LMFDB - Embedded newform 403.2.bk.a.9.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(9,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("403.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bk (of order $15$, degree $8$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$35$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.11
Character	$\chi$	$=$	403.9
Dual form			403.2.bk.a.224.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.736014 - 0.817427i) q^{2} +(2.06902 - 2.29788i) q^{3} +(0.0825875 - 0.785768i) q^{4} +(1.51346 + 2.62138i) q^{5} -3.40117 q^{6} +(2.69694 + 1.95944i) q^{7} +(-2.48286 + 1.80390i) q^{8} +(-0.685820 - 6.52514i) q^{9} +O(q^{10})$	\(q+(-0.736014 - 0.817427i) q^{2} +(2.06902 - 2.29788i) q^{3} +(0.0825875 - 0.785768i) q^{4} +(1.51346 + 2.62138i) q^{5} -3.40117 q^{6} +(2.69694 + 1.95944i) q^{7} +(-2.48286 + 1.80390i) q^{8} +(-0.685820 - 6.52514i) q^{9} +(1.02886 - 3.16652i) q^{10} +(-3.38559 - 2.45978i) q^{11} +(-1.63472 - 1.81554i) q^{12} +(3.37440 - 1.27021i) q^{13} +(-0.383287 - 3.64673i) q^{14} +(9.15499 + 1.94595i) q^{15} +(1.75632 + 0.373317i) q^{16} +(-2.06993 + 1.50389i) q^{17} +(-4.82905 + 5.36320i) q^{18} +(1.37458 - 4.23052i) q^{19} +(2.18479 - 0.972732i) q^{20} +(10.0826 - 2.14312i) q^{21} +(0.481157 + 4.57790i) q^{22} +(0.364574 + 3.46869i) q^{23} +(-0.991934 + 9.43762i) q^{24} +(-2.08110 + 3.60457i) q^{25} +(-3.52191 - 1.82343i) q^{26} +(-8.90827 - 6.47223i) q^{27} +(1.76240 - 1.95734i) q^{28} +(-5.52696 - 6.13832i) q^{29} +(-5.14753 - 8.91578i) q^{30} +(-3.69644 + 4.16370i) q^{31} +(2.08147 + 3.60521i) q^{32} +(-12.6571 + 2.69035i) q^{33} +(2.75282 + 0.585130i) q^{34} +(-1.05475 + 10.0352i) q^{35} -5.18389 q^{36} +(4.67192 + 8.09201i) q^{37} +(-4.46985 + 1.99010i) q^{38} +(4.06290 - 10.3820i) q^{39} +(-8.48642 - 3.77840i) q^{40} +(1.38635 - 4.26674i) q^{41} +(-9.17277 - 6.66441i) q^{42} +(-3.09404 + 9.52246i) q^{43} +(-2.21242 + 2.45714i) q^{44} +(16.0669 - 11.6733i) q^{45} +(2.56707 - 2.85102i) q^{46} +(0.649523 + 1.99903i) q^{47} +(4.49169 - 3.26341i) q^{48} +(1.27096 + 3.91161i) q^{49} +(4.47819 - 0.951869i) q^{50} +(-0.826963 + 7.86803i) q^{51} +(-0.719408 - 2.75640i) q^{52} +(2.39885 + 1.06804i) q^{53} +(1.26603 + 12.0455i) q^{54} +(1.32407 - 12.5977i) q^{55} -10.2308 q^{56} +(-6.87719 - 11.9116i) q^{57} +(-0.949698 + 9.03578i) q^{58} +(1.04831 + 3.22637i) q^{59} +(2.28516 - 7.03299i) q^{60} +(2.67977 + 4.64150i) q^{61} +(6.12415 - 0.0429752i) q^{62} +(10.9360 - 18.9417i) q^{63} +(2.52472 - 7.77028i) q^{64} +(8.43671 + 6.92318i) q^{65} +(11.5150 + 8.36613i) q^{66} -5.71825 q^{67} +(1.01076 + 1.75069i) q^{68} +(8.72493 + 6.33903i) q^{69} +(8.97939 - 6.52391i) q^{70} +(0.456341 + 4.34179i) q^{71} +(13.4735 + 14.9639i) q^{72} +(-0.970070 + 9.22960i) q^{73} +(3.17602 - 9.77479i) q^{74} +(3.97703 + 12.2400i) q^{75} +(-3.21068 - 1.42949i) q^{76} +(-4.31095 - 13.2677i) q^{77} +(-11.4769 + 4.32021i) q^{78} +(-1.16334 - 11.0685i) q^{79} +(1.67950 + 5.16898i) q^{80} +(-14.0507 + 2.98656i) q^{81} +(-4.50812 + 2.00714i) q^{82} +(-13.7527 + 2.92322i) q^{83} +(-0.851299 - 8.09957i) q^{84} +(-7.07502 - 3.15000i) q^{85} +(10.0612 - 4.47952i) q^{86} -25.5405 q^{87} +12.8431 q^{88} +(2.16716 - 0.964881i) q^{89} +(-21.3676 - 4.54182i) q^{90} +(11.5895 + 3.18625i) q^{91} +2.75569 q^{92} +(1.91967 + 17.1087i) q^{93} +(1.15600 - 2.00225i) q^{94} +(13.1702 - 2.79941i) q^{95} +(12.5909 + 2.67628i) q^{96} +(1.24409 - 11.8367i) q^{97} +(2.26201 - 3.91791i) q^{98} +(-13.7285 + 23.7784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9}+O(q^{10}) $ 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9} - 9 q^{10} - 6 q^{11} - 50 q^{12} - 6 q^{13} - 21 q^{15} + 23 q^{16} + 3 q^{17} - 15 q^{18} - 9 q^{19} + 60 q^{20} - 34 q^{21} + 41 q^{22} - 12 q^{23} - 89 q^{24} - 112 q^{25} + 39 q^{26} + 48 q^{27} + 66 q^{28} - 11 q^{29} + 24 q^{30} - 22 q^{31} + q^{32} - 37 q^{33} - 49 q^{34} + 41 q^{35} + 134 q^{36} + 17 q^{37} - 23 q^{38} + 10 q^{39} + 31 q^{40} + q^{41} - 71 q^{42} - 7 q^{43} - 42 q^{44} - 13 q^{45} + 21 q^{46} - 20 q^{47} - 3 q^{48} - 69 q^{49} - 42 q^{50} - 71 q^{51} - 140 q^{52} - 8 q^{53} - 149 q^{54} + 5 q^{55} - 126 q^{56} + 21 q^{57} + 79 q^{58} + 77 q^{59} + 2 q^{60} + 53 q^{61} + 72 q^{62} + 17 q^{63} - 91 q^{64} - 25 q^{65} - 62 q^{66} - 14 q^{67} + 83 q^{68} - 31 q^{69} + 134 q^{70} + 32 q^{71} - 70 q^{72} - 31 q^{73} + 51 q^{74} + 79 q^{75} + 98 q^{76} - 80 q^{77} - 141 q^{78} - 142 q^{79} + 6 q^{80} + 66 q^{81} - 48 q^{82} + 94 q^{83} + 130 q^{84} + 90 q^{85} - 34 q^{86} + 22 q^{87} - 122 q^{88} - 15 q^{89} + 43 q^{90} + 56 q^{91} - 294 q^{92} - 52 q^{93} - 57 q^{94} + 94 q^{95} + 24 q^{96} + 46 q^{97} + 73 q^{98} + 12 q^{99}+O(q^{100}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9 - 9 * q^10 - 6 * q^11 - 50 * q^12 - 6 * q^13 - 21 * q^15 + 23 * q^16 + 3 * q^17 - 15 * q^18 - 9 * q^19 + 60 * q^20 - 34 * q^21 + 41 * q^22 - 12 * q^23 - 89 * q^24 - 112 * q^25 + 39 * q^26 + 48 * q^27 + 66 * q^28 - 11 * q^29 + 24 * q^30 - 22 * q^31 + q^32 - 37 * q^33 - 49 * q^34 + 41 * q^35 + 134 * q^36 + 17 * q^37 - 23 * q^38 + 10 * q^39 + 31 * q^40 + q^41 - 71 * q^42 - 7 * q^43 - 42 * q^44 - 13 * q^45 + 21 * q^46 - 20 * q^47 - 3 * q^48 - 69 * q^49 - 42 * q^50 - 71 * q^51 - 140 * q^52 - 8 * q^53 - 149 * q^54 + 5 * q^55 - 126 * q^56 + 21 * q^57 + 79 * q^58 + 77 * q^59 + 2 * q^60 + 53 * q^61 + 72 * q^62 + 17 * q^63 - 91 * q^64 - 25 * q^65 - 62 * q^66 - 14 * q^67 + 83 * q^68 - 31 * q^69 + 134 * q^70 + 32 * q^71 - 70 * q^72 - 31 * q^73 + 51 * q^74 + 79 * q^75 + 98 * q^76 - 80 * q^77 - 141 * q^78 - 142 * q^79 + 6 * q^80 + 66 * q^81 - 48 * q^82 + 94 * q^83 + 130 * q^84 + 90 * q^85 - 34 * q^86 + 22 * q^87 - 122 * q^88 - 15 * q^89 + 43 * q^90 + 56 * q^91 - 294 * q^92 - 52 * q^93 - 57 * q^94 + 94 * q^95 + 24 * q^96 + 46 * q^97 + 73 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{15}\right)$

Coefficient data

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

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

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

$2$	−0.736014	−	0.817427i	−0.520441	−	0.578008i	0.424426	−	0.905463i	$-0.360476\pi$
$2$	−0.736014	−	0.817427i	−0.520441	−	0.578008i	−0.944867	+	0.327455i	$0.893809\pi$
$3$	2.06902	−	2.29788i	1.19455	−	1.32668i	0.262246	−	0.965001i	$-0.415537\pi$
$3$	2.06902	−	2.29788i	1.19455	−	1.32668i	0.932303	−	0.361679i	$-0.117797\pi$
$4$	0.0825875	−	0.785768i	0.0412938	−	0.392884i
$5$	1.51346	+	2.62138i	0.676838	+	1.17232i	0.975928	+	0.218093i	$0.0699837\pi$
$5$	1.51346	+	2.62138i	0.676838	+	1.17232i	−0.299090	+	0.954225i	$0.596683\pi$
$6$	−3.40117			−1.38852
$7$	2.69694	+	1.95944i	1.01935	+	0.740600i	0.966149	−	0.257984i	$-0.0830583\pi$
$7$	2.69694	+	1.95944i	1.01935	+	0.740600i	0.0531988	+	0.998584i	$0.483058\pi$
$8$	−2.48286	+	1.80390i	−0.877824	+	0.637776i
$9$	−0.685820	−	6.52514i	−0.228607	−	2.17505i
$10$	1.02886	−	3.16652i	0.325355	−	1.00134i
$11$	−3.38559	−	2.45978i	−1.02079	−	0.741650i	−0.0543488	−	0.998522i	$-0.517308\pi$
$11$	−3.38559	−	2.45978i	−1.02079	−	0.741650i	−0.966446	+	0.256872i	$0.917308\pi$
$12$	−1.63472	−	1.81554i	−0.471904	−	0.524103i
$13$	3.37440	−	1.27021i	0.935890	−	0.352293i
$13$	3.37440	−	1.27021i	0.935890	−	0.352293i
$14$	−0.383287	−	3.64673i	−0.102438	−	0.974630i
$15$	9.15499	+	1.94595i	2.36381	+	0.502443i
$16$	1.75632	+	0.373317i	0.439080	+	0.0933292i
$17$	−2.06993	+	1.50389i	−0.502032	+	0.364747i	−0.809792	−	0.586716i	$-0.800420\pi$
$17$	−2.06993	+	1.50389i	−0.502032	+	0.364747i	0.307761	+	0.951464i	$0.400420\pi$
$18$	−4.82905	+	5.36320i	−1.13822	+	1.26412i
$19$	1.37458	−	4.23052i	0.315350	−	0.970548i	−0.660260	−	0.751037i	$-0.729554\pi$
$19$	1.37458	−	4.23052i	0.315350	−	0.970548i	0.975610	−	0.219511i	$-0.0704460\pi$
$20$	2.18479	−	0.972732i	0.488534	−	0.217509i
$21$	10.0826	−	2.14312i	2.20020	−	0.467667i
$22$	0.481157	+	4.57790i	0.102583	+	0.976012i
$23$	0.364574	+	3.46869i	0.0760189	+	0.723271i	0.964451	+	0.264263i	$0.0851286\pi$
$23$	0.364574	+	3.46869i	0.0760189	+	0.723271i	−0.888432	+	0.459008i	$0.848205\pi$
$24$	−0.991934	+	9.43762i	−0.202478	+	1.92645i
$25$	−2.08110	+	3.60457i	−0.416220	+	0.720914i
$26$	−3.52191	−	1.82343i	−0.690703	−	0.357604i
$27$	−8.90827	−	6.47223i	−1.71440	−	1.24558i
$28$	1.76240	−	1.95734i	0.333062	−	0.369903i
$29$	−5.52696	−	6.13832i	−1.02633	−	1.13986i	−0.990079	−	0.140514i	$-0.955125\pi$
$29$	−5.52696	−	6.13832i	−1.02633	−	1.13986i	−0.0362528	−	0.999343i	$-0.511542\pi$
$30$	−5.14753	−	8.91578i	−0.939806	−	1.62779i
$31$	−3.69644	+	4.16370i	−0.663899	+	0.747822i
$31$	−3.69644	+	4.16370i	−0.663899	+	0.747822i
$32$	2.08147	+	3.60521i	0.367955	+	0.637317i
$33$	−12.6571	+	2.69035i	−2.20332	+	0.468330i
$34$	2.75282	+	0.585130i	0.472105	+	0.100349i
$35$	−1.05475	+	10.0352i	−0.178285	+	1.69627i
$36$	−5.18389			−0.863981
$37$	4.67192	+	8.09201i	0.768059	+	1.33032i	0.938614	+	0.344969i	$0.112111\pi$
$37$	4.67192	+	8.09201i	0.768059	+	1.33032i	−0.170555	+	0.985348i	$0.554556\pi$
$38$	−4.46985	+	1.99010i	−0.725105	+	0.322838i
$39$	4.06290	−	10.3820i	0.650585	−	1.66246i
$40$	−8.48642	−	3.77840i	−1.34182	−	0.597417i
$41$	1.38635	−	4.26674i	0.216511	−	0.666352i	−0.782532	−	0.622611i	$-0.786072\pi$
$41$	1.38635	−	4.26674i	0.216511	−	0.666352i	0.999043	−	0.0437419i	$-0.0139279\pi$
$42$	−9.17277	−	6.66441i	−1.41539	−	1.02834i
$43$	−3.09404	+	9.52246i	−0.471836	+	1.45216i	0.378342	+	0.925666i	$0.376494\pi$
$43$	−3.09404	+	9.52246i	−0.471836	+	1.45216i	−0.850178	+	0.526496i	$0.823506\pi$
$44$	−2.21242	+	2.45714i	−0.333535	+	0.370428i
$45$	16.0669	−	11.6733i	2.39512	−	1.74015i
$46$	2.56707	−	2.85102i	0.378493	−	0.420359i
$47$	0.649523	+	1.99903i	0.0947426	+	0.291588i	0.987187	−	0.159571i	$-0.0510109\pi$
$47$	0.649523	+	1.99903i	0.0947426	+	0.291588i	−0.892444	+	0.451158i	$0.851011\pi$
$48$	4.49169	−	3.26341i	0.648320	−	0.471032i
$49$	1.27096	+	3.91161i	0.181565	+	0.558801i
$50$	4.47819	−	0.951869i	0.633312	−	0.134615i
$51$	−0.826963	+	7.86803i	−0.115798	+	1.10174i
$52$	−0.719408	−	2.75640i	−0.0997640	−	0.382244i
$53$	2.39885	+	1.06804i	0.329508	+	0.146706i	0.564821	−	0.825213i	$-0.308945\pi$
$53$	2.39885	+	1.06804i	0.329508	+	0.146706i	−0.235314	+	0.971919i	$0.575612\pi$
$54$	1.26603	+	12.0455i	0.172285	+	1.63919i
$55$	1.32407	−	12.5977i	0.178538	−	1.69867i
$56$	−10.2308			−1.36714
$57$	−6.87719	−	11.9116i	−0.910906	−	1.57773i
$58$	−0.949698	+	9.03578i	−0.124702	+	1.18646i
$59$	1.04831	+	3.22637i	0.136478	+	0.420038i	0.995817	−	0.0913695i	$-0.0291244\pi$
$59$	1.04831	+	3.22637i	0.136478	+	0.420038i	−0.859339	+	0.511407i	$0.829124\pi$
$60$	2.28516	−	7.03299i	0.295012	−	0.907955i
$61$	2.67977	+	4.64150i	0.343110	+	0.594284i	0.985008	−	0.172506i	$-0.0551864\pi$
$61$	2.67977	+	4.64150i	0.343110	+	0.594284i	−0.641899	+	0.766789i	$0.721853\pi$
$62$	6.12415	−	0.0429752i	0.777767	−	0.00545786i
$63$	10.9360	−	18.9417i	1.37781	−	2.38644i
$64$	2.52472	−	7.77028i	0.315590	−	0.971285i
$65$	8.43671	+	6.92318i	1.04645	+	0.858715i
$66$	11.5150	+	8.36613i	1.41740	+	1.02980i
$67$	−5.71825			−0.698595			−0.349298	−	0.937012i	$-0.613580\pi$
$67$	−5.71825			−0.698595			−0.349298	+	0.937012i	$0.613580\pi$
$68$	1.01076	+	1.75069i	0.122573	+	0.212302i
$69$	8.72493	+	6.33903i	1.05036	+	0.763130i
$70$	8.97939	−	6.52391i	1.07324	−	0.779756i
$71$	0.456341	+	4.34179i	0.0541577	+	0.515276i	0.987650	+	0.156678i	$0.0500785\pi$
$71$	0.456341	+	4.34179i	0.0541577	+	0.515276i	−0.933492	+	0.358598i	$0.883255\pi$
$72$	13.4735	+	14.9639i	1.58787	+	1.76351i
$73$	−0.970070	+	9.22960i	−0.113538	+	1.08024i	0.778301	+	0.627891i	$0.216082\pi$
$73$	−0.970070	+	9.22960i	−0.113538	+	1.08024i	−0.891839	+	0.452352i	$0.850585\pi$
$74$	3.17602	−	9.77479i	0.369205	−	1.13630i
$75$	3.97703	+	12.2400i	0.459228	+	1.41336i
$76$	−3.21068	−	1.42949i	−0.368291	−	0.163974i
$77$	−4.31095	−	13.2677i	−0.491279	−	1.51200i
$78$	−11.4769	+	4.32021i	−1.29950	+	0.489168i
$79$	−1.16334	−	11.0685i	−0.130886	−	1.24530i	−0.840930	−	0.541144i	$-0.817992\pi$
$79$	−1.16334	−	11.0685i	−0.130886	−	1.24530i	0.710044	−	0.704158i	$-0.248675\pi$
$80$	1.67950	+	5.16898i	0.187774	+	0.577910i
$81$	−14.0507	+	2.98656i	−1.56118	+	0.331840i
$82$	−4.50812	+	2.00714i	−0.497838	+	0.221652i
$83$	−13.7527	+	2.92322i	−1.50955	+	0.320865i	−0.887020	−	0.461731i	$-0.847228\pi$
$83$	−13.7527	+	2.92322i	−1.50955	+	0.320865i	−0.622530	+	0.782596i	$0.713895\pi$
$84$	−0.851299	−	8.09957i	−0.0928843	−	0.883735i
$85$	−7.07502	−	3.15000i	−0.767394	−	0.341666i
$86$	10.0612	−	4.47952i	1.08492	−	0.483039i
$87$	−25.5405			−2.73823
$88$	12.8431			1.36908
$89$	2.16716	−	0.964881i	0.229718	−	0.102277i	−0.288650	−	0.957435i	$-0.593206\pi$
$89$	2.16716	−	0.964881i	0.229718	−	0.102277i	0.518368	+	0.855158i	$0.326540\pi$
$90$	−21.3676	−	4.54182i	−2.25234	−	0.478750i
$91$	11.5895	+	3.18625i	1.21491	+	0.334010i
$92$	2.75569			0.287301
$93$	1.91967	+	17.1087i	0.199061	+	1.77409i
$94$	1.15600	−	2.00225i	0.119232	−	0.206516i
$95$	13.1702	−	2.79941i	1.35123	−	0.287213i
$96$	12.5909	+	2.67628i	1.28506	+	0.273147i
$97$	1.24409	−	11.8367i	0.126318	−	1.20184i	−0.729286	−	0.684209i	$-0.760148\pi$
$97$	1.24409	−	11.8367i	0.126318	−	1.20184i	0.855605	−	0.517630i	$-0.173186\pi$
$98$	2.26201	−	3.91791i	0.228497	−	0.395769i
$99$	−13.7285	+	23.7784i	−1.37976	+	2.38982i
$100$	2.66048	+	1.93295i	0.266048	+	0.193295i
$101$	0.844643	+	8.03624i	0.0840451	+	0.799636i	0.952637	+	0.304108i	$0.0983585\pi$
$101$	0.844643	+	8.03624i	0.0840451	+	0.799636i	−0.868592	+	0.495527i	$0.834975\pi$
$102$	7.04019	−	5.11500i	0.697083	−	0.506460i
$103$	3.53070	−	0.750473i	0.347890	−	0.0739463i	−0.0306529	−	0.999530i	$-0.509759\pi$
$103$	3.53070	−	0.750473i	0.347890	−	0.0739463i	0.378543	+	0.925584i	$0.376425\pi$
$104$	−6.08682	+	9.24085i	−0.596862	+	0.906139i
$105$	20.8775	+	23.1868i	2.03743	+	2.26280i
$106$	−0.892547	−	2.74698i	−0.0866918	−	0.266810i
$107$	2.81782	+	1.25457i	0.272409	+	0.121284i	0.538395	−	0.842693i	$-0.319031\pi$
$107$	2.81782	+	1.25457i	0.272409	+	0.121284i	−0.265986	+	0.963977i	$0.585697\pi$
$108$	−5.82139	+	6.46530i	−0.560163	+	0.622124i
$109$	0.0497629	+	0.153154i	0.00476642	+	0.0146695i	0.953411	−	0.301673i	$-0.0975451\pi$
$109$	0.0497629	+	0.153154i	0.00476642	+	0.0146695i	−0.948645	+	0.316343i	$0.897545\pi$
$110$	−11.2722	+	8.18975i	−1.07476	+	0.780862i
$111$	28.2607	+	6.00700i	2.68239	+	0.570160i
$112$	4.00519	+	4.44822i	0.378455	+	0.420317i
$113$	10.7257	−	4.77538i	1.00899	−	0.449230i	0.165402	−	0.986226i	$-0.447108\pi$
$113$	10.7257	−	4.77538i	1.00899	−	0.449230i	0.843584	+	0.536997i	$0.180441\pi$
$114$	−4.67518	+	14.3887i	−0.437871	+	1.34763i
$115$	−8.54099	+	6.20539i	−0.796451	+	0.578656i
$116$	−5.27975	+	3.83596i	−0.490213	+	0.356160i
$117$	−10.6025	−	21.1473i	−0.980205	−	1.95507i
$118$	1.86575	−	3.23157i	0.171756	−	0.297490i
$119$	−8.52927			−0.781877
$120$	−26.2409	+	11.6832i	−2.39545	+	1.06652i
$121$	2.01254	+	6.19398i	0.182959	+	0.563089i
$122$	1.82174	−	5.60673i	0.164932	−	0.507610i
$123$	−6.93606	−	12.0136i	−0.625404	−	1.08323i
$124$	2.96642	+	3.24841i	0.266392	+	0.291716i
$125$	2.53595			0.226822
$126$	−23.5326	+	5.00200i	−2.09645	+	0.445614i
$127$	−2.89530	+	3.21556i	−0.256916	+	0.285335i	−0.857780	−	0.514017i	$-0.828157\pi$
$127$	−2.89530	+	3.21556i	−0.256916	+	0.285335i	0.600864	+	0.799352i	$0.294823\pi$
$128$	−0.603803	+	0.268831i	−0.0533692	+	0.0237615i
$129$	15.4798	+	26.8119i	1.36292	+	2.36065i
$130$	−0.550350	−	11.9920i	−0.0482689	−	1.05176i
$131$	−11.6677	+	5.19481i	−1.01941	+	0.453873i	−0.847249	−	0.531196i	$-0.821743\pi$
$131$	−11.6677	+	5.19481i	−1.01941	+	0.453873i	−0.172165	+	0.985068i	$0.555076\pi$
$132$	1.06867	+	10.1677i	0.0930161	+	0.884989i
$133$	11.9966	−	8.71605i	1.04024	−	0.755778i
$134$	4.20871	+	4.67425i	0.363577	+	0.403794i
$135$	3.48393	−	33.1474i	0.299849	−	2.85288i
$136$	2.42647	−	7.46791i	0.208068	−	0.640368i
$137$	−6.80877	−	1.44725i	−0.581712	−	0.123647i	−0.0923488	−	0.995727i	$-0.529437\pi$
$137$	−6.80877	−	1.44725i	−0.581712	−	0.123647i	−0.489363	+	0.872080i	$0.662771\pi$
$138$	−1.23998	−	11.7976i	−0.105554	−	1.00428i
$139$	−2.04548	+	2.27173i	−0.173495	+	0.192686i	−0.823621	−	0.567141i	$-0.808049\pi$
$139$	−2.04548	+	2.27173i	−0.173495	+	0.192686i	0.650126	+	0.759827i	$0.274716\pi$
$140$	7.79827	+	1.65757i	0.659074	+	0.140090i
$141$	5.93739	+	2.64350i	0.500019	+	0.222623i
$142$	3.21322	−	3.56865i	0.269648	−	0.299474i
$143$	−14.5488	−	3.99985i	−1.21663	−	0.334484i
$144$	1.23143	−	11.7162i	0.102619	−	0.976354i
$145$	7.72606	−	23.7784i	0.641614	−	1.97469i
$146$	8.25851	−	6.00016i	0.683479	−	0.496577i
$147$	11.6180	+	5.17268i	0.958239	+	0.426636i
$148$	6.74428	−	3.00275i	0.554377	−	0.246824i
$149$	9.15845			0.750290			0.375145	−	0.926966i	$-0.377593\pi$
$149$	9.15845			0.750290			0.375145	+	0.926966i	$0.377593\pi$
$150$	7.07818	−	12.2598i	0.577931	−	1.00101i
$151$	−19.1371	−	13.9039i	−1.55736	−	1.13148i	−0.938136	−	0.346266i	$-0.887449\pi$
$151$	−19.1371	−	13.9039i	−1.55736	−	1.13148i	−0.619219	−	0.785219i	$-0.712551\pi$
$152$	4.21856	+	12.9834i	0.342170	+	1.05309i
$153$	11.2327	+	12.4752i	0.908110	+	1.00856i
$154$	−7.67249	+	13.2891i	−0.618267	+	1.07087i
$155$	−16.5090	−	3.38820i	−1.32604	−	0.272147i
$156$	−7.82234	−	4.04993i	−0.626288	−	0.324254i
$157$	3.32810	−	10.2428i	0.265611	−	0.817467i	−0.725941	−	0.687757i	$-0.758595\pi$
$157$	3.32810	−	10.2428i	0.265611	−	0.817467i	0.991552	−	0.129710i	$-0.0414045\pi$
$158$	−8.19143	+	9.09751i	−0.651675	+	0.723759i
$159$	7.41749	−	3.30248i	0.588245	−	0.261904i
$160$	−6.30042	+	10.9126i	−0.498092	+	0.862721i
$161$	−5.81346	+	10.0692i	−0.458165	+	0.793564i
$162$	12.7828	+	9.28723i	1.00431	+	0.729674i
$163$	12.7189	+	5.66283i	0.996223	+	0.443547i	0.839068	−	0.544027i	$-0.183101\pi$
$163$	12.7189	+	5.66283i	0.996223	+	0.443547i	0.157155	+	0.987574i	$0.449768\pi$
$164$	−3.23817	−	1.44173i	−0.252859	−	0.112580i
$165$	−26.2084	−	29.1074i	−2.04032	−	2.26601i
$166$	12.5117	+	9.09026i	0.971094	+	0.705541i
$167$	−15.1590	+	3.22215i	−1.17304	+	0.249338i	−0.752909	−	0.658125i	$-0.771350\pi$
$167$	−15.1590	+	3.22215i	−1.17304	+	0.249338i	−0.420133	+	0.907463i	$0.638017\pi$
$168$	−21.1677	+	23.5091i	−1.63312	+	1.81376i
$169$	9.77313	−	8.57240i	0.751779	−	0.659415i
$170$	2.63242	+	8.10176i	0.201898	+	0.621377i
$171$	−28.5474	−	6.06795i	−2.18308	−	0.464027i
$172$	7.22692	+	3.21763i	0.551047	+	0.245342i
$173$	−2.10069	−	0.446515i	−0.159712	−	0.0339479i	0.127362	−	0.991856i	$-0.459349\pi$
$173$	−2.10069	−	0.446515i	−0.159712	−	0.0339479i	−0.287074	+	0.957908i	$0.592682\pi$
$174$	18.7982	+	20.8775i	1.42509	+	1.58272i
$175$	−12.6756	+	5.64352i	−0.958182	+	0.426610i
$176$	−5.02790	−	5.58405i	−0.378992	−	0.420914i
$177$	9.58278	+	4.26653i	0.720286	+	0.320692i
$178$	−2.38378	−	1.06133i	−0.178672	−	0.0795498i
$179$	2.07781	−	19.7690i	0.155303	−	1.47761i	−0.588113	−	0.808779i	$-0.700129\pi$
$179$	2.07781	−	19.7690i	0.155303	−	1.47761i	0.743416	−	0.668829i	$-0.233204\pi$
$180$	−7.84559	−	13.5890i	−0.584775	−	1.01286i
$181$	4.23710	+	7.33887i	0.314941	+	0.545494i	0.979425	−	0.201809i	$-0.0646820\pi$
$181$	4.23710	+	7.33887i	0.314941	+	0.545494i	−0.664484	+	0.747302i	$0.731349\pi$
$182$	−5.92548	−	11.8187i	−0.439226	−	0.876058i
$183$	16.2101	+	3.44556i	1.19829	+	0.254703i
$184$	−7.16236	−	7.95461i	−0.528016	−	0.586421i
$185$	−14.1415	+	24.4938i	−1.03970	+	1.80082i
$186$	12.5722	−	14.1615i	0.921840	−	1.03837i
$187$	10.7072			0.782986
$188$	1.62441	−	0.345280i	0.118472	−	0.0251821i
$189$	−11.3431	−	34.9105i	−0.825089	−	2.53936i
$190$	−11.9817	−	8.70525i	−0.869247	−	0.631545i
$191$	4.07266	−	7.05405i	0.294687	−	0.510413i	−0.680225	−	0.733003i	$-0.738118\pi$
$191$	4.07266	−	7.05405i	0.294687	−	0.510413i	0.974912	+	0.222590i	$0.0714513\pi$
$192$	−12.6315	−	21.8784i	−0.911598	−	1.57893i
$193$	1.82882	−	17.4000i	0.131641	−	1.25248i	−0.706770	−	0.707444i	$-0.749848\pi$
$193$	1.82882	−	17.4000i	0.131641	−	1.25248i	0.838411	−	0.545038i	$-0.183485\pi$
$194$	−10.5913	+	7.69505i	−0.760414	+	0.552473i
$195$	33.3643	−	5.06235i	2.38927	−	0.362523i
$196$	3.17858	−	0.675628i	0.227041	−	0.0482592i
$197$	11.6994	+	8.50011i	0.833547	+	0.605607i	0.920561	−	0.390600i	$-0.127732\pi$
$197$	11.6994	+	8.50011i	0.833547	+	0.605607i	−0.0870135	+	0.996207i	$0.527732\pi$
$198$	29.5415	−	6.27923i	2.09942	−	0.446246i
$199$	−4.62354	−	0.982765i	−0.327754	−	0.0696664i	0.0410958	−	0.999155i	$-0.486915\pi$
$199$	−4.62354	−	0.982765i	−0.327754	−	0.0696664i	−0.368850	+	0.929489i	$0.620248\pi$
$200$	−1.33522	−	12.7037i	−0.0944141	−	0.898290i
$201$	−11.8312	+	13.1398i	−0.834506	+	0.926813i
$202$	5.94737	−	6.60522i	0.418455	−	0.464742i
$203$	−2.87822	−	27.3844i	−0.202012	−	1.92201i
$204$	6.11415	+	1.29960i	0.428076	+	0.0909903i
$205$	13.2829	−	2.82337i	0.927720	−	0.197193i
$206$	−3.21210	−	2.33373i	−0.223798	−	0.162598i
$207$	22.3836	−	4.75779i	1.55577	−	0.330689i
$208$	6.40071	−	0.971176i	0.443809	−	0.0673389i
$209$	−15.0599	+	10.9417i	−1.04171	+	0.756850i
$210$	3.58738	−	34.1316i	0.247553	−	2.35531i
$211$	−11.9417	−	20.6837i	−0.822102	−	1.42392i	−0.904114	−	0.427291i	$-0.859468\pi$
$211$	−11.9417	−	20.6837i	−0.822102	−	1.42392i	0.0820122	−	0.996631i	$-0.473865\pi$
$212$	1.03735	−	1.79674i	0.0712452	−	0.123400i
$213$	10.9211	+	7.93463i	0.748301	+	0.543672i
$214$	−1.04843	−	3.22675i	−0.0716695	−	0.220576i
$215$	−29.6447	+	6.30118i	−2.02175	+	0.429737i
$216$	33.7933			2.29934
$217$	−18.1276	+	3.98629i	−1.23058	+	0.270607i
$218$	0.0885663	−	0.153401i	0.00599847	−	0.0103896i
$219$	19.2014	+	21.3253i	1.29751	+	1.44103i
$220$	−9.78952	−	2.08083i	−0.660009	−	0.140289i
$221$	−5.07451	+	7.70398i	−0.341348	+	0.518226i
$222$	−15.8900	−	27.5223i	−1.06647	−	1.84718i
$223$	5.50598	+	9.53664i	0.368708	+	0.638620i	0.989364	−	0.145463i	$-0.0464670\pi$
$223$	5.50598	+	9.53664i	0.368708	+	0.638620i	−0.620656	+	0.784083i	$0.713134\pi$
$224$	−1.45060	+	13.8015i	−0.0969224	+	0.922155i
$225$	24.9476	+	11.1074i	1.66317	+	0.740492i
$226$	−11.7978	−	5.25271i	−0.784776	−	0.349405i
$227$	13.2650	+	14.7322i	0.880426	+	0.977812i	0.999887	−	0.0150271i	$-0.00478344\pi$
$227$	13.2650	+	14.7322i	0.880426	+	0.977812i	−0.119461	+	0.992839i	$0.538117\pi$
$228$	−9.92775	+	4.42012i	−0.657482	+	0.292730i
$229$	5.23338	+	5.81226i	0.345831	+	0.384085i	0.890818	−	0.454360i	$-0.150132\pi$
$229$	5.23338	+	5.81226i	0.345831	+	0.384085i	−0.544987	+	0.838445i	$0.683465\pi$
$230$	11.3587	+	2.41438i	0.748973	+	0.159199i
$231$	−39.4071	−	17.5452i	−2.59280	−	1.15439i
$232$	24.7956	+	5.27047i	1.62791	+	0.346023i
$233$	−1.91318	−	5.88816i	−0.125337	−	0.385746i	0.868626	−	0.495469i	$-0.165004\pi$
$233$	−1.91318	−	5.88816i	−0.125337	−	0.385746i	−0.993962	+	0.109723i	$0.965004\pi$
$234$	−9.48274	+	24.2315i	−0.619906	+	1.58406i
$235$	−4.25719	+	4.72809i	−0.277708	+	0.308426i
$236$	2.62176	−	0.557271i	0.170662	−	0.0362753i
$237$	−27.8410	−	20.2277i	−1.80847	−	1.31393i
$238$	6.27766	+	6.97205i	0.406920	+	0.451931i
$239$	10.6171	+	4.72704i	0.686763	+	0.305767i	0.720292	−	0.693671i	$-0.244008\pi$
$239$	10.6171	+	4.72704i	0.686763	+	0.305767i	−0.0335289	+	0.999438i	$0.510675\pi$
$240$	15.3526	+	6.83542i	0.991007	+	0.441225i
$241$	−20.5340	−	14.9188i	−1.32271	−	0.961006i	−0.999894	−	0.0145441i	$-0.995370\pi$
$241$	−20.5340	−	14.9188i	−1.32271	−	0.961006i	−0.322817	−	0.946462i	$-0.604630\pi$
$242$	3.58186	−	6.20396i	0.230251	−	0.398806i
$243$	−5.69148	+	9.85793i	−0.365109	+	0.632387i
$244$	3.86846	−	1.72235i	0.247653	−	0.110262i
$245$	−8.33028	+	9.25171i	−0.532202	+	0.591070i
$246$	−4.71521	+	14.5119i	−0.300631	+	0.925246i
$247$	−0.735277	−	16.0215i	−0.0467846	−	1.01942i
$248$	1.66683	−	17.0059i	0.105844	−	1.07987i
$249$	−21.7373	+	37.6501i	−1.37755	+	2.38598i
$250$	−1.86650	−	2.07295i	−0.118048	−	0.131105i
$251$	−6.00570	−	18.4837i	−0.379077	−	1.16668i	−0.940687	−	0.339276i	$-0.889818\pi$
$251$	−6.00570	−	18.4837i	−0.379077	−	1.16668i	0.561610	−	0.827402i	$-0.310182\pi$
$252$	−13.9806	−	10.1575i	−0.880697	−	0.639864i
$253$	7.29789	−	12.6403i	0.458815	−	0.794690i
$254$	4.75947			0.298635
$255$	−21.8767	+	9.74013i	−1.36997	+	0.609950i
$256$	−14.2635	−	6.35050i	−0.891466	−	0.396906i
$257$	3.89118	−	2.82711i	0.242725	−	0.176350i	−0.459771	−	0.888037i	$-0.652069\pi$
$257$	3.89118	−	2.82711i	0.242725	−	0.176350i	0.702497	+	0.711687i	$0.252069\pi$
$258$	10.5234	−	32.3876i	0.655155	−	2.01636i
$259$	−3.25592	+	30.9780i	−0.202313	+	1.92488i
$260$	6.13678	−	6.05753i	0.380587	−	0.375672i
$261$	−36.2629	+	40.2740i	−2.24461	+	2.49290i
$262$	12.8340	+	5.71406i	0.792887	+	0.353016i
$263$	−9.41740	−	2.00173i	−0.580702	−	0.123432i	−0.0918101	−	0.995777i	$-0.529265\pi$
$263$	−9.41740	−	2.00173i	−0.580702	−	0.123432i	−0.488891	+	0.872345i	$0.662599\pi$
$264$	26.5727	−	29.5120i	1.63544	−	1.81634i
$265$	0.830822	+	7.90474i	0.0510370	+	0.485584i
$266$	−15.9544	−	3.39122i	−0.978228	−	0.207929i
$267$	2.26671	−	6.97622i	0.138720	−	0.426938i
$268$	−0.472256	+	4.49322i	−0.0288476	+	0.274467i
$269$	−2.40696	−	2.67320i	−0.146755	−	0.162988i	0.665285	−	0.746589i	$-0.268310\pi$
$269$	−2.40696	−	2.67320i	−0.146755	−	0.162988i	−0.812040	+	0.583601i	$0.801643\pi$
$270$	−29.6598	+	21.5491i	−1.80504	+	1.31144i
$271$	3.22131	+	30.6487i	0.195680	+	1.86177i	0.447872	+	0.894098i	$0.352182\pi$
$271$	3.22131	+	30.6487i	0.195680	+	1.86177i	−0.252192	+	0.967677i	$0.581151\pi$
$272$	−4.19688	+	1.86857i	−0.254473	+	0.113299i
$273$	31.3004	−	20.0387i	1.89439	−	1.21280i
$274$	3.82833	+	6.63086i	0.231278	+	0.400585i
$275$	15.9122	−	7.08456i	0.959541	−	0.427215i
$276$	5.70158	−	6.33224i	0.343195	−	0.381156i
$277$	−17.6996	+	3.76216i	−1.06346	+	0.226046i	−0.706240	−	0.707972i	$-0.749610\pi$
$277$	−17.6996	+	3.76216i	−1.06346	+	0.226046i	−0.357224	+	0.934019i	$0.616277\pi$
$278$	3.36247			0.201668
$279$	29.7038	+	21.2642i	1.77832	+	1.27305i
$280$	−15.4838	−	26.8188i	−0.925336	−	1.60273i
$281$	2.09444	−	6.44602i	0.124944	−	0.384537i	−0.868947	−	0.494905i	$-0.835203\pi$
$281$	2.09444	−	6.44602i	0.124944	−	0.384537i	0.993891	+	0.110368i	$0.0352029\pi$
$282$	−2.20914	−	6.79904i	−0.131552	−	0.404877i
$283$	−0.185638	+	0.0826512i	−0.0110350	+	0.00491310i	−0.412247	−	0.911072i	$-0.635256\pi$
$283$	−0.185638	+	0.0826512i	−0.0110350	+	0.00491310i	0.401212	+	0.915985i	$0.368589\pi$
$284$	3.44933			0.204680
$285$	20.8166	−	36.0555i	1.23307	−	2.13574i
$286$	7.43852	+	14.8365i	0.439849	+	0.877301i
$287$	12.0993	−	8.79067i	0.714200	−	0.518897i
$288$	22.0970	−	16.0544i	1.30208	−	0.946014i
$289$	−3.23037	+	9.94206i	−0.190022	+	0.584827i
$290$	−25.1236	+	11.1857i	−1.47531	+	0.656849i
$291$	−24.6253	−	27.3492i	−1.44356	−	1.60324i
$292$	7.17221	+	1.52450i	0.419722	+	0.0892146i
$293$	−8.46511	+	6.15026i	−0.494537	+	0.359302i	−0.806926	−	0.590652i	$-0.798871\pi$
$293$	−8.46511	+	6.15026i	−0.494537	+	0.359302i	0.312390	+	0.949954i	$0.398871\pi$
$294$	−4.32275	−	13.3041i	−0.252108	−	0.775908i
$295$	−6.87098	+	7.63099i	−0.400044	+	0.444294i
$296$	−26.1969	−	11.6636i	−1.52267	−	0.677934i
$297$	14.2395	+	43.8247i	0.826260	+	2.54297i
$298$	−6.74075	−	7.48637i	−0.390481	−	0.433673i
$299$	5.63618	+	11.2416i	0.325949	+	0.650121i
$300$	9.94628	−	2.11415i	0.574249	−	0.122060i
$301$	−27.0031	+	19.6189i	−1.55644	+	1.13082i
$302$	2.71975	+	25.8767i	0.156504	+	1.48903i
$303$	20.2139	+	14.6862i	1.16126	+	0.843703i
$304$	3.99352	−	6.91698i	0.229044	−	0.396716i
$305$	−8.11144	+	14.0494i	−0.464460	+	0.804468i
$306$	1.93012	−	18.3638i	0.110337	−	1.04979i
$307$	−10.4974	−	2.23129i	−0.599118	−	0.127346i	−0.101637	−	0.994822i	$-0.532408\pi$
$307$	−10.4974	−	2.23129i	−0.599118	−	0.127346i	−0.497481	+	0.867475i	$0.665741\pi$
$308$	−10.7814	+	2.29166i	−0.614327	+	0.130579i
$309$	5.58058	−	9.66585i	0.317468	−	0.549871i
$310$	9.38128	+	15.9887i	0.532821	+	0.908097i
$311$	3.65737			0.207391			0.103695	−	0.994609i	$-0.466933\pi$
$311$	3.65737			0.207391			0.103695	+	0.994609i	$0.466933\pi$
$312$	8.64059	+	33.1063i	0.489177	+	1.87427i
$313$	22.2646	+	4.73249i	1.25847	+	0.267496i	0.788417	−	0.615141i	$-0.210901\pi$
$313$	22.2646	+	4.73249i	1.25847	+	0.267496i	0.470055	+	0.882637i	$0.344234\pi$
$314$	−10.8223	+	4.81839i	−0.610737	+	0.271918i
$315$	66.2048			3.73022
$316$	−8.79333			−0.494664
$317$	−16.0248	+	7.13469i	−0.900042	+	0.400724i	−0.803984	−	0.594651i	$-0.797290\pi$
$317$	−16.0248	+	7.13469i	−0.900042	+	0.400724i	−0.0960580	+	0.995376i	$0.530623\pi$
$318$	−8.15892	−	3.63258i	−0.457529	−	0.203705i
$319$	3.61316	+	34.3769i	0.202298	+	1.92474i
$320$	24.1899	−	5.14173i	1.35226	−	0.287431i
$321$	8.71299	−	3.87927i	0.486311	−	0.216520i
$322$	12.5096	−	2.65900i	0.697134	−	0.148180i
$323$	3.51696	+	10.8241i	0.195689	+	0.602269i
$324$	1.18633	+	11.2872i	0.0659074	+	0.627067i
$325$	−2.44389	+	14.8067i	−0.135563	+	0.821327i
$326$	−4.73236	−	14.5647i	−0.262101	−	0.806664i
$327$	0.454890	+	0.202530i	0.0251555	+	0.0111999i
$328$	4.25468	+	13.0945i	0.234925	+	0.723025i
$329$	−2.16525	+	6.66396i	−0.119374	+	0.367396i
$330$	−4.50340	+	42.8470i	−0.247904	+	2.35865i
$331$	−12.9741	−	14.4092i	−0.713119	−	0.791999i	0.272288	−	0.962216i	$-0.412220\pi$
$331$	−12.9741	−	14.4092i	−0.713119	−	0.791999i	−0.985407	+	0.170217i	$0.945553\pi$
$332$	1.16117	+	11.0478i	0.0637276	+	0.606328i
$333$	49.5974	−	36.0346i	2.71792	−	1.97468i
$334$	13.7911	+	10.0199i	0.754618	+	0.548262i
$335$	−8.65432	−	14.9897i	−0.472836	−	0.818976i
$336$	18.5083			1.00971
$337$	−17.4329	−	12.6657i	−0.949631	−	0.689947i	0.00108888	−	0.999999i	$-0.499653\pi$
$337$	−17.4329	−	12.6657i	−0.949631	−	0.689947i	−0.950719	+	0.310052i	$0.899653\pi$
$338$	−14.2005	−	1.67941i	−0.772404	−	0.0913476i
$339$	11.2184	−	34.5266i	0.609299	−	1.87523i
$340$	−3.05948	+	5.29918i	−0.165924	+	0.287388i
$341$	22.7564	−	5.00417i	1.23233	−	0.270991i
$342$	16.0512	+	27.8015i	0.867951	+	1.50333i
$343$	2.97411	−	9.15337i	0.160587	−	0.494235i
$344$	−9.49554	−	29.2243i	−0.511965	−	1.57567i
$345$	−3.41223	+	32.4652i	−0.183708	+	1.74787i
$346$	1.18114	+	2.04580i	0.0634986	+	0.109983i
$347$	33.0074			1.77193			0.885965	−	0.463753i	$-0.153497\pi$
$347$	33.0074			1.77193			0.885965	+	0.463753i	$0.153497\pi$
$348$	−2.10933	+	20.0689i	−0.113072	+	1.07581i
$349$	0.0891522	+	0.848227i	0.00477221	+	0.0454045i	0.996649	−	0.0817990i	$-0.0260665\pi$
$349$	0.0891522	+	0.848227i	0.00477221	+	0.0454045i	−0.991877	+	0.127203i	$0.959400\pi$
$350$	13.9426	+	6.20762i	0.745261	+	0.331811i
$351$	−38.2811	−	10.5245i	−2.04330	−	0.561757i
$352$	1.82101	−	17.3257i	0.0970599	−	0.923463i
$353$	0.180472	−	0.0383606i	0.00960557	−	0.00204173i	−0.203106	−	0.979157i	$-0.565104\pi$
$353$	0.180472	−	0.0383606i	0.00960557	−	0.00204173i	0.212712	+	0.977115i	$0.431770\pi$
$354$	−3.56549	−	10.9734i	−0.189504	−	0.583232i
$355$	−10.6909	+	7.76736i	−0.567411	+	0.412249i
$356$	−0.579192	−	1.78257i	−0.0306971	−	0.0944760i
$357$	−17.6472	+	19.5992i	−0.933990	+	1.03730i
$358$	−17.6890	+	12.8518i	−0.934895	+	0.679241i
$359$	19.5767	−	21.7421i	1.03322	−	1.14750i	0.0443023	−	0.999018i	$-0.485894\pi$
$359$	19.5767	−	21.7421i	1.03322	−	1.14750i	0.988915	−	0.148485i	$-0.0474398\pi$
$360$	−18.8344	+	57.9664i	−0.992661	+	3.05510i
$361$	−0.636497	−	0.462442i	−0.0334998	−	0.0243391i
$362$	2.88042	−	8.86503i	0.151392	−	0.465936i
$363$	18.3970	+	8.19087i	0.965592	+	0.429909i
$364$	3.46080	−	8.84348i	0.181395	−	0.463524i
$365$	−25.6625	+	11.4257i	−1.34324	+	0.598047i
$366$	−9.11438	−	15.7866i	−0.476416	−	0.825177i
$367$	−7.69490			−0.401670			−0.200835	−	0.979625i	$-0.564366\pi$
$367$	−7.69490			−0.401670			−0.200835	+	0.979625i	$0.564366\pi$
$368$	−0.654612	+	6.22822i	−0.0341240	+	0.324668i
$369$	−28.7918	−	6.11990i	−1.49884	−	0.318589i
$370$	30.4302	−	6.46814i	1.58199	−	0.336263i
$371$	4.37681	+	7.58085i	0.227232	+	0.393578i
$372$	13.6020	−	0.0954501i	0.705232	−	0.00494886i
$373$	3.69347	+	6.39727i	0.191240	+	0.331238i	0.945662	−	0.325153i	$-0.105416\pi$
$373$	3.69347	+	6.39727i	0.191240	+	0.331238i	−0.754421	+	0.656391i	$0.772082\pi$
$374$	−7.88063	−	8.75233i	−0.407498	−	0.452572i
$375$	5.24693	−	5.82731i	0.270950	−	0.300921i
$376$	−5.21872	−	3.79162i	−0.269135	−	0.195538i
$377$	−26.4471	−	13.6927i	−1.36210	−	0.705210i
$378$	−20.1881	+	34.9668i	−1.03836	+	1.79850i
$379$	0.856205	−	8.14625i	0.0439803	−	0.418445i	−0.950275	−	0.311412i	$-0.899198\pi$
$379$	0.856205	−	8.14625i	0.0439803	−	0.418445i	0.994255	−	0.107033i	$-0.0341351\pi$
$380$	−1.11199	−	10.5799i	−0.0570440	−	0.542737i
$381$	1.39853	+	13.3061i	0.0716487	+	0.681692i
$382$	−8.76370	+	1.86278i	−0.448390	+	0.0953082i
$383$	3.29279	−	1.46604i	0.168254	−	0.0749114i	−0.320882	−	0.947119i	$-0.603979\pi$
$383$	3.29279	−	1.46604i	0.168254	−	0.0749114i	0.489135	+	0.872208i	$0.337312\pi$
$384$	−0.631541	+	1.94368i	−0.0322282	+	0.0991881i
$385$	28.2554	−	31.3808i	1.44003	−	1.59931i
$386$	−15.5693	+	11.3118i	−0.792456	+	0.575753i
$387$	64.2573	+	13.6583i	3.26638	+	0.694291i
$388$	−9.19818	−	1.95513i	−0.466967	−	0.0992569i
$389$	2.48488	+	23.6421i	0.125988	+	1.19870i	0.856627	+	0.515936i	$0.172556\pi$
$389$	2.48488	+	23.6421i	0.125988	+	1.19870i	−0.730639	+	0.682764i	$0.760778\pi$
$390$	−28.6947	−	23.5469i	−1.45301	−	1.19235i
$391$	−5.97117	−	6.63166i	−0.301975	−	0.335377i
$392$	−10.2118	−	7.41929i	−0.515772	−	0.374731i
$393$	−12.2037	+	37.5592i	−0.615596	+	1.89461i
$394$	−1.66271	−	15.8196i	−0.0837659	−	0.796980i
$395$	27.2541	−	19.8012i	1.37130	−	0.996308i
$396$	17.5505	+	12.7512i	0.881947	+	0.640772i
$397$	−27.8781			−1.39916			−0.699582	−	0.714553i	$-0.746630\pi$
$397$	−27.8781			−1.39916			−0.699582	+	0.714553i	$0.746630\pi$
$398$	2.59966	+	4.50274i	0.130309	+	0.225702i
$399$	4.79280	−	45.6004i	0.239940	−	2.28288i
$400$	−5.00072	+	5.55386i	−0.250036	+	0.277693i
$401$	10.1979	+	11.3259i	0.509259	+	0.565590i	0.941864	−	0.335994i	$-0.109072\pi$
$401$	10.1979	+	11.3259i	0.509259	+	0.565590i	−0.432605	+	0.901584i	$0.642405\pi$
$402$	19.4488			0.970016
$403$	−7.18447	+	18.7452i	−0.357884	+	0.933766i
$404$	6.38438			0.317635
$405$	−29.0940	−	32.3121i	−1.44569	−	1.60560i
$406$	−20.2664	+	22.5081i	−1.00580	+	1.11706i
$407$	4.08731	−	38.8881i	0.202600	−	1.92761i
$408$	−12.1399	−	21.0270i	−0.601016	−	1.04099i
$409$	−22.6684			−1.12088			−0.560441	−	0.828194i	$-0.689368\pi$
$409$	−22.6684			−1.12088			−0.560441	+	0.828194i	$0.689368\pi$
$410$	−12.0843	−	8.77978i	−0.596802	−	0.433602i
$411$	−17.4131	+	12.6513i	−0.858923	+	0.624044i
$412$	−0.298106	−	2.83629i	−0.0146866	−	0.139734i
$413$	−3.49465	+	10.7554i	−0.171961	+	0.529240i
$414$	−20.3638	−	14.7952i	−1.00083	−	0.727143i
$415$	−28.4769	−	31.6268i	−1.39788	−	1.55250i
$416$	11.6031	+	9.52150i	0.568888	+	0.466830i
$417$	0.988033	+	9.40050i	0.0483842	+	0.460345i
$418$	20.0283	+	4.25715i	0.979616	+	0.208224i
$419$	8.03401	+	1.70768i	0.392487	+	0.0834257i	0.399928	−	0.916547i	$-0.369035\pi$
$419$	8.03401	+	1.70768i	0.392487	+	0.0834257i	−0.00744076	+	0.999972i	$0.502368\pi$
$420$	19.9437	−	14.4899i	0.973151	−	0.707036i
$421$	−12.3831	+	13.7529i	−0.603518	+	0.670274i	−0.965044	−	0.262088i	$-0.915589\pi$
$421$	−12.3831	+	13.7529i	−0.603518	+	0.670274i	0.361526	+	0.932362i	$0.382256\pi$
$422$	−8.11811	+	24.9850i	−0.395183	+	1.21625i
$423$	12.5985	−	5.60920i	0.612558	−	0.272729i
$424$	−7.88265	+	1.67551i	−0.382815	+	0.0813699i
$425$	−1.11315	−	10.5910i	−0.0539959	−	0.513737i
$426$	−1.55209	−	14.7672i	−0.0751992	−	0.715473i
$427$	−1.86757	+	17.7687i	−0.0903779	+	0.859889i
$428$	1.21852	−	2.11054i	0.0588995	−	0.102017i
$429$	−39.2928	+	25.1555i	−1.89708	+	1.21452i
$430$	26.9697	+	19.5946i	1.30059	+	0.944937i
$431$	13.4263	−	14.9115i	0.646724	−	0.718260i	−0.327245	−	0.944939i	$-0.606120\pi$
$431$	13.4263	−	14.9115i	0.646724	−	0.718260i	0.973969	+	0.226679i	$0.0727870\pi$
$432$	−13.2296	−	14.6929i	−0.636507	−	0.706913i
$433$	−5.03107	−	8.71406i	−0.241778	−	0.418771i	0.719443	−	0.694551i	$-0.244397\pi$
$433$	−5.03107	−	8.71406i	−0.241778	−	0.418771i	−0.961221	+	0.275780i	$0.911064\pi$
$434$	16.6007	+	11.8840i	0.796858	+	0.570451i
$435$	−38.6544	−	66.9514i	−1.85334	−	3.21007i
$436$	0.124454	−	0.0264534i	0.00596025	−	0.00126689i
$437$	15.1755	+	3.22565i	0.725941	+	0.154304i
$438$	3.29938	−	31.3915i	0.157650	−	1.49994i
$439$	14.8994			0.711111			0.355556	−	0.934655i	$-0.384292\pi$
$439$	14.8994			0.711111			0.355556	+	0.934655i	$0.384292\pi$
$440$	19.4375	+	33.6668i	0.926649	+	1.60500i
$441$	24.6521	−	10.9758i	1.17391	−	0.522659i
$442$	10.0323	−	1.52220i	0.477190	−	0.0724038i
$443$	−13.7723	−	6.13182i	−0.654341	−	0.291332i	0.0525873	−	0.998616i	$-0.483253\pi$
$443$	−13.7723	−	6.13182i	−0.654341	−	0.291332i	−0.706929	+	0.707285i	$0.749920\pi$
$444$	7.05410	−	21.7103i	0.334773	−	1.03032i
$445$	5.80922	+	4.22065i	0.275383	+	0.200078i
$446$	3.74302	−	11.5198i	0.177237	−	0.545480i
$447$	18.9490	−	21.0450i	0.896257	−	0.995395i
$448$	22.0344	−	16.0090i	1.04103	−	0.756352i
$449$	15.9983	−	17.7679i	0.755007	−	0.838521i	−0.236080	−	0.971734i	$-0.575863\pi$
$449$	15.9983	−	17.7679i	0.755007	−	0.838521i	0.991087	+	0.133213i	$0.0425294\pi$
$450$	−9.28231	−	28.5680i	−0.437572	−	1.34671i
$451$	−15.1888	+	11.0353i	−0.715214	+	0.519633i
$452$	−2.86653	−	8.82228i	−0.134830	−	0.414965i
$453$	−71.5445	+	15.2073i	−3.36145	+	0.714499i
$454$	2.27932	−	21.6863i	0.106974	−	1.01779i
$455$	9.18775	+	35.2027i	0.430728	+	1.65033i
$456$	38.5625	+	17.1691i	1.80586	+	0.804019i
$457$	−0.645030	−	6.13705i	−0.0301733	−	0.287079i	−0.999195	−	0.0401056i	$-0.987231\pi$
$457$	−0.645030	−	6.13705i	−0.0301733	−	0.287079i	0.969022	−	0.246974i	$-0.0794361\pi$
$458$	0.899252	−	8.55581i	0.0420193	−	0.399787i
$459$	28.1730			1.31500
$460$	4.17062	+	7.22372i	0.194456	+	0.336808i
$461$	1.96701	−	18.7148i	0.0916128	−	0.871637i	−0.848138	−	0.529776i	$-0.822276\pi$
$461$	1.96701	−	18.7148i	0.0916128	−	0.871637i	0.939750	−	0.341861i	$-0.111057\pi$
$462$	14.6623	+	45.1259i	0.682152	+	2.09945i
$463$	−4.82529	+	14.8507i	−0.224250	+	0.690172i	0.774116	+	0.633043i	$0.218194\pi$
$463$	−4.82529	+	14.8507i	−0.224250	+	0.690172i	−0.998367	+	0.0571284i	$0.981806\pi$
$464$	−7.41557	−	12.8441i	−0.344259	−	0.596274i
$465$	−41.9432	+	30.9255i	−1.94507	+	1.43414i
$466$	−3.40501	+	5.89765i	−0.157734	+	0.273204i
$467$	2.52343	−	7.76632i	0.116770	−	0.359382i	−0.875542	−	0.483142i	$-0.839495\pi$
$467$	2.52343	−	7.76632i	0.116770	−	0.359382i	0.992312	+	0.123760i	$0.0394953\pi$
$468$	−17.4925	+	6.58463i	−0.808591	+	0.304375i
$469$	−15.4218	−	11.2046i	−0.712112	−	0.517379i
$470$	6.99822			0.322804
$471$	−16.6509	−	28.8402i	−0.767232	−	1.32888i
$472$	−8.42287	−	6.11957i	−0.387694	−	0.281676i
$473$	33.8983	−	24.6285i	1.55864	−	1.13242i
$474$	3.95674	+	37.6458i	0.181739	+	1.72913i
$475$	12.3886	+	13.7589i	0.568426	+	0.631301i
$476$	−0.704411	+	6.70203i	−0.0322866	+	0.307187i
$477$	5.32392	−	16.3853i	0.243765	−	0.750233i
$478$	−3.95033	−	12.1579i	−0.180684	−	0.556088i
$479$	−29.6373	−	13.1954i	−1.35416	−	0.602912i	−0.404027	−	0.914747i	$-0.632390\pi$
$479$	−29.6373	−	13.1954i	−1.35416	−	0.602912i	−0.950136	+	0.311835i	$0.899056\pi$
$480$	12.0402	+	37.0561i	0.549560	+	1.69137i
$481$	26.0435	+	21.3713i	1.18748	+	0.974448i
$482$	2.91827	+	27.7655i	0.132924	+	1.26468i
$483$	11.1096	+	34.1920i	0.505507	+	1.55579i
$484$	5.03324	−	1.06985i	0.228784	−	0.0486295i
$485$	32.9115	−	14.6531i	1.49443	−	0.665365i
$486$	12.2472	−	2.60321i	0.555542	−	0.118084i
$487$	1.93684	+	18.4278i	0.0877664	+	0.835042i	0.946518	+	0.322650i	$0.104574\pi$
$487$	1.93684	+	18.4278i	0.0877664	+	0.835042i	−0.858752	+	0.512392i	$0.828760\pi$
$488$	−15.0263	−	6.69015i	−0.680210	−	0.302849i
$489$	39.3282	−	17.5100i	1.77848	−	0.791831i
$490$	13.6938			0.618623
$491$	−8.74183			−0.394513			−0.197257	−	0.980352i	$-0.563203\pi$
$491$	−8.74183			−0.394513			−0.197257	+	0.980352i	$0.563203\pi$
$492$	−10.0127	+	4.45796i	−0.451410	+	0.200980i
$493$	20.6718	+	4.39392i	0.931011	+	0.197892i
$494$	−12.5552	+	12.3931i	−0.564885	+	0.557590i
$495$	−83.1098			−3.73551
$496$	−8.04649	+	5.93283i	−0.361298	+	0.266392i
$497$	−7.27677	+	12.6037i	−0.326408	+	0.565355i
$498$	46.7752	−	9.94237i	2.09605	−	0.445528i
$499$	37.7722	+	8.02874i	1.69092	+	0.359416i	0.950017	−	0.312199i	$-0.101066\pi$
$499$	37.7722	+	8.02874i	1.69092	+	0.359416i	0.740901	+	0.671615i	$0.234399\pi$
$500$	0.209438	−	1.99267i	0.00936635	−	0.0891149i
$501$	−23.9602	+	41.5003i	−1.07046	+	1.85410i
$502$	−10.6888	+	18.5135i	−0.477062	+	0.826296i
$503$	−26.7291	−	19.4198i	−1.19179	−	0.865888i	−0.198340	−	0.980133i	$-0.563555\pi$
$503$	−26.7291	−	19.4198i	−1.19179	−	0.865888i	−0.993453	+	0.114245i	$0.963555\pi$
$504$	7.01647	+	66.7572i	0.312538	+	2.97360i
$505$	−19.7877	+	14.3766i	−0.880542	+	0.639752i
$506$	−15.7039	+	3.33797i	−0.698123	+	0.148391i
$507$	0.522453	−	40.1939i	0.0232029	−	1.78507i
$508$	2.28757	+	2.54060i	0.101494	+	0.112721i
$509$	8.13874	+	25.0485i	0.360743	+	1.11025i	0.952604	+	0.304214i	$0.0983937\pi$
$509$	8.13874	+	25.0485i	0.360743	+	1.11025i	−0.591860	+	0.806041i	$0.701606\pi$
$510$	24.0634	+	10.7137i	1.06554	+	0.474411i
$511$	−20.7011	+	22.9909i	−0.915762	+	1.01706i
$512$	5.71553	+	17.5906i	0.252593	+	0.777402i
$513$	−39.6260	+	28.7900i	−1.74953	+	1.27111i
$514$	−5.17492	−	1.09996i	−0.228256	−	0.0485173i
$515$	7.31083	+	8.11950i	0.322154	+	0.357788i
$516$	22.3464	−	9.94924i	0.983743	−	0.437991i
$517$	2.71814	−	8.36557i	0.119544	−	0.367917i
$518$	27.7187	−	20.1388i	1.21789	−	0.884848i
$519$	−5.37240	+	3.90328i	−0.235822	+	0.171335i
$520$	−33.4359	−	1.97027i	−1.46626	−	0.0864021i
$521$	7.92545	−	13.7273i	0.347220	−	0.601403i	−0.638534	−	0.769593i	$-0.720459\pi$
$521$	7.92545	−	13.7273i	0.347220	−	0.601403i	0.985755	+	0.168190i	$0.0537923\pi$
$522$	59.6110			2.60910
$523$	−6.37945	+	2.84032i	−0.278954	+	0.124198i	−0.541445	−	0.840736i	$-0.682123\pi$
$523$	−6.37945	+	2.84032i	−0.278954	+	0.124198i	0.262491	+	0.964934i	$0.415456\pi$
$524$	3.11831	+	9.59716i	0.136224	+	0.419254i
$525$	−13.2578	+	40.8034i	−0.578619	+	1.78081i
$526$	5.29507	+	9.17133i	0.230876	+	0.399889i
$527$	1.38961	−	14.1776i	0.0605324	−	0.617586i
$528$	−23.2343			−1.01114
$529$	10.5985	−	2.25279i	0.460805	−	0.0979472i
$530$	5.85005	−	6.49714i	0.254110	−	0.282218i
$531$	20.3336	−	9.05308i	0.882401	−	0.392870i
$532$	−5.85802	−	10.1464i	−0.253978	−	0.439902i
$533$	−0.741572	−	16.1586i	−0.0321211	−	0.699908i
$534$	−7.37088	+	3.28173i	−0.318969	+	0.142014i
$535$	0.975928	+	9.28533i	0.0421930	+	0.401440i
$536$	14.1976	−	10.3152i	0.613243	−	0.445547i
$537$	−41.1278	−	45.6771i	−1.77480	−	1.97111i
$538$	−0.413588	+	3.93503i	−0.0178311	+	0.169651i
$539$	5.31873	−	16.3694i	0.229094	−	0.705079i
$540$	−25.7585	−	5.47513i	−1.10847	−	0.235612i
$541$	−0.0354082	−	0.336887i	−0.00152232	−	0.0144839i	0.993734	−	0.111768i	$-0.0356512\pi$
$541$	−0.0354082	−	0.336887i	−0.00152232	−	0.0144839i	−0.995257	+	0.0972837i	$0.968985\pi$
$542$	22.6821	−	25.1911i	0.974281	−	1.08205i
$543$	25.6305	+	5.44792i	1.09991	+	0.233793i
$544$	−9.73033	−	4.33222i	−0.417185	−	0.185743i
$545$	−0.326162	+	0.362240i	−0.0139713	+	0.0155167i
$546$	−39.4178	−	10.8370i	−1.68693	−	0.463781i
$547$	−2.53437	+	24.1129i	−0.108362	+	1.03099i	0.796311	+	0.604888i	$0.206782\pi$
$547$	−2.53437	+	24.1129i	−0.108362	+	1.03099i	−0.904673	+	0.426107i	$0.859885\pi$
$548$	−1.69952	+	5.23059i	−0.0725999	+	0.223440i
$549$	28.4486	−	20.6691i	1.21416	−	0.882137i
$550$	−17.5027	−	7.79271i	−0.746318	−	0.332282i
$551$	−33.5655	+	14.9443i	−1.42994	+	0.636650i
$552$	−33.0978			−1.40873
$553$	18.5506	−	32.1305i	0.788851	−	1.36633i
$554$	16.1024	+	11.6991i	0.684127	+	0.497047i
$555$	27.0247	+	83.1736i	1.14714	+	3.53052i
$556$	1.61612	+	1.79489i	0.0685388	+	0.0761201i
$557$	9.48706	−	16.4321i	0.401980	−	0.696249i	−0.591985	−	0.805949i	$-0.701656\pi$
$557$	9.48706	−	16.4321i	0.401980	−	0.696249i	0.993965	+	0.109700i	$0.0349889\pi$
$558$	−4.48048	−	39.9314i	−0.189674	−	1.69043i
$559$	1.65503	+	36.0627i	0.0700004	+	1.52529i
$560$	−5.59880	+	17.2313i	−0.236592	+	0.728157i
$561$	22.1533	−	24.6038i	0.935315	−	1.03877i
$562$	−6.81068	+	3.03231i	−0.287291	+	0.127910i
$563$	5.61468	−	9.72491i	0.236631	−	0.409856i	−0.723115	−	0.690728i	$-0.757290\pi$
$563$	5.61468	−	9.72491i	0.236631	−	0.409856i	0.959745	+	0.280872i	$0.0906236\pi$
$564$	2.56753	−	4.44709i	0.108113	−	0.187256i
$565$	28.7509	+	20.8888i	1.20956	+	0.878797i
$566$	0.204193	+	0.0909127i	0.00858288	+	0.00382135i
$567$	−43.7458	−	19.4769i	−1.83715	−	0.817952i
$568$	−8.96521	−	9.95687i	−0.376172	−	0.417781i
$569$	−18.7732	−	13.6395i	−0.787014	−	0.571799i	0.120062	−	0.992766i	$-0.461691\pi$
$569$	−18.7732	−	13.6395i	−0.787014	−	0.571799i	−0.907076	+	0.420968i	$0.861691\pi$
$570$	−44.7941	+	9.52127i	−1.87622	+	0.398802i
$571$	9.22735	−	10.2480i	0.386153	−	0.428866i	−0.518459	−	0.855102i	$-0.673494\pi$
$571$	9.22735	−	10.2480i	0.386153	−	0.428866i	0.904612	+	0.426237i	$0.140161\pi$
$572$	−4.34450	+	11.1016i	−0.181653	+	0.464182i
$573$	−7.78294	−	23.9534i	−0.325137	−	1.00067i
$574$	−16.0910	−	3.42025i	−0.671626	−	0.142758i
$575$	−13.2618	−	5.90455i	−0.553057	−	0.246237i
$576$	−52.4337	−	11.1451i	−2.18474	−	0.464380i
$577$	−14.3801	−	15.9707i	−0.598652	−	0.664870i	0.365318	−	0.930883i	$-0.380960\pi$
$577$	−14.3801	−	15.9707i	−0.598652	−	0.664870i	−0.963970	+	0.266013i	$0.914294\pi$
$578$	10.5045	−	4.67691i	0.436930	−	0.194534i
$579$	−36.1993	−	40.2034i	−1.50439	−	1.67080i
$580$	−18.0462	−	8.03469i	−0.749328	−	0.333622i
$581$	−42.8180	−	19.0638i	−1.77639	−	0.790899i
$582$	−4.23137	+	40.2588i	−0.175396	+	1.66878i
$583$	−5.49440	−	9.51658i	−0.227555	−	0.394137i
$584$	−14.2408	−	24.6657i	−0.589287	−	1.02067i
$585$	39.3887	−	59.7988i	1.62852	−	2.47238i
$586$	11.2578	+	2.39293i	0.465057	+	0.0988508i
$587$	12.5631	+	13.9528i	0.518535	+	0.575892i	0.944360	−	0.328914i	$-0.106683\pi$
$587$	12.5631	+	13.9528i	0.518535	+	0.575892i	−0.425825	+	0.904806i	$0.640016\pi$
$588$	5.02403	−	8.70188i	0.207188	−	0.358859i
$589$	12.5336	+	21.3612i	0.516436	+	0.880172i
$590$	11.2949			0.465004
$591$	43.7385	−	9.29690i	1.79916	−	0.382423i
$592$	5.18450	+	15.9562i	0.213082	+	0.655798i
$593$	25.4307	+	18.4765i	1.04431	+	0.758738i	0.971123	−	0.238580i	$-0.0766821\pi$
$593$	25.4307	+	18.4765i	1.04431	+	0.758738i	0.0731899	+	0.997318i	$0.476682\pi$
$594$	25.3430	−	43.8953i	1.03984	−	1.80105i
$595$	−12.9087	−	22.3585i	−0.529204	−	0.916608i
$596$	0.756374	−	7.19642i	0.0309823	−	0.294777i
$597$	−11.8245	+	8.59098i	−0.483944	+	0.351606i
$598$	5.04091	−	12.8812i	0.206138	−	0.526750i
$599$	30.5729	−	6.49847i	1.24917	−	0.265520i	0.464581	−	0.885531i	$-0.346205\pi$
$599$	30.5729	−	6.49847i	1.24917	−	0.265520i	0.784594	+	0.620011i	$0.212872\pi$
$600$	−31.9542	−	23.2161i	−1.30453	−	0.947794i
$601$	40.7439	−	8.66038i	1.66198	−	0.353264i	0.721315	−	0.692607i	$-0.243538\pi$
$601$	40.7439	−	8.66038i	1.66198	−	0.353264i	0.940663	+	0.339342i	$0.110205\pi$
$602$	35.9117	+	7.63328i	1.46365	+	0.311109i
$603$	3.92169	+	37.3124i	0.159703	+	1.51948i
$604$	−12.5057	+	13.8890i	−0.508851	+	0.565137i
$605$	−13.1909	+	14.6500i	−0.536286	+	0.595606i
$606$	−2.87278	−	27.3327i	−0.116699	−	1.11031i
$607$	19.6242	+	4.17126i	0.796523	+	0.169306i	0.588159	−	0.808745i	$-0.299853\pi$
$607$	19.6242	+	4.17126i	0.796523	+	0.169306i	0.208364	+	0.978051i	$0.433186\pi$
$608$	18.1130	−	3.85005i	0.734581	−	0.156140i
$609$	−68.8812	−	50.0451i	−2.79121	−	2.02793i
$610$	17.4545	−	3.71007i	0.706712	−	0.150216i
$611$	4.73093	+	5.92048i	0.191393	+	0.239517i
$612$	10.7303	−	7.79600i	0.433746	−	0.315135i
$613$	2.10392	−	20.0174i	0.0849764	−	0.808496i	−0.866169	−	0.499752i	$-0.833425\pi$
$613$	2.10392	−	20.0174i	0.0849764	−	0.808496i	0.951145	−	0.308744i	$-0.0999088\pi$
$614$	5.90232	+	10.2231i	0.238198	+	0.412571i
$615$	20.9949	−	36.3642i	0.846594	−	1.46634i
$616$	34.6372	+	25.1654i	1.39557	+	1.01394i
$617$	−0.502559	−	1.54672i	−0.0202323	−	0.0622686i	0.940431	−	0.339986i	$-0.110422\pi$
$617$	−0.502559	−	1.54672i	−0.0202323	−	0.0622686i	−0.960663	+	0.277717i	$0.910422\pi$
$618$	−12.0085	+	2.55249i	−0.483053	+	0.102676i
$619$	−27.6736			−1.11230			−0.556148	−	0.831083i	$-0.687721\pi$
$619$	−27.6736			−1.11230			−0.556148	+	0.831083i	$0.687721\pi$
$620$	−4.02578	+	12.6924i	−0.161679	+	0.509741i
$621$	19.2024	−	33.2596i	0.770567	−	1.33466i
$622$	−2.69188	−	2.98963i	−0.107935	−	0.119873i
$623$	7.73533	+	1.64419i	0.309909	+	0.0658732i
$624$	11.0115	−	16.7174i	0.440814	−	0.669233i
$625$	14.2435	+	24.6705i	0.569742	+	0.986822i
$626$	−12.5186	−	21.6829i	−0.500345	−	0.866623i
$627$	−6.01662	+	57.2443i	−0.240281	+	2.28612i
$628$	−7.77363	−	3.46104i	−0.310201	−	0.138111i
$629$	−21.8400	−	9.72382i	−0.870820	−	0.387714i
$630$	−48.7276	−	54.1175i	−1.94136	−	2.15609i
$631$	3.99729	−	1.77971i	0.159130	−	0.0708491i	−0.325626	−	0.945499i	$-0.605575\pi$
$631$	3.99729	−	1.77971i	0.159130	−	0.0708491i	0.484756	+	0.874649i	$0.338908\pi$
$632$	22.8549	+	25.3829i	0.909119	+	1.00968i
$633$	−72.2362	−	15.3543i	−2.87113	−	0.610278i
$634$	17.6266	+	7.84785i	0.700040	+	0.311678i
$635$	−12.8111	−	2.72309i	−0.508394	−	0.108062i
$636$	−1.98239	−	6.10117i	−0.0786069	−	0.241927i
$637$	9.25729	+	11.5849i	0.366787	+	0.459012i
$638$	25.4413	−	28.2554i	1.00723	−	1.11864i
$639$	28.0178	−	5.95538i	1.10837	−	0.235591i
$640$	−1.61854	−	1.17594i	−0.0639783	−	0.0464830i
$641$	5.45953	+	6.06342i	0.215638	+	0.239491i	0.841253	−	0.540641i	$-0.181818\pi$
$641$	5.45953	+	6.06342i	0.215638	+	0.239491i	−0.625615	+	0.780132i	$0.715152\pi$
$642$	−9.58390	−	4.26703i	−0.378246	−	0.168406i
$643$	4.69607	+	2.09083i	0.185195	+	0.0824542i	0.497239	−	0.867613i	$-0.334347\pi$
$643$	4.69607	+	2.09083i	0.185195	+	0.0824542i	−0.312044	+	0.950068i	$0.601014\pi$
$644$	7.43194	+	5.39962i	0.292859	+	0.212775i
$645$	−46.8561	+	81.1572i	−1.84496	+	3.19556i
$646$	6.25937	−	10.8415i	0.246272	−	0.426555i
$647$	−5.47790	+	2.43892i	−0.215359	+	0.0958838i	−0.511581	−	0.859235i	$-0.670940\pi$
$647$	−5.47790	+	2.43892i	−0.215359	+	0.0958838i	0.296222	+	0.955119i	$0.404273\pi$
$648$	29.4983	−	32.7612i	1.15880	−	1.28698i
$649$	4.38699	−	13.5018i	0.172205	−	0.529991i
$650$	13.9021	−	8.90023i	0.545286	−	0.349096i
$651$	−28.3463	+	49.9027i	−1.11098	+	1.95584i
$652$	5.50009	−	9.52644i	0.215400	−	0.373084i
$653$	20.2695	+	22.5115i	0.793206	+	0.880944i	0.995142	−	0.0984546i	$-0.0313899\pi$
$653$	20.2695	+	22.5115i	0.793206	+	0.880944i	−0.201936	+	0.979399i	$0.564723\pi$
$654$	−0.169252	−	0.520905i	−0.00661829	−	0.0203690i
$655$	−31.2762	−	22.7235i	−1.22206	−	0.887880i
$656$	4.02771	−	6.97620i	0.157256	−	0.272375i
$657$	60.8897			2.37553
$658$	7.04095	−	3.13483i	0.274485	−	0.122209i
$659$	−0.430009	−	0.191452i	−0.0167508	−	0.00745793i	0.398344	−	0.917236i	$-0.369585\pi$
$659$	−0.430009	−	0.191452i	−0.0167508	−	0.00745793i	−0.415095	+	0.909778i	$0.636252\pi$
$660$	−25.0362	+	18.1898i	−0.974532	+	0.708039i
$661$	3.53993	−	10.8948i	0.137687	−	0.423758i	−0.858311	−	0.513130i	$-0.828486\pi$
$661$	3.53993	−	10.8948i	0.137687	−	0.423758i	0.995998	+	0.0893719i	$0.0284860\pi$
$662$	−2.22933	+	21.2107i	−0.0866455	+	0.824377i
$663$	7.20355	+	27.6003i	0.279763	+	1.07191i
$664$	28.8727	−	32.0664i	1.12048	−	1.24442i
$665$	41.0045	+	18.2564i	1.59008	+	0.707951i
$666$	−65.9600	−	14.0202i	−2.55590	−	0.543273i
$667$	19.2769	−	21.4092i	0.746405	−	0.828966i
$668$	1.27992	+	12.1776i	0.0495215	+	0.471165i
$669$	33.3060	+	7.07941i	1.28768	+	0.273706i
$670$	−5.88329	+	18.1069i	−0.227291	+	0.699531i
$671$	2.34444	−	22.3059i	0.0905062	−	0.861109i
$672$	28.7130	+	31.8890i	1.10763	+	1.23014i
$673$	4.45445	−	3.23634i	0.171706	−	0.124752i	−0.498613	−	0.866825i	$-0.666157\pi$
$673$	4.45445	−	3.23634i	0.171706	−	0.124752i	0.670319	+	0.742073i	$0.266157\pi$
$674$	2.47755	+	23.5723i	0.0954316	+	0.907971i
$675$	41.8686	−	18.6411i	1.61152	−	0.717496i
$676$	−5.92878	−	8.38738i	−0.228030	−	0.322592i
$677$	1.49685	+	2.59262i	0.0575285	+	0.0996423i	0.893355	−	0.449351i	$-0.148345\pi$
$677$	1.49685	+	2.59262i	0.0575285	+	0.0996423i	−0.835827	+	0.548993i	$0.815011\pi$
$678$	−36.4799	+	16.2419i	−1.40100	+	0.623766i
$679$	26.5486	−	29.4853i	1.01884	−	1.13154i
$680$	23.2486	−	4.94164i	0.891543	−	0.189503i
$681$	61.2983			2.34896
$682$	−20.8396	−	14.9185i	−0.797988	−	0.571260i
$683$	−12.5645	−	21.7624i	−0.480769	−	0.832716i	0.518988	−	0.854782i	$-0.326309\pi$
$683$	−12.5645	−	21.7624i	−0.480769	−	0.832716i	−0.999757	+	0.0220659i	$0.992976\pi$
$684$	−7.12566	+	21.9305i	−0.272456	+	0.838535i
$685$	−6.51098	−	20.0387i	−0.248772	−	0.765641i
$686$	−9.67120	+	4.30589i	−0.369248	+	0.164400i
$687$	24.1838			0.922670
$688$	−8.98901	+	15.5694i	−0.342703	+	0.593578i
$689$	9.45132	+	0.556935i	0.360067	+	0.0212175i
$690$	29.0494	−	21.1056i	1.10589	−	0.803477i
$691$	−9.33994	+	6.78586i	−0.355308	+	0.258146i	−0.751092	−	0.660197i	$-0.770473\pi$
$691$	−9.33994	+	6.78586i	−0.355308	+	0.258146i	0.395784	+	0.918343i	$0.370473\pi$
$692$	−0.524348	+	1.61378i	−0.0199327	+	0.0613466i
$693$	−83.6174	+	37.2288i	−3.17636	+	1.41421i
$694$	−24.2939	−	26.9811i	−0.922184	−	1.02419i
$695$	−9.05081	−	1.92381i	−0.343317	−	0.0729743i
$696$	63.4135	−	46.0726i	2.40368	−	1.74638i
$697$	3.54707	+	10.9168i	0.134355	+	0.413502i
$698$	0.627746	−	0.697183i	0.0237605	−	0.0263888i
$699$	−17.4887	−	7.78646i	−0.661482	−	0.294511i
$700$	3.38765	+	10.4261i	0.128041	+	0.394071i
$701$	26.6803	+	29.6314i	1.00770	+	1.11916i	0.992861	+	0.119273i	$0.0380565\pi$
$701$	26.6803	+	29.6314i	1.00770	+	1.11916i	0.0148377	+	0.999890i	$0.495277\pi$
$702$	19.5725	+	39.0382i	0.738715	+	1.47340i
$703$	40.6553	−	8.64155i	1.53334	−	0.325922i
$704$	−27.6608	+	20.0968i	−1.04251	+	0.757425i
$705$	2.05636	+	19.5650i	0.0774471	+	0.736860i
$706$	−0.164187	−	0.119289i	−0.00617926	−	0.00448950i
$707$	−13.4686	+	23.3283i	−0.506539	+	0.877351i
$708$	4.14392	−	7.17748i	0.155738	−	0.269746i
$709$	−0.567034	+	5.39497i	−0.0212954	+	0.202612i	−0.999996	−	0.00267857i	$-0.999147\pi$
$709$	−0.567034	+	5.39497i	−0.0212954	+	0.202612i	0.978701	+	0.205291i	$0.0658140\pi$
$710$	14.2179	+	3.02210i	0.533587	+	0.113417i
$711$	−71.4255	+	15.1820i	−2.67867	+	0.569368i
$712$	−3.64020	+	6.30501i	−0.136422	+	0.236290i
$713$	−15.7902	−	11.3038i	−0.591347	−	0.423331i
$714$	29.0095			1.08565
$715$	−11.5338	−	44.1915i	−0.431339	−	1.65267i
$716$	−15.3623	−	3.26535i	−0.574115	−	0.122032i
$717$	32.8291	−	14.6165i	1.22603	−	0.545862i
$718$	−32.1813			−1.20099
$719$	−44.8599			−1.67299			−0.836496	−	0.547974i	$-0.815399\pi$
$719$	−44.8599			−1.67299			−0.836496	+	0.547974i	$0.815399\pi$
$720$	32.5765	−	14.5040i	1.21405	−	0.540532i
$721$	10.9926	+	4.89422i	0.409385	+	0.182270i
$722$	0.0904584	+	0.860654i	0.00336651	+	0.0320302i
$723$	−76.7668	+	16.3173i	−2.85499	+	0.606847i
$724$	6.11658	−	2.72328i	0.227321	−	0.101210i
$725$	33.6281	−	7.14788i	1.24892	−	0.265466i
$726$	−6.84502	−	21.0668i	−0.254042	−	0.781862i
$727$	−1.22137	−	11.6206i	−0.0452982	−	0.430984i	−0.993544	−	0.113447i	$-0.963811\pi$
$727$	−1.22137	−	11.6206i	−0.0452982	−	0.430984i	0.948246	−	0.317537i	$-0.102856\pi$
$728$	−34.5227	+	12.9952i	−1.27950	+	0.481636i
$729$	−2.44012	−	7.50992i	−0.0903748	−	0.278145i
$730$	28.2276	+	12.5677i	1.04475	+	0.465153i
$731$	−7.91632	−	24.3639i	−0.292796	−	0.901132i
$732$	4.04617	−	12.4528i	0.149551	−	0.460270i
$733$	0.300742	−	2.86137i	0.0111082	−	0.105687i	−0.987563	−	0.157224i	$-0.949745\pi$
$733$	0.300742	−	2.86137i	0.0111082	−	0.105687i	0.998671	+	0.0515372i	$0.0164121\pi$
$734$	5.66356	+	6.29002i	0.209046	+	0.232169i
$735$	4.02380	+	38.2839i	0.148420	+	1.41212i
$736$	−11.7465	+	8.53432i	−0.432981	+	0.314579i
$737$	19.3597	+	14.0656i	0.713122	+	0.518113i
$738$	16.1886	+	28.0396i	0.595912	+	1.03215i
$739$	43.9410			1.61639			0.808197	−	0.588912i	$-0.200443\pi$
$739$	43.9410			1.61639			0.808197	+	0.588912i	$0.200443\pi$
$740$	18.0785	+	13.1348i	0.664580	+	0.482846i
$741$	−38.3367	−	31.4591i	−1.40833	−	1.15568i
$742$	2.97540	−	9.15733i	0.109230	−	0.336176i
$743$	11.4033	−	19.7511i	0.418347	−	0.724598i	−0.577426	−	0.816443i	$-0.695943\pi$
$743$	11.4033	−	19.7511i	0.418347	−	0.724598i	0.995773	+	0.0918444i	$0.0292762\pi$
$744$	−35.6288	−	39.0157i	−1.30621	−	1.43038i
$745$	13.8609	+	24.0078i	0.507825	+	0.879578i
$746$	2.51086	−	7.72762i	0.0919290	−	0.282928i
$747$	28.5062	+	87.7332i	1.04299	+	3.20999i
$748$	0.884279	−	8.41335i	0.0323325	−	0.307623i
$749$	5.14123	+	8.90487i	0.187857	+	0.325377i
$750$	−8.62521			−0.314948
$751$	4.15684	−	39.5497i	0.151685	−	1.44319i	−0.608536	−	0.793526i	$-0.708243\pi$
$751$	4.15684	−	39.5497i	0.151685	−	1.44319i	0.760222	−	0.649664i	$-0.225090\pi$
$752$	0.394499	+	3.75340i	0.0143859	+	0.136873i
$753$	−54.8991	−	24.4427i	−2.00063	−	0.890740i
$754$	8.27269	+	31.6966i	0.301274	+	1.15432i
$755$	7.48433	−	71.2086i	0.272383	−	2.59155i
$756$	−28.3683	+	6.02987i	−1.03175	+	0.219304i
$757$	1.93435	+	5.95331i	0.0703051	+	0.216377i	0.980035	−	0.198823i	$-0.0637118\pi$
$757$	1.93435	+	5.95331i	0.0703051	+	0.216377i	−0.909730	+	0.415200i	$0.863712\pi$
$758$	−7.28914	+	5.29587i	−0.264753	+	0.192355i
$759$	−13.9464	−	42.9227i	−0.506224	−	1.55800i
$760$	−27.6498	+	30.7083i	−1.00297	+	1.11391i
$761$	10.2570	−	7.45216i	0.371816	−	0.270140i	−0.386147	−	0.922437i	$-0.626194\pi$
$761$	10.2570	−	7.45216i	0.371816	−	0.270140i	0.757964	+	0.652297i	$0.226194\pi$
$762$	9.84743	−	10.9367i	0.356735	−	0.396194i
$763$	−0.165890	+	0.510556i	−0.00600561	+	0.0184834i
$764$	−5.20649	−	3.78274i	−0.188364	−	0.136855i
$765$	−15.7020	+	48.3259i	−0.567708	+	1.74722i
$766$	−3.62192	−	1.61258i	−0.130865	−	0.0582651i
$767$	7.63559	+	9.55548i	0.275705	+	0.345028i
$768$	−44.1041	+	19.6364i	−1.59147	+	0.708567i
$769$	0.352246	+	0.610108i	0.0127023	+	0.0220011i	0.872307	−	0.488959i	$-0.162623\pi$
$769$	0.352246	+	0.610108i	0.0127023	+	0.0220011i	−0.859604	+	0.510960i	$0.829290\pi$
$770$	−46.4479			−1.67387
$771$	1.55458	−	14.7908i	0.0559867	−	0.532677i
$772$	−13.5214	−	2.87405i	−0.486644	−	0.103439i
$773$	22.2698	−	4.73358i	0.800988	−	0.170255i	0.210808	−	0.977527i	$-0.432390\pi$
$773$	22.2698	−	4.73358i	0.800988	−	0.170255i	0.590179	+	0.807272i	$0.299057\pi$
$774$	−36.1297	−	62.5784i	−1.29865	−	2.24933i
$775$	−7.31569	−	21.9891i	−0.262787	−	0.789873i
$776$	18.2634	+	31.6332i	0.655619	+	1.13557i
$777$	64.4472	+	71.5758i	2.31203	+	2.56777i
$778$	17.4968	−	19.4321i	0.627289	−	0.696675i
$779$	−16.1449	−	11.7299i	−0.578450	−	0.420268i
$780$	−1.22235	−	26.6347i	−0.0437673	−	0.953676i
$781$	9.13486	−	15.8220i	0.326871	−	0.566157i
$782$	−1.02603	+	9.76199i	−0.0366906	+	0.349088i
$783$	9.50705	+	90.4535i	0.339754	+	3.23255i
$784$	0.771938	+	7.34450i	0.0275692	+	0.262303i
$785$	31.8873	−	6.77785i	1.13811	−	0.241912i
$786$	39.6840	−	17.6685i	1.41548	−	0.630213i
$787$	−0.971854	+	2.99106i	−0.0346429	+	0.106620i	−0.966883	−	0.255221i	$-0.917852\pi$
$787$	−0.971854	+	2.99106i	−0.0346429	+	0.106620i	0.932240	+	0.361841i	$0.117852\pi$
$788$	7.64534	−	8.49100i	0.272354	−	0.302480i
$789$	−24.0845	+	17.4984i	−0.857431	+	0.622960i
$790$	−36.2454	−	7.70420i	−1.28955	−	0.274103i
$791$	38.2836	+	8.13743i	1.36121	+	0.289334i
$792$	−8.80809	−	83.8033i	−0.312982	−	2.97782i
$793$	14.9383	+	12.2584i	0.530475	+	0.435309i
$794$	20.5187	+	22.7883i	0.728182	+	0.808728i
$795$	19.8831	+	14.4459i	0.705181	+	0.512344i
$796$	−1.15407	+	3.55187i	−0.0409050	+	0.125893i
$797$	1.62375	+	15.4489i	0.0575161	+	0.547229i	0.984901	+	0.173120i	$0.0553848\pi$
$797$	1.62375	+	15.4489i	0.0575161	+	0.547229i	−0.927385	+	0.374109i	$0.877948\pi$
$798$	−40.8026	+	29.6448i	−1.44440	+	1.04942i
$799$	−4.35078	−	3.16103i	−0.153920	−	0.111829i
$800$	−17.3270			−0.612601
$801$	−7.78226	−	13.4793i	−0.274973	−	0.476267i
$802$	1.75231	−	16.6721i	0.0618761	−	0.588712i
$803$	25.9870	−	28.8615i	0.917062	−	1.01850i
$804$	9.34776	+	10.3817i	0.329670	+	0.366136i
$805$	−35.1937			−1.24041
$806$	20.6107	−	7.92398i	0.725982	−	0.279110i
$807$	−11.1227			−0.391539
$808$	−16.5937	−	18.4292i	−0.583765	−	0.648337i
$809$	−8.82693	+	9.80330i	−0.310338	+	0.344666i	−0.878056	−	0.478558i	$-0.841160\pi$
$809$	−8.82693	+	9.80330i	−0.310338	+	0.344666i	0.567718	+	0.823223i	$0.307826\pi$
$810$	−4.99922	+	47.5644i	−0.175655	+	1.67124i
$811$	24.4158	+	42.2894i	0.857355	+	1.48498i	0.874443	+	0.485129i	$0.161227\pi$
$811$	24.4158	+	42.2894i	0.857355	+	1.48498i	−0.0170872	+	0.999854i	$0.505439\pi$
$812$	−21.7555			−0.763469
$813$	77.0919	+	56.0105i	2.70373	+	1.96437i
$814$	−34.7965	+	25.2811i	−1.21962	+	0.886103i
$815$	4.40509	+	41.9116i	0.154303	+	1.46810i
$816$	−4.38968	+	13.5100i	−0.153669	+	0.472946i
$817$	36.0320	+	26.1787i	1.26060	+	0.915878i
$818$	16.6843	+	18.5298i	0.583353	+	0.647879i
$819$	12.8425	−	77.8080i	0.448752	−	2.71883i
$820$	−1.12151	−	10.6705i	−0.0391649	−	0.372629i
$821$	−31.5114	−	6.69796i	−1.09976	−	0.233761i	−0.377930	−	0.925834i	$-0.623364\pi$
$821$	−31.5114	−	6.69796i	−1.09976	−	0.233761i	−0.721827	+	0.692074i	$0.756697\pi$
$822$	23.1578	+	4.92234i	0.807721	+	0.171686i
$823$	−21.8256	+	15.8573i	−0.760794	+	0.552749i	−0.899154	−	0.437633i	$-0.855817\pi$
$823$	−21.8256	+	15.8573i	−0.760794	+	0.552749i	0.138360	+	0.990382i	$0.455817\pi$
$824$	−7.41245	+	8.23235i	−0.258225	+	0.286788i
$825$	16.6432	−	51.2224i	0.579440	−	1.78333i
$826$	11.3639	−	5.05953i	0.395400	−	0.176044i
$827$	−45.0825	+	9.58258i	−1.56767	+	0.333219i	−0.908209	−	0.418517i	$-0.862550\pi$
$827$	−45.0825	+	9.58258i	−1.56767	+	0.333219i	−0.659464	+	0.751736i	$0.729217\pi$
$828$	−1.88991	−	17.9813i	−0.0656788	−	0.624892i
$829$	−4.54784	−	43.2698i	−0.157953	−	1.50282i	−0.730478	−	0.682936i	$-0.760703\pi$
$829$	−4.54784	−	43.2698i	−0.157953	−	1.50282i	0.572525	−	0.819887i	$-0.305964\pi$
$830$	−4.89319	+	46.5556i	−0.169845	+	1.61597i
$831$	−27.9758	+	48.4555i	−0.970469	+	1.68090i
$832$	−1.35050	−	29.4269i	−0.0468201	−	1.02020i
$833$	−8.51343	−	6.18537i	−0.294973	−	0.214310i
$834$	6.95702	−	7.72655i	0.240902	−	0.267549i
$835$	−31.3890	−	34.8611i	−1.08626	−	1.20642i
$836$	7.35384	+	12.7372i	0.254338	+	0.440526i
$837$	59.8772	−	13.1671i	2.06966	−	0.455122i
$838$	−4.51724	−	7.82409i	−0.156046	−	0.270279i
$839$	−39.3896	+	8.37251i	−1.35988	+	0.289051i	−0.829404	−	0.558649i	$-0.811320\pi$
$839$	−39.3896	+	8.37251i	−1.35988	+	0.289051i	−0.530475	+	0.847701i	$0.677986\pi$
$840$	−93.6626	−	19.9086i	−3.23167	−	0.686912i
$841$	−4.10026	+	39.0114i	−0.141388	+	1.34522i
$842$	20.3561			0.701519
$843$	−10.4787	−	18.1497i	−0.360907	−	0.625108i
$844$	−17.2388	+	7.67521i	−0.593384	+	0.264192i
$845$	37.2627	+	12.6452i	1.28188	+	0.435007i
$846$	−13.8578	−	6.16987i	−0.476440	−	0.212125i
$847$	−6.70902	+	20.6483i	−0.230525	+	0.709482i
$848$	3.81443	+	2.77135i	0.130988	+	0.0951684i
$849$	−0.194165	+	0.597579i	−0.00666374	+	0.0205089i
$850$	−7.83803	+	8.70502i	−0.268842	+	0.298580i
$851$	−26.3654	+	19.1556i	−0.903793	+	0.656644i
$852$	7.13673	−	7.92614i	0.244500	−	0.271545i
$853$	−7.35575	−	22.6387i	−0.251856	−	0.775133i	−0.994433	−	0.105372i	$-0.966397\pi$
$853$	−7.35575	−	22.6387i	−0.251856	−	0.775133i	0.742577	−	0.669761i	$-0.233603\pi$
$854$	15.8992	−	11.5514i	0.544059	−	0.395282i
$855$	−27.2989	−	84.0173i	−0.933602	−	2.87333i
$856$	−9.25939	+	1.96814i	−0.316479	+	0.0672698i
$857$	−2.91468	+	27.7313i	−0.0995636	+	0.947284i	0.824711	+	0.565555i	$0.191338\pi$
$857$	−2.91468	+	27.7313i	−0.0995636	+	0.947284i	−0.924274	+	0.381729i	$0.875329\pi$
$858$	49.4829	+	13.6042i	1.68932	+	0.464439i
$859$	−45.9444	−	20.4557i	−1.56760	−	0.697941i	−0.574865	−	0.818248i	$-0.694945\pi$
$859$	−45.9444	−	20.4557i	−1.56760	−	0.697941i	−0.992737	+	0.120307i	$0.961612\pi$
$860$	2.50298	+	23.8143i	0.0853509	+	0.812060i
$861$	4.83383	−	45.9908i	0.164737	−	1.56736i
$862$	−22.0710			−0.751742
$863$	−19.6902	−	34.1044i	−0.670262	−	1.16093i	−0.977830	−	0.209401i	$-0.932849\pi$
$863$	−19.6902	−	34.1044i	−0.670262	−	1.16093i	0.307568	−	0.951526i	$-0.400485\pi$
$864$	4.79148	−	45.5879i	0.163009	−	1.55093i
$865$	−2.00881	−	6.18249i	−0.0683016	−	0.210211i
$866$	−3.42017	+	10.5262i	−0.116222	+	0.357695i
$867$	16.1619	+	27.9933i	0.548888	+	0.950703i
$868$	1.63519	+	14.5733i	0.0555019	+	0.494650i
$869$	−23.2874	+	40.3349i	−0.789970	+	1.36827i
$870$	−26.2777	+	80.8744i	−0.890897	+	2.74190i
$871$	−19.2956	+	7.26338i	−0.653808	+	0.246110i
$872$	−0.399830	−	0.290493i	−0.0135400	−	0.00983735i
$873$	−78.0896			−2.64293
$874$	−8.53264	−	14.7790i	−0.288621	−	0.499906i
$875$	6.83931	+	4.96905i	0.231211	+	0.167985i
$876$	18.3426	−	13.3266i	0.619737	−	0.450266i
$877$	3.42810	+	32.6162i	0.115759	+	1.10137i	0.886021	+	0.463645i	$0.153459\pi$
$877$	3.42810	+	32.6162i	0.115759	+	1.10137i	−0.770262	+	0.637727i	$0.779875\pi$
$878$	−10.9662	−	12.1792i	−0.370091	−	0.411028i
$879$	−3.38192	+	32.1768i	−0.114069	+	1.08530i
$880$	7.02842	−	21.6313i	0.236928	−	0.729190i
$881$	−11.8290	−	36.4058i	−0.398528	−	1.22654i	−0.926180	−	0.377081i	$-0.876928\pi$
$881$	−11.8290	−	36.4058i	−0.398528	−	1.22654i	0.527652	−	0.849460i	$-0.323072\pi$
$882$	−27.1163	−	12.0729i	−0.913052	−	0.406517i
$883$	−0.192933	−	0.593786i	−0.00649270	−	0.0199825i	0.947758	−	0.318991i	$-0.103344\pi$
$883$	−0.192933	−	0.593786i	−0.00649270	−	0.0199825i	−0.954250	+	0.299009i	$0.903344\pi$
$884$	5.63445	+	4.62364i	0.189507	+	0.155510i
$885$	3.31891	+	31.5773i	0.111564	+	1.06146i
$886$	5.12429	+	15.7709i	0.172154	+	0.529835i
$887$	−26.5294	+	5.63900i	−0.890771	+	0.189339i	−0.630493	−	0.776195i	$-0.717147\pi$
$887$	−26.5294	+	5.63900i	−0.890771	+	0.189339i	−0.260278	+	0.965534i	$0.583814\pi$
$888$	−81.0035	+	36.0651i	−2.71830	+	1.21027i
$889$	−14.1092	+	2.99899i	−0.473206	+	0.100583i
$890$	−0.825601	−	7.85507i	−0.0276742	−	0.263302i
$891$	54.9160	+	24.4502i	1.83976	+	0.819112i
$892$	7.94831	−	3.53882i	0.266129	−	0.118488i
$893$	9.34974			0.312877
$894$	−31.1495			−1.04180
$895$	54.9669	−	24.4728i	1.83734	−	0.818037i
$896$	−2.15518	−	0.458098i	−0.0719995	−	0.0153040i
$897$	37.4933	+	10.3079i	1.25186	+	0.344171i
$898$	−26.2990			−0.877608
$899$	45.9881	−	0.322715i	1.53379	−	0.0107631i
$900$	10.7882	−	18.6857i	0.359606	−	0.622856i
$901$	−6.57167	+	1.39685i	−0.218934	+	0.0465359i
$902$	20.1998	+	4.29359i	0.672579	+	0.142961i
$903$	−10.7881	+	102.642i	−0.359005	+	3.41571i
$904$	−18.0160	+	31.2047i	−0.599204	+	1.03785i
$905$	−12.8253	+	22.2141i	−0.426328	+	0.738422i
$906$	65.0886	+	47.2896i	2.16242	+	1.57109i
$907$	−0.623670	−	5.93382i	−0.0207086	−	0.197029i	0.979276	−	0.202529i	$-0.0649161\pi$
$907$	−0.623670	−	5.93382i	−0.0207086	−	0.197029i	−0.999985	+	0.00549965i	$0.998249\pi$
$908$	12.6716	−	9.20648i	0.420523	−	0.305528i
$909$	51.8583	−	11.0228i	1.72003	−	0.365604i
$910$	22.0133	−	33.4200i	0.729733	−	1.10786i
$911$	33.6558	+	37.3785i	1.11507	+	1.23841i	0.968449	+	0.249213i	$0.0801719\pi$
$911$	33.6558	+	37.3785i	1.11507	+	1.23841i	0.146617	+	0.989193i	$0.453161\pi$
$912$	−7.63171	−	23.4880i	−0.252711	−	0.777765i
$913$	53.7513	+	23.9316i	1.77891	+	0.792022i
$914$	−4.54184	+	5.04423i	−0.150231	+	0.166848i
$915$	15.5011	+	47.7076i	0.512452	+	1.57717i
$916$	4.99930	−	3.63220i	0.165181	−	0.120011i
$917$	−41.6461	−	8.85216i	−1.37528	−	0.292324i
$918$	−20.7357	−	23.0294i	−0.684382	−	0.760083i
$919$	10.4242	−	4.64115i	0.343862	−	0.153097i	−0.227537	−	0.973769i	$-0.573067\pi$
$919$	10.4242	−	4.64115i	0.343862	−	0.153097i	0.571399	+	0.820672i	$0.306401\pi$
$920$	10.0122	−	30.8142i	0.330091	−	1.01592i
$921$	−26.8465	+	19.5052i	−0.884624	+	0.642717i
$922$	−16.7458	+	12.1665i	−0.551492	+	0.400683i
$923$	7.05487	+	14.0713i	0.232214	+	0.463162i
$924$	−17.0410	+	29.5158i	−0.560607	+	0.970999i
$925$	−38.8909			−1.27873
$926$	15.6909	−	6.98602i	0.515634	−	0.229575i
$927$	−7.31836	−	22.5236i	−0.240367	−	0.739772i
$928$	10.6257	−	32.7026i	0.348806	−	1.07351i
$929$	3.46787	+	6.00653i	0.113777	+	0.197068i	0.917290	−	0.398219i	$-0.130372\pi$
$929$	3.46787	+	6.00653i	0.113777	+	0.197068i	−0.803513	+	0.595287i	$0.797038\pi$
$930$	56.1501	+	11.5239i	1.84123	+	0.377882i
$931$	18.2952			0.599600
$932$	−4.78473	+	1.01703i	−0.156729	+	0.0333138i
$933$	7.56717	−	8.40420i	0.247738	−	0.275141i
$934$	−8.20568	+	3.65340i	−0.268498	+	0.119543i
$935$	16.2048	+	28.0676i	0.529955	+	0.917909i
$936$	64.4723	+	33.3798i	2.10734	+	1.09105i
$937$	−18.1135	+	8.06465i	−0.591742	+	0.263461i	−0.680685	−	0.732576i	$-0.738318\pi$
$937$	−18.1135	+	8.06465i	−0.591742	+	0.263461i	0.0889428	+	0.996037i	$0.471651\pi$
$938$	2.19173	+	20.8529i	0.0715625	+	0.680871i
$939$	56.9406	−	41.3698i	1.85819	−	1.35005i
$940$	3.36359	+	3.73564i	0.109708	+	0.121843i
$941$	−3.63720	+	34.6056i	−0.118569	+	1.12811i	0.759809	+	0.650146i	$0.225292\pi$
$941$	−3.63720	+	34.6056i	−0.118569	+	1.12811i	−0.878379	+	0.477966i	$0.841374\pi$
$942$	−11.3194	+	34.8376i	−0.368807	+	1.13507i
$943$	15.3054	+	3.25326i	0.498412	+	0.105941i
$944$	0.636709	+	6.05788i	0.0207231	+	0.197167i
$945$	74.3464	−	82.5701i	2.41849	−	2.68600i
$946$	−45.0816	−	9.58240i	−1.46573	−	0.311551i
$947$	−35.9454	−	16.0039i	−1.16807	−	0.520057i	−0.271272	−	0.962503i	$-0.587444\pi$
$947$	−35.9454	−	16.0039i	−1.16807	−	0.520057i	−0.896795	+	0.442446i	$0.854111\pi$
$948$	−18.1936	+	20.2060i	−0.590900	+	0.656261i
$949$	8.45014	+	32.3765i	0.274303	+	1.05099i
$950$	2.12873	−	20.2535i	0.0690650	−	0.657110i
$951$	−16.7609	+	51.5848i	−0.543510	+	1.67275i
$952$	21.1770	−	15.3860i	0.686350	−	0.498662i
$953$	−14.2524	−	6.34557i	−0.461680	−	0.205553i	0.162697	−	0.986676i	$-0.447981\pi$
$953$	−14.2524	−	6.34557i	−0.461680	−	0.205553i	−0.624377	+	0.781123i	$0.714647\pi$
$954$	−17.3123	+	7.70793i	−0.560506	+	0.249553i
$955$	24.6551			0.797822
$956$	4.59119	−	7.95218i	0.148490	−	0.257192i
$957$	86.4697	+	62.8239i	2.79517	+	2.03081i
$958$	11.0272	+	33.9383i	0.356274	+	1.09650i
$959$	−15.5270	−	17.2445i	−0.501394	−	0.556855i
$960$	38.2344	−	66.2239i	1.23401	−	2.13737i
$961$	−3.67273	−	30.7817i	−0.118475	−	0.992957i
$962$	−1.69889	−	37.0182i	−0.0547743	−	1.19352i
$963$	6.25376	−	19.2471i	0.201525	−	0.620229i
$964$	−13.4186	+	14.9028i	−0.432183	+	0.479988i
$965$	48.3800	−	21.5402i	1.55741	−	0.693402i
$966$	19.7726	−	34.2471i	0.636172	−	1.10188i
$967$	−21.8950	+	37.9233i	−0.704096	+	1.21953i	0.262920	+	0.964818i	$0.415314\pi$
$967$	−21.8950	+	37.9233i	−0.704096	+	1.21953i	−0.967017	+	0.254713i	$0.918019\pi$
$968$	−16.1702	−	11.7483i	−0.519730	−	0.377606i
$969$	32.1491	+	14.3137i	1.03278	+	0.459822i
$970$	−36.2012	−	16.1178i	−1.16235	−	0.517512i
$971$	−3.51547	−	3.90433i	−0.112817	−	0.125296i	0.684091	−	0.729397i	$-0.260199\pi$
$971$	−3.51547	−	3.90433i	−0.112817	−	0.125296i	−0.796908	+	0.604101i	$0.793532\pi$
$972$	7.27600	+	5.28633i	0.233378	+	0.169559i
$973$	−9.96785	+	2.11873i	−0.319555	+	0.0679234i
$974$	13.6378	−	15.1463i	0.436984	−	0.485319i
$975$	28.9675	+	36.2511i	0.927703	+	1.16096i
$976$	2.97378	+	9.15236i	0.0951885	+	0.292960i
$977$	43.9253	+	9.33662i	1.40530	+	0.298705i	0.847289	−	0.531131i	$-0.178233\pi$
$977$	43.9253	+	9.33662i	1.40530	+	0.298705i	0.558007	+	0.829836i	$0.311566\pi$
$978$	−43.2593	−	19.2603i	−1.38328	−	0.615875i
$979$	−9.71050	−	2.06403i	−0.310349	−	0.0659667i
$980$	6.58172	+	7.30974i	0.210245	+	0.233501i
$981$	0.965225	−	0.429746i	0.0308173	−	0.0137207i
$982$	6.43412	+	7.14581i	0.205321	+	0.228032i
$983$	17.0645	+	7.59760i	0.544273	+	0.242326i	0.660407	−	0.750908i	$-0.270384\pi$
$983$	17.0645	+	7.59760i	0.544273	+	0.242326i	−0.116134	+	0.993234i	$0.537050\pi$
$984$	38.8927	+	17.3161i	1.23985	+	0.552018i
$985$	−4.57552	+	43.5331i	−0.145788	+	1.38708i
$986$	−11.6230	−	20.1317i	−0.370152	−	0.641123i
$987$	10.8330	+	18.7633i	0.344819	+	0.597244i
$988$	−12.6499	−	0.745416i	−0.402446	−	0.0237148i
$989$	−34.1584	−	7.26060i	−1.08618	−	0.230874i
$990$	61.1700	+	67.9362i	1.94411	+	2.15915i
$991$	9.72686	−	16.8474i	0.308984	−	0.535176i	−0.669156	−	0.743122i	$-0.733344\pi$
$991$	9.72686	−	16.8474i	0.308984	−	0.535176i	0.978140	+	0.207946i	$0.0666777\pi$
$992$	−22.7050	−	4.65982i	−0.720884	−	0.147949i
$993$	−59.9541			−1.90258
$994$	15.6584	−	3.32830i	0.496655	−	0.105567i
$995$	−4.42133	−	13.6075i	−0.140166	−	0.431385i
$996$	27.7890	+	20.1899i	0.880529	+	0.639742i
$997$	11.0073	−	19.0652i	0.348605	−	0.603802i	−0.637397	−	0.770536i	$-0.719989\pi$
$997$	11.0073	−	19.0652i	0.348605	−	0.603802i	0.986002	+	0.166734i	$0.0533221\pi$
$998$	−21.2380	−	36.7853i	−0.672277	−	1.16442i
$999$	10.7546	−	102.323i	0.340262	−	3.23737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bk.a.9.11	yes	280
13.3	even	3		403.2.bj.a.133.25	yes	280
31.7	even	15		403.2.bj.a.100.25	✓	280
403.224	even	15	inner	403.2.bk.a.224.11	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bj.a.100.25	✓	280	31.7	even	15
403.2.bj.a.133.25	yes	280	13.3	even	3
403.2.bk.a.9.11	yes	280	1.1	even	1	trivial
403.2.bk.a.224.11	yes	280	403.224	even	15	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bk (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.736014 - 0.817427i) q^{2} +(2.06902 - 2.29788i) q^{3} +(0.0825875 - 0.785768i) q^{4} +(1.51346 + 2.62138i) q^{5} -3.40117 q^{6} +(2.69694 + 1.95944i) q^{7} +(-2.48286 + 1.80390i) q^{8} +(-0.685820 - 6.52514i) q^{9} +O(q^{10})\)	\(q+(-0.736014 - 0.817427i) q^{2} +(2.06902 - 2.29788i) q^{3} +(0.0825875 - 0.785768i) q^{4} +(1.51346 + 2.62138i) q^{5} -3.40117 q^{6} +(2.69694 + 1.95944i) q^{7} +(-2.48286 + 1.80390i) q^{8} +(-0.685820 - 6.52514i) q^{9} +(1.02886 - 3.16652i) q^{10} +(-3.38559 - 2.45978i) q^{11} +(-1.63472 - 1.81554i) q^{12} +(3.37440 - 1.27021i) q^{13} +(-0.383287 - 3.64673i) q^{14} +(9.15499 + 1.94595i) q^{15} +(1.75632 + 0.373317i) q^{16} +(-2.06993 + 1.50389i) q^{17} +(-4.82905 + 5.36320i) q^{18} +(1.37458 - 4.23052i) q^{19} +(2.18479 - 0.972732i) q^{20} +(10.0826 - 2.14312i) q^{21} +(0.481157 + 4.57790i) q^{22} +(0.364574 + 3.46869i) q^{23} +(-0.991934 + 9.43762i) q^{24} +(-2.08110 + 3.60457i) q^{25} +(-3.52191 - 1.82343i) q^{26} +(-8.90827 - 6.47223i) q^{27} +(1.76240 - 1.95734i) q^{28} +(-5.52696 - 6.13832i) q^{29} +(-5.14753 - 8.91578i) q^{30} +(-3.69644 + 4.16370i) q^{31} +(2.08147 + 3.60521i) q^{32} +(-12.6571 + 2.69035i) q^{33} +(2.75282 + 0.585130i) q^{34} +(-1.05475 + 10.0352i) q^{35} -5.18389 q^{36} +(4.67192 + 8.09201i) q^{37} +(-4.46985 + 1.99010i) q^{38} +(4.06290 - 10.3820i) q^{39} +(-8.48642 - 3.77840i) q^{40} +(1.38635 - 4.26674i) q^{41} +(-9.17277 - 6.66441i) q^{42} +(-3.09404 + 9.52246i) q^{43} +(-2.21242 + 2.45714i) q^{44} +(16.0669 - 11.6733i) q^{45} +(2.56707 - 2.85102i) q^{46} +(0.649523 + 1.99903i) q^{47} +(4.49169 - 3.26341i) q^{48} +(1.27096 + 3.91161i) q^{49} +(4.47819 - 0.951869i) q^{50} +(-0.826963 + 7.86803i) q^{51} +(-0.719408 - 2.75640i) q^{52} +(2.39885 + 1.06804i) q^{53} +(1.26603 + 12.0455i) q^{54} +(1.32407 - 12.5977i) q^{55} -10.2308 q^{56} +(-6.87719 - 11.9116i) q^{57} +(-0.949698 + 9.03578i) q^{58} +(1.04831 + 3.22637i) q^{59} +(2.28516 - 7.03299i) q^{60} +(2.67977 + 4.64150i) q^{61} +(6.12415 - 0.0429752i) q^{62} +(10.9360 - 18.9417i) q^{63} +(2.52472 - 7.77028i) q^{64} +(8.43671 + 6.92318i) q^{65} +(11.5150 + 8.36613i) q^{66} -5.71825 q^{67} +(1.01076 + 1.75069i) q^{68} +(8.72493 + 6.33903i) q^{69} +(8.97939 - 6.52391i) q^{70} +(0.456341 + 4.34179i) q^{71} +(13.4735 + 14.9639i) q^{72} +(-0.970070 + 9.22960i) q^{73} +(3.17602 - 9.77479i) q^{74} +(3.97703 + 12.2400i) q^{75} +(-3.21068 - 1.42949i) q^{76} +(-4.31095 - 13.2677i) q^{77} +(-11.4769 + 4.32021i) q^{78} +(-1.16334 - 11.0685i) q^{79} +(1.67950 + 5.16898i) q^{80} +(-14.0507 + 2.98656i) q^{81} +(-4.50812 + 2.00714i) q^{82} +(-13.7527 + 2.92322i) q^{83} +(-0.851299 - 8.09957i) q^{84} +(-7.07502 - 3.15000i) q^{85} +(10.0612 - 4.47952i) q^{86} -25.5405 q^{87} +12.8431 q^{88} +(2.16716 - 0.964881i) q^{89} +(-21.3676 - 4.54182i) q^{90} +(11.5895 + 3.18625i) q^{91} +2.75569 q^{92} +(1.91967 + 17.1087i) q^{93} +(1.15600 - 2.00225i) q^{94} +(13.1702 - 2.79941i) q^{95} +(12.5909 + 2.67628i) q^{96} +(1.24409 - 11.8367i) q^{97} +(2.26201 - 3.91791i) q^{98} +(-13.7285 + 23.7784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9}+O(q^{10}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9} - 9 q^{10} - 6 q^{11} - 50 q^{12} - 6 q^{13} - 21 q^{15} + 23 q^{16} + 3 q^{17} - 15 q^{18} - 9 q^{19} + 60 q^{20} - 34 q^{21} + 41 q^{22} - 12 q^{23} - 89 q^{24} - 112 q^{25} + 39 q^{26} + 48 q^{27} + 66 q^{28} - 11 q^{29} + 24 q^{30} - 22 q^{31} + q^{32} - 37 q^{33} - 49 q^{34} + 41 q^{35} + 134 q^{36} + 17 q^{37} - 23 q^{38} + 10 q^{39} + 31 q^{40} + q^{41} - 71 q^{42} - 7 q^{43} - 42 q^{44} - 13 q^{45} + 21 q^{46} - 20 q^{47} - 3 q^{48} - 69 q^{49} - 42 q^{50} - 71 q^{51} - 140 q^{52} - 8 q^{53} - 149 q^{54} + 5 q^{55} - 126 q^{56} + 21 q^{57} + 79 q^{58} + 77 q^{59} + 2 q^{60} + 53 q^{61} + 72 q^{62} + 17 q^{63} - 91 q^{64} - 25 q^{65} - 62 q^{66} - 14 q^{67} + 83 q^{68} - 31 q^{69} + 134 q^{70} + 32 q^{71} - 70 q^{72} - 31 q^{73} + 51 q^{74} + 79 q^{75} + 98 q^{76} - 80 q^{77} - 141 q^{78} - 142 q^{79} + 6 q^{80} + 66 q^{81} - 48 q^{82} + 94 q^{83} + 130 q^{84} + 90 q^{85} - 34 q^{86} + 22 q^{87} - 122 q^{88} - 15 q^{89} + 43 q^{90} + 56 q^{91} - 294 q^{92} - 52 q^{93} - 57 q^{94} + 94 q^{95} + 24 q^{96} + 46 q^{97} + 73 q^{98} + 12 q^{99}+O(q^{100}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9 - 9 * q^10 - 6 * q^11 - 50 * q^12 - 6 * q^13 - 21 * q^15 + 23 * q^16 + 3 * q^17 - 15 * q^18 - 9 * q^19 + 60 * q^20 - 34 * q^21 + 41 * q^22 - 12 * q^23 - 89 * q^24 - 112 * q^25 + 39 * q^26 + 48 * q^27 + 66 * q^28 - 11 * q^29 + 24 * q^30 - 22 * q^31 + q^32 - 37 * q^33 - 49 * q^34 + 41 * q^35 + 134 * q^36 + 17 * q^37 - 23 * q^38 + 10 * q^39 + 31 * q^40 + q^41 - 71 * q^42 - 7 * q^43 - 42 * q^44 - 13 * q^45 + 21 * q^46 - 20 * q^47 - 3 * q^48 - 69 * q^49 - 42 * q^50 - 71 * q^51 - 140 * q^52 - 8 * q^53 - 149 * q^54 + 5 * q^55 - 126 * q^56 + 21 * q^57 + 79 * q^58 + 77 * q^59 + 2 * q^60 + 53 * q^61 + 72 * q^62 + 17 * q^63 - 91 * q^64 - 25 * q^65 - 62 * q^66 - 14 * q^67 + 83 * q^68 - 31 * q^69 + 134 * q^70 + 32 * q^71 - 70 * q^72 - 31 * q^73 + 51 * q^74 + 79 * q^75 + 98 * q^76 - 80 * q^77 - 141 * q^78 - 142 * q^79 + 6 * q^80 + 66 * q^81 - 48 * q^82 + 94 * q^83 + 130 * q^84 + 90 * q^85 - 34 * q^86 + 22 * q^87 - 122 * q^88 - 15 * q^89 + 43 * q^90 + 56 * q^91 - 294 * q^92 - 52 * q^93 - 57 * q^94 + 94 * q^95 + 24 * q^96 + 46 * q^97 + 73 * q^98 + 12 * q^99

Introduction

L-functions

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