LMFDB - Embedded newform 750.2.o.a.619.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [750,2,Mod(19,750)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("750.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(750, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([0, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [240] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			619.12
Character	$\chi$	$=$	750.619
Dual form			750.2.o.a.229.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.248690 - 0.968583i) q^{2} +(0.982287 + 0.187381i) q^{3} +(-0.876307 - 0.481754i) q^{4} +(1.61258 - 1.54906i) q^{5} +(0.425779 - 0.904827i) q^{6} +(0.699566 + 0.962870i) q^{7} +(-0.684547 + 0.728969i) q^{8} +(0.929776 + 0.368125i) q^{9} +(-1.09936 - 1.94715i) q^{10} +(-0.289463 - 0.0743214i) q^{11} +(-0.770513 - 0.637424i) q^{12} +(1.45894 - 3.68486i) q^{13} +(1.10659 - 0.438132i) q^{14} +(1.87428 - 1.21945i) q^{15} +(0.535827 + 0.844328i) q^{16} +(-0.233766 - 0.425219i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-0.106393 - 0.557734i) q^{19} +(-2.15938 + 0.580585i) q^{20} +(0.506751 + 1.07690i) q^{21} +(-0.143973 + 0.261886i) q^{22} +(3.48258 - 0.219105i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(0.200831 - 4.99597i) q^{25} +(-3.20627 - 2.32949i) q^{26} +(0.844328 + 0.535827i) q^{27} +(-0.149168 - 1.18079i) q^{28} +(8.38529 - 1.05931i) q^{29} +(-0.715027 - 2.11866i) q^{30} +(-5.20391 + 2.86087i) q^{31} +(0.951057 - 0.309017i) q^{32} +(-0.270409 - 0.127245i) q^{33} +(-0.469995 + 0.120674i) q^{34} +(2.61965 + 0.469036i) q^{35} +(-0.637424 - 0.770513i) q^{36} +(-5.30628 + 3.36747i) q^{37} +(-0.566671 - 0.0356519i) q^{38} +(2.12357 - 3.34621i) q^{39} +(0.0253284 + 2.23592i) q^{40} +(0.0193451 - 0.307482i) q^{41} +(1.16909 - 0.223016i) q^{42} +(-3.49380 - 1.13521i) q^{43} +(0.217854 + 0.204578i) q^{44} +(2.06959 - 0.846648i) q^{45} +(0.653860 - 3.42766i) q^{46} +(2.23834 + 2.38359i) q^{47} +(0.368125 + 0.929776i) q^{48} +(1.72539 - 5.31021i) q^{49} +(-4.78906 - 1.43697i) q^{50} +(-0.149947 - 0.461491i) q^{51} +(-3.05367 + 2.52622i) q^{52} +(-6.75236 + 3.17742i) q^{53} +(0.728969 - 0.684547i) q^{54} +(-0.581910 + 0.328546i) q^{55} +(-1.18079 - 0.149168i) q^{56} -0.567791i q^{57} +(1.05931 - 8.38529i) q^{58} +(-4.63128 + 5.59825i) q^{59} +(-2.22992 + 0.165673i) q^{60} +(-0.0466440 - 0.741384i) q^{61} +(1.47683 + 5.75189i) q^{62} +(0.295984 + 1.15278i) q^{63} +(-0.0627905 - 0.998027i) q^{64} +(-3.35541 - 8.20211i) q^{65} +(-0.190495 + 0.230269i) q^{66} +(0.320716 - 2.53873i) q^{67} +0.485240i q^{68} +(3.46195 + 0.437346i) q^{69} +(1.10578 - 2.42070i) q^{70} +(-5.11472 + 4.80304i) q^{71} +(-0.904827 + 0.425779i) q^{72} +(7.91296 - 6.54617i) q^{73} +(1.94205 + 5.97703i) q^{74} +(1.13342 - 4.86984i) q^{75} +(-0.175457 + 0.540002i) q^{76} +(-0.130936 - 0.330708i) q^{77} +(-2.71297 - 2.88902i) q^{78} +(-0.548519 + 2.87544i) q^{79} +(2.17198 + 0.531519i) q^{80} +(0.728969 + 0.684547i) q^{81} +(-0.293011 - 0.0952050i) q^{82} +(14.6821 - 2.80075i) q^{83} +(0.0747315 - 1.18782i) q^{84} +(-1.03566 - 0.323582i) q^{85} +(-1.96841 + 3.10173i) q^{86} +(8.43526 + 0.530701i) q^{87} +(0.252329 - 0.160133i) q^{88} +(2.87378 + 3.47381i) q^{89} +(-0.305364 - 2.21512i) q^{90} +(4.56866 - 1.17303i) q^{91} +(-3.15736 - 1.48574i) q^{92} +(-5.64781 + 1.83508i) q^{93} +(2.86536 - 1.57524i) q^{94} +(-1.03553 - 0.734581i) q^{95} +(0.992115 - 0.125333i) q^{96} +(1.39979 + 11.0805i) q^{97} +(-4.71430 - 2.99178i) q^{98} +(-0.241776 - 0.175661i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42}+ \cdots - 20 q^{99}+O(q^{100}) $ 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{29}{50}\right)$	$1$

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 $

$2$	0.248690	−	0.968583i	0.175850	−	0.684892i
$2$	0.248690	−	0.968583i	0.175850	−	0.684892i
$3$	0.982287	+	0.187381i	0.567124	+	0.108185i
$3$	0.982287	+	0.187381i	0.567124	+	0.108185i
$4$	−0.876307	−	0.481754i	−0.438153	−	0.240877i
$5$	1.61258	−	1.54906i	0.721168	−	0.692760i
$5$	1.61258	−	1.54906i	0.721168	−	0.692760i
$6$	0.425779	−	0.904827i	0.173824	−	0.369394i
$7$	0.699566	+	0.962870i	0.264411	+	0.363931i	0.920493	−	0.390759i	$-0.127787\pi$
$7$	0.699566	+	0.962870i	0.264411	+	0.363931i	−0.656082	+	0.754690i	$0.727787\pi$
$8$	−0.684547	+	0.728969i	−0.242024	+	0.257729i
$9$	0.929776	+	0.368125i	0.309925	+	0.122708i
$10$	−1.09936	−	1.94715i	−0.347648	−	0.615744i
$11$	−0.289463	−	0.0743214i	−0.0872763	−	0.0224088i	0.204799	−	0.978804i	$-0.434346\pi$
$11$	−0.289463	−	0.0743214i	−0.0872763	−	0.0224088i	−0.292076	+	0.956395i	$0.594346\pi$
$12$	−0.770513	−	0.637424i	−0.222428	−	0.184008i
$13$	1.45894	−	3.68486i	0.404637	−	1.02200i	−0.574448	−	0.818541i	$-0.694783\pi$
$13$	1.45894	−	3.68486i	0.404637	−	1.02200i	0.979084	−	0.203454i	$-0.0652169\pi$
$14$	1.10659	−	0.438132i	0.295750	−	0.117096i
$15$	1.87428	−	1.21945i	0.483937	−	0.314862i
$16$	0.535827	+	0.844328i	0.133957	+	0.211082i
$17$	−0.233766	−	0.425219i	−0.0566966	−	0.103131i	0.846440	−	0.532484i	$-0.178741\pi$
$17$	−0.233766	−	0.425219i	−0.0566966	−	0.103131i	−0.903137	+	0.429353i	$0.858741\pi$
$18$	0.587785	−	0.809017i	0.138542	−	0.190687i
$19$	−0.106393	−	0.557734i	−0.0244083	−	0.127953i	0.967997	−	0.250960i	$-0.0807462\pi$
$19$	−0.106393	−	0.557734i	−0.0244083	−	0.127953i	−0.992406	+	0.123007i	$0.960746\pi$
$20$	−2.15938	+	0.580585i	−0.482852	+	0.129823i
$21$	0.506751	+	1.07690i	0.110582	+	0.234999i
$22$	−0.143973	+	0.261886i	−0.0306951	+	0.0558342i
$23$	3.48258	−	0.219105i	0.726168	−	0.0456866i	0.304596	−	0.952482i	$-0.401479\pi$
$23$	3.48258	−	0.219105i	0.726168	−	0.0456866i	0.421572	+	0.906795i	$0.361479\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	0.200831	−	4.99597i	0.0401661	−	0.999193i
$26$	−3.20627	−	2.32949i	−0.628801	−	0.456851i
$27$	0.844328	+	0.535827i	0.162491	+	0.103120i
$28$	−0.149168	−	1.18079i	−0.0281901	−	0.223148i
$29$	8.38529	−	1.05931i	1.55711	−	0.196709i	0.700870	−	0.713289i	$-0.252795\pi$
$29$	8.38529	−	1.05931i	1.55711	−	0.196709i	0.856239	+	0.516580i	$0.172795\pi$
$30$	−0.715027	−	2.11866i	−0.130546	−	0.386813i
$31$	−5.20391	+	2.86087i	−0.934650	+	0.513828i	−0.874856	−	0.484383i	$-0.839044\pi$
$31$	−5.20391	+	2.86087i	−0.934650	+	0.513828i	−0.0597936	+	0.998211i	$0.519044\pi$
$32$	0.951057	−	0.309017i	0.168125	−	0.0546270i
$33$	−0.270409	−	0.127245i	−0.0470722	−	0.0221505i
$34$	−0.469995	+	0.120674i	−0.0806035	+	0.0206955i
$35$	2.61965	+	0.469036i	0.442801	+	0.0792815i
$36$	−0.637424	−	0.770513i	−0.106237	−	0.128419i
$37$	−5.30628	+	3.36747i	−0.872347	+	0.553608i	−0.894965	−	0.446136i	$-0.852800\pi$
$37$	−5.30628	+	3.36747i	−0.872347	+	0.553608i	0.0226184	+	0.999744i	$0.492800\pi$
$38$	−0.566671	−	0.0356519i	−0.0919261	−	0.00578350i
$39$	2.12357	−	3.34621i	0.340043	−	0.535823i
$40$	0.0253284	+	2.23592i	0.00400478	+	0.353531i
$41$	0.0193451	−	0.307482i	0.00302120	−	0.0480206i	−0.996227	−	0.0867827i	$-0.972341\pi$
$41$	0.0193451	−	0.307482i	0.00302120	−	0.0480206i	0.999248	+	0.0387620i	$0.0123414\pi$
$42$	1.16909	−	0.223016i	0.180395	−	0.0344121i
$43$	−3.49380	−	1.13521i	−0.532800	−	0.173117i	0.0302464	−	0.999542i	$-0.490371\pi$
$43$	−3.49380	−	1.13521i	−0.532800	−	0.173117i	−0.563047	+	0.826425i	$0.690371\pi$
$44$	0.217854	+	0.204578i	0.0328427	+	0.0308413i
$45$	2.06959	−	0.846648i	0.308516	−	0.126211i
$46$	0.653860	−	3.42766i	0.0964064	−	0.505380i
$47$	2.23834	+	2.38359i	0.326495	+	0.347682i	0.871184	−	0.490956i	$-0.163352\pi$
$47$	2.23834	+	2.38359i	0.326495	+	0.347682i	−0.544689	+	0.838638i	$0.683352\pi$
$48$	0.368125	+	0.929776i	0.0531342	+	0.134202i
$49$	1.72539	−	5.31021i	0.246485	−	0.758602i
$50$	−4.78906	−	1.43697i	−0.677276	−	0.203218i
$51$	−0.149947	−	0.461491i	−0.0209968	−	0.0646216i
$52$	−3.05367	+	2.52622i	−0.423468	+	0.350323i
$53$	−6.75236	+	3.17742i	−0.927509	+	0.436452i	−0.829357	−	0.558719i	$-0.811293\pi$
$53$	−6.75236	+	3.17742i	−0.927509	+	0.436452i	−0.0981516	+	0.995171i	$0.531293\pi$
$54$	0.728969	−	0.684547i	0.0992001	−	0.0931551i
$55$	−0.581910	+	0.328546i	−0.0784648	+	0.0443011i
$56$	−1.18079	−	0.149168i	−0.157789	−	0.0199334i
$57$		−	0.567791i		−	0.0752058i
$58$	1.05931	−	8.38529i	0.139094	−	1.10104i
$59$	−4.63128	+	5.59825i	−0.602941	+	0.728830i	−0.980361	−	0.197212i	$-0.936811\pi$
$59$	−4.63128	+	5.59825i	−0.602941	+	0.728830i	0.377420	+	0.926042i	$0.376811\pi$
$60$	−2.22992	+	0.165673i	−0.287882	+	0.0213883i
$61$	−0.0466440	−	0.741384i	−0.00597215	−	0.0949245i	0.993911	−	0.110182i	$-0.0351433\pi$
$61$	−0.0466440	−	0.741384i	−0.00597215	−	0.0949245i	−0.999884	+	0.0152572i	$0.995143\pi$
$62$	1.47683	+	5.75189i	0.187558	+	0.730491i
$63$	0.295984	+	1.15278i	0.0372905	+	0.145237i
$64$	−0.0627905	−	0.998027i	−0.00784881	−	0.124753i
$65$	−3.35541	−	8.20211i	−0.416187	−	1.01735i
$66$	−0.190495	+	0.230269i	−0.0234484	+	0.0283442i
$67$	0.320716	−	2.53873i	0.0391817	−	0.310155i	−0.960329	−	0.278870i	$-0.910040\pi$
$67$	0.320716	−	2.53873i	0.0391817	−	0.310155i	0.999511	−	0.0312849i	$-0.00995992\pi$
$68$			0.485240i			0.0588440i
$69$	3.46195	+	0.437346i	0.416770	+	0.0526502i
$70$	1.10578	−	2.42070i	0.132166	−	0.289329i
$71$	−5.11472	+	4.80304i	−0.607005	+	0.570016i	−0.925897	−	0.377775i	$-0.876689\pi$
$71$	−5.11472	+	4.80304i	−0.607005	+	0.570016i	0.318892	+	0.947791i	$0.396689\pi$
$72$	−0.904827	+	0.425779i	−0.106635	+	0.0501786i
$73$	7.91296	−	6.54617i	0.926142	−	0.766171i	−0.0463941	−	0.998923i	$-0.514773\pi$
$73$	7.91296	−	6.54617i	0.926142	−	0.766171i	0.972536	+	0.232752i	$0.0747730\pi$
$74$	1.94205	+	5.97703i	0.225759	+	0.694815i
$75$	1.13342	−	4.86984i	0.130877	−	0.562321i
$76$	−0.175457	+	0.540002i	−0.0201263	+	0.0619424i
$77$	−0.130936	−	0.330708i	−0.0149216	−	0.0376876i
$78$	−2.71297	−	2.88902i	−0.307184	−	0.327117i
$79$	−0.548519	+	2.87544i	−0.0617132	+	0.323512i	−0.999734	−	0.0230674i	$-0.992657\pi$
$79$	−0.548519	+	2.87544i	−0.0617132	+	0.323512i	0.938021	+	0.346579i	$0.112657\pi$
$80$	2.17198	+	0.531519i	0.242834	+	0.0594256i
$81$	0.728969	+	0.684547i	0.0809965	+	0.0760608i
$82$	−0.293011	−	0.0952050i	−0.0323576	−	0.0105136i
$83$	14.6821	−	2.80075i	1.61157	−	0.307423i	0.698617	−	0.715496i	$-0.253799\pi$
$83$	14.6821	−	2.80075i	1.61157	−	0.307423i	0.912949	+	0.408073i	$0.133799\pi$
$84$	0.0747315	−	1.18782i	0.00815388	−	0.129602i
$85$	−1.03566	−	0.323582i	−0.112333	−	0.0350974i
$86$	−1.96841	+	3.10173i	−0.212260	+	0.334468i
$87$	8.43526	+	0.530701i	0.904355	+	0.0568972i
$88$	0.252329	−	0.160133i	0.0268984	−	0.0170702i
$89$	2.87378	+	3.47381i	0.304620	+	0.368223i	0.900504	−	0.434848i	$-0.143198\pi$
$89$	2.87378	+	3.47381i	0.304620	+	0.368223i	−0.595883	+	0.803071i	$0.703198\pi$
$90$	−0.305364	−	2.21512i	−0.0321882	−	0.233494i
$91$	4.56866	−	1.17303i	0.478926	−	0.122967i
$92$	−3.15736	−	1.48574i	−0.329178	−	0.154899i
$93$	−5.64781	+	1.83508i	−0.585650	+	0.190289i
$94$	2.86536	−	1.57524i	0.295539	−	0.162474i
$95$	−1.03553	−	0.734581i	−0.106243	−	0.0753664i
$96$	0.992115	−	0.125333i	0.101257	−	0.0127918i
$97$	1.39979	+	11.0805i	0.142127	+	1.12505i	0.888287	+	0.459288i	$0.151895\pi$
$97$	1.39979	+	11.0805i	0.142127	+	1.12505i	−0.746160	+	0.665767i	$0.768105\pi$
$98$	−4.71430	−	2.99178i	−0.476216	−	0.302216i
$99$	−0.241776	−	0.175661i	−0.0242994	−	0.0176546i
$100$	−2.58281	+	4.28125i	−0.258281	+	0.428125i
$101$	−10.7951	+	7.84307i	−1.07415	+	0.780415i	−0.976653	−	0.214821i	$-0.931083\pi$
$101$	−10.7951	+	7.84307i	−1.07415	+	0.780415i	−0.0974954	+	0.995236i	$0.531083\pi$
$102$	−0.484283	+	0.0304685i	−0.0479511	+	0.00301683i
$103$	0.733704	−	1.33460i	0.0722940	−	0.131502i	−0.837689	−	0.546147i	$-0.816094\pi$
$103$	0.733704	−	1.33460i	0.0722940	−	0.131502i	0.909983	+	0.414645i	$0.136094\pi$
$104$	1.68743	+	3.58598i	0.165466	+	0.351634i
$105$	2.48536	+	0.951601i	0.242546	+	0.0928668i
$106$	1.39835	+	7.33042i	0.135820	+	0.711993i
$107$	−11.3042	+	15.5589i	−1.09282	+	1.50413i	−0.248241	+	0.968698i	$0.579853\pi$
$107$	−11.3042	+	15.5589i	−1.09282	+	1.50413i	−0.844576	+	0.535436i	$0.820147\pi$
$108$	−0.481754	−	0.876307i	−0.0463568	−	0.0843226i
$109$	−6.25966	−	9.86364i	−0.599567	−	0.944766i	−0.999600	−	0.0282654i	$-0.991002\pi$
$109$	−6.25966	−	9.86364i	−0.599567	−	0.944766i	0.400034	−	0.916500i	$-0.368998\pi$
$110$	0.173509	+	0.645335i	0.0165434	+	0.0615302i
$111$	−5.84329	+	2.31352i	−0.554620	+	0.219590i
$112$	−0.438132	+	1.10659i	−0.0413996	+	0.104563i
$113$	9.80866	+	8.11443i	0.922721	+	0.763341i	0.971887	−	0.235449i	$-0.0756561\pi$
$113$	9.80866	+	8.11443i	0.922721	+	0.763341i	−0.0491654	+	0.998791i	$0.515656\pi$
$114$	−0.549953	−	0.141204i	−0.0515078	−	0.0132250i
$115$	5.27653	−	5.74804i	0.492039	−	0.536008i
$116$	−7.85841	−	3.11136i	−0.729635	−	0.288883i
$117$	2.71297	−	2.88902i	0.250814	−	0.267090i
$118$	4.27062	+	5.87800i	0.393142	+	0.541114i
$119$	0.245896	−	0.522555i	0.0225412	−	0.0479026i
$120$	−0.394091	+	2.20107i	−0.0359754	+	0.200929i
$121$	−9.56111	−	5.25626i	−0.869192	−	0.477842i
$122$	−0.729692	−	0.139196i	−0.0660632	−	0.0126022i
$123$	0.0766188	−	0.298411i	0.00690849	−	0.0269068i
$124$	5.93846			0.533289
$125$	−7.41519	−	8.36749i	−0.663235	−	0.748411i
$126$	1.19017			0.106029
$127$	−1.45907	+	5.68271i	−0.129472	+	0.504259i	0.870456	+	0.492246i	$0.163824\pi$
$127$	−1.45907	+	5.68271i	−0.129472	+	0.504259i	−0.999928	+	0.0120130i	$0.996176\pi$
$128$	−0.982287	−	0.187381i	−0.0868227	−	0.0165623i
$129$	−3.21920	−	1.76977i	−0.283435	−	0.155820i
$130$	−8.77888	+	1.21021i	−0.769959	+	0.106142i
$131$	−8.55368	+	18.1775i	−0.747338	+	1.58817i	0.0600788	+	0.998194i	$0.480865\pi$
$131$	−8.55368	+	18.1775i	−0.747338	+	1.58817i	−0.807417	+	0.589981i	$0.799135\pi$
$132$	0.175661	+	0.241776i	0.0152893	+	0.0210439i
$133$	0.462596	−	0.492615i	0.0401122	−	0.0427151i
$134$	−2.37921	−	0.941996i	−0.205533	−	0.0813761i
$135$	2.19157	−	0.443850i	0.188621	−	0.0382005i
$136$	0.469995	+	0.120674i	0.0403018	+	0.0103477i
$137$	7.31729	+	6.05339i	0.625158	+	0.517176i	0.895195	−	0.445674i	$-0.147036\pi$
$137$	7.31729	+	6.05339i	0.625158	+	0.517176i	−0.270037	+	0.962850i	$0.587036\pi$
$138$	1.28456	−	3.24442i	0.109349	−	0.276183i
$139$	−4.05370	+	1.60497i	−0.343830	+	0.136132i	−0.533692	−	0.845679i	$-0.679196\pi$
$139$	−4.05370	+	1.60497i	−0.343830	+	0.136132i	0.189862	+	0.981811i	$0.439196\pi$
$140$	−2.06966	−	1.67304i	−0.174918	−	0.141398i
$141$	1.75205	+	2.76079i	0.147549	+	0.232501i
$142$	3.38016	+	6.14850i	0.283657	+	0.515970i
$143$	−0.696172	+	0.958199i	−0.0582169	+	0.0801286i
$144$	0.187381	+	0.982287i	0.0156151	+	0.0818573i
$145$	11.8810	−	14.6975i	0.986665	−	1.22056i
$146$	−4.37264	−	9.29233i	−0.361882	−	0.769038i
$147$	2.68987	−	4.89285i	0.221856	−	0.403555i
$148$	6.27222	−	0.394614i	0.515573	−	0.0324371i
$149$	−8.80256	+	6.39544i	−0.721134	+	0.523935i	−0.886746	−	0.462256i	$-0.847040\pi$
$149$	−8.80256	+	6.39544i	−0.721134	+	0.523935i	0.165612	+	0.986191i	$0.447040\pi$
$150$	−4.43497	−	2.30890i	−0.362114	−	0.188521i
$151$	3.78560	+	2.75040i	0.308067	+	0.223824i	0.731067	−	0.682306i	$-0.239023\pi$
$151$	3.78560	+	2.75040i	0.308067	+	0.223824i	−0.422999	+	0.906130i	$0.639023\pi$
$152$	0.479402	+	0.304238i	0.0388846	+	0.0246769i
$153$	−0.0608167	−	0.481414i	−0.00491674	−	0.0389200i
$154$	−0.352881	+	0.0445792i	−0.0284359	+	0.00359229i
$155$	−3.96006	+	12.6746i	−0.318080	+	1.01804i
$156$	−3.47295	+	1.90927i	−0.278058	+	0.152864i
$157$	−12.3745	+	4.02072i	−0.987593	+	0.320888i	−0.757897	−	0.652374i	$-0.773773\pi$
$157$	−12.3745	+	4.02072i	−0.987593	+	0.320888i	−0.229696	+	0.973263i	$0.573773\pi$
$158$	2.64869	+	1.24638i	0.210718	+	0.0991565i
$159$	−7.22815	+	1.85587i	−0.573230	+	0.147180i
$160$	1.05497	−	1.97156i	0.0834027	−	0.155865i
$161$	2.64726	+	3.19999i	0.208634	+	0.252195i
$162$	0.844328	−	0.535827i	0.0663367	−	0.0420985i
$163$	2.55962	+	0.161038i	0.200485	+	0.0126134i	0.162715	−	0.986673i	$-0.447975\pi$
$163$	2.55962	+	0.161038i	0.200485	+	0.0126134i	0.0377694	+	0.999286i	$0.487975\pi$
$164$	−0.165083	+	0.260129i	−0.0128908	+	0.0203127i
$165$	−0.633166	+	0.213687i	−0.0492919	+	0.0166355i
$166$	0.938518	−	14.9173i	0.0728432	−	1.15781i
$167$	16.9615	−	3.23559i	1.31252	−	0.250377i	0.516836	−	0.856085i	$-0.327110\pi$
$167$	16.9615	−	3.23559i	1.31252	−	0.250377i	0.795687	+	0.605707i	$0.207110\pi$
$168$	−1.13192	−	0.367784i	−0.0873296	−	0.0283751i
$169$	−1.97308	−	1.85285i	−0.151776	−	0.142527i
$170$	−0.570974	+	0.922648i	−0.0437917	+	0.0707638i
$171$	0.106393	−	0.557734i	0.00813611	−	0.0426510i
$172$	2.51475	+	2.67794i	0.191748	+	0.204191i
$173$	5.00802	+	12.6488i	0.380753	+	0.961671i	0.986166	+	0.165760i	$0.0530078\pi$
$173$	5.00802	+	12.6488i	0.380753	+	0.961671i	−0.605413	+	0.795911i	$0.706992\pi$
$174$	2.61179	−	8.03827i	0.197999	−	0.609380i
$175$	4.95096	−	3.30163i	0.374257	−	0.249580i
$176$	−0.0923503	−	0.284225i	−0.00696116	−	0.0214243i
$177$	−5.59825	+	4.63128i	−0.420790	+	0.348108i
$178$	4.07935	−	1.91960i	0.305760	−	0.143880i
$179$	1.41243	−	1.32636i	0.105570	−	0.0991365i	−0.629965	−	0.776623i	$-0.716931\pi$
$179$	1.41243	−	1.32636i	0.105570	−	0.0991365i	0.735535	+	0.677487i	$0.236931\pi$
$180$	−2.22147	−	0.255107i	−0.165578	−	0.0190145i
$181$	−1.89147	−	0.238948i	−0.140592	−	0.0177609i	0.0547223	−	0.998502i	$-0.482573\pi$
$181$	−1.89147	−	0.238948i	−0.140592	−	0.0177609i	−0.195314	+	0.980741i	$0.562573\pi$
$182$		−	4.71685i		−	0.349636i
$183$	0.0931038	−	0.736993i	0.00688243	−	0.0544801i
$184$	−2.22427	+	2.68868i	−0.163975	+	0.198212i
$185$	−3.34039	+	13.6500i	−0.245591	+	1.00357i
$186$	0.372879	+	5.92674i	0.0273408	+	0.434570i
$187$	0.0360637	+	0.140459i	0.00263724	+	0.0102714i
$188$	−0.813169	−	3.16708i	−0.0593064	−	0.230983i
$189$	0.0747315	+	1.18782i	0.00543592	+	0.0864015i
$190$	−0.969029	+	0.820315i	−0.0703008	+	0.0595119i
$191$	0.326958	−	0.395224i	0.0236578	−	0.0285974i	−0.758552	−	0.651613i	$-0.774093\pi$
$191$	0.326958	−	0.395224i	0.0236578	−	0.0285974i	0.782209	+	0.623016i	$0.214093\pi$
$192$	0.125333	−	0.992115i	0.00904515	−	0.0715997i
$193$			21.5987i			1.55471i	0.629064	+	0.777353i	$0.283438\pi$
$193$			21.5987i			1.55471i	−0.629064	+	0.777353i	$0.716562\pi$
$194$	11.0805	+	1.39979i	0.795534	+	0.100499i
$195$	−1.75905	−	8.68557i	−0.125968	−	0.621987i
$196$	−4.07019	+	3.82216i	−0.290728	+	0.273012i
$197$	20.5640	−	9.67670i	1.46513	−	0.689436i	0.482649	−	0.875814i	$-0.339675\pi$
$197$	20.5640	−	9.67670i	1.46513	−	0.689436i	0.982478	+	0.186377i	$0.0596747\pi$
$198$	−0.230269	+	0.190495i	−0.0163645	+	0.0135379i
$199$	−2.90142	−	8.92964i	−0.205676	−	0.633005i	−0.999685	−	0.0250995i	$-0.992010\pi$
$199$	−2.90142	−	8.92964i	−0.205676	−	0.633005i	0.794009	−	0.607906i	$-0.207990\pi$
$200$	3.50442	+	3.56637i	0.247800	+	0.252181i
$201$	0.790746	−	2.43366i	0.0557749	−	0.171657i
$202$	4.91204	+	12.4064i	0.345610	+	0.872912i
$203$	6.88604	+	7.33289i	0.483305	+	0.514668i
$204$	−0.0909249	+	0.476645i	−0.00636602	+	0.0333718i
$205$	−0.445112	−	0.525806i	−0.0310880	−	0.0367239i
$206$	−1.11021	−	1.04256i	−0.0773519	−	0.0726383i
$207$	3.31868	+	1.07830i	0.230664	+	0.0749473i
$208$	3.89297	−	0.742623i	0.269929	−	0.0514916i
$209$	−0.0106546	+	0.169351i	−0.000736997	+	0.0117142i
$210$	1.53979	−	2.17062i	0.106255	−	0.149787i
$211$	−0.820617	+	1.29309i	−0.0564936	+	0.0890197i	−0.871401	−	0.490572i	$-0.836788\pi$
$211$	−0.820617	+	1.29309i	−0.0564936	+	0.0890197i	0.814907	+	0.579592i	$0.196788\pi$
$212$	7.44788	+	0.468581i	0.511522	+	0.0321823i
$213$	−5.92412	+	3.75956i	−0.405914	+	0.257601i
$214$	12.2588	+	14.8184i	0.837997	+	1.01296i
$215$	−7.39254	+	3.58150i	−0.504167	+	0.244256i
$216$	−0.968583	+	0.248690i	−0.0659037	+	0.0169212i
$217$	−6.39513	−	3.00932i	−0.434129	−	0.204286i
$218$	−11.1105	+	3.61001i	−0.752496	+	0.244501i
$219$	8.99943	−	4.94748i	0.608125	−	0.334320i
$220$	0.668210	−	0.00756945i	0.0450507	−	0.000510332i
$221$	−1.90792	+	0.241027i	−0.128341	+	0.0162132i
$222$	0.787671	+	6.23506i	0.0528650	+	0.418470i
$223$	12.4419	+	7.89588i	0.833172	+	0.528747i	0.882651	−	0.470028i	$-0.155756\pi$
$223$	12.4419	+	7.89588i	0.833172	+	0.528747i	−0.0494795	+	0.998775i	$0.515756\pi$
$224$	0.962870	+	0.699566i	0.0643344	+	0.0467417i
$225$	2.02587	−	4.57120i	0.135058	−	0.304747i
$226$	10.2988	−	7.48253i	0.685067	−	0.497730i
$227$	4.45134	−	0.280055i	0.295446	−	0.0185879i	0.0856242	−	0.996328i	$-0.472712\pi$
$227$	4.45134	−	0.280055i	0.295446	−	0.0185879i	0.209822	+	0.977740i	$0.432712\pi$
$228$	−0.273536	+	0.497559i	−0.0181153	+	0.0329517i
$229$	−2.99213	−	6.35860i	−0.197726	−	0.420188i	0.781235	−	0.624237i	$-0.214590\pi$
$229$	−2.99213	−	6.35860i	−0.197726	−	0.420188i	−0.978961	+	0.204048i	$0.934590\pi$
$230$	−4.25524	−	6.54024i	−0.280582	−	0.431251i
$231$	−0.0666488	−	0.349385i	−0.00438517	−	0.0229878i
$232$	−4.96792	+	6.83776i	−0.326160	+	0.448921i
$233$	0.364412	+	0.662863i	0.0238734	+	0.0434256i	0.887974	−	0.459893i	$-0.152112\pi$
$233$	0.364412	+	0.662863i	0.0238734	+	0.0434256i	−0.864101	+	0.503319i	$0.832112\pi$
$234$	−2.12357	−	3.34621i	−0.138822	−	0.218749i
$235$	7.30182	+	0.376409i	0.476318	+	0.0245542i
$236$	6.75540	−	2.67465i	0.439739	−	0.174105i
$237$	−1.07761	+	2.72172i	−0.0699980	+	0.176795i
$238$	−0.444986	−	0.368125i	−0.0288442	−	0.0238620i
$239$	10.9197	+	2.80371i	0.706338	+	0.181357i	0.584738	−	0.811222i	$-0.301197\pi$
$239$	10.9197	+	2.80371i	0.706338	+	0.181357i	0.121600	+	0.992579i	$0.461197\pi$
$240$	2.03391	+	0.929093i	0.131288	+	0.0599727i
$241$	−9.74417	−	3.85799i	−0.627677	−	0.248515i	0.0326808	−	0.999466i	$-0.489596\pi$
$241$	−9.74417	−	3.85799i	−0.627677	−	0.248515i	−0.660358	+	0.750951i	$0.729596\pi$
$242$	−7.46888	+	7.95355i	−0.480118	+	0.511273i
$243$	0.587785	+	0.809017i	0.0377064	+	0.0518985i
$244$	−0.316290	+	0.672151i	−0.0202484	+	0.0430301i
$245$	−5.44350	−	11.2359i	−0.347773	−	0.717834i
$246$	−0.269981	−	0.148423i	−0.0172134	−	0.00946313i
$247$	−2.21039	−	0.421655i	−0.140644	−	0.0268293i
$248$	1.47683	−	5.75189i	0.0937791	−	0.365245i
$249$	14.9468			0.947216
$250$	−9.94870	+	5.10132i	−0.629211	+	0.322636i
$251$	−9.81151			−0.619297			−0.309648	−	0.950851i	$-0.600211\pi$
$251$	−9.81151			−0.619297			−0.309648	+	0.950851i	$0.600211\pi$
$252$	0.295984	−	1.15278i	0.0186452	−	0.0726184i
$253$	−1.02436	−	0.195407i	−0.0644010	−	0.0122852i
$254$	5.14132	+	2.82647i	0.322595	+	0.177348i
$255$	−0.956679	−	0.511913i	−0.0599096	−	0.0320573i
$256$	−0.425779	+	0.904827i	−0.0266112	+	0.0565517i
$257$	−12.4645	−	17.1559i	−0.777515	−	1.07016i	−0.995552	−	0.0942170i	$-0.969965\pi$
$257$	−12.4645	−	17.1559i	−0.777515	−	1.07016i	0.218037	−	0.975941i	$-0.430035\pi$
$258$	−2.51475	+	2.67794i	−0.156562	+	0.166721i
$259$	−6.95452	−	2.75349i	−0.432133	−	0.171094i
$260$	−1.01103	+	8.80404i	−0.0627015	+	0.546004i
$261$	8.18640	+	2.10191i	0.506726	+	0.130105i
$262$	15.4792	+	12.8055i	0.956308	+	0.791127i
$263$	−0.828328	+	2.09212i	−0.0510769	+	0.129006i	−0.953075	−	0.302735i	$-0.902100\pi$
$263$	−0.828328	+	2.09212i	−0.0510769	+	0.129006i	0.901998	+	0.431740i	$0.142100\pi$
$264$	0.277865	−	0.110015i	0.0171014	−	0.00677094i
$265$	−5.96672	+	15.5837i	−0.366532	+	0.957297i
$266$	−0.362095	−	0.570571i	−0.0222015	−	0.0349840i
$267$	2.17195	+	3.95077i	0.132921	+	0.241783i
$268$	−1.50409	+	2.07020i	−0.0918768	+	0.126458i
$269$	−4.88834	−	25.6256i	−0.298047	−	1.56242i	−0.744507	−	0.667615i	$-0.767315\pi$
$269$	−4.88834	−	25.6256i	−0.298047	−	1.56242i	0.446460	−	0.894804i	$-0.352685\pi$
$270$	0.115116	−	2.23310i	0.00700576	−	0.135902i
$271$	−3.34699	−	7.11271i	−0.203315	−	0.432066i	0.777002	−	0.629499i	$-0.216740\pi$
$271$	−3.34699	−	7.11271i	−0.203315	−	0.432066i	−0.980316	+	0.197432i	$0.936740\pi$
$272$	0.233766	−	0.425219i	0.0141742	−	0.0257827i
$273$	4.70754	−	0.296173i	0.284913	−	0.0179252i
$274$	7.68295	−	5.58199i	0.464144	−	0.337220i
$275$	−0.429440	+	1.43122i	−0.0258962	+	0.0863058i
$276$	−2.82304	−	2.05106i	−0.169927	−	0.123459i
$277$	−11.6960	−	7.42249i	−0.702743	−	0.445974i	0.135852	−	0.990729i	$-0.456623\pi$
$277$	−11.6960	−	7.42249i	−0.702743	−	0.445974i	−0.838595	+	0.544755i	$0.816623\pi$
$278$	0.546435	+	4.32548i	0.0327730	+	0.259425i
$279$	−5.89163	+	0.744286i	−0.352723	+	0.0445592i
$280$	−2.13519	+	1.58856i	−0.127602	+	0.0949349i
$281$	−15.0065	+	8.24988i	−0.895212	+	0.492147i	−0.861773	−	0.507294i	$-0.830646\pi$
$281$	−15.0065	+	8.24988i	−0.895212	+	0.492147i	−0.0334387	+	0.999441i	$0.510646\pi$
$282$	3.10977	−	1.01043i	0.185184	−	0.0601701i
$283$	14.7257	+	6.92937i	0.875349	+	0.411908i	0.810329	−	0.585976i	$-0.199289\pi$
$283$	14.7257	+	6.92937i	0.875349	+	0.411908i	0.0650207	+	0.997884i	$0.479289\pi$
$284$	6.79594	−	1.74490i	0.403265	−	0.103541i
$285$	−0.879542	−	0.915609i	−0.0520996	−	0.0542360i
$286$	0.754964	+	0.912595i	0.0446420	+	0.0539629i
$287$	0.309598	−	0.196477i	0.0182750	−	0.0115977i
$288$	0.998027	+	0.0627905i	0.0588093	+	0.00369997i
$289$	8.98289	−	14.1548i	0.528405	−	0.832634i
$290$	−11.2811	−	15.1629i	−0.662448	−	0.890395i
$291$	−0.701280	+	11.1465i	−0.0411098	+	0.653421i
$292$	−10.0878	+	1.92436i	−0.590345	+	0.112614i
$293$	−5.74553	−	1.86683i	−0.335657	−	0.109062i	0.136339	−	0.990662i	$-0.456466\pi$
$293$	−5.74553	−	1.86683i	−0.335657	−	0.109062i	−0.471996	+	0.881601i	$0.656466\pi$
$294$	−4.07019	−	3.82216i	−0.237378	−	0.222913i
$295$	1.20372	+	16.2017i	0.0700832	+	0.943302i
$296$	1.17762	−	6.17330i	0.0684478	−	0.358816i
$297$	−0.204578	−	0.217854i	−0.0118708	−	0.0126411i
$298$	4.00540	+	10.1165i	0.232027	+	0.586033i
$299$	4.27350	−	13.1525i	0.247143	−	0.760627i
$300$	−3.33929	+	3.72144i	−0.192794	+	0.214858i
$301$	−1.35109	−	4.15823i	−0.0778756	−	0.239676i
$302$	3.60543	−	2.98267i	0.207469	−	0.171633i
$303$	−12.0735	+	5.68136i	−0.693604	+	0.326385i
$304$	0.413902	−	0.388680i	0.0237389	−	0.0222923i
$305$	−1.22367	−	1.12329i	−0.0700669	−	0.0643193i
$306$	−0.481414	−	0.0608167i	−0.0275206	−	0.00347666i
$307$			18.0732i			1.03149i	0.856741	+	0.515747i	$0.172486\pi$
$307$			18.0732i			1.03149i	−0.856741	+	0.515747i	$0.827514\pi$
$308$	−0.0445792	+	0.352881i	−0.00254013	+	0.0201072i
$309$	0.970787	−	1.17348i	0.0552262	−	0.0667570i
$310$	11.2915	+	6.98768i	0.641316	+	0.396874i
$311$	−0.139671	−	2.22000i	−0.00791999	−	0.125885i	−1.00000		0.000276781i	$-0.999912\pi$
$311$	−0.139671	−	2.22000i	−0.00791999	−	0.125885i	0.992080	−	0.125608i	$-0.0400881\pi$
$312$	0.985599	+	3.83865i	0.0557986	+	0.217321i
$313$	−2.66874	−	10.3940i	−0.150846	−	0.587506i	−0.998387	−	0.0567762i	$-0.981918\pi$
$313$	−2.66874	−	10.3940i	−0.150846	−	0.587506i	0.847541	−	0.530730i	$-0.178082\pi$
$314$	0.816987	+	12.9856i	0.0461053	+	0.732822i
$315$	2.26302	+	1.40046i	0.127507	+	0.0789067i
$316$	1.86592	−	2.25551i	0.104966	−	0.126882i
$317$	0.377834	−	2.99086i	0.0212213	−	0.167984i	−0.977942	−	0.208875i	$-0.933020\pi$
$317$	0.377834	−	2.99086i	0.0212213	−	0.167984i	0.999164	+	0.0408914i	$0.0130198\pi$
$318$			7.46260i			0.418482i
$319$	−2.50596	−	0.316576i	−0.140307	−	0.0177249i
$320$	−1.64726	−	1.51213i	−0.0920845	−	0.0845308i
$321$	−14.0194	+	13.1651i	−0.782487	+	0.734804i
$322$	3.75780	−	1.76829i	0.209414	−	0.0985429i
$323$	−0.212288	+	0.175620i	−0.0118120	+	0.00977175i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	−18.1164	−	8.02884i	−1.00492	−	0.445360i
$326$	0.792530	−	2.43916i	0.0438942	−	0.135092i
$327$	−4.30052	−	10.8619i	−0.237819	−	0.600663i
$328$	0.210902	+	0.224588i	0.0116451	+	0.0124008i
$329$	−0.729220	+	3.82271i	−0.0402032	+	0.210753i
$330$	0.0495118	+	0.666416i	0.00272553	+	0.0366850i
$331$	−12.8281	−	12.0464i	−0.705099	−	0.662132i	0.246617	−	0.969113i	$-0.420681\pi$
$331$	−12.8281	−	12.0464i	−0.705099	−	0.662132i	−0.951716	+	0.306981i	$0.900681\pi$
$332$	−14.2153	−	4.61882i	−0.780164	−	0.253491i
$333$	−6.17330	+	1.17762i	−0.338295	+	0.0645332i
$334$	1.08423	−	17.2333i	0.0593263	−	0.942965i
$335$	−3.41546	−	4.59071i	−0.186607	−	0.250817i
$336$	−0.637726	+	1.00490i	−0.0347908	+	0.0548216i
$337$	−9.53913	−	0.600151i	−0.519629	−	0.0326923i	−0.199189	−	0.979961i	$-0.563831\pi$
$337$	−9.53913	−	0.600151i	−0.519629	−	0.0326923i	−0.320440	+	0.947269i	$0.603831\pi$
$338$	−2.28532	+	1.45031i	−0.124305	+	0.0788865i
$339$	8.11443	+	9.80866i	0.440715	+	0.532733i
$340$	0.751666	+	0.782489i	0.0407648	+	0.0424364i
$341$	1.71896	−	0.441355i	0.0930870	−	0.0239007i
$342$	−0.513753	−	0.241754i	−0.0277806	−	0.0130725i
$343$	14.2435	−	4.62800i	0.769078	−	0.249889i
$344$	3.21920	−	1.76977i	0.173568	−	0.0954197i
$345$	6.26014	−	4.65751i	0.337035	−	0.250752i
$346$	13.4969	−	1.70505i	0.725596	−	0.0916641i
$347$	−1.56117	−	12.3579i	−0.0838080	−	0.663408i	−0.976925	−	0.213584i	$-0.931486\pi$
$347$	−1.56117	−	12.3579i	−0.0838080	−	0.663408i	0.893117	−	0.449825i	$-0.148514\pi$
$348$	−7.13620	−	4.52877i	−0.382541	−	0.242768i
$349$	−21.4083	−	15.5540i	−1.14596	−	0.832588i	−0.158021	−	0.987436i	$-0.550511\pi$
$349$	−21.4083	−	15.5540i	−1.14596	−	0.832588i	−0.987938	+	0.154847i	$0.950511\pi$
$350$	−1.96665	−	5.61650i	−0.105122	−	0.300214i
$351$	3.20627	−	2.32949i	0.171138	−	0.124339i
$352$	−0.298262	+	0.0187651i	−0.0158974	+	0.00100018i
$353$	7.15892	−	13.0220i	0.381031	−	0.693093i	−0.614357	−	0.789029i	$-0.710584\pi$
$353$	7.15892	−	13.0220i	0.381031	−	0.693093i	0.995388	+	0.0959357i	$0.0305843\pi$
$354$	3.09355	+	6.57412i	0.164420	+	0.349411i
$355$	−0.807700	+	15.6683i	−0.0428683	+	0.831586i
$356$	−0.844796	−	4.42857i	−0.0447741	−	0.234714i
$357$	0.339457	−	0.467223i	0.0179660	−	0.0247281i
$358$	−0.933430	−	1.69790i	−0.0493333	−	0.0897370i
$359$	−14.2267	−	22.4176i	−0.750854	−	1.18316i	−0.977859	−	0.209263i	$-0.932893\pi$
$359$	−14.2267	−	22.4176i	−0.750854	−	1.18316i	0.227005	−	0.973894i	$-0.427107\pi$
$360$	−0.799549	+	2.08823i	−0.0421399	+	0.110060i
$361$	17.3660	−	6.87569i	0.914000	−	0.361878i
$362$	−0.701831	+	1.77262i	−0.0368874	+	0.0931670i
$363$	−8.40683	−	6.95473i	−0.441244	−	0.365029i
$364$	−4.56866	−	1.17303i	−0.239463	−	0.0614836i
$365$	2.61988	−	22.8139i	0.137131	−	1.19413i
$366$	−0.690685	−	0.273461i	−0.0361027	−	0.0142941i
$367$	−9.60278	+	10.2259i	−0.501261	+	0.533789i	−0.928983	−	0.370121i	$-0.879316\pi$
$367$	−9.60278	+	10.2259i	−0.501261	+	0.533789i	0.427722	+	0.903910i	$0.359316\pi$
$368$	2.05106	+	2.82304i	0.106919	+	0.147161i
$369$	0.131178	−	0.278768i	0.00682887	−	0.0145121i
$370$	12.3905	+	6.63008i	0.644151	+	0.344681i
$371$	−7.78317	−	4.27883i	−0.404082	−	0.222146i
$372$	5.83327	+	1.11276i	0.302441	+	0.0576937i
$373$	−4.95354	+	19.2928i	−0.256484	+	0.998941i	0.701627	+	0.712545i	$0.252457\pi$
$373$	−4.95354	+	19.2928i	−0.256484	+	0.998941i	−0.958111	+	0.286396i	$0.907543\pi$
$374$	0.145015			0.00749854
$375$	−5.71594	−	9.60875i	−0.295170	−	0.496194i
$376$	−3.26981			−0.168628
$377$	8.33022	−	32.4441i	0.429028	−	1.67095i
$378$	1.16909	+	0.223016i	0.0601316	+	0.0114707i
$379$	−4.42148	−	2.43073i	−0.227116	−	0.124858i	0.364134	−	0.931347i	$-0.381365\pi$
$379$	−4.42148	−	2.43073i	−0.227116	−	0.124858i	−0.591250	+	0.806489i	$0.701365\pi$
$380$	0.553556	+	1.14259i	0.0283968	+	0.0586136i
$381$	−2.49806	+	5.30865i	−0.127980	+	0.271970i
$382$	−0.301496	−	0.414974i	−0.0154259	−	0.0212319i
$383$	14.4553	−	15.3934i	0.738633	−	0.786565i	−0.244462	−	0.969659i	$-0.578611\pi$
$383$	14.4553	−	15.3934i	0.738633	−	0.786565i	0.983095	+	0.183094i	$0.0586114\pi$
$384$	−0.929776	−	0.368125i	−0.0474475	−	0.0187858i
$385$	−0.723431	−	0.330464i	−0.0368695	−	0.0168420i
$386$	20.9201	+	5.37137i	1.06481	+	0.273396i
$387$	−2.83056	−	2.34164i	−0.143885	−	0.119032i
$388$	4.11143	−	10.3843i	0.208726	−	0.527182i
$389$	−1.38729	+	0.549269i	−0.0703386	+	0.0278490i	−0.403030	−	0.915187i	$-0.632043\pi$
$389$	−1.38729	+	0.549269i	−0.0703386	+	0.0278490i	0.332692	+	0.943036i	$0.392043\pi$
$390$	−8.85016	−	0.456225i	−0.448145	−	0.0231019i
$391$	−0.907277	−	1.42964i	−0.0458830	−	0.0723000i
$392$	2.68987	+	4.89285i	0.135859	+	0.247126i
$393$	−11.8083	+	16.2527i	−0.595649	+	0.819841i
$394$	−4.25862	−	22.3245i	−0.214546	−	1.12469i
$395$	3.56969	+	5.48656i	0.179611	+	0.276059i
$396$	0.127245	+	0.270409i	0.00639430	+	0.0135886i
$397$	12.7006	−	23.1023i	0.637425	−	1.15947i	−0.338417	−	0.940996i	$-0.609891\pi$
$397$	12.7006	−	23.1023i	0.637425	−	1.15947i	0.975842	−	0.218476i	$-0.0701085\pi$
$398$	−9.37065	+	0.589551i	−0.469708	+	0.0295515i
$399$	0.546709	−	0.397207i	0.0273697	−	0.0198852i
$400$	4.32584	−	2.50741i	0.216292	−	0.125370i
$401$	−3.57245	−	2.59553i	−0.178399	−	0.129615i	0.495002	−	0.868892i	$-0.335167\pi$
$401$	−3.57245	−	2.59553i	−0.178399	−	0.129615i	−0.673401	+	0.739277i	$0.735167\pi$
$402$	−2.16056	−	1.37113i	−0.107759	−	0.0683858i
$403$	2.94973	+	23.3495i	0.146936	+	1.16312i
$404$	13.2382	−	1.67238i	0.658626	−	0.0832038i
$405$	2.23592	−	0.0253284i	0.111104	−	0.00125858i
$406$	8.81500	−	4.84609i	0.437481	−	0.240507i
$407$	1.78625	−	0.580386i	0.0885409	−	0.0287687i
$408$	0.439058	+	0.206605i	0.0217366	+	0.0102285i
$409$	−17.4154	+	4.47152i	−0.861138	+	0.221103i	−0.653336	−	0.757068i	$-0.726631\pi$
$409$	−17.4154	+	4.47152i	−0.861138	+	0.221103i	−0.207802	+	0.978171i	$0.566631\pi$
$410$	−0.619982	+	0.300366i	−0.0306187	+	0.0148340i
$411$	6.05339	+	7.31729i	0.298592	+	0.360935i
$412$	−1.28590	+	0.816056i	−0.0633517	+	0.0402042i
$413$	−8.63027	−	0.542970i	−0.424668	−	0.0267178i
$414$	1.86975	−	2.94625i	0.0918931	−	0.144800i
$415$	19.3375	−	27.2598i	0.949240	−	1.33813i
$416$	0.248849	−	3.95534i	0.0122008	−	0.193927i
$417$	−4.28263	+	0.816956i	−0.209722	+	0.0400065i
$418$	0.161380	+	0.0524357i	0.00789338	+	0.00256471i
$419$	16.6879	+	15.6710i	0.815259	+	0.765579i	0.975148	−	0.221556i	$-0.0711136\pi$
$419$	16.6879	+	15.6710i	0.815259	+	0.765579i	−0.159889	+	0.987135i	$0.551114\pi$
$420$	−1.71950	−	2.03123i	−0.0839030	−	0.0991136i
$421$	4.46697	−	23.4167i	0.217707	−	1.14126i	−0.690690	−	0.723151i	$-0.742693\pi$
$421$	4.46697	−	23.4167i	0.217707	−	1.14126i	0.908397	−	0.418109i	$-0.137307\pi$
$422$	1.04838	+	1.11641i	0.0510344	+	0.0543461i
$423$	1.20370	+	3.04019i	0.0585258	+	0.147819i
$424$	2.30607	−	7.09736i	0.111993	−	0.344678i
$425$	−2.17133	+	1.08249i	−0.105325	+	0.0525085i
$426$	2.16818	+	6.67297i	0.105049	+	0.323306i
$427$	0.681226	−	0.563559i	0.0329668	−	0.0272725i
$428$	17.4015	−	8.18852i	0.841132	−	0.395807i
$429$	−0.863390	+	0.810777i	−0.0416848	+	0.0391447i
$430$	1.63053	+	8.05097i	0.0786311	+	0.388252i
$431$	−4.57442	−	0.577884i	−0.220342	−	0.0278357i	0.0143869	−	0.999897i	$-0.495420\pi$
$431$	−4.57442	−	0.577884i	−0.220342	−	0.0278357i	−0.234729	+	0.972061i	$0.575420\pi$
$432$			1.00000i			0.0481125i
$433$	2.11205	−	16.7186i	0.101499	−	0.803444i	−0.856395	−	0.516321i	$-0.827301\pi$
$433$	2.11205	−	16.7186i	0.101499	−	0.803444i	0.957894	−	0.287123i	$-0.0926988\pi$
$434$	−4.50518	+	5.44582i	−0.216255	+	0.261408i
$435$	14.4246	−	12.2109i	0.691607	−	0.585469i
$436$	0.733534	+	11.6592i	0.0351299	+	0.558374i
$437$	−0.492726	−	1.91904i	−0.0235703	−	0.0918002i
$438$	−2.55398	−	9.94709i	−0.122034	−	0.475290i
$439$	0.459180	+	7.29845i	0.0219154	+	0.348336i	0.993670	+	0.112341i	$0.0358349\pi$
$439$	0.459180	+	7.29845i	0.0219154	+	0.348336i	−0.971754	+	0.235995i	$0.924165\pi$
$440$	0.158845	−	0.649099i	0.00757266	−	0.0309446i
$441$	3.55905	−	4.30215i	0.169479	−	0.204864i
$442$	−0.241027	+	1.90792i	−0.0114645	+	0.0907506i
$443$		−	9.62444i		−	0.457271i	−0.973512	−	0.228636i	$-0.926574\pi$
$443$		−	9.62444i		−	0.457271i	0.973512	−	0.228636i	$-0.0734264\pi$
$444$	6.23506	+	0.787671i	0.295903	+	0.0373812i
$445$	10.0153	+	1.15013i	0.474772	+	0.0545215i
$446$	10.7420	−	10.0874i	0.508648	−	0.477652i
$447$	−9.84503	+	4.63272i	−0.465654	+	0.219120i
$448$	0.917044	−	0.758644i	0.0433262	−	0.0358426i
$449$	1.67631	+	5.15914i	0.0791098	+	0.243475i	0.982788	−	0.184737i	$-0.0591435\pi$
$449$	1.67631	+	5.15914i	0.0791098	+	0.243475i	−0.903678	+	0.428212i	$0.859143\pi$
$450$	−3.92378	−	3.09903i	−0.184969	−	0.146090i
$451$	−0.0284522	+	0.0875668i	−0.00133976	+	0.00412336i
$452$	−4.68624	−	11.8361i	−0.220422	−	0.556723i
$453$	3.20317	+	3.41103i	0.150498	+	0.160264i
$454$	0.835748	−	4.38114i	0.0392236	−	0.205617i
$455$	5.55024	−	8.96874i	0.260199	−	0.420461i
$456$	0.413902	+	0.388680i	0.0193827	+	0.0182016i
$457$	−38.0982	−	12.3789i	−1.78216	−	0.579059i	−0.783078	−	0.621923i	$-0.786352\pi$
$457$	−38.0982	−	12.3789i	−1.78216	−	0.579059i	−0.999081	+	0.0428649i	$0.986352\pi$
$458$	−6.90295	+	1.31681i	−0.322554	+	0.0615304i
$459$	0.0304685	−	0.484283i	0.00142215	−	0.0226044i
$460$	−7.39300	+	2.49506i	−0.344700	+	0.116333i
$461$	−0.955584	+	1.50576i	−0.0445060	+	0.0701302i	−0.865852	−	0.500299i	$-0.833223\pi$
$461$	−0.955584	+	1.50576i	−0.0445060	+	0.0701302i	0.821346	+	0.570430i	$0.193223\pi$
$462$	−0.354983	−	0.0223337i	−0.0165153	−	0.00103906i
$463$	18.6118	−	11.8114i	0.864964	−	0.548923i	−0.0277150	−	0.999616i	$-0.508823\pi$
$463$	18.6118	−	11.8114i	0.864964	−	0.548923i	0.892679	+	0.450693i	$0.148823\pi$
$464$	5.38747	+	6.51233i	0.250107	+	0.302327i
$465$	−6.26489	+	11.7080i	−0.290527	+	0.542946i
$466$	0.732663	−	0.188116i	0.0339400	−	0.00871431i
$467$	−10.7115	−	5.04047i	−0.495671	−	0.233245i	0.161661	−	0.986846i	$-0.448315\pi$
$467$	−10.7115	−	5.04047i	−0.495671	−	0.233245i	−0.657332	+	0.753601i	$0.728315\pi$
$468$	−3.76919	+	1.22469i	−0.174231	+	0.0566111i
$469$	2.66883	−	1.46720i	0.123235	−	0.0677490i
$470$	2.18047	−	6.97881i	0.100578	−	0.321909i
$471$	−12.9087	+	1.63075i	−0.594802	+	0.0751410i
$472$	−0.910623	−	7.20832i	−0.0419148	−	0.331790i
$473$	0.926956	+	0.588264i	0.0426215	+	0.0270484i
$474$	2.36822	+	1.72062i	0.108776	+	0.0790305i
$475$	−2.80779	+	0.419528i	−0.128830	+	0.0192493i
$476$	−0.467223	+	0.339457i	−0.0214151	+	0.0155590i
$477$	−7.44788	+	0.468581i	−0.341015	+	0.0214548i
$478$	5.43125	−	9.87941i	0.248420	−	0.451873i
$479$	−11.8538	−	25.1906i	−0.541613	−	1.15099i	−0.969033	−	0.246933i	$-0.920577\pi$
$479$	−11.8538	−	25.1906i	−0.541613	−	1.15099i	0.427419	−	0.904053i	$-0.359423\pi$
$480$	1.40572	−	1.73895i	0.0641619	−	0.0793720i
$481$	4.66710	+	24.4658i	0.212802	+	1.11554i
$482$	−6.16006	+	8.47860i	−0.280583	+	0.386190i
$483$	2.00075	+	3.63936i	0.0910374	+	0.165597i
$484$	5.84624	+	9.21220i	0.265738	+	0.418736i
$485$	19.4216	+	15.6998i	0.881891	+	0.712893i
$486$	0.929776	−	0.368125i	0.0421755	−	0.0166985i
$487$	2.12671	−	5.37146i	0.0963705	−	0.243404i	−0.873592	−	0.486659i	$-0.838215\pi$
$487$	2.12671	−	5.37146i	0.0963705	−	0.243404i	0.969962	+	0.243255i	$0.0782153\pi$
$488$	0.572376	+	0.473511i	0.0259102	+	0.0214348i
$489$	2.48411	+	0.637810i	0.112335	+	0.0288428i
$490$	−12.2366	+	2.47823i	−0.552795	+	0.111955i
$491$	2.25802	+	0.894014i	0.101903	+	0.0403463i	0.418523	−	0.908206i	$-0.362548\pi$
$491$	2.25802	+	0.894014i	0.101903	+	0.0403463i	−0.316620	+	0.948553i	$0.602548\pi$
$492$	−0.210902	+	0.224588i	−0.00950820	+	0.0101252i
$493$	−2.41064	−	3.31795i	−0.108570	−	0.149433i
$494$	−0.958110	+	2.03609i	−0.0431074	+	0.0916079i
$495$	−0.661992	+	0.0912587i	−0.0297543	+	0.00410177i
$496$	−5.20391	−	2.86087i	−0.233662	−	0.128457i
$497$	−8.20278	−	1.56476i	−0.367945	−	0.0701893i
$498$	3.71712	−	14.4772i	0.166568	−	0.648740i
$499$	−33.6413			−1.50599			−0.752997	−	0.658024i	$-0.771392\pi$
$499$	−33.6413			−1.50599			−0.752997	+	0.658024i	$0.771392\pi$
$500$	2.46691	+	10.9048i	0.110324	+	0.487677i
$501$	17.2674			0.771450
$502$	−2.44002	+	9.50326i	−0.108904	+	0.424151i
$503$	9.74909	+	1.85974i	0.434690	+	0.0829216i	0.400082	−	0.916479i	$-0.368982\pi$
$503$	9.74909	+	1.85974i	0.434690	+	0.0829216i	0.0346084	+	0.999401i	$0.488982\pi$
$504$	−1.04296	−	0.573370i	−0.0464570	−	0.0255399i
$505$	−5.25852	+	29.3698i	−0.234001	+	1.30694i
$506$	−0.444017	+	0.943583i	−0.0197389	+	0.0419474i
$507$	−1.59094	−	2.18975i	−0.0706563	−	0.0972501i
$508$	4.01626	−	4.27688i	0.178193	−	0.189756i
$509$	10.6623	+	4.22150i	0.472598	+	0.187115i	0.592337	−	0.805691i	$-0.298206\pi$
$509$	10.6623	+	4.22150i	0.472598	+	0.187115i	−0.119738	+	0.992805i	$0.538206\pi$
$510$	−0.733747	+	0.799315i	−0.0324909	+	0.0353943i
$511$	11.8387	+	3.03967i	0.523715	+	0.134467i
$512$	0.770513	+	0.637424i	0.0340522	+	0.0281704i
$513$	0.209018	−	0.527919i	0.00922837	−	0.0233082i
$514$	−19.7167	+	7.80641i	−0.869668	+	0.344326i
$515$	−0.884222	−	3.28870i	−0.0389635	−	0.144918i
$516$	1.96841	+	3.10173i	0.0866546	+	0.136546i
$517$	−0.470764	−	0.856317i	−0.0207042	−	0.0376608i
$518$	−4.39650	+	6.05127i	−0.193171	+	0.265877i
$519$	2.54916	+	13.3632i	0.111896	+	0.586578i
$520$	8.27602	+	3.16874i	0.362927	+	0.138959i
$521$	8.04715	+	17.1011i	0.352552	+	0.749212i	0.999916	−	0.0129697i	$-0.00412850\pi$
$521$	8.04715	+	17.1011i	0.352552	+	0.749212i	−0.647364	+	0.762181i	$0.724128\pi$
$522$	4.07175	−	7.40649i	0.178216	−	0.324173i
$523$	17.6799	−	1.11232i	0.773087	−	0.0486385i	0.328654	−	0.944451i	$-0.393405\pi$
$523$	17.6799	−	1.11232i	0.773087	−	0.0486385i	0.444433	+	0.895812i	$0.353405\pi$
$524$	16.2527	−	11.8083i	0.710003	−	0.515848i
$525$	5.48193	−	2.31543i	0.239251	−	0.101054i
$526$	1.82039	+	1.32259i	0.0793729	+	0.0576678i
$527$	2.43300	+	1.54403i	0.105983	+	0.0672588i
$528$	−0.0374561	−	0.296495i	−0.00163007	−	0.0129033i
$529$	−10.7383	+	1.35656i	−0.466882	+	0.0589810i
$530$	13.6102	+	9.65476i	0.591190	+	0.419376i
$531$	−6.36690	+	3.50024i	−0.276300	+	0.151897i
$532$	−0.642695	+	0.208824i	−0.0278644	+	0.00905368i
$533$	−1.10480	−	0.519881i	−0.0478544	−	0.0225186i
$534$	4.36679	−	1.12120i	0.188970	−	0.0485191i
$535$	5.87272	+	42.6008i	0.253900	+	1.84179i
$536$	1.63111	+	1.97167i	0.0704532	+	0.0851632i
$537$	1.63594	−	1.03820i	0.0705961	−	0.0448017i
$538$	−26.0362	−	1.63806i	−1.12250	−	0.0706217i
$539$	−0.894100	+	1.40888i	−0.0385116	+	0.0606846i
$540$	−2.13432	−	0.666850i	−0.0918464	−	0.0286967i
$541$	1.20700	−	19.1847i	0.0518929	−	0.824813i	−0.882887	−	0.469586i	$-0.844403\pi$
$541$	1.20700	−	19.1847i	0.0518929	−	0.824813i	0.934780	−	0.355228i	$-0.115597\pi$
$542$	−7.72161	+	1.47298i	−0.331672	+	0.0632697i
$543$	−1.81319	−	0.589142i	−0.0778116	−	0.0252825i
$544$	−0.353725	−	0.332170i	−0.0151658	−	0.0142417i
$545$	−25.3736	−	6.20934i	−1.08688	−	0.265979i
$546$	0.883850	−	4.63330i	0.0378253	−	0.198287i
$547$	23.9036	+	25.4548i	1.02204	+	1.08837i	0.996058	+	0.0887044i	$0.0282726\pi$
$547$	23.9036	+	25.4548i	1.02204	+	1.08837i	0.0259863	+	0.999662i	$0.491727\pi$
$548$	−3.49595	−	8.82976i	−0.149340	−	0.377189i
$549$	0.229553	−	0.706493i	0.00979710	−	0.0301524i
$550$	1.27946	+	0.771879i	0.0545563	+	0.0329130i
$551$	−1.48295	−	4.56406i	−0.0631759	−	0.194435i
$552$	−2.68868	+	2.22427i	−0.114438	+	0.0946711i
$553$	−3.15239	+	1.48340i	−0.134053	+	0.0630808i
$554$	−10.0980	+	9.48262i	−0.429022	+	0.402878i
$555$	−5.83899	+	12.7823i	−0.247851	+	0.542580i
$556$	4.32548	+	0.546435i	0.183441	+	0.0231740i
$557$			8.68696i			0.368078i	0.982919	+	0.184039i	$0.0589173\pi$
$557$			8.68696i			0.368078i	−0.982919	+	0.184039i	$0.941083\pi$
$558$	−0.744286	+	5.89163i	−0.0315081	+	0.249413i
$559$	−9.28032	+	11.2180i	−0.392516	+	0.474470i
$560$	1.00766	+	2.46316i	0.0425813	+	0.104088i
$561$	0.00910556	+	0.144729i	0.000384437	+	0.00611045i
$562$	4.25874	+	16.5867i	0.179644	+	0.699667i
$563$	2.97976	+	11.6054i	0.125582	+	0.489109i	0.999992	+	0.00392226i	$0.00124850\pi$
$563$	2.97976	+	11.6054i	0.125582	+	0.489109i	−0.874410	+	0.485187i	$0.838752\pi$
$564$	−0.205313	−	3.26336i	−0.00864524	−	0.137412i
$565$	28.3870	−	2.10903i	1.19425	−	0.0887274i
$566$	10.3738	−	12.5398i	0.436043	−	0.527085i
$567$	−0.149168	+	1.18079i	−0.00626447	+	0.0495884i
$568$		−	7.01638i		−	0.294401i
$569$	34.3798	+	4.34318i	1.44128	+	0.182075i	0.806780	−	0.590852i	$-0.201208\pi$
$569$	34.3798	+	4.34318i	1.44128	+	0.182075i	0.634495	+	0.772927i	$0.281208\pi$
$570$	−1.10558	+	0.624207i	−0.0463075	+	0.0261452i
$571$	−4.15177	+	3.89877i	−0.173746	+	0.163159i	−0.766542	−	0.642194i	$-0.778024\pi$
$571$	−4.15177	+	3.89877i	−0.173746	+	0.163159i	0.592796	+	0.805353i	$0.298024\pi$
$572$	1.07168	−	0.504293i	0.0448090	−	0.0210855i
$573$	0.395224	−	0.326958i	0.0165107	−	0.0136589i
$574$	−0.113310	−	0.348733i	−0.00472948	−	0.0145559i
$575$	−0.395234	−	17.4428i	−0.0164824	−	0.727417i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−8.54885	−	21.5919i	−0.355893	−	0.898884i	−0.991879	−	0.127183i	$-0.959406\pi$
$577$	−8.54885	−	21.5919i	−0.355893	−	0.898884i	0.635986	−	0.771701i	$-0.280594\pi$
$578$	−11.4761	−	12.2208i	−0.477344	−	0.508319i
$579$	−4.04719	+	21.2161i	−0.168195	+	0.881711i
$580$	−17.4920	+	7.15582i	−0.726316	+	0.297129i
$581$	12.9678	+	12.1776i	0.537996	+	0.505212i
$582$	10.6219	+	3.45128i	0.440294	+	0.143060i
$583$	2.19071	−	0.417900i	0.0907299	−	0.0173077i
$584$	−0.644842	+	10.2495i	−0.0266837	+	0.424126i
$585$	−0.100381	−	8.86134i	−0.00415023	−	0.366371i
$586$	−3.23704	+	5.10076i	−0.133721	+	0.210710i
$587$	42.3712	+	2.66577i	1.74885	+	0.110028i	0.904690	−	0.426070i	$-0.140102\pi$
$587$	42.3712	+	2.66577i	1.74885	+	0.110028i	0.844156	+	0.536098i	$0.180102\pi$
$588$	−4.71430	+	2.99178i	−0.194414	+	0.123379i
$589$	2.14927	+	2.59802i	0.0885591	+	0.107050i
$590$	15.9921	+	2.86331i	0.658384	+	0.117881i
$591$	22.0130	−	5.65198i	0.905495	−	0.232492i
$592$	−5.68649	−	2.67586i	−0.233713	−	0.109977i
$593$	−13.8534	+	4.50125i	−0.568893	+	0.184844i	−0.579319	−	0.815101i	$-0.696681\pi$
$593$	−13.8534	+	4.50125i	−0.568893	+	0.184844i	0.0104260	+	0.999946i	$0.496681\pi$
$594$	−0.261886	+	0.143973i	−0.0107453	+	0.00590728i
$595$	−0.412942	−	1.22357i	−0.0169290	−	0.0501615i
$596$	10.7948	−	1.36370i	0.442171	−	0.0558592i
$597$	−1.17678	−	9.31514i	−0.0481622	−	0.381243i
$598$	−11.6765	−	7.41012i	−0.477487	−	0.303022i
$599$	−3.43124	−	2.49294i	−0.140197	−	0.101859i	0.515476	−	0.856904i	$-0.327615\pi$
$599$	−3.43124	−	2.49294i	−0.140197	−	0.101859i	−0.655673	+	0.755045i	$0.727615\pi$
$600$	2.77408	+	4.15987i	0.113251	+	0.169826i
$601$	24.4566	−	17.7687i	0.997604	−	0.724802i	0.0360309	−	0.999351i	$-0.488529\pi$
$601$	24.4566	−	17.7687i	0.997604	−	0.724802i	0.961573	+	0.274549i	$0.0885285\pi$
$602$	−4.36359	+	0.274534i	−0.177847	+	0.0111892i
$603$	1.23276	−	2.24239i	0.0502020	−	0.0913171i
$604$	−1.99233	−	4.23392i	−0.0810667	−	0.172276i
$605$	−23.5603	+	6.33458i	−0.957863	+	0.257537i
$606$	2.50031	+	13.1071i	0.101568	+	0.532439i
$607$	−17.1053	+	23.5434i	−0.694282	+	0.955598i	0.305712	+	0.952124i	$0.401106\pi$
$607$	−17.1053	+	23.5434i	−0.694282	+	0.955598i	−0.999994	+	0.00347350i	$0.998894\pi$
$608$	−0.273536	−	0.497559i	−0.0110933	−	0.0201787i
$609$	5.39002	+	8.49331i	0.218415	+	0.344166i
$610$	−1.39231	+	0.905872i	−0.0563730	+	0.0366777i
$611$	12.0488	−	4.77045i	0.487442	−	0.192992i
$612$	−0.178629	+	0.451165i	−0.00722064	+	0.0182373i
$613$	−25.7587	−	21.3095i	−1.04039	−	0.860682i	−0.0499630	−	0.998751i	$-0.515910\pi$
$613$	−25.7587	−	21.3095i	−1.04039	−	0.860682i	−0.990423	+	0.138069i	$0.955910\pi$
$614$	17.5054	+	4.49463i	0.706462	+	0.181389i
$615$	−0.338702	−	0.599898i	−0.0136578	−	0.0241902i
$616$	0.330708	+	0.130936i	0.0133246	+	0.00527558i
$617$	25.7050	−	27.3731i	1.03485	−	1.10200i	0.0401435	−	0.999194i	$-0.487218\pi$
$617$	25.7050	−	27.3731i	1.03485	−	1.10200i	0.994702	−	0.102804i	$-0.0327815\pi$
$618$	−0.895188	−	1.23212i	−0.0360098	−	0.0495632i
$619$	−0.538402	+	1.14416i	−0.0216402	+	0.0459878i	−0.915355	−	0.402648i	$-0.868090\pi$
$619$	−0.538402	+	1.14416i	−0.0216402	+	0.0459878i	0.893715	+	0.448636i	$0.148090\pi$
$620$	9.57624	−	9.19902i	0.384591	−	0.369442i
$621$	3.05784	+	1.68106i	0.122707	+	0.0674587i
$622$	−2.18499	−	0.416809i	−0.0876101	−	0.0167125i
$623$	−1.33442	+	5.19723i	−0.0534625	+	0.208223i
$624$	3.96317			0.158654
$625$	−24.9193	−	2.00669i	−0.996773	−	0.0802674i
$626$	−10.7312			−0.428904
$627$	−0.0421991	+	0.164354i	−0.00168527	+	0.00656369i
$628$	12.7809	+	2.43808i	0.510012	+	0.0972899i
$629$	2.67234	+	1.46913i	0.106553	+	0.0585781i
$630$	1.91925	−	1.84365i	0.0764647	−	0.0734527i
$631$	−20.5638	+	43.7004i	−0.818633	+	1.73968i	−0.160144	+	0.987094i	$0.551196\pi$
$631$	−20.5638	+	43.7004i	−0.818633	+	1.73968i	−0.658489	+	0.752590i	$0.728804\pi$
$632$	−1.72062	−	2.36822i	−0.0684424	−	0.0942029i
$633$	−1.04838	+	1.11641i	−0.0416694	+	0.0443734i
$634$	−2.80294	−	1.10976i	−0.111319	−	0.0440743i
$635$	6.44998	+	11.4240i	0.255960	+	0.453348i
$636$	7.22815	+	1.85587i	0.286615	+	0.0735902i
$637$	−17.0501	−	14.1051i	−0.675551	−	0.558865i
$638$	−0.929837	+	2.34850i	−0.0368126	+	0.0929780i
$639$	−6.52366	+	2.58290i	−0.258072	+	0.102178i
$640$	−1.87428	+	1.21945i	−0.0740875	+	0.0482031i
$641$	10.0074	+	15.7691i	0.395268	+	0.622843i	0.982431	−	0.186626i	$-0.0597552\pi$
$641$	10.0074	+	15.7691i	0.395268	+	0.622843i	−0.587163	+	0.809469i	$0.699755\pi$
$642$	9.26501	+	16.8530i	0.365661	+	0.665134i
$643$	−17.9537	+	24.7112i	−0.708025	+	0.974513i	0.291812	+	0.956476i	$0.405742\pi$
$643$	−17.9537	+	24.7112i	−0.708025	+	0.974513i	−0.999837	+	0.0180375i	$0.994258\pi$
$644$	−0.778207	−	4.07950i	−0.0306656	−	0.160755i
$645$	−7.93270	+	2.13284i	−0.312350	+	0.0839804i
$646$	0.117309	+	0.249293i	0.00461545	+	0.00980832i
$647$	−4.72339	+	8.59181i	−0.185696	+	0.337779i	−0.952726	−	0.303832i	$-0.901734\pi$
$647$	−4.72339	+	8.59181i	−0.185696	+	0.337779i	0.767030	+	0.641611i	$0.221734\pi$
$648$	−0.998027	+	0.0627905i	−0.0392062	+	0.00246664i
$649$	1.75665	−	1.27628i	0.0689546	−	0.0500985i
$650$	−12.2820	+	15.5506i	−0.481738	+	0.609944i
$651$	−5.71796	−	4.15434i	−0.224105	−	0.162821i
$652$	−2.16543	−	1.37422i	−0.0848048	−	0.0538188i
$653$	0.765715	+	6.06126i	0.0299647	+	0.237195i	0.999983	−	0.00583683i	$-0.00185793\pi$
$653$	0.765715	+	6.06126i	0.0299647	+	0.237195i	−0.970018	+	0.243032i	$0.921858\pi$
$654$	−11.5901	+	1.46417i	−0.453210	+	0.0572537i
$655$	14.3645	+	42.5628i	0.561268	+	1.66307i
$656$	0.269981	−	0.148423i	0.0105410	−	0.00579496i
$657$	9.76709	−	3.17352i	0.381051	−	0.123811i
$658$	3.52126	+	1.65698i	0.137273	+	0.0645958i
$659$	−47.6257	+	12.2282i	−1.85524	+	0.476343i	−0.999178	−	0.0405376i	$-0.987093\pi$
$659$	−47.6257	+	12.2282i	−1.85524	+	0.476343i	−0.856057	+	0.516881i	$0.827093\pi$
$660$	0.657793	+	0.117775i	0.0256045	+	0.00458437i
$661$	−14.9154	−	18.0296i	−0.580140	−	0.701269i	0.396040	−	0.918233i	$-0.370384\pi$
$661$	−14.9154	−	18.0296i	−0.580140	−	0.701269i	−0.976179	+	0.216965i	$0.930384\pi$
$662$	−14.8582	+	9.42930i	−0.577481	+	0.366480i
$663$	−1.91929	−	0.120752i	−0.0745391	−	0.00468960i
$664$	−8.00891	+	12.6200i	−0.310806	+	0.489752i
$665$	−0.0171162	−	1.51097i	−0.000663737	−	0.0585929i
$666$	−0.394614	+	6.27222i	−0.0152910	+	0.243043i
$667$	28.9703	−	5.52639i	1.12174	−	0.213982i
$668$	−16.4223	−	5.33592i	−0.635396	−	0.206453i
$669$	10.7420	+	10.0874i	0.415309	+	0.390001i
$670$	−5.29588	+	2.16649i	−0.204598	+	0.0836990i
$671$	−0.0415991	+	0.218070i	−0.00160591	+	0.00841849i
$672$	0.814729	+	0.867598i	0.0314289	+	0.0334683i
$673$	16.4193	+	41.4705i	0.632919	+	1.59857i	0.791462	+	0.611218i	$0.209320\pi$
$673$	16.4193	+	41.4705i	0.632919	+	1.59857i	−0.158544	+	0.987352i	$0.550680\pi$
$674$	−2.95358	+	9.09019i	−0.113768	+	0.350141i
$675$	2.84654	−	4.11062i	0.109563	−	0.158218i
$676$	0.836409	+	2.57420i	0.0321696	+	0.0990078i
$677$	24.3979	−	20.1837i	0.937689	−	0.775724i	−0.0369938	−	0.999315i	$-0.511778\pi$
$677$	24.3979	−	20.1837i	0.937689	−	0.775724i	0.974683	+	0.223592i	$0.0717782\pi$
$678$	11.5185	−	5.42019i	0.442365	−	0.208161i
$679$	−9.68983	+	9.09936i	−0.371862	+	0.349201i
$680$	0.944837	−	0.533454i	0.0362328	−	0.0204570i
$681$	4.42498	+	0.559004i	0.169565	+	0.0214211i
$682$		−	1.77472i		−	0.0679575i
$683$	5.41642	−	42.8754i	0.207254	−	1.64058i	−0.454419	−	0.890788i	$-0.650153\pi$
$683$	5.41642	−	42.8754i	0.207254	−	1.64058i	0.661672	−	0.749793i	$-0.269847\pi$
$684$	−0.361924	+	0.437491i	−0.0138385	+	0.0167279i
$685$	21.1768	−	1.57334i	0.809123	−	0.0601143i
$686$	−0.940384	−	14.9470i	−0.0359040	−	0.570678i
$687$	−1.74765	−	6.80664i	−0.0666770	−	0.259690i
$688$	−0.913588	−	3.55819i	−0.0348302	−	0.135655i
$689$	1.85706	+	29.5172i	0.0707484	+	1.12451i
$690$	−2.95435	−	7.22175i	−0.112470	−	0.274927i
$691$	30.4466	−	36.8037i	1.15824	−	1.40008i	0.257195	−	0.966359i	$-0.417202\pi$
$691$	30.4466	−	36.8037i	1.15824	−	1.40008i	0.901049	−	0.433717i	$-0.142798\pi$
$692$	1.70505	−	13.4969i	0.0648163	−	0.513074i
$693$		−	0.355685i		−	0.0135114i
$694$	−12.3579	−	1.56117i	−0.469101	−	0.0592612i
$695$	−4.05071	+	8.86756i	−0.153652	+	0.336366i
$696$	−6.16120	+	5.78575i	−0.233540	+	0.219308i
$697$	−0.135269	+	0.0636530i	−0.00512370	+	0.00241103i
$698$	−20.3894	+	16.8676i	−0.771750	+	0.638447i
$699$	0.233749	+	0.719406i	0.00884120	+	0.0272104i
$700$	−5.92913	+	0.508101i	−0.224100	+	0.0192044i
$701$	7.19932	−	22.1572i	0.271915	−	0.836867i	−0.718105	−	0.695935i	$-0.754990\pi$
$701$	7.19932	−	22.1572i	0.271915	−	0.836867i	0.990019	−	0.140932i	$-0.0450099\pi$
$702$	−1.45894	−	3.68486i	−0.0550641	−	0.139076i
$703$	2.44270	+	2.60122i	0.0921283	+	0.0981067i
$704$	−0.0559992	+	0.293558i	−0.00211055	+	0.0110639i
$705$	7.10196	+	1.73797i	0.267475	+	0.0654556i
$706$	−10.8326	−	10.1725i	−0.407689	−	0.382846i
$707$	−15.1037	−	4.90749i	−0.568034	−	0.184565i
$708$	7.13692	−	1.36144i	0.268222	−	0.0511660i
$709$	0.565828	−	8.99359i	0.0212501	−	0.337761i	−0.973009	−	0.230766i	$-0.925877\pi$
$709$	0.565828	−	8.99359i	0.0212501	−	0.337761i	0.994259	−	0.106996i	$-0.0341231\pi$
$710$	14.9752	+	4.67887i	0.562008	+	0.175595i
$711$	−1.56852	+	2.47159i	−0.0588240	+	0.0926918i
$712$	−4.49954	−	0.283087i	−0.168627	−	0.0106091i
$713$	−17.4962	+	11.1034i	−0.655237	+	0.415826i
$714$	−0.368125	−	0.444986i	−0.0137767	−	0.0166532i
$715$	0.361673	+	2.62358i	0.0135258	+	0.0981165i
$716$	−1.87670	+	0.481854i	−0.0701354	+	0.0180077i
$717$	10.2009	+	4.80020i	0.380961	+	0.179267i
$718$	−25.2514	+	8.20466i	−0.942372	+	0.306195i
$719$	32.2829	−	17.7477i	1.20395	−	0.661876i	0.251879	−	0.967759i	$-0.418951\pi$
$719$	32.2829	−	17.7477i	1.20395	−	0.661876i	0.952069	+	0.305882i	$0.0989515\pi$
$720$	1.82379	+	1.29375i	0.0679686	+	0.0482153i
$721$	1.79832	−	0.227181i	0.0669730	−	0.00846066i
$722$	−2.34093	−	18.5303i	−0.0871202	−	0.689628i
$723$	−8.84866	−	5.61553i	−0.329085	−	0.208844i
$724$	1.54239	+	1.12062i	0.0573226	+	0.0416473i
$725$	−3.60824	−	42.1054i	−0.134007	−	1.56375i
$726$	−8.82693	+	6.41314i	−0.327598	+	0.238014i
$727$	−36.7124	+	2.30975i	−1.36159	+	0.0856639i	−0.726708	−	0.686946i	$-0.758951\pi$
$727$	−36.7124	+	2.30975i	−1.36159	+	0.0856639i	−0.634881	+	0.772610i	$0.718951\pi$
$728$	−2.27236	+	4.13341i	−0.0842193	+	0.153194i
$729$	0.425779	+	0.904827i	0.0157696	+	0.0335121i
$730$	−21.4456	−	8.21115i	−0.793737	−	0.303908i
$731$	0.334022	+	1.75101i	0.0123543	+	0.0647633i
$732$	−0.436636	+	0.600978i	−0.0161385	+	0.0222128i
$733$	−3.32387	−	6.04610i	−0.122770	−	0.223318i	0.807779	−	0.589486i	$-0.200670\pi$
$733$	−3.32387	−	6.04610i	−0.122770	−	0.223318i	−0.930549	+	0.366168i	$0.880670\pi$
$734$	7.51654	+	11.8442i	0.277441	+	0.437176i
$735$	−3.24169	−	12.0569i	−0.119571	−	0.444725i
$736$	3.24442	−	1.28456i	0.119591	−	0.0473494i
$737$	−0.281517	+	0.711032i	−0.0103698	+	0.0261912i
$738$	−0.237387	−	0.196384i	−0.00873835	−	0.00722899i
$739$	18.8958	+	4.85162i	0.695093	+	0.178470i	0.579675	−	0.814847i	$-0.303179\pi$
$739$	18.8958	+	4.85162i	0.695093	+	0.178470i	0.115418	+	0.993317i	$0.463179\pi$
$740$	9.50317	−	10.3524i	0.349344	−	0.380561i
$741$	−2.09223	−	0.828372i	−0.0768600	−	0.0304310i
$742$	−6.08000	+	6.47454i	−0.223204	+	0.237688i
$743$	−24.1314	−	33.2141i	−0.885297	−	1.21851i	−0.974926	−	0.222531i	$-0.928568\pi$
$743$	−24.1314	−	33.2141i	−0.885297	−	1.21851i	0.0896291	−	0.995975i	$-0.471432\pi$
$744$	2.52847	−	5.37328i	0.0926983	−	0.196994i
$745$	−4.28793	+	23.9488i	−0.157098	+	0.877418i
$746$	17.4547	+	9.59582i	0.639063	+	0.351328i
$747$	14.6821	+	2.80075i	0.537189	+	0.102474i
$748$	0.0360637	−	0.140459i	0.00131862	−	0.00513569i
$749$	−22.8892			−0.836353
$750$	−10.7284	+	3.14676i	−0.391745	+	0.114903i
$751$	−9.80633			−0.357838			−0.178919	−	0.983864i	$-0.557260\pi$
$751$	−9.80633			−0.357838			−0.178919	+	0.983864i	$0.557260\pi$
$752$	−0.813169	+	3.16708i	−0.0296532	+	0.115492i
$753$	−9.63772	−	1.83849i	−0.351218	−	0.0669984i
$754$	−29.3531	−	16.1370i	−1.06898	−	0.587676i
$755$	10.3651	−	1.42888i	0.377225	−	0.0520022i
$756$	0.506751	−	1.07690i	0.0184303	−	0.0391665i
$757$	6.99757	+	9.63133i	0.254331	+	0.350057i	0.917022	−	0.398836i	$-0.130586\pi$
$757$	6.99757	+	9.63133i	0.254331	+	0.350057i	−0.662691	+	0.748893i	$0.730586\pi$
$758$	−3.45394	+	3.67807i	−0.125453	+	0.133594i
$759$	−0.969601	−	0.383892i	−0.0351943	−	0.0139344i
$760$	1.24436	−	0.252014i	0.0451376	−	0.00914152i
$761$	53.1196	+	13.6388i	1.92558	+	0.494405i	0.989947	+	0.141436i	$0.0451719\pi$
$761$	53.1196	+	13.6388i	1.92558	+	0.494405i	0.935635	+	0.352970i	$0.114828\pi$
$762$	4.52063	+	3.73979i	0.163765	+	0.135478i
$763$	5.11836	−	12.9275i	0.185297	−	0.468007i
$764$	−0.476916	+	0.188824i	−0.0172542	+	0.00683143i
$765$	−0.843810	−	0.682110i	−0.0305080	−	0.0246617i
$766$	−11.3149	−	17.8294i	−0.408823	−	0.644201i
$767$	13.8720	+	25.2331i	0.500889	+	0.911114i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	8.89963	+	46.6535i	0.320929	+	1.68237i	0.667709	+	0.744422i	$0.267275\pi$
$769$	8.89963	+	46.6535i	0.320929	+	1.68237i	−0.346780	+	0.937946i	$0.612725\pi$
$770$	−0.499992	+	0.618520i	−0.0180185	+	0.0222899i
$771$	−9.02903	−	19.1877i	−0.325173	−	0.691027i
$772$	10.4052	−	18.9271i	0.374493	−	0.681200i
$773$	45.4790	−	2.86130i	1.63577	−	0.102914i	0.781900	−	0.623404i	$-0.214251\pi$
$773$	45.4790	−	2.86130i	1.63577	−	0.102914i	0.853867	+	0.520491i	$0.174251\pi$
$774$	−2.97201	+	2.15929i	−0.106827	+	0.0776141i
$775$	13.2477	+	26.5731i	0.475872	+	0.954534i
$776$	−9.03556	−	6.56472i	−0.324358	−	0.235660i
$777$	−6.31539	−	4.00787i	−0.226563	−	0.143781i
$778$	0.187006	+	1.48031i	0.00670450	+	0.0530716i
$779$	−0.173551	+	0.0219246i	−0.00621812	+	0.000785532i
$780$	−2.64284	+	8.45865i	−0.0946287	+	0.302868i
$781$	1.83749	−	1.01017i	0.0657505	−	0.0361467i
$782$	−1.61036	+	0.523236i	−0.0575862	+	0.0187109i
$783$	7.64754	+	3.59866i	0.273301	+	0.128606i
$784$	5.40807	−	1.38856i	0.193145	−	0.0495913i
$785$	−13.7265	+	25.6526i	−0.489921	+	0.915579i
$786$	12.8055	+	15.4792i	0.456757	+	0.552125i
$787$	−38.5723	+	24.4787i	−1.37495	+	0.872573i	−0.998547	−	0.0538814i	$-0.982841\pi$
$787$	−38.5723	+	24.4787i	−1.37495	+	0.872573i	−0.376407	+	0.926454i	$0.622841\pi$
$788$	−22.6822	−	1.42704i	−0.808020	−	0.0508363i
$789$	−1.20568	+	1.89985i	−0.0429233	+	0.0676364i
$790$	6.20193	−	2.09309i	0.220655	−	0.0744688i
$791$	−0.951335	+	15.1210i	−0.0338256	+	0.537642i
$792$	0.293558	−	0.0559992i	0.0104311	−	0.00198985i
$793$	−2.79995	−	0.909758i	−0.0994290	−	0.0323064i
$794$	−19.2180	−	18.0469i	−0.682021	−	0.640461i
$795$	−8.78112	+	14.1896i	−0.311434	+	0.503253i
$796$	−1.75936	+	9.22287i	−0.0623587	+	0.326896i
$797$	−3.09063	−	3.29119i	−0.109476	−	0.116580i	0.671897	−	0.740645i	$-0.265480\pi$
$797$	−3.09063	−	3.29119i	−0.109476	−	0.116580i	−0.781372	+	0.624065i	$0.785480\pi$
$798$	−0.248767	−	0.628315i	−0.00880627	−	0.0222421i
$799$	0.490300	−	1.50899i	0.0173456	−	0.0533841i
$800$	−1.35284	−	4.81351i	−0.0478300	−	0.170183i
$801$	1.39318	+	4.28777i	0.0492257	+	0.151501i
$802$	−3.40242	+	2.81473i	−0.120144	+	0.0993915i
$803$	−2.77703	+	1.30677i	−0.0979992	+	0.0461149i
$804$	−1.86536	+	1.75169i	−0.0657863	+	0.0617774i
$805$	9.22590	+	1.05948i	0.325170	+	0.0373416i
$806$	23.3495	+	2.94973i	0.822451	+	0.103900i
$807$		−	26.0876i		−	0.918329i
$808$	1.67238	−	13.2382i	0.0588340	−	0.465719i
$809$	−32.2263	+	38.9549i	−1.13302	+	1.36958i	−0.213303	+	0.976986i	$0.568422\pi$
$809$	−32.2263	+	38.9549i	−1.13302	+	1.36958i	−0.919712	+	0.392594i	$0.871578\pi$
$810$	0.531519	−	2.17198i	0.0186757	−	0.0763155i
$811$	0.121780	+	1.93564i	0.00427628	+	0.0679695i	0.999586	−	0.0287694i	$-0.00915883\pi$
$811$	0.121780	+	1.93564i	0.00427628	+	0.0679695i	−0.995310	+	0.0967389i	$0.969159\pi$
$812$	−2.50164	−	9.74323i	−0.0877902	−	0.341920i
$813$	−1.95491	−	7.61388i	−0.0685618	−	0.267031i
$814$	−0.117931	−	1.87446i	−0.00413349	−	0.0656999i
$815$	4.37705	−	3.70532i	0.153321	−	0.129792i
$816$	0.309304	−	0.373884i	0.0108278	−	0.0130886i
$817$	−0.261425	+	2.06939i	−0.00914610	+	0.0723989i
$818$			17.9803i			0.628667i
$819$	4.67966	+	0.591178i	0.163520	+	0.0206574i
$820$	0.136746	+	0.675202i	0.00477537	+	0.0235791i
$821$	−21.4788	+	20.1699i	−0.749615	+	0.703935i	−0.961939	−	0.273264i	$-0.911897\pi$
$821$	−21.4788	+	20.1699i	−0.749615	+	0.703935i	0.212324	+	0.977199i	$0.431897\pi$
$822$	8.59282	−	4.04348i	0.299709	−	0.141032i
$823$	9.53791	−	7.89044i	0.332471	−	0.275044i	−0.456177	−	0.889889i	$-0.650782\pi$
$823$	9.53791	−	7.89044i	0.332471	−	0.275044i	0.788648	+	0.614845i	$0.210782\pi$
$824$	0.470628	+	1.44845i	0.0163951	+	0.0504590i
$825$	−0.690018	+	1.32540i	−0.0240233	+	0.0461445i
$826$	−2.67217	+	8.22410i	−0.0929768	+	0.286153i
$827$	−9.41364	−	23.7761i	−0.327344	−	0.826777i	−0.996495	−	0.0836506i	$-0.973342\pi$
$827$	−9.41364	−	23.7761i	−0.327344	−	0.826777i	0.669151	−	0.743127i	$-0.266658\pi$
$828$	−2.38870	−	2.54371i	−0.0830131	−	0.0884000i
$829$	2.61340	−	13.6999i	0.0907670	−	0.475817i	−0.907658	−	0.419711i	$-0.862131\pi$
$829$	2.61340	−	13.6999i	0.0907670	−	0.475817i	0.998425	−	0.0561063i	$-0.0178686\pi$
$830$	−21.5944	−	25.5092i	−0.749552	−	0.885437i
$831$	−10.0980	−	9.48262i	−0.350295	−	0.328949i
$832$	−3.76919	−	1.22469i	−0.130673	−	0.0424583i
$833$	−2.66134	+	0.507678i	−0.0922101	+	0.0175900i
$834$	−0.273758	+	4.35126i	−0.00947946	+	0.150672i
$835$	22.3397	−	31.4921i	0.773098	−	1.08983i
$836$	0.0909220	−	0.143270i	0.00314460	−	0.00495510i
$837$	−5.92674	−	0.372879i	−0.204858	−	0.0128886i
$838$	19.3288	−	12.2664i	0.667702	−	0.423737i
$839$	16.4767	+	19.9169i	0.568838	+	0.687607i	0.973977	−	0.226648i	$-0.0727767\pi$
$839$	16.4767	+	19.9169i	0.568838	+	0.687607i	−0.405139	+	0.914255i	$0.632777\pi$
$840$	−2.39503	+	1.16033i	−0.0826365	+	0.0400353i
$841$	41.1020	−	10.5532i	1.41731	−	0.363904i
$842$	−21.5701	−	10.1501i	−0.743355	−	0.349797i
$843$	−16.2866	+	5.29182i	−0.560939	+	0.182260i
$844$	1.34206	−	0.737804i	0.0461956	−	0.0253963i
$845$	−6.05193	+	0.0685559i	−0.208193	+	0.00235839i
$846$	3.24403	−	0.409816i	0.111532	−	0.0140898i
$847$	−1.62753	−	12.8832i	−0.0559225	−	0.442672i
$848$	−6.30088	−	3.99866i	−0.216373	−	0.137315i
$849$	13.1664	+	9.56594i	0.451869	+	0.328302i
$850$	0.508495	+	2.37232i	0.0174412	+	0.0813698i
$851$	−17.7417	+	12.8901i	−0.608178	+	0.441867i
$852$	7.00253	−	0.440562i	0.239903	−	0.0150934i
$853$	−20.9181	+	38.0498i	−0.716221	+	1.30280i	0.228056	+	0.973648i	$0.426763\pi$
$853$	−20.9181	+	38.0498i	−0.716221	+	1.30280i	−0.944277	+	0.329153i	$0.893237\pi$
$854$	−0.376440	−	0.799976i	−0.0128815	−	0.0273746i
$855$	−0.692395	−	1.06420i	−0.0236794	−	0.0363949i
$856$	−3.60369	−	18.8912i	−0.123171	−	0.645687i
$857$	−14.2799	+	19.6546i	−0.487792	+	0.671388i	−0.979979	−	0.199101i	$-0.936198\pi$
$857$	−14.2799	+	19.6546i	−0.487792	+	0.671388i	0.492187	+	0.870490i	$0.336198\pi$
$858$	0.570589	+	1.03790i	0.0194796	+	0.0354332i
$859$	21.6430	+	34.1039i	0.738449	+	1.16361i	0.981101	+	0.193496i	$0.0619826\pi$
$859$	21.6430	+	34.1039i	0.738449	+	1.16361i	−0.242652	+	0.970113i	$0.578017\pi$
$860$	8.20353	+	0.422892i	0.279738	+	0.0144205i
$861$	0.340931	−	0.134984i	0.0116189	−	0.00460024i
$862$	−1.69734	+	4.28700i	−0.0578117	+	0.146016i
$863$	−38.6346	−	31.9613i	−1.31514	−	1.08798i	−0.989813	−	0.142373i	$-0.954527\pi$
$863$	−38.6346	−	31.9613i	−1.31514	−	1.08798i	−0.325323	−	0.945603i	$-0.605473\pi$
$864$	0.968583	+	0.248690i	0.0329519	+	0.00846060i
$865$	27.6696	+	12.6395i	0.940794	+	0.429756i
$866$	−15.6681	−	6.20344i	−0.532423	−	0.210801i
$867$	11.4761	−	12.2208i	0.389749	−	0.415041i
$868$	4.15434	+	5.71796i	0.141008	+	0.194080i
$869$	0.372482	−	0.791565i	0.0126356	−	0.0268520i
$870$	−8.24003	−	17.0082i	−0.279363	−	0.576631i
$871$	−8.88695	−	4.88564i	−0.301123	−	0.165544i
$872$	11.4753	+	2.18903i	0.388603	+	0.0741300i
$873$	−2.77751	+	10.8177i	−0.0940045	+	0.366123i
$874$	−1.98129			−0.0670180
$875$	2.86939	−	12.9935i	0.0970032	−	0.439260i
$876$	−10.2697			−0.346982
$877$	11.1709	−	43.5077i	0.377213	−	1.46915i	−0.442704	−	0.896668i	$-0.645981\pi$
$877$	11.1709	−	43.5077i	0.377213	−	1.46915i	0.819918	−	0.572482i	$-0.194019\pi$
$878$	7.18335	+	1.37030i	0.242426	+	0.0462453i
$879$	−5.29395	−	2.91037i	−0.178560	−	0.0981644i
$880$	−0.589204	−	0.315280i	−0.0198620	−	0.0106281i
$881$	−14.8070	+	31.4666i	−0.498862	+	1.06014i	0.483876	+	0.875136i	$0.339228\pi$
$881$	−14.8070	+	31.4666i	−0.498862	+	1.06014i	−0.982739	+	0.185000i	$0.940772\pi$
$882$	−3.28189	−	4.51714i	−0.110507	−	0.152100i
$883$	1.48631	−	1.58276i	0.0500184	−	0.0532642i	−0.703473	−	0.710722i	$-0.748368\pi$
$883$	1.48631	−	1.58276i	0.0500184	−	0.0532642i	0.753491	+	0.657458i	$0.228368\pi$
$884$	1.78804	+	0.707935i	0.0601383	+	0.0238104i
$885$	−1.85351	+	16.1403i	−0.0623050	+	0.542551i
$886$	−9.32207	−	2.39350i	−0.313181	−	0.0804112i
$887$	28.3652	+	23.4658i	0.952411	+	0.787903i	0.977316	−	0.211787i	$-0.0679283\pi$
$887$	28.3652	+	23.4658i	0.952411	+	0.787903i	−0.0249049	+	0.999690i	$0.507928\pi$
$888$	2.31352	−	5.84329i	0.0776367	−	0.196088i
$889$	−6.49243	+	2.57053i	−0.217749	+	0.0862129i
$890$	3.60471	−	9.41466i	0.120830	−	0.315580i
$891$	−0.160133	−	0.252329i	−0.00536465	−	0.00845334i
$892$	−7.09906	−	12.9131i	−0.237694	−	0.432364i
$893$	1.09126	−	1.50200i	0.0365178	−	0.0502624i
$894$	2.03881	+	10.6878i	0.0681882	+	0.357455i
$895$	0.223046	−	4.32679i	0.00745560	−	0.144629i
$896$	−0.506751	−	1.07690i	−0.0169294	−	0.0359767i
$897$	6.66233	−	12.1187i	0.222449	−	0.404633i
$898$	5.41394	−	0.340616i	0.180666	−	0.0113665i
$899$	−40.6057	+	29.5018i	−1.35428	+	0.983940i
$900$	−3.97747	+	3.02981i	−0.132582	+	0.100994i
$901$	2.92957	+	2.12846i	0.0975983	+	0.0709093i
$902$	0.0777400	+	0.0493353i	0.00258846	+	0.00164269i
$903$	−0.547985	−	4.33774i	−0.0182358	−	0.144351i
$904$	−12.6297	+	1.59550i	−0.420056	+	0.0530654i
$905$	−3.42029	+	2.54468i	−0.113694	+	0.0845879i
$906$	4.10046	−	2.25425i	0.136229	−	0.0748924i
$907$	39.3678	−	12.7914i	1.30719	−	0.424731i	0.429111	−	0.903252i	$-0.358827\pi$
$907$	39.3678	−	12.7914i	1.30719	−	0.424731i	0.878076	+	0.478521i	$0.158827\pi$
$908$	−4.03566	−	1.89904i	−0.133928	−	0.0630218i
$909$	−12.9242	+	3.31838i	−0.428669	+	0.110064i
$910$	−7.30668	−	7.60630i	−0.242214	−	0.252146i
$911$	4.27515	+	5.16777i	0.141642	+	0.171216i	0.836564	−	0.547870i	$-0.184561\pi$
$911$	4.27515	+	5.16777i	0.141642	+	0.171216i	−0.694922	+	0.719085i	$0.744561\pi$
$912$	0.479402	−	0.304238i	0.0158746	−	0.0100743i
$913$	−4.45807	−	0.280478i	−0.147541	−	0.00928246i
$914$	−21.4646	+	33.8228i	−0.709986	+	1.11876i
$915$	−0.991508	−	1.33268i	−0.0327782	−	0.0440571i
$916$	−0.441256	+	7.01356i	−0.0145795	+	0.231734i
$917$	−23.4864	+	4.48027i	−0.775590	+	0.147952i
$918$	−0.461491	−	0.149947i	−0.0152315	−	0.00494900i
$919$	−16.5467	−	15.5384i	−0.545824	−	0.512563i	0.361851	−	0.932236i	$-0.382145\pi$
$919$	−16.5467	−	15.5384i	−0.545824	−	0.512563i	−0.907676	+	0.419673i	$0.862145\pi$
$920$	0.578111	+	7.78123i	0.0190598	+	0.256540i
$921$	−3.38659	+	17.7531i	−0.111592	+	0.584985i
$922$	1.22081	+	1.30003i	0.0402052	+	0.0428142i
$923$	10.2365	+	25.8543i	0.336937	+	0.851006i
$924$	−0.109913	+	0.338277i	−0.00361586	+	0.0111285i
$925$	15.7581	+	27.1863i	0.518123	+	0.893879i
$926$	−6.81177	−	20.9645i	−0.223849	−	0.688935i
$927$	1.17348	−	0.970787i	0.0385421	−	0.0318848i
$928$	7.64754	−	3.59866i	0.251043	−	0.118132i
$929$	−2.41089	+	2.26398i	−0.0790988	+	0.0742787i	−0.723088	−	0.690756i	$-0.757278\pi$
$929$	−2.41089	+	2.26398i	−0.0790988	+	0.0742787i	0.643989	+	0.765034i	$0.277278\pi$
$930$	9.78217	+	8.97973i	0.320770	+	0.294457i
$931$	−3.14526	−	0.397338i	−0.103082	−	0.0130222i
$932$		−	0.756428i		−	0.0247776i
$933$	0.278790	−	2.20685i	0.00912717	−	0.0722490i
$934$	−7.54596	+	9.12150i	−0.246911	+	0.298465i
$935$	0.275735	+	0.170637i	0.00901750	+	0.00558041i
$936$	0.248849	+	3.95534i	0.00813389	+	0.129284i
$937$	−0.686902	−	2.67531i	−0.0224401	−	0.0873985i	0.956377	−	0.292136i	$-0.0943660\pi$
$937$	−0.686902	−	2.67531i	−0.0224401	−	0.0873985i	−0.978817	+	0.204737i	$0.934366\pi$
$938$	−0.757395	−	2.94986i	−0.0247298	−	0.0963163i
$939$	−0.673817	−	10.7100i	−0.0219892	−	0.349508i
$940$	−6.21730	−	3.84753i	−0.202786	−	0.125493i
$941$	−13.6285	+	16.4741i	−0.444277	+	0.537039i	−0.944349	−	0.328945i	$-0.893307\pi$
$941$	−13.6285	+	16.4741i	−0.444277	+	0.537039i	0.500072	+	0.865984i	$0.333307\pi$
$942$	−1.63075	+	12.9087i	−0.0531327	+	0.420589i
$943$		−	1.07507i		−	0.0350090i
$944$	−7.20832	−	0.910623i	−0.234611	−	0.0296382i
$945$	1.96052	+	1.79970i	0.0637757	+	0.0585442i
$946$	0.800308	−	0.751539i	0.0260202	−	0.0244346i
$947$	−25.1857	+	11.8515i	−0.818424	+	0.385121i	−0.788960	−	0.614445i	$-0.789380\pi$
$947$	−25.1857	+	11.8515i	−0.818424	+	0.385121i	−0.0294642	+	0.999566i	$0.509380\pi$
$948$	2.25551	−	1.86592i	0.0732556	−	0.0606023i
$949$	−12.5772	−	38.7086i	−0.408273	−	1.25653i
$950$	−0.291921	+	2.82391i	−0.00947115	+	0.0916197i
$951$	0.931574	−	2.86709i	0.0302084	−	0.0929717i
$952$	0.212599	+	0.536964i	0.00689038	+	0.0174031i
$953$	11.6575	+	12.4139i	0.377622	+	0.402127i	0.889503	−	0.456930i	$-0.151051\pi$
$953$	11.6575	+	12.4139i	0.377622	+	0.402127i	−0.511880	+	0.859057i	$0.671051\pi$
$954$	−1.39835	+	7.33042i	−0.0452733	+	0.237331i
$955$	−0.0849799	−	1.14381i	−0.00274988	−	0.0370128i
$956$	−8.21833	−	7.71752i	−0.265800	−	0.249603i
$957$	−2.40225	−	0.780539i	−0.0776537	−	0.0252312i
$958$	−27.3471	+	5.21673i	−0.883544	+	0.168545i
$959$	−0.709699	+	11.2803i	−0.0229174	+	0.364261i
$960$	−1.33473	−	1.79401i	−0.0430784	−	0.0579015i
$961$	2.28545	−	3.60129i	0.0737241	−	0.116171i
$962$	24.8578	+	1.56392i	0.801449	+	0.0504229i
$963$	−16.2380	+	10.3049i	−0.523261	+	0.332072i
$964$	6.68028	+	8.07507i	0.215157	+	0.260081i
$965$	33.4576	+	34.8296i	1.07704	+	1.12120i
$966$	4.02259	−	1.03282i	0.129425	−	0.0332306i
$967$	47.1487	+	22.1865i	1.51620	+	0.713470i	0.990540	−	0.137225i	$-0.0438184\pi$
$967$	47.1487	+	22.1865i	1.51620	+	0.713470i	0.525660	+	0.850695i	$0.323818\pi$
$968$	10.3767	−	3.37159i	0.333519	−	0.108367i
$969$	−0.241436	+	0.132730i	−0.00775603	+	0.00426391i
$970$	20.0366	−	14.9071i	0.643335	−	0.478637i
$971$	53.0741	−	6.70482i	1.70323	−	0.215168i	0.787318	−	0.616547i	$-0.211469\pi$
$971$	53.0741	−	6.70482i	1.70323	−	0.215168i	0.915912	+	0.401379i	$0.131469\pi$
$972$	−0.125333	−	0.992115i	−0.00402007	−	0.0318221i
$973$	−4.38121	−	2.78040i	−0.140455	−	0.0891354i
$974$	−4.67382	−	3.39573i	−0.149759	−	0.108806i
$975$	−16.2911	−	11.2813i	−0.521732	−	0.361291i
$976$	0.600978	−	0.436636i	0.0192369	−	0.0139764i
$977$	22.4669	−	1.41350i	0.718779	−	0.0452217i	0.300811	−	0.953684i	$-0.402743\pi$
$977$	22.4669	−	1.41350i	0.718779	−	0.0452217i	0.417967	+	0.908462i	$0.362743\pi$
$978$	1.23554	−	2.24745i	0.0395083	−	0.0718654i
$979$	−0.573675	−	1.21912i	−0.0183347	−	0.0389633i
$980$	−0.642751	+	12.4685i	−0.0205319	+	0.398292i
$981$	−2.18903	−	11.4753i	−0.0698905	−	0.366379i
$982$	1.42747	−	1.96475i	0.0455525	−	0.0626976i
$983$	−23.4385	−	42.6344i	−0.747572	−	1.35983i	−0.926624	−	0.375988i	$-0.877303\pi$
$983$	−23.4385	−	42.6344i	−0.747572	−	1.35983i	0.179053	−	0.983839i	$-0.442697\pi$
$984$	0.165083	+	0.260129i	0.00526265	+	0.00829261i
$985$	18.1714	−	47.4594i	0.578988	−	1.51218i
$986$	−3.81322	+	1.50976i	−0.121438	+	0.0480805i
$987$	−1.43261	+	3.61835i	−0.0456004	+	0.115173i
$988$	1.73385	+	1.43436i	0.0551610	+	0.0456332i
$989$	−12.4162	−	3.18793i	−0.394811	−	0.101370i
$990$	−0.0762392	+	0.663890i	−0.00242304	+	0.0210998i
$991$	31.8661	+	12.6167i	1.01226	+	0.400782i	0.814933	−	0.579555i	$-0.196774\pi$
$991$	31.8661	+	12.6167i	1.01226	+	0.400782i	0.197328	+	0.980338i	$0.436774\pi$
$992$	−4.06515	+	4.32895i	−0.129069	+	0.137444i
$993$	−10.3437	−	14.2368i	−0.328246	−	0.451792i
$994$	−3.55555	+	7.55594i	−0.112775	+	0.239660i
$995$	−18.5113	−	9.90530i	−0.586848	−	0.314019i
$996$	−13.0980	−	7.20068i	−0.415026	−	0.228162i
$997$	−2.84855	−	0.543390i	−0.0902144	−	0.0172093i	0.142076	−	0.989856i	$-0.454622\pi$
$997$	−2.84855	−	0.543390i	−0.0902144	−	0.0172093i	−0.232291	+	0.972646i	$0.574622\pi$
$998$	−8.36626	+	32.5844i	−0.264829	+	1.03144i
$999$	−6.28462			−0.198836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.a.619.12	yes	240
125.104	even	50	inner	750.2.o.a.229.12	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.a.229.12	✓	240	125.104	even	50	inner
750.2.o.a.619.12	yes	240	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.248690 - 0.968583i) q^{2} +(0.982287 + 0.187381i) q^{3} +(-0.876307 - 0.481754i) q^{4} +(1.61258 - 1.54906i) q^{5} +(0.425779 - 0.904827i) q^{6} +(0.699566 + 0.962870i) q^{7} +(-0.684547 + 0.728969i) q^{8} +(0.929776 + 0.368125i) q^{9} +(-1.09936 - 1.94715i) q^{10} +(-0.289463 - 0.0743214i) q^{11} +(-0.770513 - 0.637424i) q^{12} +(1.45894 - 3.68486i) q^{13} +(1.10659 - 0.438132i) q^{14} +(1.87428 - 1.21945i) q^{15} +(0.535827 + 0.844328i) q^{16} +(-0.233766 - 0.425219i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-0.106393 - 0.557734i) q^{19} +(-2.15938 + 0.580585i) q^{20} +(0.506751 + 1.07690i) q^{21} +(-0.143973 + 0.261886i) q^{22} +(3.48258 - 0.219105i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(0.200831 - 4.99597i) q^{25} +(-3.20627 - 2.32949i) q^{26} +(0.844328 + 0.535827i) q^{27} +(-0.149168 - 1.18079i) q^{28} +(8.38529 - 1.05931i) q^{29} +(-0.715027 - 2.11866i) q^{30} +(-5.20391 + 2.86087i) q^{31} +(0.951057 - 0.309017i) q^{32} +(-0.270409 - 0.127245i) q^{33} +(-0.469995 + 0.120674i) q^{34} +(2.61965 + 0.469036i) q^{35} +(-0.637424 - 0.770513i) q^{36} +(-5.30628 + 3.36747i) q^{37} +(-0.566671 - 0.0356519i) q^{38} +(2.12357 - 3.34621i) q^{39} +(0.0253284 + 2.23592i) q^{40} +(0.0193451 - 0.307482i) q^{41} +(1.16909 - 0.223016i) q^{42} +(-3.49380 - 1.13521i) q^{43} +(0.217854 + 0.204578i) q^{44} +(2.06959 - 0.846648i) q^{45} +(0.653860 - 3.42766i) q^{46} +(2.23834 + 2.38359i) q^{47} +(0.368125 + 0.929776i) q^{48} +(1.72539 - 5.31021i) q^{49} +(-4.78906 - 1.43697i) q^{50} +(-0.149947 - 0.461491i) q^{51} +(-3.05367 + 2.52622i) q^{52} +(-6.75236 + 3.17742i) q^{53} +(0.728969 - 0.684547i) q^{54} +(-0.581910 + 0.328546i) q^{55} +(-1.18079 - 0.149168i) q^{56} -0.567791i q^{57} +(1.05931 - 8.38529i) q^{58} +(-4.63128 + 5.59825i) q^{59} +(-2.22992 + 0.165673i) q^{60} +(-0.0466440 - 0.741384i) q^{61} +(1.47683 + 5.75189i) q^{62} +(0.295984 + 1.15278i) q^{63} +(-0.0627905 - 0.998027i) q^{64} +(-3.35541 - 8.20211i) q^{65} +(-0.190495 + 0.230269i) q^{66} +(0.320716 - 2.53873i) q^{67} +0.485240i q^{68} +(3.46195 + 0.437346i) q^{69} +(1.10578 - 2.42070i) q^{70} +(-5.11472 + 4.80304i) q^{71} +(-0.904827 + 0.425779i) q^{72} +(7.91296 - 6.54617i) q^{73} +(1.94205 + 5.97703i) q^{74} +(1.13342 - 4.86984i) q^{75} +(-0.175457 + 0.540002i) q^{76} +(-0.130936 - 0.330708i) q^{77} +(-2.71297 - 2.88902i) q^{78} +(-0.548519 + 2.87544i) q^{79} +(2.17198 + 0.531519i) q^{80} +(0.728969 + 0.684547i) q^{81} +(-0.293011 - 0.0952050i) q^{82} +(14.6821 - 2.80075i) q^{83} +(0.0747315 - 1.18782i) q^{84} +(-1.03566 - 0.323582i) q^{85} +(-1.96841 + 3.10173i) q^{86} +(8.43526 + 0.530701i) q^{87} +(0.252329 - 0.160133i) q^{88} +(2.87378 + 3.47381i) q^{89} +(-0.305364 - 2.21512i) q^{90} +(4.56866 - 1.17303i) q^{91} +(-3.15736 - 1.48574i) q^{92} +(-5.64781 + 1.83508i) q^{93} +(2.86536 - 1.57524i) q^{94} +(-1.03553 - 0.734581i) q^{95} +(0.992115 - 0.125333i) q^{96} +(1.39979 + 11.0805i) q^{97} +(-4.71430 - 2.99178i) q^{98} +(-0.241776 - 0.175661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42}+ \cdots - 20 q^{99}+O(q^{100}) \) 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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