LMFDB - Embedded newform 930.2.o.e.161.2

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			161.2
Character	$\chi$	$=$	930.161
Dual form			930.2.o.e.491.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.14810 + 1.29687i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.29687 + 1.14810i) q^{6} +(0.742621 + 1.28626i) q^{7} +1.00000i q^{8} +(-0.363755 - 2.97787i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.14810 + 1.29687i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.29687 + 1.14810i) q^{6} +(0.742621 + 1.28626i) q^{7} +1.00000i q^{8} +(-0.363755 - 2.97787i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.14249 - 3.71090i) q^{11} +(1.14810 - 1.29687i) 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} +(-2.97787 + 0.363755i) q^{18} +(-1.59932 - 2.77010i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-2.52071 - 0.513661i) q^{21} +(-3.71090 - 2.14249i) q^{22} +4.16867 q^{23} +(-1.29687 - 1.14810i) 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} +(0.363755 + 2.97787i) 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} +(-0.513661 + 2.52071i) q^{42} +(6.44566 - 3.72140i) q^{43} +(-2.14249 + 3.71090i) q^{44} +(1.17391 - 2.76078i) q^{45} -4.16867i q^{46} +11.9223i q^{47} +(-1.14810 + 1.29687i) q^{48} +(2.39703 - 4.15178i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-9.75543 - 1.98792i) 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} +(5.42864 + 1.10623i) 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} +(-4.78603 + 5.40624i) q^{69} +1.48524 q^{70} +(0.650013 + 0.375285i) q^{71} +(2.97787 - 0.363755i) q^{72} +(-3.41044 - 1.96902i) q^{73} +(-4.75644 - 8.23840i) q^{74} +(-1.69717 - 0.345843i) 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} +(-8.73536 + 2.16643i) q^{81} +(5.63658 - 9.76284i) q^{82} +(4.88450 - 8.46021i) q^{83} +(2.52071 + 0.513661i) q^{84} +5.74805i q^{85} +(-3.72140 - 6.44566i) q^{86} +(8.24705 - 9.31575i) q^{87} +(3.71090 + 2.14249i) q^{88} -4.38445 q^{89} +(-2.76078 - 1.17391i) q^{90} -2.52004i q^{91} -4.16867 q^{92} +(-9.32438 - 2.46087i) q^{93} +11.9223 q^{94} -3.19864i q^{95} +(1.29687 + 1.14810i) q^{96} -14.9295 q^{97} +(-4.15178 - 2.39703i) q^{98} +(-11.8299 - 5.03019i) 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
$3$	−1.14810	+	1.29687i	−0.662853	+	0.748750i
$3$	−1.14810	+	1.29687i	−0.662853	+	0.748750i
$4$	−1.00000			−0.500000
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	1.29687	+	1.14810i	0.529446	+	0.468708i
$7$	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
$9$	−0.363755	−	2.97787i	−0.121252	−	0.992622i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	2.14249	−	3.71090i	0.645986	−	1.11888i	−0.338087	−	0.941115i	$-0.609780\pi$
$11$	2.14249	−	3.71090i	0.645986	−	1.11888i	0.984073	−	0.177765i	$-0.0568867\pi$
$12$	1.14810	−	1.29687i	0.331426	−	0.374375i
$13$	−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	$0.0788392\pi$
$17$	2.87402	+	4.97796i	0.697053	+	1.20733i	−0.272430	+	0.962175i	$0.587827\pi$
$18$	−2.97787	+	0.363755i	−0.701890	+	0.0857380i
$19$	−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
$21$	−2.52071	−	0.513661i	−0.550064	−	0.112090i
$22$	−3.71090	−	2.14249i	−0.791168	−	0.456781i
$23$	4.16867			0.869228			0.434614	−	0.900617i	$-0.356885\pi$
$23$	4.16867			0.869228			0.434614	+	0.900617i	$0.356885\pi$
$24$	−1.29687	−	1.14810i	−0.264723	−	0.234354i
$25$	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	$-0.732400\pi$
$29$	−7.18325			−1.33390			−0.666948	+	0.745104i	$0.732400\pi$
$30$	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
$36$	0.363755	+	2.97787i	0.0606259	+	0.496311i
$37$	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	$0.00931590\pi$
$41$	9.76284	+	5.63658i	1.52470	+	0.880286i	0.525128	+	0.851023i	$0.324017\pi$
$42$	−0.513661	+	2.52071i	−0.0792596	+	0.388954i
$43$	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
$45$	1.17391	−	2.76078i	0.174996	−	0.411553i
$46$		−	4.16867i		−	0.614637i
$47$			11.9223i			1.73905i	0.493893	+	0.869523i	$0.335574\pi$
$47$			11.9223i			1.73905i	−0.493893	+	0.869523i	$0.664426\pi$
$48$	−1.14810	+	1.29687i	−0.165713	+	0.187187i
$49$	2.39703	−	4.15178i	0.342433	−	0.593111i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−9.75543	−	1.98792i	−1.36603	−	0.278365i
$52$	1.46940	+	0.848361i	0.203770	+	0.117647i
$53$	−3.03596	+	5.25843i	−0.417021	+	0.722302i	−0.995638	−	0.0932976i	$-0.970259\pi$
$53$	−3.03596	+	5.25843i	−0.417021	+	0.722302i	0.578617	+	0.815599i	$0.303593\pi$
$54$	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
$57$	5.42864	+	1.10623i	0.719041	+	0.146523i
$58$			7.18325i			0.943207i
$59$	−1.18138	+	0.682072i	−0.153803	+	0.0887983i	−0.574926	−	0.818205i	$-0.694969\pi$
$59$	−1.18138	+	0.682072i	−0.153803	+	0.0887983i	0.421123	+	0.907003i	$0.361636\pi$
$60$	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
$69$	−4.78603	+	5.40624i	−0.576171	+	0.650834i
$70$	1.48524			0.177520
$71$	0.650013	+	0.375285i	0.0771424	+	0.0445382i	0.538075	−	0.842897i	$-0.319152\pi$
$71$	0.650013	+	0.375285i	0.0771424	+	0.0445382i	−0.460933	+	0.887435i	$0.652485\pi$
$72$	2.97787	−	0.363755i	0.350945	−	0.0428690i
$73$	−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
$75$	−1.69717	−	0.345843i	−0.195973	−	0.0399345i
$76$	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
$81$	−8.73536	+	2.16643i	−0.970596	+	0.240714i
$82$	5.63658	−	9.76284i	0.622456	−	1.07813i
$83$	4.88450	−	8.46021i	0.536144	−	0.928628i	−0.462963	−	0.886377i	$-0.653214\pi$
$83$	4.88450	−	8.46021i	0.536144	−	0.928628i	0.999107	−	0.0422508i	$-0.0134528\pi$
$84$	2.52071	+	0.513661i	0.275032	+	0.0560450i
$85$			5.74805i			0.623463i
$86$	−3.72140	−	6.44566i	−0.401289	−	0.695053i
$87$	8.24705	−	9.31575i	0.884177	−	0.998754i
$88$	3.71090	+	2.14249i	0.395584	+	0.228390i
$89$	−4.38445			−0.464751			−0.232376	−	0.972626i	$-0.574650\pi$
$89$	−4.38445			−0.464751			−0.232376	+	0.972626i	$0.574650\pi$
$90$	−2.76078	−	1.17391i	−0.291012	−	0.123741i
$91$		−	2.52004i		−	0.264172i
$92$	−4.16867			−0.434614
$93$	−9.32438	−	2.46087i	−0.966893	−	0.255181i
$94$	11.9223			1.22969
$95$		−	3.19864i		−	0.328173i
$96$	1.29687	+	1.14810i	0.132361	+	0.117177i
$97$	−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
$99$	−11.8299	−	5.03019i	−1.18895	−	0.505553i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$			7.89451i			0.785533i	0.919638	+	0.392767i	$0.128482\pi$
$101$			7.89451i			0.785533i	−0.919638	+	0.392767i	$0.871518\pi$
$102$	−1.98792	+	9.75543i	−0.196834	+	0.965931i
$103$	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
$105$	−1.92617	−	1.70520i	−0.187975	−	0.166410i
$106$	5.25843	+	3.03596i	0.510744	+	0.294878i
$107$	15.9107	−	9.18604i	1.53814	−	0.888048i	0.539197	−	0.842180i	$-0.318728\pi$
$107$	15.9107	−	9.18604i	1.53814	−	0.888048i	0.998948	−	0.0458681i	$-0.0146054\pi$
$108$	−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
$111$	−3.28997	+	16.1450i	−0.312270	+	1.53242i
$112$	0.742621	+	1.28626i	0.0701711	+	0.121540i
$113$	13.9553	+	8.05711i	1.31281	+	0.757949i	0.982560	−	0.185946i	$-0.0595349\pi$
$113$	13.9553	+	8.05711i	1.31281	+	0.757949i	0.330246	+	0.943895i	$0.392868\pi$
$114$	1.10623	−	5.42864i	0.103608	−	0.508438i
$115$	3.61018	+	2.08434i	0.336651	+	0.194365i
$116$	7.18325			0.666948
$117$	−1.99180	+	4.68429i	−0.184142	+	0.433062i
$118$	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
$129$	−2.57405	+	12.6317i	−0.226632	+	1.11216i
$130$	−1.46940	+	0.848361i	−0.128875	+	0.0744062i
$131$	−4.66039	+	2.69068i	−0.407180	+	0.235086i	−0.689577	−	0.724212i	$-0.742204\pi$
$131$	−4.66039	+	2.69068i	−0.407180	+	0.235086i	0.282397	+	0.959298i	$0.408870\pi$
$132$	−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
$135$	2.23262	+	4.69206i	0.192154	+	0.403828i
$136$	−4.97796	+	2.87402i	−0.426856	+	0.246446i
$137$	−9.99103	+	17.3050i	−0.853591	+	1.47846i	0.0243552	+	0.999703i	$0.492247\pi$
$137$	−9.99103	+	17.3050i	−0.853591	+	1.47846i	−0.877946	+	0.478759i	$0.841087\pi$
$138$	5.40624	+	4.78603i	0.460209	+	0.407414i
$139$			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
$141$	−15.4617	−	13.6879i	−1.30211	−	1.15273i
$142$	0.375285	−	0.650013i	0.0314932	−	0.0545479i
$143$	−6.29638	+	3.63521i	−0.526529	+	0.303992i
$144$	−0.363755	−	2.97787i	−0.0303130	−	0.248155i
$145$	−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	−0.454221	−	0.890889i	$-0.650082\pi$
$149$	1.10104	−	0.635685i	0.0902006	−	0.0520773i	0.544422	+	0.838812i	$0.316749\pi$
$150$	−0.345843	+	1.69717i	−0.0282380	+	0.138574i
$151$		−	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
$162$	2.16643	+	8.73536i	0.170211	+	0.686315i
$163$	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
$165$	−1.48193	+	7.27235i	−0.115368	+	0.566152i
$166$	−8.46021	−	4.88450i	−0.656639	−	0.379111i
$167$	−6.42081	−	11.1212i	−0.496857	−	0.860581i	0.503137	−	0.864207i	$-0.332179\pi$
$167$	−6.42081	−	11.1212i	−0.496857	−	0.860581i	−0.999993	+	0.00362562i	$0.998846\pi$
$168$	0.513661	−	2.52071i	0.0396298	−	0.194477i
$169$	−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	0.722665	−	0.691198i	$-0.242917\pi$
$173$	6.38447	+	3.68607i	0.485402	+	0.280247i	−0.237263	+	0.971445i	$0.576250\pi$
$174$	−9.31575	−	8.24705i	−0.706225	−	0.625207i
$175$	−0.742621	+	1.28626i	−0.0561368	+	0.0972319i
$176$	2.14249	−	3.71090i	0.161496	−	0.279720i
$177$	0.471780	−	2.31519i	0.0354612	−	0.174020i
$178$			4.38445i			0.328629i
$179$	−8.19260	−	14.1900i	−0.612344	−	1.06061i	−0.990844	−	0.135009i	$-0.956894\pi$
$179$	−8.19260	−	14.1900i	−0.612344	−	1.06061i	0.378501	−	0.925601i	$-0.376440\pi$
$180$	−1.17391	+	2.76078i	−0.0874982	+	0.205777i
$181$	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
$183$	−16.2829	−	14.4149i	−1.20366	−	1.06558i
$184$			4.16867i			0.307319i
$185$	9.51288			0.699401
$186$	−2.46087	+	9.32438i	−0.180440	+	0.683697i
$187$	24.6303			1.80115
$188$		−	11.9223i		−	0.869523i
$189$	−0.612691	+	7.69318i	−0.0445667	+	0.559597i
$190$	−3.19864			−0.232054
$191$	0.457852	+	0.264341i	0.0331290	+	0.0191270i	0.516473	−	0.856303i	$-0.327245\pi$
$191$	0.457852	+	0.264341i	0.0331290	+	0.0191270i	−0.483344	+	0.875430i	$0.660578\pi$
$192$	1.14810	−	1.29687i	0.0828566	−	0.0935937i
$193$	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
$195$	2.87963	+	0.586800i	0.206215	+	0.0420216i
$196$	−2.39703	+	4.15178i	−0.171216	+	0.296555i
$197$	2.86622	−	4.96444i	0.204210	−	0.353702i	−0.745671	−	0.666314i	$-0.767871\pi$
$197$	2.86622	−	4.96444i	0.204210	−	0.353702i	0.949881	+	0.312613i	$0.101204\pi$
$198$	−5.03019	+	11.8299i	−0.357480	+	0.840716i
$199$	−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
$204$	9.75543	+	1.98792i	0.683016	+	0.139183i
$205$	5.63658	+	9.76284i	0.393676	+	0.681866i
$206$	−5.77095	−	3.33186i	−0.402081	−	0.232142i
$207$	−1.51638	−	12.4137i	−0.105396	−	0.862815i
$208$	−1.46940	−	0.848361i	−0.101885	−	0.0588233i
$209$	−13.7061			−0.948071
$210$	−1.70520	+	1.92617i	−0.117670	+	0.132918i
$211$	−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
$222$	16.1450	+	3.28997i	1.08358	+	0.220808i
$223$	−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	0.739474	−	0.673185i	$-0.235074\pi$
$227$	7.92824	+	4.57737i	0.526216	+	0.303811i	−0.213258	+	0.976996i	$0.568408\pi$
$228$	−5.42864	−	1.10623i	−0.359520	−	0.0732617i
$229$	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
$231$	−7.30675	+	8.25360i	−0.480749	+	0.543047i
$232$		−	7.18325i		−	0.471603i
$233$			16.7182i			1.09525i	0.836725	+	0.547623i	$0.184467\pi$
$233$			16.7182i			1.09525i	−0.836725	+	0.547623i	$0.815533\pi$
$234$	4.68429	+	1.99180i	0.306221	+	0.130208i
$235$	−5.96115	+	10.3250i	−0.388862	+	0.673530i
$236$	1.18138	−	0.682072i	0.0769016	−	0.0443991i
$237$	−3.85221	+	18.9041i	−0.250228	+	1.22795i
$238$	7.39346	+	4.26862i	0.479247	+	0.276693i
$239$	−5.18784	+	8.98561i	−0.335574	+	0.581231i	−0.983595	−	0.180392i	$-0.942264\pi$
$239$	−5.18784	+	8.98561i	−0.335574	+	0.581231i	0.648021	+	0.761622i	$0.275597\pi$
$240$	−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
$243$	7.21945	−	13.8159i	0.463128	−	0.886292i
$244$		−	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	0.587464	−	0.809250i	$-0.300126\pi$
$251$	−6.44966	−	11.1711i	−0.407099	−	0.705116i	−0.994563	+	0.104134i	$0.966793\pi$
$252$	−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
$255$	−7.45448	−	6.59931i	−0.466818	−	0.413265i
$256$	1.00000			0.0625000
$257$	−5.60986	−	3.23885i	−0.349933	−	0.202034i	0.314722	−	0.949184i	$-0.398089\pi$
$257$	−5.60986	−	3.23885i	−0.349933	−	0.202034i	−0.664656	+	0.747150i	$0.731422\pi$
$258$	12.6317	+	2.57405i	0.786417	+	0.160253i
$259$	12.2360	+	7.06446i	0.760309	+	0.438964i
$260$	0.848361	+	1.46940i	0.0526131	+	0.0911286i
$261$	2.61295	+	21.3907i	0.161737	+	1.32405i
$262$	2.69068	+	4.66039i	0.166231	+	0.287920i
$263$	−8.12970			−0.501299			−0.250649	−	0.968078i	$-0.580644\pi$
$263$	−8.12970			−0.501299			−0.250649	+	0.968078i	$0.580644\pi$
$264$	−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
$267$	5.03377	−	5.68607i	0.308062	−	0.347982i
$268$	−5.98520	+	10.3667i	−0.365604	+	0.633245i
$269$	6.17853	−	10.7015i	0.376711	−	0.652483i	−0.613870	−	0.789407i	$-0.710388\pi$
$269$	6.17853	−	10.7015i	0.376711	−	0.652483i	0.990582	+	0.136924i	$0.0437215\pi$
$270$	4.69206	−	2.23262i	0.285549	−	0.135873i
$271$		−	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
$273$	3.26817	+	2.89325i	0.197799	+	0.175107i
$274$	17.3050	+	9.99103i	1.04543	+	0.603580i
$275$	4.28498			0.258394
$276$	4.78603	−	5.40624i	0.288085	−	0.325417i
$277$			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
$279$	13.8967	−	9.26722i	0.831974	−	0.554814i
$280$	−1.48524			−0.0887601
$281$		−	26.4095i		−	1.57546i	−0.616023	−	0.787728i	$-0.711257\pi$
$281$		−	26.4095i		−	1.57546i	0.616023	−	0.787728i	$-0.288743\pi$
$282$	−13.6879	+	15.4617i	−0.815104	+	0.920731i
$283$	−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
$285$	4.14822	+	3.67234i	0.245720	+	0.217531i
$286$	3.63521	+	6.29638i	0.214955	+	0.372312i
$287$			16.7434i			0.988329i
$288$	−2.97787	+	0.363755i	−0.175472	+	0.0214345i
$289$	−8.02003	+	13.8911i	−0.471766	+	0.817123i
$290$	−3.59162	+	6.22087i	−0.210907	+	0.365302i
$291$	17.1404	−	19.3616i	1.00479	−	1.13500i
$292$	3.41044	+	1.96902i	0.199581	+	0.115228i
$293$	−9.81515	+	5.66678i	−0.573407	+	0.331057i	−0.758509	−	0.651663i	$-0.774072\pi$
$293$	−9.81515	+	5.66678i	−0.573407	+	0.331057i	0.185102	+	0.982719i	$0.440738\pi$
$294$	7.87527	−	2.63231i	0.459295	−	0.153519i
$295$	−1.36414			−0.0794236
$296$	4.75644	+	8.23840i	0.276463	+	0.478847i
$297$	20.1054	−	9.56676i	1.16663	−	0.555119i
$298$	−0.635685	−	1.10104i	−0.0368242	−	0.0637814i
$299$	−6.12547	−	3.53654i	−0.354245	−	0.204523i
$300$	1.69717	+	0.345843i	0.0979863	+	0.0199673i
$301$	9.57336	+	5.52718i	0.551799	+	0.318582i
$302$	−20.8749			−1.20121
$303$	−10.2382	−	9.06365i	−0.588168	−	0.520693i
$304$	−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	$-0.954087\pi$
$311$		−	5.06981i		−	0.287482i	0.989615	−	0.143741i	$-0.0459133\pi$
$312$	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
$315$	4.42285	−	0.540265i	0.249199	−	0.0304405i
$316$	−9.64630	+	5.56929i	−0.542647	+	0.313297i
$317$	10.9608	−	6.32820i	0.615618	−	0.355427i	−0.159543	−	0.987191i	$-0.551002\pi$
$317$	10.9608	−	6.32820i	0.615618	−	0.355427i	0.775161	+	0.631764i	$0.217669\pi$
$318$	−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
$321$	−6.35386	+	31.1806i	−0.354638	+	1.74033i
$322$	5.36198	−	3.09574i	0.298812	−	0.172519i
$323$	9.19296	−	15.9227i	0.511510	−	0.885961i
$324$	8.73536	−	2.16643i	0.485298	−	0.120357i
$325$		−	1.69672i		−	0.0941172i
$326$		−	14.8670i		−	0.823405i
$327$	−0.0866774	+	0.0979095i	−0.00479327	+	0.00541441i
$328$	−5.63658	+	9.76284i	−0.311228	+	0.539063i
$329$	−15.3351	+	8.85374i	−0.845453	+	0.488123i
$330$	7.27235	+	1.48193i	0.400330	+	0.0815777i
$331$	−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
$336$	−2.52071	−	0.513661i	−0.137516	−	0.0280225i
$337$		−	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	0.966901	−	0.255154i	$-0.0821260\pi$
$347$	4.88948	+	8.46882i	0.262481	+	0.454630i	−0.704420	+	0.709784i	$0.748793\pi$
$348$	−8.24705	+	9.31575i	−0.442088	+	0.499377i
$349$	−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
$351$	−3.78814	−	7.96112i	−0.202196	−	0.424933i
$352$	−3.71090	−	2.14249i	−0.197792	−	0.114195i
$353$	−8.84422	−	15.3186i	−0.470730	−	0.815329i	0.528709	−	0.848803i	$-0.322676\pi$
$353$	−8.84422	−	15.3186i	−0.470730	−	0.815329i	−0.999440	+	0.0334742i	$0.989343\pi$
$354$	−2.31519	−	0.471780i	−0.123051	−	0.0250748i
$355$	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	0.444377	−	0.895840i	$-0.353425\pi$
$359$	−2.07009	−	1.19517i	−0.109255	−	0.0630786i	−0.553632	+	0.832761i	$0.686759\pi$
$360$	2.76078	+	1.17391i	0.145506	+	0.0618706i
$361$	4.38436	−	7.59393i	0.230756	−	0.399681i
$362$	0.175835	−	0.304556i	0.00924170	−	0.0160071i
$363$	12.4930	+	2.54578i	0.655714	+	0.133619i
$364$			2.52004i			0.132086i
$365$	−1.96902	−	3.41044i	−0.103063	−	0.178511i
$366$	−14.4149	+	16.2829i	−0.753479	+	0.851119i
$367$	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
$369$	13.2337	−	31.1228i	0.688918	−	1.62019i
$370$		−	9.51288i		−	0.494551i
$371$	−9.01826			−0.468205
$372$	9.32438	+	2.46087i	0.483447	+	0.127590i
$373$	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
$375$	−1.29687	−	1.14810i	−0.0669702	−	0.0592874i
$376$	−11.9223			−0.614846
$377$	10.5551	+	6.09399i	0.543615	+	0.313856i
$378$	7.69318	+	0.612691i	0.395695	+	0.0315134i
$379$	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
$381$	5.93125	−	29.1067i	0.303867	−	1.49118i
$382$	0.264341	−	0.457852i	0.0135249	−	0.0234257i
$383$	−5.76820	+	9.99081i	−0.294741	+	0.510506i	−0.974925	−	0.222535i	$-0.928567\pi$
$383$	−5.76820	+	9.99081i	−0.294741	+	0.510506i	0.680184	+	0.733042i	$0.261900\pi$
$384$	−1.29687	−	1.14810i	−0.0661807	−	0.0585885i
$385$	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	0.945805	−	0.324735i	$-0.105275\pi$
$389$	3.78040	+	6.54785i	0.191674	+	0.331989i	−0.754131	+	0.656724i	$0.771942\pi$
$390$	0.586800	−	2.87963i	0.0297138	−	0.145816i
$391$	11.9809	+	20.7515i	0.605898	+	1.04945i
$392$	4.15178	+	2.39703i	0.209696	+	0.121068i
$393$	1.86111	−	9.13309i	0.0938804	−	0.460703i
$394$	−4.96444	−	2.86622i	−0.250105	−	0.144398i
$395$	11.1386			0.560443
$396$	11.8299	+	5.03019i	0.594476	+	0.252777i
$397$	−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	$-0.224848\pi$
$401$	30.4667			1.52143			0.760716	+	0.649084i	$0.224848\pi$
$402$	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
$408$	1.98792	−	9.75543i	0.0984169	−	0.482966i
$409$	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
$414$	−12.4137	+	1.51638i	−0.610102	+	0.0745259i
$415$	8.46021	−	4.88450i	0.415295	−	0.239771i
$416$	−0.848361	+	1.46940i	−0.0415943	+	0.0720435i
$417$	−10.9936	−	9.73242i	−0.538359	−	0.476599i
$418$			13.7061i			0.670388i
$419$			13.0350i			0.636804i	0.947956	+	0.318402i	$0.103146\pi$
$419$			13.0350i			0.636804i	−0.947956	+	0.318402i	$0.896854\pi$
$420$	1.92617	+	1.70520i	0.0939874	+	0.0832051i
$421$	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
$423$	35.5030	−	4.33680i	1.72621	−	0.210862i
$424$	−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
$429$	2.51443	−	12.3392i	0.121398	−	0.595741i
$430$		−	7.44281i		−	0.358924i
$431$	21.6097	−	12.4764i	1.04090	−	0.600967i	0.120815	−	0.992675i	$-0.461449\pi$
$431$	21.6097	−	12.4764i	1.04090	−	0.600967i	0.920089	+	0.391708i	$0.128116\pi$
$432$	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
$441$	−13.2354	−	5.62780i	−0.630255	−	0.267990i
$442$	−9.75284			−0.463895
$443$	−7.42343	−	4.28592i	−0.352698	−	0.203630i	0.313175	−	0.949695i	$-0.398607\pi$
$443$	−7.42343	−	4.28592i	−0.352698	−	0.203630i	−0.665873	+	0.746065i	$0.731941\pi$
$444$	3.28997	−	16.1450i	0.156135	−	0.766208i
$445$	−3.79705	−	2.19223i	−0.179997	−	0.103921i
$446$	11.1586	+	19.3273i	0.528376	+	0.915175i
$447$	−0.439695	+	2.15773i	−0.0207968	+	0.102057i
$448$	−0.742621	−	1.28626i	−0.0350855	−	0.0607699i
$449$	−40.5736			−1.91479			−0.957393	−	0.288787i	$-0.906748\pi$
$449$	−40.5736			−1.91479			−0.957393	+	0.288787i	$0.906748\pi$
$450$	−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
$453$	27.0721	+	23.9664i	1.27196	+	1.12604i
$454$	4.57737	−	7.92824i	0.214827	−	0.372091i
$455$	1.26002	−	2.18242i	0.0590707	−	0.102313i
$456$	−1.10623	+	5.42864i	−0.0518038	+	0.254219i
$457$			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
$459$	−2.37118	+	29.7735i	−0.110677	+	1.38971i
$460$	−3.61018	−	2.08434i	−0.168325	−	0.0971827i
$461$	−2.92110			−0.136049			−0.0680246	−	0.997684i	$-0.521670\pi$
$461$	−2.92110			−0.136049			−0.0680246	+	0.997684i	$0.521670\pi$
$462$	8.25360	+	7.30675i	0.383992	+	0.339941i
$463$			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
$465$	−6.84472	−	6.79337i	−0.317416	−	0.315035i
$466$	16.7182			0.774456
$467$			21.7637i			1.00711i	0.863964	+	0.503553i	$0.167974\pi$
$467$			21.7637i			1.00711i	−0.863964	+	0.503553i	$0.832026\pi$
$468$	1.99180	−	4.68429i	0.0920711	−	0.216531i
$469$	17.7789			0.820954
$470$	10.3250	+	5.96115i	0.476257	+	0.274967i
$471$	14.6018	−	16.4940i	0.672816	−	0.760004i
$472$	−0.682072	−	1.18138i	−0.0313949	−	0.0543776i
$473$		−	31.8923i		−	1.46641i
$474$	18.9041	+	3.85221i	0.868294	+	0.176938i
$475$	1.59932	−	2.77010i	0.0733818	−	0.127101i
$476$	4.26862	−	7.39346i	0.195652	−	0.338879i
$477$	16.7633	+	7.12789i	0.767537	+	0.326364i
$478$	8.98561	+	5.18784i	0.410992	+	0.237286i
$479$	1.92376	−	1.11069i	0.0878991	−	0.0507485i	−0.455406	−	0.890284i	$-0.650506\pi$
$479$	1.92376	−	1.11069i	0.0878991	−	0.0507485i	0.543305	+	0.839535i	$0.317173\pi$
$480$	0.549077	+	1.64272i	0.0250618	+	0.0749794i
$481$	−16.1407			−0.735954
$482$	4.43763	+	7.68620i	0.202129	+	0.350097i
$483$	−10.5080	−	2.14128i	−0.478131	−	0.0974318i
$484$	3.68054	+	6.37489i	0.167297	+	0.289768i
$485$	−12.9293	−	7.46473i	−0.587089	−	0.338956i
$486$	−13.8159	−	7.21945i	−0.626703	−	0.327481i
$487$	−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
$489$	−17.0687	+	19.2806i	−0.771873	+	0.871897i
$490$	−2.39703	−	4.15178i	−0.108287	−	0.187558i
$491$	3.47887	−	6.02558i	0.156999	−	0.271931i	−0.776786	−	0.629765i	$-0.783151\pi$
$491$	3.47887	−	6.02558i	0.156999	−	0.271931i	0.933785	+	0.357834i	$0.116485\pi$
$492$	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
$501$	21.7944	+	4.44119i	0.973703	+	0.198418i
$502$	−11.1711	+	6.44966i	−0.498593	+	0.287863i
$503$	2.94516	−	1.70039i	0.131318	−	0.0758166i	−0.432902	−	0.901441i	$-0.642510\pi$
$503$	2.94516	−	1.70039i	0.131318	−	0.0758166i	0.564220	+	0.825624i	$0.309177\pi$
$504$	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
$507$	17.1773	+	3.50033i	0.762871	+	0.155455i
$508$	14.8524	−	8.57505i	0.658969	−	0.380456i
$509$	1.23751	−	2.14342i	0.0548515	−	0.0950055i	−0.837296	−	0.546750i	$-0.815865\pi$
$509$	1.23751	−	2.14342i	0.0548515	−	0.0950055i	0.892147	+	0.451745i	$0.149198\pi$
$510$	−6.59931	+	7.45448i	−0.292222	+	0.330090i
$511$		−	5.84894i		−	0.258742i
$512$		−	1.00000i		−	0.0441942i
$513$	1.31950	−	16.5681i	0.0582573	−	0.731502i
$514$	−3.23885	+	5.60986i	−0.142860	+	0.247440i
$515$	5.77095	−	3.33186i	0.254299	−	0.146819i
$516$	2.57405	−	12.6317i	0.113316	−	0.556081i
$517$	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	−0.853014	−	0.521887i	$-0.825228\pi$
$521$	−18.8893	+	10.9057i	−0.827554	+	0.477789i	0.0254604	+	0.999676i	$0.491895\pi$
$522$	21.3907	−	2.61295i	0.936247	−	0.114366i
$523$		−	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
$534$	−5.68607	−	5.03377i	−0.246061	−	0.217832i
$535$	18.3721			0.794294
$536$	10.3667	+	5.98520i	0.447772	+	0.258521i
$537$	27.8085	+	5.66671i	1.20003	+	0.244537i
$538$	−10.7015	−	6.17853i	−0.461375	−	0.266375i
$539$	−10.2712	−	17.7903i	−0.442413	−	0.766282i
$540$	−2.23262	−	4.69206i	−0.0960768	−	0.201914i
$541$	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
$546$	2.89325	−	3.26817i	0.123820	−	0.139865i
$547$	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
$549$	37.3886	−	4.56713i	1.59570	−	0.194920i
$550$		−	4.28498i		−	0.182712i
$551$	11.4883	+	19.8983i	0.489418	+	0.847697i
$552$	−5.40624	−	4.78603i	−0.230105	−	0.203707i
$553$	14.3271	+	8.27174i	0.609249	+	0.351750i
$554$	0.958749			0.0407333
$555$	−10.9217	+	12.3370i	−0.463600	+	0.523676i
$556$		−	8.47702i		−	0.359506i
$557$	−16.7531			−0.709853			−0.354927	−	0.934894i	$-0.615494\pi$
$557$	−16.7531			−0.709853			−0.354927	+	0.934894i	$0.615494\pi$
$558$	−9.26722	−	13.8967i	−0.392313	−	0.588295i
$559$	−12.6284			−0.534124
$560$			1.48524i			0.0627629i
$561$	−28.2779	+	31.9423i	−1.19389	+	1.34861i
$562$	−26.4095			−1.11402
$563$	19.8195	+	11.4428i	0.835291	+	0.482255i	0.855661	−	0.517537i	$-0.173151\pi$
$563$	19.8195	+	11.4428i	0.835291	+	0.482255i	−0.0203699	+	0.999793i	$0.506484\pi$
$564$	15.4617	+	13.6879i	0.651055	+	0.576366i
$565$	8.05711	+	13.9553i	0.338965	+	0.587105i
$566$			9.06729i			0.381127i
$567$	−9.27365	−	9.62708i	−0.389457	−	0.404300i
$568$	−0.375285	+	0.650013i	−0.0157466	+	0.0272740i
$569$	−6.49170	+	11.2440i	−0.272146	+	0.471371i	−0.969411	−	0.245442i	$-0.921067\pi$
$569$	−6.49170	+	11.2440i	−0.272146	+	0.471371i	0.697265	+	0.716814i	$0.254400\pi$
$570$	3.67234	−	4.14822i	0.153817	−	0.173750i
$571$	−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
$576$	0.363755	+	2.97787i	0.0151565	+	0.124078i
$577$	−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
$579$	−6.06124	−	1.23514i	−0.251897	−	0.0513305i
$580$	6.22087	+	3.59162i	0.258308	+	0.149134i
$581$	14.5093			0.601948
$582$	−19.3616	−	17.1404i	−0.802564	−	0.710494i
$583$	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	$-0.526036\pi$
$587$	−3.95908			−0.163409			−0.0817044	+	0.996657i	$0.526036\pi$
$588$	−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	$0.190366\pi$
$593$			27.4216i			1.12607i	−0.826433	+	0.563035i	$0.809634\pi$
$594$	−9.56676	−	20.1054i	−0.392529	−	0.824934i
$595$	−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	0.867545	−	0.497358i	$-0.165697\pi$
$599$	21.3073	+	12.3018i	0.870593	+	0.502637i	0.00304762	+	0.999995i	$0.499030\pi$
$600$	0.345843	−	1.69717i	0.0141190	−	0.0692868i
$601$	−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
$603$	−33.0477	−	14.0522i	−1.34581	−	0.572249i
$604$			20.8749i			0.849387i
$605$		−	7.36109i		−	0.299271i
$606$	−9.06365	+	10.2382i	−0.368186	+	0.415897i
$607$	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
$609$	18.1069	+	3.68975i	0.733728	+	0.149516i
$610$	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
$615$	−19.1325	−	3.89875i	−0.771496	−	0.157213i
$616$			6.36423i			0.256422i
$617$	−9.02116	+	5.20837i	−0.363178	+	0.209681i	−0.670474	−	0.741933i	$-0.733909\pi$
$617$	−9.02116	+	5.20837i	−0.363178	+	0.209681i	0.307296	+	0.951614i	$0.400576\pi$
$618$	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
$627$	15.7359	−	17.7751i	0.628432	−	0.709868i
$628$	12.7183			0.507515
$629$	47.3547	+	27.3403i	1.88816	+	1.09013i
$630$	−0.540265	−	4.42285i	−0.0215247	−	0.176210i
$631$	−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
$633$	3.41072	+	0.695024i	0.135564	+	0.0276247i
$634$	−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
$639$	0.881103	−	2.07216i	0.0348559	−	0.0819735i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	0.0147605	−	0.0255660i	0.000583005	−	0.00100979i	−0.865734	−	0.500505i	$-0.833148\pi$
$641$	0.0147605	−	0.0255660i	0.000583005	−	0.00100979i	0.866317	+	0.499495i	$0.166481\pi$
$642$	31.1806	+	6.35386i	1.23060	+	0.250767i
$643$			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
$645$	−8.54505	+	9.65237i	−0.336461	+	0.380062i
$646$	−15.9227	−	9.19296i	−0.626469	−	0.361692i
$647$	−20.2804			−0.797307			−0.398653	−	0.917102i	$-0.630522\pi$
$647$	−20.2804			−0.797307			−0.398653	+	0.917102i	$0.630522\pi$
$648$	−2.16643	−	8.73536i	−0.0851054	−	0.343158i
$649$			5.84534i			0.229450i
$650$	−1.69672			−0.0665509
$651$	−3.75917	−	13.8210i	−0.147333	−	0.541689i
$652$	−14.8670			−0.582235
$653$			38.1868i			1.49436i	0.664619	+	0.747182i	$0.268594\pi$
$653$			38.1868i			1.49436i	−0.664619	+	0.747182i	$0.731406\pi$
$654$	0.0979095	+	0.0866774i	0.00382857	+	0.00338935i
$655$	−5.38136			−0.210267
$656$	9.76284	+	5.63658i	0.381175	+	0.220071i
$657$	−4.62291	+	10.8721i	−0.180357	+	0.424160i
$658$	8.85374	+	15.3351i	0.345155	+	0.597826i
$659$		−	7.51357i		−	0.292687i	−0.989234	−	0.146344i	$-0.953250\pi$
$659$		−	7.51357i		−	0.292687i	0.989234	−	0.146344i	$-0.0467505\pi$
$660$	1.48193	−	7.27235i	0.0576842	−	0.283076i
$661$	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
$663$	12.6482	+	11.1972i	0.491215	+	0.434863i
$664$	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
$669$	7.71827	−	37.8762i	0.298406	−	1.46438i
$670$	−5.98520	−	10.3667i	−0.231228	−	0.400499i
$671$	46.5922	+	26.9000i	1.79867	+	1.03846i
$672$	−0.513661	+	2.52071i	−0.0198149	+	0.0972385i
$673$	−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
$675$	−0.412519	+	5.17975i	−0.0158779	+	0.199369i
$676$	5.06057	+	8.76516i	0.194637	+	0.337121i
$677$	−10.5122	+	18.2077i	−0.404017	+	0.699778i	−0.994207	−	0.107487i	$-0.965720\pi$
$677$	−10.5122	+	18.2077i	−0.404017	+	0.699778i	0.590189	+	0.807265i	$0.299053\pi$
$678$	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	$0.0703184\pi$
$683$			11.4530i			0.438239i	−0.975698	+	0.219119i	$0.929682\pi$
$684$	7.66723	−	5.77020i	0.293164	−	0.220629i
$685$	−17.3050	+	9.99103i	−0.661189	+	0.381737i
$686$		−	17.5170i		−	0.668803i
$687$	−1.74484	+	8.56253i	−0.0665698	+	0.326681i
$688$	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
$693$	−2.31503	−	18.9518i	−0.0879405	−	0.719921i
$694$	8.46882	−	4.88948i	0.321472	−	0.185602i
$695$	−4.23851	+	7.34131i	−0.160776	+	0.278472i
$696$	9.31575	+	8.24705i	0.353113	+	0.312604i
$697$			64.7987i			2.45442i
$698$			15.4112i			0.583321i
$699$	−21.6814	−	19.1941i	−0.820065	−	0.725987i
$700$	0.742621	−	1.28626i	0.0280684	−	0.0486159i
$701$	−30.3210	+	17.5058i	−1.14521	+	0.661186i	−0.947715	−	0.319118i	$-0.896613\pi$
$701$	−30.3210	+	17.5058i	−1.14521	+	0.661186i	−0.197493	+	0.980304i	$0.563280\pi$
$702$	−7.96112	+	3.78814i	−0.300473	+	0.142974i
$703$	−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
$708$	−0.471780	+	2.31519i	−0.0177306	+	0.0870101i
$709$		−	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	0.999622	−	0.0274921i	$-0.00875211\pi$
$719$	12.7636	+	22.1072i	0.476002	+	0.824460i	−0.523620	+	0.851952i	$0.675419\pi$
$720$	1.17391	−	2.76078i	0.0437491	−	0.102888i
$721$	9.89724			0.368592
$722$	−7.59393	−	4.38436i	−0.282617	−	0.163169i
$723$	3.06945	−	15.0628i	0.114154	−	0.560193i
$724$	−0.304556	−	0.175835i	−0.0113187	−	0.00653487i
$725$	−3.59162	−	6.22087i	−0.133390	−	0.231037i
$726$	2.54578	−	12.4930i	0.0944829	−	0.463660i
$727$	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
$732$	16.2829	+	14.4149i	0.601832	+	0.532790i
$733$	−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
$735$	−1.65799	+	8.13634i	−0.0611560	+	0.300113i
$736$		−	4.16867i		−	0.153659i
$737$	−25.6465	−	44.4210i	−0.944700	−	1.63627i
$738$	−31.1228	−	13.2337i	−1.14564	−	0.487139i
$739$	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
$741$	−7.03839	−	6.23094i	−0.258562	−	0.228899i
$742$			9.01826i			0.331071i
$743$	−3.33359			−0.122298			−0.0611488	−	0.998129i	$-0.519476\pi$
$743$	−3.33359			−0.122298			−0.0611488	+	0.998129i	$0.519476\pi$
$744$	2.46087	−	9.32438i	0.0902199	−	0.341848i
$745$	1.27137			0.0465794
$746$		−	8.75126i		−	0.320406i
$747$	−26.9701	−	11.4679i	−0.986785	−	0.419590i
$748$	−24.6303			−0.900573
$749$	23.6312	+	13.6435i	0.863466	+	0.498522i
$750$	−1.14810	+	1.29687i	−0.0419225	+	0.0473551i
$751$	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
$753$	21.8924	+	4.46115i	0.797802	+	0.162573i
$754$	6.09399	−	10.5551i	0.221930	−	0.384394i
$755$	10.4374	−	18.0782i	0.379857	−	0.657932i
$756$	0.612691	−	7.69318i	0.0222833	−	0.279798i
$757$	−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	$-0.851270\pi$
$761$	−23.0756	−	39.9681i	−0.836490	−	1.44884i	0.0563208	−	0.998413i	$-0.482063\pi$
$762$	−29.1067	−	5.93125i	−1.05442	−	0.214866i
$763$	0.0560654	+	0.0971081i	0.00202970	+	0.00351555i
$764$	−0.457852	−	0.264341i	−0.0165645	−	0.00956352i
$765$	17.1169	−	2.09088i	0.618863	−	0.0755961i
$766$	9.99081	+	5.76820i	0.360983	+	0.208413i
$767$	2.31458			0.0835745
$768$	−1.14810	+	1.29687i	−0.0414283	+	0.0467968i
$769$	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	$-0.805851\pi$
$773$	−45.5792			−1.63937			−0.819684	+	0.572816i	$0.805851\pi$
$774$	−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
$780$	−2.87963	−	0.586800i	−0.103107	−	0.0210108i
$781$	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
$786$	−9.13309	−	1.86111i	−0.325766	−	0.0663835i
$787$	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
$789$	9.33366	−	10.5432i	0.332287	−	0.375347i
$790$		−	11.1386i		−	0.396293i
$791$			23.9335i			0.850977i
$792$	5.03019	−	11.8299i	0.178740	−	0.420358i
$793$	10.6516	−	18.4491i	0.378249	−	0.655147i
$794$	−24.4225	+	14.1004i	−0.866723	+	0.500403i
$795$	2.09993	−	10.3051i	0.0744769	−	0.365484i
$796$	20.8795	+	12.0548i	0.740053	+	0.427270i
$797$	7.02376	−	12.1655i	0.248794	−	0.430924i	−0.714397	−	0.699740i	$-0.753299\pi$
$797$	7.02376	−	12.1655i	0.248794	−	0.430924i	0.963192	+	0.268816i	$0.0866324\pi$
$798$	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
$801$	1.59487	+	13.0563i	0.0563519	+	0.461322i
$802$		−	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	0.689350	−	0.724428i	$-0.257896\pi$
$809$	−8.04077	−	13.9270i	−0.282698	−	0.489648i	−0.972048	+	0.234780i	$0.924563\pi$
$810$	−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
$813$	32.2897	+	28.5854i	1.13245	+	1.00253i
$814$	−40.7626			−1.42873
$815$	12.8752	+	7.43348i	0.450998	+	0.260384i
$816$	−9.75543	−	1.98792i	−0.341508	−	0.0695913i
$817$	−20.6173	−	11.9034i	−0.721309	−	0.416448i
$818$	−11.6666	−	20.2072i	−0.407913	−	0.706527i
$819$	−7.50435	+	0.916679i	−0.262223	+	0.0320314i
$820$	−5.63658	−	9.76284i	−0.196838	−	0.340933i
$821$	24.4815			0.854410			0.427205	−	0.904155i	$-0.359498\pi$
$821$	24.4815			0.854410			0.427205	+	0.904155i	$0.359498\pi$
$822$	−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
$825$	−4.91957	+	5.55708i	−0.171277	+	0.193473i
$826$	−1.01304	+	1.75464i	−0.0352482	+	0.0610517i
$827$	−22.8529	+	39.5824i	−0.794674	+	1.37642i	0.128372	+	0.991726i	$0.459025\pi$
$827$	−22.8529	+	39.5824i	−0.794674	+	1.37642i	−0.923046	+	0.384690i	$0.874308\pi$
$828$	1.51638	+	12.4137i	0.0526978	+	0.431407i
$829$			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
$831$	−1.24338	−	1.10074i	−0.0431322	−	0.0381841i
$832$	1.46940	+	0.848361i	0.0509424	+	0.0294116i
$833$	27.5565			0.954775
$834$	−9.73242	+	10.9936i	−0.337006	+	0.380678i
$835$		−	12.8416i		−	0.444402i
$836$	13.7061			0.474036
$837$	−3.93635	+	28.6619i	−0.136060	+	0.990701i
$838$	13.0350			0.450288
$839$			21.1757i			0.731067i	0.930798	+	0.365534i	$0.119113\pi$
$839$			21.1757i			0.731067i	−0.930798	+	0.365534i	$0.880887\pi$
$840$	1.70520	−	1.92617i	0.0588349	−	0.0664591i
$841$	22.5990			0.779277
$842$	−5.32469	−	3.07421i	−0.183501	−	0.105944i
$843$	34.2497	+	30.3206i	1.17962	+	1.04430i
$844$	1.00482	+	1.74041i	0.0345875	+	0.0599073i
$845$		−	10.1211i		−	0.348178i
$846$	−4.33680	−	35.5030i	−0.149102	−	1.22062i
$847$	5.46649	−	9.46825i	0.187831	−	0.325333i
$848$	−3.03596	+	5.25843i	−0.104255	+	0.180575i
$849$	10.4101	−	11.7591i	0.357274	−	0.403572i
$850$	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
$855$	−9.52511	+	1.16352i	−0.325752	+	0.0397916i
$856$	9.18604	+	15.9107i	0.313972	+	0.543816i
$857$	−12.9227	−	7.46091i	−0.441430	−	0.254860i	0.262774	−	0.964857i	$-0.415363\pi$
$857$	−12.9227	−	7.46091i	−0.441430	−	0.254860i	−0.704204	+	0.709998i	$0.748696\pi$
$858$	−12.3392	−	2.51443i	−0.421252	−	0.0858412i
$859$	−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
$861$	−21.7140	−	19.2230i	−0.740011	−	0.655117i
$862$	−12.4764	−	21.6097i	−0.424948	−	0.736031i
$863$	5.27120	−	9.12999i	0.179434	−	0.310789i	−0.762253	−	0.647279i	$-0.775907\pi$
$863$	5.27120	−	9.12999i	0.179434	−	0.310789i	0.941687	+	0.336491i	$0.109240\pi$
$864$	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
$873$	5.43067	+	44.4579i	0.183800	+	1.50467i
$874$	−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
$879$	3.91964	−	19.2350i	0.132206	−	0.648780i
$880$	3.71090	−	2.14249i	0.125095	−	0.0722234i
$881$	5.81077	−	10.0646i	0.195770	−	0.339084i	−0.751383	−	0.659867i	$-0.770613\pi$
$881$	5.81077	−	10.0646i	0.195770	−	0.339084i	0.947153	+	0.320783i	$0.103946\pi$
$882$	−5.62780	+	13.2354i	−0.189498	+	0.445658i
$883$			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
$885$	1.56617	−	1.76912i	0.0526462	−	0.0594684i
$886$	−4.28592	+	7.42343i	−0.143988	+	0.249395i
$887$	−2.95327	+	1.70507i	−0.0991612	+	0.0572507i	−0.548761	−	0.835980i	$-0.684900\pi$
$887$	−2.95327	+	1.70507i	−0.0991612	+	0.0572507i	0.449599	+	0.893230i	$0.351567\pi$
$888$	−16.1450	−	3.28997i	−0.541791	−	0.110404i
$889$	−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
$894$	2.15773	+	0.439695i	0.0721654	+	0.0147056i
$895$		−	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
$906$	23.9664	−	27.0721i	0.796229	−	0.899409i
$907$	−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
$909$	23.5088	−	2.87167i	0.779737	−	0.0952473i
$910$	−2.18242	−	1.26002i	−0.0723465	−	0.0417693i
$911$	17.9150	+	31.0297i	0.593550	+	1.02806i	0.993750	+	0.111631i	$0.0356075\pi$
$911$	17.9150	+	31.0297i	0.593550	+	1.02806i	−0.400200	+	0.916428i	$0.631059\pi$
$912$	5.42864	+	1.10623i	0.179760	+	0.0366309i
$913$	−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
$918$	29.7735	+	2.37118i	0.982671	+	0.0782606i
$919$	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
$921$	−24.8784	−	5.06963i	−0.819772	−	0.167050i
$922$			2.92110i			0.0962013i
$923$	−0.636755	−	1.10289i	−0.0209590	−	0.0363021i
$924$	7.30675	−	8.25360i	0.240374	−	0.271523i
$925$	8.23840	+	4.75644i	0.270877	+	0.156391i
$926$	23.0953			0.758959
$927$	−18.3971	−	7.82262i	−0.604240	−	0.256929i
$928$			7.18325i			0.235802i
$929$	−6.12371			−0.200912			−0.100456	−	0.994941i	$-0.532030\pi$
$929$	−6.12371			−0.200912			−0.100456	+	0.994941i	$0.532030\pi$
$930$	−6.79337	+	6.84472i	−0.222763	+	0.224447i
$931$	−15.3345			−0.502566
$932$		−	16.7182i		−	0.547623i
$933$	6.57489	+	5.82062i	0.215252	+	0.190559i
$934$	21.7637			0.712132
$935$	21.3305	+	12.3151i	0.697581	+	0.402748i
$936$	−4.68429	−	1.99180i	−0.153111	−	0.0651041i
$937$	−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
$939$	−3.55317	+	17.4366i	−0.115953	+	0.569022i
$940$	5.96115	−	10.3250i	0.194431	−	0.336765i
$941$	9.99684	−	17.3150i	0.325888	−	0.564454i	−0.655804	−	0.754931i	$-0.727670\pi$
$941$	9.99684	−	17.3150i	0.325888	−	0.564454i	0.981692	+	0.190477i	$0.0610035\pi$
$942$	−16.4940	−	14.6018i	−0.537404	−	0.475753i
$943$	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	$-0.979951\pi$
$947$	−17.0336	−	29.5031i	−0.553519	−	0.958722i	0.444499	−	0.895780i	$-0.353382\pi$
$948$	3.85221	−	18.9041i	0.125114	−	0.613976i
$949$	3.34088	+	5.78658i	0.108450	+	0.187840i
$950$	−2.77010	−	1.59932i	−0.0898740	−	0.0518888i
$951$	−4.37713	+	21.4801i	−0.141938	+	0.696539i
$952$	−7.39346	−	4.26862i	−0.239624	−	0.138347i
$953$	10.7328			0.347669			0.173835	−	0.984775i	$-0.444384\pi$
$953$	10.7328			0.347669			0.173835	+	0.984775i	$0.444384\pi$
$954$	7.12789	−	16.7633i	0.230774	−	0.542730i
$955$	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
$966$	−2.14128	+	10.5080i	−0.0688947	+	0.338090i
$967$	−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	0.260528	−	0.965466i	$-0.416103\pi$
$971$	−13.8767	−	8.01173i	−0.445325	−	0.257109i	−0.705854	+	0.708357i	$0.749437\pi$
$972$	−7.21945	+	13.8159i	−0.231564	+	0.443146i
$973$	−10.9036	+	6.29521i	−0.349554	+	0.201815i
$974$	−11.8930	+	20.5993i	−0.381077	+	0.660046i
$975$	2.20043	+	1.94800i	0.0704702	+	0.0623859i
$976$			12.5555i			0.401891i
$977$		−	20.5064i		−	0.656059i	−0.944667	−	0.328030i	$-0.893615\pi$
$977$		−	20.5064i		−	0.656059i	0.944667	−	0.328030i	$-0.106385\pi$
$978$	19.2806	+	17.0687i	0.616524	+	0.545797i
$979$	−9.39365	+	16.2703i	−0.300222	+	0.520001i
$980$	−4.15178	+	2.39703i	−0.132624	+	0.0765703i
$981$	−0.0274623	−	0.224819i	−0.000876805	−	0.00717792i
$982$	−6.02558	−	3.47887i	−0.192284	−	0.111015i
$983$	3.75211	−	6.49885i	0.119674	−	0.207281i	−0.799965	−	0.600047i	$-0.795148\pi$
$983$	3.75211	−	6.49885i	0.119674	−	0.207281i	0.919638	+	0.392766i	$0.128482\pi$
$984$	−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
$987$	6.12402	−	30.0527i	0.194930	−	0.956586i
$988$		−	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
$999$	49.2744	+	3.92425i	1.55897	+	0.124158i

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.14810 + 1.29687i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.29687 + 1.14810i) q^{6} +(0.742621 + 1.28626i) q^{7} +1.00000i q^{8} +(-0.363755 - 2.97787i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.14810 + 1.29687i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.29687 + 1.14810i) q^{6} +(0.742621 + 1.28626i) q^{7} +1.00000i q^{8} +(-0.363755 - 2.97787i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.14249 - 3.71090i) q^{11} +(1.14810 - 1.29687i) 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} +(-2.97787 + 0.363755i) q^{18} +(-1.59932 - 2.77010i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-2.52071 - 0.513661i) q^{21} +(-3.71090 - 2.14249i) q^{22} +4.16867 q^{23} +(-1.29687 - 1.14810i) 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} +(0.363755 + 2.97787i) 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} +(-0.513661 + 2.52071i) q^{42} +(6.44566 - 3.72140i) q^{43} +(-2.14249 + 3.71090i) q^{44} +(1.17391 - 2.76078i) q^{45} -4.16867i q^{46} +11.9223i q^{47} +(-1.14810 + 1.29687i) q^{48} +(2.39703 - 4.15178i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-9.75543 - 1.98792i) 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} +(5.42864 + 1.10623i) 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} +(-4.78603 + 5.40624i) q^{69} +1.48524 q^{70} +(0.650013 + 0.375285i) q^{71} +(2.97787 - 0.363755i) q^{72} +(-3.41044 - 1.96902i) q^{73} +(-4.75644 - 8.23840i) q^{74} +(-1.69717 - 0.345843i) 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} +(-8.73536 + 2.16643i) q^{81} +(5.63658 - 9.76284i) q^{82} +(4.88450 - 8.46021i) q^{83} +(2.52071 + 0.513661i) q^{84} +5.74805i q^{85} +(-3.72140 - 6.44566i) q^{86} +(8.24705 - 9.31575i) q^{87} +(3.71090 + 2.14249i) q^{88} -4.38445 q^{89} +(-2.76078 - 1.17391i) q^{90} -2.52004i q^{91} -4.16867 q^{92} +(-9.32438 - 2.46087i) q^{93} +11.9223 q^{94} -3.19864i q^{95} +(1.29687 + 1.14810i) q^{96} -14.9295 q^{97} +(-4.15178 - 2.39703i) q^{98} +(-11.8299 - 5.03019i) 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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