LMFDB - Embedded newform 990.2.t.a.461.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(131,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			461.8
Character	$\chi$	$=$	990.461
Dual form			990.2.t.a.131.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.19434 - 1.25442i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.68352 - 0.407116i) q^{6} +(-1.93804 - 1.11893i) q^{7} +1.00000 q^{8} +(-0.147126 + 2.99639i) q^{9} +1.00000i q^{10} +(2.43975 + 2.24669i) q^{11} +(-0.489190 + 1.66153i) q^{12} +(-2.70110 + 1.55948i) q^{13} +(1.93804 - 1.11893i) q^{14} +(-1.66153 - 0.489190i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.53311 q^{17} +(-2.52139 - 1.62561i) q^{18} +0.649165i q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.911067 + 3.76748i) q^{21} +(-3.16557 + 0.989540i) q^{22} +(1.72813 - 0.997734i) q^{23} +(-1.19434 - 1.25442i) q^{24} +(0.500000 - 0.866025i) q^{25} -3.11896i q^{26} +(3.93444 - 3.39414i) q^{27} +2.23785i q^{28} +(0.0531702 - 0.0920935i) q^{29} +(1.25442 - 1.19434i) q^{30} +(4.17649 + 7.23389i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.0955921 - 5.74377i) q^{33} +(1.76655 - 3.05976i) q^{34} -2.23785 q^{35} +(2.66851 - 1.37078i) q^{36} -3.00315 q^{37} +(-0.562194 - 0.324583i) q^{38} +(5.18226 + 1.52576i) q^{39} +(0.866025 - 0.500000i) q^{40} +(1.38401 + 2.39717i) q^{41} +(-3.71827 - 1.09474i) q^{42} +(10.0170 + 5.78333i) q^{43} +(0.725816 - 3.23623i) q^{44} +(1.37078 + 2.66851i) q^{45} +1.99547i q^{46} +(5.60838 + 3.23800i) q^{47} +(1.68352 - 0.407116i) q^{48} +(-0.996003 - 1.72513i) q^{49} +(0.500000 + 0.866025i) q^{50} +(4.21972 + 4.43199i) q^{51} +(2.70110 + 1.55948i) q^{52} -3.95259i q^{53} +(0.972189 + 5.10439i) q^{54} +(3.23623 + 0.725816i) q^{55} +(-1.93804 - 1.11893i) q^{56} +(0.814324 - 0.775321i) q^{57} +(0.0531702 + 0.0920935i) q^{58} +(-2.80361 + 1.61866i) q^{59} +(0.407116 + 1.68352i) q^{60} +(11.4068 + 6.58570i) q^{61} -8.35297 q^{62} +(3.63788 - 5.64250i) q^{63} +1.00000 q^{64} +(-1.55948 + 2.70110i) q^{65} +(5.02204 + 2.78910i) q^{66} +(4.91487 + 8.51280i) q^{67} +(1.76655 + 3.05976i) q^{68} +(-3.31554 - 0.976162i) q^{69} +(1.11893 - 1.93804i) q^{70} -1.16465i q^{71} +(-0.147126 + 2.99639i) q^{72} -1.40361i q^{73} +(1.50157 - 2.60080i) q^{74} +(-1.68352 + 0.407116i) q^{75} +(0.562194 - 0.324583i) q^{76} +(-2.21445 - 7.08408i) q^{77} +(-3.91248 + 3.72509i) q^{78} +(2.59056 + 1.49566i) q^{79} +1.00000i q^{80} +(-8.95671 - 0.881691i) q^{81} -2.76801 q^{82} +(-4.91742 + 8.51723i) q^{83} +(2.80720 - 2.67275i) q^{84} +(-3.05976 + 1.76655i) q^{85} +(-10.0170 + 5.78333i) q^{86} +(-0.179027 + 0.0432929i) q^{87} +(2.43975 + 2.24669i) q^{88} -0.269039i q^{89} +(-2.99639 - 0.147126i) q^{90} +6.97979 q^{91} +(-1.72813 - 0.997734i) q^{92} +(4.08619 - 13.8787i) q^{93} +(-5.60838 + 3.23800i) q^{94} +(0.324583 + 0.562194i) q^{95} +(-0.489190 + 1.66153i) q^{96} +(-2.53151 + 4.38471i) q^{97} +1.99201 q^{98} +(-7.09091 + 6.97990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{6} + 48 q^{8} + 10 q^{9} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) $ 48 * q - 24 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^6 + 48 * q^8 + 10 * q^9 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 - 40 * q^39 - 6 * q^41 + 8 * q^42 + 30 * q^43 - 6 * q^44 - 2 * q^48 + 24 * q^49 + 24 * q^50 + 22 * q^51 - 24 * q^52 + 22 * q^54 + 40 * q^57 - 54 * q^59 - 4 * q^60 - 38 * q^63 + 48 * q^64 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.19434	−	1.25442i	−0.689550	−	0.724238i
$3$	−1.19434	−	1.25442i	−0.689550	−	0.724238i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	1.68352	−	0.407116i	0.687296	−	0.166204i
$7$	−1.93804	−	1.11893i	−0.732510	−	0.422915i	0.0868297	−	0.996223i	$-0.472326\pi$
$7$	−1.93804	−	1.11893i	−0.732510	−	0.422915i	−0.819340	+	0.573308i	$0.805660\pi$
$8$	1.00000			0.353553
$9$	−0.147126	+	2.99639i	−0.0490419	+	0.998797i
$10$			1.00000i			0.316228i
$11$	2.43975	+	2.24669i	0.735612	+	0.677403i
$11$	2.43975	+	2.24669i	0.735612	+	0.677403i
$12$	−0.489190	+	1.66153i	−0.141217	+	0.479643i
$13$	−2.70110	+	1.55948i	−0.749151	+	0.432522i	−0.825387	−	0.564567i	$-0.809043\pi$
$13$	−2.70110	+	1.55948i	−0.749151	+	0.432522i	0.0762361	+	0.997090i	$0.475710\pi$
$14$	1.93804	−	1.11893i	0.517963	−	0.299046i
$15$	−1.66153	−	0.489190i	−0.429006	−	0.126308i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.53311			−0.856905			−0.428452	−	0.903564i	$-0.640941\pi$
$17$	−3.53311			−0.856905			−0.428452	+	0.903564i	$0.640941\pi$
$18$	−2.52139	−	1.62561i	−0.594297	−	0.383160i
$19$			0.649165i			0.148929i	0.997224	+	0.0744644i	$0.0237247\pi$
$19$			0.649165i			0.148929i	−0.997224	+	0.0744644i	$0.976275\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	0.911067	+	3.76748i	0.198811	+	0.822133i
$22$	−3.16557	+	0.989540i	−0.674901	+	0.210971i
$23$	1.72813	−	0.997734i	0.360339	−	0.208042i	−0.308890	−	0.951098i	$-0.599958\pi$
$23$	1.72813	−	0.997734i	0.360339	−	0.208042i	0.669230	+	0.743056i	$0.266624\pi$
$24$	−1.19434	−	1.25442i	−0.243793	−	0.256057i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		−	3.11896i		−	0.611679i
$27$	3.93444	−	3.39414i	0.757184	−	0.653202i
$28$			2.23785i			0.422915i
$29$	0.0531702	−	0.0920935i	0.00987346	−	0.0171013i	−0.861046	−	0.508526i	$-0.830190\pi$
$29$	0.0531702	−	0.0920935i	0.00987346	−	0.0171013i	0.870920	+	0.491425i	$0.163524\pi$
$30$	1.25442	−	1.19434i	0.229024	−	0.218055i
$31$	4.17649	+	7.23389i	0.750119	+	1.29924i	0.947765	+	0.318971i	$0.103337\pi$
$31$	4.17649	+	7.23389i	0.750119	+	1.29924i	−0.197646	+	0.980274i	$0.563330\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.0955921	−	5.74377i	−0.0166404	−	0.999862i
$34$	1.76655	−	3.05976i	0.302962	−	0.524745i
$35$	−2.23785			−0.378267
$36$	2.66851	−	1.37078i	0.444752	−	0.228463i
$37$	−3.00315			−0.493715			−0.246857	−	0.969052i	$-0.579398\pi$
$37$	−3.00315			−0.493715			−0.246857	+	0.969052i	$0.579398\pi$
$38$	−0.562194	−	0.324583i	−0.0911998	−	0.0526543i
$39$	5.18226	+	1.52576i	0.829826	+	0.244318i
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	1.38401	+	2.39717i	0.216146	+	0.374375i	0.953626	−	0.300993i	$-0.0973181\pi$
$41$	1.38401	+	2.39717i	0.216146	+	0.374375i	−0.737481	+	0.675368i	$0.763985\pi$
$42$	−3.71827	−	1.09474i	−0.573742	−	0.168921i
$43$	10.0170	+	5.78333i	1.52758	+	0.881950i	0.999463	+	0.0327798i	$0.0104360\pi$
$43$	10.0170	+	5.78333i	1.52758	+	0.881950i	0.528119	+	0.849170i	$0.322897\pi$
$44$	0.725816	−	3.23623i	0.109421	−	0.487880i
$45$	1.37078	+	2.66851i	0.204344	+	0.397798i
$46$			1.99547i			0.294216i
$47$	5.60838	+	3.23800i	0.818067	+	0.472311i	0.849749	−	0.527187i	$-0.176753\pi$
$47$	5.60838	+	3.23800i	0.818067	+	0.472311i	−0.0316824	+	0.999498i	$0.510087\pi$
$48$	1.68352	−	0.407116i	0.242996	−	0.0587622i
$49$	−0.996003	−	1.72513i	−0.142286	−	0.246447i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	4.21972	+	4.43199i	0.590878	+	0.620603i
$52$	2.70110	+	1.55948i	0.374575	+	0.216261i
$53$		−	3.95259i		−	0.542930i	−0.962448	−	0.271465i	$-0.912492\pi$
$53$		−	3.95259i		−	0.542930i	0.962448	−	0.271465i	$-0.0875082\pi$
$54$	0.972189	+	5.10439i	0.132298	+	0.694620i
$55$	3.23623	+	0.725816i	0.436373	+	0.0978691i
$56$	−1.93804	−	1.11893i	−0.258981	−	0.149523i
$57$	0.814324	−	0.775321i	0.107860	−	0.102694i
$58$	0.0531702	+	0.0920935i	0.00698159	+	0.0120925i
$59$	−2.80361	+	1.61866i	−0.364998	+	0.210732i	−0.671271	−	0.741212i	$-0.734251\pi$
$59$	−2.80361	+	1.61866i	−0.364998	+	0.210732i	0.306273	+	0.951944i	$0.400918\pi$
$60$	0.407116	+	1.68352i	0.0525585	+	0.217342i
$61$	11.4068	+	6.58570i	1.46049	+	0.843212i	0.999034	−	0.0439524i	$-0.0139950\pi$
$61$	11.4068	+	6.58570i	1.46049	+	0.843212i	0.461453	+	0.887165i	$0.347328\pi$
$62$	−8.35297			−1.06083
$63$	3.63788	−	5.64250i	0.458330	−	0.710888i
$64$	1.00000			0.125000
$65$	−1.55948	+	2.70110i	−0.193430	+	0.335030i
$66$	5.02204	+	2.78910i	0.618171	+	0.343314i
$67$	4.91487	+	8.51280i	0.600447	+	1.04000i	0.992753	+	0.120170i	$0.0383439\pi$
$67$	4.91487	+	8.51280i	0.600447	+	1.04000i	−0.392307	+	0.919834i	$0.628323\pi$
$68$	1.76655	+	3.05976i	0.214226	+	0.371051i
$69$	−3.31554	−	0.976162i	−0.399144	−	0.117516i
$70$	1.11893	−	1.93804i	0.133737	−	0.231640i
$71$		−	1.16465i		−	0.138219i	−0.997609	−	0.0691095i	$-0.977984\pi$
$71$		−	1.16465i		−	0.138219i	0.997609	−	0.0691095i	$-0.0220158\pi$
$72$	−0.147126	+	2.99639i	−0.0173389	+	0.353128i
$73$		−	1.40361i		−	0.164280i	−0.996621	−	0.0821400i	$-0.973825\pi$
$73$		−	1.40361i		−	0.164280i	0.996621	−	0.0821400i	$-0.0261755\pi$
$74$	1.50157	−	2.60080i	0.174554	−	0.302337i
$75$	−1.68352	+	0.407116i	−0.194397	+	0.0470097i
$76$	0.562194	−	0.324583i	0.0644880	−	0.0372322i
$77$	−2.21445	−	7.08408i	−0.252360	−	0.807306i
$78$	−3.91248	+	3.72509i	−0.443001	+	0.421783i
$79$	2.59056	+	1.49566i	0.291461	+	0.168275i	0.638601	−	0.769538i	$-0.279514\pi$
$79$	2.59056	+	1.49566i	0.291461	+	0.168275i	−0.347140	+	0.937813i	$0.612847\pi$
$80$			1.00000i			0.111803i
$81$	−8.95671	−	0.881691i	−0.995190	−	0.0979657i
$82$	−2.76801			−0.305676
$83$	−4.91742	+	8.51723i	−0.539757	+	0.934887i	0.459159	+	0.888354i	$0.348151\pi$
$83$	−4.91742	+	8.51723i	−0.539757	+	0.934887i	−0.998917	+	0.0465331i	$0.985183\pi$
$84$	2.80720	−	2.67275i	0.306291	−	0.291621i
$85$	−3.05976	+	1.76655i	−0.331878	+	0.191610i
$86$	−10.0170	+	5.78333i	−1.08016	+	0.623633i
$87$	−0.179027	+	0.0432929i	−0.0191937	+	0.00464149i
$88$	2.43975	+	2.24669i	0.260078	+	0.239498i
$89$		−	0.269039i		−	0.0285181i	−0.999898	−	0.0142590i	$-0.995461\pi$
$89$		−	0.269039i		−	0.0285181i	0.999898	−	0.0142590i	$-0.00453894\pi$
$90$	−2.99639	−	0.147126i	−0.315847	−	0.0155084i
$91$	6.97979			0.731681
$92$	−1.72813	−	0.997734i	−0.180170	−	0.104021i
$93$	4.08619	−	13.8787i	0.423718	−	1.43916i
$94$	−5.60838	+	3.23800i	−0.578461	+	0.333974i
$95$	0.324583	+	0.562194i	0.0333015	+	0.0576798i
$96$	−0.489190	+	1.66153i	−0.0499277	+	0.169580i
$97$	−2.53151	+	4.38471i	−0.257036	+	0.445200i	−0.965447	−	0.260601i	$-0.916079\pi$
$97$	−2.53151	+	4.38471i	−0.257036	+	0.445200i	0.708410	+	0.705801i	$0.249413\pi$
$98$	1.99201			0.201223
$99$	−7.09091	+	6.97990i	−0.712663	+	0.701506i
$100$	−1.00000			−0.100000
$101$	0.625489	−	1.08338i	0.0622385	−	0.107800i	−0.833227	−	0.552931i	$-0.813509\pi$
$101$	0.625489	−	1.08338i	0.0622385	−	0.107800i	0.895466	+	0.445131i	$0.146843\pi$
$102$	−5.94808	+	1.43839i	−0.588947	+	0.142421i
$103$	4.34798	+	7.53091i	0.428419	+	0.742043i	0.996733	−	0.0807686i	$-0.0257375\pi$
$103$	4.34798	+	7.53091i	0.428419	+	0.742043i	−0.568314	+	0.822812i	$0.692404\pi$
$104$	−2.70110	+	1.55948i	−0.264865	+	0.152920i
$105$	2.67275	+	2.80720i	0.260834	+	0.273955i
$106$	3.42305	+	1.97630i	0.332476	+	0.191955i
$107$	−7.47916			−0.723038			−0.361519	−	0.932365i	$-0.617742\pi$
$107$	−7.47916			−0.723038			−0.361519	+	0.932365i	$0.617742\pi$
$108$	−4.90663	−	1.71026i	−0.472141	−	0.164570i
$109$			11.4060i			1.09249i	0.837624	+	0.546247i	$0.183944\pi$
$109$			11.4060i			1.09249i	−0.837624	+	0.546247i	$0.816056\pi$
$110$	−2.24669	+	2.43975i	−0.214214	+	0.232621i
$111$	3.58677	+	3.76720i	0.340441	+	0.357567i
$112$	1.93804	−	1.11893i	0.183127	−	0.105729i
$113$	11.2536	−	6.49729i	1.05865	−	0.611214i	0.133594	−	0.991036i	$-0.457348\pi$
$113$	11.2536	−	6.49729i	1.05865	−	0.611214i	0.925059	+	0.379822i	$0.124015\pi$
$114$	0.264286	+	1.09289i	0.0247526	+	0.102358i
$115$	0.997734	−	1.72813i	0.0930392	−	0.161149i
$116$	−0.106340			−0.00987346
$117$	−4.27542	−	8.32300i	−0.395262	−	0.769461i
$118$		−	3.23733i		−	0.298020i
$119$	6.84730	+	3.95329i	0.627691	+	0.362398i
$120$	−1.66153	−	0.489190i	−0.151677	−	0.0446567i
$121$	0.904760	+	10.9627i	0.0822509	+	0.996612i
$122$	−11.4068	+	6.58570i	−1.03272	+	0.596241i
$123$	1.35408	−	4.59915i	0.122094	−	0.414691i
$124$	4.17649	−	7.23389i	0.375059	−	0.649622i
$125$		−	1.00000i		−	0.0894427i
$126$	3.06761	+	5.97174i	0.273284	+	0.532005i
$127$			3.47665i			0.308503i	0.988032	+	0.154251i	$0.0492965\pi$
$127$			3.47665i			0.308503i	−0.988032	+	0.154251i	$0.950703\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−4.70898	−	19.4728i	−0.414602	−	1.71448i
$130$	−1.55948	−	2.70110i	−0.136776	−	0.236902i
$131$	−1.86412	−	3.22874i	−0.162869	−	0.282097i	0.773028	−	0.634372i	$-0.218741\pi$
$131$	−1.86412	−	3.22874i	−0.162869	−	0.282097i	−0.935896	+	0.352276i	$0.885408\pi$
$132$	−4.92645	+	2.95467i	−0.428793	+	0.257171i
$133$	0.726369	−	1.25811i	0.0629842	−	0.109092i
$134$	−9.82974			−0.849160
$135$	1.71026	−	4.90663i	0.147195	−	0.422296i
$136$	−3.53311			−0.302962
$137$	2.31644	+	1.33740i	0.197907	+	0.114262i	0.595679	−	0.803223i	$-0.296883\pi$
$137$	2.31644	+	1.33740i	0.197907	+	0.114262i	−0.397772	+	0.917484i	$0.630216\pi$
$138$	2.50315	−	2.38326i	0.213082	−	0.202876i
$139$	6.75836	−	3.90194i	0.573237	−	0.330958i	−0.185204	−	0.982700i	$-0.559295\pi$
$139$	6.75836	−	3.90194i	0.573237	−	0.330958i	0.758441	+	0.651742i	$0.225961\pi$
$140$	1.11893	+	1.93804i	0.0945666	+	0.163794i
$141$	−2.63649	−	10.9025i	−0.222032	−	0.918158i
$142$	1.00862	+	0.582327i	0.0846415	+	0.0488678i
$143$	−10.0937	−	2.26380i	−0.844077	−	0.189308i
$144$	−2.52139	−	1.62561i	−0.210116	−	0.135467i
$145$		−	0.106340i		−	0.00883109i
$146$	1.21556	+	0.701804i	0.100601	+	0.0580817i
$147$	−0.974468	+	3.30978i	−0.0803728	+	0.272986i
$148$	1.50157	+	2.60080i	0.123429	+	0.213785i
$149$	−0.0324085	−	0.0561333i	−0.00265501	−	0.00459862i	0.864695	−	0.502298i	$-0.167512\pi$
$149$	−0.0324085	−	0.0561333i	−0.00265501	−	0.00459862i	−0.867350	+	0.497699i	$0.834178\pi$
$150$	0.489190	−	1.66153i	0.0399422	−	0.135664i
$151$	12.7926	+	7.38583i	1.04105	+	0.601050i	0.920130	−	0.391612i	$-0.128082\pi$
$151$	12.7926	+	7.38583i	1.04105	+	0.601050i	0.120919	+	0.992662i	$0.461416\pi$
$152$			0.649165i			0.0526543i
$153$	0.519810	−	10.5866i	0.0420242	−	0.855873i
$154$	7.24222	+	1.62427i	0.583594	+	0.130888i
$155$	7.23389	+	4.17649i	0.581040	+	0.335463i
$156$	−1.26978	−	5.25085i	−0.101664	−	0.420405i
$157$	−4.61431	−	7.99222i	−0.368262	−	0.637849i	0.621032	−	0.783785i	$-0.286714\pi$
$157$	−4.61431	−	7.99222i	−0.368262	−	0.637849i	−0.989294	+	0.145937i	$0.953380\pi$
$158$	−2.59056	+	1.49566i	−0.206094	+	0.118988i
$159$	−4.95820	+	4.72072i	−0.393211	+	0.374378i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−4.46557			−0.351936
$162$	5.24192	−	7.31589i	0.411844	−	0.574791i
$163$	−1.69270			−0.132582			−0.0662912	−	0.997800i	$-0.521117\pi$
$163$	−1.69270			−0.132582			−0.0662912	+	0.997800i	$0.521117\pi$
$164$	1.38401	−	2.39717i	0.108073	−	0.187188i
$165$	−2.95467	−	4.92645i	−0.230021	−	0.383524i
$166$	−4.91742	−	8.51723i	−0.381666	−	0.661065i
$167$	−8.19719	−	14.1980i	−0.634318	−	1.09867i	−0.986659	−	0.162799i	$-0.947948\pi$
$167$	−8.19719	−	14.1980i	−0.634318	−	1.09867i	0.352341	−	0.935872i	$-0.385386\pi$
$168$	0.911067	+	3.76748i	0.0702903	+	0.290668i
$169$	−1.63603	+	2.83369i	−0.125849	+	0.217976i
$170$		−	3.53311i		−	0.270977i
$171$	−1.94515	−	0.0955088i	−0.148750	−	0.00730374i
$172$		−	11.5667i		−	0.881950i
$173$	10.2188	−	17.6995i	0.776923	−	1.34567i	−0.156784	−	0.987633i	$-0.550113\pi$
$173$	10.2188	−	17.6995i	0.776923	−	1.34567i	0.933707	−	0.358037i	$-0.116554\pi$
$174$	0.0520206	−	0.176688i	0.00394367	−	0.0133947i
$175$	−1.93804	+	1.11893i	−0.146502	+	0.0845830i
$176$	−3.16557	+	0.989540i	−0.238614	+	0.0745894i
$177$	5.37892	+	1.58367i	0.404305	+	0.119036i
$178$	0.232994	+	0.134519i	0.0174637	+	0.0100827i
$179$			20.0246i			1.49671i	0.663297	+	0.748356i	$0.269156\pi$
$179$			20.0246i			1.49671i	−0.663297	+	0.748356i	$0.730844\pi$
$180$	1.62561	−	2.52139i	0.121166	−	0.187933i
$181$	−22.3978			−1.66482			−0.832408	−	0.554163i	$-0.813038\pi$
$181$	−22.3978			−1.66482			−0.832408	+	0.554163i	$0.813038\pi$
$182$	−3.48989	+	6.04467i	−0.258688	+	0.448061i
$183$	−5.36229	−	22.1744i	−0.396392	−	1.63918i
$184$	1.72813	−	0.997734i	0.127399	−	0.0735539i
$185$	−2.60080	+	1.50157i	−0.191215	+	0.110398i
$186$	9.97625	+	10.4781i	0.731494	+	0.768292i
$187$	−8.61990	−	7.93780i	−0.630350	−	0.580470i
$188$		−	6.47601i		−	0.472311i
$189$	−11.4229	+	2.17562i	−0.830893	+	0.158253i
$190$	−0.649165			−0.0470954
$191$	1.37544	+	0.794110i	0.0995233	+	0.0574598i	0.548936	−	0.835865i	$-0.315033\pi$
$191$	1.37544	+	0.794110i	0.0995233	+	0.0574598i	−0.449412	+	0.893324i	$0.648367\pi$
$192$	−1.19434	−	1.25442i	−0.0861937	−	0.0905298i
$193$	−22.3683	+	12.9144i	−1.61011	+	0.929596i	−0.620763	+	0.783998i	$0.713177\pi$
$193$	−22.3683	+	12.9144i	−1.61011	+	0.929596i	−0.989344	+	0.145597i	$0.953490\pi$
$194$	−2.53151	−	4.38471i	−0.181752	−	0.314804i
$195$	5.25085	−	1.26978i	0.376021	−	0.0909309i
$196$	−0.996003	+	1.72513i	−0.0711430	+	0.123223i
$197$	−20.0332			−1.42730			−0.713652	−	0.700500i	$-0.752960\pi$
$197$	−20.0332			−1.42730			−0.713652	+	0.700500i	$0.752960\pi$
$198$	−2.49931	−	9.63086i	−0.177618	−	0.684435i
$199$	1.63362			0.115804			0.0579022	−	0.998322i	$-0.481559\pi$
$199$	1.63362			0.115804			0.0579022	+	0.998322i	$0.481559\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	4.80860	−	16.3324i	0.339173	−	1.15200i
$202$	0.625489	+	1.08338i	0.0440092	+	0.0762262i
$203$	−0.206092	+	0.118987i	−0.0144648	+	0.00835127i
$204$	1.72836	−	5.87038i	0.121009	−	0.411009i
$205$	2.39717	+	1.38401i	0.167426	+	0.0966633i
$206$	−8.69595			−0.605876
$207$	2.73535	+	5.32493i	0.190120	+	0.370108i
$208$		−	3.11896i		−	0.216261i
$209$	−1.45847	+	1.58380i	−0.100885	+	0.109554i
$210$	−3.76748	+	0.911067i	−0.259981	+	0.0628696i
$211$	13.8809	−	8.01412i	0.955598	−	0.551715i	0.0607823	−	0.998151i	$-0.480640\pi$
$211$	13.8809	−	8.01412i	0.955598	−	0.551715i	0.894815	+	0.446437i	$0.147307\pi$
$212$	−3.42305	+	1.97630i	−0.235096	+	0.135733i
$213$	−1.46096	+	1.39099i	−0.100103	+	0.0953089i
$214$	3.73958	−	6.47714i	0.255632	−	0.442768i
$215$	11.5667			0.788840
$216$	3.93444	−	3.39414i	0.267705	−	0.230942i
$217$		−	18.6927i		−	1.26895i
$218$	−9.87786	−	5.70298i	−0.669013	−	0.386255i
$219$	−1.76071	+	1.67638i	−0.118978	+	0.113279i
$220$	−0.989540	−	3.16557i	−0.0667148	−	0.213422i
$221$	9.54329	−	5.50982i	0.641951	−	0.370630i
$222$	−5.05588	+	1.22263i	−0.339328	+	0.0820576i
$223$	−4.23876	+	7.34175i	−0.283848	+	0.491640i	−0.972329	−	0.233615i	$-0.924945\pi$
$223$	−4.23876	+	7.34175i	−0.283848	+	0.491640i	0.688481	+	0.725255i	$0.258278\pi$
$224$			2.23785i			0.149523i
$225$	2.52139	+	1.62561i	0.168092	+	0.108374i
$226$			12.9946i			0.864387i
$227$	3.63551	−	6.29688i	0.241297	−	0.417939i	−0.719787	−	0.694195i	$-0.755761\pi$
$227$	3.63551	−	6.29688i	0.241297	−	0.417939i	0.961084	+	0.276256i	$0.0890938\pi$
$228$	−1.07861	−	0.317565i	−0.0714327	−	0.0210312i
$229$	−7.10018	−	12.2979i	−0.469193	−	0.812667i	0.530186	−	0.847881i	$-0.322122\pi$
$229$	−7.10018	−	12.2979i	−0.469193	−	0.812667i	−0.999380	+	0.0352143i	$0.988789\pi$
$230$	0.997734	+	1.72813i	0.0657886	+	0.113949i
$231$	−6.24160	+	11.2386i	−0.410667	+	0.739446i
$232$	0.0531702	−	0.0920935i	0.00349080	−	0.00604623i
$233$	1.86696			0.122308			0.0611542	−	0.998128i	$-0.480522\pi$
$233$	1.86696			0.122308			0.0611542	+	0.998128i	$0.480522\pi$
$234$	9.34563	+	0.458879i	0.610943	+	0.0299979i
$235$	6.47601			0.422448
$236$	2.80361	+	1.61866i	0.182499	+	0.105366i
$237$	−1.21782	−	5.03597i	−0.0791057	−	0.327121i
$238$	−6.84730	+	3.95329i	−0.443845	+	0.256254i
$239$	−12.8822	−	22.3127i	−0.833282	−	1.44329i	−0.895421	−	0.445220i	$-0.853125\pi$
$239$	−12.8822	−	22.3127i	−0.833282	−	1.44329i	0.0621388	−	0.998068i	$-0.480208\pi$
$240$	1.25442	−	1.19434i	0.0809723	−	0.0770940i
$241$	26.3093	+	15.1897i	1.69473	+	0.978454i	0.950598	+	0.310423i	$0.100471\pi$
$241$	26.3093	+	15.1897i	1.69473	+	0.978454i	0.744134	+	0.668031i	$0.232863\pi$
$242$	−9.94638	−	4.69782i	−0.639378	−	0.301987i
$243$	9.59131	+	12.2885i	0.615283	+	0.788307i
$244$		−	13.1714i		−	0.843212i
$245$	−1.72513	−	0.996003i	−0.110214	−	0.0636323i
$246$	3.30594	+	3.47225i	0.210779	+	0.221382i
$247$	−1.01236	−	1.75346i	−0.0644150	−	0.111570i
$248$	4.17649	+	7.23389i	0.265207	+	0.459352i
$249$	16.5572	−	4.00392i	1.04927	−	0.253738i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$			0.648202i			0.0409141i	0.999791	+	0.0204571i	$0.00651214\pi$
$251$			0.648202i			0.0409141i	−0.999791	+	0.0204571i	$0.993488\pi$
$252$	−6.70549	−	0.329246i	−0.422406	−	0.0207405i
$253$	6.45780	+	1.44834i	0.405998	+	0.0910566i
$254$	−3.01086	−	1.73832i	−0.188918	−	0.109072i
$255$	5.87038	+	1.72836i	0.367617	+	0.108234i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.78451	−	1.03029i	0.111315	−	0.0642677i	−0.443309	−	0.896369i	$-0.646196\pi$
$257$	1.78451	−	1.03029i	0.111315	−	0.0642677i	0.554624	+	0.832101i	$0.312862\pi$
$258$	19.2184	+	5.65829i	1.19649	+	0.352270i
$259$	5.82022	+	3.36031i	0.361651	+	0.208799i
$260$	3.11896			0.193430
$261$	0.268125	+	0.172868i	0.0165965	+	0.0107003i
$262$	3.72823			0.230331
$263$	4.15995	−	7.20525i	0.256514	−	0.444295i	−0.708792	−	0.705418i	$-0.750759\pi$
$263$	4.15995	−	7.20525i	0.256514	−	0.444295i	0.965306	+	0.261123i	$0.0840928\pi$
$264$	−0.0955921	−	5.74377i	−0.00588329	−	0.353504i
$265$	−1.97630	−	3.42305i	−0.121403	−	0.210276i
$266$	0.726369	+	1.25811i	0.0445365	+	0.0771395i
$267$	−0.337487	+	0.321323i	−0.0206539	+	0.0196646i
$268$	4.91487	−	8.51280i	0.300223	−	0.520002i
$269$		−	7.13974i		−	0.435318i	−0.976025	−	0.217659i	$-0.930158\pi$
$269$		−	7.13974i		−	0.435318i	0.976025	−	0.217659i	$-0.0698420\pi$
$270$	3.39414	+	3.93444i	0.206561	+	0.239442i
$271$		−	25.6730i		−	1.55952i	−0.626076	−	0.779762i	$-0.715340\pi$
$271$		−	25.6730i		−	1.55952i	0.626076	−	0.779762i	$-0.284660\pi$
$272$	1.76655	−	3.05976i	0.107113	−	0.185525i
$273$	−8.33621	−	8.75557i	−0.504530	−	0.529911i
$274$	−2.31644	+	1.33740i	−0.139942	+	0.0807953i
$275$	3.16557	−	0.989540i	0.190891	−	0.0596715i
$276$	0.812388	+	3.35942i	0.0489000	+	0.202213i
$277$	15.8621	+	9.15799i	0.953061	+	0.550250i	0.894031	−	0.448006i	$-0.147866\pi$
$277$	15.8621	+	9.15799i	0.953061	+	0.550250i	0.0590307	+	0.998256i	$0.481199\pi$
$278$			7.80388i			0.468046i
$279$	−22.2900	+	11.4501i	−1.33447	+	0.685499i
$280$	−2.23785			−0.133737
$281$	−11.3351	+	19.6330i	−0.676196	+	1.17121i	0.299922	+	0.953964i	$0.403039\pi$
$281$	−11.3351	+	19.6330i	−0.676196	+	1.17121i	−0.976118	+	0.217242i	$0.930294\pi$
$282$	10.7601	+	3.16799i	0.640755	+	0.188651i
$283$	−25.3797	+	14.6530i	−1.50867	+	0.871029i	−0.508718	+	0.860933i	$0.669880\pi$
$283$	−25.3797	+	14.6530i	−1.50867	+	0.871029i	−0.999949	+	0.0100962i	$0.996786\pi$
$284$	−1.00862	+	0.582327i	−0.0598506	+	0.0345547i
$285$	0.317565	−	1.07861i	0.0188109	−	0.0638913i
$286$	7.00735	−	7.60949i	0.414353	−	0.449959i
$287$		−	6.19442i		−	0.365645i
$288$	2.66851	−	1.37078i	0.157244	−	0.0807740i
$289$	−4.51715			−0.265715
$290$	0.0920935	+	0.0531702i	0.00540792	+	0.00312226i
$291$	8.52373	−	2.06124i	0.499670	−	0.120832i
$292$	−1.21556	+	0.701804i	−0.0711353	+	0.0410700i
$293$	10.2552	+	17.7625i	0.599113	+	1.03769i	0.992952	+	0.118515i	$0.0378133\pi$
$293$	10.2552	+	17.7625i	0.599113	+	1.03769i	−0.393839	+	0.919179i	$0.628853\pi$
$294$	−2.37912	−	2.49881i	−0.138753	−	0.145733i
$295$	−1.61866	+	2.80361i	−0.0942422	+	0.163232i
$296$	−3.00315			−0.174554
$297$	17.2246	+	0.558624i	0.999475	+	0.0324146i
$298$	0.0648171			0.00375475
$299$	−3.11190	+	5.38996i	−0.179966	+	0.311710i
$300$	1.19434	+	1.25442i	0.0689550	+	0.0724238i
$301$	−12.9423	−	22.4166i	−0.745979	−	1.29207i
$302$	−12.7926	+	7.38583i	−0.736133	+	0.425007i
$303$	−2.10605	+	0.509293i	−0.120990	+	0.0292581i
$304$	−0.562194	−	0.324583i	−0.0322440	−	0.0186161i
$305$	13.1714			0.754192
$306$	8.90833	+	5.74345i	0.509256	+	0.328331i
$307$		−	21.7811i		−	1.24311i	−0.783369	−	0.621557i	$-0.786500\pi$
$307$		−	21.7811i		−	1.24311i	0.783369	−	0.621557i	$-0.213500\pi$
$308$	−5.02777	+	5.45981i	−0.286484	+	0.311101i
$309$	4.25397	−	14.4486i	0.242000	−	0.821953i
$310$	−7.23389	+	4.17649i	−0.410857	+	0.237208i
$311$	−1.76080	+	1.01660i	−0.0998460	+	0.0576461i	−0.549092	−	0.835762i	$-0.685026\pi$
$311$	−1.76080	+	1.01660i	−0.0998460	+	0.0576461i	0.449246	+	0.893408i	$0.351693\pi$
$312$	5.18226	+	1.52576i	0.293388	+	0.0863794i
$313$	−12.2823	+	21.2735i	−0.694235	+	1.20245i	0.276202	+	0.961100i	$0.410924\pi$
$313$	−12.2823	+	21.2735i	−0.694235	+	1.20245i	−0.970438	+	0.241352i	$0.922409\pi$
$314$	9.22862			0.520801
$315$	0.329246	−	6.70549i	0.0185509	−	0.377811i
$316$		−	2.99132i		−	0.168275i
$317$	15.0163	+	8.66967i	0.843400	+	0.486937i	0.858418	−	0.512950i	$-0.171447\pi$
$317$	15.0163	+	8.66967i	0.843400	+	0.486937i	−0.0150187	+	0.999887i	$0.504781\pi$
$318$	−1.60916	−	6.65429i	−0.0902375	−	0.373154i
$319$	0.336628	−	0.105228i	0.0188475	−	0.00589164i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	8.93262	+	9.38199i	0.498570	+	0.523651i
$322$	2.23278	−	3.86730i	0.124428	−	0.215516i
$323$		−	2.29357i		−	0.127618i
$324$	3.71479	+	8.19758i	0.206377	+	0.455421i
$325$			3.11896i			0.173009i
$326$	0.846349	−	1.46592i	0.0468749	−	0.0811898i
$327$	14.3078	−	13.6225i	0.791225	−	0.753329i
$328$	1.38401	+	2.39717i	0.0764190	+	0.132362i
$329$	−7.24618	−	12.5508i	−0.399495	−	0.691945i
$330$	5.74377	−	0.0955921i	0.316184	−	0.00526217i
$331$	8.70296	−	15.0740i	0.478358	−	0.828541i	−0.521334	−	0.853353i	$-0.674565\pi$
$331$	8.70296	−	15.0740i	0.478358	−	0.828541i	0.999692	+	0.0248121i	$0.00789874\pi$
$332$	9.83485			0.539757
$333$	0.441840	−	8.99861i	0.0242127	−	0.493121i
$334$	16.3944			0.897061
$335$	8.51280	+	4.91487i	0.465104	+	0.268528i
$336$	−3.71827	−	1.09474i	−0.202848	−	0.0597227i
$337$	12.1230	−	6.99923i	0.660383	−	0.381272i	−0.132040	−	0.991244i	$-0.542153\pi$
$337$	12.1230	−	6.99923i	0.660383	−	0.381272i	0.792423	+	0.609972i	$0.208819\pi$
$338$	−1.63603	−	2.83369i	−0.0889884	−	0.154132i
$339$	−21.5909	−	6.35681i	−1.17266	−	0.345255i
$340$	3.05976	+	1.76655i	0.165939	+	0.0958048i
$341$	−6.06272	+	27.0321i	−0.328315	+	1.46387i
$342$	1.05529	−	1.63680i	0.0570635	−	0.0885078i
$343$			20.1228i			1.08653i
$344$	10.0170	+	5.78333i	0.540082	+	0.311816i
$345$	−3.35942	+	0.812388i	−0.180865	+	0.0437375i
$346$	10.2188	+	17.6995i	0.549368	+	0.951533i
$347$	13.0830	+	22.6604i	0.702332	+	1.21648i	0.967646	+	0.252313i	$0.0811912\pi$
$347$	13.0830	+	22.6604i	0.702332	+	1.21648i	−0.265314	+	0.964162i	$0.585475\pi$
$348$	0.127006	+	0.133395i	0.00680824	+	0.00715074i
$349$	−27.7358	−	16.0132i	−1.48466	−	0.857170i	−0.484814	−	0.874618i	$-0.661113\pi$
$349$	−27.7358	−	16.0132i	−1.48466	−	0.857170i	−0.999848	+	0.0174479i	$0.994446\pi$
$350$		−	2.23785i		−	0.119618i
$351$	−5.33423	+	15.3036i	−0.284720	+	0.816846i
$352$	0.725816	−	3.23623i	0.0386861	−	0.172492i
$353$	−20.2217	−	11.6750i	−1.07629	−	0.621397i	−0.146398	−	0.989226i	$-0.546768\pi$
$353$	−20.2217	−	11.6750i	−1.07629	−	0.621397i	−0.929894	+	0.367829i	$0.880101\pi$
$354$	−4.06096	+	3.86645i	−0.215837	+	0.205500i
$355$	−0.582327	−	1.00862i	−0.0309067	−	0.0535320i
$356$	−0.232994	+	0.134519i	−0.0123487	+	0.00712952i
$357$	−3.21890	−	13.3109i	−0.170362	−	0.704489i
$358$	−17.3418	−	10.0123i	−0.916545	−	0.529168i
$359$	18.2033			0.960731			0.480366	−	0.877068i	$-0.340504\pi$
$359$	18.2033			0.960731			0.480366	+	0.877068i	$0.340504\pi$
$360$	1.37078	+	2.66851i	0.0722465	+	0.140643i
$361$	18.5786			0.977820
$362$	11.1989	−	19.3971i	0.588602	−	1.01949i
$363$	12.6712	−	14.2281i	0.665068	−	0.746783i
$364$	−3.48989	−	6.04467i	−0.182920	−	0.316827i
$365$	−0.701804	−	1.21556i	−0.0367341	−	0.0636253i
$366$	21.8847	+	6.44331i	1.14393	+	0.336797i
$367$	−10.7997	+	18.7057i	−0.563741	+	0.976428i	0.433425	+	0.901190i	$0.357305\pi$
$367$	−10.7997	+	18.7057i	−0.563741	+	0.976428i	−0.997166	+	0.0752382i	$0.976028\pi$
$368$			1.99547i			0.104021i
$369$	−7.38648	+	3.79434i	−0.384525	+	0.197526i
$370$		−	3.00315i		−	0.156126i
$371$	−4.42266	+	7.66028i	−0.229613	+	0.397702i
$372$	−14.0624	+	3.40063i	−0.729103	+	0.176314i
$373$	−5.03375	+	2.90624i	−0.260638	+	0.150479i	−0.624626	−	0.780924i	$-0.714748\pi$
$373$	−5.03375	+	2.90624i	−0.260638	+	0.150479i	0.363988	+	0.931404i	$0.381415\pi$
$374$	11.1843	−	3.49615i	0.578326	−	0.180782i
$375$	−1.25442	+	1.19434i	−0.0647778	+	0.0616752i
$376$	5.60838	+	3.23800i	0.289230	+	0.166987i
$377$			0.331672i			0.0170820i
$378$	3.82731	−	10.9803i	0.196855	−	0.564767i
$379$	−35.6346			−1.83043			−0.915213	−	0.402970i	$-0.867978\pi$
$379$	−35.6346			−1.83043			−0.915213	+	0.402970i	$0.867978\pi$
$380$	0.324583	−	0.562194i	0.0166507	−	0.0288399i
$381$	4.36117	−	4.15228i	0.223429	−	0.212728i
$382$	−1.37544	+	0.794110i	−0.0703736	+	0.0406302i
$383$	−24.4144	+	14.0957i	−1.24752	+	0.720254i	−0.970614	−	0.240644i	$-0.922641\pi$
$383$	−24.4144	+	14.0957i	−1.24752	+	0.720254i	−0.276903	+	0.960898i	$0.589308\pi$
$384$	1.68352	−	0.407116i	0.0859120	−	0.0207756i
$385$	−5.45981	−	5.02777i	−0.278258	−	0.256239i
$386$		−	25.8287i		−	1.31465i
$387$	−18.8029	+	29.1640i	−0.955804	+	1.48249i
$388$	5.06302			0.257036
$389$	−1.82484	−	1.05357i	−0.0925229	−	0.0534181i	0.453025	−	0.891498i	$-0.350345\pi$
$389$	−1.82484	−	1.05357i	−0.0925229	−	0.0534181i	−0.545548	+	0.838080i	$0.683678\pi$
$390$	−1.52576	+	5.18226i	−0.0772601	+	0.262414i
$391$	−6.10566	+	3.52510i	−0.308776	+	0.178272i
$392$	−0.996003	−	1.72513i	−0.0503057	−	0.0871321i
$393$	−1.82381	+	6.19458i	−0.0919991	+	0.312475i
$394$	10.0166	−	17.3492i	0.504628	−	0.874042i
$395$	2.99132			0.150510
$396$	9.59022	+	2.65096i	0.481927	+	0.133216i
$397$	10.4728			0.525615			0.262808	−	0.964848i	$-0.415352\pi$
$397$	10.4728			0.525615			0.262808	+	0.964848i	$0.415352\pi$
$398$	−0.816811	+	1.41476i	−0.0409430	+	0.0709154i
$399$	−2.44572	+	0.591433i	−0.122439	+	0.0296087i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−21.0553	+	12.1563i	−1.05145	+	0.607055i	−0.923055	−	0.384668i	$-0.874316\pi$
$401$	−21.0553	+	12.1563i	−1.05145	+	0.607055i	−0.128396	+	0.991723i	$0.540983\pi$
$402$	11.7400	+	12.3306i	0.585538	+	0.614994i
$403$	−22.5622	−	13.0263i	−1.12390	−	0.648887i
$404$	−1.25098			−0.0622385
$405$	−8.19758	+	3.71479i	−0.407341	+	0.184589i
$406$		−	0.237974i		−	0.0118105i
$407$	−7.32693	−	6.74715i	−0.363183	−	0.334444i
$408$	4.21972	+	4.43199i	0.208907	+	0.219416i
$409$	−26.4890	+	15.2934i	−1.30980	+	0.756212i	−0.982062	−	0.188557i	$-0.939619\pi$
$409$	−26.4890	+	15.2934i	−1.30980	+	0.756212i	−0.327736	+	0.944769i	$0.606286\pi$
$410$	−2.39717	+	1.38401i	−0.118388	+	0.0683513i
$411$	−1.08895	−	4.50309i	−0.0537142	−	0.222121i
$412$	4.34798	−	7.53091i	0.214209	−	0.371022i
$413$	7.24466			0.356487
$414$	−5.97920	−	0.293584i	−0.293862	−	0.0144289i
$415$			9.83485i			0.482774i
$416$	2.70110	+	1.55948i	0.132432	+	0.0764599i
$417$	−12.9664	−	3.81758i	−0.634968	−	0.186948i
$418$	−0.642375	−	2.05498i	−0.0314196	−	0.100512i
$419$	17.5066	−	10.1075i	0.855255	−	0.493782i	−0.00716547	−	0.999974i	$-0.502281\pi$
$419$	17.5066	−	10.1075i	0.855255	−	0.493782i	0.862420	+	0.506193i	$0.168948\pi$
$420$	1.09474	−	3.71827i	0.0534176	−	0.181433i
$421$	−4.03827	+	6.99449i	−0.196813	+	0.340891i	−0.947493	−	0.319775i	$-0.896393\pi$
$421$	−4.03827	+	6.99449i	−0.196813	+	0.340891i	0.750680	+	0.660666i	$0.229726\pi$
$422$			16.0282i			0.780242i
$423$	−10.5275	+	16.3285i	−0.511862	+	0.793920i
$424$		−	3.95259i		−	0.191955i
$425$	−1.76655	+	3.05976i	−0.0856905	+	0.148420i
$426$	−0.474149	−	1.96072i	−0.0229726	−	0.0949974i
$427$	−14.7378	−	25.5267i	−0.713214	−	1.23532i
$428$	3.73958	+	6.47714i	0.180759	+	0.313084i
$429$	9.21551	+	15.3654i	0.444929	+	0.741850i
$430$	−5.78333	+	10.0170i	−0.278897	+	0.483064i
$431$	17.0692			0.822197			0.411098	−	0.911591i	$-0.365145\pi$
$431$	17.0692			0.822197			0.411098	+	0.911591i	$0.365145\pi$
$432$	0.972189	+	5.10439i	0.0467745	+	0.245585i
$433$	−40.2925			−1.93634			−0.968168	−	0.250303i	$-0.919470\pi$
$433$	−40.2925			−1.93634			−0.968168	+	0.250303i	$0.919470\pi$
$434$	16.1884	+	9.34637i	0.777067	+	0.448640i
$435$	−0.133395	+	0.127006i	−0.00639581	+	0.00608948i
$436$	9.87786	−	5.70298i	0.473063	−	0.273123i
$437$	0.647694	+	1.12184i	0.0309834	+	0.0536649i
$438$	−0.571432	−	2.36301i	−0.0273041	−	0.112909i
$439$	18.7045	+	10.7991i	0.892719	+	0.515411i	0.874831	−	0.484429i	$-0.160972\pi$
$439$	18.7045	+	10.7991i	0.892719	+	0.515411i	0.0178880	+	0.999840i	$0.494306\pi$
$440$	3.23623	+	0.725816i	0.154281	+	0.0346019i
$441$	5.31569	−	2.73060i	0.253128	−	0.130029i
$442$			11.0196i			0.524151i
$443$	−14.2248	−	8.21271i	−0.675842	−	0.390198i	0.122445	−	0.992475i	$-0.460927\pi$
$443$	−14.2248	−	8.21271i	−0.675842	−	0.390198i	−0.798287	+	0.602278i	$0.794260\pi$
$444$	1.46911	−	4.98983i	0.0697208	−	0.236807i
$445$	−0.134519	−	0.232994i	−0.00637683	−	0.0110450i
$446$	−4.23876	−	7.34175i	−0.200711	−	0.347642i
$447$	−0.0317078	+	0.107696i	−0.00149973	+	0.00509384i
$448$	−1.93804	−	1.11893i	−0.0915637	−	0.0528644i
$449$			22.2449i			1.04980i	0.851163	+	0.524901i	$0.175898\pi$
$449$			22.2449i			1.04980i	−0.851163	+	0.524901i	$0.824102\pi$
$450$	−2.66851	+	1.37078i	−0.125795	+	0.0646192i
$451$	−2.00907	+	8.95794i	−0.0946034	+	0.421813i
$452$	−11.2536	−	6.49729i	−0.529327	−	0.305607i
$453$	−6.01378	−	24.8685i	−0.282552	−	1.16842i
$454$	3.63551	+	6.29688i	0.170623	+	0.295527i
$455$	6.04467	−	3.48989i	0.283379	−	0.163609i
$456$	0.814324	−	0.775321i	0.0381342	−	0.0363077i
$457$	9.07476	+	5.23932i	0.424500	+	0.245085i	0.697001	−	0.717071i	$-0.254517\pi$
$457$	9.07476	+	5.23932i	0.424500	+	0.245085i	−0.272501	+	0.962155i	$0.587851\pi$
$458$	14.2004			0.663540
$459$	−13.9008	+	11.9919i	−0.648834	+	0.559732i
$460$	−1.99547			−0.0930392
$461$	13.9519	−	24.1654i	0.649804	−	1.12549i	−0.333365	−	0.942798i	$-0.608184\pi$
$461$	13.9519	−	24.1654i	0.649804	−	1.12549i	0.983169	−	0.182696i	$-0.0584825\pi$
$462$	−6.61212	−	11.0247i	−0.307624	−	0.512915i
$463$	20.7852	+	36.0010i	0.965970	+	1.67311i	0.706986	+	0.707227i	$0.250054\pi$
$463$	20.7852	+	36.0010i	0.965970	+	1.67311i	0.258983	+	0.965882i	$0.416613\pi$
$464$	0.0531702	+	0.0920935i	0.00246837	+	0.00427533i
$465$	−3.40063	−	14.0624i	−0.157700	−	0.652130i
$466$	−0.933478	+	1.61683i	−0.0432425	+	0.0748983i
$467$		−	34.8128i		−	1.61095i	−0.592632	−	0.805473i	$-0.701911\pi$
$467$		−	34.8128i		−	1.61095i	0.592632	−	0.805473i	$-0.298089\pi$
$468$	−5.07022	+	7.86412i	−0.234371	+	0.363519i
$469$		−	21.9975i		−	1.01575i
$470$	−3.23800	+	5.60838i	−0.149358	+	0.258696i
$471$	−4.51455	+	15.3337i	−0.208019	+	0.706538i
$472$	−2.80361	+	1.61866i	−0.129046	+	0.0745050i
$473$	11.4457	+	36.6150i	0.526273	+	1.68356i
$474$	4.97018	+	1.46332i	0.228288	+	0.0672127i
$475$	0.562194	+	0.324583i	0.0257952	+	0.0148929i
$476$		−	7.90658i		−	0.362398i
$477$	11.8435	+	0.581527i	0.542277	+	0.0266263i
$478$	25.7645			1.17844
$479$	−18.0153	+	31.2034i	−0.823139	+	1.42572i	0.0801944	+	0.996779i	$0.474446\pi$
$479$	−18.0153	+	31.2034i	−0.823139	+	1.42572i	−0.903333	+	0.428939i	$0.858887\pi$
$480$	0.407116	+	1.68352i	0.0185822	+	0.0768421i
$481$	8.11181	−	4.68336i	0.369867	−	0.213543i
$482$	−26.3093	+	15.1897i	−1.19836	+	0.691872i
$483$	5.33339	+	5.60169i	0.242678	+	0.254886i
$484$	9.04162	−	6.26491i	0.410983	−	0.284769i
$485$			5.06302i			0.229900i
$486$	−15.4378	+	2.16207i	−0.700272	+	0.0980736i
$487$	23.2302			1.05266			0.526331	−	0.850280i	$-0.323567\pi$
$487$	23.2302			1.05266			0.526331	+	0.850280i	$0.323567\pi$
$488$	11.4068	+	6.58570i	0.516360	+	0.298121i
$489$	2.02165	+	2.12335i	0.0914221	+	0.0960212i
$490$	1.72513	−	0.996003i	0.0779333	−	0.0449948i
$491$	−14.0156	−	24.2757i	−0.632514	−	1.09555i	−0.987036	−	0.160499i	$-0.948690\pi$
$491$	−14.0156	−	24.2757i	−0.632514	−	1.09555i	0.354521	−	0.935048i	$-0.384644\pi$
$492$	−4.66002	+	1.12690i	−0.210090	+	0.0508047i
$493$	−0.187856	+	0.325376i	−0.00846061	+	0.0146542i
$494$	2.02472			0.0910966
$495$	−2.65096	+	9.59022i	−0.119152	+	0.431049i
$496$	−8.35297			−0.375059
$497$	−1.30316	+	2.25714i	−0.0584549	+	0.101247i
$498$	−4.81110	+	16.3409i	−0.215591	+	0.732254i
$499$	9.73187	+	16.8561i	0.435658	+	0.754582i	0.997349	−	0.0727649i	$-0.0231823\pi$
$499$	9.73187	+	16.8561i	0.435658	+	0.754582i	−0.561691	+	0.827347i	$0.689849\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	−8.01996	+	27.2398i	−0.358305	+	1.21699i
$502$	−0.561359	−	0.324101i	−0.0250547	−	0.0144653i
$503$	25.6161			1.14217			0.571083	−	0.820892i	$-0.306523\pi$
$503$	25.6161			1.14217			0.571083	+	0.820892i	$0.306523\pi$
$504$	3.63788	−	5.64250i	0.162044	−	0.251337i
$505$		−	1.25098i		−	0.0556678i
$506$	−4.48320	+	4.86844i	−0.199303	+	0.216429i
$507$	5.50860	−	1.33211i	0.244646	−	0.0591611i
$508$	3.01086	−	1.73832i	0.133586	−	0.0771256i
$509$	−6.65944	+	3.84483i	−0.295175	+	0.170419i	−0.640273	−	0.768147i	$-0.721179\pi$
$509$	−6.65944	+	3.84483i	−0.295175	+	0.170419i	0.345098	+	0.938566i	$0.387846\pi$
$510$	−4.43199	+	4.21972i	−0.196252	+	0.186852i
$511$	−1.57054	+	2.72025i	−0.0694764	+	0.120337i
$512$	1.00000			0.0441942
$513$	2.20336	+	2.55410i	0.0972806	+	0.112766i
$514$			2.06058i			0.0908883i
$515$	7.53091	+	4.34798i	0.331852	+	0.191595i
$516$	−14.5094	+	13.8145i	−0.638742	+	0.608148i
$517$	6.40827	+	20.5002i	0.281835	+	0.901599i
$518$	−5.82022	+	3.36031i	−0.255726	+	0.147643i
$519$	−34.4073	+	8.32050i	−1.51031	+	0.365229i
$520$	−1.55948	+	2.70110i	−0.0683878	+	0.118451i
$521$			9.19977i			0.403049i	0.979483	+	0.201525i	$0.0645896\pi$
$521$			9.19977i			0.403049i	−0.979483	+	0.201525i	$0.935410\pi$
$522$	−0.283771	+	0.145769i	−0.0124203	+	0.00638015i
$523$		−	19.8490i		−	0.867937i	−0.900928	−	0.433968i	$-0.857113\pi$
$523$		−	19.8490i		−	0.867937i	0.900928	−	0.433968i	$-0.142887\pi$
$524$	−1.86412	+	3.22874i	−0.0814343	+	0.141048i
$525$	3.71827	+	1.09474i	0.162279	+	0.0477782i
$526$	4.15995	+	7.20525i	0.181383	+	0.314164i
$527$	−14.7560	−	25.5581i	−0.642780	−	1.11333i
$528$	5.02204	+	2.78910i	0.218556	+	0.121380i
$529$	−9.50905	+	16.4702i	−0.413437	+	0.716094i
$530$	3.95259			0.171690
$531$	−4.43766	−	8.63884i	−0.192578	−	0.374894i
$532$	−1.45274			−0.0629842
$533$	−7.47669	−	4.31667i	−0.323851	−	0.186976i
$534$	−0.109530	−	0.452934i	−0.00473983	−	0.0196004i
$535$	−6.47714	+	3.73958i	−0.280031	+	0.161676i
$536$	4.91487	+	8.51280i	0.212290	+	0.367697i
$537$	25.1193	−	23.9161i	1.08398	−	1.03206i
$538$	6.18320	+	3.56987i	0.266577	+	0.153908i
$539$	1.44583	−	6.44659i	0.0622763	−	0.277674i
$540$	−5.10439	+	0.972189i	−0.219658	+	0.0418364i
$541$		−	21.7443i		−	0.934859i	−0.884030	−	0.467429i	$-0.845180\pi$
$541$		−	21.7443i		−	0.934859i	0.884030	−	0.467429i	$-0.154820\pi$
$542$	22.2335	+	12.8365i	0.955009	+	0.551375i
$543$	26.7505	+	28.0962i	1.14797	+	1.20572i
$544$	1.76655	+	3.05976i	0.0757404	+	0.131186i
$545$	5.70298	+	9.87786i	0.244289	+	0.423121i
$546$	11.7506	−	2.84159i	0.502881	−	0.121609i
$547$	19.2159	+	11.0943i	0.821611	+	0.474357i	0.850972	−	0.525211i	$-0.176014\pi$
$547$	19.2159	+	11.0943i	0.821611	+	0.474357i	−0.0293606	+	0.999569i	$0.509347\pi$
$548$		−	2.67480i		−	0.114262i
$549$	−21.4115	+	33.2102i	−0.913823	+	1.41738i
$550$	−0.725816	+	3.23623i	−0.0309489	+	0.137993i
$551$	0.0597839	+	0.0345163i	0.00254688	+	0.00147044i
$552$	−3.31554	−	0.976162i	−0.141119	−	0.0415482i
$553$	−3.34707	−	5.79730i	−0.142332	−	0.246526i
$554$	−15.8621	+	9.15799i	−0.673916	+	0.389086i
$555$	4.98983	+	1.46911i	0.211807	+	0.0623602i
$556$	−6.75836	−	3.90194i	−0.286618	−	0.165479i
$557$	−10.9699			−0.464808			−0.232404	−	0.972619i	$-0.574659\pi$
$557$	−10.9699			−0.464808			−0.232404	+	0.972619i	$0.574659\pi$
$558$	1.22894	−	25.0288i	0.0520250	−	1.05955i
$559$	−36.0760			−1.52585
$560$	1.11893	−	1.93804i	0.0472833	−	0.0818971i
$561$	0.337737	+	20.2933i	0.0142593	+	0.856786i
$562$	−11.3351	−	19.6330i	−0.478143	−	0.828168i
$563$	11.9763	+	20.7435i	0.504740	+	0.874236i	0.999985	+	0.00548240i	$0.00174511\pi$
$563$	11.9763	+	20.7435i	0.504740	+	0.874236i	−0.495245	+	0.868754i	$0.664922\pi$
$564$	−8.12361	+	7.73452i	−0.342066	+	0.325682i
$565$	6.49729	−	11.2536i	0.273343	−	0.473444i
$566$		−	29.3060i		−	1.23182i
$567$	16.3719	+	11.7307i	0.687555	+	0.492641i
$568$		−	1.16465i		−	0.0488678i
$569$	7.37244	−	12.7694i	0.309069	−	0.535322i	−0.669090	−	0.743181i	$-0.733316\pi$
$569$	7.37244	−	12.7694i	0.309069	−	0.535322i	0.978159	+	0.207859i	$0.0666494\pi$
$570$	0.775321	+	0.814324i	0.0324746	+	0.0341083i
$571$	16.8538	−	9.73053i	0.705309	−	0.407210i	−0.104013	−	0.994576i	$-0.533168\pi$
$571$	16.8538	−	9.73053i	0.705309	−	0.407210i	0.809322	+	0.587366i	$0.199835\pi$
$572$	3.08634	+	9.87329i	0.129046	+	0.412823i
$573$	−0.646590	−	2.67381i	−0.0270117	−	0.111700i
$574$	5.36452	+	3.09721i	0.223911	+	0.129275i
$575$		−	1.99547i		−	0.0832168i
$576$	−0.147126	+	2.99639i	−0.00613023	+	0.124850i
$577$	−30.7153			−1.27869			−0.639347	−	0.768919i	$-0.720795\pi$
$577$	−30.7153			−1.27869			−0.639347	+	0.768919i	$0.720795\pi$
$578$	2.25857	−	3.91197i	0.0939443	−	0.162716i
$579$	42.9153	+	12.6351i	1.78350	+	0.525098i
$580$	−0.0920935	+	0.0531702i	−0.00382397	+	0.00220777i
$581$	19.0603	−	11.0045i	0.790755	−	0.456543i
$582$	−2.47678	+	8.41238i	−0.102666	+	0.348704i
$583$	8.88025	−	9.64334i	0.367783	−	0.399386i
$584$		−	1.40361i		−	0.0580817i
$585$	−7.86412	−	5.07022i	−0.325141	−	0.209628i
$586$	−20.5103			−0.847274
$587$	−16.3401	−	9.43395i	−0.674427	−	0.389381i	0.123325	−	0.992366i	$-0.460644\pi$
$587$	−16.3401	−	9.43395i	−0.674427	−	0.389381i	−0.797752	+	0.602986i	$0.793978\pi$
$588$	3.35359	−	0.810978i	0.138300	−	0.0334442i
$589$	−4.69599	+	2.71123i	−0.193495	+	0.111714i
$590$	−1.61866	−	2.80361i	−0.0666393	−	0.115423i
$591$	23.9263	+	25.1300i	0.984197	+	1.03371i
$592$	1.50157	−	2.60080i	0.0617143	−	0.106892i
$593$	17.7380			0.728413			0.364206	−	0.931318i	$-0.381340\pi$
$593$	17.7380			0.728413			0.364206	+	0.931318i	$0.381340\pi$
$594$	−9.09610	+	14.6377i	−0.373217	+	0.600590i
$595$	7.90658			0.324138
$596$	−0.0324085	+	0.0561333i	−0.00132751	+	0.00229931i
$597$	−1.95109	−	2.04924i	−0.0798529	−	0.0838699i
$598$	−3.11190	−	5.38996i	−0.127255	−	0.220412i
$599$	31.6791	−	18.2899i	1.29437	−	0.747306i	0.314946	−	0.949109i	$-0.398013\pi$
$599$	31.6791	−	18.2899i	1.29437	−	0.747306i	0.979426	+	0.201803i	$0.0646801\pi$
$600$	−1.68352	+	0.407116i	−0.0687296	+	0.0166204i
$601$	−18.8025	−	10.8556i	−0.766971	−	0.442811i	0.0648219	−	0.997897i	$-0.479352\pi$
$601$	−18.8025	−	10.8556i	−0.766971	−	0.442811i	−0.831793	+	0.555086i	$0.812685\pi$
$602$	25.8845			1.05497
$603$	−26.2308	+	13.4744i	−1.06820	+	0.548720i
$604$		−	14.7717i		−	0.601050i
$605$	6.26491	+	9.04162i	0.254705	+	0.367594i
$606$	0.611965	−	2.07854i	0.0248594	−	0.0844350i
$607$	−2.44027	+	1.40889i	−0.0990475	+	0.0571851i	−0.548706	−	0.836016i	$-0.684879\pi$
$607$	−2.44027	+	1.40889i	−0.0990475	+	0.0571851i	0.449658	+	0.893201i	$0.351546\pi$
$608$	0.562194	−	0.324583i	0.0228000	−	0.0131636i
$609$	0.395403	+	0.116415i	0.0160225	+	0.00471736i
$610$	−6.58570	+	11.4068i	−0.266647	+	0.461846i
$611$	−20.1984			−0.817141
$612$	−9.42814	+	4.84312i	−0.381110	+	0.195771i
$613$			2.12088i			0.0856617i	0.999082	+	0.0428308i	$0.0136377\pi$
$613$			2.12088i			0.0856617i	−0.999082	+	0.0428308i	$0.986362\pi$
$614$	18.8630	+	10.8906i	0.761249	+	0.439507i
$615$	−1.12690	−	4.66002i	−0.0454411	−	0.187910i
$616$	−2.21445	−	7.08408i	−0.0892226	−	0.285426i
$617$	38.0414	−	21.9632i	1.53149	−	0.884206i	0.532197	−	0.846620i	$-0.321367\pi$
$617$	38.0414	−	21.9632i	1.53149	−	0.884206i	0.999293	−	0.0375859i	$-0.0119668\pi$
$618$	10.3859	+	10.9084i	0.417781	+	0.438798i
$619$	12.8087	−	22.1853i	0.514825	−	0.891703i	−0.485027	−	0.874499i	$-0.661190\pi$
$619$	12.8087	−	22.1853i	0.514825	−	0.891703i	0.999852	−	0.0172042i	$-0.00547653\pi$
$620$		−	8.35297i		−	0.335463i
$621$	3.41276	−	9.79103i	0.136949	−	0.392900i
$622$		−	2.03320i		−	0.0815239i
$623$	−0.301035	+	0.521408i	−0.0120607	+	0.0208898i
$624$	−3.91248	+	3.72509i	−0.156625	+	0.149123i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−12.2823	−	21.2735i	−0.490899	−	0.850261i
$627$	3.72865	−	0.0620551i	0.148908	−	0.00247824i
$628$	−4.61431	+	7.99222i	−0.184131	+	0.318924i
$629$	10.6104			0.423066
$630$	5.64250	+	3.63788i	0.224803	+	0.144937i
$631$	20.1742			0.803122			0.401561	−	0.915832i	$-0.368468\pi$
$631$	20.1742			0.803122			0.401561	+	0.915832i	$0.368468\pi$
$632$	2.59056	+	1.49566i	0.103047	+	0.0594942i
$633$	−26.6314	−	7.84084i	−1.05850	−	0.311646i
$634$	−15.0163	+	8.66967i	−0.596374	+	0.344316i
$635$	1.73832	+	3.01086i	0.0689833	+	0.119483i
$636$	6.56736	+	1.93357i	0.260413	+	0.0766709i
$637$	5.38061	+	3.10650i	0.213187	+	0.123084i
$638$	−0.0771836	+	0.344142i	−0.00305573	+	0.0136247i
$639$	3.48976	+	0.171350i	0.138053	+	0.00677851i
$640$			1.00000i			0.0395285i
$641$	−15.9881	−	9.23075i	−0.631493	−	0.364593i	0.149837	−	0.988711i	$-0.452125\pi$
$641$	−15.9881	−	9.23075i	−0.631493	−	0.364593i	−0.781330	+	0.624118i	$0.785458\pi$
$642$	−12.5914	+	3.04489i	−0.496941	+	0.120172i
$643$	10.0429	+	17.3949i	0.396054	+	0.685986i	0.993235	−	0.116120i	$-0.0370459\pi$
$643$	10.0429	+	17.3949i	0.396054	+	0.685986i	−0.597181	+	0.802107i	$0.703713\pi$
$644$	2.23278	+	3.86730i	0.0879840	+	0.152393i
$645$	−13.8145	−	14.5094i	−0.543945	−	0.571308i
$646$	1.98629	+	1.14679i	0.0781496	+	0.0451197i
$647$		−	3.97837i		−	0.156406i	−0.996937	−	0.0782030i	$-0.975082\pi$
$647$		−	3.97837i		−	0.156406i	0.996937	−	0.0782030i	$-0.0249182\pi$
$648$	−8.95671	−	0.881691i	−0.351853	−	0.0346361i
$649$	−10.4767	−	2.34970i	−0.411248	−	0.0922339i
$650$	−2.70110	−	1.55948i	−0.105946	−	0.0611679i
$651$	−23.4485	+	22.3254i	−0.919019	+	0.875001i
$652$	0.846349	+	1.46592i	0.0331456	+	0.0574098i
$653$	36.6216	−	21.1435i	1.43311	−	0.827409i	0.435757	−	0.900064i	$-0.356481\pi$
$653$	36.6216	−	21.1435i	1.43311	−	0.827409i	0.997357	+	0.0726555i	$0.0231474\pi$
$654$	4.64355	+	19.2022i	0.181577	+	0.750866i
$655$	−3.22874	−	1.86412i	−0.126157	−	0.0728370i
$656$	−2.76801			−0.108073
$657$	4.20576	+	0.206507i	0.164082	+	0.00805659i
$658$	14.4924			0.564971
$659$	11.5514	−	20.0076i	0.449978	−	0.779384i	−0.548406	−	0.836212i	$-0.684765\pi$
$659$	11.5514	−	20.0076i	0.449978	−	0.779384i	0.998384	+	0.0568277i	$0.0180986\pi$
$660$	−2.78910	+	5.02204i	−0.108566	+	0.195483i
$661$	−8.61084	−	14.9144i	−0.334923	−	0.580104i	0.648547	−	0.761175i	$-0.275377\pi$
$661$	−8.61084	−	14.9144i	−0.334923	−	0.580104i	−0.983470	+	0.181071i	$0.942044\pi$
$662$	8.70296	+	15.0740i	0.338250	+	0.585867i
$663$	−18.3095	−	5.39069i	−0.711082	−	0.209357i
$664$	−4.91742	+	8.51723i	−0.190833	+	0.330532i
$665$		−	1.45274i		−	0.0563348i
$666$	7.57210	+	4.88195i	0.293413	+	0.189172i
$667$		−	0.212199i		−	0.00821638i
$668$	−8.19719	+	14.1980i	−0.317159	+	0.549335i
$669$	14.2721	−	3.45134i	0.551792	−	0.133436i
$670$	−8.51280	+	4.91487i	−0.328878	+	0.189878i
$671$	13.0336	+	41.6949i	0.503158	+	1.60962i
$672$	2.80720	−	2.67275i	0.108290	−	0.103104i
$673$	10.9871	+	6.34342i	0.423522	+	0.244521i	0.696583	−	0.717476i	$-0.254703\pi$
$673$	10.9871	+	6.34342i	0.423522	+	0.244521i	−0.273061	+	0.961997i	$0.588036\pi$
$674$			13.9985i			0.539200i
$675$	−0.972189	−	5.10439i	−0.0374196	−	0.196468i
$676$	3.27206			0.125849
$677$	4.74555	−	8.21953i	0.182386	−	0.315902i	−0.760306	−	0.649565i	$-0.774951\pi$
$677$	4.74555	−	8.21953i	0.182386	−	0.315902i	0.942693	+	0.333662i	$0.108285\pi$
$678$	16.3006	−	15.5199i	0.626022	−	0.596038i
$679$	9.81234	−	5.66516i	0.376563	−	0.217409i
$680$	−3.05976	+	1.76655i	−0.117336	+	0.0677443i
$681$	−12.2409	+	2.96015i	−0.469074	+	0.113433i
$682$	−20.3792	−	18.7665i	−0.780358	−	0.718608i
$683$			27.3499i			1.04651i	0.852175	+	0.523257i	$0.175283\pi$
$683$			27.3499i			1.04651i	−0.852175	+	0.523257i	$0.824717\pi$
$684$	0.889863	+	1.73231i	0.0340248	+	0.0662364i
$685$	2.67480			0.102199
$686$	−17.4269	−	10.0614i	−0.665361	−	0.384146i
$687$	−6.94667	+	23.5944i	−0.265032	+	0.900182i
$688$	−10.0170	+	5.78333i	−0.381896	+	0.220487i
$689$	6.16400	+	10.6764i	0.234830	+	0.406737i
$690$	0.976162	−	3.31554i	0.0371619	−	0.126220i
$691$	18.0682	−	31.2950i	0.687346	−	1.19052i	−0.285348	−	0.958424i	$-0.592109\pi$
$691$	18.0682	−	31.2950i	0.687346	−	1.19052i	0.972693	−	0.232093i	$-0.0745575\pi$
$692$	−20.4377			−0.776923
$693$	21.5525	−	5.59310i	0.818710	−	0.212464i
$694$	−26.1660			−0.993248
$695$	3.90194	−	6.75836i	0.148009	−	0.256359i
$696$	−0.179027	+	0.0432929i	−0.00678599	+	0.00164101i
$697$	−4.88985	−	8.46946i	−0.185216	−	0.320804i
$698$	27.7358	−	16.0132i	1.04981	−	0.606110i
$699$	−2.22977	−	2.34194i	−0.0843377	−	0.0885804i
$700$	1.93804	+	1.11893i	0.0732510	+	0.0422915i
$701$	8.65997			0.327083			0.163541	−	0.986536i	$-0.447708\pi$
$701$	8.65997			0.327083			0.163541	+	0.986536i	$0.447708\pi$
$702$	−10.5862	−	12.2714i	−0.399550	−	0.463153i
$703$		−	1.94954i		−	0.0735283i
$704$	2.43975	+	2.24669i	0.0919515	+	0.0846753i
$705$	−7.73452	−	8.12361i	−0.291299	−	0.305953i
$706$	20.2217	−	11.6750i	0.761053	−	0.439394i
$707$	−2.42444	+	1.39975i	−0.0911806	+	0.0526431i
$708$	−1.31797	−	5.45012i	−0.0495323	−	0.204828i
$709$	14.0217	−	24.2864i	0.526598	−	0.912094i	−0.472922	−	0.881104i	$-0.656801\pi$
$709$	14.0217	−	24.2864i	0.526598	−	0.912094i	0.999520	−	0.0309898i	$-0.00986594\pi$
$710$	1.16465			0.0437087
$711$	−4.86272	+	7.54228i	−0.182366	+	0.282858i
$712$		−	0.269039i		−	0.0100827i
$713$	14.4350	+	8.33405i	0.540595	+	0.312112i
$714$	13.1371	+	3.86782i	0.491642	+	0.144749i
$715$	−9.87329	+	3.08634i	−0.369240	+	0.115423i
$716$	17.3418	−	10.0123i	0.648095	−	0.374178i
$717$	−12.6037	+	42.8085i	−0.470694	+	1.59871i
$718$	−9.10163	+	15.7645i	−0.339670	+	0.588325i
$719$		−	25.5223i		−	0.951820i	−0.879494	−	0.475910i	$-0.842119\pi$
$719$		−	25.5223i		−	0.951820i	0.879494	−	0.475910i	$-0.157881\pi$
$720$	−2.99639	−	0.147126i	−0.111669	−	0.00548305i
$721$		−	19.4603i		−	0.724739i
$722$	−9.28929	+	16.0895i	−0.345712	+	0.598790i
$723$	−12.3679	−	51.1445i	−0.459969	−	1.90208i
$724$	11.1989	+	19.3971i	0.416204	+	0.720887i
$725$	−0.0531702	−	0.0920935i	−0.00197469	−	0.00342027i
$726$	5.98629	+	18.0877i	0.222172	+	0.671297i
$727$	−22.7537	+	39.4106i	−0.843889	+	1.46166i	0.0426928	+	0.999088i	$0.486406\pi$
$727$	−22.7537	+	39.4106i	−0.843889	+	1.46166i	−0.886582	+	0.462571i	$0.846927\pi$
$728$	6.97979			0.258688
$729$	3.95965	−	26.7081i	0.146654	−	0.989188i
$730$	1.40361			0.0519499
$731$	−35.3912	−	20.4331i	−1.30899	−	0.755747i
$732$	−16.5224	+	15.7311i	−0.610687	+	0.581437i
$733$	1.96896	−	1.13678i	0.0727253	−	0.0419880i	−0.463196	−	0.886256i	$-0.653298\pi$
$733$	1.96896	−	1.13678i	0.0727253	−	0.0419880i	0.535922	+	0.844268i	$0.319964\pi$
$734$	−10.7997	−	18.7057i	−0.398625	−	0.690439i
$735$	0.810978	+	3.35359i	0.0299134	+	0.123699i
$736$	−1.72813	−	0.997734i	−0.0636996	−	0.0367770i
$737$	−7.13458	+	31.8113i	−0.262806	+	1.17178i
$738$	0.407246	−	8.29405i	0.0149909	−	0.305308i
$739$			2.04843i			0.0753526i	0.999290	+	0.0376763i	$0.0119956\pi$
$739$			2.04843i			0.0753526i	−0.999290	+	0.0376763i	$0.988004\pi$
$740$	2.60080	+	1.50157i	0.0956074	+	0.0551990i
$741$	−0.990473	+	3.36415i	−0.0363859	+	0.123585i
$742$	−4.42266	−	7.66028i	−0.162361	−	0.281218i
$743$	23.2197	+	40.2176i	0.851847	+	1.47544i	0.879540	+	0.475825i	$0.157851\pi$
$743$	23.2197	+	40.2176i	0.851847	+	1.47544i	−0.0276930	+	0.999616i	$0.508816\pi$
$744$	4.08619	−	13.8787i	0.149807	−	0.508819i
$745$	−0.0561333	−	0.0324085i	−0.00205656	−	0.00118736i
$746$		−	5.81248i		−	0.212810i
$747$	−24.7975	−	15.9876i	−0.907291	−	0.584956i
$748$	−2.56439	+	11.4340i	−0.0937633	+	0.418067i
$749$	14.4949	+	8.36864i	0.529632	+	0.305783i
$750$	−0.407116	−	1.68352i	−0.0148658	−	0.0614736i
$751$	3.66422	+	6.34662i	0.133709	+	0.231592i	0.925104	−	0.379715i	$-0.123978\pi$
$751$	3.66422	+	6.34662i	0.133709	+	0.231592i	−0.791394	+	0.611306i	$0.790644\pi$
$752$	−5.60838	+	3.23800i	−0.204517	+	0.118078i
$753$	0.813115	−	0.774170i	0.0296316	−	0.0282123i
$754$	−0.287236	−	0.165836i	−0.0104605	−	0.00603939i
$755$	14.7717			0.537596
$756$	7.59559	+	8.80471i	0.276249	+	0.320224i
$757$	32.5935			1.18463			0.592315	−	0.805706i	$-0.298214\pi$
$757$	32.5935			1.18463			0.592315	+	0.805706i	$0.298214\pi$
$758$	17.8173	−	30.8605i	0.647153	−	1.12090i
$759$	−5.89595	−	9.83058i	−0.214009	−	0.356827i
$760$	0.324583	+	0.562194i	0.0117738	+	0.0203929i
$761$	−26.8972	−	46.5873i	−0.975023	−	1.68879i	−0.679858	−	0.733343i	$-0.737959\pi$
$761$	−26.8972	−	46.5873i	−0.975023	−	1.68879i	−0.295165	−	0.955446i	$-0.595375\pi$
$762$	1.41540	+	5.85302i	0.0512745	+	0.212033i
$763$	12.7624	−	22.1052i	0.462032	−	0.800262i
$764$		−	1.58822i		−	0.0574598i
$765$	−4.84312	−	9.42814i	−0.175103	−	0.340875i
$766$		−	28.1913i		−	1.01859i
$767$	5.04855	−	8.74435i	0.182293	−	0.315740i
$768$	−0.489190	+	1.66153i	−0.0176521	+	0.0599554i
$769$	46.7234	−	26.9758i	1.68489	−	0.972771i	0.726560	−	0.687103i	$-0.241118\pi$
$769$	46.7234	−	26.9758i	1.68489	−	0.972771i	0.958329	−	0.285668i	$-0.0922156\pi$
$770$	7.08408	−	2.21445i	0.255292	−	0.0798031i
$771$	−3.42372	−	1.00801i	−0.123302	−	0.0363027i
$772$	22.3683	+	12.9144i	0.805053	+	0.464798i
$773$		−	19.9741i		−	0.718417i	−0.933257	−	0.359209i	$-0.883047\pi$
$773$		−	19.9741i		−	0.718417i	0.933257	−	0.359209i	$-0.116953\pi$
$774$	−15.8554	−	30.8658i	−0.569909	−	1.10945i
$775$	8.35297			0.300048
$776$	−2.53151	+	4.38471i	−0.0908760	+	0.157402i
$777$	−2.73607	−	11.3143i	−0.0981560	−	0.405899i
$778$	1.82484	−	1.05357i	0.0654236	−	0.0377723i
$779$	−1.55616	+	0.898450i	−0.0557552	+	0.0321903i
$780$	−3.72509	−	3.91248i	−0.133380	−	0.140089i
$781$	2.61662	−	2.84146i	0.0936299	−	0.101676i
$782$		−	7.05021i		−	0.252115i
$783$	−0.103383	−	0.542803i	−0.00369461	−	0.0193982i
$784$	1.99201			0.0711430
$785$	−7.99222	−	4.61431i	−0.285255	−	0.164692i
$786$	−4.45276	−	4.67676i	−0.158825	−	0.166814i
$787$	−33.9688	+	19.6119i	−1.21086	+	0.699088i	−0.962946	−	0.269696i	$-0.913077\pi$
$787$	−33.9688	+	19.6119i	−1.21086	+	0.699088i	−0.247910	+	0.968783i	$0.579744\pi$
$788$	10.0166	+	17.3492i	0.356826	+	0.618041i
$789$	−14.0068	+	3.38717i	−0.498654	+	0.120586i
$790$	−1.49566	+	2.59056i	−0.0532133	+	0.0921681i
$791$	−29.0800			−1.03397
$792$	−7.09091	+	6.97990i	−0.251965	+	0.248020i
$793$	−41.0811			−1.45883
$794$	−5.23641	+	9.06972i	−0.185833	+	0.321872i
$795$	−1.93357	+	6.56736i	−0.0685765	+	0.232920i
$796$	−0.816811	−	1.41476i	−0.0289511	−	0.0501448i
$797$	28.2733	−	16.3236i	1.00149	−	0.578212i	0.0928024	−	0.995685i	$-0.470418\pi$
$797$	28.2733	−	16.3236i	1.00149	−	0.578212i	0.908689	+	0.417473i	$0.137084\pi$
$798$	0.710664	−	2.41377i	0.0251572	−	0.0854466i
$799$	−19.8150	−	11.4402i	−0.701005	−	0.404726i
$800$	−1.00000			−0.0353553
$801$	0.806145	+	0.0395825i	0.0284837	+	0.00139858i
$802$		−	24.3125i		−	0.858506i
$803$	3.15347	−	3.42445i	0.111284	−	0.120846i
$804$	−16.5486	+	4.00185i	−0.583624	+	0.141134i
$805$	−3.86730	+	2.23278i	−0.136304	+	0.0786953i
$806$	22.5622	−	13.0263i	0.794721	−	0.458832i
$807$	−8.95622	+	8.52725i	−0.315274	+	0.300173i
$808$	0.625489	−	1.08338i	0.0220046	−	0.0381131i
$809$	0.748177			0.0263045			0.0131523	−	0.999914i	$-0.495813\pi$
$809$	0.748177			0.0263045			0.0131523	+	0.999914i	$0.495813\pi$
$810$	0.881691	−	8.95671i	0.0309795	−	0.314707i
$811$		−	26.0618i		−	0.915155i	−0.889170	−	0.457577i	$-0.848717\pi$
$811$		−	26.0618i		−	0.915155i	0.889170	−	0.457577i	$-0.151283\pi$
$812$	0.206092	+	0.118987i	0.00723241	+	0.00417563i
$813$	−32.2047	+	30.6622i	−1.12947	+	1.07537i
$814$	9.50667	−	2.97174i	0.333209	−	0.104159i
$815$	−1.46592	+	0.846349i	−0.0513489	+	0.0296463i
$816$	−5.94808	+	1.43839i	−0.208224	+	0.0503536i
$817$	−3.75434	+	6.50270i	−0.131348	+	0.227501i
$818$		−	30.5869i		−	1.06945i
$819$	−1.02691	+	20.9142i	−0.0358830	+	0.730800i
$820$		−	2.76801i		−	0.0966633i
$821$	8.01351	−	13.8798i	0.279673	−	0.484409i	−0.691630	−	0.722252i	$-0.743107\pi$
$821$	8.01351	−	13.8798i	0.279673	−	0.484409i	0.971304	+	0.237843i	$0.0764405\pi$
$822$	4.44427	+	1.30848i	0.155012	+	0.0456386i
$823$	21.2864	+	36.8691i	0.741997	+	1.28518i	0.951585	+	0.307387i	$0.0994546\pi$
$823$	21.2864	+	36.8691i	0.741997	+	1.28518i	−0.209587	+	0.977790i	$0.567212\pi$
$824$	4.34798	+	7.53091i	0.151469	+	0.262352i
$825$	−5.02204	−	2.78910i	−0.174845	−	0.0971039i
$826$	−3.62233	+	6.27406i	−0.126037	+	0.218303i
$827$	26.1822			0.910444			0.455222	−	0.890378i	$-0.349560\pi$
$827$	26.1822			0.910444			0.455222	+	0.890378i	$0.349560\pi$
$828$	3.24385	−	5.03135i	0.112732	−	0.174851i
$829$	32.5134			1.12924			0.564618	−	0.825353i	$-0.309024\pi$
$829$	32.5134			1.12924			0.564618	+	0.825353i	$0.309024\pi$
$830$	−8.51723	−	4.91742i	−0.295637	−	0.170686i
$831$	−7.45673	−	30.8354i	−0.258671	−	1.06967i
$832$	−2.70110	+	1.55948i	−0.0936439	+	0.0540653i
$833$	3.51898	+	6.09506i	0.121926	+	0.211181i
$834$	9.78933	−	9.32045i	0.338977	−	0.322741i
$835$	−14.1980	−	8.19719i	−0.491340	−	0.283676i
$836$	2.10085	+	0.471175i	0.0726594	+	0.0162959i
$837$	40.9849	+	14.2857i	1.41665	+	0.493787i
$838$			20.2149i			0.698313i
$839$	−44.5464	−	25.7189i	−1.53791	−	0.887915i	−0.998961	−	0.0455791i	$-0.985487\pi$
$839$	−44.5464	−	25.7189i	−1.53791	−	0.887915i	−0.538953	−	0.842336i	$-0.681180\pi$
$840$	2.67275	+	2.80720i	0.0922186	+	0.0968577i
$841$	14.4943	+	25.1049i	0.499805	+	0.865688i
$842$	−4.03827	−	6.99449i	−0.139168	−	0.241046i
$843$	38.1659	−	9.22941i	1.31450	−	0.317878i
$844$	−13.8809	−	8.01412i	−0.477799	−	0.275857i
$845$			3.27206i			0.112562i
$846$	−8.87718	−	17.2813i	−0.305204	−	0.594143i
$847$	10.5130	−	22.2586i	0.361232	−	0.764813i
$848$	3.42305	+	1.97630i	0.117548	+	0.0678663i
$849$	48.6928	+	14.3362i	1.67113	+	0.492016i
$850$	−1.76655	−	3.05976i	−0.0605923	−	0.104949i
$851$	−5.18982	+	2.99634i	−0.177905	+	0.102713i
$852$	1.93511	+	0.569736i	0.0662958	+	0.0195188i
$853$	−24.8106	−	14.3244i	−0.849498	−	0.490458i	0.0109834	−	0.999940i	$-0.496504\pi$
$853$	−24.8106	−	14.3244i	−0.849498	−	0.490458i	−0.860481	+	0.509482i	$0.829837\pi$
$854$	29.4757			1.00864
$855$	−1.73231	+	0.889863i	−0.0592436	+	0.0304327i
$856$	−7.47916			−0.255632
$857$	13.3156	−	23.0633i	0.454852	−	0.787826i	−0.543828	−	0.839197i	$-0.683026\pi$
$857$	13.3156	−	23.0633i	0.454852	−	0.787826i	0.998680	+	0.0513704i	$0.0163589\pi$
$858$	−17.9146	+	0.298148i	−0.611594	+	0.0101786i
$859$	21.2715	+	36.8433i	0.725773	+	1.25708i	0.958655	+	0.284571i	$0.0918512\pi$
$859$	21.2715	+	36.8433i	0.725773	+	1.25708i	−0.232882	+	0.972505i	$0.574815\pi$
$860$	−5.78333	−	10.0170i	−0.197210	−	0.341578i
$861$	−7.77038	+	7.39821i	−0.264814	+	0.252130i
$862$	−8.53462	+	14.7824i	−0.290690	+	0.503491i
$863$		−	18.5594i		−	0.631770i	−0.948797	−	0.315885i	$-0.897699\pi$
$863$		−	18.5594i		−	0.631770i	0.948797	−	0.315885i	$-0.102301\pi$
$864$	−4.90663	−	1.71026i	−0.166927	−	0.0581841i
$865$		−	20.4377i		−	0.694901i
$866$	20.1463	−	34.8943i	0.684598	−	1.18576i
$867$	5.39499	+	5.66639i	0.183223	+	0.192441i
$868$	−16.1884	+	9.34637i	−0.549470	+	0.317236i
$869$	2.96003	+	9.46923i	0.100412	+	0.321222i
$870$	−0.0432929	−	0.179027i	−0.00146777	−	0.00606958i
$871$	−26.5511	−	15.3293i	−0.899650	−	0.519413i
$872$			11.4060i			0.386255i
$873$	−12.7658	−	8.23050i	−0.432058	−	0.278560i
$874$	−1.29539			−0.0438172
$875$	−1.11893	+	1.93804i	−0.0378267	+	0.0655177i
$876$	2.33214	+	0.686630i	0.0787958	+	0.0231991i
$877$	37.5715	−	21.6919i	1.26870	−	0.732484i	0.293957	−	0.955819i	$-0.405028\pi$
$877$	37.5715	−	21.6919i	1.26870	−	0.732484i	0.974742	+	0.223335i	$0.0716944\pi$
$878$	−18.7045	+	10.7991i	−0.631248	+	0.364451i
$879$	10.0334	−	34.0786i	0.338419	−	1.14944i
$880$	−2.24669	+	2.43975i	−0.0757359	+	0.0822440i
$881$			54.3837i			1.83223i	0.400913	+	0.916116i	$0.368693\pi$
$881$			54.3837i			1.83223i	−0.400913	+	0.916116i	$0.631307\pi$
$882$	−0.293075	+	5.96882i	−0.00986834	+	0.200981i
$883$	22.5423			0.758607			0.379304	−	0.925272i	$-0.376164\pi$
$883$	22.5423			0.758607			0.379304	+	0.925272i	$0.376164\pi$
$884$	−9.54329	−	5.50982i	−0.320975	−	0.185315i
$885$	5.45012	−	1.31797i	0.183204	−	0.0443030i
$886$	14.2248	−	8.21271i	0.477892	−	0.275911i
$887$	8.42281	+	14.5887i	0.282810	+	0.489842i	0.972076	−	0.234667i	$-0.0754000\pi$
$887$	8.42281	+	14.5887i	0.282810	+	0.489842i	−0.689266	+	0.724509i	$0.742067\pi$
$888$	3.58677	+	3.76720i	0.120364	+	0.126419i
$889$	3.89012	−	6.73788i	0.130470	−	0.225981i
$890$	0.269039			0.00901820
$891$	−19.8712	−	22.2741i	−0.665712	−	0.746209i
$892$	8.47752			0.283848
$893$	−2.10200	+	3.64077i	−0.0703407	+	0.121834i
$894$	−0.0774134	−	0.0813077i	−0.00258909	−	0.00271934i
$895$	10.0123	+	17.3418i	0.334675	+	0.579674i
$896$	1.93804	−	1.11893i	0.0647453	−	0.0373807i
$897$	10.4779	−	2.53381i	0.349847	−	0.0846014i
$898$	−19.2646	−	11.1224i	−0.642870	−	0.371161i
$899$	0.888258			0.0296251
$900$	0.147126	−	2.99639i	0.00490419	−	0.0998797i
$901$			13.9649i			0.465239i
$902$	−6.75326	−	6.21887i	−0.224859	−	0.207066i
$903$	−12.6624	+	43.0080i	−0.421379	+	1.43122i
$904$	11.2536	−	6.49729i	0.374290	−	0.216097i
$905$	−19.3971	+	11.1989i	−0.644781	+	0.372264i
$906$	24.5436	+	7.22614i	0.815407	+	0.240073i
$907$	6.38593	−	11.0608i	0.212041	−	0.367266i	−0.740312	−	0.672264i	$-0.765322\pi$
$907$	6.38593	−	11.0608i	0.212041	−	0.367266i	0.952353	+	0.304997i	$0.0986555\pi$
$908$	−7.27102			−0.241297
$909$	3.15420	+	2.03360i	0.104618	+	0.0674503i
$910$			6.97979i			0.231378i
$911$	−3.35433	−	1.93662i	−0.111134	−	0.0641632i	0.443403	−	0.896323i	$-0.353771\pi$
$911$	−3.35433	−	1.93662i	−0.111134	−	0.0641632i	−0.554537	+	0.832159i	$0.687104\pi$
$912$	0.264286	+	1.09289i	0.00875137	+	0.0361891i
$913$	−31.1329	+	9.73197i	−1.03035	+	0.322081i
$914$	−9.07476	+	5.23932i	−0.300166	+	0.173301i
$915$	−15.7311	−	16.5224i	−0.520053	−	0.546215i
$916$	−7.10018	+	12.2979i	−0.234597	+	0.406333i
$917$			8.34324i			0.275518i
$918$	−3.43485	−	18.0344i	−0.113367	−	0.595223i
$919$		−	21.9222i		−	0.723147i	−0.932344	−	0.361573i	$-0.882240\pi$
$919$		−	21.9222i		−	0.723147i	0.932344	−	0.361573i	$-0.117760\pi$
$920$	0.997734	−	1.72813i	0.0328943	−	0.0569746i
$921$	−27.3226	+	26.0140i	−0.900311	+	0.857190i
$922$	13.9519	+	24.1654i	0.459481	+	0.795845i
$923$	1.81626	+	3.14585i	0.0597828	+	0.103547i
$924$	12.8537	−	0.213921i	0.422856	−	0.00703749i
$925$	−1.50157	+	2.60080i	−0.0493715	+	0.0855139i
$926$	−41.5704			−1.36609
$927$	−23.2053	+	11.9202i	−0.762161	+	0.391512i
$928$	−0.106340			−0.00349080
$929$	−16.3628	−	9.44708i	−0.536847	−	0.309949i	0.206953	−	0.978351i	$-0.433645\pi$
$929$	−16.3628	−	9.44708i	−0.536847	−	0.309949i	−0.743800	+	0.668402i	$0.766979\pi$
$930$	13.8787	+	4.08619i	0.455102	+	0.133991i
$931$	1.11989	−	0.646570i	0.0367030	−	0.0211905i
$932$	−0.933478	−	1.61683i	−0.0305771	−	0.0529611i
$933$	3.37823	+	0.994621i	0.110598	+	0.0325624i
$934$	30.1488	+	17.4064i	0.986499	+	0.569556i
$935$	−11.4340	−	2.56439i	−0.373930	−	0.0838644i
$936$	−4.27542	−	8.32300i	−0.139746	−	0.272046i
$937$			19.5862i			0.639854i	0.947442	+	0.319927i	$0.103658\pi$
$937$			19.5862i			0.639854i	−0.947442	+	0.319927i	$0.896342\pi$
$938$	19.0504	+	10.9988i	0.622018	+	0.359122i
$939$	41.3550	−	10.0006i	1.34957	−	0.326358i
$940$	−3.23800	−	5.60838i	−0.105612	−	0.182925i
$941$	−26.7009	−	46.2473i	−0.870424	−	1.50762i	−0.861559	−	0.507658i	$-0.830512\pi$
$941$	−26.7009	−	46.2473i	−0.870424	−	1.50762i	−0.00886483	−	0.999961i	$-0.502822\pi$
$942$	−11.0221	−	11.5765i	−0.359119	−	0.377184i
$943$	4.78348	+	2.76174i	0.155772	+	0.0899347i
$944$		−	3.23733i		−	0.105366i
$945$	−8.80471	+	7.59559i	−0.286417	+	0.247085i
$946$	−37.4324	−	8.39527i	−1.21703	−	0.272954i
$947$	−25.8265	−	14.9109i	−0.839248	−	0.484540i	0.0177602	−	0.999842i	$-0.494346\pi$
$947$	−25.8265	−	14.9109i	−0.839248	−	0.484540i	−0.857009	+	0.515302i	$0.827680\pi$
$948$	−3.75237	+	3.57264i	−0.121871	+	0.116034i
$949$	2.18890	+	3.79129i	0.0710548	+	0.123070i
$950$	−0.562194	+	0.324583i	−0.0182400	+	0.0105309i
$951$	−7.05912	−	29.1912i	−0.228908	−	0.946590i
$952$	6.84730	+	3.95329i	0.221922	+	0.128127i
$953$	1.51910			0.0492084			0.0246042	−	0.999697i	$-0.492167\pi$
$953$	1.51910			0.0492084			0.0246042	+	0.999697i	$0.492167\pi$
$954$	−6.42537	+	9.96602i	−0.208029	+	0.322662i
$955$	1.58822			0.0513936
$956$	−12.8822	+	22.3127i	−0.416641	+	0.721644i
$957$	−0.534046	−	0.296594i	−0.0172633	−	0.00958752i
$958$	−18.0153	−	31.2034i	−0.582047	−	1.00814i
$959$	−2.99291	−	5.18387i	−0.0966460	−	0.167396i
$960$	−1.66153	−	0.489190i	−0.0536258	−	0.0157885i
$961$	−19.3861	+	33.5777i	−0.625357	+	1.08315i
$962$			9.36671i			0.301995i
$963$	1.10038	−	22.4105i	0.0354591	−	0.722168i
$964$		−	30.3794i		−	0.978454i
$965$	−12.9144	+	22.3683i	−0.415728	+	0.720062i
$966$	−7.51790	+	1.81801i	−0.241884	+	0.0584934i
$967$	−13.6284	+	7.86838i	−0.438261	+	0.253030i	−0.702860	−	0.711329i	$-0.748094\pi$
$967$	−13.6284	+	7.86838i	−0.438261	+	0.253030i	0.264599	+	0.964359i	$0.414760\pi$
$968$	0.904760	+	10.9627i	0.0290801	+	0.352355i
$969$	−2.87709	+	2.73929i	−0.0924256	+	0.0879988i
$970$	−4.38471	−	2.53151i	−0.140784	−	0.0812819i
$971$			18.6803i			0.599480i	0.954021	+	0.299740i	$0.0969000\pi$
$971$			18.6803i			0.599480i	−0.954021	+	0.299740i	$0.903100\pi$
$972$	5.84649	−	14.4506i	0.187526	−	0.463502i
$973$	−17.4640			−0.559869
$974$	−11.6151	+	20.1179i	−0.372172	+	0.644621i
$975$	3.91248	−	3.72509i	0.125300	−	0.119298i
$976$	−11.4068	+	6.58570i	−0.365122	+	0.210803i
$977$	41.0917	−	23.7243i	1.31464	−	0.759007i	0.331779	−	0.943357i	$-0.392351\pi$
$977$	41.0917	−	23.7243i	1.31464	−	0.759007i	0.982861	+	0.184350i	$0.0590179\pi$
$978$	−2.84970	+	0.689125i	−0.0911233	+	0.0220358i
$979$	0.604447	−	0.656388i	0.0193182	−	0.0209782i
$980$			1.99201i			0.0636323i
$981$	−34.1767	−	1.67811i	−1.09118	−	0.0535779i
$982$	28.0312			0.894511
$983$	15.3785	+	8.87879i	0.490498	+	0.283189i	0.724781	−	0.688979i	$-0.241941\pi$
$983$	15.3785	+	8.87879i	0.490498	+	0.283189i	−0.234283	+	0.972168i	$0.575274\pi$
$984$	1.35408	−	4.59915i	0.0431666	−	0.146616i
$985$	−17.3492	+	10.0166i	−0.552793	+	0.319155i
$986$	−0.187856	−	0.325376i	−0.00598256	−	0.0103621i
$987$	−7.08951	+	24.0795i	−0.225662	+	0.766460i
$988$	−1.01236	+	1.75346i	−0.0322075	+	0.0557850i
$989$	23.0809			0.733930
$990$	−6.97990	−	7.09091i	−0.221836	−	0.225364i
$991$	19.1821			0.609338			0.304669	−	0.952458i	$-0.401454\pi$
$991$	19.1821			0.609338			0.304669	+	0.952458i	$0.401454\pi$
$992$	4.17649	−	7.23389i	0.132604	−	0.229676i
$993$	−29.3033	+	7.08624i	−0.929913	+	0.224875i
$994$	−1.30316	−	2.25714i	−0.0413338	−	0.0715923i
$995$	1.41476	−	0.816811i	0.0448508	−	0.0258946i
$996$	−11.7461	−	12.3370i	−0.372190	−	0.390913i
$997$	4.14157	+	2.39114i	0.131165	+	0.0757280i	0.564147	−	0.825675i	$-0.309205\pi$
$997$	4.14157	+	2.39114i	0.131165	+	0.0757280i	−0.432982	+	0.901403i	$0.642539\pi$
$998$	−19.4637			−0.616114
$999$	−11.8157	+	10.1931i	−0.373833	+	0.322496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.t.a.461.8	yes	48
3.2	odd	2		2970.2.t.b.791.9		48
9.4	even	3		2970.2.t.a.2771.9		48
9.5	odd	6		990.2.t.b.131.8	yes	48
11.10	odd	2		990.2.t.b.461.8	yes	48
33.32	even	2		2970.2.t.a.791.9		48
99.32	even	6	inner	990.2.t.a.131.8	✓	48
99.76	odd	6		2970.2.t.b.2771.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.8	✓	48	99.32	even	6	inner
990.2.t.a.461.8	yes	48	1.1	even	1	trivial
990.2.t.b.131.8	yes	48	9.5	odd	6
990.2.t.b.461.8	yes	48	11.10	odd	2
2970.2.t.a.791.9		48	33.32	even	2
2970.2.t.a.2771.9		48	9.4	even	3
2970.2.t.b.791.9		48	3.2	odd	2
2970.2.t.b.2771.9		48	99.76	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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.19434 - 1.25442i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.68352 - 0.407116i) q^{6} +(-1.93804 - 1.11893i) q^{7} +1.00000 q^{8} +(-0.147126 + 2.99639i) q^{9} +1.00000i q^{10} +(2.43975 + 2.24669i) q^{11} +(-0.489190 + 1.66153i) q^{12} +(-2.70110 + 1.55948i) q^{13} +(1.93804 - 1.11893i) q^{14} +(-1.66153 - 0.489190i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.53311 q^{17} +(-2.52139 - 1.62561i) q^{18} +0.649165i q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.911067 + 3.76748i) q^{21} +(-3.16557 + 0.989540i) q^{22} +(1.72813 - 0.997734i) q^{23} +(-1.19434 - 1.25442i) q^{24} +(0.500000 - 0.866025i) q^{25} -3.11896i q^{26} +(3.93444 - 3.39414i) q^{27} +2.23785i q^{28} +(0.0531702 - 0.0920935i) q^{29} +(1.25442 - 1.19434i) q^{30} +(4.17649 + 7.23389i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.0955921 - 5.74377i) q^{33} +(1.76655 - 3.05976i) q^{34} -2.23785 q^{35} +(2.66851 - 1.37078i) q^{36} -3.00315 q^{37} +(-0.562194 - 0.324583i) q^{38} +(5.18226 + 1.52576i) q^{39} +(0.866025 - 0.500000i) q^{40} +(1.38401 + 2.39717i) q^{41} +(-3.71827 - 1.09474i) q^{42} +(10.0170 + 5.78333i) q^{43} +(0.725816 - 3.23623i) q^{44} +(1.37078 + 2.66851i) q^{45} +1.99547i q^{46} +(5.60838 + 3.23800i) q^{47} +(1.68352 - 0.407116i) q^{48} +(-0.996003 - 1.72513i) q^{49} +(0.500000 + 0.866025i) q^{50} +(4.21972 + 4.43199i) q^{51} +(2.70110 + 1.55948i) q^{52} -3.95259i q^{53} +(0.972189 + 5.10439i) q^{54} +(3.23623 + 0.725816i) q^{55} +(-1.93804 - 1.11893i) q^{56} +(0.814324 - 0.775321i) q^{57} +(0.0531702 + 0.0920935i) q^{58} +(-2.80361 + 1.61866i) q^{59} +(0.407116 + 1.68352i) q^{60} +(11.4068 + 6.58570i) q^{61} -8.35297 q^{62} +(3.63788 - 5.64250i) q^{63} +1.00000 q^{64} +(-1.55948 + 2.70110i) q^{65} +(5.02204 + 2.78910i) q^{66} +(4.91487 + 8.51280i) q^{67} +(1.76655 + 3.05976i) q^{68} +(-3.31554 - 0.976162i) q^{69} +(1.11893 - 1.93804i) q^{70} -1.16465i q^{71} +(-0.147126 + 2.99639i) q^{72} -1.40361i q^{73} +(1.50157 - 2.60080i) q^{74} +(-1.68352 + 0.407116i) q^{75} +(0.562194 - 0.324583i) q^{76} +(-2.21445 - 7.08408i) q^{77} +(-3.91248 + 3.72509i) q^{78} +(2.59056 + 1.49566i) q^{79} +1.00000i q^{80} +(-8.95671 - 0.881691i) q^{81} -2.76801 q^{82} +(-4.91742 + 8.51723i) q^{83} +(2.80720 - 2.67275i) q^{84} +(-3.05976 + 1.76655i) q^{85} +(-10.0170 + 5.78333i) q^{86} +(-0.179027 + 0.0432929i) q^{87} +(2.43975 + 2.24669i) q^{88} -0.269039i q^{89} +(-2.99639 - 0.147126i) q^{90} +6.97979 q^{91} +(-1.72813 - 0.997734i) q^{92} +(4.08619 - 13.8787i) q^{93} +(-5.60838 + 3.23800i) q^{94} +(0.324583 + 0.562194i) q^{95} +(-0.489190 + 1.66153i) q^{96} +(-2.53151 + 4.38471i) q^{97} +1.99201 q^{98} +(-7.09091 + 6.97990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{6} + 48 q^{8} + 10 q^{9} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^6 + 48 * q^8 + 10 * q^9 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 - 40 * q^39 - 6 * q^41 + 8 * q^42 + 30 * q^43 - 6 * q^44 - 2 * q^48 + 24 * q^49 + 24 * q^50 + 22 * q^51 - 24 * q^52 + 22 * q^54 + 40 * q^57 - 54 * q^59 - 4 * q^60 - 38 * q^63 + 48 * q^64 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * q^99

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