LMFDB - Embedded newform 840.2.cq.b.11.24

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			11.24
Character	$\chi$	$=$	840.11
Dual form			840.2.cq.b.611.24

$q$-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} +(0.125358 - 1.72751i) q^{3} +(-1.31022 - 1.51107i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.14884 + 1.17579i) q^{6} +(2.48277 - 0.914246i) q^{7} +(2.71346 - 0.798201i) q^{8} +(-2.96857 - 0.433114i) q^{9} +(-1.40779 + 0.134661i) q^{10} +(-5.52569 - 3.19026i) q^{11} +(-2.77463 + 2.07399i) 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} +(2.30057 - 3.56474i) q^{18} +(-0.410032 - 0.710197i) q^{19} +(0.653513 - 1.89022i) q^{20} +(-1.26813 - 4.40362i) q^{21} +(7.34939 - 5.23530i) q^{22} +(-3.24378 - 5.61839i) q^{23} +(-1.03874 - 4.78759i) 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} +(0.0561511 + 2.44885i) q^{30} +(-1.54758 - 0.893495i) q^{31} +(-4.76137 - 3.05441i) q^{32} +(-6.20389 + 9.14575i) q^{33} +(-8.01360 + 5.70845i) q^{34} +(2.03315 + 1.69302i) q^{35} +(3.23501 + 5.05319i) q^{36} +(-5.90797 + 3.41097i) q^{37} +(1.15448 - 0.110431i) q^{38} +(-5.04676 - 0.366223i) q^{39} +(2.04799 + 1.95083i) q^{40} -4.67787i q^{41} +(6.41004 + 0.954664i) q^{42} -8.45307 q^{43} +(2.41917 + 12.5296i) q^{44} +(-1.10920 - 2.78741i) q^{45} +(9.13310 - 0.873623i) q^{46} +(-3.56339 - 6.17197i) q^{47} +(6.76931 + 1.47527i) q^{48} +(5.32831 - 4.53973i) q^{49} +(-0.820514 - 1.15185i) q^{50} +(6.76457 - 9.97231i) q^{51} +(-4.41445 + 3.82769i) q^{52} +(4.72056 - 8.17625i) q^{53} +(-5.86973 - 4.42112i) 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} +(-3.18344 - 1.36590i) q^{60} +(7.43114 - 4.29037i) q^{61} +(2.05834 - 1.46625i) q^{62} +(-7.76626 + 1.63868i) q^{63} +(6.72575 - 4.33178i) q^{64} +(2.53002 - 1.46071i) q^{65} +(-8.12272 - 13.3524i) 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} +(-8.40082 + 1.19428i) q^{72} +(-2.19598 + 3.80355i) q^{73} +(-0.918651 - 9.60383i) q^{74} +(1.43339 + 0.972318i) q^{75} +(-0.535923 + 1.55010i) q^{76} +(-16.6357 - 2.86884i) q^{77} +(3.43498 - 6.27764i) q^{78} +(14.1532 - 8.17134i) q^{79} +(-3.71249 + 1.48910i) q^{80} +(8.62482 + 2.57146i) q^{81} +(6.01813 + 2.74719i) q^{82} -9.26784i q^{83} +(-4.99263 + 7.68594i) q^{84} +6.95716i q^{85} +(4.96427 - 10.8750i) q^{86} +(-0.170921 + 2.35539i) q^{87} +(-17.5402 - 4.24603i) q^{88} +(-11.1758 + 6.45237i) q^{89} +(4.23744 + 0.209981i) q^{90} +(-2.67089 - 7.25320i) q^{91} +(-4.23970 + 12.2629i) q^{92} +(-1.73752 + 2.56145i) q^{93} +(10.0330 - 0.959702i) q^{94} +(0.410032 - 0.710197i) q^{95} +(-5.87339 + 7.84240i) 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} + 2 q^{12} + 6 q^{14} + 8 q^{16} - 4 q^{18} - 8 q^{21} + 4 q^{22} + 20 q^{24} - 64 q^{25} + 16 q^{26} - 6 q^{28} + 10 q^{32} + 24 q^{34} + 20 q^{36} + 16 q^{38} + 18 q^{42} - 6 q^{44} + 8 q^{46}+ \cdots - 14 q^{98}+O(q^{100}) $ 128 * q + 64 * q^5 + 2 * q^12 + 6 * q^14 + 8 * q^16 - 4 * q^18 - 8 * q^21 + 4 * q^22 + 20 * q^24 - 64 * q^25 + 16 * q^26 - 6 * q^28 + 10 * q^32 + 24 * q^34 + 20 * q^36 + 16 * q^38 + 18 * q^42 - 6 * q^44 + 8 * q^46 - 44 * q^48 + 8 * q^49 + 20 * q^51 - 6 * q^52 - 16 * q^54 + 18 * q^56 - 8 * q^58 - 2 * q^60 + 20 * q^62 + 28 * q^63 + 22 * q^66 + 32 * q^67 + 2 * q^68 - 40 * q^69 - 6 * q^70 + 48 * q^71 - 54 * q^72 - 8 * q^73 + 26 * q^74 - 24 * q^76 - 84 * q^78 - 8 * q^80 + 4 * q^81 - 12 * q^82 + 6 * q^84 - 46 * q^86 + 36 * q^87 - 20 * q^88 - 8 * q^90 - 24 * q^91 + 40 * q^92 + 12 * q^94 + 22 * q^96 + 32 * q^97 - 14 * q^98

Character values

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

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$-1$	$-1$

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
$3$	0.125358	−	1.72751i	0.0723756	−	0.997377i
$3$	0.125358	−	1.72751i	0.0723756	−	0.997377i
$4$	−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
$6$	2.14884	+	1.17579i	0.877260	+	0.480016i
$7$	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
$9$	−2.96857	−	0.433114i	−0.989524	−	0.144371i
$10$	−1.40779	+	0.134661i	−0.445182	+	0.0425837i
$11$	−5.52569	−	3.19026i	−1.66606	−	0.961899i	−0.969732	−	0.244173i	$-0.921483\pi$
$11$	−5.52569	−	3.19026i	−1.66606	−	0.961899i	−0.696326	−	0.717725i	$-0.745183\pi$
$12$	−2.77463	+	2.07399i	−0.800966	+	0.598709i
$13$		−	2.92141i		−	0.810254i	−0.914260	−	0.405127i	$-0.867227\pi$
$13$		−	2.92141i		−	0.810254i	0.914260	−	0.405127i	$-0.132773\pi$
$14$	−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	$-0.0137180\pi$
$17$	6.02508	+	3.47858i	1.46130	+	0.843680i	0.462225	+	0.886763i	$0.347051\pi$
$18$	2.30057	−	3.56474i	0.542249	−	0.840218i
$19$	−0.410032	−	0.710197i	−0.0940679	−	0.162930i	0.815151	−	0.579248i	$-0.196654\pi$
$19$	−0.410032	−	0.710197i	−0.0940679	−	0.162930i	−0.909219	+	0.416318i	$0.863320\pi$
$20$	0.653513	−	1.89022i	0.146130	−	0.422665i
$21$	−1.26813	−	4.40362i	−0.276729	−	0.960948i
$22$	7.34939	−	5.23530i	1.56690	−	1.11617i
$23$	−3.24378	−	5.61839i	−0.676374	−	1.17151i	−0.976065	−	0.217478i	$-0.930217\pi$
$23$	−3.24378	−	5.61839i	−0.676374	−	1.17151i	0.299691	−	0.954036i	$-0.403116\pi$
$24$	−1.03874	−	4.78759i	−0.212033	−	0.977263i
$25$	−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	$-0.540405\pi$
$29$	−1.36346			−0.253189			−0.126594	+	0.991955i	$0.540405\pi$
$30$	0.0561511	+	2.44885i	0.0102517	+	0.447096i
$31$	−1.54758	−	0.893495i	−0.277953	−	0.160476i	0.354543	−	0.935040i	$-0.384636\pi$
$31$	−1.54758	−	0.893495i	−0.277953	−	0.160476i	−0.632496	+	0.774563i	$0.717970\pi$
$32$	−4.76137	−	3.05441i	−0.841698	−	0.539948i
$33$	−6.20389	+	9.14575i	−1.07996	+	1.59207i
$34$	−8.01360	+	5.70845i	−1.37432	+	0.978991i
$35$	2.03315	+	1.69302i	0.343664	+	0.286173i
$36$	3.23501	+	5.05319i	0.539169	+	0.842198i
$37$	−5.90797	+	3.41097i	−0.971264	+	0.560760i	−0.899621	−	0.436671i	$-0.856157\pi$
$37$	−5.90797	+	3.41097i	−0.971264	+	0.560760i	−0.0716426	+	0.997430i	$0.522824\pi$
$38$	1.15448	−	0.110431i	0.187281	−	0.0179143i
$39$	−5.04676	−	0.366223i	−0.808129	−	0.0586426i
$40$	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	$-0.119027\pi$
$42$	6.41004	+	0.954664i	0.989091	+	0.147308i
$43$	−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
$45$	−1.10920	−	2.78741i	−0.165349	−	0.415523i
$46$	9.13310	−	0.873623i	1.34660	−	0.128809i
$47$	−3.56339	−	6.17197i	−0.519774	−	0.900274i	−0.999736	−	0.0229852i	$-0.992683\pi$
$47$	−3.56339	−	6.17197i	−0.519774	−	0.900274i	0.479962	−	0.877289i	$-0.340650\pi$
$48$	6.76931	+	1.47527i	0.977066	+	0.212937i
$49$	5.32831	−	4.53973i	0.761187	−	0.648532i
$50$	−0.820514	−	1.15185i	−0.116038	−	0.162896i
$51$	6.76457	−	9.97231i	0.947229	−	1.39640i
$52$	−4.41445	+	3.82769i	−0.612174	+	0.530805i
$53$	4.72056	−	8.17625i	0.648419	−	1.12309i	−0.335081	−	0.942189i	$-0.608764\pi$
$53$	4.72056	−	8.17625i	0.648419	−	1.12309i	0.983500	−	0.180906i	$-0.0579028\pi$
$54$	−5.86973	−	4.42112i	−0.798768	−	0.601639i
$55$		−	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	$-0.279026\pi$
$59$	2.25883	+	1.30414i	0.294075	+	0.169784i	−0.345703	+	0.938344i	$0.612360\pi$
$60$	−3.18344	−	1.36590i	−0.410981	−	0.176337i
$61$	7.43114	−	4.29037i	0.951460	−	0.549326i	0.0579259	−	0.998321i	$-0.481551\pi$
$61$	7.43114	−	4.29037i	0.951460	−	0.549326i	0.893534	+	0.448995i	$0.148218\pi$
$62$	2.05834	−	1.46625i	0.261410	−	0.186214i
$63$	−7.76626	+	1.63868i	−0.978456	+	0.206454i
$64$	6.72575	−	4.33178i	0.840719	−	0.541472i
$65$	2.53002	−	1.46071i	0.313810	−	0.181178i
$66$	−8.12272	−	13.3524i	−0.999838	−	1.64357i
$67$	0.191019	−	0.330854i	0.0233367	−	0.0404203i	−0.854121	−	0.520074i	$-0.825904\pi$
$67$	0.191019	−	0.330854i	0.0233367	−	0.0404203i	0.877458	+	0.479654i	$0.159238\pi$
$68$	−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	$-0.541736\pi$
$71$	−2.20330			−0.261484			−0.130742	+	0.991416i	$0.541736\pi$
$72$	−8.40082	+	1.19428i	−0.990046	+	0.140747i
$73$	−2.19598	+	3.80355i	−0.257020	+	0.445172i	−0.965442	−	0.260617i	$-0.916074\pi$
$73$	−2.19598	+	3.80355i	−0.257020	+	0.445172i	0.708422	+	0.705789i	$0.249407\pi$
$74$	−0.918651	−	9.60383i	−0.106791	−	1.11642i
$75$	1.43339	+	0.972318i	0.165513	+	0.112274i
$76$	−0.535923	+	1.55010i	−0.0614746	+	0.177809i
$77$	−16.6357	−	2.86884i	−1.89581	−	0.326935i
$78$	3.43498	−	6.27764i	0.388935	−	0.710803i
$79$	14.1532	−	8.17134i	1.59236	−	0.919347i	0.599454	−	0.800409i	$-0.295384\pi$
$79$	14.1532	−	8.17134i	1.59236	−	0.919347i	0.992902	−	0.118938i	$-0.0379491\pi$
$80$	−3.71249	+	1.48910i	−0.415069	+	0.166486i
$81$	8.62482	+	2.57146i	0.958314	+	0.285718i
$82$	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	$-0.169851\pi$
$84$	−4.99263	+	7.68594i	−0.544741	+	0.838604i
$85$			6.95716i			0.754610i
$86$	4.96427	−	10.8750i	0.535311	−	1.17268i
$87$	−0.170921	+	2.35539i	−0.0183247	+	0.252525i
$88$	−17.5402	−	4.24603i	−1.86979	−	0.452629i
$89$	−11.1758	+	6.45237i	−1.18464	+	0.683950i	−0.957083	−	0.289815i	$-0.906406\pi$
$89$	−11.1758	+	6.45237i	−1.18464	+	0.683950i	−0.227554	+	0.973765i	$0.573073\pi$
$90$	4.23744	+	0.209981i	0.446666	+	0.0221340i
$91$	−2.67089	−	7.25320i	−0.279985	−	0.760342i
$92$	−4.23970	+	12.2629i	−0.442020	+	1.27849i
$93$	−1.73752	+	2.56145i	−0.180173	+	0.265610i
$94$	10.0330	−	0.959702i	1.03482	−	0.0989857i
$95$	0.410032	−	0.710197i	0.0420684	−	0.0728647i
$96$	−5.87339	+	7.84240i	−0.599450	+	0.800412i
$97$	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	$-0.813746\pi$
$101$	0.618018	−	1.07044i	0.0614951	−	0.106513i	0.895134	+	0.445797i	$0.147080\pi$
$102$	8.85682	+	14.5592i	0.876956	+	1.44157i
$103$	8.36863	−	4.83163i	0.824586	−	0.476075i	−0.0274096	−	0.999624i	$-0.508726\pi$
$103$	8.36863	−	4.83163i	0.824586	−	0.476075i	0.851995	+	0.523550i	$0.175392\pi$
$104$	−2.33187	−	7.92714i	−0.228659	−	0.777320i
$105$	3.17958	−	3.30004i	0.310295	−	0.322051i
$106$	7.74657	+	10.8748i	0.752414	+	1.05625i
$107$	2.73656	−	1.57996i	0.264554	−	0.152740i	−0.361856	−	0.932234i	$-0.617857\pi$
$107$	2.73656	−	1.57996i	0.264554	−	0.152740i	0.626410	+	0.779494i	$0.284524\pi$
$108$	9.13496	−	4.95505i	0.879012	−	0.476800i
$109$	−10.1325	−	5.85000i	−0.970517	−	0.560328i	−0.0711229	−	0.997468i	$-0.522658\pi$
$109$	−10.1325	−	5.85000i	−0.970517	−	0.560328i	−0.899394	+	0.437140i	$0.855992\pi$
$110$	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	$0.881852\pi$
$114$	−0.0460475	−	2.00821i	−0.00431274	−	0.188086i
$115$	3.24378	−	5.61839i	0.302484	−	0.523917i
$116$	1.78644	+	2.06028i	0.165866	+	0.191293i
$117$	−1.26531	+	8.67242i	−0.116978	+	0.801765i
$118$	−3.00434	+	2.14012i	−0.276572	+	0.197014i
$119$	18.1392	+	3.12812i	1.66282	+	0.286754i
$120$	3.62680	−	3.29337i	0.331080	−	0.300642i
$121$	14.8555	+	25.7305i	1.35050	+	2.33913i
$122$	1.15549	+	12.0799i	0.104614	+	1.09366i
$123$	−8.08106	−	0.586409i	−0.728644	−	0.0528747i
$124$	0.677536	+	3.50917i	0.0608445	+	0.315133i
$125$	−1.00000			−0.0894427
$126$	2.45274	−	10.9537i	0.218507	−	0.975835i
$127$		−	1.18634i		−	0.105271i	−0.998614	−	0.0526355i	$-0.983238\pi$
$127$		−	1.18634i		−	0.105271i	0.998614	−	0.0526355i	$-0.0167621\pi$
$128$	1.62302	+	11.1967i	0.143456	+	0.989657i
$129$	−1.05966	+	14.6028i	−0.0932980	+	1.28570i
$130$	0.393401	+	4.11273i	0.0345036	+	0.360710i
$131$	−3.38447	+	1.95403i	−0.295703	+	0.170724i	−0.640511	−	0.767949i	$-0.721277\pi$
$131$	−3.38447	+	1.95403i	−0.295703	+	0.170724i	0.344808	+	0.938673i	$0.387944\pi$
$132$	21.9483	−	2.60844i	1.91035	−	0.227036i
$133$	−1.66731	−	1.38839i	−0.144574	−	0.120388i
$134$	0.313467	+	0.440050i	0.0270794	+	0.0380145i
$135$	−4.95433	+	1.56672i	−0.426401	+	0.134842i
$136$	19.1254	+	4.62977i	1.63999	+	0.397000i
$137$	−3.91683	−	2.26138i	−0.334637	−	0.193203i	0.323261	−	0.946310i	$-0.395221\pi$
$137$	−3.91683	−	2.26138i	−0.334637	−	0.193203i	−0.657898	+	0.753107i	$0.728554\pi$
$138$	−0.364283	−	15.8870i	−0.0310098	−	1.35239i
$139$	−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
$144$	3.39713	−	11.5091i	0.283094	−	0.959092i
$145$	−0.681731	−	1.18079i	−0.0566147	−	0.0980596i
$146$	−3.60366	−	5.05888i	−0.298241	−	0.418675i
$147$	−7.17447	−	9.77379i	−0.591740	−	0.806129i
$148$	12.8949	+	4.45822i	1.05996	+	0.366464i
$149$	−5.89838	−	10.2163i	−0.483214	−	0.836952i	0.516600	−	0.856227i	$-0.327197\pi$
$149$	−5.89838	−	10.2163i	−0.483214	−	0.836952i	−0.999814	+	0.0192752i	$0.993864\pi$
$150$	−2.09269	+	1.27305i	−0.170867	+	0.103944i
$151$	4.99959	+	2.88652i	0.406861	+	0.234901i	0.689440	−	0.724343i	$-0.257857\pi$
$151$	4.99959	+	2.88652i	0.406861	+	0.234901i	−0.282579	+	0.959244i	$0.591190\pi$
$152$	−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
$156$	6.05898	+	8.10583i	0.485107	+	0.648986i
$157$	−1.44853	−	0.836307i	−0.115605	−	0.0667446i	0.441083	−	0.897467i	$-0.354595\pi$
$157$	−1.44853	−	0.836307i	−0.115605	−	0.0667446i	−0.556688	+	0.830722i	$0.687928\pi$
$158$	2.20073	+	23.0070i	0.175080	+	1.83034i
$159$	−13.5328	−	9.17977i	−1.07322	−	0.728003i
$160$	0.264511	−	5.65067i	0.0209114	−	0.446724i
$161$	−13.1901	−	10.9836i	−1.03953	−	0.865626i
$162$	−8.37334	+	9.58578i	−0.657872	+	0.753130i
$163$	10.7871	+	18.6838i	0.844913	+	1.46343i	0.885697	+	0.464264i	$0.153681\pi$
$163$	10.7871	+	18.6838i	0.844913	+	1.46343i	−0.0407840	+	0.999168i	$0.512986\pi$
$164$	−7.06858	+	6.12903i	−0.551963	+	0.478597i
$165$	−11.0224	−	0.799850i	−0.858092	−	0.0622682i
$166$	11.9232	+	5.44276i	0.925417	+	0.422440i
$167$	0.435572			0.0337055			0.0168528	−	0.999858i	$-0.494635\pi$
$167$	0.435572			0.0337055			0.0168528	+	0.999858i	$0.494635\pi$
$168$	−6.95600	−	10.9368i	−0.536667	−	0.843794i
$169$	4.46535			0.343489
$170$	−8.95046	−	4.08576i	−0.686469	−	0.313363i
$171$	0.909614	+	2.28586i	0.0695599	+	0.174804i
$172$	11.0754	+	12.7732i	0.844490	+	0.973945i
$173$	1.75807	+	3.04506i	0.133663	+	0.231512i	0.925086	−	0.379758i	$-0.123993\pi$
$173$	1.75807	+	3.04506i	0.133663	+	0.231512i	−0.791423	+	0.611269i	$0.790659\pi$
$174$	−2.92986	−	1.60315i	−0.222112	−	0.121535i
$175$	−0.449626	+	2.60727i	−0.0339885	+	0.197091i
$176$	15.7635	−	20.0721i	1.18822	−	1.51299i
$177$	2.53607	−	3.73866i	0.190623	−	0.281015i
$178$	−1.73777	−	18.1671i	−0.130251	−	1.36168i
$179$	18.6434	+	10.7638i	1.39347	+	0.804521i	0.993698	−	0.112093i	$-0.0357555\pi$
$179$	18.6434	+	10.7638i	1.39347	+	0.804521i	0.399773	+	0.916614i	$0.369089\pi$
$180$	−2.75868	+	5.32820i	−0.205620	+	0.397140i
$181$			6.00703i			0.446499i	0.974761	+	0.223249i	$0.0716665\pi$
$181$			6.00703i			0.446499i	−0.974761	+	0.223249i	$0.928334\pi$
$182$	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
$186$	−2.27493	−	3.73961i	−0.166806	−	0.274202i
$187$	−22.1951	−	38.4431i	−1.62307	−	2.81124i
$188$	−4.65744	+	13.4712i	−0.339679	+	0.982485i
$189$	1.85727	+	13.6217i	0.135096	+	0.990832i
$190$	0.672875	+	0.944591i	0.0488155	+	0.0685278i
$191$	9.09052	+	15.7452i	0.657767	+	1.13929i	0.981192	+	0.193032i	$0.0618321\pi$
$191$	9.09052	+	15.7452i	0.657767	+	1.13929i	−0.323426	+	0.946254i	$0.604835\pi$
$192$	−6.64005	−	12.1618i	−0.479204	−	0.877703i
$193$	−5.39964	+	9.35245i	−0.388675	+	0.673204i	−0.992272	−	0.124086i	$-0.960400\pi$
$193$	−5.39964	+	9.35245i	−0.388675	+	0.673204i	0.603597	+	0.797290i	$0.293734\pi$
$194$	−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	$-0.154808\pi$
$197$	24.8164			1.76810			0.884048	+	0.467396i	$0.154808\pi$
$198$	−24.0847	+	12.3582i	−1.71162	+	0.878262i
$199$	19.4351	+	11.2209i	1.37772	+	0.795428i	0.991885	−	0.127140i	$-0.0405797\pi$
$199$	19.4351	+	11.2209i	1.37772	+	0.795428i	0.385836	+	0.922567i	$0.373913\pi$
$200$	−0.665469	+	2.74903i	−0.0470557	+	0.194386i
$201$	−0.547608	−	0.371462i	−0.0386253	−	0.0262009i
$202$	1.01418	+	1.42373i	0.0713578	+	0.100173i
$203$	−3.38517	+	1.24654i	−0.237592	+	0.0874899i
$204$	−23.9319	+	2.84418i	−1.67557	+	0.199133i
$205$	4.05115	−	2.33893i	0.282945	−	0.163358i
$206$	1.30127	+	13.6038i	0.0906637	+	0.947823i
$207$	7.19598	+	18.0835i	0.500155	+	1.25689i
$208$	11.5678	+	1.65542i	0.802082	+	0.114783i
$209$			5.23244i			0.361935i
$210$	2.37826	+	6.02859i	0.164115	+	0.416012i
$211$	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
$213$	−0.276202	+	3.80622i	−0.0189250	+	0.260798i
$214$	0.425518	+	4.44848i	0.0290878	+	0.304092i
$215$	−4.22654	−	7.32058i	−0.288247	−	0.499259i
$216$	1.01001	+	14.6622i	0.0687226	+	0.997636i
$217$	−4.65916	−	0.803477i	−0.316284	−	0.0545435i
$218$	13.4766	−	9.60001i	0.912752	−	0.650195i
$219$	6.29538	+	4.27038i	0.425402	+	0.288565i
$220$	−9.64139	+	8.35987i	−0.650022	+	0.563623i
$221$	10.1624	−	17.6017i	0.683595	−	1.18402i
$222$	−16.7059	+	0.383059i	−1.12122	+	0.0257092i
$223$			1.31355i			0.0879621i	0.999032	+	0.0439811i	$0.0140041\pi$
$223$			1.31355i			0.0879621i	−0.999032	+	0.0439811i	$0.985996\pi$
$224$	−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	$-0.311489\pi$
$227$	1.78947	+	1.03315i	0.118771	+	0.0685725i	−0.439438	+	0.898273i	$0.644822\pi$
$228$	2.61063	+	1.12013i	0.172893	+	0.0741824i
$229$	10.1601	−	5.86594i	0.671399	−	0.387632i	−0.125208	−	0.992131i	$-0.539960\pi$
$229$	10.1601	−	5.86594i	0.671399	−	0.387632i	0.796606	+	0.604498i	$0.206626\pi$
$230$	5.32313	+	7.47268i	0.350997	+	0.492734i
$231$	−7.04137	+	28.3787i	−0.463288	+	1.86718i
$232$	−3.69970	+	1.08832i	−0.242897	+	0.0714515i
$233$	−9.28303	+	5.35956i	−0.608151	+	0.351116i	−0.772242	−	0.635329i	$-0.780865\pi$
$233$	−9.28303	+	5.35956i	−0.608151	+	0.351116i	0.164090	+	0.986445i	$0.447531\pi$
$234$	−10.4141	−	6.72091i	−0.680789	−	0.439360i
$235$	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	$-0.430912\pi$
$239$	6.65836			0.430694			0.215347	+	0.976538i	$0.430912\pi$
$240$	2.10703	+	6.60003i	0.136009	+	0.426030i
$241$	0.781481	−	1.35357i	0.0503396	−	0.0871908i	−0.839758	−	0.542961i	$-0.817303\pi$
$241$	0.781481	−	1.35357i	0.0503396	−	0.0871908i	0.890097	+	0.455771i	$0.150636\pi$
$242$	−41.8268	+	4.00092i	−2.68873	+	0.257189i
$243$	5.52341	−	14.5771i	0.354327	−	0.935122i
$244$	−16.2195	−	5.60763i	−1.03834	−	0.358992i
$245$	6.59567	+	2.34459i	0.421382	+	0.149790i
$246$	5.50021	−	10.0520i	0.350681	−	0.640891i
$247$	−2.07478	+	1.19787i	−0.132015	+	0.0762189i
$248$	−4.91248	−	1.18919i	−0.311943	−	0.0755134i
$249$	−16.0103	−	1.16180i	−1.01461	−	0.0736260i
$250$	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	$-0.00634808\pi$
$252$	12.6517	+	9.58831i	0.796979	+	0.604007i
$253$			41.3939i			2.60241i
$254$	1.52624	+	0.696708i	0.0957651	+	0.0437154i
$255$	12.0186	+	0.872137i	0.752631	+	0.0546153i
$256$	−15.3578	−	4.48749i	−0.959863	−	0.280468i
$257$	−9.92146	+	5.72816i	−0.618883	+	0.357313i	−0.776434	−	0.630198i	$-0.782974\pi$
$257$	−9.92146	+	5.72816i	−0.618883	+	0.357313i	0.157551	+	0.987511i	$0.449640\pi$
$258$	−18.1643	−	9.93908i	−1.13086	−	0.618780i
$259$	−11.5497	+	13.8700i	−0.717662	+	0.861839i
$260$	−5.52210	−	1.90918i	−0.342466	−	0.118402i
$261$	4.04754	+	0.590535i	0.250536	+	0.0365532i
$262$	−0.526264	−	5.50171i	−0.0325127	−	0.339897i
$263$	1.93094	−	3.34449i	0.119067	−	0.206230i	−0.800331	−	0.599558i	$-0.795343\pi$
$263$	1.93094	−	3.34449i	0.119067	−	0.206230i	0.919398	+	0.393328i	$0.128676\pi$
$264$	−9.53387	+	29.7686i	−0.586769	+	1.83213i
$265$	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	$-0.769524\pi$
$269$	3.26588	−	5.65667i	0.199124	−	0.344893i	0.948245	+	0.317540i	$0.102857\pi$
$270$	0.893942	−	7.29389i	0.0544036	−	0.443892i
$271$	−13.6039	+	7.85424i	−0.826381	+	0.477111i	−0.852612	−	0.522545i	$-0.824983\pi$
$271$	−13.6039	+	7.85424i	−0.826381	+	0.477111i	0.0262311	+	0.999656i	$0.491649\pi$
$272$	−17.1881	+	21.8861i	−1.04218	+	1.32704i
$273$	−12.8648	+	3.70473i	−0.778612	+	0.224221i
$274$	5.20954	−	3.71099i	0.314720	−	0.224189i
$275$	5.52569	−	3.19026i	0.333212	−	0.192380i
$276$	20.6528	+	8.86138i	1.24315	+	0.533392i
$277$	7.51404	+	4.33823i	0.451475	+	0.260659i	0.708453	−	0.705758i	$-0.249393\pi$
$277$	7.51404	+	4.33823i	0.451475	+	0.260659i	−0.256978	+	0.966417i	$0.582727\pi$
$278$	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	$-0.195215\pi$
$282$	−0.400176	−	17.4524i	−0.0238301	−	1.03927i
$283$	11.5640	−	20.0294i	0.687406	−	1.19062i	−0.285268	−	0.958448i	$-0.592083\pi$
$283$	11.5640	−	20.0294i	0.687406	−	1.19062i	0.972674	−	0.232174i	$-0.0745839\pi$
$284$	2.88681	+	3.32934i	0.171300	+	0.197560i
$285$	−1.17547	−	0.797363i	−0.0696289	−	0.0472317i
$286$	−15.2945	−	21.4706i	−0.904381	−	1.26958i
$287$	−4.27672	−	11.6141i	−0.252447	−	0.685557i
$288$	12.8115	+	11.1294i	0.754927	+	0.655808i
$289$	15.7011	+	27.1950i	0.923591	+	1.59971i
$290$	1.91947	−	0.183606i	0.112715	−	0.0107817i
$291$	0.154407	−	2.12782i	0.00905150	−	0.124735i
$292$	8.62463	−	1.66521i	0.504719	−	0.0974490i
$293$	26.2233			1.53198			0.765991	−	0.642851i	$-0.222249\pi$
$293$	26.2233			1.53198			0.765991	+	0.642851i	$0.222249\pi$
$294$	16.7875	−	3.49014i	0.979065	−	0.203549i
$295$			2.60827i			0.151859i
$296$	−13.3084	+	13.9713i	−0.773536	+	0.812064i
$297$	22.3778	−	24.4628i	1.29849	−	1.41948i
$298$	16.6073	−	1.58857i	0.962037	−	0.0920233i
$299$	−16.4136	+	9.47641i	−0.949224	+	0.548035i
$300$	−0.408814	−	3.43989i	−0.0236029	−	0.198602i
$301$	−20.9870	+	7.72819i	−1.20967	+	0.445445i
$302$	−6.64966	+	4.73685i	−0.382645	+	0.272575i
$303$	−1.77172	−	1.20182i	−0.101782	−	0.0690427i
$304$	3.04448	−	1.22116i	0.174613	−	0.0700381i
$305$	7.43114	+	4.29037i	0.425506	+	0.245666i
$306$	26.2614	−	13.4751i	1.50126	−	0.770322i
$307$	−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	$-0.706409\pi$
$311$	6.84705	−	11.8594i	0.388261	−	0.672487i	0.992216	+	0.124531i	$0.0397427\pi$
$312$	−13.9865	+	3.03460i	−0.791831	+	0.171800i
$313$	13.4268	+	23.2558i	0.758926	+	1.31450i	0.943399	+	0.331660i	$0.107609\pi$
$313$	13.4268	+	23.2558i	0.758926	+	1.31450i	−0.184473	+	0.982837i	$0.559058\pi$
$314$	1.92660	−	1.37240i	0.108724	−	0.0774492i
$315$	−5.30227	−	5.90644i	−0.298749	−	0.332790i
$316$	−30.8912	−	10.6802i	−1.73777	−	0.600806i
$317$	−8.36597	−	14.4903i	−0.469880	−	0.813855i	0.529527	−	0.848293i	$-0.322369\pi$
$317$	−8.36597	−	14.4903i	−0.469880	−	0.813855i	−0.999407	+	0.0344376i	$0.989036\pi$
$318$	19.7573	−	12.0190i	1.10794	−	0.673994i
$319$	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
$324$	−7.41476	−	16.4019i	−0.411931	−	0.911215i
$325$	2.53002	+	1.46071i	0.140340	+	0.0810254i
$326$	−30.3720	+	2.90522i	−1.68215	+	0.160905i
$327$	−11.3761	+	16.7706i	−0.629100	+	0.927417i
$328$	−3.73388	−	12.6932i	−0.206169	−	0.700866i
$329$	−14.4898	−	12.0658i	−0.798847	−	0.665208i
$330$	7.50218	−	13.7107i	0.412981	−	0.754749i
$331$	4.38007	+	7.58651i	0.240751	+	0.416992i	0.960928	−	0.276797i	$-0.0892731\pi$
$331$	4.38007	+	7.58651i	0.240751	+	0.416992i	−0.720178	+	0.693790i	$0.755940\pi$
$332$	−14.0043	+	12.1429i	−0.768587	+	0.666428i
$333$	19.0156	−	7.56687i	1.04205	−	0.414662i
$334$	−0.255800	+	0.560367i	−0.0139967	+	0.0306619i
$335$	0.382037			0.0208729
$336$	18.1554	−	2.52606i	0.990459	−	0.137808i
$337$	−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
$339$	13.3213	+	0.966671i	0.723513	+	0.0525023i
$340$	10.5127	−	9.11541i	0.570133	−	0.494352i
$341$	5.70096	+	9.87435i	0.308724	+	0.534726i
$342$	−3.47498	−	0.172198i	−0.187905	−	0.00931142i
$343$	9.07855	−	16.1425i	0.490196	−	0.871612i
$344$	−22.9371	+	6.74725i	−1.23669	+	0.363787i
$345$	−9.29918	−	6.30796i	−0.500651	−	0.339609i
$346$	−4.94997	+	0.473488i	−0.266112	+	0.0254548i
$347$	4.41107	+	2.54673i	0.236799	+	0.136716i	0.613705	−	0.789536i	$-0.289679\pi$
$347$	4.41107	+	2.54673i	0.236799	+	0.136716i	−0.376906	+	0.926252i	$0.623012\pi$
$348$	3.78310	−	2.82781i	0.202796	−	0.151586i
$349$		−	8.94593i		−	0.478865i	−0.970913	−	0.239432i	$-0.923039\pi$
$349$		−	8.94593i		−	0.478865i	0.970913	−	0.239432i	$-0.0769613\pi$
$350$	−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	$-0.187619\pi$
$353$	14.3822	+	8.30355i	0.765486	+	0.441953i	−0.0657762	+	0.997834i	$0.520952\pi$
$354$	3.32046	+	5.45830i	0.176481	+	0.290105i
$355$	−1.10165	−	1.90811i	−0.0584695	−	0.101272i
$356$	24.3928	+	8.43342i	1.29281	+	0.446971i
$357$	7.67775	−	30.9434i	0.406349	−	1.63770i
$358$	−24.7964	+	17.6636i	−1.31053	+	0.933552i
$359$	−0.562490	−	0.974262i	−0.0296871	−	0.0514196i	0.850800	−	0.525489i	$-0.176118\pi$
$359$	−0.562490	−	0.974262i	−0.0296871	−	0.0514196i	−0.880487	+	0.474070i	$0.842784\pi$
$360$	−5.23468	−	6.67818i	−0.275892	−	0.351971i
$361$	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
$366$	21.0129	−	0.481818i	1.09836	−	0.0251850i
$367$	−20.7127	−	11.9585i	−1.08120	−	0.624229i	−0.149977	−	0.988689i	$-0.547920\pi$
$367$	−20.7127	−	11.9585i	−1.08120	−	0.624229i	−0.931219	+	0.364461i	$0.881253\pi$
$368$	24.0850	−	9.66059i	1.25552	−	0.503593i
$369$	−2.02605	+	13.8866i	−0.105472	+	0.722907i
$370$	7.85784	−	5.59749i	0.408510	−	0.291000i
$371$	4.24497	−	24.6155i	0.220388	−	1.27797i
$372$	6.14705	−	0.730546i	0.318710	−	0.0378770i
$373$	−19.1223	+	11.0402i	−0.990113	+	0.571642i	−0.905308	−	0.424756i	$-0.860360\pi$
$373$	−19.1223	+	11.0402i	−0.990113	+	0.571642i	−0.0848047	+	0.996398i	$0.527027\pi$
$374$	62.4921	−	5.97766i	3.23139	−	0.309097i
$375$	−0.125358	+	1.72751i	−0.00647347	+	0.0892082i
$376$	−14.5956	−	13.9031i	−0.752710	−	0.716998i
$377$			3.98324i			0.205147i
$378$	−18.6152	−	5.61027i	−0.957461	−	0.288561i
$379$	−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
$381$	−2.04942	−	0.148718i	−0.104995	−	0.00761905i
$382$	−25.5950	+	2.44828i	−1.30956	+	0.125265i
$383$	6.74338	+	11.6799i	0.344571	+	0.596814i	0.985276	−	0.170973i	$-0.0546911\pi$
$383$	6.74338	+	11.6799i	0.344571	+	0.596814i	−0.640705	+	0.767787i	$0.721358\pi$
$384$	19.5458	−	1.40018i	0.997444	−	0.0714528i
$385$	−5.83336	−	15.8414i	−0.297295	−	0.807351i
$386$	−8.86096	−	12.4391i	−0.451011	−	0.633136i
$387$	25.0935	+	3.66115i	1.27558	+	0.186107i
$388$	−1.61383	−	1.86122i	−0.0819299	−	0.0944893i
$389$	−11.3548	+	19.6672i	−0.575713	+	0.997165i	0.420250	+	0.907408i	$0.361942\pi$
$389$	−11.3548	+	19.6672i	−0.575713	+	0.997165i	−0.995964	+	0.0897567i	$0.971391\pi$
$390$	7.15409	−	0.164040i	0.362261	−	0.00830651i
$391$		−	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
$396$	−1.75471	−	38.2429i	−0.0881775	−	1.92178i
$397$	2.80762	−	1.62098i	0.140911	−	0.0813548i	−0.427887	−	0.903832i	$-0.640742\pi$
$397$	2.80762	−	1.62098i	0.140911	−	0.0813548i	0.568798	+	0.822477i	$0.307409\pi$
$398$	−25.8495	+	18.4138i	−1.29572	+	0.923000i
$399$	−2.60746	+	2.70625i	−0.130536	+	0.135482i
$400$	−3.14584	−	2.47056i	−0.157292	−	0.123528i
$401$	26.1429	−	15.0936i	1.30552	−	0.753740i	0.324171	−	0.945999i	$-0.394915\pi$
$401$	26.1429	−	15.0936i	1.30552	−	0.753740i	0.981344	+	0.192259i	$0.0615814\pi$
$402$	0.799485	−	0.486353i	0.0398747	−	0.0242571i
$403$	−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
$408$	10.3955	−	32.4590i	0.514654	−	1.60696i
$409$	10.2794	−	17.8045i	0.508285	−	0.880375i	−0.491669	−	0.870782i	$-0.663613\pi$
$409$	10.2794	−	17.8045i	0.508285	−	0.880375i	0.999954	−	0.00959312i	$-0.00305363\pi$
$410$	0.629928	+	6.58545i	0.0311099	+	0.325232i
$411$	−4.39756	+	6.48287i	−0.216916	+	0.319776i
$412$	−18.2657	−	6.31507i	−0.899885	−	0.311121i
$413$	6.80046	+	1.17275i	0.334629	+	0.0577071i
$414$	−27.4906	−	1.36227i	−1.35109	−	0.0669517i
$415$	8.02618	−	4.63392i	0.393990	−	0.227470i
$416$	−8.92318	+	13.9099i	−0.437495	+	0.681989i
$417$	−1.52539	+	21.0208i	−0.0746987	+	1.02939i
$418$	−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	$-0.198591\pi$
$420$	−9.15253	−	0.480779i	−0.446598	−	0.0234596i
$421$		−	14.9328i		−	0.727780i	−0.931442	−	0.363890i	$-0.881448\pi$
$421$		−	14.9328i		−	0.727780i	0.931442	−	0.363890i	$-0.118552\pi$
$422$	−6.30017	+	13.8015i	−0.306688	+	0.671845i
$423$	7.90500	+	19.8653i	0.384354	+	0.965883i
$424$	6.28277	−	25.9539i	0.305118	−	1.26043i
$425$	−6.02508	+	3.47858i	−0.292259	+	0.168736i
$426$	−4.73454	−	2.59063i	−0.229389	−	0.125516i
$427$	14.5274	−	17.4459i	0.703029	−	0.844266i
$428$	−5.97292	−	2.06504i	−0.288712	−	0.0998177i
$429$	26.7185	+	18.1241i	1.28998	+	0.875040i
$430$	11.9001	−	1.13830i	0.573875	−	0.0548938i
$431$	6.78400	−	11.7502i	0.326774	−	0.565989i	−0.655096	−	0.755546i	$-0.727372\pi$
$431$	6.78400	−	11.7502i	0.326774	−	0.565989i	0.981870	+	0.189557i	$0.0607052\pi$
$432$	−19.4562	−	7.31133i	−0.936088	−	0.351766i
$433$	−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
$438$	−9.19100	+	5.59119i	−0.439163	+	0.267157i
$439$	−23.4308	+	13.5278i	−1.11829	+	0.645644i	−0.940964	−	0.338508i	$-0.890078\pi$
$439$	−23.4308	+	13.5278i	−1.11829	+	0.645644i	−0.177325	+	0.984152i	$0.556744\pi$
$440$	−5.09293	−	17.3133i	−0.242796	−	0.825379i
$441$	−17.7837	+	11.1687i	−0.846842	+	0.531844i
$442$	16.6767	+	23.4110i	0.793231	+	1.11355i
$443$	−28.7921	+	16.6231i	−1.36795	+	0.789789i	−0.990667	−	0.136307i	$-0.956477\pi$
$443$	−28.7921	+	16.6231i	−1.36795	+	0.789789i	−0.377288	+	0.926096i	$0.623143\pi$
$444$	9.31811	−	21.7172i	0.442218	−	1.03065i
$445$	−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	$-0.204977\pi$
$450$	1.93687	+	3.77472i	0.0913050	+	0.177942i
$451$	−14.9236	+	25.8484i	−0.702725	+	1.21716i
$452$	11.6523	−	10.1035i	0.548076	−	0.475227i
$453$	5.61322	−	8.27499i	0.263732	−	0.388793i
$454$	−2.38006	+	1.69543i	−0.111702	+	0.0795703i
$455$	4.94601	−	5.93966i	0.231873	−	0.278455i
$456$	−2.97421	+	2.70078i	−0.139280	+	0.126476i
$457$	−14.4703	−	25.0633i	−0.676893	−	1.17241i	−0.975912	−	0.218166i	$-0.929993\pi$
$457$	−14.4703	−	25.0633i	−0.676893	−	1.17241i	0.299019	−	0.954247i	$-0.403341\pi$
$458$	1.57983	+	16.5160i	0.0738207	+	0.771742i
$459$	−24.4003	+	26.6737i	−1.13891	+	1.24502i
$460$	−12.7398	+	2.45975i	−0.593997	+	0.114687i
$461$	21.8992			1.01995			0.509974	−	0.860190i	$-0.329655\pi$
$461$	21.8992			1.01995			0.509974	+	0.860190i	$0.329655\pi$
$462$	−32.3743	−	25.7249i	−1.50619	−	1.19683i
$463$		−	36.8724i		−	1.71361i	−0.515643	−	0.856804i	$-0.672447\pi$
$463$		−	36.8724i		−	1.71361i	0.515643	−	0.856804i	$-0.327553\pi$
$464$	0.772607	−	5.39885i	0.0358674	−	0.250635i
$465$	−3.08704	−	0.224014i	−0.143158	−	0.0103884i
$466$	−1.44345	−	15.0902i	−0.0668666	−	0.699042i
$467$	8.16932	−	4.71656i	0.378031	−	0.218256i	−0.298930	−	0.954275i	$-0.596630\pi$
$467$	8.16932	−	4.71656i	0.378031	−	0.218256i	0.676961	+	0.736019i	$0.263296\pi$
$468$	14.7624	−	9.45081i	0.682394	−	0.436864i
$469$	0.171774	−	0.996073i	0.00793178	−	0.0459944i
$470$	5.84762	+	8.20897i	0.269731	+	0.378652i
$471$	−1.62631	+	2.39750i	−0.0749365	+	0.110471i
$472$	7.17021	+	1.73572i	0.330036	+	0.0798932i
$473$	46.7090	+	26.9675i	2.14768	+	1.23997i
$474$	40.0207	−	0.917659i	1.83821	−	0.0421495i
$475$	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	−0.0298420	−	0.999555i	$-0.509500\pi$
$479$	18.6189	−	32.2489i	0.850719	−	1.47349i	0.880561	−	0.473933i	$-0.157166\pi$
$480$	−9.72842	−	1.16530i	−0.444039	−	0.0531885i
$481$	9.96484	+	17.2596i	0.454358	+	0.786970i
$482$	1.28243	+	1.80030i	0.0584132	+	0.0820013i
$483$	−20.6277	+	21.4092i	−0.938592	+	0.974153i
$484$	19.4165	−	56.1602i	0.882569	−	2.55274i
$485$	0.615864	+	1.06671i	0.0279649	+	0.0484367i
$486$	15.5098	+	15.6667i	0.703541	+	0.710655i
$487$	−19.4552	−	11.2324i	−0.881598	−	0.508991i	−0.0104127	−	0.999946i	$-0.503315\pi$
$487$	−19.4552	−	11.2324i	−0.881598	−	0.508991i	−0.871185	+	0.490955i	$0.836648\pi$
$488$	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	$0.894264\pi$
$492$	9.70185	+	12.9793i	0.437393	+	0.585154i
$493$	−8.21497	−	4.74292i	−0.369984	−	0.213610i
$494$	−0.322615	−	3.37270i	−0.0145151	−	0.151745i
$495$	−2.76349	+	18.9410i	−0.124210	+	0.851335i
$496$	4.41487	−	5.62158i	0.198234	−	0.252417i
$497$	−5.47029	+	2.01436i	−0.245376	+	0.0903563i
$498$	10.8971	−	19.9151i	0.488310	−	0.892416i
$499$	−3.45358	−	5.98178i	−0.154604	−	0.267781i	0.778311	−	0.627879i	$-0.216077\pi$
$499$	−3.45358	−	5.98178i	−0.154604	−	0.267781i	−0.932915	+	0.360098i	$0.882743\pi$
$500$	1.31022	+	1.51107i	0.0585948	+	0.0675770i
$501$	0.0546024	−	0.752454i	0.00243946	−	0.0336171i
$502$	0.812912	+	0.371083i	0.0362820	+	0.0165622i
$503$	−10.9067			−0.486307			−0.243153	−	0.969988i	$-0.578182\pi$
$503$	−10.9067			−0.486307			−0.243153	+	0.969988i	$0.578182\pi$
$504$	−19.7654	+	10.6455i	−0.880423	+	0.474189i
$505$	1.23604			0.0550029
$506$	−53.2537	−	24.3096i	−2.36742	−	1.08069i
$507$	0.559768	−	7.71394i	0.0248602	−	0.342588i
$508$	−1.79265	+	1.55437i	−0.0795358	+	0.0689640i
$509$	16.6483	+	28.8356i	0.737921	+	1.27812i	0.953430	+	0.301615i	$0.0975258\pi$
$509$	16.6483	+	28.8356i	0.737921	+	1.27812i	−0.215508	+	0.976502i	$0.569141\pi$
$510$	−8.18019	+	14.9498i	−0.362225	+	0.661989i
$511$	−1.97474	+	11.4510i	−0.0873573	+	0.506563i
$512$	14.7924	−	17.1226i	0.653740	−	0.756719i
$513$	4.06287	−	1.28481i	0.179380	−	0.0567259i
$514$	−1.54272	−	16.1281i	−0.0680466	−	0.711378i
$515$	8.36863	+	4.83163i	0.368766	+	0.212907i
$516$	23.4541	−	17.5316i	1.03251	−	0.771785i
$517$			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	$-0.276533\pi$
$521$	7.01740	+	4.05150i	0.307438	+	0.177499i	−0.338341	+	0.941023i	$0.609866\pi$
$522$	−3.13674	+	4.86039i	−0.137291	+	0.212734i
$523$	−0.335720	−	0.581484i	−0.0146800	−	0.0254265i	0.858592	−	0.512659i	$-0.171340\pi$
$523$	−0.335720	−	0.581484i	−0.0146800	−	0.0254265i	−0.873272	+	0.487233i	$0.838006\pi$
$524$	7.38706	+	2.55396i	0.322705	+	0.111570i
$525$	4.44771	+	1.10357i	0.194114	+	0.0481639i
$526$	3.16873	+	4.44830i	0.138163	+	0.193955i
$527$	−6.21619	−	10.7668i	−0.270781	−	0.469007i
$528$	−32.6986	−	29.7477i	−1.42302	−	1.29460i
$529$	−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
$534$	−31.6017	+	0.724615i	−1.36754	+	0.0313572i
$535$	2.73656	+	1.57996i	0.118312	+	0.0683074i
$536$	0.254234	−	1.05023i	0.0109812	−	0.0453631i
$537$	20.9316	−	30.8573i	0.903264	−	1.33159i
$538$	5.35940	+	7.52360i	0.231060	+	0.324366i
$539$	−43.9255	+	8.08643i	−1.89200	+	0.348307i
$540$	8.85868	+	5.43358i	0.381217	+	0.233824i
$541$	−1.27385	+	0.735460i	−0.0547673	+	0.0316199i	−0.527134	−	0.849782i	$-0.676733\pi$
$541$	−1.27385	+	0.735460i	−0.0547673	+	0.0316199i	0.472366	+	0.881402i	$0.343400\pi$
$542$	−2.11533	−	22.1142i	−0.0908610	−	0.949887i
$543$	10.3772	+	0.753030i	0.445328	+	0.0323156i
$544$	−18.0626	−	34.9658i	−0.774428	−	1.49915i
$545$		−	11.7000i		−	0.501173i
$546$	2.78897	−	18.7264i	0.119357	−	0.801415i
$547$	−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
$549$	−23.9181	+	9.51773i	−1.02080	+	0.406207i
$550$	0.859209	+	8.98241i	0.0366368	+	0.383011i
$551$	0.559064	+	0.968327i	0.0238169	+	0.0412521i
$552$	−23.5291	+	21.3659i	−1.00146	+	0.909395i
$553$	27.6685	−	33.2270i	1.17658	−	1.41296i
$554$	−9.99398	+	7.11916i	−0.424604	+	0.302464i
$555$	−6.63309	+	9.77847i	−0.281559	+	0.415073i
$556$	15.9431	+	18.3871i	0.676137	+	0.779785i
$557$	−1.92197	+	3.32895i	−0.0814365	+	0.141052i	−0.903867	−	0.427813i	$-0.859284\pi$
$557$	−1.92197	+	3.32895i	−0.0814365	+	0.141052i	0.822431	+	0.568865i	$0.192617\pi$
$558$	−6.74539	+	3.46117i	−0.285555	+	0.146523i
$559$			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	$-0.168334\pi$
$563$	20.3620	+	11.7560i	0.858157	+	0.495457i	−0.00523745	+	0.999986i	$0.501667\pi$
$564$	22.6877	+	9.73449i	0.955324	+	0.409896i
$565$	−6.67816	+	3.85564i	−0.280952	+	0.162208i
$566$	18.9768	+	26.6399i	0.797653	+	1.11976i
$567$	23.7644	−	1.50085i	0.998012	−	0.0630300i
$568$	−5.97857	+	1.75868i	−0.250855	+	0.0737924i
$569$	5.00053	−	2.88706i	0.209633	−	0.121032i	−0.391508	−	0.920175i	$-0.628046\pi$
$569$	5.00053	−	2.88706i	0.209633	−	0.121032i	0.601141	+	0.799143i	$0.294713\pi$
$570$	1.71614	−	1.04398i	0.0718812	−	0.0437277i
$571$	8.56780	−	14.8399i	0.358551	−	0.621029i	−0.629168	−	0.777269i	$-0.716604\pi$
$571$	8.56780	−	14.8399i	0.358551	−	0.621029i	0.987719	+	0.156241i	$0.0499375\pi$
$572$	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
$576$	−21.8420	+	9.94616i	−0.910084	+	0.414423i
$577$	4.31045	−	7.46593i	0.179447	−	0.310811i	−0.762245	−	0.647289i	$-0.775903\pi$
$577$	4.31045	−	7.46593i	0.179447	−	0.310811i	0.941691	+	0.336479i	$0.109236\pi$
$578$	−44.2075	+	4.22865i	−1.83879	+	0.175889i
$579$	15.4795	+	10.5003i	0.643308	+	0.436379i
$580$	−0.891041	+	2.57724i	−0.0369985	+	0.107014i
$581$	−8.47308	−	23.0099i	−0.351523	−	0.954612i
$582$	2.64678	+	1.44826i	0.109713	+	0.0600322i
$583$	−52.1687	+	30.1196i	−2.16061	+	1.24743i
$584$	−2.92271	+	12.0736i	−0.120943	+	0.499610i
$585$	−8.14319	+	3.24042i	−0.336679	+	0.133975i
$586$	−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	$-0.320176\pi$
$588$	−5.36873	+	23.6469i	−0.221403	+	0.975182i
$589$			1.46545i			0.0603827i
$590$	−3.35557	−	1.53177i	−0.138147	−	0.0630620i
$591$	3.11094	−	42.8706i	0.127967	−	1.76346i
$592$	−10.1585	−	25.3264i	−0.417512	−	1.04091i
$593$	−14.7231	+	8.50037i	−0.604604	+	0.349068i	−0.770851	−	0.637016i	$-0.780169\pi$
$593$	−14.7231	+	8.50037i	−0.604604	+	0.349068i	0.166247	+	0.986084i	$0.446835\pi$
$594$	18.3298	+	43.1557i	0.752079	+	1.77070i
$595$	6.36056	+	17.2730i	0.260757	+	0.708126i
$596$	−7.70934	+	22.2984i	−0.315787	+	0.913380i
$597$	21.8205	−	32.1677i	0.893055	−	1.31654i
$598$	−2.55221	−	26.6815i	−0.104368	−	1.09109i
$599$	0.0838877	−	0.145298i	0.00342756	−	0.00593671i	−0.864307	−	0.502965i	$-0.832242\pi$
$599$	0.0838877	−	0.145298i	0.00342756	−	0.00593671i	0.867734	+	0.497029i	$0.165576\pi$
$600$	4.66555	+	1.49422i	0.190470	+	0.0610011i
$601$	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
$606$	2.58664	−	1.57354i	0.105075	−	0.0639206i
$607$	−22.6024	+	13.0495i	−0.917405	+	0.529664i	−0.882806	−	0.469737i	$-0.844349\pi$
$607$	−22.6024	+	13.0495i	−0.917405	+	0.529664i	−0.0345985	+	0.999401i	$0.511015\pi$
$608$	−0.216916	+	4.63391i	−0.00879710	+	0.187930i
$609$	1.72905	+	6.00417i	0.0700646	+	0.243301i
$610$	−9.88372	+	7.04062i	−0.400180	+	0.285066i
$611$	−18.0309	+	10.4101i	−0.729451	+	0.421149i
$612$	1.91329	+	41.6991i	0.0773403	+	1.68559i
$613$	38.6345	+	22.3056i	1.56043	+	0.900916i	0.997213	+	0.0746079i	$0.0237705\pi$
$613$	38.6345	+	22.3056i	1.56043	+	0.900916i	0.563219	+	0.826308i	$0.309563\pi$
$614$	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	$-0.0680249\pi$
$618$	23.6638	−	0.542603i	0.951899	−	0.0218267i
$619$	−16.5158	+	28.6062i	−0.663826	+	1.14978i	0.315776	+	0.948834i	$0.397735\pi$
$619$	−16.5158	+	28.6062i	−0.663826	+	1.14978i	−0.979602	+	0.200947i	$0.935598\pi$
$620$	−2.70026	+	2.34135i	−0.108445	+	0.0940308i
$621$	32.1415	−	10.1642i	1.28979	−	0.407875i
$622$	11.2362	+	15.7735i	0.450531	+	0.632461i
$623$	−21.8480	+	26.2372i	−0.875322	+	1.05117i
$624$	4.30987	−	19.7759i	0.172533	−	0.791671i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−37.8041	+	3.61613i	−1.51095	+	0.144530i
$627$	9.03908	+	0.655928i	0.360986	+	0.0261953i
$628$	0.634171	+	3.28457i	0.0253062	+	0.131068i
$629$	−47.4613			−1.89241
$630$	10.7126	−	3.35273i	0.426799	−	0.133576i
$631$			21.2155i			0.844577i	0.906462	+	0.422288i	$0.138773\pi$
$631$			21.2155i			0.844577i	−0.906462	+	0.422288i	$0.861227\pi$
$632$	31.8817	−	33.4697i	1.26819	−	1.33135i
$633$	1.34482	−	18.5324i	0.0534518	−	0.736598i
$634$	23.5550	−	2.25315i	0.935489	−	0.0894839i
$635$	1.02740	−	0.593172i	0.0407713	−	0.0235393i
$636$	3.85966	+	32.4765i	0.153046	+	1.28778i
$637$	−13.2624	−	15.5662i	−0.525476	−	0.616755i
$638$	−10.0206	+	7.13814i	−0.396720	+	0.282602i
$639$	6.54065	+	0.954281i	0.258744	+	0.0377508i
$640$	−8.88511	+	7.00392i	−0.351215	+	0.276854i
$641$	12.4072	+	7.16330i	0.490055	+	0.282934i	0.724597	−	0.689172i	$-0.242026\pi$
$641$	12.4072	+	7.16330i	0.490055	+	0.282934i	−0.234542	+	0.972106i	$0.575359\pi$
$642$	7.73813	−	0.177432i	0.305400	−	0.00700270i
$643$	−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	0.335794	+	0.941936i	$0.390995\pi$
$647$	−16.4787	+	28.5419i	−0.647843	+	1.12210i	−0.983637	+	0.180162i	$0.942338\pi$
$648$	25.4557	+	0.0932225i	0.999993	+	0.00366213i
$649$	−8.32106	−	14.4125i	−0.326630	−	0.565740i
$650$	−3.36503	+	2.39706i	−0.131987	+	0.0940204i
$651$	−1.97208	+	7.94801i	−0.0772917	+	0.311507i
$652$	14.0991	−	40.7800i	0.552162	−	1.59707i
$653$	−9.82718	−	17.0212i	−0.384567	−	0.666090i	0.607142	−	0.794594i	$-0.292316\pi$
$653$	−9.82718	−	17.0212i	−0.384567	−	0.666090i	−0.991709	+	0.128503i	$0.958983\pi$
$654$	−14.8947	−	24.4844i	−0.582428	−	0.957417i
$655$	−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	$0.860417\pi$
$660$	13.2331	+	17.7036i	0.515099	+	0.689110i
$661$	−10.2511	−	5.91846i	−0.398720	−	0.230201i	0.287211	−	0.957867i	$-0.407272\pi$
$661$	−10.2511	−	5.91846i	−0.398720	−	0.230201i	−0.685932	+	0.727666i	$0.740605\pi$
$662$	−12.3324	+	1.17965i	−0.479313	+	0.0458485i
$663$	−29.1332	−	19.7621i	−1.13144	−	0.767496i
$664$	−7.39759	−	25.1479i	−0.287082	−	0.975929i
$665$	0.368722	−	2.13813i	0.0142984	−	0.0829130i
$666$	−1.43248	+	28.9075i	−0.0555074	+	1.12014i
$667$	4.42277	+	7.66046i	0.171250	+	0.296614i
$668$	−0.570694	−	0.658178i	−0.0220808	−	0.0254657i
$669$	2.26918	+	0.164665i	0.0877314	+	0.00636631i
$670$	−0.224361	+	0.491495i	−0.00866780	+	0.0189881i
$671$	−54.7496			−2.11358
$672$	−7.41240	+	24.8406i	−0.285939	+	0.958248i
$673$	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
$675$	−3.83399	−	3.50721i	−0.147570	−	0.134993i
$676$	−5.85059	−	6.74745i	−0.225023	−	0.259517i
$677$	22.8224	+	39.5296i	0.877136	+	1.51924i	0.854470	+	0.519501i	$0.173882\pi$
$677$	22.8224	+	39.5296i	0.877136	+	1.51924i	0.0226662	+	0.999743i	$0.492785\pi$
$678$	−9.06687	+	16.5703i	−0.348211	+	0.636378i
$679$	3.05810	−	1.12610i	0.117359	−	0.0432158i
$680$	5.55321	+	18.8780i	0.212956	+	0.723938i
$681$	2.00910	−	2.96180i	0.0769888	−	0.113497i
$682$	−16.0515	+	1.53540i	−0.614643	+	0.0587934i
$683$	−2.77195	−	1.60039i	−0.106066	−	0.0612371i	0.446029	−	0.895019i	$-0.352838\pi$
$683$	−2.77195	−	1.60039i	−0.106066	−	0.0612371i	−0.552094	+	0.833782i	$0.686171\pi$
$684$	2.26230	−	4.36947i	0.0865011	−	0.167071i
$685$		−	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
$690$	13.5764	−	8.25899i	0.516846	−	0.314414i
$691$	1.26606	+	2.19288i	0.0481633	+	0.0834212i	0.889102	−	0.457709i	$-0.151330\pi$
$691$	1.26606	+	2.19288i	0.0481633	+	0.0834212i	−0.840939	+	0.541130i	$0.817997\pi$
$692$	2.29784	−	6.64626i	0.0873508	−	0.252653i
$693$	48.1417	+	15.7215i	1.82875	+	0.597212i
$694$	−5.86691	+	4.17926i	−0.222705	+	0.158643i
$695$	−6.08413	−	10.5380i	−0.230784	−	0.399730i
$696$	1.41629	+	6.52770i	0.0536843	+	0.247432i
$697$	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	$-0.556237\pi$
$701$	−9.30680			−0.351513			−0.175756	+	0.984434i	$0.556237\pi$
$702$	−12.9159	+	17.1479i	−0.487480	+	0.647205i
$703$	4.84492	+	2.79721i	0.182729	+	0.105499i
$704$	−50.9839	+	2.47916i	−1.92153	+	0.0934369i
$705$	−10.2154	−	6.92949i	−0.384735	−	0.260980i
$706$	−19.1289	+	13.6264i	−0.719925	+	0.512835i
$707$	0.555753	−	3.22267i	0.0209013	−	0.121201i
$708$	−8.97218	+	1.06630i	−0.337195	+	0.0400739i
$709$	−30.9906	+	17.8924i	−1.16388	+	0.671964i	−0.952230	−	0.305383i	$-0.901216\pi$
$709$	−30.9906	+	17.8924i	−1.16388	+	0.671964i	−0.211646	+	0.977347i	$0.567882\pi$
$710$	3.10178	−	0.296700i	0.116408	−	0.0111349i
$711$	−45.5538	+	18.1272i	−1.70840	+	0.679825i
$712$	−25.1749	+	26.4288i	−0.943470	+	0.990462i
$713$			11.5932i			0.434168i
$714$	35.3001	+	28.0498i	1.32107	+	1.04974i
$715$	−18.6401			−0.697101
$716$	−8.16214	−	42.2743i	−0.305034	−	1.57986i
$717$	0.834680	−	11.5024i	0.0311717	−	0.429564i
$718$	1.58373	−	0.151491i	0.0591044	−	0.00565361i
$719$	3.84834	+	6.66553i	0.143519	+	0.248582i	0.928819	−	0.370533i	$-0.120825\pi$
$719$	3.84834	+	6.66553i	0.143519	+	0.248582i	−0.785300	+	0.619115i	$0.787492\pi$
$720$	11.6657	−	2.81255i	0.434757	−	0.104818i
$721$	16.3601	−	19.6468i	0.609282	−	0.731686i
$722$	15.0380	+	21.1105i	0.559655	+	0.785652i
$723$	−2.24033	−	1.51970i	−0.0833188	−	0.0565181i
$724$	9.07703	−	7.87052i	0.337345	−	0.292506i
$725$	0.681731	−	1.18079i	0.0253189	−	0.0438536i
$726$	1.66830	+	72.7576i	0.0619165	+	2.70029i
$727$		−	1.90494i		−	0.0706503i	−0.999376	−	0.0353252i	$-0.988753\pi$
$727$		−	1.90494i		−	0.0706503i	0.999376	−	0.0353252i	$-0.0112467\pi$
$728$	−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
$732$	−11.7205	+	27.3163i	−0.433201	+	1.00964i
$733$	29.4946	−	17.0287i	1.08941	−	0.628969i	0.155988	−	0.987759i	$-0.450144\pi$
$733$	29.4946	−	17.0287i	1.08941	−	0.628969i	0.933418	+	0.358790i	$0.116811\pi$
$734$	27.5488	−	19.6242i	1.01684	−	0.724344i
$735$	4.87712	−	11.1002i	0.179895	−	0.409436i
$736$	−1.71603	+	36.6590i	−0.0632536	+	1.35127i
$737$	−2.11102	+	1.21880i	−0.0777604	+	0.0448950i
$738$	−16.6754	−	10.7618i	−0.613830	−	0.396146i
$739$	−10.9793	+	19.0167i	−0.403880	+	0.699541i	−0.994190	−	0.107635i	$-0.965672\pi$
$739$	−10.9793	+	19.0167i	−0.403880	+	0.699541i	0.590310	+	0.807177i	$0.299005\pi$
$740$	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	$-0.620568\pi$
$743$	−20.1591			−0.739567			−0.369783	+	0.929118i	$0.620568\pi$
$744$	−2.67015	+	8.33728i	−0.0978924	+	0.305660i
$745$	5.89838	−	10.2163i	0.216100	−	0.374296i
$746$	−2.97339	−	31.0846i	−0.108863	−	1.13809i
$747$	−4.01403	+	27.5122i	−0.146866	+	1.00662i
$748$	−29.0096	+	83.9073i	−1.06070	+	3.06795i
$749$	5.34979	−	6.42456i	0.195477	−	0.234748i
$750$	−2.14884	−	1.17579i	−0.0784645	−	0.0429340i
$751$	27.2412	−	15.7277i	0.994046	−	0.573913i	0.0875647	−	0.996159i	$-0.472092\pi$
$751$	27.2412	−	15.7277i	0.994046	−	0.573913i	0.906481	+	0.422246i	$0.138758\pi$
$752$	26.4581	−	10.6125i	0.964828	−	0.386996i
$753$	−1.09157	−	0.0792105i	−0.0397789	−	0.00288659i
$754$	−5.12448	−	2.33925i	−0.186622	−	0.0851904i
$755$			5.77303i			0.210102i
$756$	18.1499	−	20.6539i	0.660105	−	0.751174i
$757$		−	7.57270i		−	0.275234i	−0.990485	−	0.137617i	$-0.956056\pi$
$757$		−	7.57270i		−	0.275234i	0.990485	−	0.137617i	$-0.0439444\pi$
$758$	1.53001	−	3.35171i	0.0555723	−	0.121739i
$759$	71.5084	+	5.18907i	2.59559	+	0.188351i
$760$	0.545727	−	2.25438i	0.0197956	−	0.0817750i
$761$	−38.1931	+	22.0508i	−1.38450	+	0.799342i	−0.992689	−	0.120704i	$-0.961485\pi$
$761$	−38.1931	+	22.0508i	−1.38450	+	0.799342i	−0.391812	+	0.920045i	$0.628152\pi$
$762$	1.39490	−	2.54926i	0.0505318	−	0.0923500i
$763$	−30.5050	−	5.26062i	−1.10435	−	0.190447i
$764$	11.8816	−	34.3661i	0.429859	−	1.24332i
$765$	3.01325	−	20.6528i	0.108944	−	0.746705i
$766$	−18.9865	+	1.81615i	−0.686010	+	0.0656201i
$767$	3.80992	−	6.59897i	0.137568	−	0.238275i
$768$	−9.67740	+	25.9682i	−0.349203	+	0.937047i
$769$	−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	−0.0904620	−	0.995900i	$-0.528834\pi$
$773$	22.7217	−	39.3552i	0.817244	−	1.41551i	0.907706	−	0.419608i	$-0.137832\pi$
$774$	−19.4469	+	30.1330i	−0.699004	+	1.08311i
$775$	1.54758	−	0.893495i	0.0555907	−	0.0320953i
$776$	3.34224	−	0.983166i	0.119980	−	0.0352936i
$777$	22.5127	+	21.6909i	0.807638	+	0.778156i
$778$	−18.6336	−	26.1581i	−0.668048	−	0.937815i
$779$	−3.32221	+	1.91808i	−0.119030	+	0.0687223i
$780$	−3.99037	+	9.30015i	−0.142878	+	0.332999i
$781$	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
$786$	−9.57021	+	0.219441i	−0.341358	+	0.00782721i
$787$	−8.93783	+	15.4808i	−0.318599	+	0.551830i	−0.980196	−	0.198030i	$-0.936546\pi$
$787$	−8.93783	+	15.4808i	−0.318599	+	0.551830i	0.661597	+	0.749860i	$0.269879\pi$
$788$	−32.5149	−	37.4993i	−1.15830	−	1.33586i
$789$	−5.53557	−	3.75497i	−0.197071	−	0.133681i
$790$	−18.8243	+	13.4094i	−0.669738	+	0.477085i
$791$	7.05000	+	19.1453i	0.250669	+	0.680729i
$792$	50.2303	+	20.2016i	1.78486	+	0.717832i
$793$	−12.5339	−	21.7094i	−0.445093	−	0.770924i
$794$	0.436567	+	4.56400i	0.0154932	+	0.161970i
$795$	1.18352	−	16.3096i	0.0419752	−	0.578443i
$796$	−8.50878	−	44.0696i	−0.301586	−	1.56201i
$797$	−24.0379			−0.851466			−0.425733	−	0.904849i	$-0.639984\pi$
$797$	−24.0379			−0.851466			−0.425733	+	0.904849i	$0.639984\pi$
$798$	−1.95032	−	4.94383i	−0.0690408	−	0.175010i
$799$		−	49.5821i		−	1.75409i
$800$	5.02588	−	2.59626i	0.177692	−	0.0917917i
$801$	35.9709	−	14.3139i	1.27097	−	0.505757i
$802$	4.06506	+	42.4972i	0.143542	+	1.50063i
$803$	24.2686	−	14.0115i	0.856420	−	0.494454i
$804$	0.156182	+	1.31417i	0.00550812	+	0.0463471i
$805$	2.91697	−	16.9148i	0.102810	−	0.596168i
$806$	−4.28352	−	6.01327i	−0.150881	−	0.211808i
$807$	−9.36254	−	6.35095i	−0.329577	−	0.223564i
$808$	0.822543	−	3.39790i	0.0289370	−	0.119538i
$809$	12.9599	+	7.48239i	0.455645	+	0.263067i	0.710211	−	0.703989i	$-0.248599\pi$
$809$	12.9599	+	7.48239i	0.455645	+	0.263067i	−0.254566	+	0.967055i	$0.581933\pi$
$810$	−12.4882	−	2.45864i	−0.438791	−	0.0863879i
$811$	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
$816$	35.6538	+	32.4362i	1.24813	+	1.13549i
$817$	3.46603	+	6.00335i	0.121261	+	0.210031i
$818$	16.8688	+	23.6807i	0.589805	+	0.827976i
$819$	4.78725	+	22.6884i	0.167280	+	0.792798i
$820$	−8.84219	−	3.05705i	−0.308783	−	0.106757i
$821$	1.14316	+	1.98002i	0.0398967	+	0.0691031i	0.885284	−	0.465050i	$-0.153964\pi$
$821$	1.14316	+	1.98002i	0.0398967	+	0.0691031i	−0.845388	+	0.534153i	$0.820630\pi$
$822$	−5.75771	−	9.46473i	−0.200823	−	0.330120i
$823$	−2.59074	−	1.49577i	−0.0903076	−	0.0521391i	0.454166	−	0.890917i	$-0.349937\pi$
$823$	−2.59074	−	1.49577i	−0.0903076	−	0.0521391i	−0.544474	+	0.838778i	$0.683271\pi$
$824$	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	$-0.0125828\pi$
$828$	17.8971	−	34.5670i	0.621967	−	1.20129i
$829$	44.5776	+	25.7369i	1.54824	+	0.893879i	0.998276	+	0.0586924i	$0.0186931\pi$
$829$	44.5776	+	25.7369i	1.54824	+	0.893879i	0.549967	+	0.835186i	$0.314640\pi$
$830$	1.24802	+	13.0471i	0.0433194	+	0.452873i
$831$	8.43628	−	12.4367i	0.292651	−	0.431426i
$832$	−12.6549	−	19.6487i	−0.438730	−	0.681196i
$833$	47.8953	−	8.81725i	1.65947	−	0.305500i
$834$	−26.1476	−	14.3074i	−0.905418	−	0.495424i
$835$	0.217786	+	0.377216i	0.00753679	+	0.0130541i
$836$	7.90656	−	6.85564i	0.273454	−	0.237107i
$837$	6.26735	−	6.85129i	0.216631	−	0.236815i
$838$	30.7688	+	14.0455i	1.06289	+	0.485194i
$839$	15.5868			0.538116			0.269058	−	0.963124i	$-0.413288\pi$
$839$	15.5868			0.538116			0.269058	+	0.963124i	$0.413288\pi$
$840$	5.99357	−	11.4925i	0.206798	−	0.396528i
$841$	−27.1410			−0.935895
$842$	19.2112	+	8.76964i	0.662062	+	0.302222i
$843$	−33.3344	−	2.41894i	−1.14810	−	0.0833126i
$844$	−14.0558	−	16.2105i	−0.483821	−	0.557988i
$845$	2.23268	+	3.86711i	0.0768064	+	0.133033i
$846$	−30.1993	−	1.49649i	−1.03827	−	0.0514504i
$847$	60.4068	+	50.3013i	2.07560	+	1.72837i
$848$	29.7003	+	23.3249i	1.01991	+	0.800980i
$849$	−33.1512	−	22.4877i	−1.13775	−	0.771775i
$850$	−0.936861	−	9.79421i	−0.0321341	−	0.335939i
$851$	38.3283	+	22.1288i	1.31388	+	0.758567i
$852$	6.11334	−	4.56962i	0.209440	−	0.156553i
$853$		−	53.4140i		−	1.82886i	−0.404745	−	0.914430i	$-0.632640\pi$
$853$		−	53.4140i		−	1.82886i	0.404745	−	0.914430i	$-0.367360\pi$
$854$	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	$-0.383410\pi$
$857$	−7.94413	−	4.58655i	−0.271366	−	0.156673i	−0.629508	+	0.776994i	$0.716744\pi$
$858$	−39.0079	+	23.7298i	−1.33171	+	0.810123i
$859$	−8.80275	−	15.2468i	−0.300346	−	0.520214i	0.675868	−	0.737022i	$-0.263769\pi$
$859$	−8.80275	−	15.2468i	−0.300346	−	0.520214i	−0.976214	+	0.216808i	$0.930435\pi$
$860$	−5.52420	+	15.9781i	−0.188374	+	0.544850i
$861$	−20.5995	+	5.93215i	−0.702031	+	0.202167i
$862$	11.1327	+	15.6283i	0.379182	+	0.532302i
$863$	−6.70607	−	11.6153i	−0.228277	−	0.395388i	0.729020	−	0.684492i	$-0.239976\pi$
$863$	−6.70607	−	11.6153i	−0.228277	−	0.395388i	−0.957298	+	0.289104i	$0.906643\pi$
$864$	20.8322	−	20.7369i	0.708727	−	0.705483i
$865$	−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
$870$	−0.0765599	−	3.33891i	−0.00259562	−	0.113200i
$871$	−0.966561	−	0.558044i	−0.0327507	−	0.0189086i
$872$	−32.1636	−	7.78598i	−1.08920	−	0.263667i
$873$	−3.65647	−	0.533479i	−0.123753	−	0.0180555i
$874$	−4.36531	−	6.12809i	−0.147659	−	0.207286i
$875$	−2.48277	+	0.914246i	−0.0839330	+	0.0309071i
$876$	−1.79549	−	15.1079i	−0.0606641	−	0.510448i
$877$	−1.44864	+	0.836371i	−0.0489170	+	0.0282422i	−0.524259	−	0.851559i	$-0.675658\pi$
$877$	−1.44864	+	0.836371i	−0.0489170	+	0.0282422i	0.475342	+	0.879801i	$0.342324\pi$
$878$	−3.64333	−	38.0884i	−0.122956	−	1.28542i
$879$	3.28731	−	45.3010i	0.110878	−	1.52796i
$880$	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	$0.894543\pi$
$882$	−3.92480	−	29.4380i	−0.132155	−	0.991229i
$883$	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
$885$	4.50581	+	0.326968i	0.151461	+	0.0109909i
$886$	−4.47699	−	46.8037i	−0.150407	−	1.57240i
$887$	−25.5507	−	44.2552i	−0.857910	−	1.48594i	−0.873919	−	0.486072i	$-0.838429\pi$
$887$	−25.5507	−	44.2552i	−0.857910	−	1.48594i	0.0160090	−	0.999872i	$-0.494904\pi$
$888$	22.4672	+	24.7418i	0.753949	+	0.830281i
$889$	−1.08461	−	2.94542i	−0.0363766	−	0.0987862i
$890$	14.8643	−	10.5885i	0.498253	−	0.354928i
$891$	−39.4545	−	41.7245i	−1.32177	−	1.39782i
$892$	1.98487	−	1.72104i	0.0664583	−	0.0576248i
$893$	−2.92221	+	5.06142i	−0.0977880	+	0.169374i
$894$	−0.662401	−	28.8885i	−0.0221540	−	0.966175i
$895$			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
$900$	−5.99369	+	0.275011i	−0.199790	+	0.00916702i
$901$	56.8835	−	32.8417i	1.89506	−	1.09412i
$902$	−24.4901	−	34.3795i	−0.815430	−	1.14471i
$903$	10.7196	+	37.2241i	0.356726	+	1.23874i
$904$	6.15514	+	20.9242i	0.204717	+	0.695930i
$905$	−5.20224	+	3.00351i	−0.172928	+	0.0998402i
$906$	7.34936	+	12.0811i	0.244166	+	0.401369i
$907$	−24.0881	+	41.7219i	−0.799833	+	1.38535i	0.119891	+	0.992787i	$0.461746\pi$
$907$	−24.0881	+	41.7219i	−0.799833	+	1.38535i	−0.919724	+	0.392565i	$0.871588\pi$
$908$	−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	$-0.557130\pi$
$911$	−10.7764			−0.357037			−0.178518	+	0.983937i	$0.557130\pi$
$912$	−1.72791	−	5.41245i	−0.0572167	−	0.179224i
$913$	−29.5668	+	51.2112i	−0.978518	+	1.69484i
$914$	40.7423	−	3.89719i	1.34764	−	0.128908i
$915$	8.34321	−	12.2995i	0.275818	−	0.406610i
$916$	−22.1758	−	7.66694i	−0.732709	−	0.253323i
$917$	−6.61641	+	7.94564i	−0.218493	+	0.262388i
$918$	−19.9863	−	47.0559i	−0.659647	−	1.55308i
$919$	46.5187	−	26.8576i	1.53451	−	0.885949i	0.535363	−	0.844622i	$-0.320175\pi$
$919$	46.5187	−	26.8576i	1.53451	−	0.885949i	0.999146	−	0.0413275i	$-0.0131587\pi$
$920$	4.31726	−	17.8345i	0.142336	−	0.587985i
$921$	−2.78746	+	38.4128i	−0.0918498	+	1.26574i
$922$	−12.8608	+	28.1736i	−0.423549	+	0.927847i
$923$			6.43675i			0.211868i
$924$	52.1079	−	26.5423i	1.71422	−	0.873178i
$925$		−	6.82193i		−	0.224304i
$926$	47.4368	+	21.6542i	1.55887	+	0.711602i
$927$	−26.9355	+	10.7185i	−0.884679	+	0.352041i
$928$	6.49194	+	4.16457i	0.213109	+	0.136709i
$929$	22.7512	−	13.1354i	0.746442	−	0.430958i	−0.0779650	−	0.996956i	$-0.524842\pi$
$929$	22.7512	−	13.1354i	0.746442	−	0.430958i	0.824407	+	0.565998i	$0.191509\pi$
$930$	2.10113	−	3.83995i	0.0688989	−	0.125917i
$931$	−5.40888	−	1.92271i	−0.177269	−	0.0630144i
$932$	20.2615	+	7.00509i	0.663686	+	0.229459i
$933$	−19.6289	−	13.3150i	−0.642623	−	0.435914i
$934$	1.27028	+	13.2798i	0.0415647	+	0.434529i
$935$	22.1951	−	38.4431i	0.725859	−	1.25722i
$936$	3.48897	+	24.5422i	0.114041	+	0.802188i
$937$	−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	$-0.795722\pi$
$941$	3.61622	−	6.26348i	0.117886	−	0.204184i	0.918930	+	0.394422i	$0.129055\pi$
$942$	−2.12932	−	3.50026i	−0.0693771	−	0.114045i
$943$	−26.2821	+	15.1740i	−0.855862	+	0.494132i
$944$	−6.44390	+	8.20521i	−0.209731	+	0.267057i
$945$	−10.8681	+	8.41929i	−0.353539	+	0.273879i
$946$	−62.1249	+	44.2544i	−2.01986	+	1.43883i
$947$	34.1683	−	19.7271i	1.11032	−	0.641044i	0.171408	−	0.985200i	$-0.445168\pi$
$947$	34.1683	−	19.7271i	1.11032	−	0.641044i	0.938912	+	0.344156i	$0.111835\pi$
$948$	−22.3225	+	52.0260i	−0.725002	+	1.68972i
$949$	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	$-0.0118601\pi$
$954$	−18.2862	−	35.6376i	−0.592039	−	1.15381i
$955$	−9.09052	+	15.7452i	−0.294162	+	0.509504i
$956$	−8.72392	−	10.0612i	−0.282152	−	0.325404i
$957$	8.45877	−	12.4699i	0.273433	−	0.403094i
$958$	30.5541	+	42.8923i	0.987159	+	1.38579i
$959$	−11.7920	−	2.03355i	−0.380785	−	0.0656668i
$960$	7.21242	−	11.8314i	0.232780	−	0.381855i
$961$	−13.9033	−	24.0813i	−0.448495	−	0.776816i
$962$	−28.0568	+	2.68376i	−0.904586	+	0.0865279i
$963$	−8.80798	+	3.50496i	−0.283833	+	0.112946i
$964$	−3.06924	+	0.592596i	−0.0988536	+	0.0190862i
$965$	−10.7993			−0.347641
$966$	−15.4291	−	39.1108i	−0.496422	−	1.25837i
$967$			2.39354i			0.0769711i	0.999259	+	0.0384855i	$0.0122534\pi$
$967$			2.39354i			0.0769711i	−0.999259	+	0.0384855i	$0.987747\pi$
$968$	60.8479	+	57.9610i	1.95572	+	1.86294i
$969$	−9.85599	−	0.715209i	−0.316620	−	0.0229758i
$970$	−1.73401	+	0.165866i	−0.0556757	+	0.00532564i
$971$	−20.9662	+	12.1048i	−0.672836	+	0.388462i	−0.797151	−	0.603781i	$-0.793660\pi$
$971$	−20.9662	+	12.1048i	−0.672836	+	0.388462i	0.124314	+	0.992243i	$0.460327\pi$
$972$	−29.2639	+	10.7529i	−0.938639	+	0.344901i
$973$	−30.2110	+	11.1248i	−0.968520	+	0.356644i
$974$	25.8762	−	18.4328i	0.829126	−	0.590624i
$975$	2.84054	−	4.18751i	0.0909701	−	0.134108i
$976$	12.7775	+	31.8559i	0.408999	+	1.01968i
$977$	5.92602	+	3.42139i	0.189590	+	0.109460i	0.591791	−	0.806092i	$-0.298421\pi$
$977$	5.92602	+	3.42139i	0.189590	+	0.109460i	−0.402201	+	0.915552i	$0.631755\pi$
$978$	1.21142	+	52.8320i	0.0387369	+	1.68938i
$979$	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	0.456793	+	0.889573i	$0.348998\pi$
$983$	−16.9931	+	29.4329i	−0.541996	+	0.938765i	−0.998789	+	0.0491921i	$0.984335\pi$
$984$	−22.3957	+	4.85911i	−0.713949	+	0.154903i
$985$	12.4082	+	21.4916i	0.395358	+	0.684781i
$986$	10.9262	−	7.78326i	0.347963	−	0.247869i
$987$	−22.6601	+	23.5187i	−0.721280	+	0.748607i
$988$	4.52848	+	1.56565i	0.144070	+	0.0498100i
$989$	27.4199	+	47.4926i	0.871902	+	1.51018i
$990$	−22.7449	−	14.6788i	−0.722880	−	0.466524i
$991$	−6.57484	−	3.79598i	−0.208857	−	0.120583i	0.391923	−	0.919998i	$-0.371810\pi$
$991$	−6.57484	−	3.79598i	−0.208857	−	0.120583i	−0.600780	+	0.799414i	$0.705143\pi$
$992$	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
$996$	19.2214	+	25.7148i	0.609053	+	0.814805i
$997$	−36.1075	−	20.8467i	−1.14354	−	0.660221i	−0.196232	−	0.980557i	$-0.562871\pi$
$997$	−36.1075	−	20.8467i	−1.14354	−	0.660221i	−0.947304	+	0.320337i	$0.896204\pi$
$998$	9.72382	−	0.930129i	0.307802	−	0.0294427i
$999$	−10.6881	−	33.7981i	−0.338156	−	1.06932i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cq.a.11.3	✓	128	8.3	odd	2
840.2.cq.a.11.41	yes	128	3.2	odd	2
840.2.cq.a.611.3	yes	128	21.2	odd	6
840.2.cq.a.611.41	yes	128	56.51	odd	6
840.2.cq.b.11.24	yes	128	1.1	even	1	trivial
840.2.cq.b.11.62	yes	128	24.11	even	2	inner
840.2.cq.b.611.24	yes	128	168.107	even	6	inner
840.2.cq.b.611.62	yes	128	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.587274 + 1.28651i) q^{2} +(0.125358 - 1.72751i) q^{3} +(-1.31022 - 1.51107i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.14884 + 1.17579i) q^{6} +(2.48277 - 0.914246i) q^{7} +(2.71346 - 0.798201i) q^{8} +(-2.96857 - 0.433114i) q^{9} +(-1.40779 + 0.134661i) q^{10} +(-5.52569 - 3.19026i) q^{11} +(-2.77463 + 2.07399i) 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} +(2.30057 - 3.56474i) q^{18} +(-0.410032 - 0.710197i) q^{19} +(0.653513 - 1.89022i) q^{20} +(-1.26813 - 4.40362i) q^{21} +(7.34939 - 5.23530i) q^{22} +(-3.24378 - 5.61839i) q^{23} +(-1.03874 - 4.78759i) 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} +(0.0561511 + 2.44885i) q^{30} +(-1.54758 - 0.893495i) q^{31} +(-4.76137 - 3.05441i) q^{32} +(-6.20389 + 9.14575i) q^{33} +(-8.01360 + 5.70845i) q^{34} +(2.03315 + 1.69302i) q^{35} +(3.23501 + 5.05319i) q^{36} +(-5.90797 + 3.41097i) q^{37} +(1.15448 - 0.110431i) q^{38} +(-5.04676 - 0.366223i) q^{39} +(2.04799 + 1.95083i) q^{40} -4.67787i q^{41} +(6.41004 + 0.954664i) q^{42} -8.45307 q^{43} +(2.41917 + 12.5296i) q^{44} +(-1.10920 - 2.78741i) q^{45} +(9.13310 - 0.873623i) q^{46} +(-3.56339 - 6.17197i) q^{47} +(6.76931 + 1.47527i) q^{48} +(5.32831 - 4.53973i) q^{49} +(-0.820514 - 1.15185i) q^{50} +(6.76457 - 9.97231i) q^{51} +(-4.41445 + 3.82769i) q^{52} +(4.72056 - 8.17625i) q^{53} +(-5.86973 - 4.42112i) 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} +(-3.18344 - 1.36590i) q^{60} +(7.43114 - 4.29037i) q^{61} +(2.05834 - 1.46625i) q^{62} +(-7.76626 + 1.63868i) q^{63} +(6.72575 - 4.33178i) q^{64} +(2.53002 - 1.46071i) q^{65} +(-8.12272 - 13.3524i) 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} +(-8.40082 + 1.19428i) q^{72} +(-2.19598 + 3.80355i) q^{73} +(-0.918651 - 9.60383i) q^{74} +(1.43339 + 0.972318i) q^{75} +(-0.535923 + 1.55010i) q^{76} +(-16.6357 - 2.86884i) q^{77} +(3.43498 - 6.27764i) q^{78} +(14.1532 - 8.17134i) q^{79} +(-3.71249 + 1.48910i) q^{80} +(8.62482 + 2.57146i) q^{81} +(6.01813 + 2.74719i) q^{82} -9.26784i q^{83} +(-4.99263 + 7.68594i) q^{84} +6.95716i q^{85} +(4.96427 - 10.8750i) q^{86} +(-0.170921 + 2.35539i) q^{87} +(-17.5402 - 4.24603i) q^{88} +(-11.1758 + 6.45237i) q^{89} +(4.23744 + 0.209981i) q^{90} +(-2.67089 - 7.25320i) q^{91} +(-4.23970 + 12.2629i) q^{92} +(-1.73752 + 2.56145i) q^{93} +(10.0330 - 0.959702i) q^{94} +(0.410032 - 0.710197i) q^{95} +(-5.87339 + 7.84240i) q^{96} +1.23173 q^{97} +(2.71123 + 9.52099i) q^{98} +(15.0217 + 11.8638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 64 q^{5} + 2 q^{12} + 6 q^{14} + 8 q^{16} - 4 q^{18} - 8 q^{21} + 4 q^{22} + 20 q^{24} - 64 q^{25} + 16 q^{26} - 6 q^{28} + 10 q^{32} + 24 q^{34} + 20 q^{36} + 16 q^{38} + 18 q^{42} - 6 q^{44} + 8 q^{46}+ \cdots - 14 q^{98}+O(q^{100}) \) 128 * q + 64 * q^5 + 2 * q^12 + 6 * q^14 + 8 * q^16 - 4 * q^18 - 8 * q^21 + 4 * q^22 + 20 * q^24 - 64 * q^25 + 16 * q^26 - 6 * q^28 + 10 * q^32 + 24 * q^34 + 20 * q^36 + 16 * q^38 + 18 * q^42 - 6 * q^44 + 8 * q^46 - 44 * q^48 + 8 * q^49 + 20 * q^51 - 6 * q^52 - 16 * q^54 + 18 * q^56 - 8 * q^58 - 2 * q^60 + 20 * q^62 + 28 * q^63 + 22 * q^66 + 32 * q^67 + 2 * q^68 - 40 * q^69 - 6 * q^70 + 48 * q^71 - 54 * q^72 - 8 * q^73 + 26 * q^74 - 24 * q^76 - 84 * q^78 - 8 * q^80 + 4 * q^81 - 12 * q^82 + 6 * q^84 - 46 * q^86 + 36 * q^87 - 20 * q^88 - 8 * q^90 - 24 * q^91 + 40 * q^92 + 12 * q^94 + 22 * q^96 + 32 * q^97 - 14 * q^98

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