LMFDB - Embedded newform 273.2.bt.b.145.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(136,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("273.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
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			145.9
Character	$\chi$	$=$	273.145
Dual form			273.2.bt.b.241.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.55234 - 1.55234i) q^{2} +(0.866025 + 0.500000i) q^{3} -2.81950i q^{4} +(-0.926472 + 0.248247i) q^{5} +(2.12053 - 0.568195i) q^{6} +(0.619609 - 2.57218i) q^{7} +(-1.27214 - 1.27214i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.05283 + 1.82356i) q^{10} +(2.73309 - 0.732330i) 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} +1.68943 q^{16} -5.07475 q^{17} +(2.12053 + 0.568195i) q^{18} +(-0.114981 + 0.429116i) q^{19} +(0.699933 + 2.61219i) q^{20} +(1.82268 - 1.91776i) q^{21} +(3.10586 - 5.37950i) q^{22} +3.37529i q^{23} +(-0.465634 - 1.73777i) q^{24} +(-3.53340 + 2.04001i) q^{25} +(-1.45968 + 7.77964i) q^{26} +1.00000i q^{27} +(-7.25224 - 1.74699i) q^{28} +(4.91269 + 8.50903i) q^{29} +(-1.82356 + 1.05283i) q^{30} +(0.861462 - 3.21502i) q^{31} +(5.16683 - 5.16683i) q^{32} +(2.73309 + 0.732330i) q^{33} +(-7.87771 + 7.87771i) q^{34} +(0.0644856 + 2.53686i) q^{35} +(2.44176 - 1.40975i) q^{36} +(-3.72714 - 3.72714i) q^{37} +(0.487643 + 0.844623i) q^{38} +(-3.59505 + 0.274938i) q^{39} +(1.49440 + 0.862793i) q^{40} +(-1.13047 + 4.21899i) q^{41} +(-0.147596 - 5.80644i) q^{42} +(-2.57983 - 1.48947i) q^{43} +(-2.06480 - 7.70594i) q^{44} +(-0.678225 - 0.678225i) q^{45} +(5.23958 + 5.23958i) q^{46} +(2.43887 + 9.10199i) q^{47} +(1.46309 + 0.844715i) q^{48} +(-6.23217 - 3.18749i) q^{49} +(-2.31825 + 8.65182i) q^{50} +(-4.39486 - 2.53737i) q^{51} +(5.73945 + 8.39065i) q^{52} +(-4.30074 - 7.44911i) q^{53} +(1.55234 + 1.55234i) q^{54} +(-2.35033 + 1.35697i) q^{55} +(-4.06038 + 2.48393i) q^{56} +(-0.314135 + 0.314135i) q^{57} +(20.8350 + 5.58273i) q^{58} +(-2.07289 + 2.07289i) q^{59} +(-0.699933 + 2.61219i) q^{60} +(11.1799 - 6.45472i) q^{61} +(-3.65351 - 6.32807i) q^{62} +(2.53737 - 0.749491i) q^{63} -12.6625i q^{64} +(2.25178 - 2.62472i) q^{65} +(5.37950 - 3.10586i) q^{66} +(-2.60877 - 9.73605i) q^{67} +14.3082i q^{68} +(-1.68764 + 2.92308i) q^{69} +(4.03817 + 3.83796i) q^{70} +(-0.206463 - 0.770529i) q^{71} +(0.465634 - 1.73777i) q^{72} +(-3.79881 - 1.01789i) q^{73} -11.5715 q^{74} -4.08002 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} +(-1.56521 + 0.419397i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.79441 + 8.30417i) q^{82} +(2.86668 + 2.86668i) q^{83} +(-5.40713 - 5.13905i) q^{84} +(4.70161 - 1.25979i) q^{85} +(-6.31692 + 1.69261i) q^{86} +9.82538i q^{87} +(-4.40848 - 2.54524i) q^{88} +(7.38686 - 7.38686i) q^{89} -2.10567 q^{90} +(3.39208 + 8.91593i) q^{91} +9.51661 q^{92} +(2.35356 - 2.35356i) q^{93} +(17.9153 + 10.3434i) q^{94} -0.426108i q^{95} +(7.05803 - 1.89119i) q^{96} +(-4.64555 + 1.24477i) q^{97} +(-14.6225 + 4.72638i) q^{98} +(2.00076 + 2.00076i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{7} + 20 q^{9} - 8 q^{11} + 24 q^{12} - 18 q^{14} - 64 q^{16} + 8 q^{17} - 14 q^{19} - 14 q^{20} - 8 q^{21} + 4 q^{22} + 18 q^{24} - 24 q^{25} - 10 q^{26} - 2 q^{28} + 8 q^{29} - 8 q^{31} + 10 q^{32}+ \cdots - 4 q^{99}+O(q^{100}) $ 40 * q - 2 * q^7 + 20 * q^9 - 8 * q^11 + 24 * q^12 - 18 * q^14 - 64 * q^16 + 8 * q^17 - 14 * q^19 - 14 * q^20 - 8 * q^21 + 4 * q^22 + 18 * q^24 - 24 * q^25 - 10 * q^26 - 2 * q^28 + 8 * q^29 - 8 * q^31 + 10 * q^32 - 8 * q^33 + 24 * q^34 - 22 * q^35 + 12 * q^37 + 8 * q^38 - 24 * q^39 - 30 * q^40 + 2 * q^41 + 6 * q^42 - 66 * q^43 + 28 * q^44 + 40 * q^46 + 10 * q^47 - 24 * q^48 + 38 * q^49 - 20 * q^50 + 40 * q^52 - 8 * q^53 + 42 * q^55 + 20 * q^56 - 14 * q^57 - 48 * q^58 - 26 * q^59 + 14 * q^60 - 12 * q^61 - 24 * q^62 - 4 * q^63 - 44 * q^65 - 18 * q^66 + 46 * q^67 - 4 * q^69 + 32 * q^70 - 6 * q^71 - 18 * q^72 + 10 * q^73 + 40 * q^74 + 48 * q^75 + 64 * q^76 - 24 * q^77 + 8 * q^78 + 34 * q^80 - 20 * q^81 + 24 * q^82 + 12 * q^83 + 20 * q^84 + 2 * q^85 + 12 * q^86 - 84 * q^88 - 16 * q^89 + 26 * q^91 + 236 * q^92 + 22 * q^93 + 30 * q^94 + 26 * q^96 + 62 * q^97 - 14 * q^98 - 4 * q^99

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.55234	−	1.55234i	1.09767	−	1.09767i	0.102985	−	0.994683i	$-0.467161\pi$
$2$	1.55234	−	1.55234i	1.09767	−	1.09767i	0.994683	−	0.102985i	$-0.0328393\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		−	2.81950i		−	1.40975i
$5$	−0.926472	+	0.248247i	−0.414331	+	0.111020i	−0.459962	−	0.887939i	$-0.652137\pi$
$5$	−0.926472	+	0.248247i	−0.414331	+	0.111020i	0.0456309	+	0.998958i	$0.485470\pi$
$6$	2.12053	−	0.568195i	0.865703	−	0.231964i
$7$	0.619609	−	2.57218i	0.234190	−	0.972191i
$7$	0.619609	−	2.57218i	0.234190	−	0.972191i
$8$	−1.27214	−	1.27214i	−0.449768	−	0.449768i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.05283	+	1.82356i	−0.332935	+	0.576660i
$11$	2.73309	−	0.732330i	0.824058	−	0.220806i	0.177938	−	0.984042i	$-0.443057\pi$
$11$	2.73309	−	0.732330i	0.824058	−	0.220806i	0.646120	+	0.763236i	$0.276391\pi$
$12$	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
$16$	1.68943			0.422358
$17$	−5.07475			−1.23081			−0.615403	−	0.788212i	$-0.711007\pi$
$17$	−5.07475			−1.23081			−0.615403	+	0.788212i	$0.711007\pi$
$18$	2.12053	+	0.568195i	0.499814	+	0.133925i
$19$	−0.114981	+	0.429116i	−0.0263785	+	0.0984460i	−0.977860	−	0.209260i	$-0.932895\pi$
$19$	−0.114981	+	0.429116i	−0.0263785	+	0.0984460i	0.951482	+	0.307706i	$0.0995612\pi$
$20$	0.699933	+	2.61219i	0.156510	+	0.584102i
$21$	1.82268	−	1.91776i	0.397742	−	0.418491i
$22$	3.10586	−	5.37950i	0.662171	−	1.14691i
$23$			3.37529i			0.703796i	0.936038	+	0.351898i	$0.114464\pi$
$23$			3.37529i			0.703796i	−0.936038	+	0.351898i	$0.885536\pi$
$24$	−0.465634	−	1.73777i	−0.0950471	−	0.354721i
$25$	−3.53340	+	2.04001i	−0.706681	+	0.408002i
$26$	−1.45968	+	7.77964i	−0.286266	+	1.52571i
$27$			1.00000i			0.192450i
$28$	−7.25224	−	1.74699i	−1.37054	−	0.330149i
$29$	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	$0.467666\pi$
$30$	−1.82356	+	1.05283i	−0.332935	+	0.192220i
$31$	0.861462	−	3.21502i	0.154723	−	0.577435i	−0.844406	−	0.535704i	$-0.820046\pi$
$31$	0.861462	−	3.21502i	0.154723	−	0.577435i	0.999129	−	0.0417306i	$-0.0132871\pi$
$32$	5.16683	−	5.16683i	0.913376	−	0.913376i
$33$	2.73309	+	0.732330i	0.475770	+	0.127482i
$34$	−7.87771	+	7.87771i	−1.35102	+	1.35102i
$35$	0.0644856	+	2.53686i	0.0109001	+	0.428808i
$36$	2.44176	−	1.40975i	0.406959	−	0.234958i
$37$	−3.72714	−	3.72714i	−0.612737	−	0.612737i	0.330921	−	0.943658i	$-0.392641\pi$
$37$	−3.72714	−	3.72714i	−0.612737	−	0.612737i	−0.943658	+	0.330921i	$0.892641\pi$
$38$	0.487643	+	0.844623i	0.0791061	+	0.137016i
$39$	−3.59505	+	0.274938i	−0.575669	+	0.0440253i
$40$	1.49440	+	0.862793i	0.236286	+	0.136420i
$41$	−1.13047	+	4.21899i	−0.176550	+	0.658895i	0.819732	+	0.572747i	$0.194122\pi$
$41$	−1.13047	+	4.21899i	−0.176550	+	0.658895i	−0.996282	+	0.0861478i	$0.972544\pi$
$42$	−0.147596	−	5.80644i	−0.0227746	−	0.895952i
$43$	−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	$0.739605\pi$
$44$	−2.06480	−	7.70594i	−0.311281	−	1.16171i
$45$	−0.678225	−	0.678225i	−0.101104	−	0.101104i
$46$	5.23958	+	5.23958i	0.772534	+	0.772534i
$47$	2.43887	+	9.10199i	0.355746	+	1.32766i	0.879543	+	0.475819i	$0.157848\pi$
$47$	2.43887	+	9.10199i	0.355746	+	1.32766i	−0.523797	+	0.851843i	$0.675485\pi$
$48$	1.46309	+	0.844715i	0.211179	+	0.121924i
$49$	−6.23217	−	3.18749i	−0.890310	−	0.455355i
$50$	−2.31825	+	8.65182i	−0.327850	+	1.22355i
$51$	−4.39486	−	2.53737i	−0.615403	−	0.355303i
$52$	5.73945	+	8.39065i	0.795919	+	1.16357i
$53$	−4.30074	−	7.44911i	−0.590753	−	1.02321i	−0.994131	−	0.108180i	$-0.965498\pi$
$53$	−4.30074	−	7.44911i	−0.590753	−	1.02321i	0.403379	−	0.915033i	$-0.367836\pi$
$54$	1.55234	+	1.55234i	0.211246	+	0.211246i
$55$	−2.35033	+	1.35697i	−0.316919	+	0.182973i
$56$	−4.06038	+	2.48393i	−0.542591	+	0.331929i
$57$	−0.314135	+	0.314135i	−0.0416082	+	0.0416082i
$58$	20.8350	+	5.58273i	2.73577	+	0.733048i
$59$	−2.07289	+	2.07289i	−0.269867	+	0.269867i	−0.829046	−	0.559180i	$-0.811116\pi$
$59$	−2.07289	+	2.07289i	−0.269867	+	0.269867i	0.559180	+	0.829046i	$0.311116\pi$
$60$	−0.699933	+	2.61219i	−0.0903609	+	0.337232i
$61$	11.1799	−	6.45472i	1.43144	−	0.826443i	0.434210	−	0.900812i	$-0.357028\pi$
$61$	11.1799	−	6.45472i	1.43144	−	0.826443i	0.997231	+	0.0743693i	$0.0236944\pi$
$62$	−3.65351	−	6.32807i	−0.463997	−	0.803666i
$63$	2.53737	−	0.749491i	0.319679	−	0.0944269i
$64$		−	12.6625i		−	1.58281i
$65$	2.25178	−	2.62472i	0.279299	−	0.325557i
$66$	5.37950	−	3.10586i	0.662171	−	0.382304i
$67$	−2.60877	−	9.73605i	−0.318712	−	1.18945i	−0.920484	−	0.390780i	$-0.872205\pi$
$67$	−2.60877	−	9.73605i	−0.318712	−	1.18945i	0.601772	−	0.798668i	$-0.294461\pi$
$68$			14.3082i			1.73513i
$69$	−1.68764	+	2.92308i	−0.203168	+	0.351898i
$70$	4.03817	+	3.83796i	0.482654	+	0.458724i
$71$	−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	$0.931740\pi$
$72$	0.465634	−	1.73777i	0.0548755	−	0.204798i
$73$	−3.79881	−	1.01789i	−0.444617	−	0.119135i	0.0295626	−	0.999563i	$-0.490589\pi$
$73$	−3.79881	−	1.01789i	−0.444617	−	0.119135i	−0.474179	+	0.880428i	$0.657255\pi$
$74$	−11.5715			−1.34516
$75$	−4.08002			−0.471120
$76$	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	−0.694747	−	0.719254i	$-0.744484\pi$
$79$	2.44887	−	4.24156i	0.275519	−	0.477213i	0.970266	+	0.242041i	$0.0778169\pi$
$80$	−1.56521	+	0.419397i	−0.174996	+	0.0468900i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.79441	+	8.30417i	0.529454	+	0.917042i
$83$	2.86668	+	2.86668i	0.314659	+	0.314659i	0.846712	−	0.532052i	$-0.178579\pi$
$83$	2.86668	+	2.86668i	0.314659	+	0.314659i	−0.532052	+	0.846712i	$0.678579\pi$
$84$	−5.40713	−	5.13905i	−0.589966	−	0.560717i
$85$	4.70161	−	1.25979i	0.509961	−	0.136644i
$86$	−6.31692	+	1.69261i	−0.681171	+	0.182519i
$87$			9.82538i			1.05339i
$88$	−4.40848	−	2.54524i	−0.469946	−	0.271323i
$89$	7.38686	−	7.38686i	0.783006	−	0.783006i	−0.197331	−	0.980337i	$-0.563227\pi$
$89$	7.38686	−	7.38686i	0.783006	−	0.783006i	0.980337	+	0.197331i	$0.0632274\pi$
$90$	−2.10567			−0.221957
$91$	3.39208	+	8.91593i	0.355586	+	0.934643i
$92$	9.51661			0.992175
$93$	2.35356	−	2.35356i	0.244053	−	0.244053i
$94$	17.9153	+	10.3434i	1.84782	+	1.06684i
$95$		−	0.426108i		−	0.0437178i
$96$	7.05803	−	1.89119i	0.720357	−	0.193019i
$97$	−4.64555	+	1.24477i	−0.471684	+	0.126387i	−0.486828	−	0.873498i	$-0.661846\pi$
$97$	−4.64555	+	1.24477i	−0.471684	+	0.126387i	0.0151437	+	0.999885i	$0.495179\pi$
$98$	−14.6225	+	4.72638i	−1.47709	+	0.477436i
$99$	2.00076	+	2.00076i	0.201084	+	0.201084i
$100$	5.75181	+	9.96242i	0.575181	+	0.996242i
$101$	3.84276	−	6.65585i	0.382369	−	0.662282i	−0.609032	−	0.793146i	$-0.708442\pi$
$101$	3.84276	−	6.65585i	0.382369	−	0.662282i	0.991400	+	0.130864i	$0.0417750\pi$
$102$	−10.7612	+	2.88344i	−1.06551	+	0.285503i
$103$	2.89145	−	5.00814i	0.284903	−	0.493466i	−0.687683	−	0.726011i	$-0.741372\pi$
$103$	2.89145	−	5.00814i	0.284903	−	0.493466i	0.972586	+	0.232545i	$0.0747053\pi$
$104$	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
$107$	−10.4484			−1.01009			−0.505043	−	0.863094i	$-0.668523\pi$
$107$	−10.4484			−1.01009			−0.505043	+	0.863094i	$0.668523\pi$
$108$	2.81950			0.271306
$109$	13.1113	+	3.51317i	1.25584	+	0.336501i	0.824589	−	0.565732i	$-0.191406\pi$
$109$	13.1113	+	3.51317i	1.25584	+	0.336501i	0.431249	+	0.902233i	$0.358073\pi$
$110$	−1.54204	+	5.75498i	−0.147028	+	0.548715i
$111$	−1.36423	−	5.09136i	−0.129487	−	0.483251i
$112$	1.04679	−	4.34551i	0.0989120	−	0.410612i
$113$	−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	$0.193470\pi$
$114$			0.975286i			0.0913439i
$115$	−0.837906	−	3.12711i	−0.0781352	−	0.291604i
$116$	23.9912	−	13.8513i	2.22753	−	1.28606i
$117$	−3.25088	−	1.55942i	−0.300544	−	0.144169i
$118$			6.43563i			0.592448i
$119$	−3.14436	+	13.0531i	−0.288243	+	1.19658i
$120$	0.862793	+	1.49440i	0.0787619	+	0.136420i
$121$	−2.59280	+	1.49695i	−0.235709	+	0.136087i
$122$	7.33508	−	27.3749i	0.664087	−	2.47841i
$123$	−3.08851	+	3.08851i	−0.278482	+	0.278482i
$124$	−9.06474	−	2.42889i	−0.814038	−	0.218121i
$125$	6.15829	−	6.15829i	0.550815	−	0.550815i
$126$	2.77540	−	5.10232i	0.247252	−	0.454551i
$127$	−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	$0.401557\pi$
$128$	−9.32275	−	9.32275i	−0.824022	−	0.824022i
$129$	−1.48947	−	2.57983i	−0.131140	−	0.227141i
$130$	−0.578927	−	7.56998i	−0.0507753	−	0.663931i
$131$	−13.6712	−	7.89309i	−1.19446	−	0.689623i	−0.235146	−	0.971960i	$-0.575557\pi$
$131$	−13.6712	−	7.89309i	−1.19446	−	0.689623i	−0.959315	+	0.282337i	$0.908890\pi$
$132$	2.06480	−	7.70594i	0.179718	−	0.670716i
$133$	1.03252	+	0.561636i	0.0895307	+	0.0487001i
$134$	−19.1633	−	11.0639i	−1.65546	−	0.955779i
$135$	−0.248247	−	0.926472i	−0.0213657	−	0.0797380i
$136$	6.45576	+	6.45576i	0.553577	+	0.553577i
$137$	11.4704	+	11.4704i	0.979985	+	0.979985i	0.999804	−	0.0198182i	$-0.00630874\pi$
$137$	11.4704	+	11.4704i	0.979985	+	0.979985i	−0.0198182	+	0.999804i	$0.506309\pi$
$138$	1.91782	+	7.15740i	0.163256	+	0.609278i
$139$	−14.0656	−	8.12080i	−1.19303	−	0.688797i	−0.234038	−	0.972227i	$-0.575194\pi$
$139$	−14.0656	−	8.12080i	−1.19303	−	0.688797i	−0.958993	+	0.283431i	$0.908527\pi$
$140$	7.15268	−	0.181817i	0.604512	−	0.0153663i
$141$	−2.43887	+	9.10199i	−0.205390	+	0.766526i
$142$	−1.51662	−	0.875620i	−0.127272	−	0.0734804i
$143$	−6.64276	+	7.74293i	−0.555495	+	0.647496i
$144$	0.844715	+	1.46309i	0.0703929	+	0.121924i
$145$	−6.66382	−	6.66382i	−0.553400	−	0.553400i
$146$	−7.47713	+	4.31692i	−0.618812	+	0.357271i
$147$	−3.80347	−	5.87653i	−0.313705	−	0.484688i
$148$	−10.5086	+	10.5086i	−0.863806	+	0.863806i
$149$	−12.2507	−	3.28257i	−1.00362	−	0.268918i	−0.280657	−	0.959808i	$-0.590552\pi$
$149$	−12.2507	−	3.28257i	−1.00362	−	0.268918i	−0.722960	+	0.690890i	$0.757219\pi$
$150$	−6.33357	+	6.33357i	−0.517134	+	0.517134i
$151$	5.17632	−	19.3183i	0.421243	−	1.57210i	−0.350750	−	0.936469i	$-0.614073\pi$
$151$	5.17632	−	19.3183i	0.421243	−	1.57210i	0.771993	−	0.635631i	$-0.219260\pi$
$152$	0.692166	−	0.399622i	0.0561421	−	0.0324136i
$153$	−2.53737	−	4.39486i	−0.205134	−	0.355303i
$154$	−11.9126	−	11.3220i	−0.959945	−	0.912352i
$155$			3.19248i			0.256426i
$156$	0.775187	+	10.1362i	0.0620646	+	0.811549i
$157$	2.66290	−	1.53742i	0.212522	−	0.122700i	−0.389961	−	0.920831i	$-0.627511\pi$
$157$	2.66290	−	1.53742i	0.212522	−	0.122700i	0.602483	+	0.798132i	$0.294178\pi$
$158$	−2.78287	−	10.3858i	−0.221393	−	0.826250i
$159$		−	8.60149i		−	0.682142i
$160$	−3.50427	+	6.06958i	−0.277037	+	0.479842i
$161$	8.68183	+	2.09136i	0.684224	+	0.164822i
$162$	0.568195	+	2.12053i	0.0446416	+	0.166605i
$163$	−5.49272	+	20.4991i	−0.430223	+	1.60561i	0.322024	+	0.946732i	$0.395637\pi$
$163$	−5.49272	+	20.4991i	−0.430223	+	1.60561i	−0.752246	+	0.658882i	$0.771030\pi$
$164$	11.8954	+	3.18737i	0.928877	+	0.248892i
$165$	−2.71393			−0.211279
$166$	8.90011			0.690783
$167$	22.6114	+	6.05871i	1.74972	+	0.468837i	0.984567	−	0.175007i	$-0.0559948\pi$
$167$	22.6114	+	6.05871i	1.74972	+	0.468837i	0.765157	+	0.643844i	$0.222661\pi$
$168$	−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
$171$	−0.429116	+	0.114981i	−0.0328153	+	0.00879284i
$172$	−4.19954	+	7.27383i	−0.320212	+	0.554624i
$173$	−8.33256	−	14.4324i	−0.633513	−	1.09728i	−0.986828	−	0.161772i	$-0.948279\pi$
$173$	−8.33256	−	14.4324i	−0.633513	−	1.09728i	0.353315	−	0.935504i	$-0.385054\pi$
$174$	15.2523	+	15.2523i	1.15627	+	1.15627i
$175$	3.05794	+	10.3525i	0.231158	+	0.782579i
$176$	4.61737	−	1.23722i	0.348047	−	0.0932589i
$177$	−2.83161	+	0.758729i	−0.212837	+	0.0570296i
$178$		−	22.9338i		−	1.71896i
$179$	−10.4842	−	6.05306i	−0.783627	−	0.452427i	0.0540872	−	0.998536i	$-0.482775\pi$
$179$	−10.4842	−	6.05306i	−0.783627	−	0.452427i	−0.837714	+	0.546109i	$0.816108\pi$
$180$	−1.91225	+	1.91225i	−0.142531	+	0.142531i
$181$	−11.9791			−0.890400			−0.445200	−	0.895431i	$-0.646867\pi$
$181$	−11.9791			−0.890400			−0.445200	+	0.895431i	$0.646867\pi$
$182$	19.1062	+	8.57487i	1.41624	+	0.635612i
$183$	12.9094			0.954294
$184$	4.29382	−	4.29382i	0.316545	−	0.316545i
$185$	4.37834	+	2.52783i	0.321902	+	0.185850i
$186$		−	7.30703i		−	0.535777i
$187$	−13.8697	+	3.71639i	−1.01426	+	0.271769i
$188$	25.6630	−	6.87639i	1.87167	−	0.501512i
$189$	2.57218	+	0.619609i	0.187098	+	0.0450699i
$190$	−0.661463	−	0.661463i	−0.0479876	−	0.0479876i
$191$	3.96796	+	6.87270i	0.287111	+	0.497291i	0.973119	−	0.230303i	$-0.0739717\pi$
$191$	3.96796	+	6.87270i	0.287111	+	0.497291i	−0.686008	+	0.727594i	$0.740638\pi$
$192$	6.33124	−	10.9660i	0.456918	−	0.791404i
$193$	−0.843813	+	0.226099i	−0.0607390	+	0.0162750i	−0.289061	−	0.957311i	$-0.593343\pi$
$193$	−0.843813	+	0.226099i	−0.0607390	+	0.0162750i	0.228322	+	0.973586i	$0.426676\pi$
$194$	−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	$0.383125\pi$
$198$	6.21171			0.441447
$199$	21.9852			1.55849			0.779246	−	0.626718i	$-0.215602\pi$
$199$	21.9852			1.55849			0.779246	+	0.626718i	$0.215602\pi$
$200$	7.09014	+	1.89980i	0.501348	+	0.134336i
$201$	2.60877	−	9.73605i	0.184008	−	0.686728i
$202$	−4.36687	−	16.2974i	−0.307252	−	1.14668i
$203$	24.9307	−	7.36403i	1.74979	−	0.516854i
$204$	−7.15412	+	12.3913i	−0.500888	+	0.867564i
$205$		−	4.18941i		−	0.292601i
$206$	−3.28581	−	12.2628i	−0.228933	−	0.854391i
$207$	−2.92308	+	1.68764i	−0.203168	+	0.117299i
$208$	−5.02764	+	3.43905i	−0.348604	+	0.238456i
$209$			1.25702i			0.0869498i
$210$	1.57818	+	5.34286i	0.108905	+	0.368692i
$211$	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	$0.542884\pi$
$212$	−21.0027	+	12.1259i	−1.44247	+	0.832813i
$213$	0.206463	−	0.770529i	0.0141466	−	0.0527958i
$214$	−16.2194	+	16.2194i	−1.10874	+	1.10874i
$215$	2.75990	+	0.739512i	0.188223	+	0.0504343i
$216$	1.27214	−	1.27214i	0.0865578	−	0.0865578i
$217$	−7.73583	−	4.20789i	−0.525142	−	0.285650i
$218$	25.8068	−	14.8996i	1.74786	−	1.00913i
$219$	−2.78092	−	2.78092i	−0.187917	−	0.187917i
$220$	3.82596	+	6.62676i	0.257946	+	0.446776i
$221$	15.1021	−	10.3303i	1.01588	−	0.694892i
$222$	−10.0212	−	5.78577i	−0.672582	−	0.388315i
$223$	−5.97549	+	22.3008i	−0.400148	+	1.49337i	0.412683	+	0.910875i	$0.364592\pi$
$223$	−5.97549	+	22.3008i	−0.400148	+	1.49337i	−0.812832	+	0.582499i	$0.802075\pi$
$224$	−10.0886	−	16.4914i	−0.674072	−	1.10188i
$225$	−3.53340	−	2.04001i	−0.235560	−	0.136001i
$226$	1.01601	+	3.79178i	0.0675837	+	0.252226i
$227$	11.7069	+	11.7069i	0.777014	+	0.777014i	0.979322	−	0.202308i	$-0.0648443\pi$
$227$	11.7069	+	11.7069i	0.777014	+	0.777014i	−0.202308	+	0.979322i	$0.564844\pi$
$228$	0.885702	+	0.885702i	0.0586571	+	0.0586571i
$229$	−1.94891	−	7.27341i	−0.128787	−	0.480641i	0.871159	−	0.491001i	$-0.163369\pi$
$229$	−1.94891	−	7.27341i	−0.128787	−	0.480641i	−0.999946	+	0.0103602i	$0.996702\pi$
$230$	−6.15504	−	3.55361i	−0.405851	−	0.234318i
$231$	3.57713	−	6.57623i	0.235358	−	0.432684i
$232$	4.57503	−	17.0742i	0.300366	−	1.12098i
$233$	−4.12931	−	2.38406i	−0.270520	−	0.156185i	0.358604	−	0.933490i	$-0.383253\pi$
$233$	−4.12931	−	2.38406i	−0.270520	−	0.156185i	−0.629124	+	0.777305i	$0.716586\pi$
$234$	−7.46720	+	2.62570i	−0.488146	+	0.171648i
$235$	−4.51909	−	7.82730i	−0.294793	−	0.510596i
$236$	5.84450	+	5.84450i	0.380444	+	0.380444i
$237$	4.24156	−	2.44887i	0.275519	−	0.159071i
$238$	15.3818	+	25.1440i	0.997051	+	1.62984i
$239$	−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	$0.298100\pi$
$240$	−1.56521	−	0.419397i	−0.101034	−	0.0270719i
$241$	−4.63321	+	4.63321i	−0.298451	+	0.298451i	−0.840407	−	0.541956i	$-0.817684\pi$
$241$	−4.63321	+	4.63321i	−0.298451	+	0.298451i	0.541956	+	0.840407i	$0.317684\pi$
$242$	−1.70112	+	6.34867i	−0.109352	+	0.408108i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−18.1991	−	31.5217i	−1.16508	−	2.01797i
$245$	6.56522	+	1.40600i	0.419436	+	0.0898258i
$246$			9.58882i			0.611361i
$247$	−0.531344	−	1.51108i	−0.0338086	−	0.0961479i
$248$	−5.18584	+	2.99404i	−0.329301	+	0.190122i
$249$	1.04928	+	3.91596i	0.0664953	+	0.248164i
$250$		−	19.1195i		−	1.20922i
$251$	−9.74305	+	16.8755i	−0.614976	+	1.06517i	0.375413	+	0.926858i	$0.377501\pi$
$251$	−9.74305	+	16.8755i	−0.614976	+	1.06517i	−0.990389	+	0.138312i	$0.955832\pi$
$252$	−2.11319	−	7.15412i	−0.133118	−	0.450667i
$253$	2.47182	+	9.22497i	0.155402	+	0.579969i
$254$	−2.72384	+	10.1655i	−0.170909	+	0.637841i
$255$	4.70161	+	1.25979i	0.294426	+	0.0788913i
$256$	−3.61914			−0.226196
$257$	7.80061			0.486589			0.243294	−	0.969953i	$-0.421772\pi$
$257$	7.80061			0.486589			0.243294	+	0.969953i	$0.421772\pi$
$258$	−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
$262$	−33.4751	+	8.96963i	−2.06810	+	0.554145i
$263$	−8.05497	+	13.9516i	−0.496691	+	0.860294i	−0.999993	−	0.00381668i	$-0.998785\pi$
$263$	−8.05497	+	13.9516i	−0.496691	+	0.860294i	0.503302	+	0.864111i	$0.332118\pi$
$264$	−2.54524	−	4.40848i	−0.156649	−	0.271323i
$265$	5.83374	+	5.83374i	0.358364	+	0.358364i
$266$	2.47466	−	0.730968i	0.151731	−	0.0448185i
$267$	10.0906	−	2.70378i	0.617537	−	0.165469i
$268$	−27.4508	+	7.35541i	−1.67682	+	0.449303i
$269$			4.34460i			0.264895i	0.991190	+	0.132447i	$0.0422836\pi$
$269$			4.34460i			0.264895i	−0.991190	+	0.132447i	$0.957716\pi$
$270$	−1.82356	−	1.05283i	−0.110978	−	0.0640734i
$271$	0.977513	−	0.977513i	0.0593797	−	0.0593797i	−0.676793	−	0.736173i	$-0.736631\pi$
$271$	0.977513	−	0.977513i	0.0593797	−	0.0593797i	0.736173	+	0.676793i	$0.236631\pi$
$272$	−8.57343			−0.519841
$273$	−1.52034	+	9.41746i	−0.0920151	+	0.569971i
$274$	35.6119			2.15140
$275$	−8.16315	+	8.16315i	−0.492257	+	0.492257i
$276$	8.24163	+	4.75831i	0.496088	+	0.286416i
$277$		−	17.6238i		−	1.05891i	−0.848337	−	0.529456i	$-0.822396\pi$
$277$		−	17.6238i		−	1.05891i	0.848337	−	0.529456i	$-0.177604\pi$
$278$	−34.4408	+	9.22838i	−2.06562	+	0.553482i
$279$	3.21502	−	0.861462i	0.192478	−	0.0515744i
$280$	3.14520	−	3.30927i	0.187962	−	0.197767i
$281$	−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	$0.759740\pi$
$282$	10.3434	+	17.9153i	0.615941	+	1.06684i
$283$	−5.65398	+	9.79298i	−0.336094	+	0.582132i	−0.983694	−	0.179848i	$-0.942439\pi$
$283$	−5.65398	+	9.79298i	−0.336094	+	0.582132i	0.647600	+	0.761980i	$0.275773\pi$
$284$	−2.17250	+	0.582121i	−0.128914	+	0.0345425i
$285$	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
$289$	8.75306			0.514886
$290$	−20.6890			−1.21490
$291$	−4.64555	−	1.24477i	−0.272327	−	0.0729698i
$292$	−2.86993	+	10.7107i	−0.167950	+	0.626798i
$293$	0.591222	+	2.20647i	0.0345396	+	0.128903i	0.981043	−	0.193790i	$-0.0620782\pi$
$293$	0.591222	+	2.20647i	0.0345396	+	0.128903i	−0.946503	+	0.322694i	$0.895412\pi$
$294$	−15.0266	−	3.21808i	−0.876370	−	0.187682i
$295$	1.40588	−	2.43506i	0.0818536	−	0.141775i
$296$			9.48284i			0.551179i
$297$	0.732330	+	2.73309i	0.0424941	+	0.158590i
$298$	−24.1129	+	13.9216i	−1.39682	+	0.806455i
$299$	−6.87083	−	10.0446i	−0.397351	−	0.580897i
$300$			11.5036i			0.664161i
$301$	−5.42965	+	5.71289i	−0.312960	+	0.329285i
$302$	−21.9531	−	38.0239i	−1.26326	−	2.18803i
$303$	6.65585	−	3.84276i	0.382369	−	0.220761i
$304$	−0.194253	+	0.724962i	−0.0111412	+	0.0415794i
$305$	−8.75550	+	8.75550i	−0.501339	+	0.501339i
$306$	−10.7612	−	2.88344i	−0.615174	−	0.164836i
$307$	16.5239	−	16.5239i	0.943069	−	0.943069i	−0.0553956	−	0.998464i	$-0.517642\pi$
$307$	16.5239	−	16.5239i	0.943069	−	0.943069i	0.998464	+	0.0553956i	$0.0176420\pi$
$308$	−21.1004	+	0.536360i	−1.20231	+	0.0305619i
$309$	5.00814	−	2.89145i	0.284903	−	0.164489i
$310$	4.95581	+	4.95581i	0.281471	+	0.281471i
$311$	5.06256	+	8.76860i	0.287071	+	0.497222i	0.973109	−	0.230344i	$-0.0739850\pi$
$311$	5.06256	+	8.76860i	0.287071	+	0.497222i	−0.686038	+	0.727566i	$0.740652\pi$
$312$	4.92315	+	4.22364i	0.278719	+	0.239116i
$313$	−7.40644	−	4.27611i	−0.418637	−	0.241700i	0.275857	−	0.961199i	$-0.411038\pi$
$313$	−7.40644	−	4.27611i	−0.418637	−	0.241700i	−0.694494	+	0.719499i	$0.744372\pi$
$314$	1.74711	−	6.52031i	0.0985953	−	0.367963i
$315$	−2.16475	+	1.32428i	−0.121970	+	0.0746146i
$316$	−11.9591	−	6.90458i	−0.672751	−	0.388413i
$317$	−8.41365	−	31.4002i	−0.472558	−	1.76361i	−0.630528	−	0.776166i	$-0.717162\pi$
$317$	−8.41365	−	31.4002i	−0.472558	−	1.76361i	0.157970	−	0.987444i	$-0.449505\pi$
$318$	−13.3524	−	13.3524i	−0.748766	−	0.748766i
$319$	19.6583	+	19.6583i	1.10065	+	1.10065i
$320$	3.14343	+	11.7314i	0.175723	+	0.655807i
$321$	−9.04858	−	5.22420i	−0.505043	−	0.291587i
$322$	16.7236	−	10.2306i	0.931970	−	0.570131i
$323$	0.583501	−	2.17766i	0.0324669	−	0.121168i
$324$	2.44176	+	1.40975i	0.135653	+	0.0783194i
$325$	6.36248	−	13.2637i	0.352927	−	0.735735i
$326$	23.2950	+	40.3480i	1.29019	+	2.23467i
$327$	9.59816	+	9.59816i	0.530780	+	0.530780i
$328$	6.80524	−	3.92901i	0.375757	−	0.216943i
$329$	24.9231	−	0.633529i	1.37405	−	0.0349276i
$330$	−4.21293	+	4.21293i	−0.231914	+	0.231914i
$331$	24.3360	+	6.52082i	1.33763	+	0.358416i	0.855554	−	0.517714i	$-0.173217\pi$
$331$	24.3360	+	6.52082i	1.33763	+	0.358416i	0.482074	+	0.876130i	$0.339883\pi$
$332$	8.08260	−	8.08260i	0.443591	−	0.443591i
$333$	1.36423	−	5.09136i	0.0747591	−	0.279005i
$334$	44.5057	−	25.6954i	2.43524	−	1.40599i
$335$	4.83390	+	8.37256i	0.264104	+	0.457442i
$336$	3.07930	−	3.23993i	0.167989	−	0.176753i
$337$			18.3271i			0.998342i	0.866504	+	0.499171i	$0.166362\pi$
$337$			18.3271i			0.998342i	−0.866504	+	0.499171i	$0.833638\pi$
$338$	−11.4926	−	26.1231i	−0.625113	−	1.42091i
$339$	−1.54857	+	0.894065i	−0.0841065	+	0.0485589i
$340$	−3.55198	−	13.2562i	−0.192633	−	0.718917i
$341$		−	9.41782i		−	0.510004i
$342$	−0.487643	+	0.844623i	−0.0263687	+	0.0456720i
$343$	−12.0603	+	14.0552i	−0.651194	+	0.758912i
$344$	1.38709	+	5.17670i	0.0747870	+	0.279109i
$345$	0.837906	−	3.12711i	0.0451114	−	0.168358i
$346$	−35.3389	−	9.46903i	−1.89983	−	0.509058i
$347$	−18.3083			−0.982844			−0.491422	−	0.870922i	$-0.663523\pi$
$347$	−18.3083			−0.982844			−0.491422	+	0.870922i	$0.663523\pi$
$348$	27.7026			1.48502
$349$	24.2335	+	6.49336i	1.29719	+	0.347581i	0.840387	−	0.541986i	$-0.182327\pi$
$349$	24.2335	+	6.49336i	1.29719	+	0.347581i	0.456804	+	0.889567i	$0.348994\pi$
$350$	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
$353$	22.0724	−	5.91428i	1.17480	−	0.314785i	0.381935	−	0.924189i	$-0.375258\pi$
$353$	22.0724	−	5.91428i	1.17480	−	0.314785i	0.792860	+	0.609404i	$0.208591\pi$
$354$	−3.21782	+	5.57342i	−0.171025	+	0.296224i
$355$	0.382563	+	0.662619i	0.0203044	+	0.0351682i
$356$	−20.8272	−	20.8272i	−1.10384	−	1.10384i
$357$	−9.24966	+	9.73217i	−0.489544	+	0.515081i
$358$	−25.6714	+	6.87864i	−1.35678	+	0.363547i
$359$	−21.4867	+	5.75735i	−1.13403	+	0.303861i	−0.776547	−	0.630060i	$-0.783030\pi$
$359$	−21.4867	+	5.75735i	−1.13403	+	0.303861i	−0.357479	+	0.933921i	$0.616364\pi$
$360$			1.72559i			0.0909464i
$361$	16.2836	+	9.40132i	0.857030	+	0.494806i
$362$	−18.5956	+	18.5956i	−0.977364	+	0.977364i
$363$	−2.99390			−0.157139
$364$	25.1384	−	9.56396i	1.31761	−	0.501288i
$365$	3.77218			0.197445
$366$	20.0398	−	20.0398i	1.04750	−	1.04750i
$367$	−14.1199	−	8.15212i	−0.737052	−	0.425537i	0.0839445	−	0.996470i	$-0.473248\pi$
$367$	−14.1199	−	8.15212i	−0.737052	−	0.425537i	−0.820996	+	0.570933i	$0.806582\pi$
$368$			5.70231i			0.297254i
$369$	−4.21899	+	1.13047i	−0.219632	+	0.0588501i
$370$	10.7207	−	2.87260i	0.557343	−	0.149340i
$371$	−21.8252	+	6.44673i	−1.13311	+	0.334698i
$372$	−6.63585	−	6.63585i	−0.344053	−	0.344053i
$373$	17.5521	+	30.4011i	0.908813	+	1.57411i	0.815716	+	0.578453i	$0.196343\pi$
$373$	17.5521	+	30.4011i	0.908813	+	1.57411i	0.0930969	+	0.995657i	$0.470323\pi$
$374$	−15.7614	+	27.2996i	−0.815004	+	1.41163i
$375$	8.41239	−	2.25409i	0.434414	−	0.116401i
$376$	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	$0.377011\pi$
$380$	−1.20141			−0.0616310
$381$	−4.79386			−0.245597
$382$	16.8284	+	4.50914i	0.861013	+	0.230708i
$383$	2.30873	−	8.61631i	0.117971	−	0.440273i	−0.881521	−	0.472145i	$-0.843480\pi$
$383$	2.30873	−	8.61631i	0.117971	−	0.440273i	0.999492	+	0.0318714i	$0.0101467\pi$
$384$	−3.41236	−	12.7351i	−0.174136	−	0.649886i
$385$	2.03407	+	6.88626i	0.103666	+	0.350956i
$386$	−0.958900	+	1.66086i	−0.0488067	+	0.0845357i
$387$		−	2.97893i		−	0.151428i
$388$	3.50963	+	13.0981i	0.178174	+	0.664956i
$389$	13.7424	−	7.93420i	0.696770	−	0.402280i	−0.109374	−	0.994001i	$-0.534884\pi$
$389$	13.7424	−	7.93420i	0.696770	−	0.402280i	0.806143	+	0.591721i	$0.201551\pi$
$390$	3.28362	−	6.84526i	0.166273	−	0.346623i
$391$		−	17.1287i		−	0.866237i
$392$	3.87325	+	11.9831i	0.195629	+	0.605237i
$393$	−7.89309	−	13.6712i	−0.398154	−	0.689623i
$394$	31.3982	−	18.1278i	1.58182	−	0.913263i
$395$	−1.21585	+	4.53762i	−0.0611761	+	0.228312i
$396$	5.64114	−	5.64114i	0.283478	−	0.283478i
$397$	−33.1918	−	8.89372i	−1.66585	−	0.446363i	−0.701863	−	0.712312i	$-0.747648\pi$
$397$	−33.1918	−	8.89372i	−1.66585	−	0.446363i	−0.963987	+	0.265949i	$0.914315\pi$
$398$	34.1285	−	34.1285i	1.71071	−	1.71071i
$399$	0.613369	+	1.00265i	0.0307069	+	0.0501953i
$400$	−5.96944	+	3.44646i	−0.298472	+	0.172323i
$401$	−12.5570	−	12.5570i	−0.627069	−	0.627069i	0.320261	−	0.947329i	$-0.396230\pi$
$401$	−12.5570	−	12.5570i	−0.627069	−	0.627069i	−0.947329	+	0.320261i	$0.896230\pi$
$402$	−11.0639	−	19.1633i	−0.551819	−	0.955779i
$403$	3.98093	+	11.3213i	0.198304	+	0.563955i
$404$	−18.7662	−	10.8346i	−0.933651	−	0.539044i
$405$	0.248247	−	0.926472i	0.0123355	−	0.0460368i
$406$	27.2693	−	50.1322i	1.35335	−	2.48802i
$407$	−12.9161	−	7.45711i	−0.640227	−	0.369635i
$408$	2.36297	+	8.81874i	0.116985	+	0.436593i
$409$	−7.70016	−	7.70016i	−0.380748	−	0.380748i	0.490623	−	0.871372i	$-0.336769\pi$
$409$	−7.70016	−	7.70016i	−0.380748	−	0.380748i	−0.871372	+	0.490623i	$0.836769\pi$
$410$	−6.50338	−	6.50338i	−0.321179	−	0.321179i
$411$	4.19847	+	15.6689i	0.207095	+	0.772890i
$412$	−14.1204	−	8.15243i	−0.695664	−	0.401642i
$413$	4.04745	+	6.61620i	0.199162	+	0.325562i
$414$	−1.91782	+	7.15740i	−0.0942557	+	0.351767i
$415$	−3.36755	−	1.94425i	−0.165306	−	0.0954397i
$416$	−4.85842	+	25.8939i	−0.238204	+	1.26956i
$417$	−8.12080	−	14.0656i	−0.397677	−	0.688797i
$418$	1.95132	+	1.95132i	0.0954419	+	0.0954419i
$419$	26.8756	−	15.5166i	1.31296	−	0.758037i	0.330374	−	0.943850i	$-0.392825\pi$
$419$	26.8756	−	15.5166i	1.31296	−	0.758037i	0.982585	+	0.185813i	$0.0594918\pi$
$420$	6.28531	+	3.41888i	0.306692	+	0.166824i
$421$	−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	$0.904591\pi$
$422$	48.7308	+	13.0574i	2.37218	+	0.635623i
$423$	−6.66312	+	6.66312i	−0.323972	+	0.323972i
$424$	−4.00514	+	14.9474i	−0.194507	+	0.725910i
$425$	17.9311	−	10.3525i	0.869787	−	0.502172i
$426$	−0.875620	−	1.51662i	−0.0424239	−	0.0734804i
$427$	−9.67551	−	32.7561i	−0.468231	−	1.58518i
$428$			29.4592i			1.42397i
$429$	−9.62426	+	3.38419i	−0.464664	+	0.163390i
$430$	5.43226	−	3.13632i	0.261967	−	0.151247i
$431$	−0.0514894	−	0.192161i	−0.00248016	−	0.00925608i	0.964675	−	0.263444i	$-0.0848585\pi$
$431$	−0.0514894	−	0.192161i	−0.00248016	−	0.00925608i	−0.967155	+	0.254188i	$0.918192\pi$
$432$			1.68943i			0.0812827i
$433$	14.8795	−	25.7720i	0.715062	−	1.23852i	−0.247873	−	0.968792i	$-0.579732\pi$
$433$	14.8795	−	25.7720i	0.715062	−	1.23852i	0.962936	−	0.269731i	$-0.0869349\pi$
$434$	−18.5407	+	5.47655i	−0.889980	+	0.262883i
$435$	−2.43913	−	9.10294i	−0.116947	−	0.436453i
$436$	9.90538	−	36.9674i	0.474382	−	1.77042i
$437$	−1.44839	−	0.388095i	−0.0692859	−	0.0185651i
$438$	−8.63385			−0.412541
$439$	37.7557			1.80198			0.900992	−	0.433836i	$-0.142840\pi$
$439$	37.7557			1.80198			0.900992	+	0.433836i	$0.142840\pi$
$440$	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	−0.331204	−	0.943559i	$-0.607455\pi$
$443$	13.7134	−	23.7524i	0.651545	−	1.12851i	0.982748	−	0.184949i	$-0.0592120\pi$
$444$	−14.3551	+	3.84643i	−0.681262	+	0.182544i
$445$	−5.00995	+	8.67749i	−0.237494	+	0.411352i
$446$	25.3424	+	43.8943i	1.20000	+	2.07846i
$447$	−8.96814	−	8.96814i	−0.424179	−	0.424179i
$448$	−32.5701	−	7.84578i	−1.53879	−	0.370678i
$449$	−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	$0.443182\pi$
$450$	−8.65182	+	2.31825i	−0.407850	+	0.109283i
$451$			12.3588i			0.581951i
$452$	4.36618	+	2.52081i	0.205368	+	0.118569i
$453$	14.1420	−	14.1420i	0.664448	−	0.664448i
$454$	36.3461			1.70581
$455$	−5.35602	−	7.41828i	−0.251094	−	0.347775i
$456$	0.799244			0.0374280
$457$	−9.15420	+	9.15420i	−0.428215	+	0.428215i	−0.888020	−	0.459805i	$-0.847919\pi$
$457$	−9.15420	+	9.15420i	−0.428215	+	0.428215i	0.459805	+	0.888020i	$0.347919\pi$
$458$	−14.3161	−	8.26543i	−0.668949	−	0.386218i
$459$		−	5.07475i		−	0.236869i
$460$	−8.81687	+	2.36247i	−0.411089	+	0.110151i
$461$	−20.6542	+	5.53427i	−0.961961	+	0.257757i	−0.705430	−	0.708779i	$-0.749246\pi$
$461$	−20.6542	+	5.53427i	−0.961961	+	0.257757i	−0.256531	+	0.966536i	$0.582580\pi$
$462$	−4.65562	−	15.7614i	−0.216599	−	0.733288i
$463$	−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	$0.899390\pi$
$464$	8.29965	+	14.3754i	0.385302	+	0.667362i
$465$	−1.59624	+	2.76477i	−0.0740239	+	0.128213i
$466$	−10.1109	+	2.70922i	−0.468380	+	0.125502i
$467$	−9.10881	+	15.7769i	−0.421505	+	0.730069i	−0.996087	−	0.0883787i	$-0.971831\pi$
$467$	−9.10881	+	15.7769i	−0.421505	+	0.730069i	0.574582	+	0.818447i	$0.305165\pi$
$468$	−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
$471$	3.07485			0.141682
$472$	5.27398			0.242755
$473$	−8.14169	−	2.18156i	−0.374355	−	0.100308i
$474$	2.78287	−	10.3858i	0.127821	−	0.477036i
$475$	−0.469127	−	1.75080i	−0.0215250	−	0.0803324i
$476$	36.8033	+	8.86551i	1.68688	+	0.406350i
$477$	4.30074	−	7.44911i	0.196918	−	0.341071i
$478$			10.2181i			0.467366i
$479$	−5.27554	−	19.6886i	−0.241045	−	0.899594i	−0.975330	−	0.220752i	$-0.929149\pi$
$479$	−5.27554	−	19.6886i	−0.241045	−	0.899594i	0.734285	−	0.678842i	$-0.237518\pi$
$480$	−6.06958	+	3.50427i	−0.277037	+	0.159947i
$481$	18.6788	+	3.50466i	0.851680	+	0.159799i
$482$			14.3846i			0.655201i
$483$	6.47300	+	6.15208i	0.294532	+	0.279929i
$484$	4.22065	+	7.31039i	0.191848	+	0.332290i
$485$	3.99496	−	2.30649i	0.181402	−	0.104732i
$486$	−0.568195	+	2.12053i	−0.0257738	+	0.0961892i
$487$	3.46627	−	3.46627i	0.157072	−	0.157072i	−0.624196	−	0.781268i	$-0.714573\pi$
$487$	3.46627	−	3.46627i	0.157072	−	0.157072i	0.781268	+	0.624196i	$0.214573\pi$
$488$	−22.4336	−	6.01107i	−1.01552	−	0.272109i
$489$	−15.0064	+	15.0064i	−0.678612	+	0.678612i
$490$	12.3740	−	8.00885i	0.559000	−	0.361803i
$491$	−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	$0.458455\pi$
$492$	8.70806	+	8.70806i	0.392589	+	0.392589i
$493$	−24.9307	−	43.1812i	−1.12282	−	1.94478i
$494$	−3.17053	−	1.52088i	−0.142649	−	0.0684278i
$495$	−2.35033	−	1.35697i	−0.105640	−	0.0609911i
$496$	1.45538	−	5.43155i	0.0653485	−	0.243884i
$497$	−2.10986	+	0.0536314i	−0.0946402	+	0.00240570i
$498$	7.70772	+	4.45006i	0.345391	+	0.199412i
$499$	−5.72138	−	21.3525i	−0.256124	−	0.955868i	−0.967462	−	0.253018i	$-0.918577\pi$
$499$	−5.72138	−	21.3525i	−0.256124	−	0.955868i	0.711337	−	0.702851i	$-0.248090\pi$
$500$	−17.3633	−	17.3633i	−0.776510	−	0.776510i
$501$	16.5527	+	16.5527i	0.739520	+	0.739520i
$502$	11.0719	+	41.3209i	0.494163	+	1.84424i
$503$	2.07668	+	1.19897i	0.0925946	+	0.0534595i	0.545582	−	0.838057i	$-0.316309\pi$
$503$	2.07668	+	1.19897i	0.0925946	+	0.0534595i	−0.452988	+	0.891517i	$0.649642\pi$
$504$	−4.18134	−	2.27443i	−0.186251	−	0.101311i
$505$	−1.90791	+	7.12042i	−0.0849009	+	0.316854i
$506$	18.1574	+	10.4832i	0.807193	+	0.466033i
$507$	10.1390	−	8.13640i	0.450288	−	0.361350i
$508$	6.75813	+	11.7054i	0.299844	+	0.519344i
$509$	18.5719	+	18.5719i	0.823185	+	0.823185i	0.986564	−	0.163378i	$-0.0522391\pi$
$509$	18.5719	+	18.5719i	0.823185	+	0.823185i	−0.163378	+	0.986564i	$0.552239\pi$
$510$	9.25410	−	5.34286i	0.409779	−	0.236586i
$511$	−4.97196	+	9.14051i	−0.219947	+	0.404352i
$512$	13.0274	−	13.0274i	0.575734	−	0.575734i
$513$	−0.429116	−	0.114981i	−0.0189459	−	0.00507655i
$514$	12.1092	−	12.1092i	0.534113	−	0.534113i
$515$	−1.43559	+	5.35769i	−0.0632596	+	0.236088i
$516$	−7.27383	+	4.19954i	−0.320212	+	0.184875i
$517$	13.3313	+	23.0905i	0.586311	+	1.01552i
$518$	−7.16983	+	29.7640i	−0.315024	+	1.30776i
$519$		−	16.6651i		−	0.731518i
$520$	−6.20358	+	0.474429i	−0.272045	+	0.0208051i
$521$	−1.07001	+	0.617770i	−0.0468780	+	0.0270650i	−0.523256	−	0.852176i	$-0.675283\pi$
$521$	−1.07001	+	0.617770i	−0.0468780	+	0.0270650i	0.476378	+	0.879241i	$0.341949\pi$
$522$	5.58273	+	20.8350i	0.244349	+	0.911925i
$523$			8.47306i			0.370501i	0.982691	+	0.185251i	$0.0593097\pi$
$523$			8.47306i			0.370501i	−0.982691	+	0.185251i	$0.940690\pi$
$524$	−22.2546	+	38.5460i	−0.972195	+	1.68389i
$525$	−2.52802	+	10.4945i	−0.110332	+	0.458019i
$526$	9.15359	+	34.1616i	0.399115	+	1.48952i
$527$	−4.37170	+	16.3154i	−0.190434	+	0.710711i
$528$	4.61737	+	1.23722i	0.200945	+	0.0538431i
$529$	11.6074			0.504671
$530$	18.1119			0.786729
$531$	−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
$535$	9.68015	−	2.59379i	0.418510	−	0.112139i
$536$	−9.06687	+	15.7043i	−0.391629	+	0.678322i
$537$	−6.05306	−	10.4842i	−0.261209	−	0.452427i
$538$	6.74428	+	6.74428i	0.290766	+	0.290766i
$539$	−19.3674	−	4.14769i	−0.834212	−	0.178653i
$540$	−2.61219	+	0.699933i	−0.112411	+	0.0301203i
$541$	−26.5160	+	7.10493i	−1.14001	+	0.305465i	−0.778955	−	0.627080i	$-0.784250\pi$
$541$	−26.5160	+	7.10493i	−1.14001	+	0.305465i	−0.361055	+	0.932545i	$0.617583\pi$
$542$		−	3.03486i		−	0.130358i
$543$	−10.3742	−	5.98956i	−0.445200	−	0.257036i
$544$	−26.2204	+	26.2204i	−1.12419	+	1.12419i
$545$	−13.0194			−0.557691
$546$	12.2590	+	16.9791i	0.524636	+	0.726640i
$547$	−46.7525			−1.99899			−0.999495	−	0.0317618i	$-0.989888\pi$
$547$	−46.7525			−1.99899			−0.999495	+	0.0317618i	$0.989888\pi$
$548$	32.3409	−	32.3409i	1.38153	−	1.38153i
$549$	11.1799	+	6.45472i	0.477147	+	0.275481i
$550$			25.3439i			1.08067i
$551$	−4.21623	+	1.12974i	−0.179618	+	0.0481284i
$552$	5.86547	−	1.57165i	0.249651	−	0.0668938i
$553$	−9.39271	−	8.92703i	−0.399418	−	0.379616i
$554$	−27.3581	−	27.3581i	−1.16233	−	1.16233i
$555$	2.52783	+	4.37834i	0.107301	+	0.185850i
$556$	−22.8966	+	39.6580i	−0.971030	+	1.68187i
$557$	−22.5933	+	6.05387i	−0.957311	+	0.256511i	−0.703462	−	0.710733i	$-0.748363\pi$
$557$	−22.5933	+	6.05387i	−0.957311	+	0.256511i	−0.253849	+	0.967244i	$0.581697\pi$
$558$	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
$562$	−2.25188			−0.0949896
$563$	−35.9933			−1.51694			−0.758468	−	0.651710i	$-0.774052\pi$
$563$	−35.9933			−1.51694			−0.758468	+	0.651710i	$0.774052\pi$
$564$	25.6630	+	6.87639i	1.08061	+	0.289548i
$565$	0.443899	−	1.65665i	0.0186750	−	0.0696959i
$566$	6.42512	+	23.9789i	0.270068	+	1.00791i
$567$	1.91776	+	1.82268i	0.0805385	+	0.0765456i
$568$	−0.717568	+	1.24286i	−0.0301085	+	0.0521495i
$569$		−	1.80622i		−	0.0757209i	−0.999283	−	0.0378604i	$-0.987946\pi$
$569$		−	1.80622i		−	0.0757209i	0.999283	−	0.0378604i	$-0.0120542\pi$
$570$	−0.242112	−	0.903575i	−0.0101410	−	0.0378466i
$571$	−10.6308	+	6.13767i	−0.444883	+	0.256853i	−0.705667	−	0.708544i	$-0.749352\pi$
$571$	−10.6308	+	6.13767i	−0.444883	+	0.256853i	0.260784	+	0.965397i	$0.416019\pi$
$572$	21.8312	+	18.7292i	0.912807	+	0.783109i
$573$			7.93591i			0.331528i
$574$	24.3304	−	7.18673i	1.01553	−	0.299968i
$575$	−6.88562	−	11.9262i	−0.287150	−	0.497359i
$576$	10.9660	−	6.33124i	0.456918	−	0.263801i
$577$	1.00503	−	3.75081i	0.0418398	−	0.156148i	−0.941845	−	0.336046i	$-0.890910\pi$
$577$	1.00503	−	3.75081i	0.0418398	−	0.156148i	0.983685	+	0.179898i	$0.0575768\pi$
$578$	13.5877	−	13.5877i	0.565173	−	0.565173i
$579$	−0.843813	−	0.226099i	−0.0350677	−	0.00939635i
$580$	−18.7886	+	18.7886i	−0.780155	+	0.780155i
$581$	9.14983	−	5.59739i	0.379599	−	0.232219i
$582$	−9.14376	+	5.27915i	−0.379021	+	0.218828i
$583$	−17.2095	−	17.2095i	−0.712746	−	0.712746i
$584$	3.53771	+	6.12749i	0.146391	+	0.253557i
$585$	3.39897	+	0.637740i	0.140530	+	0.0263673i
$586$	4.34296	+	2.50741i	0.179406	+	0.103580i
$587$	1.54556	−	5.76812i	0.0637922	−	0.238076i	−0.926667	−	0.375884i	$-0.877339\pi$
$587$	1.54556	−	5.76812i	0.0637922	−	0.238076i	0.990459	+	0.137808i	$0.0440058\pi$
$588$	−16.5689	+	10.7239i	−0.683288	+	0.442246i
$589$	1.28057	+	0.739335i	0.0527648	+	0.0304638i
$590$	−1.59763	−	5.96243i	−0.0657734	−	0.245470i
$591$	11.6777	+	11.6777i	0.480357	+	0.480357i
$592$	−6.29674	−	6.29674i	−0.258794	−	0.258794i
$593$	3.44195	+	12.8455i	0.141344	+	0.527502i	0.999891	+	0.0147677i	$0.00470087\pi$
$593$	3.44195	+	12.8455i	0.141344	+	0.527502i	−0.858547	+	0.512735i	$0.828632\pi$
$594$	5.37950	+	3.10586i	0.220724	+	0.127435i
$595$	−0.327248	−	12.8739i	−0.0134159	−	0.527780i
$596$	−9.25519	+	34.5408i	−0.379107	+	1.41485i
$597$	19.0398	+	10.9926i	0.779246	+	0.449898i
$598$	−26.2585	−	4.92682i	−1.07379	−	0.201473i
$599$	9.76222	+	16.9087i	0.398873	+	0.690869i	0.993587	−	0.113069i	$-0.0360680\pi$
$599$	9.76222	+	16.9087i	0.398873	+	0.690869i	−0.594714	+	0.803937i	$0.702735\pi$
$600$	5.19034	+	5.19034i	0.211895	+	0.211895i
$601$	−38.3090	+	22.1177i	−1.56266	+	0.902201i	−0.565671	+	0.824631i	$0.691383\pi$
$601$	−38.3090	+	22.1177i	−1.56266	+	0.902201i	−0.996987	+	0.0775697i	$0.975284\pi$
$602$	0.439679	+	17.2970i	0.0179200	+	0.704972i
$603$	7.12728	−	7.12728i	0.290245	−	0.290245i
$604$	−54.4679	−	14.5946i	−2.21627	−	0.593847i
$605$	2.03054	−	2.03054i	0.0825532	−	0.0825532i
$606$	4.36687	−	16.2974i	0.177392	−	0.662036i
$607$	−27.2066	+	15.7077i	−1.10428	+	0.637557i	−0.937342	−	0.348411i	$-0.886721\pi$
$607$	−27.2066	+	15.7077i	−1.10428	+	0.637557i	−0.166938	+	0.985967i	$0.553388\pi$
$608$	1.62308	+	2.81126i	0.0658247	+	0.114012i
$609$	25.2726	+	6.08789i	1.02410	+	0.246694i
$610$			27.1830i			1.10061i
$611$	−25.7862	−	22.1223i	−1.04320	−	0.894974i
$612$	−12.3913	+	7.15412i	−0.500888	+	0.289188i
$613$	8.67343	+	32.3697i	0.350317	+	1.30740i	0.886277	+	0.463156i	$0.153283\pi$
$613$	8.67343	+	32.3697i	0.350317	+	1.30740i	−0.535960	+	0.844243i	$0.680050\pi$
$614$		−	51.3013i		−	2.07035i
$615$	2.09471	−	3.62814i	0.0844667	−	0.146301i
$616$	−9.27834	+	9.76234i	−0.373835	+	0.393336i
$617$	−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	$0.975697\pi$
$618$	3.28581	−	12.2628i	0.132175	−	0.493283i
$619$	8.21409	+	2.20096i	0.330152	+	0.0884640i	0.420088	−	0.907484i	$-0.361999\pi$
$619$	8.21409	+	2.20096i	0.330152	+	0.0884640i	−0.0899353	+	0.995948i	$0.528666\pi$
$620$	9.00119			0.361497
$621$	−3.37529			−0.135446
$622$	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
$626$	−18.1353	+	4.85933i	−0.724831	+	0.194218i
$627$	−0.628509	+	1.08861i	−0.0251002	+	0.0434749i
$628$	−4.33476	−	7.50803i	−0.172976	−	0.299603i
$629$	18.9143	+	18.9143i	0.754161	+	0.754161i
$630$	−1.30469	+	5.41614i	−0.0519801	+	0.215784i
$631$	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	$0.152373\pi$
$632$	−8.51114	+	2.28055i	−0.338555	+	0.0907155i
$633$			22.9805i			0.913391i
$634$	−61.8045	−	35.6828i	−2.45457	−	1.41715i
$635$	3.25131	−	3.25131i	0.129024	−	0.129024i
$636$	−24.2519			−0.961649
$637$	25.0351	−	3.20063i	0.991927	−	0.126814i
$638$	61.0324			2.41630
$639$	0.564066	−	0.564066i	0.0223141	−	0.0223141i
$640$	10.9516	+	6.32292i	0.432900	+	0.249935i
$641$		−	20.3828i		−	0.805072i	−0.915404	−	0.402536i	$-0.868129\pi$
$641$		−	20.3828i		−	0.805072i	0.915404	−	0.402536i	$-0.131871\pi$
$642$	−22.1562	+	5.93673i	−0.874434	+	0.234304i
$643$	2.81166	−	0.753382i	0.110881	−	0.0297105i	−0.202952	−	0.979189i	$-0.565053\pi$
$643$	2.81166	−	0.753382i	0.110881	−	0.0297105i	0.313833	+	0.949478i	$0.398387\pi$
$644$	5.89658	−	24.4784i	0.232358	−	0.964584i
$645$	2.02038	+	2.02038i	0.0795526	+	0.0795526i
$646$	−2.47466	−	4.28625i	−0.0973644	−	0.168640i
$647$	−7.89093	+	13.6675i	−0.310224	+	0.537324i	−0.978411	−	0.206669i	$-0.933738\pi$
$647$	−7.89093	+	13.6675i	−0.310224	+	0.537324i	0.668186	+	0.743994i	$0.267071\pi$
$648$	1.73777	−	0.465634i	0.0682660	−	0.0182918i
$649$	−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
$653$	37.0166			1.44857			0.724287	−	0.689499i	$-0.242169\pi$
$653$	37.0166			1.44857			0.724287	+	0.689499i	$0.242169\pi$
$654$	29.7992			1.16524
$655$	14.6255	+	3.91888i	0.571464	+	0.153123i
$656$	−1.90986	+	7.12769i	−0.0745674	+	0.278289i
$657$	−1.01789	−	3.79881i	−0.0397116	−	0.148206i
$658$	37.7055	−	39.6724i	1.46991	−	1.54659i
$659$	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	$0.157976\pi$
$660$			7.65192i			0.297851i
$661$	7.16393	+	26.7362i	0.278645	+	1.03992i	0.953359	+	0.301837i	$0.0976000\pi$
$661$	7.16393	+	26.7362i	0.278645	+	1.03992i	−0.674715	+	0.738079i	$0.735733\pi$
$662$	47.9002	−	27.6552i	1.86169	−	1.07485i
$663$	18.2440	−	1.39524i	0.708538	−	0.0541867i
$664$		−	7.29362i		−	0.283047i
$665$	−1.09602	−	0.264020i	−0.0425020	−	0.0102383i
$666$	−5.78577	−	10.0212i	−0.224194	−	0.388315i
$667$	−28.7204	+	16.5817i	−1.11206	+	0.642048i
$668$	17.0825	−	63.7528i	0.660942	−	2.46667i
$669$	−16.3253	+	16.3253i	−0.631174	+	0.631174i
$670$	20.5009	+	5.49319i	0.792018	+	0.212220i
$671$	25.8287	−	25.8287i	0.997107	−	0.997107i
$672$	−0.491263	−	19.3263i	−0.0189509	−	0.745528i
$673$	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	$0.270398\pi$
$674$	28.4499	+	28.4499i	1.09585	+	1.09585i
$675$	−2.04001	−	3.53340i	−0.0785201	−	0.136001i
$676$	−34.1605	−	13.2867i	−1.31387	−	0.511025i
$677$	−42.6758	−	24.6389i	−1.64016	−	0.946949i	−0.980774	−	0.195148i	$-0.937481\pi$
$677$	−42.6758	−	24.6389i	−1.64016	−	0.946949i	−0.659390	−	0.751801i	$-0.729185\pi$
$678$	−1.01601	+	3.79178i	−0.0390195	+	0.145623i
$679$	0.323346	+	12.7204i	0.0124089	+	0.488166i
$680$	−7.58371	−	4.37846i	−0.290822	−	0.167906i
$681$	4.28502	+	15.9919i	0.164202	+	0.612811i
$682$	−14.6196	−	14.6196i	−0.559814	−	0.559814i
$683$	0.298763	+	0.298763i	0.0114319	+	0.0114319i	0.712800	−	0.701368i	$-0.247427\pi$
$683$	0.298763	+	0.298763i	0.0114319	+	0.0114319i	−0.701368	+	0.712800i	$0.747427\pi$
$684$	0.324190	+	1.20989i	0.0123957	+	0.0462614i
$685$	−13.4745	−	7.77953i	−0.514836	−	0.297241i
$686$	3.09685	+	40.5401i	0.118238	+	1.54783i
$687$	1.94891	−	7.27341i	0.0743554	−	0.277498i
$688$	−4.35844	−	2.51635i	−0.166164	−	0.0959349i
$689$	27.9624	+	13.4134i	1.06528	+	0.511008i
$690$	−3.55361	−	6.15504i	−0.135284	−	0.234318i
$691$	−21.1989	−	21.1989i	−0.806444	−	0.806444i	0.177650	−	0.984094i	$-0.443151\pi$
$691$	−21.1989	−	21.1989i	−0.806444	−	0.806444i	−0.984094	+	0.177650i	$0.943151\pi$
$692$	−40.6922	+	23.4936i	−1.54688	+	0.893094i
$693$	6.38600	−	3.90662i	0.242584	−	0.148400i
$694$	−28.4207	+	28.4207i	−1.07884	+	1.07884i
$695$	15.0474	+	4.03193i	0.570780	+	0.152940i
$696$	12.4992	−	12.4992i	0.473782	−	0.473782i
$697$	5.73687	−	21.4103i	0.217300	−	0.810973i
$698$	47.6985	−	27.5387i	1.80541	−	1.04236i
$699$	−2.38406	−	4.12931i	−0.0901734	−	0.156185i
$700$	29.1890	−	8.62185i	1.10324	−	0.325875i
$701$			35.9119i			1.35637i	0.734889	+	0.678187i	$0.237234\pi$
$701$			35.9119i			1.35637i	−0.734889	+	0.678187i	$0.762766\pi$
$702$	−7.77964	−	1.45968i	−0.293624	−	0.0550919i
$703$	2.02793	−	1.17082i	0.0764847	−	0.0441584i
$704$	−9.27310	−	34.6077i	−0.349493	−	1.30433i
$705$		−	9.03818i		−	0.340398i
$706$	25.0828	−	43.4447i	0.944005	−	1.63506i
$707$	−14.7390	−	14.0083i	−0.554318	−	0.526835i
$708$	2.13923	+	7.98373i	0.0803973	+	0.300047i
$709$	9.67773	−	36.1178i	0.363455	−	1.35643i	−0.506049	−	0.862505i	$-0.668894\pi$
$709$	9.67773	−	36.1178i	0.363455	−	1.35643i	0.869503	−	0.493927i	$-0.164439\pi$
$710$	1.62248	+	0.434741i	0.0608904	+	0.0163155i
$711$	4.89774			0.183679
$712$	−18.7942			−0.704341
$713$	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
$717$	−4.49587	+	1.20467i	−0.167901	+	0.0449890i
$718$	−24.4173	+	42.2920i	−0.911245	+	1.57832i
$719$	14.8053	+	25.6436i	0.552145	+	0.956344i	0.998120	+	0.0612978i	$0.0195239\pi$
$719$	14.8053	+	25.6436i	0.552145	+	0.956344i	−0.445974	+	0.895046i	$0.647143\pi$
$720$	−1.14581	−	1.14581i	−0.0427019	−	0.0427019i
$721$	−11.0902	−	10.5404i	−0.413022	−	0.392545i
$722$	39.8716	−	10.6836i	1.48387	−	0.397601i
$723$	−6.32909	+	1.69587i	−0.235381	+	0.0630702i
$724$			33.7751i			1.25524i
$725$	−34.7170	−	20.0439i	−1.28936	−	0.744412i
$726$	−4.64755	+	4.64755i	−0.172487	+	0.172487i
$727$	49.3431			1.83004			0.915018	−	0.403414i	$-0.132176\pi$
$727$	49.3431			1.83004			0.915018	+	0.403414i	$0.132176\pi$
$728$	7.02709	−	15.6575i	0.260441	−	0.580304i
$729$	−1.00000			−0.0370370
$730$	5.85569	−	5.85569i	0.216729	−	0.216729i
$731$	13.0920	+	7.55866i	0.484225	+	0.279567i
$732$		−	36.3981i		−	1.34531i
$733$	33.3610	−	8.93904i	1.23221	−	0.330171i	0.416773	−	0.909010i	$-0.363161\pi$
$733$	33.3610	−	8.93904i	1.23221	−	0.330171i	0.815442	+	0.578839i	$0.196494\pi$
$734$	−34.5736	+	9.26398i	−1.27614	+	0.341940i
$735$	4.98265	+	4.50024i	0.183788	+	0.165994i
$736$	17.4395	+	17.4395i	0.642830	+	0.642830i
$737$	−14.2600	−	24.6990i	−0.525274	−	0.909801i
$738$	−4.79441	+	8.30417i	−0.176485	+	0.305681i
$739$	−4.94223	+	1.32427i	−0.181803	+	0.0487139i	−0.348572	−	0.937282i	$-0.613333\pi$
$739$	−4.94223	+	1.32427i	−0.181803	+	0.0487139i	0.166769	+	0.985996i	$0.446667\pi$
$740$	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	$0.633036\pi$
$744$	−5.98809			−0.219534
$745$	12.1648			0.445685
$746$	74.4395	+	19.9460i	2.72542	+	0.730275i
$747$	−1.04928	+	3.91596i	−0.0383911	+	0.143278i
$748$	10.4783	+	39.1057i	0.383126	+	1.42985i
$749$	−6.47392	+	26.8751i	−0.236552	+	0.981996i
$750$	9.55975	−	16.5580i	0.349073	−	0.604611i
$751$			10.9271i			0.398734i	0.979925	+	0.199367i	$0.0638885\pi$
$751$			10.9271i			0.398734i	−0.979925	+	0.199367i	$0.936111\pi$
$752$	4.12030	+	15.3772i	0.150252	+	0.560748i
$753$	−16.8755	+	9.74305i	−0.614976	+	0.355057i
$754$	−73.3681	+	25.7986i	−2.67191	+	0.939528i
$755$			19.1829i			0.698136i
$756$	1.74699	−	7.25224i	0.0635372	−	0.263761i
$757$	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	$0.746957\pi$
$758$	44.6920	−	25.8029i	1.62329	−	0.937205i
$759$	−2.47182	+	9.22497i	−0.0897215	+	0.334845i
$760$	−0.542067	+	0.542067i	−0.0196628	+	0.0196628i
$761$	−1.48997	−	0.399237i	−0.0540114	−	0.0144723i	0.231712	−	0.972784i	$-0.425567\pi$
$761$	−1.48997	−	0.399237i	−0.0540114	−	0.0144723i	−0.285724	+	0.958312i	$0.592234\pi$
$762$	−7.44168	+	7.44168i	−0.269584	+	0.269584i
$763$	17.1604	−	31.5479i	0.621248	−	1.14211i
$764$	19.3776	−	11.1876i	0.701056	−	0.404755i
$765$	3.44182	+	3.44182i	0.124439	+	0.124439i
$766$	−9.79149	−	16.9594i	−0.353781	−	0.612766i
$767$	1.94915	−	10.3884i	0.0703798	−	0.375104i
$768$	−3.13427	−	1.80957i	−0.113098	−	0.0652972i
$769$	3.95534	−	14.7615i	0.142633	−	0.532315i	−0.857216	−	0.514957i	$-0.827808\pi$
$769$	3.95534	−	14.7615i	0.142633	−	0.532315i	0.999849	−	0.0173579i	$-0.00552546\pi$
$770$	13.8473	+	7.53223i	0.499024	+	0.271443i
$771$	6.75553	+	3.90031i	0.243294	+	0.140466i
$772$	0.637485	+	2.37913i	0.0229436	+	0.0856267i
$773$	−10.0488	−	10.0488i	−0.361429	−	0.361429i	0.502910	−	0.864339i	$-0.332263\pi$
$773$	−10.0488	−	10.0488i	−0.361429	−	0.361429i	−0.864339	+	0.502910i	$0.832263\pi$
$774$	−4.62430	−	4.62430i	−0.166217	−	0.166217i
$775$	3.51479	+	13.1174i	0.126255	+	0.471189i
$776$	7.49329	+	4.32625i	0.268993	+	0.155303i
$777$	−13.9412	+	0.354376i	−0.500136	+	0.0127132i
$778$	9.01634	−	33.6495i	0.323252	−	1.20639i
$779$	−1.68045	−	0.970210i	−0.0602085	−	0.0347614i
$780$	−3.23449	−	9.19851i	−0.115813	−	0.329359i
$781$	−1.12856	−	1.95473i	−0.0403831	−	0.0699456i
$782$	−26.5895	−	26.5895i	−0.950840	−	0.950840i
$783$	−8.50903	+	4.91269i	−0.304088	+	0.175565i
$784$	−10.5288	−	5.38503i	−0.376029	−	0.192323i
$785$	−2.08544	+	2.08544i	−0.0744325	+	0.0744325i
$786$	−33.4751	−	8.96963i	−1.19402	−	0.319936i
$787$	12.7726	−	12.7726i	0.455294	−	0.455294i	−0.441813	−	0.897107i	$-0.645665\pi$
$787$	12.7726	−	12.7726i	0.455294	−	0.455294i	0.897107	+	0.441813i	$0.145665\pi$
$788$	12.0515	−	44.9768i	0.429317	−	1.60223i
$789$	−13.9516	+	8.05497i	−0.496691	+	0.286765i
$790$	5.15650	+	8.93132i	0.183460	+	0.317762i
$791$	3.42921	+	3.25920i	0.121929	+	0.115884i
$792$		−	5.09048i		−	0.180882i
$793$	−20.1313	+	41.9670i	−0.714883	+	1.49029i
$794$	−65.3309	+	37.7188i	−2.31851	+	1.33859i
$795$	2.13530	+	7.96904i	0.0757312	+	0.282633i
$796$		−	61.9873i		−	2.19708i
$797$	19.4574	−	33.7012i	0.689215	−	1.19376i	−0.282877	−	0.959156i	$-0.591289\pi$
$797$	19.4574	−	33.7012i	0.689215	−	1.19376i	0.972092	−	0.234600i	$-0.0753780\pi$
$798$	2.50861	+	0.604296i	0.0888037	+	0.0213918i
$799$	−12.3767	−	46.1903i	−0.437855	−	1.63410i
$800$	−7.71611	+	28.7969i	−0.272806	+	1.01812i
$801$	10.0906	+	2.70378i	0.356535	+	0.0955333i
$802$	−38.9855			−1.37663
$803$	−11.1279			−0.392696
$804$	−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
$808$	−13.3557	+	3.57864i	−0.469850	+	0.125896i
$809$	−18.7088	+	32.4046i	−0.657766	+	1.13928i	0.323426	+	0.946253i	$0.395165\pi$
$809$	−18.7088	+	32.4046i	−0.657766	+	1.13928i	−0.981193	+	0.193031i	$0.938168\pi$
$810$	−1.05283	−	1.82356i	−0.0369928	−	0.0640734i
$811$	−16.1489	−	16.1489i	−0.567064	−	0.567064i	0.364241	−	0.931305i	$-0.381329\pi$
$811$	−16.1489	−	16.1489i	−0.567064	−	0.567064i	−0.931305	+	0.364241i	$0.881329\pi$
$812$	−20.7629	−	70.2919i	−0.728634	−	2.46676i
$813$	1.33531	−	0.357794i	0.0468313	−	0.0125484i
$814$	−31.6261	+	8.47418i	−1.10849	+	0.297020i
$815$		−	20.3554i		−	0.713018i
$816$	−7.42481	−	4.28672i	−0.259920	−	0.150065i
$817$	0.935786	−	0.935786i	0.0327390	−	0.0327390i
$818$	−23.9065			−0.835870
$819$	−6.02538	+	7.39559i	−0.210544	+	0.258423i
$820$	−11.8120			−0.412494
$821$	−9.63196	+	9.63196i	−0.336158	+	0.336158i	−0.854919	−	0.518761i	$-0.826393\pi$
$821$	−9.63196	+	9.63196i	−0.336158	+	0.336158i	0.518761	+	0.854919i	$0.326393\pi$
$822$	30.8409	+	17.8060i	1.07570	+	0.621055i
$823$		−	24.9602i		−	0.870058i	−0.900416	−	0.435029i	$-0.856738\pi$
$823$		−	24.9602i		−	0.870058i	0.900416	−	0.435029i	$-0.143262\pi$
$824$	−10.0493	+	2.69271i	−0.350085	+	0.0938051i
$825$	−11.1511	+	2.98792i	−0.388231	+	0.104026i
$826$	16.5536	+	3.98758i	0.575973	+	0.138745i
$827$	−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	$0.785948\pi$
$828$	4.75831	+	8.24163i	0.165363	+	0.286416i
$829$	7.02010	−	12.1592i	0.243818	−	0.422306i	−0.717980	−	0.696063i	$-0.754933\pi$
$829$	7.02010	−	12.1592i	0.243818	−	0.422306i	0.961799	+	0.273758i	$0.0882666\pi$
$830$	−8.24571	+	2.20943i	−0.286213	+	0.0766904i
$831$	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
$835$	−22.4529			−0.777015
$836$	3.54416			0.122577
$837$	3.21502	+	0.861462i	0.111127	+	0.0297765i
$838$	17.6329	−	65.8070i	0.609120	−	2.27327i
$839$	8.57855	+	32.0156i	0.296165	+	1.10530i	0.940288	+	0.340380i	$0.110556\pi$
$839$	8.57855	+	32.0156i	0.296165	+	1.10530i	−0.644123	+	0.764922i	$0.722778\pi$
$840$	4.37846	−	1.29331i	0.151071	−	0.0446235i
$841$	−33.7691	+	58.4898i	−1.16445	+	2.01689i
$842$			79.6717i			2.74567i
$843$	−0.265485	−	0.990803i	−0.00914378	−	0.0341251i
$844$	56.1127	−	32.3967i	1.93148	−	1.11514i
$845$	−1.35820	+	12.3948i	−0.0467237	+	0.426395i
$846$			20.6868i			0.711227i
$847$	2.24390	+	7.59665i	0.0771014	+	0.261024i
$848$	−7.26581	−	12.5847i	−0.249509	−	0.432162i
$849$	−9.79298	+	5.65398i	−0.336094	+	0.194044i
$850$	11.7645	−	43.9058i	0.403520	−	1.50596i
$851$	12.5801	−	12.5801i	0.431242	−	0.431242i
$852$	−2.17250	−	0.582121i	−0.0744287	−	0.0199431i
$853$	9.18368	−	9.18368i	0.314443	−	0.314443i	−0.532185	−	0.846628i	$-0.678629\pi$
$853$	9.18368	−	9.18368i	0.314443	−	0.314443i	0.846628	+	0.532185i	$0.178629\pi$
$854$	−65.8681	−	35.8288i	−2.25396	−	1.22604i
$855$	0.369020	−	0.213054i	0.0126202	−	0.00728629i
$856$	13.2918	+	13.2918i	0.454304	+	0.454304i
$857$	17.6781	+	30.6194i	0.603873	+	1.04594i	0.992229	+	0.124429i	$0.0397098\pi$
$857$	17.6781	+	30.6194i	0.603873	+	1.04594i	−0.388356	+	0.921510i	$0.626957\pi$
$858$	−9.68669	+	20.1935i	−0.330698	+	0.689395i
$859$	20.5980	+	11.8923i	0.702795	+	0.405759i	0.808388	−	0.588651i	$-0.200341\pi$
$859$	20.5980	+	11.8923i	0.702795	+	0.405759i	−0.105593	+	0.994409i	$0.533674\pi$
$860$	2.08505	−	7.78152i	0.0710997	−	0.265348i
$861$	6.03053	+	9.85787i	0.205520	+	0.335955i
$862$	−0.378228	−	0.218370i	−0.0128825	−	0.00743771i
$863$	7.41873	+	27.6871i	0.252537	+	0.942480i	0.969444	+	0.245311i	$0.0788902\pi$
$863$	7.41873	+	27.6871i	0.252537	+	0.942480i	−0.716908	+	0.697168i	$0.754443\pi$
$864$	5.16683	+	5.16683i	0.175779	+	0.175779i
$865$	11.3027	+	11.3027i	0.384303	+	0.384303i
$866$	−16.9089	−	63.1048i	−0.574587	−	2.14439i
$867$	7.58037	+	4.37653i	0.257443	+	0.148635i
$868$	−11.8641	+	21.8111i	−0.402695	+	0.740318i
$869$	3.58676	−	13.3860i	0.121672	−	0.454088i
$870$	−17.9172	−	10.3445i	−0.607449	−	0.350711i
$871$	27.5825	+	23.6634i	0.934598	+	0.801804i
$872$	−12.2102	−	21.1486i	−0.413488	−	0.716183i
$873$	−3.40078	−	3.40078i	−0.115099	−	0.115099i
$874$	−2.85084	+	1.64593i	−0.0964312	+	0.0556746i
$875$	−12.0245	−	19.6559i	−0.406502	−	0.664492i
$876$	−7.84080	+	7.84080i	−0.264916	+	0.264916i
$877$	19.6352	+	5.26123i	0.663033	+	0.177659i	0.574614	−	0.818424i	$-0.305152\pi$
$877$	19.6352	+	5.26123i	0.663033	+	0.177659i	0.0884184	+	0.996083i	$0.471819\pi$
$878$	58.6096	−	58.6096i	1.97798	−	1.97798i
$879$	−0.591222	+	2.20647i	−0.0199414	+	0.0744225i
$880$	−3.97072	+	2.29250i	−0.133853	+	0.0772801i
$881$	−17.8814	−	30.9716i	−0.602441	−	1.04346i	−0.992450	−	0.122648i	$-0.960861\pi$
$881$	−17.8814	−	30.9716i	−0.602441	−	1.04346i	0.390009	−	0.920811i	$-0.372472\pi$
$882$	−11.4044	−	10.3002i	−0.384006	−	0.346827i
$883$		−	12.9519i		−	0.435865i	−0.975964	−	0.217932i	$-0.930069\pi$
$883$		−	12.9519i		−	0.435865i	0.975964	−	0.217932i	$-0.0699312\pi$
$884$	−29.1263	−	42.5804i	−0.979623	−	1.43213i
$885$	2.43506	−	1.40588i	0.0818536	−	0.0472582i
$886$	−15.5838	−	58.1595i	−0.523548	−	1.95391i
$887$			39.0095i			1.30981i	0.755711	+	0.654905i	$0.227291\pi$
$887$			39.0095i			1.30981i	−0.755711	+	0.654905i	$0.772709\pi$
$888$	−4.74142	+	8.21238i	−0.159112	+	0.275589i
$889$	3.59295	+	12.1638i	0.120504	+	0.407961i
$890$	5.69325	+	21.2475i	0.190838	+	0.712218i
$891$	−0.732330	+	2.73309i	−0.0245340	+	0.0915620i
$892$	62.8771	+	16.8479i	2.10528	+	0.564108i
$893$	−4.18624			−0.140087
$894$	−27.8431			−0.931214
$895$	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
$899$	31.5888	−	8.46420i	1.05355	−	0.282297i
$900$	−5.75181	+	9.96242i	−0.191727	+	0.332081i
$901$	21.8252	+	37.8023i	0.727102	+	1.25938i
$902$	19.1850	+	19.1850i	0.638789	+	0.638789i
$903$	−7.55866	+	2.23268i	−0.251537	+	0.0742990i
$904$	3.10736	−	0.832614i	0.103349	−	0.0276923i
$905$	11.0983	−	2.97378i	0.368920	−	0.0988519i
$906$		−	43.9062i		−	1.45869i
$907$	−14.2393	−	8.22105i	−0.472808	−	0.272976i	0.244607	−	0.969622i	$-0.421341\pi$
$907$	−14.2393	−	8.22105i	−0.472808	−	0.272976i	−0.717414	+	0.696647i	$0.754674\pi$
$908$	33.0075	−	33.0075i	1.09539	−	1.09539i
$909$	7.68552			0.254913
$910$	−19.8300	−	3.20132i	−0.657359	−	0.106123i
$911$	−13.9789			−0.463141			−0.231570	−	0.972818i	$-0.574386\pi$
$911$	−13.9789			−0.463141			−0.231570	+	0.972818i	$0.574386\pi$
$912$	−0.530709	+	0.530709i	−0.0175735	+	0.0175735i
$913$	9.93426	+	5.73555i	0.328776	+	0.189819i
$914$			28.4208i			0.940076i
$915$	−11.9602	+	3.20474i	−0.395393	+	0.105945i
$916$	−20.5074	+	5.49493i	−0.677583	+	0.181558i
$917$	−28.7732	+	30.2742i	−0.950176	+	0.999742i
$918$	−7.87771	−	7.87771i	−0.260003	−	0.260003i
$919$	9.76278	+	16.9096i	0.322044	+	0.557797i	0.980910	−	0.194464i	$-0.0622966\pi$
$919$	9.76278	+	16.9096i	0.322044	+	0.557797i	−0.658865	+	0.752261i	$0.728963\pi$
$920$	−2.91217	+	5.04403i	−0.0960116	+	0.166297i
$921$	22.5721	−	6.04817i	0.743775	−	0.199294i
$922$	−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
$926$	−42.7297			−1.40419
$927$	5.78290			0.189935
$928$	69.3478	+	18.5817i	2.27645	+	0.609974i
$929$	0.600618	−	2.24154i	0.0197057	−	0.0735425i	−0.955373	−	0.295403i	$-0.904546\pi$
$929$	0.600618	−	2.24154i	0.0197057	−	0.0735425i	0.975078	+	0.221860i	$0.0712129\pi$
$930$	1.81395	+	6.76976i	0.0594818	+	0.221989i
$931$	2.08438	−	2.30782i	0.0683130	−	0.0756359i
$932$	−6.72185	+	11.6426i	−0.220181	+	0.381365i
$933$			10.1251i			0.331481i
$934$	10.3511	+	38.6310i	0.338700	+	1.26405i
$935$	11.9273	−	6.88626i	0.390066	−	0.225205i
$936$	2.15176	+	6.11935i	0.0703324	+	0.200017i
$937$		−	18.7950i		−	0.614006i	−0.951709	−	0.307003i	$-0.900674\pi$
$937$		−	18.7950i		−	0.614006i	0.951709	−	0.307003i	$-0.0993262\pi$
$938$	−40.3322	+	42.4361i	−1.31689	+	1.38559i
$939$	−4.27611	−	7.40644i	−0.139546	−	0.241700i
$940$	−22.0690	+	12.7416i	−0.719813	+	0.415584i
$941$	6.59642	−	24.6182i	0.215037	−	0.802530i	−0.771116	−	0.636694i	$-0.780301\pi$
$941$	6.59642	−	24.6182i	0.215037	−	0.802530i	0.986153	−	0.165835i	$-0.0530320\pi$
$942$	4.77320	−	4.77320i	0.155519	−	0.155519i
$943$	−14.2403	−	3.81568i	−0.463728	−	0.124255i
$944$	−3.50200	+	3.50200i	−0.113980	+	0.113980i
$945$	−2.53686	+	0.0644856i	−0.0825242	+	0.00209772i
$946$	−16.0252	+	9.25213i	−0.521023	+	0.300813i
$947$	8.73075	+	8.73075i	0.283711	+	0.283711i	0.834587	−	0.550876i	$-0.185706\pi$
$947$	8.73075	+	8.73075i	0.283711	+	0.283711i	−0.550876	+	0.834587i	$0.685706\pi$
$948$	−6.90458	−	11.9591i	−0.224250	−	0.388413i
$949$	13.3771	−	4.70380i	0.434238	−	0.152692i
$950$	−3.44608	−	1.98959i	−0.111806	−	0.0645510i
$951$	8.41365	−	31.4002i	0.272831	−	1.01822i
$952$	20.6054	−	12.6053i	0.667825	−	0.408540i
$953$	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	$0.394023\pi$
$954$	−4.88732	−	18.2397i	−0.158233	−	0.590533i
$955$	−5.38233	−	5.38233i	−0.174168	−	0.174168i
$956$	9.27955	+	9.27955i	0.300122	+	0.300122i
$957$	7.19542	+	26.8537i	0.232595	+	0.868056i
$958$	−38.7527	−	22.3739i	−1.25204	−	0.722867i
$959$	36.6112	−	22.3968i	1.18224	−	0.723230i
$960$	−3.14343	+	11.7314i	−0.101454	+	0.378630i
$961$	17.2525	+	9.96076i	0.556534	+	0.321315i
$962$	34.4362	−	23.5554i	1.11027	−	0.759456i
$963$	−5.22420	−	9.04858i	−0.168348	−	0.291587i
$964$	13.0633	+	13.0633i	0.420741	+	0.420741i
$965$	0.725640	−	0.418949i	0.0233592	−	0.0134864i
$966$	19.5984	−	0.498179i	0.630568	−	0.0160287i
$967$	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	$-0.0806741\pi$
$968$	5.20272	+	1.39406i	0.167222	+	0.0448069i
$969$	1.59416	−	1.59416i	0.0512116	−	0.0512116i
$970$	2.62107	−	9.78197i	0.0841575	−	0.314080i
$971$	5.31932	−	3.07111i	0.170705	−	0.0985567i	−0.412213	−	0.911087i	$-0.635244\pi$
$971$	5.31932	−	3.07111i	0.170705	−	0.0985567i	0.582918	+	0.812531i	$0.301911\pi$
$972$	1.40975	+	2.44176i	0.0452177	+	0.0783194i
$973$	−29.6033	+	31.1475i	−0.949038	+	0.998544i
$974$		−	10.7616i		−	0.344825i
$975$	12.1419	−	8.30542i	0.388852	−	0.265986i
$976$	18.8877	−	10.9048i	0.604580	−	0.349054i
$977$	−11.0172	−	41.1167i	−0.352471	−	1.31544i	−0.883638	−	0.468171i	$-0.844913\pi$
$977$	−11.0172	−	41.1167i	−0.352471	−	1.31544i	0.531167	−	0.847267i	$-0.321754\pi$
$978$			46.5899i			1.48978i
$979$	14.7793	−	25.5986i	0.472350	−	0.818134i
$980$	3.96420	−	18.5106i	0.126632	−	0.591300i
$981$	3.51317	+	13.1113i	0.112167	+	0.418613i
$982$	−9.64510	+	35.9960i	−0.307788	+	1.14868i
$983$	−7.30592	−	1.95762i	−0.233023	−	0.0624383i	0.140418	−	0.990092i	$-0.455155\pi$
$983$	−7.30592	−	1.95762i	−0.233023	−	0.0624383i	−0.373441	+	0.927654i	$0.621822\pi$
$984$	7.85801			0.250504
$985$	−15.8402			−0.504712
$986$	−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
$990$	−5.75498	+	1.54204i	−0.182905	+	0.0490093i
$991$	−4.75483	+	8.23561i	−0.151042	+	0.261613i	−0.931611	−	0.363457i	$-0.881596\pi$
$991$	−4.75483	+	8.23561i	−0.151042	+	0.261613i	0.780569	+	0.625070i	$0.214930\pi$
$992$	−12.1604	−	21.0625i	−0.386095	−	0.668735i
$993$	17.8152	+	17.8152i	0.565348	+	0.565348i
$994$	−3.19196	+	3.35847i	−0.101243	+	0.106524i
$995$	−20.3687	+	5.45778i	−0.645732	+	0.173023i
$996$	11.0410	−	2.95844i	0.349849	−	0.0937417i
$997$		−	11.3440i		−	0.359269i	−0.983733	−	0.179634i	$-0.942509\pi$
$997$		−	11.3440i		−	0.359269i	0.983733	−	0.179634i	$-0.0574915\pi$
$998$	−42.0277	−	24.2647i	−1.33037	−	0.768087i
$999$	3.72714	−	3.72714i	0.117921	−	0.117921i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.9	✓	40	1.1	even	1	trivial
273.2.bt.b.241.9	yes	40	91.59	even	12	inner
273.2.cg.b.124.9	yes	40	13.7	odd	12
273.2.cg.b.262.9	yes	40	7.3	odd	6
819.2.et.d.145.2		40	3.2	odd	2
819.2.et.d.514.2		40	273.59	odd	12
819.2.gh.d.262.2		40	21.17	even	6
819.2.gh.d.397.2		40	39.20	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.55234 - 1.55234i) q^{2} +(0.866025 + 0.500000i) q^{3} -2.81950i q^{4} +(-0.926472 + 0.248247i) q^{5} +(2.12053 - 0.568195i) q^{6} +(0.619609 - 2.57218i) q^{7} +(-1.27214 - 1.27214i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.05283 + 1.82356i) q^{10} +(2.73309 - 0.732330i) 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} +1.68943 q^{16} -5.07475 q^{17} +(2.12053 + 0.568195i) q^{18} +(-0.114981 + 0.429116i) q^{19} +(0.699933 + 2.61219i) q^{20} +(1.82268 - 1.91776i) q^{21} +(3.10586 - 5.37950i) q^{22} +3.37529i q^{23} +(-0.465634 - 1.73777i) q^{24} +(-3.53340 + 2.04001i) q^{25} +(-1.45968 + 7.77964i) q^{26} +1.00000i q^{27} +(-7.25224 - 1.74699i) q^{28} +(4.91269 + 8.50903i) q^{29} +(-1.82356 + 1.05283i) q^{30} +(0.861462 - 3.21502i) q^{31} +(5.16683 - 5.16683i) q^{32} +(2.73309 + 0.732330i) q^{33} +(-7.87771 + 7.87771i) q^{34} +(0.0644856 + 2.53686i) q^{35} +(2.44176 - 1.40975i) q^{36} +(-3.72714 - 3.72714i) q^{37} +(0.487643 + 0.844623i) q^{38} +(-3.59505 + 0.274938i) q^{39} +(1.49440 + 0.862793i) q^{40} +(-1.13047 + 4.21899i) q^{41} +(-0.147596 - 5.80644i) q^{42} +(-2.57983 - 1.48947i) q^{43} +(-2.06480 - 7.70594i) q^{44} +(-0.678225 - 0.678225i) q^{45} +(5.23958 + 5.23958i) q^{46} +(2.43887 + 9.10199i) q^{47} +(1.46309 + 0.844715i) q^{48} +(-6.23217 - 3.18749i) q^{49} +(-2.31825 + 8.65182i) q^{50} +(-4.39486 - 2.53737i) q^{51} +(5.73945 + 8.39065i) q^{52} +(-4.30074 - 7.44911i) q^{53} +(1.55234 + 1.55234i) q^{54} +(-2.35033 + 1.35697i) q^{55} +(-4.06038 + 2.48393i) q^{56} +(-0.314135 + 0.314135i) q^{57} +(20.8350 + 5.58273i) q^{58} +(-2.07289 + 2.07289i) q^{59} +(-0.699933 + 2.61219i) q^{60} +(11.1799 - 6.45472i) q^{61} +(-3.65351 - 6.32807i) q^{62} +(2.53737 - 0.749491i) q^{63} -12.6625i q^{64} +(2.25178 - 2.62472i) q^{65} +(5.37950 - 3.10586i) q^{66} +(-2.60877 - 9.73605i) q^{67} +14.3082i q^{68} +(-1.68764 + 2.92308i) q^{69} +(4.03817 + 3.83796i) q^{70} +(-0.206463 - 0.770529i) q^{71} +(0.465634 - 1.73777i) q^{72} +(-3.79881 - 1.01789i) q^{73} -11.5715 q^{74} -4.08002 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} +(-1.56521 + 0.419397i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.79441 + 8.30417i) q^{82} +(2.86668 + 2.86668i) q^{83} +(-5.40713 - 5.13905i) q^{84} +(4.70161 - 1.25979i) q^{85} +(-6.31692 + 1.69261i) q^{86} +9.82538i q^{87} +(-4.40848 - 2.54524i) q^{88} +(7.38686 - 7.38686i) q^{89} -2.10567 q^{90} +(3.39208 + 8.91593i) q^{91} +9.51661 q^{92} +(2.35356 - 2.35356i) q^{93} +(17.9153 + 10.3434i) q^{94} -0.426108i q^{95} +(7.05803 - 1.89119i) q^{96} +(-4.64555 + 1.24477i) q^{97} +(-14.6225 + 4.72638i) q^{98} +(2.00076 + 2.00076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{7} + 20 q^{9} - 8 q^{11} + 24 q^{12} - 18 q^{14} - 64 q^{16} + 8 q^{17} - 14 q^{19} - 14 q^{20} - 8 q^{21} + 4 q^{22} + 18 q^{24} - 24 q^{25} - 10 q^{26} - 2 q^{28} + 8 q^{29} - 8 q^{31} + 10 q^{32}+ \cdots - 4 q^{99}+O(q^{100}) \) 40 * q - 2 * q^7 + 20 * q^9 - 8 * q^11 + 24 * q^12 - 18 * q^14 - 64 * q^16 + 8 * q^17 - 14 * q^19 - 14 * q^20 - 8 * q^21 + 4 * q^22 + 18 * q^24 - 24 * q^25 - 10 * q^26 - 2 * q^28 + 8 * q^29 - 8 * q^31 + 10 * q^32 - 8 * q^33 + 24 * q^34 - 22 * q^35 + 12 * q^37 + 8 * q^38 - 24 * q^39 - 30 * q^40 + 2 * q^41 + 6 * q^42 - 66 * q^43 + 28 * q^44 + 40 * q^46 + 10 * q^47 - 24 * q^48 + 38 * q^49 - 20 * q^50 + 40 * q^52 - 8 * q^53 + 42 * q^55 + 20 * q^56 - 14 * q^57 - 48 * q^58 - 26 * q^59 + 14 * q^60 - 12 * q^61 - 24 * q^62 - 4 * q^63 - 44 * q^65 - 18 * q^66 + 46 * q^67 - 4 * q^69 + 32 * q^70 - 6 * q^71 - 18 * q^72 + 10 * q^73 + 40 * q^74 + 48 * q^75 + 64 * q^76 - 24 * q^77 + 8 * q^78 + 34 * q^80 - 20 * q^81 + 24 * q^82 + 12 * q^83 + 20 * q^84 + 2 * q^85 + 12 * q^86 - 84 * q^88 - 16 * q^89 + 26 * q^91 + 236 * q^92 + 22 * q^93 + 30 * q^94 + 26 * q^96 + 62 * q^97 - 14 * q^98 - 4 * q^99

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