LMFDB - Embedded newform 357.2.u.a.127.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(43,357)] 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("357.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.u (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			127.8
Character	$\chi$	$=$	357.127
Dual form			357.2.u.a.253.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.84429 - 1.84429i) q^{2} +(-0.382683 + 0.923880i) q^{3} -4.80284i q^{4} +(-3.30307 - 1.36818i) q^{5} +(0.998125 + 2.40969i) q^{6} +(0.923880 - 0.382683i) q^{7} +(-5.16926 - 5.16926i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-8.61515 + 3.56851i) q^{10} +(-1.52650 - 3.68530i) q^{11} +(4.43724 + 1.83797i) q^{12} +3.65518i q^{13} +(0.998125 - 2.40969i) q^{14} +(2.52806 - 2.52806i) q^{15} -9.46158 q^{16} +(3.89777 - 1.34439i) q^{17} -2.60823 q^{18} +(5.47708 - 5.47708i) q^{19} +(-6.57113 + 15.8641i) q^{20} +1.00000i q^{21} +(-9.61209 - 3.98146i) q^{22} +(0.504796 + 1.21869i) q^{23} +(6.75396 - 2.79758i) q^{24} +(5.50283 + 5.50283i) q^{25} +(6.74122 + 6.74122i) q^{26} +(0.923880 - 0.382683i) q^{27} +(-1.83797 - 4.43724i) q^{28} +(3.24579 + 1.34445i) q^{29} -9.32497i q^{30} +(-3.83447 + 9.25723i) q^{31} +(-7.11142 + 7.11142i) q^{32} +3.98894 q^{33} +(4.70919 - 9.66808i) q^{34} -3.57522 q^{35} +(-3.39612 + 3.39612i) q^{36} +(2.89433 - 6.98754i) q^{37} -20.2027i q^{38} +(-3.37695 - 1.39878i) q^{39} +(10.0020 + 24.1469i) q^{40} +(-6.72787 + 2.78677i) q^{41} +(1.84429 + 1.84429i) q^{42} +(2.83064 + 2.83064i) q^{43} +(-17.6999 + 7.33154i) q^{44} +(1.36818 + 3.30307i) q^{45} +(3.17861 + 1.31662i) q^{46} -7.29870i q^{47} +(3.62079 - 8.74136i) q^{48} +(0.707107 - 0.707107i) q^{49} +20.2977 q^{50} +(-0.249561 + 4.11555i) q^{51} +17.5552 q^{52} +(2.23241 - 2.23241i) q^{53} +(0.998125 - 2.40969i) q^{54} +14.2613i q^{55} +(-6.75396 - 2.79758i) q^{56} +(2.96417 + 7.15615i) q^{57} +(8.46575 - 3.50663i) q^{58} +(1.11936 + 1.11936i) q^{59} +(-12.1419 - 12.1419i) q^{60} +(3.77713 - 1.56454i) q^{61} +(10.0012 + 24.1449i) q^{62} +(-0.923880 - 0.382683i) q^{63} +7.30793i q^{64} +(5.00093 - 12.0733i) q^{65} +(7.35677 - 7.35677i) q^{66} +2.11711 q^{67} +(-6.45687 - 18.7204i) q^{68} -1.31910 q^{69} +(-6.59375 + 6.59375i) q^{70} +(-1.03719 + 2.50401i) q^{71} +7.31043i q^{72} +(-4.39581 - 1.82080i) q^{73} +(-7.54907 - 18.2251i) q^{74} +(-7.18979 + 2.97811i) q^{75} +(-26.3055 - 26.3055i) q^{76} +(-2.82061 - 2.82061i) q^{77} +(-8.80783 + 3.64832i) q^{78} +(4.87513 + 11.7696i) q^{79} +(31.2523 + 12.9451i) q^{80} +1.00000i q^{81} +(-7.26853 + 17.5478i) q^{82} +(3.38316 - 3.38316i) q^{83} +4.80284 q^{84} +(-14.7140 - 0.892235i) q^{85} +10.4411 q^{86} +(-2.48422 + 2.48422i) q^{87} +(-11.1594 + 26.9411i) q^{88} +8.81120i q^{89} +(8.61515 + 3.56851i) q^{90} +(1.39878 + 3.37695i) q^{91} +(5.85315 - 2.42445i) q^{92} +(-7.08518 - 7.08518i) q^{93} +(-13.4609 - 13.4609i) q^{94} +(-25.5848 + 10.5976i) q^{95} +(-3.84867 - 9.29152i) q^{96} +(-10.2663 - 4.25244i) q^{97} -2.60823i q^{98} +(-1.52650 + 3.68530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{6} - 32 q^{10} + 8 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} + 8 q^{19} - 16 q^{20} - 8 q^{23} - 8 q^{24} + 24 q^{25} - 32 q^{26} + 24 q^{29} + 8 q^{31} - 40 q^{32} + 8 q^{33} - 8 q^{34} - 8 q^{35}+ \cdots + 96 q^{97}+O(q^{100}) $ 32 * q + 8 * q^6 - 32 * q^10 + 8 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 + 8 * q^19 - 16 * q^20 - 8 * q^23 - 8 * q^24 + 24 * q^25 - 32 * q^26 + 24 * q^29 + 8 * q^31 - 40 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^35 - 8 * q^36 + 72 * q^37 - 16 * q^39 + 40 * q^40 + 8 * q^41 - 32 * q^43 - 48 * q^44 + 8 * q^45 + 40 * q^46 + 32 * q^48 + 56 * q^50 - 16 * q^51 - 56 * q^53 + 8 * q^54 + 8 * q^56 + 16 * q^57 - 32 * q^58 - 48 * q^59 - 48 * q^60 + 8 * q^61 - 24 * q^62 + 16 * q^66 + 96 * q^67 - 16 * q^68 + 8 * q^69 - 16 * q^70 + 24 * q^71 - 24 * q^73 - 32 * q^74 - 16 * q^75 - 48 * q^76 - 24 * q^77 - 72 * q^78 - 48 * q^79 + 72 * q^80 + 96 * q^82 - 24 * q^83 + 24 * q^84 - 136 * q^85 - 32 * q^87 + 16 * q^88 + 32 * q^90 + 8 * q^91 + 136 * q^92 + 8 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 + 96 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$1$

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 $

$2$	1.84429	−	1.84429i	1.30411	−	1.30411i	0.378519	−	0.925593i	$-0.376433\pi$
$2$	1.84429	−	1.84429i	1.30411	−	1.30411i	0.925593	−	0.378519i	$-0.123567\pi$
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$4$		−	4.80284i		−	2.40142i
$5$	−3.30307	−	1.36818i	−1.47718	−	0.611867i	−0.508695	−	0.860947i	$-0.669872\pi$
$5$	−3.30307	−	1.36818i	−1.47718	−	0.611867i	−0.968483	+	0.249080i	$0.919872\pi$
$6$	0.998125	+	2.40969i	0.407483	+	0.983750i
$7$	0.923880	−	0.382683i	0.349194	−	0.144641i
$7$	0.923880	−	0.382683i	0.349194	−	0.144641i
$8$	−5.16926	−	5.16926i	−1.82761	−	1.82761i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	−8.61515	+	3.56851i	−2.72435	+	1.12846i
$11$	−1.52650	−	3.68530i	−0.460257	−	1.11116i	−0.968292	−	0.249823i	$-0.919628\pi$
$11$	−1.52650	−	3.68530i	−0.460257	−	1.11116i	0.508034	−	0.861337i	$-0.330372\pi$
$12$	4.43724	+	1.83797i	1.28092	+	0.530575i
$13$			3.65518i			1.01376i	0.862015	+	0.506882i	$0.169202\pi$
$13$			3.65518i			1.01376i	−0.862015	+	0.506882i	$0.830798\pi$
$14$	0.998125	−	2.40969i	0.266760	−	0.644016i
$15$	2.52806	−	2.52806i	0.652742	−	0.652742i
$16$	−9.46158			−2.36540
$17$	3.89777	−	1.34439i	0.945348	−	0.326062i
$17$	3.89777	−	1.34439i	0.945348	−	0.326062i
$18$	−2.60823			−0.614765
$19$	5.47708	−	5.47708i	1.25653	−	1.25653i	0.303789	−	0.952739i	$-0.401748\pi$
$19$	5.47708	−	5.47708i	1.25653	−	1.25653i	0.952739	−	0.303789i	$-0.0982519\pi$
$20$	−6.57113	+	15.8641i	−1.46935	+	3.54732i
$21$			1.00000i			0.218218i
$22$	−9.61209	−	3.98146i	−2.04930	−	0.848850i
$23$	0.504796	+	1.21869i	0.105257	+	0.254113i	0.967730	−	0.251991i	$-0.0810852\pi$
$23$	0.504796	+	1.21869i	0.105257	+	0.254113i	−0.862472	+	0.506104i	$0.831085\pi$
$24$	6.75396	−	2.79758i	1.37865	−	0.571054i
$25$	5.50283	+	5.50283i	1.10057	+	1.10057i
$26$	6.74122	+	6.74122i	1.32206	+	1.32206i
$27$	0.923880	−	0.382683i	0.177801	−	0.0736475i
$28$	−1.83797	−	4.43724i	−0.347343	−	0.838560i
$29$	3.24579	+	1.34445i	0.602728	+	0.249658i	0.663116	−	0.748517i	$-0.269234\pi$
$29$	3.24579	+	1.34445i	0.602728	+	0.249658i	−0.0603877	+	0.998175i	$0.519234\pi$
$30$		−	9.32497i		−	1.70250i
$31$	−3.83447	+	9.25723i	−0.688691	+	1.66265i	0.0587110	+	0.998275i	$0.481301\pi$
$31$	−3.83447	+	9.25723i	−0.688691	+	1.66265i	−0.747402	+	0.664372i	$0.768699\pi$
$32$	−7.11142	+	7.11142i	−1.25713	+	1.25713i
$33$	3.98894			0.694385
$34$	4.70919	−	9.66808i	0.807620	−	1.65806i
$35$	−3.57522			−0.604322
$36$	−3.39612	+	3.39612i	−0.566020	+	0.566020i
$37$	2.89433	−	6.98754i	0.475825	−	1.14874i	−0.485724	−	0.874112i	$-0.661444\pi$
$37$	2.89433	−	6.98754i	0.475825	−	1.14874i	0.961549	−	0.274632i	$-0.0885560\pi$
$38$		−	20.2027i		−	3.27731i
$39$	−3.37695	−	1.39878i	−0.540744	−	0.223984i
$40$	10.0020	+	24.1469i	1.58145	+	3.81796i
$41$	−6.72787	+	2.78677i	−1.05072	+	0.435221i	−0.840147	−	0.542358i	$-0.817532\pi$
$41$	−6.72787	+	2.78677i	−1.05072	+	0.435221i	−0.210569	+	0.977579i	$0.567532\pi$
$42$	1.84429	+	1.84429i	0.284581	+	0.284581i
$43$	2.83064	+	2.83064i	0.431668	+	0.431668i	0.889196	−	0.457527i	$-0.151265\pi$
$43$	2.83064	+	2.83064i	0.431668	+	0.431668i	−0.457527	+	0.889196i	$0.651265\pi$
$44$	−17.6999	+	7.33154i	−2.66836	+	1.10527i
$45$	1.36818	+	3.30307i	0.203956	+	0.492393i
$46$	3.17861	+	1.31662i	0.468660	+	0.194125i
$47$		−	7.29870i		−	1.06462i	−0.846548	−	0.532312i	$-0.821323\pi$
$47$		−	7.29870i		−	1.06462i	0.846548	−	0.532312i	$-0.178677\pi$
$48$	3.62079	−	8.74136i	0.522616	−	1.26171i
$49$	0.707107	−	0.707107i	0.101015	−	0.101015i
$50$	20.2977			2.87052
$51$	−0.249561	+	4.11555i	−0.0349456	+	0.576292i
$52$	17.5552			2.43447
$53$	2.23241	−	2.23241i	0.306646	−	0.306646i	−0.536961	−	0.843607i	$-0.680428\pi$
$53$	2.23241	−	2.23241i	0.306646	−	0.306646i	0.843607	+	0.536961i	$0.180428\pi$
$54$	0.998125	−	2.40969i	0.135828	−	0.327917i
$55$			14.2613i			1.92300i
$56$	−6.75396	−	2.79758i	−0.902536	−	0.373843i
$57$	2.96417	+	7.15615i	0.392615	+	0.947855i
$58$	8.46575	−	3.50663i	1.11161	−	0.460443i
$59$	1.11936	+	1.11936i	0.145728	+	0.145728i	0.776207	−	0.630478i	$-0.217141\pi$
$59$	1.11936	+	1.11936i	0.145728	+	0.145728i	−0.630478	+	0.776207i	$0.717141\pi$
$60$	−12.1419	−	12.1419i	−1.56751	−	1.56751i
$61$	3.77713	−	1.56454i	0.483611	−	0.200318i	−0.127538	−	0.991834i	$-0.540707\pi$
$61$	3.77713	−	1.56454i	0.483611	−	0.200318i	0.611149	+	0.791515i	$0.290707\pi$
$62$	10.0012	+	24.1449i	1.27015	+	3.06641i
$63$	−0.923880	−	0.382683i	−0.116398	−	0.0482136i
$64$			7.30793i			0.913491i
$65$	5.00093	−	12.0733i	0.620289	−	1.49751i
$66$	7.35677	−	7.35677i	0.905556	−	0.905556i
$67$	2.11711			0.258646			0.129323	−	0.991603i	$-0.458720\pi$
$67$	2.11711			0.258646			0.129323	+	0.991603i	$0.458720\pi$
$68$	−6.45687	−	18.7204i	−0.783011	−	2.27018i
$69$	−1.31910			−0.158800
$70$	−6.59375	+	6.59375i	−0.788104	+	0.788104i
$71$	−1.03719	+	2.50401i	−0.123092	+	0.297171i	−0.973399	−	0.229116i	$-0.926416\pi$
$71$	−1.03719	+	2.50401i	−0.123092	+	0.297171i	0.850307	+	0.526287i	$0.176416\pi$
$72$			7.31043i			0.861543i
$73$	−4.39581	−	1.82080i	−0.514491	−	0.213109i	0.110304	−	0.993898i	$-0.464817\pi$
$73$	−4.39581	−	1.82080i	−0.514491	−	0.213109i	−0.624795	+	0.780789i	$0.714817\pi$
$74$	−7.54907	−	18.2251i	−0.877562	−	2.11862i
$75$	−7.18979	+	2.97811i	−0.830206	+	0.343883i
$76$	−26.3055	−	26.3055i	−3.01745	−	3.01745i
$77$	−2.82061	−	2.82061i	−0.321438	−	0.321438i
$78$	−8.80783	+	3.64832i	−0.997291	+	0.413091i
$79$	4.87513	+	11.7696i	0.548495	+	1.32418i	0.918598	+	0.395194i	$0.129323\pi$
$79$	4.87513	+	11.7696i	0.548495	+	1.32418i	−0.370102	+	0.928991i	$0.620677\pi$
$80$	31.2523	+	12.9451i	3.49411	+	1.44731i
$81$			1.00000i			0.111111i
$82$	−7.26853	+	17.5478i	−0.802675	+	1.93783i
$83$	3.38316	−	3.38316i	0.371350	−	0.371350i	−0.496619	−	0.867969i	$-0.665425\pi$
$83$	3.38316	−	3.38316i	0.371350	−	0.371350i	0.867969	+	0.496619i	$0.165425\pi$
$84$	4.80284			0.524033
$85$	−14.7140	−	0.892235i	−1.59595	−	0.0967765i
$86$	10.4411			1.12589
$87$	−2.48422	+	2.48422i	−0.266336	+	0.266336i
$88$	−11.1594	+	26.9411i	−1.18959	+	2.87193i
$89$			8.81120i			0.933986i	0.884261	+	0.466993i	$0.154663\pi$
$89$			8.81120i			0.933986i	−0.884261	+	0.466993i	$0.845337\pi$
$90$	8.61515	+	3.56851i	0.908117	+	0.376154i
$91$	1.39878	+	3.37695i	0.146632	+	0.354000i
$92$	5.85315	−	2.42445i	0.610233	−	0.252767i
$93$	−7.08518	−	7.08518i	−0.734698	−	0.734698i
$94$	−13.4609	−	13.4609i	−1.38839	−	1.38839i
$95$	−25.5848	+	10.5976i	−2.62494	+	1.08729i
$96$	−3.84867	−	9.29152i	−0.392804	−	0.948312i
$97$	−10.2663	−	4.25244i	−1.04239	−	0.431770i	−0.205217	−	0.978716i	$-0.565790\pi$
$97$	−10.2663	−	4.25244i	−1.04239	−	0.431770i	−0.837168	+	0.546946i	$0.815790\pi$
$98$		−	2.60823i		−	0.263471i
$99$	−1.52650	+	3.68530i	−0.153419	+	0.370386i
$100$	26.4292	−	26.4292i	2.64292	−	2.64292i
$101$	−5.61190			−0.558405			−0.279202	−	0.960232i	$-0.590070\pi$
$101$	−5.61190			−0.558405			−0.279202	+	0.960232i	$0.590070\pi$
$102$	7.13001	+	8.05054i	0.705976	+	0.797122i
$103$	−5.56986			−0.548814			−0.274407	−	0.961614i	$-0.588482\pi$
$103$	−5.56986			−0.548814			−0.274407	+	0.961614i	$0.588482\pi$
$104$	18.8946	−	18.8946i	1.85276	−	1.85276i
$105$	1.36818	−	3.30307i	0.133520	−	0.322347i
$106$		−	8.23445i		−	0.799801i
$107$	7.27825	+	3.01475i	0.703615	+	0.291447i	0.705659	−	0.708551i	$-0.250651\pi$
$107$	7.27825	+	3.01475i	0.703615	+	0.291447i	−0.00204484	+	0.999998i	$0.500651\pi$
$108$	−1.83797	−	4.43724i	−0.176858	−	0.426974i
$109$	6.20019	−	2.56820i	0.593870	−	0.245989i	−0.0654444	−	0.997856i	$-0.520846\pi$
$109$	6.20019	−	2.56820i	0.593870	−	0.245989i	0.659315	+	0.751867i	$0.270846\pi$
$110$	26.3021	+	26.3021i	2.50780	+	2.50780i
$111$	5.34803	+	5.34803i	0.507613	+	0.507613i
$112$	−8.74136	+	3.62079i	−0.825981	+	0.342133i
$113$	−0.777241	−	1.87643i	−0.0731167	−	0.176519i	0.883096	−	0.469193i	$-0.155455\pi$
$113$	−0.777241	−	1.87643i	−0.0731167	−	0.176519i	−0.956212	+	0.292674i	$0.905455\pi$
$114$	18.6649	+	7.73124i	1.74812	+	0.724097i
$115$		−	4.71605i		−	0.439774i
$116$	6.45718	−	15.5890i	0.599534	−	1.44740i
$117$	2.58460	−	2.58460i	0.238947	−	0.238947i
$118$	4.12886			0.380092
$119$	3.08660	−	2.73366i	0.282948	−	0.250595i
$120$	−26.1364			−2.38591
$121$	−3.47305	+	3.47305i	−0.315732	+	0.315732i
$122$	4.08066	−	9.85159i	0.369446	−	0.891921i
$123$		−	7.28219i		−	0.656613i
$124$	44.4610	+	18.4163i	3.99271	+	1.65384i
$125$	−3.80651	−	9.18972i	−0.340464	−	0.821954i
$126$	−2.40969	+	0.998125i	−0.214672	+	0.0889200i
$127$	5.34935	+	5.34935i	0.474678	+	0.474678i	0.903425	−	0.428747i	$-0.141045\pi$
$127$	5.34935	+	5.34935i	0.474678	+	0.474678i	−0.428747	+	0.903425i	$0.641045\pi$
$128$	−0.744868	−	0.744868i	−0.0658377	−	0.0658377i
$129$	−3.69841	+	1.53193i	−0.325627	+	0.134879i
$130$	−13.0436	−	31.4899i	−1.14400	−	2.76185i
$131$	3.24886	+	1.34572i	0.283854	+	0.117576i	0.520068	−	0.854125i	$-0.325907\pi$
$131$	3.24886	+	1.34572i	0.283854	+	0.117576i	−0.236214	+	0.971701i	$0.575907\pi$
$132$		−	19.1582i		−	1.66751i
$133$	2.96417	−	7.15615i	0.257027	−	0.620517i
$134$	3.90457	−	3.90457i	0.337303	−	0.337303i
$135$	−3.57522			−0.307706
$136$	−27.0981	−	13.1991i	−2.32364	−	1.13181i
$137$	−5.11399			−0.436918			−0.218459	−	0.975846i	$-0.570103\pi$
$137$	−5.11399			−0.436918			−0.218459	+	0.975846i	$0.570103\pi$
$138$	−2.43280	+	2.43280i	−0.207094	+	0.207094i
$139$	4.59447	−	11.0920i	0.389698	−	0.940814i	−0.600306	−	0.799771i	$-0.704954\pi$
$139$	4.59447	−	11.0920i	0.389698	−	0.940814i	0.990003	−	0.141043i	$-0.0450456\pi$
$140$			17.1712i			1.45123i
$141$	6.74312	+	2.79309i	0.567873	+	0.235221i
$142$	2.70524	+	6.53102i	0.227018	+	0.548071i
$143$	13.4704	−	5.57963i	1.12645	−	0.466592i
$144$	6.69035	+	6.69035i	0.557529	+	0.557529i
$145$	−8.88163	−	8.88163i	−0.737579	−	0.737579i
$146$	−11.4653	+	4.74907i	−0.948872	+	0.393036i
$147$	0.382683	+	0.923880i	0.0315632	+	0.0762003i
$148$	−33.5600	−	13.9010i	−2.75862	−	1.14266i
$149$			4.82241i			0.395067i	0.980296	+	0.197534i	$0.0632932\pi$
$149$			4.82241i			0.395067i	−0.980296	+	0.197534i	$0.936707\pi$
$150$	−7.76758	+	18.7526i	−0.634220	+	1.53114i
$151$	−15.5780	+	15.5780i	−1.26772	+	1.26772i	−0.320455	+	0.947264i	$0.603836\pi$
$151$	−15.5780	+	15.5780i	−1.26772	+	1.26772i	−0.947264	+	0.320455i	$0.896164\pi$
$152$	−56.6249			−4.59288
$153$	−3.70677	−	1.80552i	−0.299674	−	0.145967i
$154$	−10.4040			−0.838382
$155$	25.3310	−	25.3310i	2.03464	−	2.03464i
$156$	−6.71810	+	16.2189i	−0.537878	+	1.29855i
$157$			6.89784i			0.550508i	0.961372	+	0.275254i	$0.0887619\pi$
$157$			6.89784i			0.550508i	−0.961372	+	0.275254i	$0.911238\pi$
$158$	30.6978	+	12.7154i	2.44219	+	1.01159i
$159$	1.20817	+	2.91679i	0.0958144	+	0.231316i
$160$	33.2192	−	13.7598i	2.62621	−	1.08781i
$161$	0.932741	+	0.932741i	0.0735103	+	0.0735103i
$162$	1.84429	+	1.84429i	0.144901	+	0.144901i
$163$	−13.3943	+	5.54811i	−1.04912	+	0.434562i	−0.839579	−	0.543237i	$-0.817198\pi$
$163$	−13.3943	+	5.54811i	−1.04912	+	0.434562i	−0.209545	+	0.977799i	$0.567198\pi$
$164$	13.3844	+	32.3129i	1.04515	+	2.52321i
$165$	−13.1757	−	5.45757i	−1.02573	−	0.424871i
$166$		−	12.4791i		−	0.968564i
$167$	3.78716	−	9.14302i	0.293059	−	0.707508i	−0.706940	−	0.707273i	$-0.749925\pi$
$167$	3.78716	−	9.14302i	0.293059	−	0.707508i	1.00000		0.000235168i	$-7.48563e-5\pi$
$168$	5.16926	−	5.16926i	0.398817	−	0.398817i
$169$	−0.360335			−0.0277181
$170$	−28.7824	+	25.4913i	−2.20751	+	1.95510i
$171$	−7.74576			−0.592333
$172$	13.5951	−	13.5951i	1.03662	−	1.03662i
$173$	1.43914	−	3.47439i	0.109416	−	0.264153i	−0.859682	−	0.510829i	$-0.829338\pi$
$173$	1.43914	−	3.47439i	0.109416	−	0.264153i	0.969098	+	0.246676i	$0.0793384\pi$
$174$			9.16326i			0.694665i
$175$	7.18979	+	2.97811i	0.543497	+	0.225124i
$176$	14.4431	+	34.8688i	1.08869	+	2.62833i
$177$	−1.46252	+	0.605794i	−0.109929	+	0.0455342i
$178$	16.2504	+	16.2504i	1.21802	+	1.21802i
$179$	11.5973	+	11.5973i	0.866820	+	0.866820i	0.992119	−	0.125299i	$-0.0399889\pi$
$179$	11.5973	+	11.5973i	0.866820	+	0.866820i	−0.125299	+	0.992119i	$0.539989\pi$
$180$	15.8641	−	6.57113i	1.18244	−	0.489783i
$181$	3.80492	+	9.18589i	0.282817	+	0.682782i	0.999899	−	0.0142074i	$-0.00452251\pi$
$181$	3.80492	+	9.18589i	0.282817	+	0.682782i	−0.717082	+	0.696989i	$0.754523\pi$
$182$	8.80783	+	3.64832i	0.652880	+	0.270432i
$183$			4.08833i			0.302218i
$184$	3.69028	−	8.90912i	0.272051	−	0.656789i
$185$	−19.1204	+	19.1204i	−1.40576	+	1.40576i
$186$	−26.1343			−1.91626
$187$	−10.9044	−	12.3122i	−0.797410	−	0.900361i
$188$	−35.0545			−2.55661
$189$	0.707107	−	0.707107i	0.0514344	−	0.0514344i
$190$	−27.6408	+	66.7309i	−2.00528	+	4.84117i
$191$			3.73169i			0.270016i	0.990845	+	0.135008i	$0.0431060\pi$
$191$			3.73169i			0.270016i	−0.990845	+	0.135008i	$0.956894\pi$
$192$	−6.75165	−	2.79662i	−0.487258	−	0.201829i
$193$	7.17922	+	17.3322i	0.516772	+	1.24760i	0.939876	+	0.341516i	$0.110940\pi$
$193$	7.17922	+	17.3322i	0.516772	+	1.24760i	−0.423104	+	0.906081i	$0.639060\pi$
$194$	−26.7768	+	11.0913i	−1.92246	+	0.796311i
$195$	9.24051	+	9.24051i	0.661727	+	0.661727i
$196$	−3.39612	−	3.39612i	−0.242580	−	0.242580i
$197$	−9.67031	+	4.00557i	−0.688981	+	0.285385i	−0.699576	−	0.714559i	$-0.746628\pi$
$197$	−9.67031	+	4.00557i	−0.688981	+	0.285385i	0.0105947	+	0.999944i	$0.496628\pi$
$198$	3.98146	+	9.61209i	0.282950	+	0.683101i
$199$	−6.02134	−	2.49412i	−0.426842	−	0.176804i	0.158912	−	0.987293i	$-0.449201\pi$
$199$	−6.02134	−	2.49412i	−0.426842	−	0.176804i	−0.585754	+	0.810489i	$0.699201\pi$
$200$		−	56.8911i		−	4.02281i
$201$	−0.810182	+	1.95595i	−0.0571458	+	0.137962i
$202$	−10.3500	+	10.3500i	−0.728223	+	0.728223i
$203$	3.51322			0.246580
$204$	19.7663	+	1.19860i	1.38392	+	0.0839189i
$205$	26.0354			1.81839
$206$	−10.2725	+	10.2725i	−0.715716	+	0.715716i
$207$	0.504796	−	1.21869i	0.0350857	−	0.0847045i
$208$		−	34.5838i		−	2.39795i
$209$	−28.5454	−	11.8239i	−1.97453	−	0.817877i
$210$	−3.56851	−	8.61515i	−0.246251	−	0.594502i
$211$	21.8230	−	9.03937i	1.50235	−	0.622296i	0.528391	−	0.849001i	$-0.322795\pi$
$211$	21.8230	−	9.03937i	1.50235	−	0.622296i	0.973963	+	0.226705i	$0.0727954\pi$
$212$	−10.7219	−	10.7219i	−0.736385	−	0.736385i
$213$	−1.91649	−	1.91649i	−0.131315	−	0.131315i
$214$	18.9833	−	7.86314i	1.29767	−	0.537513i
$215$	−5.47698	−	13.2226i	−0.373527	−	0.901774i
$216$	−6.75396	−	2.79758i	−0.459549	−	0.190351i
$217$			10.0200i			0.680199i
$218$	6.69845	−	16.1715i	0.453676	−	1.09527i
$219$	3.36441	−	3.36441i	0.227346	−	0.227346i
$220$	68.4948			4.61792
$221$	4.91397	+	14.2471i	0.330550	+	0.958361i
$222$	19.7267			1.32397
$223$	−4.10711	+	4.10711i	−0.275033	+	0.275033i	−0.831122	−	0.556090i	$-0.812301\pi$
$223$	−4.10711	+	4.10711i	−0.275033	+	0.275033i	0.556090	+	0.831122i	$0.312301\pi$
$224$	−3.84867	+	9.29152i	−0.257150	+	0.620816i
$225$		−	7.78218i		−	0.518812i
$226$	−4.89414	−	2.02722i	−0.325553	−	0.134849i
$227$	−3.25228	−	7.85170i	−0.215861	−	0.521135i	0.778443	−	0.627716i	$-0.216010\pi$
$227$	−3.25228	−	7.85170i	−0.215861	−	0.521135i	−0.994304	+	0.106580i	$0.966010\pi$
$228$	34.3698	−	14.2365i	2.27620	−	0.942832i
$229$	−11.5607	−	11.5607i	−0.763953	−	0.763953i	0.213081	−	0.977035i	$-0.431650\pi$
$229$	−11.5607	−	11.5607i	−0.763953	−	0.763953i	−0.977035	+	0.213081i	$0.931650\pi$
$230$	−8.69778	−	8.69778i	−0.573515	−	0.573515i
$231$	3.68530	−	1.52650i	0.242475	−	0.100436i
$232$	−9.82851	−	23.7281i	−0.645274	−	1.55783i
$233$	−17.3745	−	7.19674i	−1.13824	−	0.471474i	−0.267665	−	0.963512i	$-0.586252\pi$
$233$	−17.3745	−	7.19674i	−1.13824	−	0.471474i	−0.870574	+	0.492038i	$0.836252\pi$
$234$		−	9.53353i		−	0.623226i
$235$	−9.98591	+	24.1081i	−0.651409	+	1.57264i
$236$	5.37611	−	5.37611i	0.349955	−	0.349955i
$237$	−12.7393			−0.827509
$238$	0.650912	−	10.7343i	0.0421923	−	0.695799i
$239$	10.1524			0.656701			0.328351	−	0.944556i	$-0.393507\pi$
$239$	10.1524			0.656701			0.328351	+	0.944556i	$0.393507\pi$
$240$	−23.9194	+	23.9194i	−1.54399	+	1.54399i
$241$	5.96211	−	14.3938i	0.384053	−	0.927186i	−0.607120	−	0.794610i	$-0.707675\pi$
$241$	5.96211	−	14.3938i	0.384053	−	0.927186i	0.991173	−	0.132576i	$-0.0423248\pi$
$242$			12.8106i			0.823499i
$243$	−0.923880	−	0.382683i	−0.0592669	−	0.0245492i
$244$	−7.51422	−	18.1409i	−0.481048	−	1.16135i
$245$	−3.30307	+	1.36818i	−0.211025	+	0.0874096i
$246$	−13.4305	−	13.4305i	−0.856297	−	0.856297i
$247$	20.0197	+	20.0197i	1.27382	+	1.27382i
$248$	67.6744	−	28.0316i	4.29733	−	1.78001i
$249$	1.83095	+	4.42031i	0.116032	+	0.280126i
$250$	−23.9689	−	9.92823i	−1.51592	−	0.627916i
$251$			7.00108i			0.441904i	0.975285	+	0.220952i	$0.0709165\pi$
$251$			7.00108i			0.441904i	−0.975285	+	0.220952i	$0.929084\pi$
$252$	−1.83797	+	4.43724i	−0.115781	+	0.279520i
$253$	3.72065	−	3.72065i	0.233915	−	0.233915i
$254$	19.7315			1.23807
$255$	6.45511	−	13.2525i	0.404235	−	0.829903i
$256$	−17.3634			−1.08521
$257$	−8.72575	+	8.72575i	−0.544298	+	0.544298i	−0.924786	−	0.380488i	$-0.875756\pi$
$257$	−8.72575	+	8.72575i	−0.544298	+	0.544298i	0.380488	+	0.924786i	$0.375756\pi$
$258$	−3.99562	+	9.64628i	−0.248756	+	0.600551i
$259$		−	7.56326i		−	0.469958i
$260$	−57.9862	−	24.0187i	−3.59615	−	1.48957i
$261$	−1.34445	−	3.24579i	−0.0832194	−	0.200909i
$262$	8.47375	−	3.50994i	0.523510	−	0.216845i
$263$	20.8032	+	20.8032i	1.28278	+	1.28278i	0.939079	+	0.343701i	$0.111681\pi$
$263$	20.8032	+	20.8032i	1.28278	+	1.28278i	0.343701	+	0.939079i	$0.388319\pi$
$264$	−20.6199	−	20.6199i	−1.26906	−	1.26906i
$265$	−10.4282	+	4.31948i	−0.640596	+	0.265344i
$266$	−7.73124	−	18.6649i	−0.474032	−	1.14442i
$267$	−8.14049	−	3.37190i	−0.498190	−	0.206357i
$268$		−	10.1681i		−	0.621117i
$269$	8.65360	−	20.8916i	0.527619	−	1.27378i	−0.405460	−	0.914113i	$-0.632889\pi$
$269$	8.65360	−	20.8916i	0.527619	−	1.27378i	0.933079	−	0.359672i	$-0.117111\pi$
$270$	−6.59375	+	6.59375i	−0.401283	+	0.401283i
$271$	23.8972			1.45165			0.725826	−	0.687878i	$-0.241458\pi$
$271$	23.8972			1.45165			0.725826	+	0.687878i	$0.241458\pi$
$272$	−36.8791	+	12.7200i	−2.23612	+	0.771265i
$273$	−3.65518			−0.221222
$274$	−9.43170	+	9.43170i	−0.569790	+	0.569790i
$275$	11.8795	−	28.6796i	0.716361	−	1.72945i
$276$			6.33540i			0.381346i
$277$	3.15437	+	1.30658i	0.189528	+	0.0785051i	0.475429	−	0.879754i	$-0.342293\pi$
$277$	3.15437	+	1.30658i	0.189528	+	0.0785051i	−0.285901	+	0.958259i	$0.592293\pi$
$278$	−11.9834	−	28.9305i	−0.718717	−	1.73514i
$279$	9.25723	−	3.83447i	0.554216	−	0.229564i
$280$	18.4812	+	18.4812i	1.10446	+	1.10446i
$281$	−17.0512	−	17.0512i	−1.01719	−	1.01719i	−0.999850	−	0.0173378i	$-0.994481\pi$
$281$	−17.0512	−	17.0512i	−1.01719	−	1.01719i	−0.0173378	−	0.999850i	$-0.505519\pi$
$282$	17.5876	−	7.28501i	1.04732	−	0.433816i
$283$	11.9039	+	28.7386i	0.707613	+	1.70833i	0.705880	+	0.708331i	$0.250552\pi$
$283$	11.9039	+	28.7386i	0.707613	+	1.70833i	0.00173335	+	0.999998i	$0.499448\pi$
$284$	12.0264	+	4.98148i	0.713633	+	0.295596i
$285$		−	27.6928i		−	1.64038i
$286$	14.5529	−	35.1339i	0.860533	−	2.07751i
$287$	−5.14929	+	5.14929i	−0.303953	+	0.303953i
$288$	10.0571			0.592618
$289$	13.3852	−	10.4802i	0.787368	−	0.616484i
$290$	−32.7607			−1.92377
$291$	7.85749	−	7.85749i	0.460614	−	0.460614i
$292$	−8.74503	+	21.1124i	−0.511764	+	1.23551i
$293$			16.7577i			0.978997i	0.872004	+	0.489499i	$0.162820\pi$
$293$			16.7577i			0.978997i	−0.872004	+	0.489499i	$0.837180\pi$
$294$	2.40969	+	0.998125i	0.140536	+	0.0582118i
$295$	−2.16584	−	5.22881i	−0.126100	−	0.304433i
$296$	−51.0819	+	21.1588i	−2.96908	+	1.22983i
$297$	−2.82061	−	2.82061i	−0.163668	−	0.163668i
$298$	8.89394	+	8.89394i	0.515212	+	0.515212i
$299$	−4.45451	+	1.84512i	−0.257611	+	0.106706i
$300$	14.3034	+	34.5314i	0.825806	+	1.99367i
$301$	3.69841	+	1.53193i	0.213173	+	0.0882990i
$302$			57.4608i			3.30650i
$303$	2.14758	−	5.18472i	0.123375	−	0.297854i
$304$	−51.8218	+	51.8218i	−2.97219	+	2.97219i
$305$	−14.6167			−0.836948
$306$	−10.1663	+	3.50646i	−0.581167	+	0.200451i
$307$	3.41030			0.194636			0.0973181	−	0.995253i	$-0.468974\pi$
$307$	3.41030			0.194636			0.0973181	+	0.995253i	$0.468974\pi$
$308$	−13.5469	+	13.5469i	−0.771907	+	0.771907i
$309$	2.13149	−	5.14588i	0.121256	−	0.292739i
$310$		−	93.4358i		−	5.30679i
$311$	31.3087	+	12.9685i	1.77535	+	0.735376i	0.993753	+	0.111598i	$0.0355968\pi$
$311$	31.3087	+	12.9685i	1.77535	+	0.735376i	0.781601	+	0.623778i	$0.214403\pi$
$312$	10.2257	+	24.6869i	0.578914	+	1.39762i
$313$	13.9549	−	5.78031i	0.788778	−	0.326722i	0.0483256	−	0.998832i	$-0.484611\pi$
$313$	13.9549	−	5.78031i	0.788778	−	0.326722i	0.740452	+	0.672109i	$0.234611\pi$
$314$	12.7216	+	12.7216i	0.717924	+	0.717924i
$315$	2.52806	+	2.52806i	0.142440	+	0.142440i
$316$	56.5276	−	23.4145i	3.17992	−	1.31717i
$317$	3.01305	+	7.27414i	0.169230	+	0.408556i	0.985627	−	0.168933i	$-0.0540323\pi$
$317$	3.01305	+	7.27414i	0.169230	+	0.408556i	−0.816398	+	0.577490i	$0.804032\pi$
$318$	7.60764	+	3.15119i	0.426615	+	0.176710i
$319$		−	14.0140i		−	0.784634i
$320$	9.99854	−	24.1386i	0.558935	−	1.34939i
$321$	−5.57053	+	5.57053i	−0.310917	+	0.310917i
$322$	3.44050			0.191731
$323$	13.9851	−	28.7117i	0.778151	−	1.59756i
$324$	4.80284			0.266824
$325$	−20.1138	+	20.1138i	−1.11571	+	1.11571i
$326$	−14.4707	+	34.9354i	−0.801459	+	1.93489i
$327$			6.71104i			0.371121i
$328$	49.1836	+	20.3725i	2.71571	+	1.12488i
$329$	−2.79309	−	6.74312i	−0.153988	−	0.371760i
$330$	−34.3653	+	14.2346i	−1.89175	+	0.783588i
$331$	−5.09916	−	5.09916i	−0.280275	−	0.280275i	0.552944	−	0.833219i	$-0.313504\pi$
$331$	−5.09916	−	5.09916i	−0.280275	−	0.280275i	−0.833219	+	0.552944i	$0.813504\pi$
$332$	−16.2488	−	16.2488i	−0.891767	−	0.891767i
$333$	−6.98754	+	2.89433i	−0.382915	+	0.158608i
$334$	−9.87777	−	23.8471i	−0.540488	−	1.30485i
$335$	−6.99295	−	2.89658i	−0.382066	−	0.158257i
$336$		−	9.46158i		−	0.516172i
$337$	8.07671	−	19.4989i	0.439967	−	1.06217i	−0.535993	−	0.844222i	$-0.680063\pi$
$337$	8.07671	−	19.4989i	0.439967	−	1.06217i	0.975960	−	0.217951i	$-0.0699372\pi$
$338$	−0.664564	+	0.664564i	−0.0361475	+	0.0361475i
$339$	2.03103			0.110310
$340$	−4.28526	+	70.6688i	−0.232401	+	3.83256i
$341$	39.9690			2.16444
$342$	−14.2855	+	14.2855i	−0.772469	+	0.772469i
$343$	0.382683	−	0.923880i	0.0206630	−	0.0498848i
$344$		−	29.2646i		−	1.57784i
$345$	4.35706	+	1.80475i	0.234576	+	0.0971647i
$346$	−3.75360	−	9.06200i	−0.201795	−	0.487176i
$347$	−0.547943	+	0.226966i	−0.0294151	+	0.0121842i	−0.397343	−	0.917670i	$-0.630068\pi$
$347$	−0.547943	+	0.226966i	−0.0294151	+	0.0121842i	0.367927	+	0.929855i	$0.380068\pi$
$348$	11.9313	+	11.9313i	0.639585	+	0.639585i
$349$	21.7323	+	21.7323i	1.16330	+	1.16330i	0.983748	+	0.179555i	$0.0574658\pi$
$349$	21.7323	+	21.7323i	1.16330	+	1.16330i	0.179555	+	0.983748i	$0.442534\pi$
$350$	18.7526	−	7.76758i	1.00237	−	0.415195i
$351$	1.39878	+	3.37695i	0.0746612	+	0.180248i
$352$	37.0633	+	15.3521i	1.97548	+	0.818271i
$353$			4.17538i			0.222233i	0.993807	+	0.111117i	$0.0354427\pi$
$353$			4.17538i			0.222233i	−0.993807	+	0.111117i	$0.964557\pi$
$354$	−1.58005	+	3.81457i	−0.0839785	+	0.202742i
$355$	6.85185	−	6.85185i	0.363659	−	0.363659i
$356$	42.3188			2.24289
$357$	1.34439	+	3.89777i	0.0711525	+	0.206292i
$358$	42.7775			2.26086
$359$	−12.7364	+	12.7364i	−0.672201	+	0.672201i	−0.958223	−	0.286022i	$-0.907667\pi$
$359$	−12.7364	+	12.7364i	−0.672201	+	0.672201i	0.286022	+	0.958223i	$0.407667\pi$
$360$	10.0020	−	24.1469i	0.527150	−	1.27265i
$361$		−	40.9968i		−	2.15773i
$362$	23.9589	+	9.92409i	1.25925	+	0.521599i
$363$	−1.87960	−	4.53775i	−0.0986534	−	0.238170i
$364$	16.2189	−	6.71810i	0.850103	−	0.352124i
$365$	12.0285	+	12.0285i	0.629600	+	0.629600i
$366$	7.54008	+	7.54008i	0.394127	+	0.394127i
$367$	23.7960	−	9.85662i	1.24214	−	0.514511i	0.337757	−	0.941233i	$-0.390332\pi$
$367$	23.7960	−	9.85662i	1.24214	−	0.514511i	0.904383	+	0.426722i	$0.140332\pi$
$368$	−4.77617	−	11.5307i	−0.248975	−	0.601079i
$369$	6.72787	+	2.78677i	0.350239	+	0.145074i
$370$			70.5272i			3.66653i
$371$	1.20817	−	2.91679i	0.0627252	−	0.151432i
$372$	−34.0290	+	34.0290i	−1.76432	+	1.76432i
$373$	−35.0014			−1.81230			−0.906151	−	0.422954i	$-0.860993\pi$
$373$	−35.0014			−1.81230			−0.906151	+	0.422954i	$0.860993\pi$
$374$	−42.8183	−	2.59645i	−2.21408	−	0.134259i
$375$	9.94688			0.513655
$376$	−37.7289	+	37.7289i	−1.94572	+	1.94572i
$377$	−4.91421	+	11.8639i	−0.253095	+	0.611024i
$378$		−	2.60823i		−	0.134153i
$379$	−34.9518	−	14.4775i	−1.79536	−	0.743660i	−0.988170	−	0.153362i	$-0.950990\pi$
$379$	−34.9518	−	14.4775i	−1.79536	−	0.743660i	−0.807185	−	0.590298i	$-0.799010\pi$
$380$	50.8984	+	122.880i	2.61103	+	6.30359i
$381$	−6.98926	+	2.89504i	−0.358070	+	0.148318i
$382$	6.88234	+	6.88234i	0.352131	+	0.352131i
$383$	−0.837527	−	0.837527i	−0.0427956	−	0.0427956i	0.685385	−	0.728181i	$-0.259634\pi$
$383$	−0.837527	−	0.837527i	−0.0427956	−	0.0427956i	−0.728181	+	0.685385i	$0.759634\pi$
$384$	0.973217	−	0.403120i	0.0496643	−	0.0205716i
$385$	5.45757	+	13.1757i	0.278144	+	0.671498i
$386$	45.2062	+	18.7250i	2.30094	+	0.953079i
$387$		−	4.00313i		−	0.203490i
$388$	−20.4238	+	49.3074i	−1.03686	+	2.50320i
$389$	−17.4349	+	17.4349i	−0.883986	+	0.883986i	−0.993937	−	0.109951i	$-0.964931\pi$
$389$	−17.4349	+	17.4349i	−0.883986	+	0.883986i	0.109951	+	0.993937i	$0.464931\pi$
$390$	34.0844			1.72593
$391$	3.60596	+	4.07152i	0.182361	+	0.205905i
$392$	−7.31043			−0.369233
$393$	−2.48657	+	2.48657i	−0.125431	+	0.125431i
$394$	−10.4474	+	25.2223i	−0.526334	+	1.27068i
$395$		−	45.5459i		−	2.29166i
$396$	17.6999	+	7.33154i	0.889453	+	0.368424i
$397$	−10.9014	−	26.3183i	−0.547126	−	1.32088i	−0.919607	−	0.392839i	$-0.871493\pi$
$397$	−10.9014	−	26.3183i	−0.547126	−	1.32088i	0.372481	−	0.928040i	$-0.378507\pi$
$398$	−15.7050	+	6.50523i	−0.787221	+	0.326078i
$399$	5.47708	+	5.47708i	0.274197	+	0.274197i
$400$	−52.0655	−	52.0655i	−2.60327	−	2.60327i
$401$	12.0052	−	4.97270i	0.599509	−	0.248325i	−0.0622268	−	0.998062i	$-0.519820\pi$
$401$	12.0052	−	4.97270i	0.599509	−	0.248325i	0.661735	+	0.749737i	$0.269820\pi$
$402$	2.11314	+	5.10156i	0.105394	+	0.254443i
$403$	−33.8368	−	14.0157i	−1.68553	−	0.698170i
$404$			26.9531i			1.34096i
$405$	1.36818	−	3.30307i	0.0679852	−	0.164131i
$406$	6.47941	−	6.47941i	0.321567	−	0.321567i
$407$	−30.1694			−1.49544
$408$	22.5644	−	19.9843i	1.11710	−	0.989369i
$409$	−14.0112			−0.692808			−0.346404	−	0.938085i	$-0.612597\pi$
$409$	−14.0112			−0.692808			−0.346404	+	0.938085i	$0.612597\pi$
$410$	48.0169	−	48.0169i	2.37139	−	2.37139i
$411$	1.95704	−	4.72471i	0.0965336	−	0.233053i
$412$			26.7511i			1.31793i
$413$	1.46252	+	0.605794i	0.0719657	+	0.0298092i
$414$	−1.31662	−	3.17861i	−0.0647084	−	0.156220i
$415$	−15.8036	+	6.54605i	−0.775766	+	0.321333i
$416$	−25.9935	−	25.9935i	−1.27444	−	1.27444i
$417$	8.48947	+	8.48947i	0.415731	+	0.415731i
$418$	−74.4529	+	30.8394i	−3.64161	+	1.50841i
$419$	−2.69072	−	6.49597i	−0.131450	−	0.317349i	0.844426	−	0.535672i	$-0.179941\pi$
$419$	−2.69072	−	6.49597i	−0.131450	−	0.317349i	−0.975877	+	0.218323i	$0.929941\pi$
$420$	−15.8641	−	6.57113i	−0.774089	−	0.320638i
$421$		−	40.4733i		−	1.97255i	−0.165124	−	0.986273i	$-0.552802\pi$
$421$		−	40.4733i		−	1.97255i	0.165124	−	0.986273i	$-0.447198\pi$
$422$	23.5767	−	56.9192i	1.14770	−	2.77078i
$423$	−5.16096	+	5.16096i	−0.250934	+	0.250934i
$424$	−23.0798			−1.12086
$425$	28.8467	+	14.0508i	1.39927	+	0.681566i
$426$	−7.06913			−0.342500
$427$	2.89089	−	2.89089i	0.139900	−	0.139900i
$428$	14.4793	−	34.9562i	0.699886	−	1.68967i
$429$			14.5803i			0.703943i
$430$	−34.4875	−	14.2852i	−1.66314	−	0.688894i
$431$	12.4942	+	30.1636i	0.601823	+	1.45293i	0.871702	+	0.490036i	$0.163016\pi$
$431$	12.4942	+	30.1636i	0.601823	+	1.45293i	−0.269879	+	0.962894i	$0.586984\pi$
$432$	−8.74136	+	3.62079i	−0.420569	+	0.174205i
$433$	−18.9429	−	18.9429i	−0.910335	−	0.910335i	0.0859629	−	0.996298i	$-0.472603\pi$
$433$	−18.9429	−	18.9429i	−0.910335	−	0.910335i	−0.996298	+	0.0859629i	$0.972603\pi$
$434$	18.4797	+	18.4797i	0.887056	+	0.887056i
$435$	11.6044	−	4.80670i	0.556389	−	0.230464i
$436$	−12.3347	−	29.7785i	−0.590723	−	1.42613i
$437$	9.43964	+	3.91003i	0.451559	+	0.187042i
$438$		−	12.4099i		−	0.592969i
$439$	−6.60076	+	15.9356i	−0.315037	+	0.760567i	0.684466	+	0.729045i	$0.260035\pi$
$439$	−6.60076	+	15.9356i	−0.315037	+	0.760567i	−0.999503	+	0.0315220i	$0.989965\pi$
$440$	73.7204	−	73.7204i	3.51448	−	3.51448i
$441$	−1.00000			−0.0476190
$442$	35.3386	+	17.2129i	1.68088	+	0.818736i
$443$	0.848219			0.0403001			0.0201500	−	0.999797i	$-0.493586\pi$
$443$	0.848219			0.0403001			0.0201500	+	0.999797i	$0.493586\pi$
$444$	25.6857	−	25.6857i	1.21899	−	1.21899i
$445$	12.0553	−	29.1040i	0.571475	−	1.37966i
$446$			15.1494i			0.717347i
$447$	−4.45533	−	1.84546i	−0.210730	−	0.0872871i
$448$	2.79662	+	6.75165i	0.132128	+	0.318985i
$449$	−8.26534	+	3.42362i	−0.390066	+	0.161570i	−0.569092	−	0.822274i	$-0.692705\pi$
$449$	−8.26534	+	3.42362i	−0.390066	+	0.161570i	0.179026	+	0.983844i	$0.442705\pi$
$450$	−14.3526	−	14.3526i	−0.676589	−	0.676589i
$451$	20.5402	+	20.5402i	0.967199	+	0.967199i
$452$	−9.01217	+	3.73296i	−0.423897	+	0.175584i
$453$	−8.43074	−	20.3536i	−0.396111	−	0.956296i
$454$	−20.4790	−	8.48268i	−0.961127	−	0.398112i
$455$		−	13.0681i		−	0.612640i
$456$	21.6694	−	52.3146i	1.01476	−	2.44985i
$457$	10.1569	−	10.1569i	0.475119	−	0.475119i	−0.428447	−	0.903567i	$-0.640939\pi$
$457$	10.1569	−	10.1569i	0.475119	−	0.475119i	0.903567	+	0.428447i	$0.140939\pi$
$458$	−42.6427			−1.99256
$459$	3.08660	−	2.73366i	0.144070	−	0.127597i
$460$	−22.6504			−1.05608
$461$	−5.34397	+	5.34397i	−0.248893	+	0.248893i	−0.820516	−	0.571623i	$-0.806314\pi$
$461$	−5.34397	+	5.34397i	−0.248893	+	0.248893i	0.571623	+	0.820516i	$0.306314\pi$
$462$	3.98146	−	9.61209i	0.185234	−	0.447195i
$463$			2.51316i			0.116797i	0.998293	+	0.0583983i	$0.0185993\pi$
$463$			2.51316i			0.116797i	−0.998293	+	0.0583983i	$0.981401\pi$
$464$	−30.7103	−	12.7206i	−1.42569	−	0.590540i
$465$	13.7091	+	33.0966i	0.635742	+	1.53482i
$466$	−45.3165	+	18.7707i	−2.09925	+	0.869536i
$467$	−19.4929	−	19.4929i	−0.902024	−	0.902024i	0.0935872	−	0.995611i	$-0.470167\pi$
$467$	−19.4929	−	19.4929i	−0.902024	−	0.902024i	−0.995611	+	0.0935872i	$0.970167\pi$
$468$	−12.4134	−	12.4134i	−0.573811	−	0.573811i
$469$	1.95595	−	0.810182i	0.0903175	−	0.0374107i
$470$	26.0455	+	62.8794i	1.20139	+	2.90041i
$471$	−6.37277	−	2.63969i	−0.293642	−	0.121630i
$472$		−	11.5725i		−	0.532669i
$473$	6.11077	−	14.7527i	0.280974	−	0.678331i
$474$	−23.4951	+	23.4951i	−1.07916	+	1.07916i
$475$	60.2789			2.76578
$476$	−13.1293	−	14.8244i	−0.601783	−	0.679476i
$477$	−3.15711			−0.144554
$478$	18.7239	−	18.7239i	0.856412	−	0.856412i
$479$	−12.2367	+	29.5421i	−0.559111	+	1.34981i	0.351361	+	0.936240i	$0.385719\pi$
$479$	−12.2367	+	29.5421i	−0.559111	+	1.34981i	−0.910471	+	0.413572i	$0.864281\pi$
$480$			35.9562i			1.64117i
$481$	25.5407	+	10.5793i	1.16456	+	0.482375i
$482$	−15.5505	−	37.5423i	−0.708307	−	1.71000i
$483$	−1.21869	+	0.504796i	−0.0554521	+	0.0229690i
$484$	16.6805	+	16.6805i	0.758204	+	0.758204i
$485$	28.0922	+	28.0922i	1.27560	+	1.27560i
$486$	−2.40969	+	0.998125i	−0.109306	+	0.0452758i
$487$	−4.67839	−	11.2946i	−0.211998	−	0.511808i	0.781732	−	0.623614i	$-0.214336\pi$
$487$	−4.67839	−	11.2946i	−0.211998	−	0.511808i	−0.993730	+	0.111806i	$0.964336\pi$
$488$	−27.6124	−	11.4374i	−1.24996	−	0.517749i
$489$		−	14.4979i		−	0.655618i
$490$	−3.56851	+	8.61515i	−0.161209	+	0.389193i
$491$	−17.3008	+	17.3008i	−0.780774	+	0.780774i	−0.979961	−	0.199187i	$-0.936170\pi$
$491$	−17.3008	+	17.3008i	−0.780774	+	0.780774i	0.199187	+	0.979961i	$0.436170\pi$
$492$	−34.9752			−1.57680
$493$	14.4588	+	0.876763i	0.651192	+	0.0394874i
$494$	73.8445			3.32242
$495$	10.0843	−	10.0843i	0.453255	−	0.453255i
$496$	36.2801	−	87.5880i	1.62903	−	3.93282i
$497$			2.71032i			0.121574i
$498$	11.5292	+	4.77554i	0.516634	+	0.213997i
$499$	−5.50789	−	13.2972i	−0.246567	−	0.595265i	0.751341	−	0.659914i	$-0.229407\pi$
$499$	−5.50789	−	13.2972i	−0.246567	−	0.595265i	−0.997908	+	0.0646488i	$0.979407\pi$
$500$	−44.1368	+	18.2820i	−1.97386	+	0.817598i
$501$	6.99777	+	6.99777i	0.312637	+	0.312637i
$502$	12.9121	+	12.9121i	0.576293	+	0.576293i
$503$	−18.3356	+	7.59486i	−0.817545	+	0.338638i	−0.751960	−	0.659209i	$-0.770891\pi$
$503$	−18.3356	+	7.59486i	−0.817545	+	0.338638i	−0.0655851	+	0.997847i	$0.520891\pi$
$504$	2.79758	+	6.75396i	0.124614	+	0.300845i
$505$	18.5365	+	7.67807i	0.824863	+	0.341670i
$506$		−	13.7239i		−	0.610103i
$507$	0.137894	−	0.332907i	0.00612410	−	0.0147849i
$508$	25.6920	−	25.6920i	1.13990	−	1.13990i
$509$	3.02225			0.133959			0.0669794	−	0.997754i	$-0.478664\pi$
$509$	3.02225			0.133959			0.0669794	+	0.997754i	$0.478664\pi$
$510$	−12.5364	−	36.3466i	−0.555120	−	1.60945i
$511$	−4.75799			−0.210481
$512$	−30.5334	+	30.5334i	−1.34940	+	1.34940i
$513$	2.96417	−	7.15615i	0.130872	−	0.315952i
$514$			32.1857i			1.41965i
$515$	18.3976	+	7.62055i	0.810696	+	0.335801i
$516$	7.35761	+	17.7628i	0.323901	+	0.781966i
$517$	−26.8979	+	11.1415i	−1.18297	+	0.490001i
$518$	−13.9489	−	13.9489i	−0.612878	−	0.612878i
$519$	2.65919	+	2.65919i	0.116725	+	0.116725i
$520$	−88.2612	+	36.5590i	−3.87051	+	1.60322i
$521$	−8.66237	−	20.9128i	−0.379506	−	0.916207i	−0.992058	−	0.125778i	$-0.959857\pi$
$521$	−8.66237	−	20.9128i	−0.379506	−	0.916207i	0.612553	−	0.790430i	$-0.290143\pi$
$522$	−8.46575	−	3.50663i	−0.370536	−	0.153481i
$523$			13.0194i			0.569296i	0.958632	+	0.284648i	$0.0918768\pi$
$523$			13.0194i			0.569296i	−0.958632	+	0.284648i	$0.908123\pi$
$524$	6.46328	−	15.6037i	0.282349	−	0.681652i
$525$	−5.50283	+	5.50283i	−0.240163	+	0.240163i
$526$	76.7344			3.34578
$527$	−2.50059	+	41.2376i	−0.108927	+	1.79634i
$528$	−37.7417			−1.64250
$529$	15.0331	−	15.0331i	0.653612	−	0.653612i
$530$	−11.2662	+	27.1990i	−0.489372	+	1.18145i
$531$		−	1.58301i		−	0.0686970i
$532$	−34.3698	−	14.2365i	−1.49012	−	0.617228i
$533$	−10.1862	−	24.5916i	−0.441211	−	1.06518i
$534$	−21.2322	+	8.79468i	−0.918809	+	0.380583i
$535$	−19.9158	−	19.9158i	−0.861037	−	0.861037i
$536$	−10.9439	−	10.9439i	−0.472703	−	0.472703i
$537$	−15.1526	+	6.27639i	−0.653881	+	0.270846i
$538$	−22.5705	−	54.4901i	−0.973084	−	2.34923i
$539$	−3.68530	−	1.52650i	−0.158737	−	0.0657510i
$540$			17.1712i			0.738930i
$541$	0.585159	−	1.41270i	0.0251579	−	0.0607366i	−0.910801	−	0.412845i	$-0.864535\pi$
$541$	0.585159	−	1.41270i	0.0251579	−	0.0607366i	0.935959	+	0.352108i	$0.114535\pi$
$542$	44.0735	−	44.0735i	1.89312	−	1.89312i
$543$	−9.94274			−0.426684
$544$	−18.1582	+	37.2792i	−0.778526	+	1.59833i
$545$	−23.9934			−1.02776
$546$	−6.74122	+	6.74122i	−0.288498	+	0.288498i
$547$	−1.82294	+	4.40098i	−0.0779435	+	0.188172i	−0.958048	−	0.286608i	$-0.907472\pi$
$547$	−1.82294	+	4.40098i	−0.0779435	+	0.188172i	0.880105	+	0.474780i	$0.157472\pi$
$548$			24.5617i			1.04922i
$549$	−3.77713	−	1.56454i	−0.161204	−	0.0667728i
$550$	−30.9844	−	74.8030i	−1.32118	−	3.18961i
$551$	25.1411	−	10.4138i	1.07105	−	0.443642i
$552$	6.81874	+	6.81874i	0.290225	+	0.290225i
$553$	9.00807	+	9.00807i	0.383062	+	0.383062i
$554$	8.22732	−	3.40787i	0.349545	−	0.144786i
$555$	−10.3479	−	24.9820i	−0.439243	−	1.06043i
$556$	−53.2732	−	22.0665i	−2.25929	−	0.935828i
$557$		−	3.04299i		−	0.128936i	−0.997920	−	0.0644678i	$-0.979465\pi$
$557$		−	3.04299i		−	0.128936i	0.997920	−	0.0644678i	$-0.0205350\pi$
$558$	10.0012	−	24.1449i	0.423383	−	1.02214i
$559$	−10.3465	+	10.3465i	−0.437610	+	0.437610i
$560$	33.8272			1.42946
$561$	15.5480	−	5.36268i	0.656436	−	0.226412i
$562$	−62.8947			−2.65305
$563$	−28.1538	+	28.1538i	−1.18654	+	1.18654i	−0.208526	+	0.978017i	$0.566867\pi$
$563$	−28.1538	+	28.1538i	−1.18654	+	1.18654i	−0.978017	+	0.208526i	$0.933133\pi$
$564$	13.4148	−	32.3861i	0.564864	−	1.36370i
$565$			7.26137i			0.305488i
$566$	74.9566	+	31.0481i	3.15066	+	1.30505i
$567$	0.382683	+	0.923880i	0.0160712	+	0.0387993i
$568$	18.3054	−	7.58234i	0.768077	−	0.318148i
$569$	3.41189	+	3.41189i	0.143034	+	0.143034i	0.774998	−	0.631964i	$-0.217751\pi$
$569$	3.41189	+	3.41189i	0.143034	+	0.143034i	−0.631964	+	0.774998i	$0.717751\pi$
$570$	−51.0736	−	51.0736i	−2.13924	−	2.13924i
$571$	−0.0424839	+	0.0175974i	−0.00177790	+	0.000736429i	−0.383572	−	0.923511i	$-0.625306\pi$
$571$	−0.0424839	+	0.0175974i	−0.00177790	+	0.000736429i	0.381794	+	0.924247i	$0.375306\pi$
$572$	−26.7981	−	64.6963i	−1.12048	−	2.70509i
$573$	−3.44763	−	1.42806i	−0.144027	−	0.0596579i
$574$			18.9936i			0.792777i
$575$	−3.92841	+	9.48402i	−0.163826	+	0.395511i
$576$	5.16749	−	5.16749i	0.215312	−	0.215312i
$577$	−6.15357			−0.256177			−0.128088	−	0.991763i	$-0.540884\pi$
$577$	−6.15357			−0.256177			−0.128088	+	0.991763i	$0.540884\pi$
$578$	5.35771	−	44.0149i	0.222852	−	1.83078i
$579$	−18.7602			−0.779648
$580$	−42.6570	+	42.6570i	−1.77124	+	1.77124i
$581$	1.83095	−	4.42031i	0.0759607	−	0.183385i
$582$		−	28.9830i		−	1.20139i
$583$	−11.6349	−	4.81933i	−0.481868	−	0.199596i
$584$	13.3109	+	32.1353i	0.550808	+	1.32977i
$585$	−12.0733	+	5.00093i	−0.499170	+	0.206763i
$586$	30.9062	+	30.9062i	1.27672	+	1.27672i
$587$	3.07750	+	3.07750i	0.127022	+	0.127022i	0.767760	−	0.640738i	$-0.221371\pi$
$587$	3.07750	+	3.07750i	0.127022	+	0.127022i	−0.640738	+	0.767760i	$0.721371\pi$
$588$	4.43724	−	1.83797i	0.182989	−	0.0757965i
$589$	29.7009	+	71.7043i	1.22380	+	2.95452i
$590$	−13.6379	−	5.64901i	−0.561464	−	0.232566i
$591$		−	10.4671i		−	0.430558i
$592$	−27.3850	+	66.1132i	−1.12552	+	2.71723i
$593$	−12.4168	+	12.4168i	−0.509897	+	0.509897i	−0.914495	−	0.404598i	$-0.867411\pi$
$593$	−12.4168	+	12.4168i	−0.509897	+	0.509897i	0.404598	+	0.914495i	$0.367411\pi$
$594$	−10.4040			−0.426883
$595$	−13.9354	+	4.80647i	−0.571295	+	0.197046i
$596$	23.1613			0.948722
$597$	4.60854	−	4.60854i	0.188615	−	0.188615i
$598$	−4.81249	+	11.6184i	−0.196797	+	0.475111i
$599$		−	8.68704i		−	0.354943i	−0.984126	−	0.177471i	$-0.943208\pi$
$599$		−	8.68704i		−	0.354943i	0.984126	−	0.177471i	$-0.0567917\pi$
$600$	52.5605	+	21.7713i	2.14577	+	0.888809i
$601$	−1.53013	−	3.69407i	−0.0624154	−	0.150684i	0.889595	−	0.456751i	$-0.150987\pi$
$601$	−1.53013	−	3.69407i	−0.0624154	−	0.150684i	−0.952010	+	0.306067i	$0.900987\pi$
$602$	9.64628	−	3.99562i	0.393153	−	0.162849i
$603$	−1.49702	−	1.49702i	−0.0609634	−	0.0609634i
$604$	74.8185	+	74.8185i	3.04432	+	3.04432i
$605$	16.2235	−	6.71998i	0.659577	−	0.273206i
$606$	−5.60138	−	13.5229i	−0.227540	−	0.549331i
$607$	37.0764	+	15.3575i	1.50488	+	0.623343i	0.974494	−	0.224412i	$-0.0720460\pi$
$607$	37.0764	+	15.3575i	1.50488	+	0.623343i	0.530389	+	0.847755i	$0.322046\pi$
$608$			77.8996i			3.15925i
$609$	−1.34445	+	3.24579i	−0.0544799	+	0.131526i
$610$	−26.9574	+	26.9574i	−1.09147	+	1.09147i
$611$	26.6781			1.07928
$612$	−8.67160	+	17.8030i	−0.350529	+	0.719644i
$613$	−23.1547			−0.935210			−0.467605	−	0.883937i	$-0.654883\pi$
$613$	−23.1547			−0.935210			−0.467605	+	0.883937i	$0.654883\pi$
$614$	6.28960	−	6.28960i	0.253827	−	0.253827i
$615$	−9.96332	+	24.0536i	−0.401760	+	0.969934i
$616$			29.1609i			1.17493i
$617$	−23.9886	−	9.93642i	−0.965747	−	0.400025i	−0.156619	−	0.987659i	$-0.550060\pi$
$617$	−23.9886	−	9.93642i	−0.965747	−	0.400025i	−0.809127	+	0.587634i	$0.800060\pi$
$618$	−5.55941	−	13.4216i	−0.223632	−	0.539896i
$619$	7.34033	−	3.04046i	0.295033	−	0.122207i	−0.230257	−	0.973130i	$-0.573957\pi$
$619$	7.34033	−	3.04046i	0.295033	−	0.122207i	0.525290	+	0.850923i	$0.323957\pi$
$620$	−121.661	−	121.661i	−4.88602	−	4.88602i
$621$	0.932741	+	0.932741i	0.0374296	+	0.0374296i
$622$	81.6602	−	33.8248i	3.27428	−	1.35625i
$623$	3.37190	+	8.14049i	0.135092	+	0.326142i
$624$	31.9512	+	13.2346i	1.27907	+	0.529810i
$625$		−	3.34861i		−	0.133944i
$626$	15.0763	−	36.3975i	0.602572	−	1.45474i
$627$	21.8477	−	21.8477i	0.872515	−	0.872515i
$628$	33.1292			1.32200
$629$	1.88750	−	31.1269i	0.0752594	−	1.24111i
$630$	9.32497			0.371516
$631$	−25.4307	+	25.4307i	−1.01238	+	1.01238i	−0.0124589	+	0.999922i	$0.503966\pi$
$631$	−25.4307	+	25.4307i	−1.01238	+	1.01238i	−0.999922	+	0.0124589i	$0.996034\pi$
$632$	35.6393	−	86.0410i	1.41766	−	3.42253i
$633$			23.6210i			0.938851i
$634$	18.9726	+	7.85871i	0.753498	+	0.312109i
$635$	−10.3504	−	24.9881i	−0.410744	−	0.991623i
$636$	14.0089	−	5.80266i	0.555488	−	0.230091i
$637$	2.58460	+	2.58460i	0.102406	+	0.102406i
$638$	−25.8459	−	25.8459i	−1.02325	−	1.02325i
$639$	2.50401	−	1.03719i	0.0990571	−	0.0410308i
$640$	1.44124	+	3.47946i	0.0569701	+	0.137538i
$641$	30.0648	+	12.4533i	1.18749	+	0.491874i	0.886937	−	0.461891i	$-0.152829\pi$
$641$	30.0648	+	12.4533i	1.18749	+	0.491874i	0.300553	+	0.953765i	$0.402829\pi$
$642$			20.5474i			0.810940i
$643$	4.54922	−	10.9828i	0.179404	−	0.433119i	−0.808438	−	0.588581i	$-0.799687\pi$
$643$	4.54922	−	10.9828i	0.179404	−	0.433119i	0.987842	+	0.155462i	$0.0496868\pi$
$644$	4.47981	−	4.47981i	0.176529	−	0.176529i
$645$	14.3120			0.563536
$646$	−27.1602	−	78.7455i	−1.06860	−	3.09820i
$647$	−7.26653			−0.285677			−0.142838	−	0.989746i	$-0.545623\pi$
$647$	−7.26653			−0.285677			−0.142838	+	0.989746i	$0.545623\pi$
$648$	5.16926	−	5.16926i	0.203068	−	0.203068i
$649$	2.41647	−	5.83388i	0.0948549	−	0.229000i
$650$			74.1916i			2.91003i
$651$	−9.25723	−	3.83447i	−0.362819	−	0.150285i
$652$	26.6467	+	64.3308i	1.04356	+	2.51939i
$653$	−8.33099	+	3.45081i	−0.326017	+	0.135041i	−0.539688	−	0.841865i	$-0.681458\pi$
$653$	−8.33099	+	3.45081i	−0.326017	+	0.135041i	0.213671	+	0.976906i	$0.431458\pi$
$654$	12.3771	+	12.3771i	0.483984	+	0.483984i
$655$	−8.89001	−	8.89001i	−0.347362	−	0.347362i
$656$	63.6562	−	26.3673i	2.48536	−	1.02947i
$657$	1.82080	+	4.39581i	0.0710363	+	0.171497i
$658$	−17.5876	−	7.28501i	−0.685635	−	0.283999i
$659$		−	2.22036i		−	0.0864929i	−0.999064	−	0.0432464i	$-0.986230\pi$
$659$		−	2.22036i		−	0.0864929i	0.999064	−	0.0432464i	$-0.0137701\pi$
$660$	−26.2118	+	63.2810i	−1.02029	+	2.46321i
$661$	−32.4649	+	32.4649i	−1.26274	+	1.26274i	−0.312980	+	0.949760i	$0.601327\pi$
$661$	−32.4649	+	32.4649i	−1.26274	+	1.26274i	−0.949760	+	0.312980i	$0.898673\pi$
$662$	−18.8087			−0.731020
$663$	−15.0431	−	0.912191i	−0.584224	−	0.0354266i
$664$	−34.9768			−1.35736
$665$	−19.5818	+	19.5818i	−0.759348	+	0.759348i
$666$	−7.54907	+	18.2251i	−0.292521	+	0.706207i
$667$			4.63427i			0.179440i
$668$	−43.9125	−	18.1891i	−1.69902	−	0.703759i
$669$	−2.22275	−	5.36620i	−0.0859366	−	0.207469i
$670$	−18.2392	+	7.55492i	−0.704642	+	0.291872i
$671$	−11.5316	−	11.5316i	−0.445171	−	0.445171i
$672$	−7.11142	−	7.11142i	−0.274329	−	0.274329i
$673$	−16.3206	+	6.76020i	−0.629112	+	0.260587i	−0.674376	−	0.738388i	$-0.735587\pi$
$673$	−16.3206	+	6.76020i	−0.629112	+	0.260587i	0.0452638	+	0.998975i	$0.485587\pi$
$674$	−21.0659	−	50.8575i	−0.811427	−	1.95896i
$675$	7.18979	+	2.97811i	0.276735	+	0.114628i
$676$			1.73063i			0.0665628i
$677$	−16.7168	+	40.3579i	−0.642478	+	1.55108i	0.180848	+	0.983511i	$0.442116\pi$
$677$	−16.7168	+	40.3579i	−0.642478	+	1.55108i	−0.823326	+	0.567569i	$0.807884\pi$
$678$	3.74581	−	3.74581i	0.143857	−	0.143857i
$679$	−11.1122			−0.426446
$680$	71.4481	+	80.6725i	2.73991	+	3.09365i
$681$	8.49861			0.325668
$682$	73.7145	−	73.7145i	2.82267	−	2.82267i
$683$	−15.8609	+	38.2916i	−0.606900	+	1.46519i	0.259453	+	0.965756i	$0.416458\pi$
$683$	−15.8609	+	38.2916i	−0.606900	+	1.46519i	−0.866354	+	0.499431i	$0.833542\pi$
$684$			37.2016i			1.42244i
$685$	16.8919	+	6.99684i	0.645405	+	0.267335i
$686$	−0.998125	−	2.40969i	−0.0381086	−	0.0920022i
$687$	15.1048	−	6.25661i	0.576284	−	0.238705i
$688$	−26.7823	−	26.7823i	−1.02107	−	1.02107i
$689$	8.15987	+	8.15987i	0.310866	+	0.310866i
$690$	11.3642	−	4.70721i	0.432628	−	0.179200i
$691$	1.82654	+	4.40965i	0.0694848	+	0.167751i	0.954807	−	0.297228i	$-0.0960620\pi$
$691$	1.82654	+	4.40965i	0.0694848	+	0.167751i	−0.885322	+	0.464979i	$0.846062\pi$
$692$	−16.6869	−	6.91196i	−0.634343	−	0.262753i
$693$			3.98894i			0.151527i
$694$	−0.591977	+	1.42916i	−0.0224712	+	0.0542502i
$695$	−30.3517	+	30.3517i	−1.15131	+	1.15131i
$696$	25.6831			0.973517
$697$	−22.4772	+	19.9071i	−0.851384	+	0.754034i
$698$	80.1615			3.03416
$699$	13.2978	−	13.2978i	0.502970	−	0.502970i
$700$	14.3034	−	34.5314i	0.540617	−	1.30516i
$701$			39.9843i			1.51019i	0.655618	+	0.755093i	$0.272408\pi$
$701$			39.9843i			1.51019i	−0.655618	+	0.755093i	$0.727592\pi$
$702$	8.80783	+	3.64832i	0.332430	+	0.137697i
$703$	−22.4188	−	54.1238i	−0.845542	−	2.04132i
$704$	26.9319	−	11.1556i	1.01503	−	0.420441i
$705$	−18.4516	−	18.4516i	−0.694926	−	0.694926i
$706$	7.70063	+	7.70063i	0.289817	+	0.289817i
$707$	−5.18472	+	2.14758i	−0.194991	+	0.0807681i
$708$	2.90953	+	7.02422i	0.109347	+	0.263986i
$709$	7.09904	+	2.94052i	0.266610	+	0.110434i	0.511984	−	0.858995i	$-0.328911\pi$
$709$	7.09904	+	2.94052i	0.266610	+	0.110434i	−0.245374	+	0.969429i	$0.578911\pi$
$710$		−	25.2737i		−	0.948503i
$711$	4.87513	−	11.7696i	0.182832	−	0.441395i
$712$	45.5474	−	45.5474i	1.70696	−	1.70696i
$713$	−13.2173			−0.494991
$714$	9.66808	+	4.70919i	0.361819	+	0.176237i
$715$	−52.1277			−1.94946
$716$	55.6998	−	55.6998i	2.08160	−	2.08160i
$717$	−3.88514	+	9.37955i	−0.145093	+	0.350286i
$718$			46.9793i			1.75325i
$719$	−32.9736	−	13.6581i	−1.22971	−	0.509362i	−0.329225	−	0.944252i	$-0.606787\pi$
$719$	−32.9736	−	13.6581i	−1.22971	−	0.509362i	−0.900484	+	0.434890i	$0.856787\pi$
$720$	−12.9451	−	31.2523i	−0.482436	−	1.16470i
$721$	−5.14588	+	2.13149i	−0.191642	+	0.0793809i
$722$	−75.6102	−	75.6102i	−2.81392	−	2.81392i
$723$	11.0165	+	11.0165i	0.409709	+	0.409709i
$724$	44.1183	−	18.2744i	1.63965	−	0.679163i
$725$	10.4627	+	25.2593i	0.388577	+	0.938107i
$726$	−11.8355	−	4.90242i	−0.439256	−	0.181946i
$727$			40.7667i			1.51195i	0.654598	+	0.755977i	$0.272838\pi$
$727$			40.7667i			1.51195i	−0.654598	+	0.755977i	$0.727162\pi$
$728$	10.2257	−	24.6869i	0.378988	−	0.914959i
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	44.3681			1.64214
$731$	14.8387	+	7.22771i	0.548827	+	0.267326i
$732$	19.6356			0.725753
$733$	25.7018	−	25.7018i	0.949318	−	0.949318i	−0.0494584	−	0.998776i	$-0.515750\pi$
$733$	25.7018	−	25.7018i	0.949318	−	0.949318i	0.998776	+	0.0494584i	$0.0157495\pi$
$734$	25.7083	−	62.0653i	0.948910	−	2.29087i
$735$		−	3.57522i		−	0.131874i
$736$	−12.2564	−	5.07677i	−0.451777	−	0.187132i
$737$	−3.23177	−	7.80217i	−0.119044	−	0.287397i
$738$	17.5478	−	7.26853i	0.645943	−	0.267558i
$739$	−2.44106	−	2.44106i	−0.0897959	−	0.0897959i	0.660782	−	0.750578i	$-0.270225\pi$
$739$	−2.44106	−	2.44106i	−0.0897959	−	0.0897959i	−0.750578	+	0.660782i	$0.770225\pi$
$740$	91.8321	+	91.8321i	3.37581	+	3.37581i
$741$	−26.1570	+	10.8346i	−0.960902	+	0.398019i
$742$	−3.15119	−	7.60764i	−0.115684	−	0.279285i
$743$	14.3381	+	5.93905i	0.526015	+	0.217883i	0.629857	−	0.776711i	$-0.283113\pi$
$743$	14.3381	+	5.93905i	0.526015	+	0.217883i	−0.103842	+	0.994594i	$0.533113\pi$
$744$			73.2502i			2.68548i
$745$	6.59791	−	15.9288i	0.241729	−	0.583585i
$746$	−64.5528	+	64.5528i	−2.36345	+	2.36345i
$747$	−4.78451			−0.175056
$748$	−59.1337	+	52.3722i	−2.16214	+	1.91492i
$749$	7.87792			0.287853
$750$	18.3450	−	18.3450i	0.669864	−	0.669864i
$751$	0.366468	−	0.884733i	0.0133726	−	0.0322844i	−0.917052	−	0.398767i	$-0.869438\pi$
$751$	0.366468	−	0.884733i	0.0133726	−	0.0322844i	0.930425	+	0.366483i	$0.119438\pi$
$752$			69.0572i			2.51826i
$753$	−6.46816	−	2.67920i	−0.235713	−	0.0976354i
$754$	12.8174	+	30.9438i	0.466781	+	1.12691i
$755$	72.7686	−	30.1417i	2.64832	−	1.09697i
$756$	−3.39612	−	3.39612i	−0.123516	−	0.123516i
$757$	−28.1640	−	28.1640i	−1.02364	−	1.02364i	−0.999714	−	0.0239248i	$-0.992384\pi$
$757$	−28.1640	−	28.1640i	−1.02364	−	1.02364i	−0.0239248	−	0.999714i	$-0.507616\pi$
$758$	−91.1623	+	37.7606i	−3.31116	+	1.37153i
$759$	2.01360	+	4.86126i	0.0730890	+	0.176453i
$760$	187.036	+	77.4728i	6.78451	+	2.81023i
$761$		−	25.8068i		−	0.935495i	−0.883862	−	0.467748i	$-0.845066\pi$
$761$		−	25.8068i		−	0.935495i	0.883862	−	0.467748i	$-0.154934\pi$
$762$	−7.55093	+	18.2296i	−0.273541	+	0.660387i
$763$	4.74542	−	4.74542i	0.171796	−	0.171796i
$764$	17.9227			0.648421
$765$	9.77344	+	11.0353i	0.353360	+	0.398980i
$766$	−3.08929			−0.111621
$767$	−4.09146	+	4.09146i	−0.147734	+	0.147734i
$768$	6.64468	−	16.0417i	0.239769	−	0.578854i
$769$		−	21.3172i		−	0.768716i	−0.923184	−	0.384358i	$-0.874423\pi$
$769$		−	21.3172i		−	0.768716i	0.923184	−	0.384358i	$-0.125577\pi$
$770$	34.3653	+	14.2346i	1.23844	+	0.512978i
$771$	−4.72234	−	11.4007i	−0.170071	−	0.410588i
$772$	83.2436	−	34.4806i	2.99600	−	1.24099i
$773$	−20.0155	−	20.0155i	−0.719907	−	0.719907i	0.248679	−	0.968586i	$-0.420004\pi$
$773$	−20.0155	−	20.0155i	−0.719907	−	0.719907i	−0.968586	+	0.248679i	$0.920004\pi$
$774$	−7.38294	−	7.38294i	−0.265374	−	0.265374i
$775$	−72.0414	+	29.8405i	−2.58780	+	1.07190i
$776$	31.0872	+	75.0511i	1.11597	+	2.69418i
$777$	6.98754	+	2.89433i	0.250677	+	0.103834i
$778$			64.3103i			2.30564i
$779$	−21.5857	+	52.1124i	−0.773387	+	1.86712i
$780$	44.3807	−	44.3807i	1.58908	−	1.58908i
$781$	10.8113			0.386859
$782$	14.1595	+	0.858615i	0.506344	+	0.0307040i
$783$	3.51322			0.125552
$784$	−6.69035	+	6.69035i	−0.238941	+	0.238941i
$785$	9.43746	−	22.7840i	0.336837	−	0.813198i
$786$			9.17192i			0.327151i
$787$	−41.5085	−	17.1934i	−1.47962	−	0.612878i	−0.510589	−	0.859825i	$-0.670573\pi$
$787$	−41.5085	−	17.1934i	−1.47962	−	0.612878i	−0.969029	+	0.246947i	$0.920573\pi$
$788$	19.2381	+	46.4449i	0.685330	+	1.65453i
$789$	−27.1807	+	11.2586i	−0.967658	+	0.400817i
$790$	−84.0000	−	84.0000i	−2.98859	−	2.98859i
$791$	−1.43615	−	1.43615i	−0.0510638	−	0.0510638i
$792$	26.9411	−	11.1594i	0.957311	−	0.396531i
$793$	5.71866	+	13.8061i	0.203076	+	0.490268i
$794$	−68.6441	−	28.4333i	−2.43609	−	1.00906i
$795$		−	11.2874i		−	0.400321i
$796$	−11.9789	+	28.9195i	−0.424580	+	1.02503i
$797$	24.7606	−	24.7606i	0.877064	−	0.877064i	−0.116166	−	0.993230i	$-0.537060\pi$
$797$	24.7606	−	24.7606i	0.877064	−	0.877064i	0.993230	+	0.116166i	$0.0370604\pi$
$798$	20.2027			0.715167
$799$	−9.81228	−	28.4487i	−0.347133	−	1.00644i
$800$	−78.2659			−2.76712
$801$	6.23046	−	6.23046i	0.220143	−	0.220143i
$802$	12.9699	−	31.3121i	0.457984	−	1.10567i
$803$			18.9793i			0.669766i
$804$	9.39412	+	3.89117i	0.331305	+	0.137231i
$805$	−1.80475	−	4.35706i	−0.0636092	−	0.153566i
$806$	−88.2541	+	36.5560i	−3.10862	+	1.28763i
$807$	15.9898	+	15.9898i	0.562866	+	0.562866i
$808$	29.0094	+	29.0094i	1.02055	+	1.02055i
$809$	7.66252	−	3.17392i	0.269400	−	0.111589i	−0.243894	−	0.969802i	$-0.578425\pi$
$809$	7.66252	−	3.17392i	0.269400	−	0.111589i	0.513294	+	0.858213i	$0.328425\pi$
$810$	−3.56851	−	8.61515i	−0.125385	−	0.302706i
$811$	41.4017	+	17.1491i	1.45381	+	0.602187i	0.963102	−	0.269137i	$-0.0867386\pi$
$811$	41.4017	+	17.1491i	1.45381	+	0.602187i	0.490707	+	0.871325i	$0.336739\pi$
$812$		−	16.8734i		−	0.592141i
$813$	−9.14507	+	22.0781i	−0.320731	+	0.774314i
$814$	−55.6412	+	55.6412i	−1.95022	+	1.95022i
$815$	51.8332			1.81564
$816$	2.36124	−	38.9396i	0.0826601	−	1.36316i
$817$	31.0073			1.08481
$818$	−25.8407	+	25.8407i	−0.903499	+	0.903499i
$819$	1.39878	−	3.37695i	0.0488772	−	0.118000i
$820$		−	125.044i		−	4.36672i
$821$	18.4147	+	7.62762i	0.642678	+	0.266206i	0.680129	−	0.733093i	$-0.261924\pi$
$821$	18.4147	+	7.62762i	0.642678	+	0.266206i	−0.0374511	+	0.999298i	$0.511924\pi$
$822$	−5.10440	−	12.3231i	−0.178036	−	0.429818i
$823$	16.1286	−	6.68067i	0.562207	−	0.232874i	−0.0834363	−	0.996513i	$-0.526590\pi$
$823$	16.1286	−	6.68067i	0.562207	−	0.232874i	0.645643	+	0.763640i	$0.276590\pi$
$824$	28.7920	+	28.7920i	1.00302	+	1.00302i
$825$	21.9504	+	21.9504i	0.764217	+	0.764217i
$826$	3.81457	−	1.58005i	0.132726	−	0.0549768i
$827$	7.37383	+	17.8020i	0.256413	+	0.619036i	0.998696	−	0.0510506i	$-0.0162570\pi$
$827$	7.37383	+	17.8020i	0.256413	+	0.619036i	−0.742283	+	0.670087i	$0.766257\pi$
$828$	−5.85315	−	2.42445i	−0.203411	−	0.0842556i
$829$			1.79073i			0.0621945i	0.999516	+	0.0310973i	$0.00990016\pi$
$829$			1.79073i			0.0621945i	−0.999516	+	0.0310973i	$0.990100\pi$
$830$	−17.0736	+	41.2193i	−0.592632	+	1.43074i
$831$	−2.41425	+	2.41425i	−0.0837495	+	0.0837495i
$832$	−26.7118			−0.926065
$833$	1.80552	−	3.70677i	0.0625574	−	0.128432i
$834$	31.3142			1.08432
$835$	−25.0185	+	25.0185i	−0.865802	+	0.865802i
$836$	−56.7883	+	137.099i	−1.96407	+	4.74167i
$837$			10.0200i			0.346340i
$838$	−16.9429	−	7.01800i	−0.585284	−	0.242433i
$839$	1.95314	+	4.71530i	0.0674299	+	0.162790i	0.954002	−	0.299800i	$-0.0969200\pi$
$839$	1.95314	+	4.71530i	0.0674299	+	0.162790i	−0.886572	+	0.462590i	$0.846920\pi$
$840$	−24.1469	+	10.0020i	−0.833146	+	0.345101i
$841$	−11.7785	−	11.7785i	−0.406155	−	0.406155i
$842$	−74.6446	−	74.6446i	−2.57242	−	2.57242i
$843$	22.2784	−	9.22803i	0.767310	−	0.317830i
$844$	−43.4146	−	104.812i	−1.49439	−	3.60778i
$845$	1.19021	+	0.493002i	0.0409446	+	0.0169598i
$846$			19.0367i			0.654494i
$847$	−1.87960	+	4.53775i	−0.0645838	+	0.155919i
$848$	−21.1222	+	21.1222i	−0.725338	+	0.725338i
$849$	−31.1064			−1.06757
$850$	79.1157	−	27.2879i	2.71365	−	0.935968i
$851$	9.97666			0.341995
$852$	−9.20457	+	9.20457i	−0.315343	+	0.315343i
$853$	3.54772	−	8.56495i	0.121472	−	0.293258i	−0.851434	−	0.524462i	$-0.824266\pi$
$853$	3.54772	−	8.56495i	0.121472	−	0.293258i	0.972905	+	0.231204i	$0.0742664\pi$
$854$		−	10.6633i		−	0.364890i
$855$	25.5848	+	10.5976i	0.874981	+	0.362429i
$856$	−22.0391	−	53.2071i	−0.753282	−	1.81858i
$857$	−10.8950	+	4.51284i	−0.372165	+	0.154156i	−0.560923	−	0.827868i	$-0.689554\pi$
$857$	−10.8950	+	4.51284i	−0.372165	+	0.154156i	0.188758	+	0.982024i	$0.439554\pi$
$858$	26.8903	+	26.8903i	0.918021	+	0.918021i
$859$	4.57505	+	4.57505i	0.156099	+	0.156099i	0.780835	−	0.624737i	$-0.214794\pi$
$859$	4.57505	+	4.57505i	0.156099	+	0.156099i	−0.624737	+	0.780835i	$0.714794\pi$
$860$	−63.5060	+	26.3051i	−2.16554	+	0.896995i
$861$	−2.78677	−	6.72787i	−0.0949730	−	0.229285i
$862$	78.6735	+	32.5876i	2.67963	+	1.10994i
$863$		−	42.6513i		−	1.45187i	−0.687764	−	0.725934i	$-0.741408\pi$
$863$		−	42.6513i		−	1.45187i	0.687764	−	0.725934i	$-0.258592\pi$
$864$	−3.84867	+	9.29152i	−0.130935	+	0.316104i
$865$	−9.50716	+	9.50716i	−0.323253	+	0.323253i
$866$	−69.8724			−2.37436
$867$	4.56015	+	16.3770i	0.154871	+	0.556191i
$868$	48.1242			1.63344
$869$	35.9326	−	35.9326i	1.21893	−	1.21893i
$870$	12.5370	−	30.2669i	0.425043	−	1.02614i
$871$			7.73841i			0.262206i
$872$	−45.3261	−	18.7747i	−1.53493	−	0.635791i
$873$	4.25244	+	10.2663i	0.143923	+	0.347462i
$874$	24.6207	−	10.1982i	0.832808	−	0.344960i
$875$	−7.03351	−	7.03351i	−0.237776	−	0.237776i
$876$	−16.1587	−	16.1587i	−0.545952	−	0.545952i
$877$	29.8295	−	12.3558i	1.00727	−	0.417226i	0.182813	−	0.983148i	$-0.441480\pi$
$877$	29.8295	−	12.3558i	1.00727	−	0.417226i	0.824459	+	0.565922i	$0.191480\pi$
$878$	17.2163	+	41.5637i	0.581021	+	1.40271i
$879$	−15.4821	−	6.41291i	−0.522199	−	0.216302i
$880$		−	134.935i		−	4.54865i
$881$	−10.2535	+	24.7541i	−0.345449	+	0.833988i	0.651696	+	0.758480i	$0.274058\pi$
$881$	−10.2535	+	24.7541i	−0.345449	+	0.833988i	−0.997145	+	0.0755075i	$0.975942\pi$
$882$	−1.84429	+	1.84429i	−0.0621006	+	0.0621006i
$883$	−3.62374			−0.121949			−0.0609743	−	0.998139i	$-0.519421\pi$
$883$	−3.62374			−0.121949			−0.0609743	+	0.998139i	$0.519421\pi$
$884$	68.4263	−	23.6010i	2.30143	−	0.793788i
$885$	5.65962			0.190246
$886$	1.56436	−	1.56436i	0.0525559	−	0.0525559i
$887$	14.5911	−	35.2261i	0.489922	−	1.18278i	−0.464837	−	0.885396i	$-0.653887\pi$
$887$	14.5911	−	35.2261i	0.489922	−	1.18278i	0.954759	−	0.297381i	$-0.0961131\pi$
$888$		−	55.2907i		−	1.85543i
$889$	6.98926	+	2.89504i	0.234412	+	0.0970967i
$890$	−31.4429	−	75.9098i	−1.05397	−	2.54450i
$891$	3.68530	−	1.52650i	0.123462	−	0.0511397i
$892$	19.7258	+	19.7258i	0.660469	+	0.660469i
$893$	−39.9756	−	39.9756i	−1.33773	−	1.33773i
$894$	−11.6205	+	4.81337i	−0.388647	+	0.160983i
$895$	−22.4395	−	54.1737i	−0.750069	−	1.81083i
$896$	−0.973217	−	0.403120i	−0.0325129	−	0.0134673i
$897$		−	4.82153i		−	0.160986i
$898$	−8.92957	+	21.5579i	−0.297983	+	0.719396i
$899$	−24.8918	+	24.8918i	−0.830187	+	0.830187i
$900$	−37.3765			−1.24588
$901$	5.70021	−	11.7027i	0.189902	−	0.389872i
$902$	75.7643			2.52267
$903$	−2.83064	+	2.83064i	−0.0941977	+	0.0941977i
$904$	−5.68197	+	13.7175i	−0.188980	+	0.456237i
$905$		−	35.5474i		−	1.18164i
$906$	−53.0868	−	21.9893i	−1.76369	−	0.730545i
$907$	−0.478534	−	1.15528i	−0.0158895	−	0.0383606i	0.915736	−	0.401781i	$-0.131609\pi$
$907$	−0.478534	−	1.15528i	−0.0158895	−	0.0383606i	−0.931625	+	0.363421i	$0.881609\pi$
$908$	−37.7104	+	15.6202i	−1.25146	+	0.518374i
$909$	3.96821	+	3.96821i	0.131617	+	0.131617i
$910$	−24.1013	−	24.1013i	−0.798952	−	0.798952i
$911$	−2.30785	+	0.955945i	−0.0764626	+	0.0316719i	−0.420587	−	0.907252i	$-0.638176\pi$
$911$	−2.30785	+	0.955945i	−0.0764626	+	0.0316719i	0.344124	+	0.938924i	$0.388176\pi$
$912$	−28.0458	−	67.7085i	−0.928689	−	2.24205i
$913$	−17.6323	−	7.30356i	−0.583545	−	0.241712i
$914$		−	37.4646i		−	1.23922i
$915$	5.59356	−	13.5040i	0.184917	−	0.446430i
$916$	−55.5242	+	55.5242i	−1.83457	+	1.83457i
$917$	3.51654			0.116126
$918$	0.650912	−	10.7343i	0.0214833	−	0.354284i
$919$	−1.86154			−0.0614064			−0.0307032	−	0.999529i	$-0.509775\pi$
$919$	−1.86154			−0.0614064			−0.0307032	+	0.999529i	$0.509775\pi$
$920$	−24.3785	+	24.3785i	−0.803735	+	0.803735i
$921$	−1.30507	+	3.15071i	−0.0430034	+	0.103819i
$922$			19.7117i			0.649170i
$923$	−9.15260	−	3.79113i	−0.301262	−	0.124787i
$924$	−7.33154	−	17.6999i	−0.241190	−	0.582284i
$925$	54.3783	−	22.5242i	1.78795	−	0.740592i
$926$	4.63501	+	4.63501i	0.152316	+	0.152316i
$927$	3.93848	+	3.93848i	0.129357	+	0.129357i
$928$	−32.6431	+	13.5212i	−1.07156	+	0.443856i
$929$	19.6992	+	47.5582i	0.646311	+	1.56033i	0.818023	+	0.575185i	$0.195070\pi$
$929$	19.6992	+	47.5582i	0.646311	+	1.56033i	−0.171712	+	0.985147i	$0.554930\pi$
$930$	86.3234	+	35.7563i	2.83066	+	1.17250i
$931$		−	7.74576i		−	0.253857i
$932$	−34.5648	+	83.4467i	−1.13221	+	2.73339i
$933$	−23.9627	+	23.9627i	−0.784502	+	0.784502i
$934$	−71.9013			−2.35268
$935$	19.1727	+	55.5874i	0.627015	+	1.81790i
$936$	−26.7209			−0.873401
$937$	−18.7884	+	18.7884i	−0.613791	+	0.613791i	−0.943932	−	0.330141i	$-0.892904\pi$
$937$	−18.7884	+	18.7884i	−0.613791	+	0.613791i	0.330141	+	0.943932i	$0.392904\pi$
$938$	2.11314	−	5.10156i	0.0689964	−	0.166572i
$939$			15.1047i			0.492922i
$940$	115.787	+	47.9607i	3.77657	+	1.56431i
$941$	−1.95939	−	4.73038i	−0.0638742	−	0.154206i	0.888719	−	0.458451i	$-0.151596\pi$
$941$	−1.95939	−	4.73038i	−0.0638742	−	0.154206i	−0.952594	+	0.304245i	$0.901596\pi$
$942$	−16.6216	+	6.88490i	−0.541562	+	0.224322i
$943$	−6.79240	−	6.79240i	−0.221191	−	0.221191i
$944$	−10.5909	−	10.5909i	−0.344705	−	0.344705i
$945$	−3.30307	+	1.36818i	−0.107449	+	0.0445068i
$946$	−15.9383	−	38.4784i	−0.518198	−	1.25104i
$947$	−44.5530	−	18.4545i	−1.44778	−	0.599690i	−0.486109	−	0.873898i	$-0.661584\pi$
$947$	−44.5530	−	18.4545i	−1.44778	−	0.599690i	−0.961670	+	0.274208i	$0.911584\pi$
$948$			61.1850i			1.98720i
$949$	6.65537	−	16.0675i	0.216042	−	0.521572i
$950$	111.172	−	111.172i	3.60689	−	3.60689i
$951$	−7.87347			−0.255315
$952$	−30.0864	−	1.82440i	−0.975107	−	0.0591292i
$953$	17.0323			0.551729			0.275864	−	0.961197i	$-0.411036\pi$
$953$	17.0323			0.551729			0.275864	+	0.961197i	$0.411036\pi$
$954$	−5.82264	+	5.82264i	−0.188515	+	0.188515i
$955$	5.10561	−	12.3260i	0.165214	−	0.398861i
$956$		−	48.7601i		−	1.57702i
$957$	12.9473	+	5.36293i	0.418525	+	0.173359i
$958$	31.9162	+	77.0524i	1.03116	+	2.48945i
$959$	−4.72471	+	1.95704i	−0.152569	+	0.0631961i
$960$	18.4749	+	18.4749i	0.596274	+	0.596274i
$961$	−49.0728	−	49.0728i	−1.58299	−	1.58299i
$962$	66.6159	−	27.5932i	2.14778	−	0.889641i
$963$	−3.01475	−	7.27825i	−0.0971489	−	0.234538i
$964$	−69.1311	−	28.6350i	−2.22656	−	0.922273i
$965$		−	67.0718i		−	2.15912i
$966$	−1.31662	+	3.17861i	−0.0423616	+	0.102270i
$967$	−12.8879	+	12.8879i	−0.414448	+	0.414448i	−0.883285	−	0.468837i	$-0.844673\pi$
$967$	−12.8879	+	12.8879i	−0.414448	+	0.414448i	0.468837	+	0.883285i	$0.344673\pi$
$968$	35.9061			1.15407
$969$	21.1743	+	23.9080i	0.680217	+	0.768037i
$970$	103.621			3.32706
$971$	31.6820	−	31.6820i	1.01672	−	1.01672i	0.0168653	−	0.999858i	$-0.494631\pi$
$971$	31.6820	−	31.6820i	1.01672	−	1.01672i	0.999858	−	0.0168653i	$-0.00536865\pi$
$972$	−1.83797	+	4.43724i	−0.0589528	+	0.142325i
$973$		−	12.0059i		−	0.384892i
$974$	−29.4589	−	12.2023i	−0.943925	−	0.390986i
$975$	−10.8855	−	26.2800i	−0.348616	−	0.841633i
$976$	−35.7376	+	14.8030i	−1.14393	+	0.473832i
$977$	41.2736	+	41.2736i	1.32046	+	1.32046i	0.913402	+	0.407059i	$0.133446\pi$
$977$	41.2736	+	41.2736i	1.32046	+	1.32046i	0.407059	+	0.913402i	$0.366554\pi$
$978$	−26.7384	−	26.7384i	−0.855000	−	0.855000i
$979$	32.4719	−	13.4503i	1.03781	−	0.429874i
$980$	6.57113	+	15.8641i	0.209907	+	0.506760i
$981$	−6.20019	−	2.56820i	−0.197957	−	0.0819964i
$982$			63.8155i			2.03644i
$983$	11.9526	−	28.8562i	0.381230	−	0.920371i	−0.610498	−	0.792018i	$-0.709031\pi$
$983$	11.9526	−	28.8562i	0.381230	−	0.920371i	0.991728	−	0.128354i	$-0.0409692\pi$
$984$	−37.6435	+	37.6435i	−1.20003	+	1.20003i
$985$	37.4220			1.19236
$986$	28.2833	−	25.0493i	0.900724	−	0.797732i
$987$	7.29870			0.232320
$988$	96.1514	−	96.1514i	3.05898	−	3.05898i
$989$	−2.02076	+	4.87855i	−0.0642565	+	0.155129i
$990$		−	37.1967i		−	1.18219i
$991$	5.88695	+	2.43845i	0.187005	+	0.0774600i	0.474221	−	0.880406i	$-0.342730\pi$
$991$	5.88695	+	2.43845i	0.187005	+	0.0774600i	−0.287216	+	0.957866i	$0.592730\pi$
$992$	−38.5635	−	93.1006i	−1.22439	−	2.95595i
$993$	6.66237	−	2.75964i	0.211424	−	0.0875746i
$994$	4.99863	+	4.99863i	0.158547	+	0.158547i
$995$	16.4765	+	16.4765i	0.522341	+	0.522341i
$996$	21.2300	−	8.79377i	0.672699	−	0.278641i
$997$	−5.74952	−	13.8806i	−0.182089	−	0.439602i	0.806308	−	0.591496i	$-0.201463\pi$
$997$	−5.74952	−	13.8806i	−0.182089	−	0.439602i	−0.988397	+	0.151894i	$0.951463\pi$
$998$	−34.6821	−	14.3658i	−1.09784	−	0.454742i
$999$		−	7.56326i		−	0.239291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.u.a.127.8	✓	32
17.7	odd	16		6069.2.a.bk.1.1		16
17.10	odd	16		6069.2.a.bj.1.1		16
17.15	even	8	inner	357.2.u.a.253.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.u.a.127.8	✓	32	1.1	even	1	trivial
357.2.u.a.253.8	yes	32	17.15	even	8	inner
6069.2.a.bj.1.1		16	17.10	odd	16
6069.2.a.bk.1.1		16	17.7	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.84429 - 1.84429i) q^{2} +(-0.382683 + 0.923880i) q^{3} -4.80284i q^{4} +(-3.30307 - 1.36818i) q^{5} +(0.998125 + 2.40969i) q^{6} +(0.923880 - 0.382683i) q^{7} +(-5.16926 - 5.16926i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-8.61515 + 3.56851i) q^{10} +(-1.52650 - 3.68530i) q^{11} +(4.43724 + 1.83797i) q^{12} +3.65518i q^{13} +(0.998125 - 2.40969i) q^{14} +(2.52806 - 2.52806i) q^{15} -9.46158 q^{16} +(3.89777 - 1.34439i) q^{17} -2.60823 q^{18} +(5.47708 - 5.47708i) q^{19} +(-6.57113 + 15.8641i) q^{20} +1.00000i q^{21} +(-9.61209 - 3.98146i) q^{22} +(0.504796 + 1.21869i) q^{23} +(6.75396 - 2.79758i) q^{24} +(5.50283 + 5.50283i) q^{25} +(6.74122 + 6.74122i) q^{26} +(0.923880 - 0.382683i) q^{27} +(-1.83797 - 4.43724i) q^{28} +(3.24579 + 1.34445i) q^{29} -9.32497i q^{30} +(-3.83447 + 9.25723i) q^{31} +(-7.11142 + 7.11142i) q^{32} +3.98894 q^{33} +(4.70919 - 9.66808i) q^{34} -3.57522 q^{35} +(-3.39612 + 3.39612i) q^{36} +(2.89433 - 6.98754i) q^{37} -20.2027i q^{38} +(-3.37695 - 1.39878i) q^{39} +(10.0020 + 24.1469i) q^{40} +(-6.72787 + 2.78677i) q^{41} +(1.84429 + 1.84429i) q^{42} +(2.83064 + 2.83064i) q^{43} +(-17.6999 + 7.33154i) q^{44} +(1.36818 + 3.30307i) q^{45} +(3.17861 + 1.31662i) q^{46} -7.29870i q^{47} +(3.62079 - 8.74136i) q^{48} +(0.707107 - 0.707107i) q^{49} +20.2977 q^{50} +(-0.249561 + 4.11555i) q^{51} +17.5552 q^{52} +(2.23241 - 2.23241i) q^{53} +(0.998125 - 2.40969i) q^{54} +14.2613i q^{55} +(-6.75396 - 2.79758i) q^{56} +(2.96417 + 7.15615i) q^{57} +(8.46575 - 3.50663i) q^{58} +(1.11936 + 1.11936i) q^{59} +(-12.1419 - 12.1419i) q^{60} +(3.77713 - 1.56454i) q^{61} +(10.0012 + 24.1449i) q^{62} +(-0.923880 - 0.382683i) q^{63} +7.30793i q^{64} +(5.00093 - 12.0733i) q^{65} +(7.35677 - 7.35677i) q^{66} +2.11711 q^{67} +(-6.45687 - 18.7204i) q^{68} -1.31910 q^{69} +(-6.59375 + 6.59375i) q^{70} +(-1.03719 + 2.50401i) q^{71} +7.31043i q^{72} +(-4.39581 - 1.82080i) q^{73} +(-7.54907 - 18.2251i) q^{74} +(-7.18979 + 2.97811i) q^{75} +(-26.3055 - 26.3055i) q^{76} +(-2.82061 - 2.82061i) q^{77} +(-8.80783 + 3.64832i) q^{78} +(4.87513 + 11.7696i) q^{79} +(31.2523 + 12.9451i) q^{80} +1.00000i q^{81} +(-7.26853 + 17.5478i) q^{82} +(3.38316 - 3.38316i) q^{83} +4.80284 q^{84} +(-14.7140 - 0.892235i) q^{85} +10.4411 q^{86} +(-2.48422 + 2.48422i) q^{87} +(-11.1594 + 26.9411i) q^{88} +8.81120i q^{89} +(8.61515 + 3.56851i) q^{90} +(1.39878 + 3.37695i) q^{91} +(5.85315 - 2.42445i) q^{92} +(-7.08518 - 7.08518i) q^{93} +(-13.4609 - 13.4609i) q^{94} +(-25.5848 + 10.5976i) q^{95} +(-3.84867 - 9.29152i) q^{96} +(-10.2663 - 4.25244i) q^{97} -2.60823i q^{98} +(-1.52650 + 3.68530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{6} - 32 q^{10} + 8 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} + 8 q^{19} - 16 q^{20} - 8 q^{23} - 8 q^{24} + 24 q^{25} - 32 q^{26} + 24 q^{29} + 8 q^{31} - 40 q^{32} + 8 q^{33} - 8 q^{34} - 8 q^{35}+ \cdots + 96 q^{97}+O(q^{100}) \) 32 * q + 8 * q^6 - 32 * q^10 + 8 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 + 8 * q^19 - 16 * q^20 - 8 * q^23 - 8 * q^24 + 24 * q^25 - 32 * q^26 + 24 * q^29 + 8 * q^31 - 40 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^35 - 8 * q^36 + 72 * q^37 - 16 * q^39 + 40 * q^40 + 8 * q^41 - 32 * q^43 - 48 * q^44 + 8 * q^45 + 40 * q^46 + 32 * q^48 + 56 * q^50 - 16 * q^51 - 56 * q^53 + 8 * q^54 + 8 * q^56 + 16 * q^57 - 32 * q^58 - 48 * q^59 - 48 * q^60 + 8 * q^61 - 24 * q^62 + 16 * q^66 + 96 * q^67 - 16 * q^68 + 8 * q^69 - 16 * q^70 + 24 * q^71 - 24 * q^73 - 32 * q^74 - 16 * q^75 - 48 * q^76 - 24 * q^77 - 72 * q^78 - 48 * q^79 + 72 * q^80 + 96 * q^82 - 24 * q^83 + 24 * q^84 - 136 * q^85 - 32 * q^87 + 16 * q^88 + 32 * q^90 + 8 * q^91 + 136 * q^92 + 8 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 + 96 * q^97

Introduction

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