LMFDB - Embedded newform 740.2.cc.a.17.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(17,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 9, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.cc (of order $36$, degree $12$, 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:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$19$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.12
Character	$\chi$	$=$	740.17
Dual form			740.2.cc.a.653.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.485165 - 0.339716i) q^{3} +(-2.23102 + 0.150100i) q^{5} +(-0.237390 - 2.71338i) q^{7} +(-0.906082 + 2.48944i) q^{9} +(1.31542 - 0.759457i) q^{11} +(-6.23147 + 2.26807i) q^{13} +(-1.03142 + 0.830738i) q^{15} +(-2.74794 + 7.54989i) q^{17} +(4.57036 + 6.52714i) q^{19} +(-1.03695 - 1.23579i) q^{21} +(2.69018 - 4.65953i) q^{23} +(4.95494 - 0.669752i) q^{25} +(0.865982 + 3.23189i) q^{27} +(0.649359 - 2.42344i) q^{29} +(-3.79745 + 3.79745i) q^{31} +(0.380195 - 0.815330i) q^{33} +(0.936899 + 6.01797i) q^{35} +(-2.32101 + 5.62254i) q^{37} +(-2.25279 + 3.21732i) q^{39} +(-1.74051 - 4.78200i) q^{41} -4.91223 q^{43} +(1.64783 - 5.69001i) q^{45} +(-12.8506 + 3.44332i) q^{47} +(-0.412398 + 0.0727169i) q^{49} +(1.23162 + 4.59646i) q^{51} +(-0.164199 + 1.87681i) q^{53} +(-2.82073 + 1.89181i) q^{55} +(4.43475 + 1.61412i) q^{57} +(0.177529 - 2.02916i) q^{59} +(-2.17623 + 4.66693i) q^{61} +(6.96988 + 1.86757i) q^{63} +(13.5621 - 5.99546i) q^{65} +(5.57549 - 0.487792i) q^{67} +(-0.277736 - 3.17454i) q^{69} +(1.59542 - 9.04807i) q^{71} +(0.0302762 + 0.0302762i) q^{73} +(2.17644 - 2.00821i) q^{75} +(-2.37296 - 3.38893i) q^{77} +(-5.23171 + 0.457716i) q^{79} +(-4.57016 - 3.83482i) q^{81} +(-4.40599 + 2.05455i) q^{83} +(4.99747 - 17.2565i) q^{85} +(-0.508236 - 1.39637i) q^{87} +(-7.73603 - 0.676815i) q^{89} +(7.63341 + 16.3699i) q^{91} +(-0.552335 + 3.13244i) q^{93} +(-11.1763 - 13.8762i) q^{95} +(-1.56183 - 0.901725i) q^{97} +(0.698746 + 3.96278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q + 6 q^{3} - 12 q^{25} + 12 q^{27} - 36 q^{31} + 6 q^{33} + 24 q^{35} + 24 q^{37} - 72 q^{39} - 54 q^{41} - 12 q^{45} + 36 q^{49} - 6 q^{53} - 72 q^{57} - 36 q^{61} + 18 q^{65} + 42 q^{67} + 96 q^{69}+ \cdots + 72 q^{97}+O(q^{100}) $ 228 * q + 6 * q^3 - 12 * q^25 + 12 * q^27 - 36 * q^31 + 6 * q^33 + 24 * q^35 + 24 * q^37 - 72 * q^39 - 54 * q^41 - 12 * q^45 + 36 * q^49 - 6 * q^53 - 72 * q^57 - 36 * q^61 + 18 * q^65 + 42 * q^67 + 96 * q^69 - 48 * q^71 - 6 * q^73 - 96 * q^75 - 114 * q^77 + 48 * q^79 - 36 * q^81 - 12 * q^83 + 72 * q^87 - 12 * q^89 + 24 * q^91 - 6 * q^93 + 90 * q^95 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.485165	−	0.339716i	0.280110	−	0.196135i	−0.425076	−	0.905158i	$-0.639752\pi$
$3$	0.485165	−	0.339716i	0.280110	−	0.196135i	0.705186	+	0.709023i	$0.250864\pi$
$4$		0			0
$5$	−2.23102	+	0.150100i	−0.997744	+	0.0671266i
$5$	−2.23102	+	0.150100i	−0.997744	+	0.0671266i
$6$		0			0
$7$	−0.237390	−	2.71338i	−0.0897248	−	1.02556i	−0.898947	−	0.438057i	$-0.855667\pi$
$7$	−0.237390	−	2.71338i	−0.0897248	−	1.02556i	0.809222	−	0.587502i	$-0.199889\pi$
$8$		0			0
$9$	−0.906082	+	2.48944i	−0.302027	+	0.829814i
$10$		0			0
$11$	1.31542	−	0.759457i	0.396613	−	0.228985i	−0.288408	−	0.957507i	$-0.593126\pi$
$11$	1.31542	−	0.759457i	0.396613	−	0.228985i	0.685022	+	0.728523i	$0.259793\pi$
$12$		0			0
$13$	−6.23147	+	2.26807i	−1.72830	+	0.629049i	−0.998507	−	0.0546200i	$-0.982605\pi$
$13$	−6.23147	+	2.26807i	−1.72830	+	0.629049i	−0.729792	+	0.683669i	$0.760383\pi$
$14$		0			0
$15$	−1.03142	+	0.830738i	−0.266312	+	0.214496i
$16$		0			0
$17$	−2.74794	+	7.54989i	−0.666472	+	1.83112i	−0.121636	+	0.992575i	$0.538814\pi$
$17$	−2.74794	+	7.54989i	−0.666472	+	1.83112i	−0.544836	+	0.838542i	$0.683408\pi$
$18$		0			0
$19$	4.57036	+	6.52714i	1.04851	+	1.49743i	0.856575	+	0.516022i	$0.172588\pi$
$19$	4.57036	+	6.52714i	1.04851	+	1.49743i	0.191936	+	0.981407i	$0.438523\pi$
$20$		0			0
$21$	−1.03695	−	1.23579i	−0.226281	−	0.269671i
$22$		0			0
$23$	2.69018	−	4.65953i	0.560942	−	0.971580i	−0.436473	−	0.899717i	$-0.643772\pi$
$23$	2.69018	−	4.65953i	0.560942	−	0.971580i	0.997415	−	0.0718623i	$-0.0228942\pi$
$24$		0			0
$25$	4.95494	−	0.669752i	0.990988	−	0.133950i
$26$		0			0
$27$	0.865982	+	3.23189i	0.166658	+	0.621977i
$28$		0			0
$29$	0.649359	−	2.42344i	0.120583	−	0.450022i	−0.879061	−	0.476710i	$-0.841829\pi$
$29$	0.649359	−	2.42344i	0.120583	−	0.450022i	0.999644	+	0.0266878i	$0.00849600\pi$
$30$		0			0
$31$	−3.79745	+	3.79745i	−0.682042	+	0.682042i	−0.960460	−	0.278418i	$-0.910190\pi$
$31$	−3.79745	+	3.79745i	−0.682042	+	0.682042i	0.278418	+	0.960460i	$0.410190\pi$
$32$		0			0
$33$	0.380195	−	0.815330i	0.0661834	−	0.141931i
$34$		0			0
$35$	0.936899	+	6.01797i	0.158365	+	1.01722i
$36$		0			0
$37$	−2.32101	+	5.62254i	−0.381572	+	0.924339i
$37$	−2.32101	+	5.62254i	−0.381572	+	0.924339i
$38$		0			0
$39$	−2.25279	+	3.21732i	−0.360735	+	0.515184i
$40$		0			0
$41$	−1.74051	−	4.78200i	−0.271821	−	0.746823i	−0.998225	−	0.0595549i	$-0.981032\pi$
$41$	−1.74051	−	4.78200i	−0.271821	−	0.746823i	0.726404	−	0.687268i	$-0.241190\pi$
$42$		0			0
$43$	−4.91223			−0.749108			−0.374554	−	0.927205i	$-0.622204\pi$
$43$	−4.91223			−0.749108			−0.374554	+	0.927205i	$0.622204\pi$
$44$		0			0
$45$	1.64783	−	5.69001i	0.245644	−	0.848216i
$46$		0			0
$47$	−12.8506	+	3.44332i	−1.87446	+	0.502259i	−0.874609	+	0.484830i	$0.838882\pi$
$47$	−12.8506	+	3.44332i	−1.87446	+	0.502259i	−0.999848	+	0.0174296i	$0.994452\pi$
$48$		0			0
$49$	−0.412398	+	0.0727169i	−0.0589140	+	0.0103881i
$50$		0			0
$51$	1.23162	+	4.59646i	0.172461	+	0.643633i
$52$		0			0
$53$	−0.164199	+	1.87681i	−0.0225545	+	0.257799i	0.976543	+	0.215323i	$0.0690804\pi$
$53$	−0.164199	+	1.87681i	−0.0225545	+	0.257799i	−0.999097	+	0.0424767i	$0.986475\pi$
$54$		0			0
$55$	−2.82073	+	1.89181i	−0.380348	+	0.255092i
$56$		0			0
$57$	4.43475	+	1.61412i	0.587397	+	0.213795i
$58$		0			0
$59$	0.177529	−	2.02916i	0.0231123	−	0.264174i	−0.975843	−	0.218473i	$-0.929892\pi$
$59$	0.177529	−	2.02916i	0.0231123	−	0.264174i	0.998955	−	0.0457010i	$-0.0145521\pi$
$60$		0			0
$61$	−2.17623	+	4.66693i	−0.278637	+	0.597539i	−0.994965	−	0.100225i	$-0.968044\pi$
$61$	−2.17623	+	4.66693i	−0.278637	+	0.597539i	0.716328	+	0.697764i	$0.245822\pi$
$62$		0			0
$63$	6.96988	+	1.86757i	0.878123	+	0.235292i
$64$		0			0
$65$	13.5621	−	5.99546i	1.68217	−	0.743645i
$66$		0			0
$67$	5.57549	−	0.487792i	0.681154	−	0.0595933i	0.258673	−	0.965965i	$-0.416715\pi$
$67$	5.57549	−	0.487792i	0.681154	−	0.0595933i	0.422481	+	0.906372i	$0.361159\pi$
$68$		0			0
$69$	−0.277736	−	3.17454i	−0.0334355	−	0.382170i
$70$		0			0
$71$	1.59542	−	9.04807i	0.189341	−	1.07381i	−0.730908	−	0.682476i	$-0.760903\pi$
$71$	1.59542	−	9.04807i	0.189341	−	1.07381i	0.920249	−	0.391332i	$-0.127986\pi$
$72$		0			0
$73$	0.0302762	+	0.0302762i	0.00354356	+	0.00354356i	0.708876	−	0.705333i	$-0.249202\pi$
$73$	0.0302762	+	0.0302762i	0.00354356	+	0.00354356i	−0.705333	+	0.708876i	$0.749202\pi$
$74$		0			0
$75$	2.17644	−	2.00821i	0.251313	−	0.231889i
$76$		0			0
$77$	−2.37296	−	3.38893i	−0.270424	−	0.386205i
$78$		0			0
$79$	−5.23171	+	0.457716i	−0.588614	+	0.0514970i	−0.377572	−	0.925980i	$-0.623241\pi$
$79$	−5.23171	+	0.457716i	−0.588614	+	0.0514970i	−0.211041	+	0.977477i	$0.567685\pi$
$80$		0			0
$81$	−4.57016	−	3.83482i	−0.507796	−	0.426091i
$82$		0			0
$83$	−4.40599	+	2.05455i	−0.483620	+	0.225516i	−0.649108	−	0.760696i	$-0.724858\pi$
$83$	−4.40599	+	2.05455i	−0.483620	+	0.225516i	0.165488	+	0.986212i	$0.447080\pi$
$84$		0			0
$85$	4.99747	−	17.2565i	0.542052	−	1.87173i
$86$		0			0
$87$	−0.508236	−	1.39637i	−0.0544886	−	0.149706i
$88$		0			0
$89$	−7.73603	−	0.676815i	−0.820018	−	0.0717422i	−0.330577	−	0.943779i	$-0.607243\pi$
$89$	−7.73603	−	0.676815i	−0.820018	−	0.0717422i	−0.489440	+	0.872037i	$0.662799\pi$
$90$		0			0
$91$	7.63341	+	16.3699i	0.800199	+	1.71603i
$92$		0			0
$93$	−0.552335	+	3.13244i	−0.0572744	+	0.324819i
$94$		0			0
$95$	−11.1763	−	13.8762i	−1.14666	−	1.42367i
$96$		0			0
$97$	−1.56183	−	0.901725i	−0.158580	−	0.0915563i	0.418610	−	0.908166i	$-0.362517\pi$
$97$	−1.56183	−	0.901725i	−0.158580	−	0.0915563i	−0.577190	+	0.816610i	$0.695851\pi$
$98$		0			0
$99$	0.698746	+	3.96278i	0.0702266	+	0.398275i
$100$		0			0
$101$	8.53973	+	4.93042i	0.849735	+	0.490595i	0.860561	−	0.509347i	$-0.170113\pi$
$101$	8.53973	+	4.93042i	0.849735	+	0.490595i	−0.0108265	+	0.999941i	$0.503446\pi$
$102$		0			0
$103$	7.56078	−	4.36522i	0.744986	−	0.430118i	−0.0788935	−	0.996883i	$-0.525139\pi$
$103$	7.56078	−	4.36522i	0.744986	−	0.430118i	0.823879	+	0.566765i	$0.191805\pi$
$104$		0			0
$105$	2.49895	+	2.60143i	0.243873	+	0.253874i
$106$		0			0
$107$	−10.2321	−	4.77131i	−0.989175	−	0.461260i	−0.140446	−	0.990088i	$-0.544854\pi$
$107$	−10.2321	−	4.77131i	−0.989175	−	0.461260i	−0.848729	+	0.528829i	$0.822631\pi$
$108$		0			0
$109$	12.4168	+	8.69435i	1.18932	+	0.832768i	0.989138	−	0.146992i	$-0.0469590\pi$
$109$	12.4168	+	8.69435i	1.18932	+	0.832768i	0.200178	+	0.979760i	$0.435848\pi$
$110$		0			0
$111$	0.783994	+	3.51634i	0.0744134	+	0.333757i
$112$		0			0
$113$	−0.126362	+	0.0222811i	−0.0118872	+	0.00209603i	−0.179589	−	0.983742i	$-0.557477\pi$
$113$	−0.126362	+	0.0222811i	−0.0118872	+	0.00209603i	0.167701	+	0.985838i	$0.446366\pi$
$114$		0			0
$115$	−5.30247	+	10.7993i	−0.494458	+	1.00704i
$116$		0			0
$117$		−	17.5679i		−	1.62416i
$118$		0			0
$119$	21.1380	+	5.66391i	1.93772	+	0.519210i
$120$		0			0
$121$	−4.34645	+	7.52828i	−0.395132	+	0.684389i
$122$		0			0
$123$	−2.46896	−	1.72878i	−0.222618	−	0.155879i
$124$		0			0
$125$	−10.9541	+	2.23797i	−0.979761	+	0.200170i
$126$		0			0
$127$	5.23193	+	0.457735i	0.464259	+	0.0406174i	0.316886	−	0.948464i	$-0.397363\pi$
$127$	5.23193	+	0.457735i	0.464259	+	0.0406174i	0.147373	+	0.989081i	$0.452918\pi$
$128$		0			0
$129$	−2.38324	+	1.66876i	−0.209833	+	0.146926i
$130$		0			0
$131$	−5.93935	+	2.76957i	−0.518924	+	0.241978i	−0.664391	−	0.747385i	$-0.731309\pi$
$131$	−5.93935	+	2.76957i	−0.518924	+	0.241978i	0.145468	+	0.989363i	$0.453531\pi$
$132$		0			0
$133$	16.6256	−	13.9506i	1.44163	−	1.20967i
$134$		0			0
$135$	−2.41713	−	7.08044i	−0.208034	−	0.609387i
$136$		0			0
$137$	3.04413	−	11.3609i	0.260078	−	0.970623i	−0.705117	−	0.709091i	$-0.749106\pi$
$137$	3.04413	−	11.3609i	0.260078	−	0.970623i	0.965195	−	0.261532i	$-0.0842278\pi$
$138$		0			0
$139$	11.4777	+	4.17754i	0.973527	+	0.354335i	0.779320	−	0.626626i	$-0.215565\pi$
$139$	11.4777	+	4.17754i	0.973527	+	0.354335i	0.194206	+	0.980961i	$0.437787\pi$
$140$		0			0
$141$	−5.06493	+	6.03614i	−0.426544	+	0.508335i
$142$		0			0
$143$	−6.47448	+	7.71599i	−0.541424	+	0.645243i
$144$		0			0
$145$	−1.08498	+	5.50423i	−0.0901025	+	0.457101i
$146$		0			0
$147$	−0.175378	+	0.175378i	−0.0144649	+	0.0144649i
$148$		0			0
$149$			0.830468i			0.0680346i	0.999421	+	0.0340173i	$0.0108301\pi$
$149$			0.830468i			0.0680346i	−0.999421	+	0.0340173i	$0.989170\pi$
$150$		0			0
$151$	−2.48966	−	0.438994i	−0.202606	−	0.0357249i	0.0714241	−	0.997446i	$-0.477246\pi$
$151$	−2.48966	−	0.438994i	−0.202606	−	0.0357249i	−0.274030	+	0.961721i	$0.588357\pi$
$152$		0			0
$153$	−16.3051	−	13.6816i	−1.31819	−	1.10610i
$154$		0			0
$155$	7.90221	−	9.04220i	0.634720	−	0.726287i
$156$		0			0
$157$	−6.42658	−	13.7818i	−0.512897	−	1.09991i	−0.976825	−	0.214038i	$-0.931338\pi$
$157$	−6.42658	−	13.7818i	−0.512897	−	1.09991i	0.463929	−	0.885873i	$-0.346439\pi$
$158$		0			0
$159$	0.557918	+	0.966343i	0.0442458	+	0.0766360i
$160$		0			0
$161$	−13.2817	−	6.19335i	−1.04674	−	0.488104i
$162$		0			0
$163$	5.64159	+	6.72338i	0.441883	+	0.526616i	0.940311	−	0.340315i	$-0.110534\pi$
$163$	5.64159	+	6.72338i	0.441883	+	0.526616i	−0.498428	+	0.866931i	$0.666089\pi$
$164$		0			0
$165$	−0.725843	+	1.87609i	−0.0565068	+	0.146053i
$166$		0			0
$167$	−9.20117	−	1.62242i	−0.712008	−	0.125546i	−0.194099	−	0.980982i	$-0.562178\pi$
$167$	−9.20117	−	1.62242i	−0.712008	−	0.125546i	−0.517909	+	0.855436i	$0.673289\pi$
$168$		0			0
$169$	23.7285	−	19.9106i	1.82527	−	1.53158i
$170$		0			0
$171$	−20.3901	+	5.46350i	−1.55927	+	0.417804i
$172$		0			0
$173$	10.8902	−	15.5528i	0.827967	−	1.18246i	−0.152988	−	0.988228i	$-0.548890\pi$
$173$	10.8902	−	15.5528i	0.827967	−	1.18246i	0.980956	−	0.194232i	$-0.0622214\pi$
$174$		0			0
$175$	−2.99354	−	13.2856i	−0.226290	−	1.00430i
$176$		0			0
$177$	−0.603209	−	1.04479i	−0.0453399	−	0.0785311i
$178$		0			0
$179$	−7.98563	−	7.98563i	−0.596874	−	0.596874i	0.342605	−	0.939479i	$-0.388691\pi$
$179$	−7.98563	−	7.98563i	−0.596874	−	0.596874i	−0.939479	+	0.342605i	$0.888691\pi$
$180$		0			0
$181$	−9.24448	+	3.36472i	−0.687137	+	0.250097i	−0.661909	−	0.749584i	$-0.730253\pi$
$181$	−9.24448	+	3.36472i	−0.687137	+	0.250097i	−0.0252281	+	0.999682i	$0.508031\pi$
$182$		0			0
$183$	0.529604	+	3.00353i	0.0391494	+	0.222027i
$184$		0			0
$185$	4.33429	−	12.8924i	0.318663	−	0.947868i
$186$		0			0
$187$	2.11913	+	12.0182i	0.154966	+	0.878857i
$188$		0			0
$189$	8.56375	−	3.11695i	0.622921	−	0.226725i
$190$		0			0
$191$	10.3257	+	10.3257i	0.747145	+	0.747145i	0.973942	−	0.226797i	$-0.0728255\pi$
$191$	10.3257	+	10.3257i	0.747145	+	0.747145i	−0.226797	+	0.973942i	$0.572825\pi$
$192$		0			0
$193$	−2.76848	−	4.79514i	−0.199279	−	0.345162i	0.749016	−	0.662552i	$-0.230527\pi$
$193$	−2.76848	−	4.79514i	−0.199279	−	0.345162i	−0.948295	+	0.317391i	$0.897193\pi$
$194$		0			0
$195$	4.54312	−	7.51606i	0.325339	−	0.538237i
$196$		0			0
$197$	−10.7222	+	15.3129i	−0.763925	+	1.09100i	0.229135	+	0.973395i	$0.426410\pi$
$197$	−10.7222	+	15.3129i	−0.763925	+	1.09100i	−0.993061	+	0.117604i	$0.962479\pi$
$198$		0			0
$199$	18.1894	−	4.87383i	1.28941	−	0.345496i	0.451974	−	0.892031i	$-0.350720\pi$
$199$	18.1894	−	4.87383i	1.28941	−	0.345496i	0.837436	+	0.546535i	$0.184053\pi$
$200$		0			0
$201$	2.53932	−	2.13074i	0.179110	−	0.150291i
$202$		0			0
$203$	−6.72986	−	1.18666i	−0.472343	−	0.0832869i
$204$		0			0
$205$	4.60089	+	10.4075i	0.321340	+	0.726892i
$206$		0			0
$207$	9.16210	+	10.9190i	0.636810	+	0.758921i
$208$		0			0
$209$	10.9690	+	5.11493i	0.758742	+	0.353807i
$210$		0			0
$211$	8.22186	+	14.2407i	0.566016	+	0.980369i	0.996954	+	0.0779871i	$0.0248493\pi$
$211$	8.22186	+	14.2407i	0.566016	+	0.980369i	−0.430938	+	0.902381i	$0.641817\pi$
$212$		0			0
$213$	−2.29973	−	4.93180i	−0.157575	−	0.337921i
$214$		0			0
$215$	10.9593	−	0.737324i	0.747418	−	0.0502851i
$216$		0			0
$217$	11.2054	+	9.40243i	0.760671	+	0.638278i
$218$		0			0
$219$	0.0249743	+	0.00440363i	0.00168760	+	0.000297570i
$220$		0			0
$221$		−	53.2794i		−	3.58396i
$222$		0			0
$223$	7.78963	−	7.78963i	0.521632	−	0.521632i	−0.396432	−	0.918064i	$-0.629752\pi$
$223$	7.78963	−	7.78963i	0.521632	−	0.521632i	0.918064	+	0.396432i	$0.129752\pi$
$224$		0			0
$225$	−2.82228	+	12.9419i	−0.188152	+	0.862792i
$226$		0			0
$227$	−3.90354	+	4.65206i	−0.259087	+	0.308768i	−0.879870	−	0.475215i	$-0.842370\pi$
$227$	−3.90354	+	4.65206i	−0.259087	+	0.308768i	0.620783	+	0.783983i	$0.286815\pi$
$228$		0			0
$229$	−14.1312	+	16.8409i	−0.933814	+	1.11288i	0.0595915	+	0.998223i	$0.481020\pi$
$229$	−14.1312	+	16.8409i	−0.933814	+	1.11288i	−0.993406	+	0.114653i	$0.963424\pi$
$230$		0			0
$231$	−2.30255	−	0.838060i	−0.151497	−	0.0551403i
$232$		0			0
$233$	−0.948448	+	3.53965i	−0.0621349	+	0.231890i	−0.990009	−	0.141002i	$-0.954967\pi$
$233$	−0.948448	+	3.53965i	−0.0621349	+	0.231890i	0.927874	+	0.372893i	$0.121634\pi$
$234$		0			0
$235$	28.1532	−	9.61100i	1.83651	−	0.626952i
$236$		0			0
$237$	−2.38275	+	1.99937i	−0.154776	+	0.129873i
$238$		0			0
$239$	−6.11692	+	2.85237i	−0.395671	+	0.184504i	−0.610262	−	0.792200i	$-0.708936\pi$
$239$	−6.11692	+	2.85237i	−0.395671	+	0.184504i	0.214591	+	0.976704i	$0.431158\pi$
$240$		0			0
$241$	7.24807	−	5.07515i	0.466889	−	0.326919i	−0.316347	−	0.948644i	$-0.602456\pi$
$241$	7.24807	−	5.07515i	0.466889	−	0.326919i	0.783236	+	0.621724i	$0.213568\pi$
$242$		0			0
$243$	−13.5195	−	1.18281i	−0.867278	−	0.0758770i
$244$		0			0
$245$	0.909155	−	0.224134i	0.0580838	−	0.0143194i
$246$		0			0
$247$	−43.2841	−	30.3078i	−2.75410	−	1.92844i
$248$		0			0
$249$	−1.43967	+	2.49358i	−0.0912353	+	0.158024i
$250$		0			0
$251$	11.7525	+	3.14906i	0.741808	+	0.198767i	0.609882	−	0.792493i	$-0.291217\pi$
$251$	11.7525	+	3.14906i	0.741808	+	0.198767i	0.131927	+	0.991259i	$0.457884\pi$
$252$		0			0
$253$		−	8.17231i		−	0.513789i
$254$		0			0
$255$	−3.43770	−	10.0700i	−0.215277	−	0.630605i
$256$		0			0
$257$	1.35036	−	0.238105i	0.0842333	−	0.0148526i	−0.131373	−	0.991333i	$-0.541938\pi$
$257$	1.35036	−	0.238105i	0.0842333	−	0.0148526i	0.215606	+	0.976480i	$0.430827\pi$
$258$		0			0
$259$	15.8070	+	4.96304i	0.982201	+	0.308388i
$260$		0			0
$261$	5.44464	+	3.81238i	0.337015	+	0.235980i
$262$		0			0
$263$	16.1199	+	7.51684i	0.993997	+	0.463508i	0.850405	−	0.526129i	$-0.176357\pi$
$263$	16.1199	+	7.51684i	0.993997	+	0.463508i	0.143592	+	0.989637i	$0.454135\pi$
$264$		0			0
$265$	0.0846246	−	4.21185i	0.00519845	−	0.258732i
$266$		0			0
$267$	−3.98318	+	2.29969i	−0.243766	+	0.140739i
$268$		0			0
$269$	27.1435	+	15.6713i	1.65497	+	0.955496i	0.974986	+	0.222268i	$0.0713459\pi$
$269$	27.1435	+	15.6713i	1.65497	+	0.955496i	0.679982	+	0.733229i	$0.261987\pi$
$270$		0			0
$271$	−1.83696	−	10.4179i	−0.111587	−	0.632844i	−0.988383	−	0.151981i	$-0.951435\pi$
$271$	−1.83696	−	10.4179i	−0.111587	−	0.632844i	0.876796	−	0.480863i	$-0.159676\pi$
$272$		0			0
$273$	9.26459	+	5.34891i	0.560718	+	0.323731i
$274$		0			0
$275$	6.00917	−	4.64407i	0.362366	−	0.280048i
$276$		0			0
$277$	−2.63799	+	14.9608i	−0.158501	+	0.898905i	0.797013	+	0.603962i	$0.206412\pi$
$277$	−2.63799	+	14.9608i	−0.158501	+	0.898905i	−0.955515	+	0.294944i	$0.904699\pi$
$278$		0			0
$279$	−6.01272	−	12.8943i	−0.359972	−	0.771963i
$280$		0			0
$281$	−7.82990	−	0.685027i	−0.467093	−	0.0408653i	−0.148820	−	0.988864i	$-0.547547\pi$
$281$	−7.82990	−	0.685027i	−0.467093	−	0.0408653i	−0.318273	+	0.947999i	$0.603103\pi$
$282$		0			0
$283$	6.01234	+	16.5188i	0.357396	+	0.981938i	0.979929	+	0.199345i	$0.0638814\pi$
$283$	6.01234	+	16.5188i	0.357396	+	0.981938i	−0.622533	+	0.782593i	$0.713896\pi$
$284$		0			0
$285$	−10.1363	−	2.93548i	−0.600424	−	0.173883i
$286$		0			0
$287$	−12.5622	+	5.85784i	−0.741523	+	0.345778i
$288$		0			0
$289$	−36.4269	−	30.5658i	−2.14276	−	1.79799i
$290$		0			0
$291$	−1.06408	+	0.0930947i	−0.0623773	+	0.00545731i
$292$		0			0
$293$	10.9479	+	15.6352i	0.639582	+	0.913417i	0.999811	−	0.0194466i	$-0.00619043\pi$
$293$	10.9479	+	15.6352i	0.639582	+	0.913417i	−0.360229	+	0.932864i	$0.617302\pi$
$294$		0			0
$295$	−0.0914942	+	4.55376i	−0.00532700	+	0.265130i
$296$		0			0
$297$	3.59361	+	3.59361i	0.208522	+	0.208522i
$298$		0			0
$299$	−6.19565	+	35.1373i	−0.358304	+	2.03204i
$300$		0			0
$301$	1.16611	+	13.3287i	0.0672136	+	0.768255i
$302$		0			0
$303$	5.81812	−	0.509020i	0.334242	−	0.0292424i
$304$		0			0
$305$	4.15471	−	10.7387i	0.237898	−	0.614896i
$306$		0			0
$307$	9.18968	+	2.46237i	0.524483	+	0.140535i	0.511339	−	0.859379i	$-0.329150\pi$
$307$	9.18968	+	2.46237i	0.524483	+	0.140535i	0.0131435	+	0.999914i	$0.495816\pi$
$308$		0			0
$309$	2.18529	−	4.68637i	0.124317	−	0.266598i
$310$		0			0
$311$	−2.29155	+	26.1925i	−0.129942	+	1.48524i	0.599046	+	0.800714i	$0.295547\pi$
$311$	−2.29155	+	26.1925i	−0.129942	+	1.48524i	−0.728988	+	0.684526i	$0.760009\pi$
$312$		0			0
$313$	−2.52839	−	0.920261i	−0.142913	−	0.0520162i	0.269573	−	0.962980i	$-0.413117\pi$
$313$	−2.52839	−	0.920261i	−0.142913	−	0.0520162i	−0.412487	+	0.910964i	$0.635340\pi$
$314$		0			0
$315$	−15.8303	−	3.12043i	−0.891936	−	0.175816i
$316$		0			0
$317$	−0.246203	+	2.81411i	−0.0138281	+	0.158056i	−0.999969	−	0.00785290i	$-0.997500\pi$
$317$	−0.246203	+	2.81411i	−0.0138281	+	0.158056i	0.986141	+	0.165909i	$0.0530559\pi$
$318$		0			0
$319$	−0.986320	−	3.68100i	−0.0552233	−	0.206096i
$320$		0			0
$321$	−6.58515	+	1.16114i	−0.367547	+	0.0648085i
$322$		0			0
$323$	−61.8383	+	16.5695i	−3.44077	+	0.921952i
$324$		0			0
$325$	−29.3575	+	15.4117i	−1.62846	+	0.854887i
$326$		0			0
$327$	8.97782			0.496475
$328$		0			0
$329$	12.3936	+	34.0512i	0.683282	+	1.87730i
$330$		0			0
$331$	16.8144	−	24.0135i	0.924205	−	1.31990i	−0.0231554	−	0.999732i	$-0.507371\pi$
$331$	16.8144	−	24.0135i	0.924205	−	1.31990i	0.947360	−	0.320169i	$-0.103740\pi$
$332$		0			0
$333$	−11.8939	−	10.8725i	−0.651784	−	0.595809i
$334$		0			0
$335$	−12.3658	+	1.92516i	−0.675618	+	0.105182i
$336$		0			0
$337$	−10.3254	+	22.1429i	−0.562461	+	1.20620i	0.395277	+	0.918562i	$0.370649\pi$
$337$	−10.3254	+	22.1429i	−0.562461	+	1.20620i	−0.957738	+	0.287641i	$0.907129\pi$
$338$		0			0
$339$	−0.0537373	+	0.0537373i	−0.00291861	+	0.00291861i
$340$		0			0
$341$	−2.11123	+	7.87923i	−0.114330	+	0.426684i
$342$		0			0
$343$	−4.63948	−	17.3148i	−0.250509	−	0.934911i
$344$		0			0
$345$	1.09613	+	7.04079i	0.0590139	+	0.379063i
$346$		0			0
$347$	17.1354	−	29.6794i	0.919877	−	1.59327i	0.120276	−	0.992740i	$-0.461622\pi$
$347$	17.1354	−	29.6794i	0.919877	−	1.59327i	0.799600	−	0.600533i	$-0.205045\pi$
$348$		0			0
$349$	−4.96003	−	5.91113i	−0.265504	−	0.316416i	0.616777	−	0.787138i	$-0.288438\pi$
$349$	−4.96003	−	5.91113i	−0.265504	−	0.316416i	−0.882282	+	0.470722i	$0.843993\pi$
$350$		0			0
$351$	−12.7265	−	18.1753i	−0.679290	−	0.970126i
$352$		0			0
$353$	6.35288	−	17.4544i	0.338130	−	0.929004i	−0.647795	−	0.761815i	$-0.724309\pi$
$353$	6.35288	−	17.4544i	0.338130	−	0.929004i	0.985925	−	0.167189i	$-0.0534690\pi$
$354$		0			0
$355$	−2.20130	+	20.4259i	−0.116833	+	1.08410i
$356$		0			0
$357$	12.1796	−	4.43299i	0.644610	−	0.234619i
$358$		0			0
$359$	−24.6250	+	14.2172i	−1.29966	+	0.750356i	−0.980344	−	0.197294i	$-0.936785\pi$
$359$	−24.6250	+	14.2172i	−1.29966	+	0.750356i	−0.319311	+	0.947650i	$0.603451\pi$
$360$		0			0
$361$	−15.2171	+	41.8086i	−0.800899	+	2.20045i
$362$		0			0
$363$	0.448731	+	5.12902i	0.0235523	+	0.269204i
$364$		0			0
$365$	−0.0720913	−	0.0630024i	−0.00377343	−	0.00329770i
$366$		0			0
$367$	−7.23136	+	5.06345i	−0.377474	+	0.264310i	−0.746881	−	0.664958i	$-0.768450\pi$
$367$	−7.23136	+	5.06345i	−0.377474	+	0.264310i	0.369407	+	0.929268i	$0.379561\pi$
$368$		0			0
$369$	13.4816			0.701822
$370$		0			0
$371$	5.13147			0.266412
$372$		0			0
$373$	−2.22424	+	1.55743i	−0.115167	+	0.0806407i	−0.629741	−	0.776805i	$-0.716839\pi$
$373$	−2.22424	+	1.55743i	−0.115167	+	0.0806407i	0.514574	+	0.857446i	$0.327950\pi$
$374$		0			0
$375$	−4.55425	+	4.80706i	−0.235181	+	0.248235i
$376$		0			0
$377$	1.45007	+	16.5744i	0.0746825	+	0.853625i
$378$		0			0
$379$	−10.7917	+	29.6499i	−0.554331	+	1.52301i	0.273408	+	0.961898i	$0.411849\pi$
$379$	−10.7917	+	29.6499i	−0.554331	+	1.52301i	−0.827739	+	0.561113i	$0.810373\pi$
$380$		0			0
$381$	2.69385	−	1.55530i	0.138010	−	0.0796802i
$382$		0			0
$383$	1.32370	−	0.481786i	0.0676377	−	0.0246181i	−0.307980	−	0.951393i	$-0.599653\pi$
$383$	1.32370	−	0.481786i	0.0676377	−	0.0246181i	0.375617	+	0.926775i	$0.377431\pi$
$384$		0			0
$385$	5.80280	+	7.20461i	0.295738	+	0.367181i
$386$		0			0
$387$	4.45088	−	12.2287i	0.226251	−	0.621620i
$388$		0			0
$389$	−17.8733	−	25.5257i	−0.906211	−	1.29420i	−0.955370	−	0.295412i	$-0.904543\pi$
$389$	−17.8733	−	25.5257i	−0.906211	−	1.29420i	0.0491591	−	0.998791i	$-0.484346\pi$
$390$		0			0
$391$	27.7865	+	33.1147i	1.40522	+	1.67468i
$392$		0			0
$393$	−1.94070	+	3.36139i	−0.0978954	+	0.169560i
$394$		0			0
$395$	11.6034	−	1.80645i	0.583829	−	0.0908925i
$396$		0			0
$397$	5.02027	+	18.7359i	0.251960	+	0.940328i	0.969756	+	0.244075i	$0.0784842\pi$
$397$	5.02027	+	18.7359i	0.251960	+	0.940328i	−0.717796	+	0.696253i	$0.754849\pi$
$398$		0			0
$399$	3.32694	−	12.4163i	0.166556	−	0.621594i
$400$		0			0
$401$	−12.2769	+	12.2769i	−0.613081	+	0.613081i	−0.943748	−	0.330666i	$-0.892726\pi$
$401$	−12.2769	+	12.2769i	−0.613081	+	0.613081i	0.330666	+	0.943748i	$0.392726\pi$
$402$		0			0
$403$	15.0508	−	32.2766i	0.749734	−	1.60781i
$404$		0			0
$405$	10.7718	+	7.86960i	0.535253	+	0.391044i
$406$		0			0
$407$	1.21697	+	9.15869i	0.0603232	+	0.453979i
$408$		0			0
$409$	7.59468	−	10.8463i	0.375533	−	0.536316i	−0.586250	−	0.810130i	$-0.699396\pi$
$409$	7.59468	−	10.8463i	0.375533	−	0.536316i	0.961783	+	0.273814i	$0.0882853\pi$
$410$		0			0
$411$	−2.38256	−	6.54603i	−0.117523	−	0.322892i
$412$		0			0
$413$	−5.54802			−0.273000
$414$		0			0
$415$	9.52148	−	5.24508i	0.467391	−	0.257471i
$416$		0			0
$417$	6.98776	−	1.87237i	0.342192	−	0.0916901i
$418$		0			0
$419$	8.73085	−	1.53948i	0.426530	−	0.0752087i	0.0437373	−	0.999043i	$-0.486074\pi$
$419$	8.73085	−	1.53948i	0.426530	−	0.0752087i	0.382792	+	0.923834i	$0.374962\pi$
$420$		0			0
$421$	4.35148	+	16.2399i	0.212078	+	0.791486i	0.987175	+	0.159643i	$0.0510344\pi$
$421$	4.35148	+	16.2399i	0.212078	+	0.791486i	−0.775097	+	0.631843i	$0.782299\pi$
$422$		0			0
$423$	3.07180	−	35.1108i	0.149356	−	1.70715i
$424$		0			0
$425$	−8.55930	+	39.2497i	−0.415187	+	1.90389i
$426$		0			0
$427$	13.1798	+	4.79704i	0.637813	+	0.232145i
$428$		0			0
$429$	−0.519947	+	5.94302i	−0.0251033	+	0.286932i
$430$		0			0
$431$	8.98621	−	19.2710i	0.432850	−	0.928251i	−0.562023	−	0.827122i	$-0.689977\pi$
$431$	8.98621	−	19.2710i	0.432850	−	0.928251i	0.994873	−	0.101129i	$-0.0322455\pi$
$432$		0			0
$433$	−5.27337	−	1.41299i	−0.253422	−	0.0679042i	0.129872	−	0.991531i	$-0.458543\pi$
$433$	−5.27337	−	1.41299i	−0.253422	−	0.0679042i	−0.383293	+	0.923627i	$0.625210\pi$
$434$		0			0
$435$	1.34348	+	3.03904i	0.0644150	+	0.145711i
$436$		0			0
$437$	42.7085	−	3.73651i	2.04303	−	0.178742i
$438$		0			0
$439$	1.63865	+	18.7298i	0.0782083	+	0.893925i	0.929401	+	0.369072i	$0.120324\pi$
$439$	1.63865	+	18.7298i	0.0782083	+	0.893925i	−0.851193	+	0.524853i	$0.824120\pi$
$440$		0			0
$441$	0.192642	−	1.09253i	0.00917343	−	0.0520251i
$442$		0			0
$443$	−13.1619	−	13.1619i	−0.625342	−	0.625342i	0.321550	−	0.946892i	$-0.395796\pi$
$443$	−13.1619	−	13.1619i	−0.625342	−	0.625342i	−0.946892	+	0.321550i	$0.895796\pi$
$444$		0			0
$445$	17.3609	+	0.348815i	0.822984	+	0.0165354i
$446$		0			0
$447$	0.282123	+	0.402914i	0.0133440	+	0.0190572i
$448$		0			0
$449$	4.05722	−	0.354961i	0.191472	−	0.0167517i	0.00898380	−	0.999960i	$-0.497140\pi$
$449$	4.05722	−	0.354961i	0.191472	−	0.0167517i	0.182488	+	0.983208i	$0.441585\pi$
$450$		0			0
$451$	−5.92121	−	4.96849i	−0.278819	−	0.233957i
$452$		0			0
$453$	−1.35703	+	0.632794i	−0.0637588	+	0.0297312i
$454$		0			0
$455$	−19.4874	−	35.3759i	−0.913586	−	1.65845i
$456$		0			0
$457$	0.799872	+	2.19763i	0.0374164	+	0.102801i	0.956994	−	0.290108i	$-0.0936911\pi$
$457$	0.799872	+	2.19763i	0.0374164	+	0.102801i	−0.919578	+	0.392908i	$0.871469\pi$
$458$		0			0
$459$	−26.7801	−	2.34295i	−1.24999	−	0.109360i
$460$		0			0
$461$	−4.86824	−	10.4400i	−0.226737	−	0.486238i	0.759722	−	0.650248i	$-0.225335\pi$
$461$	−4.86824	−	10.4400i	−0.226737	−	0.486238i	−0.986459	+	0.164010i	$0.947557\pi$
$462$		0			0
$463$	−5.90192	+	33.4714i	−0.274285	+	1.55555i	0.466937	+	0.884291i	$0.345357\pi$
$463$	−5.90192	+	33.4714i	−0.274285	+	1.55555i	−0.741223	+	0.671259i	$0.765754\pi$
$464$		0			0
$465$	0.762093	−	7.07147i	0.0353412	−	0.327931i
$466$		0			0
$467$	2.09501	+	1.20955i	0.0969454	+	0.0559714i	0.547689	−	0.836682i	$-0.315508\pi$
$467$	2.09501	+	1.20955i	0.0969454	+	0.0559714i	−0.450744	+	0.892654i	$0.648841\pi$
$468$		0			0
$469$	−2.64713	−	15.0126i	−0.122233	−	0.693217i
$470$		0			0
$471$	−7.79986	−	4.50325i	−0.359399	−	0.207499i
$472$		0			0
$473$	−6.46163	+	3.73062i	−0.297106	+	0.171534i
$474$		0			0
$475$	27.0174	+	29.2806i	1.23964	+	1.34349i
$476$		0			0
$477$	−4.52343	−	2.10931i	−0.207113	−	0.0965786i
$478$		0			0
$479$	−10.0862	−	7.06246i	−0.460852	−	0.322692i	0.319990	−	0.947421i	$-0.396321\pi$
$479$	−10.0862	−	7.06246i	−0.460852	−	0.322692i	−0.780842	+	0.624729i	$0.785209\pi$
$480$		0			0
$481$	1.71100	−	40.3009i	0.0780149	−	1.83756i
$482$		0			0
$483$	−8.54779	+	1.50721i	−0.388938	+	0.0685803i
$484$		0			0
$485$	3.61984	+	1.77734i	0.164368	+	0.0807048i
$486$		0			0
$487$			4.22723i			0.191554i	0.995403	+	0.0957770i	$0.0305336\pi$
$487$			4.22723i			0.191554i	−0.995403	+	0.0957770i	$0.969466\pi$
$488$		0			0
$489$	5.02114	+	1.34541i	0.227064	+	0.0608416i
$490$		0			0
$491$	−9.18545	+	15.9097i	−0.414534	+	0.717993i	−0.995379	−	0.0960203i	$-0.969389\pi$
$491$	−9.18545	+	15.9097i	−0.414534	+	0.717993i	0.580846	+	0.814014i	$0.302722\pi$
$492$		0			0
$493$	16.5123	+	11.5621i	0.743677	+	0.520729i
$494$		0			0
$495$	−2.15373	−	8.73619i	−0.0968030	−	0.392662i
$496$		0			0
$497$	−24.9295	−	2.18105i	−1.11824	−	0.0978335i
$498$		0			0
$499$	−25.0551	+	17.5437i	−1.12162	+	0.785366i	−0.978888	−	0.204396i	$-0.934477\pi$
$499$	−25.0551	+	17.5437i	−1.12162	+	0.785366i	−0.142730	+	0.989762i	$0.545588\pi$
$500$		0			0
$501$	−5.01525	+	2.33865i	−0.224065	+	0.104483i
$502$		0			0
$503$	1.99627	−	1.67507i	0.0890093	−	0.0746877i	−0.597197	−	0.802094i	$-0.703719\pi$
$503$	1.99627	−	1.67507i	0.0890093	−	0.0746877i	0.686207	+	0.727407i	$0.259275\pi$
$504$		0			0
$505$	−19.7924	−	9.71807i	−0.880750	−	0.432448i
$506$		0			0
$507$	4.74830	−	17.7209i	0.210879	−	0.787012i
$508$		0			0
$509$	10.7298	+	3.90534i	0.475592	+	0.173101i	0.568684	−	0.822556i	$-0.307453\pi$
$509$	10.7298	+	3.90534i	0.475592	+	0.173101i	−0.0930920	+	0.995658i	$0.529675\pi$
$510$		0			0
$511$	0.0749634	−	0.0893379i	0.00331618	−	0.00395207i
$512$		0			0
$513$	−17.1372	+	20.4233i	−0.756624	+	0.901709i
$514$		0			0
$515$	−16.2131	+	10.8738i	−0.714433	+	0.479156i
$516$		0			0
$517$	−14.2889	+	14.2889i	−0.628425	+	0.628425i
$518$		0			0
$519$		−	11.2453i		−	0.493613i
$520$		0			0
$521$	−11.6369	−	2.05189i	−0.509820	−	0.0898951i	−0.0871800	−	0.996193i	$-0.527786\pi$
$521$	−11.6369	−	2.05189i	−0.509820	−	0.0898951i	−0.422640	+	0.906298i	$0.638897\pi$
$522$		0			0
$523$	12.8506	+	10.7829i	0.561918	+	0.471505i	0.878953	−	0.476909i	$-0.158243\pi$
$523$	12.8506	+	10.7829i	0.561918	+	0.471505i	−0.317035	+	0.948414i	$0.602687\pi$
$524$		0			0
$525$	−5.96570	−	5.42876i	−0.260365	−	0.236931i
$526$		0			0
$527$	−18.2352	−	39.1055i	−0.794337	−	1.70346i
$528$		0			0
$529$	−2.97416	−	5.15140i	−0.129311	−	0.223974i
$530$		0			0
$531$	4.89062	+	2.28054i	0.212235	+	0.0989668i
$532$		0			0
$533$	21.6918	+	25.8513i	0.939577	+	1.11974i
$534$		0			0
$535$	23.5442	+	9.10907i	1.01791	+	0.393819i
$536$		0			0
$537$	−6.58720	−	1.16150i	−0.284259	−	0.0501224i
$538$		0			0
$539$	−0.487250	+	0.408851i	−0.0209873	+	0.0176105i
$540$		0			0
$541$	−10.4862	+	2.80977i	−0.450837	+	0.120802i	−0.477091	−	0.878854i	$-0.658309\pi$
$541$	−10.4862	+	2.80977i	−0.450837	+	0.120802i	0.0262537	+	0.999655i	$0.491642\pi$
$542$		0			0
$543$	−3.34205	+	4.77294i	−0.143421	+	0.204827i
$544$		0			0
$545$	−29.0073	−	17.5336i	−1.24253	−	0.751055i
$546$		0			0
$547$	20.0562	+	34.7383i	0.857540	+	1.48530i	0.874268	+	0.485444i	$0.161342\pi$
$547$	20.0562	+	34.7383i	0.857540	+	1.48530i	−0.0167275	+	0.999860i	$0.505325\pi$
$548$		0			0
$549$	−9.64621	−	9.64621i	−0.411690	−	0.411690i
$550$		0			0
$551$	18.7860	−	6.83753i	0.800308	−	0.291288i
$552$		0			0
$553$	2.48391	+	14.0869i	0.105627	+	0.599038i
$554$		0			0
$555$	−2.27691	−	7.72737i	−0.0966495	−	0.328009i
$556$		0			0
$557$	−3.45307	−	19.5833i	−0.146311	−	0.829772i	−0.966305	−	0.257400i	$-0.917134\pi$
$557$	−3.45307	−	19.5833i	−0.146311	−	0.829772i	0.819994	−	0.572372i	$-0.193977\pi$
$558$		0			0
$559$	30.6104	−	11.1413i	1.29468	−	0.471226i
$560$		0			0
$561$	5.11090	+	5.11090i	0.215783	+	0.215783i
$562$		0			0
$563$	8.18042	+	14.1689i	0.344764	+	0.597148i	0.985311	−	0.170771i	$-0.0546258\pi$
$563$	8.18042	+	14.1689i	0.344764	+	0.597148i	−0.640547	+	0.767919i	$0.721292\pi$
$564$		0			0
$565$	0.278573	−	0.0686765i	0.0117196	−	0.00288924i
$566$		0			0
$567$	−9.32040	+	13.3109i	−0.391420	+	0.559006i
$568$		0			0
$569$	10.1761	−	2.72668i	0.426605	−	0.114308i	−0.0391271	−	0.999234i	$-0.512458\pi$
$569$	10.1761	−	2.72668i	0.426605	−	0.114308i	0.465732	+	0.884926i	$0.345791\pi$
$570$		0			0
$571$	20.2735	−	17.0115i	0.848418	−	0.711907i	−0.111023	−	0.993818i	$-0.535413\pi$
$571$	20.2735	−	17.0115i	0.848418	−	0.711907i	0.959441	+	0.281911i	$0.0909682\pi$
$572$		0			0
$573$	8.51751	+	1.50187i	0.355824	+	0.0627414i
$574$		0			0
$575$	10.2090	−	24.8895i	0.425743	−	1.03796i
$576$		0			0
$577$	−15.1428	−	18.0465i	−0.630404	−	0.751286i	0.352418	−	0.935843i	$-0.385359\pi$
$577$	−15.1428	−	18.0465i	−0.630404	−	0.751286i	−0.982822	+	0.184557i	$0.940915\pi$
$578$		0			0
$579$	−2.97215	−	1.38594i	−0.123519	−	0.0575976i
$580$		0			0
$581$	6.62069	+	11.4674i	0.274673	+	0.475747i
$582$		0			0
$583$	1.20936	+	2.59349i	0.0500867	+	0.107411i
$584$		0			0
$585$	2.63694	+	39.1945i	0.109024	+	1.62049i
$586$		0			0
$587$	−8.61671	−	7.23028i	−0.355650	−	0.298426i	0.447404	−	0.894332i	$-0.352349\pi$
$587$	−8.61671	−	7.23028i	−0.355650	−	0.298426i	−0.803054	+	0.595906i	$0.796793\pi$
$588$		0			0
$589$	−42.1422	−	7.43080i	−1.73644	−	0.306181i
$590$		0			0
$591$			11.0718i			0.455432i
$592$		0			0
$593$	26.9937	−	26.9937i	1.10850	−	1.10850i	0.115151	−	0.993348i	$-0.463265\pi$
$593$	26.9937	−	26.9937i	1.10850	−	1.10850i	0.993348	−	0.115151i	$-0.0367352\pi$
$594$		0			0
$595$	−48.0096	−	9.46352i	−1.96820	−	0.387967i
$596$		0			0
$597$	7.16913	−	8.54383i	0.293413	−	0.349676i
$598$		0			0
$599$	20.9501	−	24.9674i	0.855999	−	1.02014i	−0.143536	−	0.989645i	$-0.545847\pi$
$599$	20.9501	−	24.9674i	0.855999	−	1.02014i	0.999535	−	0.0304950i	$-0.00970837\pi$
$600$		0			0
$601$	5.43626	+	1.97864i	0.221750	+	0.0807103i	0.450506	−	0.892773i	$-0.351244\pi$
$601$	5.43626	+	1.97864i	0.221750	+	0.0807103i	−0.228756	+	0.973484i	$0.573466\pi$
$602$		0			0
$603$	−3.83752	+	14.3218i	−0.156276	+	0.583230i
$604$		0			0
$605$	8.56705	−	17.4482i	0.348300	−	0.709369i
$606$		0			0
$607$	27.2128	−	22.8343i	1.10453	−	0.926815i	0.106813	−	0.994279i	$-0.465935\pi$
$607$	27.2128	−	22.8343i	1.10453	−	0.926815i	0.997722	+	0.0674646i	$0.0214910\pi$
$608$		0			0
$609$	−3.66822	+	1.71052i	−0.148644	+	0.0693137i
$610$		0			0
$611$	72.2686	−	50.6030i	2.92368	−	2.04718i
$612$		0			0
$613$	32.9363	+	2.88155i	1.33029	+	0.116385i	0.730025	−	0.683420i	$-0.239508\pi$
$613$	32.9363	+	2.88155i	1.33029	+	0.116385i	0.600260	+	0.799805i	$0.295064\pi$
$614$		0			0
$615$	5.76779	+	3.48637i	0.232580	+	0.140584i
$616$		0			0
$617$	16.3425	+	11.4432i	0.657926	+	0.460684i	0.854255	−	0.519853i	$-0.174013\pi$
$617$	16.3425	+	11.4432i	0.657926	+	0.460684i	−0.196330	+	0.980538i	$0.562902\pi$
$618$		0			0
$619$	−12.3677	+	21.4214i	−0.497098	+	0.860999i	−0.999994	−	0.00334748i	$-0.998934\pi$
$619$	−12.3677	+	21.4214i	−0.497098	+	0.860999i	0.502896	+	0.864347i	$0.332268\pi$
$620$		0			0
$621$	17.3887	+	4.65930i	0.697786	+	0.186971i
$622$		0			0
$623$			21.1514i			0.847414i
$624$		0			0
$625$	24.1029	−	6.63717i	0.964115	−	0.265487i
$626$		0			0
$627$	7.05940	−	1.24476i	0.281925	−	0.0497111i
$628$		0			0
$629$	−36.0715	−	32.9737i	−1.43827	−	1.31475i
$630$		0			0
$631$	−21.5124	−	15.0631i	−0.856395	−	0.599654i	0.0607742	−	0.998152i	$-0.480643\pi$
$631$	−21.5124	−	15.0631i	−0.856395	−	0.599654i	−0.917170	+	0.398497i	$0.869532\pi$
$632$		0			0
$633$	8.82675	+	4.11598i	0.350832	+	0.163596i
$634$		0			0
$635$	−11.7413	−	0.235906i	−0.465938	−	0.00936164i
$636$		0			0
$637$	2.40492	−	1.38848i	0.0952863	−	0.0550136i
$638$		0			0
$639$	21.0790	+	12.1700i	0.833874	+	0.481438i
$640$		0			0
$641$	−4.47953	−	25.4047i	−0.176931	−	1.00343i	−0.935891	−	0.352288i	$-0.885404\pi$
$641$	−4.47953	−	25.4047i	−0.176931	−	1.00343i	0.758961	−	0.651137i	$-0.225708\pi$
$642$		0			0
$643$	29.8850	+	17.2541i	1.17855	+	0.680437i	0.955679	−	0.294411i	$-0.0951235\pi$
$643$	29.8850	+	17.2541i	1.17855	+	0.680437i	0.222872	+	0.974848i	$0.428457\pi$
$644$		0			0
$645$	5.06659	−	4.08078i	0.199497	−	0.160680i
$646$		0			0
$647$	3.10340	−	17.6003i	0.122007	−	0.691938i	−0.861033	−	0.508549i	$-0.830182\pi$
$647$	3.10340	−	17.6003i	0.122007	−	0.691938i	0.983040	−	0.183389i	$-0.0587068\pi$
$648$		0			0
$649$	−1.30754	−	2.80402i	−0.0513253	−	0.110067i
$650$		0			0
$651$	8.63062	+	0.755081i	0.338261	+	0.0295940i
$652$		0			0
$653$	12.0804	+	33.1906i	0.472743	+	1.29885i	0.915540	+	0.402228i	$0.131764\pi$
$653$	12.0804	+	33.1906i	0.472743	+	1.29885i	−0.442797	+	0.896622i	$0.646014\pi$
$654$		0			0
$655$	12.8351	−	7.07046i	0.501510	−	0.276266i
$656$		0			0
$657$	−0.102803	+	0.0479380i	−0.00401074	+	0.00187024i
$658$		0			0
$659$	−10.2900	−	8.63437i	−0.400843	−	0.336347i	0.419976	−	0.907535i	$-0.362038\pi$
$659$	−10.2900	−	8.63437i	−0.400843	−	0.336347i	−0.820819	+	0.571188i	$0.806483\pi$
$660$		0			0
$661$	−40.1961	+	3.51671i	−1.56345	+	0.136784i	−0.835749	−	0.549112i	$-0.814966\pi$
$661$	−40.1961	+	3.51671i	−1.56345	+	0.136784i	−0.727699	+	0.685896i	$0.759410\pi$
$662$		0			0
$663$	−18.0999	−	25.8493i	−0.702941	−	1.00390i
$664$		0			0
$665$	−34.9982	+	33.6196i	−1.35717	+	1.30371i
$666$		0			0
$667$	−9.54521	−	9.54521i	−0.369592	−	0.369592i
$668$		0			0
$669$	1.13299	−	6.42552i	0.0438040	−	0.248425i
$670$		0			0
$671$	0.681686	+	7.79171i	0.0263162	+	0.300796i
$672$		0			0
$673$	8.39488	−	0.734457i	0.323599	−	0.0283112i	0.0758009	−	0.997123i	$-0.475849\pi$
$673$	8.39488	−	0.734457i	0.323599	−	0.0283112i	0.247798	+	0.968812i	$0.420293\pi$
$674$		0			0
$675$	6.45545	+	15.4338i	0.248471	+	0.594048i
$676$		0			0
$677$	4.03603	+	1.08145i	0.155117	+	0.0415635i	0.335542	−	0.942025i	$-0.391081\pi$
$677$	4.03603	+	1.08145i	0.155117	+	0.0415635i	−0.180425	+	0.983589i	$0.557747\pi$
$678$		0			0
$679$	−2.07595	+	4.45190i	−0.0796678	+	0.170848i
$680$		0			0
$681$	−0.313482	+	3.58311i	−0.0120126	+	0.137305i
$682$		0			0
$683$	−15.2815	−	5.56200i	−0.584729	−	0.212824i	0.0326806	−	0.999466i	$-0.489596\pi$
$683$	−15.2815	−	5.56200i	−0.584729	−	0.212824i	−0.617409	+	0.786642i	$0.711818\pi$
$684$		0			0
$685$	−5.08627	+	25.8033i	−0.194336	+	0.985892i
$686$		0			0
$687$	−1.13483	+	12.9712i	−0.0432966	+	0.494882i
$688$		0			0
$689$	−3.23353	−	12.0677i	−0.123188	−	0.459742i
$690$		0			0
$691$	−0.438048	+	0.0772397i	−0.0166641	+	0.00293834i	−0.181974	−	0.983303i	$-0.558249\pi$
$691$	−0.438048	+	0.0772397i	−0.0166641	+	0.00293834i	0.165310	+	0.986242i	$0.447138\pi$
$692$		0			0
$693$	10.5866	−	2.83668i	0.402153	−	0.107757i
$694$		0			0
$695$	−26.2341	−	7.59740i	−0.995116	−	0.288186i
$696$		0			0
$697$	40.8864			1.54868
$698$		0			0
$699$	0.742325	+	2.03952i	0.0280773	+	0.0771417i
$700$		0			0
$701$	−19.0487	+	27.2043i	−0.719458	+	1.02749i	0.278296	+	0.960495i	$0.410231\pi$
$701$	−19.0487	+	27.2043i	−0.719458	+	1.02749i	−0.997753	+	0.0669966i	$0.978658\pi$
$702$		0			0
$703$	−47.3069	+	10.5474i	−1.78422	+	0.397804i
$704$		0			0
$705$	10.3940	−	14.2270i	0.391459	−	0.535821i
$706$		0			0
$707$	11.3508	−	24.3419i	0.426892	−	0.915472i
$708$		0			0
$709$	8.00887	−	8.00887i	0.300780	−	0.300780i	−0.540539	−	0.841319i	$-0.681780\pi$
$709$	8.00887	−	8.00887i	0.300780	−	0.300780i	0.841319	+	0.540539i	$0.181780\pi$
$710$		0			0
$711$	3.60091	−	13.4388i	0.135045	−	0.503993i
$712$		0			0
$713$	7.47851	+	27.9102i	0.280072	+	1.04524i
$714$		0			0
$715$	13.2866	−	18.1864i	0.496889	−	0.680132i
$716$		0			0
$717$	−1.99872	+	3.46189i	−0.0746436	+	0.129287i
$718$		0			0
$719$	−26.8017	−	31.9410i	−0.999534	−	1.19120i	−0.981520	−	0.191360i	$-0.938710\pi$
$719$	−26.8017	−	31.9410i	−0.999534	−	1.19120i	−0.0180139	−	0.999838i	$-0.505734\pi$
$720$		0			0
$721$	−13.6393	−	19.4790i	−0.507955	−	0.725435i
$722$		0			0
$723$	1.79240	−	4.92457i	0.0666600	−	0.183147i
$724$		0			0
$725$	1.59443	−	12.4429i	0.0592157	−	0.462118i
$726$		0			0
$727$	−33.0751	+	12.0384i	−1.22669	+	0.446478i	−0.872462	−	0.488682i	$-0.837478\pi$
$727$	−33.0751	+	12.0384i	−1.22669	+	0.446478i	−0.354226	+	0.935160i	$0.615256\pi$
$728$		0			0
$729$	8.53890	−	4.92994i	0.316256	−	0.182590i
$730$		0			0
$731$	13.4985	−	37.0868i	0.499259	−	1.37170i
$732$		0			0
$733$	−2.21174	−	25.2803i	−0.0816923	−	0.933748i	−0.920865	−	0.389882i	$-0.872516\pi$
$733$	−2.21174	−	25.2803i	−0.0816923	−	0.933748i	0.839172	−	0.543866i	$-0.183040\pi$
$734$		0			0
$735$	0.364948	−	0.417597i	0.0134613	−	0.0154033i
$736$		0			0
$737$	6.96364	−	4.87599i	0.256509	−	0.179609i
$738$		0			0
$739$	−12.3808			−0.455436			−0.227718	−	0.973727i	$-0.573126\pi$
$739$	−12.3808			−0.455436			−0.227718	+	0.973727i	$0.573126\pi$
$740$		0			0
$741$	−31.2960			−1.14969
$742$		0			0
$743$	3.79813	−	2.65948i	0.139340	−	0.0975668i	−0.501828	−	0.864967i	$-0.667339\pi$
$743$	3.79813	−	2.65948i	0.139340	−	0.0975668i	0.641168	+	0.767400i	$0.278450\pi$
$744$		0			0
$745$	−0.124653	−	1.85279i	−0.00456693	−	0.0678811i
$746$		0			0
$747$	−1.12248	−	12.8300i	−0.0410695	−	0.469427i
$748$		0			0
$749$	−10.5174	+	28.8962i	−0.384296	+	1.05584i
$750$		0			0
$751$	23.2196	−	13.4059i	0.847297	−	0.489187i	−0.0124412	−	0.999923i	$-0.503960\pi$
$751$	23.2196	−	13.4059i	0.847297	−	0.489187i	0.859738	+	0.510736i	$0.170627\pi$
$752$		0			0
$753$	6.77167	−	2.46469i	0.246773	−	0.0898181i
$754$		0			0
$755$	5.62039	+	0.605710i	0.204547	+	0.0220440i
$756$		0			0
$757$	4.10102	−	11.2675i	0.149054	−	0.409523i	−0.842585	−	0.538563i	$-0.818967\pi$
$757$	4.10102	−	11.2675i	0.149054	−	0.409523i	0.991639	+	0.129040i	$0.0411895\pi$
$758$		0			0
$759$	−2.77627	−	3.96492i	−0.100772	−	0.143917i
$760$		0			0
$761$	−2.79685	−	3.33316i	−0.101386	−	0.120827i	0.712966	−	0.701199i	$-0.247352\pi$
$761$	−2.79685	−	3.33316i	−0.101386	−	0.120827i	−0.814351	+	0.580372i	$0.802907\pi$
$762$		0			0
$763$	20.6434	−	35.7554i	0.747342	−	1.29443i
$764$		0			0
$765$	38.4308	+	28.0767i	1.38947	+	1.01511i
$766$		0			0
$767$	3.49602	+	13.0473i	0.126234	+	0.471111i
$768$		0			0
$769$	5.89200	−	21.9893i	0.212471	−	0.792953i	−0.774570	−	0.632488i	$-0.782034\pi$
$769$	5.89200	−	21.9893i	0.212471	−	0.792953i	0.987042	−	0.160465i	$-0.0512994\pi$
$770$		0			0
$771$	0.574261	−	0.574261i	0.0206815	−	0.0206815i
$772$		0			0
$773$	−8.38185	+	17.9749i	−0.301474	+	0.646514i	−0.997436	−	0.0715653i	$-0.977201\pi$
$773$	−8.38185	+	17.9749i	−0.301474	+	0.646514i	0.695962	+	0.718079i	$0.254978\pi$
$774$		0			0
$775$	−16.2728	+	21.3595i	−0.584536	+	0.767255i
$776$		0			0
$777$	9.35505	−	2.96201i	0.335610	−	0.106262i
$778$		0			0
$779$	23.2581	−	33.2160i	0.833307	−	1.19009i
$780$		0			0
$781$	−4.77297	−	13.1136i	−0.170790	−	0.469243i
$782$		0			0
$783$	8.39463			0.299999
$784$		0			0
$785$	16.4065	+	29.7830i	0.585573	+	1.06300i
$786$		0			0
$787$	−10.6108	+	2.84316i	−0.378235	+	0.101348i	−0.442928	−	0.896557i	$-0.646060\pi$
$787$	−10.6108	+	2.84316i	−0.378235	+	0.101348i	0.0646922	+	0.997905i	$0.479393\pi$
$788$		0			0
$789$	10.3744	−	1.82929i	0.369339	−	0.0651244i
$790$		0			0
$791$	0.0904540	+	0.337579i	0.00321617	+	0.0120029i
$792$		0			0
$793$	2.97616	−	34.0177i	0.105687	−	1.20800i
$794$		0			0
$795$	−1.38978	−	2.07219i	−0.0492903	−	0.0734931i
$796$		0			0
$797$	12.3122	+	4.48128i	0.436121	+	0.158735i	0.550744	−	0.834674i	$-0.314344\pi$
$797$	12.3122	+	4.48128i	0.436121	+	0.158735i	−0.114624	+	0.993409i	$0.536566\pi$
$798$		0			0
$799$	9.31604	−	106.483i	0.329578	−	3.76709i
$800$		0			0
$801$	8.69437	−	18.6451i	0.307201	−	0.658794i
$802$		0			0
$803$	0.0628192	+	0.0168324i	0.00221684	+	0.000594001i
$804$		0			0
$805$	30.5614	+	11.8239i	1.07715	+	0.416739i
$806$		0			0
$807$	18.4929	−	1.61792i	0.650980	−	0.0569534i
$808$		0			0
$809$	1.58171	+	18.0790i	0.0556099	+	0.635624i	0.971944	+	0.235211i	$0.0755780\pi$
$809$	1.58171	+	18.0790i	0.0556099	+	0.635624i	−0.916335	+	0.400414i	$0.868866\pi$
$810$		0			0
$811$	1.73343	−	9.83075i	0.0608688	−	0.345204i	−0.939130	−	0.343562i	$-0.888366\pi$
$811$	1.73343	−	9.83075i	0.0608688	−	0.345204i	0.999999	−	0.00164179i	$-0.000522598\pi$
$812$		0			0
$813$	−4.43037	−	4.43037i	−0.155380	−	0.155380i
$814$		0			0
$815$	−13.5957	−	14.1532i	−0.476236	−	0.495766i
$816$		0			0
$817$	−22.4506	−	32.0628i	−0.785448	−	1.12174i
$818$		0			0
$819$	−47.6684	+	4.17045i	−1.66567	+	0.145727i
$820$		0			0
$821$	−10.4075	−	8.73290i	−0.363223	−	0.304780i	0.442851	−	0.896595i	$-0.353967\pi$
$821$	−10.4075	−	8.73290i	−0.363223	−	0.304780i	−0.806074	+	0.591815i	$0.798412\pi$
$822$		0			0
$823$	−41.0591	+	19.1462i	−1.43123	+	0.667394i	−0.974946	−	0.222441i	$-0.928598\pi$
$823$	−41.0591	+	19.1462i	−1.43123	+	0.667394i	−0.456284	+	0.889834i	$0.650820\pi$
$824$		0			0
$825$	1.33777	−	4.29455i	0.0465753	−	0.149517i
$826$		0			0
$827$	4.77137	+	13.1092i	0.165917	+	0.455853i	0.994590	−	0.103880i	$-0.0331259\pi$
$827$	4.77137	+	13.1092i	0.165917	+	0.455853i	−0.828673	+	0.559733i	$0.810904\pi$
$828$		0			0
$829$	42.7026	+	3.73600i	1.48312	+	0.129757i	0.799759	−	0.600321i	$-0.204960\pi$
$829$	42.7026	+	3.73600i	1.48312	+	0.129757i	0.683365	+	0.730077i	$0.260516\pi$
$830$		0			0
$831$	3.80256	+	8.15461i	0.131909	+	0.282880i
$832$		0			0
$833$	0.584238	−	3.31338i	0.0202427	−	0.114802i
$834$		0			0
$835$	20.7716	+	2.23855i	0.718830	+	0.0774684i
$836$		0			0
$837$	−15.5615	−	8.98441i	−0.537882	−	0.310547i
$838$		0			0
$839$	4.08845	+	23.1868i	0.141149	+	0.800496i	0.970379	+	0.241588i	$0.0776683\pi$
$839$	4.08845	+	23.1868i	0.141149	+	0.800496i	−0.829230	+	0.558908i	$0.811221\pi$
$840$		0			0
$841$	19.6633	+	11.3526i	0.678046	+	0.391470i
$842$		0			0
$843$	−4.03151	+	2.32759i	−0.138853	+	0.0801665i
$844$		0			0
$845$	−49.9503	+	47.9826i	−1.71834	+	1.65065i
$846$		0			0
$847$	21.4588	+	10.0064i	0.737334	+	0.343825i
$848$		0			0
$849$	8.52867	+	5.97184i	0.292703	+	0.204953i
$850$		0			0
$851$	19.9545	+	25.9405i	0.684030	+	0.889228i
$852$		0			0
$853$	−11.7676	+	2.07494i	−0.402915	+	0.0710447i	−0.371433	−	0.928460i	$-0.621134\pi$
$853$	−11.7676	+	2.07494i	−0.402915	+	0.0710447i	−0.0314813	+	0.999504i	$0.510022\pi$
$854$		0			0
$855$	44.6706	−	15.2497i	1.52770	−	0.521530i
$856$		0			0
$857$			40.8866i			1.39666i	0.715775	+	0.698331i	$0.246073\pi$
$857$			40.8866i			1.39666i	−0.715775	+	0.698331i	$0.753927\pi$
$858$		0			0
$859$	−51.4244	−	13.7791i	−1.75458	−	0.470138i	−0.768984	−	0.639269i	$-0.779237\pi$
$859$	−51.4244	−	13.7791i	−1.75458	−	0.470138i	−0.985594	+	0.169131i	$0.945904\pi$
$860$		0			0
$861$	−4.10473	+	7.10960i	−0.139889	+	0.242295i
$862$		0			0
$863$	9.02798	+	6.32146i	0.307316	+	0.215185i	0.717053	−	0.697019i	$-0.245491\pi$
$863$	9.02798	+	6.32146i	0.307316	+	0.215185i	−0.409737	+	0.912204i	$0.634379\pi$
$864$		0			0
$865$	−21.9619	+	36.3334i	−0.746725	+	1.23537i
$866$		0			0
$867$	−28.0568	−	2.45465i	−0.952858	−	0.0833643i
$868$		0			0
$869$	−6.53427	+	4.57535i	−0.221660	+	0.155208i
$870$		0			0
$871$	−33.6372	+	15.6853i	−1.13975	+	0.531475i
$872$		0			0
$873$	3.65994	−	3.07105i	0.123870	−	0.103939i
$874$		0			0
$875$	8.67283	+	29.1912i	0.293195	+	0.986843i
$876$		0			0
$877$	−3.42091	+	12.7670i	−0.115516	+	0.431111i	−0.999325	−	0.0367365i	$-0.988304\pi$
$877$	−3.42091	+	12.7670i	−0.115516	+	0.431111i	0.883809	+	0.467848i	$0.154970\pi$
$878$		0			0
$879$	10.6231	+	3.86647i	0.358307	+	0.130413i
$880$		0			0
$881$	12.5295	−	14.9320i	0.422128	−	0.503073i	−0.512506	−	0.858684i	$-0.671283\pi$
$881$	12.5295	−	14.9320i	0.422128	−	0.503073i	0.934634	+	0.355611i	$0.115727\pi$
$882$		0			0
$883$	−5.62166	+	6.69964i	−0.189184	+	0.225461i	−0.852296	−	0.523059i	$-0.824791\pi$
$883$	−5.62166	+	6.69964i	−0.189184	+	0.225461i	0.663112	+	0.748520i	$0.269235\pi$
$884$		0			0
$885$	1.50260	+	2.24041i	0.0505092	+	0.0753104i
$886$		0			0
$887$	−1.61341	+	1.61341i	−0.0541730	+	0.0541730i	−0.733674	−	0.679501i	$-0.762196\pi$
$887$	−1.61341	+	1.61341i	−0.0541730	+	0.0541730i	0.679501	+	0.733674i	$0.262196\pi$
$888$		0			0
$889$		−	14.3049i		−	0.479770i
$890$		0			0
$891$	−8.92405	−	1.57355i	−0.298967	−	0.0527159i
$892$		0			0
$893$	−81.2069	−	68.1407i	−2.71749	−	2.28024i
$894$		0			0
$895$	19.0148	+	16.6175i	0.635594	+	0.555462i
$896$		0			0
$897$	8.93079	+	19.1521i	0.298190	+	0.639471i
$898$		0			0
$899$	6.73699	+	11.6688i	0.224691	+	0.389176i
$900$		0			0
$901$	−13.7185	−	6.39704i	−0.457029	−	0.213116i
$902$		0			0
$903$	5.09374	+	6.07048i	0.169509	+	0.202013i
$904$		0			0
$905$	20.1196	−	8.89436i	0.668799	−	0.295659i
$906$		0			0
$907$	42.7120	+	7.53128i	1.41823	+	0.250072i	0.829612	−	0.558340i	$-0.188562\pi$
$907$	42.7120	+	7.53128i	1.41823	+	0.250072i	0.588617	+	0.808412i	$0.299673\pi$
$908$		0			0
$909$	−20.0117	+	16.7918i	−0.663745	+	0.556949i
$910$		0			0
$911$	11.1785	−	2.99528i	0.370361	−	0.0992380i	−0.0688375	−	0.997628i	$-0.521929\pi$
$911$	11.1785	−	2.99528i	0.370361	−	0.0992380i	0.439199	+	0.898390i	$0.355262\pi$
$912$		0			0
$913$	−4.23538	+	6.04874i	−0.140170	+	0.200184i
$914$		0			0
$915$	−1.63239	−	6.62146i	−0.0539651	−	0.218899i
$916$		0			0
$917$	8.92481	+	15.4582i	0.294723	+	0.510476i
$918$		0			0
$919$	28.4606	+	28.4606i	0.938828	+	0.938828i	0.998234	−	0.0594061i	$-0.0189207\pi$
$919$	28.4606	+	28.4606i	0.938828	+	0.938828i	−0.0594061	+	0.998234i	$0.518921\pi$
$920$		0			0
$921$	5.29502	−	1.92723i	0.174477	−	0.0635044i
$922$		0			0
$923$	10.5798	+	60.0013i	0.348240	+	1.97497i
$924$		0			0
$925$	−7.73476	+	29.4138i	−0.254317	+	0.967121i
$926$		0			0
$927$	4.01626	+	22.7774i	0.131911	+	0.748107i
$928$		0			0
$929$	21.7675	−	7.92270i	0.714167	−	0.259935i	0.0407195	−	0.999171i	$-0.487035\pi$
$929$	21.7675	−	7.92270i	0.714167	−	0.259935i	0.673447	+	0.739235i	$0.264813\pi$
$930$		0			0
$931$	−2.35944	−	2.35944i	−0.0773275	−	0.0773275i
$932$		0			0
$933$	7.78624	+	13.4862i	0.254910	+	0.441517i
$934$		0			0
$935$	−6.53176	−	26.4948i	−0.213611	−	0.866473i
$936$		0			0
$937$	33.1956	−	47.4082i	1.08445	−	1.54876i	0.275117	−	0.961411i	$-0.411283\pi$
$937$	33.1956	−	47.4082i	1.08445	−	1.54876i	0.809335	−	0.587348i	$-0.199828\pi$
$938$		0			0
$939$	−1.53932	+	0.412459i	−0.0502337	+	0.0134601i
$940$		0			0
$941$	9.44916	−	7.92879i	0.308034	−	0.258471i	−0.475645	−	0.879637i	$-0.657785\pi$
$941$	9.44916	−	7.92879i	0.308034	−	0.258471i	0.783679	+	0.621166i	$0.213341\pi$
$942$		0			0
$943$	−26.9642	−	4.75451i	−0.878074	−	0.154828i
$944$		0			0
$945$	−18.6381	+	8.23941i	−0.606297	+	0.268028i
$946$		0			0
$947$	−2.25944	−	2.69269i	−0.0734219	−	0.0875008i	0.728083	−	0.685489i	$-0.240411\pi$
$947$	−2.25944	−	2.69269i	−0.0734219	−	0.0875008i	−0.801505	+	0.597988i	$0.795967\pi$
$948$		0			0
$949$	−0.257334	−	0.119997i	−0.00835340	−	0.00389526i
$950$		0			0
$951$	0.836551	+	1.44895i	0.0271270	+	0.0469854i
$952$		0			0
$953$	14.2850	+	30.6343i	0.462737	+	0.992342i	0.989793	+	0.142512i	$0.0455180\pi$
$953$	14.2850	+	30.6343i	0.462737	+	0.992342i	−0.527056	+	0.849830i	$0.676704\pi$
$954$		0			0
$955$	−24.5869	−	21.4871i	−0.795613	−	0.695306i
$956$		0			0
$957$	−1.72902	−	1.45082i	−0.0558914	−	0.0468984i
$958$		0			0
$959$	−31.5489	−	5.56292i	−1.01877	−	0.179636i
$960$		0			0
$961$			2.15876i			0.0696376i
$962$		0			0
$963$	21.1490	−	21.1490i	0.681518	−	0.681518i
$964$		0			0
$965$	6.89628	+	10.2825i	0.221999	+	0.331006i
$966$		0			0
$967$	19.4553	−	23.1860i	0.625642	−	0.745611i	−0.356388	−	0.934338i	$-0.615992\pi$
$967$	19.4553	−	23.1860i	0.625642	−	0.745611i	0.982030	+	0.188727i	$0.0604362\pi$
$968$		0			0
$969$	−24.3728	+	29.0464i	−0.782968	+	0.933105i
$970$		0			0
$971$	38.9861	+	14.1898i	1.25113	+	0.455372i	0.880782	−	0.473523i	$-0.157018\pi$
$971$	38.9861	+	14.1898i	1.25113	+	0.455372i	0.370343	+	0.928895i	$0.379240\pi$
$972$		0			0
$973$	8.61056	−	32.1350i	0.276042	−	1.03020i
$974$		0			0
$975$	−9.00764	+	17.4504i	−0.288475	+	0.558861i
$976$		0			0
$977$	−0.374886	+	0.314567i	−0.0119937	+	0.0100639i	−0.648765	−	0.760989i	$-0.724714\pi$
$977$	−0.374886	+	0.314567i	−0.0119937	+	0.0100639i	0.636771	+	0.771053i	$0.280270\pi$
$978$		0			0
$979$	−10.6901	+	4.98488i	−0.341658	+	0.159318i
$980$		0			0
$981$	−32.8947	+	23.0331i	−1.05025	+	0.735392i
$982$		0			0
$983$	−40.6612	−	3.55740i	−1.29689	−	0.113463i	−0.582282	−	0.812987i	$-0.697840\pi$
$983$	−40.6612	−	3.55740i	−1.29689	−	0.113463i	−0.714610	+	0.699523i	$0.753396\pi$
$984$		0			0
$985$	21.6230	−	35.7728i	0.688967	−	1.13982i
$986$		0			0
$987$	17.5807	+	12.3101i	0.559599	+	0.391836i
$988$		0			0
$989$	−13.2148	+	22.8887i	−0.420206	+	0.727818i
$990$		0			0
$991$	−34.1249	−	9.14375i	−1.08401	−	0.290461i	−0.327775	−	0.944756i	$-0.606299\pi$
$991$	−34.1249	−	9.14375i	−1.08401	−	0.290461i	−0.756239	+	0.654295i	$0.772965\pi$
$992$		0			0
$993$		−	17.3626i		−	0.550987i
$994$		0			0
$995$	−39.8494	+	13.6038i	−1.26331	+	0.431271i
$996$		0			0
$997$	−5.68914	+	1.00315i	−0.180177	+	0.0317701i	−0.263009	−	0.964794i	$-0.584715\pi$
$997$	−5.68914	+	1.00315i	−0.180177	+	0.0317701i	0.0828316	+	0.996564i	$0.473604\pi$
$998$		0			0
$999$	−20.1814	−	2.63223i	−0.638510	−	0.0832801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.cc.a.17.12	✓	228
5.3	odd	4		740.2.ch.a.313.12	yes	228
37.24	odd	36		740.2.ch.a.357.12	yes	228
185.98	even	36	inner	740.2.cc.a.653.12	yes	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.cc.a.17.12	✓	228	1.1	even	1	trivial
740.2.cc.a.653.12	yes	228	185.98	even	36	inner
740.2.ch.a.313.12	yes	228	5.3	odd	4
740.2.ch.a.357.12	yes	228	37.24	odd	36

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.cc (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.485165 - 0.339716i) q^{3} +(-2.23102 + 0.150100i) q^{5} +(-0.237390 - 2.71338i) q^{7} +(-0.906082 + 2.48944i) q^{9} +(1.31542 - 0.759457i) q^{11} +(-6.23147 + 2.26807i) q^{13} +(-1.03142 + 0.830738i) q^{15} +(-2.74794 + 7.54989i) q^{17} +(4.57036 + 6.52714i) q^{19} +(-1.03695 - 1.23579i) q^{21} +(2.69018 - 4.65953i) q^{23} +(4.95494 - 0.669752i) q^{25} +(0.865982 + 3.23189i) q^{27} +(0.649359 - 2.42344i) q^{29} +(-3.79745 + 3.79745i) q^{31} +(0.380195 - 0.815330i) q^{33} +(0.936899 + 6.01797i) q^{35} +(-2.32101 + 5.62254i) q^{37} +(-2.25279 + 3.21732i) q^{39} +(-1.74051 - 4.78200i) q^{41} -4.91223 q^{43} +(1.64783 - 5.69001i) q^{45} +(-12.8506 + 3.44332i) q^{47} +(-0.412398 + 0.0727169i) q^{49} +(1.23162 + 4.59646i) q^{51} +(-0.164199 + 1.87681i) q^{53} +(-2.82073 + 1.89181i) q^{55} +(4.43475 + 1.61412i) q^{57} +(0.177529 - 2.02916i) q^{59} +(-2.17623 + 4.66693i) q^{61} +(6.96988 + 1.86757i) q^{63} +(13.5621 - 5.99546i) q^{65} +(5.57549 - 0.487792i) q^{67} +(-0.277736 - 3.17454i) q^{69} +(1.59542 - 9.04807i) q^{71} +(0.0302762 + 0.0302762i) q^{73} +(2.17644 - 2.00821i) q^{75} +(-2.37296 - 3.38893i) q^{77} +(-5.23171 + 0.457716i) q^{79} +(-4.57016 - 3.83482i) q^{81} +(-4.40599 + 2.05455i) q^{83} +(4.99747 - 17.2565i) q^{85} +(-0.508236 - 1.39637i) q^{87} +(-7.73603 - 0.676815i) q^{89} +(7.63341 + 16.3699i) q^{91} +(-0.552335 + 3.13244i) q^{93} +(-11.1763 - 13.8762i) q^{95} +(-1.56183 - 0.901725i) q^{97} +(0.698746 + 3.96278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q + 6 q^{3} - 12 q^{25} + 12 q^{27} - 36 q^{31} + 6 q^{33} + 24 q^{35} + 24 q^{37} - 72 q^{39} - 54 q^{41} - 12 q^{45} + 36 q^{49} - 6 q^{53} - 72 q^{57} - 36 q^{61} + 18 q^{65} + 42 q^{67} + 96 q^{69}+ \cdots + 72 q^{97}+O(q^{100}) \) 228 * q + 6 * q^3 - 12 * q^25 + 12 * q^27 - 36 * q^31 + 6 * q^33 + 24 * q^35 + 24 * q^37 - 72 * q^39 - 54 * q^41 - 12 * q^45 + 36 * q^49 - 6 * q^53 - 72 * q^57 - 36 * q^61 + 18 * q^65 + 42 * q^67 + 96 * q^69 - 48 * q^71 - 6 * q^73 - 96 * q^75 - 114 * q^77 + 48 * q^79 - 36 * q^81 - 12 * q^83 + 72 * q^87 - 12 * q^89 + 24 * q^91 - 6 * q^93 + 90 * q^95 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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