LMFDB - Embedded newform 621.2.s.a.44.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [621,2,Mod(17,621)] 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("621.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(621, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 21])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 621 = 3^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	621.s (of order $66$, degree $20$, 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:	$4.95870996552$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	no (minimal twist has level 207)
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			44.18
Character	$\chi$	$=$	621.44
Dual form			621.2.s.a.494.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.82640 + 0.0870020i) q^{2} +(1.33722 + 0.127689i) q^{4} +(0.497778 - 0.474630i) q^{5} +(0.727727 - 3.77580i) q^{7} +(-1.18854 - 0.170886i) q^{8} +(0.950434 - 0.823555i) q^{10} +(3.80876 + 1.96355i) q^{11} +(0.691689 - 0.133312i) q^{13} +(1.65762 - 6.83281i) q^{14} +(-4.79392 - 0.923952i) q^{16} +(3.30816 - 7.24386i) q^{17} +(-1.89153 + 0.863831i) q^{19} +(0.726241 - 0.571122i) q^{20} +(6.78547 + 3.91760i) q^{22} +(4.04740 + 2.57265i) q^{23} +(-0.215401 + 4.52182i) q^{25} +(1.27490 - 0.183303i) q^{26} +(1.45525 - 4.95614i) q^{28} +(0.711492 + 7.45108i) q^{29} +(-3.93002 - 3.09060i) q^{31} +(-6.34139 - 1.53841i) q^{32} +(6.67225 - 12.9424i) q^{34} +(-1.42986 - 2.22491i) q^{35} +(-0.969499 - 3.30181i) q^{37} +(-3.52983 + 1.41313i) q^{38} +(-0.672735 + 0.479052i) q^{40} +(-0.863301 - 0.905404i) q^{41} +(1.04122 + 1.32402i) q^{43} +(4.84241 + 3.11203i) q^{44} +(7.16834 + 5.05081i) q^{46} +(-0.172200 + 0.0994197i) q^{47} +(-7.22854 - 2.89387i) q^{49} +(-0.786815 + 8.23989i) q^{50} +(0.941960 - 0.0899462i) q^{52} +(-7.10983 + 8.20518i) q^{53} +(2.82787 - 0.830339i) q^{55} +(-1.51016 + 4.36333i) q^{56} +(0.651208 + 13.6705i) q^{58} +(1.40276 + 7.27823i) q^{59} +(3.81925 + 9.54002i) q^{61} +(-6.90889 - 5.98659i) q^{62} +(-2.07929 - 0.610536i) q^{64} +(0.281033 - 0.394656i) q^{65} +(1.99939 + 3.87827i) q^{67} +(5.34868 - 9.26419i) q^{68} +(-2.41793 - 4.18797i) q^{70} +(-0.172587 + 0.268551i) q^{71} +(-4.97498 - 10.8937i) q^{73} +(-1.48343 - 6.11477i) q^{74} +(-2.63968 + 0.913602i) q^{76} +(10.1857 - 12.9522i) q^{77} +(-15.2755 - 5.28691i) q^{79} +(-2.82484 + 1.81542i) q^{80} +(-1.49796 - 1.72874i) q^{82} +(2.43239 + 2.31928i) q^{83} +(-1.79143 - 5.17599i) q^{85} +(1.78649 + 2.50877i) q^{86} +(-4.19131 - 2.98462i) q^{88} +(1.65318 + 11.4981i) q^{89} -2.70870i q^{91} +(5.08375 + 3.95699i) q^{92} +(-0.323155 + 0.166598i) q^{94} +(-0.531559 + 1.32777i) q^{95} +(-4.69126 + 1.13809i) q^{97} +(-12.9504 - 5.91426i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 27 q^{2} - 29 q^{4} + 33 q^{5} - 11 q^{7} - 44 q^{10} + 33 q^{11} - 9 q^{13} + 33 q^{14} + 3 q^{16} - 44 q^{19} + 33 q^{20} + 27 q^{23} + 11 q^{25} - 44 q^{28} - 27 q^{29} - 3 q^{31} + 33 q^{32}+ \cdots + 22 q^{97}+O(q^{100}) $ 440 * q + 27 * q^2 - 29 * q^4 + 33 * q^5 - 11 * q^7 - 44 * q^10 + 33 * q^11 - 9 * q^13 + 33 * q^14 + 3 * q^16 - 44 * q^19 + 33 * q^20 + 27 * q^23 + 11 * q^25 - 44 * q^28 - 27 * q^29 - 3 * q^31 + 33 * q^32 - 11 * q^34 - 44 * q^37 + 33 * q^38 - 77 * q^40 - 9 * q^41 - 11 * q^43 - 36 * q^46 + 120 * q^47 + 35 * q^49 + 3 * q^50 - 38 * q^52 - 44 * q^55 - 165 * q^56 - 10 * q^58 + 9 * q^59 - 11 * q^61 - 22 * q^64 - 198 * q^65 - 11 * q^67 - 70 * q^70 - 36 * q^73 - 231 * q^74 - 11 * q^76 - 39 * q^77 - 11 * q^79 - 10 * q^82 - 66 * q^83 + q^85 + 33 * q^86 - 99 * q^88 - 63 * q^92 - 42 * q^94 + 93 * q^95 + 22 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/621\mathbb{Z}\right)^\times$.

$n$	$28$	$461$
$\chi(n)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.82640	+	0.0870020i	1.29146	+	0.0615197i	0.682032	−	0.731323i	$-0.261097\pi$
$2$	1.82640	+	0.0870020i	1.29146	+	0.0615197i	0.609427	+	0.792842i	$0.291400\pi$
$3$		0			0
$3$		0			0
$4$	1.33722	+	0.127689i	0.668608	+	0.0638443i
$5$	0.497778	−	0.474630i	0.222613	−	0.212261i	−0.570563	−	0.821254i	$-0.693275\pi$
$5$	0.497778	−	0.474630i	0.222613	−	0.212261i	0.793175	+	0.608993i	$0.208426\pi$
$6$		0			0
$7$	0.727727	−	3.77580i	0.275055	−	1.42712i	−0.537021	−	0.843569i	$-0.680451\pi$
$7$	0.727727	−	3.77580i	0.275055	−	1.42712i	0.812076	−	0.583551i	$-0.198337\pi$
$8$	−1.18854	−	0.170886i	−0.420211	−	0.0604173i
$9$		0			0
$10$	0.950434	−	0.823555i	0.300553	−	0.260431i
$11$	3.80876	+	1.96355i	1.14838	+	0.592033i	0.923972	−	0.382461i	$-0.124923\pi$
$11$	3.80876	+	1.96355i	1.14838	+	0.592033i	0.224412	+	0.974494i	$0.427954\pi$
$12$		0			0
$13$	0.691689	−	0.133312i	0.191840	−	0.0369741i	−0.0924261	−	0.995720i	$-0.529462\pi$
$13$	0.691689	−	0.133312i	0.191840	−	0.0369741i	0.284266	+	0.958745i	$0.408250\pi$
$14$	1.65762	−	6.83281i	0.443018	−	1.82614i
$15$		0			0
$16$	−4.79392	−	0.923952i	−1.19848	−	0.230988i
$17$	3.30816	−	7.24386i	0.802347	−	1.75689i	0.165037	−	0.986287i	$-0.447226\pi$
$17$	3.30816	−	7.24386i	0.802347	−	1.75689i	0.637310	−	0.770607i	$-0.280047\pi$
$18$		0			0
$19$	−1.89153	+	0.863831i	−0.433946	+	0.198176i	−0.620397	−	0.784288i	$-0.713029\pi$
$19$	−1.89153	+	0.863831i	−0.433946	+	0.198176i	0.186451	+	0.982464i	$0.440301\pi$
$20$	0.726241	−	0.571122i	0.162392	−	0.127707i
$21$		0			0
$22$	6.78547	+	3.91760i	1.44667	+	0.835234i
$23$	4.04740	+	2.57265i	0.843942	+	0.536434i
$23$	4.04740	+	2.57265i	0.843942	+	0.536434i
$24$		0			0
$25$	−0.215401	+	4.52182i	−0.0430801	+	0.904363i
$26$	1.27490	−	0.183303i	0.250028	−	0.0359486i
$27$		0			0
$28$	1.45525	−	4.95614i	0.275017	−	0.936623i
$29$	0.711492	+	7.45108i	0.132121	+	1.38363i	0.781851	+	0.623465i	$0.214276\pi$
$29$	0.711492	+	7.45108i	0.132121	+	1.38363i	−0.649730	+	0.760165i	$0.725118\pi$
$30$		0			0
$31$	−3.93002	−	3.09060i	−0.705853	−	0.555089i	0.199423	−	0.979914i	$-0.436093\pi$
$31$	−3.93002	−	3.09060i	−0.705853	−	0.555089i	−0.905276	+	0.424825i	$0.860336\pi$
$32$	−6.34139	−	1.53841i	−1.12101	−	0.271954i
$33$		0			0
$34$	6.67225	−	12.9424i	1.14428	−	2.21960i
$35$	−1.42986	−	2.22491i	−0.241691	−	0.376079i
$36$		0			0
$37$	−0.969499	−	3.30181i	−0.159385	−	0.542814i	−0.999999	−	0.00118053i	$-0.999624\pi$
$37$	−0.969499	−	3.30181i	−0.159385	−	0.542814i	0.840615	−	0.541634i	$-0.182194\pi$
$38$	−3.52983	+	1.41313i	−0.572615	+	0.229240i
$39$		0			0
$40$	−0.672735	+	0.479052i	−0.106369	+	0.0757448i
$41$	−0.863301	−	0.905404i	−0.134825	−	0.141400i	0.652860	−	0.757479i	$-0.273569\pi$
$41$	−0.863301	−	0.905404i	−0.134825	−	0.141400i	−0.787685	+	0.616078i	$0.788720\pi$
$42$		0			0
$43$	1.04122	+	1.32402i	0.158785	+	0.201911i	0.858935	−	0.512084i	$-0.171126\pi$
$43$	1.04122	+	1.32402i	0.158785	+	0.201911i	−0.700151	+	0.713995i	$0.746884\pi$
$44$	4.84241	+	3.11203i	0.730020	+	0.469156i
$45$		0			0
$46$	7.16834	+	5.05081i	1.05691	+	0.744702i
$47$	−0.172200	+	0.0994197i	−0.0251179	+	0.0145018i	−0.512506	−	0.858683i	$-0.671283\pi$
$47$	−0.172200	+	0.0994197i	−0.0251179	+	0.0145018i	0.487388	+	0.873185i	$0.337950\pi$
$48$		0			0
$49$	−7.22854	−	2.89387i	−1.03265	−	0.413410i
$50$	−0.786815	+	8.23989i	−0.111272	+	1.16530i
$51$		0			0
$52$	0.941960	−	0.0899462i	0.130626	−	0.0124733i
$53$	−7.10983	+	8.20518i	−0.976610	+	1.12707i	0.0152691	+	0.999883i	$0.495139\pi$
$53$	−7.10983	+	8.20518i	−0.976610	+	1.12707i	−0.991879	+	0.127185i	$0.959406\pi$
$54$		0			0
$55$	2.82787	−	0.830339i	0.381311	−	0.111963i
$56$	−1.51016	+	4.36333i	−0.201804	+	0.583074i
$57$		0			0
$58$	0.651208	+	13.6705i	0.0855078	+	1.79503i
$59$	1.40276	+	7.27823i	0.182624	+	0.947545i	0.951384	+	0.308007i	$0.0996620\pi$
$59$	1.40276	+	7.27823i	0.182624	+	0.947545i	−0.768760	+	0.639538i	$0.779126\pi$
$60$		0			0
$61$	3.81925	+	9.54002i	0.489005	+	1.22147i	0.943693	+	0.330824i	$0.107327\pi$
$61$	3.81925	+	9.54002i	0.489005	+	1.22147i	−0.454688	+	0.890651i	$0.650249\pi$
$62$	−6.90889	−	5.98659i	−0.877430	−	0.760298i
$63$		0			0
$64$	−2.07929	−	0.610536i	−0.259912	−	0.0763170i
$65$	0.281033	−	0.394656i	0.0348579	−	0.0489511i
$66$		0			0
$67$	1.99939	+	3.87827i	0.244264	+	0.473807i	0.978815	−	0.204747i	$-0.0656373\pi$
$67$	1.99939	+	3.87827i	0.244264	+	0.473807i	−0.734551	+	0.678554i	$0.762607\pi$
$68$	5.34868	−	9.26419i	0.648623	−	1.12345i
$69$		0			0
$70$	−2.41793	−	4.18797i	−0.288998	−	0.500559i
$71$	−0.172587	+	0.268551i	−0.0204823	+	0.0318711i	−0.851344	−	0.524608i	$-0.824212\pi$
$71$	−0.172587	+	0.268551i	−0.0204823	+	0.0318711i	0.830861	+	0.556479i	$0.187848\pi$
$72$		0			0
$73$	−4.97498	−	10.8937i	−0.582277	−	1.27501i	−0.939998	−	0.341181i	$-0.889173\pi$
$73$	−4.97498	−	10.8937i	−0.582277	−	1.27501i	0.357721	−	0.933829i	$-0.383554\pi$
$74$	−1.48343	−	6.11477i	−0.172445	−	0.710827i
$75$		0			0
$76$	−2.63968	+	0.913602i	−0.302792	+	0.104797i
$77$	10.1857	−	12.9522i	1.16077	−	1.47604i
$78$		0			0
$79$	−15.2755	−	5.28691i	−1.71863	−	0.594823i	−0.723228	−	0.690610i	$-0.757342\pi$
$79$	−15.2755	−	5.28691i	−1.71863	−	0.594823i	−0.995402	+	0.0957862i	$0.969463\pi$
$80$	−2.82484	+	1.81542i	−0.315827	+	0.202970i
$81$		0			0
$82$	−1.49796	−	1.72874i	−0.165422	−	0.190907i
$83$	2.43239	+	2.31928i	0.266990	+	0.254574i	0.811733	−	0.584029i	$-0.198524\pi$
$83$	2.43239	+	2.31928i	0.266990	+	0.254574i	−0.544743	+	0.838603i	$0.683373\pi$
$84$		0			0
$85$	−1.79143	−	5.17599i	−0.194307	−	0.561414i
$86$	1.78649	+	2.50877i	0.192642	+	0.270528i
$87$		0			0
$88$	−4.19131	−	2.98462i	−0.446795	−	0.318161i
$89$	1.65318	+	11.4981i	0.175237	+	1.21880i	0.867604	+	0.497256i	$0.165659\pi$
$89$	1.65318	+	11.4981i	0.175237	+	1.21880i	−0.692367	+	0.721546i	$0.743432\pi$
$90$		0			0
$91$		−	2.70870i		−	0.283949i
$92$	5.08375	+	3.95699i	0.530018	+	0.412545i
$93$		0			0
$94$	−0.323155	+	0.166598i	−0.0333309	+	0.0171833i
$95$	−0.531559	+	1.32777i	−0.0545368	+	0.136226i
$96$		0			0
$97$	−4.69126	+	1.13809i	−0.476326	+	0.115555i	−0.466732	−	0.884399i	$-0.654569\pi$
$97$	−4.69126	+	1.13809i	−0.476326	+	0.115555i	−0.00959340	+	0.999954i	$0.503054\pi$
$98$	−12.9504	−	5.91426i	−1.30819	−	0.597430i
$99$		0			0
$100$	−0.865421	+	6.01914i	−0.0865421	+	0.601914i
$101$	−1.99639	+	2.09375i	−0.198648	+	0.208336i	−0.815522	−	0.578726i	$-0.803550\pi$
$101$	−1.99639	+	2.09375i	−0.198648	+	0.208336i	0.616874	+	0.787062i	$0.288399\pi$
$102$		0			0
$103$	6.92991	−	0.330112i	0.682824	−	0.0325269i	0.296696	−	0.954972i	$-0.404115\pi$
$103$	6.92991	−	0.330112i	0.682824	−	0.0325269i	0.386128	+	0.922445i	$0.373812\pi$
$104$	−0.844880	+	0.0402466i	−0.0828473	+	0.00394650i
$105$		0			0
$106$	−13.6992	+	14.3673i	−1.33059	+	1.39548i
$107$	1.45241	−	10.1017i	0.140410	−	0.976572i	−0.790796	−	0.612079i	$-0.790333\pi$
$107$	1.45241	−	10.1017i	0.140410	−	0.976572i	0.931206	−	0.364493i	$-0.118758\pi$
$108$		0			0
$109$	−2.47709	−	1.13125i	−0.237262	−	0.108354i	0.293236	−	0.956040i	$-0.405268\pi$
$109$	−2.47709	−	1.13125i	−0.237262	−	0.108354i	−0.530498	+	0.847686i	$0.677995\pi$
$110$	5.23706	−	1.27050i	0.499335	−	0.121137i
$111$		0			0
$112$	−6.97733	+	17.4285i	−0.659295	+	1.64684i
$113$	−0.523879	+	0.270079i	−0.0492824	+	0.0254069i	−0.482692	−	0.875790i	$-0.660341\pi$
$113$	−0.523879	+	0.270079i	−0.0492824	+	0.0254069i	0.433409	+	0.901197i	$0.357310\pi$
$114$		0			0
$115$	3.23576	−	0.640412i	0.301736	−	0.0597187i
$116$			10.0545i			0.933541i
$117$		0			0
$118$	1.92878	+	13.4150i	0.177559	+	1.23495i
$119$	−24.9440	−	17.7625i	−2.28661	−	1.62829i
$120$		0			0
$121$	4.27048	+	5.99705i	0.388225	+	0.545186i
$122$	6.14547	+	17.7562i	0.556384	+	1.60757i
$123$		0			0
$124$	−4.86065	−	4.63462i	−0.436499	−	0.416201i
$125$	4.29100	+	4.95208i	0.383799	+	0.442928i
$126$		0			0
$127$	13.9757	−	8.98161i	1.24014	−	0.796989i	0.254701	−	0.967020i	$-0.418023\pi$
$127$	13.9757	−	8.98161i	1.24014	−	0.796989i	0.985439	+	0.170031i	$0.0543866\pi$
$128$	8.58839	+	2.97247i	0.759114	+	0.262732i
$129$		0			0
$130$	0.547615	−	0.696349i	0.0480290	−	0.0610738i
$131$	−5.39981	+	1.86889i	−0.471783	+	0.163286i	−0.552606	−	0.833443i	$-0.686367\pi$
$131$	−5.39981	+	1.86889i	−0.471783	+	0.163286i	0.0808225	+	0.996729i	$0.474245\pi$
$132$		0			0
$133$	1.88514	+	7.77066i	0.163463	+	0.673802i
$134$	3.31426	+	7.25722i	0.286309	+	0.626929i
$135$		0			0
$136$	−5.16975	+	8.04428i	−0.443302	+	0.689792i
$137$	−0.705864	−	1.22259i	−0.0603060	−	0.104453i	0.834296	−	0.551317i	$-0.185874\pi$
$137$	−0.705864	−	1.22259i	−0.0603060	−	0.104453i	−0.894602	+	0.446863i	$0.852541\pi$
$138$		0			0
$139$	7.64739	−	13.2457i	0.648643	−	1.12348i	−0.334804	−	0.942288i	$-0.608670\pi$
$139$	7.64739	−	13.2457i	0.648643	−	1.12348i	0.983447	−	0.181196i	$-0.0579967\pi$
$140$	−1.62794	−	3.15776i	−0.137586	−	0.266880i
$141$		0			0
$142$	−0.338577	+	0.475466i	−0.0284128	+	0.0399002i
$143$	2.89624	+	0.850413i	0.242196	+	0.0711151i
$144$		0			0
$145$	3.89067	+	3.37128i	0.323102	+	0.279970i
$146$	−8.13852	−	20.3290i	−0.673548	−	1.68244i
$147$		0			0
$148$	−0.874825	−	4.53902i	−0.0719102	−	0.373105i
$149$	0.364633	+	7.65459i	0.0298719	+	0.627089i	0.963317	+	0.268367i	$0.0864841\pi$
$149$	0.364633	+	7.65459i	0.0298719	+	0.627089i	−0.933445	+	0.358721i	$0.883213\pi$
$150$		0			0
$151$	−3.21483	+	9.28863i	−0.261619	+	0.755898i	0.735320	+	0.677720i	$0.237032\pi$
$151$	−3.21483	+	9.28863i	−0.261619	+	0.755898i	−0.996939	+	0.0781786i	$0.975090\pi$
$152$	2.39577	−	0.703460i	0.194322	−	0.0570582i
$153$		0			0
$154$	19.7300	−	22.7697i	1.58989	−	1.83483i
$155$	−3.42317	+	0.326873i	−0.274956	+	0.0262551i
$156$		0			0
$157$	−0.657534	+	6.88601i	−0.0524770	+	0.549564i	0.930558	+	0.366145i	$0.119322\pi$
$157$	−0.657534	+	6.88601i	−0.0524770	+	0.549564i	−0.983035	+	0.183419i	$0.941284\pi$
$158$	−27.4392	−	10.9850i	−2.18294	−	0.873919i
$159$		0			0
$160$	−3.88678	+	2.24403i	−0.307277	+	0.177406i
$161$	12.6592	−	13.4100i	0.997687	−	1.05686i
$162$		0			0
$163$	7.94124	+	5.10352i	0.622006	+	0.399739i	0.813342	−	0.581786i	$-0.197646\pi$
$163$	7.94124	+	5.10352i	0.622006	+	0.399739i	−0.191336	+	0.981525i	$0.561282\pi$
$164$	−1.03881	−	1.32095i	−0.0811174	−	0.103149i
$165$		0			0
$166$	4.24073	+	4.44755i	0.329145	+	0.345197i
$167$	−6.05282	+	4.31020i	−0.468382	+	0.333533i	−0.789758	−	0.613419i	$-0.789794\pi$
$167$	−6.05282	+	4.31020i	−0.468382	+	0.333533i	0.321376	+	0.946952i	$0.395855\pi$
$168$		0			0
$169$	−11.6081	+	4.64719i	−0.892932	+	0.357476i
$170$	−2.82153	−	9.60926i	−0.216402	−	0.736997i
$171$		0			0
$172$	1.22327	+	1.90345i	0.0932737	+	0.145137i
$173$	−4.76457	+	9.24197i	−0.362243	+	0.702654i	−0.997576	−	0.0695845i	$-0.977833\pi$
$173$	−4.76457	+	9.24197i	−0.362243	+	0.702654i	0.635333	+	0.772239i	$0.280863\pi$
$174$		0			0
$175$	16.9167	+	4.10396i	1.27879	+	0.310230i
$176$	−16.4447	−	12.9322i	−1.23956	−	0.974803i
$177$		0			0
$178$	2.01901	+	21.1440i	0.151331	+	1.58481i
$179$	2.75416	−	9.37982i	0.205856	−	0.701080i	−0.790240	−	0.612798i	$-0.790044\pi$
$179$	2.75416	−	9.37982i	0.205856	−	0.701080i	0.996095	−	0.0882825i	$-0.0281378\pi$
$180$		0			0
$181$	4.57265	−	0.657447i	0.339882	−	0.0488677i	0.0297394	−	0.999558i	$-0.490532\pi$
$181$	4.57265	−	0.657447i	0.339882	−	0.0488677i	0.310143	+	0.950690i	$0.399623\pi$
$182$	0.235662	−	4.94716i	0.0174684	−	0.366708i
$183$		0			0
$184$	−4.37086	−	3.74933i	−0.322224	−	0.276405i
$185$	−2.04973	−	1.18341i	−0.150699	−	0.0870063i
$186$		0			0
$187$	26.8237	−	21.0944i	1.96154	−	1.54257i
$188$	−0.242963	+	0.110958i	−0.0177199	+	0.00809241i
$189$		0			0
$190$	−1.08636	+	2.37879i	−0.0788126	+	0.172576i
$191$	20.6911	+	3.98788i	1.49715	+	0.288553i	0.871053	−	0.491189i	$-0.163438\pi$
$191$	20.6911	+	3.98788i	1.49715	+	0.288553i	0.626101	+	0.779742i	$0.284650\pi$
$192$		0			0
$193$	3.01877	−	12.4435i	0.217296	−	0.895706i	−0.753817	−	0.657084i	$-0.771789\pi$
$193$	3.01877	−	12.4435i	0.217296	−	0.895706i	0.971113	−	0.238621i	$-0.0766954\pi$
$194$	−8.66713	+	1.67045i	−0.622264	+	0.119932i
$195$		0			0
$196$	−9.29660	−	4.79273i	−0.664043	−	0.342338i
$197$	−12.7308	+	11.0313i	−0.907034	+	0.785950i	−0.977362	−	0.211574i	$-0.932141\pi$
$197$	−12.7308	+	11.0313i	−0.907034	+	0.785950i	0.0703277	+	0.997524i	$0.477596\pi$
$198$		0			0
$199$	−4.85097	−	0.697464i	−0.343876	−	0.0494419i	−0.0317868	−	0.999495i	$-0.510120\pi$
$199$	−4.85097	−	0.697464i	−0.343876	−	0.0494419i	−0.312089	+	0.950053i	$0.601029\pi$
$200$	1.02873	−	5.33754i	0.0727419	−	0.377421i
$201$		0			0
$202$	−3.82836	+	3.65033i	−0.269362	+	0.256836i
$203$	28.6516	+	2.73589i	2.01095	+	0.192022i
$204$		0			0
$205$	−0.859464	−	0.0409413i	−0.0600275	−	0.00285946i
$206$	12.6855			0.883840
$207$		0			0
$208$	−3.43908			−0.238457
$209$	−8.90054	−	0.423985i	−0.615663	−	0.0293277i
$210$		0			0
$211$	−21.0335	−	2.00845i	−1.44800	−	0.138268i	−0.658763	−	0.752351i	$-0.728920\pi$
$211$	−21.0335	−	2.00845i	−1.44800	−	0.138268i	−0.789241	+	0.614083i	$0.789526\pi$
$212$	−10.5551	+	10.0642i	−0.724926	+	0.691215i
$213$		0			0
$214$	3.53155	−	18.3234i	0.241412	−	1.25256i
$215$	1.14672	+	0.164873i	0.0782053	+	0.0112442i
$216$		0			0
$217$	−14.5295	+	12.5899i	−0.986326	+	0.854657i
$218$	−4.42573	−	2.28162i	−0.299749	−	0.154531i
$219$		0			0
$220$	3.88750	−	0.749255i	0.262095	−	0.0505147i
$221$	1.32252	−	5.45152i	0.0889626	−	0.366709i
$222$		0			0
$223$	20.0900	+	3.87204i	1.34533	+	0.259291i	0.810534	−	0.585691i	$-0.199177\pi$
$223$	20.0900	+	3.87204i	1.34533	+	0.259291i	0.534794	+	0.844982i	$0.320389\pi$
$224$	−10.4235	+	22.8243i	−0.696451	+	1.52501i
$225$		0			0
$226$	−0.980310	+	0.447692i	−0.0652092	+	0.0297801i
$227$	2.07842	−	1.63448i	0.137949	−	0.108485i	−0.546800	−	0.837263i	$-0.684154\pi$
$227$	2.07842	−	1.63448i	0.137949	−	0.108485i	0.684749	+	0.728779i	$0.259912\pi$
$228$		0			0
$229$	5.44939	+	3.14621i	0.360106	+	0.207907i	0.669127	−	0.743148i	$-0.266668\pi$
$229$	5.44939	+	3.14621i	0.360106	+	0.207907i	−0.309021	+	0.951055i	$0.600001\pi$
$230$	5.96551	−	0.888129i	0.393354	−	0.0585615i
$231$		0			0
$232$	0.427649	−	8.97747i	0.0280766	−	0.589400i
$233$	15.1039	−	2.17161i	0.989488	−	0.142267i	0.371482	−	0.928440i	$-0.378850\pi$
$233$	15.1039	−	2.17161i	0.989488	−	0.142267i	0.618006	+	0.786173i	$0.287941\pi$
$234$		0			0
$235$	−0.0385297	+	0.131220i	−0.00251340	+	0.00855986i
$236$	0.946450	+	9.91167i	0.0616087	+	0.645195i
$237$		0			0
$238$	−44.0122	−	34.6116i	−2.85289	−	2.24354i
$239$	10.1974	+	2.47386i	0.659614	+	0.160021i	0.551574	−	0.834126i	$-0.314027\pi$
$239$	10.1974	+	2.47386i	0.659614	+	0.160021i	0.108040	+	0.994147i	$0.465543\pi$
$240$		0			0
$241$	3.34809	−	6.49439i	0.215669	−	0.418340i	−0.756038	−	0.654527i	$-0.772868\pi$
$241$	3.34809	−	6.49439i	0.215669	−	0.418340i	0.971708	+	0.236187i	$0.0758979\pi$
$242$	7.27784	+	11.3245i	0.467837	+	0.727969i
$243$		0			0
$244$	3.88901	+	13.2447i	0.248968	+	0.847907i
$245$	−4.97172	+	1.99038i	−0.317632	+	0.127161i
$246$		0			0
$247$	−1.19319	+	0.849666i	−0.0759208	+	0.0540629i
$248$	4.14284	+	4.34488i	0.263070	+	0.275900i
$249$		0			0
$250$	7.40624	+	9.41780i	0.468412	+	0.595634i
$251$	−2.09511	−	1.34645i	−0.132242	−	0.0849871i	0.472847	−	0.881145i	$-0.343226\pi$
$251$	−2.09511	−	1.34645i	−0.132242	−	0.0849871i	−0.605089	+	0.796157i	$0.706863\pi$
$252$		0			0
$253$	10.3641	+	17.7459i	0.651582	+	1.11567i
$254$	26.3065	−	15.1881i	1.65062	−	0.952985i
$255$		0			0
$256$	19.4509	+	7.78696i	1.21568	+	0.486685i
$257$	1.93438	−	20.2578i	0.120663	−	1.26364i	−0.708931	−	0.705278i	$-0.750822\pi$
$257$	1.93438	−	20.2578i	0.120663	−	1.26364i	0.829594	−	0.558366i	$-0.188572\pi$
$258$		0			0
$259$	−13.1725	+	1.25782i	−0.818500	+	0.0781573i
$260$	0.426195	−	0.491856i	0.0264315	−	0.0305036i
$261$		0			0
$262$	−10.0248	+	2.94354i	−0.619334	+	0.181853i
$263$	3.97236	−	11.4774i	0.244946	−	0.707726i	−0.753773	−	0.657135i	$-0.771768\pi$
$263$	3.97236	−	11.4774i	0.244946	−	0.707726i	0.998719	−	0.0505910i	$-0.0161105\pi$
$264$		0			0
$265$	0.355311	+	7.45889i	0.0218266	+	0.458196i
$266$	2.76696	+	14.3563i	0.169653	+	0.880243i
$267$		0			0
$268$	2.17840	+	5.44139i	0.133067	+	0.332386i
$269$	−9.86711	−	8.54990i	−0.601609	−	0.521297i	0.299949	−	0.953955i	$-0.403030\pi$
$269$	−9.86711	−	8.54990i	−0.601609	−	0.521297i	−0.901558	+	0.432658i	$0.857576\pi$
$270$		0			0
$271$	−9.43054	−	2.76906i	−0.572864	−	0.168208i	−0.0175461	−	0.999846i	$-0.505585\pi$
$271$	−9.43054	−	2.76906i	−0.572864	−	0.168208i	−0.555318	+	0.831638i	$0.687404\pi$
$272$	−22.5520	+	31.6699i	−1.36742	+	1.92027i
$273$		0			0
$274$	−1.18282	−	2.29435i	−0.0714568	−	0.138607i
$275$	−9.69923	+	16.7996i	−0.584885	+	1.01305i
$276$		0			0
$277$	−4.91170	−	8.50732i	−0.295116	−	0.511155i	0.679896	−	0.733308i	$-0.262025\pi$
$277$	−4.91170	−	8.50732i	−0.295116	−	0.511155i	−0.975012	+	0.222153i	$0.928692\pi$
$278$	15.1196	−	23.5265i	0.906812	−	1.41103i
$279$		0			0
$280$	1.31924	+	2.88873i	0.0788397	+	0.172635i
$281$	−3.71993	−	15.3338i	−0.221912	−	0.914735i	−0.968413	−	0.249351i	$-0.919783\pi$
$281$	−3.71993	−	15.3338i	−0.221912	−	0.914735i	0.746501	−	0.665384i	$-0.231732\pi$
$282$		0			0
$283$	18.8674	−	6.53008i	1.12155	−	0.388173i	0.297520	−	0.954716i	$-0.403840\pi$
$283$	18.8674	−	6.53008i	1.12155	−	0.388173i	0.824033	+	0.566542i	$0.191719\pi$
$284$	−0.265077	+	0.337073i	−0.0157294	+	0.0200016i
$285$		0			0
$286$	5.21570	+	1.80517i	0.308411	+	0.106742i
$287$	−4.04687	+	2.60077i	−0.238879	+	0.153519i
$288$		0			0
$289$	−30.3970	−	35.0800i	−1.78806	−	2.06353i
$290$	6.81260	+	6.49580i	0.400050	+	0.381447i
$291$		0			0
$292$	−5.26162	−	15.2024i	−0.307913	−	0.889656i
$293$	2.67432	+	3.75555i	0.156235	+	0.219402i	0.885273	−	0.465072i	$-0.153972\pi$
$293$	2.67432	+	3.75555i	0.156235	+	0.219402i	−0.729038	+	0.684474i	$0.760032\pi$
$294$		0			0
$295$	4.15273	+	2.95715i	0.241781	+	0.172172i
$296$	0.588053	+	4.09000i	0.0341799	+	0.237726i
$297$		0			0
$298$			14.0121i			0.811696i
$299$	3.14251	+	1.23991i	0.181736	+	0.0717056i
$300$		0			0
$301$	5.75696	−	2.96792i	0.331826	−	0.171068i
$302$	−6.67968	+	16.6850i	−0.384373	+	0.960116i
$303$		0			0
$304$	9.86596	−	2.39346i	0.565852	−	0.137274i
$305$	6.42912	+	2.93608i	0.368130	+	0.168119i
$306$		0			0
$307$	3.22232	−	22.4117i	0.183908	−	1.27910i	−0.663506	−	0.748171i	$-0.730932\pi$
$307$	3.22232	−	22.4117i	0.183908	−	1.27910i	0.847413	−	0.530934i	$-0.178159\pi$
$308$	15.2743	−	16.0193i	0.870337	−	0.912783i
$309$		0			0
$310$	−6.28051	+	0.299177i	−0.356709	+	0.0169921i
$311$	21.5965	−	1.02877i	1.22462	−	0.0583361i	0.574719	−	0.818351i	$-0.305111\pi$
$311$	21.5965	−	1.02877i	1.22462	−	0.0583361i	0.649906	+	0.760015i	$0.274808\pi$
$312$		0			0
$313$	12.9438	−	13.5750i	0.731624	−	0.767305i	−0.247867	−	0.968794i	$-0.579730\pi$
$313$	12.9438	−	13.5750i	0.731624	−	0.767305i	0.979491	+	0.201489i	$0.0645780\pi$
$314$	−1.80002	+	12.5194i	−0.101581	+	0.706510i
$315$		0			0
$316$	−19.7516	−	9.02024i	−1.11111	−	0.507428i
$317$	−27.7410	+	6.72988i	−1.55809	+	0.377988i	−0.919982	−	0.391961i	$-0.871797\pi$
$317$	−27.7410	+	6.72988i	−1.55809	+	0.377988i	−0.638106	+	0.769949i	$0.720282\pi$
$318$		0			0
$319$	−11.9207	+	29.7764i	−0.667430	+	1.66716i
$320$	−1.32480	+	0.682984i	−0.0740588	+	0.0381800i
$321$		0			0
$322$	24.2875	−	23.3907i	1.35349	−	1.30351i
$323$			16.5596i			0.921403i
$324$		0			0
$325$	0.453823	+	3.15641i	0.0251736	+	0.175086i
$326$	14.0598	+	10.0120i	0.778703	+	0.554512i
$327$		0			0
$328$	0.871344	+	1.22363i	0.0481119	+	0.0675638i
$329$	0.250075	+	0.722544i	0.0137871	+	0.0398351i
$330$		0			0
$331$	14.8418	+	14.1516i	0.815779	+	0.777844i	0.977932	−	0.208922i	$-0.0669955\pi$
$331$	14.8418	+	14.1516i	0.815779	+	0.777844i	−0.162153	+	0.986766i	$0.551844\pi$
$332$	2.95648	+	3.41197i	0.162258	+	0.187256i
$333$		0			0
$334$	−11.4299	+	7.34552i	−0.625414	+	0.401929i
$335$	2.83600	+	0.981548i	0.154947	+	0.0536277i
$336$		0			0
$337$	−15.5934	+	19.8286i	−0.849424	+	1.08013i	0.146435	+	0.989220i	$0.453220\pi$
$337$	−15.5934	+	19.8286i	−0.849424	+	1.08013i	−0.995859	+	0.0909103i	$0.971022\pi$
$338$	−21.6054	+	7.47769i	−1.17518	+	0.406733i
$339$		0			0
$340$	−1.73461	−	7.15015i	−0.0940723	−	0.387771i
$341$	−8.89994	−	19.4882i	−0.481959	−	1.05534i
$342$		0			0
$343$	−1.63463	+	2.54353i	−0.0882617	+	0.137338i
$344$	−1.01127	−	1.75158i	−0.0545242	−	0.0944387i
$345$		0			0
$346$	−9.50607	+	16.4650i	−0.511049	+	0.885163i
$347$	−10.3882	−	20.1503i	−0.557669	−	1.08173i	−0.984168	−	0.177238i	$-0.943284\pi$
$347$	−10.3882	−	20.1503i	−0.557669	−	1.08173i	0.426499	−	0.904488i	$-0.359747\pi$
$348$		0			0
$349$	−5.02038	+	7.05014i	−0.268735	+	0.377386i	−0.926787	−	0.375587i	$-0.877441\pi$
$349$	−5.02038	+	7.05014i	−0.268735	+	0.377386i	0.658052	+	0.752972i	$0.271381\pi$
$350$	30.5396	+	8.96725i	1.63241	+	0.479320i
$351$		0			0
$352$	−21.1321	−	18.3111i	−1.12634	−	0.975983i
$353$	−8.65884	−	21.6287i	−0.460864	−	1.15118i	−0.958829	−	0.283985i	$-0.908343\pi$
$353$	−8.65884	−	21.6287i	−0.460864	−	1.15118i	0.497965	−	0.867197i	$-0.334081\pi$
$354$		0			0
$355$	0.0415523	+	0.215594i	0.00220537	+	0.0114425i
$356$	0.742481	+	15.5866i	0.0393514	+	0.826088i
$357$		0			0
$358$	5.84626	−	16.8917i	0.308984	−	0.892752i
$359$	11.1076	−	3.26148i	0.586235	−	0.172134i	0.0248533	−	0.999691i	$-0.492088\pi$
$359$	11.1076	−	3.26148i	0.586235	−	0.172134i	0.561382	+	0.827557i	$0.310270\pi$
$360$		0			0
$361$	−9.61069	+	11.0913i	−0.505826	+	0.583754i
$362$	8.40867	−	0.802930i	0.441950	−	0.0422011i
$363$		0			0
$364$	0.345870	−	3.62211i	0.0181285	−	0.189850i
$365$	−7.64690	−	3.06136i	−0.400257	−	0.160239i
$366$		0			0
$367$	−18.6842	+	10.7873i	−0.975308	+	0.563094i	−0.900850	−	0.434130i	$-0.857056\pi$
$367$	−18.6842	+	10.7873i	−0.975308	+	0.563094i	−0.0744577	+	0.997224i	$0.523723\pi$
$368$	−17.0259	−	16.0727i	−0.887538	−	0.837846i
$369$		0			0
$370$	−3.64067	−	2.33971i	−0.189269	−	0.121636i
$371$	25.8071	+	32.8164i	1.33984	+	1.70375i
$372$		0			0
$373$	−24.2002	−	25.3805i	−1.25304	−	1.31415i	−0.929905	−	0.367799i	$-0.880111\pi$
$373$	−24.2002	−	25.3805i	−1.25304	−	1.31415i	−0.323136	−	0.946352i	$-0.604737\pi$
$374$	50.8260	−	36.1930i	2.62815	−	1.87150i
$375$		0			0
$376$	0.221655	−	0.0887374i	0.0114310	−	0.00457628i
$377$	1.48545	+	5.05898i	0.0765046	+	0.260551i
$378$		0			0
$379$	6.54282	+	10.1808i	0.336082	+	0.522954i	0.967627	−	0.252386i	$-0.0812152\pi$
$379$	6.54282	+	10.1808i	0.336082	+	0.522954i	−0.631545	+	0.775339i	$0.717579\pi$
$380$	−0.880350	+	1.70764i	−0.0451610	+	0.0876001i
$381$		0			0
$382$	37.4432	+	9.08362i	1.91576	+	0.464758i
$383$	−12.6744	−	9.96723i	−0.647630	−	0.509302i	0.239455	−	0.970907i	$-0.423031\pi$
$383$	−12.6744	−	9.96723i	−0.647630	−	0.509302i	−0.887085	+	0.461606i	$0.847274\pi$
$384$		0			0
$385$	−1.07728	−	11.2818i	−0.0549032	−	0.574972i
$386$	6.59609	−	22.4642i	0.335732	−	1.14340i
$387$		0			0
$388$	−6.41855	+	0.922848i	−0.325853	+	0.0468505i
$389$	−0.533965	+	11.2093i	−0.0270731	+	0.568335i	0.944057	+	0.329783i	$0.106976\pi$
$389$	−0.533965	+	11.2093i	−0.0270731	+	0.568335i	−0.971130	+	0.238551i	$0.923327\pi$
$390$		0			0
$391$	32.0254	−	20.8081i	1.61959	−	1.05231i
$392$	8.09687	+	4.67473i	0.408954	+	0.236109i
$393$		0			0
$394$	−24.2113	+	19.0400i	−1.21975	+	0.959221i
$395$	−10.1131	+	4.61851i	−0.508847	+	0.232383i
$396$		0			0
$397$	0.386564	−	0.846457i	0.0194011	−	0.0424825i	−0.899683	−	0.436543i	$-0.856203\pi$
$397$	0.386564	−	0.846457i	0.0194011	−	0.0424825i	0.919085	+	0.394060i	$0.128930\pi$
$398$	−8.79912	−	1.69589i	−0.441060	−	0.0850074i
$399$		0			0
$400$	5.21056	−	21.4782i	0.260528	−	1.07391i
$401$	−23.7964	+	4.58639i	−1.18834	+	0.229033i	−0.744841	−	0.667243i	$-0.767474\pi$
$401$	−23.7964	+	4.58639i	−1.18834	+	0.229033i	−0.443497	+	0.896276i	$0.646262\pi$
$402$		0			0
$403$	−3.13037	−	1.61382i	−0.155935	−	0.0803899i
$404$	−2.93695	+	2.54488i	−0.146119	+	0.126613i
$405$		0			0
$406$	52.0912	+	7.48958i	2.58524	+	0.371702i
$407$	2.79069	−	14.4795i	0.138329	−	0.717720i
$408$		0			0
$409$	16.3095	−	15.5511i	0.806453	−	0.768952i	−0.169824	−	0.985474i	$-0.554320\pi$
$409$	16.3095	−	15.5511i	0.806453	−	0.768952i	0.976278	+	0.216523i	$0.0694715\pi$
$410$	−1.56616	−	0.149550i	−0.0773471	−	0.00738576i
$411$		0			0
$412$	9.30893	+	0.443439i	0.458618	+	0.0218467i
$413$	28.5020			1.40249
$414$		0			0
$415$	2.31159			0.113471
$416$	−4.59136	−	0.218714i	−0.225110	−	0.0107233i
$417$		0			0
$418$	−16.2190	−	1.54873i	−0.793299	−	0.0757509i
$419$	12.3790	−	11.8033i	0.604752	−	0.576630i	−0.324588	−	0.945856i	$-0.605226\pi$
$419$	12.3790	−	11.8033i	0.604752	−	0.576630i	0.929340	+	0.369226i	$0.120377\pi$
$420$		0			0
$421$	−6.89914	+	35.7961i	−0.336243	+	1.74460i	0.282744	+	0.959196i	$0.408755\pi$
$421$	−6.89914	+	35.7961i	−0.336243	+	1.74460i	−0.618987	+	0.785401i	$0.712457\pi$
$422$	−38.2407	−	5.49819i	−1.86153	−	0.267648i
$423$		0			0
$424$	9.85244	−	8.53719i	0.478477	−	0.414603i
$425$	32.0428	+	16.5192i	1.55431	+	0.801300i
$426$		0			0
$427$	38.8006	−	7.47821i	1.87769	−	0.361896i
$428$	3.23206	−	13.3227i	0.156228	−	0.643979i
$429$		0			0
$430$	2.08001	+	0.400890i	0.100307	+	0.0193326i
$431$	−1.29293	+	2.83113i	−0.0622783	+	0.136371i	−0.938212	−	0.346061i	$-0.887519\pi$
$431$	−1.29293	+	2.83113i	−0.0622783	+	0.136371i	0.875934	+	0.482432i	$0.160246\pi$
$432$		0			0
$433$	−28.0657	+	12.8172i	−1.34875	+	0.615954i	−0.953158	−	0.302471i	$-0.902188\pi$
$433$	−28.0657	+	12.8172i	−1.34875	+	0.615954i	−0.395593	+	0.918426i	$0.629461\pi$
$434$	−27.6320	+	21.7300i	−1.32638	+	1.04307i
$435$		0			0
$436$	−3.16796	−	1.82902i	−0.151718	−	0.0875942i
$437$	−9.87810	−	1.36996i	−0.472534	−	0.0655341i
$438$		0			0
$439$	0.407501	−	8.55450i	0.0194490	−	0.408284i	−0.968060	−	0.250720i	$-0.919333\pi$
$439$	0.407501	−	8.55450i	0.0194490	−	0.408284i	0.987509	−	0.157564i	$-0.0503642\pi$
$440$	−3.50293	+	0.503645i	−0.166996	+	0.0240103i
$441$		0			0
$442$	2.88975	−	9.84158i	0.137451	−	0.468116i
$443$	1.77405	+	18.5787i	0.0842877	+	0.882701i	0.934430	+	0.356148i	$0.115910\pi$
$443$	1.77405	+	18.5787i	0.0842877	+	0.882701i	−0.850142	+	0.526554i	$0.823484\pi$
$444$		0			0
$445$	6.28028	+	4.93887i	0.297714	+	0.234125i
$446$	36.3555	+	8.81976i	1.72148	+	0.417628i
$447$		0			0
$448$	−3.81842	+	7.40670i	−0.180403	+	0.349934i
$449$	−21.5862	−	33.5888i	−1.01872	−	1.58515i	−0.791370	−	0.611338i	$-0.790632\pi$
$449$	−21.5862	−	33.5888i	−1.01872	−	1.58515i	−0.227346	−	0.973814i	$-0.573005\pi$
$450$		0			0
$451$	−1.51030	−	5.14360i	−0.0711171	−	0.242203i
$452$	−0.735026	+	0.294260i	−0.0345727	+	0.0138408i
$453$		0			0
$454$	3.93822	−	2.80439i	0.184830	−	0.131617i
$455$	−1.28563	−	1.34833i	−0.0602712	−	0.0632106i
$456$		0			0
$457$	7.10588	+	9.03586i	0.332399	+	0.422680i	0.923309	−	0.384058i	$-0.125474\pi$
$457$	7.10588	+	9.03586i	0.332399	+	0.422680i	−0.590910	+	0.806737i	$0.701231\pi$
$458$	9.67902	+	6.22033i	0.452271	+	0.290657i
$459$		0			0
$460$	4.40869	−	0.443199i	0.205556	−	0.0206642i
$461$	1.94634	−	1.12372i	0.0906502	−	0.0523369i	−0.453990	−	0.891007i	$-0.650000\pi$
$461$	1.94634	−	1.12372i	0.0906502	−	0.0523369i	0.544640	+	0.838670i	$0.316666\pi$
$462$		0			0
$463$	−3.53910	−	1.41684i	−0.164476	−	0.0658462i	0.287963	−	0.957641i	$-0.407022\pi$
$463$	−3.53910	−	1.41684i	−0.164476	−	0.0658462i	−0.452439	+	0.891795i	$0.649446\pi$
$464$	3.47361	−	36.3773i	0.161258	−	1.68877i
$465$		0			0
$466$	27.7746	−	2.65215i	1.28663	−	0.122859i
$467$	−5.27043	+	6.08240i	−0.243886	+	0.281460i	−0.864474	−	0.502677i	$-0.832349\pi$
$467$	−5.27043	+	6.08240i	−0.243886	+	0.281460i	0.620588	+	0.784137i	$0.286894\pi$
$468$		0			0
$469$	16.0986	−	4.72698i	0.743365	−	0.218272i
$470$	−0.0817870	+	0.236308i	−0.00377255	+	0.0109001i
$471$		0			0
$472$	−0.423490	−	8.89016i	−0.0194927	−	0.409203i
$473$	1.36598	+	7.08736i	0.0628077	+	0.325877i
$474$		0			0
$475$	−3.49865	−	8.73920i	−0.160529	−	0.400982i
$476$	−31.0874	−	26.9374i	−1.42489	−	1.23467i
$477$		0			0
$478$	18.4092	+	5.40544i	0.842019	+	0.247239i
$479$	6.51917	−	9.15489i	0.297868	−	0.418298i	−0.638334	−	0.769760i	$-0.720376\pi$
$479$	6.51917	−	9.15489i	0.297868	−	0.418298i	0.936202	+	0.351462i	$0.114315\pi$
$480$		0			0
$481$	−1.11076	−	2.15458i	−0.0506464	−	0.0982404i
$482$	6.67997	−	11.5700i	0.304264	−	0.527001i
$483$		0			0
$484$	4.94479	+	8.56464i	0.224763	+	0.389302i
$485$	−1.79504	+	2.79313i	−0.0815084	+	0.126829i
$486$		0			0
$487$	11.1988	+	24.5219i	0.507466	+	1.11119i	0.973970	+	0.226676i	$0.0727858\pi$
$487$	11.1988	+	24.5219i	0.507466	+	1.11119i	−0.466505	+	0.884519i	$0.654487\pi$
$488$	−2.90906	−	11.9913i	−0.131687	−	0.542822i
$489$		0			0
$490$	−9.25351	+	3.20267i	−0.418031	+	0.144682i
$491$	−1.80173	+	2.29108i	−0.0813108	+	0.103395i	−0.825007	−	0.565123i	$-0.808829\pi$
$491$	−1.80173	+	2.29108i	−0.0813108	+	0.103395i	0.743696	+	0.668518i	$0.233071\pi$
$492$		0			0
$493$	56.3283	+	19.4954i	2.53690	+	0.878029i
$494$	−2.25316	+	1.44802i	−0.101374	+	0.0651494i
$495$		0			0
$496$	15.9846	+	18.4473i	0.717731	+	0.828306i
$497$	0.888400	+	0.847088i	0.0398502	+	0.0379971i
$498$		0			0
$499$	−13.2568	−	38.3030i	−0.593456	−	1.71468i	−0.694215	−	0.719768i	$-0.744248\pi$
$499$	−13.2568	−	38.3030i	−0.593456	−	1.71468i	0.100759	−	0.994911i	$-0.467873\pi$
$500$	5.10567	+	7.16991i	0.228333	+	0.320648i
$501$		0			0
$502$	−3.70937	−	2.64143i	−0.165557	−	0.117893i
$503$	1.21107	+	8.42315i	0.0539988	+	0.375570i	0.998845	+	0.0480546i	$0.0153021\pi$
$503$	1.21107	+	8.42315i	0.0539988	+	0.375570i	−0.944846	+	0.327515i	$0.893789\pi$
$504$		0			0
$505$			1.98977i			0.0885435i
$506$	17.3850	+	33.3127i	0.772855	+	1.48093i
$507$		0			0
$508$	19.8353	−	10.2258i	0.880050	−	0.453697i
$509$	−9.97524	+	24.9169i	−0.442145	+	1.10442i	0.525205	+	0.850976i	$0.323989\pi$
$509$	−9.97524	+	24.9169i	−0.442145	+	1.10442i	−0.967349	+	0.253448i	$0.918435\pi$
$510$		0			0
$511$	−44.7528	+	10.8569i	−1.97975	+	0.480282i
$512$	18.3137	+	8.36358i	0.809358	+	0.369621i
$513$		0			0
$514$	5.29542	−	36.8304i	0.233571	−	1.62452i
$515$	3.29287	−	3.45346i	0.145101	−	0.152178i
$516$		0			0
$517$	−0.851083	+	0.0405421i	−0.0374306	+	0.00178304i
$518$	−24.1677	+	1.15125i	−1.06187	+	0.0505830i
$519$		0			0
$520$	−0.401460	+	0.421039i	−0.0176052	+	0.0184638i
$521$	0.983411	−	6.83977i	0.0430840	−	0.299656i	−0.956874	−	0.290503i	$-0.906177\pi$
$521$	0.983411	−	6.83977i	0.0430840	−	0.299656i	0.999958	−	0.00915296i	$-0.00291352\pi$
$522$		0			0
$523$	−39.2907	−	17.9435i	−1.71806	−	0.784613i	−0.995652	−	0.0931477i	$-0.970307\pi$
$523$	−39.2907	−	17.9435i	−1.71806	−	0.784613i	−0.722410	−	0.691465i	$-0.756966\pi$
$524$	−7.45934	+	1.80962i	−0.325863	+	0.0790535i
$525$		0			0
$526$	8.25366	−	20.6167i	0.359877	−	0.898929i
$527$	−35.3891	+	18.2443i	−1.54157	+	0.794735i
$528$		0			0
$529$	9.76295	+	20.8251i	0.424476	+	0.905439i
$530$			13.6538i			0.593084i
$531$		0			0
$532$	1.52862	+	10.6318i	0.0662739	+	0.460945i
$533$	−0.717837	−	0.511169i	−0.0310930	−	0.0221412i
$534$		0			0
$535$	−4.07161	−	5.71778i	−0.176031	−	0.247201i
$536$	−1.71361	−	4.95114i	−0.0740165	−	0.213857i
$537$		0			0
$538$	−17.2774	−	16.4740i	−0.744882	−	0.710244i
$539$	−21.8495	−	25.2157i	−0.941124	−	1.08612i
$540$		0			0
$541$	−24.4970	+	15.7433i	−1.05321	+	0.676855i	−0.948219	−	0.317618i	$-0.897117\pi$
$541$	−24.4970	+	15.7433i	−1.05321	+	0.676855i	−0.104989	+	0.994473i	$0.533481\pi$
$542$	−16.9830	−	5.87787i	−0.729482	−	0.252476i
$543$		0			0
$544$	−32.1224	+	40.8469i	−1.37723	+	1.75130i
$545$	−1.76997	+	0.612591i	−0.0758170	+	0.0262405i
$546$		0			0
$547$	−5.67335	−	23.3859i	−0.242575	−	0.999907i	−0.954633	−	0.297786i	$-0.903752\pi$
$547$	−5.67335	−	23.3859i	−0.242575	−	0.999907i	0.712058	−	0.702121i	$-0.247763\pi$
$548$	−0.787781	−	1.72500i	−0.0336523	−	0.0736883i
$549$		0			0
$550$	−19.1762	+	29.8388i	−0.817678	+	1.27233i
$551$	−7.78228	−	13.4793i	−0.331536	−	0.574237i
$552$		0			0
$553$	−31.0787	+	53.8299i	−1.32160	+	2.28908i
$554$	−8.23057	−	15.9651i	−0.349683	−	0.678291i
$555$		0			0
$556$	11.9175	−	16.7358i	0.505416	−	0.709757i
$557$	−30.6458	−	8.99841i	−1.29850	−	0.381275i	−0.441813	−	0.897107i	$-0.645664\pi$
$557$	−30.6458	−	8.99841i	−1.29850	−	0.381275i	−0.856689	+	0.515833i	$0.827483\pi$
$558$		0			0
$559$	0.896709	+	0.777002i	0.0379267	+	0.0328637i
$560$	4.79894	+	11.9872i	0.202792	+	0.506551i
$561$		0			0
$562$	−5.46000	−	28.3292i	−0.230316	−	1.19499i
$563$	−0.520129	−	10.9188i	−0.0219208	−	0.460175i	−0.982966	−	0.183785i	$-0.941165\pi$
$563$	−0.520129	−	10.9188i	−0.0219208	−	0.460175i	0.961046	−	0.276390i	$-0.0891380\pi$
$564$		0			0
$565$	−0.132588	+	0.383088i	−0.00557802	+	0.0161166i
$566$	35.0276	−	10.2850i	1.47232	−	0.432312i
$567$		0			0
$568$	0.251018	−	0.289690i	0.0105325	−	0.0121551i
$569$	−16.2143	+	1.54828i	−0.679738	+	0.0649071i	−0.429213	−	0.903203i	$-0.641209\pi$
$569$	−16.2143	+	1.54828i	−0.679738	+	0.0649071i	−0.250525	+	0.968110i	$0.580603\pi$
$570$		0			0
$571$	0.370369	−	3.87867i	0.0154994	−	0.162317i	−0.984408	−	0.175898i	$-0.943717\pi$
$571$	0.370369	−	3.87867i	0.0154994	−	0.162317i	0.999908	+	0.0135809i	$0.00432306\pi$
$572$	3.76431	+	1.50700i	0.157394	+	0.0630109i
$573$		0			0
$574$	−7.61747	+	4.39795i	−0.317947	+	0.183567i
$575$	−12.5049	+	17.7475i	−0.521489	+	0.740120i
$576$		0			0
$577$	23.9241	+	15.3751i	0.995972	+	0.640072i	0.933726	−	0.357989i	$-0.116537\pi$
$577$	23.9241	+	15.3751i	0.995972	+	0.640072i	0.0622458	+	0.998061i	$0.480174\pi$
$578$	−52.4650	−	66.7146i	−2.18225	−	2.77496i
$579$		0			0
$580$	4.77219	+	5.00493i	0.198154	+	0.207818i
$581$	10.5273	−	7.49643i	0.436745	−	0.311004i
$582$		0			0
$583$	−43.1909	+	17.2910i	−1.78878	+	0.716121i
$584$	4.05137	+	13.7977i	0.167647	+	0.570953i
$585$		0			0
$586$	4.55762	+	7.09180i	0.188274	+	0.292960i
$587$	−12.1250	+	23.5191i	−0.500451	+	0.970739i	0.494385	+	0.869243i	$0.335393\pi$
$587$	−12.1250	+	23.5191i	−0.500451	+	0.970739i	−0.994836	+	0.101496i	$0.967637\pi$
$588$		0			0
$589$	10.1035	+	2.45108i	0.416307	+	0.100995i
$590$	7.32726	+	5.76222i	0.301658	+	0.237227i
$591$		0			0
$592$	1.59698	+	16.7244i	0.0656357	+	0.687368i
$593$	−10.3740	+	35.3306i	−0.426009	+	1.45085i	0.414995	+	0.909824i	$0.363783\pi$
$593$	−10.3740	+	35.3306i	−0.426009	+	1.45085i	−0.841004	+	0.541029i	$0.818035\pi$
$594$		0			0
$595$	−20.8472	+	2.99737i	−0.854651	+	0.122880i
$596$	−0.489811	+	10.2824i	−0.0200634	+	0.421183i
$597$		0			0
$598$	5.63160	+	2.53797i	0.230293	+	0.103785i
$599$	16.3246	+	9.42499i	0.667004	+	0.385095i	0.794940	−	0.606688i	$-0.207502\pi$
$599$	16.3246	+	9.42499i	0.667004	+	0.385095i	−0.127937	+	0.991782i	$0.540835\pi$
$600$		0			0
$601$	13.5827	−	10.6816i	0.554051	−	0.435711i	−0.301472	−	0.953475i	$-0.597478\pi$
$601$	13.5827	−	10.6816i	0.554051	−	0.435711i	0.855523	+	0.517764i	$0.173236\pi$
$602$	10.7727	−	4.91973i	0.439063	−	0.200513i
$603$		0			0
$604$	−5.48497	+	12.0104i	−0.223180	+	0.488696i
$605$	4.97213	+	0.958299i	0.202146	+	0.0389604i
$606$		0			0
$607$	−1.99971	+	8.24293i	−0.0811658	+	0.334570i	−0.997888	−	0.0649547i	$-0.979310\pi$
$607$	−1.99971	+	8.24293i	−0.0811658	+	0.334570i	0.916722	+	0.399525i	$0.130825\pi$
$608$	13.3238	−	2.56796i	0.540353	−	0.104144i
$609$		0			0
$610$	11.4867	+	5.92179i	0.465082	+	0.239766i
$611$	−0.105855	+	0.0917238i	−0.00428243	+	0.00371075i
$612$		0			0
$613$	−16.6964	−	2.40059i	−0.674363	−	0.0969587i	−0.203378	−	0.979100i	$-0.565192\pi$
$613$	−16.6964	−	2.40059i	−0.674363	−	0.0969587i	−0.470985	+	0.882141i	$0.656101\pi$
$614$	7.83510	−	40.6524i	0.316199	−	1.64060i
$615$		0			0
$616$	−14.3195	+	13.6536i	−0.576947	+	0.550118i
$617$	45.2101	+	4.31704i	1.82009	+	0.173798i	0.948571	−	0.316563i	$-0.102529\pi$
$617$	45.2101	+	4.31704i	1.82009	+	0.173798i	0.871520	+	0.490361i	$0.163135\pi$
$618$		0			0
$619$	17.0176	+	0.810648i	0.683995	+	0.0325827i	0.386703	−	0.922204i	$-0.373614\pi$
$619$	17.0176	+	0.810648i	0.683995	+	0.0325827i	0.297291	+	0.954787i	$0.403917\pi$
$620$	−4.61925			−0.185514
$621$		0			0
$622$	39.5333			1.58514
$623$	44.6178	+	2.12541i	1.78758	+	0.0851527i
$624$		0			0
$625$	−18.0459	−	1.72317i	−0.721834	−	0.0689268i
$626$	24.8215	−	23.6672i	0.992066	−	0.945933i
$627$		0			0
$628$	−1.75853	+	9.12412i	−0.0701730	+	0.364092i
$629$	−27.1251	−	3.90000i	−1.08155	−	0.155503i
$630$		0			0
$631$	−0.534040	+	0.462748i	−0.0212598	+	0.0184217i	−0.665426	−	0.746464i	$-0.731750\pi$
$631$	−0.534040	+	0.462748i	−0.0212598	+	0.0184217i	0.644166	+	0.764886i	$0.277205\pi$
$632$	17.2521	+	8.89406i	0.686250	+	0.353787i
$633$		0			0
$634$	−51.2515	+	9.87793i	−2.03546	+	0.392303i
$635$	2.69383	−	11.1041i	0.106901	−	0.440653i
$636$		0			0
$637$	−5.38569	−	1.03801i	−0.213389	−	0.0411273i
$638$	−24.3625	+	53.3464i	−0.964521	+	2.11201i
$639$		0			0
$640$	5.68593	−	2.59668i	0.224756	−	0.102643i
$641$	−25.7812	+	20.2746i	−1.01830	+	0.800797i	−0.980106	−	0.198473i	$-0.936402\pi$
$641$	−25.7812	+	20.2746i	−1.01830	+	0.800797i	−0.0381900	+	0.999270i	$0.512159\pi$
$642$		0			0
$643$	−14.4108	−	8.32011i	−0.568308	−	0.328113i	0.188165	−	0.982137i	$-0.439746\pi$
$643$	−14.4108	−	8.32011i	−0.568308	−	0.328113i	−0.756473	+	0.654024i	$0.773079\pi$
$644$	18.6404	−	16.3156i	0.734535	−	0.642927i
$645$		0			0
$646$	−1.44072	+	30.2445i	−0.0566845	+	1.18995i
$647$	−4.37389	+	0.628871i	−0.171955	+	0.0247235i	−0.227755	−	0.973719i	$-0.573138\pi$
$647$	−4.37389	+	0.628871i	−0.171955	+	0.0247235i	0.0557992	+	0.998442i	$0.482229\pi$
$648$		0			0
$649$	−8.94839	+	30.4754i	−0.351255	+	1.19626i
$650$	0.554247	+	5.80434i	0.0217394	+	0.227665i
$651$		0			0
$652$	9.96749	+	7.83852i	0.390357	+	0.306980i
$653$	−39.2063	−	9.51134i	−1.53426	−	0.372208i	−0.622397	−	0.782701i	$-0.713841\pi$
$653$	−39.2063	−	9.51134i	−1.53426	−	0.372208i	−0.911863	+	0.410494i	$0.865356\pi$
$654$		0			0
$655$	−1.80087	+	3.49320i	−0.0703659	+	0.136491i
$656$	3.30204	+	5.13808i	0.128923	+	0.200608i
$657$		0			0
$658$	0.393873	+	1.34141i	0.0153548	+	0.0522936i
$659$	15.6766	−	6.27595i	0.610672	−	0.244476i	−0.0456496	−	0.998958i	$-0.514536\pi$
$659$	15.6766	−	6.27595i	0.610672	−	0.244476i	0.656321	+	0.754481i	$0.272112\pi$
$660$		0			0
$661$	4.72808	−	3.36685i	0.183901	−	0.130955i	−0.484399	−	0.874847i	$-0.660962\pi$
$661$	4.72808	−	3.36685i	0.183901	−	0.130955i	0.668300	+	0.743892i	$0.267022\pi$
$662$	25.8758	+	27.1378i	1.00569	+	1.05474i
$663$		0			0
$664$	−2.49466	−	3.17221i	−0.0968114	−	0.123106i
$665$	4.62657	+	2.97332i	0.179411	+	0.115300i
$666$		0			0
$667$	−16.2893	+	31.9879i	−0.630725	+	1.23858i
$668$	−8.64429	+	4.99078i	−0.334458	+	0.193099i
$669$		0			0
$670$	5.09426	+	2.03943i	0.196808	+	0.0787902i
$671$	−4.18573	+	43.8349i	−0.161588	+	1.69223i
$672$		0			0
$673$	−8.70790	+	0.831504i	−0.335665	+	0.0320521i	−0.261528	−	0.965196i	$-0.584226\pi$
$673$	−8.70790	+	0.831504i	−0.335665	+	0.0320521i	−0.0741371	+	0.997248i	$0.523620\pi$
$674$	−30.2048	+	34.8582i	−1.16345	+	1.34269i
$675$		0			0
$676$	−16.1160	+	4.73207i	−0.619844	+	0.182003i
$677$	−0.831292	+	2.40186i	−0.0319491	+	0.0923110i	−0.959848	−	0.280522i	$-0.909492\pi$
$677$	−0.831292	+	2.40186i	−0.0319491	+	0.0923110i	0.927898	+	0.372833i	$0.121614\pi$
$678$		0			0
$679$	0.883241	+	18.5415i	0.0338957	+	0.711558i
$680$	1.24467	+	6.45798i	0.0477311	+	0.247652i
$681$		0			0
$682$	−14.5593	−	36.3674i	−0.557505	−	1.39258i
$683$	24.5834	+	21.3017i	0.940659	+	0.815086i	0.982922	−	0.184021i	$-0.0589114\pi$
$683$	24.5834	+	21.3017i	0.940659	+	0.815086i	−0.0422633	+	0.999107i	$0.513457\pi$
$684$		0			0
$685$	−0.931642	−	0.273555i	−0.0355962	−	0.0104520i
$686$	−3.20678	+	4.50329i	−0.122435	+	0.171936i
$687$		0			0
$688$	−3.76820	−	7.30928i	−0.143661	−	0.278664i
$689$	−3.82394	+	6.62326i	−0.145681	+	0.252326i
$690$		0			0
$691$	−16.1522	−	27.9765i	−0.614460	−	1.06428i	−0.990479	−	0.137663i	$-0.956041\pi$
$691$	−16.1522	−	27.9765i	−0.614460	−	1.06428i	0.376019	−	0.926612i	$-0.377293\pi$
$692$	−7.55135	+	11.7501i	−0.287059	+	0.446673i
$693$		0			0
$694$	−17.2199	−	37.7063i	−0.653658	−	1.43131i
$695$	−2.48009	−	10.2231i	−0.0940753	−	0.387784i
$696$		0			0
$697$	−9.41456	+	3.25841i	−0.356602	+	0.123421i
$698$	−9.78260	+	12.4396i	−0.370277	+	0.470845i
$699$		0			0
$700$	22.0973	+	7.64795i	0.835199	+	0.289065i
$701$	29.4895	−	18.9518i	1.11380	−	0.715798i	0.151685	−	0.988429i	$-0.451530\pi$
$701$	29.4895	−	18.9518i	1.11380	−	0.715798i	0.962119	+	0.272630i	$0.0878936\pi$
$702$		0			0
$703$	4.68604	+	5.40797i	0.176737	+	0.203966i
$704$	−6.72071	−	6.40818i	−0.253296	−	0.241517i
$705$		0			0
$706$	−13.9327	−	40.2560i	−0.524366	−	1.51506i
$707$	6.45277	+	9.06165i	0.242681	+	0.340798i
$708$		0			0
$709$	17.9176	+	12.7591i	0.672911	+	0.479178i	0.864720	−	0.502255i	$-0.167496\pi$
$709$	17.9176	+	12.7591i	0.672911	+	0.479178i	−0.191809	+	0.981432i	$0.561435\pi$
$710$	0.0571339	+	0.397375i	0.00214420	+	0.0149132i
$711$		0			0
$712$		−	13.9485i		−	0.522741i
$713$	−7.95535	−	22.6195i	−0.297930	−	0.847106i
$714$		0			0
$715$	1.84532	−	0.951326i	0.0690109	−	0.0355776i
$716$	4.88060	−	12.1912i	0.182397	−	0.455605i
$717$		0			0
$718$	20.5706	−	4.99037i	0.767688	−	0.186239i
$719$	−34.9109	−	15.9433i	−1.30196	−	0.594583i	−0.360827	−	0.932633i	$-0.617505\pi$
$719$	−34.9109	−	15.9433i	−1.30196	−	0.594583i	−0.941128	+	0.338050i	$0.890233\pi$
$720$		0			0
$721$	3.79664	−	26.4062i	0.141394	−	0.983418i
$722$	−18.5179	+	19.4210i	−0.689165	+	0.722776i
$723$		0			0
$724$	6.19856	−	0.295274i	0.230368	−	0.0109738i
$725$	−33.8457	+	1.61227i	−1.25700	+	0.0598781i
$726$		0			0
$727$	−28.4361	+	29.8230i	−1.05464	+	1.10607i	−0.0604761	+	0.998170i	$0.519262\pi$
$727$	−28.4361	+	29.8230i	−1.05464	+	1.10607i	−0.994161	+	0.107902i	$0.965587\pi$
$728$	−0.462878	+	3.21939i	−0.0171554	+	0.119318i
$729$		0			0
$730$	−13.6999	−	6.25655i	−0.507057	−	0.231565i
$731$	13.0355	−	3.16239i	0.482137	−	0.116965i
$732$		0			0
$733$	−5.53644	+	13.8294i	−0.204493	+	0.510799i	−0.994792	−	0.101922i	$-0.967501\pi$
$733$	−5.53644	+	13.8294i	−0.204493	+	0.510799i	0.790299	+	0.612721i	$0.209925\pi$
$734$	−35.0633	+	18.0764i	−1.29421	+	0.667212i
$735$		0			0
$736$	−21.7084	−	22.5407i	−0.800182	−	0.830862i
$737$			18.6973i			0.688724i
$738$		0			0
$739$	−1.85257	−	12.8849i	−0.0681480	−	0.473979i	−0.995106	−	0.0988142i	$-0.968495\pi$
$739$	−1.85257	−	12.8849i	−0.0681480	−	0.473979i	0.926958	−	0.375165i	$-0.122414\pi$
$740$	−2.58983	−	1.84421i	−0.0952039	−	0.0677944i
$741$		0			0
$742$	44.2790	+	62.1812i	1.62553	+	2.28274i
$743$	−4.62943	−	13.3759i	−0.169837	−	0.490713i	0.827675	−	0.561208i	$-0.189663\pi$
$743$	−4.62943	−	13.3759i	−0.169837	−	0.490713i	−0.997512	+	0.0704953i	$0.977542\pi$
$744$		0			0
$745$	3.81460	+	3.63722i	0.139756	+	0.133257i
$746$	−41.9911	−	48.4603i	−1.53740	−	1.77426i
$747$		0			0
$748$	38.5625	−	24.7826i	1.40999	−	0.906143i
$749$	−37.0852	−	12.8353i	−1.35506	−	0.468992i
$750$		0			0
$751$	18.1504	−	23.0801i	0.662318	−	0.842206i	−0.332581	−	0.943075i	$-0.607920\pi$
$751$	18.1504	−	23.0801i	0.662318	−	0.842206i	0.994900	+	0.100868i	$0.0321620\pi$
$752$	0.917372	−	0.317505i	0.0334531	−	0.0115782i
$753$		0			0
$754$	2.27288	+	9.36894i	0.0827735	+	0.341197i
$755$	2.80839	+	6.14953i	0.102208	+	0.223804i
$756$		0			0
$757$	13.7741	−	21.4329i	0.500628	−	0.778993i	−0.495340	−	0.868699i	$-0.664957\pi$
$757$	13.7741	−	21.4329i	0.500628	−	0.778993i	0.995968	+	0.0897066i	$0.0285929\pi$
$758$	11.0640	+	19.1635i	0.401864	+	0.696049i
$759$		0			0
$760$	0.858675	−	1.48727i	0.0311474	−	0.0539489i
$761$	0.503166	+	0.976006i	0.0182398	+	0.0353802i	0.897779	−	0.440446i	$-0.145180\pi$
$761$	0.503166	+	0.976006i	0.0182398	+	0.0353802i	−0.879540	+	0.475826i	$0.842149\pi$
$762$		0			0
$763$	−6.07402	+	8.52977i	−0.219894	+	0.308799i
$764$	27.1592	+	7.97467i	0.982586	+	0.288513i
$765$		0			0
$766$	−22.2813	−	19.3068i	−0.805055	−	0.697584i
$767$	1.94055	+	4.84727i	0.0700693	+	0.175025i
$768$		0			0
$769$	−4.25832	−	22.0942i	−0.153559	−	0.796739i	−0.974268	−	0.225393i	$-0.927633\pi$
$769$	−4.25832	−	22.0942i	−0.153559	−	0.796739i	0.820709	−	0.571346i	$-0.193579\pi$
$770$	−0.986001	−	20.6987i	−0.0355330	−	0.745930i
$771$		0			0
$772$	5.62564	−	16.2542i	0.202471	−	0.585002i
$773$	21.4593	−	6.30101i	0.771836	−	0.226632i	0.127979	−	0.991777i	$-0.459151\pi$
$773$	21.4593	−	6.30101i	0.771836	−	0.226632i	0.643858	+	0.765145i	$0.277333\pi$
$774$		0			0
$775$	14.8217	−	17.1051i	0.532410	−	0.614434i
$776$	5.77023	−	0.550990i	0.207139	−	0.0197794i
$777$		0			0
$778$	−1.95047	+	20.4262i	−0.0699276	+	0.732315i
$779$	2.41507	+	0.966849i	0.0865289	+	0.0346410i
$780$		0			0
$781$	−1.18466	+	0.683962i	−0.0423904	+	0.0244741i
$782$	60.3014	−	35.2176i	2.15637	−	1.25938i
$783$		0			0
$784$	31.9792	+	20.5518i	1.14212	+	0.733993i
$785$	2.94100	+	3.73979i	0.104969	+	0.133479i
$786$		0			0
$787$	8.31925	+	8.72498i	0.296549	+	0.311012i	0.855105	−	0.518455i	$-0.173493\pi$
$787$	8.31925	+	8.72498i	0.296549	+	0.311012i	−0.558556	+	0.829467i	$0.688644\pi$
$788$	−18.4324	+	13.1257i	−0.656628	+	0.467583i
$789$		0			0
$790$	−18.8724	+	7.55538i	−0.671451	+	0.268808i
$791$	0.638523	+	2.17461i	0.0227033	+	0.0773202i
$792$		0			0
$793$	3.91353	+	6.08958i	0.138974	+	0.216247i
$794$	0.779663	−	1.51234i	0.0276692	−	0.0536708i
$795$		0			0
$796$	−6.39774	−	1.55207i	−0.226762	−	0.0550118i
$797$	7.37897	+	5.80289i	0.261377	+	0.205549i	0.740244	−	0.672338i	$-0.234710\pi$
$797$	7.37897	+	5.80289i	0.261377	+	0.205549i	−0.478867	+	0.877887i	$0.658952\pi$
$798$		0			0
$799$	0.150517	+	1.57629i	0.00532492	+	0.0557651i
$800$	8.32233	−	28.3432i	0.294239	−	1.00209i
$801$		0			0
$802$	−43.8608	+	6.30623i	−1.54878	+	0.222681i
$803$	2.44182	−	51.2600i	0.0861698	−	1.80893i
$804$		0			0
$805$	−0.0633193	−	12.6837i	−0.00223171	−	0.447040i
$806$	−5.57689	−	3.21982i	−0.196438	−	0.113413i
$807$		0			0
$808$	2.73057	−	2.14735i	0.0960612	−	0.0755434i
$809$	7.44835	−	3.40155i	0.261870	−	0.119592i	−0.280154	−	0.959955i	$-0.590385\pi$
$809$	7.44835	−	3.40155i	0.261870	−	0.119592i	0.542024	+	0.840363i	$0.317658\pi$
$810$		0			0
$811$	12.1769	−	26.6638i	0.427590	−	0.936291i	−0.566122	−	0.824322i	$-0.691557\pi$
$811$	12.1769	−	26.6638i	0.427590	−	0.936291i	0.993712	−	0.111970i	$-0.0357159\pi$
$812$	37.9640	+	7.31696i	1.33228	+	0.256775i
$813$		0			0
$814$	6.35664	−	26.2024i	0.222800	−	0.918395i
$815$	6.37526	−	1.22873i	0.223316	−	0.0430405i
$816$		0			0
$817$	−3.11322	−	1.60498i	−0.108918	−	0.0561511i
$818$	31.1406	−	26.9835i	1.08881	−	0.943456i
$819$		0			0
$820$	−1.14406	−	0.164491i	−0.0399523	−	0.00574427i
$821$	−6.03426	+	31.3087i	−0.210597	+	1.09268i	0.710603	+	0.703593i	$0.248422\pi$
$821$	−6.03426	+	31.3087i	−0.210597	+	1.09268i	−0.921200	+	0.389088i	$0.872790\pi$
$822$		0			0
$823$	18.2680	−	17.4185i	0.636783	−	0.607171i	−0.301322	−	0.953522i	$-0.597428\pi$
$823$	18.2680	−	17.4185i	0.636783	−	0.607171i	0.938105	+	0.346351i	$0.112579\pi$
$824$	−8.29286	−	0.791872i	−0.288896	−	0.0275862i
$825$		0			0
$826$	52.0560	+	2.47973i	1.81126	+	0.0862809i
$827$	11.5329			0.401037			0.200518	−	0.979690i	$-0.435737\pi$
$827$	11.5329			0.401037			0.200518	+	0.979690i	$0.435737\pi$
$828$		0			0
$829$	27.0765			0.940405			0.470203	−	0.882558i	$-0.344181\pi$
$829$	27.0765			0.940405			0.470203	+	0.882558i	$0.344181\pi$
$830$	4.22188	+	0.201113i	0.146544	+	0.00698073i
$831$		0			0
$832$	−1.51962	−	0.145106i	−0.0526832	−	0.00503064i
$833$	−44.8760	+	42.7892i	−1.55486	+	1.48256i
$834$		0			0
$835$	−0.967212	+	5.01837i	−0.0334717	+	0.173668i
$836$	−11.8478	−	1.70346i	−0.409765	−	0.0589153i
$837$		0			0
$838$	23.6358	−	20.4805i	0.816486	−	0.707489i
$839$	−34.8493	−	17.9661i	−1.20313	−	0.620257i	−0.264235	−	0.964458i	$-0.585119\pi$
$839$	−34.8493	−	17.9661i	−1.20313	−	0.620257i	−0.938896	+	0.344201i	$0.888150\pi$
$840$		0			0
$841$	−26.5364	+	5.11447i	−0.915048	+	0.176361i
$842$	−15.7149	+	64.7777i	−0.541571	+	2.23239i
$843$		0			0
$844$	−27.8698	−	5.37147i	−0.959319	−	0.184894i
$845$	−3.57257	+	7.82283i	−0.122900	+	0.269114i
$846$		0			0
$847$	25.7514	−	11.7603i	0.884829	−	0.404088i
$848$	41.6651	−	32.7658i	1.43079	−	1.12518i
$849$		0			0
$850$	57.0858	+	32.9585i	1.95803	+	1.13047i
$851$	4.57044	−	15.8579i	0.156673	−	0.543603i
$852$		0			0
$853$	2.21807	−	46.5631i	0.0759454	−	1.59429i	−0.563937	−	0.825817i	$-0.690714\pi$
$853$	2.21807	−	46.5631i	0.0759454	−	1.59429i	0.639883	−	0.768472i	$-0.278983\pi$
$854$	71.5160	−	10.2824i	2.44723	−	0.351858i
$855$		0			0
$856$	−3.45249	+	11.7581i	−0.118004	+	0.401883i
$857$	1.70902	+	17.8977i	0.0583790	+	0.611372i	0.976565	+	0.215223i	$0.0690478\pi$
$857$	1.70902	+	17.8977i	0.0583790	+	0.611372i	−0.918186	+	0.396150i	$0.870346\pi$
$858$		0			0
$859$	42.3897	+	33.3357i	1.44632	+	1.13740i	0.965444	+	0.260609i	$0.0839233\pi$
$859$	42.3897	+	33.3357i	1.44632	+	1.13740i	0.480875	+	0.876789i	$0.340319\pi$
$860$	1.51235	+	0.366893i	0.0515708	+	0.0125109i
$861$		0			0
$862$	−2.60772	+	5.05827i	−0.0888193	+	0.172285i
$863$	11.8456	+	18.4322i	0.403230	+	0.627438i	0.982184	−	0.187922i	$-0.0601752\pi$
$863$	11.8456	+	18.4322i	0.403230	+	0.627438i	−0.578954	+	0.815360i	$0.696539\pi$
$864$		0			0
$865$	2.01482	+	6.86185i	0.0685060	+	0.233310i
$866$	−52.3743	+	20.9675i	−1.77975	+	0.712504i
$867$		0			0
$868$	−21.0366	+	14.9801i	−0.714030	+	0.508459i
$869$	−47.7996	−	50.1308i	−1.62149	−	1.70057i
$870$		0			0
$871$	1.89998	+	2.41602i	0.0643783	+	0.0818636i
$872$	2.75080	+	1.76783i	0.0931539	+	0.0598664i
$873$		0			0
$874$	−17.9222	−	3.36151i	−0.606226	−	0.113705i
$875$	21.8208	−	12.5982i	0.737677	−	0.425898i
$876$		0			0
$877$	−11.9736	−	4.79350i	−0.404319	−	0.161865i	0.160584	−	0.987022i	$-0.448662\pi$
$877$	−11.9736	−	4.79350i	−0.404319	−	0.161865i	−0.564903	+	0.825157i	$0.691086\pi$
$878$	1.48852	−	15.5885i	0.0502351	−	0.526085i
$879$		0			0
$880$	−14.3238	+	1.36776i	−0.482855	+	0.0461071i
$881$	−33.9904	+	39.2270i	−1.14516	+	1.32159i	−0.205831	+	0.978588i	$0.565990\pi$
$881$	−33.9904	+	39.2270i	−1.14516	+	1.32159i	−0.939334	+	0.343003i	$0.888556\pi$
$882$		0			0
$883$	5.75369	−	1.68944i	0.193627	−	0.0568540i	−0.183481	−	0.983023i	$-0.558737\pi$
$883$	5.75369	−	1.68944i	0.193627	−	0.0568540i	0.377108	+	0.926169i	$0.376918\pi$
$884$	2.46460	−	7.12098i	0.0828933	−	0.239505i
$885$		0			0
$886$	1.62374	+	34.0865i	0.0545505	+	1.14516i
$887$	−2.04269	−	10.5985i	−0.0685870	−	0.355863i	0.931380	−	0.364050i	$-0.118606\pi$
$887$	−2.04269	−	10.5985i	−0.0685870	−	0.355863i	−0.999966	+	0.00818669i	$0.997394\pi$
$888$		0			0
$889$	−23.7424	−	59.3055i	−0.796293	−	1.98904i
$890$	11.0406	+	9.56674i	0.370082	+	0.320678i
$891$		0			0
$892$	26.3703	+	7.74302i	0.882943	+	0.259255i
$893$	0.239839	−	0.336806i	0.00802590	−	0.0112708i
$894$		0			0
$895$	−3.08098	−	5.97627i	−0.102986	−	0.199765i
$896$	17.4735	−	30.2649i	0.583748	−	1.01108i
$897$		0			0
$898$	−36.5027	−	63.2245i	−1.21811	−	2.10983i
$899$	20.2321	−	31.4818i	0.674780	−	1.04998i
$900$		0			0
$901$	35.9167	+	78.6467i	1.19656	+	2.62010i
$902$	−2.31090	−	9.52566i	−0.0769445	−	0.317170i
$903$		0			0
$904$	0.668803	−	0.231475i	0.0222441	−	0.00769874i
$905$	1.96412	−	2.49758i	0.0652894	−	0.0830223i
$906$		0			0
$907$	−15.2489	−	5.27770i	−0.506332	−	0.175243i	0.0619466	−	0.998079i	$-0.480269\pi$
$907$	−15.2489	−	5.27770i	−0.506332	−	0.175243i	−0.568278	+	0.822836i	$0.692390\pi$
$908$	2.98799	−	1.92027i	0.0991601	−	0.0637263i
$909$		0			0
$910$	−2.23076	−	2.57444i	−0.0739491	−	0.0853418i
$911$	12.3736	+	11.7982i	0.409956	+	0.390892i	0.866801	−	0.498654i	$-0.166172\pi$
$911$	12.3736	+	11.7982i	0.409956	+	0.390892i	−0.456845	+	0.889546i	$0.651021\pi$
$912$		0			0
$913$	4.71036	+	13.6097i	0.155890	+	0.450415i
$914$	12.1920	+	17.1213i	0.403276	+	0.566322i
$915$		0			0
$916$	6.88527	+	4.90298i	0.227496	+	0.161999i
$917$	3.12699	+	21.7487i	0.103262	+	0.718204i
$918$		0			0
$919$		−	32.0171i		−	1.05615i	−0.849198	−	0.528074i	$-0.822914\pi$
$919$		−	32.0171i		−	1.05615i	0.849198	−	0.528074i	$-0.177086\pi$
$920$	−3.95526	+	0.208207i	−0.130401	+	0.00686439i
$921$		0			0
$922$	3.65256	−	1.88303i	0.120291	−	0.0620142i
$923$	−0.0835756	+	0.208762i	−0.00275093	+	0.00687148i
$924$		0			0
$925$	15.1390	−	3.67268i	0.497767	−	0.120757i
$926$	−6.34054	−	2.89563i	−0.208363	−	0.0951562i
$927$		0			0
$928$	6.95093	−	48.3448i	0.228175	−	1.58700i
$929$	23.6958	−	24.8515i	0.777435	−	0.815351i	−0.209272	−	0.977857i	$-0.567109\pi$
$929$	23.6958	−	24.8515i	0.777435	−	0.815351i	0.986707	+	0.162507i	$0.0519579\pi$
$930$		0			0
$931$	16.1728	−	0.770405i	0.530042	−	0.0252490i
$932$	20.4744	−	0.975317i	0.670662	−	0.0319476i
$933$		0			0
$934$	−10.1551	+	10.6503i	−0.332284	+	0.348490i
$935$	3.34020	−	23.2316i	0.109236	−	0.759756i
$936$		0			0
$937$	16.6128	+	7.58683i	0.542718	+	0.247851i	0.667859	−	0.744288i	$-0.267211\pi$
$937$	16.6128	+	7.58683i	0.542718	+	0.247851i	−0.125141	+	0.992139i	$0.539938\pi$
$938$	29.8137	−	7.23273i	0.973453	−	0.236157i
$939$		0			0
$940$	−0.0682778	+	0.170550i	−0.00222698	+	0.00556272i
$941$	37.7729	−	19.4733i	1.23136	−	0.634811i	0.285188	−	0.958471i	$-0.407944\pi$
$941$	37.7729	−	19.4733i	1.23136	−	0.634811i	0.946173	+	0.323660i	$0.104914\pi$
$942$		0			0
$943$	−1.16484	−	5.88550i	−0.0379324	−	0.191658i
$944$		−	36.1873i		−	1.17780i
$945$		0			0
$946$	1.87820	+	13.0632i	0.0610656	+	0.424721i
$947$	18.0529	+	12.8554i	0.586640	+	0.417744i	0.834465	−	0.551060i	$-0.185777\pi$
$947$	18.0529	+	12.8554i	0.586640	+	0.417744i	−0.247826	+	0.968805i	$0.579716\pi$
$948$		0			0
$949$	−4.89340	−	6.87182i	−0.158846	−	0.223069i
$950$	−5.62960	−	16.2656i	−0.182648	−	0.527727i
$951$		0			0
$952$	26.6115	+	25.3740i	0.862483	+	0.822376i
$953$	12.7163	+	14.6754i	0.411921	+	0.475382i	0.923359	−	0.383938i	$-0.125433\pi$
$953$	12.7163	+	14.6754i	0.411921	+	0.475382i	−0.511438	+	0.859320i	$0.670887\pi$
$954$		0			0
$955$	12.1923	−	7.83553i	0.394534	−	0.253552i
$956$	13.3202	+	4.61017i	0.430806	+	0.149104i
$957$		0			0
$958$	12.7031	−	16.1533i	0.410418	−	0.521889i
$959$	−5.12994	+	1.77549i	−0.165655	+	0.0573336i
$960$		0			0
$961$	−1.41529	−	5.83388i	−0.0456544	−	0.188190i
$962$	−1.84124	−	4.03176i	−0.0593640	−	0.129989i
$963$		0			0
$964$	5.30637	−	8.25688i	0.170907	−	0.265936i
$965$	−4.40340	−	7.62691i	−0.141750	−	0.245519i
$966$		0			0
$967$	−3.78066	+	6.54830i	−0.121578	+	0.210579i	−0.920390	−	0.391001i	$-0.872129\pi$
$967$	−3.78066	+	6.54830i	−0.121578	+	0.210579i	0.798812	+	0.601581i	$0.205462\pi$
$968$	−4.05081	−	7.85748i	−0.130198	−	0.252549i
$969$		0			0
$970$	−3.52146	+	4.94519i	−0.113067	+	0.158781i
$971$	47.2669	+	13.8788i	1.51687	+	0.445392i	0.931001	−	0.365016i	$-0.118936\pi$
$971$	47.2669	+	13.8788i	1.51687	+	0.445392i	0.585866	+	0.810408i	$0.300755\pi$
$972$		0			0
$973$	−44.4479	−	38.5143i	−1.42493	−	1.23471i
$974$	18.3200	+	45.7611i	0.587010	+	1.46628i
$975$		0			0
$976$	−9.49465	−	49.2629i	−0.303916	−	1.57687i
$977$	0.427563	+	8.97565i	0.0136789	+	0.287156i	0.995334	+	0.0964904i	$0.0307617\pi$
$977$	0.427563	+	8.97565i	0.0136789	+	0.287156i	−0.981655	+	0.190666i	$0.938935\pi$
$978$		0			0
$979$	−16.2806	+	47.0398i	−0.520331	+	1.50340i
$980$	−6.90241	+	2.02673i	−0.220489	+	0.0647415i
$981$		0			0
$982$	−3.49000	+	4.02767i	−0.111370	+	0.128528i
$983$	−29.9087	+	2.85594i	−0.953940	+	0.0910902i	−0.560404	−	0.828219i	$-0.689354\pi$
$983$	−29.9087	+	2.85594i	−0.953940	+	0.0910902i	−0.393536	+	0.919309i	$0.628748\pi$
$984$		0			0
$985$	−1.10132	+	11.5336i	−0.0350911	+	0.367490i
$986$	101.182	+	40.5071i	3.22228	+	1.29001i
$987$		0			0
$988$	−1.70404	+	0.983830i	−0.0542128	+	0.0312998i
$989$	0.808002	+	8.03753i	0.0256930	+	0.255579i
$990$		0			0
$991$	−18.6828	−	12.0067i	−0.593478	−	0.381405i	0.209151	−	0.977883i	$-0.432930\pi$
$991$	−18.6828	−	12.0067i	−0.593478	−	0.381405i	−0.802629	+	0.596478i	$0.796566\pi$
$992$	20.1672	+	25.6447i	0.640310	+	0.814220i
$993$		0			0
$994$	1.54887	+	1.62441i	0.0491273	+	0.0515232i
$995$	−2.74574	+	1.95523i	−0.0870459	+	0.0619851i
$996$		0			0
$997$	45.0476	−	18.0343i	1.42667	−	0.571153i	0.475472	−	0.879731i	$-0.342277\pi$
$997$	45.0476	−	18.0343i	1.42667	−	0.571153i	0.951199	+	0.308578i	$0.0998532\pi$
$998$	−20.8798	−	71.1099i	−0.660937	−	2.25094i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	621.2.s.a.44.18		440
3.2	odd	2		207.2.o.a.113.5	yes	440
9.2	odd	6	inner	621.2.s.a.251.18		440
9.7	even	3		207.2.o.a.182.5	yes	440
23.11	odd	22	inner	621.2.s.a.287.18		440
69.11	even	22		207.2.o.a.149.5	yes	440
207.11	even	66	inner	621.2.s.a.494.18		440
207.34	odd	66		207.2.o.a.11.5	✓	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.5	✓	440	207.34	odd	66
207.2.o.a.113.5	yes	440	3.2	odd	2
207.2.o.a.149.5	yes	440	69.11	even	22
207.2.o.a.182.5	yes	440	9.7	even	3
621.2.s.a.44.18		440	1.1	even	1	trivial
621.2.s.a.251.18		440	9.2	odd	6	inner
621.2.s.a.287.18		440	23.11	odd	22	inner
621.2.s.a.494.18		440	207.11	even	66	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:	\( N \)	\(=\)	\( 621 = 3^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	621.s (of order \(66\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.82640 + 0.0870020i) q^{2} +(1.33722 + 0.127689i) q^{4} +(0.497778 - 0.474630i) q^{5} +(0.727727 - 3.77580i) q^{7} +(-1.18854 - 0.170886i) q^{8} +(0.950434 - 0.823555i) q^{10} +(3.80876 + 1.96355i) q^{11} +(0.691689 - 0.133312i) q^{13} +(1.65762 - 6.83281i) q^{14} +(-4.79392 - 0.923952i) q^{16} +(3.30816 - 7.24386i) q^{17} +(-1.89153 + 0.863831i) q^{19} +(0.726241 - 0.571122i) q^{20} +(6.78547 + 3.91760i) q^{22} +(4.04740 + 2.57265i) q^{23} +(-0.215401 + 4.52182i) q^{25} +(1.27490 - 0.183303i) q^{26} +(1.45525 - 4.95614i) q^{28} +(0.711492 + 7.45108i) q^{29} +(-3.93002 - 3.09060i) q^{31} +(-6.34139 - 1.53841i) q^{32} +(6.67225 - 12.9424i) q^{34} +(-1.42986 - 2.22491i) q^{35} +(-0.969499 - 3.30181i) q^{37} +(-3.52983 + 1.41313i) q^{38} +(-0.672735 + 0.479052i) q^{40} +(-0.863301 - 0.905404i) q^{41} +(1.04122 + 1.32402i) q^{43} +(4.84241 + 3.11203i) q^{44} +(7.16834 + 5.05081i) q^{46} +(-0.172200 + 0.0994197i) q^{47} +(-7.22854 - 2.89387i) q^{49} +(-0.786815 + 8.23989i) q^{50} +(0.941960 - 0.0899462i) q^{52} +(-7.10983 + 8.20518i) q^{53} +(2.82787 - 0.830339i) q^{55} +(-1.51016 + 4.36333i) q^{56} +(0.651208 + 13.6705i) q^{58} +(1.40276 + 7.27823i) q^{59} +(3.81925 + 9.54002i) q^{61} +(-6.90889 - 5.98659i) q^{62} +(-2.07929 - 0.610536i) q^{64} +(0.281033 - 0.394656i) q^{65} +(1.99939 + 3.87827i) q^{67} +(5.34868 - 9.26419i) q^{68} +(-2.41793 - 4.18797i) q^{70} +(-0.172587 + 0.268551i) q^{71} +(-4.97498 - 10.8937i) q^{73} +(-1.48343 - 6.11477i) q^{74} +(-2.63968 + 0.913602i) q^{76} +(10.1857 - 12.9522i) q^{77} +(-15.2755 - 5.28691i) q^{79} +(-2.82484 + 1.81542i) q^{80} +(-1.49796 - 1.72874i) q^{82} +(2.43239 + 2.31928i) q^{83} +(-1.79143 - 5.17599i) q^{85} +(1.78649 + 2.50877i) q^{86} +(-4.19131 - 2.98462i) q^{88} +(1.65318 + 11.4981i) q^{89} -2.70870i q^{91} +(5.08375 + 3.95699i) q^{92} +(-0.323155 + 0.166598i) q^{94} +(-0.531559 + 1.32777i) q^{95} +(-4.69126 + 1.13809i) q^{97} +(-12.9504 - 5.91426i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 27 q^{2} - 29 q^{4} + 33 q^{5} - 11 q^{7} - 44 q^{10} + 33 q^{11} - 9 q^{13} + 33 q^{14} + 3 q^{16} - 44 q^{19} + 33 q^{20} + 27 q^{23} + 11 q^{25} - 44 q^{28} - 27 q^{29} - 3 q^{31} + 33 q^{32}+ \cdots + 22 q^{97}+O(q^{100}) \) 440 * q + 27 * q^2 - 29 * q^4 + 33 * q^5 - 11 * q^7 - 44 * q^10 + 33 * q^11 - 9 * q^13 + 33 * q^14 + 3 * q^16 - 44 * q^19 + 33 * q^20 + 27 * q^23 + 11 * q^25 - 44 * q^28 - 27 * q^29 - 3 * q^31 + 33 * q^32 - 11 * q^34 - 44 * q^37 + 33 * q^38 - 77 * q^40 - 9 * q^41 - 11 * q^43 - 36 * q^46 + 120 * q^47 + 35 * q^49 + 3 * q^50 - 38 * q^52 - 44 * q^55 - 165 * q^56 - 10 * q^58 + 9 * q^59 - 11 * q^61 - 22 * q^64 - 198 * q^65 - 11 * q^67 - 70 * q^70 - 36 * q^73 - 231 * q^74 - 11 * q^76 - 39 * q^77 - 11 * q^79 - 10 * q^82 - 66 * q^83 + q^85 + 33 * q^86 - 99 * q^88 - 63 * q^92 - 42 * q^94 + 93 * q^95 + 22 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more