LMFDB - Embedded newform 273.2.cg.b.262.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [273,2,Mod(19,273)] 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("273.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(273, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 10, 5])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$273 = 3 \cdot 7 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [40] 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			262.9
Character	$\chi$	$=$	273.262
Dual form			273.2.cg.b.124.9

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.568195 + 2.12053i) q^{2} +1.00000i q^{3} +(-2.44176 + 1.40975i) q^{4} +(-0.248247 + 0.926472i) q^{5} +(-2.12053 + 0.568195i) q^{6} +(1.82268 + 1.91776i) q^{7} +(-1.27214 - 1.27214i) q^{8} -1.00000 q^{9} -2.10567 q^{10} +(-2.00076 - 2.00076i) q^{11} +(-1.40975 - 2.44176i) q^{12} +(2.97594 - 2.03563i) q^{13} +(-3.03104 + 4.95472i) q^{14} +(-0.926472 - 0.248247i) q^{15} +(-0.844715 + 1.46309i) q^{16} +(-2.53737 - 4.39486i) q^{17} +(-0.568195 - 2.12053i) q^{18} +(0.314135 + 0.314135i) q^{19} +(-0.699933 - 2.61219i) q^{20} +(-1.91776 + 1.82268i) q^{21} +(3.10586 - 5.37950i) q^{22} +(-2.92308 - 1.68764i) q^{23} +(1.27214 - 1.27214i) q^{24} +(3.53340 + 2.04001i) q^{25} +(6.00753 + 5.15394i) q^{26} -1.00000i q^{27} +(-7.15412 - 2.11319i) q^{28} +(4.91269 + 8.50903i) q^{29} -2.10567i q^{30} +(3.21502 - 0.861462i) q^{31} +(-7.05803 - 1.89119i) q^{32} +(2.00076 - 2.00076i) q^{33} +(7.87771 - 7.87771i) q^{34} +(-2.22923 + 1.21259i) q^{35} +(2.44176 - 1.40975i) q^{36} +(5.09136 - 1.36423i) q^{37} +(-0.487643 + 0.844623i) q^{38} +(2.03563 + 2.97594i) q^{39} +(1.49440 - 0.862793i) q^{40} +(1.13047 - 4.21899i) q^{41} +(-4.95472 - 3.03104i) q^{42} +(-2.57983 - 1.48947i) q^{43} +(7.70594 + 2.06480i) q^{44} +(0.248247 - 0.926472i) q^{45} +(1.91782 - 7.15740i) q^{46} +(9.10199 + 2.43887i) q^{47} +(-1.46309 - 0.844715i) q^{48} +(-0.355642 + 6.99096i) q^{49} +(-2.31825 + 8.65182i) q^{50} +(4.39486 - 2.53737i) q^{51} +(-4.39679 + 9.16584i) q^{52} +(-4.30074 + 7.44911i) q^{53} +(2.12053 - 0.568195i) q^{54} +(2.35033 - 1.35697i) q^{55} +(0.120955 - 4.75836i) q^{56} +(-0.314135 + 0.314135i) q^{57} +(-15.2523 + 15.2523i) q^{58} +(-2.83161 - 0.758729i) q^{59} +(2.61219 - 0.699933i) q^{60} -12.9094i q^{61} +(3.65351 + 6.32807i) q^{62} +(-1.82268 - 1.91776i) q^{63} -12.6625i q^{64} +(1.14719 + 3.26246i) q^{65} +(5.37950 + 3.10586i) q^{66} +(-7.12728 + 7.12728i) q^{67} +(12.3913 + 7.15412i) q^{68} +(1.68764 - 2.92308i) q^{69} +(-3.83796 - 4.03817i) q^{70} +(-0.206463 - 0.770529i) q^{71} +(1.27214 + 1.27214i) q^{72} +(-1.01789 - 3.79881i) q^{73} +(5.78577 + 10.0212i) q^{74} +(-2.04001 + 3.53340i) q^{75} +(-1.20989 - 0.324190i) q^{76} +(0.190232 - 7.48375i) q^{77} +(-5.15394 + 6.00753i) q^{78} +(2.44887 + 4.24156i) q^{79} +(-1.14581 - 1.14581i) q^{80} +1.00000 q^{81} +9.58882 q^{82} +(-2.86668 - 2.86668i) q^{83} +(2.11319 - 7.15412i) q^{84} +(4.70161 - 1.25979i) q^{85} +(1.69261 - 6.31692i) q^{86} +(-8.50903 + 4.91269i) q^{87} +5.09048i q^{88} +(-2.70378 - 10.0906i) q^{89} +2.10567 q^{90} +(9.32806 + 1.99684i) q^{91} +9.51661 q^{92} +(0.861462 + 3.21502i) q^{93} +20.6868i q^{94} +(-0.369020 + 0.213054i) q^{95} +(1.89119 - 7.05803i) q^{96} +(4.64555 - 1.24477i) q^{97} +(-15.0266 + 3.21808i) q^{98} +(2.00076 + 2.00076i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32}+ \cdots - 4 q^{99}+O(q^{100})$ 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$ .

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.568195	+	2.12053i	0.401774	+	1.49944i	0.809928	+	0.586529i	$0.199506\pi$
$2$	0.568195	+	2.12053i	0.401774	+	1.49944i	−0.408154	+	0.912913i	$0.633827\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−2.44176	+	1.40975i	−1.22088	+	0.704874i
$5$	−0.248247	+	0.926472i	−0.111020	+	0.414331i	−0.998958	−	0.0456309i	$-0.985470\pi$
$5$	−0.248247	+	0.926472i	−0.111020	+	0.414331i	0.887939	+	0.459962i	$0.152137\pi$
$6$	−2.12053	+	0.568195i	−0.865703	+	0.231964i
$7$	1.82268	+	1.91776i	0.688910	+	0.724847i
$7$	1.82268	+	1.91776i	0.688910	+	0.724847i
$8$	−1.27214	−	1.27214i	−0.449768	−	0.449768i
$9$	−1.00000			−0.333333
$10$	−2.10567			−0.665870
$11$	−2.00076	−	2.00076i	−0.603252	−	0.603252i	0.337922	−	0.941174i	$-0.390276\pi$
$11$	−2.00076	−	2.00076i	−0.603252	−	0.603252i	−0.941174	+	0.337922i	$0.890276\pi$
$12$	−1.40975	−	2.44176i	−0.406959	−	0.704874i
$13$	2.97594	−	2.03563i	0.825377	−	0.564582i
$13$	2.97594	−	2.03563i	0.825377	−	0.564582i
$14$	−3.03104	+	4.95472i	−0.810079	+	1.32421i
$15$	−0.926472	−	0.248247i	−0.239214	−	0.0640972i
$16$	−0.844715	+	1.46309i	−0.211179	+	0.365772i
$17$	−2.53737	−	4.39486i	−0.615403	−	1.06591i	−0.990314	−	0.138849i	$-0.955660\pi$
$17$	−2.53737	−	4.39486i	−0.615403	−	1.06591i	0.374910	−	0.927061i	$-0.377674\pi$
$18$	−0.568195	−	2.12053i	−0.133925	−	0.499814i
$19$	0.314135	+	0.314135i	0.0720675	+	0.0720675i	0.742222	−	0.670154i	$-0.233772\pi$
$19$	0.314135	+	0.314135i	0.0720675	+	0.0720675i	−0.670154	+	0.742222i	$0.733772\pi$
$20$	−0.699933	−	2.61219i	−0.156510	−	0.584102i
$21$	−1.91776	+	1.82268i	−0.418491	+	0.397742i
$22$	3.10586	−	5.37950i	0.662171	−	1.14691i
$23$	−2.92308	−	1.68764i	−0.609505	−	0.351898i	0.163267	−	0.986582i	$-0.447797\pi$
$23$	−2.92308	−	1.68764i	−0.609505	−	0.351898i	−0.772772	+	0.634684i	$0.781130\pi$
$24$	1.27214	−	1.27214i	0.259674	−	0.259674i
$25$	3.53340	+	2.04001i	0.706681	+	0.408002i
$26$	6.00753	+	5.15394i	1.17817	+	1.01077i
$27$		−	1.00000i		−	0.192450i
$28$	−7.15412	−	2.11319i	−1.35200	−	0.399355i
$29$	4.91269	+	8.50903i	0.912264	+	1.58009i	0.810858	+	0.585242i	$0.199001\pi$
$29$	4.91269	+	8.50903i	0.912264	+	1.58009i	0.101406	+	0.994845i	$0.467666\pi$
$30$		−	2.10567i		−	0.384440i
$31$	3.21502	−	0.861462i	0.577435	−	0.154723i	0.0417306	−	0.999129i	$-0.486713\pi$
$31$	3.21502	−	0.861462i	0.577435	−	0.154723i	0.535704	+	0.844406i	$0.320046\pi$
$32$	−7.05803	−	1.89119i	−1.24769	−	0.334319i
$33$	2.00076	−	2.00076i	0.348288	−	0.348288i
$34$	7.87771	−	7.87771i	1.35102	−	1.35102i
$35$	−2.22923	+	1.21259i	−0.376809	+	0.204964i
$36$	2.44176	−	1.40975i	0.406959	−	0.234958i
$37$	5.09136	−	1.36423i	0.837015	−	0.224277i	0.185243	−	0.982693i	$-0.440693\pi$
$37$	5.09136	−	1.36423i	0.837015	−	0.224277i	0.651772	+	0.758415i	$0.274026\pi$
$38$	−0.487643	+	0.844623i	−0.0791061	+	0.137016i
$39$	2.03563	+	2.97594i	0.325962	+	0.476532i
$40$	1.49440	−	0.862793i	0.236286	−	0.136420i
$41$	1.13047	−	4.21899i	0.176550	−	0.658895i	−0.819732	−	0.572747i	$-0.805878\pi$
$41$	1.13047	−	4.21899i	0.176550	−	0.658895i	0.996282	−	0.0861478i	$-0.0274557\pi$
$42$	−4.95472	−	3.03104i	−0.764530	−	0.467700i
$43$	−2.57983	−	1.48947i	−0.393420	−	0.227141i	0.290221	−	0.956960i	$-0.406271\pi$
$43$	−2.57983	−	1.48947i	−0.393420	−	0.227141i	−0.683641	+	0.729818i	$0.739605\pi$
$44$	7.70594	+	2.06480i	1.16171	+	0.311281i
$45$	0.248247	−	0.926472i	0.0370065	−	0.138110i
$46$	1.91782	−	7.15740i	0.282767	−	1.05530i
$47$	9.10199	+	2.43887i	1.32766	+	0.355746i	0.851843	−	0.523797i	$-0.175485\pi$
$47$	9.10199	+	2.43887i	1.32766	+	0.355746i	0.475819	+	0.879543i	$0.342152\pi$
$48$	−1.46309	−	0.844715i	−0.211179	−	0.121924i
$49$	−0.355642	+	6.99096i	−0.0508060	+	0.998709i
$50$	−2.31825	+	8.65182i	−0.327850	+	1.22355i
$51$	4.39486	−	2.53737i	0.615403	−	0.355303i
$52$	−4.39679	+	9.16584i	−0.609725	+	1.27107i
$53$	−4.30074	+	7.44911i	−0.590753	+	1.02321i	0.403379	+	0.915033i	$0.367836\pi$
$53$	−4.30074	+	7.44911i	−0.590753	+	1.02321i	−0.994131	+	0.108180i	$0.965498\pi$
$54$	2.12053	−	0.568195i	0.288568	−	0.0773215i
$55$	2.35033	−	1.35697i	0.316919	−	0.182973i
$56$	0.120955	−	4.75836i	0.0161632	−	0.635862i
$57$	−0.314135	+	0.314135i	−0.0416082	+	0.0416082i
$58$	−15.2523	+	15.2523i	−2.00273	+	2.00273i
$59$	−2.83161	−	0.758729i	−0.368645	−	0.0987781i	0.0697406	−	0.997565i	$-0.477783\pi$
$59$	−2.83161	−	0.758729i	−0.368645	−	0.0987781i	−0.438385	+	0.898787i	$0.644450\pi$
$60$	2.61219	−	0.699933i	0.337232	−	0.0903609i
$61$		−	12.9094i		−	1.65289i	−0.563021	−	0.826443i	$-0.690361\pi$
$61$		−	12.9094i		−	1.65289i	0.563021	−	0.826443i	$-0.309639\pi$
$62$	3.65351	+	6.32807i	0.463997	+	0.803666i
$63$	−1.82268	−	1.91776i	−0.229637	−	0.241616i
$64$		−	12.6625i		−	1.58281i
$65$	1.14719	+	3.26246i	0.142291	+	0.404659i
$66$	5.37950	+	3.10586i	0.662171	+	0.382304i
$67$	−7.12728	+	7.12728i	−0.870736	+	0.870736i	−0.992553	−	0.121816i	$-0.961128\pi$
$67$	−7.12728	+	7.12728i	−0.870736	+	0.870736i	0.121816	+	0.992553i	$0.461128\pi$
$68$	12.3913	+	7.15412i	1.50267	+	0.867564i
$69$	1.68764	−	2.92308i	0.203168	−	0.351898i
$70$	−3.83796	−	4.03817i	−0.458724	−	0.482654i
$71$	−0.206463	−	0.770529i	−0.0245026	−	0.0914449i	0.952592	−	0.304251i	$-0.0984063\pi$
$71$	−0.206463	−	0.770529i	−0.0245026	−	0.0914449i	−0.977094	+	0.212806i	$0.931740\pi$
$72$	1.27214	+	1.27214i	0.149923	+	0.149923i
$73$	−1.01789	−	3.79881i	−0.119135	−	0.444617i	0.880428	−	0.474179i	$-0.157255\pi$
$73$	−1.01789	−	3.79881i	−0.119135	−	0.444617i	−0.999563	+	0.0295626i	$0.990589\pi$
$74$	5.78577	+	10.0212i	0.672582	+	1.16495i
$75$	−2.04001	+	3.53340i	−0.235560	+	0.408002i
$76$	−1.20989	−	0.324190i	−0.138784	−	0.0371871i
$77$	0.190232	−	7.48375i	0.0216790	−	0.852852i
$78$	−5.15394	+	6.00753i	−0.583568	+	0.680219i
$79$	2.44887	+	4.24156i	0.275519	+	0.477213i	0.970266	−	0.242041i	$-0.0778169\pi$
$79$	2.44887	+	4.24156i	0.275519	+	0.477213i	−0.694747	+	0.719254i	$0.744484\pi$
$80$	−1.14581	−	1.14581i	−0.128106	−	0.128106i
$81$	1.00000			0.111111
$82$	9.58882			1.05891
$83$	−2.86668	−	2.86668i	−0.314659	−	0.314659i	0.532052	−	0.846712i	$-0.321421\pi$
$83$	−2.86668	−	2.86668i	−0.314659	−	0.314659i	−0.846712	+	0.532052i	$0.821421\pi$
$84$	2.11319	−	7.15412i	0.230568	−	0.780578i
$85$	4.70161	−	1.25979i	0.509961	−	0.136644i
$86$	1.69261	−	6.31692i	0.182519	−	0.681171i
$87$	−8.50903	+	4.91269i	−0.912264	+	0.526696i
$88$			5.09048i			0.542647i
$89$	−2.70378	−	10.0906i	−0.286600	−	1.06961i	−0.947662	−	0.319275i	$-0.896561\pi$
$89$	−2.70378	−	10.0906i	−0.286600	−	1.06961i	0.661062	−	0.750331i	$-0.270106\pi$
$90$	2.10567			0.221957
$91$	9.32806	+	1.99684i	0.977846	+	0.209326i
$92$	9.51661			0.992175
$93$	0.861462	+	3.21502i	0.0893295	+	0.333382i
$94$			20.6868i			2.13368i
$95$	−0.369020	+	0.213054i	−0.0378607	+	0.0218589i
$96$	1.89119	−	7.05803i	0.193019	−	0.720357i
$97$	4.64555	−	1.24477i	0.471684	−	0.126387i	−0.0151437	−	0.999885i	$-0.504821\pi$
$97$	4.64555	−	1.24477i	0.471684	−	0.126387i	0.486828	+	0.873498i	$0.338154\pi$
$98$	−15.0266	+	3.21808i	−1.51792	+	0.325075i
$99$	2.00076	+	2.00076i	0.201084	+	0.201084i
$100$	−11.5036			−1.15036
$101$	7.68552			0.764738			0.382369	−	0.924010i	$-0.375108\pi$
$101$	7.68552			0.764738			0.382369	+	0.924010i	$0.375108\pi$
$102$	7.87771	+	7.87771i	0.780010	+	0.780010i
$103$	−2.89145	−	5.00814i	−0.284903	−	0.493466i	0.687683	−	0.726011i	$-0.258628\pi$
$103$	−2.89145	−	5.00814i	−0.284903	−	0.493466i	−0.972586	+	0.232545i	$0.925295\pi$
$104$	−6.37539	−	1.19620i	−0.625159	−	0.117297i
$105$	−1.21259	−	2.22923i	−0.118336	−	0.217551i
$106$	−18.2397	−	4.88732i	−1.77160	−	0.474698i
$107$	5.22420	−	9.04858i	0.505043	−	0.874760i	−0.494940	−	0.868927i	$-0.664810\pi$
$107$	5.22420	−	9.04858i	0.505043	−	0.874760i	0.999983	−	0.00583257i	$-0.00185657\pi$
$108$	1.40975	+	2.44176i	0.135653	+	0.234958i
$109$	−3.51317	−	13.1113i	−0.336501	−	1.25584i	−0.902233	−	0.431249i	$-0.858073\pi$
$109$	−3.51317	−	13.1113i	−0.336501	−	1.25584i	0.565732	−	0.824589i	$-0.308594\pi$
$110$	4.21293	+	4.21293i	0.401688	+	0.401688i
$111$	1.36423	+	5.09136i	0.129487	+	0.483251i
$112$	−4.34551	+	1.04679i	−0.410612	+	0.0989120i
$113$	−0.894065	+	1.54857i	−0.0841065	+	0.145677i	−0.905010	−	0.425390i	$-0.860137\pi$
$113$	−0.894065	+	1.54857i	−0.0841065	+	0.145677i	0.820904	+	0.571067i	$0.193470\pi$
$114$	−0.844623	−	0.487643i	−0.0791061	−	0.0456720i
$115$	2.28920	−	2.28920i	0.213469	−	0.213469i
$116$	−23.9912	−	13.8513i	−2.22753	−	1.28606i
$117$	−2.97594	+	2.03563i	−0.275126	+	0.188194i
$118$		−	6.43563i		−	0.592448i
$119$	3.80347	−	12.8765i	0.348664	−	1.18039i
$120$	0.862793	+	1.49440i	0.0787619	+	0.136420i
$121$		−	2.99390i		−	0.272173i
$122$	27.3749	−	7.33508i	2.47841	−	0.664087i
$123$	4.21899	+	1.13047i	0.380413	+	0.101931i
$124$	−6.63585	+	6.63585i	−0.595917	+	0.595917i
$125$	−6.15829	+	6.15829i	−0.550815	+	0.550815i
$126$	3.03104	−	4.95472i	0.270026	−	0.441402i
$127$	−4.15160	+	2.39693i	−0.368395	+	0.212693i	−0.672757	−	0.739863i	$-0.734890\pi$
$127$	−4.15160	+	2.39693i	−0.368395	+	0.212693i	0.304362	+	0.952556i	$0.401557\pi$
$128$	12.7351	−	3.41236i	1.12564	−	0.301613i
$129$	1.48947	−	2.57983i	0.131140	−	0.227141i
$130$	−6.26633	+	4.28636i	−0.549594	+	0.375938i
$131$	−13.6712	+	7.89309i	−1.19446	+	0.689623i	−0.959315	−	0.282337i	$-0.908890\pi$
$131$	−13.6712	+	7.89309i	−1.19446	+	0.689623i	−0.235146	+	0.971960i	$0.575557\pi$
$132$	−2.06480	+	7.70594i	−0.179718	+	0.670716i
$133$	−0.0298679	+	1.17501i	−0.00258988	+	0.101886i
$134$	−19.1633	−	11.0639i	−1.65546	−	0.955779i
$135$	0.926472	+	0.248247i	0.0797380	+	0.0213657i
$136$	−2.36297	+	8.81874i	−0.202623	+	0.756201i
$137$	4.19847	−	15.6689i	0.358700	−	1.33868i	−0.517065	−	0.855946i	$-0.672975\pi$
$137$	4.19847	−	15.6689i	0.358700	−	1.33868i	0.875764	−	0.482739i	$-0.160358\pi$
$138$	7.15740	+	1.91782i	0.609278	+	0.163256i
$139$	14.0656	+	8.12080i	1.19303	+	0.688797i	0.958993	−	0.283431i	$-0.0914725\pi$
$139$	14.0656	+	8.12080i	1.19303	+	0.688797i	0.234038	+	0.972227i	$0.424806\pi$
$140$	3.73380	−	6.10350i	0.315564	−	0.515840i
$141$	−2.43887	+	9.10199i	−0.205390	+	0.766526i
$142$	1.51662	−	0.875620i	0.127272	−	0.0734804i
$143$	−10.0270	−	1.88133i	−0.838496	−	0.157325i
$144$	0.844715	−	1.46309i	0.0703929	−	0.121924i
$145$	−9.10294	+	2.43913i	−0.755958	+	0.202558i
$146$	7.47713	−	4.31692i	0.618812	−	0.357271i
$147$	−6.99096	−	0.355642i	−0.576605	−	0.0293328i
$148$	−10.5086	+	10.5086i	−0.863806	+	0.863806i
$149$	8.96814	−	8.96814i	0.734699	−	0.734699i	−0.236848	−	0.971547i	$-0.576114\pi$
$149$	8.96814	−	8.96814i	0.734699	−	0.734699i	0.971547	+	0.236848i	$0.0761143\pi$
$150$	−8.65182	−	2.31825i	−0.706418	−	0.189284i
$151$	−19.3183	+	5.17632i	−1.57210	+	0.421243i	−0.936469	−	0.350750i	$-0.885927\pi$
$151$	−19.3183	+	5.17632i	−1.57210	+	0.421243i	−0.635631	+	0.771993i	$0.719260\pi$
$152$		−	0.799244i		−	0.0648273i
$153$	2.53737	+	4.39486i	0.205134	+	0.355303i
$154$	15.9776	−	3.84883i	1.28751	−	0.310148i
$155$			3.19248i			0.256426i
$156$	−9.16584	−	4.39679i	−0.733854	−	0.352025i
$157$	2.66290	+	1.53742i	0.212522	+	0.122700i	0.602483	−	0.798132i	$-0.294178\pi$
$157$	2.66290	+	1.53742i	0.212522	+	0.122700i	−0.389961	+	0.920831i	$0.627511\pi$
$158$	−7.60294	+	7.60294i	−0.604857	+	0.604857i
$159$	−7.44911	−	4.30074i	−0.590753	−	0.341071i
$160$	3.50427	−	6.06958i	0.277037	−	0.479842i
$161$	−2.09136	−	8.68183i	−0.164822	−	0.684224i
$162$	0.568195	+	2.12053i	0.0446416	+	0.166605i
$163$	−15.0064	−	15.0064i	−1.17539	−	1.17539i	−0.980905	−	0.194485i	$-0.937696\pi$
$163$	−15.0064	−	15.0064i	−1.17539	−	1.17539i	−0.194485	−	0.980905i	$-0.562304\pi$
$164$	3.18737	+	11.8954i	0.248892	+	0.928877i
$165$	1.35697	+	2.35033i	0.105640	+	0.182973i
$166$	4.45006	−	7.70772i	0.345391	−	0.598235i
$167$	−22.6114	−	6.05871i	−1.74972	−	0.468837i	−0.765157	−	0.643844i	$-0.777339\pi$
$167$	−22.6114	−	6.05871i	−1.74972	−	0.468837i	−0.984567	+	0.175007i	$0.944005\pi$
$168$	4.75836	+	0.120955i	0.367115	+	0.00933185i
$169$	4.71242	−	12.1158i	0.362494	−	0.931986i
$170$	5.34286	+	9.25410i	0.409779	+	0.709757i
$171$	−0.314135	−	0.314135i	−0.0240225	−	0.0240225i
$172$	8.39909			0.640425
$173$	−16.6651			−1.26703			−0.633513	−	0.773732i	$-0.718388\pi$
$173$	−16.6651			−1.26703			−0.633513	+	0.773732i	$0.718388\pi$
$174$	−15.2523	−	15.2523i	−1.15627	−	1.15627i
$175$	2.52802	+	10.4945i	0.191100	+	0.793312i
$176$	4.61737	−	1.23722i	0.348047	−	0.0932589i
$177$	0.758729	−	2.83161i	0.0570296	−	0.212837i
$178$	19.8612	−	11.4669i	1.48866	−	0.859480i
$179$			12.1061i			0.904854i	0.891801	+	0.452427i	$0.149442\pi$
$179$			12.1061i			0.904854i	−0.891801	+	0.452427i	$0.850558\pi$
$180$	0.699933	+	2.61219i	0.0521699	+	0.194701i
$181$	11.9791			0.890400			0.445200	−	0.895431i	$-0.353133\pi$
$181$	11.9791			0.890400			0.445200	+	0.895431i	$0.353133\pi$
$182$	1.06579	+	20.9150i	0.0790019	+	1.55032i
$183$	12.9094			0.954294
$184$	1.57165	+	5.86547i	0.115863	+	0.432408i
$185$			5.05567i			0.371700i
$186$	−6.32807	+	3.65351i	−0.463997	+	0.267889i
$187$	−3.71639	+	13.8697i	−0.271769	+	1.01426i
$188$	−25.6630	+	6.87639i	−1.87167	+	0.501512i
$189$	1.91776	−	1.82268i	0.139497	−	0.132581i
$190$	−0.661463	−	0.661463i	−0.0479876	−	0.0479876i
$191$	−7.93591			−0.574223			−0.287111	−	0.957897i	$-0.592695\pi$
$191$	−7.93591			−0.574223			−0.287111	+	0.957897i	$0.592695\pi$
$192$	12.6625			0.913835
$193$	0.617714	+	0.617714i	0.0444640	+	0.0444640i	0.728989	−	0.684525i	$-0.239990\pi$
$193$	0.617714	+	0.617714i	0.0444640	+	0.0444640i	−0.684525	+	0.728989i	$0.739990\pi$
$194$	5.27915	+	9.14376i	0.379021	+	0.656484i
$195$	−3.26246	+	1.14719i	−0.233630	+	0.0821516i
$196$	−8.98710	−	17.5716i	−0.641936	−	1.25511i
$197$	15.9521	+	4.27434i	1.13654	+	0.304534i	0.777558	−	0.628811i	$-0.216458\pi$
$197$	15.9521	+	4.27434i	1.13654	+	0.304534i	0.358980	+	0.933345i	$0.383125\pi$
$198$	−3.10586	+	5.37950i	−0.220724	+	0.382304i
$199$	10.9926	+	19.0398i	0.779246	+	1.34969i	0.932377	+	0.361488i	$0.117731\pi$
$199$	10.9926	+	19.0398i	0.779246	+	1.34969i	−0.153130	+	0.988206i	$0.548935\pi$
$200$	−1.89980	−	7.09014i	−0.134336	−	0.501348i
$201$	−7.12728	−	7.12728i	−0.502720	−	0.502720i
$202$	4.36687	+	16.2974i	0.307252	+	1.14668i
$203$	−7.36403	+	24.9307i	−0.516854	+	1.74979i
$204$	−7.15412	+	12.3913i	−0.500888	+	0.867564i
$205$	3.62814	+	2.09471i	0.253400	+	0.146301i
$206$	8.97700	−	8.97700i	0.625458	−	0.625458i
$207$	2.92308	+	1.68764i	0.203168	+	0.117299i
$208$	0.464489	+	6.07359i	0.0322065	+	0.421128i
$209$		−	1.25702i		−	0.0869498i
$210$	4.03817	−	3.83796i	0.278660	−	0.264845i
$211$	11.4902	+	19.9017i	0.791020	+	1.37009i	0.925336	+	0.379148i	$0.123783\pi$
$211$	11.4902	+	19.9017i	0.791020	+	1.37009i	−0.134316	+	0.990939i	$0.542884\pi$
$212$		−	24.2519i		−	1.66563i
$213$	0.770529	−	0.206463i	0.0527958	−	0.0141466i
$214$	22.1562	+	5.93673i	1.51456	+	0.405826i
$215$	2.02038	−	2.02038i	0.137789	−	0.137789i
$216$	−1.27214	+	1.27214i	−0.0865578	+	0.0865578i
$217$	7.51205	+	4.59548i	0.509951	+	0.311961i
$218$	25.8068	−	14.8996i	1.74786	−	1.00913i
$219$	3.79881	−	1.01789i	0.256700	−	0.0687825i
$220$	−3.82596	+	6.62676i	−0.257946	+	0.446776i
$221$	−16.4974	−	7.91368i	−1.10973	−	0.532332i
$222$	−10.0212	+	5.78577i	−0.672582	+	0.388315i
$223$	5.97549	−	22.3008i	0.400148	−	1.49337i	−0.412683	−	0.910875i	$-0.635408\pi$
$223$	5.97549	−	22.3008i	0.400148	−	1.49337i	0.812832	−	0.582499i	$-0.197925\pi$
$224$	−9.23770	−	16.9827i	−0.617219	−	1.13470i
$225$	−3.53340	−	2.04001i	−0.235560	−	0.136001i
$226$	−3.79178	−	1.01601i	−0.252226	−	0.0675837i
$227$	−4.28502	+	15.9919i	−0.284407	+	1.06142i	0.664865	+	0.746964i	$0.268489\pi$
$227$	−4.28502	+	15.9919i	−0.284407	+	1.06142i	−0.949272	+	0.314457i	$0.898178\pi$
$228$	0.324190	−	1.20989i	0.0214700	−	0.0801271i
$229$	−7.27341	−	1.94891i	−0.480641	−	0.128787i	0.0103602	−	0.999946i	$-0.496702\pi$
$229$	−7.27341	−	1.94891i	−0.480641	−	0.128787i	−0.491001	+	0.871159i	$0.663369\pi$
$230$	6.15504	+	3.55361i	0.405851	+	0.234318i
$231$	7.48375	+	0.190232i	0.492394	+	0.0125164i
$232$	4.57503	−	17.0742i	0.300366	−	1.12098i
$233$	4.12931	−	2.38406i	0.270520	−	0.156185i	−0.358604	−	0.933490i	$-0.616747\pi$
$233$	4.12931	−	2.38406i	0.270520	−	0.156185i	0.629124	+	0.777305i	$0.283414\pi$
$234$	−6.00753	−	5.15394i	−0.392724	−	0.336923i
$235$	−4.51909	+	7.82730i	−0.294793	+	0.510596i
$236$	7.98373	−	2.13923i	0.519697	−	0.139252i
$237$	−4.24156	+	2.44887i	−0.275519	+	0.159071i
$238$	29.4662	+	0.749013i	1.91001	+	0.0485513i
$239$	−3.29121	+	3.29121i	−0.212890	+	0.212890i	−0.805494	−	0.592604i	$-0.798100\pi$
$239$	−3.29121	+	3.29121i	−0.212890	+	0.212890i	0.592604	+	0.805494i	$0.298100\pi$
$240$	1.14581	−	1.14581i	0.0739619	−	0.0739619i
$241$	−6.32909	−	1.69587i	−0.407692	−	0.109241i	0.0491438	−	0.998792i	$-0.484351\pi$
$241$	−6.32909	−	1.69587i	−0.407692	−	0.109241i	−0.456836	+	0.889551i	$0.651017\pi$
$242$	6.34867	−	1.70112i	0.408108	−	0.109352i
$243$			1.00000i			0.0641500i
$244$	18.1991	+	31.5217i	1.16508	+	2.01797i
$245$	−6.38864	−	2.06498i	−0.408155	−	0.131927i
$246$			9.58882i			0.611361i
$247$	1.57431	+	0.295384i	0.100171	+	0.0187948i
$248$	−5.18584	−	2.99404i	−0.329301	−	0.190122i
$249$	2.86668	−	2.86668i	0.181669	−	0.181669i
$250$	−16.5580	−	9.55975i	−1.04722	−	0.604611i
$251$	9.74305	−	16.8755i	0.614976	−	1.06517i	−0.375413	−	0.926858i	$-0.622499\pi$
$251$	9.74305	−	16.8755i	0.614976	−	1.06517i	0.990389	−	0.138312i	$-0.0441676\pi$
$252$	7.15412	+	2.11319i	0.450667	+	0.133118i
$253$	2.47182	+	9.22497i	0.155402	+	0.579969i
$254$	−7.44168	−	7.44168i	−0.466932	−	0.466932i
$255$	1.25979	+	4.70161i	0.0788913	+	0.294426i
$256$	1.80957	+	3.13427i	0.113098	+	0.195892i
$257$	3.90031	−	6.75553i	0.243294	−	0.421398i	−0.718356	−	0.695675i	$-0.755105\pi$
$257$	3.90031	−	6.75553i	0.243294	−	0.421398i	0.961651	+	0.274277i	$0.0884386\pi$
$258$	6.31692	+	1.69261i	0.393274	+	0.105377i
$259$	11.8962	+	7.27748i	0.739195	+	0.452201i
$260$	−7.40040	−	6.34890i	−0.458953	−	0.393742i
$261$	−4.91269	−	8.50903i	−0.304088	−	0.526696i
$262$	−24.5055	−	24.5055i	−1.51395	−	1.51395i
$263$	16.1099			0.993382			0.496691	−	0.867927i	$-0.334548\pi$
$263$	16.1099			0.993382			0.496691	+	0.867927i	$0.334548\pi$
$264$	−5.09048			−0.313297
$265$	−5.83374	−	5.83374i	−0.358364	−	0.358364i
$266$	−2.50861	+	0.604296i	−0.153813	+	0.0370518i
$267$	10.0906	−	2.70378i	0.617537	−	0.165469i
$268$	7.35541	−	27.4508i	0.449303	−	1.67682i
$269$	−3.76253	+	2.17230i	−0.229406	+	0.132447i	−0.610298	−	0.792172i	$-0.708950\pi$
$269$	−3.76253	+	2.17230i	−0.229406	+	0.132447i	0.380892	+	0.924619i	$0.375617\pi$
$270$			2.10567i			0.128147i
$271$	−0.357794	−	1.33531i	−0.0217345	−	0.0811141i	0.954207	−	0.299148i	$-0.0967024\pi$
$271$	−0.357794	−	1.33531i	−0.0217345	−	0.0811141i	−0.975941	+	0.218034i	$0.930036\pi$
$272$	8.57343			0.519841
$273$	−1.99684	+	9.32806i	−0.120854	+	0.564560i
$274$	35.6119			2.15140
$275$	−2.98792	−	11.1511i	−0.180178	−	0.672435i
$276$			9.51661i			0.572833i
$277$	−15.2627	+	8.81191i	−0.917045	+	0.529456i	−0.882691	−	0.469953i	$-0.844271\pi$
$277$	−15.2627	+	8.81191i	−0.917045	+	0.529456i	−0.0343541	+	0.999410i	$0.510937\pi$
$278$	−9.22838	+	34.4408i	−0.553482	+	2.06562i
$279$	−3.21502	+	0.861462i	−0.192478	+	0.0515744i
$280$	4.37846	+	1.29331i	0.261663	+	0.0772901i
$281$	−0.725318	−	0.725318i	−0.0432688	−	0.0432688i	0.685141	−	0.728410i	$-0.259740\pi$
$281$	−0.725318	−	0.725318i	−0.0432688	−	0.0432688i	−0.728410	+	0.685141i	$0.759740\pi$
$282$	−20.6868			−1.23188
$283$	−11.3080			−0.672188			−0.336094	−	0.941828i	$-0.609106\pi$
$283$	−11.3080			−0.672188			−0.336094	+	0.941828i	$0.609106\pi$
$284$	1.59038	+	1.59038i	0.0943719	+	0.0943719i
$285$	−0.213054	−	0.369020i	−0.0126202	−	0.0218589i
$286$	−1.70784	−	22.3314i	−0.100986	−	1.32049i
$287$	10.1515	−	5.52190i	0.599226	−	0.325947i
$288$	7.05803	+	1.89119i	0.415898	+	0.111440i
$289$	−4.37653	+	7.58037i	−0.257443	+	0.445904i
$290$	−10.3445	−	17.9172i	−0.607449	−	1.05213i
$291$	1.24477	+	4.64555i	0.0729698	+	0.272327i
$292$	7.84080	+	7.84080i	0.458848	+	0.458848i
$293$	−0.591222	−	2.20647i	−0.0345396	−	0.128903i	0.946503	−	0.322694i	$-0.104588\pi$
$293$	−0.591222	−	2.20647i	−0.0345396	−	0.128903i	−0.981043	+	0.193790i	$0.937922\pi$
$294$	−3.21808	−	15.0266i	−0.187682	−	0.876370i
$295$	1.40588	−	2.43506i	0.0818536	−	0.141775i
$296$	−8.21238	−	4.74142i	−0.477335	−	0.275589i
$297$	−2.00076	+	2.00076i	−0.116096	+	0.116096i
$298$	24.1129	+	13.9216i	1.39682	+	0.806455i
$299$	−12.1343	+	0.927995i	−0.701747	+	0.0536673i
$300$		−	11.5036i		−	0.664161i
$301$	−1.84577	−	7.66233i	−0.106389	−	0.441650i
$302$	−21.9531	−	38.0239i	−1.26326	−	2.18803i
$303$			7.68552i			0.441522i
$304$	−0.724962	+	0.194253i	−0.0415794	+	0.0111412i
$305$	11.9602	+	3.20474i	0.684841	+	0.183503i
$306$	−7.87771	+	7.87771i	−0.450339	+	0.450339i
$307$	−16.5239	+	16.5239i	−0.943069	+	0.943069i	−0.998464	−	0.0553956i	$-0.982358\pi$
$307$	−16.5239	+	16.5239i	−0.943069	+	0.943069i	0.0553956	+	0.998464i	$0.482358\pi$
$308$	10.0857	+	18.5417i	0.574686	+	1.05651i
$309$	5.00814	−	2.89145i	0.284903	−	0.164489i
$310$	−6.76976	+	1.81395i	−0.384496	+	0.103026i
$311$	−5.06256	+	8.76860i	−0.287071	+	0.497222i	−0.973109	−	0.230344i	$-0.926015\pi$
$311$	−5.06256	+	8.76860i	−0.287071	+	0.497222i	0.686038	+	0.727566i	$0.259348\pi$
$312$	1.19620	−	6.37539i	0.0677215	−	0.360936i
$313$	−7.40644	+	4.27611i	−0.418637	+	0.241700i	−0.694494	−	0.719499i	$-0.744372\pi$
$313$	−7.40644	+	4.27611i	−0.418637	+	0.241700i	0.275857	+	0.961199i	$0.411038\pi$
$314$	−1.74711	+	6.52031i	−0.0985953	+	0.367963i
$315$	2.22923	−	1.21259i	0.125603	−	0.0683215i
$316$	−11.9591	−	6.90458i	−0.672751	−	0.388413i
$317$	31.4002	+	8.41365i	1.76361	+	0.472558i	0.987444	−	0.157970i	$-0.0504950\pi$
$317$	31.4002	+	8.41365i	1.76361	+	0.472558i	0.776166	+	0.630528i	$0.217162\pi$
$318$	4.88732	−	18.2397i	0.274067	−	1.02283i
$319$	7.19542	−	26.8537i	0.402866	−	1.50352i
$320$	11.7314	+	3.14343i	0.655807	+	0.175723i
$321$	9.04858	+	5.22420i	0.505043	+	0.291587i
$322$	17.2218	−	9.36776i	0.959733	−	0.522045i
$323$	0.583501	−	2.17766i	0.0324669	−	0.121168i
$324$	−2.44176	+	1.40975i	−0.135653	+	0.0783194i
$325$	14.6679	−	1.12175i	0.813629	−	0.0622237i
$326$	23.2950	−	40.3480i	1.29019	−	2.23467i
$327$	13.1113	−	3.51317i	0.725059	−	0.194279i
$328$	−6.80524	+	3.92901i	−0.375757	+	0.216943i
$329$	11.9129	+	21.9008i	0.656778	+	1.20743i
$330$	−4.21293	+	4.21293i	−0.231914	+	0.231914i
$331$	−17.8152	+	17.8152i	−0.979212	+	0.979212i	−0.999788	−	0.0205764i	$-0.993450\pi$
$331$	−17.8152	+	17.8152i	−0.979212	+	0.979212i	0.0205764	+	0.999788i	$0.493450\pi$
$332$	11.0410	+	2.95844i	0.605956	+	0.162365i
$333$	−5.09136	+	1.36423i	−0.279005	+	0.0747591i
$334$		−	51.3907i		−	2.81198i
$335$	−4.83390	−	8.37256i	−0.264104	−	0.457442i
$336$	−1.04679	−	4.34551i	−0.0571069	−	0.237067i
$337$			18.3271i			0.998342i	0.866504	+	0.499171i	$0.166362\pi$
$337$			18.3271i			0.998342i	−0.866504	+	0.499171i	$0.833638\pi$
$338$	28.3695	+	3.10869i	1.54310	+	0.169091i
$339$	−1.54857	−	0.894065i	−0.0841065	−	0.0485589i
$340$	−9.70420	+	9.70420i	−0.526284	+	0.526284i
$341$	−8.15607	−	4.70891i	−0.441676	−	0.255002i
$342$	0.487643	−	0.844623i	0.0263687	−	0.0456720i
$343$	−14.0552	+	12.0603i	−0.758912	+	0.651194i
$344$	1.38709	+	5.17670i	0.0747870	+	0.279109i
$345$	2.28920	+	2.28920i	0.123247	+	0.123247i
$346$	−9.46903	−	35.3389i	−0.509058	−	1.89983i
$347$	9.15417	+	15.8555i	0.491422	+	0.851167i	0.999951	−	0.00987715i	$-0.00314404\pi$
$347$	9.15417	+	15.8555i	0.491422	+	0.851167i	−0.508529	+	0.861045i	$0.669811\pi$
$348$	13.8513	−	23.9912i	0.742509	−	1.28606i
$349$	−24.2335	−	6.49336i	−1.29719	−	0.347581i	−0.456804	−	0.889567i	$-0.651006\pi$
$349$	−24.2335	−	6.49336i	−1.29719	−	0.347581i	−0.840387	+	0.541986i	$0.817673\pi$
$350$	−20.8176	+	11.3237i	−1.11275	+	0.605276i
$351$	−2.03563	−	2.97594i	−0.108654	−	0.158844i
$352$	10.3376	+	17.9053i	0.550996	+	0.954353i
$353$	16.1581	+	16.1581i	0.860010	+	0.860010i	0.991339	−	0.131329i	$-0.0419244\pi$
$353$	16.1581	+	16.1581i	0.860010	+	0.860010i	−0.131329	+	0.991339i	$0.541924\pi$
$354$	6.43563			0.342050
$355$	0.765127			0.0406087
$356$	20.8272	+	20.8272i	1.10384	+	1.10384i
$357$	12.8765	+	3.80347i	0.681498	+	0.201301i
$358$	−25.6714	+	6.87864i	−1.35678	+	0.363547i
$359$	5.75735	−	21.4867i	0.303861	−	1.13403i	−0.630060	−	0.776547i	$-0.716970\pi$
$359$	5.75735	−	21.4867i	0.303861	−	1.13403i	0.933921	−	0.357479i	$-0.116364\pi$
$360$	−1.49440	+	0.862793i	−0.0787619	+	0.0454732i
$361$		−	18.8026i		−	0.989613i
$362$	6.80647	+	25.4021i	0.357740	+	1.33510i
$363$	2.99390			0.157139
$364$	−25.5919	+	8.27442i	−1.34138	+	0.433698i
$365$	3.77218			0.197445
$366$	7.33508	+	27.3749i	0.383411	+	1.43091i
$367$		−	16.3042i		−	0.851074i	−0.904941	−	0.425537i	$-0.860085\pi$
$367$		−	16.3042i		−	0.851074i	0.904941	−	0.425537i	$-0.139915\pi$
$368$	4.93835	−	2.85116i	0.257429	−	0.148627i
$369$	−1.13047	+	4.21899i	−0.0588501	+	0.219632i
$370$	−10.7207	+	2.87260i	−0.557343	+	0.149340i
$371$	−22.1245	+	5.32956i	−1.14865	+	0.276697i
$372$	−6.63585	−	6.63585i	−0.344053	−	0.344053i
$373$	−35.1042			−1.81763			−0.908813	−	0.417204i	$-0.863010\pi$
$373$	−35.1042			−1.81763			−0.908813	+	0.417204i	$0.863010\pi$
$374$	−31.5229			−1.63001
$375$	−6.15829	−	6.15829i	−0.318013	−	0.318013i
$376$	−8.47639	−	14.6815i	−0.437136	−	0.757142i
$377$	31.9411	+	15.3219i	1.64505	+	0.789120i
$378$	4.95472	+	3.03104i	0.254843	+	0.155900i
$379$	22.7061	+	6.08407i	1.16633	+	0.312518i	0.789492	−	0.613760i	$-0.210344\pi$
$379$	22.7061	+	6.08407i	1.16633	+	0.312518i	0.376840	+	0.926278i	$0.377011\pi$
$380$	0.600705	−	1.04045i	0.0308155	−	0.0533740i
$381$	−2.39693	−	4.15160i	−0.122798	−	0.212693i
$382$	−4.50914	−	16.8284i	−0.230708	−	0.861013i
$383$	−6.30758	−	6.30758i	−0.322302	−	0.322302i	0.527347	−	0.849650i	$-0.323187\pi$
$383$	−6.30758	−	6.30758i	−0.322302	−	0.322302i	−0.849650	+	0.527347i	$0.823187\pi$
$384$	3.41236	+	12.7351i	0.174136	+	0.649886i
$385$	6.88626	+	2.03407i	0.350956	+	0.103666i
$386$	−0.958900	+	1.66086i	−0.0488067	+	0.0845357i
$387$	2.57983	+	1.48947i	0.131140	+	0.0757138i
$388$	−9.58849	+	9.58849i	−0.486782	+	0.486782i
$389$	−13.7424	−	7.93420i	−0.696770	−	0.402280i	0.109374	−	0.994001i	$-0.465116\pi$
$389$	−13.7424	−	7.93420i	−0.696770	−	0.402280i	−0.806143	+	0.591721i	$0.798449\pi$
$390$	−4.28636	−	6.26633i	−0.217048	−	0.317308i
$391$			17.1287i			0.866237i
$392$	9.34587	−	8.44102i	0.472038	−	0.426336i
$393$	−7.89309	−	13.6712i	−0.398154	−	0.689623i
$394$			36.2555i			1.82653i
$395$	−4.53762	+	1.21585i	−0.228312	+	0.0611761i
$396$	−7.70594	−	2.06480i	−0.387238	−	0.103760i
$397$	−24.2981	+	24.2981i	−1.21949	+	1.21949i	−0.251675	+	0.967812i	$0.580981\pi$
$397$	−24.2981	+	24.2981i	−1.21949	+	1.21949i	−0.967812	+	0.251675i	$0.919019\pi$
$398$	−34.1285	+	34.1285i	−1.71071	+	1.71071i
$399$	−1.17501	−	0.0298679i	−0.0588239	−	0.00149527i
$400$	−5.96944	+	3.44646i	−0.298472	+	0.172323i
$401$	17.1532	−	4.59620i	0.856592	−	0.229523i	0.196311	−	0.980542i	$-0.437104\pi$
$401$	17.1532	−	4.59620i	0.856592	−	0.229523i	0.660281	+	0.751019i	$0.270437\pi$
$402$	11.0639	−	19.1633i	0.551819	−	0.955779i
$403$	7.81409	−	9.10825i	0.389247	−	0.453714i
$404$	−18.7662	+	10.8346i	−0.933651	+	0.539044i
$405$	−0.248247	+	0.926472i	−0.0123355	+	0.0460368i
$406$	−57.0505	−	1.45019i	−2.83137	−	0.0719716i
$407$	−12.9161	−	7.45711i	−0.640227	−	0.369635i
$408$	−8.81874	−	2.36297i	−0.436593	−	0.116985i
$409$	2.81845	−	10.5186i	0.139364	−	0.520112i	−0.860578	−	0.509318i	$-0.829898\pi$
$409$	2.81845	−	10.5186i	0.139364	−	0.520112i	0.999942	−	0.0107935i	$-0.00343574\pi$
$410$	−2.38040	+	8.88378i	−0.117560	+	0.438738i
$411$	15.6689	+	4.19847i	0.772890	+	0.207095i
$412$	14.1204	+	8.15243i	0.695664	+	0.401642i
$413$	−3.70608	−	6.81329i	−0.182364	−	0.335260i
$414$	−1.91782	+	7.15740i	−0.0942557	+	0.351767i
$415$	3.36755	−	1.94425i	0.165306	−	0.0954397i
$416$	−24.8540	+	8.73946i	−1.21857	+	0.428487i
$417$	−8.12080	+	14.0656i	−0.397677	+	0.688797i
$418$	2.66555	−	0.714231i	0.130376	−	0.0349342i
$419$	−26.8756	+	15.5166i	−1.31296	+	0.758037i	−0.982585	−	0.185813i	$-0.940508\pi$
$419$	−26.8756	+	15.5166i	−1.31296	+	0.758037i	−0.330374	+	0.943850i	$0.607175\pi$
$420$	6.10350	+	3.73380i	0.297820	+	0.182191i
$421$	−25.6619	+	25.6619i	−1.25068	+	1.25068i	−0.295269	+	0.955414i	$0.595409\pi$
$421$	−25.6619	+	25.6619i	−1.25068	+	1.25068i	−0.955414	+	0.295269i	$0.904591\pi$
$422$	−35.6734	+	35.6734i	−1.73655	+	1.73655i
$423$	−9.10199	−	2.43887i	−0.442554	−	0.118582i
$424$	14.9474	−	4.00514i	0.725910	−	0.194507i
$425$		−	20.7051i		−	1.00434i
$426$	0.875620	+	1.51662i	0.0424239	+	0.0734804i
$427$	24.7573	−	23.5298i	1.19809	−	1.13869i
$428$			29.4592i			1.42397i
$429$	1.88133	−	10.0270i	0.0908316	−	0.484106i
$430$	5.43226	+	3.13632i	0.261967	+	0.151247i
$431$	−0.140672	+	0.140672i	−0.00677592	+	0.00677592i	−0.710487	−	0.703711i	$-0.751525\pi$
$431$	−0.140672	+	0.140672i	−0.00677592	+	0.00677592i	0.703711	+	0.710487i	$0.251525\pi$
$432$	1.46309	+	0.844715i	0.0703929	+	0.0406414i
$433$	−14.8795	+	25.7720i	−0.715062	+	1.23852i	0.247873	+	0.968792i	$0.420268\pi$
$433$	−14.8795	+	25.7720i	−0.715062	+	1.23852i	−0.962936	+	0.269731i	$0.913065\pi$
$434$	−5.47655	+	18.5407i	−0.262883	+	0.889980i
$435$	−2.43913	−	9.10294i	−0.116947	−	0.436453i
$436$	27.0620	+	27.0620i	1.29603	+	1.29603i
$437$	−0.388095	−	1.44839i	−0.0185651	−	0.0692859i
$438$	4.31692	+	7.47713i	0.206271	+	0.357271i
$439$	18.8779	−	32.6974i	0.900992	−	1.56056i	0.0747826	−	0.997200i	$-0.476174\pi$
$439$	18.8779	−	32.6974i	0.900992	−	1.56056i	0.826209	−	0.563364i	$-0.190493\pi$
$440$	−4.71619	−	1.26370i	−0.224835	−	0.0602445i
$441$	0.355642	−	6.99096i	0.0169353	−	0.332903i
$442$	7.40748	−	39.4797i	0.352338	−	1.87786i
$443$	13.7134	+	23.7524i	0.651545	+	1.12851i	0.982748	+	0.184949i	$0.0592120\pi$
$443$	13.7134	+	23.7524i	0.651545	+	1.12851i	−0.331204	+	0.943559i	$0.607455\pi$
$444$	−10.5086	−	10.5086i	−0.498718	−	0.498718i
$445$	10.0199			0.474989
$446$	50.6848			2.40000
$447$	8.96814	+	8.96814i	0.424179	+	0.424179i
$448$	24.2836	−	23.0797i	1.14729	−	1.09041i
$449$	−3.40594	+	0.912619i	−0.160736	+	0.0430691i	−0.338290	−	0.941042i	$-0.609848\pi$
$449$	−3.40594	+	0.912619i	−0.160736	+	0.0430691i	0.177553	+	0.984111i	$0.443182\pi$
$450$	2.31825	−	8.65182i	0.109283	−	0.407850i
$451$	−10.7030	+	6.17938i	−0.503985	+	0.290976i
$452$		−	5.04163i		−	0.237138i
$453$	−5.17632	−	19.3183i	−0.243205	−	0.907652i
$454$	−36.3461			−1.70581
$455$	−4.16568	+	8.14647i	−0.195290	+	0.381913i
$456$	0.799244			0.0374280
$457$	−3.35067	−	12.5049i	−0.156738	−	0.584953i	−0.998950	−	0.0458075i	$-0.985414\pi$
$457$	−3.35067	−	12.5049i	−0.156738	−	0.584953i	0.842213	−	0.539146i	$-0.181253\pi$
$458$		−	16.5309i		−	0.772436i
$459$	−4.39486	+	2.53737i	−0.205134	+	0.118434i
$460$	−2.36247	+	8.81687i	−0.110151	+	0.411089i
$461$	20.6542	−	5.53427i	0.961961	−	0.257757i	0.256531	−	0.966536i	$-0.417420\pi$
$461$	20.6542	−	5.53427i	0.961961	−	0.257757i	0.705430	+	0.708779i	$0.250754\pi$
$462$	3.84883	+	15.9776i	0.179064	+	0.743346i
$463$	−13.7630	−	13.7630i	−0.639622	−	0.639622i	0.310840	−	0.950462i	$-0.399390\pi$
$463$	−13.7630	−	13.7630i	−0.639622	−	0.639622i	−0.950462	+	0.310840i	$0.899390\pi$
$464$	−16.5993			−0.770603
$465$	−3.19248			−0.148048
$466$	7.40172	+	7.40172i	0.342878	+	0.342878i
$467$	9.10881	+	15.7769i	0.421505	+	0.730069i	0.996087	−	0.0883787i	$-0.0281686\pi$
$467$	9.10881	+	15.7769i	0.421505	+	0.730069i	−0.574582	+	0.818447i	$0.694835\pi$
$468$	4.39679	−	9.16584i	0.203242	−	0.423691i
$469$	−26.6592	−	0.677662i	−1.23101	−	0.0312915i
$470$	−19.1657	−	5.13545i	−0.884050	−	0.236880i
$471$	−1.53742	+	2.66290i	−0.0708408	+	0.122700i
$472$	2.63699	+	4.56740i	0.121377	+	0.210232i
$473$	2.18156	+	8.14169i	0.100308	+	0.374355i
$474$	−7.60294	−	7.60294i	−0.349214	−	0.349214i
$475$	0.469127	+	1.75080i	0.0215250	+	0.0803324i
$476$	8.86551	+	36.8033i	0.406350	+	1.68688i
$477$	4.30074	−	7.44911i	0.196918	−	0.341071i
$478$	−8.84915	−	5.10906i	−0.404751	−	0.233683i
$479$	14.4130	−	14.4130i	0.658548	−	0.658548i	−0.296488	−	0.955037i	$-0.595816\pi$
$479$	14.4130	−	14.4130i	0.658548	−	0.658548i	0.955037	+	0.296488i	$0.0958155\pi$
$480$	6.06958	+	3.50427i	0.277037	+	0.159947i
$481$	12.3745	−	14.4240i	0.564230	−	0.657677i
$482$		−	14.3846i		−	0.655201i
$483$	8.68183	−	2.09136i	0.395037	−	0.0951601i
$484$	4.22065	+	7.31039i	0.191848	+	0.332290i
$485$			4.61298i			0.209465i
$486$	−2.12053	+	0.568195i	−0.0961892	+	0.0257738i
$487$	−4.73501	−	1.26874i	−0.214564	−	0.0574922i	0.149936	−	0.988696i	$-0.452093\pi$
$487$	−4.73501	−	1.26874i	−0.214564	−	0.0574922i	−0.364500	+	0.931204i	$0.618760\pi$
$488$	−16.4226	+	16.4226i	−0.743414	+	0.743414i
$489$	15.0064	−	15.0064i	0.678612	−	0.678612i
$490$	0.748863	−	14.7206i	0.0338302	−	0.665010i
$491$	−14.7008	+	8.48750i	−0.663437	+	0.383035i	−0.793585	−	0.608459i	$-0.791788\pi$
$491$	−14.7008	+	8.48750i	−0.663437	+	0.383035i	0.130148	+	0.991495i	$0.458455\pi$
$492$	−11.8954	+	3.18737i	−0.536287	+	0.143698i
$493$	24.9307	−	43.1812i	1.12282	−	1.94478i
$494$	0.268143	+	3.50621i	0.0120643	+	0.157752i
$495$	−2.35033	+	1.35697i	−0.105640	+	0.0609911i
$496$	−1.45538	+	5.43155i	−0.0653485	+	0.243884i
$497$	1.10138	−	1.80038i	0.0494035	−	0.0807580i
$498$	7.70772	+	4.45006i	0.345391	+	0.199412i
$499$	21.3525	+	5.72138i	0.955868	+	0.256124i	0.702851	−	0.711337i	$-0.251910\pi$
$499$	21.3525	+	5.72138i	0.955868	+	0.256124i	0.253018	+	0.967462i	$0.418577\pi$
$500$	6.35541	−	23.7187i	0.284222	−	1.06073i
$501$	6.05871	−	22.6114i	0.270683	−	1.01020i
$502$	41.3209	+	11.0719i	1.84424	+	0.494163i
$503$	−2.07668	−	1.19897i	−0.0925946	−	0.0534595i	0.452988	−	0.891517i	$-0.350358\pi$
$503$	−2.07668	−	1.19897i	−0.0925946	−	0.0534595i	−0.545582	+	0.838057i	$0.683691\pi$
$504$	−0.120955	+	4.75836i	−0.00538775	+	0.211954i
$505$	−1.90791	+	7.12042i	−0.0849009	+	0.316854i
$506$	−18.1574	+	10.4832i	−0.807193	+	0.466033i
$507$	12.1158	+	4.71242i	0.538082	+	0.209286i
$508$	6.75813	−	11.7054i	0.299844	−	0.519344i
$509$	25.3697	−	6.79779i	1.12449	−	0.301307i	0.351792	−	0.936078i	$-0.385572\pi$
$509$	25.3697	−	6.79779i	1.12449	−	0.301307i	0.772700	+	0.634771i	$0.218906\pi$
$510$	−9.25410	+	5.34286i	−0.409779	+	0.236586i
$511$	5.42993	−	8.87610i	0.240206	−	0.392655i
$512$	13.0274	−	13.0274i	0.575734	−	0.575734i
$513$	0.314135	−	0.314135i	0.0138694	−	0.0138694i
$514$	16.5414	+	4.43226i	0.729612	+	0.195499i
$515$	5.35769	−	1.43559i	0.236088	−	0.0632596i
$516$			8.39909i			0.369749i
$517$	−13.3313	−	23.0905i	−0.586311	−	1.01552i
$518$	−8.67276	+	29.3613i	−0.381059	+	1.29006i
$519$		−	16.6651i		−	0.731518i
$520$	2.69092	−	5.60967i	0.118005	−	0.246000i
$521$	−1.07001	−	0.617770i	−0.0468780	−	0.0270650i	0.476378	−	0.879241i	$-0.341949\pi$
$521$	−1.07001	−	0.617770i	−0.0468780	−	0.0270650i	−0.523256	+	0.852176i	$0.675283\pi$
$522$	15.2523	−	15.2523i	0.667575	−	0.667575i
$523$	7.33789	+	4.23653i	0.320863	+	0.185251i	0.651777	−	0.758410i	$-0.274024\pi$
$523$	7.33789	+	4.23653i	0.320863	+	0.185251i	−0.330914	+	0.943661i	$0.607357\pi$
$524$	22.2546	−	38.5460i	0.972195	−	1.68389i
$525$	−10.4945	+	2.52802i	−0.458019	+	0.110332i
$526$	9.15359	+	34.1616i	0.399115	+	1.48952i
$527$	−11.9437	−	11.9437i	−0.520276	−	0.520276i
$528$	1.23722	+	4.61737i	0.0538431	+	0.200945i
$529$	−5.80372	−	10.0523i	−0.252336	−	0.437058i
$530$	9.05593	−	15.6853i	0.393364	−	0.681327i
$531$	2.83161	+	0.758729i	0.122882	+	0.0329260i
$532$	−1.58353	−	2.91118i	−0.0686548	−	0.126216i
$533$	−5.22408	−	14.8567i	−0.226280	−	0.643514i
$534$	11.4669	+	19.8612i	0.496221	+	0.859480i
$535$	7.08636	+	7.08636i	0.306370	+	0.306370i
$536$	18.1337			0.783258
$537$	−12.1061			−0.522418
$538$	−6.74428	−	6.74428i	−0.290766	−	0.290766i
$539$	14.6988	−	13.2757i	0.633122	−	0.571824i
$540$	−2.61219	+	0.699933i	−0.112411	+	0.0301203i
$541$	7.10493	−	26.5160i	0.305465	−	1.14001i	−0.627080	−	0.778955i	$-0.715750\pi$
$541$	7.10493	−	26.5160i	0.305465	−	1.14001i	0.932545	−	0.361055i	$-0.117583\pi$
$542$	2.62826	−	1.51743i	0.112894	−	0.0651791i
$543$			11.9791i			0.514073i
$544$	9.59732	+	35.8177i	0.411482	+	1.53567i
$545$	13.0194			0.557691
$546$	−20.9150	+	1.06579i	−0.895080	+	0.0456118i
$547$	−46.7525			−1.99899			−0.999495	−	0.0317618i	$-0.989888\pi$
$547$	−46.7525			−1.99899			−0.999495	+	0.0317618i	$0.989888\pi$
$548$	11.8376	+	44.1784i	0.505676	+	1.88721i
$549$			12.9094i			0.550962i
$550$	21.9485	−	12.6720i	0.935886	−	0.540334i
$551$	−1.12974	+	4.21623i	−0.0481284	+	0.179618i
$552$	−5.86547	+	1.57165i	−0.249651	+	0.0668938i
$553$	−3.67081	+	12.4274i	−0.156099	+	0.528466i
$554$	−27.3581	−	27.3581i	−1.16233	−	1.16233i
$555$	−5.05567			−0.214601
$556$	−45.7931			−1.94206
$557$	16.5395	+	16.5395i	0.700800	+	0.700800i	0.964582	−	0.263782i	$-0.0849700\pi$
$557$	16.5395	+	16.5395i	0.700800	+	0.700800i	−0.263782	+	0.964582i	$0.584970\pi$
$558$	−3.65351	−	6.32807i	−0.154666	−	0.267889i
$559$	−10.7094	+	0.819022i	−0.452960	+	0.0346409i
$560$	0.108944	−	4.28586i	0.00460372	−	0.181110i
$561$	−13.8697	−	3.71639i	−0.585581	−	0.156906i
$562$	1.12594	−	1.95018i	0.0474948	−	0.0822634i
$563$	−17.9966	−	31.1711i	−0.758468	−	1.31370i	−0.943632	−	0.330997i	$-0.892615\pi$
$563$	−17.9966	−	31.1711i	−0.758468	−	1.31370i	0.185164	−	0.982708i	$-0.440718\pi$
$564$	−6.87639	−	25.6630i	−0.289548	−	1.08061i
$565$	−1.21275	−	1.21275i	−0.0510209	−	0.0510209i
$566$	−6.42512	−	23.9789i	−0.270068	−	1.00791i
$567$	1.82268	+	1.91776i	0.0765456	+	0.0805385i
$568$	−0.717568	+	1.24286i	−0.0301085	+	0.0521495i
$569$	1.56424	+	0.903112i	0.0655762	+	0.0378604i	0.532430	−	0.846474i	$-0.321279\pi$
$569$	1.56424	+	0.903112i	0.0655762	+	0.0378604i	−0.466853	+	0.884335i	$0.654612\pi$
$570$	0.661463	−	0.661463i	0.0277056	−	0.0277056i
$571$	10.6308	+	6.13767i	0.444883	+	0.256853i	0.705667	−	0.708544i	$-0.250648\pi$
$571$	10.6308	+	6.13767i	0.444883	+	0.256853i	−0.260784	+	0.965397i	$0.583981\pi$
$572$	27.1356	−	9.54173i	1.13460	−	0.398960i
$573$		−	7.93591i		−	0.331528i
$574$	17.4774	+	18.3891i	0.729493	+	0.767547i
$575$	−6.88562	−	11.9262i	−0.287150	−	0.497359i
$576$			12.6625i			0.527603i
$577$	3.75081	−	1.00503i	0.156148	−	0.0418398i	−0.179898	−	0.983685i	$-0.557577\pi$
$577$	3.75081	−	1.00503i	0.156148	−	0.0418398i	0.336046	+	0.941845i	$0.390910\pi$
$578$	−18.5611	−	4.97344i	−0.772041	−	0.206868i
$579$	−0.617714	+	0.617714i	−0.0256713	+	0.0256713i
$580$	18.7886	−	18.7886i	0.780155	−	0.780155i
$581$	0.272564	−	10.7227i	0.0113079	−	0.444852i
$582$	−9.14376	+	5.27915i	−0.379021	+	0.218828i
$583$	23.5087	−	6.29912i	0.973629	−	0.260883i
$584$	−3.53771	+	6.12749i	−0.146391	+	0.253557i
$585$	−1.14719	−	3.26246i	−0.0474303	−	0.134886i
$586$	4.34296	−	2.50741i	0.179406	−	0.103580i
$587$	−1.54556	+	5.76812i	−0.0637922	+	0.238076i	−0.990459	−	0.137808i	$-0.955994\pi$
$587$	−1.54556	+	5.76812i	−0.0637922	+	0.238076i	0.926667	+	0.375884i	$0.122661\pi$
$588$	17.5716	−	8.98710i	0.724640	−	0.370622i
$589$	1.28057	+	0.739335i	0.0527648	+	0.0304638i
$590$	5.96243	+	1.59763i	0.245470	+	0.0657734i
$591$	−4.27434	+	15.9521i	−0.175823	+	0.656181i
$592$	−2.30477	+	8.60150i	−0.0947253	+	0.353519i
$593$	12.8455	+	3.44195i	0.527502	+	0.141344i	0.512735	−	0.858547i	$-0.328632\pi$
$593$	12.8455	+	3.44195i	0.527502	+	0.141344i	0.0147677	+	0.999891i	$0.495299\pi$
$594$	−5.37950	−	3.10586i	−0.220724	−	0.127435i
$595$	10.9855	+	6.72038i	0.450363	+	0.275509i
$596$	−9.25519	+	34.5408i	−0.379107	+	1.41485i
$597$	−19.0398	+	10.9926i	−0.779246	+	0.449898i
$598$	−8.86251	−	25.2040i	−0.362415	−	1.03067i
$599$	9.76222	−	16.9087i	0.398873	−	0.690869i	−0.594714	−	0.803937i	$-0.702735\pi$
$599$	9.76222	−	16.9087i	0.398873	−	0.690869i	0.993587	+	0.113069i	$0.0360680\pi$
$600$	7.09014	−	1.89980i	0.289454	−	0.0775589i
$601$	38.3090	−	22.1177i	1.56266	−	0.902201i	0.565671	−	0.824631i	$-0.308617\pi$
$601$	38.3090	−	22.1177i	1.56266	−	0.902201i	0.996987	−	0.0775697i	$-0.0247160\pi$
$602$	15.1995	−	8.26771i	0.619484	−	0.336967i
$603$	7.12728	−	7.12728i	0.290245	−	0.290245i
$604$	39.8732	−	39.8732i	1.62242	−	1.62242i
$605$	2.77377	+	0.743229i	0.112770	+	0.0302166i
$606$	−16.2974	+	4.36687i	−0.662036	+	0.177392i
$607$			31.4154i			1.27511i	0.770404	+	0.637557i	$0.220055\pi$
$607$			31.4154i			1.27511i	−0.770404	+	0.637557i	$0.779945\pi$
$608$	−1.62308	−	2.81126i	−0.0658247	−	0.114012i
$609$	−24.9307	−	7.36403i	−1.01024	−	0.298406i
$610$			27.1830i			1.10061i
$611$	32.0516	−	11.2704i	1.29667	−	0.455950i
$612$	−12.3913	−	7.15412i	−0.500888	−	0.289188i
$613$	23.6963	−	23.6963i	0.957083	−	0.957083i	−0.0420336	−	0.999116i	$-0.513384\pi$
$613$	23.6963	−	23.6963i	0.957083	−	0.957083i	0.999116	+	0.0420336i	$0.0133837\pi$
$614$	−44.4282	−	25.6507i	−1.79298	−	1.03518i
$615$	−2.09471	+	3.62814i	−0.0844667	+	0.146301i
$616$	−9.76234	+	9.27834i	−0.393336	+	0.373835i
$617$	−2.37085	−	8.84813i	−0.0954468	−	0.356212i	0.901640	−	0.432487i	$-0.142364\pi$
$617$	−2.37085	−	8.84813i	−0.0954468	−	0.356212i	−0.997087	+	0.0762750i	$0.975697\pi$
$618$	8.97700	+	8.97700i	0.361108	+	0.361108i
$619$	2.20096	+	8.21409i	0.0884640	+	0.330152i	0.995948	−	0.0899353i	$-0.0286660\pi$
$619$	2.20096	+	8.21409i	0.0884640	+	0.330152i	−0.907484	+	0.420088i	$0.861999\pi$
$620$	−4.50060	−	7.79526i	−0.180748	−	0.313065i
$621$	−1.68764	+	2.92308i	−0.0677228	+	0.117299i
$622$	−21.4706	−	5.75303i	−0.860893	−	0.230676i
$623$	14.4233	−	23.5773i	0.577859	−	0.944603i
$624$	−6.07359	+	0.464489i	−0.243138	+	0.0185944i
$625$	6.02335	+	10.4327i	0.240934	+	0.417310i
$626$	−13.2759	−	13.2759i	−0.530613	−	0.530613i
$627$	1.25702			0.0502005
$628$	−8.66953			−0.345952
$629$	−18.9143	−	18.9143i	−0.754161	−	0.754161i
$630$	3.83796	+	4.03817i	0.152908	+	0.160885i
$631$	35.8199	−	9.59792i	1.42597	−	0.382087i	0.538371	−	0.842708i	$-0.319040\pi$
$631$	35.8199	−	9.59792i	1.42597	−	0.382087i	0.887597	+	0.460621i	$0.152373\pi$
$632$	2.28055	−	8.51114i	0.0907155	−	0.338555i
$633$	−19.9017	+	11.4902i	−0.791020	+	0.456696i
$634$			71.3657i			2.83429i
$635$	−1.19006	−	4.44137i	−0.0472262	−	0.176250i
$636$	24.2519			0.961649
$637$	13.1726	+	21.5286i	0.521919	+	0.852995i
$638$	61.0324			2.41630
$639$	0.206463	+	0.770529i	0.00816753	+	0.0304816i
$640$			12.6458i			0.499870i
$641$	−17.6520	+	10.1914i	−0.697213	+	0.402536i	−0.806308	−	0.591495i	$-0.798538\pi$
$641$	−17.6520	+	10.1914i	−0.697213	+	0.402536i	0.109096	+	0.994031i	$0.465204\pi$
$642$	−5.93673	+	22.1562i	−0.234304	+	0.874434i
$643$	−2.81166	+	0.753382i	−0.110881	+	0.0297105i	−0.313833	−	0.949478i	$-0.601613\pi$
$643$	−2.81166	+	0.753382i	−0.110881	+	0.0297105i	0.202952	+	0.979189i	$0.434947\pi$
$644$	17.3458	+	18.2506i	0.683519	+	0.719175i
$645$	2.02038	+	2.02038i	0.0795526	+	0.0795526i
$646$	4.94933			0.194729
$647$	−15.7819			−0.620449			−0.310224	−	0.950663i	$-0.600404\pi$
$647$	−15.7819			−0.620449			−0.310224	+	0.950663i	$0.600404\pi$
$648$	−1.27214	−	1.27214i	−0.0499742	−	0.0499742i
$649$	4.14735	+	7.18342i	0.162798	+	0.281974i
$650$	10.7129	+	30.4664i	0.420196	+	1.19499i
$651$	−4.59548	+	7.51205i	−0.180111	+	0.294420i
$652$	57.7972	+	15.4867i	2.26351	+	0.606506i
$653$	−18.5083	+	32.0574i	−0.724287	+	1.25450i	0.234980	+	0.972000i	$0.424497\pi$
$653$	−18.5083	+	32.0574i	−0.724287	+	1.25450i	−0.959267	+	0.282501i	$0.908836\pi$
$654$	14.8996	+	25.8068i	0.582620	+	1.00913i
$655$	−3.91888	−	14.6255i	−0.153123	−	0.571464i
$656$	5.21783	+	5.21783i	0.203722	+	0.203722i
$657$	1.01789	+	3.79881i	0.0397116	+	0.148206i
$658$	−39.6724	+	37.7055i	−1.54659	+	1.46991i
$659$	0.700795	−	1.21381i	0.0272991	−	0.0472834i	−0.852053	−	0.523455i	$-0.824643\pi$
$659$	0.700795	−	1.21381i	0.0272991	−	0.0472834i	0.879352	+	0.476172i	$0.157976\pi$
$660$	−6.62676	−	3.82596i	−0.257946	−	0.148925i
$661$	−19.5722	+	19.5722i	−0.761271	+	0.761271i	−0.976552	−	0.215281i	$-0.930933\pi$
$661$	−19.5722	+	19.5722i	−0.761271	+	0.761271i	0.215281	+	0.976552i	$0.430933\pi$
$662$	−47.9002	−	27.6552i	−1.86169	−	1.07485i
$663$	7.91368	−	16.4974i	0.307342	−	0.640705i
$664$			7.29362i			0.283047i
$665$	−1.08120	−	0.319364i	−0.0419269	−	0.0123844i
$666$	−5.78577	−	10.0212i	−0.224194	−	0.388315i
$667$		−	33.1635i		−	1.28410i
$668$	63.7528	−	17.0825i	2.46667	−	0.660942i
$669$	22.3008	+	5.97549i	0.862200	+	0.231026i
$670$	15.0077	−	15.0077i	0.579797	−	0.579797i
$671$	−25.8287	+	25.8287i	−0.997107	+	0.997107i
$672$	16.9827	−	9.23770i	0.655121	−	0.356352i
$673$	8.82634	−	5.09589i	0.340230	−	0.196432i	−0.320143	−	0.947369i	$-0.603731\pi$
$673$	8.82634	−	5.09589i	0.340230	−	0.196432i	0.660374	+	0.750937i	$0.270398\pi$
$674$	−38.8632	+	10.4134i	−1.49696	+	0.401108i
$675$	2.04001	−	3.53340i	0.0785201	−	0.136001i
$676$	5.57368	+	36.2272i	0.214372	+	1.39335i
$677$	−42.6758	+	24.6389i	−1.64016	+	0.946949i	−0.659390	+	0.751801i	$0.729185\pi$
$677$	−42.6758	+	24.6389i	−1.64016	+	0.946949i	−0.980774	+	0.195148i	$0.937481\pi$
$678$	1.01601	−	3.79178i	0.0390195	−	0.145623i
$679$	10.8546	+	6.64025i	0.416559	+	0.254829i
$680$	−7.58371	−	4.37846i	−0.290822	−	0.167906i
$681$	−15.9919	−	4.28502i	−0.612811	−	0.164202i
$682$	5.35115	−	19.9708i	0.204906	−	0.764721i
$683$	0.109355	−	0.408118i	0.00418435	−	0.0156162i	−0.963802	−	0.266619i	$-0.914094\pi$
$683$	0.109355	−	0.408118i	0.00418435	−	0.0156162i	0.967986	+	0.251002i	$0.0807602\pi$
$684$	1.20989	+	0.324190i	0.0462614	+	0.0123957i
$685$	13.4745	+	7.77953i	0.514836	+	0.297241i
$686$	−33.5603	−	22.9520i	−1.28134	−	0.876311i
$687$	1.94891	−	7.27341i	0.0743554	−	0.277498i
$688$	4.35844	−	2.51635i	0.166164	−	0.0959349i
$689$	2.36488	+	30.9228i	0.0900946	+	1.17807i
$690$	−3.55361	+	6.15504i	−0.135284	+	0.234318i
$691$	−28.9582	+	7.75933i	−1.10162	+	0.295179i	−0.763425	−	0.645896i	$-0.776484\pi$
$691$	−28.9582	+	7.75933i	−1.10162	+	0.295179i	−0.338198	+	0.941075i	$0.609817\pi$
$692$	40.6922	−	23.4936i	1.54688	−	0.893094i
$693$	−0.190232	+	7.48375i	−0.00722633	+	0.284284i
$694$	−28.4207	+	28.4207i	−1.07884	+	1.07884i
$695$	−11.0154	+	11.0154i	−0.417840	+	0.417840i
$696$	17.0742	+	4.57503i	0.647198	+	0.173416i
$697$	−21.4103	+	5.73687i	−0.810973	+	0.217300i
$698$		−	55.0774i		−	2.08471i
$699$	2.38406	+	4.12931i	0.0901734	+	0.156185i
$700$	−20.9675	−	22.0612i	−0.792495	−	0.833836i
$701$			35.9119i			1.35637i	0.734889	+	0.678187i	$0.237234\pi$
$701$			35.9119i			1.35637i	−0.734889	+	0.678187i	$0.762766\pi$
$702$	5.15394	−	6.00753i	0.194523	−	0.226740i
$703$	2.02793	+	1.17082i	0.0764847	+	0.0441584i
$704$	−25.3346	+	25.3346i	−0.954833	+	0.954833i
$705$	−7.82730	−	4.51909i	−0.294793	−	0.170199i
$706$	−25.0828	+	43.4447i	−0.944005	+	1.63506i
$707$	14.0083	+	14.7390i	0.526835	+	0.554318i
$708$	2.13923	+	7.98373i	0.0803973	+	0.300047i
$709$	26.4401	+	26.4401i	0.992977	+	0.992977i	0.999976	−	0.00699848i	$-0.00222770\pi$
$709$	26.4401	+	26.4401i	0.992977	+	0.992977i	−0.00699848	+	0.999976i	$0.502228\pi$
$710$	0.434741	+	1.62248i	0.0163155	+	0.0608904i
$711$	−2.44887	−	4.24156i	−0.0918397	−	0.159071i
$712$	−9.39709	+	16.2762i	−0.352171	+	0.609978i
$713$	−10.8516	−	2.90768i	−0.406396	−	0.108894i
$714$	−0.749013	+	29.4662i	−0.0280311	+	1.10274i
$715$	4.23217	−	8.82266i	0.158274	−	0.329949i
$716$	−17.0666	−	29.5602i	−0.637809	−	1.10472i
$717$	−3.29121	−	3.29121i	−0.122912	−	0.122912i
$718$	48.8346			1.82249
$719$	29.6106			1.10429			0.552145	−	0.833748i	$-0.313809\pi$
$719$	29.6106			1.10429			0.552145	+	0.833748i	$0.313809\pi$
$720$	1.14581	+	1.14581i	0.0427019	+	0.0427019i
$721$	4.33423	−	14.6734i	0.161415	−	0.546465i
$722$	39.8716	−	10.6836i	1.48387	−	0.397601i
$723$	1.69587	−	6.32909i	0.0630702	−	0.235381i
$724$	−29.2501	+	16.8875i	−1.08707	+	0.627620i
$725$			40.0878i			1.48882i
$726$	1.70112	+	6.34867i	0.0631345	+	0.235621i
$727$	−49.3431			−1.83004			−0.915018	−	0.403414i	$-0.867824\pi$
$727$	−49.3431			−1.83004			−0.915018	+	0.403414i	$0.867824\pi$
$728$	−9.32630	−	14.4068i	−0.345656	−	0.533951i
$729$	−1.00000			−0.0370370
$730$	2.14333	+	7.99902i	0.0793282	+	0.296057i
$731$			15.1173i			0.559134i
$732$	−31.5217	+	18.1991i	−1.16508	+	0.672657i
$733$	8.93904	−	33.3610i	0.330171	−	1.23221i	−0.578839	−	0.815442i	$-0.696494\pi$
$733$	8.93904	−	33.3610i	0.330171	−	1.23221i	0.909010	−	0.416773i	$-0.136839\pi$
$734$	34.5736	−	9.26398i	1.27614	−	0.341940i
$735$	2.06498	−	6.38864i	0.0761679	−	0.235649i
$736$	17.4395	+	17.4395i	0.642830	+	0.642830i
$737$	28.5200			1.05055
$738$	−9.58882			−0.352970
$739$	3.61796	+	3.61796i	0.133089	+	0.133089i	0.770513	−	0.637424i	$-0.220000\pi$
$739$	3.61796	+	3.61796i	0.133089	+	0.133089i	−0.637424	+	0.770513i	$0.720000\pi$
$740$	−7.12722	−	12.3447i	−0.262002	−	0.453801i
$741$	−0.295384	+	1.57431i	−0.0108512	+	0.0578337i
$742$	−23.8725	−	43.8875i	−0.876388	−	1.61116i
$743$	−8.18894	−	2.19422i	−0.300423	−	0.0804981i	0.105459	−	0.994424i	$-0.466369\pi$
$743$	−8.18894	−	2.19422i	−0.300423	−	0.0804981i	−0.405882	+	0.913926i	$0.633036\pi$
$744$	2.99404	−	5.18584i	0.109767	−	0.190122i
$745$	6.08241	+	10.5351i	0.222842	+	0.385974i
$746$	−19.9460	−	74.4395i	−0.730275	−	2.72542i
$747$	2.86668	+	2.86668i	0.104886	+	0.104886i
$748$	−10.4783	−	39.1057i	−0.383126	−	1.42985i
$749$	26.8751	−	6.47392i	0.981996	−	0.236552i
$750$	9.55975	−	16.5580i	0.349073	−	0.604611i
$751$	−9.46310	−	5.46353i	−0.345314	−	0.199367i	0.317306	−	0.948323i	$-0.397222\pi$
$751$	−9.46310	−	5.46353i	−0.345314	−	0.199367i	−0.662619	+	0.748956i	$0.730555\pi$
$752$	−11.2569	+	11.2569i	−0.410496	+	0.410496i
$753$	16.8755	+	9.74305i	0.614976	+	0.355057i
$754$	−14.3419	+	76.4380i	−0.522300	+	2.78371i
$755$		−	19.1829i		−	0.698136i
$756$	−2.11319	+	7.15412i	−0.0768558	+	0.260193i
$757$	7.37479	+	12.7735i	0.268041	+	0.464261i	0.968356	−	0.249573i	$-0.0802903\pi$
$757$	7.37479	+	12.7735i	0.268041	+	0.464261i	−0.700315	+	0.713834i	$0.746957\pi$
$758$			51.6059i			1.87441i
$759$	−9.22497	+	2.47182i	−0.334845	+	0.0897215i
$760$	0.740477	+	0.198410i	0.0268599	+	0.00719710i
$761$	−1.09073	+	1.09073i	−0.0395391	+	0.0395391i	−0.726600	−	0.687061i	$-0.758901\pi$
$761$	−1.09073	+	1.09073i	−0.0395391	+	0.0395391i	0.687061	+	0.726600i	$0.258901\pi$
$762$	7.44168	−	7.44168i	0.269584	−	0.269584i
$763$	18.7411	−	30.6353i	0.678472	−	1.10907i
$764$	19.3776	−	11.1876i	0.701056	−	0.404755i
$765$	−4.70161	+	1.25979i	−0.169987	+	0.0455479i
$766$	9.79149	−	16.9594i	0.353781	−	0.612766i
$767$	−9.97120	+	3.50619i	−0.360039	+	0.126601i
$768$	−3.13427	+	1.80957i	−0.113098	+	0.0652972i
$769$	−3.95534	+	14.7615i	−0.142633	+	0.532315i	0.857216	+	0.514957i	$0.172192\pi$
$769$	−3.95534	+	14.7615i	−0.142633	+	0.532315i	−0.999849	+	0.0173579i	$0.994475\pi$
$770$	−0.400566	+	15.7583i	−0.0144354	+	0.567889i
$771$	6.75553	+	3.90031i	0.243294	+	0.140466i
$772$	−2.37913	−	0.637485i	−0.0856267	−	0.0229436i
$773$	3.67811	−	13.7269i	0.132292	−	0.493722i	−0.867702	−	0.497085i	$-0.834404\pi$
$773$	3.67811	−	13.7269i	0.132292	−	0.493722i	0.999994	+	0.00336300i	$0.00107048\pi$
$774$	−1.69261	+	6.31692i	−0.0608397	+	0.227057i
$775$	13.1174	+	3.51479i	0.471189	+	0.126255i
$776$	−7.49329	−	4.32625i	−0.268993	−	0.155303i
$777$	−7.27748	+	11.8962i	−0.261078	+	0.426774i
$778$	9.01634	−	33.6495i	0.323252	−	1.20639i
$779$	1.68045	−	0.970210i	0.0602085	−	0.0347614i
$780$	6.34890	−	7.40040i	0.227327	−	0.264977i
$781$	−1.12856	+	1.95473i	−0.0403831	+	0.0699456i
$782$	−36.3220	+	9.73245i	−1.29887	+	0.348032i
$783$	8.50903	−	4.91269i	0.304088	−	0.175565i
$784$	−9.92798	−	6.42571i	−0.354571	−	0.229489i
$785$	−2.08544	+	2.08544i	−0.0744325	+	0.0744325i
$786$	24.5055	−	24.5055i	0.874081	−	0.874081i
$787$	17.4477	+	4.67509i	0.621943	+	0.166649i	0.556011	−	0.831175i	$-0.312331\pi$
$787$	17.4477	+	4.67509i	0.621943	+	0.166649i	0.0659321	+	0.997824i	$0.478998\pi$
$788$	−44.9768	+	12.0515i	−1.60223	+	0.429317i
$789$			16.1099i			0.573529i
$790$	−5.15650	−	8.93132i	−0.183460	−	0.317762i
$791$	−4.59938	+	1.10794i	−0.163535	+	0.0393938i
$792$		−	5.09048i		−	0.180882i
$793$	−26.2789	−	38.4177i	−0.933189	−	1.36425i
$794$	−65.3309	−	37.7188i	−2.31851	−	1.33859i
$795$	5.83374	−	5.83374i	0.206901	−	0.206901i
$796$	−53.6826	−	30.9937i	−1.90273	−	1.09854i
$797$	−19.4574	+	33.7012i	−0.689215	+	1.19376i	0.282877	+	0.959156i	$0.408711\pi$
$797$	−19.4574	+	33.7012i	−0.689215	+	1.19376i	−0.972092	+	0.234600i	$0.924622\pi$
$798$	−0.604296	−	2.50861i	−0.0213918	−	0.0888037i
$799$	−12.3767	−	46.1903i	−0.437855	−	1.63410i
$800$	−21.0808	−	21.0808i	−0.745319	−	0.745319i
$801$	2.70378	+	10.0906i	0.0955333	+	0.356535i
$802$	19.4928	+	33.7624i	0.688313	+	1.19219i
$803$	−5.56396	+	9.63706i	−0.196348	+	0.340084i
$804$	27.4508	+	7.35541i	0.968114	+	0.259405i
$805$	8.56264	+	0.217657i	0.301794	+	0.00767141i
$806$	23.7543	+	11.3948i	0.836708	+	0.401363i
$807$	−2.17230	−	3.76253i	−0.0764685	−	0.132447i
$808$	−9.77702	−	9.77702i	−0.343954	−	0.343954i
$809$	37.4176			1.31553			0.657766	−	0.753222i	$-0.271501\pi$
$809$	37.4176			1.31553			0.657766	+	0.753222i	$0.271501\pi$
$810$	−2.10567			−0.0739855
$811$	16.1489	+	16.1489i	0.567064	+	0.567064i	0.931305	−	0.364241i	$-0.118671\pi$
$811$	16.1489	+	16.1489i	0.567064	+	0.567064i	−0.364241	+	0.931305i	$0.618671\pi$
$812$	−17.1648	−	71.2560i	−0.602366	−	2.50060i
$813$	1.33531	−	0.357794i	0.0468313	−	0.0125484i
$814$	8.47418	−	31.6261i	0.297020	−	1.10849i
$815$	17.6283	−	10.1777i	0.617492	−	0.356509i
$816$			8.57343i			0.300130i
$817$	−0.342522	−	1.27831i	−0.0119833	−	0.0447223i
$818$	23.9065			0.835870
$819$	−9.32806	−	1.99684i	−0.325949	−	0.0697752i
$820$	−11.8120			−0.412494
$821$	−3.52554	−	13.1575i	−0.123042	−	0.459200i	0.876720	−	0.481001i	$-0.159727\pi$
$821$	−3.52554	−	13.1575i	−0.123042	−	0.459200i	−0.999762	+	0.0218010i	$0.993060\pi$
$822$			35.6119i			1.24211i
$823$	−21.6162	+	12.4801i	−0.753492	+	0.435029i	−0.826954	−	0.562269i	$-0.809929\pi$
$823$	−21.6162	+	12.4801i	−0.753492	+	0.435029i	0.0734621	+	0.997298i	$0.476595\pi$
$824$	−2.69271	+	10.0493i	−0.0938051	+	0.350085i
$825$	11.1511	−	2.98792i	0.388231	−	0.104026i
$826$	12.3420	−	11.7301i	0.429434	−	0.408143i
$827$	−4.58320	−	4.58320i	−0.159374	−	0.159374i	0.622916	−	0.782289i	$-0.285948\pi$
$827$	−4.58320	−	4.58320i	−0.159374	−	0.159374i	−0.782289	+	0.622916i	$0.785948\pi$
$828$	−9.51661			−0.330725
$829$	14.0402			0.487636			0.243818	−	0.969821i	$-0.421600\pi$
$829$	14.0402			0.487636			0.243818	+	0.969821i	$0.421600\pi$
$830$	6.03628	+	6.03628i	0.209522	+	0.209522i
$831$	−8.81191	−	15.2627i	−0.305682	−	0.529456i
$832$	−25.7761	−	37.6827i	−0.893626	−	1.30641i
$833$	31.6267	−	16.1757i	1.09580	−	0.560454i
$834$	−34.4408	−	9.22838i	−1.19259	−	0.319553i
$835$	11.2265	−	19.4448i	0.388507	−	0.672914i
$836$	1.77208	+	3.06933i	0.0612887	+	0.106155i
$837$	−0.861462	−	3.21502i	−0.0297765	−	0.111127i
$838$	−48.1741	−	48.1741i	−1.66415	−	1.66415i
$839$	−8.57855	−	32.0156i	−0.296165	−	1.10530i	−0.940288	−	0.340380i	$-0.889444\pi$
$839$	−8.57855	−	32.0156i	−0.296165	−	1.10530i	0.644123	−	0.764922i	$-0.277222\pi$
$840$	−1.29331	+	4.37846i	−0.0446235	+	0.151071i
$841$	−33.7691	+	58.4898i	−1.16445	+	2.01689i
$842$	−68.9977	−	39.8359i	−2.37782	−	1.37283i
$843$	0.725318	−	0.725318i	0.0249813	−	0.0249813i
$844$	−56.1127	−	32.3967i	−1.93148	−	1.11514i
$845$	10.0551	+	7.37365i	0.345907	+	0.253661i
$846$		−	20.6868i		−	0.711227i
$847$	5.74160	−	5.45694i	0.197284	−	0.187503i
$848$	−7.26581	−	12.5847i	−0.249509	−	0.432162i
$849$		−	11.3080i		−	0.388088i
$850$	43.9058	−	11.7645i	1.50596	−	0.403520i
$851$	−17.1848	−	4.60465i	−0.589088	−	0.157846i
$852$	−1.59038	+	1.59038i	−0.0544856	+	0.0544856i
$853$	−9.18368	+	9.18368i	−0.314443	+	0.314443i	−0.846628	−	0.532185i	$-0.821371\pi$
$853$	−9.18368	+	9.18368i	−0.314443	+	0.314443i	0.532185	+	0.846628i	$0.321371\pi$
$854$	63.9627	+	39.1290i	2.18876	+	1.33897i
$855$	0.369020	−	0.213054i	0.0126202	−	0.00728629i
$856$	−18.1569	+	4.86513i	−0.620591	+	0.166287i
$857$	−17.6781	+	30.6194i	−0.603873	+	1.04594i	0.388356	+	0.921510i	$0.373043\pi$
$857$	−17.6781	+	30.6194i	−0.603873	+	1.04594i	−0.992229	+	0.124429i	$0.960290\pi$
$858$	22.3314	−	1.70784i	0.762383	−	0.0583045i
$859$	20.5980	−	11.8923i	0.702795	−	0.405759i	−0.105593	−	0.994409i	$-0.533674\pi$
$859$	20.5980	−	11.8923i	0.702795	−	0.405759i	0.808388	+	0.588651i	$0.200341\pi$
$860$	−2.08505	+	7.78152i	−0.0710997	+	0.265348i
$861$	5.52190	+	10.1515i	0.188186	+	0.345963i
$862$	−0.378228	−	0.218370i	−0.0128825	−	0.00743771i
$863$	−27.6871	−	7.41873i	−0.942480	−	0.252537i	−0.245311	−	0.969444i	$-0.578890\pi$
$863$	−27.6871	−	7.41873i	−0.942480	−	0.252537i	−0.697168	+	0.716908i	$0.745557\pi$
$864$	−1.89119	+	7.05803i	−0.0643397	+	0.240119i
$865$	4.13707	−	15.4398i	0.140665	−	0.524968i
$866$	−63.1048	−	16.9089i	−2.14439	−	0.574587i
$867$	−7.58037	−	4.37653i	−0.257443	−	0.148635i
$868$	−24.8211	−	0.630937i	−0.842482	−	0.0214154i
$869$	3.58676	−	13.3860i	0.121672	−	0.454088i
$870$	17.9172	−	10.3445i	0.607449	−	0.350711i
$871$	−6.70185	+	35.7189i	−0.227083	+	1.21029i
$872$	−12.2102	+	21.1486i	−0.413488	+	0.716183i
$873$	−4.64555	+	1.24477i	−0.157228	+	0.0421291i
$874$	2.85084	−	1.64593i	0.0964312	−	0.0556746i
$875$	−23.0348	−	0.585531i	−0.778718	−	0.0197945i
$876$	−7.84080	+	7.84080i	−0.264916	+	0.264916i
$877$	−14.3739	+	14.3739i	−0.485374	+	0.485374i	−0.906843	−	0.421469i	$-0.861515\pi$
$877$	−14.3739	+	14.3739i	−0.485374	+	0.485374i	0.421469	+	0.906843i	$0.361515\pi$
$878$	80.0622	+	21.4526i	2.70197	+	0.723991i
$879$	2.20647	−	0.591222i	0.0744225	−	0.0199414i
$880$			4.58500i			0.154560i
$881$	17.8814	+	30.9716i	0.602441	+	1.04346i	0.992450	+	0.122648i	$0.0391385\pi$
$881$	17.8814	+	30.9716i	0.602441	+	1.04346i	−0.390009	+	0.920811i	$0.627528\pi$
$882$	15.0266	−	3.21808i	0.505973	−	0.108358i
$883$		−	12.9519i		−	0.435865i	−0.975964	−	0.217932i	$-0.930069\pi$
$883$		−	12.9519i		−	0.435865i	0.975964	−	0.217932i	$-0.0699312\pi$
$884$	51.4389	−	3.93388i	1.73008	−	0.132311i
$885$	2.43506	+	1.40588i	0.0818536	+	0.0472582i
$886$	−42.5757	+	42.5757i	−1.43036	+	1.43036i
$887$	33.7832	+	19.5047i	1.13433	+	0.654905i	0.945020	−	0.327013i	$-0.106042\pi$
$887$	33.7832	+	19.5047i	1.13433	+	0.654905i	0.189308	+	0.981918i	$0.439375\pi$
$888$	4.74142	−	8.21238i	0.159112	−	0.275589i
$889$	−12.1638	−	3.59295i	−0.407961	−	0.120504i
$890$	5.69325	+	21.2475i	0.190838	+	0.712218i
$891$	−2.00076	−	2.00076i	−0.0670280	−	0.0670280i
$892$	16.8479	+	62.8771i	0.564108	+	2.10528i
$893$	2.09312	+	3.62539i	0.0700435	+	0.121319i
$894$	−13.9216	+	24.1129i	−0.465607	+	0.806455i
$895$	−11.2160	−	3.00531i	−0.374909	−	0.100457i
$896$	29.7562	+	18.2033i	0.994085	+	0.608129i
$897$	−0.927995	−	12.1343i	−0.0309848	−	0.405154i
$898$	−3.87047	−	6.70386i	−0.129159	−	0.223711i
$899$	23.1246	+	23.1246i	0.771249	+	0.771249i
$900$	11.5036			0.383454
$901$	43.6504			1.45420
$902$	−19.1850	−	19.1850i	−0.638789	−	0.638789i
$903$	7.66233	−	1.84577i	0.254987	−	0.0614235i
$904$	3.10736	−	0.832614i	0.103349	−	0.0276923i
$905$	−2.97378	+	11.0983i	−0.0988519	+	0.368920i
$906$	38.0239	−	21.9531i	1.26326	−	0.729343i
$907$			16.4421i			0.545951i	0.962021	+	0.272976i	$0.0880078\pi$
$907$			16.4421i			0.545951i	−0.962021	+	0.272976i	$0.911992\pi$
$908$	−12.0816	−	45.0892i	−0.400942	−	1.49634i
$909$	−7.68552			−0.254913
$910$	−19.6418	−	4.20467i	−0.651118	−	0.139384i
$911$	−13.9789			−0.463141			−0.231570	−	0.972818i	$-0.574386\pi$
$911$	−13.9789			−0.463141			−0.231570	+	0.972818i	$0.574386\pi$
$912$	−0.194253	−	0.724962i	−0.00643236	−	0.0240059i
$913$			11.4711i			0.379638i
$914$	24.6131	−	14.2104i	0.814130	−	0.470038i
$915$	−3.20474	+	11.9602i	−0.105945	+	0.395393i
$916$	20.5074	−	5.49493i	0.677583	−	0.181558i
$917$	−40.0554	−	11.8316i	−1.32275	−	0.390714i
$918$	−7.87771	−	7.87771i	−0.260003	−	0.260003i
$919$	−19.5256			−0.644089			−0.322044	−	0.946725i	$-0.604370\pi$
$919$	−19.5256			−0.644089			−0.322044	+	0.946725i	$0.604370\pi$
$920$	−5.82435			−0.192023
$921$	−16.5239	−	16.5239i	−0.544481	−	0.544481i
$922$	23.4712	+	40.6533i	0.772982	+	1.33884i
$923$	−2.18293	−	1.87276i	−0.0718521	−	0.0616428i
$924$	−18.5417	+	10.0857i	−0.609976	+	0.331795i
$925$	20.7729	+	5.56607i	0.683008	+	0.183011i
$926$	21.3648	−	37.0050i	0.702093	−	1.21606i
$927$	2.89145	+	5.00814i	0.0949677	+	0.164489i
$928$	−18.5817	−	69.3478i	−0.609974	−	2.27645i
$929$	−1.64092	−	1.64092i	−0.0538368	−	0.0538368i	0.679676	−	0.733513i	$-0.262120\pi$
$929$	−1.64092	−	1.64092i	−0.0538368	−	0.0538368i	−0.733513	+	0.679676i	$0.762120\pi$
$930$	−1.81395	−	6.76976i	−0.0594818	−	0.221989i
$931$	−2.30782	+	2.08438i	−0.0756359	+	0.0683130i
$932$	−6.72185	+	11.6426i	−0.220181	+	0.381365i
$933$	−8.76860	−	5.06256i	−0.287071	−	0.165741i
$934$	−28.2799	+	28.2799i	−0.925345	+	0.925345i
$935$	−11.9273	−	6.88626i	−0.390066	−	0.225205i
$936$	6.37539	+	1.19620i	0.208386	+	0.0390990i
$937$			18.7950i			0.614006i	0.951709	+	0.307003i	$0.0993262\pi$
$937$			18.7950i			0.614006i	−0.951709	+	0.307003i	$0.900674\pi$
$938$	−13.7106	−	56.9168i	−0.447668	−	1.85840i
$939$	−4.27611	−	7.40644i	−0.139546	−	0.241700i
$940$		−	25.4831i		−	0.831168i
$941$	24.6182	−	6.59642i	0.802530	−	0.215037i	0.165835	−	0.986153i	$-0.446968\pi$
$941$	24.6182	−	6.59642i	0.802530	−	0.215037i	0.636694	+	0.771116i	$0.280301\pi$
$942$	−6.52031	−	1.74711i	−0.212443	−	0.0569240i
$943$	−10.4246	+	10.4246i	−0.339472	+	0.339472i
$944$	3.50200	−	3.50200i	0.113980	−	0.113980i
$945$	1.21259	+	2.22923i	0.0394454	+	0.0725169i
$946$	−16.0252	+	9.25213i	−0.521023	+	0.300813i
$947$	−11.9264	+	3.19567i	−0.387557	+	0.103845i	−0.447336	−	0.894366i	$-0.647627\pi$
$947$	−11.9264	+	3.19567i	−0.387557	+	0.103845i	0.0597791	+	0.998212i	$0.480960\pi$
$948$	6.90458	−	11.9591i	0.224250	−	0.388413i
$949$	−10.7621	−	9.23298i	−0.349354	−	0.299715i
$950$	−3.44608	+	1.98959i	−0.111806	+	0.0645510i
$951$	−8.41365	+	31.4002i	−0.272831	+	1.01822i
$952$	−21.2192	+	11.5422i	−0.687719	+	0.374083i
$953$	40.4004	+	23.3252i	1.30870	+	0.755578i	0.981879	−	0.189509i	$-0.0606896\pi$
$953$	40.4004	+	23.3252i	1.30870	+	0.755578i	0.326820	+	0.945087i	$0.394023\pi$
$954$	18.2397	+	4.88732i	0.590533	+	0.158233i
$955$	1.97007	−	7.35240i	0.0637500	−	0.237918i
$956$	3.39655	−	12.6761i	0.109852	−	0.409974i
$957$	26.8537	+	7.19542i	0.868056	+	0.232595i
$958$	38.7527	+	22.3739i	1.25204	+	0.722867i
$959$	37.7018	−	20.5078i	1.21745	−	0.662231i
$960$	−3.14343	+	11.7314i	−0.101454	+	0.378630i
$961$	−17.2525	+	9.96076i	−0.556534	+	0.321315i
$962$	37.6176	+	18.0449i	1.21284	+	0.581792i
$963$	−5.22420	+	9.04858i	−0.168348	+	0.291587i
$964$	17.8448	−	4.78151i	0.574744	−	0.154002i
$965$	−0.725640	+	0.418949i	−0.0233592	+	0.0134864i
$966$	9.36776	+	17.2218i	0.301403	+	0.554102i
$967$	37.9004	−	37.9004i	1.21879	−	1.21879i	0.250741	−	0.968054i	$-0.419326\pi$
$967$	37.9004	−	37.9004i	1.21879	−	1.21879i	0.968054	−	0.250741i	$-0.0806741\pi$
$968$	−3.80865	+	3.80865i	−0.122415	+	0.122415i
$969$	2.17766	+	0.583501i	0.0699564	+	0.0187448i
$970$	−9.78197	+	2.62107i	−0.314080	+	0.0841575i
$971$		−	6.14222i		−	0.197113i	−0.995131	−	0.0985567i	$-0.968577\pi$
$971$		−	6.14222i		−	0.197113i	0.995131	−	0.0985567i	$-0.0314226\pi$
$972$	−1.40975	−	2.44176i	−0.0452177	−	0.0783194i
$973$	10.0634	+	41.7762i	0.322619	+	1.33928i
$974$		−	10.7616i		−	0.344825i
$975$	1.12175	+	14.6679i	0.0359249	+	0.469749i
$976$	18.8877	+	10.9048i	0.604580	+	0.349054i
$977$	−30.0995	+	30.0995i	−0.962968	+	0.962968i	−0.999338	−	0.0363707i	$-0.988420\pi$
$977$	−30.0995	+	30.0995i	−0.962968	+	0.962968i	0.0363707	+	0.999338i	$0.488420\pi$
$978$	40.3480	+	23.2950i	1.29019	+	0.744891i
$979$	−14.7793	+	25.5986i	−0.472350	+	0.818134i
$980$	18.5106	−	3.96420i	0.591300	−	0.126632i
$981$	3.51317	+	13.1113i	0.112167	+	0.418613i
$982$	−26.3509	−	26.3509i	−0.840891	−	0.840891i
$983$	−1.95762	−	7.30592i	−0.0624383	−	0.233023i	0.927654	−	0.373441i	$-0.121822\pi$
$983$	−1.95762	−	7.30592i	−0.0624383	−	0.233023i	−0.990092	+	0.140418i	$0.955155\pi$
$984$	−3.92901	−	6.80524i	−0.125252	−	0.216943i
$985$	−7.92012	+	13.7181i	−0.252356	+	0.437093i
$986$	105.733	+	28.3309i	3.36721	+	0.902241i
$987$	−21.9008	+	11.9129i	−0.697109	+	0.379191i
$988$	−4.26049	+	1.49812i	−0.135544	+	0.0476617i
$989$	5.02737	+	8.70767i	0.159861	+	0.276888i
$990$	−4.21293	−	4.21293i	−0.133896	−	0.133896i
$991$	9.50967			0.302085			0.151042	−	0.988527i	$-0.451737\pi$
$991$	9.50967			0.302085			0.151042	+	0.988527i	$0.451737\pi$
$992$	−24.3209			−0.772189
$993$	−17.8152	−	17.8152i	−0.565348	−	0.565348i
$994$	4.44355	+	1.31254i	0.140941	+	0.0416312i
$995$	−20.3687	+	5.45778i	−0.645732	+	0.173023i
$996$	−2.95844	+	11.0410i	−0.0937417	+	0.349849i
$997$	9.82421	−	5.67201i	0.311136	−	0.179634i	−0.336299	−	0.941755i	$-0.609175\pi$
$997$	9.82421	−	5.67201i	0.311136	−	0.179634i	0.647435	+	0.762121i	$0.275842\pi$
$998$			48.5295i			1.53617i
$999$	−1.36423	−	5.09136i	−0.0431622	−	0.161084i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.b.262.9	yes	40
3.2	odd	2		819.2.gh.d.262.2		40
7.5	odd	6		273.2.bt.b.145.9	✓	40
13.7	odd	12		273.2.bt.b.241.9	yes	40
21.5	even	6		819.2.et.d.145.2		40
39.20	even	12		819.2.et.d.514.2		40
91.33	even	12	inner	273.2.cg.b.124.9	yes	40
273.215	odd	12		819.2.gh.d.397.2		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.9	✓	40	7.5	odd	6
273.2.bt.b.241.9	yes	40	13.7	odd	12
273.2.cg.b.124.9	yes	40	91.33	even	12	inner
273.2.cg.b.262.9	yes	40	1.1	even	1	trivial
819.2.et.d.145.2		40	21.5	even	6
819.2.et.d.514.2		40	39.20	even	12
819.2.gh.d.262.2		40	3.2	odd	2
819.2.gh.d.397.2		40	273.215	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	273.2.cg.b.262.9

Level	$273$
Weight	$2$
Character	273.262
Analytic conductor	$2.180$
Analytic rank	$0$
Dimension	$40$
Inner twists	$2$