LMFDB - Embedded newform 930.2.o.e.161.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.12
Character	$\chi$	$=$	930.161
Dual form			930.2.o.e.491.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.69717 + 0.345843i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.345843 - 1.69717i) q^{6} +(0.742621 + 1.28626i) q^{7} -1.00000i q^{8} +(2.76078 - 1.17391i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.69717 + 0.345843i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.345843 - 1.69717i) q^{6} +(0.742621 + 1.28626i) q^{7} -1.00000i q^{8} +(2.76078 - 1.17391i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.14249 + 3.71090i) q^{11} +(1.69717 - 0.345843i) q^{12} +(-1.46940 - 0.848361i) q^{13} +(-1.28626 + 0.742621i) q^{14} +(1.64272 + 0.549077i) q^{15} +1.00000 q^{16} +(-2.87402 - 4.97796i) q^{17} +(1.17391 + 2.76078i) q^{18} +(-1.59932 - 2.77010i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-1.70520 - 1.92617i) q^{21} +(-3.71090 - 2.14249i) q^{22} -4.16867 q^{23} +(0.345843 + 1.69717i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.848361 - 1.46940i) q^{26} +(-4.27954 + 2.94713i) q^{27} +(-0.742621 - 1.28626i) q^{28} +7.18325 q^{29} +(-0.549077 + 1.64272i) q^{30} +(2.50461 + 4.97262i) q^{31} +1.00000i q^{32} +(2.35279 - 7.03901i) q^{33} +(4.97796 - 2.87402i) q^{34} -1.48524i q^{35} +(-2.76078 + 1.17391i) q^{36} +(8.23840 - 4.75644i) q^{37} +(2.77010 - 1.59932i) q^{38} +(2.78723 + 0.931631i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-9.76284 - 5.63658i) q^{41} +(1.92617 - 1.70520i) q^{42} +(6.44566 - 3.72140i) q^{43} +(2.14249 - 3.71090i) q^{44} +(-2.97787 - 0.363755i) q^{45} -4.16867i q^{46} -11.9223i q^{47} +(-1.69717 + 0.345843i) q^{48} +(2.39703 - 4.15178i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(6.59931 + 7.45448i) q^{51} +(1.46940 + 0.848361i) q^{52} +(3.03596 - 5.25843i) q^{53} +(-2.94713 - 4.27954i) q^{54} +(3.71090 - 2.14249i) q^{55} +(1.28626 - 0.742621i) q^{56} +(3.67234 + 4.14822i) q^{57} +7.18325i q^{58} +(1.18138 - 0.682072i) q^{59} +(-1.64272 - 0.549077i) q^{60} +12.5555i q^{61} +(-4.97262 + 2.50461i) q^{62} +(3.56017 + 2.67931i) q^{63} -1.00000 q^{64} +(0.848361 + 1.46940i) q^{65} +(7.03901 + 2.35279i) q^{66} +(5.98520 - 10.3667i) q^{67} +(2.87402 + 4.97796i) q^{68} +(7.07495 - 1.44171i) q^{69} +1.48524 q^{70} +(-0.650013 - 0.375285i) q^{71} +(-1.17391 - 2.76078i) q^{72} +(-3.41044 - 1.96902i) q^{73} +(4.75644 + 8.23840i) q^{74} +(-1.14810 - 1.29687i) q^{75} +(1.59932 + 2.77010i) q^{76} -6.36423 q^{77} +(-0.931631 + 2.78723i) q^{78} +(9.64630 - 5.56929i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(6.24387 - 6.48183i) q^{81} +(5.63658 - 9.76284i) q^{82} +(-4.88450 + 8.46021i) q^{83} +(1.70520 + 1.92617i) q^{84} +5.74805i q^{85} +(3.72140 + 6.44566i) q^{86} +(-12.1912 + 2.48428i) q^{87} +(3.71090 + 2.14249i) q^{88} +4.38445 q^{89} +(0.363755 - 2.97787i) q^{90} -2.52004i q^{91} +4.16867 q^{92} +(-5.97051 - 7.57318i) q^{93} +11.9223 q^{94} +3.19864i q^{95} +(-0.345843 - 1.69717i) q^{96} -14.9295 q^{97} +(4.15178 + 2.39703i) q^{98} +(-1.55869 + 12.7601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.69717	+	0.345843i	−0.979863	+	0.199673i
$3$	−1.69717	+	0.345843i	−0.979863	+	0.199673i
$4$	−1.00000			−0.500000
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−0.345843	−	1.69717i	−0.141190	−	0.692868i
$7$	0.742621	+	1.28626i	0.280684	+	0.486159i	0.971553	−	0.236820i	$-0.0761053\pi$
$7$	0.742621	+	1.28626i	0.280684	+	0.486159i	−0.690869	+	0.722980i	$0.742772\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.76078	−	1.17391i	0.920262	−	0.391304i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.14249	+	3.71090i	−0.645986	+	1.11888i	0.338087	+	0.941115i	$0.390220\pi$
$11$	−2.14249	+	3.71090i	−0.645986	+	1.11888i	−0.984073	+	0.177765i	$0.943113\pi$
$12$	1.69717	−	0.345843i	0.489931	−	0.0998364i
$13$	−1.46940	−	0.848361i	−0.407540	−	0.235293i	0.282192	−	0.959358i	$-0.408938\pi$
$13$	−1.46940	−	0.848361i	−0.407540	−	0.235293i	−0.689732	+	0.724065i	$0.742272\pi$
$14$	−1.28626	+	0.742621i	−0.343767	+	0.198474i
$15$	1.64272	+	0.549077i	0.424147	+	0.141771i
$16$	1.00000			0.250000
$17$	−2.87402	−	4.97796i	−0.697053	−	1.20733i	−0.969484	−	0.245156i	$-0.921161\pi$
$17$	−2.87402	−	4.97796i	−0.697053	−	1.20733i	0.272430	−	0.962175i	$-0.412173\pi$
$18$	1.17391	+	2.76078i	0.276694	+	0.650723i
$19$	−1.59932	−	2.77010i	−0.366909	−	0.635505i	0.622172	−	0.782881i	$-0.286251\pi$
$19$	−1.59932	−	2.77010i	−0.366909	−	0.635505i	−0.989081	+	0.147376i	$0.952917\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	−1.70520	−	1.92617i	−0.372105	−	0.420324i
$22$	−3.71090	−	2.14249i	−0.791168	−	0.456781i
$23$	−4.16867			−0.869228			−0.434614	−	0.900617i	$-0.643115\pi$
$23$	−4.16867			−0.869228			−0.434614	+	0.900617i	$0.643115\pi$
$24$	0.345843	+	1.69717i	0.0705950	+	0.346434i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	0.848361	−	1.46940i	0.166377	−	0.288174i
$27$	−4.27954	+	2.94713i	−0.823597	+	0.567175i
$28$	−0.742621	−	1.28626i	−0.140342	−	0.243080i
$29$	7.18325			1.33390			0.666948	−	0.745104i	$-0.267600\pi$
$29$	7.18325			1.33390			0.666948	+	0.745104i	$0.267600\pi$
$30$	−0.549077	+	1.64272i	−0.100247	+	0.299917i
$31$	2.50461	+	4.97262i	0.449842	+	0.893108i
$31$	2.50461	+	4.97262i	0.449842	+	0.893108i
$32$			1.00000i			0.176777i
$33$	2.35279	−	7.03901i	0.409567	−	1.22533i
$34$	4.97796	−	2.87402i	0.853712	−	0.492891i
$35$		−	1.48524i		−	0.251052i
$36$	−2.76078	+	1.17391i	−0.460131	+	0.195652i
$37$	8.23840	−	4.75644i	1.35438	−	0.781954i	0.365524	−	0.930802i	$-0.380890\pi$
$37$	8.23840	−	4.75644i	1.35438	−	0.781954i	0.988860	+	0.148848i	$0.0475564\pi$
$38$	2.77010	−	1.59932i	0.449370	−	0.259444i
$39$	2.78723	+	0.931631i	0.446314	+	0.149180i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−9.76284	−	5.63658i	−1.52470	−	0.880286i	−0.999572	−	0.0292626i	$-0.990684\pi$
$41$	−9.76284	−	5.63658i	−1.52470	−	0.880286i	−0.525128	−	0.851023i	$-0.675983\pi$
$42$	1.92617	−	1.70520i	0.297214	−	0.263118i
$43$	6.44566	−	3.72140i	0.982954	−	0.567509i	0.0797934	−	0.996811i	$-0.474574\pi$
$43$	6.44566	−	3.72140i	0.982954	−	0.567509i	0.903161	+	0.429303i	$0.141241\pi$
$44$	2.14249	−	3.71090i	0.322993	−	0.559440i
$45$	−2.97787	−	0.363755i	−0.443914	−	0.0542255i
$46$		−	4.16867i		−	0.614637i
$47$		−	11.9223i		−	1.73905i	−0.493893	−	0.869523i	$-0.664426\pi$
$47$		−	11.9223i		−	1.73905i	0.493893	−	0.869523i	$-0.335574\pi$
$48$	−1.69717	+	0.345843i	−0.244966	+	0.0499182i
$49$	2.39703	−	4.15178i	0.342433	−	0.593111i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	6.59931	+	7.45448i	0.924088	+	1.04384i
$52$	1.46940	+	0.848361i	0.203770	+	0.117647i
$53$	3.03596	−	5.25843i	0.417021	−	0.722302i	−0.578617	−	0.815599i	$-0.696407\pi$
$53$	3.03596	−	5.25843i	0.417021	−	0.722302i	0.995638	+	0.0932976i	$0.0297408\pi$
$54$	−2.94713	−	4.27954i	−0.401053	−	0.582371i
$55$	3.71090	−	2.14249i	0.500378	−	0.288894i
$56$	1.28626	−	0.742621i	0.171883	−	0.0992369i
$57$	3.67234	+	4.14822i	0.486413	+	0.549446i
$58$			7.18325i			0.943207i
$59$	1.18138	−	0.682072i	0.153803	−	0.0887983i	−0.421123	−	0.907003i	$-0.638364\pi$
$59$	1.18138	−	0.682072i	0.153803	−	0.0887983i	0.574926	+	0.818205i	$0.305031\pi$
$60$	−1.64272	−	0.549077i	−0.212074	−	0.0708855i
$61$			12.5555i			1.60757i	0.594923	+	0.803783i	$0.297183\pi$
$61$			12.5555i			1.60757i	−0.594923	+	0.803783i	$0.702817\pi$
$62$	−4.97262	+	2.50461i	−0.631523	+	0.318086i
$63$	3.56017	+	2.67931i	0.448539	+	0.337561i
$64$	−1.00000			−0.125000
$65$	0.848361	+	1.46940i	0.105226	+	0.182257i
$66$	7.03901	+	2.35279i	0.866442	+	0.289608i
$67$	5.98520	−	10.3667i	0.731208	−	1.26649i	−0.225159	−	0.974322i	$-0.572290\pi$
$67$	5.98520	−	10.3667i	0.731208	−	1.26649i	0.956367	−	0.292167i	$-0.0943765\pi$
$68$	2.87402	+	4.97796i	0.348527	+	0.603666i
$69$	7.07495	−	1.44171i	0.851724	−	0.173561i
$70$	1.48524			0.177520
$71$	−0.650013	−	0.375285i	−0.0771424	−	0.0445382i	0.460933	−	0.887435i	$-0.347515\pi$
$71$	−0.650013	−	0.375285i	−0.0771424	−	0.0445382i	−0.538075	+	0.842897i	$0.680848\pi$
$72$	−1.17391	−	2.76078i	−0.138347	−	0.325362i
$73$	−3.41044	−	1.96902i	−0.399162	−	0.230456i	0.286960	−	0.957943i	$-0.407355\pi$
$73$	−3.41044	−	1.96902i	−0.399162	−	0.230456i	−0.686122	+	0.727486i	$0.740689\pi$
$74$	4.75644	+	8.23840i	0.552925	+	0.957694i
$75$	−1.14810	−	1.29687i	−0.132571	−	0.149750i
$76$	1.59932	+	2.77010i	0.183454	+	0.317752i
$77$	−6.36423			−0.725272
$78$	−0.931631	+	2.78723i	−0.105486	+	0.315592i
$79$	9.64630	−	5.56929i	1.08529	−	0.626594i	0.152974	−	0.988230i	$-0.451115\pi$
$79$	9.64630	−	5.56929i	1.08529	−	0.626594i	0.932319	+	0.361636i	$0.117782\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	6.24387	−	6.48183i	0.693763	−	0.720204i
$82$	5.63658	−	9.76284i	0.622456	−	1.07813i
$83$	−4.88450	+	8.46021i	−0.536144	+	0.928628i	0.462963	+	0.886377i	$0.346786\pi$
$83$	−4.88450	+	8.46021i	−0.536144	+	0.928628i	−0.999107	+	0.0422508i	$0.986547\pi$
$84$	1.70520	+	1.92617i	0.186052	+	0.210162i
$85$			5.74805i			0.623463i
$86$	3.72140	+	6.44566i	0.401289	+	0.695053i
$87$	−12.1912	+	2.48428i	−1.30703	+	0.266343i
$88$	3.71090	+	2.14249i	0.395584	+	0.228390i
$89$	4.38445			0.464751			0.232376	−	0.972626i	$-0.425350\pi$
$89$	4.38445			0.464751			0.232376	+	0.972626i	$0.425350\pi$
$90$	0.363755	−	2.97787i	0.0383432	−	0.313895i
$91$		−	2.52004i		−	0.264172i
$92$	4.16867			0.434614
$93$	−5.97051	−	7.57318i	−0.619113	−	0.785302i
$94$	11.9223			1.22969
$95$			3.19864i			0.328173i
$96$	−0.345843	−	1.69717i	−0.0352975	−	0.173217i
$97$	−14.9295			−1.51586			−0.757928	−	0.652338i	$-0.773788\pi$
$97$	−14.9295			−1.51586			−0.757928	+	0.652338i	$0.773788\pi$
$98$	4.15178	+	2.39703i	0.419393	+	0.242137i
$99$	−1.55869	+	12.7601i	−0.156654	+	1.28244i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$		−	7.89451i		−	0.785533i	−0.919638	−	0.392767i	$-0.871518\pi$
$101$		−	7.89451i		−	0.785533i	0.919638	−	0.392767i	$-0.128482\pi$
$102$	−7.45448	+	6.59931i	−0.738104	+	0.653429i
$103$	3.33186	−	5.77095i	0.328298	−	0.568629i	−0.653876	−	0.756602i	$-0.726858\pi$
$103$	3.33186	−	5.77095i	0.328298	−	0.568629i	0.982174	+	0.187973i	$0.0601916\pi$
$104$	−0.848361	+	1.46940i	−0.0831887	+	0.144087i
$105$	0.513661	+	2.52071i	0.0501282	+	0.245996i
$106$	5.25843	+	3.03596i	0.510744	+	0.294878i
$107$	−15.9107	+	9.18604i	−1.53814	+	0.888048i	−0.539197	+	0.842180i	$0.681272\pi$
$107$	−15.9107	+	9.18604i	−1.53814	+	0.888048i	−0.998948	+	0.0458681i	$0.985395\pi$
$108$	4.27954	−	2.94713i	0.411799	−	0.283588i
$109$	0.0754967			0.00723127			0.00361563	−	0.999993i	$-0.498849\pi$
$109$	0.0754967			0.00723127			0.00361563	+	0.999993i	$0.498849\pi$
$110$	2.14249	+	3.71090i	0.204279	+	0.353821i
$111$	−12.3370	+	10.9217i	−1.17098	+	1.03664i
$112$	0.742621	+	1.28626i	0.0701711	+	0.121540i
$113$	−13.9553	−	8.05711i	−1.31281	−	0.757949i	−0.330246	−	0.943895i	$-0.607132\pi$
$113$	−13.9553	−	8.05711i	−1.31281	−	0.757949i	−0.982560	+	0.185946i	$0.940465\pi$
$114$	−4.14822	+	3.67234i	−0.388517	+	0.343946i
$115$	3.61018	+	2.08434i	0.336651	+	0.194365i
$116$	−7.18325			−0.666948
$117$	−5.05261	−	0.617192i	−0.467114	−	0.0570594i
$118$	0.682072	+	1.18138i	0.0627899	+	0.108755i
$119$	4.26862	−	7.39346i	0.391304	−	0.677758i
$120$	0.549077	−	1.64272i	0.0501236	−	0.149959i
$121$	−3.68054	−	6.37489i	−0.334595	−	0.579535i
$122$	−12.5555			−1.13672
$123$	18.5186	+	6.18983i	1.66977	+	0.558118i
$124$	−2.50461	−	4.97262i	−0.224921	−	0.446554i
$125$		−	1.00000i		−	0.0894427i
$126$	−2.67931	+	3.56017i	−0.238692	+	0.317165i
$127$	−14.8524	+	8.57505i	−1.31794	+	0.760912i	−0.983397	−	0.181468i	$-0.941915\pi$
$127$	−14.8524	+	8.57505i	−1.31794	+	0.760912i	−0.334542	+	0.942381i	$0.608582\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−9.65237	+	8.54505i	−0.849844	+	0.752350i
$130$	−1.46940	+	0.848361i	−0.128875	+	0.0744062i
$131$	4.66039	−	2.69068i	0.407180	−	0.235086i	−0.282397	−	0.959298i	$-0.591130\pi$
$131$	4.66039	−	2.69068i	0.407180	−	0.235086i	0.689577	+	0.724212i	$0.257796\pi$
$132$	−2.35279	+	7.03901i	−0.204784	+	0.612667i
$133$	2.37537	−	4.11427i	0.205971	−	0.356752i
$134$	10.3667	+	5.98520i	0.895543	+	0.517042i
$135$	5.17975	−	0.412519i	0.445802	−	0.0355040i
$136$	−4.97796	+	2.87402i	−0.426856	+	0.246446i
$137$	9.99103	−	17.3050i	0.853591	−	1.47846i	−0.0243552	−	0.999703i	$-0.507753\pi$
$137$	9.99103	−	17.3050i	0.853591	−	1.47846i	0.877946	−	0.478759i	$-0.158913\pi$
$138$	1.44171	+	7.07495i	0.122726	+	0.602260i
$139$			8.47702i			0.719011i	0.933143	+	0.359506i	$0.117055\pi$
$139$			8.47702i			0.719011i	−0.933143	+	0.359506i	$0.882945\pi$
$140$			1.48524i			0.125526i
$141$	4.12325	+	20.2342i	0.347240	+	1.70403i
$142$	0.375285	−	0.650013i	0.0314932	−	0.0545479i
$143$	6.29638	−	3.63521i	0.526529	−	0.303992i
$144$	2.76078	−	1.17391i	0.230065	−	0.0978259i
$145$	−6.22087	−	3.59162i	−0.516615	−	0.298268i
$146$	1.96902	−	3.41044i	0.162957	−	0.282250i
$147$	−2.63231	+	7.87527i	−0.217109	+	0.649542i
$148$	−8.23840	+	4.75644i	−0.677192	+	0.390977i
$149$	−1.10104	+	0.635685i	−0.0902006	+	0.0520773i	−0.544422	−	0.838812i	$-0.683251\pi$
$149$	−1.10104	+	0.635685i	−0.0902006	+	0.0520773i	0.454221	+	0.890889i	$0.349918\pi$
$150$	1.29687	−	1.14810i	0.105889	−	0.0937416i
$151$		−	20.8749i		−	1.69877i	−0.527770	−	0.849387i	$-0.676972\pi$
$151$		−	20.8749i		−	1.69877i	0.527770	−	0.849387i	$-0.323028\pi$
$152$	−2.77010	+	1.59932i	−0.224685	+	0.129722i
$153$	−13.7782	−	10.3692i	−1.11390	−	0.838301i
$154$		−	6.36423i		−	0.512845i
$155$	0.317249	−	5.55872i	0.0254820	−	0.446487i
$156$	−2.78723	−	0.931631i	−0.223157	−	0.0745902i
$157$	−12.7183			−1.01503			−0.507515	−	0.861643i	$-0.669436\pi$
$157$	−12.7183			−1.01503			−0.507515	+	0.861643i	$0.669436\pi$
$158$	5.56929	+	9.64630i	0.443069	+	0.767418i
$159$	−3.33395	+	9.97443i	−0.264399	+	0.791024i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−3.09574	−	5.36198i	−0.243979	−	0.422583i
$162$	6.48183	+	6.24387i	0.509261	+	0.490564i
$163$	14.8670			1.16447			0.582235	−	0.813020i	$-0.302178\pi$
$163$	14.8670			1.16447			0.582235	+	0.813020i	$0.302178\pi$
$164$	9.76284	+	5.63658i	0.762350	+	0.440143i
$165$	−5.55708	+	4.91957i	−0.432618	+	0.382988i
$166$	−8.46021	−	4.88450i	−0.656639	−	0.379111i
$167$	6.42081	+	11.1212i	0.496857	+	0.860581i	0.999993	−	0.00362562i	$-0.00115407\pi$
$167$	6.42081	+	11.1212i	0.496857	+	0.860581i	−0.503137	+	0.864207i	$0.667821\pi$
$168$	−1.92617	+	1.70520i	−0.148607	+	0.131559i
$169$	−5.06057	−	8.76516i	−0.389274	−	0.674243i
$170$	−5.74805			−0.440855
$171$	−7.66723	−	5.77020i	−0.586328	−	0.441258i
$172$	−6.44566	+	3.72140i	−0.491477	+	0.283754i
$173$	−6.38447	−	3.68607i	−0.485402	−	0.280247i	0.237263	−	0.971445i	$-0.423750\pi$
$173$	−6.38447	−	3.68607i	−0.485402	−	0.280247i	−0.722665	+	0.691198i	$0.757083\pi$
$174$	−2.48428	−	12.1912i	−0.188333	−	0.924213i
$175$	−0.742621	+	1.28626i	−0.0561368	+	0.0972319i
$176$	−2.14249	+	3.71090i	−0.161496	+	0.279720i
$177$	−1.76912	+	1.56617i	−0.132975	+	0.117720i
$178$			4.38445i			0.328629i
$179$	8.19260	+	14.1900i	0.612344	+	1.06061i	0.990844	+	0.135009i	$0.0431064\pi$
$179$	8.19260	+	14.1900i	0.612344	+	1.06061i	−0.378501	+	0.925601i	$0.623560\pi$
$180$	2.97787	+	0.363755i	0.221957	+	0.0271127i
$181$	0.304556	+	0.175835i	0.0226374	+	0.0130697i	0.511276	−	0.859417i	$-0.329173\pi$
$181$	0.304556	+	0.175835i	0.0226374	+	0.0130697i	−0.488639	+	0.872486i	$0.662506\pi$
$182$	2.52004			0.186798
$183$	−4.34223	−	21.3088i	−0.320987	−	1.57519i
$184$			4.16867i			0.307319i
$185$	−9.51288			−0.699401
$186$	7.57318	−	5.97051i	0.555293	−	0.437779i
$187$	24.6303			1.80115
$188$			11.9223i			0.869523i
$189$	−6.96884	−	3.31598i	−0.506908	−	0.241202i
$190$	−3.19864			−0.232054
$191$	−0.457852	−	0.264341i	−0.0331290	−	0.0191270i	0.483344	−	0.875430i	$-0.339422\pi$
$191$	−0.457852	−	0.264341i	−0.0331290	−	0.0191270i	−0.516473	+	0.856303i	$0.672755\pi$
$192$	1.69717	−	0.345843i	0.122483	−	0.0249591i
$193$	1.78569	+	3.09290i	0.128537	+	0.222632i	0.923110	−	0.384536i	$-0.125639\pi$
$193$	1.78569	+	3.09290i	0.128537	+	0.222632i	−0.794573	+	0.607168i	$0.792305\pi$
$194$		−	14.9295i		−	1.07187i
$195$	−1.94800	−	2.20043i	−0.139499	−	0.157576i
$196$	−2.39703	+	4.15178i	−0.171216	+	0.296555i
$197$	−2.86622	+	4.96444i	−0.204210	+	0.353702i	−0.949881	−	0.312613i	$-0.898796\pi$
$197$	−2.86622	+	4.96444i	−0.204210	+	0.353702i	0.745671	+	0.666314i	$0.232129\pi$
$198$	−12.7601	−	1.55869i	−0.906821	−	0.110771i
$199$	−20.8795	−	12.0548i	−1.48011	−	0.854539i	−0.480359	−	0.877072i	$-0.659494\pi$
$199$	−20.8795	−	12.0548i	−1.48011	−	0.854539i	−0.999746	+	0.0225328i	$0.992827\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	−6.57266	+	19.6639i	−0.463600	+	1.38699i
$202$	7.89451			0.555456
$203$	5.33443	+	9.23950i	0.374403	+	0.648486i
$204$	−6.59931	−	7.45448i	−0.462044	−	0.521918i
$205$	5.63658	+	9.76284i	0.393676	+	0.681866i
$206$	5.77095	+	3.33186i	0.402081	+	0.232142i
$207$	−11.5088	+	4.89365i	−0.799917	+	0.340132i
$208$	−1.46940	−	0.848361i	−0.101885	−	0.0588233i
$209$	13.7061			0.948071
$210$	−2.52071	+	0.513661i	−0.173945	+	0.0354460i
$211$	−1.00482	−	1.74041i	−0.0691750	−	0.119815i	0.829363	−	0.558710i	$-0.188703\pi$
$211$	−1.00482	−	1.74041i	−0.0691750	−	0.119815i	−0.898538	+	0.438895i	$0.855370\pi$
$212$	−3.03596	+	5.25843i	−0.208510	+	0.361151i
$213$	1.23297	+	0.412121i	0.0844820	+	0.0282381i
$214$	−9.18604	−	15.9107i	−0.627945	−	1.08763i
$215$	−7.44281			−0.507595
$216$	2.94713	+	4.27954i	0.200527	+	0.291186i
$217$	−4.53608	+	6.91434i	−0.307929	+	0.469376i
$218$			0.0754967i			0.00511328i
$219$	6.46908	+	2.16229i	0.437140	+	0.146114i
$220$	−3.71090	+	2.14249i	−0.250189	+	0.144447i
$221$			9.75284i			0.656047i
$222$	−10.9217	−	12.3370i	−0.733016	−	0.828005i
$223$	−19.3273	+	11.1586i	−1.29425	+	0.747237i	−0.979405	−	0.201905i	$-0.935287\pi$
$223$	−19.3273	+	11.1586i	−1.29425	+	0.747237i	−0.314847	+	0.949142i	$0.601953\pi$
$224$	−1.28626	+	0.742621i	−0.0859416	+	0.0496184i
$225$	2.39703	+	1.80395i	0.159802	+	0.120264i
$226$	8.05711	−	13.9553i	0.535951	−	0.928294i
$227$	−7.92824	−	4.57737i	−0.526216	−	0.303811i	0.213258	−	0.976996i	$-0.431592\pi$
$227$	−7.92824	−	4.57737i	−0.526216	−	0.303811i	−0.739474	+	0.673185i	$0.764926\pi$
$228$	−3.67234	−	4.14822i	−0.243207	−	0.274723i
$229$	4.36925	−	2.52259i	0.288728	−	0.166697i	−0.348640	−	0.937257i	$-0.613356\pi$
$229$	4.36925	−	2.52259i	0.288728	−	0.166697i	0.637368	+	0.770559i	$0.280023\pi$
$230$	−2.08434	+	3.61018i	−0.137437	+	0.238048i
$231$	10.8012	−	2.20103i	0.710667	−	0.144817i
$232$		−	7.18325i		−	0.471603i
$233$		−	16.7182i		−	1.09525i	−0.836725	−	0.547623i	$-0.815533\pi$
$233$		−	16.7182i		−	1.09525i	0.836725	−	0.547623i	$-0.184467\pi$
$234$	0.617192	−	5.05261i	0.0403471	−	0.330299i
$235$	−5.96115	+	10.3250i	−0.388862	+	0.673530i
$236$	−1.18138	+	0.682072i	−0.0769016	+	0.0443991i
$237$	−14.4453	+	12.7882i	−0.938325	+	0.830680i
$238$	7.39346	+	4.26862i	0.479247	+	0.276693i
$239$	5.18784	−	8.98561i	0.335574	−	0.581231i	−0.648021	−	0.761622i	$-0.724403\pi$
$239$	5.18784	−	8.98561i	0.335574	−	0.581231i	0.983595	+	0.180392i	$0.0577365\pi$
$240$	1.64272	+	0.549077i	0.106037	+	0.0354428i
$241$	−7.68620	+	4.43763i	−0.495112	+	0.285853i	−0.726693	−	0.686963i	$-0.758944\pi$
$241$	−7.68620	+	4.43763i	−0.495112	+	0.285853i	0.231581	+	0.972816i	$0.425610\pi$
$242$	6.37489	−	3.68054i	0.409793	−	0.236594i
$243$	−8.35521	+	13.1602i	−0.535987	+	0.844226i
$244$		−	12.5555i		−	0.803783i
$245$	−4.15178	+	2.39703i	−0.265247	+	0.153141i
$246$	−6.18983	+	18.5186i	−0.394649	+	1.18070i
$247$			5.42720i			0.345324i
$248$	4.97262	−	2.50461i	0.315761	−	0.159043i
$249$	5.36393	−	16.0477i	0.339925	−	1.01698i
$250$	1.00000			0.0632456
$251$	6.44966	+	11.1711i	0.407099	+	0.705116i	0.994563	−	0.104134i	$-0.0332070\pi$
$251$	6.44966	+	11.1711i	0.407099	+	0.705116i	−0.587464	+	0.809250i	$0.699874\pi$
$252$	−3.56017	−	2.67931i	−0.224269	−	0.168780i
$253$	8.93135	−	15.4695i	0.561509	−	0.972562i
$254$	−8.57505	−	14.8524i	−0.538046	−	0.931923i
$255$	−1.98792	−	9.75543i	−0.124489	−	0.610908i
$256$	1.00000			0.0625000
$257$	5.60986	+	3.23885i	0.349933	+	0.202034i	0.664656	−	0.747150i	$-0.268578\pi$
$257$	5.60986	+	3.23885i	0.349933	+	0.202034i	−0.314722	+	0.949184i	$0.601911\pi$
$258$	−8.54505	−	9.65237i	−0.531992	−	0.600930i
$259$	12.2360	+	7.06446i	0.760309	+	0.438964i
$260$	−0.848361	−	1.46940i	−0.0526131	−	0.0911286i
$261$	19.8314	−	8.43249i	1.22753	−	0.521958i
$262$	2.69068	+	4.66039i	0.166231	+	0.287920i
$263$	8.12970			0.501299			0.250649	−	0.968078i	$-0.419356\pi$
$263$	8.12970			0.501299			0.250649	+	0.968078i	$0.419356\pi$
$264$	−7.03901	−	2.35279i	−0.433221	−	0.144804i
$265$	−5.25843	+	3.03596i	−0.323023	+	0.186497i
$266$	4.11427	+	2.37537i	0.252262	+	0.145644i
$267$	−7.44117	+	1.51633i	−0.455392	+	0.0927981i
$268$	−5.98520	+	10.3667i	−0.365604	+	0.633245i
$269$	−6.17853	+	10.7015i	−0.376711	+	0.652483i	−0.990582	−	0.136924i	$-0.956278\pi$
$269$	−6.17853	+	10.7015i	−0.376711	+	0.652483i	0.613870	+	0.789407i	$0.289612\pi$
$270$	0.412519	+	5.17975i	0.0251051	+	0.315230i
$271$		−	24.8981i		−	1.51245i	−0.654311	−	0.756226i	$-0.727041\pi$
$271$		−	24.8981i		−	1.51245i	0.654311	−	0.756226i	$-0.272959\pi$
$272$	−2.87402	−	4.97796i	−0.174263	−	0.301833i
$273$	0.871540	+	4.27694i	0.0527480	+	0.258852i
$274$	17.3050	+	9.99103i	1.04543	+	0.603580i
$275$	−4.28498			−0.258394
$276$	−7.07495	+	1.44171i	−0.425862	+	0.0867806i
$277$			0.958749i			0.0576056i	0.999585	+	0.0288028i	$0.00916949\pi$
$277$			0.958749i			0.0576056i	−0.999585	+	0.0288028i	$0.990831\pi$
$278$	−8.47702			−0.508418
$279$	12.7521	+	10.7881i	0.763449	+	0.645868i
$280$	−1.48524			−0.0887601
$281$			26.4095i			1.57546i	0.616023	+	0.787728i	$0.288743\pi$
$281$			26.4095i			1.57546i	−0.616023	+	0.787728i	$0.711257\pi$
$282$	−20.2342	+	4.12325i	−1.20493	+	0.245536i
$283$	−9.06729			−0.538994			−0.269497	−	0.963001i	$-0.586857\pi$
$283$	−9.06729			−0.538994			−0.269497	+	0.963001i	$0.586857\pi$
$284$	0.650013	+	0.375285i	0.0385712	+	0.0222691i
$285$	−1.10623	−	5.42864i	−0.0655273	−	0.321565i
$286$	3.63521	+	6.29638i	0.214955	+	0.372312i
$287$		−	16.7434i		−	0.988329i
$288$	1.17391	+	2.76078i	0.0691734	+	0.162681i
$289$	−8.02003	+	13.8911i	−0.471766	+	0.817123i
$290$	3.59162	−	6.22087i	0.210907	−	0.365302i
$291$	25.3378	−	5.16325i	1.48533	−	0.302675i
$292$	3.41044	+	1.96902i	0.199581	+	0.115228i
$293$	9.81515	−	5.66678i	0.573407	−	0.331057i	−0.185102	−	0.982719i	$-0.559262\pi$
$293$	9.81515	−	5.66678i	0.573407	−	0.331057i	0.758509	+	0.651663i	$0.225928\pi$
$294$	−7.87527	−	2.63231i	−0.459295	−	0.153519i
$295$	−1.36414			−0.0794236
$296$	−4.75644	−	8.23840i	−0.276463	−	0.478847i
$297$	−1.76764	−	22.1952i	−0.102569	−	1.28789i
$298$	−0.635685	−	1.10104i	−0.0368242	−	0.0637814i
$299$	6.12547	+	3.53654i	0.354245	+	0.204523i
$300$	1.14810	+	1.29687i	0.0662853	+	0.0748750i
$301$	9.57336	+	5.52718i	0.551799	+	0.318582i
$302$	20.8749			1.20121
$303$	2.73026	+	13.3983i	0.156850	+	0.769715i
$304$	−1.59932	−	2.77010i	−0.0917272	−	0.158876i
$305$	6.27775	−	10.8734i	0.359463	−	0.622608i
$306$	10.3692	−	13.7782i	0.592769	−	0.787649i
$307$	7.32937	+	12.6948i	0.418309	+	0.724533i	0.995770	−	0.0918857i	$-0.0292894\pi$
$307$	7.32937	+	12.6948i	0.418309	+	0.724533i	−0.577460	+	0.816419i	$0.695956\pi$
$308$	6.36423			0.362636
$309$	−3.65890	+	10.9466i	−0.208147	+	0.622731i
$310$	5.55872	+	0.317249i	0.315714	+	0.0180185i
$311$			5.06981i			0.287482i	0.989615	+	0.143741i	$0.0459133\pi$
$311$			5.06981i			0.287482i	−0.989615	+	0.143741i	$0.954087\pi$
$312$	0.931631	−	2.78723i	0.0527432	−	0.157796i
$313$	8.89747	−	5.13696i	0.502915	−	0.290358i	−0.227002	−	0.973894i	$-0.572892\pi$
$313$	8.89747	−	5.13696i	0.502915	−	0.290358i	0.729917	+	0.683536i	$0.239559\pi$
$314$		−	12.7183i		−	0.717735i
$315$	−1.74354	−	4.10043i	−0.0982374	−	0.231033i
$316$	−9.64630	+	5.56929i	−0.542647	+	0.313297i
$317$	−10.9608	+	6.32820i	−0.615618	+	0.355427i	−0.775161	−	0.631764i	$-0.782331\pi$
$317$	−10.9608	+	6.32820i	−0.615618	+	0.355427i	0.159543	+	0.987191i	$0.448998\pi$
$318$	−9.97443	−	3.33395i	−0.559338	−	0.186959i
$319$	−15.3900	+	26.6563i	−0.861677	+	1.49247i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	23.8262	−	21.0929i	1.32985	−	1.17729i
$322$	5.36198	−	3.09574i	0.298812	−	0.172519i
$323$	−9.19296	+	15.9227i	−0.511510	+	0.885961i
$324$	−6.24387	+	6.48183i	−0.346881	+	0.360102i
$325$		−	1.69672i		−	0.0941172i
$326$			14.8670i			0.823405i
$327$	−0.128131	+	0.0261100i	−0.00708565	+	0.00144389i
$328$	−5.63658	+	9.76284i	−0.311228	+	0.539063i
$329$	15.3351	−	8.85374i	0.845453	−	0.488123i
$330$	−4.91957	−	5.55708i	−0.270813	−	0.305907i
$331$	−27.0867	−	15.6385i	−1.48882	−	0.859570i	−0.488901	−	0.872339i	$-0.662602\pi$
$331$	−27.0867	−	15.6385i	−1.48882	−	0.859570i	−0.999918	+	0.0127687i	$0.995935\pi$
$332$	4.88450	−	8.46021i	0.268072	−	0.464314i
$333$	17.1608	−	22.8027i	0.940406	−	1.24958i
$334$	−11.1212	+	6.42081i	−0.608523	+	0.351331i
$335$	−10.3667	+	5.98520i	−0.566391	+	0.327006i
$336$	−1.70520	−	1.92617i	−0.0930262	−	0.105081i
$337$		−	9.34441i		−	0.509022i	−0.967070	−	0.254511i	$-0.918085\pi$
$337$		−	9.34441i		−	0.509022i	0.967070	−	0.254511i	$-0.0819145\pi$
$338$	8.76516	−	5.06057i	0.476762	−	0.275259i
$339$	26.4711	+	8.84794i	1.43771	+	0.480554i
$340$		−	5.74805i		−	0.311732i
$341$	−23.8190	−	1.35941i	−1.28987	−	0.0736160i
$342$	5.77020	−	7.66723i	0.312016	−	0.414596i
$343$	17.5170			0.945830
$344$	−3.72140	−	6.44566i	−0.200645	−	0.347527i
$345$	−6.84794	−	2.28892i	−0.368681	−	0.123231i
$346$	3.68607	−	6.38447i	0.198165	−	0.343231i
$347$	−4.88948	−	8.46882i	−0.262481	−	0.454630i	0.704420	−	0.709784i	$-0.251207\pi$
$347$	−4.88948	−	8.46882i	−0.262481	−	0.454630i	−0.966901	+	0.255154i	$0.917874\pi$
$348$	12.1912	−	2.48428i	0.653517	−	0.133171i
$349$	−15.4112			−0.824940			−0.412470	−	0.910971i	$-0.635334\pi$
$349$	−15.4112			−0.824940			−0.412470	+	0.910971i	$0.635334\pi$
$350$	−1.28626	−	0.742621i	−0.0687533	−	0.0396947i
$351$	8.78860	−	0.699931i	0.469101	−	0.0373595i
$352$	−3.71090	−	2.14249i	−0.197792	−	0.114195i
$353$	8.84422	+	15.3186i	0.470730	+	0.815329i	0.999440	−	0.0334742i	$-0.0106572\pi$
$353$	8.84422	+	15.3186i	0.470730	+	0.815329i	−0.528709	+	0.848803i	$0.677324\pi$
$354$	−1.56617	−	1.76912i	−0.0832409	−	0.0940278i
$355$	0.375285	+	0.650013i	0.0199181	+	0.0344991i
$356$	−4.38445			−0.232376
$357$	−4.68760	+	14.0243i	−0.248094	+	0.742242i
$358$	−14.1900	+	8.19260i	−0.749965	+	0.432992i
$359$	2.07009	+	1.19517i	0.109255	+	0.0630786i	0.553632	−	0.832761i	$-0.313241\pi$
$359$	2.07009	+	1.19517i	0.109255	+	0.0630786i	−0.444377	+	0.895840i	$0.646575\pi$
$360$	−0.363755	+	2.97787i	−0.0191716	+	0.156947i
$361$	4.38436	−	7.59393i	0.230756	−	0.399681i
$362$	−0.175835	+	0.304556i	−0.00924170	+	0.0160071i
$363$	8.45123	+	9.54639i	0.443574	+	0.501055i
$364$			2.52004i			0.132086i
$365$	1.96902	+	3.41044i	0.103063	+	0.178511i
$366$	21.3088	−	4.34223i	1.11383	−	0.226972i
$367$	24.6528	+	14.2333i	1.28687	+	0.742973i	0.978094	−	0.208163i	$-0.0667485\pi$
$367$	24.6528	+	14.2333i	1.28687	+	0.742973i	0.308773	+	0.951136i	$0.400082\pi$
$368$	−4.16867			−0.217307
$369$	−33.5699	−	4.10067i	−1.74758	−	0.213473i
$370$		−	9.51288i		−	0.494551i
$371$	9.01826			0.468205
$372$	5.97051	+	7.57318i	0.309556	+	0.392651i
$373$	8.75126			0.453123			0.226561	−	0.973997i	$-0.427252\pi$
$373$	8.75126			0.453123			0.226561	+	0.973997i	$0.427252\pi$
$374$			24.6303i			1.27360i
$375$	0.345843	+	1.69717i	0.0178593	+	0.0876416i
$376$	−11.9223			−0.614846
$377$	−10.5551	−	6.09399i	−0.543615	−	0.313856i
$378$	3.31598	−	6.96884i	0.170556	−	0.358438i
$379$	10.8559	+	18.8030i	0.557631	+	0.965846i	0.997694	+	0.0678785i	$0.0216230\pi$
$379$	10.8559	+	18.8030i	0.557631	+	0.965846i	−0.440062	+	0.897967i	$0.645044\pi$
$380$		−	3.19864i		−	0.164087i
$381$	22.2415	−	19.6899i	1.13947	−	1.00875i
$382$	0.264341	−	0.457852i	0.0135249	−	0.0234257i
$383$	5.76820	−	9.99081i	0.294741	−	0.510506i	−0.680184	−	0.733042i	$-0.738100\pi$
$383$	5.76820	−	9.99081i	0.294741	−	0.510506i	0.974925	+	0.222535i	$0.0714333\pi$
$384$	0.345843	+	1.69717i	0.0176487	+	0.0866084i
$385$	5.51159	+	3.18212i	0.280897	+	0.162176i
$386$	−3.09290	+	1.78569i	−0.157425	+	0.0908891i
$387$	13.4265	−	17.8406i	0.682507	−	0.906890i
$388$	14.9295			0.757928
$389$	−3.78040	−	6.54785i	−0.191674	−	0.331989i	0.754131	−	0.656724i	$-0.228058\pi$
$389$	−3.78040	−	6.54785i	−0.191674	−	0.331989i	−0.945805	+	0.324735i	$0.894725\pi$
$390$	2.20043	−	1.94800i	0.111423	−	0.0986407i
$391$	11.9809	+	20.7515i	0.605898	+	1.04945i
$392$	−4.15178	−	2.39703i	−0.209696	−	0.121068i
$393$	−6.97893	+	6.17831i	−0.352040	+	0.311654i
$394$	−4.96444	−	2.86622i	−0.250105	−	0.144398i
$395$	−11.1386			−0.560443
$396$	1.55869	−	12.7601i	0.0783269	−	0.641219i
$397$	−14.1004	−	24.4225i	−0.707676	−	1.22573i	−0.965717	−	0.259597i	$-0.916410\pi$
$397$	−14.1004	−	24.4225i	−0.707676	−	1.22573i	0.258041	−	0.966134i	$-0.416923\pi$
$398$	12.0548	−	20.8795i	0.604250	−	1.04659i
$399$	−2.60853	+	7.80413i	−0.130590	+	0.390695i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−30.4667			−1.52143			−0.760716	−	0.649084i	$-0.775152\pi$
$401$	−30.4667			−1.52143			−0.760716	+	0.649084i	$0.775152\pi$
$402$	−19.6639	−	6.57266i	−0.980749	−	0.327815i
$403$	0.538283	−	9.43160i	0.0268138	−	0.469822i
$404$			7.89451i			0.392767i
$405$	−8.64826	+	2.49150i	−0.429736	+	0.123804i
$406$	−9.23950	+	5.33443i	−0.458549	+	0.264743i
$407$			40.7626i			2.02052i
$408$	7.45448	−	6.59931i	0.369052	−	0.326714i
$409$	20.2072	−	11.6666i	0.999180	−	0.576877i	0.0911742	−	0.995835i	$-0.470938\pi$
$409$	20.2072	−	11.6666i	0.999180	−	0.576877i	0.908005	+	0.418958i	$0.137605\pi$
$410$	−9.76284	+	5.63658i	−0.482152	+	0.278371i
$411$	−10.9717	+	32.8248i	−0.541193	+	1.61913i
$412$	−3.33186	+	5.77095i	−0.164149	+	0.284315i
$413$	1.75464	+	1.01304i	0.0863402	+	0.0498485i
$414$	−4.89365	−	11.5088i	−0.240510	−	0.565627i
$415$	8.46021	−	4.88450i	0.415295	−	0.239771i
$416$	0.848361	−	1.46940i	0.0415943	−	0.0720435i
$417$	−2.93172	−	14.3870i	−0.143567	−	0.704532i
$418$			13.7061i			0.670388i
$419$		−	13.0350i		−	0.636804i	−0.947956	−	0.318402i	$-0.896854\pi$
$419$		−	13.0350i		−	0.636804i	0.947956	−	0.318402i	$-0.103146\pi$
$420$	−0.513661	−	2.52071i	−0.0250641	−	0.122998i
$421$	3.07421	−	5.32469i	0.149828	−	0.259510i	−0.781336	−	0.624111i	$-0.785461\pi$
$421$	3.07421	−	5.32469i	0.149828	−	0.259510i	0.931164	+	0.364601i	$0.118795\pi$
$422$	1.74041	−	1.00482i	0.0847217	−	0.0489141i
$423$	−13.9957	−	32.9149i	−0.680495	−	1.60038i
$424$	−5.25843	−	3.03596i	−0.255372	−	0.147439i
$425$	2.87402	−	4.97796i	0.139411	−	0.241466i
$426$	−0.412121	+	1.23297i	−0.0199673	+	0.0597378i
$427$	−16.1496	+	9.32397i	−0.781533	+	0.451218i
$428$	15.9107	−	9.18604i	0.769072	−	0.444024i
$429$	−9.42882	+	8.34714i	−0.455228	+	0.403004i
$430$		−	7.44281i		−	0.358924i
$431$	−21.6097	+	12.4764i	−1.04090	+	0.600967i	−0.920089	−	0.391708i	$-0.871884\pi$
$431$	−21.6097	+	12.4764i	−1.04090	+	0.600967i	−0.120815	+	0.992675i	$0.538551\pi$
$432$	−4.27954	+	2.94713i	−0.205899	+	0.141794i
$433$		−	8.45564i		−	0.406352i	−0.979142	−	0.203176i	$-0.934874\pi$
$433$		−	8.45564i		−	0.406352i	0.979142	−	0.203176i	$-0.0651264\pi$
$434$	−6.91434	−	4.53608i	−0.331899	−	0.217739i
$435$	11.8000	+	3.94415i	0.565768	+	0.189108i
$436$	−0.0754967			−0.00361563
$437$	6.66704	+	11.5476i	0.318928	+	0.552399i
$438$	−2.16229	+	6.46908i	−0.103318	+	0.309105i
$439$	−5.15491	+	8.92856i	−0.246030	+	0.426137i	−0.962421	−	0.271563i	$-0.912460\pi$
$439$	−5.15491	+	8.92856i	−0.246030	+	0.426137i	0.716390	+	0.697700i	$0.245793\pi$
$440$	−2.14249	−	3.71090i	−0.102139	−	0.176910i
$441$	1.74387	−	14.2761i	0.0830412	−	0.679812i
$442$	−9.75284			−0.463895
$443$	7.42343	+	4.28592i	0.352698	+	0.203630i	0.665873	−	0.746065i	$-0.268059\pi$
$443$	7.42343	+	4.28592i	0.352698	+	0.203630i	−0.313175	+	0.949695i	$0.601393\pi$
$444$	12.3370	−	10.9217i	0.585488	−	0.518321i
$445$	−3.79705	−	2.19223i	−0.179997	−	0.103921i
$446$	−11.1586	−	19.3273i	−0.528376	−	0.915175i
$447$	1.64880	−	1.45965i	0.0779857	−	0.0690392i
$448$	−0.742621	−	1.28626i	−0.0350855	−	0.0607699i
$449$	40.5736			1.91479			0.957393	−	0.288787i	$-0.0932521\pi$
$449$	40.5736			1.91479			0.957393	+	0.288787i	$0.0932521\pi$
$450$	−1.80395	+	2.39703i	−0.0850392	+	0.112997i
$451$	41.8336	−	24.1527i	1.96987	−	1.13730i
$452$	13.9553	+	8.05711i	0.656403	+	0.378974i
$453$	7.21944	+	35.4283i	0.339199	+	1.66457i
$454$	4.57737	−	7.92824i	0.214827	−	0.372091i
$455$	−1.26002	+	2.18242i	−0.0590707	+	0.102313i
$456$	4.14822	−	3.67234i	0.194258	−	0.171973i
$457$			33.0592i			1.54644i	0.634136	+	0.773222i	$0.281356\pi$
$457$			33.0592i			1.54644i	−0.634136	+	0.773222i	$0.718644\pi$
$458$	2.52259	+	4.36925i	0.117873	+	0.204162i
$459$	26.9702	+	12.8332i	1.25886	+	0.599004i
$460$	−3.61018	−	2.08434i	−0.168325	−	0.0971827i
$461$	2.92110			0.136049			0.0680246	−	0.997684i	$-0.478330\pi$
$461$	2.92110			0.136049			0.0680246	+	0.997684i	$0.478330\pi$
$462$	2.20103	+	10.8012i	0.102401	+	0.502517i
$463$			23.0953i			1.07333i	0.843795	+	0.536665i	$0.180316\pi$
$463$			23.0953i			1.07333i	−0.843795	+	0.536665i	$0.819684\pi$
$464$	7.18325			0.333474
$465$	1.38402	+	9.54382i	0.0641824	+	0.442584i
$466$	16.7182			0.774456
$467$		−	21.7637i		−	1.00711i	−0.863964	−	0.503553i	$-0.832026\pi$
$467$		−	21.7637i		−	1.00711i	0.863964	−	0.503553i	$-0.167974\pi$
$468$	5.05261	+	0.617192i	0.233557	+	0.0285297i
$469$	17.7789			0.820954
$470$	−10.3250	−	5.96115i	−0.476257	−	0.274967i
$471$	21.5851	−	4.39854i	0.994591	−	0.202674i
$472$	−0.682072	−	1.18138i	−0.0313949	−	0.0543776i
$473$			31.8923i			1.46641i
$474$	−12.7882	−	14.4453i	−0.587379	−	0.663496i
$475$	1.59932	−	2.77010i	0.0733818	−	0.127101i
$476$	−4.26862	+	7.39346i	−0.195652	+	0.338879i
$477$	2.20869	−	18.0814i	0.101129	−	0.827888i
$478$	8.98561	+	5.18784i	0.410992	+	0.237286i
$479$	−1.92376	+	1.11069i	−0.0878991	+	0.0507485i	−0.543305	−	0.839535i	$-0.682827\pi$
$479$	−1.92376	+	1.11069i	−0.0878991	+	0.0507485i	0.455406	+	0.890284i	$0.349494\pi$
$480$	−0.549077	+	1.64272i	−0.0250618	+	0.0749794i
$481$	−16.1407			−0.735954
$482$	−4.43763	−	7.68620i	−0.202129	−	0.350097i
$483$	7.10841	+	8.02956i	0.323444	+	0.365358i
$484$	3.68054	+	6.37489i	0.167297	+	0.289768i
$485$	12.9293	+	7.46473i	0.587089	+	0.338956i
$486$	−13.1602	−	8.35521i	−0.596958	−	0.379000i
$487$	−20.5993	−	11.8930i	−0.933445	−	0.538925i	−0.0455457	−	0.998962i	$-0.514503\pi$
$487$	−20.5993	−	11.8930i	−0.933445	−	0.538925i	−0.887900	+	0.460037i	$0.847836\pi$
$488$	12.5555			0.568360
$489$	−25.2318	+	5.14164i	−1.14102	+	0.232513i
$490$	−2.39703	−	4.15178i	−0.108287	−	0.187558i
$491$	−3.47887	+	6.02558i	−0.156999	+	0.271931i	−0.933785	−	0.357834i	$-0.883515\pi$
$491$	−3.47887	+	6.02558i	−0.156999	+	0.271931i	0.776786	+	0.629765i	$0.216849\pi$
$492$	−18.5186	−	6.18983i	−0.834883	−	0.279059i
$493$	−20.6448	−	35.7579i	−0.929796	−	1.61045i
$494$	−5.42720			−0.244181
$495$	7.72991	−	10.2712i	0.347434	−	0.461658i
$496$	2.50461	+	4.97262i	0.112460	+	0.223277i
$497$		−	1.11478i		−	0.0500046i
$498$	16.0477	+	5.36393i	0.719114	+	0.240364i
$499$	−15.0370	+	8.68160i	−0.673147	+	0.388642i	−0.797268	−	0.603626i	$-0.793722\pi$
$499$	−15.0370	+	8.68160i	−0.673147	+	0.388642i	0.124121	+	0.992267i	$0.460389\pi$
$500$			1.00000i			0.0447214i
$501$	−14.7434	−	16.6539i	−0.658686	−	0.744043i
$502$	−11.1711	+	6.44966i	−0.498593	+	0.287863i
$503$	−2.94516	+	1.70039i	−0.131318	+	0.0758166i	−0.564220	−	0.825624i	$-0.690823\pi$
$503$	−2.94516	+	1.70039i	−0.131318	+	0.0758166i	0.432902	+	0.901441i	$0.357490\pi$
$504$	2.67931	−	3.56017i	0.119346	−	0.158582i
$505$	−3.94726	+	6.83685i	−0.175651	+	0.304236i
$506$	15.4695	+	8.93135i	0.687705	+	0.397047i
$507$	11.6200	+	13.1258i	0.516063	+	0.582938i
$508$	14.8524	−	8.57505i	0.658969	−	0.380456i
$509$	−1.23751	+	2.14342i	−0.0548515	+	0.0950055i	−0.892147	−	0.451745i	$-0.850802\pi$
$509$	−1.23751	+	2.14342i	−0.0548515	+	0.0950055i	0.837296	+	0.546750i	$0.184135\pi$
$510$	9.75543	−	1.98792i	0.431977	−	0.0880268i
$511$		−	5.84894i		−	0.258742i
$512$			1.00000i			0.0441942i
$513$	15.0082	+	7.14135i	0.662628	+	0.315298i
$514$	−3.23885	+	5.60986i	−0.142860	+	0.247440i
$515$	−5.77095	+	3.33186i	−0.254299	+	0.146819i
$516$	9.65237	−	8.54505i	0.424922	−	0.376175i
$517$	44.2425	+	25.5434i	1.94578	+	1.12340i
$518$	−7.06446	+	12.2360i	−0.310395	+	0.537619i
$519$	12.1103	+	4.04788i	0.531585	+	0.177682i
$520$	1.46940	−	0.848361i	0.0644377	−	0.0372031i
$521$	18.8893	−	10.9057i	0.827554	−	0.477789i	−0.0254604	−	0.999676i	$-0.508105\pi$
$521$	18.8893	−	10.9057i	0.827554	−	0.477789i	0.853014	+	0.521887i	$0.174772\pi$
$522$	8.43249	+	19.8314i	0.369080	+	0.867997i
$523$		−	29.7300i		−	1.30000i	−0.759932	−	0.650002i	$-0.774768\pi$
$523$		−	29.7300i		−	1.30000i	0.759932	−	0.650002i	$-0.225232\pi$
$524$	−4.66039	+	2.69068i	−0.203590	+	0.117543i
$525$	0.815512	−	2.43983i	0.0355918	−	0.106483i
$526$			8.12970i			0.354472i
$527$	17.5551	−	26.7593i	0.764714	−	1.16565i
$528$	2.35279	−	7.03901i	0.102392	−	0.306334i
$529$	−5.62217			−0.244442
$530$	−3.03596	−	5.25843i	−0.131874	−	0.228412i
$531$	2.46085	−	3.26990i	0.106792	−	0.141901i
$532$	−2.37537	+	4.11427i	−0.102986	+	0.178376i
$533$	9.56371	+	16.5648i	0.414250	+	0.717503i
$534$	−1.51633	−	7.44117i	−0.0656182	−	0.322011i
$535$	18.3721			0.794294
$536$	−10.3667	−	5.98520i	−0.447772	−	0.258521i
$537$	−18.8118	−	21.2495i	−0.811787	−	0.916984i
$538$	−10.7015	−	6.17853i	−0.461375	−	0.266375i
$539$	10.2712	+	17.7903i	0.442413	+	0.766282i
$540$	−5.17975	+	0.412519i	−0.222901	+	0.0177520i
$541$	6.49989	+	11.2581i	0.279452	+	0.484026i	0.971249	−	0.238067i	$-0.0765138\pi$
$541$	6.49989	+	11.2581i	0.279452	+	0.484026i	−0.691796	+	0.722093i	$0.743180\pi$
$542$	24.8981			1.06946
$543$	−0.577695	−	0.193094i	−0.0247913	−	0.00828646i
$544$	4.97796	−	2.87402i	0.213428	−	0.123223i
$545$	−0.0653820	−	0.0377483i	−0.00280066	−	0.00161696i
$546$	−4.27694	+	0.871540i	−0.183036	+	0.0372985i
$547$	5.95679	−	10.3175i	0.254694	−	0.441143i	−0.710118	−	0.704082i	$-0.751359\pi$
$547$	5.95679	−	10.3175i	0.254694	−	0.441143i	0.964812	+	0.262939i	$0.0846919\pi$
$548$	−9.99103	+	17.3050i	−0.426795	+	0.739231i
$549$	14.7390	+	34.6630i	0.629047	+	1.47938i
$550$		−	4.28498i		−	0.182712i
$551$	−11.4883	−	19.8983i	−0.489418	−	0.847697i
$552$	−1.44171	−	7.07495i	−0.0613631	−	0.301130i
$553$	14.3271	+	8.27174i	0.609249	+	0.351750i
$554$	−0.958749			−0.0407333
$555$	16.1450	−	3.28997i	0.685317	−	0.139651i
$556$		−	8.47702i		−	0.359506i
$557$	16.7531			0.709853			0.354927	−	0.934894i	$-0.384506\pi$
$557$	16.7531			0.709853			0.354927	+	0.934894i	$0.384506\pi$
$558$	−10.7881	+	12.7521i	−0.456698	+	0.539840i
$559$	−12.6284			−0.534124
$560$		−	1.48524i		−	0.0627629i
$561$	−41.8018	+	8.51822i	−1.76488	+	0.359640i
$562$	−26.4095			−1.11402
$563$	−19.8195	−	11.4428i	−0.835291	−	0.482255i	0.0203699	−	0.999793i	$-0.493516\pi$
$563$	−19.8195	−	11.4428i	−0.835291	−	0.482255i	−0.855661	+	0.517537i	$0.826849\pi$
$564$	−4.12325	−	20.2342i	−0.173620	−	0.852013i
$565$	8.05711	+	13.9553i	0.338965	+	0.587105i
$566$		−	9.06729i		−	0.381127i
$567$	12.9741	+	3.21767i	0.544862	+	0.135129i
$568$	−0.375285	+	0.650013i	−0.0157466	+	0.0272740i
$569$	6.49170	−	11.2440i	0.272146	−	0.471371i	−0.697265	−	0.716814i	$-0.745600\pi$
$569$	6.49170	−	11.2440i	0.272146	−	0.471371i	0.969411	+	0.245442i	$0.0789332\pi$
$570$	5.42864	−	1.10623i	0.227381	−	0.0463348i
$571$	−21.3534	−	12.3284i	−0.893613	−	0.515927i	−0.0184902	−	0.999829i	$-0.505886\pi$
$571$	−21.3534	−	12.3284i	−0.893613	−	0.515927i	−0.875122	+	0.483902i	$0.839219\pi$
$572$	−6.29638	+	3.63521i	−0.263265	+	0.151996i
$573$	0.868474	+	0.290287i	0.0362810	+	0.0121269i
$574$	16.7434			0.698854
$575$	−2.08434	−	3.61018i	−0.0869228	−	0.150555i
$576$	−2.76078	+	1.17391i	−0.115033	+	0.0489130i
$577$	−3.59472	−	6.22623i	−0.149650	−	0.259202i	0.781448	−	0.623970i	$-0.214481\pi$
$577$	−3.59472	−	6.22623i	−0.149650	−	0.259202i	−0.931098	+	0.364769i	$0.881148\pi$
$578$	−13.8911	−	8.02003i	−0.577793	−	0.333589i
$579$	−4.10028	−	4.63162i	−0.170402	−	0.192484i
$580$	6.22087	+	3.59162i	0.258308	+	0.149134i
$581$	−14.5093			−0.601948
$582$	5.16325	+	25.3378i	0.214024	+	1.05029i
$583$	13.0090	+	22.5323i	0.538779	+	0.933193i
$584$	−1.96902	+	3.41044i	−0.0814787	+	0.141125i
$585$	4.06709	+	3.06081i	0.168154	+	0.126549i
$586$	5.66678	+	9.81515i	0.234092	+	0.405460i
$587$	3.95908			0.163409			0.0817044	−	0.996657i	$-0.473964\pi$
$587$	3.95908			0.163409			0.0817044	+	0.996657i	$0.473964\pi$
$588$	2.63231	−	7.87527i	0.108554	−	0.324771i
$589$	9.76897	−	14.8908i	0.402524	−	0.613566i
$590$		−	1.36414i		−	0.0561610i
$591$	3.14755	−	9.41678i	0.129473	−	0.387354i
$592$	8.23840	−	4.75644i	0.338596	−	0.195489i
$593$		−	27.4216i		−	1.12607i	−0.826433	−	0.563035i	$-0.809634\pi$
$593$		−	27.4216i		−	1.12607i	0.826433	−	0.563035i	$-0.190366\pi$
$594$	22.1952	−	1.76764i	0.910678	−	0.0725271i
$595$	−7.39346	+	4.26862i	−0.303102	+	0.174996i
$596$	1.10104	−	0.635685i	0.0451003	−	0.0260387i
$597$	39.6051	+	13.2380i	1.62093	+	0.541794i
$598$	−3.53654	+	6.12547i	−0.144620	+	0.250489i
$599$	−21.3073	−	12.3018i	−0.870593	−	0.502637i	−0.00304762	−	0.999995i	$-0.500970\pi$
$599$	−21.3073	−	12.3018i	−0.870593	−	0.502637i	−0.867545	+	0.497358i	$0.834303\pi$
$600$	−1.29687	+	1.14810i	−0.0529446	+	0.0468708i
$601$	−10.4607	+	6.03950i	−0.426701	+	0.246356i	−0.697940	−	0.716156i	$-0.745900\pi$
$601$	−10.4607	+	6.03950i	−0.426701	+	0.246356i	0.271239	+	0.962512i	$0.412567\pi$
$602$	−5.52718	+	9.57336i	−0.225271	+	0.390181i
$603$	4.35430	−	35.6462i	0.177321	−	1.45163i
$604$			20.8749i			0.849387i
$605$			7.36109i			0.299271i
$606$	−13.3983	+	2.73026i	−0.544271	+	0.110909i
$607$	14.8047	−	25.6424i	0.600903	−	1.04079i	−0.391781	−	0.920058i	$-0.628141\pi$
$607$	14.8047	−	25.6424i	0.600903	−	1.04079i	0.992685	−	0.120737i	$-0.0385256\pi$
$608$	2.77010	−	1.59932i	0.112342	−	0.0648609i
$609$	−12.2489	−	13.8361i	−0.496349	−	0.560669i
$610$	10.8734	+	6.27775i	0.440250	+	0.254178i
$611$	−10.1144	+	17.5187i	−0.409185	+	0.708730i
$612$	13.7782	+	10.3692i	0.556952	+	0.419151i
$613$	−15.6867	+	9.05675i	−0.633582	+	0.365799i	−0.782138	−	0.623105i	$-0.785871\pi$
$613$	−15.6867	+	9.05675i	−0.633582	+	0.365799i	0.148556	+	0.988904i	$0.452537\pi$
$614$	−12.6948	+	7.32937i	−0.512322	+	0.295789i
$615$	−12.9427	−	14.6198i	−0.521898	−	0.589529i
$616$			6.36423i			0.256422i
$617$	9.02116	−	5.20837i	0.363178	−	0.209681i	−0.307296	−	0.951614i	$-0.599424\pi$
$617$	9.02116	−	5.20837i	0.363178	−	0.209681i	0.670474	+	0.741933i	$0.266091\pi$
$618$	−10.9466	−	3.65890i	−0.440337	−	0.147182i
$619$		−	15.4259i		−	0.620018i	−0.950734	−	0.310009i	$-0.899668\pi$
$619$		−	15.4259i		−	0.620018i	0.950734	−	0.310009i	$-0.100332\pi$
$620$	−0.317249	+	5.55872i	−0.0127410	+	0.223244i
$621$	17.8400	−	12.2856i	0.715894	−	0.493005i
$622$	−5.06981			−0.203281
$623$	3.25598	+	5.63953i	0.130448	+	0.225943i
$624$	2.78723	+	0.931631i	0.111579	+	0.0372951i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	5.13696	+	8.89747i	0.205314	+	0.355615i
$627$	−23.2616	+	4.74017i	−0.928980	+	0.189304i
$628$	12.7183			0.507515
$629$	−47.3547	−	27.3403i	−1.88816	−	1.09013i
$630$	4.10043	−	1.74354i	0.163365	−	0.0694643i
$631$	−29.5735	−	17.0743i	−1.17730	−	0.679716i	−0.221913	−	0.975066i	$-0.571230\pi$
$631$	−29.5735	−	17.0743i	−1.17730	−	0.679716i	−0.955389	+	0.295351i	$0.904563\pi$
$632$	−5.56929	−	9.64630i	−0.221535	−	0.383709i
$633$	2.30727	+	2.60626i	0.0917057	+	0.103589i
$634$	−6.32820	−	10.9608i	−0.251325	−	0.435307i
$635$	17.1501			0.680581
$636$	3.33395	−	9.97443i	0.132200	−	0.395512i
$637$	−7.04441	+	4.06709i	−0.279110	+	0.161144i
$638$	−26.6563	−	15.3900i	−1.05533	−	0.609298i
$639$	−2.23510	−	0.273024i	−0.0884191	−	0.0108007i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−0.0147605	+	0.0255660i	−0.000583005	+	0.00100979i	−0.866317	−	0.499495i	$-0.833519\pi$
$641$	−0.0147605	+	0.0255660i	−0.000583005	+	0.00100979i	0.865734	+	0.500505i	$0.166852\pi$
$642$	21.0929	+	23.8262i	0.832470	+	0.940347i
$643$			35.8603i			1.41419i	0.707117	+	0.707097i	$0.249995\pi$
$643$			35.8603i			1.41419i	−0.707117	+	0.707097i	$0.750005\pi$
$644$	3.09574	+	5.36198i	0.121989	+	0.211292i
$645$	12.6317	−	2.57405i	0.497374	−	0.101353i
$646$	−15.9227	−	9.19296i	−0.626469	−	0.361692i
$647$	20.2804			0.797307			0.398653	−	0.917102i	$-0.369478\pi$
$647$	20.2804			0.797307			0.398653	+	0.917102i	$0.369478\pi$
$648$	−6.48183	−	6.24387i	−0.254630	−	0.245282i
$649$			5.84534i			0.229450i
$650$	1.69672			0.0665509
$651$	5.30723	−	13.3036i	0.208007	−	0.521409i
$652$	−14.8670			−0.582235
$653$		−	38.1868i		−	1.49436i	−0.664619	−	0.747182i	$-0.731406\pi$
$653$		−	38.1868i		−	1.49436i	0.664619	−	0.747182i	$-0.268594\pi$
$654$	−0.0261100	−	0.128131i	−0.00102098	−	0.00501031i
$655$	−5.38136			−0.210267
$656$	−9.76284	−	5.63658i	−0.381175	−	0.220071i
$657$	−11.7270	−	1.43248i	−0.457512	−	0.0558865i
$658$	8.85374	+	15.3351i	0.345155	+	0.597826i
$659$			7.51357i			0.292687i	0.989234	+	0.146344i	$0.0467505\pi$
$659$			7.51357i			0.292687i	−0.989234	+	0.146344i	$0.953250\pi$
$660$	5.55708	−	4.91957i	0.216309	−	0.191494i
$661$	8.34254	−	14.4497i	0.324487	−	0.562028i	−0.656921	−	0.753959i	$-0.728142\pi$
$661$	8.34254	−	14.4497i	0.324487	−	0.562028i	0.981408	+	0.191931i	$0.0614749\pi$
$662$	15.6385	−	27.0867i	0.607808	−	1.05275i
$663$	−3.37296	−	16.5522i	−0.130995	−	0.642836i
$664$	8.46021	+	4.88450i	0.328320	+	0.189555i
$665$	−4.11427	+	2.37537i	−0.159544	+	0.0921131i
$666$	22.8027	+	17.1608i	0.883585	+	0.664968i
$667$	−29.9446			−1.15946
$668$	−6.42081	−	11.1212i	−0.248428	−	0.430291i
$669$	28.9426	−	25.6223i	1.11899	−	0.990616i
$670$	−5.98520	−	10.3667i	−0.231228	−	0.400499i
$671$	−46.5922	−	26.9000i	−1.79867	−	1.03846i
$672$	1.92617	−	1.70520i	0.0743035	−	0.0657794i
$673$	−9.55123	−	5.51440i	−0.368173	−	0.212565i	0.304487	−	0.952516i	$-0.401515\pi$
$673$	−9.55123	−	5.51440i	−0.368173	−	0.212565i	−0.672660	+	0.739952i	$0.734848\pi$
$674$	9.34441			0.359933
$675$	−4.69206	−	2.23262i	−0.180597	−	0.0859337i
$676$	5.06057	+	8.76516i	0.194637	+	0.337121i
$677$	10.5122	−	18.2077i	0.404017	−	0.699778i	−0.590189	−	0.807265i	$-0.700947\pi$
$677$	10.5122	−	18.2077i	0.404017	−	0.699778i	0.994207	+	0.107487i	$0.0342803\pi$
$678$	−8.84794	+	26.4711i	−0.339803	+	1.01662i
$679$	−11.0869	−	19.2031i	−0.425477	−	0.736948i
$680$	5.74805			0.220428
$681$	15.0386	+	5.02665i	0.576282	+	0.192622i
$682$	1.35941	−	23.8190i	0.0520543	−	0.912077i
$683$		−	11.4530i		−	0.438239i	−0.975698	−	0.219119i	$-0.929682\pi$
$683$		−	11.4530i		−	0.438239i	0.975698	−	0.219119i	$-0.0703184\pi$
$684$	7.66723	+	5.77020i	0.293164	+	0.220629i
$685$	−17.3050	+	9.99103i	−0.661189	+	0.381737i
$686$			17.5170i			0.668803i
$687$	−6.54295	+	5.79234i	−0.249629	+	0.220992i
$688$	6.44566	−	3.72140i	0.245739	−	0.141877i
$689$	−8.92210	+	5.15118i	−0.339905	+	0.196244i
$690$	2.28892	−	6.84794i	0.0871377	−	0.260697i
$691$	4.67107	−	8.09053i	0.177696	−	0.307778i	−0.763395	−	0.645932i	$-0.776469\pi$
$691$	4.67107	−	8.09053i	0.177696	−	0.307778i	0.941091	+	0.338154i	$0.109802\pi$
$692$	6.38447	+	3.68607i	0.242701	+	0.140124i
$693$	−17.5703	+	7.47105i	−0.667440	+	0.283802i
$694$	8.46882	−	4.88948i	0.321472	−	0.185602i
$695$	4.23851	−	7.34131i	0.160776	−	0.278472i
$696$	2.48428	+	12.1912i	0.0941663	+	0.462106i
$697$			64.7987i			2.45442i
$698$		−	15.4112i		−	0.583321i
$699$	5.78188	+	28.3737i	0.218691	+	1.07319i
$700$	0.742621	−	1.28626i	0.0280684	−	0.0486159i
$701$	30.3210	−	17.5058i	1.14521	−	0.661186i	0.197493	−	0.980304i	$-0.436720\pi$
$701$	30.3210	−	17.5058i	1.14521	−	0.661186i	0.947715	+	0.319118i	$0.103387\pi$
$702$	0.699931	+	8.78860i	0.0264172	+	0.331704i
$703$	−26.3517	−	15.2141i	−0.993871	−	0.573812i
$704$	2.14249	−	3.71090i	0.0807482	−	0.139860i
$705$	6.54626	−	19.5849i	0.246546	−	0.737612i
$706$	−15.3186	+	8.84422i	−0.576524	+	0.332857i
$707$	10.1544	−	5.86263i	0.381894	−	0.220487i
$708$	1.76912	−	1.56617i	0.0664877	−	0.0588602i
$709$		−	22.0096i		−	0.826587i	−0.910598	−	0.413294i	$-0.864378\pi$
$709$		−	22.0096i		−	0.826587i	0.910598	−	0.413294i	$-0.135622\pi$
$710$	−0.650013	+	0.375285i	−0.0243946	+	0.0140842i
$711$	20.0935	−	26.6995i	0.753565	−	1.00131i
$712$		−	4.38445i		−	0.164314i
$713$	−10.4409	−	20.7292i	−0.391015	−	0.776315i
$714$	−14.0243	−	4.68760i	−0.524844	−	0.175429i
$715$	−7.27043			−0.271899
$716$	−8.19260	−	14.1900i	−0.306172	−	0.530305i
$717$	−5.69705	+	17.0443i	−0.212760	+	0.636531i
$718$	−1.19517	+	2.07009i	−0.0446033	+	0.0772552i
$719$	−12.7636	−	22.1072i	−0.476002	−	0.824460i	0.523620	−	0.851952i	$-0.324581\pi$
$719$	−12.7636	−	22.1072i	−0.476002	−	0.824460i	−0.999622	+	0.0274921i	$0.991248\pi$
$720$	−2.97787	−	0.363755i	−0.110978	−	0.0135564i
$721$	9.89724			0.368592
$722$	7.59393	+	4.38436i	0.282617	+	0.163169i
$723$	11.5101	−	10.1896i	0.428065	−	0.378957i
$724$	−0.304556	−	0.175835i	−0.0113187	−	0.00653487i
$725$	3.59162	+	6.22087i	0.133390	+	0.231037i
$726$	−9.54639	+	8.45123i	−0.354300	+	0.313654i
$727$	24.4903	+	42.4184i	0.908294	+	1.57321i	0.816434	+	0.577439i	$0.195948\pi$
$727$	24.4903	+	42.4184i	0.908294	+	1.57321i	0.0918596	+	0.995772i	$0.470719\pi$
$728$	−2.52004			−0.0933990
$729$	9.62887	−	25.2247i	0.356625	−	0.934248i
$730$	−3.41044	+	1.96902i	−0.126226	+	0.0728767i
$731$	−37.0500	−	21.3908i	−1.37034	−	0.791168i
$732$	4.34223	+	21.3088i	0.160494	+	0.787597i
$733$	−22.4311	+	38.8518i	−0.828511	+	1.43502i	0.0706944	+	0.997498i	$0.477479\pi$
$733$	−22.4311	+	38.8518i	−0.828511	+	1.43502i	−0.899206	+	0.437526i	$0.855855\pi$
$734$	−14.2333	+	24.6528i	−0.525361	+	0.909952i
$735$	6.21728	−	5.50403i	0.229328	−	0.203019i
$736$		−	4.16867i		−	0.153659i
$737$	25.6465	+	44.4210i	0.944700	+	1.63627i
$738$	4.10067	−	33.5699i	0.150948	−	1.23573i
$739$	11.5825	+	6.68715i	0.426068	+	0.245991i	0.697670	−	0.716419i	$-0.254220\pi$
$739$	11.5825	+	6.68715i	0.426068	+	0.245991i	−0.271602	+	0.962410i	$0.587553\pi$
$740$	9.51288			0.349701
$741$	−1.87696	−	9.21089i	−0.0689519	−	0.338371i
$742$			9.01826i			0.331071i
$743$	3.33359			0.122298			0.0611488	−	0.998129i	$-0.480524\pi$
$743$	3.33359			0.122298			0.0611488	+	0.998129i	$0.480524\pi$
$744$	−7.57318	+	5.97051i	−0.277646	+	0.218889i
$745$	1.27137			0.0465794
$746$			8.75126i			0.320406i
$747$	−3.55353	+	29.0908i	−0.130017	+	1.06438i
$748$	−24.6303			−0.900573
$749$	−23.6312	−	13.6435i	−0.863466	−	0.498522i
$750$	−1.69717	+	0.345843i	−0.0619720	+	0.0126284i
$751$	27.1330	+	46.9957i	0.990097	+	1.71490i	0.616628	+	0.787255i	$0.288498\pi$
$751$	27.1330	+	46.9957i	0.990097	+	1.71490i	0.373469	+	0.927643i	$0.378168\pi$
$752$		−	11.9223i		−	0.434761i
$753$	−14.8097	−	16.7288i	−0.539694	−	0.609631i
$754$	6.09399	−	10.5551i	0.221930	−	0.384394i
$755$	−10.4374	+	18.0782i	−0.379857	+	0.657932i
$756$	6.96884	+	3.31598i	0.253454	+	0.120601i
$757$	−21.3239	−	12.3114i	−0.775030	−	0.447464i	0.0596361	−	0.998220i	$-0.481006\pi$
$757$	−21.3239	−	12.3114i	−0.775030	−	0.447464i	−0.834666	+	0.550756i	$0.814339\pi$
$758$	−18.8030	+	10.8559i	−0.682956	+	0.394305i
$759$	−9.80799	+	29.3433i	−0.356008	+	1.06510i
$760$	3.19864			0.116027
$761$	23.0756	+	39.9681i	0.836490	+	1.44884i	0.892811	+	0.450431i	$0.148730\pi$
$761$	23.0756	+	39.9681i	0.836490	+	1.44884i	−0.0563208	+	0.998413i	$0.517937\pi$
$762$	19.6899	+	22.2415i	0.713291	+	0.805724i
$763$	0.0560654	+	0.0971081i	0.00202970	+	0.00351555i
$764$	0.457852	+	0.264341i	0.0165645	+	0.00956352i
$765$	6.74770	+	15.8691i	0.243964	+	0.573749i
$766$	9.99081	+	5.76820i	0.360983	+	0.208413i
$767$	−2.31458			−0.0835745
$768$	−1.69717	+	0.345843i	−0.0612414	+	0.0124795i
$769$	22.7611	+	39.4233i	0.820785	+	1.42164i	0.905099	+	0.425201i	$0.139797\pi$
$769$	22.7611	+	39.4233i	0.820785	+	1.42164i	−0.0843143	+	0.996439i	$0.526870\pi$
$770$	−3.18212	+	5.51159i	−0.114676	+	0.198624i
$771$	−10.6410	−	3.55676i	−0.383227	−	0.128094i
$772$	−1.78569	−	3.09290i	−0.0642683	−	0.111316i
$773$	45.5792			1.63937			0.819684	−	0.572816i	$-0.194149\pi$
$773$	45.5792			1.63937			0.819684	+	0.572816i	$0.194149\pi$
$774$	17.8406	+	13.4265i	0.641268	+	0.482605i
$775$	−3.05410	+	4.65537i	−0.109707	+	0.167226i
$776$			14.9295i			0.535936i
$777$	−23.2098	−	7.75787i	−0.832647	−	0.278312i
$778$	6.54785	−	3.78040i	0.234752	−	0.135534i
$779$			36.0587i			1.29194i
$780$	1.94800	+	2.20043i	0.0697495	+	0.0787881i
$781$	2.78530	−	1.60809i	0.0996657	−	0.0575420i
$782$	−20.7515	+	11.9809i	−0.742071	+	0.428435i
$783$	−30.7410	+	21.1699i	−1.09859	+	0.756552i
$784$	2.39703	−	4.15178i	0.0856082	−	0.148278i
$785$	11.0144	+	6.35915i	0.393120	+	0.226968i
$786$	−6.17831	−	6.97893i	−0.220373	−	0.248930i
$787$	31.4303	−	18.1463i	1.12037	−	0.646845i	0.178873	−	0.983872i	$-0.442755\pi$
$787$	31.4303	−	18.1463i	1.12037	−	0.646845i	0.941495	+	0.337027i	$0.109421\pi$
$788$	2.86622	−	4.96444i	0.102105	−	0.176851i
$789$	−13.7975	+	2.81160i	−0.491204	+	0.100096i
$790$		−	11.1386i		−	0.396293i
$791$		−	23.9335i		−	0.850977i
$792$	12.7601	+	1.55869i	0.453411	+	0.0553855i
$793$	10.6516	−	18.4491i	0.378249	−	0.655147i
$794$	24.4225	−	14.1004i	0.866723	−	0.500403i
$795$	7.87450	−	6.97114i	0.279280	−	0.247241i
$796$	20.8795	+	12.0548i	0.740053	+	0.427270i
$797$	−7.02376	+	12.1655i	−0.248794	+	0.430924i	−0.963192	−	0.268816i	$-0.913368\pi$
$797$	−7.02376	+	12.1655i	−0.248794	+	0.430924i	0.714397	+	0.699740i	$0.246701\pi$
$798$	−7.80413	−	2.60853i	−0.276263	−	0.0923408i
$799$	−59.3487	+	34.2650i	−2.09960	+	1.21221i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	12.1045	−	5.14696i	0.427693	−	0.181859i
$802$		−	30.4667i		−	1.07582i
$803$	14.6137	−	8.43722i	0.515706	−	0.297743i
$804$	6.57266	−	19.6639i	0.231800	−	0.693494i
$805$			6.19148i			0.218221i
$806$	9.43160	+	0.538283i	0.332214	+	0.0189602i
$807$	6.78497	−	20.2991i	0.238842	−	0.714563i
$808$	−7.89451			−0.277728
$809$	8.04077	+	13.9270i	0.282698	+	0.489648i	0.972048	−	0.234780i	$-0.0754371\pi$
$809$	8.04077	+	13.9270i	0.282698	+	0.489648i	−0.689350	+	0.724428i	$0.742104\pi$
$810$	−2.49150	−	8.64826i	−0.0875423	−	0.303869i
$811$	15.8659	−	27.4806i	0.557128	−	0.964974i	−0.440607	−	0.897700i	$-0.645237\pi$
$811$	15.8659	−	27.4806i	0.557128	−	0.964974i	0.997735	−	0.0672736i	$-0.0214300\pi$
$812$	−5.33443	−	9.23950i	−0.187202	−	0.324243i
$813$	8.61084	+	42.2564i	0.301995	+	1.48199i
$814$	−40.7626			−1.42873
$815$	−12.8752	−	7.43348i	−0.450998	−	0.260384i
$816$	6.59931	+	7.45448i	0.231022	+	0.260959i
$817$	−20.6173	−	11.9034i	−0.721309	−	0.416448i
$818$	11.6666	+	20.2072i	0.407913	+	0.706527i
$819$	−2.95831	−	6.95729i	−0.103372	−	0.243108i
$820$	−5.63658	−	9.76284i	−0.196838	−	0.340933i
$821$	−24.4815			−0.854410			−0.427205	−	0.904155i	$-0.640502\pi$
$821$	−24.4815			−0.854410			−0.427205	+	0.904155i	$0.640502\pi$
$822$	−32.8248	−	10.9717i	−1.14490	−	0.382681i
$823$	−24.6435	+	14.2279i	−0.859018	+	0.495954i	−0.863683	−	0.504035i	$-0.831848\pi$
$823$	−24.6435	+	14.2279i	−0.859018	+	0.495954i	0.00466530	+	0.999989i	$0.498515\pi$
$824$	−5.77095	−	3.33186i	−0.201041	−	0.116071i
$825$	7.27235	−	1.48193i	0.253191	−	0.0515943i
$826$	−1.01304	+	1.75464i	−0.0352482	+	0.0610517i
$827$	22.8529	−	39.5824i	0.794674	−	1.37642i	−0.128372	−	0.991726i	$-0.540975\pi$
$827$	22.8529	−	39.5824i	0.794674	−	1.37642i	0.923046	−	0.384690i	$-0.125692\pi$
$828$	11.5088	−	4.89365i	0.399959	−	0.170066i
$829$			13.1909i			0.458137i	0.973410	+	0.229069i	$0.0735680\pi$
$829$			13.1909i			0.458137i	−0.973410	+	0.229069i	$0.926432\pi$
$830$	4.88450	+	8.46021i	0.169544	+	0.293658i
$831$	−0.331577	−	1.62716i	−0.0115023	−	0.0564456i
$832$	1.46940	+	0.848361i	0.0509424	+	0.0294116i
$833$	−27.5565			−0.954775
$834$	14.3870	−	2.93172i	0.498180	−	0.101517i
$835$		−	12.8416i		−	0.444402i
$836$	−13.7061			−0.474036
$837$	−25.3735	−	13.8991i	−0.877037	−	0.480422i
$838$	13.0350			0.450288
$839$		−	21.1757i		−	0.731067i	−0.930798	−	0.365534i	$-0.880887\pi$
$839$		−	21.1757i		−	0.731067i	0.930798	−	0.365534i	$-0.119113\pi$
$840$	2.52071	−	0.513661i	0.0869727	−	0.0177230i
$841$	22.5990			0.779277
$842$	5.32469	+	3.07421i	0.183501	+	0.105944i
$843$	−9.13353	−	44.8214i	−0.314576	−	1.54373i
$844$	1.00482	+	1.74041i	0.0345875	+	0.0599073i
$845$			10.1211i			0.348178i
$846$	32.9149	−	13.9957i	1.13164	−	0.481183i
$847$	5.46649	−	9.46825i	0.187831	−	0.325333i
$848$	3.03596	−	5.25843i	0.104255	−	0.180575i
$849$	15.3887	−	3.13586i	0.528140	−	0.107622i
$850$	4.97796	+	2.87402i	0.170742	+	0.0985782i
$851$	−34.3432	+	19.8280i	−1.17727	+	0.679697i
$852$	−1.23297	−	0.412121i	−0.0422410	−	0.0141190i
$853$	−46.5321			−1.59323			−0.796615	−	0.604487i	$-0.793378\pi$
$853$	−46.5321			−1.59323			−0.796615	+	0.604487i	$0.793378\pi$
$854$	−9.32397	−	16.1496i	−0.319060	−	0.552627i
$855$	3.75492	+	8.83075i	0.128415	+	0.302005i
$856$	9.18604	+	15.9107i	0.313972	+	0.543816i
$857$	12.9227	+	7.46091i	0.441430	+	0.254860i	0.704204	−	0.709998i	$-0.251304\pi$
$857$	12.9227	+	7.46091i	0.441430	+	0.254860i	−0.262774	+	0.964857i	$0.584637\pi$
$858$	−8.34714	−	9.42882i	−0.284967	−	0.321894i
$859$	−6.28753	−	3.63011i	−0.214528	−	0.123858i	0.388886	−	0.921286i	$-0.372860\pi$
$859$	−6.28753	−	3.63011i	−0.214528	−	0.123858i	−0.603414	+	0.797428i	$0.706193\pi$
$860$	7.44281			0.253798
$861$	5.79058	+	28.4164i	0.197342	+	0.968427i
$862$	−12.4764	−	21.6097i	−0.424948	−	0.736031i
$863$	−5.27120	+	9.12999i	−0.179434	+	0.310789i	−0.941687	−	0.336491i	$-0.890760\pi$
$863$	−5.27120	+	9.12999i	−0.179434	+	0.310789i	0.762253	+	0.647279i	$0.224093\pi$
$864$	−2.94713	−	4.27954i	−0.100263	−	0.145593i
$865$	3.68607	+	6.38447i	0.125330	+	0.217078i
$866$	8.45564			0.287334
$867$	8.80722	−	26.3492i	0.299109	−	0.894867i
$868$	4.53608	−	6.91434i	0.153965	−	0.234688i
$869$			47.7287i			1.61908i
$870$	−3.94415	+	11.8000i	−0.133719	+	0.400059i
$871$	−17.5893	+	10.1552i	−0.595992	+	0.344096i
$872$		−	0.0754967i		−	0.00255664i
$873$	−41.2170	+	17.5259i	−1.39498	+	0.593160i
$874$	−11.5476	+	6.66704i	−0.390605	+	0.225516i
$875$	1.28626	−	0.742621i	0.0434834	−	0.0251052i
$876$	−6.46908	−	2.16229i	−0.218570	−	0.0730569i
$877$	−1.46162	+	2.53160i	−0.0493553	+	0.0854859i	−0.889648	−	0.456648i	$-0.849050\pi$
$877$	−1.46162	+	2.53160i	−0.0493553	+	0.0854859i	0.840292	+	0.542134i	$0.182383\pi$
$878$	−8.92856	−	5.15491i	−0.301324	−	0.173970i
$879$	−14.6982	+	13.0120i	−0.495757	+	0.438884i
$880$	3.71090	−	2.14249i	0.125095	−	0.0722234i
$881$	−5.81077	+	10.0646i	−0.195770	+	0.339084i	−0.947153	−	0.320783i	$-0.896054\pi$
$881$	−5.81077	+	10.0646i	−0.195770	+	0.339084i	0.751383	+	0.659867i	$0.229387\pi$
$882$	14.2761	+	1.74387i	0.480700	+	0.0587190i
$883$			37.0914i			1.24823i	0.781334	+	0.624113i	$0.214539\pi$
$883$			37.0914i			1.24823i	−0.781334	+	0.624113i	$0.785461\pi$
$884$		−	9.75284i		−	0.328024i
$885$	2.31519	−	0.471780i	0.0778242	−	0.0158587i
$886$	−4.28592	+	7.42343i	−0.143988	+	0.249395i
$887$	2.95327	−	1.70507i	0.0991612	−	0.0572507i	−0.449599	−	0.893230i	$-0.648433\pi$
$887$	2.95327	−	1.70507i	0.0991612	−	0.0572507i	0.548761	+	0.835980i	$0.315100\pi$
$888$	10.9217	+	12.3370i	0.366508	+	0.414002i
$889$	−22.0594	−	12.7360i	−0.739849	−	0.427152i
$890$	2.19223	−	3.79705i	0.0734836	−	0.127277i
$891$	10.6760	+	37.0577i	0.357661	+	1.24148i
$892$	19.3273	−	11.1586i	0.647126	−	0.373618i
$893$	−33.0260	+	19.0676i	−1.10517	+	0.638071i
$894$	1.45965	+	1.64880i	0.0488181	+	0.0551442i
$895$		−	16.3852i		−	0.547697i
$896$	1.28626	−	0.742621i	0.0429708	−	0.0248092i
$897$	−11.6191	−	3.88366i	−0.387949	−	0.129672i
$898$			40.5736i			1.35396i
$899$	17.9913	+	35.7195i	0.600042	+	1.19131i
$900$	−2.39703	−	1.80395i	−0.0799010	−	0.0601318i
$901$	−34.9017			−1.16274
$902$	24.1527	+	41.8336i	0.804195	+	1.39291i
$903$	−18.1592	−	6.06970i	−0.604300	−	0.201987i
$904$	−8.05711	+	13.9553i	−0.267975	+	0.464147i
$905$	−0.175835	−	0.304556i	−0.00584496	−	0.0101238i
$906$	−35.4283	+	7.21944i	−1.17703	+	0.239850i
$907$	−31.9698			−1.06154			−0.530770	−	0.847516i	$-0.678097\pi$
$907$	−31.9698			−1.06154			−0.530770	+	0.847516i	$0.678097\pi$
$908$	7.92824	+	4.57737i	0.263108	+	0.151905i
$909$	−9.26746	−	21.7950i	−0.307382	−	0.722896i
$910$	−2.18242	−	1.26002i	−0.0723465	−	0.0417693i
$911$	−17.9150	−	31.0297i	−0.593550	−	1.02806i	−0.993750	−	0.111631i	$-0.964393\pi$
$911$	−17.9150	−	31.0297i	−0.593550	−	1.02806i	0.400200	−	0.916428i	$-0.368941\pi$
$912$	3.67234	+	4.14822i	0.121603	+	0.137361i
$913$	−20.9300	−	36.2518i	−0.692682	−	1.19976i
$914$	−33.0592			−1.09350
$915$	−6.89393	+	20.6251i	−0.227906	+	0.681845i
$916$	−4.36925	+	2.52259i	−0.144364	+	0.0833486i
$917$	6.92180	+	3.99631i	0.228578	+	0.131970i
$918$	−12.8332	+	26.9702i	−0.423560	+	0.890148i
$919$	17.9710	−	31.1268i	0.592810	−	1.02678i	−0.401042	−	0.916060i	$-0.631352\pi$
$919$	17.9710	−	31.1268i	0.592810	−	1.02678i	0.993852	−	0.110717i	$-0.0353148\pi$
$920$	2.08434	−	3.61018i	0.0687185	−	0.119024i
$921$	−16.8296	−	19.0105i	−0.554555	−	0.626418i
$922$			2.92110i			0.0962013i
$923$	0.636755	+	1.10289i	0.0209590	+	0.0363021i
$924$	−10.8012	+	2.20103i	−0.355333	+	0.0724085i
$925$	8.23840	+	4.75644i	0.270877	+	0.156391i
$926$	−23.0953			−0.758959
$927$	2.42397	−	19.8437i	0.0796135	−	0.651752i
$928$			7.18325i			0.235802i
$929$	6.12371			0.200912			0.100456	−	0.994941i	$-0.467970\pi$
$929$	6.12371			0.200912			0.100456	+	0.994941i	$0.467970\pi$
$930$	−9.54382	+	1.38402i	−0.312954	+	0.0453838i
$931$	−15.3345			−0.502566
$932$			16.7182i			0.547623i
$933$	−1.75336	−	8.60434i	−0.0574024	−	0.281693i
$934$	21.7637			0.712132
$935$	−21.3305	−	12.3151i	−0.697581	−	0.402748i
$936$	−0.617192	+	5.05261i	−0.0201736	+	0.165150i
$937$	−10.4465	−	18.0939i	−0.341273	−	0.591103i	0.643396	−	0.765533i	$-0.277525\pi$
$937$	−10.4465	−	18.0939i	−0.341273	−	0.591103i	−0.984669	+	0.174431i	$0.944192\pi$
$938$			17.7789i			0.580502i
$939$	−13.3240	+	11.7954i	−0.434811	+	0.384929i
$940$	5.96115	−	10.3250i	0.194431	−	0.336765i
$941$	−9.99684	+	17.3150i	−0.325888	+	0.564454i	−0.981692	−	0.190477i	$-0.938997\pi$
$941$	−9.99684	+	17.3150i	−0.325888	+	0.564454i	0.655804	+	0.754931i	$0.272330\pi$
$942$	4.39854	+	21.5851i	0.143312	+	0.703282i
$943$	40.6981	+	23.4971i	1.32531	+	0.765169i
$944$	1.18138	−	0.682072i	0.0384508	−	0.0221996i
$945$	4.37720	+	6.35614i	0.142390	+	0.206765i
$946$	−31.8923			−1.03691
$947$	17.0336	+	29.5031i	0.553519	+	0.958722i	0.998017	+	0.0629427i	$0.0200485\pi$
$947$	17.0336	+	29.5031i	0.553519	+	0.958722i	−0.444499	+	0.895780i	$0.646618\pi$
$948$	14.4453	−	12.7882i	0.469162	−	0.415340i
$949$	3.34088	+	5.78658i	0.108450	+	0.187840i
$950$	2.77010	+	1.59932i	0.0898740	+	0.0518888i
$951$	16.4137	−	14.5307i	0.532252	−	0.471192i
$952$	−7.39346	−	4.26862i	−0.239624	−	0.138347i
$953$	−10.7328			−0.347669			−0.173835	−	0.984775i	$-0.555616\pi$
$953$	−10.7328			−0.347669			−0.173835	+	0.984775i	$0.555616\pi$
$954$	18.0814	+	2.20869i	0.585405	+	0.0715091i
$955$	0.264341	+	0.457852i	0.00855387	+	0.0148157i
$956$	−5.18784	+	8.98561i	−0.167787	+	0.290615i
$957$	16.9006	−	50.5629i	0.546320	−	1.63447i
$958$	−1.11069	−	1.92376i	−0.0358846	−	0.0621540i
$959$	29.6782			0.958358
$960$	−1.64272	−	0.549077i	−0.0530184	−	0.0177214i
$961$	−18.4538	+	24.9090i	−0.595285	+	0.803515i
$962$		−	16.1407i		−	0.520398i
$963$	−33.1424	+	44.0384i	−1.06800	+	1.41912i
$964$	7.68620	−	4.43763i	0.247556	−	0.142926i
$965$		−	3.57138i		−	0.114967i
$966$	−8.02956	+	7.10841i	−0.258347	+	0.228709i
$967$	−26.4826	+	15.2897i	−0.851622	+	0.491684i	−0.861198	−	0.508270i	$-0.830285\pi$
$967$	−26.4826	+	15.2897i	−0.851622	+	0.491684i	0.00957593	+	0.999954i	$0.496952\pi$
$968$	−6.37489	+	3.68054i	−0.204897	+	0.118297i
$969$	10.0953	−	30.2028i	0.324307	−	0.970255i
$970$	−7.46473	+	12.9293i	−0.239678	+	0.415134i
$971$	13.8767	+	8.01173i	0.445325	+	0.257109i	0.705854	−	0.708357i	$-0.250563\pi$
$971$	13.8767	+	8.01173i	0.445325	+	0.257109i	−0.260528	+	0.965466i	$0.583897\pi$
$972$	8.35521	−	13.1602i	0.267994	−	0.422113i
$973$	−10.9036	+	6.29521i	−0.349554	+	0.201815i
$974$	11.8930	−	20.5993i	0.381077	−	0.660046i
$975$	0.586800	+	2.87963i	0.0187926	+	0.0922220i
$976$			12.5555i			0.401891i
$977$			20.5064i			0.656059i	0.944667	+	0.328030i	$0.106385\pi$
$977$			20.5064i			0.656059i	−0.944667	+	0.328030i	$0.893615\pi$
$978$	−5.14164	−	25.2318i	−0.164412	−	0.806824i
$979$	−9.39365	+	16.2703i	−0.300222	+	0.520001i
$980$	4.15178	−	2.39703i	0.132624	−	0.0765703i
$981$	0.208430	−	0.0886264i	0.00665466	−	0.00282962i
$982$	−6.02558	−	3.47887i	−0.192284	−	0.111015i
$983$	−3.75211	+	6.49885i	−0.119674	+	0.207281i	−0.919638	−	0.392766i	$-0.871518\pi$
$983$	−3.75211	+	6.49885i	−0.119674	+	0.207281i	0.799965	+	0.600047i	$0.204852\pi$
$984$	6.18983	−	18.5186i	0.197325	−	0.590351i
$985$	4.96444	−	2.86622i	0.158180	−	0.0913254i
$986$	35.7579	−	20.6448i	1.13876	−	0.657465i
$987$	−22.9644	+	20.3299i	−0.730963	+	0.647107i
$988$		−	5.42720i		−	0.172662i
$989$	−26.8698	+	15.5133i	−0.854411	+	0.493295i
$990$	10.2712	+	7.72991i	0.326441	+	0.245673i
$991$		−	41.9790i		−	1.33351i	−0.745278	−	0.666753i	$-0.767683\pi$
$991$		−	41.9790i		−	1.33351i	0.745278	−	0.666753i	$-0.232317\pi$
$992$	−4.97262	+	2.50461i	−0.157881	+	0.0795216i
$993$	51.3793	+	17.1735i	1.63047	+	0.544984i
$994$	1.11478			0.0353586
$995$	12.0548	+	20.8795i	0.382162	+	0.661923i
$996$	−5.36393	+	16.0477i	−0.169963	+	0.508491i
$997$	14.8480	−	25.7174i	0.470240	−	0.814479i	−0.529181	−	0.848509i	$-0.677501\pi$
$997$	14.8480	−	25.7174i	0.470240	−	0.814479i	0.999421	+	0.0340296i	$0.0108341\pi$
$998$	−8.68160	−	15.0370i	−0.274811	−	0.475987i
$999$	−21.2387	+	44.6350i	−0.671962	+	1.41219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.e.161.12	yes	40
3.2	odd	2	inner	930.2.o.e.161.2	✓	40
31.26	odd	6	inner	930.2.o.e.491.12	yes	40
93.26	even	6	inner	930.2.o.e.491.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.e.161.2	✓	40	3.2	odd	2	inner
930.2.o.e.161.12	yes	40	1.1	even	1	trivial
930.2.o.e.491.2	yes	40	93.26	even	6	inner
930.2.o.e.491.12	yes	40	31.26	odd	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.69717 + 0.345843i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.345843 - 1.69717i) q^{6} +(0.742621 + 1.28626i) q^{7} -1.00000i q^{8} +(2.76078 - 1.17391i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.69717 + 0.345843i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.345843 - 1.69717i) q^{6} +(0.742621 + 1.28626i) q^{7} -1.00000i q^{8} +(2.76078 - 1.17391i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.14249 + 3.71090i) q^{11} +(1.69717 - 0.345843i) q^{12} +(-1.46940 - 0.848361i) q^{13} +(-1.28626 + 0.742621i) q^{14} +(1.64272 + 0.549077i) q^{15} +1.00000 q^{16} +(-2.87402 - 4.97796i) q^{17} +(1.17391 + 2.76078i) q^{18} +(-1.59932 - 2.77010i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-1.70520 - 1.92617i) q^{21} +(-3.71090 - 2.14249i) q^{22} -4.16867 q^{23} +(0.345843 + 1.69717i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.848361 - 1.46940i) q^{26} +(-4.27954 + 2.94713i) q^{27} +(-0.742621 - 1.28626i) q^{28} +7.18325 q^{29} +(-0.549077 + 1.64272i) q^{30} +(2.50461 + 4.97262i) q^{31} +1.00000i q^{32} +(2.35279 - 7.03901i) q^{33} +(4.97796 - 2.87402i) q^{34} -1.48524i q^{35} +(-2.76078 + 1.17391i) q^{36} +(8.23840 - 4.75644i) q^{37} +(2.77010 - 1.59932i) q^{38} +(2.78723 + 0.931631i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-9.76284 - 5.63658i) q^{41} +(1.92617 - 1.70520i) q^{42} +(6.44566 - 3.72140i) q^{43} +(2.14249 - 3.71090i) q^{44} +(-2.97787 - 0.363755i) q^{45} -4.16867i q^{46} -11.9223i q^{47} +(-1.69717 + 0.345843i) q^{48} +(2.39703 - 4.15178i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(6.59931 + 7.45448i) q^{51} +(1.46940 + 0.848361i) q^{52} +(3.03596 - 5.25843i) q^{53} +(-2.94713 - 4.27954i) q^{54} +(3.71090 - 2.14249i) q^{55} +(1.28626 - 0.742621i) q^{56} +(3.67234 + 4.14822i) q^{57} +7.18325i q^{58} +(1.18138 - 0.682072i) q^{59} +(-1.64272 - 0.549077i) q^{60} +12.5555i q^{61} +(-4.97262 + 2.50461i) q^{62} +(3.56017 + 2.67931i) q^{63} -1.00000 q^{64} +(0.848361 + 1.46940i) q^{65} +(7.03901 + 2.35279i) q^{66} +(5.98520 - 10.3667i) q^{67} +(2.87402 + 4.97796i) q^{68} +(7.07495 - 1.44171i) q^{69} +1.48524 q^{70} +(-0.650013 - 0.375285i) q^{71} +(-1.17391 - 2.76078i) q^{72} +(-3.41044 - 1.96902i) q^{73} +(4.75644 + 8.23840i) q^{74} +(-1.14810 - 1.29687i) q^{75} +(1.59932 + 2.77010i) q^{76} -6.36423 q^{77} +(-0.931631 + 2.78723i) q^{78} +(9.64630 - 5.56929i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(6.24387 - 6.48183i) q^{81} +(5.63658 - 9.76284i) q^{82} +(-4.88450 + 8.46021i) q^{83} +(1.70520 + 1.92617i) q^{84} +5.74805i q^{85} +(3.72140 + 6.44566i) q^{86} +(-12.1912 + 2.48428i) q^{87} +(3.71090 + 2.14249i) q^{88} +4.38445 q^{89} +(0.363755 - 2.97787i) q^{90} -2.52004i q^{91} +4.16867 q^{92} +(-5.97051 - 7.57318i) q^{93} +11.9223 q^{94} +3.19864i q^{95} +(-0.345843 - 1.69717i) q^{96} -14.9295 q^{97} +(4.15178 + 2.39703i) q^{98} +(-1.55869 + 12.7601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

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