LMFDB - Embedded newform 325.2.s.c.32.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(32,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.32"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.s (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] 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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.4
Character	$\chi$	$=$	325.32
Dual form			325.2.s.c.193.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.457039 + 0.791616i) q^{2} +(0.0872808 + 0.325736i) q^{3} +(0.582230 + 1.00845i) q^{4} +(-0.297749 - 0.0797815i) q^{6} +(3.61133 - 2.08500i) q^{7} -2.89257 q^{8} +(2.49959 - 1.44314i) q^{9} +(5.01101 - 1.34269i) q^{11} +(-0.277672 + 0.277672i) q^{12} +(-2.87797 + 2.17194i) q^{13} +3.81171i q^{14} +(0.157557 - 0.272897i) q^{16} +(-2.91180 - 0.780215i) q^{17} +2.63829i q^{18} +(-1.43417 + 5.35240i) q^{19} +(0.994360 + 0.994360i) q^{21} +(-1.22733 + 4.58045i) q^{22} +(1.65039 - 0.442222i) q^{23} +(-0.252465 - 0.942213i) q^{24} +(-0.403995 - 3.27090i) q^{26} +(1.40362 + 1.40362i) q^{27} +(4.20525 + 2.42790i) q^{28} +(-7.08218 - 4.08890i) q^{29} +(-2.64703 + 2.64703i) q^{31} +(-2.74855 - 4.76062i) q^{32} +(0.874729 + 1.51507i) q^{33} +(1.94844 - 1.94844i) q^{34} +(2.91067 + 1.68048i) q^{36} +(6.72122 + 3.88050i) q^{37} +(-3.58157 - 3.58157i) q^{38} +(-0.958670 - 0.747890i) q^{39} +(-0.228680 - 0.853445i) q^{41} +(-1.24161 + 0.332689i) q^{42} +(-0.224991 + 0.839677i) q^{43} +(4.27160 + 4.27160i) q^{44} +(-0.404226 + 1.50859i) q^{46} -1.44206i q^{47} +(0.102644 + 0.0275034i) q^{48} +(5.19446 - 8.99707i) q^{49} -1.01658i q^{51} +(-3.86593 - 1.63772i) q^{52} +(-0.405781 + 0.405781i) q^{53} +(-1.75263 + 0.469616i) q^{54} +(-10.4460 + 6.03100i) q^{56} -1.86865 q^{57} +(6.47367 - 3.73758i) q^{58} +(-9.44885 - 2.53181i) q^{59} +(-2.28425 - 3.95643i) q^{61} +(-0.885633 - 3.30523i) q^{62} +(6.01789 - 10.4233i) q^{63} +5.65500 q^{64} -1.59914 q^{66} +(-3.55279 + 6.15361i) q^{67} +(-0.908530 - 3.39068i) q^{68} +(0.288095 + 0.498996i) q^{69} +(-2.65984 - 0.712701i) q^{71} +(-7.23023 + 4.17437i) q^{72} +6.02847 q^{73} +(-6.14372 + 3.54708i) q^{74} +(-6.23266 + 1.67004i) q^{76} +(15.2969 - 15.2969i) q^{77} +(1.03019 - 0.417083i) q^{78} -12.5840i q^{79} +(3.99472 - 6.91905i) q^{81} +(0.780116 + 0.209031i) q^{82} -8.44351i q^{83} +(-0.423818 + 1.58171i) q^{84} +(-0.561871 - 0.561871i) q^{86} +(0.713764 - 2.66380i) q^{87} +(-14.4947 + 3.88383i) q^{88} +(3.79160 + 14.1504i) q^{89} +(-5.86479 + 13.8441i) q^{91} +(1.40687 + 1.40687i) q^{92} +(-1.09327 - 0.631199i) q^{93} +(1.14156 + 0.659078i) q^{94} +(1.31081 - 1.31081i) q^{96} +(-0.386897 - 0.670125i) q^{97} +(4.74815 + 8.22403i) q^{98} +(10.5878 - 10.5878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{4} - 12 q^{6} + 24 q^{9} + 8 q^{11} - 32 q^{16} - 24 q^{19} + 32 q^{21} + 56 q^{24} + 76 q^{26} - 36 q^{29} + 8 q^{31} + 44 q^{34} - 60 q^{36} + 44 q^{39} - 52 q^{41} - 80 q^{44} - 60 q^{46}+ \cdots + 208 q^{99}+O(q^{100}) $ 40 * q - 24 * q^4 - 12 * q^6 + 24 * q^9 + 8 * q^11 - 32 * q^16 - 24 * q^19 + 32 * q^21 + 56 * q^24 + 76 * q^26 - 36 * q^29 + 8 * q^31 + 44 * q^34 - 60 * q^36 + 44 * q^39 - 52 * q^41 - 80 * q^44 - 60 * q^46 + 28 * q^49 - 68 * q^54 + 72 * q^56 - 72 * q^59 + 144 * q^64 + 24 * q^66 - 80 * q^69 - 52 * q^71 + 168 * q^74 + 8 * q^76 - 20 * q^81 - 248 * q^84 - 168 * q^86 + 60 * q^89 - 100 * q^91 - 156 * q^94 - 36 * q^96 + 208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.457039	+	0.791616i	−0.323176	+	0.559757i	−0.981141	−	0.193291i	$-0.938084\pi$
$2$	−0.457039	+	0.791616i	−0.323176	+	0.559757i	0.657966	+	0.753048i	$0.271417\pi$
$3$	0.0872808	+	0.325736i	0.0503916	+	0.188064i	0.986534	−	0.163558i	$-0.0522970\pi$
$3$	0.0872808	+	0.325736i	0.0503916	+	0.188064i	−0.936142	+	0.351622i	$0.885630\pi$
$4$	0.582230	+	1.00845i	0.291115	+	0.504226i
$5$		0			0
$5$		0			0
$6$	−0.297749	−	0.0797815i	−0.121555	−	0.0325707i
$7$	3.61133	−	2.08500i	1.36495	−	0.788056i	0.374675	−	0.927156i	$-0.377754\pi$
$7$	3.61133	−	2.08500i	1.36495	−	0.788056i	0.990278	+	0.139100i	$0.0444209\pi$
$8$	−2.89257			−1.02268
$9$	2.49959	−	1.44314i	0.833197	−	0.481046i
$10$		0			0
$11$	5.01101	−	1.34269i	1.51088	−	0.404838i	0.594149	−	0.804355i	$-0.297489\pi$
$11$	5.01101	−	1.34269i	1.51088	−	0.404838i	0.916726	+	0.399517i	$0.130822\pi$
$12$	−0.277672	+	0.277672i	−0.0801569	+	0.0801569i
$13$	−2.87797	+	2.17194i	−0.798204	+	0.602387i
$13$	−2.87797	+	2.17194i	−0.798204	+	0.602387i
$14$			3.81171i			1.01872i
$15$		0			0
$16$	0.157557	−	0.272897i	0.0393892	−	0.0682241i
$17$	−2.91180	−	0.780215i	−0.706216	−	0.189230i	−0.112203	−	0.993685i	$-0.535791\pi$
$17$	−2.91180	−	0.780215i	−0.706216	−	0.189230i	−0.594013	+	0.804455i	$0.702457\pi$
$18$			2.63829i			0.621850i
$19$	−1.43417	+	5.35240i	−0.329022	+	1.22793i	0.581185	+	0.813771i	$0.302589\pi$
$19$	−1.43417	+	5.35240i	−0.329022	+	1.22793i	−0.910207	+	0.414154i	$0.864078\pi$
$20$		0			0
$21$	0.994360	+	0.994360i	0.216987	+	0.216987i
$22$	−1.22733	+	4.58045i	−0.261667	+	0.976556i
$23$	1.65039	−	0.442222i	0.344131	−	0.0922096i	−0.0826140	−	0.996582i	$-0.526327\pi$
$23$	1.65039	−	0.442222i	0.344131	−	0.0922096i	0.426745	+	0.904372i	$0.359660\pi$
$24$	−0.252465	−	0.942213i	−0.0515343	−	0.192329i
$25$		0			0
$26$	−0.403995	−	3.27090i	−0.0792299	−	0.641477i
$27$	1.40362	+	1.40362i	0.270126	+	0.270126i
$28$	4.20525	+	2.42790i	0.794717	+	0.458830i
$29$	−7.08218	−	4.08890i	−1.31513	−	0.759289i	−0.332187	−	0.943213i	$-0.607787\pi$
$29$	−7.08218	−	4.08890i	−1.31513	−	0.759289i	−0.982940	+	0.183924i	$0.941120\pi$
$30$		0			0
$31$	−2.64703	+	2.64703i	−0.475421	+	0.475421i	−0.903664	−	0.428243i	$-0.859133\pi$
$31$	−2.64703	+	2.64703i	−0.475421	+	0.475421i	0.428243	+	0.903664i	$0.359133\pi$
$32$	−2.74855	−	4.76062i	−0.485879	−	0.841567i
$33$	0.874729	+	1.51507i	0.152271	+	0.263741i
$34$	1.94844	−	1.94844i	0.334155	−	0.334155i
$35$		0			0
$36$	2.91067	+	1.68048i	0.485112	+	0.280080i
$37$	6.72122	+	3.88050i	1.10496	+	0.637950i	0.937520	−	0.347932i	$-0.113116\pi$
$37$	6.72122	+	3.88050i	1.10496	+	0.637950i	0.167442	+	0.985882i	$0.446449\pi$
$38$	−3.58157	−	3.58157i	−0.581008	−	0.581008i
$39$	−0.958670	−	0.747890i	−0.153510	−	0.119758i
$40$		0			0
$41$	−0.228680	−	0.853445i	−0.0357138	−	0.133286i	0.945767	−	0.324845i	$-0.105312\pi$
$41$	−0.228680	−	0.853445i	−0.0357138	−	0.133286i	−0.981481	+	0.191559i	$0.938646\pi$
$42$	−1.24161	+	0.332689i	−0.191585	+	0.0513350i
$43$	−0.224991	+	0.839677i	−0.0343108	+	0.128049i	−0.980957	−	0.194225i	$-0.937781\pi$
$43$	−0.224991	+	0.839677i	−0.0343108	+	0.128049i	0.946646	+	0.322275i	$0.104447\pi$
$44$	4.27160	+	4.27160i	0.643968	+	0.643968i
$45$		0			0
$46$	−0.404226	+	1.50859i	−0.0595998	+	0.222430i
$47$		−	1.44206i		−	0.210346i	−0.994454	−	0.105173i	$-0.966460\pi$
$47$		−	1.44206i		−	0.210346i	0.994454	−	0.105173i	$-0.0335397\pi$
$48$	0.102644	+	0.0275034i	0.0148154	+	0.00396977i
$49$	5.19446	−	8.99707i	0.742066	−	1.28530i
$50$		0			0
$51$		−	1.01658i		−	0.142349i
$52$	−3.86593	−	1.63772i	−0.536108	−	0.227111i
$53$	−0.405781	+	0.405781i	−0.0557384	+	0.0557384i	−0.734427	−	0.678688i	$-0.762549\pi$
$53$	−0.405781	+	0.405781i	−0.0557384	+	0.0557384i	0.678688	+	0.734427i	$0.262549\pi$
$54$	−1.75263	+	0.469616i	−0.238503	+	0.0639066i
$55$		0			0
$56$	−10.4460	+	6.03100i	−1.39591	+	0.805927i
$57$	−1.86865			−0.247508
$58$	6.47367	−	3.73758i	0.850035	−	0.490768i
$59$	−9.44885	−	2.53181i	−1.23014	−	0.329614i	−0.415504	−	0.909592i	$-0.636395\pi$
$59$	−9.44885	−	2.53181i	−1.23014	−	0.329614i	−0.814632	+	0.579978i	$0.803061\pi$
$60$		0			0
$61$	−2.28425	−	3.95643i	−0.292468	−	0.506569i	0.681925	−	0.731422i	$-0.261143\pi$
$61$	−2.28425	−	3.95643i	−0.292468	−	0.506569i	−0.974393	+	0.224853i	$0.927810\pi$
$62$	−0.885633	−	3.30523i	−0.112476	−	0.419764i
$63$	6.01789	−	10.4233i	0.758183	−	1.31321i
$64$	5.65500			0.706875
$65$		0			0
$66$	−1.59914			−0.196841
$67$	−3.55279	+	6.15361i	−0.434042	+	0.751783i	−0.997217	−	0.0745551i	$-0.976246\pi$
$67$	−3.55279	+	6.15361i	−0.434042	+	0.751783i	0.563175	+	0.826338i	$0.309580\pi$
$68$	−0.908530	−	3.39068i	−0.110175	−	0.411180i
$69$	0.288095	+	0.498996i	0.0346826	+	0.0600720i
$70$		0			0
$71$	−2.65984	−	0.712701i	−0.315664	−	0.0845820i	0.0975083	−	0.995235i	$-0.468913\pi$
$71$	−2.65984	−	0.712701i	−0.315664	−	0.0845820i	−0.413173	+	0.910653i	$0.635579\pi$
$72$	−7.23023	+	4.17437i	−0.852091	+	0.491955i
$73$	6.02847			0.705579			0.352789	−	0.935703i	$-0.385233\pi$
$73$	6.02847			0.705579			0.352789	+	0.935703i	$0.385233\pi$
$74$	−6.14372	+	3.54708i	−0.714193	+	0.412340i
$75$		0			0
$76$	−6.23266	+	1.67004i	−0.714935	+	0.191566i
$77$	15.2969	−	15.2969i	1.74324	−	1.74324i
$78$	1.03019	−	0.417083i	0.116646	−	0.0472253i
$79$		−	12.5840i		−	1.41582i	−0.706305	−	0.707908i	$-0.749639\pi$
$79$		−	12.5840i		−	1.41582i	0.706305	−	0.707908i	$-0.250361\pi$
$80$		0			0
$81$	3.99472	−	6.91905i	0.443857	−	0.768784i
$82$	0.780116	+	0.209031i	0.0861494	+	0.0230837i
$83$		−	8.44351i		−	0.926796i	−0.886150	−	0.463398i	$-0.846630\pi$
$83$		−	8.44351i		−	0.926796i	0.886150	−	0.463398i	$-0.153370\pi$
$84$	−0.423818	+	1.58171i	−0.0462423	+	0.172579i
$85$		0			0
$86$	−0.561871	−	0.561871i	−0.0605882	−	0.0605882i
$87$	0.713764	−	2.66380i	0.0765236	−	0.285590i
$88$	−14.4947	+	3.88383i	−1.54514	+	0.414018i
$89$	3.79160	+	14.1504i	0.401908	+	1.49994i	0.809687	+	0.586862i	$0.199637\pi$
$89$	3.79160	+	14.1504i	0.401908	+	1.49994i	−0.407779	+	0.913081i	$0.633696\pi$
$90$		0			0
$91$	−5.86479	+	13.8441i	−0.614797	+	1.45126i
$92$	1.40687	+	1.40687i	0.146676	+	0.146676i
$93$	−1.09327	−	0.631199i	−0.113367	−	0.0654523i
$94$	1.14156	+	0.659078i	0.117743	+	0.0679788i
$95$		0			0
$96$	1.31081	−	1.31081i	0.133784	−	0.133784i
$97$	−0.386897	−	0.670125i	−0.0392834	−	0.0680408i	0.845715	−	0.533634i	$-0.179174\pi$
$97$	−0.386897	−	0.670125i	−0.0392834	−	0.0680408i	−0.884999	+	0.465594i	$0.845841\pi$
$98$	4.74815	+	8.22403i	0.479635	+	0.830752i
$99$	10.5878	−	10.5878i	1.06411	−	1.06411i
$100$		0			0
$101$	−7.74418	−	4.47110i	−0.770575	−	0.444892i	0.0625048	−	0.998045i	$-0.480091\pi$
$101$	−7.74418	−	4.47110i	−0.770575	−	0.444892i	−0.833080	+	0.553153i	$0.813424\pi$
$102$	0.804739	+	0.464616i	0.0796810	+	0.0460038i
$103$	−13.3476	−	13.3476i	−1.31518	−	1.31518i	−0.917541	−	0.397641i	$-0.869829\pi$
$103$	−13.3476	−	13.3476i	−1.31518	−	1.31518i	−0.397641	−	0.917541i	$-0.630171\pi$
$104$	8.32471	−	6.28247i	0.816305	−	0.616047i
$105$		0			0
$106$	−0.135765	−	0.506681i	−0.0131866	−	0.0492132i
$107$	−4.75112	+	1.27306i	−0.459308	+	0.123071i	−0.481051	−	0.876692i	$-0.659745\pi$
$107$	−4.75112	+	1.27306i	−0.459308	+	0.123071i	0.0217436	+	0.999764i	$0.493078\pi$
$108$	−0.598251	+	2.23270i	−0.0575668	+	0.214842i
$109$	1.95993	+	1.95993i	0.187727	+	0.187727i	0.794713	−	0.606986i	$-0.207621\pi$
$109$	1.95993	+	1.95993i	0.187727	+	0.187727i	−0.606986	+	0.794713i	$0.707621\pi$
$110$		0			0
$111$	−0.677385	+	2.52804i	−0.0642946	+	0.239951i
$112$		−	1.31402i		−	0.124164i
$113$	7.83033	+	2.09813i	0.736616	+	0.197376i	0.607573	−	0.794264i	$-0.292143\pi$
$113$	7.83033	+	2.09813i	0.736616	+	0.197376i	0.129042	+	0.991639i	$0.458810\pi$
$114$	0.854045	−	1.47925i	0.0799887	−	0.138544i
$115$		0			0
$116$		−	9.52272i		−	0.884162i
$117$	−4.05933	+	9.58226i	−0.375285	+	0.885880i
$118$	6.32272	−	6.32272i	0.582054	−	0.582054i
$119$	−12.1422	+	3.25350i	−1.11308	+	0.298248i
$120$		0			0
$121$	13.7811	−	7.95650i	1.25282	−	0.723319i
$122$	4.17596			0.378074
$123$	0.258039	−	0.148979i	0.0232666	−	0.0134330i
$124$	−4.21058	−	1.12822i	−0.378122	−	0.101317i
$125$		0			0
$126$	5.50083	+	9.52771i	0.490053	+	0.848796i
$127$	0.815081	+	3.04192i	0.0723268	+	0.269927i	0.992614	−	0.121317i	$-0.0387116\pi$
$127$	0.815081	+	3.04192i	0.0723268	+	0.269927i	−0.920287	+	0.391244i	$0.872045\pi$
$128$	2.91253	−	5.04466i	0.257434	−	0.445889i
$129$	−0.293150			−0.0258105
$130$		0			0
$131$	8.63029			0.754032			0.377016	−	0.926207i	$-0.376950\pi$
$131$	8.63029			0.754032			0.377016	+	0.926207i	$0.376950\pi$
$132$	−1.01859	+	1.76424i	−0.0886566	+	0.153558i
$133$	5.98050	+	22.3195i	0.518575	+	1.93535i
$134$	−3.24753	−	5.62488i	−0.280544	−	0.485916i
$135$		0			0
$136$	8.42258	+	2.25682i	0.722231	+	0.193521i
$137$	−9.64530	+	5.56872i	−0.824054	+	0.475768i	−0.851812	−	0.523847i	$-0.824496\pi$
$137$	−9.64530	+	5.56872i	−0.824054	+	0.475768i	0.0277585	+	0.999615i	$0.491163\pi$
$138$	−0.526684			−0.0448343
$139$	−12.0068	+	6.93216i	−1.01841	+	0.587978i	−0.913642	−	0.406519i	$-0.866742\pi$
$139$	−12.0068	+	6.93216i	−1.01841	+	0.587978i	−0.104765	+	0.994497i	$0.533409\pi$
$140$		0			0
$141$	0.469731	−	0.125864i	0.0395585	−	0.0105997i
$142$	1.77983	−	1.77983i	0.149360	−	0.149360i
$143$	−11.5053	+	14.7478i	−0.962118	+	1.23327i
$144$		−	0.909506i		−	0.0757922i
$145$		0			0
$146$	−2.75525	+	4.77223i	−0.228026	+	0.394952i
$147$	3.38405	+	0.906753i	0.279111	+	0.0747877i
$148$			9.03737i			0.742867i
$149$	−4.63818	+	17.3099i	−0.379974	+	1.41808i	0.465965	+	0.884803i	$0.345707\pi$
$149$	−4.63818	+	17.3099i	−0.379974	+	1.41808i	−0.845939	+	0.533280i	$0.820959\pi$
$150$		0			0
$151$	−1.97852	−	1.97852i	−0.161010	−	0.161010i	0.622004	−	0.783014i	$-0.286319\pi$
$151$	−1.97852	−	1.97852i	−0.161010	−	0.161010i	−0.783014	+	0.622004i	$0.786319\pi$
$152$	4.14844	−	15.4822i	0.336483	−	1.25577i
$153$	−8.40427	+	2.25192i	−0.679445	+	0.182057i
$154$	5.11797	+	19.1005i	0.412417	+	1.53916i
$155$		0			0
$156$	0.196045	−	1.40222i	0.0156961	−	0.112267i
$157$	10.4990	+	10.4990i	0.837914	+	0.837914i	0.988584	−	0.150670i	$-0.0481431\pi$
$157$	10.4990	+	10.4990i	0.837914	+	0.837914i	−0.150670	+	0.988584i	$0.548143\pi$
$158$	9.96172	+	5.75140i	0.792512	+	0.457557i
$159$	−0.167595	−	0.0967608i	−0.0132911	−	0.00767363i
$160$		0			0
$161$	5.03808	−	5.03808i	0.397057	−	0.397057i
$162$	3.65149	+	6.32456i	0.286888	+	0.496904i
$163$	1.43243	+	2.48103i	0.112196	+	0.194330i	0.916655	−	0.399678i	$-0.130878\pi$
$163$	1.43243	+	2.48103i	0.112196	+	0.194330i	−0.804459	+	0.594008i	$0.797545\pi$
$164$	0.727514	−	0.727514i	0.0568093	−	0.0568093i
$165$		0			0
$166$	6.68401	+	3.85902i	0.518780	+	0.299518i
$167$	−3.15787	−	1.82320i	−0.244363	−	0.141083i	0.372817	−	0.927905i	$-0.378392\pi$
$167$	−3.15787	−	1.82320i	−0.244363	−	0.141083i	−0.617180	+	0.786822i	$0.711725\pi$
$168$	−2.87625	−	2.87625i	−0.221908	−	0.221908i
$169$	3.56538	−	12.5015i	0.274260	−	0.961656i
$170$		0			0
$171$	4.13942	+	15.4485i	0.316549	+	1.18138i
$172$	−0.977770	+	0.261993i	−0.0745542	+	0.0199767i
$173$	−1.90689	+	7.11663i	−0.144978	+	0.541067i	0.854778	+	0.518994i	$0.173693\pi$
$173$	−1.90689	+	7.11663i	−0.144978	+	0.541067i	−0.999756	+	0.0220730i	$0.992973\pi$
$174$	1.78249	+	1.78249i	0.135130	+	0.135130i
$175$		0			0
$176$	0.423102	−	1.57904i	0.0318925	−	0.119024i
$177$		−	3.29881i		−	0.247954i
$178$	−12.9346	−	3.46582i	−0.969490	−	0.259774i
$179$	5.02174	−	8.69791i	0.375343	−	0.650113i	−0.615036	−	0.788499i	$-0.710858\pi$
$179$	5.02174	−	8.69791i	0.375343	−	0.650113i	0.990378	+	0.138387i	$0.0441917\pi$
$180$		0			0
$181$		−	10.0395i		−	0.746233i	−0.927785	−	0.373116i	$-0.878289\pi$
$181$		−	10.0395i		−	0.746233i	0.927785	−	0.373116i	$-0.121711\pi$
$182$	−8.27880	−	10.9700i	−0.613665	−	0.813149i
$183$	1.08938	−	1.08938i	0.0805295	−	0.0805295i
$184$	−4.77387	+	1.27916i	−0.351935	+	0.0943006i
$185$		0			0
$186$	0.999334	−	0.576966i	0.0732747	−	0.0423052i
$187$	−15.6387			−1.14361
$188$	1.45425	−	0.839611i	0.106062	−	0.0612349i
$189$	7.99545	+	2.14238i	0.581584	+	0.155835i
$190$		0			0
$191$	−8.40440	−	14.5568i	−0.608121	−	1.05330i	−0.991550	−	0.129726i	$-0.958590\pi$
$191$	−8.40440	−	14.5568i	−0.608121	−	1.05330i	0.383429	−	0.923570i	$-0.374743\pi$
$192$	0.493573	+	1.84204i	0.0356206	+	0.132938i
$193$	8.49185	−	14.7083i	0.611257	−	1.05873i	−0.379772	−	0.925080i	$-0.623998\pi$
$193$	8.49185	−	14.7083i	0.611257	−	1.05873i	0.991029	−	0.133648i	$-0.0426691\pi$
$194$	0.707308			0.0507818
$195$		0			0
$196$	12.0975			0.864106
$197$	2.26234	−	3.91848i	0.161185	−	0.279180i	−0.774109	−	0.633052i	$-0.781802\pi$
$197$	2.26234	−	3.91848i	0.161185	−	0.279180i	0.935294	+	0.353872i	$0.115135\pi$
$198$	3.54241	+	13.2205i	0.251748	+	0.939538i
$199$	4.08425	+	7.07413i	0.289525	+	0.501472i	0.973696	−	0.227849i	$-0.0731694\pi$
$199$	4.08425	+	7.07413i	0.289525	+	0.501472i	−0.684171	+	0.729321i	$0.739836\pi$
$200$		0			0
$201$	−2.31454	−	0.620180i	−0.163255	−	0.0437441i
$202$	7.07879	−	4.08694i	0.498062	−	0.287556i
$203$	−34.1014			−2.39345
$204$	1.02517	−	0.591882i	0.0717762	−	0.0414400i
$205$		0			0
$206$	16.6666	−	4.46580i	1.16122	−	0.311147i
$207$	3.48712	−	3.48712i	0.242372	−	0.242372i
$208$	0.139271	+	1.12759i	0.00965668	+	0.0781843i
$209$			28.7466i			1.98844i
$210$		0			0
$211$	−7.05655	+	12.2223i	−0.485793	+	0.841418i	−0.999867	−	0.0163277i	$-0.994802\pi$
$211$	−7.05655	+	12.2223i	−0.485793	+	0.841418i	0.514074	+	0.857746i	$0.328136\pi$
$212$	−0.645469	−	0.172953i	−0.0443310	−	0.0118785i
$213$		−	0.928610i		−	0.0636273i
$214$	1.16368	−	4.34289i	0.0795472	−	0.296874i
$215$		0			0
$216$	−4.06005	−	4.06005i	−0.276251	−	0.276251i
$217$	−4.04023	+	15.0784i	−0.274269	+	1.02359i
$218$	−2.44727	+	0.655745i	−0.165750	+	0.0444127i
$219$	0.526169	+	1.96369i	0.0355552	+	0.132694i
$220$		0			0
$221$	10.0747	−	4.07882i	0.677694	−	0.274371i
$222$	−1.69164	−	1.69164i	−0.113536	−	0.113536i
$223$	18.3866	+	10.6155i	1.23125	+	0.710865i	0.967291	−	0.253667i	$-0.0816369\pi$
$223$	18.3866	+	10.6155i	1.23125	+	0.710865i	0.263963	+	0.964533i	$0.414970\pi$
$224$	−19.8518	−	11.4614i	−1.32640	−	0.765800i
$225$		0			0
$226$	−5.23968	+	5.23968i	−0.348539	+	0.348539i
$227$	7.72867	+	13.3865i	0.512970	+	0.888490i	0.999887	+	0.0150418i	$0.00478813\pi$
$227$	7.72867	+	13.3865i	0.512970	+	0.888490i	−0.486917	+	0.873448i	$0.661879\pi$
$228$	−1.08798	−	1.88444i	−0.0720534	−	0.124800i
$229$	4.47959	−	4.47959i	0.296020	−	0.296020i	−0.543433	−	0.839453i	$-0.682876\pi$
$229$	4.47959	−	4.47959i	0.296020	−	0.296020i	0.839453	+	0.543433i	$0.182876\pi$
$230$		0			0
$231$	6.31786	+	3.64762i	0.415685	+	0.239996i
$232$	20.4857	+	11.8274i	1.34495	+	0.776507i
$233$	−3.54772	−	3.54772i	−0.232419	−	0.232419i	0.581283	−	0.813702i	$-0.302551\pi$
$233$	−3.54772	−	3.54772i	−0.232419	−	0.232419i	−0.813702	+	0.581283i	$0.802551\pi$
$234$	−5.73019	−	7.59290i	−0.374594	−	0.496363i
$235$		0			0
$236$	−2.94819	−	11.0028i	−0.191911	−	0.716222i
$237$	4.09908	−	1.09834i	0.266264	−	0.0713452i
$238$	2.97396	−	11.0990i	0.192773	−	0.719438i
$239$	−3.55914	−	3.55914i	−0.230222	−	0.230222i	0.582563	−	0.812785i	$-0.302050\pi$
$239$	−3.55914	−	3.55914i	−0.230222	−	0.230222i	−0.812785	+	0.582563i	$0.802050\pi$
$240$		0			0
$241$	−0.187912	+	0.701296i	−0.0121044	+	0.0451744i	−0.971714	−	0.236161i	$-0.924111\pi$
$241$	−0.187912	+	0.701296i	−0.0121044	+	0.0451744i	0.959609	+	0.281335i	$0.0907774\pi$
$242$			14.5457i			0.935036i
$243$	8.35457	+	2.23860i	0.535946	+	0.143606i
$244$	2.65991	−	4.60711i	0.170284	−	0.294940i
$245$		0			0
$246$			0.272356i			0.0173648i
$247$	−7.49758	−	18.5190i	−0.477060	−	1.17833i
$248$	7.65671	−	7.65671i	0.486202	−	0.486202i
$249$	2.75036	−	0.736956i	0.174297	−	0.0467027i
$250$		0			0
$251$	−12.5444	+	7.24253i	−0.791797	+	0.457144i	−0.840595	−	0.541664i	$-0.817794\pi$
$251$	−12.5444	+	7.24253i	−0.791797	+	0.457144i	0.0487976	+	0.998809i	$0.484461\pi$
$252$	14.0152			0.882874
$253$	7.67637	−	4.43195i	0.482609	−	0.278634i
$254$	−2.78056	−	0.745049i	−0.174468	−	0.0467485i
$255$		0			0
$256$	8.31729	+	14.4060i	0.519831	+	0.900373i
$257$	−8.11269	−	30.2770i	−0.506056	−	1.88862i	−0.456219	−	0.889868i	$-0.650797\pi$
$257$	−8.11269	−	30.2770i	−0.506056	−	1.88862i	−0.0498367	−	0.998757i	$-0.515870\pi$
$258$	0.133981	−	0.232062i	0.00834131	−	0.0144476i
$259$	32.3634			2.01096
$260$		0			0
$261$	−23.6034			−1.46101
$262$	−3.94438	+	6.83187i	−0.243685	+	0.422074i
$263$	−5.25932	−	19.6281i	−0.324304	−	1.21032i	−0.915010	−	0.403431i	$-0.867817\pi$
$263$	−5.25932	−	19.6281i	−0.324304	−	1.21032i	0.590706	−	0.806887i	$-0.298849\pi$
$264$	−2.53021	−	4.38245i	−0.155724	−	0.269721i
$265$		0			0
$266$	−20.4018	−	5.46665i	−1.25092	−	0.335182i
$267$	−4.27837	+	2.47012i	−0.261832	+	0.151169i
$268$	−8.27415			−0.505424
$269$	20.6369	−	11.9147i	1.25825	−	0.726453i	0.285519	−	0.958373i	$-0.407834\pi$
$269$	20.6369	−	11.9147i	1.25825	−	0.726453i	0.972735	+	0.231919i	$0.0745006\pi$
$270$		0			0
$271$	−6.39629	+	1.71388i	−0.388547	+	0.104111i	−0.447804	−	0.894132i	$-0.647794\pi$
$271$	−6.39629	+	1.71388i	−0.388547	+	0.104111i	0.0592568	+	0.998243i	$0.481127\pi$
$272$	−0.671693	+	0.671693i	−0.0407274	+	0.0407274i
$273$	−5.02142	−	0.702047i	−0.303910	−	0.0424898i
$274$		−	10.1805i		−	0.615026i
$275$		0			0
$276$	−0.335475	+	0.581061i	−0.0201932	+	0.0349757i
$277$	−24.6232	−	6.59777i	−1.47947	−	0.396422i	−0.573301	−	0.819345i	$-0.694337\pi$
$277$	−24.6232	−	6.59777i	−1.47947	−	0.396422i	−0.906165	+	0.422923i	$0.861004\pi$
$278$		−	12.6731i		−	0.760081i
$279$	−2.79646	+	10.4365i	−0.167420	+	0.624818i
$280$		0			0
$281$	9.24115	+	9.24115i	0.551281	+	0.551281i	0.926810	−	0.375530i	$-0.122539\pi$
$281$	9.24115	+	9.24115i	0.551281	+	0.551281i	−0.375530	+	0.926810i	$0.622539\pi$
$282$	−0.115050	+	0.429371i	−0.00685111	+	0.0255687i
$283$	9.79438	−	2.62440i	0.582216	−	0.156004i	0.0443225	−	0.999017i	$-0.485887\pi$
$283$	9.79438	−	2.62440i	0.582216	−	0.156004i	0.537893	+	0.843013i	$0.319220\pi$
$284$	−0.829911	−	3.09727i	−0.0492462	−	0.183789i
$285$		0			0
$286$	−6.41625	−	15.8481i	−0.379401	−	0.937116i
$287$	−2.60527	−	2.60527i	−0.153784	−	0.153784i
$288$	−13.7405	−	7.93307i	−0.809665	−	0.467461i
$289$	−6.85257	−	3.95633i	−0.403092	−	0.232725i
$290$		0			0
$291$	0.184515	−	0.184515i	0.0108165	−	0.0108165i
$292$	3.50995	+	6.07942i	0.205405	+	0.355771i
$293$	5.91259	+	10.2409i	0.345417	+	0.598280i	0.985429	−	0.170085i	$-0.0544041\pi$
$293$	5.91259	+	10.2409i	0.345417	+	0.598280i	−0.640012	+	0.768365i	$0.721071\pi$
$294$	−2.26444	+	2.26444i	−0.132065	+	0.132065i
$295$		0			0
$296$	−19.4416	−	11.2246i	−1.13002	−	0.652416i
$297$	8.91815	+	5.14890i	0.517484	+	0.298769i
$298$	−11.5830	−	11.5830i	−0.670983	−	0.670983i
$299$	−3.78930	+	4.85725i	−0.219141	+	0.280902i
$300$		0			0
$301$	0.938212	+	3.50145i	0.0540776	+	0.201820i
$302$	2.47049	−	0.661966i	0.142161	−	0.0380918i
$303$	0.780483	−	2.91280i	0.0448376	−	0.167336i
$304$	1.23469	+	1.23469i	0.0708142	+	0.0708142i
$305$		0			0
$306$	2.05843	−	7.68217i	0.117673	−	0.439160i
$307$		−	24.7916i		−	1.41493i	−0.706747	−	0.707467i	$-0.749838\pi$
$307$		−	24.7916i		−	1.41493i	0.706747	−	0.707467i	$-0.250162\pi$
$308$	24.3324	+	6.51986i	1.38647	+	0.371503i
$309$	3.18282	−	5.51280i	0.181064	−	0.313612i
$310$		0			0
$311$			24.3734i			1.38209i	0.722812	+	0.691045i	$0.242849\pi$
$311$			24.3734i			1.38209i	−0.722812	+	0.691045i	$0.757151\pi$
$312$	2.77301	+	2.16332i	0.156991	+	0.122474i
$313$	−8.82280	+	8.82280i	−0.498694	+	0.498694i	−0.911031	−	0.412337i	$-0.864713\pi$
$313$	−8.82280	+	8.82280i	−0.498694	+	0.498694i	0.412337	+	0.911031i	$0.364713\pi$
$314$	−13.1097	+	3.51273i	−0.739822	+	0.198235i
$315$		0			0
$316$	12.6904	−	7.32681i	0.713891	−	0.412165i
$317$	−3.43365			−0.192853			−0.0964266	−	0.995340i	$-0.530741\pi$
$317$	−3.43365			−0.192853			−0.0964266	+	0.995340i	$0.530741\pi$
$318$	0.153195	−	0.0884470i	0.00859073	−	0.00495986i
$319$	−40.9790	−	10.9803i	−2.29438	−	0.614778i
$320$		0			0
$321$	−0.829362	−	1.43650i	−0.0462905	−	0.0801774i
$322$	1.68562	+	6.29083i	0.0939360	+	0.350574i
$323$	8.35205	−	14.4662i	0.464721	−	0.804920i
$324$	9.30338			0.516854
$325$		0			0
$326$	−2.61870			−0.145036
$327$	−0.467355	+	0.809483i	−0.0258448	+	0.0447645i
$328$	0.661472	+	2.46865i	0.0365237	+	0.136308i
$329$	−3.00670	−	5.20775i	−0.165765	−	0.287113i
$330$		0			0
$331$	−4.89235	−	1.31090i	−0.268908	−	0.0720536i	0.121845	−	0.992549i	$-0.461119\pi$
$331$	−4.89235	−	1.31090i	−0.268908	−	0.0720536i	−0.390753	+	0.920495i	$0.627785\pi$
$332$	8.51487	−	4.91606i	0.467314	−	0.269804i
$333$	22.4004			1.22753
$334$	2.88654	−	1.66654i	0.157944	−	0.0911893i
$335$		0			0
$336$	0.428026	−	0.114689i	0.0233507	−	0.00625680i
$337$	−6.10952	+	6.10952i	−0.332807	+	0.332807i	−0.853651	−	0.520845i	$-0.825617\pi$
$337$	−6.10952	+	6.10952i	−0.332807	+	0.332807i	0.520845	+	0.853651i	$0.325617\pi$
$338$	8.26688	+	8.53610i	0.449659	+	0.464303i
$339$			2.73375i			0.148477i
$340$		0			0
$341$	−9.71013	+	16.8184i	−0.525833	+	0.910770i
$342$	−14.1212	−	3.78375i	−0.763585	−	0.204602i
$343$		−	14.1318i		−	0.763045i
$344$	0.650800	−	2.42882i	0.0350888	−	0.130953i
$345$		0			0
$346$	−4.76211	−	4.76211i	−0.256012	−	0.256012i
$347$	−7.51485	+	28.0458i	−0.403418	+	1.50558i	0.403536	+	0.914964i	$0.367781\pi$
$347$	−7.51485	+	28.0458i	−0.403418	+	1.50558i	−0.806954	+	0.590614i	$0.798886\pi$
$348$	3.10189	−	0.831150i	0.166279	−	0.0445543i
$349$	−0.992964	−	3.70579i	−0.0531522	−	0.198367i	0.934244	−	0.356634i	$-0.116076\pi$
$349$	−0.992964	−	3.70579i	−0.0531522	−	0.198367i	−0.987396	+	0.158268i	$0.949409\pi$
$350$		0			0
$351$	−7.08812	−	0.990994i	−0.378336	−	0.0528953i
$352$	−20.1650	−	20.1650i	−1.07480	−	1.07480i
$353$	22.1433	+	12.7844i	1.17857	+	0.680446i	0.955683	−	0.294399i	$-0.0951195\pi$
$353$	22.1433	+	12.7844i	1.17857	+	0.680446i	0.222884	+	0.974845i	$0.428453\pi$
$354$	2.61139	+	1.50769i	0.138794	+	0.0801327i
$355$		0			0
$356$	−12.0624	+	12.0624i	−0.639308	+	0.639308i
$357$	−2.11957	−	3.67120i	−0.112179	−	0.194300i
$358$	4.59027	+	7.95058i	0.242603	+	0.420201i
$359$	−16.4517	+	16.4517i	−0.868286	+	0.868286i	−0.992283	−	0.123997i	$-0.960429\pi$
$359$	−16.4517	+	16.4517i	−0.868286	+	0.868286i	0.123997	+	0.992283i	$0.460429\pi$
$360$		0			0
$361$	−10.1369	−	5.85252i	−0.533519	−	0.308028i
$362$	7.94745	+	4.58846i	0.417709	+	0.241164i
$363$	3.79454	+	3.79454i	0.199162	+	0.199162i
$364$	−17.3758	+	2.14611i	−0.910740	+	0.112487i
$365$		0			0
$366$	0.364481	+	1.36026i	0.0190517	+	0.0711021i
$367$	−11.4621	+	3.07127i	−0.598319	+	0.160319i	−0.545252	−	0.838272i	$-0.683566\pi$
$367$	−11.4621	+	3.07127i	−0.598319	+	0.160319i	−0.0530664	+	0.998591i	$0.516899\pi$
$368$	0.139350	−	0.520062i	0.00726413	−	0.0271101i
$369$	−1.80325	−	1.80325i	−0.0938732	−	0.0938732i
$370$		0			0
$371$	−0.619355	+	2.31146i	−0.0321553	+	0.120005i
$372$		−	1.47001i		−	0.0762166i
$373$	−4.03365	−	1.08081i	−0.208855	−	0.0559624i	0.152875	−	0.988246i	$-0.451147\pi$
$373$	−4.03365	−	1.08081i	−0.208855	−	0.0559624i	−0.361729	+	0.932283i	$0.617814\pi$
$374$	7.14748	−	12.3798i	0.369588	−	0.640144i
$375$		0			0
$376$			4.17125i			0.215116i
$377$	29.2631	−	3.61434i	1.50713	−	0.186148i
$378$	−5.35018	+	5.35018i	−0.275183	+	0.275183i
$379$	10.7615	−	2.88353i	0.552781	−	0.148117i	0.0283931	−	0.999597i	$-0.490961\pi$
$379$	10.7615	−	2.88353i	0.552781	−	0.148117i	0.524388	+	0.851480i	$0.324294\pi$
$380$		0			0
$381$	−0.919724	+	0.531003i	−0.0471189	+	0.0272041i
$382$	15.3646			0.786119
$383$	−6.35744	+	3.67047i	−0.324850	+	0.187552i	−0.653552	−	0.756881i	$-0.726722\pi$
$383$	−6.35744	+	3.67047i	−0.324850	+	0.187552i	0.328702	+	0.944434i	$0.393389\pi$
$384$	1.89743	+	0.508416i	0.0968281	+	0.0259450i
$385$		0			0
$386$	7.76222	+	13.4446i	0.395087	+	0.684310i
$387$	0.649386	+	2.42354i	0.0330101	+	0.123195i
$388$	0.450526	−	0.780333i	0.0228720	−	0.0396154i
$389$	26.6060			1.34898			0.674488	−	0.738286i	$-0.264364\pi$
$389$	26.6060			1.34898			0.674488	+	0.738286i	$0.264364\pi$
$390$		0			0
$391$	−5.15065			−0.260480
$392$	−15.0253	+	26.0246i	−0.758893	+	1.31444i
$393$	0.753258	+	2.81120i	0.0379969	+	0.141806i
$394$	2.06796	+	3.58180i	0.104182	+	0.180449i
$395$		0			0
$396$	16.8418	+	4.51274i	0.846330	+	0.226774i
$397$	−18.3053	+	10.5686i	−0.918717	+	0.530421i	−0.883225	−	0.468949i	$-0.844633\pi$
$397$	−18.3053	+	10.5686i	−0.918717	+	0.530421i	−0.0354913	+	0.999370i	$0.511300\pi$
$398$	−7.46666			−0.374270
$399$	−6.74830	+	3.89613i	−0.337837	+	0.195050i
$400$		0			0
$401$	6.09429	−	1.63296i	0.304334	−	0.0815461i	−0.103420	−	0.994638i	$-0.532979\pi$
$401$	6.09429	−	1.63296i	0.304334	−	0.0815461i	0.407754	+	0.913092i	$0.366312\pi$
$402$	1.54878	−	1.54878i	0.0772462	−	0.0772462i
$403$	1.86888	−	13.3673i	0.0930957	−	0.665870i
$404$		−	10.4128i		−	0.518058i
$405$		0			0
$406$	15.5857	−	26.9952i	0.773505	−	1.33975i
$407$	38.8904	+	10.4206i	1.92772	+	0.516532i
$408$			2.94052i			0.145577i
$409$	3.27126	−	12.2085i	0.161753	−	0.603672i	−0.836679	−	0.547694i	$-0.815506\pi$
$409$	3.27126	−	12.2085i	0.161753	−	0.603672i	0.998432	−	0.0559775i	$-0.0178275\pi$
$410$		0			0
$411$	−2.65578	−	2.65578i	−0.131000	−	0.131000i
$412$	5.68906	−	21.2318i	0.280280	−	1.04602i
$413$	−39.4017	+	10.5577i	−1.93883	+	0.519509i
$414$	1.16671	+	4.35421i	0.0573406	+	0.213998i
$415$		0			0
$416$	18.2500	+	7.73124i	0.894780	+	0.379055i
$417$	−3.30602	−	3.30602i	−0.161897	−	0.161897i
$418$	−22.7562	−	13.1383i	−1.11304	−	0.642616i
$419$	19.9068	+	11.4932i	0.972511	+	0.561480i	0.900001	−	0.435888i	$-0.143566\pi$
$419$	19.9068	+	11.4932i	0.972511	+	0.561480i	0.0725104	+	0.997368i	$0.476899\pi$
$420$		0			0
$421$	25.2576	−	25.2576i	1.23098	−	1.23098i	0.267395	−	0.963587i	$-0.413837\pi$
$421$	25.2576	−	25.2576i	1.23098	−	1.23098i	0.963587	−	0.267395i	$-0.0861627\pi$
$422$	−6.45025	−	11.1722i	−0.313993	−	0.543852i
$423$	−2.08109	−	3.60456i	−0.101186	−	0.175260i
$424$	1.17375	−	1.17375i	0.0570023	−	0.0570023i
$425$		0			0
$426$	0.735102	+	0.424411i	0.0356158	+	0.0205628i
$427$	−16.4983	−	9.52532i	−0.798410	−	0.460962i
$428$	−4.05006	−	4.05006i	−0.195767	−	0.195767i
$429$	−5.80809	−	2.46048i	−0.280417	−	0.118793i
$430$		0			0
$431$	1.01246	+	3.77857i	0.0487687	+	0.182007i	0.986014	−	0.166664i	$-0.0532996\pi$
$431$	1.01246	+	3.77857i	0.0487687	+	0.182007i	−0.937245	+	0.348671i	$0.886633\pi$
$432$	0.604191	−	0.161892i	0.0290691	−	0.00778905i
$433$	−8.91900	+	33.2862i	−0.428620	+	1.59963i	0.327269	+	0.944931i	$0.393872\pi$
$433$	−8.91900	+	33.2862i	−0.428620	+	1.59963i	−0.755889	+	0.654700i	$0.772795\pi$
$434$	−10.0897	−	10.0897i	−0.484322	−	0.484322i
$435$		0			0
$436$	−0.835364	+	3.11762i	−0.0400067	+	0.149307i
$437$			9.46780i			0.452906i
$438$	−1.79497	−	0.480960i	−0.0857669	−	0.0229812i
$439$	−11.1274	+	19.2732i	−0.531081	+	0.919859i	0.468261	+	0.883590i	$0.344881\pi$
$439$	−11.1274	+	19.2732i	−0.531081	+	0.919859i	−0.999342	+	0.0362692i	$0.988453\pi$
$440$		0			0
$441$		−	29.9853i		−	1.42787i
$442$	−1.37566	+	9.83943i	−0.0654333	+	0.468014i
$443$	2.45786	−	2.45786i	0.116776	−	0.116776i	−0.646304	−	0.763080i	$-0.723686\pi$
$443$	2.45786	−	2.45786i	0.116776	−	0.116776i	0.763080	+	0.646304i	$0.223686\pi$
$444$	−2.94380	+	0.788788i	−0.139706	+	0.0374342i
$445$		0			0
$446$	−16.8068	+	9.70339i	−0.795823	+	0.459469i
$447$	−6.04329			−0.285838
$448$	20.4221	−	11.7907i	0.964852	−	0.557058i
$449$	27.1100	+	7.26410i	1.27940	+	0.342814i	0.833625	−	0.552331i	$-0.186262\pi$
$449$	27.1100	+	7.26410i	1.27940	+	0.342814i	0.445775	+	0.895145i	$0.352928\pi$
$450$		0			0
$451$	−2.29183	−	3.96957i	−0.107918	−	0.186920i
$452$	2.44319	+	9.11811i	0.114918	+	0.428880i
$453$	0.471789	−	0.817163i	0.0221666	−	0.0383936i
$454$	−14.1292			−0.663118
$455$		0			0
$456$	5.40518			0.253121
$457$	18.5211	−	32.0795i	0.866381	−	1.50062i	0.000712325	−	1.00000i	$-0.499773\pi$
$457$	18.5211	−	32.0795i	0.866381	−	1.50062i	0.865669	−	0.500617i	$-0.166893\pi$
$458$	1.49876	+	5.59346i	0.0700326	+	0.261365i
$459$	−2.99193	−	5.18217i	−0.139651	−	0.241883i
$460$		0			0
$461$	38.7623	+	10.3863i	1.80534	+	0.483740i	0.994792	−	0.101931i	$-0.0325020\pi$
$461$	38.7623	+	10.3863i	1.80534	+	0.483740i	0.810549	+	0.585670i	$0.199169\pi$
$462$	−5.77503	+	3.33421i	−0.268679	+	0.155122i
$463$	3.45704			0.160663			0.0803313	−	0.996768i	$-0.474402\pi$
$463$	3.45704			0.160663			0.0803313	+	0.996768i	$0.474402\pi$
$464$	−2.23169	+	1.28847i	−0.103604	+	0.0598156i
$465$		0			0
$466$	4.42988	−	1.18698i	0.205210	−	0.0549859i
$467$	−4.75622	+	4.75622i	−0.220092	+	0.220092i	−0.808537	−	0.588445i	$-0.799740\pi$
$467$	−4.75622	+	4.75622i	−0.220092	+	0.220092i	0.588445	+	0.808537i	$0.299740\pi$
$468$	−12.0267	+	1.48544i	−0.555935	+	0.0686644i
$469$			29.6302i			1.36820i
$470$		0			0
$471$	−2.50355	+	4.33628i	−0.115358	+	0.199805i
$472$	27.3314	+	7.32344i	1.25803	+	0.337088i
$473$			4.50972i			0.207357i
$474$	−1.00397	+	3.74688i	−0.0461140	+	0.172100i
$475$		0			0
$476$	−10.3506	−	10.3506i	−0.474417	−	0.474417i
$477$	−0.428688	+	1.59989i	−0.0196283	+	0.0732538i
$478$	4.44414	−	1.19080i	0.203270	−	0.0544661i
$479$	0.0302527	+	0.112905i	0.00138228	+	0.00515874i	0.966614	−	0.256239i	$-0.0824833\pi$
$479$	0.0302527	+	0.112905i	0.00138228	+	0.00515874i	−0.965231	+	0.261397i	$0.915817\pi$
$480$		0			0
$481$	−27.7716	+	3.43012i	−1.26628	+	0.156400i
$482$	−0.469273	−	0.469273i	−0.0213748	−	0.0213748i
$483$	2.08081	+	1.20136i	0.0946803	+	0.0546637i
$484$	16.0475	+	9.26503i	0.729432	+	0.421138i
$485$		0			0
$486$	−5.59048	+	5.59048i	−0.253589	+	0.253589i
$487$	5.32225	+	9.21841i	0.241174	+	0.417726i	0.961049	−	0.276378i	$-0.0891341\pi$
$487$	5.32225	+	9.21841i	0.241174	+	0.417726i	−0.719875	+	0.694104i	$0.755801\pi$
$488$	6.60734	+	11.4442i	0.299100	+	0.518057i
$489$	−0.683139	+	0.683139i	−0.0308926	+	0.0308926i
$490$		0			0
$491$	27.0138	+	15.5964i	1.21912	+	0.703857i	0.964729	−	0.263246i	$-0.0847929\pi$
$491$	27.0138	+	15.5964i	1.21912	+	0.703857i	0.254387	+	0.967102i	$0.418126\pi$
$492$	0.300476	+	0.173480i	0.0135465	+	0.00782107i
$493$	17.4317	+	17.4317i	0.785084	+	0.785084i
$494$	18.0866	+	2.52870i	0.813754	+	0.113771i
$495$		0			0
$496$	0.305308	+	1.13942i	0.0137087	+	0.0511616i
$497$	−11.0915	+	2.97196i	−0.497523	+	0.133311i
$498$	−0.673636	+	2.51404i	−0.0301863	+	0.112657i
$499$	6.58133	+	6.58133i	0.294621	+	0.294621i	0.838903	−	0.544282i	$-0.183198\pi$
$499$	6.58133	+	6.58133i	0.294621	+	0.294621i	−0.544282	+	0.838903i	$0.683198\pi$
$500$		0			0
$501$	0.318260	−	1.18776i	0.0142188	−	0.0530653i
$502$		−	13.2405i		−	0.590952i
$503$	−41.2382	−	11.0497i	−1.83872	−	0.492683i	−0.839968	−	0.542637i	$-0.817426\pi$
$503$	−41.2382	−	11.0497i	−1.83872	−	0.492683i	−0.998752	+	0.0499533i	$0.984093\pi$
$504$	−17.4072	+	30.1501i	−0.775376	+	1.34299i
$505$		0			0
$506$			8.10231i			0.360192i
$507$	4.38339	+	0.0702315i	0.194673	+	0.00311909i
$508$	−2.59307	+	2.59307i	−0.115049	+	0.115049i
$509$	−11.1097	+	2.97683i	−0.492429	+	0.131946i	−0.496484	−	0.868046i	$-0.665376\pi$
$509$	−11.1097	+	2.97683i	−0.492429	+	0.131946i	0.00405535	+	0.999992i	$0.498709\pi$
$510$		0			0
$511$	21.7708	−	12.5694i	0.963082	−	0.556036i
$512$	−3.55518			−0.157118
$513$	−9.52574	+	5.49969i	−0.420572	+	0.242817i
$514$	27.6755	+	7.41564i	1.22072	+	0.327090i
$515$		0			0
$516$	−0.170681	−	0.295628i	−0.00751381	−	0.0130143i
$517$	−1.93625	−	7.22617i	−0.0851561	−	0.317807i
$518$	−14.7913	+	25.6193i	−0.649894	+	1.12565i
$519$	−2.48458			−0.109061
$520$		0			0
$521$	9.73221			0.426376			0.213188	−	0.977011i	$-0.431615\pi$
$521$	9.73221			0.426376			0.213188	+	0.977011i	$0.431615\pi$
$522$	10.7877	−	18.6848i	0.472164	−	0.817812i
$523$	3.04051	+	11.3473i	0.132952	+	0.496184i	0.999998	−	0.00204420i	$-0.000650689\pi$
$523$	3.04051	+	11.3473i	0.132952	+	0.496184i	−0.867046	+	0.498229i	$0.833984\pi$
$524$	5.02481	+	8.70323i	0.219510	+	0.380202i
$525$		0			0
$526$	17.9416	+	4.80744i	0.782291	+	0.209614i
$527$	9.77289	−	5.64238i	0.425714	−	0.245786i
$528$	0.551278			0.0239913
$529$	−17.3903	+	10.0403i	−0.756102	+	0.436536i
$530$		0			0
$531$	−27.2720	+	7.30752i	−1.18350	+	0.317119i
$532$	−19.0261	+	19.0261i	−0.824888	+	0.824888i
$533$	2.51176	+	1.95951i	0.108796	+	0.0848757i
$534$		−	4.51577i		−	0.195416i
$535$		0			0
$536$	10.2767	−	17.7997i	0.443884	−	0.768830i
$537$	3.27153	+	0.876603i	0.141177	+	0.0378282i
$538$			21.7820i			0.939088i
$539$	13.9491	−	52.0589i	0.600832	−	2.24234i
$540$		0			0
$541$	14.8972	+	14.8972i	0.640479	+	0.640479i	0.950673	−	0.310194i	$-0.100394\pi$
$541$	14.8972	+	14.8972i	0.640479	+	0.640479i	−0.310194	+	0.950673i	$0.600394\pi$
$542$	1.56662	−	5.84671i	0.0672922	−	0.251138i
$543$	3.27024	−	0.876258i	0.140339	−	0.0376038i
$544$	4.28892	+	16.0065i	0.183886	+	0.686271i
$545$		0			0
$546$	2.85074	−	3.65417i	0.122000	−	0.156384i
$547$	32.7790	+	32.7790i	1.40153	+	1.40153i	0.795262	+	0.606266i	$0.207333\pi$
$547$	32.7790	+	32.7790i	1.40153	+	1.40153i	0.606266	+	0.795262i	$0.292667\pi$
$548$	−11.2316	−	6.48455i	−0.479789	−	0.277006i
$549$	−11.4194	−	6.59297i	−0.487367	−	0.281381i
$550$		0			0
$551$	32.0425	−	32.0425i	1.36506	−	1.36506i
$552$	−0.833335	−	1.44338i	−0.0354691	−	0.0614343i
$553$	−26.2377	−	45.4451i	−1.11574	−	1.93252i
$554$	16.4767	−	16.4767i	0.700027	−	0.700027i
$555$		0			0
$556$	−13.9815	−	8.07222i	−0.592947	−	0.342338i
$557$	−32.9089	−	18.9999i	−1.39439	−	0.805053i	−0.400595	−	0.916255i	$-0.631197\pi$
$557$	−32.9089	−	18.9999i	−1.39439	−	0.805053i	−0.993798	+	0.111202i	$0.964530\pi$
$558$	−6.98362	−	6.98362i	−0.295640	−	0.295640i
$559$	−1.17621	−	2.90523i	−0.0497483	−	0.122878i
$560$		0			0
$561$	−1.36495	−	5.09408i	−0.0576284	−	0.215072i
$562$	−11.5390	+	3.09187i	−0.486744	+	0.130423i
$563$	7.31631	−	27.3048i	0.308346	−	1.15076i	−0.621681	−	0.783270i	$-0.713550\pi$
$563$	7.31631	−	27.3048i	0.308346	−	1.15076i	0.930027	−	0.367492i	$-0.119783\pi$
$564$	0.400419	+	0.400419i	0.0168607	+	0.0168607i
$565$		0			0
$566$	−2.39891	+	8.95284i	−0.100834	+	0.376316i
$567$		−	33.3160i		−	1.39914i
$568$	7.69375	+	2.06153i	0.322823	+	0.0865000i
$569$	−7.77409	+	13.4651i	−0.325907	+	0.564487i	−0.981695	−	0.190457i	$-0.939003\pi$
$569$	−7.77409	+	13.4651i	−0.325907	+	0.564487i	0.655789	+	0.754945i	$0.272336\pi$
$570$		0			0
$571$			27.1740i			1.13720i	0.822616	+	0.568598i	$0.192514\pi$
$571$			27.1740i			1.13720i	−0.822616	+	0.568598i	$0.807486\pi$
$572$	−21.5712	−	3.01588i	−0.901936	−	0.126100i
$573$	4.00815	−	4.00815i	0.167443	−	0.167443i
$574$	3.25309	−	0.871662i	0.135781	−	0.0363825i
$575$		0			0
$576$	14.1352	−	8.16096i	0.588966	−	0.340040i
$577$	36.9310			1.53746			0.768730	−	0.639574i	$-0.220889\pi$
$577$	36.9310			1.53746			0.768730	+	0.639574i	$0.220889\pi$
$578$	6.26379	−	3.61640i	0.260539	−	0.150422i
$579$	5.53221	+	1.48235i	0.229911	+	0.0616044i
$580$		0			0
$581$	−17.6047	−	30.4923i	−0.730367	−	1.26503i
$582$	0.0617344	+	0.230396i	0.00255897	+	0.00955022i
$583$	−1.48853	+	2.57821i	−0.0616487	+	0.106779i
$584$	−17.4377			−0.721579
$585$		0			0
$586$	−10.8091			−0.446522
$587$	−12.8465	+	22.2508i	−0.530232	+	0.918388i	0.469146	+	0.883120i	$0.344562\pi$
$587$	−12.8465	+	22.2508i	−0.530232	+	0.918388i	−0.999378	+	0.0352676i	$0.988772\pi$
$588$	1.05588	+	3.94059i	0.0435436	+	0.162507i
$589$	−10.3717	−	17.9643i	−0.427357	−	0.740205i
$590$		0			0
$591$	1.47385	+	0.394917i	0.0606261	+	0.0162447i
$592$	2.11795	−	1.22280i	0.0870471	−	0.0502567i
$593$	21.2325			0.871915			0.435958	−	0.899967i	$-0.356410\pi$
$593$	21.2325			0.871915			0.435958	+	0.899967i	$0.356410\pi$
$594$	−8.15189	+	4.70650i	−0.334476	+	0.193110i
$595$		0			0
$596$	−20.1567	+	5.40097i	−0.825650	+	0.221232i
$597$	−1.94782	+	1.94782i	−0.0797191	+	0.0797191i
$598$	−2.11322	−	5.21963i	−0.0864158	−	0.213446i
$599$		−	21.3026i		−	0.870403i	−0.900333	−	0.435201i	$-0.856677\pi$
$599$		−	21.3026i		−	0.870403i	0.900333	−	0.435201i	$-0.143323\pi$
$600$		0			0
$601$	−0.552019	+	0.956124i	−0.0225173	+	0.0390011i	−0.877064	−	0.480373i	$-0.840501\pi$
$601$	−0.552019	+	0.956124i	−0.0225173	+	0.0390011i	0.854547	+	0.519374i	$0.173835\pi$
$602$	−3.20060	−	0.857599i	−0.130447	−	0.0349531i
$603$			20.5087i			0.835177i
$604$	0.843289	−	3.14720i	0.0343129	−	0.128058i
$605$		0			0
$606$	1.94911	+	1.94911i	0.0791771	+	0.0791771i
$607$	5.49058	−	20.4911i	0.222856	−	0.831709i	−0.760397	−	0.649459i	$-0.774995\pi$
$607$	5.49058	−	20.4911i	0.222856	−	0.831709i	0.983252	−	0.182250i	$-0.0583379\pi$
$608$	29.4226	−	7.88377i	1.19325	−	0.319729i
$609$	−2.97640	−	11.1081i	−0.120610	−	0.450122i
$610$		0			0
$611$	3.13206	+	4.15020i	0.126710	+	0.167899i
$612$	−7.16417	−	7.16417i	−0.289594	−	0.289594i
$613$	−7.63018	−	4.40529i	−0.308180	−	0.177928i	0.337932	−	0.941171i	$-0.390273\pi$
$613$	−7.63018	−	4.40529i	−0.308180	−	0.177928i	−0.646112	+	0.763243i	$0.723606\pi$
$614$	19.6254	+	11.3308i	0.792018	+	0.457272i
$615$		0			0
$616$	−44.2472	+	44.2472i	−1.78277	+	1.78277i
$617$	20.8856	+	36.1750i	0.840825	+	1.45635i	0.889199	+	0.457521i	$0.151263\pi$
$617$	20.8856	+	36.1750i	0.840825	+	1.45635i	−0.0483741	+	0.998829i	$0.515404\pi$
$618$	2.90935	+	5.03914i	0.117031	+	0.202704i
$619$	−0.180435	+	0.180435i	−0.00725231	+	0.00725231i	−0.710724	−	0.703471i	$-0.751632\pi$
$619$	−0.180435	+	0.180435i	−0.00725231	+	0.00725231i	0.703471	+	0.710724i	$0.251632\pi$
$620$		0			0
$621$	2.93723	+	1.69581i	0.117867	+	0.0680505i
$622$	−19.2944	−	11.1396i	−0.773634	−	0.446658i
$623$	43.1964	+	43.1964i	1.73063	+	1.73063i
$624$	−0.355141	+	0.143782i	−0.0142170	+	0.00575590i
$625$		0			0
$626$	−2.95190	−	11.0166i	−0.117982	−	0.440313i
$627$	−9.36380	+	2.50902i	−0.373954	+	0.100201i
$628$	−4.47492	+	16.7006i	−0.178569	+	0.666427i
$629$	−16.5432	−	16.5432i	−0.659622	−	0.659622i
$630$		0			0
$631$	−2.63181	+	9.82203i	−0.104771	+	0.391009i	−0.998319	−	0.0579577i	$-0.981541\pi$
$631$	−2.63181	+	9.82203i	−0.104771	+	0.391009i	0.893549	+	0.448967i	$0.148208\pi$
$632$			36.4002i			1.44792i
$633$	−4.59715	−	1.23180i	−0.182720	−	0.0489598i
$634$	1.56931	−	2.71813i	0.0623254	−	0.107951i
$635$		0			0
$636$		−	0.225348i		−	0.00893563i
$637$	4.59158	+	37.1753i	0.181925	+	1.47294i
$638$	27.4212	−	27.4212i	1.08562	−	1.08562i
$639$	−7.67702	+	2.05705i	−0.303698	+	0.0813757i
$640$		0			0
$641$	−3.87783	+	2.23887i	−0.153165	+	0.0884299i	−0.574624	−	0.818418i	$-0.694852\pi$
$641$	−3.87783	+	2.23887i	−0.153165	+	0.0884299i	0.421459	+	0.906848i	$0.361518\pi$
$642$	1.51620			0.0598398
$643$	−16.2870	+	9.40328i	−0.642295	+	0.370829i	−0.785498	−	0.618864i	$-0.787593\pi$
$643$	−16.2870	+	9.40328i	−0.642295	+	0.370829i	0.143203	+	0.989693i	$0.454260\pi$
$644$	8.01399	+	2.14734i	0.315795	+	0.0846171i
$645$		0			0
$646$	7.63443	+	13.2232i	0.300373	+	0.520261i
$647$	3.67805	+	13.7267i	0.144599	+	0.539652i	0.999773	+	0.0213101i	$0.00678373\pi$
$647$	3.67805	+	13.7267i	0.144599	+	0.539652i	−0.855174	+	0.518342i	$0.826550\pi$
$648$	−11.5550	+	20.0138i	−0.453923	+	0.786217i
$649$	−50.7477			−1.99202
$650$		0			0
$651$	−5.26420			−0.206320
$652$	−1.66800	+	2.88906i	−0.0653240	+	0.113144i
$653$	−9.80386	−	36.5885i	−0.383655	−	1.43182i	−0.840277	−	0.542158i	$-0.817607\pi$
$653$	−9.80386	−	36.5885i	−0.383655	−	1.43182i	0.456622	−	0.889661i	$-0.349059\pi$
$654$	−0.427200	−	0.739932i	−0.0167048	−	0.0289336i
$655$		0			0
$656$	−0.268932	−	0.0720602i	−0.0105000	−	0.00281348i
$657$	15.0687	−	8.69992i	0.587886	−	0.339416i
$658$	5.49672			0.214284
$659$	10.6520	−	6.14995i	0.414944	−	0.239568i	−0.277968	−	0.960590i	$-0.589661\pi$
$659$	10.6520	−	6.14995i	0.414944	−	0.239568i	0.692912	+	0.721022i	$0.256328\pi$
$660$		0			0
$661$	5.05178	−	1.35362i	0.196491	−	0.0526497i	−0.159231	−	0.987241i	$-0.550901\pi$
$661$	5.05178	−	1.35362i	0.196491	−	0.0526497i	0.355722	+	0.934592i	$0.384235\pi$
$662$	3.27373	−	3.27373i	0.127237	−	0.127237i
$663$	2.20794	+	2.92568i	0.0857494	+	0.113624i
$664$			24.4234i			0.947812i
$665$		0			0
$666$	−10.2379	+	17.7325i	−0.396709	+	0.687120i
$667$	−13.4966	−	3.61640i	−0.522590	−	0.140028i
$668$		−	4.24608i		−	0.164286i
$669$	−1.85305	+	6.91569i	−0.0716432	+	0.267376i
$670$		0			0
$671$	−16.7587	−	16.7587i	−0.646961	−	0.646961i
$672$	2.00073	−	7.46682i	0.0771797	−	0.288039i
$673$	35.0474	−	9.39092i	1.35098	−	0.361993i	0.490482	−	0.871452i	$-0.336821\pi$
$673$	35.0474	−	9.39092i	1.35098	−	0.361993i	0.860495	+	0.509458i	$0.170154\pi$
$674$	−2.04410	−	7.62868i	−0.0787357	−	0.293846i
$675$		0			0
$676$	14.6831	−	3.68325i	0.564733	−	0.141663i
$677$	−17.7672	−	17.7672i	−0.682851	−	0.682851i	0.277791	−	0.960642i	$-0.410398\pi$
$677$	−17.7672	−	17.7672i	−0.682851	−	0.682851i	−0.960642	+	0.277791i	$0.910398\pi$
$678$	−2.16408	−	1.24943i	−0.0831109	−	0.0479841i
$679$	−2.79442	−	1.61336i	−0.107240	−	0.0619151i
$680$		0			0
$681$	−3.68589	+	3.68589i	−0.141244	+	0.141244i
$682$	−8.87583	−	15.3734i	−0.339873	−	0.588677i
$683$	10.5865	+	18.3363i	0.405080	+	0.701619i	0.994331	−	0.106331i	$-0.0339103\pi$
$683$	10.5865	+	18.3363i	0.405080	+	0.701619i	−0.589251	+	0.807950i	$0.700577\pi$
$684$	−13.1690	+	13.1690i	−0.503529	+	0.503529i
$685$		0			0
$686$	11.1870	+	6.45879i	0.427120	+	0.246598i
$687$	1.85015	+	1.06818i	0.0705875	+	0.0407537i
$688$	0.193696	+	0.193696i	0.00738459	+	0.00738459i
$689$	0.286494	−	2.04916i	0.0109145	−	0.0780667i
$690$		0			0
$691$	−9.75426	−	36.4034i	−0.371069	−	1.38485i	−0.859004	−	0.511970i	$-0.828916\pi$
$691$	−9.75426	−	36.4034i	−0.371069	−	1.38485i	0.487934	−	0.872880i	$-0.337751\pi$
$692$	−8.28702	+	2.22050i	−0.315025	+	0.0844108i
$693$	16.1604	−	60.3114i	0.613882	−	2.29104i
$694$	−18.7669	−	18.7669i	−0.712382	−	0.712382i
$695$		0			0
$696$	−2.06461	+	7.70523i	−0.0782589	+	0.292066i
$697$			2.66348i			0.100887i
$698$	3.38739	+	0.907648i	0.128214	+	0.0343550i
$699$	0.845974	−	1.46527i	0.0319977	−	0.0554216i
$700$		0			0
$701$			24.9114i			0.940889i	0.882430	+	0.470445i	$0.155906\pi$
$701$			24.9114i			0.940889i	−0.882430	+	0.470445i	$0.844094\pi$
$702$	4.02404	−	5.15814i	0.151877	−	0.194682i
$703$	−30.4094	+	30.4094i	−1.14691	+	1.14691i
$704$	28.3373	−	7.59295i	1.06800	−	0.286170i
$705$		0			0
$706$	−20.2407	+	11.6860i	−0.761768	+	0.439807i
$707$	−37.2890			−1.40240
$708$	3.32669	−	1.92067i	0.125025	−	0.0721831i
$709$	17.2592	+	4.62459i	0.648183	+	0.173680i	0.567907	−	0.823092i	$-0.307753\pi$
$709$	17.2592	+	4.62459i	0.648183	+	0.173680i	0.0802760	+	0.996773i	$0.474420\pi$
$710$		0			0
$711$	−18.1605	−	31.4550i	−0.681073	−	1.17965i
$712$	−10.9674	−	40.9311i	−0.411022	−	1.53396i
$713$	−3.19807	+	5.53922i	−0.119769	+	0.207445i
$714$	3.87490			0.145014
$715$		0			0
$716$	11.6952			0.437071
$717$	0.848697	−	1.46999i	0.0316952	−	0.0548976i
$718$	−5.50433	−	20.5424i	−0.205420	−	0.766637i
$719$	−3.20390	−	5.54933i	−0.119485	−	0.206955i	0.800078	−	0.599895i	$-0.204791\pi$
$719$	−3.20390	−	5.54933i	−0.119485	−	0.206955i	−0.919564	+	0.392941i	$0.871458\pi$
$720$		0			0
$721$	−76.0325	−	20.3729i	−2.83160	−	0.758725i
$722$	9.26590	−	5.34967i	0.344841	−	0.199094i
$723$	−0.244838			−0.00910564
$724$	10.1244	−	5.84532i	0.376270	−	0.217239i
$725$		0			0
$726$	−4.73808	+	1.26956i	−0.175846	+	0.0471179i
$727$	17.2216	−	17.2216i	0.638714	−	0.638714i	−0.311524	−	0.950238i	$-0.600839\pi$
$727$	17.2216	−	17.2216i	0.638714	−	0.638714i	0.950238	+	0.311524i	$0.100839\pi$
$728$	16.9643	−	40.0451i	0.628738	−	1.48417i
$729$		−	21.0515i		−	0.779686i
$730$		0			0
$731$	1.31026	−	2.26943i	0.0484616	−	0.0839380i
$732$	1.73286	+	0.464319i	0.0640484	+	0.0171617i
$733$		−	34.7895i		−	1.28498i	−0.766295	−	0.642489i	$-0.777902\pi$
$733$		−	34.7895i		−	1.28498i	0.766295	−	0.642489i	$-0.222098\pi$
$734$	2.80738	−	10.4773i	0.103622	−	0.386724i
$735$		0			0
$736$	−6.64144	−	6.64144i	−0.244807	−	0.244807i
$737$	−9.54061	+	35.6061i	−0.351433	+	1.31157i
$738$	2.25163	−	0.603323i	0.0828837	−	0.0222086i
$739$	−10.1339	−	37.8203i	−0.372782	−	1.39124i	−0.856558	−	0.516051i	$-0.827402\pi$
$739$	−10.1339	−	37.8203i	−0.372782	−	1.39124i	0.483776	−	0.875192i	$-0.339265\pi$
$740$		0			0
$741$	5.37790	−	4.05858i	0.197562	−	0.149096i
$742$	−1.54672	−	1.54672i	−0.0567819	−	0.0567819i
$743$	−31.6228	−	18.2574i	−1.16013	−	0.669801i	−0.208794	−	0.977960i	$-0.566954\pi$
$743$	−31.6228	−	18.2574i	−1.16013	−	0.669801i	−0.951335	+	0.308159i	$0.900287\pi$
$744$	3.16235	+	1.82578i	0.115937	+	0.0669365i
$745$		0			0
$746$	2.69913	−	2.69913i	0.0988221	−	0.0988221i
$747$	−12.1852	−	21.1053i	−0.445832	−	0.772203i
$748$	−9.10529	−	15.7708i	−0.332922	−	0.576639i
$749$	−14.5035	+	14.5035i	−0.529947	+	0.529947i
$750$		0			0
$751$	−12.0184	−	6.93885i	−0.438559	−	0.253202i	0.264427	−	0.964406i	$-0.414817\pi$
$751$	−12.0184	−	6.93885i	−0.438559	−	0.253202i	−0.702986	+	0.711203i	$0.748150\pi$
$752$	−0.393533	−	0.227207i	−0.0143507	−	0.00828537i
$753$	−3.45404	−	3.45404i	−0.125872	−	0.125872i
$754$	−10.5132	+	24.8170i	−0.382869	+	0.903783i
$755$		0			0
$756$	2.49471	+	9.31038i	0.0907317	+	0.338615i
$757$	36.3019	−	9.72706i	1.31941	−	0.353536i	0.470656	−	0.882317i	$-0.344017\pi$
$757$	36.3019	−	9.72706i	1.31941	−	0.353536i	0.848758	+	0.528781i	$0.177351\pi$
$758$	−2.63578	+	9.83685i	−0.0957357	+	0.357291i
$759$	2.11365	+	2.11365i	0.0767205	+	0.0767205i
$760$		0			0
$761$	−6.97074	+	26.0152i	−0.252689	+	0.943049i	0.716672	+	0.697410i	$0.245664\pi$
$761$	−6.97074	+	26.0152i	−0.252689	+	0.943049i	−0.969361	+	0.245639i	$0.921002\pi$
$762$		−	0.970757i		−	0.0351668i
$763$	11.1644	+	2.99149i	0.404178	+	0.108299i
$764$	9.78658	−	16.9509i	0.354066	−	0.613261i
$765$		0			0
$766$		−	6.71020i		−	0.242449i
$767$	32.6924	−	13.2358i	1.18045	−	0.477919i
$768$	−3.96661	+	3.96661i	−0.143133	+	0.143133i
$769$	41.7992	−	11.2001i	1.50732	−	0.403885i	0.591775	−	0.806103i	$-0.298427\pi$
$769$	41.7992	−	11.2001i	1.50732	−	0.403885i	0.915544	+	0.402218i	$0.131761\pi$
$770$		0			0
$771$	9.15422	−	5.28519i	0.329681	−	0.190342i
$772$	19.7768			0.711784
$773$	−14.3584	+	8.28981i	−0.516435	+	0.298164i	−0.735475	−	0.677552i	$-0.763041\pi$
$773$	−14.3584	+	8.28981i	−0.516435	+	0.298164i	0.219040	+	0.975716i	$0.429708\pi$
$774$	−2.21531	−	0.593590i	−0.0796276	−	0.0213361i
$775$		0			0
$776$	1.11912	+	1.93838i	0.0401742	+	0.0695838i
$777$	2.82470	+	10.5419i	0.101336	+	0.378189i
$778$	−12.1600	+	21.0617i	−0.435956	+	0.755098i
$779$	4.89595			0.175415
$780$		0			0
$781$	−14.2854			−0.511171
$782$	2.35405	−	4.07734i	0.0841807	−	0.145805i
$783$	−4.20142	−	15.6799i	−0.150146	−	0.560354i
$784$	−1.63685	−	2.83510i	−0.0584588	−	0.101254i
$785$		0			0
$786$	−2.56966	−	0.688537i	−0.0916566	−	0.0245593i
$787$	−0.866181	+	0.500090i	−0.0308760	+	0.0178263i	−0.515359	−	0.856975i	$-0.672341\pi$
$787$	−0.866181	+	0.500090i	−0.0308760	+	0.0178263i	0.484483	+	0.874801i	$0.339008\pi$
$788$	5.26880			0.187693
$789$	5.93453	−	3.42630i	0.211275	−	0.121980i
$790$		0			0
$791$	32.6525	−	8.74921i	1.16099	−	0.311086i
$792$	−30.6258	+	30.6258i	−1.08824	+	1.08824i
$793$	15.1671	+	6.42524i	0.538600	+	0.228167i
$794$		−	19.3210i		−	0.685677i
$795$		0			0
$796$	−4.75595	+	8.23754i	−0.168570	+	0.291972i
$797$	0.462469	+	0.123918i	0.0163815	+	0.00438941i	0.267000	−	0.963696i	$-0.413967\pi$
$797$	0.462469	+	0.123918i	0.0163815	+	0.00438941i	−0.250619	+	0.968086i	$0.580634\pi$
$798$		−	7.12274i		−	0.252142i
$799$	−1.12512	+	4.19900i	−0.0398038	+	0.148550i
$800$		0			0
$801$	29.8985	+	29.8985i	1.05641	+	1.05641i
$802$	−1.49265	+	5.57066i	−0.0527074	+	0.196707i
$803$	30.2087	−	8.09439i	1.06604	−	0.285645i
$804$	−0.722174	−	2.69519i	−0.0254691	−	0.0950521i
$805$		0			0
$806$	9.72757	+	7.58880i	0.342639	+	0.267304i
$807$	5.68226	+	5.68226i	0.200025	+	0.200025i
$808$	22.4006	+	12.9330i	0.788049	+	0.454980i
$809$	17.8417	+	10.3009i	0.627280	+	0.362160i	0.779698	−	0.626156i	$-0.215373\pi$
$809$	17.8417	+	10.3009i	0.627280	+	0.362160i	−0.152418	+	0.988316i	$0.548706\pi$
$810$		0			0
$811$	−0.752500	+	0.752500i	−0.0264239	+	0.0264239i	−0.720195	−	0.693771i	$-0.755948\pi$
$811$	−0.752500	+	0.752500i	−0.0264239	+	0.0264239i	0.693771	+	0.720195i	$0.255948\pi$
$812$	−19.8549	−	34.3897i	−0.696770	−	1.20684i
$813$	−1.11655	−	1.93391i	−0.0391590	−	0.0678253i
$814$	−26.0236	+	26.0236i	−0.912126	+	0.912126i
$815$		0			0
$816$	−0.277420	−	0.160169i	−0.00971166	−	0.00560703i
$817$	−4.17161	−	2.40848i	−0.145946	−	0.0842621i
$818$	8.16934	+	8.16934i	0.285634	+	0.285634i
$819$	5.31945	+	43.0684i	0.185877	+	1.50493i
$820$		0			0
$821$	7.34022	+	27.3941i	0.256175	+	0.956059i	0.967433	+	0.253128i	$0.0814593\pi$
$821$	7.34022	+	27.3941i	0.256175	+	0.956059i	−0.711258	+	0.702931i	$0.751874\pi$
$822$	3.31616	−	0.888561i	0.115664	−	0.0309921i
$823$	0.395567	−	1.47628i	0.0137886	−	0.0514598i	−0.958689	−	0.284457i	$-0.908187\pi$
$823$	0.395567	−	1.47628i	0.0137886	−	0.0514598i	0.972477	+	0.232997i	$0.0748533\pi$
$824$	38.6089	+	38.6089i	1.34501	+	1.34501i
$825$		0			0
$826$	9.65054	−	36.0163i	0.335785	−	1.25317i
$827$			34.9791i			1.21634i	0.793806	+	0.608171i	$0.208097\pi$
$827$			34.9791i			1.21634i	−0.793806	+	0.608171i	$0.791903\pi$
$828$	5.54690	+	1.48629i	0.192768	+	0.0516521i
$829$	−5.70269	+	9.87735i	−0.198063	+	0.343055i	−0.947900	−	0.318567i	$-0.896798\pi$
$829$	−5.70269	+	9.87735i	−0.198063	+	0.343055i	0.749838	+	0.661622i	$0.230132\pi$
$830$		0			0
$831$		−	8.59653i		−	0.298210i
$832$	−16.2749	+	12.2823i	−0.564231	+	0.425813i
$833$	−22.1449	+	22.1449i	−0.767275	+	0.767275i
$834$	4.12808	−	1.10612i	0.142944	−	0.0383016i
$835$		0			0
$836$	−28.9895	+	16.7371i	−1.00262	+	0.578865i
$837$	−7.43083			−0.256847
$838$	−18.1964	+	10.5057i	−0.628584	+	0.362913i
$839$	−28.6789	−	7.68448i	−0.990105	−	0.265298i	−0.272810	−	0.962068i	$-0.587953\pi$
$839$	−28.6789	−	7.68448i	−0.990105	−	0.265298i	−0.717295	+	0.696770i	$0.754620\pi$
$840$		0			0
$841$	18.9382	+	32.8019i	0.653041	+	1.13110i
$842$	8.45060	+	31.5381i	0.291227	+	1.08687i
$843$	−2.20360	+	3.81675i	−0.0758961	+	0.131456i
$844$	−16.4341			−0.565687
$845$		0			0
$846$	3.80457			0.130804
$847$	33.1786	−	57.4671i	1.14003	−	1.97459i
$848$	0.0468027	+	0.174670i	0.00160721	+	0.00599819i
$849$	1.70972	+	2.96133i	0.0586775	+	0.101632i
$850$		0			0
$851$	12.8087	+	3.43208i	0.439077	+	0.117650i
$852$	0.936458	−	0.540664i	0.0320825	−	0.0185229i
$853$	15.2934			0.523636			0.261818	−	0.965117i	$-0.415678\pi$
$853$	15.2934			0.523636			0.261818	+	0.965117i	$0.415678\pi$
$854$	15.0808	−	8.70689i	0.516054	−	0.297944i
$855$		0			0
$856$	13.7429	−	3.68240i	0.469723	−	0.125862i
$857$	−12.3837	+	12.3837i	−0.423018	+	0.423018i	−0.886242	−	0.463223i	$-0.846693\pi$
$857$	−12.3837	+	12.3837i	−0.423018	+	0.423018i	0.463223	+	0.886242i	$0.346693\pi$
$858$	4.60228	−	3.47324i	0.157119	−	0.118574i
$859$		−	8.73070i		−	0.297888i	−0.988846	−	0.148944i	$-0.952413\pi$
$859$		−	8.73070i		−	0.297888i	0.988846	−	0.148944i	$-0.0475874\pi$
$860$		0			0
$861$	0.621241	−	1.07602i	0.0211718	−	0.0366707i
$862$	−3.45391	−	0.925473i	−0.117641	−	0.0315217i
$863$			8.33598i			0.283760i	0.989884	+	0.141880i	$0.0453147\pi$
$863$			8.33598i			0.283760i	−0.989884	+	0.141880i	$0.954685\pi$
$864$	2.82418	−	10.5400i	0.0960805	−	0.358577i
$865$		0			0
$866$	−22.2735	−	22.2735i	−0.756885	−	0.756885i
$867$	0.690623	−	2.57744i	0.0234548	−	0.0875345i
$868$	−17.5581	+	4.70469i	−0.595962	+	0.159688i
$869$	−16.8965	−	63.0587i	−0.573176	−	2.13912i
$870$		0			0
$871$	−3.14044	−	25.4263i	−0.106410	−	0.861537i
$872$	−5.66922	−	5.66922i	−0.191984	−	0.191984i
$873$	−1.93417	−	1.11669i	−0.0654616	−	0.0377943i
$874$	−7.49485	−	4.32716i	−0.253517	−	0.146368i
$875$		0			0
$876$	−1.67394	+	1.67394i	−0.0565570	+	0.0565570i
$877$	−6.18525	−	10.7132i	−0.208861	−	0.361758i	0.742495	−	0.669852i	$-0.233642\pi$
$877$	−6.18525	−	10.7132i	−0.208861	−	0.361758i	−0.951356	+	0.308094i	$0.900309\pi$
$878$	−10.1713	−	17.6172i	−0.343265	−	0.594552i
$879$	−2.81978	+	2.81978i	−0.0951088	+	0.0951088i
$880$		0			0
$881$	12.0765	+	6.97237i	0.406868	+	0.234905i	0.689443	−	0.724340i	$-0.257855\pi$
$881$	12.0765	+	6.97237i	0.406868	+	0.234905i	−0.282575	+	0.959245i	$0.591189\pi$
$882$	23.7368	+	13.7045i	0.799261	+	0.461453i
$883$	−8.89171	−	8.89171i	−0.299230	−	0.299230i	0.541482	−	0.840712i	$-0.317863\pi$
$883$	−8.89171	−	8.89171i	−0.299230	−	0.299230i	−0.840712	+	0.541482i	$0.817863\pi$
$884$	9.97906	+	7.78499i	0.335632	+	0.261838i
$885$		0			0
$886$	0.822340	+	3.06901i	0.0276270	+	0.103106i
$887$	51.6144	−	13.8300i	1.73304	−	0.464367i	0.752160	−	0.658980i	$-0.229012\pi$
$887$	51.6144	−	13.8300i	1.73304	−	0.464367i	0.980880	+	0.194613i	$0.0623452\pi$
$888$	1.95938	−	7.31251i	0.0657526	−	0.245392i
$889$	9.28594	+	9.28594i	0.311440	+	0.311440i
$890$		0			0
$891$	10.7274	−	40.0351i	0.359381	−	1.34123i
$892$			24.7226i			0.827774i
$893$	7.71849	+	2.06816i	0.258289	+	0.0692084i
$894$	2.76202	−	4.78396i	0.0923758	−	0.160000i
$895$		0			0
$896$		−	24.2905i		−	0.811490i
$897$	−1.91292	−	0.810368i	−0.0638704	−	0.0270574i
$898$	−18.1407	+	18.1407i	−0.605363	+	0.605363i
$899$	29.5702	−	7.92331i	0.986221	−	0.264257i
$900$		0			0
$901$	1.49815	−	0.864959i	0.0499107	−	0.0288160i
$902$	4.18983			0.139506
$903$	−1.05866	+	0.611219i	−0.0352301	+	0.0203401i
$904$	−22.6498	−	6.06898i	−0.753320	−	0.201851i
$905$		0			0
$906$	0.431252	+	0.746951i	0.0143274	+	0.0248158i
$907$	10.8433	+	40.4677i	0.360045	+	1.34371i	0.874015	+	0.485899i	$0.161508\pi$
$907$	10.8433	+	40.4677i	0.360045	+	1.34371i	−0.513970	+	0.857808i	$0.671826\pi$
$908$	−8.99973	+	15.5880i	−0.298666	+	0.517306i
$909$	−25.8097			−0.856054
$910$		0			0
$911$	13.0974			0.433937			0.216968	−	0.976179i	$-0.430383\pi$
$911$	13.0974			0.433937			0.216968	+	0.976179i	$0.430383\pi$
$912$	−0.294418	+	0.509947i	−0.00974916	+	0.0168860i
$913$	−11.3371	−	42.3105i	−0.375202	−	1.40027i
$914$	16.9298	+	29.3232i	0.559987	+	0.969926i
$915$		0			0
$916$	7.12560	+	1.90930i	0.235437	+	0.0630850i
$917$	31.1668	−	17.9942i	1.02922	−	0.594220i
$918$	5.46972			0.180528
$919$	31.8713	−	18.4009i	1.05134	−	0.606990i	0.128314	−	0.991734i	$-0.459043\pi$
$919$	31.8713	−	18.4009i	1.05134	−	0.606990i	0.923023	+	0.384744i	$0.125710\pi$
$920$		0			0
$921$	8.07553	−	2.16383i	0.266098	−	0.0713007i
$922$	−25.9379	+	25.9379i	−0.854219	+	0.854219i
$923$	9.20286	−	3.72587i	0.302916	−	0.122638i
$924$			8.49502i			0.279465i
$925$		0			0
$926$	−1.58001	+	2.73665i	−0.0519222	+	0.0899319i
$927$	−52.6261	−	14.1011i	−1.72847	−	0.463142i
$928$			44.9541i			1.47569i
$929$	−10.4741	+	39.0897i	−0.343643	+	1.28249i	0.550547	+	0.834804i	$0.314419\pi$
$929$	−10.4741	+	39.0897i	−0.343643	+	1.28249i	−0.894190	+	0.447688i	$0.852248\pi$
$930$		0			0
$931$	40.7062	+	40.7062i	1.33409	+	1.33409i
$932$	1.51212	−	5.64330i	0.0495310	−	0.184852i
$933$	−7.93930	+	2.12733i	−0.259921	+	0.0696456i
$934$	−1.59132	−	5.93888i	−0.0520695	−	0.194326i
$935$		0			0
$936$	11.7419	−	27.7173i	0.383795	−	0.905969i
$937$	−17.2306	−	17.2306i	−0.562898	−	0.562898i	0.367232	−	0.930129i	$-0.380306\pi$
$937$	−17.2306	−	17.2306i	−0.562898	−	0.562898i	−0.930129	+	0.367232i	$0.880306\pi$
$938$	−23.4558	−	13.5422i	−0.765858	−	0.442168i
$939$	−3.64397	−	2.10385i	−0.118916	−	0.0686564i
$940$		0			0
$941$	17.6729	−	17.6729i	0.576119	−	0.576119i	−0.357712	−	0.933832i	$-0.616443\pi$
$941$	17.6729	−	17.6729i	0.576119	−	0.576119i	0.933832	+	0.357712i	$0.116443\pi$
$942$	−2.28844	−	3.96370i	−0.0745615	−	0.129144i
$943$	−0.754824	−	1.30739i	−0.0245805	−	0.0425746i
$944$	−2.17965	+	2.17965i	−0.0709417	+	0.0709417i
$945$		0			0
$946$	−3.56996	−	2.06112i	−0.116070	−	0.0670128i
$947$	−15.8254	−	9.13678i	−0.514255	−	0.296905i	0.220326	−	0.975426i	$-0.429288\pi$
$947$	−15.8254	−	9.13678i	−0.514255	−	0.296905i	−0.734581	+	0.678521i	$0.762621\pi$
$948$	3.49423	+	3.49423i	0.113487	+	0.113487i
$949$	−17.3497	+	13.0934i	−0.563196	+	0.425031i
$950$		0			0
$951$	−0.299692	−	1.11846i	−0.00971817	−	0.0362687i
$952$	35.1222	−	9.41096i	1.13832	−	0.305011i
$953$	−15.3289	+	57.2081i	−0.496551	+	1.85315i	0.0246142	+	0.999697i	$0.492164\pi$
$953$	−15.3289	+	57.2081i	−0.496551	+	1.85315i	−0.521165	+	0.853456i	$0.674502\pi$
$954$	−1.07057	−	1.07057i	−0.0346609	−	0.0346609i
$955$		0			0
$956$	1.51698	−	5.66146i	0.0490628	−	0.183105i
$957$		−	14.3067i		−	0.462470i
$958$	−0.103204	−	0.0276534i	−0.00333436	−	0.000893439i
$959$	−23.2216	+	40.2209i	−0.749864	+	1.29880i
$960$		0			0
$961$			16.9865i			0.547950i
$962$	9.97740	−	23.5522i	0.321684	−	0.759352i
$963$	−10.0386	+	10.0386i	−0.323491	+	0.323491i
$964$	−0.816630	+	0.218815i	−0.0263019	+	0.00704757i
$965$		0			0
$966$	−1.90203	+	1.09814i	−0.0611967	+	0.0353320i
$967$	−53.6313			−1.72467			−0.862333	−	0.506341i	$-0.830998\pi$
$967$	−53.6313			−1.72467			−0.862333	+	0.506341i	$0.830998\pi$
$968$	−39.8627	+	23.0147i	−1.28123	+	0.739721i
$969$	5.44113	+	1.45795i	0.174794	+	0.0468360i
$970$		0			0
$971$	5.90908	+	10.2348i	0.189631	+	0.328451i	0.945127	−	0.326702i	$-0.105937\pi$
$971$	5.90908	+	10.2348i	0.189631	+	0.328451i	−0.755496	+	0.655153i	$0.772604\pi$
$972$	2.60676	+	9.72856i	0.0836119	+	0.312044i
$973$	−28.9071	+	50.0686i	−0.926719	+	1.60512i
$974$	−9.72992			−0.311767
$975$		0			0
$976$	−1.43960			−0.0460803
$977$	−10.2104	+	17.6850i	−0.326661	+	0.565793i	−0.981847	−	0.189674i	$-0.939257\pi$
$977$	−10.2104	+	17.6850i	−0.326661	+	0.565793i	0.655186	+	0.755467i	$0.272590\pi$
$978$	−0.228562	−	0.853005i	−0.00730861	−	0.0272761i
$979$	37.9994	+	65.8169i	1.21447	+	2.10352i
$980$		0			0
$981$	7.72746	+	2.07057i	0.246719	+	0.0661081i
$982$	−24.6927	+	14.2564i	−0.787977	+	0.454939i
$983$	25.2690			0.805957			0.402979	−	0.915209i	$-0.367975\pi$
$983$	25.2690			0.805957			0.402979	+	0.915209i	$0.367975\pi$
$984$	−0.746394	+	0.430931i	−0.0237942	+	0.0137376i
$985$		0			0
$986$	−21.7662	+	5.83223i	−0.693176	+	0.185736i
$987$	1.43393	−	1.43393i	0.0456424	−	0.0456424i
$988$	14.3102	−	18.3432i	0.455267	−	0.583576i
$989$			1.48529i			0.0472296i
$990$		0			0
$991$	10.5834	−	18.3311i	0.336194	−	0.582305i	−0.647519	−	0.762049i	$-0.724193\pi$
$991$	10.5834	−	18.3311i	0.336194	−	0.582305i	0.983713	+	0.179744i	$0.0575268\pi$
$992$	19.8770	+	5.32603i	0.631095	+	0.169102i
$993$		−	1.70803i		−	0.0542027i
$994$	2.71661	−	10.1385i	0.0861656	−	0.321574i
$995$		0			0
$996$	2.34452	+	2.34452i	0.0742891	+	0.0742891i
$997$	−2.41168	+	9.00051i	−0.0763786	+	0.285049i	−0.993542	−	0.113462i	$-0.963806\pi$
$997$	−2.41168	+	9.00051i	−0.0763786	+	0.285049i	0.917164	+	0.398511i	$0.130473\pi$
$998$	−8.21781	+	2.20196i	−0.260130	+	0.0697017i
$999$	3.98728	+	14.8807i	0.126152	+	0.470805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.s.c.32.4	✓	40
5.2	odd	4		325.2.x.c.318.4	yes	40
5.3	odd	4		325.2.x.c.318.7	yes	40
5.4	even	2	inner	325.2.s.c.32.7	yes	40
13.11	odd	12		325.2.x.c.232.7	yes	40
65.24	odd	12		325.2.x.c.232.4	yes	40
65.37	even	12	inner	325.2.s.c.193.7	yes	40
65.63	even	12	inner	325.2.s.c.193.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.s.c.32.4	✓	40	1.1	even	1	trivial
325.2.s.c.32.7	yes	40	5.4	even	2	inner
325.2.s.c.193.4	yes	40	65.63	even	12	inner
325.2.s.c.193.7	yes	40	65.37	even	12	inner
325.2.x.c.232.4	yes	40	65.24	odd	12
325.2.x.c.232.7	yes	40	13.11	odd	12
325.2.x.c.318.4	yes	40	5.2	odd	4
325.2.x.c.318.7	yes	40	5.3	odd	4

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.s (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.457039 + 0.791616i) q^{2} +(0.0872808 + 0.325736i) q^{3} +(0.582230 + 1.00845i) q^{4} +(-0.297749 - 0.0797815i) q^{6} +(3.61133 - 2.08500i) q^{7} -2.89257 q^{8} +(2.49959 - 1.44314i) q^{9} +(5.01101 - 1.34269i) q^{11} +(-0.277672 + 0.277672i) q^{12} +(-2.87797 + 2.17194i) q^{13} +3.81171i q^{14} +(0.157557 - 0.272897i) q^{16} +(-2.91180 - 0.780215i) q^{17} +2.63829i q^{18} +(-1.43417 + 5.35240i) q^{19} +(0.994360 + 0.994360i) q^{21} +(-1.22733 + 4.58045i) q^{22} +(1.65039 - 0.442222i) q^{23} +(-0.252465 - 0.942213i) q^{24} +(-0.403995 - 3.27090i) q^{26} +(1.40362 + 1.40362i) q^{27} +(4.20525 + 2.42790i) q^{28} +(-7.08218 - 4.08890i) q^{29} +(-2.64703 + 2.64703i) q^{31} +(-2.74855 - 4.76062i) q^{32} +(0.874729 + 1.51507i) q^{33} +(1.94844 - 1.94844i) q^{34} +(2.91067 + 1.68048i) q^{36} +(6.72122 + 3.88050i) q^{37} +(-3.58157 - 3.58157i) q^{38} +(-0.958670 - 0.747890i) q^{39} +(-0.228680 - 0.853445i) q^{41} +(-1.24161 + 0.332689i) q^{42} +(-0.224991 + 0.839677i) q^{43} +(4.27160 + 4.27160i) q^{44} +(-0.404226 + 1.50859i) q^{46} -1.44206i q^{47} +(0.102644 + 0.0275034i) q^{48} +(5.19446 - 8.99707i) q^{49} -1.01658i q^{51} +(-3.86593 - 1.63772i) q^{52} +(-0.405781 + 0.405781i) q^{53} +(-1.75263 + 0.469616i) q^{54} +(-10.4460 + 6.03100i) q^{56} -1.86865 q^{57} +(6.47367 - 3.73758i) q^{58} +(-9.44885 - 2.53181i) q^{59} +(-2.28425 - 3.95643i) q^{61} +(-0.885633 - 3.30523i) q^{62} +(6.01789 - 10.4233i) q^{63} +5.65500 q^{64} -1.59914 q^{66} +(-3.55279 + 6.15361i) q^{67} +(-0.908530 - 3.39068i) q^{68} +(0.288095 + 0.498996i) q^{69} +(-2.65984 - 0.712701i) q^{71} +(-7.23023 + 4.17437i) q^{72} +6.02847 q^{73} +(-6.14372 + 3.54708i) q^{74} +(-6.23266 + 1.67004i) q^{76} +(15.2969 - 15.2969i) q^{77} +(1.03019 - 0.417083i) q^{78} -12.5840i q^{79} +(3.99472 - 6.91905i) q^{81} +(0.780116 + 0.209031i) q^{82} -8.44351i q^{83} +(-0.423818 + 1.58171i) q^{84} +(-0.561871 - 0.561871i) q^{86} +(0.713764 - 2.66380i) q^{87} +(-14.4947 + 3.88383i) q^{88} +(3.79160 + 14.1504i) q^{89} +(-5.86479 + 13.8441i) q^{91} +(1.40687 + 1.40687i) q^{92} +(-1.09327 - 0.631199i) q^{93} +(1.14156 + 0.659078i) q^{94} +(1.31081 - 1.31081i) q^{96} +(-0.386897 - 0.670125i) q^{97} +(4.74815 + 8.22403i) q^{98} +(10.5878 - 10.5878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{4} - 12 q^{6} + 24 q^{9} + 8 q^{11} - 32 q^{16} - 24 q^{19} + 32 q^{21} + 56 q^{24} + 76 q^{26} - 36 q^{29} + 8 q^{31} + 44 q^{34} - 60 q^{36} + 44 q^{39} - 52 q^{41} - 80 q^{44} - 60 q^{46}+ \cdots + 208 q^{99}+O(q^{100}) \) 40 * q - 24 * q^4 - 12 * q^6 + 24 * q^9 + 8 * q^11 - 32 * q^16 - 24 * q^19 + 32 * q^21 + 56 * q^24 + 76 * q^26 - 36 * q^29 + 8 * q^31 + 44 * q^34 - 60 * q^36 + 44 * q^39 - 52 * q^41 - 80 * q^44 - 60 * q^46 + 28 * q^49 - 68 * q^54 + 72 * q^56 - 72 * q^59 + 144 * q^64 + 24 * q^66 - 80 * q^69 - 52 * q^71 + 168 * q^74 + 8 * q^76 - 20 * q^81 - 248 * q^84 - 168 * q^86 + 60 * q^89 - 100 * q^91 - 156 * q^94 - 36 * q^96 + 208 * q^99

Introduction

L-functions

Modular forms

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