LMFDB - Embedded newform 735.2.q.g.214.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(79,735)] 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("735.79"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.27814731656356152999936.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} - 14 x^{12} + 38 x^{11} - 40 x^{10} + 64 x^{9} + 291 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 2x^14 - 4x^13 - 14x^12 + 38x^11 - 40x^10 + 64x^9 + 291x^8 - 630x^7 + 584x^6 - 800x^5 + 734x^4 - 188x^3 + 32x^2 - 8*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			214.6
Root			$0.526774 - 1.96595i$ of defining polynomial
Character	$\chi$	$=$	735.214
Dual form			735.2.q.g.79.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34443 - 0.776205i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.204988 - 0.355049i) q^{4} +(-1.88899 + 1.19655i) q^{5} +1.55241 q^{6} +2.46837i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.61083 + 3.07491i) q^{10} +(-2.21538 + 3.83715i) q^{11} +(0.355049 - 0.204988i) q^{12} -1.73246i q^{13} +(-2.23418 + 0.0917505i) q^{15} +(2.32594 + 4.02864i) q^{16} +(2.36638 + 1.36623i) q^{17} +(1.34443 + 0.776205i) q^{18} +(0.152578 + 0.264273i) q^{19} +(0.0376154 + 0.915960i) q^{20} +6.87834i q^{22} +(-6.08316 + 3.51212i) q^{23} +(-1.23418 + 2.13767i) q^{24} +(2.13653 - 4.52053i) q^{25} +(-1.34474 - 2.32916i) q^{26} +1.00000i q^{27} +7.79430 q^{29} +(-2.93248 + 1.85754i) q^{30} +(-2.64243 + 4.57683i) q^{31} +(1.97875 + 1.14243i) q^{32} +(-3.83715 + 2.21538i) q^{33} +4.24190 q^{34} +0.409975 q^{36} +(3.18183 - 1.83703i) q^{37} +(0.410260 + 0.236864i) q^{38} +(0.866230 - 1.50035i) q^{39} +(-2.95353 - 4.66271i) q^{40} +6.71562 q^{41} -9.71562i q^{43} +(0.908250 + 1.57313i) q^{44} +(-1.98074 - 1.03763i) q^{45} +(-5.45224 + 9.44356i) q^{46} +(1.57313 - 0.908250i) q^{47} +4.65187i q^{48} +(-0.636449 - 7.73591i) q^{50} +(1.36623 + 2.36638i) q^{51} +(-0.615108 - 0.355133i) q^{52} +(1.48535 + 0.857566i) q^{53} +(0.776205 + 1.34443i) q^{54} +(-0.406524 - 9.89912i) q^{55} +0.305156i q^{57} +(10.4789 - 6.04998i) q^{58} +(0.571217 - 0.989377i) q^{59} +(-0.425404 + 0.812053i) q^{60} +(4.77818 + 8.27604i) q^{61} +8.20428i q^{62} -5.75669 q^{64} +(2.07298 + 3.27259i) q^{65} +(-3.43917 + 5.95682i) q^{66} +(-7.26104 - 4.19216i) q^{67} +(0.970157 - 0.560120i) q^{68} -7.02423 q^{69} +10.2888 q^{71} +(-2.13767 + 1.23418i) q^{72} +(-11.1028 - 6.41022i) q^{73} +(2.85183 - 4.93951i) q^{74} +(4.11056 - 2.84663i) q^{75} +0.125106 q^{76} -2.68949i q^{78} +(3.35686 + 5.81425i) q^{79} +(-9.21413 - 4.82694i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(9.02866 - 5.21270i) q^{82} -5.09946i q^{83} +(-6.10482 + 0.250704i) q^{85} +(-7.54131 - 13.0619i) q^{86} +(6.75007 + 3.89715i) q^{87} +(-9.47149 - 5.46837i) q^{88} +(-2.03533 - 3.52529i) q^{89} +(-3.46837 + 0.142434i) q^{90} +2.87976i q^{92} +(-4.57683 + 2.64243i) q^{93} +(1.40998 - 2.44215i) q^{94} +(-0.604434 - 0.316641i) q^{95} +(1.14243 + 1.97875i) q^{96} -2.87834i q^{97} -4.43075 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 2 q^{5} + 8 q^{6} + 8 q^{9} + 4 q^{10} - 4 q^{15} + 24 q^{19} + 8 q^{20} + 12 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} - 12 q^{30} - 16 q^{31} - 16 q^{34} + 16 q^{36} - 4 q^{39} - 32 q^{40}+ \cdots - 8 q^{96}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^5 + 8 * q^6 + 8 * q^9 + 4 * q^10 - 4 * q^15 + 24 * q^19 + 8 * q^20 + 12 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 - 12 * q^30 - 16 * q^31 - 16 * q^34 + 16 * q^36 - 4 * q^39 - 32 * q^40 - 16 * q^41 + 20 * q^44 + 2 * q^45 - 32 * q^46 - 40 * q^50 + 4 * q^51 + 4 * q^54 - 8 * q^55 - 4 * q^59 + 16 * q^60 - 16 * q^61 + 16 * q^64 + 30 * q^65 - 28 * q^66 - 40 * q^69 - 56 * q^71 + 40 * q^74 - 8 * q^75 + 64 * q^76 - 16 * q^79 - 52 * q^80 - 8 * q^81 - 64 * q^85 - 48 * q^86 - 16 * q^89 + 8 * q^90 + 32 * q^94 - 22 * q^95 - 8 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.34443	−	0.776205i	0.950653	−	0.548860i	0.0573691	−	0.998353i	$-0.481729\pi$
$2$	1.34443	−	0.776205i	0.950653	−	0.548860i	0.893284	+	0.449493i	$0.148395\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.204988	−	0.355049i	0.102494	−	0.177524i
$5$	−1.88899	+	1.19655i	−0.844780	+	0.535114i
$5$	−1.88899	+	1.19655i	−0.844780	+	0.535114i
$6$	1.55241			0.633769
$7$		0			0
$7$		0			0
$8$			2.46837i			0.872700i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.61083	+	3.07491i	−0.509390	+	0.972373i
$11$	−2.21538	+	3.83715i	−0.667961	+	1.15694i	0.310512	+	0.950569i	$0.399500\pi$
$11$	−2.21538	+	3.83715i	−0.667961	+	1.15694i	−0.978473	+	0.206373i	$0.933834\pi$
$12$	0.355049	−	0.204988i	0.102494	−	0.0591748i
$13$		−	1.73246i		−	0.480498i	−0.970711	−	0.240249i	$-0.922771\pi$
$13$		−	1.73246i		−	0.480498i	0.970711	−	0.240249i	$-0.0772291\pi$
$14$		0			0
$15$	−2.23418	+	0.0917505i	−0.576864	+	0.0236899i
$16$	2.32594	+	4.02864i	0.581484	+	1.00716i
$17$	2.36638	+	1.36623i	0.573931	+	0.331359i	0.758718	−	0.651419i	$-0.225826\pi$
$17$	2.36638	+	1.36623i	0.573931	+	0.331359i	−0.184787	+	0.982779i	$0.559159\pi$
$18$	1.34443	+	0.776205i	0.316884	+	0.182953i
$19$	0.152578	+	0.264273i	0.0350038	+	0.0606284i	0.882997	−	0.469379i	$-0.155522\pi$
$19$	0.152578	+	0.264273i	0.0350038	+	0.0606284i	−0.847993	+	0.530008i	$0.822189\pi$
$20$	0.0376154	+	0.915960i	0.00841106	+	0.204815i
$21$		0			0
$22$			6.87834i			1.46647i
$23$	−6.08316	+	3.51212i	−1.26843	+	0.732327i	−0.974690	−	0.223560i	$-0.928232\pi$
$23$	−6.08316	+	3.51212i	−1.26843	+	0.732327i	−0.293737	+	0.955886i	$0.594899\pi$
$24$	−1.23418	+	2.13767i	−0.251927	+	0.436350i
$25$	2.13653	−	4.52053i	0.427307	−	0.904107i
$26$	−1.34474	−	2.32916i	−0.263726	−	0.456786i
$27$			1.00000i			0.192450i
$28$		0			0
$29$	7.79430			1.44737			0.723683	−	0.690132i	$-0.242448\pi$
$29$	7.79430			1.44737			0.723683	+	0.690132i	$0.242448\pi$
$30$	−2.93248	+	1.85754i	−0.535395	+	0.339138i
$31$	−2.64243	+	4.57683i	−0.474595	+	0.822023i	−0.999577	−	0.0290906i	$-0.990739\pi$
$31$	−2.64243	+	4.57683i	−0.474595	+	0.822023i	0.524982	+	0.851114i	$0.324072\pi$
$32$	1.97875	+	1.14243i	0.349798	+	0.201956i
$33$	−3.83715	+	2.21538i	−0.667961	+	0.385648i
$34$	4.24190			0.727479
$35$		0			0
$36$	0.409975			0.0683292
$37$	3.18183	−	1.83703i	0.523090	−	0.302006i	−0.215108	−	0.976590i	$-0.569010\pi$
$37$	3.18183	−	1.83703i	0.523090	−	0.302006i	0.738198	+	0.674584i	$0.235677\pi$
$38$	0.410260	+	0.236864i	0.0665530	+	0.0384244i
$39$	0.866230	−	1.50035i	0.138708	−	0.240249i
$40$	−2.95353	−	4.66271i	−0.466994	−	0.737240i
$41$	6.71562			1.04880			0.524402	−	0.851471i	$-0.324289\pi$
$41$	6.71562			1.04880			0.524402	+	0.851471i	$0.324289\pi$
$42$		0			0
$43$		−	9.71562i		−	1.48162i	−0.671715	−	0.740809i	$-0.734442\pi$
$43$		−	9.71562i		−	1.48162i	0.671715	−	0.740809i	$-0.265558\pi$
$44$	0.908250	+	1.57313i	0.136924	+	0.237159i
$45$	−1.98074	−	1.03763i	−0.295271	−	0.154681i
$46$	−5.45224	+	9.44356i	−0.803889	+	1.39238i
$47$	1.57313	−	0.908250i	0.229465	−	0.132482i	−0.380860	−	0.924633i	$-0.624372\pi$
$47$	1.57313	−	0.908250i	0.229465	−	0.132482i	0.610325	+	0.792151i	$0.291039\pi$
$48$			4.65187i			0.671440i
$49$		0			0
$50$	−0.636449	−	7.73591i	−0.0900075	−	1.09402i
$51$	1.36623	+	2.36638i	0.191310	+	0.331359i
$52$	−0.615108	−	0.355133i	−0.0853001	−	0.0492480i
$53$	1.48535	+	0.857566i	0.204028	+	0.117796i	0.598533	−	0.801098i	$-0.295751\pi$
$53$	1.48535	+	0.857566i	0.204028	+	0.117796i	−0.394505	+	0.918894i	$0.629084\pi$
$54$	0.776205	+	1.34443i	0.105628	+	0.182953i
$55$	−0.406524	−	9.89912i	−0.0548157	−	1.33480i
$56$		0			0
$57$			0.305156i			0.0404189i
$58$	10.4789	−	6.04998i	1.37594	−	0.794401i
$59$	0.571217	−	0.989377i	0.0743661	−	0.128806i	−0.826444	−	0.563018i	$-0.809640\pi$
$59$	0.571217	−	0.989377i	0.0743661	−	0.128806i	0.900810	+	0.434213i	$0.142973\pi$
$60$	−0.425404	+	0.812053i	−0.0549194	+	0.104836i
$61$	4.77818	+	8.27604i	0.611783	+	1.05964i	0.990940	+	0.134307i	$0.0428807\pi$
$61$	4.77818	+	8.27604i	0.611783	+	1.05964i	−0.379157	+	0.925332i	$0.623786\pi$
$62$			8.20428i			1.04194i
$63$		0			0
$64$	−5.75669			−0.719586
$65$	2.07298	+	3.27259i	0.257121	+	0.405915i
$66$	−3.43917	+	5.95682i	−0.423333	+	0.733234i
$67$	−7.26104	−	4.19216i	−0.887078	−	0.512154i	−0.0140921	−	0.999901i	$-0.504486\pi$
$67$	−7.26104	−	4.19216i	−0.887078	−	0.512154i	−0.872985	+	0.487746i	$0.837819\pi$
$68$	0.970157	−	0.560120i	0.117649	−	0.0679245i
$69$	−7.02423			−0.845618
$70$		0			0
$71$	10.2888			1.22106			0.610529	−	0.791994i	$-0.290957\pi$
$71$	10.2888			1.22106			0.610529	+	0.791994i	$0.290957\pi$
$72$	−2.13767	+	1.23418i	−0.251927	+	0.145450i
$73$	−11.1028	−	6.41022i	−1.29949	−	0.750260i	−0.319172	−	0.947697i	$-0.603405\pi$
$73$	−11.1028	−	6.41022i	−1.29949	−	0.750260i	−0.980316	+	0.197437i	$0.936738\pi$
$74$	2.85183	−	4.93951i	0.331518	−	0.574206i
$75$	4.11056	−	2.84663i	0.474646	−	0.328701i
$76$	0.125106			0.0143507
$77$		0			0
$78$		−	2.68949i		−	0.304524i
$79$	3.35686	+	5.81425i	0.377676	+	0.654154i	0.990724	−	0.135892i	$-0.0433900\pi$
$79$	3.35686	+	5.81425i	0.377676	+	0.654154i	−0.613048	+	0.790046i	$0.710057\pi$
$80$	−9.21413	−	4.82694i	−1.03017	−	0.539668i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	9.02866	−	5.21270i	0.997049	−	0.575646i
$83$		−	5.09946i		−	0.559739i	−0.960038	−	0.279869i	$-0.909709\pi$
$83$		−	5.09946i		−	0.559739i	0.960038	−	0.279869i	$-0.0902911\pi$
$84$		0			0
$85$	−6.10482	+	0.250704i	−0.662161	+	0.0271927i
$86$	−7.54131	−	13.0619i	−0.813201	−	1.40850i
$87$	6.75007	+	3.89715i	0.723683	+	0.417819i
$88$	−9.47149	−	5.46837i	−1.00966	−	0.582930i
$89$	−2.03533	−	3.52529i	−0.215744	−	0.373680i	0.737758	−	0.675065i	$-0.235884\pi$
$89$	−2.03533	−	3.52529i	−0.215744	−	0.373680i	−0.953503	+	0.301385i	$0.902551\pi$
$90$	−3.46837	+	0.142434i	−0.365598	+	0.0150139i
$91$		0			0
$92$			2.87976i			0.300236i
$93$	−4.57683	+	2.64243i	−0.474595	+	0.274008i
$94$	1.40998	−	2.44215i	0.145428	−	0.251888i
$95$	−0.604434	−	0.316641i	−0.0620136	−	0.0324866i
$96$	1.14243	+	1.97875i	0.116599	+	0.201956i
$97$		−	2.87834i		−	0.292252i	−0.989266	−	0.146126i	$-0.953320\pi$
$97$		−	2.87834i		−	0.292252i	0.989266	−	0.146126i	$-0.0466804\pi$
$98$		0			0
$99$	−4.43075			−0.445308
$100$	−1.16705	−	1.68523i	−0.116705	−	0.168523i
$101$	3.60883	−	6.25068i	0.359092	−	0.621966i	−0.628717	−	0.777634i	$-0.716420\pi$
$101$	3.60883	−	6.25068i	0.359092	−	0.621966i	0.987809	+	0.155668i	$0.0497530\pi$
$102$	3.67359	+	2.12095i	0.363740	+	0.210005i
$103$	9.76304	−	5.63670i	0.961981	−	0.555400i	0.0651989	−	0.997872i	$-0.479232\pi$
$103$	9.76304	−	5.63670i	0.961981	−	0.555400i	0.896782	+	0.442472i	$0.145898\pi$
$104$	4.27635			0.419331
$105$		0			0
$106$	2.66259			0.258613
$107$	5.98940	−	3.45798i	0.579017	−	0.334296i	−0.181726	−	0.983349i	$-0.558168\pi$
$107$	5.98940	−	3.45798i	0.579017	−	0.334296i	0.760743	+	0.649054i	$0.224835\pi$
$108$	0.355049	+	0.204988i	0.0341646	+	0.0197249i
$109$	2.21097	−	3.82952i	0.211773	−	0.366801i	−0.740497	−	0.672060i	$-0.765410\pi$
$109$	2.21097	−	3.82952i	0.211773	−	0.366801i	0.952269	+	0.305259i	$0.0987430\pi$
$110$	−8.23029	−	12.9931i	−0.784727	−	1.23884i
$111$	3.67406			0.348727
$112$		0			0
$113$			2.86151i			0.269188i	0.990901	+	0.134594i	$0.0429730\pi$
$113$			2.86151i			0.269188i	−0.990901	+	0.134594i	$0.957027\pi$
$114$	0.236864	+	0.410260i	0.0221843	+	0.0384244i
$115$	7.28858	−	13.9131i	0.679664	−	1.29741i
$116$	1.59774	−	2.76736i	0.148346	−	0.256943i
$117$	1.50035	−	0.866230i	0.138708	−	0.0800830i
$118$		−	1.77353i		−	0.163266i
$119$		0			0
$120$	−0.226474	−	5.51479i	−0.0206742	−	0.503430i
$121$	−4.31579	−	7.47517i	−0.392345	−	0.679561i
$122$	12.8478	+	7.41769i	1.16319	+	0.671566i
$123$	5.81590	+	3.35781i	0.524402	+	0.302764i
$124$	1.08333	+	1.87639i	0.0972861	+	0.168504i
$125$	1.37317	+	11.0957i	0.122820	+	0.992429i
$126$		0			0
$127$			13.7325i			1.21856i	0.792956	+	0.609279i	$0.208541\pi$
$127$			13.7325i			1.21856i	−0.792956	+	0.609279i	$0.791459\pi$
$128$	−11.6970	+	6.75324i	−1.03387	+	0.596908i
$129$	4.85781	−	8.41398i	0.427706	−	0.740809i
$130$	5.32716	+	2.79070i	0.467223	+	0.244761i
$131$	10.9909	+	19.0368i	0.960277	+	1.66325i	0.721801	+	0.692100i	$0.243314\pi$
$131$	10.9909	+	19.0368i	0.960277	+	1.66325i	0.238476	+	0.971148i	$0.423352\pi$
$132$			1.81650i			0.158106i
$133$		0			0
$134$	−13.0159			−1.12440
$135$	−1.19655	−	1.88899i	−0.102983	−	0.162578i
$136$	−3.37236	+	5.84110i	−0.289177	+	0.500870i
$137$	−2.59973	−	1.50095i	−0.222110	−	0.128235i	0.384817	−	0.922993i	$-0.374265\pi$
$137$	−2.59973	−	1.50095i	−0.222110	−	0.128235i	−0.606927	+	0.794758i	$0.707598\pi$
$138$	−9.44356	+	5.45224i	−0.803889	+	0.464126i
$139$	−21.7364			−1.84366			−0.921829	−	0.387597i	$-0.873305\pi$
$139$	−21.7364			−1.84366			−0.921829	+	0.387597i	$0.873305\pi$
$140$		0			0
$141$	1.81650			0.152977
$142$	13.8325	−	7.98622i	1.16080	−	0.670189i
$143$	6.64770	+	3.83805i	0.555908	+	0.320954i
$144$	−2.32594	+	4.02864i	−0.193828	+	0.335720i
$145$	−14.7233	+	9.32628i	−1.22271	+	0.774505i
$146$	−19.9026			−1.64715
$147$		0			0
$148$		−	1.50628i		−	0.123815i
$149$	−2.60654	−	4.51467i	−0.213536	−	0.369856i	0.739282	−	0.673396i	$-0.235165\pi$
$149$	−2.60654	−	4.51467i	−0.213536	−	0.369856i	−0.952819	+	0.303540i	$0.901832\pi$
$150$	3.31677	−	7.01772i	0.270813	−	0.572994i
$151$	4.85686	−	8.41233i	0.395246	−	0.684585i	−0.597887	−	0.801580i	$-0.703993\pi$
$151$	4.85686	−	8.41233i	0.395246	−	0.684585i	0.993132	+	0.116995i	$0.0373262\pi$
$152$	−0.652324	+	0.376619i	−0.0529104	+	0.0305478i
$153$			2.73246i			0.220906i
$154$		0			0
$155$	−0.484889	−	11.8074i	−0.0389472	−	0.948391i
$156$	−0.355133	−	0.615108i	−0.0284334	−	0.0492480i
$157$	8.20284	+	4.73591i	0.654658	+	0.377967i	0.790238	−	0.612800i	$-0.209957\pi$
$157$	8.20284	+	4.73591i	0.654658	+	0.377967i	−0.135581	+	0.990766i	$0.543290\pi$
$158$	9.02610	+	5.21122i	0.718078	+	0.414582i
$159$	0.857566	+	1.48535i	0.0680094	+	0.117796i
$160$	−5.10482	+	0.209638i	−0.403571	+	0.0165733i
$161$		0			0
$162$			1.55241i			0.121969i
$163$	4.67358	−	2.69830i	0.366063	−	0.211347i	−0.305674	−	0.952136i	$-0.598882\pi$
$163$	4.67358	−	2.69830i	0.366063	−	0.211347i	0.671737	+	0.740789i	$0.265548\pi$
$164$	1.37662	−	2.38437i	0.107496	−	0.186188i
$165$	4.59750	−	8.77615i	0.357915	−	0.683223i
$166$	−3.95823	−	6.85585i	−0.307218	−	0.532117i
$167$		−	0.312550i		−	0.0241859i	−0.999927	−	0.0120929i	$-0.996151\pi$
$167$		−	0.312550i		−	0.0241859i	0.999927	−	0.0120929i	$-0.00384939\pi$
$168$		0			0
$169$	9.99859			0.769122
$170$	−8.01288	+	5.07564i	−0.614560	+	0.389284i
$171$	−0.152578	+	0.264273i	−0.0116679	+	0.0202095i
$172$	−3.44952	−	1.99158i	−0.263024	−	0.151857i
$173$	−8.32661	+	4.80737i	−0.633061	+	0.365498i	−0.781937	−	0.623358i	$-0.785768\pi$
$173$	−8.32661	+	4.80737i	−0.633061	+	0.365498i	0.148876	+	0.988856i	$0.452435\pi$
$174$	12.1000			0.917295
$175$		0			0
$176$	−20.6113			−1.55363
$177$	0.989377	−	0.571217i	0.0743661	−	0.0429353i
$178$	−5.47269	−	3.15966i	−0.410196	−	0.236827i
$179$	−4.42730	+	7.66831i	−0.330912	+	0.573157i	−0.982691	−	0.185252i	$-0.940690\pi$
$179$	−4.42730	+	7.66831i	−0.330912	+	0.573157i	0.651779	+	0.758409i	$0.274023\pi$
$180$	−0.774437	+	0.490556i	−0.0577231	+	0.0365639i
$181$	16.9234			1.25790			0.628952	−	0.777445i	$-0.283484\pi$
$181$	16.9234			1.25790			0.628952	+	0.777445i	$0.283484\pi$
$182$		0			0
$183$			9.55635i			0.706426i
$184$	−8.66920	−	15.0155i	−0.639102	−	1.10696i
$185$	−3.81233	+	7.27735i	−0.280288	+	0.535042i
$186$	−4.10214	+	7.10511i	−0.300784	+	0.520972i
$187$	−10.4848	+	6.05343i	−0.766728	+	0.442670i
$188$		−	0.744719i		−	0.0543142i
$189$		0			0
$190$	−1.05839	+	0.0434647i	−0.0767840	+	0.00315326i
$191$	−0.159271	−	0.275865i	−0.0115244	−	0.0199609i	0.860206	−	0.509947i	$-0.170335\pi$
$191$	−0.159271	−	0.275865i	−0.0115244	−	0.0199609i	−0.871730	+	0.489986i	$0.837002\pi$
$192$	−4.98544	−	2.87834i	−0.359793	−	0.207727i
$193$	−1.81289	−	1.04667i	−0.130494	−	0.0753410i	0.433332	−	0.901234i	$-0.357338\pi$
$193$	−1.81289	−	1.04667i	−0.130494	−	0.0753410i	−0.563826	+	0.825894i	$0.690671\pi$
$194$	−2.23418	−	3.86972i	−0.160405	−	0.277830i
$195$	0.158954	+	3.87063i	0.0113829	+	0.277182i
$196$		0			0
$197$			22.5798i			1.60874i	0.594126	+	0.804372i	$0.297498\pi$
$197$			22.5798i			1.60874i	−0.594126	+	0.804372i	$0.702502\pi$
$198$	−5.95682	+	3.43917i	−0.423333	+	0.244411i
$199$	3.75204	−	6.49872i	0.265975	−	0.460682i	−0.701844	−	0.712331i	$-0.747639\pi$
$199$	3.75204	−	6.49872i	0.265975	−	0.460682i	0.967819	+	0.251649i	$0.0809728\pi$
$200$	11.1583	+	5.27375i	0.789014	+	0.372911i
$201$	−4.19216	−	7.26104i	−0.295693	−	0.512154i
$202$		−	11.2048i		−	0.788365i
$203$		0			0
$204$	1.12024			0.0784325
$205$	−12.6857	+	8.03558i	−0.886009	+	0.561229i
$206$	8.75046	−	15.1562i	0.609673	−	1.05599i
$207$	−6.08316	−	3.51212i	−0.422809	−	0.244109i
$208$	6.97945	−	4.02959i	0.483938	−	0.279402i
$209$	−1.35207			−0.0935248
$210$		0			0
$211$	7.67216			0.528173			0.264087	−	0.964499i	$-0.414930\pi$
$211$	7.67216			0.528173			0.264087	+	0.964499i	$0.414930\pi$
$212$	0.608955	−	0.351581i	0.0418232	−	0.0241467i
$213$	8.91037	+	5.14441i	0.610529	+	0.352489i
$214$	5.36820	−	9.29800i	0.366963	−	0.635598i
$215$	11.6252	+	18.3527i	0.792834	+	1.25164i
$216$	−2.46837			−0.167951
$217$		0			0
$218$		−	6.86467i		−	0.464934i
$219$	−6.41022	−	11.1028i	−0.433163	−	0.750260i
$220$	−3.59801	−	1.88486i	−0.242577	−	0.127077i
$221$	2.36694	−	4.09966i	0.159217	−	0.275773i
$222$	4.93951	−	2.85183i	0.331518	−	0.191402i
$223$		−	6.90208i		−	0.462198i	−0.972930	−	0.231099i	$-0.925768\pi$
$223$		−	6.90208i		−	0.462198i	0.972930	−	0.231099i	$-0.0742321\pi$
$224$		0			0
$225$	4.98316	−	0.409975i	0.332211	−	0.0273317i
$226$	2.22112	+	3.84709i	0.147746	+	0.255904i
$227$	−5.49684	−	3.17360i	−0.364838	−	0.210639i	0.306363	−	0.951915i	$-0.400888\pi$
$227$	−5.49684	−	3.17360i	−0.364838	−	0.210639i	−0.671201	+	0.741275i	$0.734221\pi$
$228$	0.108345	+	0.0625532i	0.00717535	+	0.00414269i
$229$	−3.37834	−	5.85146i	−0.223247	−	0.386676i	0.732545	−	0.680719i	$-0.238332\pi$
$229$	−3.37834	−	5.85146i	−0.223247	−	0.386676i	−0.955792	+	0.294043i	$0.904999\pi$
$230$	−1.00049	−	24.3626i	−0.0659705	−	1.60642i
$231$		0			0
$232$			19.2392i			1.26312i
$233$	6.41899	−	3.70601i	0.420522	−	0.242789i	−0.274779	−	0.961508i	$-0.588605\pi$
$233$	6.41899	−	3.70601i	0.420522	−	0.242789i	0.695301	+	0.718719i	$0.255271\pi$
$234$	1.34474	−	2.32916i	0.0879086	−	0.152262i
$235$	−1.88486	+	3.59801i	−0.122955	+	0.234708i
$236$	−0.234185	−	0.405620i	−0.0152441	−	0.0264036i
$237$			6.71372i			0.436103i
$238$		0			0
$239$	−7.36355			−0.476309			−0.238154	−	0.971227i	$-0.576542\pi$
$239$	−7.36355			−0.476309			−0.238154	+	0.971227i	$0.576542\pi$
$240$	−5.56620	−	8.78732i	−0.359297	−	0.567219i
$241$	6.84002	−	11.8473i	0.440605	−	0.763149i	−0.557130	−	0.830425i	$-0.688097\pi$
$241$	6.84002	−	11.8473i	0.440605	−	0.763149i	0.997734	+	0.0672759i	$0.0214308\pi$
$242$	−11.6045	−	6.69988i	−0.745967	−	0.430684i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	3.91787			0.250816
$245$		0			0
$246$	10.4254			0.664699
$247$	0.457842	−	0.264335i	0.0291318	−	0.0168193i
$248$	−11.2973	−	6.52250i	−0.717380	−	0.414179i
$249$	2.54973	−	4.41626i	0.161583	−	0.279869i
$250$	10.4587	+	13.8515i	0.661463	+	0.876044i
$251$	−23.4843			−1.48231			−0.741157	−	0.671331i	$-0.765723\pi$
$251$	−23.4843			−1.48231			−0.741157	+	0.671331i	$0.765723\pi$
$252$		0			0
$253$		−	31.1226i		−	1.95666i
$254$	10.6592	+	18.4623i	0.668818	+	1.15843i
$255$	−5.41228	−	2.83529i	−0.338930	−	0.177553i
$256$	−4.72710	+	8.18758i	−0.295444	+	0.511724i
$257$	12.6417	−	7.29871i	0.788570	−	0.455281i	−0.0508890	−	0.998704i	$-0.516205\pi$
$257$	12.6417	−	7.29871i	0.788570	−	0.455281i	0.839459	+	0.543423i	$0.182872\pi$
$258$		−	15.0826i		−	0.939003i
$259$		0			0
$260$	1.58686	−	0.0651672i	0.0984131	−	0.00404150i
$261$	3.89715	+	6.75007i	0.241228	+	0.417819i
$262$	29.5528	+	17.0623i	1.82578	+	1.05411i
$263$	4.40755	+	2.54470i	0.271781	+	0.156913i	0.629697	−	0.776841i	$-0.283179\pi$
$263$	4.40755	+	2.54470i	0.271781	+	0.156913i	−0.357916	+	0.933754i	$0.616512\pi$
$264$	−5.46837	−	9.47149i	−0.336555	−	0.582930i
$265$	−3.83192	+	0.157364i	−0.235393	+	0.00966680i
$266$		0			0
$267$		−	4.07065i		−	0.249120i
$268$	−2.97685	+	1.71868i	−0.181840	+	0.104985i
$269$	−15.2550	+	26.4224i	−0.930112	+	1.61100i	−0.146984	+	0.989139i	$0.546957\pi$
$269$	−15.2550	+	26.4224i	−0.930112	+	1.61100i	−0.783127	+	0.621862i	$0.786377\pi$
$270$	−3.07491	−	1.61083i	−0.187133	−	0.0980322i
$271$	−9.74401	−	16.8771i	−0.591907	−	1.02521i	−0.993975	−	0.109603i	$-0.965042\pi$
$271$	−9.74401	−	16.8771i	−0.591907	−	1.02521i	0.402069	−	0.915609i	$-0.368291\pi$
$272$			12.7110i			0.770720i
$273$		0			0
$274$	−4.66019			−0.281532
$275$	12.6127	+	18.2129i	0.760576	+	1.09828i
$276$	−1.43988	+	2.49395i	−0.0866706	+	0.150118i
$277$	22.0665	+	12.7401i	1.32585	+	0.765478i	0.984655	−	0.174515i	$-0.0558357\pi$
$277$	22.0665	+	12.7401i	1.32585	+	0.765478i	0.341193	+	0.939993i	$0.389169\pi$
$278$	−29.2230	+	16.8719i	−1.75268	+	1.01191i
$279$	−5.28487			−0.316397
$280$		0			0
$281$	−22.1914			−1.32383			−0.661914	−	0.749580i	$-0.730255\pi$
$281$	−22.1914			−1.32383			−0.661914	+	0.749580i	$0.730255\pi$
$282$	2.44215	−	1.40998i	0.145428	−	0.0839628i
$283$	−15.6960	−	9.06209i	−0.933031	−	0.538685i	−0.0452618	−	0.998975i	$-0.514412\pi$
$283$	−15.6960	−	9.06209i	−0.933031	−	0.538685i	−0.887769	+	0.460290i	$0.847746\pi$
$284$	2.10908	−	3.65303i	0.125151	−	0.216768i
$285$	−0.365135	−	0.576436i	−0.0216287	−	0.0341451i
$286$	11.9165			0.704635
$287$		0			0
$288$			2.28487i			0.134637i
$289$	−4.76683	−	8.25640i	−0.280402	−	0.485670i
$290$	−12.5553	+	23.9668i	−0.737274	+	1.40738i
$291$	1.43917	−	2.49272i	0.0843658	−	0.146126i
$292$	−4.55188	+	2.62803i	−0.266379	+	0.153794i
$293$			13.8958i			0.811801i	0.913917	+	0.405901i	$0.133042\pi$
$293$			13.8958i			0.811801i	−0.913917	+	0.405901i	$0.866958\pi$
$294$		0			0
$295$	0.104819	+	2.55241i	0.00610279	+	0.148607i
$296$	4.53447	+	7.85394i	0.263561	+	0.456501i
$297$	−3.83715	−	2.21538i	−0.222654	−	0.128549i
$298$	−7.00861	−	4.04642i	−0.405998	−	0.234403i
$299$	6.08460	+	10.5388i	0.351881	+	0.609476i
$300$	−0.168080	−	2.04297i	−0.00970408	−	0.117951i
$301$		0			0
$302$		−	15.0797i		−	0.867737i
$303$	6.25068	−	3.60883i	0.359092	−	0.207322i
$304$	−0.709774	+	1.22936i	−0.0407083	+	0.0705089i
$305$	−18.9286	−	9.91600i	−1.08385	−	0.567788i
$306$	2.12095	+	3.67359i	0.121247	+	0.210005i
$307$			29.8332i			1.70267i	0.524622	+	0.851335i	$0.324207\pi$
$307$			29.8332i			1.70267i	−0.524622	+	0.851335i	$0.675793\pi$
$308$		0			0
$309$	11.2734			0.641321
$310$	−9.81684	−	15.4978i	−0.557559	−	0.880214i
$311$	6.75662	−	11.7028i	0.383133	−	0.663606i	−0.608375	−	0.793650i	$-0.708178\pi$
$311$	6.75662	−	11.7028i	0.383133	−	0.663606i	0.991508	+	0.130044i	$0.0415117\pi$
$312$	3.70343	+	2.13817i	0.209665	+	0.121050i
$313$	25.1023	−	14.4928i	1.41887	−	0.819184i	0.422669	−	0.906284i	$-0.361093\pi$
$313$	25.1023	−	14.4928i	1.41887	−	0.819184i	0.996200	+	0.0871001i	$0.0277600\pi$
$314$	14.7041			0.829803
$315$		0			0
$316$	2.75246			0.154838
$317$	−1.00341	+	0.579319i	−0.0563571	+	0.0325378i	−0.527914	−	0.849298i	$-0.677026\pi$
$317$	−1.00341	+	0.579319i	−0.0563571	+	0.0325378i	0.471557	+	0.881836i	$0.343692\pi$
$318$	2.30587	+	1.33129i	0.129307	+	0.0746552i
$319$	−17.2673	+	29.9079i	−0.966785	+	1.67452i
$320$	10.8743	−	6.88817i	0.607892	−	0.385060i
$321$	6.91596			0.386011
$322$		0			0
$323$			0.833827i			0.0463954i
$324$	0.204988	+	0.355049i	0.0113882	+	0.0197249i
$325$	−7.83164	−	3.70146i	−0.434421	−	0.205320i
$326$	4.18886	−	7.25532i	0.231999	−	0.401835i
$327$	3.82952	−	2.21097i	0.211773	−	0.122267i
$328$			16.5766i			0.915292i
$329$		0			0
$330$	−0.631092	−	15.3675i	−0.0347404	−	0.845953i
$331$	14.1746	+	24.5511i	0.779104	+	1.34945i	0.932459	+	0.361277i	$0.117659\pi$
$331$	14.1746	+	24.5511i	0.779104	+	1.34945i	−0.153355	+	0.988171i	$0.549008\pi$
$332$	−1.81056	−	1.04533i	−0.0993673	−	0.0573697i
$333$	3.18183	+	1.83703i	0.174363	+	0.100669i
$334$	−0.242603	−	0.420201i	−0.0132746	−	0.0229924i
$335$	18.7321	−	0.769266i	1.02345	−	0.0420295i
$336$		0			0
$337$		−	15.9729i		−	0.870101i	−0.900406	−	0.435051i	$-0.856730\pi$
$337$		−	15.9729i		−	0.870101i	0.900406	−	0.435051i	$-0.143270\pi$
$338$	13.4424	−	7.76095i	0.731168	−	0.422140i
$339$	−1.43075	+	2.47814i	−0.0777079	+	0.134594i
$340$	−1.16240	+	2.21890i	−0.0630400	+	0.120337i
$341$	−11.7080	−	20.2788i	−0.634023	−	1.09816i
$342$			0.473727i			0.0256162i
$343$		0			0
$344$	23.9817			1.29301
$345$	13.2687	−	8.40485i	0.714361	−	0.452502i
$346$	−7.46301	+	12.9263i	−0.401214	+	0.694923i
$347$	11.2687	+	6.50599i	0.604935	+	0.349260i	0.770981	−	0.636859i	$-0.219766\pi$
$347$	11.2687	+	6.50599i	0.604935	+	0.349260i	−0.166045	+	0.986118i	$0.553100\pi$
$348$	2.76736	−	1.59774i	0.148346	−	0.0856476i
$349$	32.0724			1.71680			0.858398	−	0.512984i	$-0.171460\pi$
$349$	32.0724			1.71680			0.858398	+	0.512984i	$0.171460\pi$
$350$		0			0
$351$	1.73246			0.0924718
$352$	−8.76737	+	5.06185i	−0.467303	+	0.269797i
$353$	11.5778	+	6.68445i	0.616225	+	0.355778i	0.775398	−	0.631473i	$-0.217549\pi$
$353$	11.5778	+	6.68445i	0.616225	+	0.355778i	−0.159173	+	0.987251i	$0.550883\pi$
$354$	0.886763	−	1.53592i	0.0471309	−	0.0816331i
$355$	−19.4354	+	12.3111i	−1.03152	+	0.653405i
$356$	−1.66887			−0.0884498
$357$		0			0
$358$			13.7460i			0.726497i
$359$	−6.55974	−	11.3618i	−0.346210	−	0.599653i	0.639363	−	0.768905i	$-0.279198\pi$
$359$	−6.55974	−	11.3618i	−0.346210	−	0.599653i	−0.985573	+	0.169252i	$0.945865\pi$
$360$	2.56126	−	4.88919i	0.134991	−	0.257683i
$361$	9.45344	−	16.3738i	0.497549	−	0.861781i
$362$	22.7522	−	13.1360i	1.19583	−	0.690412i
$363$		−	8.63158i		−	0.453041i
$364$		0			0
$365$	28.6432	−	1.17628i	1.49926	−	0.0615694i
$366$	7.41769	+	12.8478i	0.387729	+	0.671566i
$367$	−11.3761	−	6.56798i	−0.593826	−	0.342846i	0.172783	−	0.984960i	$-0.444724\pi$
$367$	−11.3761	−	6.56798i	−0.593826	−	0.342846i	−0.766609	+	0.642114i	$0.778057\pi$
$368$	−28.2981	−	16.3379i	−1.47514	−	0.851672i
$369$	3.35781	+	5.81590i	0.174801	+	0.302764i
$370$	0.523313	+	12.7430i	0.0272057	+	0.662478i
$371$		0			0
$372$			2.16666i			0.112336i
$373$	−25.6514	+	14.8099i	−1.32818	+	0.766826i	−0.985018	−	0.172450i	$-0.944832\pi$
$373$	−25.6514	+	14.8099i	−1.32818	+	0.766826i	−0.343163	+	0.939276i	$0.611498\pi$
$374$	−9.39740	+	16.2768i	−0.485928	+	0.841652i
$375$	−4.35865	+	10.2957i	−0.225080	+	0.531670i
$376$	2.24190	+	3.88308i	0.115617	+	0.200254i
$377$		−	13.5033i		−	0.695456i
$378$		0			0
$379$	−7.47689			−0.384062			−0.192031	−	0.981389i	$-0.561507\pi$
$379$	−7.47689			−0.384062			−0.192031	+	0.981389i	$0.561507\pi$
$380$	−0.236324	+	0.149696i	−0.0121232	+	0.00767925i
$381$	−6.86623	+	11.8927i	−0.351768	+	0.609279i
$382$	−0.428255	−	0.247253i	−0.0219114	−	0.0126506i
$383$	20.5586	−	11.8695i	1.05050	−	0.606505i	0.127709	−	0.991812i	$-0.459238\pi$
$383$	20.5586	−	11.8695i	1.05050	−	0.606505i	0.922789	+	0.385307i	$0.125904\pi$
$384$	−13.5065			−0.689250
$385$		0			0
$386$	−3.24972			−0.165406
$387$	8.41398	−	4.85781i	0.427706	−	0.246936i
$388$	−1.02195	−	0.590025i	−0.0518818	−	0.0299540i
$389$	−7.06523	+	12.2373i	−0.358221	+	0.620458i	−0.987664	−	0.156589i	$-0.949950\pi$
$389$	−7.06523	+	12.2373i	−0.358221	+	0.620458i	0.629442	+	0.777047i	$0.283283\pi$
$390$	3.21811	+	5.08040i	0.162955	+	0.257256i
$391$	−19.1934			−0.970653
$392$		0			0
$393$			21.9817i			1.10883i
$394$	17.5265	+	30.3569i	0.882975	+	1.52936i
$395$	−13.2981	−	6.96638i	−0.669100	−	0.350517i
$396$	−0.908250	+	1.57313i	−0.0456413	+	0.0790530i
$397$	9.75974	−	5.63479i	0.489827	−	0.282802i	−0.234676	−	0.972074i	$-0.575403\pi$
$397$	9.75974	−	5.63479i	0.489827	−	0.282802i	0.724503	+	0.689272i	$0.242069\pi$
$398$		−	11.6494i		−	0.583932i
$399$		0			0
$400$	23.1810	−	1.90715i	1.15905	−	0.0953576i
$401$	−11.6484	−	20.1757i	−0.581694	−	1.00752i	−0.995279	−	0.0970583i	$-0.969057\pi$
$401$	−11.6484	−	20.1757i	−0.581694	−	1.00752i	0.413584	−	0.910466i	$-0.364277\pi$
$402$	−11.2721	−	6.50796i	−0.562202	−	0.324587i
$403$	7.92917	+	4.57791i	0.394980	+	0.228042i
$404$	−1.47953	−	2.56262i	−0.0736094	−	0.127495i
$405$	−0.0917505	−	2.23418i	−0.00455912	−	0.111018i
$406$		0			0
$407$			16.2789i			0.806914i
$408$	−5.84110	+	3.37236i	−0.289177	+	0.166957i
$409$	−10.3239	+	17.8815i	−0.510484	+	0.884184i	0.489443	+	0.872036i	$0.337200\pi$
$409$	−10.3239	+	17.8815i	−0.510484	+	0.884184i	−0.999926	+	0.0121481i	$0.996133\pi$
$410$	−10.8177	+	20.6500i	−0.534250	+	1.01983i
$411$	−1.50095	−	2.59973i	−0.0740366	−	0.128235i
$412$		−	4.62181i		−	0.227700i
$413$		0			0
$414$	−10.9045			−0.535926
$415$	6.10176	+	9.63281i	0.299524	+	0.472856i
$416$	1.97922	−	3.42811i	0.0970393	−	0.168077i
$417$	−18.8243	−	10.8682i	−0.921829	−	0.532218i
$418$	−1.81776	+	1.04948i	−0.0889096	+	0.0513320i
$419$	−5.48254			−0.267839			−0.133920	−	0.990992i	$-0.542756\pi$
$419$	−5.48254			−0.267839			−0.133920	+	0.990992i	$0.542756\pi$
$420$		0			0
$421$	−3.78079			−0.184264			−0.0921322	−	0.995747i	$-0.529368\pi$
$421$	−3.78079			−0.184264			−0.0921322	+	0.995747i	$0.529368\pi$
$422$	10.3146	−	5.95517i	0.502109	−	0.289893i
$423$	1.57313	+	0.908250i	0.0764884	+	0.0441606i
$424$	−2.11679	+	3.66639i	−0.102800	+	0.178055i
$425$	11.2319	−	7.77830i	0.544829	−	0.377303i
$426$	15.9724			0.773868
$427$		0			0
$428$		−	2.83537i		−	0.137053i
$429$	3.83805	+	6.64770i	0.185303	+	0.320954i
$430$	29.8747	+	15.6502i	1.44069	+	0.754722i
$431$	13.7564	−	23.8267i	0.662621	−	1.14769i	−0.317303	−	0.948324i	$-0.602777\pi$
$431$	13.7564	−	23.8267i	0.662621	−	1.14769i	0.979924	−	0.199369i	$-0.0638894\pi$
$432$	−4.02864	+	2.32594i	−0.193828	+	0.111907i
$433$		−	8.75514i		−	0.420745i	−0.977621	−	0.210373i	$-0.932532\pi$
$433$		−	8.75514i		−	0.420745i	0.977621	−	0.210373i	$-0.0674677\pi$
$434$		0			0
$435$	−17.4139	+	0.715131i	−0.834933	+	0.0342879i
$436$	−0.906444	−	1.57001i	−0.0434108	−	0.0751897i
$437$	−1.85631	−	1.07174i	−0.0887996	−	0.0512685i
$438$	−17.2361	−	9.95129i	−0.823574	−	0.475491i
$439$	5.30636	+	9.19088i	0.253259	+	0.438657i	0.964421	−	0.264371i	$-0.0851643\pi$
$439$	5.30636	+	9.19088i	0.253259	+	0.438657i	−0.711163	+	0.703028i	$0.751831\pi$
$440$	24.4347	−	1.00345i	1.16488	−	0.0478377i
$441$		0			0
$442$		−	7.34891i		−	0.349552i
$443$	17.3080	−	9.99278i	0.822328	−	0.474771i	−0.0288905	−	0.999583i	$-0.509197\pi$
$443$	17.3080	−	9.99278i	0.822328	−	0.474771i	0.851219	+	0.524811i	$0.175864\pi$
$444$	0.753138	−	1.30447i	0.0357423	−	0.0619075i
$445$	8.06289	+	4.22385i	0.382218	+	0.200230i
$446$	−5.35743	−	9.27934i	−0.253682	−	0.439390i
$447$		−	5.21309i		−	0.246571i
$448$		0			0
$449$	−3.02578			−0.142795			−0.0713976	−	0.997448i	$-0.522746\pi$
$449$	−3.02578			−0.142795			−0.0713976	+	0.997448i	$0.522746\pi$
$450$	6.38127	−	4.41914i	0.300816	−	0.208320i
$451$	−14.8776	+	25.7688i	−0.700561	+	1.21341i
$452$	1.01598	+	0.586574i	0.0477875	+	0.0275901i
$453$	8.41233	−	4.85686i	0.395246	−	0.228195i
$454$	−9.85346			−0.462446
$455$		0			0
$456$	−0.753238			−0.0352736
$457$	1.97570	−	1.14067i	0.0924195	−	0.0533584i	−0.453078	−	0.891471i	$-0.649674\pi$
$457$	1.97570	−	1.14067i	0.0924195	−	0.0533584i	0.545497	+	0.838112i	$0.316341\pi$
$458$	−9.08387	−	5.24457i	−0.424461	−	0.245063i
$459$	−1.36623	+	2.36638i	−0.0637701	+	0.110453i
$460$	−3.44578	−	5.43982i	−0.160660	−	0.253633i
$461$	24.0678			1.12095			0.560475	−	0.828171i	$-0.310619\pi$
$461$	24.0678			1.12095			0.560475	+	0.828171i	$0.310619\pi$
$462$		0			0
$463$		−	11.1290i		−	0.517211i	−0.965983	−	0.258605i	$-0.916737\pi$
$463$		−	11.1290i		−	0.517211i	0.965983	−	0.258605i	$-0.0832629\pi$
$464$	18.1290	+	31.4004i	0.841620	+	1.45773i
$465$	5.48376	−	10.4679i	0.254303	−	0.485439i
$466$	5.75324	−	9.96490i	0.266514	−	0.461615i
$467$	−24.7481	+	14.2883i	−1.14521	+	0.661185i	−0.947714	−	0.319120i	$-0.896613\pi$
$467$	−24.7481	+	14.2883i	−1.14521	+	0.661185i	−0.197491	+	0.980305i	$0.563279\pi$
$468$		−	0.710265i		−	0.0328320i
$469$		0			0
$470$	0.258732	+	6.30029i	0.0119344	+	0.290611i
$471$	4.73591	+	8.20284i	0.218219	+	0.377967i
$472$	2.44215	+	1.40998i	0.112409	+	0.0648994i
$473$	37.2803	+	21.5238i	1.71415	+	0.989664i
$474$	5.21122	+	9.02610i	0.239359	+	0.414582i
$475$	1.52064	−	0.125106i	0.0697719	−	0.00574028i
$476$		0			0
$477$			1.71513i			0.0785305i
$478$	−9.89975	+	5.71562i	−0.452804	+	0.261427i
$479$	2.79005	−	4.83250i	0.127480	−	0.220803i	−0.795219	−	0.606322i	$-0.792644\pi$
$479$	2.79005	−	4.83250i	0.127480	−	0.220803i	0.922700	+	0.385519i	$0.125978\pi$
$480$	−4.52572	−	2.37086i	−0.206570	−	0.108214i
$481$	−3.18258	−	5.51240i	−0.145113	−	0.251344i
$482$		−	21.2370i		−	0.967320i
$483$		0			0
$484$	−3.53873			−0.160852
$485$	3.44409	+	5.43715i	0.156388	+	0.246888i
$486$	−0.776205	+	1.34443i	−0.0352094	+	0.0609844i
$487$	−7.22858	−	4.17342i	−0.327558	−	0.189116i	0.327198	−	0.944956i	$-0.393895\pi$
$487$	−7.22858	−	4.17342i	−0.327558	−	0.189116i	−0.654756	+	0.755840i	$0.727229\pi$
$488$	−20.4283	+	11.7943i	−0.924747	+	0.533903i
$489$	5.39659			0.244042
$490$		0			0
$491$	0.557405			0.0251554			0.0125777	−	0.999921i	$-0.495996\pi$
$491$	0.557405			0.0251554			0.0125777	+	0.999921i	$0.495996\pi$
$492$	2.38437	−	1.37662i	0.107496	−	0.0620628i
$493$	18.4443	+	10.6488i	0.830689	+	0.479598i
$494$	0.410357	−	0.710759i	0.0184628	−	0.0319785i
$495$	8.36963	−	5.30162i	0.376187	−	0.238290i
$496$	−24.5845			−1.10388
$497$		0			0
$498$		−	7.91645i		−	0.354745i
$499$	−13.0168	−	22.5458i	−0.582713	−	1.00929i	−0.995156	−	0.0983057i	$-0.968658\pi$
$499$	−13.0168	−	22.5458i	−0.582713	−	1.00929i	0.412443	−	0.910983i	$-0.364676\pi$
$500$	4.22100	+	1.78694i	0.188769	+	0.0799143i
$501$	0.156275	−	0.270676i	0.00698186	−	0.0120929i
$502$	−31.5729	+	18.2286i	−1.40917	+	0.813583i
$503$			5.52409i			0.246307i	0.992388	+	0.123154i	$0.0393008\pi$
$503$			5.52409i			0.246307i	−0.992388	+	0.123154i	$0.960699\pi$
$504$		0			0
$505$	0.662224	+	16.1256i	0.0294686	+	0.717580i
$506$	−24.1575	−	41.8421i	−1.07393	−	1.86011i
$507$	8.65903	+	4.99929i	0.384561	+	0.222026i
$508$	4.87569	+	2.81498i	0.216324	+	0.124895i
$509$	−11.4446	−	19.8227i	−0.507274	−	0.878625i	−0.999965	−	0.00842016i	$-0.997320\pi$
$509$	−11.4446	−	19.8227i	−0.507274	−	0.878625i	0.492690	−	0.870205i	$-0.336014\pi$
$510$	−9.47718	+	0.389196i	−0.419657	+	0.0172339i
$511$		0			0
$512$		−	12.3362i		−	0.545186i
$513$	−0.264273	+	0.152578i	−0.0116679	+	0.00673649i
$514$	11.3306	−	19.6251i	0.499771	−	0.865628i
$515$	−11.6977	+	22.3296i	−0.515460	+	0.983960i
$516$	−1.99158	−	3.44952i	−0.0876745	−	0.151857i
$517$			8.04846i			0.353971i
$518$		0			0
$519$	−9.61475			−0.422041
$520$	−8.07796	+	5.11687i	−0.354242	+	0.224390i
$521$	13.0995	−	22.6889i	0.573898	−	0.994020i	−0.422263	−	0.906474i	$-0.638764\pi$
$521$	13.0995	−	22.6889i	0.573898	−	0.994020i	0.996160	−	0.0875466i	$-0.0279027\pi$
$522$	10.4789	+	6.04998i	0.458648	+	0.264800i
$523$	−23.2753	+	13.4380i	−1.01776	+	0.587603i	−0.913454	−	0.406943i	$-0.866595\pi$
$523$	−23.2753	+	13.4380i	−1.01776	+	0.587603i	−0.104304	+	0.994545i	$0.533262\pi$
$524$	9.01197			0.393690
$525$		0			0
$526$	7.90083			0.344493
$527$	−12.5060	+	7.22034i	−0.544770	+	0.314523i
$528$	−17.8499	−	10.3056i	−0.776817	−	0.448496i
$529$	13.1699	−	22.8109i	0.572605	−	0.991780i
$530$	−5.02959	+	3.18592i	−0.218471	+	0.138387i
$531$	1.14243			0.0495774
$532$		0			0
$533$		−	11.6345i		−	0.503948i
$534$	−3.15966	−	5.47269i	−0.136732	−	0.236827i
$535$	−7.17624	+	13.6987i	−0.310256	+	0.592246i
$536$	10.3478	−	17.9229i	0.446957	−	0.774153i
$537$	−7.66831	+	4.42730i	−0.330912	+	0.191052i
$538$			47.3639i			2.04200i
$539$		0			0
$540$	−0.915960	+	0.0376154i	−0.0394167	+	0.00161871i
$541$	9.39222	+	16.2678i	0.403803	+	0.699408i	0.994181	−	0.107719i	$-0.0343547\pi$
$541$	9.39222	+	16.2678i	0.403803	+	0.699408i	−0.590378	+	0.807127i	$0.701021\pi$
$542$	−26.2002	−	15.1267i	−1.12540	−	0.649747i
$543$	14.6561	+	8.46168i	0.628952	+	0.363125i
$544$	3.12166	+	5.40687i	0.133840	+	0.231817i
$545$	0.405716	+	9.87944i	0.0173789	+	0.423189i
$546$		0			0
$547$		−	13.4126i		−	0.573483i	−0.958008	−	0.286742i	$-0.907428\pi$
$547$		−	13.4126i		−	0.573483i	0.958008	−	0.286742i	$-0.0925721\pi$
$548$	−1.06582	+	0.615353i	−0.0455297	+	0.0262866i
$549$	−4.77818	+	8.27604i	−0.203928	+	0.353213i
$550$	31.0938	+	14.6958i	1.32584	+	0.626631i
$551$	1.18924	+	2.05982i	0.0506633	+	0.0877515i
$552$		−	17.3384i		−	0.737971i
$553$		0			0
$554$	39.5557			1.68056
$555$	−6.94026	+	4.39620i	−0.294597	+	0.186608i
$556$	−4.45569	+	7.71749i	−0.188963	+	0.327294i
$557$	−34.8008	−	20.0922i	−1.47456	−	0.851336i	−0.474968	−	0.880003i	$-0.657540\pi$
$557$	−34.8008	−	20.0922i	−1.47456	−	0.851336i	−0.999589	+	0.0286677i	$0.990874\pi$
$558$	−7.10511	+	4.10214i	−0.300784	+	0.173657i
$559$	−16.8319			−0.711914
$560$		0			0
$561$	−12.1069			−0.511152
$562$	−29.8347	+	17.2251i	−1.25850	+	0.726595i
$563$	21.8134	+	12.5940i	0.919325	+	0.530772i	0.883420	−	0.468583i	$-0.155235\pi$
$563$	21.8134	+	12.5940i	0.919325	+	0.530772i	0.0359052	+	0.999355i	$0.488569\pi$
$564$	0.372360	−	0.644946i	0.0156792	−	0.0271571i
$565$	−3.42394	−	5.40535i	−0.144046	−	0.227405i
$566$	−28.1362			−1.18265
$567$		0			0
$568$			25.3966i			1.06562i
$569$	−5.51757	−	9.55672i	−0.231309	−	0.400638i	0.726885	−	0.686759i	$-0.240967\pi$
$569$	−5.51757	−	9.55672i	−0.231309	−	0.400638i	−0.958194	+	0.286121i	$0.907634\pi$
$570$	−0.938329	−	0.491556i	−0.0393023	−	0.0205890i
$571$	−14.3573	+	24.8677i	−0.600836	+	1.04068i	0.391858	+	0.920026i	$0.371832\pi$
$571$	−14.3573	+	24.8677i	−0.600836	+	1.04068i	−0.992695	+	0.120654i	$0.961501\pi$
$572$	2.72539	−	1.57351i	0.113954	−	0.0657916i
$573$		−	0.318541i		−	0.0133073i
$574$		0			0
$575$	2.87976	+	35.0029i	0.120094	+	1.45972i
$576$	−2.87834	−	4.98544i	−0.119931	−	0.207727i
$577$	−5.94444	−	3.43202i	−0.247470	−	0.142877i	0.371135	−	0.928579i	$-0.378969\pi$
$577$	−5.94444	−	3.43202i	−0.247470	−	0.142877i	−0.618605	+	0.785702i	$0.712302\pi$
$578$	−12.8173	−	7.40008i	−0.533130	−	0.307803i
$579$	−1.04667	−	1.81289i	−0.0434981	−	0.0753410i
$580$	0.293186	+	7.13927i	0.0121739	+	0.296442i
$581$		0			0
$582$		−	4.46837i		−	0.185220i
$583$	−6.58121	+	3.79966i	−0.272566	+	0.157366i
$584$	15.8228	−	27.4059i	0.654752	−	1.13406i
$585$	−1.79766	+	3.43154i	−0.0743240	+	0.141877i
$586$	10.7860	+	18.6819i	0.445565	+	0.771741i
$587$		−	9.03965i		−	0.373106i	−0.982445	−	0.186553i	$-0.940268\pi$
$587$		−	9.03965i		−	0.373106i	0.982445	−	0.186553i	$-0.0597317\pi$
$588$		0			0
$589$	−1.61271			−0.0664506
$590$	2.12211	+	3.35016i	0.0873660	+	0.137924i
$591$	−11.2899	+	19.5547i	−0.464404	+	0.804372i
$592$	14.8015	+	8.54564i	0.608337	+	0.351224i
$593$	−4.42364	+	2.55399i	−0.181657	+	0.104880i	−0.588071	−	0.808809i	$-0.700112\pi$
$593$	−4.42364	+	2.55399i	−0.181657	+	0.104880i	0.406414	+	0.913689i	$0.366779\pi$
$594$	−6.87834			−0.282222
$595$		0			0
$596$	−2.13724			−0.0875446
$597$	6.49872	−	3.75204i	0.265975	−	0.153561i
$598$	16.3606	+	9.44578i	0.669034	+	0.386267i
$599$	−14.9721	+	25.9325i	−0.611745	+	1.05957i	0.379202	+	0.925314i	$0.376199\pi$
$599$	−14.9721	+	25.9325i	−0.611745	+	1.05957i	−0.990946	+	0.134259i	$0.957135\pi$
$600$	7.02654	+	10.1464i	0.286857	+	0.414224i
$601$	12.5387			0.511466			0.255733	−	0.966747i	$-0.417683\pi$
$601$	12.5387			0.511466			0.255733	+	0.966747i	$0.417683\pi$
$602$		0			0
$603$		−	8.38433i		−	0.341436i
$604$	−1.99119	−	3.44884i	−0.0810204	−	0.140331i
$605$	17.0969	+	8.95643i	0.695087	+	0.364130i
$606$	5.60239	−	9.70362i	0.227581	−	0.394182i
$607$	−8.31216	+	4.79903i	−0.337380	+	0.194786i	−0.659113	−	0.752044i	$-0.729068\pi$
$607$	−8.31216	+	4.79903i	−0.337380	+	0.194786i	0.321733	+	0.946831i	$0.395735\pi$
$608$			0.697242i			0.0282769i
$609$		0			0
$610$	−33.1450	+	1.36115i	−1.34200	+	0.0551115i
$611$	−1.57351	−	2.72539i	−0.0636572	−	0.110258i
$612$	0.970157	+	0.560120i	0.0392163	+	0.0226415i
$613$	23.9583	+	13.8323i	0.967665	+	0.558682i	0.898524	−	0.438925i	$-0.144641\pi$
$613$	23.9583	+	13.8323i	0.967665	+	0.558682i	0.0691416	+	0.997607i	$0.477974\pi$
$614$	23.1567	+	40.1085i	0.934527	+	1.61865i
$615$	−15.0039	+	0.616162i	−0.605017	+	0.0248460i
$616$		0			0
$617$		−	20.4155i		−	0.821896i	−0.911659	−	0.410948i	$-0.865198\pi$
$617$		−	20.4155i		−	0.821896i	0.911659	−	0.410948i	$-0.134802\pi$
$618$	15.1562	−	8.75046i	0.609673	−	0.351995i
$619$	7.72112	−	13.3734i	0.310338	−	0.537521i	−0.668098	−	0.744074i	$-0.732891\pi$
$619$	7.72112	−	13.3734i	0.310338	−	0.537521i	0.978435	+	0.206553i	$0.0662245\pi$
$620$	−4.29159	−	2.24821i	−0.172354	−	0.0902901i
$621$	−3.51212	−	6.08316i	−0.140936	−	0.244109i
$622$		−	20.9781i		−	0.841145i
$623$		0			0
$624$	8.05918			0.322625
$625$	−15.8705	−	19.3165i	−0.634818	−	0.772662i
$626$	22.4988	−	38.9691i	0.899234	−	1.55752i
$627$	−1.17093	−	0.676036i	−0.0467624	−	0.0269983i
$628$	3.36296	−	1.94161i	0.134197	−	0.0774785i
$629$	10.0392			0.400290
$630$		0			0
$631$	−38.1722			−1.51961			−0.759805	−	0.650151i	$-0.774705\pi$
$631$	−38.1722			−1.51961			−0.759805	+	0.650151i	$0.774705\pi$
$632$	−14.3517	+	8.28597i	−0.570881	+	0.329598i
$633$	6.64428	+	3.83608i	0.264087	+	0.152470i
$634$	−0.899340	+	1.55770i	−0.0357173	+	0.0618643i
$635$	−16.4316	−	25.9404i	−0.652067	−	1.02941i
$636$	0.703161			0.0278822
$637$		0			0
$638$			53.6119i			2.12252i
$639$	5.14441	+	8.91037i	0.203510	+	0.352489i
$640$	14.0148	−	26.7528i	0.553983	−	1.05750i
$641$	8.39007	−	14.5320i	0.331388	−	0.573981i	−0.651396	−	0.758738i	$-0.725816\pi$
$641$	8.39007	−	14.5320i	0.331388	−	0.573981i	0.982784	+	0.184757i	$0.0591498\pi$
$642$	9.29800	−	5.36820i	0.366963	−	0.211866i
$643$		−	14.2002i		−	0.560001i	−0.960000	−	0.280001i	$-0.909665\pi$
$643$		−	14.2002i		−	0.560001i	0.960000	−	0.280001i	$-0.0903346\pi$
$644$		0			0
$645$	0.891413	+	21.7065i	0.0350994	+	0.854692i
$646$	0.647220	+	1.12102i	0.0254645	+	0.0441059i
$647$	12.5474	+	7.24426i	0.493290	+	0.284801i	0.725938	−	0.687760i	$-0.241406\pi$
$647$	12.5474	+	7.24426i	0.493290	+	0.284801i	−0.232648	+	0.972561i	$0.574739\pi$
$648$	−2.13767	−	1.23418i	−0.0839756	−	0.0484834i
$649$	2.53092	+	4.38369i	0.0993474	+	0.172075i
$650$	−13.4021	+	1.10262i	−0.525676	+	0.0432484i
$651$		0			0
$652$		−	2.21247i		−	0.0866469i
$653$	−8.90562	+	5.14166i	−0.348504	+	0.201209i	−0.664026	−	0.747709i	$-0.731154\pi$
$653$	−8.90562	+	5.14166i	−0.348504	+	0.201209i	0.315522	+	0.948918i	$0.397820\pi$
$654$	3.43233	−	5.94498i	0.134215	−	0.232467i
$655$	−43.5400	−	22.8090i	−1.70125	−	0.891222i
$656$	15.6201	+	27.0548i	0.609863	+	1.05631i
$657$		−	12.8204i		−	0.500173i
$658$		0			0
$659$	−14.9773			−0.583433			−0.291717	−	0.956505i	$-0.594226\pi$
$659$	−14.9773			−0.583433			−0.291717	+	0.956505i	$0.594226\pi$
$660$	−2.17353	−	3.43134i	−0.0846047	−	0.133565i
$661$	1.22323	−	2.11870i	0.0475782	−	0.0824079i	−0.841256	−	0.540638i	$-0.818183\pi$
$661$	1.22323	−	2.11870i	0.0475782	−	0.0824079i	0.888834	+	0.458230i	$0.151516\pi$
$662$	38.1133	+	22.0047i	1.48131	+	0.855238i
$663$	4.09966	−	2.36694i	0.159217	−	0.0919242i
$664$	12.5874			0.488484
$665$		0			0
$666$	5.70365			0.221012
$667$	−47.4140	+	27.3745i	−1.83588	+	1.05994i
$668$	−0.110971	−	0.0640689i	−0.00429358	−	0.00247890i
$669$	3.45104	−	5.97738i	0.133425	−	0.231099i
$670$	24.5869	−	15.5742i	0.949874	−	0.601684i
$671$	−42.3418			−1.63459
$672$		0			0
$673$		−	17.2596i		−	0.665310i	−0.943049	−	0.332655i	$-0.892055\pi$
$673$		−	17.2596i		−	0.665310i	0.943049	−	0.332655i	$-0.107945\pi$
$674$	−12.3983	−	21.4744i	−0.477564	−	0.827164i
$675$	4.52053	+	2.13653i	0.173995	+	0.0822352i
$676$	2.04959	−	3.54999i	0.0788302	−	0.136538i
$677$	−10.0791	+	5.81918i	−0.387372	+	0.223649i	−0.681021	−	0.732264i	$-0.738464\pi$
$677$	−10.0791	+	5.81918i	−0.387372	+	0.223649i	0.293649	+	0.955913i	$0.405130\pi$
$678$			4.44223i			0.170603i
$679$		0			0
$680$	−0.618831	−	15.0689i	−0.0237311	−	0.577868i
$681$	−3.17360	−	5.49684i	−0.121613	−	0.210639i
$682$	−31.4810	−	18.1756i	−1.20547	−	0.695979i
$683$	−26.9299	−	15.5480i	−1.03044	−	0.594928i	−0.113333	−	0.993557i	$-0.536153\pi$
$683$	−26.9299	−	15.5480i	−1.03044	−	0.594928i	−0.917112	+	0.398629i	$0.869486\pi$
$684$	0.0625532	+	0.108345i	0.00239178	+	0.00414269i
$685$	6.70681	−	0.275426i	0.256254	−	0.0105235i
$686$		0			0
$687$		−	6.75669i		−	0.257784i
$688$	39.1407	−	22.5979i	1.49223	−	0.861537i
$689$	1.48570	−	2.57330i	0.0566006	−	0.0980351i
$690$	11.3149	−	21.5989i	0.430749	−	0.822256i
$691$	−8.96695	−	15.5312i	−0.341119	−	0.590835i	0.643522	−	0.765428i	$-0.277473\pi$
$691$	−8.96695	−	15.5312i	−0.341119	−	0.590835i	−0.984641	+	0.174592i	$0.944139\pi$
$692$			3.94181i			0.149845i
$693$		0			0
$694$	20.1999			0.766778
$695$	41.0597	−	26.0087i	1.55749	−	0.986566i
$696$	−9.61961	+	16.6617i	−0.364630	+	0.631559i
$697$	15.8917	+	9.17508i	0.601941	+	0.347531i
$698$	43.1190	−	24.8947i	1.63208	−	0.942280i
$699$	7.41201			0.280348
$700$		0			0
$701$	7.04488			0.266081			0.133041	−	0.991111i	$-0.457526\pi$
$701$	7.04488			0.266081			0.133041	+	0.991111i	$0.457526\pi$
$702$	2.32916	−	1.34474i	0.0879086	−	0.0507541i
$703$	0.970956	+	0.560582i	0.0366203	+	0.0211427i
$704$	12.7532	−	22.0893i	0.480656	−	0.832520i
$705$	−3.43134	+	2.17353i	−0.129232	+	0.0818600i
$706$	20.7540			0.781088
$707$		0			0
$708$		−	0.468370i		−	0.0176024i
$709$	−12.9622	−	22.4511i	−0.486804	−	0.843170i	0.513080	−	0.858341i	$-0.328504\pi$
$709$	−12.9622	−	22.4511i	−0.486804	−	0.843170i	−0.999885	+	0.0151705i	$0.995171\pi$
$710$	−16.5736	+	31.6372i	−0.621995	+	1.18732i
$711$	−3.35686	+	5.81425i	−0.125892	+	0.218051i
$712$	8.70172	−	5.02394i	0.326111	−	0.188280i
$713$		−	37.1221i		−	1.39023i
$714$		0			0
$715$	−17.1498	+	0.704286i	−0.641367	+	0.0263388i
$716$	1.81508	+	3.14382i	0.0678329	+	0.117490i
$717$	−6.37702	−	3.68178i	−0.238154	−	0.137498i
$718$	−17.6382	−	10.1834i	−0.658251	−	0.380041i
$719$	−15.6427	−	27.0940i	−0.583376	−	1.01044i	−0.995076	−	0.0991173i	$-0.968398\pi$
$719$	−15.6427	−	27.0940i	−0.583376	−	1.01044i	0.411700	−	0.911320i	$-0.364935\pi$
$720$	−0.426811	−	10.3931i	−0.0159063	−	0.387329i
$721$		0			0
$722$		−	29.3512i		−	1.09234i
$723$	11.8473	−	6.84002i	0.440605	−	0.254383i
$724$	3.46908	−	6.00862i	0.128927	−	0.223309i
$725$	16.6528	−	35.2344i	0.618469	−	1.30857i
$726$	−6.69988	−	11.6045i	−0.248656	−	0.430684i
$727$			22.8312i			0.846761i	0.905952	+	0.423380i	$0.139157\pi$
$727$			22.8312i			0.846761i	−0.905952	+	0.423380i	$0.860843\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	37.5957	−	23.8144i	1.39148	−	0.881412i
$731$	13.2738	−	22.9908i	0.490948	−	0.850347i
$732$	3.39297	+	1.95893i	0.125408	+	0.0724043i
$733$	5.15661	−	2.97717i	0.190464	−	0.109964i	−0.401736	−	0.915756i	$-0.631593\pi$
$733$	5.15661	−	2.97717i	0.190464	−	0.109964i	0.592200	+	0.805791i	$0.298260\pi$
$734$	−20.3924			−0.752696
$735$		0			0
$736$	−16.0494			−0.591590
$737$	32.1719	−	18.5745i	1.18507	−	0.684199i
$738$	9.02866	+	5.21270i	0.332350	+	0.191882i
$739$	20.7539	−	35.9469i	0.763446	−	1.32233i	−0.177618	−	0.984099i	$-0.556839\pi$
$739$	20.7539	−	35.9469i	0.763446	−	1.32233i	0.941064	−	0.338228i	$-0.109827\pi$
$740$	1.80233	+	2.84533i	0.0662551	+	0.104596i
$741$	0.528671			0.0194212
$742$		0			0
$743$		−	6.80015i		−	0.249473i	−0.992190	−	0.124737i	$-0.960191\pi$
$743$		−	6.80015i		−	0.249473i	0.992190	−	0.124737i	$-0.0398086\pi$
$744$	−6.52250	−	11.2973i	−0.239127	−	0.414179i
$745$	10.3258	+	5.40928i	0.378306	+	0.198181i
$746$	−22.9910	+	39.8216i	−0.841760	+	1.45797i
$747$	4.41626	−	2.54973i	0.161583	−	0.0932898i
$748$			4.96351i			0.181484i
$749$		0			0
$750$	2.13172	+	17.2251i	0.0778394	+	0.628970i
$751$	−11.8056	−	20.4480i	−0.430794	−	0.746157i	0.566148	−	0.824304i	$-0.308433\pi$
$751$	−11.8056	−	20.4480i	−0.430794	−	0.746157i	−0.996942	+	0.0781464i	$0.975100\pi$
$752$	7.31802	+	4.22506i	0.266861	+	0.154072i
$753$	−20.3380	−	11.7421i	−0.741157	−	0.427907i
$754$	−10.4813	−	18.1542i	−0.381708	−	0.661137i
$755$	0.891238	+	21.7022i	0.0324355	+	0.789825i
$756$		0			0
$757$		−	16.2267i		−	0.589769i	−0.955533	−	0.294884i	$-0.904719\pi$
$757$		−	16.2267i		−	0.589769i	0.955533	−	0.294884i	$-0.0952811\pi$
$758$	−10.0521	+	5.80360i	−0.365110	+	0.210796i
$759$	15.5613	−	26.9530i	0.564840	−	0.978332i
$760$	0.781586	−	1.49197i	0.0283511	−	0.0541193i
$761$	−1.27754	−	2.21276i	−0.0463108	−	0.0802126i	0.841941	−	0.539570i	$-0.181413\pi$
$761$	−1.27754	−	2.21276i	−0.0463108	−	0.0802126i	−0.888252	+	0.459357i	$0.848080\pi$
$762$			21.3184i			0.772284i
$763$		0			0
$764$	−0.130594			−0.00472473
$765$	−3.26953	−	5.16158i	−0.118210	−	0.186617i
$766$	18.4264	−	31.9154i	0.665772	−	1.15315i
$767$	−1.71406	−	0.989610i	−0.0618910	−	0.0357328i
$768$	−8.18758	+	4.72710i	−0.295444	+	0.170575i
$769$	−45.4525			−1.63906			−0.819530	−	0.573037i	$-0.805765\pi$
$769$	−45.4525			−1.63906			−0.819530	+	0.573037i	$0.805765\pi$
$770$		0			0
$771$	14.5974			0.525713
$772$	−0.743238	+	0.429109i	−0.0267497	+	0.0154440i
$773$	−44.5909	−	25.7446i	−1.60382	−	0.925968i	−0.990713	−	0.135970i	$-0.956585\pi$
$773$	−44.5909	−	25.7446i	−1.60382	−	0.925968i	−0.613110	−	0.789997i	$-0.710082\pi$
$774$	7.54131	−	13.0619i	0.271067	−	0.469502i
$775$	15.0441	+	21.7238i	0.540399	+	0.780341i
$776$	7.10482			0.255048
$777$		0			0
$778$			21.9363i			0.786453i
$779$	1.02466	+	1.77476i	0.0367121	+	0.0635873i
$780$	1.40685	+	0.736995i	0.0503732	+	0.0263887i
$781$	−22.7936	+	39.4797i	−0.815619	+	1.41269i
$782$	−25.8041	+	14.8980i	−0.922754	+	0.532752i
$783$			7.79430i			0.278546i
$784$		0			0
$785$	−21.1618	+	0.869044i	−0.755297	+	0.0310175i
$786$	17.0623	+	29.5528i	0.608593	+	1.05411i
$787$	−17.4517	−	10.0757i	−0.622085	−	0.359161i	0.155596	−	0.987821i	$-0.450270\pi$
$787$	−17.4517	−	10.0757i	−0.622085	−	0.359161i	−0.777680	+	0.628660i	$0.783604\pi$
$788$	8.01693	+	4.62858i	0.285591	+	0.164886i
$789$	2.54470	+	4.40755i	0.0905937	+	0.156913i
$790$	−23.2857	+	0.956264i	−0.828466	+	0.0340223i
$791$		0			0
$792$		−	10.9367i		−	0.388620i
$793$	14.3379	−	8.27800i	0.509154	−	0.293960i
$794$	8.74750	−	15.1511i	0.310437	−	0.537693i
$795$	−3.39722	−	1.77968i	−0.120487	−	0.0631187i
$796$	−1.53824	−	2.66431i	−0.0545216	−	0.0944341i
$797$		−	13.0702i		−	0.462971i	−0.972838	−	0.231486i	$-0.925641\pi$
$797$		−	13.0702i		−	0.462971i	0.972838	−	0.231486i	$-0.0743587\pi$
$798$		0			0
$799$	4.96351			0.175596
$800$	9.39209	−	6.50418i	0.332060	−	0.229957i
$801$	2.03533	−	3.52529i	0.0719148	−	0.124560i
$802$	−31.3209	−	18.0831i	−1.10598	−	0.638537i
$803$	49.1939	−	28.4021i	1.73602	−	1.00229i
$804$	−3.43737			−0.121227
$805$		0			0
$806$	14.2136			0.500652
$807$	−26.4224	+	15.2550i	−0.930112	+	0.537000i
$808$	15.4290	+	8.90793i	0.542790	+	0.313380i
$809$	−0.868598	+	1.50446i	−0.0305383	+	0.0528938i	−0.880891	−	0.473320i	$-0.843055\pi$
$809$	−0.868598	+	1.50446i	−0.0305383	+	0.0528938i	0.850352	+	0.526214i	$0.176389\pi$
$810$	−1.85754	−	2.93248i	−0.0652672	−	0.103037i
$811$	27.9004			0.979715			0.489858	−	0.871802i	$-0.337049\pi$
$811$	27.9004			0.979715			0.489858	+	0.871802i	$0.337049\pi$
$812$		0			0
$813$		−	19.4880i		−	0.683475i
$814$	12.6357	+	21.8857i	0.442883	+	0.767095i
$815$	−5.59969	+	10.6892i	−0.196148	+	0.374427i
$816$	−6.35552	+	11.0081i	−0.222488	+	0.385360i
$817$	2.56758	−	1.48239i	0.0898282	−	0.0518623i
$818$			32.0538i			1.12074i
$819$		0			0
$820$	0.252611	+	6.15124i	0.00882156	+	0.214811i
$821$	−8.46799	−	14.6670i	−0.295535	−	0.511881i	0.679574	−	0.733607i	$-0.262165\pi$
$821$	−8.46799	−	14.6670i	−0.295535	−	0.511881i	−0.975109	+	0.221725i	$0.928831\pi$
$822$	−4.03584	−	2.33009i	−0.140766	−	0.0812714i
$823$	−8.56526	−	4.94516i	−0.298566	−	0.172377i	0.343232	−	0.939251i	$-0.388478\pi$
$823$	−8.56526	−	4.94516i	−0.298566	−	0.172377i	−0.641799	+	0.766873i	$0.721812\pi$
$824$	13.9134	+	24.0988i	0.484698	+	0.839521i
$825$	1.81650	+	22.0792i	0.0632424	+	0.768698i
$826$		0			0
$827$		−	35.3201i		−	1.22820i	−0.789228	−	0.614101i	$-0.789519\pi$
$827$		−	35.3201i		−	1.22820i	0.789228	−	0.614101i	$-0.210481\pi$
$828$	−2.49395	+	1.43988i	−0.0866706	+	0.0500393i
$829$	−4.64975	+	8.05361i	−0.161493	+	0.279713i	−0.935404	−	0.353580i	$-0.884964\pi$
$829$	−4.64975	+	8.05361i	−0.161493	+	0.279713i	0.773912	+	0.633294i	$0.218297\pi$
$830$	15.6804	+	8.21438i	0.544275	+	0.285125i
$831$	12.7401	+	22.0665i	0.441949	+	0.765478i
$832$			9.97323i			0.345760i
$833$		0			0
$834$	−33.7438			−1.16845
$835$	0.373982	+	0.590403i	0.0129422	+	0.0204317i
$836$	−0.277158	+	0.480052i	−0.00958571	+	0.0166029i
$837$	−4.57683	−	2.64243i	−0.158198	−	0.0913359i
$838$	−7.37086	+	4.25557i	−0.254622	+	0.147006i
$839$	−7.93405			−0.273914			−0.136957	−	0.990577i	$-0.543732\pi$
$839$	−7.93405			−0.273914			−0.136957	+	0.990577i	$0.543732\pi$
$840$		0			0
$841$	31.7512			1.09487
$842$	−5.08299	+	2.93467i	−0.175171	+	0.101135i
$843$	−19.2183	−	11.0957i	−0.661914	−	0.382156i
$844$	1.57270	−	2.72399i	0.0541345	−	0.0937636i
$845$	−18.8872	+	11.9638i	−0.649739	+	0.411568i
$846$	2.81995			0.0969519
$847$		0			0
$848$			7.97857i			0.273985i
$849$	−9.06209	−	15.6960i	−0.311010	−	0.538685i
$850$	9.06295	−	19.1756i	0.310857	−	0.657719i
$851$	−12.9037	+	22.3499i	−0.442334	+	0.766146i
$852$	3.65303	−	2.10908i	0.125151	−	0.0722558i
$853$		−	30.0757i		−	1.02977i	−0.857258	−	0.514887i	$-0.827834\pi$
$853$		−	30.0757i		−	1.02977i	0.857258	−	0.514887i	$-0.172166\pi$
$854$		0			0
$855$	−0.0279982	−	0.681775i	−0.000957519	−	0.0233162i
$856$	8.53557	+	14.7840i	0.291740	+	0.505308i
$857$	−40.8221	−	23.5686i	−1.39446	−	0.805090i	−0.400652	−	0.916230i	$-0.631216\pi$
$857$	−40.8221	−	23.5686i	−1.39446	−	0.805090i	−0.993805	+	0.111141i	$0.964550\pi$
$858$	10.3199	+	5.95823i	0.352317	+	0.203410i
$859$	16.3183	+	28.2642i	0.556774	+	0.964361i	0.997763	+	0.0668485i	$0.0212944\pi$
$859$	16.3183	+	28.2642i	0.556774	+	0.964361i	−0.440989	+	0.897512i	$0.645372\pi$
$860$	8.89912	−	0.365457i	0.303458	−	0.0124620i
$861$		0			0
$862$		−	42.7110i		−	1.45474i
$863$	−32.3982	+	18.7051i	−1.10285	+	0.636728i	−0.936967	−	0.349418i	$-0.886379\pi$
$863$	−32.3982	+	18.7051i	−1.10285	+	0.636728i	−0.165879	+	0.986146i	$0.553046\pi$
$864$	−1.14243	+	1.97875i	−0.0388664	+	0.0673186i
$865$	9.97659	−	19.0443i	0.339214	−	0.647525i
$866$	−6.79578	−	11.7706i	−0.230930	−	0.399983i
$867$		−	9.53367i		−	0.323780i
$868$		0			0
$869$	−29.7468			−1.00909
$870$	−22.8566	+	14.4782i	−0.774913	+	0.490857i
$871$	−7.26275	+	12.5795i	−0.246089	+	0.426239i
$872$	9.45266	+	5.45750i	0.320108	+	0.184814i
$873$	2.49272	−	1.43917i	0.0843658	−	0.0487086i
$874$	−3.32757			−0.112557
$875$		0			0
$876$	−5.25606			−0.177586
$877$	29.0687	−	16.7828i	0.981581	−	0.566716i	0.0788336	−	0.996888i	$-0.474880\pi$
$877$	29.0687	−	16.7828i	0.981581	−	0.566716i	0.902747	+	0.430172i	$0.141547\pi$
$878$	14.2680	+	8.23764i	0.481522	+	0.278007i
$879$	−6.94790	+	12.0341i	−0.234347	+	0.405901i
$880$	38.9344	−	24.6625i	1.31248	−	0.831371i
$881$	12.1952			0.410867			0.205433	−	0.978671i	$-0.434140\pi$
$881$	12.1952			0.410867			0.205433	+	0.978671i	$0.434140\pi$
$882$		0			0
$883$			11.0408i			0.371552i	0.982592	+	0.185776i	$0.0594799\pi$
$883$			11.0408i			0.371552i	−0.982592	+	0.185776i	$0.940520\pi$
$884$	−0.970385	−	1.68076i	−0.0326376	−	0.0565300i
$885$	−1.18543	+	2.26286i	−0.0398478	+	0.0760652i
$886$	15.5129	−	26.8691i	0.521166	−	0.902685i
$887$	−1.35180	+	0.780464i	−0.0453891	+	0.0262054i	−0.522523	−	0.852625i	$-0.675009\pi$
$887$	−1.35180	+	0.780464i	−0.0453891	+	0.0262054i	0.477134	+	0.878831i	$0.341676\pi$
$888$			9.06895i			0.304334i
$889$		0			0
$890$	14.1185	−	0.579801i	0.473254	−	0.0194350i
$891$	−2.21538	−	3.83715i	−0.0742179	−	0.128549i
$892$	−2.45058	−	1.41484i	−0.0820514	−	0.0473724i
$893$	0.480052	+	0.277158i	0.0160643	+	0.00927474i
$894$	−4.04642	−	7.00861i	−0.135333	−	0.234403i
$895$	−0.812414	−	19.7828i	−0.0271560	−	0.661267i
$896$		0			0
$897$			12.1692i			0.406318i
$898$	−4.06793	+	2.34862i	−0.135749	+	0.0783745i
$899$	−20.5959	+	35.6732i	−0.686913	+	1.18977i
$900$	0.875925	−	1.85331i	0.0291975	−	0.0617769i
$901$	2.34326	+	4.05865i	0.0780654	+	0.135213i
$902$			46.1924i			1.53804i
$903$		0			0
$904$	−7.06326			−0.234921
$905$	−31.9680	+	20.2497i	−1.06265	+	0.673121i
$906$	7.53983	−	13.0594i	0.250494	−	0.433869i
$907$	15.0756	+	8.70390i	0.500577	+	0.289008i	0.728952	−	0.684565i	$-0.240008\pi$
$907$	15.0756	+	8.70390i	0.500577	+	0.289008i	−0.228375	+	0.973573i	$0.573341\pi$
$908$	−2.25357	+	1.30110i	−0.0747873	+	0.0431785i
$909$	7.21767			0.239395
$910$		0			0
$911$	−18.3203			−0.606978			−0.303489	−	0.952835i	$-0.598152\pi$
$911$	−18.3203			−0.606978			−0.303489	+	0.952835i	$0.598152\pi$
$912$	−1.22936	+	0.709774i	−0.0407083	+	0.0235030i
$913$	19.5674	+	11.2972i	0.647586	+	0.373884i
$914$	1.77079	−	3.06710i	0.0585726	−	0.101451i
$915$	−11.4347	−	18.0518i	−0.378018	−	0.596774i
$916$	−2.77007			−0.0915258
$917$		0			0
$918$			4.24190i			0.140003i
$919$	11.2963	+	19.5658i	0.372632	+	0.645417i	0.989970	−	0.141281i	$-0.0451221\pi$
$919$	11.2963	+	19.5658i	0.372632	+	0.645417i	−0.617338	+	0.786698i	$0.711789\pi$
$920$	34.3428	+	17.9909i	1.13225	+	0.593143i
$921$	−14.9166	+	25.8363i	−0.491519	+	0.851335i
$922$	32.3574	−	18.6816i	1.06563	−	0.615244i
$923$		−	17.8249i		−	0.586715i
$924$		0			0
$925$	−1.50628	−	18.3085i	−0.0495260	−	0.601979i
$926$	−8.63842	−	14.9622i	−0.283876	−	0.491688i
$927$	9.76304	+	5.63670i	0.320660	+	0.185133i
$928$	15.4230	+	8.90448i	0.506285	+	0.292304i
$929$	−19.3356	−	33.4903i	−0.634381	−	1.09878i	−0.986646	−	0.162880i	$-0.947922\pi$
$929$	−19.3356	−	33.4903i	−0.634381	−	1.09878i	0.352265	−	0.935900i	$-0.385412\pi$
$930$	−0.752747	−	18.3299i	−0.0246835	−	0.601060i
$931$		0			0
$932$		−	3.03874i		−	0.0995372i
$933$	11.7028	−	6.75662i	0.383133	−	0.221202i
$934$	−22.1813	+	38.4192i	−0.725795	+	1.25711i
$935$	12.5625	−	23.9805i	0.410837	−	0.784246i
$936$	2.13817	+	3.70343i	0.0698884	+	0.121050i
$937$		−	46.7921i		−	1.52863i	−0.644842	−	0.764316i	$-0.723077\pi$
$937$		−	46.7921i		−	1.52863i	0.644842	−	0.764316i	$-0.276923\pi$
$938$		0			0
$939$	28.9857			0.945912
$940$	0.891095	+	1.40676i	0.0290643	+	0.0458836i
$941$	−20.9461	+	36.2797i	−0.682824	+	1.18268i	0.291292	+	0.956634i	$0.405915\pi$
$941$	−20.9461	+	36.2797i	−0.682824	+	1.18268i	−0.974116	+	0.226051i	$0.927418\pi$
$942$	12.7342	+	7.35207i	0.414901	+	0.239543i
$943$	−40.8522	+	23.5860i	−1.33033	+	0.768067i
$944$	5.31446			0.172971
$945$		0			0
$946$	66.8274			2.17275
$947$	−48.5967	+	28.0573i	−1.57918	+	0.911740i	−0.584206	+	0.811605i	$0.698594\pi$
$947$	−48.5967	+	28.0573i	−1.57918	+	0.911740i	−0.994974	+	0.100134i	$0.968073\pi$
$948$	2.38370	+	1.37623i	0.0774189	+	0.0446978i
$949$	−11.1054	+	19.2352i	−0.360498	+	0.624401i
$950$	1.94728	−	1.34853i	0.0631782	−	0.0437520i
$951$	−1.15864			−0.0375714
$952$		0			0
$953$			17.7705i			0.575643i	0.957684	+	0.287821i	$0.0929309\pi$
$953$			17.7705i			0.575643i	−0.957684	+	0.287821i	$0.907069\pi$
$954$	1.33129	+	2.30587i	0.0431022	+	0.0746552i
$955$	0.630946	+	0.330529i	0.0204169	+	0.0106957i
$956$	−1.50944	+	2.61442i	−0.0488187	+	0.0845564i
$957$	−29.9079	+	17.2673i	−0.966785	+	0.558173i
$958$		−	8.66259i		−	0.279875i
$959$		0			0
$960$	12.8615	−	0.528179i	0.415103	−	0.0170469i
$961$	1.53508	+	2.65884i	0.0495188	+	0.0857690i
$962$	−8.55750	−	4.94067i	−0.275905	−	0.159294i
$963$	5.98940	+	3.45798i	0.193006	+	0.111432i
$964$	−2.80424	−	4.85708i	−0.0903185	−	0.156436i
$965$	4.67691	−	0.192065i	0.150555	−	0.00618279i
$966$		0			0
$967$			22.5942i			0.726579i	0.931676	+	0.363290i	$0.118346\pi$
$967$			22.5942i			0.726579i	−0.931676	+	0.363290i	$0.881654\pi$
$968$	18.4515	−	10.6530i	0.593053	−	0.342399i
$969$	−0.416913	+	0.722115i	−0.0133932	+	0.0231977i
$970$	8.85066	+	4.63653i	0.284178	+	0.148870i
$971$	20.5244	+	35.5493i	0.658660	+	1.14083i	0.980963	+	0.194196i	$0.0622096\pi$
$971$	20.5244	+	35.5493i	0.658660	+	1.14083i	−0.322303	+	0.946637i	$0.604457\pi$
$972$			0.409975i			0.0131500i
$973$		0			0
$974$	−12.9577			−0.415192
$975$	−4.93167	−	7.12138i	−0.157940	−	0.228067i
$976$	−22.2275	+	38.4991i	−0.711484	+	1.23233i
$977$	−16.8644	−	9.73668i	−0.539541	−	0.311504i	0.205352	−	0.978688i	$-0.434166\pi$
$977$	−16.8644	−	9.73668i	−0.539541	−	0.311504i	−0.744893	+	0.667184i	$0.767499\pi$
$978$	7.25532	−	4.18886i	0.231999	−	0.133945i
$979$	18.0361			0.576435
$980$		0			0
$981$	4.42195			0.141182
$982$	0.749390	−	0.432661i	0.0239140	−	0.0138068i
$983$	44.7970	+	25.8636i	1.42880	+	0.824920i	0.997026	−	0.0770602i	$-0.0245534\pi$
$983$	44.7970	+	25.8636i	1.42880	+	0.824920i	0.431777	+	0.901980i	$0.357887\pi$
$984$	−8.28832	+	14.3558i	−0.264222	+	0.457646i
$985$	−27.0179	−	42.6529i	−0.860861	−	1.35903i
$986$	33.0626			1.05293
$987$		0			0
$988$		−	0.216742i		−	0.00689548i
$989$	34.1224	+	59.1017i	1.08503	+	1.87932i
$990$	7.13721	−	13.6242i	0.226835	−	0.433005i
$991$	−17.9749	+	31.1335i	−0.570992	+	0.988988i	0.425472	+	0.904972i	$0.360108\pi$
$991$	−17.9749	+	31.1335i	−0.570992	+	0.988988i	−0.996464	+	0.0840162i	$0.973225\pi$
$992$	−10.4575	+	6.03762i	−0.332025	+	0.191694i
$993$			28.3491i			0.899632i
$994$		0			0
$995$	0.688503	+	16.7655i	0.0218270	+	0.531502i
$996$	−1.04533	−	1.81056i	−0.0331224	−	0.0573697i
$997$	−48.5493	−	28.0300i	−1.53757	−	0.887718i	−0.998980	−	0.0451513i	$-0.985623\pi$
$997$	−48.5493	−	28.0300i	−1.53757	−	0.887718i	−0.538592	−	0.842567i	$-0.681044\pi$
$998$	−35.0003	−	20.2075i	−1.10792	−	0.639656i
$999$	1.83703	+	3.18183i	0.0581211	+	0.100669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.q.g.214.6		16
5.4	even	2	inner	735.2.q.g.214.3		16
7.2	even	3	inner	735.2.q.g.79.3		16
7.3	odd	6		735.2.d.d.589.6		8
7.4	even	3		735.2.d.e.589.6		8
7.5	odd	6		105.2.q.a.79.3	yes	16
7.6	odd	2		105.2.q.a.4.6	yes	16
21.5	even	6		315.2.bf.b.289.6		16
21.11	odd	6		2205.2.d.o.1324.3		8
21.17	even	6		2205.2.d.s.1324.3		8
21.20	even	2		315.2.bf.b.109.3		16
28.19	even	6		1680.2.di.d.289.1		16
28.27	even	2		1680.2.di.d.529.8		16
35.3	even	12		3675.2.a.bz.1.3		4
35.4	even	6		735.2.d.e.589.3		8
35.9	even	6	inner	735.2.q.g.79.6		16
35.12	even	12		525.2.i.k.226.3		8
35.13	even	4		525.2.i.h.151.2		8
35.17	even	12		3675.2.a.bp.1.2		4
35.18	odd	12		3675.2.a.cb.1.3		4
35.19	odd	6		105.2.q.a.79.6	yes	16
35.24	odd	6		735.2.d.d.589.3		8
35.27	even	4		525.2.i.k.151.3		8
35.32	odd	12		3675.2.a.bn.1.2		4
35.33	even	12		525.2.i.h.226.2		8
35.34	odd	2		105.2.q.a.4.3	✓	16
105.59	even	6		2205.2.d.s.1324.6		8
105.74	odd	6		2205.2.d.o.1324.6		8
105.89	even	6		315.2.bf.b.289.3		16
105.104	even	2		315.2.bf.b.109.6		16
140.19	even	6		1680.2.di.d.289.8		16
140.139	even	2		1680.2.di.d.529.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.3	✓	16	35.34	odd	2
105.2.q.a.4.6	yes	16	7.6	odd	2
105.2.q.a.79.3	yes	16	7.5	odd	6
105.2.q.a.79.6	yes	16	35.19	odd	6
315.2.bf.b.109.3		16	21.20	even	2
315.2.bf.b.109.6		16	105.104	even	2
315.2.bf.b.289.3		16	105.89	even	6
315.2.bf.b.289.6		16	21.5	even	6
525.2.i.h.151.2		8	35.13	even	4
525.2.i.h.226.2		8	35.33	even	12
525.2.i.k.151.3		8	35.27	even	4
525.2.i.k.226.3		8	35.12	even	12
735.2.d.d.589.3		8	35.24	odd	6
735.2.d.d.589.6		8	7.3	odd	6
735.2.d.e.589.3		8	35.4	even	6
735.2.d.e.589.6		8	7.4	even	3
735.2.q.g.79.3		16	7.2	even	3	inner
735.2.q.g.79.6		16	35.9	even	6	inner
735.2.q.g.214.3		16	5.4	even	2	inner
735.2.q.g.214.6		16	1.1	even	1	trivial
1680.2.di.d.289.1		16	28.19	even	6
1680.2.di.d.289.8		16	140.19	even	6
1680.2.di.d.529.1		16	140.139	even	2
1680.2.di.d.529.8		16	28.27	even	2
2205.2.d.o.1324.3		8	21.11	odd	6
2205.2.d.o.1324.6		8	105.74	odd	6
2205.2.d.s.1324.3		8	21.17	even	6
2205.2.d.s.1324.6		8	105.59	even	6
3675.2.a.bn.1.2		4	35.32	odd	12
3675.2.a.bp.1.2		4	35.17	even	12
3675.2.a.bz.1.3		4	35.3	even	12
3675.2.a.cb.1.3		4	35.18	odd	12

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.34443 - 0.776205i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.204988 - 0.355049i) q^{4} +(-1.88899 + 1.19655i) q^{5} +1.55241 q^{6} +2.46837i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.61083 + 3.07491i) q^{10} +(-2.21538 + 3.83715i) q^{11} +(0.355049 - 0.204988i) q^{12} -1.73246i q^{13} +(-2.23418 + 0.0917505i) q^{15} +(2.32594 + 4.02864i) q^{16} +(2.36638 + 1.36623i) q^{17} +(1.34443 + 0.776205i) q^{18} +(0.152578 + 0.264273i) q^{19} +(0.0376154 + 0.915960i) q^{20} +6.87834i q^{22} +(-6.08316 + 3.51212i) q^{23} +(-1.23418 + 2.13767i) q^{24} +(2.13653 - 4.52053i) q^{25} +(-1.34474 - 2.32916i) q^{26} +1.00000i q^{27} +7.79430 q^{29} +(-2.93248 + 1.85754i) q^{30} +(-2.64243 + 4.57683i) q^{31} +(1.97875 + 1.14243i) q^{32} +(-3.83715 + 2.21538i) q^{33} +4.24190 q^{34} +0.409975 q^{36} +(3.18183 - 1.83703i) q^{37} +(0.410260 + 0.236864i) q^{38} +(0.866230 - 1.50035i) q^{39} +(-2.95353 - 4.66271i) q^{40} +6.71562 q^{41} -9.71562i q^{43} +(0.908250 + 1.57313i) q^{44} +(-1.98074 - 1.03763i) q^{45} +(-5.45224 + 9.44356i) q^{46} +(1.57313 - 0.908250i) q^{47} +4.65187i q^{48} +(-0.636449 - 7.73591i) q^{50} +(1.36623 + 2.36638i) q^{51} +(-0.615108 - 0.355133i) q^{52} +(1.48535 + 0.857566i) q^{53} +(0.776205 + 1.34443i) q^{54} +(-0.406524 - 9.89912i) q^{55} +0.305156i q^{57} +(10.4789 - 6.04998i) q^{58} +(0.571217 - 0.989377i) q^{59} +(-0.425404 + 0.812053i) q^{60} +(4.77818 + 8.27604i) q^{61} +8.20428i q^{62} -5.75669 q^{64} +(2.07298 + 3.27259i) q^{65} +(-3.43917 + 5.95682i) q^{66} +(-7.26104 - 4.19216i) q^{67} +(0.970157 - 0.560120i) q^{68} -7.02423 q^{69} +10.2888 q^{71} +(-2.13767 + 1.23418i) q^{72} +(-11.1028 - 6.41022i) q^{73} +(2.85183 - 4.93951i) q^{74} +(4.11056 - 2.84663i) q^{75} +0.125106 q^{76} -2.68949i q^{78} +(3.35686 + 5.81425i) q^{79} +(-9.21413 - 4.82694i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(9.02866 - 5.21270i) q^{82} -5.09946i q^{83} +(-6.10482 + 0.250704i) q^{85} +(-7.54131 - 13.0619i) q^{86} +(6.75007 + 3.89715i) q^{87} +(-9.47149 - 5.46837i) q^{88} +(-2.03533 - 3.52529i) q^{89} +(-3.46837 + 0.142434i) q^{90} +2.87976i q^{92} +(-4.57683 + 2.64243i) q^{93} +(1.40998 - 2.44215i) q^{94} +(-0.604434 - 0.316641i) q^{95} +(1.14243 + 1.97875i) q^{96} -2.87834i q^{97} -4.43075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 2 q^{5} + 8 q^{6} + 8 q^{9} + 4 q^{10} - 4 q^{15} + 24 q^{19} + 8 q^{20} + 12 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} - 12 q^{30} - 16 q^{31} - 16 q^{34} + 16 q^{36} - 4 q^{39} - 32 q^{40}+ \cdots - 8 q^{96}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^5 + 8 * q^6 + 8 * q^9 + 4 * q^10 - 4 * q^15 + 24 * q^19 + 8 * q^20 + 12 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 - 12 * q^30 - 16 * q^31 - 16 * q^34 + 16 * q^36 - 4 * q^39 - 32 * q^40 - 16 * q^41 + 20 * q^44 + 2 * q^45 - 32 * q^46 - 40 * q^50 + 4 * q^51 + 4 * q^54 - 8 * q^55 - 4 * q^59 + 16 * q^60 - 16 * q^61 + 16 * q^64 + 30 * q^65 - 28 * q^66 - 40 * q^69 - 56 * q^71 + 40 * q^74 - 8 * q^75 + 64 * q^76 - 16 * q^79 - 52 * q^80 - 8 * q^81 - 64 * q^85 - 48 * q^86 - 16 * q^89 + 8 * q^90 + 32 * q^94 - 22 * q^95 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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