LMFDB - Embedded newform 930.2.br.b.761.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			761.4
Character	$\chi$	$=$	930.761
Dual form			930.2.br.b.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(-1.05992 - 1.36988i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.584727 + 1.63037i) q^{6} +(0.140936 - 1.34092i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.753142 + 2.90392i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(-1.05992 - 1.36988i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.584727 + 1.63037i) q^{6} +(0.140936 - 1.34092i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.753142 + 2.90392i) q^{9} +(0.669131 + 0.743145i) q^{10} +(3.37088 - 1.50081i) q^{11} +(-0.0522975 - 1.73126i) q^{12} +(-1.36284 + 6.41167i) q^{13} +(-0.548405 + 1.23174i) q^{14} +(0.232977 + 1.71631i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-5.12286 - 2.28084i) q^{17} +(1.61364 - 2.52906i) q^{18} +(-1.80634 + 0.383949i) q^{19} +(-0.406737 - 0.913545i) q^{20} +(-1.98628 + 1.22820i) q^{21} +(-3.66968 + 0.385699i) q^{22} +(-4.04207 + 2.93674i) q^{23} +(-0.485251 + 1.66269i) q^{24} +(0.500000 + 0.866025i) q^{25} +(3.27746 - 5.67672i) q^{26} +(4.77630 - 2.04621i) q^{27} +(0.902193 - 1.00199i) q^{28} +(-0.419623 + 1.29147i) q^{29} +(0.308795 - 1.70430i) q^{30} +(4.68202 + 3.01308i) q^{31} -1.00000i q^{32} +(-5.62880 - 3.02697i) q^{33} +(4.16731 + 3.75226i) q^{34} +(-0.792514 + 1.09080i) q^{35} +(-2.31619 + 1.90664i) q^{36} +(-3.11169 + 1.79653i) q^{37} +(1.83658 + 0.193032i) q^{38} +(10.2277 - 4.92892i) q^{39} +(0.104528 + 0.994522i) q^{40} +(-1.81154 + 1.63112i) q^{41} +(2.26860 - 0.554294i) q^{42} +(2.02409 + 9.52259i) q^{43} +(3.60926 + 0.767172i) q^{44} +(2.10420 - 2.13830i) q^{45} +(4.75174 - 1.54393i) q^{46} +(2.26952 - 0.737413i) q^{47} +(0.975300 - 1.43136i) q^{48} +(5.06883 + 1.07741i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(2.30534 + 9.43521i) q^{51} +(-4.87125 + 4.38609i) q^{52} +(-0.959748 - 9.13139i) q^{53} +(-5.17484 + 0.470106i) q^{54} +(-3.66968 - 0.385699i) q^{55} +(-1.16767 + 0.674153i) q^{56} +(2.44054 + 2.06751i) q^{57} +(0.798170 - 1.09859i) q^{58} +(7.31627 + 6.58760i) q^{59} +(-0.820340 + 1.52546i) q^{60} +1.70177i q^{61} +(-3.52177 - 4.31244i) q^{62} +(3.78779 + 1.41917i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(4.38609 - 4.87125i) q^{65} +(4.41793 + 4.61821i) q^{66} +(-0.0499869 + 0.0865799i) q^{67} +(-2.80383 - 4.85638i) q^{68} +(8.30724 + 2.42445i) q^{69} +(1.09080 - 0.792514i) q^{70} +(-8.04344 + 0.845399i) q^{71} +(2.79201 - 1.09758i) q^{72} +(1.50175 + 3.37300i) q^{73} +(3.51455 - 0.747040i) q^{74} +(0.656391 - 1.60286i) q^{75} +(-1.68704 - 0.751118i) q^{76} +(-1.53739 - 4.73161i) q^{77} +(-11.2503 + 1.52714i) q^{78} +(0.331778 - 0.745186i) q^{79} +(0.207912 - 0.978148i) q^{80} +(-7.86555 - 4.37414i) q^{81} +(2.22693 - 0.991491i) q^{82} +(3.07491 + 3.41503i) q^{83} +(-2.32885 - 0.173871i) q^{84} +(3.29610 + 4.53670i) q^{85} +(1.01762 - 9.68200i) q^{86} +(2.21392 - 0.794017i) q^{87} +(-3.19554 - 1.84495i) q^{88} +(9.31870 + 6.77043i) q^{89} +(-2.66199 + 1.38341i) q^{90} +(8.40546 + 2.73110i) q^{91} -4.99627 q^{92} +(-0.835004 - 9.60743i) q^{93} -2.38632 q^{94} +(1.75631 + 0.570660i) q^{95} +(-1.36988 + 1.05992i) q^{96} +(13.8287 + 10.0471i) q^{97} +(-4.48780 - 2.59104i) q^{98} +(1.81950 + 10.9191i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{30}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	−1.05992	−	1.36988i	−0.611945	−	0.790901i
$3$	−1.05992	−	1.36988i	−0.611945	−	0.790901i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	0.584727	+	1.63037i	0.238714	+	0.665594i
$7$	0.140936	−	1.34092i	0.0532689	−	0.506820i	−0.935060	−	0.354488i	$-0.884655\pi$
$7$	0.140936	−	1.34092i	0.0532689	−	0.506820i	0.988329	−	0.152332i	$-0.0486782\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−0.753142	+	2.90392i	−0.251047	+	0.967975i
$10$	0.669131	+	0.743145i	0.211598	+	0.235003i
$11$	3.37088	−	1.50081i	1.01636	−	0.452513i	0.170182	−	0.985413i	$-0.445564\pi$
$11$	3.37088	−	1.50081i	1.01636	−	0.452513i	0.846178	+	0.532900i	$0.178898\pi$
$12$	−0.0522975	−	1.73126i	−0.0150970	−	0.499772i
$13$	−1.36284	+	6.41167i	−0.377985	+	1.77828i	0.218690	+	0.975794i	$0.429822\pi$
$13$	−1.36284	+	6.41167i	−0.377985	+	1.77828i	−0.596675	+	0.802483i	$0.703512\pi$
$14$	−0.548405	+	1.23174i	−0.146568	+	0.329196i
$15$	0.232977	+	1.71631i	0.0601544	+	0.443149i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−5.12286	−	2.28084i	−1.24248	−	0.553186i	−0.323025	−	0.946390i	$-0.604700\pi$
$17$	−5.12286	−	2.28084i	−1.24248	−	0.553186i	−0.919451	+	0.393204i	$0.871366\pi$
$18$	1.61364	−	2.52906i	0.380339	−	0.596106i
$19$	−1.80634	+	0.383949i	−0.414403	+	0.0880840i	−0.410395	−	0.911908i	$-0.634609\pi$
$19$	−1.80634	+	0.383949i	−0.414403	+	0.0880840i	−0.00400785	+	0.999992i	$0.501276\pi$
$20$	−0.406737	−	0.913545i	−0.0909491	−	0.204275i
$21$	−1.98628	+	1.22820i	−0.433442	+	0.268015i
$22$	−3.66968	+	0.385699i	−0.782378	+	0.0822313i
$23$	−4.04207	+	2.93674i	−0.842830	+	0.612352i	−0.923160	−	0.384417i	$-0.874403\pi$
$23$	−4.04207	+	2.93674i	−0.842830	+	0.612352i	0.0803298	+	0.996768i	$0.474403\pi$
$24$	−0.485251	+	1.66269i	−0.0990515	+	0.339395i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	3.27746	−	5.67672i	0.642762	−	1.11330i
$27$	4.77630	−	2.04621i	0.919199	−	0.393794i
$28$	0.902193	−	1.00199i	0.170498	−	0.189358i
$29$	−0.419623	+	1.29147i	−0.0779220	+	0.239819i	−0.982428	−	0.186641i	$-0.940240\pi$
$29$	−0.419623	+	1.29147i	−0.0779220	+	0.239819i	0.904506	+	0.426461i	$0.140240\pi$
$30$	0.308795	−	1.70430i	0.0563779	−	0.311162i
$31$	4.68202	+	3.01308i	0.840916	+	0.541166i
$31$	4.68202	+	3.01308i	0.840916	+	0.541166i
$32$		−	1.00000i		−	0.176777i
$33$	−5.62880	−	3.02697i	−0.979849	−	0.526927i
$34$	4.16731	+	3.75226i	0.714688	+	0.643508i
$35$	−0.792514	+	1.09080i	−0.133959	+	0.184379i
$36$	−2.31619	+	1.90664i	−0.386031	+	0.317773i
$37$	−3.11169	+	1.79653i	−0.511558	+	0.295348i	−0.733474	−	0.679718i	$-0.762102\pi$
$37$	−3.11169	+	1.79653i	−0.511558	+	0.295348i	0.221916	+	0.975066i	$0.428769\pi$
$38$	1.83658	+	0.193032i	0.297932	+	0.0313139i
$39$	10.2277	−	4.92892i	1.63775	−	0.789259i
$40$	0.104528	+	0.994522i	0.0165274	+	0.157248i
$41$	−1.81154	+	1.63112i	−0.282916	+	0.254738i	−0.798354	−	0.602188i	$-0.794296\pi$
$41$	−1.81154	+	1.63112i	−0.282916	+	0.254738i	0.515439	+	0.856927i	$0.327629\pi$
$42$	2.26860	−	0.554294i	0.350053	−	0.0855295i
$43$	2.02409	+	9.52259i	0.308671	+	1.45218i	0.809747	+	0.586779i	$0.199604\pi$
$43$	2.02409	+	9.52259i	0.308671	+	1.45218i	−0.501077	+	0.865403i	$0.667063\pi$
$44$	3.60926	+	0.767172i	0.544116	+	0.115656i
$45$	2.10420	−	2.13830i	0.313676	−	0.318759i
$46$	4.75174	−	1.54393i	0.700606	−	0.227641i
$47$	2.26952	−	0.737413i	0.331044	−	0.107563i	−0.138779	−	0.990323i	$-0.544318\pi$
$47$	2.26952	−	0.737413i	0.331044	−	0.107563i	0.469823	+	0.882761i	$0.344318\pi$
$48$	0.975300	−	1.43136i	0.140772	−	0.206599i
$49$	5.06883	+	1.07741i	0.724119	+	0.153916i
$50$	−0.207912	−	0.978148i	−0.0294032	−	0.138331i
$51$	2.30534	+	9.43521i	0.322812	+	1.32119i
$52$	−4.87125	+	4.38609i	−0.675521	+	0.608241i
$53$	−0.959748	−	9.13139i	−0.131832	−	1.25429i	−0.837771	−	0.546021i	$-0.816142\pi$
$53$	−0.959748	−	9.13139i	−0.131832	−	1.25429i	0.705940	−	0.708272i	$-0.250525\pi$
$54$	−5.17484	+	0.470106i	−0.704207	+	0.0639733i
$55$	−3.66968	−	0.385699i	−0.494819	−	0.0520076i
$56$	−1.16767	+	0.674153i	−0.156036	+	0.0900875i
$57$	2.44054	+	2.06751i	0.323257	+	0.273849i
$58$	0.798170	−	1.09859i	0.104805	−	0.144251i
$59$	7.31627	+	6.58760i	0.952497	+	0.857632i	0.989914	−	0.141667i	$-0.0452463\pi$
$59$	7.31627	+	6.58760i	0.952497	+	0.857632i	−0.0374170	+	0.999300i	$0.511913\pi$
$60$	−0.820340	+	1.52546i	−0.105905	+	0.196937i
$61$			1.70177i			0.217889i	0.994048	+	0.108944i	$0.0347471\pi$
$61$			1.70177i			0.217889i	−0.994048	+	0.108944i	$0.965253\pi$
$62$	−3.52177	−	4.31244i	−0.447266	−	0.547680i
$63$	3.78779	+	1.41917i	0.477216	+	0.178799i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	4.38609	−	4.87125i	0.544028	−	0.604204i
$66$	4.41793	+	4.61821i	0.543809	+	0.568462i
$67$	−0.0499869	+	0.0865799i	−0.00610687	+	0.0105774i	−0.869063	−	0.494702i	$-0.835277\pi$
$67$	−0.0499869	+	0.0865799i	−0.00610687	+	0.0105774i	0.862956	+	0.505279i	$0.168611\pi$
$68$	−2.80383	−	4.85638i	−0.340015	−	0.588923i
$69$	8.30724	+	2.42445i	1.00007	+	0.291869i
$70$	1.09080	−	0.792514i	0.130376	−	0.0947236i
$71$	−8.04344	+	0.845399i	−0.954580	+	0.100330i	−0.568994	−	0.822341i	$-0.692667\pi$
$71$	−8.04344	+	0.845399i	−0.954580	+	0.100330i	−0.385586	+	0.922672i	$0.626001\pi$
$72$	2.79201	−	1.09758i	0.329042	−	0.129351i
$73$	1.50175	+	3.37300i	0.175767	+	0.394779i	0.979849	−	0.199739i	$-0.0640094\pi$
$73$	1.50175	+	3.37300i	0.175767	+	0.394779i	−0.804082	+	0.594518i	$0.797343\pi$
$74$	3.51455	−	0.747040i	0.408558	−	0.0868417i
$75$	0.656391	−	1.60286i	0.0757935	−	0.185082i
$76$	−1.68704	−	0.751118i	−0.193517	−	0.0861591i
$77$	−1.53739	−	4.73161i	−0.175202	−	0.539217i
$78$	−11.2503	+	1.52714i	−1.27384	+	0.172915i
$79$	0.331778	−	0.745186i	0.0373280	−	0.0838400i	−0.893919	−	0.448228i	$-0.852055\pi$
$79$	0.331778	−	0.745186i	0.0373280	−	0.0838400i	0.931247	+	0.364388i	$0.118722\pi$
$80$	0.207912	−	0.978148i	0.0232452	−	0.109360i
$81$	−7.86555	−	4.37414i	−0.873950	−	0.486015i
$82$	2.22693	−	0.991491i	0.245923	−	0.109492i
$83$	3.07491	+	3.41503i	0.337515	+	0.374849i	0.887880	−	0.460076i	$-0.152178\pi$
$83$	3.07491	+	3.41503i	0.337515	+	0.374849i	−0.550364	+	0.834925i	$0.685511\pi$
$84$	−2.32885	−	0.173871i	−0.254099	−	0.0189709i
$85$	3.29610	+	4.53670i	0.357513	+	0.492074i
$86$	1.01762	−	9.68200i	0.109733	−	1.04404i
$87$	2.21392	−	0.794017i	0.237357	−	0.0851275i
$88$	−3.19554	−	1.84495i	−0.340646	−	0.196672i
$89$	9.31870	+	6.77043i	0.987780	+	0.717664i	0.959434	−	0.281934i	$-0.0909759\pi$
$89$	9.31870	+	6.77043i	0.987780	+	0.717664i	0.0283463	+	0.999598i	$0.490976\pi$
$90$	−2.66199	+	1.38341i	−0.280598	+	0.145824i
$91$	8.40546	+	2.73110i	0.881132	+	0.286297i
$92$	−4.99627			−0.520898
$93$	−0.835004	−	9.60743i	−0.0865858	−	0.996244i
$94$	−2.38632			−0.246130
$95$	1.75631	+	0.570660i	0.180194	+	0.0585485i
$96$	−1.36988	+	1.05992i	−0.139813	+	0.108178i
$97$	13.8287	+	10.0471i	1.40409	+	1.02013i	0.994149	+	0.108016i	$0.0344497\pi$
$97$	13.8287	+	10.0471i	1.40409	+	1.02013i	0.409938	+	0.912113i	$0.365550\pi$
$98$	−4.48780	−	2.59104i	−0.453337	−	0.261734i
$99$	1.81950	+	10.9191i	0.182866	+	1.09741i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	7.89339	+	10.8643i	0.785422	+	1.08104i	0.994663	+	0.103177i	$0.0329007\pi$
$101$	7.89339	+	10.8643i	0.785422	+	1.08104i	−0.209241	+	0.977864i	$0.567099\pi$
$102$	0.723137	−	9.68581i	0.0716012	−	0.959038i
$103$	5.22200	+	5.79962i	0.514539	+	0.571453i	0.943290	−	0.331969i	$-0.107713\pi$
$103$	5.22200	+	5.79962i	0.514539	+	0.571453i	−0.428751	+	0.903423i	$0.641046\pi$
$104$	5.98821	−	2.66612i	0.587192	−	0.261435i
$105$	2.33427	−	0.0705131i	0.227801	−	0.00688137i
$106$	−1.90898	+	8.98105i	−0.185417	+	0.872317i
$107$	2.63935	−	5.92808i	0.255156	−	0.573089i	−0.739865	−	0.672755i	$-0.765111\pi$
$107$	2.63935	−	5.92808i	0.255156	−	0.573089i	0.995021	+	0.0996658i	$0.0317774\pi$
$108$	5.06684	+	1.15202i	0.487557	+	0.110853i
$109$	−6.04369	−	18.6006i	−0.578880	−	1.78161i	−0.622569	−	0.782565i	$-0.713911\pi$
$109$	−6.04369	−	18.6006i	−0.578880	−	1.78161i	0.0436890	−	0.999045i	$-0.486089\pi$
$110$	3.37088	+	1.50081i	0.321401	+	0.143097i
$111$	5.75917	+	2.35846i	0.546636	+	0.223855i
$112$	1.31884	−	0.280329i	0.124619	−	0.0264886i
$113$	6.93720	+	15.5812i	0.652597	+	1.46576i	0.871693	+	0.490053i	$0.163023\pi$
$113$	6.93720	+	15.5812i	0.652597	+	1.46576i	−0.219096	+	0.975703i	$0.570311\pi$
$114$	−1.68219	−	2.72049i	−0.157552	−	0.254797i
$115$	4.96890	−	0.522253i	0.463353	−	0.0487003i
$116$	−1.09859	+	0.798170i	−0.102001	+	0.0741082i
$117$	−17.5926	−	8.78649i	−1.62644	−	0.812311i
$118$	−4.92251	−	8.52603i	−0.453153	−	0.784885i
$119$	−3.78043	+	6.54789i	−0.346551	+	0.600244i
$120$	1.25158	−	1.19730i	0.114253	−	0.109298i
$121$	1.74998	−	1.94355i	0.159089	−	0.176687i
$122$	0.525875	−	1.61848i	0.0476105	−	0.146530i
$123$	4.15453	+	0.752741i	0.374602	+	0.0678723i
$124$	2.01679	+	5.18966i	0.181113	+	0.466045i
$125$		−	1.00000i		−	0.0894427i
$126$	−3.16385	−	2.52020i	−0.281858	−	0.224517i
$127$	−13.4400	−	12.1014i	−1.19261	−	1.07383i	−0.995627	−	0.0934189i	$-0.970220\pi$
$127$	−13.4400	−	12.1014i	−1.19261	−	1.07383i	−0.196979	−	0.980408i	$-0.563113\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	10.8994	−	12.8659i	0.959642	−	1.13278i
$130$	−5.67672	+	3.27746i	−0.497881	+	0.287452i
$131$	−12.7882	−	1.34410i	−1.11731	−	0.117434i	−0.472178	−	0.881503i	$-0.656532\pi$
$131$	−12.7882	−	1.34410i	−1.11731	−	0.117434i	−0.645135	+	0.764069i	$0.723199\pi$
$132$	−2.77459	−	5.75739i	−0.241497	−	0.501117i
$133$	0.260266	+	2.47627i	0.0225679	+	0.214720i
$134$	0.0742950	−	0.0668956i	0.00641811	−	0.00577890i
$135$	−5.15950	−	0.616078i	−0.444059	−	0.0530235i
$136$	1.16590	+	5.48513i	0.0999751	+	0.470346i
$137$	−3.58631	−	0.762293i	−0.306399	−	0.0651271i	0.0521463	−	0.998639i	$-0.483394\pi$
$137$	−3.58631	−	0.762293i	−0.306399	−	0.0651271i	−0.358545	+	0.933512i	$0.616727\pi$
$138$	−7.15146	−	4.87287i	−0.608773	−	0.414806i
$139$	6.94795	−	2.25753i	0.589318	−	0.191481i	0.000847313	−	1.00000i	$-0.499730\pi$
$139$	6.94795	−	2.25753i	0.589318	−	0.191481i	0.588471	+	0.808519i	$0.299730\pi$
$140$	−1.28232	+	0.416649i	−0.108375	+	0.0352133i
$141$	−3.41568	−	2.32738i	−0.287652	−	0.196000i
$142$	7.91101	+	1.68154i	0.663877	+	0.141111i
$143$	5.02874	+	23.6584i	0.420525	+	1.97841i
$144$	−2.99453	+	0.181081i	−0.249544	+	0.0150901i
$145$	1.00914	−	0.908631i	0.0838042	−	0.0754577i
$146$	−0.385940	−	3.67198i	−0.0319407	−	0.303895i
$147$	−3.89662	−	8.08566i	−0.321388	−	0.666894i
$148$	−3.57338	−	0.375578i	−0.293730	−	0.0308723i
$149$	−19.0580	+	11.0032i	−1.56130	+	0.901414i	−0.564169	+	0.825659i	$0.690803\pi$
$149$	−19.0580	+	11.0032i	−1.56130	+	0.901414i	−0.997126	+	0.0757551i	$0.975863\pi$
$150$	−1.11958	+	1.32157i	−0.0914129	+	0.107906i
$151$	−11.7273	+	16.1412i	−0.954354	+	1.31356i	−0.00478737	+	0.999989i	$0.501524\pi$
$151$	−11.7273	+	16.1412i	−0.954354	+	1.31356i	−0.949566	+	0.313567i	$0.898476\pi$
$152$	1.37236	+	1.23568i	0.111313	+	0.100227i
$153$	10.4816	−	13.1586i	0.847390	−	1.06381i
$154$			4.97511i			0.400905i
$155$	−2.54821	−	4.95042i	−0.204677	−	0.397627i
$156$	11.1715	+	2.02412i	0.894440	+	0.162059i
$157$	2.69616	−	8.29793i	0.215177	−	0.662247i	−0.783964	−	0.620807i	$-0.786805\pi$
$157$	2.69616	−	8.29793i	0.215177	−	0.662247i	0.999141	−	0.0414407i	$-0.0131948\pi$
$158$	−0.545815	+	0.606189i	−0.0434227	+	0.0482258i
$159$	−11.4917	+	10.9933i	−0.911348	+	0.871824i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	3.36825	+	5.83399i	0.265456	+	0.459782i
$162$	6.12890	+	6.59064i	0.481532	+	0.517810i
$163$	−7.44782	+	5.41116i	−0.583358	+	0.423835i	−0.839933	−	0.542690i	$-0.817406\pi$
$163$	−7.44782	+	5.41116i	−0.583358	+	0.423835i	0.256575	+	0.966524i	$0.417406\pi$
$164$	−2.42432	+	0.254806i	−0.189308	+	0.0198970i
$165$	3.36120	+	5.43583i	0.261669	+	0.423179i
$166$	−1.86911	−	4.19809i	−0.145071	−	0.325835i
$167$	−4.72701	+	1.00476i	−0.365787	+	0.0777504i	−0.387138	−	0.922022i	$-0.626536\pi$
$167$	−4.72701	+	1.00476i	−0.365787	+	0.0777504i	0.0213516	+	0.999772i	$0.493203\pi$
$168$	2.16114	+	0.885016i	0.166736	+	0.0682805i
$169$	−27.3761	−	12.1886i	−2.10585	−	0.937586i
$170$	−1.73286	−	5.33321i	−0.132905	−	0.409038i
$171$	0.245470	−	5.53464i	0.0187716	−	0.423245i
$172$	−3.95972	+	8.89367i	−0.301926	+	0.678136i
$173$	3.24242	−	15.2544i	0.246517	−	1.15977i	−0.664463	−	0.747321i	$-0.731340\pi$
$173$	3.24242	−	15.2544i	0.246517	−	1.15977i	0.910980	−	0.412450i	$-0.135327\pi$
$174$	−2.35093	+	0.0710163i	−0.178223	+	0.00538373i
$175$	1.23174	−	0.548405i	0.0931107	−	0.0414556i
$176$	2.46902	+	2.74212i	0.186109	+	0.206695i
$177$	1.26956	−	17.0047i	0.0954263	−	1.27815i
$178$	−6.77043	−	9.31870i	−0.507465	−	0.698466i
$179$	−1.50880	+	14.3553i	−0.112773	+	1.07296i	0.781026	+	0.624498i	$0.214696\pi$
$179$	−1.50880	+	14.3553i	−0.112773	+	1.07296i	−0.893800	+	0.448467i	$0.851970\pi$
$180$	2.95920	−	0.493103i	0.220566	−	0.0367537i
$181$	−8.35728	−	4.82508i	−0.621192	−	0.358645i	0.156141	−	0.987735i	$-0.450095\pi$
$181$	−8.35728	−	4.82508i	−0.621192	−	0.358645i	−0.777333	+	0.629089i	$0.783428\pi$
$182$	−7.15011	−	5.19486i	−0.530002	−	0.385069i
$183$	2.33122	−	1.80373i	0.172328	−	0.133336i
$184$	4.75174	+	1.54393i	0.350303	+	0.113820i
$185$	3.59307			0.264167
$186$	−2.17472	+	9.39524i	−0.159459	+	0.688893i
$187$	−20.6917			−1.51313
$188$	2.26952	+	0.737413i	0.165522	+	0.0537814i
$189$	−2.07065	−	6.69302i	−0.150618	−	0.486845i
$190$	−1.49401	−	1.08546i	−0.108387	−	0.0787475i
$191$	6.84297	+	3.95079i	0.495140	+	0.285869i	0.726704	−	0.686951i	$-0.241051\pi$
$191$	6.84297	+	3.95079i	0.495140	+	0.285869i	−0.231564	+	0.972820i	$0.574384\pi$
$192$	1.63037	−	0.584727i	0.117662	−	0.0421990i
$193$	0.947966	−	9.01929i	0.0682361	−	0.649223i	−0.905936	−	0.423415i	$-0.860831\pi$
$193$	0.947966	−	9.01929i	0.0682361	−	0.649223i	0.974172	−	0.225808i	$-0.0725022\pi$
$194$	−10.0471	−	13.8287i	−0.721340	−	0.992840i
$195$	−11.3219	−	0.845289i	−0.810780	−	0.0605324i
$196$	3.46748	+	3.85103i	0.247677	+	0.275074i
$197$	9.03839	−	4.02415i	0.643958	−	0.286709i	−0.0586575	−	0.998278i	$-0.518682\pi$
$197$	9.03839	−	4.02415i	0.643958	−	0.286709i	0.702616	+	0.711569i	$0.252015\pi$
$198$	1.64375	−	10.9470i	0.116816	−	0.777966i
$199$	−0.000289787		0.00136334i	−2.05424e−5		9.66446e-5i	−0.978158	−	0.207863i	$-0.933349\pi$
$199$	−0.000289787		0.00136334i	−2.05424e−5		9.66446e-5i	0.978137	+	0.207960i	$0.0666824\pi$
$200$	0.406737	−	0.913545i	0.0287606	−	0.0645974i
$201$	0.171586	−	0.0232916i	0.0121028	−	0.00164286i
$202$	−4.14980	−	12.7718i	−0.291979	−	0.898619i
$203$	1.67261	+	0.744695i	0.117394	+	0.0522673i
$204$	−3.68082	+	8.98829i	−0.257709	+	0.629306i
$205$	2.38440	−	0.506821i	0.166534	−	0.0353979i
$206$	−3.17424	−	7.12945i	−0.221160	−	0.496732i
$207$	−5.48381	−	13.9496i	−0.381151	−	0.969567i
$208$	−6.51900	+	0.685175i	−0.452011	+	0.0475083i
$209$	−5.51272	+	4.00523i	−0.381323	+	0.277047i
$210$	−2.24181	−	0.654267i	−0.154700	−	0.0451487i
$211$	−6.86283	−	11.8868i	−0.472457	−	0.818319i	0.527046	−	0.849837i	$-0.323299\pi$
$211$	−6.86283	−	11.8868i	−0.472457	−	0.818319i	−0.999503	+	0.0315172i	$0.989966\pi$
$212$	4.59085	−	7.95158i	0.315301	−	0.546117i
$213$	9.68349	+	10.1225i	0.663502	+	0.693581i
$214$	−4.34205	+	4.82234i	−0.296817	+	0.329648i
$215$	3.00838	−	9.25885i	0.205170	−	0.631448i
$216$	−4.46286	−	2.66137i	−0.303659	−	0.181083i
$217$	4.70017	−	5.85356i	0.319068	−	0.397366i
$218$			19.5578i			1.32462i
$219$	3.02886	−	5.63233i	0.204671	−	0.380597i
$220$	−2.74212	−	2.46902i	−0.184874	−	0.166461i
$221$	21.6057	−	29.7377i	1.45335	−	2.00037i
$222$	−4.74849	−	4.02271i	−0.318698	−	0.269986i
$223$	−10.9442	+	6.31865i	−0.732880	+	0.423128i	−0.819475	−	0.573115i	$-0.805735\pi$
$223$	−10.9442	+	6.31865i	−0.732880	+	0.423128i	0.0865949	+	0.996244i	$0.472401\pi$
$224$	−1.34092	−	0.140936i	−0.0895940	−	0.00941671i
$225$	−2.89144	+	0.799722i	−0.192763	+	0.0533148i
$226$	−1.78281	−	16.9623i	−0.118591	−	1.12832i
$227$	−8.30198	+	7.47513i	−0.551022	+	0.496142i	−0.896958	−	0.442116i	$-0.854228\pi$
$227$	−8.30198	+	7.47513i	−0.551022	+	0.496142i	0.345936	+	0.938258i	$0.387561\pi$
$228$	0.759183	+	3.10716i	0.0502781	+	0.205777i
$229$	2.48323	+	11.6827i	0.164096	+	0.772013i	0.980809	+	0.194969i	$0.0624606\pi$
$229$	2.48323	+	11.6827i	0.164096	+	0.772013i	−0.816713	+	0.577044i	$0.804206\pi$
$230$	−4.88709	−	1.03878i	−0.322245	−	0.0684954i
$231$	−4.85222	+	7.12116i	−0.319253	+	0.468538i
$232$	1.29147	−	0.419623i	0.0847889	−	0.0275496i
$233$	−10.9052	+	3.54332i	−0.714424	+	0.232130i	−0.643604	−	0.765359i	$-0.722562\pi$
$233$	−10.9052	+	3.54332i	−0.714424	+	0.232130i	−0.0708198	+	0.997489i	$0.522562\pi$
$234$	14.0164	+	13.7929i	0.916279	+	0.901667i
$235$	−2.33417	−	0.496143i	−0.152265	−	0.0323648i
$236$	2.04689	+	9.62988i	0.133241	+	0.626852i
$237$	−1.37247	+	0.335341i	−0.0891518	+	0.0217827i
$238$	5.61881	−	5.05920i	0.364213	−	0.327939i
$239$	1.50610	+	14.3295i	0.0974212	+	0.926901i	0.928647	+	0.370966i	$0.120973\pi$
$239$	1.50610	+	14.3295i	0.0974212	+	0.926901i	−0.831225	+	0.555936i	$0.812360\pi$
$240$	−1.56031	+	0.751943i	−0.100718	+	0.0485377i
$241$	−12.5968	−	1.32397i	−0.811429	−	0.0852846i	−0.310279	−	0.950645i	$-0.600423\pi$
$241$	−12.5968	−	1.32397i	−0.811429	−	0.0852846i	−0.501149	+	0.865361i	$0.667089\pi$
$242$	−2.26492	+	1.30765i	−0.145595	+	0.0840592i
$243$	2.34481	+	15.4111i	0.150420	+	0.988622i
$244$	−1.00027	+	1.37676i	−0.0640359	+	0.0881379i
$245$	−3.85103	−	3.46748i	−0.246033	−	0.221529i
$246$	−3.71859	−	1.99972i	−0.237088	−	0.127497i
$247$		−	12.1049i		−	0.770217i
$248$	−0.314388	−	5.55888i	−0.0199637	−	0.352989i
$249$	1.41903	−	7.83192i	0.0899273	−	0.496328i
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−1.34486	+	1.49361i	−0.0848865	+	0.0942760i	−0.784092	−	0.620645i	$-0.786871\pi$
$251$	−1.34486	+	1.49361i	−0.0848865	+	0.0942760i	0.699205	+	0.714921i	$0.253537\pi$
$252$	2.23021	+	3.37454i	0.140490	+	0.212576i
$253$	−9.21786	+	15.9658i	−0.579522	+	1.00376i
$254$	9.04264	+	15.6623i	0.567386	+	0.982741i
$255$	2.72113	−	9.32380i	0.170404	−	0.583879i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	3.03046	−	0.318514i	0.189035	−	0.0198684i	−0.00953794	−	0.999955i	$-0.503036\pi$
$257$	3.03046	−	0.318514i	0.189035	−	0.0198684i	0.198573	+	0.980086i	$0.436369\pi$
$258$	−14.3418	+	8.86812i	−0.892880	+	0.552105i
$259$	1.97046	+	4.42572i	0.122438	+	0.275001i
$260$	6.41167	−	1.36284i	0.397635	−	0.0845199i
$261$	−3.43428	−	2.19121i	−0.212577	−	0.135632i
$262$	11.7470	+	5.23009i	0.725731	+	0.323116i
$263$	0.850313	+	2.61699i	0.0524325	+	0.161371i	0.973844	−	0.227218i	$-0.0729629\pi$
$263$	0.850313	+	2.61699i	0.0524325	+	0.161371i	−0.921411	+	0.388588i	$0.872963\pi$
$264$	0.859661	+	6.33300i	0.0529085	+	0.389769i
$265$	−3.73453	+	8.38789i	−0.229410	+	0.515264i
$266$	0.517681	−	2.43550i	0.0317411	−	0.149330i
$267$	−0.602391	−	19.9416i	−0.0368658	−	1.22041i
$268$	−0.0913306	+	0.0406630i	−0.00557891	+	0.00248389i
$269$	−15.4577	−	17.1675i	−0.942473	−	1.04672i	−0.998832	−	0.0483118i	$-0.984616\pi$
$269$	−15.4577	−	17.1675i	−0.942473	−	1.04672i	0.0563592	−	0.998411i	$-0.482051\pi$
$270$	4.71660	+	2.18030i	0.287043	+	0.132689i
$271$	11.5470	+	15.8931i	0.701431	+	0.965437i	0.999939	+	0.0110298i	$0.00351096\pi$
$271$	11.5470	+	15.8931i	0.701431	+	0.965437i	−0.298508	+	0.954407i	$0.596489\pi$
$272$	0.586161	−	5.57695i	0.0355412	−	0.338152i
$273$	−5.16783	−	14.4092i	−0.312771	−	0.872086i
$274$	3.17522	+	1.83321i	0.191822	+	0.110748i
$275$	2.98519	+	2.16886i	0.180013	+	0.130787i
$276$	5.29565	+	6.84429i	0.318760	+	0.411978i
$277$	−1.45337	−	0.472230i	−0.0873248	−	0.0283736i	0.265029	−	0.964241i	$-0.414619\pi$
$277$	−1.45337	−	0.472230i	−0.0873248	−	0.0283736i	−0.352354	+	0.935867i	$0.614619\pi$
$278$	−7.30551			−0.438156
$279$	−12.2760	+	11.3270i	−0.734944	+	0.678127i
$280$	1.34831			0.0805767
$281$	−14.8517	−	4.82562i	−0.885980	−	0.287872i	−0.169542	−	0.985523i	$-0.554229\pi$
$281$	−14.8517	−	4.82562i	−0.885980	−	0.287872i	−0.716438	+	0.697650i	$0.754229\pi$
$282$	2.52930	+	3.26897i	0.150618	+	0.194664i
$283$	20.2186	+	14.6897i	1.20187	+	0.873209i	0.994467	−	0.105047i	$-0.0334992\pi$
$283$	20.2186	+	14.6897i	1.20187	+	0.873209i	0.207402	+	0.978256i	$0.433499\pi$
$284$	−7.00419	−	4.04387i	−0.415622	−	0.239960i
$285$	−1.07981	−	3.01079i	−0.0639625	−	0.178344i
$286$	2.52822	−	24.0544i	0.149497	−	1.42237i
$287$	1.93189	+	2.65902i	0.114036	+	0.156957i
$288$	2.90392	+	0.753142i	0.171115	+	0.0443793i
$289$	9.66622	+	10.7354i	0.568601	+	0.631496i
$290$	−1.24053	+	0.552319i	−0.0728463	+	0.0324333i
$291$	−0.893930	−	29.5927i	−0.0524031	−	1.73476i
$292$	−0.767652	+	3.61152i	−0.0449235	+	0.211348i
$293$	−7.63171	+	17.1411i	−0.445850	+	1.00139i	0.541188	+	0.840902i	$0.317975\pi$
$293$	−7.63171	+	17.1411i	−0.445850	+	1.00139i	−0.987037	+	0.160493i	$0.948692\pi$
$294$	1.20730	+	8.89404i	0.0704114	+	0.518711i
$295$	−3.04228	−	9.36316i	−0.177128	−	0.545144i
$296$	3.28243	+	1.46143i	0.190787	+	0.0849440i
$297$	13.0294	−	14.0659i	0.756040	−	0.816185i
$298$	21.5254	−	4.57537i	1.24694	−	0.265044i
$299$	−13.3207	−	29.9187i	−0.770355	−	1.73024i
$300$	1.47317	−	0.910922i	0.0850534	−	0.0525921i
$301$	13.0543	−	1.37206i	0.752437	−	0.0790844i
$302$	16.1412	−	11.7273i	0.928824	−	0.674830i
$303$	6.51646	−	22.3283i	0.374361	−	1.28273i
$304$	−0.923347	−	1.59928i	−0.0529576	−	0.0917252i
$305$	0.850883	−	1.47377i	0.0487214	−	0.0843880i
$306$	−14.0349	+	9.27557i	−0.802320	+	0.530249i
$307$	7.18730	−	7.98230i	0.410201	−	0.455574i	−0.502273	−	0.864709i	$-0.667503\pi$
$307$	7.18730	−	7.98230i	0.410201	−	0.455574i	0.912474	+	0.409135i	$0.134169\pi$
$308$	1.53739	−	4.73161i	0.0876010	−	0.269608i
$309$	2.40988	−	13.3006i	0.137093	−	0.756647i
$310$	0.893727	+	5.49557i	0.0507603	+	0.312127i
$311$		−	8.76227i		−	0.496863i	−0.968649	−	0.248431i	$-0.920085\pi$
$311$		−	8.76227i		−	0.496863i	0.968649	−	0.248431i	$-0.0799151\pi$
$312$	−9.99929	−	5.37725i	−0.566098	−	0.304427i
$313$	6.50542	+	5.85750i	0.367708	+	0.331086i	0.832184	−	0.554500i	$-0.187091\pi$
$313$	6.50542	+	5.85750i	0.367708	+	0.331086i	−0.464476	+	0.885586i	$0.653757\pi$
$314$	−5.12841	+	7.05864i	−0.289413	+	0.398342i
$315$	−2.57073	−	3.12293i	−0.144844	−	0.175957i
$316$	0.706424	−	0.407854i	0.0397394	−	0.0229436i
$317$	−22.0209	−	2.31449i	−1.23682	−	0.129995i	−0.536546	−	0.843871i	$-0.680271\pi$
$317$	−22.0209	−	2.31449i	−1.23682	−	0.129995i	−0.700272	+	0.713876i	$0.746938\pi$
$318$	14.3263	−	6.90411i	0.803380	−	0.387163i
$319$	0.523751	+	4.98316i	0.0293244	+	0.279003i
$320$	0.743145	−	0.669131i	0.0415431	−	0.0374055i
$321$	−10.9183	+	2.66769i	−0.609398	+	0.148896i
$322$	−1.40060	−	6.58930i	−0.0780523	−	0.367207i
$323$	10.1293	+	2.15306i	0.563612	+	0.119799i
$324$	−3.79231	−	8.16201i	−0.210684	−	0.453445i
$325$	−6.23409	+	2.02558i	−0.345805	+	0.112359i
$326$	8.75544	−	2.84481i	0.484919	−	0.157560i
$327$	−19.0747	+	27.9942i	−1.05483	+	1.54808i
$328$	2.38440	+	0.506821i	0.131657	+	0.0279845i
$329$	−0.668953	−	3.14718i	−0.0368806	−	0.173509i
$330$	−1.51693	−	6.20845i	−0.0835043	−	0.341764i
$331$	17.6480	−	15.8903i	0.970023	−	0.873412i	−0.0219636	−	0.999759i	$-0.506992\pi$
$331$	17.6480	−	15.8903i	0.970023	−	0.873412i	0.991986	+	0.126347i	$0.0403251\pi$
$332$	0.480348	+	4.57021i	0.0263625	+	0.250823i
$333$	−2.87345	−	10.3891i	−0.157464	−	0.569322i
$334$	4.80614	+	0.505145i	0.262980	+	0.0276403i
$335$	0.0865799	−	0.0499869i	0.00473036	−	0.00273108i
$336$	−1.78188	−	1.50953i	−0.0972097	−	0.0823516i
$337$	−13.0598	+	17.9753i	−0.711413	+	0.979176i	0.288353	+	0.957524i	$0.406892\pi$
$337$	−13.0598	+	17.9753i	−0.711413	+	0.979176i	−0.999766	+	0.0216513i	$0.993108\pi$
$338$	22.2697	+	20.0517i	1.21131	+	1.09067i
$339$	13.9915	−	26.0179i	0.759914	−	1.41310i
$340$			5.60767i			0.304119i
$341$	20.3046	+	3.12991i	1.09956	+	0.169494i
$342$	−1.94375	+	5.18790i	−0.105106	+	0.280530i
$343$	5.07565	−	15.6213i	0.274060	−	0.843469i
$344$	6.51421	−	7.23476i	0.351223	−	0.390072i
$345$	−5.98206	−	6.25326i	−0.322063	−	0.336664i
$346$	−7.79760	+	13.5058i	−0.419201	+	0.726078i
$347$	12.6018	+	21.8270i	0.676500	+	1.17173i	0.976028	+	0.217645i	$0.0698376\pi$
$347$	12.6018	+	21.8270i	0.676500	+	1.17173i	−0.299528	+	0.954088i	$0.596829\pi$
$348$	2.25781	+	0.658936i	0.121031	+	0.0353227i
$349$	28.7820	−	20.9114i	1.54067	−	1.11936i	0.590749	−	0.806855i	$-0.298832\pi$
$349$	28.7820	−	20.9114i	1.54067	−	1.11936i	0.949917	−	0.312504i	$-0.101168\pi$
$350$	−1.34092	+	0.140936i	−0.0716752	+	0.00753337i
$351$	6.61029	+	33.4127i	0.352831	+	1.78344i
$352$	−1.50081	−	3.37088i	−0.0799937	−	0.179669i
$353$	−27.9373	+	5.93825i	−1.48695	+	0.316061i	−0.878581	−	0.477593i	$-0.841509\pi$
$353$	−27.9373	+	5.93825i	−1.48695	+	0.316061i	−0.608369	+	0.793654i	$0.708176\pi$
$354$	−6.46218	+	15.7801i	−0.343461	+	0.838705i
$355$	7.38852	+	3.28958i	0.392142	+	0.174593i
$356$	3.55943	+	10.9548i	0.188649	+	0.580603i
$357$	12.9768	−	1.76151i	0.686804	−	0.0932288i
$358$	5.87098	−	13.1864i	0.310291	−	0.696925i
$359$	−6.16257	+	28.9926i	−0.325248	+	1.53017i	0.446816	+	0.894626i	$0.352558\pi$
$359$	−6.16257	+	28.9926i	−0.325248	+	1.53017i	−0.772064	+	0.635545i	$0.780775\pi$
$360$	−2.96674	−	0.445473i	−0.156361	−	0.0234785i
$361$	−14.2419	+	6.34091i	−0.749575	+	0.333732i
$362$	6.45722	+	7.17147i	0.339384	+	0.376924i
$363$	−4.51728	−	0.337257i	−0.237096	−	0.0177014i
$364$	5.19486	+	7.15011i	0.272285	+	0.374768i
$365$	0.385940	−	3.67198i	0.0202010	−	0.192200i
$366$	−2.77450	+	0.995069i	−0.145026	+	0.0520131i
$367$	13.0415	+	7.52949i	0.680759	+	0.393036i	0.800141	−	0.599812i	$-0.204758\pi$
$367$	13.0415	+	7.52949i	0.680759	+	0.393036i	−0.119382	+	0.992848i	$0.538091\pi$
$368$	−4.04207	−	2.93674i	−0.210707	−	0.153088i
$369$	−3.37230	−	6.48905i	−0.175555	−	0.337807i
$370$	−3.41721	−	1.11032i	−0.177652	−	0.0577227i
$371$	−12.3797			−0.642724
$372$	4.97158	−	8.26338i	0.257764	−	0.428436i
$373$	−7.27462			−0.376665			−0.188333	−	0.982105i	$-0.560308\pi$
$373$	−7.27462			−0.376665			−0.188333	+	0.982105i	$0.560308\pi$
$374$	19.6790	+	6.39409i	1.01758	+	0.330630i
$375$	−1.36988	+	1.05992i	−0.0707403	+	0.0547340i
$376$	−1.93057	−	1.40264i	−0.0995616	−	0.0723358i
$377$	−7.70857	−	4.45055i	−0.397012	−	0.229215i
$378$	−0.0989495	+	7.00531i	−0.00508941	+	0.360314i
$379$	2.67747	−	25.4745i	0.137533	−	1.30853i	−0.680238	−	0.732991i	$-0.738124\pi$
$379$	2.67747	−	25.4745i	0.137533	−	1.30853i	0.817771	−	0.575544i	$-0.195210\pi$
$380$	1.08546	+	1.49401i	0.0556829	+	0.0766409i
$381$	−2.33219	+	31.2377i	−0.119482	+	1.60035i
$382$	−5.28719	−	5.87202i	−0.270516	−	0.300438i
$383$	−9.47373	+	4.21798i	−0.484085	+	0.215528i	−0.634243	−	0.773133i	$-0.718688\pi$
$383$	−9.47373	+	4.21798i	−0.484085	+	0.215528i	0.150158	+	0.988662i	$0.452022\pi$
$384$	−1.73126	+	0.0522975i	−0.0883480	+	0.00266880i
$385$	−1.03438	+	4.86639i	−0.0527170	+	0.248014i
$386$	−3.68868	+	8.28492i	−0.187749	+	0.421691i
$387$	−29.1773	−	1.29406i	−1.48317	−	0.0657808i
$388$	5.28208	+	16.2566i	0.268157	+	0.825302i
$389$	−5.12581	−	2.28216i	−0.259889	−	0.115710i	0.272657	−	0.962111i	$-0.412098\pi$
$389$	−5.12581	−	2.28216i	−0.259889	−	0.115710i	−0.532545	+	0.846401i	$0.678764\pi$
$390$	10.5066	+	4.30259i	0.532022	+	0.217870i
$391$	27.4052	−	5.82515i	1.38594	−	0.294591i
$392$	−2.10774	−	4.73406i	−0.106457	−	0.239106i
$393$	11.7132	+	18.9430i	0.590855	+	0.955547i
$394$	−9.83955	+	1.03418i	−0.495709	+	0.0521011i
$395$	−0.659922	+	0.479461i	−0.0332043	+	0.0241243i
$396$	−4.94609	+	9.90323i	−0.248551	+	0.497656i
$397$	9.09073	+	15.7456i	0.456251	+	0.790249i	0.998759	−	0.0498011i	$-0.0158588\pi$
$397$	9.09073	+	15.7456i	0.456251	+	0.790249i	−0.542509	+	0.840050i	$0.682525\pi$
$398$	0.000696899	−	0.00120706i	3.49324e−5	−	6.05047e-5i
$399$	3.11633	−	2.98118i	0.156012	−	0.149246i
$400$	−0.669131	+	0.743145i	−0.0334565	+	0.0371572i
$401$	4.54601	−	13.9912i	0.227017	−	0.698686i	−0.771064	−	0.636758i	$-0.780275\pi$
$401$	4.54601	−	13.9912i	0.227017	−	0.698686i	0.998081	−	0.0619279i	$-0.0197249\pi$
$402$	−0.170386	−	0.0308714i	−0.00849806	−	0.00153973i
$403$	−25.6998	+	25.9132i	−1.28020	+	1.29083i
$404$			13.4290i			0.668120i
$405$	4.62470	+	7.72089i	0.229803	+	0.383654i
$406$	−1.36063	−	1.22511i	−0.0675267	−	0.0608013i
$407$	−7.79287	+	10.7260i	−0.386278	+	0.531667i
$408$	6.27821	−	7.41094i	0.310818	−	0.366896i
$409$	14.5021	−	8.37278i	0.717082	−	0.414007i	−0.0965959	−	0.995324i	$-0.530795\pi$
$409$	14.5021	−	8.37278i	0.717082	−	0.414007i	0.813678	+	0.581316i	$0.197462\pi$
$410$	−2.42432	−	0.254806i	−0.119729	−	0.0125840i
$411$	2.75695	+	5.72078i	0.135990	+	0.282185i
$412$	0.815757	+	7.76141i	0.0401894	+	0.382377i
$413$	9.86457	−	8.88210i	0.485404	−	0.437060i
$414$	0.904732	+	14.9615i	0.0444652	+	0.735317i
$415$	−0.955433	−	4.49496i	−0.0469004	−	0.220649i
$416$	6.41167	+	1.36284i	0.314358	+	0.0668189i
$417$	−10.4568	−	7.12507i	−0.512072	−	0.348916i
$418$	6.48060	−	2.10567i	0.316976	−	0.102992i
$419$	35.0985	−	11.4042i	1.71468	−	0.557132i	0.723575	−	0.690246i	$-0.242498\pi$
$419$	35.0985	−	11.4042i	1.71468	−	0.557132i	0.991101	+	0.133114i	$0.0424976\pi$
$420$	1.92991	+	1.31500i	0.0941700	+	0.0641656i
$421$	−26.3891	−	5.60917i	−1.28613	−	0.273374i	−0.486398	−	0.873737i	$-0.661689\pi$
$421$	−26.3891	−	5.60917i	−1.28613	−	0.273374i	−0.799728	+	0.600363i	$0.795023\pi$
$422$	2.85373	+	13.4257i	0.138917	+	0.653554i
$423$	0.432118	+	7.14590i	0.0210103	+	0.347446i
$424$	−6.82333	+	6.14375i	−0.331370	+	0.298367i
$425$	−0.586161	−	5.57695i	−0.0284330	−	0.270522i
$426$	−6.08153	−	12.6194i	−0.294651	−	0.611413i
$427$	2.28193	+	0.239841i	0.110430	+	0.0116067i
$428$	5.61972	−	3.24455i	0.271639	−	0.156831i
$429$	27.0791	−	31.9647i	1.30739	−	1.54327i
$430$	−5.72228	+	7.87605i	−0.275953	+	0.379817i
$431$	18.9781	+	17.0880i	0.914144	+	0.823099i	0.984673	−	0.174411i	$-0.0558021\pi$
$431$	18.9781	+	17.0880i	0.914144	+	0.823099i	−0.0705290	+	0.997510i	$0.522469\pi$
$432$	3.42202	+	3.91021i	0.164642	+	0.188130i
$433$			24.3011i			1.16783i	0.811813	+	0.583917i	$0.198481\pi$
$433$			24.3011i			1.16783i	−0.811813	+	0.583917i	$0.801519\pi$
$434$	−6.27898	+	4.11464i	−0.301401	+	0.197509i
$435$	−2.31432	−	0.419321i	−0.110963	−	0.0201049i
$436$	6.04369	−	18.6006i	0.289440	−	0.890805i
$437$	6.17379	−	6.85669i	0.295333	−	0.328000i
$438$	−4.62110	+	4.42069i	−0.220805	+	0.211229i
$439$	−13.2566	+	22.9611i	−0.632702	+	1.09587i	0.354295	+	0.935134i	$0.384721\pi$
$439$	−13.2566	+	22.9611i	−0.632702	+	1.09587i	−0.986997	+	0.160738i	$0.948612\pi$
$440$	1.84495	+	3.19554i	0.0879544	+	0.152341i
$441$	−6.94628	+	13.9081i	−0.330775	+	0.662288i
$442$	−29.7377	+	21.6057i	−1.41448	+	1.02768i
$443$	20.8207	−	2.18835i	0.989223	−	0.103972i	0.403927	−	0.914791i	$-0.367645\pi$
$443$	20.8207	−	2.18835i	0.989223	−	0.103972i	0.585296	+	0.810820i	$0.300978\pi$
$444$	3.27300	+	5.29319i	0.155330	+	0.251204i
$445$	−4.68501	−	10.5227i	−0.222091	−	0.498825i
$446$	12.3612	−	2.62744i	0.585318	−	0.124413i
$447$	35.2730	+	14.4448i	1.66836	+	0.683214i
$448$	1.23174	+	0.548405i	0.0581942	+	0.0259097i
$449$	4.74159	+	14.5931i	0.223770	+	0.688692i	0.998414	+	0.0562953i	$0.0179288\pi$
$449$	4.74159	+	14.5931i	0.223770	+	0.688692i	−0.774644	+	0.632397i	$0.782071\pi$
$450$	2.99705	+	0.132924i	0.141282	+	0.00626611i
$451$	−3.65850	+	8.21712i	−0.172272	+	0.386929i
$452$	−3.54609	+	16.6830i	−0.166794	+	0.784704i
$453$	34.5415	−	1.04342i	1.62290	−	0.0490243i
$454$	10.2056	−	4.54382i	0.478972	−	0.213252i
$455$	−5.91379	−	6.56793i	−0.277243	−	0.307909i
$456$	0.238140	−	3.18969i	0.0111519	−	0.149371i
$457$	−14.7381	−	20.2853i	−0.689420	−	0.948906i	0.310578	−	0.950548i	$-0.399477\pi$
$457$	−14.7381	−	20.2853i	−0.689420	−	0.948906i	−0.999999	+	0.00164220i	$0.999477\pi$
$458$	1.24845	−	11.8782i	0.0583364	−	0.555034i
$459$	−29.1354	−	0.411536i	−1.35992	−	0.0192088i
$460$	4.32690	+	2.49814i	0.201743	+	0.116476i
$461$	−2.19286	−	1.59321i	−0.102132	−	0.0742030i	0.535547	−	0.844505i	$-0.320105\pi$
$461$	−2.19286	−	1.59321i	−0.102132	−	0.0742030i	−0.637679	+	0.770302i	$0.720105\pi$
$462$	6.81530	−	5.27321i	0.317076	−	0.245332i
$463$	−5.76377	−	1.87276i	−0.267865	−	0.0870346i	0.172005	−	0.985096i	$-0.444975\pi$
$463$	−5.76377	−	1.87276i	−0.267865	−	0.0870346i	−0.439870	+	0.898061i	$0.644975\pi$
$464$	−1.35793			−0.0630402
$465$	−4.08058	+	8.73778i	−0.189232	+	0.405205i
$466$	11.4664			0.531171
$467$	−38.1428	−	12.3933i	−1.76504	−	0.573495i	−0.767335	−	0.641247i	$-0.778417\pi$
$467$	−38.1428	−	12.3933i	−1.76504	−	0.573495i	−0.997702	+	0.0677518i	$0.978417\pi$
$468$	−9.06814	−	17.4491i	−0.419175	−	0.806584i
$469$	0.109052	+	0.0792307i	0.00503554	+	0.00365853i
$470$	2.06661	+	1.19316i	0.0953257	+	0.0550363i
$471$	−14.2249	+	5.10172i	−0.655448	+	0.235075i
$472$	1.02908	−	9.79108i	0.0473674	−	0.450671i
$473$	21.1146	+	29.0618i	0.970851	+	1.33626i
$474$	1.40893	+	0.105190i	0.0647141	+	0.00483152i
$475$	−1.23568	−	1.37236i	−0.0566969	−	0.0629682i
$476$	−6.90718	+	3.07528i	−0.316590	+	0.140955i
$477$	27.2397	+	4.09020i	1.24722	+	0.187277i
$478$	2.99569	−	14.0936i	0.137020	−	0.644627i
$479$	−6.66205	+	14.9632i	−0.304397	+	0.683687i	−0.999375	−	0.0353439i	$-0.988747\pi$
$479$	−6.66205	+	14.9632i	−0.304397	+	0.683687i	0.694978	+	0.719031i	$0.255414\pi$
$480$	1.71631	−	0.232977i	0.0783385	−	0.0106339i
$481$	−7.27804	−	22.3995i	−0.331850	−	1.02133i
$482$	11.5711	+	5.15179i	0.527049	+	0.234657i
$483$	4.42178	−	10.7977i	0.201198	−	0.491310i
$484$	2.55816	−	0.543754i	0.116280	−	0.0247161i
$485$	−6.95241	−	15.6154i	−0.315693	−	0.709058i
$486$	2.53224	−	15.3814i	0.114865	−	0.697715i
$487$	16.9421	−	1.78068i	0.767719	−	0.0806905i	0.287431	−	0.957801i	$-0.407199\pi$
$487$	16.9421	−	1.78068i	0.767719	−	0.0806905i	0.480288	+	0.877111i	$0.340532\pi$
$488$	1.37676	−	1.00027i	0.0623229	−	0.0452802i
$489$	15.3067	+	4.46723i	0.692194	+	0.202015i
$490$	2.59104	+	4.48780i	0.117051	+	0.202738i
$491$	17.0000	−	29.4448i	0.767197	−	1.32882i	−0.171880	−	0.985118i	$-0.554984\pi$
$491$	17.0000	−	29.4448i	0.767197	−	1.32882i	0.939077	−	0.343706i	$-0.111682\pi$
$492$	2.91864	+	3.05095i	0.131582	+	0.137548i
$493$	5.09530	−	5.65890i	0.229481	−	0.254864i
$494$	−3.74062	+	11.5125i	−0.168299	+	0.517970i
$495$	3.88383	−	10.3660i	0.174565	−	0.465916i
$496$	−1.41879	+	5.38396i	−0.0637055	+	0.241747i
$497$			10.9048i			0.489145i
$498$	−3.76977	+	7.01009i	−0.168928	+	0.314130i
$499$	23.7219	+	21.3593i	1.06194	+	0.956175i	0.999124	−	0.0418500i	$-0.0133252\pi$
$499$	23.7219	+	21.3593i	1.06194	+	0.956175i	0.0628161	+	0.998025i	$0.479992\pi$
$500$	0.587785	−	0.809017i	0.0262866	−	0.0361803i
$501$	6.38664	+	5.41047i	0.285334	+	0.241722i
$502$	1.74059	−	1.00493i	0.0776861	−	0.0448521i
$503$	14.4287	+	1.51652i	0.643344	+	0.0676182i	0.420582	−	0.907255i	$-0.361826\pi$
$503$	14.4287	+	1.51652i	0.643344	+	0.0676182i	0.222762	+	0.974873i	$0.428493\pi$
$504$	−1.07827	−	3.89855i	−0.0480300	−	0.173655i
$505$	−1.40372	−	13.3555i	−0.0624646	−	0.594311i
$506$	13.7004	−	12.3359i	0.609057	−	0.548398i
$507$	12.3195	+	50.4209i	0.547128	+	2.23927i
$508$	−3.76014	−	17.6901i	−0.166829	−	0.784870i
$509$	−22.9726	−	4.88298i	−1.01824	−	0.216434i	−0.331593	−	0.943423i	$-0.607586\pi$
$509$	−22.9726	−	4.88298i	−1.01824	−	0.216434i	−0.686650	+	0.726989i	$0.740919\pi$
$510$	−5.46916	+	8.02659i	−0.242178	+	0.355423i
$511$	4.73457	−	1.53835i	0.209445	−	0.0680528i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−7.84197	+	5.53001i	−0.346231	+	0.244156i
$514$	−2.98056	−	0.633538i	−0.131467	−	0.0279442i
$515$	−1.62258	−	7.63362i	−0.0714992	−	0.336377i
$516$	16.3802	−	4.00224i	0.721100	−	0.176189i
$517$	6.54358	−	5.89187i	0.287786	−	0.259124i
$518$	−0.506394	−	4.81801i	−0.0222497	−	0.211691i
$519$	−24.3334	+	11.7267i	−1.06812	+	0.514745i
$520$	−6.51900	−	0.685175i	−0.285877	−	0.0300469i
$521$	−0.279080	+	0.161127i	−0.0122267	+	0.00705909i	−0.506101	−	0.862474i	$-0.668914\pi$
$521$	−0.279080	+	0.161127i	−0.0122267	+	0.00705909i	0.493874	+	0.869533i	$0.335580\pi$
$522$	2.58908	+	3.14522i	0.113321	+	0.137662i
$523$	−2.32621	+	3.20175i	−0.101718	+	0.140003i	−0.856842	−	0.515579i	$-0.827577\pi$
$523$	−2.32621	+	3.20175i	−0.101718	+	0.140003i	0.755124	+	0.655582i	$0.227577\pi$
$524$	−9.55586	−	8.60413i	−0.417449	−	0.375873i
$525$	−2.05679	−	1.10607i	−0.0897658	−	0.0482728i
$526$		−	2.75167i		−	0.119978i
$527$	−17.1130	−	26.1146i	−0.745453	−	1.13757i
$528$	1.13942	−	6.28869i	0.0495869	−	0.273680i
$529$	0.606523	−	1.86669i	0.0263706	−	0.0811603i
$530$	6.14375	−	6.82333i	0.266867	−	0.296386i
$531$	−24.6401	+	16.2845i	−1.06929	+	0.706687i
$532$	−1.24495	+	2.15632i	−0.0539756	+	0.0934885i
$533$	−7.98937	−	13.8380i	−0.346058	−	0.599390i
$534$	−5.58939	+	19.1517i	−0.241876	+	0.828777i
$535$	−5.24979	+	3.81419i	−0.226968	+	0.164902i
$536$	0.0994262	−	0.0104501i	0.00429456	−	0.000451376i
$537$	21.2642	−	13.1486i	0.917619	−	0.567403i
$538$	9.39610	+	21.1040i	0.405095	+	0.909857i
$539$	18.7034	−	3.97554i	0.805614	−	0.171239i
$540$	−3.81200	−	3.53110i	−0.164042	−	0.151954i
$541$	−21.9320	−	9.76476i	−0.942931	−	0.419820i	−0.123080	−	0.992397i	$-0.539277\pi$
$541$	−21.9320	−	9.76476i	−0.942931	−	0.419820i	−0.819851	+	0.572577i	$0.805944\pi$
$542$	−6.07062	−	18.6835i	−0.260756	−	0.802523i
$543$	2.24827	+	16.5627i	0.0964823	+	0.710772i
$544$	−2.28084	+	5.12286i	−0.0977904	+	0.219641i
$545$	−4.06629	+	19.1304i	−0.174181	+	0.819456i
$546$	0.462207	+	15.3009i	0.0197806	+	0.654819i
$547$	35.6735	−	15.8829i	1.52529	−	0.679103i	0.538726	−	0.842481i	$-0.318906\pi$
$547$	35.6735	−	15.8829i	1.52529	−	0.679103i	0.986564	+	0.163378i	$0.0522390\pi$
$548$	−2.45332	−	2.72469i	−0.104801	−	0.116393i
$549$	−4.94180	−	1.28167i	−0.210911	−	0.0547004i
$550$	−2.16886	−	2.98519i	−0.0924807	−	0.127289i
$551$	0.262124	−	2.49394i	0.0111668	−	0.106245i
$552$	−2.92146	−	8.14576i	−0.124345	−	0.346706i
$553$	−0.952476	−	0.549912i	−0.0405034	−	0.0233846i
$554$	1.23631	+	0.898235i	0.0525260	+	0.0381624i
$555$	−3.80836	−	4.92207i	−0.161656	−	0.208930i
$556$	6.94795	+	2.25753i	0.294659	+	0.0957405i
$557$	−7.27305			−0.308169			−0.154085	−	0.988058i	$-0.549243\pi$
$557$	−7.27305			−0.308169			−0.154085	+	0.988058i	$0.549243\pi$
$558$	15.1754	−	6.97909i	0.642425	−	0.295448i
$559$	−63.8142			−2.69905
$560$	−1.28232	−	0.416649i	−0.0541877	−	0.0176067i
$561$	21.9315	+	28.3451i	0.925950	+	1.19673i
$562$	12.6336	+	9.17888i	0.532918	+	0.387188i
$563$	−7.52484	−	4.34447i	−0.317134	−	0.183098i	0.332980	−	0.942934i	$-0.391946\pi$
$563$	−7.52484	−	4.34447i	−0.317134	−	0.183098i	−0.650114	+	0.759836i	$0.725279\pi$
$564$	−1.39534	−	3.89057i	−0.0587546	−	0.163823i
$565$	1.78281	−	16.9623i	0.0750034	−	0.713610i
$566$	−14.6897	−	20.2186i	−0.617452	−	0.849850i
$567$	−6.97391	+	9.93060i	−0.292877	+	0.417046i
$568$	5.41176	+	6.01036i	0.227072	+	0.252189i
$569$	−31.4886	+	14.0196i	−1.32007	+	0.587734i	−0.941242	−	0.337732i	$-0.890340\pi$
$569$	−31.4886	+	14.0196i	−1.32007	+	0.587734i	−0.378830	+	0.925466i	$0.623674\pi$
$570$	0.0965775	+	3.19711i	0.00404519	+	0.133912i
$571$	3.60439	−	16.9573i	0.150839	−	0.709641i	−0.836104	−	0.548571i	$-0.815172\pi$
$571$	3.60439	−	16.9573i	0.150839	−	0.709641i	0.986943	−	0.161070i	$-0.0514946\pi$
$572$	−9.83771	+	22.0959i	−0.411335	+	0.923874i
$573$	−1.84089	−	13.5616i	−0.0769041	−	0.566542i
$574$	−1.01566	−	3.12587i	−0.0423926	−	0.130471i
$575$	−4.56432	−	2.03217i	−0.190345	−	0.0847472i
$576$	−2.52906	−	1.61364i	−0.105378	−	0.0672351i
$577$	34.1756	−	7.26426i	1.42275	−	0.302415i	0.568674	−	0.822563i	$-0.307456\pi$
$577$	34.1756	−	7.26426i	1.42275	−	0.302415i	0.854076	+	0.520148i	$0.174123\pi$
$578$	−5.87569	−	13.1970i	−0.244397	−	0.548924i
$579$	−13.3601	+	8.26113i	−0.555228	+	0.343321i
$580$	1.35049	−	0.141942i	0.0560760	−	0.00589382i
$581$	5.01265	−	3.64191i	0.207960	−	0.151092i
$582$	−8.29448	+	28.4206i	−0.343817	+	1.17807i
$583$	−16.9397	−	29.3405i	−0.701572	−	1.21516i
$584$	1.84610	−	3.19754i	0.0763922	−	0.132315i
$585$	10.8424	+	16.4056i	0.448278	+	0.678289i
$586$	12.5551	−	13.9438i	0.518646	−	0.576015i
$587$	−3.57253	+	10.9951i	−0.147454	+	0.453817i	−0.997318	−	0.0731846i	$-0.976684\pi$
$587$	−3.57253	+	10.9951i	−0.147454	+	0.453817i	0.849864	+	0.527001i	$0.176684\pi$
$588$	1.60020	−	8.83181i	0.0659910	−	0.364218i
$589$	−9.61419	−	3.64499i	−0.396146	−	0.150189i
$590$			9.84501i			0.405313i
$591$	−15.0926	−	8.11623i	−0.620825	−	0.333857i
$592$	−2.67017	−	2.40423i	−0.109743	−	0.0988133i
$593$	23.8530	−	32.8309i	0.979527	−	1.34820i	0.0424432	−	0.999099i	$-0.486486\pi$
$593$	23.8530	−	32.8309i	0.979527	−	1.34820i	0.937084	−	0.349104i	$-0.113514\pi$
$594$	−16.7383	+	9.35115i	−0.686779	+	0.383682i
$595$	6.54789	−	3.78043i	0.268437	−	0.154982i
$596$	−21.8858	−	2.30029i	−0.896476	−	0.0942235i
$597$	0.00217476	−	0.00104806i	8.90071e−5	−	4.28941e-5i
$598$	3.42332	+	32.5707i	0.139990	+	1.33192i
$599$	14.6629	−	13.2025i	0.599109	−	0.539440i	−0.312807	−	0.949817i	$-0.601269\pi$
$599$	14.6629	−	13.2025i	0.599109	−	0.539440i	0.911916	+	0.410377i	$0.134603\pi$
$600$	−1.68256	+	0.411104i	−0.0686900	+	0.0167833i
$601$	−4.27992	−	20.1354i	−0.174581	−	0.821341i	−0.975053	−	0.221971i	$-0.928751\pi$
$601$	−4.27992	−	20.1354i	−0.174581	−	0.821341i	0.800472	−	0.599370i	$-0.204582\pi$
$602$	−12.8394	−	2.72909i	−0.523294	−	0.111229i
$603$	−0.213774	−	0.210365i	−0.00870556	−	0.00856673i
$604$	−18.9752	+	6.16540i	−0.772088	+	0.250867i
$605$	−2.48731	+	0.808175i	−0.101123	+	0.0328570i
$606$	−13.0973	+	19.2218i	−0.532043	+	0.780832i
$607$	11.6656	+	2.47959i	0.473491	+	0.100644i	0.438475	−	0.898743i	$-0.355519\pi$
$607$	11.6656	+	2.47959i	0.473491	+	0.100644i	0.0350154	+	0.999387i	$0.488852\pi$
$608$	0.383949	+	1.80634i	0.0155712	+	0.0732567i
$609$	−0.752691	−	3.08059i	−0.0305006	−	0.124832i
$610$	−1.26466	+	1.13870i	−0.0512045	+	0.0461048i
$611$	1.63504	+	15.5564i	0.0661468	+	0.629345i
$612$	16.2143	−	4.48458i	0.655422	−	0.181278i
$613$	6.57914	+	0.691495i	0.265729	+	0.0279292i	0.236456	−	0.971642i	$-0.424014\pi$
$613$	6.57914	+	0.691495i	0.265729	+	0.0279292i	0.0292730	+	0.999571i	$0.490681\pi$
$614$	−9.30219	+	5.37062i	−0.375406	+	0.216741i
$615$	−3.22156	−	2.72916i	−0.129906	−	0.110050i
$616$	−2.92429	+	4.02494i	−0.117823	+	0.162170i
$617$	25.7361	+	23.1729i	1.03610	+	0.932905i	0.997796	−	0.0663609i	$-0.0211389\pi$
$617$	25.7361	+	23.1729i	1.03610	+	0.932905i	0.0383007	+	0.999266i	$0.487806\pi$
$618$	−6.40206	+	11.9050i	−0.257529	+	0.478888i
$619$			27.1275i			1.09035i	0.838323	+	0.545174i	$0.183536\pi$
$619$			27.1275i			1.09035i	−0.838323	+	0.545174i	$0.816464\pi$
$620$	0.848238	−	5.50277i	0.0340661	−	0.220997i
$621$	−13.2969	+	22.2977i	−0.533588	+	0.894774i
$622$	−2.70769	+	8.33342i	−0.108569	+	0.334140i
$623$	10.3919	−	11.5414i	0.416345	−	0.462398i
$624$	7.84822	+	8.20402i	0.314180	+	0.328424i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.37695	−	7.58110i	−0.174938	−	0.303002i
$627$	11.3297	+	3.30655i	0.452466	+	0.132051i
$628$	7.05864	−	5.12841i	0.281671	−	0.204646i
$629$	20.0383	−	2.10611i	0.798981	−	0.0839763i
$630$	1.47987	+	3.76448i	0.0589595	+	0.149981i
$631$	5.92265	+	13.3025i	0.235777	+	0.529564i	0.992220	−	0.124496i	$-0.0397313\pi$
$631$	5.92265	+	13.3025i	0.235777	+	0.529564i	−0.756443	+	0.654059i	$0.773065\pi$
$632$	−0.797883	+	0.169595i	−0.0317381	+	0.00674614i
$633$	−9.00941	+	22.0003i	−0.358092	+	0.874433i
$634$	20.2279	+	9.00605i	0.803353	+	0.357676i
$635$	5.58866	+	17.2001i	0.221779	+	0.682566i
$636$	−15.7586	+	2.13912i	−0.624870	+	0.0848218i
$637$	−13.8160	+	31.0313i	−0.547411	+	1.22951i
$638$	1.04176	−	4.90111i	0.0412438	−	0.194037i
$639$	3.60287	−	23.9942i	0.142528	−	0.949197i
$640$	−0.913545	+	0.406737i	−0.0361111	+	0.0160777i
$641$	21.8840	+	24.3046i	0.864364	+	0.959974i	0.999524	−	0.0308500i	$-0.00982142\pi$
$641$	21.8840	+	24.3046i	0.864364	+	0.959974i	−0.135160	+	0.990824i	$0.543155\pi$
$642$	11.2082	+	0.836801i	0.442354	+	0.0330259i
$643$	−4.77787	−	6.57618i	−0.188421	−	0.259339i	0.704347	−	0.709856i	$-0.251240\pi$
$643$	−4.77787	−	6.57618i	−0.188421	−	0.259339i	−0.892768	+	0.450516i	$0.851240\pi$
$644$	−0.704157	+	6.69960i	−0.0277477	+	0.264001i
$645$	−15.8722	+	5.69251i	−0.624966	+	0.224142i
$646$	−8.96825	−	5.17782i	−0.352851	−	0.203719i
$647$	23.6320	+	17.1696i	0.929068	+	0.675008i	0.945764	−	0.324853i	$-0.105315\pi$
$647$	23.6320	+	17.1696i	0.929068	+	0.675008i	−0.0166963	+	0.999861i	$0.505315\pi$
$648$	1.08451	+	8.93442i	0.0426035	+	0.350977i
$649$	34.5491	+	11.2257i	1.35617	+	0.440646i
$650$	6.55491			0.257105
$651$	−13.0005	−	0.234364i	−0.509529	−	0.00918544i
$652$	−9.20601			−0.360535
$653$	−33.8569	−	11.0008i	−1.32492	−	0.430493i	−0.440739	−	0.897635i	$-0.645284\pi$
$653$	−33.8569	−	11.0008i	−1.32492	−	0.430493i	−0.884182	+	0.467142i	$0.845284\pi$
$654$	26.7918	−	20.7297i	1.04764	−	0.810594i
$655$	10.4029	+	7.55814i	0.406474	+	0.295321i
$656$	−2.11109	−	1.21884i	−0.0824241	−	0.0475876i
$657$	−10.9260	+	1.82064i	−0.426262	+	0.0710298i
$658$	−0.336319	+	3.19986i	−0.0131111	+	0.124744i
$659$	3.17686	+	4.37258i	0.123753	+	0.170331i	0.866398	−	0.499354i	$-0.166429\pi$
$659$	3.17686	+	4.37258i	0.123753	+	0.170331i	−0.742645	+	0.669685i	$0.766429\pi$
$660$	−0.475830	+	6.37334i	−0.0185217	+	0.248082i
$661$	17.8559	+	19.8310i	0.694513	+	0.771335i	0.982493	−	0.186302i	$-0.0596502\pi$
$661$	17.8559	+	19.8310i	0.694513	+	0.771335i	−0.287979	+	0.957637i	$0.592983\pi$
$662$	−21.6946	+	9.65908i	−0.843186	+	0.375411i
$663$	−63.6373	+	1.92234i	−2.47147	+	0.0746575i
$664$	0.955433	−	4.49496i	0.0370780	−	0.174438i
$665$	1.01274	−	2.27464i	0.0392723	−	0.0882069i
$666$	−0.477606	+	10.7686i	−0.0185068	+	0.417275i
$667$	−2.09655	−	6.45252i	−0.0811787	−	0.249842i
$668$	−4.41481	−	1.96560i	−0.170814	−	0.0760513i
$669$	20.2558	+	8.29502i	0.783134	+	0.320704i
$670$	−0.0977892	+	0.0207857i	−0.00377793	+	0.000803023i
$671$	2.55404	+	5.73646i	0.0985975	+	0.221454i
$672$	1.22820	+	1.98628i	0.0473789	+	0.0766224i
$673$	−0.998611	+	0.104958i	−0.0384936	+	0.00404584i	−0.123756	−	0.992313i	$-0.539494\pi$
$673$	−0.998611	+	0.104958i	−0.0384936	+	0.00404584i	0.0852621	+	0.996359i	$0.472827\pi$
$674$	17.9753	−	13.0598i	0.692382	−	0.503045i
$675$	4.16022	+	3.11329i	0.160127	+	0.119831i
$676$	−14.9834	−	25.9521i	−0.576286	−	0.998156i
$677$	−0.696025	+	1.20555i	−0.0267504	+	0.0463331i	−0.879091	−	0.476655i	$-0.841849\pi$
$677$	−0.696025	+	1.20555i	−0.0267504	+	0.0463331i	0.852340	+	0.522988i	$0.175183\pi$
$678$	−21.3467	+	20.4209i	−0.819815	+	0.784261i
$679$	15.4213	−	17.1271i	0.591816	−	0.657278i
$680$	1.73286	−	5.33321i	0.0664523	−	0.204519i
$681$	19.0395	+	3.44967i	0.729594	+	0.132192i
$682$	−18.3437	−	9.25120i	−0.702415	−	0.354247i
$683$		−	35.0354i		−	1.34059i	−0.742093	−	0.670297i	$-0.766167\pi$
$683$		−	35.0354i		−	1.34059i	0.742093	−	0.670297i	$-0.233833\pi$
$684$	3.45177	−	4.33333i	0.131982	−	0.165689i
$685$	2.72469	+	2.45332i	0.104105	+	0.0937365i
$686$	−9.65447	+	13.2882i	−0.368609	+	0.507347i
$687$	13.3718	−	15.7844i	0.510167	−	0.602213i
$688$	−8.43104	+	4.86767i	−0.321431	+	0.185578i
$689$	59.8555	+	6.29106i	2.28031	+	0.239670i
$690$	3.75692	+	7.79576i	0.143023	+	0.296779i
$691$	−3.69038	−	35.1116i	−0.140389	−	1.33571i	−0.807110	−	0.590402i	$-0.798969\pi$
$691$	−3.69038	−	35.1116i	−0.140389	−	1.33571i	0.666721	−	0.745307i	$-0.267697\pi$
$692$	11.5895	−	10.4352i	0.440566	−	0.396688i
$693$	14.8981	−	0.900899i	0.565932	−	0.0342223i
$694$	−5.24013	−	24.6529i	−0.198912	−	0.935809i
$695$	−7.14587	−	1.51890i	−0.271058	−	0.0576152i
$696$	−1.94368	−	1.32439i	−0.0736751	−	0.0502008i
$697$	13.0006	−	4.22416i	0.492434	−	0.160001i
$698$	−33.8353	+	10.9937i	−1.28068	+	0.416120i
$699$	16.4126	+	11.1832i	0.620780	+	0.422987i
$700$	1.31884	+	0.280329i	0.0498476	+	0.0105954i
$701$	−7.03182	−	33.0821i	−0.265588	−	1.24949i	−0.885432	−	0.464769i	$-0.846138\pi$
$701$	−7.03182	−	33.0821i	−0.265588	−	1.24949i	0.619844	−	0.784725i	$-0.287196\pi$
$702$	4.03833	−	33.8201i	0.152417	−	1.27646i
$703$	4.93098	−	4.43988i	0.185976	−	0.167453i
$704$	0.385699	+	3.66968i	0.0145366	+	0.138306i
$705$	1.79438	+	3.72341i	0.0675801	+	0.140232i
$706$	28.4049	+	2.98548i	1.06903	+	0.112360i
$707$	15.6807	−	9.05323i	0.589732	−	0.340482i
$708$	11.0222	−	13.0109i	0.414241	−	0.488979i
$709$	10.7375	−	14.7790i	0.403257	−	0.555035i	−0.558301	−	0.829639i	$-0.688547\pi$
$709$	10.7375	−	14.7790i	0.403257	−	0.555035i	0.961558	+	0.274603i	$0.0885465\pi$
$710$	−6.01036	−	5.41176i	−0.225565	−	0.203100i
$711$	1.91409	+	1.52469i	0.0717839	+	0.0571804i
$712$		−	11.5185i		−	0.431676i
$713$	−27.7737	+	1.57077i	−1.04013	+	0.0588258i
$714$	−12.8860	−	2.33475i	−0.482246	−	0.0873759i
$715$	7.47417	−	23.0031i	0.279518	−	0.860268i
$716$	−9.65847	+	10.7268i	−0.360954	+	0.400880i
$717$	18.0334	−	17.2513i	0.673470	−	0.644263i
$718$	14.8202	−	25.6693i	0.553083	−	0.957969i
$719$	−12.9139	−	22.3676i	−0.481608	−	0.834170i	0.518169	−	0.855278i	$-0.326614\pi$
$719$	−12.9139	−	22.3676i	−0.481608	−	0.834170i	−0.999777	+	0.0211085i	$0.993280\pi$
$720$	2.68388	+	1.34044i	0.100022	+	0.0499554i
$721$	8.51279	−	6.18491i	0.317033	−	0.230338i
$722$	15.5043	−	1.62957i	0.577011	−	0.0606463i
$723$	11.5379	+	18.6594i	0.429098	+	0.693949i
$724$	−3.92507	−	8.81586i	−0.145874	−	0.327639i
$725$	−1.32825	+	0.282329i	−0.0493301	+	0.0104854i
$726$	4.19197	+	1.71667i	0.155579	+	0.0637115i
$727$	−18.0501	−	8.03641i	−0.669440	−	0.298054i	0.0437315	−	0.999043i	$-0.486075\pi$
$727$	−18.0501	−	8.03641i	−0.669440	−	0.298054i	−0.713172	+	0.700989i	$0.752742\pi$
$728$	−2.73110	−	8.40546i	−0.101221	−	0.311527i
$729$	18.6260	−	19.5466i	0.689853	−	0.723949i
$730$	−1.50175	+	3.37300i	−0.0555824	+	0.124840i
$731$	11.3504	−	53.3995i	0.419811	−	1.97505i
$732$	2.94620	−	0.0889982i	0.108895	−	0.00328947i
$733$	25.0288	−	11.1435i	0.924459	−	0.411596i	0.111399	−	0.993776i	$-0.464467\pi$
$733$	25.0288	−	11.1435i	0.924459	−	0.411596i	0.813060	+	0.582180i	$0.197800\pi$
$734$	−10.0764	−	11.1910i	−0.371928	−	0.413068i
$735$	−0.668254	+	8.95070i	−0.0246489	+	0.330151i
$736$	2.93674	+	4.04207i	0.108250	+	0.148993i
$737$	−0.0385598	+	0.366872i	−0.00142037	+	0.0135139i
$738$	1.20202	+	7.21356i	0.0442471	+	0.265535i
$739$	−33.9689	−	19.6120i	−1.24957	−	0.721438i	−0.278545	−	0.960423i	$-0.589852\pi$
$739$	−33.9689	−	19.6120i	−1.24957	−	0.721438i	−0.971023	+	0.238985i	$0.923185\pi$
$740$	2.90685	+	2.11195i	0.106858	+	0.0776369i
$741$	−16.5823	+	12.8302i	−0.609165	+	0.471330i
$742$	11.7738	+	3.82555i	0.432231	+	0.140440i
$743$	−44.4963			−1.63241			−0.816206	−	0.577761i	$-0.803927\pi$
$743$	−44.4963			−1.63241			−0.816206	+	0.577761i	$0.803927\pi$
$744$	−7.28177	+	6.32264i	−0.266963	+	0.231799i
$745$	22.0063			0.806250
$746$	6.91857	+	2.24798i	0.253307	+	0.0823044i
$747$	−12.2328	+	6.35730i	−0.447576	+	0.232601i
$748$	−16.7399	−	12.1623i	−0.612073	−	0.444697i
$749$	−7.57710	−	4.37464i	−0.276861	−	0.159846i
$750$	1.63037	−	0.584727i	0.0595326	−	0.0213512i
$751$	−2.67618	+	25.4622i	−0.0976552	+	0.929127i	0.830521	+	0.556987i	$0.188043\pi$
$751$	−2.67618	+	25.4622i	−0.0976552	+	0.929127i	−0.928176	+	0.372140i	$0.878624\pi$
$752$	1.40264	+	1.93057i	0.0511491	+	0.0704007i
$753$	3.47151	+	0.259181i	0.126509	+	0.00944508i
$754$	5.95599	+	6.61480i	0.216905	+	0.240897i
$755$	18.2268	−	8.11507i	0.663339	−	0.295338i
$756$	2.25886	−	6.63186i	0.0821541	−	0.241199i
$757$	−3.34305	+	15.7278i	−0.121505	+	0.571637i	0.874705	+	0.484656i	$0.161055\pi$
$757$	−3.34305	+	15.7278i	−0.121505	+	0.571637i	−0.996210	+	0.0869808i	$0.972278\pi$
$758$	−10.4185	+	23.4003i	−0.378416	+	0.849936i
$759$	31.6414	−	4.29510i	1.14851	−	0.155902i
$760$	−0.570660	−	1.75631i	−0.0207000	−	0.0637081i
$761$	−41.2290	−	18.3564i	−1.49455	−	0.665417i	−0.513311	−	0.858203i	$-0.671581\pi$
$761$	−41.2290	−	18.3564i	−1.49455	−	0.665417i	−0.981241	+	0.192786i	$0.938248\pi$
$762$	11.8710	−	28.9881i	0.430042	−	1.05013i
$763$	−25.7936	+	5.48261i	−0.933792	+	0.198484i
$764$	3.21386	+	7.21845i	0.116273	+	0.261154i
$765$	−15.6567	+	6.15486i	−0.566068	+	0.222529i
$766$	10.3135	−	1.08399i	0.372641	−	0.0391662i
$767$	−52.2084	+	37.9317i	−1.88514	+	1.36963i
$768$	1.66269	+	0.485251i	0.0599971	+	0.0175100i
$769$	−22.4501	−	38.8847i	−0.809571	−	1.40222i	−0.913162	−	0.407597i	$-0.866367\pi$
$769$	−22.4501	−	38.8847i	−0.809571	−	1.40222i	0.103591	−	0.994620i	$-0.466967\pi$
$770$	2.48755	−	4.30857i	0.0896452	−	0.155270i
$771$	−3.64837	−	3.81376i	−0.131393	−	0.137349i
$772$	6.06833	−	6.73956i	0.218404	−	0.242562i
$773$	−0.132270	+	0.407084i	−0.00475741	+	0.0146418i	−0.953407	−	0.301687i	$-0.902450\pi$
$773$	−0.132270	+	0.407084i	−0.00475741	+	0.0146418i	0.948650	+	0.316329i	$0.102450\pi$
$774$	27.3494	+	10.2470i	0.983053	+	0.368321i
$775$	−0.268395	+	5.56129i	−0.00964105	+	0.199767i
$776$		−	17.0932i		−	0.613609i
$777$	3.97418	−	7.39019i	0.142573	−	0.265122i
$778$	4.16971	+	3.75442i	0.149491	+	0.134603i
$779$	2.64600	−	3.64190i	0.0948026	−	0.130485i
$780$	−8.66278	−	7.33872i	−0.310177	−	0.262768i
$781$	−25.8447	+	14.9215i	−0.924797	+	0.533932i
$782$	−27.8640	−	2.92862i	−0.996413	−	0.104727i
$783$	0.638369	+	7.02706i	0.0228135	+	0.251127i
$784$	0.541674	+	5.15368i	0.0193455	+	0.184060i
$785$	−6.48391	+	5.83814i	−0.231421	+	0.208372i
$786$	−5.28625	−	21.6354i	−0.188554	−	0.771710i
$787$	−0.941742	−	4.43055i	−0.0335695	−	0.157932i	0.958170	−	0.286199i	$-0.0923919\pi$
$787$	−0.941742	−	4.43055i	−0.0335695	−	0.157932i	−0.991740	+	0.128267i	$0.959059\pi$
$788$	9.67754	+	2.05703i	0.344748	+	0.0732785i
$789$	2.68370	−	3.93863i	0.0955424	−	0.140219i
$790$	0.775784	−	0.252068i	0.0276012	−	0.00896816i
$791$	21.8708	−	7.10627i	0.777638	−	0.252670i
$792$	7.76428	−	7.89010i	0.275892	−	0.280363i
$793$	−10.9112	−	2.31924i	−0.387467	−	0.0823586i
$794$	−3.78014	−	17.7841i	−0.134152	−	0.631136i
$795$	15.4487	−	3.77463i	0.547909	−	0.133872i
$796$	−0.00103579		0.000932633i	−3.67127e−5		3.30563e-5i
$797$	2.04193	+	19.4276i	0.0723288	+	0.688162i	0.969268	+	0.246008i	$0.0791189\pi$
$797$	2.04193	+	19.4276i	0.0723288	+	0.688162i	−0.896939	+	0.442154i	$0.854214\pi$
$798$	−3.88504	+	1.87227i	−0.137529	+	0.0662777i
$799$	−13.3084	−	1.39877i	−0.470816	−	0.0494848i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−26.6791	+	21.9617i	−0.942660	+	0.775979i
$802$	−8.64702	+	11.9016i	−0.305337	+	0.420260i
$803$	10.1245	+	9.11613i	0.357285	+	0.321701i
$804$	0.152507	+	0.0820125i	0.00537849	+	0.00289236i
$805$		−	6.73651i		−	0.237431i
$806$	32.4495	−	16.7033i	1.14299	−	0.588348i
$807$	−7.13352	+	39.3714i	−0.251112	+	1.38594i
$808$	4.14980	−	12.7718i	0.145990	−	0.449310i
$809$	−24.1219	+	26.7901i	−0.848081	+	0.941889i	−0.998910	−	0.0466704i	$-0.985139\pi$
$809$	−24.1219	+	26.7901i	−0.848081	+	0.941889i	0.150829	+	0.988560i	$0.451806\pi$
$810$	−2.01247	−	8.77211i	−0.0707109	−	0.308221i
$811$	8.66146	−	15.0021i	0.304145	−	0.526794i	−0.672926	−	0.739710i	$-0.734963\pi$
$811$	8.66146	−	15.0021i	0.304145	−	0.526794i	0.977071	+	0.212916i	$0.0682960\pi$
$812$	0.915451	+	1.58561i	0.0321260	+	0.0556439i
$813$	9.53273	−	32.6634i	0.334328	−	1.14556i
$814$	10.7260	−	7.79287i	0.375945	−	0.273140i
$815$	9.15558	−	0.962290i	0.320706	−	0.0337076i
$816$	−8.26103	+	5.10815i	−0.289194	+	0.178821i
$817$	−7.31238	−	16.4239i	−0.255828	−	0.574599i
$818$	−16.3796	+	3.48160i	−0.572700	+	0.121731i
$819$	−14.2614	+	22.3519i	−0.498334	+	0.781039i
$820$	2.22693	+	0.991491i	0.0777676	+	0.0346244i
$821$	3.74543	+	11.5272i	0.130716	+	0.402303i	0.994899	−	0.100874i	$-0.0321640\pi$
$821$	3.74543	+	11.5272i	0.130716	+	0.402303i	−0.864183	+	0.503178i	$0.832164\pi$
$822$	−0.854194	−	6.29273i	−0.0297934	−	0.219484i
$823$	−11.0633	+	24.8485i	−0.385641	+	0.866164i	0.611546	+	0.791209i	$0.290548\pi$
$823$	−11.0633	+	24.8485i	−0.385641	+	0.866164i	−0.997187	+	0.0749553i	$0.976119\pi$
$824$	1.62258	−	7.63362i	0.0565251	−	0.265930i
$825$	−0.192972	−	6.38817i	−0.00671843	−	0.222407i
$826$	−12.1265	+	5.39906i	−0.421934	+	0.187857i
$827$	20.3136	+	22.5605i	0.706373	+	0.784506i	0.984377	−	0.176074i	$-0.0563396\pi$
$827$	20.3136	+	22.5605i	0.706373	+	0.784506i	−0.278004	+	0.960580i	$0.589673\pi$
$828$	3.76290	−	14.5088i	0.130770	−	0.504216i
$829$	−29.0086	−	39.9269i	−1.00751	−	1.38672i	−0.920602	−	0.390502i	$-0.872301\pi$
$829$	−29.0086	−	39.9269i	−1.00751	−	1.38672i	−0.0869083	−	0.996216i	$-0.527699\pi$
$830$	−0.480348	+	4.57021i	−0.0166731	+	0.158634i
$831$	0.893562	+	2.49148i	0.0309973	+	0.0864283i
$832$	−5.67672	−	3.27746i	−0.196805	−	0.113625i
$833$	−23.5095	−	17.0806i	−0.814556	−	0.591809i
$834$	7.74325	+	10.0077i	0.268127	+	0.346537i
$835$	4.59609	+	1.49336i	0.159054	+	0.0516798i
$836$	−6.81410			−0.235671
$837$	28.5281	+	4.81097i	0.986077	+	0.166292i
$838$	−36.9048			−1.27485
$839$	−23.0855	−	7.50095i	−0.797002	−	0.258961i	−0.117919	−	0.993023i	$-0.537622\pi$
$839$	−23.0855	−	7.50095i	−0.797002	−	0.258961i	−0.679083	+	0.734062i	$0.737622\pi$
$840$	−1.42910	−	1.84702i	−0.0493085	−	0.0637282i
$841$	21.9697	+	15.9619i	0.757576	+	0.550411i
$842$	23.3642	+	13.4893i	0.805183	+	0.464873i
$843$	9.13112	+	25.4599i	0.314493	+	0.876884i
$844$	1.43472	−	13.6505i	0.0493852	−	0.469869i
$845$	17.6141	+	24.2437i	0.605943	+	0.834008i
$846$	1.79724	−	6.92969i	0.0617903	−	0.238248i
$847$	−2.35951	−	2.62051i	−0.0810739	−	0.0900416i
$848$	8.38789	−	3.73453i	0.288041	−	0.128244i
$849$	−1.30700	−	43.2669i	−0.0448560	−	1.48491i
$850$	−1.16590	+	5.48513i	−0.0399900	+	0.188138i
$851$	7.30171	−	16.3999i	0.250299	−	0.562182i
$852$	1.88426	+	13.8811i	0.0645536	+	0.475558i
$853$	−13.8830	−	42.7275i	−0.475345	−	1.46296i	−0.845491	−	0.533989i	$-0.820692\pi$
$853$	−13.8830	−	42.7275i	−0.475345	−	1.46296i	0.370146	−	0.928974i	$-0.379308\pi$
$854$	−2.09613	−	0.933258i	−0.0717281	−	0.0319354i
$855$	−2.97990	+	4.67040i	−0.101911	+	0.159724i
$856$	−6.34729	+	1.34916i	−0.216946	+	0.0461133i
$857$	12.9651	+	29.1201i	0.442879	+	0.994722i	0.987727	+	0.156188i	$0.0499205\pi$
$857$	12.9651	+	29.1201i	0.442879	+	0.994722i	−0.544849	+	0.838534i	$0.683413\pi$
$858$	−35.6314	+	22.0324i	−1.21644	+	0.752173i
$859$	23.3886	−	2.45824i	0.798007	−	0.0838739i	0.303257	−	0.952909i	$-0.401926\pi$
$859$	23.3886	−	2.45824i	0.798007	−	0.0838739i	0.494751	+	0.869035i	$0.335259\pi$
$860$	7.87605	−	5.72228i	0.268571	−	0.195128i
$861$	1.59489	−	5.46481i	0.0543537	−	0.186240i
$862$	−12.7688	−	22.1162i	−0.434907	−	0.753281i
$863$	−12.5904	+	21.8072i	−0.428582	+	0.742326i	−0.996747	−	0.0805883i	$-0.974320\pi$
$863$	−12.5904	+	21.8072i	−0.428582	+	0.742326i	0.568165	+	0.822914i	$0.307653\pi$
$864$	−2.04621	−	4.77630i	−0.0696135	−	0.162493i
$865$	−10.4352	+	11.5895i	−0.354808	+	0.394054i
$866$	7.50944	−	23.1117i	0.255181	−	0.785367i
$867$	4.46083	−	24.6203i	0.151498	−	0.836148i
$868$	7.24316	−	1.97294i	0.245849	−	0.0669660i
$869$		−	3.00988i		−	0.102103i
$870$	2.07147	+	1.11396i	0.0702294	+	0.0377668i
$871$	−0.486997	−	0.438494i	−0.0165013	−	0.0148578i
$872$	−11.4958	+	15.8226i	−0.389296	+	0.535820i
$873$	−39.5910	+	32.5905i	−1.33995	+	1.10302i
$874$	−7.99046	+	4.61329i	−0.270281	+	0.156047i
$875$	−1.34092	−	0.140936i	−0.0453314	−	0.00476452i
$876$	5.76100	−	2.77633i	0.194646	−	0.0938035i
$877$	3.94150	+	37.5009i	0.133095	+	1.26631i	0.833480	+	0.552549i	$0.186345\pi$
$877$	3.94150	+	37.5009i	0.133095	+	1.26631i	−0.700385	+	0.713765i	$0.746989\pi$
$878$	19.7031	−	17.7408i	0.664948	−	0.598722i
$879$	31.5703	−	7.71366i	1.06484	−	0.260175i
$880$	−0.767172	−	3.60926i	−0.0258614	−	0.121668i
$881$	−9.45978	−	2.01074i	−0.318708	−	0.0677435i	0.0457800	−	0.998952i	$-0.485423\pi$
$881$	−9.45978	−	2.01074i	−0.318708	−	0.0677435i	−0.364488	+	0.931208i	$0.618756\pi$
$882$	10.9041	−	11.0808i	0.367161	−	0.373111i
$883$	−37.8679	+	12.3040i	−1.27436	+	0.414064i	−0.866589	−	0.499022i	$-0.833693\pi$
$883$	−37.8679	+	12.3040i	−1.27436	+	0.414064i	−0.407768	+	0.913086i	$0.633693\pi$
$884$	34.9587	−	11.3588i	1.17579	−	0.382037i
$885$	−9.60184	+	14.0918i	−0.322762	+	0.473689i
$886$	−20.4779	−	4.35272i	−0.687970	−	0.146233i
$887$	−8.85496	−	41.6593i	−0.297320	−	1.39878i	−0.832491	−	0.554039i	$-0.813086\pi$
$887$	−8.85496	−	41.6593i	−0.297320	−	1.39878i	0.535171	−	0.844744i	$-0.320247\pi$
$888$	−1.47712	−	6.04553i	−0.0495690	−	0.202875i
$889$	−18.1212	+	16.3164i	−0.607766	+	0.547235i
$890$	1.20402	+	11.4554i	0.0403587	+	0.383987i
$891$	−33.0786	−	2.93997i	−1.10818	−	0.0984926i
$892$	−12.5681	−	1.32096i	−0.420810	−	0.0442290i
$893$	−3.81640	+	2.20340i	−0.127711	+	0.0737339i
$894$	−29.0829	−	24.6377i	−0.972679	−	0.824009i
$895$	8.48430	−	11.6776i	0.283599	−	0.390341i
$896$	−1.00199	−	0.902193i	−0.0334740	−	0.0301401i
$897$	−26.8662	+	49.9592i	−0.897037	+	1.66809i
$898$		−	15.3441i		−	0.512040i
$899$	−5.85598	+	4.78231i	−0.195308	+	0.159499i
$900$	−2.80929	−	1.05256i	−0.0936431	−	0.0350853i
$901$	−15.9106	+	48.9679i	−0.530060	+	1.63136i
$902$	6.01867	−	6.68441i	0.200400	−	0.222566i
$903$	−15.7161	−	16.4285i	−0.522998	−	0.546708i
$904$	8.52787	−	14.7707i	0.283633	−	0.491267i
$905$	4.82508	+	8.35728i	0.160391	+	0.277806i
$906$	−33.1734	−	9.68157i	−1.10211	−	0.321649i
$907$	−48.3277	+	35.1121i	−1.60469	+	1.16588i	−0.727023	+	0.686613i	$0.759097\pi$
$907$	−48.3277	+	35.1121i	−1.60469	+	1.16588i	−0.877670	+	0.479265i	$0.840903\pi$
$908$	−11.1102	+	1.16773i	−0.368705	+	0.0387525i
$909$	−37.4940	+	14.7394i	−1.24360	+	0.488876i
$910$	3.59475	+	8.07394i	0.119165	+	0.267648i
$911$	−16.0098	+	3.40298i	−0.530428	+	0.112746i	−0.465337	−	0.885133i	$-0.654067\pi$
$911$	−16.0098	+	3.40298i	−0.530428	+	0.112746i	−0.0650905	+	0.997879i	$0.520734\pi$
$912$	−1.21215	+	2.95999i	−0.0401384	+	0.0980149i
$913$	15.4905	+	6.89682i	0.512661	+	0.228251i
$914$	7.74829	+	23.8468i	0.256291	+	0.788781i
$915$	−2.92076	+	0.396473i	−0.0965573	+	0.0131070i
$916$	−4.85793	+	10.9111i	−0.160510	+	0.360512i
$917$	−3.60465	+	16.9586i	−0.119036	+	0.560021i
$918$	27.5822	+	9.39473i	0.910349	+	0.310072i
$919$	−6.94664	+	3.09284i	−0.229149	+	0.102024i	−0.518099	−	0.855320i	$-0.673360\pi$
$919$	−6.94664	+	3.09284i	−0.229149	+	0.102024i	0.288951	+	0.957344i	$0.406694\pi$
$920$	−3.34316	−	3.71295i	−0.110221	−	0.122412i
$921$	−18.5527	−	1.38514i	−0.611334	−	0.0456418i
$922$	1.59321	+	2.19286i	0.0524694	+	0.0722180i
$923$	5.54152	−	52.7240i	0.182401	−	1.73543i
$924$	−8.11124	+	2.90908i	−0.266840	+	0.0957017i
$925$	−3.11169	−	1.79653i	−0.102312	−	0.0590696i
$926$	4.90295	+	3.56220i	0.161121	+	0.117061i
$927$	−20.7746	+	10.7964i	−0.682326	+	0.354599i
$928$	1.29147	+	0.419623i	0.0423944	+	0.0137748i
$929$	12.7080			0.416935			0.208468	−	0.978029i	$-0.433152\pi$
$929$	12.7080			0.416935			0.208468	+	0.978029i	$0.433152\pi$
$930$	6.58099	−	7.04916i	0.215799	−	0.231151i
$931$	−9.56970			−0.313634
$932$	−10.9052	−	3.54332i	−0.357212	−	0.116065i
$933$	−12.0033	+	9.28730i	−0.392969	+	0.304053i
$934$	32.4462	+	23.5735i	1.06167	+	0.771349i
$935$	17.9195	+	10.3458i	0.586031	+	0.338345i
$936$	3.23225	+	19.3973i	0.105649	+	0.634020i
$937$	5.57929	−	53.0834i	0.182267	−	1.73416i	−0.395948	−	0.918273i	$-0.629584\pi$
$937$	5.57929	−	53.0834i	0.182267	−	1.73416i	0.578215	−	0.815885i	$-0.303750\pi$
$938$	−0.0792307	−	0.109052i	−0.00258697	−	0.00356066i
$939$	1.12886	−	15.1201i	0.0368389	−	0.493426i
$940$	−1.59676	−	1.77338i	−0.0520805	−	0.0578413i
$941$	−43.9165	+	19.5529i	−1.43164	+	0.637406i	−0.968530	−	0.248897i	$-0.919932\pi$
$941$	−43.9165	+	19.5529i	−1.43164	+	0.637406i	−0.463107	+	0.886303i	$0.653265\pi$
$942$	15.1052	−	0.456294i	0.492154	−	0.0148669i
$943$	2.53222	−	11.9131i	0.0824603	−	0.387945i
$944$	−4.00433	+	8.99387i	−0.130330	+	0.292725i
$945$	−1.55327	+	6.83165i	−0.0505279	+	0.222234i
$946$	−11.1006	−	34.1642i	−0.360912	−	1.11077i
$947$	11.5723	+	5.15233i	0.376050	+	0.167428i	0.586053	−	0.810272i	$-0.300681\pi$
$947$	11.5723	+	5.15233i	0.376050	+	0.167428i	−0.210003	+	0.977701i	$0.567348\pi$
$948$	−1.30746	−	0.535424i	−0.0424644	−	0.0173897i
$949$	−23.6732	+	5.03189i	−0.768464	+	0.163342i
$950$	0.751118	+	1.68704i	0.0243695	+	0.0547348i
$951$	20.1698	+	32.6192i	0.654051	+	1.05775i
$952$	7.51943	−	0.790324i	0.243706	−	0.0256146i
$953$	37.9206	−	27.5509i	1.22837	−	0.892462i	0.231602	−	0.972811i	$-0.425603\pi$
$953$	37.9206	−	27.5509i	1.22837	−	0.892462i	0.996767	+	0.0803485i	$0.0256033\pi$
$954$	−24.6426	−	12.3075i	−0.797832	−	0.398471i
$955$	−3.95079	−	6.84297i	−0.127845	−	0.221433i
$956$	−7.20424	+	12.4781i	−0.233002	+	0.403571i
$957$	6.27119	−	5.99922i	0.202719	−	0.193927i
$958$	10.9599	−	12.1722i	0.354098	−	0.393265i
$959$	−1.52762	+	4.70152i	−0.0493293	+	0.151820i
$960$	−1.70430	−	0.308795i	−0.0550061	−	0.00996631i
$961$	12.8427	+	28.2146i	0.414279	+	0.910150i
$962$			23.5522i			0.759354i
$963$	15.2269	+	12.1292i	0.490680	+	0.390857i
$964$	−9.41278	−	8.47531i	−0.303165	−	0.272971i
$965$	−5.33061	+	7.33696i	−0.171598	+	0.236185i
$966$	−7.54202	+	8.90278i	−0.242661	+	0.286442i
$967$	32.7635	−	18.9160i	1.05360	−	0.608299i	0.129948	−	0.991521i	$-0.458519\pi$
$967$	32.7635	−	18.9160i	1.05360	−	0.608299i	0.923656	+	0.383222i	$0.125186\pi$
$968$	−2.60098	−	0.273374i	−0.0835988	−	0.00878658i
$969$	−7.78686	−	16.1581i	−0.250150	−	0.519072i
$970$	1.78672	+	16.9995i	0.0573682	+	0.545822i
$971$	27.4472	−	24.7136i	0.880824	−	0.793097i	−0.0985548	−	0.995132i	$-0.531422\pi$
$971$	27.4472	−	24.7136i	0.880824	−	0.793097i	0.979378	+	0.202035i	$0.0647553\pi$
$972$	−7.16142	+	13.8461i	−0.229703	+	0.444113i
$973$	−2.04794	−	9.63482i	−0.0656541	−	0.308878i
$974$	−16.6631	−	3.54186i	−0.533921	−	0.113489i
$975$	9.38243	+	6.39301i	0.300478	+	0.204740i
$976$	−1.61848	+	0.525875i	−0.0518061	+	0.0168328i
$977$	−38.1953	+	12.4104i	−1.22198	+	0.397044i	−0.847801	−	0.530314i	$-0.822074\pi$
$977$	−38.1953	+	12.4104i	−1.22198	+	0.397044i	−0.374175	+	0.927358i	$0.622074\pi$
$978$	−13.1771	−	8.97862i	−0.421358	−	0.287105i
$979$	41.5734	+	8.83670i	1.32869	+	0.282422i
$980$	−1.07741	−	5.06883i	−0.0344167	−	0.161918i
$981$	58.5664	−	3.54155i	1.86988	−	0.113073i
$982$	−25.2669	+	22.7504i	−0.806298	+	0.725994i
$983$	2.12031	+	20.1734i	0.0676273	+	0.643431i	0.974863	+	0.222807i	$0.0715220\pi$
$983$	2.12031	+	20.1734i	0.0676273	+	0.643431i	−0.907235	+	0.420624i	$0.861811\pi$
$984$	−1.83299	−	3.80354i	−0.0584337	−	0.121252i
$985$	−9.83955	−	1.03418i	−0.313514	−	0.0329516i
$986$	−6.59462	+	3.80740i	−0.210015	+	0.121252i
$987$	−3.60222	+	4.25214i	−0.114660	+	0.135347i
$988$	7.11509	−	9.79308i	0.226361	−	0.311559i
$989$	−36.1468	−	32.5468i	−1.14940	−	1.03493i
$990$	−6.89701	+	8.65847i	−0.219201	+	0.275184i
$991$		−	57.7953i		−	1.83593i	−0.396663	−	0.917964i	$-0.629832\pi$
$991$		−	57.7953i		−	1.83593i	0.396663	−	0.917964i	$-0.370168\pi$
$992$	3.01308	−	4.68202i	0.0956655	−	0.148654i
$993$	−40.4733	−	7.33318i	−1.28438	−	0.232711i
$994$	3.36975	−	10.3710i	0.106882	−	0.328949i
$995$	0.000932633	−	0.00103579i	2.95664e−5	−	3.28369e-5i
$996$	5.75150	−	5.50207i	0.182243	−	0.174340i
$997$	11.8843	−	20.5842i	0.376380	−	0.651909i	−0.614153	−	0.789187i	$-0.710502\pi$
$997$	11.8843	−	20.5842i	0.376380	−	0.651909i	0.990533	+	0.137278i	$0.0438354\pi$
$998$	−15.9605	−	27.6444i	−0.505221	−	0.875069i
$999$	−11.1863	+	14.9479i	−0.353917	+	0.472932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.761.4	yes	176
3.2	odd	2	inner	930.2.br.b.761.14	yes	176
31.11	odd	30	inner	930.2.br.b.11.14	yes	176
93.11	even	30	inner	930.2.br.b.11.4	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.4	✓	176	93.11	even	30	inner
930.2.br.b.11.14	yes	176	31.11	odd	30	inner
930.2.br.b.761.4	yes	176	1.1	even	1	trivial
930.2.br.b.761.14	yes	176	3.2	odd	2	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-1.05992 - 1.36988i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.584727 + 1.63037i) q^{6} +(0.140936 - 1.34092i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.753142 + 2.90392i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-1.05992 - 1.36988i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.584727 + 1.63037i) q^{6} +(0.140936 - 1.34092i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.753142 + 2.90392i) q^{9} +(0.669131 + 0.743145i) q^{10} +(3.37088 - 1.50081i) q^{11} +(-0.0522975 - 1.73126i) q^{12} +(-1.36284 + 6.41167i) q^{13} +(-0.548405 + 1.23174i) q^{14} +(0.232977 + 1.71631i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-5.12286 - 2.28084i) q^{17} +(1.61364 - 2.52906i) q^{18} +(-1.80634 + 0.383949i) q^{19} +(-0.406737 - 0.913545i) q^{20} +(-1.98628 + 1.22820i) q^{21} +(-3.66968 + 0.385699i) q^{22} +(-4.04207 + 2.93674i) q^{23} +(-0.485251 + 1.66269i) q^{24} +(0.500000 + 0.866025i) q^{25} +(3.27746 - 5.67672i) q^{26} +(4.77630 - 2.04621i) q^{27} +(0.902193 - 1.00199i) q^{28} +(-0.419623 + 1.29147i) q^{29} +(0.308795 - 1.70430i) q^{30} +(4.68202 + 3.01308i) q^{31} -1.00000i q^{32} +(-5.62880 - 3.02697i) q^{33} +(4.16731 + 3.75226i) q^{34} +(-0.792514 + 1.09080i) q^{35} +(-2.31619 + 1.90664i) q^{36} +(-3.11169 + 1.79653i) q^{37} +(1.83658 + 0.193032i) q^{38} +(10.2277 - 4.92892i) q^{39} +(0.104528 + 0.994522i) q^{40} +(-1.81154 + 1.63112i) q^{41} +(2.26860 - 0.554294i) q^{42} +(2.02409 + 9.52259i) q^{43} +(3.60926 + 0.767172i) q^{44} +(2.10420 - 2.13830i) q^{45} +(4.75174 - 1.54393i) q^{46} +(2.26952 - 0.737413i) q^{47} +(0.975300 - 1.43136i) q^{48} +(5.06883 + 1.07741i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(2.30534 + 9.43521i) q^{51} +(-4.87125 + 4.38609i) q^{52} +(-0.959748 - 9.13139i) q^{53} +(-5.17484 + 0.470106i) q^{54} +(-3.66968 - 0.385699i) q^{55} +(-1.16767 + 0.674153i) q^{56} +(2.44054 + 2.06751i) q^{57} +(0.798170 - 1.09859i) q^{58} +(7.31627 + 6.58760i) q^{59} +(-0.820340 + 1.52546i) q^{60} +1.70177i q^{61} +(-3.52177 - 4.31244i) q^{62} +(3.78779 + 1.41917i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(4.38609 - 4.87125i) q^{65} +(4.41793 + 4.61821i) q^{66} +(-0.0499869 + 0.0865799i) q^{67} +(-2.80383 - 4.85638i) q^{68} +(8.30724 + 2.42445i) q^{69} +(1.09080 - 0.792514i) q^{70} +(-8.04344 + 0.845399i) q^{71} +(2.79201 - 1.09758i) q^{72} +(1.50175 + 3.37300i) q^{73} +(3.51455 - 0.747040i) q^{74} +(0.656391 - 1.60286i) q^{75} +(-1.68704 - 0.751118i) q^{76} +(-1.53739 - 4.73161i) q^{77} +(-11.2503 + 1.52714i) q^{78} +(0.331778 - 0.745186i) q^{79} +(0.207912 - 0.978148i) q^{80} +(-7.86555 - 4.37414i) q^{81} +(2.22693 - 0.991491i) q^{82} +(3.07491 + 3.41503i) q^{83} +(-2.32885 - 0.173871i) q^{84} +(3.29610 + 4.53670i) q^{85} +(1.01762 - 9.68200i) q^{86} +(2.21392 - 0.794017i) q^{87} +(-3.19554 - 1.84495i) q^{88} +(9.31870 + 6.77043i) q^{89} +(-2.66199 + 1.38341i) q^{90} +(8.40546 + 2.73110i) q^{91} -4.99627 q^{92} +(-0.835004 - 9.60743i) q^{93} -2.38632 q^{94} +(1.75631 + 0.570660i) q^{95} +(-1.36988 + 1.05992i) q^{96} +(13.8287 + 10.0471i) q^{97} +(-4.48780 - 2.59104i) q^{98} +(1.81950 + 10.9191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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