LMFDB - Embedded newform 325.2.x.c.318.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(7,325)] 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, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.x (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			318.4
Character	$\chi$	$=$	325.318
Dual form			325.2.x.c.232.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.791616 - 0.457039i) q^{2} +(0.325736 - 0.0872808i) q^{3} +(-0.582230 - 1.00845i) q^{4} +(-0.297749 - 0.0797815i) q^{6} +(2.08500 + 3.61133i) q^{7} +2.89257i q^{8} +(-2.49959 + 1.44314i) q^{9} +(5.01101 - 1.34269i) q^{11} +(-0.277672 - 0.277672i) q^{12} +(2.17194 + 2.87797i) q^{13} -3.81171i q^{14} +(0.157557 - 0.272897i) q^{16} +(0.780215 - 2.91180i) q^{17} +2.63829 q^{18} +(1.43417 - 5.35240i) q^{19} +(0.994360 + 0.994360i) q^{21} +(-4.58045 - 1.22733i) q^{22} +(-0.442222 - 1.65039i) q^{23} +(0.252465 + 0.942213i) q^{24} +(-0.403995 - 3.27090i) q^{26} +(-1.40362 + 1.40362i) q^{27} +(2.42790 - 4.20525i) q^{28} +(7.08218 + 4.08890i) q^{29} +(-2.64703 + 2.64703i) q^{31} +(4.76062 - 2.74855i) q^{32} +(1.51507 - 0.874729i) q^{33} +(-1.94844 + 1.94844i) q^{34} +(2.91067 + 1.68048i) q^{36} +(-3.88050 + 6.72122i) q^{37} +(-3.58157 + 3.58157i) q^{38} +(0.958670 + 0.747890i) q^{39} +(-0.228680 - 0.853445i) q^{41} +(-0.332689 - 1.24161i) q^{42} +(0.839677 + 0.224991i) q^{43} +(-4.27160 - 4.27160i) q^{44} +(-0.404226 + 1.50859i) q^{46} +1.44206 q^{47} +(0.0275034 - 0.102644i) q^{48} +(-5.19446 + 8.99707i) q^{49} -1.01658i q^{51} +(1.63772 - 3.86593i) q^{52} +(0.405781 + 0.405781i) q^{53} +(1.75263 - 0.469616i) q^{54} +(-10.4460 + 6.03100i) q^{56} -1.86865i q^{57} +(-3.73758 - 6.47367i) q^{58} +(9.44885 + 2.53181i) q^{59} +(-2.28425 - 3.95643i) q^{61} +(3.30523 - 0.885633i) q^{62} +(-10.4233 - 6.01789i) q^{63} -5.65500 q^{64} -1.59914 q^{66} +(-6.15361 - 3.55279i) q^{67} +(-3.39068 + 0.908530i) q^{68} +(-0.288095 - 0.498996i) q^{69} +(-2.65984 - 0.712701i) q^{71} +(-4.17437 - 7.23023i) q^{72} -6.02847i q^{73} +(6.14372 - 3.54708i) q^{74} +(-6.23266 + 1.67004i) q^{76} +(15.2969 + 15.2969i) q^{77} +(-0.417083 - 1.03019i) q^{78} +12.5840i q^{79} +(3.99472 - 6.91905i) q^{81} +(-0.209031 + 0.780116i) q^{82} -8.44351 q^{83} +(0.423818 - 1.58171i) q^{84} +(-0.561871 - 0.561871i) q^{86} +(2.66380 + 0.713764i) q^{87} +(3.88383 + 14.4947i) q^{88} +(-3.79160 - 14.1504i) q^{89} +(-5.86479 + 13.8441i) q^{91} +(-1.40687 + 1.40687i) q^{92} +(-0.631199 + 1.09327i) q^{93} +(-1.14156 - 0.659078i) q^{94} +(1.31081 - 1.31081i) q^{96} +(0.670125 - 0.386897i) q^{97} +(8.22403 - 4.74815i) 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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.791616	−	0.457039i	−0.559757	−	0.323176i	0.193291	−	0.981141i	$-0.438084\pi$
$2$	−0.791616	−	0.457039i	−0.559757	−	0.323176i	−0.753048	+	0.657966i	$0.771417\pi$
$3$	0.325736	−	0.0872808i	0.188064	−	0.0503916i	−0.163558	−	0.986534i	$-0.552297\pi$
$3$	0.325736	−	0.0872808i	0.188064	−	0.0503916i	0.351622	+	0.936142i	$0.385630\pi$
$4$	−0.582230	−	1.00845i	−0.291115	−	0.504226i
$5$		0			0
$5$		0			0
$6$	−0.297749	−	0.0797815i	−0.121555	−	0.0325707i
$7$	2.08500	+	3.61133i	0.788056	+	1.36495i	0.927156	+	0.374675i	$0.122246\pi$
$7$	2.08500	+	3.61133i	0.788056	+	1.36495i	−0.139100	+	0.990278i	$0.544421\pi$
$8$			2.89257i			1.02268i
$9$	−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
$13$	2.17194	+	2.87797i	0.602387	+	0.798204i
$13$	2.17194	+	2.87797i	0.602387	+	0.798204i
$14$		−	3.81171i		−	1.01872i
$15$		0			0
$16$	0.157557	−	0.272897i	0.0393892	−	0.0682241i
$17$	0.780215	−	2.91180i	0.189230	−	0.706216i	−0.804455	−	0.594013i	$-0.797543\pi$
$17$	0.780215	−	2.91180i	0.189230	−	0.706216i	0.993685	−	0.112203i	$-0.0357907\pi$
$18$	2.63829			0.621850
$19$	1.43417	−	5.35240i	0.329022	−	1.22793i	−0.581185	−	0.813771i	$-0.697411\pi$
$19$	1.43417	−	5.35240i	0.329022	−	1.22793i	0.910207	−	0.414154i	$-0.135922\pi$
$20$		0			0
$21$	0.994360	+	0.994360i	0.216987	+	0.216987i
$22$	−4.58045	−	1.22733i	−0.976556	−	0.261667i
$23$	−0.442222	−	1.65039i	−0.0922096	−	0.344131i	0.904372	−	0.426745i	$-0.140340\pi$
$23$	−0.442222	−	1.65039i	−0.0922096	−	0.344131i	−0.996582	+	0.0826140i	$0.973673\pi$
$24$	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
$28$	2.42790	−	4.20525i	0.458830	−	0.794717i
$29$	7.08218	+	4.08890i	1.31513	+	0.759289i	0.982940	−	0.183924i	$-0.0588800\pi$
$29$	7.08218	+	4.08890i	1.31513	+	0.759289i	0.332187	+	0.943213i	$0.392213\pi$
$30$		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	$0.359133\pi$
$32$	4.76062	−	2.74855i	0.841567	−	0.485879i
$33$	1.51507	−	0.874729i	0.263741	−	0.152271i
$34$	−1.94844	+	1.94844i	−0.334155	+	0.334155i
$35$		0			0
$36$	2.91067	+	1.68048i	0.485112	+	0.280080i
$37$	−3.88050	+	6.72122i	−0.637950	+	1.10496i	0.347932	+	0.937520i	$0.386884\pi$
$37$	−3.88050	+	6.72122i	−0.637950	+	1.10496i	−0.985882	+	0.167442i	$0.946449\pi$
$38$	−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	$0.938646\pi$
$42$	−0.332689	−	1.24161i	−0.0513350	−	0.191585i
$43$	0.839677	+	0.224991i	0.128049	+	0.0343108i	0.322275	−	0.946646i	$-0.395553\pi$
$43$	0.839677	+	0.224991i	0.128049	+	0.0343108i	−0.194225	+	0.980957i	$0.562219\pi$
$44$	−4.27160	−	4.27160i	−0.643968	−	0.643968i
$45$		0			0
$46$	−0.404226	+	1.50859i	−0.0595998	+	0.222430i
$47$	1.44206			0.210346			0.105173	−	0.994454i	$-0.466460\pi$
$47$	1.44206			0.210346			0.105173	+	0.994454i	$0.466460\pi$
$48$	0.0275034	−	0.102644i	0.00396977	−	0.0148154i
$49$	−5.19446	+	8.99707i	−0.742066	+	1.28530i
$50$		0			0
$51$		−	1.01658i		−	0.142349i
$52$	1.63772	−	3.86593i	0.227111	−	0.536108i
$53$	0.405781	+	0.405781i	0.0557384	+	0.0557384i	0.734427	−	0.678688i	$-0.237451\pi$
$53$	0.405781	+	0.405781i	0.0557384	+	0.0557384i	−0.678688	+	0.734427i	$0.737451\pi$
$54$	1.75263	−	0.469616i	0.238503	−	0.0639066i
$55$		0			0
$56$	−10.4460	+	6.03100i	−1.39591	+	0.805927i
$57$		−	1.86865i		−	0.247508i
$58$	−3.73758	−	6.47367i	−0.490768	−	0.850035i
$59$	9.44885	+	2.53181i	1.23014	+	0.329614i	0.814632	−	0.579978i	$-0.196939\pi$
$59$	9.44885	+	2.53181i	1.23014	+	0.329614i	0.415504	+	0.909592i	$0.363605\pi$
$60$		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	$0.927810\pi$
$62$	3.30523	−	0.885633i	0.419764	−	0.112476i
$63$	−10.4233	−	6.01789i	−1.31321	−	0.758183i
$64$	−5.65500			−0.706875
$65$		0			0
$66$	−1.59914			−0.196841
$67$	−6.15361	−	3.55279i	−0.751783	−	0.434042i	0.0745551	−	0.997217i	$-0.476246\pi$
$67$	−6.15361	−	3.55279i	−0.751783	−	0.434042i	−0.826338	+	0.563175i	$0.809580\pi$
$68$	−3.39068	+	0.908530i	−0.411180	+	0.110175i
$69$	−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	$0.635579\pi$
$72$	−4.17437	−	7.23023i	−0.491955	−	0.852091i
$73$		−	6.02847i		−	0.705579i	−0.935703	−	0.352789i	$-0.885233\pi$
$73$		−	6.02847i		−	0.705579i	0.935703	−	0.352789i	$-0.114767\pi$
$74$	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
$78$	−0.417083	−	1.03019i	−0.0472253	−	0.116646i
$79$			12.5840i			1.41582i	0.706305	+	0.707908i	$0.250361\pi$
$79$			12.5840i			1.41582i	−0.706305	+	0.707908i	$0.749639\pi$
$80$		0			0
$81$	3.99472	−	6.91905i	0.443857	−	0.768784i
$82$	−0.209031	+	0.780116i	−0.0230837	+	0.0861494i
$83$	−8.44351			−0.926796			−0.463398	−	0.886150i	$-0.653370\pi$
$83$	−8.44351			−0.926796			−0.463398	+	0.886150i	$0.653370\pi$
$84$	0.423818	−	1.58171i	0.0462423	−	0.172579i
$85$		0			0
$86$	−0.561871	−	0.561871i	−0.0605882	−	0.0605882i
$87$	2.66380	+	0.713764i	0.285590	+	0.0765236i
$88$	3.88383	+	14.4947i	0.414018	+	1.54514i
$89$	−3.79160	−	14.1504i	−0.401908	−	1.49994i	−0.809687	−	0.586862i	$-0.800363\pi$
$89$	−3.79160	−	14.1504i	−0.401908	−	1.49994i	0.407779	−	0.913081i	$-0.366304\pi$
$90$		0			0
$91$	−5.86479	+	13.8441i	−0.614797	+	1.45126i
$92$	−1.40687	+	1.40687i	−0.146676	+	0.146676i
$93$	−0.631199	+	1.09327i	−0.0654523	+	0.113367i
$94$	−1.14156	−	0.659078i	−0.117743	−	0.0679788i
$95$		0			0
$96$	1.31081	−	1.31081i	0.133784	−	0.133784i
$97$	0.670125	−	0.386897i	0.0680408	−	0.0392834i	−0.465594	−	0.884999i	$-0.654159\pi$
$97$	0.670125	−	0.386897i	0.0680408	−	0.0392834i	0.533634	+	0.845715i	$0.320826\pi$
$98$	8.22403	−	4.74815i	0.830752	−	0.479635i
$99$	−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	$0.813424\pi$
$102$	−0.464616	+	0.804739i	−0.0460038	+	0.0796810i
$103$	−13.3476	+	13.3476i	−1.31518	+	1.31518i	−0.397641	+	0.917541i	$0.630171\pi$
$103$	−13.3476	+	13.3476i	−1.31518	+	1.31518i	−0.917541	+	0.397641i	$0.869829\pi$
$104$	−8.32471	+	6.28247i	−0.816305	+	0.616047i
$105$		0			0
$106$	−0.135765	−	0.506681i	−0.0131866	−	0.0492132i
$107$	−1.27306	−	4.75112i	−0.123071	−	0.459308i	0.876692	−	0.481051i	$-0.159745\pi$
$107$	−1.27306	−	4.75112i	−0.123071	−	0.459308i	−0.999764	+	0.0217436i	$0.993078\pi$
$108$	2.23270	+	0.598251i	0.214842	+	0.0575668i
$109$	−1.95993	−	1.95993i	−0.187727	−	0.187727i	0.606986	−	0.794713i	$-0.292379\pi$
$109$	−1.95993	−	1.95993i	−0.187727	−	0.187727i	−0.794713	+	0.606986i	$0.792379\pi$
$110$		0			0
$111$	−0.677385	+	2.52804i	−0.0642946	+	0.239951i
$112$	1.31402			0.124164
$113$	2.09813	−	7.83033i	0.197376	−	0.736616i	−0.794264	−	0.607573i	$-0.792143\pi$
$113$	2.09813	−	7.83033i	0.197376	−	0.736616i	0.991639	−	0.129042i	$-0.0411903\pi$
$114$	−0.854045	+	1.47925i	−0.0799887	+	0.138544i
$115$		0			0
$116$		−	9.52272i		−	0.884162i
$117$	−9.58226	−	4.05933i	−0.885880	−	0.375285i
$118$	−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
$122$			4.17596i			0.378074i
$123$	−0.148979	−	0.258039i	−0.0134330	−	0.0232666i
$124$	4.21058	+	1.12822i	0.378122	+	0.101317i
$125$		0			0
$126$	5.50083	+	9.52771i	0.490053	+	0.848796i
$127$	−3.04192	+	0.815081i	−0.269927	+	0.0723268i	−0.391244	−	0.920287i	$-0.627955\pi$
$127$	−3.04192	+	0.815081i	−0.269927	+	0.0723268i	0.121317	+	0.992614i	$0.461288\pi$
$128$	−5.04466	−	2.91253i	−0.445889	−	0.257434i
$129$	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	$0.376950\pi$
$132$	−1.76424	−	1.01859i	−0.153558	−	0.0886566i
$133$	22.3195	−	5.98050i	1.93535	−	0.518575i
$134$	3.24753	+	5.62488i	0.280544	+	0.485916i
$135$		0			0
$136$	8.42258	+	2.25682i	0.722231	+	0.193521i
$137$	−5.56872	−	9.64530i	−0.475768	−	0.824054i	0.523847	−	0.851812i	$-0.324496\pi$
$137$	−5.56872	−	9.64530i	−0.475768	−	0.824054i	−0.999615	+	0.0277585i	$0.991163\pi$
$138$			0.526684i			0.0448343i
$139$	12.0068	−	6.93216i	1.01841	−	0.587978i	0.104765	−	0.994497i	$-0.466591\pi$
$139$	12.0068	−	6.93216i	1.01841	−	0.587978i	0.913642	+	0.406519i	$0.133258\pi$
$140$		0			0
$141$	0.469731	−	0.125864i	0.0395585	−	0.0105997i
$142$	1.77983	+	1.77983i	0.149360	+	0.149360i
$143$	14.7478	+	11.5053i	1.23327	+	0.962118i
$144$			0.909506i			0.0757922i
$145$		0			0
$146$	−2.75525	+	4.77223i	−0.228026	+	0.394952i
$147$	−0.906753	+	3.38405i	−0.0747877	+	0.279111i
$148$	9.03737			0.742867
$149$	4.63818	−	17.3099i	0.379974	−	1.41808i	−0.465965	−	0.884803i	$-0.654293\pi$
$149$	4.63818	−	17.3099i	0.379974	−	1.41808i	0.845939	−	0.533280i	$-0.179041\pi$
$150$		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	$0.786319\pi$
$152$	15.4822	+	4.14844i	1.25577	+	0.336483i
$153$	2.25192	+	8.40427i	0.182057	+	0.679445i
$154$	−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	$-0.951857\pi$
$157$	−10.4990	+	10.4990i	−0.837914	+	0.837914i	0.150670	+	0.988584i	$0.451857\pi$
$158$	5.75140	−	9.96172i	0.457557	−	0.792512i
$159$	0.167595	+	0.0967608i	0.0132911	+	0.00767363i
$160$		0			0
$161$	5.03808	−	5.03808i	0.397057	−	0.397057i
$162$	−6.32456	+	3.65149i	−0.496904	+	0.286888i
$163$	2.48103	−	1.43243i	0.194330	−	0.112196i	−0.399678	−	0.916655i	$-0.630878\pi$
$163$	2.48103	−	1.43243i	0.194330	−	0.112196i	0.594008	+	0.804459i	$0.297545\pi$
$164$	−0.727514	+	0.727514i	−0.0568093	+	0.0568093i
$165$		0			0
$166$	6.68401	+	3.85902i	0.518780	+	0.299518i
$167$	1.82320	−	3.15787i	0.141083	−	0.244363i	−0.786822	−	0.617180i	$-0.788275\pi$
$167$	1.82320	−	3.15787i	0.141083	−	0.244363i	0.927905	+	0.372817i	$0.121608\pi$
$168$	−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
$172$	−0.261993	−	0.977770i	−0.0199767	−	0.0745542i
$173$	7.11663	+	1.90689i	0.541067	+	0.144978i	0.518994	−	0.854778i	$-0.326307\pi$
$173$	7.11663	+	1.90689i	0.541067	+	0.144978i	0.0220730	+	0.999756i	$0.492973\pi$
$174$	−1.78249	−	1.78249i	−0.135130	−	0.135130i
$175$		0			0
$176$	0.423102	−	1.57904i	0.0318925	−	0.119024i
$177$	3.29881			0.247954
$178$	−3.46582	+	12.9346i	−0.259774	+	0.969490i
$179$	−5.02174	+	8.69791i	−0.375343	+	0.650113i	−0.990378	−	0.138387i	$-0.955808\pi$
$179$	−5.02174	+	8.69791i	−0.375343	+	0.650113i	0.615036	+	0.788499i	$0.289142\pi$
$180$		0			0
$181$		−	10.0395i		−	0.746233i	−0.927785	−	0.373116i	$-0.878289\pi$
$181$		−	10.0395i		−	0.746233i	0.927785	−	0.373116i	$-0.121711\pi$
$182$	10.9700	−	8.27880i	0.813149	−	0.613665i
$183$	−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
$187$		−	15.6387i		−	1.14361i
$188$	−0.839611	−	1.45425i	−0.0612349	−	0.106062i
$189$	−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	$-0.374743\pi$
$192$	−1.84204	+	0.493573i	−0.132938	+	0.0356206i
$193$	−14.7083	−	8.49185i	−1.05873	−	0.611257i	−0.133648	−	0.991029i	$-0.542669\pi$
$193$	−14.7083	−	8.49185i	−1.05873	−	0.611257i	−0.925080	+	0.379772i	$0.876002\pi$
$194$	−0.707308			−0.0507818
$195$		0			0
$196$	12.0975			0.864106
$197$	3.91848	+	2.26234i	0.279180	+	0.161185i	0.633052	−	0.774109i	$-0.281802\pi$
$197$	3.91848	+	2.26234i	0.279180	+	0.161185i	−0.353872	+	0.935294i	$0.615135\pi$
$198$	13.2205	−	3.54241i	0.939538	−	0.251748i
$199$	−4.08425	−	7.07413i	−0.289525	−	0.501472i	0.684171	−	0.729321i	$-0.260164\pi$
$199$	−4.08425	−	7.07413i	−0.289525	−	0.501472i	−0.973696	+	0.227849i	$0.926831\pi$
$200$		0			0
$201$	−2.31454	−	0.620180i	−0.163255	−	0.0437441i
$202$	4.08694	+	7.07879i	0.287556	+	0.498062i
$203$			34.1014i			2.39345i
$204$	−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
$208$	1.12759	−	0.139271i	0.0781843	−	0.00965668i
$209$		−	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	$0.328136\pi$
$212$	0.172953	−	0.645469i	0.0118785	−	0.0443310i
$213$	−0.928610			−0.0636273
$214$	−1.16368	+	4.34289i	−0.0795472	+	0.296874i
$215$		0			0
$216$	−4.06005	−	4.06005i	−0.276251	−	0.276251i
$217$	−15.0784	−	4.04023i	−1.02359	−	0.274269i
$218$	0.655745	+	2.44727i	0.0444127	+	0.165750i
$219$	−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
$223$	10.6155	−	18.3866i	0.710865	−	1.23125i	−0.253667	−	0.967291i	$-0.581637\pi$
$223$	10.6155	−	18.3866i	0.710865	−	1.23125i	0.964533	−	0.263963i	$-0.0850298\pi$
$224$	19.8518	+	11.4614i	1.32640	+	0.765800i
$225$		0			0
$226$	−5.23968	+	5.23968i	−0.348539	+	0.348539i
$227$	−13.3865	+	7.72867i	−0.888490	+	0.512970i	−0.873448	−	0.486917i	$-0.838121\pi$
$227$	−13.3865	+	7.72867i	−0.888490	+	0.512970i	−0.0150418	+	0.999887i	$0.504788\pi$
$228$	−1.88444	+	1.08798i	−0.124800	+	0.0720534i
$229$	−4.47959	+	4.47959i	−0.296020	+	0.296020i	−0.839453	−	0.543433i	$-0.817124\pi$
$229$	−4.47959	+	4.47959i	−0.296020	+	0.296020i	0.543433	+	0.839453i	$0.317124\pi$
$230$		0			0
$231$	6.31786	+	3.64762i	0.415685	+	0.239996i
$232$	−11.8274	+	20.4857i	−0.776507	+	1.34495i
$233$	−3.54772	+	3.54772i	−0.232419	+	0.232419i	−0.813702	−	0.581283i	$-0.802551\pi$
$233$	−3.54772	+	3.54772i	−0.232419	+	0.232419i	0.581283	+	0.813702i	$0.302551\pi$
$234$	5.73019	+	7.59290i	0.374594	+	0.496363i
$235$		0			0
$236$	−2.94819	−	11.0028i	−0.191911	−	0.716222i
$237$	1.09834	+	4.09908i	0.0713452	+	0.266264i
$238$	−11.0990	−	2.97396i	−0.719438	−	0.192773i
$239$	3.55914	+	3.55914i	0.230222	+	0.230222i	0.812785	−	0.582563i	$-0.197950\pi$
$239$	3.55914	+	3.55914i	0.230222	+	0.230222i	−0.582563	+	0.812785i	$0.697950\pi$
$240$		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	$0.0907774\pi$
$242$	−14.5457			−0.935036
$243$	2.23860	−	8.35457i	0.143606	−	0.535946i
$244$	−2.65991	+	4.60711i	−0.170284	+	0.294940i
$245$		0			0
$246$			0.272356i			0.0173648i
$247$	18.5190	−	7.49758i	1.17833	−	0.477060i
$248$	−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	$0.484461\pi$
$252$			14.0152i			0.882874i
$253$	−4.43195	−	7.67637i	−0.278634	−	0.482609i
$254$	2.78056	+	0.745049i	0.174468	+	0.0467485i
$255$		0			0
$256$	8.31729	+	14.4060i	0.519831	+	0.900373i
$257$	30.2770	−	8.11269i	1.88862	−	0.506056i	0.889868	−	0.456219i	$-0.150797\pi$
$257$	30.2770	−	8.11269i	1.88862	−	0.506056i	0.998757	−	0.0498367i	$-0.0158701\pi$
$258$	−0.232062	−	0.133981i	−0.0144476	−	0.00834131i
$259$	−32.3634			−2.01096
$260$		0			0
$261$	−23.6034			−1.46101
$262$	−6.83187	−	3.94438i	−0.422074	−	0.243685i
$263$	−19.6281	+	5.25932i	−1.21032	+	0.324304i	−0.806887	−	0.590706i	$-0.798849\pi$
$263$	−19.6281	+	5.25932i	−1.21032	+	0.324304i	−0.403431	+	0.915010i	$0.632183\pi$
$264$	2.53021	+	4.38245i	0.155724	+	0.269721i
$265$		0			0
$266$	−20.4018	−	5.46665i	−1.25092	−	0.335182i
$267$	−2.47012	−	4.27837i	−0.151169	−	0.261832i
$268$			8.27415i			0.505424i
$269$	−20.6369	+	11.9147i	−1.25825	+	0.726453i	−0.972735	−	0.231919i	$-0.925499\pi$
$269$	−20.6369	+	11.9147i	−1.25825	+	0.726453i	−0.285519	+	0.958373i	$0.592166\pi$
$270$		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
$273$	−0.702047	+	5.02142i	−0.0424898	+	0.303910i
$274$			10.1805i			0.615026i
$275$		0			0
$276$	−0.335475	+	0.581061i	−0.0201932	+	0.0349757i
$277$	6.59777	−	24.6232i	0.396422	−	1.47947i	−0.422923	−	0.906165i	$-0.638996\pi$
$277$	6.59777	−	24.6232i	0.396422	−	1.47947i	0.819345	−	0.573301i	$-0.194337\pi$
$278$	−12.6731			−0.760081
$279$	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	$0.622539\pi$
$282$	−0.429371	−	0.115050i	−0.0255687	−	0.00685111i
$283$	−2.62440	−	9.79438i	−0.156004	−	0.582216i	−0.999017	−	0.0443225i	$-0.985887\pi$
$283$	−2.62440	−	9.79438i	−0.156004	−	0.582216i	0.843013	−	0.537893i	$-0.180780\pi$
$284$	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
$288$	−7.93307	+	13.7405i	−0.467461	+	0.809665i
$289$	6.85257	+	3.95633i	0.403092	+	0.232725i
$290$		0			0
$291$	0.184515	−	0.184515i	0.0108165	−	0.0108165i
$292$	−6.07942	+	3.50995i	−0.355771	+	0.205405i
$293$	10.2409	−	5.91259i	0.598280	−	0.345417i	−0.170085	−	0.985429i	$-0.554404\pi$
$293$	10.2409	−	5.91259i	0.598280	−	0.345417i	0.768365	+	0.640012i	$0.221071\pi$
$294$	2.26444	−	2.26444i	0.132065	−	0.132065i
$295$		0			0
$296$	−19.4416	−	11.2246i	−1.13002	−	0.652416i
$297$	−5.14890	+	8.91815i	−0.298769	+	0.517484i
$298$	−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
$302$	0.661966	+	2.47049i	0.0380918	+	0.142161i
$303$	−2.91280	−	0.780483i	−0.167336	−	0.0448376i
$304$	−1.23469	−	1.23469i	−0.0708142	−	0.0708142i
$305$		0			0
$306$	2.05843	−	7.68217i	0.117673	−	0.439160i
$307$	24.7916			1.41493			0.707467	−	0.706747i	$-0.249838\pi$
$307$	24.7916			1.41493			0.707467	+	0.706747i	$0.249838\pi$
$308$	6.51986	−	24.3324i	0.371503	−	1.38647i
$309$	−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	$0.757151\pi$
$312$	−2.16332	+	2.77301i	−0.122474	+	0.156991i
$313$	8.82280	+	8.82280i	0.498694	+	0.498694i	0.911031	−	0.412337i	$-0.135287\pi$
$313$	8.82280	+	8.82280i	0.498694	+	0.498694i	−0.412337	+	0.911031i	$0.635287\pi$
$314$	13.1097	−	3.51273i	0.739822	−	0.198235i
$315$		0			0
$316$	12.6904	−	7.32681i	0.713891	−	0.412165i
$317$		−	3.43365i		−	0.192853i	−0.995340	−	0.0964266i	$-0.969259\pi$
$317$		−	3.43365i		−	0.192853i	0.995340	−	0.0964266i	$-0.0307413\pi$
$318$	−0.0884470	−	0.153195i	−0.00495986	−	0.00859073i
$319$	40.9790	+	10.9803i	2.29438	+	0.614778i
$320$		0			0
$321$	−0.829362	−	1.43650i	−0.0462905	−	0.0801774i
$322$	−6.29083	+	1.68562i	−0.350574	+	0.0939360i
$323$	−14.4662	−	8.35205i	−0.804920	−	0.464721i
$324$	−9.30338			−0.516854
$325$		0			0
$326$	−2.61870			−0.145036
$327$	−0.809483	−	0.467355i	−0.0447645	−	0.0258448i
$328$	2.46865	−	0.661472i	0.136308	−	0.0365237i
$329$	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	$0.627785\pi$
$332$	4.91606	+	8.51487i	0.269804	+	0.467314i
$333$		−	22.4004i		−	1.22753i
$334$	−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	0.520845	−	0.853651i	$-0.325617\pi$
$337$	−6.10952	−	6.10952i	−0.332807	−	0.332807i	−0.853651	+	0.520845i	$0.825617\pi$
$338$	8.53610	−	8.26688i	0.464303	−	0.449659i
$339$		−	2.73375i		−	0.148477i
$340$		0			0
$341$	−9.71013	+	16.8184i	−0.525833	+	0.910770i
$342$	3.78375	−	14.1212i	0.204602	−	0.763585i
$343$	−14.1318			−0.763045
$344$	−0.650800	+	2.42882i	−0.0350888	+	0.130953i
$345$		0			0
$346$	−4.76211	−	4.76211i	−0.256012	−	0.256012i
$347$	−28.0458	−	7.51485i	−1.50558	−	0.403418i	−0.590614	−	0.806954i	$-0.701114\pi$
$347$	−28.0458	−	7.51485i	−1.50558	−	0.403418i	−0.914964	+	0.403536i	$0.867781\pi$
$348$	−0.831150	−	3.10189i	−0.0445543	−	0.166279i
$349$	0.992964	+	3.70579i	0.0531522	+	0.198367i	0.987396	−	0.158268i	$-0.0505909\pi$
$349$	0.992964	+	3.70579i	0.0531522	+	0.198367i	−0.934244	+	0.356634i	$0.883924\pi$
$350$		0			0
$351$	−7.08812	−	0.990994i	−0.378336	−	0.0528953i
$352$	20.1650	−	20.1650i	1.07480	−	1.07480i
$353$	12.7844	−	22.1433i	0.680446	−	1.17857i	−0.294399	−	0.955683i	$-0.595119\pi$
$353$	12.7844	−	22.1433i	0.680446	−	1.17857i	0.974845	−	0.222884i	$-0.0715472\pi$
$354$	−2.61139	−	1.50769i	−0.138794	−	0.0801327i
$355$		0			0
$356$	−12.0624	+	12.0624i	−0.639308	+	0.639308i
$357$	3.67120	−	2.11957i	0.194300	−	0.112179i
$358$	7.95058	−	4.59027i	0.420201	−	0.242603i
$359$	16.4517	−	16.4517i	0.868286	−	0.868286i	−0.123997	−	0.992283i	$-0.539571\pi$
$359$	16.4517	−	16.4517i	0.868286	−	0.868286i	0.992283	+	0.123997i	$0.0395713\pi$
$360$		0			0
$361$	−10.1369	−	5.85252i	−0.533519	−	0.308028i
$362$	−4.58846	+	7.94745i	−0.241164	+	0.417709i
$363$	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
$367$	−3.07127	−	11.4621i	−0.160319	−	0.598319i	−0.998591	−	0.0530664i	$-0.983101\pi$
$367$	−3.07127	−	11.4621i	−0.160319	−	0.598319i	0.838272	−	0.545252i	$-0.183566\pi$
$368$	−0.520062	−	0.139350i	−0.0271101	−	0.00726413i
$369$	1.80325	+	1.80325i	0.0938732	+	0.0938732i
$370$		0			0
$371$	−0.619355	+	2.31146i	−0.0321553	+	0.120005i
$372$	1.47001			0.0762166
$373$	−1.08081	+	4.03365i	−0.0559624	+	0.208855i	−0.988246	−	0.152875i	$-0.951147\pi$
$373$	−1.08081	+	4.03365i	−0.0559624	+	0.208855i	0.932283	+	0.361729i	$0.117814\pi$
$374$	−7.14748	+	12.3798i	−0.369588	+	0.640144i
$375$		0			0
$376$			4.17125i			0.215116i
$377$	3.61434	+	29.2631i	0.186148	+	1.50713i
$378$	5.35018	+	5.35018i	0.275183	+	0.275183i
$379$	−10.7615	+	2.88353i	−0.552781	+	0.148117i	−0.524388	−	0.851480i	$-0.675706\pi$
$379$	−10.7615	+	2.88353i	−0.552781	+	0.148117i	−0.0283931	+	0.999597i	$0.509039\pi$
$380$		0			0
$381$	−0.919724	+	0.531003i	−0.0471189	+	0.0272041i
$382$			15.3646i			0.786119i
$383$	3.67047	+	6.35744i	0.187552	+	0.324850i	0.944434	−	0.328702i	$-0.106611\pi$
$383$	3.67047	+	6.35744i	0.187552	+	0.324850i	−0.756881	+	0.653552i	$0.773278\pi$
$384$	−1.89743	−	0.508416i	−0.0968281	−	0.0259450i
$385$		0			0
$386$	7.76222	+	13.4446i	0.395087	+	0.684310i
$387$	−2.42354	+	0.649386i	−0.123195	+	0.0330101i
$388$	−0.780333	−	0.450526i	−0.0396154	−	0.0228720i
$389$	−26.6060			−1.34898			−0.674488	−	0.738286i	$-0.735636\pi$
$389$	−26.6060			−1.34898			−0.674488	+	0.738286i	$0.735636\pi$
$390$		0			0
$391$	−5.15065			−0.260480
$392$	−26.0246	−	15.0253i	−1.31444	−	0.758893i
$393$	2.81120	−	0.753258i	0.141806	−	0.0379969i
$394$	−2.06796	−	3.58180i	−0.104182	−	0.180449i
$395$		0			0
$396$	16.8418	+	4.51274i	0.846330	+	0.226774i
$397$	−10.5686	−	18.3053i	−0.530421	−	0.918717i	−0.999370	−	0.0354913i	$-0.988700\pi$
$397$	−10.5686	−	18.3053i	−0.530421	−	0.918717i	0.468949	−	0.883225i	$-0.344633\pi$
$398$			7.46666i			0.374270i
$399$	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
$403$	−13.3673	−	1.86888i	−0.665870	−	0.0930957i
$404$			10.4128i			0.518058i
$405$		0			0
$406$	15.5857	−	26.9952i	0.773505	−	1.33975i
$407$	−10.4206	+	38.8904i	−0.516532	+	1.92772i
$408$	2.94052			0.145577
$409$	−3.27126	+	12.2085i	−0.161753	+	0.603672i	0.836679	+	0.547694i	$0.184494\pi$
$409$	−3.27126	+	12.2085i	−0.161753	+	0.603672i	−0.998432	+	0.0559775i	$0.982172\pi$
$410$		0			0
$411$	−2.65578	−	2.65578i	−0.131000	−	0.131000i
$412$	21.2318	+	5.68906i	1.04602	+	0.280280i
$413$	10.5577	+	39.4017i	0.519509	+	1.93883i
$414$	−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
$418$	−13.1383	+	22.7562i	−0.642616	+	1.11304i
$419$	−19.9068	−	11.4932i	−0.972511	−	0.561480i	−0.0725104	−	0.997368i	$-0.523101\pi$
$419$	−19.9068	−	11.4932i	−0.972511	−	0.561480i	−0.900001	+	0.435888i	$0.856434\pi$
$420$		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	$-0.0861627\pi$
$422$	11.1722	−	6.45025i	0.543852	−	0.313993i
$423$	−3.60456	+	2.08109i	−0.175260	+	0.101186i
$424$	−1.17375	+	1.17375i	−0.0570023	+	0.0570023i
$425$		0			0
$426$	0.735102	+	0.424411i	0.0356158	+	0.0205628i
$427$	9.52532	−	16.4983i	0.460962	−	0.798410i
$428$	−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	$0.886633\pi$
$432$	0.161892	+	0.604191i	0.00778905	+	0.0290691i
$433$	33.2862	+	8.91900i	1.59963	+	0.428620i	0.944931	−	0.327269i	$-0.106128\pi$
$433$	33.2862	+	8.91900i	1.59963	+	0.428620i	0.654700	+	0.755889i	$0.272795\pi$
$434$	10.0897	+	10.0897i	0.484322	+	0.484322i
$435$		0			0
$436$	−0.835364	+	3.11762i	−0.0400067	+	0.149307i
$437$	−9.46780			−0.452906
$438$	−0.480960	+	1.79497i	−0.0229812	+	0.0857669i
$439$	11.1274	−	19.2732i	0.531081	−	0.919859i	−0.468261	−	0.883590i	$-0.655119\pi$
$439$	11.1274	−	19.2732i	0.531081	−	0.919859i	0.999342	−	0.0362692i	$-0.0115474\pi$
$440$		0			0
$441$		−	29.9853i		−	1.42787i
$442$	−9.83943	−	1.37566i	−0.468014	−	0.0654333i
$443$	−2.45786	−	2.45786i	−0.116776	−	0.116776i	0.646304	−	0.763080i	$-0.276314\pi$
$443$	−2.45786	−	2.45786i	−0.116776	−	0.116776i	−0.763080	+	0.646304i	$0.776314\pi$
$444$	2.94380	−	0.788788i	0.139706	−	0.0374342i
$445$		0			0
$446$	−16.8068	+	9.70339i	−0.795823	+	0.459469i
$447$		−	6.04329i		−	0.285838i
$448$	−11.7907	−	20.4221i	−0.557058	−	0.964852i
$449$	−27.1100	−	7.26410i	−1.27940	−	0.342814i	−0.445775	−	0.895145i	$-0.647072\pi$
$449$	−27.1100	−	7.26410i	−1.27940	−	0.342814i	−0.833625	+	0.552331i	$0.813738\pi$
$450$		0			0
$451$	−2.29183	−	3.96957i	−0.107918	−	0.186920i
$452$	−9.11811	+	2.44319i	−0.428880	+	0.114918i
$453$	−0.817163	−	0.471789i	−0.0383936	−	0.0221666i
$454$	14.1292			0.663118
$455$		0			0
$456$	5.40518			0.253121
$457$	32.0795	+	18.5211i	1.50062	+	0.866381i	1.00000		0.000712325i	$0.000226740\pi$
$457$	32.0795	+	18.5211i	1.50062	+	0.866381i	0.500617	+	0.865669i	$0.333107\pi$
$458$	5.59346	−	1.49876i	0.261365	−	0.0700326i
$459$	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	$0.199169\pi$
$462$	−3.33421	−	5.77503i	−0.155122	−	0.268679i
$463$		−	3.45704i		−	0.160663i	−0.996768	−	0.0803313i	$-0.974402\pi$
$463$		−	3.45704i		−	0.160663i	0.996768	−	0.0803313i	$-0.0255978\pi$
$464$	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	0.588445	−	0.808537i	$-0.299740\pi$
$467$	−4.75622	−	4.75622i	−0.220092	−	0.220092i	−0.808537	+	0.588445i	$0.799740\pi$
$468$	1.48544	+	12.0267i	0.0686644	+	0.555935i
$469$		−	29.6302i		−	1.36820i
$470$		0			0
$471$	−2.50355	+	4.33628i	−0.115358	+	0.199805i
$472$	−7.32344	+	27.3314i	−0.337088	+	1.25803i
$473$	4.50972			0.207357
$474$	1.00397	−	3.74688i	0.0461140	−	0.172100i
$475$		0			0
$476$	−10.3506	−	10.3506i	−0.474417	−	0.474417i
$477$	−1.59989	−	0.428688i	−0.0732538	−	0.0196283i
$478$	−1.19080	−	4.44414i	−0.0544661	−	0.203270i
$479$	−0.0302527	−	0.112905i	−0.00138228	−	0.00515874i	0.965231	−	0.261397i	$-0.0841833\pi$
$479$	−0.0302527	−	0.112905i	−0.00138228	−	0.00515874i	−0.966614	+	0.256239i	$0.917517\pi$
$480$		0			0
$481$	−27.7716	+	3.43012i	−1.26628	+	0.156400i
$482$	0.469273	−	0.469273i	0.0213748	−	0.0213748i
$483$	1.20136	−	2.08081i	0.0546637	−	0.0946803i
$484$	−16.0475	−	9.26503i	−0.729432	−	0.421138i
$485$		0			0
$486$	−5.59048	+	5.59048i	−0.253589	+	0.253589i
$487$	−9.21841	+	5.32225i	−0.417726	+	0.241174i	−0.694104	−	0.719875i	$-0.744199\pi$
$487$	−9.21841	+	5.32225i	−0.417726	+	0.241174i	0.276378	+	0.961049i	$0.410866\pi$
$488$	11.4442	−	6.60734i	0.518057	−	0.299100i
$489$	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	$0.418126\pi$
$492$	−0.173480	+	0.300476i	−0.00782107	+	0.0135465i
$493$	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
$497$	−2.97196	−	11.0915i	−0.133311	−	0.497523i
$498$	2.51404	+	0.673636i	0.112657	+	0.0301863i
$499$	−6.58133	−	6.58133i	−0.294621	−	0.294621i	0.544282	−	0.838903i	$-0.316802\pi$
$499$	−6.58133	−	6.58133i	−0.294621	−	0.294621i	−0.838903	+	0.544282i	$0.816802\pi$
$500$		0			0
$501$	0.318260	−	1.18776i	0.0142188	−	0.0530653i
$502$	13.2405			0.590952
$503$	−11.0497	+	41.2382i	−0.492683	+	1.83872i	0.0499533	+	0.998752i	$0.484093\pi$
$503$	−11.0497	+	41.2382i	−0.492683	+	1.83872i	−0.542637	+	0.839968i	$0.682574\pi$
$504$	17.4072	−	30.1501i	0.775376	−	1.34299i
$505$		0			0
$506$			8.10231i			0.360192i
$507$	−0.0702315	+	4.38339i	−0.00311909	+	0.194673i
$508$	2.59307	+	2.59307i	0.115049	+	0.115049i
$509$	11.1097	−	2.97683i	0.492429	−	0.131946i	−0.00405535	−	0.999992i	$-0.501291\pi$
$509$	11.1097	−	2.97683i	0.492429	−	0.131946i	0.496484	+	0.868046i	$0.334624\pi$
$510$		0			0
$511$	21.7708	−	12.5694i	0.963082	−	0.556036i
$512$		−	3.55518i		−	0.157118i
$513$	5.49969	+	9.52574i	0.242817	+	0.420572i
$514$	−27.6755	−	7.41564i	−1.22072	−	0.327090i
$515$		0			0
$516$	−0.170681	−	0.295628i	−0.00751381	−	0.0130143i
$517$	7.22617	−	1.93625i	0.317807	−	0.0851561i
$518$	25.6193	+	14.7913i	1.12565	+	0.649894i
$519$	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	$0.431615\pi$
$522$	18.6848	+	10.7877i	0.817812	+	0.472164i
$523$	11.3473	−	3.04051i	0.496184	−	0.132952i	−0.00204420	−	0.999998i	$-0.500651\pi$
$523$	11.3473	−	3.04051i	0.496184	−	0.132952i	0.498229	+	0.867046i	$0.333984\pi$
$524$	−5.02481	−	8.70323i	−0.219510	−	0.380202i
$525$		0			0
$526$	17.9416	+	4.80744i	0.782291	+	0.209614i
$527$	5.64238	+	9.77289i	0.245786	+	0.425714i
$528$		−	0.551278i		−	0.0239913i
$529$	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
$533$	1.95951	−	2.51176i	0.0848757	−	0.108796i
$534$			4.51577i			0.195416i
$535$		0			0
$536$	10.2767	−	17.7997i	0.443884	−	0.768830i
$537$	−0.876603	+	3.27153i	−0.0378282	+	0.141177i
$538$	21.7820			0.939088
$539$	−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	$0.600394\pi$
$542$	5.84671	+	1.56662i	0.251138	+	0.0672922i
$543$	−0.876258	−	3.27024i	−0.0376038	−	0.140339i
$544$	−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	−0.606266	+	0.795262i	$0.707333\pi$
$547$	−32.7790	+	32.7790i	−1.40153	+	1.40153i	−0.795262	+	0.606266i	$0.792667\pi$
$548$	−6.48455	+	11.2316i	−0.277006	+	0.479789i
$549$	11.4194	+	6.59297i	0.487367	+	0.281381i
$550$		0			0
$551$	32.0425	−	32.0425i	1.36506	−	1.36506i
$552$	1.44338	−	0.833335i	0.0614343	−	0.0354691i
$553$	−45.4451	+	26.2377i	−1.93252	+	1.11574i
$554$	−16.4767	+	16.4767i	−0.700027	+	0.700027i
$555$		0			0
$556$	−13.9815	−	8.07222i	−0.592947	−	0.342338i
$557$	18.9999	−	32.9089i	0.805053	−	1.39439i	−0.111202	−	0.993798i	$-0.535470\pi$
$557$	18.9999	−	32.9089i	0.805053	−	1.39439i	0.916255	−	0.400595i	$-0.131197\pi$
$558$	−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
$562$	−3.09187	−	11.5390i	−0.130423	−	0.486744i
$563$	−27.3048	−	7.31631i	−1.15076	−	0.308346i	−0.367492	−	0.930027i	$-0.619783\pi$
$563$	−27.3048	−	7.31631i	−1.15076	−	0.308346i	−0.783270	+	0.621681i	$0.786450\pi$
$564$	−0.400419	−	0.400419i	−0.0168607	−	0.0168607i
$565$		0			0
$566$	−2.39891	+	8.95284i	−0.100834	+	0.376316i
$567$	33.3160			1.39914
$568$	2.06153	−	7.69375i	0.0865000	−	0.322823i
$569$	7.77409	−	13.4651i	0.325907	−	0.564487i	−0.655789	−	0.754945i	$-0.727664\pi$
$569$	7.77409	−	13.4651i	0.325907	−	0.564487i	0.981695	+	0.190457i	$0.0609971\pi$
$570$		0			0
$571$			27.1740i			1.13720i	0.822616	+	0.568598i	$0.192514\pi$
$571$			27.1740i			1.13720i	−0.822616	+	0.568598i	$0.807486\pi$
$572$	3.01588	−	21.5712i	0.126100	−	0.901936i
$573$	−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
$577$			36.9310i			1.53746i	0.639574	+	0.768730i	$0.279111\pi$
$577$			36.9310i			1.53746i	−0.639574	+	0.768730i	$0.720889\pi$
$578$	−3.61640	−	6.26379i	−0.150422	−	0.260539i
$579$	−5.53221	−	1.48235i	−0.229911	−	0.0616044i
$580$		0			0
$581$	−17.6047	−	30.4923i	−0.730367	−	1.26503i
$582$	−0.230396	+	0.0617344i	−0.00955022	+	0.00255897i
$583$	2.57821	+	1.48853i	0.106779	+	0.0616487i
$584$	17.4377			0.721579
$585$		0			0
$586$	−10.8091			−0.446522
$587$	−22.2508	−	12.8465i	−0.918388	−	0.530232i	−0.0352676	−	0.999378i	$-0.511228\pi$
$587$	−22.2508	−	12.8465i	−0.918388	−	0.530232i	−0.883120	+	0.469146i	$0.844562\pi$
$588$	3.94059	−	1.05588i	0.162507	−	0.0435436i
$589$	10.3717	+	17.9643i	0.427357	+	0.740205i
$590$		0			0
$591$	1.47385	+	0.394917i	0.0606261	+	0.0162447i
$592$	1.22280	+	2.11795i	0.0502567	+	0.0870471i
$593$		−	21.2325i		−	0.871915i	−0.899967	−	0.435958i	$-0.856410\pi$
$593$		−	21.2325i		−	0.871915i	0.899967	−	0.435958i	$-0.143590\pi$
$594$	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
$598$	−5.21963	+	2.11322i	−0.213446	+	0.0864158i
$599$			21.3026i			0.870403i	0.900333	+	0.435201i	$0.143323\pi$
$599$			21.3026i			0.870403i	−0.900333	+	0.435201i	$0.856677\pi$
$600$		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	$0.173835\pi$
$602$	0.857599	−	3.20060i	0.0349531	−	0.130447i
$603$	20.5087			0.835177
$604$	−0.843289	+	3.14720i	−0.0343129	+	0.128058i
$605$		0			0
$606$	1.94911	+	1.94911i	0.0791771	+	0.0791771i
$607$	20.4911	+	5.49058i	0.831709	+	0.222856i	0.649459	−	0.760397i	$-0.274995\pi$
$607$	20.4911	+	5.49058i	0.831709	+	0.222856i	0.182250	+	0.983252i	$0.441662\pi$
$608$	−7.88377	−	29.4226i	−0.319729	−	1.19325i
$609$	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
$613$	−4.40529	+	7.63018i	−0.177928	+	0.308180i	−0.941171	−	0.337932i	$-0.890273\pi$
$613$	−4.40529	+	7.63018i	−0.177928	+	0.308180i	0.763243	+	0.646112i	$0.223606\pi$
$614$	−19.6254	−	11.3308i	−0.792018	−	0.457272i
$615$		0			0
$616$	−44.2472	+	44.2472i	−1.78277	+	1.78277i
$617$	−36.1750	+	20.8856i	−1.45635	+	0.840825i	−0.998829	−	0.0483741i	$-0.984596\pi$
$617$	−36.1750	+	20.8856i	−1.45635	+	0.840825i	−0.457521	+	0.889199i	$0.651263\pi$
$618$	5.03914	−	2.90935i	0.202704	−	0.117031i
$619$	0.180435	−	0.180435i	0.00725231	−	0.00725231i	−0.703471	−	0.710724i	$-0.748368\pi$
$619$	0.180435	−	0.180435i	0.00725231	−	0.00725231i	0.710724	+	0.703471i	$0.248368\pi$
$620$		0			0
$621$	2.93723	+	1.69581i	0.117867	+	0.0680505i
$622$	11.1396	−	19.2944i	0.446658	−	0.773634i
$623$	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
$627$	−2.50902	−	9.36380i	−0.100201	−	0.373954i
$628$	16.7006	+	4.47492i	0.666427	+	0.178569i
$629$	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	$0.148208\pi$
$632$	−36.4002			−1.44792
$633$	−1.23180	+	4.59715i	−0.0489598	+	0.182720i
$634$	−1.56931	+	2.71813i	−0.0623254	+	0.107951i
$635$		0			0
$636$		−	0.225348i		−	0.00893563i
$637$	−37.1753	+	4.59158i	−1.47294	+	0.181925i
$638$	−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	$0.361518\pi$
$642$			1.51620i			0.0598398i
$643$	9.40328	+	16.2870i	0.370829	+	0.642295i	0.989693	−	0.143203i	$-0.0457402\pi$
$643$	9.40328	+	16.2870i	0.370829	+	0.642295i	−0.618864	+	0.785498i	$0.712407\pi$
$644$	−8.01399	−	2.14734i	−0.315795	−	0.0846171i
$645$		0			0
$646$	7.63443	+	13.2232i	0.300373	+	0.520261i
$647$	−13.7267	+	3.67805i	−0.539652	+	0.144599i	−0.518342	−	0.855174i	$-0.673450\pi$
$647$	−13.7267	+	3.67805i	−0.539652	+	0.144599i	−0.0213101	+	0.999773i	$0.506784\pi$
$648$	20.0138	+	11.5550i	0.786217	+	0.453923i
$649$	50.7477			1.99202
$650$		0			0
$651$	−5.26420			−0.206320
$652$	−2.88906	−	1.66800i	−0.113144	−	0.0653240i
$653$	−36.5885	+	9.80386i	−1.43182	+	0.383655i	−0.889661	−	0.456622i	$-0.849059\pi$
$653$	−36.5885	+	9.80386i	−1.43182	+	0.383655i	−0.542158	+	0.840277i	$0.682393\pi$
$654$	0.427200	+	0.739932i	0.0167048	+	0.0289336i
$655$		0			0
$656$	−0.268932	−	0.0720602i	−0.0105000	−	0.00281348i
$657$	8.69992	+	15.0687i	0.339416	+	0.587886i
$658$		−	5.49672i		−	0.214284i
$659$	−10.6520	+	6.14995i	−0.414944	+	0.239568i	−0.692912	−	0.721022i	$-0.743672\pi$
$659$	−10.6520	+	6.14995i	−0.414944	+	0.239568i	0.277968	+	0.960590i	$0.410339\pi$
$660$		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
$663$	2.92568	−	2.20794i	0.113624	−	0.0857494i
$664$		−	24.4234i		−	0.947812i
$665$		0			0
$666$	−10.2379	+	17.7325i	−0.396709	+	0.687120i
$667$	3.61640	−	13.4966i	0.140028	−	0.522590i
$668$	−4.24608			−0.164286
$669$	1.85305	−	6.91569i	0.0716432	−	0.267376i
$670$		0			0
$671$	−16.7587	−	16.7587i	−0.646961	−	0.646961i
$672$	7.46682	+	2.00073i	0.288039	+	0.0771797i
$673$	−9.39092	−	35.0474i	−0.361993	−	1.35098i	−0.871452	−	0.490482i	$-0.836821\pi$
$673$	−9.39092	−	35.0474i	−0.361993	−	1.35098i	0.509458	−	0.860495i	$-0.329846\pi$
$674$	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	$-0.589602\pi$
$677$	17.7672	−	17.7672i	0.682851	−	0.682851i	0.960642	+	0.277791i	$0.0896022\pi$
$678$	−1.24943	+	2.16408i	−0.0479841	+	0.0831109i
$679$	2.79442	+	1.61336i	0.107240	+	0.0619151i
$680$		0			0
$681$	−3.68589	+	3.68589i	−0.141244	+	0.141244i
$682$	15.3734	−	8.87583i	0.588677	−	0.339873i
$683$	18.3363	−	10.5865i	0.701619	−	0.405080i	−0.106331	−	0.994331i	$-0.533910\pi$
$683$	18.3363	−	10.5865i	0.701619	−	0.405080i	0.807950	+	0.589251i	$0.200577\pi$
$684$	13.1690	−	13.1690i	0.503529	−	0.503529i
$685$		0			0
$686$	11.1870	+	6.45879i	0.427120	+	0.246598i
$687$	−1.06818	+	1.85015i	−0.0407537	+	0.0705875i
$688$	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	$-0.337751\pi$
$692$	−2.22050	−	8.28702i	−0.0844108	−	0.315025i
$693$	−60.3114	−	16.1604i	−2.29104	−	0.613882i
$694$	18.7669	+	18.7669i	0.712382	+	0.712382i
$695$		0			0
$696$	−2.06461	+	7.70523i	−0.0782589	+	0.292066i
$697$	−2.66348			−0.100887
$698$	0.907648	−	3.38739i	0.0343550	−	0.128214i
$699$	−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	$0.844094\pi$
$702$	5.15814	+	4.02404i	0.194682	+	0.151877i
$703$	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
$707$		−	37.2890i		−	1.40240i
$708$	−1.92067	−	3.32669i	−0.0721831	−	0.125025i
$709$	−17.2592	−	4.62459i	−0.648183	−	0.173680i	−0.0802760	−	0.996773i	$-0.525580\pi$
$709$	−17.2592	−	4.62459i	−0.648183	−	0.173680i	−0.567907	+	0.823092i	$0.692247\pi$
$710$		0			0
$711$	−18.1605	−	31.4550i	−0.681073	−	1.17965i
$712$	40.9311	−	10.9674i	1.53396	−	0.411022i
$713$	5.53922	+	3.19807i	0.207445	+	0.119769i
$714$	−3.87490			−0.145014
$715$		0			0
$716$	11.6952			0.437071
$717$	1.46999	+	0.848697i	0.0548976	+	0.0316952i
$718$	−20.5424	+	5.50433i	−0.766637	+	0.205420i
$719$	3.20390	+	5.54933i	0.119485	+	0.206955i	0.919564	−	0.392941i	$-0.128542\pi$
$719$	3.20390	+	5.54933i	0.119485	+	0.206955i	−0.800078	+	0.599895i	$0.795209\pi$
$720$		0			0
$721$	−76.0325	−	20.3729i	−2.83160	−	0.758725i
$722$	5.34967	+	9.26590i	0.199094	+	0.344841i
$723$			0.244838i			0.00910564i
$724$	−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	0.950238	−	0.311524i	$-0.100839\pi$
$727$	17.2216	+	17.2216i	0.638714	+	0.638714i	−0.311524	+	0.950238i	$0.600839\pi$
$728$	−40.0451	−	16.9643i	−1.48417	−	0.628738i
$729$			21.0515i			0.779686i
$730$		0			0
$731$	1.31026	−	2.26943i	0.0484616	−	0.0839380i
$732$	−0.464319	+	1.73286i	−0.0171617	+	0.0640484i
$733$	−34.7895			−1.28498			−0.642489	−	0.766295i	$-0.722098\pi$
$733$	−34.7895			−1.28498			−0.642489	+	0.766295i	$0.722098\pi$
$734$	−2.80738	+	10.4773i	−0.103622	+	0.386724i
$735$		0			0
$736$	−6.64144	−	6.64144i	−0.244807	−	0.244807i
$737$	−35.6061	−	9.54061i	−1.31157	−	0.351433i
$738$	−0.603323	−	2.25163i	−0.0222086	−	0.0828837i
$739$	10.1339	+	37.8203i	0.372782	+	1.39124i	0.856558	+	0.516051i	$0.172598\pi$
$739$	10.1339	+	37.8203i	0.372782	+	1.39124i	−0.483776	+	0.875192i	$0.660735\pi$
$740$		0			0
$741$	5.37790	−	4.05858i	0.197562	−	0.149096i
$742$	1.54672	−	1.54672i	0.0567819	−	0.0567819i
$743$	−18.2574	+	31.6228i	−0.669801	+	1.16013i	0.308159	+	0.951335i	$0.400287\pi$
$743$	−18.2574	+	31.6228i	−0.669801	+	1.16013i	−0.977960	+	0.208794i	$0.933046\pi$
$744$	−3.16235	−	1.82578i	−0.115937	−	0.0669365i
$745$		0			0
$746$	2.69913	−	2.69913i	0.0988221	−	0.0988221i
$747$	21.1053	−	12.1852i	0.772203	−	0.445832i
$748$	−15.7708	+	9.10529i	−0.576639	+	0.332922i
$749$	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	$0.748150\pi$
$752$	0.227207	−	0.393533i	0.00828537	−	0.0143507i
$753$	−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
$757$	9.72706	+	36.3019i	0.353536	+	1.31941i	0.882317	+	0.470656i	$0.155983\pi$
$757$	9.72706	+	36.3019i	0.353536	+	1.31941i	−0.528781	+	0.848758i	$0.677351\pi$
$758$	9.83685	+	2.63578i	0.357291	+	0.0957357i
$759$	−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	$0.921002\pi$
$762$	0.970757			0.0351668
$763$	2.99149	−	11.1644i	0.108299	−	0.404178i
$764$	−9.78658	+	16.9509i	−0.354066	+	0.613261i
$765$		0			0
$766$		−	6.71020i		−	0.242449i
$767$	13.2358	+	32.6924i	0.477919	+	1.18045i
$768$	3.96661	+	3.96661i	0.143133	+	0.143133i
$769$	−41.7992	+	11.2001i	−1.50732	+	0.403885i	−0.915544	−	0.402218i	$-0.868239\pi$
$769$	−41.7992	+	11.2001i	−1.50732	+	0.403885i	−0.591775	+	0.806103i	$0.701573\pi$
$770$		0			0
$771$	9.15422	−	5.28519i	0.329681	−	0.190342i
$772$			19.7768i			0.711784i
$773$	8.28981	+	14.3584i	0.298164	+	0.516435i	0.975716	−	0.219040i	$-0.0702925\pi$
$773$	8.28981	+	14.3584i	0.298164	+	0.516435i	−0.677552	+	0.735475i	$0.736959\pi$
$774$	2.21531	+	0.593590i	0.0796276	+	0.0213361i
$775$		0			0
$776$	1.11912	+	1.93838i	0.0401742	+	0.0695838i
$777$	−10.5419	+	2.82470i	−0.378189	+	0.101336i
$778$	21.0617	+	12.1600i	0.755098	+	0.435956i
$779$	−4.89595			−0.175415
$780$		0			0
$781$	−14.2854			−0.511171
$782$	4.07734	+	2.35405i	0.145805	+	0.0841807i
$783$	−15.6799	+	4.20142i	−0.560354	+	0.150146i
$784$	1.63685	+	2.83510i	0.0584588	+	0.101254i
$785$		0			0
$786$	−2.56966	−	0.688537i	−0.0916566	−	0.0245593i
$787$	−0.500090	−	0.866181i	−0.0178263	−	0.0308760i	0.856975	−	0.515359i	$-0.172341\pi$
$787$	−0.500090	−	0.866181i	−0.0178263	−	0.0308760i	−0.874801	+	0.484483i	$0.839008\pi$
$788$		−	5.26880i		−	0.187693i
$789$	−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
$793$	6.42524	−	15.1671i	0.228167	−	0.538600i
$794$			19.3210i			0.685677i
$795$		0			0
$796$	−4.75595	+	8.23754i	−0.168570	+	0.291972i
$797$	−0.123918	+	0.462469i	−0.00438941	+	0.0163815i	−0.968086	−	0.250619i	$-0.919366\pi$
$797$	−0.123918	+	0.462469i	−0.00438941	+	0.0163815i	0.963696	+	0.267000i	$0.0860325\pi$
$798$	−7.12274			−0.252142
$799$	1.12512	−	4.19900i	0.0398038	−	0.148550i
$800$		0			0
$801$	29.8985	+	29.8985i	1.05641	+	1.05641i
$802$	−5.57066	−	1.49265i	−0.196707	−	0.0527074i
$803$	−8.09439	−	30.2087i	−0.285645	−	1.06604i
$804$	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
$808$	12.9330	−	22.4006i	0.454980	−	0.788049i
$809$	−17.8417	−	10.3009i	−0.627280	−	0.362160i	0.152418	−	0.988316i	$-0.451294\pi$
$809$	−17.8417	−	10.3009i	−0.627280	−	0.362160i	−0.779698	+	0.626156i	$0.784627\pi$
$810$		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	$0.255948\pi$
$812$	34.3897	−	19.8549i	1.20684	−	0.696770i
$813$	−1.93391	+	1.11655i	−0.0678253	+	0.0391590i
$814$	26.0236	−	26.0236i	0.912126	−	0.912126i
$815$		0			0
$816$	−0.277420	−	0.160169i	−0.00971166	−	0.00560703i
$817$	2.40848	−	4.17161i	0.0842621	−	0.145946i
$818$	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	$0.751874\pi$
$822$	0.888561	+	3.31616i	0.0309921	+	0.115664i
$823$	−1.47628	−	0.395567i	−0.0514598	−	0.0137886i	0.232997	−	0.972477i	$-0.425147\pi$
$823$	−1.47628	−	0.395567i	−0.0514598	−	0.0137886i	−0.284457	+	0.958689i	$0.591813\pi$
$824$	−38.6089	−	38.6089i	−1.34501	−	1.34501i
$825$		0			0
$826$	9.65054	−	36.0163i	0.335785	−	1.25317i
$827$	−34.9791			−1.21634			−0.608171	−	0.793806i	$-0.708097\pi$
$827$	−34.9791			−1.21634			−0.608171	+	0.793806i	$0.708097\pi$
$828$	1.48629	−	5.54690i	0.0516521	−	0.192768i
$829$	5.70269	−	9.87735i	0.198063	−	0.343055i	−0.749838	−	0.661622i	$-0.769868\pi$
$829$	5.70269	−	9.87735i	0.198063	−	0.343055i	0.947900	+	0.318567i	$0.103202\pi$
$830$		0			0
$831$		−	8.59653i		−	0.298210i
$832$	−12.2823	−	16.2749i	−0.425813	−	0.564231i
$833$	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
$837$		−	7.43083i		−	0.256847i
$838$	10.5057	+	18.1964i	0.362913	+	0.628584i
$839$	28.6789	+	7.68448i	0.990105	+	0.265298i	0.717295	−	0.696770i	$-0.245380\pi$
$839$	28.6789	+	7.68448i	0.990105	+	0.265298i	0.272810	+	0.962068i	$0.412047\pi$
$840$		0			0
$841$	18.9382	+	32.8019i	0.653041	+	1.13110i
$842$	−31.5381	+	8.45060i	−1.08687	+	0.291227i
$843$	3.81675	+	2.20360i	0.131456	+	0.0758961i
$844$	16.4341			0.565687
$845$		0			0
$846$	3.80457			0.130804
$847$	57.4671	+	33.1786i	1.97459	+	1.14003i
$848$	0.174670	−	0.0468027i	0.00599819	−	0.00160721i
$849$	−1.70972	−	2.96133i	−0.0586775	−	0.101632i
$850$		0			0
$851$	12.8087	+	3.43208i	0.439077	+	0.117650i
$852$	0.540664	+	0.936458i	0.0185229	+	0.0320825i
$853$		−	15.2934i		−	0.523636i	−0.965117	−	0.261818i	$-0.915678\pi$
$853$		−	15.2934i		−	0.523636i	0.965117	−	0.261818i	$-0.0843220\pi$
$854$	−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	0.463223	−	0.886242i	$-0.346693\pi$
$857$	−12.3837	−	12.3837i	−0.423018	−	0.423018i	−0.886242	+	0.463223i	$0.846693\pi$
$858$	−3.47324	−	4.60228i	−0.118574	−	0.157119i
$859$			8.73070i			0.297888i	0.988846	+	0.148944i	$0.0475874\pi$
$859$			8.73070i			0.297888i	−0.988846	+	0.148944i	$0.952413\pi$
$860$		0			0
$861$	0.621241	−	1.07602i	0.0211718	−	0.0366707i
$862$	0.925473	−	3.45391i	0.0315217	−	0.117641i
$863$	8.33598			0.283760			0.141880	−	0.989884i	$-0.454685\pi$
$863$	8.33598			0.283760			0.141880	+	0.989884i	$0.454685\pi$
$864$	−2.82418	+	10.5400i	−0.0960805	+	0.358577i
$865$		0			0
$866$	−22.2735	−	22.2735i	−0.756885	−	0.756885i
$867$	2.57744	+	0.690623i	0.0875345	+	0.0234548i
$868$	4.70469	+	17.5581i	0.159688	+	0.595962i
$869$	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
$873$	−1.11669	+	1.93417i	−0.0377943	+	0.0654616i
$874$	7.49485	+	4.32716i	0.253517	+	0.146368i
$875$		0			0
$876$	−1.67394	+	1.67394i	−0.0565570	+	0.0565570i
$877$	10.7132	−	6.18525i	0.361758	−	0.208861i	−0.308094	−	0.951356i	$-0.599691\pi$
$877$	10.7132	−	6.18525i	0.361758	−	0.208861i	0.669852	+	0.742495i	$0.266358\pi$
$878$	−17.6172	+	10.1713i	−0.594552	+	0.343265i
$879$	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	$0.591189\pi$
$882$	−13.7045	+	23.7368i	−0.461453	+	0.799261i
$883$	−8.89171	+	8.89171i	−0.299230	+	0.299230i	−0.840712	−	0.541482i	$-0.817863\pi$
$883$	−8.89171	+	8.89171i	−0.299230	+	0.299230i	0.541482	+	0.840712i	$0.317863\pi$
$884$	−9.97906	−	7.78499i	−0.335632	−	0.261838i
$885$		0			0
$886$	0.822340	+	3.06901i	0.0276270	+	0.103106i
$887$	13.8300	+	51.6144i	0.464367	+	1.73304i	0.658980	+	0.752160i	$0.270988\pi$
$887$	13.8300	+	51.6144i	0.464367	+	1.73304i	−0.194613	+	0.980880i	$0.562345\pi$
$888$	−7.31251	−	1.95938i	−0.245392	−	0.0657526i
$889$	−9.28594	−	9.28594i	−0.311440	−	0.311440i
$890$		0			0
$891$	10.7274	−	40.0351i	0.359381	−	1.34123i
$892$	−24.7226			−0.827774
$893$	2.06816	−	7.71849i	0.0692084	−	0.258289i
$894$	−2.76202	+	4.78396i	−0.0923758	+	0.160000i
$895$		0			0
$896$		−	24.2905i		−	0.811490i
$897$	0.810368	−	1.91292i	0.0270574	−	0.0638704i
$898$	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
$902$			4.18983i			0.139506i
$903$	0.611219	+	1.05866i	0.0203401	+	0.0352301i
$904$	22.6498	+	6.06898i	0.753320	+	0.201851i
$905$		0			0
$906$	0.431252	+	0.746951i	0.0143274	+	0.0248158i
$907$	−40.4677	+	10.8433i	−1.34371	+	0.360045i	−0.857808	−	0.513970i	$-0.828174\pi$
$907$	−40.4677	+	10.8433i	−1.34371	+	0.360045i	−0.485899	+	0.874015i	$0.661508\pi$
$908$	15.5880	+	8.99973i	0.517306	+	0.298666i
$909$	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	$0.430383\pi$
$912$	−0.509947	−	0.294418i	−0.0168860	−	0.00974916i
$913$	−42.3105	+	11.3371i	−1.40027	+	0.375202i
$914$	−16.9298	−	29.3232i	−0.559987	−	0.969926i
$915$		0			0
$916$	7.12560	+	1.90930i	0.235437	+	0.0630850i
$917$	17.9942	+	31.1668i	0.594220	+	1.02922i
$918$		−	5.46972i		−	0.180528i
$919$	−31.8713	+	18.4009i	−1.05134	+	0.606990i	−0.923023	−	0.384744i	$-0.874290\pi$
$919$	−31.8713	+	18.4009i	−1.05134	+	0.606990i	−0.128314	+	0.991734i	$0.540957\pi$
$920$		0			0
$921$	8.07553	−	2.16383i	0.266098	−	0.0713007i
$922$	−25.9379	−	25.9379i	−0.854219	−	0.854219i
$923$	−3.72587	−	9.20286i	−0.122638	−	0.302916i
$924$		−	8.49502i		−	0.279465i
$925$		0			0
$926$	−1.58001	+	2.73665i	−0.0519222	+	0.0899319i
$927$	14.1011	−	52.6261i	0.463142	−	1.72847i
$928$	44.9541			1.47569
$929$	10.4741	−	39.0897i	0.343643	−	1.28249i	−0.550547	−	0.834804i	$-0.685581\pi$
$929$	10.4741	−	39.0897i	0.343643	−	1.28249i	0.894190	−	0.447688i	$-0.147752\pi$
$930$		0			0
$931$	40.7062	+	40.7062i	1.33409	+	1.33409i
$932$	5.64330	+	1.51212i	0.184852	+	0.0495310i
$933$	2.12733	+	7.93930i	0.0696456	+	0.259921i
$934$	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	$-0.619694\pi$
$937$	17.2306	−	17.2306i	0.562898	−	0.562898i	0.930129	+	0.367232i	$0.119694\pi$
$938$	−13.5422	+	23.4558i	−0.442168	+	0.765858i
$939$	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	$0.116443\pi$
$942$	3.96370	−	2.28844i	0.129144	−	0.0745615i
$943$	−1.30739	+	0.754824i	−0.0425746	+	0.0245805i
$944$	2.17965	−	2.17965i	0.0709417	−	0.0709417i
$945$		0			0
$946$	−3.56996	−	2.06112i	−0.116070	−	0.0670128i
$947$	9.13678	−	15.8254i	0.296905	−	0.514255i	−0.678521	−	0.734581i	$-0.737379\pi$
$947$	9.13678	−	15.8254i	0.296905	−	0.514255i	0.975426	+	0.220326i	$0.0707121\pi$
$948$	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
$952$	9.41096	+	35.1222i	0.305011	+	1.13832i
$953$	57.2081	+	15.3289i	1.85315	+	0.496551i	0.999697	−	0.0246142i	$-0.00783574\pi$
$953$	57.2081	+	15.3289i	1.85315	+	0.496551i	0.853456	+	0.521165i	$0.174502\pi$
$954$	1.07057	+	1.07057i	0.0346609	+	0.0346609i
$955$		0			0
$956$	1.51698	−	5.66146i	0.0490628	−	0.183105i
$957$	14.3067			0.462470
$958$	−0.0276534	+	0.103204i	−0.000893439	+	0.00333436i
$959$	23.2216	−	40.2209i	0.749864	−	1.29880i
$960$		0			0
$961$			16.9865i			0.547950i
$962$	23.5522	+	9.97740i	0.759352	+	0.321684i
$963$	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
$967$		−	53.6313i		−	1.72467i	−0.506341	−	0.862333i	$-0.669002\pi$
$967$		−	53.6313i		−	1.72467i	0.506341	−	0.862333i	$-0.330998\pi$
$968$	23.0147	+	39.8627i	0.739721	+	1.28123i
$969$	−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	$0.772604\pi$
$972$	−9.72856	+	2.60676i	−0.312044	+	0.0836119i
$973$	50.0686	+	28.9071i	1.60512	+	0.926719i
$974$	9.72992			0.311767
$975$		0			0
$976$	−1.43960			−0.0460803
$977$	−17.6850	−	10.2104i	−0.565793	−	0.326661i	0.189674	−	0.981847i	$-0.439257\pi$
$977$	−17.6850	−	10.2104i	−0.565793	−	0.326661i	−0.755467	+	0.655186i	$0.772590\pi$
$978$	−0.853005	+	0.228562i	−0.0272761	+	0.00730861i
$979$	−37.9994	−	65.8169i	−1.21447	−	2.10352i
$980$		0			0
$981$	7.72746	+	2.07057i	0.246719	+	0.0661081i
$982$	−14.2564	−	24.6927i	−0.454939	−	0.787977i
$983$		−	25.2690i		−	0.805957i	−0.915209	−	0.402979i	$-0.867975\pi$
$983$		−	25.2690i		−	0.805957i	0.915209	−	0.402979i	$-0.132025\pi$
$984$	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
$988$	−18.3432	−	14.3102i	−0.583576	−	0.455267i
$989$		−	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	$0.0575268\pi$
$992$	−5.32603	+	19.8770i	−0.169102	+	0.631095i
$993$	−1.70803			−0.0542027
$994$	−2.71661	+	10.1385i	−0.0861656	+	0.321574i
$995$		0			0
$996$	2.34452	+	2.34452i	0.0742891	+	0.0742891i
$997$	−9.00051	−	2.41168i	−0.285049	−	0.0763786i	0.113462	−	0.993542i	$-0.463806\pi$
$997$	−9.00051	−	2.41168i	−0.285049	−	0.0763786i	−0.398511	+	0.917164i	$0.630473\pi$
$998$	2.20196	+	8.21781i	0.0697017	+	0.260130i
$999$	−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.x.c.318.4	yes	40
5.2	odd	4		325.2.s.c.32.7	yes	40
5.3	odd	4		325.2.s.c.32.4	✓	40
5.4	even	2	inner	325.2.x.c.318.7	yes	40
13.11	odd	12		325.2.s.c.193.7	yes	40
65.24	odd	12		325.2.s.c.193.4	yes	40
65.37	even	12	inner	325.2.x.c.232.4	yes	40
65.63	even	12	inner	325.2.x.c.232.7	yes	40

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Varieties

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Database

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