LMFDB - Embedded newform 425.3.u.e.401.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(126,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.126"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.u (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,0,0,0,0,0,192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			401.9
Character	$\chi$	$=$	425.401
Dual form			425.3.u.e.301.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.552543 - 1.33396i) q^{2} +(3.95654 + 2.64368i) q^{3} +(1.35429 + 1.35429i) q^{4} +(5.71272 - 3.81711i) q^{6} +(-8.88293 - 1.76692i) q^{7} +(7.89070 - 3.26843i) q^{8} +(5.22106 + 12.6047i) q^{9} +(11.2168 + 16.7872i) q^{11} +(1.77800 + 8.93861i) q^{12} +(-4.55740 + 4.55740i) q^{13} +(-7.26520 + 10.8731i) q^{14} -4.67078i q^{16} +(-10.6179 + 13.2763i) q^{17} +19.6991 q^{18} +(4.69451 - 11.3335i) q^{19} +(-30.4745 - 30.4745i) q^{21} +(28.5912 - 5.68714i) q^{22} +(27.7049 - 18.5118i) q^{23} +(39.8606 + 7.92876i) q^{24} +(3.56121 + 8.59753i) q^{26} +(-4.31053 + 21.6705i) q^{27} +(-9.63713 - 14.4230i) q^{28} +(-1.76764 - 8.88650i) q^{29} +(5.24039 - 7.84280i) q^{31} +(25.3322 + 10.4929i) q^{32} +96.0730i q^{33} +(11.8432 + 21.4995i) q^{34} +(-9.99965 + 24.1413i) q^{36} +(-30.8010 - 20.5805i) q^{37} +(-12.5245 - 12.5245i) q^{38} +(-30.0798 + 5.98325i) q^{39} +(-20.0419 - 3.98659i) q^{41} +(-57.4902 + 23.8132i) q^{42} +(1.42655 + 3.44400i) q^{43} +(-7.54387 + 37.9256i) q^{44} +(-9.38582 - 47.1857i) q^{46} +(59.9421 - 59.9421i) q^{47} +(12.3481 - 18.4802i) q^{48} +(30.5143 + 12.6394i) q^{49} +(-77.1084 + 24.4581i) q^{51} -12.3441 q^{52} +(-31.5824 + 76.2466i) q^{53} +(26.5258 + 17.7239i) q^{54} +(-75.8676 + 15.0910i) q^{56} +(48.5363 - 32.4309i) q^{57} +(-12.8309 - 2.55223i) q^{58} +(-10.2158 + 4.23153i) q^{59} +(13.7504 - 69.1280i) q^{61} +(-7.56642 - 11.3239i) q^{62} +(-24.1066 - 121.192i) q^{63} +(41.2052 - 41.2052i) q^{64} +(128.157 + 53.0845i) q^{66} +53.5283i q^{67} +(-32.3597 + 3.60031i) q^{68} +158.555 q^{69} +(32.2384 + 21.5410i) q^{71} +(82.3956 + 82.3956i) q^{72} +(41.3536 - 8.22574i) q^{73} +(-44.4724 + 29.7155i) q^{74} +(21.7066 - 8.99117i) q^{76} +(-69.9767 - 168.939i) q^{77} +(-8.63900 + 43.4312i) q^{78} +(-29.3762 - 43.9646i) q^{79} +(12.4807 - 12.4807i) q^{81} +(-16.3920 + 24.5323i) q^{82} +(2.25342 + 0.933397i) q^{83} -82.5426i q^{84} +5.38238 q^{86} +(16.4993 - 39.8329i) q^{87} +(143.377 + 95.8012i) q^{88} +(-109.152 - 109.152i) q^{89} +(48.5356 - 32.4304i) q^{91} +(62.5908 + 12.4501i) q^{92} +(41.4677 - 17.1765i) q^{93} +(-46.8396 - 113.081i) q^{94} +(72.4879 + 108.486i) q^{96} +(-14.7702 - 74.2547i) q^{97} +(33.7209 - 33.7209i) q^{98} +(-153.035 + 229.033i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 192 q^{12} + 48 q^{13} - 64 q^{14} - 16 q^{17} - 128 q^{18} + 48 q^{19} - 192 q^{22} - 112 q^{23} + 240 q^{24} - 224 q^{26} + 288 q^{27} + 480 q^{28} - 64 q^{31} + 80 q^{32} + 64 q^{34} + 192 q^{36}+ \cdots - 592 q^{99}+O(q^{100}) $ 96 * q + 192 * q^12 + 48 * q^13 - 64 * q^14 - 16 * q^17 - 128 * q^18 + 48 * q^19 - 192 * q^22 - 112 * q^23 + 240 * q^24 - 224 * q^26 + 288 * q^27 + 480 * q^28 - 64 * q^31 + 80 * q^32 + 64 * q^34 + 192 * q^36 - 256 * q^37 - 208 * q^38 + 16 * q^39 - 432 * q^41 - 864 * q^42 - 256 * q^43 - 32 * q^44 - 48 * q^46 + 320 * q^48 - 32 * q^49 + 64 * q^51 - 192 * q^53 - 976 * q^54 + 80 * q^56 + 1120 * q^57 - 512 * q^58 - 224 * q^59 - 224 * q^61 + 560 * q^62 - 624 * q^63 + 160 * q^64 + 48 * q^66 + 384 * q^69 + 48 * q^71 - 1040 * q^72 + 672 * q^74 + 496 * q^76 - 960 * q^77 + 768 * q^79 + 1424 * q^81 - 1200 * q^82 + 288 * q^83 + 64 * q^86 + 1344 * q^87 + 1664 * q^88 - 1152 * q^89 + 336 * q^91 + 2016 * q^92 + 1024 * q^93 - 1344 * q^94 + 768 * q^96 + 256 * q^97 + 816 * q^98 - 592 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{16}\right)$

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 $

$2$	0.552543	−	1.33396i	0.276272	−	0.666979i	−0.723455	−	0.690372i	$-0.757447\pi$
$2$	0.552543	−	1.33396i	0.276272	−	0.666979i	0.999726	+	0.0233932i	$0.00744696\pi$
$3$	3.95654	+	2.64368i	1.31885	+	0.881226i	0.997830	−	0.0658467i	$-0.0209748\pi$
$3$	3.95654	+	2.64368i	1.31885	+	0.881226i	0.321018	+	0.947073i	$0.395975\pi$
$4$	1.35429	+	1.35429i	0.338572	+	0.338572i
$5$		0			0
$5$		0			0
$6$	5.71272	−	3.81711i	0.952119	−	0.636186i
$7$	−8.88293	−	1.76692i	−1.26899	−	0.252418i	−0.485728	−	0.874110i	$-0.661445\pi$
$7$	−8.88293	−	1.76692i	−1.26899	−	0.252418i	−0.783262	+	0.621692i	$0.786445\pi$
$8$	7.89070	−	3.26843i	0.986337	−	0.408554i
$9$	5.22106	+	12.6047i	0.580118	+	1.40053i
$10$		0			0
$11$	11.2168	+	16.7872i	1.01971	+	1.52611i	0.840144	+	0.542364i	$0.182471\pi$
$11$	11.2168	+	16.7872i	1.01971	+	1.52611i	0.179570	+	0.983745i	$0.442529\pi$
$12$	1.77800	+	8.93861i	0.148167	+	0.744884i
$13$	−4.55740	+	4.55740i	−0.350569	+	0.350569i	−0.860321	−	0.509752i	$-0.829737\pi$
$13$	−4.55740	+	4.55740i	−0.350569	+	0.350569i	0.509752	+	0.860321i	$0.329737\pi$
$14$	−7.26520	+	10.8731i	−0.518943	+	0.776653i
$15$		0			0
$16$		−	4.67078i		−	0.291924i
$17$	−10.6179	+	13.2763i	−0.624581	+	0.780960i
$17$	−10.6179	+	13.2763i	−0.624581	+	0.780960i
$18$	19.6991			1.09439
$19$	4.69451	−	11.3335i	0.247079	−	0.596502i	−0.750874	−	0.660445i	$-0.770368\pi$
$19$	4.69451	−	11.3335i	0.247079	−	0.596502i	0.997954	+	0.0639429i	$0.0203676\pi$
$20$		0			0
$21$	−30.4745	−	30.4745i	−1.45117	−	1.45117i
$22$	28.5912	−	5.68714i	1.29960	−	0.258506i
$23$	27.7049	−	18.5118i	1.20456	−	0.804861i	0.219256	−	0.975667i	$-0.429637\pi$
$23$	27.7049	−	18.5118i	1.20456	−	0.804861i	0.985305	+	0.170806i	$0.0546371\pi$
$24$	39.8606	+	7.92876i	1.66086	+	0.330365i
$25$		0			0
$26$	3.56121	+	8.59753i	0.136970	+	0.330674i
$27$	−4.31053	+	21.6705i	−0.159649	+	0.802611i
$28$	−9.63713	−	14.4230i	−0.344183	−	0.515106i
$29$	−1.76764	−	8.88650i	−0.0609530	−	0.306431i	0.938267	−	0.345911i	$-0.112430\pi$
$29$	−1.76764	−	8.88650i	−0.0609530	−	0.306431i	−0.999220	+	0.0394795i	$0.987430\pi$
$30$		0			0
$31$	5.24039	−	7.84280i	0.169045	−	0.252993i	−0.737268	−	0.675600i	$-0.763885\pi$
$31$	5.24039	−	7.84280i	0.169045	−	0.252993i	0.906313	+	0.422606i	$0.138885\pi$
$32$	25.3322	+	10.4929i	0.791630	+	0.327904i
$33$			96.0730i			2.91130i
$34$	11.8432	+	21.4995i	0.348330	+	0.632339i
$35$		0			0
$36$	−9.99965	+	24.1413i	−0.277768	+	0.670592i
$37$	−30.8010	−	20.5805i	−0.832458	−	0.556231i	0.0647178	−	0.997904i	$-0.479385\pi$
$37$	−30.8010	−	20.5805i	−0.832458	−	0.556231i	−0.897176	+	0.441673i	$0.854385\pi$
$38$	−12.5245	−	12.5245i	−0.329593	−	0.329593i
$39$	−30.0798	+	5.98325i	−0.771278	+	0.153417i
$40$		0			0
$41$	−20.0419	−	3.98659i	−0.488828	−	0.0972338i	−0.0554783	−	0.998460i	$-0.517668\pi$
$41$	−20.0419	−	3.98659i	−0.488828	−	0.0972338i	−0.433349	+	0.901226i	$0.642668\pi$
$42$	−57.4902	+	23.8132i	−1.36881	+	0.566981i
$43$	1.42655	+	3.44400i	0.0331756	+	0.0800931i	0.939599	−	0.342277i	$-0.111198\pi$
$43$	1.42655	+	3.44400i	0.0331756	+	0.0800931i	−0.906423	+	0.422370i	$0.861198\pi$
$44$	−7.54387	+	37.9256i	−0.171452	+	0.861945i
$45$		0			0
$46$	−9.38582	−	47.1857i	−0.204040	−	1.02578i
$47$	59.9421	−	59.9421i	1.27536	−	1.27536i	0.332129	−	0.943234i	$-0.392233\pi$
$47$	59.9421	−	59.9421i	1.27536	−	1.27536i	0.943234	−	0.332129i	$-0.107767\pi$
$48$	12.3481	−	18.4802i	0.257251	−	0.385004i
$49$	30.5143	+	12.6394i	0.622741	+	0.257948i
$50$		0			0
$51$	−77.1084	+	24.4581i	−1.51193	+	0.479571i
$52$	−12.3441			−0.237386
$53$	−31.5824	+	76.2466i	−0.595894	+	1.43862i	0.281837	+	0.959462i	$0.409056\pi$
$53$	−31.5824	+	76.2466i	−0.595894	+	1.43862i	−0.877731	+	0.479154i	$0.840944\pi$
$54$	26.5258	+	17.7239i	0.491218	+	0.328221i
$55$		0			0
$56$	−75.8676	+	15.0910i	−1.35478	+	0.269482i
$57$	48.5363	−	32.4309i	0.851514	−	0.568963i
$58$	−12.8309	−	2.55223i	−0.221223	−	0.0440039i
$59$	−10.2158	+	4.23153i	−0.173149	+	0.0717208i	−0.467574	−	0.883954i	$-0.654872\pi$
$59$	−10.2158	+	4.23153i	−0.173149	+	0.0717208i	0.294425	+	0.955675i	$0.404872\pi$
$60$		0			0
$61$	13.7504	−	69.1280i	0.225417	−	1.13325i	−0.687840	−	0.725862i	$-0.741441\pi$
$61$	13.7504	−	69.1280i	0.225417	−	1.13325i	0.913257	−	0.407384i	$-0.133559\pi$
$62$	−7.56642	−	11.3239i	−0.122039	−	0.182644i
$63$	−24.1066	−	121.192i	−0.382645	−	1.92369i
$64$	41.2052	−	41.2052i	0.643831	−	0.643831i
$65$		0			0
$66$	128.157	+	53.0845i	1.94178	+	0.804311i
$67$			53.5283i			0.798931i	0.916748	+	0.399465i	$0.130804\pi$
$67$			53.5283i			0.798931i	−0.916748	+	0.399465i	$0.869196\pi$
$68$	−32.3597	+	3.60031i	−0.475877	+	0.0529458i
$69$	158.555			2.29790
$70$		0			0
$71$	32.2384	+	21.5410i	0.454063	+	0.303395i	0.761490	−	0.648177i	$-0.224468\pi$
$71$	32.2384	+	21.5410i	0.454063	+	0.303395i	−0.307427	+	0.951572i	$0.599468\pi$
$72$	82.3956	+	82.3956i	1.14438	+	1.14438i
$73$	41.3536	−	8.22574i	0.566487	−	0.112681i	0.0964658	−	0.995336i	$-0.469246\pi$
$73$	41.3536	−	8.22574i	0.566487	−	0.112681i	0.470021	+	0.882655i	$0.344246\pi$
$74$	−44.4724	+	29.7155i	−0.600979	+	0.401561i
$75$		0			0
$76$	21.7066	−	8.99117i	0.285613	−	0.118305i
$77$	−69.9767	−	168.939i	−0.908789	−	2.19401i
$78$	−8.63900	+	43.4312i	−0.110756	+	0.556810i
$79$	−29.3762	−	43.9646i	−0.371851	−	0.556514i	0.597602	−	0.801793i	$-0.296120\pi$
$79$	−29.3762	−	43.9646i	−0.371851	−	0.556514i	−0.969453	+	0.245279i	$0.921120\pi$
$80$		0			0
$81$	12.4807	−	12.4807i	0.154083	−	0.154083i
$82$	−16.3920	+	24.5323i	−0.199902	+	0.299175i
$83$	2.25342	+	0.933397i	0.0271496	+	0.0112458i	0.396217	−	0.918157i	$-0.370323\pi$
$83$	2.25342	+	0.933397i	0.0271496	+	0.0112458i	−0.369067	+	0.929403i	$0.620323\pi$
$84$		−	82.5426i		−	0.982650i
$85$		0			0
$86$	5.38238			0.0625859
$87$	16.4993	−	39.8329i	0.189648	−	0.457850i
$88$	143.377	+	95.8012i	1.62928	+	1.08865i
$89$	−109.152	−	109.152i	−1.22643	−	1.22643i	−0.965306	−	0.261121i	$-0.915908\pi$
$89$	−109.152	−	109.152i	−1.22643	−	1.22643i	−0.261121	−	0.965306i	$-0.584092\pi$
$90$		0			0
$91$	48.5356	−	32.4304i	0.533358	−	0.356379i
$92$	62.5908	+	12.4501i	0.680335	+	0.135327i
$93$	41.4677	−	17.1765i	0.445889	−	0.184693i
$94$	−46.8396	−	113.081i	−0.498293	−	1.20299i
$95$		0			0
$96$	72.4879	+	108.486i	0.755082	+	1.13006i
$97$	−14.7702	−	74.2547i	−0.152270	−	0.765512i	−0.979151	−	0.203135i	$-0.934887\pi$
$97$	−14.7702	−	74.2547i	−0.152270	−	0.765512i	0.826881	−	0.562377i	$-0.190113\pi$
$98$	33.7209	−	33.7209i	0.344091	−	0.344091i
$99$	−153.035	+	229.033i	−1.54580	+	2.31346i
$100$		0			0
$101$		−	104.483i		−	1.03448i	−0.855839	−	0.517242i	$-0.826959\pi$
$101$		−	104.483i		−	1.03448i	0.855839	−	0.517242i	$-0.173041\pi$
$102$	−9.97964	+	116.374i	−0.0978396	+	1.14092i
$103$	29.4081			0.285515			0.142758	−	0.989758i	$-0.454403\pi$
$103$	29.4081			0.285515			0.142758	+	0.989758i	$0.454403\pi$
$104$	−21.0655	+	50.8566i	−0.202553	+	0.489005i
$105$		0			0
$106$	84.2591	+	84.2591i	0.794897	+	0.794897i
$107$	−97.6936	+	19.4325i	−0.913024	+	0.181612i	−0.629181	−	0.777259i	$-0.716610\pi$
$107$	−97.6936	+	19.4325i	−0.913024	+	0.181612i	−0.283843	+	0.958871i	$0.591610\pi$
$108$	−35.1858	+	23.5104i	−0.325795	+	0.217689i
$109$	−50.5798	−	10.0609i	−0.464035	−	0.0923023i	−0.0424645	−	0.999098i	$-0.513521\pi$
$109$	−50.5798	−	10.0609i	−0.464035	−	0.0923023i	−0.421570	+	0.906796i	$0.638521\pi$
$110$		0			0
$111$	−67.4570	−	162.856i	−0.607721	−	1.46717i
$112$	−8.25292	+	41.4902i	−0.0736868	+	0.370449i
$113$	−53.9070	−	80.6775i	−0.477053	−	0.713960i	0.512411	−	0.858740i	$-0.328752\pi$
$113$	−53.9070	−	80.6775i	−0.477053	−	0.713960i	−0.989464	+	0.144780i	$0.953752\pi$
$114$	−16.4430	−	82.6648i	−0.144237	−	0.725130i
$115$		0			0
$116$	9.64101	−	14.4288i	0.0831121	−	0.124386i
$117$	−81.2393	−	33.6504i	−0.694353	−	0.287610i
$118$			15.9655i			0.135301i
$119$	117.776	−	99.1717i	0.989715	−	0.833375i
$120$		0			0
$121$	−109.688	+	264.810i	−0.906510	+	2.18851i
$122$	−84.6161	−	56.5387i	−0.693575	−	0.463432i
$123$	−68.7575	−	68.7575i	−0.559004	−	0.559004i
$124$	17.7184	−	3.52441i	0.142890	−	0.0284227i
$125$		0			0
$126$	−174.985	−	34.8067i	−1.38877	−	0.276244i
$127$	−49.6315	+	20.5580i	−0.390799	+	0.161874i	−0.569426	−	0.822043i	$-0.692835\pi$
$127$	−49.6315	+	20.5580i	−0.390799	+	0.161874i	0.178627	+	0.983917i	$0.442835\pi$
$128$	9.77337	+	23.5950i	0.0763545	+	0.184336i
$129$	−3.46062	+	17.3977i	−0.0268265	+	0.134866i
$130$		0			0
$131$	−8.34298	−	41.9430i	−0.0636869	−	0.320176i	0.935789	−	0.352562i	$-0.114689\pi$
$131$	−8.34298	−	41.9430i	−0.0636869	−	0.320176i	−0.999475	+	0.0323862i	$0.989689\pi$
$132$	−130.111	+	130.111i	−0.985687	+	0.985687i
$133$	−61.7265	+	92.3802i	−0.464109	+	0.694588i
$134$	71.4045	+	29.5767i	0.532870	+	0.220722i
$135$		0			0
$136$	−40.3896	+	139.463i	−0.296983	+	1.02547i
$137$	175.836			1.28347			0.641736	−	0.766925i	$-0.278214\pi$
$137$	175.836			1.28347			0.641736	+	0.766925i	$0.278214\pi$
$138$	87.6084	−	211.505i	0.634844	−	1.53265i
$139$	51.2893	+	34.2704i	0.368988	+	0.246550i	0.726215	−	0.687468i	$-0.241278\pi$
$139$	51.2893	+	34.2704i	0.368988	+	0.246550i	−0.357227	+	0.934018i	$0.616278\pi$
$140$		0			0
$141$	395.631	−	78.6959i	2.80589	−	0.558127i
$142$	46.5480	−	31.1024i	0.327803	−	0.219031i
$143$	−127.626	−	25.3863i	−0.892486	−	0.177527i
$144$	58.8741	−	24.3864i	0.408848	−	0.169350i
$145$		0			0
$146$	11.8769	−	59.7090i	0.0813483	−	0.408966i
$147$	87.3166	+	130.679i	0.593990	+	0.888970i
$148$	−13.8414	−	69.5854i	−0.0935230	−	0.470172i
$149$	5.89178	−	5.89178i	0.0395421	−	0.0395421i	−0.687059	−	0.726601i	$-0.741099\pi$
$149$	5.89178	−	5.89178i	0.0395421	−	0.0395421i	0.726601	+	0.687059i	$0.241099\pi$
$150$		0			0
$151$	−69.9385	−	28.9695i	−0.463169	−	0.191851i	0.138881	−	0.990309i	$-0.455649\pi$
$151$	−69.9385	−	28.9695i	−0.463169	−	0.191851i	−0.602050	+	0.798458i	$0.705649\pi$
$152$		−	104.773i		−	0.689298i
$153$	−222.781	−	64.5192i	−1.45609	−	0.421694i
$154$	−264.022			−1.71443
$155$		0			0
$156$	−48.8398	−	32.6337i	−0.313076	−	0.209191i
$157$	167.491	+	167.491i	1.06682	+	1.06682i	0.997602	+	0.0692173i	$0.0220502\pi$
$157$	167.491	+	167.491i	1.06682	+	1.06682i	0.0692173	+	0.997602i	$0.477950\pi$
$158$	−74.8786	+	14.8943i	−0.473915	+	0.0942676i
$159$	−326.529	+	218.180i	−2.05364	+	1.37220i
$160$		0			0
$161$	−278.810	+	115.487i	−1.73174	+	0.717309i
$162$	−9.75260	−	23.5449i	−0.0602012	−	0.145339i
$163$	−19.1933	+	96.4915i	−0.117751	+	0.591972i	0.876182	+	0.481981i	$0.160082\pi$
$163$	−19.1933	+	96.4915i	−0.117751	+	0.591972i	−0.993933	+	0.109992i	$0.964918\pi$
$164$	−21.7436	−	32.5416i	−0.132583	−	0.198424i
$165$		0			0
$166$	2.49022	−	2.49022i	0.0150014	−	0.0150014i
$167$	52.0905	−	77.9590i	0.311919	−	0.466820i	−0.642076	−	0.766641i	$-0.721927\pi$
$167$	52.0905	−	77.9590i	0.311919	−	0.466820i	0.953996	+	0.299821i	$0.0969268\pi$
$168$	−340.069	−	140.861i	−2.02422	−	0.838460i
$169$			127.460i			0.754203i
$170$		0			0
$171$	167.367			0.978753
$172$	−2.73221	+	6.59614i	−0.0158849	+	0.0383496i
$173$	−167.941	−	112.214i	−0.970755	−	0.648638i	−0.0342948	−	0.999412i	$-0.510919\pi$
$173$	−167.941	−	112.214i	−0.970755	−	0.648638i	−0.936460	+	0.350774i	$0.885919\pi$
$174$	−44.0188	−	44.0188i	−0.252982	−	0.252982i
$175$		0			0
$176$	78.4094	−	52.3915i	0.445508	−	0.297679i
$177$	−51.6061	−	10.2651i	−0.291560	−	0.0579949i
$178$	−205.915	+	85.2929i	−1.15683	+	0.479174i
$179$	−17.0542	−	41.1724i	−0.0952747	−	0.230013i	0.869056	−	0.494714i	$-0.164727\pi$
$179$	−17.0542	−	41.1724i	−0.0952747	−	0.230013i	−0.964331	+	0.264700i	$0.914727\pi$
$180$		0			0
$181$	115.362	+	172.651i	0.637358	+	0.953873i	0.999761	+	0.0218520i	$0.00695625\pi$
$181$	115.362	+	172.651i	0.637358	+	0.953873i	−0.362403	+	0.932021i	$0.618044\pi$
$182$	−16.4428	−	82.6636i	−0.0903451	−	0.454196i
$183$	237.156	−	237.156i	1.29594	−	1.29594i
$184$	158.106	−	236.623i	0.859273	−	1.28599i
$185$		0			0
$186$		−	64.8068i		−	0.348424i
$187$	−341.971	−	29.3258i	−1.82872	−	0.156823i
$188$	162.358			0.863605
$189$	76.5802	−	184.881i	0.405186	−	0.978207i
$190$		0			0
$191$	−22.5345	−	22.5345i	−0.117982	−	0.117982i	0.645651	−	0.763633i	$-0.276586\pi$
$191$	−22.5345	−	22.5345i	−0.117982	−	0.117982i	−0.763633	+	0.645651i	$0.776586\pi$
$192$	271.963	−	54.0969i	1.41648	−	0.281755i
$193$	95.2863	−	63.6683i	0.493712	−	0.329888i	−0.283665	−	0.958924i	$-0.591550\pi$
$193$	95.2863	−	63.6683i	0.493712	−	0.329888i	0.777376	+	0.629036i	$0.216550\pi$
$194$	−107.214	−	21.3261i	−0.552648	−	0.109928i
$195$		0			0
$196$	24.2077	+	58.4427i	0.123509	+	0.298177i
$197$	25.4103	−	127.746i	0.128986	−	0.648458i	−0.861150	−	0.508351i	$-0.830255\pi$
$197$	25.4103	−	127.746i	0.128986	−	0.648458i	0.990136	−	0.140107i	$-0.0447447\pi$
$198$	220.961	+	330.692i	1.11597	+	1.67016i
$199$	−5.01500	−	25.2121i	−0.0252010	−	0.126694i	0.966137	−	0.258030i	$-0.0830733\pi$
$199$	−5.01500	−	25.2121i	−0.0252010	−	0.126694i	−0.991338	+	0.131336i	$0.958073\pi$
$200$		0			0
$201$	−141.512	+	211.787i	−0.704039	+	1.05367i
$202$	−139.376	−	57.7313i	−0.689978	−	0.285798i
$203$			82.0615i			0.404244i
$204$	−137.550	−	71.3037i	−0.674267	−	0.349528i
$205$		0			0
$206$	16.2492	−	39.2291i	0.0788797	−	0.190432i
$207$	377.986	+	252.562i	1.82602	+	1.22011i
$208$	21.2866	+	21.2866i	0.102339	+	0.102339i
$209$	242.916	−	48.3190i	1.16228	−	0.231191i
$210$		0			0
$211$	−366.478	−	72.8971i	−1.73686	−	0.345484i	−0.777765	−	0.628555i	$-0.783647\pi$
$211$	−366.478	−	72.8971i	−1.73686	−	0.345484i	−0.959099	+	0.283071i	$0.908647\pi$
$212$	−146.032	+	60.4883i	−0.688829	+	0.285322i
$213$	70.6053	+	170.456i	0.331480	+	0.800264i
$214$	−28.0579	+	141.056i	−0.131111	+	0.659142i
$215$		0			0
$216$	36.8155	+	185.084i	0.170442	+	0.856870i
$217$	−60.4076	+	60.4076i	−0.278376	+	0.278376i
$218$	−41.3684	+	61.9122i	−0.189763	+	0.284001i
$219$	185.363	+	76.7801i	0.846409	+	0.350594i
$220$		0			0
$221$	−12.1156	−	108.895i	−0.0548218	−	0.492739i
$222$	−254.515			−1.14647
$223$	47.5229	−	114.730i	0.213107	−	0.514486i	−0.780790	−	0.624793i	$-0.785183\pi$
$223$	47.5229	−	114.730i	0.213107	−	0.514486i	0.993898	+	0.110307i	$0.0351833\pi$
$224$	−206.484	−	137.968i	−0.921802	−	0.615928i
$225$		0			0
$226$	−137.406	+	27.3318i	−0.607992	+	0.120937i
$227$	59.4422	−	39.7180i	0.261860	−	0.174969i	−0.417709	−	0.908581i	$-0.637167\pi$
$227$	59.4422	−	39.7180i	0.261860	−	0.174969i	0.679569	+	0.733612i	$0.262167\pi$
$228$	109.653	+	21.8113i	0.480934	+	0.0956637i
$229$	47.7547	−	19.7807i	0.208536	−	0.0863784i	−0.275971	−	0.961166i	$-0.588999\pi$
$229$	47.7547	−	19.7807i	0.208536	−	0.0863784i	0.484506	+	0.874788i	$0.338999\pi$
$230$		0			0
$231$	169.754	−	853.410i	0.734865	−	3.69442i
$232$	−42.9928	−	64.3433i	−0.185314	−	0.277342i
$233$	63.7358	+	320.422i	0.273544	+	1.37520i	0.836162	+	0.548483i	$0.184794\pi$
$233$	63.7358	+	320.422i	0.273544	+	1.37520i	−0.562617	+	0.826717i	$0.690206\pi$
$234$	−89.7764	+	89.7764i	−0.383660	+	0.383660i
$235$		0			0
$236$	−19.5659	−	8.10445i	−0.0829062	−	0.0343409i
$237$		−	251.609i		−	1.06164i
$238$	−67.2144	−	211.905i	−0.282413	−	0.890357i
$239$	92.6253			0.387554			0.193777	−	0.981046i	$-0.437926\pi$
$239$	92.6253			0.387554			0.193777	+	0.981046i	$0.437926\pi$
$240$		0			0
$241$	140.562	+	93.9207i	0.583246	+	0.389713i	0.811901	−	0.583795i	$-0.198433\pi$
$241$	140.562	+	93.9207i	0.583246	+	0.389713i	−0.228655	+	0.973508i	$0.573433\pi$
$242$	292.637	+	292.637i	1.20925	+	1.20925i
$243$	277.410	−	55.1803i	1.14160	−	0.227079i
$244$	112.241	−	74.9973i	0.460005	−	0.307366i
$245$		0			0
$246$	−129.711	+	53.7281i	−0.527281	+	0.218407i
$247$	30.2567	+	73.0462i	0.122497	+	0.295733i
$248$	15.7167	−	79.0130i	0.0633736	−	0.318601i
$249$	6.44816	+	9.65035i	0.0258962	+	0.0387564i
$250$		0			0
$251$	255.770	−	255.770i	1.01900	−	1.01900i	0.0191867	−	0.999816i	$-0.493892\pi$
$251$	255.770	−	255.770i	1.01900	−	1.01900i	0.999816	−	0.0191867i	$-0.00610770\pi$
$252$	131.482	−	196.777i	0.521754	−	0.780860i
$253$	621.523	+	257.443i	2.45661	+	1.01756i
$254$			77.5655i			0.305376i
$255$		0			0
$256$	269.967			1.05456
$257$	−182.440	+	440.449i	−0.709883	+	1.71381i	−0.00958789	+	0.999954i	$0.503052\pi$
$257$	−182.440	+	440.449i	−0.709883	+	1.71381i	−0.700295	+	0.713854i	$0.746948\pi$
$258$	21.2956	+	14.2293i	0.0825412	+	0.0551523i
$259$	237.238	+	237.238i	0.915979	+	0.915979i
$260$		0			0
$261$	102.783	−	68.6776i	0.393806	−	0.263132i
$262$	−60.5600	−	12.0461i	−0.231145	−	0.0459776i
$263$	−484.648	+	200.748i	−1.84277	+	0.763300i	−0.893280	+	0.449500i	$0.851602\pi$
$263$	−484.648	+	200.748i	−1.84277	+	0.763300i	−0.949489	+	0.313800i	$0.898398\pi$
$264$	314.008	+	758.083i	1.18943	+	2.87153i
$265$		0			0
$266$	89.1247	+	133.385i	0.335055	+	0.501446i
$267$	−143.302	−	720.428i	−0.536712	−	2.69823i
$268$	−72.4929	+	72.4929i	−0.270496	+	0.270496i
$269$	99.6815	−	149.184i	0.370563	−	0.554587i	−0.598587	−	0.801058i	$-0.704271\pi$
$269$	99.6815	−	149.184i	0.370563	−	0.554587i	0.969150	+	0.246471i	$0.0792709\pi$
$270$		0			0
$271$			523.206i			1.93065i	0.261055	+	0.965324i	$0.415929\pi$
$271$			523.206i			1.93065i	−0.261055	+	0.965324i	$0.584071\pi$
$272$	62.0108	+	49.5938i	0.227981	+	0.182330i
$273$	277.769			1.01747
$274$	97.1568	−	234.557i	0.354587	−	0.856049i
$275$		0			0
$276$	214.729	+	214.729i	0.778004	+	0.778004i
$277$	−55.2918	+	10.9982i	−0.199609	+	0.0397048i	−0.293882	−	0.955842i	$-0.594947\pi$
$277$	−55.2918	+	10.9982i	−0.199609	+	0.0397048i	0.0942729	+	0.995546i	$0.469947\pi$
$278$	74.0548	−	49.4819i	0.266384	−	0.177992i
$279$	126.217	+	25.1061i	0.452390	+	0.0899860i
$280$		0			0
$281$	−5.36180	−	12.9445i	−0.0190812	−	0.0460660i	0.914052	−	0.405597i	$-0.132937\pi$
$281$	−5.36180	−	12.9445i	−0.0190812	−	0.0460660i	−0.933133	+	0.359531i	$0.882937\pi$
$282$	113.626	−	571.238i	0.402930	−	2.02567i
$283$	−130.918	−	195.932i	−0.462606	−	0.692339i	0.524679	−	0.851300i	$-0.324185\pi$
$283$	−130.918	−	195.932i	−0.462606	−	0.692339i	−0.987285	+	0.158961i	$0.949185\pi$
$284$	14.4874	+	72.8330i	0.0510119	+	0.256454i
$285$		0			0
$286$	−104.383	+	156.220i	−0.364975	+	0.546224i
$287$	170.987	+	70.8252i	0.595774	+	0.246778i
$288$			374.090i			1.29892i
$289$	−63.5216	−	281.933i	−0.219798	−	0.975545i
$290$		0			0
$291$	137.867	−	332.839i	0.473768	−	1.14378i
$292$	67.1447	+	44.8647i	0.229948	+	0.153646i
$293$	58.7301	+	58.7301i	0.200444	+	0.200444i	0.800190	−	0.599746i	$-0.204732\pi$
$293$	58.7301	+	58.7301i	0.200444	+	0.200444i	−0.599746	+	0.800190i	$0.704732\pi$
$294$	222.566	−	44.2711i	0.757026	−	0.150582i
$295$		0			0
$296$	−310.307	−	61.7239i	−1.04834	−	0.208527i
$297$	−412.137	+	170.713i	−1.38767	+	0.574791i
$298$	−4.60392	−	11.1148i	−0.0154494	−	0.0372981i
$299$	−41.8965	+	210.628i	−0.140122	+	0.704441i
$300$		0			0
$301$	−6.58667	−	33.1134i	−0.0218826	−	0.110011i
$302$	−77.2881	+	77.2881i	−0.255921	+	0.255921i
$303$	276.219	−	413.391i	0.911614	−	1.36433i
$304$	−52.9365	−	21.9270i	−0.174133	−	0.0721284i
$305$		0			0
$306$	−209.162	+	261.531i	−0.683536	+	0.854677i
$307$	350.474			1.14161			0.570804	−	0.821086i	$-0.306631\pi$
$307$	350.474			1.14161			0.570804	+	0.821086i	$0.306631\pi$
$308$	134.023	−	323.561i	0.435140	−	1.05052i
$309$	116.354	+	77.7454i	0.376551	+	0.251603i
$310$		0			0
$311$	−298.600	+	59.3951i	−0.960127	+	0.190981i	−0.650186	−	0.759775i	$-0.725309\pi$
$311$	−298.600	+	59.3951i	−0.960127	+	0.190981i	−0.309941	+	0.950756i	$0.600309\pi$
$312$	−217.795	+	145.526i	−0.698061	+	0.466429i
$313$	−383.620	−	76.3067i	−1.22562	−	0.243791i	−0.460490	−	0.887665i	$-0.652326\pi$
$313$	−383.620	−	76.3067i	−1.22562	−	0.243791i	−0.765132	+	0.643873i	$0.777326\pi$
$314$	315.971	−	130.879i	1.00628	−	0.416814i
$315$		0			0
$316$	19.7569	−	99.3248i	0.0625219	−	0.314319i
$317$	−26.0395	−	38.9709i	−0.0821435	−	0.122936i	0.788123	−	0.615518i	$-0.211053\pi$
$317$	−26.0395	−	38.9709i	−0.0821435	−	0.122936i	−0.870266	+	0.492582i	$0.836053\pi$
$318$	110.621	+	556.129i	0.347865	+	1.74883i
$319$	129.352	−	129.352i	0.405493	−	0.405493i
$320$		0			0
$321$	−437.902	−	181.385i	−1.36418	−	0.565063i
$322$			435.731i			1.35320i
$323$	100.622	+	182.664i	0.311524	+	0.565523i
$324$	33.8050			0.104336
$325$		0			0
$326$	118.110	+	78.9188i	0.362302	+	0.242082i
$327$	−173.523	−	173.523i	−0.530652	−	0.530652i
$328$	−171.175	+	34.0488i	−0.521874	+	0.103807i
$329$	−638.374	+	426.548i	−1.94035	+	1.29650i
$330$		0			0
$331$	−135.561	+	56.1513i	−0.409550	+	0.169641i	−0.577940	−	0.816079i	$-0.696143\pi$
$331$	−135.561	+	56.1513i	−0.409550	+	0.169641i	0.168390	+	0.985720i	$0.446143\pi$
$332$	1.78769	+	4.31587i	0.00538462	+	0.0129996i
$333$	98.5990	−	495.691i	0.296093	−	1.48856i
$334$	−75.2117	−	112.562i	−0.225185	−	0.337013i
$335$		0			0
$336$	−142.340	+	142.340i	−0.423631	+	0.423631i
$337$	−10.2204	+	15.2959i	−0.0303277	+	0.0453886i	−0.846324	−	0.532669i	$-0.821189\pi$
$337$	−10.2204	+	15.2959i	−0.0303277	+	0.0453886i	0.815996	+	0.578058i	$0.196189\pi$
$338$	170.027	+	70.4273i	0.503037	+	0.208365i
$339$		−	461.717i		−	1.36200i
$340$		0			0
$341$	190.439			0.558473
$342$	92.4774	−	223.260i	0.270402	−	0.652807i
$343$	120.275	+	80.3653i	0.350656	+	0.234301i
$344$	22.5130	+	22.5130i	0.0654447	+	0.0654447i
$345$		0			0
$346$	−242.484	+	162.022i	−0.700819	+	0.468273i
$347$	−551.034	−	109.607i	−1.58799	−	0.315872i	−0.679469	−	0.733704i	$-0.737790\pi$
$347$	−551.034	−	109.607i	−1.58799	−	0.315872i	−0.908524	+	0.417832i	$0.862790\pi$
$348$	76.2902	−	31.6004i	0.219225	−	0.0908058i
$349$	89.2578	+	215.487i	0.255753	+	0.617442i	0.998649	−	0.0519647i	$-0.0165483\pi$
$349$	89.2578	+	215.487i	0.255753	+	0.617442i	−0.742896	+	0.669407i	$0.766548\pi$
$350$		0			0
$351$	−79.1162	−	118.406i	−0.225402	−	0.337338i
$352$	108.000	+	542.953i	0.306819	+	1.54248i
$353$	−35.0592	+	35.0592i	−0.0993178	+	0.0993178i	−0.755020	−	0.655702i	$-0.772373\pi$
$353$	−35.0592	+	35.0592i	−0.0993178	+	0.0993178i	0.655702	+	0.755020i	$0.272373\pi$
$354$	−42.2078	+	63.1684i	−0.119231	+	0.178442i
$355$		0			0
$356$		−	295.647i		−	0.830469i
$357$	728.164	−	81.0150i	2.03968	−	0.226933i
$358$	−64.3454			−0.179736
$359$	−107.336	+	259.133i	−0.298987	+	0.721819i	0.700976	+	0.713185i	$0.252748\pi$
$359$	−107.336	+	259.133i	−0.298987	+	0.721819i	−0.999963	+	0.00863338i	$0.997252\pi$
$360$		0			0
$361$	148.855	+	148.855i	0.412340	+	0.412340i
$362$	294.051	−	58.4905i	0.812297	−	0.161576i
$363$	−1134.06	+	757.752i	−3.12412	+	2.08747i
$364$	109.651	+	21.8110i	0.301240	+	0.0599204i
$365$		0			0
$366$	−185.317	−	447.396i	−0.506331	−	1.22239i
$367$	−119.018	+	598.342i	−0.324299	+	1.63036i	0.383214	+	0.923660i	$0.374817\pi$
$367$	−119.018	+	598.342i	−0.324299	+	1.63036i	−0.707513	+	0.706701i	$0.750183\pi$
$368$	−86.4647	−	129.404i	−0.234958	−	0.351640i
$369$	−54.3901	−	273.438i	−0.147399	−	0.741024i
$370$		0			0
$371$	415.266	−	621.490i	1.11932	−	1.67517i
$372$	79.4211	+	32.8973i	0.213498	+	0.0884336i
$373$		−	250.623i		−	0.671912i	−0.941878	−	0.335956i	$-0.890941\pi$
$373$		−	250.623i		−	0.671912i	0.941878	−	0.335956i	$-0.109059\pi$
$374$	−228.073	+	439.971i	−0.609822	+	1.17639i
$375$		0			0
$376$	277.068	−	668.901i	0.736883	−	1.77899i
$377$	48.5551	+	32.4435i	0.128793	+	0.0860570i
$378$	−204.310	−	204.310i	−0.540501	−	0.540501i
$379$	−532.918	+	106.004i	−1.40612	+	0.279694i	−0.839084	−	0.544002i	$-0.816909\pi$
$379$	−532.918	+	106.004i	−1.40612	+	0.279694i	−0.567032	+	0.823696i	$0.691909\pi$
$380$		0			0
$381$	−250.718	−	49.8709i	−0.658053	−	0.130895i
$382$	−42.5113	+	17.6088i	−0.111286	+	0.0460963i
$383$	0.487893	+	1.17788i	0.00127387	+	0.00307540i	0.924515	−	0.381145i	$-0.124470\pi$
$383$	0.487893	+	1.17788i	0.00127387	+	0.00307540i	−0.923241	+	0.384221i	$0.874470\pi$
$384$	−23.7088	+	119.192i	−0.0617418	+	0.310397i
$385$		0			0
$386$	−32.2810	−	162.287i	−0.0836294	−	0.420434i
$387$	−35.9627	+	35.9627i	−0.0929268	+	0.0929268i
$388$	80.5592	−	120.565i	0.207627	−	0.310735i
$389$	427.876	+	177.232i	1.09994	+	0.455609i	0.857461	−	0.514548i	$-0.172040\pi$
$389$	427.876	+	177.232i	1.09994	+	0.455609i	0.242476	+	0.970157i	$0.422040\pi$
$390$		0			0
$391$	−48.3981	+	564.375i	−0.123780	+	1.44341i
$392$	282.090			0.719618
$393$	77.8744	−	188.006i	0.198154	−	0.478386i
$394$	−156.368	−	104.482i	−0.396872	−	0.265182i
$395$		0			0
$396$	−517.429	+	102.923i	−1.30664	+	0.259907i
$397$	349.464	−	233.505i	0.880263	−	0.588173i	−0.0312191	−	0.999513i	$-0.509939\pi$
$397$	349.464	−	233.505i	0.880263	−	0.588173i	0.911482	+	0.411340i	$0.134939\pi$
$398$	−36.4029	−	7.24098i	−0.0914645	−	0.0181934i
$399$	−488.447	+	202.321i	−1.22418	+	0.507071i
$400$		0			0
$401$	−101.827	+	511.917i	−0.253932	+	1.27660i	0.617689	+	0.786422i	$0.288069\pi$
$401$	−101.827	+	511.917i	−0.253932	+	1.27660i	−0.871621	+	0.490180i	$0.836931\pi$
$402$	204.324	+	305.792i	0.508268	+	0.760677i
$403$	11.8602	+	59.6253i	0.0294298	+	0.147953i
$404$	141.500	−	141.500i	0.350247	−	0.350247i
$405$		0			0
$406$	109.466	+	45.3425i	0.269622	+	0.111681i
$407$		−	747.911i		−	1.83762i
$408$	−528.499	+	445.015i	−1.29534	+	1.09072i
$409$	12.0816			0.0295393			0.0147696	−	0.999891i	$-0.495299\pi$
$409$	12.0816			0.0295393			0.0147696	+	0.999891i	$0.495299\pi$
$410$		0			0
$411$	695.702	+	464.853i	1.69271	+	1.13103i
$412$	39.8270	+	39.8270i	0.0966675	+	0.0966675i
$413$	98.2231	−	19.5378i	0.237828	−	0.0473070i
$414$	545.760	−	364.665i	1.31826	−	0.880834i
$415$		0			0
$416$	−163.269	+	67.6283i	−0.392474	+	0.162568i
$417$	112.328	+	271.185i	0.269373	+	0.650323i
$418$	69.7661	−	350.738i	0.166905	−	0.839086i
$419$	162.741	+	243.559i	0.388403	+	0.581287i	0.973219	−	0.229880i	$-0.0738332\pi$
$419$	162.741	+	243.559i	0.388403	+	0.581287i	−0.584816	+	0.811166i	$0.698833\pi$
$420$		0			0
$421$	−338.834	+	338.834i	−0.804832	+	0.804832i	−0.983846	−	0.179015i	$-0.942709\pi$
$421$	−338.834	+	338.834i	−0.804832	+	0.804832i	0.179015	+	0.983846i	$0.442709\pi$
$422$	−299.737	+	448.588i	−0.710277	+	1.06300i
$423$	1068.52	+	442.594i	2.52604	+	1.04632i
$424$			704.864i			1.66242i
$425$		0			0
$426$	266.394			0.625337
$427$	−244.288	+	589.763i	−0.572103	+	1.38118i
$428$	−158.623	−	105.988i	−0.370613	−	0.247636i
$429$	−437.843	−	437.843i	−1.02061	−	1.02061i
$430$		0			0
$431$	126.914	−	84.8015i	0.294465	−	0.196755i	−0.399558	−	0.916708i	$-0.630836\pi$
$431$	126.914	−	84.8015i	0.294465	−	0.196755i	0.694023	+	0.719953i	$0.255836\pi$
$432$	101.218	+	20.1336i	0.234301	+	0.0466054i
$433$	570.937	−	236.490i	1.31856	−	0.546165i	0.391190	−	0.920310i	$-0.372064\pi$
$433$	570.937	−	236.490i	1.31856	−	0.546165i	0.927370	+	0.374145i	$0.122064\pi$
$434$	47.2034	+	113.959i	0.108764	+	0.262578i
$435$		0			0
$436$	−54.8742	−	82.1251i	−0.125858	−	0.188360i
$437$	−79.7436	−	400.898i	−0.182480	−	0.917388i
$438$	204.843	−	204.843i	0.467677	−	0.467677i
$439$	263.064	−	393.703i	0.599235	−	0.896818i	−0.400576	−	0.916263i	$-0.631190\pi$
$439$	263.064	−	393.703i	0.599235	−	0.896818i	0.999811	+	0.0194454i	$0.00619006\pi$
$440$		0			0
$441$			450.616i			1.02181i
$442$	−151.956	−	44.0076i	−0.343792	−	0.0995648i
$443$	405.016			0.914257			0.457129	−	0.889401i	$-0.348878\pi$
$443$	405.016			0.914257			0.457129	+	0.889401i	$0.348878\pi$
$444$	129.197	−	311.910i	0.290985	−	0.702500i
$445$		0			0
$446$	−126.787	−	126.787i	−0.284276	−	0.284276i
$447$	38.8871	−	7.73512i	0.0869957	−	0.0173045i
$448$	−438.829	+	293.216i	−0.979530	+	0.654501i
$449$	557.010	+	110.796i	1.24056	+	0.246762i	0.771399	−	0.636352i	$-0.219557\pi$
$449$	557.010	+	110.796i	1.24056	+	0.246762i	0.469158	+	0.883114i	$0.344557\pi$
$450$		0			0
$451$	−157.884	−	381.165i	−0.350075	−	0.845155i
$452$	36.2550	−	182.266i	0.0802102	−	0.403244i
$453$	−200.129	−	299.514i	−0.441786	−	0.661179i
$454$	−20.1377	−	101.239i	−0.0443563	−	0.222994i
$455$		0			0
$456$	276.987	−	414.540i	0.607427	−	0.909079i
$457$	−455.582	−	188.708i	−0.996898	−	0.412929i	−0.176239	−	0.984347i	$-0.556393\pi$
$457$	−455.582	−	188.708i	−0.996898	−	0.412929i	−0.820659	+	0.571419i	$0.806393\pi$
$458$		−	74.6324i		−	0.162953i
$459$	−241.936	−	287.322i	−0.527093	−	0.625975i
$460$		0			0
$461$	−128.852	+	311.076i	−0.279505	+	0.674785i	−0.999822	−	0.0188600i	$-0.993996\pi$
$461$	−128.852	+	311.076i	−0.279505	+	0.674785i	0.720317	+	0.693645i	$0.243996\pi$
$462$	−1044.62	−	697.990i	−2.26107	−	1.51080i
$463$	−229.089	−	229.089i	−0.494792	−	0.494792i	0.415020	−	0.909812i	$-0.363775\pi$
$463$	−229.089	−	229.089i	−0.494792	−	0.494792i	−0.909812	+	0.415020i	$0.863775\pi$
$464$	−41.5070	+	8.25625i	−0.0894546	+	0.0177936i
$465$		0			0
$466$	462.646	+	92.0259i	0.992802	+	0.197481i
$467$	1.34121	−	0.555546i	0.00287196	−	0.00118961i	−0.381247	−	0.924473i	$-0.624505\pi$
$467$	1.34121	−	0.555546i	0.00287196	−	0.00118961i	0.384119	+	0.923284i	$0.374505\pi$
$468$	−64.4491	−	155.594i	−0.137712	−	0.332465i
$469$	94.5805	−	475.488i	0.201664	−	1.01383i
$470$		0			0
$471$	219.893	+	1105.48i	0.466863	+	2.34708i
$472$	−66.7794	+	66.7794i	−0.141482	+	0.141482i
$473$	−41.8137	+	62.5787i	−0.0884011	+	0.132302i
$474$	−335.636	−	139.025i	−0.708093	−	0.293302i
$475$		0			0
$476$	293.810	+	25.1957i	0.617248	+	0.0529322i
$477$	−1125.96			−2.36051
$478$	51.1795	−	123.558i	0.107070	−	0.258490i
$479$	−603.522	−	403.261i	−1.25996	−	0.841880i	−0.267397	−	0.963587i	$-0.586163\pi$
$479$	−603.522	−	403.261i	−1.25996	−	0.841880i	−0.992566	+	0.121706i	$0.961163\pi$
$480$		0			0
$481$	234.166	−	46.5785i	0.486831	−	0.0968368i
$482$	202.953	−	135.609i	0.421064	−	0.281346i
$483$	−1408.43	−	280.155i	−2.91601	−	0.580030i
$484$	−507.178	+	210.080i	−1.04789	+	0.434049i
$485$		0			0
$486$	79.6728	−	400.542i	0.163936	−	0.824161i
$487$	167.730	+	251.026i	0.344416	+	0.515454i	0.962726	−	0.270480i	$-0.0871824\pi$
$487$	167.730	+	251.026i	0.344416	+	0.515454i	−0.618310	+	0.785934i	$0.712182\pi$
$488$	−117.440	−	590.410i	−0.240656	−	1.20986i
$489$	−331.032	+	331.032i	−0.676957	+	0.676957i
$490$		0			0
$491$	299.474	+	124.046i	0.609927	+	0.252640i	0.666197	−	0.745776i	$-0.267921\pi$
$491$	299.474	+	124.046i	0.609927	+	0.252640i	−0.0562705	+	0.998416i	$0.517921\pi$
$492$		−	186.235i		−	0.378527i
$493$	136.749	+	70.8881i	0.277381	+	0.143789i
$494$	114.159			0.231090
$495$		0			0
$496$	−36.6320	−	24.4767i	−0.0738549	−	0.0493483i
$497$	−248.310	−	248.310i	−0.499619	−	0.499619i
$498$	16.4360	−	3.26933i	0.0330041	−	0.00656492i
$499$	−1.17493	+	0.785065i	−0.00235457	+	0.00157328i	−0.556747	−	0.830682i	$-0.687951\pi$
$499$	−1.17493	+	0.785065i	−0.00235457	+	0.00157328i	0.554392	+	0.832255i	$0.312951\pi$
$500$		0			0
$501$	412.197	−	170.738i	0.822748	−	0.340793i
$502$	−199.862	−	482.510i	−0.398131	−	0.961174i
$503$	16.5439	−	83.1720i	0.0328905	−	0.165352i	−0.960849	−	0.277072i	$-0.910636\pi$
$503$	16.5439	−	83.1720i	0.0328905	−	0.165352i	0.993740	+	0.111720i	$0.0356360\pi$
$504$	−586.327	−	877.501i	−1.16335	−	1.74107i
$505$		0			0
$506$	686.837	−	686.837i	1.35738	−	1.35738i
$507$	−336.964	+	504.302i	−0.664623	+	0.994679i
$508$	−95.0570	−	39.3739i	−0.187120	−	0.0775076i
$509$		−	118.487i		−	0.232784i	−0.993203	−	0.116392i	$-0.962867\pi$
$509$		−	118.487i		−	0.232784i	0.993203	−	0.116392i	$-0.0371329\pi$
$510$		0			0
$511$	−381.875			−0.747309
$512$	110.075	−	265.744i	0.214990	−	0.519031i
$513$	225.368	+	150.586i	0.439313	+	0.293540i
$514$	486.734	+	486.734i	0.946953	+	0.946953i
$515$		0			0
$516$	−28.2482	+	18.8748i	−0.0547445	+	0.0365791i
$517$	1678.62	+	333.898i	3.24685	+	0.645838i
$518$	447.550	−	185.381i	0.863997	−	0.357879i
$519$	−367.806	−	887.962i	−0.708682	−	1.71091i
$520$		0			0
$521$	−200.786	−	300.498i	−0.385386	−	0.576772i	0.587163	−	0.809469i	$-0.300245\pi$
$521$	−200.786	−	300.498i	−0.385386	−	0.576772i	−0.972549	+	0.232697i	$0.925245\pi$
$522$	−34.8208	−	175.056i	−0.0667064	−	0.335356i
$523$	−280.565	+	280.565i	−0.536453	+	0.536453i	−0.922485	−	0.386032i	$-0.873845\pi$
$523$	−280.565	+	280.565i	−0.536453	+	0.536453i	0.386032	+	0.922485i	$0.373845\pi$
$524$	45.5041	−	68.1018i	0.0868400	−	0.129965i
$525$		0			0
$526$			757.422i			1.43997i
$527$	48.4817	+	152.847i	0.0919957	+	0.290032i
$528$	448.737			0.849880
$529$	222.434	−	537.003i	0.420480	−	1.01513i
$530$		0			0
$531$	−106.675	−	106.675i	−0.200894	−	0.200894i
$532$	−208.705	+	41.5140i	−0.392303	+	0.0780339i
$533$	109.507	−	73.1705i	0.205455	−	0.137281i
$534$	−1040.20	−	206.909i	−1.94794	−	0.387469i
$535$		0			0
$536$	174.954	+	422.376i	0.326406	+	0.788015i
$537$	41.3710	−	207.986i	0.0770410	−	0.387311i
$538$	−143.927	−	215.401i	−0.267522	−	0.400374i
$539$	130.094	+	654.024i	0.241361	+	1.21340i
$540$		0			0
$541$	9.85351	−	14.7468i	0.0182135	−	0.0272584i	−0.822251	−	0.569125i	$-0.807282\pi$
$541$	9.85351	−	14.7468i	0.0182135	−	0.0272584i	0.840465	+	0.541866i	$0.182282\pi$
$542$	697.934	+	289.094i	1.28770	+	0.533383i
$543$			988.081i			1.81967i
$544$	−408.281	+	224.905i	−0.750517	+	0.413429i
$545$		0			0
$546$	153.479	−	370.532i	0.281098	−	0.678630i
$547$	−367.596	−	245.620i	−0.672021	−	0.449030i	0.172174	−	0.985067i	$-0.444921\pi$
$547$	−367.596	−	245.620i	−0.672021	−	0.449030i	−0.844195	+	0.536036i	$0.819921\pi$
$548$	238.132	+	238.132i	0.434548	+	0.434548i
$549$	943.133	−	187.601i	1.71791	−	0.341714i
$550$		0			0
$551$	−109.014	−	21.6842i	−0.197847	−	0.0393542i
$552$	1251.11	−	518.226i	2.26650	−	0.938815i
$553$	183.265	+	442.440i	0.331401	+	0.800073i
$554$	−15.8799	+	79.8339i	−0.0286642	+	0.144104i
$555$		0			0
$556$	23.0485	+	115.873i	0.0414541	+	0.208404i
$557$	286.858	−	286.858i	0.515005	−	0.515005i	−0.401051	−	0.916056i	$-0.631355\pi$
$557$	286.858	−	286.858i	0.515005	−	0.515005i	0.916056	+	0.401051i	$0.131355\pi$
$558$	103.231	−	154.496i	0.185001	−	0.276874i
$559$	−22.1970	−	9.19432i	−0.0397085	−	0.0164478i
$560$		0			0
$561$	−1275.50	−	1020.09i	−2.27361	−	1.81834i
$562$	−20.2301			−0.0359966
$563$	331.993	−	801.501i	0.589685	−	1.42362i	−0.294120	−	0.955769i	$-0.595026\pi$
$563$	331.993	−	801.501i	0.589685	−	1.42362i	0.883805	−	0.467856i	$-0.154974\pi$
$564$	642.376	+	429.222i	1.13896	+	0.761032i
$565$		0			0
$566$	−333.702	+	66.3775i	−0.589580	+	0.117275i
$567$	−132.918	+	88.8128i	−0.234423	+	0.156636i
$568$	324.789	+	64.6046i	0.571812	+	0.113740i
$569$	−731.591	+	303.035i	−1.28575	+	0.532575i	−0.917716	−	0.397238i	$-0.869969\pi$
$569$	−731.591	+	303.035i	−1.28575	+	0.532575i	−0.368033	+	0.929813i	$0.619969\pi$
$570$		0			0
$571$	−128.468	+	645.854i	−0.224988	+	1.13109i	0.688816	+	0.724936i	$0.258131\pi$
$571$	−128.468	+	645.854i	−0.224988	+	1.13109i	−0.913804	+	0.406156i	$0.866869\pi$
$572$	−138.461	−	207.222i	−0.242066	−	0.362277i
$573$	−29.5848	−	148.733i	−0.0516314	−	0.259568i
$574$	188.955	−	188.955i	0.329191	−	0.329191i
$575$		0			0
$576$	734.516	+	304.246i	1.27520	+	0.528206i
$577$			156.835i			0.271810i	0.990722	+	0.135905i	$0.0433943\pi$
$577$			156.835i			0.271810i	−0.990722	+	0.135905i	$0.956606\pi$
$578$	−411.184	−	71.0449i	−0.711392	−	0.122915i
$579$	545.323			0.941836
$580$		0			0
$581$	−18.3677	−	12.2729i	−0.0316140	−	0.0211238i
$582$	−367.816	−	367.816i	−0.631987	−	0.631987i
$583$	−1634.22	+	325.067i	−2.80313	+	0.557576i
$584$	299.423	−	200.068i	0.512711	−	0.342583i
$585$		0			0
$586$	110.794	−	45.8925i	0.189069	−	0.0783149i
$587$	341.417	+	824.253i	0.581630	+	1.40418i	0.891335	+	0.453346i	$0.149770\pi$
$587$	341.417	+	824.253i	0.581630	+	1.40418i	−0.309705	+	0.950833i	$0.600230\pi$
$588$	−58.7246	+	295.228i	−0.0998717	+	0.502089i
$589$	−64.2856	−	96.2103i	−0.109144	−	0.163345i
$590$		0			0
$591$	438.257	−	438.257i	0.741552	−	0.741552i
$592$	−96.1273	+	143.865i	−0.162377	+	0.243015i
$593$	−523.732	−	216.937i	−0.883191	−	0.365830i	−0.105457	−	0.994424i	$-0.533631\pi$
$593$	−523.732	−	216.937i	−0.883191	−	0.365830i	−0.777733	+	0.628594i	$0.783631\pi$
$594$			644.100i			1.08434i
$595$		0			0
$596$	15.9583			0.0267758
$597$	46.8106	−	113.011i	0.0784098	−	0.189298i
$598$	257.819	+	172.269i	0.431135	+	0.288075i
$599$	−825.842	−	825.842i	−1.37870	−	1.37870i	−0.846818	−	0.531883i	$-0.821484\pi$
$599$	−825.842	−	825.842i	−1.37870	−	1.37870i	−0.531883	−	0.846818i	$-0.678516\pi$
$600$		0			0
$601$	159.974	−	106.891i	0.266180	−	0.177856i	−0.415317	−	0.909677i	$-0.636329\pi$
$601$	159.974	−	106.891i	0.266180	−	0.177856i	0.681497	+	0.731821i	$0.261329\pi$
$602$	−47.8113	−	9.51026i	−0.0794208	−	0.0157978i
$603$	−674.711	+	279.475i	−1.11892	+	0.463474i
$604$	−55.4839	−	133.950i	−0.0918608	−	0.221772i
$605$		0			0
$606$	−398.823	−	596.881i	−0.658124	−	0.984952i
$607$	70.8263	+	356.068i	0.116682	+	0.586602i	0.994244	+	0.107139i	$0.0341689\pi$
$607$	70.8263	+	356.068i	0.116682	+	0.586602i	−0.877562	+	0.479464i	$0.840831\pi$
$608$	237.844	−	237.844i	0.391191	−	0.391191i
$609$	−216.944	+	324.680i	−0.356230	+	0.533136i
$610$		0			0
$611$			546.359i			0.894205i
$612$	−214.333	−	389.088i	−0.350217	−	0.635765i
$613$	372.159			0.607111			0.303556	−	0.952814i	$-0.401826\pi$
$613$	372.159			0.607111			0.303556	+	0.952814i	$0.401826\pi$
$614$	193.652	−	467.517i	0.315394	−	0.761429i
$615$		0			0
$616$	−1104.33	−	1104.33i	−1.79274	−	1.79274i
$617$	−157.929	+	31.4141i	−0.255963	+	0.0509143i	−0.321404	−	0.946942i	$-0.604155\pi$
$617$	−157.929	+	31.4141i	−0.255963	+	0.0509143i	0.0654406	+	0.997856i	$0.479155\pi$
$618$	168.000	−	112.254i	0.271844	−	0.181641i
$619$	764.806	+	152.129i	1.23555	+	0.245766i	0.769301	−	0.638887i	$-0.220605\pi$
$619$	764.806	+	152.129i	1.23555	+	0.245766i	0.466250	+	0.884653i	$0.345605\pi$
$620$		0			0
$621$	281.737	+	680.174i	0.453683	+	1.09529i
$622$	−85.7586	+	431.137i	−0.137876	+	0.693147i
$623$	776.726	+	1162.45i	1.24675	+	1.86590i
$624$	27.9465	+	140.496i	0.0447860	+	0.225154i
$625$		0			0
$626$	−313.756	+	469.570i	−0.501208	+	0.750111i
$627$	1088.85	+	451.016i	1.73660	+	0.719323i
$628$			453.661i			0.722391i
$629$	600.275	−	190.402i	0.954332	−	0.302706i
$630$		0			0
$631$	−158.851	+	383.501i	−0.251745	+	0.607766i	−0.998345	−	0.0575068i	$-0.981685\pi$
$631$	−158.851	+	383.501i	−0.251745	+	0.607766i	0.746600	+	0.665273i	$0.231685\pi$
$632$	−375.494	−	250.897i	−0.594137	−	0.396989i
$633$	−1257.27	−	1257.27i	−1.98621	−	1.98621i
$634$	−66.3734	+	13.2025i	−0.104690	+	0.0208241i
$635$		0			0
$636$	−737.693	−	146.736i	−1.15989	−	0.230717i
$637$	−196.669	+	81.4628i	−0.308742	+	0.127885i
$638$	−101.078	−	244.023i	−0.158429	−	0.382481i
$639$	−103.201	+	518.825i	−0.161503	+	0.811932i
$640$		0			0
$641$	176.168	+	885.657i	0.274833	+	1.38168i	0.833606	+	0.552359i	$0.186272\pi$
$641$	176.168	+	885.657i	0.274833	+	1.38168i	−0.558773	+	0.829321i	$0.688728\pi$
$642$	−483.920	+	483.920i	−0.753769	+	0.753769i
$643$	−318.185	+	476.198i	−0.494845	+	0.740587i	−0.991885	−	0.127140i	$-0.959420\pi$
$643$	−318.185	+	476.198i	−0.494845	+	0.740587i	0.497040	+	0.867728i	$0.334420\pi$
$644$	−533.991	−	221.186i	−0.829179	−	0.343457i
$645$		0			0
$646$	299.264	−	33.2959i	0.463257	−	0.0515416i
$647$	178.146			0.275342			0.137671	−	0.990478i	$-0.456038\pi$
$647$	178.146			0.275342			0.137671	+	0.990478i	$0.456038\pi$
$648$	57.6891	−	139.274i	0.0890264	−	0.214929i
$649$	−185.625	−	124.030i	−0.286016	−	0.191110i
$650$		0			0
$651$	−398.704	+	79.3071i	−0.612448	+	0.121824i
$652$	−156.671	+	104.684i	−0.240293	+	0.160558i
$653$	−1242.54	−	247.157i	−1.90282	−	0.378495i	−0.904025	−	0.427479i	$-0.859402\pi$
$653$	−1242.54	−	247.157i	−1.90282	−	0.378495i	−0.998800	+	0.0489839i	$0.984402\pi$
$654$	−327.352	+	135.594i	−0.500538	+	0.207330i
$655$		0			0
$656$	−18.6205	+	93.6115i	−0.0283849	+	0.142701i
$657$	319.593	+	478.304i	0.486443	+	0.728013i
$658$	216.267	+	1087.25i	0.328674	+	1.65236i
$659$	−399.585	+	399.585i	−0.606351	+	0.606351i	−0.941990	−	0.335640i	$-0.891047\pi$
$659$	−399.585	+	399.585i	−0.606351	+	0.606351i	0.335640	+	0.941990i	$0.391047\pi$
$660$		0			0
$661$	−438.279	−	181.541i	−0.663054	−	0.274646i	0.0256692	−	0.999670i	$-0.491828\pi$
$661$	−438.279	−	181.541i	−0.663054	−	0.274646i	−0.688723	+	0.725025i	$0.741828\pi$
$662$			211.859i			0.320028i
$663$	239.948	−	462.879i	0.361913	−	0.698158i
$664$	20.8318			0.0313732
$665$		0			0
$666$	−606.750	−	405.417i	−0.911036	−	0.608735i
$667$	−213.477	−	213.477i	−0.320056	−	0.320056i
$668$	176.125	−	35.0334i	0.263660	−	0.0524451i
$669$	491.337	−	328.301i	0.734435	−	0.490734i
$670$		0			0
$671$	1314.70	−	544.567i	1.95932	−	0.811576i
$672$	−452.219	−	1091.75i	−0.672944	−	1.62463i
$673$	167.516	−	842.162i	0.248910	−	1.25135i	−0.630838	−	0.775914i	$-0.717289\pi$
$673$	167.516	−	842.162i	0.248910	−	1.25135i	0.879748	−	0.475440i	$-0.157711\pi$
$674$	14.7569	+	22.0853i	0.0218945	+	0.0327675i
$675$		0			0
$676$	−172.618	+	172.618i	−0.255352	+	0.255352i
$677$	177.774	−	266.057i	0.262591	−	0.392995i	−0.676622	−	0.736331i	$-0.736557\pi$
$677$	177.774	−	266.057i	0.262591	−	0.392995i	0.939213	+	0.343336i	$0.111557\pi$
$678$	−615.910	−	255.118i	−0.908422	−	0.376281i
$679$			685.697i			1.00986i
$680$		0			0
$681$	340.187			0.499541
$682$	105.226	−	254.038i	0.154290	−	0.372490i
$683$	412.510	+	275.630i	0.603968	+	0.403558i	0.819616	−	0.572913i	$-0.194187\pi$
$683$	412.510	+	275.630i	0.603968	+	0.403558i	−0.215649	+	0.976471i	$0.569187\pi$
$684$	226.663	+	226.663i	0.331379	+	0.331379i
$685$		0			0
$686$	173.661	−	116.037i	0.253150	−	0.169150i
$687$	241.237	+	47.9851i	0.351146	+	0.0698473i
$688$	16.0862	−	6.66312i	0.0233811	−	0.00968477i
$689$	−203.553	−	491.420i	−0.295432	−	0.713236i
$690$		0			0
$691$	274.571	+	410.925i	0.397354	+	0.594682i	0.975163	−	0.221490i	$-0.0710921\pi$
$691$	274.571	+	410.925i	0.397354	+	0.594682i	−0.577809	+	0.816172i	$0.696092\pi$
$692$	−75.4695	−	379.411i	−0.109060	−	0.548281i
$693$	1764.08	−	1764.08i	2.54557	−	2.54557i
$694$	−450.682	+	674.493i	−0.649397	+	0.971891i
$695$		0			0
$696$		−	368.236i		−	0.529075i
$697$	265.730	−	223.754i	0.381248	−	0.321024i
$698$	336.770			0.482478
$699$	−594.918	+	1436.26i	−0.851099	+	2.05474i
$700$		0			0
$701$	−681.196	−	681.196i	−0.971749	−	0.971749i	0.0278623	−	0.999612i	$-0.491130\pi$
$701$	−681.196	−	681.196i	−0.971749	−	0.971749i	−0.999612	+	0.0278623i	$0.991130\pi$
$702$	−201.663	+	40.1133i	−0.287270	+	0.0571415i
$703$	−377.846	+	252.469i	−0.537476	+	0.359130i
$704$	1153.91	+	229.527i	1.63908	+	0.326033i
$705$		0			0
$706$	27.3957	+	66.1392i	0.0388042	+	0.0936816i
$707$	−184.613	+	928.114i	−0.261122	+	1.31275i
$708$	−55.9877	−	83.7915i	−0.0790786	−	0.118350i
$709$	−252.171	−	1267.75i	−0.355672	−	1.78808i	−0.581110	−	0.813825i	$-0.697381\pi$
$709$	−252.171	−	1267.75i	−0.355672	−	1.78808i	0.225438	−	0.974258i	$-0.427619\pi$
$710$		0			0
$711$	400.788	−	599.822i	0.563697	−	0.843631i
$712$	−1218.04	−	504.529i	−1.71073	−	0.708609i
$713$		−	314.293i		−	0.440804i
$714$	294.272	−	1016.10i	0.412145	−	1.42312i
$715$		0			0
$716$	32.6631	−	78.8556i	0.0456188	−	0.110134i
$717$	366.476	+	244.872i	0.511125	+	0.341522i
$718$	286.364	+	286.364i	0.398836	+	0.398836i
$719$	−1045.14	+	207.892i	−1.45361	+	0.289141i	−0.857799	−	0.513985i	$-0.828169\pi$
$719$	−1045.14	+	207.892i	−1.45361	+	0.289141i	−0.595810	+	0.803126i	$0.703169\pi$
$720$		0			0
$721$	−261.230	−	51.9618i	−0.362316	−	0.0720691i
$722$	280.815	−	116.317i	0.388940	−	0.161104i
$723$	307.845	+	743.203i	0.425788	+	1.02794i
$724$	−77.5863	+	390.053i	−0.107163	+	0.538747i
$725$		0			0
$726$	384.194	+	1931.47i	0.529192	+	2.66043i
$727$	2.23924	−	2.23924i	0.00308011	−	0.00308011i	−0.705565	−	0.708645i	$-0.749307\pi$
$727$	2.23924	−	2.23924i	0.00308011	−	0.00308011i	0.708645	+	0.705565i	$0.249307\pi$
$728$	276.983	−	414.534i	0.380471	−	0.569415i
$729$	1096.70	+	454.269i	1.50439	+	0.623140i
$730$		0			0
$731$	−60.8706	−	17.6286i	−0.0832704	−	0.0241157i
$732$	642.357			0.877536
$733$	−206.148	+	497.685i	−0.281238	+	0.678969i	−0.999865	−	0.0164266i	$-0.994771\pi$
$733$	−206.148	+	497.685i	−0.281238	+	0.678969i	0.718627	+	0.695396i	$0.244771\pi$
$734$	732.401	+	489.374i	0.997821	+	0.666723i
$735$		0			0
$736$	896.068	−	178.239i	1.21748	−	0.242172i
$737$	−898.591	+	600.419i	−1.21926	+	0.814680i
$738$	−394.807	−	78.5320i	−0.534969	−	0.106412i
$739$	893.274	−	370.006i	1.20876	−	0.500685i	0.314941	−	0.949111i	$-0.398015\pi$
$739$	893.274	−	370.006i	1.20876	−	0.500685i	0.893820	+	0.448426i	$0.148015\pi$
$740$		0			0
$741$	−73.3986	+	368.999i	−0.0990534	+	0.497975i
$742$	−599.588	−	897.347i	−0.808070	−	1.20936i
$743$	229.986	+	1156.22i	0.309537	+	1.55615i	0.751879	+	0.659302i	$0.229148\pi$
$743$	229.986	+	1156.22i	0.309537	+	1.55615i	−0.442341	+	0.896847i	$0.645852\pi$
$744$	271.069	−	271.069i	0.364340	−	0.364340i
$745$		0			0
$746$	−334.321	−	138.480i	−0.448151	−	0.185630i
$747$			33.2771i			0.0445477i
$748$	−423.412	−	502.844i	−0.566059	−	0.672251i
$749$	902.141			1.20446
$750$		0			0
$751$	−450.127	−	300.765i	−0.599370	−	0.400486i	0.218544	−	0.975827i	$-0.429869\pi$
$751$	−450.127	−	300.765i	−0.599370	−	0.400486i	−0.817914	+	0.575341i	$0.804869\pi$
$752$	−279.976	−	279.976i	−0.372309	−	0.372309i
$753$	1688.14	−	335.791i	2.24188	−	0.445938i
$754$	70.1070	−	46.8440i	0.0929802	−	0.0621274i
$755$		0			0
$756$	354.094	−	146.671i	0.468379	−	0.194009i
$757$	158.525	+	382.713i	0.209412	+	0.505565i	0.993331	−	0.115298i	$-0.0367823\pi$
$757$	158.525	+	382.713i	0.209412	+	0.505565i	−0.783919	+	0.620863i	$0.786782\pi$
$758$	−153.055	+	769.462i	−0.201920	+	1.01512i
$759$	1778.49	+	2661.69i	2.34320	+	3.50684i
$760$		0			0
$761$	1002.23	−	1002.23i	1.31699	−	1.31699i	0.400840	−	0.916148i	$-0.368718\pi$
$761$	1002.23	−	1002.23i	1.31699	−	1.31699i	0.916148	−	0.400840i	$-0.131282\pi$
$762$	−205.058	+	306.891i	−0.269105	+	0.402745i
$763$	431.520	+	178.741i	0.565557	+	0.234261i
$764$		−	61.0364i		−	0.0798906i
$765$		0			0
$766$	1.84082			0.00240316
$767$	27.2727	−	65.8422i	0.0355577	−	0.0858438i
$768$	1068.14	+	713.705i	1.39080	+	0.929304i
$769$	865.325	+	865.325i	1.12526	+	1.12526i	0.990938	+	0.134322i	$0.0428857\pi$
$769$	865.325	+	865.325i	1.12526	+	1.12526i	0.134322	+	0.990938i	$0.457114\pi$
$770$		0			0
$771$	−1886.24	+	1260.34i	−2.44648	+	1.63469i
$772$	215.271	+	42.8200i	0.278848	+	0.0554663i
$773$	1118.10	−	463.133i	1.44645	−	0.599138i	0.485094	−	0.874462i	$-0.338785\pi$
$773$	1118.10	−	463.133i	1.44645	−	0.599138i	0.961351	+	0.275324i	$0.0887852\pi$
$774$	28.1017	+	67.8436i	0.0363072	+	0.0876532i
$775$		0			0
$776$	−359.243	−	537.646i	−0.462942	−	0.692842i
$777$	311.462	+	1565.83i	0.400852	+	2.01522i
$778$	472.840	−	472.840i	0.607763	−	0.607763i
$779$	−139.269	+	208.431i	−0.178779	+	0.267562i
$780$		0			0
$781$			782.816i			1.00233i
$782$	726.110	+	376.403i	0.928530	+	0.481333i
$783$	200.194			0.255676
$784$	59.0361	−	142.526i	0.0753011	−	0.181793i
$785$		0			0
$786$	−207.762	−	207.762i	−0.264329	−	0.264329i
$787$	−788.186	+	156.780i	−1.00151	+	0.199212i	−0.668500	−	0.743712i	$-0.733063\pi$
$787$	−788.186	+	156.780i	−1.00151	+	0.199212i	−0.333007	+	0.942924i	$0.608063\pi$
$788$	207.418	−	138.592i	0.263221	−	0.175879i
$789$	−2448.25	−	486.986i	−3.10297	−	0.617220i
$790$		0			0
$791$	336.301	+	811.902i	0.425159	+	1.02642i
$792$	−458.972	+	2307.41i	−0.579510	+	2.91340i
$793$	252.378	+	377.710i	0.318257	+	0.476305i
$794$	−118.391	−	595.192i	−0.149107	−	0.749612i
$795$		0			0
$796$	27.3527	−	40.9362i	0.0343627	−	0.0514274i
$797$	−475.120	−	196.801i	−0.596135	−	0.246927i	0.0641526	−	0.997940i	$-0.479566\pi$
$797$	−475.120	−	196.801i	−0.596135	−	0.246927i	−0.660288	+	0.751013i	$0.729566\pi$
$798$			763.359i			0.956590i
$799$	159.353	+	1432.27i	0.199441	+	1.79257i
$800$		0			0
$801$	805.945	−	1945.72i	1.00617	−	2.42912i
$802$	626.612	+	418.689i	0.781312	+	0.522056i
$803$	601.944	+	601.944i	0.749619	+	0.749619i
$804$	−478.469	+	95.1734i	−0.595111	+	0.118375i
$805$		0			0
$806$	86.0908	+	17.1245i	0.106812	+	0.0212463i
$807$	788.789	−	326.727i	0.977433	−	0.404866i
$808$	−341.495	−	824.442i	−0.422643	−	1.02035i
$809$	220.058	−	1106.31i	0.272013	−	1.36750i	−0.567148	−	0.823616i	$-0.691953\pi$
$809$	220.058	−	1106.31i	0.272013	−	1.36750i	0.839160	−	0.543884i	$-0.183047\pi$
$810$		0			0
$811$	−37.4732	−	188.390i	−0.0462061	−	0.232294i	0.950781	−	0.309864i	$-0.100284\pi$
$811$	−37.4732	−	188.390i	−0.0462061	−	0.232294i	−0.996987	+	0.0775706i	$0.975284\pi$
$812$	−111.135	+	111.135i	−0.136866	+	0.136866i
$813$	−1383.19	+	2070.09i	−1.70134	+	2.54623i
$814$	−997.681	−	413.253i	−1.22565	−	0.507682i
$815$		0			0
$816$	114.239	+	360.157i	0.139998	+	0.441369i
$817$	45.7297			0.0559727
$818$	6.67558	−	16.1163i	0.00816086	−	0.0197021i
$819$	662.185	+	442.458i	0.808528	+	0.540241i
$820$		0			0
$821$	165.070	−	32.8346i	0.201060	−	0.0399934i	−0.0935327	−	0.995616i	$-0.529816\pi$
$821$	165.070	−	32.8346i	0.201060	−	0.0399934i	0.294593	+	0.955623i	$0.404816\pi$
$822$	1004.50	−	671.185i	1.22202	−	0.816527i
$823$	382.561	+	76.0962i	0.464838	+	0.0924620i	0.421952	−	0.906618i	$-0.361345\pi$
$823$	382.561	+	76.0962i	0.464838	+	0.0924620i	0.0428854	+	0.999080i	$0.486345\pi$
$824$	232.050	−	96.1183i	0.281614	−	0.116648i
$825$		0			0
$826$	28.2099	−	141.821i	0.0341524	−	0.171696i
$827$	−802.763	−	1201.42i	−0.970693	−	1.45274i	−0.889976	−	0.456007i	$-0.849279\pi$
$827$	−802.763	−	1201.42i	−0.970693	−	1.45274i	−0.0807169	−	0.996737i	$-0.525721\pi$
$828$	169.860	+	853.944i	0.205145	+	1.03133i
$829$	660.591	−	660.591i	0.796853	−	0.796853i	−0.185745	−	0.982598i	$-0.559470\pi$
$829$	660.591	−	660.591i	0.796853	−	0.796853i	0.982598	+	0.185745i	$0.0594699\pi$
$830$		0			0
$831$	−247.840	−	102.659i	−0.298243	−	0.123536i
$832$			375.577i			0.451414i
$833$	−491.802	+	270.914i	−0.590399	+	0.325227i
$834$	423.815			0.508172
$835$		0			0
$836$	394.416	+	263.541i	0.471790	+	0.315240i
$837$	147.368	+	147.368i	0.176067	+	0.176067i
$838$	414.819	−	82.5126i	0.495010	−	0.0984637i
$839$	−1004.02	+	670.862i	−1.19668	+	0.799597i	−0.984112	−	0.177549i	$-0.943183\pi$
$839$	−1004.02	+	670.862i	−1.19668	+	0.799597i	−0.212569	+	0.977146i	$0.568183\pi$
$840$		0			0
$841$	701.137	−	290.421i	0.833695	−	0.345328i
$842$	264.770	+	639.211i	0.314453	+	0.759157i
$843$	13.0070	−	65.3905i	0.0154294	−	0.0775688i
$844$	−397.594	−	595.041i	−0.471083	−	0.705025i
$845$		0			0
$846$	1180.80	−	1180.80i	1.39575	−	1.39575i
$847$	1442.25	−	2158.47i	1.70277	−	2.54838i
$848$	356.132	+	147.515i	0.419967	+	0.173956i
$849$		−	1121.32i		−	1.32075i
$850$		0			0
$851$	−1234.32			−1.45044
$852$	−135.227	+	326.467i	−0.158717	+	0.383177i
$853$	635.070	+	424.340i	0.744514	+	0.497468i	0.869036	−	0.494749i	$-0.164740\pi$
$853$	635.070	+	424.340i	0.744514	+	0.497468i	−0.124523	+	0.992217i	$0.539740\pi$
$854$	651.739	+	651.739i	0.763161	+	0.763161i
$855$		0			0
$856$	−707.357	+	472.641i	−0.826351	+	0.552150i
$857$	−851.226	−	169.319i	−0.993262	−	0.197572i	−0.328401	−	0.944539i	$-0.606510\pi$
$857$	−851.226	−	169.319i	−0.993262	−	0.197572i	−0.664862	+	0.746966i	$0.731510\pi$
$858$	−825.991	+	342.137i	−0.962693	+	0.398761i
$859$	156.442	+	377.684i	0.182121	+	0.439679i	0.988403	−	0.151852i	$-0.0485237\pi$
$859$	156.442	+	377.684i	0.182121	+	0.439679i	−0.806282	+	0.591531i	$0.798524\pi$
$860$		0			0
$861$	489.279	+	732.258i	0.568268	+	0.850473i
$862$	−42.9959	−	216.155i	−0.0498792	−	0.250760i
$863$	−74.8375	+	74.8375i	−0.0867179	+	0.0867179i	−0.749135	−	0.662417i	$-0.769531\pi$
$863$	−74.8375	+	74.8375i	−0.0867179	+	0.0867179i	0.662417	+	0.749135i	$0.269531\pi$
$864$	−336.582	+	503.730i	−0.389562	+	0.583021i
$865$		0			0
$866$		−	892.276i		−	1.03034i
$867$	494.013	−	1283.41i	0.569796	−	1.48029i
$868$	−163.619			−0.188501
$869$	408.534	−	986.289i	0.470120	−	1.13497i
$870$		0			0
$871$	−243.950	−	243.950i	−0.280080	−	0.280080i
$872$	−431.993	+	85.9288i	−0.495405	+	0.0985422i
$873$	858.845	−	573.862i	0.983786	−	0.657345i
$874$	−578.843	−	115.139i	−0.662292	−	0.131738i
$875$		0			0
$876$	147.053	+	355.018i	0.167869	+	0.405272i
$877$	277.754	−	1396.37i	0.316710	−	1.59221i	−0.414497	−	0.910051i	$-0.636042\pi$
$877$	277.754	−	1396.37i	0.316710	−	1.59221i	0.731206	−	0.682156i	$-0.238958\pi$
$878$	−379.829	−	568.454i	−0.432607	−	0.647442i
$879$	77.1047	+	387.632i	0.0877187	+	0.440992i
$880$		0			0
$881$	−695.799	+	1041.34i	−0.789783	+	1.18199i	0.189971	+	0.981790i	$0.439161\pi$
$881$	−695.799	+	1041.34i	−0.789783	+	1.18199i	−0.979754	+	0.200204i	$0.935839\pi$
$882$	601.103	+	248.985i	0.681523	+	0.282296i
$883$		−	1212.52i		−	1.37319i	−0.727042	−	0.686593i	$-0.759105\pi$
$883$		−	1212.52i		−	1.37319i	0.727042	−	0.686593i	$-0.240895\pi$
$884$	131.068	−	163.884i	0.148267	−	0.185389i
$885$		0			0
$886$	223.789	−	540.274i	0.252583	−	0.609790i
$887$	−630.801	−	421.488i	−0.711163	−	0.475184i	0.146622	−	0.989193i	$-0.453160\pi$
$887$	−630.801	−	421.488i	−0.711163	−	0.475184i	−0.857785	+	0.514009i	$0.828160\pi$
$888$	−1064.57	−	1064.57i	−1.19884	−	1.19884i
$889$	477.198	−	94.9205i	0.536780	−	0.106772i
$890$		0			0
$891$	349.510	+	69.5219i	0.392267	+	0.0780268i
$892$	219.738	−	91.0184i	0.246343	−	0.102039i
$893$	−397.957	−	960.754i	−0.445641	−	1.07587i
$894$	11.1685	−	56.1477i	0.0124927	−	0.0628050i
$895$		0			0
$896$	−45.1256	−	226.862i	−0.0503634	−	0.253194i
$897$	−722.597	+	722.597i	−0.805571	+	0.805571i
$898$	455.570	−	681.808i	0.507316	−	0.759252i
$899$	−78.9582	−	32.7055i	−0.0878289	−	0.0363799i
$900$		0			0
$901$	−676.937	−	1228.88i	−0.751318	−	1.36390i
$902$	−595.695			−0.660416
$903$	61.4808	−	148.428i	0.0680851	−	0.164372i
$904$	−689.053	−	460.410i	−0.762226	−	0.509303i
$905$		0			0
$906$	−510.119	+	101.469i	−0.563045	+	0.111997i
$907$	−104.077	+	69.5418i	−0.114748	+	0.0766724i	−0.611620	−	0.791152i	$-0.709482\pi$
$907$	−104.077	+	69.5418i	−0.114748	+	0.0766724i	0.496872	+	0.867824i	$0.334482\pi$
$908$	134.292	+	26.7123i	0.147898	+	0.0294188i
$909$	1316.98	−	545.511i	1.44882	−	0.600122i
$910$		0			0
$911$	0.463584	−	2.33060i	0.000508874	−	0.00255828i	−0.980530	−	0.196369i	$-0.937085\pi$
$911$	0.463584	−	2.33060i	0.000508874	−	0.00255828i	0.981039	+	0.193811i	$0.0620849\pi$
$912$	−151.478	−	226.702i	−0.166094	−	0.248577i
$913$	9.60715	+	48.2984i	0.0105226	+	0.0529008i
$914$	−503.458	+	503.458i	−0.550829	+	0.550829i
$915$		0			0
$916$	91.4624	+	37.8850i	0.0998498	+	0.0413592i
$917$			387.318i			0.422375i
$918$	−516.956	+	163.974i	−0.563133	+	0.178621i
$919$	−910.398			−0.990640			−0.495320	−	0.868711i	$-0.664949\pi$
$919$	−910.398			−0.990640			−0.495320	+	0.868711i	$0.664949\pi$
$920$		0			0
$921$	1386.67	+	926.540i	1.50561	+	1.00602i
$922$	343.766	+	343.766i	0.372848	+	0.372848i
$923$	−245.094	+	48.7523i	−0.265541	+	0.0528194i
$924$	1385.66	−	925.868i	1.49963	−	1.00202i
$925$		0			0
$926$	−432.176	+	179.013i	−0.466713	+	0.193319i
$927$	153.541	+	370.681i	0.165632	+	0.399872i
$928$	48.4674	−	243.662i	0.0522278	−	0.262567i
$929$	−103.190	−	154.434i	−0.111076	−	0.166237i	0.771767	−	0.635906i	$-0.219373\pi$
$929$	−103.190	−	154.434i	−0.111076	−	0.166237i	−0.882843	+	0.469669i	$0.844373\pi$
$930$		0			0
$931$	286.499	−	286.499i	0.307733	−	0.307733i
$932$	−347.627	+	520.260i	−0.372990	+	0.558219i
$933$	−1338.44	−	554.402i	−1.43456	−	0.594214i
$934$		−	2.09608i		−	0.00224419i
$935$		0			0
$936$	−751.018			−0.802370
$937$	39.9492	−	96.4460i	0.0426353	−	0.102931i	−0.901127	−	0.433555i	$-0.857259\pi$
$937$	39.9492	−	96.4460i	0.0426353	−	0.102931i	0.943763	+	0.330624i	$0.107259\pi$
$938$	−582.021	−	388.894i	−0.620492	−	0.414599i
$939$	−1316.08	−	1316.08i	−1.40157	−	1.40157i
$940$		0			0
$941$	−839.481	+	560.923i	−0.892116	+	0.596093i	−0.914915	−	0.403647i	$-0.867742\pi$
$941$	−839.481	+	560.923i	−0.892116	+	0.596093i	0.0227989	+	0.999740i	$0.492742\pi$
$942$	1596.16	+	317.495i	1.69443	+	0.337044i
$943$	−629.058	+	260.564i	−0.667082	+	0.276314i
$944$	19.7645	+	47.7158i	0.0209370	+	0.0505464i
$945$		0			0
$946$	60.3734	+	90.3551i	0.0638196	+	0.0955128i
$947$	−166.428	−	836.688i	−0.175742	−	0.883515i	−0.963537	−	0.267577i	$-0.913777\pi$
$947$	−166.428	−	836.688i	−0.175742	−	0.883515i	0.787795	−	0.615938i	$-0.211223\pi$
$948$	340.752	−	340.752i	0.359443	−	0.359443i
$949$	−150.977	+	225.953i	−0.159090	+	0.238095i
$950$		0			0
$951$		−	223.030i		−	0.234522i
$952$	605.199	−	1167.48i	0.635713	−	1.22634i
$953$	−518.720			−0.544302			−0.272151	−	0.962255i	$-0.587735\pi$
$953$	−518.720			−0.544302			−0.272151	+	0.962255i	$0.587735\pi$
$954$	−622.143	+	1501.99i	−0.652142	+	1.57441i
$955$		0			0
$956$	125.441	+	125.441i	0.131215	+	0.131215i
$957$	853.754	−	169.822i	0.892115	−	0.177453i
$958$	−871.405	+	582.254i	−0.909608	+	0.607781i
$959$	−1561.94	−	310.688i	−1.62871	−	0.323971i
$960$		0			0
$961$	333.711	+	805.650i	0.347254	+	0.838345i
$962$	67.2530	−	338.104i	0.0699096	−	0.351459i
$963$	−755.005	−	1129.95i	−0.784014	−	1.17336i
$964$	63.1662	+	317.558i	0.0655251	+	0.329417i
$965$		0			0
$966$	−1151.93	+	1723.99i	−1.19248	+	1.78467i
$967$	−645.244	−	267.269i	−0.667264	−	0.276390i	0.0232278	−	0.999730i	$-0.492606\pi$
$967$	−645.244	−	267.269i	−0.667264	−	0.276390i	−0.690491	+	0.723341i	$0.742606\pi$
$968$			2448.04i			2.52897i
$969$	−84.7888	+	988.731i	−0.0875014	+	1.02036i
$970$		0			0
$971$	14.0507	−	33.9214i	0.0144703	−	0.0349345i	−0.916479	−	0.400082i	$-0.868982\pi$
$971$	14.0507	−	33.9214i	0.0144703	−	0.0349345i	0.930950	+	0.365148i	$0.118982\pi$
$972$	450.423	+	300.963i	0.463398	+	0.309633i
$973$	−395.046	−	395.046i	−0.406008	−	0.406008i
$974$	427.537	−	85.0423i	0.438949	−	0.0873125i
$975$		0			0
$976$	−322.882	−	64.2252i	−0.330822	−	0.0658045i
$977$	−328.508	+	136.073i	−0.336242	+	0.139276i	−0.544415	−	0.838816i	$-0.683248\pi$
$977$	−328.508	+	136.073i	−0.336242	+	0.139276i	0.208173	+	0.978092i	$0.433248\pi$
$978$	258.673	+	624.492i	0.264492	+	0.638540i
$979$	608.015	−	3056.70i	0.621057	−	3.12227i
$980$		0			0
$981$	−137.264	−	690.074i	−0.139923	−	0.703440i
$982$	330.945	−	330.945i	0.337011	−	0.337011i
$983$	104.396	−	156.240i	0.106202	−	0.158942i	−0.774562	−	0.632498i	$-0.782030\pi$
$983$	104.396	−	156.240i	0.106202	−	0.158942i	0.880764	+	0.473556i	$0.157030\pi$
$984$	−767.274	−	317.815i	−0.779750	−	0.322983i
$985$		0			0
$986$	170.121	−	143.248i	0.172537	−	0.145282i
$987$	−3653.41			−3.70153
$988$	−57.9493	+	139.902i	−0.0586531	+	0.141601i
$989$	103.277	+	69.0076i	0.104426	+	0.0697751i
$990$		0			0
$991$	−97.8933	+	19.4722i	−0.0987824	+	0.0196490i	−0.244234	−	0.969716i	$-0.578536\pi$
$991$	−97.8933	+	19.4722i	−0.0987824	+	0.0196490i	0.145452	+	0.989365i	$0.453536\pi$
$992$	215.044	−	143.688i	0.216778	−	0.144847i
$993$	−684.800	−	136.215i	−0.689627	−	0.137175i
$994$	−468.438	+	194.033i	−0.471265	+	0.195204i
$995$		0			0
$996$	−4.33669	+	21.8020i	−0.00435411	+	0.0218896i
$997$	−467.853	−	700.191i	−0.469261	−	0.702298i	0.519051	−	0.854743i	$-0.326285\pi$
$997$	−467.853	−	700.191i	−0.469261	−	0.702298i	−0.988312	+	0.152445i	$0.951285\pi$
$998$	0.398042	+	2.00109i	0.000398840	+	0.00200510i
$999$	578.759	−	578.759i	0.579338	−	0.579338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.u.e.401.9		96
5.2	odd	4		425.3.t.e.299.9		96
5.3	odd	4		425.3.t.h.299.4		96
5.4	even	2		85.3.q.a.61.4	yes	96
17.12	odd	16	inner	425.3.u.e.301.9		96
85.12	even	16		425.3.t.h.199.4		96
85.29	odd	16		85.3.q.a.46.4	✓	96
85.63	even	16		425.3.t.e.199.9		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.3.q.a.46.4	✓	96	85.29	odd	16
85.3.q.a.61.4	yes	96	5.4	even	2
425.3.t.e.199.9		96	85.63	even	16
425.3.t.e.299.9		96	5.2	odd	4
425.3.t.h.199.4		96	85.12	even	16
425.3.t.h.299.4		96	5.3	odd	4
425.3.u.e.301.9		96	17.12	odd	16	inner
425.3.u.e.401.9		96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.u (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.552543 - 1.33396i) q^{2} +(3.95654 + 2.64368i) q^{3} +(1.35429 + 1.35429i) q^{4} +(5.71272 - 3.81711i) q^{6} +(-8.88293 - 1.76692i) q^{7} +(7.89070 - 3.26843i) q^{8} +(5.22106 + 12.6047i) q^{9} +(11.2168 + 16.7872i) q^{11} +(1.77800 + 8.93861i) q^{12} +(-4.55740 + 4.55740i) q^{13} +(-7.26520 + 10.8731i) q^{14} -4.67078i q^{16} +(-10.6179 + 13.2763i) q^{17} +19.6991 q^{18} +(4.69451 - 11.3335i) q^{19} +(-30.4745 - 30.4745i) q^{21} +(28.5912 - 5.68714i) q^{22} +(27.7049 - 18.5118i) q^{23} +(39.8606 + 7.92876i) q^{24} +(3.56121 + 8.59753i) q^{26} +(-4.31053 + 21.6705i) q^{27} +(-9.63713 - 14.4230i) q^{28} +(-1.76764 - 8.88650i) q^{29} +(5.24039 - 7.84280i) q^{31} +(25.3322 + 10.4929i) q^{32} +96.0730i q^{33} +(11.8432 + 21.4995i) q^{34} +(-9.99965 + 24.1413i) q^{36} +(-30.8010 - 20.5805i) q^{37} +(-12.5245 - 12.5245i) q^{38} +(-30.0798 + 5.98325i) q^{39} +(-20.0419 - 3.98659i) q^{41} +(-57.4902 + 23.8132i) q^{42} +(1.42655 + 3.44400i) q^{43} +(-7.54387 + 37.9256i) q^{44} +(-9.38582 - 47.1857i) q^{46} +(59.9421 - 59.9421i) q^{47} +(12.3481 - 18.4802i) q^{48} +(30.5143 + 12.6394i) q^{49} +(-77.1084 + 24.4581i) q^{51} -12.3441 q^{52} +(-31.5824 + 76.2466i) q^{53} +(26.5258 + 17.7239i) q^{54} +(-75.8676 + 15.0910i) q^{56} +(48.5363 - 32.4309i) q^{57} +(-12.8309 - 2.55223i) q^{58} +(-10.2158 + 4.23153i) q^{59} +(13.7504 - 69.1280i) q^{61} +(-7.56642 - 11.3239i) q^{62} +(-24.1066 - 121.192i) q^{63} +(41.2052 - 41.2052i) q^{64} +(128.157 + 53.0845i) q^{66} +53.5283i q^{67} +(-32.3597 + 3.60031i) q^{68} +158.555 q^{69} +(32.2384 + 21.5410i) q^{71} +(82.3956 + 82.3956i) q^{72} +(41.3536 - 8.22574i) q^{73} +(-44.4724 + 29.7155i) q^{74} +(21.7066 - 8.99117i) q^{76} +(-69.9767 - 168.939i) q^{77} +(-8.63900 + 43.4312i) q^{78} +(-29.3762 - 43.9646i) q^{79} +(12.4807 - 12.4807i) q^{81} +(-16.3920 + 24.5323i) q^{82} +(2.25342 + 0.933397i) q^{83} -82.5426i q^{84} +5.38238 q^{86} +(16.4993 - 39.8329i) q^{87} +(143.377 + 95.8012i) q^{88} +(-109.152 - 109.152i) q^{89} +(48.5356 - 32.4304i) q^{91} +(62.5908 + 12.4501i) q^{92} +(41.4677 - 17.1765i) q^{93} +(-46.8396 - 113.081i) q^{94} +(72.4879 + 108.486i) q^{96} +(-14.7702 - 74.2547i) q^{97} +(33.7209 - 33.7209i) q^{98} +(-153.035 + 229.033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 192 q^{12} + 48 q^{13} - 64 q^{14} - 16 q^{17} - 128 q^{18} + 48 q^{19} - 192 q^{22} - 112 q^{23} + 240 q^{24} - 224 q^{26} + 288 q^{27} + 480 q^{28} - 64 q^{31} + 80 q^{32} + 64 q^{34} + 192 q^{36}+ \cdots - 592 q^{99}+O(q^{100}) \) 96 * q + 192 * q^12 + 48 * q^13 - 64 * q^14 - 16 * q^17 - 128 * q^18 + 48 * q^19 - 192 * q^22 - 112 * q^23 + 240 * q^24 - 224 * q^26 + 288 * q^27 + 480 * q^28 - 64 * q^31 + 80 * q^32 + 64 * q^34 + 192 * q^36 - 256 * q^37 - 208 * q^38 + 16 * q^39 - 432 * q^41 - 864 * q^42 - 256 * q^43 - 32 * q^44 - 48 * q^46 + 320 * q^48 - 32 * q^49 + 64 * q^51 - 192 * q^53 - 976 * q^54 + 80 * q^56 + 1120 * q^57 - 512 * q^58 - 224 * q^59 - 224 * q^61 + 560 * q^62 - 624 * q^63 + 160 * q^64 + 48 * q^66 + 384 * q^69 + 48 * q^71 - 1040 * q^72 + 672 * q^74 + 496 * q^76 - 960 * q^77 + 768 * q^79 + 1424 * q^81 - 1200 * q^82 + 288 * q^83 + 64 * q^86 + 1344 * q^87 + 1664 * q^88 - 1152 * q^89 + 336 * q^91 + 2016 * q^92 + 1024 * q^93 - 1344 * q^94 + 768 * q^96 + 256 * q^97 + 816 * q^98 - 592 * q^99

Introduction

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