LMFDB - Embedded newform 840.2.cq.a.611.41

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(11,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 3, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.cq (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,0,0,-64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			611.41
Character	$\chi$	$=$	840.611
Dual form			840.2.cq.a.11.41

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.587274 + 1.28651i) q^{2} +(1.43339 + 0.972318i) q^{3} +(-1.31022 + 1.51107i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.409106 + 2.41508i) q^{6} +(2.48277 + 0.914246i) q^{7} +(-2.71346 - 0.798201i) q^{8} +(1.10920 + 2.78741i) q^{9} +(-1.40779 - 0.134661i) q^{10} +(5.52569 - 3.19026i) q^{11} +(-3.34729 + 0.891996i) q^{12} +2.92141i q^{13} +(0.281880 + 3.73102i) q^{14} +(-1.55875 + 0.755191i) q^{15} +(-0.566651 - 3.95966i) q^{16} +(-6.02508 + 3.47858i) q^{17} +(-2.93464 + 3.06397i) q^{18} +(-0.410032 + 0.710197i) q^{19} +(-0.653513 - 1.89022i) q^{20} +(2.66984 + 3.72451i) q^{21} +(7.34939 + 5.23530i) q^{22} +(3.24378 - 5.61839i) q^{23} +(-3.11334 - 3.78248i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.75843 + 1.71567i) q^{26} +(-1.12034 + 5.07394i) q^{27} +(-4.63446 + 2.55377i) q^{28} +1.36346 q^{29} +(-1.88697 - 1.56184i) q^{30} +(-1.54758 + 0.893495i) q^{31} +(4.76137 - 3.05441i) q^{32} +(11.0224 + 0.799850i) q^{33} +(-8.01360 - 5.70845i) q^{34} +(-2.03315 + 1.69302i) q^{35} +(-5.66526 - 1.97605i) q^{36} +(-5.90797 - 3.41097i) q^{37} +(-1.15448 - 0.110431i) q^{38} +(-2.84054 + 4.18751i) q^{39} +(2.04799 - 1.95083i) q^{40} -4.67787i q^{41} +(-3.22370 + 5.62208i) q^{42} -8.45307 q^{43} +(-2.41917 + 12.5296i) q^{44} +(-2.96857 - 0.433114i) q^{45} +(9.13310 + 0.873623i) q^{46} +(3.56339 - 6.17197i) q^{47} +(3.03782 - 6.22669i) q^{48} +(5.32831 + 4.53973i) q^{49} +(0.820514 - 1.15185i) q^{50} +(-12.0186 - 0.872137i) q^{51} +(-4.41445 - 3.82769i) q^{52} +(-4.72056 - 8.17625i) q^{53} +(-7.18562 + 1.53846i) q^{54} +6.38052i q^{55} +(-6.00715 - 4.46252i) q^{56} +(-1.27827 + 0.619305i) q^{57} +(0.800726 + 1.75411i) q^{58} +(-2.25883 + 1.30414i) q^{59} +(0.901154 - 3.34484i) q^{60} +(7.43114 + 4.29037i) q^{61} +(-2.05834 - 1.46625i) q^{62} +(0.205501 + 7.93459i) q^{63} +(6.72575 + 4.33178i) q^{64} +(-2.53002 - 1.46071i) q^{65} +(5.44415 + 14.6502i) q^{66} +(0.191019 + 0.330854i) q^{67} +(2.63780 - 13.6620i) q^{68} +(10.1124 - 4.89934i) q^{69} +(-3.37210 - 1.62140i) q^{70} +2.20330 q^{71} +(-0.784847 - 8.44891i) q^{72} +(-2.19598 - 3.80355i) q^{73} +(0.918651 - 9.60383i) q^{74} +(0.125358 - 1.72751i) q^{75} +(-0.535923 - 1.55010i) q^{76} +(16.6357 - 2.86884i) q^{77} +(-7.05546 - 1.19517i) q^{78} +(14.1532 + 8.17134i) q^{79} +(3.71249 + 1.48910i) q^{80} +(-6.53936 + 6.18359i) q^{81} +(6.01813 - 2.74719i) q^{82} -9.26784i q^{83} +(-9.12606 - 0.845623i) q^{84} -6.95716i q^{85} +(-4.96427 - 10.8750i) q^{86} +(1.95437 + 1.32572i) q^{87} +(-17.5402 + 4.24603i) q^{88} +(11.1758 + 6.45237i) q^{89} +(-1.18616 - 4.07345i) q^{90} +(-2.67089 + 7.25320i) q^{91} +(4.23970 + 12.2629i) q^{92} +(-3.08704 - 0.224014i) q^{93} +(10.0330 + 0.959702i) q^{94} +(-0.410032 - 0.710197i) q^{95} +(9.79473 + 0.251413i) q^{96} +1.23173 q^{97} +(-2.71123 + 9.52099i) q^{98} +(15.0217 + 11.8638i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 64 q^{5} - 12 q^{12} - 6 q^{14} + 8 q^{16} + 14 q^{18} + 8 q^{21} + 4 q^{22} - 64 q^{25} - 16 q^{26} - 6 q^{28} - 10 q^{32} + 24 q^{34} + 20 q^{36} - 16 q^{38} + 16 q^{42} + 6 q^{44} + 8 q^{46}+ \cdots + 14 q^{98}+O(q^{100}) $ 128 * q - 64 * q^5 - 12 * q^12 - 6 * q^14 + 8 * q^16 + 14 * q^18 + 8 * q^21 + 4 * q^22 - 64 * q^25 - 16 * q^26 - 6 * q^28 - 10 * q^32 + 24 * q^34 + 20 * q^36 - 16 * q^38 + 16 * q^42 + 6 * q^44 + 8 * q^46 - 80 * q^48 + 8 * q^49 + 20 * q^51 - 6 * q^52 - 32 * q^54 - 18 * q^56 - 8 * q^58 - 12 * q^60 - 20 * q^62 - 28 * q^63 - 14 * q^66 + 32 * q^67 - 2 * q^68 + 40 * q^69 - 6 * q^70 - 48 * q^71 + 4 * q^72 - 8 * q^73 - 26 * q^74 - 24 * q^76 - 12 * q^78 + 8 * q^80 + 4 * q^81 - 12 * q^82 - 22 * q^84 + 46 * q^86 - 36 * q^87 - 20 * q^88 - 28 * q^90 - 24 * q^91 - 40 * q^92 + 12 * q^94 + 34 * q^96 + 32 * q^97 + 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$-1$	$-1$

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 $

$2$	0.587274	+	1.28651i	0.415265	+	0.909700i
$2$	0.587274	+	1.28651i	0.415265	+	0.909700i
$3$	1.43339	+	0.972318i	0.827566	+	0.561368i
$3$	1.43339	+	0.972318i	0.827566	+	0.561368i
$4$	−1.31022	+	1.51107i	−0.655110	+	0.755534i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.409106	+	2.41508i	−0.167017	+	0.985954i
$7$	2.48277	+	0.914246i	0.938399	+	0.345552i
$7$	2.48277	+	0.914246i	0.938399	+	0.345552i
$8$	−2.71346	−	0.798201i	−0.959354	−	0.282207i
$9$	1.10920	+	2.78741i	0.369732	+	0.929138i
$10$	−1.40779	−	0.134661i	−0.445182	−	0.0425837i
$11$	5.52569	−	3.19026i	1.66606	−	0.961899i	0.696326	−	0.717725i	$-0.254817\pi$
$11$	5.52569	−	3.19026i	1.66606	−	0.961899i	0.969732	−	0.244173i	$-0.0785166\pi$
$12$	−3.34729	+	0.891996i	−0.966279	+	0.257497i
$13$			2.92141i			0.810254i	0.914260	+	0.405127i	$0.132773\pi$
$13$			2.92141i			0.810254i	−0.914260	+	0.405127i	$0.867227\pi$
$14$	0.281880	+	3.73102i	0.0753355	+	0.997158i
$15$	−1.55875	+	0.755191i	−0.402466	+	0.194989i
$16$	−0.566651	−	3.95966i	−0.141663	−	0.989915i
$17$	−6.02508	+	3.47858i	−1.46130	+	0.843680i	−0.999071	−	0.0430830i	$-0.986282\pi$
$17$	−6.02508	+	3.47858i	−1.46130	+	0.843680i	−0.462225	+	0.886763i	$0.652949\pi$
$18$	−2.93464	+	3.06397i	−0.691700	+	0.722184i
$19$	−0.410032	+	0.710197i	−0.0940679	+	0.162930i	−0.909219	−	0.416318i	$-0.863320\pi$
$19$	−0.410032	+	0.710197i	−0.0940679	+	0.162930i	0.815151	+	0.579248i	$0.196654\pi$
$20$	−0.653513	−	1.89022i	−0.146130	−	0.422665i
$21$	2.66984	+	3.72451i	0.582606	+	0.812755i
$22$	7.34939	+	5.23530i	1.56690	+	1.11617i
$23$	3.24378	−	5.61839i	0.676374	−	1.17151i	−0.299691	−	0.954036i	$-0.596884\pi$
$23$	3.24378	−	5.61839i	0.676374	−	1.17151i	0.976065	−	0.217478i	$-0.0697831\pi$
$24$	−3.11334	−	3.78248i	−0.635507	−	0.772095i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.75843	+	1.71567i	−0.737088	+	0.336470i
$27$	−1.12034	+	5.07394i	−0.215610	+	0.976480i
$28$	−4.63446	+	2.55377i	−0.875831	+	0.482618i
$29$	1.36346			0.253189			0.126594	−	0.991955i	$-0.459595\pi$
$29$	1.36346			0.253189			0.126594	+	0.991955i	$0.459595\pi$
$30$	−1.88697	−	1.56184i	−0.344512	−	0.285151i
$31$	−1.54758	+	0.893495i	−0.277953	+	0.160476i	−0.632496	−	0.774563i	$-0.717970\pi$
$31$	−1.54758	+	0.893495i	−0.277953	+	0.160476i	0.354543	+	0.935040i	$0.384636\pi$
$32$	4.76137	−	3.05441i	0.841698	−	0.539948i
$33$	11.0224	+	0.799850i	1.91875	+	0.139236i
$34$	−8.01360	−	5.70845i	−1.37432	−	0.978991i
$35$	−2.03315	+	1.69302i	−0.343664	+	0.286173i
$36$	−5.66526	−	1.97605i	−0.944211	−	0.329342i
$37$	−5.90797	−	3.41097i	−0.971264	−	0.560760i	−0.0716426	−	0.997430i	$-0.522824\pi$
$37$	−5.90797	−	3.41097i	−0.971264	−	0.560760i	−0.899621	+	0.436671i	$0.856157\pi$
$38$	−1.15448	−	0.110431i	−0.187281	−	0.0179143i
$39$	−2.84054	+	4.18751i	−0.454850	+	0.670539i
$40$	2.04799	−	1.95083i	0.323816	−	0.308453i
$41$		−	4.67787i		−	0.730560i	−0.930898	−	0.365280i	$-0.880973\pi$
$41$		−	4.67787i		−	0.730560i	0.930898	−	0.365280i	$-0.119027\pi$
$42$	−3.22370	+	5.62208i	−0.497427	+	0.867506i
$43$	−8.45307			−1.28908			−0.644541	−	0.764570i	$-0.722951\pi$
$43$	−8.45307			−1.28908			−0.644541	+	0.764570i	$0.722951\pi$
$44$	−2.41917	+	12.5296i	−0.364703	+	1.88891i
$45$	−2.96857	−	0.433114i	−0.442528	−	0.0645649i
$46$	9.13310	+	0.873623i	1.34660	+	0.128809i
$47$	3.56339	−	6.17197i	0.519774	−	0.900274i	−0.479962	−	0.877289i	$-0.659350\pi$
$47$	3.56339	−	6.17197i	0.519774	−	0.900274i	0.999736	−	0.0229852i	$-0.00731705\pi$
$48$	3.03782	−	6.22669i	0.438471	−	0.898745i
$49$	5.32831	+	4.53973i	0.761187	+	0.648532i
$50$	0.820514	−	1.15185i	0.116038	−	0.162896i
$51$	−12.0186	−	0.872137i	−1.68293	−	0.122124i
$52$	−4.41445	−	3.82769i	−0.612174	−	0.530805i
$53$	−4.72056	−	8.17625i	−0.648419	−	1.12309i	−0.983500	−	0.180906i	$-0.942097\pi$
$53$	−4.72056	−	8.17625i	−0.648419	−	1.12309i	0.335081	−	0.942189i	$-0.391236\pi$
$54$	−7.18562	+	1.53846i	−0.977839	+	0.209357i
$55$			6.38052i			0.860349i
$56$	−6.00715	−	4.46252i	−0.802740	−	0.596329i
$57$	−1.27827	+	0.619305i	−0.169311	+	0.0820290i
$58$	0.800726	+	1.75411i	0.105140	+	0.230326i
$59$	−2.25883	+	1.30414i	−0.294075	+	0.169784i	−0.639778	−	0.768560i	$-0.720974\pi$
$59$	−2.25883	+	1.30414i	−0.294075	+	0.169784i	0.345703	+	0.938344i	$0.387640\pi$
$60$	0.901154	−	3.34484i	0.116338	−	0.431816i
$61$	7.43114	+	4.29037i	0.951460	+	0.549326i	0.893534	−	0.448995i	$-0.148218\pi$
$61$	7.43114	+	4.29037i	0.951460	+	0.549326i	0.0579259	+	0.998321i	$0.481551\pi$
$62$	−2.05834	−	1.46625i	−0.261410	−	0.186214i
$63$	0.205501	+	7.93459i	0.0258907	+	0.999665i
$64$	6.72575	+	4.33178i	0.840719	+	0.541472i
$65$	−2.53002	−	1.46071i	−0.313810	−	0.181178i
$66$	5.44415	+	14.6502i	0.670128	+	1.80331i
$67$	0.191019	+	0.330854i	0.0233367	+	0.0404203i	0.877458	−	0.479654i	$-0.159238\pi$
$67$	0.191019	+	0.330854i	0.0233367	+	0.0404203i	−0.854121	+	0.520074i	$0.825904\pi$
$68$	2.63780	−	13.6620i	0.319881	−	1.65676i
$69$	10.1124	−	4.89934i	1.21740	−	0.589811i
$70$	−3.37210	−	1.62140i	−0.403043	−	0.193794i
$71$	2.20330			0.261484			0.130742	−	0.991416i	$-0.458264\pi$
$71$	2.20330			0.261484			0.130742	+	0.991416i	$0.458264\pi$
$72$	−0.784847	−	8.44891i	−0.0924951	−	0.995713i
$73$	−2.19598	−	3.80355i	−0.257020	−	0.445172i	0.708422	−	0.705789i	$-0.249407\pi$
$73$	−2.19598	−	3.80355i	−0.257020	−	0.445172i	−0.965442	+	0.260617i	$0.916074\pi$
$74$	0.918651	−	9.60383i	0.106791	−	1.11642i
$75$	0.125358	−	1.72751i	0.0144751	−	0.199475i
$76$	−0.535923	−	1.55010i	−0.0614746	−	0.177809i
$77$	16.6357	−	2.86884i	1.89581	−	0.326935i
$78$	−7.05546	−	1.19517i	−0.798873	−	0.135326i
$79$	14.1532	+	8.17134i	1.59236	+	0.919347i	0.992902	+	0.118938i	$0.0379491\pi$
$79$	14.1532	+	8.17134i	1.59236	+	0.919347i	0.599454	+	0.800409i	$0.295384\pi$
$80$	3.71249	+	1.48910i	0.415069	+	0.166486i
$81$	−6.53936	+	6.18359i	−0.726596	+	0.687065i
$82$	6.01813	−	2.74719i	0.664591	−	0.303376i
$83$		−	9.26784i		−	1.01728i	−0.860980	−	0.508639i	$-0.830149\pi$
$83$		−	9.26784i		−	1.01728i	0.860980	−	0.508639i	$-0.169851\pi$
$84$	−9.12606	−	0.845623i	−0.995734	−	0.0922650i
$85$		−	6.95716i		−	0.754610i
$86$	−4.96427	−	10.8750i	−0.535311	−	1.17268i
$87$	1.95437	+	1.32572i	0.209530	+	0.142132i
$88$	−17.5402	+	4.24603i	−1.86979	+	0.452629i
$89$	11.1758	+	6.45237i	1.18464	+	0.683950i	0.957083	−	0.289815i	$-0.0935939\pi$
$89$	11.1758	+	6.45237i	1.18464	+	0.683950i	0.227554	+	0.973765i	$0.426927\pi$
$90$	−1.18616	−	4.07345i	−0.125032	−	0.429380i
$91$	−2.67089	+	7.25320i	−0.279985	+	0.760342i
$92$	4.23970	+	12.2629i	0.442020	+	1.27849i
$93$	−3.08704	−	0.224014i	−0.320111	−	0.0232291i
$94$	10.0330	+	0.959702i	1.03482	+	0.0989857i
$95$	−0.410032	−	0.710197i	−0.0420684	−	0.0728647i
$96$	9.79473	+	0.251413i	0.999671	+	0.0256597i
$97$	1.23173			0.125063			0.0625315	−	0.998043i	$-0.480083\pi$
$97$	1.23173			0.125063			0.0625315	+	0.998043i	$0.480083\pi$
$98$	−2.71123	+	9.52099i	−0.273876	+	0.961765i
$99$	15.0217	+	11.8638i	1.50973	+	1.19235i
$100$	1.96373	+	0.379149i	0.196373	+	0.0379149i
$101$	−0.618018	−	1.07044i	−0.0614951	−	0.106513i	0.833639	−	0.552310i	$-0.186254\pi$
$101$	−0.618018	−	1.07044i	−0.0614951	−	0.106513i	−0.895134	+	0.445797i	$0.852920\pi$
$102$	−5.93617	−	15.9742i	−0.587768	−	1.58168i
$103$	8.36863	+	4.83163i	0.824586	+	0.476075i	0.851995	−	0.523550i	$-0.175392\pi$
$103$	8.36863	+	4.83163i	0.824586	+	0.476075i	−0.0274096	+	0.999624i	$0.508726\pi$
$104$	2.33187	−	7.92714i	0.228659	−	0.777320i
$105$	−4.56044	+	0.449890i	−0.445053	+	0.0439048i
$106$	7.74657	−	10.8748i	0.752414	−	1.05625i
$107$	−2.73656	−	1.57996i	−0.264554	−	0.152740i	0.361856	−	0.932234i	$-0.382143\pi$
$107$	−2.73656	−	1.57996i	−0.264554	−	0.152740i	−0.626410	+	0.779494i	$0.715476\pi$
$108$	−6.19917	−	8.34088i	−0.596515	−	0.802602i
$109$	−10.1325	+	5.85000i	−0.970517	+	0.560328i	−0.899394	−	0.437140i	$-0.855992\pi$
$109$	−10.1325	+	5.85000i	−0.970517	+	0.560328i	−0.0711229	+	0.997468i	$0.522658\pi$
$110$	−8.20860	+	3.74711i	−0.782659	+	0.357273i
$111$	−5.15186	−	10.6337i	−0.488993	−	1.00930i
$112$	2.21324	−	10.3490i	0.209131	−	0.977888i
$113$			7.71127i			0.725415i	0.931903	+	0.362708i	$0.118148\pi$
$113$			7.71127i			0.725415i	−0.931903	+	0.362708i	$0.881852\pi$
$114$	−1.54744	−	1.28081i	−0.144931	−	0.119959i
$115$	3.24378	+	5.61839i	0.302484	+	0.523917i
$116$	−1.78644	+	2.06028i	−0.165866	+	0.191293i
$117$	−8.14319	+	3.24042i	−0.752838	+	0.299577i
$118$	−3.00434	−	2.14012i	−0.276572	−	0.197014i
$119$	−18.1392	+	3.12812i	−1.66282	+	0.286754i
$120$	4.83239	−	0.804990i	0.441135	−	0.0734852i
$121$	14.8555	−	25.7305i	1.35050	−	2.33913i
$122$	−1.15549	+	12.0799i	−0.104614	+	1.09366i
$123$	4.54837	−	6.70520i	0.410113	−	0.604587i
$124$	0.677536	−	3.50917i	0.0608445	−	0.315133i
$125$	1.00000			0.0894427
$126$	−10.0873	+	4.92416i	−0.898644	+	0.438679i
$127$			1.18634i			0.105271i	0.998614	+	0.0526355i	$0.0167621\pi$
$127$			1.18634i			0.105271i	−0.998614	+	0.0526355i	$0.983238\pi$
$128$	−1.62302	+	11.1967i	−0.143456	+	0.989657i
$129$	−12.1165	−	8.21907i	−1.06680	−	0.723649i
$130$	0.393401	−	4.11273i	0.0345036	−	0.360710i
$131$	3.38447	+	1.95403i	0.295703	+	0.170724i	0.640511	−	0.767949i	$-0.278723\pi$
$131$	3.38447	+	1.95403i	0.295703	+	0.170724i	−0.344808	+	0.938673i	$0.612056\pi$
$132$	−15.6504	+	15.6076i	−1.36219	+	1.35847i
$133$	−1.66731	+	1.38839i	−0.144574	+	0.120388i
$134$	−0.313467	+	0.440050i	−0.0270794	+	0.0380145i
$135$	−3.83399	−	3.50721i	−0.329977	−	0.301853i
$136$	19.1254	−	4.62977i	1.63999	−	0.397000i
$137$	3.91683	−	2.26138i	0.334637	−	0.193203i	−0.323261	−	0.946310i	$-0.604779\pi$
$137$	3.91683	−	2.26138i	0.334637	−	0.193203i	0.657898	+	0.753107i	$0.271446\pi$
$138$	12.2418	+	10.1325i	1.04209	+	0.862537i
$139$	−12.1683			−1.03210			−0.516049	−	0.856559i	$-0.672598\pi$
$139$	−12.1683			−1.03210			−0.516049	+	0.856559i	$0.672598\pi$
$140$	0.105598	−	5.29045i	0.00892470	−	0.447125i
$141$	11.1088	−	5.38208i	0.935532	−	0.453253i
$142$	1.29394	+	2.83457i	0.108585	+	0.237872i
$143$	9.32006	+	16.1428i	0.779382	+	1.34993i
$144$	10.4087	−	5.97153i	0.867391	−	0.497628i
$145$	−0.681731	+	1.18079i	−0.0566147	+	0.0980596i
$146$	3.60366	−	5.05888i	0.298241	−	0.418675i
$147$	3.22347	+	11.6880i	0.265868	+	0.964010i
$148$	12.8949	−	4.45822i	1.05996	−	0.366464i
$149$	5.89838	−	10.2163i	0.483214	−	0.836952i	−0.516600	−	0.856227i	$-0.672803\pi$
$149$	5.89838	−	10.2163i	0.483214	−	0.836952i	0.999814	+	0.0192752i	$0.00613586\pi$
$150$	2.29608	−	0.853246i	0.187474	−	0.0696672i
$151$	4.99959	−	2.88652i	0.406861	−	0.234901i	−0.282579	−	0.959244i	$-0.591190\pi$
$151$	4.99959	−	2.88652i	0.406861	−	0.234901i	0.689440	+	0.724343i	$0.257857\pi$
$152$	1.67949	−	1.59980i	0.136224	−	0.129761i
$153$	−16.3792	−	12.9360i	−1.32418	−	1.04581i
$154$	13.4605	+	19.7172i	1.08468	+	1.58886i
$155$		−	1.78699i		−	0.143534i
$156$	−2.60589	−	9.77881i	−0.208638	−	0.782931i
$157$	−1.44853	+	0.836307i	−0.115605	+	0.0667446i	−0.556688	−	0.830722i	$-0.687928\pi$
$157$	−1.44853	+	0.836307i	−0.115605	+	0.0667446i	0.441083	+	0.897467i	$0.354595\pi$
$158$	−2.20073	+	23.0070i	−0.175080	+	1.83034i
$159$	1.18352	−	16.3096i	0.0938594	−	1.29344i
$160$	0.264511	+	5.65067i	0.0209114	+	0.446724i
$161$	13.1901	−	10.9836i	1.03953	−	0.865626i
$162$	−11.7956	−	4.78150i	−0.926753	−	0.375670i
$163$	10.7871	−	18.6838i	0.844913	−	1.46343i	−0.0407840	−	0.999168i	$-0.512986\pi$
$163$	10.7871	−	18.6838i	0.844913	−	1.46343i	0.885697	−	0.464264i	$-0.153681\pi$
$164$	7.06858	+	6.12903i	0.551963	+	0.478597i
$165$	−6.20389	+	9.14575i	−0.482972	+	0.711996i
$166$	11.9232	−	5.44276i	0.925417	−	0.422440i
$167$	−0.435572			−0.0337055			−0.0168528	−	0.999858i	$-0.505365\pi$
$167$	−0.435572			−0.0337055			−0.0168528	+	0.999858i	$0.505365\pi$
$168$	−4.27159	−	12.2374i	−0.329560	−	0.944135i
$169$	4.46535			0.343489
$170$	8.95046	−	4.08576i	0.686469	−	0.313363i
$171$	−2.43442	−	0.355182i	−0.186165	−	0.0271614i
$172$	11.0754	−	12.7732i	0.844490	−	0.973945i
$173$	−1.75807	+	3.04506i	−0.133663	+	0.231512i	−0.925086	−	0.379758i	$-0.876007\pi$
$173$	−1.75807	+	3.04506i	−0.133663	+	0.231512i	0.791423	+	0.611269i	$0.209341\pi$
$174$	−0.557801	+	3.29288i	−0.0422868	+	0.249632i
$175$	−0.449626	−	2.60727i	−0.0339885	−	0.197091i
$176$	−15.7635	−	20.0721i	−1.18822	−	1.51299i
$177$	−4.50581	−	0.326968i	−0.338678	−	0.0245764i
$178$	−1.73777	+	18.1671i	−0.130251	+	1.36168i
$179$	−18.6434	+	10.7638i	−1.39347	+	0.804521i	−0.993698	−	0.112093i	$-0.964244\pi$
$179$	−18.6434	+	10.7638i	−1.39347	+	0.804521i	−0.399773	+	0.916614i	$0.630911\pi$
$180$	4.54394	−	3.91824i	0.338686	−	0.292048i
$181$		−	6.00703i		−	0.446499i	−0.974761	−	0.223249i	$-0.928334\pi$
$181$		−	6.00703i		−	0.446499i	0.974761	−	0.223249i	$-0.0716665\pi$
$182$	−10.8999	+	0.823486i	−0.807951	+	0.0610409i
$183$	6.48010	+	13.3752i	0.479023	+	0.988723i
$184$	−13.2865	+	12.6561i	−0.979491	+	0.933020i
$185$	5.90797	−	3.41097i	0.434362	−	0.250779i
$186$	−1.52474	−	4.10307i	−0.111799	−	0.300851i
$187$	−22.1951	+	38.4431i	−1.62307	+	2.81124i
$188$	4.65744	+	13.4712i	0.339679	+	0.982485i
$189$	−7.42038	+	11.5732i	−0.539753	+	0.841823i
$190$	0.672875	−	0.944591i	0.0488155	−	0.0685278i
$191$	−9.09052	+	15.7452i	−0.657767	+	1.13929i	0.323426	+	0.946254i	$0.395165\pi$
$191$	−9.09052	+	15.7452i	−0.657767	+	1.13929i	−0.981192	+	0.193032i	$0.938168\pi$
$192$	5.42874	+	12.7487i	0.391786	+	0.920056i
$193$	−5.39964	−	9.35245i	−0.388675	−	0.673204i	0.603597	−	0.797290i	$-0.293734\pi$
$193$	−5.39964	−	9.35245i	−0.388675	−	0.673204i	−0.992272	+	0.124086i	$0.960400\pi$
$194$	0.723361	+	1.58463i	0.0519343	+	0.113770i
$195$	−2.20622	−	4.55374i	−0.157991	−	0.326100i
$196$	−13.8411	+	2.10340i	−0.988649	+	0.150243i
$197$	−24.8164			−1.76810			−0.884048	−	0.467396i	$-0.845192\pi$
$197$	−24.8164			−1.76810			−0.884048	+	0.467396i	$0.845192\pi$
$198$	−6.44104	+	26.2928i	−0.457744	+	1.86855i
$199$	19.4351	−	11.2209i	1.37772	−	0.795428i	0.385836	−	0.922567i	$-0.373913\pi$
$199$	19.4351	−	11.2209i	1.37772	−	0.795428i	0.991885	+	0.127140i	$0.0405797\pi$
$200$	0.665469	+	2.74903i	0.0470557	+	0.194386i
$201$	−0.0478915	+	0.659973i	−0.00337801	+	0.0465509i
$202$	1.01418	−	1.42373i	0.0713578	−	0.100173i
$203$	3.38517	+	1.24654i	0.237592	+	0.0874899i
$204$	17.0648	−	17.0182i	1.19478	−	1.19151i
$205$	4.05115	+	2.33893i	0.282945	+	0.163358i
$206$	−1.30127	+	13.6038i	−0.0906637	+	0.947823i
$207$	19.2588	+	2.80985i	1.33858	+	0.195298i
$208$	11.5678	−	1.65542i	0.802082	−	0.114783i
$209$			5.23244i			0.361935i
$210$	−3.25701	−	5.60284i	−0.224755	−	0.386633i
$211$	10.7278			0.738534			0.369267	−	0.929323i	$-0.379609\pi$
$211$	10.7278			0.738534			0.369267	+	0.929323i	$0.379609\pi$
$212$	18.5398	+	3.57960i	1.27332	+	0.245848i
$213$	3.15818	+	2.14231i	0.216395	+	0.146789i
$214$	0.425518	−	4.44848i	0.0290878	−	0.304092i
$215$	4.22654	−	7.32058i	0.288247	−	0.499259i
$216$	7.09003	−	12.8737i	0.482415	−	0.875943i
$217$	−4.65916	+	0.803477i	−0.316284	+	0.0545435i
$218$	−13.4766	−	9.60001i	−0.912752	−	0.650195i
$219$	0.550568	−	7.58715i	0.0372039	−	0.512692i
$220$	−9.64139	−	8.35987i	−0.650022	−	0.563623i
$221$	−10.1624	−	17.6017i	−0.683595	−	1.18402i
$222$	10.6548	−	12.8728i	0.715101	−	0.863965i
$223$		−	1.31355i		−	0.0879621i	−0.999032	−	0.0439811i	$-0.985996\pi$
$223$		−	1.31355i		−	0.0879621i	0.999032	−	0.0439811i	$-0.0140041\pi$
$224$	14.6139	−	3.23034i	0.976430	−	0.215836i
$225$	1.85937	−	2.35430i	0.123958	−	0.156953i
$226$	−9.92063	+	4.52863i	−0.659911	+	0.301240i
$227$	−1.78947	+	1.03315i	−0.118771	+	0.0685725i	−0.558209	−	0.829701i	$-0.688511\pi$
$227$	−1.78947	+	1.03315i	−0.118771	+	0.0685725i	0.439438	+	0.898273i	$0.355178\pi$
$228$	0.739004	−	2.74298i	0.0489418	−	0.181658i
$229$	10.1601	+	5.86594i	0.671399	+	0.387632i	0.796606	−	0.604498i	$-0.206626\pi$
$229$	10.1601	+	5.86594i	0.671399	+	0.387632i	−0.125208	+	0.992131i	$0.539960\pi$
$230$	−5.32313	+	7.47268i	−0.350997	+	0.492734i
$231$	26.6348	+	12.0630i	1.75244	+	0.793688i
$232$	−3.69970	−	1.08832i	−0.242897	−	0.0714515i
$233$	9.28303	+	5.35956i	0.608151	+	0.351116i	0.772242	−	0.635329i	$-0.219135\pi$
$233$	9.28303	+	5.35956i	0.608151	+	0.351116i	−0.164090	+	0.986445i	$0.552469\pi$
$234$	−8.95112	−	8.57328i	−0.585153	−	0.560453i
$235$	3.56339	+	6.17197i	0.232450	+	0.402615i
$236$	0.988925	−	5.12195i	0.0643735	−	0.333411i
$237$	12.3418	+	25.4741i	0.801689	+	1.65472i
$238$	−14.6770	−	21.4992i	−0.951370	−	1.39358i
$239$	−6.65836			−0.430694			−0.215347	−	0.976538i	$-0.569088\pi$
$239$	−6.65836			−0.430694			−0.215347	+	0.976538i	$0.569088\pi$
$240$	3.87356	+	5.74417i	0.250037	+	0.370785i
$241$	0.781481	+	1.35357i	0.0503396	+	0.0871908i	0.890097	−	0.455771i	$-0.150636\pi$
$241$	0.781481	+	1.35357i	0.0503396	+	0.0871908i	−0.839758	+	0.542961i	$0.817303\pi$
$242$	41.8268	+	4.00092i	2.68873	+	0.257189i
$243$	−15.3858	+	2.50513i	−0.987003	+	0.160704i
$244$	−16.2195	+	5.60763i	−1.03834	+	0.358992i
$245$	−6.59567	+	2.34459i	−0.421382	+	0.149790i
$246$	11.2974	+	1.91375i	0.720299	+	0.122016i
$247$	−2.07478	−	1.19787i	−0.132015	−	0.0762189i
$248$	4.91248	−	1.18919i	0.311943	−	0.0755134i
$249$	9.01128	−	13.2844i	0.571067	−	0.841864i
$250$	0.587274	+	1.28651i	0.0371424	+	0.0813661i
$251$		−	0.631874i		−	0.0398835i	−0.999801	−	0.0199418i	$-0.993652\pi$
$251$		−	0.631874i		−	0.0398835i	0.999801	−	0.0199418i	$-0.00634808\pi$
$252$	−12.2590	−	10.0855i	−0.772242	−	0.635329i
$253$		−	41.3939i		−	2.60241i
$254$	−1.52624	+	0.696708i	−0.0957651	+	0.0437154i
$255$	6.76457	−	9.97231i	0.423614	−	0.624490i
$256$	−15.3578	+	4.48749i	−0.959863	+	0.280468i
$257$	9.92146	+	5.72816i	0.618883	+	0.357313i	0.776434	−	0.630198i	$-0.217026\pi$
$257$	9.92146	+	5.72816i	0.618883	+	0.357313i	−0.157551	+	0.987511i	$0.550360\pi$
$258$	3.45821	−	20.4149i	0.215299	−	1.27098i
$259$	−11.5497	−	13.8700i	−0.717662	−	0.861839i
$260$	5.52210	−	1.90918i	0.342466	−	0.118402i
$261$	1.51235	+	3.80054i	0.0936121	+	0.235247i
$262$	−0.526264	+	5.50171i	−0.0325127	+	0.339897i
$263$	−1.93094	−	3.34449i	−0.119067	−	0.206230i	0.800331	−	0.599558i	$-0.204657\pi$
$263$	−1.93094	−	3.34449i	−0.119067	−	0.206230i	−0.919398	+	0.393328i	$0.871324\pi$
$264$	−29.2704	−	10.9684i	−1.80147	−	0.675061i
$265$	9.44112			0.579964
$266$	−2.76534	−	1.32965i	−0.169554	−	0.0815261i
$267$	9.74555	+	20.1152i	0.596418	+	1.23103i
$268$	−0.750219	−	0.144849i	−0.0458269	−	0.00884808i
$269$	−3.26588	−	5.65667i	−0.199124	−	0.344893i	0.749120	−	0.662434i	$-0.230476\pi$
$269$	−3.26588	−	5.65667i	−0.199124	−	0.344893i	−0.948245	+	0.317540i	$0.897143\pi$
$270$	2.26047	−	6.99216i	0.137568	−	0.425529i
$271$	−13.6039	−	7.85424i	−0.826381	−	0.477111i	0.0262311	−	0.999656i	$-0.491649\pi$
$271$	−13.6039	−	7.85424i	−0.826381	−	0.477111i	−0.852612	+	0.522545i	$0.824983\pi$
$272$	17.1881	+	21.8861i	1.04218	+	1.32704i
$273$	−10.8808	+	7.79969i	−0.658538	+	0.472059i
$274$	5.20954	+	3.71099i	0.314720	+	0.224189i
$275$	−5.52569	−	3.19026i	−0.333212	−	0.192380i
$276$	−5.84628	+	21.6998i	−0.351905	+	1.30617i
$277$	7.51404	−	4.33823i	0.451475	−	0.260659i	−0.256978	−	0.966417i	$-0.582727\pi$
$277$	7.51404	−	4.33823i	0.451475	−	0.260659i	0.708453	+	0.705758i	$0.249393\pi$
$278$	−7.14610	−	15.6546i	−0.428594	−	0.938900i
$279$	−4.20711	−	3.32268i	−0.251873	−	0.198924i
$280$	6.86823	−	2.97109i	0.410455	−	0.177556i
$281$		−	19.2962i		−	1.15112i	−0.817761	−	0.575558i	$-0.804785\pi$
$281$		−	19.2962i		−	1.15112i	0.817761	−	0.575558i	$-0.195215\pi$
$282$	13.4480	+	11.1309i	0.800818	+	0.662834i
$283$	11.5640	+	20.0294i	0.687406	+	1.19062i	0.972674	+	0.232174i	$0.0745839\pi$
$283$	11.5640	+	20.0294i	0.687406	+	1.19062i	−0.285268	+	0.958448i	$0.592083\pi$
$284$	−2.88681	+	3.32934i	−0.171300	+	0.197560i
$285$	0.102802	−	1.41667i	0.00608945	−	0.0839162i
$286$	−15.2945	+	21.4706i	−0.904381	+	1.26958i
$287$	4.27672	−	11.6141i	0.252447	−	0.685557i
$288$	13.7952	+	9.88396i	0.812889	+	0.582418i
$289$	15.7011	−	27.1950i	0.923591	−	1.59971i
$290$	−1.91947	−	0.183606i	−0.112715	−	0.0107817i
$291$	1.76554	+	1.19763i	0.103498	+	0.0702063i
$292$	8.62463	+	1.66521i	0.504719	+	0.0974490i
$293$	−26.2233			−1.53198			−0.765991	−	0.642851i	$-0.777751\pi$
$293$	−26.2233			−1.53198			−0.765991	+	0.642851i	$0.777751\pi$
$294$	−13.1437	+	11.0111i	−0.766554	+	0.642180i
$295$		−	2.60827i		−	0.151859i
$296$	13.3084	+	13.9713i	0.773536	+	0.812064i
$297$	9.99650	+	31.6112i	0.580056	+	1.83427i
$298$	16.6073	+	1.58857i	0.962037	+	0.0920233i
$299$	16.4136	+	9.47641i	0.949224	+	0.548035i
$300$	2.44614	+	2.45284i	0.141228	+	0.141615i
$301$	−20.9870	−	7.72819i	−1.20967	−	0.445445i
$302$	6.64966	+	4.73685i	0.382645	+	0.272575i
$303$	0.154947	−	2.13526i	0.00890148	−	0.122668i
$304$	3.04448	+	1.22116i	0.174613	+	0.0700381i
$305$	−7.43114	+	4.29037i	−0.425506	+	0.245666i
$306$	7.02315	−	28.6690i	0.401487	−	1.63890i
$307$	−22.2359			−1.26907			−0.634536	−	0.772893i	$-0.718809\pi$
$307$	−22.2359			−1.26907			−0.634536	+	0.772893i	$0.718809\pi$
$308$	−17.4614	+	28.8965i	−0.994956	+	1.64653i
$309$	7.29761	+	15.0626i	0.415146	+	0.856879i
$310$	2.29898	−	1.04945i	0.130573	−	0.0596049i
$311$	−6.84705	−	11.8594i	−0.388261	−	0.672487i	0.603955	−	0.797018i	$-0.293591\pi$
$311$	−6.84705	−	11.8594i	−0.388261	−	0.672487i	−0.992216	+	0.124531i	$0.960257\pi$
$312$	11.0502	−	9.09534i	0.625593	−	0.514922i
$313$	13.4268	−	23.2558i	0.758926	−	1.31450i	−0.184473	−	0.982837i	$-0.559058\pi$
$313$	13.4268	−	23.2558i	0.758926	−	1.31450i	0.943399	−	0.331660i	$-0.107609\pi$
$314$	−1.92660	−	1.37240i	−0.108724	−	0.0774492i
$315$	−6.97431	−	3.78933i	−0.392958	−	0.213504i
$316$	−30.8912	+	10.6802i	−1.73777	+	0.600806i
$317$	8.36597	−	14.4903i	0.469880	−	0.813855i	−0.529527	−	0.848293i	$-0.677631\pi$
$317$	8.36597	−	14.4903i	0.469880	−	0.813855i	0.999407	+	0.0344376i	$0.0109640\pi$
$318$	21.6776	−	8.05560i	1.21562	−	0.451735i
$319$	7.53407	−	4.34980i	0.421827	−	0.243542i
$320$	−7.11430	+	3.65878i	−0.397702	+	0.204532i
$321$	−2.38634	−	4.92550i	−0.133192	−	0.274914i
$322$	21.8767	+	10.5189i	1.21914	+	0.586196i
$323$		−	5.70532i		−	0.317453i
$324$	−0.775816	−	17.9833i	−0.0431009	−	0.999071i
$325$	2.53002	−	1.46071i	0.140340	−	0.0810254i
$326$	30.3720	+	2.90522i	1.68215	+	0.160905i
$327$	−20.2118	−	1.46669i	−1.11772	−	0.0811081i
$328$	−3.73388	+	12.6932i	−0.206169	+	0.700866i
$329$	14.4898	−	12.0658i	0.798847	−	0.665208i
$330$	−15.4095	−	2.61031i	−0.848264	−	0.143693i
$331$	4.38007	−	7.58651i	0.240751	−	0.416992i	−0.720178	−	0.693790i	$-0.755940\pi$
$331$	4.38007	−	7.58651i	0.240751	−	0.416992i	0.960928	+	0.276797i	$0.0892731\pi$
$332$	14.0043	+	12.1429i	0.768587	+	0.666428i
$333$	2.95468	−	20.2514i	0.161915	−	1.10977i
$334$	−0.255800	−	0.560367i	−0.0139967	−	0.0306619i
$335$	−0.382037			−0.0208729
$336$	13.2349	−	12.6821i	0.722025	−	0.691867i
$337$	−15.2545			−0.830965			−0.415482	−	0.909601i	$-0.636387\pi$
$337$	−15.2545			−0.830965			−0.415482	+	0.909601i	$0.636387\pi$
$338$	2.62238	+	5.74472i	0.142639	+	0.312472i
$339$	−7.49780	+	11.0532i	−0.407225	+	0.600329i
$340$	10.5127	+	9.11541i	0.570133	+	0.494352i
$341$	−5.70096	+	9.87435i	−0.308724	+	0.534726i
$342$	−0.972726	−	3.34050i	−0.0525990	−	0.180633i
$343$	9.07855	+	16.1425i	0.490196	+	0.871612i
$344$	22.9371	+	6.74725i	1.23669	+	0.363787i
$345$	−0.813268	+	11.2073i	−0.0437849	+	0.603381i
$346$	−4.94997	−	0.473488i	−0.266112	−	0.0254548i
$347$	−4.41107	+	2.54673i	−0.236799	+	0.136716i	−0.613705	−	0.789536i	$-0.710321\pi$
$347$	−4.41107	+	2.54673i	−0.236799	+	0.136716i	0.376906	+	0.926252i	$0.376988\pi$
$348$	−4.56390	+	1.21620i	−0.244651	+	0.0651953i
$349$			8.94593i			0.478865i	0.970913	+	0.239432i	$0.0769613\pi$
$349$			8.94593i			0.478865i	−0.970913	+	0.239432i	$0.923039\pi$
$350$	3.09022	−	2.10963i	0.165179	−	0.112764i
$351$	−14.8231	−	3.27298i	−0.791196	−	0.174699i
$352$	16.5655	−	32.0677i	0.882943	−	1.70921i
$353$	−14.3822	+	8.30355i	−0.765486	+	0.441953i	−0.831262	−	0.555881i	$-0.812381\pi$
$353$	−14.3822	+	8.30355i	−0.765486	+	0.441953i	0.0657762	+	0.997834i	$0.479048\pi$
$354$	−2.22550	−	5.98880i	−0.118284	−	0.318301i
$355$	−1.10165	+	1.90811i	−0.0584695	+	0.101272i
$356$	−24.3928	+	8.43342i	−1.29281	+	0.446971i
$357$	−29.0420	−	13.1532i	−1.53706	−	0.696143i
$358$	−24.7964	−	17.6636i	−1.31053	−	0.933552i
$359$	0.562490	−	0.974262i	0.0296871	−	0.0514196i	−0.850800	−	0.525489i	$-0.823882\pi$
$359$	0.562490	−	0.974262i	0.0296871	−	0.0514196i	0.880487	+	0.474070i	$0.157216\pi$
$360$	7.70939	+	3.54476i	0.406321	+	0.186825i
$361$	9.16375	+	15.8721i	0.482302	+	0.835372i
$362$	7.72811	−	3.52777i	0.406180	−	0.185415i
$363$	46.3118	−	22.4375i	2.43074	−	1.17766i
$364$	−7.46062	−	13.5392i	−0.391043	−	0.709645i
$365$	4.39196			0.229886
$366$	−13.4017	+	16.1916i	−0.700520	+	0.846349i
$367$	−20.7127	+	11.9585i	−1.08120	+	0.624229i	−0.931219	−	0.364461i	$-0.881253\pi$
$367$	−20.7127	+	11.9585i	−1.08120	+	0.624229i	−0.149977	+	0.988689i	$0.547920\pi$
$368$	−24.0850	−	9.66059i	−1.25552	−	0.503593i
$369$	13.0392	−	5.18868i	0.678792	−	0.270112i
$370$	7.85784	+	5.59749i	0.408510	+	0.291000i
$371$	−4.24497	−	24.6155i	−0.220388	−	1.27797i
$372$	4.38320	−	4.37122i	0.227258	−	0.226637i
$373$	−19.1223	−	11.0402i	−0.990113	−	0.571642i	−0.0848047	−	0.996398i	$-0.527027\pi$
$373$	−19.1223	−	11.0402i	−0.990113	−	0.571642i	−0.905308	+	0.424756i	$0.860360\pi$
$374$	−62.4921	−	5.97766i	−3.23139	−	0.309097i
$375$	1.43339	+	0.972318i	0.0740198	+	0.0502103i
$376$	−14.5956	+	13.9031i	−0.752710	+	0.716998i
$377$			3.98324i			0.205147i
$378$	−19.2468	−	2.74979i	−0.989948	−	0.141434i
$379$	−2.60527			−0.133824			−0.0669118	−	0.997759i	$-0.521315\pi$
$379$	−2.60527			−0.133824			−0.0669118	+	0.997759i	$0.521315\pi$
$380$	1.61039	+	0.310927i	0.0826112	+	0.0159502i
$381$	−1.15350	+	1.70049i	−0.0590957	+	0.0871187i
$382$	−25.5950	−	2.44828i	−1.30956	−	0.125265i
$383$	−6.74338	+	11.6799i	−0.344571	+	0.596814i	−0.985276	−	0.170973i	$-0.945309\pi$
$383$	−6.74338	+	11.6799i	−0.344571	+	0.596814i	0.640705	+	0.767787i	$0.278642\pi$
$384$	−13.2131	+	14.4711i	−0.674281	+	0.738475i
$385$	−5.83336	+	15.8414i	−0.297295	+	0.807351i
$386$	8.86096	−	12.4391i	0.451011	−	0.633136i
$387$	−9.37612	−	23.5622i	−0.476615	−	1.19774i
$388$	−1.61383	+	1.86122i	−0.0819299	+	0.0944893i
$389$	11.3548	+	19.6672i	0.575713	+	0.997165i	0.995964	+	0.0897567i	$0.0286090\pi$
$389$	11.3548	+	19.6672i	0.575713	+	0.997165i	−0.420250	+	0.907408i	$0.638058\pi$
$390$	4.56277	−	5.51262i	0.231045	−	0.279142i
$391$			45.1350i			2.28257i
$392$	−10.8346	−	16.5714i	−0.547228	−	0.836984i
$393$	2.95132	+	6.09166i	0.148875	+	0.307283i
$394$	−14.5740	−	31.9266i	−0.734229	−	1.60844i
$395$	−14.1532	+	8.17134i	−0.712123	+	0.411145i
$396$	−37.6086	+	7.15460i	−1.88990	+	0.359532i
$397$	2.80762	+	1.62098i	0.140911	+	0.0813548i	0.568798	−	0.822477i	$-0.307409\pi$
$397$	2.80762	+	1.62098i	0.140911	+	0.0813548i	−0.427887	+	0.903832i	$0.640742\pi$
$398$	25.8495	+	18.4138i	1.29572	+	0.923000i
$399$	−3.73985	+	0.368939i	−0.187227	+	0.0184701i
$400$	−3.14584	+	2.47056i	−0.157292	+	0.123528i
$401$	−26.1429	−	15.0936i	−1.30552	−	0.753740i	−0.324171	−	0.945999i	$-0.605085\pi$
$401$	−26.1429	−	15.0936i	−1.30552	−	0.753740i	−0.981344	+	0.192259i	$0.938419\pi$
$402$	−0.877188	+	0.325972i	−0.0437501	+	0.0162580i
$403$	−2.61027	−	4.52111i	−0.130027	−	0.225213i
$404$	2.42724	+	0.468642i	0.120760	+	0.0233158i
$405$	−2.08546	−	8.75505i	−0.103627	−	0.435042i
$406$	0.384332	+	5.08711i	0.0190741	+	0.252469i
$407$	−43.5275			−2.15758
$408$	31.9158	+	11.9597i	1.58007	+	0.592095i
$409$	10.2794	+	17.8045i	0.508285	+	0.880375i	0.999954	+	0.00959312i	$0.00305363\pi$
$409$	10.2794	+	17.8045i	0.508285	+	0.880375i	−0.491669	+	0.870782i	$0.663613\pi$
$410$	−0.629928	+	6.58545i	−0.0311099	+	0.325232i
$411$	7.81311	+	0.566965i	0.385392	+	0.0279663i
$412$	−18.2657	+	6.31507i	−0.899885	+	0.311121i
$413$	−6.80046	+	1.17275i	−0.334629	+	0.0577071i
$414$	7.69526	+	26.4268i	0.378201	+	1.29880i
$415$	8.02618	+	4.63392i	0.393990	+	0.227470i
$416$	8.92318	+	13.9099i	0.437495	+	0.681989i
$417$	−17.4418	−	11.8314i	−0.854130	−	0.579386i
$418$	−6.73158	+	3.07287i	−0.329253	+	0.150299i
$419$		−	23.9165i		−	1.16840i	−0.811611	−	0.584198i	$-0.801409\pi$
$419$		−	23.9165i		−	1.16840i	0.811611	−	0.584198i	$-0.198591\pi$
$420$	5.29536	−	7.48059i	0.258387	−	0.365015i
$421$			14.9328i			0.727780i	0.931442	+	0.363890i	$0.118552\pi$
$421$			14.9328i			0.727780i	−0.931442	+	0.363890i	$0.881448\pi$
$422$	6.30017	+	13.8015i	0.306688	+	0.671845i
$423$	21.1563	+	3.08671i	1.02866	+	0.150081i
$424$	6.28277	+	25.9539i	0.305118	+	1.26043i
$425$	6.02508	+	3.47858i	0.292259	+	0.168736i
$426$	−0.901384	+	5.32116i	−0.0436722	+	0.257811i
$427$	14.5274	+	17.4459i	0.703029	+	0.844266i
$428$	5.97292	−	2.06504i	0.288712	−	0.0998177i
$429$	−2.33669	+	32.2010i	−0.112816	+	1.55468i
$430$	11.9001	+	1.13830i	0.573875	+	0.0548938i
$431$	−6.78400	−	11.7502i	−0.326774	−	0.565989i	0.655096	−	0.755546i	$-0.272628\pi$
$431$	−6.78400	−	11.7502i	−0.326774	−	0.565989i	−0.981870	+	0.189557i	$0.939295\pi$
$432$	20.7259	+	1.56103i	0.997176	+	0.0751050i
$433$	−20.4637			−0.983421			−0.491710	−	0.870759i	$-0.663628\pi$
$433$	−20.4637			−0.983421			−0.491710	+	0.870759i	$0.663628\pi$
$434$	−3.76988	−	5.52219i	−0.180960	−	0.265074i
$435$	−2.12529	+	1.02967i	−0.101900	+	0.0493691i
$436$	4.43604	−	22.9757i	0.212448	−	1.10033i
$437$	2.66011	+	4.60744i	0.127250	+	0.220404i
$438$	10.0843	−	3.74742i	0.481846	−	0.179059i
$439$	−23.4308	−	13.5278i	−1.11829	−	0.645644i	−0.177325	−	0.984152i	$-0.556744\pi$
$439$	−23.4308	−	13.5278i	−1.11829	−	0.645644i	−0.940964	+	0.338508i	$0.890078\pi$
$440$	5.09293	−	17.3133i	0.242796	−	0.825379i
$441$	−6.74395	+	19.8877i	−0.321141	+	0.947031i
$442$	16.6767	−	23.4110i	0.793231	−	1.11355i
$443$	28.7921	+	16.6231i	1.36795	+	0.789789i	0.990667	−	0.136307i	$-0.0435233\pi$
$443$	28.7921	+	16.6231i	1.36795	+	0.789789i	0.377288	+	0.926096i	$0.376857\pi$
$444$	22.8182	+	6.14761i	1.08291	+	0.291753i
$445$	−11.1758	+	6.45237i	−0.529786	+	0.305872i
$446$	1.68990	−	0.771416i	0.0800192	−	0.0365276i
$447$	18.3882	−	8.90881i	0.869730	−	0.421372i
$448$	12.7382	+	16.9038i	0.601823	+	0.798629i
$449$		−	25.4429i		−	1.20072i	−0.799728	−	0.600362i	$-0.795023\pi$
$449$		−	25.4429i		−	1.20072i	0.799728	−	0.600362i	$-0.204977\pi$
$450$	4.12079	+	1.00949i	0.194256	+	0.0475876i
$451$	−14.9236	−	25.8484i	−0.702725	−	1.21716i
$452$	−11.6523	−	10.1035i	−0.548076	−	0.475227i
$453$	9.97296	+	0.723696i	0.468570	+	0.0340022i
$454$	−2.38006	−	1.69543i	−0.111702	−	0.0795703i
$455$	−4.94601	−	5.93966i	−0.231873	−	0.278455i
$456$	3.96287	−	0.660144i	0.185579	−	0.0309141i
$457$	−14.4703	+	25.0633i	−0.676893	+	1.17241i	0.299019	+	0.954247i	$0.403341\pi$
$457$	−14.4703	+	25.0633i	−0.676893	+	1.17241i	−0.975912	+	0.218166i	$0.929993\pi$
$458$	−1.57983	+	16.5160i	−0.0738207	+	0.771742i
$459$	−10.8999	−	34.4681i	−0.508766	−	1.60883i
$460$	−12.7398	−	2.45975i	−0.593997	−	0.114687i
$461$	−21.8992			−1.01995			−0.509974	−	0.860190i	$-0.670345\pi$
$461$	−21.8992			−1.01995			−0.509974	+	0.860190i	$0.670345\pi$
$462$	0.122730	+	41.3503i	0.00570989	+	1.92379i
$463$			36.8724i			1.71361i	0.515643	+	0.856804i	$0.327553\pi$
$463$			36.8724i			1.71361i	−0.515643	+	0.856804i	$0.672447\pi$
$464$	−0.772607	−	5.39885i	−0.0358674	−	0.250635i
$465$	1.73752	−	2.56145i	0.0805756	−	0.118784i
$466$	−1.44345	+	15.0902i	−0.0668666	+	0.699042i
$467$	−8.16932	−	4.71656i	−0.378031	−	0.218256i	0.298930	−	0.954275i	$-0.403370\pi$
$467$	−8.16932	−	4.71656i	−0.378031	−	0.218256i	−0.676961	+	0.736019i	$0.736704\pi$
$468$	5.77286	−	16.5506i	0.266851	−	0.765050i
$469$	0.171774	+	0.996073i	0.00793178	+	0.0459944i
$470$	−5.84762	+	8.20897i	−0.269731	+	0.378652i
$471$	−2.88945	−	0.209676i	−0.133139	−	0.00966135i
$472$	7.17021	−	1.73572i	0.330036	−	0.0798932i
$473$	−46.7090	+	26.9675i	−2.14768	+	1.23997i
$474$	−25.5246	+	30.8382i	−1.17238	+	1.41644i
$475$	0.820065			0.0376272
$476$	19.0395	−	31.5080i	0.872674	−	1.44417i
$477$	17.5546	−	22.2272i	0.803769	−	1.01772i
$478$	−3.91028	−	8.56605i	−0.178852	−	0.391802i
$479$	−18.6189	−	32.2489i	−0.850719	−	1.47349i	−0.880561	−	0.473933i	$-0.842834\pi$
$479$	−18.6189	−	32.2489i	−0.850719	−	1.47349i	0.0298420	−	0.999555i	$-0.490500\pi$
$480$	−5.11510	+	8.35678i	−0.233471	+	0.381433i
$481$	9.96484	−	17.2596i	0.454358	−	0.786970i
$482$	−1.28243	+	1.80030i	−0.0584132	+	0.0820013i
$483$	29.5861	−	2.91869i	1.34621	−	0.132805i
$484$	19.4165	+	56.1602i	0.882569	+	2.55274i
$485$	−0.615864	+	1.06671i	−0.0279649	+	0.0484367i
$486$	−12.2586	−	18.3229i	−0.556061	−	0.831142i
$487$	−19.4552	+	11.2324i	−0.881598	+	0.508991i	−0.871185	−	0.490955i	$-0.836648\pi$
$487$	−19.4552	+	11.2324i	−0.881598	+	0.508991i	−0.0104127	+	0.999946i	$0.503315\pi$
$488$	−16.7395	−	17.5733i	−0.757763	−	0.795506i
$489$	33.6288	−	16.2927i	1.52075	−	0.736780i
$490$	−6.88980	−	7.10849i	−0.311250	−	0.321129i
$491$			14.4520i			0.652208i	0.945334	+	0.326104i	$0.105736\pi$
$491$			14.4520i			0.652208i	−0.945334	+	0.326104i	$0.894264\pi$
$492$	4.17264	+	15.6582i	0.188117	+	0.705925i
$493$	−8.21497	+	4.74292i	−0.369984	+	0.213610i
$494$	0.322615	−	3.37270i	0.0145151	−	0.151745i
$495$	−17.7851	+	7.07725i	−0.799383	+	0.318099i
$496$	4.41487	+	5.62158i	0.198234	+	0.252417i
$497$	5.47029	+	2.01436i	0.245376	+	0.0903563i
$498$	22.3826	+	3.79153i	1.00299	+	0.169903i
$499$	−3.45358	+	5.98178i	−0.154604	+	0.267781i	−0.932915	−	0.360098i	$-0.882743\pi$
$499$	−3.45358	+	5.98178i	−0.154604	+	0.267781i	0.778311	+	0.627879i	$0.216077\pi$
$500$	−1.31022	+	1.51107i	−0.0585948	+	0.0675770i
$501$	−0.624343	−	0.423514i	−0.0278936	−	0.0189212i
$502$	0.812912	−	0.371083i	0.0362820	−	0.0165622i
$503$	10.9067			0.486307			0.243153	−	0.969988i	$-0.421818\pi$
$503$	10.9067			0.486307			0.243153	+	0.969988i	$0.421818\pi$
$504$	5.77578	−	21.6942i	0.257274	−	0.966339i
$505$	1.23604			0.0550029
$506$	53.2537	−	24.3096i	2.36742	−	1.08069i
$507$	6.40058	+	4.34174i	0.284260	+	0.192824i
$508$	−1.79265	−	1.55437i	−0.0795358	−	0.0689640i
$509$	−16.6483	+	28.8356i	−0.737921	+	1.27812i	0.215508	+	0.976502i	$0.430859\pi$
$509$	−16.6483	+	28.8356i	−0.737921	+	1.27812i	−0.953430	+	0.301615i	$0.902474\pi$
$510$	16.8021	+	2.84622i	0.744011	+	0.126033i
$511$	−1.97474	−	11.4510i	−0.0873573	−	0.506563i
$512$	−14.7924	−	17.1226i	−0.653740	−	0.756719i
$513$	−3.14412	−	2.87614i	−0.138816	−	0.126985i
$514$	−1.54272	+	16.1281i	−0.0680466	+	0.711378i
$515$	−8.36863	+	4.83163i	−0.368766	+	0.212907i
$516$	28.2949	−	7.54010i	1.24561	−	0.331935i
$517$		−	45.4725i		−	1.99988i
$518$	11.0611	−	23.0043i	0.485995	−	1.01075i
$519$	−5.48076	+	2.65535i	−0.240579	+	0.116557i
$520$	5.69917	+	5.98303i	0.249925	+	0.262373i
$521$	−7.01740	+	4.05150i	−0.307438	+	0.177499i	−0.645779	−	0.763524i	$-0.723467\pi$
$521$	−7.01740	+	4.05150i	−0.307438	+	0.177499i	0.338341	+	0.941023i	$0.390134\pi$
$522$	−4.00127	+	4.17761i	−0.175131	+	0.182849i
$523$	−0.335720	+	0.581484i	−0.0146800	+	0.0254265i	−0.873272	−	0.487233i	$-0.838006\pi$
$523$	−0.335720	+	0.581484i	−0.0146800	+	0.0254265i	0.858592	+	0.512659i	$0.171340\pi$
$524$	−7.38706	+	2.55396i	−0.322705	+	0.111570i
$525$	1.89060	−	4.17440i	0.0825127	−	0.182186i
$526$	3.16873	−	4.44830i	0.138163	−	0.193955i
$527$	6.21619	−	10.7668i	0.270781	−	0.469007i
$528$	−3.07872	−	44.0982i	−0.133984	−	1.91913i
$529$	−9.54418	−	16.5310i	−0.414964	−	0.718740i
$530$	5.54452	+	12.1461i	0.240839	+	0.527593i
$531$	−6.14066	−	4.84975i	−0.266482	−	0.210461i
$532$	0.0865975	−	4.33851i	0.00375448	−	0.188098i
$533$	13.6660			0.591939
$534$	−20.1551	+	24.3509i	−0.872198	+	1.05377i
$535$	2.73656	−	1.57996i	0.118312	−	0.0683074i
$536$	−0.254234	−	1.05023i	−0.0109812	−	0.0453631i
$537$	−37.1890	−	2.69865i	−1.60482	−	0.116455i
$538$	5.35940	−	7.52360i	0.231060	−	0.324366i
$539$	43.9255	+	8.08643i	1.89200	+	0.348307i
$540$	10.3230	−	1.19819i	0.444231	−	0.0515620i
$541$	−1.27385	−	0.735460i	−0.0547673	−	0.0316199i	0.472366	−	0.881402i	$-0.343400\pi$
$541$	−1.27385	−	0.735460i	−0.0547673	−	0.0316199i	−0.527134	+	0.849782i	$0.676733\pi$
$542$	2.11533	−	22.1142i	0.0908610	−	0.949887i
$543$	5.84074	−	8.61040i	0.250650	−	0.369508i
$544$	−18.0626	+	34.9658i	−0.774428	+	1.49915i
$545$		−	11.7000i		−	0.501173i
$546$	−16.4244	−	9.41775i	−0.702900	−	0.403042i
$547$	−5.10594			−0.218314			−0.109157	−	0.994025i	$-0.534815\pi$
$547$	−5.10594			−0.218314			−0.109157	+	0.994025i	$0.534815\pi$
$548$	−1.71480	+	8.88150i	−0.0732528	+	0.379399i
$549$	−3.71644	+	25.4725i	−0.158614	+	1.08714i
$550$	0.859209	−	8.98241i	0.0366368	−	0.383011i
$551$	−0.559064	+	0.968327i	−0.0238169	+	0.0412521i
$552$	−31.3504	+	5.22242i	−1.33436	+	0.222281i
$553$	27.6685	+	33.2270i	1.17658	+	1.41296i
$554$	9.99398	+	7.11916i	0.424604	+	0.302464i
$555$	11.7849	+	0.855185i	0.500243	+	0.0363006i
$556$	15.9431	−	18.3871i	0.676137	−	0.779785i
$557$	1.92197	+	3.32895i	0.0814365	+	0.141052i	0.903867	−	0.427813i	$-0.140716\pi$
$557$	1.92197	+	3.32895i	0.0814365	+	0.141052i	−0.822431	+	0.568865i	$0.807383\pi$
$558$	1.80394	−	7.36381i	0.0763668	−	0.311735i
$559$		−	24.6949i		−	1.04448i
$560$	7.85587	+	7.09121i	0.331971	+	0.299659i
$561$	−69.1931	+	33.5231i	−2.92134	+	1.41535i
$562$	24.8248	−	11.3322i	1.04717	−	0.478018i
$563$	−20.3620	+	11.7560i	−0.858157	+	0.495457i	−0.863395	−	0.504529i	$-0.831666\pi$
$563$	−20.3620	+	11.7560i	−0.858157	+	0.495457i	0.00523745	+	0.999986i	$0.498333\pi$
$564$	−6.42232	+	23.8379i	−0.270428	+	1.00376i
$565$	−6.67816	−	3.85564i	−0.280952	−	0.162208i
$566$	−18.9768	+	26.6399i	−0.797653	+	1.11976i
$567$	−21.8891	+	9.37385i	−0.919254	+	0.393665i
$568$	−5.97857	−	1.75868i	−0.250855	−	0.0737924i
$569$	−5.00053	−	2.88706i	−0.209633	−	0.121032i	0.391508	−	0.920175i	$-0.371954\pi$
$569$	−5.00053	−	2.88706i	−0.209633	−	0.121032i	−0.601141	+	0.799143i	$0.705287\pi$
$570$	1.88293	−	0.699717i	0.0788674	−	0.0293079i
$571$	8.56780	+	14.8399i	0.358551	+	0.621029i	0.987719	−	0.156241i	$-0.0499375\pi$
$571$	8.56780	+	14.8399i	0.358551	+	0.621029i	−0.629168	+	0.777269i	$0.716604\pi$
$572$	−36.6042	−	7.06739i	−1.53050	−	0.295502i
$573$	−28.3396	+	13.7302i	−1.18390	+	0.573585i
$574$	17.4532	−	1.31860i	0.728484	−	0.0550371i
$575$	−6.48755			−0.270550
$576$	−4.61427	+	23.5523i	−0.192261	+	0.981344i
$577$	4.31045	+	7.46593i	0.179447	+	0.310811i	0.941691	−	0.336479i	$-0.109236\pi$
$577$	4.31045	+	7.46593i	0.179447	+	0.310811i	−0.762245	+	0.647289i	$0.775903\pi$
$578$	44.2075	+	4.22865i	1.83879	+	0.175889i
$579$	1.35378	−	18.6558i	0.0562611	−	0.775310i
$580$	−0.891041	−	2.57724i	−0.0369985	−	0.107014i
$581$	8.47308	−	23.0099i	0.351523	−	0.954612i
$582$	−0.503907	+	2.97473i	−0.0208876	+	0.123306i
$583$	−52.1687	−	30.1196i	−2.16061	−	1.24743i
$584$	2.92271	+	12.0736i	0.120943	+	0.499610i
$585$	1.26531	−	8.67242i	0.0523140	−	0.358560i
$586$	−15.4003	−	33.7366i	−0.636179	−	1.39365i
$587$		−	40.9272i		−	1.68925i	−0.535360	−	0.844624i	$-0.679824\pi$
$587$		−	40.9272i		−	1.68925i	0.535360	−	0.844624i	$-0.320176\pi$
$588$	−21.8848	−	10.4429i	−0.902514	−	0.430660i
$589$		−	1.46545i		−	0.0603827i
$590$	3.35557	−	1.53177i	0.138147	−	0.0630620i
$591$	−35.5715	−	24.1294i	−1.46322	−	0.992552i
$592$	−10.1585	+	25.3264i	−0.417512	+	1.04091i
$593$	14.7231	+	8.50037i	0.604604	+	0.349068i	0.770851	−	0.637016i	$-0.219831\pi$
$593$	14.7231	+	8.50037i	0.604604	+	0.349068i	−0.166247	+	0.986084i	$0.553165\pi$
$594$	−34.7974	+	31.4250i	−1.42776	+	1.28938i
$595$	6.36056	−	17.2730i	0.260757	−	0.708126i
$596$	7.70934	+	22.2984i	0.315787	+	0.913380i
$597$	38.7684	+	2.81326i	1.58668	+	0.115139i
$598$	−2.55221	+	26.6815i	−0.104368	+	1.09109i
$599$	−0.0838877	−	0.145298i	−0.00342756	−	0.00593671i	0.864307	−	0.502965i	$-0.167758\pi$
$599$	−0.0838877	−	0.145298i	−0.00342756	−	0.00593671i	−0.867734	+	0.497029i	$0.834424\pi$
$600$	−1.71905	+	4.58747i	−0.0701801	+	0.187283i
$601$	42.9062			1.75018			0.875091	−	0.483958i	$-0.160801\pi$
$601$	42.9062			1.75018			0.875091	+	0.483958i	$0.160801\pi$
$602$	−2.38275	−	31.5386i	−0.0971136	−	1.28542i
$603$	−0.710350	+	0.899431i	−0.0289277	+	0.0366277i
$604$	−2.18884	+	11.3367i	−0.0890627	+	0.461283i
$605$	14.8555	+	25.7305i	0.603962	+	1.04609i
$606$	2.83803	−	1.05464i	0.115287	−	0.0428419i
$607$	−22.6024	−	13.0495i	−0.917405	−	0.529664i	−0.0345985	−	0.999401i	$-0.511015\pi$
$607$	−22.6024	−	13.0495i	−0.917405	−	0.529664i	−0.882806	+	0.469737i	$0.844349\pi$
$608$	0.216916	+	4.63391i	0.00879710	+	0.187930i
$609$	3.64022	+	5.07823i	0.147509	+	0.205780i
$610$	−9.88372	−	7.04062i	−0.400180	−	0.285066i
$611$	18.0309	+	10.4101i	0.729451	+	0.421149i
$612$	41.0075	−	7.80121i	1.65763	−	0.315345i
$613$	38.6345	−	22.3056i	1.56043	−	0.900916i	0.563219	−	0.826308i	$-0.309563\pi$
$613$	38.6345	−	22.3056i	1.56043	−	0.900916i	0.997213	−	0.0746079i	$-0.0237705\pi$
$614$	−13.0586	−	28.6068i	−0.527002	−	1.15448i
$615$	3.53268	+	7.29161i	0.142452	+	0.294026i
$616$	−47.4303	−	5.49413i	−1.91102	−	0.221365i
$617$		−	10.5361i		−	0.424167i	−0.977252	−	0.212084i	$-0.931975\pi$
$617$		−	10.5361i		−	0.424167i	0.977252	−	0.212084i	$-0.0680249\pi$
$618$	−15.0925	+	18.2343i	−0.607108	+	0.733491i
$619$	−16.5158	−	28.6062i	−0.663826	−	1.14978i	−0.979602	−	0.200947i	$-0.935598\pi$
$619$	−16.5158	−	28.6062i	−0.663826	−	1.14978i	0.315776	−	0.948834i	$-0.397735\pi$
$620$	2.70026	+	2.34135i	0.108445	+	0.0940308i
$621$	24.8732	+	22.7532i	0.998127	+	0.913056i
$622$	11.2362	−	15.7735i	0.450531	−	0.632461i
$623$	21.8480	+	26.2372i	0.875322	+	1.05117i
$624$	18.1907	+	8.87471i	0.728212	+	0.355273i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	37.8041	+	3.61613i	1.51095	+	0.144530i
$627$	−5.08759	+	7.50011i	−0.203179	+	0.299525i
$628$	0.634171	−	3.28457i	0.0253062	−	0.131068i
$629$	47.4613			1.89241
$630$	0.779181	−	11.1979i	0.0310433	−	0.446135i
$631$		−	21.2155i		−	0.844577i	−0.906462	−	0.422288i	$-0.861227\pi$
$631$		−	21.2155i		−	0.844577i	0.906462	−	0.422288i	$-0.138773\pi$
$632$	−31.8817	−	33.4697i	−1.26819	−	1.33135i
$633$	15.3771	+	10.4309i	0.611186	+	0.414589i
$634$	23.5550	+	2.25315i	0.935489	+	0.0894839i
$635$	−1.02740	−	0.593172i	−0.0407713	−	0.0235393i
$636$	23.0943	+	23.1576i	0.915747	+	0.918257i
$637$	−13.2624	+	15.5662i	−0.525476	+	0.616755i
$638$	10.0206	+	7.13814i	0.396720	+	0.282602i
$639$	2.44389	+	6.14151i	0.0966790	+	0.242954i
$640$	−8.88511	−	7.00392i	−0.351215	−	0.276854i
$641$	−12.4072	+	7.16330i	−0.490055	+	0.282934i	−0.724597	−	0.689172i	$-0.757974\pi$
$641$	−12.4072	+	7.16330i	−0.490055	+	0.282934i	0.234542	+	0.972106i	$0.424641\pi$
$642$	4.93527	−	5.96266i	0.194780	−	0.235327i
$643$	−10.1712			−0.401111			−0.200556	−	0.979682i	$-0.564275\pi$
$643$	−10.1712			−0.401111			−0.200556	+	0.979682i	$0.564275\pi$
$644$	−0.685076	+	34.3221i	−0.0269958	+	1.35248i
$645$	13.1762	−	6.38368i	0.518812	−	0.251357i
$646$	7.33996	−	3.35059i	0.288787	−	0.131827i
$647$	16.4787	+	28.5419i	0.647843	+	1.12210i	0.983637	+	0.180162i	$0.0576622\pi$
$647$	16.4787	+	28.5419i	0.647843	+	1.12210i	−0.335794	+	0.941936i	$0.609005\pi$
$648$	22.6801	−	11.5592i	0.890957	−	0.454088i
$649$	−8.32106	+	14.4125i	−0.326630	+	0.565740i
$650$	3.36503	+	2.39706i	0.131987	+	0.0940204i
$651$	−7.45961	−	3.37849i	−0.292365	−	0.132413i
$652$	14.0991	+	40.7800i	0.552162	+	1.59707i
$653$	9.82718	−	17.0212i	0.384567	−	0.666090i	−0.607142	−	0.794594i	$-0.707684\pi$
$653$	9.82718	−	17.0212i	0.384567	−	0.666090i	0.991709	+	0.128503i	$0.0410173\pi$
$654$	−9.98297	−	26.8641i	−0.390365	−	1.05047i
$655$	−3.38447	+	1.95403i	−0.132242	+	0.0763501i
$656$	−18.5228	+	2.65072i	−0.723193	+	0.103493i
$657$	8.16629	−	10.3400i	0.318597	−	0.403401i
$658$	24.0322	+	11.5553i	0.936873	+	0.450474i
$659$			21.7995i			0.849188i	0.905384	+	0.424594i	$0.139583\pi$
$659$			21.7995i			0.849188i	−0.905384	+	0.424594i	$0.860417\pi$
$660$	−5.69139	−	21.3574i	−0.221537	−	0.831337i
$661$	−10.2511	+	5.91846i	−0.398720	+	0.230201i	−0.685932	−	0.727666i	$-0.740605\pi$
$661$	−10.2511	+	5.91846i	−0.398720	+	0.230201i	0.287211	+	0.957867i	$0.407272\pi$
$662$	12.3324	+	1.17965i	0.479313	+	0.0458485i
$663$	2.54787	−	35.1111i	0.0989511	−	1.36360i
$664$	−7.39759	+	25.1479i	−0.287082	+	0.975929i
$665$	−0.368722	−	2.13813i	−0.0142984	−	0.0829130i
$666$	27.7888	−	8.09188i	1.07680	−	0.313554i
$667$	4.42277	−	7.66046i	0.171250	−	0.296614i
$668$	0.570694	−	0.658178i	0.0220808	−	0.0254657i
$669$	1.27719	−	1.88283i	0.0493791	−	0.0727945i
$670$	−0.224361	−	0.491495i	−0.00866780	−	0.0189881i
$671$	54.7496			2.11358
$672$	24.0882	+	9.57899i	0.929224	+	0.369518i
$673$	29.8607			1.15105			0.575524	−	0.817785i	$-0.304798\pi$
$673$	29.8607			1.15105			0.575524	+	0.817785i	$0.304798\pi$
$674$	−8.95856	−	19.6251i	−0.345071	−	0.755929i
$675$	4.95433	−	1.56672i	0.190692	−	0.0603032i
$676$	−5.85059	+	6.74745i	−0.225023	+	0.259517i
$677$	−22.8224	+	39.5296i	−0.877136	+	1.51924i	−0.0226662	+	0.999743i	$0.507215\pi$
$677$	−22.8224	+	39.5296i	−0.877136	+	1.51924i	−0.854470	+	0.519501i	$0.826118\pi$
$678$	−18.6234	−	3.15473i	−0.715226	−	0.121157i
$679$	3.05810	+	1.12610i	0.117359	+	0.0432158i
$680$	−5.55321	+	18.8780i	−0.212956	+	0.723938i
$681$	−3.56955	−	0.259027i	−0.136785	−	0.00992595i
$682$	−16.0515	−	1.53540i	−0.614643	−	0.0587934i
$683$	2.77195	−	1.60039i	0.106066	−	0.0612371i	−0.446029	−	0.895019i	$-0.647162\pi$
$683$	2.77195	−	1.60039i	0.106066	−	0.0612371i	0.552094	+	0.833782i	$0.313829\pi$
$684$	3.72633	−	3.21321i	0.142480	−	0.122860i
$685$			4.52276i			0.172806i
$686$	−15.4359	+	21.1597i	−0.589345	+	0.807881i
$687$	8.85981	+	18.2870i	0.338023	+	0.697693i
$688$	4.78994	+	33.4713i	0.182615	+	1.27608i
$689$	23.8862	−	13.7907i	0.909992	−	0.525384i
$690$	−14.8959	+	5.53548i	−0.567078	+	0.210732i
$691$	1.26606	−	2.19288i	0.0481633	−	0.0834212i	−0.840939	−	0.541130i	$-0.817997\pi$
$691$	1.26606	−	2.19288i	0.0481633	−	0.0834212i	0.889102	+	0.457709i	$0.151330\pi$
$692$	−2.29784	−	6.64626i	−0.0873508	−	0.252653i
$693$	26.4489	+	43.1885i	1.00471	+	1.64060i
$694$	−5.86691	−	4.17926i	−0.222705	−	0.158643i
$695$	6.08413	−	10.5380i	0.230784	−	0.399730i
$696$	−4.24492	−	5.15727i	−0.160903	−	0.195486i
$697$	16.2723	+	28.1845i	0.616359	+	1.06757i
$698$	−11.5090	+	5.25371i	−0.435623	+	0.198856i
$699$	8.09498	+	16.7084i	0.306180	+	0.631969i
$700$	4.52886	+	2.73668i	0.171175	+	0.103437i
$701$	9.30680			0.351513			0.175756	−	0.984434i	$-0.443763\pi$
$701$	9.30680			0.351513			0.175756	+	0.984434i	$0.443763\pi$
$702$	−4.49446	−	20.9922i	−0.169633	−	0.792298i
$703$	4.84492	−	2.79721i	0.182729	−	0.105499i
$704$	50.9839	+	2.47916i	1.92153	+	0.0934369i
$705$	−0.893400	+	12.3116i	−0.0336474	+	0.463680i
$706$	−19.1289	−	13.6264i	−0.719925	−	0.512835i
$707$	−0.555753	−	3.22267i	−0.0209013	−	0.121201i
$708$	6.39767	−	6.38019i	0.240439	−	0.239782i
$709$	−30.9906	−	17.8924i	−1.16388	−	0.671964i	−0.211646	−	0.977347i	$-0.567882\pi$
$709$	−30.9906	−	17.8924i	−1.16388	−	0.671964i	−0.952230	+	0.305383i	$0.901216\pi$
$710$	−3.10178	−	0.296700i	−0.116408	−	0.0111349i
$711$	−7.07825	+	48.5144i	−0.265455	+	1.81943i
$712$	−25.1749	−	26.4288i	−0.943470	−	0.990462i
$713$			11.5932i			0.434168i
$714$	−0.133821	−	45.0874i	−0.00500814	−	1.68735i
$715$	−18.6401			−0.697101
$716$	8.16214	−	42.2743i	0.305034	−	1.57986i
$717$	−9.54401	−	6.47404i	−0.356428	−	0.241778i
$718$	1.58373	+	0.151491i	0.0591044	+	0.00565361i
$719$	−3.84834	+	6.66553i	−0.143519	+	0.248582i	−0.928819	−	0.370533i	$-0.879175\pi$
$719$	−3.84834	+	6.66553i	−0.143519	+	0.248582i	0.785300	+	0.619115i	$0.212508\pi$
$720$	−0.0328432	+	12.0000i	−0.00122399	+	0.447212i
$721$	16.3601	+	19.6468i	0.609282	+	0.731686i
$722$	−15.0380	+	21.1105i	−0.559655	+	0.785652i
$723$	−0.195930	+	2.70003i	−0.00728672	+	0.100415i
$724$	9.07703	+	7.87052i	0.337345	+	0.292506i
$725$	−0.681731	−	1.18079i	−0.0253189	−	0.0438536i
$726$	56.0638	+	46.4038i	2.08072	+	1.72220i
$727$			1.90494i			0.0706503i	0.999376	+	0.0353252i	$0.0112467\pi$
$727$			1.90494i			0.0706503i	−0.999376	+	0.0353252i	$0.988753\pi$
$728$	13.0369	−	17.5494i	0.483178	−	0.650423i
$729$	−24.4897	−	11.3691i	−0.907024	−	0.421078i
$730$	2.57928	+	5.65030i	0.0954635	+	0.209127i
$731$	50.9304	−	29.4047i	1.88373	−	1.08757i
$732$	−28.7012	−	7.73257i	−1.06083	−	0.285804i
$733$	29.4946	+	17.0287i	1.08941	+	0.628969i	0.933418	−	0.358790i	$-0.116811\pi$
$733$	29.4946	+	17.0287i	1.08941	+	0.628969i	0.155988	+	0.987759i	$0.450144\pi$
$734$	−27.5488	−	19.6242i	−1.01684	−	0.724344i
$735$	−11.7338	−	3.05239i	−0.432809	−	0.112589i
$736$	−1.71603	−	36.6590i	−0.0632536	−	1.35127i
$737$	2.11102	+	1.21880i	0.0777604	+	0.0448950i
$738$	14.3328	+	13.7278i	0.527599	+	0.505329i
$739$	−10.9793	−	19.0167i	−0.403880	−	0.699541i	0.590310	−	0.807177i	$-0.299005\pi$
$739$	−10.9793	−	19.0167i	−0.403880	−	0.699541i	−0.994190	+	0.107635i	$0.965672\pi$
$740$	−2.58653	+	13.3965i	−0.0950828	+	0.492463i
$741$	−1.80925	−	3.73436i	−0.0664643	−	0.137185i
$742$	29.1752	−	19.9172i	1.07105	−	0.731185i
$743$	20.1591			0.739567			0.369783	−	0.929118i	$-0.379432\pi$
$743$	20.1591			0.739567			0.369783	+	0.929118i	$0.379432\pi$
$744$	8.19776	+	3.07193i	0.300544	+	0.112622i
$745$	5.89838	+	10.2163i	0.216100	+	0.374296i
$746$	2.97339	−	31.0846i	0.108863	−	1.13809i
$747$	25.8333	−	10.2799i	0.945191	−	0.376120i
$748$	−29.0096	−	83.9073i	−1.06070	−	3.06795i
$749$	−5.34979	−	6.42456i	−0.195477	−	0.234748i
$750$	−0.409106	+	2.41508i	−0.0149385	+	0.0881864i
$751$	27.2412	+	15.7277i	0.994046	+	0.573913i	0.906481	−	0.422246i	$-0.138758\pi$
$751$	27.2412	+	15.7277i	0.994046	+	0.573913i	0.0875647	+	0.996159i	$0.472092\pi$
$752$	−26.4581	−	10.6125i	−0.964828	−	0.386996i
$753$	0.614382	−	0.905720i	0.0223893	−	0.0330063i
$754$	−5.12448	+	2.33925i	−0.186622	+	0.0851904i
$755$			5.77303i			0.210102i
$756$	−7.76549	−	26.3761i	−0.282428	−	0.959288i
$757$			7.57270i			0.275234i	0.990485	+	0.137617i	$0.0439444\pi$
$757$			7.57270i			0.275234i	−0.990485	+	0.137617i	$0.956056\pi$
$758$	−1.53001	−	3.35171i	−0.0555723	−	0.121739i
$759$	40.2481	−	59.3335i	1.46091	−	2.15367i
$760$	0.545727	+	2.25438i	0.0197956	+	0.0817750i
$761$	38.1931	+	22.0508i	1.38450	+	0.799342i	0.992689	−	0.120704i	$-0.0385151\pi$
$761$	38.1931	+	22.0508i	1.38450	+	0.799342i	0.391812	+	0.920045i	$0.371848\pi$
$762$	−2.86512	−	0.485341i	−0.103792	−	0.0175820i
$763$	−30.5050	+	5.26062i	−1.10435	+	0.190447i
$764$	−11.8816	−	34.3661i	−0.429859	−	1.24332i
$765$	19.3925	−	7.71686i	0.701137	−	0.279004i
$766$	−18.9865	−	1.81615i	−0.686010	−	0.0656201i
$767$	−3.80992	−	6.59897i	−0.137568	−	0.238275i
$768$	−26.3770	−	8.50036i	−0.951796	−	0.306730i
$769$	−38.7044			−1.39572			−0.697859	−	0.716235i	$-0.745864\pi$
$769$	−38.7044			−1.39572			−0.697859	+	0.716235i	$0.745864\pi$
$770$	−23.8059	+	1.79854i	−0.857904	+	0.0648148i
$771$	8.65170	+	17.8575i	0.311583	+	0.643121i
$772$	21.2069	+	4.09454i	0.763253	+	0.147366i
$773$	−22.7217	−	39.3552i	−0.817244	−	1.41551i	−0.907706	−	0.419608i	$-0.862168\pi$
$773$	−22.7217	−	39.3552i	−0.817244	−	1.41551i	0.0904620	−	0.995900i	$-0.471166\pi$
$774$	24.8067	−	25.9000i	0.891658	−	0.930955i
$775$	1.54758	+	0.893495i	0.0555907	+	0.0320953i
$776$	−3.34224	−	0.983166i	−0.119980	−	0.0352936i
$777$	−3.06912	−	31.1110i	−0.110104	−	1.11610i
$778$	−18.6336	+	26.1581i	−0.668048	+	0.937815i
$779$	3.32221	+	1.91808i	0.119030	+	0.0687223i
$780$	9.77164	+	2.63264i	0.349881	+	0.0942637i
$781$	12.1748	−	7.02910i	0.435647	−	0.251521i
$782$	−58.0666	+	26.5066i	−2.07646	+	0.947873i
$783$	−1.52755	+	6.91812i	−0.0545901	+	0.247234i
$784$	14.9565	−	23.6707i	0.534160	−	0.845383i
$785$		−	1.67261i		−	0.0596982i
$786$	−6.10374	+	7.37438i	−0.217713	+	0.263035i
$787$	−8.93783	−	15.4808i	−0.318599	−	0.551830i	0.661597	−	0.749860i	$-0.269879\pi$
$787$	−8.93783	−	15.4808i	−0.318599	−	0.551830i	−0.980196	+	0.198030i	$0.936546\pi$
$788$	32.5149	−	37.4993i	1.15830	−	1.33586i
$789$	0.484118	−	6.67143i	0.0172351	−	0.237509i
$790$	−18.8243	−	13.4094i	−0.669738	−	0.477085i
$791$	−7.05000	+	19.1453i	−0.250669	+	0.680729i
$792$	−31.2910	−	44.1822i	−1.11188	−	1.56994i
$793$	−12.5339	+	21.7094i	−0.445093	+	0.770924i
$794$	−0.436567	+	4.56400i	−0.0154932	+	0.161970i
$795$	13.5328	+	9.17977i	0.479958	+	0.325573i
$796$	−8.50878	+	44.0696i	−0.301586	+	1.56201i
$797$	24.0379			0.851466			0.425733	−	0.904849i	$-0.360016\pi$
$797$	24.0379			0.851466			0.425733	+	0.904849i	$0.360016\pi$
$798$	−2.67096	−	4.59469i	−0.0945510	−	0.162650i
$799$			49.5821i			1.75409i
$800$	−5.02588	−	2.59626i	−0.177692	−	0.0917917i
$801$	−5.58923	+	38.3087i	−0.197486	+	1.35357i
$802$	4.06506	−	42.4972i	0.143542	−	1.50063i
$803$	−24.2686	−	14.0115i	−0.856420	−	0.494454i
$804$	−0.934515	−	0.937077i	−0.0329578	−	0.0330481i
$805$	2.91697	+	16.9148i	0.102810	+	0.596168i
$806$	4.28352	−	6.01327i	0.150881	−	0.211808i
$807$	0.818809	−	11.2837i	0.0288235	−	0.397204i
$808$	0.822543	+	3.39790i	0.0289370	+	0.119538i
$809$	−12.9599	+	7.48239i	−0.455645	+	0.263067i	−0.710211	−	0.703989i	$-0.751401\pi$
$809$	−12.9599	+	7.48239i	−0.455645	+	0.263067i	0.254566	+	0.967055i	$0.418067\pi$
$810$	10.0387	−	7.82458i	0.352725	−	0.274928i
$811$	2.38700			0.0838191			0.0419095	−	0.999121i	$-0.486656\pi$
$811$	2.38700			0.0838191			0.0419095	+	0.999121i	$0.486656\pi$
$812$	−6.31892	+	3.48198i	−0.221751	+	0.122193i
$813$	−11.8629	−	24.4855i	−0.416050	−	0.858745i
$814$	−25.5625	−	55.9985i	−0.895966	−	1.96275i
$815$	10.7871	+	18.6838i	0.377857	+	0.654467i
$816$	3.35696	+	48.0836i	0.117517	+	1.68326i
$817$	3.46603	−	6.00335i	0.121261	−	0.210031i
$818$	−16.8688	+	23.6807i	−0.589805	+	0.827976i
$819$	−23.1802	+	0.600354i	−0.809982	+	0.0209781i
$820$	−8.84219	+	3.05705i	−0.308783	+	0.106757i
$821$	−1.14316	+	1.98002i	−0.0398967	+	0.0691031i	−0.885284	−	0.465050i	$-0.846036\pi$
$821$	−1.14316	+	1.98002i	−0.0398967	+	0.0691031i	0.845388	+	0.534153i	$0.179370\pi$
$822$	3.85903	+	10.3846i	0.134599	+	0.362205i
$823$	−2.59074	+	1.49577i	−0.0903076	+	0.0521391i	−0.544474	−	0.838778i	$-0.683271\pi$
$823$	−2.59074	+	1.49577i	−0.0903076	+	0.0521391i	0.454166	+	0.890917i	$0.349937\pi$
$824$	−18.8513	−	19.7903i	−0.656718	−	0.689428i
$825$	−4.81851	−	9.94560i	−0.167759	−	0.346261i
$826$	−5.50248	−	8.06014i	−0.191456	−	0.280448i
$827$		−	2.27298i		−	0.0790393i	−0.999219	−	0.0395196i	$-0.987417\pi$
$827$		−	2.27298i		−	0.0790393i	0.999219	−	0.0395196i	$-0.0125828\pi$
$828$	−29.4791	+	25.4198i	−1.02447	+	0.883398i
$829$	44.5776	−	25.7369i	1.54824	−	0.893879i	0.549967	−	0.835186i	$-0.314640\pi$
$829$	44.5776	−	25.7369i	1.54824	−	0.893879i	0.998276	−	0.0586924i	$-0.0186931\pi$
$830$	−1.24802	+	13.0471i	−0.0433194	+	0.452873i
$831$	14.9887	+	1.08767i	0.519951	+	0.0377307i
$832$	−12.6549	+	19.6487i	−0.438730	+	0.681196i
$833$	−47.8953	−	8.81725i	−1.65947	−	0.305500i
$834$	4.97811	−	29.3874i	0.172378	−	1.01760i
$835$	0.217786	−	0.377216i	0.00753679	−	0.0130541i
$836$	−7.90656	−	6.85564i	−0.273454	−	0.237107i
$837$	−2.79972	−	8.85333i	−0.0967723	−	0.306016i
$838$	30.7688	−	14.0455i	1.06289	−	0.485194i
$839$	−15.5868			−0.538116			−0.269058	−	0.963124i	$-0.586712\pi$
$839$	−15.5868			−0.538116			−0.269058	+	0.963124i	$0.586712\pi$
$840$	12.7337	+	2.41939i	0.439354	+	0.0834767i
$841$	−27.1410			−0.935895
$842$	−19.2112	+	8.76964i	−0.662062	+	0.302222i
$843$	18.7620	−	27.6589i	0.646199	−	0.952624i
$844$	−14.0558	+	16.2105i	−0.483821	+	0.557988i
$845$	−2.23268	+	3.86711i	−0.0768064	+	0.133033i
$846$	8.45348	+	29.0306i	0.290636	+	0.998093i
$847$	60.4068	−	50.3013i	2.07560	−	1.72837i
$848$	−29.7003	+	23.3249i	−1.01991	+	0.800980i
$849$	−2.89927	+	39.9537i	−0.0995028	+	1.37121i
$850$	−0.936861	+	9.79421i	−0.0321341	+	0.335939i
$851$	−38.3283	+	22.1288i	−1.31388	+	0.758567i
$852$	−7.37508	+	1.96533i	−0.252666	+	0.0673312i
$853$			53.4140i			1.82886i	0.404745	+	0.914430i	$0.367360\pi$
$853$			53.4140i			1.82886i	−0.404745	+	0.914430i	$0.632640\pi$
$854$	−13.9128	+	28.9351i	−0.476086	+	0.990140i
$855$	1.52481	−	1.93068i	0.0521473	−	0.0660278i
$856$	6.16444	+	6.47148i	0.210696	+	0.221190i
$857$	7.94413	−	4.58655i	0.271366	−	0.156673i	−0.358142	−	0.933667i	$-0.616590\pi$
$857$	7.94413	−	4.58655i	0.271366	−	0.156673i	0.629508	+	0.776994i	$0.283256\pi$
$858$	−42.7991	+	15.9046i	−1.46114	+	0.542974i
$859$	−8.80275	+	15.2468i	−0.300346	+	0.520214i	−0.976214	−	0.216808i	$-0.930435\pi$
$859$	−8.80275	+	15.2468i	−0.300346	+	0.520214i	0.675868	+	0.737022i	$0.263769\pi$
$860$	5.52420	+	15.9781i	0.188374	+	0.544850i
$861$	17.4228	−	12.4891i	0.593766	−	0.425629i
$862$	11.1327	−	15.6283i	0.379182	−	0.532302i
$863$	6.70607	−	11.6153i	0.228277	−	0.395388i	−0.729020	−	0.684492i	$-0.760024\pi$
$863$	6.70607	−	11.6153i	0.228277	−	0.395388i	0.957298	+	0.289104i	$0.0933574\pi$
$864$	10.1635	+	27.5809i	0.345769	+	0.938320i
$865$	−1.75807	−	3.04506i	−0.0597761	−	0.103535i
$866$	−12.0178	−	26.3267i	−0.408380	−	0.894618i
$867$	48.9479	−	23.7146i	1.66236	−	0.805389i
$868$	4.89041	−	8.09303i	0.165991	−	0.274695i
$869$	104.275			3.53728
$870$	−2.57281	−	2.12951i	−0.0872266	−	0.0721971i
$871$	−0.966561	+	0.558044i	−0.0327507	+	0.0189086i
$872$	32.1636	−	7.78598i	1.08920	−	0.263667i
$873$	1.36623	+	3.43333i	0.0462398	+	0.116201i
$874$	−4.36531	+	6.12809i	−0.147659	+	0.207286i
$875$	2.48277	+	0.914246i	0.0839330	+	0.0309071i
$876$	10.7433	+	10.7728i	0.362983	+	0.363978i
$877$	−1.44864	−	0.836371i	−0.0489170	−	0.0282422i	0.475342	−	0.879801i	$-0.342324\pi$
$877$	−1.44864	−	0.836371i	−0.0489170	−	0.0282422i	−0.524259	+	0.851559i	$0.675658\pi$
$878$	3.64333	−	38.0884i	0.122956	−	1.28542i
$879$	−37.5882	−	25.4974i	−1.26782	−	0.860006i
$880$	25.2647	−	3.61552i	0.851672	−	0.121879i
$881$			19.3094i			0.650551i	0.945619	+	0.325276i	$0.105457\pi$
$881$			19.3094i			0.650551i	−0.945619	+	0.325276i	$0.894543\pi$
$882$	−29.5462	+	3.00333i	−0.994873	+	0.101127i
$883$	13.3201			0.448257			0.224128	−	0.974560i	$-0.428047\pi$
$883$	13.3201			0.448257			0.224128	+	0.974560i	$0.428047\pi$
$884$	39.9123	+	7.70611i	1.34240	+	0.259185i
$885$	2.53607	−	3.73866i	0.0852490	−	0.125674i
$886$	−4.47699	+	46.8037i	−0.150407	+	1.57240i
$887$	25.5507	−	44.2552i	0.857910	−	1.48594i	−0.0160090	−	0.999872i	$-0.505096\pi$
$887$	25.5507	−	44.2552i	0.857910	−	1.48594i	0.873919	−	0.486072i	$-0.161571\pi$
$888$	5.49159	+	32.9662i	0.184286	+	1.10627i
$889$	−1.08461	+	2.94542i	−0.0363766	+	0.0987862i
$890$	−14.8643	−	10.5885i	−0.498253	−	0.354928i
$891$	−16.4073	+	55.0308i	−0.549664	+	1.84360i
$892$	1.98487	+	1.72104i	0.0664583	+	0.0576248i
$893$	2.92221	+	5.06142i	0.0977880	+	0.169374i
$894$	22.2602	+	18.4246i	0.744491	+	0.616212i
$895$		−	21.5275i		−	0.719585i
$896$	−14.2661	+	26.3150i	−0.476597	+	0.879122i
$897$	14.3130	+	29.5426i	0.477897	+	0.986399i
$898$	32.7325	−	14.9419i	1.09230	−	0.498619i
$899$	−2.11007	+	1.21825i	−0.0703746	+	0.0406308i
$900$	1.12132	+	5.89429i	0.0373773	+	0.196476i
$901$	56.8835	+	32.8417i	1.89506	+	1.09412i
$902$	24.4901	−	34.3795i	0.815430	−	1.14471i
$903$	−22.5683	−	31.4836i	−0.751027	−	1.04771i
$904$	6.15514	−	20.9242i	0.204717	−	0.695930i
$905$	5.20224	+	3.00351i	0.172928	+	0.0998402i
$906$	4.92581	+	13.2553i	0.163649	+	0.440379i
$907$	−24.0881	−	41.7219i	−0.799833	−	1.38535i	−0.919724	−	0.392565i	$-0.871588\pi$
$907$	−24.0881	−	41.7219i	−0.799833	−	1.38535i	0.119891	−	0.992787i	$-0.461746\pi$
$908$	0.783436	−	4.05766i	0.0259992	−	0.134658i
$909$	2.29825	−	2.91000i	0.0762282	−	0.0965186i
$910$	4.73677	−	9.85130i	0.157022	−	0.326567i
$911$	10.7764			0.357037			0.178518	−	0.983937i	$-0.442870\pi$
$911$	10.7764			0.357037			0.178518	+	0.983937i	$0.442870\pi$
$912$	3.17657	+	4.71059i	0.105187	+	0.155983i
$913$	−29.5668	−	51.2112i	−0.978518	−	1.69484i
$914$	−40.7423	−	3.89719i	−1.34764	−	0.128908i
$915$	−14.8233	−	1.07567i	−0.490043	−	0.0355604i
$916$	−22.1758	+	7.66694i	−0.732709	+	0.253323i
$917$	6.61641	+	7.94564i	0.218493	+	0.262388i
$918$	37.9423	−	34.2651i	1.25228	−	1.13092i
$919$	46.5187	+	26.8576i	1.53451	+	0.885949i	0.999146	+	0.0413275i	$0.0131587\pi$
$919$	46.5187	+	26.8576i	1.53451	+	0.885949i	0.535363	+	0.844622i	$0.320175\pi$
$920$	−4.31726	−	17.8345i	−0.142336	−	0.587985i
$921$	−31.8727	−	21.6204i	−1.05024	−	0.712416i
$922$	−12.8608	−	28.1736i	−0.423549	−	0.927847i
$923$			6.43675i			0.211868i
$924$	−53.1255	+	24.4418i	−1.74770	+	0.804077i
$925$			6.82193i			0.224304i
$926$	−47.4368	+	21.6542i	−1.55887	+	0.711602i
$927$	−4.18530	+	28.6861i	−0.137463	+	0.942174i
$928$	6.49194	−	4.16457i	0.213109	−	0.136709i
$929$	−22.7512	−	13.1354i	−0.746442	−	0.430958i	0.0779650	−	0.996956i	$-0.475158\pi$
$929$	−22.7512	−	13.1354i	−0.746442	−	0.430958i	−0.824407	+	0.565998i	$0.808491\pi$
$930$	4.31573	+	0.731069i	0.141518	+	0.0239727i
$931$	−5.40888	+	1.92271i	−0.177269	+	0.0630144i
$932$	−20.2615	+	7.00509i	−0.663686	+	0.229459i
$933$	1.71667	−	23.6567i	0.0562012	−	0.774485i
$934$	1.27028	−	13.2798i	0.0415647	−	0.434529i
$935$	−22.1951	−	38.4431i	−0.725859	−	1.25722i
$936$	24.6827	−	2.29286i	0.806780	−	0.0749445i
$937$	−15.5368			−0.507566			−0.253783	−	0.967261i	$-0.581675\pi$
$937$	−15.5368			−0.507566			−0.253783	+	0.967261i	$0.581675\pi$
$938$	−1.18058	+	0.805957i	−0.0385473	+	0.0263154i
$939$	41.8578	−	20.2795i	1.36598	−	0.661798i
$940$	−13.9951	−	2.70211i	−0.456469	−	0.0881332i
$941$	−3.61622	−	6.26348i	−0.117886	−	0.204184i	0.801044	−	0.598605i	$-0.204278\pi$
$941$	−3.61622	−	6.26348i	−0.117886	−	0.204184i	−0.918930	+	0.394422i	$0.870945\pi$
$942$	−1.42715	−	3.84045i	−0.0464991	−	0.125129i
$943$	−26.2821	−	15.1740i	−0.855862	−	0.494132i
$944$	6.44390	+	8.20521i	0.209731	+	0.267057i
$945$	−6.31246	−	12.2128i	−0.205344	−	0.397283i
$946$	−62.1249	−	44.2544i	−2.01986	−	1.43883i
$947$	−34.1683	−	19.7271i	−1.11032	−	0.641044i	−0.171408	−	0.985200i	$-0.554832\pi$
$947$	−34.1683	−	19.7271i	−1.11032	−	0.641044i	−0.938912	+	0.344156i	$0.888165\pi$
$948$	−54.6635	−	14.7273i	−1.77539	−	0.478319i
$949$	11.1117	−	6.41536i	0.360702	−	0.208251i
$950$	0.481602	+	1.05502i	0.0156252	+	0.0342294i
$951$	26.0808	−	12.6358i	0.845729	−	0.409744i
$952$	51.7168	+	5.99067i	1.67615	+	0.194159i
$953$		−	2.29992i		−	0.0745017i	−0.999306	−	0.0372508i	$-0.988140\pi$
$953$		−	2.29992i		−	0.0745017i	0.999306	−	0.0372508i	$-0.0118601\pi$
$954$	38.9049	+	9.53067i	1.25959	+	0.308567i
$955$	−9.09052	−	15.7452i	−0.294162	−	0.509504i
$956$	8.72392	−	10.0612i	0.282152	−	0.325404i
$957$	15.0286	+	1.09057i	0.485806	+	0.0352530i
$958$	30.5541	−	42.8923i	0.987159	−	1.38579i
$959$	11.7920	−	2.03355i	0.380785	−	0.0656668i
$960$	−13.7550	−	1.67291i	−0.443942	−	0.0539929i
$961$	−13.9033	+	24.0813i	−0.448495	+	0.776816i
$962$	28.0568	+	2.68376i	0.904586	+	0.0865279i
$963$	1.36860	−	9.38042i	0.0441026	−	0.302280i
$964$	−3.06924	−	0.592596i	−0.0988536	−	0.0190862i
$965$	10.7993			0.347641
$966$	21.1301	+	36.3488i	0.679848	+	1.16950i
$967$		−	2.39354i		−	0.0769711i	−0.999259	−	0.0384855i	$-0.987747\pi$
$967$		−	2.39354i		−	0.0769711i	0.999259	−	0.0384855i	$-0.0122534\pi$
$968$	−60.8479	+	57.9610i	−1.95572	+	1.86294i
$969$	5.54739	−	8.17794i	0.178208	−	0.262713i
$970$	−1.73401	−	0.165866i	−0.0556757	−	0.00532564i
$971$	20.9662	+	12.1048i	0.672836	+	0.388462i	0.797151	−	0.603781i	$-0.206340\pi$
$971$	20.9662	+	12.1048i	0.672836	+	0.388462i	−0.124314	+	0.992243i	$0.539673\pi$
$972$	16.3734	−	26.5313i	0.525177	−	0.850993i
$973$	−30.2110	−	11.1248i	−0.968520	−	0.356644i
$974$	−25.8762	−	18.4328i	−0.829126	−	0.590624i
$975$	5.04676	+	0.366223i	0.161626	+	0.0117285i
$976$	12.7775	−	31.8559i	0.408999	−	1.01968i
$977$	−5.92602	+	3.42139i	−0.189590	+	0.109460i	−0.591791	−	0.806092i	$-0.701579\pi$
$977$	−5.92602	+	3.42139i	−0.189590	+	0.109460i	0.402201	+	0.915552i	$0.368245\pi$
$978$	40.7100	+	33.6955i	1.30176	+	1.07746i
$979$	82.3389			2.63156
$980$	5.09895	−	13.0384i	0.162880	−	0.416497i
$981$	−27.5453	−	21.7547i	−0.879454	−	0.694573i
$982$	−18.5926	+	8.48726i	−0.593314	+	0.270839i
$983$	16.9931	+	29.4329i	0.541996	+	0.938765i	0.998789	+	0.0491921i	$0.0156647\pi$
$983$	16.9931	+	29.4329i	0.541996	+	0.938765i	−0.456793	+	0.889573i	$0.651002\pi$
$984$	−17.6939	+	14.5638i	−0.564062	+	0.464276i
$985$	12.4082	−	21.4916i	0.395358	−	0.684781i
$986$	−10.9262	−	7.78326i	−0.347963	−	0.247869i
$987$	32.5012	−	3.20627i	1.03453	−	0.102057i
$988$	4.52848	−	1.56565i	0.144070	−	0.0498100i
$989$	−27.4199	+	47.4926i	−0.871902	+	1.51018i
$990$	−19.5497	−	18.7245i	−0.621330	−	0.595103i
$991$	−6.57484	+	3.79598i	−0.208857	+	0.120583i	−0.600780	−	0.799414i	$-0.705143\pi$
$991$	−6.57484	+	3.79598i	−0.208857	+	0.120583i	0.391923	+	0.919998i	$0.371810\pi$
$992$	−4.63949	+	8.98119i	−0.147304	+	0.285153i
$993$	13.6548	−	6.61558i	0.433323	−	0.209939i
$994$	0.621065	+	8.22057i	0.0196990	+	0.260741i
$995$			22.4418i			0.711452i
$996$	8.26687	+	31.0221i	0.261946	+	0.982974i
$997$	−36.1075	+	20.8467i	−1.14354	+	0.660221i	−0.947304	−	0.320337i	$-0.896204\pi$
$997$	−36.1075	+	20.8467i	−1.14354	+	0.660221i	−0.196232	+	0.980557i	$0.562871\pi$
$998$	−9.72382	−	0.930129i	−0.307802	−	0.0294427i
$999$	23.9260	−	26.1552i	0.756985	−	0.827514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cq.a.611.41	yes	128
3.2	odd	2		840.2.cq.b.611.24	yes	128
7.4	even	3	inner	840.2.cq.a.11.3	✓	128
8.3	odd	2		840.2.cq.b.611.62	yes	128
21.11	odd	6		840.2.cq.b.11.62	yes	128
24.11	even	2	inner	840.2.cq.a.611.3	yes	128
56.11	odd	6		840.2.cq.b.11.24	yes	128
168.11	even	6	inner	840.2.cq.a.11.41	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cq.a.11.3	✓	128	7.4	even	3	inner
840.2.cq.a.11.41	yes	128	168.11	even	6	inner
840.2.cq.a.611.3	yes	128	24.11	even	2	inner
840.2.cq.a.611.41	yes	128	1.1	even	1	trivial
840.2.cq.b.11.24	yes	128	56.11	odd	6
840.2.cq.b.11.62	yes	128	21.11	odd	6
840.2.cq.b.611.24	yes	128	3.2	odd	2
840.2.cq.b.611.62	yes	128	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587274 + 1.28651i) q^{2} +(1.43339 + 0.972318i) q^{3} +(-1.31022 + 1.51107i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.409106 + 2.41508i) q^{6} +(2.48277 + 0.914246i) q^{7} +(-2.71346 - 0.798201i) q^{8} +(1.10920 + 2.78741i) q^{9} +(-1.40779 - 0.134661i) q^{10} +(5.52569 - 3.19026i) q^{11} +(-3.34729 + 0.891996i) q^{12} +2.92141i q^{13} +(0.281880 + 3.73102i) q^{14} +(-1.55875 + 0.755191i) q^{15} +(-0.566651 - 3.95966i) q^{16} +(-6.02508 + 3.47858i) q^{17} +(-2.93464 + 3.06397i) q^{18} +(-0.410032 + 0.710197i) q^{19} +(-0.653513 - 1.89022i) q^{20} +(2.66984 + 3.72451i) q^{21} +(7.34939 + 5.23530i) q^{22} +(3.24378 - 5.61839i) q^{23} +(-3.11334 - 3.78248i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.75843 + 1.71567i) q^{26} +(-1.12034 + 5.07394i) q^{27} +(-4.63446 + 2.55377i) q^{28} +1.36346 q^{29} +(-1.88697 - 1.56184i) q^{30} +(-1.54758 + 0.893495i) q^{31} +(4.76137 - 3.05441i) q^{32} +(11.0224 + 0.799850i) q^{33} +(-8.01360 - 5.70845i) q^{34} +(-2.03315 + 1.69302i) q^{35} +(-5.66526 - 1.97605i) q^{36} +(-5.90797 - 3.41097i) q^{37} +(-1.15448 - 0.110431i) q^{38} +(-2.84054 + 4.18751i) q^{39} +(2.04799 - 1.95083i) q^{40} -4.67787i q^{41} +(-3.22370 + 5.62208i) q^{42} -8.45307 q^{43} +(-2.41917 + 12.5296i) q^{44} +(-2.96857 - 0.433114i) q^{45} +(9.13310 + 0.873623i) q^{46} +(3.56339 - 6.17197i) q^{47} +(3.03782 - 6.22669i) q^{48} +(5.32831 + 4.53973i) q^{49} +(0.820514 - 1.15185i) q^{50} +(-12.0186 - 0.872137i) q^{51} +(-4.41445 - 3.82769i) q^{52} +(-4.72056 - 8.17625i) q^{53} +(-7.18562 + 1.53846i) q^{54} +6.38052i q^{55} +(-6.00715 - 4.46252i) q^{56} +(-1.27827 + 0.619305i) q^{57} +(0.800726 + 1.75411i) q^{58} +(-2.25883 + 1.30414i) q^{59} +(0.901154 - 3.34484i) q^{60} +(7.43114 + 4.29037i) q^{61} +(-2.05834 - 1.46625i) q^{62} +(0.205501 + 7.93459i) q^{63} +(6.72575 + 4.33178i) q^{64} +(-2.53002 - 1.46071i) q^{65} +(5.44415 + 14.6502i) q^{66} +(0.191019 + 0.330854i) q^{67} +(2.63780 - 13.6620i) q^{68} +(10.1124 - 4.89934i) q^{69} +(-3.37210 - 1.62140i) q^{70} +2.20330 q^{71} +(-0.784847 - 8.44891i) q^{72} +(-2.19598 - 3.80355i) q^{73} +(0.918651 - 9.60383i) q^{74} +(0.125358 - 1.72751i) q^{75} +(-0.535923 - 1.55010i) q^{76} +(16.6357 - 2.86884i) q^{77} +(-7.05546 - 1.19517i) q^{78} +(14.1532 + 8.17134i) q^{79} +(3.71249 + 1.48910i) q^{80} +(-6.53936 + 6.18359i) q^{81} +(6.01813 - 2.74719i) q^{82} -9.26784i q^{83} +(-9.12606 - 0.845623i) q^{84} -6.95716i q^{85} +(-4.96427 - 10.8750i) q^{86} +(1.95437 + 1.32572i) q^{87} +(-17.5402 + 4.24603i) q^{88} +(11.1758 + 6.45237i) q^{89} +(-1.18616 - 4.07345i) q^{90} +(-2.67089 + 7.25320i) q^{91} +(4.23970 + 12.2629i) q^{92} +(-3.08704 - 0.224014i) q^{93} +(10.0330 + 0.959702i) q^{94} +(-0.410032 - 0.710197i) q^{95} +(9.79473 + 0.251413i) q^{96} +1.23173 q^{97} +(-2.71123 + 9.52099i) q^{98} +(15.0217 + 11.8638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 64 q^{5} - 12 q^{12} - 6 q^{14} + 8 q^{16} + 14 q^{18} + 8 q^{21} + 4 q^{22} - 64 q^{25} - 16 q^{26} - 6 q^{28} - 10 q^{32} + 24 q^{34} + 20 q^{36} - 16 q^{38} + 16 q^{42} + 6 q^{44} + 8 q^{46}+ \cdots + 14 q^{98}+O(q^{100}) \) 128 * q - 64 * q^5 - 12 * q^12 - 6 * q^14 + 8 * q^16 + 14 * q^18 + 8 * q^21 + 4 * q^22 - 64 * q^25 - 16 * q^26 - 6 * q^28 - 10 * q^32 + 24 * q^34 + 20 * q^36 - 16 * q^38 + 16 * q^42 + 6 * q^44 + 8 * q^46 - 80 * q^48 + 8 * q^49 + 20 * q^51 - 6 * q^52 - 32 * q^54 - 18 * q^56 - 8 * q^58 - 12 * q^60 - 20 * q^62 - 28 * q^63 - 14 * q^66 + 32 * q^67 - 2 * q^68 + 40 * q^69 - 6 * q^70 - 48 * q^71 + 4 * q^72 - 8 * q^73 - 26 * q^74 - 24 * q^76 - 12 * q^78 + 8 * q^80 + 4 * q^81 - 12 * q^82 - 22 * q^84 + 46 * q^86 - 36 * q^87 - 20 * q^88 - 28 * q^90 - 24 * q^91 - 40 * q^92 + 12 * q^94 + 34 * q^96 + 32 * q^97 + 14 * q^98

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