LMFDB - Embedded newform 200.2.q.a.89.2

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			89.2
Character	$\chi$	$=$	200.89
Dual form			200.2.q.a.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.57764 - 0.837527i) q^{3} +(1.74676 + 1.39601i) q^{5} +0.760910i q^{7} +(3.51574 + 2.55433i) q^{9} +O(q^{10})$	\(q+(-2.57764 - 0.837527i) q^{3} +(1.74676 + 1.39601i) q^{5} +0.760910i q^{7} +(3.51574 + 2.55433i) q^{9} +(5.24785 - 3.81279i) q^{11} +(3.36896 - 4.63698i) q^{13} +(-3.33333 - 5.06136i) q^{15} +(-2.59513 + 0.843208i) q^{17} +(1.72249 + 5.30128i) q^{19} +(0.637282 - 1.96135i) q^{21} +(1.70948 + 2.35290i) q^{23} +(1.10234 + 4.87697i) q^{25} +(-2.14378 - 2.95066i) q^{27} +(0.466898 - 1.43697i) q^{29} +(-0.669886 - 2.06170i) q^{31} +(-16.7204 + 5.43279i) q^{33} +(-1.06223 + 1.32913i) q^{35} +(0.877654 - 1.20799i) q^{37} +(-12.5676 + 9.13087i) q^{39} +(-3.64017 - 2.64474i) q^{41} -0.0184418i q^{43} +(2.57529 + 9.36980i) q^{45} +(-8.13150 - 2.64208i) q^{47} +6.42102 q^{49} +7.39552 q^{51} +(-5.02803 - 1.63371i) q^{53} +(14.4894 + 0.666007i) q^{55} -15.1074i q^{57} +(-6.40413 - 4.65287i) q^{59} +(-2.94396 + 2.13891i) q^{61} +(-1.94362 + 2.67516i) q^{63} +(12.3580 - 3.39659i) q^{65} +(4.63317 - 1.50541i) q^{67} +(-2.43582 - 7.49667i) q^{69} +(-2.25528 + 6.94103i) q^{71} +(6.59077 + 9.07141i) q^{73} +(1.24316 - 13.4943i) q^{75} +(2.90119 + 3.99314i) q^{77} +(-1.47673 + 4.54492i) q^{79} +(-0.974034 - 2.99777i) q^{81} +(4.47952 - 1.45549i) q^{83} +(-5.71018 - 2.14993i) q^{85} +(-2.40699 + 3.31294i) q^{87} +(-7.97974 + 5.79762i) q^{89} +(3.52832 + 2.56347i) q^{91} +5.87537i q^{93} +(-4.39184 + 11.6647i) q^{95} +(-0.725911 - 0.235863i) q^{97} +28.1892 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{5} + 10 q^{9}+O(q^{10}) $ 32 * q + 2 * q^5 + 10 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$151$	$177$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

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
$3$	−2.57764	−	0.837527i	−1.48820	−	0.483546i	−0.551651	−	0.834075i	$-0.686002\pi$
$3$	−2.57764	−	0.837527i	−1.48820	−	0.483546i	−0.936552	+	0.350529i	$0.886002\pi$
$4$		0			0
$5$	1.74676	+	1.39601i	0.781175	+	0.624313i
$5$	1.74676	+	1.39601i	0.781175	+	0.624313i
$6$		0			0
$7$			0.760910i			0.287597i	0.989607	+	0.143798i	$0.0459317\pi$
$7$			0.760910i			0.287597i	−0.989607	+	0.143798i	$0.954068\pi$
$8$		0			0
$9$	3.51574	+	2.55433i	1.17191	+	0.851444i
$10$		0			0
$11$	5.24785	−	3.81279i	1.58229	−	1.14960i	0.668273	−	0.743916i	$-0.267034\pi$
$11$	5.24785	−	3.81279i	1.58229	−	1.14960i	0.914014	−	0.405683i	$-0.132966\pi$
$12$		0			0
$13$	3.36896	−	4.63698i	0.934381	−	1.28607i	−0.0237445	−	0.999718i	$-0.507559\pi$
$13$	3.36896	−	4.63698i	0.934381	−	1.28607i	0.958126	−	0.286348i	$-0.0924412\pi$
$14$		0			0
$15$	−3.33333	−	5.06136i	−0.860662	−	1.30684i
$16$		0			0
$17$	−2.59513	+	0.843208i	−0.629411	+	0.204508i	−0.606314	−	0.795225i	$-0.707353\pi$
$17$	−2.59513	+	0.843208i	−0.629411	+	0.204508i	−0.0230966	+	0.999733i	$0.507353\pi$
$18$		0			0
$19$	1.72249	+	5.30128i	0.395166	+	1.21620i	0.928832	+	0.370501i	$0.120814\pi$
$19$	1.72249	+	5.30128i	0.395166	+	1.21620i	−0.533666	+	0.845695i	$0.679186\pi$
$20$		0			0
$21$	0.637282	−	1.96135i	0.139066	−	0.428002i
$22$		0			0
$23$	1.70948	+	2.35290i	0.356451	+	0.490613i	0.949156	−	0.314807i	$-0.101940\pi$
$23$	1.70948	+	2.35290i	0.356451	+	0.490613i	−0.592704	+	0.805420i	$0.701940\pi$
$24$		0			0
$25$	1.10234	+	4.87697i	0.220467	+	0.975394i
$26$		0			0
$27$	−2.14378	−	2.95066i	−0.412571	−	0.567855i
$28$		0			0
$29$	0.466898	−	1.43697i	0.0867009	−	0.266838i	−0.898301	−	0.439380i	$-0.855198\pi$
$29$	0.466898	−	1.43697i	0.0867009	−	0.266838i	0.985002	+	0.172542i	$0.0551981\pi$
$30$		0			0
$31$	−0.669886	−	2.06170i	−0.120315	−	0.370292i	0.872703	−	0.488251i	$-0.162365\pi$
$31$	−0.669886	−	2.06170i	−0.120315	−	0.370292i	−0.993018	+	0.117959i	$0.962365\pi$
$32$		0			0
$33$	−16.7204	+	5.43279i	−2.91065	+	0.945727i
$34$		0			0
$35$	−1.06223	+	1.32913i	−0.179550	+	0.224663i
$36$		0			0
$37$	0.877654	−	1.20799i	0.144285	−	0.198592i	−0.730758	−	0.682637i	$-0.760833\pi$
$37$	0.877654	−	1.20799i	0.144285	−	0.198592i	0.875043	+	0.484045i	$0.160833\pi$
$38$		0			0
$39$	−12.5676	+	9.13087i	−2.01242	+	1.46211i
$40$		0			0
$41$	−3.64017	−	2.64474i	−0.568500	−	0.413039i	0.266060	−	0.963956i	$-0.414278\pi$
$41$	−3.64017	−	2.64474i	−0.568500	−	0.413039i	−0.834560	+	0.550917i	$0.814278\pi$
$42$		0			0
$43$		−	0.0184418i		−	0.00281235i	−0.999999	−	0.00140617i	$-0.999552\pi$
$43$		−	0.0184418i		−	0.00281235i	0.999999	−	0.00140617i	$-0.000447599\pi$
$44$		0			0
$45$	2.57529	+	9.36980i	0.383901	+	1.39677i
$46$		0			0
$47$	−8.13150	−	2.64208i	−1.18610	−	0.385388i	−0.351471	−	0.936199i	$-0.614318\pi$
$47$	−8.13150	−	2.64208i	−1.18610	−	0.385388i	−0.834630	+	0.550811i	$0.814318\pi$
$48$		0			0
$49$	6.42102			0.917288
$50$		0			0
$51$	7.39552			1.03558
$52$		0			0
$53$	−5.02803	−	1.63371i	−0.690654	−	0.224407i	−0.0573999	−	0.998351i	$-0.518281\pi$
$53$	−5.02803	−	1.63371i	−0.690654	−	0.224407i	−0.633254	+	0.773944i	$0.718281\pi$
$54$		0			0
$55$	14.4894	+	0.666007i	1.95375	+	0.0898044i
$56$		0			0
$57$		−	15.1074i		−	2.00103i
$58$		0			0
$59$	−6.40413	−	4.65287i	−0.833746	−	0.605752i	0.0868706	−	0.996220i	$-0.472313\pi$
$59$	−6.40413	−	4.65287i	−0.833746	−	0.605752i	−0.920617	+	0.390468i	$0.872313\pi$
$60$		0			0
$61$	−2.94396	+	2.13891i	−0.376935	+	0.273860i	−0.760081	−	0.649828i	$-0.774841\pi$
$61$	−2.94396	+	2.13891i	−0.376935	+	0.273860i	0.383146	+	0.923688i	$0.374841\pi$
$62$		0			0
$63$	−1.94362	+	2.67516i	−0.244873	+	0.337038i
$64$		0			0
$65$	12.3580	−	3.39659i	1.53282	−	0.421296i
$66$		0			0
$67$	4.63317	−	1.50541i	0.566032	−	0.183915i	−0.0120015	−	0.999928i	$-0.503820\pi$
$67$	4.63317	−	1.50541i	0.566032	−	0.183915i	0.578033	+	0.816013i	$0.303820\pi$
$68$		0			0
$69$	−2.43582	−	7.49667i	−0.293238	−	0.902493i
$70$		0			0
$71$	−2.25528	+	6.94103i	−0.267652	+	0.823749i	0.723418	+	0.690410i	$0.242570\pi$
$71$	−2.25528	+	6.94103i	−0.267652	+	0.823749i	−0.991071	+	0.133339i	$0.957430\pi$
$72$		0			0
$73$	6.59077	+	9.07141i	0.771391	+	1.06173i	0.996180	+	0.0873214i	$0.0278307\pi$
$73$	6.59077	+	9.07141i	0.771391	+	1.06173i	−0.224789	+	0.974407i	$0.572169\pi$
$74$		0			0
$75$	1.24316	−	13.4943i	0.143548	−	1.55819i
$76$		0			0
$77$	2.90119	+	3.99314i	0.330621	+	0.455061i
$78$		0			0
$79$	−1.47673	+	4.54492i	−0.166146	+	0.511344i	−0.999119	−	0.0419696i	$-0.986637\pi$
$79$	−1.47673	+	4.54492i	−0.166146	+	0.511344i	0.832973	+	0.553313i	$0.186637\pi$
$80$		0			0
$81$	−0.974034	−	2.99777i	−0.108226	−	0.333085i
$82$		0			0
$83$	4.47952	−	1.45549i	0.491692	−	0.159760i	−0.0526683	−	0.998612i	$-0.516773\pi$
$83$	4.47952	−	1.45549i	0.491692	−	0.159760i	0.544360	+	0.838852i	$0.316773\pi$
$84$		0			0
$85$	−5.71018	−	2.14993i	−0.619356	−	0.233193i
$86$		0			0
$87$	−2.40699	+	3.31294i	−0.258057	+	0.355185i
$88$		0			0
$89$	−7.97974	+	5.79762i	−0.845850	+	0.614546i	−0.923999	−	0.382395i	$-0.875099\pi$
$89$	−7.97974	+	5.79762i	−0.845850	+	0.614546i	0.0781483	+	0.996942i	$0.475099\pi$
$90$		0			0
$91$	3.52832	+	2.56347i	0.369868	+	0.268725i
$92$		0			0
$93$			5.87537i			0.609247i
$94$		0			0
$95$	−4.39184	+	11.6647i	−0.450593	+	1.19677i
$96$		0			0
$97$	−0.725911	−	0.235863i	−0.0737050	−	0.0239482i	0.271932	−	0.962316i	$-0.412337\pi$
$97$	−0.725911	−	0.235863i	−0.0737050	−	0.0239482i	−0.345637	+	0.938368i	$0.612337\pi$
$98$		0			0
$99$	28.1892			2.83312
$100$		0			0
$101$	−16.8574			−1.67737			−0.838685	−	0.544617i	$-0.816675\pi$
$101$	−16.8574			−1.67737			−0.838685	+	0.544617i	$0.816675\pi$
$102$		0			0
$103$	2.86381	+	0.930507i	0.282179	+	0.0916856i	0.446687	−	0.894690i	$-0.352604\pi$
$103$	2.86381	+	0.930507i	0.282179	+	0.0916856i	−0.164508	+	0.986376i	$0.552604\pi$
$104$		0			0
$105$	3.85124	−	2.53636i	0.375842	−	0.247524i
$106$		0			0
$107$		−	11.8596i		−	1.14651i	−0.819377	−	0.573255i	$-0.805680\pi$
$107$		−	11.8596i		−	1.14651i	0.819377	−	0.573255i	$-0.194320\pi$
$108$		0			0
$109$	−11.4038	−	8.28532i	−1.09228	−	0.793590i	−0.112499	−	0.993652i	$-0.535886\pi$
$109$	−11.4038	−	8.28532i	−1.09228	−	0.793590i	−0.979783	+	0.200062i	$0.935886\pi$
$110$		0			0
$111$	−3.27400	+	2.37870i	−0.310754	+	0.225776i
$112$		0			0
$113$	3.48429	−	4.79571i	0.327774	−	0.451143i	−0.613047	−	0.790047i	$-0.710056\pi$
$113$	3.48429	−	4.79571i	0.327774	−	0.451143i	0.940821	+	0.338904i	$0.110056\pi$
$114$		0			0
$115$	−0.298607	+	6.49639i	−0.0278453	+	0.605792i
$116$		0			0
$117$	23.6888	−	7.69694i	2.19003	−	0.711583i
$118$		0			0
$119$	−0.641605	−	1.97466i	−0.0588158	−	0.181017i
$120$		0			0
$121$	9.60342	−	29.5563i	0.873038	−	2.68693i
$122$		0			0
$123$	7.16802	+	9.86594i	0.646319	+	0.889582i
$124$		0			0
$125$	−4.88276	+	10.0578i	−0.436727	+	0.899594i
$126$		0			0
$127$	5.33820	+	7.34741i	0.473689	+	0.651977i	0.977277	−	0.211967i	$-0.0679870\pi$
$127$	5.33820	+	7.34741i	0.473689	+	0.651977i	−0.503588	+	0.863944i	$0.667987\pi$
$128$		0			0
$129$	−0.0154455	+	0.0475363i	−0.00135990	+	0.00418534i
$130$		0			0
$131$	1.92225	+	5.91608i	0.167948	+	0.516891i	0.999241	−	0.0389431i	$-0.0123991\pi$
$131$	1.92225	+	5.91608i	0.167948	+	0.516891i	−0.831293	+	0.555834i	$0.812399\pi$
$132$		0			0
$133$	−4.03379	+	1.31066i	−0.349774	+	0.113649i
$134$		0			0
$135$	0.374470	−	8.14683i	0.0322292	−	0.701167i
$136$		0			0
$137$	−9.54916	+	13.1433i	−0.815840	+	1.12291i	0.174556	+	0.984647i	$0.444151\pi$
$137$	−9.54916	+	13.1433i	−0.815840	+	1.12291i	−0.990396	+	0.138260i	$0.955849\pi$
$138$		0			0
$139$	−8.19880	+	5.95678i	−0.695413	+	0.505247i	−0.878435	−	0.477862i	$-0.841412\pi$
$139$	−8.19880	+	5.95678i	−0.695413	+	0.505247i	0.183022	+	0.983109i	$0.441412\pi$
$140$		0			0
$141$	18.7473	+	13.6207i	1.57881	+	1.14707i
$142$		0			0
$143$		−	37.1793i		−	3.10909i
$144$		0			0
$145$	2.82157	−	1.85824i	0.234319	−	0.154318i
$146$		0			0
$147$	−16.5511	−	5.37777i	−1.36511	−	0.443551i
$148$		0			0
$149$	12.0280			0.985371			0.492686	−	0.870207i	$-0.336015\pi$
$149$	12.0280			0.985371			0.492686	+	0.870207i	$0.336015\pi$
$150$		0			0
$151$	12.4820			1.01577			0.507884	−	0.861425i	$-0.330428\pi$
$151$	12.4820			1.01577			0.507884	+	0.861425i	$0.330428\pi$
$152$		0			0
$153$	−11.2776	−	3.66432i	−0.911741	−	0.296243i
$154$		0			0
$155$	1.70801	−	4.53646i	0.137191	−	0.364377i
$156$		0			0
$157$			21.7736i			1.73772i	0.495056	+	0.868861i	$0.335148\pi$
$157$			21.7736i			1.73772i	−0.495056	+	0.868861i	$0.664852\pi$
$158$		0			0
$159$	11.5922	+	8.42223i	0.919321	+	0.667926i
$160$		0			0
$161$	−1.79034	+	1.30076i	−0.141099	+	0.102514i
$162$		0			0
$163$	3.80505	−	5.23721i	0.298035	−	0.410210i	−0.633568	−	0.773687i	$-0.718410\pi$
$163$	3.80505	−	5.23721i	0.298035	−	0.410210i	0.931603	+	0.363477i	$0.118410\pi$
$164$		0			0
$165$	−36.7907	−	13.8520i	−2.86415	−	1.07838i
$166$		0			0
$167$	−14.4627	+	4.69922i	−1.11916	+	0.363637i	−0.809446	−	0.587194i	$-0.800233\pi$
$167$	−14.4627	+	4.69922i	−1.11916	+	0.363637i	−0.309712	+	0.950830i	$0.600233\pi$
$168$		0			0
$169$	−6.13443	−	18.8798i	−0.471879	−	1.45229i
$170$		0			0
$171$	−7.48541	+	23.0377i	−0.572423	+	1.76174i
$172$		0			0
$173$	0.0649280	+	0.0893657i	0.00493639	+	0.00679435i	0.811478	−	0.584383i	$-0.198663\pi$
$173$	0.0649280	+	0.0893657i	0.00493639	+	0.00679435i	−0.806542	+	0.591177i	$0.798663\pi$
$174$		0			0
$175$	−3.71094	+	0.838779i	−0.280520	+	0.0634058i
$176$		0			0
$177$	12.6106	+	17.3571i	0.947874	+	1.30464i
$178$		0			0
$179$	2.59428	−	7.98437i	0.193906	−	0.596780i	−0.806082	−	0.591804i	$-0.798416\pi$
$179$	2.59428	−	7.98437i	0.193906	−	0.596780i	0.999988	−	0.00497610i	$-0.00158395\pi$
$180$		0			0
$181$	1.60141	+	4.92862i	0.119032	+	0.366341i	0.992767	−	0.120061i	$-0.0383090\pi$
$181$	1.60141	+	4.92862i	0.119032	+	0.366341i	−0.873735	+	0.486402i	$0.838309\pi$
$182$		0			0
$183$	9.37987	−	3.04771i	0.693380	−	0.225293i
$184$		0			0
$185$	3.21941	−	0.884853i	0.236696	−	0.0650557i
$186$		0			0
$187$	−10.4039	+	14.3197i	−0.760806	+	1.04716i
$188$		0			0
$189$	2.24519	−	1.63122i	0.163313	−	0.118654i
$190$		0			0
$191$	−21.5347	−	15.6459i	−1.55819	−	1.13209i	−0.937470	−	0.348065i	$-0.886839\pi$
$191$	−21.5347	−	15.6459i	−1.55819	−	1.13209i	−0.620724	−	0.784029i	$-0.713161\pi$
$192$		0			0
$193$			21.8300i			1.57136i	0.618635	+	0.785678i	$0.287686\pi$
$193$			21.8300i			1.57136i	−0.618635	+	0.785678i	$0.712314\pi$
$194$		0			0
$195$	−34.6993	−	1.59495i	−2.48487	−	0.114217i
$196$		0			0
$197$	4.31270	+	1.40128i	0.307267	+	0.0998372i	0.458592	−	0.888647i	$-0.348354\pi$
$197$	4.31270	+	1.40128i	0.307267	+	0.0998372i	−0.151325	+	0.988484i	$0.548354\pi$
$198$		0			0
$199$	−15.5338			−1.10116			−0.550582	−	0.834781i	$-0.685594\pi$
$199$	−15.5338			−1.10116			−0.550582	+	0.834781i	$0.685594\pi$
$200$		0			0
$201$	−13.2035			−0.931302
$202$		0			0
$203$	1.09340	+	0.355268i	0.0767417	+	0.0249349i
$204$		0			0
$205$	−2.66643	−	9.70143i	−0.186232	−	0.677577i
$206$		0			0
$207$			12.6388i			0.878455i
$208$		0			0
$209$	29.2520	+	21.2528i	2.02340	+	1.47009i
$210$		0			0
$211$	−8.26475	+	6.00469i	−0.568969	+	0.413380i	−0.834730	−	0.550659i	$-0.814377\pi$
$211$	−8.26475	+	6.00469i	−0.568969	+	0.413380i	0.265762	+	0.964039i	$0.414377\pi$
$212$		0			0
$213$	11.6266	−	16.0026i	0.796641	−	1.09648i
$214$		0			0
$215$	0.0257448	−	0.0322134i	0.00175578	−	0.00219693i
$216$		0			0
$217$	1.56877	−	0.509723i	0.106495	−	0.0346023i
$218$		0			0
$219$	−9.39109	−	28.9028i	−0.634591	−	1.95307i
$220$		0			0
$221$	−4.83294	+	14.8743i	−0.325099	+	1.00055i
$222$		0			0
$223$	−9.88289	−	13.6026i	−0.661808	−	0.910900i	0.337732	−	0.941242i	$-0.390340\pi$
$223$	−9.88289	−	13.6026i	−0.661808	−	0.910900i	−0.999540	+	0.0303424i	$0.990340\pi$
$224$		0			0
$225$	−8.58188	+	19.9619i	−0.572125	+	1.33079i
$226$		0			0
$227$	−0.938426	−	1.29163i	−0.0622855	−	0.0857287i	0.776738	−	0.629824i	$-0.216873\pi$
$227$	−0.938426	−	1.29163i	−0.0622855	−	0.0857287i	−0.839023	+	0.544095i	$0.816873\pi$
$228$		0			0
$229$	−2.04935	+	6.30726i	−0.135425	+	0.416795i	−0.995656	−	0.0931095i	$-0.970319\pi$
$229$	−2.04935	+	6.30726i	−0.135425	+	0.416795i	0.860231	+	0.509905i	$0.170319\pi$
$230$		0			0
$231$	−4.13386	−	12.7227i	−0.271988	−	0.837093i
$232$		0			0
$233$	20.4823	−	6.65512i	1.34184	−	0.435991i	0.451902	−	0.892067i	$-0.350745\pi$
$233$	20.4823	−	6.65512i	1.34184	−	0.435991i	0.889941	+	0.456076i	$0.150745\pi$
$234$		0			0
$235$	−10.5154	−	15.9667i	−0.685950	−	1.04155i
$236$		0			0
$237$	7.61299	−	10.4784i	0.494517	−	0.680644i
$238$		0			0
$239$	2.84987	−	2.07055i	0.184343	−	0.133933i	−0.491787	−	0.870716i	$-0.663656\pi$
$239$	2.84987	−	2.07055i	0.184343	−	0.133933i	0.676129	+	0.736783i	$0.263656\pi$
$240$		0			0
$241$	−4.20876	−	3.05784i	−0.271110	−	0.196973i	0.443921	−	0.896066i	$-0.353587\pi$
$241$	−4.20876	−	3.05784i	−0.271110	−	0.196973i	−0.715031	+	0.699093i	$0.753587\pi$
$242$		0			0
$243$			19.4846i			1.24994i
$244$		0			0
$245$	11.2160	+	8.96377i	0.716562	+	0.572675i
$246$		0			0
$247$	30.3849	+	9.87265i	1.93334	+	0.628181i
$248$		0			0
$249$	−12.7656			−0.808988
$250$		0			0
$251$	10.9106			0.688669			0.344335	−	0.938847i	$-0.388105\pi$
$251$	10.9106			0.688669			0.344335	+	0.938847i	$0.388105\pi$
$252$		0			0
$253$	17.9422	+	5.82978i	1.12802	+	0.366515i
$254$		0			0
$255$	12.9182	+	10.3242i	0.808968	+	0.646525i
$256$		0			0
$257$		−	13.2429i		−	0.826069i	−0.910715	−	0.413034i	$-0.864469\pi$
$257$		−	13.2429i		−	0.826069i	0.910715	−	0.413034i	$-0.135531\pi$
$258$		0			0
$259$	0.919169	+	0.667816i	0.0571144	+	0.0414960i
$260$		0			0
$261$	5.31198	−	3.85938i	0.328803	−	0.238890i
$262$		0			0
$263$	−9.23506	+	12.7110i	−0.569458	+	0.783792i	−0.992490	−	0.122322i	$-0.960966\pi$
$263$	−9.23506	+	12.7110i	−0.569458	+	0.783792i	0.423032	+	0.906115i	$0.360966\pi$
$264$		0			0
$265$	−6.50210	−	9.87286i	−0.399421	−	0.606485i
$266$		0			0
$267$	25.4246	−	8.26094i	1.55596	−	0.505562i
$268$		0			0
$269$	−6.76458	−	20.8192i	−0.412444	−	1.26937i	−0.914517	−	0.404547i	$-0.867429\pi$
$269$	−6.76458	−	20.8192i	−0.412444	−	1.26937i	0.502073	−	0.864825i	$-0.332571\pi$
$270$		0			0
$271$	1.10735	−	3.40807i	0.0672667	−	0.207026i	−0.911773	−	0.410694i	$-0.865286\pi$
$271$	1.10735	−	3.40807i	0.0672667	−	0.207026i	0.979040	+	0.203668i	$0.0652864\pi$
$272$		0			0
$273$	−6.94777	−	9.56278i	−0.420498	−	0.578766i
$274$		0			0
$275$	24.3798	+	21.3906i	1.47015	+	1.28990i
$276$		0			0
$277$	−6.10945	−	8.40894i	−0.367082	−	0.505244i	0.585023	−	0.811017i	$-0.301085\pi$
$277$	−6.10945	−	8.40894i	−0.367082	−	0.505244i	−0.952105	+	0.305772i	$0.901085\pi$
$278$		0			0
$279$	2.91112	−	8.95951i	0.174284	−	0.536392i
$280$		0			0
$281$	7.41608	+	22.8243i	0.442406	+	1.36159i	0.885303	+	0.465014i	$0.153951\pi$
$281$	7.41608	+	22.8243i	0.442406	+	1.36159i	−0.442897	+	0.896572i	$0.646049\pi$
$282$		0			0
$283$	−3.22778	+	1.04877i	−0.191871	+	0.0623428i	−0.403376	−	0.915034i	$-0.632163\pi$
$283$	−3.22778	+	1.04877i	−0.191871	+	0.0623428i	0.211505	+	0.977377i	$0.432163\pi$
$284$		0			0
$285$	21.0900	−	26.3890i	1.24927	−	1.56315i
$286$		0			0
$287$	2.01241	−	2.76984i	0.118789	−	0.163499i
$288$		0			0
$289$	−7.72961	+	5.61589i	−0.454683	+	0.330346i
$290$		0			0
$291$	1.67360	+	1.21594i	0.0981080	+	0.0712796i
$292$		0			0
$293$			0.853181i			0.0498434i	0.999689	+	0.0249217i	$0.00793364\pi$
$293$			0.853181i			0.0498434i	−0.999689	+	0.0249217i	$0.992066\pi$
$294$		0			0
$295$	−4.69104	−	17.0676i	−0.273123	−	0.993716i
$296$		0			0
$297$	−22.5005	−	7.31085i	−1.30561	−	0.424219i
$298$		0			0
$299$	16.6695			0.964022
$300$		0			0
$301$	0.0140325			0.000808822
$302$		0			0
$303$	43.4522	+	14.1185i	2.49627	+	0.811086i
$304$		0			0
$305$	−8.12832	−	0.373619i	−0.465426	−	0.0213934i
$306$		0			0
$307$		−	32.9825i		−	1.88241i	−0.337832	−	0.941207i	$-0.609693\pi$
$307$		−	32.9825i		−	1.88241i	0.337832	−	0.941207i	$-0.390307\pi$
$308$		0			0
$309$	−6.60254	−	4.79703i	−0.375605	−	0.272893i
$310$		0			0
$311$	−2.63887	+	1.91725i	−0.149637	+	0.108718i	−0.660085	−	0.751191i	$-0.729480\pi$
$311$	−2.63887	+	1.91725i	−0.149637	+	0.108718i	0.510448	+	0.859909i	$0.329480\pi$
$312$		0			0
$313$	3.07735	−	4.23561i	0.173942	−	0.239411i	−0.713141	−	0.701021i	$-0.752728\pi$
$313$	3.07735	−	4.23561i	0.173942	−	0.239411i	0.887083	+	0.461610i	$0.152728\pi$
$314$		0			0
$315$	−7.12957	+	1.95956i	−0.401706	+	0.110409i
$316$		0			0
$317$	−20.5415	+	6.67432i	−1.15372	+	0.374867i	−0.822544	−	0.568701i	$-0.807446\pi$
$317$	−20.5415	+	6.67432i	−1.15372	+	0.374867i	−0.331179	+	0.943568i	$0.607446\pi$
$318$		0			0
$319$	−3.02863	−	9.32117i	−0.169571	−	0.521885i
$320$		0			0
$321$	−9.93273	+	30.5698i	−0.554391	+	1.70624i
$322$		0			0
$323$	−8.94015	−	12.3051i	−0.497443	−	0.684672i
$324$		0			0
$325$	26.3281	+	11.3188i	1.46042	+	0.627855i
$326$		0			0
$327$	22.4557	+	30.9076i	1.24180	+	1.70919i
$328$		0			0
$329$	2.01039	−	6.18734i	0.110836	−	0.341119i
$330$		0			0
$331$	1.88002	+	5.78610i	0.103335	+	0.318033i	0.989336	−	0.145651i	$-0.0465275\pi$
$331$	1.88002	+	5.78610i	0.103335	+	0.318033i	−0.886001	+	0.463683i	$0.846528\pi$
$332$		0			0
$333$	6.17120	−	2.00515i	0.338180	−	0.109881i
$334$		0			0
$335$	10.1946	+	3.83835i	0.556990	+	0.209711i
$336$		0			0
$337$	−5.70265	+	7.84902i	−0.310643	+	0.427564i	−0.935582	−	0.353110i	$-0.885124\pi$
$337$	−5.70265	+	7.84902i	−0.310643	+	0.427564i	0.624939	+	0.780674i	$0.285124\pi$
$338$		0			0
$339$	−12.9978	+	9.44345i	−0.705943	+	0.512898i
$340$		0			0
$341$	−11.3763	−	8.26535i	−0.616060	−	0.447594i
$342$		0			0
$343$			10.2122i			0.551406i
$344$		0			0
$345$	6.21061	−	16.4953i	0.334368	−	0.888076i
$346$		0			0
$347$	1.81431	+	0.589504i	0.0973971	+	0.0316462i	0.357310	−	0.933986i	$-0.383694\pi$
$347$	1.81431	+	0.589504i	0.0973971	+	0.0316462i	−0.259913	+	0.965632i	$0.583694\pi$
$348$		0			0
$349$	1.02648			0.0549462			0.0274731	−	0.999623i	$-0.491254\pi$
$349$	1.02648			0.0549462			0.0274731	+	0.999623i	$0.491254\pi$
$350$		0			0
$351$	−20.9045			−1.11580
$352$		0			0
$353$	1.83452	+	0.596071i	0.0976415	+	0.0317256i	0.357430	−	0.933940i	$-0.383653\pi$
$353$	1.83452	+	0.596071i	0.0976415	+	0.0317256i	−0.259789	+	0.965665i	$0.583653\pi$
$354$		0			0
$355$	−13.6291	+	8.97593i	−0.723360	+	0.476393i
$356$		0			0
$357$			5.62732i			0.297829i
$358$		0			0
$359$	−17.7540	−	12.8990i	−0.937021	−	0.680786i	0.0106806	−	0.999943i	$-0.496600\pi$
$359$	−17.7540	−	12.8990i	−0.937021	−	0.680786i	−0.947702	+	0.319157i	$0.896600\pi$
$360$		0			0
$361$	−9.76524	+	7.09486i	−0.513960	+	0.373414i
$362$		0			0
$363$	−49.5083	+	68.1424i	−2.59851	+	3.57655i
$364$		0			0
$365$	−1.15126	+	25.0463i	−0.0602596	+	1.31098i
$366$		0			0
$367$	18.0351	−	5.85995i	0.941423	−	0.305887i	0.202198	−	0.979345i	$-0.435192\pi$
$367$	18.0351	−	5.85995i	0.941423	−	0.305887i	0.739226	+	0.673458i	$0.235192\pi$
$368$		0			0
$369$	−6.04235	−	18.5964i	−0.314552	−	0.968092i
$370$		0			0
$371$	1.24310	−	3.82588i	0.0645387	−	0.198630i
$372$		0			0
$373$	−6.47975	−	8.91860i	−0.335508	−	0.461788i	0.607614	−	0.794232i	$-0.292127\pi$
$373$	−6.47975	−	8.91860i	−0.335508	−	0.461788i	−0.943123	+	0.332444i	$0.892127\pi$
$374$		0			0
$375$	21.0097	−	21.8359i	1.08493	−	1.12760i
$376$		0			0
$377$	−5.09021	−	7.00608i	−0.262159	−	0.360831i
$378$		0			0
$379$	−0.606433	+	1.86641i	−0.0311504	+	0.0958710i	−0.965423	−	0.260689i	$-0.916050\pi$
$379$	−0.606433	+	1.86641i	−0.0311504	+	0.0958710i	0.934273	+	0.356560i	$0.116050\pi$
$380$		0			0
$381$	−7.60633	−	23.4099i	−0.389684	−	1.19932i
$382$		0			0
$383$	26.1420	−	8.49404i	1.33579	−	0.434025i	0.447903	−	0.894082i	$-0.352171\pi$
$383$	26.1420	−	8.49404i	1.33579	−	0.434025i	0.887890	+	0.460057i	$0.152171\pi$
$384$		0			0
$385$	−0.506771	+	11.0251i	−0.0258275	+	0.561893i
$386$		0			0
$387$	0.0471065	−	0.0648365i	0.00239456	−	0.00329582i
$388$		0			0
$389$	26.1122	−	18.9716i	1.32394	−	0.961898i	0.324064	−	0.946035i	$-0.394951\pi$
$389$	26.1122	−	18.9716i	1.32394	−	0.961898i	0.999874	−	0.0158627i	$-0.00504945\pi$
$390$		0			0
$391$	−6.42030	−	4.66462i	−0.324689	−	0.235900i
$392$		0			0
$393$		−	16.8595i		−	0.850448i
$394$		0			0
$395$	−8.92424	+	5.87736i	−0.449027	+	0.295722i
$396$		0			0
$397$	−23.4105	−	7.60652i	−1.17494	−	0.381760i	−0.344454	−	0.938803i	$-0.611936\pi$
$397$	−23.4105	−	7.60652i	−1.17494	−	0.381760i	−0.830484	+	0.557043i	$0.811936\pi$
$398$		0			0
$399$	11.4954			0.575489
$400$		0			0
$401$	18.5748			0.927581			0.463791	−	0.885945i	$-0.346489\pi$
$401$	18.5748			0.927581			0.463791	+	0.885945i	$0.346489\pi$
$402$		0			0
$403$	−11.8169	−	3.83953i	−0.588640	−	0.191261i
$404$		0			0
$405$	2.48350	−	6.59614i	0.123406	−	0.327765i
$406$		0			0
$407$		−	9.68565i		−	0.480100i
$408$		0			0
$409$	20.3731	+	14.8019i	1.00739	+	0.731908i	0.963659	−	0.267135i	$-0.0860771\pi$
$409$	20.3731	+	14.8019i	1.00739	+	0.731908i	0.0437262	+	0.999044i	$0.486077\pi$
$410$		0			0
$411$	35.6222	−	25.8810i	1.75711	−	1.27662i
$412$		0			0
$413$	3.54041	−	4.87296i	0.174212	−	0.239783i
$414$		0			0
$415$	9.85652	+	3.71106i	0.483837	+	0.182169i
$416$		0			0
$417$	26.1225	−	8.48773i	1.27923	−	0.415646i
$418$		0			0
$419$	3.57875	+	11.0143i	0.174833	+	0.538081i	0.999626	−	0.0273540i	$-0.00870815\pi$
$419$	3.57875	+	11.0143i	0.174833	+	0.538081i	−0.824793	+	0.565435i	$0.808708\pi$
$420$		0			0
$421$	7.20740	−	22.1821i	0.351267	−	1.08109i	−0.606875	−	0.794797i	$-0.707577\pi$
$421$	7.20740	−	22.1821i	0.351267	−	1.08109i	0.958142	−	0.286292i	$-0.0924228\pi$
$422$		0			0
$423$	−21.8395	−	30.0594i	−1.06187	−	1.46154i
$424$		0			0
$425$	−6.97301	−	11.7269i	−0.338240	−	0.568836i
$426$		0			0
$427$	−1.62752	−	2.24009i	−0.0787612	−	0.108405i
$428$		0			0
$429$	−31.1387	+	95.8349i	−1.50339	+	4.62695i
$430$		0			0
$431$	3.08204	+	9.48554i	0.148457	+	0.456902i	0.997439	−	0.0715183i	$-0.0227844\pi$
$431$	3.08204	+	9.48554i	0.148457	+	0.456902i	−0.848983	+	0.528421i	$0.822784\pi$
$432$		0			0
$433$	−1.15579	+	0.375539i	−0.0555437	+	0.0180472i	−0.336657	−	0.941627i	$-0.609296\pi$
$433$	−1.15579	+	0.375539i	−0.0555437	+	0.0180472i	0.281113	+	0.959675i	$0.409296\pi$
$434$		0			0
$435$	−8.82933	+	2.42674i	−0.423334	+	0.116353i
$436$		0			0
$437$	−9.52880	+	13.1153i	−0.455825	+	0.627389i
$438$		0			0
$439$	−18.0946	+	13.1465i	−0.863607	+	0.627447i	−0.928864	−	0.370421i	$-0.879213\pi$
$439$	−18.0946	+	13.1465i	−0.863607	+	0.627447i	0.0652568	+	0.997869i	$0.479213\pi$
$440$		0			0
$441$	22.5746	+	16.4014i	1.07498	+	0.781020i
$442$		0			0
$443$			7.44696i			0.353816i	0.984227	+	0.176908i	$0.0566095\pi$
$443$			7.44696i			0.353816i	−0.984227	+	0.176908i	$0.943390\pi$
$444$		0			0
$445$	−22.0322	−	1.01271i	−1.04443	−	0.0480071i
$446$		0			0
$447$	−31.0039	−	10.0738i	−1.46643	−	0.476473i
$448$		0			0
$449$	−7.86162			−0.371013			−0.185506	−	0.982643i	$-0.559393\pi$
$449$	−7.86162			−0.371013			−0.185506	+	0.982643i	$0.559393\pi$
$450$		0			0
$451$	−29.1869			−1.37436
$452$		0			0
$453$	−32.1741	−	10.4540i	−1.51167	−	0.491171i
$454$		0			0
$455$	2.58450	+	9.40333i	0.121163	+	0.440835i
$456$		0			0
$457$		−	29.4630i		−	1.37822i	−0.724657	−	0.689109i	$-0.758002\pi$
$457$		−	29.4630i		−	1.37822i	0.724657	−	0.689109i	$-0.241998\pi$
$458$		0			0
$459$	8.05140	+	5.84969i	0.375807	+	0.273040i
$460$		0			0
$461$	−9.17606	+	6.66680i	−0.427372	+	0.310504i	−0.780597	−	0.625035i	$-0.785085\pi$
$461$	−9.17606	+	6.66680i	−0.427372	+	0.310504i	0.353225	+	0.935538i	$0.385085\pi$
$462$		0			0
$463$	−10.9175	+	15.0267i	−0.507380	+	0.698349i	−0.983475	−	0.181045i	$-0.942052\pi$
$463$	−10.9175	+	15.0267i	−0.507380	+	0.698349i	0.476095	+	0.879394i	$0.342052\pi$
$464$		0			0
$465$	−8.20205	+	10.2629i	−0.380361	+	0.475929i
$466$		0			0
$467$	−8.75253	+	2.84387i	−0.405019	+	0.131599i	−0.504440	−	0.863447i	$-0.668301\pi$
$467$	−8.75253	+	2.84387i	−0.405019	+	0.131599i	0.0994209	+	0.995045i	$0.468301\pi$
$468$		0			0
$469$	1.14548	+	3.52543i	0.0528934	+	0.162789i
$470$		0			0
$471$	18.2360	−	56.1246i	0.840269	−	2.58608i
$472$		0			0
$473$	−0.0703146	−	0.0967798i	−0.00323307	−	0.00444994i
$474$		0			0
$475$	−23.9554	+	14.2443i	−1.09915	+	0.653574i
$476$		0			0
$477$	−13.5042	−	18.5870i	−0.618316	−	0.851039i
$478$		0			0
$479$	−8.50620	+	26.1794i	−0.388658	+	1.19617i	0.545133	+	0.838349i	$0.316479\pi$
$479$	−8.50620	+	26.1794i	−0.388658	+	1.19617i	−0.933792	+	0.357818i	$0.883521\pi$
$480$		0			0
$481$	−2.64463	−	8.13932i	−0.120585	−	0.371121i
$482$		0			0
$483$	5.70429	−	1.85344i	0.259554	−	0.0843342i
$484$		0			0
$485$	−0.938726	−	1.42537i	−0.0426253	−	0.0647227i
$486$		0			0
$487$	2.65881	−	3.65953i	0.120482	−	0.165829i	−0.744516	−	0.667605i	$-0.767320\pi$
$487$	2.65881	−	3.65953i	0.120482	−	0.165829i	0.864998	+	0.501775i	$0.167320\pi$
$488$		0			0
$489$	−14.1944	+	10.3128i	−0.641892	+	0.466362i
$490$		0			0
$491$	24.3841	+	17.7161i	1.10044	+	0.799515i	0.981131	−	0.193343i	$-0.0619329\pi$
$491$	24.3841	+	17.7161i	1.10044	+	0.799515i	0.119306	+	0.992857i	$0.461933\pi$
$492$		0			0
$493$			4.12280i			0.185682i
$494$		0			0
$495$	49.2398	+	39.3523i	2.21316	+	1.76875i
$496$		0			0
$497$	−5.28150	−	1.71606i	−0.236908	−	0.0769759i
$498$		0			0
$499$	15.3588			0.687556			0.343778	−	0.939051i	$-0.388293\pi$
$499$	15.3588			0.687556			0.343778	+	0.939051i	$0.388293\pi$
$500$		0			0
$501$	41.2154			1.84137
$502$		0			0
$503$	−23.0809	−	7.49943i	−1.02913	−	0.334383i	−0.254681	−	0.967025i	$-0.581970\pi$
$503$	−23.0809	−	7.49943i	−1.02913	−	0.334383i	−0.774444	+	0.632642i	$0.781970\pi$
$504$		0			0
$505$	−29.4457	−	23.5330i	−1.31032	−	1.04720i
$506$		0			0
$507$			53.8032i			2.38948i
$508$		0			0
$509$	27.0435	+	19.6483i	1.19868	+	0.870895i	0.994155	−	0.107966i	$-0.0344337\pi$
$509$	27.0435	+	19.6483i	1.19868	+	0.870895i	0.204529	+	0.978860i	$0.434434\pi$
$510$		0			0
$511$	−6.90253	+	5.01498i	−0.305350	+	0.221850i
$512$		0			0
$513$	11.9496	−	16.4473i	0.527589	−	0.726164i
$514$		0			0
$515$	3.70339	+	5.62326i	0.163191	+	0.247790i
$516$		0			0
$517$	−52.7466	+	17.1384i	−2.31979	+	0.753747i
$518$		0			0
$519$	−0.0925150	−	0.284732i	−0.00406096	−	0.0124983i
$520$		0			0
$521$	−3.76193	+	11.5780i	−0.164813	+	0.507243i	−0.999022	−	0.0442049i	$-0.985925\pi$
$521$	−3.76193	+	11.5780i	−0.164813	+	0.507243i	0.834209	+	0.551448i	$0.185925\pi$
$522$		0			0
$523$	−19.8098	−	27.2659i	−0.866224	−	1.19226i	−0.980049	−	0.198754i	$-0.936310\pi$
$523$	−19.8098	−	27.2659i	−0.866224	−	1.19226i	0.113825	−	0.993501i	$-0.463690\pi$
$524$		0			0
$525$	10.2680	+	0.945935i	0.448131	+	0.0412840i
$526$		0			0
$527$	3.47688	+	4.78552i	0.151455	+	0.208460i
$528$		0			0
$529$	4.49358	−	13.8298i	0.195373	−	0.601297i
$530$		0			0
$531$	−10.6302	−	32.7165i	−0.461314	−	1.41978i
$532$		0			0
$533$	−24.5272	+	7.96937i	−1.06239	+	0.345192i
$534$		0			0
$535$	16.5561	−	20.7159i	0.715781	−	0.895625i
$536$		0			0
$537$	−13.3742	+	18.4081i	−0.577141	+	0.794367i
$538$		0			0
$539$	33.6965	−	24.4820i	1.45141	−	1.05451i
$540$		0			0
$541$	11.4465	+	8.31634i	0.492122	+	0.357547i	0.806000	−	0.591916i	$-0.201628\pi$
$541$	11.4465	+	8.31634i	0.492122	+	0.357547i	−0.313878	+	0.949463i	$0.601628\pi$
$542$		0			0
$543$		−	14.0454i		−	0.602748i
$544$		0			0
$545$	−8.35328	−	30.3922i	−0.357815	−	1.30186i
$546$		0			0
$547$	14.5967	+	4.74276i	0.624111	+	0.202786i	0.603964	−	0.797011i	$-0.293587\pi$
$547$	14.5967	+	4.74276i	0.624111	+	0.202786i	0.0201461	+	0.999797i	$0.493587\pi$
$548$		0			0
$549$	−15.8137			−0.674912
$550$		0			0
$551$	8.42198			0.358788
$552$		0			0
$553$	−3.45828	−	1.12366i	−0.147061	−	0.0477830i
$554$		0			0
$555$	−9.03957	−	0.415505i	−0.383708	−	0.0176372i
$556$		0			0
$557$		−	27.6553i		−	1.17179i	−0.810386	−	0.585896i	$-0.800743\pi$
$557$		−	27.6553i		−	1.17179i	0.810386	−	0.585896i	$-0.199257\pi$
$558$		0			0
$559$	−0.0855141	−	0.0621296i	−0.00361686	−	0.00262780i
$560$		0			0
$561$	38.8106	−	28.1975i	1.63858	−	1.19050i
$562$		0			0
$563$	10.3282	−	14.2156i	0.435283	−	0.599115i	−0.533873	−	0.845565i	$-0.679264\pi$
$563$	10.3282	−	14.2156i	0.435283	−	0.599115i	0.969156	+	0.246450i	$0.0792640\pi$
$564$		0			0
$565$	12.7811	−	3.51287i	0.537703	−	0.147788i
$566$		0			0
$567$	2.28103	−	0.741152i	0.0957943	−	0.0311255i
$568$		0			0
$569$	2.53587	+	7.80461i	0.106309	+	0.327186i	0.990035	−	0.140818i	$-0.0449732\pi$
$569$	2.53587	+	7.80461i	0.106309	+	0.327186i	−0.883726	+	0.468004i	$0.844973\pi$
$570$		0			0
$571$	4.01983	−	12.3718i	0.168225	−	0.517743i	−0.831035	−	0.556221i	$-0.812251\pi$
$571$	4.01983	−	12.3718i	0.168225	−	0.517743i	0.999259	+	0.0384780i	$0.0122509\pi$
$572$		0			0
$573$	42.4049	+	58.3653i	1.77149	+	2.43824i
$574$		0			0
$575$	−9.59060	+	10.9308i	−0.399956	+	0.455845i
$576$		0			0
$577$	24.5187	+	33.7471i	1.02073	+	1.40491i	0.911694	+	0.410870i	$0.134775\pi$
$577$	24.5187	+	33.7471i	1.02073	+	1.40491i	0.109032	+	0.994038i	$0.465225\pi$
$578$		0			0
$579$	18.2832	−	56.2699i	0.759824	−	2.33850i
$580$		0			0
$581$	1.10749	+	3.40851i	0.0459466	+	0.141409i
$582$		0			0
$583$	−32.6154	+	10.5974i	−1.35079	+	0.438898i
$584$		0			0
$585$	52.1235	+	19.6249i	2.15504	+	0.811391i
$586$		0			0
$587$	11.3426	−	15.6117i	0.468158	−	0.644364i	−0.508017	−	0.861347i	$-0.669621\pi$
$587$	11.3426	−	15.6117i	0.468158	−	0.644364i	0.976176	+	0.216982i	$0.0696214\pi$
$588$		0			0
$589$	9.77576	−	7.10251i	0.402803	−	0.292654i
$590$		0			0
$591$	−9.94299	−	7.22401i	−0.409000	−	0.297156i
$592$		0			0
$593$		−	22.3316i		−	0.917049i	−0.888682	−	0.458525i	$-0.848378\pi$
$593$		−	22.3316i		−	0.917049i	0.888682	−	0.458525i	$-0.151622\pi$
$594$		0			0
$595$	1.63590	−	4.34494i	0.0670655	−	0.178125i
$596$		0			0
$597$	40.0406	+	13.0100i	1.63875	+	0.532463i
$598$		0			0
$599$	23.3783			0.955212			0.477606	−	0.878574i	$-0.341505\pi$
$599$	23.3783			0.955212			0.477606	+	0.878574i	$0.341505\pi$
$600$		0			0
$601$	21.1044			0.860866			0.430433	−	0.902623i	$-0.358361\pi$
$601$	21.1044			0.860866			0.430433	+	0.902623i	$0.358361\pi$
$602$		0			0
$603$	20.1343	+	6.54204i	0.819933	+	0.266412i
$604$		0			0
$605$	58.0356	−	38.2213i	2.35948	−	1.55392i
$606$		0			0
$607$		−	27.5146i		−	1.11678i	−0.829578	−	0.558391i	$-0.811419\pi$
$607$		−	27.5146i		−	1.11678i	0.829578	−	0.558391i	$-0.188581\pi$
$608$		0			0
$609$	−2.52085	−	1.83151i	−0.102150	−	0.0742164i
$610$		0			0
$611$	−39.6460	+	28.8045i	−1.60390	+	1.16530i
$612$		0			0
$613$	−13.4265	+	18.4800i	−0.542292	+	0.746401i	−0.988941	−	0.148309i	$-0.952617\pi$
$613$	−13.4265	+	18.4800i	−0.542292	+	0.746401i	0.446649	+	0.894709i	$0.352617\pi$
$614$		0			0
$615$	−1.25209	+	27.2400i	−0.0504892	+	1.09842i
$616$		0			0
$617$	25.0330	−	8.13371i	1.00779	−	0.327451i	0.241816	−	0.970322i	$-0.422257\pi$
$617$	25.0330	−	8.13371i	1.00779	−	0.327451i	0.765974	+	0.642872i	$0.222257\pi$
$618$		0			0
$619$	12.0565	+	37.1060i	0.484590	+	1.49141i	0.832574	+	0.553914i	$0.186866\pi$
$619$	12.0565	+	37.1060i	0.484590	+	1.49141i	−0.347984	+	0.937501i	$0.613134\pi$
$620$		0			0
$621$	3.27786	−	10.0882i	0.131536	−	0.404826i
$622$		0			0
$623$	−4.41146	−	6.07186i	−0.176742	−	0.243264i
$624$		0			0
$625$	−22.5697	+	10.7521i	−0.902788	+	0.430085i
$626$		0			0
$627$	−57.6014	−	79.2815i	−2.30038	−	3.16620i
$628$		0			0
$629$	−1.25904	+	3.87492i	−0.0502012	+	0.154503i
$630$		0			0
$631$	1.86801	+	5.74913i	0.0743641	+	0.228869i	0.981329	−	0.192337i	$-0.0616068\pi$
$631$	1.86801	+	5.74913i	0.0743641	+	0.228869i	−0.906965	+	0.421207i	$0.861607\pi$
$632$		0			0
$633$	26.3326	−	8.55600i	1.04663	−	0.340070i
$634$		0			0
$635$	−0.932463	+	20.2863i	−0.0370036	+	0.805038i
$636$		0			0
$637$	21.6321	−	29.7741i	0.857097	−	1.17969i
$638$		0			0
$639$	−25.6587	+	18.6421i	−1.01504	+	0.737471i
$640$		0			0
$641$	−25.8796	−	18.8027i	−1.02218	−	0.742660i	−0.0554545	−	0.998461i	$-0.517661\pi$
$641$	−25.8796	−	18.8027i	−1.02218	−	0.742660i	−0.966729	+	0.255801i	$0.917661\pi$
$642$		0			0
$643$			9.81465i			0.387052i	0.981095	+	0.193526i	$0.0619924\pi$
$643$			9.81465i			0.387052i	−0.981095	+	0.193526i	$0.938008\pi$
$644$		0			0
$645$	−0.0933405	+	0.0614725i	−0.00367528	+	0.00242048i
$646$		0			0
$647$	−24.7452	−	8.04019i	−0.972832	−	0.316092i	−0.220874	−	0.975302i	$-0.570891\pi$
$647$	−24.7452	−	8.04019i	−0.972832	−	0.316092i	−0.751959	+	0.659210i	$0.770891\pi$
$648$		0			0
$649$	−51.3483			−2.01560
$650$		0			0
$651$	−4.47063			−0.175218
$652$		0			0
$653$	−36.1617	−	11.7496i	−1.41512	−	0.459799i	−0.501069	−	0.865408i	$-0.667060\pi$
$653$	−36.1617	−	11.7496i	−1.41512	−	0.459799i	−0.914047	+	0.405609i	$0.867060\pi$
$654$		0			0
$655$	−4.90117	+	13.0174i	−0.191505	+	0.508634i
$656$		0			0
$657$			48.7277i			1.90105i
$658$		0			0
$659$	6.74023	+	4.89706i	0.262562	+	0.190762i	0.711276	−	0.702913i	$-0.248118\pi$
$659$	6.74023	+	4.89706i	0.262562	+	0.190762i	−0.448714	+	0.893676i	$0.648118\pi$
$660$		0			0
$661$	21.1227	−	15.3465i	0.821576	−	0.596910i	−0.0955874	−	0.995421i	$-0.530473\pi$
$661$	21.1227	−	15.3465i	0.821576	−	0.596910i	0.917164	+	0.398511i	$0.130473\pi$
$662$		0			0
$663$	24.9152	−	34.2928i	0.967626	−	1.33182i
$664$		0			0
$665$	−8.87575	−	3.34179i	−0.344187	−	0.129589i
$666$		0			0
$667$	4.17919	−	1.35790i	0.161819	−	0.0525781i
$668$		0			0
$669$	14.0820	+	43.3399i	0.544441	+	1.67562i
$670$		0			0
$671$	−7.29425	+	22.4494i	−0.281591	+	0.866649i
$672$		0			0
$673$	28.5875	+	39.3473i	1.10197	+	1.51673i	0.832750	+	0.553649i	$0.186765\pi$
$673$	28.5875	+	39.3473i	1.10197	+	1.51673i	0.269217	+	0.963079i	$0.413235\pi$
$674$		0			0
$675$	12.0271	−	13.7078i	0.462924	−	0.527613i
$676$		0			0
$677$	−18.4652	−	25.4152i	−0.709677	−	0.976786i	−0.999804	−	0.0197980i	$-0.993698\pi$
$677$	−18.4652	−	25.4152i	−0.709677	−	0.976786i	0.290127	−	0.956988i	$-0.406302\pi$
$678$		0			0
$679$	0.179470	−	0.552352i	0.00688743	−	0.0211973i
$680$		0			0
$681$	1.33715	+	4.11532i	0.0512397	+	0.157700i
$682$		0			0
$683$	−32.1915	+	10.4597i	−1.23177	+	0.400228i	−0.851357	−	0.524587i	$-0.824220\pi$
$683$	−32.1915	+	10.4597i	−1.23177	+	0.400228i	−0.380417	+	0.924815i	$0.624220\pi$
$684$		0			0
$685$	−35.0282	+	9.62749i	−1.33836	+	0.367847i
$686$		0			0
$687$	10.5650	−	14.5415i	0.403080	−	0.554791i
$688$		0			0
$689$	−24.5147	+	17.8110i	−0.933936	+	0.678544i
$690$		0			0
$691$	36.6495	+	26.6274i	1.39421	+	1.01296i	0.995388	+	0.0959289i	$0.0305822\pi$
$691$	36.6495	+	26.6274i	1.39421	+	1.01296i	0.398826	+	0.917027i	$0.369418\pi$
$692$		0			0
$693$			21.4494i			0.814797i
$694$		0			0
$695$	−22.6370	−	1.04051i	−0.858671	−	0.0394689i
$696$		0			0
$697$	11.6768	+	3.79402i	0.442289	+	0.143709i
$698$		0			0
$699$	−58.3700			−2.20776
$700$		0			0
$701$	3.00762			0.113596			0.0567982	−	0.998386i	$-0.481911\pi$
$701$	3.00762			0.113596			0.0567982	+	0.998386i	$0.481911\pi$
$702$		0			0
$703$	7.91562	+	2.57194i	0.298543	+	0.0970026i
$704$		0			0
$705$	13.7324	+	49.9634i	0.517193	+	1.88173i
$706$		0			0
$707$		−	12.8269i		−	0.482406i
$708$		0			0
$709$	−22.1169	−	16.0688i	−0.830616	−	0.603478i	0.0891173	−	0.996021i	$-0.471595\pi$
$709$	−22.1169	−	16.0688i	−0.830616	−	0.603478i	−0.919734	+	0.392543i	$0.871595\pi$
$710$		0			0
$711$	−16.8011	+	12.2067i	−0.630089	+	0.457786i
$712$		0			0
$713$	3.70581	−	5.10061i	0.138784	−	0.191019i
$714$		0			0
$715$	51.9025	−	64.9433i	1.94104	−	2.42874i
$716$		0			0
$717$	−9.08008	+	2.95030i	−0.339102	+	0.110181i
$718$		0			0
$719$	2.15179	+	6.62252i	0.0802482	+	0.246978i	0.983129	−	0.182912i	$-0.0585523\pi$
$719$	2.15179	+	6.62252i	0.0802482	+	0.246978i	−0.902881	+	0.429890i	$0.858552\pi$
$720$		0			0
$721$	−0.708032	+	2.17910i	−0.0263685	+	0.0811538i
$722$		0			0
$723$	8.28765	+	11.4070i	0.308221	+	0.424230i
$724$		0			0
$725$	7.52272	+	0.693029i	0.279387	+	0.0257385i
$726$		0			0
$727$	23.2038	+	31.9373i	0.860581	+	1.18449i	0.981431	+	0.191817i	$0.0614379\pi$
$727$	23.2038	+	31.9373i	0.860581	+	1.18449i	−0.120850	+	0.992671i	$0.538562\pi$
$728$		0			0
$729$	13.3968	−	41.2311i	0.496177	−	1.52708i
$730$		0			0
$731$	0.0155503	+	0.0478588i	0.000575147	+	0.00177012i
$732$		0			0
$733$	1.38560	−	0.450207i	0.0511781	−	0.0166288i	−0.283316	−	0.959027i	$-0.591435\pi$
$733$	1.38560	−	0.450207i	0.0511781	−	0.0166288i	0.334494	+	0.942398i	$0.391435\pi$
$734$		0			0
$735$	−21.4034	−	32.4991i	−0.789475	−	1.19875i
$736$		0			0
$737$	18.5744	−	25.5655i	0.684197	−	0.941716i
$738$		0			0
$739$	9.21835	−	6.69753i	0.339103	−	0.246372i	−0.405181	−	0.914237i	$-0.632791\pi$
$739$	9.21835	−	6.69753i	0.339103	−	0.246372i	0.744283	+	0.667864i	$0.232791\pi$
$740$		0			0
$741$	−70.0528	−	50.8963i	−2.57345	−	1.86972i
$742$		0			0
$743$			38.1536i			1.39972i	0.714280	+	0.699860i	$0.246754\pi$
$743$			38.1536i			1.39972i	−0.714280	+	0.699860i	$0.753246\pi$
$744$		0			0
$745$	21.0100	+	16.7911i	0.769747	+	0.615180i
$746$		0			0
$747$	19.4666	+	6.32509i	0.712247	+	0.231423i
$748$		0			0
$749$	9.02408			0.329733
$750$		0			0
$751$	−47.6723			−1.73959			−0.869794	−	0.493415i	$-0.835749\pi$
$751$	−47.6723			−1.73959			−0.869794	+	0.493415i	$0.835749\pi$
$752$		0			0
$753$	−28.1236	−	9.13790i	−1.02488	−	0.333004i
$754$		0			0
$755$	21.8030	+	17.4249i	0.793493	+	0.634157i
$756$		0			0
$757$		−	11.0241i		−	0.400676i	−0.979727	−	0.200338i	$-0.935796\pi$
$757$		−	11.0241i		−	0.400676i	0.979727	−	0.200338i	$-0.0642041\pi$
$758$		0			0
$759$	−41.3660	−	30.0542i	−1.50149	−	1.09090i
$760$		0			0
$761$	−41.2225	+	29.9499i	−1.49431	+	1.08568i	−0.521736	+	0.853107i	$0.674716\pi$
$761$	−41.2225	+	29.9499i	−1.49431	+	1.08568i	−0.972578	+	0.232576i	$0.925284\pi$
$762$		0			0
$763$	6.30438	−	8.67724i	0.228234	−	0.314137i
$764$		0			0
$765$	−14.5839	−	22.1443i	−0.527281	−	0.800629i
$766$		0			0
$767$	−43.1505	+	14.0204i	−1.55807	+	0.506249i
$768$		0			0
$769$	−9.84334	−	30.2947i	−0.354960	−	1.09245i	−0.956033	−	0.293260i	$-0.905260\pi$
$769$	−9.84334	−	30.2947i	−0.354960	−	1.09245i	0.601073	−	0.799194i	$-0.294740\pi$
$770$		0			0
$771$	−11.0913	+	34.1354i	−0.399442	+	1.22936i
$772$		0			0
$773$	−8.96948	−	12.3454i	−0.322610	−	0.444034i	0.616652	−	0.787236i	$-0.288489\pi$
$773$	−8.96948	−	12.3454i	−0.322610	−	0.444034i	−0.939262	+	0.343201i	$0.888489\pi$
$774$		0			0
$775$	9.31640	−	5.53970i	0.334655	−	0.198992i
$776$		0			0
$777$	−1.80998	−	2.49122i	−0.0649325	−	0.0893720i
$778$		0			0
$779$	7.75034	−	23.8531i	0.277685	−	0.854626i
$780$		0			0
$781$	14.6293	+	45.0244i	0.523478	+	1.61110i
$782$		0			0
$783$	−5.24093	+	1.70288i	−0.187295	+	0.0608560i
$784$		0			0
$785$	−30.3961	+	38.0332i	−1.08488	+	1.35746i
$786$		0			0
$787$	−3.77478	+	5.19554i	−0.134556	+	0.185201i	−0.870978	−	0.491322i	$-0.836514\pi$
$787$	−3.77478	+	5.19554i	−0.134556	+	0.185201i	0.736422	+	0.676523i	$0.236514\pi$
$788$		0			0
$789$	34.4505	−	25.0297i	1.22647	−	0.891082i
$790$		0			0
$791$	3.64910	+	2.65123i	0.129747	+	0.0942669i
$792$		0			0
$793$			20.8570i			0.740653i
$794$		0			0
$795$	8.49131	+	30.8944i	0.301156	+	1.09571i
$796$		0			0
$797$	18.7417	+	6.08953i	0.663864	+	0.215702i	0.621517	−	0.783401i	$-0.286517\pi$
$797$	18.7417	+	6.08953i	0.663864	+	0.215702i	0.0423465	+	0.999103i	$0.486517\pi$
$798$		0			0
$799$	23.3301			0.825360
$800$		0			0
$801$	−42.8637			−1.51451
$802$		0			0
$803$	69.1748	+	22.4762i	2.44112	+	0.793169i
$804$		0			0
$805$	−4.94317	−	0.227213i	−0.174224	−	0.00800822i
$806$		0			0
$807$			59.3301i			2.08852i
$808$		0			0
$809$	−13.9154	−	10.1101i	−0.489238	−	0.355452i	0.315653	−	0.948875i	$-0.397776\pi$
$809$	−13.9154	−	10.1101i	−0.489238	−	0.355452i	−0.804891	+	0.593422i	$0.797776\pi$
$810$		0			0
$811$	32.7484	−	23.7931i	1.14995	−	0.835488i	0.161477	−	0.986877i	$-0.448374\pi$
$811$	32.7484	−	23.7931i	1.14995	−	0.835488i	0.988474	+	0.151388i	$0.0483743\pi$
$812$		0			0
$813$	−5.70871	+	7.85736i	−0.200213	+	0.275570i
$814$		0			0
$815$	13.9577	−	3.83627i	0.488916	−	0.134379i
$816$		0			0
$817$	0.0977650	−	0.0317658i	0.00342036	−	0.00111134i
$818$		0			0
$819$	5.85668	+	18.0250i	0.204649	+	0.629845i
$820$		0			0
$821$	−4.34057	+	13.3589i	−0.151487	+	0.466229i	−0.997788	−	0.0664761i	$-0.978824\pi$
$821$	−4.34057	+	13.3589i	−0.151487	+	0.466229i	0.846301	+	0.532705i	$0.178824\pi$
$822$		0			0
$823$	9.13984	+	12.5799i	0.318595	+	0.438508i	0.938038	−	0.346534i	$-0.112641\pi$
$823$	9.13984	+	12.5799i	0.318595	+	0.438508i	−0.619443	+	0.785042i	$0.712641\pi$
$824$		0			0
$825$	−44.9271	−	75.5561i	−1.56416	−	2.63053i
$826$		0			0
$827$	−3.32447	−	4.57574i	−0.115603	−	0.159114i	0.747294	−	0.664493i	$-0.231353\pi$
$827$	−3.32447	−	4.57574i	−0.115603	−	0.159114i	−0.862897	+	0.505379i	$0.831353\pi$
$828$		0			0
$829$	15.5431	−	47.8369i	0.539835	−	1.66144i	−0.193127	−	0.981174i	$-0.561863\pi$
$829$	15.5431	−	47.8369i	0.539835	−	1.66144i	0.732963	−	0.680269i	$-0.238137\pi$
$830$		0			0
$831$	8.70527	+	26.7921i	0.301983	+	0.929407i
$832$		0			0
$833$	−16.6634	+	5.41425i	−0.577351	+	0.187593i
$834$		0			0
$835$	−31.8230	−	11.9816i	−1.10128	−	0.414641i
$836$		0			0
$837$	−4.64729	+	6.39644i	−0.160634	+	0.221093i
$838$		0			0
$839$	11.6370	−	8.45479i	0.401755	−	0.291892i	−0.368501	−	0.929627i	$-0.620129\pi$
$839$	11.6370	−	8.45479i	0.401755	−	0.291892i	0.770255	+	0.637736i	$0.220129\pi$
$840$		0			0
$841$	21.6146	+	15.7039i	0.745332	+	0.541515i
$842$		0			0
$843$		−	65.0442i		−	2.24024i
$844$		0			0
$845$	15.6410	−	41.5422i	0.538066	−	1.42910i
$846$		0			0
$847$	22.4897	+	7.30733i	0.772754	+	0.251083i
$848$		0			0
$849$	9.19842			0.315689
$850$		0			0
$851$	4.34261			0.148863
$852$		0			0
$853$	18.7911	+	6.10561i	0.643397	+	0.209052i	0.612500	−	0.790470i	$-0.290164\pi$
$853$	18.7911	+	6.10561i	0.643397	+	0.209052i	0.0308964	+	0.999523i	$0.490164\pi$
$854$		0			0
$855$	−45.2360	+	29.7917i	−1.54704	+	1.01885i
$856$		0			0
$857$			22.9746i			0.784798i	0.919795	+	0.392399i	$0.128355\pi$
$857$			22.9746i			0.784798i	−0.919795	+	0.392399i	$0.871645\pi$
$858$		0			0
$859$	−13.0816	−	9.50433i	−0.446338	−	0.324284i	0.341810	−	0.939769i	$-0.388960\pi$
$859$	−13.0816	−	9.50433i	−0.446338	−	0.324284i	−0.788148	+	0.615485i	$0.788960\pi$
$860$		0			0
$861$	−7.50709	+	5.45422i	−0.255841	+	0.185879i
$862$		0			0
$863$	10.6331	−	14.6352i	0.361954	−	0.498187i	−0.588738	−	0.808324i	$-0.700375\pi$
$863$	10.6331	−	14.6352i	0.361954	−	0.498187i	0.950692	+	0.310137i	$0.100375\pi$
$864$		0			0
$865$	−0.0113414	+	0.246740i	−0.000385621	+	0.00838942i
$866$		0			0
$867$	24.6276	−	8.00200i	0.836398	−	0.271762i
$868$		0			0
$869$	9.57914	+	29.4816i	0.324950	+	1.00009i
$870$		0			0
$871$	8.62842	−	26.5556i	0.292363	−	0.899801i
$872$		0			0
$873$	−1.94964	−	2.68345i	−0.0659853	−	0.0908210i
$874$		0			0
$875$	−7.65305	−	3.71534i	−0.258720	−	0.125601i
$876$		0			0
$877$	3.09212	+	4.25593i	0.104413	+	0.143713i	0.858026	−	0.513606i	$-0.171691\pi$
$877$	3.09212	+	4.25593i	0.104413	+	0.143713i	−0.753613	+	0.657318i	$0.771691\pi$
$878$		0			0
$879$	0.714562	−	2.19920i	0.0241016	−	0.0741771i
$880$		0			0
$881$	−12.6144	−	38.8233i	−0.424991	−	1.30799i	−0.903002	−	0.429635i	$-0.858642\pi$
$881$	−12.6144	−	38.8233i	−0.424991	−	1.30799i	0.478011	−	0.878354i	$-0.341358\pi$
$882$		0			0
$883$	−23.2943	+	7.56879i	−0.783917	+	0.254710i	−0.673512	−	0.739177i	$-0.735215\pi$
$883$	−23.2943	+	7.56879i	−0.783917	+	0.254710i	−0.110405	+	0.993887i	$0.535215\pi$
$884$		0			0
$885$	−2.20279	+	47.9231i	−0.0740460	+	1.61092i
$886$		0			0
$887$	−15.6478	+	21.5374i	−0.525403	+	0.723155i	−0.986421	−	0.164235i	$-0.947484\pi$
$887$	−15.6478	+	21.5374i	−0.525403	+	0.723155i	0.461018	+	0.887391i	$0.347484\pi$
$888$		0			0
$889$	−5.59071	+	4.06189i	−0.187507	+	0.136231i
$890$		0			0
$891$	−16.5414	−	12.0181i	−0.554159	−	0.402620i
$892$		0			0
$893$		−	47.6583i		−	1.59482i
$894$		0			0
$895$	15.6778	−	10.3251i	0.524051	−	0.345132i
$896$		0			0
$897$	−42.9680	−	13.9612i	−1.43466	−	0.466150i
$898$		0			0
$899$	−3.27536			−0.109239
$900$		0			0
$901$	14.4259			0.480598
$902$		0			0
$903$	−0.0361709	−	0.0117526i	−0.00120369	−	0.000391103i
$904$		0			0
$905$	−4.08311	+	10.8447i	−0.135727	+	0.360490i
$906$		0			0
$907$			12.8213i			0.425723i	0.977082	+	0.212862i	$0.0682784\pi$
$907$			12.8213i			0.425723i	−0.977082	+	0.212862i	$0.931722\pi$
$908$		0			0
$909$	−59.2661	−	43.0593i	−1.96573	−	1.42819i
$910$		0			0
$911$	18.1249	−	13.1685i	0.600505	−	0.436292i	−0.245553	−	0.969383i	$-0.578970\pi$
$911$	18.1249	−	13.1685i	0.600505	−	0.436292i	0.846058	+	0.533091i	$0.178970\pi$
$912$		0			0
$913$	17.9584	−	24.7176i	0.594337	−	0.818035i
$914$		0			0
$915$	20.6390	+	7.77075i	0.682304	+	0.256893i
$916$		0			0
$917$	−4.50161	+	1.46266i	−0.148656	+	0.0483013i
$918$		0			0
$919$	18.6498	+	57.3983i	0.615201	+	1.89339i	0.398557	+	0.917144i	$0.369511\pi$
$919$	18.6498	+	57.3983i	0.615201	+	1.89339i	0.216644	+	0.976251i	$0.430489\pi$
$920$		0			0
$921$	−27.6238	+	85.0172i	−0.910234	+	2.80141i
$922$		0			0
$923$	24.5874	+	33.8417i	0.809306	+	1.11391i
$924$		0			0
$925$	6.85879	+	2.94868i	0.225516	+	0.0969522i
$926$		0			0
$927$	7.69156	+	10.5865i	0.252624	+	0.347707i
$928$		0			0
$929$	9.21921	−	28.3738i	0.302472	−	0.930914i	−0.678136	−	0.734936i	$-0.737212\pi$
$929$	9.21921	−	28.3738i	0.302472	−	0.930914i	0.980608	−	0.195978i	$-0.0627880\pi$
$930$		0			0
$931$	11.0601	+	34.0396i	0.362481	+	1.11560i
$932$		0			0
$933$	8.40783	−	2.73187i	0.275260	−	0.0894374i
$934$		0			0
$935$	−38.1634	+	10.4892i	−1.24808	+	0.343034i
$936$		0			0
$937$	−1.51541	+	2.08578i	−0.0495063	+	0.0681396i	−0.833052	−	0.553194i	$-0.813409\pi$
$937$	−1.51541	+	2.08578i	−0.0495063	+	0.0681396i	0.783546	+	0.621334i	$0.213409\pi$
$938$		0			0
$939$	−11.4798	+	8.34053i	−0.374628	+	0.272183i
$940$		0			0
$941$	6.78087	+	4.92659i	0.221050	+	0.160602i	0.692799	−	0.721131i	$-0.256377\pi$
$941$	6.78087	+	4.92659i	0.221050	+	0.160602i	−0.471749	+	0.881733i	$0.656377\pi$
$942$		0			0
$943$		−	13.0861i		−	0.426142i
$944$		0			0
$945$	6.19900	+	0.284938i	0.201653	+	0.00926902i
$946$		0			0
$947$	31.0314	+	10.0827i	1.00839	+	0.327644i	0.766212	−	0.642588i	$-0.222139\pi$
$947$	31.0314	+	10.0827i	1.00839	+	0.327644i	0.242174	+	0.970233i	$0.422139\pi$
$948$		0			0
$949$	64.2680			2.08623
$950$		0			0
$951$	58.5384			1.89824
$952$		0			0
$953$	−4.57148	−	1.48536i	−0.148085	−	0.0481156i	0.234037	−	0.972228i	$-0.424806\pi$
$953$	−4.57148	−	1.48536i	−0.148085	−	0.0481156i	−0.382121	+	0.924112i	$0.624806\pi$
$954$		0			0
$955$	−15.7742	−	57.3921i	−0.510441	−	1.85716i
$956$		0			0
$957$			26.5632i			0.858666i
$958$		0			0
$959$	−10.0009	−	7.26605i	−0.322945	−	0.234633i
$960$		0			0
$961$	21.2777	−	15.4591i	0.686377	−	0.498682i
$962$		0			0
$963$	30.2934	−	41.6952i	0.976190	−	1.34361i
$964$		0			0
$965$	−30.4748	+	38.1317i	−0.981018	+	1.22750i
$966$		0			0
$967$	−20.7425	+	6.73963i	−0.667033	+	0.216732i	−0.622909	−	0.782294i	$-0.714049\pi$
$967$	−20.7425	+	6.73963i	−0.667033	+	0.216732i	−0.0441233	+	0.999026i	$0.514049\pi$
$968$		0			0
$969$	12.7387	+	39.2057i	0.409226	+	1.25947i
$970$		0			0
$971$	7.43033	−	22.8682i	0.238451	−	0.733876i	−0.758194	−	0.652029i	$-0.773918\pi$
$971$	7.43033	−	22.8682i	0.238451	−	0.733876i	0.996645	−	0.0818470i	$-0.0260819\pi$
$972$		0			0
$973$	−4.53257	−	6.23855i	−0.145308	−	0.199999i
$974$		0			0
$975$	−58.3847	−	51.2264i	−1.86981	−	1.64056i
$976$		0			0
$977$	−1.71728	−	2.36363i	−0.0549406	−	0.0756192i	0.780663	−	0.624953i	$-0.214882\pi$
$977$	−1.71728	−	2.36363i	−0.0549406	−	0.0756192i	−0.835603	+	0.549333i	$0.814882\pi$
$978$		0			0
$979$	−19.7714	+	60.8501i	−0.631896	+	1.94478i
$980$		0			0
$981$	−18.9292	−	58.2580i	−0.604362	−	1.86004i
$982$		0			0
$983$	−0.802072	+	0.260609i	−0.0255821	+	0.00831213i	−0.321780	−	0.946814i	$-0.604281\pi$
$983$	−0.802072	+	0.260609i	−0.0255821	+	0.00831213i	0.296198	+	0.955127i	$0.404281\pi$
$984$		0			0
$985$	5.57706	+	8.46826i	0.177700	+	0.269821i
$986$		0			0
$987$	−10.3641	+	14.2650i	−0.329894	+	0.454060i
$988$		0			0
$989$	0.0433917	−	0.0315259i	0.00137977	−	0.00100246i
$990$		0			0
$991$	−5.03874	−	3.66086i	−0.160061	−	0.116291i	0.504872	−	0.863194i	$-0.331540\pi$
$991$	−5.03874	−	3.66086i	−0.160061	−	0.116291i	−0.664933	+	0.746903i	$0.731540\pi$
$992$		0			0
$993$		−	16.4891i		−	0.523265i
$994$		0			0
$995$	−27.1338	−	21.6853i	−0.860201	−	0.687470i
$996$		0			0
$997$	49.9219	+	16.2206i	1.58104	+	0.513712i	0.962325	−	0.271902i	$-0.0876527\pi$
$997$	49.9219	+	16.2206i	1.58104	+	0.513712i	0.618717	+	0.785614i	$0.287653\pi$
$998$		0			0
$999$	−5.44586			−0.172299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.q.a.89.2	yes	32
4.3	odd	2		400.2.y.d.289.7		32
5.2	odd	4		1000.2.m.d.801.1		32
5.3	odd	4		1000.2.m.e.801.8		32
5.4	even	2		1000.2.q.c.449.7		32
25.3	odd	20		5000.2.a.q.1.15		16
25.9	even	10	inner	200.2.q.a.9.2	✓	32
25.12	odd	20		1000.2.m.d.201.1		32
25.13	odd	20		1000.2.m.e.201.8		32
25.16	even	5		1000.2.q.c.49.7		32
25.22	odd	20		5000.2.a.r.1.2		16
100.3	even	20		10000.2.a.br.1.2		16
100.47	even	20		10000.2.a.bq.1.15		16
100.59	odd	10		400.2.y.d.209.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.q.a.9.2	✓	32	25.9	even	10	inner
200.2.q.a.89.2	yes	32	1.1	even	1	trivial
400.2.y.d.209.7		32	100.59	odd	10
400.2.y.d.289.7		32	4.3	odd	2
1000.2.m.d.201.1		32	25.12	odd	20
1000.2.m.d.801.1		32	5.2	odd	4
1000.2.m.e.201.8		32	25.13	odd	20
1000.2.m.e.801.8		32	5.3	odd	4
1000.2.q.c.49.7		32	25.16	even	5
1000.2.q.c.449.7		32	5.4	even	2
5000.2.a.q.1.15		16	25.3	odd	20
5000.2.a.r.1.2		16	25.22	odd	20
10000.2.a.bq.1.15		16	100.47	even	20
10000.2.a.br.1.2		16	100.3	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)

\(f(q)\)	\(=\)	\(q+(-2.57764 - 0.837527i) q^{3} +(1.74676 + 1.39601i) q^{5} +0.760910i q^{7} +(3.51574 + 2.55433i) q^{9} +O(q^{10})\)	\(q+(-2.57764 - 0.837527i) q^{3} +(1.74676 + 1.39601i) q^{5} +0.760910i q^{7} +(3.51574 + 2.55433i) q^{9} +(5.24785 - 3.81279i) q^{11} +(3.36896 - 4.63698i) q^{13} +(-3.33333 - 5.06136i) q^{15} +(-2.59513 + 0.843208i) q^{17} +(1.72249 + 5.30128i) q^{19} +(0.637282 - 1.96135i) q^{21} +(1.70948 + 2.35290i) q^{23} +(1.10234 + 4.87697i) q^{25} +(-2.14378 - 2.95066i) q^{27} +(0.466898 - 1.43697i) q^{29} +(-0.669886 - 2.06170i) q^{31} +(-16.7204 + 5.43279i) q^{33} +(-1.06223 + 1.32913i) q^{35} +(0.877654 - 1.20799i) q^{37} +(-12.5676 + 9.13087i) q^{39} +(-3.64017 - 2.64474i) q^{41} -0.0184418i q^{43} +(2.57529 + 9.36980i) q^{45} +(-8.13150 - 2.64208i) q^{47} +6.42102 q^{49} +7.39552 q^{51} +(-5.02803 - 1.63371i) q^{53} +(14.4894 + 0.666007i) q^{55} -15.1074i q^{57} +(-6.40413 - 4.65287i) q^{59} +(-2.94396 + 2.13891i) q^{61} +(-1.94362 + 2.67516i) q^{63} +(12.3580 - 3.39659i) q^{65} +(4.63317 - 1.50541i) q^{67} +(-2.43582 - 7.49667i) q^{69} +(-2.25528 + 6.94103i) q^{71} +(6.59077 + 9.07141i) q^{73} +(1.24316 - 13.4943i) q^{75} +(2.90119 + 3.99314i) q^{77} +(-1.47673 + 4.54492i) q^{79} +(-0.974034 - 2.99777i) q^{81} +(4.47952 - 1.45549i) q^{83} +(-5.71018 - 2.14993i) q^{85} +(-2.40699 + 3.31294i) q^{87} +(-7.97974 + 5.79762i) q^{89} +(3.52832 + 2.56347i) q^{91} +5.87537i q^{93} +(-4.39184 + 11.6647i) q^{95} +(-0.725911 - 0.235863i) q^{97} +28.1892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 32 * q + 2 * q^5 + 10 * q^9	\( 32 q + 2 q^{5} + 10 q^{9} + 6 q^{11} + 12 q^{15} - 6 q^{19} - 4 q^{21} - 30 q^{23} + 6 q^{25} - 2 q^{29} + 6 q^{31} + 8 q^{35} - 40 q^{37} - 12 q^{39} - 12 q^{45} - 20 q^{47} - 60 q^{49} - 60 q^{51} - 30 q^{53} - 28 q^{55} - 30 q^{59} + 14 q^{61} - 20 q^{63} - 26 q^{65} - 4 q^{69} + 12 q^{71} + 40 q^{73} + 16 q^{75} + 16 q^{79} - 52 q^{81} + 30 q^{83} + 60 q^{85} + 110 q^{87} + 24 q^{89} - 4 q^{91} + 68 q^{95} + 30 q^{97} + 92 q^{99}+O(q^{100}) \) 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

Related objects

Downloads

Learn more