LMFDB - Embedded newform 630.2.i.e.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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([2, 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("630.121");

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.i (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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	630.151
Dual form			630.2.i.e.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.12132 + 3.67423i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(1.62132 + 2.09077i) q^{14} +(-1.50000 + 0.866025i) q^{15} +1.00000 q^{16} +(1.50000 + 2.59808i) q^{18} +(1.12132 + 1.94218i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.621320 - 4.54026i) q^{21} +(2.12132 + 3.67423i) q^{22} +(4.24264 - 7.34847i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} -5.19615i q^{27} +(1.62132 + 2.09077i) q^{28} +(-0.621320 + 1.07616i) q^{29} +(-1.50000 + 0.866025i) q^{30} +6.24264 q^{31} +1.00000 q^{32} -7.34847i q^{33} +(2.62132 - 0.358719i) q^{35} +(1.50000 + 2.59808i) q^{36} +(4.12132 + 7.13834i) q^{37} +(1.12132 + 1.94218i) q^{38} +3.46410i q^{39} +(0.500000 - 0.866025i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(-0.621320 - 4.54026i) q^{42} +(0.500000 - 0.866025i) q^{43} +(2.12132 + 3.67423i) q^{44} +3.00000 q^{45} +(4.24264 - 7.34847i) q^{46} +1.24264 q^{47} +(-1.50000 - 0.866025i) q^{48} +(-1.74264 + 6.77962i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(-0.878680 + 1.52192i) q^{53} -5.19615i q^{54} +4.24264 q^{55} +(1.62132 + 2.09077i) q^{56} -3.88437i q^{57} +(-0.621320 + 1.07616i) q^{58} +1.75736 q^{59} +(-1.50000 + 0.866025i) q^{60} -12.4853 q^{61} +6.24264 q^{62} +(-3.00000 + 7.34847i) q^{63} +1.00000 q^{64} -2.00000 q^{65} -7.34847i q^{66} -6.48528 q^{67} +(-12.7279 + 7.34847i) q^{69} +(2.62132 - 0.358719i) q^{70} +4.24264 q^{71} +(1.50000 + 2.59808i) q^{72} +(-2.24264 + 3.88437i) q^{73} +(4.12132 + 7.13834i) q^{74} +1.73205i q^{75} +(1.12132 + 1.94218i) q^{76} +(-4.24264 + 10.3923i) q^{77} +3.46410i q^{78} -10.7279 q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 - 7.79423i) q^{82} +(4.50000 - 7.79423i) q^{83} +(-0.621320 - 4.54026i) q^{84} +(0.500000 - 0.866025i) q^{86} +(1.86396 - 1.07616i) q^{87} +(2.12132 + 3.67423i) q^{88} +3.00000 q^{90} +(2.00000 - 4.89898i) q^{91} +(4.24264 - 7.34847i) q^{92} +(-9.36396 - 5.40629i) q^{93} +1.24264 q^{94} +2.24264 q^{95} +(-1.50000 - 0.866025i) q^{96} +(3.24264 - 5.61642i) q^{97} +(-1.74264 + 6.77962i) q^{98} +(-6.36396 + 11.0227i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 6 q^{3} + 4 q^{4} + 2 q^{5} - 6 q^{6} - 2 q^{7} + 4 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 6 * q^3 + 4 * q^4 + 2 * q^5 - 6 * q^6 - 2 * q^7 + 4 * q^8 + 6 * q^9	$ 4 q + 4 q^{2} - 6 q^{3} + 4 q^{4} + 2 q^{5} - 6 q^{6} - 2 q^{7} + 4 q^{8} + 6 q^{9} + 2 q^{10} - 6 q^{12} - 4 q^{13} - 2 q^{14} - 6 q^{15} + 4 q^{16} + 6 q^{18} - 4 q^{19} + 2 q^{20} + 6 q^{21} - 6 q^{24} - 2 q^{25} - 4 q^{26} - 2 q^{28} + 6 q^{29} - 6 q^{30} + 8 q^{31} + 4 q^{32} + 2 q^{35} + 6 q^{36} + 8 q^{37} - 4 q^{38} + 2 q^{40} - 18 q^{41} + 6 q^{42} + 2 q^{43} + 12 q^{45} - 12 q^{47} - 6 q^{48} + 10 q^{49} - 2 q^{50} - 4 q^{52} - 12 q^{53} - 2 q^{56} + 6 q^{58} + 24 q^{59} - 6 q^{60} - 16 q^{61} + 8 q^{62} - 12 q^{63} + 4 q^{64} - 8 q^{65} + 8 q^{67} + 2 q^{70} + 6 q^{72} + 8 q^{73} + 8 q^{74} - 4 q^{76} + 8 q^{79} + 2 q^{80} - 18 q^{81} - 18 q^{82} + 18 q^{83} + 6 q^{84} + 2 q^{86} - 18 q^{87} + 12 q^{90} + 8 q^{91} - 12 q^{93} - 12 q^{94} - 8 q^{95} - 6 q^{96} - 4 q^{97} + 10 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 6 * q^3 + 4 * q^4 + 2 * q^5 - 6 * q^6 - 2 * q^7 + 4 * q^8 + 6 * q^9 + 2 * q^10 - 6 * q^12 - 4 * q^13 - 2 * q^14 - 6 * q^15 + 4 * q^16 + 6 * q^18 - 4 * q^19 + 2 * q^20 + 6 * q^21 - 6 * q^24 - 2 * q^25 - 4 * q^26 - 2 * q^28 + 6 * q^29 - 6 * q^30 + 8 * q^31 + 4 * q^32 + 2 * q^35 + 6 * q^36 + 8 * q^37 - 4 * q^38 + 2 * q^40 - 18 * q^41 + 6 * q^42 + 2 * q^43 + 12 * q^45 - 12 * q^47 - 6 * q^48 + 10 * q^49 - 2 * q^50 - 4 * q^52 - 12 * q^53 - 2 * q^56 + 6 * q^58 + 24 * q^59 - 6 * q^60 - 16 * q^61 + 8 * q^62 - 12 * q^63 + 4 * q^64 - 8 * q^65 + 8 * q^67 + 2 * q^70 + 6 * q^72 + 8 * q^73 + 8 * q^74 - 4 * q^76 + 8 * q^79 + 2 * q^80 - 18 * q^81 - 18 * q^82 + 18 * q^83 + 6 * q^84 + 2 * q^86 - 18 * q^87 + 12 * q^90 + 8 * q^91 - 12 * q^93 - 12 * q^94 - 8 * q^95 - 6 * q^96 - 4 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	1.00000			0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$8$	1.00000			0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	2.12132	+	3.67423i	0.639602	+	1.10782i	0.985520	+	0.169559i	$0.0542342\pi$
$11$	2.12132	+	3.67423i	0.639602	+	1.10782i	−0.345918	+	0.938265i	$0.612432\pi$
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	1.62132	+	2.09077i	0.433316	+	0.558782i
$15$	−1.50000	+	0.866025i	−0.387298	+	0.223607i
$16$	1.00000			0.250000
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	1.50000	+	2.59808i	0.353553	+	0.612372i
$19$	1.12132	+	1.94218i	0.257249	+	0.445568i	0.965504	−	0.260389i	$-0.0838508\pi$
$19$	1.12132	+	1.94218i	0.257249	+	0.445568i	−0.708255	+	0.705956i	$0.750517\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−0.621320	−	4.54026i	−0.135583	−	0.990766i
$22$	2.12132	+	3.67423i	0.452267	+	0.783349i
$23$	4.24264	−	7.34847i	0.884652	−	1.53226i	0.0385394	−	0.999257i	$-0.487729\pi$
$23$	4.24264	−	7.34847i	0.884652	−	1.53226i	0.846112	−	0.533005i	$-0.178937\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$		−	5.19615i		−	1.00000i
$28$	1.62132	+	2.09077i	0.306401	+	0.395118i
$29$	−0.621320	+	1.07616i	−0.115376	+	0.199838i	−0.917930	−	0.396742i	$-0.870141\pi$
$29$	−0.621320	+	1.07616i	−0.115376	+	0.199838i	0.802554	+	0.596580i	$0.203474\pi$
$30$	−1.50000	+	0.866025i	−0.273861	+	0.158114i
$31$	6.24264			1.12121			0.560606	−	0.828083i	$-0.310568\pi$
$31$	6.24264			1.12121			0.560606	+	0.828083i	$0.310568\pi$
$32$	1.00000			0.176777
$33$		−	7.34847i		−	1.27920i
$34$		0			0
$35$	2.62132	−	0.358719i	0.443084	−	0.0606347i
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	4.12132	+	7.13834i	0.677541	+	1.17354i	0.975719	+	0.219025i	$0.0702877\pi$
$37$	4.12132	+	7.13834i	0.677541	+	1.17354i	−0.298178	+	0.954510i	$0.596379\pi$
$38$	1.12132	+	1.94218i	0.181902	+	0.315064i
$39$			3.46410i			0.554700i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$	−0.621320	−	4.54026i	−0.0958718	−	0.700577i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	2.12132	+	3.67423i	0.319801	+	0.553912i
$45$	3.00000			0.447214
$46$	4.24264	−	7.34847i	0.625543	−	1.08347i
$47$	1.24264			0.181258			0.0906289	−	0.995885i	$-0.471112\pi$
$47$	1.24264			0.181258			0.0906289	+	0.995885i	$0.471112\pi$
$48$	−1.50000	−	0.866025i	−0.216506	−	0.125000i
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−0.878680	+	1.52192i	−0.120696	+	0.209051i	−0.920042	−	0.391819i	$-0.871846\pi$
$53$	−0.878680	+	1.52192i	−0.120696	+	0.209051i	0.799346	+	0.600871i	$0.205179\pi$
$54$		−	5.19615i		−	0.707107i
$55$	4.24264			0.572078
$56$	1.62132	+	2.09077i	0.216658	+	0.279391i
$57$		−	3.88437i		−	0.514497i
$58$	−0.621320	+	1.07616i	−0.0815834	+	0.141307i
$59$	1.75736			0.228789			0.114394	−	0.993435i	$-0.463507\pi$
$59$	1.75736			0.228789			0.114394	+	0.993435i	$0.463507\pi$
$60$	−1.50000	+	0.866025i	−0.193649	+	0.111803i
$61$	−12.4853			−1.59858			−0.799288	−	0.600948i	$-0.794790\pi$
$61$	−12.4853			−1.59858			−0.799288	+	0.600948i	$0.794790\pi$
$62$	6.24264			0.792816
$63$	−3.00000	+	7.34847i	−0.377964	+	0.925820i
$64$	1.00000			0.125000
$65$	−2.00000			−0.248069
$66$		−	7.34847i		−	0.904534i
$67$	−6.48528			−0.792303			−0.396152	−	0.918185i	$-0.629655\pi$
$67$	−6.48528			−0.792303			−0.396152	+	0.918185i	$0.629655\pi$
$68$		0			0
$69$	−12.7279	+	7.34847i	−1.53226	+	0.884652i
$70$	2.62132	−	0.358719i	0.313308	−	0.0428752i
$71$	4.24264			0.503509			0.251754	−	0.967791i	$-0.418992\pi$
$71$	4.24264			0.503509			0.251754	+	0.967791i	$0.418992\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	−2.24264	+	3.88437i	−0.262481	+	0.454631i	−0.966901	−	0.255153i	$-0.917874\pi$
$73$	−2.24264	+	3.88437i	−0.262481	+	0.454631i	0.704419	+	0.709784i	$0.251207\pi$
$74$	4.12132	+	7.13834i	0.479094	+	0.829815i
$75$			1.73205i			0.200000i
$76$	1.12132	+	1.94218i	0.128624	+	0.222784i
$77$	−4.24264	+	10.3923i	−0.483494	+	1.18431i
$78$			3.46410i			0.392232i
$79$	−10.7279			−1.20699			−0.603493	−	0.797368i	$-0.706225\pi$
$79$	−10.7279			−1.20699			−0.603493	+	0.797368i	$0.706225\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−4.50000	−	7.79423i	−0.496942	−	0.860729i
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$	−0.621320	−	4.54026i	−0.0677916	−	0.495383i
$85$		0			0
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$	1.86396	−	1.07616i	0.199838	−	0.115376i
$88$	2.12132	+	3.67423i	0.226134	+	0.391675i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$	3.00000			0.316228
$91$	2.00000	−	4.89898i	0.209657	−	0.513553i
$92$	4.24264	−	7.34847i	0.442326	−	0.766131i
$93$	−9.36396	−	5.40629i	−0.970998	−	0.560606i
$94$	1.24264			0.128169
$95$	2.24264			0.230090
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	3.24264	−	5.61642i	0.329240	−	0.570261i	−0.653121	−	0.757254i	$-0.726541\pi$
$97$	3.24264	−	5.61642i	0.329240	−	0.570261i	0.982361	+	0.186993i	$0.0598741\pi$
$98$	−1.74264	+	6.77962i	−0.176033	+	0.684845i
$99$	−6.36396	+	11.0227i	−0.639602	+	1.10782i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	6.62132	+	11.4685i	0.658846	+	1.14115i	0.980915	+	0.194438i	$0.0622885\pi$
$101$	6.62132	+	11.4685i	0.658846	+	1.14115i	−0.322069	+	0.946716i	$0.604378\pi$
$102$		0			0
$103$	−1.62132	+	2.80821i	−0.159753	+	0.276701i	−0.934780	−	0.355228i	$-0.884403\pi$
$103$	−1.62132	+	2.80821i	−0.159753	+	0.276701i	0.775026	+	0.631929i	$0.217737\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$	−4.24264	−	1.73205i	−0.414039	−	0.169031i
$106$	−0.878680	+	1.52192i	−0.0853449	+	0.147822i
$107$	−7.50000	−	12.9904i	−0.725052	−	1.25583i	−0.958952	−	0.283567i	$-0.908482\pi$
$107$	−7.50000	−	12.9904i	−0.725052	−	1.25583i	0.233900	−	0.972261i	$-0.424851\pi$
$108$		−	5.19615i		−	0.500000i
$109$	−8.86396	+	15.3528i	−0.849013	+	1.47053i	0.0330761	+	0.999453i	$0.489470\pi$
$109$	−8.86396	+	15.3528i	−0.849013	+	1.47053i	−0.882090	+	0.471082i	$0.843864\pi$
$110$	4.24264			0.404520
$111$		−	14.2767i		−	1.35508i
$112$	1.62132	+	2.09077i	0.153200	+	0.197559i
$113$	−6.36396	−	11.0227i	−0.598671	−	1.03693i	−0.993018	−	0.117967i	$-0.962362\pi$
$113$	−6.36396	−	11.0227i	−0.598671	−	1.03693i	0.394346	−	0.918962i	$-0.370971\pi$
$114$		−	3.88437i		−	0.363804i
$115$	−4.24264	−	7.34847i	−0.395628	−	0.685248i
$116$	−0.621320	+	1.07616i	−0.0576881	+	0.0999188i
$117$	3.00000	−	5.19615i	0.277350	−	0.480384i
$118$	1.75736			0.161778
$119$		0			0
$120$	−1.50000	+	0.866025i	−0.136931	+	0.0790569i
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$	−12.4853			−1.13036
$123$			15.5885i			1.40556i
$124$	6.24264			0.560606
$125$	−1.00000			−0.0894427
$126$	−3.00000	+	7.34847i	−0.267261	+	0.654654i
$127$	6.75736			0.599619			0.299809	−	0.953999i	$-0.403077\pi$
$127$	6.75736			0.599619			0.299809	+	0.953999i	$0.403077\pi$
$128$	1.00000			0.0883883
$129$	−1.50000	+	0.866025i	−0.132068	+	0.0762493i
$130$	−2.00000			−0.175412
$131$	−1.75736	+	3.04384i	−0.153541	+	0.265941i	−0.932527	−	0.361101i	$-0.882401\pi$
$131$	−1.75736	+	3.04384i	−0.153541	+	0.265941i	0.778986	+	0.627042i	$0.215734\pi$
$132$		−	7.34847i		−	0.639602i
$133$	−2.24264	+	5.49333i	−0.194462	+	0.476332i
$134$	−6.48528			−0.560243
$135$	−4.50000	−	2.59808i	−0.387298	−	0.223607i
$136$		0			0
$137$	−9.36396	−	16.2189i	−0.800017	−	1.38567i	−0.919604	−	0.392847i	$-0.871490\pi$
$137$	−9.36396	−	16.2189i	−0.800017	−	1.38567i	0.119587	−	0.992824i	$-0.461843\pi$
$138$	−12.7279	+	7.34847i	−1.08347	+	0.625543i
$139$	7.12132	+	12.3345i	0.604023	+	1.04620i	0.992205	+	0.124615i	$0.0397696\pi$
$139$	7.12132	+	12.3345i	0.604023	+	1.04620i	−0.388183	+	0.921582i	$0.626897\pi$
$140$	2.62132	−	0.358719i	0.221542	−	0.0303173i
$141$	−1.86396	−	1.07616i	−0.156974	−	0.0906289i
$142$	4.24264			0.356034
$143$	4.24264	−	7.34847i	0.354787	−	0.614510i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	0.621320	+	1.07616i	0.0515978	+	0.0893701i
$146$	−2.24264	+	3.88437i	−0.185602	+	0.321473i
$147$	8.48528	−	8.66025i	0.699854	−	0.714286i
$148$	4.12132	+	7.13834i	0.338770	+	0.586768i
$149$	−7.24264	+	12.5446i	−0.593340	+	1.02770i	0.400439	+	0.916324i	$0.368858\pi$
$149$	−7.24264	+	12.5446i	−0.593340	+	1.02770i	−0.993779	+	0.111372i	$0.964476\pi$
$150$			1.73205i			0.141421i
$151$	−0.121320	−	0.210133i	−0.00987291	−	0.0171004i	0.861047	−	0.508526i	$-0.169809\pi$
$151$	−0.121320	−	0.210133i	−0.00987291	−	0.0171004i	−0.870920	+	0.491425i	$0.836476\pi$
$152$	1.12132	+	1.94218i	0.0909511	+	0.157532i
$153$		0			0
$154$	−4.24264	+	10.3923i	−0.341882	+	0.837436i
$155$	3.12132	−	5.40629i	0.250710	−	0.434243i
$156$			3.46410i			0.277350i
$157$	−16.7279			−1.33503			−0.667517	−	0.744595i	$-0.732643\pi$
$157$	−16.7279			−1.33503			−0.667517	+	0.744595i	$0.732643\pi$
$158$	−10.7279			−0.853468
$159$	2.63604	−	1.52192i	0.209051	−	0.120696i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	22.2426	−	3.04384i	1.75297	−	0.239888i
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$	7.48528	+	12.9649i	0.586292	+	1.01549i	0.994713	+	0.102694i	$0.0327464\pi$
$163$	7.48528	+	12.9649i	0.586292	+	1.01549i	−0.408420	+	0.912794i	$0.633920\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$	−6.36396	−	3.67423i	−0.495434	−	0.286039i
$166$	4.50000	−	7.79423i	0.349268	−	0.604949i
$167$	−10.2426	−	17.7408i	−0.792599	−	1.37282i	−0.924352	−	0.381540i	$-0.875394\pi$
$167$	−10.2426	−	17.7408i	−0.792599	−	1.37282i	0.131753	−	0.991283i	$-0.457939\pi$
$168$	−0.621320	−	4.54026i	−0.0479359	−	0.350289i
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	−3.36396	+	5.82655i	−0.257249	+	0.445568i
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	−10.2426			−0.778734			−0.389367	−	0.921083i	$-0.627306\pi$
$173$	−10.2426			−0.778734			−0.389367	+	0.921083i	$0.627306\pi$
$174$	1.86396	−	1.07616i	0.141307	−	0.0815834i
$175$	1.00000	−	2.44949i	0.0755929	−	0.185164i
$176$	2.12132	+	3.67423i	0.159901	+	0.276956i
$177$	−2.63604	−	1.52192i	−0.198137	−	0.114394i
$178$		0			0
$179$	−0.878680	+	1.52192i	−0.0656756	+	0.113753i	−0.896993	−	0.442044i	$-0.854254\pi$
$179$	−0.878680	+	1.52192i	−0.0656756	+	0.113753i	0.831318	+	0.555797i	$0.187587\pi$
$180$	3.00000			0.223607
$181$	−23.2426			−1.72761			−0.863806	−	0.503825i	$-0.831926\pi$
$181$	−23.2426			−1.72761			−0.863806	+	0.503825i	$0.831926\pi$
$182$	2.00000	−	4.89898i	0.148250	−	0.363137i
$183$	18.7279	+	10.8126i	1.38441	+	0.799288i
$184$	4.24264	−	7.34847i	0.312772	−	0.541736i
$185$	8.24264			0.606011
$186$	−9.36396	−	5.40629i	−0.686599	−	0.396408i
$187$		0			0
$188$	1.24264			0.0906289
$189$	10.8640	−	8.42463i	0.790237	−	0.612801i
$190$	2.24264			0.162698
$191$	14.4853			1.04812			0.524059	−	0.851682i	$-0.324417\pi$
$191$	14.4853			1.04812			0.524059	+	0.851682i	$0.324417\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$	0.242641			0.0174657			0.00873283	−	0.999962i	$-0.497220\pi$
$193$	0.242641			0.0174657			0.00873283	+	0.999962i	$0.497220\pi$
$194$	3.24264	−	5.61642i	0.232808	−	0.403235i
$195$	3.00000	+	1.73205i	0.214834	+	0.124035i
$196$	−1.74264	+	6.77962i	−0.124474	+	0.484258i
$197$	27.2132			1.93886			0.969430	−	0.245367i	$-0.0789085\pi$
$197$	27.2132			1.93886			0.969430	+	0.245367i	$0.0789085\pi$
$198$	−6.36396	+	11.0227i	−0.452267	+	0.783349i
$199$	−2.24264	+	3.88437i	−0.158977	+	0.275356i	−0.934500	−	0.355963i	$-0.884153\pi$
$199$	−2.24264	+	3.88437i	−0.158977	+	0.275356i	0.775523	+	0.631319i	$0.217486\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	9.72792	+	5.61642i	0.686155	+	0.396152i
$202$	6.62132	+	11.4685i	0.465874	+	0.806918i
$203$	−3.25736	+	0.445759i	−0.228622	+	0.0312862i
$204$		0			0
$205$	−9.00000			−0.628587
$206$	−1.62132	+	2.80821i	−0.112963	+	0.195657i
$207$	25.4558			1.76930
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	−4.75736	+	8.23999i	−0.329073	+	0.569972i
$210$	−4.24264	−	1.73205i	−0.292770	−	0.119523i
$211$	−1.87868	−	3.25397i	−0.129334	−	0.224012i	0.794085	−	0.607807i	$-0.207950\pi$
$211$	−1.87868	−	3.25397i	−0.129334	−	0.224012i	−0.923419	+	0.383794i	$0.874617\pi$
$212$	−0.878680	+	1.52192i	−0.0603480	+	0.104526i
$213$	−6.36396	−	3.67423i	−0.436051	−	0.251754i
$214$	−7.50000	−	12.9904i	−0.512689	−	0.888004i
$215$	−0.500000	−	0.866025i	−0.0340997	−	0.0590624i
$216$		−	5.19615i		−	0.353553i
$217$	10.1213	+	13.0519i	0.687080	+	0.886023i
$218$	−8.86396	+	15.3528i	−0.600343	+	1.03982i
$219$	6.72792	−	3.88437i	0.454631	−	0.262481i
$220$	4.24264			0.286039
$221$		0			0
$222$		−	14.2767i		−	0.958188i
$223$	−5.86396	+	10.1567i	−0.392680	+	0.680141i	−0.992802	−	0.119767i	$-0.961785\pi$
$223$	−5.86396	+	10.1567i	−0.392680	+	0.680141i	0.600122	+	0.799908i	$0.295119\pi$
$224$	1.62132	+	2.09077i	0.108329	+	0.139695i
$225$	1.50000	−	2.59808i	0.100000	−	0.173205i
$226$	−6.36396	−	11.0227i	−0.423324	−	0.733219i
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	0.993210	+	0.116331i	$0.0371134\pi$
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	−0.395860	+	0.918311i	$0.629553\pi$
$228$		−	3.88437i		−	0.257249i
$229$	14.6213	−	25.3249i	0.966204	−	1.67351i	0.259859	−	0.965646i	$-0.416324\pi$
$229$	14.6213	−	25.3249i	0.966204	−	1.67351i	0.706345	−	0.707868i	$-0.250343\pi$
$230$	−4.24264	−	7.34847i	−0.279751	−	0.484544i
$231$	15.3640	−	11.9142i	1.01087	−	0.783898i
$232$	−0.621320	+	1.07616i	−0.0407917	+	0.0706533i
$233$	−9.87868	−	17.1104i	−0.647174	−	1.12094i	−0.983795	−	0.179298i	$-0.942617\pi$
$233$	−9.87868	−	17.1104i	−0.647174	−	1.12094i	0.336621	−	0.941640i	$-0.390716\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$	0.621320	−	1.07616i	0.0405305	−	0.0702008i
$236$	1.75736			0.114394
$237$	16.0919	+	9.29065i	1.04528	+	0.603493i
$238$		0			0
$239$	−11.1213	−	19.2627i	−0.719378	−	1.24600i	−0.961246	−	0.275691i	$-0.911093\pi$
$239$	−11.1213	−	19.2627i	−0.719378	−	1.24600i	0.241868	−	0.970309i	$-0.422240\pi$
$240$	−1.50000	+	0.866025i	−0.0968246	+	0.0559017i
$241$	−3.74264	−	6.48244i	−0.241085	−	0.417571i	0.719939	−	0.694037i	$-0.244170\pi$
$241$	−3.74264	−	6.48244i	−0.241085	−	0.417571i	−0.961024	+	0.276467i	$0.910836\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	−12.4853			−0.799288
$245$	5.00000	+	4.89898i	0.319438	+	0.312984i
$246$			15.5885i			0.993884i
$247$	2.24264	−	3.88437i	0.142696	−	0.247156i
$248$	6.24264			0.396408
$249$	−13.5000	+	7.79423i	−0.855528	+	0.493939i
$250$	−1.00000			−0.0632456
$251$	−9.51472			−0.600564			−0.300282	−	0.953851i	$-0.597081\pi$
$251$	−9.51472			−0.600564			−0.300282	+	0.953851i	$0.597081\pi$
$252$	−3.00000	+	7.34847i	−0.188982	+	0.462910i
$253$	36.0000			2.26330
$254$	6.75736			0.423994
$255$		0			0
$256$	1.00000			0.0625000
$257$	−8.48528	+	14.6969i	−0.529297	+	0.916770i	0.470119	+	0.882603i	$0.344211\pi$
$257$	−8.48528	+	14.6969i	−0.529297	+	0.916770i	−0.999416	+	0.0341667i	$0.989122\pi$
$258$	−1.50000	+	0.866025i	−0.0933859	+	0.0539164i
$259$	−8.24264	+	20.1903i	−0.512173	+	1.25456i
$260$	−2.00000			−0.124035
$261$	−3.72792			−0.230753
$262$	−1.75736	+	3.04384i	−0.108570	+	0.188049i
$263$	7.86396	+	13.6208i	0.484913	+	0.839893i	0.999850	−	0.0173347i	$-0.00551807\pi$
$263$	7.86396	+	13.6208i	0.484913	+	0.839893i	−0.514937	+	0.857228i	$0.672185\pi$
$264$		−	7.34847i		−	0.452267i
$265$	0.878680	+	1.52192i	0.0539769	+	0.0934907i
$266$	−2.24264	+	5.49333i	−0.137505	+	0.336817i
$267$		0			0
$268$	−6.48528			−0.396152
$269$	11.4853	−	19.8931i	0.700270	−	1.21290i	−0.268102	−	0.963391i	$-0.586396\pi$
$269$	11.4853	−	19.8931i	0.700270	−	1.21290i	0.968372	−	0.249513i	$-0.0802704\pi$
$270$	−4.50000	−	2.59808i	−0.273861	−	0.158114i
$271$	−10.3640	−	17.9509i	−0.629566	−	1.09044i	−0.987639	−	0.156746i	$-0.949899\pi$
$271$	−10.3640	−	17.9509i	−0.629566	−	1.09044i	0.358073	−	0.933694i	$-0.383434\pi$
$272$		0			0
$273$	−7.24264	+	5.61642i	−0.438345	+	0.339921i
$274$	−9.36396	−	16.2189i	−0.565698	−	0.979817i
$275$	2.12132	−	3.67423i	0.127920	−	0.221565i
$276$	−12.7279	+	7.34847i	−0.766131	+	0.442326i
$277$	−4.87868	−	8.45012i	−0.293131	−	0.507719i	0.681417	−	0.731895i	$-0.261364\pi$
$277$	−4.87868	−	8.45012i	−0.293131	−	0.507719i	−0.974548	+	0.224177i	$0.928031\pi$
$278$	7.12132	+	12.3345i	0.427108	+	0.739773i
$279$	9.36396	+	16.2189i	0.560606	+	0.970998i
$280$	2.62132	−	0.358719i	0.156654	−	0.0214376i
$281$	−3.98528	+	6.90271i	−0.237742	+	0.411781i	−0.960066	−	0.279774i	$-0.909741\pi$
$281$	−3.98528	+	6.90271i	−0.237742	+	0.411781i	0.722324	+	0.691555i	$0.243074\pi$
$282$	−1.86396	−	1.07616i	−0.110997	−	0.0640843i
$283$	1.48528			0.0882908			0.0441454	−	0.999025i	$-0.485944\pi$
$283$	1.48528			0.0882908			0.0441454	+	0.999025i	$0.485944\pi$
$284$	4.24264			0.251754
$285$	−3.36396	−	1.94218i	−0.199264	−	0.115045i
$286$	4.24264	−	7.34847i	0.250873	−	0.434524i
$287$	9.00000	−	22.0454i	0.531253	−	1.30130i
$288$	1.50000	+	2.59808i	0.0883883	+	0.153093i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	0.621320	+	1.07616i	0.0364852	+	0.0631942i
$291$	−9.72792	+	5.61642i	−0.570261	+	0.329240i
$292$	−2.24264	+	3.88437i	−0.131241	+	0.227315i
$293$	−10.2426	−	17.7408i	−0.598381	−	1.03643i	−0.993060	−	0.117608i	$-0.962477\pi$
$293$	−10.2426	−	17.7408i	−0.598381	−	1.03643i	0.394679	−	0.918819i	$-0.370856\pi$
$294$	8.48528	−	8.66025i	0.494872	−	0.505076i
$295$	0.878680	−	1.52192i	0.0511587	−	0.0886095i
$296$	4.12132	+	7.13834i	0.239547	+	0.414907i
$297$	19.0919	−	11.0227i	1.10782	−	0.639602i
$298$	−7.24264	+	12.5446i	−0.419555	+	0.726690i
$299$	−16.9706			−0.981433
$300$			1.73205i			0.100000i
$301$	2.62132	−	0.358719i	0.151090	−	0.0206762i
$302$	−0.121320	−	0.210133i	−0.00698120	−	0.0120918i
$303$		−	22.9369i		−	1.31769i
$304$	1.12132	+	1.94218i	0.0643121	+	0.111392i
$305$	−6.24264	+	10.8126i	−0.357453	+	0.619126i
$306$		0			0
$307$	−29.9706			−1.71051			−0.855255	−	0.518207i	$-0.826600\pi$
$307$	−29.9706			−1.71051			−0.855255	+	0.518207i	$0.826600\pi$
$308$	−4.24264	+	10.3923i	−0.241747	+	0.592157i
$309$	4.86396	−	2.80821i	0.276701	−	0.159753i
$310$	3.12132	−	5.40629i	0.177279	−	0.307056i
$311$	24.7279			1.40219			0.701096	−	0.713067i	$-0.252694\pi$
$311$	24.7279			1.40219			0.701096	+	0.713067i	$0.252694\pi$
$312$			3.46410i			0.196116i
$313$	17.2132			0.972948			0.486474	−	0.873695i	$-0.338283\pi$
$313$	17.2132			0.972948			0.486474	+	0.873695i	$0.338283\pi$
$314$	−16.7279			−0.944011
$315$	4.86396	+	6.27231i	0.274053	+	0.353405i
$316$	−10.7279			−0.603493
$317$	−31.4558			−1.76674			−0.883368	−	0.468680i	$-0.844730\pi$
$317$	−31.4558			−1.76674			−0.883368	+	0.468680i	$0.844730\pi$
$318$	2.63604	−	1.52192i	0.147822	−	0.0853449i
$319$	−5.27208			−0.295180
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$			25.9808i			1.45010i
$322$	22.2426	−	3.04384i	1.23953	−	0.169626i
$323$		0			0
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$	7.48528	+	12.9649i	0.414571	+	0.718059i
$327$	26.5919	−	15.3528i	1.47053	−	0.849013i
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$	2.01472	+	2.59808i	0.111075	+	0.143237i
$330$	−6.36396	−	3.67423i	−0.350325	−	0.202260i
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$	4.50000	−	7.79423i	0.246970	−	0.427764i
$333$	−12.3640	+	21.4150i	−0.677541	+	1.17354i
$334$	−10.2426	−	17.7408i	−0.560452	−	0.970732i
$335$	−3.24264	+	5.61642i	−0.177164	+	0.306858i
$336$	−0.621320	−	4.54026i	−0.0338958	−	0.247691i
$337$	−5.24264	−	9.08052i	−0.285585	−	0.494647i	0.687166	−	0.726500i	$-0.258855\pi$
$337$	−5.24264	−	9.08052i	−0.285585	−	0.494647i	−0.972751	+	0.231853i	$0.925521\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$			22.0454i			1.19734i
$340$		0			0
$341$	13.2426	+	22.9369i	0.717129	+	1.24210i
$342$	−3.36396	+	5.82655i	−0.181902	+	0.315064i
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	0.500000	−	0.866025i	0.0269582	−	0.0466930i
$345$			14.6969i			0.791257i
$346$	−10.2426			−0.550648
$347$	−9.00000			−0.483145			−0.241573	−	0.970383i	$-0.577663\pi$
$347$	−9.00000			−0.483145			−0.241573	+	0.970383i	$0.577663\pi$
$348$	1.86396	−	1.07616i	0.0999188	−	0.0576881i
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	0.274011	+	0.961727i	$0.411649\pi$
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	−0.969885	+	0.243563i	$0.921684\pi$
$350$	1.00000	−	2.44949i	0.0534522	−	0.130931i
$351$	−9.00000	+	5.19615i	−0.480384	+	0.277350i
$352$	2.12132	+	3.67423i	0.113067	+	0.195837i
$353$	0.878680	+	1.52192i	0.0467674	+	0.0810035i	0.888462	−	0.458951i	$-0.151775\pi$
$353$	0.878680	+	1.52192i	0.0467674	+	0.0810035i	−0.841694	+	0.539955i	$0.818441\pi$
$354$	−2.63604	−	1.52192i	−0.140104	−	0.0808890i
$355$	2.12132	−	3.67423i	0.112588	−	0.195008i
$356$		0			0
$357$		0			0
$358$	−0.878680	+	1.52192i	−0.0464397	+	0.0804359i
$359$	−5.12132	−	8.87039i	−0.270293	−	0.468161i	0.698644	−	0.715470i	$-0.253787\pi$
$359$	−5.12132	−	8.87039i	−0.270293	−	0.468161i	−0.968937	+	0.247309i	$0.920454\pi$
$360$	3.00000			0.158114
$361$	6.98528	−	12.0989i	0.367646	−	0.636782i
$362$	−23.2426			−1.22161
$363$	10.5000	−	6.06218i	0.551107	−	0.318182i
$364$	2.00000	−	4.89898i	0.104828	−	0.256776i
$365$	2.24264	+	3.88437i	0.117385	+	0.203317i
$366$	18.7279	+	10.8126i	0.978924	+	0.565182i
$367$	15.8640	+	27.4772i	0.828092	+	1.43430i	0.899533	+	0.436853i	$0.143907\pi$
$367$	15.8640	+	27.4772i	0.828092	+	1.43430i	−0.0714411	+	0.997445i	$0.522760\pi$
$368$	4.24264	−	7.34847i	0.221163	−	0.383065i
$369$	13.5000	−	23.3827i	0.702782	−	1.21725i
$370$	8.24264			0.428514
$371$	−4.60660	+	0.630399i	−0.239163	+	0.0327287i
$372$	−9.36396	−	5.40629i	−0.485499	−	0.280303i
$373$	16.8492	−	29.1837i	0.872421	−	1.51108i	0.0129355	−	0.999916i	$-0.495882\pi$
$373$	16.8492	−	29.1837i	0.872421	−	1.51108i	0.859485	−	0.511161i	$-0.170784\pi$
$374$		0			0
$375$	1.50000	+	0.866025i	0.0774597	+	0.0447214i
$376$	1.24264			0.0640843
$377$	2.48528			0.127999
$378$	10.8640	−	8.42463i	0.558782	−	0.433316i
$379$	34.4853			1.77139			0.885695	−	0.464268i	$-0.153682\pi$
$379$	34.4853			1.77139			0.885695	+	0.464268i	$0.153682\pi$
$380$	2.24264			0.115045
$381$	−10.1360	−	5.85204i	−0.519285	−	0.299809i
$382$	14.4853			0.741131
$383$	−4.13604	+	7.16383i	−0.211342	+	0.366055i	−0.952135	−	0.305679i	$-0.901117\pi$
$383$	−4.13604	+	7.16383i	−0.211342	+	0.366055i	0.740793	+	0.671733i	$0.234450\pi$
$384$	−1.50000	−	0.866025i	−0.0765466	−	0.0441942i
$385$	6.87868	+	8.87039i	0.350570	+	0.452077i
$386$	0.242641			0.0123501
$387$	3.00000			0.152499
$388$	3.24264	−	5.61642i	0.164620	−	0.285130i
$389$	−15.1066	−	26.1654i	−0.765935	−	1.32664i	−0.939751	−	0.341860i	$-0.888943\pi$
$389$	−15.1066	−	26.1654i	−0.765935	−	1.32664i	0.173816	−	0.984778i	$-0.444390\pi$
$390$	3.00000	+	1.73205i	0.151911	+	0.0877058i
$391$		0			0
$392$	−1.74264	+	6.77962i	−0.0880166	+	0.342422i
$393$	5.27208	−	3.04384i	0.265941	−	0.153541i
$394$	27.2132			1.37098
$395$	−5.36396	+	9.29065i	−0.269890	+	0.467463i
$396$	−6.36396	+	11.0227i	−0.319801	+	0.553912i
$397$	−15.1213	−	26.1909i	−0.758917	−	1.31448i	−0.943403	−	0.331648i	$-0.892395\pi$
$397$	−15.1213	−	26.1909i	−0.758917	−	1.31448i	0.184486	−	0.982835i	$-0.440938\pi$
$398$	−2.24264	+	3.88437i	−0.112413	+	0.194706i
$399$	8.12132	−	6.29780i	0.406575	−	0.315285i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	3.25736	−	5.64191i	0.162665	−	0.281744i	−0.773159	−	0.634213i	$-0.781324\pi$
$401$	3.25736	−	5.64191i	0.162665	−	0.281744i	0.935824	+	0.352469i	$0.114658\pi$
$402$	9.72792	+	5.61642i	0.485185	+	0.280121i
$403$	−6.24264	−	10.8126i	−0.310968	−	0.538613i
$404$	6.62132	+	11.4685i	0.329423	+	0.570577i
$405$	4.50000	+	7.79423i	0.223607	+	0.387298i
$406$	−3.25736	+	0.445759i	−0.161660	+	0.0221227i
$407$	−17.4853	+	30.2854i	−0.866713	+	1.50119i
$408$		0			0
$409$	1.48528			0.0734424			0.0367212	−	0.999326i	$-0.488309\pi$
$409$	1.48528			0.0734424			0.0367212	+	0.999326i	$0.488309\pi$
$410$	−9.00000			−0.444478
$411$			32.4377i			1.60003i
$412$	−1.62132	+	2.80821i	−0.0798767	+	0.138351i
$413$	2.84924	+	3.67423i	0.140202	+	0.180797i
$414$	25.4558			1.25109
$415$	−4.50000	−	7.79423i	−0.220896	−	0.382604i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$		−	24.6690i		−	1.20805i
$418$	−4.75736	+	8.23999i	−0.232690	+	0.403031i
$419$	17.4853	+	30.2854i	0.854212	+	1.47954i	0.877374	+	0.479807i	$0.159293\pi$
$419$	17.4853	+	30.2854i	0.854212	+	1.47954i	−0.0231623	+	0.999732i	$0.507373\pi$
$420$	−4.24264	−	1.73205i	−0.207020	−	0.0845154i
$421$	20.1066	−	34.8257i	0.979936	−	1.69730i	0.317357	−	0.948306i	$-0.397204\pi$
$421$	20.1066	−	34.8257i	0.979936	−	1.69730i	0.662578	−	0.748993i	$-0.269462\pi$
$422$	−1.87868	−	3.25397i	−0.0914527	−	0.158401i
$423$	1.86396	+	3.22848i	0.0906289	+	0.156974i
$424$	−0.878680	+	1.52192i	−0.0426725	+	0.0739109i
$425$		0			0
$426$	−6.36396	−	3.67423i	−0.308335	−	0.178017i
$427$	−20.2426	−	26.1039i	−0.979610	−	1.26325i
$428$	−7.50000	−	12.9904i	−0.362526	−	0.627914i
$429$	−12.7279	+	7.34847i	−0.614510	+	0.354787i
$430$	−0.500000	−	0.866025i	−0.0241121	−	0.0417635i
$431$	7.24264	−	12.5446i	0.348866	−	0.604253i	−0.637183	−	0.770713i	$-0.719900\pi$
$431$	7.24264	−	12.5446i	0.348866	−	0.604253i	0.986048	+	0.166460i	$0.0532336\pi$
$432$		−	5.19615i		−	0.250000i
$433$	27.4558			1.31944			0.659722	−	0.751510i	$-0.270674\pi$
$433$	27.4558			1.31944			0.659722	+	0.751510i	$0.270674\pi$
$434$	10.1213	+	13.0519i	0.485839	+	0.626513i
$435$		−	2.15232i		−	0.103196i
$436$	−8.86396	+	15.3528i	−0.424507	+	0.735267i
$437$	19.0294			0.910301
$438$	6.72792	−	3.88437i	0.321473	−	0.185602i
$439$	13.2721			0.633442			0.316721	−	0.948519i	$-0.397418\pi$
$439$	13.2721			0.633442			0.316721	+	0.948519i	$0.397418\pi$
$440$	4.24264			0.202260
$441$	−20.2279	+	5.64191i	−0.963234	+	0.268662i
$442$		0			0
$443$	12.5147			0.594592			0.297296	−	0.954785i	$-0.403915\pi$
$443$	12.5147			0.594592			0.297296	+	0.954785i	$0.403915\pi$
$444$		−	14.2767i		−	0.677541i
$445$		0			0
$446$	−5.86396	+	10.1567i	−0.277667	+	0.480933i
$447$	21.7279	−	12.5446i	1.02770	−	0.593340i
$448$	1.62132	+	2.09077i	0.0766002	+	0.0987796i
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$	1.50000	−	2.59808i	0.0707107	−	0.122474i
$451$	19.0919	−	33.0681i	0.899002	−	1.55712i
$452$	−6.36396	−	11.0227i	−0.299336	−	0.518464i
$453$			0.420266i			0.0197458i
$454$	9.00000	+	15.5885i	0.422391	+	0.731603i
$455$	−3.24264	−	4.18154i	−0.152017	−	0.196034i
$456$		−	3.88437i		−	0.181902i
$457$	18.9706			0.887405			0.443703	−	0.896174i	$-0.353665\pi$
$457$	18.9706			0.887405			0.443703	+	0.896174i	$0.353665\pi$
$458$	14.6213	−	25.3249i	0.683209	−	1.18335i
$459$		0			0
$460$	−4.24264	−	7.34847i	−0.197814	−	0.342624i
$461$	−15.1066	+	26.1654i	−0.703585	+	1.21864i	0.263615	+	0.964628i	$0.415085\pi$
$461$	−15.1066	+	26.1654i	−0.703585	+	1.21864i	−0.967200	+	0.254016i	$0.918248\pi$
$462$	15.3640	−	11.9142i	0.714796	−	0.554300i
$463$	−2.86396	−	4.96053i	−0.133100	−	0.230535i	0.791770	−	0.610819i	$-0.209160\pi$
$463$	−2.86396	−	4.96053i	−0.133100	−	0.230535i	−0.924870	+	0.380284i	$0.875826\pi$
$464$	−0.621320	+	1.07616i	−0.0288441	+	0.0499594i
$465$	−9.36396	+	5.40629i	−0.434243	+	0.250710i
$466$	−9.87868	−	17.1104i	−0.457621	−	0.792623i
$467$	−0.985281	−	1.70656i	−0.0455934	−	0.0789701i	0.842328	−	0.538965i	$-0.181185\pi$
$467$	−0.985281	−	1.70656i	−0.0455934	−	0.0789701i	−0.887921	+	0.459995i	$0.847851\pi$
$468$	3.00000	−	5.19615i	0.138675	−	0.240192i
$469$	−10.5147	−	13.5592i	−0.485525	−	0.626107i
$470$	0.621320	−	1.07616i	0.0286594	−	0.0496395i
$471$	25.0919	+	14.4868i	1.15617	+	0.667517i
$472$	1.75736			0.0808890
$473$	4.24264			0.195077
$474$	16.0919	+	9.29065i	0.739125	+	0.426734i
$475$	1.12132	−	1.94218i	0.0514497	−	0.0891135i
$476$		0			0
$477$	−5.27208			−0.241392
$478$	−11.1213	−	19.2627i	−0.508677	−	0.881055i
$479$	−7.24264	−	12.5446i	−0.330925	−	0.573178i	0.651769	−	0.758418i	$-0.274027\pi$
$479$	−7.24264	−	12.5446i	−0.330925	−	0.573178i	−0.982693	+	0.185239i	$0.940694\pi$
$480$	−1.50000	+	0.866025i	−0.0684653	+	0.0395285i
$481$	8.24264	−	14.2767i	0.375832	−	0.650960i
$482$	−3.74264	−	6.48244i	−0.170473	−	0.295267i
$483$	−36.0000	−	14.6969i	−1.63806	−	0.668734i
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$	−3.24264	−	5.61642i	−0.147241	−	0.255028i
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$	−6.48528	+	11.2328i	−0.293876	+	0.509008i	−0.974723	−	0.223418i	$-0.928279\pi$
$487$	−6.48528	+	11.2328i	−0.293876	+	0.509008i	0.680847	+	0.732426i	$0.261612\pi$
$488$	−12.4853			−0.565182
$489$		−	25.9298i		−	1.17258i
$490$	5.00000	+	4.89898i	0.225877	+	0.221313i
$491$	−11.1213	−	19.2627i	−0.501898	−	0.869313i	−0.999998	−	0.00219320i	$-0.999302\pi$
$491$	−11.1213	−	19.2627i	−0.501898	−	0.869313i	0.498099	−	0.867120i	$-0.334031\pi$
$492$			15.5885i			0.702782i
$493$		0			0
$494$	2.24264	−	3.88437i	0.100901	−	0.174766i
$495$	6.36396	+	11.0227i	0.286039	+	0.495434i
$496$	6.24264			0.280303
$497$	6.87868	+	8.87039i	0.308551	+	0.397891i
$498$	−13.5000	+	7.79423i	−0.604949	+	0.349268i
$499$	−12.8492	+	22.2555i	−0.575211	+	0.996295i	0.420808	+	0.907150i	$0.361747\pi$
$499$	−12.8492	+	22.2555i	−0.575211	+	0.996295i	−0.996019	+	0.0891449i	$0.971587\pi$
$500$	−1.00000			−0.0447214
$501$			35.4815i			1.58520i
$502$	−9.51472			−0.424663
$503$	4.75736			0.212120			0.106060	−	0.994360i	$-0.466176\pi$
$503$	4.75736			0.212120			0.106060	+	0.994360i	$0.466176\pi$
$504$	−3.00000	+	7.34847i	−0.133631	+	0.327327i
$505$	13.2426			0.589290
$506$	36.0000			1.60040
$507$	−13.5000	+	7.79423i	−0.599556	+	0.346154i
$508$	6.75736			0.299809
$509$	−15.6213	+	27.0569i	−0.692403	+	1.19928i	0.278646	+	0.960394i	$0.410115\pi$
$509$	−15.6213	+	27.0569i	−0.692403	+	1.19928i	−0.971048	+	0.238883i	$0.923219\pi$
$510$		0			0
$511$	−11.7574	+	1.60896i	−0.520115	+	0.0711761i
$512$	1.00000			0.0441942
$513$	10.0919	−	5.82655i	0.445568	−	0.257249i
$514$	−8.48528	+	14.6969i	−0.374270	+	0.648254i
$515$	1.62132	+	2.80821i	0.0714439	+	0.123744i
$516$	−1.50000	+	0.866025i	−0.0660338	+	0.0381246i
$517$	2.63604	+	4.56575i	0.115933	+	0.200802i
$518$	−8.24264	+	20.1903i	−0.362161	+	0.887109i
$519$	15.3640	+	8.87039i	0.674403	+	0.389367i
$520$	−2.00000			−0.0877058
$521$	−17.2279	+	29.8396i	−0.754769	+	1.30730i	0.190720	+	0.981644i	$0.438918\pi$
$521$	−17.2279	+	29.8396i	−0.754769	+	1.30730i	−0.945489	+	0.325654i	$0.894416\pi$
$522$	−3.72792			−0.163167
$523$	−1.25736	−	2.17781i	−0.0549805	−	0.0952290i	0.837225	−	0.546858i	$-0.184176\pi$
$523$	−1.25736	−	2.17781i	−0.0549805	−	0.0952290i	−0.892206	+	0.451629i	$0.850843\pi$
$524$	−1.75736	+	3.04384i	−0.0767706	+	0.132971i
$525$	−3.62132	+	2.80821i	−0.158047	+	0.122560i
$526$	7.86396	+	13.6208i	0.342885	+	0.593894i
$527$		0			0
$528$		−	7.34847i		−	0.319801i
$529$	−24.5000	−	42.4352i	−1.06522	−	1.84501i
$530$	0.878680	+	1.52192i	0.0381674	+	0.0661079i
$531$	2.63604	+	4.56575i	0.114394	+	0.198137i
$532$	−2.24264	+	5.49333i	−0.0972308	+	0.238166i
$533$	−9.00000	+	15.5885i	−0.389833	+	0.675211i
$534$		0			0
$535$	−15.0000			−0.648507
$536$	−6.48528			−0.280121
$537$	2.63604	−	1.52192i	0.113753	−	0.0656756i
$538$	11.4853	−	19.8931i	0.495166	−	0.857652i
$539$	−28.6066	+	7.97887i	−1.23217	+	0.343674i
$540$	−4.50000	−	2.59808i	−0.193649	−	0.111803i
$541$	−10.7279	−	18.5813i	−0.461229	−	0.798873i	0.537793	−	0.843077i	$-0.319258\pi$
$541$	−10.7279	−	18.5813i	−0.461229	−	0.798873i	−0.999023	+	0.0442041i	$0.985925\pi$
$542$	−10.3640	−	17.9509i	−0.445170	−	0.771057i
$543$	34.8640	+	20.1287i	1.49616	+	0.863806i
$544$		0			0
$545$	8.86396	+	15.3528i	0.379690	+	0.657643i
$546$	−7.24264	+	5.61642i	−0.309956	+	0.240361i
$547$	−6.22792	+	10.7871i	−0.266287	+	0.461222i	−0.967900	−	0.251336i	$-0.919130\pi$
$547$	−6.22792	+	10.7871i	−0.266287	+	0.461222i	0.701613	+	0.712558i	$0.252463\pi$
$548$	−9.36396	−	16.2189i	−0.400009	−	0.692835i
$549$	−18.7279	−	32.4377i	−0.799288	−	1.38441i
$550$	2.12132	−	3.67423i	0.0904534	−	0.156670i
$551$	−2.78680			−0.118722
$552$	−12.7279	+	7.34847i	−0.541736	+	0.312772i
$553$	−17.3934	−	22.4296i	−0.739643	−	0.953804i
$554$	−4.87868	−	8.45012i	−0.207275	−	0.359011i
$555$	−12.3640	−	7.13834i	−0.524821	−	0.303005i
$556$	7.12132	+	12.3345i	0.302011	+	0.523099i
$557$	−20.4853	+	35.4815i	−0.867989	+	1.50340i	−0.00394110	+	0.999992i	$0.501254\pi$
$557$	−20.4853	+	35.4815i	−0.867989	+	1.50340i	−0.864048	+	0.503409i	$0.832079\pi$
$558$	9.36396	+	16.2189i	0.396408	+	0.686599i
$559$	−2.00000			−0.0845910
$560$	2.62132	−	0.358719i	0.110771	−	0.0151587i
$561$		0			0
$562$	−3.98528	+	6.90271i	−0.168109	+	0.291173i
$563$	−4.97056			−0.209484			−0.104742	−	0.994499i	$-0.533402\pi$
$563$	−4.97056			−0.209484			−0.104742	+	0.994499i	$0.533402\pi$
$564$	−1.86396	−	1.07616i	−0.0784869	−	0.0453144i
$565$	−12.7279			−0.535468
$566$	1.48528			0.0624310
$567$	−23.5919	+	3.22848i	−0.990766	+	0.135583i
$568$	4.24264			0.178017
$569$	4.97056			0.208377			0.104188	−	0.994558i	$-0.466776\pi$
$569$	4.97056			0.208377			0.104188	+	0.994558i	$0.466776\pi$
$570$	−3.36396	−	1.94218i	−0.140901	−	0.0813491i
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$	4.24264	−	7.34847i	0.177394	−	0.307255i
$573$	−21.7279	−	12.5446i	−0.907697	−	0.524059i
$574$	9.00000	−	22.0454i	0.375653	−	0.920158i
$575$	−8.48528			−0.353861
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−18.4853	+	32.0174i	−0.769552	+	1.33290i	0.168254	+	0.985744i	$0.446187\pi$
$577$	−18.4853	+	32.0174i	−0.769552	+	1.33290i	−0.937806	+	0.347160i	$0.887146\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$	−0.363961	−	0.210133i	−0.0151257	−	0.00873283i
$580$	0.621320	+	1.07616i	0.0257989	+	0.0446850i
$581$	23.5919	−	3.22848i	0.978756	−	0.133940i
$582$	−9.72792	+	5.61642i	−0.403235	+	0.232808i
$583$	−7.45584			−0.308790
$584$	−2.24264	+	3.88437i	−0.0928011	+	0.160736i
$585$	−3.00000	−	5.19615i	−0.124035	−	0.214834i
$586$	−10.2426	−	17.7408i	−0.423120	−	0.732865i
$587$	−2.22792	+	3.85887i	−0.0919562	+	0.159273i	−0.908334	−	0.418245i	$-0.862645\pi$
$587$	−2.22792	+	3.85887i	−0.0919562	+	0.159273i	0.816378	+	0.577518i	$0.195979\pi$
$588$	8.48528	−	8.66025i	0.349927	−	0.357143i
$589$	7.00000	+	12.1244i	0.288430	+	0.499575i
$590$	0.878680	−	1.52192i	0.0361747	−	0.0626564i
$591$	−40.8198	−	23.5673i	−1.67910	−	0.969430i
$592$	4.12132	+	7.13834i	0.169385	+	0.293384i
$593$	4.75736	+	8.23999i	0.195361	+	0.338376i	0.947019	−	0.321178i	$-0.104079\pi$
$593$	4.75736	+	8.23999i	0.195361	+	0.338376i	−0.751658	+	0.659554i	$0.770745\pi$
$594$	19.0919	−	11.0227i	0.783349	−	0.452267i
$595$		0			0
$596$	−7.24264	+	12.5446i	−0.296670	+	0.513848i
$597$	6.72792	−	3.88437i	0.275356	−	0.158977i
$598$	−16.9706			−0.693978
$599$	−33.9411			−1.38680			−0.693398	−	0.720554i	$-0.743887\pi$
$599$	−33.9411			−1.38680			−0.693398	+	0.720554i	$0.743887\pi$
$600$			1.73205i			0.0707107i
$601$	8.00000	−	13.8564i	0.326327	−	0.565215i	−0.655453	−	0.755236i	$-0.727522\pi$
$601$	8.00000	−	13.8564i	0.326327	−	0.565215i	0.981780	+	0.190021i	$0.0608557\pi$
$602$	2.62132	−	0.358719i	0.106837	−	0.0146203i
$603$	−9.72792	−	16.8493i	−0.396152	−	0.686155i
$604$	−0.121320	−	0.210133i	−0.00493645	−	0.00855019i
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$		−	22.9369i		−	0.931749i
$607$	−22.6213	+	39.1813i	−0.918171	+	1.59032i	−0.115980	+	0.993252i	$0.537001\pi$
$607$	−22.6213	+	39.1813i	−0.918171	+	1.59032i	−0.802191	+	0.597067i	$0.796332\pi$
$608$	1.12132	+	1.94218i	0.0454755	+	0.0787660i
$609$	5.27208	+	2.15232i	0.213635	+	0.0872163i
$610$	−6.24264	+	10.8126i	−0.252757	+	0.437788i
$611$	−1.24264	−	2.15232i	−0.0502719	−	0.0870734i
$612$		0			0
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	−0.747208	−	0.664590i	$-0.768606\pi$
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	0.949156	+	0.314806i	$0.101939\pi$
$614$	−29.9706			−1.20951
$615$	13.5000	+	7.79423i	0.544373	+	0.314294i
$616$	−4.24264	+	10.3923i	−0.170941	+	0.418718i
$617$	1.75736	+	3.04384i	0.0707486	+	0.122540i	0.899230	−	0.437477i	$-0.144128\pi$
$617$	1.75736	+	3.04384i	0.0707486	+	0.122540i	−0.828481	+	0.560017i	$0.810795\pi$
$618$	4.86396	−	2.80821i	0.195657	−	0.112963i
$619$	18.2426	+	31.5972i	0.733234	+	1.27000i	0.955494	+	0.295011i	$0.0953232\pi$
$619$	18.2426	+	31.5972i	0.733234	+	1.27000i	−0.222260	+	0.974987i	$0.571343\pi$
$620$	3.12132	−	5.40629i	0.125355	−	0.217122i
$621$	−38.1838	−	22.0454i	−1.53226	−	0.884652i
$622$	24.7279			0.991499
$623$		0			0
$624$			3.46410i			0.138675i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	17.2132			0.687978
$627$	14.2721	−	8.23999i	0.569972	−	0.329073i
$628$	−16.7279			−0.667517
$629$		0			0
$630$	4.86396	+	6.27231i	0.193785	+	0.249895i
$631$	−7.51472			−0.299156			−0.149578	−	0.988750i	$-0.547792\pi$
$631$	−7.51472			−0.299156			−0.149578	+	0.988750i	$0.547792\pi$
$632$	−10.7279			−0.426734
$633$			6.50794i			0.258667i
$634$	−31.4558			−1.24927
$635$	3.37868	−	5.85204i	0.134079	−	0.232231i
$636$	2.63604	−	1.52192i	0.104526	−	0.0603480i
$637$	13.4853	−	3.76127i	0.534306	−	0.149027i
$638$	−5.27208			−0.208724
$639$	6.36396	+	11.0227i	0.251754	+	0.436051i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	5.48528	+	9.50079i	0.216656	+	0.375258i	0.953783	−	0.300495i	$-0.0971518\pi$
$641$	5.48528	+	9.50079i	0.216656	+	0.375258i	−0.737128	+	0.675753i	$0.763818\pi$
$642$			25.9808i			1.02538i
$643$	−18.2279	−	31.5717i	−0.718839	−	1.24507i	−0.961460	−	0.274945i	$-0.911340\pi$
$643$	−18.2279	−	31.5717i	−0.718839	−	1.24507i	0.242621	−	0.970121i	$-0.421993\pi$
$644$	22.2426	−	3.04384i	0.876483	−	0.119944i
$645$			1.73205i			0.0681994i
$646$		0			0
$647$	−7.13604	+	12.3600i	−0.280547	+	0.485921i	−0.971519	−	0.236960i	$-0.923849\pi$
$647$	−7.13604	+	12.3600i	−0.280547	+	0.485921i	0.690973	+	0.722881i	$0.257182\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$	3.72792	+	6.45695i	0.146334	+	0.253457i
$650$	−1.00000	+	1.73205i	−0.0392232	+	0.0679366i
$651$	−3.87868	−	28.3432i	−0.152017	−	1.11086i
$652$	7.48528	+	12.9649i	0.293146	+	0.507744i
$653$	−18.7279	+	32.4377i	−0.732880	+	1.26939i	0.222767	+	0.974872i	$0.428491\pi$
$653$	−18.7279	+	32.4377i	−0.732880	+	1.26939i	−0.955647	+	0.294514i	$0.904842\pi$
$654$	26.5919	−	15.3528i	1.03982	−	0.600343i
$655$	1.75736	+	3.04384i	0.0686657	+	0.118932i
$656$	−4.50000	−	7.79423i	−0.175695	−	0.304314i
$657$	−13.4558			−0.524962
$658$	2.01472	+	2.59808i	0.0785419	+	0.101284i
$659$	11.8492	−	20.5235i	0.461581	−	0.799482i	−0.537459	−	0.843290i	$-0.680616\pi$
$659$	11.8492	−	20.5235i	0.461581	−	0.799482i	0.999040	+	0.0438082i	$0.0139491\pi$
$660$	−6.36396	−	3.67423i	−0.247717	−	0.143019i
$661$	−5.24264			−0.203915			−0.101958	−	0.994789i	$-0.532511\pi$
$661$	−5.24264			−0.203915			−0.101958	+	0.994789i	$0.532511\pi$
$662$	−4.00000			−0.155464
$663$		0			0
$664$	4.50000	−	7.79423i	0.174634	−	0.302475i
$665$	3.63604	+	4.68885i	0.141000	+	0.181826i
$666$	−12.3640	+	21.4150i	−0.479094	+	0.829815i
$667$	5.27208	+	9.13151i	0.204136	+	0.353573i
$668$	−10.2426	−	17.7408i	−0.396300	−	0.686411i
$669$	17.5919	−	10.1567i	0.680141	−	0.392680i
$670$	−3.24264	+	5.61642i	−0.125274	+	0.216981i
$671$	−26.4853	−	45.8739i	−1.02245	−	1.77094i
$672$	−0.621320	−	4.54026i	−0.0239680	−	0.175144i
$673$	−13.3640	+	23.1471i	−0.515143	+	0.892254i	0.484703	+	0.874679i	$0.338928\pi$
$673$	−13.3640	+	23.1471i	−0.515143	+	0.892254i	−0.999846	+	0.0175746i	$0.994406\pi$
$674$	−5.24264	−	9.08052i	−0.201939	−	0.349769i
$675$	−4.50000	+	2.59808i	−0.173205	+	0.100000i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−0.727922			−0.0279763			−0.0139882	−	0.999902i	$-0.504453\pi$
$677$	−0.727922			−0.0279763			−0.0139882	+	0.999902i	$0.504453\pi$
$678$			22.0454i			0.846649i
$679$	17.0000	−	2.32640i	0.652400	−	0.0892789i
$680$		0			0
$681$		−	31.1769i		−	1.19470i
$682$	13.2426	+	22.9369i	0.507087	+	0.878300i
$683$	17.7426	−	30.7312i	0.678903	−	1.17589i	−0.296408	−	0.955061i	$-0.595789\pi$
$683$	17.7426	−	30.7312i	0.678903	−	1.17589i	0.975311	−	0.220834i	$-0.0708778\pi$
$684$	−3.36396	+	5.82655i	−0.128624	+	0.222784i
$685$	−18.7279			−0.715557
$686$	−17.0000	+	7.34847i	−0.649063	+	0.280566i
$687$	−43.8640	+	25.3249i	−1.67351	+	0.966204i
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	3.51472			0.133900
$690$			14.6969i			0.559503i
$691$	0.970563			0.0369219			0.0184610	−	0.999830i	$-0.494123\pi$
$691$	0.970563			0.0369219			0.0184610	+	0.999830i	$0.494123\pi$
$692$	−10.2426			−0.389367
$693$	−33.3640	+	4.56575i	−1.26739	+	0.173439i
$694$	−9.00000			−0.341635
$695$	14.2426			0.540254
$696$	1.86396	−	1.07616i	0.0706533	−	0.0407917i
$697$		0			0
$698$	−13.0000	+	22.5167i	−0.492057	+	0.852268i
$699$			34.2208i			1.29435i
$700$	1.00000	−	2.44949i	0.0377964	−	0.0925820i
$701$	−20.6985			−0.781771			−0.390885	−	0.920439i	$-0.627831\pi$
$701$	−20.6985			−0.781771			−0.390885	+	0.920439i	$0.627831\pi$
$702$	−9.00000	+	5.19615i	−0.339683	+	0.196116i
$703$	−9.24264	+	16.0087i	−0.348593	+	0.603780i
$704$	2.12132	+	3.67423i	0.0799503	+	0.138478i
$705$	−1.86396	+	1.07616i	−0.0702008	+	0.0405305i
$706$	0.878680	+	1.52192i	0.0330695	+	0.0572781i
$707$	−13.2426	+	32.4377i	−0.498041	+	1.21995i
$708$	−2.63604	−	1.52192i	−0.0990684	−	0.0571972i
$709$	18.9706			0.712454			0.356227	−	0.934399i	$-0.384063\pi$
$709$	18.9706			0.712454			0.356227	+	0.934399i	$0.384063\pi$
$710$	2.12132	−	3.67423i	0.0796117	−	0.137892i
$711$	−16.0919	−	27.8720i	−0.603493	−	1.04528i
$712$		0			0
$713$	26.4853	−	45.8739i	0.991882	−	1.71799i
$714$		0			0
$715$	−4.24264	−	7.34847i	−0.158666	−	0.274817i
$716$	−0.878680	+	1.52192i	−0.0328378	+	0.0568767i
$717$			38.5254i			1.43876i
$718$	−5.12132	−	8.87039i	−0.191126	−	0.331040i
$719$	16.2426	+	28.1331i	0.605748	+	1.04919i	0.991933	+	0.126765i	$0.0404595\pi$
$719$	16.2426	+	28.1331i	0.605748	+	1.04919i	−0.386184	+	0.922422i	$0.626207\pi$
$720$	3.00000			0.111803
$721$	−8.50000	+	1.16320i	−0.316557	+	0.0433198i
$722$	6.98528	−	12.0989i	0.259965	−	0.450273i
$723$			12.9649i			0.482169i
$724$	−23.2426			−0.863806
$725$	1.24264			0.0461505
$726$	10.5000	−	6.06218i	0.389692	−	0.224989i
$727$	−3.48528	+	6.03668i	−0.129262	+	0.223888i	−0.923391	−	0.383861i	$-0.874594\pi$
$727$	−3.48528	+	6.03668i	−0.129262	+	0.223888i	0.794129	+	0.607749i	$0.207927\pi$
$728$	2.00000	−	4.89898i	0.0741249	−	0.181568i
$729$	−27.0000			−1.00000
$730$	2.24264	+	3.88437i	0.0830039	+	0.143767i
$731$		0			0
$732$	18.7279	+	10.8126i	0.692204	+	0.399644i
$733$	4.12132	−	7.13834i	0.152224	−	0.263660i	−0.779820	−	0.626003i	$-0.784690\pi$
$733$	4.12132	−	7.13834i	0.152224	−	0.263660i	0.932045	+	0.362343i	$0.118023\pi$
$734$	15.8640	+	27.4772i	0.585549	+	1.01420i
$735$	−3.25736	−	11.6786i	−0.120150	−	0.430772i
$736$	4.24264	−	7.34847i	0.156386	−	0.270868i
$737$	−13.7574	−	23.8284i	−0.506759	−	0.877732i
$738$	13.5000	−	23.3827i	0.496942	−	0.860729i
$739$	16.4853	−	28.5533i	0.606421	−	1.05035i	−0.385404	−	0.922748i	$-0.625938\pi$
$739$	16.4853	−	28.5533i	0.606421	−	1.05035i	0.991825	−	0.127604i	$-0.0407286\pi$
$740$	8.24264			0.303005
$741$	−6.72792	+	3.88437i	−0.247156	+	0.142696i
$742$	−4.60660	+	0.630399i	−0.169114	+	0.0231427i
$743$	−5.37868	−	9.31615i	−0.197325	−	0.341776i	0.750335	−	0.661057i	$-0.229892\pi$
$743$	−5.37868	−	9.31615i	−0.197325	−	0.341776i	−0.947660	+	0.319281i	$0.896559\pi$
$744$	−9.36396	−	5.40629i	−0.343299	−	0.198204i
$745$	7.24264	+	12.5446i	0.265350	+	0.459599i
$746$	16.8492	−	29.1837i	0.616895	−	1.06849i
$747$	27.0000			0.987878
$748$		0			0
$749$	15.0000	−	36.7423i	0.548088	−	1.34254i
$750$	1.50000	+	0.866025i	0.0547723	+	0.0316228i
$751$	−2.75736	+	4.77589i	−0.100617	+	0.174275i	−0.911939	−	0.410325i	$-0.865415\pi$
$751$	−2.75736	+	4.77589i	−0.100617	+	0.174275i	0.811322	+	0.584600i	$0.198748\pi$
$752$	1.24264			0.0453144
$753$	14.2721	+	8.23999i	0.520103	+	0.300282i
$754$	2.48528			0.0905086
$755$	−0.242641			−0.00883060
$756$	10.8640	−	8.42463i	0.395118	−	0.306401i
$757$	4.78680			0.173979			0.0869895	−	0.996209i	$-0.472275\pi$
$757$	4.78680			0.173979			0.0869895	+	0.996209i	$0.472275\pi$
$758$	34.4853			1.25256
$759$	−54.0000	−	31.1769i	−1.96008	−	1.13165i
$760$	2.24264			0.0813491
$761$	−7.50000	+	12.9904i	−0.271875	+	0.470901i	−0.969342	−	0.245716i	$-0.920977\pi$
$761$	−7.50000	+	12.9904i	−0.271875	+	0.470901i	0.697467	+	0.716617i	$0.254310\pi$
$762$	−10.1360	−	5.85204i	−0.367190	−	0.211997i
$763$	−46.4706	+	6.35935i	−1.68235	+	0.230224i
$764$	14.4853			0.524059
$765$		0			0
$766$	−4.13604	+	7.16383i	−0.149441	+	0.258840i
$767$	−1.75736	−	3.04384i	−0.0634546	−	0.109907i
$768$	−1.50000	−	0.866025i	−0.0541266	−	0.0312500i
$769$	4.74264	+	8.21449i	0.171024	+	0.296222i	0.938778	−	0.344522i	$-0.111959\pi$
$769$	4.74264	+	8.21449i	0.171024	+	0.296222i	−0.767754	+	0.640745i	$0.778626\pi$
$770$	6.87868	+	8.87039i	0.247890	+	0.319667i
$771$	25.4558	−	14.6969i	0.916770	−	0.529297i
$772$	0.242641			0.00873283
$773$	4.75736	−	8.23999i	0.171110	−	0.296372i	−0.767698	−	0.640812i	$-0.778598\pi$
$773$	4.75736	−	8.23999i	0.171110	−	0.296372i	0.938808	+	0.344440i	$0.111931\pi$
$774$	3.00000			0.107833
$775$	−3.12132	−	5.40629i	−0.112121	−	0.194200i
$776$	3.24264	−	5.61642i	0.116404	−	0.201618i
$777$	29.8492	−	23.1471i	1.07084	−	0.830396i
$778$	−15.1066	−	26.1654i	−0.541598	−	0.938075i
$779$	10.0919	−	17.4797i	0.361579	−	0.626274i
$780$	3.00000	+	1.73205i	0.107417	+	0.0620174i
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$		0			0
$783$	5.59188	+	3.22848i	0.199838	+	0.115376i
$784$	−1.74264	+	6.77962i	−0.0622372	+	0.242129i
$785$	−8.36396	+	14.4868i	−0.298523	+	0.517056i
$786$	5.27208	−	3.04384i	0.188049	−	0.108570i
$787$	20.5147			0.731271			0.365635	−	0.930758i	$-0.380852\pi$
$787$	20.5147			0.731271			0.365635	+	0.930758i	$0.380852\pi$
$788$	27.2132			0.969430
$789$		−	27.2416i		−	0.969825i
$790$	−5.36396	+	9.29065i	−0.190841	+	0.330547i
$791$	12.7279	−	31.1769i	0.452553	−	1.10852i
$792$	−6.36396	+	11.0227i	−0.226134	+	0.391675i
$793$	12.4853	+	21.6251i	0.443365	+	0.767931i
$794$	−15.1213	−	26.1909i	−0.536636	−	0.929480i
$795$		−	3.04384i		−	0.107954i
$796$	−2.24264	+	3.88437i	−0.0794883	+	0.137678i
$797$	1.24264	+	2.15232i	0.0440166	+	0.0762390i	0.887194	−	0.461396i	$-0.152651\pi$
$797$	1.24264	+	2.15232i	0.0440166	+	0.0762390i	−0.843178	+	0.537635i	$0.819318\pi$
$798$	8.12132	−	6.29780i	0.287492	−	0.222940i
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	3.25736	−	5.64191i	0.115021	−	0.199223i
$803$	−19.0294			−0.671534
$804$	9.72792	+	5.61642i	0.343077	+	0.198076i
$805$	8.48528	−	20.7846i	0.299067	−	0.732561i
$806$	−6.24264	−	10.8126i	−0.219888	−	0.380857i
$807$	−34.4558	+	19.8931i	−1.21290	+	0.700270i
$808$	6.62132	+	11.4685i	0.232937	+	0.403459i
$809$	−9.98528	+	17.2950i	−0.351064	+	0.608060i	−0.986436	−	0.164146i	$-0.947513\pi$
$809$	−9.98528	+	17.2950i	−0.351064	+	0.608060i	0.635372	+	0.772206i	$0.280847\pi$
$810$	4.50000	+	7.79423i	0.158114	+	0.273861i
$811$	27.4558			0.964105			0.482053	−	0.876142i	$-0.339891\pi$
$811$	27.4558			0.964105			0.482053	+	0.876142i	$0.339891\pi$
$812$	−3.25736	+	0.445759i	−0.114311	+	0.0156431i
$813$			35.9018i			1.25913i
$814$	−17.4853	+	30.2854i	−0.612859	+	1.06150i
$815$	14.9706			0.524396
$816$		0			0
$817$	2.24264			0.0784601
$818$	1.48528			0.0519316
$819$	15.7279	−	2.15232i	0.549578	−	0.0752080i
$820$	−9.00000			−0.314294
$821$	32.6985			1.14118			0.570592	−	0.821233i	$-0.306714\pi$
$821$	32.6985			1.14118			0.570592	+	0.821233i	$0.306714\pi$
$822$			32.4377i			1.13140i
$823$	30.7574			1.07213			0.536067	−	0.844175i	$-0.319909\pi$
$823$	30.7574			1.07213			0.536067	+	0.844175i	$0.319909\pi$
$824$	−1.62132	+	2.80821i	−0.0564814	+	0.0978286i
$825$	−6.36396	+	3.67423i	−0.221565	+	0.127920i
$826$	2.84924	+	3.67423i	0.0991378	+	0.127843i
$827$	−36.9411			−1.28457			−0.642284	−	0.766466i	$-0.722013\pi$
$827$	−36.9411			−1.28457			−0.642284	+	0.766466i	$0.722013\pi$
$828$	25.4558			0.884652
$829$	6.86396	−	11.8887i	0.238395	−	0.412913i	−0.721859	−	0.692040i	$-0.756712\pi$
$829$	6.86396	−	11.8887i	0.238395	−	0.412913i	0.960254	+	0.279128i	$0.0900453\pi$
$830$	−4.50000	−	7.79423i	−0.156197	−	0.270542i
$831$			16.9002i			0.586263i
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$		0			0
$834$		−	24.6690i		−	0.854217i
$835$	−20.4853			−0.708922
$836$	−4.75736	+	8.23999i	−0.164537	+	0.284986i
$837$		−	32.4377i		−	1.12121i
$838$	17.4853	+	30.2854i	0.604019	+	1.04619i
$839$	25.0919	−	43.4604i	0.866268	−	1.50042i	0.000485409	−	1.00000i	$-0.499845\pi$
$839$	25.0919	−	43.4604i	0.866268	−	1.50042i	0.865783	−	0.500420i	$-0.166821\pi$
$840$	−4.24264	−	1.73205i	−0.146385	−	0.0597614i
$841$	13.7279	+	23.7775i	0.473377	+	0.819912i
$842$	20.1066	−	34.8257i	0.692919	−	1.20017i
$843$	11.9558	−	6.90271i	0.411781	−	0.237742i
$844$	−1.87868	−	3.25397i	−0.0646668	−	0.112006i
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$	1.86396	+	3.22848i	0.0640843	+	0.110997i
$847$	−18.3492	+	2.51104i	−0.630487	+	0.0862802i
$848$	−0.878680	+	1.52192i	−0.0301740	+	0.0522629i
$849$	−2.22792	−	1.28629i	−0.0764621	−	0.0441454i
$850$		0			0
$851$	69.9411			2.39755
$852$	−6.36396	−	3.67423i	−0.218026	−	0.125877i
$853$	1.27208	−	2.20330i	0.0435551	−	0.0754397i	−0.843426	−	0.537245i	$-0.819465\pi$
$853$	1.27208	−	2.20330i	0.0435551	−	0.0754397i	0.886981	+	0.461806i	$0.152798\pi$
$854$	−20.2426	−	26.1039i	−0.692689	−	0.893256i
$855$	3.36396	+	5.82655i	0.115045	+	0.199264i
$856$	−7.50000	−	12.9904i	−0.256345	−	0.444002i
$857$	19.0919	+	33.0681i	0.652166	+	1.12959i	0.982596	+	0.185755i	$0.0594730\pi$
$857$	19.0919	+	33.0681i	0.652166	+	1.12959i	−0.330430	+	0.943831i	$0.607194\pi$
$858$	−12.7279	+	7.34847i	−0.434524	+	0.250873i
$859$	−0.636039	+	1.10165i	−0.0217014	+	0.0375879i	−0.876672	−	0.481088i	$-0.840242\pi$
$859$	−0.636039	+	1.10165i	−0.0217014	+	0.0375879i	0.854971	+	0.518676i	$0.173575\pi$
$860$	−0.500000	−	0.866025i	−0.0170499	−	0.0295312i
$861$	−32.5919	+	25.2739i	−1.11073	+	0.861332i
$862$	7.24264	−	12.5446i	0.246685	−	0.427272i
$863$	25.9706	+	44.9823i	0.884048	+	1.53122i	0.846801	+	0.531910i	$0.178526\pi$
$863$	25.9706	+	44.9823i	0.884048	+	1.53122i	0.0372476	+	0.999306i	$0.488141\pi$
$864$		−	5.19615i		−	0.176777i
$865$	−5.12132	+	8.87039i	−0.174130	+	0.301602i
$866$	27.4558			0.932988
$867$		−	29.4449i		−	1.00000i
$868$	10.1213	+	13.0519i	0.343540	+	0.443011i
$869$	−22.7574	−	39.4169i	−0.771991	−	1.33713i
$870$		−	2.15232i		−	0.0729704i
$871$	6.48528	+	11.2328i	0.219745	+	0.380610i
$872$	−8.86396	+	15.3528i	−0.300172	+	0.519912i
$873$	19.4558			0.658481
$874$	19.0294			0.643680
$875$	−1.62132	−	2.09077i	−0.0548106	−	0.0706809i
$876$	6.72792	−	3.88437i	0.227315	−	0.131241i
$877$	−12.8492	+	22.2555i	−0.433888	+	0.751516i	−0.997204	−	0.0747253i	$-0.976192\pi$
$877$	−12.8492	+	22.2555i	−0.433888	+	0.751516i	0.563316	+	0.826241i	$0.309525\pi$
$878$	13.2721			0.447911
$879$			35.4815i			1.19676i
$880$	4.24264			0.143019
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	−20.2279	+	5.64191i	−0.681110	+	0.189973i
$883$	26.9411			0.906641			0.453321	−	0.891348i	$-0.350239\pi$
$883$	26.9411			0.906641			0.453321	+	0.891348i	$0.350239\pi$
$884$		0			0
$885$	−2.63604	+	1.52192i	−0.0886095	+	0.0511587i
$886$	12.5147			0.420440
$887$	0.621320	−	1.07616i	0.0208619	−	0.0361339i	−0.855406	−	0.517958i	$-0.826692\pi$
$887$	0.621320	−	1.07616i	0.0208619	−	0.0361339i	0.876268	+	0.481824i	$0.160026\pi$
$888$		−	14.2767i		−	0.479094i
$889$	10.9558	+	14.1281i	0.367447	+	0.473841i
$890$		0			0
$891$	−38.1838			−1.27920
$892$	−5.86396	+	10.1567i	−0.196340	+	0.340071i
$893$	1.39340	+	2.41344i	0.0466283	+	0.0807626i
$894$	21.7279	−	12.5446i	0.726690	−	0.419555i
$895$	0.878680	+	1.52192i	0.0293710	+	0.0508721i
$896$	1.62132	+	2.09077i	0.0541645	+	0.0698477i
$897$	25.4558	+	14.6969i	0.849946	+	0.490716i
$898$	9.00000			0.300334
$899$	−3.87868	+	6.71807i	−0.129361	+	0.224060i
$900$	1.50000	−	2.59808i	0.0500000	−	0.0866025i
$901$		0			0
$902$	19.0919	−	33.0681i	0.635690	−	1.10105i
$903$	−4.24264	−	1.73205i	−0.141186	−	0.0576390i
$904$	−6.36396	−	11.0227i	−0.211662	−	0.366610i
$905$	−11.6213	+	20.1287i	−0.386306	+	0.669101i
$906$			0.420266i			0.0139624i
$907$	25.2279	+	43.6960i	0.837679	+	1.45090i	0.891830	+	0.452371i	$0.149422\pi$
$907$	25.2279	+	43.6960i	0.837679	+	1.45090i	−0.0541507	+	0.998533i	$0.517245\pi$
$908$	9.00000	+	15.5885i	0.298675	+	0.517321i
$909$	−19.8640	+	34.4054i	−0.658846	+	1.14115i
$910$	−3.24264	−	4.18154i	−0.107492	−	0.138617i
$911$	23.3345	−	40.4166i	0.773107	−	1.33906i	−0.162745	−	0.986668i	$-0.552035\pi$
$911$	23.3345	−	40.4166i	0.773107	−	1.33906i	0.935852	−	0.352393i	$-0.114632\pi$
$912$		−	3.88437i		−	0.128624i
$913$	38.1838			1.26370
$914$	18.9706			0.627490
$915$	18.7279	−	10.8126i	0.619126	−	0.357453i
$916$	14.6213	−	25.3249i	0.483102	−	0.836757i
$917$	−9.21320	+	1.26080i	−0.304247	+	0.0416352i
$918$		0			0
$919$	4.12132	+	7.13834i	0.135950	+	0.235472i	0.925960	−	0.377622i	$-0.123258\pi$
$919$	4.12132	+	7.13834i	0.135950	+	0.235472i	−0.790010	+	0.613094i	$0.789925\pi$
$920$	−4.24264	−	7.34847i	−0.139876	−	0.242272i
$921$	44.9558	+	25.9553i	1.48135	+	0.855255i
$922$	−15.1066	+	26.1654i	−0.497509	+	0.861712i
$923$	−4.24264	−	7.34847i	−0.139648	−	0.241878i
$924$	15.3640	−	11.9142i	0.505437	−	0.391949i
$925$	4.12132	−	7.13834i	0.135508	−	0.234707i
$926$	−2.86396	−	4.96053i	−0.0941156	−	0.163013i
$927$	−9.72792			−0.319507
$928$	−0.621320	+	1.07616i	−0.0203958	+	0.0353266i
$929$	53.9117			1.76879			0.884393	−	0.466744i	$-0.154573\pi$
$929$	53.9117			1.76879			0.884393	+	0.466744i	$0.154573\pi$
$930$	−9.36396	+	5.40629i	−0.307056	+	0.177279i
$931$	−15.1213	+	4.21759i	−0.495581	+	0.138226i
$932$	−9.87868	−	17.1104i	−0.323587	−	0.560469i
$933$	−37.0919	−	21.4150i	−1.21433	−	0.701096i
$934$	−0.985281	−	1.70656i	−0.0322394	−	0.0558403i
$935$		0			0
$936$	3.00000	−	5.19615i	0.0980581	−	0.169842i
$937$	−2.24264			−0.0732639			−0.0366319	−	0.999329i	$-0.511663\pi$
$937$	−2.24264			−0.0732639			−0.0366319	+	0.999329i	$0.511663\pi$
$938$	−10.5147	−	13.5592i	−0.343318	−	0.442725i
$939$	−25.8198	−	14.9071i	−0.842597	−	0.486474i
$940$	0.621320	−	1.07616i	0.0202652	−	0.0351004i
$941$	13.2426			0.431698			0.215849	−	0.976427i	$-0.430748\pi$
$941$	13.2426			0.431698			0.215849	+	0.976427i	$0.430748\pi$
$942$	25.0919	+	14.4868i	0.817538	+	0.472006i
$943$	−76.3675			−2.48687
$944$	1.75736			0.0571972
$945$	−1.86396	−	13.6208i	−0.0606347	−	0.443084i
$946$	4.24264			0.137940
$947$	14.4853			0.470708			0.235354	−	0.971910i	$-0.424375\pi$
$947$	14.4853			0.470708			0.235354	+	0.971910i	$0.424375\pi$
$948$	16.0919	+	9.29065i	0.522640	+	0.301746i
$949$	8.97056			0.291197
$950$	1.12132	−	1.94218i	0.0363804	−	0.0630128i
$951$	47.1838	+	27.2416i	1.53004	+	0.883368i
$952$		0			0
$953$	50.1838			1.62561			0.812806	−	0.582535i	$-0.197939\pi$
$953$	50.1838			1.62561			0.812806	+	0.582535i	$0.197939\pi$
$954$	−5.27208			−0.170690
$955$	7.24264	−	12.5446i	0.234366	−	0.405934i
$956$	−11.1213	−	19.2627i	−0.359689	−	0.623000i
$957$	7.90812	+	4.56575i	0.255633	+	0.147590i
$958$	−7.24264	−	12.5446i	−0.233999	−	0.405298i
$959$	18.7279	−	45.8739i	0.604756	−	1.48134i
$960$	−1.50000	+	0.866025i	−0.0484123	+	0.0279508i
$961$	7.97056			0.257115
$962$	8.24264	−	14.2767i	0.265753	−	0.460298i
$963$	22.5000	−	38.9711i	0.725052	−	1.25583i
$964$	−3.74264	−	6.48244i	−0.120542	−	0.208785i
$965$	0.121320	−	0.210133i	0.00390544	−	0.00676442i
$966$	−36.0000	−	14.6969i	−1.15828	−	0.472866i
$967$	−21.4853	−	37.2136i	−0.690920	−	1.19671i	−0.971537	−	0.236889i	$-0.923872\pi$
$967$	−21.4853	−	37.2136i	−0.690920	−	1.19671i	0.280617	−	0.959820i	$-0.409461\pi$
$968$	−3.50000	+	6.06218i	−0.112494	+	0.194846i
$969$		0			0
$970$	−3.24264	−	5.61642i	−0.104115	−	0.180332i
$971$	4.75736	+	8.23999i	0.152671	+	0.264434i	0.932209	−	0.361922i	$-0.117879\pi$
$971$	4.75736	+	8.23999i	0.152671	+	0.264434i	−0.779538	+	0.626355i	$0.784546\pi$
$972$	13.5000	−	7.79423i	0.433013	−	0.250000i
$973$	−14.2426	+	34.8872i	−0.456598	+	1.11843i
$974$	−6.48528	+	11.2328i	−0.207802	+	0.359923i
$975$	3.00000	−	1.73205i	0.0960769	−	0.0554700i
$976$	−12.4853			−0.399644
$977$	−39.5147			−1.26419			−0.632094	−	0.774892i	$-0.717804\pi$
$977$	−39.5147			−1.26419			−0.632094	+	0.774892i	$0.717804\pi$
$978$		−	25.9298i		−	0.829143i
$979$		0			0
$980$	5.00000	+	4.89898i	0.159719	+	0.156492i
$981$	−53.1838			−1.69803
$982$	−11.1213	−	19.2627i	−0.354896	−	0.614697i
$983$	1.86396	+	3.22848i	0.0594511	+	0.102972i	0.894219	−	0.447629i	$-0.147732\pi$
$983$	1.86396	+	3.22848i	0.0594511	+	0.102972i	−0.834768	+	0.550602i	$0.814398\pi$
$984$			15.5885i			0.496942i
$985$	13.6066	−	23.5673i	0.433542	−	0.750917i
$986$		0			0
$987$	−0.772078	−	5.64191i	−0.0245755	−	0.179584i
$988$	2.24264	−	3.88437i	0.0713479	−	0.123578i
$989$	−4.24264	−	7.34847i	−0.134908	−	0.233668i
$990$	6.36396	+	11.0227i	0.202260	+	0.350325i
$991$	−3.12132	+	5.40629i	−0.0991520	+	0.171736i	−0.911334	−	0.411668i	$-0.864946\pi$
$991$	−3.12132	+	5.40629i	−0.0991520	+	0.171736i	0.812182	+	0.583404i	$0.198280\pi$
$992$	6.24264			0.198204
$993$	6.00000	+	3.46410i	0.190404	+	0.109930i
$994$	6.87868	+	8.87039i	0.218178	+	0.281352i
$995$	2.24264	+	3.88437i	0.0710965	+	0.123143i
$996$	−13.5000	+	7.79423i	−0.427764	+	0.246970i
$997$	−22.3640	−	38.7355i	−0.708274	−	1.22677i	−0.965497	−	0.260414i	$-0.916141\pi$
$997$	−22.3640	−	38.7355i	−0.708274	−	1.22677i	0.257223	−	0.966352i	$-0.417192\pi$
$998$	−12.8492	+	22.2555i	−0.406736	+	0.704487i
$999$	37.0919	−	21.4150i	1.17354	−	0.677541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.e.151.2	yes	4
3.2	odd	2		1890.2.i.e.991.2		4
7.2	even	3		630.2.l.e.331.1	yes	4
9.4	even	3		630.2.l.e.571.1	yes	4
9.5	odd	6		1890.2.l.e.361.1		4
21.2	odd	6		1890.2.l.e.1801.1		4
63.23	odd	6		1890.2.i.e.1171.2		4
63.58	even	3	inner	630.2.i.e.121.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.e.121.2	✓	4	63.58	even	3	inner
630.2.i.e.151.2	yes	4	1.1	even	1	trivial
630.2.l.e.331.1	yes	4	7.2	even	3
630.2.l.e.571.1	yes	4	9.4	even	3
1890.2.i.e.991.2		4	3.2	odd	2
1890.2.i.e.1171.2		4	63.23	odd	6
1890.2.l.e.361.1		4	9.5	odd	6
1890.2.l.e.1801.1		4	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.12132 + 3.67423i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(1.62132 + 2.09077i) q^{14} +(-1.50000 + 0.866025i) q^{15} +1.00000 q^{16} +(1.50000 + 2.59808i) q^{18} +(1.12132 + 1.94218i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.621320 - 4.54026i) q^{21} +(2.12132 + 3.67423i) q^{22} +(4.24264 - 7.34847i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} -5.19615i q^{27} +(1.62132 + 2.09077i) q^{28} +(-0.621320 + 1.07616i) q^{29} +(-1.50000 + 0.866025i) q^{30} +6.24264 q^{31} +1.00000 q^{32} -7.34847i q^{33} +(2.62132 - 0.358719i) q^{35} +(1.50000 + 2.59808i) q^{36} +(4.12132 + 7.13834i) q^{37} +(1.12132 + 1.94218i) q^{38} +3.46410i q^{39} +(0.500000 - 0.866025i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(-0.621320 - 4.54026i) q^{42} +(0.500000 - 0.866025i) q^{43} +(2.12132 + 3.67423i) q^{44} +3.00000 q^{45} +(4.24264 - 7.34847i) q^{46} +1.24264 q^{47} +(-1.50000 - 0.866025i) q^{48} +(-1.74264 + 6.77962i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(-0.878680 + 1.52192i) q^{53} -5.19615i q^{54} +4.24264 q^{55} +(1.62132 + 2.09077i) q^{56} -3.88437i q^{57} +(-0.621320 + 1.07616i) q^{58} +1.75736 q^{59} +(-1.50000 + 0.866025i) q^{60} -12.4853 q^{61} +6.24264 q^{62} +(-3.00000 + 7.34847i) q^{63} +1.00000 q^{64} -2.00000 q^{65} -7.34847i q^{66} -6.48528 q^{67} +(-12.7279 + 7.34847i) q^{69} +(2.62132 - 0.358719i) q^{70} +4.24264 q^{71} +(1.50000 + 2.59808i) q^{72} +(-2.24264 + 3.88437i) q^{73} +(4.12132 + 7.13834i) q^{74} +1.73205i q^{75} +(1.12132 + 1.94218i) q^{76} +(-4.24264 + 10.3923i) q^{77} +3.46410i q^{78} -10.7279 q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 - 7.79423i) q^{82} +(4.50000 - 7.79423i) q^{83} +(-0.621320 - 4.54026i) q^{84} +(0.500000 - 0.866025i) q^{86} +(1.86396 - 1.07616i) q^{87} +(2.12132 + 3.67423i) q^{88} +3.00000 q^{90} +(2.00000 - 4.89898i) q^{91} +(4.24264 - 7.34847i) q^{92} +(-9.36396 - 5.40629i) q^{93} +1.24264 q^{94} +2.24264 q^{95} +(-1.50000 - 0.866025i) q^{96} +(3.24264 - 5.61642i) q^{97} +(-1.74264 + 6.77962i) q^{98} +(-6.36396 + 11.0227i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 6 q^{3} + 4 q^{4} + 2 q^{5} - 6 q^{6} - 2 q^{7} + 4 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 6 * q^3 + 4 * q^4 + 2 * q^5 - 6 * q^6 - 2 * q^7 + 4 * q^8 + 6 * q^9	\( 4 q + 4 q^{2} - 6 q^{3} + 4 q^{4} + 2 q^{5} - 6 q^{6} - 2 q^{7} + 4 q^{8} + 6 q^{9} + 2 q^{10} - 6 q^{12} - 4 q^{13} - 2 q^{14} - 6 q^{15} + 4 q^{16} + 6 q^{18} - 4 q^{19} + 2 q^{20} + 6 q^{21} - 6 q^{24} - 2 q^{25} - 4 q^{26} - 2 q^{28} + 6 q^{29} - 6 q^{30} + 8 q^{31} + 4 q^{32} + 2 q^{35} + 6 q^{36} + 8 q^{37} - 4 q^{38} + 2 q^{40} - 18 q^{41} + 6 q^{42} + 2 q^{43} + 12 q^{45} - 12 q^{47} - 6 q^{48} + 10 q^{49} - 2 q^{50} - 4 q^{52} - 12 q^{53} - 2 q^{56} + 6 q^{58} + 24 q^{59} - 6 q^{60} - 16 q^{61} + 8 q^{62} - 12 q^{63} + 4 q^{64} - 8 q^{65} + 8 q^{67} + 2 q^{70} + 6 q^{72} + 8 q^{73} + 8 q^{74} - 4 q^{76} + 8 q^{79} + 2 q^{80} - 18 q^{81} - 18 q^{82} + 18 q^{83} + 6 q^{84} + 2 q^{86} - 18 q^{87} + 12 q^{90} + 8 q^{91} - 12 q^{93} - 12 q^{94} - 8 q^{95} - 6 q^{96} - 4 q^{97} + 10 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 6 * q^3 + 4 * q^4 + 2 * q^5 - 6 * q^6 - 2 * q^7 + 4 * q^8 + 6 * q^9 + 2 * q^10 - 6 * q^12 - 4 * q^13 - 2 * q^14 - 6 * q^15 + 4 * q^16 + 6 * q^18 - 4 * q^19 + 2 * q^20 + 6 * q^21 - 6 * q^24 - 2 * q^25 - 4 * q^26 - 2 * q^28 + 6 * q^29 - 6 * q^30 + 8 * q^31 + 4 * q^32 + 2 * q^35 + 6 * q^36 + 8 * q^37 - 4 * q^38 + 2 * q^40 - 18 * q^41 + 6 * q^42 + 2 * q^43 + 12 * q^45 - 12 * q^47 - 6 * q^48 + 10 * q^49 - 2 * q^50 - 4 * q^52 - 12 * q^53 - 2 * q^56 + 6 * q^58 + 24 * q^59 - 6 * q^60 - 16 * q^61 + 8 * q^62 - 12 * q^63 + 4 * q^64 - 8 * q^65 + 8 * q^67 + 2 * q^70 + 6 * q^72 + 8 * q^73 + 8 * q^74 - 4 * q^76 + 8 * q^79 + 2 * q^80 - 18 * q^81 - 18 * q^82 + 18 * q^83 + 6 * q^84 + 2 * q^86 - 18 * q^87 + 12 * q^90 + 8 * q^91 - 12 * q^93 - 12 * q^94 - 8 * q^95 - 6 * q^96 - 4 * q^97 + 10 * q^98

Introduction

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