LMFDB - Embedded newform 840.2.cq.a.11.3

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			11.3
Character	$\chi$	$=$	840.11
Dual form			840.2.cq.a.611.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40779 - 0.134661i) q^{2} +(0.125358 - 1.72751i) q^{3} +(1.96373 + 0.379149i) 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} +(-2.96857 - 0.433114i) q^{9} +(0.587274 + 1.28651i) q^{10} +(-5.52569 - 3.19026i) q^{11} +(0.901154 - 3.34484i) q^{12} +2.92141i q^{13} +(3.61833 - 0.952730i) q^{14} +(-1.55875 + 0.755191i) q^{15} +(3.71249 + 1.48910i) q^{16} +(6.02508 + 3.47858i) q^{17} +(4.12079 + 1.00949i) 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} +(-1.71905 + 4.58747i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.393401 - 4.11273i) q^{26} +(-1.12034 + 5.07394i) q^{27} +(-5.22214 + 0.853993i) q^{28} +1.36346 q^{29} +(2.29608 - 0.853246i) q^{30} +(1.54758 + 0.893495i) q^{31} +(-5.02588 - 2.59626i) q^{32} +(-6.20389 + 9.14575i) 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} +(0.481602 + 1.05502i) q^{38} +(5.04676 + 0.366223i) q^{39} +(0.665469 + 2.74903i) q^{40} -4.67787i q^{41} +(-1.19226 - 6.37013i) q^{42} -8.45307 q^{43} +(-9.64139 - 8.35987i) q^{44} +(1.10920 + 2.78741i) q^{45} +(-3.80997 - 8.34631i) 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} +(6.76457 - 9.97231i) q^{51} +(-1.10765 + 5.73687i) q^{52} +(-4.72056 + 8.17625i) q^{53} +(2.26047 - 6.99216i) q^{54} +6.38052i q^{55} +(7.46666 - 0.499020i) q^{56} +(-1.27827 + 0.619305i) q^{57} +(-1.91947 - 0.183606i) q^{58} +(2.25883 + 1.30414i) q^{59} +(-3.34729 + 0.891996i) 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} +(9.96534 - 12.0398i) q^{66} +(0.191019 - 0.330854i) q^{67} +(10.5127 + 9.11541i) q^{68} +(10.1124 - 4.89934i) q^{69} +(-2.63425 - 2.65720i) q^{70} +2.20330 q^{71} +(7.70939 + 3.54476i) q^{72} +(-2.19598 + 3.80355i) q^{73} +(-8.77649 + 4.00634i) q^{74} +(1.43339 + 0.972318i) 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} +(-0.566651 - 3.95966i) q^{80} +(8.62482 + 2.57146i) q^{81} +(-0.629928 + 6.58545i) q^{82} -9.26784i q^{83} +(0.820642 + 9.12834i) q^{84} -6.95716i q^{85} +(11.9001 + 1.13830i) q^{86} +(0.170921 - 2.35539i) q^{87} +(12.4473 + 13.0673i) 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} +(1.73752 - 2.56145i) q^{93} +(-4.18537 - 9.16867i) q^{94} +(-0.410032 + 0.710197i) q^{95} +(-5.11510 + 8.35678i) q^{96} +1.23173 q^{97} +(-8.11246 + 5.67345i) 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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.40779	−	0.134661i	−0.995456	−	0.0952200i
$2$	−1.40779	−	0.134661i	−0.995456	−	0.0952200i
$3$	0.125358	−	1.72751i	0.0723756	−	0.997377i
$3$	0.125358	−	1.72751i	0.0723756	−	0.997377i
$4$	1.96373	+	0.379149i	0.981866	+	0.189575i
$5$	−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
$9$	−2.96857	−	0.433114i	−0.989524	−	0.144371i
$10$	0.587274	+	1.28651i	0.185712	+	0.406830i
$11$	−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	$-0.745183\pi$
$12$	0.901154	−	3.34484i	0.260141	−	0.965571i
$13$			2.92141i			0.810254i	0.914260	+	0.405127i	$0.132773\pi$
$13$			2.92141i			0.810254i	−0.914260	+	0.405127i	$0.867227\pi$
$14$	3.61833	−	0.952730i	0.967039	−	0.254628i
$15$	−1.55875	+	0.755191i	−0.402466	+	0.194989i
$16$	3.71249	+	1.48910i	0.928123	+	0.372274i
$17$	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	$0.347051\pi$
$18$	4.12079	+	1.00949i	0.971280	+	0.237938i
$19$	−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	$0.0697831\pi$
$23$	3.24378	+	5.61839i	0.676374	+	1.17151i	−0.299691	+	0.954036i	$0.596884\pi$
$24$	−1.71905	+	4.58747i	−0.350900	+	0.936413i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.393401	−	4.11273i	0.0771524	−	0.806572i
$27$	−1.12034	+	5.07394i	−0.215610	+	0.976480i
$28$	−5.22214	+	0.853993i	−0.986891	+	0.161389i
$29$	1.36346			0.253189			0.126594	−	0.991955i	$-0.459595\pi$
$29$	1.36346			0.253189			0.126594	+	0.991955i	$0.459595\pi$
$30$	2.29608	−	0.853246i	0.419204	−	0.155781i
$31$	1.54758	+	0.893495i	0.277953	+	0.160476i	0.632496	−	0.774563i	$-0.282030\pi$
$31$	1.54758	+	0.893495i	0.277953	+	0.160476i	−0.354543	+	0.935040i	$0.615364\pi$
$32$	−5.02588	−	2.59626i	−0.888458	−	0.458958i
$33$	−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
$36$	−5.66526	−	1.97605i	−0.944211	−	0.329342i
$37$	5.90797	−	3.41097i	0.971264	−	0.560760i	0.0716426	−	0.997430i	$-0.477176\pi$
$37$	5.90797	−	3.41097i	0.971264	−	0.560760i	0.899621	+	0.436671i	$0.143843\pi$
$38$	0.481602	+	1.05502i	0.0781262	+	0.171147i
$39$	5.04676	+	0.366223i	0.808129	+	0.0586426i
$40$	0.665469	+	2.74903i	0.105220	+	0.434659i
$41$		−	4.67787i		−	0.730560i	−0.930898	−	0.365280i	$-0.880973\pi$
$41$		−	4.67787i		−	0.730560i	0.930898	−	0.365280i	$-0.119027\pi$
$42$	−1.19226	−	6.37013i	−0.183970	−	0.982932i
$43$	−8.45307			−1.28908			−0.644541	−	0.764570i	$-0.722951\pi$
$43$	−8.45307			−1.28908			−0.644541	+	0.764570i	$0.722951\pi$
$44$	−9.64139	−	8.35987i	−1.45349	−	1.26030i
$45$	1.10920	+	2.78741i	0.165349	+	0.415523i
$46$	−3.80997	−	8.34631i	−0.561749	−	1.23060i
$47$	3.56339	+	6.17197i	0.519774	+	0.900274i	0.999736	+	0.0229852i	$0.00731705\pi$
$47$	3.56339	+	6.17197i	0.519774	+	0.900274i	−0.479962	+	0.877289i	$0.659350\pi$
$48$	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
$51$	6.76457	−	9.97231i	0.947229	−	1.39640i
$52$	−1.10765	+	5.73687i	−0.153604	+	0.795561i
$53$	−4.72056	+	8.17625i	−0.648419	+	1.12309i	0.335081	+	0.942189i	$0.391236\pi$
$53$	−4.72056	+	8.17625i	−0.648419	+	1.12309i	−0.983500	+	0.180906i	$0.942097\pi$
$54$	2.26047	−	6.99216i	0.307611	−	0.951512i
$55$			6.38052i			0.860349i
$56$	7.46666	−	0.499020i	0.997774	−	0.0666844i
$57$	−1.27827	+	0.619305i	−0.169311	+	0.0820290i
$58$	−1.91947	−	0.183606i	−0.252038	−	0.0241086i
$59$	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	$0.612360\pi$
$60$	−3.34729	+	0.891996i	−0.432133	+	0.115156i
$61$	−7.43114	+	4.29037i	−0.951460	+	0.549326i	−0.893534	−	0.448995i	$-0.851782\pi$
$61$	−7.43114	+	4.29037i	−0.951460	+	0.549326i	−0.0579259	+	0.998321i	$0.518449\pi$
$62$	−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
$66$	9.96534	−	12.0398i	1.22665	−	1.48200i
$67$	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	$0.159238\pi$
$68$	10.5127	+	9.11541i	1.27486	+	1.10541i
$69$	10.1124	−	4.89934i	1.21740	−	0.589811i
$70$	−2.63425	−	2.65720i	−0.314853	−	0.317596i
$71$	2.20330			0.261484			0.130742	−	0.991416i	$-0.458264\pi$
$71$	2.20330			0.261484			0.130742	+	0.991416i	$0.458264\pi$
$72$	7.70939	+	3.54476i	0.908560	+	0.417753i
$73$	−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	$0.249407\pi$
$74$	−8.77649	+	4.00634i	−1.02025	+	0.465728i
$75$	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
$78$	−7.05546	−	1.19517i	−0.798873	−	0.135326i
$79$	−14.1532	+	8.17134i	−1.59236	+	0.919347i	−0.599454	+	0.800409i	$0.704616\pi$
$79$	−14.1532	+	8.17134i	−1.59236	+	0.919347i	−0.992902	+	0.118938i	$0.962051\pi$
$80$	−0.566651	−	3.95966i	−0.0633535	−	0.442703i
$81$	8.62482	+	2.57146i	0.958314	+	0.285718i
$82$	−0.629928	+	6.58545i	−0.0695640	+	0.727241i
$83$		−	9.26784i		−	1.01728i	−0.860980	−	0.508639i	$-0.830149\pi$
$83$		−	9.26784i		−	1.01728i	0.860980	−	0.508639i	$-0.169851\pi$
$84$	0.820642	+	9.12834i	0.0895394	+	0.995983i
$85$		−	6.95716i		−	0.754610i
$86$	11.9001	+	1.13830i	1.28322	+	0.122746i
$87$	0.170921	−	2.35539i	0.0183247	−	0.252525i
$88$	12.4473	+	13.0673i	1.32688	+	1.39297i
$89$	−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	$0.573073\pi$
$90$	−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
$93$	1.73752	−	2.56145i	0.180173	−	0.265610i
$94$	−4.18537	−	9.16867i	−0.431688	−	0.945677i
$95$	−0.410032	+	0.710197i	−0.0420684	+	0.0728647i
$96$	−5.11510	+	8.35678i	−0.522057	+	0.852910i
$97$	1.23173			0.125063			0.0625315	−	0.998043i	$-0.480083\pi$
$97$	1.23173			0.125063			0.0625315	+	0.998043i	$0.480083\pi$
$98$	−8.11246	+	5.67345i	−0.819482	+	0.573105i
$99$	15.0217	+	11.8638i	1.50973	+	1.19235i
$100$	−1.31022	+	1.51107i	−0.131022	+	0.151107i
$101$	−0.618018	+	1.07044i	−0.0614951	+	0.106513i	−0.895134	−	0.445797i	$-0.852920\pi$
$101$	−0.618018	+	1.07044i	−0.0614951	+	0.106513i	0.833639	+	0.552310i	$0.186254\pi$
$102$	−10.8660	+	13.1280i	−1.07589	+	1.29986i
$103$	−8.36863	+	4.83163i	−0.824586	+	0.476075i	−0.851995	−	0.523550i	$-0.824608\pi$
$103$	−8.36863	+	4.83163i	−0.824586	+	0.476075i	0.0274096	+	0.999624i	$0.491274\pi$
$104$	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	$0.284524\pi$
$108$	−4.12383	+	9.53908i	−0.396816	+	0.917898i
$109$	10.1325	+	5.85000i	0.970517	+	0.560328i	0.899394	−	0.437140i	$-0.144008\pi$
$109$	10.1325	+	5.85000i	0.970517	+	0.560328i	0.0711229	+	0.997468i	$0.477342\pi$
$110$	0.859209	−	8.98241i	0.0819224	−	0.856439i
$111$	−5.15186	−	10.6337i	−0.488993	−	1.00930i
$112$	−10.5787	−	0.302956i	−0.999590	−	0.0286266i
$113$			7.71127i			0.725415i	0.931903	+	0.362708i	$0.118148\pi$
$113$			7.71127i			0.725415i	−0.931903	+	0.362708i	$0.881852\pi$
$114$	1.88293	−	0.699717i	0.176353	−	0.0655345i
$115$	3.24378	−	5.61839i	0.302484	−	0.523917i
$116$	2.67748	+	0.516956i	0.248597	+	0.0479982i
$117$	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
$120$	4.83239	−	0.804990i	0.441135	−	0.0734852i
$121$	14.8555	+	25.7305i	1.35050	+	2.33913i
$122$	11.0392	−	5.03924i	0.999444	−	0.456232i
$123$	−8.08106	−	0.586409i	−0.728644	−	0.0528747i
$124$	2.70026	+	2.34135i	0.242491	+	0.210259i
$125$	1.00000			0.0894427
$126$	−11.1539	+	1.26110i	−0.993669	+	0.112347i
$127$			1.18634i			0.105271i	0.998614	+	0.0526355i	$0.0167621\pi$
$127$			1.18634i			0.105271i	−0.998614	+	0.0526355i	$0.983238\pi$
$128$	−8.88511	−	7.00392i	−0.785340	−	0.619065i
$129$	−1.05966	+	14.6028i	−0.0932980	+	1.28570i
$130$	−3.75843	+	1.71567i	−0.329636	+	0.150474i
$131$	−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	$0.387944\pi$
$132$	−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
$135$	4.95433	−	1.56672i	0.426401	−	0.134842i
$136$	−13.5722	−	14.2482i	−1.16381	−	1.22177i
$137$	−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	$0.728554\pi$
$138$	−14.8959	+	5.53548i	−1.26803	+	0.471211i
$139$	−12.1683			−1.03210			−0.516049	−	0.856559i	$-0.672598\pi$
$139$	−12.1683			−1.03210			−0.516049	+	0.856559i	$0.672598\pi$
$140$	3.35065	+	4.09551i	0.283181	+	0.346133i
$141$	11.1088	−	5.38208i	0.935532	−	0.453253i
$142$	−3.10178	−	0.296700i	−0.260296	−	0.0248985i
$143$	9.32006	−	16.1428i	0.779382	−	1.34993i
$144$	−10.3758	−	6.02842i	−0.864654	−	0.502368i
$145$	−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	0.999814	−	0.0192752i	$-0.00613586\pi$
$149$	5.89838	+	10.2163i	0.483214	+	0.836952i	−0.516600	+	0.856227i	$0.672803\pi$
$150$	−1.88697	−	1.56184i	−0.154071	−	0.127524i
$151$	−4.99959	−	2.88652i	−0.406861	−	0.234901i	0.282579	−	0.959244i	$-0.408810\pi$
$151$	−4.99959	−	2.88652i	−0.406861	−	0.234901i	−0.689440	+	0.724343i	$0.742143\pi$
$152$	0.545727	+	2.25438i	0.0442643	+	0.182854i
$153$	−16.3792	−	12.9360i	−1.32418	−	1.04581i
$154$	−23.0332	−	6.27891i	−1.85607	−	0.505969i
$155$		−	1.78699i		−	0.143534i
$156$	9.77164	+	2.63264i	0.782357	+	0.210780i
$157$	1.44853	+	0.836307i	0.115605	+	0.0667446i	0.556688	−	0.830722i	$-0.312072\pi$
$157$	1.44853	+	0.836307i	0.115605	+	0.0667446i	−0.441083	+	0.897467i	$0.645405\pi$
$158$	21.0250	−	9.59762i	1.67266	−	0.763546i
$159$	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
$162$	−11.7956	−	4.78150i	−0.926753	−	0.375670i
$163$	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	$0.512986\pi$
$164$	1.77361	−	9.18608i	0.138496	−	0.717313i
$165$	11.0224	+	0.799850i	0.858092	+	0.0622682i
$166$	−1.24802	+	13.0471i	−0.0968651	+	1.01265i
$167$	−0.435572			−0.0337055			−0.0168528	−	0.999858i	$-0.505365\pi$
$167$	−0.435572			−0.0337055			−0.0168528	+	0.999858i	$0.505365\pi$
$168$	0.0739445	−	12.9613i	0.00570494	−	0.999984i
$169$	4.46535			0.343489
$170$	−0.936861	+	9.79421i	−0.0718540	+	0.751181i
$171$	0.909614	+	2.28586i	0.0695599	+	0.174804i
$172$	−16.5996	−	3.20498i	−1.26571	−	0.244377i
$173$	−1.75807	−	3.04506i	−0.133663	−	0.231512i	0.791423	−	0.611269i	$-0.209341\pi$
$173$	−1.75807	−	3.04506i	−0.133663	−	0.231512i	−0.925086	+	0.379758i	$0.876007\pi$
$174$	−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
$177$	2.53607	−	3.73866i	0.190623	−	0.281015i
$178$	16.6021	−	7.57862i	1.24438	−	0.568041i
$179$	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	$0.369089\pi$
$180$	1.12132	+	5.89429i	0.0835783	+	0.439334i
$181$		−	6.00703i		−	0.446499i	−0.974761	−	0.223249i	$-0.928334\pi$
$181$		−	6.00703i		−	0.446499i	0.974761	−	0.223249i	$-0.0716665\pi$
$182$	2.78332	+	10.5706i	0.206313	+	0.783547i
$183$	6.48010	+	13.3752i	0.479023	+	0.988723i
$184$	−4.31726	−	17.8345i	−0.318273	−	1.31477i
$185$	−5.90797	−	3.41097i	−0.434362	−	0.250779i
$186$	−2.79099	+	3.37200i	−0.204645	+	0.247247i
$187$	−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	$-0.938168\pi$
$191$	−9.09052	−	15.7452i	−0.657767	−	1.13929i	0.323426	−	0.946254i	$-0.395165\pi$
$192$	8.32631	−	11.0758i	0.600899	−	0.799325i
$193$	−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	$0.293734\pi$
$194$	−1.73401	−	0.165866i	−0.124495	−	0.0119085i
$195$	−2.20622	−	4.55374i	−0.157991	−	0.326100i
$196$	12.1846	−	6.89458i	0.870329	−	0.492470i
$197$	−24.8164			−1.76810			−0.884048	−	0.467396i	$-0.845192\pi$
$197$	−24.8164			−1.76810			−0.884048	+	0.467396i	$0.845192\pi$
$198$	−19.5497	−	18.7245i	−1.38934	−	1.33069i
$199$	−19.4351	−	11.2209i	−1.37772	−	0.795428i	−0.385836	−	0.922567i	$-0.626087\pi$
$199$	−19.4351	−	11.2209i	−1.37772	−	0.795428i	−0.991885	+	0.127140i	$0.959420\pi$
$200$	2.04799	−	1.95083i	0.144815	−	0.137944i
$201$	−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
$204$	17.0648	−	17.0182i	1.19478	−	1.19151i
$205$	−4.05115	+	2.33893i	−0.282945	+	0.163358i
$206$	12.4319	−	5.67498i	0.866171	−	0.395395i
$207$	−7.19598	−	18.0835i	−0.500155	−	1.25689i
$208$	−4.35026	+	10.8457i	−0.301636	+	0.752015i
$209$			5.23244i			0.361935i
$210$	−4.92056	+	4.21759i	−0.339551	+	0.291042i
$211$	10.7278			0.738534			0.369267	−	0.929323i	$-0.379609\pi$
$211$	10.7278			0.738534			0.369267	+	0.929323i	$0.379609\pi$
$212$	−12.3699	+	14.2662i	−0.849571	+	0.979805i
$213$	0.276202	−	3.80622i	0.0189250	−	0.260798i
$214$	−4.06526	+	1.85573i	−0.277895	+	0.126855i
$215$	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
$219$	6.29538	+	4.27038i	0.425402	+	0.288565i
$220$	−2.41917	+	12.5296i	−0.163100	+	0.844747i
$221$	−10.1624	+	17.6017i	−0.683595	+	1.18402i
$222$	5.82079	+	15.6637i	0.390666	+	1.05128i
$223$		−	1.31355i		−	0.0879621i	−0.999032	−	0.0439811i	$-0.985996\pi$
$223$		−	1.31355i		−	0.0879621i	0.999032	−	0.0439811i	$-0.0140041\pi$
$224$	14.8517	+	1.85104i	0.992322	+	0.123678i
$225$	1.85937	−	2.35430i	0.123958	−	0.156953i
$226$	1.03841	−	10.8558i	0.0690740	−	0.722119i
$227$	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	$0.644822\pi$
$228$	−2.74499	+	0.731494i	−0.181792	+	0.0484444i
$229$	−10.1601	+	5.86594i	−0.671399	+	0.387632i	−0.796606	−	0.604498i	$-0.793374\pi$
$229$	−10.1601	+	5.86594i	−0.671399	+	0.387632i	0.125208	+	0.992131i	$0.460040\pi$
$230$	−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	$0.447531\pi$
$234$	−2.94912	+	12.0385i	−0.192790	+	0.786984i
$235$	3.56339	−	6.17197i	0.232450	−	0.402615i
$236$	3.94128	+	3.41741i	0.256555	+	0.222454i
$237$	12.3418	+	25.4741i	0.801689	+	1.65472i
$238$	25.1149	+	6.84638i	1.62796	+	0.443785i
$239$	−6.65836			−0.430694			−0.215347	−	0.976538i	$-0.569088\pi$
$239$	−6.65836			−0.430694			−0.215347	+	0.976538i	$0.569088\pi$
$240$	−6.91138	+	0.482518i	−0.446128	+	0.0311464i
$241$	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	$0.150636\pi$
$242$	−17.4485	−	38.2235i	−1.12163	−	2.45710i
$243$	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
$246$	11.2974	+	1.91375i	0.720299	+	0.122016i
$247$	2.07478	−	1.19787i	0.132015	−	0.0762189i
$248$	−3.48611	−	3.65974i	−0.221368	−	0.232394i
$249$	−16.0103	−	1.16180i	−1.01461	−	0.0736260i
$250$	−1.40779	−	0.134661i	−0.0890363	−	0.00851674i
$251$		−	0.631874i		−	0.0398835i	−0.999801	−	0.0199418i	$-0.993652\pi$
$251$		−	0.631874i		−	0.0398835i	0.999801	−	0.0199418i	$-0.00634808\pi$
$252$	15.8722	−	0.273355i	0.999852	−	0.0172198i
$253$		−	41.3939i		−	2.60241i
$254$	0.159755	−	1.67012i	0.0100239	−	0.104793i
$255$	−12.0186	−	0.872137i	−0.752631	−	0.0546153i
$256$	11.5652	+	11.0565i	0.722824	+	0.691032i
$257$	−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	$0.449640\pi$
$258$	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
$261$	−4.04754	−	0.590535i	−0.250536	−	0.0365532i
$262$	5.02775	−	2.29510i	0.310615	−	0.141791i
$263$	−1.93094	+	3.34449i	−0.119067	+	0.206230i	−0.919398	−	0.393328i	$-0.871324\pi$
$263$	−1.93094	+	3.34449i	−0.119067	+	0.206230i	0.800331	+	0.599558i	$0.204657\pi$
$264$	24.1342	−	19.8647i	1.48535	−	1.22259i
$265$	9.44112			0.579964
$266$	−2.16026	−	2.17908i	−0.132454	−	0.133608i
$267$	9.74555	+	20.1152i	0.596418	+	1.23103i
$268$	0.500553	−	0.577284i	0.0305761	−	0.0352633i
$269$	−3.26588	+	5.65667i	−0.199124	+	0.344893i	−0.948245	−	0.317540i	$-0.897143\pi$
$269$	−3.26588	+	5.65667i	−0.199124	+	0.344893i	0.749120	+	0.662434i	$0.230476\pi$
$270$	−7.18562	+	1.53846i	−0.437303	+	0.0936274i
$271$	13.6039	−	7.85424i	0.826381	−	0.477111i	−0.0262311	−	0.999656i	$-0.508351\pi$
$271$	13.6039	−	7.85424i	0.826381	−	0.477111i	0.852612	+	0.522545i	$0.175017\pi$
$272$	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
$276$	21.7157	−	5.78687i	1.30713	−	0.348329i
$277$	−7.51404	−	4.33823i	−0.451475	−	0.260659i	0.256978	−	0.966417i	$-0.417273\pi$
$277$	−7.51404	−	4.33823i	−0.451475	−	0.260659i	−0.708453	+	0.705758i	$0.750607\pi$
$278$	17.1303	+	1.63859i	1.02741	+	0.0982764i
$279$	−4.20711	−	3.32268i	−0.251873	−	0.198924i
$280$	−4.16549	−	6.21681i	−0.248936	−	0.371525i
$281$		−	19.2962i		−	1.15112i	−0.817761	−	0.575558i	$-0.804785\pi$
$281$		−	19.2962i		−	1.15112i	0.817761	−	0.575558i	$-0.195215\pi$
$282$	−16.3636	+	6.08089i	−0.974440	+	0.362112i
$283$	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	$-0.0745839\pi$
$284$	4.32669	+	0.835380i	0.256742	+	0.0495707i
$285$	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
$288$	13.7952	+	9.88396i	0.812889	+	0.582418i
$289$	15.7011	+	27.1950i	0.923591	+	1.59971i
$290$	0.800726	+	1.75411i	0.0470202	+	0.103005i
$291$	0.154407	−	2.12782i	0.00905150	−	0.124735i
$292$	−5.75443	+	6.63655i	−0.336753	+	0.388375i
$293$	−26.2233			−1.53198			−0.765991	−	0.642851i	$-0.777751\pi$
$293$	−26.2233			−1.53198			−0.765991	+	0.642851i	$0.777751\pi$
$294$	8.78398	+	14.7255i	0.512292	+	0.858811i
$295$		−	2.60827i		−	0.151859i
$296$	−18.7537	+	4.53978i	−1.09004	+	0.263870i
$297$	22.3778	−	24.4628i	1.29849	−	1.41948i
$298$	−6.92793	−	15.1767i	−0.401324	−	0.879160i
$299$	−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
$303$	1.77172	+	1.20182i	0.101782	+	0.0690427i
$304$	−0.464690	−	3.24718i	−0.0266518	−	0.186238i
$305$	7.43114	+	4.29037i	0.425506	+	0.245666i
$306$	21.3165	+	20.4167i	1.21858	+	1.16715i
$307$	−22.2359			−1.26907			−0.634536	−	0.772893i	$-0.718809\pi$
$307$	−22.2359			−1.26907			−0.634536	+	0.772893i	$0.718809\pi$
$308$	31.5803	+	11.9411i	1.79946	+	0.680405i
$309$	7.29761	+	15.0626i	0.415146	+	0.856879i
$310$	−0.240639	+	2.51570i	−0.0136673	+	0.142882i
$311$	−6.84705	+	11.8594i	−0.388261	+	0.672487i	−0.992216	−	0.124531i	$-0.960257\pi$
$311$	−6.84705	+	11.8594i	−0.388261	+	0.672487i	0.603955	+	0.797018i	$0.293591\pi$
$312$	−13.4019	−	5.02206i	−0.758732	−	0.284318i
$313$	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	0.999407	−	0.0344376i	$-0.0109640\pi$
$317$	8.36597	+	14.4903i	0.469880	+	0.813855i	−0.529527	+	0.848293i	$0.677631\pi$
$318$	−17.8151	−	14.7455i	−0.999023	−	0.826887i
$319$	−7.53407	−	4.34980i	−0.421827	−	0.243542i
$320$	0.388552	−	7.99056i	0.0217207	−	0.446686i
$321$	−2.38634	−	4.92550i	−0.133192	−	0.274914i
$322$	17.0899	+	17.2387i	0.952381	+	0.960677i
$323$		−	5.70532i		−	0.317453i
$324$	15.9619	+	8.31976i	0.886771	+	0.462209i
$325$	−2.53002	−	1.46071i	−0.140340	−	0.0810254i
$326$	−12.6700	−	27.7555i	−0.701726	−	1.53724i
$327$	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
$330$	−15.4095	−	2.61031i	−0.848264	−	0.143693i
$331$	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	$0.755940\pi$
$332$	3.51389	−	18.1996i	0.192850	−	0.998830i
$333$	−19.0156	+	7.56687i	−1.04205	+	0.414662i
$334$	0.613192	+	0.0586547i	0.0335524	+	0.00320944i
$335$	−0.382037			−0.0208729
$336$	−1.84948	+	18.2368i	−0.100897	+	0.994897i
$337$	−15.2545			−0.830965			−0.415482	−	0.909601i	$-0.636387\pi$
$337$	−15.2545			−0.830965			−0.415482	+	0.909601i	$0.636387\pi$
$338$	−6.28627	−	0.601311i	−0.341928	−	0.0327070i
$339$	13.3213	+	0.966671i	0.723513	+	0.0525023i
$340$	2.63780	−	13.6620i	0.143055	−	0.740926i
$341$	−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
$345$	−9.29918	−	6.30796i	−0.500651	−	0.339609i
$346$	2.06493	+	4.52354i	0.111011	+	0.243187i
$347$	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	$0.623012\pi$
$348$	1.22869	−	4.56056i	0.0658647	−	0.244472i
$349$			8.94593i			0.478865i	0.970913	+	0.239432i	$0.0769613\pi$
$349$			8.94593i			0.478865i	−0.970913	+	0.239432i	$0.923039\pi$
$350$	−0.984076	+	3.60993i	−0.0526011	+	0.192959i
$351$	−14.8231	−	3.27298i	−0.791196	−	0.174699i
$352$	19.4887	+	30.3800i	1.03875	+	1.61926i
$353$	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	$0.520952\pi$
$354$	−4.07370	+	4.92173i	−0.216515	+	0.261587i
$355$	−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	0.880487	−	0.474070i	$-0.157216\pi$
$359$	0.562490	+	0.974262i	0.0296871	+	0.0514196i	−0.850800	+	0.525489i	$0.823882\pi$
$360$	−0.784847	−	8.44891i	−0.0413651	−	0.445296i
$361$	9.16375	−	15.8721i	0.482302	−	0.835372i
$362$	−0.808915	+	8.45662i	−0.0425156	+	0.444470i
$363$	46.3118	−	22.4375i	2.43074	−	1.17766i
$364$	−2.49486	−	15.2560i	−0.130766	−	0.799632i
$365$	4.39196			0.229886
$366$	−7.32148	−	19.7020i	−0.382700	−	1.02984i
$367$	20.7127	+	11.9585i	1.08120	+	0.624229i	0.931219	−	0.364461i	$-0.118747\pi$
$367$	20.7127	+	11.9585i	1.08120	+	0.624229i	0.149977	+	0.988689i	$0.452080\pi$
$368$	3.67618	+	25.6885i	0.191634	+	1.33911i
$369$	−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
$372$	4.38320	−	4.37122i	0.227258	−	0.226637i
$373$	19.1223	−	11.0402i	0.990113	−	0.571642i	0.0848047	−	0.996398i	$-0.472973\pi$
$373$	19.1223	−	11.0402i	0.990113	−	0.571642i	0.905308	+	0.424756i	$0.139640\pi$
$374$	26.0692	+	57.1086i	1.34801	+	2.95301i
$375$	0.125358	−	1.72751i	0.00647347	−	0.0892082i
$376$	−4.74265	−	19.5917i	−0.244583	−	1.01037i
$377$			3.98324i			0.205147i
$378$	0.780322	+	19.4266i	0.0401354	+	0.999194i
$379$	−2.60527			−0.133824			−0.0669118	−	0.997759i	$-0.521315\pi$
$379$	−2.60527			−0.133824			−0.0669118	+	0.997759i	$0.521315\pi$
$380$	−1.07446	+	1.23917i	−0.0551189	+	0.0635683i
$381$	2.04942	+	0.148718i	0.104995	+	0.00761905i
$382$	10.6772	+	23.3901i	0.546295	+	1.19674i
$383$	−6.74338	−	11.6799i	−0.344571	−	0.596814i	0.640705	−	0.767787i	$-0.278642\pi$
$383$	−6.74338	−	11.6799i	−0.344571	−	0.596814i	−0.985276	+	0.170973i	$0.945309\pi$
$384$	−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
$387$	25.0935	+	3.66115i	1.27558	+	0.186107i
$388$	2.41878	+	0.467009i	0.122795	+	0.0237088i
$389$	11.3548	−	19.6672i	0.575713	−	0.997165i	−0.420250	−	0.907408i	$-0.638058\pi$
$389$	11.3548	−	19.6672i	0.575713	−	0.997165i	0.995964	−	0.0897567i	$-0.0286090\pi$
$390$	2.49268	+	6.70779i	0.126222	+	0.339662i
$391$			45.1350i			2.28257i
$392$	−18.0818	+	8.06531i	−0.913268	+	0.407360i
$393$	2.95132	+	6.09166i	0.148875	+	0.307283i
$394$	34.9362	+	3.34181i	1.76006	+	0.168358i
$395$	14.1532	+	8.17134i	0.712123	+	0.411145i
$396$	25.0004	+	28.9927i	1.25632	+	1.45694i
$397$	−2.80762	+	1.62098i	−0.140911	+	0.0813548i	−0.568798	−	0.822477i	$-0.692591\pi$
$397$	−2.80762	+	1.62098i	−0.140911	+	0.0813548i	0.427887	+	0.903832i	$0.359258\pi$
$398$	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	$0.0615814\pi$
$402$	0.720894	+	0.596681i	0.0359549	+	0.0297597i
$403$	−2.61027	+	4.52111i	−0.130027	+	0.225213i
$404$	−1.61948	+	1.86773i	−0.0805720	+	0.0929232i
$405$	−2.08546	−	8.75505i	−0.103627	−	0.435042i
$406$	4.93346	−	1.29901i	0.244843	−	0.0644689i
$407$	−43.5275			−2.15758
$408$	−26.3153	+	21.6600i	−1.30280	+	1.07233i
$409$	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	$-0.00305363\pi$
$410$	6.01813	−	2.74719i	0.297214	−	0.135674i
$411$	−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
$414$	7.69526	+	26.4268i	0.378201	+	1.29880i
$415$	−8.02618	+	4.63392i	−0.393990	+	0.227470i
$416$	7.58475	−	14.6827i	0.371873	−	0.719876i
$417$	−1.52539	+	21.0208i	−0.0746987	+	1.02939i
$418$	0.704607	−	7.36616i	0.0344635	−	0.360291i
$419$		−	23.9165i		−	1.16840i	−0.811611	−	0.584198i	$-0.801409\pi$
$419$		−	23.9165i		−	1.16840i	0.811611	−	0.584198i	$-0.198591\pi$
$420$	7.49505	−	5.27487i	0.365721	−	0.257387i
$421$			14.9328i			0.727780i	0.931442	+	0.363890i	$0.118552\pi$
$421$			14.9328i			0.727780i	−0.931442	+	0.363890i	$0.881448\pi$
$422$	−15.1025	−	1.44463i	−0.735179	−	0.0703233i
$423$	−7.90500	−	19.8653i	−0.384354	−	0.965883i
$424$	19.3354	−	18.4180i	0.939008	−	0.894457i
$425$	−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
$429$	−26.7185	−	18.1241i	−1.28998	−	0.875040i
$430$	−4.96427	−	10.8750i	−0.239398	−	0.524438i
$431$	−6.78400	+	11.7502i	−0.326774	+	0.565989i	−0.981870	−	0.189557i	$-0.939295\pi$
$431$	−6.78400	+	11.7502i	−0.326774	+	0.565989i	0.655096	+	0.755546i	$0.272628\pi$
$432$	−11.7148	+	17.1686i	−0.563631	+	0.826027i
$433$	−20.4637			−0.983421			−0.491710	−	0.870759i	$-0.663628\pi$
$433$	−20.4637			−0.983421			−0.491710	+	0.870759i	$0.663628\pi$
$434$	6.45091	+	1.75853i	0.309653	+	0.0844123i
$435$	−2.12529	+	1.02967i	−0.101900	+	0.0493691i
$436$	17.6795	+	15.3296i	0.846693	+	0.734153i
$437$	2.66011	−	4.60744i	0.127250	−	0.220404i
$438$	−8.28750	−	6.85953i	−0.395992	−	0.327761i
$439$	23.4308	−	13.5278i	1.11829	−	0.645644i	0.177325	−	0.984152i	$-0.443256\pi$
$439$	23.4308	−	13.5278i	1.11829	−	0.645644i	0.940964	+	0.338508i	$0.109922\pi$
$440$	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	$0.623143\pi$
$444$	−6.08514	−	22.8350i	−0.288788	−	1.08370i
$445$	11.1758	+	6.45237i	0.529786	+	0.305872i
$446$	−0.176885	+	1.84921i	−0.00837575	+	0.0875624i
$447$	18.3882	−	8.90881i	0.869730	−	0.421372i
$448$	−20.6588	−	4.60582i	−0.976037	−	0.217605i
$449$		−	25.4429i		−	1.20072i	−0.799728	−	0.600362i	$-0.795023\pi$
$449$		−	25.4429i		−	1.20072i	0.799728	−	0.600362i	$-0.204977\pi$
$450$	−2.93464	+	3.06397i	−0.138340	+	0.144437i
$451$	−14.9236	+	25.8484i	−0.702725	+	1.21716i
$452$	−2.92372	+	15.1429i	−0.137520	+	0.712261i
$453$	−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
$456$	3.96287	−	0.660144i	0.185579	−	0.0309141i
$457$	−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	$-0.403341\pi$
$458$	15.0932	−	6.88982i	0.705258	−	0.321940i
$459$	−24.4003	+	26.6737i	−1.13891	+	1.24502i
$460$	8.50012	−	9.80313i	0.396320	−	0.457073i
$461$	−21.8992			−1.01995			−0.509974	−	0.860190i	$-0.670345\pi$
$461$	−21.8992			−1.01995			−0.509974	+	0.860190i	$0.670345\pi$
$462$	−13.7343	+	39.0030i	−0.638976	+	1.81458i
$463$			36.8724i			1.71361i	0.515643	+	0.856804i	$0.327553\pi$
$463$			36.8724i			1.71361i	−0.515643	+	0.856804i	$0.672447\pi$
$464$	5.06184	+	2.03033i	0.234990	+	0.0942556i
$465$	−3.08704	−	0.224014i	−0.143158	−	0.0103884i
$466$	13.7903	−	6.29505i	0.638821	−	0.291613i
$467$	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	$0.263296\pi$
$468$	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
$471$	1.62631	−	2.39750i	0.0749365	−	0.110471i
$472$	−5.08829	−	5.34172i	−0.234207	−	0.245873i
$473$	46.7090	+	26.9675i	2.14768	+	1.23997i
$474$	−13.9443	−	37.5240i	−0.640484	−	1.72354i
$475$	0.820065			0.0376272
$476$	−34.4345	−	13.0202i	−1.57830	−	0.596782i
$477$	17.5546	−	22.2272i	0.803769	−	1.01772i
$478$	9.37356	+	0.896625i	0.428737	+	0.0410107i
$479$	−18.6189	+	32.2489i	−0.850719	+	1.47349i	0.0298420	+	0.999555i	$0.490500\pi$
$479$	−18.6189	+	32.2489i	−0.850719	+	1.47349i	−0.880561	+	0.473933i	$0.842834\pi$
$480$	9.79473	+	0.251413i	0.447066	+	0.0114754i
$481$	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
$486$	−9.73877	+	19.7777i	−0.441759	+	0.897134i
$487$	19.4552	+	11.2324i	0.881598	+	0.508991i	0.871185	−	0.490955i	$-0.163352\pi$
$487$	19.4552	+	11.2324i	0.881598	+	0.508991i	0.0104127	+	0.999946i	$0.496685\pi$
$488$	23.5887	−	5.71022i	1.06781	−	0.258489i
$489$	33.6288	−	16.2927i	1.52075	−	0.736780i
$490$	8.96958	+	4.18887i	0.405204	+	0.189234i
$491$			14.4520i			0.652208i	0.945334	+	0.326104i	$0.105736\pi$
$491$			14.4520i			0.652208i	−0.945334	+	0.326104i	$0.894264\pi$
$492$	−15.6467	−	4.21548i	−0.705408	−	0.190048i
$493$	8.21497	+	4.74292i	0.369984	+	0.213610i
$494$	−3.08215	+	1.40696i	−0.138673	+	0.0633021i
$495$	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
$498$	22.3826	+	3.79153i	1.00299	+	0.169903i
$499$	−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	$0.882743\pi$
$500$	1.96373	+	0.379149i	0.0878208	+	0.0169561i
$501$	−0.0546024	+	0.752454i	−0.00243946	+	0.0336171i
$502$	−0.0850890	+	0.889544i	−0.00379771	+	0.0397023i
$503$	10.9067			0.486307			0.243153	−	0.969988i	$-0.421818\pi$
$503$	10.9067			0.486307			0.243153	+	0.969988i	$0.421818\pi$
$504$	−22.3814	−	1.75254i	−0.996948	−	0.0780644i
$505$	1.23604			0.0550029
$506$	−5.57417	+	58.2739i	−0.247802	+	2.59059i
$507$	0.559768	−	7.71394i	0.0248602	−	0.342588i
$508$	−0.449802	+	2.32966i	−0.0199567	+	0.103362i
$509$	−16.6483	−	28.8356i	−0.737921	−	1.27812i	−0.953430	−	0.301615i	$-0.902474\pi$
$509$	−16.6483	−	28.8356i	−0.737921	−	1.27812i	0.215508	−	0.976502i	$-0.430859\pi$
$510$	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
$513$	4.06287	−	1.28481i	0.179380	−	0.0567259i
$514$	14.7387	−	6.72799i	0.650095	−	0.296759i
$515$	8.36863	+	4.83163i	0.368766	+	0.212907i
$516$	−7.61752	+	28.2741i	−0.335343	+	1.24470i
$517$		−	45.4725i		−	1.99988i
$518$	18.1272	−	17.9707i	0.796465	−	0.789587i
$519$	−5.48076	+	2.65535i	−0.240579	+	0.116557i
$520$	−8.03104	+	1.94411i	−0.352184	+	0.0852548i
$521$	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	$0.609866\pi$
$522$	5.61855	+	1.37640i	0.245917	+	0.0602432i
$523$	−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
$528$	−36.6508	+	24.7153i	−1.59502	+	1.07560i
$529$	−9.54418	+	16.5310i	−0.414964	+	0.718740i
$530$	−13.2911	−	1.27136i	−0.577328	−	0.0552241i
$531$	−6.14066	−	4.84975i	−0.266482	−	0.210461i
$532$	2.74775	+	3.35858i	0.119130	+	0.145613i
$533$	13.6660			0.591939
$534$	−11.0109	−	29.6303i	−0.476489	−	1.28223i
$535$	−2.73656	−	1.57996i	−0.118312	−	0.0683074i
$536$	−0.782410	+	0.745289i	−0.0337950	+	0.0321916i
$537$	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
$540$	10.3230	−	1.19819i	0.444231	−	0.0515620i
$541$	1.27385	−	0.735460i	0.0547673	−	0.0316199i	−0.472366	−	0.881402i	$-0.656600\pi$
$541$	1.27385	−	0.735460i	0.0547673	−	0.0316199i	0.527134	+	0.849782i	$0.323267\pi$
$542$	−20.2091	+	9.22518i	−0.868056	+	0.396255i
$543$	−10.3772	−	0.753030i	−0.445328	−	0.0323156i
$544$	−21.2500	−	33.1256i	−0.911086	−	1.42025i
$545$		−	11.7000i		−	0.501173i
$546$	18.6098	−	3.48309i	0.796424	−	0.149062i
$547$	−5.10594			−0.218314			−0.109157	−	0.994025i	$-0.534815\pi$
$547$	−5.10594			−0.218314			−0.109157	+	0.994025i	$0.534815\pi$
$548$	−6.83420	−	5.92581i	−0.291943	−	0.253138i
$549$	23.9181	−	9.51773i	1.02080	−	0.406207i
$550$	−8.20860	+	3.74711i	−0.350016	+	0.159777i
$551$	−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
$555$	−6.63309	+	9.77847i	−0.281559	+	0.415073i
$556$	−23.8952	−	4.61359i	−1.01338	−	0.195660i
$557$	1.92197	−	3.32895i	0.0814365	−	0.141052i	−0.822431	−	0.568865i	$-0.807383\pi$
$557$	1.92197	−	3.32895i	0.0814365	−	0.141052i	0.903867	+	0.427813i	$0.140716\pi$
$558$	5.47528	+	5.24416i	0.231787	+	0.222003i
$559$		−	24.6949i		−	1.04448i
$560$	5.02697	+	9.31287i	0.212428	+	0.393541i
$561$	−69.1931	+	33.5231i	−2.92134	+	1.41535i
$562$	−2.59845	+	27.1650i	−0.109609	+	1.14588i
$563$	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	$0.501667\pi$
$564$	23.8554	−	6.35705i	1.00449	−	0.267680i
$565$	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	$0.294713\pi$
$570$	−1.54744	−	1.28081i	−0.0648151	−	0.0536472i
$571$	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	$0.0499375\pi$
$572$	24.4226	−	28.1665i	1.02116	−	1.17770i
$573$	−28.3396	+	13.7302i	−1.18390	+	0.573585i
$574$	−4.45675	−	16.9261i	−0.186021	−	0.706480i
$575$	−6.48755			−0.270550
$576$	−18.0897	−	15.7722i	−0.753738	−	0.657175i
$577$	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	$0.109236\pi$
$578$	−18.4416	−	40.3991i	−0.767071	−	1.68038i
$579$	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
$582$	−0.503907	+	2.97473i	−0.0208876	+	0.123306i
$583$	52.1687	−	30.1196i	2.16061	−	1.24743i
$584$	8.99470	−	8.56795i	0.372203	−	0.354544i
$585$	−8.14319	+	3.24042i	−0.336679	+	0.133975i
$586$	36.9169	+	3.53127i	1.52502	+	0.145875i
$587$		−	40.9272i		−	1.68925i	−0.535360	−	0.844624i	$-0.679824\pi$
$587$		−	40.9272i		−	1.68925i	0.535360	−	0.844624i	$-0.320176\pi$
$588$	−10.3830	−	21.9133i	−0.428188	−	0.903690i
$589$		−	1.46545i		−	0.0603827i
$590$	−0.351234	+	3.67189i	−0.0144601	+	0.151169i
$591$	−3.11094	+	42.8706i	−0.127967	+	1.76346i
$592$	27.0125	−	3.86565i	1.11021	−	0.158877i
$593$	−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	$0.446835\pi$
$594$	−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
$597$	−21.8205	+	32.1677i	−0.893055	+	1.31654i
$598$	24.3830	−	11.1305i	0.997095	−	0.455160i
$599$	−0.0838877	+	0.145298i	−0.00342756	+	0.00593671i	−0.867734	−	0.497029i	$-0.834424\pi$
$599$	−0.0838877	+	0.145298i	−0.00342756	+	0.00593671i	0.864307	+	0.502965i	$0.167758\pi$
$600$	−3.11334	−	3.78248i	−0.127101	−	0.154419i
$601$	42.9062			1.75018			0.875091	−	0.483958i	$-0.160801\pi$
$601$	42.9062			1.75018			0.875091	+	0.483958i	$0.160801\pi$
$602$	−30.5860	+	8.05350i	−1.24659	+	0.328236i
$603$	−0.710350	+	0.899431i	−0.0289277	+	0.0366277i
$604$	−8.72344	−	7.56394i	−0.354952	−	0.307772i
$605$	14.8555	−	25.7305i	0.603962	−	1.04609i
$606$	−2.33236	−	1.93049i	−0.0947458	−	0.0784207i
$607$	22.6024	−	13.0495i	0.917405	−	0.529664i	0.0345985	−	0.999401i	$-0.488985\pi$
$607$	22.6024	−	13.0495i	0.917405	−	0.529664i	0.882806	+	0.469737i	$0.155651\pi$
$608$	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
$612$	−27.2598	−	31.6130i	−1.10191	−	1.27788i
$613$	−38.6345	−	22.3056i	−1.56043	−	0.900916i	−0.997213	−	0.0746079i	$-0.976229\pi$
$613$	−38.6345	−	22.3056i	−1.56043	−	0.900916i	−0.563219	−	0.826308i	$-0.690437\pi$
$614$	31.3035	+	2.99432i	1.26331	+	0.120841i
$615$	3.53268	+	7.29161i	0.142452	+	0.294026i
$616$	−42.8504	−	21.0631i	−1.72649	−	0.848658i
$617$		−	10.5361i		−	0.424167i	−0.977252	−	0.212084i	$-0.931975\pi$
$617$		−	10.5361i		−	0.424167i	0.977252	−	0.212084i	$-0.0680249\pi$
$618$	−8.24514	−	22.1876i	−0.331668	−	0.892516i
$619$	−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	$0.935598\pi$
$620$	0.677536	−	3.50917i	0.0272105	−	0.140932i
$621$	−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
$624$	18.1907	+	8.87471i	0.728212	+	0.355273i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−15.7704	−	34.5473i	−0.630311	−	1.38079i
$627$	9.03908	+	0.655928i	0.360986	+	0.0261953i
$628$	2.52743	+	2.19149i	0.100856	+	0.0874500i
$629$	47.4613			1.89241
$630$	6.66909	+	9.02902i	0.265703	+	0.359725i
$631$		−	21.2155i		−	0.844577i	−0.906462	−	0.422288i	$-0.861227\pi$
$631$		−	21.2155i		−	0.844577i	0.906462	−	0.422288i	$-0.138773\pi$
$632$	44.9265	−	10.8755i	1.78708	−	0.432606i
$633$	1.34482	−	18.5324i	0.0534518	−	0.736598i
$634$	−9.82623	−	21.5258i	−0.390249	−	0.854899i
$635$	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
$639$	−6.54065	−	0.954281i	−0.258744	−	0.0377508i
$640$	−1.62302	+	11.1967i	−0.0641554	+	0.442588i
$641$	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	$0.575359\pi$
$642$	2.69618	+	7.25540i	0.106410	+	0.286348i
$643$	−10.1712			−0.401111			−0.200556	−	0.979682i	$-0.564275\pi$
$643$	−10.1712			−0.401111			−0.200556	+	0.979682i	$0.564275\pi$
$644$	−21.7375	−	26.5698i	−0.856578	−	1.04700i
$645$	13.1762	−	6.38368i	0.518812	−	0.251357i
$646$	−0.768287	+	8.03188i	−0.0302278	+	0.316010i
$647$	16.4787	−	28.5419i	0.647843	−	1.12210i	−0.335794	−	0.941936i	$-0.609005\pi$
$647$	16.4787	−	28.5419i	0.647843	−	1.12210i	0.983637	−	0.180162i	$-0.0576622\pi$
$648$	−21.3506	−	13.8619i	−0.838730	−	0.544547i
$649$	−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	0.991709	−	0.128503i	$-0.0410173\pi$
$653$	9.82718	+	17.0212i	0.384567	+	0.666090i	−0.607142	+	0.794594i	$0.707684\pi$
$654$	−18.2735	+	22.0775i	−0.714550	+	0.863300i
$655$	3.38447	+	1.95403i	0.132242	+	0.0763501i
$656$	6.96580	−	17.3665i	0.271969	−	0.678050i
$657$	8.16629	−	10.3400i	0.318597	−	0.403401i
$658$	18.7737	+	18.9373i	0.731876	+	0.738252i
$659$			21.7995i			0.849188i	0.905384	+	0.424594i	$0.139583\pi$
$659$			21.7995i			0.849188i	−0.905384	+	0.424594i	$0.860417\pi$
$660$	21.3418	+	5.74982i	0.830727	+	0.223812i
$661$	10.2511	+	5.91846i	0.398720	+	0.230201i	0.685932	−	0.727666i	$-0.259395\pi$
$661$	10.2511	+	5.91846i	0.398720	+	0.230201i	−0.287211	+	0.957867i	$0.592728\pi$
$662$	−5.14460	−	11.2700i	−0.199951	−	0.438022i
$663$	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
$666$	27.7888	−	8.09188i	1.07680	−	0.313554i
$667$	4.42277	+	7.66046i	0.171250	+	0.296614i
$668$	−0.855346	−	0.165147i	−0.0330943	−	0.00638972i
$669$	−2.26918	−	0.164665i	−0.0877314	−	0.00636631i
$670$	0.537828	+	0.0514457i	0.0207781	+	0.00198752i
$671$	54.7496			2.11358
$672$	5.05946	−	25.4244i	0.195173	−	0.980769i
$673$	29.8607			1.15105			0.575524	−	0.817785i	$-0.304798\pi$
$673$	29.8607			1.15105			0.575524	+	0.817785i	$0.304798\pi$
$674$	21.4751	+	2.05419i	0.827189	+	0.0791245i
$675$	−3.83399	−	3.50721i	−0.147570	−	0.134993i
$676$	8.76876	+	1.69304i	0.337260	+	0.0651168i
$677$	−22.8224	−	39.5296i	−0.877136	−	1.51924i	−0.854470	−	0.519501i	$-0.826118\pi$
$677$	−22.8224	−	39.5296i	−0.877136	−	1.51924i	−0.0226662	−	0.999743i	$-0.507215\pi$
$678$	−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
$681$	2.00910	−	2.96180i	0.0769888	−	0.113497i
$682$	6.69604	+	14.6687i	0.256405	+	0.561693i
$683$	−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	$0.686171\pi$
$684$	0.919555	+	4.83370i	0.0351601	+	0.184821i
$685$			4.52276i			0.172806i
$686$	14.9544	−	21.5027i	0.570963	−	0.820976i
$687$	8.85981	+	18.2870i	0.338023	+	0.697693i
$688$	−31.3820	−	12.5874i	−1.19643	−	0.479892i
$689$	−23.8862	−	13.7907i	−0.909992	−	0.525384i
$690$	12.2418	+	10.1325i	0.466038	+	0.385738i
$691$	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
$696$	−2.34387	+	6.25484i	−0.0888440	+	0.237089i
$697$	16.2723	−	28.1845i	0.616359	−	1.06757i
$698$	1.20467	−	12.5940i	0.0455975	−	0.476689i
$699$	8.09498	+	16.7084i	0.306180	+	0.631969i
$700$	1.87149	−	4.94950i	0.0707356	−	0.187073i
$701$	9.30680			0.351513			0.175756	−	0.984434i	$-0.443763\pi$
$701$	9.30680			0.351513			0.175756	+	0.984434i	$0.443763\pi$
$702$	20.4270	+	6.60376i	0.770966	+	0.249243i
$703$	−4.84492	−	2.79721i	−0.182729	−	0.105499i
$704$	−23.3449	−	45.3929i	−0.879845	−	1.71081i
$705$	−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
$708$	6.39767	−	6.38019i	0.240439	−	0.239782i
$709$	30.9906	−	17.8924i	1.16388	−	0.671964i	0.211646	−	0.977347i	$-0.432118\pi$
$709$	30.9906	−	17.8924i	1.16388	−	0.671964i	0.952230	+	0.305383i	$0.0987844\pi$
$710$	1.29394	+	2.83457i	0.0485607	+	0.106379i
$711$	45.5538	−	18.1272i	1.70840	−	0.679825i
$712$	35.4755	−	8.58771i	1.32950	−	0.321838i
$713$			11.5932i			0.434168i
$714$	14.9755	−	42.5279i	0.560445	−	1.59157i
$715$	−18.6401			−0.697101
$716$	32.5295	+	28.2058i	1.21569	+	1.05410i
$717$	−0.834680	+	11.5024i	−0.0311717	+	0.429564i
$718$	−0.660672	−	1.44730i	−0.0246560	−	0.0540127i
$719$	−3.84834	−	6.66553i	−0.143519	−	0.248582i	0.785300	−	0.619115i	$-0.212508\pi$
$719$	−3.84834	−	6.66553i	−0.143519	−	0.248582i	−0.928819	+	0.370533i	$0.879175\pi$
$720$	−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
$723$	−2.24033	−	1.51970i	−0.0833188	−	0.0565181i
$724$	2.27756	−	11.7962i	0.0846449	−	0.438402i
$725$	−0.681731	+	1.18079i	−0.0253189	+	0.0438536i
$726$	−68.2187	+	25.3508i	−2.53183	+	0.940855i
$727$			1.90494i			0.0706503i	0.999376	+	0.0353252i	$0.0112467\pi$
$727$			1.90494i			0.0706503i	−0.999376	+	0.0353252i	$0.988753\pi$
$728$	1.45784	+	21.8132i	0.0540313	+	0.808450i
$729$	−24.4897	−	11.3691i	−0.907024	−	0.421078i
$730$	−6.18295	−	0.591427i	−0.228841	−	0.0218897i
$731$	−50.9304	−	29.4047i	−1.88373	−	1.08757i
$732$	7.65398	+	28.7222i	0.282899	+	1.06160i
$733$	−29.4946	+	17.0287i	−1.08941	+	0.628969i	−0.933418	−	0.358790i	$-0.883189\pi$
$733$	−29.4946	+	17.0287i	−1.08941	+	0.628969i	−0.155988	+	0.987759i	$0.549856\pi$
$734$	−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
$738$	4.72224	−	19.2765i	0.173828	−	0.709579i
$739$	−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	$0.299005\pi$
$740$	−10.3084	−	8.93823i	−0.378944	−	0.328576i
$741$	−1.80925	−	3.73436i	−0.0664643	−	0.137185i
$742$	−9.29078	+	34.0818i	−0.341075	+	1.25118i
$743$	20.1591			0.739567			0.369783	−	0.929118i	$-0.379432\pi$
$743$	20.1591			0.739567			0.369783	+	0.929118i	$0.379432\pi$
$744$	−6.75925	+	5.56350i	−0.247806	+	0.203968i
$745$	5.89838	−	10.2163i	0.216100	−	0.374296i
$746$	−28.4068	+	12.9673i	−1.04005	+	0.474766i
$747$	−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
$750$	−0.409106	+	2.41508i	−0.0149385	+	0.0881864i
$751$	−27.2412	+	15.7277i	−0.994046	+	0.573913i	−0.906481	−	0.422246i	$-0.861242\pi$
$751$	−27.2412	+	15.7277i	−0.994046	+	0.573913i	−0.0875647	+	0.996159i	$0.527908\pi$
$752$	4.03839	+	28.2196i	0.147265	+	1.02906i
$753$	−1.09157	−	0.0792105i	−0.0397789	−	0.00288659i
$754$	0.536388	−	5.60755i	0.0195341	−	0.204215i
$755$			5.77303i			0.210102i
$756$	1.51748	−	27.4535i	0.0551902	−	0.998476i
$757$			7.57270i			0.275234i	0.990485	+	0.137617i	$0.0439444\pi$
$757$			7.57270i			0.275234i	−0.990485	+	0.137617i	$0.956056\pi$
$758$	3.66766	+	0.350829i	0.133216	+	0.0127427i
$759$	−71.5084	−	5.18907i	−2.59559	−	0.188351i
$760$	1.67949	−	1.59980i	0.0609214	−	0.0580310i
$761$	−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	$0.628152\pi$
$762$	−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
$765$	−3.01325	+	20.6528i	−0.108944	+	0.746705i
$766$	7.92042	+	17.3509i	0.286176	+	0.626912i
$767$	−3.80992	+	6.59897i	−0.137568	+	0.238275i
$768$	20.5500	−	18.5929i	0.741535	−	0.670915i
$769$	−38.7044			−1.39572			−0.697859	−	0.716235i	$-0.745864\pi$
$769$	−38.7044			−1.39572			−0.697859	+	0.716235i	$0.745864\pi$
$770$	6.07891	+	23.0868i	0.219069	+	0.831991i
$771$	8.65170	+	17.8575i	0.311583	+	0.643121i
$772$	−14.1494	+	16.3184i	−0.509249	+	0.587313i
$773$	−22.7217	+	39.3552i	−0.817244	+	1.41551i	0.0904620	+	0.995900i	$0.471166\pi$
$773$	−22.7217	+	39.3552i	−0.817244	+	1.41551i	−0.907706	+	0.419608i	$0.862168\pi$
$774$	−34.8334	−	8.53325i	−1.25206	−	0.306721i
$775$	−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
$780$	−2.60589	−	9.77881i	−0.0933057	−	0.350138i
$781$	−12.1748	−	7.02910i	−0.435647	−	0.251521i
$782$	6.07794	−	63.5405i	0.217347	−	2.27220i
$783$	−1.52755	+	6.91812i	−0.0545901	+	0.247234i
$784$	26.5414	−	8.91933i	0.947907	−	0.318548i
$785$		−	1.67261i		−	0.0596982i
$786$	−3.33453	−	8.97319i	−0.118939	−	0.320063i
$787$	−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	$0.269879\pi$
$788$	−48.7328	−	9.40913i	−1.73603	−	0.335186i
$789$	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
$792$	−31.2910	−	44.1822i	−1.11188	−	1.56994i
$793$	−12.5339	−	21.7094i	−0.445093	−	0.770924i
$794$	4.17082	−	1.90392i	0.148017	−	0.0675676i
$795$	1.18352	−	16.3096i	0.0419752	−	0.578443i
$796$	−33.9110	−	29.4036i	−1.20194	−	1.04218i
$797$	24.0379			0.851466			0.425733	−	0.904849i	$-0.360016\pi$
$797$	24.0379			0.851466			0.425733	+	0.904849i	$0.360016\pi$
$798$	−4.03518	+	3.45870i	−0.142844	+	0.122437i
$799$			49.5821i			1.75409i
$800$	4.76137	−	3.05441i	0.168340	−	0.107990i
$801$	35.9709	−	14.3139i	1.27097	−	0.505757i
$802$	−38.8362	+	17.7282i	−1.37135	+	0.626004i
$803$	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
$807$	9.36254	+	6.35095i	0.329577	+	0.223564i
$808$	2.53139	−	2.41129i	0.0890541	−	0.0848289i
$809$	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	$0.581933\pi$
$810$	1.75692	+	12.6061i	0.0617318	+	0.442932i
$811$	2.38700			0.0838191			0.0419095	−	0.999121i	$-0.486656\pi$
$811$	2.38700			0.0838191			0.0419095	+	0.999121i	$0.486656\pi$
$812$	−7.12019	+	1.16439i	−0.249870	+	0.0408620i
$813$	−11.8629	−	24.4855i	−0.416050	−	0.858745i
$814$	61.2774	+	5.86147i	2.14777	+	0.205444i
$815$	10.7871	−	18.6838i	0.377857	−	0.654467i
$816$	39.9631	−	26.9490i	1.39899	−	0.943404i
$817$	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	0.845388	−	0.534153i	$-0.179370\pi$
$821$	−1.14316	−	1.98002i	−0.0398967	−	0.0691031i	−0.885284	+	0.465050i	$0.846036\pi$
$822$	7.06383	−	8.53432i	0.246379	−	0.297669i
$823$	2.59074	+	1.49577i	0.0903076	+	0.0521391i	0.544474	−	0.838778i	$-0.316729\pi$
$823$	2.59074	+	1.49577i	0.0903076	+	0.0521391i	−0.454166	+	0.890917i	$0.650063\pi$
$824$	26.5646	−	6.43060i	0.925421	−	0.224021i
$825$	−4.81851	−	9.94560i	−0.167759	−	0.346261i
$826$	9.41568	+	2.56674i	0.327613	+	0.0893082i
$827$		−	2.27298i		−	0.0790393i	−0.999219	−	0.0395196i	$-0.987417\pi$
$827$		−	2.27298i		−	0.0790393i	0.999219	−	0.0395196i	$-0.0125828\pi$
$828$	−7.27463	−	38.2395i	−0.252811	−	1.32892i
$829$	−44.5776	−	25.7369i	−1.54824	−	0.893879i	−0.998276	−	0.0586924i	$-0.981307\pi$
$829$	−44.5776	−	25.7369i	−1.54824	−	0.893879i	−0.549967	−	0.835186i	$-0.685360\pi$
$830$	11.9232	−	5.44276i	0.413859	−	0.188921i
$831$	−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
$834$	4.97811	−	29.3874i	0.172378	−	1.01760i
$835$	0.217786	+	0.377216i	0.00753679	+	0.0130541i
$836$	−1.98387	+	10.2751i	−0.0686137	+	0.355372i
$837$	−6.26735	+	6.85129i	−0.216631	+	0.236815i
$838$	−3.22063	+	33.6693i	−0.111255	+	1.16309i
$839$	−15.5868			−0.538116			−0.269058	−	0.963124i	$-0.586712\pi$
$839$	−15.5868			−0.538116			−0.269058	+	0.963124i	$0.586712\pi$
$840$	−11.2618	+	6.41660i	−0.388568	+	0.221394i
$841$	−27.1410			−0.935895
$842$	2.01087	−	21.0222i	0.0692992	−	0.724473i
$843$	−33.3344	−	2.41894i	−1.14810	−	0.0833126i
$844$	21.0666	+	4.06745i	0.725142	+	0.140007i
$845$	−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
$849$	−33.1512	−	22.4877i	−1.13775	−	0.771775i
$850$	8.95046	−	4.08576i	0.306998	−	0.140140i
$851$	38.3283	+	22.1288i	1.31388	+	0.758567i
$852$	1.98551	−	7.36968i	0.0680225	−	0.252481i
$853$			53.4140i			1.82886i	0.404745	+	0.914430i	$0.367360\pi$
$853$			53.4140i			1.82886i	−0.404745	+	0.914430i	$0.632640\pi$
$854$	−22.8007	+	22.6038i	−0.780225	+	0.773488i
$855$	1.52481	−	1.93068i	0.0521473	−	0.0660278i
$856$	−8.68668	+	2.10282i	−0.296905	+	0.0718730i
$857$	−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	$0.716744\pi$
$858$	35.1734	+	29.1128i	1.20080	+	0.993896i
$859$	−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	0.957298	−	0.289104i	$-0.0933574\pi$
$863$	6.70607	+	11.6153i	0.228277	+	0.395388i	−0.729020	+	0.684492i	$0.760024\pi$
$864$	18.8040	−	22.5923i	0.639724	−	0.768605i
$865$	−1.75807	+	3.04506i	−0.0597761	+	0.103535i
$866$	28.8085	+	2.75567i	0.978952	+	0.0936413i
$867$	48.9479	−	23.7146i	1.66236	−	0.805389i
$868$	−8.84470	−	3.34433i	−0.300209	−	0.113514i
$869$	104.275			3.53728
$870$	3.13062	−	1.16337i	0.106138	−	0.0394419i
$871$	0.966561	+	0.558044i	0.0327507	+	0.0189086i
$872$	−22.8247	−	23.9615i	−0.772940	−	0.811439i
$873$	−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
$876$	10.7433	+	10.7728i	0.362983	+	0.363978i
$877$	1.44864	−	0.836371i	0.0489170	−	0.0282422i	−0.475342	−	0.879801i	$-0.657676\pi$
$877$	1.44864	−	0.836371i	0.0489170	−	0.0282422i	0.524259	+	0.851559i	$0.324342\pi$
$878$	−34.8072	+	15.8890i	−1.17469	+	0.536227i
$879$	−3.28731	+	45.3010i	−0.110878	+	1.52796i
$880$	−9.50120	+	23.6876i	−0.320285	+	0.798509i
$881$			19.3094i			0.650551i	0.945619	+	0.325276i	$0.105457\pi$
$881$			19.3094i			0.650551i	−0.945619	+	0.325276i	$0.894543\pi$
$882$	26.5397	−	13.3284i	0.893637	−	0.448791i
$883$	13.3201			0.448257			0.224128	−	0.974560i	$-0.428047\pi$
$883$	13.3201			0.448257			0.224128	+	0.974560i	$0.428047\pi$
$884$	−26.6299	+	30.7120i	−0.895659	+	1.03296i
$885$	−4.50581	−	0.326968i	−0.151461	−	0.0109909i
$886$	42.7717	−	19.5247i	1.43694	−	0.655944i
$887$	25.5507	+	44.2552i	0.857910	+	1.48594i	0.873919	+	0.486072i	$0.161571\pi$
$887$	25.5507	+	44.2552i	0.857910	+	1.48594i	−0.0160090	+	0.999872i	$0.505096\pi$
$888$	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
$891$	−39.4545	−	41.7245i	−1.32177	−	1.39782i
$892$	0.498033	−	2.57947i	0.0166754	−	0.0863670i
$893$	2.92221	−	5.06142i	0.0977880	−	0.169374i
$894$	−27.0863	+	10.0655i	−0.905901	+	0.336642i
$895$		−	21.5275i		−	0.719585i
$896$	28.4630	+	9.26596i	0.950882	+	0.309554i
$897$	14.3130	+	29.5426i	0.477897	+	0.986399i
$898$	−3.42618	+	35.8182i	−0.114333	+	1.19527i
$899$	2.11007	+	1.21825i	0.0703746	+	0.0406308i
$900$	4.54394	−	3.91824i	0.151465	−	0.130608i
$901$	−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
$906$	9.01654	−	10.8935i	0.299555	−	0.361914i
$907$	−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	$0.871588\pi$
$908$	3.12232	+	2.70730i	0.103618	+	0.0898450i
$909$	2.29825	−	2.91000i	0.0762282	−	0.0965186i
$910$	7.76277	−	7.69574i	0.257333	−	0.255111i
$911$	10.7764			0.357037			0.178518	−	0.983937i	$-0.442870\pi$
$911$	10.7764			0.357037			0.178518	+	0.983937i	$0.442870\pi$
$912$	−5.66778	+	0.395696i	−0.187679	+	0.0131028i
$913$	−29.5668	+	51.2112i	−0.978518	+	1.69484i
$914$	16.9961	+	37.2324i	0.562180	+	1.23154i
$915$	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
$918$	37.9423	−	34.2651i	1.25228	−	1.13092i
$919$	−46.5187	+	26.8576i	−1.53451	+	0.885949i	−0.535363	+	0.844622i	$0.679825\pi$
$919$	−46.5187	+	26.8576i	−1.53451	+	0.885949i	−0.999146	+	0.0413275i	$0.986841\pi$
$920$	−13.2865	+	12.6561i	−0.438042	+	0.417259i
$921$	−2.78746	+	38.4128i	−0.0918498	+	1.26574i
$922$	30.8294	+	2.94898i	1.01531	+	0.0971194i
$923$			6.43675i			0.211868i
$924$	24.5871	−	53.0584i	0.808857	−	1.74549i
$925$			6.82193i			0.224304i
$926$	4.96529	−	51.9086i	0.163170	−	1.70582i
$927$	26.9355	−	10.7185i	0.884679	−	0.352041i
$928$	−6.85259	−	3.53990i	−0.224947	−	0.116203i
$929$	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	$0.191509\pi$
$930$	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
$933$	19.6289	+	13.3150i	0.642623	+	0.435914i
$934$	−12.1358	+	5.53982i	−0.397096	+	0.181268i
$935$	−22.1951	+	38.4431i	−0.725859	+	1.25722i
$936$	−10.3557	+	22.5223i	−0.338486	+	0.736165i
$937$	−15.5368			−0.507566			−0.253783	−	0.967261i	$-0.581675\pi$
$937$	−15.5368			−0.507566			−0.253783	+	0.967261i	$0.581675\pi$
$938$	0.375954	−	1.37913i	0.0122753	−	0.0450301i
$939$	41.8578	−	20.2795i	1.36598	−	0.661798i
$940$	9.33764	−	10.7690i	0.304560	−	0.351247i
$941$	−3.61622	+	6.26348i	−0.117886	+	0.204184i	−0.918930	−	0.394422i	$-0.870945\pi$
$941$	−3.61622	+	6.26348i	−0.117886	+	0.204184i	0.801044	+	0.598605i	$0.204278\pi$
$942$	−2.61235	+	3.15617i	−0.0851151	+	0.102834i
$943$	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	$0.111835\pi$
$948$	14.5776	+	54.7037i	0.473458	+	1.77669i
$949$	−11.1117	−	6.41536i	−0.360702	−	0.208251i
$950$	−1.15448	−	0.110431i	−0.0374562	−	0.00358286i
$951$	26.0808	−	12.6358i	0.845729	−	0.409744i
$952$	46.7231	+	22.9667i	1.51430	+	0.744356i
$953$		−	2.29992i		−	0.0745017i	−0.999306	−	0.0372508i	$-0.988140\pi$
$953$		−	2.29992i		−	0.0745017i	0.999306	−	0.0372508i	$-0.0118601\pi$
$954$	−27.7063	+	28.9273i	−0.897023	+	0.936556i
$955$	−9.09052	+	15.7452i	−0.294162	+	0.509504i
$956$	−13.0752	−	2.52451i	−0.422884	−	0.0816486i
$957$	−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
$960$	−13.7550	−	1.67291i	−0.443942	−	0.0539929i
$961$	−13.9033	−	24.0813i	−0.448495	−	0.776816i
$962$	−11.7042	−	25.6397i	−0.377358	−	0.826658i
$963$	−8.80798	+	3.50496i	−0.283833	+	0.112946i
$964$	2.04782	−	2.36174i	0.0659560	−	0.0760666i
$965$	10.7993			0.347641
$966$	31.9224	−	27.3619i	1.02709	−	0.880354i
$967$		−	2.39354i		−	0.0769711i	−0.999259	−	0.0384855i	$-0.987747\pi$
$967$		−	2.39354i		−	0.0769711i	0.999259	−	0.0384855i	$-0.0122534\pi$
$968$	−19.7717	−	81.6763i	−0.635487	−	2.62518i
$969$	−9.85599	−	0.715209i	−0.316620	−	0.0229758i
$970$	0.723361	+	1.58463i	0.0232257	+	0.0508794i
$971$	−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	$0.460327\pi$
$972$	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
$975$	−2.84054	+	4.18751i	−0.0909701	+	0.134108i
$976$	−33.9768	+	4.86228i	−1.08757	+	0.155638i
$977$	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	$0.631755\pi$
$978$	−49.5362	+	18.4081i	−1.58399	+	0.588627i
$979$	82.3389			2.63156
$980$	−12.0632	−	7.10489i	−0.385344	−	0.226957i
$981$	−27.5453	−	21.7547i	−0.879454	−	0.694573i
$982$	1.94612	−	20.3453i	0.0621032	−	0.649244i
$983$	16.9931	−	29.4329i	0.541996	−	0.938765i	−0.456793	−	0.889573i	$-0.651002\pi$
$983$	16.9931	−	29.4329i	0.541996	−	0.938765i	0.998789	−	0.0491921i	$-0.0156647\pi$
$984$	21.4596	+	8.04151i	0.684106	+	0.256354i
$985$	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
$990$	−6.44104	+	26.2928i	−0.204710	+	0.835640i
$991$	6.57484	+	3.79598i	0.208857	+	0.120583i	0.600780	−	0.799414i	$-0.294857\pi$
$991$	6.57484	+	3.79598i	0.208857	+	0.120583i	−0.391923	+	0.919998i	$0.628190\pi$
$992$	−5.45819	−	8.50851i	−0.173298	−	0.270145i
$993$	13.6548	−	6.61558i	0.433323	−	0.209939i
$994$	7.97227	−	2.09915i	0.252865	−	0.0665810i
$995$			22.4418i			0.711452i
$996$	−30.9994	−	8.35174i	−0.982253	−	0.264635i
$997$	36.1075	+	20.8467i	1.14354	+	0.660221i	0.947304	−	0.320337i	$-0.103796\pi$
$997$	36.1075	+	20.8467i	1.14354	+	0.660221i	0.196232	+	0.980557i	$0.437129\pi$
$998$	4.05640	+	8.88614i	0.128403	+	0.281286i
$999$	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.a.11.3	✓	128
3.2	odd	2		840.2.cq.b.11.62	yes	128
7.2	even	3	inner	840.2.cq.a.611.41	yes	128
8.3	odd	2		840.2.cq.b.11.24	yes	128
21.2	odd	6		840.2.cq.b.611.24	yes	128
24.11	even	2	inner	840.2.cq.a.11.41	yes	128
56.51	odd	6		840.2.cq.b.611.62	yes	128
168.107	even	6	inner	840.2.cq.a.611.3	yes	128

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

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+(-1.40779 - 0.134661i) q^{2} +(0.125358 - 1.72751i) q^{3} +(1.96373 + 0.379149i) 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} +(-2.96857 - 0.433114i) q^{9} +(0.587274 + 1.28651i) q^{10} +(-5.52569 - 3.19026i) q^{11} +(0.901154 - 3.34484i) q^{12} +2.92141i q^{13} +(3.61833 - 0.952730i) q^{14} +(-1.55875 + 0.755191i) q^{15} +(3.71249 + 1.48910i) q^{16} +(6.02508 + 3.47858i) q^{17} +(4.12079 + 1.00949i) 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} +(-1.71905 + 4.58747i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.393401 - 4.11273i) q^{26} +(-1.12034 + 5.07394i) q^{27} +(-5.22214 + 0.853993i) q^{28} +1.36346 q^{29} +(2.29608 - 0.853246i) q^{30} +(1.54758 + 0.893495i) q^{31} +(-5.02588 - 2.59626i) q^{32} +(-6.20389 + 9.14575i) 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} +(0.481602 + 1.05502i) q^{38} +(5.04676 + 0.366223i) q^{39} +(0.665469 + 2.74903i) q^{40} -4.67787i q^{41} +(-1.19226 - 6.37013i) q^{42} -8.45307 q^{43} +(-9.64139 - 8.35987i) q^{44} +(1.10920 + 2.78741i) q^{45} +(-3.80997 - 8.34631i) 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} +(6.76457 - 9.97231i) q^{51} +(-1.10765 + 5.73687i) q^{52} +(-4.72056 + 8.17625i) q^{53} +(2.26047 - 6.99216i) q^{54} +6.38052i q^{55} +(7.46666 - 0.499020i) q^{56} +(-1.27827 + 0.619305i) q^{57} +(-1.91947 - 0.183606i) q^{58} +(2.25883 + 1.30414i) q^{59} +(-3.34729 + 0.891996i) 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} +(9.96534 - 12.0398i) q^{66} +(0.191019 - 0.330854i) q^{67} +(10.5127 + 9.11541i) q^{68} +(10.1124 - 4.89934i) q^{69} +(-2.63425 - 2.65720i) q^{70} +2.20330 q^{71} +(7.70939 + 3.54476i) q^{72} +(-2.19598 + 3.80355i) q^{73} +(-8.77649 + 4.00634i) q^{74} +(1.43339 + 0.972318i) 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} +(-0.566651 - 3.95966i) q^{80} +(8.62482 + 2.57146i) q^{81} +(-0.629928 + 6.58545i) q^{82} -9.26784i q^{83} +(0.820642 + 9.12834i) q^{84} -6.95716i q^{85} +(11.9001 + 1.13830i) q^{86} +(0.170921 - 2.35539i) q^{87} +(12.4473 + 13.0673i) 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} +(1.73752 - 2.56145i) q^{93} +(-4.18537 - 9.16867i) q^{94} +(-0.410032 + 0.710197i) q^{95} +(-5.11510 + 8.35678i) q^{96} +1.23173 q^{97} +(-8.11246 + 5.67345i) 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

Introduction

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