LMFDB - Embedded newform 729.2.i.a.10.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(10,729)] 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("729.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			10.7
Character	$\chi$	$=$	729.10
Dual form			729.2.i.a.73.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.44758 - 0.226398i) q^{2} +(0.139748 + 0.0448082i) q^{4} +(-3.00496 - 1.36592i) q^{5} +(-0.603573 - 4.41893i) q^{7} +(2.42652 + 1.21864i) q^{8} +(4.04068 + 2.65760i) q^{10} +(4.13243 - 0.321198i) q^{11} +(-0.395167 - 1.15492i) q^{13} +(-0.126716 + 6.53342i) q^{14} +(-3.47547 - 2.48412i) q^{16} +(2.88846 - 6.69621i) q^{17} +(0.997513 - 1.33989i) q^{19} +(-0.358731 - 0.325531i) q^{20} +(-6.05476 - 0.470613i) q^{22} +(-0.314079 - 0.243430i) q^{23} +(3.87642 + 4.44188i) q^{25} +(0.310566 + 1.76131i) q^{26} +(0.113657 - 0.644580i) q^{28} +(-8.76723 + 5.29105i) q^{29} +(-4.29487 + 0.166661i) q^{31} +(0.591517 + 0.580156i) q^{32} +(-5.69730 + 9.03938i) q^{34} +(-4.22220 + 14.1031i) q^{35} +(2.55472 - 2.70785i) q^{37} +(-1.74733 + 1.71377i) q^{38} +(-5.62700 - 6.97639i) q^{40} +(0.944402 - 2.44606i) q^{41} +(-0.0744696 - 0.289109i) q^{43} +(0.591889 + 0.140280i) q^{44} +(0.399544 + 0.423492i) q^{46} +(3.26932 + 0.126864i) q^{47} +(-12.4191 + 3.45709i) q^{49} +(-4.60581 - 7.30761i) q^{50} +(-0.00347372 - 0.179104i) q^{52} +(-7.96306 + 2.89832i) q^{53} +(-12.8565 - 4.67938i) q^{55} +(3.92052 - 11.4581i) q^{56} +(13.8892 - 5.67436i) q^{58} +(-3.24305 - 6.78226i) q^{59} +(1.62786 - 0.521952i) q^{61} +(6.25492 + 0.731096i) q^{62} +(4.37717 + 5.87956i) q^{64} +(-0.390068 + 4.01025i) q^{65} +(7.10449 + 4.28758i) q^{67} +(0.703701 - 0.806352i) q^{68} +(9.30491 - 19.4596i) q^{70} +(-0.445964 + 7.65690i) q^{71} +(4.00185 - 2.63206i) q^{73} +(-4.31123 + 3.34145i) q^{74} +(0.199438 - 0.142550i) q^{76} +(-3.91357 - 18.0671i) q^{77} +(-0.497565 + 0.616884i) q^{79} +(7.05054 + 12.2119i) q^{80} +(-1.92089 + 3.32707i) q^{82} +(3.45919 + 8.95953i) q^{83} +(-17.8262 + 16.1764i) q^{85} +(0.0423473 + 0.435369i) q^{86} +(10.4188 + 4.25656i) q^{88} +(-0.648276 - 11.1305i) q^{89} +(-4.86500 + 2.44330i) q^{91} +(-0.0329841 - 0.0480920i) q^{92} +(-4.70389 - 0.923814i) q^{94} +(-4.82767 + 2.66380i) q^{95} +(-13.9384 + 6.33577i) q^{97} +(18.7603 - 2.19277i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26}+ \cdots - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{81}\right)$

Coefficient data

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

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

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

$2$	−1.44758	−	0.226398i	−1.02360	−	0.160088i	−0.379628	−	0.925139i	$-0.623948\pi$
$2$	−1.44758	−	0.226398i	−1.02360	−	0.160088i	−0.643969	+	0.765052i	$0.722713\pi$
$3$		0			0
$3$		0			0
$4$	0.139748	+	0.0448082i	0.0698738	+	0.0224041i
$5$	−3.00496	−	1.36592i	−1.34386	−	0.610858i	−0.392729	−	0.919654i	$-0.628469\pi$
$5$	−3.00496	−	1.36592i	−1.34386	−	0.610858i	−0.951128	+	0.308796i	$0.900074\pi$
$6$		0			0
$7$	−0.603573	−	4.41893i	−0.228129	−	1.67020i	−0.647256	−	0.762272i	$-0.724084\pi$
$7$	−0.603573	−	4.41893i	−0.228129	−	1.67020i	0.419127	−	0.907927i	$-0.362336\pi$
$8$	2.42652	+	1.21864i	0.857903	+	0.430855i
$9$		0			0
$10$	4.04068	+	2.65760i	1.27778	+	0.840407i
$11$	4.13243	−	0.321198i	1.24597	−	0.0968448i	0.562486	−	0.826807i	$-0.309845\pi$
$11$	4.13243	−	0.321198i	1.24597	−	0.0968448i	0.683488	+	0.729962i	$0.260462\pi$
$12$		0			0
$13$	−0.395167	−	1.15492i	−0.109600	−	0.320317i	0.877694	−	0.479221i	$-0.159081\pi$
$13$	−0.395167	−	1.15492i	−0.109600	−	0.320317i	−0.987294	+	0.158904i	$0.949204\pi$
$14$	−0.126716	+	6.53342i	−0.0338662	+	1.74613i
$15$		0			0
$16$	−3.47547	−	2.48412i	−0.868868	−	0.621030i
$17$	2.88846	−	6.69621i	0.700555	−	1.62407i	−0.0783486	−	0.996926i	$-0.524965\pi$
$17$	2.88846	−	6.69621i	0.700555	−	1.62407i	0.778904	−	0.627143i	$-0.215776\pi$
$18$		0			0
$19$	0.997513	−	1.33989i	0.228845	−	0.307393i	−0.672838	−	0.739790i	$-0.734925\pi$
$19$	0.997513	−	1.33989i	0.228845	−	0.307393i	0.901683	+	0.432397i	$0.142332\pi$
$20$	−0.358731	−	0.325531i	−0.0802146	−	0.0727909i
$21$		0			0
$22$	−6.05476	−	0.470613i	−1.29088	−	0.100335i
$23$	−0.314079	−	0.243430i	−0.0654900	−	0.0507586i	0.579330	−	0.815093i	$-0.303314\pi$
$23$	−0.314079	−	0.243430i	−0.0654900	−	0.0507586i	−0.644820	+	0.764335i	$0.723068\pi$
$24$		0			0
$25$	3.87642	+	4.44188i	0.775283	+	0.888376i
$26$	0.310566	+	1.76131i	0.0609070	+	0.345421i
$27$		0			0
$28$	0.113657	−	0.644580i	0.0214791	−	0.121814i
$29$	−8.76723	+	5.29105i	−1.62803	+	0.982524i	−0.653892	+	0.756588i	$0.726865\pi$
$29$	−8.76723	+	5.29105i	−1.62803	+	0.982524i	−0.974142	+	0.225936i	$0.927456\pi$
$30$		0			0
$31$	−4.29487	+	0.166661i	−0.771382	+	0.0299331i	−0.421462	−	0.906846i	$-0.638483\pi$
$31$	−4.29487	+	0.166661i	−0.771382	+	0.0299331i	−0.349921	+	0.936779i	$0.613791\pi$
$32$	0.591517	+	0.580156i	0.104566	+	0.102558i
$33$		0			0
$34$	−5.69730	+	9.03938i	−0.977079	+	1.55024i
$35$	−4.22220	+	14.1031i	−0.713682	+	2.38386i
$36$		0			0
$37$	2.55472	−	2.70785i	0.419994	−	0.445168i	−0.482483	−	0.875905i	$-0.660265\pi$
$37$	2.55472	−	2.70785i	0.419994	−	0.445168i	0.902477	+	0.430738i	$0.141747\pi$
$38$	−1.74733	+	1.71377i	−0.283455	+	0.278011i
$39$		0			0
$40$	−5.62700	−	6.97639i	−0.889708	−	1.10306i
$41$	0.944402	−	2.44606i	0.147491	−	0.382011i	−0.839375	−	0.543553i	$-0.817079\pi$
$41$	0.944402	−	2.44606i	0.147491	−	0.382011i	0.986866	+	0.161542i	$0.0516467\pi$
$42$		0			0
$43$	−0.0744696	−	0.289109i	−0.0113565	−	0.0440886i	0.962461	−	0.271421i	$-0.0874935\pi$
$43$	−0.0744696	−	0.289109i	−0.0113565	−	0.0440886i	−0.973817	+	0.227332i	$0.927000\pi$
$44$	0.591889	+	0.140280i	0.0892306	+	0.0211481i
$45$		0			0
$46$	0.399544	+	0.423492i	0.0589095	+	0.0624405i
$47$	3.26932	+	0.126864i	0.476879	+	0.0185051i	0.276095	−	0.961130i	$-0.410960\pi$
$47$	3.26932	+	0.126864i	0.476879	+	0.0185051i	0.200784	+	0.979635i	$0.435651\pi$
$48$		0			0
$49$	−12.4191	+	3.45709i	−1.77415	+	0.493869i
$50$	−4.60581	−	7.30761i	−0.651359	−	1.03345i
$51$		0			0
$52$	−0.00347372	−	0.179104i	−0.000481718	−	0.0248373i
$53$	−7.96306	+	2.89832i	−1.09381	+	0.398114i	−0.825031	−	0.565087i	$-0.808842\pi$
$53$	−7.96306	+	2.89832i	−1.09381	+	0.398114i	−0.268779	+	0.963202i	$0.586620\pi$
$54$		0			0
$55$	−12.8565	−	4.67938i	−1.73357	−	0.630968i
$56$	3.92052	−	11.4581i	0.523901	−	1.53116i
$57$		0			0
$58$	13.8892	−	5.67436i	1.82374	−	0.745080i
$59$	−3.24305	−	6.78226i	−0.422209	−	0.882975i	−0.997867	−	0.0652841i	$-0.979205\pi$
$59$	−3.24305	−	6.78226i	−0.422209	−	0.882975i	0.575658	−	0.817691i	$-0.304746\pi$
$60$		0			0
$61$	1.62786	−	0.521952i	0.208426	−	0.0668291i	−0.199279	−	0.979943i	$-0.563860\pi$
$61$	1.62786	−	0.521952i	0.208426	−	0.0668291i	0.407705	+	0.913114i	$0.366329\pi$
$62$	6.25492	+	0.731096i	0.794376	+	0.0928492i
$63$		0			0
$64$	4.37717	+	5.87956i	0.547146	+	0.734944i
$65$	−0.390068	+	4.01025i	−0.0483820	+	0.497410i
$66$		0			0
$67$	7.10449	+	4.28758i	0.867951	+	0.523811i	0.879378	−	0.476123i	$-0.157958\pi$
$67$	7.10449	+	4.28758i	0.867951	+	0.523811i	−0.0114272	+	0.999935i	$0.503637\pi$
$68$	0.703701	−	0.806352i	0.0853363	−	0.0977845i
$69$		0			0
$70$	9.30491	−	19.4596i	1.11215	−	2.32586i
$71$	−0.445964	+	7.65690i	−0.0529262	+	0.908707i	0.862459	+	0.506127i	$0.168923\pi$
$71$	−0.445964	+	7.65690i	−0.0529262	+	0.908707i	−0.915385	+	0.402580i	$0.868114\pi$
$72$		0			0
$73$	4.00185	−	2.63206i	0.468381	−	0.308059i	−0.293289	−	0.956024i	$-0.594750\pi$
$73$	4.00185	−	2.63206i	0.468381	−	0.308059i	0.761670	+	0.647965i	$0.224380\pi$
$74$	−4.31123	+	3.34145i	−0.501170	+	0.388436i
$75$		0			0
$76$	0.199438	−	0.142550i	0.0228771	−	0.0163516i
$77$	−3.91357	−	18.0671i	−0.445993	−	2.05893i
$78$		0			0
$79$	−0.497565	+	0.616884i	−0.0559804	+	0.0694048i	−0.805581	−	0.592485i	$-0.798147\pi$
$79$	−0.497565	+	0.616884i	−0.0559804	+	0.0694048i	0.749601	+	0.661890i	$0.230246\pi$
$80$	7.05054	+	12.2119i	0.788274	+	1.36533i
$81$		0			0
$82$	−1.92089	+	3.32707i	−0.212126	+	0.367414i
$83$	3.45919	+	8.95953i	0.379696	+	0.983436i	0.982618	+	0.185637i	$0.0594348\pi$
$83$	3.45919	+	8.95953i	0.379696	+	0.983436i	−0.602923	+	0.797800i	$0.705997\pi$
$84$		0			0
$85$	−17.8262	+	16.1764i	−1.93352	+	1.75458i
$86$	0.0423473	+	0.435369i	0.00456643	+	0.0469470i
$87$		0			0
$88$	10.4188	+	4.25656i	1.11065	+	0.453751i
$89$	−0.648276	−	11.1305i	−0.0687171	−	1.17983i	−0.839729	−	0.543006i	$-0.817286\pi$
$89$	−0.648276	−	11.1305i	−0.0687171	−	1.17983i	0.771012	−	0.636821i	$-0.219751\pi$
$90$		0			0
$91$	−4.86500	+	2.44330i	−0.509991	+	0.256127i
$92$	−0.0329841	−	0.0480920i	−0.00343883	−	0.00501394i
$93$		0			0
$94$	−4.70389	−	0.923814i	−0.485169	−	0.0952842i
$95$	−4.82767	+	2.66380i	−0.495309	+	0.273300i
$96$		0			0
$97$	−13.9384	+	6.33577i	−1.41523	+	0.643300i	−0.967961	−	0.251100i	$-0.919208\pi$
$97$	−13.9384	+	6.33577i	−1.41523	+	0.643300i	−0.447267	+	0.894400i	$0.647603\pi$
$98$	18.7603	−	2.19277i	1.89508	−	0.221503i
$99$		0			0
$100$	0.342687	+	0.794437i	0.0342687	+	0.0794437i
$101$	−1.21067	+	5.58909i	−0.120466	+	0.556135i	0.876709	+	0.481022i	$0.159734\pi$
$101$	−1.21067	+	5.58909i	−0.120466	+	0.556135i	−0.997175	+	0.0751130i	$0.976068\pi$
$102$		0			0
$103$	1.08919	−	1.58808i	0.107321	−	0.156478i	−0.767295	−	0.641295i	$-0.778398\pi$
$103$	1.08919	−	1.58808i	0.107321	−	0.156478i	0.874616	+	0.484817i	$0.161114\pi$
$104$	0.448554	−	3.28400i	0.0439844	−	0.322022i
$105$		0			0
$106$	12.1834	−	2.39274i	1.18335	−	0.232403i
$107$	−4.93126	+	4.13782i	−0.476723	+	0.400018i	−0.849240	−	0.528007i	$-0.822939\pi$
$107$	−4.93126	+	4.13782i	−0.476723	+	0.400018i	0.372517	+	0.928026i	$0.378495\pi$
$108$		0			0
$109$	−5.82284	−	4.88594i	−0.557727	−	0.467989i	0.319821	−	0.947478i	$-0.396377\pi$
$109$	−5.82284	−	4.88594i	−0.557727	−	0.467989i	−0.877548	+	0.479490i	$0.840822\pi$
$110$	17.5515	+	9.68448i	1.67347	+	0.923379i
$111$		0			0
$112$	−8.87945	+	16.8572i	−0.839030	+	1.59286i
$113$	1.30320	−	5.05934i	0.122595	−	0.475943i	−0.877398	−	0.479764i	$-0.840722\pi$
$113$	1.30320	−	5.05934i	0.122595	−	0.475943i	0.999993	+	0.00382089i	$0.00121623\pi$
$114$		0			0
$115$	0.611289	+	1.16050i	0.0570029	+	0.108217i
$116$	−1.46228	+	0.346567i	−0.135770	+	0.0321780i
$117$		0			0
$118$	3.15909	+	10.5521i	0.290818	+	0.971400i
$119$	−31.3335	−	8.72228i	−2.87234	−	0.799570i
$120$		0			0
$121$	6.10591	−	0.954947i	0.555083	−	0.0868134i
$122$	−2.47463	+	0.387026i	−0.224043	+	0.0350396i
$123$		0			0
$124$	−0.607666	−	0.169155i	−0.0545700	−	0.0151906i
$125$	−0.847759	−	2.83171i	−0.0758259	−	0.253276i
$126$		0			0
$127$	10.1674	−	2.40972i	0.902213	−	0.213828i	0.246771	−	0.969074i	$-0.420630\pi$
$127$	10.1674	−	2.40972i	0.902213	−	0.213828i	0.655442	+	0.755245i	$0.272482\pi$
$128$	−5.77747	−	10.9682i	−0.510661	−	0.969465i
$129$		0			0
$130$	1.47257	−	5.71686i	0.129153	−	0.501402i
$131$	1.17168	−	2.22438i	0.102370	−	0.194345i	−0.828224	−	0.560397i	$-0.810649\pi$
$131$	1.17168	−	2.22438i	0.102370	−	0.194345i	0.930595	+	0.366052i	$0.119291\pi$
$132$		0			0
$133$	−6.52297	−	3.59922i	−0.565613	−	0.312092i
$134$	−9.31364	−	7.81507i	−0.804576	−	0.675120i
$135$		0			0
$136$	15.1692	−	12.7285i	1.30075	−	1.09146i
$137$	−2.13263	+	0.418835i	−0.182203	+	0.0357835i	−0.282981	−	0.959125i	$-0.591323\pi$
$137$	−2.13263	+	0.418835i	−0.182203	+	0.0357835i	0.100778	+	0.994909i	$0.467867\pi$
$138$		0			0
$139$	−1.16330	+	8.51684i	−0.0986696	+	0.722389i	0.873283	+	0.487213i	$0.161986\pi$
$139$	−1.16330	+	8.51684i	−0.0986696	+	0.722389i	−0.971953	+	0.235176i	$0.924433\pi$
$140$	−1.22198	+	1.78169i	−0.103276	+	0.150580i
$141$		0			0
$142$	2.37908	−	10.9830i	0.199648	−	0.921676i
$143$	−2.00396	−	4.64570i	−0.167579	−	0.388493i
$144$		0			0
$145$	33.5723	−	3.92404i	2.78803	−	0.325874i
$146$	−6.38890	+	2.90411i	−0.528749	+	0.240346i
$147$		0			0
$148$	0.478350	−	0.263943i	0.0393201	−	0.0216959i
$149$	18.1500	+	3.56455i	1.48691	+	0.292019i	0.869228	−	0.494412i	$-0.164616\pi$
$149$	18.1500	+	3.56455i	1.48691	+	0.292019i	0.617679	+	0.786431i	$0.288073\pi$
$150$		0			0
$151$	2.59903	+	3.78948i	0.211506	+	0.308383i	0.915885	−	0.401441i	$-0.131490\pi$
$151$	2.59903	+	3.78948i	0.211506	+	0.308383i	−0.704379	+	0.709824i	$0.748774\pi$
$152$	4.05333	−	2.03566i	0.328769	−	0.165114i
$153$		0			0
$154$	1.57488	+	27.0396i	0.126907	+	2.17891i
$155$	13.1336	+	5.36565i	1.05491	+	0.430979i
$156$		0			0
$157$	1.78401	+	18.3412i	0.142380	+	1.46379i	0.745695	+	0.666287i	$0.232118\pi$
$157$	1.78401	+	18.3412i	0.142380	+	1.46379i	−0.603316	+	0.797502i	$0.706154\pi$
$158$	0.859928	−	0.780343i	0.0684122	−	0.0620808i
$159$		0			0
$160$	−0.985037	−	2.55131i	−0.0778740	−	0.201699i
$161$	−0.886130	+	1.53482i	−0.0698368	+	0.120961i
$162$		0			0
$163$	3.43080	+	5.94232i	0.268721	+	0.465438i	0.968532	−	0.248890i	$-0.0800657\pi$
$163$	3.43080	+	5.94232i	0.268721	+	0.465438i	−0.699811	+	0.714328i	$0.746732\pi$
$164$	0.241582	−	0.299514i	0.0188644	−	0.0233881i
$165$		0			0
$166$	−2.97905	−	13.7528i	−0.231219	−	1.06743i
$167$	−0.776428	+	0.554958i	−0.0600818	+	0.0429439i	−0.611136	−	0.791525i	$-0.709287\pi$
$167$	−0.776428	+	0.554958i	−0.0600818	+	0.0429439i	0.551055	+	0.834469i	$0.314226\pi$
$168$		0			0
$169$	9.09742	−	7.05103i	0.699802	−	0.542387i
$170$	29.4672	−	19.3809i	2.26003	−	1.48645i
$171$		0			0
$172$	0.00254751	−	0.0437391i	0.000194246	−	0.00333507i
$173$	6.86641	−	14.3599i	0.522043	−	1.09176i	−0.457254	−	0.889336i	$-0.651167\pi$
$173$	6.86641	−	14.3599i	0.522043	−	1.09176i	0.979298	−	0.202425i	$-0.0648822\pi$
$174$		0			0
$175$	17.2887	−	19.8106i	1.30690	−	1.49754i
$176$	−15.1600	−	9.14913i	−1.14273	−	0.689642i
$177$		0			0
$178$	−1.58148	+	16.2590i	−0.118537	+	1.21867i
$179$	−2.24540	−	3.01610i	−0.167829	−	0.225434i	0.710249	−	0.703950i	$-0.248582\pi$
$179$	−2.24540	−	3.01610i	−0.167829	−	0.225434i	−0.878079	+	0.478516i	$0.841175\pi$
$180$		0			0
$181$	−7.22734	−	0.844754i	−0.537204	−	0.0627901i	−0.156835	−	0.987625i	$-0.550129\pi$
$181$	−7.22734	−	0.844754i	−0.537204	−	0.0627901i	−0.380369	+	0.924835i	$0.624203\pi$
$182$	7.59566	−	2.43545i	0.563027	−	0.180527i
$183$		0			0
$184$	−0.465464	−	0.973436i	−0.0343145	−	0.0717627i
$185$	−11.3755	+	4.64742i	−0.836346	+	0.341685i
$186$		0			0
$187$	9.78556	−	28.5994i	0.715591	−	2.09139i
$188$	0.451195	+	0.164221i	0.0329068	+	0.0119771i
$189$		0			0
$190$	7.59154	−	2.76309i	0.550748	−	0.200456i
$191$	−0.107490	−	5.54217i	−0.00777773	−	0.401018i	−0.983389	−	0.181511i	$-0.941901\pi$
$191$	−0.107490	−	5.54217i	−0.00777773	−	0.401018i	0.975611	−	0.219506i	$-0.0704446\pi$
$192$		0			0
$193$	−3.53392	−	5.60694i	−0.254377	−	0.403597i	0.694377	−	0.719611i	$-0.255680\pi$
$193$	−3.53392	−	5.60694i	−0.254377	−	0.403597i	−0.948754	+	0.316014i	$0.897655\pi$
$194$	21.6114	−	6.01594i	1.55161	−	0.431919i
$195$		0			0
$196$	−1.89044	−	0.0733577i	−0.135032	−	0.00523984i
$197$	−4.09408	−	4.33947i	−0.291691	−	0.309174i	0.564911	−	0.825152i	$-0.308910\pi$
$197$	−4.09408	−	4.33947i	−0.291691	−	0.309174i	−0.856602	+	0.515977i	$0.827429\pi$
$198$		0			0
$199$	−22.3347	−	5.29342i	−1.58326	−	0.375241i	−0.657534	−	0.753425i	$-0.728401\pi$
$199$	−22.3347	−	5.29342i	−1.58326	−	0.375241i	−0.925731	+	0.378184i	$0.876549\pi$
$200$	3.99312	+	15.5023i	0.282356	+	1.09617i
$201$		0			0
$202$	3.01791	−	7.81658i	0.212339	−	0.549973i
$203$	28.6725	+	35.5483i	2.01241	+	2.49500i
$204$		0			0
$205$	−6.17901	+	6.06033i	−0.431561	+	0.423272i
$206$	−1.93623	+	2.05229i	−0.134904	+	0.142990i
$207$		0			0
$208$	−1.49556	+	4.99553i	−0.103699	+	0.346378i
$209$	3.69178	−	5.85741i	0.255366	−	0.405166i
$210$		0			0
$211$	−8.04302	−	7.88854i	−0.553704	−	0.543069i	0.368573	−	0.929599i	$-0.379847\pi$
$211$	−8.04302	−	7.88854i	−0.553704	−	0.543069i	−0.922277	+	0.386530i	$0.873674\pi$
$212$	−1.24269	+	0.0482219i	−0.0853481	+	0.00331189i
$213$		0			0
$214$	8.07521	−	4.87342i	0.552010	−	0.333140i
$215$	−0.171121	+	0.970478i	−0.0116704	+	0.0661860i
$216$		0			0
$217$	3.32873	+	18.8782i	0.225969	+	1.28153i
$218$	7.32288	+	8.39109i	0.495968	+	0.568317i
$219$		0			0
$220$	−1.58699	−	1.23001i	−0.106995	−	0.0829272i
$221$	−8.87501	−	0.689820i	−0.596998	−	0.0464023i
$222$		0			0
$223$	−19.2509	−	17.4693i	−1.28914	−	1.16983i	−0.975430	−	0.220309i	$-0.929293\pi$
$223$	−19.2509	−	17.4693i	−1.28914	−	1.16983i	−0.313707	−	0.949520i	$-0.601571\pi$
$224$	2.20665	−	2.96404i	0.147438	−	0.198043i
$225$		0			0
$226$	−3.03192	+	7.02878i	−0.201680	+	0.467547i
$227$	−7.42236	−	5.30519i	−0.492640	−	0.352118i	0.307879	−	0.951426i	$-0.400381\pi$
$227$	−7.42236	−	5.30519i	−0.492640	−	0.352118i	−0.800519	+	0.599308i	$0.795443\pi$
$228$		0			0
$229$	0.218762	−	11.2793i	0.0144562	−	0.745357i	−0.920530	−	0.390672i	$-0.872243\pi$
$229$	0.218762	−	11.2793i	0.0144562	−	0.745357i	0.934986	−	0.354685i	$-0.115412\pi$
$230$	−0.622156	−	1.81832i	−0.0410238	−	0.119896i
$231$		0			0
$232$	−27.7217	+	2.15470i	−1.82002	+	0.141463i
$233$	21.2468	+	13.9742i	1.39192	+	0.915482i	0.999990	−	0.00451107i	$-0.00143592\pi$
$233$	21.2468	+	13.9742i	1.39192	+	0.915482i	0.391934	+	0.919994i	$0.371806\pi$
$234$		0			0
$235$	−9.65087	−	4.84685i	−0.629554	−	0.316174i
$236$	−0.149307	−	1.09312i	−0.00971904	−	0.0711560i
$237$		0			0
$238$	43.3832	+	19.7201i	2.81211	+	1.27826i
$239$	20.7307	+	6.64704i	1.34096	+	0.429961i	0.887291	−	0.461210i	$-0.152584\pi$
$239$	20.7307	+	6.64704i	1.34096	+	0.429961i	0.453668	+	0.891171i	$0.350115\pi$
$240$		0			0
$241$	24.9176	+	3.89704i	1.60508	+	0.251030i	0.892663	−	0.450724i	$-0.148834\pi$
$241$	24.9176	+	3.89704i	1.60508	+	0.251030i	0.712419	+	0.701754i	$0.247600\pi$
$242$	−9.05502			−0.582079
$243$		0			0
$244$	0.250877			0.0160608
$245$	42.0409	+	6.57507i	2.68589	+	0.420066i
$246$		0			0
$247$	−1.94165	−	0.622566i	−0.123544	−	0.0396129i
$248$	−10.6247	−	4.82951i	−0.674668	−	0.306674i
$249$		0			0
$250$	0.586108	+	4.29107i	0.0370687	+	0.271391i
$251$	−0.593703	−	0.298169i	−0.0374742	−	0.0188203i	0.429963	−	0.902846i	$-0.358526\pi$
$251$	−0.593703	−	0.298169i	−0.0374742	−	0.0188203i	−0.467438	+	0.884026i	$0.654823\pi$
$252$		0			0
$253$	−1.37610	−	0.905075i	−0.0865146	−	0.0569015i
$254$	−15.2638	+	1.18639i	−0.957733	+	0.0744409i
$255$		0			0
$256$	1.13424	+	3.31495i	0.0708902	+	0.207185i
$257$	0.128067	−	6.60312i	0.00798863	−	0.411892i	−0.974377	−	0.224921i	$-0.927788\pi$
$257$	0.128067	−	6.60312i	0.00798863	−	0.411892i	0.982366	−	0.186970i	$-0.0598668\pi$
$258$		0			0
$259$	−13.5078	−	9.65477i	−0.839331	−	0.599918i
$260$	−0.234203	+	0.542944i	−0.0145247	+	0.0336720i
$261$		0			0
$262$	−2.19970	+	2.95471i	−0.135898	+	0.182543i
$263$	−15.7966	−	14.3346i	−0.974058	−	0.883910i	0.0192025	−	0.999816i	$-0.493887\pi$
$263$	−15.7966	−	14.3346i	−0.974058	−	0.883910i	−0.993260	+	0.115905i	$0.963023\pi$
$264$		0			0
$265$	27.8875	+	2.16759i	1.71312	+	0.133154i
$266$	8.62769	+	6.68696i	0.528998	+	0.410004i
$267$		0			0
$268$	0.800716	+	0.917518i	0.0489115	+	0.0560464i
$269$	0.101529	+	0.575801i	0.00619034	+	0.0351072i	0.987746	−	0.156067i	$-0.0498816\pi$
$269$	0.101529	+	0.575801i	0.00619034	+	0.0351072i	−0.981556	+	0.191174i	$0.938770\pi$
$270$		0			0
$271$	4.47675	−	25.3889i	0.271943	−	1.54227i	−0.476564	−	0.879140i	$-0.658118\pi$
$271$	4.47675	−	25.3889i	0.271943	−	1.54227i	0.748507	−	0.663127i	$-0.230771\pi$
$272$	−26.6730	+	16.0972i	−1.61729	+	0.976037i
$273$		0			0
$274$	3.18198	−	0.123476i	0.192231	−	0.00745943i
$275$	17.4457	+	17.1107i	1.05202	+	1.03181i
$276$		0			0
$277$	−0.924144	+	1.46625i	−0.0555264	+	0.0880987i	−0.872602	−	0.488432i	$-0.837569\pi$
$277$	−0.924144	+	1.46625i	−0.0555264	+	0.0880987i	0.817076	+	0.576531i	$0.195594\pi$
$278$	3.61217	−	12.0655i	0.216643	−	0.723639i
$279$		0			0
$280$	−27.4319	+	29.0761i	−1.63937	+	1.73763i
$281$	−18.8923	+	18.5294i	−1.12702	+	1.10537i	−0.133575	+	0.991039i	$0.542646\pi$
$281$	−18.8923	+	18.5294i	−1.12702	+	1.10537i	−0.993443	+	0.114332i	$0.963527\pi$
$282$		0			0
$283$	−0.137372	−	0.170315i	−0.00816593	−	0.0101242i	0.774265	−	0.632861i	$-0.218120\pi$
$283$	−0.137372	−	0.170315i	−0.00816593	−	0.0101242i	−0.782431	+	0.622737i	$0.786021\pi$
$284$	−0.405415	+	1.05005i	−0.0240569	+	0.0623090i
$285$		0			0
$286$	1.84912	+	7.17873i	0.109341	+	0.424487i
$287$	−11.3790	−	2.69687i	−0.671681	−	0.159191i
$288$		0			0
$289$	−24.8299	−	26.3182i	−1.46058	−	1.54813i
$290$	−49.4871	−	1.92033i	−2.90598	−	0.112765i
$291$		0			0
$292$	0.677186	−	0.188508i	0.0396293	−	0.0110316i
$293$	7.43996	+	11.8043i	0.434647	+	0.689615i	0.989852	−	0.142099i	$-0.0453850\pi$
$293$	7.43996	+	11.8043i	0.434647	+	0.689615i	−0.555205	+	0.831713i	$0.687360\pi$
$294$		0			0
$295$	0.481192	+	24.8101i	0.0280161	+	1.44450i
$296$	9.49897	−	3.45734i	0.552117	−	0.200954i
$297$		0			0
$298$	−25.4667	−	9.26910i	−1.47524	−	0.536945i
$299$	−0.157028	+	0.458932i	−0.00908116	+	0.0265407i
$300$		0			0
$301$	−1.23260	+	0.503574i	−0.0710461	+	0.0290255i
$302$	−2.90438	−	6.07400i	−0.167128	−	0.349519i
$303$		0			0
$304$	−6.79528	+	2.17882i	−0.389736	+	0.124964i
$305$	−5.60459	−	0.655083i	−0.320918	−	0.0375099i
$306$		0			0
$307$	3.74146	+	5.02565i	0.213536	+	0.286829i	0.895966	−	0.444122i	$-0.146484\pi$
$307$	3.74146	+	5.02565i	0.213536	+	0.286829i	−0.682430	+	0.730951i	$0.739077\pi$
$308$	0.262641	−	2.70019i	0.0149654	−	0.153857i
$309$		0			0
$310$	−17.7971	−	10.7406i	−1.01081	−	0.610027i
$311$	−3.77734	+	4.32835i	−0.214193	+	0.245438i	−0.850471	−	0.526022i	$-0.823683\pi$
$311$	−3.77734	+	4.32835i	−0.214193	+	0.245438i	0.636278	+	0.771460i	$0.280473\pi$
$312$		0			0
$313$	4.31560	−	9.02530i	0.243932	−	0.510140i	−0.743393	−	0.668855i	$-0.766785\pi$
$313$	4.31560	−	9.02530i	0.243932	−	0.510140i	0.987324	+	0.158715i	$0.0507352\pi$
$314$	1.56991	−	26.9544i	0.0885953	−	1.52112i
$315$		0			0
$316$	−0.0971749	+	0.0639130i	−0.00546652	+	0.00359539i
$317$	−8.08596	+	6.26709i	−0.454153	+	0.351995i	−0.813851	−	0.581074i	$-0.802633\pi$
$317$	−8.08596	+	6.26709i	−0.454153	+	0.351995i	0.359698	+	0.933069i	$0.382880\pi$
$318$		0			0
$319$	−34.5305	+	24.6809i	−1.93334	+	1.38187i
$320$	−5.12219	−	23.6467i	−0.286339	−	1.32189i
$321$		0			0
$322$	1.63023	−	2.02117i	0.0908491	−	0.112635i
$323$	−6.09092	−	10.5498i	−0.338908	−	0.587006i
$324$		0			0
$325$	3.59818	−	6.23224i	0.199591	−	0.345702i
$326$	−3.62104	−	9.37873i	−0.200551	−	0.519440i
$327$		0			0
$328$	5.27248	−	4.78452i	0.291124	−	0.264181i
$329$	−1.41267	−	14.5235i	−0.0778828	−	0.800705i
$330$		0			0
$331$	−20.0615	−	8.19602i	−1.10268	−	0.450494i	−0.247532	−	0.968880i	$-0.579620\pi$
$331$	−20.0615	−	8.19602i	−1.10268	−	0.450494i	−0.855147	+	0.518386i	$0.826533\pi$
$332$	0.0819527	+	1.40707i	0.00449774	+	0.0772232i
$333$		0			0
$334$	1.24959	−	0.627566i	0.0683743	−	0.0343389i
$335$	−15.4922	−	22.5882i	−0.846428	−	1.23412i
$336$		0			0
$337$	20.4180	+	4.00997i	1.11224	+	0.218437i	0.714895	−	0.699232i	$-0.246474\pi$
$337$	20.4180	+	4.00997i	1.11224	+	0.218437i	0.397346	+	0.917669i	$0.369931\pi$
$338$	−14.7656	+	8.14733i	−0.803144	+	0.443156i
$339$		0			0
$340$	−3.21600	+	1.46185i	−0.174412	+	0.0792801i
$341$	−17.6947	+	2.06822i	−0.958223	+	0.112000i
$342$		0			0
$343$	10.4069	+	24.1260i	0.561922	+	1.30268i
$344$	0.171618	−	0.792278i	0.00925304	−	0.0427168i
$345$		0			0
$346$	−13.1907	+	19.2326i	−0.709139	+	1.03395i
$347$	2.51954	−	18.4463i	0.135256	−	0.990250i	−0.790589	−	0.612347i	$-0.790226\pi$
$347$	2.51954	−	18.4463i	0.135256	−	0.990250i	0.925845	−	0.377903i	$-0.123355\pi$
$348$		0			0
$349$	3.04894	−	0.598793i	0.163206	−	0.0320527i	−0.110442	−	0.993883i	$-0.535227\pi$
$349$	3.04894	−	0.598793i	0.163206	−	0.0320527i	0.273648	+	0.961830i	$0.411770\pi$
$350$	−29.5119	+	24.7634i	−1.57748	+	1.32366i
$351$		0			0
$352$	2.63075	+	2.20746i	0.140219	+	0.117658i
$353$	13.8001	+	7.61455i	0.734503	+	0.405281i	0.805811	−	0.592173i	$-0.201730\pi$
$353$	13.8001	+	7.61455i	0.734503	+	0.405281i	−0.0713082	+	0.997454i	$0.522717\pi$
$354$		0			0
$355$	11.7988	−	22.3995i	0.626216	−	1.18884i
$356$	0.408142	−	1.58450i	0.0216315	−	0.0839785i
$357$		0			0
$358$	2.56757	+	4.87441i	0.135700	+	0.257621i
$359$	−33.8900	+	8.03208i	−1.78865	+	0.423917i	−0.985193	−	0.171450i	$-0.945155\pi$
$359$	−33.8900	+	8.03208i	−1.78865	+	0.423917i	−0.803454	+	0.595367i	$0.797007\pi$
$360$		0			0
$361$	4.64898	+	15.5287i	0.244683	+	0.817299i
$362$	10.2709	+	2.85911i	0.539828	+	0.150271i
$363$		0			0
$364$	−0.789352	+	0.123452i	−0.0413733	+	0.00647066i
$365$	−15.6206	+	2.44301i	−0.817617	+	0.127873i
$366$		0			0
$367$	−3.26104	−	0.907772i	−0.170225	−	0.0473853i	0.182012	−	0.983296i	$-0.441739\pi$
$367$	−3.26104	−	0.907772i	−0.170225	−	0.0473853i	−0.352236	+	0.935911i	$0.614579\pi$
$368$	0.486865	+	1.62624i	0.0253796	+	0.0847738i
$369$		0			0
$370$	17.5192	−	4.15213i	0.910780	−	0.215859i
$371$	17.6138	+	33.4389i	0.914460	+	1.73606i
$372$		0			0
$373$	1.00759	−	3.91170i	0.0521709	−	0.202540i	−0.936995	−	0.349343i	$-0.886405\pi$
$373$	1.00759	−	3.91170i	0.0521709	−	0.202540i	0.989166	+	0.146803i	$0.0468985\pi$
$374$	−20.6403	+	39.1846i	−1.06728	+	2.02619i
$375$		0			0
$376$	7.77845	+	4.29197i	0.401143	+	0.221341i
$377$	9.57527	+	8.03460i	0.493151	+	0.413803i
$378$		0			0
$379$	4.02335	−	3.37599i	0.206665	−	0.173413i	−0.533580	−	0.845750i	$-0.679154\pi$
$379$	4.02335	−	3.37599i	0.206665	−	0.173413i	0.740246	+	0.672337i	$0.234709\pi$
$380$	−0.794015	+	0.155939i	−0.0407321	+	0.00799953i
$381$		0			0
$382$	−1.09914	+	8.04710i	−0.0562367	+	0.411725i
$383$	0.364701	−	0.531747i	0.0186354	−	0.0271710i	−0.815245	−	0.579116i	$-0.803398\pi$
$383$	0.364701	−	0.531747i	0.0186354	−	0.0271710i	0.833881	+	0.551945i	$0.186114\pi$
$384$		0			0
$385$	−12.9180	+	59.6364i	−0.658365	+	3.03935i
$386$	3.84624	+	8.91659i	0.195769	+	0.453843i
$387$		0			0
$388$	−2.23175	+	0.260854i	−0.113300	+	0.0132429i
$389$	21.5335	−	9.78820i	1.09179	−	0.496281i	0.214739	−	0.976671i	$-0.431110\pi$
$389$	21.5335	−	9.78820i	1.09179	−	0.496281i	0.877055	+	0.480390i	$0.159505\pi$
$390$		0			0
$391$	−2.53726	+	1.40000i	−0.128315	+	0.0708012i
$392$	−34.3480	−	6.74573i	−1.73484	−	0.340711i
$393$		0			0
$394$	4.94407	+	7.20864i	0.249079	+	0.363166i
$395$	2.33777	−	1.17407i	0.117626	−	0.0590741i
$396$		0			0
$397$	2.16590	+	37.1871i	0.108704	+	1.86637i	0.409014	+	0.912528i	$0.365873\pi$
$397$	2.16590	+	37.1871i	0.108704	+	1.86637i	−0.300311	+	0.953841i	$0.597090\pi$
$398$	31.1329	+	12.7192i	1.56055	+	0.637556i
$399$		0			0
$400$	−2.43822	−	25.0671i	−0.121911	−	1.25336i
$401$	−26.6209	+	24.1572i	−1.32939	+	1.20635i	−0.368430	+	0.929656i	$0.620104\pi$
$401$	−26.6209	+	24.1572i	−1.32939	+	1.20635i	−0.960957	+	0.276698i	$0.910760\pi$
$402$		0			0
$403$	1.88967	+	4.89438i	0.0941313	+	0.243806i
$404$	−0.419626	+	0.726813i	−0.0208772	+	0.0361603i
$405$		0			0
$406$	−33.4577	−	57.9505i	−1.66048	−	2.87604i
$407$	9.68746	−	12.0106i	0.480189	−	0.595341i
$408$		0			0
$409$	−2.47783	−	11.4389i	−0.122521	−	0.565619i	−0.996782	−	0.0801625i	$-0.974456\pi$
$409$	−2.47783	−	11.4389i	−0.122521	−	0.565619i	0.874261	−	0.485456i	$-0.161346\pi$
$410$	10.3167	−	7.37393i	0.509505	−	0.364172i
$411$		0			0
$412$	0.223371	−	0.173125i	0.0110047	−	0.00852927i
$413$	−28.0129	+	18.4244i	−1.37843	+	0.906605i
$414$		0			0
$415$	1.84329	−	31.6480i	0.0904833	−	1.55354i
$416$	0.436286	−	0.912414i	0.0213907	−	0.0447348i
$417$		0			0
$418$	−6.67027	+	7.64328i	−0.326254	+	0.373845i
$419$	−3.22860	−	1.94847i	−0.157728	−	0.0951891i	0.435639	−	0.900122i	$-0.356522\pi$
$419$	−3.22860	−	1.94847i	−0.157728	−	0.0951891i	−0.593366	+	0.804932i	$0.702201\pi$
$420$		0			0
$421$	1.66536	−	17.1214i	0.0811647	−	0.834446i	−0.863051	−	0.505117i	$-0.831449\pi$
$421$	1.66536	−	17.1214i	0.0811647	−	0.834446i	0.944215	−	0.329329i	$-0.106822\pi$
$422$	9.85700	+	13.2402i	0.479831	+	0.644525i
$423$		0			0
$424$	−22.8545	−	2.67131i	−1.10991	−	0.129730i
$425$	40.9406	−	13.1271i	1.98591	−	0.636757i
$426$		0			0
$427$	−3.28900	−	6.87837i	−0.159166	−	0.332868i
$428$	−0.874540	+	0.357289i	−0.0422725	+	0.0172702i
$429$		0			0
$430$	0.467427	−	1.36611i	0.0225413	−	0.0658795i
$431$	−6.06973	−	2.20920i	−0.292369	−	0.106413i	0.191672	−	0.981459i	$-0.438609\pi$
$431$	−6.06973	−	2.20920i	−0.292369	−	0.106413i	−0.484041	+	0.875046i	$0.660831\pi$
$432$		0			0
$433$	6.77948	−	2.46753i	0.325801	−	0.118582i	−0.173941	−	0.984756i	$-0.555650\pi$
$433$	6.77948	−	2.46753i	0.325801	−	0.118582i	0.499742	+	0.866174i	$0.333428\pi$
$434$	−0.544637	−	28.0814i	−0.0261434	−	1.34795i
$435$		0			0
$436$	−0.594797	−	0.943710i	−0.0284856	−	0.0451955i
$437$	−0.639468	+	0.178008i	−0.0305899	+	0.00851528i
$438$		0			0
$439$	26.1244	+	1.01375i	1.24685	+	0.0483835i	0.653729	−	0.756729i	$-0.273204\pi$
$439$	26.1244	+	1.01375i	1.24685	+	0.0483835i	0.593123	+	0.805112i	$0.297895\pi$
$440$	−25.4940	−	27.0221i	−1.21538	−	1.28823i
$441$		0			0
$442$	12.6912	+	3.00786i	0.603656	+	0.143069i
$443$	−5.03072	−	19.5304i	−0.239017	−	0.927919i	−0.969520	−	0.245011i	$-0.921209\pi$
$443$	−5.03072	−	19.5304i	−0.239017	−	0.927919i	0.730504	−	0.682909i	$-0.239285\pi$
$444$		0			0
$445$	−13.2553	+	34.3320i	−0.628361	+	1.62749i
$446$	23.9123	+	29.6466i	1.13228	+	1.40381i
$447$		0			0
$448$	23.3394	−	22.8911i	1.10268	−	1.08150i
$449$	−8.49977	+	9.00923i	−0.401129	+	0.425172i	−0.896179	−	0.443693i	$-0.853668\pi$
$449$	−8.49977	+	9.00923i	−0.401129	+	0.425172i	0.495050	+	0.868864i	$0.335150\pi$
$450$		0			0
$451$	3.11701	−	10.4115i	0.146774	−	0.490259i
$452$	0.408820	−	0.648636i	0.0192293	−	0.0305093i
$453$		0			0
$454$	9.54341	+	9.36011i	0.447894	+	0.439292i
$455$	17.9565	−	0.696792i	0.841812	−	0.0326661i
$456$		0			0
$457$	−16.8230	+	10.1528i	−0.786949	+	0.474926i	−0.852375	−	0.522931i	$-0.824838\pi$
$457$	−16.8230	+	10.1528i	−0.786949	+	0.474926i	0.0654260	+	0.997857i	$0.479159\pi$
$458$	−2.87029	+	16.2782i	−0.134120	+	0.760631i
$459$		0			0
$460$	0.0334260	+	0.189568i	0.00155849	+	0.00883866i
$461$	2.00099	+	2.29288i	0.0931953	+	0.106790i	0.798139	−	0.602473i	$-0.205818\pi$
$461$	2.00099	+	2.29288i	0.0931953	+	0.106790i	−0.704944	+	0.709263i	$0.749028\pi$
$462$		0			0
$463$	17.6293	+	13.6637i	0.819303	+	0.635008i	0.933551	−	0.358444i	$-0.116693\pi$
$463$	17.6293	+	13.6637i	0.819303	+	0.635008i	−0.114248	+	0.993452i	$0.536446\pi$
$464$	43.6139	+	3.38994i	2.02472	+	0.157374i
$465$		0			0
$466$	−27.5928	−	25.0391i	−1.27821	−	1.15991i
$467$	15.1401	−	20.3366i	0.700598	−	0.941067i	−0.299316	−	0.954154i	$-0.596759\pi$
$467$	15.1401	−	20.3366i	0.700598	−	0.941067i	0.999914	+	0.0130874i	$0.00416598\pi$
$468$		0			0
$469$	14.6585	−	33.9821i	0.676865	−	1.56915i
$470$	12.8731	+	9.20116i	0.593793	+	0.424418i
$471$		0			0
$472$	0.395839	−	20.4094i	0.0182200	−	0.939417i
$473$	−0.400601	−	1.17080i	−0.0184197	−	0.0538335i
$474$		0			0
$475$	9.81842	−	0.763148i	0.450500	−	0.0350156i
$476$	−3.98795	−	2.62292i	−0.182787	−	0.120221i
$477$		0			0
$478$	−28.5046	−	14.3155i	−1.30377	−	0.654778i
$479$	−5.15642	−	37.7517i	−0.235603	−	1.72492i	−0.605499	−	0.795846i	$-0.707026\pi$
$479$	−5.15642	−	37.7517i	−0.235603	−	1.72492i	0.369896	−	0.929073i	$-0.379393\pi$
$480$		0			0
$481$	−4.13689	−	1.88045i	−0.188626	−	0.0857410i
$482$	−35.1880	−	11.2826i	−1.60277	−	0.513908i
$483$		0			0
$484$	0.896076	+	0.140144i	0.0407307	+	0.00637017i
$485$	50.5384			2.29483
$486$		0			0
$487$	−37.9752			−1.72082			−0.860410	−	0.509603i	$-0.829792\pi$
$487$	−37.9752			−1.72082			−0.860410	+	0.509603i	$0.829792\pi$
$488$	4.58610	+	0.717253i	0.207603	+	0.0324685i
$489$		0			0
$490$	−59.3691	−	19.0359i	−2.68202	−	0.859956i
$491$	−24.1707	−	10.9869i	−1.09081	−	0.495834i	−0.214079	−	0.976816i	$-0.568675\pi$
$491$	−24.1707	−	10.9869i	−1.09081	−	0.495834i	−0.876730	+	0.480982i	$0.840280\pi$
$492$		0			0
$493$	10.1062	+	73.9903i	0.455159	+	3.33235i
$494$	2.66976	+	1.34080i	0.120118	+	0.0603256i
$495$		0			0
$496$	15.3407	+	10.0898i	0.688819	+	0.453043i
$497$	34.1045	−	2.65081i	1.52980	−	0.118905i
$498$		0			0
$499$	−4.50770	−	13.1742i	−0.201792	−	0.589760i	0.798127	−	0.602490i	$-0.205825\pi$
$499$	−4.50770	−	13.1742i	−0.201792	−	0.589760i	−0.999919	+	0.0127294i	$0.995948\pi$
$500$	0.00841182	−	0.433711i	0.000376188	−	0.0193962i
$501$		0			0
$502$	0.791930	+	0.566038i	0.0353456	+	0.0252635i
$503$	−1.20465	+	2.79268i	−0.0537125	+	0.124520i	−0.942959	−	0.332908i	$-0.891970\pi$
$503$	−1.20465	+	2.79268i	−0.0537125	+	0.124520i	0.889247	+	0.457428i	$0.151229\pi$
$504$		0			0
$505$	11.2723	−	15.1413i	0.501609	−	0.673778i
$506$	1.78711	+	1.62172i	0.0794468	+	0.0720941i
$507$		0			0
$508$	1.52885	+	0.118831i	0.0678317	+	0.00527229i
$509$	−8.73789	−	6.77238i	−0.387300	−	0.300180i	0.400280	−	0.916393i	$-0.368913\pi$
$509$	−8.73789	−	6.77238i	−0.387300	−	0.300180i	−0.787580	+	0.616213i	$0.788666\pi$
$510$		0			0
$511$	−14.0463	−	16.0953i	−0.621371	−	0.712012i
$512$	3.41396	+	19.3615i	0.150877	+	0.855667i
$513$		0			0
$514$	−1.68032	+	9.52958i	−0.0741158	+	0.420332i
$515$	−5.44216	+	3.28436i	−0.239810	+	0.144726i
$516$		0			0
$517$	13.5510	−	0.525840i	0.595971	−	0.0231264i
$518$	17.3678	+	17.0342i	0.763097	+	0.748441i
$519$		0			0
$520$	−5.83356	+	9.25558i	−0.255819	+	0.405884i
$521$	2.45775	−	8.20946i	0.107676	−	0.359663i	−0.887121	−	0.461536i	$-0.847298\pi$
$521$	2.45775	−	8.20946i	0.107676	−	0.359663i	0.994797	+	0.101873i	$0.0324836\pi$
$522$		0			0
$523$	12.9105	−	13.6843i	0.564536	−	0.598373i	−0.380725	−	0.924688i	$-0.624326\pi$
$523$	12.9105	−	13.6843i	0.564536	−	0.598373i	0.945261	+	0.326315i	$0.105807\pi$
$524$	0.263410	−	0.258351i	0.0115071	−	0.0112861i
$525$		0			0
$526$	19.6215	+	24.3269i	0.855539	+	1.06070i
$527$	−11.2896	+	29.2408i	−0.491782	+	1.27375i
$528$		0			0
$529$	−5.69776	−	22.1201i	−0.247729	−	0.961742i
$530$	−39.8788	−	9.45144i	−1.73222	−	0.410544i
$531$		0			0
$532$	−0.750294	−	0.795265i	−0.0325294	−	0.0344791i
$533$	−3.19820	−	0.124105i	−0.138530	−	0.00537558i
$534$		0			0
$535$	20.4702	−	5.69826i	0.885002	−	0.246357i
$536$	12.0141	+	19.0617i	0.518931	+	0.823340i
$537$		0			0
$538$	−0.0166119	−	0.856506i	−0.000716190	−	0.0369266i
$539$	−50.2105	+	18.2751i	−2.16272	+	0.787166i
$540$		0			0
$541$	−9.42109	−	3.42900i	−0.405044	−	0.147424i	0.131460	−	0.991321i	$-0.458033\pi$
$541$	−9.42109	−	3.42900i	−0.405044	−	0.147424i	−0.536505	+	0.843897i	$0.680256\pi$
$542$	−12.2285	+	35.7391i	−0.525258	+	1.53512i
$543$		0			0
$544$	5.59342	−	2.28517i	0.239816	−	0.0979756i
$545$	10.8236	+	22.6356i	0.463631	+	0.969602i
$546$		0			0
$547$	32.7705	−	10.5074i	1.40116	−	0.449265i	0.493788	−	0.869583i	$-0.335612\pi$
$547$	32.7705	−	10.5074i	1.40116	−	0.449265i	0.907377	+	0.420317i	$0.138081\pi$
$548$	−0.316797	−	0.0370283i	−0.0135329	−	0.00158177i
$549$		0			0
$550$	−21.3804	−	28.7188i	−0.911661	−	1.22457i
$551$	−1.65599	+	17.0251i	−0.0705475	+	0.725292i
$552$		0			0
$553$	3.02628	+	1.82637i	0.128691	+	0.0776652i
$554$	1.66973	−	1.91330i	0.0709402	−	0.0812884i
$555$		0			0
$556$	−0.544193	+	1.13808i	−0.0230789	+	0.0482655i
$557$	−1.20705	+	20.7243i	−0.0511444	+	0.878116i	0.871003	+	0.491277i	$0.163470\pi$
$557$	−1.20705	+	20.7243i	−0.0511444	+	0.878116i	−0.922148	+	0.386838i	$0.873567\pi$
$558$		0			0
$559$	−0.304469	+	0.200253i	−0.0128777	+	0.00846978i
$560$	49.7080	−	38.5266i	2.10055	−	1.62805i
$561$		0			0
$562$	31.5431	−	22.5457i	1.33057	−	0.951032i
$563$	−1.62760	−	7.51382i	−0.0685950	−	0.316670i	0.930125	−	0.367242i	$-0.119698\pi$
$563$	−1.62760	−	7.51382i	−0.0685950	−	0.316670i	−0.998720	+	0.0505723i	$0.983895\pi$
$564$		0			0
$565$	−10.8267	+	13.4230i	−0.455484	+	0.564711i
$566$	0.160299	+	0.277646i	0.00673786	+	0.0116703i
$567$		0			0
$568$	−10.4132	+	18.0361i	−0.436926	+	0.756779i
$569$	−9.74838	−	25.2489i	−0.408673	−	1.05849i	−0.972563	−	0.232640i	$-0.925264\pi$
$569$	−9.74838	−	25.2489i	−0.408673	−	1.05849i	0.563890	−	0.825850i	$-0.309304\pi$
$570$		0			0
$571$	−11.7960	+	10.7043i	−0.493646	+	0.447960i	−0.880406	−	0.474220i	$-0.842730\pi$
$571$	−11.7960	+	10.7043i	−0.493646	+	0.447960i	0.386760	+	0.922180i	$0.373594\pi$
$572$	−0.0718827	−	0.739019i	−0.00300557	−	0.0308999i
$573$		0			0
$574$	15.8615	+	6.48014i	0.662046	+	0.270476i
$575$	−0.136216	−	2.33874i	−0.00568060	−	0.0975321i
$576$		0			0
$577$	41.3521	−	20.7678i	1.72151	−	0.864576i	0.740141	−	0.672452i	$-0.234759\pi$
$577$	41.3521	−	20.7678i	1.72151	−	0.864576i	0.981371	−	0.192124i	$-0.0615376\pi$
$578$	29.9850	+	43.7192i	1.24721	+	1.81848i
$579$		0			0
$580$	4.86748	+	0.955941i	0.202111	+	0.0396933i
$581$	37.5037	−	20.6937i	1.55592	−	0.858518i
$582$		0			0
$583$	−31.9758	+	14.5348i	−1.32430	+	0.601970i
$584$	12.9181	−	1.50991i	0.534554	−	0.0624804i
$585$		0			0
$586$	−8.09750	−	18.7721i	−0.334505	−	0.775469i
$587$	4.31716	−	19.9302i	0.178188	−	0.822609i	−0.797478	−	0.603348i	$-0.793833\pi$
$587$	4.31716	−	19.9302i	0.178188	−	0.822609i	0.975666	−	0.219261i	$-0.0703646\pi$
$588$		0			0
$589$	−4.06089	+	5.92092i	−0.167326	+	0.243967i
$590$	4.92040	−	36.0237i	0.202570	−	1.48307i
$591$		0			0
$592$	−15.6055	+	3.06482i	−0.641382	+	0.125963i
$593$	33.6479	−	28.2339i	1.38175	−	1.15943i	0.413194	−	0.910643i	$-0.364413\pi$
$593$	33.6479	−	28.2339i	1.38175	−	1.15943i	0.968559	−	0.248785i	$-0.0800311\pi$
$594$		0			0
$595$	82.2419	+	69.0091i	3.37159	+	2.82910i
$596$	2.37670	+	1.31141i	0.0973533	+	0.0537173i
$597$		0			0
$598$	0.331212	−	0.628791i	0.0135443	−	0.0257132i
$599$	−1.07574	+	4.17628i	−0.0439535	+	0.170638i	−0.986601	−	0.163152i	$-0.947834\pi$
$599$	−1.07574	+	4.17628i	−0.0439535	+	0.170638i	0.942647	+	0.333790i	$0.108328\pi$
$600$		0			0
$601$	−5.35154	−	10.1597i	−0.218294	−	0.414421i	0.751008	−	0.660293i	$-0.229568\pi$
$601$	−5.35154	−	10.1597i	−0.218294	−	0.414421i	−0.969302	+	0.245872i	$0.920926\pi$
$602$	1.89831	−	0.449907i	0.0773691	−	0.0183368i
$603$		0			0
$604$	0.193408	+	0.646028i	0.00786966	+	0.0262865i
$605$	−19.6524	−	5.47061i	−0.798983	−	0.222412i
$606$		0			0
$607$	−22.1328	+	3.46150i	−0.898342	+	0.140498i	−0.586798	−	0.809734i	$-0.699612\pi$
$607$	−22.1328	+	3.46150i	−0.898342	+	0.140498i	−0.311544	+	0.950232i	$0.600846\pi$
$608$	1.36739	−	0.213856i	0.0554551	−	0.00867303i
$609$		0			0
$610$	7.96481	+	2.21716i	0.322486	+	0.0897700i
$611$	−1.14541	−	3.82593i	−0.0463383	−	0.154781i
$612$		0			0
$613$	−13.3094	+	3.15439i	−0.537562	+	0.127404i	−0.490424	−	0.871484i	$-0.663158\pi$
$613$	−13.3094	+	3.15439i	−0.537562	+	0.127404i	−0.0471376	+	0.998888i	$0.515010\pi$
$614$	−4.27828	−	8.12211i	−0.172657	−	0.327782i
$615$		0			0
$616$	12.5209	−	48.6092i	0.504483	−	1.95852i
$617$	5.87245	−	11.1486i	0.236416	−	0.448824i	−0.737621	−	0.675215i	$-0.764051\pi$
$617$	5.87245	−	11.1486i	0.236416	−	0.448824i	0.974037	+	0.226391i	$0.0726927\pi$
$618$		0			0
$619$	14.4627	+	7.98020i	0.581306	+	0.320751i	0.746369	−	0.665532i	$-0.231795\pi$
$619$	14.4627	+	7.98020i	0.581306	+	0.320751i	−0.165063	+	0.986283i	$0.552783\pi$
$620$	1.59496	+	1.33833i	0.0640550	+	0.0537485i
$621$		0			0
$622$	6.44794	−	5.41047i	0.258539	−	0.216940i
$623$	−48.7935	+	9.58273i	−1.95487	+	0.383924i
$624$		0			0
$625$	2.66881	−	19.5392i	0.106753	−	0.781567i
$626$	−8.29050	+	12.0878i	−0.331355	+	0.483127i
$627$		0			0
$628$	−0.572527	+	2.64308i	−0.0228463	+	0.105470i
$629$	−10.7531	−	24.9285i	−0.428754	−	0.993964i
$630$		0			0
$631$	−23.6062	+	2.75917i	−0.939749	+	0.109841i	−0.572155	−	0.820146i	$-0.693892\pi$
$631$	−23.6062	+	2.75917i	−0.939749	+	0.109841i	−0.367594	+	0.929986i	$0.619818\pi$
$632$	−1.95911	+	0.890524i	−0.0779292	+	0.0354232i
$633$		0			0
$634$	13.1240	−	7.24149i	0.521219	−	0.287596i
$635$	−33.8442	−	6.64678i	−1.34306	−	0.263769i
$636$		0			0
$637$	8.90027	+	12.9769i	0.352641	+	0.514164i
$638$	55.5735	−	27.9101i	2.20018	−	1.10497i
$639$		0			0
$640$	2.37928	+	40.8507i	0.0940493	+	1.61476i
$641$	−8.42088	−	3.44031i	−0.332605	−	0.135884i	0.205745	−	0.978606i	$-0.434038\pi$
$641$	−8.42088	−	3.44031i	−0.332605	−	0.135884i	−0.538349	+	0.842722i	$0.680952\pi$
$642$		0			0
$643$	−0.322183	−	3.31233i	−0.0127056	−	0.130625i	0.986805	−	0.161915i	$-0.0517670\pi$
$643$	−0.322183	−	3.31233i	−0.0127056	−	0.130625i	−0.999510	+	0.0312895i	$0.990039\pi$
$644$	−0.192607	+	0.174782i	−0.00758979	+	0.00688736i
$645$		0			0
$646$	6.42867	+	16.6507i	0.252933	+	0.655112i
$647$	8.58782	−	14.8745i	0.337622	−	0.584779i	−0.646363	−	0.763030i	$-0.723711\pi$
$647$	8.58782	−	14.8745i	0.337622	−	0.584779i	0.983985	+	0.178252i	$0.0570441\pi$
$648$		0			0
$649$	−15.5801	−	26.9855i	−0.611573	−	1.05927i
$650$	−6.61964	+	8.20706i	−0.259644	+	0.321907i
$651$		0			0
$652$	0.213181	+	0.984152i	0.00834881	+	0.0385424i
$653$	38.0973	−	27.2303i	1.49086	−	1.06561i	0.512507	−	0.858683i	$-0.328717\pi$
$653$	38.0973	−	27.2303i	1.49086	−	1.06561i	0.978357	−	0.206923i	$-0.0663449\pi$
$654$		0			0
$655$	−6.55918	+	5.08375i	−0.256288	+	0.198638i
$656$	−9.35856	+	6.15522i	−0.365390	+	0.240321i
$657$		0			0
$658$	−1.24313	+	21.3438i	−0.0484624	+	0.832067i
$659$	−8.42815	+	17.6260i	−0.328314	+	0.686611i	−0.998452	−	0.0556263i	$-0.982284\pi$
$659$	−8.42815	+	17.6260i	−0.328314	+	0.686611i	0.670138	+	0.742237i	$0.266235\pi$
$660$		0			0
$661$	23.0093	−	26.3658i	0.894959	−	1.02551i	−0.104561	−	0.994518i	$-0.533344\pi$
$661$	23.0093	−	26.3658i	0.894959	−	1.02551i	0.999520	−	0.0309905i	$-0.00986617\pi$
$662$	27.1851	+	16.4063i	1.05658	+	0.637649i
$663$		0			0
$664$	−2.52468	+	25.9560i	−0.0979765	+	1.00729i
$665$	14.6850	+	19.7254i	0.569459	+	0.764917i
$666$		0			0
$667$	4.04161	+	0.472396i	0.156492	+	0.0182912i
$668$	−0.133371	+	0.0427636i	−0.00516027	+	0.00165457i
$669$		0			0
$670$	17.3123	+	36.2056i	0.668833	+	1.39875i
$671$	6.55937	−	2.67980i	0.253222	−	0.103452i
$672$		0			0
$673$	7.31903	−	21.3907i	0.282128	−	0.824550i	−0.710538	−	0.703659i	$-0.751548\pi$
$673$	7.31903	−	21.3907i	0.282128	−	0.824550i	0.992666	−	0.120891i	$-0.0385751\pi$
$674$	−28.6490	−	10.4274i	−1.10352	−	0.401647i
$675$		0			0
$676$	1.58729	−	0.577725i	0.0610495	−	0.0222202i
$677$	0.0818179	+	4.21851i	0.00314452	+	0.162131i	0.998092	+	0.0617378i	$0.0196643\pi$
$677$	0.0818179	+	4.21851i	0.00314452	+	0.162131i	−0.994948	+	0.100393i	$0.967990\pi$
$678$		0			0
$679$	36.4102	+	57.7687i	1.39729	+	2.21696i
$680$	−62.9688	+	17.5286i	−2.41474	+	0.672189i
$681$		0			0
$682$	26.0828	+	1.01213i	0.998764	+	0.0387566i
$683$	26.5516	+	28.1431i	1.01597	+	1.07686i	0.997028	+	0.0770438i	$0.0245481\pi$
$683$	26.5516	+	28.1431i	1.01597	+	1.07686i	0.0189414	+	0.999821i	$0.493970\pi$
$684$		0			0
$685$	6.98056	+	1.65442i	0.266713	+	0.0632122i
$686$	−9.60284	−	37.2805i	−0.366638	−	1.42338i
$687$		0			0
$688$	−0.459363	+	1.18978i	−0.0175131	+	0.0453599i
$689$	6.49406	+	8.05138i	0.247404	+	0.306733i
$690$		0			0
$691$	−13.2683	+	13.0135i	−0.504750	+	0.495055i	−0.907382	−	0.420307i	$-0.861922\pi$
$691$	−13.2683	+	13.0135i	−0.504750	+	0.495055i	0.402632	+	0.915362i	$0.368095\pi$
$692$	1.60300	−	1.69909i	0.0609371	−	0.0645895i
$693$		0			0
$694$	−7.82346	+	26.1322i	−0.296974	+	0.991964i
$695$	15.1290	−	24.0038i	0.573875	−	0.910515i
$696$		0			0
$697$	−13.6515	−	13.3893i	−0.517087	−	0.507155i
$698$	−4.54917	+	0.176528i	−0.172189	+	0.00668170i
$699$		0			0
$700$	3.30373	−	1.99381i	0.124869	−	0.0753590i
$701$	5.58713	−	31.6862i	0.211023	−	1.19677i	−0.676653	−	0.736302i	$-0.736570\pi$
$701$	5.58713	−	31.6862i	0.211023	−	1.19677i	0.887676	−	0.460468i	$-0.152319\pi$
$702$		0			0
$703$	−1.07986	−	6.12417i	−0.0407276	−	0.230977i
$704$	19.9768	+	22.8909i	0.752905	+	0.862734i
$705$		0			0
$706$	−18.2528	−	14.1470i	−0.686954	−	0.532429i
$707$	25.4285	+	1.97646i	0.956338	+	0.0743325i
$708$		0			0
$709$	13.8646	+	12.5815i	0.520697	+	0.472507i	0.889458	−	0.457017i	$-0.151082\pi$
$709$	13.8646	+	12.5815i	0.520697	+	0.472507i	−0.368761	+	0.929524i	$0.620218\pi$
$710$	−22.1510	+	29.7539i	−0.831312	+	1.11665i
$711$		0			0
$712$	11.9910	−	27.7983i	0.449382	−	1.04178i
$713$	1.38950	+	0.993155i	0.0520372	+	0.0371940i
$714$		0			0
$715$	−0.323845	+	16.6974i	−0.0121111	+	0.624446i
$716$	−0.178643	−	0.522105i	−0.00667622	−	0.0195120i
$717$		0			0
$718$	50.8771	−	3.95448i	1.89872	−	0.147580i
$719$	18.3277	+	12.0543i	0.683510	+	0.449551i	0.843189	−	0.537618i	$-0.180676\pi$
$719$	18.3277	+	12.0543i	0.683510	+	0.449551i	−0.159679	+	0.987169i	$0.551046\pi$
$720$		0			0
$721$	−7.67502	−	3.85454i	−0.285833	−	0.143551i
$722$	−3.21413	−	23.5316i	−0.119617	−	0.875755i
$723$		0			0
$724$	−0.972150	−	0.441897i	−0.0361297	−	0.0164230i
$725$	−57.4877	−	18.4327i	−2.13504	−	0.684573i
$726$		0			0
$727$	−34.9083	−	5.45956i	−1.29468	−	0.202484i	−0.530608	−	0.847617i	$-0.678036\pi$
$727$	−34.9083	−	5.45956i	−1.29468	−	0.202484i	−0.764070	+	0.645133i	$0.776802\pi$
$728$	−14.7825			−0.547876
$729$		0			0
$730$	23.1652			0.857381
$731$	−2.15103	−	0.336416i	−0.0795589	−	0.0124428i
$732$		0			0
$733$	18.1888	+	5.83202i	0.671820	+	0.215411i	0.621609	−	0.783328i	$-0.286479\pi$
$733$	18.1888	+	5.83202i	0.671820	+	0.215411i	0.0502119	+	0.998739i	$0.484010\pi$
$734$	4.51511	+	2.05237i	0.166656	+	0.0757543i
$735$		0			0
$736$	−0.0445560	−	0.326208i	−0.00164236	−	0.0120242i
$737$	30.7360	+	15.4362i	1.13217	+	0.568599i
$738$		0			0
$739$	−4.57338	−	3.00796i	−0.168235	−	0.110650i	0.462600	−	0.886567i	$-0.346917\pi$
$739$	−4.57338	−	3.00796i	−0.168235	−	0.110650i	−0.630834	+	0.775918i	$0.717287\pi$
$740$	−1.79795	+	0.139747i	−0.0660938	+	0.00513722i
$741$		0			0
$742$	−17.9269	−	52.3933i	−0.658117	−	1.92342i
$743$	0.0215372	−	1.11045i	0.000790123	−	0.0407385i	−0.999209	−	0.0397566i	$-0.987342\pi$
$743$	0.0215372	−	1.11045i	0.000790123	−	0.0407385i	1.00000		0.000981966i	$-0.000312570\pi$
$744$		0			0
$745$	−49.6711	−	35.5028i	−1.81981	−	1.30072i
$746$	−2.34417	+	5.43439i	−0.0858261	+	0.198967i
$747$		0			0
$748$	2.64900	−	3.55822i	0.0968569	−	0.130101i
$749$	21.2611	+	19.2934i	0.776865	+	0.704967i
$750$		0			0
$751$	4.40395	+	0.342302i	0.160702	+	0.0124908i	0.157591	−	0.987504i	$-0.449627\pi$
$751$	4.40395	+	0.342302i	0.160702	+	0.0124908i	0.00311079	+	0.999995i	$0.499010\pi$
$752$	−11.0473	−	8.56229i	−0.402853	−	0.312235i
$753$		0			0
$754$	−12.0420	−	13.7986i	−0.438543	−	0.502515i
$755$	−2.63384	−	14.9373i	−0.0958554	−	0.543623i
$756$		0			0
$757$	−1.07142	+	6.07635i	−0.0389416	+	0.220849i	−0.998068	−	0.0621288i	$-0.980211\pi$
$757$	−1.07142	+	6.07635i	−0.0389416	+	0.220849i	0.959127	+	0.282977i	$0.0913221\pi$
$758$	−6.58845	+	3.97615i	−0.239303	+	0.144420i
$759$		0			0
$760$	−14.9606	+	0.580541i	−0.542679	+	0.0210584i
$761$	12.5188	+	12.2783i	0.453805	+	0.445089i	0.890814	−	0.454368i	$-0.150135\pi$
$761$	12.5188	+	12.2783i	0.453805	+	0.445089i	−0.437009	+	0.899457i	$0.643962\pi$
$762$		0			0
$763$	−18.0762	+	28.6798i	−0.654401	+	1.03828i
$764$	0.233314	−	0.779322i	0.00844099	−	0.0281949i
$765$		0			0
$766$	−0.648322	+	0.687181i	−0.0234248	+	0.0248289i
$767$	−6.55142	+	6.42558i	−0.236558	+	0.232014i
$768$		0			0
$769$	15.4275	+	19.1271i	0.556329	+	0.689740i	0.975959	−	0.217955i	$-0.0699387\pi$
$769$	15.4275	+	19.1271i	0.556329	+	0.689740i	−0.419629	+	0.907696i	$0.637840\pi$
$770$	32.2015	−	83.4040i	1.16046	−	3.00567i
$771$		0			0
$772$	−0.242619	−	0.941905i	−0.00873205	−	0.0338999i
$773$	14.0887	+	3.33907i	0.506734	+	0.120098i	0.476028	−	0.879430i	$-0.342076\pi$
$773$	14.0887	+	3.33907i	0.506734	+	0.120098i	0.0307062	+	0.999528i	$0.490224\pi$
$774$		0			0
$775$	−17.3890	−	18.4313i	−0.624632	−	0.662071i
$776$	−41.5427	−	1.61205i	−1.49130	−	0.0578691i
$777$		0			0
$778$	−33.3876	+	9.29408i	−1.19700	+	0.333209i
$779$	−2.33541	−	3.70538i	−0.0836747	−	0.132759i
$780$		0			0
$781$	0.616466	+	31.7848i	0.0220589	+	1.13735i
$782$	3.98986	−	1.45219i	0.142677	−	0.0519302i
$783$		0			0
$784$	51.7500	+	18.8354i	1.84821	+	0.672695i
$785$	19.6918	−	57.5514i	0.702830	−	2.05410i
$786$		0			0
$787$	−18.2700	+	7.46410i	−0.651254	+	0.266067i	−0.679657	−	0.733530i	$-0.737871\pi$
$787$	−18.2700	+	7.46410i	−0.651254	+	0.266067i	0.0284031	+	0.999597i	$0.490958\pi$
$788$	−0.377693	−	0.789879i	−0.0134548	−	0.0281383i
$789$		0			0
$790$	−3.64993	+	1.17030i	−0.129859	+	0.0416375i
$791$	−23.1435	−	2.70508i	−0.822887	−	0.0961817i
$792$		0			0
$793$	−1.24609	−	1.67379i	−0.0442500	−	0.0594380i
$794$	5.28377	−	54.3219i	0.187514	−	1.92781i
$795$		0			0
$796$	−2.88403	−	1.74052i	−0.102222	−	0.0616911i
$797$	1.84214	−	2.11086i	0.0652521	−	0.0747706i	−0.719882	−	0.694097i	$-0.755804\pi$
$797$	1.84214	−	2.11086i	0.0652521	−	0.0747706i	0.785134	+	0.619326i	$0.212594\pi$
$798$		0			0
$799$	10.2928	−	21.5256i	0.364134	−	0.761521i
$800$	−0.284017	+	4.87638i	−0.0100415	+	0.172406i
$801$		0			0
$802$	44.0052	−	28.9427i	1.55388	−	1.02200i
$803$	15.6919	−	12.1622i	0.553757	−	0.429194i
$804$		0			0
$805$	4.75923	−	3.40169i	0.167741	−	0.119894i
$806$	−1.62738	−	7.51284i	−0.0573221	−	0.264628i
$807$		0			0
$808$	−9.74881	+	12.0866i	−0.342962	+	0.425206i
$809$	1.59300	+	2.75915i	0.0560067	+	0.0970065i	0.892669	−	0.450712i	$-0.148830\pi$
$809$	1.59300	+	2.75915i	0.0560067	+	0.0970065i	−0.836663	+	0.547718i	$0.815497\pi$
$810$		0			0
$811$	−17.7017	+	30.6603i	−0.621591	+	1.07663i	0.367598	+	0.929985i	$0.380180\pi$
$811$	−17.7017	+	30.6603i	−0.621591	+	1.07663i	−0.989189	+	0.146643i	$0.953153\pi$
$812$	2.41405	+	6.25255i	0.0847166	+	0.219421i
$813$		0			0
$814$	−16.7426	+	15.1931i	−0.586827	+	0.532517i
$815$	−2.19267	−	22.5426i	−0.0768058	−	0.789633i
$816$		0			0
$817$	−0.461659	−	0.188608i	−0.0161514	−	0.00659857i
$818$	0.997114	+	17.1198i	0.0348633	+	0.598579i
$819$		0			0
$820$	−1.13506	+	0.570046i	−0.0396378	+	0.0199069i
$821$	29.4648	+	42.9607i	1.02833	+	1.49934i	0.857798	+	0.513987i	$0.171832\pi$
$821$	29.4648	+	42.9607i	1.02833	+	1.49934i	0.170530	+	0.985352i	$0.445452\pi$
$822$		0			0
$823$	34.7203	+	6.81885i	1.21027	+	0.237690i	0.756840	−	0.653600i	$-0.226742\pi$
$823$	34.7203	+	6.81885i	1.21027	+	0.237690i	0.453434	+	0.891290i	$0.350199\pi$
$824$	4.57824	−	2.52616i	0.159490	−	0.0880031i
$825$		0			0
$826$	44.7223	−	20.3288i	1.55609	−	0.707329i
$827$	13.1203	−	1.53355i	0.456239	−	0.0533267i	0.115130	−	0.993350i	$-0.463272\pi$
$827$	13.1203	−	1.53355i	0.456239	−	0.0533267i	0.341109	+	0.940024i	$0.389198\pi$
$828$		0			0
$829$	−13.2172	−	30.6410i	−0.459053	−	1.06420i	−0.977850	−	0.209307i	$-0.932879\pi$
$829$	−13.2172	−	30.6410i	−0.459053	−	1.06420i	0.518797	−	0.854897i	$-0.326380\pi$
$830$	−9.83335	+	45.3958i	−0.341321	+	1.57571i
$831$		0			0
$832$	5.06070	−	7.37868i	0.175448	−	0.255810i
$833$	−12.7227	+	93.1464i	−0.440814	+	3.22733i
$834$		0			0
$835$	3.09116	−	0.607084i	0.106974	−	0.0210090i
$836$	0.778378	−	0.653137i	0.0269208	−	0.0225892i
$837$		0			0
$838$	4.23254	+	3.55152i	0.146211	+	0.122685i
$839$	−44.0558	−	24.3090i	−1.52098	−	0.839239i	−0.521078	−	0.853509i	$-0.674470\pi$
$839$	−44.0558	−	24.3090i	−1.52098	−	0.839239i	−0.999898	+	0.0142694i	$0.995458\pi$
$840$		0			0
$841$	35.3539	−	67.1177i	1.21910	−	2.31440i
$842$	−6.28700	+	24.4076i	−0.216664	+	0.841143i
$843$		0			0
$844$	−0.770521	−	1.46280i	−0.0265224	−	0.0503516i
$845$	−36.9685	+	8.76170i	−1.27176	+	0.301412i
$846$		0			0
$847$	−7.90521	−	26.4052i	−0.271626	−	0.907295i
$848$	34.8752	+	9.70816i	1.19762	+	0.333380i
$849$		0			0
$850$	−62.2370	+	9.73368i	−2.13471	+	0.333863i
$851$	−1.46156	+	0.228583i	−0.0501015	+	0.00783573i
$852$		0			0
$853$	46.7056	+	13.0014i	1.59917	+	0.445160i	0.949167	−	0.314772i	$-0.101928\pi$
$853$	46.7056	+	13.0014i	1.59917	+	0.445160i	0.650003	+	0.759931i	$0.274768\pi$
$854$	3.20386	+	10.7016i	0.109634	+	0.366203i
$855$		0			0
$856$	−17.0083	+	4.03104i	−0.581332	+	0.137778i
$857$	−23.5881	−	44.7808i	−0.805753	−	1.52968i	−0.847646	−	0.530562i	$-0.821981\pi$
$857$	−23.5881	−	44.7808i	−0.805753	−	1.52968i	0.0418927	−	0.999122i	$-0.486661\pi$
$858$		0			0
$859$	−6.57681	+	25.5328i	−0.224398	+	0.871167i	0.752698	+	0.658366i	$0.228752\pi$
$859$	−6.57681	+	25.5328i	−0.224398	+	0.871167i	−0.977096	+	0.212800i	$0.931742\pi$
$860$	−0.0673992	+	0.127954i	−0.00229829	+	0.00436320i
$861$		0			0
$862$	8.28629	+	4.57218i	0.282232	+	0.155729i
$863$	−33.1201	−	27.7910i	−1.12742	−	0.946018i	−0.128465	−	0.991714i	$-0.541005\pi$
$863$	−33.1201	−	27.7910i	−1.12742	−	0.946018i	−0.998955	+	0.0456963i	$0.985449\pi$
$864$		0			0
$865$	−40.2477	+	33.7718i	−1.36846	+	1.14828i
$866$	−10.3725	+	2.03709i	−0.352472	+	0.0692233i
$867$		0			0
$868$	−0.380716	+	2.78733i	−0.0129223	+	0.0946082i
$869$	−1.85801	+	2.70904i	−0.0630287	+	0.0918980i
$870$		0			0
$871$	2.14435	−	9.89942i	0.0726585	−	0.335429i
$872$	−8.17500	−	18.9518i	−0.276840	−	0.641788i
$873$		0			0
$874$	0.965984	−	0.112907i	0.0326749	−	0.00381915i
$875$	−12.0015	+	5.45533i	−0.405723	+	0.184424i
$876$		0			0
$877$	−2.80677	+	1.54871i	−0.0947778	+	0.0522962i	−0.529793	−	0.848127i	$-0.677731\pi$
$877$	−2.80677	+	1.54871i	−0.0947778	+	0.0522962i	0.435016	+	0.900423i	$0.356743\pi$
$878$	−37.5878	−	7.38201i	−1.26853	−	0.249131i
$879$		0			0
$880$	33.0583	+	48.2001i	1.11439	+	1.62483i
$881$	−21.2466	+	10.6704i	−0.715815	+	0.359496i	−0.769139	−	0.639081i	$-0.779315\pi$
$881$	−21.2466	+	10.6704i	−0.715815	+	0.359496i	0.0533240	+	0.998577i	$0.483018\pi$
$882$		0			0
$883$	−0.148703	−	2.55313i	−0.00500425	−	0.0859197i	0.994881	−	0.101051i	$-0.0322205\pi$
$883$	−0.148703	−	2.55313i	−0.00500425	−	0.0859197i	−0.999886	+	0.0151311i	$0.995183\pi$
$884$	−1.20935	−	0.494074i	−0.0406749	−	0.0166175i
$885$		0			0
$886$	2.86073	+	29.4109i	0.0961081	+	0.988078i
$887$	8.88147	−	8.05951i	0.298211	−	0.270612i	−0.509140	−	0.860684i	$-0.670036\pi$
$887$	8.88147	−	8.05951i	0.298211	−	0.270612i	0.807351	+	0.590072i	$0.200901\pi$
$888$		0			0
$889$	−16.7852	−	43.4747i	−0.562957	−	1.45810i
$890$	26.9608	−	46.6975i	0.903729	−	1.56531i
$891$		0			0
$892$	−1.90750	−	3.30389i	−0.0638679	−	0.110622i
$893$	3.43117	−	4.25399i	0.114820	−	0.142354i
$894$		0			0
$895$	2.62759	+	12.1303i	0.0878305	+	0.405471i
$896$	−44.9808	+	32.1504i	−1.50270	+	1.07407i
$897$		0			0
$898$	14.3438	−	11.1173i	0.478659	−	0.370988i
$899$	36.7724	−	24.1856i	1.22643	−	0.806634i
$900$		0			0
$901$	−3.59327	+	61.6940i	−0.119709	+	2.05533i
$902$	−6.86928	+	14.3659i	−0.228722	+	0.478331i
$903$		0			0
$904$	9.32776	−	10.6884i	0.310237	−	0.355492i
$905$	20.5640	+	12.4104i	0.683569	+	0.412536i
$906$		0			0
$907$	−2.23227	+	22.9497i	−0.0741213	+	0.762033i	0.882425	+	0.470453i	$0.155909\pi$
$907$	−2.23227	+	22.9497i	−0.0741213	+	0.762033i	−0.956546	+	0.291580i	$0.905819\pi$
$908$	−0.799541	−	1.07397i	−0.0265337	−	0.0356409i
$909$		0			0
$910$	−26.1512	−	3.05664i	−0.866905	−	0.101327i
$911$	−47.8682	+	15.3483i	−1.58594	+	0.508513i	−0.962022	−	0.272973i	$-0.911993\pi$
$911$	−47.8682	+	15.3483i	−1.58594	+	0.508513i	−0.623923	+	0.781486i	$0.714462\pi$
$912$		0			0
$913$	17.1726	+	35.9135i	0.568332	+	1.18856i
$914$	26.6513	−	10.8883i	0.881548	−	0.360152i
$915$		0			0
$916$	0.535977	−	1.56645i	0.0177092	−	0.0517570i
$917$	−10.5366	−	3.83501i	−0.347949	−	0.126643i
$918$		0			0
$919$	−16.7839	+	6.10884i	−0.553649	+	0.201512i	−0.603667	−	0.797236i	$-0.706294\pi$
$919$	−16.7839	+	6.10884i	−0.553649	+	0.201512i	0.0500178	+	0.998748i	$0.484072\pi$
$920$	0.0690640	+	3.56092i	0.00227697	+	0.117400i
$921$		0			0
$922$	−2.37750	−	3.77215i	−0.0782986	−	0.124229i
$923$	9.01934	−	2.51070i	0.296875	−	0.0826408i
$924$		0			0
$925$	21.9311	+	0.851027i	0.721090	+	0.0279816i
$926$	−22.4265	−	23.7706i	−0.736979	−	0.781152i
$927$		0			0
$928$	−8.25561	−	1.95662i	−0.271004	−	0.0642290i
$929$	9.52107	+	36.9631i	0.312376	+	1.21272i	0.911243	+	0.411870i	$0.135124\pi$
$929$	9.52107	+	36.9631i	0.312376	+	1.21272i	−0.598867	+	0.800849i	$0.704382\pi$
$930$		0			0
$931$	−7.75607	+	20.0887i	−0.254195	+	0.658381i
$932$	2.34303	+	2.90490i	0.0767484	+	0.0951530i
$933$		0			0
$934$	−26.5207	+	26.0113i	−0.867783	+	0.851115i
$935$	−68.4696	+	72.5736i	−2.23920	+	2.37341i
$936$		0			0
$937$	−8.95792	+	29.9215i	−0.292642	+	0.977494i	0.677615	+	0.735417i	$0.263014\pi$
$937$	−8.95792	+	29.9215i	−0.292642	+	0.977494i	−0.970257	+	0.242077i	$0.922171\pi$
$938$	−28.9128	+	45.8733i	−0.944037	+	1.49782i
$939$		0			0
$940$	−1.13151	−	1.10977i	−0.0369057	−	0.0361968i
$941$	31.5886	−	1.22578i	1.02976	−	0.0399593i	0.481648	−	0.876365i	$-0.340039\pi$
$941$	31.5886	−	1.22578i	1.02976	−	0.0399593i	0.548111	+	0.836406i	$0.315347\pi$
$942$		0			0
$943$	−0.892062	+	0.538362i	−0.0290495	+	0.0175315i
$944$	−5.57681	+	31.6277i	−0.181510	+	1.02939i
$945$		0			0
$946$	0.314837	+	1.78553i	0.0102362	+	0.0580525i
$947$	18.2529	+	20.9154i	0.593138	+	0.679661i	0.969013	−	0.247010i	$-0.0794479\pi$
$947$	18.2529	+	20.9154i	0.593138	+	0.679661i	−0.375875	+	0.926670i	$0.622658\pi$
$948$		0			0
$949$	−4.62121	−	3.58171i	−0.150011	−	0.116267i
$950$	−14.3858	−	1.11815i	−0.466736	−	0.0362776i
$951$		0			0
$952$	−65.4019	−	59.3491i	−2.11969	−	1.92351i
$953$	16.5053	−	22.1705i	0.534660	−	0.718173i	−0.449928	−	0.893065i	$-0.648550\pi$
$953$	16.5053	−	22.1705i	0.534660	−	0.718173i	0.984588	+	0.174892i	$0.0559577\pi$
$954$		0			0
$955$	−7.24716	+	16.8008i	−0.234513	+	0.543662i
$956$	2.59923	+	1.85781i	0.0840650	+	0.0600860i
$957$		0			0
$958$	−1.08255	+	55.8162i	−0.0349757	+	1.80334i
$959$	3.13800	+	9.17115i	0.101331	+	0.296152i
$960$		0			0
$961$	−12.4886	+	0.970692i	−0.402859	+	0.0313126i
$962$	5.56277	+	3.65869i	0.179351	+	0.117961i
$963$		0			0
$964$	3.30755	+	1.66111i	0.106529	+	0.0535009i
$965$	2.96063	+	21.6757i	0.0953062	+	0.697764i
$966$		0			0
$967$	−35.4994	−	16.1365i	−1.14158	−	0.518913i	−0.248423	−	0.968652i	$-0.579912\pi$
$967$	−35.4994	−	16.1365i	−1.14158	−	0.518913i	−0.893160	+	0.449738i	$0.851517\pi$
$968$	15.9798	+	5.12373i	0.513611	+	0.164683i
$969$		0			0
$970$	−73.1586	−	11.4418i	−2.34898	−	0.367374i
$971$	51.0557			1.63846			0.819228	−	0.573468i	$-0.194402\pi$
$971$	51.0557			1.63846			0.819228	+	0.573468i	$0.194402\pi$
$972$		0			0
$973$	38.3375			1.22904
$974$	54.9722	+	8.59750i	1.76142	+	0.275482i
$975$		0			0
$976$	−6.95418	−	2.22977i	−0.222598	−	0.0713731i
$977$	−36.3490	−	16.5226i	−1.16291	−	0.528606i	−0.263046	−	0.964783i	$-0.584727\pi$
$977$	−36.3490	−	16.5226i	−1.16291	−	0.528606i	−0.899861	+	0.436178i	$0.856332\pi$
$978$		0			0
$979$	−6.25403	−	45.7876i	−0.199880	−	1.46338i
$980$	5.58049	+	2.80263i	0.178262	+	0.0895267i
$981$		0			0
$982$	32.5017	+	21.3767i	1.03717	+	0.682159i
$983$	23.1825	−	1.80188i	0.739405	−	0.0574711i	0.297735	−	0.954649i	$-0.403769\pi$
$983$	23.1825	−	1.80188i	0.739405	−	0.0574711i	0.441670	+	0.897177i	$0.354386\pi$
$984$		0			0
$985$	6.37516	+	18.6321i	0.203129	+	0.593668i
$986$	2.12172	−	109.395i	0.0675692	−	3.48385i
$987$		0			0
$988$	−0.243445	−	0.174004i	−0.00774502	−	0.00553581i
$989$	−0.0469883	+	0.108931i	−0.00149414	+	0.00346381i
$990$		0			0
$991$	27.0024	−	36.2706i	0.857761	−	1.15217i	−0.129265	−	0.991610i	$-0.541262\pi$
$991$	27.0024	−	36.2706i	0.857761	−	1.15217i	0.987026	−	0.160563i	$-0.0513308\pi$
$992$	−2.63718	−	2.39311i	−0.0837306	−	0.0759815i
$993$		0			0
$994$	−49.9693	−	3.88392i	−1.58493	−	0.123190i
$995$	59.8844	+	46.4139i	1.89846	+	1.47142i
$996$		0			0
$997$	−25.4862	−	29.2039i	−0.807156	−	0.924898i	0.191239	−	0.981544i	$-0.438750\pi$
$997$	−25.4862	−	29.2039i	−0.807156	−	0.924898i	−0.998394	+	0.0566458i	$0.981959\pi$
$998$	3.54265	+	20.0914i	0.112141	+	0.635981i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.10.7		1404
3.2	odd	2		243.2.i.a.13.20	✓	1404
243.56	odd	162		243.2.i.a.187.20	yes	1404
243.187	even	81	inner	729.2.i.a.73.7		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.13.20	✓	1404	3.2	odd	2
243.2.i.a.187.20	yes	1404	243.56	odd	162
729.2.i.a.10.7		1404	1.1	even	1	trivial
729.2.i.a.73.7		1404	243.187	even	81	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.44758 - 0.226398i) q^{2} +(0.139748 + 0.0448082i) q^{4} +(-3.00496 - 1.36592i) q^{5} +(-0.603573 - 4.41893i) q^{7} +(2.42652 + 1.21864i) q^{8} +(4.04068 + 2.65760i) q^{10} +(4.13243 - 0.321198i) q^{11} +(-0.395167 - 1.15492i) q^{13} +(-0.126716 + 6.53342i) q^{14} +(-3.47547 - 2.48412i) q^{16} +(2.88846 - 6.69621i) q^{17} +(0.997513 - 1.33989i) q^{19} +(-0.358731 - 0.325531i) q^{20} +(-6.05476 - 0.470613i) q^{22} +(-0.314079 - 0.243430i) q^{23} +(3.87642 + 4.44188i) q^{25} +(0.310566 + 1.76131i) q^{26} +(0.113657 - 0.644580i) q^{28} +(-8.76723 + 5.29105i) q^{29} +(-4.29487 + 0.166661i) q^{31} +(0.591517 + 0.580156i) q^{32} +(-5.69730 + 9.03938i) q^{34} +(-4.22220 + 14.1031i) q^{35} +(2.55472 - 2.70785i) q^{37} +(-1.74733 + 1.71377i) q^{38} +(-5.62700 - 6.97639i) q^{40} +(0.944402 - 2.44606i) q^{41} +(-0.0744696 - 0.289109i) q^{43} +(0.591889 + 0.140280i) q^{44} +(0.399544 + 0.423492i) q^{46} +(3.26932 + 0.126864i) q^{47} +(-12.4191 + 3.45709i) q^{49} +(-4.60581 - 7.30761i) q^{50} +(-0.00347372 - 0.179104i) q^{52} +(-7.96306 + 2.89832i) q^{53} +(-12.8565 - 4.67938i) q^{55} +(3.92052 - 11.4581i) q^{56} +(13.8892 - 5.67436i) q^{58} +(-3.24305 - 6.78226i) q^{59} +(1.62786 - 0.521952i) q^{61} +(6.25492 + 0.731096i) q^{62} +(4.37717 + 5.87956i) q^{64} +(-0.390068 + 4.01025i) q^{65} +(7.10449 + 4.28758i) q^{67} +(0.703701 - 0.806352i) q^{68} +(9.30491 - 19.4596i) q^{70} +(-0.445964 + 7.65690i) q^{71} +(4.00185 - 2.63206i) q^{73} +(-4.31123 + 3.34145i) q^{74} +(0.199438 - 0.142550i) q^{76} +(-3.91357 - 18.0671i) q^{77} +(-0.497565 + 0.616884i) q^{79} +(7.05054 + 12.2119i) q^{80} +(-1.92089 + 3.32707i) q^{82} +(3.45919 + 8.95953i) q^{83} +(-17.8262 + 16.1764i) q^{85} +(0.0423473 + 0.435369i) q^{86} +(10.4188 + 4.25656i) q^{88} +(-0.648276 - 11.1305i) q^{89} +(-4.86500 + 2.44330i) q^{91} +(-0.0329841 - 0.0480920i) q^{92} +(-4.70389 - 0.923814i) q^{94} +(-4.82767 + 2.66380i) q^{95} +(-13.9384 + 6.33577i) q^{97} +(18.7603 - 2.19277i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26}+ \cdots - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

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Representations

Groups

Database

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