LMFDB - Embedded newform 200.2.q.a.129.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,2,Mod(9,200)] 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("200.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.q (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			129.5
Character	$\chi$	$=$	200.129
Dual form			200.2.q.a.169.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0350089 - 0.0481856i) q^{3} +(-0.243712 + 2.22275i) q^{5} +1.71675i q^{7} +(0.925955 + 2.84980i) q^{9} +(0.573356 - 1.76461i) q^{11} +(0.533844 - 0.173457i) q^{13} +(0.0985723 + 0.0895593i) q^{15} +(2.29552 + 3.15952i) q^{17} +(4.69249 - 3.40929i) q^{19} +(0.0827227 + 0.0601016i) q^{21} +(-6.95461 - 2.25969i) q^{23} +(-4.88121 - 1.08342i) q^{25} +(0.339673 + 0.110366i) q^{27} +(2.13709 + 1.55269i) q^{29} +(1.56235 - 1.13511i) q^{31} +(-0.0649561 - 0.0894045i) q^{33} +(-3.81590 - 0.418393i) q^{35} +(0.725506 - 0.235731i) q^{37} +(0.0103312 - 0.0317961i) q^{39} +(-3.00636 - 9.25262i) q^{41} -9.68774i q^{43} +(-6.56004 + 1.36363i) q^{45} +(-6.11994 + 8.42338i) q^{47} +4.05276 q^{49} +0.232607 q^{51} +(0.654009 - 0.900166i) q^{53} +(3.78254 + 1.70448i) q^{55} -0.345466i q^{57} +(-1.56343 - 4.81174i) q^{59} +(4.18521 - 12.8808i) q^{61} +(-4.89239 + 1.58963i) q^{63} +(0.255446 + 1.22887i) q^{65} +(0.733847 + 1.01005i) q^{67} +(-0.352358 + 0.256003i) q^{69} +(10.8951 + 7.91578i) q^{71} +(-3.88964 - 1.26382i) q^{73} +(-0.223091 + 0.197275i) q^{75} +(3.02939 + 0.984309i) q^{77} +(5.25455 + 3.81765i) q^{79} +(-7.25533 + 5.27131i) q^{81} +(0.536761 + 0.738788i) q^{83} +(-7.58225 + 4.33236i) q^{85} +(0.149634 - 0.0486192i) q^{87} +(-1.61785 + 4.97923i) q^{89} +(0.297782 + 0.916478i) q^{91} -0.115022i q^{93} +(6.43438 + 11.2611i) q^{95} +(8.54098 - 11.7557i) q^{97} +5.55967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{5} + 10 q^{9} + 6 q^{11} + 12 q^{15} - 6 q^{19} - 4 q^{21} - 30 q^{23} + 6 q^{25} - 2 q^{29} + 6 q^{31} + 8 q^{35} - 40 q^{37} - 12 q^{39} - 12 q^{45} - 20 q^{47} - 60 q^{49} - 60 q^{51} - 30 q^{53}+ \cdots + 92 q^{99}+O(q^{100}) $ 32 * q + 2 * q^5 + 10 * q^9 + 6 * q^11 + 12 * q^15 - 6 * q^19 - 4 * q^21 - 30 * q^23 + 6 * q^25 - 2 * q^29 + 6 * q^31 + 8 * q^35 - 40 * q^37 - 12 * q^39 - 12 * q^45 - 20 * q^47 - 60 * q^49 - 60 * q^51 - 30 * q^53 - 28 * q^55 - 30 * q^59 + 14 * q^61 - 20 * q^63 - 26 * q^65 - 4 * q^69 + 12 * q^71 + 40 * q^73 + 16 * q^75 + 16 * q^79 - 52 * q^81 + 30 * q^83 + 60 * q^85 + 110 * q^87 + 24 * q^89 - 4 * q^91 + 68 * q^95 + 30 * q^97 + 92 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{10}\right)$

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			0
$2$		0			0
$3$	0.0350089	−	0.0481856i	0.0202124	−	0.0278200i	−0.798791	−	0.601608i	$-0.794527\pi$
$3$	0.0350089	−	0.0481856i	0.0202124	−	0.0278200i	0.819004	+	0.573788i	$0.194527\pi$
$4$		0			0
$5$	−0.243712	+	2.22275i	−0.108991	+	0.994043i
$5$	−0.243712	+	2.22275i	−0.108991	+	0.994043i
$6$		0			0
$7$			1.71675i			0.648871i	0.945908	+	0.324436i	$0.105174\pi$
$7$			1.71675i			0.648871i	−0.945908	+	0.324436i	$0.894826\pi$
$8$		0			0
$9$	0.925955	+	2.84980i	0.308652	+	0.949932i
$10$		0			0
$11$	0.573356	−	1.76461i	0.172873	−	0.532049i	−0.826657	−	0.562707i	$-0.809760\pi$
$11$	0.573356	−	1.76461i	0.172873	−	0.532049i	0.999530	+	0.0306574i	$0.00976008\pi$
$12$		0			0
$13$	0.533844	−	0.173457i	0.148062	−	0.0481082i	−0.234048	−	0.972225i	$-0.575197\pi$
$13$	0.533844	−	0.173457i	0.148062	−	0.0481082i	0.382110	+	0.924117i	$0.375197\pi$
$14$		0			0
$15$	0.0985723	+	0.0895593i	0.0254513	+	0.0231241i
$16$		0			0
$17$	2.29552	+	3.15952i	0.556746	+	0.766295i	0.990908	−	0.134539i	$-0.0429555\pi$
$17$	2.29552	+	3.15952i	0.556746	+	0.766295i	−0.434162	+	0.900835i	$0.642955\pi$
$18$		0			0
$19$	4.69249	−	3.40929i	1.07653	−	0.782145i	0.0994556	−	0.995042i	$-0.468290\pi$
$19$	4.69249	−	3.40929i	1.07653	−	0.782145i	0.977075	+	0.212897i	$0.0682899\pi$
$20$		0			0
$21$	0.0827227	+	0.0601016i	0.0180516	+	0.0131152i
$22$		0			0
$23$	−6.95461	−	2.25969i	−1.45014	−	0.471178i	−0.525094	−	0.851044i	$-0.675970\pi$
$23$	−6.95461	−	2.25969i	−1.45014	−	0.471178i	−0.925041	+	0.379866i	$0.875970\pi$
$24$		0			0
$25$	−4.88121	−	1.08342i	−0.976242	−	0.216684i
$26$		0			0
$27$	0.339673	+	0.110366i	0.0653700	+	0.0212400i
$28$		0			0
$29$	2.13709	+	1.55269i	0.396848	+	0.288327i	0.768256	−	0.640143i	$-0.221125\pi$
$29$	2.13709	+	1.55269i	0.396848	+	0.288327i	−0.371408	+	0.928470i	$0.621125\pi$
$30$		0			0
$31$	1.56235	−	1.13511i	0.280607	−	0.203873i	−0.438575	−	0.898694i	$-0.644517\pi$
$31$	1.56235	−	1.13511i	0.280607	−	0.203873i	0.719182	+	0.694822i	$0.244517\pi$
$32$		0			0
$33$	−0.0649561	−	0.0894045i	−0.0113074	−	0.0155633i
$34$		0			0
$35$	−3.81590	−	0.418393i	−0.645006	−	0.0707213i
$36$		0			0
$37$	0.725506	−	0.235731i	0.119272	−	0.0387539i	−0.248773	−	0.968562i	$-0.580027\pi$
$37$	0.725506	−	0.235731i	0.119272	−	0.0387539i	0.368045	+	0.929808i	$0.380027\pi$
$38$		0			0
$39$	0.0103312	−	0.0317961i	0.00165431	−	0.00509146i
$40$		0			0
$41$	−3.00636	−	9.25262i	−0.469514	−	1.44502i	−0.853215	−	0.521559i	$-0.825351\pi$
$41$	−3.00636	−	9.25262i	−0.469514	−	1.44502i	0.383701	−	0.923457i	$-0.374649\pi$
$42$		0			0
$43$		−	9.68774i		−	1.47737i	−0.674053	−	0.738683i	$-0.735448\pi$
$43$		−	9.68774i		−	1.47737i	0.674053	−	0.738683i	$-0.264552\pi$
$44$		0			0
$45$	−6.56004	+	1.36363i	−0.977913	+	0.203278i
$46$		0			0
$47$	−6.11994	+	8.42338i	−0.892685	+	1.22868i	0.0800577	+	0.996790i	$0.474490\pi$
$47$	−6.11994	+	8.42338i	−0.892685	+	1.22868i	−0.972743	+	0.231886i	$0.925510\pi$
$48$		0			0
$49$	4.05276			0.578966
$50$		0			0
$51$	0.232607			0.0325715
$52$		0			0
$53$	0.654009	−	0.900166i	0.0898351	−	0.123647i	−0.761734	−	0.647890i	$-0.775652\pi$
$53$	0.654009	−	0.900166i	0.0898351	−	0.123647i	0.851569	+	0.524243i	$0.175652\pi$
$54$		0			0
$55$	3.78254	+	1.70448i	0.510038	+	0.229832i
$56$		0			0
$57$		−	0.345466i		−	0.0457581i
$58$		0			0
$59$	−1.56343	−	4.81174i	−0.203541	−	0.626435i	−0.999770	−	0.0214397i	$-0.993175\pi$
$59$	−1.56343	−	4.81174i	−0.203541	−	0.626435i	0.796229	−	0.604995i	$-0.206825\pi$
$60$		0			0
$61$	4.18521	−	12.8808i	0.535862	−	1.64921i	−0.205918	−	0.978569i	$-0.566018\pi$
$61$	4.18521	−	12.8808i	0.535862	−	1.64921i	0.741780	−	0.670643i	$-0.233982\pi$
$62$		0			0
$63$	−4.89239	+	1.58963i	−0.616383	+	0.200275i
$64$		0			0
$65$	0.255446	+	1.22887i	0.0316841	+	0.152423i
$66$		0			0
$67$	0.733847	+	1.01005i	0.0896537	+	0.123398i	0.851488	−	0.524375i	$-0.175701\pi$
$67$	0.733847	+	1.01005i	0.0896537	+	0.123398i	−0.761834	+	0.647772i	$0.775701\pi$
$68$		0			0
$69$	−0.352358	+	0.256003i	−0.0424189	+	0.0308191i
$70$		0			0
$71$	10.8951	+	7.91578i	1.29302	+	0.939430i	0.999862	−	0.0166349i	$-0.00529530\pi$
$71$	10.8951	+	7.91578i	1.29302	+	0.939430i	0.293154	+	0.956065i	$0.405295\pi$
$72$		0			0
$73$	−3.88964	−	1.26382i	−0.455248	−	0.147919i	0.0724119	−	0.997375i	$-0.476930\pi$
$73$	−3.88964	−	1.26382i	−0.455248	−	0.147919i	−0.527660	+	0.849456i	$0.676930\pi$
$74$		0			0
$75$	−0.223091	+	0.197275i	−0.0257603	+	0.0227793i
$76$		0			0
$77$	3.02939	+	0.984309i	0.345231	+	0.112172i
$78$		0			0
$79$	5.25455	+	3.81765i	0.591183	+	0.429520i	0.842738	−	0.538323i	$-0.180942\pi$
$79$	5.25455	+	3.81765i	0.591183	+	0.429520i	−0.251555	+	0.967843i	$0.580942\pi$
$80$		0			0
$81$	−7.25533	+	5.27131i	−0.806148	+	0.585701i
$82$		0			0
$83$	0.536761	+	0.738788i	0.0589172	+	0.0810925i	0.837459	−	0.546500i	$-0.184040\pi$
$83$	0.536761	+	0.738788i	0.0589172	+	0.0810925i	−0.778542	+	0.627593i	$0.784040\pi$
$84$		0			0
$85$	−7.58225	+	4.33236i	−0.822411	+	0.469910i
$86$		0			0
$87$	0.149634	−	0.0486192i	0.0160425	−	0.00521252i
$88$		0			0
$89$	−1.61785	+	4.97923i	−0.171492	+	0.527797i	−0.999456	−	0.0329839i	$-0.989499\pi$
$89$	−1.61785	+	4.97923i	−0.171492	+	0.527797i	0.827964	+	0.560781i	$0.189499\pi$
$90$		0			0
$91$	0.297782	+	0.916478i	0.0312160	+	0.0960730i
$92$		0			0
$93$		−	0.115022i		−	0.0119272i
$94$		0			0
$95$	6.43438	+	11.2611i	0.660153	+	1.15536i
$96$		0			0
$97$	8.54098	−	11.7557i	0.867205	−	1.19361i	−0.112598	−	0.993641i	$-0.535917\pi$
$97$	8.54098	−	11.7557i	0.867205	−	1.19361i	0.979803	−	0.199965i	$-0.0640828\pi$
$98$		0			0
$99$	5.55967			0.558768
$100$		0			0
$101$	−1.84989			−0.184071			−0.0920354	−	0.995756i	$-0.529337\pi$
$101$	−1.84989			−0.184071			−0.0920354	+	0.995756i	$0.529337\pi$
$102$		0			0
$103$	−6.06351	+	8.34571i	−0.597456	+	0.822327i	−0.995472	−	0.0950510i	$-0.969699\pi$
$103$	−6.06351	+	8.34571i	−0.597456	+	0.822327i	0.398017	+	0.917378i	$0.369699\pi$
$104$		0			0
$105$	−0.153751	+	0.169224i	−0.0150046	+	0.0165146i
$106$		0			0
$107$			15.1159i			1.46131i	0.682746	+	0.730656i	$0.260786\pi$
$107$			15.1159i			1.46131i	−0.682746	+	0.730656i	$0.739214\pi$
$108$		0			0
$109$	1.40146	+	4.31325i	0.134235	+	0.413134i	0.995470	−	0.0950729i	$-0.0303084\pi$
$109$	1.40146	+	4.31325i	0.134235	+	0.413134i	−0.861235	+	0.508207i	$0.830308\pi$
$110$		0			0
$111$	0.0140403	−	0.0432116i	0.00133265	−	0.00410146i
$112$		0			0
$113$	14.8637	−	4.82952i	1.39826	−	0.454323i	0.489633	−	0.871929i	$-0.337131\pi$
$113$	14.8637	−	4.82952i	1.39826	−	0.454323i	0.908628	+	0.417606i	$0.137131\pi$
$114$		0			0
$115$	6.71764	−	14.9076i	0.626423	−	1.39014i
$116$		0			0
$117$	0.988632	+	1.36073i	0.0913990	+	0.125800i
$118$		0			0
$119$	−5.42411	+	3.94084i	−0.497227	+	0.361257i
$120$		0			0
$121$	6.11408	+	4.44214i	0.555826	+	0.403831i
$122$		0			0
$123$	−0.551092	−	0.179061i	−0.0496903	−	0.0161454i
$124$		0			0
$125$	3.59778	−	10.5856i	0.321795	−	0.946809i
$126$		0			0
$127$	−1.27621	−	0.414665i	−0.113245	−	0.0367956i	0.251846	−	0.967767i	$-0.418962\pi$
$127$	−1.27621	−	0.414665i	−0.113245	−	0.0367956i	−0.365091	+	0.930972i	$0.618962\pi$
$128$		0			0
$129$	−0.466810	−	0.339157i	−0.0411003	−	0.0298611i
$130$		0			0
$131$	−11.2000	+	8.13727i	−0.978548	+	0.710957i	−0.957384	−	0.288819i	$-0.906737\pi$
$131$	−11.2000	+	8.13727i	−0.978548	+	0.710957i	−0.0211645	+	0.999776i	$0.506737\pi$
$132$		0			0
$133$	5.85291	+	8.05583i	0.507511	+	0.698529i
$134$		0			0
$135$	−0.328099	+	0.728109i	−0.0282382	+	0.0626656i
$136$		0			0
$137$	−8.02147	+	2.60633i	−0.685320	+	0.222674i	−0.630923	−	0.775845i	$-0.717324\pi$
$137$	−8.02147	+	2.60633i	−0.685320	+	0.222674i	−0.0543972	+	0.998519i	$0.517324\pi$
$138$		0			0
$139$	4.91470	−	15.1259i	0.416860	−	1.28296i	−0.493717	−	0.869622i	$-0.664362\pi$
$139$	4.91470	−	15.1259i	0.416860	−	1.28296i	0.910577	−	0.413340i	$-0.135638\pi$
$140$		0			0
$141$	0.191633	+	0.589786i	0.0161384	+	0.0496690i
$142$		0			0
$143$		−	1.04148i		−	0.0870928i
$144$		0			0
$145$	−3.97207	+	4.37181i	−0.329862	+	0.363059i
$146$		0			0
$147$	0.141883	−	0.195285i	0.0117023	−	0.0161068i
$148$		0			0
$149$	−8.35969			−0.684852			−0.342426	−	0.939545i	$-0.611249\pi$
$149$	−8.35969			−0.684852			−0.342426	+	0.939545i	$0.611249\pi$
$150$		0			0
$151$	−5.35624			−0.435885			−0.217942	−	0.975962i	$-0.569934\pi$
$151$	−5.35624			−0.435885			−0.217942	+	0.975962i	$0.569934\pi$
$152$		0			0
$153$	−6.87843	+	9.46734i	−0.556088	+	0.765389i
$154$		0			0
$155$	2.14231	+	3.74935i	0.172074	+	0.301155i
$156$		0			0
$157$		−	13.3180i		−	1.06289i	−0.847092	−	0.531446i	$-0.821649\pi$
$157$		−	13.3180i		−	1.06289i	0.847092	−	0.531446i	$-0.178351\pi$
$158$		0			0
$159$	−0.0204789	−	0.0630277i	−0.00162408	−	0.00499842i
$160$		0			0
$161$	3.87932	−	11.9393i	0.305734	−	0.940951i
$162$		0			0
$163$	13.4848	−	4.38148i	1.05621	−	0.343184i	0.271109	−	0.962549i	$-0.412610\pi$
$163$	13.4848	−	4.38148i	1.05621	−	0.343184i	0.785104	+	0.619364i	$0.212610\pi$
$164$		0			0
$165$	0.214554	−	0.122592i	0.0167030	−	0.00954379i
$166$		0			0
$167$	−13.3299	−	18.3470i	−1.03150	−	1.41973i	−0.903818	−	0.427916i	$-0.859248\pi$
$167$	−13.3299	−	18.3470i	−1.03150	−	1.41973i	−0.127677	−	0.991816i	$-0.540752\pi$
$168$		0			0
$169$	−10.2623	+	7.45601i	−0.789409	+	0.573539i
$170$		0			0
$171$	14.0608	+	10.2158i	1.07526	+	0.781220i
$172$		0			0
$173$	6.43969	+	2.09238i	0.489601	+	0.159081i	0.543405	−	0.839471i	$-0.317135\pi$
$173$	6.43969	+	2.09238i	0.489601	+	0.159081i	−0.0538045	+	0.998551i	$0.517135\pi$
$174$		0			0
$175$	1.85996	−	8.37982i	0.140600	−	0.633455i
$176$		0			0
$177$	−0.286590	−	0.0931189i	−0.0215415	−	0.00699924i
$178$		0			0
$179$	−20.3012	−	14.7497i	−1.51739	−	1.10245i	−0.962764	−	0.270342i	$-0.912863\pi$
$179$	−20.3012	−	14.7497i	−1.51739	−	1.10245i	−0.554621	−	0.832103i	$-0.687137\pi$
$180$		0			0
$181$	−20.3908	+	14.8148i	−1.51564	+	1.10117i	−0.552039	+	0.833818i	$0.686150\pi$
$181$	−20.3908	+	14.8148i	−1.51564	+	1.10117i	−0.963598	+	0.267356i	$0.913850\pi$
$182$		0			0
$183$	−0.474148	−	0.652608i	−0.0350500	−	0.0482422i
$184$		0			0
$185$	0.347156	+	1.67007i	0.0255234	+	0.122786i
$186$		0			0
$187$	6.89146	−	2.23917i	0.503953	−	0.163744i
$188$		0			0
$189$	−0.189472	+	0.583133i	−0.0137820	+	0.0424167i
$190$		0			0
$191$	−6.14957	−	18.9264i	−0.444967	−	1.36947i	−0.882520	−	0.470275i	$-0.844155\pi$
$191$	−6.14957	−	18.9264i	−0.444967	−	1.36947i	0.437552	−	0.899193i	$-0.355845\pi$
$192$		0			0
$193$		−	4.79198i		−	0.344934i	−0.985015	−	0.172467i	$-0.944826\pi$
$193$		−	4.79198i		−	0.344934i	0.985015	−	0.172467i	$-0.0551738\pi$
$194$		0			0
$195$	0.0681569	+	0.0307127i	0.00488082	+	0.00219938i
$196$		0			0
$197$	0.393872	−	0.542119i	0.0280622	−	0.0386244i	−0.794755	−	0.606930i	$-0.792401\pi$
$197$	0.393872	−	0.542119i	0.0280622	−	0.0386244i	0.822818	+	0.568306i	$0.192401\pi$
$198$		0			0
$199$	−9.41311			−0.667278			−0.333639	−	0.942701i	$-0.608277\pi$
$199$	−9.41311			−0.667278			−0.333639	+	0.942701i	$0.608277\pi$
$200$		0			0
$201$	0.0743612			0.00524504
$202$		0			0
$203$	−2.66558	+	3.66886i	−0.187087	+	0.257503i
$204$		0			0
$205$	21.2989	−	4.42740i	1.48758	−	0.309223i
$206$		0			0
$207$		−	21.9116i		−	1.52296i
$208$		0			0
$209$	−3.32560	−	10.2351i	−0.230036	−	0.707979i
$210$		0			0
$211$	−3.80217	+	11.7019i	−0.261752	+	0.805589i	0.730672	+	0.682729i	$0.239207\pi$
$211$	−3.80217	+	11.7019i	−0.261752	+	0.805589i	−0.992424	+	0.122861i	$0.960793\pi$
$212$		0			0
$213$	0.762854	−	0.247866i	0.0522699	−	0.0169835i
$214$		0			0
$215$	21.5334	+	2.36102i	1.46857	+	0.161020i
$216$		0			0
$217$	1.94871	+	2.68217i	0.132287	+	0.182078i
$218$		0			0
$219$	−0.197070	+	0.143180i	−0.0133168	+	0.00967519i
$220$		0			0
$221$	1.77349	+	1.28852i	0.119298	+	0.0866750i
$222$		0			0
$223$	−13.4389	−	4.36656i	−0.899934	−	0.292406i	−0.177724	−	0.984080i	$-0.556873\pi$
$223$	−13.4389	−	4.36656i	−0.899934	−	0.292406i	−0.722210	+	0.691674i	$0.756873\pi$
$224$		0			0
$225$	−1.43225	−	14.9136i	−0.0954834	−	0.994243i
$226$		0			0
$227$	−3.72885	−	1.21158i	−0.247492	−	0.0804151i	0.182644	−	0.983179i	$-0.441534\pi$
$227$	−3.72885	−	1.21158i	−0.247492	−	0.0804151i	−0.430136	+	0.902764i	$0.641534\pi$
$228$		0			0
$229$	2.16082	+	1.56993i	0.142791	+	0.103744i	0.656887	−	0.753989i	$-0.271873\pi$
$229$	2.16082	+	1.56993i	0.142791	+	0.103744i	−0.514096	+	0.857732i	$0.671873\pi$
$230$		0			0
$231$	0.153485	−	0.111514i	0.0100986	−	0.00733705i
$232$		0			0
$233$	13.1641	+	18.1188i	0.862409	+	1.18700i	0.980990	+	0.194059i	$0.0621654\pi$
$233$	13.1641	+	18.1188i	0.862409	+	1.18700i	−0.118581	+	0.992944i	$0.537835\pi$
$234$		0			0
$235$	−17.2315	−	15.6560i	−1.12406	−	1.02128i
$236$		0			0
$237$	0.367912	−	0.119542i	0.0238985	−	0.00776508i
$238$		0			0
$239$	−6.69719	+	20.6118i	−0.433205	+	1.33327i	0.461710	+	0.887031i	$0.347236\pi$
$239$	−6.69719	+	20.6118i	−0.433205	+	1.33327i	−0.894915	+	0.446237i	$0.852764\pi$
$240$		0			0
$241$	5.45316	+	16.7831i	0.351269	+	1.08109i	0.958141	+	0.286296i	$0.0924239\pi$
$241$	5.45316	+	16.7831i	0.351269	+	1.08109i	−0.606872	+	0.794799i	$0.707576\pi$
$242$		0			0
$243$			1.60560i			0.103000i
$244$		0			0
$245$	−0.987708	+	9.00827i	−0.0631023	+	0.575517i
$246$		0			0
$247$	1.91369	−	2.63397i	0.121765	−	0.167596i
$248$		0			0
$249$	0.0543904			0.00344685
$250$		0			0
$251$	−16.2475			−1.02553			−0.512766	−	0.858528i	$-0.671379\pi$
$251$	−16.2475			−1.02553			−0.512766	+	0.858528i	$0.671379\pi$
$252$		0			0
$253$	−7.97493	+	10.9765i	−0.501379	+	0.690090i
$254$		0			0
$255$	−0.0566891	+	0.517027i	−0.00355001	+	0.0323775i
$256$		0			0
$257$		−	9.12754i		−	0.569361i	−0.958623	−	0.284680i	$-0.908113\pi$
$257$		−	9.12754i		−	0.569361i	0.958623	−	0.284680i	$-0.0918874\pi$
$258$		0			0
$259$	0.404692	+	1.24551i	0.0251463	+	0.0773924i
$260$		0			0
$261$	−2.44599	+	7.52800i	−0.151403	+	0.465971i
$262$		0			0
$263$	18.2735	−	5.93742i	1.12679	−	0.366117i	0.314436	−	0.949279i	$-0.398184\pi$
$263$	18.2735	−	5.93742i	1.12679	−	0.366117i	0.812356	+	0.583161i	$0.198184\pi$
$264$		0			0
$265$	1.84145	+	1.67308i	0.113120	+	0.102776i
$266$		0			0
$267$	0.183288	+	0.252274i	0.0112170	+	0.0154389i
$268$		0			0
$269$	4.36357	−	3.17032i	0.266052	−	0.193298i	−0.446759	−	0.894654i	$-0.647422\pi$
$269$	4.36357	−	3.17032i	0.266052	−	0.193298i	0.712811	+	0.701356i	$0.247422\pi$
$270$		0			0
$271$	17.3290	+	12.5902i	1.05266	+	0.764803i	0.972717	−	0.231996i	$-0.0745258\pi$
$271$	17.3290	+	12.5902i	1.05266	+	0.764803i	0.0799442	+	0.996799i	$0.474526\pi$
$272$		0			0
$273$	0.0545861	+	0.0177361i	0.00330370	+	0.00107344i
$274$		0			0
$275$	−4.71048	+	7.99223i	−0.284053	+	0.481950i
$276$		0			0
$277$	−13.7152	−	4.45635i	−0.824068	−	0.267756i	−0.133524	−	0.991046i	$-0.542629\pi$
$277$	−13.7152	−	4.45635i	−0.824068	−	0.267756i	−0.690545	+	0.723290i	$0.742629\pi$
$278$		0			0
$279$	4.68151	+	3.40132i	0.280275	+	0.203632i
$280$		0			0
$281$	−10.6166	+	7.71340i	−0.633332	+	0.460143i	−0.857553	−	0.514395i	$-0.828016\pi$
$281$	−10.6166	+	7.71340i	−0.633332	+	0.460143i	0.224221	+	0.974538i	$0.428016\pi$
$282$		0			0
$283$	15.5938	+	21.4630i	0.926953	+	1.27584i	0.961036	+	0.276423i	$0.0891490\pi$
$283$	15.5938	+	21.4630i	0.926953	+	1.27584i	−0.0340827	+	0.999419i	$0.510851\pi$
$284$		0			0
$285$	0.767883	+	0.0841942i	0.0454855	+	0.00498723i
$286$		0			0
$287$	15.8844	−	5.16117i	0.937629	−	0.304654i
$288$		0			0
$289$	0.540169	−	1.66247i	0.0317747	−	0.0977923i
$290$		0			0
$291$	−0.267443	−	0.823105i	−0.0156778	−	0.0482513i
$292$		0			0
$293$		−	24.1828i		−	1.41277i	−0.707827	−	0.706386i	$-0.750324\pi$
$293$		−	24.1828i		−	1.41277i	0.707827	−	0.706386i	$-0.249676\pi$
$294$		0			0
$295$	11.0763	−	2.30243i	0.644887	−	0.134053i
$296$		0			0
$297$	0.389506	−	0.536110i	0.0226015	−	0.0311082i
$298$		0			0
$299$	−4.10464			−0.237377
$300$		0			0
$301$	16.6314			0.958621
$302$		0			0
$303$	−0.0647625	+	0.0891380i	−0.00372051	+	0.00512084i
$304$		0			0
$305$	27.6107	+	12.4419i	1.58098	+	0.712419i
$306$		0			0
$307$			19.1169i			1.09106i	0.838091	+	0.545530i	$0.183672\pi$
$307$			19.1169i			1.09106i	−0.838091	+	0.545530i	$0.816328\pi$
$308$		0			0
$309$	0.189866	+	0.584348i	0.0108011	+	0.0332424i
$310$		0			0
$311$	7.01668	−	21.5951i	0.397879	−	1.22455i	−0.528817	−	0.848736i	$-0.677364\pi$
$311$	7.01668	−	21.5951i	0.397879	−	1.22455i	0.926696	−	0.375811i	$-0.122636\pi$
$312$		0			0
$313$	−12.7661	+	4.14797i	−0.721585	+	0.234457i	−0.646710	−	0.762736i	$-0.723856\pi$
$313$	−12.7661	+	4.14797i	−0.721585	+	0.234457i	−0.0748747	+	0.997193i	$0.523856\pi$
$314$		0			0
$315$	−2.34102	−	11.2620i	−0.131902	−	0.634540i
$316$		0			0
$317$	15.9915	+	22.0105i	0.898174	+	1.23623i	0.971047	+	0.238889i	$0.0767832\pi$
$317$	15.9915	+	22.0105i	0.898174	+	1.23623i	−0.0728730	+	0.997341i	$0.523217\pi$
$318$		0			0
$319$	3.96520	−	2.88089i	0.222009	−	0.161299i
$320$		0			0
$321$	0.728370	+	0.529192i	0.0406537	+	0.0295366i
$322$		0			0
$323$	21.5434	+	6.99988i	1.19871	+	0.389484i
$324$		0			0
$325$	−2.79373	+	0.268300i	−0.154968	+	0.0148826i
$326$		0			0
$327$	0.256900	+	0.0834719i	0.0142066	+	0.00461601i
$328$		0			0
$329$	−14.4608	−	10.5064i	−0.797252	−	0.579238i
$330$		0			0
$331$	−23.3469	+	16.9625i	−1.28326	+	0.932344i	−0.999646	−	0.0265941i	$-0.991534\pi$
$331$	−23.3469	+	16.9625i	−1.28326	+	0.932344i	−0.283615	+	0.958938i	$0.591534\pi$
$332$		0			0
$333$	1.34357	+	1.84927i	0.0736272	+	0.101339i
$334$		0			0
$335$	−2.42394	+	1.38499i	−0.132434	+	0.0756703i
$336$		0			0
$337$	−19.9562	+	6.48418i	−1.08709	+	0.353216i	−0.797120	−	0.603821i	$-0.793644\pi$
$337$	−19.9562	+	6.48418i	−1.08709	+	0.353216i	−0.289966	+	0.957037i	$0.593644\pi$
$338$		0			0
$339$	0.287649	−	0.885294i	0.0156230	−	0.0480825i
$340$		0			0
$341$	−1.10725	−	3.40776i	−0.0599609	−	0.184541i
$342$		0			0
$343$			18.9748i			1.02455i
$344$		0			0
$345$	−0.483156	−	0.845593i	−0.0260122	−	0.0455252i
$346$		0			0
$347$	−10.3583	+	14.2570i	−0.556063	+	0.765355i	−0.990819	−	0.135193i	$-0.956835\pi$
$347$	−10.3583	+	14.2570i	−0.556063	+	0.765355i	0.434756	+	0.900548i	$0.356835\pi$
$348$		0			0
$349$	−13.6103			−0.728544			−0.364272	−	0.931293i	$-0.618682\pi$
$349$	−13.6103			−0.728544			−0.364272	+	0.931293i	$0.618682\pi$
$350$		0			0
$351$	0.200476			0.0107006
$352$		0			0
$353$	7.66202	−	10.5459i	0.407808	−	0.561299i	−0.554874	−	0.831934i	$-0.687234\pi$
$353$	7.66202	−	10.5459i	0.407808	−	0.561299i	0.962682	+	0.270635i	$0.0872336\pi$
$354$		0			0
$355$	−20.2501	+	22.2880i	−1.07476	+	1.18292i
$356$		0			0
$357$			0.399328i			0.0211347i
$358$		0			0
$359$	4.59073	+	14.1288i	0.242289	+	0.745690i	0.996070	+	0.0885643i	$0.0282279\pi$
$359$	4.59073	+	14.1288i	0.242289	+	0.745690i	−0.753781	+	0.657126i	$0.771772\pi$
$360$		0			0
$361$	4.52484	−	13.9260i	0.238150	−	0.732949i
$362$		0			0
$363$	0.428095	−	0.139096i	0.0224691	−	0.00730067i
$364$		0			0
$365$	3.75711	−	8.33768i	0.196656	−	0.436414i
$366$		0			0
$367$	−15.5525	−	21.4062i	−0.811836	−	1.11740i	−0.991038	−	0.133584i	$-0.957351\pi$
$367$	−15.5525	−	21.4062i	−0.811836	−	1.11740i	0.179202	−	0.983812i	$-0.442649\pi$
$368$		0			0
$369$	23.5843	−	17.1350i	1.22775	−	0.892013i
$370$		0			0
$371$	1.54536	+	1.12277i	0.0802312	+	0.0582914i
$372$		0			0
$373$	−31.8132	−	10.3367i	−1.64722	−	0.535215i	−0.669088	−	0.743183i	$-0.733315\pi$
$373$	−31.8132	−	10.3367i	−1.64722	−	0.535215i	−0.978136	+	0.207968i	$0.933315\pi$
$374$		0			0
$375$	−0.384122	−	0.543953i	−0.0198360	−	0.0280896i
$376$		0			0
$377$	1.41020	+	0.458201i	0.0726289	+	0.0235986i
$378$		0			0
$379$	19.6075	+	14.2457i	1.00717	+	0.731753i	0.963614	−	0.267298i	$-0.0861309\pi$
$379$	19.6075	+	14.2457i	1.00717	+	0.731753i	0.0435574	+	0.999051i	$0.486131\pi$
$380$		0			0
$381$	−0.0646596	+	0.0469779i	−0.00331261	+	0.00240675i
$382$		0			0
$383$	−1.50232	−	2.06777i	−0.0767650	−	0.105658i	0.768908	−	0.639360i	$-0.220800\pi$
$383$	−1.50232	−	2.06777i	−0.0767650	−	0.105658i	−0.845673	+	0.533702i	$0.820800\pi$
$384$		0			0
$385$	−2.92617	+	6.49369i	−0.149131	+	0.330949i
$386$		0			0
$387$	27.6081	−	8.97041i	1.40340	−	0.455992i
$388$		0			0
$389$	3.92452	−	12.0784i	0.198981	−	0.612400i	−0.800926	−	0.598763i	$-0.795659\pi$
$389$	3.92452	−	12.0784i	0.198981	−	0.612400i	0.999907	−	0.0136371i	$-0.00434096\pi$
$390$		0			0
$391$	−8.82494	−	27.1604i	−0.446296	−	1.37356i
$392$		0			0
$393$			0.824556i			0.0415933i
$394$		0			0
$395$	−9.76628	+	10.7491i	−0.491395	+	0.540847i
$396$		0			0
$397$	11.7770	−	16.2097i	0.591072	−	0.813541i	−0.403782	−	0.914855i	$-0.632305\pi$
$397$	11.7770	−	16.2097i	0.591072	−	0.813541i	0.994855	+	0.101314i	$0.0323046\pi$
$398$		0			0
$399$	0.593079			0.0296911
$400$		0			0
$401$	0.685119			0.0342132			0.0171066	−	0.999854i	$-0.494555\pi$
$401$	0.685119			0.0342132			0.0171066	+	0.999854i	$0.494555\pi$
$402$		0			0
$403$	0.637160	−	0.876975i	0.0317392	−	0.0436852i
$404$		0			0
$405$	−9.94857	−	17.4115i	−0.494349	−	0.865182i
$406$		0			0
$407$		−	1.41539i		−	0.0701583i
$408$		0			0
$409$	0.120676	+	0.371402i	0.00596704	+	0.0183647i	0.953996	−	0.299820i	$-0.0969267\pi$
$409$	0.120676	+	0.371402i	0.00596704	+	0.0183647i	−0.948029	+	0.318185i	$0.896927\pi$
$410$		0			0
$411$	−0.155235	+	0.477764i	−0.00765718	+	0.0235664i
$412$		0			0
$413$	8.26056	−	2.68402i	0.406476	−	0.132072i
$414$		0			0
$415$	−1.77295	+	1.01303i	−0.0870309	+	0.0497278i
$416$		0			0
$417$	−0.556792	−	0.766359i	−0.0272662	−	0.0375288i
$418$		0			0
$419$	−13.9723	+	10.1515i	−0.682591	+	0.495931i	−0.874216	−	0.485537i	$-0.838624\pi$
$419$	−13.9723	+	10.1515i	−0.682591	+	0.495931i	0.191625	+	0.981468i	$0.438624\pi$
$420$		0			0
$421$	14.0506	+	10.2083i	0.684784	+	0.497524i	0.874941	−	0.484229i	$-0.160900\pi$
$421$	14.0506	+	10.2083i	0.684784	+	0.497524i	−0.190158	+	0.981754i	$0.560900\pi$
$422$		0			0
$423$	−29.6717	−	9.64092i	−1.44269	−	0.468758i
$424$		0			0
$425$	−7.78184	−	17.9093i	−0.377475	−	0.868728i
$426$		0			0
$427$	22.1131	+	7.18497i	1.07013	+	0.347705i
$428$		0			0
$429$	−0.0501843	−	0.0364610i	−0.00242292	−	0.00176035i
$430$		0			0
$431$	27.9780	−	20.3272i	1.34765	−	0.979126i	0.348526	−	0.937299i	$-0.386682\pi$
$431$	27.9780	−	20.3272i	1.34765	−	0.979126i	0.999125	−	0.0418269i	$-0.0133178\pi$
$432$		0			0
$433$	−22.3305	−	30.7353i	−1.07314	−	1.47704i	−0.866861	−	0.498550i	$-0.833866\pi$
$433$	−22.3305	−	30.7353i	−1.07314	−	1.47704i	−0.206275	−	0.978494i	$-0.566134\pi$
$434$		0			0
$435$	0.0716004	+	0.344449i	0.00343298	+	0.0165151i
$436$		0			0
$437$	−40.3383	+	13.1067i	−1.92964	+	0.626979i
$438$		0			0
$439$	−1.45680	+	4.48356i	−0.0695291	+	0.213989i	−0.979783	−	0.200061i	$-0.935886\pi$
$439$	−1.45680	+	4.48356i	−0.0695291	+	0.213989i	0.910254	+	0.414050i	$0.135886\pi$
$440$		0			0
$441$	3.75268	+	11.5495i	0.178699	+	0.549979i
$442$		0			0
$443$		−	30.4179i		−	1.44520i	−0.691267	−	0.722600i	$-0.742947\pi$
$443$		−	30.4179i		−	1.44520i	0.691267	−	0.722600i	$-0.257053\pi$
$444$		0			0
$445$	−10.6733	−	4.80957i	−0.505962	−	0.227995i
$446$		0			0
$447$	−0.292663	+	0.402817i	−0.0138425	+	0.0190526i
$448$		0			0
$449$	13.7761			0.650133			0.325067	−	0.945691i	$-0.394613\pi$
$449$	13.7761			0.650133			0.325067	+	0.945691i	$0.394613\pi$
$450$		0			0
$451$	−18.0510			−0.849986
$452$		0			0
$453$	−0.187516	+	0.258094i	−0.00881027	+	0.0121263i
$454$		0			0
$455$	−2.10967	+	0.438537i	−0.0989030	+	0.0205589i
$456$		0			0
$457$			14.6462i			0.685122i	0.939496	+	0.342561i	$0.111294\pi$
$457$			14.6462i			0.685122i	−0.939496	+	0.342561i	$0.888706\pi$
$458$		0			0
$459$	0.431022	+	1.32655i	0.0201184	+	0.0619180i
$460$		0			0
$461$	6.89410	−	21.2179i	0.321090	−	0.988215i	−0.652084	−	0.758147i	$-0.726105\pi$
$461$	6.89410	−	21.2179i	0.321090	−	0.988215i	0.973175	−	0.230068i	$-0.0738949\pi$
$462$		0			0
$463$	−15.2144	+	4.94346i	−0.707073	+	0.229742i	−0.640410	−	0.768033i	$-0.721235\pi$
$463$	−15.2144	+	4.94346i	−0.707073	+	0.229742i	−0.0666636	+	0.997776i	$0.521235\pi$
$464$		0			0
$465$	0.255665	+	0.0280322i	0.0118562	+	0.00129996i
$466$		0			0
$467$	5.04792	+	6.94787i	0.233590	+	0.321509i	0.909680	−	0.415310i	$-0.136327\pi$
$467$	5.04792	+	6.94787i	0.233590	+	0.321509i	−0.676090	+	0.736819i	$0.736327\pi$
$468$		0			0
$469$	−1.73401	+	1.25983i	−0.0800692	+	0.0581737i
$470$		0			0
$471$	−0.641736	−	0.466248i	−0.0295696	−	0.0214836i
$472$		0			0
$473$	−17.0951	−	5.55452i	−0.786032	−	0.255397i
$474$		0			0
$475$	−26.5987	+	11.5575i	−1.22043	+	0.530296i
$476$		0			0
$477$	3.17087	+	1.03028i	0.145184	+	0.0471732i
$478$		0			0
$479$	3.64835	+	2.65068i	0.166697	+	0.121113i	0.668006	−	0.744156i	$-0.267148\pi$
$479$	3.64835	+	2.65068i	0.166697	+	0.121113i	−0.501309	+	0.865268i	$0.667148\pi$
$480$		0			0
$481$	0.346418	−	0.251687i	0.0157953	−	0.0114760i
$482$		0			0
$483$	−0.439493	−	0.604910i	−0.0199976	−	0.0275244i
$484$		0			0
$485$	24.0483	+	21.8494i	1.09198	+	0.992132i
$486$		0			0
$487$	6.69405	−	2.17503i	0.303336	−	0.0985599i	−0.153394	−	0.988165i	$-0.549020\pi$
$487$	6.69405	−	2.17503i	0.303336	−	0.0985599i	0.456730	+	0.889605i	$0.349020\pi$
$488$		0			0
$489$	0.260964	−	0.803165i	0.0118012	−	0.0363204i
$490$		0			0
$491$	−7.80243	−	24.0134i	−0.352119	−	1.08371i	−0.957661	−	0.287897i	$-0.907044\pi$
$491$	−7.80243	−	24.0134i	−0.352119	−	1.08371i	0.605543	−	0.795813i	$-0.292956\pi$
$492$		0			0
$493$			10.3164i			0.464628i
$494$		0			0
$495$	−1.35496	+	12.3577i	−0.0609009	+	0.555439i
$496$		0			0
$497$	−13.5894	+	18.7042i	−0.609569	+	0.839000i
$498$		0			0
$499$	22.8665			1.02364			0.511822	−	0.859092i	$-0.328971\pi$
$499$	22.8665			1.02364			0.511822	+	0.859092i	$0.328971\pi$
$500$		0			0
$501$	−1.35072			−0.0603459
$502$		0			0
$503$	5.18231	−	7.13284i	0.231068	−	0.318038i	−0.677701	−	0.735338i	$-0.737024\pi$
$503$	5.18231	−	7.13284i	0.231068	−	0.318038i	0.908769	+	0.417300i	$0.137024\pi$
$504$		0			0
$505$	0.450840	−	4.11183i	0.0200621	−	0.182974i
$506$		0			0
$507$			0.755523i			0.0335539i
$508$		0			0
$509$	−6.02799	−	18.5522i	−0.267186	−	0.822314i	−0.991182	−	0.132509i	$-0.957697\pi$
$509$	−6.02799	−	18.5522i	−0.267186	−	0.822314i	0.723996	−	0.689804i	$-0.242303\pi$
$510$		0			0
$511$	2.16967	−	6.67755i	0.0959804	−	0.295397i
$512$		0			0
$513$	1.97018	−	0.640150i	0.0869856	−	0.0282633i
$514$		0			0
$515$	−17.0727	−	15.5116i	−0.752311	−	0.683523i
$516$		0			0
$517$	11.3551	+	15.6289i	0.499395	+	0.687358i
$518$		0			0
$519$	0.326269	−	0.237048i	0.0143216	−	0.0104053i
$520$		0			0
$521$	−10.7036	−	7.77662i	−0.468933	−	0.340700i	0.328092	−	0.944646i	$-0.393594\pi$
$521$	−10.7036	−	7.77662i	−0.468933	−	0.340700i	−0.797025	+	0.603946i	$0.793594\pi$
$522$		0			0
$523$	40.6072	+	13.1941i	1.77563	+	0.576937i	0.998618	−	0.0525482i	$-0.0167343\pi$
$523$	40.6072	+	13.1941i	1.77563	+	0.576937i	0.777012	+	0.629486i	$0.216734\pi$
$524$		0			0
$525$	−0.338672	−	0.382992i	−0.0147808	−	0.0167151i
$526$		0			0
$527$	7.17283	+	2.33059i	0.312453	+	0.101522i
$528$		0			0
$529$	24.6530	+	17.9114i	1.07187	+	0.778758i
$530$		0			0
$531$	12.2648	−	8.91090i	0.532247	−	0.386700i
$532$		0			0
$533$	−3.20985	−	4.41799i	−0.139034	−	0.191364i
$534$		0			0
$535$	−33.5989	−	3.68393i	−1.45261	−	0.159270i
$536$		0			0
$537$	−1.42145	+	0.461856i	−0.0613400	+	0.0199306i
$538$		0			0
$539$	2.32368	−	7.15154i	0.100088	−	0.308039i
$540$		0			0
$541$	2.59118	+	7.97483i	0.111404	+	0.342865i	0.991180	−	0.132523i	$-0.0423078\pi$
$541$	2.59118	+	7.97483i	0.111404	+	0.342865i	−0.879776	+	0.475388i	$0.842308\pi$
$542$		0			0
$543$			1.50119i			0.0644224i
$544$		0			0
$545$	−9.92881	+	2.06390i	−0.425304	+	0.0884077i
$546$		0			0
$547$	−8.49189	+	11.6881i	−0.363087	+	0.499747i	−0.951006	−	0.309174i	$-0.899948\pi$
$547$	−8.49189	+	11.6881i	−0.363087	+	0.499747i	0.587918	+	0.808920i	$0.299948\pi$
$548$		0			0
$549$	40.5829			1.73203
$550$		0			0
$551$	15.3218			0.652732
$552$		0			0
$553$	−6.55396	+	9.02076i	−0.278703	+	0.383602i
$554$		0			0
$555$	0.0926267	+	0.0417392i	0.00393178	+	0.00177173i
$556$		0			0
$557$			17.2330i			0.730187i	0.930971	+	0.365093i	$0.118963\pi$
$557$			17.2330i			0.730187i	−0.930971	+	0.365093i	$0.881037\pi$
$558$		0			0
$559$	−1.68040	−	5.17175i	−0.0710734	−	0.218742i
$560$		0			0
$561$	0.133367	−	0.410460i	0.00563074	−	0.0173296i
$562$		0			0
$563$	−6.78168	+	2.20350i	−0.285814	+	0.0928665i	−0.448415	−	0.893825i	$-0.648011\pi$
$563$	−6.78168	+	2.20350i	−0.285814	+	0.0928665i	0.162602	+	0.986692i	$0.448011\pi$
$564$		0			0
$565$	7.11232	+	34.2153i	0.299218	+	1.43945i
$566$		0			0
$567$	−9.04953	−	12.4556i	−0.380044	−	0.523086i
$568$		0			0
$569$	−11.5916	+	8.42179i	−0.485945	+	0.353060i	−0.803623	−	0.595139i	$-0.797097\pi$
$569$	−11.5916	+	8.42179i	−0.485945	+	0.353060i	0.317678	+	0.948199i	$0.397097\pi$
$570$		0			0
$571$	−8.30283	−	6.03236i	−0.347462	−	0.252446i	0.400341	−	0.916366i	$-0.368892\pi$
$571$	−8.30283	−	6.03236i	−0.347462	−	0.252446i	−0.747804	+	0.663920i	$0.768892\pi$
$572$		0			0
$573$	−1.12727	−	0.366273i	−0.0470924	−	0.0153013i
$574$		0			0
$575$	31.4987	+	18.5648i	1.31359	+	0.774205i
$576$		0			0
$577$	9.12639	+	2.96534i	0.379937	+	0.123449i	0.492758	−	0.870166i	$-0.335989\pi$
$577$	9.12639	+	2.96534i	0.379937	+	0.123449i	−0.112821	+	0.993615i	$0.535989\pi$
$578$		0			0
$579$	−0.230904	−	0.167762i	−0.00959606	−	0.00697194i
$580$		0			0
$581$	−1.26832	+	0.921485i	−0.0526186	+	0.0382296i
$582$		0			0
$583$	−1.21346	−	1.67019i	−0.0502564	−	0.0691720i
$584$		0			0
$585$	−3.26551	+	1.86585i	−0.135012	+	0.0771434i
$586$		0			0
$587$	5.03134	−	1.63478i	0.207666	−	0.0674747i	−0.203337	−	0.979109i	$-0.565179\pi$
$587$	5.03134	−	1.63478i	0.207666	−	0.0674747i	0.411003	+	0.911634i	$0.365179\pi$
$588$		0			0
$589$	3.46138	−	10.6530i	0.142624	−	0.438950i
$590$		0			0
$591$	−0.0123333	−	0.0379580i	−0.000507324	−	0.00156138i
$592$		0			0
$593$		−	2.21453i		−	0.0909397i	−0.998966	−	0.0454699i	$-0.985522\pi$
$593$		−	2.21453i		−	0.0909397i	0.998966	−	0.0454699i	$-0.0144785\pi$
$594$		0			0
$595$	−7.43758	−	13.0168i	−0.304911	−	0.533639i
$596$		0			0
$597$	−0.329543	+	0.453577i	−0.0134873	+	0.0185637i
$598$		0			0
$599$	−1.85018			−0.0755964			−0.0377982	−	0.999285i	$-0.512034\pi$
$599$	−1.85018			−0.0755964			−0.0377982	+	0.999285i	$0.512034\pi$
$600$		0			0
$601$	32.8477			1.33988			0.669942	−	0.742413i	$-0.266319\pi$
$601$	32.8477			1.33988			0.669942	+	0.742413i	$0.266319\pi$
$602$		0			0
$603$	−2.19894	+	3.02658i	−0.0895477	+	0.123252i
$604$		0			0
$605$	−11.3638	+	12.5075i	−0.462006	+	0.508500i
$606$		0			0
$607$			29.1371i			1.18264i	0.806438	+	0.591319i	$0.201392\pi$
$607$			29.1371i			1.18264i	−0.806438	+	0.591319i	$0.798608\pi$
$608$		0			0
$609$	0.0834671	+	0.256885i	0.00338226	+	0.0104095i
$610$		0			0
$611$	−1.80601	+	5.55832i	−0.0730632	+	0.224865i
$612$		0			0
$613$	−3.61632	+	1.17501i	−0.146062	+	0.0474584i	−0.381136	−	0.924519i	$-0.624467\pi$
$613$	−3.61632	+	1.17501i	−0.146062	+	0.0474584i	0.235074	+	0.971978i	$0.424467\pi$
$614$		0			0
$615$	0.532315	−	1.18130i	0.0214650	−	0.0476346i
$616$		0			0
$617$	28.9502	+	39.8466i	1.16549	+	1.60416i	0.688456	+	0.725278i	$0.258289\pi$
$617$	28.9502	+	39.8466i	1.16549	+	1.60416i	0.477035	+	0.878884i	$0.341711\pi$
$618$		0			0
$619$	5.13396	−	3.73004i	0.206351	−	0.149923i	−0.479810	−	0.877372i	$-0.659294\pi$
$619$	5.13396	−	3.73004i	0.206351	−	0.149923i	0.686161	+	0.727449i	$0.259294\pi$
$620$		0			0
$621$	−2.11290	−	1.53511i	−0.0847876	−	0.0616018i
$622$		0			0
$623$	−8.54810	−	2.77745i	−0.342472	−	0.111276i
$624$		0			0
$625$	22.6524	+	10.5768i	0.906096	+	0.423072i
$626$		0			0
$627$	−0.609612	−	0.198075i	−0.0243455	−	0.00791035i
$628$		0			0
$629$	2.41021	+	1.75112i	0.0961014	+	0.0698218i
$630$		0			0
$631$	4.48099	−	3.25563i	0.178385	−	0.129604i	−0.495010	−	0.868888i	$-0.664835\pi$
$631$	4.48099	−	3.25563i	0.178385	−	0.129604i	0.673395	+	0.739283i	$0.264835\pi$
$632$		0			0
$633$	0.430752	+	0.592879i	0.0171208	+	0.0235648i
$634$		0			0
$635$	1.23272	−	2.73563i	0.0489191	−	0.108560i
$636$		0			0
$637$	2.16355	−	0.702979i	0.0857228	−	0.0278530i
$638$		0			0
$639$	−12.4700	+	38.3786i	−0.493304	+	1.51823i
$640$		0			0
$641$	3.16032	+	9.72646i	0.124825	+	0.384172i	0.993869	−	0.110563i	$-0.0352653\pi$
$641$	3.16032	+	9.72646i	0.124825	+	0.384172i	−0.869044	+	0.494735i	$0.835265\pi$
$642$		0			0
$643$		−	20.5779i		−	0.811515i	−0.913981	−	0.405757i	$-0.867008\pi$
$643$		−	20.5779i		−	0.811515i	0.913981	−	0.405757i	$-0.132992\pi$
$644$		0			0
$645$	0.867628	−	0.954943i	0.0341628	−	0.0376009i
$646$		0			0
$647$	4.06226	−	5.59123i	0.159704	−	0.219814i	−0.721665	−	0.692243i	$-0.756623\pi$
$647$	4.06226	−	5.59123i	0.159704	−	0.219814i	0.881369	+	0.472429i	$0.156623\pi$
$648$		0			0
$649$	−9.38723			−0.368481
$650$		0			0
$651$	0.197464			0.00773923
$652$		0			0
$653$	0.974775	−	1.34166i	0.0381459	−	0.0525033i	−0.789518	−	0.613727i	$-0.789669\pi$
$653$	0.974775	−	1.34166i	0.0381459	−	0.0525033i	0.827664	+	0.561224i	$0.189669\pi$
$654$		0			0
$655$	−15.3575	−	26.8779i	−0.600068	−	1.05021i
$656$		0			0
$657$		−	12.2549i		−	0.478110i
$658$		0			0
$659$	0.956983	+	2.94529i	0.0372788	+	0.114732i	0.967964	−	0.251088i	$-0.0807884\pi$
$659$	0.956983	+	2.94529i	0.0372788	+	0.114732i	−0.930685	+	0.365820i	$0.880788\pi$
$660$		0			0
$661$	−4.38102	+	13.4834i	−0.170402	+	0.524443i	−0.999394	−	0.0348175i	$-0.988915\pi$
$661$	−4.38102	+	13.4834i	−0.170402	+	0.524443i	0.828992	+	0.559261i	$0.188915\pi$
$662$		0			0
$663$	0.124176	−	0.0403472i	0.00482259	−	0.00156696i
$664$		0			0
$665$	−19.3325	+	11.0462i	−0.749682	+	0.428354i
$666$		0			0
$667$	−11.3540	−	15.6275i	−0.439630	−	0.605099i
$668$		0			0
$669$	−0.680886	+	0.494692i	−0.0263246	+	0.0191259i
$670$		0			0
$671$	−20.3299	−	14.7705i	−0.784826	−	0.570210i
$672$		0			0
$673$	4.87403	+	1.58367i	0.187880	+	0.0610460i	0.401446	−	0.915883i	$-0.368508\pi$
$673$	4.87403	+	1.58367i	0.187880	+	0.0610460i	−0.213566	+	0.976929i	$0.568508\pi$
$674$		0			0
$675$	−1.53844	−	0.906729i	−0.0592146	−	0.0349000i
$676$		0			0
$677$	−25.7566	−	8.36884i	−0.989908	−	0.321641i	−0.231082	−	0.972934i	$-0.574227\pi$
$677$	−25.7566	−	8.36884i	−0.989908	−	0.321641i	−0.758826	+	0.651294i	$0.774227\pi$
$678$		0			0
$679$	20.1815	+	14.6627i	0.774496	+	0.562704i
$680$		0			0
$681$	−0.188923	+	0.137261i	−0.00723956	+	0.00525985i
$682$		0			0
$683$	−8.64040	−	11.8925i	−0.330616	−	0.455053i	0.611056	−	0.791588i	$-0.290745\pi$
$683$	−8.64040	−	11.8925i	−0.330616	−	0.455053i	−0.941671	+	0.336534i	$0.890745\pi$
$684$		0			0
$685$	−3.83829	−	18.4649i	−0.146654	−	0.705507i
$686$		0			0
$687$	0.151296	−	0.0491590i	0.00577229	−	0.00187553i
$688$		0			0
$689$	0.192999	−	0.593991i	0.00735269	−	0.0226293i
$690$		0			0
$691$	4.25630	+	13.0995i	0.161917	+	0.498330i	0.998796	−	0.0490586i	$-0.0156221\pi$
$691$	4.25630	+	13.0995i	0.161917	+	0.498330i	−0.836879	+	0.547388i	$0.815622\pi$
$692$		0			0
$693$			9.54458i			0.362569i
$694$		0			0
$695$	32.4233	+	14.6105i	1.22988	+	0.554208i
$696$		0			0
$697$	22.3326	−	30.7382i	0.845909	−	1.16429i
$698$		0			0
$699$	1.33393			0.0504538
$700$		0			0
$701$	3.95616			0.149422			0.0747111	−	0.997205i	$-0.476197\pi$
$701$	3.95616			0.149422			0.0747111	+	0.997205i	$0.476197\pi$
$702$		0			0
$703$	2.60075	−	3.57962i	0.0980891	−	0.135008i
$704$		0			0
$705$	−1.35765	+	0.282214i	−0.0511320	+	0.0106288i
$706$		0			0
$707$		−	3.17580i		−	0.119438i
$708$		0			0
$709$	10.5384	+	32.4338i	0.395777	+	1.21808i	0.928355	+	0.371696i	$0.121224\pi$
$709$	10.5384	+	32.4338i	0.395777	+	1.21808i	−0.532577	+	0.846381i	$0.678776\pi$
$710$		0			0
$711$	−6.01406	+	18.5094i	−0.225545	+	0.694156i
$712$		0			0
$713$	−13.4305	+	4.36385i	−0.502978	+	0.163427i
$714$		0			0
$715$	2.31494	+	0.253821i	0.0865739	+	0.00949236i
$716$		0			0
$717$	0.758732	+	1.04431i	0.0283354	+	0.0390003i
$718$		0			0
$719$	18.8977	−	13.7300i	0.704766	−	0.512043i	−0.176715	−	0.984262i	$-0.556547\pi$
$719$	18.8977	−	13.7300i	0.704766	−	0.512043i	0.881481	+	0.472220i	$0.156547\pi$
$720$		0			0
$721$	−14.3275	−	10.4095i	−0.533584	−	0.387672i
$722$		0			0
$723$	0.999614	+	0.324794i	0.0371760	+	0.0120792i
$724$		0			0
$725$	−8.74938	−	9.89437i	−0.324944	−	0.367468i
$726$		0			0
$727$	−12.1847	−	3.95904i	−0.451904	−	0.146833i	0.0742170	−	0.997242i	$-0.476354\pi$
$727$	−12.1847	−	3.95904i	−0.451904	−	0.146833i	−0.526121	+	0.850409i	$0.676354\pi$
$728$		0			0
$729$	−21.6886	−	15.7577i	−0.803283	−	0.583619i
$730$		0			0
$731$	30.6086	−	22.2384i	1.13210	−	0.822518i
$732$		0			0
$733$	−15.7602	−	21.6920i	−0.582115	−	0.801213i	0.411810	−	0.911270i	$-0.364897\pi$
$733$	−15.7602	−	21.6920i	−0.582115	−	0.801213i	−0.993925	+	0.110057i	$0.964897\pi$
$734$		0			0
$735$	0.399490	+	0.362963i	0.0147354	+	0.0133881i
$736$		0			0
$737$	2.20310	−	0.715832i	0.0811524	−	0.0263680i
$738$		0			0
$739$	15.7123	−	48.3574i	0.577986	−	1.77886i	−0.0477941	−	0.998857i	$-0.515219\pi$
$739$	15.7123	−	48.3574i	0.577986	−	1.77886i	0.625780	−	0.780000i	$-0.284781\pi$
$740$		0			0
$741$	−0.0599233	−	0.184425i	−0.00220134	−	0.00677502i
$742$		0			0
$743$			25.4540i			0.933816i	0.884306	+	0.466908i	$0.154632\pi$
$743$			25.4540i			0.933816i	−0.884306	+	0.466908i	$0.845368\pi$
$744$		0			0
$745$	2.03736	−	18.5815i	0.0746430	−	0.680772i
$746$		0			0
$747$	−1.60838	+	2.21374i	−0.0588475	+	0.0809966i
$748$		0			0
$749$	−25.9503			−0.948203
$750$		0			0
$751$	−21.1719			−0.772574			−0.386287	−	0.922379i	$-0.626243\pi$
$751$	−21.1719			−0.772574			−0.386287	+	0.922379i	$0.626243\pi$
$752$		0			0
$753$	−0.568806	+	0.782895i	−0.0207285	+	0.0285303i
$754$		0			0
$755$	1.30538	−	11.9056i	0.0475077	−	0.433288i
$756$		0			0
$757$		−	34.8326i		−	1.26601i	−0.774147	−	0.633006i	$-0.781821\pi$
$757$		−	34.8326i		−	1.26601i	0.774147	−	0.633006i	$-0.218179\pi$
$758$		0			0
$759$	0.249718	+	0.768554i	0.00906420	+	0.0278967i
$760$		0			0
$761$	−2.49606	+	7.68209i	−0.0904822	+	0.278476i	−0.986050	−	0.166450i	$-0.946770\pi$
$761$	−2.49606	+	7.68209i	−0.0904822	+	0.278476i	0.895568	+	0.444925i	$0.146770\pi$
$762$		0			0
$763$	−7.40478	+	2.40596i	−0.268071	+	0.0871015i
$764$		0			0
$765$	−19.3672	−	17.5963i	−0.700221	−	0.636196i
$766$		0			0
$767$	−1.66926	−	2.29753i	−0.0602733	−	0.0829591i
$768$		0			0
$769$	−10.2491	+	7.44644i	−0.369593	+	0.268525i	−0.757042	−	0.653366i	$-0.773356\pi$
$769$	−10.2491	+	7.44644i	−0.369593	+	0.268525i	0.387449	+	0.921891i	$0.373356\pi$
$770$		0			0
$771$	−0.439816	−	0.319545i	−0.0158396	−	0.0115081i
$772$		0			0
$773$	38.9161	+	12.6446i	1.39971	+	0.454795i	0.909098	−	0.416582i	$-0.136772\pi$
$773$	38.9161	+	12.6446i	1.39971	+	0.454795i	0.490615	+	0.871376i	$0.336772\pi$
$774$		0			0
$775$	−8.85597	+	3.84805i	−0.318116	+	0.138226i
$776$		0			0
$777$	0.0741836	+	0.0241037i	0.00266132	+	0.000864716i
$778$		0			0
$779$	−45.6522	−	33.1682i	−1.63566	−	1.18838i
$780$		0			0
$781$	20.2150	−	14.6871i	0.723351	−	0.525545i
$782$		0			0
$783$	0.554547	+	0.763269i	0.0198179	+	0.0272770i
$784$		0			0
$785$	29.6025	+	3.24576i	1.05656	+	0.115846i
$786$		0			0
$787$	−2.46599	+	0.801249i	−0.0879031	+	0.0285615i	−0.352638	−	0.935760i	$-0.614715\pi$
$787$	−2.46599	+	0.801249i	−0.0879031	+	0.0285615i	0.264735	+	0.964321i	$0.414715\pi$
$788$		0			0
$789$	0.353637	−	1.08838i	0.0125898	−	0.0387474i
$790$		0			0
$791$	8.29108	+	25.5173i	0.294797	+	0.907291i
$792$		0			0
$793$		−	7.60228i		−	0.269965i
$794$		0			0
$795$	0.145086	−	0.0301589i	0.00514565	−	0.00106963i
$796$		0			0
$797$	−12.6487	+	17.4095i	−0.448041	+	0.616676i	−0.971975	−	0.235083i	$-0.924464\pi$
$797$	−12.6487	+	17.4095i	−0.448041	+	0.616676i	0.523934	+	0.851759i	$0.324464\pi$
$798$		0			0
$799$	−40.6623			−1.43853
$800$		0			0
$801$	−15.6878			−0.554302
$802$		0			0
$803$	−4.46029	+	6.13907i	−0.157400	+	0.216643i
$804$		0			0
$805$	25.5927	+	11.5325i	0.902023	+	0.406468i
$806$		0			0
$807$		−	0.321251i		−	0.0113086i
$808$		0			0
$809$	1.07271	+	3.30147i	0.0377146	+	0.116074i	0.968141	−	0.250404i	$-0.0805636\pi$
$809$	1.07271	+	3.30147i	0.0377146	+	0.116074i	−0.930427	+	0.366478i	$0.880564\pi$
$810$		0			0
$811$	−11.3665	+	34.9826i	−0.399133	+	1.22841i	0.526563	+	0.850136i	$0.323481\pi$
$811$	−11.3665	+	34.9826i	−0.399133	+	1.22841i	−0.925696	+	0.378269i	$0.876519\pi$
$812$		0			0
$813$	1.21334	−	0.394237i	0.0425536	−	0.0138265i
$814$		0			0
$815$	6.45252	+	31.0412i	0.226022	+	1.08732i
$816$		0			0
$817$	−33.0283	−	45.4596i	−1.15552	−	1.59043i
$818$		0			0
$819$	−2.33604	+	1.69723i	−0.0816280	+	0.0593062i
$820$		0			0
$821$	−38.2615	−	27.7986i	−1.33534	−	0.970179i	−0.999602	−	0.0282220i	$-0.991015\pi$
$821$	−38.2615	−	27.7986i	−1.33534	−	0.970179i	−0.335735	−	0.941957i	$-0.608985\pi$
$822$		0			0
$823$	−9.96867	−	3.23902i	−0.347486	−	0.112905i	0.130074	−	0.991504i	$-0.458479\pi$
$823$	−9.96867	−	3.23902i	−0.347486	−	0.112905i	−0.477560	+	0.878599i	$0.658479\pi$
$824$		0			0
$825$	0.220202	+	0.506777i	0.00766645	+	0.0176437i
$826$		0			0
$827$	5.48824	+	1.78324i	0.190845	+	0.0620093i	0.402880	−	0.915253i	$-0.368009\pi$
$827$	5.48824	+	1.78324i	0.190845	+	0.0620093i	−0.212035	+	0.977262i	$0.568009\pi$
$828$		0			0
$829$	−23.6650	−	17.1936i	−0.821919	−	0.597159i	0.0953427	−	0.995445i	$-0.469605\pi$
$829$	−23.6650	−	17.1936i	−0.821919	−	0.597159i	−0.917261	+	0.398286i	$0.869605\pi$
$830$		0			0
$831$	−0.694887	+	0.504865i	−0.0241054	+	0.0175136i
$832$		0			0
$833$	9.30322	+	12.8048i	0.322337	+	0.443659i
$834$		0			0
$835$	44.0294	−	25.1575i	1.52370	−	0.870612i
$836$		0			0
$837$	0.655966	−	0.213136i	0.0226735	−	0.00736707i
$838$		0			0
$839$	−4.96033	+	15.2663i	−0.171250	+	0.527052i	−0.999442	−	0.0333911i	$-0.989369\pi$
$839$	−4.96033	+	15.2663i	−0.171250	+	0.527052i	0.828193	+	0.560444i	$0.189369\pi$
$840$		0			0
$841$	−6.80517	−	20.9442i	−0.234661	−	0.722212i
$842$		0			0
$843$			0.781604i			0.0269199i
$844$		0			0
$845$	−14.0718	−	24.6277i	−0.484084	−	0.847217i
$846$		0			0
$847$	−7.62605	+	10.4964i	−0.262034	+	0.360659i
$848$		0			0
$849$	1.58013			0.0542298
$850$		0			0
$851$	−5.57828			−0.191221
$852$		0			0
$853$	19.7934	−	27.2433i	0.677713	−	0.932792i	−0.322190	−	0.946675i	$-0.604419\pi$
$853$	19.7934	−	27.2433i	0.677713	−	0.932792i	0.999904	+	0.0138826i	$0.00441911\pi$
$854$		0			0
$855$	−26.1339	+	28.7639i	−0.893760	+	0.983705i
$856$		0			0
$857$		−	18.5384i		−	0.633260i	−0.948549	−	0.316630i	$-0.897449\pi$
$857$		−	18.5384i		−	0.633260i	0.948549	−	0.316630i	$-0.102551\pi$
$858$		0			0
$859$	0.00514740	+	0.0158421i	0.000175627	+	0.000540524i	0.951144	−	0.308747i	$-0.0999095\pi$
$859$	0.00514740	+	0.0158421i	0.000175627	+	0.000540524i	−0.950969	+	0.309287i	$0.899910\pi$
$860$		0			0
$861$	0.307403	−	0.946089i	0.0104763	−	0.0322426i
$862$		0			0
$863$	31.6593	−	10.2867i	1.07769	−	0.350164i	0.284214	−	0.958761i	$-0.408267\pi$
$863$	31.6593	−	10.2867i	1.07769	−	0.350164i	0.793480	+	0.608597i	$0.208267\pi$
$864$		0			0
$865$	−6.22027	+	13.8039i	−0.211495	+	0.469345i
$866$		0			0
$867$	−0.0611964	−	0.0842296i	−0.00207834	−	0.00286059i
$868$		0			0
$869$	9.74939	−	7.08335i	0.330725	−	0.240286i
$870$		0			0
$871$	0.566961	+	0.411921i	0.0192107	+	0.0139574i
$872$		0			0
$873$	41.4098	+	13.4548i	1.40151	+	0.455378i
$874$		0			0
$875$	18.1729	+	6.17649i	0.614357	+	0.208804i
$876$		0			0
$877$	38.7660	+	12.5958i	1.30903	+	0.425331i	0.878715	−	0.477346i	$-0.158401\pi$
$877$	38.7660	+	12.5958i	1.30903	+	0.425331i	0.430319	+	0.902677i	$0.358401\pi$
$878$		0			0
$879$	−1.16526	−	0.846612i	−0.0393033	−	0.0285555i
$880$		0			0
$881$	−20.0854	+	14.5929i	−0.676694	+	0.491647i	−0.872259	−	0.489044i	$-0.837346\pi$
$881$	−20.0854	+	14.5929i	−0.676694	+	0.491647i	0.195565	+	0.980691i	$0.437346\pi$
$882$		0			0
$883$	0.996201	+	1.37115i	0.0335248	+	0.0461430i	0.825450	−	0.564475i	$-0.190921\pi$
$883$	0.996201	+	1.37115i	0.0335248	+	0.0461430i	−0.791926	+	0.610618i	$0.790921\pi$
$884$		0			0
$885$	0.276825	−	0.614324i	0.00930538	−	0.0206503i
$886$		0			0
$887$	11.5402	−	3.74964i	0.387482	−	0.125901i	−0.108796	−	0.994064i	$-0.534700\pi$
$887$	11.5402	−	3.74964i	0.387482	−	0.125901i	0.496278	+	0.868164i	$0.334700\pi$
$888$		0			0
$889$	0.711877	−	2.19093i	0.0238756	−	0.0734816i
$890$		0			0
$891$	5.14190	+	15.8252i	0.172260	+	0.530163i
$892$		0			0
$893$			60.3913i			2.02092i
$894$		0			0
$895$	37.7325	−	41.5298i	1.26126	−	1.38819i
$896$		0			0
$897$	−0.143699	+	0.197784i	−0.00479796	+	0.00660383i
$898$		0			0
$899$	5.10137			0.170140
$900$		0			0
$901$	4.34538			0.144766
$902$		0			0
$903$	0.582249	−	0.801396i	0.0193760	−	0.0266688i
$904$		0			0
$905$	−27.9600	−	48.9341i	−0.929423	−	1.62663i
$906$		0			0
$907$		−	14.9224i		−	0.495491i	−0.968825	−	0.247746i	$-0.920310\pi$
$907$		−	14.9224i		−	0.495491i	0.968825	−	0.247746i	$-0.0796898\pi$
$908$		0			0
$909$	−1.71291	−	5.27180i	−0.0568137	−	0.174855i
$910$		0			0
$911$	−14.2166	+	43.7543i	−0.471018	+	1.44964i	0.380236	+	0.924890i	$0.375843\pi$
$911$	−14.2166	+	43.7543i	−0.471018	+	1.44964i	−0.851254	+	0.524754i	$0.824157\pi$
$912$		0			0
$913$	1.61143	−	0.523584i	0.0533304	−	0.0173281i
$914$		0			0
$915$	1.56614	−	0.894862i	0.0517750	−	0.0295832i
$916$		0			0
$917$	−13.9697	−	19.2276i	−0.461319	−	0.634952i
$918$		0			0
$919$	−4.67512	+	3.39667i	−0.154218	+	0.112046i	−0.662218	−	0.749311i	$-0.730385\pi$
$919$	−4.67512	+	3.39667i	−0.154218	+	0.112046i	0.508000	+	0.861357i	$0.330385\pi$
$920$		0			0
$921$	0.921160	+	0.669262i	0.0303532	+	0.0220529i
$922$		0			0
$923$	7.18935	+	2.33596i	0.236640	+	0.0768891i
$924$		0			0
$925$	−3.79674	+	0.364625i	−0.124836	+	0.0119888i
$926$		0			0
$927$	−29.3981	−	9.55202i	−0.965560	−	0.313730i
$928$		0			0
$929$	11.1761	+	8.11994i	0.366677	+	0.266406i	0.755832	−	0.654766i	$-0.227233\pi$
$929$	11.1761	+	8.11994i	0.366677	+	0.266406i	−0.389155	+	0.921172i	$0.627233\pi$
$930$		0			0
$931$	19.0175	−	13.8171i	0.623275	−	0.452836i
$932$		0			0
$933$	−0.794928	−	1.09412i	−0.0260248	−	0.0358200i
$934$		0			0
$935$	3.29758	+	15.8637i	0.107842	+	0.518798i
$936$		0			0
$937$	−2.29684	+	0.746290i	−0.0750346	+	0.0243802i	−0.346294	−	0.938126i	$-0.612560\pi$
$937$	−2.29684	+	0.746290i	−0.0750346	+	0.0243802i	0.271259	+	0.962506i	$0.412560\pi$
$938$		0			0
$939$	−0.247056	+	0.760360i	−0.00806237	+	0.0248134i
$940$		0			0
$941$	9.18367	+	28.2644i	0.299379	+	0.921394i	0.981715	+	0.190356i	$0.0609641\pi$
$941$	9.18367	+	28.2644i	0.299379	+	0.921394i	−0.682336	+	0.731039i	$0.739036\pi$
$942$		0			0
$943$			71.1417i			2.31669i
$944$		0			0
$945$	−1.24998	−	0.563264i	−0.0406619	−	0.0183230i
$946$		0			0
$947$	−5.37375	+	7.39633i	−0.174623	+	0.240348i	−0.887353	−	0.461090i	$-0.847458\pi$
$947$	−5.37375	+	7.39633i	−0.174623	+	0.240348i	0.712730	+	0.701438i	$0.247458\pi$
$948$		0			0
$949$	−2.29568			−0.0745209
$950$		0			0
$951$	1.62043			0.0525461
$952$		0			0
$953$	17.2277	−	23.7118i	0.558059	−	0.768102i	−0.433019	−	0.901385i	$-0.642552\pi$
$953$	17.2277	−	23.7118i	0.558059	−	0.768102i	0.991078	+	0.133283i	$0.0425518\pi$
$954$		0			0
$955$	43.5674	−	9.05634i	1.40981	−	0.293056i
$956$		0			0
$957$		−	0.291922i		−	0.00943651i
$958$		0			0
$959$	−4.47443	−	13.7709i	−0.144487	−	0.444685i
$960$		0			0
$961$	−8.42707	+	25.9359i	−0.271841	+	0.836640i
$962$		0			0
$963$	−43.0773	+	13.9967i	−1.38815	+	0.451036i
$964$		0			0
$965$	10.6514	+	1.16786i	0.342879	+	0.0375948i
$966$		0			0
$967$	20.3443	+	28.0016i	0.654230	+	0.900470i	0.999273	−	0.0381168i	$-0.0121359\pi$
$967$	20.3443	+	28.0016i	0.654230	+	0.900470i	−0.345044	+	0.938587i	$0.612136\pi$
$968$		0			0
$969$	1.09151	−	0.793025i	0.0350642	−	0.0254756i
$970$		0			0
$971$	24.0628	+	17.4826i	0.772211	+	0.561044i	0.902631	−	0.430415i	$-0.141633\pi$
$971$	24.0628	+	17.4826i	0.772211	+	0.561044i	−0.130420	+	0.991459i	$0.541633\pi$
$972$		0			0
$973$	25.9674	+	8.43732i	0.832477	+	0.270488i
$974$		0			0
$975$	−0.0848773	+	0.144011i	−0.00271825	+	0.00461203i
$976$		0			0
$977$	−40.1184	−	13.0352i	−1.28350	−	0.417035i	−0.413689	−	0.910418i	$-0.635760\pi$
$977$	−40.1184	−	13.0352i	−1.28350	−	0.417035i	−0.869812	+	0.493384i	$0.835760\pi$
$978$		0			0
$979$	7.85878	+	5.70974i	0.251168	+	0.182484i
$980$		0			0
$981$	−10.9942	+	7.98775i	−0.351017	+	0.255029i
$982$		0			0
$983$	−13.6846	−	18.8353i	−0.436472	−	0.600752i	0.532952	−	0.846146i	$-0.321083\pi$
$983$	−13.6846	−	18.8353i	−0.436472	−	0.600752i	−0.969424	+	0.245394i	$0.921083\pi$
$984$		0			0
$985$	1.10900	+	1.00760i	0.0353357	+	0.0321048i
$986$		0			0
$987$	−1.01252	+	0.328987i	−0.0322288	+	0.0104718i
$988$		0			0
$989$	−21.8913	+	67.3744i	−0.696102	+	2.14238i
$990$		0			0
$991$	16.3062	+	50.1854i	0.517984	+	1.59419i	0.777786	+	0.628529i	$0.216343\pi$
$991$	16.3062	+	50.1854i	0.517984	+	1.59419i	−0.259802	+	0.965662i	$0.583657\pi$
$992$		0			0
$993$			1.71882i			0.0545452i
$994$		0			0
$995$	2.29409	−	20.9230i	0.0727275	−	0.663303i
$996$		0			0
$997$	34.7408	−	47.8165i	1.10025	−	1.51437i	0.265199	−	0.964194i	$-0.414562\pi$
$997$	34.7408	−	47.8165i	1.10025	−	1.51437i	0.835052	−	0.550171i	$-0.185438\pi$
$998$		0			0
$999$	0.272451			0.00861997

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.q.a.129.5	✓	32
4.3	odd	2		400.2.y.d.129.4		32
5.2	odd	4		1000.2.m.e.601.4		32
5.3	odd	4		1000.2.m.d.601.5		32
5.4	even	2		1000.2.q.c.649.4		32
25.6	even	5		1000.2.q.c.849.4		32
25.8	odd	20		1000.2.m.d.401.5		32
25.12	odd	20		5000.2.a.q.1.9		16
25.13	odd	20		5000.2.a.r.1.8		16
25.17	odd	20		1000.2.m.e.401.4		32
25.19	even	10	inner	200.2.q.a.169.5	yes	32
100.19	odd	10		400.2.y.d.369.4		32
100.63	even	20		10000.2.a.bq.1.9		16
100.87	even	20		10000.2.a.br.1.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.q.a.129.5	✓	32	1.1	even	1	trivial
200.2.q.a.169.5	yes	32	25.19	even	10	inner
400.2.y.d.129.4		32	4.3	odd	2
400.2.y.d.369.4		32	100.19	odd	10
1000.2.m.d.401.5		32	25.8	odd	20
1000.2.m.d.601.5		32	5.3	odd	4
1000.2.m.e.401.4		32	25.17	odd	20
1000.2.m.e.601.4		32	5.2	odd	4
1000.2.q.c.649.4		32	5.4	even	2
1000.2.q.c.849.4		32	25.6	even	5
5000.2.a.q.1.9		16	25.12	odd	20
5000.2.a.r.1.8		16	25.13	odd	20
10000.2.a.bq.1.9		16	100.63	even	20
10000.2.a.br.1.8		16	100.87	even	20

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.q (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0350089 - 0.0481856i) q^{3} +(-0.243712 + 2.22275i) q^{5} +1.71675i q^{7} +(0.925955 + 2.84980i) q^{9} +(0.573356 - 1.76461i) q^{11} +(0.533844 - 0.173457i) q^{13} +(0.0985723 + 0.0895593i) q^{15} +(2.29552 + 3.15952i) q^{17} +(4.69249 - 3.40929i) q^{19} +(0.0827227 + 0.0601016i) q^{21} +(-6.95461 - 2.25969i) q^{23} +(-4.88121 - 1.08342i) q^{25} +(0.339673 + 0.110366i) q^{27} +(2.13709 + 1.55269i) q^{29} +(1.56235 - 1.13511i) q^{31} +(-0.0649561 - 0.0894045i) q^{33} +(-3.81590 - 0.418393i) q^{35} +(0.725506 - 0.235731i) q^{37} +(0.0103312 - 0.0317961i) q^{39} +(-3.00636 - 9.25262i) q^{41} -9.68774i q^{43} +(-6.56004 + 1.36363i) q^{45} +(-6.11994 + 8.42338i) q^{47} +4.05276 q^{49} +0.232607 q^{51} +(0.654009 - 0.900166i) q^{53} +(3.78254 + 1.70448i) q^{55} -0.345466i q^{57} +(-1.56343 - 4.81174i) q^{59} +(4.18521 - 12.8808i) q^{61} +(-4.89239 + 1.58963i) q^{63} +(0.255446 + 1.22887i) q^{65} +(0.733847 + 1.01005i) q^{67} +(-0.352358 + 0.256003i) q^{69} +(10.8951 + 7.91578i) q^{71} +(-3.88964 - 1.26382i) q^{73} +(-0.223091 + 0.197275i) q^{75} +(3.02939 + 0.984309i) q^{77} +(5.25455 + 3.81765i) q^{79} +(-7.25533 + 5.27131i) q^{81} +(0.536761 + 0.738788i) q^{83} +(-7.58225 + 4.33236i) q^{85} +(0.149634 - 0.0486192i) q^{87} +(-1.61785 + 4.97923i) q^{89} +(0.297782 + 0.916478i) q^{91} -0.115022i q^{93} +(6.43438 + 11.2611i) q^{95} +(8.54098 - 11.7557i) q^{97} +5.55967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{5} + 10 q^{9} + 6 q^{11} + 12 q^{15} - 6 q^{19} - 4 q^{21} - 30 q^{23} + 6 q^{25} - 2 q^{29} + 6 q^{31} + 8 q^{35} - 40 q^{37} - 12 q^{39} - 12 q^{45} - 20 q^{47} - 60 q^{49} - 60 q^{51} - 30 q^{53}+ \cdots + 92 q^{99}+O(q^{100}) \) 32 * q + 2 * q^5 + 10 * q^9 + 6 * q^11 + 12 * q^15 - 6 * q^19 - 4 * q^21 - 30 * q^23 + 6 * q^25 - 2 * q^29 + 6 * q^31 + 8 * q^35 - 40 * q^37 - 12 * q^39 - 12 * q^45 - 20 * q^47 - 60 * q^49 - 60 * q^51 - 30 * q^53 - 28 * q^55 - 30 * q^59 + 14 * q^61 - 20 * q^63 - 26 * q^65 - 4 * q^69 + 12 * q^71 + 40 * q^73 + 16 * q^75 + 16 * q^79 - 52 * q^81 + 30 * q^83 + 60 * q^85 + 110 * q^87 + 24 * q^89 - 4 * q^91 + 68 * q^95 + 30 * q^97 + 92 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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