LMFDB - Embedded newform 55.2.l.a.8.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,2,Mod(2,55)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("55.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	55.l (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.439177211117$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			8.3
Character	$\chi$	$=$	55.8
Dual form			55.2.l.a.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.482327 + 0.0763931i) q^{2} +(0.517260 - 1.01518i) q^{3} +(-1.67531 - 0.544341i) q^{4} +(2.05331 + 0.885381i) q^{5} +(0.327041 - 0.450133i) q^{6} +(-2.59854 + 1.32402i) q^{7} +(-1.63669 - 0.833936i) q^{8} +(1.00032 + 1.37683i) q^{9} +(0.922733 + 0.583903i) q^{10} +(-3.15977 + 1.00788i) q^{11} +(-1.41917 + 1.41917i) q^{12} +(0.457808 - 2.89049i) q^{13} +(-1.35449 + 0.440102i) q^{14} +(1.96092 - 1.62651i) q^{15} +(2.12449 + 1.54353i) q^{16} +(-0.824113 - 5.20325i) q^{17} +(0.377304 + 0.740500i) q^{18} +(1.26677 + 3.89873i) q^{19} +(-2.95799 - 2.60099i) q^{20} +3.32285i q^{21} +(-1.60104 + 0.244743i) q^{22} +(-2.12046 - 2.12046i) q^{23} +(-1.69319 + 1.23017i) q^{24} +(3.43220 + 3.63593i) q^{25} +(0.441627 - 1.35919i) q^{26} +(5.29116 - 0.838037i) q^{27} +(5.07408 - 0.803656i) q^{28} +(0.817241 - 2.51521i) q^{29} +(1.07006 - 0.634710i) q^{30} +(5.45328 - 3.96204i) q^{31} +(3.50456 + 3.50456i) q^{32} +(-0.611244 + 3.72907i) q^{33} -2.57262i q^{34} +(-6.50789 + 0.417937i) q^{35} +(-0.926389 - 2.85113i) q^{36} +(-0.528116 - 1.03649i) q^{37} +(0.313163 + 1.97724i) q^{38} +(-2.69755 - 1.95989i) q^{39} +(-2.62229 - 3.16143i) q^{40} +(-3.38136 + 1.09867i) q^{41} +(-0.253843 + 1.60270i) q^{42} +(-5.07292 + 5.07292i) q^{43} +(5.84223 + 0.0314826i) q^{44} +(0.834964 + 3.71273i) q^{45} +(-0.860769 - 1.18475i) q^{46} +(-3.28041 - 1.67145i) q^{47} +(2.66588 - 1.35833i) q^{48} +(0.884888 - 1.21794i) q^{49} +(1.37768 + 2.01591i) q^{50} +(-5.70851 - 1.85481i) q^{51} +(-2.34038 + 4.59325i) q^{52} +(-1.45955 - 0.231169i) q^{53} +2.61609 q^{54} +(-7.38037 - 0.728107i) q^{55} +5.35716 q^{56} +(4.61316 + 0.730652i) q^{57} +(0.586323 - 1.15072i) q^{58} +(-1.52672 - 0.496061i) q^{59} +(-4.17052 + 1.65750i) q^{60} +(-4.07810 + 5.61302i) q^{61} +(2.93294 - 1.49441i) q^{62} +(-4.42234 - 2.25330i) q^{63} +(-1.66445 - 2.29092i) q^{64} +(3.49920 - 5.52974i) q^{65} +(-0.579695 + 1.75194i) q^{66} +(1.31471 - 1.31471i) q^{67} +(-1.45170 + 9.16564i) q^{68} +(-3.24948 + 1.05582i) q^{69} +(-3.17086 - 0.295576i) q^{70} +(-2.32441 - 1.68878i) q^{71} +(-0.489036 - 3.08765i) q^{72} +(6.71992 + 13.1886i) q^{73} +(-0.175544 - 0.540270i) q^{74} +(5.46646 - 1.60358i) q^{75} -7.22113i q^{76} +(6.87635 - 6.80264i) q^{77} +(-1.15138 - 1.15138i) q^{78} +(12.3342 - 8.96129i) q^{79} +(2.99564 + 5.05035i) q^{80} +(0.308439 - 0.949277i) q^{81} +(-1.71486 + 0.271606i) q^{82} +(6.60041 - 1.04540i) q^{83} +(1.80876 - 5.56680i) q^{84} +(2.91469 - 11.4136i) q^{85} +(-2.83434 + 2.05927i) q^{86} +(-2.13066 - 2.13066i) q^{87} +(6.01208 + 0.985459i) q^{88} +11.1726i q^{89} +(0.119098 + 1.85454i) q^{90} +(2.63744 + 8.11720i) q^{91} +(2.39818 + 4.70669i) q^{92} +(-1.20142 - 7.58545i) q^{93} +(-1.45454 - 1.05679i) q^{94} +(-0.850775 + 9.12689i) q^{95} +(5.37052 - 1.74499i) q^{96} +(-1.57505 + 9.94447i) q^{97} +(0.519848 - 0.519848i) q^{98} +(-4.54848 - 3.34226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 4 q^{3} - 2 q^{5} - 20 q^{6} - 10 q^{8} - 24 q^{11} + 12 q^{12} - 10 q^{13} + 14 q^{15} - 8 q^{16} - 10 q^{18} + 16 q^{20} + 10 q^{22} - 24 q^{23} + 16 q^{25} + 20 q^{26} - 16 q^{27} + 50 q^{28}+ \cdots - 8 q^{97}+O(q^{100}) $ 32 * q - 10 * q^2 - 4 * q^3 - 2 * q^5 - 20 * q^6 - 10 * q^8 - 24 * q^11 + 12 * q^12 - 10 * q^13 + 14 * q^15 - 8 * q^16 - 10 * q^18 + 16 * q^20 + 10 * q^22 - 24 * q^23 + 16 * q^25 + 20 * q^26 - 16 * q^27 + 50 * q^28 + 30 * q^30 - 28 * q^31 + 66 * q^33 - 10 * q^35 + 24 * q^36 - 8 * q^37 + 10 * q^38 - 50 * q^40 + 40 * q^41 - 10 * q^42 - 28 * q^45 + 60 * q^46 - 28 * q^47 - 54 * q^48 - 50 * q^50 + 20 * q^51 - 50 * q^52 - 24 * q^53 - 64 * q^55 - 80 * q^56 + 30 * q^57 - 50 * q^58 + 34 * q^60 - 60 * q^61 + 100 * q^62 - 30 * q^63 - 100 * q^66 - 8 * q^67 - 30 * q^68 + 30 * q^70 + 24 * q^71 + 80 * q^72 + 50 * q^73 + 34 * q^75 + 70 * q^77 + 60 * q^78 + 98 * q^80 - 12 * q^81 - 10 * q^82 + 90 * q^83 + 30 * q^85 + 100 * q^86 + 170 * q^88 - 20 * q^90 + 20 * q^91 - 68 * q^92 - 8 * q^93 - 40 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.482327	+	0.0763931i	0.341057	+	0.0540181i	0.324614	−	0.945847i	$-0.394766\pi$
$2$	0.482327	+	0.0763931i	0.341057	+	0.0540181i	0.0164432	+	0.999865i	$0.494766\pi$
$3$	0.517260	−	1.01518i	0.298640	−	0.586114i	−0.692114	−	0.721789i	$-0.743320\pi$
$3$	0.517260	−	1.01518i	0.298640	−	0.586114i	0.990753	+	0.135675i	$0.0433202\pi$
$4$	−1.67531	−	0.544341i	−0.837655	−	0.272170i
$5$	2.05331	+	0.885381i	0.918270	+	0.395954i
$5$	2.05331	+	0.885381i	0.918270	+	0.395954i
$6$	0.327041	−	0.450133i	0.133514	−	0.183766i
$7$	−2.59854	+	1.32402i	−0.982157	+	0.500434i	−0.869891	−	0.493244i	$-0.835811\pi$
$7$	−2.59854	+	1.32402i	−0.982157	+	0.500434i	−0.112266	+	0.993678i	$0.535811\pi$
$8$	−1.63669	−	0.833936i	−0.578658	−	0.294841i
$9$	1.00032	+	1.37683i	0.333442	+	0.458943i
$10$	0.922733	+	0.583903i	0.291794	+	0.184646i
$11$	−3.15977	+	1.00788i	−0.952708	+	0.303888i
$11$	−3.15977	+	1.00788i	−0.952708	+	0.303888i
$12$	−1.41917	+	1.41917i	−0.409680	+	0.409680i
$13$	0.457808	−	2.89049i	0.126973	−	0.801677i	−0.839208	−	0.543811i	$-0.816981\pi$
$13$	0.457808	−	2.89049i	0.126973	−	0.801677i	0.966181	−	0.257866i	$-0.0830192\pi$
$14$	−1.35449	+	0.440102i	−0.362004	+	0.117622i
$15$	1.96092	−	1.62651i	0.506306	−	0.419963i
$16$	2.12449	+	1.54353i	0.531123	+	0.385884i
$17$	−0.824113	−	5.20325i	−0.199877	−	1.26197i	−0.859797	−	0.510636i	$-0.829410\pi$
$17$	−0.824113	−	5.20325i	−0.199877	−	1.26197i	0.659920	−	0.751336i	$-0.270590\pi$
$18$	0.377304	+	0.740500i	0.0889313	+	0.174538i
$19$	1.26677	+	3.89873i	0.290618	+	0.894429i	0.984658	+	0.174494i	$0.0558288\pi$
$19$	1.26677	+	3.89873i	0.290618	+	0.894429i	−0.694041	+	0.719936i	$0.744171\pi$
$20$	−2.95799	−	2.60099i	−0.661426	−	0.581599i
$21$			3.32285i			0.725105i
$22$	−1.60104	+	0.244743i	−0.341343	+	0.0521795i
$23$	−2.12046	−	2.12046i	−0.442147	−	0.442147i	0.450586	−	0.892733i	$-0.351215\pi$
$23$	−2.12046	−	2.12046i	−0.442147	−	0.442147i	−0.892733	+	0.450586i	$0.851215\pi$
$24$	−1.69319	+	1.23017i	−0.345621	+	0.251108i
$25$	3.43220	+	3.63593i	0.686440	+	0.727186i
$26$	0.441627	−	1.35919i	0.0866101	−	0.266558i
$27$	5.29116	−	0.838037i	1.01828	−	0.161280i
$28$	5.07408	−	0.803656i	0.958912	−	0.151877i
$29$	0.817241	−	2.51521i	0.151758	−	0.467063i	−0.846060	−	0.533088i	$-0.821032\pi$
$29$	0.817241	−	2.51521i	0.151758	−	0.467063i	0.997818	+	0.0660248i	$0.0210316\pi$
$30$	1.07006	−	0.634710i	0.195365	−	0.115882i
$31$	5.45328	−	3.96204i	0.979438	−	0.711603i	0.0218548	−	0.999761i	$-0.493043\pi$
$31$	5.45328	−	3.96204i	0.979438	−	0.711603i	0.957583	+	0.288158i	$0.0930429\pi$
$32$	3.50456	+	3.50456i	0.619524	+	0.619524i
$33$	−0.611244	+	3.72907i	−0.106404	+	0.649148i
$34$		−	2.57262i		−	0.441201i
$35$	−6.50789	+	0.417937i	−1.10003	+	0.0706442i
$36$	−0.926389	−	2.85113i	−0.154398	−	0.475189i
$37$	−0.528116	−	1.03649i	−0.0868218	−	0.170397i	0.843513	−	0.537109i	$-0.180484\pi$
$37$	−0.528116	−	1.03649i	−0.0868218	−	0.170397i	−0.930335	+	0.366712i	$0.880484\pi$
$38$	0.313163	+	1.97724i	0.0508018	+	0.320750i
$39$	−2.69755	−	1.95989i	−0.431954	−	0.313833i
$40$	−2.62229	−	3.16143i	−0.414621	−	0.499866i
$41$	−3.38136	+	1.09867i	−0.528080	+	0.171584i	−0.560909	−	0.827877i	$-0.689548\pi$
$41$	−3.38136	+	1.09867i	−0.528080	+	0.171584i	0.0328289	+	0.999461i	$0.489548\pi$
$42$	−0.253843	+	1.60270i	−0.0391688	+	0.247302i
$43$	−5.07292	+	5.07292i	−0.773613	+	0.773613i	−0.978736	−	0.205123i	$-0.934241\pi$
$43$	−5.07292	+	5.07292i	−0.773613	+	0.773613i	0.205123	+	0.978736i	$0.434241\pi$
$44$	5.84223	+	0.0314826i	0.880749	+	0.00474618i
$45$	0.834964	+	3.71273i	0.124469	+	0.553461i
$46$	−0.860769	−	1.18475i	−0.126913	−	0.174681i
$47$	−3.28041	−	1.67145i	−0.478497	−	0.243806i	0.198070	−	0.980188i	$-0.436533\pi$
$47$	−3.28041	−	1.67145i	−0.478497	−	0.243806i	−0.676566	+	0.736382i	$0.736533\pi$
$48$	2.66588	−	1.35833i	0.384786	−	0.196058i
$49$	0.884888	−	1.21794i	0.126413	−	0.173992i
$50$	1.37768	+	2.01591i	0.194834	+	0.285092i
$51$	−5.70851	−	1.85481i	−0.799351	−	0.259725i
$52$	−2.34038	+	4.59325i	−0.324552	+	0.636970i
$53$	−1.45955	−	0.231169i	−0.200484	−	0.0317536i	0.0553847	−	0.998465i	$-0.482361\pi$
$53$	−1.45955	−	0.231169i	−0.200484	−	0.0317536i	−0.255869	+	0.966712i	$0.582361\pi$
$54$	2.61609			0.356005
$55$	−7.38037	−	0.728107i	−0.995169	−	0.0981780i
$56$	5.35716			0.715881
$57$	4.61316	+	0.730652i	0.611028	+	0.0967773i
$58$	0.586323	−	1.15072i	0.0769879	−	0.151097i
$59$	−1.52672	−	0.496061i	−0.198762	−	0.0645817i	0.207944	−	0.978141i	$-0.433323\pi$
$59$	−1.52672	−	0.496061i	−0.198762	−	0.0645817i	−0.406706	+	0.913559i	$0.633323\pi$
$60$	−4.17052	+	1.65750i	−0.538412	+	0.213982i
$61$	−4.07810	+	5.61302i	−0.522147	+	0.718674i	−0.985908	−	0.167286i	$-0.946500\pi$
$61$	−4.07810	+	5.61302i	−0.522147	+	0.718674i	0.463761	+	0.885960i	$0.346500\pi$
$62$	2.93294	−	1.49441i	0.372483	−	0.189790i
$63$	−4.42234	−	2.25330i	−0.557163	−	0.283889i
$64$	−1.66445	−	2.29092i	−0.208056	−	0.286365i
$65$	3.49920	−	5.52974i	0.434023	−	0.685880i
$66$	−0.579695	+	1.75194i	−0.0713556	+	0.215649i
$67$	1.31471	−	1.31471i	0.160617	−	0.160617i	−0.622223	−	0.782840i	$-0.713770\pi$
$67$	1.31471	−	1.31471i	0.160617	−	0.160617i	0.782840	+	0.622223i	$0.213770\pi$
$68$	−1.45170	+	9.16564i	−0.176044	+	1.11150i
$69$	−3.24948	+	1.05582i	−0.391192	+	0.127106i
$70$	−3.17086	−	0.295576i	−0.378990	−	0.0353281i
$71$	−2.32441	−	1.68878i	−0.275857	−	0.200422i	0.441251	−	0.897384i	$-0.354535\pi$
$71$	−2.32441	−	1.68878i	−0.275857	−	0.200422i	−0.717108	+	0.696962i	$0.754535\pi$
$72$	−0.489036	−	3.08765i	−0.0576334	−	0.363883i
$73$	6.71992	+	13.1886i	0.786507	+	1.54361i	0.838464	+	0.544957i	$0.183454\pi$
$73$	6.71992	+	13.1886i	0.786507	+	1.54361i	−0.0519568	+	0.998649i	$0.516546\pi$
$74$	−0.175544	−	0.540270i	−0.0204066	−	0.0628051i
$75$	5.46646	−	1.60358i	0.631212	−	0.185165i
$76$		−	7.22113i		−	0.828321i
$77$	6.87635	−	6.80264i	0.783633	−	0.775232i
$78$	−1.15138	−	1.15138i	−0.130368	−	0.130368i
$79$	12.3342	−	8.96129i	1.38770	−	1.00822i	0.391589	−	0.920140i	$-0.371926\pi$
$79$	12.3342	−	8.96129i	1.38770	−	1.00822i	0.996113	−	0.0880839i	$-0.0280744\pi$
$80$	2.99564	+	5.05035i	0.334922	+	0.564646i
$81$	0.308439	−	0.949277i	0.0342710	−	0.105475i
$82$	−1.71486	+	0.271606i	−0.189374	+	0.0299939i
$83$	6.60041	−	1.04540i	0.724489	−	0.114748i	0.216711	−	0.976236i	$-0.430467\pi$
$83$	6.60041	−	1.04540i	0.724489	−	0.114748i	0.507778	+	0.861488i	$0.330467\pi$
$84$	1.80876	−	5.56680i	0.197352	−	0.607388i
$85$	2.91469	−	11.4136i	0.316143	−	1.23797i
$86$	−2.83434	+	2.05927i	−0.305635	+	0.222057i
$87$	−2.13066	−	2.13066i	−0.228431	−	0.228431i
$88$	6.01208	+	0.985459i	0.640890	+	0.105050i
$89$			11.1726i			1.18429i	0.805830	+	0.592147i	$0.201719\pi$
$89$			11.1726i			1.18429i	−0.805830	+	0.592147i	$0.798281\pi$
$90$	0.119098	+	1.85454i	0.0125541	+	0.195485i
$91$	2.63744	+	8.11720i	0.276479	+	0.850914i
$92$	2.39818	+	4.70669i	0.250027	+	0.490706i
$93$	−1.20142	−	7.58545i	−0.124581	−	0.786575i
$94$	−1.45454	−	1.05679i	−0.150025	−	0.108999i
$95$	−0.850775	+	9.12689i	−0.0872876	+	0.936399i
$96$	5.37052	−	1.74499i	0.548126	−	0.178097i
$97$	−1.57505	+	9.94447i	−0.159922	+	1.00971i	0.768951	+	0.639308i	$0.220779\pi$
$97$	−1.57505	+	9.94447i	−0.159922	+	1.00971i	−0.928873	+	0.370400i	$0.879221\pi$
$98$	0.519848	−	0.519848i	0.0525126	−	0.0525126i
$99$	−4.54848	−	3.34226i	−0.457140	−	0.335910i
$100$	−3.77081	−	7.95960i	−0.377081	−	0.795960i
$101$	−1.12216	−	1.54452i	−0.111659	−	0.153686i	0.749530	−	0.661971i	$-0.230280\pi$
$101$	−1.12216	−	1.54452i	−0.111659	−	0.153686i	−0.861189	+	0.508285i	$0.830280\pi$
$102$	−2.61167	−	1.33071i	−0.258594	−	0.131760i
$103$	−5.49869	+	2.80172i	−0.541802	+	0.276062i	−0.703399	−	0.710795i	$-0.748335\pi$
$103$	−5.49869	+	2.80172i	−0.541802	+	0.276062i	0.161597	+	0.986857i	$0.448335\pi$
$104$	−3.15977	+	4.34905i	−0.309841	+	0.426459i
$105$	−2.94199	+	6.82286i	−0.287109	+	0.665842i
$106$	−0.686319	−	0.222999i	−0.0666612	−	0.0216595i
$107$	0.197726	−	0.388059i	0.0191149	−	0.0375151i	−0.881252	−	0.472647i	$-0.843298\pi$
$107$	0.197726	−	0.388059i	0.0191149	−	0.0375151i	0.900367	+	0.435132i	$0.143298\pi$
$108$	−9.32051	−	1.47622i	−0.896866	−	0.142050i
$109$	−9.46672			−0.906748			−0.453374	−	0.891320i	$-0.649780\pi$
$109$	−9.46672			−0.906748			−0.453374	+	0.891320i	$0.649780\pi$
$110$	−3.50413	−	0.914996i	−0.334106	−	0.0872414i
$111$	−1.32539			−0.125801
$112$	−7.56426	−	1.19806i	−0.714755	−	0.113206i
$113$	9.20080	−	18.0576i	0.865538	−	1.69871i	0.163539	−	0.986537i	$-0.447709\pi$
$113$	9.20080	−	18.0576i	0.865538	−	1.69871i	0.701999	−	0.712178i	$-0.252291\pi$
$114$	2.16923	+	0.704827i	0.203167	+	0.0660131i
$115$	−2.47656	−	6.23140i	−0.230941	−	0.581081i
$116$	−2.73826	+	3.76890i	−0.254241	+	0.349933i
$117$	4.43766	−	2.26110i	0.410262	−	0.209039i
$118$	−0.698483	−	0.355895i	−0.0643005	−	0.0327628i
$119$	9.03071	+	12.4297i	0.827844	+	1.13943i
$120$	−4.56582	+	1.02682i	−0.416800	+	0.0937351i
$121$	8.96835	−	6.36935i	0.815305	−	0.579032i
$122$	−2.39578	+	2.39578i	−0.216903	+	0.216903i
$123$	−0.633694	+	4.00099i	−0.0571383	+	0.360757i
$124$	−11.2926	+	3.66920i	−1.01411	+	0.329504i
$125$	3.82821	+	10.5045i	0.342405	+	0.939552i
$126$	−1.96088	−	1.42466i	−0.174689	−	0.126919i
$127$	1.47513	+	9.31359i	0.130896	+	0.826447i	0.962540	+	0.271138i	$0.0874000\pi$
$127$	1.47513	+	9.31359i	0.130896	+	0.826447i	−0.831644	+	0.555309i	$0.812600\pi$
$128$	−5.12793	−	10.0641i	−0.453249	−	0.889551i
$129$	2.52591	+	7.77394i	0.222394	+	0.684457i
$130$	2.11020	−	2.39983i	0.185076	−	0.210479i
$131$		−	7.51676i		−	0.656743i	−0.944549	−	0.328371i	$-0.893500\pi$
$131$		−	7.51676i		−	0.656743i	0.944549	−	0.328371i	$-0.106500\pi$
$132$	3.05391	−	5.91462i	0.265809	−	0.514802i
$133$	−8.45377	−	8.45377i	−0.733035	−	0.733035i
$134$	0.734554	−	0.533685i	0.0634558	−	0.0461034i
$135$	11.6064	+	2.96394i	0.998920	+	0.255095i
$136$	−2.99035	+	9.20336i	−0.256421	+	0.789182i
$137$	−15.1801	+	2.40429i	−1.29692	+	0.205413i	−0.766458	−	0.642294i	$-0.777983\pi$
$137$	−15.1801	+	2.40429i	−1.29692	+	0.205413i	−0.530466	+	0.847706i	$0.677983\pi$
$138$	−1.64797	+	0.261013i	−0.140285	+	0.0222189i
$139$	1.28625	−	3.95867i	0.109098	−	0.335770i	−0.881572	−	0.472049i	$-0.843514\pi$
$139$	1.28625	−	3.95867i	0.109098	−	0.335770i	0.990670	+	0.136279i	$0.0435145\pi$
$140$	11.1302	+	2.84234i	0.940676	+	0.240221i
$141$	−3.39364	+	2.46563i	−0.285796	+	0.207643i
$142$	−0.992116	−	0.992116i	−0.0832565	−	0.0832565i
$143$	1.46670	+	9.59470i	0.122651	+	0.802349i
$144$			4.46910i			0.372425i
$145$	3.90497	−	4.44095i	0.324290	−	0.368801i
$146$	2.23368	+	6.87457i	0.184861	+	0.568943i
$147$	−0.778714	−	1.52831i	−0.0642273	−	0.126053i
$148$	0.320556	+	2.02391i	0.0263495	+	0.166364i
$149$	−14.5440	−	10.5669i	−1.19149	−	0.865672i	−0.198073	−	0.980187i	$-0.563468\pi$
$149$	−14.5440	−	10.5669i	−1.19149	−	0.865672i	−0.993421	+	0.114516i	$0.963468\pi$
$150$	2.75912	−	0.355850i	0.225282	−	0.0290550i
$151$	16.9214	−	5.49808i	1.37704	−	0.447427i	0.475345	−	0.879800i	$-0.342323\pi$
$151$	16.9214	−	5.49808i	1.37704	−	0.447427i	0.901695	+	0.432372i	$0.142323\pi$
$152$	1.17797	−	7.43742i	0.0955461	−	0.603254i
$153$	6.33960	−	6.33960i	0.512526	−	0.512526i
$154$	3.83633	−	2.75579i	0.309140	−	0.222068i
$155$	14.7052	−	3.30708i	1.18115	−	0.265631i
$156$	3.45239	+	4.75181i	0.276413	+	0.380449i
$157$	−19.1253	−	9.74483i	−1.52636	−	0.777722i	−0.528887	−	0.848693i	$-0.677390\pi$
$157$	−19.1253	−	9.74483i	−1.52636	−	0.777722i	−0.997478	+	0.0709708i	$0.977390\pi$
$158$	6.63368	−	3.38003i	0.527748	−	0.268901i
$159$	−0.989642	+	1.36213i	−0.0784837	+	0.108024i
$160$	4.09309	+	10.2988i	0.323587	+	0.814193i
$161$	8.31766	+	2.70257i	0.655524	+	0.212993i
$162$	0.221287	−	0.434300i	0.0173859	−	0.0341218i
$163$	−10.2967	−	1.63083i	−0.806497	−	0.127737i	−0.260446	−	0.965488i	$-0.583870\pi$
$163$	−10.2967	−	1.63083i	−0.806497	−	0.127737i	−0.546051	+	0.837752i	$0.683870\pi$
$164$	6.26288			0.489049
$165$	−4.55673	+	7.11578i	−0.354741	+	0.553962i
$166$	3.26342			0.253290
$167$	11.1538	+	1.76660i	0.863110	+	0.136703i	0.572267	−	0.820067i	$-0.306064\pi$
$167$	11.1538	+	1.76660i	0.863110	+	0.136703i	0.290843	+	0.956771i	$0.406064\pi$
$168$	2.77104	−	5.43848i	0.213791	−	0.419588i
$169$	4.21842	+	1.37065i	0.324493	+	0.105434i
$170$	2.27775	−	5.28241i	0.174696	−	0.405142i
$171$	−4.10070	+	5.64412i	−0.313588	+	0.431617i
$172$	11.2601	−	5.73731i	0.858575	−	0.437466i
$173$	−11.7632	−	5.99367i	−0.894343	−	0.455691i	−0.0544963	−	0.998514i	$-0.517355\pi$
$173$	−11.7632	−	5.99367i	−0.894343	−	0.455691i	−0.839847	+	0.542823i	$0.817355\pi$
$174$	−0.864909	−	1.19044i	−0.0655686	−	0.0902474i
$175$	−13.7328	−	4.90381i	−1.03810	−	0.370693i
$176$	−8.26862	−	2.73598i	−0.623270	−	0.206233i
$177$	−1.29330	+	1.29330i	−0.0972104	+	0.0972104i
$178$	−0.853510	+	5.38885i	−0.0639733	+	0.403912i
$179$	2.11776	−	0.688100i	0.158288	−	0.0514310i	−0.228801	−	0.973473i	$-0.573480\pi$
$179$	2.11776	−	0.688100i	0.158288	−	0.0514310i	0.387089	+	0.922042i	$0.373480\pi$
$180$	0.622170	−	6.67448i	0.0463738	−	0.497486i
$181$	−3.50687	−	2.54789i	−0.260664	−	0.189383i	0.449776	−	0.893141i	$-0.351504\pi$
$181$	−3.50687	−	2.54789i	−0.260664	−	0.189383i	−0.710440	+	0.703758i	$0.751504\pi$
$182$	0.652010	+	4.11663i	0.0483302	+	0.305145i
$183$	3.58879	+	7.04339i	0.265291	+	0.520663i
$184$	1.70221	+	5.23888i	0.125489	+	0.386215i
$185$	−0.166703	−	2.59582i	−0.0122563	−	0.190848i
$186$		−	3.75045i		−	0.274996i
$187$	7.84826	+	15.6105i	0.573922	+	1.14155i
$188$	4.58586	+	4.58586i	0.334458	+	0.334458i
$189$	−12.6397	+	9.18329i	−0.919404	+	0.667986i
$190$	−1.10758	+	4.33716i	−0.0803526	+	0.314650i
$191$	−1.26010	+	3.87820i	−0.0911779	+	0.280617i	−0.986239	−	0.165327i	$-0.947132\pi$
$191$	−1.26010	+	3.87820i	−0.0911779	+	0.280617i	0.895061	+	0.445944i	$0.147132\pi$
$192$	−3.18664	+	0.504715i	−0.229976	+	0.0364247i
$193$	20.6434	−	3.26960i	1.48595	−	0.235351i	0.639899	−	0.768459i	$-0.278976\pi$
$193$	20.6434	−	3.26960i	1.48595	−	0.235351i	0.846047	+	0.533108i	$0.178976\pi$
$194$	−1.51938	+	4.67617i	−0.109085	+	0.335729i
$195$	−3.80368	−	6.41263i	−0.272387	−	0.459218i
$196$	−2.14544	+	1.55875i	−0.153246	+	0.111339i
$197$	−0.213782	−	0.213782i	−0.0152313	−	0.0152313i	0.699450	−	0.714681i	$-0.253428\pi$
$197$	−0.213782	−	0.213782i	−0.0152313	−	0.0152313i	−0.714681	+	0.699450i	$0.753428\pi$
$198$	−1.93853	−	1.95954i	−0.137765	−	0.139258i
$199$		−	11.0815i		−	0.785549i	−0.919635	−	0.392775i	$-0.871515\pi$
$199$		−	11.0815i		−	0.785549i	0.919635	−	0.392775i	$-0.128485\pi$
$200$	−2.58532	−	8.81313i	−0.182810	−	0.623182i
$201$	−0.654619	−	2.01471i	−0.0461733	−	0.142107i
$202$	−0.423258	−	0.830691i	−0.0297803	−	0.0584472i
$203$	1.20656	+	7.61793i	0.0846840	+	0.534674i
$204$	8.55387	+	6.21475i	0.598890	+	0.435119i
$205$	−7.91575	−	0.737876i	−0.552860	−	0.0515355i
$206$	−2.86620	+	0.931285i	−0.199698	+	0.0648857i
$207$	0.798364	−	5.04067i	0.0554901	−	0.350351i
$208$	5.43417	−	5.43417i	0.376792	−	0.376792i
$209$	−7.93217	−	11.0423i	−0.548680	−	0.763815i
$210$	−1.94022	+	3.06610i	−0.133888	+	0.211581i
$211$	−5.20512	−	7.16423i	−0.358335	−	0.493206i	0.591349	−	0.806416i	$-0.298596\pi$
$211$	−5.20512	−	7.16423i	−0.358335	−	0.493206i	−0.949684	+	0.313210i	$0.898596\pi$
$212$	2.31936	+	1.18177i	0.159294	+	0.0811644i
$213$	−2.91674	+	1.48615i	−0.199852	+	0.101830i
$214$	0.125014	−	0.172067i	0.00854576	−	0.0117622i
$215$	−14.9078	+	5.92483i	−1.01670	+	0.404070i
$216$	−9.35886	−	3.04088i	−0.636790	−	0.206906i
$217$	−8.92474	+	17.5158i	−0.605851	+	1.18905i
$218$	−4.56606	−	0.723193i	−0.309253	−	0.0489808i
$219$	16.8647			1.13961
$220$	11.9681	+	5.23724i	0.806887	+	0.353095i
$221$	−15.4172			−1.03707
$222$	−0.639273	−	0.101251i	−0.0429052	−	0.00679551i
$223$	−2.80667	+	5.50839i	−0.187948	+	0.368869i	−0.965683	−	0.259723i	$-0.916369\pi$
$223$	−2.80667	+	5.50839i	−0.187948	+	0.368869i	0.777735	+	0.628593i	$0.216369\pi$
$224$	−13.7469	−	4.46662i	−0.918500	−	0.298439i
$225$	−1.57274	+	8.36267i	−0.104849	+	0.557511i
$226$	5.81727	−	8.00679i	0.386959	−	0.532604i
$227$	−2.95522	+	1.50576i	−0.196145	+	0.0999406i	−0.549304	−	0.835622i	$-0.685107\pi$
$227$	−2.95522	+	1.50576i	−0.196145	+	0.0999406i	0.353160	+	0.935563i	$0.385107\pi$
$228$	−7.33074	−	3.73520i	−0.485490	−	0.247370i
$229$	3.13876	+	4.32013i	0.207415	+	0.285482i	0.900032	−	0.435823i	$-0.143543\pi$
$229$	3.13876	+	4.32013i	0.207415	+	0.285482i	−0.692618	+	0.721305i	$0.743543\pi$
$230$	−0.718477	−	3.19477i	−0.0473750	−	0.210657i
$231$	−3.34904	−	10.4995i	−0.220350	−	0.690813i
$232$	−3.43509	+	3.43509i	−0.225525	+	0.225525i
$233$	−0.691167	+	4.36386i	−0.0452799	+	0.285886i	−0.999930	−	0.0118446i	$-0.996230\pi$
$233$	−0.691167	+	4.36386i	−0.0452799	+	0.285886i	0.954650	+	0.297730i	$0.0962297\pi$
$234$	2.31314	−	0.751584i	0.151215	−	0.0491326i
$235$	−5.25584	−	6.33642i	−0.342853	−	0.413343i
$236$	2.28770	+	1.66211i	0.148917	+	0.108194i
$237$	−2.71735	−	17.1567i	−0.176511	−	1.11445i
$238$	3.40621	+	6.68507i	0.220792	+	0.433329i
$239$	−3.23012	−	9.94128i	−0.208939	−	0.643048i	−0.999529	−	0.0307017i	$-0.990226\pi$
$239$	−3.23012	−	9.94128i	−0.208939	−	0.643048i	0.790590	−	0.612346i	$-0.209774\pi$
$240$	6.67653	−	0.428767i	0.430968	−	0.0276768i
$241$			27.8579i			1.79449i	0.441536	+	0.897243i	$0.354434\pi$
$241$			27.8579i			1.79449i	−0.441536	+	0.897243i	$0.645566\pi$
$242$	4.81226	−	2.38699i	0.309344	−	0.153442i
$243$	10.5600	+	10.5600i	0.677425	+	0.677425i
$244$	9.88748	−	7.18367i	0.632981	−	0.459888i
$245$	2.89530	−	1.71736i	0.184974	−	0.109718i
$246$	−0.611296	+	1.88138i	−0.0389748	+	0.119952i
$247$	11.8492	−	1.87672i	0.753944	−	0.119413i
$248$	−12.2294	+	1.93695i	−0.776569	+	0.122996i
$249$	2.35285	−	7.24134i	0.149106	−	0.458901i
$250$	1.04398	+	5.35906i	0.0660268	+	0.338937i
$251$	8.04670	−	5.84627i	0.507903	−	0.369013i	−0.304124	−	0.952632i	$-0.598364\pi$
$251$	8.04670	−	5.84627i	0.507903	−	0.369013i	0.812028	+	0.583619i	$0.198364\pi$
$252$	6.18223	+	6.18223i	0.389444	+	0.389444i
$253$	8.83737	+	4.56302i	0.555601	+	0.286874i
$254$			4.60489i			0.288936i
$255$	−10.0791	−	8.86270i	−0.631181	−	0.555004i
$256$	0.0455968	+	0.140332i	0.00284980	+	0.00877078i
$257$	−1.92513	−	3.77828i	−0.120086	−	0.235683i	0.823136	−	0.567844i	$-0.192222\pi$
$257$	−1.92513	−	3.77828i	−0.120086	−	0.235683i	−0.943223	+	0.332161i	$0.892222\pi$
$258$	0.624438	+	3.94254i	0.0388758	+	0.245452i
$259$	2.74467	+	1.99412i	0.170545	+	0.123908i
$260$	−8.87232	+	7.35927i	−0.550238	+	0.456402i
$261$	4.28052	−	1.39083i	0.264958	−	0.0860899i
$262$	0.574229	−	3.62554i	0.0354760	−	0.223987i
$263$	−16.1830	+	16.1830i	−0.997884	+	0.997884i	−0.999998	−	0.00211364i	$-0.999327\pi$
$263$	−16.1830	+	16.1830i	−0.997884	+	0.997884i	0.00211364	+	0.999998i	$0.499327\pi$
$264$	4.11022	−	5.59360i	0.252967	−	0.344262i
$265$	−2.79223	−	1.76692i	−0.171526	−	0.108541i
$266$	−3.43167	−	4.72330i	−0.210409	−	0.289604i
$267$	11.3422	+	5.77914i	0.694131	+	0.353677i
$268$	−2.91819	+	1.48689i	−0.178257	+	0.0908265i
$269$	13.4435	−	18.5034i	0.819666	−	1.12817i	−0.170094	−	0.985428i	$-0.554407\pi$
$269$	13.4435	−	18.5034i	0.819666	−	1.12817i	0.989759	−	0.142745i	$-0.0455930\pi$
$270$	5.37166	+	2.31624i	0.326909	+	0.140962i
$271$	−1.32229	−	0.429640i	−0.0803237	−	0.0260987i	0.268580	−	0.963258i	$-0.413446\pi$
$271$	−1.32229	−	0.429640i	−0.0803237	−	0.0260987i	−0.348903	+	0.937159i	$0.613446\pi$
$272$	6.28057	−	12.3263i	0.380815	−	0.747392i
$273$	9.60465	+	1.52123i	0.581300	+	0.0920688i
$274$	−7.50545			−0.453421
$275$	−14.5096	−	8.02947i	−0.874960	−	0.484195i
$276$	6.01861			0.362278
$277$	14.0803	+	2.23010i	0.846002	+	0.133994i	0.564363	−	0.825527i	$-0.309122\pi$
$277$	14.0803	+	2.23010i	0.846002	+	0.133994i	0.281639	+	0.959520i	$0.409122\pi$
$278$	0.922808	−	1.81111i	0.0553464	−	0.108623i
$279$	10.9101	+	3.54491i	0.653171	+	0.212228i
$280$	10.9999	+	4.74313i	0.657372	+	0.283456i
$281$	14.9161	−	20.5302i	0.889818	−	1.22473i	−0.0837853	−	0.996484i	$-0.526701\pi$
$281$	14.9161	−	20.5302i	0.889818	−	1.22473i	0.973604	−	0.228246i	$-0.0732990\pi$
$282$	−1.82520	+	0.929988i	−0.108689	+	0.0553800i
$283$	6.60300	+	3.36440i	0.392508	+	0.199993i	0.639095	−	0.769128i	$-0.279309\pi$
$283$	6.60300	+	3.36440i	0.392508	+	0.199993i	−0.246587	+	0.969121i	$0.579309\pi$
$284$	2.97484	+	4.09451i	0.176524	+	0.242964i
$285$	8.82536	+	5.58466i	0.522769	+	0.330807i
$286$	−0.0255420	+	4.73983i	−0.00151033	+	0.280272i
$287$	7.33195	−	7.33195i	0.432791	−	0.432791i
$288$	−1.31948	+	8.33087i	−0.0777511	+	0.490901i
$289$	−10.2266	+	3.32284i	−0.601567	+	0.195461i
$290$	2.22273	−	1.84368i	0.130523	−	0.108264i
$291$	9.28071	+	6.74283i	0.544045	+	0.395272i
$292$	−4.07886	−	25.7529i	−0.238697	−	1.50707i
$293$	−6.66340	−	13.0777i	−0.389280	−	0.764005i	0.610324	−	0.792152i	$-0.291039\pi$
$293$	−6.66340	−	13.0777i	−0.389280	−	0.764005i	−0.999604	+	0.0281472i	$0.991039\pi$
$294$	−0.258843	−	0.796636i	−0.0150960	−	0.0464607i
$295$	−2.69563	−	2.37030i	−0.156946	−	0.138004i
$296$			2.13682i			0.124200i
$297$	−15.8742	+	7.98087i	−0.921116	+	0.463097i
$298$	−6.20775	−	6.20775i	−0.359606	−	0.359606i
$299$	−7.09994	+	5.15841i	−0.410600	+	0.298318i
$300$	−10.0309	−	0.289127i	−0.579134	−	0.0166928i
$301$	6.46553	−	19.8989i	0.372667	−	1.14695i
$302$	8.58165	−	1.35920i	0.493818	−	0.0782131i
$303$	−2.14842	+	0.340276i	−0.123423	+	0.0195483i
$304$	−3.32657	+	10.2381i	−0.190792	+	0.587197i
$305$	−13.3433	+	7.91463i	−0.764034	+	0.453191i
$306$	3.54206	−	2.57346i	0.202486	−	0.147115i
$307$	0.874954	+	0.874954i	0.0499363	+	0.0499363i	0.731634	−	0.681698i	$-0.238758\pi$
$307$	0.874954	+	0.874954i	0.0499363	+	0.0499363i	−0.681698	+	0.731634i	$0.738758\pi$
$308$	−15.2230	+	7.65344i	−0.867409	+	0.436095i
$309$			7.03137i			0.400001i
$310$	7.34536	−	0.471719i	0.417189	−	0.0267919i
$311$	4.37162	+	13.4545i	0.247892	+	0.762933i	0.995147	+	0.0983958i	$0.0313711\pi$
$311$	4.37162	+	13.4545i	0.247892	+	0.762933i	−0.747256	+	0.664537i	$0.768629\pi$
$312$	2.78064	+	5.45732i	0.157423	+	0.308960i
$313$	0.115706	+	0.730542i	0.00654011	+	0.0412927i	0.990743	−	0.135754i	$-0.0433457\pi$
$313$	0.115706	+	0.730542i	0.00654011	+	0.0412927i	−0.984202	+	0.177047i	$0.943346\pi$
$314$	−8.48022	−	6.16124i	−0.478566	−	0.347699i
$315$	−7.08543	−	8.54218i	−0.399219	−	0.481297i
$316$	−25.5415	+	8.29895i	−1.43682	+	0.466852i
$317$	−2.66972	+	16.8560i	−0.149947	+	0.946726i	0.791892	+	0.610661i	$0.209096\pi$
$317$	−2.66972	+	16.8560i	−0.149947	+	0.946726i	−0.941839	+	0.336065i	$0.890904\pi$
$318$	−0.581389	+	0.581389i	−0.0326027	+	0.0326027i
$319$	−0.0472661	+	8.77118i	−0.00264640	+	0.491092i
$320$	−1.38930	−	6.17765i	−0.0776644	−	0.345341i
$321$	−0.291674	−	0.401454i	−0.0162796	−	0.0224070i
$322$	3.80538	+	1.93894i	0.212065	+	0.108053i
$323$	19.2421	−	9.80433i	1.07066	−	0.545527i
$324$	−1.03346	+	1.42244i	−0.0574145	+	0.0790243i
$325$	12.0809	−	8.25617i	0.670128	−	0.457970i
$326$	−4.84178	−	1.57319i	−0.268161	−	0.0871309i
$327$	−4.89675	+	9.61042i	−0.270791	+	0.531457i
$328$	6.45047	+	1.02165i	0.356168	+	0.0564114i
$329$	10.7373			0.591967
$330$	−2.74143	+	3.08403i	−0.150911	+	0.169770i
$331$	−14.9189			−0.820016			−0.410008	−	0.912082i	$-0.634474\pi$
$331$	−14.9189			−0.820016			−0.410008	+	0.912082i	$0.634474\pi$
$332$	−11.6268	−	1.84150i	−0.638102	−	0.101065i
$333$	0.898777	−	1.76395i	0.0492527	−	0.0966638i
$334$	5.24485	+	1.70415i	0.286985	+	0.0932472i
$335$	3.86353	−	1.53549i	0.211087	−	0.0838929i
$336$	−5.12893	+	7.05937i	−0.279806	+	0.385120i
$337$	−8.40891	+	4.28455i	−0.458062	+	0.233394i	−0.667767	−	0.744370i	$-0.732750\pi$
$337$	−8.40891	+	4.28455i	−0.458062	+	0.233394i	0.209705	+	0.977765i	$0.432750\pi$
$338$	1.92995	+	0.983358i	0.104975	+	0.0534876i
$339$	−13.5725	−	18.6809i	−0.737156	−	1.01461i
$340$	−11.0959	+	17.5346i	−0.601758	+	0.950950i
$341$	−13.2379	+	18.0154i	−0.716871	+	0.975589i
$342$	−2.40905	+	2.40905i	−0.130267	+	0.130267i
$343$	2.50676	−	15.8271i	0.135352	−	0.854581i
$344$	12.5333	−	4.07231i	0.675750	−	0.219564i
$345$	−7.60701	−	0.709097i	−0.409548	−	0.0381765i
$346$	−5.21586	−	3.78954i	−0.280406	−	0.203727i
$347$	3.00971	+	19.0026i	0.161570	+	1.02011i	0.926581	+	0.376094i	$0.122733\pi$
$347$	3.00971	+	19.0026i	0.161570	+	1.02011i	−0.765012	+	0.644016i	$0.777267\pi$
$348$	2.40971	+	4.72933i	0.129174	+	0.253518i
$349$	4.59599	+	14.1450i	0.246018	+	0.757164i	0.995467	+	0.0951031i	$0.0303181\pi$
$349$	4.59599	+	14.1450i	0.246018	+	0.757164i	−0.749450	+	0.662061i	$0.769682\pi$
$350$	−6.24908	−	3.41433i	−0.334027	−	0.182504i
$351$		−	15.6777i		−	0.836813i
$352$	−14.6058	−	7.54143i	−0.778491	−	0.401960i
$353$	1.78406	+	1.78406i	0.0949560	+	0.0949560i	0.752989	−	0.658033i	$-0.228611\pi$
$353$	1.78406	+	1.78406i	0.0949560	+	0.0949560i	−0.658033	+	0.752989i	$0.728611\pi$
$354$	−0.722594	+	0.524995i	−0.0384054	+	0.0279032i
$355$	−3.27753	−	5.52560i	−0.173953	−	0.293268i
$356$	6.08171	−	18.7176i	0.322330	−	0.992029i
$357$	17.2896	−	2.73840i	0.915063	−	0.144932i
$358$	1.07402	−	0.170108i	0.0567636	−	0.00899047i
$359$	−2.62416	+	8.07635i	−0.138498	+	0.426253i	−0.996118	−	0.0880312i	$-0.971942\pi$
$359$	−2.62416	+	8.07635i	−0.138498	+	0.426253i	0.857620	+	0.514285i	$0.171942\pi$
$360$	1.72960	−	6.77290i	0.0911580	−	0.356963i
$361$	1.77596	−	1.29031i	0.0934717	−	0.0679111i
$362$	−1.49682	−	1.49682i	−0.0786711	−	0.0786711i
$363$	−1.82707	−	12.3991i	−0.0958962	−	0.650783i
$364$		−	15.0345i		−	0.788021i
$365$	2.12119	+	33.0300i	0.111028	+	1.72887i
$366$	1.19290	+	3.67138i	0.0623541	+	0.191906i
$367$	−9.63799	−	18.9156i	−0.503099	−	0.987387i	−0.993277	−	0.115765i	$-0.963068\pi$
$367$	−9.63799	−	18.9156i	−0.503099	−	0.987387i	0.490178	−	0.871622i	$-0.336932\pi$
$368$	−1.23190	−	7.77792i	−0.0642173	−	0.405452i
$369$	−4.89515	−	3.55653i	−0.254831	−	0.185146i
$370$	0.117897	−	1.26477i	0.00612917	−	0.0657522i
$371$	4.09877	−	1.33177i	0.212797	−	0.0691420i
$372$	−2.11633	+	13.3620i	−0.109726	+	0.692786i
$373$	−2.57445	+	2.57445i	−0.133300	+	0.133300i	−0.770609	−	0.637309i	$-0.780048\pi$
$373$	−2.57445	+	2.57445i	−0.133300	+	0.133300i	0.637309	+	0.770609i	$0.280048\pi$
$374$	2.59290	+	8.12891i	0.134076	+	0.420336i
$375$	12.6441	+	1.54725i	0.652940	+	0.0798995i
$376$	3.97513	+	5.47130i	0.205002	+	0.282161i
$377$	−6.89604	−	3.51371i	−0.355164	−	0.180965i
$378$	−6.79802	+	3.46377i	−0.349653	+	0.178157i
$379$	−9.74713	+	13.4158i	−0.500677	+	0.689122i	−0.982312	−	0.187249i	$-0.940043\pi$
$379$	−9.74713	+	13.4158i	−0.500677	+	0.689122i	0.481636	+	0.876371i	$0.340043\pi$
$380$	6.39345	−	14.8273i	0.327977	−	0.760622i
$381$	10.2180	+	3.32002i	0.523483	+	0.170090i
$382$	−0.904051	+	1.77430i	−0.0462553	+	0.0907810i
$383$	11.2007	+	1.77402i	0.572330	+	0.0906481i	0.435890	−	0.900000i	$-0.356434\pi$
$383$	11.2007	+	1.77402i	0.572330	+	0.0906481i	0.136440	+	0.990648i	$0.456434\pi$
$384$	−12.8694			−0.656736
$385$	20.1422	−	7.87977i	1.02654	−	0.401590i
$386$	10.2067			0.519505
$387$	−12.0591	−	1.90998i	−0.612999	−	0.0970895i
$388$	8.05188	−	15.8027i	0.408772	−	0.802260i
$389$	0.777554	+	0.252643i	0.0394236	+	0.0128095i	0.328662	−	0.944447i	$-0.393402\pi$
$389$	0.777554	+	0.252643i	0.0394236	+	0.0128095i	−0.289239	+	0.957257i	$0.593402\pi$
$390$	−1.34474	−	3.38356i	−0.0680935	−	0.171333i
$391$	−9.28580	+	12.7808i	−0.469603	+	0.646353i
$392$	−2.46398	+	1.25546i	−0.124450	+	0.0634102i
$393$	−7.63086	−	3.88812i	−0.384926	−	0.196130i
$394$	−0.0867814	−	0.119444i	−0.00437198	−	0.00601752i
$395$	33.2601	−	7.47992i	1.67350	−	0.376356i
$396$	5.80078	+	8.07525i	0.291500	+	0.405796i
$397$	11.8504	−	11.8504i	0.594752	−	0.594752i	−0.344159	−	0.938911i	$-0.611836\pi$
$397$	11.8504	−	11.8504i	0.594752	−	0.594752i	0.938911	+	0.344159i	$0.111836\pi$
$398$	0.846553	−	5.34493i	0.0424339	−	0.267917i
$399$	−12.9549	+	4.20930i	−0.648555	+	0.210728i
$400$	1.67950	+	13.0222i	0.0839751	+	0.651111i
$401$	23.0228	+	16.7270i	1.14970	+	0.835308i	0.988441	−	0.151603i	$-0.0484436\pi$
$401$	23.0228	+	16.7270i	1.14970	+	0.835308i	0.161262	+	0.986912i	$0.448444\pi$
$402$	−0.161831	−	1.02176i	−0.00807137	−	0.0509607i
$403$	−8.95566	−	17.5765i	−0.446113	−	0.875547i
$404$	1.03922	+	3.19839i	0.0517032	+	0.159126i
$405$	1.47379	−	1.67608i	0.0732334	−	0.0832850i
$406$			3.76651i			0.186929i
$407$	2.71338	+	2.74279i	0.134497	+	0.135955i
$408$	7.79627	+	7.79627i	0.385973	+	0.385973i
$409$	1.95998	−	1.42401i	0.0969146	−	0.0704126i	−0.538273	−	0.842771i	$-0.680923\pi$
$409$	1.95998	−	1.42401i	0.0969146	−	0.0704126i	0.635187	+	0.772358i	$0.280923\pi$
$410$	−3.76161	−	0.960607i	−0.185773	−	0.0474410i
$411$	−5.41127	+	16.6542i	−0.266918	+	0.821490i
$412$	10.7371	−	1.70059i	0.528979	−	0.0837820i
$413$	4.62404	−	0.732376i	0.227534	−	0.0360379i
$414$	0.770145	−	2.37026i	0.0378506	−	0.116492i
$415$	14.4783	+	3.69733i	0.710711	+	0.181495i
$416$	11.7343	−	8.52546i	0.575321	−	0.417995i
$417$	−3.35343	−	3.35343i	−0.164218	−	0.164218i
$418$	−2.98234	−	5.93199i	−0.145871	−	0.290143i
$419$			16.4371i			0.803006i	0.915858	+	0.401503i	$0.131512\pi$
$419$			16.4371i			0.803006i	−0.915858	+	0.401503i	$0.868488\pi$
$420$	8.64270	−	9.82895i	0.421720	−	0.479604i
$421$	−3.85294	−	11.8581i	−0.187781	−	0.577930i	0.812204	−	0.583373i	$-0.198267\pi$
$421$	−3.85294	−	11.8581i	−0.187781	−	0.577930i	−0.999985	+	0.00544310i	$0.998267\pi$
$422$	−1.96327	−	3.85314i	−0.0955707	−	0.187568i
$423$	−0.980171	−	6.18855i	−0.0476575	−	0.300898i
$424$	2.19605	+	1.59552i	0.106649	+	0.0774853i
$425$	16.0901	−	20.8550i	0.780485	−	1.01162i
$426$	−1.52036	+	0.493994i	−0.0736615	+	0.0239341i
$427$	3.16534	−	19.9852i	0.153182	−	0.967151i
$428$	−0.542488	+	0.542488i	−0.0262222	+	0.0262222i
$429$	10.4990	+	3.47399i	0.506896	+	0.167726i
$430$	−7.64304	+	1.71886i	−0.368580	+	0.0828907i
$431$	−11.6588	−	16.0470i	−0.561586	−	0.772957i	0.429941	−	0.902857i	$-0.358534\pi$
$431$	−11.6588	−	16.0470i	−0.561586	−	0.772957i	−0.991527	+	0.129900i	$0.958534\pi$
$432$	12.5346	+	6.38668i	0.603070	+	0.307279i
$433$	−25.5054	+	12.9956i	−1.22571	+	0.624531i	−0.942397	−	0.334496i	$-0.891434\pi$
$433$	−25.5054	+	12.9956i	−1.22571	+	0.624531i	−0.283314	+	0.959027i	$0.591434\pi$
$434$	−5.64273	+	7.76656i	−0.270860	+	0.372807i
$435$	−2.48847	−	6.26137i	−0.119313	−	0.300210i
$436$	15.8597	+	5.15313i	0.759541	+	0.246790i
$437$	5.58097	−	10.9533i	0.266974	−	0.523966i
$438$	8.13431	+	1.28835i	0.388672	+	0.0615597i
$439$	3.12279			0.149043			0.0745214	−	0.997219i	$-0.476257\pi$
$439$	3.12279			0.149043			0.0745214	+	0.997219i	$0.476257\pi$
$440$	11.4722	+	7.34644i	0.546915	+	0.350228i
$441$	2.56208			0.122004
$442$	−7.43613	−	1.17777i	−0.353701	−	0.0560207i
$443$	−14.4087	+	28.2787i	−0.684579	+	1.34356i	0.243033	+	0.970018i	$0.421858\pi$
$443$	−14.4087	+	28.2787i	−0.684579	+	1.34356i	−0.927612	+	0.373545i	$0.878142\pi$
$444$	2.22044	+	0.721465i	0.105378	+	0.0342392i
$445$	−9.89201	+	22.9409i	−0.468926	+	1.08750i
$446$	−1.77454	+	2.44244i	−0.0840267	+	0.115653i
$447$	−18.2503	+	9.29900i	−0.863210	+	0.439827i
$448$	7.35837	+	3.74928i	0.347650	+	0.177137i
$449$	−20.5693	−	28.3112i	−0.970726	−	1.33609i	−0.941679	−	0.336511i	$-0.890753\pi$
$449$	−20.5693	−	28.3112i	−0.970726	−	1.33609i	−0.0290462	−	0.999578i	$-0.509247\pi$
$450$	−1.39743	+	3.91340i	−0.0658753	+	0.184479i
$451$	9.57702	−	6.87957i	0.450964	−	0.323946i
$452$	−25.2437	+	25.2437i	−1.18736	+	1.18736i
$453$	3.17119	−	20.0221i	0.148996	−	0.940722i
$454$	−1.54041	+	0.500510i	−0.0722951	+	0.0234901i
$455$	−1.77132	+	19.0023i	−0.0830409	+	0.890842i
$456$	−6.94099	−	5.04293i	−0.325042	−	0.236157i
$457$	0.797826	+	5.03728i	0.0373207	+	0.235634i	0.999297	−	0.0375006i	$-0.0119396\pi$
$457$	0.797826	+	5.03728i	0.0373207	+	0.235634i	−0.961976	+	0.273134i	$0.911940\pi$
$458$	1.18388	+	2.32350i	0.0553191	+	0.108570i
$459$	−8.72103	−	26.8406i	−0.407063	−	1.25281i
$460$	0.757001	+	11.7876i	0.0352954	+	0.549600i
$461$			12.4703i			0.580801i	0.956905	+	0.290400i	$0.0937885\pi$
$461$			12.4703i			0.580801i	−0.956905	+	0.290400i	$0.906211\pi$
$462$	−0.813245	−	5.32002i	−0.0378356	−	0.247510i
$463$	−19.2728	−	19.2728i	−0.895684	−	0.895684i	0.0993669	−	0.995051i	$-0.468318\pi$
$463$	−19.2728	−	19.2728i	−0.895684	−	0.895684i	−0.995051	+	0.0993669i	$0.968318\pi$
$464$	5.61854	−	4.08211i	0.260834	−	0.189507i
$465$	4.24913	−	16.6390i	0.197049	−	0.771617i
$466$	−0.666738	+	2.05201i	−0.0308860	+	0.0950574i
$467$	−39.2044	+	6.20937i	−1.81416	+	0.287335i	−0.968980	−	0.247141i	$-0.920509\pi$
$467$	−39.2044	+	6.20937i	−1.81416	+	0.287335i	−0.845184	+	0.534476i	$0.820509\pi$
$468$	−8.66527	+	1.37244i	−0.400552	+	0.0634412i
$469$	−1.67562	+	5.15703i	−0.0773730	+	0.238130i
$470$	−2.05097	−	3.45774i	−0.0946044	−	0.159494i
$471$	−19.7855	+	14.3750i	−0.911667	+	0.662365i
$472$	2.08508	+	2.08508i	0.0959738	+	0.0959738i
$473$	10.9164	−	21.1422i	0.501936	−	0.972119i
$474$		−	8.48273i		−	0.389625i
$475$	−9.82768	+	17.9871i	−0.450925	+	0.825306i
$476$	−8.36324	−	25.7394i	−0.383328	−	1.17976i
$477$	−1.14174	−	2.24079i	−0.0522767	−	0.102599i
$478$	−0.798528	−	5.04171i	−0.0365238	−	0.230602i
$479$	30.9491	+	22.4858i	1.41410	+	1.02740i	0.992711	+	0.120523i	$0.0384570\pi$
$479$	30.9491	+	22.4858i	1.41410	+	1.02740i	0.421388	+	0.906880i	$0.361543\pi$
$480$	12.5723	+	1.17195i	0.573846	+	0.0534918i
$481$	−3.23773	+	1.05200i	−0.147628	+	0.0479671i
$482$	−2.12815	+	13.4366i	−0.0969348	+	0.612022i
$483$	7.04599	−	7.04599i	0.320603	−	0.320603i
$484$	−18.4919	+	5.78879i	−0.840539	+	0.263127i
$485$	−12.0387	+	19.0246i	−0.546650	+	0.863863i
$486$	4.28667	+	5.90009i	0.194447	+	0.267634i
$487$	24.2169	+	12.3391i	1.09737	+	0.559139i	0.906384	−	0.422454i	$-0.138831\pi$
$487$	24.2169	+	12.3391i	1.09737	+	0.559139i	0.190987	+	0.981593i	$0.438831\pi$
$488$	11.3555	−	5.78591i	0.514039	−	0.261916i
$489$	−6.98164	+	9.60940i	−0.315720	+	0.434552i
$490$	1.52768	−	0.607148i	0.0690134	−	0.0274282i
$491$	3.77748	+	1.22738i	0.170475	+	0.0553907i	0.393011	−	0.919534i	$-0.371433\pi$
$491$	3.77748	+	1.22738i	0.170475	+	0.0553907i	−0.222536	+	0.974925i	$0.571433\pi$
$492$	3.23954	−	6.35795i	0.146050	−	0.286638i
$493$	−13.7608	−	2.17949i	−0.619753	−	0.0981593i
$494$	5.85854			0.263588
$495$	−6.38029	−	10.8899i	−0.286773	−	0.489462i
$496$	17.7010			0.794798
$497$	8.27608	+	1.31080i	0.371233	+	0.0587975i
$498$	1.68803	−	3.31295i	0.0756426	−	0.148457i
$499$	−6.11060	−	1.98546i	−0.273548	−	0.0888812i	0.169031	−	0.985611i	$-0.445936\pi$
$499$	−6.11060	−	1.98546i	−0.273548	−	0.0888812i	−0.442579	+	0.896730i	$0.645936\pi$
$500$	−0.695390	−	19.6822i	−0.0310988	−	0.880213i
$501$	7.56284	−	10.4094i	0.337883	−	0.465056i
$502$	4.32776	−	2.20510i	0.193157	−	0.0984186i
$503$	36.2878	+	18.4896i	1.61799	+	0.824409i	0.999246	+	0.0388190i	$0.0123596\pi$
$503$	36.2878	+	18.4896i	1.61799	+	0.824409i	0.618747	+	0.785590i	$0.287640\pi$
$504$	5.35890	+	7.37590i	0.238704	+	0.328549i
$505$	−0.936660	−	4.16493i	−0.0416808	−	0.185337i
$506$	3.91392	+	2.87598i	0.173995	+	0.127853i
$507$	3.57347	−	3.57347i	0.158703	−	0.158703i
$508$	2.59847	−	16.4061i	0.115289	−	0.727904i
$509$	8.83124	−	2.86944i	0.391438	−	0.127186i	−0.106684	−	0.994293i	$-0.534023\pi$
$509$	8.83124	−	2.86944i	0.391438	−	0.127186i	0.498122	+	0.867107i	$0.334023\pi$
$510$	−4.18440	−	5.04470i	−0.185288	−	0.223383i
$511$	−34.9240	−	25.3738i	−1.54495	−	1.12247i
$512$	3.54520	+	22.3835i	0.156677	+	0.989220i
$513$	9.96998	+	19.5672i	0.440185	+	0.863912i
$514$	−0.639909	−	1.96944i	−0.0282252	−	0.0868681i
$515$	−13.7711	+	0.884383i	−0.606828	+	0.0389706i
$516$		−	14.3987i		−	0.633868i
$517$	12.0500	+	1.97515i	0.529957	+	0.0868669i
$518$	1.17149	+	1.17149i	0.0514723	+	0.0514723i
$519$	−12.1693	+	8.84152i	−0.534173	+	0.388099i
$520$	−10.3386	+	6.13237i	−0.453376	+	0.268922i
$521$	−4.57564	+	14.0824i	−0.200462	+	0.616960i	0.799407	+	0.600790i	$0.205147\pi$
$521$	−4.57564	+	14.0824i	−0.200462	+	0.616960i	−0.999869	+	0.0161698i	$0.994853\pi$
$522$	2.17086	−	0.343831i	0.0950160	−	0.0150491i
$523$	−38.3651	+	6.07643i	−1.67759	+	0.265704i	−0.921390	−	0.388640i	$-0.872945\pi$
$523$	−38.3651	+	6.07643i	−1.67759	+	0.265704i	−0.756197	+	0.654344i	$0.772945\pi$
$524$	−4.09168	+	12.5929i	−0.178746	+	0.550124i
$525$	−12.0817	+	11.4047i	−0.527286	+	0.497741i
$526$	−9.04175	+	6.56922i	−0.394239	+	0.286431i
$527$	−25.1096	−	25.1096i	−1.09379	−	1.09379i
$528$	−7.05453	+	6.97891i	−0.307009	+	0.303718i
$529$		−	14.0073i		−	0.609011i
$530$	−1.21179	−	1.06554i	−0.0526368	−	0.0462841i
$531$	−0.844224	−	2.59825i	−0.0366362	−	0.112755i
$532$	9.56095	+	18.7644i	0.414520	+	0.813541i
$533$	1.62768	+	10.2768i	0.0705027	+	0.445136i
$534$	5.02916	+	3.65390i	0.217633	+	0.158120i
$535$	0.749573	−	0.621744i	0.0324069	−	0.0268804i
$536$	−3.24815	+	1.05539i	−0.140299	+	0.0455859i
$537$	0.396884	−	2.50583i	0.0171268	−	0.108134i
$538$	7.89771	−	7.89771i	0.340495	−	0.340495i
$539$	−1.56850	+	4.74029i	−0.0675603	+	0.204179i
$540$	−17.8309	−	11.2833i	−0.767320	−	0.485558i
$541$	10.2392	+	14.0930i	0.440217	+	0.605907i	0.970260	−	0.242064i	$-0.0778243\pi$
$541$	10.2392	+	14.0930i	0.440217	+	0.605907i	−0.530043	+	0.847971i	$0.677824\pi$
$542$	−0.604957	−	0.308241i	−0.0259851	−	0.0132401i
$543$	−4.40053	+	2.24218i	−0.188845	+	0.0962213i
$544$	15.3469	−	21.1232i	0.657994	−	0.905650i
$545$	−19.4382	−	8.38166i	−0.832639	−	0.359031i
$546$	4.51637	+	1.46746i	0.193283	+	0.0628014i
$547$	17.7994	−	34.9333i	0.761048	−	1.49364i	−0.105430	−	0.994427i	$-0.533622\pi$
$547$	17.7994	−	34.9333i	0.761048	−	1.49364i	0.866478	−	0.499215i	$-0.166378\pi$
$548$	26.7401	+	4.23522i	1.14228	+	0.180920i
$549$	−11.8076			−0.503936
$550$	−6.38496	−	4.98127i	−0.272256	−	0.212402i
$551$	10.8414			0.461858
$552$	6.19888	+	0.981807i	0.263842	+	0.0417885i
$553$	−20.1859	+	39.6170i	−0.858391	+	1.68469i
$554$	6.62094	+	2.15127i	0.281297	+	0.0913989i
$555$	−2.72145	−	1.17348i	−0.115519	−	0.0498113i
$556$	−4.30973	+	5.93184i	−0.182773	+	0.251566i
$557$	32.7010	−	16.6620i	1.38558	−	0.705991i	0.407307	−	0.913291i	$-0.366468\pi$
$557$	32.7010	−	16.6620i	1.38558	−	0.705991i	0.978277	+	0.207301i	$0.0664678\pi$
$558$	4.99143	+	2.54326i	0.211304	+	0.107665i
$559$	12.3408	+	16.9856i	0.521959	+	0.718416i
$560$	−14.4711	−	9.15725i	−0.611514	−	0.386964i
$561$	19.9070	+	0.107275i	0.840475	+	0.00452915i
$562$	8.76280	−	8.76280i	0.369636	−	0.369636i
$563$	−2.64077	+	16.6732i	−0.111295	+	0.702690i	0.867437	+	0.497547i	$0.165766\pi$
$563$	−2.64077	+	16.6732i	−0.111295	+	0.702690i	−0.978732	+	0.205143i	$0.934234\pi$
$564$	7.02754	−	2.28339i	0.295913	−	0.0961480i
$565$	34.8800	−	28.9317i	1.46741	−	1.21717i
$566$	2.92779	+	2.12716i	0.123064	+	0.0894114i
$567$	0.455374	+	2.87512i	0.0191239	+	0.120744i
$568$	2.39601	+	4.70243i	0.100534	+	0.197310i
$569$	0.818531	+	2.51918i	0.0343146	+	0.105609i	0.966747	−	0.255736i	$-0.0823176\pi$
$569$	0.818531	+	2.51918i	0.0343146	+	0.105609i	−0.932432	+	0.361345i	$0.882318\pi$
$570$	3.83008	+	3.36783i	0.160424	+	0.141063i
$571$		−	29.8675i		−	1.24992i	−0.780658	−	0.624959i	$-0.785116\pi$
$571$		−	29.8675i		−	1.24992i	0.780658	−	0.624959i	$-0.214884\pi$
$572$	2.76562	−	16.8725i	0.115636	−	0.705473i
$573$	3.28527	+	3.28527i	0.137244	+	0.137244i
$574$	4.09651	−	2.97629i	0.170985	−	0.124228i
$575$	0.432001	−	14.9877i	0.0180157	−	0.625031i
$576$	1.48921	−	4.58332i	0.0620505	−	0.190972i
$577$	−0.354477	+	0.0561437i	−0.0147571	+	0.00233729i	−0.163809	−	0.986492i	$-0.552378\pi$
$577$	−0.354477	+	0.0561437i	−0.0147571	+	0.00233729i	0.149052	+	0.988829i	$0.452378\pi$
$578$	−5.18643	+	0.821450i	−0.215727	+	0.0341678i
$579$	7.35878	−	22.6480i	0.305821	−	0.941219i
$580$	−8.95943	+	5.31432i	−0.372020	+	0.220665i
$581$	−15.7673	+	11.4556i	−0.654138	+	0.475259i
$582$	3.96123	+	3.96123i	0.164198	+	0.164198i
$583$	4.84483	−	0.740605i	0.200652	−	0.0306727i
$584$		−	27.1896i		−	1.12511i
$585$	11.1139	−	0.713732i	0.459501	−	0.0295092i
$586$	−2.21490	−	6.81675i	−0.0914965	−	0.281597i
$587$	11.7343	+	23.0298i	0.484326	+	0.950543i	0.995827	+	0.0912603i	$0.0290895\pi$
$587$	11.7343	+	23.0298i	0.484326	+	0.950543i	−0.511501	+	0.859282i	$0.670910\pi$
$588$	0.472664	+	2.98428i	0.0194923	+	0.123070i
$589$	22.3550	+	16.2418i	0.921121	+	0.669233i
$590$	−1.11910	−	1.34919i	−0.0460727	−	0.0555451i
$591$	−0.327608	+	0.106446i	−0.0134760	+	0.00437861i
$592$	0.477873	−	3.01717i	0.0196405	−	0.124005i
$593$	9.56872	−	9.56872i	0.392940	−	0.392940i	−0.482794	−	0.875734i	$-0.660378\pi$
$593$	9.56872	−	9.56872i	0.392940	−	0.392940i	0.875734	+	0.482794i	$0.160378\pi$
$594$	−8.26626	+	2.63671i	−0.339169	+	0.108185i
$595$	7.53787	+	33.5177i	0.309022	+	1.37409i
$596$	18.6138	+	25.6197i	0.762451	+	1.04942i
$597$	−11.2497	−	5.73203i	−0.460421	−	0.234596i
$598$	−3.81856	+	1.94565i	−0.156153	+	0.0795637i
$599$	6.65542	−	9.16040i	0.271933	−	0.374284i	−0.651108	−	0.758985i	$-0.725696\pi$
$599$	6.65542	−	9.16040i	0.271933	−	0.374284i	0.923041	+	0.384701i	$0.125696\pi$
$600$	−10.2842	−	1.93411i	−0.419850	−	0.0789598i
$601$	−15.6822	−	5.09545i	−0.639689	−	0.207848i	−0.0288267	−	0.999584i	$-0.509177\pi$
$601$	−15.6822	−	5.09545i	−0.639689	−	0.207848i	−0.610862	+	0.791737i	$0.709177\pi$
$602$	4.63864	−	9.10384i	0.189057	−	0.371045i
$603$	3.12526	+	0.494993i	0.127271	+	0.0201577i
$604$	−31.3413			−1.27526
$605$	24.0542	−	5.13788i	0.977940	−	0.208884i
$606$	−1.06223			−0.0431503
$607$	4.92298	+	0.779724i	0.199818	+	0.0316480i	0.255541	−	0.966798i	$-0.417746\pi$
$607$	4.92298	+	0.779724i	0.199818	+	0.0316480i	−0.0557232	+	0.998446i	$0.517746\pi$
$608$	−9.22383	+	18.1028i	−0.374076	+	0.734165i
$609$	8.35766	+	2.71557i	0.338670	+	0.110040i
$610$	−7.04046	+	2.79811i	−0.285060	+	0.113292i
$611$	−6.33310	+	8.71677i	−0.256210	+	0.352643i
$612$	−14.0717	+	7.16989i	−0.568814	+	0.289825i
$613$	16.2873	+	8.29879i	0.657837	+	0.335185i	0.750843	−	0.660481i	$-0.229648\pi$
$613$	16.2873	+	8.29879i	0.657837	+	0.335185i	−0.0930058	+	0.995666i	$0.529648\pi$
$614$	0.355174	+	0.488855i	0.0143337	+	0.0197286i
$615$	−4.84357	+	7.65423i	−0.195312	+	0.308648i
$616$	−16.9274	+	5.39938i	−0.682025	+	0.217547i
$617$	15.4942	−	15.4942i	0.623773	−	0.623773i	−0.322721	−	0.946494i	$-0.604598\pi$
$617$	15.4942	−	15.4942i	0.623773	−	0.623773i	0.946494	+	0.322721i	$0.104598\pi$
$618$	−0.537149	+	3.39142i	−0.0216073	+	0.136423i
$619$	46.8070	−	15.2085i	1.88133	−	0.611282i	0.895114	−	0.445837i	$-0.147094\pi$
$619$	46.8070	−	15.2085i	1.88133	−	0.611282i	0.986219	−	0.165445i	$-0.0529061\pi$
$620$	−26.4360	−	2.46426i	−1.06169	−	0.0989671i
$621$	−12.9967	−	9.44269i	−0.521541	−	0.378922i
$622$	1.08072	+	6.82342i	0.0433330	+	0.273594i
$623$	−14.7928	−	29.0325i	−0.592661	−	1.16316i
$624$	−2.70578	−	8.32754i	−0.108318	−	0.333368i
$625$	−1.43999	+	24.9585i	−0.0575995	+	0.998340i
$626$			0.361199i			0.0144364i
$627$	−15.3129	+	2.34082i	−0.611540	+	0.0934832i
$628$	26.7363	+	26.7363i	1.06689	+	1.06689i
$629$	−4.95787	+	3.60210i	−0.197683	+	0.143625i
$630$	−2.76493	−	4.66141i	−0.110158	−	0.185715i
$631$	−2.79731	+	8.60924i	−0.111359	+	0.342729i	−0.991170	−	0.132595i	$-0.957669\pi$
$631$	−2.79731	+	8.60924i	−0.111359	+	0.342729i	0.879811	+	0.475324i	$0.157669\pi$
$632$	−27.6604	+	4.38097i	−1.10027	+	0.174266i
$633$	−9.96538	+	1.57836i	−0.396088	+	0.0627342i
$634$	−2.57536	+	7.92615i	−0.102281	+	0.314788i
$635$	−5.21717	+	20.4298i	−0.207037	+	0.810731i
$636$	2.39942	−	1.74328i	0.0951431	−	0.0691255i
$637$	−3.11534	−	3.11534i	−0.123434	−	0.123434i
$638$	−0.692856	+	4.22697i	−0.0274304	+	0.167347i
$639$		−	4.88965i		−	0.193432i
$640$	−1.61866	−	25.2050i	−0.0639833	−	0.996314i
$641$	−8.63030	−	26.5613i	−0.340876	−	1.04911i	−0.963755	−	0.266791i	$-0.914037\pi$
$641$	−8.63030	−	26.5613i	−0.340876	−	1.04911i	0.622878	−	0.782319i	$-0.285963\pi$
$642$	−0.110014	−	0.215914i	−0.00434190	−	0.00852146i
$643$	−1.50637	−	9.51085i	−0.0594055	−	0.375071i	−0.999424	−	0.0339470i	$-0.989192\pi$
$643$	−1.50637	−	9.51085i	−0.0594055	−	0.375071i	0.940018	−	0.341124i	$-0.110808\pi$
$644$	−12.4635	−	9.05529i	−0.491132	−	0.356828i
$645$	−1.69642	+	18.1987i	−0.0667964	+	0.716574i
$646$	10.0300	−	3.25893i	0.394624	−	0.128221i
$647$	4.84185	−	30.5702i	0.190353	−	1.20184i	−0.688675	−	0.725070i	$-0.741807\pi$
$647$	4.84185	−	30.5702i	0.190353	−	1.20184i	0.879028	−	0.476770i	$-0.158193\pi$
$648$	−1.29645	+	1.29645i	−0.0509296	+	0.0509296i
$649$	5.32406	+	0.0286903i	0.208988	+	0.00112619i
$650$	6.45766	−	3.05928i	0.253290	−	0.119995i
$651$	13.1653	+	18.1204i	0.515987	+	0.710195i
$652$	16.3624	+	8.33705i	0.640800	+	0.326504i
$653$	−5.44440	+	2.77406i	−0.213056	+	0.108557i	−0.557262	−	0.830337i	$-0.688148\pi$
$653$	−5.44440	+	2.77406i	−0.213056	+	0.108557i	0.344206	+	0.938894i	$0.388148\pi$
$654$	−3.09601	+	4.26129i	−0.121063	+	0.166630i
$655$	6.65520	−	15.4343i	0.260040	−	0.603067i
$656$	−8.87952	−	2.88513i	−0.346687	−	0.112645i
$657$	−11.4363	+	22.4450i	−0.446173	+	0.875665i
$658$	5.17890	+	0.820257i	0.201895	+	0.0319770i
$659$	−12.0647			−0.469975			−0.234988	−	0.971998i	$-0.575505\pi$
$659$	−12.0647			−0.469975			−0.234988	+	0.971998i	$0.575505\pi$
$660$	11.5073	−	9.44071i	0.447922	−	0.367479i
$661$	−29.6228			−1.15219			−0.576097	−	0.817382i	$-0.695425\pi$
$661$	−29.6228			−1.15219			−0.576097	+	0.817382i	$0.695425\pi$
$662$	−7.19579	−	1.13970i	−0.279672	−	0.0442957i
$663$	−7.97469	+	15.6512i	−0.309711	+	0.607843i
$664$	−11.6746	−	3.79331i	−0.453063	−	0.147209i
$665$	−9.87344	−	24.8431i	−0.382876	−	0.963373i
$666$	0.568258	−	0.782140i	0.0220196	−	0.0303073i
$667$	−7.06635	+	3.60048i	−0.273610	+	0.139411i
$668$	−17.7245	−	9.03109i	−0.685782	−	0.349423i
$669$	4.14023	+	5.69854i	0.160071	+	0.220318i
$670$	1.98079	−	0.445463i	0.0765244	−	0.0172097i
$671$	7.22862	−	21.8461i	0.279058	−	0.843361i
$672$	−11.6451	+	11.6451i	−0.449220	+	0.449220i
$673$	0.787773	−	4.97380i	0.0303664	−	0.191726i	−0.967842	−	0.251559i	$-0.919057\pi$
$673$	0.787773	−	4.97380i	0.0303664	−	0.191726i	0.998208	+	0.0598329i	$0.0190568\pi$
$674$	−4.38316	+	1.42417i	−0.168833	+	0.0548571i
$675$	21.2074	+	16.3620i	0.816272	+	0.629773i
$676$	−6.32105	−	4.59251i	−0.243117	−	0.176635i
$677$	5.69516	+	35.9579i	0.218883	+	1.38197i	0.815180	+	0.579208i	$0.196638\pi$
$677$	5.69516	+	35.9579i	0.218883	+	1.38197i	−0.596297	+	0.802764i	$0.703362\pi$
$678$	−5.11928	−	10.0472i	−0.196605	−	0.385859i
$679$	−9.07388	−	27.9265i	−0.348223	−	1.07172i
$680$	−14.2886	+	16.2498i	−0.547944	+	0.623151i
$681$			3.77894i			0.144809i
$682$	−7.76124	+	7.67804i	−0.297193	+	0.294007i
$683$	−8.07353	−	8.07353i	−0.308925	−	0.308925i	0.535567	−	0.844492i	$-0.320098\pi$
$683$	−8.07353	−	8.07353i	−0.308925	−	0.308925i	−0.844492	+	0.535567i	$0.820098\pi$
$684$	9.94226	−	7.22348i	0.380152	−	0.276197i
$685$	−33.2983	−	8.50341i	−1.27226	−	0.324898i
$686$	2.41816	−	7.44232i	0.0923257	−	0.284149i
$687$	6.00926	−	0.951773i	0.229267	−	0.0363124i
$688$	−18.6076	+	2.94716i	−0.709408	+	0.112359i
$689$	−1.33638	+	4.11297i	−0.0509122	+	0.156692i
$690$	−3.61490	−	0.923140i	−0.137617	−	0.0351434i
$691$	9.61076	−	6.98263i	0.365611	−	0.265632i	−0.389778	−	0.920909i	$-0.627448\pi$
$691$	9.61076	−	6.98263i	0.365611	−	0.265632i	0.755388	+	0.655277i	$0.227448\pi$
$692$	16.4445	+	16.4445i	0.625125	+	0.625125i
$693$	16.2447	+	2.66271i	0.617083	+	0.101148i
$694$			9.39538i			0.356644i
$695$	6.14600	−	6.98957i	0.233131	−	0.265130i
$696$	1.71040	+	5.26407i	0.0648326	+	0.199534i
$697$	8.50329	+	16.6886i	0.322085	+	0.632127i
$698$	1.13619	+	7.17362i	0.0430054	+	0.271526i
$699$	4.07258	+	2.95891i	0.154039	+	0.111916i
$700$	20.3373	+	15.6907i	0.768678	+	0.593053i
$701$	−25.2475	+	8.20342i	−0.953586	+	0.309839i	−0.744172	−	0.667988i	$-0.767156\pi$
$701$	−25.2475	+	8.20342i	−0.953586	+	0.309839i	−0.209414	+	0.977827i	$0.567156\pi$
$702$	1.19767	−	7.56177i	0.0452030	−	0.285401i
$703$	3.37197	−	3.37197i	0.127176	−	0.127176i
$704$	7.56826	+	5.56122i	0.285239	+	0.209596i
$705$	−9.15124	+	2.05804i	−0.344655	+	0.0775102i
$706$	0.724212	+	0.996792i	0.0272561	+	0.0375148i
$707$	4.96097	+	2.52774i	0.186576	+	0.0950654i
$708$	2.87068	−	1.46268i	0.107887	−	0.0549710i
$709$	−10.4984	+	14.4498i	−0.394275	+	0.542673i	−0.959296	−	0.282404i	$-0.908868\pi$
$709$	−10.4984	+	14.4498i	−0.394275	+	0.542673i	0.565021	+	0.825077i	$0.308868\pi$
$710$	−1.15873	−	2.91553i	−0.0434862	−	0.109418i
$711$	24.6763	+	8.01783i	0.925435	+	0.300692i
$712$	9.31723	−	18.2861i	0.349178	−	0.685301i
$713$	−19.9648	−	3.16212i	−0.747689	−	0.118422i
$714$	8.54844			0.319917
$715$	−5.48338	+	20.9995i	−0.205067	+	0.785338i
$716$	−3.92246			−0.146589
$717$	−11.7630	−	1.86307i	−0.439297	−	0.0695778i
$718$	−1.88268	+	3.69497i	−0.0702611	+	0.137895i
$719$	−31.1609	−	10.1248i	−1.16211	−	0.377592i	−0.336416	−	0.941714i	$-0.609215\pi$
$719$	−31.1609	−	10.1248i	−1.16211	−	0.377592i	−0.825691	+	0.564122i	$0.809215\pi$
$720$	−3.95685	+	9.17647i	−0.147463	+	0.341987i
$721$	10.5790	−	14.5608i	0.393984	−	0.542272i
$722$	0.955166	−	0.486681i	0.0355476	−	0.0181124i
$723$	28.2808	+	14.4098i	1.05177	+	0.535905i
$724$	4.48818	+	6.17744i	0.166802	+	0.229583i
$725$	11.9501	−	5.66127i	0.443814	−	0.210254i
$726$	0.0659608	−	6.12000i	0.00244803	−	0.227134i
$727$	0.964903	−	0.964903i	0.0357863	−	0.0357863i	−0.688987	−	0.724773i	$-0.741944\pi$
$727$	0.964903	−	0.964903i	0.0357863	−	0.0357863i	0.724773	+	0.688987i	$0.241944\pi$
$728$	2.45255	−	15.4848i	0.0908976	−	0.573905i
$729$	19.0304	−	6.18335i	0.704830	−	0.229013i
$730$	−1.50016	+	16.0933i	−0.0555233	+	0.595640i
$731$	30.5763	+	22.2150i	1.13091	+	0.821651i
$732$	−2.17832	−	13.7534i	−0.0805131	−	0.508340i
$733$	−5.35405	−	10.5079i	−0.197756	−	0.388119i	0.770739	−	0.637151i	$-0.219887\pi$
$733$	−5.35405	−	10.5079i	−0.197756	−	0.388119i	−0.968495	+	0.249033i	$0.919887\pi$
$734$	−3.20364	−	9.85979i	−0.118249	−	0.363932i
$735$	−0.245806	−	3.82757i	−0.00906671	−	0.141182i
$736$		−	14.8626i		−	0.547842i
$737$	−2.82911	+	5.47925i	−0.104212	+	0.201831i
$738$	−2.08937	−	2.08937i	−0.0769107	−	0.0769107i
$739$	−34.8645	+	25.3305i	−1.28251	+	0.931798i	−0.999626	−	0.0273561i	$-0.991291\pi$
$739$	−34.8645	+	25.3305i	−1.28251	+	0.931798i	−0.282884	+	0.959154i	$0.591291\pi$
$740$	−1.13373	+	4.43954i	−0.0416767	+	0.163201i
$741$	4.22388	−	12.9998i	0.155168	−	0.477558i
$742$	2.07868	−	0.329231i	0.0763109	−	0.0120865i
$743$	37.4472	−	5.93105i	1.37380	−	0.217589i	0.574494	−	0.818509i	$-0.305199\pi$
$743$	37.4472	−	5.93105i	1.37380	−	0.217589i	0.799309	+	0.600920i	$0.205199\pi$
$744$	−4.35943	+	13.4170i	−0.159825	+	0.491889i
$745$	−20.5078	−	34.5741i	−0.751348	−	1.26670i
$746$	−1.43840	+	1.04506i	−0.0526636	+	0.0382623i
$747$	8.04189	+	8.04189i	0.294237	+	0.294237i
$748$	−4.65085	−	30.4245i	−0.170052	−	1.11243i
$749$			1.27018i			0.0464114i
$750$	5.98041	+	1.71220i	0.218374	+	0.0625209i
$751$	10.7881	+	33.2025i	0.393665	+	1.21158i	0.929996	+	0.367569i	$0.119810\pi$
$751$	10.7881	+	33.2025i	0.393665	+	1.21158i	−0.536331	+	0.844008i	$0.680190\pi$
$752$	−4.38926	−	8.61441i	−0.160060	−	0.314135i
$753$	−1.77278	−	11.1929i	−0.0646036	−	0.407891i
$754$	−3.05772	−	2.22157i	−0.111356	−	0.0809047i
$755$	39.6128	+	3.69255i	1.44166	+	0.134386i
$756$	26.1743	−	8.50454i	0.951950	−	0.309307i
$757$	5.39320	−	34.0513i	0.196019	−	1.23762i	−0.671798	−	0.740734i	$-0.734478\pi$
$757$	5.39320	−	34.0513i	0.196019	−	1.23762i	0.867818	−	0.496883i	$-0.165522\pi$
$758$	−5.72618	+	5.72618i	−0.207984	+	0.207984i
$759$	9.20349	−	6.61125i	0.334065	−	0.239973i
$760$	9.00370	−	14.2284i	0.326598	−	0.516119i
$761$	−8.17878	−	11.2571i	−0.296481	−	0.408071i	0.634625	−	0.772820i	$-0.281155\pi$
$761$	−8.17878	−	11.2571i	−0.296481	−	0.408071i	−0.931106	+	0.364750i	$0.881155\pi$
$762$	4.67478	+	2.38192i	0.169350	+	0.0862879i
$763$	24.5997	−	12.5342i	0.890568	−	0.453767i
$764$	4.22213	−	5.81126i	0.152751	−	0.210244i
$765$	18.6302	−	7.40423i	0.673575	−	0.267701i
$766$	5.26689	+	1.71132i	0.190300	+	0.0618323i
$767$	−2.13280	+	4.18586i	−0.0770110	+	0.151143i
$768$	0.166048	+	0.0262994i	0.00599174	+	0.000948998i
$769$	13.3273			0.480596			0.240298	−	0.970699i	$-0.422755\pi$
$769$	13.3273			0.480596			0.240298	+	0.970699i	$0.422755\pi$
$770$	10.3171	−	2.26190i	0.371803	−	0.0815131i
$771$	−4.83143			−0.174000
$772$	−36.3639	−	5.75948i	−1.30877	−	0.207288i
$773$	−5.67471	+	11.1372i	−0.204105	+	0.400579i	−0.970256	−	0.242082i	$-0.922170\pi$
$773$	−5.67471	+	11.1372i	−0.204105	+	0.400579i	0.766151	+	0.642661i	$0.222170\pi$
$774$	−5.67053	−	1.84247i	−0.203823	−	0.0662261i
$775$	33.1224	+	6.22923i	1.18979	+	0.223760i
$776$	10.8709	−	14.9625i	0.390243	−	0.537124i
$777$	3.44409	−	1.75485i	0.123556	−	0.0629549i
$778$	0.355735	+	0.181256i	0.0127537	+	0.00649835i
$779$	−8.56685	−	11.7913i	−0.306939	−	0.422465i
$780$	2.88168	+	12.8136i	0.103181	+	0.458802i
$781$	9.04671	+	2.99345i	0.323717	+	0.107114i
$782$	−5.45516	+	5.45516i	−0.195076	+	0.195076i
$783$	2.21631	−	13.9933i	0.0792046	−	0.500078i
$784$	3.75988	−	1.22166i	0.134281	−	0.0436306i
$785$	−30.6424	−	36.9424i	−1.09367	−	1.31853i
$786$	−3.38355	−	2.45829i	−0.120687	−	0.0876843i
$787$	0.984406	+	6.21530i	0.0350903	+	0.221551i	0.999002	−	0.0446718i	$-0.0142242\pi$
$787$	0.984406	+	6.21530i	0.0350903	+	0.221551i	−0.963911	+	0.266223i	$0.914224\pi$
$788$	0.241781	+	0.474521i	0.00861308	+	0.0169041i
$789$	8.05781	+	24.7994i	0.286866	+	0.882882i
$790$	16.6137	−	1.06693i	0.591087	−	0.0379597i
$791$			59.1055i			2.10155i
$792$	4.65723	+	9.26339i	0.165487	+	0.329160i
$793$	14.3574	+	14.3574i	0.509846	+	0.509846i
$794$	6.62104	−	4.81046i	0.234972	−	0.170717i
$795$	−3.23805	+	1.92066i	−0.114842	+	0.0681189i
$796$	−6.03213	+	18.5650i	−0.213803	+	0.658019i
$797$	−1.74680	+	0.276667i	−0.0618750	+	0.00980003i	−0.187295	−	0.982304i	$-0.559972\pi$
$797$	−1.74680	+	0.276667i	−0.0618750	+	0.00980003i	0.125420	+	0.992104i	$0.459972\pi$
$798$	−6.57006	+	1.04059i	−0.232577	+	0.0368367i
$799$	−5.99354	+	18.4462i	−0.212036	+	0.652581i
$800$	−0.713981	+	24.7707i	−0.0252430	+	0.875775i
$801$	−15.3828	+	11.1762i	−0.543523	+	0.394893i
$802$	9.82669	+	9.82669i	0.346992	+	0.346992i
$803$	−34.5259	−	34.9001i	−1.21839	−	1.23160i
$804$			3.73160i			0.131603i
$805$	14.6860	+	12.9135i	0.517613	+	0.455142i
$806$	−2.97684	−	9.16176i	−0.104855	−	0.322709i
$807$	−11.8305	−	23.2186i	−0.416453	−	0.817335i
$808$	0.548599	+	3.46372i	0.0192996	+	0.121853i
$809$	−14.9294	−	10.8468i	−0.524889	−	0.381354i	0.293553	−	0.955943i	$-0.405162\pi$
$809$	−14.9294	−	10.8468i	−0.524889	−	0.381354i	−0.818443	+	0.574588i	$0.805162\pi$
$810$	0.838892	−	0.695831i	0.0294756	−	0.0244490i
$811$	−12.4057	+	4.03086i	−0.435624	+	0.141543i	−0.518616	−	0.855007i	$-0.673552\pi$
$811$	−12.4057	+	4.03086i	−0.435624	+	0.141543i	0.0829918	+	0.996550i	$0.473552\pi$
$812$	2.12539	−	13.4192i	0.0745865	−	0.470920i
$813$	−1.12013	+	1.12013i	−0.0392847	+	0.0392847i
$814$	1.09921	+	1.53020i	0.0385273	+	0.0536336i
$815$	−19.6984	−	12.4651i	−0.690004	−	0.436633i
$816$	−9.26472	−	12.7518i	−0.324330	−	0.446402i
$817$	−26.2042	−	13.3517i	−0.916768	−	0.467117i
$818$	1.05413	−	0.537108i	0.0368569	−	0.0187796i
$819$	−8.53770	+	11.7511i	−0.298331	+	0.410618i
$820$	12.8597	+	5.54504i	0.449079	+	0.193641i
$821$	−24.7703	−	8.04835i	−0.864489	−	0.280889i	−0.156987	−	0.987601i	$-0.550178\pi$
$821$	−24.7703	−	8.04835i	−0.864489	−	0.280889i	−0.707502	+	0.706711i	$0.750178\pi$
$822$	−3.88227	+	7.61938i	−0.135410	+	0.265756i
$823$	4.96237	+	0.785962i	0.172977	+	0.0273969i	0.242322	−	0.970196i	$-0.422091\pi$
$823$	4.96237	+	0.785962i	0.172977	+	0.0273969i	−0.0693449	+	0.997593i	$0.522091\pi$
$824$	11.3361			0.394912
$825$	−15.6566	+	10.5765i	−0.545092	+	0.368226i
$826$	2.28625			0.0795488
$827$	−12.0210	−	1.90393i	−0.418010	−	0.0662062i	−0.0561130	−	0.998424i	$-0.517871\pi$
$827$	−12.0210	−	1.90393i	−0.418010	−	0.0662062i	−0.361897	+	0.932218i	$0.617871\pi$
$828$	−4.08135	+	8.01010i	−0.141837	+	0.278370i
$829$	10.4727	+	3.40277i	0.363730	+	0.118183i	0.485180	−	0.874415i	$-0.338754\pi$
$829$	10.4727	+	3.40277i	0.363730	+	0.118183i	−0.121449	+	0.992598i	$0.538754\pi$
$830$	6.70082	+	2.88937i	0.232589	+	0.100291i
$831$	9.54711	−	13.1405i	0.331185	−	0.455838i
$832$	−7.38386	+	3.76227i	−0.255989	+	0.130433i
$833$	−7.06651	−	3.60057i	−0.244840	−	0.124752i
$834$	−1.36127	−	1.87363i	−0.0471370	−	0.0648785i
$835$	21.3382	+	13.5028i	0.738440	+	0.467283i
$836$	7.27804	+	22.8171i	0.251716	+	0.789148i
$837$	25.5338	−	25.5338i	0.882578	−	0.882578i
$838$	−1.25568	+	7.92807i	−0.0433769	+	0.273871i
$839$	−8.83685	+	2.87127i	−0.305082	+	0.0991272i	−0.457557	−	0.889180i	$-0.651276\pi$
$839$	−8.83685	+	2.87127i	−0.305082	+	0.0991272i	0.152475	+	0.988307i	$0.451276\pi$
$840$	10.5049	−	8.71348i	0.362455	−	0.300644i
$841$	17.8031	+	12.9347i	0.613900	+	0.446024i
$842$	−0.952498	−	6.01384i	−0.0328253	−	0.207251i
$843$	−13.1264	−	25.7619i	−0.452096	−	0.887288i
$844$	4.82040	+	14.8357i	0.165925	+	0.510665i
$845$	7.44819	+	6.54927i	0.256225	+	0.225302i
$846$		−	3.05979i		−	0.105198i
$847$	−14.8715	+	28.4253i	−0.510990	+	0.976706i
$848$	−2.74398	−	2.74398i	−0.0942286	−	0.0942286i
$849$	6.83093	−	4.96296i	0.234437	−	0.170328i
$850$	9.35388	−	8.82976i	0.320836	−	0.302858i
$851$	−1.07798	+	3.31768i	−0.0369527	+	0.113729i
$852$	5.69542	−	0.902066i	0.195122	−	0.0309043i
$853$	−26.7133	+	4.23097i	−0.914645	+	0.144866i	−0.595978	−	0.803001i	$-0.703235\pi$
$853$	−26.7133	+	4.23097i	−0.914645	+	0.144866i	−0.318667	+	0.947867i	$0.603235\pi$
$854$	3.05346	−	9.39759i	0.104487	−	0.321579i
$855$	−13.4172	+	7.95848i	−0.458859	+	0.272174i
$856$	−0.647232	+	0.470242i	−0.0221220	+	0.0160725i
$857$	−33.1497	−	33.1497i	−1.13237	−	1.13237i	−0.989782	−	0.142591i	$-0.954457\pi$
$857$	−33.1497	−	33.1497i	−1.13237	−	1.13237i	−0.142591	−	0.989782i	$-0.545543\pi$
$858$	4.79856	+	2.47765i	0.163820	+	0.0845857i
$859$			47.2517i			1.61221i	0.591775	+	0.806103i	$0.298427\pi$
$859$			47.2517i			1.61221i	−0.591775	+	0.806103i	$0.701573\pi$
$860$	28.2003	−	1.81102i	0.961621	−	0.0617553i
$861$	−3.65072	−	11.2358i	−0.124416	−	0.382914i
$862$	−4.39749	−	8.63057i	−0.149779	−	0.293958i
$863$	2.43422	+	15.3690i	0.0828617	+	0.523168i	0.993850	+	0.110736i	$0.0353207\pi$
$863$	2.43422	+	15.3690i	0.0828617	+	0.523168i	−0.910988	+	0.412432i	$0.864679\pi$
$864$	21.4801	+	15.6062i	0.730768	+	0.530934i
$865$	−18.8470	−	22.7219i	−0.640816	−	0.772566i
$866$	−13.2947	+	4.31972i	−0.451773	+	0.146790i
$867$	−1.91655	+	12.1006i	−0.0650896	+	0.410959i
$868$	24.4863	−	24.4863i	0.831118	−	0.831118i
$869$	−29.9413	+	40.7470i	−1.01569	+	1.38225i
$870$	−0.721933	−	3.21013i	−0.0244758	−	0.108834i
$871$	−3.19826	−	4.40203i	−0.108369	−	0.149157i
$872$	15.4941	+	7.89464i	0.524696	+	0.267346i
$873$	−15.2674	+	7.77913i	−0.516723	+	0.263284i
$874$	3.52861	−	4.85671i	0.119357	−	0.164281i
$875$	−23.8560	−	22.2278i	−0.806479	−	0.751437i
$876$	−28.2536	−	9.18015i	−0.954601	−	0.310169i
$877$	−13.2254	+	25.9562i	−0.446589	+	0.876480i	0.552488	+	0.833521i	$0.313679\pi$
$877$	−13.2254	+	25.9562i	−0.446589	+	0.876480i	−0.999077	+	0.0429592i	$0.986321\pi$
$878$	1.50621	+	0.238560i	0.0508321	+	0.00805101i
$879$	−16.7229			−0.564048
$880$	−14.5557	−	12.9387i	−0.490672	−	0.436164i
$881$	4.18815			0.141102			0.0705512	−	0.997508i	$-0.477524\pi$
$881$	4.18815			0.141102			0.0705512	+	0.997508i	$0.477524\pi$
$882$	1.23576	+	0.195725i	0.0416102	+	0.00659041i
$883$	20.7555	−	40.7349i	0.698477	−	1.37084i	−0.220053	−	0.975488i	$-0.570623\pi$
$883$	20.7555	−	40.7349i	0.698477	−	1.37084i	0.918530	−	0.395351i	$-0.129377\pi$
$884$	25.8286	+	8.39221i	0.868709	+	0.282261i
$885$	−3.80062	+	1.51049i	−0.127756	+	0.0507745i
$886$	−9.11003	+	12.5389i	−0.306057	+	0.421252i
$887$	−30.7027	+	15.6438i	−1.03090	+	0.525267i	−0.885760	−	0.464144i	$-0.846362\pi$
$887$	−30.7027	+	15.6438i	−1.03090	+	0.525267i	−0.145136	+	0.989412i	$0.546362\pi$
$888$	2.16926	+	1.10529i	0.0727955	+	0.0370912i
$889$	−16.1646	−	22.2487i	−0.542143	−	0.746196i
$890$	−6.52371	+	10.3093i	−0.218675	+	0.345569i
$891$	−0.0178389	+	3.31037i	−0.000597626	+	0.110902i
$892$	7.70048	−	7.70048i	0.257831	−	0.257831i
$893$	2.36100	−	14.9068i	0.0790078	−	0.498836i
$894$	−9.51300	+	3.09096i	−0.318162	+	0.103377i
$895$	4.95765	+	0.462133i	0.165716	+	0.0154474i
$896$	26.6503	+	19.3626i	0.890323	+	0.646857i
$897$	1.56420	+	9.87594i	0.0522270	+	0.329748i
$898$	−7.75836	−	15.2266i	−0.258900	−	0.508119i
$899$	−5.50871	−	16.9541i	−0.183726	−	0.565450i
$900$	7.18697	−	13.1539i	0.239566	−	0.438465i
$901$			7.78489i			0.259352i
$902$	5.14481	−	2.58659i	0.171303	−	0.0861239i
$903$	−16.8566	−	16.8566i	−0.560951	−	0.560951i
$904$	−30.1177	+	21.8818i	−1.00170	+	0.727778i
$905$	−4.94486	−	8.33654i	−0.164373	−	0.277116i
$906$	3.05911	−	9.41497i	0.101632	−	0.312791i
$907$	38.0387	−	6.02474i	1.26306	−	0.200048i	0.511249	−	0.859433i	$-0.329183\pi$
$907$	38.0387	−	6.02474i	1.26306	−	0.200048i	0.751806	+	0.659384i	$0.229183\pi$
$908$	5.77055	−	0.913965i	0.191502	−	0.0303310i
$909$	1.00402	−	3.09005i	0.0333012	−	0.102490i
$910$	−2.30600	+	9.03001i	−0.0764432	+	0.299342i
$911$	29.8280	−	21.6713i	0.988244	−	0.718002i	0.0287085	−	0.999588i	$-0.490861\pi$
$911$	29.8280	−	21.6713i	0.988244	−	0.718002i	0.959536	+	0.281586i	$0.0908605\pi$
$912$	8.67283	+	8.67283i	0.287186	+	0.287186i
$913$	−19.8022	+	9.95566i	−0.655356	+	0.329484i
$914$			2.49056i			0.0823805i
$915$	1.13283	+	17.6397i	0.0374500	+	0.583152i
$916$	−2.90677	−	8.94611i	−0.0960423	−	0.295588i
$917$	9.95237	+	19.5326i	0.328656	+	0.645024i
$918$	−2.15595	−	13.6122i	−0.0711571	−	0.449268i
$919$	−24.5973	−	17.8710i	−0.811392	−	0.589510i	0.102842	−	0.994698i	$-0.467206\pi$
$919$	−24.5973	−	17.8710i	−0.811392	−	0.589510i	−0.914234	+	0.405187i	$0.867206\pi$
$920$	−1.14322	+	12.2642i	−0.0376908	+	0.404338i
$921$	1.34081	−	0.435657i	0.0441813	−	0.0143554i
$922$	−0.952647	+	6.01478i	−0.0313738	+	0.198086i
$923$	−5.94554	+	5.94554i	−0.195700	+	0.195700i
$924$	−0.104612	+	19.4129i	−0.00344148	+	0.638636i
$925$	1.95599	−	5.47762i	0.0643126	−	0.180103i
$926$	−7.82350	−	10.7681i	−0.257096	−	0.353862i
$927$	−9.35797	−	4.76812i	−0.307356	−	0.156606i
$928$	11.6788	−	5.95063i	0.383374	−	0.195339i
$929$	13.6936	−	18.8477i	0.449273	−	0.618372i	−0.522968	−	0.852352i	$-0.675175\pi$
$929$	13.6936	−	18.8477i	0.449273	−	0.618372i	0.972241	+	0.233981i	$0.0751752\pi$
$930$	3.32058	−	7.70086i	0.108886	−	0.252521i
$931$	5.86938	+	1.90708i	0.192361	+	0.0625020i
$932$	3.53335	−	6.93458i	0.115739	−	0.227150i
$933$	15.9199	+	2.52147i	0.521196	+	0.0825493i
$934$	−19.3837			−0.634254
$935$	2.29374	+	39.0019i	0.0750132	+	1.27550i
$936$	−9.14869			−0.299034
$937$	−7.94449	−	1.25828i	−0.259535	−	0.0411063i	0.0253108	−	0.999680i	$-0.491942\pi$
$937$	−7.94449	−	1.25828i	−0.259535	−	0.0411063i	−0.284846	+	0.958573i	$0.591942\pi$
$938$	−1.20216	+	2.35937i	−0.0392519	+	0.0770362i
$939$	0.801481	+	0.260417i	0.0261553	+	0.00849838i
$940$	5.35598	+	13.4764i	0.174693	+	0.439553i
$941$	28.1490	−	38.7438i	0.917631	−	1.26301i	−0.0468615	−	0.998901i	$-0.514922\pi$
$941$	28.1490	−	38.7438i	0.917631	−	1.26301i	0.964493	−	0.264110i	$-0.0850781\pi$
$942$	−10.6412	+	5.42198i	−0.346710	+	0.176658i
$943$	9.49976	+	4.84037i	0.309355	+	0.157624i
$944$	−2.47782	−	3.41042i	−0.0806460	−	0.111000i
$945$	−34.0840	+	7.66523i	−1.10875	+	0.249350i
$946$	6.88039	−	9.36352i	0.223701	−	0.304434i
$947$	9.38618	−	9.38618i	0.305010	−	0.305010i	−0.537960	−	0.842970i	$-0.680805\pi$
$947$	9.38618	−	9.38618i	0.305010	−	0.305010i	0.842970	+	0.537960i	$0.180805\pi$
$948$	−4.78668	+	30.2219i	−0.155464	+	0.981563i
$949$	41.1978	−	13.3860i	1.33734	−	0.434528i
$950$	−6.11425	+	7.92491i	−0.198373	+	0.257118i
$951$	15.7309	+	11.4292i	0.510109	+	0.370616i
$952$	−4.41491	−	27.8746i	−0.143088	−	0.903422i
$953$	24.1733	+	47.4428i	0.783051	+	1.53682i	0.842564	+	0.538597i	$0.181045\pi$
$953$	24.1733	+	47.4428i	0.783051	+	1.53682i	−0.0595128	+	0.998228i	$0.518955\pi$
$954$	−0.379511	−	1.16802i	−0.0122871	−	0.0378159i
$955$	−6.02108	+	6.84750i	−0.194837	+	0.221580i
$956$			18.4130i			0.595519i
$957$	8.87987	+	4.58496i	0.287045	+	0.148211i
$958$	13.2098	+	13.2098i	0.426790	+	0.426790i
$959$	36.2628	−	26.3465i	1.17099	−	0.850772i
$960$	−6.99005	−	1.78506i	−0.225603	−	0.0576124i
$961$	4.46097	−	13.7294i	0.143902	−	0.442885i
$962$	−1.64201	+	0.260069i	−0.0529405	+	0.00838495i
$963$	0.732081	−	0.115950i	0.0235910	−	0.00373644i
$964$	15.1642	−	46.6706i	0.488406	−	1.50316i
$965$	45.2823	+	11.5638i	1.45769	+	0.372251i
$966$	3.93674	−	2.86021i	0.126662	−	0.0920256i
$967$	38.6475	+	38.6475i	1.24282	+	1.24282i	0.958826	+	0.283994i	$0.0916596\pi$
$967$	38.6475	+	38.6475i	1.24282	+	1.24282i	0.283994	+	0.958826i	$0.408340\pi$
$968$	−19.9901	+	2.94563i	−0.642505	+	0.0946763i
$969$		−	24.6055i		−	0.790443i
$970$	−7.25995	+	8.25641i	−0.233103	+	0.265097i
$971$	2.55556	+	7.86521i	0.0820119	+	0.252407i	0.983652	−	0.180081i	$-0.0576360\pi$
$971$	2.55556	+	7.86521i	0.0820119	+	0.252407i	−0.901640	+	0.432487i	$0.857636\pi$
$972$	−11.9430	−	23.4395i	−0.383073	−	0.751823i
$973$	1.89900	+	11.9898i	0.0608790	+	0.384375i
$974$	10.7378	+	7.80149i	0.344062	+	0.249976i
$975$	−2.13253	−	16.5349i	−0.0682957	−	0.529539i
$976$	−17.3278	+	5.63014i	−0.554649	+	0.180216i
$977$	−8.56551	+	54.0805i	−0.274035	+	1.73019i	0.339575	+	0.940579i	$0.389717\pi$
$977$	−8.56551	+	54.0805i	−0.274035	+	1.73019i	−0.613610	+	0.789610i	$0.710283\pi$
$978$	−4.10153	+	4.10153i	−0.131152	+	0.131152i
$979$	−11.2607	−	35.3029i	−0.359892	−	1.12829i
$980$	−5.78535	+	1.30108i	−0.184806	+	0.0415614i
$981$	−9.46980	−	13.0341i	−0.302347	−	0.416145i
$982$	1.72822	+	0.880571i	0.0551496	+	0.0281001i
$983$	12.1525	−	6.19202i	0.387606	−	0.197495i	−0.249318	−	0.968422i	$-0.580207\pi$
$983$	12.1525	−	6.19202i	0.387606	−	0.197495i	0.636924	+	0.770927i	$0.280207\pi$
$984$	4.37373	−	6.01992i	0.139429	−	0.191908i
$985$	−0.249683	−	0.628240i	−0.00795557	−	0.0200174i
$986$	−6.47069	−	2.10245i	−0.206069	−	0.0669558i
$987$	5.55398	−	10.9003i	0.176785	−	0.346960i
$988$	−20.8726	−	3.30589i	−0.664045	−	0.105174i
$989$	21.5139			0.684102
$990$	−2.24548	−	5.73988i	−0.0713659	−	0.182425i
$991$	6.43457			0.204401			0.102200	−	0.994764i	$-0.467412\pi$
$991$	6.43457			0.204401			0.102200	+	0.994764i	$0.467412\pi$
$992$	32.9965	+	5.22613i	1.04764	+	0.165930i
$993$	−7.71694	+	15.1453i	−0.244890	+	0.480623i
$994$	3.89164	+	1.26447i	0.123435	+	0.0401066i
$995$	9.81138	−	22.7539i	0.311042	−	0.721346i
$996$	−7.88351	+	10.8507i	−0.249799	+	0.343818i
$997$	−18.9575	+	9.65934i	−0.600391	+	0.305914i	−0.727643	−	0.685956i	$-0.759384\pi$
$997$	−18.9575	+	9.65934i	−0.600391	+	0.305914i	0.127252	+	0.991870i	$0.459384\pi$
$998$	−2.79564	−	1.42445i	−0.0884943	−	0.0450901i
$999$	−3.66296	−	5.04163i	−0.115891	−	0.159510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.2.l.a.8.3	yes	32
3.2	odd	2		495.2.bj.a.118.2		32
4.3	odd	2		880.2.cm.a.833.2		32
5.2	odd	4	inner	55.2.l.a.52.2	yes	32
5.3	odd	4		275.2.bm.b.107.3		32
5.4	even	2		275.2.bm.b.118.2		32
11.2	odd	10		605.2.e.b.483.9		32
11.3	even	5		605.2.m.c.578.3		32
11.4	even	5		605.2.m.e.403.3		32
11.5	even	5		605.2.m.d.233.2		32
11.6	odd	10		605.2.m.c.233.3		32
11.7	odd	10	inner	55.2.l.a.18.2	yes	32
11.8	odd	10		605.2.m.d.578.2		32
11.9	even	5		605.2.e.b.483.8		32
11.10	odd	2		605.2.m.e.118.2		32
15.2	even	4		495.2.bj.a.217.3		32
20.7	even	4		880.2.cm.a.657.3		32
33.29	even	10		495.2.bj.a.73.3		32
44.7	even	10		880.2.cm.a.513.3		32
55.2	even	20		605.2.e.b.362.8		32
55.7	even	20	inner	55.2.l.a.7.3	✓	32
55.17	even	20		605.2.m.c.112.3		32
55.18	even	20		275.2.bm.b.7.2		32
55.27	odd	20		605.2.m.d.112.2		32
55.29	odd	10		275.2.bm.b.18.3		32
55.32	even	4		605.2.m.e.602.3		32
55.37	odd	20		605.2.m.e.282.2		32
55.42	odd	20		605.2.e.b.362.9		32
55.47	odd	20		605.2.m.c.457.3		32
55.52	even	20		605.2.m.d.457.2		32
165.62	odd	20		495.2.bj.a.172.2		32
220.7	odd	20		880.2.cm.a.337.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.3	✓	32	55.7	even	20	inner
55.2.l.a.8.3	yes	32	1.1	even	1	trivial
55.2.l.a.18.2	yes	32	11.7	odd	10	inner
55.2.l.a.52.2	yes	32	5.2	odd	4	inner
275.2.bm.b.7.2		32	55.18	even	20
275.2.bm.b.18.3		32	55.29	odd	10
275.2.bm.b.107.3		32	5.3	odd	4
275.2.bm.b.118.2		32	5.4	even	2
495.2.bj.a.73.3		32	33.29	even	10
495.2.bj.a.118.2		32	3.2	odd	2
495.2.bj.a.172.2		32	165.62	odd	20
495.2.bj.a.217.3		32	15.2	even	4
605.2.e.b.362.8		32	55.2	even	20
605.2.e.b.362.9		32	55.42	odd	20
605.2.e.b.483.8		32	11.9	even	5
605.2.e.b.483.9		32	11.2	odd	10
605.2.m.c.112.3		32	55.17	even	20
605.2.m.c.233.3		32	11.6	odd	10
605.2.m.c.457.3		32	55.47	odd	20
605.2.m.c.578.3		32	11.3	even	5
605.2.m.d.112.2		32	55.27	odd	20
605.2.m.d.233.2		32	11.5	even	5
605.2.m.d.457.2		32	55.52	even	20
605.2.m.d.578.2		32	11.8	odd	10
605.2.m.e.118.2		32	11.10	odd	2
605.2.m.e.282.2		32	55.37	odd	20
605.2.m.e.403.3		32	11.4	even	5
605.2.m.e.602.3		32	55.32	even	4
880.2.cm.a.337.2		32	220.7	odd	20
880.2.cm.a.513.3		32	44.7	even	10
880.2.cm.a.657.3		32	20.7	even	4
880.2.cm.a.833.2		32	4.3	odd	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	55.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.482327 + 0.0763931i) q^{2} +(0.517260 - 1.01518i) q^{3} +(-1.67531 - 0.544341i) q^{4} +(2.05331 + 0.885381i) q^{5} +(0.327041 - 0.450133i) q^{6} +(-2.59854 + 1.32402i) q^{7} +(-1.63669 - 0.833936i) q^{8} +(1.00032 + 1.37683i) q^{9} +(0.922733 + 0.583903i) q^{10} +(-3.15977 + 1.00788i) q^{11} +(-1.41917 + 1.41917i) q^{12} +(0.457808 - 2.89049i) q^{13} +(-1.35449 + 0.440102i) q^{14} +(1.96092 - 1.62651i) q^{15} +(2.12449 + 1.54353i) q^{16} +(-0.824113 - 5.20325i) q^{17} +(0.377304 + 0.740500i) q^{18} +(1.26677 + 3.89873i) q^{19} +(-2.95799 - 2.60099i) q^{20} +3.32285i q^{21} +(-1.60104 + 0.244743i) q^{22} +(-2.12046 - 2.12046i) q^{23} +(-1.69319 + 1.23017i) q^{24} +(3.43220 + 3.63593i) q^{25} +(0.441627 - 1.35919i) q^{26} +(5.29116 - 0.838037i) q^{27} +(5.07408 - 0.803656i) q^{28} +(0.817241 - 2.51521i) q^{29} +(1.07006 - 0.634710i) q^{30} +(5.45328 - 3.96204i) q^{31} +(3.50456 + 3.50456i) q^{32} +(-0.611244 + 3.72907i) q^{33} -2.57262i q^{34} +(-6.50789 + 0.417937i) q^{35} +(-0.926389 - 2.85113i) q^{36} +(-0.528116 - 1.03649i) q^{37} +(0.313163 + 1.97724i) q^{38} +(-2.69755 - 1.95989i) q^{39} +(-2.62229 - 3.16143i) q^{40} +(-3.38136 + 1.09867i) q^{41} +(-0.253843 + 1.60270i) q^{42} +(-5.07292 + 5.07292i) q^{43} +(5.84223 + 0.0314826i) q^{44} +(0.834964 + 3.71273i) q^{45} +(-0.860769 - 1.18475i) q^{46} +(-3.28041 - 1.67145i) q^{47} +(2.66588 - 1.35833i) q^{48} +(0.884888 - 1.21794i) q^{49} +(1.37768 + 2.01591i) q^{50} +(-5.70851 - 1.85481i) q^{51} +(-2.34038 + 4.59325i) q^{52} +(-1.45955 - 0.231169i) q^{53} +2.61609 q^{54} +(-7.38037 - 0.728107i) q^{55} +5.35716 q^{56} +(4.61316 + 0.730652i) q^{57} +(0.586323 - 1.15072i) q^{58} +(-1.52672 - 0.496061i) q^{59} +(-4.17052 + 1.65750i) q^{60} +(-4.07810 + 5.61302i) q^{61} +(2.93294 - 1.49441i) q^{62} +(-4.42234 - 2.25330i) q^{63} +(-1.66445 - 2.29092i) q^{64} +(3.49920 - 5.52974i) q^{65} +(-0.579695 + 1.75194i) q^{66} +(1.31471 - 1.31471i) q^{67} +(-1.45170 + 9.16564i) q^{68} +(-3.24948 + 1.05582i) q^{69} +(-3.17086 - 0.295576i) q^{70} +(-2.32441 - 1.68878i) q^{71} +(-0.489036 - 3.08765i) q^{72} +(6.71992 + 13.1886i) q^{73} +(-0.175544 - 0.540270i) q^{74} +(5.46646 - 1.60358i) q^{75} -7.22113i q^{76} +(6.87635 - 6.80264i) q^{77} +(-1.15138 - 1.15138i) q^{78} +(12.3342 - 8.96129i) q^{79} +(2.99564 + 5.05035i) q^{80} +(0.308439 - 0.949277i) q^{81} +(-1.71486 + 0.271606i) q^{82} +(6.60041 - 1.04540i) q^{83} +(1.80876 - 5.56680i) q^{84} +(2.91469 - 11.4136i) q^{85} +(-2.83434 + 2.05927i) q^{86} +(-2.13066 - 2.13066i) q^{87} +(6.01208 + 0.985459i) q^{88} +11.1726i q^{89} +(0.119098 + 1.85454i) q^{90} +(2.63744 + 8.11720i) q^{91} +(2.39818 + 4.70669i) q^{92} +(-1.20142 - 7.58545i) q^{93} +(-1.45454 - 1.05679i) q^{94} +(-0.850775 + 9.12689i) q^{95} +(5.37052 - 1.74499i) q^{96} +(-1.57505 + 9.94447i) q^{97} +(0.519848 - 0.519848i) q^{98} +(-4.54848 - 3.34226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 4 q^{3} - 2 q^{5} - 20 q^{6} - 10 q^{8} - 24 q^{11} + 12 q^{12} - 10 q^{13} + 14 q^{15} - 8 q^{16} - 10 q^{18} + 16 q^{20} + 10 q^{22} - 24 q^{23} + 16 q^{25} + 20 q^{26} - 16 q^{27} + 50 q^{28}+ \cdots - 8 q^{97}+O(q^{100}) \) 32 * q - 10 * q^2 - 4 * q^3 - 2 * q^5 - 20 * q^6 - 10 * q^8 - 24 * q^11 + 12 * q^12 - 10 * q^13 + 14 * q^15 - 8 * q^16 - 10 * q^18 + 16 * q^20 + 10 * q^22 - 24 * q^23 + 16 * q^25 + 20 * q^26 - 16 * q^27 + 50 * q^28 + 30 * q^30 - 28 * q^31 + 66 * q^33 - 10 * q^35 + 24 * q^36 - 8 * q^37 + 10 * q^38 - 50 * q^40 + 40 * q^41 - 10 * q^42 - 28 * q^45 + 60 * q^46 - 28 * q^47 - 54 * q^48 - 50 * q^50 + 20 * q^51 - 50 * q^52 - 24 * q^53 - 64 * q^55 - 80 * q^56 + 30 * q^57 - 50 * q^58 + 34 * q^60 - 60 * q^61 + 100 * q^62 - 30 * q^63 - 100 * q^66 - 8 * q^67 - 30 * q^68 + 30 * q^70 + 24 * q^71 + 80 * q^72 + 50 * q^73 + 34 * q^75 + 70 * q^77 + 60 * q^78 + 98 * q^80 - 12 * q^81 - 10 * q^82 + 90 * q^83 + 30 * q^85 + 100 * q^86 + 170 * q^88 - 20 * q^90 + 20 * q^91 - 68 * q^92 - 8 * q^93 - 40 * q^95 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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