LMFDB - Embedded newform 930.2.bn.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(19,930)]

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([0, 15, 4]))

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

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

chi := DirichletCharacter("930.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bn (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:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	930.19
Dual form			930.2.bn.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.39553 + 1.74714i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.99915 + 1.80004i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.39553 + 1.74714i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.99915 + 1.80004i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(-0.593198 - 2.15595i) q^{10} +(2.18694 + 0.464849i) q^{11} +(0.994522 + 0.104528i) q^{12} +(6.18846 - 0.650433i) q^{13} +(-2.63134 + 0.559308i) q^{14} +(-1.02848 - 1.98550i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.966552 + 4.54727i) q^{17} +(0.994522 - 0.104528i) q^{18} +(0.107482 - 1.02262i) q^{19} +(2.09287 + 0.787328i) q^{20} +(-2.45755 + 1.09417i) q^{21} +(-1.66152 + 1.49604i) q^{22} +(5.07160 + 1.64786i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-1.10501 - 4.87637i) q^{25} +(-3.11127 + 5.38888i) q^{26} +(0.951057 - 0.309017i) q^{27} +(1.09417 - 2.45755i) q^{28} +(-1.01677 - 0.738726i) q^{29} +(2.21083 + 0.334990i) q^{30} +(-2.26830 + 5.08476i) q^{31} -1.00000i q^{32} +(-1.31417 + 1.80880i) q^{33} +(-4.24695 - 1.89086i) q^{34} +(-5.93480 + 0.980792i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.21386 - 2.43287i) q^{37} +(0.764144 + 0.688039i) q^{38} +(-1.92287 + 5.91799i) q^{39} +(-1.86712 + 1.23039i) q^{40} +(-4.73221 + 2.10691i) q^{41} +(0.559308 - 2.63134i) q^{42} +(-4.16692 - 0.437961i) q^{43} +(-0.233705 - 2.22355i) q^{44} +(2.23217 - 0.131988i) q^{45} +(-4.31416 + 3.13442i) q^{46} +(-1.08223 - 1.48956i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(0.0247479 + 0.235460i) q^{49} +(4.59457 + 1.97228i) q^{50} +(-4.54727 - 0.966552i) q^{51} +(-2.53094 - 5.68458i) q^{52} +(-8.11750 + 7.30903i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-3.86410 + 3.17219i) q^{55} +(1.34506 + 2.32971i) q^{56} +(0.890497 + 0.514129i) q^{57} +(1.19528 - 0.388371i) q^{58} +(-4.91747 - 2.18940i) q^{59} +(-1.57051 + 1.59170i) q^{60} +7.29862 q^{61} +(-2.78039 - 4.82384i) q^{62} -2.69012i q^{63} +(0.809017 + 0.587785i) q^{64} +(-7.49976 + 11.7198i) q^{65} +(-0.690901 - 2.12637i) q^{66} +(2.45697 + 1.41853i) q^{67} +(4.02603 - 2.32443i) q^{68} +(-3.56821 + 3.96289i) q^{69} +(2.69491 - 5.37785i) q^{70} +(0.744274 + 0.826600i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(-0.265023 + 1.24683i) q^{73} +(-0.508609 + 4.83909i) q^{74} +(4.90423 + 0.973919i) q^{75} +(-1.00579 + 0.213787i) q^{76} +(3.53528 + 4.86590i) q^{77} +(-3.65752 - 5.03414i) q^{78} +(1.42766 - 0.303459i) q^{79} +(0.102060 - 2.23374i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(1.07699 - 5.06685i) q^{82} +(2.99758 + 6.73268i) q^{83} +(1.80004 + 1.99915i) q^{84} +(-9.29358 - 4.65713i) q^{85} +(2.80357 - 3.11368i) q^{86} +(1.08842 - 0.628398i) q^{87} +(1.93626 + 1.11790i) q^{88} +(-3.33425 - 10.2618i) q^{89} +(-1.20526 + 1.88344i) q^{90} +(13.5425 + 9.83918i) q^{91} -5.33260i q^{92} +(-3.72256 - 4.14035i) q^{93} +1.84120 q^{94} +(1.63668 + 1.61489i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-16.5749 + 5.38551i) q^{97} +(-0.205038 - 0.118379i) q^{98} +(-1.11790 - 1.93626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{15}\right)$

Coefficient data

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

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

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

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−1.39553	+	1.74714i	−0.624098	+	0.781346i
$5$	−1.39553	+	1.74714i	−0.624098	+	0.781346i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	1.99915	+	1.80004i	0.755608	+	0.680352i	0.954012	−	0.299768i	$-0.0969092\pi$
$7$	1.99915	+	1.80004i	0.755608	+	0.680352i	−0.198404	+	0.980120i	$0.563576\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	−0.669131	−	0.743145i	−0.223044	−	0.247715i
$10$	−0.593198	−	2.15595i	−0.187586	−	0.681771i
$11$	2.18694	+	0.464849i	0.659389	+	0.140157i	0.525440	−	0.850831i	$-0.323901\pi$
$11$	2.18694	+	0.464849i	0.659389	+	0.140157i	0.133949	+	0.990988i	$0.457234\pi$
$12$	0.994522	+	0.104528i	0.287094	+	0.0301748i
$13$	6.18846	−	0.650433i	1.71637	−	0.180398i	0.805361	−	0.592785i	$-0.201972\pi$
$13$	6.18846	−	0.650433i	1.71637	−	0.180398i	0.911008	+	0.412388i	$0.135305\pi$
$14$	−2.63134	+	0.559308i	−0.703254	+	0.149481i
$15$	−1.02848	−	1.98550i	−0.265553	−	0.512655i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.966552	+	4.54727i	0.234423	+	1.10288i	0.925104	+	0.379715i	$0.123978\pi$
$17$	0.966552	+	4.54727i	0.234423	+	1.10288i	−0.690680	+	0.723160i	$0.742689\pi$
$18$	0.994522	−	0.104528i	0.234411	−	0.0246376i
$19$	0.107482	−	1.02262i	0.0246581	−	0.234606i	−0.975251	−	0.221102i	$-0.929035\pi$
$19$	0.107482	−	1.02262i	0.0246581	−	0.234606i	0.999909	−	0.0135043i	$-0.00429868\pi$
$20$	2.09287	+	0.787328i	0.467980	+	0.176052i
$21$	−2.45755	+	1.09417i	−0.536281	+	0.238768i
$22$	−1.66152	+	1.49604i	−0.354238	+	0.318958i
$23$	5.07160	+	1.64786i	1.05750	+	0.343603i	0.785609	−	0.618724i	$-0.212350\pi$
$23$	5.07160	+	1.64786i	1.05750	+	0.343603i	0.271894	+	0.962327i	$0.412350\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	−1.10501	−	4.87637i	−0.221002	−	0.975273i
$26$	−3.11127	+	5.38888i	−0.610171	+	1.05685i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	1.09417	−	2.45755i	0.206779	−	0.464433i
$29$	−1.01677	−	0.738726i	−0.188809	−	0.137178i	0.489365	−	0.872079i	$-0.337229\pi$
$29$	−1.01677	−	0.738726i	−0.188809	−	0.137178i	−0.678174	+	0.734901i	$0.737229\pi$
$30$	2.21083	+	0.334990i	0.403641	+	0.0611606i
$31$	−2.26830	+	5.08476i	−0.407398	+	0.913251i
$31$	−2.26830	+	5.08476i	−0.407398	+	0.913251i
$32$		−	1.00000i		−	0.176777i
$33$	−1.31417	+	1.80880i	−0.228768	+	0.314872i
$34$	−4.24695	−	1.89086i	−0.728345	−	0.324280i
$35$	−5.93480	+	0.980792i	−1.00316	+	0.165784i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	4.21386	−	2.43287i	0.692754	−	0.399962i	−0.111889	−	0.993721i	$-0.535690\pi$
$37$	4.21386	−	2.43287i	0.692754	−	0.399962i	0.804643	+	0.593759i	$0.202357\pi$
$38$	0.764144	+	0.688039i	0.123961	+	0.111615i
$39$	−1.92287	+	5.91799i	−0.307906	+	0.947637i
$40$	−1.86712	+	1.23039i	−0.295218	+	0.194542i
$41$	−4.73221	+	2.10691i	−0.739047	+	0.329045i	−0.741501	−	0.670952i	$-0.765886\pi$
$41$	−4.73221	+	2.10691i	−0.739047	+	0.329045i	0.00245395	+	0.999997i	$0.499219\pi$
$42$	0.559308	−	2.63134i	0.0863031	−	0.406024i
$43$	−4.16692	−	0.437961i	−0.635449	−	0.0667884i	−0.218674	−	0.975798i	$-0.570173\pi$
$43$	−4.16692	−	0.437961i	−0.635449	−	0.0667884i	−0.416775	+	0.909010i	$0.636840\pi$
$44$	−0.233705	−	2.22355i	−0.0352323	−	0.335213i
$45$	2.23217	−	0.131988i	0.332752	−	0.0196756i
$46$	−4.31416	+	3.13442i	−0.636089	+	0.462146i
$47$	−1.08223	−	1.48956i	−0.157859	−	0.217275i	0.722760	−	0.691099i	$-0.242873\pi$
$47$	−1.08223	−	1.48956i	−0.157859	−	0.217275i	−0.880619	+	0.473824i	$0.842873\pi$
$48$	−0.207912	−	0.978148i	−0.0300095	−	0.141183i
$49$	0.0247479	+	0.235460i	0.00353541	+	0.0336372i
$50$	4.59457	+	1.97228i	0.649771	+	0.278923i
$51$	−4.54727	−	0.966552i	−0.636745	−	0.135344i
$52$	−2.53094	−	5.68458i	−0.350978	−	0.788309i
$53$	−8.11750	+	7.30903i	−1.11502	+	1.00397i	−0.115080	+	0.993356i	$0.536713\pi$
$53$	−8.11750	+	7.30903i	−1.11502	+	1.00397i	−0.999944	+	0.0106161i	$0.996621\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	−3.86410	+	3.17219i	−0.521035	+	0.427738i
$56$	1.34506	+	2.32971i	0.179741	+	0.311321i
$57$	0.890497	+	0.514129i	0.117949	+	0.0680980i
$58$	1.19528	−	0.388371i	0.156948	−	0.0509956i
$59$	−4.91747	−	2.18940i	−0.640200	−	0.285035i	0.0608508	−	0.998147i	$-0.480619\pi$
$59$	−4.91747	−	2.18940i	−0.640200	−	0.285035i	−0.701051	+	0.713112i	$0.747285\pi$
$60$	−1.57051	+	1.59170i	−0.202752	+	0.205487i
$61$	7.29862			0.934493			0.467247	−	0.884127i	$-0.345246\pi$
$61$	7.29862			0.934493			0.467247	+	0.884127i	$0.345246\pi$
$62$	−2.78039	−	4.82384i	−0.353110	−	0.612628i
$63$		−	2.69012i		−	0.338924i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−7.49976	+	11.7198i	−0.930230	+	1.45366i
$66$	−0.690901	−	2.12637i	−0.0850440	−	0.261739i
$67$	2.45697	+	1.41853i	0.300167	+	0.173301i	0.642518	−	0.766271i	$-0.277890\pi$
$67$	2.45697	+	1.41853i	0.300167	+	0.173301i	−0.342351	+	0.939572i	$0.611223\pi$
$68$	4.02603	−	2.32443i	0.488228	−	0.281879i
$69$	−3.56821	+	3.96289i	−0.429562	+	0.477076i
$70$	2.69491	−	5.37785i	0.322103	−	0.642776i
$71$	0.744274	+	0.826600i	0.0883291	+	0.0980994i	0.785689	−	0.618622i	$-0.212309\pi$
$71$	0.744274	+	0.826600i	0.0883291	+	0.0980994i	−0.697360	+	0.716721i	$0.745642\pi$
$72$	−0.406737	−	0.913545i	−0.0479344	−	0.107662i
$73$	−0.265023	+	1.24683i	−0.0310186	+	0.145931i	−0.990932	−	0.134367i	$-0.957100\pi$
$73$	−0.265023	+	1.24683i	−0.0310186	+	0.145931i	0.959913	+	0.280298i	$0.0904332\pi$
$74$	−0.508609	+	4.83909i	−0.0591246	+	0.562533i
$75$	4.90423	+	0.973919i	0.566292	+	0.112458i
$76$	−1.00579	+	0.213787i	−0.115372	+	0.0245230i
$77$	3.53528	+	4.86590i	0.402883	+	0.554521i
$78$	−3.65752	−	5.03414i	−0.414133	−	0.570005i
$79$	1.42766	−	0.303459i	0.160625	−	0.0341418i	−0.126897	−	0.991916i	$-0.540502\pi$
$79$	1.42766	−	0.303459i	0.160625	−	0.0341418i	0.287522	+	0.957774i	$0.407169\pi$
$80$	0.102060	−	2.23374i	0.0114107	−	0.249739i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	1.07699	−	5.06685i	0.118934	−	0.559540i
$83$	2.99758	+	6.73268i	0.329027	+	0.739008i	0.999997	−	0.00247722i	$-0.000788525\pi$
$83$	2.99758	+	6.73268i	0.329027	+	0.739008i	−0.670969	+	0.741485i	$0.734122\pi$
$84$	1.80004	+	1.99915i	0.196401	+	0.218125i
$85$	−9.29358	−	4.65713i	−1.00803	−	0.505137i
$86$	2.80357	−	3.11368i	0.302317	−	0.335757i
$87$	1.08842	−	0.628398i	0.116691	−	0.0673713i
$88$	1.93626	+	1.11790i	0.206406	+	0.119169i
$89$	−3.33425	−	10.2618i	−0.353430	−	1.08775i	−0.956914	−	0.290371i	$-0.906221\pi$
$89$	−3.33425	−	10.2618i	−0.353430	−	1.08775i	0.603484	−	0.797375i	$-0.293779\pi$
$90$	−1.20526	+	1.88344i	−0.127045	+	0.198532i
$91$	13.5425	+	9.83918i	1.41964	+	1.03143i
$92$		−	5.33260i		−	0.555962i
$93$	−3.72256	−	4.14035i	−0.386012	−	0.429335i
$94$	1.84120			0.189905
$95$	1.63668	+	1.61489i	0.167919	+	0.165684i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	−16.5749	+	5.38551i	−1.68293	+	0.546816i	−0.985476	−	0.169817i	$-0.945682\pi$
$97$	−16.5749	+	5.38551i	−1.68293	+	0.546816i	−0.697450	+	0.716633i	$0.745682\pi$
$98$	−0.205038	−	0.118379i	−0.0207120	−	0.0119581i
$99$	−1.11790	−	1.93626i	−0.112353	−	0.194602i
$100$	−4.29623	+	2.55781i	−0.429623	+	0.255781i
$101$	−3.66526	+	11.2805i	−0.364707	+	1.12245i	0.585458	+	0.810703i	$0.300915\pi$
$101$	−3.66526	+	11.2805i	−0.364707	+	1.12245i	−0.950164	+	0.311749i	$0.899085\pi$
$102$	3.45478	−	3.11069i	0.342074	−	0.308005i
$103$	−5.37430	−	12.0709i	−0.529546	−	1.18938i	−0.958249	−	0.285934i	$-0.907696\pi$
$103$	−5.37430	−	12.0709i	−0.529546	−	1.18938i	0.428703	−	0.903445i	$-0.358971\pi$
$104$	6.08657	+	1.29374i	0.596837	+	0.126862i
$105$	1.51790	−	5.82063i	0.148132	−	0.568036i
$106$	−1.14178	−	10.8633i	−0.110900	−	1.05514i
$107$	1.95079	+	9.17775i	0.188590	+	0.887247i	0.966058	+	0.258325i	$0.0831704\pi$
$107$	1.95079	+	9.17775i	0.188590	+	0.887247i	−0.777468	+	0.628922i	$0.783496\pi$
$108$	−0.587785	−	0.809017i	−0.0565597	−	0.0778477i
$109$	9.15572	−	6.65202i	0.876959	−	0.637148i	−0.0554859	−	0.998459i	$-0.517671\pi$
$109$	9.15572	−	6.65202i	0.876959	−	0.637148i	0.932445	+	0.361311i	$0.117671\pi$
$110$	−0.295099	−	4.99069i	−0.0281366	−	0.475843i
$111$	0.508609	+	4.83909i	0.0482750	+	0.459306i
$112$	−2.67539	−	0.281194i	−0.252800	−	0.0265704i
$113$	1.66308	−	7.82417i	0.156449	−	0.736036i	−0.828051	−	0.560653i	$-0.810550\pi$
$113$	1.66308	−	7.82417i	0.156449	−	0.736036i	0.984500	−	0.175383i	$-0.0561164\pi$
$114$	−0.939360	+	0.418230i	−0.0879791	+	0.0391708i
$115$	−9.95661	+	6.56118i	−0.928459	+	0.611833i
$116$	−0.388371	+	1.19528i	−0.0360594	+	0.110979i
$117$	−4.62425	−	4.16369i	−0.427512	−	0.384934i
$118$	4.66168	−	2.69142i	0.429142	−	0.247765i
$119$	−6.25300	+	10.8305i	−0.573212	+	0.992832i
$120$	−0.364590	−	2.20614i	−0.0332824	−	0.201393i
$121$	−5.48236	−	2.44090i	−0.498396	−	0.221900i
$122$	−4.29002	+	5.90471i	−0.388400	+	0.534587i
$123$		−	5.18005i		−	0.467069i
$124$	5.53684	+	0.585999i	0.497223	+	0.0526243i
$125$	10.0618	+	4.87449i	0.899953	+	0.435987i
$126$	2.17635	+	1.58121i	0.193885	+	0.140866i
$127$	3.83663	−	8.61722i	0.340446	−	0.764654i	−0.659470	−	0.751730i	$-0.729219\pi$
$127$	3.83663	−	8.61722i	0.340446	−	0.764654i	0.999916	−	0.0129238i	$-0.00411390\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	2.09493	−	3.62853i	0.184449	−	0.319475i
$130$	−5.07328	−	12.9562i	−0.444956	−	1.13633i
$131$	1.91823	−	2.13041i	0.167597	−	0.186135i	−0.653496	−	0.756930i	$-0.726698\pi$
$131$	1.91823	−	2.13041i	0.167597	−	0.186135i	0.821093	+	0.570795i	$0.193365\pi$
$132$	2.12637	+	0.690901i	0.185077	+	0.0601352i
$133$	2.05564	−	1.85091i	0.178247	−	0.160494i
$134$	−2.59179	+	1.15394i	−0.223896	+	0.0996851i
$135$	−0.787328	+	2.09287i	−0.0677624	+	0.180126i
$136$	−0.485938	+	4.62339i	−0.0416689	+	0.396453i
$137$	11.4924	−	1.20790i	0.981860	−	0.103198i	0.400025	−	0.916504i	$-0.369001\pi$
$137$	11.4924	−	1.20790i	0.981860	−	0.103198i	0.581835	+	0.813307i	$0.302335\pi$
$138$	−1.10871	−	5.21607i	−0.0943797	−	0.444021i
$139$	−4.41936	+	3.21085i	−0.374845	+	0.272341i	−0.759217	−	0.650837i	$-0.774418\pi$
$139$	−4.41936	+	3.21085i	−0.374845	+	0.272341i	0.384372	+	0.923178i	$0.374418\pi$
$140$	2.76674	+	5.34125i	0.233832	+	0.451418i
$141$	1.80096	−	0.382806i	0.151668	−	0.0322381i
$142$	−1.10621	+	0.116267i	−0.0928308	+	0.00975691i
$143$	13.8362	+	1.45424i	1.15704	+	0.121610i
$144$	0.978148	+	0.207912i	0.0815123	+	0.0173260i
$145$	2.70959	−	0.745528i	0.225019	−	0.0619128i
$146$	−0.852934	−	0.947279i	−0.0705893	−	0.0783974i
$147$	−0.225170	−	0.0731620i	−0.0185717	−	0.00603430i
$148$	−3.61595	−	3.25582i	−0.297230	−	0.267627i
$149$	−10.1343	−	17.5530i	−0.830231	−	1.43800i	−0.897855	−	0.440291i	$-0.854875\pi$
$149$	−10.1343	−	17.5530i	−0.830231	−	1.43800i	0.0676248	−	0.997711i	$-0.478458\pi$
$150$	−3.67055	+	3.39515i	−0.299699	+	0.277213i
$151$	0.936187	+	2.88129i	0.0761858	+	0.234476i	0.981896	−	0.189422i	$-0.0606615\pi$
$151$	0.936187	+	2.88129i	0.0761858	+	0.234476i	−0.905710	+	0.423898i	$0.860662\pi$
$152$	0.418230	−	0.939360i	0.0339229	−	0.0761922i
$153$	2.73253	−	3.76101i	0.220912	−	0.304059i
$154$	−6.01458			−0.484669
$155$	−5.71834	−	11.0590i	−0.459308	−	0.888277i
$156$	6.22254			0.498202
$157$	−5.77163	+	7.94397i	−0.460627	+	0.633998i	−0.974639	−	0.223785i	$-0.928159\pi$
$157$	−5.77163	+	7.94397i	−0.460627	+	0.633998i	0.514012	+	0.857783i	$0.328159\pi$
$158$	−0.593656	+	1.33337i	−0.0472287	+	0.106077i
$159$	−3.37545	−	10.3886i	−0.267690	−	0.823866i
$160$	1.74714	+	1.39553i	0.138124	+	0.110326i
$161$	7.17267	+	12.4234i	0.565286	+	0.979104i
$162$	−0.743145	−	0.669131i	−0.0583870	−	0.0525719i
$163$	8.17280	+	2.65551i	0.640143	+	0.207995i	0.611063	−	0.791582i	$-0.290742\pi$
$163$	8.17280	+	2.65551i	0.640143	+	0.207995i	0.0290803	+	0.999577i	$0.490742\pi$
$164$	3.46613	+	3.84952i	0.270659	+	0.300597i
$165$	−1.32627	−	4.82028i	−0.103250	−	0.375258i
$166$	−7.20879	−	1.53228i	−0.559510	−	0.118928i
$167$	17.9517	+	1.88680i	1.38915	+	0.146005i	0.769385	−	0.638785i	$-0.220563\pi$
$167$	17.9517	+	1.88680i	1.38915	+	0.146005i	0.619762	+	0.784790i	$0.287229\pi$
$168$	−2.67539	+	0.281194i	−0.206410	+	0.0216946i
$169$	25.1580	−	5.34750i	1.93523	−	0.411346i
$170$	9.23033	−	4.78127i	0.707934	−	0.366707i
$171$	−0.831878	+	0.604395i	−0.0636153	+	0.0462192i
$172$	0.871123	+	4.09831i	0.0664225	+	0.312493i
$173$	−19.1559	+	2.01337i	−1.45640	+	0.153074i	−0.799391	−	0.600811i	$-0.794844\pi$
$173$	−19.1559	+	2.01337i	−1.45640	+	0.153074i	−0.657007	+	0.753885i	$0.728178\pi$
$174$	−0.131371	+	1.24991i	−0.00995920	+	0.0947555i
$175$	6.56859	−	11.7377i	0.496538	−	0.887284i
$176$	−2.04251	+	0.909383i	−0.153960	+	0.0685473i
$177$	4.00023	−	3.60182i	0.300676	−	0.270730i
$178$	10.2618	+	3.33425i	0.769152	+	0.249913i
$179$	16.6635	−	18.5067i	1.24549	−	1.38325i	0.350870	−	0.936424i	$-0.385886\pi$
$179$	16.6635	−	18.5067i	1.24549	−	1.38325i	0.894619	−	0.446831i	$-0.147447\pi$
$180$	−0.815306	−	2.08213i	−0.0607693	−	0.155193i
$181$	−8.59982	+	14.8953i	−0.639220	+	1.10716i	0.346385	+	0.938093i	$0.387409\pi$
$181$	−8.59982	+	14.8953i	−0.639220	+	1.10716i	−0.985604	+	0.169068i	$0.945924\pi$
$182$	−15.9201	+	5.17276i	−1.18008	+	0.383431i
$183$	−2.96862	+	6.66762i	−0.219447	+	0.492885i
$184$	4.31416	+	3.13442i	0.318044	+	0.231073i
$185$	−1.62998	+	10.7574i	−0.119838	+	0.790896i
$186$	5.53768	−	0.577980i	0.406043	−	0.0423795i
$187$			10.3939i			0.760080i
$188$	−1.08223	+	1.48956i	−0.0789296	+	0.108637i
$189$	2.45755	+	1.09417i	0.178760	+	0.0795892i
$190$	−2.26849	+	0.374893i	−0.164573	+	0.0271976i
$191$	9.27026	−	16.0566i	0.670773	−	1.16181i	−0.306913	−	0.951738i	$-0.599296\pi$
$191$	9.27026	−	16.0566i	0.670773	−	1.16181i	0.977685	−	0.210075i	$-0.0673707\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	9.45958	+	8.51745i	0.680916	+	0.613099i	0.935238	−	0.354020i	$-0.115186\pi$
$193$	9.45958	+	8.51745i	0.680916	+	0.613099i	−0.254322	+	0.967120i	$0.581852\pi$
$194$	5.38551	−	16.5749i	0.386657	−	1.19001i
$195$	−7.65615	−	11.6182i	−0.548269	−	0.832000i
$196$	0.216289	−	0.0962979i	0.0154492	−	0.00687842i
$197$	−3.40065	+	15.9988i	−0.242286	+	1.13987i	0.673809	+	0.738906i	$0.264657\pi$
$197$	−3.40065	+	15.9988i	−0.242286	+	1.13987i	−0.916095	+	0.400961i	$0.868676\pi$
$198$	2.22355	+	0.233705i	0.158021	+	0.0166087i
$199$	0.579541	+	5.51396i	0.0410825	+	0.390874i	0.995671	+	0.0929469i	$0.0296287\pi$
$199$	0.579541	+	5.51396i	0.0410825	+	0.390874i	−0.954589	+	0.297927i	$0.903705\pi$
$200$	0.455952	−	4.97917i	0.0322407	−	0.352080i
$201$	−2.29523	+	1.66759i	−0.161893	+	0.117622i
$202$	−6.97173	−	9.59577i	−0.490530	−	0.675156i
$203$	−0.702936	−	3.30705i	−0.0493364	−	0.232110i
$204$	0.485938	+	4.62339i	0.0340225	+	0.323702i
$205$	2.92284	−	11.2081i	0.204140	−	0.782807i
$206$	12.9245	+	2.74718i	0.900492	+	0.191405i
$207$	−2.16896	−	4.87157i	−0.150753	−	0.338598i
$208$	−4.62425	+	4.16369i	−0.320634	+	0.288700i
$209$	0.710424	−	2.18646i	0.0491411	−	0.151241i
$210$	3.81679	+	4.64929i	0.263384	+	0.320832i
$211$	2.77687	+	4.80968i	0.191168	+	0.331112i	0.945638	−	0.325223i	$-0.105439\pi$
$211$	2.77687	+	4.80968i	0.191168	+	0.331112i	−0.754470	+	0.656335i	$0.772106\pi$
$212$	9.45974	+	5.46159i	0.649698	+	0.375103i
$213$	−1.05786	+	0.343720i	−0.0724834	+	0.0235513i
$214$	−8.57161	−	3.81633i	−0.585943	−	0.260879i
$215$	6.58022	−	6.66901i	0.448767	−	0.454823i
$216$	1.00000			0.0680414
$217$	−13.6875	+	6.08218i	−0.929165	+	0.412885i
$218$			11.3171i			0.766491i
$219$	−1.03125	−	0.749244i	−0.0696851	−	0.0506292i
$220$	4.21101	+	2.69471i	0.283906	+	0.181678i
$221$	8.93916	+	27.5119i	0.601313	+	1.85065i
$222$	−4.21386	−	2.43287i	−0.282816	−	0.163284i
$223$	11.4691	−	6.62170i	0.768029	−	0.443422i	−0.0641418	−	0.997941i	$-0.520431\pi$
$223$	11.4691	−	6.62170i	0.768029	−	0.443422i	0.832171	+	0.554519i	$0.187098\pi$
$224$	1.80004	−	1.99915i	0.120270	−	0.133574i
$225$	−2.88445	+	4.08411i	−0.192297	+	0.272274i
$226$	5.35235	+	5.94439i	0.356033	+	0.395415i
$227$	6.83858	+	15.3597i	0.453893	+	1.01946i	0.985063	+	0.172194i	$0.0550857\pi$
$227$	6.83858	+	15.3597i	0.453893	+	1.01946i	−0.531170	+	0.847265i	$0.678248\pi$
$228$	0.213787	−	1.00579i	0.0141584	−	0.0666099i
$229$	1.12792	−	10.7315i	0.0745354	−	0.709157i	−0.891898	−	0.452237i	$-0.850626\pi$
$229$	1.12792	−	10.7315i	0.0745354	−	0.709157i	0.966433	−	0.256919i	$-0.0827074\pi$
$230$	0.544247	−	11.9116i	0.0358866	−	0.785430i
$231$	−5.88315	+	1.25050i	−0.387083	+	0.0822770i
$232$	−0.738726	−	1.01677i	−0.0484997	−	0.0667541i
$233$	−7.83531	−	10.7844i	−0.513308	−	0.706508i	0.471164	−	0.882045i	$-0.343834\pi$
$233$	−7.83531	−	10.7844i	−0.513308	−	0.706508i	−0.984473	+	0.175537i	$0.943834\pi$
$234$	6.08657	−	1.29374i	0.397891	−	0.0845744i
$235$	4.11275	+	0.187913i	0.268286	+	0.0122581i
$236$	−0.562660	+	5.35335i	−0.0366260	+	0.348473i
$237$	−0.303459	+	1.42766i	−0.0197118	+	0.0927367i
$238$	−5.08665	−	11.4248i	−0.329719	−	0.740560i
$239$	−4.81681	−	5.34961i	−0.311574	−	0.346038i	0.566936	−	0.823762i	$-0.308129\pi$
$239$	−4.81681	−	5.34961i	−0.311574	−	0.346038i	−0.878510	+	0.477724i	$0.841462\pi$
$240$	1.99911	+	1.00178i	0.129042	+	0.0646646i
$241$	−9.84764	+	10.9369i	−0.634342	+	0.704508i	−0.971527	−	0.236930i	$-0.923859\pi$
$241$	−9.84764	+	10.9369i	−0.634342	+	0.704508i	0.337185	+	0.941439i	$0.390525\pi$
$242$	5.19718	−	3.00059i	0.334088	−	0.192886i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−2.25540	−	6.94140i	−0.144387	−	0.444378i
$245$	−0.445919	−	0.285353i	−0.0284887	−	0.0182305i
$246$	4.19075	+	3.04475i	0.267192	+	0.194126i
$247$		−	6.39838i		−	0.407119i
$248$	−3.72856	+	4.13496i	−0.236764	+	0.262570i
$249$	−7.36984			−0.467044
$250$	−9.85771	+	5.27500i	−0.623456	+	0.333620i
$251$	22.0776	+	9.82959i	1.39353	+	0.620438i	0.959820	−	0.280616i	$-0.0905387\pi$
$251$	22.0776	+	9.82959i	1.39353	+	0.620438i	0.433707	+	0.901054i	$0.357205\pi$
$252$	−2.55846	+	0.831293i	−0.161168	+	0.0523666i
$253$	10.3253	+	5.96132i	0.649147	+	0.374785i
$254$	4.71636	+	8.16897i	0.295931	+	0.512567i
$255$	8.03454	−	6.59588i	0.503143	−	0.413050i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	15.9591	−	14.3697i	0.995503	−	0.896355i	0.000888918	−	1.00000i	$-0.499717\pi$
$257$	15.9591	−	14.3697i	0.995503	−	0.896355i	0.994614	+	0.103644i	$0.0330504\pi$
$258$	1.70417	+	3.82764i	0.106097	+	0.238298i
$259$	12.8034	+	2.72145i	0.795566	+	0.169103i
$260$	13.4638	+	3.51107i	0.834987	+	0.217747i
$261$	0.131371	+	1.24991i	0.00813165	+	0.0773675i
$262$	0.596032	+	2.80411i	0.0368230	+	0.173238i
$263$	−8.78871	−	12.0966i	−0.541935	−	0.745910i	0.446955	−	0.894556i	$-0.352508\pi$
$263$	−8.78871	−	12.0966i	−0.541935	−	0.745910i	−0.988890	+	0.148647i	$0.952508\pi$
$264$	−1.80880	+	1.31417i	−0.111324	+	0.0808817i
$265$	−1.44173	−	24.3824i	−0.0885646	−	1.49780i
$266$	0.289140	+	2.75099i	0.0177283	+	0.168674i
$267$	10.7308	+	1.12785i	0.656712	+	0.0690232i
$268$	0.589859	−	2.77507i	0.0360314	−	0.169514i
$269$	−11.8460	+	5.27417i	−0.722263	+	0.321572i	−0.734739	−	0.678350i	$-0.762695\pi$
$269$	−11.8460	+	5.27417i	−0.722263	+	0.321572i	0.0124762	+	0.999922i	$0.496029\pi$
$270$	−1.23039	−	1.86712i	−0.0748791	−	0.113629i
$271$	7.84282	−	24.1377i	0.476417	−	1.46626i	−0.367620	−	0.929976i	$-0.619827\pi$
$271$	7.84282	−	24.1377i	0.476417	−	1.46626i	0.844037	−	0.536285i	$-0.180173\pi$
$272$	−3.45478	−	3.11069i	−0.209477	−	0.188614i
$273$	−14.4967	+	8.36970i	−0.877383	+	0.506557i
$274$	−5.77784	+	10.0075i	−0.349052	+	0.604576i
$275$	−0.149822	−	11.1780i	−0.00903463	−	0.674059i
$276$	4.87157	+	2.16896i	0.293234	+	0.130556i
$277$	7.40450	−	10.1914i	0.444893	−	0.612343i	−0.526397	−	0.850239i	$-0.676458\pi$
$277$	7.40450	−	10.1914i	0.444893	−	0.612343i	0.971291	+	0.237896i	$0.0764576\pi$
$278$		−	5.46262i		−	0.327626i
$279$	5.29650	−	1.71670i	0.317093	−	0.102776i
$280$	−5.94741	−	0.901165i	−0.355426	−	0.0538549i
$281$	−10.8196	−	7.86093i	−0.645446	−	0.468944i	0.216271	−	0.976333i	$-0.430611\pi$
$281$	−10.8196	−	7.86093i	−0.645446	−	0.468944i	−0.861717	+	0.507389i	$0.830611\pi$
$282$	−0.748882	+	1.68202i	−0.0445953	+	0.100163i
$283$	19.8048	−	6.43497i	1.17727	−	0.382519i	0.345920	−	0.938264i	$-0.387567\pi$
$283$	19.8048	−	6.43497i	1.17727	−	0.382519i	0.831353	+	0.555745i	$0.187567\pi$
$284$	0.556150	−	0.963280i	0.0330014	−	0.0571602i
$285$	−2.14097	+	0.838345i	−0.126820	+	0.0496593i
$286$	−9.30920	+	10.3389i	−0.550464	+	0.611353i
$287$	−13.2529	−	4.30614i	−0.782296	−	0.254183i
$288$	−0.743145	+	0.669131i	−0.0437902	+	0.0394289i
$289$	−4.21319	+	1.87583i	−0.247834	+	0.110343i
$290$	−0.989510	+	2.63031i	−0.0581060	+	0.154457i
$291$	1.82171	−	17.3324i	0.106790	−	1.01604i
$292$	1.26771	−	0.133241i	0.0741869	−	0.00779736i
$293$	−0.296629	−	1.39553i	−0.0173293	−	0.0815278i	0.968633	−	0.248495i	$-0.0799360\pi$
$293$	−0.296629	−	1.39553i	−0.0173293	−	0.0815278i	−0.985962	+	0.166967i	$0.946603\pi$
$294$	0.191541	−	0.139162i	0.0111709	−	0.00811612i
$295$	10.6876	−	5.53615i	0.622259	−	0.322327i
$296$	4.75942	−	1.01165i	0.276636	−	0.0588007i
$297$	2.22355	−	0.233705i	0.129024	−	0.0135609i
$298$	20.1575	+	2.11864i	1.16769	+	0.122729i
$299$	32.4572	+	6.89900i	1.87705	+	0.398979i
$300$	−0.589239	−	4.96516i	−0.0340197	−	0.286664i
$301$	−7.54195	−	8.37618i	−0.434711	−	0.482795i
$302$	−2.88129	−	0.936187i	−0.165799	−	0.0538715i
$303$	−8.81446	−	7.93657i	−0.506377	−	0.455944i
$304$	0.514129	+	0.890497i	0.0294873	+	0.0510735i
$305$	−10.1854	+	12.7517i	−0.583216	+	0.730162i
$306$	1.43658	+	4.42133i	0.0821236	+	0.252751i
$307$	10.1543	−	22.8070i	0.579539	−	1.30167i	−0.351309	−	0.936260i	$-0.614263\pi$
$307$	10.1543	−	22.8070i	0.579539	−	1.30167i	0.930848	−	0.365407i	$-0.119070\pi$
$308$	3.53528	−	4.86590i	0.201441	−	0.277260i
$309$	13.2132			0.751674
$310$	12.3080	+	1.87406i	0.699050	+	0.106439i
$311$	20.6224			1.16939			0.584695	−	0.811253i	$-0.301214\pi$
$311$	20.6224			1.16939			0.584695	+	0.811253i	$0.301214\pi$
$312$	−3.65752	+	5.03414i	−0.207066	+	0.285002i
$313$	−3.03957	+	6.82699i	−0.171807	+	0.385885i	−0.978842	−	0.204619i	$-0.934404\pi$
$313$	−3.03957	+	6.82699i	−0.171807	+	0.385885i	0.807035	+	0.590504i	$0.201071\pi$
$314$	−3.03433	−	9.33870i	−0.171237	−	0.527013i
$315$	4.70003	+	3.75414i	0.264816	+	0.211522i
$316$	−0.729779	−	1.26401i	−0.0410533	−	0.0711064i
$317$	−3.36966	−	3.03406i	−0.189259	−	0.170410i	0.569054	−	0.822300i	$-0.307310\pi$
$317$	−3.36966	−	3.03406i	−0.189259	−	0.170410i	−0.758313	+	0.651890i	$0.773976\pi$
$318$	10.3886	+	3.37545i	0.582561	+	0.189286i
$319$	−1.88022	−	2.08820i	−0.105272	−	0.116917i
$320$	−2.15595	+	0.593198i	−0.120521	+	0.0331608i
$321$	−9.17775	−	1.95079i	−0.512252	−	0.108883i
$322$	−14.2668	−	1.49950i	−0.795056	−	0.0835637i
$323$	4.75404	−	0.499670i	0.264522	−	0.0278024i
$324$	0.978148	−	0.207912i	0.0543415	−	0.0115506i
$325$	−10.0101	−	29.4584i	−0.555258	−	1.63406i
$326$	−6.95220	+	5.05107i	−0.385047	+	0.279753i
$327$	2.35296	+	11.0698i	0.130119	+	0.612161i
$328$	−5.15167	+	0.541462i	−0.284453	+	0.0298973i
$329$	0.517734	−	4.92591i	0.0285436	−	0.271574i
$330$	4.67925	+	1.76031i	0.257584	+	0.0969019i
$331$	−28.0406	+	12.4845i	−1.54125	+	0.686208i	−0.989060	−	0.147511i	$-0.952874\pi$
$331$	−28.0406	+	12.4845i	−1.54125	+	0.686208i	−0.552188	+	0.833719i	$0.686207\pi$
$332$	5.47686	−	4.93138i	0.300582	−	0.270645i
$333$	−4.62760	−	1.50360i	−0.253591	−	0.0823967i
$334$	−12.0782	+	13.4142i	−0.660891	+	0.733994i
$335$	−5.90715	+	2.31308i	−0.322742	+	0.126377i
$336$	1.34506	−	2.32971i	0.0733791	−	0.127096i
$337$	−26.2145	+	8.51760i	−1.42799	+	0.463983i	−0.918132	−	0.396274i	$-0.870303\pi$
$337$	−26.2145	+	8.51760i	−1.42799	+	0.463983i	−0.509861	+	0.860257i	$0.670303\pi$
$338$	−10.4613	+	23.4964i	−0.569019	+	1.27804i
$339$	6.47130	+	4.70167i	0.351473	+	0.255360i
$340$	−1.55732	+	10.2779i	−0.0844577	+	0.557395i
$341$	−7.32429	+	10.0657i	−0.396632	+	0.545087i
$342$		−	1.02826i		−	0.0556018i
$343$	10.6941	−	14.7192i	0.577429	−	0.794763i
$344$	−3.82764	−	1.70417i	−0.206372	−	0.0918829i
$345$	−1.94421	−	11.7645i	−0.104673	−	0.633379i
$346$	9.63072	−	16.6809i	0.517751	−	0.896770i
$347$	−25.6919	+	14.8332i	−1.37921	+	0.796290i	−0.992065	−	0.125727i	$-0.959874\pi$
$347$	−25.6919	+	14.8332i	−1.37921	+	0.796290i	−0.387150	+	0.922017i	$0.626540\pi$
$348$	−0.933981	−	0.840960i	−0.0500666	−	0.0450802i
$349$	−8.66646	+	26.6726i	−0.463905	+	1.42775i	0.396449	+	0.918057i	$0.370242\pi$
$349$	−8.66646	+	26.6726i	−0.463905	+	1.42775i	−0.860354	+	0.509697i	$0.829758\pi$
$350$	5.63505	+	12.2133i	0.301206	+	0.652829i
$351$	5.68458	−	2.53094i	0.303420	−	0.135091i
$352$	0.464849	−	2.18694i	0.0247766	−	0.116565i
$353$	−23.3668	−	2.45595i	−1.24369	−	0.130717i	−0.540270	−	0.841492i	$-0.681678\pi$
$353$	−23.3668	−	2.45595i	−1.24369	−	0.130717i	−0.703420	+	0.710775i	$0.748345\pi$
$354$	0.562660	+	5.35335i	0.0299050	+	0.284527i
$355$	−2.48284	+	0.146810i	−0.131776	+	0.00779188i
$356$	−8.72918	+	6.34212i	−0.462646	+	0.336132i
$357$	−7.35084	−	10.1176i	−0.389048	−	0.535479i
$358$	5.17767	+	24.3590i	0.273648	+	1.28741i
$359$	−2.19115	−	20.8474i	−0.115645	−	1.10028i	−0.886325	−	0.463063i	$-0.846750\pi$
$359$	−2.19115	−	20.8474i	−0.115645	−	1.10028i	0.770681	−	0.637222i	$-0.219916\pi$
$360$	2.16371	+	0.564250i	0.114037	+	0.0297386i
$361$	17.5506	+	3.73049i	0.923716	+	0.196342i
$362$	−6.99573	−	15.7127i	−0.367687	−	0.825839i
$363$	4.45975	−	4.01558i	0.234076	−	0.210763i
$364$	5.17276	−	15.9201i	0.271126	−	0.834441i
$365$	−1.80855	−	2.20302i	−0.0946639	−	0.115311i
$366$	−3.64931	−	6.32079i	−0.190753	−	0.330393i
$367$	17.7783	+	10.2643i	0.928017	+	0.535791i	0.886184	−	0.463334i	$-0.153347\pi$
$367$	17.7783	+	10.2643i	0.928017	+	0.535791i	0.0418333	+	0.999125i	$0.486680\pi$
$368$	−5.07160	+	1.64786i	−0.264376	+	0.0859009i
$369$	4.73221	+	2.10691i	0.246349	+	0.109682i
$370$	−7.74480	−	7.64169i	−0.402633	−	0.397273i
$371$	−29.3847			−1.52558
$372$	−2.78737	+	4.81981i	−0.144519	+	0.249895i
$373$			22.5401i			1.16708i	0.812084	+	0.583540i	$0.198333\pi$
$373$			22.5401i			1.16708i	−0.812084	+	0.583540i	$0.801667\pi$
$374$	−8.40887	−	6.10940i	−0.434812	−	0.315910i
$375$	−8.54556	+	7.20926i	−0.441291	+	0.372285i
$376$	−0.568961	−	1.75108i	−0.0293419	−	0.0903052i
$377$	−6.77272	−	3.91023i	−0.348813	−	0.201387i
$378$	−2.32971	+	1.34506i	−0.119828	+	0.0691825i
$379$	−6.38092	+	7.08673i	−0.327766	+	0.364021i	−0.884394	−	0.466741i	$-0.845428\pi$
$379$	−6.38092	+	7.08673i	−0.327766	+	0.364021i	0.556628	+	0.830762i	$0.312095\pi$
$380$	1.03009	−	2.05560i	0.0528424	−	0.105450i
$381$	6.31172	+	7.00988i	0.323359	+	0.359127i
$382$	7.54111	+	16.9376i	0.385837	+	0.866604i
$383$	−0.771437	+	3.62932i	−0.0394186	+	0.185450i	−0.993452	−	0.114250i	$-0.963553\pi$
$383$	−0.771437	+	3.62932i	−0.0394186	+	0.185450i	0.954033	+	0.299700i	$0.0968867\pi$
$384$	0.104528	−	0.994522i	0.00533420	−	0.0507515i
$385$	−13.4350	−	0.613850i	−0.684711	−	0.0312847i
$386$	−12.4510	+	2.64653i	−0.633737	+	0.134705i
$387$	2.46274	+	3.38968i	0.125188	+	0.172307i
$388$	10.2439	+	14.0995i	0.520053	+	0.715791i
$389$	−13.6988	+	2.91178i	−0.694559	+	0.147633i	−0.541646	−	0.840607i	$-0.682199\pi$
$389$	−13.6988	+	2.91178i	−0.694559	+	0.147633i	−0.152913	+	0.988240i	$0.548865\pi$
$390$	13.8995	+	0.635075i	0.703830	+	0.0321583i
$391$	−2.59131	+	24.6547i	−0.131048	+	1.24684i
$392$	−0.0492246	+	0.231584i	−0.00248622	+	0.0116967i
$393$	1.16601	+	2.61891i	0.0588176	+	0.132107i
$394$	−10.9444	−	12.1550i	−0.551373	−	0.612362i
$395$	−1.46216	+	2.91782i	−0.0735690	+	0.146811i
$396$	−1.49604	+	1.66152i	−0.0751790	+	0.0834948i
$397$	12.9491	−	7.47615i	0.649895	−	0.375217i	−0.138521	−	0.990360i	$-0.544235\pi$
$397$	12.9491	−	7.47615i	0.649895	−	0.375217i	0.788416	+	0.615142i	$0.210901\pi$
$398$	−4.80153	−	2.77217i	−0.240679	−	0.138956i
$399$	0.854784	+	2.63075i	0.0427927	+	0.131702i
$400$	3.76023	+	3.29555i	0.188011	+	0.164778i
$401$	−12.5142	−	9.09207i	−0.624928	−	0.454036i	0.229712	−	0.973259i	$-0.426222\pi$
$401$	−12.5142	−	9.09207i	−0.624928	−	0.454036i	−0.854639	+	0.519222i	$0.826222\pi$
$402$		−	2.83707i		−	0.141500i
$403$	−10.7300	+	32.9422i	−0.534497	+	1.64097i
$404$	11.8610			0.590108
$405$	−1.59170	−	1.57051i	−0.0790922	−	0.0780392i
$406$	3.08864	+	1.37515i	0.153286	+	0.0682475i
$407$	10.3464	−	3.36175i	0.512852	−	0.166636i
$408$	−4.02603	−	2.32443i	−0.199318	−	0.115076i
$409$	−8.95670	−	15.5135i	−0.442880	−	0.767091i	0.555022	−	0.831836i	$-0.312710\pi$
$409$	−8.95670	−	15.5135i	−0.442880	−	0.767091i	−0.997902	+	0.0647448i	$0.979377\pi$
$410$	7.34954	+	8.95258i	0.362968	+	0.442136i
$411$	−3.57090	+	10.9901i	−0.176140	+	0.542102i
$412$	−9.81934	+	8.84137i	−0.483764	+	0.435583i
$413$	−5.88975	−	13.2286i	−0.289816	−	0.650936i
$414$	5.21607	+	1.10871i	0.256356	+	0.0544901i
$415$	−15.9462	−	4.15843i	−0.782766	−	0.204129i
$416$	−0.650433	−	6.18846i	−0.0318901	−	0.303414i
$417$	−1.13574	−	5.34325i	−0.0556176	−	0.261660i
$418$	1.35131	+	1.85991i	0.0660946	+	0.0909714i
$419$	−11.1787	+	8.12184i	−0.546118	+	0.396778i	−0.826352	−	0.563154i	$-0.809588\pi$
$419$	−11.1787	+	8.12184i	−0.546118	+	0.396778i	0.280234	+	0.959932i	$0.409588\pi$
$420$	−6.00481	+	0.355064i	−0.293005	+	0.0173253i
$421$	2.38802	+	22.7205i	0.116385	+	1.10733i	0.884346	+	0.466832i	$0.154605\pi$
$421$	2.38802	+	22.7205i	0.116385	+	1.10733i	−0.767961	+	0.640497i	$0.778728\pi$
$422$	−5.52332	−	0.580524i	−0.268871	−	0.0282595i
$423$	−0.382806	+	1.80096i	−0.0186127	+	0.0875658i
$424$	−9.97881	+	4.44285i	−0.484614	+	0.215764i
$425$	21.1061	−	9.73805i	1.02380	−	0.472365i
$426$	0.343720	−	1.05786i	0.0166533	−	0.0512535i
$427$	14.5910	+	13.1378i	0.706110	+	0.635785i
$428$	8.12574	−	4.69140i	0.392772	−	0.226767i
$429$	−6.95619	+	12.0485i	−0.335848	+	0.581706i
$430$	1.52759	+	9.24346i	0.0736667	+	0.445759i
$431$	−23.4108	−	10.4231i	−1.12766	−	0.502065i	−0.243801	−	0.969825i	$-0.578394\pi$
$431$	−23.4108	−	10.4231i	−1.12766	−	0.502065i	−0.883855	+	0.467760i	$0.845061\pi$
$432$	−0.587785	+	0.809017i	−0.0282798	+	0.0389238i
$433$			9.58706i			0.460725i	0.973105	+	0.230362i	$0.0739912\pi$
$433$			9.58706i			0.460725i	−0.973105	+	0.230362i	$0.926009\pi$
$434$	3.12470	−	14.6484i	0.149991	−	0.703146i
$435$	−0.421014	+	2.77856i	−0.0201861	+	0.133222i
$436$	−9.15572	−	6.65202i	−0.438480	−	0.318574i
$437$	2.23025	−	5.00923i	0.106688	−	0.239624i
$438$	1.21230	−	0.393901i	0.0579260	−	0.0188213i
$439$	−19.2717	+	33.3795i	−0.919786	+	1.59312i	−0.120048	+	0.992768i	$0.538305\pi$
$439$	−19.2717	+	33.3795i	−0.919786	+	1.59312i	−0.799739	+	0.600348i	$0.795029\pi$
$440$	−4.65524	+	1.82286i	−0.221930	+	0.0869016i
$441$	0.158422	−	0.175945i	0.00754389	−	0.00837833i
$442$	−27.5119	−	8.93916i	−1.30861	−	0.425193i
$443$	14.9691	−	13.4782i	0.711203	−	0.640370i	−0.231951	−	0.972728i	$-0.574511\pi$
$443$	14.9691	−	13.4782i	0.711203	−	0.640370i	0.943153	+	0.332358i	$0.107844\pi$
$444$	4.44508	−	1.97908i	0.210954	−	0.0939228i
$445$	22.5818	+	8.49516i	1.07048	+	0.402709i
$446$	−1.38431	+	13.1709i	−0.0655491	+	0.623658i
$447$	20.1575	−	2.11864i	0.953416	−	0.100208i
$448$	0.559308	+	2.63134i	0.0264248	+	0.124319i
$449$	7.35155	−	5.34122i	0.346941	−	0.252068i	−0.400643	−	0.916234i	$-0.631213\pi$
$449$	7.35155	−	5.34122i	0.346941	−	0.252068i	0.747585	+	0.664166i	$0.231213\pi$
$450$	−1.60868	−	4.73415i	−0.0758338	−	0.223170i
$451$	−11.3285	+	2.40794i	−0.533437	+	0.113386i
$452$	−7.95515	+	0.836120i	−0.374179	+	0.0393278i
$453$	−3.01297	−	0.316676i	−0.141562	−	0.0148787i
$454$	−16.4459	−	3.49568i	−0.771843	−	0.164060i
$455$	−36.0893	+	9.92978i	−1.69189	+	0.465515i
$456$	0.688039	+	0.764144i	0.0322204	+	0.0357843i
$457$	−17.4234	−	5.66120i	−0.815032	−	0.264820i	−0.128304	−	0.991735i	$-0.540953\pi$
$457$	−17.4234	−	5.66120i	−0.815032	−	0.264820i	−0.686728	+	0.726915i	$0.740953\pi$
$458$	8.01898	+	7.22032i	0.374702	+	0.337383i
$459$	2.32443	+	4.02603i	0.108495	+	0.187919i
$460$	9.31681	+	7.44179i	0.434399	+	0.346975i
$461$	−12.4033	−	38.1735i	−0.577680	−	1.77792i	−0.626865	−	0.779128i	$-0.715662\pi$
$461$	−12.4033	−	38.1735i	−0.577680	−	1.77792i	0.0491849	−	0.998790i	$-0.484338\pi$
$462$	2.44635	−	5.49459i	0.113815	−	0.255632i
$463$	15.0916	−	20.7719i	0.701368	−	0.965350i	−0.298572	−	0.954387i	$-0.596510\pi$
$463$	15.0916	−	20.7719i	0.701368	−	0.965350i	0.999940	−	0.0109630i	$-0.00348970\pi$
$464$	1.25680			0.0583453
$465$	12.4287	−	0.725878i	0.576368	−	0.0336618i
$466$	13.3302			0.617511
$467$	14.3528	−	19.7550i	0.664169	−	0.914151i	−0.335441	−	0.942061i	$-0.608885\pi$
$467$	14.3528	−	19.7550i	0.664169	−	0.914151i	0.999610	+	0.0279105i	$0.00888534\pi$
$468$	−2.53094	+	5.68458i	−0.116993	+	0.262770i
$469$	2.35843	+	7.25851i	0.108902	+	0.335167i
$470$	−2.56944	+	3.21683i	−0.118519	+	0.148381i
$471$	−4.90964	−	8.50375i	−0.226224	−	0.391832i
$472$	−4.00023	−	3.60182i	−0.184125	−	0.165787i
$473$	−8.90923	−	2.89478i	−0.409647	−	0.133102i
$474$	−0.976635	−	1.08466i	−0.0448583	−	0.0498202i
$475$	−5.10546	+	0.605889i	−0.234255	+	0.0278001i
$476$	12.2327	+	2.60014i	0.560686	+	0.119177i
$477$	10.8633	+	1.14178i	0.497398	+	0.0522786i
$478$	7.15918	−	0.752460i	0.327453	−	0.0344167i
$479$	−14.7188	+	3.12858i	−0.672520	+	0.142948i	−0.531500	−	0.847058i	$-0.678371\pi$
$479$	−14.7188	+	3.12858i	−0.672520	+	0.142948i	−0.141020	+	0.990007i	$0.545038\pi$
$480$	−1.98550	+	1.02848i	−0.0906254	+	0.0469436i
$481$	24.4949	−	17.7966i	1.11687	−	0.811453i
$482$	−3.05985	−	14.3955i	−0.139372	−	0.655695i
$483$	−14.2668	+	1.49950i	−0.649160	+	0.0682295i
$484$	−0.627295	+	5.96831i	−0.0285134	+	0.271287i
$485$	13.7215	−	36.4743i	0.623059	−	1.65621i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	23.6781	−	21.3198i	1.07296	−	0.966094i	0.0734427	−	0.997299i	$-0.476601\pi$
$487$	23.6781	−	21.3198i	1.07296	−	0.966094i	0.999513	+	0.0312058i	$0.00993473\pi$
$488$	6.94140	+	2.25540i	0.314223	+	0.102097i
$489$	−5.75010	+	6.38614i	−0.260029	+	0.288791i
$490$	0.492960	−	0.193030i	0.0222697	−	0.00872019i
$491$	−2.93473	+	5.08311i	−0.132443	+	0.229397i	−0.924618	−	0.380897i	$-0.875615\pi$
$491$	−2.93473	+	5.08311i	−0.132443	+	0.229397i	0.792175	+	0.610294i	$0.208949\pi$
$492$	−4.92652	+	1.60072i	−0.222105	+	0.0721661i
$493$	2.37643	−	5.33754i	0.107029	−	0.240391i
$494$	5.17640	+	3.76087i	0.232897	+	0.169210i
$495$	4.94298	+	0.748972i	0.222171	+	0.0336638i
$496$	−1.15366	−	5.44693i	−0.0518008	−	0.244574i
$497$			2.99222i			0.134220i
$498$	4.33188	−	5.96232i	0.194116	−	0.267178i
$499$	19.3787	+	8.62793i	0.867508	+	0.386239i	0.791720	−	0.610885i	$-0.209186\pi$
$499$	19.3787	+	8.62793i	0.867508	+	0.386239i	0.0757880	+	0.997124i	$0.475853\pi$
$500$	1.52665	−	11.0756i	0.0682740	−	0.495317i
$501$	−9.02531	+	15.6323i	−0.403221	+	0.698399i
$502$	−20.9292	+	12.0835i	−0.934116	+	0.539312i
$503$	−20.0561	−	18.0586i	−0.894257	−	0.805192i	0.0873360	−	0.996179i	$-0.472165\pi$
$503$	−20.0561	−	18.0586i	−0.894257	−	0.805192i	−0.981593	+	0.190987i	$0.938831\pi$
$504$	0.831293	−	2.55846i	0.0370288	−	0.113963i
$505$	−14.5937	−	22.1460i	−0.649410	−	0.985483i
$506$	−10.8919	+	4.84937i	−0.484203	+	0.215581i
$507$	−5.34750	+	25.1580i	−0.237491	+	1.11731i
$508$	−9.38104	−	0.985988i	−0.416217	−	0.0437461i
$509$	−3.12331	−	29.7163i	−0.138438	−	1.31715i	−0.814438	−	0.580251i	$-0.802954\pi$
$509$	−3.12331	−	29.7163i	−0.138438	−	1.31715i	0.675999	−	0.736902i	$-0.263712\pi$
$510$	0.613594	+	10.3770i	0.0271704	+	0.459503i
$511$	−2.77418	+	2.01556i	−0.122722	+	0.0891630i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	−0.213787	−	1.00579i	−0.00943892	−	0.0444066i
$514$	2.24476	+	21.3575i	0.0990122	+	0.942038i
$515$	28.5895	+	7.45557i	1.25981	+	0.328531i
$516$	−4.09831	−	0.871123i	−0.180418	−	0.0383490i
$517$	−1.67435	−	3.76066i	−0.0736379	−	0.165394i
$518$	−9.72736	+	8.75855i	−0.427396	+	0.384829i
$519$	5.95211	−	18.3187i	0.261269	−	0.804102i
$520$	−10.7543	+	8.82865i	−0.471608	+	0.387162i
$521$	17.6432	+	30.5590i	0.772964	+	1.33881i	0.935932	+	0.352182i	$0.114560\pi$
$521$	17.6432	+	30.5590i	0.772964	+	1.33881i	−0.162967	+	0.986631i	$0.552106\pi$
$522$	−1.08842	−	0.628398i	−0.0476387	−	0.0275042i
$523$	−11.0793	+	3.59987i	−0.484462	+	0.157411i	−0.541057	−	0.840986i	$-0.681976\pi$
$523$	−11.0793	+	3.59987i	−0.484462	+	0.157411i	0.0565948	+	0.998397i	$0.481976\pi$
$524$	−2.61891	−	1.16601i	−0.114408	−	0.0509376i
$525$	8.05120	+	10.7748i	0.351383	+	0.470252i
$526$	14.9522			0.651949
$527$	−25.3142	−	5.39987i	−1.10271	−	0.235222i
$528$		−	2.23580i		−	0.0973008i
$529$	4.39832	+	3.19557i	0.191231	+	0.138938i
$530$	20.5732	+	13.1652i	0.893642	+	0.571860i
$531$	1.66339	+	5.11938i	0.0721849	+	0.222162i
$532$	−2.39555	−	1.38307i	−0.103860	−	0.0599637i
$533$	−27.9147	+	16.1165i	−1.20912	+	0.698085i
$534$	−7.21983	+	8.01843i	−0.312433	+	0.346991i
$535$	−18.7572	−	9.39949i	−0.810946	−	0.406375i
$536$	1.89837	+	2.10835i	0.0819970	+	0.0910669i
$537$	10.1290	+	22.7502i	0.437101	+	0.981744i
$538$	2.69600	−	12.6837i	0.116233	−	0.546833i
$539$	−0.0553314	+	0.526443i	−0.00238329	+	0.0226755i
$540$	2.23374	+	0.102060i	0.0961248	+	0.00439198i
$541$	9.83169	−	2.08979i	0.422697	−	0.0898471i	0.00834828	−	0.999965i	$-0.497343\pi$
$541$	9.83169	−	2.08979i	0.422697	−	0.0898471i	0.414349	+	0.910118i	$0.364009\pi$
$542$	14.9179	+	20.5328i	0.640780	+	0.881957i
$543$	−10.1097	−	13.9148i	−0.433849	−	0.597141i
$544$	4.54727	−	0.966552i	0.194963	−	0.0414406i
$545$	−1.15503	+	25.2794i	−0.0494759	+	1.08285i
$546$	1.74974	−	16.6477i	0.0748821	−	0.712456i
$547$	−9.41499	+	44.2940i	−0.402556	+	1.89388i	0.0438363	+	0.999039i	$0.486042\pi$
$547$	−9.41499	+	44.2940i	−0.402556	+	1.89388i	−0.446392	+	0.894837i	$0.647291\pi$
$548$	−4.70012	−	10.5566i	−0.200779	−	0.450957i
$549$	−4.88373	−	5.42393i	−0.208433	−	0.231488i
$550$	9.13126	+	6.44906i	0.389358	+	0.274989i
$551$	−0.864724	+	0.960373i	−0.0368385	+	0.0409133i
$552$	−4.61817	+	2.66630i	−0.196562	+	0.113485i
$553$	3.40035	+	1.96319i	0.144598	+	0.0834835i
$554$	3.89278	+	11.9807i	0.165388	+	0.509013i
$555$	−9.16436	−	5.86447i	−0.389005	−	0.248933i
$556$	4.41936	+	3.21085i	0.187422	+	0.136170i
$557$			26.5657i			1.12562i	0.826585	+	0.562812i	$0.190281\pi$
$557$			26.5657i			1.12562i	−0.826585	+	0.562812i	$0.809719\pi$
$558$	−1.72437	+	5.29401i	−0.0729983	+	0.224113i
$559$	−26.0716			−1.10271
$560$	4.22486	−	4.28186i	0.178533	−	0.180942i
$561$	−9.49533	−	4.22759i	−0.400893	−	0.178489i
$562$	12.7193	−	4.13274i	0.536530	−	0.174329i
$563$	15.5389	+	8.97139i	0.654887	+	0.378099i	0.790326	−	0.612687i	$-0.209911\pi$
$563$	15.5389	+	8.97139i	0.654887	+	0.378099i	−0.135439	+	0.990786i	$0.543245\pi$
$564$	−0.920599	−	1.59452i	−0.0387642	−	0.0671415i
$565$	11.3491	+	13.8245i	0.477459	+	0.581600i
$566$	−6.43497	+	19.8048i	−0.270482	+	0.832458i
$567$	−1.99915	+	1.80004i	−0.0839564	+	0.0755947i
$568$	0.452413	+	1.01614i	0.0189828	+	0.0426362i
$569$	5.29422	+	1.12532i	0.221945	+	0.0471759i	0.317542	−	0.948244i	$-0.397143\pi$
$569$	5.29422	+	1.12532i	0.221945	+	0.0471759i	−0.0955967	+	0.995420i	$0.530476\pi$
$570$	0.580195	−	2.22485i	0.0243017	−	0.0931886i
$571$	2.47359	+	23.5346i	0.103517	+	0.984894i	0.915801	+	0.401633i	$0.131557\pi$
$571$	2.47359	+	23.5346i	0.103517	+	0.984894i	−0.812284	+	0.583262i	$0.801776\pi$
$572$	−2.89255	−	13.6084i	−0.120943	−	0.568994i
$573$	10.8978	+	14.9996i	0.455264	+	0.626617i
$574$	11.2736	−	8.19076i	0.470552	−	0.341876i
$575$	2.43141	−	26.5519i	0.101397	−	1.10729i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	13.7977	+	1.45020i	0.574406	+	0.0603725i	0.387278	−	0.921963i	$-0.373415\pi$
$577$	13.7977	+	1.45020i	0.574406	+	0.0603725i	0.187128	+	0.982335i	$0.440082\pi$
$578$	0.958869	−	4.51112i	0.0398837	−	0.187638i
$579$	−11.6286	+	5.17740i	−0.483269	+	0.215165i
$580$	−1.54635	−	2.34659i	−0.0642086	−	0.0974368i
$581$	−6.12650	+	18.8554i	−0.254170	+	0.782255i
$582$	12.9514	+	11.6615i	0.536854	+	0.483386i
$583$	−21.1501	+	12.2110i	−0.875948	+	0.505729i
$584$	−0.637345	+	1.10391i	−0.0263735	+	0.0456803i
$585$	13.7278	−	2.26868i	0.567576	−	0.0937983i
$586$	1.30336	+	0.580295i	0.0538414	+	0.0239718i
$587$	21.9812	−	30.2545i	0.907260	−	1.24874i	−0.0608334	−	0.998148i	$-0.519376\pi$
$587$	21.9812	−	30.2545i	0.907260	−	1.24874i	0.968094	−	0.250589i	$-0.0806242\pi$
$588$			0.236757i			0.00976371i
$589$	4.95601	+	2.86614i	0.204209	+	0.118097i
$590$	−1.80320	+	11.9006i	−0.0742365	+	0.489938i
$591$	−13.2325	−	9.61395i	−0.544311	−	0.395465i
$592$	−1.97908	+	4.44508i	−0.0813396	+	0.182692i
$593$	−7.53614	+	2.44864i	−0.309472	+	0.100554i	−0.459636	−	0.888108i	$-0.652020\pi$
$593$	−7.53614	+	2.44864i	−0.309472	+	0.100554i	0.150163	+	0.988661i	$0.452020\pi$
$594$	−1.11790	+	1.93626i	−0.0458680	+	0.0794458i
$595$	−10.1962	−	26.0392i	−0.418004	−	1.06750i
$596$	−13.5623	+	15.0624i	−0.555533	+	0.616982i
$597$	−5.27297	−	1.71329i	−0.215808	−	0.0701204i
$598$	−24.6593	+	22.2033i	−1.00839	+	0.907961i
$599$	−18.7013	+	8.32634i	−0.764113	+	0.340205i	−0.751515	−	0.659716i	$-0.770677\pi$
$599$	−18.7013	+	8.32634i	−0.764113	+	0.340205i	−0.0125977	+	0.999921i	$0.504010\pi$
$600$	4.36324	+	2.44174i	0.178129	+	0.0996837i
$601$	4.35787	−	41.4624i	0.177761	−	1.69129i	−0.434532	−	0.900656i	$-0.643086\pi$
$601$	4.35787	−	41.4624i	0.177761	−	1.69129i	0.612294	−	0.790630i	$-0.290247\pi$
$602$	11.2095	−	1.17817i	0.456866	−	0.0480185i
$603$	−0.589859	−	2.77507i	−0.0240209	−	0.113010i
$604$	2.45097	−	1.78073i	0.0997285	−	0.0724570i
$605$	11.9154	−	6.17211i	0.484429	−	0.250932i
$606$	11.6018	−	2.46605i	0.471292	−	0.100176i
$607$	29.3440	−	3.08418i	1.19104	−	0.125183i	0.511802	−	0.859103i	$-0.328978\pi$
$607$	29.3440	−	3.08418i	1.19104	−	0.125183i	0.679236	+	0.733920i	$0.262311\pi$
$608$	−1.02262	−	0.107482i	−0.0414729	−	0.00435898i
$609$	3.30705	+	0.702936i	0.134009	+	0.0284844i
$610$	−4.32953	−	15.7355i	−0.175297	−	0.637110i
$611$	−7.66618	−	8.51416i	−0.310141	−	0.344446i
$612$	−4.42133	−	1.43658i	−0.178722	−	0.0580702i
$613$	−15.3005	−	13.7767i	−0.617983	−	0.556434i	0.299557	−	0.954078i	$-0.403161\pi$
$613$	−15.3005	−	13.7767i	−0.617983	−	0.556434i	−0.917540	+	0.397644i	$0.869828\pi$
$614$	12.4827	+	21.6207i	0.503761	+	0.872540i
$615$	9.05028	+	7.22889i	0.364942	+	0.291497i
$616$	1.85861	+	5.72021i	0.0748854	+	0.230474i
$617$	11.0070	−	24.7222i	0.443126	−	0.995278i	−0.544544	−	0.838732i	$-0.683297\pi$
$617$	11.0070	−	24.7222i	0.443126	−	0.995278i	0.987671	−	0.156546i	$-0.0500360\pi$
$618$	−7.76654	+	10.6897i	−0.312416	+	0.430004i
$619$	3.50352			0.140818			0.0704092	−	0.997518i	$-0.477570\pi$
$619$	3.50352			0.140818			0.0704092	+	0.997518i	$0.477570\pi$
$620$	−8.75063	+	8.85587i	−0.351434	+	0.355660i
$621$	5.33260			0.213990
$622$	−12.1216	+	16.6839i	−0.486030	+	0.668963i
$623$	11.8060	−	26.5166i	0.472996	−	1.06237i
$624$	−1.92287	−	5.91799i	−0.0769765	−	0.236909i
$625$	−22.5579	+	10.7769i	−0.902316	+	0.431075i
$626$	−3.73654	−	6.47187i	−0.149342	−	0.258668i
$627$	1.70848	+	1.53832i	0.0682299	+	0.0614345i
$628$	9.33870	+	3.03433i	0.372655	+	0.121083i
$629$	15.1359	+	16.8101i	0.603506	+	0.670261i
$630$	−5.79977	+	1.59577i	−0.231068	+	0.0635772i
$631$	10.2703	+	2.18303i	0.408856	+	0.0869051i	0.407748	−	0.913094i	$-0.366314\pi$
$631$	10.2703	+	2.18303i	0.408856	+	0.0869051i	0.00110775	+	0.999999i	$0.499647\pi$
$632$	1.45156	+	0.152565i	0.0577401	+	0.00606872i
$633$	−5.52332	+	0.580524i	−0.219532	+	0.0230738i
$634$	4.43524	−	0.942740i	0.176146	−	0.0374410i
$635$	9.70138	+	18.7287i	0.384988	+	0.743226i
$636$	−8.83703	+	6.42048i	−0.350411	+	0.254589i
$637$	0.306302	+	1.44104i	0.0121361	+	0.0570961i
$638$	2.79455	−	0.293719i	0.110637	−	0.0116285i
$639$	0.116267	−	1.10621i	0.00459945	−	0.0437609i
$640$	0.787328	−	2.09287i	0.0311219	−	0.0827280i
$641$	23.2014	−	10.3299i	0.916399	−	0.408007i	0.106323	−	0.994332i	$-0.466092\pi$
$641$	23.2014	−	10.3299i	0.916399	−	0.408007i	0.810076	+	0.586324i	$0.199426\pi$
$642$	6.97277	−	6.27831i	0.275193	−	0.247785i
$643$	37.3271	+	12.1283i	1.47204	+	0.478293i	0.931723	−	0.363171i	$-0.118306\pi$
$643$	37.3271	+	12.1283i	1.47204	+	0.478293i	0.540313	+	0.841464i	$0.318306\pi$
$644$	9.59891	−	10.6607i	0.378250	−	0.420089i
$645$	3.41603	+	8.72386i	0.134506	+	0.343502i
$646$	−2.39011	+	4.13980i	−0.0940378	+	0.162878i
$647$	14.8728	−	4.83245i	0.584708	−	0.189983i	−0.00170032	−	0.999999i	$-0.500541\pi$
$647$	14.8728	−	4.83245i	0.584708	−	0.189983i	0.586409	+	0.810015i	$0.300541\pi$
$648$	−0.406737	+	0.913545i	−0.0159781	+	0.0358875i
$649$	−9.73649	−	7.07397i	−0.382191	−	0.277678i
$650$	29.7162	+	9.21693i	1.16556	+	0.361518i
$651$	0.0108460	−	14.9780i	0.000425090	−	0.587033i
$652$		−	8.59340i		−	0.336543i
$653$	6.27788	−	8.64076i	0.245673	−	0.338139i	−0.668317	−	0.743876i	$-0.732985\pi$
$653$	6.27788	−	8.64076i	0.245673	−	0.338139i	0.913990	+	0.405737i	$0.132985\pi$
$654$	−10.3387	−	4.60308i	−0.404274	−	0.179995i
$655$	1.04519	+	6.32447i	0.0408390	+	0.247118i
$656$	2.59002	−	4.48605i	0.101123	−	0.175151i
$657$	1.10391	−	0.637345i	0.0430678	−	0.0248652i
$658$	3.68083	+	3.31423i	0.143494	+	0.129202i
$659$	1.42125	−	4.37417i	0.0553642	−	0.170393i	−0.919551	−	0.392971i	$-0.871447\pi$
$659$	1.42125	−	4.37417i	0.0553642	−	0.170393i	0.974915	+	0.222578i	$0.0714472\pi$
$660$	−4.17451	+	2.75091i	−0.162493	+	0.107079i
$661$	−37.7224	+	16.7951i	−1.46723	+	0.653254i	−0.975999	−	0.217774i	$-0.930120\pi$
$661$	−37.7224	+	16.7951i	−1.46723	+	0.653254i	−0.491233	+	0.871028i	$0.663454\pi$
$662$	6.38169	−	30.0235i	0.248031	−	1.16690i
$663$	−28.7693	−	3.02377i	−1.11731	−	0.117434i
$664$	0.770358	+	7.32946i	0.0298957	+	0.284438i
$665$	0.365097	+	6.17449i	0.0141579	+	0.239436i
$666$	3.93647	−	2.86001i	0.152535	−	0.110823i
$667$	−3.93933	−	5.42202i	−0.152531	−	0.209942i
$668$	−3.75293	−	17.6562i	−0.145205	−	0.683138i
$669$	1.38431	+	13.1709i	0.0535206	+	0.509215i
$670$	1.60081	−	6.13857i	0.0618449	−	0.237154i
$671$	15.9617	+	3.39276i	0.616194	+	0.130976i
$672$	1.09417	+	2.45755i	0.0422086	+	0.0948020i
$673$	−17.7826	+	16.0115i	−0.685468	+	0.617198i	−0.936453	−	0.350793i	$-0.885912\pi$
$673$	−17.7826	+	16.0115i	−0.685468	+	0.617198i	0.250985	+	0.967991i	$0.419246\pi$
$674$	8.51760	−	26.2145i	0.328086	−	1.00974i
$675$	−2.55781	−	4.29623i	−0.0984501	−	0.165362i
$676$	−12.8600	−	22.2742i	−0.494616	−	0.856701i
$677$	21.0276	+	12.1403i	0.808154	+	0.466588i	0.846315	−	0.532683i	$-0.178816\pi$
$677$	21.0276	+	12.1403i	0.808154	+	0.466588i	−0.0381601	+	0.999272i	$0.512150\pi$
$678$	−7.60747	+	2.47182i	−0.292163	+	0.0949295i
$679$	−42.8299	−	19.0691i	−1.64366	−	0.731804i
$680$	−7.39959	−	7.30107i	−0.283761	−	0.279983i
$681$	−16.8133			−0.644287
$682$	−3.83820	−	11.8419i	−0.146972	−	0.453451i
$683$		−	39.3515i		−	1.50575i	−0.658166	−	0.752873i	$-0.728668\pi$
$683$		−	39.3515i		−	1.50575i	0.658166	−	0.752873i	$-0.271332\pi$
$684$	0.831878	+	0.604395i	0.0318077	+	0.0231096i
$685$	−13.9276	+	21.7645i	−0.532144	+	0.831578i
$686$	5.62224	+	17.3035i	0.214658	+	0.660650i
$687$	9.34493	+	5.39530i	0.356531	+	0.205844i
$688$	3.62853	−	2.09493i	0.138337	−	0.0798686i
$689$	−45.4808	+	50.5115i	−1.73268	+	1.92433i
$690$	10.6605	+	5.34209i	0.405836	+	0.203370i
$691$	26.5541	+	29.4913i	1.01016	+	1.12190i	0.992523	+	0.122057i	$0.0389491\pi$
$691$	26.5541	+	29.4913i	1.01016	+	1.12190i	0.0176415	+	0.999844i	$0.494384\pi$
$692$	7.83433	+	17.5962i	0.297817	+	0.668907i
$693$	1.25050	−	5.88315i	0.0475026	−	0.223482i
$694$	3.10099	−	29.5040i	0.117712	−	1.11996i
$695$	0.557517	−	12.2021i	0.0211478	−	0.462851i
$696$	1.22933	−	0.261302i	0.0465977	−	0.00990464i
$697$	−14.1546	−	19.4822i	−0.536145	−	0.737941i
$698$	−16.4846	−	22.6891i	−0.623951	−	0.858795i
$699$	13.0389	−	2.77151i	0.493178	−	0.104828i
$700$	−13.1930	−	2.61996i	−0.498648	−	0.0990252i
$701$	4.72270	−	44.9335i	0.178374	−	1.69712i	−0.429488	−	0.903073i	$-0.641306\pi$
$701$	4.72270	−	44.9335i	0.178374	−	1.69712i	0.607862	−	0.794043i	$-0.292027\pi$
$702$	−1.29374	+	6.08657i	−0.0488291	+	0.229723i
$703$	−2.03500	−	4.57069i	−0.0767515	−	0.172387i
$704$	1.49604	+	1.66152i	0.0563843	+	0.0626211i
$705$	−1.84447	+	3.68075i	−0.0694669	+	0.138625i
$706$	15.7216	−	17.4606i	0.591689	−	0.657137i
$707$	−27.6328	+	15.9538i	−1.03924	+	0.600004i
$708$	−4.66168	−	2.69142i	−0.175196	−	0.101150i
$709$	−11.1480	−	34.3101i	−0.418673	−	1.28854i	−0.908924	−	0.416961i	$-0.863095\pi$
$709$	−11.1480	−	34.3101i	−0.418673	−	1.28854i	0.490252	−	0.871581i	$-0.336905\pi$
$710$	1.34061	−	2.09495i	0.0503120	−	0.0786222i
$711$	−1.18081	−	0.857907i	−0.0442837	−	0.0321740i
$712$		−	10.7899i		−	0.404367i
$713$	−19.8829	+	22.0501i	−0.744621	+	0.825782i
$714$	12.5060			0.468025
$715$	−21.8495	+	22.1443i	−0.817125	+	0.828150i
$716$	−22.7502	−	10.1290i	−0.850215	−	0.378540i
$717$	6.84629	−	2.22449i	0.255679	−	0.0830753i
$718$	18.1538	+	10.4811i	0.677495	+	0.391152i
$719$	−8.39465	−	14.5400i	−0.313068	−	0.542249i	0.665957	−	0.745990i	$-0.268023\pi$
$719$	−8.39465	−	14.5400i	−0.313068	−	0.542249i	−0.979025	+	0.203741i	$0.934690\pi$
$720$	−1.72828	+	1.41882i	−0.0644093	+	0.0528762i
$721$	10.9841	−	33.8055i	0.409068	−	1.25898i
$722$	−13.3340	+	12.0060i	−0.496241	+	0.446817i
$723$	−5.98597	−	13.4447i	−0.222621	−	0.500014i
$724$	16.8238	+	3.57601i	0.625251	+	0.132901i
$725$	−2.47876	+	5.77444i	−0.0920587	+	0.214457i
$726$	0.627295	+	5.96831i	0.0232811	+	0.221505i
$727$	1.94894	+	9.16903i	0.0722821	+	0.340061i	0.999397	−	0.0347161i	$-0.0110527\pi$
$727$	1.94894	+	9.16903i	0.0722821	+	0.340061i	−0.927115	+	0.374777i	$0.877719\pi$
$728$	9.83918	+	13.5425i	0.364664	+	0.501917i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	2.84532	−	0.168244i	0.105310	−	0.00622698i
$731$	−2.03602	−	19.3714i	−0.0753048	−	0.716478i
$732$	7.25864	+	0.762914i	0.268287	+	0.0281981i
$733$	−8.20898	+	38.6202i	−0.303206	+	1.42647i	0.517776	+	0.855516i	$0.326760\pi$
$733$	−8.20898	+	38.6202i	−0.303206	+	1.42647i	−0.820982	+	0.570954i	$0.806573\pi$
$734$	−18.7538	+	8.34972i	−0.692214	+	0.308194i
$735$	0.442055	−	0.291304i	0.0163054	−	0.0107449i
$736$	1.64786	−	5.07160i	0.0607411	−	0.186942i
$737$	4.71385	+	4.24437i	0.173637	+	0.156344i
$738$	−4.48605	+	2.59002i	−0.165134	+	0.0953401i
$739$	16.1140	−	27.9103i	0.592763	−	1.02670i	−0.401095	−	0.916036i	$-0.631370\pi$
$739$	16.1140	−	27.9103i	0.592763	−	1.02670i	0.993858	−	0.110659i	$-0.0352963\pi$
$740$	10.7345	−	1.77400i	0.394610	−	0.0652136i
$741$	5.84521	+	2.60246i	0.214729	+	0.0956036i
$742$	17.2719	−	23.7727i	0.634070	−	0.872723i
$743$			12.9685i			0.475770i	0.971293	+	0.237885i	$0.0764541\pi$
$743$			12.9685i			0.475770i	−0.971293	+	0.237885i	$0.923546\pi$
$744$	−2.26093	−	5.08804i	−0.0828897	−	0.186537i
$745$	44.8103	+	6.78976i	1.64172	+	0.248757i
$746$	−18.2353	−	13.2487i	−0.667642	−	0.485070i
$747$	2.99758	−	6.73268i	0.109676	−	0.246336i
$748$	9.88522	−	3.21190i	0.361439	−	0.117439i
$749$	−12.6204	+	21.8592i	−0.461140	+	0.798719i
$750$	−0.809460	−	11.1510i	−0.0295573	−	0.407177i
$751$	23.4247	−	26.0157i	0.854778	−	0.949327i	−0.144414	−	0.989517i	$-0.546130\pi$
$751$	23.4247	−	26.0157i	0.854778	−	0.949327i	0.999192	+	0.0401902i	$0.0127964\pi$
$752$	1.75108	+	0.568961i	0.0638554	+	0.0207479i
$753$	−17.9596	+	16.1709i	−0.654482	+	0.589299i
$754$	7.14435	−	3.18087i	0.260182	−	0.115840i
$755$	−6.34049	−	2.38526i	−0.230754	−	0.0868085i
$756$	0.281194	−	2.67539i	0.0102269	−	0.0973028i
$757$	18.1514	−	1.90779i	0.659724	−	0.0693398i	0.231251	−	0.972894i	$-0.425718\pi$
$757$	18.1514	−	1.90779i	0.659724	−	0.0693398i	0.428474	+	0.903554i	$0.359052\pi$
$758$	−1.98267	−	9.32775i	−0.0720140	−	0.338799i
$759$	−9.64562	+	7.00795i	−0.350114	+	0.254373i
$760$	1.05754	+	2.04161i	0.0383612	+	0.0740570i
$761$	45.7246	−	9.71907i	1.65752	−	0.352316i	0.718324	−	0.695708i	$-0.244909\pi$
$761$	45.7246	−	9.71907i	1.65752	−	0.352316i	0.939192	+	0.343392i	$0.111576\pi$
$762$	−9.38104	+	0.985988i	−0.339839	+	0.0357186i
$763$	30.2776	+	3.18230i	1.09612	+	0.115207i
$764$	−18.1354	−	3.85479i	−0.656115	−	0.139461i
$765$	2.75769	+	10.0227i	0.0997046	+	0.362372i
$766$	−2.48275	−	2.75737i	−0.0897053	−	0.0996278i
$767$	−31.8556	−	10.3505i	−1.15024	−	0.373735i
$768$	0.743145	+	0.669131i	0.0268159	+	0.0241452i
$769$	18.7823	+	32.5319i	0.677308	+	1.17313i	0.975788	+	0.218716i	$0.0701869\pi$
$769$	18.7823	+	32.5319i	0.677308	+	1.17313i	−0.298480	+	0.954416i	$0.596480\pi$
$770$	8.39351	−	10.5083i	0.302481	−	0.378694i
$771$	6.63618	+	20.4241i	0.238996	+	0.735555i
$772$	5.17740	−	11.6286i	0.186339	−	0.418524i
$773$	−17.8249	+	24.5338i	−0.641116	+	0.882421i	−0.998675	−	0.0514702i	$-0.983609\pi$
$773$	−17.8249	+	24.5338i	−0.641116	+	0.882421i	0.357559	+	0.933891i	$0.383609\pi$
$774$	−4.18987			−0.150602
$775$	27.3017	+	5.44232i	0.980705	+	0.195494i
$776$	−17.4279			−0.625624
$777$	−7.69379	+	10.5896i	−0.276013	+	0.379899i
$778$	5.69630	−	12.7941i	0.204222	−	0.458690i
$779$	1.64596	+	5.06573i	0.0589725	+	0.181499i
$780$	−8.68373	+	10.8717i	−0.310927	+	0.389268i
$781$	1.24344	+	2.15370i	0.0444938	+	0.0770656i
$782$	−18.4229	−	16.5881i	−0.658803	−	0.593189i
$783$	−1.19528	−	0.388371i	−0.0427159	−	0.0138793i
$784$	−0.158422	−	0.175945i	−0.00565791	−	0.00628375i
$785$	−5.82478	−	21.1699i	−0.207895	−	0.755586i
$786$	−2.80411	−	0.596032i	−0.100019	−	0.0212597i
$787$	−20.4786	−	2.15239i	−0.729984	−	0.0767245i	−0.267758	−	0.963486i	$-0.586283\pi$
$787$	−20.4786	−	2.15239i	−0.729984	−	0.0767245i	−0.462227	+	0.886762i	$0.652949\pi$
$788$	16.2666	−	1.70969i	0.579474	−	0.0609052i
$789$	14.6255	−	3.10875i	0.520682	−	0.110674i
$790$	−1.50113	−	2.89796i	−0.0534078	−	0.103105i
$791$	17.4086	−	12.6481i	0.618978	−	0.449714i
$792$	−0.464849	−	2.18694i	−0.0165177	−	0.0777097i
$793$	45.1672	−	4.74727i	1.60393	−	0.168580i
$794$	−1.56294	+	14.8704i	−0.0554667	+	0.527731i
$795$	22.8608	+	8.60012i	0.810789	+	0.305015i
$796$	5.06500	−	2.25508i	0.179524	−	0.0799293i
$797$	27.6145	−	24.8642i	0.978154	−	0.880734i	−0.0147209	−	0.999892i	$-0.504686\pi$
$797$	27.6145	−	24.8642i	0.978154	−	0.880734i	0.992875	+	0.119157i	$0.0380193\pi$
$798$	−2.63075	−	0.854784i	−0.0931277	−	0.0302590i
$799$	5.72740	−	6.36093i	0.202621	−	0.225033i
$800$	−4.87637	+	1.10501i	−0.172406	+	0.0390681i
$801$	−5.39493	+	9.34430i	−0.190621	+	0.330165i
$802$	14.7113	−	4.77999i	0.519473	−	0.168787i
$803$	−1.15918	+	2.60356i	−0.0409066	+	0.0918777i
$804$	2.29523	+	1.66759i	0.0809467	+	0.0588112i
$805$	−31.7152	−	4.80555i	−1.11781	−	0.169373i
$806$	−20.3439	−	28.0437i	−0.716584	−	0.987796i
$807$		−	12.9670i		−	0.456462i
$808$	−6.97173	+	9.59577i	−0.245265	+	0.337578i
$809$	22.8768	+	10.1854i	0.804304	+	0.358099i	0.767359	−	0.641218i	$-0.221571\pi$
$809$	22.8768	+	10.1854i	0.804304	+	0.358099i	0.0369455	+	0.999317i	$0.488237\pi$
$810$	2.20614	−	0.364590i	0.0775160	−	0.0128104i
$811$	11.9855	−	20.7595i	0.420868	−	0.728964i	−0.575157	−	0.818043i	$-0.695059\pi$
$811$	11.9855	−	20.7595i	0.420868	−	0.728964i	0.996025	+	0.0890790i	$0.0283924\pi$
$812$	−2.92797	+	1.69047i	−0.102752	+	0.0593237i
$813$	18.8609	+	16.9825i	0.661482	+	0.595601i
$814$	−3.36175	+	10.3464i	−0.117829	+	0.362641i
$815$	−16.0449	+	10.5732i	−0.562029	+	0.370364i
$816$	4.24695	−	1.89086i	0.148673	−	0.0661934i
$817$	−0.895739	+	4.21412i	−0.0313379	+	0.147433i
$818$	17.8153	+	1.87246i	0.622896	+	0.0654690i
$819$	−1.74974	−	16.6477i	−0.0611410	−	0.581718i
$820$	−11.5627	+	0.683704i	−0.403788	+	0.0238760i
$821$	14.2143	−	10.3273i	0.496081	−	0.360424i	−0.311437	−	0.950267i	$-0.600810\pi$
$821$	14.2143	−	10.3273i	0.496081	−	0.360424i	0.807518	+	0.589843i	$0.200810\pi$
$822$	−6.79226	−	9.34875i	−0.236907	−	0.326075i
$823$	−7.21870	−	33.9613i	−0.251628	−	1.18382i	−0.904542	−	0.426385i	$-0.859787\pi$
$823$	−7.21870	−	33.9613i	−0.251628	−	1.18382i	0.652914	−	0.757432i	$-0.273546\pi$
$824$	−1.38116	−	13.1408i	−0.0481149	−	0.457783i
$825$	10.2726	+	4.40964i	0.357644	+	0.153524i
$826$	14.1641	+	3.01066i	0.492831	+	0.104754i
$827$	11.4928	+	25.8133i	0.399644	+	0.897615i	0.995521	+	0.0945392i	$0.0301378\pi$
$827$	11.4928	+	25.8133i	0.399644	+	0.897615i	−0.595877	+	0.803075i	$0.703196\pi$
$828$	−3.96289	+	3.56821i	−0.137720	+	0.124004i
$829$	6.72499	−	20.6974i	0.233568	−	0.718850i	−0.763740	−	0.645524i	$-0.776639\pi$
$829$	6.72499	−	20.6974i	0.233568	−	0.718850i	0.997308	−	0.0733252i	$-0.0233611\pi$
$830$	12.7372	−	10.4564i	0.442113	−	0.362949i
$831$	6.29864	+	10.9096i	0.218498	+	0.378449i
$832$	5.38888	+	3.11127i	0.186826	+	0.107864i
$833$	−1.04678	+	0.340120i	−0.0362689	+	0.0117845i
$834$	4.99035	+	2.22185i	0.172802	+	0.0769363i
$835$	−28.3486	+	28.7311i	−0.981045	+	0.994282i
$836$	−2.29898			−0.0795119
$837$	−0.585999	+	5.53684i	−0.0202551	+	0.191381i
$838$		−	13.8177i		−	0.477324i
$839$	−16.0796	−	11.6825i	−0.555130	−	0.403326i	0.274543	−	0.961575i	$-0.411473\pi$
$839$	−16.0796	−	11.6825i	−0.555130	−	0.403326i	−0.829673	+	0.558249i	$0.811473\pi$
$840$	3.24228	−	5.06669i	0.111869	−	0.174818i
$841$	−8.47339	−	26.0784i	−0.292186	−	0.899256i
$842$	−19.7849	−	11.4228i	−0.681833	−	0.393656i
$843$	11.5821	−	6.68691i	0.398908	−	0.230309i
$844$	3.71618	−	4.12724i	0.127916	−	0.142065i
$845$	−25.7658	+	51.4172i	−0.886372	+	1.76881i
$846$	−1.23200	−	1.36828i	−0.0423571	−	0.0470423i
$847$	−6.56633	−	14.7482i	−0.225622	−	0.506755i
$848$	2.27105	−	10.6845i	0.0779883	−	0.366906i
$849$	−2.17670	+	20.7099i	−0.0747042	+	0.710763i
$850$	−4.52761	+	22.7991i	−0.155296	+	0.782002i
$851$	25.3801	−	5.39470i	0.870018	−	0.184928i
$852$	0.653794	+	0.899870i	0.0223986	+	0.0308290i
$853$	1.68468	+	2.31876i	0.0576823	+	0.0793929i	0.836884	−	0.547381i	$-0.184375\pi$
$853$	1.68468	+	2.31876i	0.0576823	+	0.0793929i	−0.779201	+	0.626774i	$0.784375\pi$
$854$	−19.2051	+	4.08218i	−0.657186	+	0.139689i
$855$	0.104944	−	2.29686i	0.00358902	−	0.0785509i
$856$	−0.980769	+	9.33139i	−0.0335220	+	0.318940i
$857$	4.20738	−	19.7942i	0.143721	−	0.676156i	−0.846004	−	0.533176i	$-0.820998\pi$
$857$	4.20738	−	19.7942i	0.143721	−	0.676156i	0.989726	−	0.142980i	$-0.0456683\pi$
$858$	−5.65867	−	12.7096i	−0.193184	−	0.433898i
$859$	28.0631	+	31.1673i	0.957501	+	1.06341i	0.997935	+	0.0642307i	$0.0204593\pi$
$859$	28.0631	+	31.1673i	0.957501	+	1.06341i	−0.0404338	+	0.999182i	$0.512874\pi$
$860$	−8.37601	−	4.19733i	−0.285619	−	0.143128i
$861$	9.32431	−	10.3557i	0.317771	−	0.352921i
$862$	22.1930	−	12.8131i	0.755896	−	0.436417i
$863$	−13.0786	−	7.55091i	−0.445200	−	0.257036i	0.260601	−	0.965447i	$-0.416079\pi$
$863$	−13.0786	−	7.55091i	−0.445200	−	0.257036i	−0.705801	+	0.708410i	$0.749413\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	23.2150	−	36.2778i	0.789332	−	1.23348i
$866$	−7.75610	−	5.63513i	−0.263563	−	0.191490i
$867$		−	4.61191i		−	0.156629i
$868$	10.0142	+	11.1381i	0.339902	+	0.378050i
$869$	3.26328			0.110699
$870$	−2.00044	−	1.97381i	−0.0678213	−	0.0669183i
$871$	16.1275	+	7.18043i	0.546460	+	0.243300i
$872$	10.7632	−	3.49718i	0.364488	−	0.118429i
$873$	15.0930	+	8.71394i	0.510820	+	0.294922i
$874$	2.74164	+	4.74867i	0.0927375	+	0.160626i
$875$	11.3407	+	27.8565i	0.383386	+	0.941720i
$876$	−0.393901	+	1.21230i	−0.0133087	+	0.0409599i
$877$	15.7583	−	14.1888i	0.532119	−	0.479123i	−0.358717	−	0.933446i	$-0.616786\pi$
$877$	15.7583	−	14.1888i	0.532119	−	0.479123i	0.890837	+	0.454324i	$0.150119\pi$
$878$	−15.6770	−	35.2111i	−0.529072	−	1.18832i
$879$	1.39553	+	0.296629i	0.0470701	+	0.0100051i
$880$	1.26155	−	4.83762i	0.0425269	−	0.163076i
$881$	−4.73056	−	45.0082i	−0.159376	−	1.51637i	−0.723297	−	0.690537i	$-0.757374\pi$
$881$	−4.73056	−	45.0082i	−0.159376	−	1.51637i	0.563921	−	0.825829i	$-0.309292\pi$
$882$	0.0492246	+	0.231584i	0.00165748	+	0.00779783i
$883$	20.9909	+	28.8916i	0.706402	+	0.972278i	0.999867	+	0.0163087i	$0.00519146\pi$
$883$	20.9909	+	28.8916i	0.706402	+	0.972278i	−0.293465	+	0.955970i	$0.594809\pi$
$884$	23.4030	−	17.0033i	0.787129	−	0.571883i
$885$	0.710470	+	12.0154i	0.0238822	+	0.403893i
$886$	2.10551	+	20.0325i	0.0707358	+	0.673007i
$887$	0.398795	+	0.0419150i	0.0133902	+	0.00140737i	0.111221	−	0.993796i	$-0.464524\pi$
$887$	0.398795	+	0.0419150i	0.0133902	+	0.00140737i	−0.0978310	+	0.995203i	$0.531190\pi$
$888$	−1.01165	+	4.75942i	−0.0339486	+	0.159716i
$889$	23.1814	−	10.3210i	0.777478	−	0.346156i
$890$	−20.1460	+	13.2757i	−0.675295	+	0.445004i
$891$	−0.690901	+	2.12637i	−0.0231460	+	0.0712362i
$892$	−9.84177	−	8.86157i	−0.329527	−	0.296707i
$893$	−1.63958	+	0.946613i	−0.0548665	+	0.0316772i
$894$	−10.1343	+	17.5530i	−0.338940	+	0.587062i
$895$	9.07946	+	54.9401i	0.303493	+	1.83644i
$896$	−2.45755	−	1.09417i	−0.0821009	−	0.0365537i
$897$	−19.5041	+	26.8451i	−0.651223	+	0.896331i
$898$			9.08702i			0.303238i
$899$	6.06258	−	3.49438i	0.202198	−	0.116544i
$900$	4.77556	+	1.48122i	0.159185	+	0.0493738i
$901$	−41.0821	−	29.8479i	−1.36864	−	0.994378i
$902$	4.71064	−	10.5803i	0.156847	−	0.352285i
$903$	10.7196	−	3.48301i	0.356726	−	0.115907i
$904$	3.99948	−	6.92731i	0.133021	−	0.230399i
$905$	−14.0230	−	35.8119i	−0.466140	−	1.19043i
$906$	2.02717	−	2.25140i	0.0673483	−	0.0747979i
$907$	−10.3272	−	3.35553i	−0.342911	−	0.111418i	0.132499	−	0.991183i	$-0.457700\pi$
$907$	−10.3272	−	3.35553i	−0.342911	−	0.111418i	−0.475409	+	0.879765i	$0.657700\pi$
$908$	12.4947	−	11.2503i	0.414651	−	0.373354i
$909$	10.8356	−	4.82431i	0.359394	−	0.160012i
$910$	13.1794	−	35.0334i	0.436893	−	1.16135i
$911$	1.09901	−	10.4564i	0.0364119	−	0.346436i	−0.961115	−	0.276149i	$-0.910942\pi$
$911$	1.09901	−	10.4564i	0.0364119	−	0.346436i	0.997527	−	0.0702872i	$-0.0223916\pi$
$912$	−1.02262	+	0.107482i	−0.0338625	+	0.00355909i
$913$	3.42586	+	16.1174i	0.113380	+	0.533409i
$914$	14.8212	−	10.7682i	0.490243	−	0.356182i
$915$	−7.50650	−	14.4914i	−0.248157	−	0.479072i
$916$	−10.5548	+	2.24349i	−0.348740	+	0.0741270i
$917$	7.66967	−	0.806115i	0.253275	−	0.0266203i
$918$	−4.62339	−	0.485938i	−0.152595	−	0.0160384i
$919$	48.2392	+	10.2536i	1.59127	+	0.338234i	0.916574	−	0.399866i	$-0.130943\pi$
$919$	48.2392	+	10.2536i	1.59127	+	0.338234i	0.674692	+	0.738100i	$0.264277\pi$
$920$	−11.4968	+	3.16329i	−0.379039	+	0.104290i
$921$	16.7051	+	18.5529i	0.550453	+	0.611340i
$922$	38.1735	+	12.4033i	1.25718	+	0.408482i
$923$	5.14356	+	4.63128i	0.169302	+	0.152440i
$924$	3.00729	+	5.20878i	0.0989326	+	0.171356i
$925$	−16.5199	−	17.8600i	−0.543172	−	0.587232i
$926$	7.93414	+	24.4188i	0.260732	+	0.802451i
$927$	−5.37430	+	12.0709i	−0.176515	+	0.396460i
$928$	−0.738726	+	1.01677i	−0.0242499	+	0.0333771i
$929$	8.37303			0.274710			0.137355	−	0.990522i	$-0.456140\pi$
$929$	8.37303			0.274710			0.137355	+	0.990522i	$0.456140\pi$
$930$	−6.71817	+	10.4817i	−0.220298	+	0.343709i
$931$	0.243448			0.00797867
$932$	−7.83531	+	10.7844i	−0.256654	+	0.353254i
$933$	−8.38790	+	18.8395i	−0.274607	+	0.616779i
$934$	7.54572	+	23.2234i	0.246904	+	0.759891i
$935$	−18.1597	−	14.5050i	−0.593885	−	0.474365i
$936$	−3.11127	−	5.38888i	−0.101695	−	0.176141i
$937$	0.871875	+	0.785040i	0.0284829	+	0.0256461i	0.683249	−	0.730185i	$-0.260566\pi$
$937$	0.871875	+	0.785040i	0.0284829	+	0.0256461i	−0.654766	+	0.755831i	$0.727233\pi$
$938$	−7.25851	−	2.35843i	−0.236999	−	0.0770056i
$939$	−5.00046	−	5.55358i	−0.163184	−	0.181234i
$940$	−1.09219	−	3.96953i	−0.0356234	−	0.129472i
$941$	27.8554	+	5.92085i	0.908060	+	0.193014i	0.638187	−	0.769882i	$-0.279685\pi$
$941$	27.8554	+	5.92085i	0.908060	+	0.193014i	0.269874	+	0.962896i	$0.413018\pi$
$942$	9.76550	+	1.02640i	0.318177	+	0.0334418i
$943$	−27.4718	+	2.88740i	−0.894605	+	0.0940267i
$944$	5.26521	−	1.11916i	0.171368	−	0.0364254i
$945$	−5.34125	+	2.76674i	−0.173751	+	0.0900021i
$946$	7.57864	−	5.50621i	0.246403	−	0.179022i
$947$	2.83068	+	13.3173i	0.0919846	+	0.432753i	0.999907	+	0.0136158i	$0.00433419\pi$
$947$	2.83068	+	13.3173i	0.0919846	+	0.432753i	−0.907923	+	0.419138i	$0.862332\pi$
$948$	1.45156	−	0.152565i	0.0471446	−	0.00495509i
$949$	−0.829100	+	7.88836i	−0.0269137	+	0.256067i
$950$	2.51074	−	4.48654i	0.0814592	−	0.145563i
$951$	4.14232	−	1.84428i	0.134324	−	0.0598048i
$952$	−9.29377	+	8.36815i	−0.301213	+	0.271213i
$953$	34.1808	+	11.1060i	1.10723	+	0.359759i	0.804879	−	0.593439i	$-0.202230\pi$
$953$	34.1808	+	11.1060i	1.10723	+	0.359759i	0.302346	+	0.953198i	$0.402230\pi$
$954$	−7.30903	+	8.11750i	−0.236639	+	0.262814i
$955$	15.1162	+	38.6038i	0.489149	+	1.24919i
$956$	−3.59931	+	6.23419i	−0.116410	+	0.201628i
$957$	2.67242	−	0.868321i	0.0863870	−	0.0280688i
$958$	6.12042	−	13.7467i	0.197742	−	0.444136i
$959$	25.1493	+	18.2720i	0.812112	+	0.590034i
$960$	0.334990	−	2.21083i	0.0108118	−	0.0713543i
$961$	−20.7097	−	23.0675i	−0.668054	−	0.744113i
$962$			30.2773i			0.976180i
$963$	5.51507	−	7.59084i	0.177721	−	0.244611i
$964$	13.4447	+	5.98597i	0.433025	+	0.192795i
$965$	−28.0823	+	4.64091i	−0.904001	+	0.149396i
$966$	7.17267	−	12.4234i	0.230777	−	0.399717i
$967$	−33.7487	+	19.4848i	−1.08528	+	0.626589i	−0.932317	−	0.361642i	$-0.882216\pi$
$967$	−33.7487	+	19.4848i	−1.08528	+	0.626589i	−0.152967	+	0.988231i	$0.548883\pi$
$968$	−4.45975	−	4.01558i	−0.143342	−	0.129066i
$969$	−1.47717	+	4.54627i	−0.0474536	+	0.146047i
$970$	21.4431	+	32.5400i	0.688496	+	1.04480i
$971$	50.6464	−	22.5492i	1.62532	−	0.723639i	0.626860	−	0.779132i	$-0.284340\pi$
$971$	50.6464	−	22.5492i	1.62532	−	0.723639i	0.998459	+	0.0554933i	$0.0176732\pi$
$972$	−0.207912	+	0.978148i	−0.00666877	+	0.0313741i
$973$	−14.6146	−	1.53606i	−0.468523	−	0.0492438i
$974$	3.33048	+	31.6874i	0.106716	+	1.01533i
$975$	30.9831	+	2.83718i	0.992253	+	0.0908625i
$976$	−5.90471	+	4.29002i	−0.189005	+	0.137320i
$977$	23.6905	+	32.6071i	0.757926	+	1.04320i	0.997384	+	0.0722883i	$0.0230302\pi$
$977$	23.6905	+	32.6071i	0.757926	+	1.04320i	−0.239458	+	0.970907i	$0.576970\pi$
$978$	−1.78667	−	8.40561i	−0.0571313	−	0.268782i
$979$	−2.52164	−	23.9918i	−0.0805921	−	0.766783i
$980$	−0.133590	+	0.512273i	−0.00426739	+	0.0163640i
$981$	−11.0698	−	2.35296i	−0.353431	−	0.0751241i
$982$	−2.38733	−	5.36203i	−0.0761827	−	0.171109i
$983$	−36.6580	+	33.0070i	−1.16921	+	1.05276i	−0.171494	+	0.985185i	$0.554860\pi$
$983$	−36.6580	+	33.0070i	−1.16921	+	1.05276i	−0.997714	+	0.0675751i	$0.978474\pi$
$984$	1.60072	−	4.92652i	0.0510292	−	0.157052i
$985$	−23.2065	−	28.2682i	−0.739420	−	0.900699i
$986$	2.92133	+	5.05990i	0.0930342	+	0.161140i
$987$	4.28946	+	2.47652i	0.136535	+	0.0788286i
$988$	−6.08522	+	1.97721i	−0.193597	+	0.0629034i
$989$	−20.4113	−	9.08768i	−0.649040	−	0.288971i
$990$	−3.51134	+	3.55872i	−0.111598	+	0.113104i
$991$	−55.1238			−1.75106			−0.875532	−	0.483160i	$-0.839489\pi$
$991$	−55.1238			−1.75106			−0.875532	+	0.483160i	$0.839489\pi$
$992$	5.08476	+	2.26830i	0.161441	+	0.0720185i
$993$		−	30.6942i		−	0.974052i
$994$	−2.42076	−	1.75878i	−0.0767818	−	0.0557853i
$995$	−10.4424	−	6.68234i	−0.331048	−	0.211844i
$996$	2.27740	+	7.00913i	0.0721623	+	0.222093i
$997$	−15.5161	−	8.95824i	−0.491401	−	0.283710i	0.233755	−	0.972296i	$-0.424899\pi$
$997$	−15.5161	−	8.95824i	−0.491401	−	0.283710i	−0.725155	+	0.688585i	$0.758232\pi$
$998$	−18.3706	+	10.6063i	−0.581512	+	0.335736i
$999$	3.25582	−	3.61595i	0.103010	−	0.114404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bn.b.19.2	✓	144
5.4	even	2	inner	930.2.bn.b.19.13	yes	144
31.18	even	15	inner	930.2.bn.b.49.13	yes	144
155.49	even	30	inner	930.2.bn.b.49.2	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bn.b.19.2	✓	144	1.1	even	1	trivial
930.2.bn.b.19.13	yes	144	5.4	even	2	inner
930.2.bn.b.49.2	yes	144	155.49	even	30	inner
930.2.bn.b.49.13	yes	144	31.18	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.39553 + 1.74714i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.99915 + 1.80004i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.39553 + 1.74714i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.99915 + 1.80004i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(-0.593198 - 2.15595i) q^{10} +(2.18694 + 0.464849i) q^{11} +(0.994522 + 0.104528i) q^{12} +(6.18846 - 0.650433i) q^{13} +(-2.63134 + 0.559308i) q^{14} +(-1.02848 - 1.98550i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.966552 + 4.54727i) q^{17} +(0.994522 - 0.104528i) q^{18} +(0.107482 - 1.02262i) q^{19} +(2.09287 + 0.787328i) q^{20} +(-2.45755 + 1.09417i) q^{21} +(-1.66152 + 1.49604i) q^{22} +(5.07160 + 1.64786i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-1.10501 - 4.87637i) q^{25} +(-3.11127 + 5.38888i) q^{26} +(0.951057 - 0.309017i) q^{27} +(1.09417 - 2.45755i) q^{28} +(-1.01677 - 0.738726i) q^{29} +(2.21083 + 0.334990i) q^{30} +(-2.26830 + 5.08476i) q^{31} -1.00000i q^{32} +(-1.31417 + 1.80880i) q^{33} +(-4.24695 - 1.89086i) q^{34} +(-5.93480 + 0.980792i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.21386 - 2.43287i) q^{37} +(0.764144 + 0.688039i) q^{38} +(-1.92287 + 5.91799i) q^{39} +(-1.86712 + 1.23039i) q^{40} +(-4.73221 + 2.10691i) q^{41} +(0.559308 - 2.63134i) q^{42} +(-4.16692 - 0.437961i) q^{43} +(-0.233705 - 2.22355i) q^{44} +(2.23217 - 0.131988i) q^{45} +(-4.31416 + 3.13442i) q^{46} +(-1.08223 - 1.48956i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(0.0247479 + 0.235460i) q^{49} +(4.59457 + 1.97228i) q^{50} +(-4.54727 - 0.966552i) q^{51} +(-2.53094 - 5.68458i) q^{52} +(-8.11750 + 7.30903i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-3.86410 + 3.17219i) q^{55} +(1.34506 + 2.32971i) q^{56} +(0.890497 + 0.514129i) q^{57} +(1.19528 - 0.388371i) q^{58} +(-4.91747 - 2.18940i) q^{59} +(-1.57051 + 1.59170i) q^{60} +7.29862 q^{61} +(-2.78039 - 4.82384i) q^{62} -2.69012i q^{63} +(0.809017 + 0.587785i) q^{64} +(-7.49976 + 11.7198i) q^{65} +(-0.690901 - 2.12637i) q^{66} +(2.45697 + 1.41853i) q^{67} +(4.02603 - 2.32443i) q^{68} +(-3.56821 + 3.96289i) q^{69} +(2.69491 - 5.37785i) q^{70} +(0.744274 + 0.826600i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(-0.265023 + 1.24683i) q^{73} +(-0.508609 + 4.83909i) q^{74} +(4.90423 + 0.973919i) q^{75} +(-1.00579 + 0.213787i) q^{76} +(3.53528 + 4.86590i) q^{77} +(-3.65752 - 5.03414i) q^{78} +(1.42766 - 0.303459i) q^{79} +(0.102060 - 2.23374i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(1.07699 - 5.06685i) q^{82} +(2.99758 + 6.73268i) q^{83} +(1.80004 + 1.99915i) q^{84} +(-9.29358 - 4.65713i) q^{85} +(2.80357 - 3.11368i) q^{86} +(1.08842 - 0.628398i) q^{87} +(1.93626 + 1.11790i) q^{88} +(-3.33425 - 10.2618i) q^{89} +(-1.20526 + 1.88344i) q^{90} +(13.5425 + 9.83918i) q^{91} -5.33260i q^{92} +(-3.72256 - 4.14035i) q^{93} +1.84120 q^{94} +(1.63668 + 1.61489i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-16.5749 + 5.38551i) q^{97} +(-0.205038 - 0.118379i) q^{98} +(-1.11790 - 1.93626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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