{38} +(9.51531e6 + 1.87445e6i) q^{39} +(-2.52923e7 - 4.38075e7i) q^{40} +(-1.18987e6 - 2.06092e6i) q^{41} +(2.39073e7 + 4.70958e6i) q^{42} +(-1.10625e7 + 1.91609e7i) q^{43} -8.98468e6 q^{44} +(3.43680e7 - 2.65738e7i) q^{45} -4.86841e7 q^{46} +(1.70843e7 - 2.95908e7i) q^{47} +(1.63351e7 + 4.78312e7i) q^{48} +(1.07350e7 + 1.85936e7i) q^{49} +(5.83209e7 + 1.01015e8i) q^{50} +(-3.86715e6 + 4.42610e6i) q^{51} +(3.75158e7 - 6.49792e7i) q^{52} -1.05262e8 q^{53} +(-9.87150e7 + 4.93626e7i) q^{54} +1.82699e7 q^{55} +(4.97964e7 - 8.62498e7i) q^{56} +(1.16585e6 - 1.33436e6i) q^{57} +(1.28620e8 + 2.22776e8i) q^{58} +(-4.43759e7 - 7.68614e7i) q^{59} +(-1.08626e8 - 3.18070e8i) q^{60} +(5.94329e7 - 1.02941e8i) q^{61} +2.95664e7 q^{62} +(7.91424e7 + 3.24399e7i) q^{63} -7.79534e7 q^{64} +(-7.62863e7 + 1.32132e8i) q^{65} +(-4.55399e7 - 8.97105e6i) q^{66} +(-4.90722e7 - 8.49956e7i) q^{67} +(2.27362e7 + 3.93802e7i) q^{68} +(-1.67670e8 - 3.30299e7i) q^{69} +(-1.91670e8 + 3.31982e8i) q^{70} +3.15854e8 q^{71} +(6.05323e7 + 4.47025e8i) q^{72} +4.17458e6 q^{73} +(3.28020e8 - 5.68147e8i) q^{74} +(1.32326e8 + 3.87467e8i) q^{75} +(-6.85439e6 - 1.18722e7i) q^{76} +(1.79852e7 + 3.11513e7i) q^{77} +(2.55034e8 - 2.91896e8i) q^{78} +(2.33429e8 - 4.04312e8i) q^{79} -7.95157e8 q^{80} +(-3.73469e8 + 1.03033e8i) q^{81} -9.51133e7 q^{82} +(-5.59890e6 + 9.69757e6i) q^{83} +(4.35395e8 - 4.98327e8i) q^{84} +(-4.62328e7 - 8.00776e7i) q^{85} +(4.42145e8 + 7.65817e8i) q^{86} +(2.91829e8 + 8.54512e8i) q^{87} +(-9.48548e7 + 1.64293e8i) q^{88} -7.22061e8 q^{89} +(-2.32994e8 - 1.72063e9i) q^{90} -3.00391e8 q^{91} +(-6.61068e8 + 1.14500e9i) q^{92} +(1.01828e8 + 2.00594e7i) q^{93} +(-6.82820e8 - 1.18268e9i) q^{94} +(1.39380e7 + 2.41414e7i) q^{95} +(3.66796e8 + 7.22564e7i) q^{96} +(3.48673e8 - 6.03920e8i) q^{97} +8.58111e8 q^{98} +(-1.50755e8 - 6.17933e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9}+O(q^{10}) \) 16 * q + 15 * q^2 - 3 * q^3 - 1793 * q^4 + 453 * q^5 + 2439 * q^6 - 343 * q^7 - 14478 * q^8 - 15669 * q^9	\( 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9} + 1020 q^{10} + 99150 q^{11} - 241212 q^{12} + 32435 q^{13} + 394824 q^{14} + 723843 q^{15} - 328193 q^{16} - 831078 q^{17} - 1039500 q^{18} - 170554 q^{19} + 1855164 q^{20} - 503475 q^{21} + 529359 q^{22} + 1064559 q^{23} - 2686059 q^{24} - 2293229 q^{25} + 2436312 q^{26} - 6176520 q^{27} + 1225724 q^{28} - 1309053 q^{29} + 30713544 q^{30} - 2359819 q^{31} + 5760063 q^{32} - 19931472 q^{33} + 981801 q^{34} - 31066554 q^{35} - 48894093 q^{36} + 16391516 q^{37} + 39490203 q^{38} + 74528535 q^{39} - 16760496 q^{40} + 54747318 q^{41} + 25242354 q^{42} + 15249608 q^{43} - 332509926 q^{44} - 139865967 q^{45} + 2390520 q^{46} + 156295545 q^{47} + 312045027 q^{48} + 15239583 q^{49} + 315590163 q^{50} + 3098385 q^{51} - 19773358 q^{52} - 525516228 q^{53} - 591710103 q^{54} - 7579770 q^{55} + 470339790 q^{56} + 581271465 q^{57} + 55408560 q^{58} + 307774074 q^{59} - 430082172 q^{60} + 69192125 q^{61} - 914436924 q^{62} - 693544725 q^{63} - 403588478 q^{64} + 482470359 q^{65} + 1912534074 q^{66} + 14328044 q^{67} + 915409575 q^{68} - 724756329 q^{69} - 229271934 q^{70} - 1239601392 q^{71} - 1729340037 q^{72} + 598613198 q^{73} + 1022736000 q^{74} + 1477690413 q^{75} + 119954093 q^{76} + 717995541 q^{77} + 243023958 q^{78} + 30257531 q^{79} - 2927826528 q^{80} - 1055378241 q^{81} - 202376022 q^{82} + 1176168291 q^{83} + 1383634866 q^{84} + 4818366 q^{85} + 1426944009 q^{86} + 617958567 q^{87} + 911312427 q^{88} - 3317041296 q^{89} - 981417492 q^{90} - 739230122 q^{91} - 76813998 q^{92} - 552731577 q^{93} - 1954316784 q^{94} - 391400652 q^{95} + 1854064512 q^{96} - 267311278 q^{97} + 4827300318 q^{98} + 1672014609 q^{99}+O(q^{100}) \) 16 * q + 15 * q^2 - 3 * q^3 - 1793 * q^4 + 453 * q^5 + 2439 * q^6 - 343 * q^7 - 14478 * q^8 - 15669 * q^9 + 1020 * q^10 + 99150 * q^11 - 241212 * q^12 + 32435 * q^13 + 394824 * q^14 + 723843 * q^15 - 328193 * q^16 - 831078 * q^17 - 1039500 * q^18 - 170554 * q^19 + 1855164 * q^20 - 503475 * q^21 + 529359 * q^22 + 1064559 * q^23 - 2686059 * q^24 - 2293229 * q^25 + 2436312 * q^26 - 6176520 * q^27 + 1225724 * q^28 - 1309053 * q^29 + 30713544 * q^30 - 2359819 * q^31 + 5760063 * q^32 - 19931472 * q^33 + 981801 * q^34 - 31066554 * q^35 - 48894093 * q^36 + 16391516 * q^37 + 39490203 * q^38 + 74528535 * q^39 - 16760496 * q^40 + 54747318 * q^41 + 25242354 * q^42 + 15249608 * q^43 - 332509926 * q^44 - 139865967 * q^45 + 2390520 * q^46 + 156295545 * q^47 + 312045027 * q^48 + 15239583 * q^49 + 315590163 * q^50 + 3098385 * q^51 - 19773358 * q^52 - 525516228 * q^53 - 591710103 * q^54 - 7579770 * q^55 + 470339790 * q^56 + 581271465 * q^57 + 55408560 * q^58 + 307774074 * q^59 - 430082172 * q^60 + 69192125 * q^61 - 914436924 * q^62 - 693544725 * q^63 - 403588478 * q^64 + 482470359 * q^65 + 1912534074 * q^66 + 14328044 * q^67 + 915409575 * q^68 - 724756329 * q^69 - 229271934 * q^70 - 1239601392 * q^71 - 1729340037 * q^72 + 598613198 * q^73 + 1022736000 * q^74 + 1477690413 * q^75 + 119954093 * q^76 + 717995541 * q^77 + 243023958 * q^78 + 30257531 * q^79 - 2927826528 * q^80 - 1055378241 * q^81 - 202376022 * q^82 + 1176168291 * q^83 + 1383634866 * q^84 + 4818366 * q^85 + 1426944009 * q^86 + 617958567 * q^87 + 911312427 * q^88 - 3317041296 * q^89 - 981417492 * q^90 - 739230122 * q^91 - 76813998 * q^92 - 552731577 * q^93 - 1954316784 * q^94 - 391400652 * q^95 + 1854064512 * q^96 - 267311278 * q^97 + 4827300318 * q^98 + 1672014609 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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