LMFDB - Embedded newform 702.2.bc.a.305.11

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)

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")

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);

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			305.11
Character	$\chi$	$=$	702.305
Dual form			702.2.bc.a.557.11

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.174335 + 0.650628i) q^{5} +(1.26694 + 1.26694i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.583337 + 0.336790i) q^{10} +(-0.952090 - 0.255112i) q^{11} +(2.90807 + 2.13146i) q^{13} +(1.55168 - 0.895864i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.20946 - 2.09485i) q^{17} +(6.33213 + 1.69669i) q^{19} +(0.476293 - 0.476293i) q^{20} +(-0.492838 + 0.853620i) q^{22} +6.32605 q^{23} +(3.93720 + 2.27315i) q^{25} +(2.81150 - 2.25732i) q^{26} +(-0.463733 - 1.73068i) q^{28} +(-3.71748 + 2.14629i) q^{29} +(-5.59289 - 1.49861i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-2.33650 + 0.626062i) q^{34} +(-1.04518 + 0.603436i) q^{35} +(6.83094 - 1.83034i) q^{37} +(3.27775 - 5.67724i) q^{38} +(-0.336790 - 0.583337i) q^{40} +(3.51849 + 3.51849i) q^{41} +0.892279i q^{43} +(0.696978 + 0.696978i) q^{44} +(1.63730 - 6.11049i) q^{46} +(0.981707 + 3.66378i) q^{47} -3.78971i q^{49} +(3.21471 - 3.21471i) q^{50} +(-1.45273 - 3.29993i) q^{52} -9.00014i q^{53} +(0.331966 - 0.574981i) q^{55} -1.79173 q^{56} +(1.11100 + 4.14631i) q^{58} +(-1.22237 - 4.56196i) q^{59} +4.76398 q^{61} +(-2.89509 + 5.01445i) q^{62} -1.00000i q^{64} +(-1.89377 + 1.52048i) q^{65} +(-7.82927 + 7.82927i) q^{67} +2.41892i q^{68} +(0.312361 + 1.16575i) q^{70} +(-1.70900 + 6.37808i) q^{71} +(-8.01788 - 8.01788i) q^{73} -7.07190i q^{74} +(-4.63544 - 4.63544i) q^{76} +(-0.883031 - 1.52946i) q^{77} +(-0.807117 + 1.39797i) q^{79} +(-0.650628 + 0.174335i) q^{80} +(4.30925 - 2.48795i) q^{82} +(7.31055 - 1.95885i) q^{83} +(1.57382 - 0.421703i) q^{85} +(0.861875 + 0.230939i) q^{86} +(0.853620 - 0.492838i) q^{88} +(-0.440877 - 1.64537i) q^{89} +(0.983920 + 6.38480i) q^{91} +(-5.47852 - 3.16302i) q^{92} +3.79302 q^{94} +(-2.20783 + 3.82407i) q^{95} +(-1.35833 + 1.35833i) q^{97} +(-3.66058 - 0.980849i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100})$ 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
$5$	−0.174335	+	0.650628i	−0.0779651	+	0.290970i	−0.993889	−	0.110382i	$-0.964793\pi$
$5$	−0.174335	+	0.650628i	−0.0779651	+	0.290970i	0.915924	+	0.401351i	$0.131459\pi$
$6$		0			0
$7$	1.26694	+	1.26694i	0.478859	+	0.478859i	0.904767	−	0.425907i	$-0.140045\pi$
$7$	1.26694	+	1.26694i	0.478859	+	0.478859i	−0.425907	+	0.904767i	$0.640045\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	0.583337	+	0.336790i	0.184467	+	0.106502i
$11$	−0.952090	−	0.255112i	−0.287066	−	0.0769190i	0.112413	−	0.993662i	$-0.464142\pi$
$11$	−0.952090	−	0.255112i	−0.287066	−	0.0769190i	−0.399479	+	0.916743i	$0.630809\pi$
$12$		0			0
$13$	2.90807	+	2.13146i	0.806554	+	0.591161i
$13$	2.90807	+	2.13146i	0.806554	+	0.591161i
$14$	1.55168	−	0.895864i	0.414704	−	0.239430i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.20946	−	2.09485i	−0.293337	−	0.508075i	0.681260	−	0.732042i	$-0.261432\pi$
$17$	−1.20946	−	2.09485i	−0.293337	−	0.508075i	−0.974597	+	0.223967i	$0.928099\pi$
$18$		0			0
$19$	6.33213	+	1.69669i	1.45269	+	0.389247i	0.896959	−	0.442114i	$-0.145771\pi$
$19$	6.33213	+	1.69669i	1.45269	+	0.389247i	0.555732	+	0.831361i	$0.312438\pi$
$20$	0.476293	−	0.476293i	0.106502	−	0.106502i
$21$		0			0
$22$	−0.492838	+	0.853620i	−0.105073	+	0.181992i
$23$	6.32605			1.31907			0.659536	−	0.751673i	$-0.270753\pi$
$23$	6.32605			1.31907			0.659536	+	0.751673i	$0.270753\pi$
$24$		0			0
$25$	3.93720	+	2.27315i	0.787441	+	0.454629i
$26$	2.81150	−	2.25732i	0.551380	−	0.442696i
$27$		0			0
$28$	−0.463733	−	1.73068i	−0.0876374	−	0.327067i
$29$	−3.71748	+	2.14629i	−0.690318	+	0.398555i	−0.803731	−	0.594993i	$-0.797155\pi$
$29$	−3.71748	+	2.14629i	−0.690318	+	0.398555i	0.113413	+	0.993548i	$0.463822\pi$
$30$		0			0
$31$	−5.59289	−	1.49861i	−1.00451	−	0.269158i	−0.281178	−	0.959656i	$-0.590725\pi$
$31$	−5.59289	−	1.49861i	−1.00451	−	0.269158i	−0.723335	+	0.690498i	$0.757392\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$		0			0
$34$	−2.33650	+	0.626062i	−0.400706	+	0.107369i
$35$	−1.04518	+	0.603436i	−0.176668	+	0.101999i
$36$		0			0
$37$	6.83094	−	1.83034i	1.12300	−	0.300907i	0.350902	−	0.936412i	$-0.385875\pi$
$37$	6.83094	−	1.83034i	1.12300	−	0.300907i	0.772096	+	0.635505i	$0.219208\pi$
$38$	3.27775	−	5.67724i	0.531722	−	0.920969i
$39$		0			0
$40$	−0.336790	−	0.583337i	−0.0532512	−	0.0922337i
$41$	3.51849	+	3.51849i	0.549496	+	0.549496i	0.926295	−	0.376799i	$-0.122975\pi$
$41$	3.51849	+	3.51849i	0.549496	+	0.549496i	−0.376799	+	0.926295i	$0.622975\pi$
$42$		0			0
$43$			0.892279i			0.136071i	0.997683	+	0.0680356i	$0.0216731\pi$
$43$			0.892279i			0.136071i	−0.997683	+	0.0680356i	$0.978327\pi$
$44$	0.696978	+	0.696978i	0.105073	+	0.105073i
$45$		0			0
$46$	1.63730	−	6.11049i	0.241407	−	0.900943i
$47$	0.981707	+	3.66378i	0.143197	+	0.534417i	0.999829	+	0.0184899i	$0.00588585\pi$
$47$	0.981707	+	3.66378i	0.143197	+	0.534417i	−0.856632	+	0.515927i	$0.827447\pi$
$48$		0			0
$49$		−	3.78971i		−	0.541387i
$50$	3.21471	−	3.21471i	0.454629	−	0.454629i
$51$		0			0
$52$	−1.45273	−	3.29993i	−0.201458	−	0.457619i
$53$		−	9.00014i		−	1.23626i	−0.786074	−	0.618132i	$-0.787890\pi$
$53$		−	9.00014i		−	1.23626i	0.786074	−	0.618132i	$-0.212110\pi$
$54$		0			0
$55$	0.331966	−	0.574981i	0.0447622	−	0.0775305i
$56$	−1.79173			−0.239430
$57$		0			0
$58$	1.11100	+	4.14631i	0.145881	+	0.544437i
$59$	−1.22237	−	4.56196i	−0.159139	−	0.593917i	−0.998715	−	0.0506741i	$-0.983863\pi$
$59$	−1.22237	−	4.56196i	−0.159139	−	0.593917i	0.839576	−	0.543243i	$-0.182804\pi$
$60$		0			0
$61$	4.76398			0.609965			0.304982	−	0.952358i	$-0.401349\pi$
$61$	4.76398			0.609965			0.304982	+	0.952358i	$0.401349\pi$
$62$	−2.89509	+	5.01445i	−0.367677	+	0.636835i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−1.89377	+	1.52048i	−0.234893	+	0.188593i
$66$		0			0
$67$	−7.82927	+	7.82927i	−0.956498	+	0.956498i	−0.999092	−	0.0425948i	$-0.986438\pi$
$67$	−7.82927	+	7.82927i	−0.956498	+	0.956498i	0.0425948	+	0.999092i	$0.486438\pi$
$68$			2.41892i			0.293337i
$69$		0			0
$70$	0.312361	+	1.16575i	0.0373343	+	0.139334i
$71$	−1.70900	+	6.37808i	−0.202821	+	0.756939i	0.787281	+	0.616594i	$0.211488\pi$
$71$	−1.70900	+	6.37808i	−0.202821	+	0.756939i	−0.990103	+	0.140345i	$0.955179\pi$
$72$		0			0
$73$	−8.01788	−	8.01788i	−0.938421	−	0.938421i	0.0597896	−	0.998211i	$-0.480957\pi$
$73$	−8.01788	−	8.01788i	−0.938421	−	0.938421i	−0.998211	+	0.0597896i	$0.980957\pi$
$74$		−	7.07190i		−	0.822092i
$75$		0			0
$76$	−4.63544	−	4.63544i	−0.531722	−	0.531722i
$77$	−0.883031	−	1.52946i	−0.100631	−	0.174298i
$78$		0			0
$79$	−0.807117	+	1.39797i	−0.0908078	+	0.157284i	−0.907851	−	0.419292i	$-0.862278\pi$
$79$	−0.807117	+	1.39797i	−0.0908078	+	0.157284i	0.817043	+	0.576576i	$0.195612\pi$
$80$	−0.650628	+	0.174335i	−0.0727424	+	0.0194913i
$81$		0			0
$82$	4.30925	−	2.48795i	0.475877	−	0.274748i
$83$	7.31055	−	1.95885i	0.802437	−	0.215012i	0.165783	−	0.986162i	$-0.446985\pi$
$83$	7.31055	−	1.95885i	0.802437	−	0.215012i	0.636653	+	0.771150i	$0.280318\pi$
$84$		0			0
$85$	1.57382	−	0.421703i	0.170704	−	0.0457401i
$86$	0.861875	+	0.230939i	0.0929384	+	0.0249028i
$87$		0			0
$88$	0.853620	−	0.492838i	0.0909962	−	0.0525367i
$89$	−0.440877	−	1.64537i	−0.0467329	−	0.174409i	0.938615	−	0.344967i	$-0.112110\pi$
$89$	−0.440877	−	1.64537i	−0.0467329	−	0.174409i	−0.985348	+	0.170557i	$0.945443\pi$
$90$		0			0
$91$	0.983920	+	6.38480i	0.103143	+	0.669309i
$92$	−5.47852	−	3.16302i	−0.571175	−	0.329768i
$93$		0			0
$94$	3.79302			0.391220
$95$	−2.20783	+	3.82407i	−0.226518	+	0.392341i
$96$		0			0
$97$	−1.35833	+	1.35833i	−0.137917	+	0.137917i	−0.772695	−	0.634778i	$-0.781092\pi$
$97$	−1.35833	+	1.35833i	−0.137917	+	0.137917i	0.634778	+	0.772695i	$0.281092\pi$
$98$	−3.66058	−	0.980849i	−0.369774	−	0.0990807i
$99$		0			0
$100$	−2.27315	−	3.93720i	−0.227315	−	0.393720i
$101$	7.44597	+	12.8968i	0.740902	+	1.28328i	0.952085	+	0.305833i	$0.0989349\pi$
$101$	7.44597	+	12.8968i	0.740902	+	1.28328i	−0.211183	+	0.977446i	$0.567732\pi$
$102$		0			0
$103$	−9.08751	+	5.24668i	−0.895419	+	0.516971i	−0.875711	−	0.482835i	$-0.839607\pi$
$103$	−9.08751	+	5.24668i	−0.895419	+	0.516971i	−0.0197081	+	0.999806i	$0.506274\pi$
$104$	−3.56349	+	0.549146i	−0.349429	+	0.0538482i
$105$		0			0
$106$	−8.69347	−	2.32941i	−0.844384	−	0.226252i
$107$	−1.87899	−	1.08484i	−0.181649	−	0.104875i	0.406418	−	0.913687i	$-0.366778\pi$
$107$	−1.87899	−	1.08484i	−0.181649	−	0.104875i	−0.588067	+	0.808812i	$0.700111\pi$
$108$		0			0
$109$	−8.28528	+	8.28528i	−0.793586	+	0.793586i	−0.982075	−	0.188489i	$-0.939641\pi$
$109$	−8.28528	+	8.28528i	−0.793586	+	0.793586i	0.188489	+	0.982075i	$0.439641\pi$
$110$	−0.469470	−	0.469470i	−0.0447622	−	0.0447622i
$111$		0			0
$112$	−0.463733	+	1.73068i	−0.0438187	+	0.163534i
$113$	−9.60049	−	5.54284i	−0.903138	−	0.521427i	−0.0249209	−	0.999689i	$-0.507933\pi$
$113$	−9.60049	−	5.54284i	−0.903138	−	0.521427i	−0.878217	+	0.478263i	$0.841267\pi$
$114$		0			0
$115$	−1.10285	+	4.11590i	−0.102842	+	0.383810i
$116$	4.29257			0.398555
$117$		0			0
$118$	−4.72289			−0.434777
$119$	1.12173	−	4.18637i	0.102829	−	0.383764i
$120$		0			0
$121$	−8.68489	−	5.01422i	−0.789535	−	0.455838i
$122$	1.23301	−	4.60165i	0.111631	−	0.416614i
$123$		0			0
$124$	4.09428	+	4.09428i	0.367677	+	0.367677i
$125$	−4.54683	+	4.54683i	−0.406681	+	0.406681i
$126$		0			0
$127$	4.33197	+	2.50106i	0.384400	+	0.221933i	0.679731	−	0.733462i	$-0.262097\pi$
$127$	4.33197	+	2.50106i	0.384400	+	0.221933i	−0.295331	+	0.955395i	$0.595430\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$		0			0
$130$	0.978531	+	2.22277i	0.0858229	+	0.194950i
$131$	−19.0361	+	10.9905i	−1.66319	+	0.960242i	−0.692010	+	0.721888i	$0.743275\pi$
$131$	−19.0361	+	10.9905i	−1.66319	+	0.960242i	−0.971178	+	0.238354i	$0.923392\pi$
$132$		0			0
$133$	5.87284	+	10.1721i	0.509240	+	0.882030i
$134$	5.53613	+	9.58886i	0.478249	+	0.828351i
$135$		0			0
$136$	2.33650	+	0.626062i	0.200353	+	0.0536844i
$137$	8.90180	−	8.90180i	0.760532	−	0.760532i	−0.215886	−	0.976419i	$-0.569264\pi$
$137$	8.90180	−	8.90180i	0.760532	−	0.760532i	0.976419	+	0.215886i	$0.0692641\pi$
$138$		0			0
$139$	9.84823	−	17.0576i	0.835316	−	1.44681i	−0.0584566	−	0.998290i	$-0.518618\pi$
$139$	9.84823	−	17.0576i	0.835316	−	1.44681i	0.893773	−	0.448520i	$-0.148049\pi$
$140$	1.20687			0.101999
$141$		0			0
$142$	5.71843	+	3.30154i	0.479880	+	0.277059i
$143$	−2.22498	−	2.77122i	−0.186062	−	0.231741i
$144$		0			0
$145$	−0.748347	−	2.79287i	−0.0621468	−	0.231935i
$146$	−9.81985	+	5.66949i	−0.812697	+	0.469211i
$147$		0			0
$148$	−6.83094	−	1.83034i	−0.561499	−	0.150453i
$149$	9.34027	−	2.50272i	0.765185	−	0.205031i	0.144942	−	0.989440i	$-0.453701\pi$
$149$	9.34027	−	2.50272i	0.765185	−	0.205031i	0.620243	+	0.784410i	$0.287034\pi$
$150$		0			0
$151$	4.80308	−	1.28698i	0.390869	−	0.104733i	−0.0580316	−	0.998315i	$-0.518482\pi$
$151$	4.80308	−	1.28698i	0.390869	−	0.104733i	0.448900	+	0.893582i	$0.351816\pi$
$152$	−5.67724	+	3.27775i	−0.460485	+	0.265861i
$153$		0			0
$154$	−1.70589	+	0.457091i	−0.137464	+	0.0368334i
$155$	1.95008	−	3.37763i	0.156634	−	0.271298i
$156$		0			0
$157$	−4.86181	−	8.42090i	−0.388015	−	0.672061i	0.604168	−	0.796857i	$-0.293506\pi$
$157$	−4.86181	−	8.42090i	−0.388015	−	0.672061i	−0.992182	+	0.124796i	$0.960172\pi$
$158$	1.14144	+	1.14144i	0.0908078	+	0.0908078i
$159$		0			0
$160$			0.673580i			0.0532512i
$161$	8.01474	+	8.01474i	0.631650	+	0.631650i
$162$		0			0
$163$	1.24717	−	4.65451i	0.0976861	−	0.364570i	−0.899727	−	0.436453i	$-0.856234\pi$
$163$	1.24717	−	4.65451i	0.0976861	−	0.364570i	0.997413	+	0.0718838i	$0.0229011\pi$
$164$	−1.28786	−	4.80634i	−0.100565	−	0.375312i
$165$		0			0
$166$		−	7.56843i		−	0.587424i
$167$	−10.0054	+	10.0054i	−0.774242	+	0.774242i	−0.978845	−	0.204603i	$-0.934410\pi$
$167$	−10.0054	+	10.0054i	−0.774242	+	0.774242i	0.204603	+	0.978845i	$0.434410\pi$
$168$		0			0
$169$	3.91375	+	12.3969i	0.301058	+	0.953606i
$170$		−	1.62934i		−	0.124964i
$171$		0			0
$172$	0.446139	−	0.772736i	0.0340178	−	0.0589206i
$173$	−23.1979			−1.76370			−0.881852	−	0.471527i	$-0.843703\pi$
$173$	−23.1979			−1.76370			−0.881852	+	0.471527i	$0.843703\pi$
$174$		0			0
$175$	2.10827	+	7.86816i	0.159370	+	0.594777i
$176$	−0.255112	−	0.952090i	−0.0192298	−	0.0717664i
$177$		0			0
$178$	−1.70342			−0.127677
$179$	−2.78545	+	4.82455i	−0.208194	+	0.360603i	−0.951146	−	0.308742i	$-0.900092\pi$
$179$	−2.78545	+	4.82455i	−0.208194	+	0.360603i	0.742951	+	0.669345i	$0.233425\pi$
$180$		0			0
$181$		−	20.8410i		−	1.54910i	−0.632514	−	0.774549i	$-0.717977\pi$
$181$		−	20.8410i		−	1.54910i	0.632514	−	0.774549i	$-0.282023\pi$
$182$	6.42190	+	0.702114i	0.476023	+	0.0520441i
$183$		0			0
$184$	−4.47319	+	4.47319i	−0.329768	+	0.329768i
$185$			4.76349i			0.350219i
$186$		0			0
$187$	0.617094	+	2.30303i	0.0451264	+	0.168414i
$188$	0.981707	−	3.66378i	0.0715983	−	0.267209i
$189$		0			0
$190$	3.12234	+	3.12234i	0.226518	+	0.226518i
$191$			18.0727i			1.30769i	0.756626	+	0.653847i	$0.226846\pi$
$191$			18.0727i			1.30769i	−0.756626	+	0.653847i	$0.773154\pi$
$192$		0			0
$193$	5.20610	+	5.20610i	0.374743	+	0.374743i	0.869201	−	0.494458i	$-0.164634\pi$
$193$	5.20610	+	5.20610i	0.374743	+	0.374743i	−0.494458	+	0.869201i	$0.664634\pi$
$194$	0.960483	+	1.66361i	0.0689587	+	0.119440i
$195$		0			0
$196$	−1.89486	+	3.28199i	−0.135347	+	0.234428i
$197$	23.6473	−	6.33628i	1.68480	−	0.451441i	0.715761	−	0.698345i	$-0.246080\pi$
$197$	23.6473	−	6.33628i	1.68480	−	0.451441i	0.969040	+	0.246904i	$0.0794132\pi$
$198$		0			0
$199$	−6.97794	+	4.02871i	−0.494653	+	0.285588i	−0.726503	−	0.687164i	$-0.758856\pi$
$199$	−6.97794	+	4.02871i	−0.494653	+	0.285588i	0.231850	+	0.972752i	$0.425522\pi$
$200$	−4.39138	+	1.17667i	−0.310517	+	0.0832029i
$201$		0			0
$202$	14.3845	−	3.85432i	1.01209	−	0.271189i
$203$	−7.42905	−	1.99061i	−0.521417	−	0.139713i
$204$		0			0
$205$	−2.90262	+	1.67583i	−0.202728	+	0.117045i
$206$	2.71588	+	10.1358i	0.189224	+	0.706195i
$207$		0			0
$208$	−0.391864	+	3.58419i	−0.0271709	+	0.248519i
$209$	−5.59591	−	3.23080i	−0.387077	−	0.223479i
$210$		0			0
$211$	−14.0818			−0.969432			−0.484716	−	0.874672i	$-0.661077\pi$
$211$	−14.0818			−0.969432			−0.484716	+	0.874672i	$0.661077\pi$
$212$	−4.50007	+	7.79435i	−0.309066	+	0.535318i
$213$		0			0
$214$	−1.53419	+	1.53419i	−0.104875	+	0.104875i
$215$	−0.580542	−	0.155556i	−0.0395926	−	0.0106088i
$216$		0			0
$217$	−5.18722	−	8.98452i	−0.352131	−	0.609909i
$218$	5.85858	+	10.1474i	0.396793	+	0.687265i
$219$		0			0
$220$	−0.574981	+	0.331966i	−0.0387652	+	0.0223811i
$221$	0.947887	−	8.66987i	0.0637618	−	0.583199i
$222$		0			0
$223$	−22.9327	−	6.14479i	−1.53568	−	0.411485i	−0.610816	−	0.791773i	$-0.709158\pi$
$223$	−22.9327	−	6.14479i	−1.53568	−	0.411485i	−0.924868	+	0.380287i	$0.875825\pi$
$224$	1.55168	+	0.895864i	0.103676	+	0.0598574i
$225$		0			0
$226$	−7.83876	+	7.83876i	−0.521427	+	0.521427i
$227$	16.9292	+	16.9292i	1.12363	+	1.12363i	0.991191	+	0.132438i	$0.0422806\pi$
$227$	16.9292	+	16.9292i	1.12363	+	1.12363i	0.132438	+	0.991191i	$0.457719\pi$
$228$		0			0
$229$	5.31509	−	19.8362i	0.351231	−	1.31081i	−0.533930	−	0.845529i	$-0.679286\pi$
$229$	5.31509	−	19.8362i	0.351231	−	1.31081i	0.885161	−	0.465284i	$-0.154048\pi$
$230$	3.69022	+	2.13055i	0.243326	+	0.140484i
$231$		0			0
$232$	1.11100	−	4.14631i	0.0729407	−	0.272218i
$233$	2.79071			0.182825			0.0914126	−	0.995813i	$-0.470862\pi$
$233$	2.79071			0.182825			0.0914126	+	0.995813i	$0.470862\pi$
$234$		0			0
$235$	−2.55490			−0.166664
$236$	−1.22237	+	4.56196i	−0.0795697	+	0.296958i
$237$		0			0
$238$	−3.75339	−	2.16702i	−0.243296	−	0.140467i
$239$	−2.03334	+	7.58852i	−0.131526	+	0.490861i	−0.999988	−	0.00489453i	$-0.998442\pi$
$239$	−2.03334	+	7.58852i	−0.131526	+	0.490861i	0.868462	+	0.495755i	$0.165109\pi$
$240$		0			0
$241$	−16.4615	−	16.4615i	−1.06038	−	1.06038i	−0.998056	−	0.0623240i	$-0.980149\pi$
$241$	−16.4615	−	16.4615i	−1.06038	−	1.06038i	−0.0623240	−	0.998056i	$-0.519851\pi$
$242$	−7.09118	+	7.09118i	−0.455838	+	0.455838i
$243$		0			0
$244$	−4.12572	−	2.38199i	−0.264122	−	0.152491i
$245$	2.46569	+	0.660680i	0.157527	+	0.0422093i
$246$		0			0
$247$	14.7979	+	18.4308i	0.941566	+	1.17272i
$248$	5.01445	−	2.89509i	0.318418	−	0.183839i
$249$		0			0
$250$	3.21509	+	5.56871i	0.203340	+	0.352196i
$251$	−13.0241	−	22.5583i	−0.822071	−	1.42387i	−0.904138	−	0.427241i	$-0.859485\pi$
$251$	−13.0241	−	22.5583i	−0.822071	−	1.42387i	0.0820668	−	0.996627i	$-0.473848\pi$
$252$		0			0
$253$	−6.02296	−	1.61385i	−0.378660	−	0.101462i
$254$	3.53704	−	3.53704i	0.221933	−	0.221933i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.20155			0.449220			0.224610	−	0.974449i	$-0.427889\pi$
$257$	7.20155			0.449220			0.224610	+	0.974449i	$0.427889\pi$
$258$		0			0
$259$	10.9733	+	6.33546i	0.681851	+	0.393667i
$260$	2.40029	−	0.369894i	0.148860	−	0.0229398i
$261$		0			0
$262$	5.68909	+	21.2320i	0.351473	+	1.31172i
$263$	−9.92027	+	5.72747i	−0.611710	+	0.353171i	−0.773634	−	0.633632i	$-0.781563\pi$
$263$	−9.92027	+	5.72747i	−0.611710	+	0.353171i	0.161924	+	0.986803i	$0.448230\pi$
$264$		0			0
$265$	5.85574	+	1.56904i	0.359715	+	0.0963855i
$266$	11.3455	−	3.04001i	0.695635	−	0.186395i
$267$		0			0
$268$	10.6950	−	2.86571i	0.653300	−	0.175051i
$269$	21.7795	−	12.5744i	1.32792	−	0.766674i	0.342941	−	0.939357i	$-0.388577\pi$
$269$	21.7795	−	12.5744i	1.32792	−	0.766674i	0.984977	+	0.172683i	$0.0552437\pi$
$270$		0			0
$271$	6.17248	−	1.65391i	0.374952	−	0.100468i	−0.0664215	−	0.997792i	$-0.521158\pi$
$271$	6.17248	−	1.65391i	0.374952	−	0.100468i	0.441373	+	0.897324i	$0.354492\pi$
$272$	1.20946	−	2.09485i	0.0733343	−	0.127019i
$273$		0			0
$274$	−6.29452	−	10.9024i	−0.380266	−	0.658640i
$275$	−3.16866	−	3.16866i	−0.191078	−	0.191078i
$276$		0			0
$277$		−	19.4429i		−	1.16821i	−0.811679	−	0.584104i	$-0.801446\pi$
$277$		−	19.4429i		−	1.16821i	0.811679	−	0.584104i	$-0.198554\pi$
$278$	−13.9275	−	13.9275i	−0.835316	−	0.835316i
$279$		0			0
$280$	0.312361	−	1.16575i	0.0186672	−	0.0696668i
$281$	−7.71478	−	28.7919i	−0.460225	−	1.71758i	−0.672255	−	0.740320i	$-0.734674\pi$
$281$	−7.71478	−	28.7919i	−0.460225	−	1.71758i	0.212030	−	0.977263i	$-0.431993\pi$
$282$		0			0
$283$			22.0759i			1.31228i	0.754640	+	0.656139i	$0.227812\pi$
$283$			22.0759i			1.31228i	−0.754640	+	0.656139i	$0.772188\pi$
$284$	4.66908	−	4.66908i	0.277059	−	0.277059i
$285$		0			0
$286$	−3.25267	+	1.43192i	−0.192334	+	0.0846714i
$287$			8.91545i			0.526262i
$288$		0			0
$289$	5.57442	−	9.65517i	0.327907	−	0.567951i
$290$	−2.89139			−0.169788
$291$		0			0
$292$	2.93475	+	10.9526i	0.171743	+	0.640954i
$293$	−2.45563	−	9.16452i	−0.143459	−	0.535397i	−0.999819	−	0.0190176i	$-0.993946\pi$
$293$	−2.45563	−	9.16452i	−0.143459	−	0.535397i	0.856360	−	0.516379i	$-0.172721\pi$
$294$		0			0
$295$	3.18124			0.185219
$296$	−3.53595	+	6.12445i	−0.205523	+	0.355976i
$297$		0			0
$298$		−	9.66976i		−	0.560154i
$299$	18.3966	+	13.4837i	1.06390	+	0.779784i
$300$		0			0
$301$	−1.13047	+	1.13047i	−0.0651590	+	0.0651590i
$302$		−	4.97251i		−	0.286136i
$303$		0			0
$304$	1.69669	+	6.33213i	0.0973119	+	0.363173i
$305$	−0.830529	+	3.09958i	−0.0475560	+	0.177481i
$306$		0			0
$307$	3.35703	+	3.35703i	0.191596	+	0.191596i	0.796385	−	0.604790i	$-0.206743\pi$
$307$	3.35703	+	3.35703i	0.191596	+	0.191596i	−0.604790	+	0.796385i	$0.706743\pi$
$308$			1.76606i			0.100631i
$309$		0			0
$310$	−2.75782	−	2.75782i	−0.156634	−	0.156634i
$311$	−10.5634	−	18.2964i	−0.598996	−	1.03749i	−0.992970	−	0.118370i	$-0.962233\pi$
$311$	−10.5634	−	18.2964i	−0.598996	−	1.03749i	0.393973	−	0.919122i	$-0.371100\pi$
$312$		0			0
$313$	−5.16590	+	8.94760i	−0.291994	+	0.505748i	−0.974281	−	0.225336i	$-0.927652\pi$
$313$	−5.16590	+	8.94760i	−0.291994	+	0.505748i	0.682287	+	0.731084i	$0.260985\pi$
$314$	−9.39229	+	2.51666i	−0.530038	+	0.142023i
$315$		0			0
$316$	1.39797	−	0.807117i	0.0786419	−	0.0454039i
$317$	16.1862	−	4.33708i	0.909108	−	0.243595i	0.226185	−	0.974084i	$-0.427375\pi$
$317$	16.1862	−	4.33708i	0.909108	−	0.243595i	0.682924	+	0.730490i	$0.260708\pi$
$318$		0			0
$319$	4.08691	−	1.09509i	0.228823	−	0.0613130i
$320$	0.650628	+	0.174335i	0.0363712	+	0.00974564i
$321$		0			0
$322$	9.81601	−	5.66728i	0.547025	−	0.315825i
$323$	−4.10416	−	15.3169i	−0.228361	−	0.852256i
$324$		0			0
$325$	6.60454	+	15.0025i	0.366354	+	0.832187i
$326$	−4.17312	−	2.40935i	−0.231128	−	0.133442i
$327$		0			0
$328$	−4.97589			−0.274748
$329$	−3.39803	+	5.88557i	−0.187340	+	0.324482i
$330$		0			0
$331$	10.4331	−	10.4331i	0.573455	−	0.573455i	−0.359637	−	0.933092i	$-0.617100\pi$
$331$	10.4331	−	10.4331i	0.573455	−	0.573455i	0.933092	+	0.359637i	$0.117100\pi$
$332$	−7.31055	−	1.95885i	−0.401218	−	0.107506i
$333$		0			0
$334$	7.07490	+	12.2541i	0.387121	+	0.670513i
$335$	−3.72903	−	6.45886i	−0.203738	−	0.352885i
$336$		0			0
$337$	−3.36489	+	1.94272i	−0.183297	+	0.105827i	−0.588841	−	0.808249i	$-0.700416\pi$
$337$	−3.36489	+	1.94272i	−0.183297	+	0.105827i	0.405544	+	0.914076i	$0.367082\pi$
$338$	12.9874	−	0.571843i	0.706422	−	0.0311042i
$339$		0			0
$340$	−1.57382	−	0.421703i	−0.0853522	−	0.0228701i
$341$	4.94262	+	2.85362i	0.267658	+	0.154532i
$342$		0			0
$343$	13.6699	−	13.6699i	0.738108	−	0.738108i
$344$	−0.630936	−	0.630936i	−0.0340178	−	0.0340178i
$345$		0			0
$346$	−6.00406	+	22.4074i	−0.322780	+	1.20463i
$347$	−27.9881	−	16.1590i	−1.50248	−	0.867459i	−0.999996	−	0.00287338i	$-0.999085\pi$
$347$	−27.9881	−	16.1590i	−1.50248	−	0.867459i	−0.502486	−	0.864585i	$-0.667581\pi$
$348$		0			0
$349$	4.90845	−	18.3186i	0.262743	−	0.980571i	−0.700874	−	0.713285i	$-0.747207\pi$
$349$	4.90845	−	18.3186i	0.262743	−	0.980571i	0.963617	−	0.267286i	$-0.0861268\pi$
$350$	8.14572			0.435407
$351$		0			0
$352$	−0.985676			−0.0525367
$353$	−5.07215	+	18.9295i	−0.269963	+	1.00752i	0.689178	+	0.724592i	$0.257972\pi$
$353$	−5.07215	+	18.9295i	−0.269963	+	1.00752i	−0.959142	+	0.282926i	$0.908695\pi$
$354$		0			0
$355$	−3.85182	−	2.22385i	−0.204433	−	0.118030i
$356$	−0.440877	+	1.64537i	−0.0233664	+	0.0872047i
$357$		0			0
$358$	3.93922	+	3.93922i	0.208194	+	0.208194i
$359$	19.2085	−	19.2085i	1.01379	−	1.01379i	0.0138835	−	0.999904i	$-0.495581\pi$
$359$	19.2085	−	19.2085i	1.01379	−	1.01379i	0.999904	−	0.0138835i	$-0.00441940\pi$
$360$		0			0
$361$	20.7627	+	11.9873i	1.09277	+	0.630913i
$362$	−20.1308	−	5.39404i	−1.05805	−	0.283504i
$363$		0			0
$364$	2.34030	−	6.02136i	0.122665	−	0.315605i
$365$	6.61445	−	3.81886i	0.346216	−	0.199888i
$366$		0			0
$367$	−3.84715	−	6.66345i	−0.200819	−	0.347829i	0.747973	−	0.663729i	$-0.231027\pi$
$367$	−3.84715	−	6.66345i	−0.200819	−	0.347829i	−0.948793	+	0.315899i	$0.897694\pi$
$368$	3.16302	+	5.47852i	0.164884	+	0.285587i
$369$		0			0
$370$	4.60118	+	1.23288i	0.239204	+	0.0640945i
$371$	11.4027	−	11.4027i	0.591997	−	0.591997i
$372$		0			0
$373$	8.04898	−	13.9412i	0.416760	−	0.721850i	−0.578851	−	0.815433i	$-0.696499\pi$
$373$	8.04898	−	13.9412i	0.416760	−	0.721850i	0.995611	+	0.0935830i	$0.0298321\pi$
$374$	2.38427			0.123288
$375$		0			0
$376$	−3.28485	−	1.89651i	−0.169403	−	0.0978051i
$377$	−15.3854	−	1.68210i	−0.792389	−	0.0866328i
$378$		0			0
$379$	6.71919	+	25.0764i	0.345142	+	1.28809i	0.892446	+	0.451153i	$0.148987\pi$
$379$	6.71919	+	25.0764i	0.345142	+	1.28809i	−0.547305	+	0.836933i	$0.684346\pi$
$380$	3.82407	−	2.20783i	0.196171	−	0.113259i
$381$		0			0
$382$	17.4569	+	4.67756i	0.893172	+	0.239325i
$383$	30.3863	−	8.14198i	1.55267	−	0.416036i	0.622334	−	0.782752i	$-0.286185\pi$
$383$	30.3863	−	8.14198i	1.55267	−	0.416036i	0.930333	+	0.366716i	$0.119518\pi$
$384$		0			0
$385$	1.14905	−	0.307887i	0.0585610	−	0.0156914i
$386$	6.37614	−	3.68127i	0.324537	−	0.187372i
$387$		0			0
$388$	1.85551	−	0.497183i	0.0941993	−	0.0252406i
$389$	12.6984	−	21.9943i	0.643836	−	1.11516i	−0.340733	−	0.940160i	$-0.610675\pi$
$389$	12.6984	−	21.9943i	0.643836	−	1.11516i	0.984569	−	0.174997i	$-0.0559915\pi$
$390$		0			0
$391$	−7.65110	−	13.2521i	−0.386933	−	0.670187i
$392$	2.67973	+	2.67973i	0.135347	+	0.135347i
$393$		0			0
$394$		−	24.4815i		−	1.23336i
$395$	−0.768848	−	0.768848i	−0.0386850	−	0.0386850i
$396$		0			0
$397$	0.337126	−	1.25817i	0.0169199	−	0.0631458i	−0.956950	−	0.290254i	$-0.906260\pi$
$397$	0.337126	−	1.25817i	0.0169199	−	0.0631458i	0.973870	+	0.227108i	$0.0729270\pi$
$398$	2.08542	+	7.78288i	0.104532	+	0.390120i
$399$		0			0
$400$			4.54629i			0.227315i
$401$	−1.01652	+	1.01652i	−0.0507627	+	0.0507627i	−0.732032	−	0.681270i	$-0.761428\pi$
$401$	−1.01652	+	1.01652i	−0.0507627	+	0.0507627i	0.681270	+	0.732032i	$0.261428\pi$
$402$		0			0
$403$	−13.0703	−	16.2791i	−0.651077	−	0.810919i
$404$		−	14.8919i		−	0.740902i
$405$		0			0
$406$	−3.84556	+	6.66071i	−0.190852	+	0.330565i
$407$	−6.97060			−0.345520
$408$		0			0
$409$	5.94553	+	22.1890i	0.293987	+	1.09718i	0.942018	+	0.335562i	$0.108926\pi$
$409$	5.94553	+	22.1890i	0.293987	+	1.09718i	−0.648031	+	0.761614i	$0.724407\pi$
$410$	0.867474	+	3.23746i	0.0428415	+	0.159887i
$411$		0			0
$412$	10.4934			0.516971
$413$	4.23107	−	7.32842i	0.208197	−	0.360608i
$414$		0			0
$415$			5.09794i			0.250248i
$416$	3.36064	+	1.30617i	0.164769	+	0.0640402i
$417$		0			0
$418$	−4.56904	+	4.56904i	−0.223479	+	0.223479i
$419$		−	6.60549i		−	0.322699i	−0.986897	−	0.161350i	$-0.948415\pi$
$419$		−	6.60549i		−	0.322699i	0.986897	−	0.161350i	$-0.0515847\pi$
$420$		0			0
$421$	−2.43480	−	9.08681i	−0.118665	−	0.442864i	0.880870	−	0.473359i	$-0.156958\pi$
$421$	−2.43480	−	9.08681i	−0.118665	−	0.442864i	−0.999535	+	0.0304944i	$0.990292\pi$
$422$	−3.64464	+	13.6020i	−0.177418	+	0.662134i
$423$		0			0
$424$	6.36406	+	6.36406i	0.309066	+	0.309066i
$425$		−	10.9971i		−	0.533438i
$426$		0			0
$427$	6.03569	+	6.03569i	0.292087	+	0.292087i
$428$	1.08484	+	1.87899i	0.0524376	+	0.0908246i
$429$		0			0
$430$	−0.300510	+	0.520499i	−0.0144919	+	0.0251007i
$431$	−1.92865	+	0.516780i	−0.0928998	+	0.0248924i	−0.304970	−	0.952362i	$-0.598646\pi$
$431$	−1.92865	+	0.516780i	−0.0928998	+	0.0248924i	0.212070	+	0.977255i	$0.431980\pi$
$432$		0			0
$433$	−27.7623	+	16.0286i	−1.33417	+	0.770285i	−0.985936	−	0.167122i	$-0.946553\pi$
$433$	−27.7623	+	16.0286i	−1.33417	+	0.770285i	−0.348236	+	0.937407i	$0.613219\pi$
$434$	−10.0209	+	2.68510i	−0.481020	+	0.128889i
$435$		0			0
$436$	11.3179	−	3.03262i	0.542029	−	0.145236i
$437$	40.0574	+	10.7333i	1.91620	+	0.513445i
$438$		0			0
$439$	−22.6287	+	13.0647i	−1.08001	+	0.623542i	−0.930898	−	0.365278i	$-0.880974\pi$
$439$	−22.6287	+	13.0647i	−1.08001	+	0.623542i	−0.149109	+	0.988821i	$0.547640\pi$
$440$	0.171838	+	0.641308i	0.00819206	+	0.0305732i
$441$		0			0
$442$	−8.12912	−	3.15952i	−0.386663	−	0.150283i
$443$	−9.85727	−	5.69110i	−0.468333	−	0.270392i	0.247209	−	0.968962i	$-0.420487\pi$
$443$	−9.85727	−	5.69110i	−0.468333	−	0.270392i	−0.715542	+	0.698570i	$0.753820\pi$
$444$		0			0
$445$	1.14739			0.0543914
$446$	−11.8708	+	20.5609i	−0.562099	+	0.973585i
$447$		0			0
$448$	1.26694	−	1.26694i	0.0598574	−	0.0598574i
$449$	13.3760	+	3.58409i	0.631253	+	0.169144i	0.560238	−	0.828331i	$-0.310710\pi$
$449$	13.3760	+	3.58409i	0.631253	+	0.169144i	0.0710148	+	0.997475i	$0.477376\pi$
$450$		0			0
$451$	−2.45231	−	4.24752i	−0.115475	−	0.200008i
$452$	5.54284	+	9.60049i	0.260713	+	0.451569i
$453$		0			0
$454$	20.7339	−	11.9707i	0.973092	−	0.561815i
$455$	−4.32566	−	0.472930i	−0.202790	−	0.0221713i
$456$		0			0
$457$	−32.5303	−	8.71648i	−1.52171	−	0.407740i	−0.601402	−	0.798946i	$-0.705391\pi$
$457$	−32.5303	−	8.71648i	−1.52171	−	0.407740i	−0.920303	+	0.391207i	$0.872058\pi$
$458$	−17.7846	−	10.2680i	−0.831022	−	0.479791i
$459$		0			0
$460$	3.01305	−	3.01305i	0.140484	−	0.140484i
$461$	−6.35961	−	6.35961i	−0.296196	−	0.296196i	0.543326	−	0.839522i	$-0.317165\pi$
$461$	−6.35961	−	6.35961i	−0.296196	−	0.296196i	−0.839522	+	0.543326i	$0.817165\pi$
$462$		0			0
$463$	4.90786	−	18.3164i	0.228087	−	0.851234i	−0.753057	−	0.657956i	$-0.771421\pi$
$463$	4.90786	−	18.3164i	0.228087	−	0.851234i	0.981144	−	0.193278i	$-0.0619120\pi$
$464$	−3.71748	−	2.14629i	−0.172580	−	0.0996388i
$465$		0			0
$466$	0.722288	−	2.69562i	0.0334593	−	0.124872i
$467$	−33.1417			−1.53362			−0.766808	−	0.641877i	$-0.778156\pi$
$467$	−33.1417			−1.53362			−0.766808	+	0.641877i	$0.778156\pi$
$468$		0			0
$469$	−19.8385			−0.916056
$470$	−0.661258	+	2.46785i	−0.0305015	+	0.113833i
$471$		0			0
$472$	4.09014	+	2.36144i	0.188264	+	0.108694i
$473$	0.227631	−	0.849529i	0.0104665	−	0.0390614i
$474$		0			0
$475$	21.0741	+	21.0741i	0.966945	+	0.966945i
$476$	−3.06463	+	3.06463i	−0.140467	+	0.140467i
$477$		0			0
$478$	6.80368	+	3.92811i	0.311193	+	0.179667i
$479$	29.7832	+	7.98038i	1.36083	+	0.364633i	0.864120	−	0.503285i	$-0.167876\pi$
$479$	29.7832	+	7.98038i	1.36083	+	0.364633i	0.496707	+	0.867918i	$0.334542\pi$
$480$		0			0
$481$	23.7661	+	9.23710i	1.08364	+	0.421176i
$482$	−20.1612	+	11.6401i	−0.918316	+	0.530190i
$483$		0			0
$484$	5.01422	+	8.68489i	0.227919	+	0.394768i
$485$	−0.646962	−	1.12057i	−0.0293770	−	0.0508825i
$486$		0			0
$487$	−19.5417	−	5.23619i	−0.885520	−	0.237274i	−0.212733	−	0.977110i	$-0.568236\pi$
$487$	−19.5417	−	5.23619i	−0.885520	−	0.237274i	−0.672787	+	0.739836i	$0.734903\pi$
$488$	−3.36864	+	3.36864i	−0.152491	+	0.152491i
$489$		0			0
$490$	1.27634	−	2.21068i	0.0576590	−	0.0998683i
$491$	15.1024			0.681562			0.340781	−	0.940143i	$-0.389309\pi$
$491$	15.1024			0.681562			0.340781	+	0.940143i	$0.389309\pi$
$492$		0			0
$493$	8.99228	+	5.19169i	0.404992	+	0.233822i
$494$	21.6327	−	9.52340i	0.973303	−	0.428478i
$495$		0			0
$496$	−1.49861	−	5.59289i	−0.0672896	−	0.251128i
$497$	−10.2459	+	5.91546i	−0.459590	+	0.265345i
$498$		0			0
$499$	40.4871	+	10.8485i	1.81245	+	0.485645i	0.995805	−	0.0914956i	$-0.0291647\pi$
$499$	40.4871	+	10.8485i	1.81245	+	0.485645i	0.816645	+	0.577140i	$0.195831\pi$
$500$	6.21109	−	1.66426i	0.277768	−	0.0744278i
$501$		0			0
$502$	−25.1605	+	6.74174i	−1.12297	+	0.300899i
$503$	−10.9025	+	6.29458i	−0.486120	+	0.280661i	−0.722963	−	0.690886i	$-0.757220\pi$
$503$	−10.9025	+	6.29458i	−0.486120	+	0.280661i	0.236843	+	0.971548i	$0.423887\pi$
$504$		0			0
$505$	−9.68912	+	2.59619i	−0.431160	+	0.115529i
$506$	−3.11771	+	5.40004i	−0.138599	+	0.240061i
$507$		0			0
$508$	−2.50106	−	4.33197i	−0.110967	−	0.192200i
$509$	23.4868	+	23.4868i	1.04103	+	1.04103i	0.999121	+	0.0419113i	$0.0133447\pi$
$509$	23.4868	+	23.4868i	1.04103	+	1.04103i	0.0419113	+	0.999121i	$0.486655\pi$
$510$		0			0
$511$		−	20.3164i		−	0.898744i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	1.86390	−	6.95616i	0.0822130	−	0.306823i
$515$	−1.82936	−	6.82727i	−0.0806113	−	0.300846i
$516$		0			0
$517$		−	3.73869i		−	0.164427i
$518$	8.95970	−	8.95970i	0.393667	−	0.393667i
$519$		0			0
$520$	0.263952	−	2.41424i	0.0115750	−	0.105871i
$521$			17.5549i			0.769094i	0.923105	+	0.384547i	$0.125642\pi$
$521$			17.5549i			0.769094i	−0.923105	+	0.384547i	$0.874358\pi$
$522$		0			0
$523$	−4.19432	+	7.26477i	−0.183405	+	0.317666i	−0.943038	−	0.332686i	$-0.892045\pi$
$523$	−4.19432	+	7.26477i	−0.183405	+	0.317666i	0.759633	+	0.650352i	$0.225379\pi$
$524$	21.9809			0.960242
$525$		0			0
$526$	2.96476	+	11.0646i	0.129270	+	0.482440i
$527$	3.62502	+	13.5287i	0.157908	+	0.589321i
$528$		0			0
$529$	17.0189			0.739951
$530$	3.03116	−	5.25012i	0.131665	−	0.228050i
$531$		0			0
$532$		−	11.7457i		−	0.509240i
$533$	2.73249	+	17.7315i	0.118357	+	0.768038i
$534$		0			0
$535$	1.03340	−	1.03340i	0.0446778	−	0.0446778i
$536$		−	11.0723i		−	0.478249i
$537$		0			0
$538$	−6.50898	−	24.2918i	−0.280622	−	1.04730i
$539$	−0.966799	+	3.60814i	−0.0416430	+	0.155414i
$540$		0			0
$541$	1.43745	+	1.43745i	0.0618007	+	0.0618007i	0.737332	−	0.675531i	$-0.236086\pi$
$541$	1.43745	+	1.43745i	0.0618007	+	0.0618007i	−0.675531	+	0.737332i	$0.736086\pi$
$542$		−	6.39022i		−	0.274484i
$543$		0			0
$544$	−1.71043	−	1.71043i	−0.0733343	−	0.0733343i
$545$	−3.94622	−	6.83505i	−0.169037	−	0.292781i
$546$		0			0
$547$	5.93332	−	10.2768i	0.253691	−	0.439405i	−0.710848	−	0.703345i	$-0.751689\pi$
$547$	5.93332	−	10.2768i	0.253691	−	0.439405i	0.964539	+	0.263940i	$0.0850222\pi$
$548$	−12.1601	+	3.25829i	−0.519453	+	0.139187i
$549$		0			0
$550$	−3.88080	+	2.24058i	−0.165478	+	0.0955388i
$551$	−27.1811	+	7.28317i	−1.15796	+	0.310273i
$552$		0			0
$553$	−2.79372	+	0.748574i	−0.118801	+	0.0318326i
$554$	−18.7804	−	5.03218i	−0.797901	−	0.213797i
$555$		0			0
$556$	−17.0576	+	9.84823i	−0.723405	+	0.417658i
$557$	9.18337	+	34.2728i	0.389112	+	1.45219i	0.831582	+	0.555402i	$0.187436\pi$
$557$	9.18337	+	34.2728i	0.389112	+	1.45219i	−0.442470	+	0.896783i	$0.645898\pi$
$558$		0			0
$559$	−1.90186	+	2.59481i	−0.0804400	+	0.109749i
$560$	−1.04518	−	0.603436i	−0.0441670	−	0.0254998i
$561$		0			0
$562$	−29.8076			−1.25736
$563$	−18.4876	+	32.0214i	−0.779159	+	1.34954i	0.153268	+	0.988185i	$0.451020\pi$
$563$	−18.4876	+	32.0214i	−0.779159	+	1.34954i	−0.932427	+	0.361358i	$0.882313\pi$
$564$		0			0
$565$	5.28003	−	5.28003i	0.222133	−	0.222133i
$566$	21.3237	+	5.71368i	0.896303	+	0.240164i
$567$		0			0
$568$	−3.30154	−	5.71843i	−0.138529	−	0.239940i
$569$	−12.2655	−	21.2445i	−0.514198	−	0.890616i	−0.999864	−	0.0164722i	$-0.994756\pi$
$569$	−12.2655	−	21.2445i	−0.514198	−	0.890616i	0.485667	−	0.874144i	$-0.338577\pi$
$570$		0			0
$571$	7.42838	−	4.28878i	0.310868	−	0.179480i	−0.336447	−	0.941702i	$-0.609225\pi$
$571$	7.42838	−	4.28878i	0.310868	−	0.179480i	0.647315	+	0.762223i	$0.275892\pi$
$572$	0.541280	+	3.51244i	0.0226320	+	0.146863i
$573$		0			0
$574$	8.61166	+	2.30749i	0.359444	+	0.0963127i
$575$	24.9069	+	14.3800i	1.03869	+	0.599688i
$576$		0			0
$577$	−0.991168	+	0.991168i	−0.0412629	+	0.0412629i	−0.727437	−	0.686174i	$-0.759289\pi$
$577$	−0.991168	+	0.991168i	−0.0412629	+	0.0412629i	0.686174	+	0.727437i	$0.259289\pi$
$578$	−7.88341	−	7.88341i	−0.327907	−	0.327907i
$579$		0			0
$580$	−0.748347	+	2.79287i	−0.0310734	+	0.115968i
$581$	11.7438	+	6.78029i	0.487215	+	0.281294i
$582$		0			0
$583$	−2.29604	+	8.56894i	−0.0950923	+	0.354889i
$584$	11.3390			0.469211
$585$		0			0
$586$	−9.48781			−0.391938
$587$	−9.87397	+	36.8502i	−0.407543	+	1.52097i	0.391775	+	0.920061i	$0.371861\pi$
$587$	−9.87397	+	36.8502i	−0.407543	+	1.52097i	−0.799318	+	0.600908i	$0.794806\pi$
$588$		0			0
$589$	−32.8722	−	18.9788i	−1.35448	−	0.782008i
$590$	0.823366	−	3.07284i	0.0338975	−	0.126507i
$591$		0			0
$592$	5.00059	+	5.00059i	0.205523	+	0.205523i
$593$	−22.4411	+	22.4411i	−0.921547	+	0.921547i	−0.997139	−	0.0755923i	$-0.975915\pi$
$593$	−22.4411	+	22.4411i	−0.921547	+	0.921547i	0.0755923	+	0.997139i	$0.475915\pi$
$594$		0			0
$595$	2.52821	+	1.45966i	0.103647	+	0.0598403i
$596$	−9.34027	−	2.50272i	−0.382592	−	0.102515i
$597$		0			0
$598$	17.7857	−	14.2799i	0.727310	−	0.583948i
$599$	−12.9383	+	7.46992i	−0.528644	+	0.305213i	−0.740464	−	0.672096i	$-0.765394\pi$
$599$	−12.9383	+	7.46992i	−0.528644	+	0.305213i	0.211820	+	0.977309i	$0.432061\pi$
$600$		0			0
$601$	4.71759	+	8.17110i	0.192434	+	0.333306i	0.946056	−	0.324002i	$-0.105028\pi$
$601$	4.71759	+	8.17110i	0.192434	+	0.333306i	−0.753622	+	0.657308i	$0.771695\pi$
$602$	0.799360	+	1.38453i	0.0325795	+	0.0564293i
$603$		0			0
$604$	−4.80308	−	1.28698i	−0.195434	−	0.0523665i
$605$	4.77648	−	4.77648i	0.194191	−	0.194191i
$606$		0			0
$607$	−4.11465	+	7.12678i	−0.167008	+	0.289267i	−0.937367	−	0.348344i	$-0.886744\pi$
$607$	−4.11465	+	7.12678i	−0.167008	+	0.289267i	0.770358	+	0.637611i	$0.220077\pi$
$608$	6.55551			0.265861
$609$		0			0
$610$	2.77901	+	1.60446i	0.112519	+	0.0649627i
$611$	−4.95433	+	12.7470i	−0.200431	+	0.515688i
$612$		0			0
$613$	−5.26589	−	19.6526i	−0.212687	−	0.793760i	−0.986968	−	0.160918i	$-0.948555\pi$
$613$	−5.26589	−	19.6526i	−0.212687	−	0.793760i	0.774280	−	0.632843i	$-0.218112\pi$
$614$	4.11150	−	2.37378i	0.165927	−	0.0957979i
$615$		0			0
$616$	1.70589	+	0.457091i	0.0687321	+	0.0184167i
$617$	−31.6362	+	8.47690i	−1.27363	+	0.341267i	−0.831419	−	0.555646i	$-0.812471\pi$
$617$	−31.6362	+	8.47690i	−1.27363	+	0.341267i	−0.442207	+	0.896913i	$0.645805\pi$
$618$		0			0
$619$	−9.36687	+	2.50985i	−0.376486	+	0.100879i	−0.442100	−	0.896966i	$-0.645766\pi$
$619$	−9.36687	+	2.50985i	−0.376486	+	0.100879i	0.0656133	+	0.997845i	$0.479100\pi$
$620$	−3.37763	+	1.95008i	−0.135649	+	0.0783169i
$621$		0			0
$622$	−20.4069	+	5.46802i	−0.818244	+	0.219248i
$623$	1.52603	−	2.64316i	0.0611391	−	0.105896i
$624$		0			0
$625$	9.20010	+	15.9350i	0.368004	+	0.637402i
$626$	7.30568	+	7.30568i	0.291994	+	0.291994i
$627$		0			0
$628$			9.72362i			0.388015i
$629$	−12.0960	−	12.0960i	−0.482300	−	0.482300i
$630$		0			0
$631$	−5.85572	+	21.8539i	−0.233113	+	0.869988i	0.745878	+	0.666083i	$0.232030\pi$
$631$	−5.85572	+	21.8539i	−0.233113	+	0.869988i	−0.978991	+	0.203906i	$0.934636\pi$
$632$	−0.417795	−	1.55923i	−0.0166190	−	0.0620229i
$633$		0			0
$634$		−	16.7572i		−	0.665514i
$635$	−2.38248	+	2.38248i	−0.0945457	+	0.0945457i
$636$		0			0
$637$	8.07762	−	11.0207i	0.320047	−	0.436658i
$638$		−	4.23108i		−	0.167510i
$639$		0			0
$640$	0.336790	−	0.583337i	0.0133128	−	0.0230584i
$641$	−10.7880			−0.426100			−0.213050	−	0.977041i	$-0.568340\pi$
$641$	−10.7880			−0.426100			−0.213050	+	0.977041i	$0.568340\pi$
$642$		0			0
$643$	2.77540	+	10.3579i	0.109451	+	0.408477i	0.998812	−	0.0487289i	$-0.0155170\pi$
$643$	2.77540	+	10.3579i	0.109451	+	0.408477i	−0.889361	+	0.457206i	$0.848850\pi$
$644$	−2.93360	−	10.9483i	−0.115600	−	0.431425i
$645$		0			0
$646$	−15.8572			−0.623895
$647$	2.44136	−	4.22856i	0.0959799	−	0.166242i	−0.814037	−	0.580813i	$-0.802735\pi$
$647$	2.44136	−	4.22856i	0.0959799	−	0.166242i	0.910017	+	0.414571i	$0.136068\pi$
$648$		0			0
$649$			4.65524i			0.182734i
$650$	16.2006	−	2.49658i	0.635442	−	0.0979238i
$651$		0			0
$652$	−3.40734	+	3.40734i	−0.133442	+	0.133442i
$653$		−	21.9436i		−	0.858719i	−0.903134	−	0.429360i	$-0.858739\pi$
$653$		−	21.9436i		−	0.858719i	0.903134	−	0.429360i	$-0.141261\pi$
$654$		0			0
$655$	−3.83206	−	14.3014i	−0.149731	−	0.558803i
$656$	−1.28786	+	4.80634i	−0.0502823	+	0.187656i
$657$		0			0
$658$	4.80554	+	4.80554i	0.187340	+	0.187340i
$659$		−	42.3078i		−	1.64808i	−0.566534	−	0.824038i	$-0.691716\pi$
$659$		−	42.3078i		−	1.64808i	0.566534	−	0.824038i	$-0.308284\pi$
$660$		0			0
$661$	−22.1456	−	22.1456i	−0.861363	−	0.861363i	0.130133	−	0.991497i	$-0.458460\pi$
$661$	−22.1456	−	22.1456i	−0.861363	−	0.861363i	−0.991497	+	0.130133i	$0.958460\pi$
$662$	−7.37732	−	12.7779i	−0.286728	−	0.496627i
$663$		0			0
$664$	−3.78422	+	6.55446i	−0.146856	+	0.254362i
$665$	−7.64207	+	2.04769i	−0.296347	+	0.0794059i
$666$		0			0
$667$	−23.5169	+	13.5775i	−0.910579	+	0.525723i
$668$	13.6676	−	3.66224i	0.528817	−	0.141696i
$669$		0			0
$670$	−7.20392	+	1.93029i	−0.278312	+	0.0745734i
$671$	−4.53573	−	1.21535i	−0.175100	−	0.0469179i
$672$		0			0
$673$	−32.9394	+	19.0176i	−1.26972	+	0.733075i	−0.974935	−	0.222488i	$-0.928582\pi$
$673$	−32.9394	+	19.0176i	−1.26972	+	0.733075i	−0.294787	+	0.955563i	$0.595249\pi$
$674$	1.00563	+	3.75304i	0.0387352	+	0.144562i
$675$		0			0
$676$	2.80903	−	12.6929i	0.108040	−	0.488188i
$677$	4.73877	+	2.73593i	0.182126	+	0.105150i	0.588291	−	0.808649i	$-0.299801\pi$
$677$	4.73877	+	2.73593i	0.182126	+	0.105150i	−0.406165	+	0.913800i	$0.633134\pi$
$678$		0			0
$679$	−3.44185			−0.132086
$680$	−0.814668	+	1.41105i	−0.0312411	+	0.0541111i
$681$		0			0
$682$	4.03563	−	4.03563i	0.154532	−	0.154532i
$683$	−24.9699	−	6.69067i	−0.955447	−	0.256011i	−0.252775	−	0.967525i	$-0.581343\pi$
$683$	−24.9699	−	6.69067i	−0.955447	−	0.256011i	−0.702672	+	0.711514i	$0.748010\pi$
$684$		0			0
$685$	4.23986	+	7.34366i	0.161997	+	0.280587i
$686$	−9.66611	−	16.7422i	−0.369054	−	0.639220i
$687$		0			0
$688$	−0.772736	+	0.446139i	−0.0294603	+	0.0170089i
$689$	19.1834	−	26.1730i	0.730831	−	0.997113i
$690$		0			0
$691$	32.7059	+	8.76352i	1.24419	+	0.333380i	0.820090	−	0.572235i	$-0.193923\pi$
$691$	32.7059	+	8.76352i	1.24419	+	0.333380i	0.424101	+	0.905615i	$0.360590\pi$
$692$	20.0900	+	11.5989i	0.763706	+	0.440926i
$693$		0			0
$694$	−22.8522	+	22.8522i	−0.867459	+	0.867459i
$695$	9.38129	+	9.38129i	0.355852	+	0.355852i
$696$		0			0
$697$	3.11522	−	11.6262i	0.117997	−	0.440372i
$698$	−16.4240	−	9.48239i	−0.621657	−	0.358914i
$699$		0			0
$700$	2.10827	−	7.86816i	0.0796850	−	0.297388i
$701$	−29.4689			−1.11303			−0.556513	−	0.830839i	$-0.687861\pi$
$701$	−29.4689			−1.11303			−0.556513	+	0.830839i	$0.687861\pi$
$702$		0			0
$703$	46.3599			1.74850
$704$	−0.255112	+	0.952090i	−0.00961488	+	0.0358832i
$705$		0			0
$706$	16.9718	+	9.79865i	0.638740	+	0.368777i
$707$	−6.90589	+	25.7731i	−0.259723	+	0.969298i
$708$		0			0
$709$	9.17695	+	9.17695i	0.344648	+	0.344648i	0.858111	−	0.513464i	$-0.171638\pi$
$709$	9.17695	+	9.17695i	0.344648	+	0.344648i	−0.513464	+	0.858111i	$0.671638\pi$
$710$	−3.14500	+	3.14500i	−0.118030	+	0.118030i
$711$		0			0
$712$	1.47520	+	0.851709i	0.0552856	+	0.0319191i
$713$	−35.3809	−	9.48027i	−1.32502	−	0.355039i
$714$		0			0
$715$	2.19093	−	0.964514i	0.0819361	−	0.0360708i
$716$	4.82455	−	2.78545i	0.180302	−	0.104097i
$717$		0			0
$718$	−13.5825	−	23.5255i	−0.506894	−	0.877965i
$719$	1.46802	+	2.54269i	0.0547480	+	0.0948263i	0.892101	−	0.451837i	$-0.149231\pi$
$719$	1.46802	+	2.54269i	0.0547480	+	0.0948263i	−0.837353	+	0.546663i	$0.815898\pi$
$720$		0			0
$721$	−18.1606	−	4.86612i	−0.676336	−	0.181224i
$722$	16.9527	−	16.9527i	0.630913	−	0.630913i
$723$		0			0
$724$	−10.4205	+	18.0488i	−0.387274	+	0.670779i
$725$	−19.5153			−0.724779
$726$		0			0
$727$	34.7895	+	20.0857i	1.29027	+	0.744938i	0.978702	−	0.205285i	$-0.0658122\pi$
$727$	34.7895	+	20.0857i	1.29027	+	0.744938i	0.311569	+	0.950224i	$0.399146\pi$
$728$	−5.21047	−	3.81900i	−0.193113	−	0.141541i
$729$		0			0
$730$	−1.97679	−	7.37746i	−0.0731641	−	0.273052i
$731$	1.86919	−	1.07917i	0.0691343	−	0.0399147i
$732$		0			0
$733$	12.6590	+	3.39197i	0.467571	+	0.125285i	0.484909	−	0.874564i	$-0.338853\pi$
$733$	12.6590	+	3.39197i	0.467571	+	0.125285i	−0.0173384	+	0.999850i	$0.505519\pi$
$734$	−7.43211	+	1.99143i	−0.274324	+	0.0735050i
$735$		0			0
$736$	6.11049	−	1.63730i	0.225236	−	0.0603517i
$737$	9.45150	−	5.45683i	0.348151	−	0.201005i
$738$		0			0
$739$	−20.2177	+	5.41732i	−0.743721	+	0.199279i	−0.610731	−	0.791838i	$-0.709124\pi$
$739$	−20.2177	+	5.41732i	−0.743721	+	0.199279i	−0.132990	+	0.991117i	$0.542458\pi$
$740$	2.38175	−	4.12531i	0.0875547	−	0.151649i
$741$		0			0
$742$	−8.06290	−	13.9654i	−0.295998	−	0.512684i
$743$	−11.8437	−	11.8437i	−0.434502	−	0.434502i	0.455655	−	0.890157i	$-0.349405\pi$
$743$	−11.8437	−	11.8437i	−0.434502	−	0.434502i	−0.890157	+	0.455655i	$0.849405\pi$
$744$		0			0
$745$			6.51335i			0.238631i
$746$	−11.3830	−	11.3830i	−0.416760	−	0.416760i
$747$		0			0
$748$	0.617094	−	2.30303i	0.0225632	−	0.0842070i
$749$	−1.00615	−	3.75500i	−0.0367639	−	0.137205i
$750$		0			0
$751$		−	9.36886i		−	0.341875i	−0.985282	−	0.170937i	$-0.945320\pi$
$751$		−	9.36886i		−	0.341875i	0.985282	−	0.170937i	$-0.0546796\pi$
$752$	−2.68207	+	2.68207i	−0.0978051	+	0.0978051i
$753$		0			0
$754$	−5.60683	+	14.4258i	−0.204189	+	0.525357i
$755$			3.34938i			0.121897i
$756$		0			0
$757$	1.46922	−	2.54477i	0.0533999	−	0.0924913i	−0.838090	−	0.545532i	$-0.816328\pi$
$757$	1.46922	−	2.54477i	0.0533999	−	0.0924913i	0.891490	+	0.453041i	$0.149661\pi$
$758$	25.9610			0.942945
$759$		0			0
$760$	−1.14286	−	4.26520i	−0.0414558	−	0.154715i
$761$	−2.67639	−	9.98843i	−0.0970191	−	0.362080i	0.900299	−	0.435273i	$-0.143348\pi$
$761$	−2.67639	−	9.98843i	−0.0970191	−	0.362080i	−0.997318	+	0.0731923i	$0.976681\pi$
$762$		0			0
$763$	−20.9940			−0.760032
$764$	9.03635	−	15.6514i	0.326924	−	0.566248i
$765$		0			0
$766$		−	31.4582i		−	1.13663i
$767$	6.16889	−	15.8719i	0.222746	−	0.573103i
$768$		0			0
$769$	0.0494190	−	0.0494190i	0.00178210	−	0.00178210i	−0.706215	−	0.707997i	$-0.749599\pi$
$769$	0.0494190	−	0.0494190i	0.00178210	−	0.00178210i	0.707997	+	0.706215i	$0.249599\pi$
$770$		−	1.18958i		−	0.0428696i
$771$		0			0
$772$	−1.90556	−	7.11166i	−0.0685827	−	0.255954i
$773$	−6.52883	+	24.3659i	−0.234826	+	0.876382i	0.743402	+	0.668845i	$0.233211\pi$
$773$	−6.52883	+	24.3659i	−0.234826	+	0.876382i	−0.978227	+	0.207536i	$0.933456\pi$
$774$		0			0
$775$	−18.6138	−	18.6138i	−0.668627	−	0.668627i
$776$		−	1.92097i		−	0.0689587i
$777$		0			0
$778$	−17.9583	−	17.9583i	−0.643836	−	0.643836i
$779$	16.3098	+	28.2493i	0.584358	+	1.01214i
$780$		0			0
$781$	3.25425	−	5.63652i	0.116446	−	0.201691i
$782$	−14.7808	+	3.96050i	−0.528560	+	0.141627i
$783$		0			0
$784$	3.28199	−	1.89486i	0.117214	−	0.0676734i
$785$	6.32646	−	1.69517i	0.225801	−	0.0605032i
$786$		0			0
$787$	−29.0692	+	7.78906i	−1.03620	+	0.277650i	−0.736539	−	0.676395i	$-0.763541\pi$
$787$	−29.0692	+	7.78906i	−1.03620	+	0.277650i	−0.299664	+	0.954045i	$0.596875\pi$
$788$	−23.6473	−	6.33628i	−0.842401	−	0.225721i
$789$		0			0
$790$	−0.941643	+	0.543658i	−0.0335022	+	0.0193425i
$791$	−5.14080	−	19.1857i	−0.182786	−	0.682166i
$792$		0			0
$793$	13.8540	+	10.1542i	0.491969	+	0.360587i
$794$	−1.12805	−	0.651278i	−0.0400329	−	0.0231130i
$795$		0			0
$796$	8.05743			0.285588
$797$	13.7961	−	23.8955i	0.488682	−	0.846422i	−0.511233	−	0.859442i	$-0.670811\pi$
$797$	13.7961	−	23.8955i	0.488682	−	0.846422i	0.999915	+	0.0130203i	$0.00414459\pi$
$798$		0			0
$799$	6.48772	−	6.48772i	0.229519	−	0.229519i
$800$	4.39138	+	1.17667i	0.155259	+	0.0416014i
$801$		0			0
$802$	0.718789	+	1.24498i	0.0253813	+	0.0439618i
$803$	5.58828	+	9.67919i	0.197206	+	0.341571i
$804$		0			0
$805$	−6.61187	+	3.81736i	−0.233038	+	0.134544i
$806$	−19.1072	+	8.41159i	−0.673023	+	0.296286i
$807$		0			0
$808$	−14.3845	−	3.85432i	−0.506045	−	0.135594i
$809$	31.3309	+	18.0889i	1.10154	+	0.635972i	0.936624	−	0.350336i	$-0.113933\pi$
$809$	31.3309	+	18.0889i	1.10154	+	0.635972i	0.164912	+	0.986308i	$0.447266\pi$
$810$		0			0
$811$	0.803239	−	0.803239i	0.0282055	−	0.0282055i	−0.692863	−	0.721069i	$-0.743651\pi$
$811$	0.803239	−	0.803239i	0.0282055	−	0.0282055i	0.721069	+	0.692863i	$0.243651\pi$
$812$	5.43845	+	5.43845i	0.190852	+	0.190852i
$813$		0			0
$814$	−1.80412	+	6.73309i	−0.0632345	+	0.235995i
$815$	2.81093	+	1.62289i	0.0984626	+	0.0568474i
$816$		0			0
$817$	−1.51392	+	5.65003i	−0.0529654	+	0.197669i
$818$	22.9718			0.803189
$819$		0			0
$820$	3.35166			0.117045
$821$	−12.5434	+	46.8128i	−0.437769	+	1.63378i	0.296582	+	0.955007i	$0.404153\pi$
$821$	−12.5434	+	46.8128i	−0.437769	+	1.63378i	−0.734351	+	0.678770i	$0.762514\pi$
$822$		0			0
$823$	−24.4935	−	14.1414i	−0.853791	−	0.492937i	0.00813687	−	0.999967i	$-0.497410\pi$
$823$	−24.4935	−	14.1414i	−0.853791	−	0.492937i	−0.861928	+	0.507030i	$0.830743\pi$
$824$	2.71588	−	10.1358i	0.0946122	−	0.353098i
$825$		0			0
$826$	−5.98363	−	5.98363i	−0.208197	−	0.208197i
$827$	13.1080	−	13.1080i	0.455810	−	0.455810i	−0.441467	−	0.897277i	$-0.645542\pi$
$827$	13.1080	−	13.1080i	0.455810	−	0.455810i	0.897277	+	0.441467i	$0.145542\pi$
$828$		0			0
$829$	46.5863	+	26.8966i	1.61801	+	0.934159i	0.987434	+	0.158032i	$0.0505148\pi$
$829$	46.5863	+	26.8966i	1.61801	+	0.934159i	0.630577	+	0.776127i	$0.282818\pi$
$830$	4.92424	+	1.31945i	0.170923	+	0.0457986i
$831$		0			0
$832$	2.13146	−	2.90807i	0.0738951	−	0.100819i
$833$	−7.93886	+	4.58350i	−0.275065	+	0.158809i
$834$		0			0
$835$	−4.76551	−	8.25410i	−0.164917	−	0.285645i
$836$	3.23080	+	5.59591i	0.111740	+	0.193539i
$837$		0			0
$838$	−6.38041	−	1.70963i	−0.220408	−	0.0590581i
$839$	−3.08099	+	3.08099i	−0.106368	+	0.106368i	−0.758288	−	0.651920i	$-0.773964\pi$
$839$	−3.08099	+	3.08099i	−0.106368	+	0.106368i	0.651920	+	0.758288i	$0.273964\pi$
$840$		0			0
$841$	−5.28691	+	9.15719i	−0.182307	+	0.315765i
$842$	−9.40736			−0.324199
$843$		0			0
$844$	12.1952	+	7.04091i	0.419776	+	0.242358i
$845$	−8.74806	+	0.385182i	−0.300942	+	0.0132507i
$846$		0			0
$847$	−4.65052	−	17.3560i	−0.159794	−	0.596359i
$848$	7.79435	−	4.50007i	0.267659	−	0.154533i
$849$		0			0
$850$	−10.6224	−	2.84626i	−0.364345	−	0.0976260i
$851$	43.2128	−	11.5788i	1.48132	−	0.396917i
$852$		0			0
$853$	−10.9121	+	2.92390i	−0.373625	+	0.100112i	−0.440745	−	0.897632i	$-0.645286\pi$
$853$	−10.9121	+	2.92390i	−0.373625	+	0.100112i	0.0671200	+	0.997745i	$0.478619\pi$
$854$	7.39218	−	4.26788i	0.252955	−	0.146044i
$855$		0			0
$856$	2.09574	−	0.561553i	0.0716311	−	0.0191935i
$857$	−8.91122	+	15.4347i	−0.304401	+	0.527239i	−0.977128	−	0.212653i	$-0.931790\pi$
$857$	−8.91122	+	15.4347i	−0.304401	+	0.527239i	0.672726	+	0.739891i	$0.265123\pi$
$858$		0			0
$859$	−12.6436	−	21.8993i	−0.431393	−	0.747194i	0.565601	−	0.824679i	$-0.308644\pi$
$859$	−12.6436	−	21.8993i	−0.431393	−	0.747194i	−0.996994	+	0.0774851i	$0.975311\pi$
$860$	0.424986	+	0.424986i	0.0144919	+	0.0144919i
$861$		0			0
$862$			1.99669i			0.0680074i
$863$	9.09474	+	9.09474i	0.309589	+	0.309589i	0.844750	−	0.535161i	$-0.179749\pi$
$863$	9.09474	+	9.09474i	0.309589	+	0.309589i	−0.535161	+	0.844750i	$0.679749\pi$
$864$		0			0
$865$	4.04421	−	15.0932i	0.137507	−	0.513184i
$866$	8.29701	+	30.9649i	0.281944	+	1.05223i
$867$		0			0
$868$			10.3744i			0.352131i
$869$	1.12509	−	1.12509i	0.0381659	−	0.0381659i
$870$		0			0
$871$	−39.4559	+	6.08029i	−1.33691	+	0.206023i
$872$		−	11.7172i		−	0.396793i
$873$		0			0
$874$	20.7352	−	35.9145i	0.701379	−	1.21482i
$875$	−11.5211			−0.389486
$876$		0			0
$877$	13.3656	+	49.8810i	0.451323	+	1.68436i	0.698678	+	0.715436i	$0.253772\pi$
$877$	13.3656	+	49.8810i	0.451323	+	1.68436i	−0.247355	+	0.968925i	$0.579561\pi$
$878$	6.76277	+	25.2390i	0.228232	+	0.851775i
$879$		0			0
$880$	0.663931			0.0223811
$881$	−21.3121	+	36.9136i	−0.718023	+	1.24365i	0.243759	+	0.969836i	$0.421619\pi$
$881$	−21.3121	+	36.9136i	−0.718023	+	1.24365i	−0.961782	+	0.273816i	$0.911714\pi$
$882$		0			0
$883$		−	33.4740i		−	1.12649i	−0.826290	−	0.563245i	$-0.809553\pi$
$883$		−	33.4740i		−	1.12649i	0.826290	−	0.563245i	$-0.190447\pi$
$884$	−5.15583	+	7.03439i	−0.173409	+	0.236592i
$885$		0			0
$886$	−8.04843	+	8.04843i	−0.270392	+	0.270392i
$887$		−	4.71119i		−	0.158186i	−0.996867	−	0.0790931i	$-0.974798\pi$
$887$		−	4.71119i		−	0.158186i	0.996867	−	0.0790931i	$-0.0252024\pi$
$888$		0			0
$889$	2.31965	+	8.65706i	0.0777987	+	0.290349i
$890$	0.296966	−	1.10829i	0.00995431	−	0.0371500i
$891$		0			0
$892$	16.7879	+	16.7879i	0.562099	+	0.562099i
$893$			24.8652i			0.832082i
$894$		0			0
$895$	−2.65338	−	2.65338i	−0.0886928	−	0.0886928i
$896$	−0.895864	−	1.55168i	−0.0299287	−	0.0518381i
$897$		0			0
$898$	6.92393	−	11.9926i	0.231055	−	0.400198i
$899$	24.0079	−	6.43289i	0.800708	−	0.214549i
$900$		0			0
$901$	−18.8539	+	10.8853i	−0.628115	+	0.362642i
$902$	−4.73750	+	1.26941i	−0.157741	+	0.0422667i
$903$		0			0
$904$	10.7080	−	2.86919i	0.356141	−	0.0954277i
$905$	13.5597	+	3.63332i	0.450740	+	0.120776i
$906$		0			0
$907$	1.92854	−	1.11344i	0.0640360	−	0.0369712i	−0.467640	−	0.883919i	$-0.654896\pi$
$907$	1.92854	−	1.11344i	0.0640360	−	0.0369712i	0.531676	+	0.846948i	$0.321562\pi$
$908$	−6.19651	−	23.1257i	−0.205638	−	0.767453i
$909$		0			0
$910$	−1.57638	+	4.05587i	−0.0522564	+	0.134451i
$911$	10.3509	+	5.97609i	0.342940	+	0.197997i	0.661571	−	0.749882i	$-0.269890\pi$
$911$	10.3509	+	5.97609i	0.342940	+	0.197997i	−0.318631	+	0.947879i	$0.603223\pi$
$912$		0			0
$913$	−7.46002			−0.246891
$914$	−16.8389	+	29.1659i	−0.556983	+	0.964722i
$915$		0			0
$916$	−14.5211	+	14.5211i	−0.479791	+	0.479791i
$917$	−38.0419	−	10.1933i	−1.25625	−	0.336612i
$918$		0			0
$919$	2.28777	+	3.96254i	0.0754667	+	0.130712i	0.901289	−	0.433218i	$-0.142622\pi$
$919$	2.28777	+	3.96254i	0.0754667	+	0.130712i	−0.825822	+	0.563930i	$0.809289\pi$
$920$	−2.13055	−	3.69022i	−0.0702421	−	0.121663i
$921$		0			0
$922$	−7.78890	+	4.49692i	−0.256514	+	0.148098i
$923$	−18.5645	+	14.9052i	−0.611059	+	0.490612i
$924$		0			0
$925$	31.0554	+	8.32127i	1.02110	+	0.273602i
$926$	−16.4220	−	9.48125i	−0.539661	−	0.311573i
$927$		0			0
$928$	−3.03531	+	3.03531i	−0.0996388	+	0.0996388i
$929$	−33.3985	−	33.3985i	−1.09577	−	1.09577i	−0.994900	−	0.100868i	$-0.967838\pi$
$929$	−33.3985	−	33.3985i	−1.09577	−	1.09577i	−0.100868	−	0.994900i	$-0.532162\pi$
$930$		0			0
$931$	6.42997	−	23.9970i	0.210734	−	0.786469i
$932$	−2.41682	−	1.39535i	−0.0791657	−	0.0457063i
$933$		0			0
$934$	−8.57771	+	32.0124i	−0.280671	+	1.04748i
$935$	−1.60600			−0.0525217
$936$		0			0
$937$	34.1939			1.11707			0.558533	−	0.829482i	$-0.311365\pi$
$937$	34.1939			1.11707			0.558533	+	0.829482i	$0.311365\pi$
$938$	−5.13458	+	19.1625i	−0.167650	+	0.625678i
$939$		0			0
$940$	2.21261	+	1.27745i	0.0721674	+	0.0416659i
$941$	7.56472	−	28.2319i	0.246603	−	0.920334i	−0.725968	−	0.687728i	$-0.758608\pi$
$941$	7.56472	−	28.2319i	0.246603	−	0.920334i	0.972571	−	0.232606i	$-0.0747253\pi$
$942$		0			0
$943$	22.2581	+	22.2581i	0.724824	+	0.724824i
$944$	3.33959	−	3.33959i	0.108694	−	0.108694i
$945$		0			0
$946$	−0.761667	−	0.439749i	−0.0247639	−	0.0142975i
$947$	26.6581	+	7.14301i	0.866271	+	0.232117i	0.664474	−	0.747311i	$-0.268655\pi$
$947$	26.6581	+	7.14301i	0.866271	+	0.232117i	0.201796	+	0.979428i	$0.435322\pi$
$948$		0			0
$949$	−6.22676	−	40.4063i	−0.202129	−	1.31165i
$950$	25.8104	−	14.9016i	0.837399	−	0.483472i
$951$		0			0
$952$	2.16702	+	3.75339i	0.0702336	+	0.121648i
$953$	−8.06765	−	13.9736i	−0.261337	−	0.452649i	0.705261	−	0.708948i	$-0.250830\pi$
$953$	−8.06765	−	13.9736i	−0.261337	−	0.452649i	−0.966597	+	0.256299i	$0.917497\pi$
$954$		0			0
$955$	−11.7586	−	3.15071i	−0.380500	−	0.101955i
$956$	5.55518	−	5.55518i	0.179667	−	0.179667i
$957$		0			0
$958$	15.4169	−	26.7029i	0.498097	−	0.862730i
$959$	22.5561			0.728376
$960$		0			0
$961$	2.18777	+	1.26311i	0.0705733	+	0.0407455i
$962$	15.0735	−	20.5656i	0.485989	−	0.663061i
$963$		0			0
$964$	6.02534	+	22.4869i	0.194063	+	0.724253i
$965$	−4.29484	+	2.47963i	−0.138256	+	0.0798220i
$966$		0			0
$967$	31.3117	+	8.38995i	1.00692	+	0.269803i	0.724341	−	0.689442i	$-0.242144\pi$
$967$	31.3117	+	8.38995i	1.00692	+	0.269803i	0.282576	+	0.959245i	$0.408811\pi$
$968$	9.68673	−	2.59555i	0.311343	−	0.0834242i
$969$		0			0
$970$	−1.24983	+	0.334892i	−0.0401298	+	0.0107527i
$971$	23.3310	−	13.4701i	0.748727	−	0.432278i	−0.0765068	−	0.997069i	$-0.524377\pi$
$971$	23.3310	−	13.4701i	0.748727	−	0.432278i	0.825234	+	0.564791i	$0.191043\pi$
$972$		0			0
$973$	34.0882	−	9.13391i	1.09282	−	0.292820i
$974$	−10.1155	+	17.5206i	−0.324123	+	0.561397i
$975$		0			0
$976$	2.38199	+	4.12572i	0.0762456	+	0.132061i
$977$	10.8073	+	10.8073i	0.345755	+	0.345755i	0.858526	−	0.512771i	$-0.171381\pi$
$977$	10.8073	+	10.8073i	0.345755	+	0.345755i	−0.512771	+	0.858526i	$0.671381\pi$
$978$		0			0
$979$			1.67902i			0.0536616i
$980$	−1.80501	−	1.80501i	−0.0576590	−	0.0576590i
$981$		0			0
$982$	3.90879	−	14.5878i	0.124735	−	0.465516i
$983$	0.756578	+	2.82359i	0.0241311	+	0.0900584i	0.976941	−	0.213508i	$-0.0684891\pi$
$983$	0.756578	+	2.82359i	0.0241311	+	0.0900584i	−0.952810	+	0.303567i	$0.901822\pi$
$984$		0			0
$985$			16.4902i			0.525423i
$986$	7.34216	−	7.34216i	0.233822	−	0.233822i
$987$		0			0
$988$	−3.59993	−	23.3605i	−0.114529	−	0.743195i
$989$			5.64460i			0.179488i
$990$		0			0
$991$	20.0775	−	34.7753i	0.637784	−	1.10467i	−0.348134	−	0.937445i	$-0.613185\pi$
$991$	20.0775	−	34.7753i	0.637784	−	1.10467i	0.985918	−	0.167229i	$-0.0534821\pi$
$992$	−5.79018			−0.183839
$993$		0			0
$994$	3.06207	+	11.4278i	0.0971229	+	0.362467i
$995$	−1.40469	−	5.24239i	−0.0445318	−	0.166195i
$996$		0			0
$997$	15.6393			0.495303			0.247651	−	0.968849i	$-0.420341\pi$
$997$	15.6393			0.495303			0.247651	+	0.968849i	$0.420341\pi$
$998$	20.9577	−	36.2997i	0.663403	−	1.14905i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bc.a.305.11		56
3.2	odd	2		234.2.z.a.227.1	yes	56
9.4	even	3		234.2.y.a.149.13	yes	56
9.5	odd	6		702.2.bb.a.71.4		56
13.11	odd	12		702.2.bb.a.89.4		56
39.11	even	12		234.2.y.a.11.13	✓	56
117.50	even	12	inner	702.2.bc.a.557.11		56
117.76	odd	12		234.2.z.a.167.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.13	✓	56	39.11	even	12
234.2.y.a.149.13	yes	56	9.4	even	3
234.2.z.a.167.1	yes	56	117.76	odd	12
234.2.z.a.227.1	yes	56	3.2	odd	2
702.2.bb.a.71.4		56	9.5	odd	6
702.2.bb.a.89.4		56	13.11	odd	12
702.2.bc.a.305.11		56	1.1	even	1	trivial
702.2.bc.a.557.11		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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	702.2.bc.a.305.11

Level	$702$
Weight	$2$
Character	702.305
Analytic conductor	$5.605$
Analytic rank	$0$
Dimension	$56$
Inner twists	$2$