LMFDB - Embedded newform 200.2.q.a.169.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,2,Mod(9,200)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			169.5
Character	$\chi$	$=$	200.169
Dual form			200.2.q.a.129.5

$q$-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 $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{10}\right)$

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	0.819004	−	0.573788i	$-0.194527\pi$
$3$	0.0350089	+	0.0481856i	0.0202124	+	0.0278200i	−0.798791	+	0.601608i	$0.794527\pi$
$4$		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	$-0.894826\pi$
$7$		−	1.71675i		−	0.648871i	0.945908	−	0.324436i	$-0.105174\pi$
$8$		0			0
$9$	0.925955	−	2.84980i	0.308652	−	0.949932i
$10$		0			0
$11$	0.573356	+	1.76461i	0.172873	+	0.532049i	0.999530	−	0.0306574i	$-0.00976008\pi$
$11$	0.573356	+	1.76461i	0.172873	+	0.532049i	−0.826657	+	0.562707i	$0.809760\pi$
$12$		0			0
$13$	0.533844	+	0.173457i	0.148062	+	0.0481082i	0.382110	−	0.924117i	$-0.375197\pi$
$13$	0.533844	+	0.173457i	0.148062	+	0.0481082i	−0.234048	+	0.972225i	$0.575197\pi$
$14$		0			0
$15$	0.0985723	−	0.0895593i	0.0254513	−	0.0231241i
$16$		0			0
$17$	2.29552	−	3.15952i	0.556746	−	0.766295i	−0.434162	−	0.900835i	$-0.642955\pi$
$17$	2.29552	−	3.15952i	0.556746	−	0.766295i	0.990908	+	0.134539i	$0.0429555\pi$
$18$		0			0
$19$	4.69249	+	3.40929i	1.07653	+	0.782145i	0.977075	−	0.212897i	$-0.0682899\pi$
$19$	4.69249	+	3.40929i	1.07653	+	0.782145i	0.0994556	+	0.995042i	$0.468290\pi$
$20$		0			0
$21$	0.0827227	−	0.0601016i	0.0180516	−	0.0131152i
$22$		0			0
$23$	−6.95461	+	2.25969i	−1.45014	+	0.471178i	−0.925041	−	0.379866i	$-0.875970\pi$
$23$	−6.95461	+	2.25969i	−1.45014	+	0.471178i	−0.525094	+	0.851044i	$0.675970\pi$
$24$		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	−0.371408	−	0.928470i	$-0.621125\pi$
$29$	2.13709	−	1.55269i	0.396848	−	0.288327i	0.768256	+	0.640143i	$0.221125\pi$
$30$		0			0
$31$	1.56235	+	1.13511i	0.280607	+	0.203873i	0.719182	−	0.694822i	$-0.244517\pi$
$31$	1.56235	+	1.13511i	0.280607	+	0.203873i	−0.438575	+	0.898694i	$0.644517\pi$
$32$		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	0.368045	−	0.929808i	$-0.380027\pi$
$37$	0.725506	+	0.235731i	0.119272	+	0.0387539i	−0.248773	+	0.968562i	$0.580027\pi$
$38$		0			0
$39$	0.0103312	+	0.0317961i	0.00165431	+	0.00509146i
$40$		0			0
$41$	−3.00636	+	9.25262i	−0.469514	+	1.44502i	0.383701	+	0.923457i	$0.374649\pi$
$41$	−3.00636	+	9.25262i	−0.469514	+	1.44502i	−0.853215	+	0.521559i	$0.825351\pi$
$42$		0			0
$43$			9.68774i			1.47737i	0.674053	+	0.738683i	$0.264552\pi$
$43$			9.68774i			1.47737i	−0.674053	+	0.738683i	$0.735448\pi$
$44$		0			0
$45$	−6.56004	−	1.36363i	−0.977913	−	0.203278i
$46$		0			0
$47$	−6.11994	−	8.42338i	−0.892685	−	1.22868i	−0.972743	−	0.231886i	$-0.925510\pi$
$47$	−6.11994	−	8.42338i	−0.892685	−	1.22868i	0.0800577	−	0.996790i	$-0.474490\pi$
$48$		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	0.851569	−	0.524243i	$-0.175652\pi$
$53$	0.654009	+	0.900166i	0.0898351	+	0.123647i	−0.761734	+	0.647890i	$0.775652\pi$
$54$		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	0.796229	+	0.604995i	$0.206825\pi$
$59$	−1.56343	+	4.81174i	−0.203541	+	0.626435i	−0.999770	+	0.0214397i	$0.993175\pi$
$60$		0			0
$61$	4.18521	+	12.8808i	0.535862	+	1.64921i	0.741780	+	0.670643i	$0.233982\pi$
$61$	4.18521	+	12.8808i	0.535862	+	1.64921i	−0.205918	+	0.978569i	$0.566018\pi$
$62$		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	−0.761834	−	0.647772i	$-0.775701\pi$
$67$	0.733847	−	1.01005i	0.0896537	−	0.123398i	0.851488	+	0.524375i	$0.175701\pi$
$68$		0			0
$69$	−0.352358	−	0.256003i	−0.0424189	−	0.0308191i
$70$		0			0
$71$	10.8951	−	7.91578i	1.29302	−	0.939430i	0.293154	−	0.956065i	$-0.405295\pi$
$71$	10.8951	−	7.91578i	1.29302	−	0.939430i	0.999862	+	0.0166349i	$0.00529530\pi$
$72$		0			0
$73$	−3.88964	+	1.26382i	−0.455248	+	0.147919i	−0.527660	−	0.849456i	$-0.676930\pi$
$73$	−3.88964	+	1.26382i	−0.455248	+	0.147919i	0.0724119	+	0.997375i	$0.476930\pi$
$74$		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	−0.251555	−	0.967843i	$-0.580942\pi$
$79$	5.25455	−	3.81765i	0.591183	−	0.429520i	0.842738	+	0.538323i	$0.180942\pi$
$80$		0			0
$81$	−7.25533	−	5.27131i	−0.806148	−	0.585701i
$82$		0			0
$83$	0.536761	−	0.738788i	0.0589172	−	0.0810925i	−0.778542	−	0.627593i	$-0.784040\pi$
$83$	0.536761	−	0.738788i	0.0589172	−	0.0810925i	0.837459	+	0.546500i	$0.184040\pi$
$84$		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	0.827964	−	0.560781i	$-0.189499\pi$
$89$	−1.61785	−	4.97923i	−0.171492	−	0.527797i	−0.999456	+	0.0329839i	$0.989499\pi$
$90$		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	0.979803	+	0.199965i	$0.0640828\pi$
$97$	8.54098	+	11.7557i	0.867205	+	1.19361i	−0.112598	+	0.993641i	$0.535917\pi$
$98$		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	0.398017	−	0.917378i	$-0.369699\pi$
$103$	−6.06351	−	8.34571i	−0.597456	−	0.822327i	−0.995472	+	0.0950510i	$0.969699\pi$
$104$		0			0
$105$	−0.153751	−	0.169224i	−0.0150046	−	0.0165146i
$106$		0			0
$107$		−	15.1159i		−	1.46131i	−0.682746	−	0.730656i	$-0.739214\pi$
$107$		−	15.1159i		−	1.46131i	0.682746	−	0.730656i	$-0.260786\pi$
$108$		0			0
$109$	1.40146	−	4.31325i	0.134235	−	0.413134i	−0.861235	−	0.508207i	$-0.830308\pi$
$109$	1.40146	−	4.31325i	0.134235	−	0.413134i	0.995470	+	0.0950729i	$0.0303084\pi$
$110$		0			0
$111$	0.0140403	+	0.0432116i	0.00133265	+	0.00410146i
$112$		0			0
$113$	14.8637	+	4.82952i	1.39826	+	0.454323i	0.908628	−	0.417606i	$-0.137131\pi$
$113$	14.8637	+	4.82952i	1.39826	+	0.454323i	0.489633	+	0.871929i	$0.337131\pi$
$114$		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	−0.365091	−	0.930972i	$-0.618962\pi$
$127$	−1.27621	+	0.414665i	−0.113245	+	0.0367956i	0.251846	+	0.967767i	$0.418962\pi$
$128$		0			0
$129$	−0.466810	+	0.339157i	−0.0411003	+	0.0298611i
$130$		0			0
$131$	−11.2000	−	8.13727i	−0.978548	−	0.710957i	−0.0211645	−	0.999776i	$-0.506737\pi$
$131$	−11.2000	−	8.13727i	−0.978548	−	0.710957i	−0.957384	+	0.288819i	$0.906737\pi$
$132$		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	−0.0543972	−	0.998519i	$-0.517324\pi$
$137$	−8.02147	−	2.60633i	−0.685320	−	0.222674i	−0.630923	+	0.775845i	$0.717324\pi$
$138$		0			0
$139$	4.91470	+	15.1259i	0.416860	+	1.28296i	0.910577	+	0.413340i	$0.135638\pi$
$139$	4.91470	+	15.1259i	0.416860	+	1.28296i	−0.493717	+	0.869622i	$0.664362\pi$
$140$		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	$0.178351\pi$
$157$			13.3180i			1.06289i	−0.847092	+	0.531446i	$0.821649\pi$
$158$		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	0.785104	−	0.619364i	$-0.212610\pi$
$163$	13.4848	+	4.38148i	1.05621	+	0.343184i	0.271109	+	0.962549i	$0.412610\pi$
$164$		0			0
$165$	0.214554	+	0.122592i	0.0167030	+	0.00954379i
$166$		0			0
$167$	−13.3299	+	18.3470i	−1.03150	+	1.41973i	−0.127677	+	0.991816i	$0.540752\pi$
$167$	−13.3299	+	18.3470i	−1.03150	+	1.41973i	−0.903818	+	0.427916i	$0.859248\pi$
$168$		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	−0.0538045	−	0.998551i	$-0.517135\pi$
$173$	6.43969	−	2.09238i	0.489601	−	0.159081i	0.543405	+	0.839471i	$0.317135\pi$
$174$		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	−0.554621	+	0.832103i	$0.687137\pi$
$179$	−20.3012	+	14.7497i	−1.51739	+	1.10245i	−0.962764	+	0.270342i	$0.912863\pi$
$180$		0			0
$181$	−20.3908	−	14.8148i	−1.51564	−	1.10117i	−0.963598	−	0.267356i	$-0.913850\pi$
$181$	−20.3908	−	14.8148i	−1.51564	−	1.10117i	−0.552039	−	0.833818i	$-0.686150\pi$
$182$		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	0.437552	+	0.899193i	$0.355845\pi$
$191$	−6.14957	+	18.9264i	−0.444967	+	1.36947i	−0.882520	+	0.470275i	$0.844155\pi$
$192$		0			0
$193$			4.79198i			0.344934i	0.985015	+	0.172467i	$0.0551738\pi$
$193$			4.79198i			0.344934i	−0.985015	+	0.172467i	$0.944826\pi$
$194$		0			0
$195$	0.0681569	−	0.0307127i	0.00488082	−	0.00219938i
$196$		0			0
$197$	0.393872	+	0.542119i	0.0280622	+	0.0386244i	0.822818	−	0.568306i	$-0.192401\pi$
$197$	0.393872	+	0.542119i	0.0280622	+	0.0386244i	−0.794755	+	0.606930i	$0.792401\pi$
$198$		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	−0.992424	−	0.122861i	$-0.960793\pi$
$211$	−3.80217	−	11.7019i	−0.261752	−	0.805589i	0.730672	−	0.682729i	$-0.239207\pi$
$212$		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	−0.722210	−	0.691674i	$-0.756873\pi$
$223$	−13.4389	+	4.36656i	−0.899934	+	0.292406i	−0.177724	+	0.984080i	$0.556873\pi$
$224$		0			0
$225$	−1.43225	+	14.9136i	−0.0954834	+	0.994243i
$226$		0			0
$227$	−3.72885	+	1.21158i	−0.247492	+	0.0804151i	−0.430136	−	0.902764i	$-0.641534\pi$
$227$	−3.72885	+	1.21158i	−0.247492	+	0.0804151i	0.182644	+	0.983179i	$0.441534\pi$
$228$		0			0
$229$	2.16082	−	1.56993i	0.142791	−	0.103744i	−0.514096	−	0.857732i	$-0.671873\pi$
$229$	2.16082	−	1.56993i	0.142791	−	0.103744i	0.656887	+	0.753989i	$0.271873\pi$
$230$		0			0
$231$	0.153485	+	0.111514i	0.0100986	+	0.00733705i
$232$		0			0
$233$	13.1641	−	18.1188i	0.862409	−	1.18700i	−0.118581	−	0.992944i	$-0.537835\pi$
$233$	13.1641	−	18.1188i	0.862409	−	1.18700i	0.980990	−	0.194059i	$-0.0621654\pi$
$234$		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	−0.894915	−	0.446237i	$-0.852764\pi$
$239$	−6.69719	−	20.6118i	−0.433205	−	1.33327i	0.461710	−	0.887031i	$-0.347236\pi$
$240$		0			0
$241$	5.45316	−	16.7831i	0.351269	−	1.08109i	−0.606872	−	0.794799i	$-0.707576\pi$
$241$	5.45316	−	16.7831i	0.351269	−	1.08109i	0.958141	−	0.286296i	$-0.0924239\pi$
$242$		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	$0.0918874\pi$
$257$			9.12754i			0.569361i	−0.958623	+	0.284680i	$0.908113\pi$
$258$		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	0.812356	−	0.583161i	$-0.198184\pi$
$263$	18.2735	+	5.93742i	1.12679	+	0.366117i	0.314436	+	0.949279i	$0.398184\pi$
$264$		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	0.712811	−	0.701356i	$-0.247422\pi$
$269$	4.36357	+	3.17032i	0.266052	+	0.193298i	−0.446759	+	0.894654i	$0.647422\pi$
$270$		0			0
$271$	17.3290	−	12.5902i	1.05266	−	0.764803i	0.0799442	−	0.996799i	$-0.474526\pi$
$271$	17.3290	−	12.5902i	1.05266	−	0.764803i	0.972717	+	0.231996i	$0.0745258\pi$
$272$		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	−0.690545	−	0.723290i	$-0.742629\pi$
$277$	−13.7152	+	4.45635i	−0.824068	+	0.267756i	−0.133524	+	0.991046i	$0.542629\pi$
$278$		0			0
$279$	4.68151	−	3.40132i	0.280275	−	0.203632i
$280$		0			0
$281$	−10.6166	−	7.71340i	−0.633332	−	0.460143i	0.224221	−	0.974538i	$-0.428016\pi$
$281$	−10.6166	−	7.71340i	−0.633332	−	0.460143i	−0.857553	+	0.514395i	$0.828016\pi$
$282$		0			0
$283$	15.5938	−	21.4630i	0.926953	−	1.27584i	−0.0340827	−	0.999419i	$-0.510851\pi$
$283$	15.5938	−	21.4630i	0.926953	−	1.27584i	0.961036	−	0.276423i	$-0.0891490\pi$
$284$		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	$0.249676\pi$
$293$			24.1828i			1.41277i	−0.707827	+	0.706386i	$0.750324\pi$
$294$		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	$-0.816328\pi$
$307$		−	19.1169i		−	1.09106i	0.838091	−	0.545530i	$-0.183672\pi$
$308$		0			0
$309$	0.189866	−	0.584348i	0.0108011	−	0.0332424i
$310$		0			0
$311$	7.01668	+	21.5951i	0.397879	+	1.22455i	0.926696	+	0.375811i	$0.122636\pi$
$311$	7.01668	+	21.5951i	0.397879	+	1.22455i	−0.528817	+	0.848736i	$0.677364\pi$
$312$		0			0
$313$	−12.7661	−	4.14797i	−0.721585	−	0.234457i	−0.0748747	−	0.997193i	$-0.523856\pi$
$313$	−12.7661	−	4.14797i	−0.721585	−	0.234457i	−0.646710	+	0.762736i	$0.723856\pi$
$314$		0			0
$315$	−2.34102	+	11.2620i	−0.131902	+	0.634540i
$316$		0			0
$317$	15.9915	−	22.0105i	0.898174	−	1.23623i	−0.0728730	−	0.997341i	$-0.523217\pi$
$317$	15.9915	−	22.0105i	0.898174	−	1.23623i	0.971047	−	0.238889i	$-0.0767832\pi$
$318$		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	−0.283615	−	0.958938i	$-0.591534\pi$
$331$	−23.3469	−	16.9625i	−1.28326	−	0.932344i	−0.999646	+	0.0265941i	$0.991534\pi$
$332$		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	−0.289966	−	0.957037i	$-0.593644\pi$
$337$	−19.9562	−	6.48418i	−1.08709	−	0.353216i	−0.797120	+	0.603821i	$0.793644\pi$
$338$		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	0.434756	−	0.900548i	$-0.356835\pi$
$347$	−10.3583	−	14.2570i	−0.556063	−	0.765355i	−0.990819	+	0.135193i	$0.956835\pi$
$348$		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	0.962682	−	0.270635i	$-0.0872336\pi$
$353$	7.66202	+	10.5459i	0.407808	+	0.561299i	−0.554874	+	0.831934i	$0.687234\pi$
$354$		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	−0.753781	−	0.657126i	$-0.771772\pi$
$359$	4.59073	−	14.1288i	0.242289	−	0.745690i	0.996070	−	0.0885643i	$-0.0282279\pi$
$360$		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	0.179202	+	0.983812i	$0.442649\pi$
$367$	−15.5525	+	21.4062i	−0.811836	+	1.11740i	−0.991038	+	0.133584i	$0.957351\pi$
$368$		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	−0.978136	−	0.207968i	$-0.933315\pi$
$373$	−31.8132	+	10.3367i	−1.64722	+	0.535215i	−0.669088	+	0.743183i	$0.733315\pi$
$374$		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	0.0435574	−	0.999051i	$-0.486131\pi$
$379$	19.6075	−	14.2457i	1.00717	−	0.731753i	0.963614	+	0.267298i	$0.0861309\pi$
$380$		0			0
$381$	−0.0646596	−	0.0469779i	−0.00331261	−	0.00240675i
$382$		0			0
$383$	−1.50232	+	2.06777i	−0.0767650	+	0.105658i	−0.845673	−	0.533702i	$-0.820800\pi$
$383$	−1.50232	+	2.06777i	−0.0767650	+	0.105658i	0.768908	+	0.639360i	$0.220800\pi$
$384$		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	0.999907	+	0.0136371i	$0.00434096\pi$
$389$	3.92452	+	12.0784i	0.198981	+	0.612400i	−0.800926	+	0.598763i	$0.795659\pi$
$390$		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	0.994855	−	0.101314i	$-0.0323046\pi$
$397$	11.7770	+	16.2097i	0.591072	+	0.813541i	−0.403782	+	0.914855i	$0.632305\pi$
$398$		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	−0.948029	−	0.318185i	$-0.896927\pi$
$409$	0.120676	−	0.371402i	0.00596704	−	0.0183647i	0.953996	+	0.299820i	$0.0969267\pi$
$410$		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	0.191625	−	0.981468i	$-0.438624\pi$
$419$	−13.9723	−	10.1515i	−0.682591	−	0.495931i	−0.874216	+	0.485537i	$0.838624\pi$
$420$		0			0
$421$	14.0506	−	10.2083i	0.684784	−	0.497524i	−0.190158	−	0.981754i	$-0.560900\pi$
$421$	14.0506	−	10.2083i	0.684784	−	0.497524i	0.874941	+	0.484229i	$0.160900\pi$
$422$		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	0.999125	+	0.0418269i	$0.0133178\pi$
$431$	27.9780	+	20.3272i	1.34765	+	0.979126i	0.348526	+	0.937299i	$0.386682\pi$
$432$		0			0
$433$	−22.3305	+	30.7353i	−1.07314	+	1.47704i	−0.206275	+	0.978494i	$0.566134\pi$
$433$	−22.3305	+	30.7353i	−1.07314	+	1.47704i	−0.866861	+	0.498550i	$0.833866\pi$
$434$		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	0.910254	−	0.414050i	$-0.135886\pi$
$439$	−1.45680	−	4.48356i	−0.0695291	−	0.213989i	−0.979783	+	0.200061i	$0.935886\pi$
$440$		0			0
$441$	3.75268	−	11.5495i	0.178699	−	0.549979i
$442$		0			0
$443$			30.4179i			1.44520i	0.691267	+	0.722600i	$0.257053\pi$
$443$			30.4179i			1.44520i	−0.691267	+	0.722600i	$0.742947\pi$
$444$		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	$-0.888706\pi$
$457$		−	14.6462i		−	0.685122i	0.939496	−	0.342561i	$-0.111294\pi$
$458$		0			0
$459$	0.431022	−	1.32655i	0.0201184	−	0.0619180i
$460$		0			0
$461$	6.89410	+	21.2179i	0.321090	+	0.988215i	0.973175	+	0.230068i	$0.0738949\pi$
$461$	6.89410	+	21.2179i	0.321090	+	0.988215i	−0.652084	+	0.758147i	$0.726105\pi$
$462$		0			0
$463$	−15.2144	−	4.94346i	−0.707073	−	0.229742i	−0.0666636	−	0.997776i	$-0.521235\pi$
$463$	−15.2144	−	4.94346i	−0.707073	−	0.229742i	−0.640410	+	0.768033i	$0.721235\pi$
$464$		0			0
$465$	0.255665	−	0.0280322i	0.0118562	−	0.00129996i
$466$		0			0
$467$	5.04792	−	6.94787i	0.233590	−	0.321509i	−0.676090	−	0.736819i	$-0.736327\pi$
$467$	5.04792	−	6.94787i	0.233590	−	0.321509i	0.909680	+	0.415310i	$0.136327\pi$
$468$		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	−0.501309	−	0.865268i	$-0.667148\pi$
$479$	3.64835	−	2.65068i	0.166697	−	0.121113i	0.668006	+	0.744156i	$0.267148\pi$
$480$		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	0.456730	−	0.889605i	$-0.349020\pi$
$487$	6.69405	+	2.17503i	0.303336	+	0.0985599i	−0.153394	+	0.988165i	$0.549020\pi$
$488$		0			0
$489$	0.260964	+	0.803165i	0.0118012	+	0.0363204i
$490$		0			0
$491$	−7.80243	+	24.0134i	−0.352119	+	1.08371i	0.605543	+	0.795813i	$0.292956\pi$
$491$	−7.80243	+	24.0134i	−0.352119	+	1.08371i	−0.957661	+	0.287897i	$0.907044\pi$
$492$		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	0.908769	−	0.417300i	$-0.137024\pi$
$503$	5.18231	+	7.13284i	0.231068	+	0.318038i	−0.677701	+	0.735338i	$0.737024\pi$
$504$		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	0.723996	+	0.689804i	$0.242303\pi$
$509$	−6.02799	+	18.5522i	−0.267186	+	0.822314i	−0.991182	+	0.132509i	$0.957697\pi$
$510$		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	−0.797025	−	0.603946i	$-0.793594\pi$
$521$	−10.7036	+	7.77662i	−0.468933	+	0.340700i	0.328092	+	0.944646i	$0.393594\pi$
$522$		0			0
$523$	40.6072	−	13.1941i	1.77563	−	0.576937i	0.777012	−	0.629486i	$-0.216734\pi$
$523$	40.6072	−	13.1941i	1.77563	−	0.576937i	0.998618	+	0.0525482i	$0.0167343\pi$
$524$		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	−0.879776	−	0.475388i	$-0.842308\pi$
$541$	2.59118	−	7.97483i	0.111404	−	0.342865i	0.991180	+	0.132523i	$0.0423078\pi$
$542$		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	0.587918	−	0.808920i	$-0.299948\pi$
$547$	−8.49189	−	11.6881i	−0.363087	−	0.499747i	−0.951006	+	0.309174i	$0.899948\pi$
$548$		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	$-0.881037\pi$
$557$		−	17.2330i		−	0.730187i	0.930971	−	0.365093i	$-0.118963\pi$
$558$		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	0.162602	−	0.986692i	$-0.448011\pi$
$563$	−6.78168	−	2.20350i	−0.285814	−	0.0928665i	−0.448415	+	0.893825i	$0.648011\pi$
$564$		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	0.317678	−	0.948199i	$-0.397097\pi$
$569$	−11.5916	−	8.42179i	−0.485945	−	0.353060i	−0.803623	+	0.595139i	$0.797097\pi$
$570$		0			0
$571$	−8.30283	+	6.03236i	−0.347462	+	0.252446i	−0.747804	−	0.663920i	$-0.768892\pi$
$571$	−8.30283	+	6.03236i	−0.347462	+	0.252446i	0.400341	+	0.916366i	$0.368892\pi$
$572$		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	−0.112821	−	0.993615i	$-0.535989\pi$
$577$	9.12639	−	2.96534i	0.379937	−	0.123449i	0.492758	+	0.870166i	$0.335989\pi$
$578$		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	0.411003	−	0.911634i	$-0.365179\pi$
$587$	5.03134	+	1.63478i	0.207666	+	0.0674747i	−0.203337	+	0.979109i	$0.565179\pi$
$588$		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	$0.0144785\pi$
$593$			2.21453i			0.0909397i	−0.998966	+	0.0454699i	$0.985522\pi$
$594$		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	$-0.798608\pi$
$607$		−	29.1371i		−	1.18264i	0.806438	−	0.591319i	$-0.201392\pi$
$608$		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	0.235074	−	0.971978i	$-0.424467\pi$
$613$	−3.61632	−	1.17501i	−0.146062	−	0.0474584i	−0.381136	+	0.924519i	$0.624467\pi$
$614$		0			0
$615$	0.532315	+	1.18130i	0.0214650	+	0.0476346i
$616$		0			0
$617$	28.9502	−	39.8466i	1.16549	−	1.60416i	0.477035	−	0.878884i	$-0.341711\pi$
$617$	28.9502	−	39.8466i	1.16549	−	1.60416i	0.688456	−	0.725278i	$-0.258289\pi$
$618$		0			0
$619$	5.13396	+	3.73004i	0.206351	+	0.149923i	0.686161	−	0.727449i	$-0.259294\pi$
$619$	5.13396	+	3.73004i	0.206351	+	0.149923i	−0.479810	+	0.877372i	$0.659294\pi$
$620$		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	0.673395	−	0.739283i	$-0.264835\pi$
$631$	4.48099	+	3.25563i	0.178385	+	0.129604i	−0.495010	+	0.868888i	$0.664835\pi$
$632$		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	−0.869044	−	0.494735i	$-0.835265\pi$
$641$	3.16032	−	9.72646i	0.124825	−	0.384172i	0.993869	+	0.110563i	$0.0352653\pi$
$642$		0			0
$643$			20.5779i			0.811515i	0.913981	+	0.405757i	$0.132992\pi$
$643$			20.5779i			0.811515i	−0.913981	+	0.405757i	$0.867008\pi$
$644$		0			0
$645$	0.867628	+	0.954943i	0.0341628	+	0.0376009i
$646$		0			0
$647$	4.06226	+	5.59123i	0.159704	+	0.219814i	0.881369	−	0.472429i	$-0.156623\pi$
$647$	4.06226	+	5.59123i	0.159704	+	0.219814i	−0.721665	+	0.692243i	$0.756623\pi$
$648$		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	0.827664	−	0.561224i	$-0.189669\pi$
$653$	0.974775	+	1.34166i	0.0381459	+	0.0525033i	−0.789518	+	0.613727i	$0.789669\pi$
$654$		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	−0.930685	−	0.365820i	$-0.880788\pi$
$659$	0.956983	−	2.94529i	0.0372788	−	0.114732i	0.967964	+	0.251088i	$0.0807884\pi$
$660$		0			0
$661$	−4.38102	−	13.4834i	−0.170402	−	0.524443i	0.828992	−	0.559261i	$-0.188915\pi$
$661$	−4.38102	−	13.4834i	−0.170402	−	0.524443i	−0.999394	+	0.0348175i	$0.988915\pi$
$662$		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	−0.213566	−	0.976929i	$-0.568508\pi$
$673$	4.87403	−	1.58367i	0.187880	−	0.0610460i	0.401446	+	0.915883i	$0.368508\pi$
$674$		0			0
$675$	−1.53844	+	0.906729i	−0.0592146	+	0.0349000i
$676$		0			0
$677$	−25.7566	+	8.36884i	−0.989908	+	0.321641i	−0.758826	−	0.651294i	$-0.774227\pi$
$677$	−25.7566	+	8.36884i	−0.989908	+	0.321641i	−0.231082	+	0.972934i	$0.574227\pi$
$678$		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	−0.941671	−	0.336534i	$-0.890745\pi$
$683$	−8.64040	+	11.8925i	−0.330616	+	0.455053i	0.611056	+	0.791588i	$0.290745\pi$
$684$		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	−0.836879	−	0.547388i	$-0.815622\pi$
$691$	4.25630	−	13.0995i	0.161917	−	0.498330i	0.998796	+	0.0490586i	$0.0156221\pi$
$692$		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	−0.532577	−	0.846381i	$-0.678776\pi$
$709$	10.5384	−	32.4338i	0.395777	−	1.21808i	0.928355	−	0.371696i	$-0.121224\pi$
$710$		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	0.881481	−	0.472220i	$-0.156547\pi$
$719$	18.8977	+	13.7300i	0.704766	+	0.512043i	−0.176715	+	0.984262i	$0.556547\pi$
$720$		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	−0.526121	−	0.850409i	$-0.676354\pi$
$727$	−12.1847	+	3.95904i	−0.451904	+	0.146833i	0.0742170	+	0.997242i	$0.476354\pi$
$728$		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	−0.993925	−	0.110057i	$-0.964897\pi$
$733$	−15.7602	+	21.6920i	−0.582115	+	0.801213i	0.411810	+	0.911270i	$0.364897\pi$
$734$		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	0.625780	+	0.780000i	$0.284781\pi$
$739$	15.7123	+	48.3574i	0.577986	+	1.77886i	−0.0477941	+	0.998857i	$0.515219\pi$
$740$		0			0
$741$	−0.0599233	+	0.184425i	−0.00220134	+	0.00677502i
$742$		0			0
$743$		−	25.4540i		−	0.933816i	−0.884306	−	0.466908i	$-0.845368\pi$
$743$		−	25.4540i		−	0.933816i	0.884306	−	0.466908i	$-0.154632\pi$
$744$		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	$0.218179\pi$
$757$			34.8326i			1.26601i	−0.774147	+	0.633006i	$0.781821\pi$
$758$		0			0
$759$	0.249718	−	0.768554i	0.00906420	−	0.0278967i
$760$		0			0
$761$	−2.49606	−	7.68209i	−0.0904822	−	0.278476i	0.895568	−	0.444925i	$-0.146770\pi$
$761$	−2.49606	−	7.68209i	−0.0904822	−	0.278476i	−0.986050	+	0.166450i	$0.946770\pi$
$762$		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	0.387449	−	0.921891i	$-0.373356\pi$
$769$	−10.2491	−	7.44644i	−0.369593	−	0.268525i	−0.757042	+	0.653366i	$0.773356\pi$
$770$		0			0
$771$	−0.439816	+	0.319545i	−0.0158396	+	0.0115081i
$772$		0			0
$773$	38.9161	−	12.6446i	1.39971	−	0.454795i	0.490615	−	0.871376i	$-0.336772\pi$
$773$	38.9161	−	12.6446i	1.39971	−	0.454795i	0.909098	+	0.416582i	$0.136772\pi$
$774$		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	0.264735	−	0.964321i	$-0.414715\pi$
$787$	−2.46599	−	0.801249i	−0.0879031	−	0.0285615i	−0.352638	+	0.935760i	$0.614715\pi$
$788$		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	0.523934	−	0.851759i	$-0.324464\pi$
$797$	−12.6487	−	17.4095i	−0.448041	−	0.616676i	−0.971975	+	0.235083i	$0.924464\pi$
$798$		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	−0.930427	−	0.366478i	$-0.880564\pi$
$809$	1.07271	−	3.30147i	0.0377146	−	0.116074i	0.968141	+	0.250404i	$0.0805636\pi$
$810$		0			0
$811$	−11.3665	−	34.9826i	−0.399133	−	1.22841i	−0.925696	−	0.378269i	$-0.876519\pi$
$811$	−11.3665	−	34.9826i	−0.399133	−	1.22841i	0.526563	−	0.850136i	$-0.323481\pi$
$812$		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	−0.335735	+	0.941957i	$0.608985\pi$
$821$	−38.2615	+	27.7986i	−1.33534	+	0.970179i	−0.999602	+	0.0282220i	$0.991015\pi$
$822$		0			0
$823$	−9.96867	+	3.23902i	−0.347486	+	0.112905i	−0.477560	−	0.878599i	$-0.658479\pi$
$823$	−9.96867	+	3.23902i	−0.347486	+	0.112905i	0.130074	+	0.991504i	$0.458479\pi$
$824$		0			0
$825$	0.220202	−	0.506777i	0.00766645	−	0.0176437i
$826$		0			0
$827$	5.48824	−	1.78324i	0.190845	−	0.0620093i	−0.212035	−	0.977262i	$-0.568009\pi$
$827$	5.48824	−	1.78324i	0.190845	−	0.0620093i	0.402880	+	0.915253i	$0.368009\pi$
$828$		0			0
$829$	−23.6650	+	17.1936i	−0.821919	+	0.597159i	−0.917261	−	0.398286i	$-0.869605\pi$
$829$	−23.6650	+	17.1936i	−0.821919	+	0.597159i	0.0953427	+	0.995445i	$0.469605\pi$
$830$		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	0.828193	−	0.560444i	$-0.189369\pi$
$839$	−4.96033	−	15.2663i	−0.171250	−	0.527052i	−0.999442	+	0.0333911i	$0.989369\pi$
$840$		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	0.999904	−	0.0138826i	$-0.00441911\pi$
$853$	19.7934	+	27.2433i	0.677713	+	0.932792i	−0.322190	+	0.946675i	$0.604419\pi$
$854$		0			0
$855$	−26.1339	−	28.7639i	−0.893760	−	0.983705i
$856$		0			0
$857$			18.5384i			0.633260i	0.948549	+	0.316630i	$0.102551\pi$
$857$			18.5384i			0.633260i	−0.948549	+	0.316630i	$0.897449\pi$
$858$		0			0
$859$	0.00514740	−	0.0158421i	0.000175627	−	0.000540524i	−0.950969	−	0.309287i	$-0.899910\pi$
$859$	0.00514740	−	0.0158421i	0.000175627	−	0.000540524i	0.951144	+	0.308747i	$0.0999095\pi$
$860$		0			0
$861$	0.307403	+	0.946089i	0.0104763	+	0.0322426i
$862$		0			0
$863$	31.6593	+	10.2867i	1.07769	+	0.350164i	0.793480	−	0.608597i	$-0.208267\pi$
$863$	31.6593	+	10.2867i	1.07769	+	0.350164i	0.284214	+	0.958761i	$0.408267\pi$
$864$		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	0.430319	−	0.902677i	$-0.358401\pi$
$877$	38.7660	−	12.5958i	1.30903	−	0.425331i	0.878715	+	0.477346i	$0.158401\pi$
$878$		0			0
$879$	−1.16526	+	0.846612i	−0.0393033	+	0.0285555i
$880$		0			0
$881$	−20.0854	−	14.5929i	−0.676694	−	0.491647i	0.195565	−	0.980691i	$-0.437346\pi$
$881$	−20.0854	−	14.5929i	−0.676694	−	0.491647i	−0.872259	+	0.489044i	$0.837346\pi$
$882$		0			0
$883$	0.996201	−	1.37115i	0.0335248	−	0.0461430i	−0.791926	−	0.610618i	$-0.790921\pi$
$883$	0.996201	−	1.37115i	0.0335248	−	0.0461430i	0.825450	+	0.564475i	$0.190921\pi$
$884$		0			0
$885$	0.276825	+	0.614324i	0.00930538	+	0.0206503i
$886$		0			0
$887$	11.5402	+	3.74964i	0.387482	+	0.125901i	0.496278	−	0.868164i	$-0.334700\pi$
$887$	11.5402	+	3.74964i	0.387482	+	0.125901i	−0.108796	+	0.994064i	$0.534700\pi$
$888$		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	$0.0796898\pi$
$907$			14.9224i			0.495491i	−0.968825	+	0.247746i	$0.920310\pi$
$908$		0			0
$909$	−1.71291	+	5.27180i	−0.0568137	+	0.174855i
$910$		0			0
$911$	−14.2166	−	43.7543i	−0.471018	−	1.44964i	−0.851254	−	0.524754i	$-0.824157\pi$
$911$	−14.2166	−	43.7543i	−0.471018	−	1.44964i	0.380236	−	0.924890i	$-0.375843\pi$
$912$		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	0.508000	−	0.861357i	$-0.330385\pi$
$919$	−4.67512	−	3.39667i	−0.154218	−	0.112046i	−0.662218	+	0.749311i	$0.730385\pi$
$920$		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	−0.389155	−	0.921172i	$-0.627233\pi$
$929$	11.1761	−	8.11994i	0.366677	−	0.266406i	0.755832	+	0.654766i	$0.227233\pi$
$930$		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	0.271259	−	0.962506i	$-0.412560\pi$
$937$	−2.29684	−	0.746290i	−0.0750346	−	0.0243802i	−0.346294	+	0.938126i	$0.612560\pi$
$938$		0			0
$939$	−0.247056	−	0.760360i	−0.00806237	−	0.0248134i
$940$		0			0
$941$	9.18367	−	28.2644i	0.299379	−	0.921394i	−0.682336	−	0.731039i	$-0.739036\pi$
$941$	9.18367	−	28.2644i	0.299379	−	0.921394i	0.981715	−	0.190356i	$-0.0609641\pi$
$942$		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	0.712730	−	0.701438i	$-0.247458\pi$
$947$	−5.37375	−	7.39633i	−0.174623	−	0.240348i	−0.887353	+	0.461090i	$0.847458\pi$
$948$		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	0.991078	−	0.133283i	$-0.0425518\pi$
$953$	17.2277	+	23.7118i	0.558059	+	0.768102i	−0.433019	+	0.901385i	$0.642552\pi$
$954$		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	−0.345044	−	0.938587i	$-0.612136\pi$
$967$	20.3443	−	28.0016i	0.654230	−	0.900470i	0.999273	+	0.0381168i	$0.0121359\pi$
$968$		0			0
$969$	1.09151	+	0.793025i	0.0350642	+	0.0254756i
$970$		0			0
$971$	24.0628	−	17.4826i	0.772211	−	0.561044i	−0.130420	−	0.991459i	$-0.541633\pi$
$971$	24.0628	−	17.4826i	0.772211	−	0.561044i	0.902631	+	0.430415i	$0.141633\pi$
$972$		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	−0.869812	−	0.493384i	$-0.835760\pi$
$977$	−40.1184	+	13.0352i	−1.28350	+	0.417035i	−0.413689	+	0.910418i	$0.635760\pi$
$978$		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	−0.969424	−	0.245394i	$-0.921083\pi$
$983$	−13.6846	+	18.8353i	−0.436472	+	0.600752i	0.532952	+	0.846146i	$0.321083\pi$
$984$		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	−0.259802	−	0.965662i	$-0.583657\pi$
$991$	16.3062	−	50.1854i	0.517984	−	1.59419i	0.777786	−	0.628529i	$-0.216343\pi$
$992$		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	0.835052	+	0.550171i	$0.185438\pi$
$997$	34.7408	+	47.8165i	1.10025	+	1.51437i	0.265199	+	0.964194i	$0.414562\pi$
$998$		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.169.5	yes	32
4.3	odd	2		400.2.y.d.369.4		32
5.2	odd	4		1000.2.m.d.401.5		32
5.3	odd	4		1000.2.m.e.401.4		32
5.4	even	2		1000.2.q.c.849.4		32
25.2	odd	20		5000.2.a.r.1.8		16
25.3	odd	20		1000.2.m.e.601.4		32
25.4	even	10	inner	200.2.q.a.129.5	✓	32
25.21	even	5		1000.2.q.c.649.4		32
25.22	odd	20		1000.2.m.d.601.5		32
25.23	odd	20		5000.2.a.q.1.9		16
100.23	even	20		10000.2.a.br.1.8		16
100.27	even	20		10000.2.a.bq.1.9		16
100.79	odd	10		400.2.y.d.129.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.q.a.129.5	✓	32	25.4	even	10	inner
200.2.q.a.169.5	yes	32	1.1	even	1	trivial
400.2.y.d.129.4		32	100.79	odd	10
400.2.y.d.369.4		32	4.3	odd	2
1000.2.m.d.401.5		32	5.2	odd	4
1000.2.m.d.601.5		32	25.22	odd	20
1000.2.m.e.401.4		32	5.3	odd	4
1000.2.m.e.601.4		32	25.3	odd	20
1000.2.q.c.649.4		32	25.21	even	5
1000.2.q.c.849.4		32	5.4	even	2
5000.2.a.q.1.9		16	25.23	odd	20
5000.2.a.r.1.8		16	25.2	odd	20
10000.2.a.bq.1.9		16	100.27	even	20
10000.2.a.br.1.8		16	100.23	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 $\F_{q}$

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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