LMFDB - Embedded newform 425.2.j.c.149.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(149,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("425.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.j (of order $4$, degree $2$, not 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			149.5
Root			$1.52346i$ of defining polynomial
Character	$\chi$	$=$	425.149
Dual form			425.2.j.c.174.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.07061 q^{2} +(1.78436 - 1.78436i) q^{3} +2.28744 q^{4} +(3.69471 - 3.69471i) q^{6} +(-0.260895 - 0.260895i) q^{7} +0.595174 q^{8} -3.36786i q^{9} +(-1.76642 + 1.76642i) q^{11} +(4.08161 - 4.08161i) q^{12} +4.68778i q^{13} +(-0.540212 - 0.540212i) q^{14} -3.34250 q^{16} +(1.48711 + 3.84558i) q^{17} -6.97354i q^{18} -7.16938i q^{19} -0.931060 q^{21} +(-3.65758 + 3.65758i) q^{22} +(-4.73801 - 4.73801i) q^{23} +(1.06200 - 1.06200i) q^{24} +9.70657i q^{26} +(-0.656399 - 0.656399i) q^{27} +(-0.596781 - 0.596781i) q^{28} +(4.79535 + 4.79535i) q^{29} +(3.40685 + 3.40685i) q^{31} -8.11138 q^{32} +6.30387i q^{33} +(3.07922 + 7.96272i) q^{34} -7.70378i q^{36} +(1.37133 - 1.37133i) q^{37} -14.8450i q^{38} +(8.36467 + 8.36467i) q^{39} +(1.66858 - 1.66858i) q^{41} -1.92786 q^{42} -11.7105 q^{43} +(-4.04059 + 4.04059i) q^{44} +(-9.81058 - 9.81058i) q^{46} -1.65317i q^{47} +(-5.96422 + 5.96422i) q^{48} -6.86387i q^{49} +(9.51543 + 4.20836i) q^{51} +10.7230i q^{52} +6.81536 q^{53} +(-1.35915 - 1.35915i) q^{54} +(-0.155278 - 0.155278i) q^{56} +(-12.7927 - 12.7927i) q^{57} +(9.92932 + 9.92932i) q^{58} +0.484372i q^{59} +(4.86706 - 4.86706i) q^{61} +(7.05427 + 7.05427i) q^{62} +(-0.878658 + 0.878658i) q^{63} -10.1105 q^{64} +13.0529i q^{66} -1.87478i q^{67} +(3.40167 + 8.79653i) q^{68} -16.9086 q^{69} +(1.21593 + 1.21593i) q^{71} -2.00446i q^{72} +(0.202452 - 0.202452i) q^{73} +(2.83949 - 2.83949i) q^{74} -16.3995i q^{76} +0.921703 q^{77} +(17.3200 + 17.3200i) q^{78} +(-3.80821 + 3.80821i) q^{79} +7.76109 q^{81} +(3.45498 - 3.45498i) q^{82} -9.94985 q^{83} -2.12974 q^{84} -24.2479 q^{86} +17.1132 q^{87} +(-1.05133 + 1.05133i) q^{88} +4.30781 q^{89} +(1.22302 - 1.22302i) q^{91} +(-10.8379 - 10.8379i) q^{92} +12.1581 q^{93} -3.42308i q^{94} +(-14.4736 + 14.4736i) q^{96} +(-9.01275 + 9.01275i) q^{97} -14.2124i q^{98} +(5.94908 + 5.94908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} - 4 q^{3} + 12 q^{4} + 12 q^{8} - 4 q^{11} + 8 q^{12} + 4 q^{14} + 4 q^{16} + 8 q^{17} - 16 q^{21} - 20 q^{22} - 12 q^{23} - 4 q^{24} - 4 q^{27} - 4 q^{28} + 12 q^{29} - 12 q^{32} + 12 q^{34}+ \cdots - 4 q^{97}+O(q^{100}) $ 12 * q + 4 * q^2 - 4 * q^3 + 12 * q^4 + 12 * q^8 - 4 * q^11 + 8 * q^12 + 4 * q^14 + 4 * q^16 + 8 * q^17 - 16 * q^21 - 20 * q^22 - 12 * q^23 - 4 * q^24 - 4 * q^27 - 4 * q^28 + 12 * q^29 - 12 * q^32 + 12 * q^34 - 12 * q^37 + 20 * q^39 - 24 * q^41 + 16 * q^42 + 16 * q^43 - 8 * q^44 - 24 * q^46 - 20 * q^48 + 32 * q^51 - 28 * q^54 + 40 * q^56 - 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 - 28 * q^64 + 60 * q^68 + 28 * q^71 - 48 * q^73 - 28 * q^74 - 48 * q^77 + 92 * q^78 + 8 * q^79 + 28 * q^81 - 40 * q^82 - 40 * q^83 - 96 * q^86 + 48 * q^87 - 72 * q^88 - 24 * q^89 - 36 * q^91 - 16 * q^92 + 72 * q^93 - 32 * q^96 - 4 * q^97

Character values

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

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.07061			1.46414			0.732072	−	0.681227i	$-0.238553\pi$
$2$	2.07061			1.46414			0.732072	+	0.681227i	$0.238553\pi$
$3$	1.78436	−	1.78436i	1.03020	−	1.03020i	0.0306697	−	0.999530i	$-0.490236\pi$
$3$	1.78436	−	1.78436i	1.03020	−	1.03020i	0.999530	−	0.0306697i	$-0.00976400\pi$
$4$	2.28744			1.14372
$5$		0			0
$5$		0			0
$6$	3.69471	−	3.69471i	1.50836	−	1.50836i
$7$	−0.260895	−	0.260895i	−0.0986090	−	0.0986090i	0.656081	−	0.754690i	$-0.272213\pi$
$7$	−0.260895	−	0.260895i	−0.0986090	−	0.0986090i	−0.754690	+	0.656081i	$0.772213\pi$
$8$	0.595174			0.210426
$9$		−	3.36786i		−	1.12262i
$10$		0			0
$11$	−1.76642	+	1.76642i	−0.532597	+	0.532597i	−0.921344	−	0.388747i	$-0.872908\pi$
$11$	−1.76642	+	1.76642i	−0.532597	+	0.532597i	0.388747	+	0.921344i	$0.372908\pi$
$12$	4.08161	−	4.08161i	1.17826	−	1.17826i
$13$			4.68778i			1.30016i	0.759868	+	0.650078i	$0.225264\pi$
$13$			4.68778i			1.30016i	−0.759868	+	0.650078i	$0.774736\pi$
$14$	−0.540212	−	0.540212i	−0.144378	−	0.144378i
$15$		0			0
$16$	−3.34250			−0.835626
$17$	1.48711	+	3.84558i	0.360676	+	0.932691i
$17$	1.48711	+	3.84558i	0.360676	+	0.932691i
$18$		−	6.97354i		−	1.64368i
$19$		−	7.16938i		−	1.64477i	−0.568933	−	0.822384i	$-0.692644\pi$
$19$		−	7.16938i		−	1.64477i	0.568933	−	0.822384i	$-0.307356\pi$
$20$		0			0
$21$	−0.931060			−0.203174
$22$	−3.65758	+	3.65758i	−0.779799	+	0.779799i
$23$	−4.73801	−	4.73801i	−0.987943	−	0.987943i	0.0119854	−	0.999928i	$-0.496185\pi$
$23$	−4.73801	−	4.73801i	−0.987943	−	0.987943i	−0.999928	+	0.0119854i	$0.996185\pi$
$24$	1.06200	−	1.06200i	0.216780	−	0.216780i
$25$		0			0
$26$			9.70657i			1.90361i
$27$	−0.656399	−	0.656399i	−0.126324	−	0.126324i
$28$	−0.596781	−	0.596781i	−0.112781	−	0.112781i
$29$	4.79535	+	4.79535i	0.890475	+	0.890475i	0.994568	−	0.104093i	$-0.0331940\pi$
$29$	4.79535	+	4.79535i	0.890475	+	0.890475i	−0.104093	+	0.994568i	$0.533194\pi$
$30$		0			0
$31$	3.40685	+	3.40685i	0.611888	+	0.611888i	0.943438	−	0.331549i	$-0.107571\pi$
$31$	3.40685	+	3.40685i	0.611888	+	0.611888i	−0.331549	+	0.943438i	$0.607571\pi$
$32$	−8.11138			−1.43390
$33$			6.30387i			1.09736i
$34$	3.07922	+	7.96272i	0.528083	+	1.36559i
$35$		0			0
$36$		−	7.70378i		−	1.28396i
$37$	1.37133	−	1.37133i	0.225445	−	0.225445i	−0.585342	−	0.810787i	$-0.699040\pi$
$37$	1.37133	−	1.37133i	0.225445	−	0.225445i	0.810787	+	0.585342i	$0.199040\pi$
$38$		−	14.8450i		−	2.40818i
$39$	8.36467	+	8.36467i	1.33942	+	1.33942i
$40$		0			0
$41$	1.66858	−	1.66858i	0.260588	−	0.260588i	−0.564705	−	0.825293i	$-0.691010\pi$
$41$	1.66858	−	1.66858i	0.260588	−	0.260588i	0.825293	+	0.564705i	$0.191010\pi$
$42$	−1.92786			−0.297476
$43$	−11.7105			−1.78584			−0.892918	−	0.450218i	$-0.851346\pi$
$43$	−11.7105			−1.78584			−0.892918	+	0.450218i	$0.851346\pi$
$44$	−4.04059	+	4.04059i	−0.609142	+	0.609142i
$45$		0			0
$46$	−9.81058	−	9.81058i	−1.44649	−	1.44649i
$47$		−	1.65317i		−	0.241140i	−0.992705	−	0.120570i	$-0.961528\pi$
$47$		−	1.65317i		−	0.241140i	0.992705	−	0.120570i	$-0.0384723\pi$
$48$	−5.96422	+	5.96422i	−0.860861	+	0.860861i
$49$		−	6.86387i		−	0.980553i
$50$		0			0
$51$	9.51543	+	4.20836i	1.33243	+	0.589289i
$52$			10.7230i			1.48701i
$53$	6.81536			0.936162			0.468081	−	0.883686i	$-0.344946\pi$
$53$	6.81536			0.936162			0.468081	+	0.883686i	$0.344946\pi$
$54$	−1.35915	−	1.35915i	−0.184957	−	0.184957i
$55$		0			0
$56$	−0.155278	−	0.155278i	−0.0207499	−	0.0207499i
$57$	−12.7927	−	12.7927i	−1.69444	−	1.69444i
$58$	9.92932	+	9.92932i	1.30378	+	1.30378i
$59$			0.484372i			0.0630598i	0.999503	+	0.0315299i	$0.0100379\pi$
$59$			0.484372i			0.0630598i	−0.999503	+	0.0315299i	$0.989962\pi$
$60$		0			0
$61$	4.86706	−	4.86706i	0.623164	−	0.623164i	−0.323175	−	0.946339i	$-0.604750\pi$
$61$	4.86706	−	4.86706i	0.623164	−	0.623164i	0.946339	+	0.323175i	$0.104750\pi$
$62$	7.05427	+	7.05427i	0.895893	+	0.895893i
$63$	−0.878658	+	0.878658i	−0.110701	+	0.110701i
$64$	−10.1105			−1.26381
$65$		0			0
$66$			13.0529i			1.60670i
$67$		−	1.87478i		−	0.229041i	−0.993421	−	0.114520i	$-0.963467\pi$
$67$		−	1.87478i		−	0.229041i	0.993421	−	0.114520i	$-0.0365331\pi$
$68$	3.40167	+	8.79653i	0.412513	+	1.06674i
$69$	−16.9086			−2.03556
$70$		0			0
$71$	1.21593	+	1.21593i	0.144304	+	0.144304i	0.775568	−	0.631264i	$-0.217464\pi$
$71$	1.21593	+	1.21593i	0.144304	+	0.144304i	−0.631264	+	0.775568i	$0.717464\pi$
$72$		−	2.00446i		−	0.236228i
$73$	0.202452	−	0.202452i	0.0236952	−	0.0236952i	−0.695160	−	0.718855i	$-0.744666\pi$
$73$	0.202452	−	0.202452i	0.0236952	−	0.0236952i	0.718855	+	0.695160i	$0.244666\pi$
$74$	2.83949	−	2.83949i	0.330084	−	0.330084i
$75$		0			0
$76$		−	16.3995i		−	1.88115i
$77$	0.921703			0.105038
$78$	17.3200	+	17.3200i	1.96110	+	1.96110i
$79$	−3.80821	+	3.80821i	−0.428458	+	0.428458i	−0.888103	−	0.459645i	$-0.847977\pi$
$79$	−3.80821	+	3.80821i	−0.428458	+	0.428458i	0.459645	+	0.888103i	$0.347977\pi$
$80$		0			0
$81$	7.76109			0.862343
$82$	3.45498	−	3.45498i	0.381538	−	0.381538i
$83$	−9.94985			−1.09214			−0.546069	−	0.837740i	$-0.683876\pi$
$83$	−9.94985			−1.09214			−0.546069	+	0.837740i	$0.683876\pi$
$84$	−2.12974			−0.232374
$85$		0			0
$86$	−24.2479			−2.61472
$87$	17.1132			1.83473
$88$	−1.05133	+	1.05133i	−0.112072	+	0.112072i
$89$	4.30781			0.456627			0.228314	−	0.973588i	$-0.426679\pi$
$89$	4.30781			0.456627			0.228314	+	0.973588i	$0.426679\pi$
$90$		0			0
$91$	1.22302	−	1.22302i	0.128207	−	0.128207i
$92$	−10.8379	−	10.8379i	−1.12993	−	1.12993i
$93$	12.1581			1.26073
$94$		−	3.42308i		−	0.353064i
$95$		0			0
$96$	−14.4736	+	14.4736i	−1.47721	+	1.47721i
$97$	−9.01275	+	9.01275i	−0.915106	+	0.915106i	−0.996668	−	0.0815619i	$-0.974009\pi$
$97$	−9.01275	+	9.01275i	−0.915106	+	0.915106i	0.0815619	+	0.996668i	$0.474009\pi$
$98$		−	14.2124i		−	1.43567i
$99$	5.94908	+	5.94908i	0.597905	+	0.597905i
$100$		0			0
$101$	−9.08552			−0.904043			−0.452021	−	0.892007i	$-0.649297\pi$
$101$	−9.08552			−0.904043			−0.452021	+	0.892007i	$0.649297\pi$
$102$	19.7028	+	8.71389i	1.95086	+	0.862804i
$103$		−	4.77811i		−	0.470801i	−0.971898	−	0.235401i	$-0.924360\pi$
$103$		−	4.77811i		−	0.470801i	0.971898	−	0.235401i	$-0.0756402\pi$
$104$			2.79004i			0.273586i
$105$		0			0
$106$	14.1120			1.37068
$107$	−2.01673	+	2.01673i	−0.194965	+	0.194965i	−0.797837	−	0.602873i	$-0.794023\pi$
$107$	−2.01673	+	2.01673i	−0.194965	+	0.194965i	0.602873	+	0.797837i	$0.294023\pi$
$108$	−1.50147	−	1.50147i	−0.144479	−	0.144479i
$109$	6.68119	−	6.68119i	0.639942	−	0.639942i	−0.310599	−	0.950541i	$-0.600530\pi$
$109$	6.68119	−	6.68119i	0.639942	−	0.639942i	0.950541	+	0.310599i	$0.100530\pi$
$110$		0			0
$111$		−	4.89387i		−	0.464506i
$112$	0.872042	+	0.872042i	0.0824002	+	0.0824002i
$113$	7.55112	+	7.55112i	0.710349	+	0.710349i	0.966608	−	0.256259i	$-0.0824900\pi$
$113$	7.55112	+	7.55112i	0.710349	+	0.710349i	−0.256259	+	0.966608i	$0.582490\pi$
$114$	−26.4888	−	26.4888i	−2.48090	−	2.48090i
$115$		0			0
$116$	10.9691	+	10.9691i	1.01845	+	1.01845i
$117$	15.7878			1.45958
$118$			1.00295i			0.0923287i
$119$	0.615314	−	1.39127i	0.0564058	−	0.127538i
$120$		0			0
$121$			4.75949i			0.432681i
$122$	10.0778	−	10.0778i	0.912402	−	0.912402i
$123$		−	5.95468i		−	0.536915i
$124$	7.79296	+	7.79296i	0.699829	+	0.699829i
$125$		0			0
$126$	−1.81936	+	1.81936i	−0.162082	+	0.162082i
$127$	−15.7315			−1.39595			−0.697974	−	0.716124i	$-0.745915\pi$
$127$	−15.7315			−1.39595			−0.697974	+	0.716124i	$0.745915\pi$
$128$	−4.71221			−0.416505
$129$	−20.8957	+	20.8957i	−1.83977	+	1.83977i
$130$		0			0
$131$	−2.89320	−	2.89320i	−0.252780	−	0.252780i	0.569329	−	0.822109i	$-0.307203\pi$
$131$	−2.89320	−	2.89320i	−0.252780	−	0.252780i	−0.822109	+	0.569329i	$0.807203\pi$
$132$			14.4197i			1.25507i
$133$	−1.87045	+	1.87045i	−0.162189	+	0.162189i
$134$		−	3.88194i		−	0.335348i
$135$		0			0
$136$	0.885087	+	2.28879i	0.0758956	+	0.196262i
$137$		−	16.2144i		−	1.38529i	−0.721280	−	0.692644i	$-0.756446\pi$
$137$		−	16.2144i		−	1.38529i	0.721280	−	0.692644i	$-0.243554\pi$
$138$	−35.0112			−2.98035
$139$	−7.57109	−	7.57109i	−0.642172	−	0.642172i	0.308917	−	0.951089i	$-0.400033\pi$
$139$	−7.57109	−	7.57109i	−0.642172	−	0.642172i	−0.951089	+	0.308917i	$0.900033\pi$
$140$		0			0
$141$	−2.94985	−	2.94985i	−0.248422	−	0.248422i
$142$	2.51772	+	2.51772i	0.211282	+	0.211282i
$143$	−8.28060	−	8.28060i	−0.692459	−	0.692459i
$144$			11.2571i			0.938091i
$145$		0			0
$146$	0.419200	−	0.419200i	0.0346932	−	0.0346932i
$147$	−12.2476	−	12.2476i	−1.01016	−	1.01016i
$148$	3.13683	−	3.13683i	0.257845	−	0.257845i
$149$	11.1290			0.911719			0.455860	−	0.890052i	$-0.349332\pi$
$149$	11.1290			0.911719			0.455860	+	0.890052i	$0.349332\pi$
$150$		0			0
$151$		−	16.0861i		−	1.30907i	−0.756032	−	0.654535i	$-0.772865\pi$
$151$		−	16.0861i		−	1.30907i	0.756032	−	0.654535i	$-0.227135\pi$
$152$		−	4.26702i		−	0.346101i
$153$	12.9514	−	5.00837i	1.04706	−	0.404903i
$154$	1.90849			0.153790
$155$		0			0
$156$	19.1337	+	19.1337i	1.53192	+	1.53192i
$157$		−	2.63326i		−	0.210157i	−0.994464	−	0.105079i	$-0.966491\pi$
$157$		−	2.63326i		−	0.210157i	0.994464	−	0.105079i	$-0.0335094\pi$
$158$	−7.88534	+	7.88534i	−0.627324	+	0.627324i
$159$	12.1610	−	12.1610i	0.964434	−	0.964434i
$160$		0			0
$161$			2.47224i			0.194840i
$162$	16.0702			1.26259
$163$	13.5013	+	13.5013i	1.05751	+	1.05751i	0.998242	+	0.0592626i	$0.0188749\pi$
$163$	13.5013	+	13.5013i	1.05751	+	1.05751i	0.0592626	+	0.998242i	$0.481125\pi$
$164$	3.81677	−	3.81677i	0.298039	−	0.298039i
$165$		0			0
$166$	−20.6023			−1.59905
$167$	−2.81953	+	2.81953i	−0.218182	+	0.218182i	−0.807732	−	0.589550i	$-0.799305\pi$
$167$	−2.81953	+	2.81953i	−0.218182	+	0.218182i	0.589550	+	0.807732i	$0.299305\pi$
$168$	−0.554142			−0.0427530
$169$	−8.97524			−0.690403
$170$		0			0
$171$	−24.1455			−1.84645
$172$	−26.7871			−2.04250
$173$	−10.3293	+	10.3293i	−0.785322	+	0.785322i	−0.980723	−	0.195401i	$-0.937399\pi$
$173$	−10.3293	+	10.3293i	−0.785322	+	0.785322i	0.195401	+	0.980723i	$0.437399\pi$
$174$	35.4349			2.68631
$175$		0			0
$176$	5.90428	−	5.90428i	0.445052	−	0.445052i
$177$	0.864292	+	0.864292i	0.0649642	+	0.0649642i
$178$	8.91981			0.668568
$179$		−	14.7452i		−	1.10211i	−0.834469	−	0.551054i	$-0.814226\pi$
$179$		−	14.7452i		−	1.10211i	0.834469	−	0.551054i	$-0.185774\pi$
$180$		0			0
$181$	7.96307	−	7.96307i	0.591890	−	0.591890i	−0.346252	−	0.938142i	$-0.612546\pi$
$181$	7.96307	−	7.96307i	0.591890	−	0.591890i	0.938142	+	0.346252i	$0.112546\pi$
$182$	2.53239	−	2.53239i	0.187714	−	0.187714i
$183$		−	17.3692i		−	1.28397i
$184$	−2.81994	−	2.81994i	−0.207888	−	0.207888i
$185$		0			0
$186$	25.1747			1.84590
$187$	−9.41980	−	4.16607i	−0.688844	−	0.304653i
$188$		−	3.78153i		−	0.275797i
$189$			0.342503i			0.0249134i
$190$		0			0
$191$	21.4934			1.55521			0.777604	−	0.628754i	$-0.216435\pi$
$191$	21.4934			1.55521			0.777604	+	0.628754i	$0.216435\pi$
$192$	−18.0408	+	18.0408i	−1.30198	+	1.30198i
$193$	1.00556	+	1.00556i	0.0723819	+	0.0723819i	0.742371	−	0.669989i	$-0.233701\pi$
$193$	1.00556	+	1.00556i	0.0723819	+	0.0723819i	−0.669989	+	0.742371i	$0.733701\pi$
$194$	−18.6619	+	18.6619i	−1.33985	+	1.33985i
$195$		0			0
$196$		−	15.7007i		−	1.12148i
$197$	12.3127	+	12.3127i	0.877240	+	0.877240i	0.993248	−	0.116008i	$-0.0370098\pi$
$197$	12.3127	+	12.3127i	0.877240	+	0.877240i	−0.116008	+	0.993248i	$0.537010\pi$
$198$	12.3182	+	12.3182i	0.875419	+	0.875419i
$199$	12.6485	+	12.6485i	0.896626	+	0.896626i	0.995136	−	0.0985101i	$-0.0314077\pi$
$199$	12.6485	+	12.6485i	0.896626	+	0.896626i	−0.0985101	+	0.995136i	$0.531408\pi$
$200$		0			0
$201$	−3.34527	−	3.34527i	−0.235957	−	0.235957i
$202$	−18.8126			−1.32365
$203$		−	2.50217i		−	0.175618i
$204$	21.7660	+	9.62637i	1.52392	+	0.673981i
$205$		0			0
$206$		−	9.89362i		−	0.689321i
$207$	−15.9570	+	15.9570i	−1.10909	+	1.10909i
$208$		−	15.6689i		−	1.08644i
$209$	12.6642	+	12.6642i	0.875999	+	0.875999i
$210$		0			0
$211$	−5.07688	+	5.07688i	−0.349507	+	0.349507i	−0.859926	−	0.510419i	$-0.829490\pi$
$211$	−5.07688	+	5.07688i	−0.349507	+	0.349507i	0.510419	+	0.859926i	$0.329490\pi$
$212$	15.5897			1.07071
$213$	4.33930			0.297324
$214$	−4.17587	+	4.17587i	−0.285457	+	0.285457i
$215$		0			0
$216$	−0.390672	−	0.390672i	−0.0265818	−	0.0265818i
$217$		−	1.77766i		−	0.120675i
$218$	13.8342	−	13.8342i	0.936967	−	0.936967i
$219$		−	0.722494i		−	0.0488216i
$220$		0			0
$221$	−18.0272	+	6.97123i	−1.21264	+	0.468935i
$222$		−	10.1333i		−	0.680104i
$223$	3.93334			0.263396			0.131698	−	0.991290i	$-0.457957\pi$
$223$	3.93334			0.263396			0.131698	+	0.991290i	$0.457957\pi$
$224$	2.11622	+	2.11622i	0.141396	+	0.141396i
$225$		0			0
$226$	15.6354	+	15.6354i	1.04005	+	1.04005i
$227$	2.46062	+	2.46062i	0.163317	+	0.163317i	0.784034	−	0.620717i	$-0.213159\pi$
$227$	2.46062	+	2.46062i	0.163317	+	0.163317i	−0.620717	+	0.784034i	$0.713159\pi$
$228$	−29.2626	−	29.2626i	−1.93796	−	1.93796i
$229$		−	4.41164i		−	0.291529i	−0.989319	−	0.145765i	$-0.953436\pi$
$229$		−	4.41164i		−	0.291529i	0.989319	−	0.145765i	$-0.0465642\pi$
$230$		0			0
$231$	1.64465	−	1.64465i	0.108210	−	0.108210i
$232$	2.85407	+	2.85407i	0.187379	+	0.187379i
$233$	−11.0779	+	11.0779i	−0.725739	+	0.725739i	−0.969768	−	0.244029i	$-0.921531\pi$
$233$	−11.0779	+	11.0779i	−0.725739	+	0.725739i	0.244029	+	0.969768i	$0.421531\pi$
$234$	32.6904			2.13704
$235$		0			0
$236$			1.10797i			0.0721227i
$237$			13.5904i			0.882793i
$238$	1.27408	−	2.88079i	0.0825862	−	0.186734i
$239$	6.59116			0.426346			0.213173	−	0.977014i	$-0.431620\pi$
$239$	6.59116			0.426346			0.213173	+	0.977014i	$0.431620\pi$
$240$		0			0
$241$	3.09742	+	3.09742i	0.199523	+	0.199523i	0.799795	−	0.600273i	$-0.204941\pi$
$241$	3.09742	+	3.09742i	0.199523	+	0.199523i	−0.600273	+	0.799795i	$0.704941\pi$
$242$			9.85506i			0.633507i
$243$	15.8178	−	15.8178i	1.01471	−	1.01471i
$244$	11.1331	−	11.1331i	0.712724	−	0.712724i
$245$		0			0
$246$		−	12.3298i		−	0.786121i
$247$	33.6084			2.13845
$248$	2.02767	+	2.02767i	0.128757	+	0.128757i
$249$	−17.7541	+	17.7541i	−1.12512	+	1.12512i
$250$		0			0
$251$	−4.30290			−0.271597			−0.135798	−	0.990736i	$-0.543360\pi$
$251$	−4.30290			−0.271597			−0.135798	+	0.990736i	$0.543360\pi$
$252$	−2.00988	+	2.00988i	−0.126610	+	0.126610i
$253$	16.7387			1.05235
$254$	−32.5739			−2.04387
$255$		0			0
$256$	10.4639			0.653991
$257$	10.5366			0.657254			0.328627	−	0.944460i	$-0.393414\pi$
$257$	10.5366			0.657254			0.328627	+	0.944460i	$0.393414\pi$
$258$	−43.2670	+	43.2670i	−2.69369	+	2.69369i
$259$	−0.715544			−0.0444618
$260$		0			0
$261$	16.1501	−	16.1501i	0.999665	−	0.999665i
$262$	−5.99070	−	5.99070i	−0.370107	−	0.370107i
$263$	13.6253			0.840173			0.420086	−	0.907484i	$-0.362000\pi$
$263$	13.6253			0.840173			0.420086	+	0.907484i	$0.362000\pi$
$264$			3.75189i			0.230913i
$265$		0			0
$266$	−3.87299	+	3.87299i	−0.237468	+	0.237468i
$267$	7.68668	−	7.68668i	0.470417	−	0.470417i
$268$		−	4.28844i		−	0.261958i
$269$	−11.0360	−	11.0360i	−0.672878	−	0.672878i	0.285501	−	0.958378i	$-0.407840\pi$
$269$	−11.0360	−	11.0360i	−0.672878	−	0.672878i	−0.958378	+	0.285501i	$0.907840\pi$
$270$		0			0
$271$	−9.66560			−0.587143			−0.293572	−	0.955937i	$-0.594844\pi$
$271$	−9.66560			−0.587143			−0.293572	+	0.955937i	$0.594844\pi$
$272$	−4.97066	−	12.8539i	−0.301391	−	0.779381i
$273$		−	4.36460i		−	0.264158i
$274$		−	33.5737i		−	2.02826i
$275$		0			0
$276$	−38.6774			−2.32810
$277$	0.955063	−	0.955063i	0.0573842	−	0.0573842i	−0.677832	−	0.735217i	$-0.737080\pi$
$277$	0.955063	−	0.955063i	0.0573842	−	0.0573842i	0.735217	+	0.677832i	$0.237080\pi$
$278$	−15.6768	−	15.6768i	−0.940232	−	0.940232i
$279$	11.4738	−	11.4738i	0.686919	−	0.686919i
$280$		0			0
$281$		−	15.8582i		−	0.946020i	−0.881057	−	0.473010i	$-0.843167\pi$
$281$		−	15.8582i		−	0.946020i	0.881057	−	0.473010i	$-0.156833\pi$
$282$	−6.10801	−	6.10801i	−0.363726	−	0.363726i
$283$	−20.7458	−	20.7458i	−1.23321	−	1.23321i	−0.962725	−	0.270483i	$-0.912816\pi$
$283$	−20.7458	−	20.7458i	−1.23321	−	1.23321i	−0.270483	−	0.962725i	$-0.587184\pi$
$284$	2.78136	+	2.78136i	0.165044	+	0.165044i
$285$		0			0
$286$	−17.1459	−	17.1459i	−1.01386	−	1.01386i
$287$	−0.870646			−0.0513926
$288$			27.3180i			1.60973i
$289$	−12.5770	+	11.4376i	−0.739825	+	0.672799i
$290$		0			0
$291$			32.1639i			1.88548i
$292$	0.463096	−	0.463096i	0.0271007	−	0.0271007i
$293$			20.6478i			1.20626i	0.797644	+	0.603129i	$0.206080\pi$
$293$			20.6478i			1.20626i	−0.797644	+	0.603129i	$0.793920\pi$
$294$	−25.3600	−	25.3600i	−1.47903	−	1.47903i
$295$		0			0
$296$	0.816177	−	0.816177i	0.0474393	−	0.0474393i
$297$	2.31896			0.134560
$298$	23.0437			1.33489
$299$	22.2107	−	22.2107i	1.28448	−	1.28448i
$300$		0			0
$301$	3.05521	+	3.05521i	0.176100	+	0.176100i
$302$		−	33.3081i		−	1.91667i
$303$	−16.2118	+	16.2118i	−0.931344	+	0.931344i
$304$			23.9637i			1.37441i
$305$		0			0
$306$	26.8173	−	10.3704i	1.53305	−	0.592837i
$307$			16.3437i			0.932787i	0.884577	+	0.466393i	$0.154447\pi$
$307$			16.3437i			0.932787i	−0.884577	+	0.466393i	$0.845553\pi$
$308$	2.10834			0.120134
$309$	−8.52586	−	8.52586i	−0.485019	−	0.485019i
$310$		0			0
$311$	24.8266	+	24.8266i	1.40778	+	1.40778i	0.771238	+	0.636547i	$0.219638\pi$
$311$	24.8266	+	24.8266i	1.40778	+	1.40778i	0.636547	+	0.771238i	$0.280362\pi$
$312$	4.97843	+	4.97843i	0.281848	+	0.281848i
$313$	−22.1419	−	22.1419i	−1.25153	−	1.25153i	−0.955032	−	0.296502i	$-0.904180\pi$
$313$	−22.1419	−	22.1419i	−1.25153	−	1.25153i	−0.296502	−	0.955032i	$-0.595820\pi$
$314$		−	5.45247i		−	0.307701i
$315$		0			0
$316$	−8.71105	+	8.71105i	−0.490035	+	0.490035i
$317$	8.87399	+	8.87399i	0.498413	+	0.498413i	0.910944	−	0.412531i	$-0.135355\pi$
$317$	8.87399	+	8.87399i	0.498413	+	0.498413i	−0.412531	+	0.910944i	$0.635355\pi$
$318$	25.1808	−	25.1808i	1.41207	−	1.41207i
$319$	−16.9413			−0.948528
$320$		0			0
$321$			7.19714i			0.401705i
$322$			5.11906i			0.285274i
$323$	27.5704	−	10.6616i	1.53406	−	0.593229i
$324$	17.7530			0.986278
$325$		0			0
$326$	27.9560	+	27.9560i	1.54834	+	1.54834i
$327$		−	23.8433i		−	1.31854i
$328$	0.993093	−	0.993093i	0.0548344	−	0.0548344i
$329$	−0.431305	+	0.431305i	−0.0237786	+	0.0237786i
$330$		0			0
$331$		−	0.497450i		−	0.0273423i	−0.999907	−	0.0136712i	$-0.995648\pi$
$331$		−	0.497450i		−	0.0273423i	0.999907	−	0.0136712i	$-0.00435180\pi$
$332$	−22.7597			−1.24910
$333$	−4.61844	−	4.61844i	−0.253089	−	0.253089i
$334$	−5.83816	+	5.83816i	−0.319450	+	0.319450i
$335$		0			0
$336$	3.11207			0.169777
$337$	23.7358	−	23.7358i	1.29297	−	1.29297i	0.360031	−	0.932940i	$-0.382766\pi$
$337$	23.7358	−	23.7358i	1.29297	−	1.29297i	0.932940	−	0.360031i	$-0.117234\pi$
$338$	−18.5843			−1.01085
$339$	26.9478			1.46360
$340$		0			0
$341$	−12.0359			−0.651780
$342$	−49.9959			−2.70347
$343$	−3.61701	+	3.61701i	−0.195300	+	0.195300i
$344$	−6.96979			−0.375786
$345$		0			0
$346$	−21.3880	+	21.3880i	−1.14983	+	1.14983i
$347$	18.5976	+	18.5976i	0.998370	+	0.998370i	0.999999	−	0.00162819i	$-0.000518270\pi$
$347$	18.5976	+	18.5976i	0.998370	+	0.998370i	−0.00162819	+	0.999999i	$0.500518\pi$
$348$	39.1455			2.09842
$349$		−	16.7865i		−	0.898560i	−0.893391	−	0.449280i	$-0.851681\pi$
$349$		−	16.7865i		−	0.898560i	0.893391	−	0.449280i	$-0.148319\pi$
$350$		0			0
$351$	3.07705	−	3.07705i	0.164241	−	0.164241i
$352$	14.3281	−	14.3281i	0.763692	−	0.763692i
$353$			23.4532i			1.24829i	0.781309	+	0.624144i	$0.214552\pi$
$353$			23.4532i			1.24829i	−0.781309	+	0.624144i	$0.785448\pi$
$354$	1.78962	+	1.78962i	0.0951170	+	0.0951170i
$355$		0			0
$356$	9.85386			0.522253
$357$	−1.38459	−	3.58047i	−0.0732800	−	0.189498i
$358$		−	30.5316i		−	1.61365i
$359$			18.1568i			0.958279i	0.877739	+	0.479139i	$0.159051\pi$
$359$			18.1568i			0.958279i	−0.877739	+	0.479139i	$0.840949\pi$
$360$		0			0
$361$	−32.4000			−1.70526
$362$	16.4884	−	16.4884i	0.866613	−	0.866613i
$363$	8.49263	+	8.49263i	0.445747	+	0.445747i
$364$	2.79758	−	2.79758i	0.146633	−	0.146633i
$365$		0			0
$366$		−	35.9648i		−	1.87991i
$367$	−9.68061	−	9.68061i	−0.505324	−	0.505324i	0.407764	−	0.913087i	$-0.366309\pi$
$367$	−9.68061	−	9.68061i	−0.505324	−	0.505324i	−0.913087	+	0.407764i	$0.866309\pi$
$368$	15.8368	+	15.8368i	0.825550	+	0.825550i
$369$	−5.61954	−	5.61954i	−0.292541	−	0.292541i
$370$		0			0
$371$	−1.77809	−	1.77809i	−0.0923140	−	0.0923140i
$372$	27.8109			1.44193
$373$			10.1594i			0.526035i	0.964791	+	0.263018i	$0.0847177\pi$
$373$			10.1594i			0.526035i	−0.964791	+	0.263018i	$0.915282\pi$
$374$	−19.5048	−	8.62632i	−1.00857	−	0.446056i
$375$		0			0
$376$		−	0.983925i		−	0.0507421i
$377$	−22.4795	+	22.4795i	−1.15775	+	1.15775i
$378$			0.709190i			0.0364768i
$379$	2.94447	+	2.94447i	0.151247	+	0.151247i	0.778675	−	0.627428i	$-0.215892\pi$
$379$	2.94447	+	2.94447i	0.151247	+	0.151247i	−0.627428	+	0.778675i	$0.715892\pi$
$380$		0			0
$381$	−28.0707	+	28.0707i	−1.43810	+	1.43810i
$382$	44.5045			2.27705
$383$	0.813273			0.0415563			0.0207782	−	0.999784i	$-0.493386\pi$
$383$	0.813273			0.0415563			0.0207782	+	0.999784i	$0.493386\pi$
$384$	−8.40828	+	8.40828i	−0.429083	+	0.429083i
$385$		0			0
$386$	2.08213	+	2.08213i	0.105978	+	0.105978i
$387$			39.4394i			2.00482i
$388$	−20.6161	+	20.6161i	−1.04662	+	1.04662i
$389$			3.11676i			0.158026i	0.996874	+	0.0790131i	$0.0251769\pi$
$389$			3.11676i			0.158026i	−0.996874	+	0.0790131i	$0.974823\pi$
$390$		0			0
$391$	11.1745	−	25.2663i	0.565118	−	1.27777i
$392$		−	4.08519i		−	0.206333i
$393$	−10.3250			−0.520828
$394$	25.4947	+	25.4947i	1.28441	+	1.28441i
$395$		0			0
$396$	13.6081	+	13.6081i	0.683835	+	0.683835i
$397$	11.5998	+	11.5998i	0.582177	+	0.582177i	0.935501	−	0.353324i	$-0.114949\pi$
$397$	11.5998	+	11.5998i	0.582177	+	0.582177i	−0.353324	+	0.935501i	$0.614949\pi$
$398$	26.1901	+	26.1901i	1.31279	+	1.31279i
$399$			6.67512i			0.334174i
$400$		0			0
$401$	10.2143	−	10.2143i	0.510075	−	0.510075i	−0.404474	−	0.914549i	$-0.632545\pi$
$401$	10.2143	−	10.2143i	0.510075	−	0.510075i	0.914549	+	0.404474i	$0.132545\pi$
$402$	−6.92677	−	6.92677i	−0.345476	−	0.345476i
$403$	−15.9706	+	15.9706i	−0.795550	+	0.795550i
$404$	−20.7826			−1.03397
$405$		0			0
$406$		−	5.18102i		−	0.257130i
$407$			4.84469i			0.240142i
$408$	5.66333	+	2.50471i	0.280377	+	0.124001i
$409$	−32.2867			−1.59648			−0.798238	−	0.602342i	$-0.794235\pi$
$409$	−32.2867			−1.59648			−0.798238	+	0.602342i	$0.794235\pi$
$410$		0			0
$411$	−28.9323	−	28.9323i	−1.42712	−	1.42712i
$412$		−	10.9296i		−	0.538464i
$413$	0.126370	−	0.126370i	0.00621827	−	0.00621827i
$414$	−33.0407	+	33.0407i	−1.62386	+	1.62386i
$415$		0			0
$416$		−	38.0243i		−	1.86430i
$417$	−27.0191			−1.32313
$418$	26.2226	+	26.2226i	1.28259	+	1.28259i
$419$	−13.3485	+	13.3485i	−0.652115	+	0.652115i	−0.953502	−	0.301387i	$-0.902550\pi$
$419$	−13.3485	+	13.3485i	−0.652115	+	0.652115i	0.301387	+	0.953502i	$0.402550\pi$
$420$		0			0
$421$	−2.06006			−0.100401			−0.0502006	−	0.998739i	$-0.515986\pi$
$421$	−2.06006			−0.100401			−0.0502006	+	0.998739i	$0.515986\pi$
$422$	−10.5122	+	10.5122i	−0.511728	+	0.511728i
$423$	−5.56766			−0.270709
$424$	4.05632			0.196993
$425$		0			0
$426$	8.98502			0.435326
$427$	−2.53958			−0.122899
$428$	−4.61315	+	4.61315i	−0.222985	+	0.222985i
$429$	−29.5511			−1.42674
$430$		0			0
$431$	−2.63581	+	2.63581i	−0.126962	+	0.126962i	−0.767733	−	0.640770i	$-0.778615\pi$
$431$	−2.63581	+	2.63581i	−0.126962	+	0.126962i	0.640770	+	0.767733i	$0.278615\pi$
$432$	2.19402	+	2.19402i	0.105560	+	0.105560i
$433$	−27.9634			−1.34383			−0.671917	−	0.740626i	$-0.734529\pi$
$433$	−27.9634			−1.34383			−0.671917	+	0.740626i	$0.734529\pi$
$434$		−	3.68085i		−	0.176686i
$435$		0			0
$436$	15.2828	−	15.2828i	0.731914	−	0.731914i
$437$	−33.9686	+	33.9686i	−1.62494	+	1.62494i
$438$		−	1.49600i		−	0.0714819i
$439$	−8.87022	−	8.87022i	−0.423353	−	0.423353i	0.463004	−	0.886356i	$-0.346772\pi$
$439$	−8.87022	−	8.87022i	−0.423353	−	0.423353i	−0.886356	+	0.463004i	$0.846772\pi$
$440$		0			0
$441$	−23.1166			−1.10079
$442$	−37.3274	+	14.4347i	−1.77548	+	0.686589i
$443$			19.9529i			0.947991i	0.880527	+	0.473995i	$0.157189\pi$
$443$			19.9529i			0.947991i	−0.880527	+	0.473995i	$0.842811\pi$
$444$		−	11.1944i		−	0.531264i
$445$		0			0
$446$	8.14442			0.385649
$447$	19.8580	−	19.8580i	0.939252	−	0.939252i
$448$	2.63778	+	2.63778i	0.124624	+	0.124624i
$449$	−14.2737	+	14.2737i	−0.673618	+	0.673618i	−0.958548	−	0.284930i	$-0.908030\pi$
$449$	−14.2737	+	14.2737i	−0.673618	+	0.673618i	0.284930	+	0.958548i	$0.408030\pi$
$450$		0			0
$451$			5.89483i			0.277577i
$452$	17.2727	+	17.2727i	0.812440	+	0.812440i
$453$	−28.7034	−	28.7034i	−1.34860	−	1.34860i
$454$	5.09499	+	5.09499i	0.239120	+	0.239120i
$455$		0			0
$456$	−7.61389	−	7.61389i	−0.356553	−	0.356553i
$457$	−37.7391			−1.76536			−0.882681	−	0.469973i	$-0.844263\pi$
$457$	−37.7391			−1.76536			−0.882681	+	0.469973i	$0.844263\pi$
$458$		−	9.13479i		−	0.426841i
$459$	1.54810	−	3.50038i	0.0722592	−	0.163384i
$460$		0			0
$461$			38.1740i			1.77794i	0.457966	+	0.888970i	$0.348578\pi$
$461$			38.1740i			1.77794i	−0.457966	+	0.888970i	$0.651422\pi$
$462$	3.40543	−	3.40543i	0.158435	−	0.158435i
$463$		−	13.1481i		−	0.611044i	−0.952185	−	0.305522i	$-0.901169\pi$
$463$		−	13.1481i		−	0.611044i	0.952185	−	0.305522i	$-0.0988310\pi$
$464$	−16.0285	−	16.0285i	−0.744103	−	0.744103i
$465$		0			0
$466$	−22.9381	+	22.9381i	−1.06259	+	1.06259i
$467$	16.2167			0.750422			0.375211	−	0.926940i	$-0.377570\pi$
$467$	16.2167			0.750422			0.375211	+	0.926940i	$0.377570\pi$
$468$	36.1136			1.66935
$469$	−0.489120	+	0.489120i	−0.0225855	+	0.0225855i
$470$		0			0
$471$	−4.69869	−	4.69869i	−0.216504	−	0.216504i
$472$			0.288285i			0.0132694i
$473$	20.6857	−	20.6857i	0.951132	−	0.951132i
$474$			28.1405i			1.29254i
$475$		0			0
$476$	1.40749	−	3.18245i	0.0645124	−	0.145867i
$477$		−	22.9532i		−	1.05096i
$478$	13.6477			0.624233
$479$	−1.46724	−	1.46724i	−0.0670398	−	0.0670398i	0.672792	−	0.739832i	$-0.265095\pi$
$479$	−1.46724	−	1.46724i	−0.0670398	−	0.0670398i	−0.739832	+	0.672792i	$0.765095\pi$
$480$		0			0
$481$	6.42847	+	6.42847i	0.293113	+	0.293113i
$482$	6.41356	+	6.41356i	0.292130	+	0.292130i
$483$	4.41137	+	4.41137i	0.200724	+	0.200724i
$484$			10.8870i			0.494865i
$485$		0			0
$486$	32.7524	−	32.7524i	1.48568	−	1.48568i
$487$	−16.9890	−	16.9890i	−0.769843	−	0.769843i	0.208236	−	0.978079i	$-0.433228\pi$
$487$	−16.9890	−	16.9890i	−0.769843	−	0.769843i	−0.978079	+	0.208236i	$0.933228\pi$
$488$	2.89675	−	2.89675i	0.131130	−	0.131130i
$489$	48.1824			2.17888
$490$		0			0
$491$			22.3803i			1.01001i	0.863116	+	0.505005i	$0.168509\pi$
$491$			22.3803i			1.01001i	−0.863116	+	0.505005i	$0.831491\pi$
$492$		−	13.6210i		−	0.614080i
$493$	−11.3097	+	25.5721i	−0.509364	+	1.15171i
$494$	69.5901			3.13100
$495$		0			0
$496$	−11.3874	−	11.3874i	−0.511310	−	0.511310i
$497$		−	0.634459i		−	0.0284594i
$498$	−36.7619	+	36.7619i	−1.64734	+	1.64734i
$499$	2.61493	−	2.61493i	0.117060	−	0.117060i	−0.646150	−	0.763210i	$-0.723622\pi$
$499$	2.61493	−	2.61493i	0.117060	−	0.117060i	0.763210	+	0.646150i	$0.223622\pi$
$500$		0			0
$501$			10.0621i			0.449541i
$502$	−8.90965			−0.397657
$503$	13.0544	+	13.0544i	0.582066	+	0.582066i	0.935471	−	0.353404i	$-0.114976\pi$
$503$	13.0544	+	13.0544i	0.582066	+	0.582066i	−0.353404	+	0.935471i	$0.614976\pi$
$504$	−0.522954	+	0.522954i	−0.0232942	+	0.0232942i
$505$		0			0
$506$	34.6593			1.54079
$507$	−16.0150	+	16.0150i	−0.711253	+	0.711253i
$508$	−35.9849			−1.59657
$509$	17.3588			0.769415			0.384708	−	0.923039i	$-0.374302\pi$
$509$	17.3588			0.769415			0.384708	+	0.923039i	$0.374302\pi$
$510$		0			0
$511$	−0.105637			−0.00467312
$512$	31.0910			1.37404
$513$	−4.70598	+	4.70598i	−0.207774	+	0.207774i
$514$	21.8172			0.962314
$515$		0			0
$516$	−47.7977	+	47.7977i	−2.10418	+	2.10418i
$517$	2.92021	+	2.92021i	0.128431	+	0.128431i
$518$	−1.48162			−0.0650984
$519$			36.8623i			1.61808i
$520$		0			0
$521$	9.87476	−	9.87476i	0.432621	−	0.432621i	−0.456898	−	0.889519i	$-0.651040\pi$
$521$	9.87476	−	9.87476i	0.432621	−	0.432621i	0.889519	+	0.456898i	$0.151040\pi$
$522$	33.4406	−	33.4406i	1.46365	−	1.46365i
$523$		−	5.59638i		−	0.244712i	−0.992486	−	0.122356i	$-0.960955\pi$
$523$		−	5.59638i		−	0.244712i	0.992486	−	0.122356i	$-0.0390450\pi$
$524$	−6.61802	−	6.61802i	−0.289109	−	0.289109i
$525$		0			0
$526$	28.2127			1.23013
$527$	−8.03498	+	18.1677i	−0.350009	+	0.791397i
$528$		−	21.0707i		−	0.916984i
$529$			21.8974i			0.952062i
$530$		0			0
$531$	1.63130			0.0707923
$532$	−4.27855	+	4.27855i	−0.185499	+	0.185499i
$533$	7.82191	+	7.82191i	0.338805	+	0.338805i
$534$	15.9161	−	15.9161i	0.688759	−	0.688759i
$535$		0			0
$536$		−	1.11582i		−	0.0481960i
$537$	−26.3107	−	26.3107i	−1.13539	−	1.13539i
$538$	−22.8513	−	22.8513i	−0.985190	−	0.985190i
$539$	12.1245	+	12.1245i	0.522239	+	0.522239i
$540$		0			0
$541$	27.6477	+	27.6477i	1.18867	+	1.18867i	0.977436	+	0.211234i	$0.0677481\pi$
$541$	27.6477	+	27.6477i	1.18867	+	1.18867i	0.211234	+	0.977436i	$0.432252\pi$
$542$	−20.0137			−0.859662
$543$		−	28.4179i		−	1.21953i
$544$	−12.0625	−	31.1930i	−0.517175	−	1.33739i
$545$		0			0
$546$		−	9.03740i		−	0.386765i
$547$	−20.7878	+	20.7878i	−0.888823	+	0.888823i	−0.994410	−	0.105588i	$-0.966328\pi$
$547$	−20.7878	+	20.7878i	−0.888823	+	0.888823i	0.105588	+	0.994410i	$0.466328\pi$
$548$		−	37.0894i		−	1.58438i
$549$	−16.3916	−	16.3916i	−0.699577	−	0.699577i
$550$		0			0
$551$	34.3797	−	34.3797i	1.46462	−	1.46462i
$552$	−10.0635			−0.428333
$553$	1.98709			0.0844995
$554$	1.97757	−	1.97757i	0.0840187	−	0.0840187i
$555$		0			0
$556$	−17.3184	−	17.3184i	−0.734464	−	0.734464i
$557$		−	27.9399i		−	1.18385i	−0.805992	−	0.591927i	$-0.798368\pi$
$557$		−	27.9399i		−	1.18385i	0.805992	−	0.591927i	$-0.201632\pi$
$558$	23.7578	−	23.7578i	1.00575	−	1.00575i
$559$		−	54.8963i		−	2.32186i
$560$		0			0
$561$	−24.2420	+	9.37453i	−1.02350	+	0.395793i
$562$		−	32.8362i		−	1.38511i
$563$	11.2994			0.476213			0.238106	−	0.971239i	$-0.423473\pi$
$563$	11.2994			0.476213			0.238106	+	0.971239i	$0.423473\pi$
$564$	−6.74761	−	6.74761i	−0.284126	−	0.284126i
$565$		0			0
$566$	−42.9565	−	42.9565i	−1.80559	−	1.80559i
$567$	−2.02483	−	2.02483i	−0.0850348	−	0.0850348i
$568$	0.723689	+	0.723689i	0.0303653	+	0.0303653i
$569$			12.1204i			0.508114i	0.967189	+	0.254057i	$0.0817650\pi$
$569$			12.1204i			0.508114i	−0.967189	+	0.254057i	$0.918235\pi$
$570$		0			0
$571$	−7.74264	+	7.74264i	−0.324019	+	0.324019i	−0.850307	−	0.526287i	$-0.823584\pi$
$571$	−7.74264	+	7.74264i	−0.324019	+	0.324019i	0.526287	+	0.850307i	$0.323584\pi$
$572$	−18.9414	−	18.9414i	−0.791978	−	0.791978i
$573$	38.3519	−	38.3519i	1.60217	−	1.60217i
$574$	−1.80277			−0.0752462
$575$		0			0
$576$			34.0508i			1.41878i
$577$		−	9.09883i		−	0.378789i	−0.981901	−	0.189395i	$-0.939347\pi$
$577$		−	9.09883i		−	0.378789i	0.981901	−	0.189395i	$-0.0606525\pi$
$578$	−26.0421	+	23.6828i	−1.08321	+	0.985076i
$579$	3.58856			0.149135
$580$		0			0
$581$	2.59587	+	2.59587i	0.107695	+	0.107695i
$582$			66.5991i			2.76062i
$583$	−12.0388	+	12.0388i	−0.498597	+	0.498597i
$584$	0.120494	−	0.120494i	0.00498608	−	0.00498608i
$585$		0			0
$586$			42.7536i			1.76614i
$587$	−11.2991			−0.466362			−0.233181	−	0.972433i	$-0.574913\pi$
$587$	−11.2991			−0.466362			−0.233181	+	0.972433i	$0.574913\pi$
$588$	−28.0156	−	28.0156i	−1.15534	−	1.15534i
$589$	24.4250	−	24.4250i	1.00641	−	1.00641i
$590$		0			0
$591$	43.9403			1.80746
$592$	−4.58366	+	4.58366i	−0.188387	+	0.188387i
$593$	−42.8620			−1.76013			−0.880066	−	0.474851i	$-0.842502\pi$
$593$	−42.8620			−1.76013			−0.880066	+	0.474851i	$0.842502\pi$
$594$	4.80167			0.197015
$595$		0			0
$596$	25.4568			1.04275
$597$	45.1388			1.84741
$598$	45.9898	−	45.9898i	1.88066	−	1.88066i
$599$	−21.0108			−0.858478			−0.429239	−	0.903191i	$-0.641218\pi$
$599$	−21.0108			−0.858478			−0.429239	+	0.903191i	$0.641218\pi$
$600$		0			0
$601$	−13.7533	+	13.7533i	−0.561009	+	0.561009i	−0.929594	−	0.368585i	$-0.879842\pi$
$601$	−13.7533	+	13.7533i	−0.561009	+	0.561009i	0.368585	+	0.929594i	$0.379842\pi$
$602$	6.32617	+	6.32617i	0.257835	+	0.257835i
$603$	−6.31399			−0.257126
$604$		−	36.7960i		−	1.49721i
$605$		0			0
$606$	−33.5684	+	33.5684i	−1.36362	+	1.36362i
$607$	19.3965	−	19.3965i	0.787281	−	0.787281i	−0.193767	−	0.981048i	$-0.562071\pi$
$607$	19.3965	−	19.3965i	0.787281	−	0.787281i	0.981048	+	0.193767i	$0.0620706\pi$
$608$			58.1535i			2.35844i
$609$	−4.46476	−	4.46476i	−0.180921	−	0.180921i
$610$		0			0
$611$	7.74971			0.313520
$612$	29.6255	−	11.4563i	1.19754	−	0.463095i
$613$		−	0.297602i		−	0.0120200i	−0.999982	−	0.00601001i	$-0.998087\pi$
$613$		−	0.297602i		−	0.0120200i	0.999982	−	0.00601001i	$-0.00191306\pi$
$614$			33.8416i			1.36573i
$615$		0			0
$616$	0.548573			0.0221026
$617$	−8.95764	+	8.95764i	−0.360621	+	0.360621i	−0.864041	−	0.503421i	$-0.832075\pi$
$617$	−8.95764	+	8.95764i	−0.360621	+	0.360621i	0.503421	+	0.864041i	$0.332075\pi$
$618$	−17.6538	−	17.6538i	−0.710138	−	0.710138i
$619$	−6.89991	+	6.89991i	−0.277331	+	0.277331i	−0.832043	−	0.554712i	$-0.812829\pi$
$619$	−6.89991	+	6.89991i	−0.277331	+	0.277331i	0.554712	+	0.832043i	$0.312829\pi$
$620$		0			0
$621$			6.22005i			0.249602i
$622$	51.4062	+	51.4062i	2.06120	+	2.06120i
$623$	−1.12389	−	1.12389i	−0.0450276	−	0.0450276i
$624$	−27.9589	−	27.9589i	−1.11925	−	1.11925i
$625$		0			0
$626$	−45.8473	−	45.8473i	−1.83243	−	1.83243i
$627$	45.1948			1.80491
$628$		−	6.02343i		−	0.240361i
$629$	7.31286	+	3.23424i	0.291583	+	0.128958i
$630$		0			0
$631$		−	40.9574i		−	1.63049i	−0.579117	−	0.815244i	$-0.696603\pi$
$631$		−	40.9574i		−	1.63049i	0.579117	−	0.815244i	$-0.303397\pi$
$632$	−2.26655	+	2.26655i	−0.0901584	+	0.0901584i
$633$			18.1179i			0.720123i
$634$	18.3746	+	18.3746i	0.729748	+	0.729748i
$635$		0			0
$636$	27.8176	−	27.8176i	1.10304	−	1.10304i
$637$	32.1763			1.27487
$638$	−35.0788			−1.38878
$639$	4.09508	−	4.09508i	0.161999	−	0.161999i
$640$		0			0
$641$	2.80367	+	2.80367i	0.110738	+	0.110738i	0.760305	−	0.649567i	$-0.225050\pi$
$641$	2.80367	+	2.80367i	0.110738	+	0.110738i	−0.649567	+	0.760305i	$0.725050\pi$
$642$			14.9025i			0.588154i
$643$	10.9095	−	10.9095i	0.430227	−	0.430227i	−0.458478	−	0.888706i	$-0.651605\pi$
$643$	10.9095	−	10.9095i	0.430227	−	0.430227i	0.888706	+	0.458478i	$0.151605\pi$
$644$			5.65511i			0.222842i
$645$		0			0
$646$	57.0877	−	22.0761i	2.24609	−	0.868573i
$647$		−	10.5735i		−	0.415687i	−0.978162	−	0.207843i	$-0.933356\pi$
$647$		−	10.5735i		−	0.415687i	0.978162	−	0.207843i	$-0.0666445\pi$
$648$	4.61919			0.181459
$649$	−0.855606	−	0.855606i	−0.0335855	−	0.0335855i
$650$		0			0
$651$	−3.17198	−	3.17198i	−0.124320	−	0.124320i
$652$	30.8834	+	30.8834i	1.20949	+	1.20949i
$653$	10.3029	+	10.3029i	0.403184	+	0.403184i	0.879354	−	0.476169i	$-0.157975\pi$
$653$	10.3029	+	10.3029i	0.403184	+	0.403184i	−0.476169	+	0.879354i	$0.657975\pi$
$654$		−	49.3702i		−	1.93053i
$655$		0			0
$656$	−5.57722	+	5.57722i	−0.217754	+	0.217754i
$657$	−0.681831	−	0.681831i	−0.0266007	−	0.0266007i
$658$	−0.893065	+	0.893065i	−0.0348153	+	0.0348153i
$659$	−23.7883			−0.926660			−0.463330	−	0.886186i	$-0.653346\pi$
$659$	−23.7883			−0.926660			−0.463330	+	0.886186i	$0.653346\pi$
$660$		0			0
$661$		−	9.91502i		−	0.385650i	−0.981233	−	0.192825i	$-0.938235\pi$
$661$		−	9.91502i		−	0.385650i	0.981233	−	0.192825i	$-0.0617649\pi$
$662$		−	1.03003i		−	0.0400331i
$663$	−19.7279	+	44.6062i	−0.766167	+	1.73236i
$664$	−5.92189			−0.229814
$665$		0			0
$666$	−9.56300	−	9.56300i	−0.370559	−	0.370559i
$667$		−	45.4408i		−	1.75948i
$668$	−6.44950	+	6.44950i	−0.249539	+	0.249539i
$669$	7.01848	−	7.01848i	0.271350	−	0.271350i
$670$		0			0
$671$			17.1946i			0.663790i
$672$	7.55218			0.291331
$673$	2.81097	+	2.81097i	0.108355	+	0.108355i	0.759206	−	0.650851i	$-0.225588\pi$
$673$	2.81097	+	2.81097i	0.108355	+	0.108355i	−0.650851	+	0.759206i	$0.725588\pi$
$674$	49.1477	−	49.1477i	1.89310	−	1.89310i
$675$		0			0
$676$	−20.5303			−0.789627
$677$	14.4022	−	14.4022i	0.553523	−	0.553523i	−0.373933	−	0.927456i	$-0.621991\pi$
$677$	14.4022	−	14.4022i	0.553523	−	0.553523i	0.927456	+	0.373933i	$0.121991\pi$
$678$	55.7984			2.14293
$679$	4.70276			0.180475
$680$		0			0
$681$	8.78125			0.336498
$682$	−24.9217			−0.954300
$683$	20.4617	−	20.4617i	0.782944	−	0.782944i	−0.197383	−	0.980327i	$-0.563244\pi$
$683$	20.4617	−	20.4617i	0.782944	−	0.782944i	0.980327	+	0.197383i	$0.0632442\pi$
$684$	−55.2313			−2.11182
$685$		0			0
$686$	−7.48943	+	7.48943i	−0.285948	+	0.285948i
$687$	−7.87193	−	7.87193i	−0.300333	−	0.300333i
$688$	39.1424			1.49229
$689$			31.9489i			1.21716i
$690$		0			0
$691$	−3.76661	+	3.76661i	−0.143289	+	0.143289i	−0.775112	−	0.631824i	$-0.782307\pi$
$691$	−3.76661	+	3.76661i	−0.143289	+	0.143289i	0.631824	+	0.775112i	$0.282307\pi$
$692$	−23.6276	+	23.6276i	−0.898188	+	0.898188i
$693$		−	3.10417i		−	0.117918i
$694$	38.5084	+	38.5084i	1.46176	+	1.46176i
$695$		0			0
$696$	10.1854			0.386075
$697$	8.89800	+	3.93530i	0.337036	+	0.149060i
$698$		−	34.7583i		−	1.31562i
$699$			39.5340i			1.49531i
$700$		0			0
$701$	−42.2699			−1.59651			−0.798256	−	0.602318i	$-0.794244\pi$
$701$	−42.2699			−1.59651			−0.798256	+	0.602318i	$0.794244\pi$
$702$	6.37139	−	6.37139i	0.240473	−	0.240473i
$703$	−9.83156	−	9.83156i	−0.370804	−	0.370804i
$704$	17.8595	−	17.8595i	0.673104	−	0.673104i
$705$		0			0
$706$			48.5625i			1.82768i
$707$	2.37037	+	2.37037i	0.0891468	+	0.0891468i
$708$	1.97702	+	1.97702i	0.0743008	+	0.0743008i
$709$	34.1983	+	34.1983i	1.28435	+	1.28435i	0.938170	+	0.346176i	$0.112520\pi$
$709$	34.1983	+	34.1983i	1.28435	+	1.28435i	0.346176	+	0.938170i	$0.387480\pi$
$710$		0			0
$711$	12.8255	+	12.8255i	0.480995	+	0.480995i
$712$	2.56390			0.0960861
$713$		−	32.2834i		−	1.20902i
$714$	−2.86694	−	7.41376i	−0.107293	−	0.277453i
$715$		0			0
$716$		−	33.7288i		−	1.26050i
$717$	11.7610	−	11.7610i	0.439222	−	0.439222i
$718$			37.5957i			1.40306i
$719$	−5.83066	−	5.83066i	−0.217447	−	0.217447i	0.589975	−	0.807422i	$-0.299138\pi$
$719$	−5.83066	−	5.83066i	−0.217447	−	0.217447i	−0.807422	+	0.589975i	$0.799138\pi$
$720$		0			0
$721$	−1.24658	+	1.24658i	−0.0464252	+	0.0464252i
$722$	−67.0878			−2.49675
$723$	11.0538			0.411096
$724$	18.2150	−	18.2150i	0.676956	−	0.676956i
$725$		0			0
$726$	17.5849	+	17.5849i	0.652638	+	0.652638i
$727$			6.46089i			0.239621i	0.992797	+	0.119811i	$0.0382288\pi$
$727$			6.46089i			0.239621i	−0.992797	+	0.119811i	$0.961771\pi$
$728$	0.727907	−	0.727907i	0.0269780	−	0.0269780i
$729$		−	33.1658i		−	1.22836i
$730$		0			0
$731$	−17.4148	−	45.0338i	−0.644109	−	1.66563i
$732$		−	39.7309i		−	1.46850i
$733$	15.9605			0.589515			0.294758	−	0.955572i	$-0.404761\pi$
$733$	15.9605			0.589515			0.294758	+	0.955572i	$0.404761\pi$
$734$	−20.0448	−	20.0448i	−0.739867	−	0.739867i
$735$		0			0
$736$	38.4318	+	38.4318i	1.41661	+	1.41661i
$737$	3.31165	+	3.31165i	0.121986	+	0.121986i
$738$	−11.6359	−	11.6359i	−0.428323	−	0.428323i
$739$			0.760943i			0.0279918i	0.999902	+	0.0139959i	$0.00445517\pi$
$739$			0.760943i			0.0279918i	−0.999902	+	0.0139959i	$0.995545\pi$
$740$		0			0
$741$	59.9695	−	59.9695i	2.20303	−	2.20303i
$742$	−3.68174	−	3.68174i	−0.135161	−	0.135161i
$743$	27.8096	−	27.8096i	1.02024	−	1.02024i	0.0204461	−	0.999791i	$-0.493491\pi$
$743$	27.8096	−	27.8096i	1.02024	−	1.02024i	0.999791	−	0.0204461i	$-0.00650865\pi$
$744$	7.23617			0.265291
$745$		0			0
$746$			21.0362i			0.770191i
$747$			33.5097i			1.22606i
$748$	−21.5472	−	9.52963i	−0.787844	−	0.348438i
$749$	1.05231			0.0384506
$750$		0			0
$751$	−23.8937	−	23.8937i	−0.871892	−	0.871892i	0.120786	−	0.992679i	$-0.461458\pi$
$751$	−23.8937	−	23.8937i	−0.871892	−	0.871892i	−0.992679	+	0.120786i	$0.961458\pi$
$752$			5.52574i			0.201503i
$753$	−7.67792	+	7.67792i	−0.279799	+	0.279799i
$754$	−46.5464	+	46.5464i	−1.69512	+	1.69512i
$755$		0			0
$756$			0.783454i			0.0284939i
$757$	−23.0663			−0.838359			−0.419180	−	0.907903i	$-0.637682\pi$
$757$	−23.0663			−0.838359			−0.419180	+	0.907903i	$0.637682\pi$
$758$	6.09685	+	6.09685i	0.221448	+	0.221448i
$759$	29.8678	−	29.8678i	1.08413	−	1.08413i
$760$		0			0
$761$	22.8435			0.828076			0.414038	−	0.910260i	$-0.364118\pi$
$761$	22.8435			0.828076			0.414038	+	0.910260i	$0.364118\pi$
$762$	−58.1235	+	58.1235i	−2.10559	+	2.10559i
$763$	−3.48618			−0.126208
$764$	49.1648			1.77872
$765$		0			0
$766$	1.68397			0.0608445
$767$	−2.27063			−0.0819876
$768$	18.6713	−	18.6713i	0.673741	−	0.673741i
$769$	−3.68785			−0.132987			−0.0664936	−	0.997787i	$-0.521181\pi$
$769$	−3.68785			−0.132987			−0.0664936	+	0.997787i	$0.521181\pi$
$770$		0			0
$771$	18.8010	−	18.8010i	0.677102	−	0.677102i
$772$	2.30016	+	2.30016i	0.0827845	+	0.0827845i
$773$	−5.04027			−0.181286			−0.0906430	−	0.995883i	$-0.528892\pi$
$773$	−5.04027			−0.181286			−0.0906430	+	0.995883i	$0.528892\pi$
$774$			81.6638i			2.93534i
$775$		0			0
$776$	−5.36415	+	5.36415i	−0.192562	+	0.192562i
$777$	−1.27679	+	1.27679i	−0.0458045	+	0.0458045i
$778$			6.45361i			0.231373i
$779$	−11.9627	−	11.9627i	−0.428607	−	0.428607i
$780$		0			0
$781$	−4.29569			−0.153712
$782$	23.1380	−	52.3168i	0.827414	−	1.87084i
$783$		−	6.29533i		−	0.224977i
$784$			22.9425i			0.819375i
$785$		0			0
$786$	−21.3791			−0.762567
$787$	9.65129	−	9.65129i	0.344031	−	0.344031i	−0.513849	−	0.857880i	$-0.671781\pi$
$787$	9.65129	−	9.65129i	0.344031	−	0.344031i	0.857880	+	0.513849i	$0.171781\pi$
$788$	28.1644	+	28.1644i	1.00332	+	1.00332i
$789$	24.3124	−	24.3124i	0.865545	−	0.865545i
$790$		0			0
$791$		−	3.94010i		−	0.140094i
$792$	3.54073	+	3.54073i	0.125814	+	0.125814i
$793$	22.8157	+	22.8157i	0.810209	+	0.810209i
$794$	24.0187	+	24.0187i	0.852391	+	0.852391i
$795$		0			0
$796$	28.9326	+	28.9326i	1.02549	+	1.02549i
$797$	−16.6869			−0.591081			−0.295541	−	0.955330i	$-0.595500\pi$
$797$	−16.6869			−0.591081			−0.295541	+	0.955330i	$0.595500\pi$
$798$			13.8216i			0.489279i
$799$	6.35742	−	2.45845i	0.224909	−	0.0869736i
$800$		0			0
$801$		−	14.5081i		−	0.512619i
$802$	21.1498	−	21.1498i	0.746824	−	0.746824i
$803$			0.715232i			0.0252400i
$804$	−7.65211	−	7.65211i	−0.269869	−	0.269869i
$805$		0			0
$806$	−33.0688	+	33.0688i	−1.16480	+	1.16480i
$807$	−39.3844			−1.38640
$808$	−5.40746			−0.190234
$809$	21.7364	−	21.7364i	0.764211	−	0.764211i	−0.212870	−	0.977081i	$-0.568281\pi$
$809$	21.7364	−	21.7364i	0.764211	−	0.764211i	0.977081	+	0.212870i	$0.0682810\pi$
$810$		0			0
$811$	15.1208	+	15.1208i	0.530962	+	0.530962i	0.920859	−	0.389896i	$-0.127489\pi$
$811$	15.1208	+	15.1208i	0.530962	+	0.530962i	−0.389896	+	0.920859i	$0.627489\pi$
$812$		−	5.72355i		−	0.200857i
$813$	−17.2469	+	17.2469i	−0.604874	+	0.604874i
$814$			10.0315i			0.351603i
$815$		0			0
$816$	−31.8053	−	14.0665i	−1.11341	−	0.492425i
$817$			83.9571i			2.93729i
$818$	−66.8534			−2.33747
$819$	−4.11895	−	4.11895i	−0.143928	−	0.143928i
$820$		0			0
$821$	−8.42091	−	8.42091i	−0.293892	−	0.293892i	0.544724	−	0.838616i	$-0.316634\pi$
$821$	−8.42091	−	8.42091i	−0.293892	−	0.293892i	−0.838616	+	0.544724i	$0.816634\pi$
$822$	−59.9075	−	59.9075i	−2.08951	−	2.08951i
$823$	13.8553	+	13.8553i	0.482965	+	0.482965i	0.906077	−	0.423113i	$-0.139063\pi$
$823$	13.8553	+	13.8553i	0.482965	+	0.482965i	−0.423113	+	0.906077i	$0.639063\pi$
$824$		−	2.84381i		−	0.0990686i
$825$		0			0
$826$	0.261664	−	0.261664i	0.00910444	−	0.00910444i
$827$	24.8128	+	24.8128i	0.862827	+	0.862827i	0.991666	−	0.128838i	$-0.0411248\pi$
$827$	24.8128	+	24.8128i	0.862827	+	0.862827i	−0.128838	+	0.991666i	$0.541125\pi$
$828$	−36.5006	+	36.5006i	−1.26848	+	1.26848i
$829$	−46.3683			−1.61044			−0.805219	−	0.592978i	$-0.797952\pi$
$829$	−46.3683			−1.61044			−0.805219	+	0.592978i	$0.797952\pi$
$830$		0			0
$831$		−	3.40835i		−	0.118234i
$832$		−	47.3958i		−	1.64315i
$833$	26.3956	−	10.2073i	0.914552	−	0.353662i
$834$	−55.9460			−1.93725
$835$		0			0
$836$	28.9685	+	28.9685i	1.00190	+	1.00190i
$837$		−	4.47251i		−	0.154593i
$838$	−27.6395	+	27.6395i	−0.954791	+	0.954791i
$839$	17.6001	−	17.6001i	0.607623	−	0.607623i	−0.334701	−	0.942324i	$-0.608635\pi$
$839$	17.6001	−	17.6001i	0.607623	−	0.607623i	0.942324	+	0.334701i	$0.108635\pi$
$840$		0			0
$841$			16.9908i			0.585890i
$842$	−4.26559			−0.147002
$843$	−28.2967	−	28.2967i	−0.974589	−	0.974589i
$844$	−11.6130	+	11.6130i	−0.399737	+	0.399737i
$845$		0			0
$846$	−11.5285			−0.396357
$847$	1.24173	−	1.24173i	0.0426662	−	0.0426662i
$848$	−22.7804			−0.782281
$849$	−74.0357			−2.54090
$850$		0			0
$851$	−12.9947			−0.445453
$852$	9.92589			0.340055
$853$	−19.8742	+	19.8742i	−0.680478	+	0.680478i	−0.960108	−	0.279629i	$-0.909788\pi$
$853$	−19.8742	+	19.8742i	−0.680478	+	0.680478i	0.279629	+	0.960108i	$0.409788\pi$
$854$	−5.25850			−0.179942
$855$		0			0
$856$	−1.20031	+	1.20031i	−0.0410256	+	0.0410256i
$857$	−17.3313	−	17.3313i	−0.592025	−	0.592025i	0.346153	−	0.938178i	$-0.387488\pi$
$857$	−17.3313	−	17.3313i	−0.592025	−	0.592025i	−0.938178	+	0.346153i	$0.887488\pi$
$858$	−61.1889			−2.08896
$859$			12.8979i			0.440069i	0.975492	+	0.220034i	$0.0706170\pi$
$859$			12.8979i			0.440069i	−0.975492	+	0.220034i	$0.929383\pi$
$860$		0			0
$861$	−1.55354	+	1.55354i	−0.0529447	+	0.0529447i
$862$	−5.45773	+	5.45773i	−0.185891	+	0.185891i
$863$			5.83668i			0.198683i	0.995053	+	0.0993414i	$0.0316736\pi$
$863$			5.83668i			0.198683i	−0.995053	+	0.0993414i	$0.968326\pi$
$864$	5.32430	+	5.32430i	0.181136	+	0.181136i
$865$		0			0
$866$	−57.9014			−1.96757
$867$	−2.03316	+	42.8507i	−0.0690496	+	1.45528i
$868$		−	4.06629i		−	0.138019i
$869$		−	13.4538i		−	0.456390i
$870$		0			0
$871$	8.78854			0.297788
$872$	3.97647	−	3.97647i	0.134660	−	0.134660i
$873$	30.3537	+	30.3537i	1.02732	+	1.02732i
$874$	−70.3357	+	70.3357i	−2.37914	+	2.37914i
$875$		0			0
$876$		−	1.65266i		−	0.0558382i
$877$	−13.2827	−	13.2827i	−0.448526	−	0.448526i	0.446338	−	0.894864i	$-0.352728\pi$
$877$	−13.2827	−	13.2827i	−0.448526	−	0.448526i	−0.894864	+	0.446338i	$0.852728\pi$
$878$	−18.3668	−	18.3668i	−0.619850	−	0.619850i
$879$	36.8431	+	36.8431i	1.24269	+	1.24269i
$880$		0			0
$881$	−32.3447	−	32.3447i	−1.08972	−	1.08972i	−0.995557	−	0.0941649i	$-0.969982\pi$
$881$	−32.3447	−	32.3447i	−1.08972	−	1.08972i	−0.0941649	−	0.995557i	$-0.530018\pi$
$882$	−47.8655			−1.61171
$883$		−	6.15932i		−	0.207277i	−0.994615	−	0.103639i	$-0.966951\pi$
$883$		−	6.15932i		−	0.207277i	0.994615	−	0.103639i	$-0.0330486\pi$
$884$	−41.2362	+	15.9462i	−1.38692	+	0.536330i
$885$		0			0
$886$			41.3147i			1.38800i
$887$	11.8423	−	11.8423i	0.397627	−	0.397627i	−0.479768	−	0.877395i	$-0.659279\pi$
$887$	11.8423	−	11.8423i	0.397627	−	0.397627i	0.877395	+	0.479768i	$0.159279\pi$
$888$		−	2.91270i		−	0.0977440i
$889$	4.10428	+	4.10428i	0.137653	+	0.137653i
$890$		0			0
$891$	−13.7094	+	13.7094i	−0.459281	+	0.459281i
$892$	8.99726			0.301251
$893$	−11.8522			−0.396620
$894$	41.1183	−	41.1183i	1.37520	−	1.37520i
$895$		0			0
$896$	1.22939	+	1.22939i	0.0410711	+	0.0410711i
$897$		−	79.2637i		−	2.64654i
$898$	−29.5553	+	29.5553i	−0.986274	+	0.986274i
$899$			32.6741i			1.08974i
$900$		0			0
$901$	10.1352	+	26.2091i	0.337652	+	0.873150i
$902$			12.2059i			0.406412i
$903$	10.9032			0.362835
$904$	4.49422	+	4.49422i	0.149476	+	0.149476i
$905$		0			0
$906$	−59.4336	−	59.4336i	−1.97455	−	1.97455i
$907$	5.74762	+	5.74762i	0.190847	+	0.190847i	0.796062	−	0.605215i	$-0.206913\pi$
$907$	5.74762	+	5.74762i	0.190847	+	0.190847i	−0.605215	+	0.796062i	$0.706913\pi$
$908$	5.62851	+	5.62851i	0.186789	+	0.186789i
$909$			30.5988i			1.01490i
$910$		0			0
$911$	−25.2063	+	25.2063i	−0.835121	+	0.835121i	−0.988212	−	0.153091i	$-0.951077\pi$
$911$	−25.2063	+	25.2063i	−0.835121	+	0.835121i	0.153091	+	0.988212i	$0.451077\pi$
$912$	42.7597	+	42.7597i	1.41592	+	1.41592i
$913$	17.5757	−	17.5757i	0.581670	−	0.581670i
$914$	−78.1431			−2.58474
$915$		0			0
$916$		−	10.0913i		−	0.333427i
$917$			1.50964i			0.0498528i
$918$	3.20552	−	7.24792i	0.105798	−	0.239217i
$919$	24.2398			0.799596			0.399798	−	0.916603i	$-0.369080\pi$
$919$	24.2398			0.799596			0.399798	+	0.916603i	$0.369080\pi$
$920$		0			0
$921$	29.1631	+	29.1631i	0.960956	+	0.960956i
$922$			79.0435i			2.60316i
$923$	−5.70000	+	5.70000i	−0.187618	+	0.187618i
$924$	3.76203	−	3.76203i	0.123762	−	0.123762i
$925$		0			0
$926$		−	27.2246i		−	0.894657i
$927$	−16.0920			−0.528531
$928$	−38.8969	−	38.8969i	−1.27685	−	1.27685i
$929$	23.6454	−	23.6454i	0.775781	−	0.775781i	−0.203329	−	0.979110i	$-0.565176\pi$
$929$	23.6454	−	23.6454i	0.775781	−	0.775781i	0.979110	+	0.203329i	$0.0651761\pi$
$930$		0			0
$931$	−49.2097			−1.61278
$932$	−25.3401	+	25.3401i	−0.830042	+	0.830042i
$933$	88.5989			2.90060
$934$	33.5786			1.09873
$935$		0			0
$936$	9.39647			0.307133
$937$	25.6264			0.837177			0.418588	−	0.908176i	$-0.362525\pi$
$937$	25.6264			0.837177			0.418588	+	0.908176i	$0.362525\pi$
$938$	−1.01278	+	1.01278i	−0.0330684	+	0.0330684i
$939$	−79.0181			−2.57866
$940$		0			0
$941$	37.8063	−	37.8063i	1.23245	−	1.23245i	0.269429	−	0.963020i	$-0.413165\pi$
$941$	37.8063	−	37.8063i	1.23245	−	1.23245i	0.963020	−	0.269429i	$-0.0868348\pi$
$942$	−9.72916	−	9.72916i	−0.316993	−	0.316993i
$943$	−15.8115			−0.514892
$944$		−	1.61901i		−	0.0526944i
$945$		0			0
$946$	42.8322	−	42.8322i	1.39259	−	1.39259i
$947$	8.32772	−	8.32772i	0.270615	−	0.270615i	−0.558733	−	0.829348i	$-0.688712\pi$
$947$	8.32772	−	8.32772i	0.270615	−	0.270615i	0.829348	+	0.558733i	$0.188712\pi$
$948$			31.0873i			1.00967i
$949$	0.949050	+	0.949050i	0.0308075	+	0.0308075i
$950$		0			0
$951$	31.6687			1.02693
$952$	0.366219	−	0.828048i	0.0118692	−	0.0268372i
$953$		−	23.9735i		−	0.776576i	−0.921538	−	0.388288i	$-0.873067\pi$
$953$		−	23.9735i		−	0.776576i	0.921538	−	0.388288i	$-0.126933\pi$
$954$		−	47.5272i		−	1.53875i
$955$		0			0
$956$	15.0769			0.487621
$957$	−30.2293	+	30.2293i	−0.977173	+	0.977173i
$958$	−3.03808	−	3.03808i	−0.0981560	−	0.0981560i
$959$	−4.23025	+	4.23025i	−0.136602	+	0.136602i
$960$		0			0
$961$		−	7.78674i		−	0.251185i
$962$	13.3109	+	13.3109i	0.429160	+	0.429160i
$963$	6.79208	+	6.79208i	0.218872	+	0.218872i
$964$	7.08516	+	7.08516i	0.228198	+	0.228198i
$965$		0			0
$966$	9.13423	+	9.13423i	0.293889	+	0.293889i
$967$	45.6312			1.46740			0.733700	−	0.679473i	$-0.237792\pi$
$967$	45.6312			1.46740			0.733700	+	0.679473i	$0.237792\pi$
$968$			2.83272i			0.0910471i
$969$	30.1714	−	68.2197i	0.969243	−	2.19153i
$970$		0			0
$971$			58.9182i			1.89078i	0.325946	+	0.945388i	$0.394317\pi$
$971$			58.9182i			1.89078i	−0.325946	+	0.945388i	$0.605683\pi$
$972$	36.1821	−	36.1821i	1.16054	−	1.16054i
$973$			3.95052i			0.126648i
$974$	−35.1776	−	35.1776i	−1.12716	−	1.12716i
$975$		0			0
$976$	−16.2682	+	16.2682i	−0.520731	+	0.520731i
$977$	24.7610			0.792176			0.396088	−	0.918213i	$-0.370368\pi$
$977$	24.7610			0.792176			0.396088	+	0.918213i	$0.370368\pi$
$978$	99.7670			3.19020
$979$	−7.60943	+	7.60943i	−0.243198	+	0.243198i
$980$		0			0
$981$	−22.5013	−	22.5013i	−0.718412	−	0.718412i
$982$			46.3410i			1.47880i
$983$	6.99814	−	6.99814i	0.223206	−	0.223206i	−0.586641	−	0.809847i	$-0.699550\pi$
$983$	6.99814	−	6.99814i	0.223206	−	0.223206i	0.809847	+	0.586641i	$0.199550\pi$
$984$		−	3.54406i		−	0.112981i
$985$		0			0
$986$	−23.4181	+	52.9500i	−0.745783	+	1.68627i
$987$			1.53920i			0.0489934i
$988$	76.8772			2.44579
$989$	55.4845	+	55.4845i	1.76430	+	1.76430i
$990$		0			0
$991$	0.624955	+	0.624955i	0.0198524	+	0.0198524i	0.716963	−	0.697111i	$-0.245532\pi$
$991$	0.624955	+	0.624955i	0.0198524	+	0.0198524i	−0.697111	+	0.716963i	$0.745532\pi$
$992$	−27.6342	−	27.6342i	−0.877388	−	0.877388i
$993$	−0.887628	−	0.887628i	−0.0281680	−	0.0281680i
$994$		−	1.31372i		−	0.0416687i
$995$		0			0
$996$	−40.6114	+	40.6114i	−1.28682	+	1.28682i
$997$	−20.5067	−	20.5067i	−0.649455	−	0.649455i	0.303407	−	0.952861i	$-0.401876\pi$
$997$	−20.5067	−	20.5067i	−0.649455	−	0.649455i	−0.952861	+	0.303407i	$0.901876\pi$
$998$	5.41451	−	5.41451i	0.171393	−	0.171393i
$999$	−1.80028			−0.0569582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.j.c.149.5		12
5.2	odd	4		425.2.e.f.251.5		12
5.3	odd	4		85.2.e.a.81.2	yes	12
5.4	even	2		425.2.j.b.149.2		12
15.8	even	4		765.2.k.b.676.5		12
17.4	even	4		425.2.j.b.174.2		12
20.3	even	4		1360.2.bt.d.81.1		12
85.2	odd	8		7225.2.a.z.1.2		6
85.4	even	4	inner	425.2.j.c.174.5		12
85.8	odd	8		1445.2.d.g.866.3		12
85.32	odd	8		7225.2.a.bb.1.2		6
85.38	odd	4		85.2.e.a.21.5	✓	12
85.43	odd	8		1445.2.d.g.866.4		12
85.53	odd	8		1445.2.a.o.1.5		6
85.72	odd	4		425.2.e.f.276.2		12
85.83	odd	8		1445.2.a.n.1.5		6
255.38	even	4		765.2.k.b.361.2		12
340.123	even	4		1360.2.bt.d.1041.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.5	✓	12	85.38	odd	4
85.2.e.a.81.2	yes	12	5.3	odd	4
425.2.e.f.251.5		12	5.2	odd	4
425.2.e.f.276.2		12	85.72	odd	4
425.2.j.b.149.2		12	5.4	even	2
425.2.j.b.174.2		12	17.4	even	4
425.2.j.c.149.5		12	1.1	even	1	trivial
425.2.j.c.174.5		12	85.4	even	4	inner
765.2.k.b.361.2		12	255.38	even	4
765.2.k.b.676.5		12	15.8	even	4
1360.2.bt.d.81.1		12	20.3	even	4
1360.2.bt.d.1041.1		12	340.123	even	4
1445.2.a.n.1.5		6	85.83	odd	8
1445.2.a.o.1.5		6	85.53	odd	8
1445.2.d.g.866.3		12	85.8	odd	8
1445.2.d.g.866.4		12	85.43	odd	8
7225.2.a.z.1.2		6	85.2	odd	8
7225.2.a.bb.1.2		6	85.32	odd	8

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.07061 q^{2} +(1.78436 - 1.78436i) q^{3} +2.28744 q^{4} +(3.69471 - 3.69471i) q^{6} +(-0.260895 - 0.260895i) q^{7} +0.595174 q^{8} -3.36786i q^{9} +(-1.76642 + 1.76642i) q^{11} +(4.08161 - 4.08161i) q^{12} +4.68778i q^{13} +(-0.540212 - 0.540212i) q^{14} -3.34250 q^{16} +(1.48711 + 3.84558i) q^{17} -6.97354i q^{18} -7.16938i q^{19} -0.931060 q^{21} +(-3.65758 + 3.65758i) q^{22} +(-4.73801 - 4.73801i) q^{23} +(1.06200 - 1.06200i) q^{24} +9.70657i q^{26} +(-0.656399 - 0.656399i) q^{27} +(-0.596781 - 0.596781i) q^{28} +(4.79535 + 4.79535i) q^{29} +(3.40685 + 3.40685i) q^{31} -8.11138 q^{32} +6.30387i q^{33} +(3.07922 + 7.96272i) q^{34} -7.70378i q^{36} +(1.37133 - 1.37133i) q^{37} -14.8450i q^{38} +(8.36467 + 8.36467i) q^{39} +(1.66858 - 1.66858i) q^{41} -1.92786 q^{42} -11.7105 q^{43} +(-4.04059 + 4.04059i) q^{44} +(-9.81058 - 9.81058i) q^{46} -1.65317i q^{47} +(-5.96422 + 5.96422i) q^{48} -6.86387i q^{49} +(9.51543 + 4.20836i) q^{51} +10.7230i q^{52} +6.81536 q^{53} +(-1.35915 - 1.35915i) q^{54} +(-0.155278 - 0.155278i) q^{56} +(-12.7927 - 12.7927i) q^{57} +(9.92932 + 9.92932i) q^{58} +0.484372i q^{59} +(4.86706 - 4.86706i) q^{61} +(7.05427 + 7.05427i) q^{62} +(-0.878658 + 0.878658i) q^{63} -10.1105 q^{64} +13.0529i q^{66} -1.87478i q^{67} +(3.40167 + 8.79653i) q^{68} -16.9086 q^{69} +(1.21593 + 1.21593i) q^{71} -2.00446i q^{72} +(0.202452 - 0.202452i) q^{73} +(2.83949 - 2.83949i) q^{74} -16.3995i q^{76} +0.921703 q^{77} +(17.3200 + 17.3200i) q^{78} +(-3.80821 + 3.80821i) q^{79} +7.76109 q^{81} +(3.45498 - 3.45498i) q^{82} -9.94985 q^{83} -2.12974 q^{84} -24.2479 q^{86} +17.1132 q^{87} +(-1.05133 + 1.05133i) q^{88} +4.30781 q^{89} +(1.22302 - 1.22302i) q^{91} +(-10.8379 - 10.8379i) q^{92} +12.1581 q^{93} -3.42308i q^{94} +(-14.4736 + 14.4736i) q^{96} +(-9.01275 + 9.01275i) q^{97} -14.2124i q^{98} +(5.94908 + 5.94908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} - 4 q^{3} + 12 q^{4} + 12 q^{8} - 4 q^{11} + 8 q^{12} + 4 q^{14} + 4 q^{16} + 8 q^{17} - 16 q^{21} - 20 q^{22} - 12 q^{23} - 4 q^{24} - 4 q^{27} - 4 q^{28} + 12 q^{29} - 12 q^{32} + 12 q^{34}+ \cdots - 4 q^{97}+O(q^{100}) \) 12 * q + 4 * q^2 - 4 * q^3 + 12 * q^4 + 12 * q^8 - 4 * q^11 + 8 * q^12 + 4 * q^14 + 4 * q^16 + 8 * q^17 - 16 * q^21 - 20 * q^22 - 12 * q^23 - 4 * q^24 - 4 * q^27 - 4 * q^28 + 12 * q^29 - 12 * q^32 + 12 * q^34 - 12 * q^37 + 20 * q^39 - 24 * q^41 + 16 * q^42 + 16 * q^43 - 8 * q^44 - 24 * q^46 - 20 * q^48 + 32 * q^51 - 28 * q^54 + 40 * q^56 - 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 - 28 * q^64 + 60 * q^68 + 28 * q^71 - 48 * q^73 - 28 * q^74 - 48 * q^77 + 92 * q^78 + 8 * q^79 + 28 * q^81 - 40 * q^82 - 40 * q^83 - 96 * q^86 + 48 * q^87 - 72 * q^88 - 24 * q^89 - 36 * q^91 - 16 * q^92 + 72 * q^93 - 32 * q^96 - 4 * q^97

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