LMFDB - Embedded newform 930.2.br.b.761.17

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			761.17
Character	$\chi$	$=$	930.761
Dual form			930.2.br.b.11.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(-0.358377 - 1.69457i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.182814 - 1.72238i) q^{6} +(-0.113415 + 1.07907i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.74313 + 1.21459i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(-0.358377 - 1.69457i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.182814 - 1.72238i) q^{6} +(-0.113415 + 1.07907i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.74313 + 1.21459i) q^{9} +(0.669131 + 0.743145i) q^{10} +(2.56206 - 1.14070i) q^{11} +(0.706110 - 1.58158i) q^{12} +(1.02862 - 4.83927i) q^{13} +(-0.441316 + 0.991212i) q^{14} +(0.536921 - 1.64673i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.58997 + 0.707901i) q^{17} +(-2.98420 + 0.307470i) q^{18} +(1.90535 - 0.404995i) q^{19} +(0.406737 + 0.913545i) q^{20} +(1.86921 - 0.194526i) q^{21} +(2.78916 - 0.293153i) q^{22} +(4.13404 - 3.00356i) q^{23} +(1.16029 - 1.28598i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.47369 - 4.28455i) q^{26} +(3.04128 + 4.21314i) q^{27} +(-0.726018 + 0.806325i) q^{28} +(0.677305 - 2.08453i) q^{29} +(1.01951 - 1.40021i) q^{30} +(0.859116 + 5.50108i) q^{31} +1.00000i q^{32} +(-2.85119 - 3.93279i) q^{33} +(1.29340 + 1.16458i) q^{34} +(-0.637757 + 0.877797i) q^{35} +(-2.93316 - 0.629748i) q^{36} +(2.45281 - 1.41613i) q^{37} +(1.93725 + 0.203613i) q^{38} +(-8.56910 - 0.00878069i) q^{39} +(0.104528 + 0.994522i) q^{40} +(0.267518 - 0.240874i) q^{41} +(1.83784 + 0.392613i) q^{42} +(-0.350040 - 1.64681i) q^{43} +(2.74324 + 0.583094i) q^{44} +(-2.98292 - 0.319699i) q^{45} +(4.85986 - 1.57906i) q^{46} +(-4.18402 + 1.35947i) q^{47} +(1.50089 - 0.864488i) q^{48} +(5.69550 + 1.21062i) q^{49} +(0.207912 + 0.978148i) q^{50} +(0.629778 - 2.94801i) q^{51} +(3.67662 - 3.31044i) q^{52} +(-0.556631 - 5.29599i) q^{53} +(1.59050 + 4.94675i) q^{54} +(2.78916 + 0.293153i) q^{55} +(-0.939652 + 0.542509i) q^{56} +(-1.36913 - 3.08361i) q^{57} +(1.28831 - 1.77321i) q^{58} +(-8.37326 - 7.53932i) q^{59} +(1.40230 - 1.01664i) q^{60} -2.17337i q^{61} +(-0.882860 + 5.49732i) q^{62} +(-0.999520 - 3.09779i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(3.31044 - 3.67662i) q^{65} +(-1.49634 - 4.62137i) q^{66} +(0.967850 - 1.67637i) q^{67} +(0.870221 + 1.50727i) q^{68} +(-6.57128 - 5.92901i) q^{69} +(-0.877797 + 0.637757i) q^{70} +(-9.83673 + 1.03388i) q^{71} +(-2.59500 - 1.50532i) q^{72} +(5.48528 + 12.3201i) q^{73} +(2.77037 - 0.588861i) q^{74} +(1.28835 - 1.15765i) q^{75} +(1.77951 + 0.792289i) q^{76} +(0.940326 + 2.89403i) q^{77} +(-8.14699 - 2.65635i) q^{78} +(-6.34492 + 14.2509i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(6.04954 - 6.66356i) q^{81} +(0.328859 - 0.146417i) q^{82} +(-8.96001 - 9.95110i) q^{83} +(1.62656 + 0.941320i) q^{84} +(1.02301 + 1.40805i) q^{85} +(0.175984 - 1.67438i) q^{86} +(-3.77511 - 0.400692i) q^{87} +(2.42879 + 1.40226i) q^{88} +(-5.49395 - 3.99159i) q^{89} +(-2.73813 - 1.22582i) q^{90} +(5.10526 + 1.65880i) q^{91} +5.10996 q^{92} +(9.01408 - 3.42730i) q^{93} -4.39934 q^{94} +(1.85258 + 0.601940i) q^{95} +(1.69457 - 0.358377i) q^{96} +(-5.71138 - 4.14956i) q^{97} +(5.04264 + 2.91137i) q^{98} +(-5.64259 + 6.24096i) 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
$3$	−0.358377	−	1.69457i	−0.206909	−	0.978360i
$3$	−0.358377	−	1.69457i	−0.206909	−	0.978360i
$4$	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
$6$	0.182814	−	1.72238i	0.0746333	−	0.703157i
$7$	−0.113415	+	1.07907i	−0.0428669	+	0.407851i	0.951957	+	0.306233i	$0.0990687\pi$
$7$	−0.113415	+	1.07907i	−0.0428669	+	0.407851i	−0.994823	+	0.101618i	$0.967598\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	−2.74313	+	1.21459i	−0.914377	+	0.404864i
$10$	0.669131	+	0.743145i	0.211598	+	0.235003i
$11$	2.56206	−	1.14070i	0.772491	−	0.343935i	0.0176510	−	0.999844i	$-0.494381\pi$
$11$	2.56206	−	1.14070i	0.772491	−	0.343935i	0.754840	+	0.655909i	$0.227715\pi$
$12$	0.706110	−	1.58158i	0.203836	−	0.456564i
$13$	1.02862	−	4.83927i	0.285287	−	1.34217i	−0.568986	−	0.822347i	$-0.692664\pi$
$13$	1.02862	−	4.83927i	0.285287	−	1.34217i	0.854274	−	0.519824i	$-0.174002\pi$
$14$	−0.441316	+	0.991212i	−0.117947	+	0.264913i
$15$	0.536921	−	1.64673i	0.138632	−	0.425184i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.58997	+	0.707901i	0.385625	+	0.171691i	0.590387	−	0.807121i	$-0.298975\pi$
$17$	1.58997	+	0.707901i	0.385625	+	0.171691i	−0.204762	+	0.978812i	$0.565642\pi$
$18$	−2.98420	+	0.307470i	−0.703383	+	0.0724714i
$19$	1.90535	−	0.404995i	0.437117	−	0.0929122i	0.0159036	−	0.999874i	$-0.494938\pi$
$19$	1.90535	−	0.404995i	0.437117	−	0.0929122i	0.421214	+	0.906961i	$0.361604\pi$
$20$	0.406737	+	0.913545i	0.0909491	+	0.204275i
$21$	1.86921	−	0.194526i	0.407895	−	0.0424490i
$22$	2.78916	−	0.293153i	0.594652	−	0.0625004i
$23$	4.13404	−	3.00356i	0.862007	−	0.626285i	−0.0664232	−	0.997792i	$-0.521159\pi$
$23$	4.13404	−	3.00356i	0.862007	−	0.626285i	0.928430	+	0.371507i	$0.121159\pi$
$24$	1.16029	−	1.28598i	0.236842	−	0.262499i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	2.47369	−	4.28455i	0.485130	−	0.840270i
$27$	3.04128	+	4.21314i	0.585296	+	0.810820i
$28$	−0.726018	+	0.806325i	−0.137205	+	0.152381i
$29$	0.677305	−	2.08453i	0.125772	−	0.387087i	−0.868269	−	0.496094i	$-0.834767\pi$
$29$	0.677305	−	2.08453i	0.125772	−	0.387087i	0.994041	+	0.109007i	$0.0347670\pi$
$30$	1.01951	−	1.40021i	0.186136	−	0.255643i
$31$	0.859116	+	5.50108i	0.154302	+	0.988024i
$31$	0.859116	+	5.50108i	0.154302	+	0.988024i
$32$			1.00000i			0.176777i
$33$	−2.85119	−	3.93279i	−0.496328	−	0.684611i
$34$	1.29340	+	1.16458i	0.221816	+	0.199724i
$35$	−0.637757	+	0.877797i	−0.107801	+	0.148375i
$36$	−2.93316	−	0.629748i	−0.488860	−	0.104958i
$37$	2.45281	−	1.41613i	0.403240	−	0.232811i	−0.284641	−	0.958634i	$-0.591874\pi$
$37$	2.45281	−	1.41613i	0.403240	−	0.232811i	0.687881	+	0.725824i	$0.258541\pi$
$38$	1.93725	+	0.203613i	0.314263	+	0.0330304i
$39$	−8.56910	−	0.00878069i	−1.37215	−	0.00140604i
$40$	0.104528	+	0.994522i	0.0165274	+	0.157248i
$41$	0.267518	−	0.240874i	0.0417792	−	0.0376182i	−0.647977	−	0.761660i	$-0.724385\pi$
$41$	0.267518	−	0.240874i	0.0417792	−	0.0376182i	0.689756	+	0.724042i	$0.257718\pi$
$42$	1.83784	+	0.392613i	0.283584	+	0.0605815i
$43$	−0.350040	−	1.64681i	−0.0533806	−	0.251136i	0.943364	−	0.331759i	$-0.107642\pi$
$43$	−0.350040	−	1.64681i	−0.0533806	−	0.251136i	−0.996745	+	0.0806234i	$0.974309\pi$
$44$	2.74324	+	0.583094i	0.413559	+	0.0879047i
$45$	−2.98292	−	0.319699i	−0.444667	−	0.0476579i
$46$	4.85986	−	1.57906i	0.716547	−	0.232820i
$47$	−4.18402	+	1.35947i	−0.610302	+	0.198299i	−0.597830	−	0.801623i	$-0.703970\pi$
$47$	−4.18402	+	1.35947i	−0.610302	+	0.198299i	−0.0124720	+	0.999922i	$0.503970\pi$
$48$	1.50089	−	0.864488i	0.216634	−	0.124778i
$49$	5.69550	+	1.21062i	0.813642	+	0.172945i
$50$	0.207912	+	0.978148i	0.0294032	+	0.138331i
$51$	0.629778	−	2.94801i	0.0881865	−	0.412805i
$52$	3.67662	−	3.31044i	0.509855	−	0.459076i
$53$	−0.556631	−	5.29599i	−0.0764592	−	0.727461i	−0.963850	−	0.266444i	$-0.914151\pi$
$53$	−0.556631	−	5.29599i	−0.0764592	−	0.727461i	0.887391	−	0.461017i	$-0.152515\pi$
$54$	1.59050	+	4.94675i	0.216440	+	0.673167i
$55$	2.78916	+	0.293153i	0.376091	+	0.0395287i
$56$	−0.939652	+	0.542509i	−0.125566	+	0.0724958i
$57$	−1.36913	−	3.08361i	−0.181345	−	0.408434i
$58$	1.28831	−	1.77321i	0.169163	−	0.232833i
$59$	−8.37326	−	7.53932i	−1.09011	−	0.981536i	−0.0902095	−	0.995923i	$-0.528754\pi$
$59$	−8.37326	−	7.53932i	−1.09011	−	0.981536i	−0.999897	+	0.0143869i	$0.995420\pi$
$60$	1.40230	−	1.01664i	0.181036	−	0.131247i
$61$		−	2.17337i		−	0.278271i	−0.990273	−	0.139136i	$-0.955568\pi$
$61$		−	2.17337i		−	0.278271i	0.990273	−	0.139136i	$-0.0444324\pi$
$62$	−0.882860	+	5.49732i	−0.112123	+	0.698161i
$63$	−0.999520	−	3.09779i	−0.125928	−	0.390285i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	3.31044	−	3.67662i	0.410610	−	0.456028i
$66$	−1.49634	−	4.62137i	−0.184187	−	0.568851i
$67$	0.967850	−	1.67637i	0.118242	−	0.204801i	−0.800829	−	0.598893i	$-0.795608\pi$
$67$	0.967850	−	1.67637i	0.118242	−	0.204801i	0.919071	+	0.394092i	$0.128941\pi$
$68$	0.870221	+	1.50727i	0.105530	+	0.182783i
$69$	−6.57128	−	5.92901i	−0.791089	−	0.713769i
$70$	−0.877797	+	0.637757i	−0.104917	+	0.0762265i
$71$	−9.83673	+	1.03388i	−1.16741	+	0.122699i	−0.668334	−	0.743862i	$-0.732992\pi$
$71$	−9.83673	+	1.03388i	−1.16741	+	0.122699i	−0.499072	+	0.866561i	$0.666326\pi$
$72$	−2.59500	−	1.50532i	−0.305823	−	0.177404i
$73$	5.48528	+	12.3201i	0.642004	+	1.44196i	0.882028	+	0.471197i	$0.156178\pi$
$73$	5.48528	+	12.3201i	0.642004	+	1.44196i	−0.240024	+	0.970767i	$0.577155\pi$
$74$	2.77037	−	0.588861i	0.322049	−	0.0684537i
$75$	1.28835	−	1.15765i	0.148766	−	0.133674i
$76$	1.77951	+	0.792289i	0.204124	+	0.0908818i
$77$	0.940326	+	2.89403i	0.107160	+	0.329805i
$78$	−8.14699	−	2.65635i	−0.922465	−	0.300772i
$79$	−6.34492	+	14.2509i	−0.713859	+	1.60335i	0.0811108	+	0.996705i	$0.474153\pi$
$79$	−6.34492	+	14.2509i	−0.713859	+	1.60335i	−0.794970	+	0.606649i	$0.792513\pi$
$80$	−0.207912	+	0.978148i	−0.0232452	+	0.109360i
$81$	6.04954	−	6.66356i	0.672171	−	0.740396i
$82$	0.328859	−	0.146417i	0.0363164	−	0.0161691i
$83$	−8.96001	−	9.95110i	−0.983489	−	1.09228i	−0.995727	−	0.0923505i	$-0.970562\pi$
$83$	−8.96001	−	9.95110i	−0.983489	−	1.09228i	0.0122372	−	0.999925i	$-0.496105\pi$
$84$	1.62656	+	0.941320i	0.177472	+	0.102706i
$85$	1.02301	+	1.40805i	0.110961	+	0.152724i
$86$	0.175984	−	1.67438i	0.0189768	−	0.180553i
$87$	−3.77511	−	0.400692i	−0.404734	−	0.0429586i
$88$	2.42879	+	1.40226i	0.258910	+	0.149482i
$89$	−5.49395	−	3.99159i	−0.582358	−	0.423108i	0.257216	−	0.966354i	$-0.417195\pi$
$89$	−5.49395	−	3.99159i	−0.582358	−	0.423108i	−0.839573	+	0.543246i	$0.817195\pi$
$90$	−2.73813	−	1.22582i	−0.288624	−	0.129213i
$91$	5.10526	+	1.65880i	0.535177	+	0.173889i
$92$	5.10996			0.532750
$93$	9.01408	−	3.42730i	0.934717	−	0.355394i
$94$	−4.39934			−0.453757
$95$	1.85258	+	0.601940i	0.190071	+	0.0617577i
$96$	1.69457	−	0.358377i	0.172951	−	0.0365767i
$97$	−5.71138	−	4.14956i	−0.579903	−	0.421324i	0.258786	−	0.965935i	$-0.416677\pi$
$97$	−5.71138	−	4.14956i	−0.579903	−	0.421324i	−0.838689	+	0.544611i	$0.816677\pi$
$98$	5.04264	+	2.91137i	0.509383	+	0.294093i
$99$	−5.64259	+	6.24096i	−0.567101	+	0.627240i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	2.22301	+	3.05971i	0.221198	+	0.304452i	0.905165	−	0.425060i	$-0.139747\pi$
$101$	2.22301	+	3.05971i	0.221198	+	0.304452i	−0.683968	+	0.729512i	$0.739747\pi$
$102$	1.50994	−	2.60912i	0.149506	−	0.258341i
$103$	8.12338	+	9.02192i	0.800420	+	0.888957i	0.995780	−	0.0917750i	$-0.0292541\pi$
$103$	8.12338	+	9.02192i	0.800420	+	0.888957i	−0.195360	+	0.980732i	$0.562587\pi$
$104$	4.51965	−	2.01228i	0.443189	−	0.197320i
$105$	1.71605	+	0.766141i	0.167469	+	0.0747677i
$106$	1.10716	−	5.20880i	0.107537	−	0.505923i
$107$	−0.518603	+	1.16480i	−0.0501353	+	0.112606i	−0.936876	−	0.349661i	$-0.886297\pi$
$107$	−0.518603	+	1.16480i	−0.0501353	+	0.112606i	0.886741	+	0.462266i	$0.152964\pi$
$108$	−0.0159733	+	5.19613i	−0.00153703	+	0.499998i
$109$	3.02851	+	9.32081i	0.290079	+	0.892771i	0.984830	+	0.173521i	$0.0555145\pi$
$109$	3.02851	+	9.32081i	0.290079	+	0.892771i	−0.694751	+	0.719250i	$0.744486\pi$
$110$	2.56206	+	1.14070i	0.244283	+	0.108762i
$111$	−3.27877	−	3.64895i	−0.311207	−	0.346343i
$112$	−1.06131	+	0.225588i	−0.100284	+	0.0213160i
$113$	5.22443	+	11.7343i	0.491473	+	1.10387i	0.973703	+	0.227821i	$0.0731601\pi$
$113$	5.22443	+	11.7343i	0.491473	+	1.10387i	−0.482230	+	0.876044i	$0.660173\pi$
$114$	−0.349229	−	3.35577i	−0.0327083	−	0.314297i
$115$	5.08196	−	0.534136i	0.473895	−	0.0498084i
$116$	1.77321	−	1.28831i	0.164638	−	0.119617i
$117$	3.05609	+	14.5241i	0.282536	+	1.34275i
$118$	−5.63367	−	9.75780i	−0.518621	−	0.898278i
$119$	−0.944204	+	1.63541i	−0.0865551	+	0.149918i
$120$	1.64783	−	0.533545i	0.150425	−	0.0487058i
$121$	−2.09748	+	2.32948i	−0.190680	+	0.211771i
$122$	0.671608	−	2.06700i	0.0608045	−	0.187137i
$123$	−0.504050	−	0.367004i	−0.0454487	−	0.0330916i
$124$	−2.53842	+	4.95545i	−0.227956	+	0.445012i
$125$			1.00000i			0.0894427i
$126$	0.00667084	−	3.25504i	0.000594286	−	0.289982i
$127$	2.48363	+	2.23627i	0.220387	+	0.198437i	0.771927	−	0.635711i	$-0.219293\pi$
$127$	2.48363	+	2.23627i	0.220387	+	0.198437i	−0.551540	+	0.834148i	$0.685960\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	−2.66519	+	1.18335i	−0.234656	+	0.104188i
$130$	4.28455	−	2.47369i	0.375780	−	0.216957i
$131$	−8.72067	−	0.916579i	−0.761928	−	0.0800819i	−0.284409	−	0.958703i	$-0.591797\pi$
$131$	−8.72067	−	0.916579i	−0.761928	−	0.0800819i	−0.477519	+	0.878621i	$0.658464\pi$
$132$	0.00497752	−	4.85758i	0.000433238	−	0.422798i
$133$	0.220923	+	2.10195i	0.0191565	+	0.182262i
$134$	1.43851	−	1.29524i	0.124268	−	0.111891i
$135$	0.527257	+	5.16933i	0.0453791	+	0.444905i
$136$	0.361858	+	1.70241i	0.0310291	+	0.145980i
$137$	6.54191	+	1.39053i	0.558914	+	0.118801i	0.478703	−	0.877977i	$-0.341107\pi$
$137$	6.54191	+	1.39053i	0.558914	+	0.118801i	0.0802110	+	0.996778i	$0.474441\pi$
$138$	−4.41749	−	7.66946i	−0.376042	−	0.652868i
$139$	−12.3210	+	4.00333i	−1.04505	+	0.339558i	−0.780725	−	0.624875i	$-0.785150\pi$
$139$	−12.3210	+	4.00333i	−1.04505	+	0.339558i	−0.264327	+	0.964433i	$0.585150\pi$
$140$	−1.03191	+	0.335289i	−0.0872125	+	0.0283371i
$141$	3.80317	+	6.60290i	0.320285	+	0.556065i
$142$	−9.67478	−	2.05644i	−0.811889	−	0.172572i
$143$	−2.88479	−	13.5718i	−0.241238	−	1.13494i
$144$	−2.00282	−	2.23354i	−0.166902	−	0.186129i
$145$	1.62883	−	1.46660i	0.135267	−	0.121795i
$146$	1.40968	+	13.4122i	0.116666	+	1.11000i
$147$	0.0103343	−	10.0853i	0.000852358	−	0.831819i
$148$	2.81675	+	0.296052i	0.231535	+	0.0243353i
$149$	−13.9398	+	8.04813i	−1.14199	+	0.659329i	−0.946923	−	0.321461i	$-0.895826\pi$
$149$	−13.9398	+	8.04813i	−1.14199	+	0.659329i	−0.195068	+	0.980790i	$0.562493\pi$
$150$	1.58303	−	0.702867i	0.129254	−	0.0573888i
$151$	−5.36846	+	7.38905i	−0.436879	+	0.601312i	−0.969515	−	0.245032i	$-0.921201\pi$
$151$	−5.36846	+	7.38905i	−0.436879	+	0.601312i	0.532636	+	0.846344i	$0.321201\pi$
$152$	1.44758	+	1.30341i	0.117415	+	0.105721i
$153$	−5.22131	−	0.0107005i	−0.422118	−	0.000865083i
$154$			3.04296i			0.245209i
$155$	−2.00653	+	5.19364i	−0.161168	+	0.417163i
$156$	−6.92739	−	5.04390i	−0.554635	−	0.403835i
$157$	5.24115	−	16.1306i	0.418289	−	1.28736i	−0.490986	−	0.871167i	$-0.663364\pi$
$157$	5.24115	−	16.1306i	0.418289	−	1.28736i	0.909276	−	0.416195i	$-0.136636\pi$
$158$	−10.4382	+	11.5927i	−0.830415	+	0.922269i
$159$	−8.77495	+	2.84122i	−0.695898	+	0.225323i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	2.77219	+	4.80158i	0.218480	+	0.378418i
$162$	7.81261	−	4.46802i	0.613816	−	0.351040i
$163$	−11.5080	+	8.36106i	−0.901377	+	0.654889i	−0.938819	−	0.344410i	$-0.888079\pi$
$163$	−11.5080	+	8.36106i	−0.901377	+	0.654889i	0.0374423	+	0.999299i	$0.488079\pi$
$164$	0.358009	−	0.0376282i	0.0279558	−	0.00293827i
$165$	−0.502805	−	4.83149i	−0.0391433	−	0.376131i
$166$	−5.44642	−	12.2329i	−0.422724	−	0.949454i
$167$	−9.78410	+	2.07968i	−0.757117	+	0.160930i	−0.570268	−	0.821459i	$-0.693161\pi$
$167$	−9.78410	+	2.07968i	−0.757117	+	0.160930i	−0.186849	+	0.982389i	$0.559827\pi$
$168$	1.25607	+	1.39788i	0.0969078	+	0.107849i
$169$	−10.4843	−	4.66793i	−0.806488	−	0.359072i
$170$	0.537826	+	1.65526i	0.0412494	+	0.126952i
$171$	−4.73472	+	3.42518i	−0.362073	+	0.261930i
$172$	0.684782	−	1.53804i	0.0522141	−	0.117275i
$173$	3.30095	−	15.5298i	0.250967	−	1.18071i	−0.654424	−	0.756127i	$-0.727089\pi$
$173$	3.30095	−	15.5298i	0.250967	−	1.18071i	0.905391	−	0.424578i	$-0.139578\pi$
$174$	−3.46652	−	1.54765i	−0.262796	−	0.117327i
$175$	−0.991212	+	0.441316i	−0.0749286	+	0.0333604i
$176$	1.87659	+	2.08417i	0.141454	+	0.157100i
$177$	−9.77511	+	16.8910i	−0.734743	+	1.26961i
$178$	−3.99159	−	5.49395i	−0.299182	−	0.411789i
$179$	−2.74109	+	26.0797i	−0.204878	+	1.94929i	0.0954047	+	0.995439i	$0.469585\pi$
$179$	−2.74109	+	26.0797i	−0.204878	+	1.94929i	−0.300283	+	0.953850i	$0.597081\pi$
$180$	−2.22532	−	2.01196i	−0.165865	−	0.149962i
$181$	8.18523	+	4.72575i	0.608404	+	0.351262i	0.772340	−	0.635209i	$-0.219086\pi$
$181$	8.18523	+	4.72575i	0.608404	+	0.351262i	−0.163937	+	0.986471i	$0.552419\pi$
$182$	4.34279	+	3.15522i	0.321909	+	0.233881i
$183$	−3.68292	+	0.778886i	−0.272249	+	0.0575769i
$184$	4.85986	+	1.57906i	0.358273	+	0.116410i
$185$	2.83226			0.208232
$186$	9.63199	−	0.474049i	0.706252	−	0.0347589i
$187$	4.88111			0.356942
$188$	−4.18402	−	1.35947i	−0.305151	−	0.0991495i
$189$	−4.89122	+	2.80393i	−0.355784	+	0.203956i
$190$	1.57590	+	1.14496i	0.114328	+	0.0830639i
$191$	5.63445	+	3.25305i	0.407694	+	0.235382i	0.689799	−	0.724001i	$-0.257699\pi$
$191$	5.63445	+	3.25305i	0.407694	+	0.235382i	−0.282104	+	0.959384i	$0.591032\pi$
$192$	1.72238	+	0.182814i	0.124302	+	0.0131934i
$193$	−1.15411	+	10.9807i	−0.0830749	+	0.790405i	0.871090	+	0.491123i	$0.163414\pi$
$193$	−1.15411	+	10.9807i	−0.0830749	+	0.790405i	−0.954165	+	0.299281i	$0.903253\pi$
$194$	−4.14956	−	5.71138i	−0.297921	−	0.410053i
$195$	−7.41667	−	4.29216i	−0.531119	−	0.307368i
$196$	3.89617	+	4.32714i	0.278298	+	0.309081i
$197$	19.6057	−	8.72900i	1.39685	−	0.621916i	0.436240	−	0.899830i	$-0.356310\pi$
$197$	19.6057	−	8.72900i	1.39685	−	0.621916i	0.960606	+	0.277915i	$0.0896432\pi$
$198$	−7.29498	+	4.19185i	−0.518432	+	0.297902i
$199$	−0.723398	+	3.40332i	−0.0512803	+	0.241255i	−0.996321	−	0.0856971i	$-0.972688\pi$
$199$	−0.723398	+	3.40332i	−0.0512803	+	0.241255i	0.945041	+	0.326952i	$0.106022\pi$
$200$	−0.406737	+	0.913545i	−0.0287606	+	0.0645974i
$201$	−3.18757	−	1.03932i	−0.224834	−	0.0733078i
$202$	1.16870	+	3.59690i	0.0822297	+	0.253077i
$203$	2.17254	+	0.967279i	0.152483	+	0.0678896i
$204$	2.24230	−	2.01482i	0.156992	−	0.141066i
$205$	0.352114	−	0.0748442i	0.0245927	−	0.00522734i
$206$	4.93786	+	11.0906i	0.344037	+	0.772720i
$207$	−7.69212	+	13.2603i	−0.534640	+	0.921656i
$208$	4.92028	−	0.517142i	0.341160	−	0.0358573i
$209$	4.41965	−	3.21106i	0.305713	−	0.222114i
$210$	1.39531	+	1.25893i	0.0962853	+	0.0868745i
$211$	−5.90668	−	10.2307i	−0.406633	−	0.704308i	0.587877	−	0.808950i	$-0.299964\pi$
$211$	−5.90668	−	10.2307i	−0.406633	−	0.704308i	−0.994510	+	0.104642i	$0.966630\pi$
$212$	2.66258	−	4.61173i	0.182867	−	0.316735i
$213$	5.27725	+	16.2985i	0.361591	+	1.11676i
$214$	−0.853164	+	0.947535i	−0.0583211	+	0.0647722i
$215$	0.520261	−	1.60120i	0.0354815	−	0.109201i
$216$	−1.62088	+	4.93688i	−0.110287	+	0.335912i
$217$	−6.03351	+	0.303143i	−0.409581	+	0.0205787i
$218$			9.80048i			0.663772i
$219$	18.9115	−	13.7105i	1.27792	−	0.926467i
$220$	2.08417	+	1.87659i	0.140515	+	0.126520i
$221$	5.06119	−	6.96614i	0.340453	−	0.468593i
$222$	−1.99070	−	4.48355i	−0.133607	−	0.300916i
$223$	−19.6581	+	11.3496i	−1.31640	+	0.760025i	−0.983148	−	0.182812i	$-0.941480\pi$
$223$	−19.6581	+	11.3496i	−1.31640	+	0.760025i	−0.333254	+	0.942837i	$0.608147\pi$
$224$	−1.07907	−	0.113415i	−0.0720986	−	0.00757787i
$225$	−2.42343	−	1.76833i	−0.161562	−	0.117888i
$226$	1.34264	+	12.7744i	0.0893111	+	0.849739i
$227$	11.1638	−	10.0519i	0.740969	−	0.667171i	−0.209564	−	0.977795i	$-0.567205\pi$
$227$	11.1638	−	10.0519i	0.740969	−	0.667171i	0.950533	+	0.310624i	$0.100538\pi$
$228$	0.704853	−	3.29944i	0.0466800	−	0.218511i
$229$	−4.47148	−	21.0367i	−0.295484	−	1.39014i	−0.835964	−	0.548785i	$-0.815091\pi$
$229$	−4.47148	−	21.0367i	−0.295484	−	1.39014i	0.540480	−	0.841357i	$-0.318243\pi$
$230$	4.99829	+	1.06242i	0.329578	+	0.0700539i
$231$	4.56714	−	2.63060i	0.300496	−	0.173081i
$232$	2.08453	−	0.677305i	0.136856	−	0.0444672i
$233$	−15.7270	+	5.11001i	−1.03031	+	0.334768i	−0.774913	−	0.632068i	$-0.782206\pi$
$233$	−15.7270	+	5.11001i	−1.03031	+	0.334768i	−0.255397	+	0.966836i	$0.582206\pi$
$234$	−1.58167	+	14.7576i	−0.103397	+	0.964736i
$235$	−4.30320	−	0.914673i	−0.280710	−	0.0596667i
$236$	−2.34261	−	11.0211i	−0.152491	−	0.717414i
$237$	26.4231	+	5.64470i	1.71636	+	0.366663i
$238$	−1.40336	+	1.26359i	−0.0909664	+	0.0819065i
$239$	0.171834	+	1.63489i	0.0111150	+	0.105752i	0.998673	−	0.0515046i	$-0.0164017\pi$
$239$	0.171834	+	1.63489i	0.0111150	+	0.105752i	−0.987558	+	0.157257i	$0.949735\pi$
$240$	1.73205	+	0.00177482i	0.111803	+	0.000114564i
$241$	5.82709	+	0.612452i	0.375356	+	0.0394515i	0.290328	−	0.956927i	$-0.406236\pi$
$241$	5.82709	+	0.612452i	0.375356	+	0.0394515i	0.0850275	+	0.996379i	$0.472902\pi$
$242$	−2.71467	+	1.56732i	−0.174506	+	0.100751i
$243$	−13.4599	−	7.86329i	−0.863452	−	0.504430i
$244$	1.27747	−	1.75829i	0.0817819	−	0.112563i
$245$	4.32714	+	3.89617i	0.276451	+	0.248917i
$246$	−0.365970	−	0.504801i	−0.0233334	−	0.0321849i
$247$		−	9.63708i		−	0.613193i
$248$	−3.94549	+	3.92850i	−0.250539	+	0.249460i
$249$	−13.6518	+	18.7496i	−0.865146	+	1.18821i
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−4.26731	+	4.73932i	−0.269350	+	0.299143i	−0.862612	−	0.505866i	$-0.831173\pi$
$251$	−4.26731	+	4.73932i	−0.269350	+	0.299143i	0.593262	+	0.805009i	$0.297840\pi$
$252$	1.01221	−	3.09367i	0.0637631	−	0.194883i
$253$	7.16550	−	12.4110i	0.450491	−	0.780274i
$254$	1.67103	+	2.89430i	0.104850	+	0.181605i
$255$	2.01941	−	2.23817i	0.126460	−	0.140159i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	21.3550	−	2.24450i	1.33209	−	0.140008i	0.588420	−	0.808555i	$-0.299750\pi$
$257$	21.3550	−	2.24450i	1.33209	−	0.140008i	0.743670	+	0.668547i	$0.233083\pi$
$258$	−2.90042	+	0.301841i	−0.180572	+	0.0187918i
$259$	1.24992	+	2.80737i	0.0776665	+	0.174442i
$260$	4.83927	−	1.02862i	0.300119	−	0.0637922i
$261$	0.673915	+	6.54079i	0.0417143	+	0.404864i
$262$	−8.01061	−	3.56655i	−0.494897	−	0.220342i
$263$	−6.72329	−	20.6922i	−0.414576	−	1.27593i	−0.912630	−	0.408788i	$-0.865952\pi$
$263$	−6.72329	−	20.6922i	−0.414576	−	1.27593i	0.498053	−	0.867146i	$-0.334048\pi$
$264$	1.50581	−	4.61829i	0.0926761	−	0.284236i
$265$	2.16594	−	4.86478i	0.133053	−	0.298841i
$266$	−0.439426	+	2.06734i	−0.0269430	+	0.126757i
$267$	−4.79512	+	10.7404i	−0.293456	+	0.657301i
$268$	1.76835	−	0.787320i	0.108019	−	0.0480932i
$269$	−15.0429	−	16.7068i	−0.917181	−	1.01863i	−0.999757	−	0.0220477i	$-0.992981\pi$
$269$	−15.0429	−	16.7068i	−0.917181	−	1.01863i	0.0825761	−	0.996585i	$-0.473685\pi$
$270$	−1.09596	+	5.07926i	−0.0666980	+	0.309114i
$271$	−15.5909	−	21.4591i	−0.947082	−	1.30355i	−0.952811	−	0.303563i	$-0.901824\pi$
$271$	−15.5909	−	21.4591i	−0.947082	−	1.30355i	0.00572905	−	0.999984i	$-0.498176\pi$
$272$	−0.181926	+	1.73091i	−0.0110309	+	0.104952i
$273$	0.981342	−	9.24570i	0.0593935	−	0.559575i
$274$	5.79203	+	3.34403i	0.349910	+	0.202020i
$275$	2.26891	+	1.64846i	0.136820	+	0.0994058i
$276$	−1.83129	−	8.65917i	−0.110231	−	0.521221i
$277$	16.9181	+	5.49703i	1.01651	+	0.330285i	0.769445	−	0.638713i	$-0.220533\pi$
$277$	16.9181	+	5.49703i	1.01651	+	0.330285i	0.247067	+	0.968998i	$0.420533\pi$
$278$	−12.9551			−0.776992
$279$	−9.03823	−	14.0467i	−0.541105	−	0.840955i
$280$	−1.08502			−0.0648422
$281$	0.545324	+	0.177186i	0.0325313	+	0.0105701i	0.325237	−	0.945632i	$-0.394556\pi$
$281$	0.545324	+	0.177186i	0.0325313	+	0.0105701i	−0.292706	+	0.956202i	$0.594556\pi$
$282$	1.57662	+	7.45498i	0.0938865	+	0.443938i
$283$	22.5931	+	16.4149i	1.34302	+	0.975762i	0.999327	+	0.0366809i	$0.0116785\pi$
$283$	22.5931	+	16.4149i	1.34302	+	0.975762i	0.343695	+	0.939081i	$0.388321\pi$
$284$	−8.56578	−	4.94546i	−0.508286	−	0.293459i
$285$	0.356106	−	3.35505i	0.0210939	−	0.198736i
$286$	1.45034	−	13.7990i	0.0857603	−	0.815955i
$287$	0.229580	+	0.315990i	0.0135517	+	0.0186523i
$288$	−1.21459	−	2.74313i	−0.0715704	−	0.161641i
$289$	−9.34833	−	10.3824i	−0.549902	−	0.610728i
$290$	2.00231	−	0.891487i	0.117580	−	0.0523499i
$291$	−4.98489	+	11.1654i	−0.292219	+	0.654530i
$292$	−2.80391	+	13.1914i	−0.164087	+	0.771967i
$293$	−6.04617	+	13.5799i	−0.353221	+	0.793347i	0.646320	+	0.763066i	$0.276307\pi$
$293$	−6.04617	+	13.5799i	−0.353221	+	0.793347i	−0.999541	+	0.0302813i	$0.990360\pi$
$294$	3.12635	−	9.58847i	0.182332	−	0.559211i
$295$	−3.48180	−	10.7159i	−0.202718	−	0.623902i
$296$	2.58740	+	1.15199i	0.150390	+	0.0669578i
$297$	12.5979	+	7.32514i	0.731005	+	0.425047i
$298$	−15.7445	+	3.34660i	−0.912056	+	0.193863i
$299$	−10.2827	−	23.0952i	−0.594662	−	1.33563i
$300$	1.72275	−	0.179283i	0.0994628	−	0.0103509i
$301$	1.81673	−	0.190946i	0.104714	−	0.0110059i
$302$	−7.38905	+	5.36846i	−0.425192	+	0.308920i
$303$	4.38821	−	4.86357i	0.252096	−	0.279405i
$304$	0.973959	+	1.68695i	0.0558604	+	0.0967530i
$305$	1.08668	−	1.88219i	0.0622233	−	0.107774i
$306$	−4.96246	−	1.62365i	−0.283685	−	0.0928179i
$307$	5.33919	−	5.92977i	0.304723	−	0.338430i	−0.571262	−	0.820768i	$-0.693546\pi$
$307$	5.33919	−	5.92977i	0.304723	−	0.338430i	0.875985	+	0.482338i	$0.160212\pi$
$308$	−0.940326	+	2.89403i	−0.0535801	+	0.164902i
$309$	12.3770	−	16.9989i	0.704105	−	0.967033i
$310$	−3.51324	+	4.31939i	−0.199539	+	0.245325i
$311$		−	1.63084i		−	0.0924767i	−0.998930	−	0.0462384i	$-0.985277\pi$
$311$		−	1.63084i		−	0.0924767i	0.998930	−	0.0462384i	$-0.0147234\pi$
$312$	−5.02969	−	6.93771i	−0.284750	−	0.392771i
$313$	8.87925	+	7.99491i	0.501885	+	0.451899i	0.880770	−	0.473545i	$-0.157026\pi$
$313$	8.87925	+	7.99491i	0.501885	+	0.451899i	−0.378885	+	0.925444i	$0.623692\pi$
$314$	9.96926	−	13.7215i	0.562598	−	0.774349i
$315$	0.683287	−	3.18253i	0.0384989	−	0.179315i
$316$	−13.5096	+	7.79979i	−0.759976	+	0.438772i
$317$	−15.7851	−	1.65908i	−0.886580	−	0.0931833i	−0.349719	−	0.936854i	$-0.613723\pi$
$317$	−15.7851	−	1.65908i	−0.886580	−	0.0931833i	−0.536860	+	0.843671i	$0.680390\pi$
$318$	−9.22345	−	0.00945119i	−0.517226	−	0.000529997i
$319$	−0.642534	−	6.11330i	−0.0359750	−	0.342279i
$320$	−0.743145	+	0.669131i	−0.0415431	+	0.0374055i
$321$	2.15969	+	0.461370i	0.120542	+	0.0257512i
$322$	1.15274	+	5.42323i	0.0642399	+	0.302225i
$323$	3.31615	+	0.704870i	0.184516	+	0.0392200i
$324$	8.81092	−	1.83511i	0.489496	−	0.101950i
$325$	4.70524	−	1.52882i	0.261000	−	0.0848039i
$326$	−13.5285	+	4.39567i	−0.749273	+	0.243454i
$327$	14.7094	−	8.47239i	0.813432	−	0.468524i
$328$	0.352114	+	0.0748442i	0.0194423	+	0.00413258i
$329$	−0.992436	−	4.66905i	−0.0547148	−	0.257413i
$330$	1.01482	−	4.75040i	0.0558638	−	0.261501i
$331$	−4.94172	+	4.44955i	−0.271622	+	0.244569i	−0.793673	−	0.608345i	$-0.791834\pi$
$331$	−4.94172	+	4.44955i	−0.271622	+	0.244569i	0.522051	+	0.852914i	$0.325167\pi$
$332$	−1.39969	−	13.3172i	−0.0768181	−	0.730875i
$333$	−5.00837	+	6.86380i	−0.274457	+	0.376134i
$334$	−9.94789	−	1.04557i	−0.544324	−	0.0572108i
$335$	1.67637	−	0.967850i	0.0915896	−	0.0528793i
$336$	0.762622	+	1.71761i	0.0416045	+	0.0937035i
$337$	3.31825	−	4.56717i	0.180756	−	0.248790i	−0.709018	−	0.705190i	$-0.750862\pi$
$337$	3.31825	−	4.56717i	0.180756	−	0.248790i	0.889774	+	0.456400i	$0.150862\pi$
$338$	−8.52874	−	7.67931i	−0.463902	−	0.417699i
$339$	18.0122	−	13.0584i	0.978288	−	0.709237i
$340$			1.74044i			0.0943887i
$341$	8.47622	+	13.1141i	0.459013	+	0.710170i
$342$	−5.56143	+	1.79443i	−0.300728	+	0.0970314i
$343$	−4.29932	+	13.2319i	−0.232141	+	0.714458i
$344$	1.12655	−	1.25116i	0.0607394	−	0.0674579i
$345$	−2.72639	−	8.42032i	−0.146784	−	0.453335i
$346$	7.93835	−	13.7496i	0.426768	−	0.739185i
$347$	1.02223	+	1.77056i	0.0548764	+	0.0950487i	0.892159	−	0.451722i	$-0.149190\pi$
$347$	1.02223	+	1.77056i	0.0548764	+	0.0950487i	−0.837282	+	0.546771i	$0.815857\pi$
$348$	−2.81861	−	2.54312i	−0.151093	−	0.136326i
$349$	−0.0904382	+	0.0657072i	−0.00484104	+	0.00351722i	−0.590203	−	0.807255i	$-0.700952\pi$
$349$	−0.0904382	+	0.0657072i	−0.00484104	+	0.00351722i	0.585362	+	0.810772i	$0.300952\pi$
$350$	−1.07907	+	0.113415i	−0.0576789	+	0.00606230i
$351$	23.5168	−	10.3839i	1.25524	−	0.554250i
$352$	1.14070	+	2.56206i	0.0607997	+	0.136558i
$353$	−22.5622	+	4.79575i	−1.20087	+	0.255252i	−0.764564	−	0.644548i	$-0.777046\pi$
$353$	−22.5622	+	4.79575i	−1.20087	+	0.255252i	−0.436302	+	0.899800i	$0.643712\pi$
$354$	−14.5163	+	13.0436i	−0.771532	+	0.693260i
$355$	−9.03580	−	4.02300i	−0.479571	−	0.213519i
$356$	−2.09850	−	6.45853i	−0.111220	−	0.342301i
$357$	3.10970	+	1.01393i	0.164583	+	0.0536626i
$358$	−10.6660	+	23.9562i	−0.563716	+	1.26613i
$359$	3.33381	−	15.6843i	0.175952	−	0.827787i	−0.798289	−	0.602275i	$-0.794261\pi$
$359$	3.33381	−	15.6843i	0.175952	−	0.827787i	0.974240	−	0.225512i	$-0.0724055\pi$
$360$	−1.49467	−	2.60114i	−0.0787762	−	0.137092i
$361$	−13.8910	+	6.18468i	−0.731106	+	0.325510i
$362$	6.32428	+	7.02383i	0.332397	+	0.369164i
$363$	4.69916	+	2.71949i	0.246642	+	0.142736i
$364$	3.15522	+	4.34279i	0.165379	+	0.227624i
$365$	−1.40968	+	13.4122i	−0.0737860	+	0.702027i
$366$	−3.74336	−	0.397321i	−0.195668	−	0.0207683i
$367$	7.58642	+	4.38002i	0.396008	+	0.228635i	0.684760	−	0.728769i	$-0.259907\pi$
$367$	7.58642	+	4.38002i	0.396008	+	0.228635i	−0.288752	+	0.957404i	$0.593240\pi$
$368$	4.13404	+	3.00356i	0.215502	+	0.156571i
$369$	−0.441273	+	0.985674i	−0.0229717	+	0.0513121i
$370$	2.69364	+	0.875218i	0.140036	+	0.0455004i
$371$	5.77790			0.299973
$372$	9.30706	+	2.52560i	0.482548	+	0.130946i
$373$	14.7122			0.761766			0.380883	−	0.924623i	$-0.375620\pi$
$373$	14.7122			0.761766			0.380883	+	0.924623i	$0.375620\pi$
$374$	4.64221	+	1.50835i	0.240043	+	0.0779948i
$375$	1.69457	−	0.358377i	0.0875072	−	0.0185065i
$376$	−3.55914	−	2.58586i	−0.183549	−	0.133356i
$377$	−9.39090	−	5.42184i	−0.483656	−	0.279239i
$378$	−5.51829	+	1.15523i	−0.283830	+	0.0594186i
$379$	0.414328	−	3.94207i	0.0212826	−	0.202490i	−0.978714	−	0.205231i	$-0.934206\pi$
$379$	0.414328	−	3.94207i	0.0212826	−	0.202490i	0.999996	+	0.00274017i	$0.000872223\pi$
$380$	1.14496	+	1.57590i	0.0587351	+	0.0808419i
$381$	2.89944	−	5.01011i	0.148543	−	0.256676i
$382$	4.35343	+	4.83498i	0.222741	+	0.247379i
$383$	24.8097	−	11.0460i	1.26771	−	0.564423i	0.340955	−	0.940080i	$-0.389250\pi$
$383$	24.8097	−	11.0460i	1.26771	−	0.564423i	0.926759	+	0.375657i	$0.122583\pi$
$384$	1.58158	+	0.706110i	0.0807099	+	0.0360335i
$385$	−0.632667	+	2.97646i	−0.0322437	+	0.151695i
$386$	−4.49083	+	10.0866i	−0.228577	+	0.513393i
$387$	2.96040	+	4.09226i	0.150486	+	0.208021i
$388$	−2.18155	−	6.71413i	−0.110752	−	0.340858i
$389$	8.00756	+	3.56520i	0.405999	+	0.180763i	0.599567	−	0.800324i	$-0.295339\pi$
$389$	8.00756	+	3.56520i	0.405999	+	0.180763i	−0.193568	+	0.981087i	$0.562006\pi$
$390$	−5.72733	−	6.37396i	−0.290014	−	0.322758i
$391$	8.69923	−	1.84908i	0.439939	−	0.0935119i
$392$	2.36832	+	5.31934i	0.119618	+	0.268667i
$393$	1.57208	+	15.1063i	0.0793011	+	0.762010i
$394$	21.3435	−	2.24329i	1.07527	−	0.113015i
$395$	−12.6203	+	9.16920i	−0.634997	+	0.461353i
$396$	−8.23329	+	1.73241i	−0.413738	+	0.0870570i
$397$	−14.7542	−	25.5550i	−0.740490	−	1.28257i	−0.952272	−	0.305250i	$-0.901260\pi$
$397$	−14.7542	−	25.5550i	−0.740490	−	1.28257i	0.211782	−	0.977317i	$-0.432073\pi$
$398$	−1.73968	+	3.01321i	−0.0872021	+	0.151038i
$399$	3.48272	−	1.12766i	0.174354	−	0.0564536i
$400$	−0.669131	+	0.743145i	−0.0334565	+	0.0371572i
$401$	−0.313174	+	0.963850i	−0.0156392	+	0.0481324i	−0.958572	−	0.284852i	$-0.908056\pi$
$401$	−0.313174	+	0.963850i	−0.0156392	+	0.0481324i	0.942932	+	0.332984i	$0.108056\pi$
$402$	−2.71040	−	1.97346i	−0.135182	−	0.0984275i
$403$	27.5049	+	1.50102i	1.37012	+	0.0747711i
$404$			3.78201i			0.188162i
$405$	8.57084	−	2.74605i	0.425888	−	0.136452i
$406$	1.76731	+	1.59129i	0.0877099	+	0.0789744i
$407$	4.66887	−	6.42615i	0.231427	−	0.318532i
$408$	2.75517	−	1.22330i	0.136401	−	0.0605623i
$409$	4.27001	−	2.46529i	0.211139	−	0.121901i	−0.390702	−	0.920517i	$-0.627768\pi$
$409$	4.27001	−	2.46529i	0.211139	−	0.121901i	0.601840	+	0.798616i	$0.294434\pi$
$410$	0.358009	+	0.0376282i	0.0176808	+	0.00185833i
$411$	0.0118701	−	11.5841i	0.000585508	−	0.571400i
$412$	1.26900	+	12.0737i	0.0625190	+	0.594828i
$413$	9.08513	−	8.18029i	0.447050	−	0.402526i
$414$	−11.4133	+	10.2343i	−0.560934	+	0.502989i
$415$	−2.78405	−	13.0979i	−0.136664	−	0.642951i
$416$	4.83927	+	1.02862i	0.237265	+	0.0504321i
$417$	11.1995	+	19.4441i	0.548441	+	0.952180i
$418$	5.19561	−	1.68816i	0.254126	−	0.0825704i
$419$	−23.6581	+	7.68698i	−1.15577	+	0.375533i	−0.823315	−	0.567585i	$-0.807878\pi$
$419$	−23.6581	+	7.68698i	−1.15577	+	0.375533i	−0.332458	+	0.943118i	$0.607878\pi$
$420$	0.937984	+	1.62849i	0.0457689	+	0.0794621i
$421$	14.4470	+	3.07081i	0.704104	+	0.149662i	0.546030	−	0.837765i	$-0.316138\pi$
$421$	14.4470	+	3.07081i	0.704104	+	0.149662i	0.158074	+	0.987427i	$0.449472\pi$
$422$	−2.45614	−	11.5552i	−0.119563	−	0.562499i
$423$	9.82611	−	8.81107i	0.477762	−	0.428409i
$424$	3.95737	−	3.56323i	0.192187	−	0.173046i
$425$	0.181926	+	1.73091i	0.00882469	+	0.0839613i
$426$	−0.0175546	+	17.1316i	−0.000850521	+	0.830027i
$427$	2.34522	+	0.246493i	0.113493	+	0.0119286i
$428$	−1.10421	+	0.637517i	−0.0533741	+	0.0308156i
$429$	−21.9646	+	9.75231i	−1.06046	+	0.470846i
$430$	0.989595	−	1.36206i	0.0477225	−	0.0656844i
$431$	13.4771	+	12.1349i	0.649171	+	0.584517i	0.926517	−	0.376254i	$-0.122788\pi$
$431$	13.4771	+	12.1349i	0.649171	+	0.584517i	−0.277345	+	0.960770i	$0.589455\pi$
$432$	−3.06713	+	4.19437i	−0.147567	+	0.201802i
$433$			8.16389i			0.392331i	0.980571	+	0.196166i	$0.0628490\pi$
$433$			8.16389i			0.392331i	−0.980571	+	0.196166i	$0.937151\pi$
$434$	−5.83188	−	1.57615i	−0.279939	−	0.0756576i
$435$	−3.06900	−	2.23456i	−0.147147	−	0.107139i
$436$	−3.02851	+	9.32081i	−0.145039	+	0.446386i
$437$	6.66037	−	7.39709i	0.318609	−	0.353851i
$438$	22.2227	−	7.19543i	1.06184	−	0.343811i
$439$	−2.29185	+	3.96959i	−0.109384	+	0.189458i	−0.915521	−	0.402271i	$-0.868221\pi$
$439$	−2.29185	+	3.96959i	−0.109384	+	0.189458i	0.806137	+	0.591729i	$0.201554\pi$
$440$	1.40226	+	2.42879i	0.0668503	+	0.115788i
$441$	−17.0939	+	3.59682i	−0.813995	+	0.171277i
$442$	6.96614	−	5.06119i	0.331345	−	0.240736i
$443$	−4.47518	+	0.470360i	−0.212622	+	0.0223475i	−0.210241	−	0.977650i	$-0.567425\pi$
$443$	−4.47518	+	0.470360i	−0.212622	+	0.0223475i	−0.00238159	+	0.999997i	$0.500758\pi$
$444$	−0.507778	−	4.87927i	−0.0240981	−	0.231560i
$445$	−2.76211	−	6.20379i	−0.130936	−	0.294088i
$446$	−22.2032	+	4.71943i	−1.05135	+	0.223471i
$447$	18.6338	+	20.7376i	0.881349	+	0.980857i
$448$	−0.991212	−	0.441316i	−0.0468304	−	0.0208502i
$449$	0.686178	+	2.11184i	0.0323827	+	0.0996638i	0.965941	−	0.258761i	$-0.0833141\pi$
$449$	0.686178	+	2.11184i	0.0323827	+	0.0996638i	−0.933559	+	0.358424i	$0.883314\pi$
$450$	−1.75838	−	2.43066i	−0.0828907	−	0.114582i
$451$	0.410631	−	0.922293i	0.0193359	−	0.0434291i
$452$	−2.67057	+	12.5640i	−0.125613	+	0.590963i
$453$	14.4452	+	6.44916i	0.678694	+	0.303008i
$454$	13.7236	−	6.11016i	0.644083	−	0.286764i
$455$	3.59189	+	3.98919i	0.168390	+	0.187016i
$456$	1.68994	−	2.92015i	0.0791386	−	0.136748i
$457$	−9.91273	−	13.6437i	−0.463698	−	0.638225i	0.511573	−	0.859240i	$-0.329063\pi$
$457$	−9.91273	−	13.6437i	−0.463698	−	0.638225i	−0.975270	+	0.221015i	$0.929063\pi$
$458$	2.24805	−	21.3888i	0.105045	−	0.999434i
$459$	1.85307	+	8.85171i	0.0864938	+	0.413162i
$460$	4.42535	+	2.55498i	0.206333	+	0.119126i
$461$	6.56002	+	4.76613i	0.305531	+	0.221981i	0.729976	−	0.683472i	$-0.239531\pi$
$461$	6.56002	+	4.76613i	0.305531	+	0.221981i	−0.424446	+	0.905453i	$0.639531\pi$
$462$	5.15651	−	1.09053i	0.239902	−	0.0507359i
$463$	35.9129	+	11.6688i	1.66902	+	0.542296i	0.982731	−	0.185038i	$-0.0592407\pi$
$463$	35.9129	+	11.6688i	1.66902	+	0.542296i	0.686284	+	0.727334i	$0.259241\pi$
$464$	2.19180			0.101752
$465$	9.52007	+	1.53891i	0.441483	+	0.0713654i
$466$	−16.5364			−0.766032
$467$	−15.8957	−	5.16483i	−0.735566	−	0.239000i	−0.0828070	−	0.996566i	$-0.526388\pi$
$467$	−15.8957	−	5.16483i	−0.735566	−	0.239000i	−0.652759	+	0.757566i	$0.726388\pi$
$468$	−6.06461	+	13.5466i	−0.280337	+	0.626190i
$469$	1.69915	+	1.23451i	0.0784596	+	0.0570042i
$470$	−3.80994	−	2.19967i	−0.175739	−	0.101463i
$471$	−29.2127	−	3.10065i	−1.34605	−	0.142870i
$472$	1.17776	−	11.2056i	0.0542107	−	0.515780i
$473$	−2.77535	−	3.81993i	−0.127611	−	0.175641i
$474$	23.3855	+	13.5336i	1.07413	+	0.621619i
$475$	1.30341	+	1.44758i	0.0598046	+	0.0664197i
$476$	−1.72515	+	0.768085i	−0.0790720	+	0.0352051i
$477$	7.95938	+	13.8515i	0.364435	+	0.634218i
$478$	−0.341784	+	1.60797i	−0.0156329	+	0.0735468i
$479$	7.56381	−	16.9886i	0.345599	−	0.776229i	−0.654203	−	0.756319i	$-0.726996\pi$
$479$	7.56381	−	16.9886i	0.345599	−	0.776229i	0.999802	−	0.0199093i	$-0.00633774\pi$
$480$	1.64673	+	0.536921i	0.0751625	+	0.0245070i
$481$	−4.33003	−	13.3265i	−0.197432	−	0.607635i
$482$	5.35263	+	2.38315i	0.243806	+	0.108549i
$483$	7.14312	−	6.41845i	0.325023	−	0.292050i
$484$	−3.06613	+	0.651726i	−0.139370	+	0.0296239i
$485$	−2.87142	−	6.44931i	−0.130384	−	0.292848i
$486$	−10.3712	−	11.6378i	−0.470448	−	0.527900i
$487$	1.00228	−	0.105344i	0.0454176	−	0.00477358i	−0.0817924	−	0.996649i	$-0.526064\pi$
$487$	1.00228	−	0.105344i	0.0454176	−	0.00477358i	0.127210	+	0.991876i	$0.459398\pi$
$488$	1.75829	−	1.27747i	0.0795941	−	0.0578285i
$489$	18.2926	+	16.5047i	0.827220	+	0.746369i
$490$	2.91137	+	5.04264i	0.131522	+	0.227803i
$491$	−13.0997	+	22.6894i	−0.591182	+	1.02396i	0.402892	+	0.915248i	$0.368005\pi$
$491$	−13.0997	+	22.6894i	−0.591182	+	1.02396i	−0.994074	+	0.108710i	$0.965328\pi$
$492$	−0.192066	−	0.593185i	−0.00865899	−	0.0267429i
$493$	2.55254	−	2.83488i	0.114960	−	0.127677i
$494$	2.97802	−	9.16541i	0.133988	−	0.412371i
$495$	−8.00710	+	2.58353i	−0.359892	+	0.116121i
$496$	−4.96636	+	2.51700i	−0.222996	+	0.113016i
$497$		−	10.7318i		−	0.481388i
$498$	−18.7776	+	13.6133i	−0.841442	+	0.610027i
$499$	−2.63585	−	2.37333i	−0.117997	−	0.106245i	0.608020	−	0.793922i	$-0.291964\pi$
$499$	−2.63585	−	2.37333i	−0.117997	−	0.106245i	−0.726017	+	0.687677i	$0.758631\pi$
$500$	−0.587785	+	0.809017i	−0.0262866	+	0.0361803i
$501$	7.03056	+	15.8345i	0.314102	+	0.707435i
$502$	−5.52298	+	3.18869i	−0.246503	+	0.142318i
$503$	−3.78395	−	0.397709i	−0.168718	−	0.0177330i	0.0197927	−	0.999804i	$-0.493699\pi$
$503$	−3.78395	−	0.397709i	−0.168718	−	0.0177330i	−0.188511	+	0.982071i	$0.560366\pi$
$504$	1.91866	−	2.62947i	0.0854641	−	0.117126i
$505$	0.395327	+	3.76129i	0.0175918	+	0.167375i
$506$	10.6500	−	9.58931i	0.473451	−	0.426297i
$507$	−4.15278	+	19.4393i	−0.184432	+	0.863331i
$508$	0.694852	+	3.26902i	0.0308291	+	0.145039i
$509$	−2.63097	−	0.559230i	−0.116616	−	0.0247874i	0.149234	−	0.988802i	$-0.452319\pi$
$509$	−2.63097	−	0.559230i	−0.116616	−	0.0247874i	−0.265850	+	0.964014i	$0.585653\pi$
$510$	2.61220	−	1.50459i	0.115670	−	0.0666244i
$511$	−13.9165	+	4.52173i	−0.615628	+	0.200030i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	7.50102	+	6.79581i	0.331178	+	0.300043i
$514$	21.0034	+	4.46442i	0.926422	+	0.196917i
$515$	2.52409	+	11.8749i	0.111225	+	0.523271i
$516$	−2.85173	−	0.609209i	−0.125541	−	0.0268190i
$517$	−9.16896	+	8.25577i	−0.403250	+	0.363088i
$518$	0.321222	+	3.05622i	0.0141137	+	0.134283i
$519$	−27.4992	−	0.0281782i	−1.20708	−	0.00123689i
$520$	4.92028	+	0.517142i	0.215768	+	0.0226782i
$521$	−6.74136	+	3.89213i	−0.295345	+	0.170517i	−0.640350	−	0.768084i	$-0.721211\pi$
$521$	−6.74136	+	3.89213i	−0.295345	+	0.170517i	0.345005	+	0.938601i	$0.387877\pi$
$522$	−1.38028	+	6.42891i	−0.0604133	+	0.281386i
$523$	−18.3331	+	25.2333i	−0.801650	+	1.10338i	0.190909	+	0.981608i	$0.438857\pi$
$523$	−18.3331	+	25.2333i	−0.801650	+	1.10338i	−0.992559	+	0.121768i	$0.961143\pi$
$524$	−6.51642	−	5.86741i	−0.284671	−	0.256319i
$525$	1.10307	+	1.52152i	0.0481419	+	0.0664046i
$526$		−	21.7570i		−	0.948652i
$527$	−2.52825	+	9.35474i	−0.110132	+	0.407499i
$528$	2.85924	−	3.92694i	0.124432	−	0.170898i
$529$	0.961551	−	2.95935i	0.0418066	−	0.128667i
$530$	3.56323	−	3.95737i	0.154777	−	0.171897i
$531$	32.1261	+	10.5113i	1.39416	+	0.456150i
$532$	−1.05676	+	1.83037i	−0.0458164	+	0.0793564i
$533$	−0.890480	−	1.54236i	−0.0385710	−	0.0668069i
$534$	−7.87939	+	8.73293i	−0.340974	+	0.377911i
$535$	−1.03152	+	0.749446i	−0.0445967	+	0.0324014i
$536$	1.92510	−	0.202336i	0.0831515	−	0.00873958i
$537$	45.1762	−	4.70141i	1.94950	−	0.202881i
$538$	−9.14394	−	20.5376i	−0.394223	−	0.885440i
$539$	15.9732	−	3.39520i	0.688013	−	0.146242i
$540$	−2.61190	+	4.49199i	−0.112398	+	0.193305i
$541$	−0.457481	−	0.203684i	−0.0196686	−	0.00875704i	0.396879	−	0.917871i	$-0.370093\pi$
$541$	−0.457481	−	0.203684i	−0.0196686	−	0.00875704i	−0.416547	+	0.909114i	$0.636760\pi$
$542$	−8.19664	−	25.2267i	−0.352076	−	1.08358i
$543$	5.07470	−	15.5640i	0.217776	−	0.667917i
$544$	−0.707901	+	1.58997i	−0.0303510	+	0.0681695i
$545$	−2.03763	+	9.58631i	−0.0872826	+	0.410632i
$546$	3.79039	−	8.48993i	0.162214	−	0.363335i
$547$	−18.9537	+	8.43872i	−0.810400	+	0.360814i	−0.769738	−	0.638359i	$-0.779613\pi$
$547$	−18.9537	+	8.43872i	−0.810400	+	0.360814i	−0.0406620	+	0.999173i	$0.512947\pi$
$548$	4.47519	+	4.97020i	0.191171	+	0.212316i
$549$	2.63975	+	5.96183i	0.112662	+	0.254445i
$550$	1.64846	+	2.26891i	0.0702905	+	0.0967466i
$551$	0.446279	−	4.24606i	0.0190121	−	0.180888i
$552$	0.934169	−	8.80126i	0.0397609	−	0.374607i
$553$	−14.6582	−	8.46290i	−0.623329	−	0.359879i
$554$	14.3914	+	10.4560i	0.611433	+	0.444232i
$555$	−1.01502	−	4.79947i	−0.0430852	−	0.203726i
$556$	−12.3210	−	4.00333i	−0.522526	−	0.169779i
$557$	−4.13618			−0.175256			−0.0876278	−	0.996153i	$-0.527929\pi$
$557$	−4.13618			−0.175256			−0.0876278	+	0.996153i	$0.527929\pi$
$558$	−4.25520	−	16.1522i	−0.180137	−	0.683777i
$559$	−8.32940			−0.352296
$560$	−1.03191	−	0.335289i	−0.0436063	−	0.0141685i
$561$	−1.74928	−	8.27139i	−0.0738547	−	0.349218i
$562$	0.463880	+	0.337029i	0.0195676	+	0.0142167i
$563$	17.7173	+	10.2291i	0.746695	+	0.431104i	0.824498	−	0.565864i	$-0.191457\pi$
$563$	17.7173	+	10.2291i	0.746695	+	0.431104i	−0.0778036	+	0.996969i	$0.524791\pi$
$564$	−0.804259	+	7.57731i	−0.0338654	+	0.319062i
$565$	−1.34264	+	12.7744i	−0.0564853	+	0.537422i
$566$	16.4149	+	22.5931i	0.689968	+	0.949660i
$567$	6.50436	+	7.28364i	0.273158	+	0.305884i
$568$	−6.61831	−	7.35038i	−0.277698	−	0.308415i
$569$	−1.72660	+	0.768730i	−0.0723827	+	0.0322268i	−0.442609	−	0.896715i	$-0.645947\pi$
$569$	−1.72660	+	0.768730i	−0.0723827	+	0.0322268i	0.370226	+	0.928942i	$0.379280\pi$
$570$	1.37544	−	3.08080i	0.0576110	−	0.129040i
$571$	7.23443	−	34.0353i	0.302752	−	1.42433i	−0.519139	−	0.854690i	$-0.673747\pi$
$571$	7.23443	−	34.0353i	0.302752	−	1.42433i	0.821891	−	0.569645i	$-0.192919\pi$
$572$	5.64349	−	12.6755i	0.235966	−	0.529989i
$573$	3.49326	−	10.7138i	0.145933	−	0.447575i
$574$	0.120697	+	0.371468i	0.00503781	+	0.0155048i
$575$	4.66818	+	2.07841i	0.194676	+	0.0866755i
$576$	−0.307470	−	2.98420i	−0.0128113	−	0.124342i
$577$	35.3759	−	7.51938i	1.47272	−	0.313036i	0.599503	−	0.800372i	$-0.295365\pi$
$577$	35.3759	−	7.51938i	1.47272	−	0.313036i	0.873214	+	0.487336i	$0.162031\pi$
$578$	−5.68246	−	12.7630i	−0.236359	−	0.530872i
$579$	19.0211	−	1.97949i	0.790489	−	0.0822649i
$580$	2.17980	−	0.229106i	0.0905111	−	0.00951310i
$581$	11.7542	−	8.53991i	0.487645	−	0.354295i
$582$	−8.19122	+	9.07855i	−0.339537	+	0.376318i
$583$	−7.46728	−	12.9337i	−0.309263	−	0.535660i
$584$	−6.74304	+	11.6793i	−0.279029	+	0.483292i
$585$	−4.61539	+	14.1063i	−0.190823	+	0.583223i
$586$	−9.94668	+	11.0469i	−0.410893	+	0.456343i
$587$	4.48366	−	13.7993i	0.185060	−	0.569557i	−0.814889	−	0.579617i	$-0.803202\pi$
$587$	4.48366	−	13.7993i	0.185060	−	0.569557i	0.999949	+	0.0100599i	$0.00320222\pi$
$588$	5.93634	−	8.15308i	0.244810	−	0.336227i
$589$	3.86483	+	10.1336i	0.159247	+	0.417546i
$590$		−	11.2673i		−	0.463869i
$591$	−21.8181	−	30.0949i	−0.897478	−	1.23794i
$592$	2.10478	+	1.89515i	0.0865060	+	0.0778904i
$593$	20.9768	−	28.8721i	0.861415	−	1.18564i	−0.119815	−	0.992796i	$-0.538230\pi$
$593$	20.9768	−	28.8721i	0.861415	−	1.18564i	0.981230	−	0.192840i	$-0.0617698\pi$
$594$	9.71773	+	10.8596i	0.398723	+	0.445574i
$595$	−1.63541	+	0.944204i	−0.0670453	+	0.0387086i
$596$	−16.0081	−	1.68252i	−0.655717	−	0.0689186i
$597$	6.02641	+	0.00617522i	0.246645	+	0.000252735i
$598$	−2.64257	−	25.1424i	−0.108063	−	1.02815i
$599$	25.2394	−	22.7256i	1.03125	−	0.928545i	0.0337688	−	0.999430i	$-0.489249\pi$
$599$	25.2394	−	22.7256i	1.03125	−	0.928545i	0.997484	+	0.0708851i	$0.0225824\pi$
$600$	1.69383	+	0.361849i	0.0691504	+	0.0147724i
$601$	5.94082	+	27.9493i	0.242331	+	1.14008i	0.916042	+	0.401083i	$0.131366\pi$
$601$	5.94082	+	27.9493i	0.242331	+	1.14008i	−0.673711	+	0.738995i	$0.735301\pi$
$602$	1.78682	+	0.379799i	0.0728252	+	0.0154795i
$603$	−0.618842	+	5.77403i	−0.0252012	+	0.235137i
$604$	−8.68634	+	2.82236i	−0.353442	+	0.114840i
$605$	−2.98121	+	0.968654i	−0.121203	+	0.0393814i
$606$	5.67636	−	3.26950i	0.230586	−	0.132814i
$607$	13.1165	+	2.78800i	0.532383	+	0.113161i	0.466256	−	0.884650i	$-0.345603\pi$
$607$	13.1165	+	2.78800i	0.532383	+	0.113161i	0.0661266	+	0.997811i	$0.478936\pi$
$608$	0.404995	+	1.90535i	0.0164247	+	0.0772722i
$609$	0.860530	−	4.02818i	0.0348704	−	0.163230i
$610$	1.61513	−	1.45427i	0.0653946	−	0.0588815i
$611$	2.27508	+	21.6459i	0.0920399	+	0.875701i
$612$	−4.21784	−	3.07767i	−0.170496	−	0.124407i
$613$	−26.2377	−	2.75769i	−1.05973	−	0.111382i	−0.441407	−	0.897307i	$-0.645521\pi$
$613$	−26.2377	−	2.75769i	−1.05973	−	0.111382i	−0.618322	+	0.785925i	$0.712187\pi$
$614$	6.91027	−	3.98964i	0.278876	−	0.161009i
$615$	−0.253018	−	0.569859i	−0.0102027	−	0.0229789i
$616$	−1.78861	+	2.46181i	−0.0720650	+	0.0991890i
$617$	−25.4085	−	22.8780i	−1.02291	−	0.921032i	−0.0260056	−	0.999662i	$-0.508279\pi$
$617$	−25.4085	−	22.8780i	−1.02291	−	0.921032i	−0.996904	+	0.0786300i	$0.974945\pi$
$618$	17.0242	−	12.3422i	0.684814	−	0.496475i
$619$		−	14.6854i		−	0.590258i	−0.955457	−	0.295129i	$-0.904637\pi$
$619$		−	14.6854i		−	0.590258i	0.955457	−	0.295129i	$-0.0953626\pi$
$620$	−4.67606	+	3.02233i	−0.187795	+	0.121380i
$621$	25.2272	+	8.28264i	1.01233	+	0.332371i
$622$	0.503959	−	1.55103i	0.0202069	−	0.0621905i
$623$	4.93032	−	5.47567i	0.197529	−	0.219378i
$624$	−2.63965	−	8.15242i	−0.105670	−	0.326358i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	5.97410	+	10.3474i	0.238773	+	0.413567i
$627$	−7.02527	−	6.33863i	−0.280562	−	0.253140i
$628$	13.7215	−	9.96926i	0.547548	−	0.397817i
$629$	4.90238	−	0.515261i	0.195471	−	0.0205448i
$630$	1.63330	−	2.81562i	0.0650722	−	0.112177i
$631$	−19.0814	−	42.8575i	−0.759618	−	1.70613i	−0.706680	−	0.707533i	$-0.749808\pi$
$631$	−19.0814	−	42.8575i	−0.759618	−	1.70613i	−0.0529380	−	0.998598i	$-0.516859\pi$
$632$	−15.2587	+	3.24333i	−0.606958	+	0.129013i
$633$	−15.2198	+	13.6757i	−0.604931	+	0.543561i
$634$	−14.4998	−	6.45574i	−0.575862	−	0.256390i
$635$	1.03275	+	3.17848i	0.0409835	+	0.126134i
$636$	−8.76910	−	2.85919i	−0.347718	−	0.113374i
$637$	11.7170	−	26.3168i	0.464244	−	1.04271i
$638$	1.27803	−	6.01265i	0.0505976	−	0.238043i
$639$	25.7277	−	14.7837i	1.01777	−	0.584833i
$640$	−0.913545	+	0.406737i	−0.0361111	+	0.0160777i
$641$	19.4832	+	21.6383i	0.769540	+	0.854661i	0.992761	−	0.120107i	$-0.0383237\pi$
$641$	19.4832	+	21.6383i	0.769540	+	0.854661i	−0.223221	+	0.974768i	$0.571657\pi$
$642$	1.91142	+	1.10617i	0.0754377	+	0.0436571i
$643$	−20.0333	−	27.5735i	−0.790037	−	1.08739i	−0.994103	−	0.108436i	$-0.965416\pi$
$643$	−20.0333	−	27.5735i	−0.790037	−	1.08739i	0.204066	−	0.978957i	$-0.434584\pi$
$644$	−0.579546	+	5.51402i	−0.0228373	+	0.217283i
$645$	−2.89979	−	0.307785i	−0.114179	−	0.0121190i
$646$	2.93603	+	1.69512i	0.115517	+	0.0666935i
$647$	−16.4963	−	11.9853i	−0.648537	−	0.471189i	0.214236	−	0.976782i	$-0.431274\pi$
$647$	−16.4963	−	11.9853i	−0.648537	−	0.471189i	−0.862772	+	0.505593i	$0.831274\pi$
$648$	8.94677	+	0.977435i	0.351462	+	0.0383973i
$649$	−30.0530	−	9.76480i	−1.17968	−	0.383302i
$650$	4.94738			0.194052
$651$	2.67597	+	10.1156i	0.104880	+	0.396460i
$652$	−14.2247			−0.557082
$653$	11.2157	+	3.64421i	0.438906	+	0.142609i	0.520131	−	0.854087i	$-0.325883\pi$
$653$	11.2157	+	3.64421i	0.438906	+	0.142609i	−0.0812250	+	0.996696i	$0.525883\pi$
$654$	16.6076	−	3.51227i	0.649408	−	0.137341i
$655$	−7.09403	−	5.15411i	−0.277187	−	0.201388i
$656$	0.311752	+	0.179990i	0.0121719	+	0.00702744i
$657$	−30.0108	−	27.1334i	−1.17083	−	1.05858i
$658$	0.498951	−	4.74721i	0.0194512	−	0.185065i
$659$	−11.4444	−	15.7518i	−0.445810	−	0.613604i	0.525681	−	0.850682i	$-0.323810\pi$
$659$	−11.4444	−	15.7518i	−0.445810	−	0.613604i	−0.971491	+	0.237077i	$0.923810\pi$
$660$	2.43310	−	4.20430i	0.0947083	−	0.163652i
$661$	23.5186	+	26.1201i	0.914769	+	1.01595i	0.999808	+	0.0195761i	$0.00623167\pi$
$661$	23.5186	+	26.1201i	0.914769	+	1.01595i	−0.0850395	+	0.996378i	$0.527102\pi$
$662$	−6.07484	+	2.70469i	−0.236105	+	0.105121i
$663$	−13.6184	−	6.08004i	−0.528896	−	0.236129i
$664$	2.78405	−	13.0979i	0.108042	−	0.508298i
$665$	−0.859648	+	1.93080i	−0.0333357	+	0.0748732i
$666$	−6.88427	+	4.98019i	−0.266760	+	0.192978i
$667$	−3.46100	−	10.6519i	−0.134010	−	0.412441i
$668$	−9.13791	−	4.06846i	−0.353556	−	0.157413i
$669$	26.2777	+	29.2445i	1.01595	+	1.13066i
$670$	1.89340	−	0.402455i	0.0731485	−	0.0155482i
$671$	−2.47917	−	5.56830i	−0.0957073	−	0.214962i
$672$	0.194526	+	1.86921i	0.00750399	+	0.0721063i
$673$	32.8783	−	3.45564i	1.26736	−	0.133205i	0.553119	−	0.833102i	$-0.313437\pi$
$673$	32.8783	−	3.45564i	1.26736	−	0.133205i	0.714244	+	0.699897i	$0.246771\pi$
$674$	4.56717	−	3.31825i	0.175921	−	0.127814i
$675$	−2.12805	+	4.74040i	−0.0819086	+	0.182458i
$676$	−5.73827	−	9.93898i	−0.220703	−	0.382268i
$677$	24.1819	−	41.8844i	0.929388	−	1.60975i	0.145040	−	0.989426i	$-0.453669\pi$
$677$	24.1819	−	41.8844i	0.929388	−	1.60975i	0.784348	−	0.620321i	$-0.212998\pi$
$678$	21.1659	−	6.85324i	0.812871	−	0.263197i
$679$	5.12544	−	5.69237i	0.196696	−	0.218453i
$680$	−0.537826	+	1.65526i	−0.0206247	+	0.0634762i
$681$	−21.0346	−	15.3155i	−0.806047	−	0.586890i
$682$	4.00887	+	15.0916i	0.153508	+	0.577886i
$683$			33.7863i			1.29280i	0.763000	+	0.646399i	$0.223726\pi$
$683$			33.7863i			1.29280i	−0.763000	+	0.646399i	$0.776274\pi$
$684$	−5.84374	−	0.0119761i	−0.223441	−	0.000457917i
$685$	4.97020	+	4.47519i	0.189902	+	0.170988i
$686$	−8.17779	+	11.2558i	−0.312230	+	0.429747i
$687$	−34.0456	+	15.1163i	−1.29892	+	0.576723i
$688$	1.45804	−	0.841800i	0.0555872	−	0.0320933i
$689$	−26.2013	−	2.75387i	−0.998189	−	0.104914i
$690$	0.00906924	−	8.85070i	0.000345260	−	0.336940i
$691$	3.59410	+	34.1955i	0.136726	+	1.30086i	0.820703	+	0.571356i	$0.193582\pi$
$691$	3.59410	+	34.1955i	0.136726	+	1.30086i	−0.683977	+	0.729504i	$0.739751\pi$
$692$	11.7987	−	10.6236i	0.448519	−	0.403848i
$693$	−6.09450	−	6.79658i	−0.231511	−	0.258181i
$694$	0.425069	+	1.99979i	0.0161354	+	0.0759110i
$695$	−12.6720	−	2.69351i	−0.480675	−	0.102171i
$696$	−1.89479	−	3.28965i	−0.0718218	−	0.124694i
$697$	0.595861	−	0.193607i	0.0225698	−	0.00733338i
$698$	−0.106316	+	0.0345443i	−0.00402414	+	0.00130752i
$699$	14.2955	+	24.8192i	0.540705	+	0.938748i
$700$	−1.06131	−	0.225588i	−0.0401136	−	0.00852642i
$701$	−2.72702	−	12.8296i	−0.102998	−	0.484568i	−0.999165	−	0.0408516i	$-0.986993\pi$
$701$	−2.72702	−	12.8296i	−0.102998	−	0.484568i	0.896167	−	0.443717i	$-0.146340\pi$
$702$	25.5746	−	2.60854i	0.965253	−	0.0984531i
$703$	4.09994	−	3.69160i	0.154632	−	0.139231i
$704$	0.293153	+	2.78916i	0.0110486	+	0.105121i
$705$	−0.00780802	+	7.61987i	−0.000294067	+	0.286981i
$706$	−22.9399	−	2.41108i	−0.863355	−	0.0907423i
$707$	−3.55377	+	2.05177i	−0.133653	+	0.0771648i
$708$	−17.8365	+	7.91944i	−0.670337	+	0.297631i
$709$	−19.1273	+	26.3264i	−0.718340	+	0.988710i	0.281237	+	0.959638i	$0.409255\pi$
$709$	−19.1273	+	26.3264i	−0.718340	+	0.988710i	−0.999577	+	0.0290721i	$0.990745\pi$
$710$	−7.35038	−	6.61831i	−0.275855	−	0.248381i
$711$	0.0959084	−	46.7986i	0.00359685	−	1.75509i
$712$		−	6.79090i		−	0.254500i
$713$	20.0744	+	20.1613i	0.751794	+	0.755047i
$714$	2.64418	+	1.92525i	0.0989558	+	0.0720507i
$715$	4.28763	−	13.1960i	0.160348	−	0.493501i
$716$	−17.5469	+	19.4878i	−0.655757	+	0.728292i
$717$	2.70885	−	0.877090i	0.101164	−	0.0327555i
$718$	8.01736	−	13.8865i	0.299205	−	0.518239i
$719$	7.06188	+	12.2315i	0.263364	+	0.456159i	0.967134	−	0.254269i	$-0.0818348\pi$
$719$	7.06188	+	12.2315i	0.263364	+	0.456159i	−0.703770	+	0.710428i	$0.748501\pi$
$720$	−0.617720	−	2.93571i	−0.0230211	−	0.109408i
$721$	−10.6566	+	7.74250i	−0.396874	+	0.288346i
$722$	−15.1223	+	1.58942i	−0.562794	+	0.0591521i
$723$	−1.05045	−	10.0939i	−0.0390668	−	0.375396i
$724$	3.84427	+	8.63437i	0.142871	+	0.320894i
$725$	2.14391	−	0.455702i	0.0796227	−	0.0169243i
$726$	3.62880	+	4.03851i	0.134677	+	0.149883i
$727$	−26.7278	−	11.9000i	−0.991279	−	0.441346i	−0.153970	−	0.988076i	$-0.549206\pi$
$727$	−26.7278	−	11.9000i	−0.991279	−	0.441346i	−0.837309	+	0.546730i	$0.815872\pi$
$728$	1.65880	+	5.10526i	0.0614792	+	0.189214i
$729$	−8.50118	+	25.6267i	−0.314858	+	0.949139i
$730$	−5.48528	+	12.3201i	−0.203019	+	0.455989i
$731$	0.609224	−	2.86617i	0.0225330	−	0.106009i
$732$	−3.43736	−	1.53464i	−0.127049	−	0.0567218i
$733$	−6.10586	+	2.71850i	−0.225525	+	0.100410i	−0.516389	−	0.856354i	$-0.672724\pi$
$733$	−6.10586	+	2.71850i	−0.225525	+	0.100410i	0.290864	+	0.956765i	$0.406057\pi$
$734$	5.86161	+	6.50998i	0.216356	+	0.240288i
$735$	5.05159	−	8.72894i	0.186331	−	0.321972i
$736$	3.00356	+	4.13404i	0.110713	+	0.152383i
$737$	0.567456	−	5.39898i	0.0209025	−	0.198874i
$738$	−0.724265	+	0.801070i	−0.0266606	+	0.0294878i
$739$	20.4177	+	11.7881i	0.751076	+	0.433634i	0.826082	−	0.563549i	$-0.190564\pi$
$739$	20.4177	+	11.7881i	0.751076	+	0.433634i	−0.0750067	+	0.997183i	$0.523898\pi$
$740$	2.29135	+	1.66476i	0.0842317	+	0.0611979i
$741$	−16.3307	+	3.45371i	−0.599923	+	0.126875i
$742$	5.49511	+	1.78547i	0.201732	+	0.0655466i
$743$	14.7228			0.540127			0.270064	−	0.962842i	$-0.412955\pi$
$743$	14.7228			0.540127			0.270064	+	0.962842i	$0.412955\pi$
$744$	8.07108	+	5.27803i	0.295900	+	0.193502i
$745$	−16.0963			−0.589721
$746$	13.9921	+	4.54630i	0.512287	+	0.166452i
$747$	36.6650	+	16.4144i	1.34150	+	0.600573i
$748$	3.94890	+	2.86905i	0.144386	+	0.104903i
$749$	−1.19809	−	0.691717i	−0.0437772	−	0.0252748i
$750$	1.72238	+	0.182814i	0.0628923	+	0.00667541i
$751$	4.63143	−	44.0651i	0.169003	−	1.60796i	−0.500897	−	0.865507i	$-0.666997\pi$
$751$	4.63143	−	44.0651i	0.169003	−	1.60796i	0.669901	−	0.742451i	$-0.266337\pi$
$752$	−2.58586	−	3.55914i	−0.0942968	−	0.129788i
$753$	9.56042	+	5.53278i	0.348401	+	0.201626i
$754$	−7.25584	−	8.05843i	−0.264242	−	0.293471i
$755$	−8.34374	+	3.71487i	−0.303660	+	0.135198i
$756$	−5.60519	−	0.606556i	−0.203859	−	0.0220602i
$757$	−8.60153	+	40.4670i	−0.312628	+	1.47080i	0.488636	+	0.872488i	$0.337495\pi$
$757$	−8.60153	+	40.4670i	−0.312628	+	1.47080i	−0.801264	+	0.598311i	$0.795839\pi$
$758$	1.61222	−	3.62110i	0.0585583	−	0.131524i
$759$	−23.5993	−	7.69462i	−0.856600	−	0.279297i
$760$	0.601940	+	1.85258i	0.0218346	+	0.0672001i
$761$	29.3063	+	13.0480i	1.06235	+	0.472990i	0.862092	−	0.506752i	$-0.169154\pi$
$761$	29.3063	+	13.0480i	1.06235	+	0.472990i	0.200262	+	0.979742i	$0.435821\pi$
$762$	4.30574	−	3.86893i	0.155981	−	0.140156i
$763$	−10.4013	+	2.21087i	−0.376553	+	0.0800388i
$764$	2.64627	+	5.94362i	0.0957387	+	0.215033i
$765$	−4.51644	−	2.61992i	−0.163292	−	0.0947235i
$766$	27.0088	−	2.83874i	0.975867	−	0.102568i
$767$	−45.0977	+	32.7654i	−1.62838	+	1.18309i
$768$	1.28598	+	1.16029i	0.0464037	+	0.0418682i
$769$	−26.7784	−	46.3816i	−0.965654	−	1.67256i	−0.707847	−	0.706366i	$-0.750333\pi$
$769$	−26.7784	−	46.3816i	−0.965654	−	1.67256i	−0.257807	−	0.966196i	$-0.583000\pi$
$770$	−1.52148	+	2.63528i	−0.0548303	+	0.0949689i
$771$	−11.4566	−	35.3832i	−0.412600	−	1.27430i
$772$	−7.38796	+	8.20516i	−0.265899	+	0.295310i
$773$	−6.87899	+	21.1714i	−0.247420	+	0.761481i	0.747809	+	0.663914i	$0.231106\pi$
$773$	−6.87899	+	21.1714i	−0.247420	+	0.761481i	−0.995229	+	0.0975666i	$0.968894\pi$
$774$	1.55093	+	4.80678i	0.0557472	+	0.172776i
$775$	−4.33452	+	3.49456i	−0.155701	+	0.125528i
$776$		−	7.05965i		−	0.253427i
$777$	4.30935	−	3.12418i	0.154597	−	0.112079i
$778$	6.51394	+	5.86517i	0.233536	+	0.210277i
$779$	0.412162	−	0.567293i	0.0147672	−	0.0203254i
$780$	−3.47735	−	7.83184i	−0.124509	−	0.280425i
$781$	−24.0230	+	13.8697i	−0.859609	+	0.496296i
$782$	8.84486	+	0.929632i	0.316291	+	0.0332436i
$783$	10.8423	−	3.48606i	0.387472	−	0.124582i
$784$	0.608642	+	5.79084i	0.0217372	+	0.206816i
$785$	12.6043	−	11.3489i	0.449866	−	0.405061i
$786$	−3.17295	+	14.8527i	−0.113175	+	0.529778i
$787$	−2.83663	−	13.3453i	−0.101115	−	0.475708i	−0.999345	−	0.0361828i	$-0.988480\pi$
$787$	−2.83663	−	13.3453i	−0.101115	−	0.475708i	0.898230	−	0.439525i	$-0.144853\pi$
$788$	20.9921	+	4.46201i	0.747812	+	0.158952i
$789$	−32.6548	+	18.8087i	−1.16254	+	0.669607i
$790$	−14.8361	+	4.82053i	−0.527844	+	0.171507i
$791$	−13.2546	+	4.30670i	−0.471281	+	0.153128i
$792$	−8.36567	−	0.896605i	−0.297261	−	0.0318595i
$793$	−10.5175	−	2.23556i	−0.373488	−	0.0793872i
$794$	−6.13513	−	28.8635i	−0.217727	−	1.02433i
$795$	−9.01993	−	1.92691i	−0.319904	−	0.0683404i
$796$	−2.58566	+	2.32814i	−0.0916464	+	0.0825188i
$797$	−3.50578	−	33.3553i	−0.124181	−	1.18150i	−0.862144	−	0.506663i	$-0.830879\pi$
$797$	−3.50578	−	33.3553i	−0.124181	−	1.18150i	0.737963	−	0.674841i	$-0.235788\pi$
$798$	3.66073	+	0.00375112i	0.129588	+	0.000132788i
$799$	−7.61484	−	0.800352i	−0.269394	−	0.0283144i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	19.9188	+	4.27655i	0.703795	+	0.151105i
$802$	−0.595692	+	0.819900i	−0.0210346	+	0.0289517i
$803$	28.1073	+	25.3079i	0.991884	+	0.893097i
$804$	−1.96791	−	2.71443i	−0.0694027	−	0.0957307i
$805$			5.54439i			0.195414i
$806$	25.6949	+	9.92704i	0.905064	+	0.349665i
$807$	−22.9198	+	31.4786i	−0.806816	+	1.10810i
$808$	−1.16870	+	3.59690i	−0.0411149	+	0.126539i
$809$	−21.3388	+	23.6992i	−0.750233	+	0.833218i	−0.990503	−	0.137488i	$-0.956097\pi$
$809$	−21.3388	+	23.6992i	−0.750233	+	0.833218i	0.240271	+	0.970706i	$0.422764\pi$
$810$	8.99992	+	0.0368888i	0.316225	+	0.00129614i
$811$	−13.9954	+	24.2407i	−0.491444	+	0.851206i	−0.999951	−	0.00985161i	$-0.996864\pi$
$811$	−13.9954	+	24.2407i	−0.491444	+	0.851206i	0.508507	+	0.861058i	$0.330197\pi$
$812$	1.18907	+	2.05953i	0.0417283	+	0.0722755i
$813$	−30.7765	+	34.1104i	−1.07938	+	1.19630i
$814$	6.42615	−	4.66887i	0.225236	−	0.163644i
$815$	−14.1468	+	1.48688i	−0.495539	+	0.0520833i
$816$	2.99834	−	0.312032i	0.104963	−	0.0109233i
$817$	−1.33390	−	2.99598i	−0.0466672	−	0.104816i
$818$	4.82284	−	1.02513i	0.168627	−	0.0358427i
$819$	−16.0192	+	1.65050i	−0.559755	+	0.0576730i
$820$	0.328859	+	0.146417i	0.0114842	+	0.00511311i
$821$	11.4323	+	35.1849i	0.398989	+	1.22796i	0.925811	+	0.377987i	$0.123383\pi$
$821$	11.4323	+	35.1849i	0.398989	+	1.22796i	−0.526822	+	0.849976i	$0.676617\pi$
$822$	3.59096	−	11.0134i	0.125249	−	0.384137i
$823$	14.2072	−	31.9100i	0.495233	−	1.11231i	−0.477129	−	0.878833i	$-0.658323\pi$
$823$	14.2072	−	31.9100i	0.495233	−	1.11231i	0.972362	−	0.233478i	$-0.0750108\pi$
$824$	−2.52409	+	11.8749i	−0.0879308	+	0.413682i
$825$	1.98030	−	4.43560i	0.0689453	−	0.154428i
$826$	11.1683	−	4.97246i	0.388596	−	0.173014i
$827$	15.3405	+	17.0373i	0.533440	+	0.592445i	0.948274	−	0.317452i	$-0.102827\pi$
$827$	15.3405	+	17.0373i	0.533440	+	0.592445i	−0.414834	+	0.909897i	$0.636160\pi$
$828$	−14.0173	+	6.20650i	−0.487134	+	0.215691i
$829$	24.0543	+	33.1080i	0.835442	+	1.14989i	0.986886	+	0.161421i	$0.0516078\pi$
$829$	24.0543	+	33.1080i	0.835442	+	1.14989i	−0.151444	+	0.988466i	$0.548392\pi$
$830$	1.39969	−	13.3172i	0.0485840	−	0.462246i
$831$	3.25203	−	30.6390i	0.112812	−	1.06285i
$832$	4.28455	+	2.47369i	0.148540	+	0.0857597i
$833$	8.19869	+	5.95669i	0.284068	+	0.206387i
$834$	4.64280	+	21.9532i	0.160767	+	0.760178i
$835$	−9.51312	−	3.09100i	−0.329215	−	0.106968i
$836$	5.46299			0.188941
$837$	−20.5640	+	20.3499i	−0.710797	+	0.703397i
$838$	−24.8756			−0.859313
$839$	39.7746	+	12.9236i	1.37317	+	0.446171i	0.900419	−	0.435024i	$-0.143260\pi$
$839$	39.7746	+	12.9236i	1.37317	+	0.446171i	0.472754	+	0.881195i	$0.343260\pi$
$840$	0.388846	+	1.83864i	0.0134164	+	0.0634390i
$841$	19.5750	+	14.2220i	0.674999	+	0.490416i
$842$	12.7910	+	7.38488i	0.440807	+	0.254500i
$843$	0.104823	−	0.987589i	0.00361030	−	0.0340144i
$844$	1.23483	−	11.7486i	0.0425047	−	0.404405i
$845$	−6.74574	−	9.28472i	−0.232061	−	0.319404i
$846$	12.0680	−	5.34339i	0.414905	−	0.183710i
$847$	−2.27580	−	2.52753i	−0.0781974	−	0.0868470i
$848$	4.86478	−	2.16594i	0.167057	−	0.0743787i
$849$	19.7193	−	44.1683i	0.676763	−	1.51585i
$850$	−0.361858	+	1.70241i	−0.0124116	+	0.0583921i
$851$	5.88659	−	13.2215i	0.201790	−	0.453227i
$852$	−5.31064	+	16.2877i	−0.181939	+	0.558006i
$853$	−14.0868	−	43.3547i	−0.482323	−	1.48444i	−0.835821	−	0.549003i	$-0.815008\pi$
$853$	−14.0868	−	43.3547i	−0.482323	−	1.48444i	0.353497	−	0.935436i	$-0.384992\pi$
$854$	2.15427	+	0.959142i	0.0737176	+	0.0328212i
$855$	−5.81298	+	0.598927i	−0.198800	+	0.0204829i
$856$	−1.24717	+	0.265095i	−0.0426274	+	0.00906074i
$857$	−14.5907	−	32.7713i	−0.498410	−	1.11945i	−0.971199	−	0.238271i	$-0.923419\pi$
$857$	−14.5907	−	32.7713i	−0.498410	−	1.11945i	0.472789	−	0.881176i	$-0.343247\pi$
$858$	−23.9032	+	2.48757i	−0.816042	+	0.0849241i
$859$	31.1115	−	3.26995i	1.06151	−	0.111569i	0.442356	−	0.896839i	$-0.354143\pi$
$859$	31.1115	−	3.26995i	1.06151	−	0.111569i	0.619153	+	0.785270i	$0.287476\pi$
$860$	1.36206	−	0.989595i	0.0464459	−	0.0337449i
$861$	0.453191	−	0.502283i	0.0154447	−	0.0171178i
$862$	9.06765	+	15.7056i	0.308845	+	0.534936i
$863$	−19.7831	+	34.2653i	−0.673424	+	1.16640i	0.303503	+	0.952831i	$0.401844\pi$
$863$	−19.7831	+	34.2653i	−0.673424	+	1.16640i	−0.976927	+	0.213574i	$0.931489\pi$
$864$	−4.21314	+	3.04128i	−0.143334	+	0.103467i
$865$	10.6236	−	11.7987i	0.361213	−	0.401168i
$866$	−2.52278	+	7.76432i	−0.0857275	+	0.263842i
$867$	−14.2434	+	19.5622i	−0.483732	+	0.664367i
$868$	−5.05939	−	3.30116i	−0.171727	−	0.112049i
$869$			43.7494i			1.48410i
$870$	−2.22827	−	3.07357i	−0.0755454	−	0.104204i
$871$	−7.11683	−	6.40802i	−0.241145	−	0.217128i
$872$	−5.76057	+	7.92875i	−0.195078	+	0.268501i
$873$	20.7071	+	4.44580i	0.700829	+	0.150468i
$874$	8.62022	−	4.97689i	0.291583	−	0.168346i
$875$	−1.07907	−	0.113415i	−0.0364793	−	0.00383413i
$876$	23.3586	+	0.0239353i	0.789213	+	0.000808700i
$877$	−4.18683	−	39.8350i	−0.141379	−	1.34513i	−0.803307	−	0.595566i	$-0.796928\pi$
$877$	−4.18683	−	39.8350i	−0.141379	−	1.34513i	0.661927	−	0.749568i	$-0.269739\pi$
$878$	−3.40635	+	3.06709i	−0.114959	+	0.103509i
$879$	25.1789	+	5.37892i	0.849264	+	0.181426i
$880$	0.583094	+	2.74324i	0.0196561	+	0.0924746i
$881$	−28.0145	−	5.95467i	−0.943833	−	0.200618i	−0.289803	−	0.957086i	$-0.593590\pi$
$881$	−28.0145	−	5.95467i	−0.943833	−	0.200618i	−0.654030	+	0.756469i	$0.726923\pi$
$882$	−17.3687	−	1.86152i	−0.584836	−	0.0626808i
$883$	−29.8618	+	9.70267i	−1.00493	+	0.326521i	−0.764833	−	0.644228i	$-0.777179\pi$
$883$	−29.8618	+	9.70267i	−1.00493	+	0.326521i	−0.240095	+	0.970749i	$0.577179\pi$
$884$	8.18919	−	2.66083i	0.275432	−	0.0894933i
$885$	−16.9110	+	9.74048i	−0.568457	+	0.327423i
$886$	−4.40150	−	0.935567i	−0.147871	−	0.0314310i
$887$	3.22444	+	15.1698i	0.108266	+	0.509352i	0.998544	+	0.0539354i	$0.0171765\pi$
$887$	3.22444	+	15.1698i	0.108266	+	0.509352i	−0.890278	+	0.455417i	$0.849490\pi$
$888$	1.02485	−	4.79738i	0.0343918	−	0.160989i
$889$	−2.69478	+	2.42639i	−0.0903801	+	0.0813786i
$890$	−0.709842	−	6.75370i	−0.0237940	−	0.226384i
$891$	7.89814	−	23.9732i	0.264598	−	0.803132i
$892$	−22.5748	−	2.37271i	−0.755861	−	0.0794442i
$893$	−7.42144	+	4.28477i	−0.248349	+	0.143384i
$894$	11.3135	+	25.4808i	0.378381	+	0.852207i
$895$	−15.4137	+	21.2151i	−0.515223	+	0.709144i
$896$	−0.806325	−	0.726018i	−0.0269374	−	0.0242546i
$897$	−35.4514	+	25.7015i	−1.18369	+	0.858148i
$898$			2.22052i			0.0740997i
$899$	12.0491	+	1.93506i	0.401858	+	0.0645377i
$900$	−0.921202	−	2.85506i	−0.0307067	−	0.0951688i
$901$	2.86401	−	8.81452i	0.0954141	−	0.293654i
$902$	0.675538	−	0.750260i	0.0224929	−	0.0249809i
$903$	−0.974645	−	3.01014i	−0.0324341	−	0.100171i
$904$	−6.42237	+	11.1239i	−0.213605	+	0.369974i
$905$	4.72575	+	8.18523i	0.157089	+	0.272086i
$906$	11.7453	+	10.5973i	0.390211	+	0.352072i
$907$	−33.7651	+	24.5318i	−1.12115	+	0.814564i	−0.984383	−	0.176039i	$-0.943671\pi$
$907$	−33.7651	+	24.5318i	−1.12115	+	0.814564i	−0.136768	+	0.990603i	$0.543671\pi$
$908$	14.9401	−	1.57027i	0.495805	−	0.0521112i
$909$	−9.81429	−	5.69313i	−0.325520	−	0.188829i
$910$	2.18336	+	4.90390i	0.0723776	+	0.162563i
$911$	−20.9363	+	4.45014i	−0.693649	+	0.147440i	−0.541228	−	0.840876i	$-0.682040\pi$
$911$	−20.9363	+	4.45014i	−0.693649	+	0.147440i	−0.152421	+	0.988316i	$0.548707\pi$
$912$	2.50960	−	2.25500i	0.0831012	−	0.0746706i
$913$	−34.3074	−	15.2746i	−1.13541	−	0.505516i
$914$	−5.21143	−	16.0391i	−0.172379	−	0.530527i
$915$	−3.57895	−	1.16693i	−0.118316	−	0.0385774i
$916$	8.74753	−	19.6473i	0.289027	−	0.649165i
$917$	1.97811	−	9.30628i	0.0653230	−	0.307321i
$918$	−0.972957	+	8.99111i	−0.0321124	+	0.296751i
$919$	−40.3252	+	17.9540i	−1.33021	+	0.592246i	−0.943933	−	0.330138i	$-0.892905\pi$
$919$	−40.3252	+	17.9540i	−1.33021	+	0.592246i	−0.386274	+	0.922384i	$0.626238\pi$
$920$	3.41923	+	3.79744i	0.112729	+	0.125198i
$921$	−11.9618	−	6.92253i	−0.394156	−	0.228105i
$922$	4.76613	+	6.56002i	0.156964	+	0.216043i
$923$	−5.11501	+	48.6660i	−0.168362	+	1.60186i
$924$	5.24112	+	0.556294i	0.172420	+	0.0183007i
$925$	2.45281	+	1.41613i	0.0806480	+	0.0465621i
$926$	30.5494	+	22.1954i	1.00391	+	0.729387i
$927$	−33.2414	−	14.8817i	−1.09179	−	0.488781i
$928$	2.08453	+	0.677305i	0.0684280	+	0.0222336i
$929$	32.2565			1.05830			0.529150	−	0.848528i	$-0.322511\pi$
$929$	32.2565			1.05830			0.529150	+	0.848528i	$0.322511\pi$
$930$	8.57857	+	4.40546i	0.281303	+	0.144461i
$931$	11.3422			0.371726
$932$	−15.7270	−	5.11001i	−0.515155	−	0.167384i
$933$	−2.76358	+	0.584458i	−0.0904755	+	0.0191343i
$934$	−13.5217	−	9.82409i	−0.442444	−	0.321454i
$935$	4.22717	+	2.44056i	0.138243	+	0.0798147i
$936$	−9.95391	+	11.0095i	−0.325354	+	0.359856i
$937$	−1.36887	+	13.0239i	−0.0447190	+	0.425473i	0.949143	+	0.314846i	$0.101953\pi$
$937$	−1.36887	+	13.0239i	−0.0447190	+	0.425473i	−0.993862	+	0.110628i	$0.964714\pi$
$938$	1.23451	+	1.69915i	0.0403081	+	0.0554793i
$939$	10.3658	−	17.9117i	0.338275	−	0.584526i
$940$	−2.94373	−	3.26934i	−0.0960139	−	0.106634i
$941$	45.4533	−	20.2371i	1.48174	−	0.659711i	0.502897	−	0.864346i	$-0.332268\pi$
$941$	45.4533	−	20.2371i	1.48174	−	0.659711i	0.978838	+	0.204636i	$0.0656009\pi$
$942$	−26.8248	−	11.9761i	−0.873999	−	0.390203i
$943$	0.382450	−	1.79929i	0.0124543	−	0.0585929i
$944$	4.58284	−	10.2932i	0.149159	−	0.335016i
$945$	−5.63789	−	0.0173313i	−0.183400	−	0.000563788i
$946$	−1.45909	−	4.49060i	−0.0474390	−	0.146002i
$947$	45.6791	+	20.3377i	1.48437	+	0.660885i	0.979341	−	0.202216i	$-0.0648142\pi$
$947$	45.6791	+	20.3377i	1.48437	+	0.660885i	0.505031	+	0.863101i	$0.331481\pi$
$948$	18.0588	+	20.0977i	0.586523	+	0.652744i
$949$	65.2627	−	13.8720i	2.11852	−	0.450305i
$950$	0.792289	+	1.77951i	0.0257053	+	0.0577350i
$951$	2.84560	+	27.3435i	0.0922748	+	0.886675i
$952$	−1.87806	+	0.197392i	−0.0608684	+	0.00639753i
$953$	6.79690	−	4.93824i	0.220173	−	0.159965i	−0.472231	−	0.881475i	$-0.656551\pi$
$953$	6.79690	−	4.93824i	0.220173	−	0.159965i	0.692405	+	0.721509i	$0.256551\pi$
$954$	3.28946	+	15.6332i	0.106500	+	0.506143i
$955$	3.25305	+	5.63445i	0.105266	+	0.182326i
$956$	−0.821946	+	1.42365i	−0.0265836	+	0.0460442i
$957$	−10.1291	+	3.27969i	−0.327429	+	0.106017i
$958$	12.4434	−	13.8198i	0.402027	−	0.446496i
$959$	−2.24243	+	6.90150i	−0.0724119	+	0.222861i
$960$	1.40021	+	1.01951i	0.0451917	+	0.0329045i
$961$	−29.5238	+	9.45214i	−0.952382	+	0.304908i
$962$		−	14.0123i		−	0.451774i
$963$	0.00783909	−	3.82509i	0.000252611	−	0.123262i
$964$	4.35422	+	3.92056i	0.140240	+	0.126273i
$965$	−6.48982	+	8.93247i	−0.208915	+	0.287546i
$966$	8.77692	−	3.89697i	0.282393	−	0.125383i
$967$	−29.2570	+	16.8915i	−0.940841	+	0.543195i	−0.890224	−	0.455523i	$-0.849452\pi$
$967$	−29.2570	+	16.8915i	−0.940841	+	0.543195i	−0.0506171	+	0.998718i	$0.516119\pi$
$968$	−3.11746	−	0.327658i	−0.100199	−	0.0105313i
$969$	0.00601705	−	5.87206i	0.000193295	−	0.188638i
$970$	−0.737935	−	7.02098i	−0.0236937	−	0.225430i
$971$	−33.6709	+	30.3174i	−1.08055	+	0.972931i	−0.999717	−	0.0237970i	$-0.992424\pi$
$971$	−33.6709	+	30.3174i	−1.08055	+	0.972931i	−0.0808323	+	0.996728i	$0.525758\pi$
$972$	−6.26735	−	14.2731i	−0.201025	−	0.457809i
$973$	−2.92250	−	13.7493i	−0.0936911	−	0.440782i
$974$	0.985777	+	0.209533i	0.0315863	+	0.00671388i
$975$	−4.27695	−	7.42545i	−0.136972	−	0.237805i
$976$	2.06700	−	0.671608i	0.0661629	−	0.0214976i
$977$	−27.3012	+	8.87071i	−0.873444	+	0.283799i	−0.711232	−	0.702957i	$-0.751863\pi$
$977$	−27.3012	+	8.87071i	−0.873444	+	0.283799i	−0.162211	+	0.986756i	$0.551863\pi$
$978$	12.2971	+	21.3496i	0.393217	+	0.682686i
$979$	−18.6291	−	3.95973i	−0.595388	−	0.126554i
$980$	1.21062	+	5.69550i	0.0386717	+	0.181936i
$981$	−19.6286	−	21.8898i	−0.626692	−	0.698887i
$982$	−19.4700	+	17.5308i	−0.621312	+	0.559432i
$983$	−6.42601	−	61.1394i	−0.204958	−	1.95004i	−0.298451	−	0.954425i	$-0.596470\pi$
$983$	−6.42601	−	61.1394i	−0.204958	−	1.95004i	0.0934931	−	0.995620i	$-0.470197\pi$
$984$	0.000638900	−	0.623504i	2.03674e−5	−	0.0198766i
$985$	21.3435	+	2.24329i	0.680061	+	0.0714773i
$986$	3.30363	−	1.90735i	0.105209	−	0.0607425i
$987$	−7.55636	+	3.35503i	−0.240521	+	0.106792i
$988$	5.66454	−	7.79656i	0.180213	−	0.248042i
$989$	−6.39336	−	5.75661i	−0.203297	−	0.183050i
$990$	−8.41356	−	0.0172426i	−0.267401	−	0.000548007i
$991$		−	11.6788i		−	0.370990i	−0.982645	−	0.185495i	$-0.940611\pi$
$991$		−	11.6788i		−	0.370990i	0.982645	−	0.185495i	$-0.0593889\pi$
$992$	−5.50108	+	0.859116i	−0.174660	+	0.0272770i
$993$	9.31107	+	6.77948i	0.295478	+	0.215140i
$994$	3.31631	−	10.2066i	0.105187	−	0.323732i
$995$	−2.32814	+	2.58566i	−0.0738071	+	0.0819710i
$996$	−22.0653	+	7.14445i	−0.699165	+	0.226381i
$997$	−22.1905	+	38.4350i	−0.702779	+	1.21725i	0.264708	+	0.964329i	$0.414724\pi$
$997$	−22.1905	+	38.4350i	−0.702779	+	1.21725i	−0.967487	+	0.252921i	$0.918609\pi$
$998$	−1.77344	−	3.07169i	−0.0561373	−	0.0972326i
$999$	13.4261	+	6.02719i	0.424782	+	0.190692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.761.17	yes	176
3.2	odd	2	inner	930.2.br.b.761.1	yes	176
31.11	odd	30	inner	930.2.br.b.11.1	✓	176
93.11	even	30	inner	930.2.br.b.11.17	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.1	✓	176	31.11	odd	30	inner
930.2.br.b.11.17	yes	176	93.11	even	30	inner
930.2.br.b.761.1	yes	176	3.2	odd	2	inner
930.2.br.b.761.17	yes	176	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.358377 - 1.69457i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.182814 - 1.72238i) q^{6} +(-0.113415 + 1.07907i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.74313 + 1.21459i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.358377 - 1.69457i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(0.182814 - 1.72238i) q^{6} +(-0.113415 + 1.07907i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.74313 + 1.21459i) q^{9} +(0.669131 + 0.743145i) q^{10} +(2.56206 - 1.14070i) q^{11} +(0.706110 - 1.58158i) q^{12} +(1.02862 - 4.83927i) q^{13} +(-0.441316 + 0.991212i) q^{14} +(0.536921 - 1.64673i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.58997 + 0.707901i) q^{17} +(-2.98420 + 0.307470i) q^{18} +(1.90535 - 0.404995i) q^{19} +(0.406737 + 0.913545i) q^{20} +(1.86921 - 0.194526i) q^{21} +(2.78916 - 0.293153i) q^{22} +(4.13404 - 3.00356i) q^{23} +(1.16029 - 1.28598i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.47369 - 4.28455i) q^{26} +(3.04128 + 4.21314i) q^{27} +(-0.726018 + 0.806325i) q^{28} +(0.677305 - 2.08453i) q^{29} +(1.01951 - 1.40021i) q^{30} +(0.859116 + 5.50108i) q^{31} +1.00000i q^{32} +(-2.85119 - 3.93279i) q^{33} +(1.29340 + 1.16458i) q^{34} +(-0.637757 + 0.877797i) q^{35} +(-2.93316 - 0.629748i) q^{36} +(2.45281 - 1.41613i) q^{37} +(1.93725 + 0.203613i) q^{38} +(-8.56910 - 0.00878069i) q^{39} +(0.104528 + 0.994522i) q^{40} +(0.267518 - 0.240874i) q^{41} +(1.83784 + 0.392613i) q^{42} +(-0.350040 - 1.64681i) q^{43} +(2.74324 + 0.583094i) q^{44} +(-2.98292 - 0.319699i) q^{45} +(4.85986 - 1.57906i) q^{46} +(-4.18402 + 1.35947i) q^{47} +(1.50089 - 0.864488i) q^{48} +(5.69550 + 1.21062i) q^{49} +(0.207912 + 0.978148i) q^{50} +(0.629778 - 2.94801i) q^{51} +(3.67662 - 3.31044i) q^{52} +(-0.556631 - 5.29599i) q^{53} +(1.59050 + 4.94675i) q^{54} +(2.78916 + 0.293153i) q^{55} +(-0.939652 + 0.542509i) q^{56} +(-1.36913 - 3.08361i) q^{57} +(1.28831 - 1.77321i) q^{58} +(-8.37326 - 7.53932i) q^{59} +(1.40230 - 1.01664i) q^{60} -2.17337i q^{61} +(-0.882860 + 5.49732i) q^{62} +(-0.999520 - 3.09779i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(3.31044 - 3.67662i) q^{65} +(-1.49634 - 4.62137i) q^{66} +(0.967850 - 1.67637i) q^{67} +(0.870221 + 1.50727i) q^{68} +(-6.57128 - 5.92901i) q^{69} +(-0.877797 + 0.637757i) q^{70} +(-9.83673 + 1.03388i) q^{71} +(-2.59500 - 1.50532i) q^{72} +(5.48528 + 12.3201i) q^{73} +(2.77037 - 0.588861i) q^{74} +(1.28835 - 1.15765i) q^{75} +(1.77951 + 0.792289i) q^{76} +(0.940326 + 2.89403i) q^{77} +(-8.14699 - 2.65635i) q^{78} +(-6.34492 + 14.2509i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(6.04954 - 6.66356i) q^{81} +(0.328859 - 0.146417i) q^{82} +(-8.96001 - 9.95110i) q^{83} +(1.62656 + 0.941320i) q^{84} +(1.02301 + 1.40805i) q^{85} +(0.175984 - 1.67438i) q^{86} +(-3.77511 - 0.400692i) q^{87} +(2.42879 + 1.40226i) q^{88} +(-5.49395 - 3.99159i) q^{89} +(-2.73813 - 1.22582i) q^{90} +(5.10526 + 1.65880i) q^{91} +5.10996 q^{92} +(9.01408 - 3.42730i) q^{93} -4.39934 q^{94} +(1.85258 + 0.601940i) q^{95} +(1.69457 - 0.358377i) q^{96} +(-5.71138 - 4.14956i) q^{97} +(5.04264 + 2.91137i) q^{98} +(-5.64259 + 6.24096i) 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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