LMFDB - Embedded newform 880.2.w.a.221.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(221,880)] 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("880.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			221.8
Character	$\chi$	$=$	880.221
Dual form			880.2.w.a.661.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.941762 + 1.05503i) q^{2} +(2.08238 + 2.08238i) q^{3} +(-0.226170 - 1.98717i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-4.15807 + 0.235864i) q^{6} -0.495497i q^{7} +(2.30952 + 1.63283i) q^{8} +5.67259i q^{9} +(0.0800917 + 1.41194i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(3.66707 - 4.60901i) q^{12} +(1.75771 + 1.75771i) q^{13} +(0.522764 + 0.466640i) q^{14} +2.94493 q^{15} +(-3.89769 + 0.898877i) q^{16} -1.66948 q^{17} +(-5.98475 - 5.34223i) q^{18} +(4.04661 + 4.04661i) q^{19} +(-1.56507 - 1.24522i) q^{20} +(1.03181 - 1.03181i) q^{21} +(-0.0800917 - 1.41194i) q^{22} -3.80821i q^{23} +(1.40913 + 8.20945i) q^{24} -1.00000i q^{25} +(-3.50978 + 0.199090i) q^{26} +(-5.56535 + 5.56535i) q^{27} +(-0.984637 + 0.112067i) q^{28} +(3.95594 + 3.95594i) q^{29} +(-2.77342 + 3.10698i) q^{30} -0.0391615 q^{31} +(2.72236 - 4.95871i) q^{32} -2.94493 q^{33} +(1.57225 - 1.76135i) q^{34} +(-0.350369 - 0.350369i) q^{35} +(11.2724 - 1.28297i) q^{36} +(-4.67922 + 4.67922i) q^{37} +(-8.08022 + 0.458346i) q^{38} +7.32043i q^{39} +(2.78766 - 0.478495i) q^{40} +4.35195i q^{41} +(0.116870 + 2.06031i) q^{42} +(-8.78390 + 8.78390i) q^{43} +(1.56507 + 1.24522i) q^{44} +(4.01113 + 4.01113i) q^{45} +(4.01777 + 3.58643i) q^{46} +7.95512 q^{47} +(-9.98827 - 6.24467i) q^{48} +6.75448 q^{49} +(1.05503 + 0.941762i) q^{50} +(-3.47649 - 3.47649i) q^{51} +(3.09533 - 3.89041i) q^{52} +(5.94910 - 5.94910i) q^{53} +(-0.630369 - 11.1128i) q^{54} +1.00000i q^{55} +(0.809060 - 1.14436i) q^{56} +16.8531i q^{57} +(-7.89919 + 0.448077i) q^{58} +(-3.29326 + 3.29326i) q^{59} +(-0.666054 - 5.85207i) q^{60} +(1.73897 + 1.73897i) q^{61} +(0.0368808 - 0.0413165i) q^{62} +2.81075 q^{63} +(2.66776 + 7.54208i) q^{64} +2.48578 q^{65} +(2.77342 - 3.10698i) q^{66} +(-5.75068 - 5.75068i) q^{67} +(0.377586 + 3.31754i) q^{68} +(7.93014 - 7.93014i) q^{69} +(0.699614 - 0.0396852i) q^{70} -16.2629i q^{71} +(-9.26235 + 13.1010i) q^{72} -7.01028i q^{73} +(-0.530000 - 9.34341i) q^{74} +(2.08238 - 2.08238i) q^{75} +(7.12608 - 8.95652i) q^{76} +(0.350369 + 0.350369i) q^{77} +(-7.72326 - 6.89410i) q^{78} -11.1174 q^{79} +(-2.12048 + 3.39169i) q^{80} -6.16053 q^{81} +(-4.59143 - 4.09850i) q^{82} +(-6.25445 - 6.25445i) q^{83} +(-2.28375 - 1.81702i) q^{84} +(-1.18050 + 1.18050i) q^{85} +(-0.994924 - 17.5396i) q^{86} +16.4755i q^{87} +(-2.78766 + 0.478495i) q^{88} -7.69163i q^{89} +(-8.00938 + 0.454328i) q^{90} +(0.870940 - 0.870940i) q^{91} +(-7.56757 + 0.861303i) q^{92} +(-0.0815490 - 0.0815490i) q^{93} +(-7.49182 + 8.39288i) q^{94} +5.72277 q^{95} +(15.9949 - 4.65692i) q^{96} -7.89397 q^{97} +(-6.36111 + 7.12617i) q^{98} +(-4.01113 - 4.01113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) $ 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.941762	+	1.05503i	−0.665926	+	0.746018i
$2$	−0.941762	+	1.05503i	−0.665926	+	0.746018i
$3$	2.08238	+	2.08238i	1.20226	+	1.20226i	0.973477	+	0.228784i	$0.0734750\pi$
$3$	2.08238	+	2.08238i	1.20226	+	1.20226i	0.228784	+	0.973477i	$0.426525\pi$
$4$	−0.226170	−	1.98717i	−0.113085	−	0.993585i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−4.15807	+	0.235864i	−1.69753	+	0.0962912i
$7$		−	0.495497i		−	0.187280i	−0.995606	−	0.0936402i	$-0.970150\pi$
$7$		−	0.495497i		−	0.187280i	0.995606	−	0.0936402i	$-0.0298503\pi$
$8$	2.30952	+	1.63283i	0.816539	+	0.577291i
$9$			5.67259i			1.89086i
$10$	0.0800917	+	1.41194i	0.0253272	+	0.446496i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	3.66707	−	4.60901i	1.05859	−	1.33051i
$13$	1.75771	+	1.75771i	0.487501	+	0.487501i	0.907517	−	0.420016i	$-0.137975\pi$
$13$	1.75771	+	1.75771i	0.487501	+	0.487501i	−0.420016	+	0.907517i	$0.637975\pi$
$14$	0.522764	+	0.466640i	0.139714	+	0.124715i
$15$	2.94493			0.760377
$16$	−3.89769	+	0.898877i	−0.974424	+	0.224719i
$17$	−1.66948			−0.404908			−0.202454	−	0.979292i	$-0.564892\pi$
$17$	−1.66948			−0.404908			−0.202454	+	0.979292i	$0.564892\pi$
$18$	−5.98475	−	5.34223i	−1.41062	−	1.25918i
$19$	4.04661	+	4.04661i	0.928355	+	0.928355i	0.997600	−	0.0692445i	$-0.0220589\pi$
$19$	4.04661	+	4.04661i	0.928355	+	0.928355i	−0.0692445	+	0.997600i	$0.522059\pi$
$20$	−1.56507	−	1.24522i	−0.349960	−	0.278439i
$21$	1.03181	−	1.03181i	0.225160	−	0.225160i
$22$	−0.0800917	−	1.41194i	−0.0170756	−	0.301027i
$23$		−	3.80821i		−	0.794067i	−0.917804	−	0.397034i	$-0.870040\pi$
$23$		−	3.80821i		−	0.794067i	0.917804	−	0.397034i	$-0.129960\pi$
$24$	1.40913	+	8.20945i	0.287638	+	1.67575i
$25$		−	1.00000i		−	0.200000i
$26$	−3.50978	+	0.199090i	−0.688324	+	0.0390448i
$27$	−5.56535	+	5.56535i	−1.07105	+	1.07105i
$28$	−0.984637	+	0.112067i	−0.186079	+	0.0211786i
$29$	3.95594	+	3.95594i	0.734600	+	0.734600i	0.971527	−	0.236927i	$-0.0761403\pi$
$29$	3.95594	+	3.95594i	0.734600	+	0.734600i	−0.236927	+	0.971527i	$0.576140\pi$
$30$	−2.77342	+	3.10698i	−0.506355	+	0.567255i
$31$	−0.0391615			−0.00703361			−0.00351680	−	0.999994i	$-0.501119\pi$
$31$	−0.0391615			−0.00703361			−0.00351680	+	0.999994i	$0.501119\pi$
$32$	2.72236	−	4.95871i	0.481249	−	0.876584i
$33$	−2.94493			−0.512646
$34$	1.57225	−	1.76135i	0.269639	−	0.302069i
$35$	−0.350369	−	0.350369i	−0.0592232	−	0.0592232i
$36$	11.2724	−	1.28297i	1.87874	−	0.213828i
$37$	−4.67922	+	4.67922i	−0.769258	+	0.769258i	−0.977976	−	0.208718i	$-0.933071\pi$
$37$	−4.67922	+	4.67922i	−0.769258	+	0.769258i	0.208718	+	0.977976i	$0.433071\pi$
$38$	−8.08022	+	0.458346i	−1.31079	+	0.0743536i
$39$			7.32043i			1.17221i
$40$	2.78766	−	0.478495i	0.440768	−	0.0756567i
$41$			4.35195i			0.679660i	0.940487	+	0.339830i	$0.110370\pi$
$41$			4.35195i			0.679660i	−0.940487	+	0.339830i	$0.889630\pi$
$42$	0.116870	+	2.06031i	0.0180334	+	0.317913i
$43$	−8.78390	+	8.78390i	−1.33953	+	1.33953i	−0.443021	+	0.896511i	$0.646093\pi$
$43$	−8.78390	+	8.78390i	−1.33953	+	1.33953i	−0.896511	+	0.443021i	$0.853907\pi$
$44$	1.56507	+	1.24522i	0.235943	+	0.187723i
$45$	4.01113	+	4.01113i	0.597944	+	0.597944i
$46$	4.01777	+	3.58643i	0.592388	+	0.528790i
$47$	7.95512			1.16037			0.580187	−	0.814484i	$-0.302980\pi$
$47$	7.95512			1.16037			0.580187	+	0.814484i	$0.302980\pi$
$48$	−9.98827	−	6.24467i	−1.44168	−	0.901340i
$49$	6.75448			0.964926
$50$	1.05503	+	0.941762i	0.149204	+	0.133185i
$51$	−3.47649	−	3.47649i	−0.486806	−	0.486806i
$52$	3.09533	−	3.89041i	0.429245	−	0.539503i
$53$	5.94910	−	5.94910i	0.817172	−	0.817172i	−0.168525	−	0.985697i	$-0.553901\pi$
$53$	5.94910	−	5.94910i	0.817172	−	0.817172i	0.985697	+	0.168525i	$0.0539005\pi$
$54$	−0.630369	−	11.1128i	−0.0857824	−	1.51226i
$55$			1.00000i			0.134840i
$56$	0.809060	−	1.14436i	0.108115	−	0.152922i
$57$			16.8531i			2.23225i
$58$	−7.89919	+	0.448077i	−1.03721	+	0.0588354i
$59$	−3.29326	+	3.29326i	−0.428746	+	0.428746i	−0.888201	−	0.459455i	$-0.848045\pi$
$59$	−3.29326	+	3.29326i	−0.428746	+	0.428746i	0.459455	+	0.888201i	$0.348045\pi$
$60$	−0.666054	−	5.85207i	−0.0859872	−	0.755499i
$61$	1.73897	+	1.73897i	0.222652	+	0.222652i	0.809614	−	0.586962i	$-0.199676\pi$
$61$	1.73897	+	1.73897i	0.222652	+	0.222652i	−0.586962	+	0.809614i	$0.699676\pi$
$62$	0.0368808	−	0.0413165i	0.00468386	−	0.00524720i
$63$	2.81075			0.354122
$64$	2.66776	+	7.54208i	0.333470	+	0.942761i
$65$	2.48578			0.308323
$66$	2.77342	−	3.10698i	0.341384	−	0.382443i
$67$	−5.75068	−	5.75068i	−0.702557	−	0.702557i	0.262402	−	0.964959i	$-0.415485\pi$
$67$	−5.75068	−	5.75068i	−0.702557	−	0.702557i	−0.964959	+	0.262402i	$0.915485\pi$
$68$	0.377586	+	3.31754i	0.0457891	+	0.402311i
$69$	7.93014	−	7.93014i	0.954676	−	0.954676i
$70$	0.699614	−	0.0396852i	0.0836199	−	0.00474329i
$71$		−	16.2629i		−	1.93005i	−0.262160	−	0.965025i	$-0.584435\pi$
$71$		−	16.2629i		−	1.93005i	0.262160	−	0.965025i	$-0.415565\pi$
$72$	−9.26235	+	13.1010i	−1.09158	+	1.54396i
$73$		−	7.01028i		−	0.820491i	−0.911975	−	0.410246i	$-0.865443\pi$
$73$		−	7.01028i		−	0.820491i	0.911975	−	0.410246i	$-0.134557\pi$
$74$	−0.530000	−	9.34341i	−0.0616112	−	1.08615i
$75$	2.08238	−	2.08238i	0.240452	−	0.240452i
$76$	7.12608	−	8.95652i	0.817417	−	1.02738i
$77$	0.350369	+	0.350369i	0.0399283	+	0.0399283i
$78$	−7.72326	−	6.89410i	−0.874487	−	0.780603i
$79$	−11.1174			−1.25081			−0.625403	−	0.780302i	$-0.715065\pi$
$79$	−11.1174			−1.25081			−0.625403	+	0.780302i	$0.715065\pi$
$80$	−2.12048	+	3.39169i	−0.237077	+	0.379202i
$81$	−6.16053			−0.684504
$82$	−4.59143	−	4.09850i	−0.507039	−	0.452604i
$83$	−6.25445	−	6.25445i	−0.686515	−	0.686515i	0.274945	−	0.961460i	$-0.411340\pi$
$83$	−6.25445	−	6.25445i	−0.686515	−	0.686515i	−0.961460	+	0.274945i	$0.911340\pi$
$84$	−2.28375	−	1.81702i	−0.249178	−	0.198253i
$85$	−1.18050	+	1.18050i	−0.128043	+	0.128043i
$86$	−0.994924	−	17.5396i	−0.107285	−	1.89134i
$87$			16.4755i			1.76636i
$88$	−2.78766	+	0.478495i	−0.297165	+	0.0510078i
$89$		−	7.69163i		−	0.815311i	−0.913136	−	0.407655i	$-0.866346\pi$
$89$		−	7.69163i		−	0.815311i	0.913136	−	0.407655i	$-0.133654\pi$
$90$	−8.00938	+	0.454328i	−0.844263	+	0.0478904i
$91$	0.870940	−	0.870940i	0.0912993	−	0.0912993i
$92$	−7.56757	+	0.861303i	−0.788973	+	0.0897971i
$93$	−0.0815490	−	0.0815490i	−0.00845623	−	0.00845623i
$94$	−7.49182	+	8.39288i	−0.772723	+	0.865659i
$95$	5.72277			0.587143
$96$	15.9949	−	4.65692i	1.63247	−	0.475295i
$97$	−7.89397			−0.801511			−0.400755	−	0.916185i	$-0.631252\pi$
$97$	−7.89397			−0.801511			−0.400755	+	0.916185i	$0.631252\pi$
$98$	−6.36111	+	7.12617i	−0.642569	+	0.719852i
$99$	−4.01113	−	4.01113i	−0.403134	−	0.403134i
$100$	−1.98717	+	0.226170i	−0.198717	+	0.0226170i
$101$	5.07411	−	5.07411i	0.504893	−	0.504893i	−0.408061	−	0.912954i	$-0.633795\pi$
$101$	5.07411	−	5.07411i	0.504893	−	0.504893i	0.912954	+	0.408061i	$0.133795\pi$
$102$	6.94181	−	0.393771i	0.687342	−	0.0389891i
$103$		−	10.4324i		−	1.02793i	−0.857811	−	0.513966i	$-0.828176\pi$
$103$		−	10.4324i		−	1.02793i	0.857811	−	0.513966i	$-0.171824\pi$
$104$	1.18943	+	6.92950i	0.116633	+	0.679493i
$105$		−	1.45920i		−	0.142404i
$106$	0.673836	+	11.8791i	0.0654487	+	1.15380i
$107$	−1.16620	+	1.16620i	−0.112741	+	0.112741i	−0.761227	−	0.648486i	$-0.775402\pi$
$107$	−1.16620	+	1.16620i	−0.112741	+	0.112741i	0.648486	+	0.761227i	$0.275402\pi$
$108$	12.3180	+	9.80058i	1.18530	+	0.943061i
$109$	13.0979	+	13.0979i	1.25455	+	1.25455i	0.953659	+	0.300890i	$0.0972836\pi$
$109$	13.0979	+	13.0979i	1.25455	+	1.25455i	0.300890	+	0.953659i	$0.402716\pi$
$110$	−1.05503	−	0.941762i	−0.100593	−	0.0897934i
$111$	−19.4878			−1.84970
$112$	0.445391	+	1.93130i	0.0420855	+	0.182490i
$113$	2.98283			0.280601			0.140301	−	0.990109i	$-0.455193\pi$
$113$	2.98283			0.280601			0.140301	+	0.990109i	$0.455193\pi$
$114$	−17.7805	−	15.8716i	−1.66530	−	1.48651i
$115$	−2.69281	−	2.69281i	−0.251106	−	0.251106i
$116$	6.96642	−	8.75585i	0.646816	−	0.812960i
$117$	−9.97077	+	9.97077i	−0.921798	+	0.921798i
$118$	−0.373017	−	6.57596i	−0.0343390	−	0.605366i
$119$			0.827222i			0.0758314i
$120$	6.80137	+	4.80855i	0.620877	+	0.438959i
$121$		−	1.00000i		−	0.0909091i
$122$	−3.47235	+	0.196967i	−0.314372	+	0.0178326i
$123$	−9.06240	+	9.06240i	−0.817129	+	0.817129i
$124$	0.00885715	+	0.0778205i	0.000795396	+	0.00698849i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−2.64706	+	2.96543i	−0.235819	+	0.264181i
$127$	3.64412			0.323364			0.161682	−	0.986843i	$-0.448308\pi$
$127$	3.64412			0.323364			0.161682	+	0.986843i	$0.448308\pi$
$128$	−10.4695	−	4.28828i	−0.925383	−	0.379034i
$129$	−36.5828			−3.22094
$130$	−2.34101	+	2.62257i	−0.205320	+	0.230014i
$131$	−2.84040	−	2.84040i	−0.248167	−	0.248167i	0.572051	−	0.820218i	$-0.306148\pi$
$131$	−2.84040	−	2.84040i	−0.248167	−	0.248167i	−0.820218	+	0.572051i	$0.806148\pi$
$132$	0.666054	+	5.85207i	0.0579726	+	0.509357i
$133$	2.00508	−	2.00508i	0.173863	−	0.173863i
$134$	11.4829	−	0.651361i	0.991971	−	0.0562690i
$135$			7.87059i			0.677393i
$136$	−3.85570	−	2.72597i	−0.330623	−	0.233750i
$137$		−	13.1825i		−	1.12625i	−0.826370	−	0.563127i	$-0.809598\pi$
$137$		−	13.1825i		−	1.12625i	0.826370	−	0.563127i	$-0.190402\pi$
$138$	0.898221	+	15.8348i	0.0764617	+	1.34795i
$139$	4.06270	−	4.06270i	0.344594	−	0.344594i	−0.513497	−	0.858091i	$-0.671650\pi$
$139$	4.06270	−	4.06270i	0.344594	−	0.344594i	0.858091	+	0.513497i	$0.171650\pi$
$140$	−0.617001	+	0.775487i	−0.0521461	+	0.0655406i
$141$	16.5656	+	16.5656i	1.39507	+	1.39507i
$142$	17.1578	+	15.3158i	1.43985	+	1.28527i
$143$	−2.48578			−0.207871
$144$	−5.09896	−	22.1100i	−0.424914	−	1.84250i
$145$	5.59455			0.464602
$146$	7.39605	+	6.60201i	0.612101	+	0.546387i
$147$	14.0654	+	14.0654i	1.16009	+	1.16009i
$148$	10.3567	+	8.24010i	0.851315	+	0.677332i
$149$	12.4246	−	12.4246i	1.01786	−	1.01786i	0.0180265	−	0.999838i	$-0.494262\pi$
$149$	12.4246	−	12.4246i	1.01786	−	1.01786i	0.999838	−	0.0180265i	$-0.00573833\pi$
$150$	0.235864	+	4.15807i	0.0192582	+	0.339505i
$151$			2.38220i			0.193861i	0.995291	+	0.0969303i	$0.0309024\pi$
$151$			2.38220i			0.193861i	−0.995291	+	0.0969303i	$0.969098\pi$
$152$	2.73832	+	15.9531i	0.222107	+	1.29397i
$153$		−	9.47028i		−	0.765627i
$154$	−0.699614	+	0.0396852i	−0.0563765	+	0.00319793i
$155$	−0.0276913	+	0.0276913i	−0.00222422	+	0.00222422i
$156$	14.5469	−	1.65566i	1.16469	−	0.132559i
$157$	−3.07201	−	3.07201i	−0.245173	−	0.245173i	0.573813	−	0.818986i	$-0.305464\pi$
$157$	−3.07201	−	3.07201i	−0.245173	−	0.245173i	−0.818986	+	0.573813i	$0.805464\pi$
$158$	10.4699	−	11.7292i	0.832944	−	0.933123i
$159$	24.7766			1.96491
$160$	−1.58134	−	5.43133i	−0.125016	−	0.429385i
$161$	−1.88696			−0.148713
$162$	5.80175	−	6.49954i	0.455829	−	0.510652i
$163$	14.8523	+	14.8523i	1.16332	+	1.16332i	0.983744	+	0.179575i	$0.0574722\pi$
$163$	14.8523	+	14.8523i	1.16332	+	1.16332i	0.179575	+	0.983744i	$0.442528\pi$
$164$	8.64807	−	0.984281i	0.675301	−	0.0768594i
$165$	−2.08238	+	2.08238i	−0.162113	+	0.162113i
$166$	12.4888	−	0.708421i	0.969320	−	0.0549841i
$167$			9.27763i			0.717925i	0.933352	+	0.358962i	$0.116869\pi$
$167$			9.27763i			0.717925i	−0.933352	+	0.358962i	$0.883131\pi$
$168$	4.06776	−	0.698222i	0.313835	−	0.0538690i
$169$		−	6.82091i		−	0.524686i
$170$	−0.133712	−	2.35721i	−0.0102552	−	0.180790i
$171$	−22.9548	+	22.9548i	−1.75539	+	1.75539i
$172$	19.4418	+	15.4685i	1.48242	+	1.17946i
$173$	−12.9441	−	12.9441i	−0.984122	−	0.984122i	0.0157539	−	0.999876i	$-0.494985\pi$
$173$	−12.9441	−	12.9441i	−0.984122	−	0.984122i	−0.999876	+	0.0157539i	$0.994985\pi$
$174$	−17.3822	−	15.5160i	−1.31774	−	1.17627i
$175$	−0.495497			−0.0374561
$176$	2.12048	−	3.39169i	0.159838	−	0.255658i
$177$	−13.7156			−1.03093
$178$	8.11488	+	7.24368i	0.608236	+	0.542937i
$179$	3.05751	+	3.05751i	0.228529	+	0.228529i	0.812078	−	0.583549i	$-0.198336\pi$
$179$	3.05751	+	3.05751i	0.228529	+	0.228529i	−0.583549	+	0.812078i	$0.698336\pi$
$180$	7.06360	−	8.87800i	0.526490	−	0.661727i
$181$	5.38539	−	5.38539i	0.400293	−	0.400293i	−0.478043	−	0.878336i	$-0.658654\pi$
$181$	5.38539	−	5.38539i	0.400293	−	0.400293i	0.878336	+	0.478043i	$0.158654\pi$
$182$	0.0986486	+	1.73908i	0.00731232	+	0.128910i
$183$			7.24237i			0.535372i
$184$	6.21815	−	8.79514i	0.458408	−	0.648386i
$185$			6.61741i			0.486522i
$186$	0.162836	−	0.00923679i	0.0119397	−	0.000677274i
$187$	1.18050	−	1.18050i	0.0863267	−	0.0863267i
$188$	−1.79921	−	15.8082i	−0.131221	−	1.15293i
$189$	2.75761	+	2.75761i	0.200587	+	0.200587i
$190$	−5.38948	+	6.03768i	−0.390994	+	0.438019i
$191$	−23.6408			−1.71059			−0.855296	−	0.518140i	$-0.826625\pi$
$191$	−23.6408			−1.71059			−0.855296	+	0.518140i	$0.826625\pi$
$192$	−10.1502	+	21.2608i	−0.732526	+	1.53436i
$193$	−12.8720			−0.926548			−0.463274	−	0.886215i	$-0.653325\pi$
$193$	−12.8720			−0.926548			−0.463274	+	0.886215i	$0.653325\pi$
$194$	7.43423	−	8.32836i	0.533747	−	0.597941i
$195$	5.17633	+	5.17633i	0.370684	+	0.370684i
$196$	−1.52766	−	13.4223i	−0.109119	−	0.958736i
$197$	5.00396	−	5.00396i	0.356517	−	0.356517i	−0.506010	−	0.862527i	$-0.668880\pi$
$197$	5.00396	−	5.00396i	0.356517	−	0.356517i	0.862527	+	0.506010i	$0.168880\pi$
$198$	8.00938	−	0.454328i	0.569202	−	0.0322877i
$199$			12.8467i			0.910678i	0.890318	+	0.455339i	$0.150482\pi$
$199$			12.8467i			0.910678i	−0.890318	+	0.455339i	$0.849518\pi$
$200$	1.63283	−	2.30952i	0.115458	−	0.163308i
$201$		−	23.9502i		−	1.68931i
$202$	0.574728	+	10.1319i	0.0404378	+	0.712881i
$203$	1.96016	−	1.96016i	0.137576	−	0.137576i
$204$	−6.12210	+	7.69465i	−0.428632	+	0.538733i
$205$	3.07729	+	3.07729i	0.214927	+	0.214927i
$206$	11.0064	+	9.82480i	0.766855	+	0.684526i
$207$	21.6024			1.50147
$208$	−8.43098	−	5.27105i	−0.584583	−	0.365482i
$209$	−5.72277			−0.395852
$210$	1.53950	+	1.37422i	0.106236	+	0.0948303i
$211$	−7.96843	−	7.96843i	−0.548570	−	0.548570i	0.377457	−	0.926027i	$-0.376798\pi$
$211$	−7.96843	−	7.96843i	−0.548570	−	0.548570i	−0.926027	+	0.377457i	$0.876798\pi$
$212$	−13.1674	−	10.4764i	−0.904340	−	0.719520i
$213$	33.8655	−	33.8655i	2.32042	−	2.32042i
$214$	−0.132091	−	2.32865i	−0.00902958	−	0.159183i
$215$			12.4223i			0.847195i
$216$	−21.9405	+	3.76604i	−1.49286	+	0.256247i
$217$			0.0194044i			0.00131726i
$218$	−26.1537	+	1.48355i	−1.77135	+	0.100479i
$219$	14.5981	−	14.5981i	0.986445	−	0.986445i
$220$	1.98717	−	0.226170i	0.133975	−	0.0152484i
$221$	−2.93446	−	2.93446i	−0.197393	−	0.197393i
$222$	18.3528	−	20.5602i	1.23176	−	1.37991i
$223$	13.3382			0.893189			0.446595	−	0.894736i	$-0.352637\pi$
$223$	13.3382			0.893189			0.446595	+	0.894736i	$0.352637\pi$
$224$	−2.45702	−	1.34892i	−0.164167	−	0.0901286i
$225$	5.67259			0.378173
$226$	−2.80911	+	3.14697i	−0.186860	+	0.209333i
$227$	−6.77859	−	6.77859i	−0.449911	−	0.449911i	0.445414	−	0.895325i	$-0.353057\pi$
$227$	−6.77859	−	6.77859i	−0.449911	−	0.449911i	−0.895325	+	0.445414i	$0.853057\pi$
$228$	33.4900	−	3.81167i	2.21793	−	0.252434i
$229$	2.54907	−	2.54907i	0.168447	−	0.168447i	−0.617849	−	0.786297i	$-0.711996\pi$
$229$	2.54907	−	2.54907i	0.168447	−	0.168447i	0.786297	+	0.617849i	$0.211996\pi$
$230$	5.37698	−	0.305006i	0.354548	−	0.0201115i
$231$			1.45920i			0.0960085i
$232$	2.67697	+	15.5957i	0.175751	+	1.02391i
$233$		−	17.9298i		−	1.17462i	−0.809362	−	0.587310i	$-0.800187\pi$
$233$		−	17.9298i		−	1.17462i	0.809362	−	0.587310i	$-0.199813\pi$
$234$	−1.12936	−	19.9095i	−0.0738284	−	1.30153i
$235$	5.62512	−	5.62512i	0.366942	−	0.366942i
$236$	7.28911	+	5.79944i	0.474481	+	0.377511i
$237$	−23.1506	−	23.1506i	−1.50380	−	1.50380i
$238$	−0.872743	−	0.779046i	−0.0565715	−	0.0504981i
$239$	−12.0110			−0.776929			−0.388465	−	0.921464i	$-0.626994\pi$
$239$	−12.0110			−0.776929			−0.388465	+	0.921464i	$0.626994\pi$
$240$	−11.4784	+	2.64713i	−0.740929	+	0.170871i
$241$	20.8475			1.34290			0.671452	−	0.741048i	$-0.265671\pi$
$241$	20.8475			1.34290			0.671452	+	0.741048i	$0.265671\pi$
$242$	1.05503	+	0.941762i	0.0678198	+	0.0605387i
$243$	3.86749	+	3.86749i	0.248099	+	0.248099i
$244$	3.06232	−	3.84893i	0.196045	−	0.246402i
$245$	4.77614	−	4.77614i	0.305136	−	0.305136i
$246$	−1.02647	−	18.0957i	−0.0654453	−	1.15374i
$247$			14.2255i			0.905148i
$248$	−0.0904442	−	0.0639438i	−0.00574321	−	0.00406044i
$249$		−	26.0482i		−	1.65074i
$250$	1.41194	−	0.0800917i	0.0892992	−	0.00506545i
$251$	1.41176	−	1.41176i	0.0891093	−	0.0891093i	−0.661147	−	0.750256i	$-0.729930\pi$
$251$	1.41176	−	1.41176i	0.0891093	−	0.0891093i	0.750256	+	0.661147i	$0.229930\pi$
$252$	−0.635708	−	5.58545i	−0.0400459	−	0.351850i
$253$	2.69281	+	2.69281i	0.169296	+	0.169296i
$254$	−3.43190	+	3.84465i	−0.215336	+	0.241235i
$255$	−4.91650			−0.307883
$256$	14.3840	−	7.00709i	0.899003	−	0.437943i
$257$	5.27037			0.328757			0.164378	−	0.986397i	$-0.447438\pi$
$257$	5.27037			0.328757			0.164378	+	0.986397i	$0.447438\pi$
$258$	34.4523	−	38.5959i	2.14491	−	2.40288i
$259$	2.31854	+	2.31854i	0.144067	+	0.144067i
$260$	−0.562208	−	4.93966i	−0.0348667	−	0.306345i
$261$	−22.4405	+	22.4405i	−1.38903	+	1.38903i
$262$	5.67168	−	0.321723i	0.350398	−	0.0198761i
$263$			9.03862i			0.557345i	0.960386	+	0.278673i	$0.0898944\pi$
$263$			9.03862i			0.557345i	−0.960386	+	0.278673i	$0.910106\pi$
$264$	−6.80137	−	4.80855i	−0.418595	−	0.295946i
$265$		−	8.41330i		−	0.516825i
$266$	0.227109	+	4.00373i	0.0139250	+	0.245484i
$267$	16.0169	−	16.0169i	0.980217	−	0.980217i
$268$	−10.1269	+	12.7282i	−0.618602	+	0.777499i
$269$	15.7359	+	15.7359i	0.959437	+	0.959437i	0.999209	−	0.0397715i	$-0.0126630\pi$
$269$	15.7359	+	15.7359i	0.959437	+	0.959437i	−0.0397715	+	0.999209i	$0.512663\pi$
$270$	−8.30370	−	7.41222i	−0.505347	−	0.451093i
$271$	15.7523			0.956882			0.478441	−	0.878120i	$-0.341202\pi$
$271$	15.7523			0.956882			0.478441	+	0.878120i	$0.341202\pi$
$272$	6.50712	−	1.50066i	0.394552	−	0.0909907i
$273$	3.62725			0.219531
$274$	13.9079	+	12.4147i	0.840206	+	0.750002i
$275$	0.707107	+	0.707107i	0.0426401	+	0.0426401i
$276$	−17.5521	−	13.9650i	−1.05651	−	0.840593i
$277$	6.72480	−	6.72480i	0.404054	−	0.404054i	−0.475605	−	0.879659i	$-0.657771\pi$
$277$	6.72480	−	6.72480i	0.404054	−	0.404054i	0.879659	+	0.475605i	$0.157771\pi$
$278$	0.460169	+	8.11236i	0.0275991	+	0.486547i
$279$		−	0.222147i		−	0.0132996i
$280$	−0.237093	−	1.38128i	−0.0141690	−	0.0825471i
$281$			22.4355i			1.33839i	0.743087	+	0.669194i	$0.233361\pi$
$281$			22.4355i			1.33839i	−0.743087	+	0.669194i	$0.766639\pi$
$282$	−33.0779	+	1.87633i	−1.96976	+	0.111734i
$283$	19.8752	−	19.8752i	1.18146	−	1.18146i	0.202090	−	0.979367i	$-0.435227\pi$
$283$	19.8752	−	19.8752i	1.18146	−	1.18146i	0.979367	−	0.202090i	$-0.0647734\pi$
$284$	−32.3171	+	3.67818i	−1.91767	+	0.218260i
$285$	11.9170	+	11.9170i	0.705900	+	0.705900i
$286$	2.34101	−	2.62257i	0.138427	−	0.155076i
$287$	2.15638			0.127287
$288$	28.1287	+	15.4428i	1.65750	+	0.909978i
$289$	−14.2128			−0.836049
$290$	−5.26873	+	5.90241i	−0.309391	+	0.346601i
$291$	−16.4382	−	16.4382i	−0.963625	−	0.963625i
$292$	−13.9306	+	1.58552i	−0.815228	+	0.0927853i
$293$	7.62093	−	7.62093i	0.445220	−	0.445220i	−0.448542	−	0.893762i	$-0.648057\pi$
$293$	7.62093	−	7.62093i	0.445220	−	0.445220i	0.893762	+	0.448542i	$0.148057\pi$
$294$	−28.0856	+	1.59314i	−1.63799	+	0.0929139i
$295$			4.65738i			0.271163i
$296$	−18.4471	+	3.16640i	−1.07221	+	0.184043i
$297$		−	7.87059i		−	0.456698i
$298$	1.40730	+	24.8093i	0.0815225	+	1.43717i
$299$	6.69373	−	6.69373i	0.387108	−	0.387108i
$300$	−4.60901	−	3.66707i	−0.266101	−	0.211718i
$301$	4.35240	+	4.35240i	0.250868	+	0.250868i
$302$	−2.51329	−	2.24346i	−0.144623	−	0.129097i
$303$	21.1324			1.21403
$304$	−19.4098	−	12.1350i	−1.11323	−	0.695992i
$305$	2.45927			0.140817
$306$	9.99141	+	8.91875i	0.571171	+	0.509851i
$307$	4.96078	+	4.96078i	0.283126	+	0.283126i	0.834355	−	0.551228i	$-0.185841\pi$
$307$	4.96078	+	4.96078i	0.283126	+	0.283126i	−0.551228	+	0.834355i	$0.685841\pi$
$308$	0.617001	−	0.775487i	0.0351569	−	0.0441875i
$309$	21.7241	−	21.7241i	1.23584	−	1.23584i
$310$	−0.00313651	−	0.0552938i	−0.000178142	−	0.00314048i
$311$		−	30.3121i		−	1.71884i	−0.511270	−	0.859420i	$-0.670825\pi$
$311$		−	30.3121i		−	1.71884i	0.511270	−	0.859420i	$-0.329175\pi$
$312$	−11.9530	+	16.9067i	−0.676704	+	0.957152i
$313$			29.6637i			1.67669i	0.545139	+	0.838346i	$0.316477\pi$
$313$			29.6637i			1.67669i	−0.545139	+	0.838346i	$0.683523\pi$
$314$	6.13415	−	0.347956i	0.346170	−	0.0196363i
$315$	1.98750	−	1.98750i	0.111983	−	0.111983i
$316$	2.51442	+	22.0922i	0.141447	+	1.24278i
$317$	−0.130729	−	0.130729i	−0.00734245	−	0.00734245i	0.703426	−	0.710768i	$-0.251653\pi$
$317$	−0.130729	−	0.130729i	−0.00734245	−	0.00734245i	−0.710768	+	0.703426i	$0.751653\pi$
$318$	−23.3336	+	26.1400i	−1.30848	+	1.46586i
$319$	−5.59455			−0.313235
$320$	7.21945	+	3.44667i	0.403580	+	0.192674i
$321$	−4.85692			−0.271087
$322$	1.77707	−	1.99079i	0.0990320	−	0.110943i
$323$	−6.75573	−	6.75573i	−0.375899	−	0.375899i
$324$	1.39333	+	12.2420i	0.0774071	+	0.680113i
$325$	1.75771	−	1.75771i	0.0975002	−	0.0975002i
$326$	−29.6569	+	1.68227i	−1.64254	+	0.0931722i
$327$			54.5494i			3.01659i
$328$	−7.10597	+	10.0509i	−0.392362	+	0.554969i
$329$		−	3.94174i		−	0.217315i
$330$	−0.235864	−	4.15807i	−0.0129839	−	0.228894i
$331$	−10.5719	+	10.5719i	−0.581086	+	0.581086i	−0.935202	−	0.354116i	$-0.884782\pi$
$331$	−10.5719	+	10.5719i	−0.581086	+	0.581086i	0.354116	+	0.935202i	$0.384782\pi$
$332$	−11.0141	+	13.8432i	−0.604476	+	0.759745i
$333$	−26.5433	−	26.5433i	−1.45456	−	1.45456i
$334$	−9.78817	−	8.73732i	−0.535585	−	0.478085i
$335$	−8.13269			−0.444336
$336$	−3.09422	+	4.94916i	−0.168803	+	0.269999i
$337$	19.5166			1.06314			0.531569	−	0.847015i	$-0.321602\pi$
$337$	19.5166			1.06314			0.531569	+	0.847015i	$0.321602\pi$
$338$	7.19626	+	6.42368i	0.391425	+	0.349402i
$339$	6.21138	+	6.21138i	0.337356	+	0.337356i
$340$	2.61285	+	2.07886i	0.141702	+	0.112742i
$341$	0.0276913	−	0.0276913i	0.00149957	−	0.00149957i
$342$	−2.60001	−	45.8358i	−0.140593	−	2.47852i
$343$		−	6.81531i		−	0.367992i
$344$	−34.6292	+	5.94402i	−1.86708	+	0.320480i
$345$		−	11.2149i		−	0.603790i
$346$	25.8467	−	1.46614i	1.38952	−	0.0788200i
$347$	−8.62592	+	8.62592i	−0.463063	+	0.463063i	−0.899658	−	0.436595i	$-0.856184\pi$
$347$	−8.62592	+	8.62592i	−0.463063	+	0.463063i	0.436595	+	0.899658i	$0.356184\pi$
$348$	32.7397	−	3.72627i	1.75503	−	0.199749i
$349$	−17.1141	−	17.1141i	−0.916098	−	0.916098i	0.0806449	−	0.996743i	$-0.474302\pi$
$349$	−17.1141	−	17.1141i	−0.916098	−	0.916098i	−0.996743	+	0.0806449i	$0.974302\pi$
$350$	0.466640	−	0.522764i	0.0249430	−	0.0279429i
$351$	−19.5645			−1.04428
$352$	1.58134	+	5.43133i	0.0842855	+	0.289491i
$353$	7.17153			0.381702			0.190851	−	0.981619i	$-0.438875\pi$
$353$	7.17153			0.381702			0.190851	+	0.981619i	$0.438875\pi$
$354$	12.9169	−	14.4704i	0.686523	−	0.769092i
$355$	−11.4996	−	11.4996i	−0.610335	−	0.610335i
$356$	−15.2846	+	1.73962i	−0.810081	+	0.0921994i
$357$	−1.72259	+	1.72259i	−0.0911691	+	0.0911691i
$358$	−6.10520	+	0.346314i	−0.322670	+	0.0183033i
$359$			9.98964i			0.527233i	0.964628	+	0.263617i	$0.0849153\pi$
$359$			9.98964i			0.527233i	−0.964628	+	0.263617i	$0.915085\pi$
$360$	2.71431	+	15.8133i	0.143057	+	0.833432i
$361$			13.7500i			0.723687i
$362$	0.609986	+	10.7535i	0.0320601	+	0.565191i
$363$	2.08238	−	2.08238i	0.109296	−	0.109296i
$364$	−1.92769	−	1.53373i	−0.101038	−	0.0803891i
$365$	−4.95702	−	4.95702i	−0.259462	−	0.259462i
$366$	−7.64091	−	6.82059i	−0.399397	−	0.356518i
$367$	−13.6414			−0.712074			−0.356037	−	0.934472i	$-0.615872\pi$
$367$	−13.6414			−0.712074			−0.356037	+	0.934472i	$0.615872\pi$
$368$	3.42311	+	14.8432i	0.178442	+	0.773758i
$369$	−24.6868			−1.28515
$370$	−6.98156	−	6.23202i	−0.362954	−	0.323987i
$371$	−2.94776	−	2.94776i	−0.153040	−	0.153040i
$372$	−0.143608	+	0.180496i	−0.00744572	+	0.00935826i
$373$	−25.8721	+	25.8721i	−1.33961	+	1.33961i	−0.443171	+	0.896437i	$0.646147\pi$
$373$	−25.8721	+	25.8721i	−1.33961	+	1.33961i	−0.896437	+	0.443171i	$0.853853\pi$
$374$	0.133712	+	2.35721i	0.00691406	+	0.121888i
$375$		−	2.94493i		−	0.152075i
$376$	18.3725	+	12.9893i	0.947489	+	0.669873i
$377$			13.9068i			0.716237i
$378$	−5.50638	+	0.312346i	−0.283217	+	0.0160654i
$379$	−18.1809	+	18.1809i	−0.933889	+	0.933889i	−0.997946	−	0.0640574i	$-0.979596\pi$
$379$	−18.1809	+	18.1809i	−0.933889	+	0.933889i	0.0640574	+	0.997946i	$0.479596\pi$
$380$	−1.29432	−	11.3721i	−0.0663971	−	0.583377i
$381$	7.58844	+	7.58844i	0.388768	+	0.388768i
$382$	22.2640	−	24.9418i	1.13913	−	1.27613i
$383$	−12.8491			−0.656559			−0.328279	−	0.944581i	$-0.606469\pi$
$383$	−12.8491			−0.656559			−0.328279	+	0.944581i	$0.606469\pi$
$384$	−12.8717	−	30.7313i	−0.656854	−	1.56825i
$385$	0.495497			0.0252529
$386$	12.1224	−	13.5803i	0.617013	−	0.691221i
$387$	−49.8275	−	49.8275i	−2.53287	−	2.53287i
$388$	1.78538	+	15.6867i	0.0906389	+	0.796369i
$389$	18.0189	−	18.0189i	0.913593	−	0.913593i	−0.0829597	−	0.996553i	$-0.526437\pi$
$389$	18.0189	−	18.0189i	0.913593	−	0.913593i	0.996553	+	0.0829597i	$0.0264373\pi$
$390$	−10.3360	+	0.586306i	−0.523386	+	0.0296888i
$391$			6.35773i			0.321524i
$392$	15.5996	+	11.0289i	0.787899	+	0.557043i
$393$		−	11.8296i		−	0.596723i
$394$	0.566782	+	9.99185i	0.0285541	+	0.503382i
$395$	−7.86119	+	7.86119i	−0.395540	+	0.395540i
$396$	−7.06360	+	8.87800i	−0.354959	+	0.446136i
$397$	−17.0632	−	17.0632i	−0.856375	−	0.856375i	0.134534	−	0.990909i	$-0.457046\pi$
$397$	−17.0632	−	17.0632i	−0.856375	−	0.856375i	−0.990909	+	0.134534i	$0.957046\pi$
$398$	−13.5536	−	12.0985i	−0.679382	−	0.606444i
$399$	8.35068			0.418057
$400$	0.898877	+	3.89769i	0.0449438	+	0.194885i
$401$	25.9937			1.29806			0.649032	−	0.760761i	$-0.275174\pi$
$401$	25.9937			1.29806			0.649032	+	0.760761i	$0.275174\pi$
$402$	25.2681	+	22.5554i	1.26026	+	1.12496i
$403$	−0.0688345	−	0.0688345i	−0.00342889	−	0.00342889i
$404$	−11.2307	−	8.93551i	−0.558750	−	0.444558i
$405$	−4.35616	+	4.35616i	−0.216459	+	0.216459i
$406$	0.222021	+	3.91403i	0.0110187	+	0.194250i
$407$		−	6.61741i		−	0.328013i
$408$	−2.35252	−	13.7055i	−0.116467	−	0.678524i
$409$			39.0238i			1.92960i	0.262979	+	0.964802i	$0.415295\pi$
$409$			39.0238i			1.92960i	−0.262979	+	0.964802i	$0.584705\pi$
$410$	−6.14471	+	0.348555i	−0.303466	+	0.0172139i
$411$	27.4509	−	27.4509i	1.35405	−	1.35405i
$412$	−20.7309	+	2.35949i	−1.02134	+	0.116244i
$413$	1.63180	+	1.63180i	0.0802958	+	0.0802958i
$414$	−20.3443	+	22.7912i	−0.999870	+	1.12013i
$415$	−8.84512			−0.434190
$416$	13.5011	−	3.93085i	0.661945	−	0.192726i
$417$	16.9202			0.828584
$418$	5.38948	−	6.03768i	0.263608	−	0.295313i
$419$	13.8337	+	13.8337i	0.675818	+	0.675818i	0.959051	−	0.283233i	$-0.0914069\pi$
$419$	13.8337	+	13.8337i	0.675818	+	0.675818i	−0.283233	+	0.959051i	$0.591407\pi$
$420$	−2.89969	+	0.330028i	−0.141490	+	0.0161037i
$421$	22.0639	−	22.0639i	1.07533	−	1.07533i	0.0784053	−	0.996922i	$-0.475017\pi$
$421$	22.0639	−	22.0639i	1.07533	−	1.07533i	0.996922	−	0.0784053i	$-0.0249828\pi$
$422$	15.9113	−	0.902559i	0.774549	−	0.0439359i
$423$			45.1261i			2.19411i
$424$	23.4534	−	4.02572i	1.13900	−	0.195506i
$425$			1.66948i			0.0809817i
$426$	3.83583	+	67.6222i	0.185847	+	3.27631i
$427$	0.861653	−	0.861653i	0.0416983	−	0.0416983i
$428$	2.58119	+	2.05367i	0.124767	+	0.0992681i
$429$	−5.17633	−	5.17633i	−0.249915	−	0.249915i
$430$	−13.1059	−	11.6989i	−0.632022	−	0.564169i
$431$	−26.5081			−1.27685			−0.638426	−	0.769683i	$-0.720414\pi$
$431$	−26.5081			−1.27685			−0.638426	+	0.769683i	$0.720414\pi$
$432$	16.6895	−	26.6946i	0.802972	−	1.28434i
$433$	−19.2552			−0.925347			−0.462674	−	0.886529i	$-0.653110\pi$
$433$	−19.2552			−0.925347			−0.462674	+	0.886529i	$0.653110\pi$
$434$	−0.0204722	−	0.0182743i	−0.000982697	−	0.000877195i
$435$	11.6500	+	11.6500i	0.558573	+	0.558573i
$436$	23.0654	−	28.9901i	1.10463	−	1.38837i
$437$	15.4103	−	15.4103i	0.737176	−	0.737176i
$438$	1.65347	+	29.1492i	0.0790061	+	1.39280i
$439$		−	5.99325i		−	0.286042i	−0.989720	−	0.143021i	$-0.954318\pi$
$439$		−	5.99325i		−	0.286042i	0.989720	−	0.143021i	$-0.0456817\pi$
$440$	−1.63283	+	2.30952i	−0.0778419	+	0.110102i
$441$			38.3154i			1.82454i
$442$	5.85950	−	0.332377i	0.278708	−	0.0158096i
$443$	−26.5068	+	26.5068i	−1.25938	+	1.25938i	−0.307985	+	0.951391i	$0.599655\pi$
$443$	−26.5068	+	26.5068i	−1.25938	+	1.25938i	−0.951391	+	0.307985i	$0.900345\pi$
$444$	4.40755	+	38.7256i	0.209173	+	1.83783i
$445$	−5.43880	−	5.43880i	−0.257824	−	0.257824i
$446$	−12.5614	+	14.0721i	−0.594798	+	0.666335i
$447$	51.7455			2.44748
$448$	3.73708	−	1.32187i	0.176561	−	0.0624525i
$449$	−15.1730			−0.716058			−0.358029	−	0.933710i	$-0.616551\pi$
$449$	−15.1730			−0.716058			−0.358029	+	0.933710i	$0.616551\pi$
$450$	−5.34223	+	5.98475i	−0.251835	+	0.282124i
$451$	−3.07729	−	3.07729i	−0.144904	−	0.144904i
$452$	−0.674627	−	5.92739i	−0.0317318	−	0.278801i
$453$	−4.96064	+	4.96064i	−0.233071	+	0.233071i
$454$	13.5354	−	0.767789i	0.635249	−	0.0360341i
$455$		−	1.23170i		−	0.0577428i
$456$	−27.5182	+	38.9226i	−1.28866	+	1.82272i
$457$		−	17.6989i		−	0.827921i	−0.910295	−	0.413960i	$-0.864145\pi$
$457$		−	17.6989i		−	0.827921i	0.910295	−	0.413960i	$-0.135855\pi$
$458$	0.288725	+	5.08996i	0.0134912	+	0.237838i
$459$	9.29124	−	9.29124i	0.433678	−	0.433678i
$460$	−4.74204	+	5.96011i	−0.221099	+	0.277892i
$461$	0.421398	+	0.421398i	0.0196265	+	0.0196265i	0.716852	−	0.697225i	$-0.245582\pi$
$461$	0.421398	+	0.421398i	0.0196265	+	0.0196265i	−0.697225	+	0.716852i	$0.745582\pi$
$462$	−1.53950	−	1.37422i	−0.0716240	−	0.0639346i
$463$	−36.2607			−1.68518			−0.842589	−	0.538558i	$-0.818969\pi$
$463$	−36.2607			−1.68518			−0.842589	+	0.538558i	$0.818969\pi$
$464$	−18.9750	−	11.8632i	−0.880890	−	0.550733i
$465$	−0.115328			−0.00534819
$466$	18.9164	+	16.8856i	0.876287	+	0.782210i
$467$	−29.9973	−	29.9973i	−1.38811	−	1.38811i	−0.829285	−	0.558826i	$-0.811252\pi$
$467$	−29.9973	−	29.9973i	−1.38811	−	1.38811i	−0.558826	−	0.829285i	$-0.688748\pi$
$468$	22.0687	+	17.5585i	1.02013	+	0.811644i
$469$	−2.84945	+	2.84945i	−0.131575	+	0.131575i
$470$	0.637139	+	11.2322i	0.0293890	+	0.518102i
$471$		−	12.7942i		−	0.589524i
$472$	−12.9832	+	2.22853i	−0.597599	+	0.102577i
$473$		−	12.4223i		−	0.571179i
$474$	46.2270	−	2.62220i	2.12327	−	0.120442i
$475$	4.04661	−	4.04661i	0.185671	−	0.185671i
$476$	1.64383	−	0.187093i	0.0753449	−	0.00857539i
$477$	33.7468	+	33.7468i	1.54516	+	1.54516i
$478$	11.3115	−	12.6720i	0.517377	−	0.579603i
$479$	31.9593			1.46026			0.730130	−	0.683308i	$-0.239460\pi$
$479$	31.9593			1.46026			0.730130	+	0.683308i	$0.239460\pi$
$480$	8.01715	−	14.6030i	0.365931	−	0.666534i
$481$	−16.4494			−0.750028
$482$	−19.6334	+	21.9947i	−0.894275	+	1.00183i
$483$	−3.92936	−	3.92936i	−0.178792	−	0.178792i
$484$	−1.98717	+	0.226170i	−0.0903259	+	0.0102805i
$485$	−5.58188	+	5.58188i	−0.253460	+	0.253460i
$486$	−7.72256	+	0.438058i	−0.350302	+	0.0198707i
$487$			12.6981i			0.575404i	0.957720	+	0.287702i	$0.0928913\pi$
$487$			12.6981i			0.575404i	−0.957720	+	0.287702i	$0.907109\pi$
$488$	1.17675	+	6.85561i	0.0532689	+	0.310339i
$489$			61.8560i			2.79723i
$490$	0.540978	+	9.53695i	0.0244389	+	0.430835i
$491$	28.0560	−	28.0560i	1.26615	−	1.26615i	0.318090	−	0.948061i	$-0.396959\pi$
$491$	28.0560	−	28.0560i	1.26615	−	1.26615i	0.948061	−	0.318090i	$-0.103041\pi$
$492$	20.0582	+	15.9589i	0.904293	+	0.719483i
$493$	−6.60437	−	6.60437i	−0.297446	−	0.297446i
$494$	−15.0083	−	13.3970i	−0.675257	−	0.602762i
$495$	−5.67259			−0.254964
$496$	0.152639	−	0.0352013i	0.00685371	−	0.00158059i
$497$	−8.05821			−0.361460
$498$	27.4816	+	24.5312i	1.23148	+	1.09927i
$499$	24.5202	+	24.5202i	1.09767	+	1.09767i	0.994682	+	0.102991i	$0.0328413\pi$
$499$	24.5202	+	24.5202i	1.09767	+	1.09767i	0.102991	+	0.994682i	$0.467159\pi$
$500$	−1.24522	+	1.56507i	−0.0556877	+	0.0699920i
$501$	−19.3195	+	19.3195i	−0.863133	+	0.863133i
$502$	0.159905	+	2.81898i	0.00713691	+	0.125817i
$503$		−	9.35068i		−	0.416926i	−0.978030	−	0.208463i	$-0.933154\pi$
$503$		−	9.35068i		−	0.416926i	0.978030	−	0.208463i	$-0.0668461\pi$
$504$	6.49149	+	4.58947i	0.289154	+	0.204431i
$505$		−	7.17588i		−	0.319322i
$506$	−5.37698	+	0.305006i	−0.239036	+	0.0135592i
$507$	14.2037	−	14.2037i	0.630809	−	0.630809i
$508$	−0.824192	−	7.24150i	−0.0365676	−	0.321289i
$509$	−10.8623	−	10.8623i	−0.481463	−	0.481463i	0.424135	−	0.905599i	$-0.360578\pi$
$509$	−10.8623	−	10.8623i	−0.481463	−	0.481463i	−0.905599	+	0.424135i	$0.860578\pi$
$510$	4.63017	−	5.18704i	0.205027	−	0.229686i
$511$	−3.47357			−0.153662
$512$	−6.15365	+	21.7746i	−0.271956	+	0.962310i
$513$	−45.0415			−1.98863
$514$	−4.96343	+	5.56039i	−0.218928	+	0.245258i
$515$	−7.37679	−	7.37679i	−0.325060	−	0.325060i
$516$	8.27393	+	72.6963i	0.364240	+	3.20027i
$517$	−5.62512	+	5.62512i	−0.247392	+	0.247392i
$518$	−4.62963	+	0.262613i	−0.203414	+	0.0115386i
$519$		−	53.9090i		−	2.36634i
$520$	5.74095	+	4.05884i	0.251757	+	0.177992i
$521$		−	7.65580i		−	0.335407i	−0.985838	−	0.167703i	$-0.946365\pi$
$521$		−	7.65580i		−	0.335407i	0.985838	−	0.167703i	$-0.0536350\pi$
$522$	−2.54176	−	44.8089i	−0.111250	−	1.96123i
$523$	−26.8166	+	26.8166i	−1.17261	+	1.17261i	−0.191022	+	0.981586i	$0.561180\pi$
$523$	−26.8166	+	26.8166i	−1.17261	+	1.17261i	−0.981586	+	0.191022i	$0.938820\pi$
$524$	−5.00194	+	6.28677i	−0.218511	+	0.274639i
$525$	−1.03181	−	1.03181i	−0.0450320	−	0.0450320i
$526$	−9.53600	−	8.51223i	−0.415789	−	0.371151i
$527$	0.0653793			0.00284797
$528$	11.4784	−	2.64713i	0.499534	−	0.115201i
$529$	8.49752			0.369457
$530$	8.87627	+	7.92332i	0.385561	+	0.344167i
$531$	−18.6813	−	18.6813i	−0.810701	−	0.810701i
$532$	−4.43793	−	3.53095i	−0.192409	−	0.153086i
$533$	−7.64946	+	7.64946i	−0.331335	+	0.331335i
$534$	1.81418	+	31.9823i	0.0785072	+	1.38401i
$535$			1.64925i			0.0713034i
$536$	−3.89145	−	22.6712i	−0.168085	−	0.979245i
$537$			12.7338i			0.549503i
$538$	−31.4214	+	1.78236i	−1.35467	+	0.0768430i
$539$	−4.77614	+	4.77614i	−0.205723	+	0.205723i
$540$	15.6402	−	1.78009i	0.673047	−	0.0766030i
$541$	8.56909	+	8.56909i	0.368414	+	0.368414i	0.866899	−	0.498485i	$-0.166110\pi$
$541$	8.56909	+	8.56909i	0.368414	+	0.368414i	−0.498485	+	0.866899i	$0.666110\pi$
$542$	−14.8349	+	16.6191i	−0.637213	+	0.713851i
$543$	22.4288			0.962513
$544$	−4.54492	+	8.27846i	−0.194862	+	0.354936i
$545$	18.5232			0.793446
$546$	−3.41601	+	3.82685i	−0.146192	+	0.163774i
$547$	−18.2995	−	18.2995i	−0.782430	−	0.782430i	0.197810	−	0.980240i	$-0.436617\pi$
$547$	−18.2995	−	18.2995i	−0.782430	−	0.782430i	−0.980240	+	0.197810i	$0.936617\pi$
$548$	−26.1958	+	2.98148i	−1.11903	+	0.127362i
$549$	−9.86445	+	9.86445i	−0.421005	+	0.421005i
$550$	−1.41194	+	0.0800917i	−0.0602055	+	0.00341512i
$551$			32.0163i			1.36394i
$552$	31.2633	−	5.36628i	1.33066	−	0.228404i
$553$			5.50864i			0.234251i
$554$	0.761696	+	13.4280i	0.0323614	+	0.570501i
$555$	−13.7799	+	13.7799i	−0.584926	+	0.584926i
$556$	−8.99214	−	7.15442i	−0.381352	−	0.303415i
$557$	−9.68836	−	9.68836i	−0.410509	−	0.410509i	0.471407	−	0.881916i	$-0.343746\pi$
$557$	−9.68836	−	9.68836i	−0.410509	−	0.410509i	−0.881916	+	0.471407i	$0.843746\pi$
$558$	0.234372	+	0.209210i	0.00992174	+	0.00885655i
$559$	−30.8791			−1.30605
$560$	1.68057	+	1.05069i	0.0710171	+	0.0443999i
$561$	4.91650			0.207575
$562$	−23.6701	−	21.1289i	−0.998462	−	0.891268i
$563$	−23.7784	−	23.7784i	−1.00214	−	1.00214i	−0.999998	−	0.00214229i	$-0.999318\pi$
$563$	−23.7784	−	23.7784i	−1.00214	−	1.00214i	−0.00214229	−	0.999998i	$-0.500682\pi$
$564$	29.1720	−	36.6652i	1.22836	−	1.54388i
$565$	2.10918	−	2.10918i	0.0887338	−	0.0887338i
$566$	2.25120	+	39.6866i	0.0946249	+	1.66815i
$567$			3.05253i			0.128194i
$568$	26.5544	−	37.5594i	1.11420	−	1.57596i
$569$			21.3048i			0.893142i	0.894748	+	0.446571i	$0.147355\pi$
$569$			21.3048i			0.893142i	−0.894748	+	0.446571i	$0.852645\pi$
$570$	−23.7957	+	1.34980i	−0.996691	+	0.0565367i
$571$	27.9153	−	27.9153i	1.16822	−	1.16822i	0.185591	−	0.982627i	$-0.440580\pi$
$571$	27.9153	−	27.9153i	1.16822	−	1.16822i	0.982627	−	0.185591i	$-0.0594199\pi$
$572$	0.562208	+	4.93966i	0.0235071	+	0.206538i
$573$	−49.2292	−	49.2292i	−2.05658	−	2.05658i
$574$	−2.03080	+	2.27504i	−0.0847638	+	0.0949584i
$575$	−3.80821			−0.158813
$576$	−42.7832	+	15.1331i	−1.78263	+	0.630547i
$577$	26.5519			1.10537			0.552686	−	0.833390i	$-0.313603\pi$
$577$	26.5519			1.10537			0.552686	+	0.833390i	$0.313603\pi$
$578$	13.3851	−	14.9949i	0.556747	−	0.623708i
$579$	−26.8044	−	26.8044i	−1.11395	−	1.11395i
$580$	−1.26532	−	11.1173i	−0.0525395	−	0.461622i
$581$	−3.09906	+	3.09906i	−0.128571	+	0.128571i
$582$	32.8237	−	1.86190i	1.36058	−	0.0771784i
$583$			8.41330i			0.348443i
$584$	11.4466	−	16.1904i	0.473662	−	0.669963i
$585$			14.1008i			0.582996i
$586$	0.863198	+	15.2174i	0.0356584	+	0.628625i
$587$	16.5276	−	16.5276i	0.682166	−	0.682166i	−0.278322	−	0.960488i	$-0.589778\pi$
$587$	16.5276	−	16.5276i	0.682166	−	0.682166i	0.960488	+	0.278322i	$0.0897782\pi$
$588$	24.7691	−	31.1315i	1.02146	−	1.28384i
$589$	−0.158471	−	0.158471i	−0.00652969	−	0.00652969i
$590$	−4.91367	−	4.38614i	−0.202292	−	0.180574i
$591$	20.8403			0.857254
$592$	14.0321	−	22.4442i	0.576716	−	0.922450i
$593$	−32.8909			−1.35067			−0.675334	−	0.737512i	$-0.736001\pi$
$593$	−32.8909			−1.35067			−0.675334	+	0.737512i	$0.736001\pi$
$594$	8.30370	+	7.41222i	0.340705	+	0.304127i
$595$	0.584935	+	0.584935i	0.0239800	+	0.0239800i
$596$	−27.4999	−	21.8798i	−1.12644	−	0.896230i
$597$	−26.7517	+	26.7517i	−1.09487	+	1.09487i
$598$	0.758178	+	13.3660i	0.0310042	+	0.546575i
$599$		−	32.6742i		−	1.33503i	−0.744596	−	0.667515i	$-0.767358\pi$
$599$		−	32.6742i		−	1.33503i	0.744596	−	0.667515i	$-0.232642\pi$
$600$	8.20945	−	1.40913i	0.335149	−	0.0575276i
$601$		−	39.0898i		−	1.59451i	−0.603646	−	0.797253i	$-0.706286\pi$
$601$		−	39.0898i		−	1.59451i	0.603646	−	0.797253i	$-0.293714\pi$
$602$	−8.69083	+	0.492982i	−0.354212	+	0.0200925i
$603$	32.6213	−	32.6213i	1.32844	−	1.32844i
$604$	4.73384	−	0.538782i	0.192617	−	0.0219227i
$605$	−0.707107	−	0.707107i	−0.0287480	−	0.0287480i
$606$	−19.9017	+	22.2953i	−0.808452	+	0.905685i
$607$	−29.5352			−1.19880			−0.599399	−	0.800450i	$-0.704594\pi$
$607$	−29.5352			−1.19880			−0.599399	+	0.800450i	$0.704594\pi$
$608$	31.0822	−	9.04962i	1.26055	−	0.367011i
$609$	8.16358			0.330805
$610$	−2.31605	+	2.59460i	−0.0937740	+	0.105052i
$611$	13.9828	+	13.9828i	0.565683	+	0.565683i
$612$	−18.8191	+	2.14189i	−0.760715	+	0.0865809i
$613$	−8.28527	+	8.28527i	−0.334639	+	0.334639i	−0.854345	−	0.519706i	$-0.826041\pi$
$613$	−8.28527	+	8.28527i	−0.334639	+	0.334639i	0.519706	+	0.854345i	$0.326041\pi$
$614$	−9.90563	+	0.561891i	−0.399759	+	0.0226761i
$615$			12.8162i			0.516798i
$616$	0.237093	+	1.38128i	0.00955275	+	0.0556532i
$617$			42.5560i			1.71324i	0.515948	+	0.856620i	$0.327440\pi$
$617$			42.5560i			1.71324i	−0.515948	+	0.856620i	$0.672560\pi$
$618$	2.46062	+	43.3785i	0.0989807	+	1.74494i
$619$	−1.99452	+	1.99452i	−0.0801664	+	0.0801664i	−0.746053	−	0.665887i	$-0.768053\pi$
$619$	−1.99452	+	1.99452i	−0.0801664	+	0.0801664i	0.665887	+	0.746053i	$0.268053\pi$
$620$	0.0612904	+	0.0487645i	0.00246148	+	0.00195843i
$621$	21.1940	+	21.1940i	0.850487	+	0.850487i
$622$	31.9801	+	28.5468i	1.28229	+	1.14462i
$623$	−3.81118			−0.152692
$624$	−6.58017	−	28.5328i	−0.263417	−	1.14223i
$625$	−1.00000			−0.0400000
$626$	−31.2961	−	27.9361i	−1.25084	−	1.11655i
$627$	−11.9170	−	11.9170i	−0.475918	−	0.475918i
$628$	−5.40981	+	6.79940i	−0.215875	+	0.271326i
$629$	7.81185	−	7.81185i	0.311479	−	0.311479i
$630$	0.225118	+	3.96863i	0.00896892	+	0.158114i
$631$		−	7.23730i		−	0.288112i	−0.989570	−	0.144056i	$-0.953985\pi$
$631$		−	7.23730i		−	0.288112i	0.989570	−	0.144056i	$-0.0460146\pi$
$632$	−25.6759	−	18.1528i	−1.02133	−	0.722079i
$633$		−	33.1866i		−	1.31905i
$634$	0.261038	−	0.0148072i	0.0103671	−	0.000588070i
$635$	2.57678	−	2.57678i	0.102257	−	0.102257i
$636$	−5.60371	−	49.2352i	−0.222202	−	1.95230i
$637$	11.8724	+	11.8724i	0.470402	+	0.470402i
$638$	5.26873	−	5.90241i	0.208591	−	0.233679i
$639$	92.2527			3.64946
$640$	−10.4353	+	4.37079i	−0.412493	+	0.172771i
$641$	6.88961			0.272123			0.136062	−	0.990700i	$-0.456556\pi$
$641$	6.88961			0.272123			0.136062	+	0.990700i	$0.456556\pi$
$642$	4.57407	−	5.12419i	0.180524	−	0.202236i
$643$	−10.7221	−	10.7221i	−0.422840	−	0.422840i	0.463340	−	0.886180i	$-0.346651\pi$
$643$	−10.7221	−	10.7221i	−0.422840	−	0.422840i	−0.886180	+	0.463340i	$0.846651\pi$
$644$	0.426773	+	3.74971i	0.0168172	+	0.147759i
$645$	−25.8679	+	25.8679i	−1.01855	+	1.01855i
$646$	13.4898	−	0.765200i	0.530748	−	0.0301064i
$647$		−	0.763574i		−	0.0300192i	−0.999887	−	0.0150096i	$-0.995222\pi$
$647$		−	0.763574i		−	0.0300192i	0.999887	−	0.0150096i	$-0.00477788\pi$
$648$	−14.2279	−	10.0591i	−0.558924	−	0.395158i
$649$		−	4.65738i		−	0.182818i
$650$	0.199090	+	3.50978i	0.00780896	+	0.137665i
$651$	−0.0404073	+	0.0404073i	−0.00158369	+	0.00158369i
$652$	26.1548	−	32.8731i	1.02430	−	1.28741i
$653$	19.8790	+	19.8790i	0.777925	+	0.777925i	0.979478	−	0.201553i	$-0.0645987\pi$
$653$	19.8790	+	19.8790i	0.777925	+	0.777925i	−0.201553	+	0.979478i	$0.564599\pi$
$654$	−57.5512	−	51.3726i	−2.25043	−	2.00883i
$655$	−4.01693			−0.156954
$656$	−3.91187	−	16.9626i	−0.152733	−	0.662277i
$657$	39.7665			1.55144
$658$	4.15865	+	3.71218i	0.162121	+	0.144716i
$659$	2.13897	+	2.13897i	0.0833224	+	0.0833224i	0.747540	−	0.664217i	$-0.231235\pi$
$659$	2.13897	+	2.13897i	0.0833224	+	0.0833224i	−0.664217	+	0.747540i	$0.731235\pi$
$660$	4.60901	+	3.66707i	0.179406	+	0.142740i
$661$	4.27773	−	4.27773i	0.166384	−	0.166384i	−0.619004	−	0.785388i	$-0.712463\pi$
$661$	4.27773	−	4.27773i	0.166384	−	0.166384i	0.785388	+	0.619004i	$0.212463\pi$
$662$	−1.19745	−	21.1099i	−0.0465402	−	0.820460i
$663$		−	12.2213i		−	0.474636i
$664$	−4.23235	−	24.6572i	−0.164247	−	0.956884i
$665$		−	2.83561i		−	0.109960i
$666$	53.0014	−	3.00647i	2.05376	−	0.116498i
$667$	15.0651	−	15.0651i	0.583322	−	0.583322i
$668$	18.4362	−	2.09832i	0.713320	−	0.0811865i
$669$	27.7751	+	27.7751i	1.07385	+	1.07385i
$670$	7.65905	−	8.58022i	0.295895	−	0.331483i
$671$	−2.45927			−0.0949391
$672$	−2.30749	−	7.92542i	−0.0890134	−	0.305730i
$673$	−35.2849			−1.36013			−0.680066	−	0.733151i	$-0.738049\pi$
$673$	−35.2849			−1.36013			−0.680066	+	0.733151i	$0.738049\pi$
$674$	−18.3800	+	20.5906i	−0.707972	+	0.793121i
$675$	5.56535	+	5.56535i	0.214210	+	0.214210i
$676$	−13.5543	+	1.54269i	−0.521320	+	0.0593341i
$677$	−6.58245	+	6.58245i	−0.252984	+	0.252984i	−0.822193	−	0.569209i	$-0.807250\pi$
$677$	−6.58245	+	6.58245i	−0.252984	+	0.252984i	0.569209	+	0.822193i	$0.307250\pi$
$678$	−12.4028	+	0.703543i	−0.476327	+	0.0270194i
$679$			3.91144i			0.150107i
$680$	−4.65394	+	0.798838i	−0.178470	+	0.0306340i
$681$		−	28.2312i		−	1.08182i
$682$	0.00313651	+	0.0552938i	0.000120103	+	0.00211731i
$683$	10.8946	−	10.8946i	0.416872	−	0.416872i	−0.467252	−	0.884124i	$-0.654756\pi$
$683$	10.8946	−	10.8946i	0.416872	−	0.416872i	0.884124	+	0.467252i	$0.154756\pi$
$684$	50.8067	+	40.4233i	1.94264	+	1.54562i
$685$	−9.32141	−	9.32141i	−0.356153	−	0.356153i
$686$	7.19034	+	6.41840i	0.274529	+	0.245055i
$687$	10.6163			0.405036
$688$	26.3413	−	42.1326i	1.00425	−	1.60629i
$689$	20.9136			0.796744
$690$	11.8320	+	10.5618i	0.450438	+	0.402080i
$691$	9.41167	+	9.41167i	0.358037	+	0.358037i	0.863089	−	0.505052i	$-0.168527\pi$
$691$	9.41167	+	9.41167i	0.358037	+	0.358037i	−0.505052	+	0.863089i	$0.668527\pi$
$692$	−22.7946	+	28.6497i	−0.866520	+	1.08910i
$693$	−1.98750	+	1.98750i	−0.0754990	+	0.0754990i
$694$	−0.977030	−	17.2241i	−0.0370876	−	0.653820i
$695$		−	5.74553i		−	0.217940i
$696$	−26.9017	+	38.0506i	−1.01971	+	1.44230i
$697$		−	7.26549i		−	0.275200i
$698$	34.1733	−	1.93846i	1.29348	−	0.0733719i
$699$	37.3366	−	37.3366i	1.41220	−	1.41220i
$700$	0.112067	+	0.984637i	0.00423572	+	0.0372158i
$701$	−6.42811	−	6.42811i	−0.242786	−	0.242786i	0.575216	−	0.818002i	$-0.304918\pi$
$701$	−6.42811	−	6.42811i	−0.242786	−	0.242786i	−0.818002	+	0.575216i	$0.804918\pi$
$702$	18.4251	−	20.6411i	0.695412	−	0.779050i
$703$	−37.8699			−1.42829
$704$	−7.21945	−	3.44667i	−0.272093	−	0.129901i
$705$	23.4272			0.882321
$706$	−6.75387	+	7.56617i	−0.254185	+	0.284757i
$707$	−2.51421	−	2.51421i	−0.0945565	−	0.0945565i
$708$	3.10207	+	27.2553i	0.116583	+	1.02432i
$709$	12.6885	−	12.6885i	0.476527	−	0.476527i	−0.427492	−	0.904019i	$-0.640603\pi$
$709$	12.6885	−	12.6885i	0.476527	−	0.476527i	0.904019	+	0.427492i	$0.140603\pi$
$710$	22.9623	−	1.30252i	0.861759	−	0.0488828i
$711$		−	63.0645i		−	2.36510i
$712$	12.5591	−	17.7640i	0.470672	−	0.665733i
$713$			0.149135i			0.00558516i
$714$	−0.195112	−	3.43965i	−0.00730189	−	0.128726i
$715$	−1.75771	+	1.75771i	−0.0657346	+	0.0657346i
$716$	5.38427	−	6.76731i	0.201220	−	0.252906i
$717$	−25.0115	−	25.0115i	−0.934072	−	0.934072i
$718$	−10.5394	−	9.40786i	−0.393325	−	0.351098i
$719$	−22.3853			−0.834830			−0.417415	−	0.908716i	$-0.637064\pi$
$719$	−22.3853			−0.834830			−0.417415	+	0.908716i	$0.637064\pi$
$720$	−19.2397	−	12.0286i	−0.717020	−	0.448281i
$721$	−5.16921			−0.192511
$722$	−14.5067	−	12.9493i	−0.539883	−	0.481922i
$723$	43.4123	+	43.4123i	1.61452	+	1.61452i
$724$	−11.9197	−	9.48367i	−0.442992	−	0.352458i
$725$	3.95594	−	3.95594i	0.146920	−	0.146920i
$726$	0.235864	+	4.15807i	0.00875374	+	0.154320i
$727$		−	33.7786i		−	1.25278i	−0.779510	−	0.626390i	$-0.784532\pi$
$727$		−	33.7786i		−	1.25278i	0.779510	−	0.626390i	$-0.215468\pi$
$728$	3.43355	−	0.589360i	0.127256	−	0.0218432i
$729$			34.5887i			1.28106i
$730$	9.89812	−	0.561466i	0.366346	−	0.0207808i
$731$	14.6645	−	14.6645i	0.542388	−	0.542388i
$732$	14.3918	−	1.63801i	0.531937	−	0.0605425i
$733$	−1.56513	−	1.56513i	−0.0578094	−	0.0578094i	0.677611	−	0.735420i	$-0.263015\pi$
$733$	−1.56513	−	1.56513i	−0.0578094	−	0.0578094i	−0.735420	+	0.677611i	$0.763015\pi$
$734$	12.8469	−	14.3920i	0.474189	−	0.531220i
$735$	19.8915			0.733707
$736$	−18.8838	−	10.3673i	−0.696066	−	0.382144i
$737$	8.13269			0.299571
$738$	23.2491	−	26.0453i	0.855812	−	0.958742i
$739$	15.4466	+	15.4466i	0.568211	+	0.568211i	0.931627	−	0.363416i	$-0.118390\pi$
$739$	15.4466	+	15.4466i	0.568211	+	0.568211i	−0.363416	+	0.931627i	$0.618390\pi$
$740$	13.1499	−	1.49666i	0.483401	−	0.0550183i
$741$	−29.6229	+	29.6229i	−1.08822	+	1.08822i
$742$	5.88606	−	0.333884i	0.216084	−	0.0122573i
$743$			7.15543i			0.262507i	0.991349	+	0.131254i	$0.0419003\pi$
$743$			7.15543i			0.262507i	−0.991349	+	0.131254i	$0.958100\pi$
$744$	−0.0551837	−	0.321494i	−0.00202313	−	0.0117865i
$745$		−	17.5711i		−	0.643754i
$746$	−2.93045	−	51.6612i	−0.107292	−	1.89145i
$747$	35.4789	−	35.4789i	1.29811	−	1.29811i
$748$	−2.61285	−	2.07886i	−0.0955352	−	0.0760107i
$749$	0.577847	+	0.577847i	0.0211141	+	0.0211141i
$750$	3.10698	+	2.77342i	0.113451	+	0.101271i
$751$	−54.2260			−1.97874			−0.989368	−	0.145435i	$-0.953542\pi$
$751$	−54.2260			−1.97874			−0.989368	+	0.145435i	$0.953542\pi$
$752$	−31.0066	+	7.15067i	−1.13069	+	0.260758i
$753$	5.87962			0.214265
$754$	−14.6721	−	13.0969i	−0.534325	−	0.476961i
$755$	1.68447	+	1.68447i	0.0613041	+	0.0613041i
$756$	4.85616	−	6.10354i	0.176617	−	0.221984i
$757$	2.95580	−	2.95580i	0.107430	−	0.107430i	−0.651348	−	0.758779i	$-0.725796\pi$
$757$	2.95580	−	2.95580i	0.107430	−	0.107430i	0.758779	+	0.651348i	$0.225796\pi$
$758$	−2.05929	−	36.3034i	−0.0747968	−	1.31860i
$759$			11.2149i			0.407075i
$760$	13.2168	+	9.34428i	0.479425	+	0.338953i
$761$			46.4621i			1.68425i	0.539282	+	0.842125i	$0.318696\pi$
$761$			46.4621i			1.68425i	−0.539282	+	0.842125i	$0.681304\pi$
$762$	−15.1525	+	0.859519i	−0.548918	+	0.0311371i
$763$	6.48996	−	6.48996i	0.234952	−	0.234952i
$764$	5.34685	+	46.9784i	0.193442	+	1.69962i
$765$	−6.69650	−	6.69650i	−0.242112	−	0.242112i
$766$	12.1008	−	13.5562i	0.437219	−	0.489804i
$767$	−11.5772			−0.418028
$768$	44.5444	+	15.3616i	1.60736	+	0.554314i
$769$	−28.1171			−1.01393			−0.506964	−	0.861967i	$-0.669232\pi$
$769$	−28.1171			−1.01393			−0.506964	+	0.861967i	$0.669232\pi$
$770$	−0.466640	+	0.522764i	−0.0168165	+	0.0188391i
$771$	10.9749	+	10.9749i	0.395251	+	0.395251i
$772$	2.91126	+	25.5789i	0.104779	+	0.920605i
$773$	10.7274	−	10.7274i	0.385837	−	0.385837i	−0.487363	−	0.873200i	$-0.662041\pi$
$773$	10.7274	−	10.7274i	0.385837	−	0.385837i	0.873200	+	0.487363i	$0.162041\pi$
$774$	99.4951	−	5.64380i	3.57628	−	0.202862i
$775$			0.0391615i			0.00140672i
$776$	−18.2313	−	12.8895i	−0.654464	−	0.462705i
$777$			9.65614i			0.346412i
$778$	2.04094	+	35.9799i	0.0731713	+	1.28994i
$779$	−17.6106	+	17.6106i	−0.630966	+	0.630966i
$780$	9.11551	−	11.4570i	0.326388	−	0.410225i
$781$	11.4996	+	11.4996i	0.411488	+	0.411488i
$782$	−6.70759	−	5.98747i	−0.239863	−	0.214111i
$783$	−44.0324			−1.57359
$784$	−26.3269	+	6.07145i	−0.940247	+	0.216837i
$785$	−4.34447			−0.155061
$786$	12.4805	+	11.1406i	0.445166	+	0.397373i
$787$	17.9676	+	17.9676i	0.640476	+	0.640476i	0.950673	−	0.310196i	$-0.100395\pi$
$787$	17.9676	+	17.9676i	0.640476	+	0.640476i	−0.310196	+	0.950673i	$0.600395\pi$
$788$	−11.0755	−	8.81197i	−0.394547	−	0.313914i
$789$	−18.8218	+	18.8218i	−0.670075	+	0.670075i
$790$	−0.890412	−	15.6972i	−0.0316794	−	0.558480i
$791$		−	1.47798i		−	0.0525511i
$792$	−2.71431	−	15.8133i	−0.0964488	−	0.561900i
$793$			6.11320i			0.217086i
$794$	34.0715	−	1.93269i	1.20915	−	0.0685886i
$795$	17.5197	−	17.5197i	0.621359	−	0.621359i
$796$	25.5286	−	2.90554i	0.904837	−	0.102984i
$797$	2.80688	+	2.80688i	0.0994249	+	0.0994249i	0.755070	−	0.655645i	$-0.227603\pi$
$797$	2.80688	+	2.80688i	0.0994249	+	0.0994249i	−0.655645	+	0.755070i	$0.727603\pi$
$798$	−7.86435	+	8.81020i	−0.278395	+	0.311878i
$799$	−13.2809			−0.469845
$800$	−4.95871	−	2.72236i	−0.175317	−	0.0962499i
$801$	43.6315			1.54164
$802$	−24.4799	+	27.4241i	−0.864414	+	0.968379i
$803$	4.95702	+	4.95702i	0.174929	+	0.174929i
$804$	−47.5931	+	5.41681i	−1.67848	+	0.191036i
$805$	−1.33428	+	1.33428i	−0.0470272	+	0.0470272i
$806$	0.137448	−	0.00779666i	0.00484140	−	0.000274626i
$807$			65.5363i			2.30699i
$808$	20.0039	−	3.43362i	0.703735	−	0.120794i
$809$			48.8405i			1.71714i	0.512696	+	0.858570i	$0.328647\pi$
$809$			48.8405i			1.71714i	−0.512696	+	0.858570i	$0.671353\pi$
$810$	−0.493408	−	8.69833i	−0.0173366	−	0.305628i
$811$	31.2394	−	31.2394i	1.09696	−	1.09696i	0.102201	−	0.994764i	$-0.467412\pi$
$811$	31.2394	−	31.2394i	1.09696	−	1.09696i	0.994764	−	0.102201i	$-0.0325884\pi$
$812$	−4.33850	−	3.45184i	−0.152251	−	0.121136i
$813$	32.8022	+	32.8022i	1.15042	+	1.15042i
$814$	6.98156	+	6.23202i	0.244703	+	0.218432i
$815$	21.0043			0.735748
$816$	16.6752	+	10.4253i	0.583749	+	0.364960i
$817$	−71.0900			−2.48712
$818$	−41.1712	−	36.7511i	−1.43952	−	1.28497i
$819$	4.94049	+	4.94049i	0.172635	+	0.172635i
$820$	5.41912	−	6.81110i	0.189244	−	0.237854i
$821$	−4.88622	+	4.88622i	−0.170530	+	0.170530i	−0.787212	−	0.616682i	$-0.788476\pi$
$821$	−4.88622	+	4.88622i	−0.170530	+	0.170530i	0.616682	+	0.787212i	$0.288476\pi$
$822$	3.10927	+	54.8136i	0.108448	+	1.91185i
$823$		−	10.4375i		−	0.363827i	−0.983315	−	0.181914i	$-0.941771\pi$
$823$		−	10.4375i		−	0.363827i	0.983315	−	0.181914i	$-0.0582291\pi$
$824$	17.0342	−	24.0937i	0.593415	−	0.839345i
$825$			2.94493i			0.102529i
$826$	−3.25837	+	0.184829i	−0.113373	+	0.00643103i
$827$	2.83269	−	2.83269i	0.0985021	−	0.0985021i	−0.656138	−	0.754641i	$-0.727811\pi$
$827$	2.83269	−	2.83269i	0.0985021	−	0.0985021i	0.754641	+	0.656138i	$0.227811\pi$
$828$	−4.88582	−	42.9277i	−0.169794	−	1.49184i
$829$	4.23839	+	4.23839i	0.147206	+	0.147206i	0.776868	−	0.629663i	$-0.216807\pi$
$829$	4.23839	+	4.23839i	0.147206	+	0.147206i	−0.629663	+	0.776868i	$0.716807\pi$
$830$	8.33000	−	9.33185i	0.289138	−	0.323913i
$831$	28.0071			0.971557
$832$	−8.56764	+	17.9459i	−0.297030	+	0.622164i
$833$	−11.2765			−0.390707
$834$	−15.9348	+	17.8513i	−0.551776	+	0.618138i
$835$	6.56028	+	6.56028i	0.227028	+	0.227028i
$836$	1.29432	+	11.3721i	0.0447649	+	0.393313i
$837$	0.217947	−	0.217947i	0.00753336	−	0.00753336i
$838$	−27.6229	+	1.56689i	−0.954217	+	0.0541274i
$839$			36.2986i			1.25317i	0.779355	+	0.626583i	$0.215547\pi$
$839$			36.2986i			1.25317i	−0.779355	+	0.626583i	$0.784453\pi$
$840$	2.38262	−	3.37006i	0.0822083	−	0.116278i
$841$			2.29897i			0.0792748i
$842$	2.49910	+	44.0569i	0.0861248	+	1.51830i
$843$	−46.7191	+	46.7191i	−1.60909	+	1.60909i
$844$	−14.0324	+	17.6369i	−0.483016	+	0.607086i
$845$	−4.82311	−	4.82311i	−0.165920	−	0.165920i
$846$	−47.6094	−	42.4981i	−1.63684	−	1.46111i
$847$	−0.495497			−0.0170255
$848$	−17.8403	+	28.5353i	−0.612637	+	0.979906i
$849$	82.7753			2.84084
$850$	−1.76135	−	1.57225i	−0.0604138	−	0.0539278i
$851$	17.8194	+	17.8194i	0.610843	+	0.610843i
$852$	−74.9558	−	59.6371i	−2.56794	−	2.04313i
$853$	−11.0945	+	11.0945i	−0.379868	+	0.379868i	−0.871054	−	0.491186i	$-0.836563\pi$
$853$	−11.0945	+	11.0945i	−0.379868	+	0.379868i	0.491186	+	0.871054i	$0.336563\pi$
$854$	0.0975967	+	1.72054i	0.00333969	+	0.0588757i
$855$			32.4629i			1.11021i
$856$	−4.59755	+	0.789159i	−0.157141	+	0.0269729i
$857$			7.41560i			0.253312i	0.991947	+	0.126656i	$0.0404244\pi$
$857$			7.41560i			0.253312i	−0.991947	+	0.126656i	$0.959576\pi$
$858$	10.3360	−	0.586306i	0.352866	−	0.0200162i
$859$	−29.8191	+	29.8191i	−1.01742	+	1.01742i	−0.0175698	+	0.999846i	$0.505593\pi$
$859$	−29.8191	+	29.8191i	−1.01742	+	1.01742i	−0.999846	+	0.0175698i	$0.994407\pi$
$860$	24.6853	−	2.80955i	0.841760	−	0.0958050i
$861$	4.49040	+	4.49040i	0.153032	+	0.153032i
$862$	24.9643	−	27.9668i	0.850289	−	0.952554i
$863$	4.58227			0.155982			0.0779912	−	0.996954i	$-0.475149\pi$
$863$	4.58227			0.155982			0.0779912	+	0.996954i	$0.475149\pi$
$864$	12.4461	+	42.7478i	0.423423	+	1.45431i
$865$	−18.3057			−0.622413
$866$	18.1338	−	20.3148i	0.616213	−	0.690325i
$867$	−29.5965	−	29.5965i	−1.00515	−	1.00515i
$868$	0.0385599	−	0.00438869i	0.00130881	−	0.000148962i
$869$	7.86119	−	7.86119i	0.266673	−	0.266673i
$870$	−23.2625	+	1.31955i	−0.788674	+	0.0447371i
$871$		−	20.2160i		−	0.684995i
$872$	8.86326	+	51.6363i	0.300148	+	1.74863i
$873$		−	44.7793i		−	1.51555i
$874$	1.74548	+	30.7712i	0.0590417	+	1.04085i
$875$	−0.350369	+	0.350369i	−0.0118446	+	0.0118446i
$876$	−32.3105	−	25.7072i	−1.09167	−	0.868565i
$877$	18.0407	+	18.0407i	0.609190	+	0.609190i	0.942734	−	0.333545i	$-0.108245\pi$
$877$	18.0407	+	18.0407i	0.609190	+	0.609190i	−0.333545	+	0.942734i	$0.608245\pi$
$878$	6.32305	+	5.64421i	0.213392	+	0.190483i
$879$	31.7393			1.07054
$880$	−0.898877	−	3.89769i	−0.0303011	−	0.131391i
$881$	−0.649247			−0.0218737			−0.0109369	−	0.999940i	$-0.503481\pi$
$881$	−0.649247			−0.0218737			−0.0109369	+	0.999940i	$0.503481\pi$
$882$	−40.4239	−	36.0840i	−1.36114	−	1.21501i
$883$	−5.06314	−	5.06314i	−0.170388	−	0.170388i	0.616762	−	0.787150i	$-0.288444\pi$
$883$	−5.06314	−	5.06314i	−0.170388	−	0.170388i	−0.787150	+	0.616762i	$0.788444\pi$
$884$	−5.16759	+	6.49496i	−0.173805	+	0.218449i
$885$	−9.69842	+	9.69842i	−0.326009	+	0.326009i
$886$	−3.00234	−	52.9285i	−0.100866	−	1.77817i
$887$		−	41.2108i		−	1.38372i	−0.722030	−	0.691862i	$-0.756791\pi$
$887$		−	41.2108i		−	1.38372i	0.722030	−	0.691862i	$-0.243209\pi$
$888$	−45.0074	−	31.8201i	−1.51035	−	1.06781i
$889$		−	1.80565i		−	0.0605597i
$890$	10.8601	−	0.616036i	0.364033	−	0.0206496i
$891$	4.35616	−	4.35616i	0.145937	−	0.145937i
$892$	−3.01669	−	26.5052i	−0.101006	−	0.887460i
$893$	32.1912	+	32.1912i	1.07724	+	1.07724i
$894$	−48.7319	+	54.5929i	−1.62984	+	1.82586i
$895$	4.32397			0.144534
$896$	−2.12483	+	5.18761i	−0.0709856	+	0.173306i
$897$	27.8778			0.930811
$898$	14.2894	−	16.0080i	0.476842	−	0.534192i
$899$	−0.154921	−	0.154921i	−0.00516689	−	0.00516689i
$900$	−1.28297	−	11.2724i	−0.0427657	−	0.375747i
$901$	−9.93190	+	9.93190i	−0.330880	+	0.330880i
$902$	6.14471	−	0.348555i	0.204596	−	0.0116056i
$903$			18.1267i			0.603218i
$904$	6.88890	+	4.87044i	0.229122	+	0.161988i
$905$		−	7.61609i		−	0.253167i
$906$	−0.561876	−	9.90535i	−0.0186671	−	0.329083i
$907$	−16.6937	+	16.6937i	−0.554304	+	0.554304i	−0.927680	−	0.373376i	$-0.878200\pi$
$907$	−16.6937	+	16.6937i	−0.554304	+	0.554304i	0.373376	+	0.927680i	$0.378200\pi$
$908$	−11.9371	+	15.0033i	−0.396147	+	0.497903i
$909$	28.7834	+	28.7834i	0.954684	+	0.954684i
$910$	1.29947	+	1.15996i	0.0430771	+	0.0384524i
$911$	−53.5676			−1.77478			−0.887388	−	0.461024i	$-0.847482\pi$
$911$	−53.5676			−1.77478			−0.887388	+	0.461024i	$0.847482\pi$
$912$	−15.1489	−	65.6883i	−0.501630	−	2.17516i
$913$	8.84512			0.292731
$914$	18.6729	+	16.6682i	0.617643	+	0.551334i
$915$	5.12113	+	5.12113i	0.169299	+	0.169299i
$916$	−5.64197	−	4.48892i	−0.186416	−	0.148318i
$917$	−1.40741	+	1.40741i	−0.0464768	+	0.0464768i
$918$	1.05239	+	18.5526i	0.0347340	+	0.612329i
$919$		−	10.7149i		−	0.353453i	−0.984260	−	0.176727i	$-0.943449\pi$
$919$		−	10.7149i		−	0.353453i	0.984260	−	0.176727i	$-0.0565508\pi$
$920$	−1.82221	−	10.6160i	−0.0600765	−	0.349999i
$921$			20.6604i			0.680784i
$922$	−0.841443	+	0.0477304i	−0.0277115	+	0.00157192i
$923$	28.5854	−	28.5854i	0.940901	−	0.940901i
$924$	2.89969	−	0.330028i	0.0953926	−	0.0108571i
$925$	4.67922	+	4.67922i	0.153852	+	0.153852i
$926$	34.1489	−	38.2561i	1.12220	−	1.25717i
$927$	59.1785			1.94368
$928$	30.3859	−	8.84686i	0.997464	−	0.290413i
$929$	52.8984			1.73554			0.867771	−	0.496965i	$-0.165552\pi$
$929$	52.8984			1.73554			0.867771	+	0.496965i	$0.165552\pi$
$930$	0.108611	−	0.121674i	0.00356150	−	0.00398985i
$931$	27.3327	+	27.3327i	0.895794	+	0.895794i
$932$	−35.6296	+	4.05518i	−1.16708	+	0.132832i
$933$	63.1212	−	63.1212i	2.06650	−	2.06650i
$934$	59.8984	−	3.39770i	1.95993	−	0.111176i
$935$		−	1.66948i		−	0.0545978i
$936$	−39.3082	+	6.74717i	−1.28483	+	0.220538i
$937$		−	17.1876i		−	0.561495i	−0.959782	−	0.280747i	$-0.909418\pi$
$937$		−	17.1876i		−	0.561495i	0.959782	−	0.280747i	$-0.0905823\pi$
$938$	−0.322748	−	5.68974i	−0.0105381	−	0.185777i
$939$	−61.7710	+	61.7710i	−2.01582	+	2.01582i
$940$	−12.4503	−	9.90584i	−0.406084	−	0.323093i
$941$	−6.86563	−	6.86563i	−0.223813	−	0.223813i	0.586289	−	0.810102i	$-0.300588\pi$
$941$	−6.86563	−	6.86563i	−0.223813	−	0.223813i	−0.810102	+	0.586289i	$0.800588\pi$
$942$	13.4982	+	12.0490i	0.439795	+	0.392579i
$943$	16.5732			0.539696
$944$	9.87589	−	15.7964i	0.321433	−	0.514128i
$945$	3.89986			0.126862
$946$	13.1059	+	11.6989i	0.426109	+	0.380363i
$947$	−9.78173	−	9.78173i	−0.317863	−	0.317863i	0.530083	−	0.847946i	$-0.322161\pi$
$947$	−9.78173	−	9.78173i	−0.317863	−	0.317863i	−0.847946	+	0.530083i	$0.822161\pi$
$948$	−40.7683	+	51.2402i	−1.32409	+	1.66421i
$949$	12.3220	−	12.3220i	0.399990	−	0.399990i
$950$	0.458346	+	8.08022i	0.0148707	+	0.262157i
$951$		−	0.544453i		−	0.0176551i
$952$	−1.35071	+	1.91049i	−0.0437768	+	0.0619192i
$953$			41.9394i			1.35855i	0.733884	+	0.679275i	$0.237706\pi$
$953$			41.9394i			1.35855i	−0.733884	+	0.679275i	$0.762294\pi$
$954$	−67.3853	+	3.82240i	−2.18168	+	0.123755i
$955$	−16.7166	+	16.7166i	−0.540937	+	0.540937i
$956$	2.71654	+	23.8680i	0.0878590	+	0.771945i
$957$	−11.6500	−	11.6500i	−0.376590	−	0.376590i
$958$	−30.0981	+	33.7180i	−0.972425	+	1.08938i
$959$	−6.53188			−0.210925
$960$	7.85637	+	22.2109i	0.253563	+	0.716853i
$961$	−30.9985			−0.999951
$962$	15.4914	−	17.3546i	0.499463	−	0.559534i
$963$	−6.61536	−	6.61536i	−0.213177	−	0.213177i
$964$	−4.71507	−	41.4275i	−0.151862	−	1.33429i
$965$	−9.10189	+	9.10189i	−0.293000	+	0.293000i
$966$	7.84611	−	0.445066i	0.252444	−	0.0143198i
$967$			8.30674i			0.267127i	0.991040	+	0.133563i	$0.0426420\pi$
$967$			8.30674i			0.267127i	−0.991040	+	0.133563i	$0.957358\pi$
$968$	1.63283	−	2.30952i	0.0524810	−	0.0742308i
$969$		−	28.1359i		−	0.903857i
$970$	−0.632241	−	11.1458i	−0.0203000	−	0.357871i
$971$	−43.1312	+	43.1312i	−1.38415	+	1.38415i	−0.547036	+	0.837109i	$0.684244\pi$
$971$	−43.1312	+	43.1312i	−1.38415	+	1.38415i	−0.837109	+	0.547036i	$0.815756\pi$
$972$	6.81065	−	8.56007i	0.218452	−	0.274564i
$973$	−2.01306	−	2.01306i	−0.0645357	−	0.0645357i
$974$	−13.3968	−	11.9586i	−0.429262	−	0.383177i
$975$	7.32043			0.234441
$976$	−8.34108	−	5.21484i	−0.266991	−	0.166923i
$977$	30.3740			0.971751			0.485875	−	0.874028i	$-0.338501\pi$
$977$	30.3740			0.971751			0.485875	+	0.874028i	$0.338501\pi$
$978$	−65.2599	−	58.2536i	−2.08678	−	1.86275i
$979$	5.43880	+	5.43880i	0.173825	+	0.173825i
$980$	−10.5712	−	8.41079i	−0.337685	−	0.268673i
$981$	−74.2989	+	74.2989i	−2.37218	+	2.37218i
$982$	3.17782	+	56.0220i	0.101408	+	1.78773i
$983$			4.97992i			0.158835i	0.996841	+	0.0794173i	$0.0253060\pi$
$983$			4.97992i			0.158835i	−0.996841	+	0.0794173i	$0.974694\pi$
$984$	−35.7271	+	6.13248i	−1.13894	+	0.195496i
$985$		−	7.07667i		−	0.225481i
$986$	13.1875	−	0.748055i	0.419977	−	0.0238229i
$987$	8.20819	−	8.20819i	0.261270	−	0.261270i
$988$	28.2685	−	3.21739i	0.899342	−	0.102359i
$989$	33.4510	+	33.4510i	1.06368	+	1.06368i
$990$	5.34223	−	5.98475i	0.169787	−	0.190208i
$991$	40.0138			1.27108			0.635541	−	0.772068i	$-0.280777\pi$
$991$	40.0138			1.27108			0.635541	+	0.772068i	$0.280777\pi$
$992$	−0.106612	+	0.194190i	−0.00338492	+	0.00616555i
$993$	−44.0295			−1.39723
$994$	7.58892	−	8.50164i	0.240706	−	0.269656i
$995$	9.08399	+	9.08399i	0.287982	+	0.287982i
$996$	−51.7623	+	5.89133i	−1.64015	+	0.186674i
$997$	−6.65957	+	6.65957i	−0.210911	+	0.210911i	−0.804654	−	0.593744i	$-0.797649\pi$
$997$	−6.65957	+	6.65957i	−0.210911	+	0.210911i	0.593744	+	0.804654i	$0.297649\pi$
$998$	−48.9616	+	2.77732i	−1.54985	+	0.0879146i
$999$		−	52.0829i		−	1.64783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.w.a.221.8	✓	72
16.5	even	4	inner	880.2.w.a.661.8	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.w.a.221.8	✓	72	1.1	even	1	trivial
880.2.w.a.661.8	yes	72	16.5	even	4	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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.941762 + 1.05503i) q^{2} +(2.08238 + 2.08238i) q^{3} +(-0.226170 - 1.98717i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-4.15807 + 0.235864i) q^{6} -0.495497i q^{7} +(2.30952 + 1.63283i) q^{8} +5.67259i q^{9} +(0.0800917 + 1.41194i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(3.66707 - 4.60901i) q^{12} +(1.75771 + 1.75771i) q^{13} +(0.522764 + 0.466640i) q^{14} +2.94493 q^{15} +(-3.89769 + 0.898877i) q^{16} -1.66948 q^{17} +(-5.98475 - 5.34223i) q^{18} +(4.04661 + 4.04661i) q^{19} +(-1.56507 - 1.24522i) q^{20} +(1.03181 - 1.03181i) q^{21} +(-0.0800917 - 1.41194i) q^{22} -3.80821i q^{23} +(1.40913 + 8.20945i) q^{24} -1.00000i q^{25} +(-3.50978 + 0.199090i) q^{26} +(-5.56535 + 5.56535i) q^{27} +(-0.984637 + 0.112067i) q^{28} +(3.95594 + 3.95594i) q^{29} +(-2.77342 + 3.10698i) q^{30} -0.0391615 q^{31} +(2.72236 - 4.95871i) q^{32} -2.94493 q^{33} +(1.57225 - 1.76135i) q^{34} +(-0.350369 - 0.350369i) q^{35} +(11.2724 - 1.28297i) q^{36} +(-4.67922 + 4.67922i) q^{37} +(-8.08022 + 0.458346i) q^{38} +7.32043i q^{39} +(2.78766 - 0.478495i) q^{40} +4.35195i q^{41} +(0.116870 + 2.06031i) q^{42} +(-8.78390 + 8.78390i) q^{43} +(1.56507 + 1.24522i) q^{44} +(4.01113 + 4.01113i) q^{45} +(4.01777 + 3.58643i) q^{46} +7.95512 q^{47} +(-9.98827 - 6.24467i) q^{48} +6.75448 q^{49} +(1.05503 + 0.941762i) q^{50} +(-3.47649 - 3.47649i) q^{51} +(3.09533 - 3.89041i) q^{52} +(5.94910 - 5.94910i) q^{53} +(-0.630369 - 11.1128i) q^{54} +1.00000i q^{55} +(0.809060 - 1.14436i) q^{56} +16.8531i q^{57} +(-7.89919 + 0.448077i) q^{58} +(-3.29326 + 3.29326i) q^{59} +(-0.666054 - 5.85207i) q^{60} +(1.73897 + 1.73897i) q^{61} +(0.0368808 - 0.0413165i) q^{62} +2.81075 q^{63} +(2.66776 + 7.54208i) q^{64} +2.48578 q^{65} +(2.77342 - 3.10698i) q^{66} +(-5.75068 - 5.75068i) q^{67} +(0.377586 + 3.31754i) q^{68} +(7.93014 - 7.93014i) q^{69} +(0.699614 - 0.0396852i) q^{70} -16.2629i q^{71} +(-9.26235 + 13.1010i) q^{72} -7.01028i q^{73} +(-0.530000 - 9.34341i) q^{74} +(2.08238 - 2.08238i) q^{75} +(7.12608 - 8.95652i) q^{76} +(0.350369 + 0.350369i) q^{77} +(-7.72326 - 6.89410i) q^{78} -11.1174 q^{79} +(-2.12048 + 3.39169i) q^{80} -6.16053 q^{81} +(-4.59143 - 4.09850i) q^{82} +(-6.25445 - 6.25445i) q^{83} +(-2.28375 - 1.81702i) q^{84} +(-1.18050 + 1.18050i) q^{85} +(-0.994924 - 17.5396i) q^{86} +16.4755i q^{87} +(-2.78766 + 0.478495i) q^{88} -7.69163i q^{89} +(-8.00938 + 0.454328i) q^{90} +(0.870940 - 0.870940i) q^{91} +(-7.56757 + 0.861303i) q^{92} +(-0.0815490 - 0.0815490i) q^{93} +(-7.49182 + 8.39288i) q^{94} +5.72277 q^{95} +(15.9949 - 4.65692i) q^{96} -7.89397 q^{97} +(-6.36111 + 7.12617i) q^{98} +(-4.01113 - 4.01113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) \) 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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