LMFDB - Embedded newform 432.2.be.b.239.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			239.6
Character	$\chi$	$=$	432.239
Dual form			432.2.be.b.47.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50778 - 0.852402i) q^{3} +(-2.12767 - 0.375166i) q^{5} +(-2.50142 - 2.98107i) q^{7} +(1.54682 - 2.57047i) q^{9} +O(q^{10})$	\(q+(1.50778 - 0.852402i) q^{3} +(-2.12767 - 0.375166i) q^{5} +(-2.50142 - 2.98107i) q^{7} +(1.54682 - 2.57047i) q^{9} +(-0.0357619 - 0.202816i) q^{11} +(-2.01394 + 0.733014i) q^{13} +(-3.52786 + 1.24796i) q^{15} +(-5.87137 - 3.38984i) q^{17} +(6.56062 - 3.78777i) q^{19} +(-6.31267 - 2.36260i) q^{21} +(3.99143 + 3.34921i) q^{23} +(-0.312223 - 0.113640i) q^{25} +(0.141195 - 5.19423i) q^{27} +(-0.709501 + 1.94934i) q^{29} +(1.02516 - 1.22174i) q^{31} +(-0.226802 - 0.275319i) q^{33} +(4.20380 + 7.28120i) q^{35} +(3.90071 - 6.75622i) q^{37} +(-2.41176 + 2.82191i) q^{39} +(4.12650 + 11.3375i) q^{41} +(6.15496 - 1.08528i) q^{43} +(-4.25549 + 4.88881i) q^{45} +(-3.44521 + 2.89087i) q^{47} +(-1.41417 + 8.02017i) q^{49} +(-11.7423 - 0.106374i) q^{51} -6.89537i q^{53} +0.444942i q^{55} +(6.66329 - 11.3034i) q^{57} +(-0.0937549 + 0.531710i) q^{59} +(0.695271 - 0.583402i) q^{61} +(-11.5320 + 1.81864i) q^{63} +(4.56001 - 0.804052i) q^{65} +(-1.77754 - 4.88376i) q^{67} +(8.87308 + 1.64758i) q^{69} +(5.04889 - 8.74494i) q^{71} +(1.46358 + 2.53500i) q^{73} +(-0.567631 + 0.0947951i) q^{75} +(-0.515154 + 0.613936i) q^{77} +(1.25749 - 3.45493i) q^{79} +(-4.21468 - 7.95213i) q^{81} +(10.0574 + 3.66058i) q^{83} +(11.2206 + 9.41520i) q^{85} +(0.591846 + 3.54396i) q^{87} +(-9.79768 + 5.65669i) q^{89} +(7.22287 + 4.17013i) q^{91} +(0.504309 - 2.71597i) q^{93} +(-15.3799 + 5.59782i) q^{95} +(1.67663 + 9.50863i) q^{97} +(-0.576651 - 0.221795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q + 3 * q^5 + 6 * q^9	$ 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50778	−	0.852402i	0.870519	−	0.492134i
$3$	1.50778	−	0.852402i	0.870519	−	0.492134i
$4$		0			0
$5$	−2.12767	−	0.375166i	−0.951524	−	0.167779i	−0.323722	−	0.946152i	$-0.604934\pi$
$5$	−2.12767	−	0.375166i	−0.951524	−	0.167779i	−0.627802	+	0.778373i	$0.716045\pi$
$6$		0			0
$7$	−2.50142	−	2.98107i	−0.945447	−	1.12674i	−0.991798	−	0.127815i	$-0.959204\pi$
$7$	−2.50142	−	2.98107i	−0.945447	−	1.12674i	0.0463507	−	0.998925i	$-0.485241\pi$
$8$		0			0
$9$	1.54682	−	2.57047i	0.515607	−	0.856825i
$10$		0			0
$11$	−0.0357619	−	0.202816i	−0.0107826	−	0.0611513i	0.978942	−	0.204140i	$-0.0654398\pi$
$11$	−0.0357619	−	0.202816i	−0.0107826	−	0.0611513i	−0.989724	+	0.142989i	$0.954329\pi$
$12$		0			0
$13$	−2.01394	+	0.733014i	−0.558566	+	0.203302i	−0.605848	−	0.795580i	$-0.707166\pi$
$13$	−2.01394	+	0.733014i	−0.558566	+	0.203302i	0.0472822	+	0.998882i	$0.484944\pi$
$14$		0			0
$15$	−3.52786	+	1.24796i	−0.910890	+	0.322223i
$16$		0			0
$17$	−5.87137	−	3.38984i	−1.42402	−	0.822156i	−0.427377	−	0.904074i	$-0.640562\pi$
$17$	−5.87137	−	3.38984i	−1.42402	−	0.822156i	−0.996639	+	0.0819176i	$0.973896\pi$
$18$		0			0
$19$	6.56062	−	3.78777i	1.50511	−	0.868975i	0.505127	−	0.863045i	$-0.331446\pi$
$19$	6.56062	−	3.78777i	1.50511	−	0.868975i	0.999982	−	0.00592975i	$-0.00188751\pi$
$20$		0			0
$21$	−6.31267	−	2.36260i	−1.37754	−	0.515562i
$22$		0			0
$23$	3.99143	+	3.34921i	0.832271	+	0.698358i	0.955811	−	0.293982i	$-0.0949804\pi$
$23$	3.99143	+	3.34921i	0.832271	+	0.698358i	−0.123540	+	0.992340i	$0.539425\pi$
$24$		0			0
$25$	−0.312223	−	0.113640i	−0.0624446	−	0.0227280i
$26$		0			0
$27$	0.141195	−	5.19423i	0.0271730	−	0.999631i
$28$		0			0
$29$	−0.709501	+	1.94934i	−0.131751	+	0.361983i	−0.987973	−	0.154625i	$-0.950583\pi$
$29$	−0.709501	+	1.94934i	−0.131751	+	0.361983i	0.856222	+	0.516608i	$0.172805\pi$
$30$		0			0
$31$	1.02516	−	1.22174i	0.184125	−	0.219431i	−0.666084	−	0.745876i	$-0.732031\pi$
$31$	1.02516	−	1.22174i	0.184125	−	0.219431i	0.850209	+	0.526445i	$0.176475\pi$
$32$		0			0
$33$	−0.226802	−	0.275319i	−0.0394811	−	0.0479269i
$34$		0			0
$35$	4.20380	+	7.28120i	0.710572	+	1.23075i
$36$		0			0
$37$	3.90071	−	6.75622i	0.641272	−	1.11072i	−0.343877	−	0.939015i	$-0.611740\pi$
$37$	3.90071	−	6.75622i	0.641272	−	1.11072i	0.985149	−	0.171701i	$-0.0549264\pi$
$38$		0			0
$39$	−2.41176	+	2.82191i	−0.386191	+	0.451868i
$40$		0			0
$41$	4.12650	+	11.3375i	0.644452	+	1.77062i	0.637269	+	0.770642i	$0.280064\pi$
$41$	4.12650	+	11.3375i	0.644452	+	1.77062i	0.00718287	+	0.999974i	$0.497714\pi$
$42$		0			0
$43$	6.15496	−	1.08528i	0.938622	−	0.165504i	0.316649	−	0.948543i	$-0.397442\pi$
$43$	6.15496	−	1.08528i	0.938622	−	0.165504i	0.621973	+	0.783038i	$0.286331\pi$
$44$		0			0
$45$	−4.25549	+	4.88881i	−0.634370	+	0.728781i
$46$		0			0
$47$	−3.44521	+	2.89087i	−0.502535	+	0.421677i	−0.858493	−	0.512825i	$-0.828599\pi$
$47$	−3.44521	+	2.89087i	−0.502535	+	0.421677i	0.355958	+	0.934502i	$0.384155\pi$
$48$		0			0
$49$	−1.41417	+	8.02017i	−0.202025	+	1.14574i
$50$		0			0
$51$	−11.7423	−	0.106374i	−1.64424	−	0.0148953i
$52$		0			0
$53$		−	6.89537i		−	0.947152i	−0.880753	−	0.473576i	$-0.842963\pi$
$53$		−	6.89537i		−	0.947152i	0.880753	−	0.473576i	$-0.157037\pi$
$54$		0			0
$55$			0.444942i			0.0599960i
$56$		0			0
$57$	6.66329	−	11.3034i	0.882574	−	1.49718i
$58$		0			0
$59$	−0.0937549	+	0.531710i	−0.0122058	+	0.0692228i	−0.990302	−	0.138930i	$-0.955634\pi$
$59$	−0.0937549	+	0.531710i	−0.0122058	+	0.0692228i	0.978096	+	0.208152i	$0.0667450\pi$
$60$		0			0
$61$	0.695271	−	0.583402i	0.0890203	−	0.0746969i	−0.597191	−	0.802099i	$-0.703717\pi$
$61$	0.695271	−	0.583402i	0.0890203	−	0.0746969i	0.686212	+	0.727402i	$0.259272\pi$
$62$		0			0
$63$	−11.5320	+	1.81864i	−1.45290	+	0.229127i
$64$		0			0
$65$	4.56001	−	0.804052i	0.565599	−	0.0997304i
$66$		0			0
$67$	−1.77754	−	4.88376i	−0.217161	−	0.596646i	0.782500	−	0.622650i	$-0.213944\pi$
$67$	−1.77754	−	4.88376i	−0.217161	−	0.596646i	−0.999662	+	0.0260040i	$0.991722\pi$
$68$		0			0
$69$	8.87308	+	1.64758i	1.06819	+	0.198345i
$70$		0			0
$71$	5.04889	−	8.74494i	0.599193	−	1.03783i	−0.393747	−	0.919219i	$-0.628821\pi$
$71$	5.04889	−	8.74494i	0.599193	−	1.03783i	0.992940	−	0.118614i	$-0.0378452\pi$
$72$		0			0
$73$	1.46358	+	2.53500i	0.171299	+	0.296699i	0.938874	−	0.344260i	$-0.111870\pi$
$73$	1.46358	+	2.53500i	0.171299	+	0.296699i	−0.767575	+	0.640959i	$0.778537\pi$
$74$		0			0
$75$	−0.567631	+	0.0947951i	−0.0655444	+	0.0109460i
$76$		0			0
$77$	−0.515154	+	0.613936i	−0.0587072	+	0.0699645i
$78$		0			0
$79$	1.25749	−	3.45493i	0.141479	−	0.388710i	−0.848634	−	0.528980i	$-0.822575\pi$
$79$	1.25749	−	3.45493i	0.141479	−	0.388710i	0.990113	+	0.140270i	$0.0447969\pi$
$80$		0			0
$81$	−4.21468	−	7.95213i	−0.468298	−	0.883571i
$82$		0			0
$83$	10.0574	+	3.66058i	1.10394	+	0.401800i	0.828766	−	0.559595i	$-0.189043\pi$
$83$	10.0574	+	3.66058i	1.10394	+	0.401800i	0.275171	+	0.961395i	$0.411265\pi$
$84$		0			0
$85$	11.2206	+	9.41520i	1.21704	+	1.02122i
$86$		0			0
$87$	0.591846	+	3.54396i	0.0634525	+	0.379953i
$88$		0			0
$89$	−9.79768	+	5.65669i	−1.03855	+	0.599608i	−0.919423	−	0.393270i	$-0.871344\pi$
$89$	−9.79768	+	5.65669i	−1.03855	+	0.599608i	−0.119129	+	0.992879i	$0.538010\pi$
$90$		0			0
$91$	7.22287	+	4.17013i	0.757163	+	0.437148i
$92$		0			0
$93$	0.504309	−	2.71597i	0.0522944	−	0.281633i
$94$		0			0
$95$	−15.3799	+	5.59782i	−1.57794	+	0.574324i
$96$		0			0
$97$	1.67663	+	9.50863i	0.170236	+	0.965455i	0.943500	+	0.331372i	$0.107511\pi$
$97$	1.67663	+	9.50863i	0.170236	+	0.965455i	−0.773265	+	0.634084i	$0.781378\pi$
$98$		0			0
$99$	−0.576651	−	0.221795i	−0.0579556	−	0.0222912i
$100$		0			0
$101$	5.78270	+	6.89155i	0.575400	+	0.685735i	0.972730	−	0.231941i	$-0.0745076\pi$
$101$	5.78270	+	6.89155i	0.575400	+	0.685735i	−0.397330	+	0.917676i	$0.630063\pi$
$102$		0			0
$103$	−5.36511	−	0.946015i	−0.528640	−	0.0932136i	−0.0970435	−	0.995280i	$-0.530939\pi$
$103$	−5.36511	−	0.946015i	−0.528640	−	0.0932136i	−0.431597	+	0.902067i	$0.642050\pi$
$104$		0			0
$105$	12.5449	+	7.39514i	1.22426	+	0.721692i
$106$		0			0
$107$	1.67182			0.161621			0.0808106	−	0.996729i	$-0.474249\pi$
$107$	1.67182			0.161621			0.0808106	+	0.996729i	$0.474249\pi$
$108$		0			0
$109$	15.6614			1.50009			0.750043	−	0.661389i	$-0.230033\pi$
$109$	15.6614			1.50009			0.750043	+	0.661389i	$0.230033\pi$
$110$		0			0
$111$	0.122405	−	13.5119i	0.0116181	−	1.28249i
$112$		0			0
$113$	−18.6094	−	3.28135i	−1.75063	−	0.308683i	−0.795738	−	0.605641i	$-0.792917\pi$
$113$	−18.6094	−	3.28135i	−1.75063	−	0.308683i	−0.954890	+	0.296958i	$0.904028\pi$
$114$		0			0
$115$	−7.23595	−	8.62347i	−0.674755	−	0.804142i
$116$		0			0
$117$	−1.23101	+	6.31062i	−0.113807	+	0.583417i
$118$		0			0
$119$	4.58140	+	25.9824i	0.419976	+	2.38180i
$120$		0			0
$121$	10.2968	−	3.74772i	0.936069	−	0.340701i
$122$		0			0
$123$	15.8860	+	13.5770i	1.43239	+	1.22420i
$124$		0			0
$125$	9.97689	+	5.76016i	0.892360	+	0.515205i
$126$		0			0
$127$	−13.2182	+	7.63155i	−1.17293	+	0.677191i	−0.954368	−	0.298633i	$-0.903470\pi$
$127$	−13.2182	+	7.63155i	−1.17293	+	0.677191i	−0.218561	+	0.975823i	$0.570136\pi$
$128$		0			0
$129$	8.35524	−	6.88287i	0.735638	−	0.606003i
$130$		0			0
$131$	−6.54614	−	5.49286i	−0.571939	−	0.479914i	0.310350	−	0.950622i	$-0.399554\pi$
$131$	−6.54614	−	5.49286i	−0.571939	−	0.479914i	−0.882289	+	0.470709i	$0.843998\pi$
$132$		0			0
$133$	−27.7025	−	10.0829i	−2.40211	−	0.874297i
$134$		0			0
$135$	−2.24912	+	10.9987i	−0.193573	+	0.946614i
$136$		0			0
$137$	3.62113	−	9.94898i	0.309374	−	0.849999i	−0.683405	−	0.730040i	$-0.739501\pi$
$137$	3.62113	−	9.94898i	0.309374	−	0.849999i	0.992779	−	0.119959i	$-0.0382763\pi$
$138$		0			0
$139$	−3.73633	+	4.45278i	−0.316911	+	0.377680i	−0.900859	−	0.434111i	$-0.857063\pi$
$139$	−3.73633	+	4.45278i	−0.316911	+	0.377680i	0.583948	+	0.811791i	$0.301507\pi$
$140$		0			0
$141$	−2.73044	+	7.29551i	−0.229945	+	0.614393i
$142$		0			0
$143$	0.220689	+	0.382245i	0.0184550	+	0.0319649i
$144$		0			0
$145$	2.24091	−	3.88137i	0.186098	−	0.322331i
$146$		0			0
$147$	4.70414	+	13.2981i	0.387991	+	1.09681i
$148$		0			0
$149$	2.99214	+	8.22085i	0.245126	+	0.673478i	0.999848	+	0.0174333i	$0.00554947\pi$
$149$	2.99214	+	8.22085i	0.245126	+	0.673478i	−0.754722	+	0.656045i	$0.772228\pi$
$150$		0			0
$151$	21.7992	−	3.84379i	1.77400	−	0.312803i	0.811551	−	0.584282i	$-0.198624\pi$
$151$	21.7992	−	3.84379i	1.77400	−	0.312803i	0.962445	+	0.271478i	$0.0875125\pi$
$152$		0			0
$153$	−17.7955	+	9.84873i	−1.43868	+	0.796223i
$154$		0			0
$155$	−2.63957	+	2.21486i	−0.212015	+	0.177902i
$156$		0			0
$157$	−0.835627	+	4.73908i	−0.0666903	+	0.378220i	0.933135	+	0.359526i	$0.117062\pi$
$157$	−0.835627	+	4.73908i	−0.0666903	+	0.378220i	−0.999825	+	0.0186933i	$0.994049\pi$
$158$		0			0
$159$	−5.87763	−	10.3967i	−0.466126	−	0.824514i
$160$		0			0
$161$		−	20.2765i		−	1.59801i
$162$		0			0
$163$			0.859928i			0.0673547i	0.999433	+	0.0336774i	$0.0107219\pi$
$163$			0.859928i			0.0673547i	−0.999433	+	0.0336774i	$0.989278\pi$
$164$		0			0
$165$	0.379270	+	0.670877i	0.0295261	+	0.0522277i
$166$		0			0
$167$	2.13490	−	12.1076i	0.165203	−	0.936915i	−0.783651	−	0.621201i	$-0.786645\pi$
$167$	2.13490	−	12.1076i	0.165203	−	0.936915i	0.948854	−	0.315714i	$-0.102244\pi$
$168$		0			0
$169$	−6.43994	+	5.40375i	−0.495380	+	0.415673i
$170$		0			0
$171$	0.411729	−	22.7229i	0.0314857	−	1.73766i
$172$		0			0
$173$	18.9738	−	3.34560i	1.44255	−	0.254361i	0.603045	−	0.797707i	$-0.293954\pi$
$173$	18.9738	−	3.34560i	1.44255	−	0.254361i	0.839509	+	0.543346i	$0.182843\pi$
$174$		0			0
$175$	0.442231	+	1.21502i	0.0334295	+	0.0918469i
$176$		0			0
$177$	0.311869	+	0.881621i	0.0234415	+	0.0662667i
$178$		0			0
$179$	6.93879	−	12.0183i	0.518629	−	0.898292i	−0.481136	−	0.876646i	$-0.659776\pi$
$179$	6.93879	−	12.0183i	0.518629	−	0.898292i	0.999766	−	0.0216464i	$-0.00689082\pi$
$180$		0			0
$181$	−12.0771	−	20.9182i	−0.897687	−	1.55484i	−0.830443	−	0.557103i	$-0.811913\pi$
$181$	−12.0771	−	20.9182i	−0.897687	−	1.55484i	−0.0672441	−	0.997737i	$-0.521421\pi$
$182$		0			0
$183$	0.551026	−	1.47229i	0.0407330	−	0.108835i
$184$		0			0
$185$	−10.8341	+	12.9116i	−0.796541	+	0.949281i
$186$		0			0
$187$	−0.477541	+	1.31203i	−0.0349213	+	0.0959454i
$188$		0			0
$189$	−15.8376	+	12.5720i	−1.15201	+	0.914481i
$190$		0			0
$191$	−6.84293	−	2.49062i	−0.495137	−	0.180215i	0.0823686	−	0.996602i	$-0.473752\pi$
$191$	−6.84293	−	2.49062i	−0.495137	−	0.180215i	−0.577505	+	0.816387i	$0.695974\pi$
$192$		0			0
$193$	7.46660	+	6.26522i	0.537458	+	0.450981i	0.870667	−	0.491872i	$-0.163687\pi$
$193$	7.46660	+	6.26522i	0.537458	+	0.450981i	−0.333210	+	0.942853i	$0.608132\pi$
$194$		0			0
$195$	6.19013	−	5.09929i	0.443284	−	0.365168i
$196$		0			0
$197$	−5.00953	+	2.89226i	−0.356914	+	0.206065i	−0.667726	−	0.744407i	$-0.732732\pi$
$197$	−5.00953	+	2.89226i	−0.356914	+	0.206065i	0.310812	+	0.950471i	$0.399399\pi$
$198$		0			0
$199$	3.57936	+	2.06654i	0.253734	+	0.146493i	0.621473	−	0.783436i	$-0.286535\pi$
$199$	3.57936	+	2.06654i	0.253734	+	0.146493i	−0.367739	+	0.929929i	$0.619868\pi$
$200$		0			0
$201$	−6.84307	−	5.84847i	−0.482673	−	0.412519i
$202$		0			0
$203$	7.58588	−	2.76104i	0.532425	−	0.193787i
$204$		0			0
$205$	−4.52641	−	25.6706i	−0.316138	−	1.79291i
$206$		0			0
$207$	14.7831	−	5.07924i	1.02750	−	0.353032i
$208$		0			0
$209$	−1.00284	−	1.19514i	−0.0693680	−	0.0826695i
$210$		0			0
$211$	−9.16208	−	1.61552i	−0.630744	−	0.111217i	−0.150868	−	0.988554i	$-0.548207\pi$
$211$	−9.16208	−	1.61552i	−0.630744	−	0.111217i	−0.479875	+	0.877337i	$0.659318\pi$
$212$		0			0
$213$	0.158435	−	17.4892i	0.0108558	−	1.19834i
$214$		0			0
$215$	−13.5029			−0.920890
$216$		0			0
$217$	−6.20646			−0.421322
$218$		0			0
$219$	4.36760	+	2.57467i	0.295135	+	0.173980i
$220$		0			0
$221$	14.3094	+	2.52313i	0.962553	+	0.169724i
$222$		0			0
$223$	0.613674	+	0.731349i	0.0410947	+	0.0489747i	0.786200	−	0.617972i	$-0.212045\pi$
$223$	0.613674	+	0.731349i	0.0410947	+	0.0489747i	−0.745106	+	0.666946i	$0.767601\pi$
$224$		0			0
$225$	−0.775062	+	0.626781i	−0.0516708	+	0.0417854i
$226$		0			0
$227$	−4.84335	−	27.4680i	−0.321465	−	1.82312i	−0.533436	−	0.845840i	$-0.679100\pi$
$227$	−4.84335	−	27.4680i	−0.321465	−	1.82312i	0.211972	−	0.977276i	$-0.432011\pi$
$228$		0			0
$229$	−11.0424	+	4.01909i	−0.729700	+	0.265589i	−0.680038	−	0.733177i	$-0.738037\pi$
$229$	−11.0424	+	4.01909i	−0.729700	+	0.265589i	−0.0496624	+	0.998766i	$0.515815\pi$
$230$		0			0
$231$	−0.253420	+	1.36480i	−0.0166738	+	0.0897973i
$232$		0			0
$233$	−12.8253	−	7.40471i	−0.840216	−	0.485099i	0.0171219	−	0.999853i	$-0.494550\pi$
$233$	−12.8253	−	7.40471i	−0.840216	−	0.485099i	−0.857337	+	0.514755i	$0.827883\pi$
$234$		0			0
$235$	8.41483	−	4.85831i	0.548923	−	0.316921i
$236$		0			0
$237$	−1.04896	−	6.28118i	−0.0681375	−	0.408006i
$238$		0			0
$239$	−18.1559	−	15.2346i	−1.17441	−	0.985446i	−1.00000		0.000772466i	$-0.999754\pi$
$239$	−18.1559	−	15.2346i	−1.17441	−	0.985446i	−0.174409	−	0.984673i	$-0.555801\pi$
$240$		0			0
$241$	−7.90441	−	2.87697i	−0.509168	−	0.185322i	0.0746451	−	0.997210i	$-0.476218\pi$
$241$	−7.90441	−	2.87697i	−0.509168	−	0.185322i	−0.583813	+	0.811888i	$0.698440\pi$
$242$		0			0
$243$	−13.1332	−	8.39749i	−0.842498	−	0.538700i
$244$		0			0
$245$	6.01779	−	16.5338i	0.384463	−	1.05630i
$246$		0			0
$247$	−10.4362	+	12.4374i	−0.664039	+	0.791371i
$248$		0			0
$249$	18.2846	−	3.05355i	1.15874	−	0.193511i
$250$		0			0
$251$	7.92565	+	13.7276i	0.500263	+	0.866481i	1.00000		0.000303448i	$9.65905e-5\pi$
$251$	7.92565	+	13.7276i	0.500263	+	0.866481i	−0.499737	+	0.866177i	$0.666570\pi$
$252$		0			0
$253$	0.536531	−	0.929300i	0.0337314	−	0.0584246i
$254$		0			0
$255$	24.9438	+	4.63162i	1.56204	+	0.290044i
$256$		0			0
$257$	−3.10717	−	8.53688i	−0.193820	−	0.532516i	0.804272	−	0.594261i	$-0.202555\pi$
$257$	−3.10717	−	8.53688i	−0.193820	−	0.532516i	−0.998092	+	0.0617455i	$0.980333\pi$
$258$		0			0
$259$	−29.8981	+	5.27184i	−1.85778	+	0.327576i
$260$		0			0
$261$	3.91325	+	4.83904i	0.242224	+	0.299529i
$262$		0			0
$263$	14.0506	−	11.7898i	0.866396	−	0.726993i	−0.0969397	−	0.995290i	$-0.530905\pi$
$263$	14.0506	−	11.7898i	0.866396	−	0.726993i	0.963336	+	0.268297i	$0.0864610\pi$
$264$		0			0
$265$	−2.58691	+	14.6711i	−0.158913	+	0.901238i
$266$		0			0
$267$	−9.95101	+	16.8806i	−0.608992	+	1.03308i
$268$		0			0
$269$		−	15.0367i		−	0.916806i	−0.888745	−	0.458403i	$-0.848422\pi$
$269$		−	15.0367i		−	0.916806i	0.888745	−	0.458403i	$-0.151578\pi$
$270$		0			0
$271$			17.2892i			1.05025i	0.851027	+	0.525123i	$0.175981\pi$
$271$			17.2892i			1.05025i	−0.851027	+	0.525123i	$0.824019\pi$
$272$		0			0
$273$	14.4452	+	0.130859i	0.874261	+	0.00791996i
$274$		0			0
$275$	−0.0118823	+	0.0673878i	−0.000716528	+	0.00406363i
$276$		0			0
$277$	−9.22261	+	7.73869i	−0.554133	+	0.464973i	−0.876338	−	0.481697i	$-0.840020\pi$
$277$	−9.22261	+	7.73869i	−0.554133	+	0.464973i	0.322205	+	0.946670i	$0.395576\pi$
$278$		0			0
$279$	−1.55471	−	4.52497i	−0.0930781	−	0.270903i
$280$		0			0
$281$	7.09306	−	1.25070i	0.423137	−	0.0746104i	0.0419746	−	0.999119i	$-0.486635\pi$
$281$	7.09306	−	1.25070i	0.423137	−	0.0746104i	0.381162	+	0.924508i	$0.375524\pi$
$282$		0			0
$283$	10.6550	+	29.2743i	0.633373	+	1.74018i	0.671604	+	0.740910i	$0.265605\pi$
$283$	10.6550	+	29.2743i	0.633373	+	1.74018i	−0.0382310	+	0.999269i	$0.512172\pi$
$284$		0			0
$285$	−18.4179	+	21.5502i	−1.09099	+	1.27652i
$286$		0			0
$287$	23.4757	−	40.6612i	1.38573	−	2.40015i
$288$		0			0
$289$	14.4820	+	25.0835i	0.851881	+	1.47550i
$290$		0			0
$291$	10.6332	+	12.9078i	0.623327	+	0.756668i
$292$		0			0
$293$	−14.3668	+	17.1217i	−0.839316	+	1.00026i	0.160596	+	0.987020i	$0.448658\pi$
$293$	−14.3668	+	17.1217i	−0.839316	+	1.00026i	−0.999912	+	0.0132378i	$0.995786\pi$
$294$		0			0
$295$	0.398959	−	1.09613i	0.0232283	−	0.0638193i
$296$		0			0
$297$	−1.05852	+	0.157119i	−0.0614217	+	0.00911698i
$298$		0			0
$299$	−10.4935	−	3.81933i	−0.606856	−	0.220877i
$300$		0			0
$301$	−18.6314	−	15.6336i	−1.07390	−	0.901107i
$302$		0			0
$303$	14.5934	+	5.46179i	0.838371	+	0.313771i
$304$		0			0
$305$	−1.69818	+	0.980446i	−0.0972376	+	0.0561402i
$306$		0			0
$307$	8.17802	+	4.72158i	0.466744	+	0.269475i	0.714876	−	0.699252i	$-0.246483\pi$
$307$	8.17802	+	4.72158i	0.466744	+	0.269475i	−0.248132	+	0.968726i	$0.579817\pi$
$308$		0			0
$309$	−8.89582	+	3.14685i	−0.506065	+	0.179018i
$310$		0			0
$311$	11.0789	−	4.03239i	0.628227	−	0.228656i	−0.00823228	−	0.999966i	$-0.502620\pi$
$311$	11.0789	−	4.03239i	0.628227	−	0.228656i	0.636460	+	0.771310i	$0.280398\pi$
$312$		0			0
$313$	−1.74976	−	9.92336i	−0.0989020	−	0.560901i	−0.993482	−	0.113993i	$-0.963636\pi$
$313$	−1.74976	−	9.92336i	−0.0989020	−	0.560901i	0.894580	−	0.446909i	$-0.147475\pi$
$314$		0			0
$315$	25.2187	+	0.456951i	1.42091	+	0.0257463i
$316$		0			0
$317$	9.34365	+	11.1353i	0.524792	+	0.625422i	0.961707	−	0.274080i	$-0.0883734\pi$
$317$	9.34365	+	11.1353i	0.524792	+	0.625422i	−0.436915	+	0.899503i	$0.643929\pi$
$318$		0			0
$319$	0.420730	+	0.0741861i	0.0235564	+	0.00415362i
$320$		0			0
$321$	2.52075	−	1.42506i	0.140694	−	0.0795394i
$322$		0			0
$323$	−51.3597			−2.85773
$324$		0			0
$325$	0.712098			0.0395001
$326$		0			0
$327$	23.6140	−	13.3498i	1.30585	−	0.738244i
$328$		0			0
$329$	17.2358	+	3.03914i	0.950241	+	0.167553i
$330$		0			0
$331$	−6.36795	−	7.58902i	−0.350014	−	0.417130i	0.562099	−	0.827070i	$-0.309994\pi$
$331$	−6.36795	−	7.58902i	−0.350014	−	0.417130i	−0.912113	+	0.409940i	$0.865550\pi$
$332$		0			0
$333$	−11.3330	−	20.4773i	−0.621045	−	1.12215i
$334$		0			0
$335$	1.94981	+	11.0579i	0.106529	+	0.604158i
$336$		0			0
$337$	−15.9688	+	5.81216i	−0.869874	+	0.316608i	−0.738116	−	0.674674i	$-0.764284\pi$
$337$	−15.9688	+	5.81216i	−0.869874	+	0.316608i	−0.131758	+	0.991282i	$0.542062\pi$
$338$		0			0
$339$	−30.8560	+	10.9152i	−1.67587	+	0.592830i
$340$		0			0
$341$	−0.284450	−	0.164227i	−0.0154039	−	0.00889342i
$342$		0			0
$343$	3.85511	−	2.22575i	0.208156	−	0.120179i
$344$		0			0
$345$	−18.2609	−	6.83438i	−0.983134	−	0.367951i
$346$		0			0
$347$	4.11669	+	3.45432i	0.220996	+	0.185437i	0.746563	−	0.665314i	$-0.231703\pi$
$347$	4.11669	+	3.45432i	0.220996	+	0.185437i	−0.525568	+	0.850752i	$0.676147\pi$
$348$		0			0
$349$	16.9030	+	6.15220i	0.904799	+	0.329320i	0.752174	−	0.658964i	$-0.229005\pi$
$349$	16.9030	+	6.15220i	0.904799	+	0.329320i	0.152625	+	0.988284i	$0.451227\pi$
$350$		0			0
$351$	3.52309	+	10.5644i	0.188049	+	0.563884i
$352$		0			0
$353$	−2.47242	+	6.79292i	−0.131594	+	0.361551i	−0.987937	−	0.154856i	$-0.950509\pi$
$353$	−2.47242	+	6.79292i	−0.131594	+	0.361551i	0.856343	+	0.516407i	$0.172731\pi$
$354$		0			0
$355$	−14.0232	+	16.7122i	−0.744274	+	0.886991i
$356$		0			0
$357$	29.0552	+	35.2706i	1.53776	+	1.86672i
$358$		0			0
$359$	10.4680	+	18.1311i	0.552481	+	0.956925i	0.998095	+	0.0616998i	$0.0196521\pi$
$359$	10.4680	+	18.1311i	0.552481	+	0.956925i	−0.445614	+	0.895225i	$0.647015\pi$
$360$		0			0
$361$	19.1945	−	33.2458i	1.01024	−	1.74978i
$362$		0			0
$363$	12.3307	−	14.4277i	0.647195	−	0.757259i
$364$		0			0
$365$	−2.16298	−	5.94273i	−0.113215	−	0.311057i
$366$		0			0
$367$	−10.0472	+	1.77160i	−0.524461	+	0.0924766i	−0.429609	−	0.903015i	$-0.641349\pi$
$367$	−10.0472	+	1.77160i	−0.524461	+	0.0924766i	−0.0948516	+	0.995491i	$0.530238\pi$
$368$		0			0
$369$	35.5257	+	6.92998i	1.84939	+	0.360760i
$370$		0			0
$371$	−20.5556	+	17.2482i	−1.06719	+	0.895482i
$372$		0			0
$373$	2.55154	−	14.4705i	0.132114	−	0.749254i	−0.844712	−	0.535220i	$-0.820229\pi$
$373$	2.55154	−	14.4705i	0.132114	−	0.749254i	0.976826	−	0.214034i	$-0.0686603\pi$
$374$		0			0
$375$	19.9530	+	0.180755i	1.03037	+	0.00933413i
$376$		0			0
$377$		−	4.44593i		−	0.228977i
$378$		0			0
$379$			1.47535i			0.0757834i	0.999282	+	0.0378917i	$0.0120642\pi$
$379$			1.47535i			0.0757834i	−0.999282	+	0.0378917i	$0.987936\pi$
$380$		0			0
$381$	−13.4251	+	22.7740i	−0.687788	+	1.16675i
$382$		0			0
$383$	−3.50484	+	19.8770i	−0.179089	+	1.01567i	0.754228	+	0.656613i	$0.228011\pi$
$383$	−3.50484	+	19.8770i	−0.179089	+	1.01567i	−0.933317	+	0.359053i	$0.883100\pi$
$384$		0			0
$385$	1.32641	−	1.11299i	0.0675999	−	0.0567231i
$386$		0			0
$387$	6.73092	−	17.4999i	0.342152	−	0.889570i
$388$		0			0
$389$	12.1450	−	2.14149i	0.615777	−	0.108578i	0.142945	−	0.989731i	$-0.454343\pi$
$389$	12.1450	−	2.14149i	0.615777	−	0.108578i	0.472832	+	0.881153i	$0.343232\pi$
$390$		0			0
$391$	−12.0819	−	33.1947i	−0.611008	−	1.67873i
$392$		0			0
$393$	−14.5523	−	2.70211i	−0.734066	−	0.136303i
$394$		0			0
$395$	−3.97170	+	6.87919i	−0.199838	+	0.346130i
$396$		0			0
$397$	−8.83157	−	15.2967i	−0.443244	−	0.767720i	0.554684	−	0.832061i	$-0.312839\pi$
$397$	−8.83157	−	15.2967i	−0.443244	−	0.767720i	−0.997928	+	0.0643404i	$0.979506\pi$
$398$		0			0
$399$	−50.3640	+	8.41085i	−2.52135	+	0.421069i
$400$		0			0
$401$	9.13835	−	10.8907i	0.456347	−	0.543853i	−0.487983	−	0.872853i	$-0.662267\pi$
$401$	9.13835	−	10.8907i	0.456347	−	0.543853i	0.944330	+	0.329000i	$0.106712\pi$
$402$		0			0
$403$	−1.16906	+	3.21197i	−0.0582351	+	0.160000i
$404$		0			0
$405$	5.98409	+	18.5007i	0.297352	+	0.919309i
$406$		0			0
$407$	−1.50977	−	0.549510i	−0.0748363	−	0.0272382i
$408$		0			0
$409$	14.7136	+	12.3461i	0.727539	+	0.610477i	0.929459	−	0.368925i	$-0.120274\pi$
$409$	14.7136	+	12.3461i	0.727539	+	0.610477i	−0.201921	+	0.979402i	$0.564718\pi$
$410$		0			0
$411$	−3.02065	−	18.0876i	−0.148997	−	0.892194i
$412$		0			0
$413$	1.81959	−	1.05054i	0.0895361	−	0.0516937i
$414$		0			0
$415$	−20.0254	−	11.5617i	−0.983009	−	0.567541i
$416$		0			0
$417$	−1.83801	+	9.89868i	−0.0900079	+	0.484741i
$418$		0			0
$419$	−5.36997	+	1.95451i	−0.262340	+	0.0954840i	−0.469842	−	0.882751i	$-0.655689\pi$
$419$	−5.36997	+	1.95451i	−0.262340	+	0.0954840i	0.207502	+	0.978235i	$0.433467\pi$
$420$		0			0
$421$	4.99357	+	28.3200i	0.243372	+	1.38023i	0.824244	+	0.566235i	$0.191601\pi$
$421$	4.99357	+	28.3200i	0.243372	+	1.38023i	−0.580872	+	0.813995i	$0.697288\pi$
$422$		0			0
$423$	2.10179	+	13.3275i	0.102193	+	0.648005i
$424$		0			0
$425$	1.44796	+	1.72561i	0.0702361	+	0.0837042i
$426$		0			0
$427$	−3.47833	−	0.613323i	−0.168328	−	0.0296808i
$428$		0			0
$429$	0.658578	+	0.388227i	0.0317964	+	0.0187438i
$430$		0			0
$431$	14.3077			0.689176			0.344588	−	0.938754i	$-0.388019\pi$
$431$	14.3077			0.689176			0.344588	+	0.938754i	$0.388019\pi$
$432$		0			0
$433$	2.66463			0.128054			0.0640269	−	0.997948i	$-0.479606\pi$
$433$	2.66463			0.128054			0.0640269	+	0.997948i	$0.479606\pi$
$434$		0			0
$435$	0.0703202	−	7.76243i	0.00337159	−	0.372180i
$436$		0			0
$437$	38.8723	+	6.85423i	1.85951	+	0.327882i
$438$		0			0
$439$	24.2181	+	28.8620i	1.15587	+	1.37751i	0.913257	+	0.407383i	$0.133559\pi$
$439$	24.2181	+	28.8620i	1.15587	+	1.37751i	0.242609	+	0.970124i	$0.421997\pi$
$440$		0			0
$441$	18.4282	+	16.0409i	0.877533	+	0.763851i
$442$		0			0
$443$	−3.46327	−	19.6412i	−0.164545	−	0.933179i	−0.949533	−	0.313668i	$-0.898442\pi$
$443$	−3.46327	−	19.6412i	−0.164545	−	0.933179i	0.784988	−	0.619511i	$-0.212669\pi$
$444$		0			0
$445$	22.9685	−	8.35983i	1.08881	−	0.396294i
$446$		0			0
$447$	11.5190	+	9.84475i	0.544828	+	0.465641i
$448$		0			0
$449$	24.0203	+	13.8682i	1.13359	+	0.654479i	0.944835	−	0.327546i	$-0.106222\pi$
$449$	24.0203	+	13.8682i	1.13359	+	0.654479i	0.188755	+	0.982024i	$0.439555\pi$
$450$		0			0
$451$	2.15185	−	1.24237i	0.101327	−	0.0585009i
$452$		0			0
$453$	29.5921	−	24.3773i	1.39036	−	1.14535i
$454$		0			0
$455$	−13.8034	−	11.5824i	−0.647114	−	0.542993i
$456$		0			0
$457$	−0.0182308	−	0.00663549i	−0.000852803	−	0.000310395i	0.341594	−	0.939848i	$-0.389033\pi$
$457$	−0.0182308	−	0.00663549i	−0.000852803	−	0.000310395i	−0.342447	+	0.939537i	$0.611256\pi$
$458$		0			0
$459$	−18.4366	+	30.0186i	−0.860547	+	1.40115i
$460$		0			0
$461$	−7.58160	+	20.8303i	−0.353110	+	0.970163i	0.628254	+	0.778008i	$0.283770\pi$
$461$	−7.58160	+	20.8303i	−0.353110	+	0.970163i	−0.981365	+	0.192155i	$0.938452\pi$
$462$		0			0
$463$	26.6835	−	31.8001i	1.24009	−	1.47788i	0.418068	−	0.908416i	$-0.362707\pi$
$463$	26.6835	−	31.8001i	1.24009	−	1.47788i	0.822018	−	0.569461i	$-0.192848\pi$
$464$		0			0
$465$	−2.09194	+	5.58950i	−0.0970116	+	0.259207i
$466$		0			0
$467$	11.4135	+	19.7688i	0.528154	+	0.914789i	0.999461	+	0.0328204i	$0.0104489\pi$
$467$	11.4135	+	19.7688i	0.528154	+	0.914789i	−0.471307	+	0.881969i	$0.656218\pi$
$468$		0			0
$469$	−10.1125	+	17.5153i	−0.466950	+	0.808782i
$470$		0			0
$471$	2.77965	+	7.85779i	0.128080	+	0.362068i
$472$		0			0
$473$	−0.440226	−	1.20951i	−0.0202416	−	0.0556134i
$474$		0			0
$475$	−2.47882	+	0.437082i	−0.113736	+	0.0200547i
$476$		0			0
$477$	−17.7244	−	10.6659i	−0.811543	−	0.488358i
$478$		0			0
$479$	−2.42704	+	2.03652i	−0.110894	+	0.0930512i	−0.696549	−	0.717510i	$-0.745282\pi$
$479$	−2.42704	+	2.03652i	−0.110894	+	0.0930512i	0.585655	+	0.810561i	$0.300838\pi$
$480$		0			0
$481$	−2.90338	+	16.4659i	−0.132383	+	0.750780i
$482$		0			0
$483$	−17.2837	−	30.5726i	−0.786438	−	1.39110i
$484$		0			0
$485$		−	20.8603i		−	0.947216i
$486$		0			0
$487$			26.6585i			1.20801i	0.796980	+	0.604005i	$0.206429\pi$
$487$			26.6585i			1.20801i	−0.796980	+	0.604005i	$0.793571\pi$
$488$		0			0
$489$	0.733004	+	1.29658i	0.0331476	+	0.0586336i
$490$		0			0
$491$	0.111406	−	0.631817i	0.00502770	−	0.0285135i	−0.982191	−	0.187887i	$-0.939836\pi$
$491$	0.111406	−	0.631817i	0.00502770	−	0.0285135i	0.987218	+	0.159373i	$0.0509473\pi$
$492$		0			0
$493$	10.7737	−	9.04019i	0.485222	−	0.407150i
$494$		0			0
$495$	1.14371	+	0.688247i	0.0514061	+	0.0309344i
$496$		0			0
$497$	−38.6987	+	6.82363i	−1.73587	+	0.306081i
$498$		0			0
$499$	0.174102	+	0.478340i	0.00779386	+	0.0214134i	0.943529	−	0.331291i	$-0.107484\pi$
$499$	0.174102	+	0.478340i	0.00779386	+	0.0214134i	−0.935735	+	0.352705i	$0.885262\pi$
$500$		0			0
$501$	−7.10159	−	20.0755i	−0.317276	−	0.896905i
$502$		0			0
$503$	17.3187	−	29.9969i	0.772203	−	1.33750i	−0.164150	−	0.986435i	$-0.552488\pi$
$503$	17.3187	−	29.9969i	0.772203	−	1.33750i	0.936353	−	0.351060i	$-0.114179\pi$
$504$		0			0
$505$	−9.71821	−	16.8324i	−0.432455	−	0.749034i
$506$		0			0
$507$	−5.10386	+	13.6371i	−0.226671	+	0.605645i
$508$		0			0
$509$	−6.71875	+	8.00710i	−0.297804	+	0.354908i	−0.894109	−	0.447849i	$-0.852190\pi$
$509$	−6.71875	+	8.00710i	−0.297804	+	0.354908i	0.596306	+	0.802757i	$0.296635\pi$
$510$		0			0
$511$	3.89599	−	10.7041i	0.172348	−	0.473523i
$512$		0			0
$513$	−18.7483	−	34.6122i	−0.827756	−	1.52817i
$514$		0			0
$515$	11.0603	+	4.02562i	0.487375	+	0.177390i
$516$		0			0
$517$	0.709522	+	0.595360i	0.0312048	+	0.0261839i
$518$		0			0
$519$	25.7566	−	21.2178i	1.13059	−	0.931357i
$520$		0			0
$521$	−18.6891	+	10.7902i	−0.818785	+	0.472726i	−0.849997	−	0.526787i	$-0.823397\pi$
$521$	−18.6891	+	10.7902i	−0.818785	+	0.472726i	0.0312124	+	0.999513i	$0.490063\pi$
$522$		0			0
$523$	−2.21284	−	1.27758i	−0.0967607	−	0.0558648i	0.450839	−	0.892605i	$-0.351125\pi$
$523$	−2.21284	−	1.27758i	−0.0967607	−	0.0558648i	−0.547600	+	0.836741i	$0.684458\pi$
$524$		0			0
$525$	1.70247	+	1.45503i	0.0743021	+	0.0635027i
$526$		0			0
$527$	−10.1606	+	3.69816i	−0.442603	+	0.161094i
$528$		0			0
$529$	0.720415	+	4.08568i	0.0313224	+	0.177638i
$530$		0			0
$531$	1.22173	+	1.06346i	0.0530184	+	0.0461501i
$532$		0			0
$533$	−16.6211	−	19.8082i	−0.719938	−	0.857988i
$534$		0			0
$535$	−3.55709	−	0.627211i	−0.153786	−	0.0271167i
$536$		0			0
$537$	0.217740	−	24.0357i	0.00939618	−	1.03722i
$538$		0			0
$539$	1.67719			0.0722418
$540$		0			0
$541$	−11.9264			−0.512754			−0.256377	−	0.966577i	$-0.582529\pi$
$541$	−11.9264			−0.512754			−0.256377	+	0.966577i	$0.582529\pi$
$542$		0			0
$543$	−36.0405	−	21.2456i	−1.54664	−	0.911735i
$544$		0			0
$545$	−33.3223	−	5.87561i	−1.42737	−	0.251684i
$546$		0			0
$547$	13.7484	+	16.3847i	0.587838	+	0.700558i	0.975189	−	0.221374i	$-0.0710543\pi$
$547$	13.7484	+	16.3847i	0.587838	+	0.700558i	−0.387351	+	0.921932i	$0.626610\pi$
$548$		0			0
$549$	−0.424159	−	2.68960i	−0.0181027	−	0.114789i
$550$		0			0
$551$	2.72889	+	15.4763i	0.116255	+	0.659313i
$552$		0			0
$553$	−13.4449	+	4.89355i	−0.571736	+	0.208095i
$554$		0			0
$555$	−5.32964	+	28.7030i	−0.226231	+	1.21837i
$556$		0			0
$557$	23.2042	+	13.3970i	0.983196	+	0.567648i	0.903233	−	0.429150i	$-0.141187\pi$
$557$	23.2042	+	13.3970i	0.983196	+	0.567648i	0.0799622	+	0.996798i	$0.474520\pi$
$558$		0			0
$559$	−11.6002	+	6.69737i	−0.490635	+	0.283268i
$560$		0			0
$561$	0.398351	+	2.38532i	0.0168184	+	0.100708i
$562$		0			0
$563$	22.0741	+	18.5223i	0.930311	+	0.780624i	0.975873	−	0.218338i	$-0.0700634\pi$
$563$	22.0741	+	18.5223i	0.930311	+	0.780624i	−0.0455620	+	0.998962i	$0.514508\pi$
$564$		0			0
$565$	38.3637	+	13.9633i	1.61397	+	0.587439i
$566$		0			0
$567$	−13.1632	+	32.4559i	−0.552803	+	1.36302i
$568$		0			0
$569$	−9.21939	+	25.3301i	−0.386497	+	1.06189i	0.582070	+	0.813138i	$0.302243\pi$
$569$	−9.21939	+	25.3301i	−0.386497	+	1.06189i	−0.968567	+	0.248753i	$0.919979\pi$
$570$		0			0
$571$	2.01830	−	2.40531i	0.0844631	−	0.100659i	−0.722158	−	0.691728i	$-0.756850\pi$
$571$	2.01830	−	2.40531i	0.0844631	−	0.100659i	0.806621	+	0.591069i	$0.201294\pi$
$572$		0			0
$573$	−12.4407	+	2.07761i	−0.519716	+	0.0867932i
$574$		0			0
$575$	−0.865612	−	1.49928i	−0.0360985	−	0.0625245i
$576$		0			0
$577$	−19.8980	+	34.4644i	−0.828366	+	1.43477i	0.0709533	+	0.997480i	$0.477396\pi$
$577$	−19.8980	+	34.4644i	−0.828366	+	1.43477i	−0.899319	+	0.437292i	$0.855937\pi$
$578$		0			0
$579$	16.5985	+	3.08205i	0.689811	+	0.128086i
$580$		0			0
$581$	−14.2452	−	39.1383i	−0.590990	−	1.62373i
$582$		0			0
$583$	−1.39849	+	0.246592i	−0.0579196	+	0.0102128i
$584$		0			0
$585$	4.98672	−	12.9651i	0.206176	−	0.536041i
$586$		0			0
$587$	12.9410	−	10.8588i	0.534132	−	0.448190i	−0.335394	−	0.942078i	$-0.608869\pi$
$587$	12.9410	−	10.8588i	0.534132	−	0.448190i	0.869525	+	0.493888i	$0.164425\pi$
$588$		0			0
$589$	2.09802	−	11.8985i	0.0864474	−	0.490268i
$590$		0			0
$591$	−5.08793	+	8.63103i	−0.209289	+	0.355033i
$592$		0			0
$593$			0.0610029i			0.00250509i	0.999999	+	0.00125254i	$0.000398697\pi$
$593$			0.0610029i			0.00250509i	−0.999999	+	0.00125254i	$0.999601\pi$
$594$		0			0
$595$		−	57.0008i		−	2.33680i
$596$		0			0
$597$	7.15842	+	0.0648484i	0.292975	+	0.00265407i
$598$		0			0
$599$	−4.17873	+	23.6987i	−0.170738	+	0.968304i	0.772211	+	0.635366i	$0.219151\pi$
$599$	−4.17873	+	23.6987i	−0.170738	+	0.968304i	−0.942949	+	0.332938i	$0.891960\pi$
$600$		0			0
$601$	−18.4133	+	15.4506i	−0.751095	+	0.630244i	−0.935792	−	0.352552i	$-0.885314\pi$
$601$	−18.4133	+	15.4506i	−0.751095	+	0.630244i	0.184697	+	0.982795i	$0.440870\pi$
$602$		0			0
$603$	−15.3031	−	2.98518i	−0.623191	−	0.121566i
$604$		0			0
$605$	−23.3142	+	4.11091i	−0.947855	+	0.167132i
$606$		0			0
$607$	−0.920929	−	2.53023i	−0.0373794	−	0.102699i	0.919599	−	0.392859i	$-0.128514\pi$
$607$	−0.920929	−	2.53023i	−0.0373794	−	0.102699i	−0.956978	+	0.290160i	$0.906292\pi$
$608$		0			0
$609$	9.08436	−	10.6293i	0.368117	−	0.430720i
$610$		0			0
$611$	4.81939	−	8.34743i	0.194972	−	0.337701i
$612$		0			0
$613$	13.5649	+	23.4951i	0.547880	+	0.948957i	0.998420	+	0.0562001i	$0.0178985\pi$
$613$	13.5649	+	23.4951i	0.547880	+	0.948957i	−0.450539	+	0.892757i	$0.648768\pi$
$614$		0			0
$615$	−28.7065	−	34.8473i	−1.15756	−	1.40518i
$616$		0			0
$617$	21.5765	−	25.7138i	0.868635	−	1.03520i	−0.130408	−	0.991460i	$-0.541629\pi$
$617$	21.5765	−	25.7138i	0.868635	−	1.03520i	0.999043	−	0.0437387i	$-0.0139269\pi$
$618$		0			0
$619$	15.2455	−	41.8867i	0.612769	−	1.68357i	−0.111254	−	0.993792i	$-0.535487\pi$
$619$	15.2455	−	41.8867i	0.612769	−	1.68357i	0.724022	−	0.689776i	$-0.242291\pi$
$620$		0			0
$621$	17.9601	−	20.2595i	0.720715	−	0.812987i
$622$		0			0
$623$	41.3711	+	15.0579i	1.65750	+	0.603280i
$624$		0			0
$625$	−17.7939	−	14.9309i	−0.711756	−	0.597235i
$626$		0			0
$627$	−2.53081	−	0.947188i	−0.101071	−	0.0378270i
$628$		0			0
$629$	−45.8050	+	26.4455i	−1.82636	+	1.05445i
$630$		0			0
$631$	22.8750	+	13.2069i	0.910640	+	0.525758i	0.880637	−	0.473792i	$-0.157115\pi$
$631$	22.8750	+	13.2069i	0.910640	+	0.525758i	0.0300027	+	0.999550i	$0.490448\pi$
$632$		0			0
$633$	−15.1915	+	5.37392i	−0.603808	+	0.213594i
$634$		0			0
$635$	30.9872	−	11.2784i	1.22969	−	0.447570i
$636$		0			0
$637$	−3.03084	−	17.1888i	−0.120086	−	0.681043i
$638$		0			0
$639$	−14.6689	−	26.5049i	−0.580293	−	1.04852i
$640$		0			0
$641$	−11.6135	−	13.8404i	−0.458704	−	0.546663i	0.486269	−	0.873809i	$-0.338357\pi$
$641$	−11.6135	−	13.8404i	−0.458704	−	0.546663i	−0.944974	+	0.327146i	$0.893913\pi$
$642$		0			0
$643$	42.9848	+	7.57937i	1.69515	+	0.298901i	0.935997	−	0.352007i	$-0.114501\pi$
$643$	42.9848	+	7.57937i	1.69515	+	0.298901i	0.759156	+	0.650908i	$0.225612\pi$
$644$		0			0
$645$	−20.3594	+	11.5099i	−0.801652	+	0.453201i
$646$		0			0
$647$	−44.0779			−1.73288			−0.866441	−	0.499279i	$-0.833598\pi$
$647$	−44.0779			−1.73288			−0.866441	+	0.499279i	$0.833598\pi$
$648$		0			0
$649$	0.111192			0.00436468
$650$		0			0
$651$	−9.35800	+	5.29040i	−0.366769	+	0.207347i
$652$		0			0
$653$	−14.7422	−	2.59945i	−0.576906	−	0.101724i	−0.122421	−	0.992478i	$-0.539066\pi$
$653$	−14.7422	−	2.59945i	−0.576906	−	0.101724i	−0.454486	+	0.890754i	$0.650177\pi$
$654$		0			0
$655$	11.8673	+	14.1429i	0.463694	+	0.552609i
$656$		0			0
$657$	8.78005	+	0.159091i	0.342542	+	0.00620672i
$658$		0			0
$659$	2.62215	+	14.8709i	0.102144	+	0.579290i	0.992323	+	0.123677i	$0.0394687\pi$
$659$	2.62215	+	14.8709i	0.102144	+	0.579290i	−0.890178	+	0.455613i	$0.849420\pi$
$660$		0			0
$661$	18.1294	−	6.59856i	0.705152	−	0.256654i	0.0355431	−	0.999368i	$-0.488684\pi$
$661$	18.1294	−	6.59856i	0.705152	−	0.256654i	0.669609	+	0.742714i	$0.266462\pi$
$662$		0			0
$663$	23.7262	−	8.39301i	0.921448	−	0.325957i
$664$		0			0
$665$	55.1591	+	31.8461i	2.13898	+	1.23494i
$666$		0			0
$667$	−9.36067	+	5.40438i	−0.362446	+	0.209259i
$668$		0			0
$669$	1.54869	+	0.579618i	0.0598759	+	0.0224093i
$670$		0			0
$671$	−0.143187	−	0.120148i	−0.00552769	−	0.00463828i
$672$		0			0
$673$	10.3140	+	3.75400i	0.397576	+	0.144706i	0.533068	−	0.846073i	$-0.321039\pi$
$673$	10.3140	+	3.75400i	0.397576	+	0.144706i	−0.135491	+	0.990779i	$0.543261\pi$
$674$		0			0
$675$	−0.634356	+	1.60571i	−0.0244164	+	0.0618039i
$676$		0			0
$677$	10.9926	−	30.2020i	0.422481	−	1.16076i	−0.527802	−	0.849367i	$-0.676984\pi$
$677$	10.9926	−	30.2020i	0.422481	−	1.16076i	0.950283	−	0.311388i	$-0.100794\pi$
$678$		0			0
$679$	24.1520	−	28.7832i	0.926868	−	1.10460i
$680$		0			0
$681$	−30.7165	−	37.2873i	−1.17706	−	1.42885i
$682$		0			0
$683$	16.0306	+	27.7658i	0.613394	+	1.06243i	0.990664	+	0.136327i	$0.0435297\pi$
$683$	16.0306	+	27.7658i	0.613394	+	1.06243i	−0.377270	+	0.926103i	$0.623137\pi$
$684$		0			0
$685$	−11.4371	+	19.8097i	−0.436989	+	0.756888i
$686$		0			0
$687$	−13.2236	+	15.4725i	−0.504513	+	0.590311i
$688$		0			0
$689$	5.05440	+	13.8869i	0.192557	+	0.529047i
$690$		0			0
$691$	−4.37408	+	0.771269i	−0.166398	+	0.0293405i	−0.256226	−	0.966617i	$-0.582479\pi$
$691$	−4.37408	+	0.771269i	−0.166398	+	0.0293405i	0.0898284	+	0.995957i	$0.471368\pi$
$692$		0			0
$693$	0.781257	+	2.27384i	0.0296775	+	0.0863761i
$694$		0			0
$695$	9.62021	−	8.07232i	0.364915	−	0.306200i
$696$		0			0
$697$	14.2040	−	80.5547i	0.538013	−	3.05123i
$698$		0			0
$699$	−25.6496	−	0.232361i	−0.970158	−	0.00878870i
$700$		0			0
$701$			27.5938i			1.04220i	0.853495	+	0.521101i	$0.174478\pi$
$701$			27.5938i			1.04220i	−0.853495	+	0.521101i	$0.825522\pi$
$702$		0			0
$703$		−	59.1000i		−	2.22900i
$704$		0			0
$705$	8.54652	−	14.4981i	0.321880	−	0.546030i
$706$		0			0
$707$	6.07928	−	34.4773i	0.228635	−	1.29665i
$708$		0			0
$709$	7.46960	−	6.26774i	0.280527	−	0.235390i	−0.491657	−	0.870789i	$-0.663609\pi$
$709$	7.46960	−	6.26774i	0.280527	−	0.235390i	0.772184	+	0.635399i	$0.219164\pi$
$710$		0			0
$711$	−6.93570	−	8.57652i	−0.260109	−	0.321644i
$712$		0			0
$713$	8.18373	−	1.44301i	0.306483	−	0.0540412i
$714$		0			0
$715$	−0.326149	−	0.896087i	−0.0121973	−	0.0335118i
$716$		0			0
$717$	−40.3612	−	7.49438i	−1.50732	−	0.279883i
$718$		0			0
$719$	−16.5609	+	28.6843i	−0.617616	+	1.06974i	0.372304	+	0.928111i	$0.378568\pi$
$719$	−16.5609	+	28.6843i	−0.617616	+	1.06974i	−0.989920	+	0.141631i	$0.954765\pi$
$720$		0			0
$721$	10.6003	+	18.3602i	0.394774	+	0.683769i
$722$		0			0
$723$	−14.3705	+	2.39989i	−0.534444	+	0.0892527i
$724$		0			0
$725$	0.443045	−	0.528001i	0.0164543	−	0.0196095i
$726$		0			0
$727$	−3.52972	+	9.69783i	−0.130910	+	0.359673i	−0.987779	−	0.155862i	$-0.950184\pi$
$727$	−3.52972	+	9.69783i	−0.130910	+	0.359673i	0.856869	+	0.515535i	$0.172407\pi$
$728$		0			0
$729$	−26.9601	−	1.46680i	−0.998523	−	0.0543260i
$730$		0			0
$731$	−39.8170	−	14.4922i	−1.47268	−	0.536013i
$732$		0			0
$733$	−18.0067	−	15.1094i	−0.665091	−	0.558078i	0.246517	−	0.969138i	$-0.420714\pi$
$733$	−18.0067	−	15.1094i	−0.665091	−	0.558078i	−0.911608	+	0.411061i	$0.865158\pi$
$734$		0			0
$735$	−5.01987	−	30.0589i	−0.185161	−	1.10874i
$736$		0			0
$737$	−0.926936	+	0.535166i	−0.0341441	+	0.0197131i
$738$		0			0
$739$	−18.0525	−	10.4226i	−0.664073	−	0.383403i	0.129754	−	0.991546i	$-0.458581\pi$
$739$	−18.0525	−	10.4226i	−0.664073	−	0.383403i	−0.793827	+	0.608143i	$0.791915\pi$
$740$		0			0
$741$	−5.13388	+	27.6487i	−0.188598	+	1.01570i
$742$		0			0
$743$	−17.7561	+	6.46269i	−0.651408	+	0.237093i	−0.646522	−	0.762895i	$-0.723777\pi$
$743$	−17.7561	+	6.46269i	−0.651408	+	0.237093i	−0.00488550	+	0.999988i	$0.501555\pi$
$744$		0			0
$745$	−3.28212	−	18.6138i	−0.120247	−	0.681957i
$746$		0			0
$747$	24.9664	−	20.1899i	0.913471	−	0.738710i
$748$		0			0
$749$	−4.18193	−	4.98383i	−0.152804	−	0.182105i
$750$		0			0
$751$	−0.970086	−	0.171052i	−0.0353989	−	0.00624179i	0.155921	−	0.987770i	$-0.450166\pi$
$751$	−0.970086	−	0.171052i	−0.0353989	−	0.00624179i	−0.191320	+	0.981528i	$0.561277\pi$
$752$		0			0
$753$	23.6516	+	13.9425i	0.861913	+	0.508091i
$754$		0			0
$755$	−47.8237			−1.74048
$756$		0			0
$757$	1.04898			0.0381259			0.0190630	−	0.999818i	$-0.493932\pi$
$757$	1.04898			0.0381259			0.0190630	+	0.999818i	$0.493932\pi$
$758$		0			0
$759$	0.0168364	−	1.85852i	0.000611124	−	0.0674601i
$760$		0			0
$761$	−45.5984	−	8.04023i	−1.65294	−	0.291458i	−0.732043	−	0.681259i	$-0.761433\pi$
$761$	−45.5984	−	8.04023i	−1.65294	−	0.291458i	−0.920899	+	0.389801i	$0.872544\pi$
$762$		0			0
$763$	−39.1756	−	46.6877i	−1.41825	−	1.69021i
$764$		0			0
$765$	41.5578	−	14.2786i	1.50253	−	0.516245i
$766$		0			0
$767$	−0.200935	−	1.13956i	−0.00725532	−	0.0411470i
$768$		0			0
$769$	7.85772	−	2.85997i	0.283356	−	0.103133i	−0.196432	−	0.980517i	$-0.562936\pi$
$769$	7.85772	−	2.85997i	0.283356	−	0.103133i	0.479789	+	0.877384i	$0.340713\pi$
$770$		0			0
$771$	−11.9618	−	10.2232i	−0.430793	−	0.368180i
$772$		0			0
$773$	−18.6959	−	10.7941i	−0.672445	−	0.388236i	0.124557	−	0.992212i	$-0.460249\pi$
$773$	−18.6959	−	10.7941i	−0.672445	−	0.388236i	−0.797003	+	0.603976i	$0.793582\pi$
$774$		0			0
$775$	−0.458918	+	0.264956i	−0.0164848	+	0.00951751i
$776$		0			0
$777$	−40.5861	+	33.4340i	−1.45602	+	1.19944i
$778$		0			0
$779$	70.0162	+	58.7506i	2.50859	+	2.10496i
$780$		0			0
$781$	−1.95417	−	0.711260i	−0.0699257	−	0.0254509i
$782$		0			0
$783$	10.0251	+	3.96055i	0.358269	+	0.141539i
$784$		0			0
$785$	3.55588	−	9.76971i	0.126915	−	0.348696i
$786$		0			0
$787$	0.551585	−	0.657353i	0.0196619	−	0.0234321i	−0.756124	−	0.654428i	$-0.772909\pi$
$787$	0.551585	−	0.657353i	0.0196619	−	0.0234321i	0.775786	+	0.630996i	$0.217354\pi$
$788$		0			0
$789$	11.1356	−	29.7533i	0.396436	−	1.05924i
$790$		0			0
$791$	36.7680	+	63.6841i	1.30732	+	2.26435i
$792$		0			0
$793$	−0.972592	+	1.68458i	−0.0345378	+	0.0598212i
$794$		0			0
$795$	8.60516	+	24.3259i	0.305194	+	0.862751i
$796$		0			0
$797$	3.33003	+	9.14917i	0.117956	+	0.324080i	0.984594	−	0.174857i	$-0.0559462\pi$
$797$	3.33003	+	9.14917i	0.117956	+	0.324080i	−0.866638	+	0.498937i	$0.833724\pi$
$798$		0			0
$799$	30.0277	−	5.29469i	1.06230	−	0.187313i
$800$		0			0
$801$	−0.614880	+	33.9346i	−0.0217257	+	1.19902i
$802$		0			0
$803$	0.461798	−	0.387494i	0.0162965	−	0.0136744i
$804$		0			0
$805$	−7.60706	+	43.1418i	−0.268114	+	1.52055i
$806$		0			0
$807$	−12.8173	−	22.6721i	−0.451192	−	0.798097i
$808$		0			0
$809$			10.0689i			0.354005i	0.984210	+	0.177003i	$0.0566401\pi$
$809$			10.0689i			0.354005i	−0.984210	+	0.177003i	$0.943360\pi$
$810$		0			0
$811$			18.3336i			0.643779i	0.946777	+	0.321889i	$0.104318\pi$
$811$			18.3336i			0.643779i	−0.946777	+	0.321889i	$0.895682\pi$
$812$		0			0
$813$	14.7374	+	26.0684i	0.516862	+	0.914259i
$814$		0			0
$815$	0.322616	−	1.82964i	0.0113007	−	0.0640896i
$816$		0			0
$817$	36.2695	−	30.4337i	1.26891	−	1.06474i
$818$		0			0
$819$	21.8917	−	12.1158i	0.764958	−	0.423359i
$820$		0			0
$821$	−40.0948	+	7.06979i	−1.39932	+	0.246737i	−0.821862	−	0.569686i	$-0.807065\pi$
$821$	−40.0948	+	7.06979i	−1.39932	+	0.246737i	−0.577454	+	0.816423i	$0.695954\pi$
$822$		0			0
$823$	−2.35467	−	6.46940i	−0.0820786	−	0.225509i	0.891864	−	0.452304i	$-0.149398\pi$
$823$	−2.35467	−	6.46940i	−0.0820786	−	0.225509i	−0.973943	+	0.226795i	$0.927175\pi$
$824$		0			0
$825$	0.0395255	+	0.111735i	0.00137610	+	0.00389010i
$826$		0			0
$827$	−9.10736	+	15.7744i	−0.316694	+	0.548530i	−0.979796	−	0.199999i	$-0.935906\pi$
$827$	−9.10736	+	15.7744i	−0.316694	+	0.548530i	0.663102	+	0.748529i	$0.269239\pi$
$828$		0			0
$829$	6.97068	+	12.0736i	0.242102	+	0.419333i	0.961313	−	0.275459i	$-0.0888299\pi$
$829$	6.97068	+	12.0736i	0.242102	+	0.419333i	−0.719211	+	0.694792i	$0.755497\pi$
$830$		0			0
$831$	−7.30923	+	19.5296i	−0.253554	+	0.677475i
$832$		0			0
$833$	35.4902	−	42.2956i	1.22966	−	1.46546i
$834$		0			0
$835$	−9.08473	+	24.9601i	−0.314390	+	0.863780i
$836$		0			0
$837$	−6.20126	−	5.49744i	−0.214347	−	0.190019i
$838$		0			0
$839$	−21.4902	−	7.82180i	−0.741925	−	0.270039i	−0.0567211	−	0.998390i	$-0.518065\pi$
$839$	−21.4902	−	7.82180i	−0.741925	−	0.270039i	−0.685204	+	0.728352i	$0.740287\pi$
$840$		0			0
$841$	18.9188	+	15.8747i	0.652371	+	0.547404i
$842$		0			0
$843$	9.62870	−	7.93192i	0.331630	−	0.273190i
$844$		0			0
$845$	15.7294	−	9.08136i	0.541107	−	0.312408i
$846$		0			0
$847$	−36.9287	−	21.3208i	−1.26889	−	0.732592i
$848$		0			0
$849$	41.0189	+	35.0570i	1.40777	+	1.20315i
$850$		0			0
$851$	38.1974	−	13.9027i	1.30939	−	0.476579i
$852$		0			0
$853$	4.14225	+	23.4919i	0.141828	+	0.804346i	0.969860	+	0.243664i	$0.0783496\pi$
$853$	4.14225	+	23.4919i	0.141828	+	0.804346i	−0.828032	+	0.560681i	$0.810539\pi$
$854$		0			0
$855$	−9.40089	+	48.1925i	−0.321504	+	1.64815i
$856$		0			0
$857$	9.33534	+	11.1254i	0.318889	+	0.380037i	0.901548	−	0.432680i	$-0.142432\pi$
$857$	9.33534	+	11.1254i	0.318889	+	0.380037i	−0.582659	+	0.812717i	$0.697987\pi$
$858$		0			0
$859$	30.2973	+	5.34222i	1.03373	+	0.182274i	0.664674	−	0.747133i	$-0.268570\pi$
$859$	30.2973	+	5.34222i	1.03373	+	0.182274i	0.369055	+	0.929408i	$0.379681\pi$
$860$		0			0
$861$	0.736672	−	81.3190i	0.0251057	−	2.77134i
$862$		0			0
$863$	−0.740209			−0.0251970			−0.0125985	−	0.999921i	$-0.504010\pi$
$863$	−0.740209			−0.0251970			−0.0125985	+	0.999921i	$0.504010\pi$
$864$		0			0
$865$	−41.6253			−1.41530
$866$		0			0
$867$	43.2169	+	25.4761i	1.46772	+	0.865212i
$868$		0			0
$869$	−0.745685	−	0.131484i	−0.0252956	−	0.00446030i
$870$		0			0
$871$	7.15973	+	8.53263i	0.242598	+	0.289117i
$872$		0			0
$873$	27.0351	+	10.3984i	0.915001	+	0.351934i
$874$		0			0
$875$	−7.78491	−	44.1504i	−0.263178	−	1.49256i
$876$		0			0
$877$	−0.300658	+	0.109431i	−0.0101525	+	0.00369521i	−0.347091	−	0.937831i	$-0.612831\pi$
$877$	−0.300658	+	0.109431i	−0.0101525	+	0.00369521i	0.336939	+	0.941527i	$0.390608\pi$
$878$		0			0
$879$	−7.06746	+	38.0620i	−0.238379	+	1.28380i
$880$		0			0
$881$	−2.53702	−	1.46475i	−0.0854744	−	0.0493487i	0.456654	−	0.889645i	$-0.349048\pi$
$881$	−2.53702	−	1.46475i	−0.0854744	−	0.0493487i	−0.542128	+	0.840296i	$0.682381\pi$
$882$		0			0
$883$	47.0872	−	27.1858i	1.58461	−	0.914876i	0.590438	−	0.807083i	$-0.298955\pi$
$883$	47.0872	−	27.1858i	1.58461	−	0.914876i	0.994173	−	0.107793i	$-0.0343783\pi$
$884$		0			0
$885$	−0.332800	−	1.99280i	−0.0111870	−	0.0669873i
$886$		0			0
$887$	−8.16957	−	6.85508i	−0.274307	−	0.230171i	0.495248	−	0.868752i	$-0.335077\pi$
$887$	−8.16957	−	6.85508i	−0.274307	−	0.230171i	−0.769555	+	0.638581i	$0.779522\pi$
$888$		0			0
$889$	55.8146	+	20.3148i	1.87196	+	0.681338i
$890$		0			0
$891$	−1.46209	+	1.13919i	−0.0489820	+	0.0381642i
$892$		0			0
$893$	−11.6527	+	32.0156i	−0.389943	+	1.07136i
$894$		0			0
$895$	−19.2723	+	22.9679i	−0.644203	+	0.767731i
$896$		0			0
$897$	−19.0775	+	3.18597i	−0.636981	+	0.106377i
$898$		0			0
$899$	1.65423	+	2.86522i	0.0551718	+	0.0955603i
$900$		0			0
$901$	−23.3742	+	40.4852i	−0.778706	+	1.34876i
$902$		0			0
$903$	−41.4183	−	7.69066i	−1.37831	−	0.255929i
$904$		0			0
$905$	17.8484	+	49.0381i	0.593301	+	1.63008i
$906$		0			0
$907$	−24.1993	+	4.26700i	−0.803526	+	0.141683i	−0.560304	−	0.828287i	$-0.689316\pi$
$907$	−24.1993	+	4.26700i	−0.803526	+	0.141683i	−0.243222	+	0.969971i	$0.578204\pi$
$908$		0			0
$909$	26.6594	−	4.20428i	0.884235	−	0.139447i
$910$		0			0
$911$	4.38166	−	3.67665i	0.145171	−	0.121813i	−0.567310	−	0.823504i	$-0.692016\pi$
$911$	4.38166	−	3.67665i	0.145171	−	0.121813i	0.712481	+	0.701691i	$0.247571\pi$
$912$		0			0
$913$	0.382753	−	2.17070i	0.0126673	−	0.0718397i
$914$		0			0
$915$	−1.72476	+	2.92583i	−0.0570187	+	0.0967250i
$916$		0			0
$917$			33.2545i			1.09816i
$918$		0			0
$919$			18.1413i			0.598426i	0.954186	+	0.299213i	$0.0967242\pi$
$919$			18.1413i			0.598426i	−0.954186	+	0.299213i	$0.903276\pi$
$920$		0			0
$921$	16.3554	+	0.148164i	0.538927	+	0.00488216i
$922$		0			0
$923$	−3.75800	+	21.3127i	−0.123696	+	0.701516i
$924$		0			0
$925$	−1.98567	+	1.66617i	−0.0652883	+	0.0547834i
$926$		0			0
$927$	−10.7306	+	12.3276i	−0.352439	+	0.404891i
$928$		0			0
$929$	−5.76282	+	1.01614i	−0.189072	+	0.0333385i	−0.267382	−	0.963591i	$-0.586159\pi$
$929$	−5.76282	+	1.01614i	−0.189072	+	0.0333385i	0.0783102	+	0.996929i	$0.475048\pi$
$930$		0			0
$931$	21.1008	+	57.9739i	0.691550	+	1.90002i
$932$		0			0
$933$	13.2674	−	15.5237i	0.434354	−	0.508222i
$934$		0			0
$935$	1.50828	−	2.61242i	0.0493261	−	0.0854353i
$936$		0			0
$937$	6.55013	+	11.3452i	0.213983	+	0.370630i	0.952958	−	0.303104i	$-0.0980228\pi$
$937$	6.55013	+	11.3452i	0.213983	+	0.370630i	−0.738974	+	0.673734i	$0.764690\pi$
$938$		0			0
$939$	−11.0969	−	13.4708i	−0.362135	−	0.439602i
$940$		0			0
$941$	2.91952	−	3.47934i	0.0951735	−	0.113423i	−0.716356	−	0.697735i	$-0.754191\pi$
$941$	2.91952	−	3.47934i	0.0951735	−	0.113423i	0.811529	+	0.584312i	$0.198636\pi$
$942$		0			0
$943$	−21.5009	+	59.0732i	−0.700166	+	1.92369i
$944$		0			0
$945$	38.4138	−	20.8075i	1.24960	−	0.676867i
$946$		0			0
$947$	−1.58228	−	0.575904i	−0.0514173	−	0.0187144i	0.316183	−	0.948698i	$-0.397598\pi$
$947$	−1.58228	−	0.575904i	−0.0514173	−	0.0187144i	−0.367601	+	0.929984i	$0.619821\pi$
$948$		0			0
$949$	−4.80576	−	4.03251i	−0.156001	−	0.130901i
$950$		0			0
$951$	23.5800	+	8.82512i	0.764633	+	0.286174i
$952$		0			0
$953$	20.8678	−	12.0481i	0.675975	−	0.390275i	−0.122362	−	0.992486i	$-0.539047\pi$
$953$	20.8678	−	12.0481i	0.675975	−	0.390275i	0.798337	+	0.602211i	$0.205713\pi$
$954$		0			0
$955$	13.6251	+	7.86646i	0.440898	+	0.254553i
$956$		0			0
$957$	0.697606	−	0.246775i	0.0225504	−	0.00797709i
$958$		0			0
$959$	−38.7166	+	14.0917i	−1.25023	+	0.455045i
$960$		0			0
$961$	4.94140	+	28.0241i	0.159400	+	0.904002i
$962$		0			0
$963$	2.58601	−	4.29738i	0.0833331	−	0.138481i
$964$		0			0
$965$	−13.5360	−	16.1316i	−0.435739	−	0.519293i
$966$		0			0
$967$	−26.2346	−	4.62588i	−0.843649	−	0.148758i	−0.264912	−	0.964272i	$-0.585343\pi$
$967$	−26.2346	−	4.62588i	−0.843649	−	0.148758i	−0.578737	+	0.815514i	$0.696454\pi$
$968$		0			0
$969$	−77.4394	+	43.7791i	−2.48771	+	1.40639i
$970$		0			0
$971$	−15.7928			−0.506815			−0.253408	−	0.967360i	$-0.581551\pi$
$971$	−15.7928			−0.506815			−0.253408	+	0.967360i	$0.581551\pi$
$972$		0			0
$973$	22.6202			0.725170
$974$		0			0
$975$	1.07369	−	0.606993i	0.0343856	−	0.0194393i
$976$		0			0
$977$	17.9884	+	3.17184i	0.575501	+	0.101476i	0.453821	−	0.891093i	$-0.350061\pi$
$977$	17.9884	+	3.17184i	0.575501	+	0.101476i	0.121680	+	0.992569i	$0.461172\pi$
$978$		0			0
$979$	1.49765	+	1.78483i	0.0478651	+	0.0570435i
$980$		0			0
$981$	24.2253	−	40.2572i	0.773456	−	1.28531i
$982$		0			0
$983$	−2.63000	−	14.9154i	−0.0838838	−	0.475729i	−0.997592	−	0.0693576i	$-0.977905\pi$
$983$	−2.63000	−	14.9154i	−0.0838838	−	0.475729i	0.913708	−	0.406371i	$-0.133206\pi$
$984$		0			0
$985$	11.7437	−	4.27436i	0.374186	−	0.136193i
$986$		0			0
$987$	28.5784	−	10.1095i	0.909662	−	0.321788i
$988$		0			0
$989$	28.2019	+	16.2824i	0.896769	+	0.517750i
$990$		0			0
$991$	−21.4600	+	12.3899i	−0.681698	+	0.393578i	−0.800494	−	0.599340i	$-0.795430\pi$
$991$	−21.4600	+	12.3899i	−0.681698	+	0.393578i	0.118797	+	0.992919i	$0.462096\pi$
$992$		0			0
$993$	−16.0704	−	6.01455i	−0.509978	−	0.190866i
$994$		0			0
$995$	−6.84040	−	5.73978i	−0.216855	−	0.181963i
$996$		0			0
$997$	−14.8546	−	5.40662i	−0.470448	−	0.171229i	0.0959070	−	0.995390i	$-0.469425\pi$
$997$	−14.8546	−	5.40662i	−0.470448	−	0.171229i	−0.566356	+	0.824161i	$0.691647\pi$
$998$		0			0
$999$	−34.5426	−	21.2151i	−1.09288	−	0.671217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.b.239.6	yes	36
4.3	odd	2		432.2.be.c.239.1	yes	36
27.20	odd	18		432.2.be.c.47.1	yes	36
108.47	even	18	inner	432.2.be.b.47.6	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.47.6	✓	36	108.47	even	18	inner
432.2.be.b.239.6	yes	36	1.1	even	1	trivial
432.2.be.c.47.1	yes	36	27.20	odd	18
432.2.be.c.239.1	yes	36	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50778 - 0.852402i) q^{3} +(-2.12767 - 0.375166i) q^{5} +(-2.50142 - 2.98107i) q^{7} +(1.54682 - 2.57047i) q^{9} +O(q^{10})\)	\(q+(1.50778 - 0.852402i) q^{3} +(-2.12767 - 0.375166i) q^{5} +(-2.50142 - 2.98107i) q^{7} +(1.54682 - 2.57047i) q^{9} +(-0.0357619 - 0.202816i) q^{11} +(-2.01394 + 0.733014i) q^{13} +(-3.52786 + 1.24796i) q^{15} +(-5.87137 - 3.38984i) q^{17} +(6.56062 - 3.78777i) q^{19} +(-6.31267 - 2.36260i) q^{21} +(3.99143 + 3.34921i) q^{23} +(-0.312223 - 0.113640i) q^{25} +(0.141195 - 5.19423i) q^{27} +(-0.709501 + 1.94934i) q^{29} +(1.02516 - 1.22174i) q^{31} +(-0.226802 - 0.275319i) q^{33} +(4.20380 + 7.28120i) q^{35} +(3.90071 - 6.75622i) q^{37} +(-2.41176 + 2.82191i) q^{39} +(4.12650 + 11.3375i) q^{41} +(6.15496 - 1.08528i) q^{43} +(-4.25549 + 4.88881i) q^{45} +(-3.44521 + 2.89087i) q^{47} +(-1.41417 + 8.02017i) q^{49} +(-11.7423 - 0.106374i) q^{51} -6.89537i q^{53} +0.444942i q^{55} +(6.66329 - 11.3034i) q^{57} +(-0.0937549 + 0.531710i) q^{59} +(0.695271 - 0.583402i) q^{61} +(-11.5320 + 1.81864i) q^{63} +(4.56001 - 0.804052i) q^{65} +(-1.77754 - 4.88376i) q^{67} +(8.87308 + 1.64758i) q^{69} +(5.04889 - 8.74494i) q^{71} +(1.46358 + 2.53500i) q^{73} +(-0.567631 + 0.0947951i) q^{75} +(-0.515154 + 0.613936i) q^{77} +(1.25749 - 3.45493i) q^{79} +(-4.21468 - 7.95213i) q^{81} +(10.0574 + 3.66058i) q^{83} +(11.2206 + 9.41520i) q^{85} +(0.591846 + 3.54396i) q^{87} +(-9.79768 + 5.65669i) q^{89} +(7.22287 + 4.17013i) q^{91} +(0.504309 - 2.71597i) q^{93} +(-15.3799 + 5.59782i) q^{95} +(1.67663 + 9.50863i) q^{97} +(-0.576651 - 0.221795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q + 3 * q^5 + 6 * q^9	\( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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