LMFDB - Embedded newform 85.2.e.a.81.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [85,2,Mod(21,85)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("85.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(85, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.678728417181$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.2
Root			$-1.52346i$ of defining polynomial
Character	$\chi$	$=$	85.81
Dual form			85.2.e.a.21.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.07061i q^{2} +(1.78436 + 1.78436i) q^{3} -2.28744 q^{4} +(-0.707107 - 0.707107i) q^{5} +(3.69471 - 3.69471i) q^{6} +(-0.260895 + 0.260895i) q^{7} +0.595174i q^{8} +3.36786i q^{9} +(-1.46414 + 1.46414i) q^{10} +(-1.76642 + 1.76642i) q^{11} +(-4.08161 - 4.08161i) q^{12} -4.68778 q^{13} +(0.540212 + 0.540212i) q^{14} -2.52346i q^{15} -3.34250 q^{16} +(3.84558 - 1.48711i) q^{17} +6.97354 q^{18} +7.16938i q^{19} +(1.61746 + 1.61746i) q^{20} -0.931060 q^{21} +(3.65758 + 3.65758i) q^{22} +(4.73801 - 4.73801i) q^{23} +(-1.06200 + 1.06200i) q^{24} +1.00000i q^{25} +9.70657i q^{26} +(-0.656399 + 0.656399i) q^{27} +(0.596781 - 0.596781i) q^{28} +(-4.79535 - 4.79535i) q^{29} -5.22511 q^{30} +(3.40685 + 3.40685i) q^{31} +8.11138i q^{32} -6.30387 q^{33} +(-3.07922 - 7.96272i) q^{34} +0.368961 q^{35} -7.70378i q^{36} +(-1.37133 - 1.37133i) q^{37} +14.8450 q^{38} +(-8.36467 - 8.36467i) q^{39} +(0.420851 - 0.420851i) q^{40} +(1.66858 - 1.66858i) q^{41} +1.92786i q^{42} -11.7105i q^{43} +(4.04059 - 4.04059i) q^{44} +(2.38144 - 2.38144i) q^{45} +(-9.81058 - 9.81058i) q^{46} -1.65317 q^{47} +(-5.96422 - 5.96422i) q^{48} +6.86387i q^{49} +2.07061 q^{50} +(9.51543 + 4.20836i) q^{51} +10.7230 q^{52} +6.81536i q^{53} +(1.35915 + 1.35915i) q^{54} +2.49810 q^{55} +(-0.155278 - 0.155278i) q^{56} +(-12.7927 + 12.7927i) q^{57} +(-9.92932 + 9.92932i) q^{58} -0.484372i q^{59} +5.77226i q^{60} +(4.86706 - 4.86706i) q^{61} +(7.05427 - 7.05427i) q^{62} +(-0.878658 - 0.878658i) q^{63} +10.1105 q^{64} +(3.31476 + 3.31476i) q^{65} +13.0529i q^{66} -1.87478 q^{67} +(-8.79653 + 3.40167i) q^{68} +16.9086 q^{69} -0.763976i q^{70} +(1.21593 + 1.21593i) q^{71} -2.00446 q^{72} +(0.202452 + 0.202452i) q^{73} +(-2.83949 + 2.83949i) q^{74} +(-1.78436 + 1.78436i) q^{75} -16.3995i q^{76} -0.921703i q^{77} +(-17.3200 + 17.3200i) q^{78} +(3.80821 - 3.80821i) q^{79} +(2.36351 + 2.36351i) q^{80} +7.76109 q^{81} +(-3.45498 - 3.45498i) q^{82} -9.94985i q^{83} +2.12974 q^{84} +(-3.77078 - 1.66769i) q^{85} -24.2479 q^{86} -17.1132i q^{87} +(-1.05133 - 1.05133i) q^{88} -4.30781 q^{89} +(-4.93104 - 4.93104i) q^{90} +(1.22302 - 1.22302i) q^{91} +(-10.8379 + 10.8379i) q^{92} +12.1581i q^{93} +3.42308i q^{94} +(5.06952 - 5.06952i) q^{95} +(-14.4736 + 14.4736i) q^{96} +(9.01275 + 9.01275i) q^{97} +14.2124 q^{98} +(-5.94908 - 5.94908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - 12 q^{4} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{14} + 4 q^{16} + 12 q^{17} + 28 q^{18} - 8 q^{20} - 16 q^{21} + 20 q^{22} + 12 q^{23} + 4 q^{24} - 4 q^{27} + 4 q^{28} - 12 q^{29} - 8 q^{30}+ \cdots + 44 q^{98}+O(q^{100}) $ 12 * q - 4 * q^3 - 12 * q^4 - 4 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^14 + 4 * q^16 + 12 * q^17 + 28 * q^18 - 8 * q^20 - 16 * q^21 + 20 * q^22 + 12 * q^23 + 4 * q^24 - 4 * q^27 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 16 * q^33 - 12 * q^34 + 16 * q^35 + 12 * q^37 + 24 * q^38 - 20 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 48 * q^47 - 20 * q^48 + 4 * q^50 + 32 * q^51 - 56 * q^52 + 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 + 28 * q^64 + 4 * q^65 - 8 * q^67 - 40 * q^68 + 28 * q^71 + 20 * q^72 - 48 * q^73 + 28 * q^74 + 4 * q^75 - 92 * q^78 - 8 * q^79 + 16 * q^80 + 28 * q^81 + 40 * q^82 - 4 * q^85 - 96 * q^86 - 72 * q^88 + 24 * q^89 - 16 * q^90 - 36 * q^91 - 16 * q^92 - 8 * q^95 - 32 * q^96 + 4 * q^97 + 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	2.07061i		−	1.46414i	−0.681227	−	0.732072i	$-0.738553\pi$
$2$		−	2.07061i		−	1.46414i	0.681227	−	0.732072i	$-0.261447\pi$
$3$	1.78436	+	1.78436i	1.03020	+	1.03020i	0.999530	+	0.0306697i	$0.00976400\pi$
$3$	1.78436	+	1.78436i	1.03020	+	1.03020i	0.0306697	+	0.999530i	$0.490236\pi$
$4$	−2.28744			−1.14372
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	3.69471	−	3.69471i	1.50836	−	1.50836i
$7$	−0.260895	+	0.260895i	−0.0986090	+	0.0986090i	−0.754690	−	0.656081i	$-0.772213\pi$
$7$	−0.260895	+	0.260895i	−0.0986090	+	0.0986090i	0.656081	+	0.754690i	$0.272213\pi$
$8$			0.595174i			0.210426i
$9$			3.36786i			1.12262i
$10$	−1.46414	+	1.46414i	−0.463003	+	0.463003i
$11$	−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
$13$	−4.68778			−1.30016			−0.650078	−	0.759868i	$-0.725264\pi$
$13$	−4.68778			−1.30016			−0.650078	+	0.759868i	$0.725264\pi$
$14$	0.540212	+	0.540212i	0.144378	+	0.144378i
$15$		−	2.52346i		−	0.651555i
$16$	−3.34250			−0.835626
$17$	3.84558	−	1.48711i	0.932691	−	0.360676i
$17$	3.84558	−	1.48711i	0.932691	−	0.360676i
$18$	6.97354			1.64368
$19$			7.16938i			1.64477i	0.568933	+	0.822384i	$0.307356\pi$
$19$			7.16938i			1.64477i	−0.568933	+	0.822384i	$0.692644\pi$
$20$	1.61746	+	1.61746i	0.361676	+	0.361676i
$21$	−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	$-0.503815\pi$
$23$	4.73801	−	4.73801i	0.987943	−	0.987943i	0.999928	+	0.0119854i	$0.00381516\pi$
$24$	−1.06200	+	1.06200i	−0.216780	+	0.216780i
$25$			1.00000i			0.200000i
$26$			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	0.104093	−	0.994568i	$-0.466806\pi$
$29$	−4.79535	−	4.79535i	−0.890475	−	0.890475i	−0.994568	+	0.104093i	$0.966806\pi$
$30$	−5.22511			−0.953971
$31$	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	$0.607571\pi$
$32$			8.11138i			1.43390i
$33$	−6.30387			−1.09736
$34$	−3.07922	−	7.96272i	−0.528083	−	1.36559i
$35$	0.368961			0.0623658
$36$		−	7.70378i		−	1.28396i
$37$	−1.37133	−	1.37133i	−0.225445	−	0.225445i	0.585342	−	0.810787i	$-0.300960\pi$
$37$	−1.37133	−	1.37133i	−0.225445	−	0.225445i	−0.810787	+	0.585342i	$0.800960\pi$
$38$	14.8450			2.40818
$39$	−8.36467	−	8.36467i	−1.33942	−	1.33942i
$40$	0.420851	−	0.420851i	0.0665424	−	0.0665424i
$41$	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	$0.191010\pi$
$42$			1.92786i			0.297476i
$43$		−	11.7105i		−	1.78584i	−0.450218	−	0.892918i	$-0.648654\pi$
$43$		−	11.7105i		−	1.78584i	0.450218	−	0.892918i	$-0.351346\pi$
$44$	4.04059	−	4.04059i	0.609142	−	0.609142i
$45$	2.38144	−	2.38144i	0.355004	−	0.355004i
$46$	−9.81058	−	9.81058i	−1.44649	−	1.44649i
$47$	−1.65317			−0.241140			−0.120570	−	0.992705i	$-0.538472\pi$
$47$	−1.65317			−0.241140			−0.120570	+	0.992705i	$0.538472\pi$
$48$	−5.96422	−	5.96422i	−0.860861	−	0.860861i
$49$			6.86387i			0.980553i
$50$	2.07061			0.292829
$51$	9.51543	+	4.20836i	1.33243	+	0.589289i
$52$	10.7230			1.48701
$53$			6.81536i			0.936162i	0.883686	+	0.468081i	$0.155054\pi$
$53$			6.81536i			0.936162i	−0.883686	+	0.468081i	$0.844946\pi$
$54$	1.35915	+	1.35915i	0.184957	+	0.184957i
$55$	2.49810			0.336844
$56$	−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	$-0.989962\pi$
$59$		−	0.484372i		−	0.0630598i	0.999503	−	0.0315299i	$-0.0100379\pi$
$60$			5.77226i			0.745196i
$61$	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
$65$	3.31476	+	3.31476i	0.411145	+	0.411145i
$66$			13.0529i			1.60670i
$67$	−1.87478			−0.229041			−0.114520	−	0.993421i	$-0.536533\pi$
$67$	−1.87478			−0.229041			−0.114520	+	0.993421i	$0.536533\pi$
$68$	−8.79653	+	3.40167i	−1.06674	+	0.412513i
$69$	16.9086			2.03556
$70$		−	0.763976i		−	0.0913126i
$71$	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	$0.717464\pi$
$72$	−2.00446			−0.236228
$73$	0.202452	+	0.202452i	0.0236952	+	0.0236952i	0.718855	−	0.695160i	$-0.244666\pi$
$73$	0.202452	+	0.202452i	0.0236952	+	0.0236952i	−0.695160	+	0.718855i	$0.744666\pi$
$74$	−2.83949	+	2.83949i	−0.330084	+	0.330084i
$75$	−1.78436	+	1.78436i	−0.206040	+	0.206040i
$76$		−	16.3995i		−	1.88115i
$77$		−	0.921703i		−	0.105038i
$78$	−17.3200	+	17.3200i	−1.96110	+	1.96110i
$79$	3.80821	−	3.80821i	0.428458	−	0.428458i	−0.459645	−	0.888103i	$-0.652023\pi$
$79$	3.80821	−	3.80821i	0.428458	−	0.428458i	0.888103	+	0.459645i	$0.152023\pi$
$80$	2.36351	+	2.36351i	0.264248	+	0.264248i
$81$	7.76109			0.862343
$82$	−3.45498	−	3.45498i	−0.381538	−	0.381538i
$83$		−	9.94985i		−	1.09214i	−0.837740	−	0.546069i	$-0.816124\pi$
$83$		−	9.94985i		−	1.09214i	0.837740	−	0.546069i	$-0.183876\pi$
$84$	2.12974			0.232374
$85$	−3.77078	−	1.66769i	−0.408999	−	0.180887i
$86$	−24.2479			−2.61472
$87$		−	17.1132i		−	1.83473i
$88$	−1.05133	−	1.05133i	−0.112072	−	0.112072i
$89$	−4.30781			−0.456627			−0.228314	−	0.973588i	$-0.573321\pi$
$89$	−4.30781			−0.456627			−0.228314	+	0.973588i	$0.573321\pi$
$90$	−4.93104	−	4.93104i	−0.519777	−	0.519777i
$91$	1.22302	−	1.22302i	0.128207	−	0.128207i
$92$	−10.8379	+	10.8379i	−1.12993	+	1.12993i
$93$			12.1581i			1.26073i
$94$			3.42308i			0.353064i
$95$	5.06952	−	5.06952i	0.520121	−	0.520121i
$96$	−14.4736	+	14.4736i	−1.47721	+	1.47721i
$97$	9.01275	+	9.01275i	0.915106	+	0.915106i	0.996668	−	0.0815619i	$-0.0259908\pi$
$97$	9.01275	+	9.01275i	0.915106	+	0.915106i	−0.0815619	+	0.996668i	$0.525991\pi$
$98$	14.2124			1.43567
$99$	−5.94908	−	5.94908i	−0.597905	−	0.597905i
$100$		−	2.28744i		−	0.228744i
$101$	−9.08552			−0.904043			−0.452021	−	0.892007i	$-0.649297\pi$
$101$	−9.08552			−0.904043			−0.452021	+	0.892007i	$0.649297\pi$
$102$	8.71389	−	19.7028i	0.862804	−	1.95086i
$103$	4.77811			0.470801			0.235401	−	0.971898i	$-0.424360\pi$
$103$	4.77811			0.470801			0.235401	+	0.971898i	$0.424360\pi$
$104$		−	2.79004i		−	0.273586i
$105$	0.658359	+	0.658359i	0.0642492	+	0.0642492i
$106$	14.1120			1.37068
$107$	2.01673	+	2.01673i	0.194965	+	0.194965i	0.797837	−	0.602873i	$-0.205977\pi$
$107$	2.01673	+	2.01673i	0.194965	+	0.194965i	−0.602873	+	0.797837i	$0.705977\pi$
$108$	1.50147	−	1.50147i	0.144479	−	0.144479i
$109$	−6.68119	+	6.68119i	−0.639942	+	0.639942i	−0.950541	−	0.310599i	$-0.899470\pi$
$109$	−6.68119	+	6.68119i	−0.639942	+	0.639942i	0.310599	+	0.950541i	$0.399470\pi$
$110$		−	5.17260i		−	0.493188i
$111$		−	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	$-0.917510\pi$
$113$	−7.55112	+	7.55112i	−0.710349	+	0.710349i	0.256259	+	0.966608i	$0.417510\pi$
$114$	26.4888	+	26.4888i	2.48090	+	2.48090i
$115$	−6.70055			−0.624830
$116$	10.9691	+	10.9691i	1.01845	+	1.01845i
$117$		−	15.7878i		−	1.45958i
$118$	−1.00295			−0.0923287
$119$	−0.615314	+	1.39127i	−0.0564058	+	0.127538i
$120$	1.50190			0.137104
$121$			4.75949i			0.432681i
$122$	−10.0778	−	10.0778i	−0.912402	−	0.912402i
$123$	5.95468			0.536915
$124$	−7.79296	−	7.79296i	−0.699829	−	0.699829i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−1.81936	+	1.81936i	−0.162082	+	0.162082i
$127$			15.7315i			1.39595i	0.716124	+	0.697974i	$0.245915\pi$
$127$			15.7315i			1.39595i	−0.716124	+	0.697974i	$0.754085\pi$
$128$		−	4.71221i		−	0.416505i
$129$	20.8957	−	20.8957i	1.83977	−	1.83977i
$130$	6.86358	−	6.86358i	0.601976	−	0.601976i
$131$	−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	$0.807203\pi$
$132$	14.4197			1.25507
$133$	−1.87045	−	1.87045i	−0.162189	−	0.162189i
$134$			3.88194i			0.335348i
$135$	0.928289			0.0798944
$136$	0.885087	+	2.28879i	0.0758956	+	0.196262i
$137$	−16.2144			−1.38529			−0.692644	−	0.721280i	$-0.743554\pi$
$137$	−16.2144			−1.38529			−0.692644	+	0.721280i	$0.743554\pi$
$138$		−	35.0112i		−	2.98035i
$139$	7.57109	+	7.57109i	0.642172	+	0.642172i	0.951089	−	0.308917i	$-0.0999666\pi$
$139$	7.57109	+	7.57109i	0.642172	+	0.642172i	−0.308917	+	0.951089i	$0.599967\pi$
$140$	−0.843976			−0.0713290
$141$	−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
$145$			6.78165i			0.563186i
$146$	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	$-0.650668\pi$
$149$	−11.1290			−0.911719			−0.455860	+	0.890052i	$0.650668\pi$
$150$	3.69471	+	3.69471i	0.301672	+	0.301672i
$151$		−	16.0861i		−	1.30907i	−0.756032	−	0.654535i	$-0.772865\pi$
$151$		−	16.0861i		−	1.30907i	0.756032	−	0.654535i	$-0.227135\pi$
$152$	−4.26702			−0.346101
$153$	5.00837	+	12.9514i	0.404903	+	1.04706i
$154$	−1.90849			−0.153790
$155$		−	4.81801i		−	0.386992i
$156$	19.1337	+	19.1337i	1.53192	+	1.53192i
$157$	−2.63326			−0.210157			−0.105079	−	0.994464i	$-0.533509\pi$
$157$	−2.63326			−0.210157			−0.105079	+	0.994464i	$0.533509\pi$
$158$	−7.88534	−	7.88534i	−0.627324	−	0.627324i
$159$	−12.1610	+	12.1610i	−0.964434	+	0.964434i
$160$	5.73561	−	5.73561i	0.453440	−	0.453440i
$161$			2.47224i			0.194840i
$162$		−	16.0702i		−	1.26259i
$163$	−13.5013	+	13.5013i	−1.05751	+	1.05751i	−0.0592626	+	0.998242i	$0.518875\pi$
$163$	−13.5013	+	13.5013i	−1.05751	+	1.05751i	−0.998242	+	0.0592626i	$0.981125\pi$
$164$	−3.81677	+	3.81677i	−0.298039	+	0.298039i
$165$	4.45751	+	4.45751i	0.347016	+	0.347016i
$166$	−20.6023			−1.59905
$167$	2.81953	+	2.81953i	0.218182	+	0.218182i	0.807732	−	0.589550i	$-0.200695\pi$
$167$	2.81953	+	2.81953i	0.218182	+	0.218182i	−0.589550	+	0.807732i	$0.700695\pi$
$168$		−	0.554142i		−	0.0427530i
$169$	8.97524			0.690403
$170$	−3.45315	+	7.80783i	−0.264845	+	0.598833i
$171$	−24.1455			−1.84645
$172$			26.7871i			2.04250i
$173$	−10.3293	−	10.3293i	−0.785322	−	0.785322i	0.195401	−	0.980723i	$-0.437399\pi$
$173$	−10.3293	−	10.3293i	−0.785322	−	0.785322i	−0.980723	+	0.195401i	$0.937399\pi$
$174$	−35.4349			−2.68631
$175$	−0.260895	−	0.260895i	−0.0197218	−	0.0197218i
$176$	5.90428	−	5.90428i	0.445052	−	0.445052i
$177$	0.864292	−	0.864292i	0.0649642	−	0.0649642i
$178$			8.91981i			0.668568i
$179$			14.7452i			1.10211i	0.834469	+	0.551054i	$0.185774\pi$
$179$			14.7452i			1.10211i	−0.834469	+	0.551054i	$0.814226\pi$
$180$	−5.44739	+	5.44739i	−0.406025	+	0.406025i
$181$	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
$183$	17.3692			1.28397
$184$	2.81994	+	2.81994i	0.207888	+	0.207888i
$185$			1.93935i			0.142584i
$186$	25.1747			1.84590
$187$	−4.16607	+	9.41980i	−0.304653	+	0.688844i
$188$	3.78153			0.275797
$189$		−	0.342503i		−	0.0249134i
$190$	−10.4970	−	10.4970i	−0.761533	−	0.761533i
$191$	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	$-0.766299\pi$
$193$	−1.00556	+	1.00556i	−0.0723819	+	0.0723819i	0.669989	+	0.742371i	$0.266299\pi$
$194$	18.6619	−	18.6619i	1.33985	−	1.33985i
$195$			11.8294i			0.847123i
$196$		−	15.7007i		−	1.12148i
$197$	12.3127	−	12.3127i	0.877240	−	0.877240i	−0.116008	−	0.993248i	$-0.537010\pi$
$197$	12.3127	−	12.3127i	0.877240	−	0.877240i	0.993248	+	0.116008i	$0.0370098\pi$
$198$	−12.3182	+	12.3182i	−0.875419	+	0.875419i
$199$	−12.6485	−	12.6485i	−0.896626	−	0.896626i	0.0985101	−	0.995136i	$-0.468592\pi$
$199$	−12.6485	−	12.6485i	−0.896626	−	0.896626i	−0.995136	+	0.0985101i	$0.968592\pi$
$200$	−0.595174			−0.0420851
$201$	−3.34527	−	3.34527i	−0.235957	−	0.235957i
$202$			18.8126i			1.32365i
$203$	2.50217			0.175618
$204$	−21.7660	−	9.62637i	−1.52392	−	0.673981i
$205$	−2.35972			−0.164810
$206$		−	9.89362i		−	0.689321i
$207$	15.9570	+	15.9570i	1.10909	+	1.10909i
$208$	15.6689			1.08644
$209$	−12.6642	−	12.6642i	−0.875999	−	0.875999i
$210$	1.36321	−	1.36321i	0.0940701	−	0.0940701i
$211$	−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	$0.329490\pi$
$212$		−	15.5897i		−	1.07071i
$213$			4.33930i			0.297324i
$214$	4.17587	−	4.17587i	0.285457	−	0.285457i
$215$	−8.28059	+	8.28059i	−0.564731	+	0.564731i
$216$	−0.390672	−	0.390672i	−0.0265818	−	0.0265818i
$217$	−1.77766			−0.120675
$218$	13.8342	+	13.8342i	0.936967	+	0.936967i
$219$			0.722494i			0.0488216i
$220$	−5.71425			−0.385255
$221$	−18.0272	+	6.97123i	−1.21264	+	0.468935i
$222$	−10.1333			−0.680104
$223$			3.93334i			0.263396i	0.991290	+	0.131698i	$0.0420428\pi$
$223$			3.93334i			0.263396i	−0.991290	+	0.131698i	$0.957957\pi$
$224$	−2.11622	−	2.11622i	−0.141396	−	0.141396i
$225$	−3.36786			−0.224524
$226$	15.6354	+	15.6354i	1.04005	+	1.04005i
$227$	2.46062	−	2.46062i	0.163317	−	0.163317i	−0.620717	−	0.784034i	$-0.713159\pi$
$227$	2.46062	−	2.46062i	0.163317	−	0.163317i	0.784034	+	0.620717i	$0.213159\pi$
$228$	29.2626	−	29.2626i	1.93796	−	1.93796i
$229$			4.41164i			0.291529i	0.989319	+	0.145765i	$0.0465642\pi$
$229$			4.41164i			0.291529i	−0.989319	+	0.145765i	$0.953436\pi$
$230$			13.8743i			0.914841i
$231$	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	0.244029	−	0.969768i	$-0.421531\pi$
$233$	−11.0779	−	11.0779i	−0.725739	−	0.725739i	−0.969768	+	0.244029i	$0.921531\pi$
$234$	−32.6904			−2.13704
$235$	1.16897	+	1.16897i	0.0762552	+	0.0762552i
$236$			1.10797i			0.0721227i
$237$	13.5904			0.882793
$238$	2.88079	+	1.27408i	0.186734	+	0.0825862i
$239$	−6.59116			−0.426346			−0.213173	−	0.977014i	$-0.568380\pi$
$239$	−6.59116			−0.426346			−0.213173	+	0.977014i	$0.568380\pi$
$240$			8.43468i			0.544456i
$241$	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	$0.704941\pi$
$242$	9.85506			0.633507
$243$	15.8178	+	15.8178i	1.01471	+	1.01471i
$244$	−11.1331	+	11.1331i	−0.712724	+	0.712724i
$245$	4.85349	−	4.85349i	0.310078	−	0.310078i
$246$		−	12.3298i		−	0.786121i
$247$		−	33.6084i		−	2.13845i
$248$	−2.02767	+	2.02767i	−0.128757	+	0.128757i
$249$	17.7541	−	17.7541i	1.12512	−	1.12512i
$250$	−1.46414	−	1.46414i	−0.0926006	−	0.0926006i
$251$	−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
$253$			16.7387i			1.05235i
$254$	32.5739			2.04387
$255$	−3.75266	−	9.70419i	−0.235001	−	0.607700i
$256$	10.4639			0.653991
$257$		−	10.5366i		−	0.657254i	−0.944460	−	0.328627i	$-0.893414\pi$
$257$		−	10.5366i		−	0.657254i	0.944460	−	0.328627i	$-0.106586\pi$
$258$	−43.2670	−	43.2670i	−2.69369	−	2.69369i
$259$	0.715544			0.0444618
$260$	−7.58230	−	7.58230i	−0.470235	−	0.470235i
$261$	16.1501	−	16.1501i	0.999665	−	0.999665i
$262$	−5.99070	+	5.99070i	−0.370107	+	0.370107i
$263$			13.6253i			0.840173i	0.907484	+	0.420086i	$0.138000\pi$
$263$			13.6253i			0.840173i	−0.907484	+	0.420086i	$0.862000\pi$
$264$		−	3.75189i		−	0.230913i
$265$	4.81919	−	4.81919i	0.296040	−	0.296040i
$266$	−3.87299	+	3.87299i	−0.237468	+	0.237468i
$267$	−7.68668	−	7.68668i	−0.470417	−	0.470417i
$268$	4.28844			0.261958
$269$	11.0360	+	11.0360i	0.672878	+	0.672878i	0.958378	−	0.285501i	$-0.0921599\pi$
$269$	11.0360	+	11.0360i	0.672878	+	0.672878i	−0.285501	+	0.958378i	$0.592160\pi$
$270$		−	1.92213i		−	0.116977i
$271$	−9.66560			−0.587143			−0.293572	−	0.955937i	$-0.594844\pi$
$271$	−9.66560			−0.587143			−0.293572	+	0.955937i	$0.594844\pi$
$272$	−12.8539	+	4.97066i	−0.779381	+	0.301391i
$273$	4.36460			0.264158
$274$			33.5737i			2.02826i
$275$	−1.76642	−	1.76642i	−0.106519	−	0.106519i
$276$	−38.6774			−2.32810
$277$	−0.955063	−	0.955063i	−0.0573842	−	0.0573842i	0.677832	−	0.735217i	$-0.262920\pi$
$277$	−0.955063	−	0.955063i	−0.0573842	−	0.0573842i	−0.735217	+	0.677832i	$0.762920\pi$
$278$	15.6768	−	15.6768i	0.940232	−	0.940232i
$279$	−11.4738	+	11.4738i	−0.686919	+	0.686919i
$280$			0.219596i			0.0131234i
$281$		−	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	0.270483	−	0.962725i	$-0.412816\pi$
$283$	20.7458	−	20.7458i	1.23321	−	1.23321i	0.962725	−	0.270483i	$-0.0871835\pi$
$284$	−2.78136	−	2.78136i	−0.165044	−	0.165044i
$285$	18.0917			1.07166
$286$	−17.1459	−	17.1459i	−1.01386	−	1.01386i
$287$			0.870646i			0.0513926i
$288$	−27.3180			−1.60973
$289$	12.5770	−	11.4376i	0.739825	−	0.672799i
$290$	14.0422			0.824585
$291$			32.1639i			1.88548i
$292$	−0.463096	−	0.463096i	−0.0271007	−	0.0271007i
$293$	−20.6478			−1.20626			−0.603129	−	0.797644i	$-0.706080\pi$
$293$	−20.6478			−1.20626			−0.603129	+	0.797644i	$0.706080\pi$
$294$	25.3600	+	25.3600i	1.47903	+	1.47903i
$295$	−0.342503	+	0.342503i	−0.0199413	+	0.0199413i
$296$	0.816177	−	0.816177i	0.0474393	−	0.0474393i
$297$		−	2.31896i		−	0.134560i
$298$			23.0437i			1.33489i
$299$	−22.2107	+	22.2107i	−1.28448	+	1.28448i
$300$	4.08161	−	4.08161i	0.235652	−	0.235652i
$301$	3.05521	+	3.05521i	0.176100	+	0.176100i
$302$	−33.3081			−1.91667
$303$	−16.2118	−	16.2118i	−0.931344	−	0.931344i
$304$		−	23.9637i		−	1.37441i
$305$	−6.88307			−0.394123
$306$	26.8173	−	10.3704i	1.53305	−	0.592837i
$307$	16.3437			0.932787			0.466393	−	0.884577i	$-0.345553\pi$
$307$	16.3437			0.932787			0.466393	+	0.884577i	$0.345553\pi$
$308$			2.10834i			0.120134i
$309$	8.52586	+	8.52586i	0.485019	+	0.485019i
$310$	−9.97624			−0.566613
$311$	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	0.296502	−	0.955032i	$-0.404180\pi$
$313$	22.1419	−	22.1419i	1.25153	−	1.25153i	0.955032	−	0.296502i	$-0.0958202\pi$
$314$			5.45247i			0.307701i
$315$			1.24261i			0.0700132i
$316$	−8.71105	+	8.71105i	−0.490035	+	0.490035i
$317$	8.87399	−	8.87399i	0.498413	−	0.498413i	−0.412531	−	0.910944i	$-0.635355\pi$
$317$	8.87399	−	8.87399i	0.498413	−	0.498413i	0.910944	+	0.412531i	$0.135355\pi$
$318$	25.1808	+	25.1808i	1.41207	+	1.41207i
$319$	16.9413			0.948528
$320$	−7.14921	−	7.14921i	−0.399653	−	0.399653i
$321$			7.19714i			0.401705i
$322$	5.11906			0.285274
$323$	10.6616	+	27.5704i	0.593229	+	1.53406i
$324$	−17.7530			−0.986278
$325$		−	4.68778i		−	0.260031i
$326$	27.9560	+	27.9560i	1.54834	+	1.54834i
$327$	−23.8433			−1.31854
$328$	0.993093	+	0.993093i	0.0548344	+	0.0548344i
$329$	0.431305	−	0.431305i	0.0237786	−	0.0237786i
$330$	9.22977	−	9.22977i	0.508082	−	0.508082i
$331$		−	0.497450i		−	0.0273423i	−0.999907	−	0.0136712i	$-0.995648\pi$
$331$		−	0.497450i		−	0.0273423i	0.999907	−	0.0136712i	$-0.00435180\pi$
$332$			22.7597i			1.24910i
$333$	4.61844	−	4.61844i	0.253089	−	0.253089i
$334$	5.83816	−	5.83816i	0.319450	−	0.319450i
$335$	1.32567	+	1.32567i	0.0724290	+	0.0724290i
$336$	3.11207			0.169777
$337$	−23.7358	−	23.7358i	−1.29297	−	1.29297i	−0.932940	−	0.360031i	$-0.882766\pi$
$337$	−23.7358	−	23.7358i	−1.29297	−	1.29297i	−0.360031	−	0.932940i	$-0.617234\pi$
$338$		−	18.5843i		−	1.01085i
$339$	−26.9478			−1.46360
$340$	8.62543	+	3.81475i	0.467780	+	0.206884i
$341$	−12.0359			−0.651780
$342$			49.9959i			2.70347i
$343$	−3.61701	−	3.61701i	−0.195300	−	0.195300i
$344$	6.96979			0.375786
$345$	−11.9562	−	11.9562i	−0.643699	−	0.643699i
$346$	−21.3880	+	21.3880i	−1.14983	+	1.14983i
$347$	18.5976	−	18.5976i	0.998370	−	0.998370i	−0.00162819	−	0.999999i	$-0.500518\pi$
$347$	18.5976	−	18.5976i	0.998370	−	0.998370i	0.999999	+	0.00162819i	$0.000518270\pi$
$348$			39.1455i			2.09842i
$349$			16.7865i			0.898560i	0.893391	+	0.449280i	$0.148319\pi$
$349$			16.7865i			0.898560i	−0.893391	+	0.449280i	$0.851681\pi$
$350$	−0.540212	+	0.540212i	−0.0288756	+	0.0288756i
$351$	3.07705	−	3.07705i	0.164241	−	0.164241i
$352$	−14.3281	−	14.3281i	−0.763692	−	0.763692i
$353$	−23.4532			−1.24829			−0.624144	−	0.781309i	$-0.714552\pi$
$353$	−23.4532			−1.24829			−0.624144	+	0.781309i	$0.714552\pi$
$354$	−1.78962	−	1.78962i	−0.0951170	−	0.0951170i
$355$		−	1.71958i		−	0.0912660i
$356$	9.85386			0.522253
$357$	−3.58047	+	1.38459i	−0.189498	+	0.0732800i
$358$	30.5316			1.61365
$359$		−	18.1568i		−	0.958279i	−0.877739	−	0.479139i	$-0.840949\pi$
$359$		−	18.1568i		−	0.958279i	0.877739	−	0.479139i	$-0.159051\pi$
$360$	1.41737	+	1.41737i	0.0747019	+	0.0747019i
$361$	−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
$365$		−	0.286310i		−	0.0149862i
$366$		−	35.9648i		−	1.87991i
$367$	−9.68061	+	9.68061i	−0.505324	+	0.505324i	−0.913087	−	0.407764i	$-0.866309\pi$
$367$	−9.68061	+	9.68061i	−0.505324	+	0.505324i	0.407764	+	0.913087i	$0.366309\pi$
$368$	−15.8368	+	15.8368i	−0.825550	+	0.825550i
$369$	5.61954	+	5.61954i	0.292541	+	0.292541i
$370$	4.01564			0.208763
$371$	−1.77809	−	1.77809i	−0.0923140	−	0.0923140i
$372$		−	27.8109i		−	1.44193i
$373$	−10.1594			−0.526035			−0.263018	−	0.964791i	$-0.584718\pi$
$373$	−10.1594			−0.526035			−0.263018	+	0.964791i	$0.584718\pi$
$374$	19.5048	+	8.62632i	1.00857	+	0.446056i
$375$	2.52346			0.130311
$376$		−	0.983925i		−	0.0507421i
$377$	22.4795	+	22.4795i	1.15775	+	1.15775i
$378$	−0.709190			−0.0364768
$379$	−2.94447	−	2.94447i	−0.151247	−	0.151247i	0.627428	−	0.778675i	$-0.284108\pi$
$379$	−2.94447	−	2.94447i	−0.151247	−	0.151247i	−0.778675	+	0.627428i	$0.784108\pi$
$380$	−11.5962	+	11.5962i	−0.594873	+	0.594873i
$381$	−28.0707	+	28.0707i	−1.43810	+	1.43810i
$382$		−	44.5045i		−	2.27705i
$383$			0.813273i			0.0415563i	0.999784	+	0.0207782i	$0.00661437\pi$
$383$			0.813273i			0.0415563i	−0.999784	+	0.0207782i	$0.993386\pi$
$384$	8.40828	−	8.40828i	0.429083	−	0.429083i
$385$	−0.651742	+	0.651742i	−0.0332159	+	0.0332159i
$386$	2.08213	+	2.08213i	0.105978	+	0.105978i
$387$	39.4394			2.00482
$388$	−20.6161	−	20.6161i	−1.04662	−	1.04662i
$389$		−	3.11676i		−	0.158026i	−0.996874	−	0.0790131i	$-0.974823\pi$
$389$		−	3.11676i		−	0.158026i	0.996874	−	0.0790131i	$-0.0251769\pi$
$390$	24.4942			1.24031
$391$	11.1745	−	25.2663i	0.565118	−	1.27777i
$392$	−4.08519			−0.206333
$393$		−	10.3250i		−	0.520828i
$394$	−25.4947	−	25.4947i	−1.28441	−	1.28441i
$395$	−5.38563			−0.270980
$396$	13.6081	+	13.6081i	0.683835	+	0.683835i
$397$	11.5998	−	11.5998i	0.582177	−	0.582177i	−0.353324	−	0.935501i	$-0.614949\pi$
$397$	11.5998	−	11.5998i	0.582177	−	0.582177i	0.935501	+	0.353324i	$0.114949\pi$
$398$	−26.1901	+	26.1901i	−1.31279	+	1.31279i
$399$		−	6.67512i		−	0.334174i
$400$		−	3.34250i		−	0.167125i
$401$	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
$405$	−5.48792	−	5.48792i	−0.272697	−	0.272697i
$406$		−	5.18102i		−	0.257130i
$407$	4.84469			0.240142
$408$	−2.50471	+	5.66333i	−0.124001	+	0.280377i
$409$	32.2867			1.59648			0.798238	−	0.602342i	$-0.205765\pi$
$409$	32.2867			1.59648			0.798238	+	0.602342i	$0.205765\pi$
$410$			4.88608i			0.241306i
$411$	−28.9323	−	28.9323i	−1.42712	−	1.42712i
$412$	−10.9296			−0.538464
$413$	0.126370	+	0.126370i	0.00621827	+	0.00621827i
$414$	33.0407	−	33.0407i	1.62386	−	1.62386i
$415$	−7.03561	+	7.03561i	−0.345364	+	0.345364i
$416$		−	38.0243i		−	1.86430i
$417$			27.0191i			1.32313i
$418$	−26.2226	+	26.2226i	−1.28259	+	1.28259i
$419$	13.3485	−	13.3485i	0.652115	−	0.652115i	−0.301387	−	0.953502i	$-0.597450\pi$
$419$	13.3485	−	13.3485i	0.652115	−	0.652115i	0.953502	+	0.301387i	$0.0974496\pi$
$420$	−1.50595	−	1.50595i	−0.0734831	−	0.0734831i
$421$	−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
$423$		−	5.56766i		−	0.270709i
$424$	−4.05632			−0.196993
$425$	1.48711	+	3.84558i	0.0721353	+	0.186538i
$426$	8.98502			0.435326
$427$			2.53958i			0.122899i
$428$	−4.61315	−	4.61315i	−0.222985	−	0.222985i
$429$	29.5511			1.42674
$430$	17.1459	+	17.1459i	0.826848	+	0.826848i
$431$	−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
$433$		−	27.9634i		−	1.34383i	−0.740626	−	0.671917i	$-0.765471\pi$
$433$		−	27.9634i		−	1.34383i	0.740626	−	0.671917i	$-0.234529\pi$
$434$			3.68085i			0.176686i
$435$	−12.1009	+	12.1009i	−0.580193	+	0.580193i
$436$	15.2828	−	15.2828i	0.731914	−	0.731914i
$437$	33.9686	+	33.9686i	1.62494	+	1.62494i
$438$	1.49600			0.0714819
$439$	8.87022	+	8.87022i	0.423353	+	0.423353i	0.886356	−	0.463004i	$-0.153228\pi$
$439$	8.87022	+	8.87022i	0.423353	+	0.423353i	−0.463004	+	0.886356i	$0.653228\pi$
$440$			1.48680i			0.0708806i
$441$	−23.1166			−1.10079
$442$	14.4347	+	37.3274i	0.686589	+	1.77548i
$443$	−19.9529			−0.947991			−0.473995	−	0.880527i	$-0.657189\pi$
$443$	−19.9529			−0.947991			−0.473995	+	0.880527i	$0.657189\pi$
$444$			11.1944i			0.531264i
$445$	3.04608	+	3.04608i	0.144398	+	0.144398i
$446$	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	−0.284930	−	0.958548i	$-0.591970\pi$
$449$	14.2737	−	14.2737i	0.673618	−	0.673618i	0.958548	+	0.284930i	$0.0919704\pi$
$450$			6.97354i			0.328736i
$451$			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
$455$	−1.72961			−0.0810852
$456$	−7.61389	−	7.61389i	−0.356553	−	0.356553i
$457$			37.7391i			1.76536i	0.469973	+	0.882681i	$0.344263\pi$
$457$			37.7391i			1.76536i	−0.469973	+	0.882681i	$0.655737\pi$
$458$	9.13479			0.426841
$459$	−1.54810	+	3.50038i	−0.0722592	+	0.163384i
$460$	15.3271			0.714630
$461$			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
$463$	13.1481			0.611044			0.305522	−	0.952185i	$-0.401169\pi$
$463$	13.1481			0.611044			0.305522	+	0.952185i	$0.401169\pi$
$464$	16.0285	+	16.0285i	0.744103	+	0.744103i
$465$	8.59706	−	8.59706i	0.398679	−	0.398679i
$466$	−22.9381	+	22.9381i	−1.06259	+	1.06259i
$467$		−	16.2167i		−	0.750422i	−0.926940	−	0.375211i	$-0.877570\pi$
$467$		−	16.2167i		−	0.750422i	0.926940	−	0.375211i	$-0.122430\pi$
$468$			36.1136i			1.66935i
$469$	0.489120	−	0.489120i	0.0225855	−	0.0225855i
$470$	2.42049	−	2.42049i	0.111649	−	0.111649i
$471$	−4.69869	−	4.69869i	−0.216504	−	0.216504i
$472$	0.288285			0.0132694
$473$	20.6857	+	20.6857i	0.951132	+	0.951132i
$474$		−	28.1405i		−	1.29254i
$475$	−7.16938			−0.328954
$476$	1.40749	−	3.18245i	0.0645124	−	0.145867i
$477$	−22.9532			−1.05096
$478$			13.6477i			0.624233i
$479$	1.46724	+	1.46724i	0.0670398	+	0.0670398i	0.739832	−	0.672792i	$-0.234905\pi$
$479$	1.46724	+	1.46724i	0.0670398	+	0.0670398i	−0.672792	+	0.739832i	$0.734905\pi$
$480$	20.4688			0.934267
$481$	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
$485$		−	12.7460i		−	0.578764i
$486$	32.7524	−	32.7524i	1.48568	−	1.48568i
$487$	−16.9890	+	16.9890i	−0.769843	+	0.769843i	−0.978079	−	0.208236i	$-0.933228\pi$
$487$	−16.9890	+	16.9890i	−0.769843	+	0.769843i	0.208236	+	0.978079i	$0.433228\pi$
$488$	2.89675	+	2.89675i	0.131130	+	0.131130i
$489$	−48.1824			−2.17888
$490$	−10.0497	−	10.0497i	−0.453999	−	0.453999i
$491$			22.3803i			1.01001i	0.863116	+	0.505005i	$0.168509\pi$
$491$			22.3803i			1.01001i	−0.863116	+	0.505005i	$0.831491\pi$
$492$	−13.6210			−0.614080
$493$	−25.5721	−	11.3097i	−1.15171	−	0.509364i
$494$	−69.5901			−3.13100
$495$			8.41327i			0.378148i
$496$	−11.3874	−	11.3874i	−0.511310	−	0.511310i
$497$	−0.634459			−0.0284594
$498$	−36.7619	−	36.7619i	−1.64734	−	1.64734i
$499$	−2.61493	+	2.61493i	−0.117060	+	0.117060i	−0.763210	−	0.646150i	$-0.776378\pi$
$499$	−2.61493	+	2.61493i	−0.117060	+	0.117060i	0.646150	+	0.763210i	$0.276378\pi$
$500$	−1.61746	+	1.61746i	−0.0723352	+	0.0723352i
$501$			10.0621i			0.449541i
$502$			8.90965i			0.397657i
$503$	−13.0544	+	13.0544i	−0.582066	+	0.582066i	−0.935471	−	0.353404i	$-0.885024\pi$
$503$	−13.0544	+	13.0544i	−0.582066	+	0.582066i	0.353404	+	0.935471i	$0.385024\pi$
$504$	0.522954	−	0.522954i	0.0232942	−	0.0232942i
$505$	6.42443	+	6.42443i	0.285883	+	0.285883i
$506$	34.6593			1.54079
$507$	16.0150	+	16.0150i	0.711253	+	0.711253i
$508$		−	35.9849i		−	1.59657i
$509$	−17.3588			−0.769415			−0.384708	−	0.923039i	$-0.625698\pi$
$509$	−17.3588			−0.769415			−0.384708	+	0.923039i	$0.625698\pi$
$510$	−20.0936	+	7.77031i	−0.889760	+	0.344075i
$511$	−0.105637			−0.00467312
$512$		−	31.0910i		−	1.37404i
$513$	−4.70598	−	4.70598i	−0.207774	−	0.207774i
$514$	−21.8172			−0.962314
$515$	−3.37863	−	3.37863i	−0.148880	−	0.148880i
$516$	−47.7977	+	47.7977i	−2.10418	+	2.10418i
$517$	2.92021	−	2.92021i	0.128431	−	0.128431i
$518$		−	1.48162i		−	0.0650984i
$519$		−	36.8623i		−	1.61808i
$520$	−1.97286	+	1.97286i	−0.0865155	+	0.0865155i
$521$	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
$523$	5.59638			0.244712			0.122356	−	0.992486i	$-0.460955\pi$
$523$	5.59638			0.244712			0.122356	+	0.992486i	$0.460955\pi$
$524$	6.61802	+	6.61802i	0.289109	+	0.289109i
$525$		−	0.931060i		−	0.0406348i
$526$	28.2127			1.23013
$527$	18.1677	+	8.03498i	0.791397	+	0.350009i
$528$	21.0707			0.916984
$529$		−	21.8974i		−	0.952062i
$530$	−9.97868	−	9.97868i	−0.433446	−	0.433446i
$531$	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
$535$		−	2.85209i		−	0.123307i
$536$		−	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
$540$	−2.12340			−0.0913768
$541$	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	$0.432252\pi$
$542$			20.0137i			0.859662i
$543$	28.4179			1.21953
$544$	12.0625	+	31.1930i	0.517175	+	1.33739i
$545$	9.44863			0.404735
$546$		−	9.03740i		−	0.386765i
$547$	20.7878	+	20.7878i	0.888823	+	0.888823i	0.994410	−	0.105588i	$-0.0336723\pi$
$547$	20.7878	+	20.7878i	0.888823	+	0.888823i	−0.105588	+	0.994410i	$0.533672\pi$
$548$	37.0894			1.58438
$549$	16.3916	+	16.3916i	0.699577	+	0.699577i
$550$	−3.65758	+	3.65758i	−0.155960	+	0.155960i
$551$	34.3797	−	34.3797i	1.46462	−	1.46462i
$552$			10.0635i			0.428333i
$553$			1.98709i			0.0844995i
$554$	−1.97757	+	1.97757i	−0.0840187	+	0.0840187i
$555$	−3.46049	+	3.46049i	−0.146890	+	0.146890i
$556$	−17.3184	−	17.3184i	−0.734464	−	0.734464i
$557$	−27.9399			−1.18385			−0.591927	−	0.805992i	$-0.701632\pi$
$557$	−27.9399			−1.18385			−0.591927	+	0.805992i	$0.701632\pi$
$558$	23.7578	+	23.7578i	1.00575	+	1.00575i
$559$			54.8963i			2.32186i
$560$	−1.23325			−0.0521145
$561$	−24.2420	+	9.37453i	−1.02350	+	0.395793i
$562$	−32.8362			−1.38511
$563$			11.2994i			0.476213i	0.971239	+	0.238106i	$0.0765267\pi$
$563$			11.2994i			0.476213i	−0.971239	+	0.238106i	$0.923473\pi$
$564$	6.74761	+	6.74761i	0.284126	+	0.284126i
$565$	10.6789			0.449264
$566$	−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	$-0.918235\pi$
$569$		−	12.1204i		−	0.508114i	0.967189	−	0.254057i	$-0.0817650\pi$
$570$		−	37.4608i		−	1.56906i
$571$	−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
$575$	4.73801	+	4.73801i	0.197589	+	0.197589i
$576$			34.0508i			1.41878i
$577$	−9.09883			−0.378789			−0.189395	−	0.981901i	$-0.560653\pi$
$577$	−9.09883			−0.378789			−0.189395	+	0.981901i	$0.560653\pi$
$578$	−23.6828	−	26.0421i	−0.985076	−	1.08321i
$579$	−3.58856			−0.149135
$580$		−	15.5126i		−	0.644126i
$581$	2.59587	+	2.59587i	0.107695	+	0.107695i
$582$	66.5991			2.76062
$583$	−12.0388	−	12.0388i	−0.498597	−	0.498597i
$584$	−0.120494	+	0.120494i	−0.00498608	+	0.00498608i
$585$	−11.1637	+	11.1637i	−0.461560	+	0.461560i
$586$			42.7536i			1.76614i
$587$			11.2991i			0.466362i	0.972433	+	0.233181i	$0.0749134\pi$
$587$			11.2991i			0.466362i	−0.972433	+	0.233181i	$0.925087\pi$
$588$	28.0156	−	28.0156i	1.15534	−	1.15534i
$589$	−24.4250	+	24.4250i	−1.00641	+	1.00641i
$590$	0.709190	+	0.709190i	0.0291969	+	0.0291969i
$591$	43.9403			1.80746
$592$	4.58366	+	4.58366i	0.188387	+	0.188387i
$593$		−	42.8620i		−	1.76013i	−0.474851	−	0.880066i	$-0.657498\pi$
$593$		−	42.8620i		−	1.76013i	0.474851	−	0.880066i	$-0.342502\pi$
$594$	−4.80167			−0.197015
$595$	1.41887	−	0.548685i	0.0581680	−	0.0224939i
$596$	25.4568			1.04275
$597$		−	45.1388i		−	1.84741i
$598$	45.9898	+	45.9898i	1.88066	+	1.88066i
$599$	21.0108			0.858478			0.429239	−	0.903191i	$-0.358782\pi$
$599$	21.0108			0.858478			0.429239	+	0.903191i	$0.358782\pi$
$600$	−1.06200	−	1.06200i	−0.0433561	−	0.0433561i
$601$	−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
$603$		−	6.31399i		−	0.257126i
$604$			36.7960i			1.49721i
$605$	3.36547	−	3.36547i	0.136826	−	0.136826i
$606$	−33.5684	+	33.5684i	−1.36362	+	1.36362i
$607$	−19.3965	−	19.3965i	−0.787281	−	0.787281i	0.193767	−	0.981048i	$-0.437929\pi$
$607$	−19.3965	−	19.3965i	−0.787281	−	0.787281i	−0.981048	+	0.193767i	$0.937929\pi$
$608$	−58.1535			−2.35844
$609$	4.46476	+	4.46476i	0.180921	+	0.180921i
$610$			14.2522i			0.577053i
$611$	7.74971			0.313520
$612$	−11.4563	−	29.6255i	−0.463095	−	1.19754i
$613$	0.297602			0.0120200			0.00601001	−	0.999982i	$-0.498087\pi$
$613$	0.297602			0.0120200			0.00601001	+	0.999982i	$0.498087\pi$
$614$		−	33.8416i		−	1.36573i
$615$	−4.21059	−	4.21059i	−0.169787	−	0.169787i
$616$	0.548573			0.0221026
$617$	8.95764	+	8.95764i	0.360621	+	0.360621i	0.864041	−	0.503421i	$-0.167925\pi$
$617$	8.95764	+	8.95764i	0.360621	+	0.360621i	−0.503421	+	0.864041i	$0.667925\pi$
$618$	17.6538	−	17.6538i	0.710138	−	0.710138i
$619$	6.89991	−	6.89991i	0.277331	−	0.277331i	−0.554712	−	0.832043i	$-0.687171\pi$
$619$	6.89991	−	6.89991i	0.277331	−	0.277331i	0.832043	+	0.554712i	$0.187171\pi$
$620$			11.0209i			0.442610i
$621$			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
$625$	−1.00000			−0.0400000
$626$	−45.8473	−	45.8473i	−1.83243	−	1.83243i
$627$		−	45.1948i		−	1.80491i
$628$	6.02343			0.240361
$629$	−7.31286	−	3.23424i	−0.291583	−	0.128958i
$630$	2.57297			0.102509
$631$		−	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
$633$	−18.1179			−0.720123
$634$	−18.3746	−	18.3746i	−0.729748	−	0.729748i
$635$	11.1239	−	11.1239i	0.441437	−	0.441437i
$636$	27.8176	−	27.8176i	1.10304	−	1.10304i
$637$		−	32.1763i		−	1.27487i
$638$		−	35.0788i		−	1.38878i
$639$	−4.09508	+	4.09508i	−0.161999	+	0.161999i
$640$	−3.33204	+	3.33204i	−0.131710	+	0.131710i
$641$	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	$0.725050\pi$
$642$	14.9025			0.588154
$643$	10.9095	+	10.9095i	0.430227	+	0.430227i	0.888706	−	0.458478i	$-0.151605\pi$
$643$	10.9095	+	10.9095i	0.430227	+	0.430227i	−0.458478	+	0.888706i	$0.651605\pi$
$644$		−	5.65511i		−	0.222842i
$645$	−29.5510			−1.16357
$646$	57.0877	−	22.0761i	2.24609	−	0.868573i
$647$	−10.5735			−0.415687			−0.207843	−	0.978162i	$-0.566644\pi$
$647$	−10.5735			−0.415687			−0.207843	+	0.978162i	$0.566644\pi$
$648$			4.61919i			0.181459i
$649$	0.855606	+	0.855606i	0.0335855	+	0.0335855i
$650$	−9.70657			−0.380723
$651$	−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	$-0.842025\pi$
$653$	−10.3029	+	10.3029i	−0.403184	+	0.403184i	0.476169	+	0.879354i	$0.342025\pi$
$654$			49.3702i			1.93053i
$655$			4.09160i			0.159872i
$656$	−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	$-0.346654\pi$
$659$	23.7883			0.926660			0.463330	+	0.886186i	$0.346654\pi$
$660$	−10.1963	−	10.1963i	−0.396889	−	0.396889i
$661$		−	9.91502i		−	0.385650i	−0.981233	−	0.192825i	$-0.938235\pi$
$661$		−	9.91502i		−	0.385650i	0.981233	−	0.192825i	$-0.0617649\pi$
$662$	−1.03003			−0.0400331
$663$	−44.6062	−	19.7279i	−1.73236	−	0.766167i
$664$	5.92189			0.229814
$665$			2.64522i			0.102577i
$666$	−9.56300	−	9.56300i	−0.370559	−	0.370559i
$667$	−45.4408			−1.75948
$668$	−6.44950	−	6.44950i	−0.249539	−	0.249539i
$669$	−7.01848	+	7.01848i	−0.271350	+	0.271350i
$670$	2.74495	−	2.74495i	0.106046	−	0.106046i
$671$			17.1946i			0.663790i
$672$		−	7.55218i		−	0.291331i
$673$	−2.81097	+	2.81097i	−0.108355	+	0.108355i	−0.759206	−	0.650851i	$-0.774412\pi$
$673$	−2.81097	+	2.81097i	−0.108355	+	0.108355i	0.650851	+	0.759206i	$0.274412\pi$
$674$	−49.1477	+	49.1477i	−1.89310	+	1.89310i
$675$	−0.656399	−	0.656399i	−0.0252648	−	0.0252648i
$676$	−20.5303			−0.789627
$677$	−14.4022	−	14.4022i	−0.553523	−	0.553523i	0.373933	−	0.927456i	$-0.378009\pi$
$677$	−14.4022	−	14.4022i	−0.553523	−	0.553523i	−0.927456	+	0.373933i	$0.878009\pi$
$678$			55.7984i			2.14293i
$679$	−4.70276			−0.180475
$680$	0.992568	−	2.24427i	0.0380632	−	0.0860638i
$681$	8.78125			0.336498
$682$			24.9217i			0.954300i
$683$	20.4617	+	20.4617i	0.782944	+	0.782944i	0.980327	−	0.197383i	$-0.0632442\pi$
$683$	20.4617	+	20.4617i	0.782944	+	0.782944i	−0.197383	+	0.980327i	$0.563244\pi$
$684$	55.2313			2.11182
$685$	11.4653	+	11.4653i	0.438067	+	0.438067i
$686$	−7.48943	+	7.48943i	−0.285948	+	0.285948i
$687$	−7.87193	+	7.87193i	−0.300333	+	0.300333i
$688$			39.1424i			1.49229i
$689$		−	31.9489i		−	1.21716i
$690$	−24.7566	+	24.7566i	−0.942469	+	0.942469i
$691$	−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
$693$	3.10417			0.117918
$694$	−38.5084	−	38.5084i	−1.46176	−	1.46176i
$695$		−	10.7071i		−	0.406145i
$696$	10.1854			0.386075
$697$	3.93530	−	8.89800i	0.149060	−	0.337036i
$698$	34.7583			1.31562
$699$		−	39.5340i		−	1.49531i
$700$	0.596781	+	0.596781i	0.0225562	+	0.0225562i
$701$	−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
$705$			4.17172i			0.157116i
$706$			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	$-0.887480\pi$
$709$	−34.1983	−	34.1983i	−1.28435	−	1.28435i	−0.346176	−	0.938170i	$-0.612520\pi$
$710$	−3.56059			−0.133627
$711$	12.8255	+	12.8255i	0.480995	+	0.480995i
$712$		−	2.56390i		−	0.0960861i
$713$	32.2834			1.20902
$714$	2.86694	+	7.41376i	0.107293	+	0.277453i
$715$	−11.7105			−0.437949
$716$		−	33.7288i		−	1.26050i
$717$	−11.7610	−	11.7610i	−0.439222	−	0.439222i
$718$	−37.5957			−1.40306
$719$	5.83066	+	5.83066i	0.217447	+	0.217447i	0.807422	−	0.589975i	$-0.200862\pi$
$719$	5.83066	+	5.83066i	0.217447	+	0.217447i	−0.589975	+	0.807422i	$0.700862\pi$
$720$	−7.95997	+	7.95997i	−0.296650	+	0.296650i
$721$	−1.24658	+	1.24658i	−0.0464252	+	0.0464252i
$722$			67.0878i			2.49675i
$723$			11.0538i			0.411096i
$724$	−18.2150	+	18.2150i	−0.676956	+	0.676956i
$725$	4.79535	−	4.79535i	0.178095	−	0.178095i
$726$	17.5849	+	17.5849i	0.652638	+	0.652638i
$727$	6.46089			0.239621			0.119811	−	0.992797i	$-0.461771\pi$
$727$	6.46089			0.239621			0.119811	+	0.992797i	$0.461771\pi$
$728$	0.727907	+	0.727907i	0.0269780	+	0.0269780i
$729$			33.1658i			1.22836i
$730$	−0.592838			−0.0219419
$731$	−17.4148	−	45.0338i	−0.644109	−	1.66563i
$732$	−39.7309			−1.46850
$733$			15.9605i			0.589515i	0.955572	+	0.294758i	$0.0952389\pi$
$733$			15.9605i			0.589515i	−0.955572	+	0.294758i	$0.904761\pi$
$734$	20.0448	+	20.0448i	0.739867	+	0.739867i
$735$	17.3207			0.638884
$736$	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	$-0.995545\pi$
$739$		−	0.760943i		−	0.0279918i	0.999902	−	0.0139959i	$-0.00445517\pi$
$740$		−	4.43614i		−	0.163076i
$741$	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	0.999791	+	0.0204461i	$0.00650865\pi$
$743$	27.8096	+	27.8096i	1.02024	+	1.02024i	0.0204461	+	0.999791i	$0.493491\pi$
$744$	−7.23617			−0.265291
$745$	7.86936	+	7.86936i	0.288311	+	0.288311i
$746$			21.0362i			0.770191i
$747$	33.5097			1.22606
$748$	9.52963	−	21.5472i	0.348438	−	0.787844i
$749$	−1.05231			−0.0384506
$750$		−	5.22511i		−	0.190794i
$751$	−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	$0.961458\pi$
$752$	5.52574			0.201503
$753$	−7.67792	−	7.67792i	−0.279799	−	0.279799i
$754$	46.5464	−	46.5464i	1.69512	−	1.69512i
$755$	−11.3746	+	11.3746i	−0.413964	+	0.413964i
$756$			0.783454i			0.0284939i
$757$			23.0663i			0.838359i	0.907903	+	0.419180i	$0.137682\pi$
$757$			23.0663i			0.838359i	−0.907903	+	0.419180i	$0.862318\pi$
$758$	−6.09685	+	6.09685i	−0.221448	+	0.221448i
$759$	−29.8678	+	29.8678i	−1.08413	+	1.08413i
$760$	3.01724	+	3.01724i	0.109447	+	0.109447i
$761$	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
$763$		−	3.48618i		−	0.126208i
$764$	−49.1648			−1.77872
$765$	5.61657	−	12.6995i	0.203067	−	0.459151i
$766$	1.68397			0.0608445
$767$			2.27063i			0.0819876i
$768$	18.6713	+	18.6713i	0.673741	+	0.673741i
$769$	3.68785			0.132987			0.0664936	−	0.997787i	$-0.478819\pi$
$769$	3.68785			0.132987			0.0664936	+	0.997787i	$0.478819\pi$
$770$	1.34951	+	1.34951i	0.0486328	+	0.0486328i
$771$	18.8010	−	18.8010i	0.677102	−	0.677102i
$772$	2.30016	−	2.30016i	0.0827845	−	0.0827845i
$773$		−	5.04027i		−	0.181286i	−0.995883	−	0.0906430i	$-0.971108\pi$
$773$		−	5.04027i		−	0.181286i	0.995883	−	0.0906430i	$-0.0288922\pi$
$774$		−	81.6638i		−	2.93534i
$775$	−3.40685	+	3.40685i	−0.122378	+	0.122378i
$776$	−5.36415	+	5.36415i	−0.192562	+	0.192562i
$777$	1.27679	+	1.27679i	0.0458045	+	0.0458045i
$778$	−6.45361			−0.231373
$779$	11.9627	+	11.9627i	0.428607	+	0.428607i
$780$		−	27.0591i		−	0.968871i
$781$	−4.29569			−0.153712
$782$	−52.3168	−	23.1380i	−1.87084	−	0.827414i
$783$	6.29533			0.224977
$784$		−	22.9425i		−	0.819375i
$785$	1.86200	+	1.86200i	0.0664576	+	0.0664576i
$786$	−21.3791			−0.762567
$787$	−9.65129	−	9.65129i	−0.344031	−	0.344031i	0.513849	−	0.857880i	$-0.328219\pi$
$787$	−9.65129	−	9.65129i	−0.344031	−	0.344031i	−0.857880	+	0.513849i	$0.828219\pi$
$788$	−28.1644	+	28.1644i	−1.00332	+	1.00332i
$789$	−24.3124	+	24.3124i	−0.865545	+	0.865545i
$790$			11.1516i			0.396754i
$791$		−	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
$795$	17.1983			0.609961
$796$	28.9326	+	28.9326i	1.02549	+	1.02549i
$797$			16.6869i			0.591081i	0.955330	+	0.295541i	$0.0954997\pi$
$797$			16.6869i			0.591081i	−0.955330	+	0.295541i	$0.904500\pi$
$798$	−13.8216			−0.489279
$799$	−6.35742	+	2.45845i	−0.224909	+	0.0869736i
$800$	−8.11138			−0.286780
$801$		−	14.5081i		−	0.512619i
$802$	−21.1498	−	21.1498i	−0.746824	−	0.746824i
$803$	−0.715232			−0.0252400
$804$	7.65211	+	7.65211i	0.269869	+	0.269869i
$805$	1.74814	−	1.74814i	0.0616139	−	0.0616139i
$806$	−33.0688	+	33.0688i	−1.16480	+	1.16480i
$807$			39.3844i			1.38640i
$808$		−	5.40746i		−	0.190234i
$809$	−21.7364	+	21.7364i	−0.764211	+	0.764211i	−0.977081	−	0.212870i	$-0.931719\pi$
$809$	−21.7364	+	21.7364i	−0.764211	+	0.764211i	0.212870	+	0.977081i	$0.431719\pi$
$810$	−11.3634	+	11.3634i	−0.399268	+	0.399268i
$811$	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	$0.627489\pi$
$812$	−5.72355			−0.200857
$813$	−17.2469	−	17.2469i	−0.604874	−	0.604874i
$814$		−	10.0315i		−	0.351603i
$815$	19.0937			0.668825
$816$	−31.8053	−	14.0665i	−1.11341	−	0.492425i
$817$	83.9571			2.93729
$818$		−	66.8534i		−	2.33747i
$819$	4.11895	+	4.11895i	0.143928	+	0.143928i
$820$	5.39772			0.188497
$821$	−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	$-0.860937\pi$
$823$	−13.8553	+	13.8553i	−0.482965	+	0.482965i	0.423113	+	0.906077i	$0.360937\pi$
$824$			2.84381i			0.0990686i
$825$		−	6.30387i		−	0.219472i
$826$	0.261664	−	0.261664i	0.00910444	−	0.00910444i
$827$	24.8128	−	24.8128i	0.862827	−	0.862827i	−0.128838	−	0.991666i	$-0.541125\pi$
$827$	24.8128	−	24.8128i	0.862827	−	0.862827i	0.991666	+	0.128838i	$0.0411248\pi$
$828$	−36.5006	−	36.5006i	−1.26848	−	1.26848i
$829$	46.3683			1.61044			0.805219	−	0.592978i	$-0.202048\pi$
$829$	46.3683			1.61044			0.805219	+	0.592978i	$0.202048\pi$
$830$	14.5680	+	14.5680i	0.505663	+	0.505663i
$831$		−	3.40835i		−	0.118234i
$832$	−47.3958			−1.64315
$833$	10.2073	+	26.3956i	0.353662	+	0.914552i
$834$	55.9460			1.93725
$835$		−	3.98742i		−	0.137990i
$836$	28.9685	+	28.9685i	1.00190	+	1.00190i
$837$	−4.47251			−0.154593
$838$	−27.6395	−	27.6395i	−0.954791	−	0.954791i
$839$	−17.6001	+	17.6001i	−0.607623	+	0.607623i	−0.942324	−	0.334701i	$-0.891365\pi$
$839$	−17.6001	+	17.6001i	−0.607623	+	0.607623i	0.334701	+	0.942324i	$0.391365\pi$
$840$	−0.391838	+	0.391838i	−0.0135197	+	0.0135197i
$841$			16.9908i			0.585890i
$842$			4.26559i			0.147002i
$843$	28.2967	−	28.2967i	0.974589	−	0.974589i
$844$	11.6130	−	11.6130i	0.399737	−	0.399737i
$845$	−6.34645	−	6.34645i	−0.218325	−	0.218325i
$846$	−11.5285			−0.396357
$847$	−1.24173	−	1.24173i	−0.0426662	−	0.0426662i
$848$		−	22.7804i		−	0.782281i
$849$	74.0357			2.54090
$850$	7.96272	−	3.07922i	0.273119	−	0.105617i
$851$	−12.9947			−0.445453
$852$		−	9.92589i		−	0.340055i
$853$	−19.8742	−	19.8742i	−0.680478	−	0.680478i	0.279629	−	0.960108i	$-0.409788\pi$
$853$	−19.8742	−	19.8742i	−0.680478	−	0.680478i	−0.960108	+	0.279629i	$0.909788\pi$
$854$	5.25850			0.179942
$855$	17.0734	+	17.0734i	0.583899	+	0.583899i
$856$	−1.20031	+	1.20031i	−0.0410256	+	0.0410256i
$857$	−17.3313	+	17.3313i	−0.592025	+	0.592025i	−0.938178	−	0.346153i	$-0.887488\pi$
$857$	−17.3313	+	17.3313i	−0.592025	+	0.592025i	0.346153	+	0.938178i	$0.387488\pi$
$858$		−	61.1889i		−	2.08896i
$859$		−	12.8979i		−	0.440069i	−0.975492	−	0.220034i	$-0.929383\pi$
$859$		−	12.8979i		−	0.440069i	0.975492	−	0.220034i	$-0.0706170\pi$
$860$	18.9413	−	18.9413i	0.645894	−	0.645894i
$861$	−1.55354	+	1.55354i	−0.0529447	+	0.0529447i
$862$	5.45773	+	5.45773i	0.185891	+	0.185891i
$863$	−5.83668			−0.198683			−0.0993414	−	0.995053i	$-0.531674\pi$
$863$	−5.83668			−0.198683			−0.0993414	+	0.995053i	$0.531674\pi$
$864$	−5.32430	−	5.32430i	−0.181136	−	0.181136i
$865$			14.6078i			0.496681i
$866$	−57.9014			−1.96757
$867$	42.8507	+	2.03316i	1.45528	+	0.0690496i
$868$	4.06629			0.138019
$869$			13.4538i			0.456390i
$870$	25.0563	+	25.0563i	0.849487	+	0.849487i
$871$	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
$875$			0.368961i			0.0124732i
$876$		−	1.65266i		−	0.0558382i
$877$	−13.2827	+	13.2827i	−0.448526	+	0.448526i	−0.894864	−	0.446338i	$-0.852728\pi$
$877$	−13.2827	+	13.2827i	−0.448526	+	0.448526i	0.446338	+	0.894864i	$0.352728\pi$
$878$	18.3668	−	18.3668i	0.619850	−	0.619850i
$879$	−36.8431	−	36.8431i	−1.24269	−	1.24269i
$880$	−8.34991			−0.281475
$881$	−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	$-0.530018\pi$
$882$			47.8655i			1.61171i
$883$	6.15932			0.207277			0.103639	−	0.994615i	$-0.466951\pi$
$883$	6.15932			0.207277			0.103639	+	0.994615i	$0.466951\pi$
$884$	41.2362	−	15.9462i	1.38692	−	0.536330i
$885$	−1.22229			−0.0410870
$886$			41.3147i			1.38800i
$887$	−11.8423	−	11.8423i	−0.397627	−	0.397627i	0.479768	−	0.877395i	$-0.340721\pi$
$887$	−11.8423	−	11.8423i	−0.397627	−	0.397627i	−0.877395	+	0.479768i	$0.840721\pi$
$888$	2.91270			0.0977440
$889$	−4.10428	−	4.10428i	−0.137653	−	0.137653i
$890$	6.30726	−	6.30726i	0.211420	−	0.211420i
$891$	−13.7094	+	13.7094i	−0.459281	+	0.459281i
$892$		−	8.99726i		−	0.301251i
$893$		−	11.8522i		−	0.396620i
$894$	−41.1183	+	41.1183i	−1.37520	+	1.37520i
$895$	10.4264	−	10.4264i	0.348517	−	0.348517i
$896$	1.22939	+	1.22939i	0.0410711	+	0.0410711i
$897$	−79.2637			−2.64654
$898$	−29.5553	−	29.5553i	−0.986274	−	0.986274i
$899$		−	32.6741i		−	1.08974i
$900$	7.70378			0.256793
$901$	10.1352	+	26.2091i	0.337652	+	0.873150i
$902$	12.2059			0.406412
$903$			10.9032i			0.362835i
$904$	−4.49422	−	4.49422i	−0.149476	−	0.149476i
$905$	−11.2615			−0.374344
$906$	−59.4336	−	59.4336i	−1.97455	−	1.97455i
$907$	5.74762	−	5.74762i	0.190847	−	0.190847i	−0.605215	−	0.796062i	$-0.706913\pi$
$907$	5.74762	−	5.74762i	0.190847	−	0.190847i	0.796062	+	0.605215i	$0.206913\pi$
$908$	−5.62851	+	5.62851i	−0.186789	+	0.186789i
$909$		−	30.5988i		−	1.01490i
$910$			3.58135i			0.118721i
$911$	−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
$915$	−12.2819	−	12.2819i	−0.406025	−	0.406025i
$916$		−	10.0913i		−	0.333427i
$917$	1.50964			0.0498528
$918$	7.24792	+	3.20552i	0.239217	+	0.105798i
$919$	−24.2398			−0.799596			−0.399798	−	0.916603i	$-0.630920\pi$
$919$	−24.2398			−0.799596			−0.399798	+	0.916603i	$0.630920\pi$
$920$		−	3.98799i		−	0.131480i
$921$	29.1631	+	29.1631i	0.960956	+	0.960956i
$922$	79.0435			2.60316
$923$	−5.70000	−	5.70000i	−0.187618	−	0.187618i
$924$	−3.76203	+	3.76203i	−0.123762	+	0.123762i
$925$	1.37133	−	1.37133i	0.0450889	−	0.0450889i
$926$		−	27.2246i		−	0.894657i
$927$			16.0920i			0.528531i
$928$	38.8969	−	38.8969i	1.27685	−	1.27685i
$929$	−23.6454	+	23.6454i	−0.775781	+	0.775781i	−0.979110	−	0.203329i	$-0.934824\pi$
$929$	−23.6454	+	23.6454i	−0.775781	+	0.775781i	0.203329	+	0.979110i	$0.434824\pi$
$930$	−17.8012	−	17.8012i	−0.583724	−	0.583724i
$931$	−49.2097			−1.61278
$932$	25.3401	+	25.3401i	0.830042	+	0.830042i
$933$			88.5989i			2.90060i
$934$	−33.5786			−1.09873
$935$	9.60666	−	3.71495i	0.314171	−	0.121492i
$936$	9.39647			0.307133
$937$		−	25.6264i		−	0.837177i	−0.908176	−	0.418588i	$-0.862525\pi$
$937$		−	25.6264i		−	0.837177i	0.908176	−	0.418588i	$-0.137475\pi$
$938$	−1.01278	−	1.01278i	−0.0330684	−	0.0330684i
$939$	79.0181			2.57866
$940$	−2.67395	−	2.67395i	−0.0872146	−	0.0872146i
$941$	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
$943$		−	15.8115i		−	0.514892i
$944$			1.61901i			0.0526944i
$945$	−0.242186	+	0.242186i	−0.00787831	+	0.00787831i
$946$	42.8322	−	42.8322i	1.39259	−	1.39259i
$947$	−8.32772	−	8.32772i	−0.270615	−	0.270615i	0.558733	−	0.829348i	$-0.311288\pi$
$947$	−8.32772	−	8.32772i	−0.270615	−	0.270615i	−0.829348	+	0.558733i	$0.811288\pi$
$948$	−31.0873			−1.00967
$949$	−0.949050	−	0.949050i	−0.0308075	−	0.0308075i
$950$			14.8450i			0.481636i
$951$	31.6687			1.02693
$952$	−0.828048	−	0.366219i	−0.0268372	−	0.0118692i
$953$	23.9735			0.776576			0.388288	−	0.921538i	$-0.373067\pi$
$953$	23.9735			0.776576			0.388288	+	0.921538i	$0.373067\pi$
$954$			47.5272i			1.53875i
$955$	−15.1981	−	15.1981i	−0.491800	−	0.491800i
$956$	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
$960$		−	25.5135i		−	0.823445i
$961$		−	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
$965$	1.42208			0.0457783
$966$	9.13423	+	9.13423i	0.293889	+	0.293889i
$967$		−	45.6312i		−	1.46740i	−0.679473	−	0.733700i	$-0.737792\pi$
$967$		−	45.6312i		−	1.46740i	0.679473	−	0.733700i	$-0.262208\pi$
$968$	−2.83272			−0.0910471
$969$	−30.1714	+	68.2197i	−0.969243	+	2.19153i
$970$	−26.3919			−0.847394
$971$			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
$973$	−3.95052			−0.126648
$974$	35.1776	+	35.1776i	1.12716	+	1.12716i
$975$	8.36467	−	8.36467i	0.267884	−	0.267884i
$976$	−16.2682	+	16.2682i	−0.520731	+	0.520731i
$977$		−	24.7610i		−	0.792176i	−0.918213	−	0.396088i	$-0.870368\pi$
$977$		−	24.7610i		−	0.792176i	0.918213	−	0.396088i	$-0.129632\pi$
$978$			99.7670i			3.19020i
$979$	7.60943	−	7.60943i	0.243198	−	0.243198i
$980$	−11.1021	+	11.1021i	−0.354642	+	0.354642i
$981$	−22.5013	−	22.5013i	−0.718412	−	0.718412i
$982$	46.3410			1.47880
$983$	6.99814	+	6.99814i	0.223206	+	0.223206i	0.809847	−	0.586641i	$-0.199550\pi$
$983$	6.99814	+	6.99814i	0.223206	+	0.223206i	−0.586641	+	0.809847i	$0.699550\pi$
$984$			3.54406i			0.112981i
$985$	−17.4127			−0.554815
$986$	−23.4181	+	52.9500i	−0.745783	+	1.68627i
$987$	1.53920			0.0489934
$988$			76.8772i			2.44579i
$989$	−55.4845	−	55.4845i	−1.76430	−	1.76430i
$990$	17.4206			0.553664
$991$	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
$995$			17.8876i			0.567076i
$996$	−40.6114	+	40.6114i	−1.28682	+	1.28682i
$997$	−20.5067	+	20.5067i	−0.649455	+	0.649455i	−0.952861	−	0.303407i	$-0.901876\pi$
$997$	−20.5067	+	20.5067i	−0.649455	+	0.649455i	0.303407	+	0.952861i	$0.401876\pi$
$998$	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	85.2.e.a.81.2	yes	12
3.2	odd	2		765.2.k.b.676.5		12
4.3	odd	2		1360.2.bt.d.81.1		12
5.2	odd	4		425.2.j.c.149.5		12
5.3	odd	4		425.2.j.b.149.2		12
5.4	even	2		425.2.e.f.251.5		12
17.2	even	8		1445.2.a.o.1.5		6
17.4	even	4	inner	85.2.e.a.21.5	✓	12
17.8	even	8		1445.2.d.g.866.3		12
17.9	even	8		1445.2.d.g.866.4		12
17.15	even	8		1445.2.a.n.1.5		6
51.38	odd	4		765.2.k.b.361.2		12
68.55	odd	4		1360.2.bt.d.1041.1		12
85.4	even	4		425.2.e.f.276.2		12
85.19	even	8		7225.2.a.z.1.2		6
85.38	odd	4		425.2.j.c.174.5		12
85.49	even	8		7225.2.a.bb.1.2		6
85.72	odd	4		425.2.j.b.174.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.5	✓	12	17.4	even	4	inner
85.2.e.a.81.2	yes	12	1.1	even	1	trivial
425.2.e.f.251.5		12	5.4	even	2
425.2.e.f.276.2		12	85.4	even	4
425.2.j.b.149.2		12	5.3	odd	4
425.2.j.b.174.2		12	85.72	odd	4
425.2.j.c.149.5		12	5.2	odd	4
425.2.j.c.174.5		12	85.38	odd	4
765.2.k.b.361.2		12	51.38	odd	4
765.2.k.b.676.5		12	3.2	odd	2
1360.2.bt.d.81.1		12	4.3	odd	2
1360.2.bt.d.1041.1		12	68.55	odd	4
1445.2.a.n.1.5		6	17.15	even	8
1445.2.a.o.1.5		6	17.2	even	8
1445.2.d.g.866.3		12	17.8	even	8
1445.2.d.g.866.4		12	17.9	even	8
7225.2.a.z.1.2		6	85.19	even	8
7225.2.a.bb.1.2		6	85.49	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.07061i q^{2} +(1.78436 + 1.78436i) q^{3} -2.28744 q^{4} +(-0.707107 - 0.707107i) q^{5} +(3.69471 - 3.69471i) q^{6} +(-0.260895 + 0.260895i) q^{7} +0.595174i q^{8} +3.36786i q^{9} +(-1.46414 + 1.46414i) q^{10} +(-1.76642 + 1.76642i) q^{11} +(-4.08161 - 4.08161i) q^{12} -4.68778 q^{13} +(0.540212 + 0.540212i) q^{14} -2.52346i q^{15} -3.34250 q^{16} +(3.84558 - 1.48711i) q^{17} +6.97354 q^{18} +7.16938i q^{19} +(1.61746 + 1.61746i) q^{20} -0.931060 q^{21} +(3.65758 + 3.65758i) q^{22} +(4.73801 - 4.73801i) q^{23} +(-1.06200 + 1.06200i) q^{24} +1.00000i q^{25} +9.70657i q^{26} +(-0.656399 + 0.656399i) q^{27} +(0.596781 - 0.596781i) q^{28} +(-4.79535 - 4.79535i) q^{29} -5.22511 q^{30} +(3.40685 + 3.40685i) q^{31} +8.11138i q^{32} -6.30387 q^{33} +(-3.07922 - 7.96272i) q^{34} +0.368961 q^{35} -7.70378i q^{36} +(-1.37133 - 1.37133i) q^{37} +14.8450 q^{38} +(-8.36467 - 8.36467i) q^{39} +(0.420851 - 0.420851i) q^{40} +(1.66858 - 1.66858i) q^{41} +1.92786i q^{42} -11.7105i q^{43} +(4.04059 - 4.04059i) q^{44} +(2.38144 - 2.38144i) q^{45} +(-9.81058 - 9.81058i) q^{46} -1.65317 q^{47} +(-5.96422 - 5.96422i) q^{48} +6.86387i q^{49} +2.07061 q^{50} +(9.51543 + 4.20836i) q^{51} +10.7230 q^{52} +6.81536i q^{53} +(1.35915 + 1.35915i) q^{54} +2.49810 q^{55} +(-0.155278 - 0.155278i) q^{56} +(-12.7927 + 12.7927i) q^{57} +(-9.92932 + 9.92932i) q^{58} -0.484372i q^{59} +5.77226i q^{60} +(4.86706 - 4.86706i) q^{61} +(7.05427 - 7.05427i) q^{62} +(-0.878658 - 0.878658i) q^{63} +10.1105 q^{64} +(3.31476 + 3.31476i) q^{65} +13.0529i q^{66} -1.87478 q^{67} +(-8.79653 + 3.40167i) q^{68} +16.9086 q^{69} -0.763976i q^{70} +(1.21593 + 1.21593i) q^{71} -2.00446 q^{72} +(0.202452 + 0.202452i) q^{73} +(-2.83949 + 2.83949i) q^{74} +(-1.78436 + 1.78436i) q^{75} -16.3995i q^{76} -0.921703i q^{77} +(-17.3200 + 17.3200i) q^{78} +(3.80821 - 3.80821i) q^{79} +(2.36351 + 2.36351i) q^{80} +7.76109 q^{81} +(-3.45498 - 3.45498i) q^{82} -9.94985i q^{83} +2.12974 q^{84} +(-3.77078 - 1.66769i) q^{85} -24.2479 q^{86} -17.1132i q^{87} +(-1.05133 - 1.05133i) q^{88} -4.30781 q^{89} +(-4.93104 - 4.93104i) q^{90} +(1.22302 - 1.22302i) q^{91} +(-10.8379 + 10.8379i) q^{92} +12.1581i q^{93} +3.42308i q^{94} +(5.06952 - 5.06952i) q^{95} +(-14.4736 + 14.4736i) q^{96} +(9.01275 + 9.01275i) q^{97} +14.2124 q^{98} +(-5.94908 - 5.94908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - 12 q^{4} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{14} + 4 q^{16} + 12 q^{17} + 28 q^{18} - 8 q^{20} - 16 q^{21} + 20 q^{22} + 12 q^{23} + 4 q^{24} - 4 q^{27} + 4 q^{28} - 12 q^{29} - 8 q^{30}+ \cdots + 44 q^{98}+O(q^{100}) \) 12 * q - 4 * q^3 - 12 * q^4 - 4 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^14 + 4 * q^16 + 12 * q^17 + 28 * q^18 - 8 * q^20 - 16 * q^21 + 20 * q^22 + 12 * q^23 + 4 * q^24 - 4 * q^27 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 16 * q^33 - 12 * q^34 + 16 * q^35 + 12 * q^37 + 24 * q^38 - 20 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 48 * q^47 - 20 * q^48 + 4 * q^50 + 32 * q^51 - 56 * q^52 + 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 + 28 * q^64 + 4 * q^65 - 8 * q^67 - 40 * q^68 + 28 * q^71 + 20 * q^72 - 48 * q^73 + 28 * q^74 + 4 * q^75 - 92 * q^78 - 8 * q^79 + 16 * q^80 + 28 * q^81 + 40 * q^82 - 4 * q^85 - 96 * q^86 - 72 * q^88 + 24 * q^89 - 16 * q^90 - 36 * q^91 - 16 * q^92 - 8 * q^95 - 32 * q^96 + 4 * q^97 + 44 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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