LMFDB - Embedded newform 930.2.br.b.11.4

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			11.4
Character	$\chi$	$=$	930.11
Dual form			930.2.br.b.761.4

$q$-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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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	0.988329	+	0.152332i	$0.0486782\pi$
$7$	0.140936	+	1.34092i	0.0532689	+	0.506820i	−0.935060	+	0.354488i	$0.884655\pi$
$8$	−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	0.846178	−	0.532900i	$-0.178898\pi$
$11$	3.37088	+	1.50081i	1.01636	+	0.452513i	0.170182	+	0.985413i	$0.445564\pi$
$12$	−0.0522975	+	1.73126i	−0.0150970	+	0.499772i
$13$	−1.36284	−	6.41167i	−0.377985	−	1.77828i	−0.596675	−	0.802483i	$-0.703512\pi$
$13$	−1.36284	−	6.41167i	−0.377985	−	1.77828i	0.218690	−	0.975794i	$-0.429822\pi$
$14$	−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	−0.919451	−	0.393204i	$-0.871366\pi$
$17$	−5.12286	+	2.28084i	−1.24248	+	0.553186i	−0.323025	+	0.946390i	$0.604700\pi$
$18$	1.61364	+	2.52906i	0.380339	+	0.596106i
$19$	−1.80634	−	0.383949i	−0.414403	−	0.0880840i	−0.00400785	−	0.999992i	$-0.501276\pi$
$19$	−1.80634	−	0.383949i	−0.414403	−	0.0880840i	−0.410395	+	0.911908i	$0.634609\pi$
$20$	−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	0.0803298	−	0.996768i	$-0.474403\pi$
$23$	−4.04207	−	2.93674i	−0.842830	−	0.612352i	−0.923160	+	0.384417i	$0.874403\pi$
$24$	−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	0.904506	−	0.426461i	$-0.140240\pi$
$29$	−0.419623	−	1.29147i	−0.0779220	−	0.239819i	−0.982428	+	0.186641i	$0.940240\pi$
$30$	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	0.221916	−	0.975066i	$-0.428769\pi$
$37$	−3.11169	−	1.79653i	−0.511558	−	0.295348i	−0.733474	+	0.679718i	$0.762102\pi$
$38$	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	0.515439	−	0.856927i	$-0.327629\pi$
$41$	−1.81154	−	1.63112i	−0.282916	−	0.254738i	−0.798354	+	0.602188i	$0.794296\pi$
$42$	2.26860	+	0.554294i	0.350053	+	0.0855295i
$43$	2.02409	−	9.52259i	0.308671	−	1.45218i	−0.501077	−	0.865403i	$-0.667063\pi$
$43$	2.02409	−	9.52259i	0.308671	−	1.45218i	0.809747	−	0.586779i	$-0.199604\pi$
$44$	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	0.469823	−	0.882761i	$-0.344318\pi$
$47$	2.26952	+	0.737413i	0.331044	+	0.107563i	−0.138779	+	0.990323i	$0.544318\pi$
$48$	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	0.705940	+	0.708272i	$0.250525\pi$
$53$	−0.959748	+	9.13139i	−0.131832	+	1.25429i	−0.837771	+	0.546021i	$0.816142\pi$
$54$	−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	−0.0374170	−	0.999300i	$-0.511913\pi$
$59$	7.31627	−	6.58760i	0.952497	−	0.857632i	0.989914	+	0.141667i	$0.0452463\pi$
$60$	−0.820340	−	1.52546i	−0.105905	−	0.196937i
$61$		−	1.70177i		−	0.217889i	−0.994048	−	0.108944i	$-0.965253\pi$
$61$		−	1.70177i		−	0.217889i	0.994048	−	0.108944i	$-0.0347471\pi$
$62$	−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	0.862956	−	0.505279i	$-0.168611\pi$
$67$	−0.0499869	−	0.0865799i	−0.00610687	−	0.0105774i	−0.869063	+	0.494702i	$0.835277\pi$
$68$	−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	−0.385586	−	0.922672i	$-0.626001\pi$
$71$	−8.04344	−	0.845399i	−0.954580	−	0.100330i	−0.568994	+	0.822341i	$0.692667\pi$
$72$	2.79201	+	1.09758i	0.329042	+	0.129351i
$73$	1.50175	−	3.37300i	0.175767	−	0.394779i	−0.804082	−	0.594518i	$-0.797343\pi$
$73$	1.50175	−	3.37300i	0.175767	−	0.394779i	0.979849	+	0.199739i	$0.0640094\pi$
$74$	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	0.931247	−	0.364388i	$-0.118722\pi$
$79$	0.331778	+	0.745186i	0.0373280	+	0.0838400i	−0.893919	+	0.448228i	$0.852055\pi$
$80$	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	−0.550364	−	0.834925i	$-0.685511\pi$
$83$	3.07491	−	3.41503i	0.337515	−	0.374849i	0.887880	+	0.460076i	$0.152178\pi$
$84$	−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	0.0283463	−	0.999598i	$-0.490976\pi$
$89$	9.31870	−	6.77043i	0.987780	−	0.717664i	0.959434	+	0.281934i	$0.0909759\pi$
$90$	−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	0.409938	−	0.912113i	$-0.365550\pi$
$97$	13.8287	−	10.0471i	1.40409	−	1.02013i	0.994149	−	0.108016i	$-0.0344497\pi$
$98$	−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	−0.209241	−	0.977864i	$-0.567099\pi$
$101$	7.89339	−	10.8643i	0.785422	−	1.08104i	0.994663	−	0.103177i	$-0.0329007\pi$
$102$	0.723137	+	9.68581i	0.0716012	+	0.959038i
$103$	5.22200	−	5.79962i	0.514539	−	0.571453i	−0.428751	−	0.903423i	$-0.641046\pi$
$103$	5.22200	−	5.79962i	0.514539	−	0.571453i	0.943290	+	0.331969i	$0.107713\pi$
$104$	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	0.995021	−	0.0996658i	$-0.0317774\pi$
$107$	2.63935	+	5.92808i	0.255156	+	0.573089i	−0.739865	+	0.672755i	$0.765111\pi$
$108$	5.06684	−	1.15202i	0.487557	−	0.110853i
$109$	−6.04369	+	18.6006i	−0.578880	+	1.78161i	0.0436890	+	0.999045i	$0.486089\pi$
$109$	−6.04369	+	18.6006i	−0.578880	+	1.78161i	−0.622569	+	0.782565i	$0.713911\pi$
$110$	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	−0.219096	−	0.975703i	$-0.570311\pi$
$113$	6.93720	−	15.5812i	0.652597	−	1.46576i	0.871693	−	0.490053i	$-0.163023\pi$
$114$	−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	−0.196979	+	0.980408i	$0.563113\pi$
$127$	−13.4400	+	12.1014i	−1.19261	+	1.07383i	−0.995627	+	0.0934189i	$0.970220\pi$
$128$	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	−0.645135	−	0.764069i	$-0.723199\pi$
$131$	−12.7882	+	1.34410i	−1.11731	+	0.117434i	−0.472178	+	0.881503i	$0.656532\pi$
$132$	−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	−0.358545	−	0.933512i	$-0.616727\pi$
$137$	−3.58631	+	0.762293i	−0.306399	+	0.0651271i	0.0521463	+	0.998639i	$0.483394\pi$
$138$	−7.15146	+	4.87287i	−0.608773	+	0.414806i
$139$	6.94795	+	2.25753i	0.589318	+	0.191481i	0.588471	−	0.808519i	$-0.299730\pi$
$139$	6.94795	+	2.25753i	0.589318	+	0.191481i	0.000847313		1.00000i	$0.499730\pi$
$140$	−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	−0.997126	−	0.0757551i	$-0.975863\pi$
$149$	−19.0580	−	11.0032i	−1.56130	−	0.901414i	−0.564169	−	0.825659i	$-0.690803\pi$
$150$	−1.11958	−	1.32157i	−0.0914129	−	0.107906i
$151$	−11.7273	−	16.1412i	−0.954354	−	1.31356i	−0.949566	−	0.313567i	$-0.898476\pi$
$151$	−11.7273	−	16.1412i	−0.954354	−	1.31356i	−0.00478737	−	0.999989i	$-0.501524\pi$
$152$	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	0.999141	+	0.0414407i	$0.0131948\pi$
$157$	2.69616	+	8.29793i	0.215177	+	0.662247i	−0.783964	+	0.620807i	$0.786805\pi$
$158$	−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	0.256575	−	0.966524i	$-0.417406\pi$
$163$	−7.44782	−	5.41116i	−0.583358	−	0.423835i	−0.839933	+	0.542690i	$0.817406\pi$
$164$	−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	0.0213516	−	0.999772i	$-0.493203\pi$
$167$	−4.72701	−	1.00476i	−0.365787	−	0.0777504i	−0.387138	+	0.922022i	$0.626536\pi$
$168$	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	0.910980	+	0.412450i	$0.135327\pi$
$173$	3.24242	+	15.2544i	0.246517	+	1.15977i	−0.664463	+	0.747321i	$0.731340\pi$
$174$	−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	−0.893800	−	0.448467i	$-0.851970\pi$
$179$	−1.50880	−	14.3553i	−0.112773	−	1.07296i	0.781026	−	0.624498i	$-0.214696\pi$
$180$	2.95920	+	0.493103i	0.220566	+	0.0367537i
$181$	−8.35728	+	4.82508i	−0.621192	+	0.358645i	−0.777333	−	0.629089i	$-0.783428\pi$
$181$	−8.35728	+	4.82508i	−0.621192	+	0.358645i	0.156141	+	0.987735i	$0.450095\pi$
$182$	−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	−0.231564	−	0.972820i	$-0.574384\pi$
$191$	6.84297	−	3.95079i	0.495140	−	0.285869i	0.726704	+	0.686951i	$0.241051\pi$
$192$	1.63037	+	0.584727i	0.117662	+	0.0421990i
$193$	0.947966	+	9.01929i	0.0682361	+	0.649223i	0.974172	+	0.225808i	$0.0725022\pi$
$193$	0.947966	+	9.01929i	0.0682361	+	0.649223i	−0.905936	+	0.423415i	$0.860831\pi$
$194$	−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	0.702616	−	0.711569i	$-0.252015\pi$
$197$	9.03839	+	4.02415i	0.643958	+	0.286709i	−0.0586575	+	0.998278i	$0.518682\pi$
$198$	1.64375	+	10.9470i	0.116816	+	0.777966i
$199$	−0.000289787	−	0.00136334i	−2.05424e−5	−	9.66446e-5i	0.978137	−	0.207960i	$-0.0666824\pi$
$199$	−0.000289787	−	0.00136334i	−2.05424e−5	−	9.66446e-5i	−0.978158	+	0.207863i	$0.933349\pi$
$200$	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	−0.999503	−	0.0315172i	$-0.989966\pi$
$211$	−6.86283	+	11.8868i	−0.472457	+	0.818319i	0.527046	+	0.849837i	$0.323299\pi$
$212$	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	0.0865949	−	0.996244i	$-0.472401\pi$
$223$	−10.9442	−	6.31865i	−0.732880	−	0.423128i	−0.819475	+	0.573115i	$0.805735\pi$
$224$	−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	0.345936	−	0.938258i	$-0.387561\pi$
$227$	−8.30198	−	7.47513i	−0.551022	−	0.496142i	−0.896958	+	0.442116i	$0.854228\pi$
$228$	0.759183	−	3.10716i	0.0502781	−	0.205777i
$229$	2.48323	−	11.6827i	0.164096	−	0.772013i	−0.816713	−	0.577044i	$-0.804206\pi$
$229$	2.48323	−	11.6827i	0.164096	−	0.772013i	0.980809	−	0.194969i	$-0.0624606\pi$
$230$	−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	−0.0708198	−	0.997489i	$-0.522562\pi$
$233$	−10.9052	−	3.54332i	−0.714424	−	0.232130i	−0.643604	+	0.765359i	$0.722562\pi$
$234$	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	−0.831225	−	0.555936i	$-0.812360\pi$
$239$	1.50610	−	14.3295i	0.0974212	−	0.926901i	0.928647	−	0.370966i	$-0.120973\pi$
$240$	−1.56031	−	0.751943i	−0.100718	−	0.0485377i
$241$	−12.5968	+	1.32397i	−0.811429	+	0.0852846i	−0.501149	−	0.865361i	$-0.667089\pi$
$241$	−12.5968	+	1.32397i	−0.811429	+	0.0852846i	−0.310279	+	0.950645i	$0.600423\pi$
$242$	−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	0.699205	−	0.714921i	$-0.253537\pi$
$251$	−1.34486	−	1.49361i	−0.0848865	−	0.0942760i	−0.784092	+	0.620645i	$0.786871\pi$
$252$	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	0.198573	−	0.980086i	$-0.436369\pi$
$257$	3.03046	+	0.318514i	0.189035	+	0.0198684i	−0.00953794	+	0.999955i	$0.503036\pi$
$258$	−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	−0.921411	−	0.388588i	$-0.872963\pi$
$263$	0.850313	−	2.61699i	0.0524325	−	0.161371i	0.973844	+	0.227218i	$0.0729629\pi$
$264$	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	0.0563592	+	0.998411i	$0.482051\pi$
$269$	−15.4577	+	17.1675i	−0.942473	+	1.04672i	−0.998832	+	0.0483118i	$0.984616\pi$
$270$	4.71660	−	2.18030i	0.287043	−	0.132689i
$271$	11.5470	−	15.8931i	0.701431	−	0.965437i	−0.298508	−	0.954407i	$-0.596489\pi$
$271$	11.5470	−	15.8931i	0.701431	−	0.965437i	0.999939	−	0.0110298i	$-0.00351096\pi$
$272$	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	−0.352354	−	0.935867i	$-0.614619\pi$
$277$	−1.45337	+	0.472230i	−0.0873248	+	0.0283736i	0.265029	+	0.964241i	$0.414619\pi$
$278$	−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	−0.716438	−	0.697650i	$-0.754229\pi$
$281$	−14.8517	+	4.82562i	−0.885980	+	0.287872i	−0.169542	+	0.985523i	$0.554229\pi$
$282$	2.52930	−	3.26897i	0.150618	−	0.194664i
$283$	20.2186	−	14.6897i	1.20187	−	0.873209i	0.207402	−	0.978256i	$-0.433499\pi$
$283$	20.2186	−	14.6897i	1.20187	−	0.873209i	0.994467	+	0.105047i	$0.0334992\pi$
$284$	−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	−0.987037	−	0.160493i	$-0.948692\pi$
$293$	−7.63171	−	17.1411i	−0.445850	−	1.00139i	0.541188	−	0.840902i	$-0.317975\pi$
$294$	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	0.912474	−	0.409135i	$-0.134169\pi$
$307$	7.18730	+	7.98230i	0.410201	+	0.455574i	−0.502273	+	0.864709i	$0.667503\pi$
$308$	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	$0.0799151\pi$
$311$			8.76227i			0.496863i	−0.968649	+	0.248431i	$0.920085\pi$
$312$	−9.99929	+	5.37725i	−0.566098	+	0.304427i
$313$	6.50542	−	5.85750i	0.367708	−	0.331086i	−0.464476	−	0.885586i	$-0.653757\pi$
$313$	6.50542	−	5.85750i	0.367708	−	0.331086i	0.832184	+	0.554500i	$0.187091\pi$
$314$	−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	−0.700272	−	0.713876i	$-0.746938\pi$
$317$	−22.0209	+	2.31449i	−1.23682	+	0.129995i	−0.536546	+	0.843871i	$0.680271\pi$
$318$	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	0.991986	−	0.126347i	$-0.0403251\pi$
$331$	17.6480	+	15.8903i	0.970023	+	0.873412i	−0.0219636	+	0.999759i	$0.506992\pi$
$332$	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	−0.999766	−	0.0216513i	$-0.993108\pi$
$337$	−13.0598	−	17.9753i	−0.711413	−	0.979176i	0.288353	−	0.957524i	$-0.406892\pi$
$338$	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	−0.299528	−	0.954088i	$-0.596829\pi$
$347$	12.6018	−	21.8270i	0.676500	−	1.17173i	0.976028	−	0.217645i	$-0.0698376\pi$
$348$	2.25781	−	0.658936i	0.121031	−	0.0353227i
$349$	28.7820	+	20.9114i	1.54067	+	1.11936i	0.949917	+	0.312504i	$0.101168\pi$
$349$	28.7820	+	20.9114i	1.54067	+	1.11936i	0.590749	+	0.806855i	$0.298832\pi$
$350$	−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	−0.608369	−	0.793654i	$-0.708176\pi$
$353$	−27.9373	−	5.93825i	−1.48695	−	0.316061i	−0.878581	+	0.477593i	$0.841509\pi$
$354$	−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	−0.772064	−	0.635545i	$-0.780775\pi$
$359$	−6.16257	−	28.9926i	−0.325248	−	1.53017i	0.446816	−	0.894626i	$-0.352558\pi$
$360$	−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	−0.119382	−	0.992848i	$-0.538091\pi$
$367$	13.0415	−	7.52949i	0.680759	−	0.393036i	0.800141	+	0.599812i	$0.204758\pi$
$368$	−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	0.817771	+	0.575544i	$0.195210\pi$
$379$	2.67747	+	25.4745i	0.137533	+	1.30853i	−0.680238	+	0.732991i	$0.738124\pi$
$380$	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	0.150158	−	0.988662i	$-0.452022\pi$
$383$	−9.47373	−	4.21798i	−0.484085	−	0.215528i	−0.634243	+	0.773133i	$0.718688\pi$
$384$	−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	−0.532545	−	0.846401i	$-0.678764\pi$
$389$	−5.12581	+	2.28216i	−0.259889	+	0.115710i	0.272657	+	0.962111i	$0.412098\pi$
$390$	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	−0.542509	−	0.840050i	$-0.682525\pi$
$397$	9.09073	−	15.7456i	0.456251	−	0.790249i	0.998759	+	0.0498011i	$0.0158588\pi$
$398$	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	0.998081	+	0.0619279i	$0.0197249\pi$
$401$	4.54601	+	13.9912i	0.227017	+	0.698686i	−0.771064	+	0.636758i	$0.780275\pi$
$402$	−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	0.813678	−	0.581316i	$-0.197462\pi$
$409$	14.5021	+	8.37278i	0.717082	+	0.414007i	−0.0965959	+	0.995324i	$0.530795\pi$
$410$	−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	0.991101	−	0.133114i	$-0.0424976\pi$
$419$	35.0985	+	11.4042i	1.71468	+	0.557132i	0.723575	+	0.690246i	$0.242498\pi$
$420$	1.92991	−	1.31500i	0.0941700	−	0.0641656i
$421$	−26.3891	+	5.60917i	−1.28613	+	0.273374i	−0.799728	−	0.600363i	$-0.795023\pi$
$421$	−26.3891	+	5.60917i	−1.28613	+	0.273374i	−0.486398	+	0.873737i	$0.661689\pi$
$422$	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	−0.0705290	−	0.997510i	$-0.522469\pi$
$431$	18.9781	−	17.0880i	0.914144	−	0.823099i	0.984673	+	0.174411i	$0.0558021\pi$
$432$	3.42202	−	3.91021i	0.164642	−	0.188130i
$433$		−	24.3011i		−	1.16783i	−0.811813	−	0.583917i	$-0.801519\pi$
$433$		−	24.3011i		−	1.16783i	0.811813	−	0.583917i	$-0.198481\pi$
$434$	−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	−0.986997	−	0.160738i	$-0.948612\pi$
$439$	−13.2566	−	22.9611i	−0.632702	−	1.09587i	0.354295	−	0.935134i	$-0.384721\pi$
$440$	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	0.585296	−	0.810820i	$-0.300978\pi$
$443$	20.8207	+	2.18835i	0.989223	+	0.103972i	0.403927	+	0.914791i	$0.367645\pi$
$444$	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	−0.774644	−	0.632397i	$-0.782071\pi$
$449$	4.74159	−	14.5931i	0.223770	−	0.688692i	0.998414	−	0.0562953i	$-0.0179288\pi$
$450$	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	−0.999999	−	0.00164220i	$-0.999477\pi$
$457$	−14.7381	+	20.2853i	−0.689420	+	0.948906i	0.310578	+	0.950548i	$0.399477\pi$
$458$	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	−0.637679	−	0.770302i	$-0.720105\pi$
$461$	−2.19286	+	1.59321i	−0.102132	+	0.0742030i	0.535547	+	0.844505i	$0.320105\pi$
$462$	6.81530	+	5.27321i	0.317076	+	0.245332i
$463$	−5.76377	+	1.87276i	−0.267865	+	0.0870346i	−0.439870	−	0.898061i	$-0.644975\pi$
$463$	−5.76377	+	1.87276i	−0.267865	+	0.0870346i	0.172005	+	0.985096i	$0.444975\pi$
$464$	−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	−0.997702	−	0.0677518i	$-0.978417\pi$
$467$	−38.1428	+	12.3933i	−1.76504	+	0.573495i	−0.767335	+	0.641247i	$0.778417\pi$
$468$	−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	0.694978	−	0.719031i	$-0.255414\pi$
$479$	−6.66205	−	14.9632i	−0.304397	−	0.683687i	−0.999375	+	0.0353439i	$0.988747\pi$
$480$	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	0.480288	−	0.877111i	$-0.340532\pi$
$487$	16.9421	+	1.78068i	0.767719	+	0.0806905i	0.287431	+	0.957801i	$0.407199\pi$
$488$	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	0.939077	+	0.343706i	$0.111682\pi$
$491$	17.0000	+	29.4448i	0.767197	+	1.32882i	−0.171880	+	0.985118i	$0.554984\pi$
$492$	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	0.0628161	−	0.998025i	$-0.479992\pi$
$499$	23.7219	−	21.3593i	1.06194	−	0.956175i	0.999124	+	0.0418500i	$0.0133252\pi$
$500$	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	0.222762	−	0.974873i	$-0.428493\pi$
$503$	14.4287	−	1.51652i	0.643344	−	0.0676182i	0.420582	+	0.907255i	$0.361826\pi$
$504$	−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	−0.686650	−	0.726989i	$-0.740919\pi$
$509$	−22.9726	+	4.88298i	−1.01824	+	0.216434i	−0.331593	+	0.943423i	$0.607586\pi$
$510$	−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	0.493874	−	0.869533i	$-0.335580\pi$
$521$	−0.279080	−	0.161127i	−0.0122267	−	0.00705909i	−0.506101	+	0.862474i	$0.668914\pi$
$522$	2.58908	−	3.14522i	0.113321	−	0.137662i
$523$	−2.32621	−	3.20175i	−0.101718	−	0.140003i	0.755124	−	0.655582i	$-0.227577\pi$
$523$	−2.32621	−	3.20175i	−0.101718	−	0.140003i	−0.856842	+	0.515579i	$0.827577\pi$
$524$	−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	−0.819851	−	0.572577i	$-0.805944\pi$
$541$	−21.9320	+	9.76476i	−0.942931	+	0.419820i	−0.123080	+	0.992397i	$0.539277\pi$
$542$	−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	0.986564	−	0.163378i	$-0.0522390\pi$
$547$	35.6735	+	15.8829i	1.52529	+	0.679103i	0.538726	+	0.842481i	$0.318906\pi$
$548$	−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	−0.650114	−	0.759836i	$-0.725279\pi$
$563$	−7.52484	+	4.34447i	−0.317134	+	0.183098i	0.332980	+	0.942934i	$0.391946\pi$
$564$	−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	−0.378830	−	0.925466i	$-0.623674\pi$
$569$	−31.4886	−	14.0196i	−1.32007	−	0.587734i	−0.941242	+	0.337732i	$0.890340\pi$
$570$	0.0965775	−	3.19711i	0.00404519	−	0.133912i
$571$	3.60439	+	16.9573i	0.150839	+	0.709641i	0.986943	+	0.161070i	$0.0514946\pi$
$571$	3.60439	+	16.9573i	0.150839	+	0.709641i	−0.836104	+	0.548571i	$0.815172\pi$
$572$	−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	0.854076	−	0.520148i	$-0.174123\pi$
$577$	34.1756	+	7.26426i	1.42275	+	0.302415i	0.568674	+	0.822563i	$0.307456\pi$
$578$	−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	0.849864	−	0.527001i	$-0.176684\pi$
$587$	−3.57253	−	10.9951i	−0.147454	−	0.453817i	−0.997318	+	0.0731846i	$0.976684\pi$
$588$	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	0.937084	+	0.349104i	$0.113514\pi$
$593$	23.8530	+	32.8309i	0.979527	+	1.34820i	0.0424432	+	0.999099i	$0.486486\pi$
$594$	−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	0.911916	−	0.410377i	$-0.134603\pi$
$599$	14.6629	+	13.2025i	0.599109	+	0.539440i	−0.312807	+	0.949817i	$0.601269\pi$
$600$	−1.68256	−	0.411104i	−0.0686900	−	0.0167833i
$601$	−4.27992	+	20.1354i	−0.174581	+	0.821341i	0.800472	+	0.599370i	$0.204582\pi$
$601$	−4.27992	+	20.1354i	−0.174581	+	0.821341i	−0.975053	+	0.221971i	$0.928751\pi$
$602$	−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	0.0350154	−	0.999387i	$-0.488852\pi$
$607$	11.6656	−	2.47959i	0.473491	−	0.100644i	0.438475	+	0.898743i	$0.355519\pi$
$608$	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	0.0292730	−	0.999571i	$-0.490681\pi$
$613$	6.57914	−	0.691495i	0.265729	−	0.0279292i	0.236456	+	0.971642i	$0.424014\pi$
$614$	−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	0.0383007	−	0.999266i	$-0.487806\pi$
$617$	25.7361	−	23.1729i	1.03610	−	0.932905i	0.997796	+	0.0663609i	$0.0211389\pi$
$618$	−6.40206	−	11.9050i	−0.257529	−	0.478888i
$619$		−	27.1275i		−	1.09035i	−0.838323	−	0.545174i	$-0.816464\pi$
$619$		−	27.1275i		−	1.09035i	0.838323	−	0.545174i	$-0.183536\pi$
$620$	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	−0.756443	−	0.654059i	$-0.773065\pi$
$631$	5.92265	−	13.3025i	0.235777	−	0.529564i	0.992220	+	0.124496i	$0.0397313\pi$
$632$	−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	−0.135160	−	0.990824i	$-0.543155\pi$
$641$	21.8840	−	24.3046i	0.864364	−	0.959974i	0.999524	+	0.0308500i	$0.00982142\pi$
$642$	11.2082	−	0.836801i	0.442354	−	0.0330259i
$643$	−4.77787	+	6.57618i	−0.188421	+	0.259339i	−0.892768	−	0.450516i	$-0.851240\pi$
$643$	−4.77787	+	6.57618i	−0.188421	+	0.259339i	0.704347	+	0.709856i	$0.251240\pi$
$644$	−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	−0.0166963	−	0.999861i	$-0.505315\pi$
$647$	23.6320	−	17.1696i	0.929068	−	0.675008i	0.945764	+	0.324853i	$0.105315\pi$
$648$	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	−0.884182	−	0.467142i	$-0.845284\pi$
$653$	−33.8569	+	11.0008i	−1.32492	+	0.430493i	−0.440739	+	0.897635i	$0.645284\pi$
$654$	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	−0.742645	−	0.669685i	$-0.766429\pi$
$659$	3.17686	−	4.37258i	0.123753	−	0.170331i	0.866398	+	0.499354i	$0.166429\pi$
$660$	−0.475830	−	6.37334i	−0.0185217	−	0.248082i
$661$	17.8559	−	19.8310i	0.694513	−	0.771335i	−0.287979	−	0.957637i	$-0.592983\pi$
$661$	17.8559	−	19.8310i	0.694513	−	0.771335i	0.982493	+	0.186302i	$0.0596502\pi$
$662$	−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	0.0852621	−	0.996359i	$-0.472827\pi$
$673$	−0.998611	−	0.104958i	−0.0384936	−	0.00404584i	−0.123756	+	0.992313i	$0.539494\pi$
$674$	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	0.852340	−	0.522988i	$-0.175183\pi$
$677$	−0.696025	−	1.20555i	−0.0267504	−	0.0463331i	−0.879091	+	0.476655i	$0.841849\pi$
$678$	−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	$0.233833\pi$
$683$			35.0354i			1.34059i	−0.742093	+	0.670297i	$0.766167\pi$
$684$	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	0.666721	+	0.745307i	$0.267697\pi$
$691$	−3.69038	+	35.1116i	−0.140389	+	1.33571i	−0.807110	+	0.590402i	$0.798969\pi$
$692$	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	0.619844	+	0.784725i	$0.287196\pi$
$701$	−7.03182	+	33.0821i	−0.265588	+	1.24949i	−0.885432	+	0.464769i	$0.846138\pi$
$702$	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	0.961558	−	0.274603i	$-0.0885465\pi$
$709$	10.7375	+	14.7790i	0.403257	+	0.555035i	−0.558301	+	0.829639i	$0.688547\pi$
$710$	−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	−0.999777	−	0.0211085i	$-0.993280\pi$
$719$	−12.9139	+	22.3676i	−0.481608	+	0.834170i	0.518169	+	0.855278i	$0.326614\pi$
$720$	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	−0.713172	−	0.700989i	$-0.752742\pi$
$727$	−18.0501	+	8.03641i	−0.669440	+	0.298054i	0.0437315	+	0.999043i	$0.486075\pi$
$728$	−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	0.813060	−	0.582180i	$-0.197800\pi$
$733$	25.0288	+	11.1435i	0.924459	+	0.411596i	0.111399	+	0.993776i	$0.464467\pi$
$734$	−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	−0.971023	−	0.238985i	$-0.923185\pi$
$739$	−33.9689	+	19.6120i	−1.24957	+	0.721438i	−0.278545	+	0.960423i	$0.589852\pi$
$740$	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	−0.928176	−	0.372140i	$-0.878624\pi$
$751$	−2.67618	−	25.4622i	−0.0976552	−	0.929127i	0.830521	−	0.556987i	$-0.188043\pi$
$752$	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	−0.996210	−	0.0869808i	$-0.972278\pi$
$757$	−3.34305	−	15.7278i	−0.121505	−	0.571637i	0.874705	−	0.484656i	$-0.161055\pi$
$758$	−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	−0.981241	−	0.192786i	$-0.938248\pi$
$761$	−41.2290	+	18.3564i	−1.49455	+	0.665417i	−0.513311	+	0.858203i	$0.671581\pi$
$762$	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	0.103591	+	0.994620i	$0.466967\pi$
$769$	−22.4501	+	38.8847i	−0.809571	+	1.40222i	−0.913162	+	0.407597i	$0.866367\pi$
$770$	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	0.948650	−	0.316329i	$-0.102450\pi$
$773$	−0.132270	−	0.407084i	−0.00475741	−	0.0146418i	−0.953407	+	0.301687i	$0.902450\pi$
$774$	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	−0.991740	−	0.128267i	$-0.959059\pi$
$787$	−0.941742	+	4.43055i	−0.0335695	+	0.157932i	0.958170	+	0.286199i	$0.0923919\pi$
$788$	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	−0.896939	−	0.442154i	$-0.854214\pi$
$797$	2.04193	−	19.4276i	0.0723288	−	0.688162i	0.969268	−	0.246008i	$-0.0791189\pi$
$798$	−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	0.150829	−	0.988560i	$-0.451806\pi$
$809$	−24.1219	−	26.7901i	−0.848081	−	0.941889i	−0.998910	+	0.0466704i	$0.985139\pi$
$810$	−2.01247	+	8.77211i	−0.0707109	+	0.308221i
$811$	8.66146	+	15.0021i	0.304145	+	0.526794i	0.977071	−	0.212916i	$-0.0682960\pi$
$811$	8.66146	+	15.0021i	0.304145	+	0.526794i	−0.672926	+	0.739710i	$0.734963\pi$
$812$	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	−0.864183	−	0.503178i	$-0.832164\pi$
$821$	3.74543	−	11.5272i	0.130716	−	0.402303i	0.994899	+	0.100874i	$0.0321640\pi$
$822$	−0.854194	+	6.29273i	−0.0297934	+	0.219484i
$823$	−11.0633	−	24.8485i	−0.385641	−	0.866164i	−0.997187	−	0.0749553i	$-0.976119\pi$
$823$	−11.0633	−	24.8485i	−0.385641	−	0.866164i	0.611546	−	0.791209i	$-0.290548\pi$
$824$	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	−0.278004	−	0.960580i	$-0.589673\pi$
$827$	20.3136	−	22.5605i	0.706373	−	0.784506i	0.984377	+	0.176074i	$0.0563396\pi$
$828$	3.76290	+	14.5088i	0.130770	+	0.504216i
$829$	−29.0086	+	39.9269i	−1.00751	+	1.38672i	−0.0869083	+	0.996216i	$0.527699\pi$
$829$	−29.0086	+	39.9269i	−1.00751	+	1.38672i	−0.920602	+	0.390502i	$0.872301\pi$
$830$	−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	−0.679083	−	0.734062i	$-0.737622\pi$
$839$	−23.0855	+	7.50095i	−0.797002	+	0.258961i	−0.117919	+	0.993023i	$0.537622\pi$
$840$	−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	0.370146	+	0.928974i	$0.379308\pi$
$853$	−13.8830	+	42.7275i	−0.475345	+	1.46296i	−0.845491	+	0.533989i	$0.820692\pi$
$854$	−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	−0.544849	−	0.838534i	$-0.683413\pi$
$857$	12.9651	−	29.1201i	0.442879	−	0.994722i	0.987727	−	0.156188i	$-0.0499205\pi$
$858$	−35.6314	−	22.0324i	−1.21644	−	0.752173i
$859$	23.3886	+	2.45824i	0.798007	+	0.0838739i	0.494751	−	0.869035i	$-0.335259\pi$
$859$	23.3886	+	2.45824i	0.798007	+	0.0838739i	0.303257	+	0.952909i	$0.401926\pi$
$860$	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	0.568165	−	0.822914i	$-0.307653\pi$
$863$	−12.5904	−	21.8072i	−0.428582	−	0.742326i	−0.996747	+	0.0805883i	$0.974320\pi$
$864$	−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	−0.700385	−	0.713765i	$-0.746989\pi$
$877$	3.94150	−	37.5009i	0.133095	−	1.26631i	0.833480	−	0.552549i	$-0.186345\pi$
$878$	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	−0.364488	−	0.931208i	$-0.618756\pi$
$881$	−9.45978	+	2.01074i	−0.318708	+	0.0677435i	0.0457800	+	0.998952i	$0.485423\pi$
$882$	10.9041	+	11.0808i	0.367161	+	0.373111i
$883$	−37.8679	−	12.3040i	−1.27436	−	0.414064i	−0.407768	−	0.913086i	$-0.633693\pi$
$883$	−37.8679	−	12.3040i	−1.27436	−	0.414064i	−0.866589	+	0.499022i	$0.833693\pi$
$884$	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	0.535171	+	0.844744i	$0.320247\pi$
$887$	−8.85496	+	41.6593i	−0.297320	+	1.39878i	−0.832491	+	0.554039i	$0.813086\pi$
$888$	−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	−0.877670	−	0.479265i	$-0.840903\pi$
$907$	−48.3277	−	35.1121i	−1.60469	−	1.16588i	−0.727023	−	0.686613i	$-0.759097\pi$
$908$	−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	−0.0650905	−	0.997879i	$-0.520734\pi$
$911$	−16.0098	−	3.40298i	−0.530428	−	0.112746i	−0.465337	+	0.885133i	$0.654067\pi$
$912$	−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	0.288951	−	0.957344i	$-0.406694\pi$
$919$	−6.94664	−	3.09284i	−0.229149	−	0.102024i	−0.518099	+	0.855320i	$0.673360\pi$
$920$	−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	0.578215	+	0.815885i	$0.303750\pi$
$937$	5.57929	+	53.0834i	0.182267	+	1.73416i	−0.395948	+	0.918273i	$0.629584\pi$
$938$	−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	−0.463107	−	0.886303i	$-0.653265\pi$
$941$	−43.9165	−	19.5529i	−1.43164	−	0.637406i	−0.968530	+	0.248897i	$0.919932\pi$
$942$	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	−0.210003	−	0.977701i	$-0.567348\pi$
$947$	11.5723	−	5.15233i	0.376050	−	0.167428i	0.586053	+	0.810272i	$0.300681\pi$
$948$	−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	0.996767	−	0.0803485i	$-0.0256033\pi$
$953$	37.9206	+	27.5509i	1.22837	+	0.892462i	0.231602	+	0.972811i	$0.425603\pi$
$954$	−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	0.923656	−	0.383222i	$-0.125186\pi$
$967$	32.7635	+	18.9160i	1.05360	+	0.608299i	0.129948	+	0.991521i	$0.458519\pi$
$968$	−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	0.979378	−	0.202035i	$-0.0647553\pi$
$971$	27.4472	+	24.7136i	0.880824	+	0.793097i	−0.0985548	+	0.995132i	$0.531422\pi$
$972$	−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	−0.374175	−	0.927358i	$-0.622074\pi$
$977$	−38.1953	−	12.4104i	−1.22198	−	0.397044i	−0.847801	+	0.530314i	$0.822074\pi$
$978$	−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	−0.907235	−	0.420624i	$-0.861811\pi$
$983$	2.12031	−	20.1734i	0.0676273	−	0.643431i	0.974863	−	0.222807i	$-0.0715220\pi$
$984$	−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	$0.370168\pi$
$991$			57.7953i			1.83593i	−0.396663	+	0.917964i	$0.629832\pi$
$992$	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	0.990533	−	0.137278i	$-0.0438354\pi$
$997$	11.8843	+	20.5842i	0.376380	+	0.651909i	−0.614153	+	0.789187i	$0.710502\pi$
$998$	−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.11.4	✓	176
3.2	odd	2	inner	930.2.br.b.11.14	yes	176
31.17	odd	30	inner	930.2.br.b.761.14	yes	176
93.17	even	30	inner	930.2.br.b.761.4	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.4	✓	176	1.1	even	1	trivial
930.2.br.b.11.14	yes	176	3.2	odd	2	inner
930.2.br.b.761.4	yes	176	93.17	even	30	inner
930.2.br.b.761.14	yes	176	31.17	odd	30	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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