LMFDB - Embedded newform 702.2.bc.a.305.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(305,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.305"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bc (of order $12$, degree $4$, not 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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.4
Character	$\chi$	$=$	702.305
Dual form			702.2.bc.a.557.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.175000 + 0.653109i) q^{5} +(2.85512 + 2.85512i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.585562 - 0.338074i) q^{10} +(0.686168 + 0.183858i) q^{11} +(-1.25625 - 3.37962i) q^{13} +(-3.49679 + 2.01888i) q^{14} +(0.500000 + 0.866025i) q^{16} +(3.24443 + 5.61952i) q^{17} +(-0.253608 - 0.0679541i) q^{19} +(0.478109 - 0.478109i) q^{20} +(-0.355187 + 0.615201i) q^{22} -1.72101 q^{23} +(3.93420 + 2.27141i) q^{25} +(3.58960 - 0.338733i) q^{26} +(-1.04505 - 3.90017i) q^{28} +(1.11417 - 0.643269i) q^{29} +(-3.89881 - 1.04468i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-6.26776 + 1.67944i) q^{34} +(-2.36435 + 1.36506i) q^{35} +(-7.96159 + 2.13330i) q^{37} +(0.131277 - 0.227379i) q^{38} +(0.338074 + 0.585562i) q^{40} +(6.55152 + 6.55152i) q^{41} +6.55772i q^{43} +(-0.502310 - 0.502310i) q^{44} +(0.445430 - 1.66237i) q^{46} +(2.43087 + 9.07214i) q^{47} +9.30343i q^{49} +(-3.21226 + 3.21226i) q^{50} +(-0.601867 + 3.55496i) q^{52} -6.34328i q^{53} +(-0.240159 + 0.415967i) q^{55} +4.03775 q^{56} +(0.332981 + 1.24270i) q^{58} +(-1.28969 - 4.81321i) q^{59} +3.29863 q^{61} +(2.01817 - 3.49557i) q^{62} -1.00000i q^{64} +(2.42711 - 0.229034i) q^{65} +(-7.38704 + 7.38704i) q^{67} -6.48886i q^{68} +(-0.706607 - 2.63709i) q^{70} +(-2.09577 + 7.82153i) q^{71} +(-1.40415 - 1.40415i) q^{73} -8.24244i q^{74} +(0.185654 + 0.185654i) q^{76} +(1.43416 + 2.48403i) q^{77} +(7.29283 - 12.6316i) q^{79} +(-0.653109 + 0.175000i) q^{80} +(-8.02394 + 4.63262i) q^{82} +(-3.90968 + 1.04760i) q^{83} +(-4.23794 + 1.13555i) q^{85} +(-6.33427 - 1.69726i) q^{86} +(0.615201 - 0.355187i) q^{88} +(-2.64065 - 9.85503i) q^{89} +(6.06248 - 13.2360i) q^{91} +(1.49044 + 0.860504i) q^{92} -9.39217 q^{94} +(0.0887629 - 0.153742i) q^{95} +(1.42324 - 1.42324i) q^{97} +(-8.98642 - 2.40791i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) $ 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.175000	+	0.653109i	−0.0782624	+	0.292079i	−0.993953	−	0.109804i	$-0.964978\pi$
$5$	−0.175000	+	0.653109i	−0.0782624	+	0.292079i	0.915691	+	0.401883i	$0.131644\pi$
$6$		0			0
$7$	2.85512	+	2.85512i	1.07913	+	1.07913i	0.996587	+	0.0825471i	$0.0263055\pi$
$7$	2.85512	+	2.85512i	1.07913	+	1.07913i	0.0825471	+	0.996587i	$0.473694\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−0.585562	−	0.338074i	−0.185171	−	0.106908i
$11$	0.686168	+	0.183858i	0.206887	+	0.0554353i	0.360774	−	0.932653i	$-0.382512\pi$
$11$	0.686168	+	0.183858i	0.206887	+	0.0554353i	−0.153887	+	0.988088i	$0.549179\pi$
$12$		0			0
$13$	−1.25625	−	3.37962i	−0.348421	−	0.937338i
$13$	−1.25625	−	3.37962i	−0.348421	−	0.937338i
$14$	−3.49679	+	2.01888i	−0.934558	+	0.539567i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.24443	+	5.61952i	0.786890	+	1.36293i	0.927863	+	0.372920i	$0.121644\pi$
$17$	3.24443	+	5.61952i	0.786890	+	1.36293i	−0.140973	+	0.990013i	$0.545023\pi$
$18$		0			0
$19$	−0.253608	−	0.0679541i	−0.0581817	−	0.0155897i	0.229611	−	0.973283i	$-0.426255\pi$
$19$	−0.253608	−	0.0679541i	−0.0581817	−	0.0155897i	−0.287792	+	0.957693i	$0.592921\pi$
$20$	0.478109	−	0.478109i	0.106908	−	0.106908i
$21$		0			0
$22$	−0.355187	+	0.615201i	−0.0757261	+	0.131161i
$23$	−1.72101			−0.358855			−0.179427	−	0.983771i	$-0.557425\pi$
$23$	−1.72101			−0.358855			−0.179427	+	0.983771i	$0.557425\pi$
$24$		0			0
$25$	3.93420	+	2.27141i	0.786840	+	0.454282i
$26$	3.58960	−	0.338733i	0.703979	−	0.0664310i
$27$		0			0
$28$	−1.04505	−	3.90017i	−0.197495	−	0.737062i
$29$	1.11417	−	0.643269i	0.206897	−	0.119452i	−0.392971	−	0.919551i	$-0.628553\pi$
$29$	1.11417	−	0.643269i	0.206897	−	0.119452i	0.599869	+	0.800099i	$0.295220\pi$
$30$		0			0
$31$	−3.89881	−	1.04468i	−0.700246	−	0.187630i	−0.108905	−	0.994052i	$-0.534735\pi$
$31$	−3.89881	−	1.04468i	−0.700246	−	0.187630i	−0.591341	+	0.806422i	$0.701401\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		0			0
$34$	−6.26776	+	1.67944i	−1.07491	+	0.288022i
$35$	−2.36435	+	1.36506i	−0.399648	+	0.230737i
$36$		0			0
$37$	−7.96159	+	2.13330i	−1.30888	+	0.350713i	−0.844800	−	0.535082i	$-0.820281\pi$
$37$	−7.96159	+	2.13330i	−1.30888	+	0.350713i	−0.464077	+	0.885795i	$0.653614\pi$
$38$	0.131277	−	0.227379i	0.0212960	−	0.0368857i
$39$		0			0
$40$	0.338074	+	0.585562i	0.0534542	+	0.0925854i
$41$	6.55152	+	6.55152i	1.02318	+	1.02318i	0.999725	+	0.0234500i	$0.00746506\pi$
$41$	6.55152	+	6.55152i	1.02318	+	1.02318i	0.0234500	+	0.999725i	$0.492535\pi$
$42$		0			0
$43$			6.55772i			1.00004i	0.866013	+	0.500021i	$0.166674\pi$
$43$			6.55772i			1.00004i	−0.866013	+	0.500021i	$0.833326\pi$
$44$	−0.502310	−	0.502310i	−0.0757261	−	0.0757261i
$45$		0			0
$46$	0.445430	−	1.66237i	0.0656750	−	0.245102i
$47$	2.43087	+	9.07214i	0.354579	+	1.32331i	0.881013	+	0.473092i	$0.156862\pi$
$47$	2.43087	+	9.07214i	0.354579	+	1.32331i	−0.526434	+	0.850216i	$0.676471\pi$
$48$		0			0
$49$			9.30343i			1.32906i
$50$	−3.21226	+	3.21226i	−0.454282	+	0.454282i
$51$		0			0
$52$	−0.601867	+	3.55496i	−0.0834640	+	0.492985i
$53$		−	6.34328i		−	0.871317i	−0.900112	−	0.435658i	$-0.856516\pi$
$53$		−	6.34328i		−	0.871317i	0.900112	−	0.435658i	$-0.143484\pi$
$54$		0			0
$55$	−0.240159	+	0.415967i	−0.0323830	+	0.0560890i
$56$	4.03775			0.539567
$57$		0			0
$58$	0.332981	+	1.24270i	0.0437225	+	0.163175i
$59$	−1.28969	−	4.81321i	−0.167904	−	0.626626i	−0.997652	−	0.0684878i	$-0.978183\pi$
$59$	−1.28969	−	4.81321i	−0.167904	−	0.626626i	0.829748	−	0.558138i	$-0.188484\pi$
$60$		0			0
$61$	3.29863			0.422346			0.211173	−	0.977449i	$-0.432272\pi$
$61$	3.29863			0.422346			0.211173	+	0.977449i	$0.432272\pi$
$62$	2.01817	−	3.49557i	0.256308	−	0.443938i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	2.42711	−	0.229034i	0.301045	−	0.0284081i
$66$		0			0
$67$	−7.38704	+	7.38704i	−0.902471	+	0.902471i	−0.995649	−	0.0931784i	$-0.970297\pi$
$67$	−7.38704	+	7.38704i	−0.902471	+	0.902471i	0.0931784	+	0.995649i	$0.470297\pi$
$68$		−	6.48886i		−	0.786890i
$69$		0			0
$70$	−0.706607	−	2.63709i	−0.0844556	−	0.315193i
$71$	−2.09577	+	7.82153i	−0.248722	+	0.928245i	0.722753	+	0.691106i	$0.242876\pi$
$71$	−2.09577	+	7.82153i	−0.248722	+	0.928245i	−0.971476	+	0.237139i	$0.923790\pi$
$72$		0			0
$73$	−1.40415	−	1.40415i	−0.164343	−	0.164343i	0.620145	−	0.784488i	$-0.287074\pi$
$73$	−1.40415	−	1.40415i	−0.164343	−	0.164343i	−0.784488	+	0.620145i	$0.787074\pi$
$74$		−	8.24244i		−	0.958165i
$75$		0			0
$76$	0.185654	+	0.185654i	0.0212960	+	0.0212960i
$77$	1.43416	+	2.48403i	0.163437	+	0.283081i
$78$		0			0
$79$	7.29283	−	12.6316i	0.820507	−	1.42116i	−0.0847976	−	0.996398i	$-0.527024\pi$
$79$	7.29283	−	12.6316i	0.820507	−	1.42116i	0.905305	−	0.424762i	$-0.139642\pi$
$80$	−0.653109	+	0.175000i	−0.0730198	+	0.0195656i
$81$		0			0
$82$	−8.02394	+	4.63262i	−0.886096	+	0.511588i
$83$	−3.90968	+	1.04760i	−0.429144	+	0.114989i	−0.466924	−	0.884297i	$-0.654638\pi$
$83$	−3.90968	+	1.04760i	−0.429144	+	0.114989i	0.0377806	+	0.999286i	$0.487971\pi$
$84$		0			0
$85$	−4.23794	+	1.13555i	−0.459669	+	0.123168i
$86$	−6.33427	−	1.69726i	−0.683042	−	0.183020i
$87$		0			0
$88$	0.615201	−	0.355187i	0.0655807	−	0.0378630i
$89$	−2.64065	−	9.85503i	−0.279908	−	1.04463i	−0.952481	−	0.304600i	$-0.901477\pi$
$89$	−2.64065	−	9.85503i	−0.279908	−	1.04463i	0.672573	−	0.740031i	$-0.265189\pi$
$90$		0			0
$91$	6.06248	−	13.2360i	0.635521	−	1.38751i
$92$	1.49044	+	0.860504i	0.155389	+	0.0897137i
$93$		0			0
$94$	−9.39217			−0.968729
$95$	0.0887629	−	0.153742i	0.00910688	−	0.0157736i
$96$		0			0
$97$	1.42324	−	1.42324i	0.144508	−	0.144508i	−0.631151	−	0.775660i	$-0.717417\pi$
$97$	1.42324	−	1.42324i	0.144508	−	0.144508i	0.775660	+	0.631151i	$0.217417\pi$
$98$	−8.98642	−	2.40791i	−0.907766	−	0.243235i
$99$		0			0
$100$	−2.27141	−	3.93420i	−0.227141	−	0.393420i
$101$	−7.26007	−	12.5748i	−0.722404	−	1.25124i	−0.960034	−	0.279884i	$-0.909704\pi$
$101$	−7.26007	−	12.5748i	−0.722404	−	1.25124i	0.237630	−	0.971356i	$-0.423629\pi$
$102$		0			0
$103$	16.7121	−	9.64874i	1.64669	−	0.950719i	0.668319	−	0.743874i	$-0.267014\pi$
$103$	16.7121	−	9.64874i	1.64669	−	0.950719i	0.978374	−	0.206844i	$-0.0663194\pi$
$104$	−3.27806	−	1.50145i	−0.321440	−	0.147229i
$105$		0			0
$106$	6.12714	+	1.64176i	0.595121	+	0.159462i
$107$	11.5211	+	6.65169i	1.11378	+	0.643043i	0.939807	−	0.341706i	$-0.111005\pi$
$107$	11.5211	+	6.65169i	1.11378	+	0.643043i	0.173977	+	0.984750i	$0.444338\pi$
$108$		0			0
$109$	7.63616	−	7.63616i	0.731412	−	0.731412i	−0.239488	−	0.970899i	$-0.576979\pi$
$109$	7.63616	−	7.63616i	0.731412	−	0.731412i	0.970899	+	0.239488i	$0.0769794\pi$
$110$	−0.339636	−	0.339636i	−0.0323830	−	0.0323830i
$111$		0			0
$112$	−1.04505	+	3.90017i	−0.0987476	+	0.368531i
$113$	−13.1742	−	7.60612i	−1.23932	−	0.715524i	−0.270368	−	0.962757i	$-0.587145\pi$
$113$	−13.1742	−	7.60612i	−1.23932	−	0.715524i	−0.968956	+	0.247233i	$0.920479\pi$
$114$		0			0
$115$	0.301176	−	1.12401i	0.0280849	−	0.104814i
$116$	−1.28654			−0.119452
$117$		0			0
$118$	4.98300			0.458722
$119$	−6.78117	+	25.3077i	−0.621628	+	2.31995i
$120$		0			0
$121$	−9.08926	−	5.24768i	−0.826296	−	0.477062i
$122$	−0.853749	+	3.18623i	−0.0772948	+	0.288468i
$123$		0			0
$124$	2.85412	+	2.85412i	0.256308	+	0.256308i
$125$	−4.56251	+	4.56251i	−0.408083	+	0.408083i
$126$		0			0
$127$	16.8933	+	9.75334i	1.49904	+	0.865469i	0.999999	−	0.00111133i	$-0.000353747\pi$
$127$	16.8933	+	9.75334i	1.49904	+	0.865469i	0.499037	+	0.866581i	$0.333687\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		0			0
$130$	−0.406951	+	2.40368i	−0.0356920	+	0.210817i
$131$	4.87564	−	2.81495i	0.425986	−	0.245943i	−0.271649	−	0.962396i	$-0.587569\pi$
$131$	4.87564	−	2.81495i	0.425986	−	0.245943i	0.697635	+	0.716453i	$0.254236\pi$
$132$		0			0
$133$	−0.530065	−	0.918099i	−0.0459625	−	0.0796093i
$134$	−5.22343	−	9.04724i	−0.451236	−	0.781563i
$135$		0			0
$136$	6.26776	+	1.67944i	0.537456	+	0.144011i
$137$	8.31760	−	8.31760i	0.710621	−	0.710621i	−0.256044	−	0.966665i	$-0.582419\pi$
$137$	8.31760	−	8.31760i	0.710621	−	0.710621i	0.966665	+	0.256044i	$0.0824193\pi$
$138$		0			0
$139$	−1.48106	+	2.56527i	−0.125622	+	0.217584i	−0.921976	−	0.387247i	$-0.873426\pi$
$139$	−1.48106	+	2.56527i	−0.125622	+	0.217584i	0.796354	+	0.604831i	$0.206759\pi$
$140$	2.73012			0.230737
$141$		0			0
$142$	−7.01259	−	4.04872i	−0.588484	−	0.339761i
$143$	−0.240627	−	2.54996i	−0.0201222	−	0.213238i
$144$		0			0
$145$	0.225144	+	0.840250i	0.0186972	+	0.0697790i
$146$	1.71972	−	0.992882i	0.142325	−	0.0821715i
$147$		0			0
$148$	7.96159	+	2.13330i	0.654439	+	0.175356i
$149$	22.4219	−	6.00794i	1.83688	−	0.492189i	0.838284	−	0.545234i	$-0.183559\pi$
$149$	22.4219	−	6.00794i	1.83688	−	0.492189i	0.998592	+	0.0530449i	$0.0168926\pi$
$150$		0			0
$151$	6.65733	−	1.78383i	0.541766	−	0.145166i	0.0224496	−	0.999748i	$-0.492853\pi$
$151$	6.65733	−	1.78383i	0.541766	−	0.145166i	0.519316	+	0.854582i	$0.326187\pi$
$152$	−0.227379	+	0.131277i	−0.0184429	+	0.0106480i
$153$		0			0
$154$	−2.77058	+	0.742373i	−0.223259	+	0.0598222i
$155$	1.36458	−	2.36353i	0.109606	−	0.189843i
$156$		0			0
$157$	−5.48299	−	9.49681i	−0.437590	−	0.757928i	0.559913	−	0.828551i	$-0.310835\pi$
$157$	−5.48299	−	9.49681i	−0.437590	−	0.757928i	−0.997503	+	0.0706232i	$0.977501\pi$
$158$	10.3136	+	10.3136i	0.820507	+	0.820507i
$159$		0			0
$160$		−	0.676148i		−	0.0534542i
$161$	−4.91369	−	4.91369i	−0.387253	−	0.387253i
$162$		0			0
$163$	3.31255	−	12.3626i	0.259459	−	0.968315i	−0.706096	−	0.708116i	$-0.749545\pi$
$163$	3.31255	−	12.3626i	0.259459	−	0.968315i	0.965555	−	0.260198i	$-0.0837880\pi$
$164$	−2.39802	−	8.94954i	−0.187254	−	0.698842i
$165$		0			0
$166$		−	4.04760i		−	0.314155i
$167$	0.593992	−	0.593992i	0.0459645	−	0.0459645i	−0.683751	−	0.729715i	$-0.739653\pi$
$167$	0.593992	−	0.593992i	0.0459645	−	0.0459645i	0.729715	+	0.683751i	$0.239653\pi$
$168$		0			0
$169$	−9.84368	+	8.49129i	−0.757206	+	0.653176i
$170$		−	4.38743i		−	0.336501i
$171$		0			0
$172$	3.27886	−	5.67915i	0.250011	−	0.433031i
$173$	−21.3169			−1.62070			−0.810349	−	0.585948i	$-0.800722\pi$
$173$	−21.3169			−1.62070			−0.810349	+	0.585948i	$0.800722\pi$
$174$		0			0
$175$	4.74746	+	17.7178i	0.358874	+	1.33934i
$176$	0.183858	+	0.686168i	0.0138588	+	0.0517219i
$177$		0			0
$178$	10.2027			0.764723
$179$	0.120767	−	0.209175i	0.00902656	−	0.0156345i	−0.861477	−	0.507797i	$-0.830460\pi$
$179$	0.120767	−	0.209175i	0.00902656	−	0.0156345i	0.870503	+	0.492162i	$0.163793\pi$
$180$		0			0
$181$			1.73952i			0.129298i	0.997908	+	0.0646488i	$0.0205927\pi$
$181$			1.73952i			0.129298i	−0.997908	+	0.0646488i	$0.979407\pi$
$182$	11.2159	+	9.28163i	0.831376	+	0.688000i
$183$		0			0
$184$	−1.21694	+	1.21694i	−0.0897137	+	0.0897137i
$185$		−	5.57311i		−	0.409744i
$186$		0			0
$187$	1.19303	+	4.45245i	0.0872430	+	0.325595i
$188$	2.43087	−	9.07214i	0.177290	−	0.661654i
$189$		0			0
$190$	0.125530	+	0.125530i	0.00910688	+	0.00910688i
$191$		−	8.44838i		−	0.611304i	−0.952143	−	0.305652i	$-0.901126\pi$
$191$		−	8.44838i		−	0.611304i	0.952143	−	0.305652i	$-0.0988744\pi$
$192$		0			0
$193$	0.0379467	+	0.0379467i	0.00273147	+	0.00273147i	0.708471	−	0.705740i	$-0.249385\pi$
$193$	0.0379467	+	0.0379467i	0.00273147	+	0.00273147i	−0.705740	+	0.708471i	$0.749385\pi$
$194$	1.00638	+	1.74311i	0.0722541	+	0.125148i
$195$		0			0
$196$	4.65172	−	8.05701i	0.332265	−	0.575501i
$197$	2.56942	−	0.688475i	0.183064	−	0.0490518i	−0.166122	−	0.986105i	$-0.553125\pi$
$197$	2.56942	−	0.688475i	0.183064	−	0.0490518i	0.349186	+	0.937053i	$0.386458\pi$
$198$		0			0
$199$	−1.51087	+	0.872302i	−0.107103	+	0.0618359i	−0.552595	−	0.833450i	$-0.686362\pi$
$199$	−1.51087	+	0.872302i	−0.107103	+	0.0618359i	0.445492	+	0.895286i	$0.353029\pi$
$200$	4.38803	−	1.17577i	0.310281	−	0.0831394i
$201$		0			0
$202$	14.0254	−	3.75809i	0.986822	−	0.264418i
$203$	5.01771	+	1.34449i	0.352175	+	0.0943649i
$204$		0			0
$205$	−5.42537	+	3.13234i	−0.378924	+	0.218772i
$206$	4.99456	+	18.6399i	0.347987	+	1.29871i
$207$		0			0
$208$	2.29871	−	2.77775i	0.159387	−	0.192603i
$209$	−0.161524	−	0.0932559i	−0.0111728	−	0.00645064i
$210$		0			0
$211$	−1.30223			−0.0896495			−0.0448248	−	0.998995i	$-0.514273\pi$
$211$	−1.30223			−0.0896495			−0.0448248	+	0.998995i	$0.514273\pi$
$212$	−3.17164	+	5.49344i	−0.217829	+	0.377291i
$213$		0			0
$214$	−9.40691	+	9.40691i	−0.643043	+	0.643043i
$215$	−4.28290	−	1.14760i	−0.292092	−	0.0782657i
$216$		0			0
$217$	−8.14887	−	14.1143i	−0.553181	−	0.958138i
$218$	5.39958	+	9.35235i	0.365706	+	0.633421i
$219$		0			0
$220$	0.415967	−	0.240159i	0.0280445	−	0.0161915i
$221$	14.9160	−	18.0245i	1.00336	−	1.21246i
$222$		0			0
$223$	18.4364	+	4.94002i	1.23459	+	0.330808i	0.816366	−	0.577535i	$-0.195985\pi$
$223$	18.4364	+	4.94002i	1.23459	+	0.330808i	0.418227	+	0.908343i	$0.362652\pi$
$224$	−3.49679	−	2.01888i	−0.233639	−	0.134892i
$225$		0			0
$226$	10.7567	−	10.7567i	0.715524	−	0.715524i
$227$	−11.6214	−	11.6214i	−0.771338	−	0.771338i	0.207002	−	0.978340i	$-0.433629\pi$
$227$	−11.6214	−	11.6214i	−0.771338	−	0.771338i	−0.978340	+	0.207002i	$0.933629\pi$
$228$		0			0
$229$	3.52092	−	13.1402i	0.232669	−	0.868332i	−0.746517	−	0.665366i	$-0.768275\pi$
$229$	3.52092	−	13.1402i	0.232669	−	0.868332i	0.979186	−	0.202965i	$-0.0650579\pi$
$230$	1.00776	+	0.581828i	0.0664495	+	0.0383646i
$231$		0			0
$232$	0.332981	−	1.24270i	0.0218612	−	0.0815873i
$233$	3.89618			0.255247			0.127623	−	0.991823i	$-0.459265\pi$
$233$	3.89618			0.255247			0.127623	+	0.991823i	$0.459265\pi$
$234$		0			0
$235$	−6.35050			−0.414261
$236$	−1.28969	+	4.81321i	−0.0839520	+	0.313313i
$237$		0			0
$238$	−22.6902	−	13.1002i	−1.47079	−	0.849160i
$239$	−0.407977	+	1.52259i	−0.0263898	+	0.0984882i	−0.977865	−	0.209238i	$-0.932902\pi$
$239$	−0.407977	+	1.52259i	−0.0263898	+	0.0984882i	0.951475	+	0.307727i	$0.0995682\pi$
$240$		0			0
$241$	3.65205	+	3.65205i	0.235249	+	0.235249i	0.814879	−	0.579630i	$-0.196803\pi$
$241$	3.65205	+	3.65205i	0.235249	+	0.235249i	−0.579630	+	0.814879i	$0.696803\pi$
$242$	7.42135	−	7.42135i	0.477062	−	0.477062i
$243$		0			0
$244$	−2.85670	−	1.64932i	−0.182881	−	0.105587i
$245$	−6.07616	−	1.62810i	−0.388191	−	0.104016i
$246$		0			0
$247$	0.0889359	+	0.942467i	0.00565885	+	0.0599677i
$248$	−3.49557	+	2.01817i	−0.221969	+	0.128154i
$249$		0			0
$250$	−3.22618	−	5.58791i	−0.204042	−	0.353411i
$251$	3.50515	+	6.07109i	0.221243	+	0.383204i	0.955186	−	0.296007i	$-0.0956553\pi$
$251$	3.50515	+	6.07109i	0.221243	+	0.383204i	−0.733943	+	0.679211i	$0.762322\pi$
$252$		0			0
$253$	−1.18090	−	0.316421i	−0.0742426	−	0.0198932i
$254$	−13.7933	+	13.7933i	−0.865469	+	0.865469i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.79217			−0.236549			−0.118275	−	0.992981i	$-0.537736\pi$
$257$	−3.79217			−0.236549			−0.118275	+	0.992981i	$0.537736\pi$
$258$		0			0
$259$	−28.8221	−	16.6405i	−1.79092	−	1.03399i
$260$	−2.21645	−	1.01520i	−0.137458	−	0.0629603i
$261$		0			0
$262$	1.45713	+	5.43807i	0.0900215	+	0.335965i
$263$	7.23499	−	4.17712i	0.446129	−	0.257573i	−0.260065	−	0.965591i	$-0.583744\pi$
$263$	7.23499	−	4.17712i	0.446129	−	0.257573i	0.706194	+	0.708019i	$0.250411\pi$
$264$		0			0
$265$	4.14286	+	1.11007i	0.254494	+	0.0681914i
$266$	1.02401	−	0.274382i	0.0627859	−	0.0168234i
$267$		0			0
$268$	10.0909	−	2.70385i	0.616399	−	0.165164i
$269$	3.60032	−	2.07864i	0.219515	−	0.126737i	−0.386211	−	0.922411i	$-0.626216\pi$
$269$	3.60032	−	2.07864i	0.219515	−	0.126737i	0.605726	+	0.795674i	$0.292883\pi$
$270$		0			0
$271$	−20.1972	+	5.41182i	−1.22689	+	0.328745i	−0.813368	−	0.581749i	$-0.802369\pi$
$271$	−20.1972	+	5.41182i	−1.22689	+	0.328745i	−0.413523	+	0.910494i	$0.635702\pi$
$272$	−3.24443	+	5.61952i	−0.196723	+	0.340733i
$273$		0			0
$274$	5.88143	+	10.1869i	0.355310	+	0.615416i
$275$	2.28190	+	2.28190i	0.137604	+	0.137604i
$276$		0			0
$277$		−	15.1838i		−	0.912308i	−0.889901	−	0.456154i	$-0.849227\pi$
$277$		−	15.1838i		−	0.912308i	0.889901	−	0.456154i	$-0.150773\pi$
$278$	−2.09454	−	2.09454i	−0.125622	−	0.125622i
$279$		0			0
$280$	−0.706607	+	2.63709i	−0.0422278	+	0.157596i
$281$	−7.82648	−	29.2088i	−0.466889	−	1.74245i	−0.650550	−	0.759463i	$-0.725462\pi$
$281$	−7.82648	−	29.2088i	−0.466889	−	1.74245i	0.183662	−	0.982990i	$-0.441205\pi$
$282$		0			0
$283$			19.6844i			1.17012i	0.810991	+	0.585059i	$0.198928\pi$
$283$			19.6844i			1.17012i	−0.810991	+	0.585059i	$0.801072\pi$
$284$	5.72576	−	5.72576i	0.339761	−	0.339761i
$285$		0			0
$286$	2.52535	+	0.427550i	0.149327	+	0.0252816i
$287$			37.4107i			2.20829i
$288$		0			0
$289$	−12.5527	+	21.7419i	−0.738393	+	1.27893i
$290$	−0.869891			−0.0510817
$291$		0			0
$292$	0.513954	+	1.91810i	0.0300769	+	0.112248i
$293$	2.57173	+	9.59784i	0.150242	+	0.560712i	0.999466	+	0.0326785i	$0.0104037\pi$
$293$	2.57173	+	9.59784i	0.150242	+	0.560712i	−0.849224	+	0.528033i	$0.822930\pi$
$294$		0			0
$295$	3.36924			0.196165
$296$	−4.12122	+	7.13817i	−0.239541	+	0.414897i
$297$		0			0
$298$			23.2129i			1.34469i
$299$	2.16201	+	5.81635i	0.125033	+	0.336368i
$300$		0			0
$301$	−18.7231	+	18.7231i	−1.07918	+	1.07918i
$302$			6.89217i			0.396600i
$303$		0			0
$304$	−0.0679541	−	0.253608i	−0.00389744	−	0.0145454i
$305$	−0.577261	+	2.15437i	−0.0330539	+	0.123359i
$306$		0			0
$307$	14.4825	+	14.4825i	0.826560	+	0.826560i	0.987039	−	0.160479i	$-0.0513040\pi$
$307$	14.4825	+	14.4825i	0.826560	+	0.826560i	−0.160479	+	0.987039i	$0.551304\pi$
$308$		−	2.86831i		−	0.163437i
$309$		0			0
$310$	1.92981	+	1.92981i	0.109606	+	0.109606i
$311$	−11.3091	−	19.5879i	−0.641281	−	1.11073i	−0.985147	−	0.171712i	$-0.945070\pi$
$311$	−11.3091	−	19.5879i	−0.641281	−	1.11073i	0.343866	−	0.939019i	$-0.388263\pi$
$312$		0			0
$313$	−9.43419	+	16.3405i	−0.533252	+	0.923619i	0.465994	+	0.884788i	$0.345697\pi$
$313$	−9.43419	+	16.3405i	−0.533252	+	0.923619i	−0.999246	+	0.0388313i	$0.987636\pi$
$314$	10.5923	−	2.83820i	0.597759	−	0.160169i
$315$		0			0
$316$	−12.6316	+	7.29283i	−0.710580	+	0.410254i
$317$	18.3643	−	4.92071i	1.03144	−	0.276375i	0.296881	−	0.954915i	$-0.404054\pi$
$317$	18.3643	−	4.92071i	1.03144	−	0.276375i	0.734563	+	0.678540i	$0.237387\pi$
$318$		0			0
$319$	0.882781	−	0.236541i	0.0494263	−	0.0132437i
$320$	0.653109	+	0.175000i	0.0365099	+	0.00978280i
$321$		0			0
$322$	6.01801	−	3.47450i	0.335371	−	0.193626i
$323$	−0.440945	−	1.64563i	−0.0245348	−	0.0915652i
$324$		0			0
$325$	2.73418	−	16.1496i	0.151665	−	0.895817i
$326$	11.0840	+	6.39936i	0.613887	+	0.354428i
$327$		0			0
$328$	9.26524			0.511588
$329$	−18.9616	+	32.8425i	−1.04539	+	1.81067i
$330$		0			0
$331$	−18.7189	+	18.7189i	−1.02889	+	1.02889i	−0.0293155	+	0.999570i	$0.509333\pi$
$331$	−18.7189	+	18.7189i	−1.02889	+	1.02889i	−0.999570	+	0.0293155i	$0.990667\pi$
$332$	3.90968	+	1.04760i	0.214572	+	0.0574943i
$333$		0			0
$334$	0.420016	+	0.727488i	0.0229822	+	0.0398064i
$335$	−3.53181	−	6.11728i	−0.192964	−	0.334223i
$336$		0			0
$337$	19.6500	−	11.3449i	1.07040	−	0.617996i	0.142110	−	0.989851i	$-0.454611\pi$
$337$	19.6500	−	11.3449i	1.07040	−	0.617996i	0.928291	+	0.371854i	$0.121278\pi$
$338$	−5.65423	−	11.7060i	−0.307549	−	0.636721i
$339$		0			0
$340$	4.23794	+	1.13555i	0.229834	+	0.0615839i
$341$	−2.48316	−	1.43365i	−0.134471	−	0.0776368i
$342$		0			0
$343$	−6.57658	+	6.57658i	−0.355102	+	0.355102i
$344$	4.63701	+	4.63701i	0.250011	+	0.250011i
$345$		0			0
$346$	5.51723	−	20.5906i	0.296608	−	1.10696i
$347$	−14.3861	−	8.30581i	−0.772286	−	0.445879i	0.0614037	−	0.998113i	$-0.480442\pi$
$347$	−14.3861	−	8.30581i	−0.772286	−	0.445879i	−0.833689	+	0.552234i	$0.813776\pi$
$348$		0			0
$349$	−0.581079	+	2.16862i	−0.0311044	+	0.116083i	−0.979733	−	0.200310i	$-0.935805\pi$
$349$	−0.581079	+	2.16862i	−0.0311044	+	0.116083i	0.948628	+	0.316393i	$0.102472\pi$
$350$	−18.3428			−0.980463
$351$		0			0
$352$	−0.710373			−0.0378630
$353$	−2.32242	+	8.66739i	−0.123610	+	0.461319i	−0.999786	−	0.0206720i	$-0.993419\pi$
$353$	−2.32242	+	8.66739i	−0.123610	+	0.461319i	0.876176	+	0.481991i	$0.160086\pi$
$354$		0			0
$355$	−4.74155	−	2.73754i	−0.251655	−	0.145293i
$356$	−2.64065	+	9.85503i	−0.139954	+	0.522315i
$357$		0			0
$358$	0.170790	+	0.170790i	0.00902656	+	0.00902656i
$359$	−25.1620	+	25.1620i	−1.32800	+	1.32800i	−0.420885	+	0.907114i	$0.638280\pi$
$359$	−25.1620	+	25.1620i	−1.32800	+	1.32800i	−0.907114	+	0.420885i	$0.861720\pi$
$360$		0			0
$361$	−16.3948	−	9.46553i	−0.862883	−	0.498186i
$362$	−1.68025	−	0.450221i	−0.0883119	−	0.0236631i
$363$		0			0
$364$	−11.8683	+	8.43144i	−0.622065	+	0.441928i
$365$	1.16279	−	0.671335i	0.0608631	−	0.0351393i
$366$		0			0
$367$	−11.5999	−	20.0916i	−0.605509	−	1.04877i	−0.991971	−	0.126467i	$-0.959636\pi$
$367$	−11.5999	−	20.0916i	−0.605509	−	1.04877i	0.386462	−	0.922305i	$-0.373697\pi$
$368$	−0.860504	−	1.49044i	−0.0448569	−	0.0776944i
$369$		0			0
$370$	5.38322	+	1.44243i	0.279860	+	0.0749883i
$371$	18.1108	−	18.1108i	0.940268	−	0.940268i
$372$		0			0
$373$	15.0231	−	26.0208i	0.777866	−	1.34730i	−0.155303	−	0.987867i	$-0.549635\pi$
$373$	15.0231	−	26.0208i	0.777866	−	1.34730i	0.933169	−	0.359437i	$-0.117031\pi$
$374$	−4.60952			−0.238352
$375$		0			0
$376$	8.13386	+	4.69609i	0.419472	+	0.242182i
$377$	−3.57369	−	2.95738i	−0.184054	−	0.152313i
$378$		0			0
$379$	7.34807	+	27.4234i	0.377445	+	1.40864i	0.849739	+	0.527203i	$0.176759\pi$
$379$	7.34807	+	27.4234i	0.377445	+	1.40864i	−0.472294	+	0.881441i	$0.656574\pi$
$380$	−0.153742	+	0.0887629i	−0.00788679	+	0.00455344i
$381$		0			0
$382$	8.16051	+	2.18660i	0.417528	+	0.111876i
$383$	3.58594	−	0.960849i	0.183233	−	0.0490971i	−0.166036	−	0.986120i	$-0.553097\pi$
$383$	3.58594	−	0.960849i	0.183233	−	0.0490971i	0.349269	+	0.937023i	$0.386430\pi$
$384$		0			0
$385$	−1.87332	+	0.501955i	−0.0954732	+	0.0255820i
$386$	−0.0464751	+	0.0268324i	−0.00236552	+	0.00136573i
$387$		0			0
$388$	−1.94418	+	0.520942i	−0.0987009	+	0.0264468i
$389$	1.01593	−	1.75965i	0.0515099	−	0.0892178i	−0.839121	−	0.543945i	$-0.816930\pi$
$389$	1.01593	−	1.75965i	0.0515099	−	0.0892178i	0.890631	+	0.454727i	$0.150263\pi$
$390$		0			0
$391$	−5.58369	−	9.67124i	−0.282379	−	0.489096i
$392$	6.57852	+	6.57852i	0.332265	+	0.332265i
$393$		0			0
$394$			2.66006i			0.134012i
$395$	6.97354	+	6.97354i	0.350877	+	0.350877i
$396$		0			0
$397$	−2.23806	+	8.35257i	−0.112325	+	0.419203i	−0.999073	−	0.0430503i	$-0.986292\pi$
$397$	−2.23806	+	8.35257i	−0.112325	+	0.419203i	0.886748	+	0.462254i	$0.152959\pi$
$398$	−0.451537	−	1.68516i	−0.0226335	−	0.0844694i
$399$		0			0
$400$			4.54282i			0.227141i
$401$	−27.8080	+	27.8080i	−1.38866	+	1.38866i	−0.560528	+	0.828136i	$0.689402\pi$
$401$	−27.8080	+	27.8080i	−1.38866	+	1.38866i	−0.828136	+	0.560528i	$0.810598\pi$
$402$		0			0
$403$	1.36724	+	14.4889i	0.0681072	+	0.721742i
$404$			14.5201i			0.722404i
$405$		0			0
$406$	−2.59736	+	4.49876i	−0.128905	+	0.223270i
$407$	−5.85521			−0.290232
$408$		0			0
$409$	−7.69913	−	28.7335i	−0.380697	−	1.42078i	−0.844839	−	0.535021i	$-0.820304\pi$
$409$	−7.69913	−	28.7335i	−0.380697	−	1.42078i	0.464141	−	0.885761i	$-0.346363\pi$
$410$	−1.62142	−	6.05122i	−0.0800761	−	0.298848i
$411$		0			0
$412$	−19.2975			−0.950719
$413$	10.0600	−	17.4245i	0.495023	−	0.857404i
$414$		0			0
$415$		−	2.73678i		−	0.134343i
$416$	2.08815	+	2.93932i	0.102380	+	0.144112i
$417$		0			0
$418$	0.131884	−	0.131884i	0.00645064	−	0.00645064i
$419$		−	14.0759i		−	0.687655i	−0.939033	−	0.343827i	$-0.888276\pi$
$419$		−	14.0759i		−	0.687655i	0.939033	−	0.343827i	$-0.111724\pi$
$420$		0			0
$421$	−1.25055	−	4.66713i	−0.0609482	−	0.227462i	0.928733	−	0.370750i	$-0.120899\pi$
$421$	−1.25055	−	4.66713i	−0.0609482	−	0.227462i	−0.989681	+	0.143288i	$0.954233\pi$
$422$	0.337043	−	1.25786i	0.0164070	−	0.0612318i
$423$		0			0
$424$	−4.48538	−	4.48538i	−0.217829	−	0.217829i
$425$			29.4778i			1.42988i
$426$		0			0
$427$	9.41799	+	9.41799i	0.455769	+	0.455769i
$428$	−6.65169	−	11.5211i	−0.321522	−	0.556892i
$429$		0			0
$430$	2.21699	−	3.83995i	0.106913	−	0.185179i
$431$	16.0936	−	4.31228i	0.775203	−	0.207715i	0.150534	−	0.988605i	$-0.451901\pi$
$431$	16.0936	−	4.31228i	0.775203	−	0.207715i	0.624669	+	0.780890i	$0.285234\pi$
$432$		0			0
$433$	5.53229	−	3.19407i	0.265865	−	0.153497i	−0.361142	−	0.932511i	$-0.617613\pi$
$433$	5.53229	−	3.19407i	0.265865	−	0.153497i	0.627007	+	0.779014i	$0.284280\pi$
$434$	15.7424	−	4.21817i	0.755660	−	0.202478i
$435$		0			0
$436$	−10.4312	+	2.79503i	−0.499564	+	0.133858i
$437$	0.436462	+	0.116950i	0.0208788	+	0.00559446i
$438$		0			0
$439$	−11.5041	+	6.64188i	−0.549060	+	0.317000i	−0.748743	−	0.662861i	$-0.769342\pi$
$439$	−11.5041	+	6.64188i	−0.549060	+	0.317000i	0.199683	+	0.979861i	$0.436009\pi$
$440$	0.124315	+	0.463951i	0.00592650	+	0.0221180i
$441$		0			0
$442$	13.5497	+	19.0729i	0.644496	+	0.907203i
$443$	−19.0340	−	10.9893i	−0.904332	−	0.522117i	−0.0257292	−	0.999669i	$-0.508191\pi$
$443$	−19.0340	−	10.9893i	−0.904332	−	0.522117i	−0.878603	+	0.477552i	$0.841524\pi$
$444$		0			0
$445$	6.89852			0.327021
$446$	−9.54338	+	16.5296i	−0.451892	+	0.782700i
$447$		0			0
$448$	2.85512	−	2.85512i	0.134892	−	0.134892i
$449$	8.04520	+	2.15570i	0.379676	+	0.101734i	0.443609	−	0.896220i	$-0.353698\pi$
$449$	8.04520	+	2.15570i	0.379676	+	0.101734i	−0.0639330	+	0.997954i	$0.520364\pi$
$450$		0			0
$451$	3.29089	+	5.69999i	0.154962	+	0.268402i
$452$	7.60612	+	13.1742i	0.357762	+	0.619662i
$453$		0			0
$454$	14.2332	−	8.21756i	0.667998	−	0.385669i
$455$	7.58360	+	6.27576i	0.355525	+	0.294212i
$456$		0			0
$457$	−13.1545	−	3.52474i	−0.615343	−	0.164881i	−0.0623330	−	0.998055i	$-0.519854\pi$
$457$	−13.1545	−	3.52474i	−0.615343	−	0.164881i	−0.553010	+	0.833175i	$0.686521\pi$
$458$	11.7812	+	6.80189i	0.550500	+	0.317831i
$459$		0			0
$460$	−0.822829	+	0.822829i	−0.0383646	+	0.0383646i
$461$	25.2856	+	25.2856i	1.17767	+	1.17767i	0.980337	+	0.197331i	$0.0632275\pi$
$461$	25.2856	+	25.2856i	1.17767	+	1.17767i	0.197331	+	0.980337i	$0.436773\pi$
$462$		0			0
$463$	−3.23386	+	12.0689i	−0.150290	+	0.560891i	0.849172	+	0.528116i	$0.177101\pi$
$463$	−3.23386	+	12.0689i	−0.150290	+	0.560891i	−0.999463	+	0.0327754i	$0.989565\pi$
$464$	1.11417	+	0.643269i	0.0517243	+	0.0298630i
$465$		0			0
$466$	−1.00840	+	3.76342i	−0.0467134	+	0.174337i
$467$	11.9847			0.554587			0.277293	−	0.960785i	$-0.410563\pi$
$467$	11.9847			0.554587			0.277293	+	0.960785i	$0.410563\pi$
$468$		0			0
$469$	−42.1818			−1.94777
$470$	1.64363	−	6.13412i	0.0758151	−	0.282946i
$471$		0			0
$472$	−4.31540	−	2.49150i	−0.198632	−	0.114681i
$473$	−1.20569	+	4.49970i	−0.0554377	+	0.206896i
$474$		0			0
$475$	−0.843394	−	0.843394i	−0.0386976	−	0.0386976i
$476$	18.5265	−	18.5265i	0.849160	−	0.849160i
$477$		0			0
$478$	−1.36512	−	0.788151i	−0.0624390	−	0.0360492i
$479$	−13.8839	−	3.72019i	−0.634373	−	0.169980i	−0.0727198	−	0.997352i	$-0.523168\pi$
$479$	−13.8839	−	3.72019i	−0.634373	−	0.169980i	−0.561653	+	0.827373i	$0.689835\pi$
$480$		0			0
$481$	17.2115	+	24.2272i	0.784776	+	1.10467i
$482$	−4.47282	+	2.58239i	−0.203732	+	0.117624i
$483$		0			0
$484$	5.24768	+	9.08926i	0.238531	+	0.413148i
$485$	0.680464	+	1.17860i	0.0308983	+	0.0535174i
$486$		0			0
$487$	21.7160	+	5.81879i	0.984047	+	0.263675i	0.714748	−	0.699382i	$-0.246541\pi$
$487$	21.7160	+	5.81879i	0.984047	+	0.263675i	0.269299	+	0.963057i	$0.413208\pi$
$488$	2.33248	−	2.33248i	0.105587	−	0.105587i
$489$		0			0
$490$	3.14525	−	5.44773i	0.142088	−	0.246103i
$491$	43.3748			1.95748			0.978738	−	0.205114i	$-0.0657565\pi$
$491$	43.3748			1.95748			0.978738	+	0.205114i	$0.0657565\pi$
$492$		0			0
$493$	7.22973	+	4.17409i	0.325611	+	0.187991i
$494$	−0.933371	−	0.158023i	−0.0419944	−	0.00710979i
$495$		0			0
$496$	−1.04468	−	3.89881i	−0.0469076	−	0.175062i
$497$	−28.3151	+	16.3477i	−1.27011	+	0.733296i
$498$		0			0
$499$	−27.8176	−	7.45370i	−1.24529	−	0.333673i	−0.424772	−	0.905300i	$-0.639646\pi$
$499$	−27.8176	−	7.45370i	−1.24529	−	0.333673i	−0.820514	+	0.571627i	$0.806313\pi$
$500$	6.23251	−	1.66999i	0.278726	−	0.0746844i
$501$		0			0
$502$	−6.77143	+	1.81440i	−0.302224	+	0.0809805i
$503$	13.3453	−	7.70492i	0.595038	−	0.343545i	−0.172049	−	0.985088i	$-0.555039\pi$
$503$	13.3453	−	7.70492i	0.595038	−	0.343545i	0.767087	+	0.641543i	$0.221705\pi$
$504$		0			0
$505$	9.48323	−	2.54102i	0.421998	−	0.113074i
$506$	0.611279	−	1.05877i	0.0271747	−	0.0470679i
$507$		0			0
$508$	−9.75334	−	16.8933i	−0.432735	−	0.749518i
$509$	4.97121	+	4.97121i	0.220345	+	0.220345i	0.808644	−	0.588299i	$-0.200202\pi$
$509$	4.97121	+	4.97121i	0.220345	+	0.220345i	−0.588299	+	0.808644i	$0.700202\pi$
$510$		0			0
$511$		−	8.01802i		−	0.354696i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	0.981486	−	3.66296i	0.0432915	−	0.161566i
$515$	3.37706	+	12.6034i	0.148811	+	0.555371i
$516$		0			0
$517$			6.67195i			0.293432i
$518$	23.5332	−	23.5332i	1.03399	−	1.03399i
$519$		0			0
$520$	1.55427	−	1.87817i	0.0681593	−	0.0823634i
$521$		−	42.4222i		−	1.85855i	−0.369391	−	0.929274i	$-0.620434\pi$
$521$		−	42.4222i		−	1.85855i	0.369391	−	0.929274i	$-0.379566\pi$
$522$		0			0
$523$	1.58272	−	2.74135i	0.0692074	−	0.119871i	−0.829345	−	0.558737i	$-0.811286\pi$
$523$	1.58272	−	2.74135i	0.0692074	−	0.119871i	0.898553	+	0.438866i	$0.144620\pi$
$524$	−5.62990			−0.245943
$525$		0			0
$526$	2.16224	+	8.06959i	0.0942781	+	0.351851i
$527$	−6.77880	−	25.2988i	−0.295289	−	1.10203i
$528$		0			0
$529$	−20.0381			−0.871223
$530$	−2.14450	+	3.71438i	−0.0931511	+	0.161342i
$531$		0			0
$532$			1.06013i			0.0459625i
$533$	13.9113	−	30.3720i	0.602566	−	1.31556i
$534$		0			0
$535$	−6.36047	+	6.36047i	−0.274987	+	0.274987i
$536$			10.4469i			0.451236i
$537$		0			0
$538$	1.07599	+	4.01563i	0.0463890	+	0.173126i
$539$	−1.71051	+	6.38372i	−0.0736770	+	0.274966i
$540$		0			0
$541$	−5.91918	−	5.91918i	−0.254486	−	0.254486i	0.568321	−	0.822807i	$-0.307593\pi$
$541$	−5.91918	−	5.91918i	−0.254486	−	0.254486i	−0.822807	+	0.568321i	$0.807593\pi$
$542$		−	20.9097i		−	0.898147i
$543$		0			0
$544$	−4.58832	−	4.58832i	−0.196723	−	0.196723i
$545$	3.65092	+	6.32358i	0.156388	+	0.270872i
$546$		0			0
$547$	16.9449	−	29.3493i	0.724510	−	1.25489i	−0.234666	−	0.972076i	$-0.575400\pi$
$547$	16.9449	−	29.3493i	0.724510	−	1.25489i	0.959176	−	0.282811i	$-0.0912670\pi$
$548$	−11.3621	+	3.04445i	−0.485363	+	0.130053i
$549$		0			0
$550$	−2.79475	+	1.61355i	−0.119169	+	0.0688020i
$551$	−0.326277	+	0.0874256i	−0.0138999	+	0.00372445i
$552$		0			0
$553$	56.8865	−	15.2427i	2.41906	−	0.648185i
$554$	14.6665	+	3.92987i	0.623118	+	0.166964i
$555$		0			0
$556$	2.56527	−	1.48106i	0.108792	−	0.0628110i
$557$	−2.17805	−	8.12858i	−0.0922868	−	0.344419i	0.904307	−	0.426882i	$-0.140388\pi$
$557$	−2.17805	−	8.12858i	−0.0922868	−	0.344419i	−0.996594	+	0.0824630i	$0.973721\pi$
$558$		0			0
$559$	22.1626	−	8.23812i	0.937378	−	0.348436i
$560$	−2.36435	−	1.36506i	−0.0999121	−	0.0576843i
$561$		0			0
$562$	30.2392			1.27556
$563$	−15.9438	+	27.6155i	−0.671951	+	1.16385i	0.305400	+	0.952224i	$0.401210\pi$
$563$	−15.9438	+	27.6155i	−0.671951	+	1.16385i	−0.977350	+	0.211628i	$0.932123\pi$
$564$		0			0
$565$	7.27311	−	7.27311i	0.305982	−	0.305982i
$566$	−19.0137	−	5.09470i	−0.799205	−	0.214146i
$567$		0			0
$568$	4.04872	+	7.01259i	0.169881	+	0.294242i
$569$	16.2401	+	28.1287i	0.680821	+	1.17922i	0.974731	+	0.223383i	$0.0717100\pi$
$569$	16.2401	+	28.1287i	0.680821	+	1.17922i	−0.293910	+	0.955833i	$0.594957\pi$
$570$		0			0
$571$	27.2576	−	15.7372i	1.14070	−	0.658582i	0.194094	−	0.980983i	$-0.437823\pi$
$571$	27.2576	−	15.7372i	1.14070	−	0.658582i	0.946603	+	0.322401i	$0.104490\pi$
$572$	−1.06659	+	2.32864i	−0.0445964	+	0.0973655i
$573$		0			0
$574$	−36.1360	−	9.68261i	−1.50829	−	0.404144i
$575$	−6.77079	−	3.90912i	−0.282361	−	0.163021i
$576$		0			0
$577$	3.78292	−	3.78292i	0.157485	−	0.157485i	−0.623966	−	0.781451i	$-0.714480\pi$
$577$	3.78292	−	3.78292i	0.157485	−	0.157485i	0.781451	+	0.623966i	$0.214480\pi$
$578$	−17.7522	−	17.7522i	−0.738393	−	0.738393i
$579$		0			0
$580$	0.225144	−	0.840250i	0.00934861	−	0.0348895i
$581$	−14.1536	−	8.17160i	−0.587192	−	0.339015i
$582$		0			0
$583$	1.16626	−	4.35256i	0.0483017	−	0.180265i
$584$	−1.98576			−0.0821715
$585$		0			0
$586$	−9.93642			−0.410470
$587$	−11.2947	+	42.1526i	−0.466184	+	1.73982i	0.186750	+	0.982408i	$0.440205\pi$
$587$	−11.2947	+	42.1526i	−0.466184	+	1.73982i	−0.652934	+	0.757415i	$0.726462\pi$
$588$		0			0
$589$	0.917779	+	0.529880i	0.0378164	+	0.0218333i
$590$	−0.872025	+	3.25444i	−0.0359007	+	0.133983i
$591$		0			0
$592$	−5.82829	−	5.82829i	−0.239541	−	0.239541i
$593$	−3.43157	+	3.43157i	−0.140918	+	0.140918i	−0.774047	−	0.633129i	$-0.781770\pi$
$593$	−3.43157	+	3.43157i	−0.140918	+	0.140918i	0.633129	+	0.774047i	$0.281770\pi$
$594$		0			0
$595$	−15.3420	−	8.85768i	−0.628959	−	0.363130i
$596$	−22.4219	−	6.00794i	−0.918438	−	0.246095i
$597$		0			0
$598$	−6.17774	+	0.582962i	−0.252626	+	0.0238391i
$599$	−6.49912	+	3.75227i	−0.265547	+	0.153313i	−0.626862	−	0.779130i	$-0.715661\pi$
$599$	−6.49912	+	3.75227i	−0.265547	+	0.153313i	0.361315	+	0.932444i	$0.382328\pi$
$600$		0			0
$601$	−8.71312	−	15.0916i	−0.355416	−	0.615598i	0.631773	−	0.775153i	$-0.282327\pi$
$601$	−8.71312	−	15.0916i	−0.355416	−	0.615598i	−0.987189	+	0.159555i	$0.948994\pi$
$602$	−13.2392	−	22.9310i	−0.539590	−	0.934597i
$603$		0			0
$604$	−6.65733	−	1.78383i	−0.270883	−	0.0725828i
$605$	5.01793	−	5.01793i	0.204008	−	0.204008i
$606$		0			0
$607$	15.4563	−	26.7710i	0.627350	−	1.08660i	−0.360731	−	0.932670i	$-0.617473\pi$
$607$	15.4563	−	26.7710i	0.627350	−	1.08660i	0.988081	−	0.153933i	$-0.0491939\pi$
$608$	0.262555			0.0106480
$609$		0			0
$610$	−1.93155	−	1.11518i	−0.0782063	−	0.0451524i
$611$	27.6066	−	19.6123i	1.11684	−	0.793429i
$612$		0			0
$613$	11.1528	+	41.6227i	0.450456	+	1.68113i	0.701113	+	0.713050i	$0.252687\pi$
$613$	11.1528	+	41.6227i	0.450456	+	1.68113i	−0.250657	+	0.968076i	$0.580646\pi$
$614$	−17.7374	+	10.2407i	−0.715822	+	0.413280i
$615$		0			0
$616$	2.77058	+	0.742373i	0.111630	+	0.0299111i
$617$	12.2280	−	3.27648i	0.492280	−	0.131906i	−0.00413506	−	0.999991i	$-0.501316\pi$
$617$	12.2280	−	3.27648i	0.492280	−	0.131906i	0.496415	+	0.868086i	$0.334650\pi$
$618$		0			0
$619$	−1.08632	+	0.291078i	−0.0436628	+	0.0116994i	−0.280584	−	0.959829i	$-0.590528\pi$
$619$	−1.08632	+	0.291078i	−0.0436628	+	0.0116994i	0.236922	+	0.971529i	$0.423862\pi$
$620$	−2.36353	+	1.36458i	−0.0949215	+	0.0548030i
$621$		0			0
$622$	21.8475	−	5.85403i	0.876006	−	0.234725i
$623$	20.5979	−	35.6767i	0.825239	−	1.42936i
$624$		0			0
$625$	9.17568	+	15.8927i	0.367027	+	0.635710i
$626$	−13.3420	−	13.3420i	−0.533252	−	0.533252i
$627$		0			0
$628$			10.9660i			0.437590i
$629$	−37.8190	−	37.8190i	−1.50794	−	1.50794i
$630$		0			0
$631$	−3.51015	+	13.1000i	−0.139737	+	0.521505i	0.860197	+	0.509962i	$0.170341\pi$
$631$	−3.51015	+	13.1000i	−0.139737	+	0.521505i	−0.999933	+	0.0115421i	$0.996326\pi$
$632$	−3.77505	−	14.0887i	−0.150163	−	0.560417i
$633$		0			0
$634$			19.0122i			0.755069i
$635$	−9.32632	+	9.32632i	−0.370104	+	0.370104i
$636$		0			0
$637$	31.4421	−	11.6874i	1.24578	−	0.463073i
$638$			0.913923i			0.0361825i
$639$		0			0
$640$	−0.338074	+	0.585562i	−0.0133636	+	0.0231464i
$641$	47.3161			1.86887			0.934436	−	0.356130i	$-0.115904\pi$
$641$	47.3161			1.86887			0.934436	+	0.356130i	$0.115904\pi$
$642$		0			0
$643$	2.46650	+	9.20510i	0.0972692	+	0.363014i	0.997354	−	0.0727016i	$-0.0231621\pi$
$643$	2.46650	+	9.20510i	0.0972692	+	0.363014i	−0.900084	+	0.435715i	$0.856495\pi$
$644$	1.79853	+	6.71222i	0.0708722	+	0.264498i
$645$		0			0
$646$	1.70368			0.0670304
$647$	−8.42061	+	14.5849i	−0.331048	+	0.573392i	−0.982718	−	0.185111i	$-0.940736\pi$
$647$	−8.42061	+	14.5849i	−0.331048	+	0.573392i	0.651669	+	0.758503i	$0.274069\pi$
$648$		0			0
$649$		−	3.53979i		−	0.138949i
$650$	14.8916	+	6.82083i	0.584098	+	0.267535i
$651$		0			0
$652$	−9.05006	+	9.05006i	−0.354428	+	0.354428i
$653$		−	29.2126i		−	1.14318i	−0.820540	−	0.571589i	$-0.806327\pi$
$653$		−	29.2126i		−	1.14318i	0.820540	−	0.571589i	$-0.193673\pi$
$654$		0			0
$655$	0.985233	+	3.67694i	0.0384962	+	0.143670i
$656$	−2.39802	+	8.94954i	−0.0936270	+	0.349421i
$657$		0			0
$658$	−26.8158	−	26.8158i	−1.04539	−	1.04539i
$659$			14.3659i			0.559615i	0.960056	+	0.279807i	$0.0902706\pi$
$659$			14.3659i			0.559615i	−0.960056	+	0.279807i	$0.909729\pi$
$660$		0			0
$661$	−29.3026	−	29.3026i	−1.13974	−	1.13974i	−0.988496	−	0.151245i	$-0.951672\pi$
$661$	−29.3026	−	29.3026i	−1.13974	−	1.13974i	−0.151245	−	0.988496i	$-0.548328\pi$
$662$	−13.2363	−	22.9259i	−0.514443	−	0.891041i
$663$		0			0
$664$	−2.02380	+	3.50533i	−0.0785387	+	0.136033i
$665$	0.692380	−	0.185523i	0.0268494	−	0.00719426i
$666$		0			0
$667$	−1.91750	+	1.10707i	−0.0742460	+	0.0428660i
$668$	−0.811408	+	0.217416i	−0.0313943	+	0.00841208i
$669$		0			0
$670$	6.82294	−	1.82820i	0.263593	−	0.0706296i
$671$	2.26342	+	0.606480i	0.0873782	+	0.0234129i
$672$		0			0
$673$	34.2005	−	19.7457i	1.31833	−	0.761140i	0.334873	−	0.942263i	$-0.391307\pi$
$673$	34.2005	−	19.7457i	1.31833	−	0.761140i	0.983460	+	0.181124i	$0.0579734\pi$
$674$	5.87256	+	21.9167i	0.226202	+	0.844199i
$675$		0			0
$676$	12.7705	−	2.43183i	0.491174	−	0.0935321i
$677$	−14.7062	−	8.49064i	−0.565206	−	0.326322i	0.190026	−	0.981779i	$-0.439143\pi$
$677$	−14.7062	−	8.49064i	−0.565206	−	0.326322i	−0.755232	+	0.655457i	$0.772476\pi$
$678$		0			0
$679$	8.12705			0.311888
$680$	−2.19372	+	3.79963i	−0.0841252	+	0.145709i
$681$		0			0
$682$	2.02749	−	2.02749i	0.0776368	−	0.0776368i
$683$	−1.34228	−	0.359662i	−0.0513607	−	0.0137621i	0.233047	−	0.972465i	$-0.425130\pi$
$683$	−1.34228	−	0.359662i	−0.0513607	−	0.0137621i	−0.284408	+	0.958703i	$0.591797\pi$
$684$		0			0
$685$	3.97672	+	6.88788i	0.151943	+	0.263173i
$686$	−4.65034	−	8.05463i	−0.177551	−	0.307527i
$687$		0			0
$688$	−5.67915	+	3.27886i	−0.216516	+	0.125005i
$689$	−21.4379	+	7.96874i	−0.816719	+	0.303585i
$690$		0			0
$691$	9.95590	+	2.66767i	0.378740	+	0.101483i	0.443166	−	0.896439i	$-0.353855\pi$
$691$	9.95590	+	2.66767i	0.378740	+	0.101483i	−0.0644263	+	0.997922i	$0.520522\pi$
$692$	18.4610	+	10.6585i	0.701782	+	0.405174i
$693$		0			0
$694$	11.7462	−	11.7462i	0.445879	−	0.445879i
$695$	−1.41622	−	1.41622i	−0.0537202	−	0.0537202i
$696$		0			0
$697$	−15.5604	+	58.0723i	−0.589393	+	2.19965i
$698$	−1.94433	−	1.12256i	−0.0735939	−	0.0424895i
$699$		0			0
$700$	4.74746	−	17.7178i	0.179437	−	0.669669i
$701$	−26.3023			−0.993423			−0.496712	−	0.867916i	$-0.665459\pi$
$701$	−26.3023			−0.993423			−0.496712	+	0.867916i	$0.665459\pi$
$702$		0			0
$703$	2.16409			0.0816202
$704$	0.183858	−	0.686168i	0.00692942	−	0.0258609i
$705$		0			0
$706$	−7.77097	−	4.48657i	−0.292464	−	0.168854i
$707$	15.1742	−	56.6310i	0.570685	−	2.12983i
$708$		0			0
$709$	−22.9263	−	22.9263i	−0.861016	−	0.861016i	0.130440	−	0.991456i	$-0.458361\pi$
$709$	−22.9263	−	22.9263i	−0.861016	−	0.861016i	−0.991456	+	0.130440i	$0.958361\pi$
$710$	3.87146	−	3.87146i	0.145293	−	0.145293i
$711$		0			0
$712$	−8.83578	−	5.10134i	−0.331135	−	0.191181i
$713$	6.70988	+	1.79791i	0.251287	+	0.0673321i
$714$		0			0
$715$	1.70751	+	0.289087i	0.0638573	+	0.0108113i
$716$	−0.209175	+	0.120767i	−0.00781723	+	0.00451328i
$717$		0			0
$718$	−17.7922	−	30.8170i	−0.663999	−	1.15008i
$719$	8.65353	+	14.9884i	0.322722	+	0.558971i	0.981049	−	0.193761i	$-0.0620687\pi$
$719$	8.65353	+	14.9884i	0.322722	+	0.558971i	−0.658326	+	0.752733i	$0.728735\pi$
$720$		0			0
$721$	75.2634	+	20.1668i	2.80296	+	0.751050i
$722$	13.3863	−	13.3863i	0.498186	−	0.498186i
$723$		0			0
$724$	0.869761	−	1.50647i	0.0323244	−	0.0559875i
$725$	5.84452			0.217060
$726$		0			0
$727$	−8.04825	−	4.64666i	−0.298493	−	0.172335i	0.343273	−	0.939236i	$-0.388464\pi$
$727$	−8.04825	−	4.64666i	−0.298493	−	0.172335i	−0.641766	+	0.766901i	$0.721798\pi$
$728$	−5.07242	−	13.6461i	−0.187996	−	0.505757i
$729$		0			0
$730$	0.347509	+	1.29692i	0.0128619	+	0.0480012i
$731$	−36.8512	+	21.2761i	−1.36299	+	0.786924i
$732$		0			0
$733$	−34.0522	−	9.12426i	−1.25775	−	0.337012i	−0.432422	−	0.901671i	$-0.642341\pi$
$733$	−34.0522	−	9.12426i	−1.25775	−	0.337012i	−0.825324	+	0.564659i	$0.809008\pi$
$734$	22.4093	−	6.00454i	0.827141	−	0.221632i
$735$		0			0
$736$	1.66237	−	0.445430i	0.0612756	−	0.0164188i
$737$	−6.42692	+	3.71058i	−0.236739	+	0.136681i
$738$		0			0
$739$	32.7392	−	8.77244i	1.20433	−	0.322699i	0.399795	−	0.916604i	$-0.369081\pi$
$739$	32.7392	−	8.77244i	1.20433	−	0.322699i	0.804535	+	0.593905i	$0.202415\pi$
$740$	−2.78656	+	4.82646i	−0.102436	+	0.177424i
$741$		0			0
$742$	12.8063	+	22.1812i	0.470134	+	0.814296i
$743$	−7.56862	−	7.56862i	−0.277666	−	0.277666i	0.554511	−	0.832177i	$-0.312905\pi$
$743$	−7.56862	−	7.56862i	−0.277666	−	0.277666i	−0.832177	+	0.554511i	$0.812905\pi$
$744$		0			0
$745$			15.6954i			0.575033i
$746$	21.2459	+	21.2459i	0.777866	+	0.777866i
$747$		0			0
$748$	1.19303	−	4.45245i	0.0436215	−	0.162798i
$749$	13.9027	+	51.8854i	0.507992	+	1.89585i
$750$		0			0
$751$		−	14.0001i		−	0.510871i	−0.966826	−	0.255436i	$-0.917781\pi$
$751$		−	14.0001i		−	0.510871i	0.966826	−	0.255436i	$-0.0822189\pi$
$752$	−6.64127	+	6.64127i	−0.242182	+	0.242182i
$753$		0			0
$754$	3.78155	−	2.68649i	0.137716	−	0.0978362i
$755$			4.66013i			0.169600i
$756$		0			0
$757$	−4.20269	+	7.27928i	−0.152749	+	0.264570i	−0.932237	−	0.361848i	$-0.882146\pi$
$757$	−4.20269	+	7.27928i	−0.152749	+	0.264570i	0.779488	+	0.626417i	$0.215479\pi$
$758$	−28.3908			−1.03120
$759$		0			0
$760$	−0.0459471	−	0.171477i	−0.00166667	−	0.00622012i
$761$	7.60908	+	28.3975i	0.275829	+	1.02941i	0.955284	+	0.295690i	$0.0955496\pi$
$761$	7.60908	+	28.3975i	0.275829	+	1.02941i	−0.679455	+	0.733717i	$0.737784\pi$
$762$		0			0
$763$	43.6043			1.57858
$764$	−4.22419	+	7.31652i	−0.152826	+	0.264702i
$765$		0			0
$766$			3.71244i			0.134136i
$767$	−14.6466	+	10.4053i	−0.528859	+	0.375712i
$768$		0			0
$769$	−25.7163	+	25.7163i	−0.927354	+	0.927354i	−0.997534	−	0.0701804i	$-0.977643\pi$
$769$	−25.7163	+	25.7163i	−0.927354	+	0.927354i	0.0701804	+	0.997534i	$0.477643\pi$
$770$		−	1.93940i		−	0.0698912i
$771$		0			0
$772$	−0.0138895	−	0.0518362i	−0.000499893	−	0.00186563i
$773$	−1.91671	+	7.15325i	−0.0689391	+	0.257284i	−0.991791	−	0.127871i	$-0.959186\pi$
$773$	−1.91671	+	7.15325i	−0.0689391	+	0.257284i	0.922852	+	0.385156i	$0.125852\pi$
$774$		0			0
$775$	−12.9658	−	12.9658i	−0.465745	−	0.465745i
$776$		−	2.01277i		−	0.0722541i
$777$		0			0
$778$	1.43675	+	1.43675i	0.0515099	+	0.0515099i
$779$	−1.21632	−	2.10672i	−0.0435790	−	0.0754811i
$780$		0			0
$781$	−2.87610	+	4.98156i	−0.102915	+	0.178254i
$782$	10.7869	−	2.89033i	0.385738	−	0.103358i
$783$		0			0
$784$	−8.05701	+	4.65172i	−0.287750	+	0.166133i
$785$	7.16198	−	1.91905i	0.255622	−	0.0684937i
$786$		0			0
$787$	11.7345	−	3.14426i	0.418291	−	0.112081i	−0.0435334	−	0.999052i	$-0.513862\pi$
$787$	11.7345	−	3.14426i	0.418291	−	0.112081i	0.461825	+	0.886971i	$0.347195\pi$
$788$	−2.56942	−	0.688475i	−0.0915319	−	0.0245259i
$789$		0			0
$790$	−8.54080	+	4.93103i	−0.303868	+	0.175438i
$791$	−15.8975	−	59.3303i	−0.565250	−	2.10954i
$792$		0			0
$793$	−4.14390	−	11.1481i	−0.147154	−	0.395881i
$794$	−7.48871	−	4.32361i	−0.265764	−	0.153439i
$795$		0			0
$796$	1.74460			0.0618359
$797$	16.2014	−	28.0616i	0.573883	−	0.993994i	−0.422279	−	0.906466i	$-0.638770\pi$
$797$	16.2014	−	28.0616i	0.573883	−	0.993994i	0.996162	−	0.0875286i	$-0.0278969\pi$
$798$		0			0
$799$	−43.0943	+	43.0943i	−1.52457	+	1.52457i
$800$	−4.38803	−	1.17577i	−0.155140	−	0.0415697i
$801$		0			0
$802$	−19.6632	−	34.0577i	−0.694332	−	1.20262i
$803$	−0.705317	−	1.22164i	−0.0248901	−	0.0431109i
$804$		0			0
$805$	4.06907	−	2.34928i	0.143416	−	0.0828012i
$806$	−14.3490	−	2.42934i	−0.505423	−	0.0855699i
$807$		0			0
$808$	−14.0254	−	3.75809i	−0.493411	−	0.132209i
$809$	−16.9078	−	9.76174i	−0.594448	−	0.343205i	0.172406	−	0.985026i	$-0.444846\pi$
$809$	−16.9078	−	9.76174i	−0.594448	−	0.343205i	−0.766854	+	0.641821i	$0.778179\pi$
$810$		0			0
$811$	−22.8460	+	22.8460i	−0.802232	+	0.802232i	−0.983444	−	0.181212i	$-0.941998\pi$
$811$	−22.8460	+	22.8460i	−0.802232	+	0.802232i	0.181212	+	0.983444i	$0.441998\pi$
$812$	−3.67322	−	3.67322i	−0.128905	−	0.128905i
$813$		0			0
$814$	1.51544	−	5.65570i	0.0531162	−	0.198232i
$815$	7.49444	+	4.32692i	0.262519	+	0.151565i
$816$		0			0
$817$	0.445624	−	1.66309i	0.0155904	−	0.0581842i
$818$	29.7471			1.04008
$819$		0			0
$820$	6.26468			0.218772
$821$	9.86247	−	36.8072i	0.344203	−	1.28458i	−0.549338	−	0.835600i	$-0.685120\pi$
$821$	9.86247	−	36.8072i	0.344203	−	1.28458i	0.893541	−	0.448982i	$-0.148213\pi$
$822$		0			0
$823$	−6.48184	−	3.74229i	−0.225943	−	0.130448i	0.382756	−	0.923849i	$-0.374975\pi$
$823$	−6.48184	−	3.74229i	−0.225943	−	0.130448i	−0.608699	+	0.793401i	$0.708308\pi$
$824$	4.99456	−	18.6399i	0.173994	−	0.649353i
$825$		0			0
$826$	14.2271	+	14.2271i	0.495023	+	0.495023i
$827$	−7.82102	+	7.82102i	−0.271963	+	0.271963i	−0.829890	−	0.557927i	$-0.811597\pi$
$827$	−7.82102	+	7.82102i	−0.271963	+	0.271963i	0.557927	+	0.829890i	$0.311597\pi$
$828$		0			0
$829$	−8.88429	−	5.12935i	−0.308564	−	0.178150i	0.337720	−	0.941247i	$-0.390344\pi$
$829$	−8.88429	−	5.12935i	−0.308564	−	0.178150i	−0.646284	+	0.763097i	$0.723678\pi$
$830$	2.64353	+	0.708331i	0.0917581	+	0.0245865i
$831$		0			0
$832$	−3.37962	+	1.25625i	−0.117167	+	0.0435526i
$833$	−52.2808	+	30.1843i	−1.81142	+	1.04583i
$834$		0			0
$835$	0.283993	+	0.491890i	0.00982798	+	0.0170226i
$836$	0.0932559	+	0.161524i	0.00322532	+	0.00558642i
$837$		0			0
$838$	13.5963	+	3.64312i	0.469677	+	0.125850i
$839$	8.33295	−	8.33295i	0.287685	−	0.287685i	−0.548479	−	0.836164i	$-0.684793\pi$
$839$	8.33295	−	8.33295i	0.287685	−	0.287685i	0.836164	+	0.548479i	$0.184793\pi$
$840$		0			0
$841$	−13.6724	+	23.6813i	−0.471462	+	0.816597i
$842$	4.83177			0.166514
$843$		0			0
$844$	1.12777	+	0.651117i	0.0388194	+	0.0224124i
$845$	−3.82310	−	7.91497i	−0.131518	−	0.272283i
$846$		0			0
$847$	−10.9682	−	40.9337i	−0.376870	−	1.40650i
$848$	5.49344	−	3.17164i	0.188646	−	0.108915i
$849$		0			0
$850$	−28.4733	−	7.62941i	−0.976627	−	0.261686i
$851$	13.7020	−	3.67143i	0.469697	−	0.125855i
$852$		0			0
$853$	23.8590	−	6.39301i	0.816918	−	0.218892i	0.173919	−	0.984760i	$-0.444357\pi$
$853$	23.8590	−	6.39301i	0.816918	−	0.218892i	0.642998	+	0.765868i	$0.277690\pi$
$854$	−11.5346	+	6.65953i	−0.394707	+	0.227884i
$855$		0			0
$856$	12.8501	−	3.44317i	0.439207	−	0.117685i
$857$	24.8560	−	43.0518i	0.849063	−	1.47062i	−0.0329818	−	0.999456i	$-0.510500\pi$
$857$	24.8560	−	43.0518i	0.849063	−	1.47062i	0.882045	−	0.471165i	$-0.156166\pi$
$858$		0			0
$859$	−11.5341	−	19.9776i	−0.393538	−	0.681628i	0.599375	−	0.800468i	$-0.295416\pi$
$859$	−11.5341	−	19.9776i	−0.393538	−	0.681628i	−0.992913	+	0.118840i	$0.962082\pi$
$860$	3.13530	+	3.13530i	0.106913	+	0.106913i
$861$		0			0
$862$			16.6614i			0.567488i
$863$	−4.06937	−	4.06937i	−0.138523	−	0.138523i	0.634445	−	0.772968i	$-0.281229\pi$
$863$	−4.06937	−	4.06937i	−0.138523	−	0.138523i	−0.772968	+	0.634445i	$0.781229\pi$
$864$		0			0
$865$	3.73047	−	13.9223i	0.126840	−	0.473372i
$866$	1.65337	+	6.17046i	0.0561838	+	0.209681i
$867$		0			0
$868$			16.2977i			0.553181i
$869$	7.32652	−	7.32652i	0.248535	−	0.248535i
$870$		0			0
$871$	34.2454	+	15.6854i	1.16036	+	0.531481i
$872$		−	10.7992i		−	0.365706i
$873$		0			0
$874$	−0.225929	+	0.391321i	−0.00764217	+	0.0132366i
$875$	−26.0530			−0.880753
$876$		0			0
$877$	−9.16821	−	34.2162i	−0.309589	−	1.15540i	−0.928923	−	0.370273i	$-0.879264\pi$
$877$	−9.16821	−	34.2162i	−0.309589	−	1.15540i	0.619334	−	0.785127i	$-0.287403\pi$
$878$	−3.43809	−	12.8311i	−0.116030	−	0.433030i
$879$		0			0
$880$	−0.480318			−0.0161915
$881$	−9.78090	+	16.9410i	−0.329527	+	0.570757i	−0.982418	−	0.186695i	$-0.940223\pi$
$881$	−9.78090	+	16.9410i	−0.329527	+	0.570757i	0.652891	+	0.757452i	$0.273556\pi$
$882$		0			0
$883$			7.96488i			0.268040i	0.990979	+	0.134020i	$0.0427886\pi$
$883$			7.96488i			0.268040i	−0.990979	+	0.134020i	$0.957211\pi$
$884$	−21.9299	+	8.15163i	−0.737582	+	0.274169i
$885$		0			0
$886$	15.5412	−	15.5412i	0.522117	−	0.522117i
$887$			51.2075i			1.71938i	0.510816	+	0.859690i	$0.329343\pi$
$887$			51.2075i			1.71938i	−0.510816	+	0.859690i	$0.670657\pi$
$888$		0			0
$889$	20.3854	+	76.0793i	0.683704	+	2.55162i
$890$	−1.78547	+	6.66346i	−0.0598490	+	0.223360i
$891$		0			0
$892$	−13.4964	−	13.4964i	−0.451892	−	0.451892i
$893$		−	2.46596i		−	0.0825201i
$894$		0			0
$895$	0.115480	+	0.115480i	0.00386006	+	0.00386006i
$896$	2.01888	+	3.49679i	0.0674459	+	0.116820i
$897$		0			0
$898$	−4.16450	+	7.21313i	−0.138971	+	0.240705i
$899$	−5.01596	+	1.34402i	−0.167292	+	0.0448257i
$900$		0			0
$901$	35.6462	−	20.5803i	1.18755	−	0.685631i
$902$	−6.35751	+	1.70349i	−0.211682	+	0.0567200i
$903$		0			0
$904$	−14.6939	+	3.93722i	−0.488712	+	0.130950i
$905$	−1.13610	−	0.304416i	−0.0377652	−	0.0101191i
$906$		0			0
$907$	11.1730	−	6.45076i	0.370995	−	0.214194i	−0.302898	−	0.953023i	$-0.597954\pi$
$907$	11.1730	−	6.45076i	0.370995	−	0.214194i	0.673893	+	0.738829i	$0.264621\pi$
$908$	4.25372	+	15.8751i	0.141165	+	0.526834i
$909$		0			0
$910$	−8.02470	+	5.70091i	−0.266016	+	0.188983i
$911$	6.52125	+	3.76504i	0.216059	+	0.124741i	0.604124	−	0.796890i	$-0.293523\pi$
$911$	6.52125	+	3.76504i	0.216059	+	0.124741i	−0.388065	+	0.921632i	$0.626857\pi$
$912$		0			0
$913$	−2.87531			−0.0951588
$914$	6.80928	−	11.7940i	0.225231	−	0.390112i
$915$		0			0
$916$	−9.61932	+	9.61932i	−0.317831	+	0.317831i
$917$	21.9576	+	5.88351i	0.725103	+	0.194291i
$918$		0			0
$919$	−9.25517	−	16.0304i	−0.305300	−	0.528795i	0.672028	−	0.740526i	$-0.265423\pi$
$919$	−9.25517	−	16.0304i	−0.305300	−	0.528795i	−0.977328	+	0.211731i	$0.932090\pi$
$920$	−0.581828	−	1.00776i	−0.0191823	−	0.0332247i
$921$		0			0
$922$	−30.9684	+	17.8796i	−1.01989	+	0.588834i
$923$	29.0666	−	2.74287i	0.956739	−	0.0902827i
$924$		0			0
$925$	−36.1681	−	9.69121i	−1.18920	−	0.318645i
$926$	−10.8207	−	6.24734i	−0.355591	−	0.205300i
$927$		0			0
$928$	−0.909720	+	0.909720i	−0.0298630	+	0.0298630i
$929$	−1.21244	−	1.21244i	−0.0397789	−	0.0397789i	0.686938	−	0.726716i	$-0.258955\pi$
$929$	−1.21244	−	1.21244i	−0.0397789	−	0.0397789i	−0.726716	+	0.686938i	$0.758955\pi$
$930$		0			0
$931$	0.632206	−	2.35943i	0.0207197	−	0.0773271i
$932$	−3.37419	−	1.94809i	−0.110525	−	0.0638117i
$933$		0			0
$934$	−3.10187	+	11.5764i	−0.101496	+	0.378790i
$935$	−3.11672			−0.101928
$936$		0			0
$937$	−25.3011			−0.826552			−0.413276	−	0.910606i	$-0.635616\pi$
$937$	−25.3011			−0.826552			−0.413276	+	0.910606i	$0.635616\pi$
$938$	10.9175	−	40.7445i	0.356468	−	1.33036i
$939$		0			0
$940$	5.49970	+	3.17525i	0.179380	+	0.103565i
$941$	−12.2942	+	45.8826i	−0.400779	+	1.49573i	0.410929	+	0.911667i	$0.365204\pi$
$941$	−12.2942	+	45.8826i	−0.400779	+	1.49573i	−0.811709	+	0.584062i	$0.801462\pi$
$942$		0			0
$943$	−11.2752	−	11.2752i	−0.367171	−	0.367171i
$944$	3.52351	−	3.52351i	0.114681	−	0.114681i
$945$		0			0
$946$	−4.03432	−	2.32921i	−0.131167	−	0.0757293i
$947$	39.6957	+	10.6364i	1.28994	+	0.345637i	0.837636	−	0.546229i	$-0.183937\pi$
$947$	39.6957	+	10.6364i	1.28994	+	0.345637i	0.452300	+	0.891866i	$0.350604\pi$
$948$		0			0
$949$	−2.98153	+	6.50944i	−0.0967845	+	0.211305i
$950$	1.03294	−	0.596369i	0.0335131	−	0.0193488i
$951$		0			0
$952$	13.1002	+	22.6902i	0.424580	+	0.735394i
$953$	18.5200	+	32.0775i	0.599921	+	1.03909i	0.992832	+	0.119517i	$0.0381346\pi$
$953$	18.5200	+	32.0775i	0.599921	+	1.03909i	−0.392911	+	0.919576i	$0.628532\pi$
$954$		0			0
$955$	5.51772	+	1.47847i	0.178549	+	0.0478421i
$956$	1.11461	−	1.11461i	0.0360492	−	0.0360492i
$957$		0			0
$958$	7.18685	−	12.4480i	0.232197	−	0.402177i
$959$	47.4955			1.53371
$960$		0			0
$961$	−12.7375	−	7.35397i	−0.410886	−	0.237225i
$962$	−27.8563	+	10.3546i	−0.898124	+	0.333844i
$963$		0			0
$964$	−1.33674	−	4.98879i	−0.0430536	−	0.160678i
$965$	−0.0314240	+	0.0181427i	−0.00101158	+	0.000584034i
$966$		0			0
$967$	−5.77149	−	1.54647i	−0.185599	−	0.0497310i	0.164822	−	0.986323i	$-0.447295\pi$
$967$	−5.77149	−	1.54647i	−0.185599	−	0.0497310i	−0.350421	+	0.936592i	$0.613962\pi$
$968$	−10.1377	+	2.71640i	−0.325840	+	0.0873085i
$969$		0			0
$970$	−1.31456	+	0.352234i	−0.0422079	+	0.0113096i
$971$	1.66482	−	0.961183i	0.0534266	−	0.0308458i	−0.473049	−	0.881036i	$-0.656847\pi$
$971$	1.66482	−	0.961183i	0.0534266	−	0.0308458i	0.526475	+	0.850190i	$0.323513\pi$
$972$		0			0
$973$	−11.5528	+	3.09556i	−0.370365	+	0.0992390i
$974$	−11.2410	+	19.4701i	−0.360186	+	0.623861i
$975$		0			0
$976$	1.64932	+	2.85670i	0.0527933	+	0.0914407i
$977$	2.90546	+	2.90546i	0.0929538	+	0.0929538i	0.752055	−	0.659101i	$-0.229063\pi$
$977$	2.90546	+	2.90546i	0.0929538	+	0.0929538i	−0.659101	+	0.752055i	$0.729063\pi$
$978$		0			0
$979$		−	7.24771i		−	0.231638i
$980$	4.44806	+	4.44806i	0.142088	+	0.142088i
$981$		0			0
$982$	−11.2262	+	41.8968i	−0.358243	+	1.33698i
$983$	−3.97238	−	14.8251i	−0.126699	−	0.472848i	0.873195	−	0.487370i	$-0.162044\pi$
$983$	−3.97238	−	14.8251i	−0.126699	−	0.472848i	−0.999895	+	0.0145225i	$0.995377\pi$
$984$		0			0
$985$			1.79860i			0.0573081i
$986$	−5.90305	+	5.90305i	−0.187991	+	0.187991i
$987$		0			0
$988$	0.394213	−	0.860668i	0.0125416	−	0.0273815i
$989$		−	11.2859i		−	0.358870i
$990$		0			0
$991$	−2.52005	+	4.36486i	−0.0800521	+	0.138654i	−0.903272	−	0.429068i	$-0.858842\pi$
$991$	−2.52005	+	4.36486i	−0.0800521	+	0.138654i	0.823220	+	0.567722i	$0.192175\pi$
$992$	4.03634			0.128154
$993$		0			0
$994$	−8.46221	−	31.5814i	−0.268405	−	1.00170i
$995$	−0.305306	−	1.13942i	−0.00967885	−	0.0361220i
$996$		0			0
$997$	−11.7157			−0.371041			−0.185520	−	0.982640i	$-0.559397\pi$
$997$	−11.7157			−0.371041			−0.185520	+	0.982640i	$0.559397\pi$
$998$	14.3994	−	24.9406i	0.455806	−	0.789480i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bc.a.305.4		56
3.2	odd	2		234.2.z.a.227.13	yes	56
9.4	even	3		234.2.y.a.149.2	yes	56
9.5	odd	6		702.2.bb.a.71.11		56
13.11	odd	12		702.2.bb.a.89.11		56
39.11	even	12		234.2.y.a.11.2	✓	56
117.50	even	12	inner	702.2.bc.a.557.4		56
117.76	odd	12		234.2.z.a.167.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.2	✓	56	39.11	even	12
234.2.y.a.149.2	yes	56	9.4	even	3
234.2.z.a.167.13	yes	56	117.76	odd	12
234.2.z.a.227.13	yes	56	3.2	odd	2
702.2.bb.a.71.11		56	9.5	odd	6
702.2.bb.a.89.11		56	13.11	odd	12
702.2.bc.a.305.4		56	1.1	even	1	trivial
702.2.bc.a.557.4		56	117.50	even	12	inner

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.175000 + 0.653109i) q^{5} +(2.85512 + 2.85512i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.585562 - 0.338074i) q^{10} +(0.686168 + 0.183858i) q^{11} +(-1.25625 - 3.37962i) q^{13} +(-3.49679 + 2.01888i) q^{14} +(0.500000 + 0.866025i) q^{16} +(3.24443 + 5.61952i) q^{17} +(-0.253608 - 0.0679541i) q^{19} +(0.478109 - 0.478109i) q^{20} +(-0.355187 + 0.615201i) q^{22} -1.72101 q^{23} +(3.93420 + 2.27141i) q^{25} +(3.58960 - 0.338733i) q^{26} +(-1.04505 - 3.90017i) q^{28} +(1.11417 - 0.643269i) q^{29} +(-3.89881 - 1.04468i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-6.26776 + 1.67944i) q^{34} +(-2.36435 + 1.36506i) q^{35} +(-7.96159 + 2.13330i) q^{37} +(0.131277 - 0.227379i) q^{38} +(0.338074 + 0.585562i) q^{40} +(6.55152 + 6.55152i) q^{41} +6.55772i q^{43} +(-0.502310 - 0.502310i) q^{44} +(0.445430 - 1.66237i) q^{46} +(2.43087 + 9.07214i) q^{47} +9.30343i q^{49} +(-3.21226 + 3.21226i) q^{50} +(-0.601867 + 3.55496i) q^{52} -6.34328i q^{53} +(-0.240159 + 0.415967i) q^{55} +4.03775 q^{56} +(0.332981 + 1.24270i) q^{58} +(-1.28969 - 4.81321i) q^{59} +3.29863 q^{61} +(2.01817 - 3.49557i) q^{62} -1.00000i q^{64} +(2.42711 - 0.229034i) q^{65} +(-7.38704 + 7.38704i) q^{67} -6.48886i q^{68} +(-0.706607 - 2.63709i) q^{70} +(-2.09577 + 7.82153i) q^{71} +(-1.40415 - 1.40415i) q^{73} -8.24244i q^{74} +(0.185654 + 0.185654i) q^{76} +(1.43416 + 2.48403i) q^{77} +(7.29283 - 12.6316i) q^{79} +(-0.653109 + 0.175000i) q^{80} +(-8.02394 + 4.63262i) q^{82} +(-3.90968 + 1.04760i) q^{83} +(-4.23794 + 1.13555i) q^{85} +(-6.33427 - 1.69726i) q^{86} +(0.615201 - 0.355187i) q^{88} +(-2.64065 - 9.85503i) q^{89} +(6.06248 - 13.2360i) q^{91} +(1.49044 + 0.860504i) q^{92} -9.39217 q^{94} +(0.0887629 - 0.153742i) q^{95} +(1.42324 - 1.42324i) q^{97} +(-8.98642 - 2.40791i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) \) 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more