LMFDB - Embedded newform 735.2.q.g.214.3

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			214.3
Root			$-1.96595 - 0.526774i$ of defining polynomial
Character	$\chi$	$=$	735.214
Dual form			735.2.q.g.79.3

$q$-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} +(1.98074 - 1.03763i) q^{5} +1.55241 q^{6} -2.46837i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.85754 + 2.93248i) 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} +(2.84663 - 4.11056i) q^{25} +(-1.34474 - 2.32916i) q^{26} -1.00000i q^{27} +7.79430 q^{29} +(3.07491 - 1.61083i) 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} +(-2.56126 - 4.88919i) q^{40} +6.71562 q^{41} +9.71562i q^{43} +(0.908250 + 1.57313i) q^{44} +(1.88899 + 1.19655i) 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} +(-0.490556 + 0.774437i) q^{60} +(4.77818 + 8.27604i) q^{61} -8.20428i q^{62} -5.75669 q^{64} +(1.79766 + 3.43154i) 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} +(-4.52053 + 2.13653i) q^{75} +0.125106 q^{76} +2.68949i q^{78} +(3.35686 + 5.81425i) q^{79} +(8.78732 + 5.56620i) 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} +(0.576436 + 0.365135i) 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	−0.893284	−	0.449493i	$-0.851605\pi$
$2$	−1.34443	+	0.776205i	−0.950653	+	0.548860i	−0.0573691	+	0.998353i	$0.518271\pi$
$3$	−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
$5$	1.98074	−	1.03763i	0.885812	−	0.464044i
$5$	1.98074	−	1.03763i	0.885812	−	0.464044i
$6$	1.55241			0.633769
$7$		0			0
$7$		0			0
$8$		−	2.46837i		−	0.872700i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.85754	+	2.93248i	−0.587405	+	0.927331i
$11$	−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	$0.0772291\pi$
$13$			1.73246i			0.480498i	−0.970711	+	0.240249i	$0.922771\pi$
$14$		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	0.184787	−	0.982779i	$-0.440841\pi$
$17$	−2.36638	−	1.36623i	−0.573931	−	0.331359i	−0.758718	+	0.651419i	$0.774174\pi$
$18$	−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	0.293737	−	0.955886i	$-0.405101\pi$
$23$	6.08316	−	3.51212i	1.26843	−	0.732327i	0.974690	+	0.223560i	$0.0717678\pi$
$24$	−1.23418	+	2.13767i	−0.251927	+	0.436350i
$25$	2.84663	−	4.11056i	0.569326	−	0.822112i
$26$	−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	$0.242448\pi$
$30$	3.07491	−	1.61083i	0.561400	−	0.294097i
$31$	−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	−0.738198	−	0.674584i	$-0.764323\pi$
$37$	−3.18183	+	1.83703i	−0.523090	+	0.302006i	0.215108	+	0.976590i	$0.430990\pi$
$38$	−0.410260	−	0.236864i	−0.0665530	−	0.0384244i
$39$	0.866230	−	1.50035i	0.138708	−	0.240249i
$40$	−2.56126	−	4.88919i	−0.404972	−	0.773049i
$41$	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	$0.265558\pi$
$43$			9.71562i			1.48162i	−0.671715	+	0.740809i	$0.734442\pi$
$44$	0.908250	+	1.57313i	0.136924	+	0.237159i
$45$	1.88899	+	1.19655i	0.281593	+	0.178371i
$46$	−5.45224	+	9.44356i	−0.803889	+	1.39238i
$47$	−1.57313	+	0.908250i	−0.229465	+	0.132482i	−0.610325	−	0.792151i	$-0.708961\pi$
$47$	−1.57313	+	0.908250i	−0.229465	+	0.132482i	0.380860	+	0.924633i	$0.375628\pi$
$48$		−	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	0.394505	−	0.918894i	$-0.370916\pi$
$53$	−1.48535	−	0.857566i	−0.204028	−	0.117796i	−0.598533	+	0.801098i	$0.704249\pi$
$54$	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	$0.142973\pi$
$60$	−0.490556	+	0.774437i	−0.0633305	+	0.0999794i
$61$	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
$65$	1.79766	+	3.43154i	0.222972	+	0.425631i
$66$	−3.43917	+	5.95682i	−0.423333	+	0.733234i
$67$	7.26104	+	4.19216i	0.887078	+	0.512154i	0.872985	−	0.487746i	$-0.162181\pi$
$67$	7.26104	+	4.19216i	0.887078	+	0.512154i	0.0140921	+	0.999901i	$0.495514\pi$
$68$	−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	0.980316	−	0.197437i	$-0.0632618\pi$
$73$	11.1028	+	6.41022i	1.29949	+	0.750260i	0.319172	+	0.947697i	$0.396595\pi$
$74$	2.85183	−	4.93951i	0.331518	−	0.574206i
$75$	−4.52053	+	2.13653i	−0.521986	+	0.246706i
$76$	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	$0.710057\pi$
$80$	8.78732	+	5.56620i	0.982452	+	0.622320i
$81$	−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	$0.0902911\pi$
$83$			5.09946i			0.559739i	−0.960038	+	0.279869i	$0.909709\pi$
$84$		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
$95$	0.576436	+	0.365135i	0.0591411	+	0.0374620i
$96$	1.14243	+	1.97875i	0.116599	+	0.201956i
$97$			2.87834i			0.292252i	0.989266	+	0.146126i	$0.0466804\pi$
$97$			2.87834i			0.292252i	−0.989266	+	0.146126i	$0.953320\pi$
$98$		0			0
$99$	−4.43075			−0.445308
$100$	−0.875925	−	1.85331i	−0.0875925	−	0.185331i
$101$	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	−0.896782	−	0.442472i	$-0.854102\pi$
$103$	−9.76304	+	5.63670i	−0.961981	+	0.555400i	−0.0651989	+	0.997872i	$0.520768\pi$
$104$	4.27635			0.419331
$105$		0			0
$106$	2.66259			0.258613
$107$	−5.98940	+	3.45798i	−0.579017	+	0.334296i	−0.760743	−	0.649054i	$-0.775165\pi$
$107$	−5.98940	+	3.45798i	−0.579017	+	0.334296i	0.181726	+	0.983349i	$0.441832\pi$
$108$	−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	$0.0987430\pi$
$110$	−7.13721	−	13.6242i	−0.680506	−	1.29902i
$111$	3.67406			0.348727
$112$		0			0
$113$		−	2.86151i		−	0.269188i	−0.990901	−	0.134594i	$-0.957027\pi$
$113$		−	2.86151i		−	0.269188i	0.990901	−	0.134594i	$-0.0429730\pi$
$114$	0.236864	+	0.410260i	0.0221843	+	0.0384244i
$115$	8.40485	−	13.2687i	0.783756	−	1.23731i
$116$	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	$-0.791459\pi$
$127$		−	13.7325i		−	1.21856i	0.792956	−	0.609279i	$-0.208541\pi$
$128$	11.6970	−	6.75324i	1.03387	−	0.596908i
$129$	4.85781	−	8.41398i	0.427706	−	0.740809i
$130$	−5.08040	−	3.21811i	−0.445581	−	0.282247i
$131$	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
$135$	−1.03763	−	1.98074i	−0.0893053	−	0.170475i
$136$	−3.37236	+	5.84110i	−0.289177	+	0.500870i
$137$	2.59973	+	1.50095i	0.222110	+	0.128235i	0.606927	−	0.794758i	$-0.292402\pi$
$137$	2.59973	+	1.50095i	0.222110	+	0.128235i	−0.384817	+	0.922993i	$0.625735\pi$
$138$	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
$145$	15.4385	−	8.08764i	1.28209	−	0.671642i
$146$	−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	$0.901832\pi$
$150$	4.41914	−	6.38127i	0.360821	−	0.521029i
$151$	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	0.135581	−	0.990766i	$-0.456710\pi$
$157$	−8.20284	−	4.73591i	−0.654658	−	0.377967i	−0.790238	+	0.612800i	$0.790043\pi$
$158$	−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	−0.671737	−	0.740789i	$-0.734452\pi$
$163$	−4.67358	+	2.69830i	−0.366063	+	0.211347i	0.305674	+	0.952136i	$0.401118\pi$
$164$	1.37662	−	2.38437i	0.107496	−	0.186188i
$165$	5.30162	−	8.36963i	0.412731	−	0.651575i
$166$	−3.95823	−	6.85585i	−0.307218	−	0.532117i
$167$			0.312550i			0.0241859i	0.999927	+	0.0120929i	$0.00384939\pi$
$167$			0.312550i			0.0241859i	−0.999927	+	0.0120929i	$0.996151\pi$
$168$		0			0
$169$	9.99859			0.769122
$170$	8.40208	−	4.40154i	0.644410	−	0.337582i
$171$	−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	−0.148876	−	0.988856i	$-0.547565\pi$
$173$	8.32661	−	4.80737i	0.633061	−	0.365498i	0.781937	+	0.623358i	$0.214232\pi$
$174$	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	$0.274023\pi$
$180$	0.812053	−	0.425404i	0.0605268	−	0.0317078i
$181$	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
$185$	−4.39620	+	6.94026i	−0.323215	+	0.510258i
$186$	−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	0.563826	−	0.825894i	$-0.309329\pi$
$193$	1.81289	+	1.04667i	0.130494	+	0.0753410i	−0.433332	+	0.901234i	$0.642662\pi$
$194$	−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	$-0.702502\pi$
$197$		−	22.5798i		−	1.60874i	0.594126	−	0.804372i	$-0.297498\pi$
$198$	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	$0.0809728\pi$
$200$	−10.1464	−	7.02654i	−0.717457	−	0.496851i
$201$	−4.19216	−	7.26104i	−0.295693	−	0.512154i
$202$			11.2048i			0.788365i
$203$		0			0
$204$	1.12024			0.0784325
$205$	13.3019	−	6.96836i	0.929043	−	0.486691i
$206$	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
$215$	10.0813	+	19.2441i	0.687536	+	1.31244i
$216$	−2.46837			−0.167951
$217$		0			0
$218$			6.86467i			0.464934i
$219$	−6.41022	−	11.1028i	−0.433163	−	0.750260i
$220$	3.43134	+	2.17353i	0.231341	+	0.146540i
$221$	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	$0.0742321\pi$
$223$			6.90208i			0.462198i	−0.972930	+	0.231099i	$0.925768\pi$
$224$		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	0.671201	−	0.741275i	$-0.265779\pi$
$227$	5.49684	+	3.17360i	0.364838	+	0.210639i	−0.306363	+	0.951915i	$0.599112\pi$
$228$	−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	−0.695301	−	0.718719i	$-0.744729\pi$
$233$	−6.41899	+	3.70601i	−0.420522	+	0.242789i	0.274779	+	0.961508i	$0.411395\pi$
$234$	1.34474	−	2.32916i	0.0879086	−	0.152262i
$235$	−2.17353	+	3.43134i	−0.141786	+	0.223836i
$236$	−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	$0.576542\pi$
$240$	−4.82694	−	9.21413i	−0.311578	−	0.594769i
$241$	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
$250$	6.76641	+	15.9832i	0.427945	+	1.01087i
$251$	−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
$255$	5.16158	+	3.26953i	0.323230	+	0.204746i
$256$	−4.72710	+	8.18758i	−0.295444	+	0.511724i
$257$	−12.6417	+	7.29871i	−0.788570	+	0.455281i	−0.839459	−	0.543423i	$-0.817128\pi$
$257$	−12.6417	+	7.29871i	−0.788570	+	0.455281i	0.0508890	+	0.998704i	$0.483795\pi$
$258$			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	0.357916	−	0.933754i	$-0.383488\pi$
$263$	−4.40755	−	2.54470i	−0.271781	−	0.156913i	−0.629697	+	0.776841i	$0.716821\pi$
$264$	−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	$0.786377\pi$
$270$	2.93248	+	1.85754i	0.178465	+	0.113046i
$271$	−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
$275$	9.46645	+	20.0294i	0.570849	+	1.20782i
$276$	−1.43988	+	2.49395i	−0.0866706	+	0.150118i
$277$	−22.0665	−	12.7401i	−1.32585	−	0.765478i	−0.341193	−	0.939993i	$-0.610831\pi$
$277$	−22.0665	−	12.7401i	−1.32585	−	0.765478i	−0.984655	+	0.174515i	$0.944164\pi$
$278$	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	0.887769	−	0.460290i	$-0.152254\pi$
$283$	15.6960	+	9.06209i	0.933031	+	0.538685i	0.0452618	+	0.998975i	$0.485588\pi$
$284$	2.10908	−	3.65303i	0.125151	−	0.216768i
$285$	−0.316641	−	0.604434i	−0.0187562	−	0.0358036i
$286$	11.9165			0.704635
$287$		0			0
$288$		−	2.28487i		−	0.134637i
$289$	−4.76683	−	8.25640i	−0.280402	−	0.485670i
$290$	−14.4782	+	22.8566i	−0.850190	+	1.34219i
$291$	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	$-0.866958\pi$
$293$		−	13.8958i		−	0.811801i	0.913917	−	0.405901i	$-0.133042\pi$
$294$		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
$305$	18.0518	+	11.4347i	1.03364	+	0.654747i
$306$	2.12095	+	3.67359i	0.121247	+	0.210005i
$307$		−	29.8332i		−	1.70267i	−0.524622	−	0.851335i	$-0.675793\pi$
$307$		−	29.8332i		−	1.70267i	0.524622	−	0.851335i	$-0.324207\pi$
$308$		0			0
$309$	11.2734			0.641321
$310$	−8.51304	−	16.2505i	−0.483508	−	0.922967i
$311$	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	−0.996200	−	0.0871001i	$-0.972240\pi$
$313$	−25.1023	+	14.4928i	−1.41887	+	0.819184i	−0.422669	+	0.906284i	$0.638907\pi$
$314$	14.7041			0.829803
$315$		0			0
$316$	2.75246			0.154838
$317$	1.00341	−	0.579319i	0.0563571	−	0.0325378i	−0.471557	−	0.881836i	$-0.656308\pi$
$317$	1.00341	−	0.579319i	0.0563571	−	0.0325378i	0.527914	+	0.849298i	$0.322974\pi$
$318$	−2.30587	−	1.33129i	−0.129307	−	0.0746552i
$319$	−17.2673	+	29.9079i	−0.966785	+	1.67452i
$320$	−11.4025	+	5.97334i	−0.637418	+	0.333920i
$321$	6.91596			0.386011
$322$		0			0
$323$		−	0.833827i		−	0.0463954i
$324$	0.204988	+	0.355049i	0.0113882	+	0.0197249i
$325$	7.12138	+	4.93167i	0.395023	+	0.273560i
$326$	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	$0.143270\pi$
$337$			15.9729i			0.870101i	−0.900406	+	0.435051i	$0.856730\pi$
$338$	−13.4424	+	7.76095i	−0.731168	+	0.422140i
$339$	−1.43075	+	2.47814i	−0.0777079	+	0.134594i
$340$	−1.34042	+	2.11612i	−0.0726947	+	0.114763i
$341$	−11.7080	−	20.2788i	−0.634023	−	1.09816i
$342$		−	0.473727i		−	0.0256162i
$343$		0			0
$344$	23.9817			1.29301
$345$	−13.9131	+	7.28858i	−0.749059	+	0.392404i
$346$	−7.46301	+	12.9263i	−0.401214	+	0.694923i
$347$	−11.2687	−	6.50599i	−0.604935	−	0.349260i	0.166045	−	0.986118i	$-0.446900\pi$
$347$	−11.2687	−	6.50599i	−0.604935	−	0.349260i	−0.770981	+	0.636859i	$0.780234\pi$
$348$	−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	0.159173	−	0.987251i	$-0.449117\pi$
$353$	−11.5778	−	6.68445i	−0.616225	−	0.355778i	−0.775398	+	0.631473i	$0.782451\pi$
$354$	0.886763	−	1.53592i	0.0471309	−	0.0816331i
$355$	20.3794	−	10.6760i	1.08163	−	0.566624i
$356$	−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	$0.945865\pi$
$360$	2.95353	−	4.66271i	0.155665	−	0.245747i
$361$	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	0.766609	−	0.642114i	$-0.221943\pi$
$367$	11.3761	+	6.56798i	0.593826	+	0.342846i	−0.172783	+	0.984960i	$0.555276\pi$
$368$	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	0.343163	−	0.939276i	$-0.388502\pi$
$373$	25.6514	−	14.8099i	1.32818	−	0.766826i	0.985018	+	0.172450i	$0.0551682\pi$
$374$	−9.39740	+	16.2768i	−0.485928	+	0.841652i
$375$	−6.73704	+	8.92257i	−0.347900	+	0.460759i
$376$	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	$0.561507\pi$
$380$	0.247803	−	0.129815i	0.0127120	−	0.00665936i
$381$	−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	−0.922789	−	0.385307i	$-0.874096\pi$
$383$	−20.5586	+	11.8695i	−1.05050	+	0.606505i	−0.127709	+	0.991812i	$0.540762\pi$
$384$	−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	$0.283283\pi$
$390$	2.79070	+	5.32716i	0.141313	+	0.269751i
$391$	−19.1934			−0.970653
$392$		0			0
$393$		−	21.9817i		−	1.10883i
$394$	17.5265	+	30.3569i	0.882975	+	1.52936i
$395$	12.6821	+	8.03330i	0.638106	+	0.404199i
$396$	−0.908250	+	1.57313i	−0.0456413	+	0.0790530i
$397$	−9.75974	+	5.63479i	−0.489827	+	0.282802i	−0.724503	−	0.689272i	$-0.757931\pi$
$397$	−9.75974	+	5.63479i	−0.489827	+	0.282802i	0.234676	+	0.972074i	$0.424597\pi$
$398$			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	$0.996133\pi$
$410$	−12.4745	+	19.6934i	−0.616072	+	0.972589i
$411$	−1.50095	−	2.59973i	−0.0740366	−	0.128235i
$412$			4.62181i			0.227700i
$413$		0			0
$414$	−10.9045			−0.535926
$415$	5.29138	+	10.1007i	0.259743	+	0.495823i
$416$	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
$425$	−12.3522	+	5.83799i	−0.599168	+	0.283184i
$426$	15.9724			0.773868
$427$		0			0
$428$			2.83537i			0.137053i
$429$	3.83805	+	6.64770i	0.185303	+	0.320954i
$430$	−28.4909	−	18.0471i	−1.37395	−	0.870310i
$431$	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	$0.0674677\pi$
$433$			8.75514i			0.420745i	−0.977621	+	0.210373i	$0.932532\pi$
$434$		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	−0.851219	−	0.524811i	$-0.824136\pi$
$443$	−17.3080	+	9.99278i	−0.822328	+	0.474771i	0.0288905	+	0.999583i	$0.490803\pi$
$444$	0.753138	−	1.30447i	0.0357423	−	0.0619075i
$445$	−7.68941	−	4.87074i	−0.364513	−	0.230895i
$446$	−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	$0.522746\pi$
$450$	−7.01772	+	3.31677i	−0.330818	+	0.156354i
$451$	−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	−0.545497	−	0.838112i	$-0.683659\pi$
$457$	−1.97570	+	1.14067i	−0.0924195	+	0.0533584i	0.453078	+	0.891471i	$0.350326\pi$
$458$	9.08387	+	5.24457i	0.424461	+	0.245063i
$459$	−1.36623	+	2.36638i	−0.0637701	+	0.110453i
$460$	−2.98814	−	5.70404i	−0.139323	−	0.265952i
$461$	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	$0.0832629\pi$
$463$			11.1290i			0.517211i	−0.965983	+	0.258605i	$0.916737\pi$
$464$	18.1290	+	31.4004i	0.841620	+	1.45773i
$465$	6.32361	−	9.98304i	0.293251	−	0.462952i
$466$	5.75324	−	9.96490i	0.266514	−	0.461615i
$467$	24.7481	−	14.2883i	1.14521	−	0.661185i	0.197491	−	0.980305i	$-0.436721\pi$
$467$	24.7481	−	14.2883i	1.14521	−	0.661185i	0.947714	+	0.319120i	$0.103387\pi$
$468$			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	$0.125978\pi$
$480$	4.31608	+	2.73396i	0.197001	+	0.124788i
$481$	−3.18258	−	5.51240i	−0.145113	−	0.251344i
$482$			21.2370i			0.967320i
$483$		0			0
$484$	−3.53873			−0.160852
$485$	2.98667	+	5.70124i	0.135618	+	0.258880i
$486$	−0.776205	+	1.34443i	−0.0352094	+	0.0609844i
$487$	7.22858	+	4.17342i	0.327558	+	0.189116i	0.654756	−	0.755840i	$-0.272771\pi$
$487$	7.22858	+	4.17342i	0.327558	+	0.189116i	−0.327198	+	0.944956i	$0.606105\pi$
$488$	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
$495$	−8.77615	+	4.59750i	−0.394459	+	0.206642i
$496$	−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	$-0.364676\pi$
$500$	−3.65803	−	2.76202i	−0.163592	−	0.123521i
$501$	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	$-0.960699\pi$
$503$		−	5.52409i		−	0.246307i	0.992388	−	0.123154i	$-0.0393008\pi$
$504$		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
$515$	−13.4892	+	21.2953i	−0.594404	+	0.938382i
$516$	−1.99158	−	3.44952i	−0.0876745	−	0.151857i
$517$		−	8.04846i		−	0.353971i
$518$		0			0
$519$	−9.61475			−0.422041
$520$	8.47032	−	4.43729i	0.371448	−	0.194588i
$521$	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	0.104304	−	0.994545i	$-0.466738\pi$
$523$	23.2753	−	13.4380i	1.01776	−	0.587603i	0.913454	+	0.406943i	$0.133405\pi$
$524$	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
$530$	5.27388	−	2.76279i	0.229083	−	0.120008i
$531$	1.14243			0.0495774
$532$		0			0
$533$			11.6345i			0.503948i
$534$	−3.15966	−	5.47269i	−0.136732	−	0.236827i
$535$	−8.27530	+	13.0641i	−0.357772	+	0.564812i
$536$	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	$0.0925721\pi$
$547$			13.4126i			0.573483i	−0.958008	+	0.286742i	$0.907428\pi$
$548$	1.06582	−	0.615353i	0.0455297	−	0.0262866i
$549$	−4.77818	+	8.27604i	−0.203928	+	0.353213i
$550$	−28.2738	−	19.5801i	−1.20560	−	0.834899i
$551$	1.18924	+	2.05982i	0.0506633	+	0.0877515i
$552$			17.3384i			0.737971i
$553$		0			0
$554$	39.5557			1.68056
$555$	7.27735	−	3.81233i	0.308906	−	0.161825i
$556$	−4.45569	+	7.71749i	−0.188963	+	0.327294i
$557$	34.8008	+	20.0922i	1.47456	+	0.851336i	0.999589	−	0.0286677i	$-0.00912646\pi$
$557$	34.8008	+	20.0922i	1.47456	+	0.851336i	0.474968	+	0.880003i	$0.342460\pi$
$558$	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	−0.0359052	−	0.999355i	$-0.511431\pi$
$563$	−21.8134	−	12.5940i	−0.919325	−	0.530772i	−0.883420	+	0.468583i	$0.844765\pi$
$564$	0.372360	−	0.644946i	0.0156792	−	0.0271571i
$565$	−2.96920	−	5.66789i	−0.124915	−	0.238450i
$566$	−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	$0.907634\pi$
$570$	0.894864	+	0.566839i	0.0374817	+	0.0237423i
$571$	−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	0.618605	−	0.785702i	$-0.287698\pi$
$577$	5.94444	+	3.43202i	0.247470	+	0.142877i	−0.371135	+	0.928579i	$0.621031\pi$
$578$	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
$585$	−2.07298	+	3.27259i	−0.0857070	+	0.135305i
$586$	10.7860	+	18.6819i	0.445565	+	0.771741i
$587$			9.03965i			0.373106i	0.982445	+	0.186553i	$0.0597317\pi$
$587$			9.03965i			0.373106i	−0.982445	+	0.186553i	$0.940268\pi$
$588$		0			0
$589$	−1.61271			−0.0664506
$590$	1.84027	+	3.51289i	0.0757628	+	0.144623i
$591$	−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	−0.406414	−	0.913689i	$-0.633221\pi$
$593$	4.42364	−	2.55399i	0.181657	−	0.104880i	0.588071	+	0.808809i	$0.299888\pi$
$594$	−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	$0.957135\pi$
$600$	5.27375	+	11.1583i	0.215300	+	0.455538i
$601$	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
$605$	−16.3049	−	10.3281i	−0.662890	−	0.419898i
$606$	5.60239	−	9.70362i	0.227581	−	0.394182i
$607$	8.31216	−	4.79903i	0.337380	−	0.194786i	−0.321733	−	0.946831i	$-0.604265\pi$
$607$	8.31216	−	4.79903i	0.337380	−	0.194786i	0.659113	+	0.752044i	$0.270932\pi$
$608$		−	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	−0.0691416	−	0.997607i	$-0.522026\pi$
$613$	−23.9583	−	13.8323i	−0.967665	−	0.558682i	−0.898524	+	0.438925i	$0.855359\pi$
$614$	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	$0.134802\pi$
$617$			20.4155i			0.821896i	−0.911659	+	0.410948i	$0.865198\pi$
$618$	−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	$0.0662245\pi$
$620$	4.09280	+	2.59252i	0.164371	+	0.104118i
$621$	−3.51212	−	6.08316i	−0.140936	−	0.244109i
$622$			20.9781i			0.841145i
$623$		0			0
$624$	8.05918			0.322625
$625$	−8.79339	−	23.4025i	−0.351735	−	0.936099i
$626$	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
$635$	−14.2493	−	27.2004i	−0.565465	−	1.07941i
$636$	0.703161			0.0278822
$637$		0			0
$638$		−	53.6119i		−	2.12252i
$639$	5.14441	+	8.91037i	0.203510	+	0.352489i
$640$	16.1612	−	25.5135i	0.638827	−	1.00851i
$641$	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	$0.0903346\pi$
$643$			14.2002i			0.560001i	−0.960000	+	0.280001i	$0.909665\pi$
$644$		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	0.232648	−	0.972561i	$-0.425261\pi$
$647$	−12.5474	−	7.24426i	−0.493290	−	0.284801i	−0.725938	+	0.687760i	$0.758594\pi$
$648$	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	−0.315522	−	0.948918i	$-0.602180\pi$
$653$	8.90562	−	5.14166i	0.348504	−	0.201209i	0.664026	+	0.747709i	$0.268846\pi$
$654$	3.43233	−	5.94498i	0.134215	−	0.232467i
$655$	41.5232	+	26.3023i	1.62245	+	1.02771i
$656$	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	$0.594226\pi$
$660$	−1.88486	−	3.59801i	−0.0733681	−	0.140052i
$661$	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
$670$	−25.7811	+	13.5058i	−0.996010	+	0.521773i
$671$	−42.3418			−1.63459
$672$		0			0
$673$			17.2596i			0.665310i	0.943049	+	0.332655i	$0.107945\pi$
$673$			17.2596i			0.665310i	−0.943049	+	0.332655i	$0.892055\pi$
$674$	−12.3983	−	21.4744i	−0.477564	−	0.827164i
$675$	−4.11056	−	2.84663i	−0.158215	−	0.109567i
$676$	2.04959	−	3.54999i	0.0788302	−	0.136538i
$677$	10.0791	−	5.81918i	0.387372	−	0.223649i	−0.293649	−	0.955913i	$-0.594870\pi$
$677$	10.0791	−	5.81918i	0.387372	−	0.223649i	0.681021	+	0.732264i	$0.261536\pi$
$678$		−	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	0.917112	−	0.398629i	$-0.130514\pi$
$683$	26.9299	+	15.5480i	1.03044	+	0.594928i	0.113333	+	0.993557i	$0.463847\pi$
$684$	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
$690$	13.0478	−	20.5984i	0.496720	−	0.784168i
$691$	−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
$695$	−43.0541	+	22.5544i	−1.63313	+	0.855538i
$696$	−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
$705$	3.59801	−	1.88486i	0.135509	−	0.0709880i
$706$	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	$0.995171\pi$
$710$	−19.1118	+	30.1717i	−0.717255	+	1.13232i
$711$	−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
$725$	22.1875	−	32.0389i	0.824023	−	1.18990i
$726$	−6.69988	−	11.6045i	−0.248656	−	0.430684i
$727$		−	22.8312i		−	0.846761i	−0.905952	−	0.423380i	$-0.860843\pi$
$727$		−	22.8312i		−	0.846761i	0.905952	−	0.423380i	$-0.139157\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−39.4217	+	20.6516i	−1.45906	+	0.764350i
$731$	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	−0.592200	−	0.805791i	$-0.701740\pi$
$733$	−5.15661	+	2.97717i	−0.190464	+	0.109964i	0.401736	+	0.915756i	$0.368407\pi$
$734$	−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	$-0.109827\pi$
$740$	1.56296	+	2.98353i	0.0574556	+	0.109677i
$741$	0.528671			0.0194212
$742$		0			0
$743$			6.80015i			0.249473i	0.992190	+	0.124737i	$0.0398086\pi$
$743$			6.80015i			0.249473i	−0.992190	+	0.124737i	$0.960191\pi$
$744$	−6.52250	−	11.2973i	−0.239127	−	0.414179i
$745$	−9.84745	−	6.23773i	−0.360783	−	0.228533i
$746$	−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	$0.0952811\pi$
$757$			16.2267i			0.589769i	−0.955533	+	0.294884i	$0.904719\pi$
$758$	10.0521	−	5.80360i	0.365110	−	0.210796i
$759$	15.5613	−	26.9530i	0.564840	−	0.978332i
$760$	0.901288	−	1.42286i	0.0326931	−	0.0516124i
$761$	−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
$765$	−2.83529	−	5.41228i	−0.102510	−	0.195681i
$766$	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	$0.0434152\pi$
$773$	44.5909	+	25.7446i	1.60382	+	0.925968i	0.613110	+	0.789997i	$0.289918\pi$
$774$	7.54131	−	13.0619i	0.271067	−	0.469502i
$775$	11.2913	+	23.8904i	0.405595	+	0.858170i
$776$	7.10482			0.255048
$777$		0			0
$778$		−	21.9363i		−	0.786453i
$779$	1.02466	+	1.77476i	0.0367121	+	0.0635873i
$780$	−1.34168	−	0.849868i	−0.0480399	−	0.0304302i
$781$	−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	0.777680	−	0.628660i	$-0.216396\pi$
$787$	17.4517	+	10.0757i	0.622085	+	0.359161i	−0.155596	+	0.987821i	$0.549730\pi$
$788$	−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
$795$	3.23986	+	2.05224i	0.114906	+	0.0727855i
$796$	−1.53824	−	2.66431i	−0.0545216	−	0.0944341i
$797$			13.0702i			0.462971i	0.972838	+	0.231486i	$0.0743587\pi$
$797$			13.0702i			0.462971i	−0.972838	+	0.231486i	$0.925641\pi$
$798$		0			0
$799$	4.96351			0.175596
$800$	−10.3288	+	4.88170i	−0.365179	+	0.172594i
$801$	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	$0.176389\pi$
$810$	−1.61083	−	3.07491i	−0.0565989	−	0.108041i
$811$	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
$815$	−6.45729	+	10.1941i	−0.226189	+	0.357083i
$816$	−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	0.641799	−	0.766873i	$-0.278188\pi$
$823$	8.56526	+	4.94516i	0.298566	+	0.172377i	−0.343232	+	0.939251i	$0.611522\pi$
$824$	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	$0.210481\pi$
$827$			35.3201i			1.22820i	−0.789228	+	0.614101i	$0.789519\pi$
$828$	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	$0.218297\pi$
$830$	−14.9541	−	9.47244i	−0.519063	−	0.328793i
$831$	12.7401	+	22.0665i	0.441949	+	0.765478i
$832$		−	9.97323i		−	0.345760i
$833$		0			0
$834$	−33.7438			−1.16845
$835$	0.324313	+	0.619080i	0.0112233	+	0.0214241i
$836$	−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
$845$	19.8046	−	10.3749i	0.681298	−	0.356906i
$846$	2.81995			0.0969519
$847$		0			0
$848$		−	7.97857i		−	0.273985i
$849$	−9.06209	−	15.6960i	−0.311010	−	0.538685i
$850$	12.0751	−	17.4366i	0.414173	−	0.598069i
$851$	−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	$0.172166\pi$
$853$			30.0757i			1.02977i	−0.857258	+	0.514887i	$0.827834\pi$
$854$		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	0.993805	−	0.111141i	$-0.0354505\pi$
$857$	40.8221	+	23.5686i	1.39446	+	0.805090i	0.400652	+	0.916230i	$0.368784\pi$
$858$	−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	0.165879	−	0.986146i	$-0.446954\pi$
$863$	32.3982	−	18.7051i	1.10285	−	0.636728i	0.936967	+	0.349418i	$0.113621\pi$
$864$	−1.14243	+	1.97875i	−0.0388664	+	0.0673186i
$865$	11.5045	−	18.1621i	0.391166	−	0.617531i
$866$	−6.79578	−	11.7706i	−0.230930	−	0.399983i
$867$			9.53367i			0.323780i
$868$		0			0
$869$	−29.7468			−1.00909
$870$	23.9668	−	12.5553i	0.812551	−	0.425665i
$871$	−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	−0.902747	−	0.430172i	$-0.858453\pi$
$877$	−29.0687	+	16.7828i	−0.981581	+	0.566716i	−0.0788336	+	0.996888i	$0.525120\pi$
$878$	−14.2680	−	8.23764i	−0.481522	−	0.278007i
$879$	−6.94790	+	12.0341i	−0.234347	+	0.405901i
$880$	−40.8255	+	21.3870i	−1.37623	+	0.720955i
$881$	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	$-0.940520\pi$
$883$		−	11.0408i		−	0.371552i	0.982592	−	0.185776i	$-0.0594799\pi$
$884$	−0.970385	−	1.68076i	−0.0326376	−	0.0565300i
$885$	−1.36698	+	2.15804i	−0.0459505	+	0.0725418i
$886$	15.5129	−	26.8691i	0.521166	−	0.902685i
$887$	1.35180	−	0.780464i	0.0453891	−	0.0262054i	−0.477134	−	0.878831i	$-0.658324\pi$
$887$	1.35180	−	0.780464i	0.0453891	−	0.0262054i	0.522523	+	0.852625i	$0.324991\pi$
$888$		−	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
$900$	1.16705	−	1.68523i	0.0389016	−	0.0561742i
$901$	2.34326	+	4.05865i	0.0780654	+	0.135213i
$902$		−	46.1924i		−	1.53804i
$903$		0			0
$904$	−7.06326			−0.234921
$905$	33.5207	−	17.5603i	1.11427	−	0.583722i
$906$	7.53983	−	13.0594i	0.250494	−	0.433869i
$907$	−15.0756	−	8.70390i	−0.500577	−	0.289008i	0.228375	−	0.973573i	$-0.426659\pi$
$907$	−15.0756	−	8.70390i	−0.500577	−	0.289008i	−0.728952	+	0.684565i	$0.759992\pi$
$908$	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
$915$	−9.91600	−	18.9286i	−0.327813	−	0.625761i
$916$	−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	$0.711789\pi$
$920$	−32.7520	−	20.7463i	−1.07980	−	0.683984i
$921$	−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
$935$	14.4865	−	22.8697i	0.473758	−	0.747918i
$936$	2.13817	+	3.70343i	0.0698884	+	0.121050i
$937$			46.7921i			1.52863i	0.644842	+	0.764316i	$0.276923\pi$
$937$			46.7921i			1.52863i	−0.644842	+	0.764316i	$0.723077\pi$
$938$		0			0
$939$	28.9857			0.945912
$940$	0.772746	+	1.47509i	0.0252042	+	0.0481122i
$941$	−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	$-0.301406\pi$
$947$	48.5967	−	28.0573i	1.57918	−	0.911740i	0.994974	−	0.100134i	$-0.0319273\pi$
$948$	−2.38370	−	1.37623i	−0.0774189	−	0.0446978i
$949$	−11.1054	+	19.2352i	−0.360498	+	0.624401i
$950$	−2.14150	+	1.01213i	−0.0694795	+	0.0328380i
$951$	−1.15864			−0.0375714
$952$		0			0
$953$		−	17.7705i		−	0.575643i	−0.957684	−	0.287821i	$-0.907069\pi$
$953$		−	17.7705i		−	0.575643i	0.957684	−	0.287821i	$-0.0929309\pi$
$954$	1.33129	+	2.30587i	0.0431022	+	0.0746552i
$955$	−0.601720	−	0.381151i	−0.0194712	−	0.0123337i
$956$	−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	$-0.881654\pi$
$967$		−	22.5942i		−	0.726579i	0.931676	−	0.363290i	$-0.118346\pi$
$968$	−18.4515	+	10.6530i	−0.593053	+	0.342399i
$969$	−0.416913	+	0.722115i	−0.0133932	+	0.0231977i
$970$	−8.44069	−	5.34663i	−0.271014	−	0.171670i
$971$	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
$975$	−3.70146	−	7.83164i	−0.118541	−	0.250813i
$976$	−22.2275	+	38.4991i	−0.711484	+	1.23233i
$977$	16.8644	+	9.73668i	0.539541	+	0.311504i	0.744893	−	0.667184i	$-0.232501\pi$
$977$	16.8644	+	9.73668i	0.539541	+	0.311504i	−0.205352	+	0.978688i	$0.565834\pi$
$978$	−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	−0.431777	−	0.901980i	$-0.642113\pi$
$983$	−44.7970	−	25.8636i	−1.42880	−	0.824920i	−0.997026	+	0.0770602i	$0.975447\pi$
$984$	−8.28832	+	14.3558i	−0.264222	+	0.457646i
$985$	−23.4296	−	44.7246i	−0.746528	−	1.42505i
$986$	33.0626			1.05293
$987$		0			0
$988$			0.216742i			0.00689548i
$989$	34.1224	+	59.1017i	1.08503	+	1.87932i
$990$	8.23029	−	12.9931i	0.261576	−	0.412948i
$991$	−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	$0.0143770\pi$
$997$	48.5493	+	28.0300i	1.53757	+	0.887718i	0.538592	+	0.842567i	$0.318956\pi$
$998$	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.214.3		16
5.4	even	2	inner	735.2.q.g.214.6		16
7.2	even	3	inner	735.2.q.g.79.6		16
7.3	odd	6		735.2.d.d.589.3		8
7.4	even	3		735.2.d.e.589.3		8
7.5	odd	6		105.2.q.a.79.6	yes	16
7.6	odd	2		105.2.q.a.4.3	✓	16
21.5	even	6		315.2.bf.b.289.3		16
21.11	odd	6		2205.2.d.o.1324.6		8
21.17	even	6		2205.2.d.s.1324.6		8
21.20	even	2		315.2.bf.b.109.6		16
28.19	even	6		1680.2.di.d.289.8		16
28.27	even	2		1680.2.di.d.529.1		16
35.3	even	12		3675.2.a.bp.1.2		4
35.4	even	6		735.2.d.e.589.6		8
35.9	even	6	inner	735.2.q.g.79.3		16
35.12	even	12		525.2.i.h.226.2		8
35.13	even	4		525.2.i.k.151.3		8
35.17	even	12		3675.2.a.bz.1.3		4
35.18	odd	12		3675.2.a.bn.1.2		4
35.19	odd	6		105.2.q.a.79.3	yes	16
35.24	odd	6		735.2.d.d.589.6		8
35.27	even	4		525.2.i.h.151.2		8
35.32	odd	12		3675.2.a.cb.1.3		4
35.33	even	12		525.2.i.k.226.3		8
35.34	odd	2		105.2.q.a.4.6	yes	16
105.59	even	6		2205.2.d.s.1324.3		8
105.74	odd	6		2205.2.d.o.1324.3		8
105.89	even	6		315.2.bf.b.289.6		16
105.104	even	2		315.2.bf.b.109.3		16
140.19	even	6		1680.2.di.d.289.1		16
140.139	even	2		1680.2.di.d.529.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.3	✓	16	7.6	odd	2
105.2.q.a.4.6	yes	16	35.34	odd	2
105.2.q.a.79.3	yes	16	35.19	odd	6
105.2.q.a.79.6	yes	16	7.5	odd	6
315.2.bf.b.109.3		16	105.104	even	2
315.2.bf.b.109.6		16	21.20	even	2
315.2.bf.b.289.3		16	21.5	even	6
315.2.bf.b.289.6		16	105.89	even	6
525.2.i.h.151.2		8	35.27	even	4
525.2.i.h.226.2		8	35.12	even	12
525.2.i.k.151.3		8	35.13	even	4
525.2.i.k.226.3		8	35.33	even	12
735.2.d.d.589.3		8	7.3	odd	6
735.2.d.d.589.6		8	35.24	odd	6
735.2.d.e.589.3		8	7.4	even	3
735.2.d.e.589.6		8	35.4	even	6
735.2.q.g.79.3		16	35.9	even	6	inner
735.2.q.g.79.6		16	7.2	even	3	inner
735.2.q.g.214.3		16	1.1	even	1	trivial
735.2.q.g.214.6		16	5.4	even	2	inner
1680.2.di.d.289.1		16	140.19	even	6
1680.2.di.d.289.8		16	28.19	even	6
1680.2.di.d.529.1		16	28.27	even	2
1680.2.di.d.529.8		16	140.139	even	2
2205.2.d.o.1324.3		8	105.74	odd	6
2205.2.d.o.1324.6		8	21.11	odd	6
2205.2.d.s.1324.3		8	105.59	even	6
2205.2.d.s.1324.6		8	21.17	even	6
3675.2.a.bn.1.2		4	35.18	odd	12
3675.2.a.bp.1.2		4	35.3	even	12
3675.2.a.bz.1.3		4	35.17	even	12
3675.2.a.cb.1.3		4	35.32	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} +(1.98074 - 1.03763i) q^{5} +1.55241 q^{6} -2.46837i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.85754 + 2.93248i) 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} +(2.84663 - 4.11056i) q^{25} +(-1.34474 - 2.32916i) q^{26} -1.00000i q^{27} +7.79430 q^{29} +(3.07491 - 1.61083i) 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} +(-2.56126 - 4.88919i) q^{40} +6.71562 q^{41} +9.71562i q^{43} +(0.908250 + 1.57313i) q^{44} +(1.88899 + 1.19655i) 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} +(-0.490556 + 0.774437i) q^{60} +(4.77818 + 8.27604i) q^{61} -8.20428i q^{62} -5.75669 q^{64} +(1.79766 + 3.43154i) 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} +(-4.52053 + 2.13653i) q^{75} +0.125106 q^{76} +2.68949i q^{78} +(3.35686 + 5.81425i) q^{79} +(8.78732 + 5.56620i) 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} +(0.576436 + 0.365135i) 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

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Database

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