LMFDB - Embedded newform 630.2.l.f.331.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(331,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 2]))

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

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

chi := DirichletCharacter("630.331");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.l (of order $3$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} + 14 x^{10} - 28 x^{9} + 36 x^{8} - 24 x^{7} + 33 x^{6} + 42 x^{5} + 114 x^{4} + \cdots + 79 $ x^12 - 5x^11 + 14x^10 - 28x^9 + 36x^8 - 24x^7 + 33x^6 + 42x^5 + 114x^4 + 104x^3 + 197x^2 + 166*x + 79
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.6
Root			$2.48293 + 0.894932i$ of defining polynomial
Character	$\chi$	$=$	630.331
Dual form			630.2.l.f.571.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.48293 + 0.894932i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.0335666 - 1.73173i) q^{6} +(-1.40545 - 2.24159i) q^{7} +1.00000 q^{8} +(1.39819 + 2.65425i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.48293 + 0.894932i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.0335666 - 1.73173i) q^{6} +(-1.40545 - 2.24159i) q^{7} +1.00000 q^{8} +(1.39819 + 2.65425i) q^{9} +(0.500000 + 0.866025i) q^{10} +4.07997 q^{11} +(-1.51650 + 0.836793i) q^{12} +(1.66295 + 2.88032i) q^{13} +(-1.23855 + 2.33795i) q^{14} +(-1.48293 - 0.894932i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.10964 + 3.65400i) q^{17} +(1.59955 - 2.53800i) q^{18} +(1.15581 - 2.00193i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.0781148 - 4.58191i) q^{21} +(-2.03999 - 3.53336i) q^{22} +0.730921 q^{23} +(1.48293 + 0.894932i) q^{24} +1.00000 q^{25} +(1.66295 - 2.88032i) q^{26} +(-0.301948 + 5.18737i) q^{27} +(2.64400 - 0.0963576i) q^{28} +(0.513393 - 0.889223i) q^{29} +(-0.0335666 + 1.73173i) q^{30} +(5.25926 - 9.10930i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(6.05033 + 3.65130i) q^{33} +(2.10964 - 3.65400i) q^{34} +(1.40545 + 2.24159i) q^{35} +(-2.99775 - 0.116256i) q^{36} +(0.647932 - 1.12225i) q^{37} -2.31162 q^{38} +(-0.111639 + 5.75956i) q^{39} -1.00000 q^{40} +(3.29918 + 5.71435i) q^{41} +(-3.92899 + 2.35860i) q^{42} +(1.24480 - 2.15606i) q^{43} +(-2.03999 + 3.53336i) q^{44} +(-1.39819 - 2.65425i) q^{45} +(-0.365460 - 0.632996i) q^{46} +(2.75194 + 4.76650i) q^{47} +(0.0335666 - 1.73173i) q^{48} +(-3.04944 + 6.30087i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.141627 + 7.30662i) q^{51} -3.32591 q^{52} +(2.65456 + 4.59783i) q^{53} +(4.64337 - 2.33219i) q^{54} -4.07997 q^{55} +(-1.40545 - 2.24159i) q^{56} +(3.50558 - 1.93435i) q^{57} -1.02679 q^{58} +(-2.98379 + 5.16808i) q^{59} +(1.51650 - 0.836793i) q^{60} +(-0.451622 - 0.782232i) q^{61} -10.5185 q^{62} +(3.98466 - 6.86458i) q^{63} +1.00000 q^{64} +(-1.66295 - 2.88032i) q^{65} +(0.136951 - 7.06539i) q^{66} +(-0.553942 + 0.959456i) q^{67} -4.21927 q^{68} +(1.08391 + 0.654125i) q^{69} +(1.23855 - 2.33795i) q^{70} +2.91752 q^{71} +(1.39819 + 2.65425i) q^{72} +(-5.73968 - 9.94141i) q^{73} -1.29586 q^{74} +(1.48293 + 0.894932i) q^{75} +(1.15581 + 2.00193i) q^{76} +(-5.73418 - 9.14562i) q^{77} +(5.04374 - 2.78310i) q^{78} +(-6.41876 - 11.1176i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-5.09012 + 7.42231i) q^{81} +(3.29918 - 5.71435i) q^{82} +(-6.86528 + 11.8910i) q^{83} +(4.00711 + 2.22331i) q^{84} +(-2.10964 - 3.65400i) q^{85} -2.48960 q^{86} +(1.55712 - 0.859207i) q^{87} +4.07997 q^{88} +(7.27583 - 12.6021i) q^{89} +(-1.59955 + 2.53800i) q^{90} +(4.11930 - 7.77579i) q^{91} +(-0.365460 + 0.632996i) q^{92} +(15.9514 - 8.80182i) q^{93} +(2.75194 - 4.76650i) q^{94} +(-1.15581 + 2.00193i) q^{95} +(-1.51650 + 0.836793i) q^{96} +(-7.36150 + 12.7505i) q^{97} +(6.98143 - 0.509538i) q^{98} +(5.70458 + 10.8293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 7 q^{3} - 6 q^{4} - 12 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 7 * q^3 - 6 * q^4 - 12 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - q^9	\( 12 q - 6 q^{2} - 7 q^{3} - 6 q^{4} - 12 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - q^{9} + 6 q^{10} + 14 q^{11} + 5 q^{12} + 2 q^{13} - 4 q^{14} + 7 q^{15} - 6 q^{16} + 7 q^{17} + 5 q^{18} + 14 q^{19} + 6 q^{20} - 4 q^{21} - 7 q^{22} + 18 q^{23} - 7 q^{24} + 12 q^{25} + 2 q^{26} + 11 q^{27} + 8 q^{28} - 9 q^{29} - 2 q^{30} + 9 q^{31} - 6 q^{32} + 15 q^{33} + 7 q^{34} + 4 q^{35} - 4 q^{36} - 12 q^{37} - 28 q^{38} + 25 q^{39} - 12 q^{40} + q^{41} - 7 q^{42} + 7 q^{43} - 7 q^{44} + q^{45} - 9 q^{46} + 7 q^{47} + 2 q^{48} - 6 q^{50} - 24 q^{51} - 4 q^{52} + 2 q^{53} + 17 q^{54} - 14 q^{55} - 4 q^{56} - 14 q^{57} + 18 q^{58} + 29 q^{59} - 5 q^{60} - 11 q^{61} - 18 q^{62} + 26 q^{63} + 12 q^{64} - 2 q^{65} - 18 q^{66} - 22 q^{67} - 14 q^{68} - 18 q^{69} + 4 q^{70} + 10 q^{71} - q^{72} + 6 q^{73} + 24 q^{74} - 7 q^{75} + 14 q^{76} - 11 q^{77} - 14 q^{78} + q^{79} + 6 q^{80} + 11 q^{81} + q^{82} - 26 q^{83} + 11 q^{84} - 7 q^{85} - 14 q^{86} + 18 q^{87} + 14 q^{88} + 2 q^{89} - 5 q^{90} - 4 q^{91} - 9 q^{92} + 61 q^{93} + 7 q^{94} - 14 q^{95} + 5 q^{96} + 6 q^{97} - 24 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 7 * q^3 - 6 * q^4 - 12 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - q^9 + 6 * q^10 + 14 * q^11 + 5 * q^12 + 2 * q^13 - 4 * q^14 + 7 * q^15 - 6 * q^16 + 7 * q^17 + 5 * q^18 + 14 * q^19 + 6 * q^20 - 4 * q^21 - 7 * q^22 + 18 * q^23 - 7 * q^24 + 12 * q^25 + 2 * q^26 + 11 * q^27 + 8 * q^28 - 9 * q^29 - 2 * q^30 + 9 * q^31 - 6 * q^32 + 15 * q^33 + 7 * q^34 + 4 * q^35 - 4 * q^36 - 12 * q^37 - 28 * q^38 + 25 * q^39 - 12 * q^40 + q^41 - 7 * q^42 + 7 * q^43 - 7 * q^44 + q^45 - 9 * q^46 + 7 * q^47 + 2 * q^48 - 6 * q^50 - 24 * q^51 - 4 * q^52 + 2 * q^53 + 17 * q^54 - 14 * q^55 - 4 * q^56 - 14 * q^57 + 18 * q^58 + 29 * q^59 - 5 * q^60 - 11 * q^61 - 18 * q^62 + 26 * q^63 + 12 * q^64 - 2 * q^65 - 18 * q^66 - 22 * q^67 - 14 * q^68 - 18 * q^69 + 4 * q^70 + 10 * q^71 - q^72 + 6 * q^73 + 24 * q^74 - 7 * q^75 + 14 * q^76 - 11 * q^77 - 14 * q^78 + q^79 + 6 * q^80 + 11 * q^81 + q^82 - 26 * q^83 + 11 * q^84 - 7 * q^85 - 14 * q^86 + 18 * q^87 + 14 * q^88 + 2 * q^89 - 5 * q^90 - 4 * q^91 - 9 * q^92 + 61 * q^93 + 7 * q^94 - 14 * q^95 + 5 * q^96 + 6 * q^97 - 24 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.48293	+	0.894932i	0.856173	+	0.516689i
$3$	1.48293	+	0.894932i	0.856173	+	0.516689i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.0335666	−	1.73173i	0.0137035	−	0.706974i
$7$	−1.40545	−	2.24159i	−0.531209	−	0.847241i
$7$	−1.40545	−	2.24159i	−0.531209	−	0.847241i
$8$	1.00000			0.353553
$9$	1.39819	+	2.65425i	0.466064	+	0.884751i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	4.07997			1.23016			0.615079	−	0.788466i	$-0.289124\pi$
$11$	4.07997			1.23016			0.615079	+	0.788466i	$0.289124\pi$
$12$	−1.51650	+	0.836793i	−0.437776	+	0.241561i
$13$	1.66295	+	2.88032i	0.461220	+	0.798857i	0.999022	−	0.0442145i	$-0.0140785\pi$
$13$	1.66295	+	2.88032i	0.461220	+	0.798857i	−0.537802	+	0.843071i	$0.680745\pi$
$14$	−1.23855	+	2.33795i	−0.331016	+	0.624843i
$15$	−1.48293	−	0.894932i	−0.382892	−	0.231071i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.10964	+	3.65400i	0.511662	+	0.886225i	0.999909	+	0.0135190i	$0.00430335\pi$
$17$	2.10964	+	3.65400i	0.511662	+	0.886225i	−0.488247	+	0.872706i	$0.662363\pi$
$18$	1.59955	−	2.53800i	0.377019	−	0.598212i
$19$	1.15581	−	2.00193i	0.265162	−	0.459273i	−0.702444	−	0.711739i	$-0.747908\pi$
$19$	1.15581	−	2.00193i	0.265162	−	0.459273i	0.967606	+	0.252465i	$0.0812414\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−0.0781148	−	4.58191i	−0.0170461	−	0.999855i
$22$	−2.03999	−	3.53336i	−0.434926	−	0.753315i
$23$	0.730921			0.152408			0.0762038	−	0.997092i	$-0.475720\pi$
$23$	0.730921			0.152408			0.0762038	+	0.997092i	$0.475720\pi$
$24$	1.48293	+	0.894932i	0.302703	+	0.182677i
$25$	1.00000			0.200000
$26$	1.66295	−	2.88032i	0.326132	−	0.564877i
$27$	−0.301948	+	5.18737i	−0.0581100	+	0.998310i
$28$	2.64400	−	0.0963576i	0.499668	−	0.0182099i
$29$	0.513393	−	0.889223i	0.0953347	−	0.165124i	−0.814414	−	0.580285i	$-0.802941\pi$
$29$	0.513393	−	0.889223i	0.0953347	−	0.165124i	0.909748	+	0.415160i	$0.136275\pi$
$30$	−0.0335666	+	1.73173i	−0.00612840	+	0.316168i
$31$	5.25926	−	9.10930i	0.944591	−	1.63608i	0.188022	−	0.982165i	$-0.439792\pi$
$31$	5.25926	−	9.10930i	0.944591	−	1.63608i	0.756568	−	0.653915i	$-0.226874\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	6.05033	+	3.65130i	1.05323	+	0.635609i
$34$	2.10964	−	3.65400i	0.361800	−	0.626655i
$35$	1.40545	+	2.24159i	0.237564	+	0.378898i
$36$	−2.99775	−	0.116256i	−0.499624	−	0.0193761i
$37$	0.647932	−	1.12225i	0.106519	−	0.184497i	−0.807839	−	0.589404i	$-0.799363\pi$
$37$	0.647932	−	1.12225i	0.106519	−	0.184497i	0.914358	+	0.404907i	$0.132696\pi$
$38$	−2.31162			−0.374995
$39$	−0.111639	+	5.75956i	−0.0178766	+	0.922267i
$40$	−1.00000			−0.158114
$41$	3.29918	+	5.71435i	0.515246	+	0.892432i	0.999843	+	0.0176946i	$0.00563267\pi$
$41$	3.29918	+	5.71435i	0.515246	+	0.892432i	−0.484598	+	0.874737i	$0.661034\pi$
$42$	−3.92899	+	2.35860i	−0.606257	+	0.363941i
$43$	1.24480	−	2.15606i	0.189831	−	0.328796i	−0.755363	−	0.655307i	$-0.772539\pi$
$43$	1.24480	−	2.15606i	0.189831	−	0.328796i	0.945194	+	0.326510i	$0.105873\pi$
$44$	−2.03999	+	3.53336i	−0.307539	+	0.532674i
$45$	−1.39819	−	2.65425i	−0.208430	−	0.395673i
$46$	−0.365460	−	0.632996i	−0.0538842	−	0.0933302i
$47$	2.75194	+	4.76650i	0.401412	+	0.695266i	0.993897	−	0.110316i	$-0.0351862\pi$
$47$	2.75194	+	4.76650i	0.401412	+	0.695266i	−0.592484	+	0.805582i	$0.701853\pi$
$48$	0.0335666	−	1.73173i	0.00484493	−	0.249953i
$49$	−3.04944	+	6.30087i	−0.435635	+	0.900124i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−0.141627	+	7.30662i	−0.0198317	+	1.02313i
$52$	−3.32591			−0.461220
$53$	2.65456	+	4.59783i	0.364632	+	0.631561i	0.988717	−	0.149795i	$-0.0478615\pi$
$53$	2.65456	+	4.59783i	0.364632	+	0.631561i	−0.624085	+	0.781356i	$0.714528\pi$
$54$	4.64337	−	2.33219i	0.631883	−	0.317371i
$55$	−4.07997			−0.550143
$56$	−1.40545	−	2.24159i	−0.187811	−	0.299545i
$57$	3.50558	−	1.93435i	0.464326	−	0.256211i
$58$	−1.02679			−0.134824
$59$	−2.98379	+	5.16808i	−0.388456	+	0.672826i	−0.992242	−	0.124320i	$-0.960325\pi$
$59$	−2.98379	+	5.16808i	−0.388456	+	0.672826i	0.603786	+	0.797147i	$0.293658\pi$
$60$	1.51650	−	0.836793i	0.195780	−	0.108030i
$61$	−0.451622	−	0.782232i	−0.0578242	−	0.100155i	0.835664	−	0.549241i	$-0.185083\pi$
$61$	−0.451622	−	0.782232i	−0.0578242	−	0.100155i	−0.893488	+	0.449086i	$0.851750\pi$
$62$	−10.5185			−1.33585
$63$	3.98466	−	6.86458i	0.502020	−	0.864856i
$64$	1.00000			0.125000
$65$	−1.66295	−	2.88032i	−0.206264	−	0.357260i
$66$	0.136951	−	7.06539i	0.0168575	−	0.869689i
$67$	−0.553942	+	0.959456i	−0.0676748	+	0.117216i	−0.897877	−	0.440246i	$-0.854891\pi$
$67$	−0.553942	+	0.959456i	−0.0676748	+	0.117216i	0.830203	+	0.557462i	$0.188225\pi$
$68$	−4.21927			−0.511662
$69$	1.08391	+	0.654125i	0.130487	+	0.0787473i
$70$	1.23855	−	2.33795i	0.148035	−	0.279438i
$71$	2.91752			0.346246			0.173123	−	0.984900i	$-0.444614\pi$
$71$	2.91752			0.346246			0.173123	+	0.984900i	$0.444614\pi$
$72$	1.39819	+	2.65425i	0.164779	+	0.312807i
$73$	−5.73968	−	9.94141i	−0.671778	−	1.16355i	−0.977399	−	0.211401i	$-0.932197\pi$
$73$	−5.73968	−	9.94141i	−0.671778	−	1.16355i	0.305621	−	0.952153i	$-0.401136\pi$
$74$	−1.29586			−0.150641
$75$	1.48293	+	0.894932i	0.171235	+	0.103338i
$76$	1.15581	+	2.00193i	0.132581	+	0.229637i
$77$	−5.73418	−	9.14562i	−0.653470	−	1.04224i
$78$	5.04374	−	2.78310i	0.571091	−	0.315123i
$79$	−6.41876	−	11.1176i	−0.722167	−	1.25083i	−0.960129	−	0.279556i	$-0.909813\pi$
$79$	−6.41876	−	11.1176i	−0.722167	−	1.25083i	0.237962	−	0.971274i	$-0.423521\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−5.09012	+	7.42231i	−0.565569	+	0.824701i
$82$	3.29918	−	5.71435i	0.364334	−	0.631045i
$83$	−6.86528	+	11.8910i	−0.753562	+	1.30521i	0.192524	+	0.981292i	$0.438333\pi$
$83$	−6.86528	+	11.8910i	−0.753562	+	1.30521i	−0.946086	+	0.323916i	$0.895001\pi$
$84$	4.00711	+	2.22331i	0.437211	+	0.242583i
$85$	−2.10964	−	3.65400i	−0.228822	−	0.396332i
$86$	−2.48960			−0.268461
$87$	1.55712	−	0.859207i	0.166941	−	0.0921167i
$88$	4.07997			0.434926
$89$	7.27583	−	12.6021i	0.771237	−	1.33582i	−0.165649	−	0.986185i	$-0.552972\pi$
$89$	7.27583	−	12.6021i	0.771237	−	1.33582i	0.936886	−	0.349636i	$-0.113695\pi$
$90$	−1.59955	+	2.53800i	−0.168608	+	0.267528i
$91$	4.11930	−	7.77579i	0.431820	−	0.815124i
$92$	−0.365460	+	0.632996i	−0.0381019	+	0.0659944i
$93$	15.9514	−	8.80182i	1.65408	−	0.912707i
$94$	2.75194	−	4.76650i	0.283841	−	0.491627i
$95$	−1.15581	+	2.00193i	−0.118584	+	0.205393i
$96$	−1.51650	+	0.836793i	−0.154777	+	0.0854048i
$97$	−7.36150	+	12.7505i	−0.747447	+	1.29462i	0.201596	+	0.979469i	$0.435387\pi$
$97$	−7.36150	+	12.7505i	−0.747447	+	1.29462i	−0.949043	+	0.315147i	$0.897946\pi$
$98$	6.98143	−	0.509538i	0.705231	−	0.0514711i
$99$	5.70458	+	10.8293i	0.573332	+	1.08838i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−4.51286			−0.449046			−0.224523	−	0.974469i	$-0.572082\pi$
$101$	−4.51286			−0.449046			−0.224523	+	0.974469i	$0.572082\pi$
$102$	6.39854	−	3.53066i	0.633549	−	0.349587i
$103$	−4.36460			−0.430057			−0.215028	−	0.976608i	$-0.568984\pi$
$103$	−4.36460			−0.430057			−0.215028	+	0.976608i	$0.568984\pi$
$104$	1.66295	+	2.88032i	0.163066	+	0.282438i
$105$	0.0781148	+	4.58191i	0.00762323	+	0.447149i
$106$	2.65456	−	4.59783i	0.257834	−	0.446581i
$107$	0.637368	−	1.10395i	0.0616167	−	0.106723i	−0.833571	−	0.552412i	$-0.813708\pi$
$107$	0.637368	−	1.10395i	0.0616167	−	0.106723i	0.895188	+	0.445688i	$0.147041\pi$
$108$	−4.34142	−	2.85518i	−0.417753	−	0.274740i
$109$	−8.63456	−	14.9555i	−0.827041	−	1.43248i	−0.900350	−	0.435167i	$-0.856689\pi$
$109$	−8.63456	−	14.9555i	−0.827041	−	1.43248i	0.0733089	−	0.997309i	$-0.476644\pi$
$110$	2.03999	+	3.53336i	0.194505	+	0.336893i
$111$	1.96518	−	1.08437i	0.186527	−	0.102924i
$112$	−1.23855	+	2.33795i	−0.117032	+	0.220915i
$113$	−9.68504	−	16.7750i	−0.911092	−	1.57806i	−0.812525	−	0.582927i	$-0.801907\pi$
$113$	−9.68504	−	16.7750i	−0.911092	−	1.57806i	−0.0985672	−	0.995130i	$-0.531426\pi$
$114$	−3.42799	−	2.06875i	−0.321061	−	0.193756i
$115$	−0.730921			−0.0681587
$116$	0.513393	+	0.889223i	0.0476673	+	0.0825622i
$117$	−5.31997	+	8.44114i	−0.491831	+	0.780383i
$118$	5.96758			0.549360
$119$	5.22578	−	9.86444i	0.479047	−	0.904271i
$120$	−1.48293	−	0.894932i	−0.135373	−	0.0816958i
$121$	5.64617			0.513288
$122$	−0.451622	+	0.782232i	−0.0408879	+	0.0708199i
$123$	−0.221485	+	11.4266i	−0.0199706	+	1.03030i
$124$	5.25926	+	9.10930i	0.472295	+	0.818040i
$125$	−1.00000			−0.0894427
$126$	−7.93723	−	0.0185258i	−0.707105	−	0.00165041i
$127$	−13.8367			−1.22781			−0.613903	−	0.789381i	$-0.710402\pi$
$127$	−13.8367			−1.22781			−0.613903	+	0.789381i	$0.710402\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	3.77549	−	2.08328i	0.332413	−	0.183423i
$130$	−1.66295	+	2.88032i	−0.145851	+	0.252621i
$131$	−13.4803			−1.17778			−0.588888	−	0.808215i	$-0.700434\pi$
$131$	−13.4803			−1.17778			−0.588888	+	0.808215i	$0.700434\pi$
$132$	−6.18728	+	3.41409i	−0.538534	+	0.297159i
$133$	−6.11193	+	0.222743i	−0.529971	+	0.0193142i
$134$	1.10788			0.0957066
$135$	0.301948	−	5.18737i	0.0259876	−	0.446458i
$136$	2.10964	+	3.65400i	0.180900	+	0.313328i
$137$	−16.2233			−1.38605			−0.693025	−	0.720913i	$-0.743723\pi$
$137$	−16.2233			−1.38605			−0.693025	+	0.720913i	$0.743723\pi$
$138$	0.0245345	−	1.26575i	0.00208852	−	0.107748i
$139$	8.37410	+	14.5044i	0.710282	+	1.23024i	0.964751	+	0.263164i	$0.0847660\pi$
$139$	8.37410	+	14.5044i	0.710282	+	1.23024i	−0.254469	+	0.967081i	$0.581901\pi$
$140$	−2.64400	+	0.0963576i	−0.223458	+	0.00814370i
$141$	−0.184747	+	9.53122i	−0.0155585	+	0.802673i
$142$	−1.45876	−	2.52665i	−0.122417	−	0.212032i
$143$	6.78480	+	11.7516i	0.567373	+	0.982720i
$144$	1.59955	−	2.53800i	0.133296	−	0.211500i
$145$	−0.513393	+	0.889223i	−0.0426350	+	0.0738459i
$146$	−5.73968	+	9.94141i	−0.475019	+	0.822757i
$147$	−10.1610	+	6.61473i	−0.838063	+	0.545574i
$148$	0.647932	+	1.12225i	0.0532597	+	0.0922485i
$149$	6.34809			0.520056			0.260028	−	0.965601i	$-0.416268\pi$
$149$	6.34809			0.520056			0.260028	+	0.965601i	$0.416268\pi$
$150$	0.0335666	−	1.73173i	0.00274070	−	0.141395i
$151$	17.4975			1.42392			0.711961	−	0.702219i	$-0.247807\pi$
$151$	17.4975			1.42392			0.711961	+	0.702219i	$0.247807\pi$
$152$	1.15581	−	2.00193i	0.0937488	−	0.162378i
$153$	−6.74896	+	10.7085i	−0.545621	+	0.865731i
$154$	−5.05325	+	9.53876i	−0.407202	+	0.768655i
$155$	−5.25926	+	9.10930i	−0.422434	+	0.731677i
$156$	−4.93210	−	2.97646i	−0.394884	−	0.238308i
$157$	−6.96791	+	12.0688i	−0.556099	+	0.963192i	0.441718	+	0.897154i	$0.354369\pi$
$157$	−6.96791	+	12.0688i	−0.556099	+	0.963192i	−0.997817	+	0.0660383i	$0.978964\pi$
$158$	−6.41876	+	11.1176i	−0.510649	+	0.884471i
$159$	−0.178209	+	9.19394i	−0.0141329	+	0.729127i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−1.02727	−	1.63842i	−0.0809602	−	0.129126i
$162$	8.97297	+	0.697014i	0.704983	+	0.0547626i
$163$	7.83322	−	13.5675i	0.613545	−	1.06269i	−0.377093	−	0.926176i	$-0.623076\pi$
$163$	7.83322	−	13.5675i	0.613545	−	1.06269i	0.990638	−	0.136516i	$-0.0435905\pi$
$164$	−6.59836			−0.515246
$165$	−6.05033	−	3.65130i	−0.471018	−	0.284253i
$166$	13.7306			1.06570
$167$	−11.6266	−	20.1379i	−0.899693	−	1.55831i	−0.827887	−	0.560896i	$-0.810457\pi$
$167$	−11.6266	−	20.1379i	−0.899693	−	1.55831i	−0.0718065	−	0.997419i	$-0.522876\pi$
$168$	−0.0781148	−	4.58191i	−0.00602669	−	0.353502i
$169$	0.969176	−	1.67866i	0.0745520	−	0.129128i
$170$	−2.10964	+	3.65400i	−0.161802	+	0.280249i
$171$	6.92967	+	0.268741i	0.529925	+	0.0205511i
$172$	1.24480	+	2.15606i	0.0949153	+	0.164398i
$173$	0.830725	+	1.43886i	0.0631589	+	0.109394i	0.895876	−	0.444305i	$-0.146549\pi$
$173$	0.830725	+	1.43886i	0.0631589	+	0.109394i	−0.832717	+	0.553699i	$0.813216\pi$
$174$	−1.52266	−	0.918904i	−0.115432	−	0.0696619i
$175$	−1.40545	−	2.24159i	−0.106242	−	0.169448i
$176$	−2.03999	−	3.53336i	−0.153770	−	0.266337i
$177$	−9.04985	+	4.99363i	−0.680228	+	0.375344i
$178$	−14.5517			−1.09069
$179$	3.21357	+	5.56606i	0.240193	+	0.416027i	0.960769	−	0.277349i	$-0.0894559\pi$
$179$	3.21357	+	5.56606i	0.240193	+	0.416027i	−0.720576	+	0.693376i	$0.756123\pi$
$180$	2.99775	+	0.116256i	0.223439	+	0.00866524i
$181$	3.64852			0.271193			0.135596	−	0.990764i	$-0.456705\pi$
$181$	3.64852			0.271193			0.135596	+	0.990764i	$0.456705\pi$
$182$	−8.79368	+	0.320476i	−0.651831	+	0.0237553i
$183$	0.0303188	−	1.56417i	0.00224123	−	0.115627i
$184$	0.730921			0.0538842
$185$	−0.647932	+	1.12225i	−0.0476369	+	0.0825096i
$186$	−15.5983	−	9.41336i	−1.14372	−	0.690221i
$187$	8.60726	+	14.9082i	0.629425	+	1.09020i
$188$	−5.50389			−0.401412
$189$	12.0523	−	6.61373i	0.876678	−	0.481078i
$190$	2.31162			0.167703
$191$	5.22286	+	9.04626i	0.377913	+	0.654564i	0.990758	−	0.135638i	$-0.0433086\pi$
$191$	5.22286	+	9.04626i	0.377913	+	0.654564i	−0.612846	+	0.790203i	$0.709975\pi$
$192$	1.48293	+	0.894932i	0.107022	+	0.0645862i
$193$	−9.07209	+	15.7133i	−0.653023	+	1.13107i	0.329362	+	0.944204i	$0.393166\pi$
$193$	−9.07209	+	15.7133i	−0.653023	+	1.13107i	−0.982385	+	0.186866i	$0.940167\pi$
$194$	14.7230			1.05705
$195$	0.111639	−	5.75956i	0.00799467	−	0.412450i
$196$	−3.93199	−	5.79133i	−0.280856	−	0.413666i
$197$	−8.53501			−0.608095			−0.304047	−	0.952657i	$-0.598338\pi$
$197$	−8.53501			−0.608095			−0.304047	+	0.952657i	$0.598338\pi$
$198$	6.52614	−	10.3550i	0.463792	−	0.735894i
$199$	−3.48948	−	6.04396i	−0.247363	−	0.428445i	0.715430	−	0.698684i	$-0.246231\pi$
$199$	−3.48948	−	6.04396i	−0.247363	−	0.428445i	−0.962793	+	0.270239i	$0.912897\pi$
$200$	1.00000			0.0707107
$201$	−1.68011	+	0.927070i	−0.118506	+	0.0653905i
$202$	2.25643	+	3.90825i	0.158762	+	0.274984i
$203$	−2.71482	+	0.0989386i	−0.190543	+	0.00694413i
$204$	−6.25691	−	3.77596i	−0.438071	−	0.264370i
$205$	−3.29918	−	5.71435i	−0.230425	−	0.399108i
$206$	2.18230	+	3.77985i	0.152048	+	0.263355i
$207$	1.02197	+	1.94005i	0.0710317	+	0.134843i
$208$	1.66295	−	2.88032i	0.115305	−	0.199714i
$209$	4.71568	−	8.16780i	0.326191	−	0.564979i
$210$	3.92899	−	2.35860i	0.271126	−	0.162759i
$211$	−10.4514	−	18.1024i	−0.719507	−	1.24622i	−0.961195	−	0.275869i	$-0.911034\pi$
$211$	−10.4514	−	18.1024i	−0.719507	−	1.24622i	0.241688	−	0.970354i	$-0.422299\pi$
$212$	−5.30912			−0.364632
$213$	4.32650	+	2.61099i	0.296447	+	0.178902i
$214$	−1.27474			−0.0871392
$215$	−1.24480	+	2.15606i	−0.0848948	+	0.147042i
$216$	−0.301948	+	5.18737i	−0.0205450	+	0.352956i
$217$	−27.8109	+	1.01354i	−1.88793	+	0.0688035i
$218$	−8.63456	+	14.9555i	−0.584806	+	1.01291i
$219$	0.385323	−	19.8791i	0.0260377	−	1.34330i
$220$	2.03999	−	3.53336i	0.137536	−	0.238219i
$221$	−7.01645	+	12.1529i	−0.471978	+	0.817489i
$222$	−1.92168	−	1.15971i	−0.128975	−	0.0778347i
$223$	−3.45757	+	5.98869i	−0.231536	+	0.401032i	−0.958260	−	0.285897i	$-0.907709\pi$
$223$	−3.45757	+	5.98869i	−0.231536	+	0.401032i	0.726724	+	0.686929i	$0.241042\pi$
$224$	2.64400	−	0.0963576i	0.176659	−	0.00643816i
$225$	1.39819	+	2.65425i	0.0932128	+	0.176950i
$226$	−9.68504	+	16.7750i	−0.644239	+	1.11586i
$227$	23.9477			1.58946			0.794731	−	0.606962i	$-0.207612\pi$
$227$	23.9477			1.58946			0.794731	+	0.606962i	$0.207612\pi$
$228$	−0.0775935	+	4.00310i	−0.00513875	+	0.265112i
$229$	13.4135			0.886391			0.443196	−	0.896425i	$-0.353845\pi$
$229$	13.4135			0.886391			0.443196	+	0.896425i	$0.353845\pi$
$230$	0.365460	+	0.632996i	0.0240977	+	0.0417385i
$231$	−0.318706	−	18.6941i	−0.0209693	−	1.22998i
$232$	0.513393	−	0.889223i	0.0337059	−	0.0583803i
$233$	−4.48461	+	7.76757i	−0.293797	+	0.508870i	−0.974704	−	0.223499i	$-0.928252\pi$
$233$	−4.48461	+	7.76757i	−0.293797	+	0.508870i	0.680908	+	0.732369i	$0.261585\pi$
$234$	9.97022	+	0.386658i	0.651774	+	0.0252766i
$235$	−2.75194	−	4.76650i	−0.179517	−	0.310932i
$236$	−2.98379	−	5.16808i	−0.194228	−	0.336413i
$237$	0.430913	−	22.2311i	0.0279908	−	1.44406i
$238$	−11.1557	+	0.406559i	−0.723119	+	0.0263533i
$239$	−10.2832	−	17.8110i	−0.665163	−	1.15210i	−0.979241	−	0.202699i	$-0.935029\pi$
$239$	−10.2832	−	17.8110i	−0.665163	−	1.15210i	0.314079	−	0.949397i	$-0.398304\pi$
$240$	−0.0335666	+	1.73173i	−0.00216672	+	0.111782i
$241$	16.1390			1.03961			0.519803	−	0.854286i	$-0.326005\pi$
$241$	16.1390			1.03961			0.519803	+	0.854286i	$0.326005\pi$
$242$	−2.82308	−	4.88972i	−0.181475	−	0.314323i
$243$	−14.1908	+	6.45150i	−0.910339	+	0.413864i
$244$	0.903244			0.0578242
$245$	3.04944	−	6.30087i	0.194822	−	0.402548i
$246$	10.0064	−	5.52147i	0.637987	−	0.352036i
$247$	7.68825			0.489191
$248$	5.25926	−	9.10930i	0.333963	−	0.578441i
$249$	−20.8224	+	11.4896i	−1.31957	+	0.728126i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	16.8254			1.06201			0.531005	−	0.847369i	$-0.321815\pi$
$251$	16.8254			1.06201			0.531005	+	0.847369i	$0.321815\pi$
$252$	3.95257	+	6.88311i	0.248989	+	0.433595i
$253$	2.98214			0.187485
$254$	6.91834	+	11.9829i	0.434095	+	0.751875i
$255$	0.141627	−	7.30662i	0.00886901	−	0.457559i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.5883			0.722859			0.361430	−	0.932399i	$-0.382289\pi$
$257$	11.5883			0.722859			0.361430	+	0.932399i	$0.382289\pi$
$258$	−3.69192	−	2.22803i	−0.229849	−	0.138711i
$259$	−3.42626	+	0.124866i	−0.212898	+	0.00775882i
$260$	3.32591			0.206264
$261$	3.07804	+	0.119370i	0.190526	+	0.00738884i
$262$	6.74013	+	11.6742i	0.416406	+	0.721237i
$263$	23.8152			1.46851			0.734255	−	0.678873i	$-0.237531\pi$
$263$	23.8152			1.46851			0.734255	+	0.678873i	$0.237531\pi$
$264$	6.05033	+	3.65130i	0.372372	+	0.224722i
$265$	−2.65456	−	4.59783i	−0.163068	−	0.282443i
$266$	3.24886	+	5.18171i	0.199201	+	0.317711i
$267$	22.0676	−	12.1767i	1.35052	−	0.745204i
$268$	−0.553942	−	0.959456i	−0.0338374	−	0.0586081i
$269$	−9.01902	−	15.6214i	−0.549899	−	0.952454i	−0.998281	−	0.0586113i	$-0.981333\pi$
$269$	−9.01902	−	15.6214i	−0.549899	−	0.952454i	0.448382	−	0.893842i	$-0.352001\pi$
$270$	−4.64337	+	2.33219i	−0.282587	+	0.141933i
$271$	−9.61907	+	16.6607i	−0.584317	+	1.01207i	0.410644	+	0.911796i	$0.365304\pi$
$271$	−9.61907	+	16.6607i	−0.584317	+	1.01207i	−0.994960	+	0.100270i	$0.968029\pi$
$272$	2.10964	−	3.65400i	0.127916	−	0.221556i
$273$	13.0675	−	7.84450i	0.790879	−	0.474770i
$274$	8.11165	+	14.0498i	0.490043	+	0.848779i
$275$	4.07997			0.246032
$276$	−1.10844	+	0.611630i	−0.0667204	+	0.0368158i
$277$	−17.9768			−1.08012			−0.540062	−	0.841626i	$-0.681599\pi$
$277$	−17.9768			−1.08012			−0.540062	+	0.841626i	$0.681599\pi$
$278$	8.37410	−	14.5044i	0.502245	−	0.869914i
$279$	31.5319	+	1.22285i	1.88776	+	0.0732098i
$280$	1.40545	+	2.24159i	0.0839915	+	0.133961i
$281$	−6.06170	+	10.4992i	−0.361610	+	0.626328i	−0.988226	−	0.153001i	$-0.951106\pi$
$281$	−6.06170	+	10.4992i	−0.361610	+	0.626328i	0.626616	+	0.779329i	$0.284440\pi$
$282$	8.34665	−	4.60561i	0.497036	−	0.274260i
$283$	0.620940	−	1.07550i	0.0369111	−	0.0639319i	−0.846980	−	0.531625i	$-0.821582\pi$
$283$	0.620940	−	1.07550i	0.0369111	−	0.0639319i	0.883891	+	0.467693i	$0.154915\pi$
$284$	−1.45876	+	2.52665i	−0.0865616	+	0.149929i
$285$	−3.50558	+	1.93435i	−0.207653	+	0.114581i
$286$	6.78480	−	11.7516i	0.401194	−	0.694888i
$287$	8.17240	−	15.4266i	0.482402	−	0.910605i
$288$	−2.99775	−	0.116256i	−0.176644	−	0.00685047i
$289$	−0.401134	+	0.694785i	−0.0235961	+	0.0408697i
$290$	1.02679			0.0602949
$291$	−22.3274	+	12.3201i	−1.30886	+	0.722217i
$292$	11.4794			0.671778
$293$	−3.66402	−	6.34628i	−0.214055	−	0.370753i	0.738925	−	0.673788i	$-0.235334\pi$
$293$	−3.66402	−	6.34628i	−0.214055	−	0.370753i	−0.952980	+	0.303034i	$0.902000\pi$
$294$	10.8090	+	5.49230i	0.630394	+	0.320317i
$295$	2.98379	−	5.16808i	0.173723	−	0.300897i
$296$	0.647932	−	1.12225i	0.0376603	−	0.0652296i
$297$	−1.23194	+	21.1643i	−0.0714845	+	1.22808i
$298$	−3.17404	−	5.49760i	−0.183867	−	0.318468i
$299$	1.21549	+	2.10528i	0.0702934	+	0.121752i
$300$	−1.51650	+	0.836793i	−0.0875553	+	0.0483123i
$301$	−6.58251	+	0.239892i	−0.379409	+	0.0138272i
$302$	−8.74873	−	15.1532i	−0.503433	−	0.871971i
$303$	−6.69228	−	4.03871i	−0.384461	−	0.232018i
$304$	−2.31162			−0.132581
$305$	0.451622	+	0.782232i	0.0258598	+	0.0447905i
$306$	12.6483	+	0.490518i	0.723056	+	0.0280410i
$307$	22.6002			1.28986			0.644930	−	0.764242i	$-0.276886\pi$
$307$	22.6002			1.28986			0.644930	+	0.764242i	$0.276886\pi$
$308$	10.7874	−	0.393136i	0.614671	−	0.0224010i
$309$	−6.47241	−	3.90602i	−0.368203	−	0.222206i
$310$	10.5185			0.597412
$311$	−11.3417	+	19.6445i	−0.643131	+	1.11394i	0.341599	+	0.939846i	$0.389032\pi$
$311$	−11.3417	+	19.6445i	−0.643131	+	1.11394i	−0.984730	+	0.174090i	$0.944302\pi$
$312$	−0.111639	+	5.75956i	−0.00632034	+	0.326071i
$313$	7.97587	+	13.8146i	0.450823	+	0.780848i	0.998437	−	0.0558825i	$-0.0177972\pi$
$313$	7.97587	+	13.8146i	0.450823	+	0.780848i	−0.547614	+	0.836731i	$0.684464\pi$
$314$	13.9358			0.786443
$315$	−3.98466	+	6.86458i	−0.224510	+	0.386775i
$316$	12.8375			0.722167
$317$	6.49094	+	11.2426i	0.364568	+	0.631450i	0.988707	−	0.149864i	$-0.0478835\pi$
$317$	6.49094	+	11.2426i	0.364568	+	0.631450i	−0.624139	+	0.781313i	$0.714550\pi$
$318$	8.05129	−	4.44264i	0.451494	−	0.249131i
$319$	2.09463	−	3.62800i	0.117277	−	0.203129i
$320$	−1.00000			−0.0559017
$321$	1.93314	−	1.06669i	0.107897	−	0.0595369i
$322$	−0.905282	+	1.70885i	−0.0504494	+	0.0952307i
$323$	9.75338			0.542692
$324$	−3.88285	−	8.11933i	−0.215714	−	0.451074i
$325$	1.66295	+	2.88032i	0.0922440	+	0.159771i
$326$	−15.6664			−0.867684
$327$	0.579666	−	29.9054i	0.0320556	−	1.65377i
$328$	3.29918	+	5.71435i	0.182167	+	0.315522i
$329$	6.81684	−	12.8678i	0.375824	−	0.709424i
$330$	−0.136951	+	7.06539i	−0.00753890	+	0.388937i
$331$	10.1379	+	17.5594i	0.557230	+	0.965150i	0.997726	+	0.0673959i	$0.0214690\pi$
$331$	10.1379	+	17.5594i	0.557230	+	0.965150i	−0.440497	+	0.897754i	$0.645198\pi$
$332$	−6.86528	−	11.8910i	−0.376781	−	0.652604i
$333$	3.88467	+	0.150653i	0.212879	+	0.00825571i
$334$	−11.6266	+	20.1379i	−0.636179	+	1.10189i
$335$	0.553942	−	0.959456i	0.0302651	−	0.0524207i
$336$	−3.92899	+	2.35860i	−0.214344	+	0.128672i
$337$	−17.2070	−	29.8034i	−0.937326	−	1.62350i	−0.770433	−	0.637521i	$-0.779960\pi$
$337$	−17.2070	−	29.8034i	−0.937326	−	1.62350i	−0.166892	−	0.985975i	$-0.553373\pi$
$338$	−1.93835			−0.105432
$339$	0.650188	−	33.5437i	0.0353134	−	1.82184i
$340$	4.21927			0.228822
$341$	21.4576	−	37.1657i	1.16200	−	2.01264i
$342$	−3.23210	−	6.13564i	−0.174772	−	0.331777i
$343$	18.4098	−	2.01993i	0.994035	−	0.109066i
$344$	1.24480	−	2.15606i	0.0671152	−	0.116247i
$345$	−1.08391	−	0.654125i	−0.0583556	−	0.0352169i
$346$	0.830725	−	1.43886i	0.0446601	−	0.0773535i
$347$	10.9928	−	19.0402i	0.590127	−	1.02213i	−0.404088	−	0.914720i	$-0.632411\pi$
$347$	10.9928	−	19.0402i	0.590127	−	1.02213i	0.994215	−	0.107410i	$-0.0342556\pi$
$348$	−0.0344657	+	1.77811i	−0.00184756	+	0.0953168i
$349$	9.29786	−	16.1044i	0.497703	−	0.862047i	−0.502293	−	0.864697i	$-0.667510\pi$
$349$	9.29786	−	16.1044i	0.497703	−	0.862047i	0.999996	+	0.00265023i	$0.000843597\pi$
$350$	−1.23855	+	2.33795i	−0.0662033	+	0.124969i
$351$	−15.4434	+	7.75665i	−0.824308	+	0.414019i
$352$	−2.03999	+	3.53336i	−0.108732	+	0.188329i
$353$	20.9201			1.11347			0.556733	−	0.830691i	$-0.312055\pi$
$353$	20.9201			1.11347			0.556733	+	0.830691i	$0.312055\pi$
$354$	8.84953	+	5.34058i	0.470347	+	0.283849i
$355$	−2.91752			−0.154846
$356$	7.27583	+	12.6021i	0.385618	+	0.667911i
$357$	16.5775	−	9.95160i	0.877374	−	0.526694i
$358$	3.21357	−	5.56606i	0.169842	−	0.294175i
$359$	−2.70799	+	4.69038i	−0.142922	+	0.247549i	−0.928596	−	0.371093i	$-0.878983\pi$
$359$	−2.70799	+	4.69038i	−0.142922	+	0.247549i	0.785674	+	0.618641i	$0.212317\pi$
$360$	−1.39819	−	2.65425i	−0.0736912	−	0.139891i
$361$	6.82820	+	11.8268i	0.359379	+	0.622462i
$362$	−1.82426	−	3.15971i	−0.0958810	−	0.166071i
$363$	8.37290	+	5.05294i	0.439463	+	0.265210i
$364$	4.67438	+	7.45531i	0.245004	+	0.390765i
$365$	5.73968	+	9.94141i	0.300428	+	0.520357i
$366$	−1.36977	+	0.755828i	−0.0715990	+	0.0395078i
$367$	−14.3169			−0.747337			−0.373669	−	0.927562i	$-0.621900\pi$
$367$	−14.3169			−0.747337			−0.373669	+	0.927562i	$0.621900\pi$
$368$	−0.365460	−	0.632996i	−0.0190509	−	0.0329972i
$369$	−10.5544	+	16.7466i	−0.549442	+	0.871795i
$370$	1.29586			0.0673688
$371$	6.57561	−	12.4124i	0.341389	−	0.644422i
$372$	−0.353071	+	18.2152i	−0.0183059	+	0.944413i
$373$	−25.8487			−1.33840			−0.669199	−	0.743084i	$-0.733362\pi$
$373$	−25.8487			−1.33840			−0.669199	+	0.743084i	$0.733362\pi$
$374$	8.60726	−	14.9082i	0.445071	−	0.770885i
$375$	−1.48293	−	0.894932i	−0.0765784	−	0.0462141i
$376$	2.75194	+	4.76650i	0.141921	+	0.245814i
$377$	3.41499			0.175881
$378$	−11.7538	−	7.13076i	−0.604551	−	0.366767i
$379$	19.9647			1.02552			0.512758	−	0.858533i	$-0.328624\pi$
$379$	19.9647			1.02552			0.512758	+	0.858533i	$0.328624\pi$
$380$	−1.15581	−	2.00193i	−0.0592919	−	0.102697i
$381$	−20.5189	−	12.3829i	−1.05121	−	0.634395i
$382$	5.22286	−	9.04626i	0.267225	−	0.462847i
$383$	10.1961			0.520996			0.260498	−	0.965474i	$-0.416113\pi$
$383$	10.1961			0.520996			0.260498	+	0.965474i	$0.416113\pi$
$384$	0.0335666	−	1.73173i	0.00171294	−	0.0883717i
$385$	5.73418	+	9.14562i	0.292241	+	0.466104i
$386$	18.1442			0.923515
$387$	7.46320	+	0.289432i	0.379376	+	0.0147127i
$388$	−7.36150	−	12.7505i	−0.373723	−	0.647308i
$389$	−23.2341			−1.17802			−0.589009	−	0.808127i	$-0.700482\pi$
$389$	−23.2341			−1.17802			−0.589009	+	0.808127i	$0.700482\pi$
$390$	−5.04374	+	2.78310i	−0.255400	+	0.140928i
$391$	1.54198	+	2.67078i	0.0779811	+	0.135067i
$392$	−3.04944	+	6.30087i	−0.154020	+	0.318242i
$393$	−19.9903	−	12.0639i	−1.00838	−	0.608544i
$394$	4.26751	+	7.39154i	0.214994	+	0.372380i
$395$	6.41876	+	11.1176i	0.322963	+	0.559388i
$396$	−12.2307	−	0.474323i	−0.614617	−	0.0238356i
$397$	−16.2529	+	28.1508i	−0.815708	+	1.41285i	0.0931112	+	0.995656i	$0.470319\pi$
$397$	−16.2529	+	28.1508i	−0.815708	+	1.41285i	−0.908819	+	0.417191i	$0.863015\pi$
$398$	−3.48948	+	6.04396i	−0.174912	+	0.302957i
$399$	−9.26293	−	5.13945i	−0.463726	−	0.257294i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−8.29152			−0.414059			−0.207029	−	0.978335i	$-0.566380\pi$
$401$	−8.29152			−0.414059			−0.207029	+	0.978335i	$0.566380\pi$
$402$	1.64292	+	0.991481i	0.0819414	+	0.0494506i
$403$	34.9836			1.74266
$404$	2.25643	−	3.90825i	0.112262	−	0.194443i
$405$	5.09012	−	7.42231i	0.252930	−	0.368818i
$406$	1.44309	+	2.30163i	0.0716195	+	0.114228i
$407$	2.64355	−	4.57876i	0.131036	−	0.226961i
$408$	−0.141627	+	7.30662i	−0.00701157	+	0.361732i
$409$	−8.73096	+	15.1225i	−0.431718	+	0.747758i	−0.997021	−	0.0771251i	$-0.975426\pi$
$409$	−8.73096	+	15.1225i	−0.431718	+	0.747758i	0.565303	+	0.824883i	$0.308759\pi$
$410$	−3.29918	+	5.71435i	−0.162935	+	0.282212i
$411$	−24.0581	−	14.5188i	−1.18670	−	0.716158i
$412$	2.18230	−	3.77985i	0.107514	−	0.186220i
$413$	15.7783	−	0.575022i	0.776397	−	0.0282950i
$414$	1.16915	−	1.85507i	0.0574605	−	0.0911719i
$415$	6.86528	−	11.8910i	0.337003	−	0.583707i
$416$	−3.32591			−0.163066
$417$	−0.562181	+	29.0033i	−0.0275301	+	1.42030i
$418$	−9.43136			−0.461303
$419$	−11.3255	−	19.6163i	−0.553286	−	0.958319i	−0.998035	−	0.0626640i	$-0.980040\pi$
$419$	−11.3255	−	19.6163i	−0.553286	−	0.958319i	0.444749	−	0.895655i	$-0.353293\pi$
$420$	−4.00711	−	2.22331i	−0.195527	−	0.108486i
$421$	4.80724	−	8.32639i	0.234291	−	0.405803i	−0.724776	−	0.688985i	$-0.758057\pi$
$421$	4.80724	−	8.32639i	0.234291	−	0.405803i	0.959066	+	0.283182i	$0.0913899\pi$
$422$	−10.4514	+	18.1024i	−0.508768	+	0.881213i
$423$	−8.80376	+	13.9688i	−0.428054	+	0.679188i
$424$	2.65456	+	4.59783i	0.128917	+	0.223291i
$425$	2.10964	+	3.65400i	0.102332	+	0.177245i
$426$	0.0979315	−	5.05235i	0.00474480	−	0.244787i
$427$	−1.11871	+	2.11174i	−0.0541383	+	0.102194i
$428$	0.637368	+	1.10395i	0.0308084	+	0.0533616i
$429$	−0.455486	+	23.4988i	−0.0219911	+	1.13453i
$430$	2.48960			0.120059
$431$	−3.40302	−	5.89421i	−0.163918	−	0.283914i	0.772353	−	0.635194i	$-0.219080\pi$
$431$	−3.40302	−	5.89421i	−0.163918	−	0.283914i	−0.936270	+	0.351280i	$0.885747\pi$
$432$	4.64337	−	2.33219i	0.223404	−	0.112208i
$433$	−30.4675			−1.46417			−0.732087	−	0.681211i	$-0.761454\pi$
$433$	−30.4675			−1.46417			−0.732087	+	0.681211i	$0.761454\pi$
$434$	14.7832	+	23.5782i	0.709617	+	1.13179i
$435$	−1.55712	+	0.859207i	−0.0746583	+	0.0411958i
$436$	17.2691			0.827041
$437$	0.844807	−	1.46325i	0.0404126	−	0.0699967i
$438$	−17.4085	+	9.60584i	−0.831808	+	0.458985i
$439$	6.99011	+	12.1072i	0.333620	+	0.577846i	0.983219	−	0.182431i	$-0.0583966\pi$
$439$	6.99011	+	12.1072i	0.333620	+	0.577846i	−0.649599	+	0.760277i	$0.725063\pi$
$440$	−4.07997			−0.194505
$441$	−20.9878	+	0.715830i	−0.999419	+	0.0340872i
$442$	14.0329			0.667477
$443$	4.00175	+	6.93123i	0.190129	+	0.329313i	0.945293	−	0.326223i	$-0.105776\pi$
$443$	4.00175	+	6.93123i	0.190129	+	0.329313i	−0.755164	+	0.655536i	$0.772443\pi$
$444$	−0.0434978	+	2.24408i	−0.00206432	+	0.106499i
$445$	−7.27583	+	12.6021i	−0.344908	+	0.597397i
$446$	6.91515			0.327442
$447$	9.41380	+	5.68111i	0.445257	+	0.268707i
$448$	−1.40545	−	2.24159i	−0.0664011	−	0.105905i
$449$	−37.4636			−1.76801			−0.884007	−	0.467473i	$-0.845165\pi$
$449$	−37.4636			−1.76801			−0.884007	+	0.467473i	$0.845165\pi$
$450$	1.59955	−	2.53800i	0.0754037	−	0.119642i
$451$	13.4606	+	23.3144i	0.633834	+	1.09783i
$452$	19.3701			0.911092
$453$	25.9476	+	15.6590i	1.21912	+	0.735726i
$454$	−11.9738	−	20.7393i	−0.561960	−	0.973343i
$455$	−4.11930	+	7.77579i	−0.193116	+	0.364535i
$456$	3.50558	−	1.93435i	0.164164	−	0.0905843i
$457$	−4.53133	−	7.84849i	−0.211967	−	0.367137i	0.740363	−	0.672207i	$-0.234653\pi$
$457$	−4.53133	−	7.84849i	−0.211967	−	0.367137i	−0.952330	+	0.305070i	$0.901320\pi$
$458$	−6.70677	−	11.6165i	−0.313387	−	0.542802i
$459$	−19.5916	+	9.84015i	−0.914460	+	0.459299i
$460$	0.365460	−	0.632996i	0.0170397	−	0.0295136i
$461$	−14.7896	+	25.6163i	−0.688818	+	1.19307i	0.283402	+	0.959001i	$0.408537\pi$
$461$	−14.7896	+	25.6163i	−0.688818	+	1.19307i	−0.972221	+	0.234067i	$0.924797\pi$
$462$	−16.0302	+	9.62304i	−0.745791	+	0.447704i
$463$	−8.49546	−	14.7146i	−0.394817	−	0.683844i	0.598261	−	0.801302i	$-0.295859\pi$
$463$	−8.49546	−	14.7146i	−0.394817	−	0.683844i	−0.993078	+	0.117458i	$0.962525\pi$
$464$	−1.02679			−0.0476673
$465$	−15.9514	+	8.80182i	−0.739726	+	0.408175i
$466$	8.96922			0.415491
$467$	18.5392	−	32.1108i	0.857891	−	1.48591i	−0.0160450	−	0.999871i	$-0.505108\pi$
$467$	18.5392	−	32.1108i	0.857891	−	1.48591i	0.873936	−	0.486040i	$-0.161559\pi$
$468$	−4.65026	−	8.82779i	−0.214958	−	0.408065i
$469$	2.92924	−	0.106753i	0.135260	−	0.00492940i
$470$	−2.75194	+	4.76650i	−0.126938	+	0.219862i
$471$	−21.1337	+	11.6614i	−0.973789	+	0.537329i
$472$	−2.98379	+	5.16808i	−0.137340	+	0.237880i
$473$	5.07876	−	8.79667i	0.233522	−	0.404471i
$474$	−19.4681	+	10.7424i	−0.894201	+	0.493413i
$475$	1.15581	−	2.00193i	0.0530323	−	0.0918547i
$476$	5.92996	+	9.45788i	0.271799	+	0.433501i
$477$	−8.49223	+	13.4745i	−0.388832	+	0.616956i
$478$	−10.2832	+	17.8110i	−0.470341	+	0.814655i
$479$	3.91130			0.178712			0.0893560	−	0.996000i	$-0.471519\pi$
$479$	3.91130			0.178712			0.0893560	+	0.996000i	$0.471519\pi$
$480$	1.51650	−	0.836793i	0.0692185	−	0.0381942i
$481$	4.30992			0.196516
$482$	−8.06952	−	13.9768i	−0.367556	−	0.636627i
$483$	−0.0570958	−	3.34901i	−0.00259795	−	0.152385i
$484$	−2.82308	+	4.88972i	−0.128322	+	0.222260i
$485$	7.36150	−	12.7505i	0.334268	−	0.578970i
$486$	12.6825	+	9.06383i	0.575292	+	0.411144i
$487$	−2.95611	−	5.12014i	−0.133954	−	0.232016i	0.791243	−	0.611502i	$-0.209434\pi$
$487$	−2.95611	−	5.12014i	−0.133954	−	0.232016i	−0.925198	+	0.379486i	$0.876101\pi$
$488$	−0.451622	−	0.782232i	−0.0204440	−	0.0354100i
$489$	23.7582	−	13.1096i	1.07438	−	0.592835i
$490$	−6.98143	+	0.509538i	−0.315389	+	0.0230186i
$491$	2.72890	+	4.72659i	0.123153	+	0.213308i	0.921010	−	0.389540i	$-0.127366\pi$
$491$	2.72890	+	4.72659i	0.123153	+	0.213308i	−0.797856	+	0.602848i	$0.794033\pi$
$492$	−9.78495	−	5.90509i	−0.441139	−	0.266222i
$493$	4.33229			0.195117
$494$	−3.84412	−	6.65822i	−0.172955	−	0.299567i
$495$	−5.70458	−	10.8293i	−0.256402	−	0.486740i
$496$	−10.5185			−0.472295
$497$	−4.10042	−	6.53989i	−0.183929	−	0.293354i
$498$	20.3615	+	12.2879i	0.912422	+	0.550635i
$499$	−38.0988			−1.70554			−0.852768	−	0.522290i	$-0.825078\pi$
$499$	−38.0988			−1.70554			−0.852768	+	0.522290i	$0.825078\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	0.780531	−	40.2681i	0.0348716	−	1.79905i
$502$	−8.41270	−	14.5712i	−0.375477	−	0.650346i
$503$	−32.2093			−1.43614			−0.718070	−	0.695971i	$-0.754974\pi$
$503$	−32.2093			−1.43614			−0.718070	+	0.695971i	$0.754974\pi$
$504$	3.98466	−	6.86458i	0.177491	−	0.305773i
$505$	4.51286			0.200820
$506$	−1.49107	−	2.58261i	−0.0662861	−	0.114811i
$507$	2.93951	−	1.62200i	0.130548	−	0.0720356i
$508$	6.91834	−	11.9829i	0.306952	−	0.531656i
$509$	4.02518			0.178413			0.0892066	−	0.996013i	$-0.471567\pi$
$509$	4.02518			0.178413			0.0892066	+	0.996013i	$0.471567\pi$
$510$	−6.39854	+	3.53066i	−0.283332	+	0.156340i
$511$	−14.2178	+	26.8381i	−0.628956	+	1.18725i
$512$	1.00000			0.0441942
$513$	10.0357	+	6.60011i	0.443089	+	0.291402i
$514$	−5.79416	−	10.0358i	−0.255569	−	0.442659i
$515$	4.36460			0.192327
$516$	−0.0835677	+	4.31131i	−0.00367886	+	0.189795i
$517$	11.2278	+	19.4472i	0.493800	+	0.855287i
$518$	1.82127	+	2.90480i	0.0800219	+	0.127629i
$519$	−0.0557693	+	2.87718i	−0.00244800	+	0.126294i
$520$	−1.66295	−	2.88032i	−0.0729253	−	0.126310i
$521$	15.5722	+	26.9719i	0.682232	+	1.18166i	0.974298	+	0.225262i	$0.0723239\pi$
$521$	15.5722	+	26.9719i	0.682232	+	1.18166i	−0.292066	+	0.956398i	$0.594343\pi$
$522$	−1.43564	−	2.72535i	−0.0628364	−	0.119285i
$523$	11.9779	−	20.7464i	0.523759	−	0.907177i	−0.475859	−	0.879522i	$-0.657863\pi$
$523$	11.9779	−	20.7464i	0.523759	−	0.907177i	0.999618	−	0.0276550i	$-0.00880398\pi$
$524$	6.74013	−	11.6742i	0.294444	−	0.509992i
$525$	−0.0781148	−	4.58191i	−0.00340921	−	0.199971i
$526$	−11.9076	−	20.6246i	−0.519197	−	0.899276i
$527$	44.3805			1.93325
$528$	0.136951	−	7.06539i	0.00596002	−	0.307482i
$529$	−22.4658			−0.976772
$530$	−2.65456	+	4.59783i	−0.115307	+	0.199717i
$531$	−17.8893	−	0.693769i	−0.776329	−	0.0301070i
$532$	2.86306	−	5.40446i	0.124130	−	0.234313i
$533$	−10.9728	+	19.0054i	−0.475283	+	0.823215i
$534$	−21.5792	−	13.0228i	−0.933822	−	0.563550i
$535$	−0.637368	+	1.10395i	−0.0275558	+	0.0477281i
$536$	−0.553942	+	0.959456i	−0.0239267	+	0.0414422i
$537$	−0.215737	+	11.1300i	−0.00930974	+	0.480296i
$538$	−9.01902	+	15.6214i	−0.388838	+	0.673486i
$539$	−12.4416	+	25.7074i	−0.535899	+	1.10729i
$540$	4.34142	+	2.85518i	0.186825	+	0.122867i
$541$	12.7810	−	22.1374i	0.549499	−	0.951760i	−0.448810	−	0.893627i	$-0.648152\pi$
$541$	12.7810	−	22.1374i	0.549499	−	0.951760i	0.998309	−	0.0581329i	$-0.0185147\pi$
$542$	19.2381			0.826349
$543$	5.41052	+	3.26518i	0.232188	+	0.140122i
$544$	−4.21927			−0.180900
$545$	8.63456	+	14.9555i	0.369864	+	0.640623i
$546$	−13.3273	−	7.39450i	−0.570354	−	0.316456i
$547$	−3.70248	+	6.41288i	−0.158306	+	0.274195i	−0.934258	−	0.356598i	$-0.883937\pi$
$547$	−3.70248	+	6.41288i	−0.158306	+	0.274195i	0.775952	+	0.630792i	$0.217270\pi$
$548$	8.11165	−	14.0498i	0.346513	−	0.600177i
$549$	1.44479	−	2.29243i	0.0616620	−	0.0978385i
$550$	−2.03999	−	3.53336i	−0.0869853	−	0.150663i
$551$	−1.18677	−	2.05555i	−0.0505582	−	0.0875693i
$552$	1.08391	+	0.654125i	0.0461342	+	0.0278414i
$553$	−15.8999	+	30.0135i	−0.676133	+	1.27630i
$554$	8.98842	+	15.5684i	0.381881	+	0.661438i
$555$	−1.96518	+	1.08437i	−0.0834173	+	0.0460290i
$556$	−16.7482			−0.710282
$557$	−23.3296	−	40.4080i	−0.988506	−	1.71214i	−0.625180	−	0.780480i	$-0.714975\pi$
$557$	−23.3296	−	40.4080i	−0.988506	−	1.71214i	−0.363326	−	0.931662i	$-0.618359\pi$
$558$	−14.7069	−	27.9188i	−0.622593	−	1.18190i
$559$	8.28019			0.350215
$560$	1.23855	−	2.33795i	0.0523383	−	0.0987963i
$561$	−0.577833	+	29.8108i	−0.0243961	+	1.25861i
$562$	12.1234			0.511394
$563$	−8.24534	+	14.2813i	−0.347500	+	0.601887i	−0.985805	−	0.167897i	$-0.946303\pi$
$563$	−8.24534	+	14.2813i	−0.347500	+	0.601887i	0.638305	+	0.769784i	$0.279636\pi$
$564$	−8.16190	−	4.92561i	−0.343678	−	0.207405i
$565$	9.68504	+	16.7750i	0.407453	+	0.705729i
$566$	−1.24188			−0.0522002
$567$	23.7917	+	0.978290i	0.999156	+	0.0410843i
$568$	2.91752			0.122417
$569$	−9.71635	−	16.8292i	−0.407330	−	0.705517i	0.587259	−	0.809399i	$-0.300207\pi$
$569$	−9.71635	−	16.8292i	−0.407330	−	0.705517i	−0.994590	+	0.103882i	$0.966874\pi$
$570$	3.42799	+	2.06875i	0.143583	+	0.0866503i
$571$	11.5585	−	20.0199i	0.483709	−	0.837808i	−0.516116	−	0.856519i	$-0.672623\pi$
$571$	11.5585	−	20.0199i	0.483709	−	0.837808i	0.999825	+	0.0187103i	$0.00595601\pi$
$572$	−13.5696			−0.567373
$573$	−0.350628	+	18.0891i	−0.0146477	+	0.755684i
$574$	−17.4461	+	0.635803i	−0.728184	+	0.0265379i
$575$	0.730921			0.0304815
$576$	1.39819	+	2.65425i	0.0582580	+	0.110594i
$577$	4.92535	+	8.53096i	0.205045	+	0.355149i	0.950147	−	0.311802i	$-0.100933\pi$
$577$	4.92535	+	8.53096i	0.205045	+	0.355149i	−0.745102	+	0.666951i	$0.767599\pi$
$578$	0.802269			0.0333700
$579$	−27.5157	+	15.1829i	−1.14351	+	0.630981i
$580$	−0.513393	−	0.889223i	−0.0213175	−	0.0369230i
$581$	36.3035	−	1.32304i	1.50612	−	0.0548891i
$582$	21.8332	+	13.1761i	0.905017	+	0.546166i
$583$	10.8305	+	18.7590i	0.448555	+	0.776920i
$584$	−5.73968	−	9.94141i	−0.237510	−	0.411379i
$585$	5.31997	−	8.44114i	0.219954	−	0.348998i
$586$	−3.66402	+	6.34628i	−0.151359	+	0.262162i
$587$	−21.0981	+	36.5429i	−0.870811	+	1.50829i	−0.00965097	+	0.999953i	$0.503072\pi$
$587$	−21.0981	+	36.5429i	−0.870811	+	1.50829i	−0.861160	+	0.508335i	$0.830261\pi$
$588$	−0.648037	−	12.1070i	−0.0267246	−	0.499285i
$589$	−12.1574	−	21.0573i	−0.500938	−	0.867651i
$590$	−5.96758			−0.245681
$591$	−12.6569	−	7.63826i	−0.520634	−	0.314196i
$592$	−1.29586			−0.0532597
$593$	19.0345	−	32.9687i	0.781652	−	1.35386i	−0.149326	−	0.988788i	$-0.547711\pi$
$593$	19.0345	−	32.9687i	0.781652	−	1.35386i	0.930979	−	0.365074i	$-0.118956\pi$
$594$	18.9448	−	9.51527i	0.777315	−	0.390416i
$595$	−5.22578	+	9.86444i	−0.214236	+	0.404402i
$596$	−3.17404	+	5.49760i	−0.130014	+	0.225191i
$597$	0.234260	−	12.0857i	0.00958764	−	0.494633i
$598$	1.21549	−	2.10528i	0.0497049	−	0.0860915i
$599$	−5.13032	+	8.88597i	−0.209619	+	0.363071i	−0.951595	−	0.307356i	$-0.900556\pi$
$599$	−5.13032	+	8.88597i	−0.209619	+	0.363071i	0.741976	+	0.670427i	$0.233889\pi$
$600$	1.48293	+	0.894932i	0.0605406	+	0.0365355i
$601$	23.8726	−	41.3486i	0.973785	−	1.68664i	0.289896	−	0.957058i	$-0.406379\pi$
$601$	23.8726	−	41.3486i	0.973785	−	1.68664i	0.683889	−	0.729586i	$-0.260287\pi$
$602$	3.49901	+	5.58067i	0.142609	+	0.227451i
$603$	−3.32116	−	0.128799i	−0.135248	−	0.00524508i
$604$	−8.74873	+	15.1532i	−0.355981	+	0.616577i
$605$	−5.64617			−0.229549
$606$	−0.151482	+	7.81504i	−0.00615352	+	0.317464i
$607$	39.6189			1.60808			0.804042	−	0.594573i	$-0.202679\pi$
$607$	39.6189			1.60808			0.804042	+	0.594573i	$0.202679\pi$
$608$	1.15581	+	2.00193i	0.0468744	+	0.0811888i
$609$	−4.11444	−	2.28286i	−0.166726	−	0.0925061i
$610$	0.451622	−	0.782232i	0.0182856	−	0.0316716i
$611$	−9.15270	+	15.8529i	−0.370279	+	0.641341i
$612$	−5.89936	−	11.1990i	−0.238467	−	0.452694i
$613$	8.09836	+	14.0268i	0.327090	+	0.566536i	0.981933	−	0.189229i	$-0.0605988\pi$
$613$	8.09836	+	14.0268i	0.327090	+	0.566536i	−0.654843	+	0.755765i	$0.727265\pi$
$614$	−11.3001	−	19.5723i	−0.456034	−	0.789875i
$615$	0.221485	−	11.4266i	0.00893113	−	0.460763i
$616$	−5.73418	−	9.14562i	−0.231037	−	0.368487i
$617$	10.7676	+	18.6501i	0.433488	+	0.750824i	0.997171	−	0.0751677i	$-0.0239492\pi$
$617$	10.7676	+	18.6501i	0.433488	+	0.750824i	−0.563683	+	0.825991i	$0.690616\pi$
$618$	−0.146505	+	7.55829i	−0.00589329	+	0.304039i
$619$	−14.2232			−0.571680			−0.285840	−	0.958277i	$-0.592273\pi$
$619$	−14.2232			−0.571680			−0.285840	+	0.958277i	$0.592273\pi$
$620$	−5.25926	−	9.10930i	−0.211217	−	0.365838i
$621$	−0.220700	+	3.79156i	−0.00885640	+	0.152150i
$622$	22.6835			0.909525
$623$	−38.4745	+	1.40216i	−1.54145	+	0.0561765i
$624$	5.04374	−	2.78310i	0.201911	−	0.111413i
$625$	1.00000			0.0400000
$626$	7.97587	−	13.8146i	0.318780	−	0.552143i
$627$	14.3027	−	7.89210i	0.571194	−	0.315180i
$628$	−6.96791	−	12.0688i	−0.278050	−	0.481596i
$629$	5.46761			0.218008
$630$	7.93723	+	0.0185258i	0.316227	+	0.000738086i
$631$	−3.76778			−0.149993			−0.0749965	−	0.997184i	$-0.523895\pi$
$631$	−3.76778			−0.149993			−0.0749965	+	0.997184i	$0.523895\pi$
$632$	−6.41876	−	11.1176i	−0.255325	−	0.442235i
$633$	0.701640	−	36.1981i	0.0278877	−	1.43874i
$634$	6.49094	−	11.2426i	0.257788	−	0.446502i
$635$	13.8367			0.549092
$636$	−7.87308	−	4.75130i	−0.312188	−	0.188401i
$637$	−23.2196	+	1.69468i	−0.919993	+	0.0671455i
$638$	−4.18926			−0.165854
$639$	4.07926	+	7.74385i	0.161373	+	0.306342i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	15.0808			0.595656			0.297828	−	0.954620i	$-0.403738\pi$
$641$	15.0808			0.595656			0.297828	+	0.954620i	$0.403738\pi$
$642$	−1.89035	−	1.14080i	−0.0746062	−	0.0450239i
$643$	−3.00458	−	5.20409i	−0.118489	−	0.205229i	0.800680	−	0.599092i	$-0.204472\pi$
$643$	−3.00458	−	5.20409i	−0.118489	−	0.205229i	−0.919169	+	0.393863i	$0.871138\pi$
$644$	1.93255	−	0.0704298i	0.0761532	−	0.00277532i
$645$	−3.77549	+	2.08328i	−0.148660	+	0.0820292i
$646$	−4.87669	−	8.44667i	−0.191871	−	0.332330i
$647$	22.3007	+	38.6259i	0.876731	+	1.51854i	0.854908	+	0.518780i	$0.173614\pi$
$647$	22.3007	+	38.6259i	0.876731	+	1.51854i	0.0218228	+	0.999762i	$0.493053\pi$
$648$	−5.09012	+	7.42231i	−0.199959	+	0.291576i
$649$	−12.1738	+	21.0856i	−0.477863	+	0.827682i
$650$	1.66295	−	2.88032i	0.0652264	−	0.112975i
$651$	−42.1488	−	23.3859i	−1.65194	−	0.916565i
$652$	7.83322	+	13.5675i	0.306773	+	0.531346i
$653$	−6.90678			−0.270283			−0.135142	−	0.990826i	$-0.543149\pi$
$653$	−6.90678			−0.270283			−0.135142	+	0.990826i	$0.543149\pi$
$654$	−26.1886	+	14.4507i	−1.02406	+	0.565066i
$655$	13.4803			0.526717
$656$	3.29918	−	5.71435i	0.128811	−	0.223108i
$657$	18.3618	−	29.1346i	0.716364	−	1.13665i
$658$	−14.5523	+	0.530341i	−0.567306	+	0.0206748i
$659$	−14.8057	+	25.6441i	−0.576746	+	0.998954i	0.419103	+	0.907939i	$0.362345\pi$
$659$	−14.8057	+	25.6441i	−0.576746	+	0.998954i	−0.995849	+	0.0910154i	$0.970989\pi$
$660$	6.18728	−	3.41409i	0.240840	−	0.132893i
$661$	14.8614	−	25.7407i	0.578041	−	1.00120i	−0.417662	−	0.908602i	$-0.637151\pi$
$661$	14.8614	−	25.7407i	0.578041	−	1.00120i	0.995704	−	0.0925948i	$-0.0295161\pi$
$662$	10.1379	−	17.5594i	0.394021	−	0.682464i
$663$	−21.2809	+	11.7426i	−0.826483	+	0.456046i
$664$	−6.86528	+	11.8910i	−0.266425	+	0.461461i
$665$	6.11193	−	0.222743i	0.237010	−	0.00863759i
$666$	−1.81187	−	3.43955i	−0.0702085	−	0.133280i
$667$	0.375250	−	0.649951i	0.0145297	−	0.0251662i
$668$	23.2532			0.899693
$669$	−10.4868	+	5.78655i	−0.405444	+	0.223721i
$670$	−1.10788			−0.0428013
$671$	−1.84260	−	3.19148i	−0.0711329	−	0.123206i
$672$	4.00711	+	2.22331i	0.154578	+	0.0857659i
$673$	18.6415	−	32.2880i	0.718575	−	1.24461i	−0.242989	−	0.970029i	$-0.578128\pi$
$673$	18.6415	−	32.2880i	0.718575	−	1.24461i	0.961564	−	0.274580i	$-0.0885389\pi$
$674$	−17.2070	+	29.8034i	−0.662789	+	1.14798i
$675$	−0.301948	+	5.18737i	−0.0116220	+	0.199662i
$676$	0.969176	+	1.67866i	0.0372760	+	0.0645639i
$677$	−5.28575	−	9.15519i	−0.203148	−	0.351862i	0.746393	−	0.665505i	$-0.231784\pi$
$677$	−5.28575	−	9.15519i	−0.203148	−	0.351862i	−0.949541	+	0.313643i	$0.898451\pi$
$678$	−29.3748	+	16.2087i	−1.12813	+	0.622493i
$679$	38.9275	−	1.41867i	1.49390	−	0.0544436i
$680$	−2.10964	−	3.65400i	−0.0809009	−	0.140124i
$681$	35.5128	+	21.4315i	1.36085	+	0.821258i
$682$	−42.9153			−1.64331
$683$	1.44233	+	2.49820i	0.0551894	+	0.0955909i	0.892300	−	0.451443i	$-0.149090\pi$
$683$	1.44233	+	2.49820i	0.0551894	+	0.0955909i	−0.837111	+	0.547033i	$0.815757\pi$
$684$	−3.69757	+	5.86690i	−0.141380	+	0.224326i
$685$	16.2233			0.619861
$686$	−10.9542	−	14.9334i	−0.418233	−	0.570159i
$687$	19.8914	+	12.0042i	0.758904	+	0.457989i
$688$	−2.48960			−0.0949153
$689$	−8.82882	+	15.2920i	−0.336351	+	0.582577i
$690$	−0.0245345	+	1.26575i	−0.000934014	+	0.0481864i
$691$	−25.3800	−	43.9594i	−0.965501	−	1.67230i	−0.708264	−	0.705947i	$-0.750521\pi$
$691$	−25.3800	−	43.9594i	−0.965501	−	1.67230i	−0.257236	−	0.966349i	$-0.582812\pi$
$692$	−1.66145			−0.0631589
$693$	16.2573	−	28.0073i	0.617564	−	1.06391i
$694$	−21.9857			−0.834565
$695$	−8.37410	−	14.5044i	−0.317648	−	0.550182i
$696$	1.55712	−	0.859207i	0.0590226	−	0.0325682i
$697$	−13.9202	+	24.1104i	−0.527263	+	0.913247i
$698$	−18.5957			−0.703858
$699$	−13.6018	+	7.50538i	−0.514469	+	0.283880i
$700$	2.64400	−	0.0963576i	0.0999337	−	0.00364197i
$701$	21.1533			0.798949			0.399474	−	0.916744i	$-0.369193\pi$
$701$	21.1533			0.798949			0.399474	+	0.916744i	$0.369193\pi$
$702$	14.4392	+	9.49606i	0.544971	+	0.358406i
$703$	−1.49778	−	2.59423i	−0.0564897	−	0.0978431i
$704$	4.07997			0.153770
$705$	0.184747	−	9.53122i	0.00695797	−	0.358966i
$706$	−10.4601	−	18.1174i	−0.393670	−	0.681856i
$707$	6.34258	+	10.1160i	0.238537	+	0.380451i
$708$	0.200312	−	10.3342i	0.00752817	−	0.388383i
$709$	4.34289	+	7.52210i	0.163101	+	0.282498i	0.935979	−	0.352056i	$-0.114517\pi$
$709$	4.34289	+	7.52210i	0.163101	+	0.282498i	−0.772879	+	0.634554i	$0.781184\pi$
$710$	1.45876	+	2.52665i	0.0547464	+	0.0948235i
$711$	20.5343	−	32.5816i	0.770097	−	1.22191i
$712$	7.27583	−	12.6021i	0.272673	−	0.472284i
$713$	3.84410	−	6.65818i	0.143963	−	0.249351i
$714$	−16.9071	−	9.38073i	−0.632732	−	0.351065i
$715$	−6.78480	−	11.7516i	−0.253737	−	0.439486i
$716$	−6.42713			−0.240193
$717$	0.690342	−	35.6152i	0.0257813	−	1.33008i
$718$	5.41598			0.202123
$719$	−15.4039	+	26.6804i	−0.574470	+	0.995011i	0.421629	+	0.906768i	$0.361458\pi$
$719$	−15.4039	+	26.6804i	−0.574470	+	0.995011i	−0.996099	+	0.0882427i	$0.971875\pi$
$720$	−1.59955	+	2.53800i	−0.0596119	+	0.0945855i
$721$	6.13421	+	9.78363i	0.228450	+	0.364362i
$722$	6.82820	−	11.8268i	0.254119	−	0.440147i
$723$	23.9331	+	14.4433i	0.890083	+	0.537154i
$724$	−1.82426	+	3.15971i	−0.0677981	+	0.117430i
$725$	0.513393	−	0.889223i	0.0190669	−	0.0330249i
$726$	0.189523	−	9.77761i	0.00703385	−	0.362881i
$727$	−22.6843	+	39.2904i	−0.841315	+	1.45720i	0.0474691	+	0.998873i	$0.484884\pi$
$727$	−22.6843	+	39.2904i	−0.841315	+	1.45720i	−0.888784	+	0.458327i	$0.848449\pi$
$728$	4.11930	−	7.77579i	0.152671	−	0.288190i
$729$	−26.8177	−	3.13264i	−0.993246	−	0.116024i
$730$	5.73968	−	9.94141i	0.212435	−	0.367948i
$731$	10.5043			0.388516
$732$	1.33945	+	0.808342i	0.0495076	+	0.0298772i
$733$	13.8773			0.512568			0.256284	−	0.966601i	$-0.417502\pi$
$733$	13.8773			0.512568			0.256284	+	0.966601i	$0.417502\pi$
$734$	7.15846	+	12.3988i	0.264224	+	0.457649i
$735$	10.1610	−	6.61473i	0.374793	−	0.243988i
$736$	−0.365460	+	0.632996i	−0.0134710	+	0.0233325i
$737$	−2.26007	+	3.91455i	−0.0832507	+	0.144194i
$738$	19.7802	+	0.767102i	0.728120	+	0.0282374i
$739$	−15.4756	−	26.8045i	−0.569278	−	0.986018i	−0.996638	−	0.0819362i	$-0.973890\pi$
$739$	−15.4756	−	26.8045i	−0.569278	−	0.986018i	0.427360	−	0.904082i	$-0.359444\pi$
$740$	−0.647932	−	1.12225i	−0.0238185	−	0.0412548i
$741$	11.4012	+	6.88046i	0.418832	+	0.252760i
$742$	−14.0373	+	0.511574i	−0.515325	+	0.0187805i
$743$	−11.5004	−	19.9193i	−0.421909	−	0.730768i	0.574217	−	0.818703i	$-0.305307\pi$
$743$	−11.5004	−	19.9193i	−0.421909	−	0.730768i	−0.996126	+	0.0879349i	$0.971973\pi$
$744$	15.9514	−	8.80182i	0.584805	−	0.322691i
$745$	−6.34809			−0.232576
$746$	12.9244	+	22.3857i	0.473195	+	0.819597i
$747$	−41.1607	−	1.59627i	−1.50599	−	0.0584043i
$748$	−17.2145			−0.629425
$749$	−3.37040	+	0.122831i	−0.123152	+	0.00448813i
$750$	−0.0335666	+	1.73173i	−0.00122568	+	0.0632337i
$751$	10.1445			0.370180			0.185090	−	0.982722i	$-0.440742\pi$
$751$	10.1445			0.370180			0.185090	+	0.982722i	$0.440742\pi$
$752$	2.75194	−	4.76650i	0.100353	−	0.173817i
$753$	24.9510	+	15.0576i	0.909264	+	0.548729i
$754$	−1.70750	−	2.95747i	−0.0621833	−	0.107705i
$755$	−17.4975			−0.636798
$756$	−0.298508	+	13.7445i	−0.0108566	+	0.499882i
$757$	30.7997			1.11943			0.559717	−	0.828684i	$-0.310910\pi$
$757$	30.7997			1.11943			0.559717	+	0.828684i	$0.310910\pi$
$758$	−9.98233	−	17.2899i	−0.362575	−	0.627998i
$759$	4.42231	+	2.66881i	0.160520	+	0.0968717i
$760$	−1.15581	+	2.00193i	−0.0419257	+	0.0726175i
$761$	−9.34029			−0.338585			−0.169293	−	0.985566i	$-0.554148\pi$
$761$	−9.34029			−0.338585			−0.169293	+	0.985566i	$0.554148\pi$
$762$	−0.464451	+	23.9613i	−0.0168253	+	0.868027i
$763$	−21.3887	+	40.3743i	−0.774322	+	1.46165i
$764$	−10.4457			−0.377913
$765$	6.74896	−	10.7085i	0.244009	−	0.387167i
$766$	−5.09805	−	8.83007i	−0.184200	−	0.319044i
$767$	−19.8476			−0.716656
$768$	−1.51650	+	0.836793i	−0.0547220	+	0.0301952i
$769$	18.0682	+	31.2950i	0.651555	+	1.12853i	0.982746	+	0.184962i	$0.0592162\pi$
$769$	18.0682	+	31.2950i	0.651555	+	1.12853i	−0.331191	+	0.943564i	$0.607450\pi$
$770$	5.05325	−	9.53876i	0.182106	−	0.343753i
$771$	17.1847	+	10.3708i	0.618892	+	0.373494i
$772$	−9.07209	−	15.7133i	−0.326512	−	0.565535i
$773$	−9.23468	−	15.9949i	−0.332148	−	0.575298i	0.650784	−	0.759263i	$-0.274440\pi$
$773$	−9.23468	−	15.9949i	−0.332148	−	0.575298i	−0.982933	+	0.183965i	$0.941107\pi$
$774$	−3.48095	−	6.60804i	−0.125120	−	0.237521i
$775$	5.25926	−	9.10930i	0.188918	−	0.327216i
$776$	−7.36150	+	12.7505i	−0.264262	+	0.457716i
$777$	−5.19267	−	2.88110i	−0.186286	−	0.103359i
$778$	11.6171	+	20.1214i	0.416492	+	0.721386i
$779$	15.2529			0.546493
$780$	4.93210	+	2.97646i	0.176598	+	0.106574i
$781$	11.9034			0.425938
$782$	1.54198	−	2.67078i	0.0551410	−	0.0955070i
$783$	4.45771	+	2.93166i	0.159306	+	0.104769i
$784$	6.98143	−	0.509538i	0.249337	−	0.0181978i
$785$	6.96791	−	12.0688i	0.248695	−	0.430753i
$786$	−0.452487	+	23.3441i	−0.0161397	+	0.832656i
$787$	−2.41833	+	4.18867i	−0.0862041	+	0.149310i	−0.905904	−	0.423484i	$-0.860807\pi$
$787$	−2.41833	+	4.18867i	−0.0862041	+	0.149310i	0.819700	+	0.572794i	$0.194140\pi$
$788$	4.26751	−	7.39154i	0.152024	−	0.263313i
$789$	35.3165	+	21.3130i	1.25730	+	0.758764i
$790$	6.41876	−	11.1176i	0.228369	−	0.395547i
$791$	−23.9908	+	45.2862i	−0.853015	+	1.61019i
$792$	5.70458	+	10.8293i	0.202704	+	0.384802i
$793$	1.50205	−	2.60163i	0.0533394	−	0.0923866i
$794$	32.5057			1.15358
$795$	0.178209	−	9.19394i	0.00632043	−	0.326075i
$796$	6.97897			0.247363
$797$	−6.12627	−	10.6110i	−0.217003	−	0.375861i	0.736887	−	0.676016i	$-0.236295\pi$
$797$	−6.12627	−	10.6110i	−0.217003	−	0.375861i	−0.953890	+	0.300155i	$0.902962\pi$
$798$	0.180572	+	10.5917i	0.00639219	+	0.374941i
$799$	−11.6112	+	20.1112i	−0.410775	+	0.711483i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	43.6222	+	1.69172i	1.54131	+	0.0597741i
$802$	4.14576	+	7.18067i	0.146392	+	0.253558i
$803$	−23.4177	−	40.5607i	−0.826393	−	1.43136i
$804$	0.0371879	−	1.91855i	0.00131152	−	0.0676621i
$805$	1.02727	+	1.63842i	0.0362065	+	0.0577469i
$806$	−17.4918	−	30.2967i	−0.616122	−	1.06716i
$807$	0.605476	−	31.2369i	0.0213138	−	1.09959i
$808$	−4.51286			−0.158762
$809$	−5.90000	−	10.2191i	−0.207433	−	0.359284i	0.743472	−	0.668767i	$-0.233178\pi$
$809$	−5.90000	−	10.2191i	−0.207433	−	0.359284i	−0.950905	+	0.309483i	$0.899844\pi$
$810$	−8.97297	−	0.697014i	−0.315278	−	0.0244906i
$811$	−17.2258			−0.604880			−0.302440	−	0.953168i	$-0.597801\pi$
$811$	−17.2258			−0.604880			−0.302440	+	0.953168i	$0.597801\pi$
$812$	1.27173	−	2.40057i	0.0446288	−	0.0842435i
$813$	−29.1747	+	16.0983i	−1.02320	+	0.564593i
$814$	−5.28709			−0.185312
$815$	−7.83322	+	13.5675i	−0.274386	+	0.475250i
$816$	6.39854	−	3.53066i	0.223994	−	0.123598i
$817$	−2.87752	−	4.98400i	−0.100672	−	0.174368i
$818$	17.4619			0.610542
$819$	26.3985	+	0.0616151i	0.922438	+	0.00215301i
$820$	6.59836			0.230425
$821$	−1.46463	−	2.53682i	−0.0511160	−	0.0885355i	0.839335	−	0.543614i	$-0.182944\pi$
$821$	−1.46463	−	2.53682i	−0.0511160	−	0.0885355i	−0.890451	+	0.455079i	$0.849611\pi$
$822$	−0.544562	+	28.0943i	−0.0189938	+	0.979901i
$823$	21.3103	−	36.9104i	0.742829	−	1.28662i	−0.208374	−	0.978049i	$-0.566817\pi$
$823$	21.3103	−	36.9104i	0.742829	−	1.28662i	0.951202	−	0.308568i	$-0.0998497\pi$
$824$	−4.36460			−0.152048
$825$	6.05033	+	3.65130i	0.210646	+	0.127122i
$826$	−8.38711	−	13.3769i	−0.291825	−	0.465441i
$827$	34.5649			1.20194			0.600969	−	0.799272i	$-0.294781\pi$
$827$	34.5649			1.20194			0.600969	+	0.799272i	$0.294781\pi$
$828$	−2.19112	−	0.0849742i	−0.0761465	−	0.00295306i
$829$	7.48696	+	12.9678i	0.260033	+	0.450390i	0.966250	−	0.257605i	$-0.0829332\pi$
$829$	7.48696	+	12.9678i	0.260033	+	0.450390i	−0.706217	+	0.707995i	$0.749600\pi$
$830$	−13.7306			−0.476595
$831$	−26.6585	−	16.0880i	−0.924772	−	0.558088i
$832$	1.66295	+	2.88032i	0.0576525	+	0.0998571i
$833$	−29.4566	+	2.14988i	−1.02061	+	0.0744890i
$834$	25.3987	−	14.0148i	0.879484	−	0.485292i
$835$	11.6266	+	20.1379i	0.402355	+	0.696899i
$836$	4.71568	+	8.16780i	0.163095	+	0.282489i
$837$	45.6653	+	30.0323i	1.57842	+	1.03807i
$838$	−11.3255	+	19.6163i	−0.391232	+	0.677634i
$839$	14.4123	−	24.9628i	0.497566	−	0.861810i	−0.502430	−	0.864618i	$-0.667560\pi$
$839$	14.4123	−	24.9628i	0.497566	−	0.861810i	0.999996	+	0.00280774i	$0.000893733\pi$
$840$	0.0781148	+	4.58191i	0.00269522	+	0.158091i
$841$	13.9729	+	24.2017i	0.481823	+	0.834541i
$842$	−9.61449			−0.331337
$843$	−18.3851	+	10.1448i	−0.633218	+	0.349405i
$844$	20.9029			0.719507
$845$	−0.969176	+	1.67866i	−0.0333407	+	0.0577477i
$846$	16.4993	+	0.639862i	0.567256	+	0.0219989i
$847$	−7.93538	−	12.6564i	−0.272663	−	0.434879i
$848$	2.65456	−	4.59783i	0.0911580	−	0.157890i
$849$	1.88331	−	1.03920i	0.0646352	−	0.0356652i
$850$	2.10964	−	3.65400i	0.0723599	−	0.125331i
$851$	0.473587	−	0.820277i	0.0162344	−	0.0281187i
$852$	−4.42443	+	2.44136i	−0.151578	+	0.0836398i
$853$	1.03687	−	1.79592i	0.0355019	−	0.0614911i	−0.847729	−	0.530430i	$-0.822030\pi$
$853$	1.03687	−	1.79592i	0.0355019	−	0.0614911i	0.883230	+	0.468939i	$0.155364\pi$
$854$	2.38817	−	0.0870344i	0.0817216	−	0.00297825i
$855$	−6.92967	−	0.268741i	−0.236990	−	0.00919075i
$856$	0.637368	−	1.10395i	0.0217848	−	0.0377324i
$857$	7.54259			0.257650			0.128825	−	0.991667i	$-0.458879\pi$
$857$	7.54259			0.257650			0.128825	+	0.991667i	$0.458879\pi$
$858$	20.5783	−	11.3549i	0.702532	−	0.387652i
$859$	−28.1389			−0.960086			−0.480043	−	0.877245i	$-0.659379\pi$
$859$	−28.1389			−0.960086			−0.480043	+	0.877245i	$0.659379\pi$
$860$	−1.24480	−	2.15606i	−0.0424474	−	0.0735211i
$861$	25.9249	−	15.5629i	0.883519	−	0.530383i
$862$	−3.40302	+	5.89421i	−0.115907	+	0.200758i
$863$	−18.1524	+	31.4410i	−0.617916	+	1.07026i	0.371949	+	0.928253i	$0.378690\pi$
$863$	−18.1524	+	31.4410i	−0.617916	+	1.07026i	−0.989865	+	0.142009i	$0.954644\pi$
$864$	−4.34142	−	2.85518i	−0.147698	−	0.0971352i
$865$	−0.830725	−	1.43886i	−0.0282455	−	0.0489226i
$866$	15.2337	+	26.3856i	0.517664	+	0.896620i
$867$	−1.21664	+	0.671333i	−0.0413193	+	0.0227997i
$868$	13.0277	−	24.5917i	0.442189	−	0.834698i
$869$	−26.1884	−	45.3596i	−0.888380	−	1.53872i
$870$	1.52266	+	0.918904i	0.0516229	+	0.0311538i
$871$	−3.68472			−0.124852
$872$	−8.63456	−	14.9555i	−0.292403	−	0.506457i
$873$	−44.1358	−	1.71164i	−1.49377	−	0.0579303i
$874$	−1.68961			−0.0571521
$875$	1.40545	+	2.24159i	0.0475128	+	0.0757795i
$876$	17.0231	+	10.2732i	0.575158	+	0.347101i
$877$	−12.1164			−0.409140			−0.204570	−	0.978852i	$-0.565580\pi$
$877$	−12.1164			−0.409140			−0.204570	+	0.978852i	$0.565580\pi$
$878$	6.99011	−	12.1072i	0.235905	−	0.408599i
$879$	0.245978	−	12.6902i	0.00829663	−	0.428029i
$880$	2.03999	+	3.53336i	0.0687679	+	0.119110i
$881$	−45.2200			−1.52350			−0.761750	−	0.647871i	$-0.775660\pi$
$881$	−45.2200			−1.52350			−0.761750	+	0.647871i	$0.775660\pi$
$882$	11.1138	+	17.8180i	0.374222	+	0.599965i
$883$	15.8733			0.534180			0.267090	−	0.963672i	$-0.413938\pi$
$883$	15.8733			0.534180			0.267090	+	0.963672i	$0.413938\pi$
$884$	−7.01645	−	12.1529i	−0.235989	−	0.408745i
$885$	9.04985	−	4.99363i	0.304207	−	0.167859i
$886$	4.00175	−	6.93123i	0.134441	−	0.232859i
$887$	−25.5339			−0.857346			−0.428673	−	0.903460i	$-0.641019\pi$
$887$	−25.5339			−0.857346			−0.428673	+	0.903460i	$0.641019\pi$
$888$	1.96518	−	1.08437i	0.0659472	−	0.0363891i
$889$	19.4467	+	31.0161i	0.652222	+	1.04025i
$890$	14.5517			0.487773
$891$	−20.7675	+	30.2828i	−0.695738	+	1.01451i
$892$	−3.45757	−	5.98869i	−0.115768	−	0.200516i
$893$	12.7229			0.425756
$894$	0.213084	−	10.9931i	0.00712659	−	0.367666i
$895$	−3.21357	−	5.56606i	−0.107418	−	0.186053i
$896$	−1.23855	+	2.33795i	−0.0413770	+	0.0781053i
$897$	−0.0815996	+	4.20978i	−0.00272453	+	0.140560i
$898$	18.7318	+	32.4444i	0.625088	+	1.08268i
$899$	−5.40013	−	9.35330i	−0.180104	−	0.311950i
$900$	−2.99775	−	0.116256i	−0.0999249	−	0.00387521i
$901$	−11.2003	+	19.3995i	−0.373137	+	0.646292i
$902$	13.4606	−	23.3144i	0.448188	−	0.776284i
$903$	−9.97611	−	5.53515i	−0.331984	−	0.184198i
$904$	−9.68504	−	16.7750i	−0.322120	−	0.557928i
$905$	−3.64852			−0.121281
$906$	0.587331	−	30.3008i	0.0195128	−	1.00668i
$907$	22.4746			0.746258			0.373129	−	0.927780i	$-0.378285\pi$
$907$	22.4746			0.746258			0.373129	+	0.927780i	$0.378285\pi$
$908$	−11.9738	+	20.7393i	−0.397366	+	0.688257i
$909$	−6.30985	−	11.9783i	−0.209284	−	0.397294i
$910$	8.79368	−	0.320476i	0.291508	−	0.0106237i
$911$	−17.7313	+	30.7115i	−0.587464	+	1.01752i	0.407099	+	0.913384i	$0.366540\pi$
$911$	−17.7313	+	30.7115i	−0.587464	+	1.01752i	−0.994563	+	0.104133i	$0.966793\pi$
$912$	−3.42799	−	2.06875i	−0.113512	−	0.0685031i
$913$	−28.0101	+	48.5150i	−0.927000	+	1.60561i
$914$	−4.53133	+	7.84849i	−0.149883	+	0.259605i
$915$	−0.0303188	+	1.56417i	−0.00100231	+	0.0517099i
$916$	−6.70677	+	11.6165i	−0.221598	+	0.383819i
$917$	18.9458	+	30.2172i	0.625644	+	0.997859i
$918$	18.3176	+	12.0468i	0.604572	+	0.397603i
$919$	27.2696	−	47.2323i	0.899541	−	1.55805i	0.0714595	−	0.997444i	$-0.477234\pi$
$919$	27.2696	−	47.2323i	0.899541	−	1.55805i	0.828082	−	0.560607i	$-0.189432\pi$
$920$	−0.730921			−0.0240977
$921$	33.5146	+	20.2256i	1.10434	+	0.666457i
$922$	29.5791			0.974136
$923$	4.85171	+	8.40340i	0.159696	+	0.276601i
$924$	16.3489	+	9.07102i	0.537839	+	0.298415i
$925$	0.647932	−	1.12225i	0.0213039	−	0.0368994i
$926$	−8.49546	+	14.7146i	−0.279178	+	0.483551i
$927$	−6.10255	−	11.5847i	−0.200434	−	0.380493i
$928$	0.513393	+	0.889223i	0.0168529	+	0.0291902i
$929$	−11.4801	−	19.8840i	−0.376648	−	0.652374i	0.613924	−	0.789365i	$-0.289590\pi$
$929$	−11.4801	−	19.8840i	−0.376648	−	0.652374i	−0.990572	+	0.136991i	$0.956257\pi$
$930$	15.5983	+	9.41336i	0.511488	+	0.308676i
$931$	9.08928	+	13.3874i	0.297889	+	0.438753i
$932$	−4.48461	−	7.76757i	−0.146898	−	0.254435i
$933$	−34.3995	+	18.9814i	−1.12619	+	0.621423i
$934$	−37.0784			−1.21324
$935$	−8.60726	−	14.9082i	−0.281487	−	0.487551i
$936$	−5.31997	+	8.44114i	−0.173889	+	0.275907i
$937$	−46.9601			−1.53412			−0.767059	−	0.641576i	$-0.778281\pi$
$937$	−46.9601			−1.53412			−0.767059	+	0.641576i	$0.778281\pi$
$938$	−1.55707	−	2.48342i	−0.0508402	−	0.0810866i
$939$	−0.535446	+	27.6240i	−0.0174736	+	0.901477i
$940$	5.50389			0.179517
$941$	−26.9022	+	46.5960i	−0.876988	+	1.51899i	−0.0223573	+	0.999750i	$0.507117\pi$
$941$	−26.9022	+	46.5960i	−0.876988	+	1.51899i	−0.854630	+	0.519237i	$0.826216\pi$
$942$	20.6659	+	12.4716i	0.673331	+	0.406347i
$943$	2.41144	+	4.17674i	0.0785273	+	0.136013i
$944$	5.96758			0.194228
$945$	−12.0523	+	6.61373i	−0.392062	+	0.215145i
$946$	−10.1575			−0.330249
$947$	3.84449	+	6.65886i	0.124929	+	0.216384i	0.921705	−	0.387891i	$-0.126796\pi$
$947$	3.84449	+	6.65886i	0.124929	+	0.216384i	−0.796776	+	0.604275i	$0.793463\pi$
$948$	19.0372	+	11.4887i	0.618300	+	0.373136i
$949$	19.0896	−	33.0642i	0.619675	−	1.07331i
$950$	−2.31162			−0.0749990
$951$	−0.435758	+	22.4811i	−0.0141304	+	0.728998i
$952$	5.22578	−	9.86444i	0.169369	−	0.319708i
$953$	8.60696			0.278807			0.139403	−	0.990236i	$-0.455482\pi$
$953$	8.60696			0.278807			0.139403	+	0.990236i	$0.455482\pi$
$954$	15.9154	+	0.617219i	0.515280	+	0.0199832i
$955$	−5.22286	−	9.04626i	−0.169008	−	0.292730i
$956$	20.5663			0.665163
$957$	6.35301	−	3.50554i	0.205364	−	0.113318i
$958$	−1.95565	−	3.38729i	−0.0631842	−	0.109438i
$959$	22.8010	+	36.3660i	0.736282	+	1.17432i
$960$	−1.48293	−	0.894932i	−0.0478615	−	0.0288838i
$961$	−39.8196	−	68.9696i	−1.28450	−	2.22483i
$962$	−2.15496	−	3.73250i	−0.0694788	−	0.120341i
$963$	3.82134	+	0.148196i	0.123141	+	0.00477556i
$964$	−8.06952	+	13.9768i	−0.259902	+	0.450163i
$965$	9.07209	−	15.7133i	0.292041	−	0.505830i
$966$	−2.87178	+	1.72395i	−0.0923981	+	0.0554673i
$967$	9.16552	+	15.8752i	0.294743	+	0.510510i	0.974925	−	0.222533i	$-0.0714325\pi$
$967$	9.16552	+	15.8752i	0.294743	+	0.510510i	−0.680182	+	0.733043i	$0.738099\pi$
$968$	5.64617			0.181475
$969$	14.4636	+	8.72861i	0.464639	+	0.280403i
$970$	−14.7230			−0.472727
$971$	−9.84994	+	17.0606i	−0.316100	+	0.547500i	−0.979671	−	0.200613i	$-0.935707\pi$
$971$	−9.84994	+	17.0606i	−0.316100	+	0.547500i	0.663571	+	0.748113i	$0.269040\pi$
$972$	1.50823	−	15.5153i	0.0483765	−	0.497654i
$973$	20.7435	−	39.1564i	0.665006	−	1.25530i
$974$	−2.95611	+	5.12014i	−0.0947200	+	0.164060i
$975$	−0.111639	+	5.75956i	−0.00357532	+	0.184453i
$976$	−0.451622	+	0.782232i	−0.0144561	+	0.0250386i
$977$	−12.2444	+	21.2079i	−0.391734	+	0.678502i	−0.992678	−	0.120788i	$-0.961458\pi$
$977$	−12.2444	+	21.2079i	−0.391734	+	0.678502i	0.600945	+	0.799291i	$0.294791\pi$
$978$	−23.2323	−	14.0204i	−0.742888	−	0.448323i
$979$	29.6852	−	51.4163i	0.948743	−	1.64327i
$980$	3.93199	+	5.79133i	0.125603	+	0.184997i
$981$	27.6229	−	43.8290i	0.881931	−	1.39935i
$982$	2.72890	−	4.72659i	0.0870827	−	0.150832i
$983$	−36.3119			−1.15817			−0.579084	−	0.815268i	$-0.696590\pi$
$983$	−36.3119			−1.15817			−0.579084	+	0.815268i	$0.696590\pi$
$984$	−0.221485	+	11.4266i	−0.00706068	+	0.364265i
$985$	8.53501			0.271948
$986$	−2.16614	−	3.75187i	−0.0689841	−	0.119484i
$987$	21.6247	−	12.9815i	0.688323	−	0.413205i
$988$	−3.84412	+	6.65822i	−0.122298	+	0.211826i
$989$	0.909852	−	1.57591i	0.0289316	−	0.0501110i
$990$	−6.52614	+	10.3550i	−0.207414	+	0.329102i
$991$	13.0056	+	22.5264i	0.413137	+	0.715575i	0.995231	−	0.0975469i	$-0.0310996\pi$
$991$	13.0056	+	22.5264i	0.413137	+	0.715575i	−0.582094	+	0.813122i	$0.697766\pi$
$992$	5.25926	+	9.10930i	0.166982	+	0.289221i
$993$	−0.680591	+	35.1121i	−0.0215979	+	1.11425i
$994$	−3.61350	+	6.82102i	−0.114613	+	0.216349i
$995$	3.48948	+	6.04396i	0.110624	+	0.191607i
$996$	0.460889	−	23.7776i	0.0146038	−	0.753421i
$997$	36.5268			1.15681			0.578407	−	0.815748i	$-0.303674\pi$
$997$	36.5268			1.15681			0.578407	+	0.815748i	$0.303674\pi$
$998$	19.0494	+	32.9945i	0.602998	+	1.04442i
$999$	5.62590	+	3.69993i	0.177995	+	0.117061i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.l.f.331.6	yes	12
3.2	odd	2		1890.2.l.h.1801.3		12
7.4	even	3		630.2.i.h.151.3	yes	12
9.4	even	3		630.2.i.h.121.3	✓	12
9.5	odd	6		1890.2.i.f.1171.6		12
21.11	odd	6		1890.2.i.f.991.6		12
63.4	even	3	inner	630.2.l.f.571.6	yes	12
63.32	odd	6		1890.2.l.h.361.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.h.121.3	✓	12	9.4	even	3
630.2.i.h.151.3	yes	12	7.4	even	3
630.2.l.f.331.6	yes	12	1.1	even	1	trivial
630.2.l.f.571.6	yes	12	63.4	even	3	inner
1890.2.i.f.991.6		12	21.11	odd	6
1890.2.i.f.1171.6		12	9.5	odd	6
1890.2.l.h.361.3		12	63.32	odd	6
1890.2.l.h.1801.3		12	3.2	odd	2

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.48293 + 0.894932i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.0335666 - 1.73173i) q^{6} +(-1.40545 - 2.24159i) q^{7} +1.00000 q^{8} +(1.39819 + 2.65425i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.48293 + 0.894932i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.0335666 - 1.73173i) q^{6} +(-1.40545 - 2.24159i) q^{7} +1.00000 q^{8} +(1.39819 + 2.65425i) q^{9} +(0.500000 + 0.866025i) q^{10} +4.07997 q^{11} +(-1.51650 + 0.836793i) q^{12} +(1.66295 + 2.88032i) q^{13} +(-1.23855 + 2.33795i) q^{14} +(-1.48293 - 0.894932i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.10964 + 3.65400i) q^{17} +(1.59955 - 2.53800i) q^{18} +(1.15581 - 2.00193i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.0781148 - 4.58191i) q^{21} +(-2.03999 - 3.53336i) q^{22} +0.730921 q^{23} +(1.48293 + 0.894932i) q^{24} +1.00000 q^{25} +(1.66295 - 2.88032i) q^{26} +(-0.301948 + 5.18737i) q^{27} +(2.64400 - 0.0963576i) q^{28} +(0.513393 - 0.889223i) q^{29} +(-0.0335666 + 1.73173i) q^{30} +(5.25926 - 9.10930i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(6.05033 + 3.65130i) q^{33} +(2.10964 - 3.65400i) q^{34} +(1.40545 + 2.24159i) q^{35} +(-2.99775 - 0.116256i) q^{36} +(0.647932 - 1.12225i) q^{37} -2.31162 q^{38} +(-0.111639 + 5.75956i) q^{39} -1.00000 q^{40} +(3.29918 + 5.71435i) q^{41} +(-3.92899 + 2.35860i) q^{42} +(1.24480 - 2.15606i) q^{43} +(-2.03999 + 3.53336i) q^{44} +(-1.39819 - 2.65425i) q^{45} +(-0.365460 - 0.632996i) q^{46} +(2.75194 + 4.76650i) q^{47} +(0.0335666 - 1.73173i) q^{48} +(-3.04944 + 6.30087i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.141627 + 7.30662i) q^{51} -3.32591 q^{52} +(2.65456 + 4.59783i) q^{53} +(4.64337 - 2.33219i) q^{54} -4.07997 q^{55} +(-1.40545 - 2.24159i) q^{56} +(3.50558 - 1.93435i) q^{57} -1.02679 q^{58} +(-2.98379 + 5.16808i) q^{59} +(1.51650 - 0.836793i) q^{60} +(-0.451622 - 0.782232i) q^{61} -10.5185 q^{62} +(3.98466 - 6.86458i) q^{63} +1.00000 q^{64} +(-1.66295 - 2.88032i) q^{65} +(0.136951 - 7.06539i) q^{66} +(-0.553942 + 0.959456i) q^{67} -4.21927 q^{68} +(1.08391 + 0.654125i) q^{69} +(1.23855 - 2.33795i) q^{70} +2.91752 q^{71} +(1.39819 + 2.65425i) q^{72} +(-5.73968 - 9.94141i) q^{73} -1.29586 q^{74} +(1.48293 + 0.894932i) q^{75} +(1.15581 + 2.00193i) q^{76} +(-5.73418 - 9.14562i) q^{77} +(5.04374 - 2.78310i) q^{78} +(-6.41876 - 11.1176i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-5.09012 + 7.42231i) q^{81} +(3.29918 - 5.71435i) q^{82} +(-6.86528 + 11.8910i) q^{83} +(4.00711 + 2.22331i) q^{84} +(-2.10964 - 3.65400i) q^{85} -2.48960 q^{86} +(1.55712 - 0.859207i) q^{87} +4.07997 q^{88} +(7.27583 - 12.6021i) q^{89} +(-1.59955 + 2.53800i) q^{90} +(4.11930 - 7.77579i) q^{91} +(-0.365460 + 0.632996i) q^{92} +(15.9514 - 8.80182i) q^{93} +(2.75194 - 4.76650i) q^{94} +(-1.15581 + 2.00193i) q^{95} +(-1.51650 + 0.836793i) q^{96} +(-7.36150 + 12.7505i) q^{97} +(6.98143 - 0.509538i) q^{98} +(5.70458 + 10.8293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 7 q^{3} - 6 q^{4} - 12 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 7 * q^3 - 6 * q^4 - 12 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - q^9	\( 12 q - 6 q^{2} - 7 q^{3} - 6 q^{4} - 12 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - q^{9} + 6 q^{10} + 14 q^{11} + 5 q^{12} + 2 q^{13} - 4 q^{14} + 7 q^{15} - 6 q^{16} + 7 q^{17} + 5 q^{18} + 14 q^{19} + 6 q^{20} - 4 q^{21} - 7 q^{22} + 18 q^{23} - 7 q^{24} + 12 q^{25} + 2 q^{26} + 11 q^{27} + 8 q^{28} - 9 q^{29} - 2 q^{30} + 9 q^{31} - 6 q^{32} + 15 q^{33} + 7 q^{34} + 4 q^{35} - 4 q^{36} - 12 q^{37} - 28 q^{38} + 25 q^{39} - 12 q^{40} + q^{41} - 7 q^{42} + 7 q^{43} - 7 q^{44} + q^{45} - 9 q^{46} + 7 q^{47} + 2 q^{48} - 6 q^{50} - 24 q^{51} - 4 q^{52} + 2 q^{53} + 17 q^{54} - 14 q^{55} - 4 q^{56} - 14 q^{57} + 18 q^{58} + 29 q^{59} - 5 q^{60} - 11 q^{61} - 18 q^{62} + 26 q^{63} + 12 q^{64} - 2 q^{65} - 18 q^{66} - 22 q^{67} - 14 q^{68} - 18 q^{69} + 4 q^{70} + 10 q^{71} - q^{72} + 6 q^{73} + 24 q^{74} - 7 q^{75} + 14 q^{76} - 11 q^{77} - 14 q^{78} + q^{79} + 6 q^{80} + 11 q^{81} + q^{82} - 26 q^{83} + 11 q^{84} - 7 q^{85} - 14 q^{86} + 18 q^{87} + 14 q^{88} + 2 q^{89} - 5 q^{90} - 4 q^{91} - 9 q^{92} + 61 q^{93} + 7 q^{94} - 14 q^{95} + 5 q^{96} + 6 q^{97} - 24 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 7 * q^3 - 6 * q^4 - 12 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - q^9 + 6 * q^10 + 14 * q^11 + 5 * q^12 + 2 * q^13 - 4 * q^14 + 7 * q^15 - 6 * q^16 + 7 * q^17 + 5 * q^18 + 14 * q^19 + 6 * q^20 - 4 * q^21 - 7 * q^22 + 18 * q^23 - 7 * q^24 + 12 * q^25 + 2 * q^26 + 11 * q^27 + 8 * q^28 - 9 * q^29 - 2 * q^30 + 9 * q^31 - 6 * q^32 + 15 * q^33 + 7 * q^34 + 4 * q^35 - 4 * q^36 - 12 * q^37 - 28 * q^38 + 25 * q^39 - 12 * q^40 + q^41 - 7 * q^42 + 7 * q^43 - 7 * q^44 + q^45 - 9 * q^46 + 7 * q^47 + 2 * q^48 - 6 * q^50 - 24 * q^51 - 4 * q^52 + 2 * q^53 + 17 * q^54 - 14 * q^55 - 4 * q^56 - 14 * q^57 + 18 * q^58 + 29 * q^59 - 5 * q^60 - 11 * q^61 - 18 * q^62 + 26 * q^63 + 12 * q^64 - 2 * q^65 - 18 * q^66 - 22 * q^67 - 14 * q^68 - 18 * q^69 + 4 * q^70 + 10 * q^71 - q^72 + 6 * q^73 + 24 * q^74 - 7 * q^75 + 14 * q^76 - 11 * q^77 - 14 * q^78 + q^79 + 6 * q^80 + 11 * q^81 + q^82 - 26 * q^83 + 11 * q^84 - 7 * q^85 - 14 * q^86 + 18 * q^87 + 14 * q^88 + 2 * q^89 - 5 * q^90 - 4 * q^91 - 9 * q^92 + 61 * q^93 + 7 * q^94 - 14 * q^95 + 5 * q^96 + 6 * q^97 - 24 * q^98 - 27 * q^99

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