LMFDB - Embedded newform 91.2.bb.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(5,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("91.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.bb (of order $12$, degree $4$, 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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	91.5
Dual form			91.2.bb.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.411280 - 1.53492i) q^{2} +(0.436133 - 0.251802i) q^{3} +(-0.454770 + 0.262561i) q^{4} +(-0.0769162 + 0.0206096i) q^{5} +(-0.565867 - 0.565867i) q^{6} +(1.52171 - 2.16435i) q^{7} +(-1.65723 - 1.65723i) q^{8} +(-1.37319 + 2.37844i) q^{9} +O(q^{10})$	\(q+(-0.411280 - 1.53492i) q^{2} +(0.436133 - 0.251802i) q^{3} +(-0.454770 + 0.262561i) q^{4} +(-0.0769162 + 0.0206096i) q^{5} +(-0.565867 - 0.565867i) q^{6} +(1.52171 - 2.16435i) q^{7} +(-1.65723 - 1.65723i) q^{8} +(-1.37319 + 2.37844i) q^{9} +(0.0632682 + 0.109584i) q^{10} +(-1.09384 + 4.08225i) q^{11} +(-0.132227 + 0.229023i) q^{12} +(0.565867 - 3.56087i) q^{13} +(-3.94794 - 1.44555i) q^{14} +(-0.0283562 + 0.0283562i) q^{15} +(-2.38725 + 4.13483i) q^{16} +(2.90357 + 5.02912i) q^{17} +(4.21547 + 1.12953i) q^{18} +(5.11216 - 1.36980i) q^{19} +(0.0295679 - 0.0295679i) q^{20} +(0.118683 - 1.32711i) q^{21} +6.71579 q^{22} +(0.755405 + 0.436133i) q^{23} +(-1.14006 - 0.305479i) q^{24} +(-4.32464 + 2.49683i) q^{25} +(-5.69837 + 0.595955i) q^{26} +2.89390i q^{27} +(-0.123754 + 1.38382i) q^{28} +0.362759 q^{29} +(0.0551867 + 0.0318621i) q^{30} +(-0.361057 + 1.34748i) q^{31} +(2.80082 + 0.750478i) q^{32} +(0.550859 + 2.05583i) q^{33} +(6.52511 - 6.52511i) q^{34} +(-0.0724379 + 0.197835i) q^{35} -1.44219i q^{36} +(-3.76857 + 1.00978i) q^{37} +(-4.20506 - 7.28338i) q^{38} +(-0.649839 - 1.69550i) q^{39} +(0.161623 + 0.0933128i) q^{40} +(-7.70995 - 7.70995i) q^{41} +(-2.08582 + 0.363646i) q^{42} +2.65570i q^{43} +(-0.574398 - 2.14368i) q^{44} +(0.0566020 - 0.211242i) q^{45} +(0.358745 - 1.33886i) q^{46} +(-0.748829 - 2.79467i) q^{47} +2.40445i q^{48} +(-2.36879 - 6.58702i) q^{49} +(5.61106 + 5.61106i) q^{50} +(2.53268 + 1.46224i) q^{51} +(0.677608 + 1.76795i) q^{52} +(-5.26830 - 9.12497i) q^{53} +(4.44189 - 1.19020i) q^{54} -0.336535i q^{55} +(-6.10864 + 1.06499i) q^{56} +(1.88467 - 1.88467i) q^{57} +(-0.149196 - 0.556806i) q^{58} +(-2.14179 - 0.573890i) q^{59} +(0.00545029 - 0.0203408i) q^{60} +(3.63628 + 2.09941i) q^{61} +2.21677 q^{62} +(3.05816 + 6.59136i) q^{63} +4.94130i q^{64} +(0.0298639 + 0.285551i) q^{65} +(2.92898 - 1.69105i) q^{66} +(9.76951 + 2.61773i) q^{67} +(-2.64091 - 1.52473i) q^{68} +0.439276 q^{69} +(0.333453 + 0.0298205i) q^{70} +(3.65698 - 3.65698i) q^{71} +(6.21730 - 1.66592i) q^{72} +(-11.4948 - 3.08002i) q^{73} +(3.09987 + 5.36914i) q^{74} +(-1.25741 + 2.17790i) q^{75} +(-1.96520 + 1.96520i) q^{76} +(7.17090 + 8.57944i) q^{77} +(-2.33519 + 1.69477i) q^{78} +(-4.27671 + 7.40747i) q^{79} +(0.0984006 - 0.367236i) q^{80} +(-3.39089 - 5.87319i) q^{81} +(-8.66319 + 15.0051i) q^{82} +(4.91372 + 4.91372i) q^{83} +(0.294475 + 0.634692i) q^{84} +(-0.326980 - 0.326980i) q^{85} +(4.07628 - 1.09224i) q^{86} +(0.158211 - 0.0913434i) q^{87} +(8.57795 - 4.95248i) q^{88} +(-2.08520 - 7.78209i) q^{89} -0.347518 q^{90} +(-6.84587 - 6.64335i) q^{91} -0.458047 q^{92} +(0.181829 + 0.678596i) q^{93} +(-3.98161 + 2.29878i) q^{94} +(-0.364977 + 0.210720i) q^{95} +(1.41050 - 0.377943i) q^{96} +(6.04128 + 6.04128i) q^{97} +(-9.13630 + 6.34501i) q^{98} +(-8.20733 - 8.20733i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 12 q^{3} - 6 q^{5} - 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 - 12 * q^3 - 6 * q^5 - 6 * q^7 - 16 * q^8 + 8 * q^9	$ 32 q - 2 q^{2} - 12 q^{3} - 6 q^{5} - 6 q^{7} - 16 q^{8} + 8 q^{9} - 10 q^{11} + 28 q^{14} - 44 q^{15} + 12 q^{16} - 4 q^{18} + 12 q^{19} - 26 q^{21} - 8 q^{22} - 12 q^{24} + 24 q^{26} - 6 q^{28} + 16 q^{29} + 24 q^{31} + 4 q^{32} + 48 q^{33} + 28 q^{35} - 8 q^{37} - 6 q^{39} - 132 q^{40} - 16 q^{42} - 42 q^{44} - 24 q^{45} + 12 q^{46} + 30 q^{47} + 88 q^{50} + 36 q^{52} - 12 q^{53} + 78 q^{54} + 40 q^{57} + 26 q^{58} - 54 q^{59} + 16 q^{60} - 48 q^{61} + 24 q^{63} - 8 q^{65} + 12 q^{66} + 16 q^{67} - 48 q^{68} + 50 q^{70} - 36 q^{71} + 22 q^{72} + 66 q^{73} + 12 q^{74} - 176 q^{78} - 32 q^{79} + 138 q^{80} + 16 q^{81} - 58 q^{84} - 84 q^{85} + 42 q^{86} - 24 q^{87} - 60 q^{89} + 48 q^{92} + 6 q^{93} - 72 q^{94} - 42 q^{96} - 86 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 - 12 * q^3 - 6 * q^5 - 6 * q^7 - 16 * q^8 + 8 * q^9 - 10 * q^11 + 28 * q^14 - 44 * q^15 + 12 * q^16 - 4 * q^18 + 12 * q^19 - 26 * q^21 - 8 * q^22 - 12 * q^24 + 24 * q^26 - 6 * q^28 + 16 * q^29 + 24 * q^31 + 4 * q^32 + 48 * q^33 + 28 * q^35 - 8 * q^37 - 6 * q^39 - 132 * q^40 - 16 * q^42 - 42 * q^44 - 24 * q^45 + 12 * q^46 + 30 * q^47 + 88 * q^50 + 36 * q^52 - 12 * q^53 + 78 * q^54 + 40 * q^57 + 26 * q^58 - 54 * q^59 + 16 * q^60 - 48 * q^61 + 24 * q^63 - 8 * q^65 + 12 * q^66 + 16 * q^67 - 48 * q^68 + 50 * q^70 - 36 * q^71 + 22 * q^72 + 66 * q^73 + 12 * q^74 - 176 * q^78 - 32 * q^79 + 138 * q^80 + 16 * q^81 - 58 * q^84 - 84 * q^85 + 42 * q^86 - 24 * q^87 - 60 * q^89 + 48 * q^92 + 6 * q^93 - 72 * q^94 - 42 * q^96 - 86 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.411280	−	1.53492i	−0.290819	−	1.08535i	−0.944482	−	0.328565i	$-0.893435\pi$
$2$	−0.411280	−	1.53492i	−0.290819	−	1.08535i	0.653663	−	0.756786i	$-0.273232\pi$
$3$	0.436133	−	0.251802i	0.251802	−	0.145378i	−0.368787	−	0.929514i	$-0.620227\pi$
$3$	0.436133	−	0.251802i	0.251802	−	0.145378i	0.620589	+	0.784136i	$0.286894\pi$
$4$	−0.454770	+	0.262561i	−0.227385	+	0.131281i
$5$	−0.0769162	+	0.0206096i	−0.0343980	+	0.00921691i	−0.275977	−	0.961164i	$-0.589001\pi$
$5$	−0.0769162	+	0.0206096i	−0.0343980	+	0.00921691i	0.241579	+	0.970381i	$0.422335\pi$
$6$	−0.565867	−	0.565867i	−0.231014	−	0.231014i
$7$	1.52171	−	2.16435i	0.575153	−	0.818046i
$7$	1.52171	−	2.16435i	0.575153	−	0.818046i
$8$	−1.65723	−	1.65723i	−0.585918	−	0.585918i
$9$	−1.37319	+	2.37844i	−0.457731	+	0.792813i
$10$	0.0632682	+	0.109584i	0.0200072	+	0.0346534i
$11$	−1.09384	+	4.08225i	−0.329804	+	1.23084i	0.579590	+	0.814908i	$0.303213\pi$
$11$	−1.09384	+	4.08225i	−0.329804	+	1.23084i	−0.909394	+	0.415936i	$0.863454\pi$
$12$	−0.132227	+	0.229023i	−0.0381706	+	0.0661134i
$13$	0.565867	−	3.56087i	0.156943	−	0.987608i
$13$	0.565867	−	3.56087i	0.156943	−	0.987608i
$14$	−3.94794	−	1.44555i	−1.05513	−	0.386339i
$15$	−0.0283562	+	0.0283562i	−0.00732153	+	0.00732153i
$16$	−2.38725	+	4.13483i	−0.596811	+	1.03371i
$17$	2.90357	+	5.02912i	0.704218	+	1.21974i	0.966973	+	0.254879i	$0.0820357\pi$
$17$	2.90357	+	5.02912i	0.704218	+	1.21974i	−0.262755	+	0.964863i	$0.584631\pi$
$18$	4.21547	+	1.12953i	0.993596	+	0.266233i
$19$	5.11216	−	1.36980i	1.17281	−	0.314254i	0.380740	−	0.924682i	$-0.375669\pi$
$19$	5.11216	−	1.36980i	1.17281	−	0.314254i	0.792071	+	0.610429i	$0.209003\pi$
$20$	0.0295679	−	0.0295679i	0.00661158	−	0.00661158i
$21$	0.118683	−	1.32711i	0.0258987	−	0.289600i
$22$	6.71579			1.43181
$23$	0.755405	+	0.436133i	0.157513	+	0.0909400i	0.576685	−	0.816967i	$-0.304346\pi$
$23$	0.755405	+	0.436133i	0.157513	+	0.0909400i	−0.419172	+	0.907907i	$0.637680\pi$
$24$	−1.14006	−	0.305479i	−0.232715	−	0.0623557i
$25$	−4.32464	+	2.49683i	−0.864927	+	0.499366i
$26$	−5.69837	+	0.595955i	−1.11754	+	0.116876i
$27$			2.89390i			0.556931i
$28$	−0.123754	+	1.38382i	−0.0233873	+	0.261518i
$29$	0.362759			0.0673627			0.0336814	−	0.999433i	$-0.489277\pi$
$29$	0.362759			0.0673627			0.0336814	+	0.999433i	$0.489277\pi$
$30$	0.0551867	+	0.0318621i	0.0100757	+	0.00581719i
$31$	−0.361057	+	1.34748i	−0.0648477	+	0.242015i	−0.990740	−	0.135773i	$-0.956648\pi$
$31$	−0.361057	+	1.34748i	−0.0648477	+	0.242015i	0.925892	+	0.377787i	$0.123315\pi$
$32$	2.80082	+	0.750478i	0.495120	+	0.132667i
$33$	0.550859	+	2.05583i	0.0958922	+	0.357875i
$34$	6.52511	−	6.52511i	1.11905	−	1.11905i
$35$	−0.0724379	+	0.197835i	−0.0122442	+	0.0334403i
$36$		−	1.44219i		−	0.240365i
$37$	−3.76857	+	1.00978i	−0.619549	+	0.166008i	−0.554923	−	0.831902i	$-0.687252\pi$
$37$	−3.76857	+	1.00978i	−0.619549	+	0.166008i	−0.0646262	+	0.997910i	$0.520586\pi$
$38$	−4.20506	−	7.28338i	−0.682151	−	1.18152i
$39$	−0.649839	−	1.69550i	−0.104058	−	0.271497i
$40$	0.161623	+	0.0933128i	0.0255548	+	0.0147541i
$41$	−7.70995	−	7.70995i	−1.20409	−	1.20409i	−0.972911	−	0.231182i	$-0.925741\pi$
$41$	−7.70995	−	7.70995i	−1.20409	−	1.20409i	−0.231182	−	0.972911i	$-0.574259\pi$
$42$	−2.08582	+	0.363646i	−0.321849	+	0.0561119i
$43$			2.65570i			0.404990i	0.979283	+	0.202495i	$0.0649050\pi$
$43$			2.65570i			0.404990i	−0.979283	+	0.202495i	$0.935095\pi$
$44$	−0.574398	−	2.14368i	−0.0865938	−	0.323172i
$45$	0.0566020	−	0.211242i	0.00843773	−	0.0314900i
$46$	0.358745	−	1.33886i	0.0528941	−	0.197404i
$47$	−0.748829	−	2.79467i	−0.109228	−	0.407644i	0.889563	−	0.456813i	$-0.151009\pi$
$47$	−0.748829	−	2.79467i	−0.109228	−	0.407644i	−0.998790	+	0.0491692i	$0.984343\pi$
$48$			2.40445i			0.347052i
$49$	−2.36879	−	6.58702i	−0.338399	−	0.941003i
$50$	5.61106	+	5.61106i	0.793524	+	0.793524i
$51$	2.53268	+	1.46224i	0.354646	+	0.204755i
$52$	0.677608	+	1.76795i	0.0939673	+	0.245171i
$53$	−5.26830	−	9.12497i	−0.723657	−	1.25341i	−0.959524	−	0.281625i	$-0.909127\pi$
$53$	−5.26830	−	9.12497i	−0.723657	−	1.25341i	0.235868	−	0.971785i	$-0.424207\pi$
$54$	4.44189	−	1.19020i	0.604465	−	0.161966i
$55$		−	0.336535i		−	0.0453784i
$56$	−6.10864	+	1.06499i	−0.816301	+	0.142316i
$57$	1.88467	−	1.88467i	0.249630	−	0.249630i
$58$	−0.149196	−	0.556806i	−0.0195903	−	0.0731122i
$59$	−2.14179	−	0.573890i	−0.278837	−	0.0747142i	0.116690	−	0.993168i	$-0.462772\pi$
$59$	−2.14179	−	0.573890i	−0.278837	−	0.0747142i	−0.395527	+	0.918454i	$0.629438\pi$
$60$	0.00545029	−	0.0203408i	0.000703630	−	0.00262598i
$61$	3.63628	+	2.09941i	0.465578	+	0.268802i	0.714387	−	0.699751i	$-0.246706\pi$
$61$	3.63628	+	2.09941i	0.465578	+	0.268802i	−0.248809	+	0.968553i	$0.580039\pi$
$62$	2.21677			0.281530
$63$	3.05816	+	6.59136i	0.385292	+	0.830433i
$64$			4.94130i			0.617662i
$65$	0.0298639	+	0.285551i	0.00370416	+	0.0354182i
$66$	2.92898	−	1.69105i	0.360532	−	0.208153i
$67$	9.76951	+	2.61773i	1.19354	+	0.319807i	0.800282	−	0.599623i	$-0.204683\pi$
$67$	9.76951	+	2.61773i	1.19354	+	0.319807i	0.393253	+	0.919430i	$0.371350\pi$
$68$	−2.64091	−	1.52473i	−0.320257	−	0.184901i
$69$	0.439276			0.0528826
$70$	0.333453	+	0.0298205i	0.0398553	+	0.00356423i
$71$	3.65698	−	3.65698i	0.434004	−	0.434004i	−0.455984	−	0.889988i	$-0.650713\pi$
$71$	3.65698	−	3.65698i	0.434004	−	0.434004i	0.889988	+	0.455984i	$0.150713\pi$
$72$	6.21730	−	1.66592i	0.732716	−	0.196331i
$73$	−11.4948	−	3.08002i	−1.34536	−	0.360489i	−0.486942	−	0.873434i	$-0.661888\pi$
$73$	−11.4948	−	3.08002i	−1.34536	−	0.360489i	−0.858421	+	0.512945i	$0.828554\pi$
$74$	3.09987	+	5.36914i	0.360353	+	0.624150i
$75$	−1.25741	+	2.17790i	−0.145193	+	0.251482i
$76$	−1.96520	+	1.96520i	−0.225424	+	0.225424i
$77$	7.17090	+	8.57944i	0.817200	+	0.977718i
$78$	−2.33519	+	1.69477i	−0.264408	+	0.191895i
$79$	−4.27671	+	7.40747i	−0.481167	+	0.833406i	−0.999766	−	0.0216116i	$-0.993120\pi$
$79$	−4.27671	+	7.40747i	−0.481167	+	0.833406i	0.518599	+	0.855017i	$0.326454\pi$
$80$	0.0984006	−	0.367236i	0.0110015	−	0.0410582i
$81$	−3.39089	−	5.87319i	−0.376765	−	0.652577i
$82$	−8.66319	+	15.0051i	−0.956690	+	1.65703i
$83$	4.91372	+	4.91372i	0.539351	+	0.539351i	0.923338	−	0.383987i	$-0.125449\pi$
$83$	4.91372	+	4.91372i	0.539351	+	0.539351i	−0.383987	+	0.923338i	$0.625449\pi$
$84$	0.294475	+	0.634692i	0.0321299	+	0.0692506i
$85$	−0.326980	−	0.326980i	−0.0354659	−	0.0354659i
$86$	4.07628	−	1.09224i	0.439557	−	0.117779i
$87$	0.158211	−	0.0913434i	0.0169620	−	0.00979304i
$88$	8.57795	−	4.95248i	0.914413	−	0.527936i
$89$	−2.08520	−	7.78209i	−0.221031	−	0.824899i	−0.983956	−	0.178412i	$-0.942904\pi$
$89$	−2.08520	−	7.78209i	−0.221031	−	0.824899i	0.762925	−	0.646487i	$-0.223763\pi$
$90$	−0.347518			−0.0366316
$91$	−6.84587	−	6.64335i	−0.717642	−	0.696412i
$92$	−0.458047			−0.0477547
$93$	0.181829	+	0.678596i	0.0188548	+	0.0703671i
$94$	−3.98161	+	2.29878i	−0.410671	+	0.237101i
$95$	−0.364977	+	0.210720i	−0.0374459	+	0.0216194i
$96$	1.41050	−	0.377943i	0.143959	−	0.0385736i
$97$	6.04128	+	6.04128i	0.613399	+	0.613399i	0.943830	−	0.330431i	$-0.107194\pi$
$97$	6.04128	+	6.04128i	0.613399	+	0.613399i	−0.330431	+	0.943830i	$0.607194\pi$
$98$	−9.13630	+	6.34501i	−0.922905	+	0.640943i
$99$	−8.20733	−	8.20733i	−0.824868	−	0.824868i
$100$	1.31114	−	2.27096i	0.131114	−	0.227096i
$101$	5.60987	+	9.71658i	0.558203	+	0.966836i	0.997647	+	0.0685657i	$0.0218423\pi$
$101$	5.60987	+	9.71658i	0.558203	+	0.966836i	−0.439444	+	0.898270i	$0.644824\pi$
$102$	1.20278	−	4.48885i	0.119093	−	0.444462i
$103$	4.82752	−	8.36150i	0.475669	−	0.823883i	−0.523942	−	0.851754i	$-0.675539\pi$
$103$	4.82752	−	8.36150i	0.475669	−	0.823883i	0.999612	+	0.0278704i	$0.00887259\pi$
$104$	−6.83894	+	4.96340i	−0.670613	+	0.486701i
$105$	0.0182227	+	0.104522i	0.00177835	+	0.0102003i
$106$	−11.8393	+	11.8393i	−1.14994	+	1.14994i
$107$	8.81408	−	15.2664i	0.852089	−	1.47586i	−0.0272305	−	0.999629i	$-0.508669\pi$
$107$	8.81408	−	15.2664i	0.852089	−	1.47586i	0.879319	−	0.476232i	$-0.157998\pi$
$108$	−0.759825	−	1.31606i	−0.0731142	−	0.126638i
$109$	−13.1784	−	3.53114i	−1.26226	−	0.338222i	−0.435199	−	0.900334i	$-0.643322\pi$
$109$	−13.1784	−	3.53114i	−1.26226	−	0.338222i	−0.827061	+	0.562113i	$0.809989\pi$
$110$	−0.516553	+	0.138410i	−0.0492514	+	0.0131969i
$111$	−1.38933	+	1.38933i	−0.131870	+	0.131870i
$112$	5.31651	+	11.4588i	0.502363	+	1.08276i
$113$	−6.02917			−0.567176			−0.283588	−	0.958946i	$-0.591525\pi$
$113$	−6.02917			−0.567176			−0.283588	+	0.958946i	$0.591525\pi$
$114$	−3.66793	−	2.11768i	−0.343533	−	0.198339i
$115$	−0.0670914	−	0.0179771i	−0.00625631	−	0.00167637i
$116$	−0.164972	+	0.0952466i	−0.0153173	+	0.00884343i
$117$	7.69226	+	6.23564i	0.711150	+	0.576485i
$118$			3.52350i			0.324364i
$119$	15.3032	+	1.36855i	1.40284	+	0.125455i
$120$	0.0939853			0.00857964
$121$	−5.94201	−	3.43062i	−0.540183	−	0.311875i
$122$	1.72689	−	6.44484i	0.156345	−	0.583488i
$123$	−5.30394	−	1.42119i	−0.478240	−	0.128144i
$124$	−0.189599	−	0.707593i	−0.0170265	−	0.0635438i
$125$	0.562709	−	0.562709i	0.0503302	−	0.0503302i
$126$	8.85943	−	7.40492i	0.789261	−	0.659683i
$127$		−	0.259825i		−	0.0230558i	−0.999934	−	0.0115279i	$-0.996330\pi$
$127$		−	0.259825i		−	0.0230558i	0.999934	−	0.0115279i	$-0.00366952\pi$
$128$	13.1861	−	3.53321i	1.16550	−	0.312295i
$129$	0.668709	+	1.15824i	0.0588766	+	0.101977i
$130$	0.426015	−	0.163280i	0.0373640	−	0.0143206i
$131$	0.679285	+	0.392185i	0.0593494	+	0.0342654i	0.529381	−	0.848384i	$-0.322424\pi$
$131$	0.679285	+	0.392185i	0.0593494	+	0.0342654i	−0.470032	+	0.882650i	$0.655758\pi$
$132$	−0.790296	−	0.790296i	−0.0687865	−	0.0687865i
$133$	4.81451	−	13.1489i	0.417471	−	1.14016i
$134$		−	16.0720i		−	1.38841i
$135$	−0.0596422	−	0.222588i	−0.00513318	−	0.0191573i
$136$	3.52253	−	13.1463i	0.302055	−	1.12728i
$137$	−3.57044	+	13.3251i	−0.305044	+	1.13844i	0.627864	+	0.778323i	$0.283929\pi$
$137$	−3.57044	+	13.3251i	−0.305044	+	1.13844i	−0.932908	+	0.360115i	$0.882737\pi$
$138$	−0.180665	−	0.674252i	−0.0153793	−	0.0573962i
$139$		−	3.12982i		−	0.265468i	−0.991152	−	0.132734i	$-0.957624\pi$
$139$		−	3.12982i		−	0.265468i	0.991152	−	0.132734i	$-0.0423755\pi$
$140$	−0.0190014	−	0.108989i	−0.00160591	−	0.00921124i
$141$	−1.03029	−	1.03029i	−0.0867661	−	0.0867661i
$142$	−7.11720	−	4.10912i	−0.597262	−	0.344830i
$143$	13.9174	+	6.20502i	1.16383	+	0.518890i
$144$	−6.55629	−	11.3558i	−0.546358	−	0.946319i
$145$	−0.0279021	+	0.00747634i	−0.00231714	+	0.000620876i
$146$			18.9103i			1.56503i
$147$	−2.69173	−	2.27635i	−0.222010	−	0.187750i
$148$	1.44870	−	1.44870i	0.119082	−	0.119082i
$149$	0.876694	+	3.27187i	0.0718216	+	0.268042i	0.992494	−	0.122295i	$-0.0390253\pi$
$149$	0.876694	+	3.27187i	0.0718216	+	0.268042i	−0.920672	+	0.390337i	$0.872359\pi$
$150$	3.86004	+	1.03430i	0.315171	+	0.0844499i
$151$	−4.21062	+	15.7142i	−0.342655	+	1.27881i	0.552673	+	0.833398i	$0.313608\pi$
$151$	−4.21062	+	15.7142i	−0.342655	+	1.27881i	−0.895328	+	0.445408i	$0.853059\pi$
$152$	−10.7421	−	6.20195i	−0.871299	−	0.503044i
$153$	−15.9486			−1.28937
$154$	10.2195	−	14.5353i	0.823510	−	1.17129i
$155$		−	0.111084i		−	0.00892252i
$156$	0.740700	+	0.600439i	0.0593034	+	0.0480736i
$157$	16.6451	−	9.61006i	1.32842	−	0.766966i	0.343368	−	0.939201i	$-0.388432\pi$
$157$	16.6451	−	9.61006i	1.32842	−	0.766966i	0.985056	+	0.172235i	$0.0550988\pi$
$158$	13.1288	+	3.51785i	1.04447	+	0.279865i
$159$	−4.59536	−	2.65313i	−0.364436	−	0.210407i
$160$	−0.230896			−0.0182539
$161$	2.09345	−	0.971289i	0.164987	−	0.0765483i
$162$	−7.62026	+	7.62026i	−0.598704	+	0.598704i
$163$	−1.20004	+	0.321549i	−0.0939942	+	0.0251857i	−0.305510	−	0.952189i	$-0.598827\pi$
$163$	−1.20004	+	0.321549i	−0.0939942	+	0.0251857i	0.211515	+	0.977375i	$0.432160\pi$
$164$	5.53059	+	1.48192i	0.431866	+	0.115718i
$165$	−0.0847400	−	0.146774i	−0.00659700	−	0.0114263i
$166$	5.52124	−	9.56307i	0.428532	−	0.742239i
$167$	−7.31443	+	7.31443i	−0.566007	+	0.566007i	−0.931007	−	0.365000i	$-0.881069\pi$
$167$	−7.31443	+	7.31443i	−0.566007	+	0.566007i	0.365000	+	0.931007i	$0.381069\pi$
$168$	−2.39601	+	2.00264i	−0.184856	+	0.154507i
$169$	−12.3596	−	4.02996i	−0.950738	−	0.309997i
$170$	−0.367407	+	0.636367i	−0.0281788	+	0.0488071i
$171$	−3.76200	+	14.0400i	−0.287687	+	1.07366i
$172$	−0.697284	−	1.20773i	−0.0531674	−	0.0920887i
$173$	1.58153	−	2.73929i	0.120241	−	0.208264i	−0.799621	−	0.600504i	$-0.794966\pi$
$173$	1.58153	−	2.73929i	0.120241	−	0.208264i	0.919863	+	0.392240i	$0.128300\pi$
$174$	−0.205274	−	0.205274i	−0.0155618	−	0.0155618i
$175$	−1.17684	+	13.1595i	−0.0889608	+	0.994762i
$176$	−14.2682	−	14.2682i	−1.07550	−	1.07550i
$177$	−1.07861	+	0.289013i	−0.0810734	+	0.0217235i
$178$	−11.0873	+	6.40123i	−0.831025	+	0.479793i
$179$	−5.02551	+	2.90148i	−0.375624	+	0.216867i	−0.675913	−	0.736982i	$-0.736250\pi$
$179$	−5.02551	+	2.90148i	−0.375624	+	0.216867i	0.300289	+	0.953848i	$0.402917\pi$
$180$	0.0297230	+	0.110928i	0.00221542	+	0.00826807i
$181$	13.7005			1.01835			0.509176	−	0.860662i	$-0.329950\pi$
$181$	13.7005			1.01835			0.509176	+	0.860662i	$0.329950\pi$
$182$	−7.38142	+	13.2401i	−0.547147	+	0.981423i
$183$	2.11454			0.156311
$184$	−0.529106	−	1.97465i	−0.0390062	−	0.145573i
$185$	0.269053	−	0.155338i	0.0197812	−	0.0114207i
$186$	0.966806	−	0.558186i	0.0708896	−	0.0409282i
$187$	−23.7062	+	6.35205i	−1.73357	+	0.464508i
$188$	1.07432	+	1.07432i	0.0783526	+	0.0783526i
$189$	6.26339	+	4.40367i	0.455595	+	0.320320i
$190$	0.473545	+	0.473545i	0.0343546	+	0.0343546i
$191$	4.22861	−	7.32417i	0.305972	−	0.529958i	−0.671506	−	0.740999i	$-0.734352\pi$
$191$	4.22861	−	7.32417i	0.305972	−	0.529958i	0.977477	+	0.211041i	$0.0676854\pi$
$192$	1.24423	+	2.15506i	0.0897943	+	0.155528i
$193$	0.127796	−	0.476941i	0.00919896	−	0.0343310i	−0.961174	−	0.275944i	$-0.911010\pi$
$193$	0.127796	−	0.476941i	0.00919896	−	0.0343310i	0.970373	+	0.241613i	$0.0776763\pi$
$194$	6.78820	−	11.7575i	0.487365	−	0.844140i
$195$	0.0849268	+	0.117018i	0.00608173	+	0.00837987i
$196$	2.80675	+	2.37362i	0.200482	+	0.169545i
$197$	−2.77899	+	2.77899i	−0.197995	+	0.197995i	−0.799140	−	0.601145i	$-0.794711\pi$
$197$	−2.77899	+	2.77899i	−0.197995	+	0.197995i	0.601145	+	0.799140i	$0.294711\pi$
$198$	−9.22207	+	15.9731i	−0.655384	+	1.13516i
$199$	8.03206	+	13.9119i	0.569377	+	0.986191i	0.996628	+	0.0820571i	$0.0261490\pi$
$199$	8.03206	+	13.9119i	0.569377	+	0.986191i	−0.427250	+	0.904133i	$0.640518\pi$
$200$	11.3047	+	3.02909i	0.799364	+	0.214189i
$201$	4.91995	−	1.31830i	0.347027	−	0.0929856i
$202$	12.6069	−	12.6069i	0.887020	−	0.887020i
$203$	0.552015	−	0.785137i	0.0387439	−	0.0551058i
$204$	−1.53572			−0.107522
$205$	0.751920	+	0.434121i	0.0525164	+	0.0303203i
$206$	−14.8197	−	3.97092i	−1.03254	−	0.276667i
$207$	−2.07463	+	1.19779i	−0.144197	+	0.0832521i
$208$	13.3727	+	10.8404i	0.927232	+	0.751649i
$209$			22.3675i			1.54719i
$210$	0.152939	−	0.0709583i	0.0105538	−	0.00489659i
$211$	21.0547			1.44947			0.724734	−	0.689029i	$-0.241963\pi$
$211$	21.0547			1.44947			0.724734	+	0.689029i	$0.241963\pi$
$212$	4.79173	+	2.76651i	0.329097	+	0.190004i
$213$	0.674096	−	2.51576i	0.0461883	−	0.172377i
$214$	−27.0578	−	7.25011i	−1.84963	−	0.495607i
$215$	−0.0547330	−	0.204266i	−0.00373276	−	0.0139309i
$216$	4.79584	−	4.79584i	0.326316	−	0.326316i
$217$	2.36699	+	2.83193i	0.160682	+	0.192244i
$218$			21.6800i			1.46836i
$219$	−5.78881	+	1.55111i	−0.391172	+	0.104814i
$220$	0.0883611	+	0.153046i	0.00595730	+	0.0103183i
$221$	19.5511	−	7.49340i	1.31515	−	0.504061i
$222$	2.70391	+	1.56111i	0.181475	+	0.104775i
$223$	−19.3108	−	19.3108i	−1.29314	−	1.29314i	−0.932832	−	0.360311i	$-0.882670\pi$
$223$	−19.3108	−	19.3108i	−1.29314	−	1.29314i	−0.360311	−	0.932832i	$-0.617330\pi$
$224$	5.88633	−	4.91994i	0.393297	−	0.328727i
$225$		−	13.7145i		−	0.914300i
$226$	2.47968	+	9.25428i	0.164946	+	0.615585i
$227$	0.897156	−	3.34823i	0.0595463	−	0.222230i	−0.929740	−	0.368216i	$-0.879969\pi$
$227$	0.897156	−	3.34823i	0.0595463	−	0.222230i	0.989287	+	0.145986i	$0.0466354\pi$
$228$	−0.362248	+	1.35193i	−0.0239905	+	0.0895337i
$229$	4.98883	+	18.6186i	0.329671	+	1.23035i	0.909532	+	0.415633i	$0.136440\pi$
$229$	4.98883	+	18.6186i	0.329671	+	1.23035i	−0.579861	+	0.814715i	$0.696893\pi$
$230$			0.110373i			0.00727781i
$231$	5.28778	+	1.93613i	0.347911	+	0.127388i
$232$	−0.601175	−	0.601175i	−0.0394691	−	0.0394691i
$233$	4.47705	+	2.58482i	0.293301	+	0.169337i	0.639430	−	0.768850i	$-0.279171\pi$
$233$	4.47705	+	2.58482i	0.293301	+	0.169337i	−0.346129	+	0.938187i	$0.612504\pi$
$234$	6.40752	−	14.3716i	0.418872	−	0.939500i
$235$	0.115194	+	0.199522i	0.00751444	+	0.0130154i
$236$	1.12470	−	0.301363i	0.0732119	−	0.0196171i
$237$			4.30752i			0.279804i
$238$	−4.19327	−	24.0519i	−0.271809	−	1.55906i
$239$	6.85569	−	6.85569i	0.443458	−	0.443458i	−0.449715	−	0.893172i	$-0.648474\pi$
$239$	6.85569	−	6.85569i	0.443458	−	0.443458i	0.893172	+	0.449715i	$0.148474\pi$
$240$	−0.0495548	−	0.184941i	−0.00319875	−	0.0119379i
$241$	−2.15968	−	0.578684i	−0.139117	−	0.0372763i	0.188589	−	0.982056i	$-0.439609\pi$
$241$	−2.15968	−	0.578684i	−0.139117	−	0.0372763i	−0.327706	+	0.944780i	$0.606275\pi$
$242$	−2.82189	+	10.5314i	−0.181398	+	0.676986i
$243$	−10.4763	−	6.04851i	−0.672056	−	0.388012i
$244$	−2.20490			−0.141154
$245$	0.317955	+	0.457829i	0.0203134	+	0.0292496i
$246$			8.72562i			0.556325i
$247$	−1.98487	−	18.9789i	−0.126295	−	1.20760i
$248$	2.83144	−	1.63473i	0.179796	−	0.103805i
$249$	3.38032	+	0.905754i	0.214219	+	0.0573998i
$250$	−1.09514	−	0.632281i	−0.0692629	−	0.0399890i
$251$	24.8342			1.56752			0.783759	−	0.621064i	$-0.213300\pi$
$251$	24.8342			1.56752			0.783759	+	0.621064i	$0.213300\pi$
$252$	−3.12140	−	2.19459i	−0.196629	−	0.138246i
$253$	−2.60669	+	2.60669i	−0.163881	+	0.163881i
$254$	−0.398810	+	0.106861i	−0.0250236	+	0.00670505i
$255$	−0.224941	−	0.0602727i	−0.0140863	−	0.00377442i
$256$	−5.90508	−	10.2279i	−0.369067	−	0.639244i
$257$	−6.67557	+	11.5624i	−0.416411	+	0.721244i	−0.995575	−	0.0939662i	$-0.970045\pi$
$257$	−6.67557	+	11.5624i	−0.416411	+	0.721244i	0.579165	+	0.815210i	$0.303379\pi$
$258$	1.50277	−	1.50277i	0.0935586	−	0.0935586i
$259$	−3.54915	+	9.69309i	−0.220533	+	0.602299i
$260$	−0.0885559	−	0.122019i	−0.00549200	−	0.00756729i
$261$	−0.498138	+	0.862801i	−0.0308340	+	0.0534060i
$262$	0.322596	−	1.20394i	0.0199300	−	0.0743799i
$263$	0.211897	+	0.367017i	0.0130662	+	0.0226312i	0.872485	−	0.488642i	$-0.162507\pi$
$263$	0.211897	+	0.367017i	0.0130662	+	0.0226312i	−0.859418	+	0.511273i	$0.829174\pi$
$264$	2.49409	−	4.31988i	0.153500	−	0.265870i
$265$	0.593280	+	0.593280i	0.0364449	+	0.0364449i
$266$	−22.1626	−	1.98199i	−1.35888	−	0.121524i
$267$	−2.86897	−	2.86897i	−0.175578	−	0.175578i
$268$	−5.13019	+	1.37463i	−0.313376	+	0.0839689i
$269$	−12.5697	+	7.25714i	−0.766390	+	0.442476i	−0.831585	−	0.555397i	$-0.812566\pi$
$269$	−12.5697	+	7.25714i	−0.766390	+	0.442476i	0.0651951	+	0.997873i	$0.479233\pi$
$270$	−0.317124	+	0.183092i	−0.0192996	+	0.0111426i
$271$	−5.12023	−	19.1090i	−0.311032	−	1.16079i	−0.927628	−	0.373506i	$-0.878155\pi$
$271$	−5.12023	−	19.1090i	−0.311032	−	1.16079i	0.616596	−	0.787280i	$-0.288511\pi$
$272$	−27.7261			−1.68114
$273$	−4.65851	−	1.17358i	−0.281946	−	0.0710285i
$274$	21.9213			1.32432
$275$	−5.46224	−	20.3854i	−0.329386	−	1.22928i
$276$	−0.199769	+	0.115337i	−0.0120247	+	0.00694246i
$277$	20.5717	−	11.8771i	1.23603	−	0.713623i	0.267751	−	0.963488i	$-0.413719\pi$
$277$	20.5717	−	11.8771i	1.23603	−	0.713623i	0.968281	+	0.249865i	$0.0803861\pi$
$278$	−4.80401	+	1.28723i	−0.288125	+	0.0772030i
$279$	−2.70910	−	2.70910i	−0.162190	−	0.162190i
$280$	0.447904	−	0.207812i	0.0267674	−	0.0124191i
$281$	9.66092	+	9.66092i	0.576322	+	0.576322i	0.933888	−	0.357566i	$-0.116393\pi$
$281$	9.66092	+	9.66092i	0.576322	+	0.576322i	−0.357566	+	0.933888i	$0.616393\pi$
$282$	−1.15767	+	2.00515i	−0.0689384	+	0.119405i
$283$	−13.3825	−	23.1791i	−0.795506	−	1.37786i	−0.922517	−	0.385956i	$-0.873872\pi$
$283$	−13.3825	−	23.1791i	−0.795506	−	1.37786i	0.127011	−	0.991901i	$-0.459462\pi$
$284$	−0.702902	+	2.62326i	−0.0417095	+	0.155662i
$285$	−0.106119	+	0.183804i	−0.00628595	+	0.0108876i
$286$	3.80025	−	23.9141i	0.224713	−	1.41407i
$287$	−28.4193	+	4.95469i	−1.67754	+	0.292466i
$288$	−5.63103	+	5.63103i	−0.331812	+	0.331812i
$289$	−8.36139	+	14.4824i	−0.491847	+	0.851903i
$290$	0.0229511	+	0.0397525i	0.00134774	+	0.00233435i
$291$	4.15600	+	1.11360i	0.243629	+	0.0652802i
$292$	6.03618	−	1.61739i	0.353241	−	0.0946505i
$293$	21.8755	−	21.8755i	1.27798	−	1.27798i	0.336181	−	0.941797i	$-0.390864\pi$
$293$	21.8755	−	21.8755i	1.27798	−	1.27798i	0.941797	−	0.336181i	$-0.109136\pi$
$294$	−2.38696	+	5.06780i	−0.139210	+	0.295560i
$295$	0.176566			0.0102801
$296$	7.91882	+	4.57193i	0.460272	+	0.265738i
$297$	−11.8136	−	3.16545i	−0.685495	−	0.183678i
$298$	4.66148	−	2.69131i	0.270032	−	0.155903i
$299$	1.98047	−	2.44310i	0.114534	−	0.141288i
$300$		−	1.32059i		−	0.0762443i
$301$	5.74785	+	4.04121i	0.331301	+	0.232931i
$302$	25.8518			1.48760
$303$	4.89330	+	2.82515i	0.281113	+	0.162300i
$304$	−6.54010	+	24.4080i	−0.375100	+	1.39989i
$305$	−0.322957	−	0.0865362i	−0.0184925	−	0.00495505i
$306$	6.55934	+	24.4798i	0.374973	+	1.39942i
$307$	2.49534	−	2.49534i	0.142417	−	0.142417i	−0.632304	−	0.774720i	$-0.717891\pi$
$307$	2.49534	−	2.49534i	0.142417	−	0.142417i	0.774720	+	0.632304i	$0.217891\pi$
$308$	−5.51374	−	2.01887i	−0.314174	−	0.115036i
$309$		−	4.86230i		−	0.276607i
$310$	−0.170505	+	0.0456868i	−0.00968406	+	0.00259484i
$311$	−15.1553	−	26.2497i	−0.859378	−	1.48849i	−0.872523	−	0.488572i	$-0.837518\pi$
$311$	−15.1553	−	26.2497i	−0.859378	−	1.48849i	0.0131458	−	0.999914i	$-0.495815\pi$
$312$	−1.73290	+	3.88676i	−0.0981060	+	0.220044i
$313$	16.8628	+	9.73575i	0.953143	+	0.550297i	0.894056	−	0.447956i	$-0.147848\pi$
$313$	16.8628	+	9.73575i	0.953143	+	0.550297i	0.0590869	+	0.998253i	$0.481181\pi$
$314$	−21.5964	−	21.5964i	−1.21876	−	1.21876i
$315$	−0.371068	−	0.443955i	−0.0209073	−	0.0250140i
$316$		−	4.49159i		−	0.252672i
$317$	−1.29749	−	4.84229i	−0.0728741	−	0.271970i	0.919869	−	0.392226i	$-0.128295\pi$
$317$	−1.29749	−	4.84229i	−0.0728741	−	0.271970i	−0.992743	+	0.120256i	$0.961628\pi$
$318$	−2.18236	+	8.14468i	−0.122381	+	0.456731i
$319$	−0.396799	+	1.48087i	−0.0222165	+	0.0829131i
$320$	−0.101838	−	0.380066i	−0.00569294	−	0.0212463i
$321$		−	8.87759i		−	0.495499i
$322$	−2.35184	−	2.81380i	−0.131063	−	0.156807i
$323$	21.7324	+	21.7324i	1.20922	+	1.20922i
$324$	3.08415	+	1.78063i	0.171341	+	0.0989240i
$325$	6.44372	+	16.8123i	0.357433	+	0.932581i
$326$	0.987103	+	1.70971i	0.0546706	+	0.0946922i
$327$	−6.63667	+	1.77829i	−0.367009	+	0.0983397i
$328$			25.5543i			1.41100i
$329$	−7.18813	−	2.63195i	−0.396294	−	0.145104i
$330$	−0.190434	+	0.190434i	−0.0104831	+	0.0104831i
$331$	4.96381	+	18.5252i	0.272835	+	1.01824i	0.957278	+	0.289169i	$0.0933789\pi$
$331$	4.96381	+	18.5252i	0.272835	+	1.01824i	−0.684443	+	0.729067i	$0.739954\pi$
$332$	−3.52477	−	0.944458i	−0.193447	−	0.0518339i
$333$	2.77326	−	10.3499i	0.151974	−	0.567173i
$334$	14.2353	+	8.21877i	0.778922	+	0.449711i
$335$	−0.805384			−0.0440029
$336$	5.20406	+	3.65888i	0.283905	+	0.199608i
$337$			3.01241i			0.164097i	0.996628	+	0.0820483i	$0.0261462\pi$
$337$			3.01241i			0.164097i	−0.996628	+	0.0820483i	$0.973854\pi$
$338$	−1.10241	+	20.6284i	−0.0599629	+	1.12204i
$339$	−2.62952	+	1.51815i	−0.142816	+	0.0824548i
$340$	0.234553	+	0.0628482i	0.0127204	+	0.00340842i
$341$	−5.10582	−	2.94785i	−0.276496	−	0.159635i
$342$	23.0974			1.24897
$343$	−17.8612	−	4.89665i	−0.964415	−	0.264394i
$344$	4.40110	−	4.40110i	0.237291	−	0.237291i
$345$	−0.0337874	+	0.00905332i	−0.00181905	+	0.000487414i
$346$	−4.85503	−	1.30090i	−0.261008	−	0.0699369i
$347$	4.11910	+	7.13449i	0.221125	+	0.382999i	0.955150	−	0.296123i	$-0.0956939\pi$
$347$	4.11910	+	7.13449i	0.221125	+	0.382999i	−0.734025	+	0.679122i	$0.762361\pi$
$348$	−0.0479665	+	0.0830804i	−0.00257127	+	0.00445358i
$349$	−8.06122	+	8.06122i	−0.431507	+	0.431507i	−0.889141	−	0.457634i	$-0.848697\pi$
$349$	−8.06122	+	8.06122i	−0.431507	+	0.431507i	0.457634	+	0.889141i	$0.348697\pi$
$350$	20.6827	−	3.60587i	1.10554	−	0.192742i
$351$	10.3048	+	1.63756i	0.550029	+	0.0874066i
$352$	−6.12728	+	10.6128i	−0.326585	+	0.565662i
$353$	4.37468	−	16.3265i	0.232841	−	0.868974i	−0.746270	−	0.665644i	$-0.768157\pi$
$353$	4.37468	−	16.3265i	0.232841	−	0.868974i	0.979110	−	0.203330i	$-0.0651763\pi$
$354$	0.887222	+	1.53671i	0.0471553	+	0.0816754i
$355$	−0.205912	+	0.356650i	−0.0109287	+	0.0189290i
$356$	2.99156	+	2.99156i	0.158553	+	0.158553i
$357$	7.01881	−	3.25649i	0.371475	−	0.172352i
$358$	6.52042	+	6.52042i	0.344615	+	0.344615i
$359$	21.8195	−	5.84652i	1.15159	−	0.308568i	0.367988	−	0.929831i	$-0.380047\pi$
$359$	21.8195	−	5.84652i	1.15159	−	0.308568i	0.783602	+	0.621263i	$0.213380\pi$
$360$	−0.443878	+	0.256273i	−0.0233944	+	0.0135068i
$361$	7.80339	−	4.50529i	0.410705	−	0.237120i
$362$	−5.63475	−	21.0292i	−0.296156	−	1.10527i
$363$	−3.45534			−0.181358
$364$	4.85758	+	1.22373i	0.254606	+	0.0641410i
$365$	0.947614			0.0496004
$366$	−0.869667	−	3.24564i	−0.0454582	−	0.169652i
$367$	−22.2369	+	12.8385i	−1.16076	+	0.670163i	−0.951485	−	0.307695i	$-0.900442\pi$
$367$	−22.2369	+	12.8385i	−1.16076	+	0.670163i	−0.209271	+	0.977858i	$0.567109\pi$
$368$	−3.60667	+	2.08231i	−0.188011	+	0.108548i
$369$	28.9249	−	7.75040i	1.50577	−	0.403470i
$370$	−0.349087	−	0.349087i	−0.0181481	−	0.0181481i
$371$	−27.7664	−	2.48313i	−1.44156	−	0.128918i
$372$	−0.260863	−	0.260863i	−0.0135251	−	0.0135251i
$373$	−8.31200	+	14.3968i	−0.430379	+	0.745439i	−0.996906	−	0.0786048i	$-0.974953\pi$
$373$	−8.31200	+	14.3968i	−0.430379	+	0.745439i	0.566527	+	0.824043i	$0.308287\pi$
$374$	19.4997	+	33.7745i	1.00831	+	1.74644i
$375$	0.103725	−	0.387107i	0.00535633	−	0.0199901i
$376$	−3.39042	+	5.87238i	−0.174848	+	0.302845i
$377$	0.205274	−	1.29174i	0.0105721	−	0.0665279i
$378$	4.18327	−	11.4249i	0.215164	−	0.587635i
$379$	−27.0566	+	27.0566i	−1.38980	+	1.38980i	−0.564094	+	0.825711i	$0.690774\pi$
$379$	−27.0566	+	27.0566i	−1.38980	+	1.38980i	−0.825711	+	0.564094i	$0.809226\pi$
$380$	0.110654	−	0.191658i	0.00567642	−	0.00983184i
$381$	−0.0654244	−	0.113318i	−0.00335179	−	0.00580547i
$382$	−12.9811	−	3.47829i	−0.664173	−	0.177965i
$383$	−26.0895	+	6.99065i	−1.33311	+	0.357206i	−0.853874	−	0.520480i	$-0.825753\pi$
$383$	−26.0895	+	6.99065i	−1.33311	+	0.357206i	−0.479236	+	0.877686i	$0.659086\pi$
$384$	4.86124	−	4.86124i	0.248074	−	0.248074i
$385$	−0.728378	−	0.512109i	−0.0371216	−	0.0260995i
$386$	−0.784626			−0.0399364
$387$	−6.31642	−	3.64679i	−0.321082	−	0.185377i
$388$	−4.33359	−	1.16118i	−0.220005	−	0.0589501i
$389$	−16.4981	+	9.52520i	−0.836488	+	0.482947i	−0.856069	−	0.516862i	$-0.827100\pi$
$389$	−16.4981	+	9.52520i	−0.836488	+	0.482947i	0.0195807	+	0.999808i	$0.493767\pi$
$390$	0.144685	−	0.178483i	0.00732641	−	0.00903784i
$391$			5.06536i			0.256166i
$392$	−6.99056	+	14.8418i	−0.353077	+	0.749625i
$393$	0.395011			0.0199257
$394$	5.40846	+	3.12258i	0.272474	+	0.157313i
$395$	0.176283	−	0.657896i	0.00886975	−	0.0331024i
$396$	5.88738	+	1.57752i	0.295852	+	0.0792732i
$397$	−0.881290	−	3.28902i	−0.0442307	−	0.165071i	0.940278	−	0.340408i	$-0.110565\pi$
$397$	−0.881290	−	3.28902i	−0.0442307	−	0.165071i	−0.984508	+	0.175337i	$0.943899\pi$
$398$	18.0502	−	18.0502i	0.904777	−	0.904777i
$399$	−1.21115	−	6.94699i	−0.0606335	−	0.347784i
$400$		−	23.8422i		−	1.19211i
$401$	−35.6391	+	9.54948i	−1.77973	+	0.476878i	−0.990535	−	0.137260i	$-0.956170\pi$
$401$	−35.6391	+	9.54948i	−1.77973	+	0.476878i	−0.789198	+	0.614138i	$0.789504\pi$
$402$	−4.04696	−	7.00954i	−0.201844	−	0.349604i
$403$	4.59390	+	2.04817i	0.228838	+	0.102027i
$404$	−5.10240	−	2.94587i	−0.253854	−	0.146563i
$405$	0.381859	+	0.381859i	0.0189747	+	0.0189747i
$406$	−1.43215	−	0.524386i	−0.0710766	−	0.0260249i
$407$		−	16.4888i		−	0.817318i
$408$	−1.77396	−	6.62050i	−0.0878240	−	0.327764i
$409$	1.45373	−	5.42540i	0.0718824	−	0.268269i	−0.920626	−	0.390446i	$-0.872321\pi$
$409$	1.45373	−	5.42540i	0.0718824	−	0.268269i	0.992508	+	0.122177i	$0.0389876\pi$
$410$	0.357091	−	1.33268i	0.0176354	−	0.0658164i
$411$	1.79809	+	6.71055i	0.0886931	+	0.331007i
$412$			5.07008i			0.249785i
$413$	−4.50128	+	3.76228i	−0.221494	+	0.185130i
$414$	2.69176	+	2.69176i	0.132293	+	0.132293i
$415$	−0.479215	−	0.276675i	−0.0235237	−	0.0135814i
$416$	4.25725	−	9.54869i	0.208729	−	0.468163i
$417$	−0.788093	−	1.36502i	−0.0385931	−	0.0668452i
$418$	34.3322	−	9.19929i	1.67924	−	0.449952i
$419$		−	17.2554i		−	0.842980i	−0.906833	−	0.421490i	$-0.861507\pi$
$419$		−	17.2554i		−	0.842980i	0.906833	−	0.421490i	$-0.138493\pi$
$420$	−0.0357307	−	0.0427491i	−0.00174348	−	0.00208594i
$421$	5.55993	−	5.55993i	0.270974	−	0.270974i	−0.558518	−	0.829492i	$-0.688630\pi$
$421$	5.55993	−	5.55993i	0.270974	−	0.270974i	0.829492	+	0.558518i	$0.188630\pi$
$422$	−8.65939	−	32.3173i	−0.421533	−	1.57318i
$423$	7.67523	+	2.05657i	0.373182	+	0.0999939i
$424$	−6.39137	+	23.8529i	−0.310392	+	1.15840i
$425$	−25.1137	−	14.4994i	−1.21819	−	0.703325i
$426$	−4.13873			−0.200522
$427$	10.0772	−	4.67548i	0.487671	−	0.226263i
$428$			9.25695i			0.447451i
$429$	7.63227	−	0.798208i	0.368489	−	0.0385378i
$430$	−0.291021	+	0.168021i	−0.0140343	+	0.00810271i
$431$	7.89471	+	2.11538i	0.380275	+	0.101894i	0.443892	−	0.896080i	$-0.353597\pi$
$431$	7.89471	+	2.11538i	0.380275	+	0.101894i	−0.0636179	+	0.997974i	$0.520264\pi$
$432$	−11.9658	−	6.90844i	−0.575704	−	0.332383i
$433$	−6.91474			−0.332301			−0.166151	−	0.986100i	$-0.553134\pi$
$433$	−6.91474			−0.332301			−0.166151	+	0.986100i	$0.553134\pi$
$434$	3.37328	−	4.79785i	0.161923	−	0.230304i
$435$	−0.0102865	+	0.0102865i	−0.000493198	+	0.000493198i
$436$	6.92027	−	1.85428i	0.331421	−	0.0888039i
$437$	4.45917	+	1.19483i	0.213311	+	0.0571565i
$438$	4.76164	+	8.24741i	0.227520	+	0.394077i
$439$	−2.14789	+	3.72026i	−0.102513	+	0.177558i	−0.912719	−	0.408587i	$-0.866022\pi$
$439$	−2.14789	+	3.72026i	−0.102513	+	0.177558i	0.810206	+	0.586145i	$0.199355\pi$
$440$	−0.557715	+	0.557715i	−0.0265880	+	0.0265880i
$441$	18.9196	+	3.41122i	0.900935	+	0.162439i
$442$	−19.5427	−	26.9274i	−0.929553	−	1.28081i
$443$	11.5068	−	19.9303i	0.546702	−	0.946916i	−0.451795	−	0.892122i	$-0.649216\pi$
$443$	11.5068	−	19.9303i	0.546702	−	0.946916i	0.998498	−	0.0547947i	$-0.0174504\pi$
$444$	0.267041	−	0.996611i	0.0126732	−	0.0472971i
$445$	0.320772	+	0.555593i	0.0152061	+	0.0263377i
$446$	−21.6983	+	37.5825i	−1.02744	+	1.77958i
$447$	1.20622	+	1.20622i	0.0570521	+	0.0570521i
$448$	10.6947	+	7.51923i	0.505276	+	0.355250i
$449$	−7.20816	−	7.20816i	−0.340174	−	0.340174i	0.516259	−	0.856433i	$-0.327324\pi$
$449$	−7.20816	−	7.20816i	−0.340174	−	0.340174i	−0.856433	+	0.516259i	$0.827324\pi$
$450$	−21.0506	+	5.64050i	−0.992336	+	0.265896i
$451$	39.9074	−	23.0405i	1.87916	−	1.08494i
$452$	2.74188	−	1.58303i	0.128967	−	0.0744593i
$453$	2.12048	+	7.91373i	0.0996288	+	0.371820i
$454$	−5.50824			−0.258515
$455$	0.663476	+	0.369890i	0.0311042	+	0.0173407i
$456$	−6.24664			−0.292526
$457$	4.03718	+	15.0670i	0.188851	+	0.704803i	0.993773	+	0.111422i	$0.0355405\pi$
$457$	4.03718	+	15.0670i	0.188851	+	0.704803i	−0.804922	+	0.593381i	$0.797793\pi$
$458$	26.5261	−	15.3149i	1.23949	−	0.715617i
$459$	−14.5538	+	8.40262i	−0.679312	+	0.392201i
$460$	0.0352312	−	0.00944018i	0.00164266	−	0.000440151i
$461$	−10.2849	−	10.2849i	−0.479017	−	0.479017i	0.425800	−	0.904817i	$-0.359993\pi$
$461$	−10.2849	−	10.2849i	−0.479017	−	0.479017i	−0.904817	+	0.425800i	$0.859993\pi$
$462$	0.797048	−	8.91261i	0.0370820	−	0.414652i
$463$	−15.2514	−	15.2514i	−0.708792	−	0.708792i	0.257489	−	0.966281i	$-0.417105\pi$
$463$	−15.2514	−	15.2514i	−0.708792	−	0.708792i	−0.966281	+	0.257489i	$0.917105\pi$
$464$	−0.865996	+	1.49995i	−0.0402028	+	0.0696334i
$465$	−0.0279712	−	0.0484476i	−0.00129714	−	0.00224670i
$466$	2.12617	−	7.93498i	0.0984930	−	0.367581i
$467$	8.90667	−	15.4268i	0.412152	−	0.713868i	−0.582973	−	0.812491i	$-0.698111\pi$
$467$	8.90667	−	15.4268i	0.412152	−	0.713868i	0.995125	+	0.0986238i	$0.0314441\pi$
$468$	−5.13545	−	0.816087i	−0.237386	−	0.0377237i
$469$	20.5321	−	17.1612i	0.948082	−	0.792429i
$470$	0.258873	−	0.258873i	0.0119409	−	0.0119409i
$471$	4.83965	−	8.38253i	0.222999	−	0.386246i
$472$	2.59836	+	4.50050i	0.119599	+	0.207152i
$473$	−10.8412	−	2.90490i	−0.498480	−	0.133567i
$474$	6.61169	−	1.77160i	0.303685	−	0.0813722i
$475$	−18.6881	+	18.6881i	−0.857468	+	0.857468i
$476$	−7.31874	+	3.39564i	−0.335454	+	0.155639i
$477$	28.9376			1.32496
$478$	−13.3425	−	7.70331i	−0.610273	−	0.352341i
$479$	24.4798	+	6.55934i	1.11851	+	0.299704i	0.770280	−	0.637706i	$-0.220116\pi$
$479$	24.4798	+	6.55934i	1.11851	+	0.299704i	0.348229	+	0.937409i	$0.386783\pi$
$480$	−0.100701	+	0.0581399i	−0.00459636	+	0.00265371i
$481$	1.46320	+	13.9908i	0.0667163	+	0.637925i
$482$			3.55293i			0.161832i
$483$	0.668451	−	0.950745i	0.0304156	−	0.0432604i
$484$	3.60299			0.163772
$485$	−0.589181	−	0.340164i	−0.0267533	−	0.0154460i
$486$	−4.97526	+	18.5679i	−0.225682	+	0.842258i
$487$	32.2452	+	8.64006i	1.46117	+	0.391519i	0.899893	−	0.436111i	$-0.143645\pi$
$487$	32.2452	+	8.64006i	1.46117	+	0.391519i	0.561275	+	0.827630i	$0.310311\pi$
$488$	−2.54695	−	9.50535i	−0.115295	−	0.430287i
$489$	−0.442410	+	0.442410i	−0.0200065	+	0.0200065i
$490$	0.571961	−	0.676330i	0.0258386	−	0.0305535i
$491$			14.4968i			0.654231i	0.944984	+	0.327115i	$0.106077\pi$
$491$			14.4968i			0.654231i	−0.944984	+	0.327115i	$0.893923\pi$
$492$	2.78522	−	0.746298i	0.125567	−	0.0336457i
$493$	1.05330	+	1.82436i	0.0474381	+	0.0821651i
$494$	−28.3147	+	10.8522i	−1.27394	+	0.488266i
$495$	0.800427	+	0.462127i	0.0359765	+	0.0207711i
$496$	−4.70968	−	4.70968i	−0.211471	−	0.211471i
$497$	−2.35010	−	13.4798i	−0.105417	−	0.604653i
$498$		−	5.56103i		−	0.249196i
$499$	2.56035	+	9.55534i	0.114617	+	0.427756i	0.999258	−	0.0385167i	$-0.0122633\pi$
$499$	2.56035	+	9.55534i	0.114617	+	0.427756i	−0.884641	+	0.466273i	$0.845597\pi$
$500$	−0.108157	+	0.403649i	−0.00483694	+	0.0180517i
$501$	−1.34828	+	5.03185i	−0.0602367	+	0.224806i
$502$	−10.2138	−	38.1184i	−0.455864	−	1.70131i
$503$			32.9620i			1.46970i	0.678229	+	0.734851i	$0.262748\pi$
$503$			32.9620i			1.46970i	−0.678229	+	0.734851i	$0.737252\pi$
$504$	5.85531	−	15.9915i	0.260816	−	0.712316i
$505$	−0.631745	−	0.631745i	−0.0281123	−	0.0281123i
$506$	5.07314	+	2.92898i	0.225528	+	0.130209i
$507$	−6.40517	+	1.35456i	−0.284464	+	0.0601583i
$508$	0.0682200	+	0.118161i	0.00302678	+	0.00524253i
$509$	33.3056	−	8.92421i	1.47624	−	0.395559i	0.571177	−	0.820827i	$-0.306487\pi$
$509$	33.3056	−	8.92421i	1.47624	−	0.395559i	0.905067	+	0.425268i	$0.139820\pi$
$510$			0.370054i			0.0163863i
$511$	−24.1580	+	20.1918i	−1.06869	+	0.893233i
$512$	6.03549	−	6.03549i	0.266733	−	0.266733i
$513$	3.96406	+	14.7941i	0.175018	+	0.653174i
$514$	20.4929	+	5.49105i	0.903903	+	0.242200i
$515$	−0.198987	+	0.742629i	−0.00876840	+	0.0327241i
$516$	−0.608217	−	0.351154i	−0.0267753	−	0.0154587i
$517$	12.2276			0.537770
$518$	16.3378	+	1.46108i	0.717841	+	0.0641960i
$519$		−	1.59292i		−	0.0699216i
$520$	0.423732	−	0.522714i	0.0185819	−	0.0229225i
$521$	−28.0062	+	16.1694i	−1.22697	+	0.708393i	−0.966395	−	0.257060i	$-0.917246\pi$
$521$	−28.0062	+	16.1694i	−1.22697	+	0.708393i	−0.260577	+	0.965453i	$0.583913\pi$
$522$	1.52920	+	0.409749i	0.0669314	+	0.0179342i
$523$	−16.8623	−	9.73548i	−0.737339	−	0.425703i	0.0837622	−	0.996486i	$-0.473306\pi$
$523$	−16.8623	−	9.73548i	−0.737339	−	0.425703i	−0.821101	+	0.570783i	$0.806640\pi$
$524$	−0.411891			−0.0179935
$525$	2.80031	+	6.03561i	0.122216	+	0.263415i
$526$	0.476192	−	0.476192i	0.0207629	−	0.0207629i
$527$	−7.82500	+	2.09670i	−0.340863	+	0.0913338i
$528$	−9.81556	−	2.63007i	−0.427167	−	0.114459i
$529$	−11.1196	−	19.2597i	−0.483460	−	0.837377i
$530$	0.666632	−	1.15464i	0.0289566	−	0.0501544i
$531$	4.30605	−	4.30605i	0.186867	−	0.186867i
$532$	1.26291	+	7.24384i	0.0547540	+	0.314060i
$533$	−31.8169	+	23.0913i	−1.37815	+	1.00020i
$534$	−3.22368	+	5.58358i	−0.139502	+	0.241625i
$535$	−0.363310	+	1.35589i	−0.0157073	+	0.0586203i
$536$	−11.8521	−	20.5285i	−0.511934	−	0.886695i
$537$	−1.46119	+	2.53086i	−0.0630551	+	0.109215i
$538$	16.3088	+	16.3088i	0.703122	+	0.703122i
$539$	29.4809	−	2.46488i	1.26983	−	0.106170i
$540$	0.0855664	+	0.0855664i	0.00368219	+	0.00368219i
$541$	7.40097	−	1.98308i	0.318193	−	0.0852594i	−0.0961879	−	0.995363i	$-0.530665\pi$
$541$	7.40097	−	1.98308i	0.318193	−	0.0852594i	0.414380	+	0.910104i	$0.363998\pi$
$542$	−27.2248	+	15.7183i	−1.16941	+	0.675157i
$543$	5.97525	−	3.44981i	0.256423	−	0.148046i
$544$	4.35812	+	16.2647i	0.186853	+	0.697345i
$545$	1.08641			0.0465366
$546$	0.114601	+	7.63311i	0.00490445	+	0.326667i
$547$	−17.3075			−0.740016			−0.370008	−	0.929029i	$-0.620645\pi$
$547$	−17.3075			−0.740016			−0.370008	+	0.929029i	$0.620645\pi$
$548$	−1.87492	−	6.99730i	−0.0800927	−	0.298910i
$549$	−9.98663	+	5.76578i	−0.426219	+	0.246078i
$550$	−29.0433	+	16.7682i	−1.23841	+	0.714998i
$551$	1.85449	−	0.496908i	0.0790037	−	0.0211690i
$552$	−0.727980	−	0.727980i	−0.0309849	−	0.0309849i
$553$	9.52443	+	20.5283i	0.405020	+	0.872952i
$554$	−26.6910	−	26.6910i	−1.13399	−	1.13399i
$555$	0.0782285	−	0.135496i	0.00332062	−	0.00575148i
$556$	0.821769	+	1.42335i	0.0348508	+	0.0603633i
$557$	4.30702	−	16.0740i	0.182494	−	0.681078i	−0.812659	−	0.582740i	$-0.801981\pi$
$557$	4.30702	−	16.0740i	0.182494	−	0.681078i	0.995153	−	0.0983379i	$-0.0313526\pi$
$558$	−3.04405	+	5.27245i	−0.128865	+	0.223200i
$559$	9.45660	+	1.50277i	0.399972	+	0.0635605i
$560$	−0.645089	−	0.771800i	−0.0272600	−	0.0326145i
$561$	−8.73959	+	8.73959i	−0.368986	+	0.368986i
$562$	10.8554	−	18.8021i	0.457906	−	0.793117i
$563$	−1.95468	−	3.38561i	−0.0823800	−	0.142686i	0.821892	−	0.569644i	$-0.192919\pi$
$563$	−1.95468	−	3.38561i	−0.0823800	−	0.142686i	−0.904272	+	0.426957i	$0.859585\pi$
$564$	0.739059	+	0.198030i	0.0311200	+	0.00833858i
$565$	0.463741	−	0.124259i	0.0195097	−	0.00522762i
$566$	−30.0741	+	30.0741i	−1.26411	+	1.26411i
$567$	−17.8716	−	1.59824i	−0.750536	−	0.0671198i
$568$	−12.1209			−0.508581
$569$	2.28143	+	1.31718i	0.0956424	+	0.0552192i	0.547058	−	0.837094i	$-0.315748\pi$
$569$	2.28143	+	1.31718i	0.0956424	+	0.0552192i	−0.451416	+	0.892314i	$0.649081\pi$
$570$	0.325768	+	0.0872893i	0.0136449	+	0.00365615i
$571$	16.2796	−	9.39903i	0.681280	−	0.393337i	−0.119057	−	0.992887i	$-0.537987\pi$
$571$	16.2796	−	9.39903i	0.681280	−	0.393337i	0.800337	+	0.599550i	$0.204654\pi$
$572$	−7.95841	+	0.832317i	−0.332758	+	0.0348009i
$573$		−	4.25908i		−	0.177926i
$574$	19.2933	+	41.5836i	0.805288	+	1.73566i
$575$	−4.35580			−0.181649
$576$	−11.7526	−	6.78535i	−0.489690	−	0.282723i
$577$	11.6005	−	43.2935i	0.482934	−	1.80233i	−0.106257	−	0.994339i	$-0.533886\pi$
$577$	11.6005	−	43.2935i	0.482934	−	1.80233i	0.589190	−	0.807994i	$-0.299447\pi$
$578$	25.6681	+	6.87775i	1.06765	+	0.286076i
$579$	−0.0643585	−	0.240189i	−0.00267465	−	0.00998192i
$580$	0.0107260	−	0.0107260i	0.000445374	−	0.000445374i
$581$	18.1123	−	3.15773i	0.751423	−	0.131005i
$582$		−	6.83712i		−	0.283408i
$583$	43.0130	−	11.5253i	1.78142	−	0.477330i
$584$	13.9452	+	24.1538i	0.577056	+	0.999491i
$585$	−0.720174	−	0.321087i	−0.0297755	−	0.0132753i
$586$	−42.5740	−	24.5801i	−1.75872	−	1.01539i
$587$	21.2468	+	21.2468i	0.876947	+	0.876947i	0.993218	−	0.116270i	$-0.0370939\pi$
$587$	21.2468	+	21.2468i	0.876947	+	0.876947i	−0.116270	+	0.993218i	$0.537094\pi$
$588$	1.82180	+	0.328471i	0.0751297	+	0.0135459i
$589$			7.38312i			0.304216i
$590$	−0.0726180	−	0.271014i	−0.00298964	−	0.0111575i
$591$	−0.512255	+	1.91176i	−0.0210714	+	0.0786394i
$592$	4.82121	−	17.9930i	0.198151	−	0.739508i
$593$	9.37263	+	34.9791i	0.384888	+	1.43642i	0.838344	+	0.545142i	$0.183524\pi$
$593$	9.37263	+	34.9791i	0.384888	+	1.43642i	−0.453456	+	0.891279i	$0.649809\pi$
$594$			19.4348i			0.797419i
$595$	−1.20527	+	0.210129i	−0.0494111	+	0.00861444i
$596$	−1.25776	−	1.25776i	−0.0515198	−	0.0515198i
$597$	7.00609	+	4.04497i	0.286740	+	0.165550i
$598$	−4.56449	−	2.03506i	−0.186656	−	0.0832198i
$599$	1.01128	+	1.75158i	0.0413196	+	0.0715677i	0.885946	−	0.463789i	$-0.153510\pi$
$599$	1.01128	+	1.75158i	0.0413196	+	0.0715677i	−0.844626	+	0.535357i	$0.820177\pi$
$600$	5.69309	−	1.52546i	0.232419	−	0.0622766i
$601$			16.8573i			0.687623i	0.939039	+	0.343811i	$0.111718\pi$
$601$			16.8573i			0.687623i	−0.939039	+	0.343811i	$0.888282\pi$
$602$	3.83894	−	10.4845i	0.156464	−	0.427318i
$603$	−19.6415	+	19.6415i	−0.799865	+	0.799865i
$604$	−2.21109	−	8.25190i	−0.0899680	−	0.335765i
$605$	0.527741	+	0.141408i	0.0214557	+	0.00574904i
$606$	2.32385	−	8.67274i	0.0944001	−	0.352306i
$607$	20.1392	+	11.6274i	0.817424	+	0.471940i	0.849528	−	0.527544i	$-0.176887\pi$
$607$	20.1392	+	11.6274i	0.817424	+	0.471940i	−0.0321030	+	0.999485i	$0.510220\pi$
$608$	15.3463			0.622373
$609$	0.0430533	−	0.481422i	0.00174461	−	0.0195082i
$610$			0.531303i			0.0215118i
$611$	−10.3752	+	1.08507i	−0.419735	+	0.0438973i
$612$	7.25295	−	4.18749i	0.293183	−	0.169269i
$613$	2.25163	+	0.603323i	0.0909426	+	0.0243680i	0.304003	−	0.952671i	$-0.401677\pi$
$613$	2.25163	+	0.603323i	0.0909426	+	0.0243680i	−0.213061	+	0.977039i	$0.568343\pi$
$614$	−4.85642	−	2.80386i	−0.195989	−	0.113155i
$615$	0.437249			0.0176316
$616$	2.33427	−	26.1019i	0.0940506	−	1.05168i
$617$	−8.67485	+	8.67485i	−0.349236	+	0.349236i	−0.859825	−	0.510589i	$-0.829428\pi$
$617$	−8.67485	+	8.67485i	−0.349236	+	0.349236i	0.510589	+	0.859825i	$0.329428\pi$
$618$	−7.46323	+	1.99977i	−0.300215	+	0.0804424i
$619$	25.7197	+	6.89158i	1.03376	+	0.276996i	0.735527	−	0.677496i	$-0.236935\pi$
$619$	25.7197	+	6.89158i	1.03376	+	0.276996i	0.298237	+	0.954492i	$0.403601\pi$
$620$	0.0291665	+	0.0505178i	0.00117135	+	0.00202885i
$621$	−1.26212	+	2.18606i	−0.0506473	+	0.0877237i
$622$	−34.0581	+	34.0581i	−1.36561	+	1.36561i
$623$	−20.0162	−	7.32898i	−0.801932	−	0.293629i
$624$	8.56193	+	1.36060i	0.342751	+	0.0544675i
$625$	12.4525	−	21.5683i	0.498099	−	0.862732i
$626$	8.00824	−	29.8871i	0.320074	−	1.19453i
$627$	5.63216	+	9.75519i	0.224927	+	0.389585i
$628$	−5.04646	+	8.74072i	−0.201376	+	0.348793i
$629$	−16.0206	−	16.0206i	−0.638784	−	0.638784i
$630$	−0.528821	+	0.752148i	−0.0210687	+	0.0299663i
$631$	−2.58488	−	2.58488i	−0.102903	−	0.102903i	0.653781	−	0.756684i	$-0.273182\pi$
$631$	−2.58488	−	2.58488i	−0.102903	−	0.102903i	−0.756684	+	0.653781i	$0.773182\pi$
$632$	19.3633	−	5.18839i	0.770232	−	0.206383i
$633$	9.18267	−	5.30162i	0.364978	−	0.210720i
$634$	−6.89888	+	3.98307i	−0.273989	+	0.158188i
$635$	0.00535490	+	0.0199848i	0.000212503	+	0.000793071i
$636$	2.78644			0.110490
$637$	−24.7959	+	4.70758i	−0.982451	+	0.186521i
$638$	2.43622			0.0964507
$639$	3.67616	+	13.7196i	0.145427	+	0.542740i
$640$	−0.941409	+	0.543523i	−0.0372125	+	0.0214846i
$641$	−26.8165	+	15.4825i	−1.05919	+	0.611523i	−0.925208	−	0.379461i	$-0.876109\pi$
$641$	−26.8165	+	15.4825i	−1.05919	+	0.611523i	−0.133981	+	0.990984i	$0.542776\pi$
$642$	−13.6264	+	3.65118i	−0.537790	+	0.144100i
$643$	−9.81258	−	9.81258i	−0.386970	−	0.386970i	0.486635	−	0.873605i	$-0.338224\pi$
$643$	−9.81258	−	9.81258i	−0.386970	−	0.386970i	−0.873605	+	0.486635i	$0.838224\pi$
$644$	−0.697015	+	0.991372i	−0.0274662	+	0.0390655i
$645$	−0.0753055	−	0.0753055i	−0.00296515	−	0.00296515i
$646$	24.4193	−	42.2955i	0.960766	−	1.66410i
$647$	−13.7400	−	23.7983i	−0.540174	−	0.935608i	−0.998894	−	0.0470275i	$-0.985025\pi$
$647$	−13.7400	−	23.7983i	−0.540174	−	0.935608i	0.458720	−	0.888581i	$-0.348308\pi$
$648$	−4.11374	+	15.3527i	−0.161603	+	0.603111i
$649$	4.68553	−	8.11557i	0.183923	−	0.318564i
$650$	23.1554	−	16.8051i	0.908229	−	0.659152i
$651$	1.74541	+	0.639085i	0.0684079	+	0.0250477i
$652$	0.461314	−	0.461314i	0.0180665	−	0.0180665i
$653$	−5.05778	+	8.76034i	−0.197926	+	0.342819i	−0.947856	−	0.318699i	$-0.896754\pi$
$653$	−5.05778	+	8.76034i	−0.197926	+	0.342819i	0.749930	+	0.661518i	$0.230087\pi$
$654$	5.45906	+	9.45537i	0.213466	+	0.369734i
$655$	−0.0603308	−	0.0161656i	−0.00235732	−	0.000631642i
$656$	50.2849	−	13.4738i	1.96330	−	0.526063i
$657$	23.1102	−	23.1102i	0.901615	−	0.901615i
$658$	−1.08349	+	12.1157i	−0.0422390	+	0.472317i
$659$	39.4336			1.53612			0.768058	−	0.640380i	$-0.221223\pi$
$659$	39.4336			1.53612			0.768058	+	0.640380i	$0.221223\pi$
$660$	0.0770744	+	0.0444989i	0.00300012	+	0.00173212i
$661$	−24.5270	−	6.57200i	−0.953992	−	0.255621i	−0.251936	−	0.967744i	$-0.581067\pi$
$661$	−24.5270	−	6.57200i	−0.953992	−	0.255621i	−0.702055	+	0.712123i	$0.747734\pi$
$662$	26.3931	−	15.2381i	1.02580	−	0.592244i
$663$	6.64003	−	8.19112i	0.257877	−	0.318117i
$664$		−	16.2863i		−	0.632032i
$665$	−0.0993194	+	1.11059i	−0.00385144	+	0.0430669i
$666$	−17.0269			−0.659778
$667$	0.274030	+	0.158211i	0.0106105	+	0.00612597i
$668$	1.40589	−	5.24687i	0.0543957	−	0.203007i
$669$	−13.2845	−	3.55958i	−0.513610	−	0.137621i
$670$	0.331238	+	1.23620i	0.0127969	+	0.0477585i
$671$	−12.5478	+	12.5478i	−0.484403	+	0.484403i
$672$	1.32838	−	3.62793i	0.0512433	−	0.139951i
$673$		−	20.9026i		−	0.805734i	−0.915258	−	0.402867i	$-0.868014\pi$
$673$		−	20.9026i		−	0.805734i	0.915258	−	0.402867i	$-0.131986\pi$
$674$	4.62380	−	1.23894i	0.178102	−	0.0477224i
$675$	−7.22557	−	12.5150i	−0.278112	−	0.481704i
$676$	6.67888	−	1.41245i	0.256880	−	0.0543249i
$677$	−13.6905	−	7.90421i	−0.526169	−	0.303784i	0.213286	−	0.976990i	$-0.431583\pi$
$677$	−13.6905	−	7.90421i	−0.526169	−	0.303784i	−0.739455	+	0.673206i	$0.764917\pi$
$678$	3.41171	+	3.41171i	0.131026	+	0.131026i
$679$	22.2685	−	3.88234i	0.854586	−	0.148990i
$680$			1.08376i			0.0415603i
$681$	−0.451810	−	1.68618i	−0.0173134	−	0.0646145i
$682$	−2.42478	+	9.04940i	−0.0928496	+	0.346520i
$683$	3.01723	−	11.2605i	0.115451	−	0.430870i	−0.883869	−	0.467734i	$-0.845070\pi$
$683$	3.01723	−	11.2605i	0.115451	−	0.430870i	0.999320	+	0.0368647i	$0.0117370\pi$
$684$	−1.97551	−	7.37271i	−0.0755355	−	0.281902i
$685$		−	1.09850i		−	0.0419715i
$686$	−0.170005	+	29.4294i	−0.00649081	+	1.12362i
$687$	6.86397	+	6.86397i	0.261877	+	0.261877i
$688$	−10.9809	−	6.33981i	−0.418642	−	0.241703i
$689$	−35.4740	+	13.5962i	−1.35145	+	0.517975i
$690$	0.0277922	+	0.0481375i	0.00105803	+	0.00183256i
$691$	−10.1085	+	2.70856i	−0.384545	+	0.103038i	−0.445912	−	0.895077i	$-0.647121\pi$
$691$	−10.1085	+	2.70856i	−0.384545	+	0.103038i	0.0613673	+	0.998115i	$0.480454\pi$
$692$			1.66099i			0.0631415i
$693$	−30.2527	+	5.27432i	−1.14921	+	0.200355i
$694$	9.25675	−	9.25675i	0.351381	−	0.351381i
$695$	0.0645044	+	0.240734i	0.00244679	+	0.00913155i
$696$	−0.413569	−	0.110815i	−0.0156763	−	0.00420045i
$697$	16.3880	−	61.1607i	0.620738	−	2.31663i
$698$	15.6887	+	9.05789i	0.593827	+	0.342846i
$699$	2.60345			0.0984716
$700$	−2.91998	−	6.29352i	−0.110365	−	0.237873i
$701$			36.2902i			1.37066i	0.728232	+	0.685331i	$0.240343\pi$
$701$			36.2902i			1.37066i	−0.728232	+	0.685331i	$0.759657\pi$
$702$	−1.72463	−	16.4905i	−0.0650920	−	0.622394i
$703$	−17.8823	+	10.3244i	−0.674445	+	0.389391i
$704$	−20.1716	−	5.40497i	−0.760246	−	0.203707i
$705$	0.100480	+	0.0580122i	0.00378430	+	0.00218486i
$706$	−26.8591			−1.01086
$707$	29.5666	+	2.64412i	1.11197	+	0.0994425i
$708$	0.414636	−	0.414636i	0.0155830	−	0.0155830i
$709$	−6.22549	+	1.66812i	−0.233803	+	0.0626474i	−0.373818	−	0.927502i	$-0.621952\pi$
$709$	−6.22549	+	1.66812i	−0.233803	+	0.0626474i	0.140015	+	0.990149i	$0.455285\pi$
$710$	0.632116	+	0.169375i	0.0237229	+	0.00635653i
$711$	−11.7455	−	20.3438i	−0.440490	−	0.762951i
$712$	−9.44103	+	16.3523i	−0.353818	+	0.612830i
$713$	−0.860425	+	0.860425i	−0.0322232	+	0.0322232i
$714$	−7.88514	−	9.43397i	−0.295094	−	0.353058i
$715$	−1.19836	−	0.190434i	−0.0448160	−	0.00712183i
$716$	1.52363	−	2.63901i	0.0569408	−	0.0986244i
$717$	1.26372	−	4.71627i	0.0471945	−	0.176132i
$718$	−17.9479	−	31.0866i	−0.669808	−	1.16014i
$719$	−2.59436	+	4.49357i	−0.0967533	+	0.167582i	−0.910339	−	0.413863i	$-0.864179\pi$
$719$	−2.59436	+	4.49357i	−0.0967533	+	0.167582i	0.813586	+	0.581445i	$0.197512\pi$
$720$	0.738325	+	0.738325i	0.0275158	+	0.0275158i
$721$	−10.7511	−	23.1722i	−0.400392	−	0.862978i
$722$	−10.1246	−	10.1246i	−0.376799	−	0.376799i
$723$	−1.08762	+	0.291427i	−0.0404491	+	0.0108383i
$724$	−6.23059	+	3.59723i	−0.231558	+	0.133690i
$725$	−1.56880	+	0.905748i	−0.0582639	+	0.0336387i
$726$	1.42111	+	5.30366i	0.0527424	+	0.196837i
$727$	−23.5345			−0.872848			−0.436424	−	0.899741i	$-0.643755\pi$
$727$	−23.5345			−0.872848			−0.436424	+	0.899741i	$0.643755\pi$
$728$	0.335625	+	22.3547i	0.0124391	+	0.828520i
$729$	14.2532			0.527898
$730$	−0.389735	−	1.45451i	−0.0144247	−	0.0538338i
$731$	−13.3558	+	7.71100i	−0.493984	+	0.285202i
$732$	−0.961628	+	0.555196i	−0.0355428	+	0.0205206i
$733$	−1.83255	+	0.491030i	−0.0676867	+	0.0181366i	−0.292503	−	0.956264i	$-0.594488\pi$
$733$	−1.83255	+	0.491030i	−0.0676867	+	0.0181366i	0.224817	+	0.974401i	$0.427822\pi$
$734$	28.8516	+	28.8516i	1.06493	+	1.06493i
$735$	0.253953	+	0.119613i	0.00936718	+	0.00441198i
$736$	1.78844	+	1.78844i	0.0659230	+	0.0659230i
$737$	−21.3725	+	37.0182i	−0.787265	+	1.36358i
$738$	−23.7925	−	41.2097i	−0.875812	−	1.51695i
$739$	1.69162	−	6.31322i	0.0622274	−	0.232236i	−0.927807	−	0.373060i	$-0.878309\pi$
$739$	1.69162	−	6.31322i	0.0622274	−	0.232236i	0.990035	+	0.140824i	$0.0449752\pi$
$740$	−0.0815714	+	0.141286i	−0.00299862	+	0.00519377i
$741$	−5.64458	−	7.77752i	−0.207359	−	0.285714i
$742$	7.60837	+	43.6404i	0.279312	+	1.60209i
$743$	12.2516	−	12.2516i	0.449468	−	0.449468i	−0.445709	−	0.895178i	$-0.647049\pi$
$743$	12.2516	−	12.2516i	0.449468	−	0.449468i	0.895178	+	0.445709i	$0.147049\pi$
$744$	0.823255	−	1.42592i	0.0301820	−	0.0522768i
$745$	−0.134864	−	0.233591i	−0.00494103	−	0.00855812i
$746$	25.5165	+	6.83712i	0.934225	+	0.250325i
$747$	−18.4345	+	4.93950i	−0.674482	+	0.180727i
$748$	9.11304	−	9.11304i	0.333206	−	0.333206i
$749$	−19.6294	−	42.3078i	−0.717241	−	1.54589i
$750$	−0.636837			−0.0232540
$751$	35.4951	+	20.4931i	1.29524	+	0.747805i	0.979577	−	0.201068i	$-0.0644412\pi$
$751$	35.4951	+	20.4931i	1.29524	+	0.747805i	0.315659	+	0.948873i	$0.397775\pi$
$752$	13.3431	+	3.57528i	0.486573	+	0.130377i
$753$	10.8310	−	6.25328i	0.394704	−	0.227882i
$754$	−2.06714	+	0.216188i	−0.0752807	+	0.00787311i
$755$		−	1.29546i		−	0.0471466i
$756$	−4.00464	−	0.358132i	−0.145647	−	0.0130251i
$757$	−25.7292			−0.935142			−0.467571	−	0.883955i	$-0.654871\pi$
$757$	−25.7292			−0.935142			−0.467571	+	0.883955i	$0.654871\pi$
$758$	52.6575	+	30.4018i	1.91261	+	1.10424i
$759$	−0.480496	+	1.79323i	−0.0174409	+	0.0650903i
$760$	0.954061	+	0.255640i	0.0346074	+	0.00927303i
$761$	7.34981	+	27.4299i	0.266430	+	0.994332i	0.961369	+	0.275263i	$0.0887648\pi$
$761$	7.34981	+	27.4299i	0.266430	+	0.994332i	−0.694939	+	0.719069i	$0.744568\pi$
$762$	−0.147027	+	0.147027i	−0.00532621	+	0.00532621i
$763$	−27.6963	+	23.1492i	−1.00267	+	0.838058i
$764$			4.44108i			0.160673i
$765$	1.22671	−	0.328695i	0.0443517	−	0.0118840i
$766$	21.4601	+	37.1701i	0.775387	+	1.34301i
$767$	−3.25552	+	7.30188i	−0.117550	+	0.263656i
$768$	−5.15080	−	2.97382i	−0.185864	−	0.107308i
$769$	−20.7240

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.bb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.411280 - 1.53492i) q^{2} +(0.436133 - 0.251802i) q^{3} +(-0.454770 + 0.262561i) q^{4} +(-0.0769162 + 0.0206096i) q^{5} +(-0.565867 - 0.565867i) q^{6} +(1.52171 - 2.16435i) q^{7} +(-1.65723 - 1.65723i) q^{8} +(-1.37319 + 2.37844i) q^{9} +O(q^{10})\)	\(q+(-0.411280 - 1.53492i) q^{2} +(0.436133 - 0.251802i) q^{3} +(-0.454770 + 0.262561i) q^{4} +(-0.0769162 + 0.0206096i) q^{5} +(-0.565867 - 0.565867i) q^{6} +(1.52171 - 2.16435i) q^{7} +(-1.65723 - 1.65723i) q^{8} +(-1.37319 + 2.37844i) q^{9} +(0.0632682 + 0.109584i) q^{10} +(-1.09384 + 4.08225i) q^{11} +(-0.132227 + 0.229023i) q^{12} +(0.565867 - 3.56087i) q^{13} +(-3.94794 - 1.44555i) q^{14} +(-0.0283562 + 0.0283562i) q^{15} +(-2.38725 + 4.13483i) q^{16} +(2.90357 + 5.02912i) q^{17} +(4.21547 + 1.12953i) q^{18} +(5.11216 - 1.36980i) q^{19} +(0.0295679 - 0.0295679i) q^{20} +(0.118683 - 1.32711i) q^{21} +6.71579 q^{22} +(0.755405 + 0.436133i) q^{23} +(-1.14006 - 0.305479i) q^{24} +(-4.32464 + 2.49683i) q^{25} +(-5.69837 + 0.595955i) q^{26} +2.89390i q^{27} +(-0.123754 + 1.38382i) q^{28} +0.362759 q^{29} +(0.0551867 + 0.0318621i) q^{30} +(-0.361057 + 1.34748i) q^{31} +(2.80082 + 0.750478i) q^{32} +(0.550859 + 2.05583i) q^{33} +(6.52511 - 6.52511i) q^{34} +(-0.0724379 + 0.197835i) q^{35} -1.44219i q^{36} +(-3.76857 + 1.00978i) q^{37} +(-4.20506 - 7.28338i) q^{38} +(-0.649839 - 1.69550i) q^{39} +(0.161623 + 0.0933128i) q^{40} +(-7.70995 - 7.70995i) q^{41} +(-2.08582 + 0.363646i) q^{42} +2.65570i q^{43} +(-0.574398 - 2.14368i) q^{44} +(0.0566020 - 0.211242i) q^{45} +(0.358745 - 1.33886i) q^{46} +(-0.748829 - 2.79467i) q^{47} +2.40445i q^{48} +(-2.36879 - 6.58702i) q^{49} +(5.61106 + 5.61106i) q^{50} +(2.53268 + 1.46224i) q^{51} +(0.677608 + 1.76795i) q^{52} +(-5.26830 - 9.12497i) q^{53} +(4.44189 - 1.19020i) q^{54} -0.336535i q^{55} +(-6.10864 + 1.06499i) q^{56} +(1.88467 - 1.88467i) q^{57} +(-0.149196 - 0.556806i) q^{58} +(-2.14179 - 0.573890i) q^{59} +(0.00545029 - 0.0203408i) q^{60} +(3.63628 + 2.09941i) q^{61} +2.21677 q^{62} +(3.05816 + 6.59136i) q^{63} +4.94130i q^{64} +(0.0298639 + 0.285551i) q^{65} +(2.92898 - 1.69105i) q^{66} +(9.76951 + 2.61773i) q^{67} +(-2.64091 - 1.52473i) q^{68} +0.439276 q^{69} +(0.333453 + 0.0298205i) q^{70} +(3.65698 - 3.65698i) q^{71} +(6.21730 - 1.66592i) q^{72} +(-11.4948 - 3.08002i) q^{73} +(3.09987 + 5.36914i) q^{74} +(-1.25741 + 2.17790i) q^{75} +(-1.96520 + 1.96520i) q^{76} +(7.17090 + 8.57944i) q^{77} +(-2.33519 + 1.69477i) q^{78} +(-4.27671 + 7.40747i) q^{79} +(0.0984006 - 0.367236i) q^{80} +(-3.39089 - 5.87319i) q^{81} +(-8.66319 + 15.0051i) q^{82} +(4.91372 + 4.91372i) q^{83} +(0.294475 + 0.634692i) q^{84} +(-0.326980 - 0.326980i) q^{85} +(4.07628 - 1.09224i) q^{86} +(0.158211 - 0.0913434i) q^{87} +(8.57795 - 4.95248i) q^{88} +(-2.08520 - 7.78209i) q^{89} -0.347518 q^{90} +(-6.84587 - 6.64335i) q^{91} -0.458047 q^{92} +(0.181829 + 0.678596i) q^{93} +(-3.98161 + 2.29878i) q^{94} +(-0.364977 + 0.210720i) q^{95} +(1.41050 - 0.377943i) q^{96} +(6.04128 + 6.04128i) q^{97} +(-9.13630 + 6.34501i) q^{98} +(-8.20733 - 8.20733i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 12 q^{3} - 6 q^{5} - 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 - 12 * q^3 - 6 * q^5 - 6 * q^7 - 16 * q^8 + 8 * q^9	\( 32 q - 2 q^{2} - 12 q^{3} - 6 q^{5} - 6 q^{7} - 16 q^{8} + 8 q^{9} - 10 q^{11} + 28 q^{14} - 44 q^{15} + 12 q^{16} - 4 q^{18} + 12 q^{19} - 26 q^{21} - 8 q^{22} - 12 q^{24} + 24 q^{26} - 6 q^{28} + 16 q^{29} + 24 q^{31} + 4 q^{32} + 48 q^{33} + 28 q^{35} - 8 q^{37} - 6 q^{39} - 132 q^{40} - 16 q^{42} - 42 q^{44} - 24 q^{45} + 12 q^{46} + 30 q^{47} + 88 q^{50} + 36 q^{52} - 12 q^{53} + 78 q^{54} + 40 q^{57} + 26 q^{58} - 54 q^{59} + 16 q^{60} - 48 q^{61} + 24 q^{63} - 8 q^{65} + 12 q^{66} + 16 q^{67} - 48 q^{68} + 50 q^{70} - 36 q^{71} + 22 q^{72} + 66 q^{73} + 12 q^{74} - 176 q^{78} - 32 q^{79} + 138 q^{80} + 16 q^{81} - 58 q^{84} - 84 q^{85} + 42 q^{86} - 24 q^{87} - 60 q^{89} + 48 q^{92} + 6 q^{93} - 72 q^{94} - 42 q^{96} - 86 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 - 12 * q^3 - 6 * q^5 - 6 * q^7 - 16 * q^8 + 8 * q^9 - 10 * q^11 + 28 * q^14 - 44 * q^15 + 12 * q^16 - 4 * q^18 + 12 * q^19 - 26 * q^21 - 8 * q^22 - 12 * q^24 + 24 * q^26 - 6 * q^28 + 16 * q^29 + 24 * q^31 + 4 * q^32 + 48 * q^33 + 28 * q^35 - 8 * q^37 - 6 * q^39 - 132 * q^40 - 16 * q^42 - 42 * q^44 - 24 * q^45 + 12 * q^46 + 30 * q^47 + 88 * q^50 + 36 * q^52 - 12 * q^53 + 78 * q^54 + 40 * q^57 + 26 * q^58 - 54 * q^59 + 16 * q^60 - 48 * q^61 + 24 * q^63 - 8 * q^65 + 12 * q^66 + 16 * q^67 - 48 * q^68 + 50 * q^70 - 36 * q^71 + 22 * q^72 + 66 * q^73 + 12 * q^74 - 176 * q^78 - 32 * q^79 + 138 * q^80 + 16 * q^81 - 58 * q^84 - 84 * q^85 + 42 * q^86 - 24 * q^87 - 60 * q^89 + 48 * q^92 + 6 * q^93 - 72 * q^94 - 42 * q^96 - 86 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more