LMFDB - Embedded newform 620.2.k.d.63.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [620,2,Mod(63,620)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("620.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(620, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 620 = 2^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	620.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.95072492532$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.16
Character	$\chi$	$=$	620.63
Dual form			620.2.k.d.187.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.507403 - 1.32005i) q^{2} +(-2.16272 + 2.16272i) q^{3} +(-1.48508 + 1.33960i) q^{4} +(-1.19840 - 1.88781i) q^{5} +(3.95227 + 1.75753i) q^{6} +(-0.840075 - 0.840075i) q^{7} +(2.52188 + 1.28068i) q^{8} -6.35469i q^{9} +(-1.88394 + 2.53984i) q^{10} -1.36022i q^{11} +(0.314646 - 6.10899i) q^{12} +(-1.02878 - 1.02878i) q^{13} +(-0.682688 + 1.53520i) q^{14} +(6.67461 + 1.49100i) q^{15} +(0.410953 - 3.97883i) q^{16} +(-1.40290 + 1.40290i) q^{17} +(-8.38854 + 3.22439i) q^{18} +1.98723 q^{19} +(4.30864 + 1.19818i) q^{20} +3.63369 q^{21} +(-1.79556 + 0.690178i) q^{22} +(-0.839531 + 0.839531i) q^{23} +(-8.22385 + 2.68437i) q^{24} +(-2.12767 + 4.52471i) q^{25} +(-0.836039 + 1.88005i) q^{26} +(7.25525 + 7.25525i) q^{27} +(2.37295 + 0.122219i) q^{28} +7.05033i q^{29} +(-1.41851 - 9.56738i) q^{30} +1.00000i q^{31} +(-5.46079 + 1.47639i) q^{32} +(2.94176 + 2.94176i) q^{33} +(2.56374 + 1.14007i) q^{34} +(-0.579157 + 2.59265i) q^{35} +(8.51274 + 9.43726i) q^{36} +(-3.23405 + 3.23405i) q^{37} +(-1.00833 - 2.62325i) q^{38} +4.44992 q^{39} +(-0.604547 - 6.29560i) q^{40} +11.1800 q^{41} +(-1.84375 - 4.79667i) q^{42} +(-5.01326 + 5.01326i) q^{43} +(1.82214 + 2.02004i) q^{44} +(-11.9965 + 7.61547i) q^{45} +(1.53421 + 0.682246i) q^{46} +(4.22980 + 4.22980i) q^{47} +(7.71632 + 9.49387i) q^{48} -5.58855i q^{49} +(7.05245 + 0.512785i) q^{50} -6.06815i q^{51} +(2.90598 + 0.149673i) q^{52} +(9.44159 + 9.44159i) q^{53} +(5.89599 - 13.2587i) q^{54} +(-2.56783 + 1.63009i) q^{55} +(-1.04270 - 3.19443i) q^{56} +(-4.29782 + 4.29782i) q^{57} +(9.30681 - 3.57736i) q^{58} +10.8983 q^{59} +(-11.9097 + 6.72703i) q^{60} -10.1104 q^{61} +(1.32005 - 0.507403i) q^{62} +(-5.33842 + 5.33842i) q^{63} +(4.71974 + 6.45942i) q^{64} +(-0.709252 + 3.17503i) q^{65} +(2.39063 - 5.37595i) q^{66} +(2.31705 + 2.31705i) q^{67} +(0.204102 - 3.96274i) q^{68} -3.63134i q^{69} +(3.71631 - 0.551000i) q^{70} -7.20426i q^{71} +(8.13830 - 16.0258i) q^{72} +(-5.40068 - 5.40068i) q^{73} +(5.91008 + 2.62815i) q^{74} +(-5.18413 - 14.3872i) q^{75} +(-2.95121 + 2.66209i) q^{76} +(-1.14268 + 1.14268i) q^{77} +(-2.25790 - 5.87413i) q^{78} +3.78916 q^{79} +(-8.00378 + 3.99244i) q^{80} -12.3180 q^{81} +(-5.67277 - 14.7582i) q^{82} +(-12.2588 + 12.2588i) q^{83} +(-5.39634 + 4.86769i) q^{84} +(4.32964 + 0.967173i) q^{85} +(9.16152 + 4.07403i) q^{86} +(-15.2479 - 15.2479i) q^{87} +(1.74200 - 3.43030i) q^{88} +2.73953i q^{89} +(16.1399 + 11.9719i) q^{90} +1.72850i q^{91} +(0.122140 - 2.37141i) q^{92} +(-2.16272 - 2.16272i) q^{93} +(3.43735 - 7.72977i) q^{94} +(-2.38150 - 3.75152i) q^{95} +(8.61713 - 15.0032i) q^{96} +(1.63417 - 1.63417i) q^{97} +(-7.37718 + 2.83564i) q^{98} -8.64376 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 2 q^{2} + 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{8} - 10 q^{10} - 12 q^{12} - 6 q^{13} + 22 q^{14} - 2 q^{15} + 8 q^{16} - 2 q^{17} - 24 q^{18} + 8 q^{19} + 8 q^{20} - 16 q^{21} - 16 q^{22} + 10 q^{23}+ \cdots - 8 q^{99}+O(q^{100}) $ 88 * q + 2 * q^2 + 2 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^8 - 10 * q^10 - 12 * q^12 - 6 * q^13 + 22 * q^14 - 2 * q^15 + 8 * q^16 - 2 * q^17 - 24 * q^18 + 8 * q^19 + 8 * q^20 - 16 * q^21 - 16 * q^22 + 10 * q^23 - 44 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 + 46 * q^28 + 16 * q^30 - 8 * q^32 - 8 * q^33 + 40 * q^34 - 12 * q^35 - 20 * q^36 + 10 * q^37 - 64 * q^38 + 8 * q^39 + 8 * q^41 + 28 * q^42 + 10 * q^43 - 16 * q^44 + 6 * q^45 - 24 * q^46 - 64 * q^47 + 88 * q^48 - 14 * q^50 + 20 * q^52 + 18 * q^53 + 36 * q^54 + 40 * q^55 - 24 * q^56 - 24 * q^57 - 52 * q^58 - 32 * q^60 + 20 * q^61 + 2 * q^62 - 4 * q^63 - 150 * q^64 - 18 * q^65 + 8 * q^66 + 116 * q^67 + 68 * q^68 - 6 * q^70 - 26 * q^72 + 38 * q^73 + 36 * q^74 - 70 * q^75 - 8 * q^76 + 40 * q^77 - 152 * q^78 + 32 * q^79 + 68 * q^80 - 60 * q^81 + 14 * q^82 - 14 * q^83 - 120 * q^84 + 6 * q^85 + 4 * q^86 - 44 * q^87 + 52 * q^88 - 68 * q^90 - 92 * q^92 + 2 * q^93 + 112 * q^94 + 104 * q^95 - 20 * q^96 + 16 * q^97 - 62 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/620\mathbb{Z}\right)^\times$.

$n$	$311$	$497$	$561$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.507403	−	1.32005i	−0.358788	−	0.933419i
$2$	−0.507403	−	1.32005i	−0.358788	−	0.933419i
$3$	−2.16272	+	2.16272i	−1.24865	+	1.24865i	−0.292327	+	0.956318i	$0.594430\pi$
$3$	−2.16272	+	2.16272i	−1.24865	+	1.24865i	−0.956318	+	0.292327i	$0.905570\pi$
$4$	−1.48508	+	1.33960i	−0.742542	+	0.669799i
$5$	−1.19840	−	1.88781i	−0.535941	−	0.844255i
$5$	−1.19840	−	1.88781i	−0.535941	−	0.844255i
$6$	3.95227	+	1.75753i	1.61351	+	0.717510i
$7$	−0.840075	−	0.840075i	−0.317519	−	0.317519i	0.530295	−	0.847813i	$-0.322081\pi$
$7$	−0.840075	−	0.840075i	−0.317519	−	0.317519i	−0.847813	+	0.530295i	$0.822081\pi$
$8$	2.52188	+	1.28068i	0.891619	+	0.452787i
$9$		−	6.35469i		−	2.11823i
$10$	−1.88394	+	2.53984i	−0.595755	+	0.803167i
$11$		−	1.36022i		−	0.410121i	−0.978749	−	0.205060i	$-0.934261\pi$
$11$		−	1.36022i		−	0.410121i	0.978749	−	0.205060i	$-0.0657391\pi$
$12$	0.314646	−	6.10899i	0.0908304	−	1.76351i
$13$	−1.02878	−	1.02878i	−0.285332	−	0.285332i	0.549899	−	0.835231i	$-0.314666\pi$
$13$	−1.02878	−	1.02878i	−0.285332	−	0.285332i	−0.835231	+	0.549899i	$0.814666\pi$
$14$	−0.682688	+	1.53520i	−0.182456	+	0.410300i
$15$	6.67461	+	1.49100i	1.72338	+	0.384975i
$16$	0.410953	−	3.97883i	0.102738	−	0.994708i
$17$	−1.40290	+	1.40290i	−0.340253	+	0.340253i	−0.856462	−	0.516209i	$-0.827343\pi$
$17$	−1.40290	+	1.40290i	−0.340253	+	0.340253i	0.516209	+	0.856462i	$0.327343\pi$
$18$	−8.38854	+	3.22439i	−1.97720	+	0.759996i
$19$	1.98723			0.455902			0.227951	−	0.973673i	$-0.426797\pi$
$19$	1.98723			0.455902			0.227951	+	0.973673i	$0.426797\pi$
$20$	4.30864	+	1.19818i	0.963441	+	0.267922i
$21$	3.63369			0.792936
$22$	−1.79556	+	0.690178i	−0.382815	+	0.147146i
$23$	−0.839531	+	0.839531i	−0.175054	+	0.175054i	−0.789196	−	0.614142i	$-0.789502\pi$
$23$	−0.839531	+	0.839531i	−0.175054	+	0.175054i	0.614142	+	0.789196i	$0.289502\pi$
$24$	−8.22385	+	2.68437i	−1.67869	+	0.547945i
$25$	−2.12767	+	4.52471i	−0.425534	+	0.904943i
$26$	−0.836039	+	1.88005i	−0.163961	+	0.368708i
$27$	7.25525	+	7.25525i	1.39627	+	1.39627i
$28$	2.37295	+	0.122219i	0.448445	+	0.0230973i
$29$			7.05033i			1.30921i	0.755970	+	0.654607i	$0.227166\pi$
$29$			7.05033i			1.30921i	−0.755970	+	0.654607i	$0.772834\pi$
$30$	−1.41851	−	9.56738i	−0.258984	−	1.74676i
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$	−5.46079	+	1.47639i	−0.965341	+	0.260992i
$33$	2.94176	+	2.94176i	0.512095	+	0.512095i
$34$	2.56374	+	1.14007i	0.439677	+	0.195520i
$35$	−0.579157	+	2.59265i	−0.0978954	+	0.438238i
$36$	8.51274	+	9.43726i	1.41879	+	1.57288i
$37$	−3.23405	+	3.23405i	−0.531674	+	0.531674i	−0.921070	−	0.389396i	$-0.872684\pi$
$37$	−3.23405	+	3.23405i	−0.531674	+	0.531674i	0.389396	+	0.921070i	$0.372684\pi$
$38$	−1.00833	−	2.62325i	−0.163572	−	0.425548i
$39$	4.44992			0.712557
$40$	−0.604547	−	6.29560i	−0.0955873	−	0.995421i
$41$	11.1800			1.74602			0.873012	−	0.487699i	$-0.162164\pi$
$41$	11.1800			1.74602			0.873012	+	0.487699i	$0.162164\pi$
$42$	−1.84375	−	4.79667i	−0.284496	−	0.740142i
$43$	−5.01326	+	5.01326i	−0.764515	+	0.764515i	−0.977135	−	0.212620i	$-0.931800\pi$
$43$	−5.01326	+	5.01326i	−0.764515	+	0.764515i	0.212620	+	0.977135i	$0.431800\pi$
$44$	1.82214	+	2.02004i	0.274699	+	0.304532i
$45$	−11.9965	+	7.61547i	−1.78833	+	1.13525i
$46$	1.53421	+	0.682246i	0.226206	+	0.100592i
$47$	4.22980	+	4.22980i	0.616979	+	0.616979i	0.944755	−	0.327776i	$-0.106299\pi$
$47$	4.22980	+	4.22980i	0.616979	+	0.616979i	−0.327776	+	0.944755i	$0.606299\pi$
$48$	7.71632	+	9.49387i	1.11375	+	1.37032i
$49$		−	5.58855i		−	0.798364i
$50$	7.05245	+	0.512785i	0.997367	+	0.0725188i
$51$		−	6.06815i		−	0.849710i
$52$	2.90598	+	0.149673i	0.402986	+	0.0207560i
$53$	9.44159	+	9.44159i	1.29690	+	1.29690i	0.930429	+	0.366473i	$0.119435\pi$
$53$	9.44159	+	9.44159i	1.29690	+	1.29690i	0.366473	+	0.930429i	$0.380565\pi$
$54$	5.89599	−	13.2587i	0.802342	−	1.80427i
$55$	−2.56783	+	1.63009i	−0.346247	+	0.219801i
$56$	−1.04270	−	3.19443i	−0.139337	−	0.426874i
$57$	−4.29782	+	4.29782i	−0.569260	+	0.569260i
$58$	9.30681	−	3.57736i	1.22204	−	0.469730i
$59$	10.8983			1.41884			0.709422	−	0.704784i	$-0.248956\pi$
$59$	10.8983			1.41884			0.709422	+	0.704784i	$0.248956\pi$
$60$	−11.9097	+	6.72703i	−1.53754	+	0.868456i
$61$	−10.1104			−1.29451			−0.647254	−	0.762274i	$-0.724083\pi$
$61$	−10.1104			−1.29451			−0.647254	+	0.762274i	$0.724083\pi$
$62$	1.32005	−	0.507403i	0.167647	−	0.0644402i
$63$	−5.33842	+	5.33842i	−0.672578	+	0.672578i
$64$	4.71974	+	6.45942i	0.589967	+	0.807427i
$65$	−0.709252	+	3.17503i	−0.0879719	+	0.393814i
$66$	2.39063	−	5.37595i	0.294266	−	0.661733i
$67$	2.31705	+	2.31705i	0.283073	+	0.283073i	0.834333	−	0.551261i	$-0.185853\pi$
$67$	2.31705	+	2.31705i	0.283073	+	0.283073i	−0.551261	+	0.834333i	$0.685853\pi$
$68$	0.204102	−	3.96274i	0.0247511	−	0.480553i
$69$		−	3.63134i		−	0.437161i
$70$	3.71631	−	0.551000i	0.444183	−	0.0658572i
$71$		−	7.20426i		−	0.854989i	−0.904018	−	0.427494i	$-0.859396\pi$
$71$		−	7.20426i		−	0.854989i	0.904018	−	0.427494i	$-0.140604\pi$
$72$	8.13830	−	16.0258i	0.959108	−	1.88865i
$73$	−5.40068	−	5.40068i	−0.632102	−	0.632102i	0.316493	−	0.948595i	$-0.397495\pi$
$73$	−5.40068	−	5.40068i	−0.632102	−	0.632102i	−0.948595	+	0.316493i	$0.897495\pi$
$74$	5.91008	+	2.62815i	0.687033	+	0.305516i
$75$	−5.18413	−	14.3872i	−0.598612	−	1.66129i
$76$	−2.95121	+	2.66209i	−0.338527	+	0.305363i
$77$	−1.14268	+	1.14268i	−0.130221	+	0.130221i
$78$	−2.25790	−	5.87413i	−0.255657	−	0.665115i
$79$	3.78916			0.426314			0.213157	−	0.977018i	$-0.431625\pi$
$79$	3.78916			0.426314			0.213157	+	0.977018i	$0.431625\pi$
$80$	−8.00378	+	3.99244i	−0.894849	+	0.446368i
$81$	−12.3180			−1.36867
$82$	−5.67277	−	14.7582i	−0.626452	−	1.62977i
$83$	−12.2588	+	12.2588i	−1.34558	+	1.34558i	−0.455177	+	0.890401i	$0.650424\pi$
$83$	−12.2588	+	12.2588i	−1.34558	+	1.34558i	−0.890401	+	0.455177i	$0.849576\pi$
$84$	−5.39634	+	4.86769i	−0.588789	+	0.531108i
$85$	4.32964	+	0.967173i	0.469616	+	0.104905i
$86$	9.16152	+	4.07403i	0.987912	+	0.439314i
$87$	−15.2479	−	15.2479i	−1.63474	−	1.63474i
$88$	1.74200	−	3.43030i	0.185697	−	0.365671i
$89$			2.73953i			0.290390i	0.989403	+	0.145195i	$0.0463809\pi$
$89$			2.73953i			0.290390i	−0.989403	+	0.145195i	$0.953619\pi$
$90$	16.1399	+	11.9719i	1.70129	+	1.26195i
$91$			1.72850i			0.181197i
$92$	0.122140	−	2.37141i	0.0127340	−	0.247236i
$93$	−2.16272	−	2.16272i	−0.224263	−	0.224263i
$94$	3.43735	−	7.72977i	0.354535	−	0.797265i
$95$	−2.38150	−	3.75152i	−0.244337	−	0.384898i
$96$	8.61713	−	15.0032i	0.879483	−	1.53125i
$97$	1.63417	−	1.63417i	0.165924	−	0.165924i	−0.619261	−	0.785185i	$-0.712568\pi$
$97$	1.63417	−	1.63417i	0.165924	−	0.165924i	0.785185	+	0.619261i	$0.212568\pi$
$98$	−7.37718	+	2.83564i	−0.745208	+	0.286443i
$99$	−8.64376			−0.868730
$100$	−2.90153	−	9.56980i	−0.290153	−	0.956980i
$101$	−11.5667			−1.15093			−0.575467	−	0.817825i	$-0.695180\pi$
$101$	−11.5667			−1.15093			−0.575467	+	0.817825i	$0.695180\pi$
$102$	−8.01028	+	3.07899i	−0.793136	+	0.304866i
$103$	10.4523	−	10.4523i	1.02990	−	1.02990i	0.0303584	−	0.999539i	$-0.490335\pi$
$103$	10.4523	−	10.4523i	1.02990	−	1.02990i	0.999539	−	0.0303584i	$-0.00966488\pi$
$104$	−1.27692	−	3.91199i	−0.125213	−	0.383602i
$105$	−4.35462	−	6.85973i	−0.424967	−	0.669441i
$106$	7.67272	−	17.2541i	0.745240	−	1.67587i
$107$	−1.80579	−	1.80579i	−0.174573	−	0.174573i	0.614412	−	0.788985i	$-0.289393\pi$
$107$	−1.80579	−	1.80579i	−0.174573	−	0.174573i	−0.788985	+	0.614412i	$0.789393\pi$
$108$	−20.4938	−	1.05554i	−1.97202	−	0.101569i
$109$			5.06780i			0.485407i	0.970101	+	0.242703i	$0.0780342\pi$
$109$			5.06780i			0.485407i	−0.970101	+	0.242703i	$0.921966\pi$
$110$	3.45473	+	2.56257i	0.329395	+	0.244331i
$111$		−	13.9887i		−	1.32774i
$112$	−3.68775	+	2.99729i	−0.348460	+	0.283217i
$113$	13.4980	+	13.4980i	1.26979	+	1.26979i	0.946198	+	0.323589i	$0.104889\pi$
$113$	13.4980	+	13.4980i	1.26979	+	1.26979i	0.323589	+	0.946198i	$0.395111\pi$
$114$	7.85408	+	3.49263i	0.735602	+	0.327115i
$115$	2.59097	+	0.578782i	0.241609	+	0.0539717i
$116$	−9.44461	−	10.4703i	−0.876910	−	0.972146i
$117$	−6.53758	+	6.53758i	−0.604399	+	0.604399i
$118$	−5.52985	−	14.3864i	−0.509064	−	1.32438i
$119$	2.35708			0.216073
$120$	14.9231	+	12.3081i	1.36228	+	1.12357i
$121$	9.14981			0.831801
$122$	5.13006	+	13.3463i	0.464454	+	1.20832i
$123$	−24.1792	+	24.1792i	−2.18016	+	2.18016i
$124$	−1.33960	−	1.48508i	−0.120299	−	0.133365i
$125$	11.0916	−	1.40578i	0.992064	−	0.125737i
$126$	9.75573	+	4.33827i	0.869110	+	0.386484i
$127$	1.54632	+	1.54632i	0.137214	+	0.137214i	0.772377	−	0.635164i	$-0.219067\pi$
$127$	1.54632	+	1.54632i	0.137214	+	0.137214i	−0.635164	+	0.772377i	$0.719067\pi$
$128$	6.13197	−	9.50784i	0.541995	−	0.840382i
$129$		−	21.6845i		−	1.90922i
$130$	4.55109	−	0.674771i	0.399157	−	0.0591813i
$131$			11.3974i			0.995792i	0.867237	+	0.497896i	$0.165894\pi$
$131$			11.3974i			0.995792i	−0.867237	+	0.497896i	$0.834106\pi$
$132$	−8.30955	−	0.427986i	−0.723254	−	0.0372514i
$133$	−1.66942	−	1.66942i	−0.144757	−	0.144757i
$134$	1.88295	−	4.23431i	0.162662	−	0.365788i
$135$	5.00185	−	22.3913i	0.430491	−	1.92713i
$136$	−5.33460	+	1.74128i	−0.457438	+	0.149314i
$137$	10.6430	−	10.6430i	0.909289	−	0.909289i	−0.0869261	−	0.996215i	$-0.527704\pi$
$137$	10.6430	−	10.6430i	0.909289	−	0.909289i	0.996215	+	0.0869261i	$0.0277044\pi$
$138$	−4.79356	+	1.84255i	−0.408055	+	0.156848i
$139$	10.8484			0.920152			0.460076	−	0.887880i	$-0.347822\pi$
$139$	10.8484			0.920152			0.460076	+	0.887880i	$0.347822\pi$
$140$	−2.61301	−	4.62614i	−0.220840	−	0.390981i
$141$	−18.2957			−1.54078
$142$	−9.51001	+	3.65546i	−0.798063	+	0.306760i
$143$	−1.39936	+	1.39936i	−0.117021	+	0.117021i
$144$	−25.2843	−	2.61148i	−2.10702	−	0.217623i
$145$	13.3097	−	8.44912i	1.10531	−	0.701661i
$146$	−4.38887	+	9.86952i	−0.363226	+	0.816807i
$147$	12.0864	+	12.0864i	0.996873	+	0.996873i
$148$	0.470509	−	9.13516i	0.0386756	−	0.750905i
$149$			15.4076i			1.26224i	0.775684	+	0.631121i	$0.217405\pi$
$149$			15.4076i			1.26224i	−0.775684	+	0.631121i	$0.782595\pi$
$150$	−16.3615	+	14.1434i	−1.33591	+	1.15481i
$151$			19.8489i			1.61528i	0.589677	+	0.807639i	$0.299255\pi$
$151$			19.8489i			1.61528i	−0.589677	+	0.807639i	$0.700745\pi$
$152$	5.01156	+	2.54500i	0.406491	+	0.206427i
$153$	8.91499	+	8.91499i	0.720734	+	0.720734i
$154$	2.08821	+	0.928604i	0.168272	+	0.0748290i
$155$	1.88781	−	1.19840i	0.151633	−	0.0962579i
$156$	−6.60851	+	5.96110i	−0.529104	+	0.477270i
$157$	−8.77748	+	8.77748i	−0.700520	+	0.700520i	−0.964522	−	0.264002i	$-0.914957\pi$
$157$	−8.77748	+	8.77748i	−0.700520	+	0.700520i	0.264002	+	0.964522i	$0.414957\pi$
$158$	−1.92263	−	5.00190i	−0.152956	−	0.397930i
$159$	−40.8390			−3.23874
$160$	9.33137	+	8.53964i	0.737710	+	0.675118i
$161$	1.41054			0.111166
$162$	6.25021	+	16.2605i	0.491063	+	1.27754i
$163$	11.1909	−	11.1909i	0.876541	−	0.876541i	−0.116634	−	0.993175i	$-0.537211\pi$
$163$	11.1909	−	11.1909i	0.876541	−	0.876541i	0.993175	+	0.116634i	$0.0372106\pi$
$164$	−16.6033	+	14.9767i	−1.29650	+	1.16949i
$165$	2.02808	−	9.07891i	0.157886	−	0.706792i
$166$	22.4024	+	9.96212i	1.73877	+	0.773211i
$167$	−3.68111	−	3.68111i	−0.284853	−	0.284853i	0.550188	−	0.835041i	$-0.314556\pi$
$167$	−3.68111	−	3.68111i	−0.284853	−	0.284853i	−0.835041	+	0.550188i	$0.814556\pi$
$168$	9.16373	+	4.65358i	0.706997	+	0.359031i
$169$		−	10.8832i		−	0.837171i
$170$	−0.920153	−	6.20611i	−0.0705725	−	0.475987i
$171$		−	12.6282i		−	0.965706i
$172$	0.729361	−	14.1609i	0.0556132	−	1.07976i
$173$	−14.4593	−	14.4593i	−1.09932	−	1.09932i	−0.994490	−	0.104830i	$-0.966570\pi$
$173$	−14.4593	−	14.4593i	−1.09932	−	1.09932i	−0.104830	−	0.994490i	$-0.533430\pi$
$174$	−12.3912	+	27.8648i	−0.939374	+	2.11243i
$175$	5.58850	−	2.01370i	0.422451	−	0.152221i
$176$	−5.41208	−	0.558984i	−0.407951	−	0.0421350i
$177$	−23.5700	+	23.5700i	−1.77163	+	1.77163i
$178$	3.61633	−	1.39005i	0.271055	−	0.104188i
$179$	10.7803			0.805759			0.402880	−	0.915253i	$-0.368009\pi$
$179$	10.7803			0.805759			0.402880	+	0.915253i	$0.368009\pi$
$180$	7.61409	−	27.3801i	0.567521	−	2.04079i
$181$	−10.7634			−0.800039			−0.400020	−	0.916507i	$-0.630997\pi$
$181$	−10.7634			−0.800039			−0.400020	+	0.916507i	$0.630997\pi$
$182$	2.28172	−	0.877048i	0.169132	−	0.0650112i
$183$	21.8660	−	21.8660i	1.61638	−	1.61638i
$184$	−3.19236	+	1.04203i	−0.235344	+	0.0768193i
$185$	9.98096	+	2.22959i	0.733815	+	0.163922i
$186$	−1.75753	+	3.95227i	−0.128869	+	0.289795i
$187$	1.90825	+	1.90825i	0.139545	+	0.139545i
$188$	−11.9478	−	0.615377i	−0.871385	−	0.0448810i
$189$		−	12.1899i		−	0.886686i
$190$	−3.74383	+	5.04724i	−0.271606	+	0.366165i
$191$			18.2296i			1.31904i	0.751685	+	0.659522i	$0.229241\pi$
$191$			18.2296i			1.31904i	−0.751685	+	0.659522i	$0.770759\pi$
$192$	−24.1774	−	3.76243i	−1.74485	−	0.271530i
$193$	−3.16147	−	3.16147i	−0.227568	−	0.227568i	0.584108	−	0.811676i	$-0.301444\pi$
$193$	−3.16147	−	3.16147i	−0.227568	−	0.227568i	−0.811676	+	0.584108i	$0.801444\pi$
$194$	−2.98637	−	1.32801i	−0.214409	−	0.0953453i
$195$	−5.33279	−	8.40061i	−0.381889	−	0.601580i
$196$	7.48641	+	8.29947i	0.534743	+	0.592819i
$197$	2.42122	−	2.42122i	0.172505	−	0.172505i	−0.615574	−	0.788079i	$-0.711076\pi$
$197$	2.42122	−	2.42122i	0.172505	−	0.172505i	0.788079	+	0.615574i	$0.211076\pi$
$198$	4.38587	+	11.4102i	0.311690	+	0.810889i
$199$	−11.8708			−0.841496			−0.420748	−	0.907177i	$-0.638232\pi$
$199$	−11.8708			−0.841496			−0.420748	+	0.907177i	$0.638232\pi$
$200$	−11.1604	+	8.68592i	−0.789160	+	0.614187i
$201$	−10.0222			−0.706914
$202$	5.86900	+	15.2687i	0.412941	+	1.07430i
$203$	5.92281	−	5.92281i	0.415700	−	0.415700i
$204$	8.12888	+	9.01171i	0.569135	+	0.630946i
$205$	−13.3981	−	21.1058i	−0.935766	−	1.47409i
$206$	−19.1012	−	8.49409i	−1.33084	−	0.591811i
$207$	5.33496	+	5.33496i	0.370805	+	0.370805i
$208$	−4.51612	+	3.67056i	−0.313137	+	0.254508i
$209$		−	2.70307i		−	0.186975i
$210$	−6.84566	+	9.22898i	−0.472395	+	0.636860i
$211$			23.0494i			1.58679i	0.608708	+	0.793395i	$0.291688\pi$
$211$			23.0494i			1.58679i	−0.608708	+	0.793395i	$0.708312\pi$
$212$	−26.6695	−	1.37362i	−1.83167	−	0.0943407i
$213$	15.5808	+	15.5808i	1.06758	+	1.06758i
$214$	−1.46748	+	3.30001i	−0.100315	+	0.225584i
$215$	15.4720	+	3.45620i	1.05518	+	0.235711i
$216$	9.00524	+	27.5885i	0.612729	+	1.87716i
$217$	0.840075	−	0.840075i	0.0570280	−	0.0570280i
$218$	6.68977	−	2.57142i	0.453088	−	0.174158i
$219$	23.3603			1.57854
$220$	1.62979	−	5.86068i	0.109880	−	0.395127i
$221$	2.88655			0.194170
$222$	−18.4658	+	7.09788i	−1.23934	+	0.476379i
$223$	−10.1443	+	10.1443i	−0.679310	+	0.679310i	−0.959844	−	0.280534i	$-0.909488\pi$
$223$	−10.1443	+	10.1443i	−0.679310	+	0.679310i	0.280534	+	0.959844i	$0.409488\pi$
$224$	5.82776	+	3.34720i	0.389383	+	0.223644i
$225$	28.7532	+	13.5207i	1.91688	+	0.901379i
$226$	10.9692	−	24.6670i	0.729659	−	1.64083i
$227$	11.2533	+	11.2533i	0.746910	+	0.746910i	0.973898	−	0.226988i	$-0.0728878\pi$
$227$	11.2533	+	11.2533i	0.746910	+	0.746910i	−0.226988	+	0.973898i	$0.572888\pi$
$228$	0.625274	−	12.1400i	0.0414098	−	0.803990i
$229$		−	14.3552i		−	0.948616i	−0.880359	−	0.474308i	$-0.842698\pi$
$229$		−	14.3552i		−	0.948616i	0.880359	−	0.474308i	$-0.157302\pi$
$230$	−0.550643	−	3.71390i	−0.0363084	−	0.244887i
$231$		−	4.94261i		−	0.325200i
$232$	−9.02918	+	17.7801i	−0.592795	+	1.16732i
$233$	2.55722	+	2.55722i	0.167529	+	0.167529i	0.785892	−	0.618363i	$-0.212204\pi$
$233$	2.55722	+	2.55722i	0.167529	+	0.167529i	−0.618363	+	0.785892i	$0.712204\pi$
$234$	11.9471	+	5.31277i	0.781009	+	0.347307i
$235$	2.91607	−	13.0541i	0.190223	−	0.851553i
$236$	−16.1850	+	14.5994i	−1.05355	+	0.950340i
$237$	−8.19489	+	8.19489i	−0.532315	+	0.532315i
$238$	−1.19599	−	3.11147i	−0.0775245	−	0.201687i
$239$	−8.68779			−0.561966			−0.280983	−	0.959713i	$-0.590661\pi$
$239$	−8.68779			−0.561966			−0.280983	+	0.959713i	$0.590661\pi$
$240$	8.67539	−	25.9444i	0.559994	−	1.67471i
$241$	17.4784			1.12588			0.562940	−	0.826497i	$-0.309670\pi$
$241$	17.4784			1.12588			0.562940	+	0.826497i	$0.309670\pi$
$242$	−4.64264	−	12.0782i	−0.298440	−	0.776419i
$243$	4.87468	−	4.87468i	0.312711	−	0.312711i
$244$	15.0148	−	13.5439i	0.961227	−	0.867061i
$245$	−10.5501	+	6.69732i	−0.674023	+	0.427876i
$246$	44.1864	+	19.6492i	2.81722	+	1.25279i
$247$	−2.04442	−	2.04442i	−0.130084	−	0.130084i
$248$	−1.28068	+	2.52188i	−0.0813230	+	0.160139i
$249$		−	53.0246i		−	3.36030i
$250$	−7.48362	−	13.9282i	−0.473306	−	0.880898i
$251$		−	5.75239i		−	0.363088i	−0.983383	−	0.181544i	$-0.941891\pi$
$251$		−	5.75239i		−	0.363088i	0.983383	−	0.181544i	$-0.0581095\pi$
$252$	0.776667	−	15.0793i	0.0489254	−	0.949909i
$253$	1.14194	+	1.14194i	0.0717934	+	0.0717934i
$254$	1.25662	−	2.82583i	0.0788473	−	0.177309i
$255$	−11.4555	+	7.27207i	−0.717372	+	0.455395i
$256$	−15.6622	−	3.27022i	−0.978890	−	0.204389i
$257$	−13.7537	+	13.7537i	−0.857932	+	0.857932i	−0.991094	−	0.133162i	$-0.957487\pi$
$257$	−13.7537	+	13.7537i	−0.857932	+	0.857932i	0.133162	+	0.991094i	$0.457487\pi$
$258$	−28.6247	+	11.0028i	−1.78210	+	0.685004i
$259$	5.43368			0.337633
$260$	−3.19997	−	5.66531i	−0.198454	−	0.351347i
$261$	44.8027			2.77322
$262$	15.0451	−	5.78305i	0.929491	−	0.357278i
$263$	4.25251	−	4.25251i	0.262221	−	0.262221i	−0.563735	−	0.825956i	$-0.690636\pi$
$263$	4.25251	−	4.25251i	0.262221	−	0.262221i	0.825956	+	0.563735i	$0.190636\pi$
$264$	3.65132	+	11.1862i	0.224724	+	0.688464i
$265$	6.50913	−	29.1388i	0.399853	−	1.78998i
$266$	−1.35666	+	3.05080i	−0.0831821	+	0.187057i
$267$	−5.92483	−	5.92483i	−0.362594	−	0.362594i
$268$	−6.54493	−	0.337099i	−0.399795	−	0.0205916i
$269$		−	23.4966i		−	1.43261i	−0.697785	−	0.716307i	$-0.745831\pi$
$269$		−	23.4966i		−	1.43261i	0.697785	−	0.716307i	$-0.254169\pi$
$270$	−32.0956	+	4.75868i	−1.95328	+	0.289604i
$271$			16.7654i			1.01843i	0.860640	+	0.509213i	$0.170064\pi$
$271$			16.7654i			1.01843i	−0.860640	+	0.509213i	$0.829936\pi$
$272$	5.00538	+	6.15842i	0.303495	+	0.373409i
$273$	−3.73827	−	3.73827i	−0.226250	−	0.226250i
$274$	−19.4495	−	8.64900i	−1.17499	−	0.522505i
$275$	6.15459	+	2.89409i	0.371136	+	0.174520i
$276$	4.86453	+	5.39284i	0.292810	+	0.324611i
$277$	12.1355	−	12.1355i	0.729150	−	0.729150i	−0.241300	−	0.970450i	$-0.577574\pi$
$277$	12.1355	−	12.1355i	0.729150	−	0.729150i	0.970450	+	0.241300i	$0.0775739\pi$
$278$	−5.50453	−	14.3205i	−0.330140	−	0.858887i
$279$	6.35469			0.380445
$280$	−4.78091	+	5.79664i	−0.285714	+	0.346415i
$281$	−5.22999			−0.311995			−0.155998	−	0.987757i	$-0.549859\pi$
$281$	−5.22999			−0.311995			−0.155998	+	0.987757i	$0.549859\pi$
$282$	9.28330	+	24.1513i	0.552812	+	1.43819i
$283$	6.22976	−	6.22976i	0.370321	−	0.370321i	−0.497273	−	0.867594i	$-0.665665\pi$
$283$	6.22976	−	6.22976i	0.370321	−	0.370321i	0.867594	+	0.497273i	$0.165665\pi$
$284$	9.65082	+	10.6989i	0.572671	+	0.634865i
$285$	13.2640	+	2.96296i	0.785691	+	0.175511i
$286$	2.55728	+	1.13719i	0.151215	+	0.0672437i
$287$	−9.39205	−	9.39205i	−0.554395	−	0.554395i
$288$	9.38202	+	34.7017i	0.552841	+	2.04482i
$289$			13.0638i			0.768456i
$290$	−17.9067	−	13.2824i	−1.05152	−	0.779970i
$291$			7.06848i			0.414362i
$292$	15.2552	+	0.785725i	0.892744	+	0.0459811i
$293$	12.5794	+	12.5794i	0.734898	+	0.734898i	0.971586	−	0.236688i	$-0.0760619\pi$
$293$	12.5794	+	12.5794i	0.734898	+	0.734898i	−0.236688	+	0.971586i	$0.576062\pi$
$294$	9.82206	−	22.0875i	0.572834	−	1.28817i
$295$	−13.0606	−	20.5740i	−0.760417	−	1.19787i
$296$	−12.2976	+	4.01411i	−0.714786	+	0.233315i
$297$	9.86871	−	9.86871i	0.572641	−	0.572641i
$298$	20.3389	−	7.81788i	1.17820	−	0.452878i
$299$	1.72738			0.0998972
$300$	26.9720	+	14.4216i	1.55723	+	0.832631i
$301$	8.42303			0.485496
$302$	26.2016	−	10.0714i	1.50773	−	0.579543i
$303$	25.0156	−	25.0156i	1.43711	−	1.43711i
$304$	0.816658	−	7.90686i	0.0468385	−	0.453490i
$305$	12.1164	+	19.0866i	0.693781	+	1.09290i
$306$	7.24477	−	16.2918i	0.414156	−	0.931338i
$307$	−10.2488	−	10.2488i	−0.584928	−	0.584928i	0.351325	−	0.936253i	$-0.385731\pi$
$307$	−10.2488	−	10.2488i	−0.584928	−	0.584928i	−0.936253	+	0.351325i	$0.885731\pi$
$308$	0.166245	−	3.22772i	0.00947268	−	0.183916i
$309$			45.2108i			2.57195i
$310$	−2.53984	−	1.88394i	−0.144253	−	0.107001i
$311$		−	15.1016i		−	0.856332i	−0.903700	−	0.428166i	$-0.859160\pi$
$311$		−	15.1016i		−	0.856332i	0.903700	−	0.428166i	$-0.140840\pi$
$312$	11.2222	+	5.69890i	0.635329	+	0.322637i
$313$	6.04069	+	6.04069i	0.341440	+	0.341440i	0.856909	−	0.515468i	$-0.172382\pi$
$313$	6.04069	+	6.04069i	0.341440	+	0.341440i	−0.515468	+	0.856909i	$0.672382\pi$
$314$	16.0405	+	7.13303i	0.905216	+	0.402540i
$315$	16.4755	+	3.68036i	0.928289	+	0.207365i
$316$	−5.62723	+	5.07596i	−0.316556	+	0.285545i
$317$	6.18381	−	6.18381i	0.347317	−	0.347317i	−0.511792	−	0.859109i	$-0.671018\pi$
$317$	6.18381	−	6.18381i	0.347317	−	0.347317i	0.859109	+	0.511792i	$0.171018\pi$
$318$	20.7218	+	53.9096i	1.16202	+	3.02310i
$319$	9.58997			0.536935
$320$	6.53802	−	16.6510i	0.365487	−	0.930817i
$321$	7.81085			0.435959
$322$	−0.715711	−	1.86199i	−0.0398850	−	0.103764i
$323$	−2.78788	+	2.78788i	−0.155122	+	0.155122i
$324$	18.2933	−	16.5012i	1.01630	−	0.916734i
$325$	6.84384	−	2.46603i	0.379628	−	0.136791i
$326$	−20.4509	−	9.09431i	−1.13267	−	0.503687i
$327$	−10.9602	−	10.9602i	−0.606101	−	0.606101i
$328$	28.1946	+	14.3180i	1.55679	+	0.790577i
$329$		−	7.10669i		−	0.391805i
$330$	−13.0137	+	1.92949i	−0.716381	+	0.106215i
$331$			25.3527i			1.39351i	0.717310	+	0.696754i	$0.245373\pi$
$331$			25.3527i			1.39351i	−0.717310	+	0.696754i	$0.754627\pi$
$332$	1.78349	−	34.6272i	0.0978816	−	1.90042i
$333$	20.5514	+	20.5514i	1.12621	+	1.12621i
$334$	−2.99146	+	6.72708i	−0.163685	+	0.368089i
$335$	1.59740	−	7.15091i	0.0872752	−	0.390696i
$336$	1.49327	−	14.4579i	0.0814648	−	0.788740i
$337$	13.7999	−	13.7999i	0.751726	−	0.751726i	−0.223075	−	0.974801i	$-0.571610\pi$
$337$	13.7999	−	13.7999i	0.751726	−	0.751726i	0.974801	+	0.223075i	$0.0716096\pi$
$338$	−14.3664	+	5.52218i	−0.781431	+	0.300367i
$339$	−58.3848			−3.17103
$340$	−7.72551	+	4.36365i	−0.418975	+	0.236652i
$341$	1.36022			0.0736599
$342$	−16.6700	+	6.40761i	−0.901408	+	0.346484i
$343$	−10.5753	+	10.5753i	−0.571014	+	0.571014i
$344$	−19.0632	+	6.22247i	−1.02782	+	0.335493i
$345$	−6.85528	+	4.35180i	−0.369076	+	0.234293i
$346$	−11.7504	+	26.4238i	−0.631704	+	1.42055i
$347$	−10.9948	−	10.9948i	−0.590231	−	0.590231i	0.347463	−	0.937694i	$-0.387043\pi$
$347$	−10.9948	−	10.9948i	−0.590231	−	0.590231i	−0.937694	+	0.347463i	$0.887043\pi$
$348$	43.0704	+	2.21836i	2.30882	+	0.118916i
$349$		−	7.26772i		−	0.389032i	−0.980899	−	0.194516i	$-0.937686\pi$
$349$		−	7.26772i		−	0.389032i	0.980899	−	0.194516i	$-0.0623136\pi$
$350$	−5.49381	−	6.35537i	−0.293657	−	0.339709i
$351$		−	14.9281i		−	0.796804i
$352$	2.00821	+	7.42786i	0.107038	+	0.395906i
$353$	13.7371	+	13.7371i	0.731151	+	0.731151i	0.970848	−	0.239697i	$-0.0770480\pi$
$353$	13.7371	+	13.7371i	0.731151	+	0.731151i	−0.239697	+	0.970848i	$0.577048\pi$
$354$	43.0732	+	19.1542i	2.28932	+	1.01803i
$355$	−13.6003	+	8.63360i	−0.721829	+	0.458224i
$356$	−3.66987	−	4.06843i	−0.194503	−	0.215627i
$357$	−5.09770	+	5.09770i	−0.269799	+	0.269799i
$358$	−5.46997	−	14.2306i	−0.289097	−	0.752111i
$359$	5.57287			0.294125			0.147062	−	0.989127i	$-0.453018\pi$
$359$	5.57287			0.294125			0.147062	+	0.989127i	$0.453018\pi$
$360$	−40.0066	+	3.84171i	−2.10853	+	0.202476i
$361$	−15.0509			−0.792153
$362$	5.46139	+	14.2083i	0.287044	+	0.746772i
$363$	−19.7885	+	19.7885i	−1.03862	+	1.03862i
$364$	−2.31550	−	2.56698i	−0.121365	−	0.134546i
$365$	−3.72329	+	16.6677i	−0.194886	+	0.872425i
$366$	−39.9592	−	17.7694i	−2.08870	−	0.928823i
$367$	−21.6875	−	21.6875i	−1.13208	−	1.13208i	−0.989831	−	0.142247i	$-0.954567\pi$
$367$	−21.6875	−	21.6875i	−1.13208	−	1.13208i	−0.142247	−	0.989831i	$-0.545433\pi$
$368$	2.99535	+	3.68536i	0.156143	+	0.192113i
$369$		−	71.0455i		−	3.69848i
$370$	−2.12119	−	14.3067i	−0.110276	−	0.743770i
$371$		−	15.8633i		−	0.823581i
$372$	6.10899	+	0.314646i	0.316736	+	0.0163136i
$373$	−4.46665	−	4.46665i	−0.231274	−	0.231274i	0.581950	−	0.813224i	$-0.302290\pi$
$373$	−4.46665	−	4.46665i	−0.231274	−	0.231274i	−0.813224	+	0.581950i	$0.802290\pi$
$374$	1.55074	−	3.48724i	0.0801867	−	0.180321i
$375$	−20.9477	+	27.0283i	−1.08173	+	1.39574i
$376$	5.25003	+	16.0840i	0.270750	+	0.829470i
$377$	7.25324	−	7.25324i	0.373561	−	0.373561i
$378$	−16.0913	+	6.18520i	−0.827649	+	0.318132i
$379$	−21.9896			−1.12953			−0.564766	−	0.825251i	$-0.691034\pi$
$379$	−21.9896			−1.12953			−0.564766	+	0.825251i	$0.691034\pi$
$380$	8.56226	+	2.38107i	0.439235	+	0.122146i
$381$	−6.68851			−0.342663
$382$	24.0640	−	9.24973i	1.23122	−	0.473257i
$383$	−20.1978	+	20.1978i	−1.03206	+	1.03206i	−0.0325907	+	0.999469i	$0.510376\pi$
$383$	−20.1978	+	20.1978i	−1.03206	+	1.03206i	−0.999469	+	0.0325907i	$0.989624\pi$
$384$	7.30105	+	33.8245i	0.372580	+	1.72610i
$385$	3.52657	+	0.787779i	0.179731	+	0.0401489i
$386$	−2.56917	+	5.77746i	−0.130768	+	0.294065i
$387$	31.8577	+	31.8577i	1.61942	+	1.61942i
$388$	−0.237749	+	4.61600i	−0.0120699	+	0.234342i
$389$			5.78420i			0.293271i	0.989191	+	0.146635i	$0.0468444\pi$
$389$			5.78420i			0.293271i	−0.989191	+	0.146635i	$0.953156\pi$
$390$	−8.38339	+	11.3021i	−0.424509	+	0.572302i
$391$		−	2.35555i		−	0.119125i
$392$	7.15712	−	14.0936i	0.361489	−	0.711836i
$393$	−24.6493	−	24.6493i	−1.24339	−	1.24339i
$394$	−4.42467	−	1.96761i	−0.222912	−	0.0991266i
$395$	−4.54094	−	7.15323i	−0.228479	−	0.359918i
$396$	12.8367	−	11.5792i	0.645069	−	0.581875i
$397$	−21.7503	+	21.7503i	−1.09161	+	1.09161i	−0.0962580	+	0.995356i	$0.530687\pi$
$397$	−21.7503	+	21.7503i	−1.09161	+	1.09161i	−0.995356	+	0.0962580i	$0.969313\pi$
$398$	6.02326	+	15.6701i	0.301919	+	0.785469i
$399$	7.22099			0.361501
$400$	17.1287	+	10.3251i	0.856435	+	0.516254i
$401$	−11.1257			−0.555590			−0.277795	−	0.960640i	$-0.589604\pi$
$401$	−11.1257			−0.555590			−0.277795	+	0.960640i	$0.589604\pi$
$402$	5.08531	+	13.2299i	0.253632	+	0.659847i
$403$	1.02878	−	1.02878i	0.0512472	−	0.0512472i
$404$	17.1776	−	15.4948i	0.854617	−	0.770895i
$405$	14.7619	+	23.2541i	0.733527	+	1.15551i
$406$	−10.8237	−	4.81317i	−0.537170	−	0.238874i
$407$	4.39900	+	4.39900i	0.218050	+	0.218050i
$408$	7.77133	−	15.3031i	0.384738	−	0.757618i
$409$			4.75304i			0.235023i	0.993072	+	0.117511i	$0.0374917\pi$
$409$			4.75304i			0.235023i	−0.993072	+	0.117511i	$0.962508\pi$
$410$	−21.0625	+	28.3954i	−1.04020	+	1.40235i
$411$			46.0354i			2.27076i
$412$	−1.52067	+	29.5245i	−0.0749180	+	1.45457i
$413$	−9.15543	−	9.15543i	−0.450509	−	0.450509i
$414$	4.33546	−	9.74941i	0.213076	−	0.479157i
$415$	37.8333	+	8.45135i	1.85716	+	0.414860i
$416$	7.13684	+	4.09907i	0.349912	+	0.200974i
$417$	−23.4621	+	23.4621i	−1.14894	+	1.14894i
$418$	−3.56819	+	1.37154i	−0.174526	+	0.0670844i
$419$	−10.8876			−0.531895			−0.265948	−	0.963987i	$-0.585685\pi$
$419$	−10.8876			−0.531895			−0.265948	+	0.963987i	$0.585685\pi$
$420$	15.6563	+	4.35383i	0.763947	+	0.212445i
$421$	−13.3209			−0.649221			−0.324610	−	0.945848i	$-0.605233\pi$
$421$	−13.3209			−0.649221			−0.324610	+	0.945848i	$0.605233\pi$
$422$	30.4265	−	11.6954i	1.48114	−	0.569321i
$423$	26.8791	−	26.8791i	1.30690	−	1.30690i
$424$	11.7189	+	35.9021i	0.569121	+	1.74356i
$425$	−3.36281	−	9.33262i	−0.163120	−	0.452698i
$426$	12.6617	−	28.4732i	0.613463	−	1.37953i
$427$	8.49353	+	8.49353i	0.411031	+	0.411031i
$428$	5.10080	+	0.262718i	0.246556	+	0.0126990i
$429$		−	6.05285i		−	0.292235i
$430$	−3.28817	−	22.1775i	−0.158570	−	1.06950i
$431$			36.5833i			1.76216i	0.472971	+	0.881078i	$0.343182\pi$
$431$			36.5833i			1.76216i	−0.472971	+	0.881078i	$0.656818\pi$
$432$	31.8490	−	25.8859i	1.53234	−	1.24543i
$433$	0.606656	+	0.606656i	0.0291540	+	0.0291540i	0.721534	−	0.692379i	$-0.243438\pi$
$433$	0.606656	+	0.606656i	0.0291540	+	0.0291540i	−0.692379	+	0.721534i	$0.743438\pi$
$434$	−1.53520	−	0.682688i	−0.0736920	−	0.0327701i
$435$	−10.5120	+	47.0582i	−0.504014	+	2.25627i
$436$	−6.78881	−	7.52611i	−0.325125	−	0.360435i
$437$	−1.66834	+	1.66834i	−0.0798076	+	0.0798076i
$438$	−11.8531	−	30.8369i	−0.566362	−	1.47344i
$439$	−21.5602			−1.02901			−0.514506	−	0.857487i	$-0.672025\pi$
$439$	−21.5602			−1.02901			−0.514506	+	0.857487i	$0.672025\pi$
$440$	−8.56337	+	0.822315i	−0.408243	+	0.0392023i
$441$	−35.5135			−1.69112
$442$	−1.46464	−	3.81040i	−0.0696659	−	0.181242i
$443$	10.3902	−	10.3902i	0.493654	−	0.493654i	−0.415801	−	0.909456i	$-0.636499\pi$
$443$	10.3902	−	10.3902i	0.493654	−	0.493654i	0.909456	+	0.415801i	$0.136499\pi$
$444$	18.7392	+	20.7743i	0.889322	+	0.985906i
$445$	5.17172	−	3.28306i	0.245163	−	0.155632i
$446$	18.5382	+	8.24374i	0.877809	+	0.390352i
$447$	−33.3224	−	33.3224i	−1.57609	−	1.57609i
$448$	1.46146	−	9.39133i	0.0690475	−	0.443699i
$449$			17.5258i			0.827096i	0.910482	+	0.413548i	$0.135711\pi$
$449$			17.5258i			0.827096i	−0.910482	+	0.413548i	$0.864289\pi$
$450$	3.25859	−	44.8161i	0.153611	−	2.11265i
$451$		−	15.2072i		−	0.716080i
$452$	−38.1276	−	1.96378i	−1.79337	−	0.0923683i
$453$	−42.9275	−	42.9275i	−2.01691	−	2.01691i
$454$	9.14503	−	20.5650i	0.429198	−	0.965162i
$455$	3.26309	−	2.07144i	0.152976	−	0.0971107i
$456$	−16.3427	+	5.33447i	−0.765317	+	0.249809i
$457$	−8.87041	+	8.87041i	−0.414940	+	0.414940i	−0.883455	−	0.468515i	$-0.844789\pi$
$457$	−8.87041	+	8.87041i	−0.414940	+	0.414940i	0.468515	+	0.883455i	$0.344789\pi$
$458$	−18.9496	+	7.28385i	−0.885456	+	0.340352i
$459$	−20.3568			−0.950172
$460$	−4.62315	+	2.61132i	−0.215555	+	0.121753i
$461$	21.3510			0.994414			0.497207	−	0.867632i	$-0.334359\pi$
$461$	21.3510			0.994414			0.497207	+	0.867632i	$0.334359\pi$
$462$	−6.52451	+	2.50789i	−0.303548	+	0.116678i
$463$	9.77091	−	9.77091i	0.454093	−	0.454093i	−0.442618	−	0.896710i	$-0.645950\pi$
$463$	9.77091	−	9.77091i	0.454093	−	0.454093i	0.896710	+	0.442618i	$0.145950\pi$
$464$	28.0521	+	2.89735i	1.30229	+	0.134506i
$465$	−1.49100	+	6.67461i	−0.0691435	+	0.309527i
$466$	2.07813	−	4.67322i	0.0962676	−	0.216483i
$467$	−2.05991	−	2.05991i	−0.0953214	−	0.0953214i	0.657838	−	0.753159i	$-0.271471\pi$
$467$	−2.05991	−	2.05991i	−0.0953214	−	0.0953214i	−0.753159	+	0.657838i	$0.771471\pi$
$468$	0.951128	−	18.4666i	0.0439659	−	0.853618i
$469$		−	3.89299i		−	0.179762i
$470$	−18.7117	+	2.77430i	−0.863105	+	0.127969i
$471$		−	37.9664i		−	1.74940i
$472$	27.4843	+	13.9572i	1.26507	+	0.642434i
$473$	6.81912	+	6.81912i	0.313543	+	0.313543i
$474$	14.9758	+	6.65959i	0.687862	+	0.305885i
$475$	−4.22817	+	8.99165i	−0.194002	+	0.412565i
$476$	−3.50046	+	3.15754i	−0.160444	+	0.144726i
$477$	59.9984	−	59.9984i	2.74714	−	2.74714i
$478$	4.40821	+	11.4683i	0.201627	+	0.524550i
$479$	−17.4441			−0.797041			−0.398520	−	0.917159i	$-0.630476\pi$
$479$	−17.4441			−0.797041			−0.398520	+	0.917159i	$0.630476\pi$
$480$	−38.6500	+	1.71229i	−1.76412	+	0.0781550i
$481$	6.65424			0.303407
$482$	−8.86858	−	23.0724i	−0.403953	−	1.05092i
$483$	−3.05060	+	3.05060i	−0.138807	+	0.138807i
$484$	−13.5882	+	12.2571i	−0.617647	+	0.557140i
$485$	−5.04339	−	1.12661i	−0.229008	−	0.0511568i
$486$	−8.90826	−	3.96141i	−0.404087	−	0.179693i
$487$	22.4465	+	22.4465i	1.01715	+	1.01715i	0.999850	+	0.0172963i	$0.00550586\pi$
$487$	22.4465	+	22.4465i	1.01715	+	1.01715i	0.0172963	+	0.999850i	$0.494494\pi$
$488$	−25.4973	−	12.9482i	−1.15421	−	0.586137i
$489$			48.4056i			2.18898i
$490$	14.1940	+	10.5285i	0.641219	+	0.475629i
$491$		−	4.38431i		−	0.197861i	−0.995094	−	0.0989306i	$-0.968458\pi$
$491$		−	4.38431i		−	0.197861i	0.995094	−	0.0989306i	$-0.0315422\pi$
$492$	3.51774	−	68.2986i	0.158592	−	3.07914i
$493$	−9.89090	−	9.89090i	−0.445464	−	0.445464i
$494$	−1.66140	+	3.73610i	−0.0747501	+	0.168095i
$495$	10.3587	+	16.3178i	0.465588	+	0.733430i
$496$	3.97883	+	0.410953i	0.178655	+	0.0184523i
$497$	−6.05212	+	6.05212i	−0.271475	+	0.271475i
$498$	−69.9954	+	26.9049i	−3.13657	+	1.20564i
$499$	−13.3109			−0.595878			−0.297939	−	0.954585i	$-0.596299\pi$
$499$	−13.3109			−0.595878			−0.297939	+	0.954585i	$0.596299\pi$
$500$	−14.5888	+	16.9460i	−0.652431	+	0.757848i
$501$	15.9224			0.711361
$502$	−7.59347	+	2.91878i	−0.338913	+	0.130272i
$503$	10.0701	−	10.0701i	0.449003	−	0.449003i	−0.446020	−	0.895023i	$-0.647159\pi$
$503$	10.0701	−	10.0701i	0.449003	−	0.449003i	0.895023	+	0.446020i	$0.147159\pi$
$504$	−20.2996	+	6.62606i	−0.904217	+	0.295148i
$505$	13.8616	+	21.8358i	0.616833	+	0.971682i
$506$	0.928002	−	2.08685i	0.0412547	−	0.0927719i
$507$	23.5373	+	23.5373i	1.04533	+	1.04533i
$508$	−4.36786	−	0.224968i	−0.193793	−	0.00998136i
$509$			18.2360i			0.808297i	0.914693	+	0.404149i	$0.132432\pi$
$509$			18.2360i			0.808297i	−0.914693	+	0.404149i	$0.867568\pi$
$510$	15.4121	+	11.4320i	0.682459	+	0.506219i
$511$			9.07396i			0.401408i
$512$	3.63019	+	22.3343i	0.160433	+	0.987047i
$513$	14.4179	+	14.4179i	0.636564	+	0.636564i
$514$	25.1343	+	11.1770i	1.10863	+	0.492995i
$515$	−32.2581	−	7.20594i	−1.42146	−	0.317532i
$516$	29.0486	+	32.2034i	1.27879	+	1.41767i
$517$	5.75344	−	5.75344i	0.253036	−	0.253036i
$518$	−2.75707	−	7.17276i	−0.121139	−	0.315153i
$519$	62.5428			2.74532
$520$	−5.85484	+	7.09873i	−0.256752	+	0.311300i
$521$	−29.2617			−1.28198			−0.640989	−	0.767550i	$-0.721476\pi$
$521$	−29.2617			−1.28198			−0.640989	+	0.767550i	$0.721476\pi$
$522$	−22.7330	−	59.1419i	−0.994997	−	2.58857i
$523$	19.2902	−	19.2902i	0.843503	−	0.843503i	−0.145809	−	0.989313i	$-0.546579\pi$
$523$	19.2902	−	19.2902i	0.843503	−	0.843503i	0.989313	+	0.145809i	$0.0465786\pi$
$524$	−15.2679	−	16.9260i	−0.666981	−	0.739418i
$525$	−7.73129	+	16.4414i	−0.337421	+	0.717562i
$526$	−7.77127	−	3.45580i	−0.338843	−	0.150680i
$527$	−1.40290	−	1.40290i	−0.0611112	−	0.0611112i
$528$	12.9137	−	10.4959i	0.561997	−	0.456774i
$529$			21.5904i			0.938712i
$530$	−41.7675	+	6.19268i	−1.81426	+	0.268993i
$531$		−	69.2556i		−	3.00544i
$532$	4.71559	+	0.242878i	0.204447	+	0.0105301i
$533$	−11.5018	−	11.5018i	−0.498197	−	0.498197i
$534$	−4.81482	+	10.8274i	−0.208358	+	0.468546i
$535$	−1.24493	+	5.57307i	−0.0538232	+	0.240945i
$536$	2.87593	+	8.81070i	0.124221	+	0.380564i
$537$	−23.3148	+	23.3148i	−1.00611	+	1.00611i
$538$	−31.0168	+	11.9223i	−1.33723	+	0.514005i
$539$	−7.60163			−0.327426
$540$	22.5671	+	39.9534i	0.971134	+	1.71932i
$541$	−8.79393			−0.378081			−0.189040	−	0.981969i	$-0.560538\pi$
$541$	−8.79393			−0.378081			−0.189040	+	0.981969i	$0.560538\pi$
$542$	22.1313	−	8.50682i	0.950619	−	0.365399i
$543$	23.2782	−	23.2782i	0.998965	−	0.998965i
$544$	5.58971	−	9.73217i	0.239657	−	0.417263i
$545$	9.56705	−	6.07325i	0.409807	−	0.260150i
$546$	−3.03791	+	6.83152i	−0.130010	+	0.292362i
$547$	11.0856	+	11.0856i	0.473988	+	0.473988i	0.903203	−	0.429215i	$-0.141210\pi$
$547$	11.0856	+	11.0856i	0.473988	+	0.473988i	−0.429215	+	0.903203i	$0.641210\pi$
$548$	−1.54840	+	30.0630i	−0.0661445	+	1.28423i
$549$			64.2487i			2.74207i
$550$	0.697499	−	9.59286i	0.0297414	−	0.409041i
$551$			14.0106i			0.596873i
$552$	4.65056	−	9.15779i	0.197941	−	0.389781i
$553$	−3.18318	−	3.18318i	−0.135363	−	0.135363i
$554$	−22.1771	−	9.86191i	−0.942213	−	0.418992i
$555$	−26.4080	+	16.7640i	−1.12096	+	0.711593i
$556$	−16.1108	+	14.5325i	−0.683252	+	0.616317i
$557$	−18.0908	+	18.0908i	−0.766533	+	0.766533i	−0.977494	−	0.210962i	$-0.932341\pi$
$557$	−18.0908	+	18.0908i	−0.766533	+	0.766533i	0.210962	+	0.977494i	$0.432341\pi$
$558$	−3.22439	−	8.38854i	−0.136499	−	0.355115i
$559$	10.3151			0.436281
$560$	10.0777	+	3.36983i	0.425862	+	0.142401i
$561$	−8.25399			−0.348484
$562$	2.65371	+	6.90387i	0.111940	+	0.291222i
$563$	15.9109	−	15.9109i	0.670566	−	0.670566i	−0.287281	−	0.957846i	$-0.592751\pi$
$563$	15.9109	−	15.9109i	0.670566	−	0.670566i	0.957846	+	0.287281i	$0.0927512\pi$
$564$	27.1707	−	24.5089i	1.14409	−	1.03201i
$565$	9.30568	−	41.6578i	0.391493	−	1.75256i
$566$	−11.3846	−	5.06262i	−0.478531	−	0.212798i
$567$	10.3481	+	10.3481i	0.434578	+	0.434578i
$568$	9.22632	−	18.1683i	0.387128	−	0.762324i
$569$			35.5078i			1.48856i	0.667865	+	0.744282i	$0.267208\pi$
$569$			35.5078i			1.48856i	−0.667865	+	0.744282i	$0.732792\pi$
$570$	−2.81892	−	19.0126i	−0.118071	−	0.796350i
$571$			32.0570i			1.34154i	0.741663	+	0.670772i	$0.234037\pi$
$571$			32.0570i			1.34154i	−0.741663	+	0.670772i	$0.765963\pi$
$572$	0.203588	−	3.95276i	0.00851245	−	0.165273i
$573$	−39.4254	−	39.4254i	−1.64702	−	1.64702i
$574$	−7.63246	+	17.1636i	−0.318573	+	0.716393i
$575$	−2.01239	−	5.58488i	−0.0839226	−	0.232906i
$576$	41.0476	−	29.9925i	1.71032	−	1.24969i
$577$	13.3843	−	13.3843i	0.557195	−	0.557195i	−0.371313	−	0.928508i	$-0.621092\pi$
$577$	13.3843	−	13.3843i	0.557195	−	0.557195i	0.928508	+	0.371313i	$0.121092\pi$
$578$	17.2449	−	6.62859i	0.717291	−	0.275713i
$579$	13.6747			0.568303
$580$	−8.44759	+	30.3773i	−0.350767	+	1.26135i
$581$	20.5966			0.854492
$582$	9.33077	−	3.58657i	0.386773	−	0.148668i
$583$	12.8426	−	12.8426i	0.531886	−	0.531886i
$584$	−6.70334	−	20.5364i	−0.277386	−	0.849802i
$585$	20.1764	+	4.50708i	0.834190	+	0.186345i
$586$	10.2227	−	22.9883i	0.422295	−	0.949640i
$587$	−29.1805	−	29.1805i	−1.20441	−	1.20441i	−0.972812	−	0.231594i	$-0.925606\pi$
$587$	−29.1805	−	29.1805i	−1.20441	−	1.20441i	−0.231594	−	0.972812i	$-0.574394\pi$
$588$	−34.1404	−	1.75841i	−1.40793	−	0.0725157i
$589$			1.98723i			0.0818825i
$590$	−20.5318	+	27.6800i	−0.845282	+	1.13957i
$591$			10.4728i			0.430794i
$592$	11.5387	+	14.1968i	0.474237	+	0.583484i
$593$	30.3704	+	30.3704i	1.24716	+	1.24716i	0.956968	+	0.290193i	$0.0937195\pi$
$593$	30.3704	+	30.3704i	1.24716	+	1.24716i	0.290193	+	0.956968i	$0.406281\pi$
$594$	−18.0346	−	8.01982i	−0.739970	−	0.329057i
$595$	−2.82473	−	4.44973i	−0.115803	−	0.182421i
$596$	−20.6400	−	22.8816i	−0.845449	−	0.937269i
$597$	25.6731	−	25.6731i	1.05073	−	1.05073i
$598$	−0.876480	−	2.28024i	−0.0358419	−	0.0932460i
$599$	38.6809			1.58046			0.790228	−	0.612812i	$-0.209962\pi$
$599$	38.6809			1.58046			0.790228	+	0.612812i	$0.209962\pi$
$600$	5.35162	−	42.9220i	0.218479	−	1.75228i
$601$	−38.1759			−1.55723			−0.778614	−	0.627504i	$-0.784077\pi$
$601$	−38.1759			−1.55723			−0.778614	+	0.627504i	$0.784077\pi$
$602$	−4.27387	−	11.1189i	−0.174190	−	0.453171i
$603$	14.7241	−	14.7241i	0.599613	−	0.599613i
$604$	−26.5895	−	29.4773i	−1.08191	−	1.19941i
$605$	−10.9651	−	17.2731i	−0.445797	−	0.702252i
$606$	−45.7149	−	20.3289i	−1.85704	−	0.825807i
$607$	−24.5570	−	24.5570i	−0.996740	−	0.996740i	0.00325490	−	0.999995i	$-0.498964\pi$
$607$	−24.5570	−	24.5570i	−0.996740	−	0.996740i	−0.999995	+	0.00325490i	$0.998964\pi$
$608$	−10.8519	+	2.93393i	−0.440101	+	0.118987i
$609$			25.6187i			1.03812i
$610$	19.0475	−	25.6788i	0.771209	−	1.03971i
$611$		−	8.70306i		−	0.352088i
$612$	−25.1820	−	1.29701i	−1.01792	−	0.0524285i
$613$	10.5790	+	10.5790i	0.427283	+	0.427283i	0.887702	−	0.460419i	$-0.152301\pi$
$613$	10.5790	+	10.5790i	0.427283	+	0.427283i	−0.460419	+	0.887702i	$0.652301\pi$
$614$	−8.32867	+	18.7292i	−0.336118	+	0.755848i
$615$	74.6221	+	16.6694i	3.00906	+	0.672175i
$616$	−4.34512	+	1.41830i	−0.175070	+	0.0571450i
$617$	−5.90290	+	5.90290i	−0.237642	+	0.237642i	−0.815873	−	0.578231i	$-0.803743\pi$
$617$	−5.90290	+	5.90290i	−0.237642	+	0.237642i	0.578231	+	0.815873i	$0.303743\pi$
$618$	59.6807	−	22.9401i	2.40071	−	0.922786i
$619$	−1.79366			−0.0720932			−0.0360466	−	0.999350i	$-0.511476\pi$
$619$	−1.79366			−0.0720932			−0.0360466	+	0.999350i	$0.511476\pi$
$620$	−1.19818	+	4.30864i	−0.0481202	+	0.173039i
$621$	−12.1820			−0.488847
$622$	−19.9349	+	7.66259i	−0.799317	+	0.307242i
$623$	2.30141	−	2.30141i	0.0922041	−	0.0922041i
$624$	1.82871	−	17.7055i	0.0732068	−	0.708787i
$625$	−15.9461	−	19.2542i	−0.637842	−	0.770167i
$626$	4.90897	−	11.0391i	0.196202	−	0.441211i
$627$	5.84597	+	5.84597i	0.233465	+	0.233465i
$628$	1.27700	−	24.7936i	0.0509580	−	0.989373i
$629$		−	9.07408i		−	0.361807i
$630$	−3.50144	−	23.6160i	−0.139501	−	0.940883i
$631$		−	14.4999i		−	0.577230i	−0.957445	−	0.288615i	$-0.906805\pi$
$631$		−	14.4999i		−	0.577230i	0.957445	−	0.288615i	$-0.0931948\pi$
$632$	9.55581	+	4.85269i	0.380110	+	0.193030i
$633$	−49.8494	−	49.8494i	−1.98134	−	1.98134i
$634$	−11.3006	−	5.02528i	−0.448806	−	0.199579i
$635$	1.06605	−	4.77227i	0.0423049	−	0.189382i
$636$	60.6493	−	54.7078i	2.40490	−	2.16931i
$637$	−5.74938	+	5.74938i	−0.227799	+	0.227799i
$638$	−4.86598	−	12.6593i	−0.192646	−	0.501186i
$639$	−45.7809			−1.81106
$640$	−25.2976	−	0.181799i	−0.999974	−	0.00718622i
$641$	3.98195			0.157278			0.0786388	−	0.996903i	$-0.474943\pi$
$641$	3.98195			0.157278			0.0786388	+	0.996903i	$0.474943\pi$
$642$	−3.96325	−	10.3107i	−0.156417	−	0.406932i
$643$	34.6403	−	34.6403i	1.36608	−	1.36608i	0.500130	−	0.865951i	$-0.333286\pi$
$643$	34.6403	−	34.6403i	1.36608	−	1.36608i	0.865951	−	0.500130i	$-0.166714\pi$
$644$	−2.09477	+	1.88955i	−0.0825454	+	0.0744589i
$645$	−40.9363	+	25.9868i	−1.61187	+	1.02323i
$646$	5.09474	+	2.26558i	0.200450	+	0.0891379i
$647$	−15.5511	−	15.5511i	−0.611379	−	0.611379i	0.331926	−	0.943305i	$-0.392301\pi$
$647$	−15.5511	−	15.5511i	−0.611379	−	0.611379i	−0.943305	+	0.331926i	$0.892301\pi$
$648$	−31.0646	−	15.7754i	−1.22033	−	0.619717i
$649$		−	14.8241i		−	0.581897i
$650$	−6.72787	−	7.78296i	−0.263889	−	0.305273i
$651$			3.63369i			0.142416i
$652$	−1.62813	+	31.6108i	−0.0637623	+	1.23797i
$653$	15.9231	+	15.9231i	0.623120	+	0.623120i	0.946328	−	0.323208i	$-0.104761\pi$
$653$	15.9231	+	15.9231i	0.623120	+	0.623120i	−0.323208	+	0.946328i	$0.604761\pi$
$654$	−8.90683	+	20.0293i	−0.348285	+	0.783208i
$655$	21.5161	−	13.6586i	0.840703	−	0.533686i
$656$	4.59445	−	44.4834i	0.179383	−	1.73678i
$657$	−34.3197	+	34.3197i	−1.33894	+	1.33894i
$658$	−9.38122	+	3.60596i	−0.365718	+	0.140575i
$659$	24.1520			0.940828			0.470414	−	0.882446i	$-0.344105\pi$
$659$	24.1520			0.940828			0.470414	+	0.882446i	$0.344105\pi$
$660$	9.15022	+	16.1998i	0.356172	+	0.630575i
$661$	−8.40768			−0.327021			−0.163510	−	0.986542i	$-0.552282\pi$
$661$	−8.40768			−0.327021			−0.163510	+	0.986542i	$0.552282\pi$
$662$	33.4669	−	12.8640i	1.30073	−	0.499974i
$663$	−6.24279	+	6.24279i	−0.242450	+	0.242450i
$664$	−46.6147	+	15.2157i	−1.80900	+	0.590482i
$665$	−1.15092	+	5.15220i	−0.0446307	+	0.199794i
$666$	16.7011	−	37.5567i	0.647154	−	1.45529i
$667$	−5.91897	−	5.91897i	−0.229183	−	0.229183i
$668$	10.3980	+	0.535552i	0.402310	+	0.0207211i
$669$		−	43.8783i		−	1.69643i
$670$	−10.2501	+	1.51974i	−0.395996	+	0.0587126i
$671$			13.7524i			0.530905i
$672$	−19.8428	+	5.36475i	−0.765454	+	0.206950i
$673$	−0.616732	−	0.616732i	−0.0237733	−	0.0237733i	0.695120	−	0.718893i	$-0.255351\pi$
$673$	−0.616732	−	0.616732i	−0.0237733	−	0.0237733i	−0.718893	+	0.695120i	$0.755351\pi$
$674$	−25.2186	−	11.2145i	−0.971386	−	0.431965i
$675$	−48.2647	+	17.3912i	−1.85771	+	0.669386i
$676$	14.5791	+	16.1625i	0.560737	+	0.621635i
$677$	36.3247	−	36.3247i	1.39607	−	1.39607i	0.585134	−	0.810936i	$-0.301042\pi$
$677$	36.3247	−	36.3247i	1.39607	−	1.39607i	0.810936	−	0.585134i	$-0.198958\pi$
$678$	29.6246	+	77.0711i	1.13773	+	2.95990i
$679$	−2.74565			−0.105368
$680$	9.68020	+	7.98396i	0.371219	+	0.306171i
$681$	−48.6755			−1.86525
$682$	−0.690178	−	1.79556i	−0.0264283	−	0.0687555i
$683$	−30.7122	+	30.7122i	−1.17517	+	1.17517i	−0.194211	+	0.980960i	$0.562215\pi$
$683$	−30.7122	+	30.7122i	−1.17517	+	1.17517i	−0.980960	+	0.194211i	$0.937785\pi$
$684$	16.9168	+	18.7540i	0.646829	+	0.717078i
$685$	−32.8464	−	7.33737i	−1.25500	−	0.280346i
$686$	19.3260	+	8.59405i	0.737868	+	0.328122i
$687$	31.0462	+	31.0462i	1.18449	+	1.18449i
$688$	17.8867	+	22.0071i	0.681925	+	0.839014i
$689$		−	19.4266i		−	0.740096i
$690$	9.22300	+	6.84122i	0.351113	+	0.260441i
$691$			40.2515i			1.53124i	0.643294	+	0.765619i	$0.277567\pi$
$691$			40.2515i			1.53124i	−0.643294	+	0.765619i	$0.722433\pi$
$692$	40.8429	+	2.10363i	1.55262	+	0.0799680i
$693$	7.26141	+	7.26141i	0.275838	+	0.275838i
$694$	−8.93493	+	20.0925i	−0.339165	+	0.762701i
$695$	−13.0008	−	20.4798i	−0.493148	−	0.776843i
$696$	−18.9257	−	57.9808i	−0.717377	−	2.19776i
$697$	−15.6844	+	15.6844i	−0.594090	+	0.594090i
$698$	−9.59378	+	3.68766i	−0.363130	+	0.139580i
$699$	−11.0611			−0.418369
$700$	−5.60185	+	10.4769i	−0.211730	+	0.395988i
$701$	18.0365			0.681228			0.340614	−	0.940203i	$-0.389365\pi$
$701$	18.0365			0.681228			0.340614	+	0.940203i	$0.389365\pi$
$702$	−19.7059	+	7.57457i	−0.743752	+	0.285884i
$703$	−6.42680	+	6.42680i	−0.242391	+	0.242391i
$704$	8.78620	−	6.41987i	0.331143	−	0.241958i
$705$	21.9256	+	34.5389i	0.825766	+	1.30081i
$706$	11.1635	−	25.1039i	0.420142	−	0.944799i
$707$	9.71693	+	9.71693i	0.365443	+	0.365443i
$708$	3.42912	−	66.5779i	0.128874	−	2.50215i
$709$			8.51004i			0.319601i	0.987149	+	0.159801i	$0.0510851\pi$
$709$			8.51004i			0.319601i	−0.987149	+	0.159801i	$0.948915\pi$
$710$	18.2976	+	13.5724i	0.686698	+	0.509363i
$711$		−	24.0790i		−	0.903032i
$712$	−3.50845	+	6.90876i	−0.131485	+	0.258917i
$713$	−0.839531	−	0.839531i	−0.0314407	−	0.0314407i
$714$	9.31583	+	4.14265i	0.348636	+	0.155035i
$715$	4.31873	+	0.964736i	0.161511	+	0.0360791i
$716$	−16.0097	+	14.4413i	−0.598310	+	0.539697i
$717$	18.7892	−	18.7892i	0.701697	−	0.701697i
$718$	−2.82769	−	7.35648i	−0.105528	−	0.274541i
$719$	41.8577			1.56103			0.780515	−	0.625137i	$-0.214957\pi$
$719$	41.8577			1.56103			0.780515	+	0.625137i	$0.214957\pi$
$720$	25.3707	+	50.8615i	0.945511	+	1.89550i
$721$	−17.5615			−0.654023
$722$	7.63688	+	19.8680i	0.284215	+	0.739411i
$723$	−37.8008	+	37.8008i	−1.40583	+	1.40583i
$724$	15.9846	−	14.4187i	0.594063	−	0.535866i
$725$	−31.9007	−	15.0008i	−1.18476	−	0.557114i
$726$	36.1625	+	16.0811i	1.34212	+	0.596826i
$727$	−16.9619	−	16.9619i	−0.629082	−	0.629082i	0.318755	−	0.947837i	$-0.396735\pi$
$727$	−16.9619	−	16.9619i	−0.629082	−	0.629082i	−0.947837	+	0.318755i	$0.896735\pi$
$728$	−2.21365	+	4.35908i	−0.0820435	+	0.161558i
$729$		−	15.8690i		−	0.587741i
$730$	23.8914	−	3.54228i	0.884261	−	0.131106i
$731$		−	14.0662i		−	0.520257i
$732$	−3.18120	+	61.7645i	−0.117581	+	2.28288i
$733$	11.1296	+	11.1296i	0.411080	+	0.411080i	0.882115	−	0.471035i	$-0.156119\pi$
$733$	11.1296	+	11.1296i	0.411080	+	0.411080i	−0.471035	+	0.882115i	$0.656119\pi$
$734$	−17.6244	+	39.6330i	−0.650527	+	1.46288i
$735$	8.33253	−	37.3014i	0.307350	−	1.37588i
$736$	3.34503	−	5.82398i	0.123299	−	0.214675i
$737$	3.15169	−	3.15169i	0.116094	−	0.116094i
$738$	−93.7839	+	36.0487i	−3.45223	+	1.32697i
$739$	−3.97510			−0.146226			−0.0731131	−	0.997324i	$-0.523293\pi$
$739$	−3.97510			−0.146226			−0.0731131	+	0.997324i	$0.523293\pi$
$740$	−17.8093	+	10.0593i	−0.654683	+	0.369789i
$741$	8.84302			0.324857
$742$	−20.9404	+	8.04908i	−0.768746	+	0.295491i
$743$	−6.70707	+	6.70707i	−0.246059	+	0.246059i	−0.819351	−	0.573292i	$-0.805666\pi$
$743$	−6.70707	+	6.70707i	−0.246059	+	0.246059i	0.573292	+	0.819351i	$0.305666\pi$
$744$	−2.68437	−	8.22385i	−0.0984138	−	0.301501i
$745$	29.0867	−	18.4645i	1.06566	−	0.676488i
$746$	−3.62983	+	8.16261i	−0.132897	+	0.298854i
$747$	77.9009	+	77.9009i	2.85024	+	2.85024i
$748$	−5.39019	−	0.277624i	−0.197085	−	0.0101509i
$749$			3.03401i			0.110860i
$750$	46.3078	+	13.9378i	1.69092	+	0.508938i
$751$		−	46.3331i		−	1.69072i	−0.534198	−	0.845359i	$-0.679386\pi$
$751$		−	46.3331i		−	1.69072i	0.534198	−	0.845359i	$-0.320614\pi$
$752$	18.5679	−	15.0914i	0.677102	−	0.550327i
$753$	12.4408	+	12.4408i	0.453368	+	0.453368i
$754$	−13.2550	−	5.89435i	−0.482718	−	0.214660i
$755$	37.4710	−	23.7869i	1.36371	−	0.865695i
$756$	16.3296	+	18.1031i	0.593901	+	0.658402i
$757$	−8.15291	+	8.15291i	−0.296323	+	0.296323i	−0.839572	−	0.543249i	$-0.817194\pi$
$757$	−8.15291	+	8.15291i	−0.296323	+	0.296323i	0.543249	+	0.839572i	$0.317194\pi$
$758$	11.1576	+	29.0275i	0.405263	+	1.05433i
$759$	−4.93940			−0.179289
$760$	−1.20138	−	12.5108i	−0.0435785	−	0.453815i
$761$	15.7691			0.571629			0.285815	−	0.958285i	$-0.407736\pi$
$761$	15.7691			0.571629			0.285815	+	0.958285i	$0.407736\pi$
$762$	3.39377	+	8.82919i	0.122943	+	0.319848i
$763$	4.25733	−	4.25733i	0.154126	−	0.154126i
$764$	−24.4203	−	27.0724i	−0.883495	−	0.979446i
$765$	6.14609	−	27.5136i	0.222212	−	0.994755i
$766$	36.9106	+	16.4138i	1.33363	+	0.593053i
$767$	−11.2120	−	11.2120i	−0.404842	−	0.404842i
$768$	40.9456	−	26.8004i	1.47750	−	0.967077i
$769$		−	9.46407i		−	0.341283i	−0.985333	−	0.170642i	$-0.945416\pi$
$769$		−	9.46407i		−	0.341283i	0.985333	−	0.170642i	$-0.0545840\pi$
$770$	−0.749480	−	5.05498i	−0.0270094	−	0.182169i
$771$		−	59.4907i		−	2.14251i
$772$	8.93016	+	0.459951i	0.321403	+	0.0165540i
$773$	24.7259	+	24.7259i	0.889328	+	0.889328i	0.994458	−	0.105131i	$-0.0335261\pi$
$773$	24.7259	+	24.7259i	0.889328	+	0.889328i	−0.105131	+	0.994458i	$0.533526\pi$
$774$	25.8892	−	58.2186i	0.930569	−	2.09263i
$775$	−4.52471	−	2.12767i	−0.162532	−	0.0764281i
$776$	6.21401	−	2.02833i	0.223070	−	0.0728129i
$777$	−11.7515	+	11.7515i	−0.421584	+	0.421584i
$778$	7.63546	−	2.93492i	0.273744	−	0.105222i
$779$	22.2173			0.796016
$780$	19.1731	+	5.33182i	0.686507	+	0.190910i
$781$	−9.79936			−0.350649
$782$	−3.10946	+	1.19521i	−0.111194	+	0.0427408i
$783$	−51.1519	+	51.1519i	−1.82802	+	1.82802i
$784$	−22.2359	−	2.29663i	−0.794139	−	0.0820224i
$785$	27.0892	+	6.05129i	0.966855	+	0.215980i
$786$	−20.0313	+	45.0455i	−0.714491	+	1.60672i
$787$	−9.63434	−	9.63434i	−0.343427	−	0.343427i	0.514227	−	0.857654i	$-0.328079\pi$
$787$	−9.63434	−	9.63434i	−0.343427	−	0.343427i	−0.857654	+	0.514227i	$0.828079\pi$
$788$	−0.352254	+	6.83918i	−0.0125485	+	0.243636i
$789$			18.3939i			0.654841i
$790$	−7.13856	+	9.62386i	−0.253979	+	0.342401i
$791$		−	22.6787i		−	0.806362i
$792$	−21.7985	−	11.0698i	−0.774576	−	0.393350i
$793$	10.4014	+	10.4014i	0.369365	+	0.369365i
$794$	39.7477	+	17.6754i	1.41059	+	0.627276i
$795$	48.9415	+	77.0963i	1.73578	+	2.73432i
$796$	17.6291	−	15.9021i	0.624847	−	0.563634i
$797$	15.9834	−	15.9834i	0.566161	−	0.566161i	−0.364890	−	0.931051i	$-0.618893\pi$
$797$	15.9834	−	15.9834i	0.566161	−	0.566161i	0.931051	+	0.364890i	$0.118893\pi$
$798$	−3.66395	−	9.53209i	−0.129702	−	0.337432i
$799$	−11.8680			−0.419858
$800$	4.93851	−	27.8498i	0.174603	−	0.984639i
$801$	17.4089			0.615112
$802$	5.64520	+	14.6865i	0.199339	+	0.518598i
$803$	−7.34610	+	7.34610i	−0.259238	+	0.259238i
$804$	14.8839	−	13.4258i	0.524914	−	0.473491i
$805$	−1.69039	−	2.66283i	−0.0595784	−	0.0938525i
$806$	−1.88005	−	0.836039i	−0.0662220	−	0.0294482i
$807$	50.8165	+	50.8165i	1.78883	+	1.78883i
$808$	−29.1699	−	14.8132i	−1.02619	−	0.521128i
$809$		−	4.56705i		−	0.160569i	−0.996772	−	0.0802844i	$-0.974417\pi$
$809$		−	4.56705i		−	0.160569i	0.996772	−	0.0802844i	$-0.0255828\pi$
$810$	23.2065	−	31.2858i	0.815392	−	1.09927i
$811$			19.7457i			0.693365i	0.937983	+	0.346682i	$0.112692\pi$
$811$			19.7457i			0.693365i	−0.937983	+	0.346682i	$0.887308\pi$
$812$	−0.861687	+	16.7301i	−0.0302393	+	0.587110i
$813$	−36.2589	−	36.2589i	−1.27165	−	1.27165i
$814$	3.57485	−	8.03899i	0.125299	−	0.281766i
$815$	−34.5376	−	7.71514i	−1.20980	−	0.270250i
$816$	−24.1441	−	2.49372i	−0.845214	−	0.0872977i
$817$	−9.96251	+	9.96251i	−0.348544	+	0.348544i
$818$	6.27427	−	2.41171i	0.219375	−	0.0843234i
$819$	10.9841			0.383816
$820$	48.1706	+	13.3957i	1.68219	+	0.467798i
$821$	3.44871			0.120361			0.0601803	−	0.998188i	$-0.480832\pi$
$821$	3.44871			0.120361			0.0601803	+	0.998188i	$0.480832\pi$
$822$	60.7692	−	23.3585i	2.11957	−	0.814721i
$823$	−29.6047	+	29.6047i	−1.03195	+	1.03195i	−0.0324827	+	0.999472i	$0.510341\pi$
$823$	−29.6047	+	29.6047i	−1.03195	+	1.03195i	−0.999472	+	0.0324827i	$0.989659\pi$
$824$	39.7455	−	12.9734i	1.38460	−	0.451951i
$825$	−19.5697	+	7.05154i	−0.681331	+	0.245503i
$826$	−7.44017	+	16.7311i	−0.258877	+	0.582151i
$827$	−20.2723	−	20.2723i	−0.704937	−	0.704937i	0.260529	−	0.965466i	$-0.416103\pi$
$827$	−20.2723	−	20.2723i	−0.704937	−	0.704937i	−0.965466	+	0.260529i	$0.916103\pi$
$828$	−15.0696	−	0.776163i	−0.523704	−	0.0269735i
$829$			3.23321i			0.112294i	0.998423	+	0.0561471i	$0.0178816\pi$
$829$			3.23321i			0.112294i	−0.998423	+	0.0561471i	$0.982118\pi$
$830$	−8.04047	−	54.2302i	−0.279089	−	1.88236i
$831$			52.4912i			1.82090i
$832$	1.78974	−	11.5009i	0.0620482	−	0.398722i
$833$	7.84016	+	7.84016i	0.271646	+	0.271646i
$834$	42.8760	+	19.0665i	1.48467	+	0.660219i
$835$	−2.53780	+	11.3607i	−0.0878242	+	0.393153i
$836$	3.62102	+	4.01428i	0.125236	+	0.138837i
$837$	−7.25525	+	7.25525i	−0.250778	+	0.250778i
$838$	5.52441	+	14.3723i	0.190838	+	0.496481i
$839$	16.6063			0.573312			0.286656	−	0.958034i	$-0.407456\pi$
$839$	16.6063			0.573312			0.286656	+	0.958034i	$0.407456\pi$
$840$	−2.19674	−	22.8762i	−0.0757946	−	0.789305i
$841$	−20.7071			−0.714039
$842$	6.75906	+	17.5843i	0.232933	+	0.605995i
$843$	11.3110	−	11.3110i	0.389571	−	0.389571i
$844$	−30.8770	−	34.2304i	−1.06283	−	1.17826i
$845$	−20.5455	+	13.0425i	−0.706786	+	0.448675i
$846$	−49.1203	−	21.8433i	−1.68879	−	0.750988i
$847$	−7.68653	−	7.68653i	−0.264112	−	0.264112i
$848$	41.4466	−	33.6865i	1.42328	−	1.15680i
$849$			26.9464i			0.924799i
$850$	−10.6133	+	9.17449i	−0.364032	+	0.314682i
$851$		−	5.43016i		−	0.186144i
$852$	−44.0108	−	2.26679i	−1.50778	−	0.0776589i
$853$	3.85139	+	3.85139i	0.131869	+	0.131869i	0.769961	−	0.638091i	$-0.220276\pi$
$853$	3.85139	+	3.85139i	0.131869	+	0.131869i	−0.638091	+	0.769961i	$0.720276\pi$
$854$	6.90227	−	15.5216i	0.236191	−	0.531137i
$855$	−23.8398	+	15.1337i	−0.815302	+	0.517562i
$856$	−2.24136	−	6.86663i	−0.0766080	−	0.234697i
$857$	−33.1459	+	33.1459i	−1.13224	+	1.13224i	−0.142440	+	0.989803i	$0.545495\pi$
$857$	−33.1459	+	33.1459i	−1.13224	+	1.13224i	−0.989803	+	0.142440i	$0.954505\pi$
$858$	−7.99009	+	3.07124i	−0.272777	+	0.104850i
$859$	−1.47185			−0.0502187			−0.0251094	−	0.999685i	$-0.507993\pi$
$859$	−1.47185			−0.0502187			−0.0251094	+	0.999685i	$0.507993\pi$
$860$	−27.6071	+	15.5935i	−0.941395	+	0.531734i
$861$	40.6247			1.38449
$862$	48.2919	−	18.5625i	1.64483	−	0.632240i
$863$	1.51398	−	1.51398i	0.0515366	−	0.0515366i	−0.680869	−	0.732405i	$-0.738398\pi$
$863$	1.51398	−	1.51398i	0.0515366	−	0.0515366i	0.732405	+	0.680869i	$0.238398\pi$
$864$	−50.3310	−	28.9078i	−1.71230	−	0.983464i
$865$	−9.96840	+	44.6245i	−0.338936	+	1.51728i
$866$	0.493000	−	1.10864i	0.0167528	−	0.0376731i
$867$	−28.2532	−	28.2532i	−0.959529	−	0.959529i
$868$	−0.122219	+	2.37295i	−0.00414840	+	0.0805430i
$869$		−	5.15408i		−	0.174840i
$870$	67.4532	−	10.0010i	2.28688	−	0.339065i
$871$		−	4.76747i		−	0.161539i
$872$	−6.49020	+	12.7804i	−0.219786	+	0.432798i
$873$	−10.3846	−	10.3846i	−0.351466	−	0.351466i
$874$	3.04882	+	1.35578i	0.103128	+	0.0458599i
$875$	−10.4987	−	8.13682i	−0.354923	−	0.275075i
$876$	−34.6920	+	31.2934i	−1.17214	+	1.05731i
$877$	17.7165	−	17.7165i	0.598244	−	0.598244i	−0.341601	−	0.939845i	$-0.610969\pi$
$877$	17.7165	−	17.7165i	0.598244	−	0.598244i	0.939845	+	0.341601i	$0.110969\pi$
$878$	10.9397	+	28.4606i	0.369197	+	0.960500i
$879$	−54.4115			−1.83525
$880$	5.43058	+	10.8869i	0.183065	+	0.366996i
$881$	27.8294			0.937597			0.468799	−	0.883305i	$-0.344687\pi$
$881$	27.8294			0.937597			0.468799	+	0.883305i	$0.344687\pi$
$882$	18.0197	+	46.8797i	0.606753	+	1.57852i
$883$	3.80959	−	3.80959i	0.128203	−	0.128203i	−0.640094	−	0.768297i	$-0.721105\pi$
$883$	3.80959	−	3.80959i	0.128203	−	0.128203i	0.768297	+	0.640094i	$0.221105\pi$
$884$	−4.28677	+	3.86681i	−0.144180	+	0.130055i
$885$	72.7421	+	16.2494i	2.44520	+	0.546219i
$886$	−18.9877	−	8.44362i	−0.637904	−	0.283669i
$887$	32.6415	+	32.6415i	1.09599	+	1.09599i	0.994874	+	0.101118i	$0.0322421\pi$
$887$	32.6415	+	32.6415i	1.09599	+	1.09599i	0.101118	+	0.994874i	$0.467758\pi$
$888$	17.9149	−	35.2777i	0.601186	−	1.18384i
$889$		−	2.59805i		−	0.0871358i
$890$	−6.95795	−	5.16111i	−0.233231	−	0.173001i
$891$			16.7552i			0.561320i
$892$	1.47585	−	28.6543i	0.0494151	−	0.959417i
$893$	8.40559	+	8.40559i	0.281282	+	0.281282i
$894$	−27.0795	+	60.8952i	−0.905672	+	2.03664i
$895$	−12.9192	−	20.3512i	−0.431840	−	0.680266i
$896$	−13.1386	+	2.83598i	−0.438930	+	0.0947436i
$897$	−3.73584	+	3.73584i	−0.124736	+	0.124736i
$898$	23.1351	−	8.89266i	0.772027	−	0.296752i
$899$	−7.05033			−0.235142
$900$	−60.8132	+	18.4383i	−2.02711	+	0.614611i
$901$	−26.4912			−0.882549
$902$	−20.0744	+	7.71619i	−0.668403	+	0.256921i
$903$	−18.2166	+	18.2166i	−0.606212	+	0.606212i
$904$	16.7538	+	51.3269i	0.557222	+	1.70711i
$905$	12.8989	+	20.3193i	0.428774	+	0.675437i
$906$	−34.8851	+	78.4482i	−1.15898	+	2.60627i
$907$	24.7998	+	24.7998i	0.823463	+	0.823463i	0.986603	−	0.163140i	$-0.0521623\pi$
$907$	24.7998	+	24.7998i	0.823463	+	0.823463i	−0.163140	+	0.986603i	$0.552162\pi$
$908$	−31.7871	−	1.63720i	−1.05489	−	0.0543326i
$909$			73.5031i			2.43794i
$910$	−4.39012	−	3.25640i	−0.145531	−	0.107949i
$911$		−	43.5849i		−	1.44403i	−0.691875	−	0.722017i	$-0.743215\pi$
$911$		−	43.5849i		−	1.44403i	0.691875	−	0.722017i	$-0.256785\pi$
$912$	15.3341	+	18.8665i	0.507763	+	0.624733i
$913$	16.6746	+	16.6746i	0.551849	+	0.551849i
$914$	16.2103	+	7.20855i	0.536189	+	0.238438i
$915$	−67.4832	−	15.0747i	−2.23092	−	0.498353i
$916$	19.2302	+	21.3186i	0.635382	+	0.704388i
$917$	9.57464	−	9.57464i	0.316183	−	0.316183i
$918$	10.3291	+	26.8720i	0.340910	+	0.886909i
$919$	−18.5286			−0.611204			−0.305602	−	0.952159i	$-0.598858\pi$
$919$	−18.5286			−0.611204			−0.305602	+	0.952159i	$0.598858\pi$
$920$	5.79288	+	4.77781i	0.190986	+	0.157520i
$921$	44.3304			1.46074
$922$	−10.8335	−	28.1844i	−0.356784	−	0.928205i
$923$	−7.41160	+	7.41160i	−0.243956	+	0.243956i
$924$	6.62111	+	7.34019i	0.217818	+	0.241474i
$925$	−7.75215	−	21.5141i	−0.254889	−	0.707380i
$926$	−17.8559	−	7.94034i	−0.586782	−	0.260936i
$927$	−66.4213	−	66.4213i	−2.18156	−	2.18156i
$928$	−10.4091	−	38.5004i	−0.341694	−	1.26384i
$929$		−	56.4407i		−	1.85176i	−0.377818	−	0.925880i	$-0.623325\pi$
$929$		−	56.4407i		−	1.85176i	0.377818	−	0.925880i	$-0.376675\pi$
$930$	9.56738	−	1.41851i	0.313727	−	0.0465149i
$931$		−	11.1057i		−	0.363976i
$932$	−7.22335	−	0.372041i	−0.236609	−	0.0121866i
$933$	32.6605	+	32.6605i	1.06926	+	1.06926i
$934$	−1.67399	+	3.76440i	−0.0547747	+	0.123175i
$935$	1.31557	−	5.88925i	0.0430236	−	0.192599i
$936$	−24.8595	+	8.11446i	−0.812558	+	0.265229i
$937$	−39.4329	+	39.4329i	−1.28822	+	1.28822i	−0.352347	+	0.935869i	$0.614616\pi$
$937$	−39.4329	+	39.4329i	−1.28822	+	1.28822i	−0.935869	+	0.352347i	$0.885384\pi$
$938$	−5.13896	+	1.97531i	−0.167793	+	0.0644963i
$939$	−26.1286			−0.852675
$940$	13.1566	+	23.2927i	0.429120	+	0.759725i
$941$	−30.7527			−1.00251			−0.501254	−	0.865300i	$-0.667128\pi$
$941$	−30.7527			−1.00251			−0.501254	+	0.865300i	$0.667128\pi$
$942$	−50.1177	+	19.2643i	−1.63292	+	0.627664i
$943$	−9.38596	+	9.38596i	−0.305649	+	0.305649i
$944$	4.47870	−	43.3627i	0.145769	−	1.41134i
$945$	−23.0123	+	14.6084i	−0.748589	+	0.475212i
$946$	5.54156	−	12.4616i	0.180172	−	0.405163i
$947$	−15.6520	−	15.6520i	−0.508621	−	0.508621i	0.405482	−	0.914103i	$-0.367104\pi$
$947$	−15.6520	−	15.6520i	−0.508621	−	0.508621i	−0.914103	+	0.405482i	$0.867104\pi$
$948$	1.19224	−	23.1480i	0.0387223	−	0.751811i
$949$			11.1122i			0.360718i
$950$	14.0149	+	1.01902i	0.454702	+	0.0330615i
$951$			26.7477i			0.867353i
$952$	5.94427	+	3.01866i	0.192655	+	0.0978352i
$953$	−28.6970	−	28.6970i	−0.929589	−	0.929589i	0.0680905	−	0.997679i	$-0.478309\pi$
$953$	−28.6970	−	28.6970i	−0.929589	−	0.929589i	−0.997679	+	0.0680905i	$0.978309\pi$
$954$	−109.644	−	48.7577i	−3.54987	−	1.57859i
$955$	34.4140	−	21.8463i	1.11361	−	0.706930i
$956$	12.9021	−	11.6381i	0.417284	−	0.376405i
$957$	−20.7404	+	20.7404i	−0.670442	+	0.670442i
$958$	8.85118	+	23.0271i	0.285969	+	0.743973i
$959$	−17.8818			−0.577432
$960$	21.8714	+	50.1512i	0.705897	+	1.61862i
$961$	−1.00000			−0.0322581
$962$	−3.37638	−	8.78396i	−0.108859	−	0.283206i
$963$	−11.4753	+	11.4753i	−0.369785	+	0.369785i
$964$	−25.9569	+	23.4140i	−0.836014	+	0.754114i
$965$	−2.17955	+	9.75698i	−0.0701623	+	0.314088i
$966$	5.57483	+	2.47907i	0.179367	+	0.0797628i
$967$	11.1490	+	11.1490i	0.358527	+	0.358527i	0.863270	−	0.504743i	$-0.168413\pi$
$967$	11.1490	+	11.1490i	0.358527	+	0.358527i	−0.504743	+	0.863270i	$0.668413\pi$
$968$	23.0747	+	11.7179i	0.741649	+	0.376629i
$969$		−	12.0588i		−	0.387385i
$970$	1.07184	+	7.22919i	0.0344147	+	0.232115i
$971$		−	33.7095i		−	1.08179i	−0.841090	−	0.540895i	$-0.818086\pi$
$971$		−	33.7095i		−	1.08179i	0.841090	−	0.540895i	$-0.181914\pi$
$972$	−0.709198	+	13.7694i	−0.0227476	+	0.441654i
$973$	−9.11350	−	9.11350i	−0.292165	−	0.292165i
$974$	18.2411	−	41.0200i	0.584484	−	1.31436i
$975$	−9.46795	+	20.1346i	−0.303217	+	0.644824i
$976$	−4.15491	+	40.2277i	−0.132995	+	1.28766i
$977$	14.7064	−	14.7064i	0.470500	−	0.470500i	−0.431577	−	0.902076i	$-0.642043\pi$
$977$	14.7064	−	14.7064i	0.470500	−	0.470500i	0.902076	+	0.431577i	$0.142043\pi$
$978$	63.8980	−	24.5611i	2.04323	−	0.785379i
$979$	3.72635			0.119095
$980$	6.69611	−	24.0790i	0.213899	−	0.769176i
$981$	32.2043			1.02820
$982$	−5.78753	+	2.22461i	−0.184687	+	0.0709902i
$983$	−6.27479	+	6.27479i	−0.200135	+	0.200135i	−0.800058	−	0.599923i	$-0.795198\pi$
$983$	−6.27479	+	6.27479i	−0.200135	+	0.200135i	0.599923	+	0.800058i	$0.295198\pi$
$984$	−91.9427	+	30.0113i	−2.93103	+	0.956725i
$985$	−7.47240	−	1.66921i	−0.238090	−	0.0531856i
$986$	−8.03785	+	18.0752i	−0.255977	+	0.575631i
$987$	15.3698	+	15.3698i	0.489225	+	0.489225i
$988$	5.77485	+	0.297436i	0.183722	+	0.00946269i
$989$		−	8.41757i		−	0.267663i
$990$	16.2843	−	21.9537i	0.517550	−	0.697735i
$991$		−	18.0586i		−	0.573649i	−0.957983	−	0.286824i	$-0.907400\pi$
$991$		−	18.0586i		−	0.573649i	0.957983	−	0.286824i	$-0.0925997\pi$
$992$	−1.47639	−	5.46079i	−0.0468755	−	0.173380i
$993$	−54.8307	−	54.8307i	−1.74000	−	1.74000i
$994$	11.0600	+	4.91826i	0.350802	+	0.155998i
$995$	14.2259	+	22.4098i	0.450993	+	0.710438i
$996$	71.0317	+	78.7461i	2.25073	+	2.49516i
$997$	34.5547	−	34.5547i	1.09436	−	1.09436i	0.0993026	−	0.995057i	$-0.468339\pi$
$997$	34.5547	−	34.5547i	1.09436	−	1.09436i	0.995057	−	0.0993026i	$-0.0316612\pi$
$998$	6.75399	+	17.5711i	0.213794	+	0.556203i
$999$	−46.9276			−1.48472

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	620.2.k.d.63.16	yes	88
4.3	odd	2		620.2.k.c.63.39	✓	88
5.2	odd	4		620.2.k.c.187.39	yes	88
20.7	even	4	inner	620.2.k.d.187.16	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
620.2.k.c.63.39	✓	88	4.3	odd	2
620.2.k.c.187.39	yes	88	5.2	odd	4
620.2.k.d.63.16	yes	88	1.1	even	1	trivial
620.2.k.d.187.16	yes	88	20.7	even	4	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:	\( N \)	\(=\)	\( 620 = 2^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	620.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.507403 - 1.32005i) q^{2} +(-2.16272 + 2.16272i) q^{3} +(-1.48508 + 1.33960i) q^{4} +(-1.19840 - 1.88781i) q^{5} +(3.95227 + 1.75753i) q^{6} +(-0.840075 - 0.840075i) q^{7} +(2.52188 + 1.28068i) q^{8} -6.35469i q^{9} +(-1.88394 + 2.53984i) q^{10} -1.36022i q^{11} +(0.314646 - 6.10899i) q^{12} +(-1.02878 - 1.02878i) q^{13} +(-0.682688 + 1.53520i) q^{14} +(6.67461 + 1.49100i) q^{15} +(0.410953 - 3.97883i) q^{16} +(-1.40290 + 1.40290i) q^{17} +(-8.38854 + 3.22439i) q^{18} +1.98723 q^{19} +(4.30864 + 1.19818i) q^{20} +3.63369 q^{21} +(-1.79556 + 0.690178i) q^{22} +(-0.839531 + 0.839531i) q^{23} +(-8.22385 + 2.68437i) q^{24} +(-2.12767 + 4.52471i) q^{25} +(-0.836039 + 1.88005i) q^{26} +(7.25525 + 7.25525i) q^{27} +(2.37295 + 0.122219i) q^{28} +7.05033i q^{29} +(-1.41851 - 9.56738i) q^{30} +1.00000i q^{31} +(-5.46079 + 1.47639i) q^{32} +(2.94176 + 2.94176i) q^{33} +(2.56374 + 1.14007i) q^{34} +(-0.579157 + 2.59265i) q^{35} +(8.51274 + 9.43726i) q^{36} +(-3.23405 + 3.23405i) q^{37} +(-1.00833 - 2.62325i) q^{38} +4.44992 q^{39} +(-0.604547 - 6.29560i) q^{40} +11.1800 q^{41} +(-1.84375 - 4.79667i) q^{42} +(-5.01326 + 5.01326i) q^{43} +(1.82214 + 2.02004i) q^{44} +(-11.9965 + 7.61547i) q^{45} +(1.53421 + 0.682246i) q^{46} +(4.22980 + 4.22980i) q^{47} +(7.71632 + 9.49387i) q^{48} -5.58855i q^{49} +(7.05245 + 0.512785i) q^{50} -6.06815i q^{51} +(2.90598 + 0.149673i) q^{52} +(9.44159 + 9.44159i) q^{53} +(5.89599 - 13.2587i) q^{54} +(-2.56783 + 1.63009i) q^{55} +(-1.04270 - 3.19443i) q^{56} +(-4.29782 + 4.29782i) q^{57} +(9.30681 - 3.57736i) q^{58} +10.8983 q^{59} +(-11.9097 + 6.72703i) q^{60} -10.1104 q^{61} +(1.32005 - 0.507403i) q^{62} +(-5.33842 + 5.33842i) q^{63} +(4.71974 + 6.45942i) q^{64} +(-0.709252 + 3.17503i) q^{65} +(2.39063 - 5.37595i) q^{66} +(2.31705 + 2.31705i) q^{67} +(0.204102 - 3.96274i) q^{68} -3.63134i q^{69} +(3.71631 - 0.551000i) q^{70} -7.20426i q^{71} +(8.13830 - 16.0258i) q^{72} +(-5.40068 - 5.40068i) q^{73} +(5.91008 + 2.62815i) q^{74} +(-5.18413 - 14.3872i) q^{75} +(-2.95121 + 2.66209i) q^{76} +(-1.14268 + 1.14268i) q^{77} +(-2.25790 - 5.87413i) q^{78} +3.78916 q^{79} +(-8.00378 + 3.99244i) q^{80} -12.3180 q^{81} +(-5.67277 - 14.7582i) q^{82} +(-12.2588 + 12.2588i) q^{83} +(-5.39634 + 4.86769i) q^{84} +(4.32964 + 0.967173i) q^{85} +(9.16152 + 4.07403i) q^{86} +(-15.2479 - 15.2479i) q^{87} +(1.74200 - 3.43030i) q^{88} +2.73953i q^{89} +(16.1399 + 11.9719i) q^{90} +1.72850i q^{91} +(0.122140 - 2.37141i) q^{92} +(-2.16272 - 2.16272i) q^{93} +(3.43735 - 7.72977i) q^{94} +(-2.38150 - 3.75152i) q^{95} +(8.61713 - 15.0032i) q^{96} +(1.63417 - 1.63417i) q^{97} +(-7.37718 + 2.83564i) q^{98} -8.64376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 2 q^{2} + 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{8} - 10 q^{10} - 12 q^{12} - 6 q^{13} + 22 q^{14} - 2 q^{15} + 8 q^{16} - 2 q^{17} - 24 q^{18} + 8 q^{19} + 8 q^{20} - 16 q^{21} - 16 q^{22} + 10 q^{23}+ \cdots - 8 q^{99}+O(q^{100}) \) 88 * q + 2 * q^2 + 2 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^8 - 10 * q^10 - 12 * q^12 - 6 * q^13 + 22 * q^14 - 2 * q^15 + 8 * q^16 - 2 * q^17 - 24 * q^18 + 8 * q^19 + 8 * q^20 - 16 * q^21 - 16 * q^22 + 10 * q^23 - 44 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 + 46 * q^28 + 16 * q^30 - 8 * q^32 - 8 * q^33 + 40 * q^34 - 12 * q^35 - 20 * q^36 + 10 * q^37 - 64 * q^38 + 8 * q^39 + 8 * q^41 + 28 * q^42 + 10 * q^43 - 16 * q^44 + 6 * q^45 - 24 * q^46 - 64 * q^47 + 88 * q^48 - 14 * q^50 + 20 * q^52 + 18 * q^53 + 36 * q^54 + 40 * q^55 - 24 * q^56 - 24 * q^57 - 52 * q^58 - 32 * q^60 + 20 * q^61 + 2 * q^62 - 4 * q^63 - 150 * q^64 - 18 * q^65 + 8 * q^66 + 116 * q^67 + 68 * q^68 - 6 * q^70 - 26 * q^72 + 38 * q^73 + 36 * q^74 - 70 * q^75 - 8 * q^76 + 40 * q^77 - 152 * q^78 + 32 * q^79 + 68 * q^80 - 60 * q^81 + 14 * q^82 - 14 * q^83 - 120 * q^84 + 6 * q^85 + 4 * q^86 - 44 * q^87 + 52 * q^88 - 68 * q^90 - 92 * q^92 + 2 * q^93 + 112 * q^94 + 104 * q^95 - 20 * q^96 + 16 * q^97 - 62 * q^98 - 8 * q^99

Introduction

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