LMFDB - Embedded newform 630.2.i.e.121.1

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			121.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.e.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.50000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(-2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(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} +(-2.62132 + 0.358719i) 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} +(-2.62132 + 0.358719i) q^{14} +(-1.50000 - 0.866025i) q^{15} +1.00000 q^{16} +(1.50000 - 2.59808i) q^{18} +(-3.12132 + 5.40629i) q^{19} +(0.500000 + 0.866025i) q^{20} +(3.62132 - 2.80821i) 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} +(-2.62132 + 0.358719i) q^{28} +(3.62132 + 6.27231i) q^{29} +(-1.50000 - 0.866025i) q^{30} -2.24264 q^{31} +1.00000 q^{32} -7.34847i q^{33} +(-1.62132 - 2.09077i) q^{35} +(1.50000 - 2.59808i) q^{36} +(-0.121320 + 0.210133i) q^{37} +(-3.12132 + 5.40629i) q^{38} -3.46410i q^{39} +(0.500000 + 0.866025i) q^{40} +(-4.50000 + 7.79423i) q^{41} +(3.62132 - 2.80821i) q^{42} +(0.500000 + 0.866025i) q^{43} +(-2.12132 + 3.67423i) q^{44} +3.00000 q^{45} +(-4.24264 - 7.34847i) q^{46} -7.24264 q^{47} +(-1.50000 + 0.866025i) q^{48} +(6.74264 - 1.88064i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(-5.12132 - 8.87039i) q^{53} +5.19615i q^{54} -4.24264 q^{55} +(-2.62132 + 0.358719i) q^{56} -10.8126i q^{57} +(3.62132 + 6.27231i) q^{58} +10.2426 q^{59} +(-1.50000 - 0.866025i) q^{60} +4.48528 q^{61} -2.24264 q^{62} +(-3.00000 + 7.34847i) q^{63} +1.00000 q^{64} -2.00000 q^{65} -7.34847i q^{66} +10.4853 q^{67} +(12.7279 + 7.34847i) q^{69} +(-1.62132 - 2.09077i) q^{70} -4.24264 q^{71} +(1.50000 - 2.59808i) q^{72} +(6.24264 + 10.8126i) q^{73} +(-0.121320 + 0.210133i) q^{74} -1.73205i q^{75} +(-3.12132 + 5.40629i) q^{76} +(4.24264 - 10.3923i) q^{77} -3.46410i q^{78} +14.7279 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} +(3.62132 - 2.80821i) q^{84} +(0.500000 + 0.866025i) q^{86} +(-10.8640 - 6.27231i) q^{87} +(-2.12132 + 3.67423i) q^{88} +3.00000 q^{90} +(2.00000 - 4.89898i) q^{91} +(-4.24264 - 7.34847i) q^{92} +(3.36396 - 1.94218i) q^{93} -7.24264 q^{94} -6.24264 q^{95} +(-1.50000 + 0.866025i) q^{96} +(-5.24264 - 9.08052i) q^{97} +(6.74264 - 1.88064i) 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$	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
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$8$	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	0.345918	+	0.938265i	$0.387568\pi$
$11$	−2.12132	+	3.67423i	−0.639602	+	1.10782i	−0.985520	+	0.169559i	$0.945766\pi$
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	−2.62132	+	0.358719i	−0.700577	+	0.0958718i
$15$	−1.50000	−	0.866025i	−0.387298	−	0.223607i
$16$	1.00000			0.250000
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	−3.12132	+	5.40629i	−0.716080	+	1.24029i	0.246462	+	0.969153i	$0.420732\pi$
$19$	−3.12132	+	5.40629i	−0.716080	+	1.24029i	−0.962542	+	0.271134i	$0.912601\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	3.62132	−	2.80821i	0.790237	−	0.612801i
$22$	−2.12132	+	3.67423i	−0.452267	+	0.783349i
$23$	−4.24264	−	7.34847i	−0.884652	−	1.53226i	−0.846112	−	0.533005i	$-0.821063\pi$
$23$	−4.24264	−	7.34847i	−0.884652	−	1.53226i	−0.0385394	−	0.999257i	$-0.512271\pi$
$24$	−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
$28$	−2.62132	+	0.358719i	−0.495383	+	0.0677916i
$29$	3.62132	+	6.27231i	0.672462	+	1.16474i	0.977204	+	0.212304i	$0.0680966\pi$
$29$	3.62132	+	6.27231i	0.672462	+	1.16474i	−0.304741	+	0.952435i	$0.598570\pi$
$30$	−1.50000	−	0.866025i	−0.273861	−	0.158114i
$31$	−2.24264			−0.402790			−0.201395	−	0.979510i	$-0.564548\pi$
$31$	−2.24264			−0.402790			−0.201395	+	0.979510i	$0.564548\pi$
$32$	1.00000			0.176777
$33$		−	7.34847i		−	1.27920i
$34$		0			0
$35$	−1.62132	−	2.09077i	−0.274053	−	0.353405i
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	−0.121320	+	0.210133i	−0.0199449	+	0.0345457i	−0.875826	−	0.482628i	$-0.839682\pi$
$37$	−0.121320	+	0.210133i	−0.0199449	+	0.0345457i	0.855881	+	0.517173i	$0.173016\pi$
$38$	−3.12132	+	5.40629i	−0.506345	+	0.877015i
$39$		−	3.46410i		−	0.554700i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	0.264704	+	0.964330i	$0.414726\pi$
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	−0.967486	+	0.252924i	$0.918608\pi$
$42$	3.62132	−	2.80821i	0.558782	−	0.433316i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	−2.12132	+	3.67423i	−0.319801	+	0.553912i
$45$	3.00000			0.447214
$46$	−4.24264	−	7.34847i	−0.625543	−	1.08347i
$47$	−7.24264			−1.05645			−0.528224	−	0.849105i	$-0.677142\pi$
$47$	−7.24264			−1.05645			−0.528224	+	0.849105i	$0.677142\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−5.12132	−	8.87039i	−0.703467	−	1.21844i	−0.967242	−	0.253857i	$-0.918301\pi$
$53$	−5.12132	−	8.87039i	−0.703467	−	1.21844i	0.263774	−	0.964584i	$-0.415033\pi$
$54$			5.19615i			0.707107i
$55$	−4.24264			−0.572078
$56$	−2.62132	+	0.358719i	−0.350289	+	0.0479359i
$57$		−	10.8126i		−	1.43216i
$58$	3.62132	+	6.27231i	0.475503	+	0.823595i
$59$	10.2426			1.33348			0.666739	−	0.745291i	$-0.267690\pi$
$59$	10.2426			1.33348			0.666739	+	0.745291i	$0.267690\pi$
$60$	−1.50000	−	0.866025i	−0.193649	−	0.111803i
$61$	4.48528			0.574281			0.287141	−	0.957888i	$-0.407295\pi$
$61$	4.48528			0.574281			0.287141	+	0.957888i	$0.407295\pi$
$62$	−2.24264			−0.284816
$63$	−3.00000	+	7.34847i	−0.377964	+	0.925820i
$64$	1.00000			0.125000
$65$	−2.00000			−0.248069
$66$		−	7.34847i		−	0.904534i
$67$	10.4853			1.28098			0.640490	−	0.767966i	$-0.278731\pi$
$67$	10.4853			1.28098			0.640490	+	0.767966i	$0.278731\pi$
$68$		0			0
$69$	12.7279	+	7.34847i	1.53226	+	0.884652i
$70$	−1.62132	−	2.09077i	−0.193785	−	0.249895i
$71$	−4.24264			−0.503509			−0.251754	−	0.967791i	$-0.581008\pi$
$71$	−4.24264			−0.503509			−0.251754	+	0.967791i	$0.581008\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	6.24264	+	10.8126i	0.730646	+	1.26552i	0.956608	+	0.291380i	$0.0941142\pi$
$73$	6.24264	+	10.8126i	0.730646	+	1.26552i	−0.225962	+	0.974136i	$0.572552\pi$
$74$	−0.121320	+	0.210133i	−0.0141032	+	0.0244275i
$75$		−	1.73205i		−	0.200000i
$76$	−3.12132	+	5.40629i	−0.358040	+	0.620143i
$77$	4.24264	−	10.3923i	0.483494	−	1.18431i
$78$		−	3.46410i		−	0.392232i
$79$	14.7279			1.65702			0.828510	−	0.559974i	$-0.189189\pi$
$79$	14.7279			1.65702			0.828510	+	0.559974i	$0.189189\pi$
$80$	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	0.999976	−	0.00698436i	$-0.00222321\pi$
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	−0.506036	+	0.862512i	$0.668890\pi$
$84$	3.62132	−	2.80821i	0.395118	−	0.306401i
$85$		0			0
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	−10.8640	−	6.27231i	−1.16474	−	0.672462i
$88$	−2.12132	+	3.67423i	−0.226134	+	0.391675i
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$	3.00000			0.316228
$91$	2.00000	−	4.89898i	0.209657	−	0.513553i
$92$	−4.24264	−	7.34847i	−0.442326	−	0.766131i
$93$	3.36396	−	1.94218i	0.348827	−	0.201395i
$94$	−7.24264			−0.747021
$95$	−6.24264			−0.640481
$96$	−1.50000	+	0.866025i	−0.153093	+	0.0883883i
$97$	−5.24264	−	9.08052i	−0.532310	−	0.921987i	−0.999288	−	0.0377187i	$-0.987991\pi$
$97$	−5.24264	−	9.08052i	−0.532310	−	0.921987i	0.466979	−	0.884268i	$-0.345342\pi$
$98$	6.74264	−	1.88064i	0.681110	−	0.189973i
$99$	6.36396	+	11.0227i	0.639602	+	1.10782i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	2.37868	−	4.11999i	0.236687	−	0.409955i	−0.723074	−	0.690770i	$-0.757272\pi$
$101$	2.37868	−	4.11999i	0.236687	−	0.409955i	0.959762	+	0.280816i	$0.0906049\pi$
$102$		0			0
$103$	2.62132	+	4.54026i	0.258286	+	0.447365i	0.965783	−	0.259352i	$-0.0835089\pi$
$103$	2.62132	+	4.54026i	0.258286	+	0.447365i	−0.707497	+	0.706717i	$0.750176\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$	4.24264	+	1.73205i	0.414039	+	0.169031i
$106$	−5.12132	−	8.87039i	−0.497427	−	0.861568i
$107$	−7.50000	+	12.9904i	−0.725052	+	1.25583i	0.233900	+	0.972261i	$0.424851\pi$
$107$	−7.50000	+	12.9904i	−0.725052	+	1.25583i	−0.958952	+	0.283567i	$0.908482\pi$
$108$			5.19615i			0.500000i
$109$	3.86396	+	6.69258i	0.370100	+	0.641033i	0.989581	−	0.143980i	$-0.0459900\pi$
$109$	3.86396	+	6.69258i	0.370100	+	0.641033i	−0.619480	+	0.785012i	$0.712657\pi$
$110$	−4.24264			−0.404520
$111$		−	0.420266i		−	0.0398899i
$112$	−2.62132	+	0.358719i	−0.247691	+	0.0338958i
$113$	6.36396	−	11.0227i	0.598671	−	1.03693i	−0.394346	−	0.918962i	$-0.629029\pi$
$113$	6.36396	−	11.0227i	0.598671	−	1.03693i	0.993018	−	0.117967i	$-0.0376377\pi$
$114$		−	10.8126i		−	1.01269i
$115$	4.24264	−	7.34847i	0.395628	−	0.685248i
$116$	3.62132	+	6.27231i	0.336231	+	0.582369i
$117$	3.00000	+	5.19615i	0.277350	+	0.480384i
$118$	10.2426			0.942912
$119$		0			0
$120$	−1.50000	−	0.866025i	−0.136931	−	0.0790569i
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$	4.48528			0.406078
$123$		−	15.5885i		−	1.40556i
$124$	−2.24264			−0.201395
$125$	−1.00000			−0.0894427
$126$	−3.00000	+	7.34847i	−0.267261	+	0.654654i
$127$	15.2426			1.35257			0.676283	−	0.736642i	$-0.263590\pi$
$127$	15.2426			1.35257			0.676283	+	0.736642i	$0.263590\pi$
$128$	1.00000			0.0883883
$129$	−1.50000	−	0.866025i	−0.132068	−	0.0762493i
$130$	−2.00000			−0.175412
$131$	−10.2426	−	17.7408i	−0.894904	−	1.55002i	−0.833924	−	0.551880i	$-0.813911\pi$
$131$	−10.2426	−	17.7408i	−0.894904	−	1.55002i	−0.0609799	−	0.998139i	$-0.519423\pi$
$132$		−	7.34847i		−	0.639602i
$133$	6.24264	−	15.2913i	0.541306	−	1.32592i
$134$	10.4853			0.905790
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$		0			0
$137$	3.36396	−	5.82655i	0.287403	−	0.497796i	−0.685786	−	0.727803i	$-0.740542\pi$
$137$	3.36396	−	5.82655i	0.287403	−	0.497796i	0.973189	+	0.230007i	$0.0738749\pi$
$138$	12.7279	+	7.34847i	1.08347	+	0.625543i
$139$	2.87868	−	4.98602i	0.244166	−	0.422909i	−0.717730	−	0.696321i	$-0.754819\pi$
$139$	2.87868	−	4.98602i	0.244166	−	0.422909i	0.961897	+	0.273412i	$0.0881523\pi$
$140$	−1.62132	−	2.09077i	−0.137027	−	0.176702i
$141$	10.8640	−	6.27231i	0.914911	−	0.528224i
$142$	−4.24264			−0.356034
$143$	−4.24264	−	7.34847i	−0.354787	−	0.614510i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	−3.62132	+	6.27231i	−0.300734	+	0.520887i
$146$	6.24264	+	10.8126i	0.516645	+	0.894855i
$147$	−8.48528	+	8.66025i	−0.699854	+	0.714286i
$148$	−0.121320	+	0.210133i	−0.00997247	+	0.0172728i
$149$	1.24264	+	2.15232i	0.101801	+	0.176325i	0.912427	−	0.409240i	$-0.134206\pi$
$149$	1.24264	+	2.15232i	0.101801	+	0.176325i	−0.810626	+	0.585565i	$0.800873\pi$
$150$		−	1.73205i		−	0.141421i
$151$	4.12132	−	7.13834i	0.335388	−	0.580910i	−0.648171	−	0.761495i	$-0.724466\pi$
$151$	4.12132	−	7.13834i	0.335388	−	0.580910i	0.983559	+	0.180585i	$0.0577992\pi$
$152$	−3.12132	+	5.40629i	−0.253173	+	0.438508i
$153$		0			0
$154$	4.24264	−	10.3923i	0.341882	−	0.837436i
$155$	−1.12132	−	1.94218i	−0.0900666	−	0.156000i
$156$		−	3.46410i		−	0.277350i
$157$	8.72792			0.696564			0.348282	−	0.937390i	$-0.386765\pi$
$157$	8.72792			0.696564			0.348282	+	0.937390i	$0.386765\pi$
$158$	14.7279			1.17169
$159$	15.3640	+	8.87039i	1.21844	+	0.703467i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	13.7574	+	17.7408i	1.08423	+	1.39817i
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	−9.48528	+	16.4290i	−0.742945	+	1.28682i	0.208204	+	0.978085i	$0.433238\pi$
$163$	−9.48528	+	16.4290i	−0.742945	+	1.28682i	−0.951149	+	0.308732i	$0.900095\pi$
$164$	−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
$167$	−1.75736	+	3.04384i	−0.135989	+	0.235539i	−0.925975	−	0.377586i	$-0.876754\pi$
$167$	−1.75736	+	3.04384i	−0.135989	+	0.235539i	0.789986	+	0.613125i	$0.210088\pi$
$168$	3.62132	−	2.80821i	0.279391	−	0.216658i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	9.36396	+	16.2189i	0.716080	+	1.24029i
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−1.75736			−0.133610			−0.0668048	−	0.997766i	$-0.521280\pi$
$173$	−1.75736			−0.133610			−0.0668048	+	0.997766i	$0.521280\pi$
$174$	−10.8640	−	6.27231i	−0.823595	−	0.475503i
$175$	1.00000	−	2.44949i	0.0755929	−	0.185164i
$176$	−2.12132	+	3.67423i	−0.159901	+	0.276956i
$177$	−15.3640	+	8.87039i	−1.15483	+	0.666739i
$178$		0			0
$179$	−5.12132	−	8.87039i	−0.382785	−	0.663004i	0.608674	−	0.793421i	$-0.291702\pi$
$179$	−5.12132	−	8.87039i	−0.382785	−	0.663004i	−0.991459	+	0.130417i	$0.958368\pi$
$180$	3.00000			0.223607
$181$	−14.7574			−1.09691			−0.548453	−	0.836181i	$-0.684783\pi$
$181$	−14.7574			−1.09691			−0.548453	+	0.836181i	$0.684783\pi$
$182$	2.00000	−	4.89898i	0.148250	−	0.363137i
$183$	−6.72792	+	3.88437i	−0.497342	+	0.287141i
$184$	−4.24264	−	7.34847i	−0.312772	−	0.541736i
$185$	−0.242641			−0.0178393
$186$	3.36396	−	1.94218i	0.246658	−	0.142408i
$187$		0			0
$188$	−7.24264			−0.528224
$189$	−1.86396	−	13.6208i	−0.135583	−	0.990766i
$190$	−6.24264			−0.452889
$191$	−2.48528			−0.179829			−0.0899143	−	0.995950i	$-0.528659\pi$
$191$	−2.48528			−0.179829			−0.0899143	+	0.995950i	$0.528659\pi$
$192$	−1.50000	+	0.866025i	−0.108253	+	0.0625000i
$193$	−8.24264			−0.593318			−0.296659	−	0.954983i	$-0.595873\pi$
$193$	−8.24264			−0.593318			−0.296659	+	0.954983i	$0.595873\pi$
$194$	−5.24264	−	9.08052i	−0.376400	−	0.651943i
$195$	3.00000	−	1.73205i	0.214834	−	0.124035i
$196$	6.74264	−	1.88064i	0.481617	−	0.134331i
$197$	−15.2132			−1.08390			−0.541948	−	0.840412i	$-0.682313\pi$
$197$	−15.2132			−1.08390			−0.541948	+	0.840412i	$0.682313\pi$
$198$	6.36396	+	11.0227i	0.452267	+	0.783349i
$199$	6.24264	+	10.8126i	0.442529	+	0.766483i	0.997876	−	0.0651357i	$-0.0207480\pi$
$199$	6.24264	+	10.8126i	0.442529	+	0.766483i	−0.555347	+	0.831618i	$0.687415\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−15.7279	+	9.08052i	−1.10936	+	0.640490i
$202$	2.37868	−	4.11999i	0.167363	−	0.289882i
$203$	−11.7426	−	15.1427i	−0.824172	−	1.06281i
$204$		0			0
$205$	−9.00000			−0.628587
$206$	2.62132	+	4.54026i	0.182636	+	0.316335i
$207$	−25.4558			−1.76930
$208$	−1.00000	+	1.73205i	−0.0693375	+	0.120096i
$209$	−13.2426	−	22.9369i	−0.916013	−	1.58658i
$210$	4.24264	+	1.73205i	0.292770	+	0.119523i
$211$	−6.12132	+	10.6024i	−0.421409	+	0.729902i	−0.996078	−	0.0884844i	$-0.971798\pi$
$211$	−6.12132	+	10.6024i	−0.421409	+	0.729902i	0.574668	+	0.818386i	$0.305131\pi$
$212$	−5.12132	−	8.87039i	−0.351734	−	0.609221i
$213$	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
$217$	5.87868	−	0.804479i	0.399071	−	0.0546116i
$218$	3.86396	+	6.69258i	0.261700	+	0.453278i
$219$	−18.7279	−	10.8126i	−1.26552	−	0.730646i
$220$	−4.24264			−0.286039
$221$		0			0
$222$		−	0.420266i		−	0.0282064i
$223$	6.86396	+	11.8887i	0.459645	+	0.796128i	0.998942	−	0.0459873i	$-0.0146434\pi$
$223$	6.86396	+	11.8887i	0.459645	+	0.796128i	−0.539297	+	0.842116i	$0.681310\pi$
$224$	−2.62132	+	0.358719i	−0.175144	+	0.0239680i
$225$	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	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$		−	10.8126i		−	0.716080i
$229$	10.3787	+	17.9764i	0.685842	+	1.18791i	0.973171	+	0.230082i	$0.0738994\pi$
$229$	10.3787	+	17.9764i	0.685842	+	1.18791i	−0.287329	+	0.957832i	$0.592767\pi$
$230$	4.24264	−	7.34847i	0.279751	−	0.484544i
$231$	2.63604	+	19.2627i	0.173439	+	1.26739i
$232$	3.62132	+	6.27231i	0.237751	+	0.411797i
$233$	−14.1213	+	24.4588i	−0.925118	+	1.60235i	−0.133748	+	0.991015i	$0.542701\pi$
$233$	−14.1213	+	24.4588i	−0.925118	+	1.60235i	−0.791371	+	0.611337i	$0.790632\pi$
$234$	3.00000	+	5.19615i	0.196116	+	0.339683i
$235$	−3.62132	−	6.27231i	−0.236229	−	0.409160i
$236$	10.2426			0.666739
$237$	−22.0919	+	12.7548i	−1.43502	+	0.828510i
$238$		0			0
$239$	−6.87868	+	11.9142i	−0.444945	+	0.770667i	−0.998048	−	0.0624455i	$-0.980110\pi$
$239$	−6.87868	+	11.9142i	−0.444945	+	0.770667i	0.553104	+	0.833112i	$0.313443\pi$
$240$	−1.50000	−	0.866025i	−0.0968246	−	0.0559017i
$241$	4.74264	−	8.21449i	0.305500	−	0.529142i	−0.671872	−	0.740667i	$-0.734510\pi$
$241$	4.74264	−	8.21449i	0.305500	−	0.529142i	0.977373	+	0.211525i	$0.0678430\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	4.48528			0.287141
$245$	5.00000	+	4.89898i	0.319438	+	0.312984i
$246$		−	15.5885i		−	0.993884i
$247$	−6.24264	−	10.8126i	−0.397210	−	0.687987i
$248$	−2.24264			−0.142408
$249$	−13.5000	−	7.79423i	−0.855528	−	0.493939i
$250$	−1.00000			−0.0632456
$251$	−26.4853			−1.67174			−0.835868	−	0.548930i	$-0.815035\pi$
$251$	−26.4853			−1.67174			−0.835868	+	0.548930i	$0.815035\pi$
$252$	−3.00000	+	7.34847i	−0.188982	+	0.462910i
$253$	36.0000			2.26330
$254$	15.2426			0.956408
$255$		0			0
$256$	1.00000			0.0625000
$257$	8.48528	+	14.6969i	0.529297	+	0.916770i	0.999416	+	0.0341667i	$0.0108777\pi$
$257$	8.48528	+	14.6969i	0.529297	+	0.916770i	−0.470119	+	0.882603i	$0.655789\pi$
$258$	−1.50000	−	0.866025i	−0.0933859	−	0.0539164i
$259$	0.242641	−	0.594346i	0.0150770	−	0.0369309i
$260$	−2.00000			−0.124035
$261$	21.7279			1.34492
$262$	−10.2426	−	17.7408i	−0.632792	−	1.09603i
$263$	−4.86396	+	8.42463i	−0.299925	+	0.519485i	−0.976118	−	0.217239i	$-0.930295\pi$
$263$	−4.86396	+	8.42463i	−0.299925	+	0.519485i	0.676194	+	0.736724i	$0.263628\pi$
$264$		−	7.34847i		−	0.452267i
$265$	5.12132	−	8.87039i	0.314600	−	0.544904i
$266$	6.24264	−	15.2913i	0.382761	−	0.937569i
$267$		0			0
$268$	10.4853			0.640490
$269$	−5.48528	−	9.50079i	−0.334444	−	0.579273i	0.648934	−	0.760844i	$-0.275215\pi$
$269$	−5.48528	−	9.50079i	−0.334444	−	0.579273i	−0.983378	+	0.181571i	$0.941882\pi$
$270$	−4.50000	+	2.59808i	−0.273861	+	0.158114i
$271$	2.36396	−	4.09450i	0.143600	−	0.248723i	−0.785249	−	0.619179i	$-0.787465\pi$
$271$	2.36396	−	4.09450i	0.143600	−	0.248723i	0.928850	+	0.370456i	$0.120799\pi$
$272$		0			0
$273$	1.24264	+	9.08052i	0.0752080	+	0.549578i
$274$	3.36396	−	5.82655i	0.203224	−	0.351995i
$275$	−2.12132	−	3.67423i	−0.127920	−	0.221565i
$276$	12.7279	+	7.34847i	0.766131	+	0.442326i
$277$	−9.12132	+	15.7986i	−0.548047	+	0.949245i	0.450361	+	0.892846i	$0.351295\pi$
$277$	−9.12132	+	15.7986i	−0.548047	+	0.949245i	−0.998408	+	0.0563989i	$0.982038\pi$
$278$	2.87868	−	4.98602i	0.172652	−	0.299042i
$279$	−3.36396	+	5.82655i	−0.201395	+	0.348827i
$280$	−1.62132	−	2.09077i	−0.0968924	−	0.124947i
$281$	12.9853	+	22.4912i	0.774637	+	1.34171i	0.934998	+	0.354652i	$0.115401\pi$
$281$	12.9853	+	22.4912i	0.774637	+	1.34171i	−0.160361	+	0.987058i	$0.551266\pi$
$282$	10.8640	−	6.27231i	0.646939	−	0.373511i
$283$	−15.4853			−0.920504			−0.460252	−	0.887788i	$-0.652241\pi$
$283$	−15.4853			−0.920504			−0.460252	+	0.887788i	$0.652241\pi$
$284$	−4.24264			−0.251754
$285$	9.36396	−	5.40629i	0.554673	−	0.320241i
$286$	−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
$290$	−3.62132	+	6.27231i	−0.212651	+	0.368323i
$291$	15.7279	+	9.08052i	0.921987	+	0.532310i
$292$	6.24264	+	10.8126i	0.365323	+	0.632758i
$293$	−1.75736	+	3.04384i	−0.102666	+	0.177823i	−0.912782	−	0.408447i	$-0.866071\pi$
$293$	−1.75736	+	3.04384i	−0.102666	+	0.177823i	0.810116	+	0.586269i	$0.199404\pi$
$294$	−8.48528	+	8.66025i	−0.494872	+	0.505076i
$295$	5.12132	+	8.87039i	0.298175	+	0.516454i
$296$	−0.121320	+	0.210133i	−0.00705160	+	0.0122137i
$297$	−19.0919	−	11.0227i	−1.10782	−	0.639602i
$298$	1.24264	+	2.15232i	0.0719842	+	0.124680i
$299$	16.9706			0.981433
$300$		−	1.73205i		−	0.100000i
$301$	−1.62132	−	2.09077i	−0.0934514	−	0.120510i
$302$	4.12132	−	7.13834i	0.237155	−	0.410765i
$303$			8.23999i			0.473375i
$304$	−3.12132	+	5.40629i	−0.179020	+	0.310072i
$305$	2.24264	+	3.88437i	0.128413	+	0.222418i
$306$		0			0
$307$	3.97056			0.226612			0.113306	−	0.993560i	$-0.463856\pi$
$307$	3.97056			0.226612			0.113306	+	0.993560i	$0.463856\pi$
$308$	4.24264	−	10.3923i	0.241747	−	0.592157i
$309$	−7.86396	−	4.54026i	−0.447365	−	0.258286i
$310$	−1.12132	−	1.94218i	−0.0636867	−	0.110309i
$311$	−0.727922			−0.0412767			−0.0206383	−	0.999787i	$-0.506570\pi$
$311$	−0.727922			−0.0412767			−0.0206383	+	0.999787i	$0.506570\pi$
$312$		−	3.46410i		−	0.196116i
$313$	−25.2132			−1.42513			−0.712567	−	0.701604i	$-0.752468\pi$
$313$	−25.2132			−1.42513			−0.712567	+	0.701604i	$0.752468\pi$
$314$	8.72792			0.492545
$315$	−7.86396	+	1.07616i	−0.443084	+	0.0606347i
$316$	14.7279			0.828510
$317$	19.4558			1.09275			0.546375	−	0.837541i	$-0.316008\pi$
$317$	19.4558			1.09275			0.546375	+	0.837541i	$0.316008\pi$
$318$	15.3640	+	8.87039i	0.861568	+	0.497427i
$319$	−30.7279			−1.72043
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		−	25.9808i		−	1.45010i
$322$	13.7574	+	17.7408i	0.766668	+	0.988655i
$323$		0			0
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$	−9.48528	+	16.4290i	−0.525341	+	0.909918i
$327$	−11.5919	−	6.69258i	−0.641033	−	0.370100i
$328$	−4.50000	+	7.79423i	−0.248471	+	0.430364i
$329$	18.9853	−	2.59808i	1.04669	−	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
$333$	0.363961	+	0.630399i	0.0199449	+	0.0345457i
$334$	−1.75736	+	3.04384i	−0.0961584	+	0.166551i
$335$	5.24264	+	9.08052i	0.286436	+	0.496122i
$336$	3.62132	−	2.80821i	0.197559	−	0.153200i
$337$	3.24264	−	5.61642i	0.176638	−	0.305946i	−0.764089	−	0.645111i	$-0.776811\pi$
$337$	3.24264	−	5.61642i	0.176638	−	0.305946i	0.940727	+	0.339165i	$0.110145\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$			22.0454i			1.19734i
$340$		0			0
$341$	4.75736	−	8.23999i	0.257625	−	0.446220i
$342$	9.36396	+	16.2189i	0.506345	+	0.877015i
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	0.500000	+	0.866025i	0.0269582	+	0.0466930i
$345$			14.6969i			0.791257i
$346$	−1.75736			−0.0944762
$347$	−9.00000			−0.483145			−0.241573	−	0.970383i	$-0.577663\pi$
$347$	−9.00000			−0.483145			−0.241573	+	0.970383i	$0.577663\pi$
$348$	−10.8640	−	6.27231i	−0.582369	−	0.336231i
$349$	−13.0000	−	22.5167i	−0.695874	−	1.20529i	−0.969885	−	0.243563i	$-0.921684\pi$
$349$	−13.0000	−	22.5167i	−0.695874	−	1.20529i	0.274011	−	0.961727i	$-0.411649\pi$
$350$	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
$353$	5.12132	−	8.87039i	0.272580	−	0.472123i	−0.696941	−	0.717128i	$-0.745456\pi$
$353$	5.12132	−	8.87039i	0.272580	−	0.472123i	0.969522	+	0.245005i	$0.0787896\pi$
$354$	−15.3640	+	8.87039i	−0.816585	+	0.471456i
$355$	−2.12132	−	3.67423i	−0.112588	−	0.195008i
$356$		0			0
$357$		0			0
$358$	−5.12132	−	8.87039i	−0.270670	−	0.468815i
$359$	−0.878680	+	1.52192i	−0.0463749	+	0.0803237i	−0.888281	−	0.459300i	$-0.848100\pi$
$359$	−0.878680	+	1.52192i	−0.0463749	+	0.0803237i	0.841906	+	0.539624i	$0.181434\pi$
$360$	3.00000			0.158114
$361$	−9.98528	−	17.2950i	−0.525541	−	0.910264i
$362$	−14.7574			−0.775630
$363$	10.5000	+	6.06218i	0.551107	+	0.318182i
$364$	2.00000	−	4.89898i	0.104828	−	0.256776i
$365$	−6.24264	+	10.8126i	−0.326755	+	0.565956i
$366$	−6.72792	+	3.88437i	−0.351674	+	0.203039i
$367$	3.13604	−	5.43178i	0.163700	−	0.283537i	−0.772493	−	0.635023i	$-0.780990\pi$
$367$	3.13604	−	5.43178i	0.163700	−	0.283537i	0.936193	+	0.351487i	$0.114324\pi$
$368$	−4.24264	−	7.34847i	−0.221163	−	0.383065i
$369$	13.5000	+	23.3827i	0.702782	+	1.21725i
$370$	−0.242641			−0.0126143
$371$	16.6066	+	21.4150i	0.862172	+	1.11181i
$372$	3.36396	−	1.94218i	0.174413	−	0.100698i
$373$	−12.8492	−	22.2555i	−0.665309	−	1.15235i	−0.979202	−	0.202890i	$-0.934967\pi$
$373$	−12.8492	−	22.2555i	−0.665309	−	1.15235i	0.313893	−	0.949458i	$-0.398367\pi$
$374$		0			0
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$	−7.24264			−0.373511
$377$	−14.4853			−0.746030
$378$	−1.86396	−	13.6208i	−0.0958718	−	0.700577i
$379$	17.5147			0.899671			0.449835	−	0.893112i	$-0.351483\pi$
$379$	17.5147			0.899671			0.449835	+	0.893112i	$0.351483\pi$
$380$	−6.24264			−0.320241
$381$	−22.8640	+	13.2005i	−1.17136	+	0.676283i
$382$	−2.48528			−0.127158
$383$	−16.8640	−	29.2092i	−0.861708	−	1.49252i	−0.870279	−	0.492559i	$-0.836062\pi$
$383$	−16.8640	−	29.2092i	−0.861708	−	1.49252i	0.00857088	−	0.999963i	$-0.497272\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$	11.1213	−	1.52192i	0.566795	−	0.0775641i
$386$	−8.24264			−0.419539
$387$	3.00000			0.152499
$388$	−5.24264	−	9.08052i	−0.266155	−	0.460994i
$389$	6.10660	−	10.5769i	0.309617	−	0.536272i	−0.668662	−	0.743567i	$-0.733132\pi$
$389$	6.10660	−	10.5769i	0.309617	−	0.536272i	0.978279	+	0.207294i	$0.0664658\pi$
$390$	3.00000	−	1.73205i	0.151911	−	0.0877058i
$391$		0			0
$392$	6.74264	−	1.88064i	0.340555	−	0.0949865i
$393$	30.7279	+	17.7408i	1.55002	+	0.894904i
$394$	−15.2132			−0.766430
$395$	7.36396	+	12.7548i	0.370521	+	0.641761i
$396$	6.36396	+	11.0227i	0.319801	+	0.553912i
$397$	−10.8787	+	18.8424i	−0.545985	+	0.945674i	0.452559	+	0.891735i	$0.350511\pi$
$397$	−10.8787	+	18.8424i	−0.545985	+	0.945674i	−0.998544	+	0.0539397i	$0.982822\pi$
$398$	6.24264	+	10.8126i	0.312915	+	0.541985i
$399$	3.87868	+	28.3432i	0.194177	+	1.41894i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	11.7426	+	20.3389i	0.586399	+	1.01567i	0.994699	+	0.102826i	$0.0327884\pi$
$401$	11.7426	+	20.3389i	0.586399	+	1.01567i	−0.408300	+	0.912848i	$0.633878\pi$
$402$	−15.7279	+	9.08052i	−0.784437	+	0.452895i
$403$	2.24264	−	3.88437i	0.111714	−	0.193494i
$404$	2.37868	−	4.11999i	0.118344	−	0.204977i
$405$	4.50000	−	7.79423i	0.223607	−	0.387298i
$406$	−11.7426	−	15.1427i	−0.582777	−	0.751519i
$407$	−0.514719	−	0.891519i	−0.0255137	−	0.0441909i
$408$		0			0
$409$	−15.4853			−0.765698			−0.382849	−	0.923811i	$-0.625057\pi$
$409$	−15.4853			−0.765698			−0.382849	+	0.923811i	$0.625057\pi$
$410$	−9.00000			−0.444478
$411$			11.6531i			0.574805i
$412$	2.62132	+	4.54026i	0.129143	+	0.223683i
$413$	−26.8492	+	3.67423i	−1.32116	+	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
$417$			9.97204i			0.488333i
$418$	−13.2426	−	22.9369i	−0.647719	−	1.12188i
$419$	0.514719	−	0.891519i	0.0251457	−	0.0435535i	−0.853179	−	0.521619i	$-0.825328\pi$
$419$	0.514719	−	0.891519i	0.0251457	−	0.0435535i	0.878324	+	0.478065i	$0.158662\pi$
$420$	4.24264	+	1.73205i	0.207020	+	0.0845154i
$421$	−1.10660	−	1.91669i	−0.0539325	−	0.0934138i	0.837799	−	0.545979i	$-0.183842\pi$
$421$	−1.10660	−	1.91669i	−0.0539325	−	0.0934138i	−0.891731	+	0.452565i	$0.850509\pi$
$422$	−6.12132	+	10.6024i	−0.297981	+	0.516119i
$423$	−10.8640	+	18.8169i	−0.528224	+	0.914911i
$424$	−5.12132	−	8.87039i	−0.248713	−	0.430784i
$425$		0			0
$426$	6.36396	−	3.67423i	0.308335	−	0.178017i
$427$	−11.7574	+	1.60896i	−0.568978	+	0.0778629i
$428$	−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
$431$	−1.24264	−	2.15232i	−0.0598559	−	0.103673i	0.834545	−	0.550940i	$-0.185731\pi$
$431$	−1.24264	−	2.15232i	−0.0598559	−	0.103673i	−0.894401	+	0.447267i	$0.852397\pi$
$432$			5.19615i			0.250000i
$433$	−23.4558			−1.12722			−0.563608	−	0.826042i	$-0.690587\pi$
$433$	−23.4558			−1.12722			−0.563608	+	0.826042i	$0.690587\pi$
$434$	5.87868	−	0.804479i	0.282186	−	0.0386162i
$435$		−	12.5446i		−	0.601469i
$436$	3.86396	+	6.69258i	0.185050	+	0.320516i
$437$	52.9706			2.53393
$438$	−18.7279	−	10.8126i	−0.894855	−	0.516645i
$439$	38.7279			1.84838			0.924191	−	0.381930i	$-0.124740\pi$
$439$	38.7279			1.84838			0.924191	+	0.381930i	$0.124740\pi$
$440$	−4.24264			−0.202260
$441$	5.22792	−	20.3389i	0.248949	−	0.968517i
$442$		0			0
$443$	29.4853			1.40089			0.700444	−	0.713707i	$-0.252985\pi$
$443$	29.4853			1.40089			0.700444	+	0.713707i	$0.252985\pi$
$444$		−	0.420266i		−	0.0199449i
$445$		0			0
$446$	6.86396	+	11.8887i	0.325018	+	0.562948i
$447$	−3.72792	−	2.15232i	−0.176325	−	0.101801i
$448$	−2.62132	+	0.358719i	−0.123846	+	0.0169479i
$449$	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
$453$			14.2767i			0.670777i
$454$	9.00000	−	15.5885i	0.422391	−	0.731603i
$455$	5.24264	−	0.717439i	0.245779	−	0.0336341i
$456$		−	10.8126i		−	0.506345i
$457$	−14.9706			−0.700293			−0.350147	−	0.936695i	$-0.613868\pi$
$457$	−14.9706			−0.700293			−0.350147	+	0.936695i	$0.613868\pi$
$458$	10.3787	+	17.9764i	0.484964	+	0.839982i
$459$		0			0
$460$	4.24264	−	7.34847i	0.197814	−	0.342624i
$461$	6.10660	+	10.5769i	0.284413	+	0.492617i	0.972467	−	0.233042i	$-0.0748680\pi$
$461$	6.10660	+	10.5769i	0.284413	+	0.492617i	−0.688054	+	0.725660i	$0.741535\pi$
$462$	2.63604	+	19.2627i	0.122640	+	0.896182i
$463$	9.86396	−	17.0849i	0.458417	−	0.794002i	−0.540460	−	0.841369i	$-0.681750\pi$
$463$	9.86396	−	17.0849i	0.458417	−	0.794002i	0.998878	+	0.0473677i	$0.0150832\pi$
$464$	3.62132	+	6.27231i	0.168116	+	0.291185i
$465$	3.36396	+	1.94218i	0.156000	+	0.0900666i
$466$	−14.1213	+	24.4588i	−0.654158	+	1.13303i
$467$	15.9853	−	27.6873i	0.739711	−	1.28122i	−0.212915	−	0.977071i	$-0.568296\pi$
$467$	15.9853	−	27.6873i	0.739711	−	1.28122i	0.952626	−	0.304146i	$-0.0983709\pi$
$468$	3.00000	+	5.19615i	0.138675	+	0.240192i
$469$	−27.4853	+	3.76127i	−1.26915	+	0.173680i
$470$	−3.62132	−	6.27231i	−0.167039	−	0.289320i
$471$	−13.0919	+	7.55860i	−0.603242	+	0.348282i
$472$	10.2426			0.471456
$473$	−4.24264			−0.195077
$474$	−22.0919	+	12.7548i	−1.01471	+	0.585845i
$475$	−3.12132	−	5.40629i	−0.143216	−	0.248057i
$476$		0			0
$477$	−30.7279			−1.40693
$478$	−6.87868	+	11.9142i	−0.314623	+	0.544944i
$479$	1.24264	−	2.15232i	0.0567777	−	0.0983419i	−0.836240	−	0.548364i	$-0.815251\pi$
$479$	1.24264	−	2.15232i	0.0567777	−	0.0983419i	0.893017	+	0.450022i	$0.148584\pi$
$480$	−1.50000	−	0.866025i	−0.0684653	−	0.0395285i
$481$	−0.242641	−	0.420266i	−0.0110635	−	0.0191625i
$482$	4.74264	−	8.21449i	0.216021	−	0.374160i
$483$	−36.0000	−	14.6969i	−1.63806	−	0.668734i
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$	5.24264	−	9.08052i	0.238056	−	0.412325i
$486$	13.5000	+	7.79423i	0.612372	+	0.353553i
$487$	10.4853	+	18.1610i	0.475133	+	0.822955i	0.999594	−	0.0284792i	$-0.00906645\pi$
$487$	10.4853	+	18.1610i	0.475133	+	0.822955i	−0.524461	+	0.851435i	$0.675733\pi$
$488$	4.48528			0.203039
$489$		−	32.8580i		−	1.48589i
$490$	5.00000	+	4.89898i	0.225877	+	0.221313i
$491$	−6.87868	+	11.9142i	−0.310430	+	0.537681i	−0.978456	−	0.206457i	$-0.933807\pi$
$491$	−6.87868	+	11.9142i	−0.310430	+	0.537681i	0.668025	+	0.744139i	$0.267140\pi$
$492$		−	15.5885i		−	0.702782i
$493$		0			0
$494$	−6.24264	−	10.8126i	−0.280870	−	0.486481i
$495$	−6.36396	+	11.0227i	−0.286039	+	0.495434i
$496$	−2.24264			−0.100698
$497$	11.1213	−	1.52192i	0.498859	−	0.0682673i
$498$	−13.5000	−	7.79423i	−0.604949	−	0.349268i
$499$	16.8492	+	29.1837i	0.754276	+	1.30644i	0.945734	+	0.324943i	$0.105345\pi$
$499$	16.8492	+	29.1837i	0.754276	+	1.30644i	−0.191458	+	0.981501i	$0.561322\pi$
$500$	−1.00000			−0.0447214
$501$		−	6.08767i		−	0.271977i
$502$	−26.4853			−1.18210
$503$	13.2426			0.590460			0.295230	−	0.955426i	$-0.404604\pi$
$503$	13.2426			0.590460			0.295230	+	0.955426i	$0.404604\pi$
$504$	−3.00000	+	7.34847i	−0.133631	+	0.327327i
$505$	4.75736			0.211700
$506$	36.0000			1.60040
$507$	−13.5000	−	7.79423i	−0.599556	−	0.346154i
$508$	15.2426			0.676283
$509$	−11.3787	−	19.7085i	−0.504351	−	0.873562i	−0.999987	−	0.00503154i	$-0.998398\pi$
$509$	−11.3787	−	19.7085i	−0.504351	−	0.873562i	0.495636	−	0.868530i	$-0.334935\pi$
$510$		0			0
$511$	−20.2426	−	26.1039i	−0.895482	−	1.15477i
$512$	1.00000			0.0441942
$513$	−28.0919	−	16.2189i	−1.24029	−	0.716080i
$514$	8.48528	+	14.6969i	0.374270	+	0.648254i
$515$	−2.62132	+	4.54026i	−0.115509	+	0.200068i
$516$	−1.50000	−	0.866025i	−0.0660338	−	0.0381246i
$517$	15.3640	−	26.6112i	0.675706	−	1.17036i
$518$	0.242641	−	0.594346i	0.0106610	−	0.0261141i
$519$	2.63604	−	1.52192i	0.115709	−	0.0668048i
$520$	−2.00000			−0.0877058
$521$	8.22792	+	14.2512i	0.360472	+	0.624355i	0.988039	−	0.154207i	$-0.0492824\pi$
$521$	8.22792	+	14.2512i	0.360472	+	0.624355i	−0.627567	+	0.778563i	$0.715949\pi$
$522$	21.7279			0.951005
$523$	−9.74264	+	16.8747i	−0.426016	+	0.737881i	−0.996515	−	0.0834172i	$-0.973417\pi$
$523$	−9.74264	+	16.8747i	−0.426016	+	0.737881i	0.570499	+	0.821298i	$0.306750\pi$
$524$	−10.2426	−	17.7408i	−0.447452	−	0.775009i
$525$	0.621320	+	4.54026i	0.0271166	+	0.198153i
$526$	−4.86396	+	8.42463i	−0.212079	+	0.367331i
$527$		0			0
$528$		−	7.34847i		−	0.319801i
$529$	−24.5000	+	42.4352i	−1.06522	+	1.84501i
$530$	5.12132	−	8.87039i	0.222456	−	0.385305i
$531$	15.3640	−	26.6112i	0.666739	−	1.15483i
$532$	6.24264	−	15.2913i	0.270653	−	0.662961i
$533$	−9.00000	−	15.5885i	−0.389833	−	0.675211i
$534$		0			0
$535$	−15.0000			−0.648507
$536$	10.4853			0.452895
$537$	15.3640	+	8.87039i	0.663004	+	0.382785i
$538$	−5.48528	−	9.50079i	−0.236487	−	0.409608i
$539$	−7.39340	+	28.7635i	−0.318456	+	1.23893i
$540$	−4.50000	+	2.59808i	−0.193649	+	0.111803i
$541$	14.7279	−	25.5095i	0.633203	−	1.09674i	−0.353690	−	0.935363i	$-0.615073\pi$
$541$	14.7279	−	25.5095i	0.633203	−	1.09674i	0.986893	−	0.161377i	$-0.0515934\pi$
$542$	2.36396	−	4.09450i	0.101541	−	0.175874i
$543$	22.1360	−	12.7802i	0.949948	−	0.548453i
$544$		0			0
$545$	−3.86396	+	6.69258i	−0.165514	+	0.286678i
$546$	1.24264	+	9.08052i	0.0531801	+	0.388610i
$547$	19.2279	+	33.3037i	0.822127	+	1.42397i	0.904096	+	0.427330i	$0.140546\pi$
$547$	19.2279	+	33.3037i	0.822127	+	1.42397i	−0.0819691	+	0.996635i	$0.526121\pi$
$548$	3.36396	−	5.82655i	0.143701	−	0.248898i
$549$	6.72792	−	11.6531i	0.287141	−	0.497342i
$550$	−2.12132	−	3.67423i	−0.0904534	−	0.156670i
$551$	−45.2132			−1.92615
$552$	12.7279	+	7.34847i	0.541736	+	0.312772i
$553$	−38.6066	+	5.28319i	−1.64172	+	0.224664i
$554$	−9.12132	+	15.7986i	−0.387528	+	0.671218i
$555$	0.363961	−	0.210133i	0.0154493	−	0.00891965i
$556$	2.87868	−	4.98602i	0.122083	−	0.211454i
$557$	−3.51472	−	6.08767i	−0.148923	−	0.257943i	0.781906	−	0.623396i	$-0.214247\pi$
$557$	−3.51472	−	6.08767i	−0.148923	−	0.257943i	−0.930830	+	0.365453i	$0.880914\pi$
$558$	−3.36396	+	5.82655i	−0.142408	+	0.246658i
$559$	−2.00000			−0.0845910
$560$	−1.62132	−	2.09077i	−0.0685133	−	0.0883512i
$561$		0			0
$562$	12.9853	+	22.4912i	0.547751	+	0.948733i
$563$	28.9706			1.22096			0.610482	−	0.792030i	$-0.290976\pi$
$563$	28.9706			1.22096			0.610482	+	0.792030i	$0.290976\pi$
$564$	10.8640	−	6.27231i	0.457455	−	0.264112i
$565$	12.7279			0.535468
$566$	−15.4853			−0.650895
$567$	14.5919	+	18.8169i	0.612801	+	0.790237i
$568$	−4.24264			−0.178017
$569$	−28.9706			−1.21451			−0.607255	−	0.794507i	$-0.707729\pi$
$569$	−28.9706			−1.21451			−0.607255	+	0.794507i	$0.707729\pi$
$570$	9.36396	−	5.40629i	0.392213	−	0.226444i
$571$	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
$573$	3.72792	−	2.15232i	0.155736	−	0.0899143i
$574$	9.00000	−	22.0454i	0.375653	−	0.920158i
$575$	8.48528			0.353861
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−1.51472	−	2.62357i	−0.0630586	−	0.109221i	0.832773	−	0.553615i	$-0.186752\pi$
$577$	−1.51472	−	2.62357i	−0.0630586	−	0.109221i	−0.895831	+	0.444395i	$0.853419\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$	12.3640	−	7.13834i	0.513829	−	0.296659i
$580$	−3.62132	+	6.27231i	−0.150367	+	0.260444i
$581$	−14.5919	−	18.8169i	−0.605373	−	0.780658i
$582$	15.7279	+	9.08052i	0.651943	+	0.376400i
$583$	43.4558			1.79976
$584$	6.24264	+	10.8126i	0.258322	+	0.447427i
$585$	−3.00000	+	5.19615i	−0.124035	+	0.214834i
$586$	−1.75736	+	3.04384i	−0.0725958	+	0.125740i
$587$	23.2279	+	40.2319i	0.958719	+	1.66055i	0.725618	+	0.688097i	$0.241554\pi$
$587$	23.2279	+	40.2319i	0.958719	+	1.66055i	0.233100	+	0.972453i	$0.425113\pi$
$588$	−8.48528	+	8.66025i	−0.349927	+	0.357143i
$589$	7.00000	−	12.1244i	0.288430	−	0.499575i
$590$	5.12132	+	8.87039i	0.210841	+	0.365188i
$591$	22.8198	−	13.1750i	0.938681	−	0.541948i
$592$	−0.121320	+	0.210133i	−0.00498624	+	0.00863641i
$593$	13.2426	−	22.9369i	0.543810	−	0.941907i	−0.454871	−	0.890557i	$-0.650315\pi$
$593$	13.2426	−	22.9369i	0.543810	−	0.941907i	0.998681	−	0.0513492i	$-0.0163521\pi$
$594$	−19.0919	−	11.0227i	−0.783349	−	0.452267i
$595$		0			0
$596$	1.24264	+	2.15232i	0.0509005	+	0.0881623i
$597$	−18.7279	−	10.8126i	−0.766483	−	0.442529i
$598$	16.9706			0.693978
$599$	33.9411			1.38680			0.693398	−	0.720554i	$-0.256113\pi$
$599$	33.9411			1.38680			0.693398	+	0.720554i	$0.256113\pi$
$600$		−	1.73205i		−	0.0707107i
$601$	8.00000	+	13.8564i	0.326327	+	0.565215i	0.981780	−	0.190021i	$-0.0608557\pi$
$601$	8.00000	+	13.8564i	0.326327	+	0.565215i	−0.655453	+	0.755236i	$0.727522\pi$
$602$	−1.62132	−	2.09077i	−0.0660801	−	0.0852134i
$603$	15.7279	−	27.2416i	0.640490	−	1.10936i
$604$	4.12132	−	7.13834i	0.167694	−	0.290455i
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$			8.23999i			0.334727i
$607$	−18.3787	−	31.8328i	−0.745968	−	1.29205i	−0.949741	−	0.313036i	$-0.898654\pi$
$607$	−18.3787	−	31.8328i	−0.745968	−	1.29205i	0.203774	−	0.979018i	$-0.434679\pi$
$608$	−3.12132	+	5.40629i	−0.126586	+	0.219254i
$609$	30.7279	+	12.5446i	1.24516	+	0.508334i
$610$	2.24264	+	3.88437i	0.0908019	+	0.157273i
$611$	7.24264	−	12.5446i	0.293006	−	0.507501i
$612$		0			0
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	0.949156	−	0.314806i	$-0.101939\pi$
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	−0.747208	+	0.664590i	$0.768606\pi$
$614$	3.97056			0.160239
$615$	13.5000	−	7.79423i	0.544373	−	0.314294i
$616$	4.24264	−	10.3923i	0.170941	−	0.418718i
$617$	10.2426	−	17.7408i	0.412353	−	0.714217i	−0.582793	−	0.812620i	$-0.698040\pi$
$617$	10.2426	−	17.7408i	0.412353	−	0.714217i	0.995147	+	0.0984037i	$0.0313736\pi$
$618$	−7.86396	−	4.54026i	−0.316335	−	0.182636i
$619$	9.75736	−	16.9002i	0.392181	−	0.679278i	−0.600556	−	0.799583i	$-0.705054\pi$
$619$	9.75736	−	16.9002i	0.392181	−	0.679278i	0.992737	+	0.120305i	$0.0383872\pi$
$620$	−1.12132	−	1.94218i	−0.0450333	−	0.0780000i
$621$	38.1838	−	22.0454i	1.53226	−	0.884652i
$622$	−0.727922			−0.0291870
$623$		0			0
$624$		−	3.46410i		−	0.138675i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−25.2132			−1.00772
$627$	39.7279	+	22.9369i	1.58658	+	0.916013i
$628$	8.72792			0.348282
$629$		0			0
$630$	−7.86396	+	1.07616i	−0.313308	+	0.0428752i
$631$	−24.4853			−0.974744			−0.487372	−	0.873195i	$-0.662044\pi$
$631$	−24.4853			−0.974744			−0.487372	+	0.873195i	$0.662044\pi$
$632$	14.7279			0.585845
$633$		−	21.2049i		−	0.842818i
$634$	19.4558			0.772690
$635$	7.62132	+	13.2005i	0.302443	+	0.523846i
$636$	15.3640	+	8.87039i	0.609221	+	0.351734i
$637$	−3.48528	+	13.5592i	−0.138092	+	0.537236i
$638$	−30.7279			−1.21653
$639$	−6.36396	+	11.0227i	−0.251754	+	0.436051i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−11.4853	+	19.8931i	−0.453641	+	0.785730i	−0.998609	−	0.0527272i	$-0.983209\pi$
$641$	−11.4853	+	19.8931i	−0.453641	+	0.785730i	0.544968	+	0.838457i	$0.316542\pi$
$642$		−	25.9808i		−	1.02538i
$643$	7.22792	−	12.5191i	0.285041	−	0.493706i	−0.687578	−	0.726111i	$-0.741326\pi$
$643$	7.22792	−	12.5191i	0.285041	−	0.493706i	0.972619	+	0.232404i	$0.0746593\pi$
$644$	13.7574	+	17.7408i	0.542116	+	0.699084i
$645$		−	1.73205i		−	0.0681994i
$646$		0			0
$647$	−19.8640	−	34.4054i	−0.780933	−	1.35262i	−0.931399	−	0.364000i	$-0.881411\pi$
$647$	−19.8640	−	34.4054i	−0.780933	−	1.35262i	0.150466	−	0.988615i	$-0.451923\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	−21.7279	+	37.6339i	−0.852896	+	1.47726i
$650$	−1.00000	−	1.73205i	−0.0392232	−	0.0679366i
$651$	−8.12132	+	6.29780i	−0.318300	+	0.246830i
$652$	−9.48528	+	16.4290i	−0.371472	+	0.643409i
$653$	6.72792	+	11.6531i	0.263284	+	0.456021i	0.967113	−	0.254349i	$-0.0818611\pi$
$653$	6.72792	+	11.6531i	0.263284	+	0.456021i	−0.703829	+	0.710370i	$0.748528\pi$
$654$	−11.5919	−	6.69258i	−0.453278	−	0.261700i
$655$	10.2426	−	17.7408i	0.400213	−	0.693189i
$656$	−4.50000	+	7.79423i	−0.175695	+	0.304314i
$657$	37.4558			1.46129
$658$	18.9853	−	2.59808i	0.740123	−	0.101284i
$659$	−17.8492	−	30.9158i	−0.695308	−	1.20431i	−0.970077	−	0.242798i	$-0.921935\pi$
$659$	−17.8492	−	30.9158i	−0.695308	−	1.20431i	0.274769	−	0.961510i	$-0.411399\pi$
$660$	6.36396	−	3.67423i	0.247717	−	0.143019i
$661$	3.24264			0.126124			0.0630621	−	0.998010i	$-0.479913\pi$
$661$	3.24264			0.126124			0.0630621	+	0.998010i	$0.479913\pi$
$662$	−4.00000			−0.155464
$663$		0			0
$664$	4.50000	+	7.79423i	0.174634	+	0.302475i
$665$	16.3640	−	2.23936i	0.634567	−	0.0868385i
$666$	0.363961	+	0.630399i	0.0141032	+	0.0244275i
$667$	30.7279	−	53.2223i	1.18979	−	2.06078i
$668$	−1.75736	+	3.04384i	−0.0679943	+	0.117770i
$669$	−20.5919	−	11.8887i	−0.796128	−	0.459645i
$670$	5.24264	+	9.08052i	0.202541	+	0.350811i
$671$	−9.51472	+	16.4800i	−0.367312	+	0.636202i
$672$	3.62132	−	2.80821i	0.139695	−	0.108329i
$673$	−0.636039	−	1.10165i	−0.0245175	−	0.0424656i	0.853506	−	0.521082i	$-0.174472\pi$
$673$	−0.636039	−	1.10165i	−0.0245175	−	0.0424656i	−0.878024	+	0.478617i	$0.841138\pi$
$674$	3.24264	−	5.61642i	0.124902	−	0.216336i
$675$	−4.50000	−	2.59808i	−0.173205	−	0.100000i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	24.7279			0.950371			0.475186	−	0.879886i	$-0.342381\pi$
$677$	24.7279			0.950371			0.475186	+	0.879886i	$0.342381\pi$
$678$			22.0454i			0.846649i
$679$	17.0000	+	21.9223i	0.652400	+	0.841301i
$680$		0			0
$681$			31.1769i			1.19470i
$682$	4.75736	−	8.23999i	0.182169	−	0.315525i
$683$	9.25736	+	16.0342i	0.354223	+	0.613532i	0.986985	−	0.160814i	$-0.0514120\pi$
$683$	9.25736	+	16.0342i	0.354223	+	0.613532i	−0.632762	+	0.774347i	$0.718079\pi$
$684$	9.36396	+	16.2189i	0.358040	+	0.620143i
$685$	6.72792			0.257061
$686$	−17.0000	+	7.34847i	−0.649063	+	0.280566i
$687$	−31.1360	−	17.9764i	−1.18791	−	0.685842i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	20.4853			0.780427
$690$			14.6969i			0.559503i
$691$	−32.9706			−1.25426			−0.627130	−	0.778915i	$-0.715770\pi$
$691$	−32.9706			−1.25426			−0.627130	+	0.778915i	$0.715770\pi$
$692$	−1.75736			−0.0668048
$693$	−20.6360	−	26.6112i	−0.783898	−	1.01087i
$694$	−9.00000			−0.341635
$695$	5.75736			0.218389
$696$	−10.8640	−	6.27231i	−0.411797	−	0.237751i
$697$		0			0
$698$	−13.0000	−	22.5167i	−0.492057	−	0.852268i
$699$		−	48.9177i		−	1.85024i
$700$	1.00000	−	2.44949i	0.0377964	−	0.0925820i
$701$	38.6985			1.46162			0.730811	−	0.682580i	$-0.239142\pi$
$701$	38.6985			1.46162			0.730811	+	0.682580i	$0.239142\pi$
$702$	−9.00000	−	5.19615i	−0.339683	−	0.196116i
$703$	−0.757359	−	1.31178i	−0.0285643	−	0.0494749i
$704$	−2.12132	+	3.67423i	−0.0799503	+	0.138478i
$705$	10.8640	+	6.27231i	0.409160	+	0.236229i
$706$	5.12132	−	8.87039i	0.192743	−	0.333841i
$707$	−4.75736	+	11.6531i	−0.178919	+	0.438260i
$708$	−15.3640	+	8.87039i	−0.577413	+	0.333370i
$709$	−14.9706			−0.562231			−0.281116	−	0.959674i	$-0.590704\pi$
$709$	−14.9706			−0.562231			−0.281116	+	0.959674i	$0.590704\pi$
$710$	−2.12132	−	3.67423i	−0.0796117	−	0.137892i
$711$	22.0919	−	38.2643i	0.828510	−	1.43502i
$712$		0			0
$713$	9.51472	+	16.4800i	0.356329	+	0.617180i
$714$		0			0
$715$	4.24264	−	7.34847i	0.158666	−	0.274817i
$716$	−5.12132	−	8.87039i	−0.191393	−	0.331502i
$717$		−	23.8284i		−	0.889890i
$718$	−0.878680	+	1.52192i	−0.0327920	+	0.0567975i
$719$	7.75736	−	13.4361i	0.289301	−	0.501083i	−0.684342	−	0.729161i	$-0.739911\pi$
$719$	7.75736	−	13.4361i	0.289301	−	0.501083i	0.973643	+	0.228077i	$0.0732439\pi$
$720$	3.00000			0.111803
$721$	−8.50000	−	10.9612i	−0.316557	−	0.408215i
$722$	−9.98528	−	17.2950i	−0.371614	−	0.643654i
$723$			16.4290i			0.611001i
$724$	−14.7574			−0.548453
$725$	−7.24264			−0.268985
$726$	10.5000	+	6.06218i	0.389692	+	0.224989i
$727$	13.4853	+	23.3572i	0.500141	+	0.866270i	1.00000		0.000163285i	$5.19751e-5\pi$
$727$	13.4853	+	23.3572i	0.500141	+	0.866270i	−0.499859	+	0.866107i	$0.666615\pi$
$728$	2.00000	−	4.89898i	0.0741249	−	0.181568i
$729$	−27.0000			−1.00000
$730$	−6.24264	+	10.8126i	−0.231050	+	0.400191i
$731$		0			0
$732$	−6.72792	+	3.88437i	−0.248671	+	0.143570i
$733$	−0.121320	−	0.210133i	−0.00448107	−	0.00776144i	0.863776	−	0.503876i	$-0.168093\pi$
$733$	−0.121320	−	0.210133i	−0.00448107	−	0.00776144i	−0.868257	+	0.496114i	$0.834760\pi$
$734$	3.13604	−	5.43178i	0.115753	−	0.200491i
$735$	−11.7426	−	3.01834i	−0.433134	−	0.111333i
$736$	−4.24264	−	7.34847i	−0.156386	−	0.270868i
$737$	−22.2426	+	38.5254i	−0.819318	+	1.41910i
$738$	13.5000	+	23.3827i	0.496942	+	0.860729i
$739$	−0.485281	−	0.840532i	−0.0178514	−	0.0309195i	0.856962	−	0.515380i	$-0.172349\pi$
$739$	−0.485281	−	0.840532i	−0.0178514	−	0.0309195i	−0.874813	+	0.484461i	$0.839016\pi$
$740$	−0.242641			−0.00891965
$741$	18.7279	+	10.8126i	0.687987	+	0.397210i
$742$	16.6066	+	21.4150i	0.609648	+	0.786170i
$743$	−9.62132	+	16.6646i	−0.352972	+	0.611365i	−0.986769	−	0.162134i	$-0.948162\pi$
$743$	−9.62132	+	16.6646i	−0.352972	+	0.611365i	0.633797	+	0.773500i	$0.281496\pi$
$744$	3.36396	−	1.94218i	0.123329	−	0.0712039i
$745$	−1.24264	+	2.15232i	−0.0455268	+	0.0788548i
$746$	−12.8492	−	22.2555i	−0.470444	−	0.814833i
$747$	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
$751$	−11.2426	−	19.4728i	−0.410250	−	0.710573i	0.584667	−	0.811273i	$-0.301225\pi$
$751$	−11.2426	−	19.4728i	−0.410250	−	0.710573i	−0.994917	+	0.100700i	$0.967892\pi$
$752$	−7.24264			−0.264112
$753$	39.7279	−	22.9369i	1.44777	−	0.835868i
$754$	−14.4853			−0.527523
$755$	8.24264			0.299980
$756$	−1.86396	−	13.6208i	−0.0677916	−	0.495383i
$757$	47.2132			1.71599			0.857997	−	0.513655i	$-0.171709\pi$
$757$	47.2132			1.71599			0.857997	+	0.513655i	$0.171709\pi$
$758$	17.5147			0.636163
$759$	−54.0000	+	31.1769i	−1.96008	+	1.13165i
$760$	−6.24264			−0.226444
$761$	−7.50000	−	12.9904i	−0.271875	−	0.470901i	0.697467	−	0.716617i	$-0.254310\pi$
$761$	−7.50000	−	12.9904i	−0.271875	−	0.470901i	−0.969342	+	0.245716i	$0.920977\pi$
$762$	−22.8640	+	13.2005i	−0.828274	+	0.478204i
$763$	−12.5294	−	16.1573i	−0.453596	−	0.584934i
$764$	−2.48528			−0.0899143
$765$		0			0
$766$	−16.8640	−	29.2092i	−0.609320	−	1.05537i
$767$	−10.2426	+	17.7408i	−0.369840	+	0.640582i
$768$	−1.50000	+	0.866025i	−0.0541266	+	0.0312500i
$769$	−3.74264	+	6.48244i	−0.134963	+	0.233763i	−0.925583	−	0.378544i	$-0.876425\pi$
$769$	−3.74264	+	6.48244i	−0.134963	+	0.233763i	0.790620	+	0.612307i	$0.209758\pi$
$770$	11.1213	−	1.52192i	0.400785	−	0.0548461i
$771$	−25.4558	−	14.6969i	−0.916770	−	0.529297i
$772$	−8.24264			−0.296659
$773$	13.2426	+	22.9369i	0.476305	+	0.824984i	0.999631	−	0.0271482i	$-0.00864260\pi$
$773$	13.2426	+	22.9369i	0.476305	+	0.824984i	−0.523327	+	0.852132i	$0.675309\pi$
$774$	3.00000			0.107833
$775$	1.12132	−	1.94218i	0.0402790	−	0.0697653i
$776$	−5.24264	−	9.08052i	−0.188200	−	0.325972i
$777$	0.150758	+	1.10165i	0.00540840	+	0.0395215i
$778$	6.10660	−	10.5769i	0.218932	−	0.379202i
$779$	−28.0919	−	48.6566i	−1.00650	−	1.74330i
$780$	3.00000	−	1.73205i	0.107417	−	0.0620174i
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$		0			0
$783$	−32.5919	+	18.8169i	−1.16474	+	0.672462i
$784$	6.74264	−	1.88064i	0.240809	−	0.0671656i
$785$	4.36396	+	7.55860i	0.155756	+	0.269778i
$786$	30.7279	+	17.7408i	1.09603	+	0.632792i
$787$	37.4853			1.33621			0.668103	−	0.744069i	$-0.267107\pi$
$787$	37.4853			1.33621			0.668103	+	0.744069i	$0.267107\pi$
$788$	−15.2132			−0.541948
$789$		−	16.8493i		−	0.599849i
$790$	7.36396	+	12.7548i	0.261998	+	0.453794i
$791$	−12.7279	+	31.1769i	−0.452553	+	1.10852i
$792$	6.36396	+	11.0227i	0.226134	+	0.391675i
$793$	−4.48528	+	7.76874i	−0.159277	+	0.275876i
$794$	−10.8787	+	18.8424i	−0.386070	+	0.668693i
$795$			17.7408i			0.629200i
$796$	6.24264	+	10.8126i	0.221265	+	0.383241i
$797$	−7.24264	+	12.5446i	−0.256547	+	0.444353i	−0.965315	−	0.261089i	$-0.915918\pi$
$797$	−7.24264	+	12.5446i	−0.256547	+	0.444353i	0.708767	+	0.705442i	$0.249252\pi$
$798$	3.87868	+	28.3432i	0.137304	+	1.00334i
$799$		0			0
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$		0			0
$802$	11.7426	+	20.3389i	0.414647	+	0.718190i
$803$	−52.9706			−1.86929
$804$	−15.7279	+	9.08052i	−0.554681	+	0.320245i
$805$	−8.48528	+	20.7846i	−0.299067	+	0.732561i
$806$	2.24264	−	3.88437i	0.0789936	−	0.136821i
$807$	16.4558	+	9.50079i	0.579273	+	0.334444i
$808$	2.37868	−	4.11999i	0.0836817	−	0.144941i
$809$	6.98528	+	12.0989i	0.245589	+	0.425373i	0.962297	−	0.272000i	$-0.0876852\pi$
$809$	6.98528	+	12.0989i	0.245589	+	0.425373i	−0.716708	+	0.697374i	$0.754352\pi$
$810$	4.50000	−	7.79423i	0.158114	−	0.273861i
$811$	−23.4558			−0.823646			−0.411823	−	0.911264i	$-0.635108\pi$
$811$	−23.4558			−0.823646			−0.411823	+	0.911264i	$0.635108\pi$
$812$	−11.7426	−	15.1427i	−0.412086	−	0.531405i
$813$			8.18900i			0.287201i
$814$	−0.514719	−	0.891519i	−0.0180409	−	0.0312477i
$815$	−18.9706			−0.664510
$816$		0			0
$817$	−6.24264			−0.218402
$818$	−15.4853			−0.541430
$819$	−9.72792	−	12.5446i	−0.339921	−	0.438345i
$820$	−9.00000			−0.314294
$821$	−26.6985			−0.931784			−0.465892	−	0.884842i	$-0.654266\pi$
$821$	−26.6985			−0.931784			−0.465892	+	0.884842i	$0.654266\pi$
$822$			11.6531i			0.406449i
$823$	39.2426			1.36791			0.683956	−	0.729523i	$-0.260258\pi$
$823$	39.2426			1.36791			0.683956	+	0.729523i	$0.260258\pi$
$824$	2.62132	+	4.54026i	0.0913180	+	0.158167i
$825$	6.36396	+	3.67423i	0.221565	+	0.127920i
$826$	−26.8492	+	3.67423i	−0.934205	+	0.127843i
$827$	30.9411			1.07593			0.537964	−	0.842968i	$-0.319194\pi$
$827$	30.9411			1.07593			0.537964	+	0.842968i	$0.319194\pi$
$828$	−25.4558			−0.884652
$829$	−5.86396	−	10.1567i	−0.203664	−	0.352756i	0.746042	−	0.665898i	$-0.231952\pi$
$829$	−5.86396	−	10.1567i	−0.203664	−	0.352756i	−0.949706	+	0.313142i	$0.898618\pi$
$830$	−4.50000	+	7.79423i	−0.156197	+	0.270542i
$831$		−	31.5972i		−	1.09609i
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$		0			0
$834$			9.97204i			0.345303i
$835$	−3.51472			−0.121632
$836$	−13.2426	−	22.9369i	−0.458006	−	0.793290i
$837$		−	11.6531i		−	0.402790i
$838$	0.514719	−	0.891519i	0.0177807	−	0.0307970i
$839$	−13.0919	−	22.6758i	−0.451982	−	0.782856i	0.546527	−	0.837441i	$-0.315950\pi$
$839$	−13.0919	−	22.6758i	−0.451982	−	0.782856i	−0.998509	+	0.0545856i	$0.982616\pi$
$840$	4.24264	+	1.73205i	0.146385	+	0.0597614i
$841$	−11.7279	+	20.3134i	−0.404411	+	0.700461i
$842$	−1.10660	−	1.91669i	−0.0381360	−	0.0660535i
$843$	−38.9558	−	22.4912i	−1.34171	−	0.774637i
$844$	−6.12132	+	10.6024i	−0.210705	+	0.364951i
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$	−10.8640	+	18.8169i	−0.373511	+	0.646939i
$847$	11.3492	+	14.6354i	0.389965	+	0.502878i
$848$	−5.12132	−	8.87039i	−0.175867	−	0.304610i
$849$	23.2279	−	13.4106i	0.797180	−	0.460252i
$850$		0			0
$851$	2.05887			0.0705773
$852$	6.36396	−	3.67423i	0.218026	−	0.125877i
$853$	26.7279	+	46.2941i	0.915147	+	1.58508i	0.806686	+	0.590980i	$0.201259\pi$
$853$	26.7279	+	46.2941i	0.915147	+	1.58508i	0.108460	+	0.994101i	$0.465408\pi$
$854$	−11.7574	+	1.60896i	−0.402329	+	0.0550574i
$855$	−9.36396	+	16.2189i	−0.320241	+	0.554673i
$856$	−7.50000	+	12.9904i	−0.256345	+	0.444002i
$857$	−19.0919	+	33.0681i	−0.652166	+	1.12959i	0.330430	+	0.943831i	$0.392806\pi$
$857$	−19.0919	+	33.0681i	−0.652166	+	1.12959i	−0.982596	+	0.185755i	$0.940527\pi$
$858$	12.7279	+	7.34847i	0.434524	+	0.250873i
$859$	−13.3640	−	23.1471i	−0.455972	−	0.789767i	0.542771	−	0.839881i	$-0.317375\pi$
$859$	−13.3640	−	23.1471i	−0.455972	−	0.789767i	−0.998744	+	0.0501132i	$0.984042\pi$
$860$	−0.500000	+	0.866025i	−0.0170499	+	0.0295312i
$861$	5.59188	+	40.8623i	0.190571	+	1.39258i
$862$	−1.24264	−	2.15232i	−0.0423245	−	0.0733082i
$863$	−7.97056	+	13.8054i	−0.271321	+	0.469942i	−0.969200	−	0.246273i	$-0.920794\pi$
$863$	−7.97056	+	13.8054i	−0.271321	+	0.469942i	0.697879	+	0.716215i	$0.254127\pi$
$864$			5.19615i			0.176777i
$865$	−0.878680	−	1.52192i	−0.0298760	−	0.0517468i
$866$	−23.4558			−0.797062
$867$			29.4449i			1.00000i
$868$	5.87868	−	0.804479i	0.199535	−	0.0273058i
$869$	−31.2426	+	54.1138i	−1.05983	+	1.83569i
$870$		−	12.5446i		−	0.425303i
$871$	−10.4853	+	18.1610i	−0.355280	+	0.615363i
$872$	3.86396	+	6.69258i	0.130850	+	0.226639i
$873$	−31.4558			−1.06462
$874$	52.9706			1.79176
$875$	2.62132	−	0.358719i	0.0886168	−	0.0121269i
$876$	−18.7279	−	10.8126i	−0.632758	−	0.365323i
$877$	16.8492	+	29.1837i	0.568958	+	0.985465i	0.996669	+	0.0815494i	$0.0259868\pi$
$877$	16.8492	+	29.1837i	0.568958	+	0.985465i	−0.427711	+	0.903916i	$0.640680\pi$
$878$	38.7279			1.30700
$879$		−	6.08767i		−	0.205332i
$880$	−4.24264			−0.143019
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	5.22792	−	20.3389i	0.176033	−	0.684845i
$883$	−40.9411			−1.37778			−0.688889	−	0.724867i	$-0.741901\pi$
$883$	−40.9411			−1.37778			−0.688889	+	0.724867i	$0.741901\pi$
$884$		0			0
$885$	−15.3640	−	8.87039i	−0.516454	−	0.298175i
$886$	29.4853			0.990577
$887$	−3.62132	−	6.27231i	−0.121592	−	0.210604i	0.798804	−	0.601592i	$-0.205467\pi$
$887$	−3.62132	−	6.27231i	−0.121592	−	0.210604i	−0.920396	+	0.390988i	$0.872133\pi$
$888$		−	0.420266i		−	0.0141032i
$889$	−39.9558	+	5.46783i	−1.34008	+	0.183385i
$890$		0			0
$891$	38.1838			1.27920
$892$	6.86396	+	11.8887i	0.229822	+	0.398064i
$893$	22.6066	−	39.1558i	0.756501	−	1.31030i
$894$	−3.72792	−	2.15232i	−0.124680	−	0.0719842i
$895$	5.12132	−	8.87039i	0.171187	−	0.296504i
$896$	−2.62132	+	0.358719i	−0.0875722	+	0.0119840i
$897$	−25.4558	+	14.6969i	−0.849946	+	0.490716i
$898$	9.00000			0.300334
$899$	−8.12132	−	14.0665i	−0.270861	−	0.469145i
$900$	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
$905$	−7.37868	−	12.7802i	−0.245276	−	0.424830i
$906$			14.2767i			0.474311i
$907$	−0.227922	+	0.394773i	−0.00756803	+	0.0131082i	−0.869785	−	0.493432i	$-0.835742\pi$
$907$	−0.227922	+	0.394773i	−0.00756803	+	0.0131082i	0.862217	+	0.506540i	$0.169076\pi$
$908$	9.00000	−	15.5885i	0.298675	−	0.517321i
$909$	−7.13604	−	12.3600i	−0.236687	−	0.409955i
$910$	5.24264	−	0.717439i	0.173792	−	0.0237829i
$911$	−23.3345	−	40.4166i	−0.773107	−	1.33906i	−0.935852	−	0.352393i	$-0.885368\pi$
$911$	−23.3345	−	40.4166i	−0.773107	−	1.33906i	0.162745	−	0.986668i	$-0.447965\pi$
$912$		−	10.8126i		−	0.358040i
$913$	−38.1838			−1.26370
$914$	−14.9706			−0.495182
$915$	−6.72792	−	3.88437i	−0.222418	−	0.128413i
$916$	10.3787	+	17.9764i	0.342921	+	0.593957i
$917$	33.2132	+	42.8300i	1.09680	+	1.41437i
$918$		0			0
$919$	−0.121320	+	0.210133i	−0.00400199	+	0.00693165i	−0.868019	−	0.496530i	$-0.834607\pi$
$919$	−0.121320	+	0.210133i	−0.00400199	+	0.00693165i	0.864017	+	0.503462i	$0.167941\pi$
$920$	4.24264	−	7.34847i	0.139876	−	0.242272i
$921$	−5.95584	+	3.43861i	−0.196252	+	0.113306i
$922$	6.10660	+	10.5769i	0.201110	+	0.348333i
$923$	4.24264	−	7.34847i	0.139648	−	0.241878i
$924$	2.63604	+	19.2627i	0.0867193	+	0.633696i
$925$	−0.121320	−	0.210133i	−0.00398899	−	0.00690913i
$926$	9.86396	−	17.0849i	0.324150	−	0.561444i
$927$	15.7279			0.516573
$928$	3.62132	+	6.27231i	0.118876	+	0.205899i
$929$	−47.9117			−1.57193			−0.785966	−	0.618270i	$-0.787834\pi$
$929$	−47.9117			−1.57193			−0.785966	+	0.618270i	$0.787834\pi$
$930$	3.36396	+	1.94218i	0.110309	+	0.0636867i
$931$	−10.8787	+	42.3227i	−0.356534	+	1.38707i
$932$	−14.1213	+	24.4588i	−0.462559	+	0.801176i
$933$	1.09188	−	0.630399i	0.0357466	−	0.0206383i
$934$	15.9853	−	27.6873i	0.523054	−	0.905957i
$935$		0			0
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$	6.24264			0.203938			0.101969	−	0.994788i	$-0.467486\pi$
$937$	6.24264			0.203938			0.101969	+	0.994788i	$0.467486\pi$
$938$	−27.4853	+	3.76127i	−0.897426	+	0.122810i
$939$	37.8198	−	21.8353i	1.23420	−	0.712567i
$940$	−3.62132	−	6.27231i	−0.118114	−	0.204580i
$941$	4.75736			0.155085			0.0775427	−	0.996989i	$-0.475293\pi$
$941$	4.75736			0.155085			0.0775427	+	0.996989i	$0.475293\pi$
$942$	−13.0919	+	7.55860i	−0.426557	+	0.246273i
$943$	76.3675			2.48687
$944$	10.2426			0.333370
$945$	10.8640	−	8.42463i	0.353405	−	0.274053i
$946$	−4.24264			−0.137940
$947$	−2.48528			−0.0807608			−0.0403804	−	0.999184i	$-0.512857\pi$
$947$	−2.48528			−0.0807608			−0.0403804	+	0.999184i	$0.512857\pi$
$948$	−22.0919	+	12.7548i	−0.717511	+	0.414255i
$949$	−24.9706			−0.810579
$950$	−3.12132	−	5.40629i	−0.101269	−	0.175403i
$951$	−29.1838	+	16.8493i	−0.946348	+	0.546375i
$952$		0			0
$953$	−26.1838			−0.848175			−0.424088	−	0.905621i	$-0.639405\pi$
$953$	−26.1838			−0.848175			−0.424088	+	0.905621i	$0.639405\pi$
$954$	−30.7279			−0.994853
$955$	−1.24264	−	2.15232i	−0.0402109	−	0.0696473i
$956$	−6.87868	+	11.9142i	−0.222472	+	0.385333i
$957$	46.0919	−	26.6112i	1.48994	−	0.860217i
$958$	1.24264	−	2.15232i	0.0401479	−	0.0695382i
$959$	−6.72792	+	16.4800i	−0.217256	+	0.532166i
$960$	−1.50000	−	0.866025i	−0.0484123	−	0.0279508i
$961$	−25.9706			−0.837760
$962$	−0.242641	−	0.420266i	−0.00782305	−	0.0135499i
$963$	22.5000	+	38.9711i	0.725052	+	1.25583i
$964$	4.74264	−	8.21449i	0.152750	−	0.264571i
$965$	−4.12132	−	7.13834i	−0.132670	−	0.229791i
$966$	−36.0000	−	14.6969i	−1.15828	−	0.472866i
$967$	−4.51472	+	7.81972i	−0.145184	+	0.251465i	−0.929441	−	0.368970i	$-0.879711\pi$
$967$	−4.51472	+	7.81972i	−0.145184	+	0.251465i	0.784258	+	0.620435i	$0.213044\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$		0			0
$970$	5.24264	−	9.08052i	0.168331	−	0.291558i
$971$	13.2426	−	22.9369i	0.424977	−	0.736081i	−0.571442	−	0.820643i	$-0.693616\pi$
$971$	13.2426	−	22.9369i	0.424977	−	0.736081i	0.996418	+	0.0845617i	$0.0269490\pi$
$972$	13.5000	+	7.79423i	0.433013	+	0.250000i
$973$	−5.75736	+	14.1026i	−0.184572	+	0.452108i
$974$	10.4853	+	18.1610i	0.335970	+	0.581917i
$975$	3.00000	+	1.73205i	0.0960769	+	0.0554700i
$976$	4.48528			0.143570
$977$	−56.4853			−1.80712			−0.903562	−	0.428457i	$-0.859057\pi$
$977$	−56.4853			−1.80712			−0.903562	+	0.428457i	$0.859057\pi$
$978$		−	32.8580i		−	1.05068i
$979$		0			0
$980$	5.00000	+	4.89898i	0.159719	+	0.156492i
$981$	23.1838			0.740201
$982$	−6.87868	+	11.9142i	−0.219507	+	0.380198i
$983$	−10.8640	+	18.8169i	−0.346507	+	0.600167i	−0.985626	−	0.168940i	$-0.945965\pi$
$983$	−10.8640	+	18.8169i	−0.346507	+	0.600167i	0.639120	+	0.769107i	$0.279299\pi$
$984$		−	15.5885i		−	0.496942i
$985$	−7.60660	−	13.1750i	−0.242366	−	0.419791i
$986$		0			0
$987$	−26.2279	+	20.3389i	−0.834844	+	0.647393i
$988$	−6.24264	−	10.8126i	−0.198605	−	0.343994i
$989$	4.24264	−	7.34847i	0.134908	−	0.233668i
$990$	−6.36396	+	11.0227i	−0.202260	+	0.350325i
$991$	1.12132	+	1.94218i	0.0356199	+	0.0616955i	0.883286	−	0.468835i	$-0.155326\pi$
$991$	1.12132	+	1.94218i	0.0356199	+	0.0616955i	−0.847666	+	0.530530i	$0.821993\pi$
$992$	−2.24264			−0.0712039
$993$	6.00000	−	3.46410i	0.190404	−	0.109930i
$994$	11.1213	−	1.52192i	0.352747	−	0.0482723i
$995$	−6.24264	+	10.8126i	−0.197905	+	0.342782i
$996$	−13.5000	−	7.79423i	−0.427764	−	0.246970i
$997$	−9.63604	+	16.6901i	−0.305176	+	0.528581i	−0.977301	−	0.211857i	$-0.932049\pi$
$997$	−9.63604	+	16.6901i	−0.305176	+	0.528581i	0.672124	+	0.740438i	$0.265382\pi$
$998$	16.8492	+	29.1837i	0.533353	+	0.923795i
$999$	−1.09188	−	0.630399i	−0.0345457	−	0.0199449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.e.121.1	✓	4
3.2	odd	2		1890.2.i.e.1171.1		4
7.4	even	3		630.2.l.e.571.2	yes	4
9.2	odd	6		1890.2.l.e.1801.2		4
9.7	even	3		630.2.l.e.331.2	yes	4
21.11	odd	6		1890.2.l.e.361.2		4
63.11	odd	6		1890.2.i.e.991.1		4
63.25	even	3	inner	630.2.i.e.151.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.e.121.1	✓	4	1.1	even	1	trivial
630.2.i.e.151.1	yes	4	63.25	even	3	inner
630.2.l.e.331.2	yes	4	9.7	even	3
630.2.l.e.571.2	yes	4	7.4	even	3
1890.2.i.e.991.1		4	63.11	odd	6
1890.2.i.e.1171.1		4	3.2	odd	2
1890.2.l.e.361.2		4	21.11	odd	6
1890.2.l.e.1801.2		4	9.2	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.50000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(-2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(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} +(-2.62132 + 0.358719i) 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} +(-2.62132 + 0.358719i) q^{14} +(-1.50000 - 0.866025i) q^{15} +1.00000 q^{16} +(1.50000 - 2.59808i) q^{18} +(-3.12132 + 5.40629i) q^{19} +(0.500000 + 0.866025i) q^{20} +(3.62132 - 2.80821i) 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} +(-2.62132 + 0.358719i) q^{28} +(3.62132 + 6.27231i) q^{29} +(-1.50000 - 0.866025i) q^{30} -2.24264 q^{31} +1.00000 q^{32} -7.34847i q^{33} +(-1.62132 - 2.09077i) q^{35} +(1.50000 - 2.59808i) q^{36} +(-0.121320 + 0.210133i) q^{37} +(-3.12132 + 5.40629i) q^{38} -3.46410i q^{39} +(0.500000 + 0.866025i) q^{40} +(-4.50000 + 7.79423i) q^{41} +(3.62132 - 2.80821i) q^{42} +(0.500000 + 0.866025i) q^{43} +(-2.12132 + 3.67423i) q^{44} +3.00000 q^{45} +(-4.24264 - 7.34847i) q^{46} -7.24264 q^{47} +(-1.50000 + 0.866025i) q^{48} +(6.74264 - 1.88064i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(-5.12132 - 8.87039i) q^{53} +5.19615i q^{54} -4.24264 q^{55} +(-2.62132 + 0.358719i) q^{56} -10.8126i q^{57} +(3.62132 + 6.27231i) q^{58} +10.2426 q^{59} +(-1.50000 - 0.866025i) q^{60} +4.48528 q^{61} -2.24264 q^{62} +(-3.00000 + 7.34847i) q^{63} +1.00000 q^{64} -2.00000 q^{65} -7.34847i q^{66} +10.4853 q^{67} +(12.7279 + 7.34847i) q^{69} +(-1.62132 - 2.09077i) q^{70} -4.24264 q^{71} +(1.50000 - 2.59808i) q^{72} +(6.24264 + 10.8126i) q^{73} +(-0.121320 + 0.210133i) q^{74} -1.73205i q^{75} +(-3.12132 + 5.40629i) q^{76} +(4.24264 - 10.3923i) q^{77} -3.46410i q^{78} +14.7279 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} +(3.62132 - 2.80821i) q^{84} +(0.500000 + 0.866025i) q^{86} +(-10.8640 - 6.27231i) q^{87} +(-2.12132 + 3.67423i) q^{88} +3.00000 q^{90} +(2.00000 - 4.89898i) q^{91} +(-4.24264 - 7.34847i) q^{92} +(3.36396 - 1.94218i) q^{93} -7.24264 q^{94} -6.24264 q^{95} +(-1.50000 + 0.866025i) q^{96} +(-5.24264 - 9.08052i) q^{97} +(6.74264 - 1.88064i) 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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