LMFDB - Embedded newform 630.2.l.e.571.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("630.331");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$4$
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			571.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	630.571
Dual form			630.2.l.e.331.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.50000 + 0.866025i) q^{6} +(-2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 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} -4.24264 q^{11} -1.73205i q^{12} +(-1.00000 + 1.73205i) q^{13} +(1.00000 - 2.44949i) q^{14} +(-1.50000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{18} +(1.12132 + 1.94218i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.24264 - 1.73205i) q^{21} +(2.12132 - 3.67423i) q^{22} -8.48528 q^{23} +(1.50000 + 0.866025i) q^{24} +1.00000 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} +(-3.12132 - 5.40629i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-6.36396 - 3.67423i) q^{33} +(2.62132 - 0.358719i) q^{35} +(1.50000 - 2.59808i) q^{36} +(4.12132 + 7.13834i) q^{37} -2.24264 q^{38} +(-3.00000 + 1.73205i) q^{39} -1.00000 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} +(-1.50000 - 2.59808i) q^{45} +(4.24264 - 7.34847i) q^{46} +(-0.621320 + 1.07616i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(6.74264 - 1.88064i) q^{49} +(-0.500000 + 0.866025i) q^{50} +2.00000 q^{52} +(-0.878680 + 1.52192i) q^{53} +(-4.50000 - 2.59808i) q^{54} +4.24264 q^{55} +(-2.62132 + 0.358719i) q^{56} +3.88437i q^{57} +1.24264 q^{58} +(-0.878680 - 1.52192i) q^{59} +1.73205i q^{60} +(6.24264 - 10.8126i) q^{61} +6.24264 q^{62} +(-4.86396 - 6.27231i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(6.36396 - 3.67423i) q^{66} +(3.24264 + 5.61642i) q^{67} +(-12.7279 - 7.34847i) q^{69} +(-1.00000 + 2.44949i) q^{70} +4.24264 q^{71} +(1.50000 + 2.59808i) q^{72} +(-2.24264 + 3.88437i) q^{73} -8.24264 q^{74} +(1.50000 + 0.866025i) q^{75} +(1.12132 - 1.94218i) q^{76} +(11.1213 - 1.52192i) q^{77} -3.46410i q^{78} +(5.36396 - 9.29065i) 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} -1.00000 q^{86} -2.15232i q^{87} -4.24264 q^{88} +3.00000 q^{90} +(2.00000 - 4.89898i) q^{91} +(4.24264 + 7.34847i) q^{92} -10.8126i q^{93} +(-0.621320 - 1.07616i) q^{94} +(-1.12132 - 1.94218i) q^{95} -1.73205i 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 - 2 q^{2} + 6 q^{3} - 2 q^{4} - 4 q^{5} - 6 q^{6} - 2 q^{7} + 4 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 4 * q^5 - 6 * q^6 - 2 * q^7 + 4 * q^8 + 6 * q^9	$ 4 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 4 q^{5} - 6 q^{6} - 2 q^{7} + 4 q^{8} + 6 q^{9} + 2 q^{10} - 4 q^{13} + 4 q^{14} - 6 q^{15} - 2 q^{16} - 12 q^{18} - 4 q^{19} + 2 q^{20} + 6 q^{24} + 4 q^{25} - 4 q^{26} - 2 q^{28} + 6 q^{29} + 6 q^{30} - 4 q^{31} - 2 q^{32} + 2 q^{35} + 6 q^{36} + 8 q^{37} + 8 q^{38} - 12 q^{39} - 4 q^{40} - 18 q^{41} + 6 q^{42} + 2 q^{43} - 6 q^{45} + 6 q^{47} - 6 q^{48} + 10 q^{49} - 2 q^{50} + 8 q^{52} - 12 q^{53} - 18 q^{54} - 2 q^{56} - 12 q^{58} - 12 q^{59} + 8 q^{61} + 8 q^{62} + 6 q^{63} + 4 q^{64} + 4 q^{65} - 4 q^{67} - 4 q^{70} + 6 q^{72} + 8 q^{73} - 16 q^{74} + 6 q^{75} - 4 q^{76} + 36 q^{77} - 4 q^{79} + 2 q^{80} - 18 q^{81} - 18 q^{82} + 18 q^{83} - 6 q^{84} - 4 q^{86} + 12 q^{90} + 8 q^{91} + 6 q^{94} + 4 q^{95} - 4 q^{97} + 10 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 4 * q^5 - 6 * q^6 - 2 * q^7 + 4 * q^8 + 6 * q^9 + 2 * q^10 - 4 * q^13 + 4 * q^14 - 6 * q^15 - 2 * q^16 - 12 * q^18 - 4 * q^19 + 2 * q^20 + 6 * q^24 + 4 * q^25 - 4 * q^26 - 2 * q^28 + 6 * q^29 + 6 * q^30 - 4 * q^31 - 2 * q^32 + 2 * q^35 + 6 * q^36 + 8 * q^37 + 8 * q^38 - 12 * q^39 - 4 * q^40 - 18 * q^41 + 6 * q^42 + 2 * q^43 - 6 * q^45 + 6 * q^47 - 6 * q^48 + 10 * q^49 - 2 * q^50 + 8 * q^52 - 12 * q^53 - 18 * q^54 - 2 * q^56 - 12 * q^58 - 12 * q^59 + 8 * q^61 + 8 * q^62 + 6 * q^63 + 4 * q^64 + 4 * q^65 - 4 * q^67 - 4 * q^70 + 6 * q^72 + 8 * q^73 - 16 * q^74 + 6 * q^75 - 4 * q^76 + 36 * q^77 - 4 * q^79 + 2 * q^80 - 18 * q^81 - 18 * q^82 + 18 * q^83 - 6 * q^84 - 4 * q^86 + 12 * q^90 + 8 * q^91 + 6 * q^94 + 4 * q^95 - 4 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−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
$11$	−4.24264			−1.27920			−0.639602	−	0.768706i	$-0.720901\pi$
$11$	−4.24264			−1.27920			−0.639602	+	0.768706i	$0.720901\pi$
$12$		−	1.73205i		−	0.500000i
$13$	−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	$0.256123\pi$
$14$	1.00000	−	2.44949i	0.267261	−	0.654654i
$15$	−1.50000	−	0.866025i	−0.387298	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−3.00000			−0.707107
$19$	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
$21$	−4.24264	−	1.73205i	−0.925820	−	0.377964i
$22$	2.12132	−	3.67423i	0.452267	−	0.783349i
$23$	−8.48528			−1.76930			−0.884652	−	0.466252i	$-0.845604\pi$
$23$	−8.48528			−1.76930			−0.884652	+	0.466252i	$0.845604\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	1.00000			0.200000
$26$	−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	0.802554	−	0.596580i	$-0.203474\pi$
$29$	−0.621320	−	1.07616i	−0.115376	−	0.199838i	−0.917930	+	0.396742i	$0.870141\pi$
$30$	1.50000	−	0.866025i	0.273861	−	0.158114i
$31$	−3.12132	−	5.40629i	−0.560606	−	0.970998i	−0.997444	−	0.0714573i	$-0.977235\pi$
$31$	−3.12132	−	5.40629i	−0.560606	−	0.970998i	0.436838	−	0.899540i	$-0.356098\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−6.36396	−	3.67423i	−1.10782	−	0.639602i
$34$		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	$0.596379\pi$
$38$	−2.24264			−0.363804
$39$	−3.00000	+	1.73205i	−0.480384	+	0.277350i
$40$	−1.00000			−0.158114
$41$	−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
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$	4.24264	−	7.34847i	0.625543	−	1.08347i
$47$	−0.621320	+	1.07616i	−0.0906289	+	0.156974i	−0.907776	−	0.419455i	$-0.862221\pi$
$47$	−0.621320	+	1.07616i	−0.0906289	+	0.156974i	0.817147	+	0.576429i	$0.195554\pi$
$48$	−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
$52$	2.00000			0.277350
$53$	−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	$0.205179\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$	4.24264			0.572078
$56$	−2.62132	+	0.358719i	−0.350289	+	0.0479359i
$57$			3.88437i			0.514497i
$58$	1.24264			0.163167
$59$	−0.878680	−	1.52192i	−0.114394	−	0.198137i	0.803143	−	0.595786i	$-0.203159\pi$
$59$	−0.878680	−	1.52192i	−0.114394	−	0.198137i	−0.917537	+	0.397649i	$0.869826\pi$
$60$			1.73205i			0.223607i
$61$	6.24264	−	10.8126i	0.799288	−	1.38441i	−0.120792	−	0.992678i	$-0.538543\pi$
$61$	6.24264	−	10.8126i	0.799288	−	1.38441i	0.920080	−	0.391730i	$-0.128123\pi$
$62$	6.24264			0.792816
$63$	−4.86396	−	6.27231i	−0.612801	−	0.790237i
$64$	1.00000			0.125000
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$	6.36396	−	3.67423i	0.783349	−	0.452267i
$67$	3.24264	+	5.61642i	0.396152	+	0.686155i	0.993247	−	0.116015i	$-0.0370121\pi$
$67$	3.24264	+	5.61642i	0.396152	+	0.686155i	−0.597096	+	0.802170i	$0.703679\pi$
$68$		0			0
$69$	−12.7279	−	7.34847i	−1.53226	−	0.884652i
$70$	−1.00000	+	2.44949i	−0.119523	+	0.292770i
$71$	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	$0.251207\pi$
$74$	−8.24264			−0.958188
$75$	1.50000	+	0.866025i	0.173205	+	0.100000i
$76$	1.12132	−	1.94218i	0.128624	−	0.222784i
$77$	11.1213	−	1.52192i	1.26739	−	0.173439i
$78$		−	3.46410i		−	0.392232i
$79$	5.36396	−	9.29065i	0.603493	−	1.04528i	−0.388795	−	0.921324i	$-0.627109\pi$
$79$	5.36396	−	9.29065i	0.603493	−	1.04528i	0.992288	−	0.123956i	$-0.0395581\pi$
$80$	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	$0.668890\pi$
$84$	0.621320	+	4.54026i	0.0677916	+	0.495383i
$85$		0			0
$86$	−1.00000			−0.107833
$87$		−	2.15232i		−	0.230753i
$88$	−4.24264			−0.452267
$89$		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
$93$		−	10.8126i		−	1.12121i
$94$	−0.621320	−	1.07616i	−0.0640843	−	0.110997i
$95$	−1.12132	−	1.94218i	−0.115045	−	0.199264i
$96$		−	1.73205i		−	0.176777i
$97$	3.24264	+	5.61642i	0.329240	+	0.570261i	0.982361	−	0.186993i	$-0.0598741\pi$
$97$	3.24264	+	5.61642i	0.329240	+	0.570261i	−0.653121	+	0.757254i	$0.726541\pi$
$98$	−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
$101$	−13.2426			−1.31769			−0.658846	−	0.752278i	$-0.728955\pi$
$101$	−13.2426			−1.31769			−0.658846	+	0.752278i	$0.728955\pi$
$102$		0			0
$103$	3.24264			0.319507			0.159753	−	0.987157i	$-0.448930\pi$
$103$	3.24264			0.319507			0.159753	+	0.987157i	$0.448930\pi$
$104$	−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	$-0.424851\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	−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	$0.843864\pi$
$110$	−2.12132	+	3.67423i	−0.202260	+	0.350325i
$111$			14.2767i			1.35508i
$112$	1.00000	−	2.44949i	0.0944911	−	0.231455i
$113$	−6.36396	+	11.0227i	−0.598671	+	1.03693i	0.394346	+	0.918962i	$0.370971\pi$
$113$	−6.36396	+	11.0227i	−0.598671	+	1.03693i	−0.993018	+	0.117967i	$0.962362\pi$
$114$	−3.36396	−	1.94218i	−0.315064	−	0.181902i
$115$	8.48528			0.791257
$116$	−0.621320	+	1.07616i	−0.0576881	+	0.0999188i
$117$	−6.00000			−0.554700
$118$	1.75736			0.161778
$119$		0			0
$120$	−1.50000	−	0.866025i	−0.136931	−	0.0790569i
$121$	7.00000			0.636364
$122$	6.24264	+	10.8126i	0.565182	+	0.978924i
$123$	−13.5000	+	7.79423i	−1.21725	+	0.702782i
$124$	−3.12132	+	5.40629i	−0.280303	+	0.485499i
$125$	−1.00000			−0.0894427
$126$	7.86396	−	1.07616i	0.700577	−	0.0958718i
$127$	6.75736			0.599619			0.299809	−	0.953999i	$-0.403077\pi$
$127$	6.75736			0.599619			0.299809	+	0.953999i	$0.403077\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$			1.73205i			0.152499i
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	3.51472			0.307082			0.153541	−	0.988142i	$-0.450932\pi$
$131$	3.51472			0.307082			0.153541	+	0.988142i	$0.450932\pi$
$132$			7.34847i			0.639602i
$133$	−3.63604	−	4.68885i	−0.315285	−	0.406575i
$134$	−6.48528			−0.560243
$135$		−	5.19615i		−	0.447214i
$136$		0			0
$137$	18.7279			1.60003			0.800017	−	0.599977i	$-0.204824\pi$
$137$	18.7279			1.60003			0.800017	+	0.599977i	$0.204824\pi$
$138$	12.7279	−	7.34847i	1.08347	−	0.625543i
$139$	7.12132	−	12.3345i	0.604023	−	1.04620i	−0.388183	−	0.921582i	$-0.626897\pi$
$139$	7.12132	−	12.3345i	0.604023	−	1.04620i	0.992205	−	0.124615i	$-0.0397696\pi$
$140$	−1.62132	−	2.09077i	−0.137027	−	0.176702i
$141$	−1.86396	+	1.07616i	−0.156974	+	0.0906289i
$142$	−2.12132	+	3.67423i	−0.178017	+	0.308335i
$143$	4.24264	−	7.34847i	0.354787	−	0.614510i
$144$	−3.00000			−0.250000
$145$	0.621320	+	1.07616i	0.0515978	+	0.0893701i
$146$	−2.24264	−	3.88437i	−0.185602	−	0.321473i
$147$	11.7426	+	3.01834i	0.968517	+	0.248949i
$148$	4.12132	−	7.13834i	0.338770	−	0.586768i
$149$	14.4853			1.18668			0.593340	−	0.804952i	$-0.297809\pi$
$149$	14.4853			1.18668			0.593340	+	0.804952i	$0.297809\pi$
$150$	−1.50000	+	0.866025i	−0.122474	+	0.0707107i
$151$	0.242641			0.0197458			0.00987291	−	0.999951i	$-0.496857\pi$
$151$	0.242641			0.0197458			0.00987291	+	0.999951i	$0.496857\pi$
$152$	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
$156$	3.00000	+	1.73205i	0.240192	+	0.138675i
$157$	8.36396	+	14.4868i	0.667517	+	1.15617i	0.978596	+	0.205789i	$0.0659761\pi$
$157$	8.36396	+	14.4868i	0.667517	+	1.15617i	−0.311080	+	0.950384i	$0.600691\pi$
$158$	5.36396	+	9.29065i	0.426734	+	0.739125i
$159$	−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	$0.633920\pi$
$164$	9.00000			0.702782
$165$	6.36396	+	3.67423i	0.495434	+	0.286039i
$166$	−9.00000			−0.698535
$167$	−10.2426	+	17.7408i	−0.792599	+	1.37282i	0.131753	+	0.991283i	$0.457939\pi$
$167$	−10.2426	+	17.7408i	−0.792599	+	1.37282i	−0.924352	+	0.381540i	$0.875394\pi$
$168$	−4.24264	−	1.73205i	−0.327327	−	0.133631i
$169$	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
$173$	5.12132	−	8.87039i	0.389367	−	0.674403i	−0.602998	−	0.797743i	$-0.706027\pi$
$173$	5.12132	−	8.87039i	0.389367	−	0.674403i	0.992364	+	0.123340i	$0.0393605\pi$
$174$	1.86396	+	1.07616i	0.141307	+	0.0815834i
$175$	−2.62132	+	0.358719i	−0.198153	+	0.0271166i
$176$	2.12132	−	3.67423i	0.159901	−	0.276956i
$177$		−	3.04384i		−	0.228789i
$178$		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	$0.187587\pi$
$180$	−1.50000	+	2.59808i	−0.111803	+	0.193649i
$181$	−23.2426			−1.72761			−0.863806	−	0.503825i	$-0.831926\pi$
$181$	−23.2426			−1.72761			−0.863806	+	0.503825i	$0.831926\pi$
$182$	3.24264	+	4.18154i	0.240361	+	0.309956i
$183$	18.7279	−	10.8126i	1.38441	−	0.799288i
$184$	−8.48528			−0.625543
$185$	−4.12132	−	7.13834i	−0.303005	−	0.524821i
$186$	9.36396	+	5.40629i	0.686599	+	0.396408i
$187$		0			0
$188$	1.24264			0.0906289
$189$	−1.86396	−	13.6208i	−0.135583	−	0.990766i
$190$	2.24264			0.162698
$191$	−7.24264	+	12.5446i	−0.524059	+	0.907697i	0.475549	+	0.879689i	$0.342250\pi$
$191$	−7.24264	+	12.5446i	−0.524059	+	0.907697i	−0.999608	+	0.0280075i	$0.991084\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	−0.121320	−	0.210133i	−0.00873283	−	0.0151257i	0.861626	−	0.507544i	$-0.169446\pi$
$193$	−0.121320	−	0.210133i	−0.00873283	−	0.0151257i	−0.870359	+	0.492418i	$0.836113\pi$
$194$	−6.48528			−0.465616
$195$	3.00000	−	1.73205i	0.214834	−	0.124035i
$196$	−5.00000	−	4.89898i	−0.357143	−	0.349927i
$197$	27.2132			1.93886			0.969430	−	0.245367i	$-0.0789085\pi$
$197$	27.2132			1.93886			0.969430	+	0.245367i	$0.0789085\pi$
$198$	12.7279			0.904534
$199$	−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	$0.217486\pi$
$200$	1.00000			0.0707107
$201$			11.2328i			0.792303i
$202$	6.62132	−	11.4685i	0.465874	−	0.806918i
$203$	2.01472	+	2.59808i	0.141406	+	0.182349i
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	−1.62132	+	2.80821i	−0.112963	+	0.195657i
$207$	−12.7279	−	22.0454i	−0.884652	−	1.53226i
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	−4.75736	−	8.23999i	−0.329073	−	0.569972i
$210$	−3.62132	+	2.80821i	−0.249895	+	0.193785i
$211$	−1.87868	+	3.25397i	−0.129334	+	0.224012i	−0.923419	−	0.383794i	$-0.874617\pi$
$211$	−1.87868	+	3.25397i	−0.129334	+	0.224012i	0.794085	+	0.607807i	$0.207950\pi$
$212$	1.75736			0.120696
$213$	6.36396	+	3.67423i	0.436051	+	0.251754i
$214$	15.0000			1.02538
$215$	−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
$220$	−2.12132	−	3.67423i	−0.143019	−	0.247717i
$221$		0			0
$222$	−12.3640	−	7.13834i	−0.829815	−	0.479094i
$223$	−5.86396	−	10.1567i	−0.392680	−	0.680141i	0.600122	−	0.799908i	$-0.295119\pi$
$223$	−5.86396	−	10.1567i	−0.392680	−	0.680141i	−0.992802	+	0.119767i	$0.961785\pi$
$224$	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
$227$	−18.0000			−1.19470			−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000			−1.19470			−0.597351	+	0.801980i	$0.703780\pi$
$228$	3.36396	−	1.94218i	0.222784	−	0.128624i
$229$	−29.2426			−1.93241			−0.966204	−	0.257778i	$-0.917010\pi$
$229$	−29.2426			−1.93241			−0.966204	+	0.257778i	$0.917010\pi$
$230$	−4.24264	+	7.34847i	−0.279751	+	0.484544i
$231$	18.0000	+	7.34847i	1.18431	+	0.483494i
$232$	−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
$236$	−0.878680	+	1.52192i	−0.0571972	+	0.0990684i
$237$	16.0919	−	9.29065i	1.04528	−	0.603493i
$238$		0			0
$239$	−11.1213	+	19.2627i	−0.719378	+	1.24600i	0.241868	+	0.970309i	$0.422240\pi$
$239$	−11.1213	+	19.2627i	−0.719378	+	1.24600i	−0.961246	+	0.275691i	$0.911093\pi$
$240$	1.50000	−	0.866025i	0.0968246	−	0.0559017i
$241$	7.48528			0.482169			0.241085	−	0.970504i	$-0.422497\pi$
$241$	7.48528			0.482169			0.241085	+	0.970504i	$0.422497\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	−12.4853			−0.799288
$245$	−6.74264	+	1.88064i	−0.430772	+	0.120150i
$246$		−	15.5885i		−	0.993884i
$247$	−4.48528			−0.285392
$248$	−3.12132	−	5.40629i	−0.198204	−	0.343299i
$249$			15.5885i			0.987878i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−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
$254$	−3.37868	+	5.85204i	−0.211997	+	0.367190i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	16.9706			1.05859			0.529297	−	0.848436i	$-0.322456\pi$
$257$	16.9706			1.05859			0.529297	+	0.848436i	$0.322456\pi$
$258$	−1.50000	−	0.866025i	−0.0933859	−	0.0539164i
$259$	−13.3640	−	17.2335i	−0.830396	−	1.07084i
$260$	−2.00000			−0.124035
$261$	1.86396	−	3.22848i	0.115376	−	0.199838i
$262$	−1.75736	+	3.04384i	−0.108570	+	0.188049i
$263$	−15.7279			−0.969825			−0.484913	−	0.874563i	$-0.661149\pi$
$263$	−15.7279			−0.969825			−0.484913	+	0.874563i	$0.661149\pi$
$264$	−6.36396	−	3.67423i	−0.391675	−	0.226134i
$265$	0.878680	−	1.52192i	0.0539769	−	0.0934907i
$266$	5.87868	−	0.804479i	0.360445	−	0.0493258i
$267$		0			0
$268$	3.24264	−	5.61642i	0.198076	−	0.343077i
$269$	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
$275$	−4.24264			−0.255841
$276$			14.6969i			0.884652i
$277$	9.75736			0.586263			0.293131	−	0.956072i	$-0.405303\pi$
$277$	9.75736			0.586263			0.293131	+	0.956072i	$0.405303\pi$
$278$	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	0.722324	−	0.691555i	$-0.243074\pi$
$281$	−3.98528	−	6.90271i	−0.237742	−	0.411781i	−0.960066	+	0.279774i	$0.909741\pi$
$282$		−	2.15232i		−	0.128169i
$283$	−0.742641	−	1.28629i	−0.0441454	−	0.0764621i	0.843108	−	0.537744i	$-0.180723\pi$
$283$	−0.742641	−	1.28629i	−0.0441454	−	0.0764621i	−0.887254	+	0.461282i	$0.847390\pi$
$284$	−2.12132	−	3.67423i	−0.125877	−	0.218026i
$285$		−	3.88437i		−	0.230090i
$286$	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
$290$	−1.24264			−0.0729704
$291$			11.2328i			0.658481i
$292$	4.48528			0.262481
$293$	−10.2426	+	17.7408i	−0.598381	+	1.03643i	0.394679	+	0.918819i	$0.370856\pi$
$293$	−10.2426	+	17.7408i	−0.598381	+	1.03643i	−0.993060	+	0.117608i	$0.962477\pi$
$294$	−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
$297$		−	22.0454i		−	1.27920i
$298$	−7.24264	+	12.5446i	−0.419555	+	0.726690i
$299$	8.48528	−	14.6969i	0.490716	−	0.849946i
$300$		−	1.73205i		−	0.100000i
$301$	−1.62132	−	2.09077i	−0.0934514	−	0.120510i
$302$	−0.121320	+	0.210133i	−0.00698120	+	0.0120918i
$303$	−19.8640	−	11.4685i	−1.14115	−	0.658846i
$304$	−2.24264			−0.128624
$305$	−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	$0.826600\pi$
$308$	−6.87868	−	8.87039i	−0.391949	−	0.505437i
$309$	4.86396	+	2.80821i	0.276701	+	0.159753i
$310$	−6.24264			−0.354558
$311$	−12.3640	−	21.4150i	−0.701096	−	1.21433i	−0.968082	−	0.250633i	$-0.919361\pi$
$311$	−12.3640	−	21.4150i	−0.701096	−	1.21433i	0.266986	−	0.963700i	$-0.413972\pi$
$312$	−3.00000	+	1.73205i	−0.169842	+	0.0980581i
$313$	−8.60660	+	14.9071i	−0.486474	+	0.842597i	−0.999879	−	0.0155488i	$-0.995050\pi$
$313$	−8.60660	+	14.9071i	−0.486474	+	0.842597i	0.513405	+	0.858146i	$0.328384\pi$
$314$	−16.7279			−0.944011
$315$	4.86396	+	6.27231i	0.274053	+	0.353405i
$316$	−10.7279			−0.603493
$317$	15.7279	−	27.2416i	0.883368	−	1.53004i	0.0357954	−	0.999359i	$-0.488604\pi$
$317$	15.7279	−	27.2416i	0.883368	−	1.53004i	0.847573	−	0.530679i	$-0.178063\pi$
$318$		−	3.04384i		−	0.170690i
$319$	2.63604	+	4.56575i	0.147590	+	0.255633i
$320$	−1.00000			−0.0559017
$321$		−	25.9808i		−	1.45010i
$322$	−8.48528	+	20.7846i	−0.472866	+	1.15828i
$323$		0			0
$324$	9.00000			0.500000
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$	−14.9706			−0.829143
$327$	−26.5919	+	15.3528i	−1.47053	+	0.849013i
$328$	−4.50000	+	7.79423i	−0.248471	+	0.430364i
$329$	1.24264	−	3.04384i	0.0685090	−	0.167812i
$330$	−6.36396	+	3.67423i	−0.350325	+	0.202260i
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	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
$336$	3.62132	−	2.80821i	0.197559	−	0.153200i
$337$	−5.24264	+	9.08052i	−0.285585	+	0.494647i	−0.972751	−	0.231853i	$-0.925521\pi$
$337$	−5.24264	+	9.08052i	−0.285585	+	0.494647i	0.687166	+	0.726500i	$0.258855\pi$
$338$	−9.00000			−0.489535
$339$	−19.0919	+	11.0227i	−1.03693	+	0.598671i
$340$		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
$345$	12.7279	+	7.34847i	0.685248	+	0.395628i
$346$	5.12132	+	8.87039i	0.275324	+	0.476875i
$347$	4.50000	+	7.79423i	0.241573	+	0.418416i	0.961162	−	0.275983i	$-0.0890035\pi$
$347$	4.50000	+	7.79423i	0.241573	+	0.418416i	−0.719590	+	0.694399i	$0.755670\pi$
$348$	−1.86396	+	1.07616i	−0.0999188	+	0.0576881i
$349$	−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
$353$	−1.75736			−0.0935348			−0.0467674	−	0.998906i	$-0.514892\pi$
$353$	−1.75736			−0.0935348			−0.0467674	+	0.998906i	$0.514892\pi$
$354$	2.63604	+	1.52192i	0.140104	+	0.0808890i
$355$	−4.24264			−0.225176
$356$		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	$0.920454\pi$
$360$	−1.50000	−	2.59808i	−0.0790569	−	0.136931i
$361$	6.98528	−	12.0989i	0.367646	−	0.636782i
$362$	11.6213	−	20.1287i	0.610803	−	1.05794i
$363$	10.5000	+	6.06218i	0.551107	+	0.318182i
$364$	−5.24264	+	0.717439i	−0.274789	+	0.0376040i
$365$	2.24264	−	3.88437i	0.117385	−	0.203317i
$366$			21.6251i			1.13036i
$367$	−31.7279			−1.65618			−0.828092	−	0.560592i	$-0.810574\pi$
$367$	−31.7279			−1.65618			−0.828092	+	0.560592i	$0.810574\pi$
$368$	4.24264	−	7.34847i	0.221163	−	0.383065i
$369$	−27.0000			−1.40556
$370$	8.24264			0.428514
$371$	1.75736	−	4.30463i	0.0912375	−	0.223485i
$372$	−9.36396	+	5.40629i	−0.485499	+	0.280303i
$373$	−33.6985			−1.74484			−0.872421	−	0.488756i	$-0.837451\pi$
$373$	−33.6985			−1.74484			−0.872421	+	0.488756i	$0.837451\pi$
$374$		0			0
$375$	−1.50000	−	0.866025i	−0.0774597	−	0.0447214i
$376$	−0.621320	+	1.07616i	−0.0320422	+	0.0554986i
$377$	2.48528			0.127999
$378$	12.7279	+	5.19615i	0.654654	+	0.267261i
$379$	34.4853			1.77139			0.885695	−	0.464268i	$-0.153682\pi$
$379$	34.4853			1.77139			0.885695	+	0.464268i	$0.153682\pi$
$380$	−1.12132	+	1.94218i	−0.0575225	+	0.0996319i
$381$	10.1360	+	5.85204i	0.519285	+	0.299809i
$382$	−7.24264	−	12.5446i	−0.370566	−	0.641839i
$383$	8.27208			0.422683			0.211342	−	0.977412i	$-0.432217\pi$
$383$	8.27208			0.422683			0.211342	+	0.977412i	$0.432217\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$	−11.1213	+	1.52192i	−0.566795	+	0.0775641i
$386$	0.242641			0.0123501
$387$	−1.50000	+	2.59808i	−0.0762493	+	0.132068i
$388$	3.24264	−	5.61642i	0.164620	−	0.285130i
$389$	30.2132			1.53187			0.765935	−	0.642918i	$-0.222276\pi$
$389$	30.2132			1.53187			0.765935	+	0.642918i	$0.222276\pi$
$390$			3.46410i			0.175412i
$391$		0			0
$392$	6.74264	−	1.88064i	0.340555	−	0.0949865i
$393$	5.27208	+	3.04384i	0.265941	+	0.153541i
$394$	−13.6066	+	23.5673i	−0.685491	+	1.18730i
$395$	−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
$399$	−1.39340	−	10.1822i	−0.0697572	−	0.509746i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−6.51472			−0.325330			−0.162665	−	0.986681i	$-0.552009\pi$
$401$	−6.51472			−0.325330			−0.162665	+	0.986681i	$0.552009\pi$
$402$	−9.72792	−	5.61642i	−0.485185	−	0.280121i
$403$	12.4853			0.621936
$404$	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
$409$	−0.742641	−	1.28629i	−0.0367212	−	0.0636030i	0.847081	−	0.531464i	$-0.178358\pi$
$409$	−0.742641	−	1.28629i	−0.0367212	−	0.0636030i	−0.883802	+	0.467861i	$0.845025\pi$
$410$	4.50000	+	7.79423i	0.222239	+	0.384930i
$411$	28.0919	+	16.2189i	1.38567	+	0.800017i
$412$	−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
$416$	2.00000			0.0980581
$417$	21.3640	−	12.3345i	1.04620	−	0.604023i
$418$	9.51472			0.465380
$419$	17.4853	−	30.2854i	0.854212	−	1.47954i	−0.0231623	−	0.999732i	$-0.507373\pi$
$419$	17.4853	−	30.2854i	0.854212	−	1.47954i	0.877374	−	0.479807i	$-0.159293\pi$
$420$	−0.621320	−	4.54026i	−0.0303173	−	0.221542i
$421$	20.1066	+	34.8257i	0.979936	+	1.69730i	0.662578	+	0.748993i	$0.269462\pi$
$421$	20.1066	+	34.8257i	0.979936	+	1.69730i	0.317357	+	0.948306i	$0.397204\pi$
$422$	−1.87868	−	3.25397i	−0.0914527	−	0.158401i
$423$	−3.72792			−0.181258
$424$	−0.878680	+	1.52192i	−0.0426725	+	0.0739109i
$425$		0			0
$426$	−6.36396	+	3.67423i	−0.308335	+	0.178017i
$427$	−12.4853	+	30.5826i	−0.604205	+	1.47999i
$428$	−7.50000	+	12.9904i	−0.362526	+	0.627914i
$429$	12.7279	−	7.34847i	0.614510	−	0.354787i
$430$	1.00000			0.0482243
$431$	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	$0.0532336\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	27.4558			1.31944			0.659722	−	0.751510i	$-0.270674\pi$
$433$	27.4558			1.31944			0.659722	+	0.751510i	$0.270674\pi$
$434$	−16.3640	+	2.23936i	−0.785495	+	0.107493i
$435$			2.15232i			0.103196i
$436$	17.7279			0.849013
$437$	−9.51472	−	16.4800i	−0.455151	−	0.788344i
$438$		−	7.76874i		−	0.371205i
$439$	−6.63604	+	11.4940i	−0.316721	+	0.548577i	−0.979802	−	0.199971i	$-0.935915\pi$
$439$	−6.63604	+	11.4940i	−0.316721	+	0.548577i	0.663081	+	0.748548i	$0.269249\pi$
$440$	4.24264			0.202260
$441$	15.0000	+	14.6969i	0.714286	+	0.699854i
$442$		0			0
$443$	−6.25736	+	10.8381i	−0.297296	+	0.514932i	−0.975516	−	0.219927i	$-0.929418\pi$
$443$	−6.25736	+	10.8381i	−0.297296	+	0.514932i	0.678220	+	0.734859i	$0.262752\pi$
$444$	12.3640	−	7.13834i	0.586768	−	0.338770i
$445$		0			0
$446$	11.7279			0.555333
$447$	21.7279	+	12.5446i	1.02770	+	0.593340i
$448$	−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	$0.431882\pi$
$450$	−3.00000			−0.141421
$451$	19.0919	−	33.0681i	0.899002	−	1.55712i
$452$	12.7279			0.598671
$453$	0.363961	+	0.210133i	0.0171004	+	0.00987291i
$454$	9.00000	−	15.5885i	0.422391	−	0.731603i
$455$	−2.00000	+	4.89898i	−0.0937614	+	0.229668i
$456$			3.88437i			0.181902i
$457$	−9.48528	+	16.4290i	−0.443703	+	0.768516i	−0.997961	−	0.0638292i	$-0.979669\pi$
$457$	−9.48528	+	16.4290i	−0.443703	+	0.768516i	0.554258	+	0.832345i	$0.313002\pi$
$458$	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	−0.967200	−	0.254016i	$-0.918248\pi$
$461$	−15.1066	−	26.1654i	−0.703585	−	1.21864i	0.263615	−	0.964628i	$-0.415085\pi$
$462$	−15.3640	+	11.9142i	−0.714796	+	0.554300i
$463$	−2.86396	+	4.96053i	−0.133100	+	0.230535i	−0.924870	−	0.380284i	$-0.875826\pi$
$463$	−2.86396	+	4.96053i	−0.133100	+	0.230535i	0.791770	+	0.610819i	$0.209160\pi$
$464$	1.24264			0.0576881
$465$			10.8126i			0.501421i
$466$	19.7574			0.915242
$467$	−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
$471$			28.9736i			1.33503i
$472$	−0.878680	−	1.52192i	−0.0404445	−	0.0700519i
$473$	−2.12132	−	3.67423i	−0.0975384	−	0.168941i
$474$			18.5813i			0.853468i
$475$	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
$479$	14.4853			0.661849			0.330925	−	0.943657i	$-0.392639\pi$
$479$	14.4853			0.661849			0.330925	+	0.943657i	$0.392639\pi$
$480$			1.73205i			0.0790569i
$481$	−16.4853			−0.751664
$482$	−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
$486$		−	15.5885i		−	0.707107i
$487$	−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	$0.261612\pi$
$488$	6.24264	−	10.8126i	0.282591	−	0.489462i
$489$			25.9298i			1.17258i
$490$	1.74264	−	6.77962i	0.0787245	−	0.306272i
$491$	−11.1213	+	19.2627i	−0.501898	+	0.869313i	0.498099	+	0.867120i	$0.334031\pi$
$491$	−11.1213	+	19.2627i	−0.501898	+	0.869313i	−0.999998	+	0.00219320i	$0.999302\pi$
$492$	13.5000	+	7.79423i	0.608627	+	0.351391i
$493$		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
$497$	−11.1213	+	1.52192i	−0.498859	+	0.0682673i
$498$	−13.5000	−	7.79423i	−0.604949	−	0.349268i
$499$	25.6985			1.15042			0.575211	−	0.818005i	$-0.304920\pi$
$499$	25.6985			1.15042			0.575211	+	0.818005i	$0.304920\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−30.7279	+	17.7408i	−1.37282	+	0.792599i
$502$	4.75736	−	8.23999i	0.212331	−	0.367769i
$503$	4.75736			0.212120			0.106060	−	0.994360i	$-0.466176\pi$
$503$	4.75736			0.212120			0.106060	+	0.994360i	$0.466176\pi$
$504$	−4.86396	−	6.27231i	−0.216658	−	0.279391i
$505$	13.2426			0.589290
$506$	−18.0000	+	31.1769i	−0.800198	+	1.38598i
$507$			15.5885i			0.692308i
$508$	−3.37868	−	5.85204i	−0.149905	−	0.259643i
$509$	31.2426			1.38481			0.692403	−	0.721511i	$-0.256552\pi$
$509$	31.2426			1.38481			0.692403	+	0.721511i	$0.256552\pi$
$510$		0			0
$511$	4.48528	−	10.9867i	0.198417	−	0.486021i
$512$	1.00000			0.0441942
$513$	−10.0919	+	5.82655i	−0.445568	+	0.257249i
$514$	−8.48528	+	14.6969i	−0.374270	+	0.648254i
$515$	−3.24264			−0.142888
$516$	1.50000	−	0.866025i	0.0660338	−	0.0381246i
$517$	2.63604	−	4.56575i	0.115933	−	0.200802i
$518$	21.6066	−	2.95680i	0.949340	−	0.129914i
$519$	15.3640	−	8.87039i	0.674403	−	0.389367i
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	−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	$0.894416\pi$
$522$	1.86396	+	3.22848i	0.0815834	+	0.141307i
$523$	−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
$525$	−4.24264	−	1.73205i	−0.185164	−	0.0755929i
$526$	7.86396	−	13.6208i	0.342885	−	0.593894i
$527$		0			0
$528$	6.36396	−	3.67423i	0.276956	−	0.159901i
$529$	49.0000			2.13043
$530$	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
$535$	7.50000	+	12.9904i	0.324253	+	0.561623i
$536$	3.24264	+	5.61642i	0.140061	+	0.242592i
$537$	−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	$0.985925\pi$
$542$	20.7279			0.890340
$543$	−34.8640	−	20.1287i	−1.49616	−	0.863806i
$544$		0			0
$545$	8.86396	−	15.3528i	0.379690	−	0.657643i
$546$	1.24264	+	9.08052i	0.0531801	+	0.388610i
$547$	−6.22792	−	10.7871i	−0.266287	−	0.461222i	0.701613	−	0.712558i	$-0.252463\pi$
$547$	−6.22792	−	10.7871i	−0.266287	−	0.461222i	−0.967900	+	0.251336i	$0.919130\pi$
$548$	−9.36396	−	16.2189i	−0.400009	−	0.692835i
$549$	37.4558			1.59858
$550$	2.12132	−	3.67423i	0.0904534	−	0.156670i
$551$	1.39340	−	2.41344i	0.0593608	−	0.102816i
$552$	−12.7279	−	7.34847i	−0.541736	−	0.312772i
$553$	−10.7279	+	26.2779i	−0.456198	+	1.11745i
$554$	−4.87868	+	8.45012i	−0.207275	+	0.359011i
$555$		−	14.2767i		−	0.606011i
$556$	−14.2426			−0.604023
$557$	−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
$560$	−1.00000	+	2.44949i	−0.0422577	+	0.103510i
$561$		0			0
$562$	7.97056			0.336218
$563$	2.48528	+	4.30463i	0.104742	+	0.181419i	0.913633	−	0.406540i	$-0.133265\pi$
$563$	2.48528	+	4.30463i	0.104742	+	0.181419i	−0.808891	+	0.587959i	$0.799932\pi$
$564$	1.86396	+	1.07616i	0.0784869	+	0.0453144i
$565$	6.36396	−	11.0227i	0.267734	−	0.463729i
$566$	1.48528			0.0624310
$567$	9.00000	−	22.0454i	0.377964	−	0.925820i
$568$	4.24264			0.178017
$569$	−2.48528	+	4.30463i	−0.104188	+	0.180460i	−0.913406	−	0.407049i	$-0.866558\pi$
$569$	−2.48528	+	4.30463i	−0.104188	+	0.180460i	0.809218	+	0.587509i	$0.199891\pi$
$570$	3.36396	+	1.94218i	0.140901	+	0.0813491i
$571$	−13.0000	−	22.5167i	−0.544033	−	0.942293i	−0.998667	−	0.0516146i	$-0.983563\pi$
$571$	−13.0000	−	22.5167i	−0.544033	−	0.942293i	0.454634	−	0.890678i	$-0.349770\pi$
$572$	−8.48528			−0.354787
$573$	−21.7279	+	12.5446i	−0.907697	+	0.524059i
$574$	14.5919	+	18.8169i	0.609053	+	0.785404i
$575$	−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	$0.887146\pi$
$578$	−17.0000			−0.707107
$579$		−	0.420266i		−	0.0174657i
$580$	0.621320	−	1.07616i	0.0257989	−	0.0446850i
$581$	−14.5919	−	18.8169i	−0.605373	−	0.780658i
$582$	−9.72792	−	5.61642i	−0.403235	−	0.232808i
$583$	3.72792	−	6.45695i	0.154395	−	0.267420i
$584$	−2.24264	+	3.88437i	−0.0928011	+	0.160736i
$585$	6.00000			0.248069
$586$	−10.2426	−	17.7408i	−0.423120	−	0.732865i
$587$	−2.22792	−	3.85887i	−0.0919562	−	0.159273i	0.816378	−	0.577518i	$-0.195979\pi$
$587$	−2.22792	−	3.85887i	−0.0919562	−	0.159273i	−0.908334	+	0.418245i	$0.862645\pi$
$588$	−3.25736	−	11.6786i	−0.134331	−	0.481617i
$589$	7.00000	−	12.1244i	0.288430	−	0.499575i
$590$	−1.75736			−0.0723493
$591$	40.8198	+	23.5673i	1.67910	+	0.969430i
$592$	−8.24264			−0.338770
$593$	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
$598$	8.48528	+	14.6969i	0.346989	+	0.601003i
$599$	16.9706	+	29.3939i	0.693398	+	1.20100i	0.970718	+	0.240223i	$0.0772207\pi$
$599$	16.9706	+	29.3939i	0.693398	+	1.20100i	−0.277319	+	0.960778i	$0.589446\pi$
$600$	1.50000	+	0.866025i	0.0612372	+	0.0353553i
$601$	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	$0.727522\pi$
$602$	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
$605$	−7.00000			−0.284590
$606$	19.8640	−	11.4685i	0.806918	−	0.465874i
$607$	45.2426			1.83634			0.918171	−	0.396184i	$-0.129666\pi$
$607$	45.2426			1.83634			0.918171	+	0.396184i	$0.129666\pi$
$608$	1.12132	−	1.94218i	0.0454755	−	0.0787660i
$609$	0.772078	+	5.64191i	0.0312862	+	0.228622i
$610$	−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	$0.101939\pi$
$614$	14.9853	−	25.9553i	0.604757	−	1.04747i
$615$	13.5000	−	7.79423i	0.544373	−	0.314294i
$616$	11.1213	−	1.52192i	0.448091	−	0.0613198i
$617$	1.75736	−	3.04384i	0.0707486	−	0.122540i	−0.828481	−	0.560017i	$-0.810795\pi$
$617$	1.75736	−	3.04384i	0.0707486	−	0.122540i	0.899230	+	0.437477i	$0.144128\pi$
$618$	−4.86396	+	2.80821i	−0.195657	+	0.112963i
$619$	−36.4853			−1.46647			−0.733234	−	0.679977i	$-0.761990\pi$
$619$	−36.4853			−1.46647			−0.733234	+	0.679977i	$0.761990\pi$
$620$	3.12132	−	5.40629i	0.125355	−	0.217122i
$621$		−	44.0908i		−	1.76930i
$622$	24.7279			0.991499
$623$		0			0
$624$		−	3.46410i		−	0.138675i
$625$	1.00000			0.0400000
$626$	−8.60660	−	14.9071i	−0.343989	−	0.595806i
$627$		−	16.4800i		−	0.658147i
$628$	8.36396	−	14.4868i	0.333758	−	0.578086i
$629$		0			0
$630$	−7.86396	+	1.07616i	−0.313308	+	0.0428752i
$631$	−7.51472			−0.299156			−0.149578	−	0.988750i	$-0.547792\pi$
$631$	−7.51472			−0.299156			−0.149578	+	0.988750i	$0.547792\pi$
$632$	5.36396	−	9.29065i	0.213367	−	0.369562i
$633$	−5.63604	+	3.25397i	−0.224012	+	0.129334i
$634$	15.7279	+	27.2416i	0.624636	+	1.08190i
$635$	−6.75736			−0.268158
$636$	2.63604	+	1.52192i	0.104526	+	0.0603480i
$637$	−3.48528	+	13.5592i	−0.138092	+	0.537236i
$638$	−5.27208			−0.208724
$639$	6.36396	+	11.0227i	0.251754	+	0.436051i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−10.9706			−0.433311			−0.216656	−	0.976248i	$-0.569515\pi$
$641$	−10.9706			−0.433311			−0.216656	+	0.976248i	$0.569515\pi$
$642$	22.5000	+	12.9904i	0.888004	+	0.512689i
$643$	−18.2279	+	31.5717i	−0.718839	+	1.24507i	0.242621	+	0.970121i	$0.421993\pi$
$643$	−18.2279	+	31.5717i	−0.718839	+	1.24507i	−0.961460	+	0.274945i	$0.911340\pi$
$644$	−13.7574	−	17.7408i	−0.542116	−	0.699084i
$645$		−	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
$653$	37.4558			1.46576			0.732880	−	0.680358i	$-0.238176\pi$
$653$	37.4558			1.46576			0.732880	+	0.680358i	$0.238176\pi$
$654$		−	30.7057i		−	1.20069i
$655$	−3.51472			−0.137331
$656$	−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	0.999040	−	0.0438082i	$-0.0139491\pi$
$659$	11.8492	+	20.5235i	0.461581	+	0.799482i	−0.537459	+	0.843290i	$0.680616\pi$
$660$		−	7.34847i		−	0.286039i
$661$	2.62132	+	4.54026i	0.101958	+	0.176596i	0.912491	−	0.409097i	$-0.134156\pi$
$661$	2.62132	+	4.54026i	0.101958	+	0.176596i	−0.810534	+	0.585692i	$0.800823\pi$
$662$	2.00000	+	3.46410i	0.0777322	+	0.134636i
$663$		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
$668$	20.4853			0.792599
$669$		−	20.3134i		−	0.785360i
$670$	6.48528			0.250548
$671$	−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	−0.999846	−	0.0175746i	$-0.994406\pi$
$673$	−13.3640	−	23.1471i	−0.515143	−	0.892254i	0.484703	−	0.874679i	$-0.338928\pi$
$674$	−5.24264	−	9.08052i	−0.201939	−	0.349769i
$675$			5.19615i			0.200000i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	0.363961	−	0.630399i	0.0139882	−	0.0242282i	−0.858947	−	0.512065i	$-0.828881\pi$
$677$	0.363961	−	0.630399i	0.0139882	−	0.0242282i	0.872935	+	0.487837i	$0.162214\pi$
$678$		−	22.0454i		−	0.846649i
$679$	−10.5147	−	13.5592i	−0.403518	−	0.520356i
$680$		0			0
$681$	−27.0000	−	15.5885i	−1.03464	−	0.597351i
$682$	−26.4853			−1.01417
$683$	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	$-0.0708778\pi$
$684$	6.72792			0.257249
$685$	−18.7279			−0.715557
$686$	2.13604	−	18.3967i	0.0815543	−	0.702388i
$687$	−43.8640	−	25.3249i	−1.67351	−	0.966204i
$688$	−1.00000			−0.0381246
$689$	−1.75736	−	3.04384i	−0.0669501	−	0.115961i
$690$	−12.7279	+	7.34847i	−0.484544	+	0.279751i
$691$	−0.485281	+	0.840532i	−0.0184610	+	0.0319753i	−0.875108	−	0.483927i	$-0.839210\pi$
$691$	−0.485281	+	0.840532i	−0.0184610	+	0.0319753i	0.856647	+	0.515902i	$0.172543\pi$
$692$	−10.2426			−0.389367
$693$	20.6360	+	26.6112i	0.783898	+	1.01087i
$694$	−9.00000			−0.341635
$695$	−7.12132	+	12.3345i	−0.270127	+	0.467874i
$696$		−	2.15232i		−	0.0815834i
$697$		0			0
$698$	26.0000			0.984115
$699$		−	34.2208i		−	1.29435i
$700$	1.62132	+	2.09077i	0.0612801	+	0.0790237i
$701$	−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
$704$	−4.24264			−0.159901
$705$	1.86396	−	1.07616i	0.0702008	−	0.0405305i
$706$	0.878680	−	1.52192i	0.0330695	−	0.0572781i
$707$	34.7132	−	4.75039i	1.30552	−	0.178657i
$708$	−2.63604	+	1.52192i	−0.0990684	+	0.0571972i
$709$	−9.48528	+	16.4290i	−0.356227	+	0.617004i	−0.987327	−	0.158698i	$-0.949270\pi$
$709$	−9.48528	+	16.4290i	−0.356227	+	0.617004i	0.631100	+	0.775702i	$0.282604\pi$
$710$	2.12132	−	3.67423i	0.0796117	−	0.137892i
$711$	32.1838			1.20699
$712$		0			0
$713$	26.4853	+	45.8739i	0.991882	+	1.71799i
$714$		0			0
$715$	−4.24264	+	7.34847i	−0.158666	+	0.274817i
$716$	1.75736			0.0656756
$717$	−33.3640	+	19.2627i	−1.24600	+	0.719378i
$718$	10.2426			0.382252
$719$	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
$723$	11.2279	+	6.48244i	0.417571	+	0.241085i
$724$	11.6213	+	20.1287i	0.431903	+	0.748078i
$725$	−0.621320	−	1.07616i	−0.0230753	−	0.0399675i
$726$	−10.5000	+	6.06218i	−0.389692	+	0.224989i
$727$	−3.48528	−	6.03668i	−0.129262	−	0.223888i	0.794129	−	0.607749i	$-0.207927\pi$
$727$	−3.48528	−	6.03668i	−0.129262	−	0.223888i	−0.923391	+	0.383861i	$0.874594\pi$
$728$	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
$733$	−8.24264			−0.304449			−0.152224	−	0.988346i	$-0.548644\pi$
$733$	−8.24264			−0.304449			−0.152224	+	0.988346i	$0.548644\pi$
$734$	15.8640	−	27.4772i	0.585549	−	1.01420i
$735$	−11.7426	−	3.01834i	−0.433134	−	0.111333i
$736$	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	$-0.0407286\pi$
$740$	−4.12132	+	7.13834i	−0.151503	+	0.262410i
$741$	−6.72792	−	3.88437i	−0.247156	−	0.142696i
$742$	2.84924	+	3.67423i	0.104599	+	0.134885i
$743$	−5.37868	+	9.31615i	−0.197325	+	0.341776i	−0.947660	−	0.319281i	$-0.896559\pi$
$743$	−5.37868	+	9.31615i	−0.197325	+	0.341776i	0.750335	+	0.661057i	$0.229892\pi$
$744$		−	10.8126i		−	0.396408i
$745$	−14.4853			−0.530700
$746$	16.8492	−	29.1837i	0.616895	−	1.06849i
$747$	−13.5000	+	23.3827i	−0.493939	+	0.855528i
$748$		0			0
$749$	24.3198	+	31.3616i	0.888626	+	1.14593i
$750$	1.50000	−	0.866025i	0.0547723	−	0.0316228i
$751$	5.51472			0.201235			0.100617	−	0.994925i	$-0.467918\pi$
$751$	5.51472			0.201235			0.100617	+	0.994925i	$0.467918\pi$
$752$	−0.621320	−	1.07616i	−0.0226572	−	0.0392435i
$753$	−14.2721	−	8.23999i	−0.520103	−	0.300282i
$754$	−1.24264	+	2.15232i	−0.0452543	+	0.0783828i
$755$	−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	$0.472275\pi$
$758$	−17.2426	+	29.8651i	−0.626281	+	1.08475i
$759$	54.0000	+	31.1769i	1.96008	+	1.13165i
$760$	−1.12132	−	1.94218i	−0.0406746	−	0.0704504i
$761$	15.0000			0.543750			0.271875	−	0.962333i	$-0.412356\pi$
$761$	15.0000			0.543750			0.271875	+	0.962333i	$0.412356\pi$
$762$	−10.1360	+	5.85204i	−0.367190	+	0.211997i
$763$	17.7279	−	43.4244i	0.641794	−	1.57207i
$764$	14.4853			0.524059
$765$		0			0
$766$	−4.13604	+	7.16383i	−0.149441	+	0.258840i
$767$	3.51472			0.126909
$768$		−	1.73205i		−	0.0625000i
$769$	4.74264	−	8.21449i	0.171024	−	0.296222i	−0.767754	−	0.640745i	$-0.778626\pi$
$769$	4.74264	−	8.21449i	0.171024	−	0.296222i	0.938778	+	0.344522i	$0.111959\pi$
$770$	4.24264	−	10.3923i	0.152894	−	0.374513i
$771$	25.4558	+	14.6969i	0.916770	+	0.529297i
$772$	−0.121320	+	0.210133i	−0.00436641	+	0.00756285i
$773$	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	$0.111931\pi$
$774$	−1.50000	−	2.59808i	−0.0539164	−	0.0933859i
$775$	−3.12132	−	5.40629i	−0.112121	−	0.194200i
$776$	3.24264	+	5.61642i	0.116404	+	0.201618i
$777$	−5.12132	−	37.4237i	−0.183726	−	1.34257i
$778$	−15.1066	+	26.1654i	−0.541598	+	0.938075i
$779$	−20.1838			−0.723158
$780$	−3.00000	−	1.73205i	−0.107417	−	0.0620174i
$781$	−18.0000			−0.644091
$782$		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
$787$	−10.2574	−	17.7663i	−0.365635	−	0.633299i	0.623243	−	0.782029i	$-0.285815\pi$
$787$	−10.2574	−	17.7663i	−0.365635	−	0.633299i	−0.988878	+	0.148730i	$0.952482\pi$
$788$	−13.6066	−	23.5673i	−0.484715	−	0.839551i
$789$	−23.5919	−	13.6208i	−0.839893	−	0.484913i
$790$	−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
$794$	30.2426			1.07327
$795$	2.63604	−	1.52192i	0.0934907	−	0.0539769i
$796$	4.48528			0.158977
$797$	1.24264	−	2.15232i	0.0440166	−	0.0762390i	−0.843178	−	0.537635i	$-0.819318\pi$
$797$	1.24264	−	2.15232i	0.0440166	−	0.0762390i	0.887194	+	0.461396i	$0.152651\pi$
$798$	9.51472	+	3.88437i	0.336817	+	0.137505i
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	3.25736	−	5.64191i	0.115021	−	0.199223i
$803$	9.51472	−	16.4800i	0.335767	−	0.581566i
$804$	9.72792	−	5.61642i	0.343077	−	0.198076i
$805$	−22.2426	+	3.04384i	−0.783950	+	0.107281i
$806$	−6.24264	+	10.8126i	−0.219888	+	0.380857i
$807$	34.4558	−	19.8931i	1.21290	−	0.700270i
$808$	−13.2426			−0.465874
$809$	−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	$0.339891\pi$
$812$	1.24264	−	3.04384i	0.0436081	−	0.106818i
$813$		−	35.9018i		−	1.25913i
$814$	34.9706			1.22572
$815$	−7.48528	−	12.9649i	−0.262198	−	0.454140i
$816$		0			0
$817$	−1.12132	+	1.94218i	−0.0392300	+	0.0679484i
$818$	1.48528			0.0519316
$819$	15.7279	−	2.15232i	0.549578	−	0.0752080i
$820$	−9.00000			−0.314294
$821$	−16.3492	+	28.3177i	−0.570592	+	0.988295i	0.425913	+	0.904764i	$0.359953\pi$
$821$	−16.3492	+	28.3177i	−0.570592	+	0.988295i	−0.996505	+	0.0835309i	$0.973380\pi$
$822$	−28.0919	+	16.2189i	−0.979817	+	0.565698i
$823$	−15.3787	−	26.6367i	−0.536067	−	0.928495i	−0.999111	−	0.0421600i	$-0.986576\pi$
$823$	−15.3787	−	26.6367i	−0.536067	−	0.928495i	0.463044	−	0.886335i	$-0.346757\pi$
$824$	3.24264			0.112963
$825$	−6.36396	−	3.67423i	−0.221565	−	0.127920i
$826$	−4.60660	+	0.630399i	−0.160284	+	0.0219344i
$827$	−36.9411			−1.28457			−0.642284	−	0.766466i	$-0.722013\pi$
$827$	−36.9411			−1.28457			−0.642284	+	0.766466i	$0.722013\pi$
$828$	−12.7279	+	22.0454i	−0.442326	+	0.766131i
$829$	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	$0.0900453\pi$
$830$	9.00000			0.312395
$831$	14.6360	+	8.45012i	0.507719	+	0.293131i
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$		0			0
$834$			24.6690i			0.854217i
$835$	10.2426	−	17.7408i	0.354461	−	0.613945i
$836$	−4.75736	+	8.23999i	−0.164537	+	0.284986i
$837$	28.0919	−	16.2189i	0.970998	−	0.560606i
$838$	17.4853	+	30.2854i	0.604019	+	1.04619i
$839$	25.0919	+	43.4604i	0.866268	+	1.50042i	0.865783	+	0.500420i	$0.166821\pi$
$839$	25.0919	+	43.4604i	0.866268	+	1.50042i	0.000485409		1.00000i	$0.499845\pi$
$840$	4.24264	+	1.73205i	0.146385	+	0.0597614i
$841$	13.7279	−	23.7775i	0.473377	−	0.819912i
$842$	−40.2132			−1.38584
$843$		−	13.8054i		−	0.475484i
$844$	3.75736			0.129334
$845$	−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
$849$		−	2.57258i		−	0.0882908i
$850$		0			0
$851$	−34.9706	−	60.5708i	−1.19878	−	2.07634i
$852$		−	7.34847i		−	0.251754i
$853$	1.27208	+	2.20330i	0.0435551	+	0.0754397i	0.886981	−	0.461806i	$-0.152798\pi$
$853$	1.27208	+	2.20330i	0.0435551	+	0.0754397i	−0.843426	+	0.537245i	$0.819465\pi$
$854$	−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
$857$	−38.1838			−1.30433			−0.652166	−	0.758076i	$-0.726140\pi$
$857$	−38.1838			−1.30433			−0.652166	+	0.758076i	$0.726140\pi$
$858$			14.6969i			0.501745i
$859$	1.27208			0.0434027			0.0217014	−	0.999764i	$-0.493092\pi$
$859$	1.27208			0.0434027			0.0217014	+	0.999764i	$0.493092\pi$
$860$	−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	$0.488141\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$	−5.12132	+	8.87039i	−0.174130	+	0.301602i
$866$	−13.7279	+	23.7775i	−0.466494	+	0.807991i
$867$			29.4449i			1.00000i
$868$	6.24264	−	15.2913i	0.211889	−	0.519020i
$869$	−22.7574	+	39.4169i	−0.771991	+	1.33713i
$870$	−1.86396	−	1.07616i	−0.0631942	−	0.0364852i
$871$	−12.9706			−0.439491
$872$	−8.86396	+	15.3528i	−0.300172	+	0.519912i
$873$	−9.72792	+	16.8493i	−0.329240	+	0.570261i
$874$	19.0294			0.643680
$875$	2.62132	−	0.358719i	0.0886168	−	0.0121269i
$876$	6.72792	+	3.88437i	0.227315	+	0.131241i
$877$	25.6985			0.867776			0.433888	−	0.900967i	$-0.357141\pi$
$877$	25.6985			0.867776			0.433888	+	0.900967i	$0.357141\pi$
$878$	−6.63604	−	11.4940i	−0.223955	−	0.387902i
$879$	−30.7279	+	17.7408i	−1.03643	+	0.598381i
$880$	−2.12132	+	3.67423i	−0.0715097	+	0.123858i
$881$		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
$885$			3.04384i			0.102317i
$886$	−6.25736	−	10.8381i	−0.210220	−	0.364112i
$887$	−1.24264			−0.0417238			−0.0208619	−	0.999782i	$-0.506641\pi$
$887$	−1.24264			−0.0417238			−0.0208619	+	0.999782i	$0.506641\pi$
$888$			14.2767i			0.479094i
$889$	−17.7132	+	2.42400i	−0.594082	+	0.0812982i
$890$		0			0
$891$	19.0919	−	33.0681i	0.639602	−	1.10782i
$892$	−5.86396	+	10.1567i	−0.196340	+	0.340071i
$893$	−2.78680			−0.0932566
$894$	−21.7279	+	12.5446i	−0.726690	+	0.419555i
$895$	0.878680	−	1.52192i	0.0293710	−	0.0508721i
$896$	1.00000	−	2.44949i	0.0334077	−	0.0818317i
$897$	25.4558	−	14.6969i	0.849946	−	0.490716i
$898$	−4.50000	+	7.79423i	−0.150167	+	0.260097i
$899$	−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
$903$	−0.621320	−	4.54026i	−0.0206762	−	0.151090i
$904$	−6.36396	+	11.0227i	−0.211662	+	0.366610i
$905$	23.2426			0.772612
$906$	−0.363961	+	0.210133i	−0.0120918	+	0.00698120i
$907$	−50.4558			−1.67536			−0.837679	−	0.546162i	$-0.816088\pi$
$907$	−50.4558			−1.67536			−0.837679	+	0.546162i	$0.816088\pi$
$908$	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	0.935852	+	0.352393i	$0.114632\pi$
$911$	23.3345	+	40.4166i	0.773107	+	1.33906i	−0.162745	+	0.986668i	$0.552035\pi$
$912$	−3.36396	−	1.94218i	−0.111392	−	0.0643121i
$913$	−19.0919	−	33.0681i	−0.631849	−	1.09439i
$914$	−9.48528	−	16.4290i	−0.313745	−	0.543423i
$915$	−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	$0.789925\pi$
$920$	8.48528			0.279751
$921$	−44.9558	−	25.9553i	−1.48135	−	0.855255i
$922$	30.2132			0.995019
$923$	−4.24264	+	7.34847i	−0.139648	+	0.241878i
$924$	−2.63604	−	19.2627i	−0.0867193	−	0.633696i
$925$	4.12132	+	7.13834i	0.135508	+	0.234707i
$926$	−2.86396	−	4.96053i	−0.0941156	−	0.163013i
$927$	4.86396	+	8.42463i	0.159753	+	0.276701i
$928$	−0.621320	+	1.07616i	−0.0203958	+	0.0353266i
$929$	−26.9558	+	46.6889i	−0.884393	+	1.53181i	−0.0379843	+	0.999278i	$0.512094\pi$
$929$	−26.9558	+	46.6889i	−0.884393	+	1.53181i	−0.846408	+	0.532535i	$0.821240\pi$
$930$	−9.36396	−	5.40629i	−0.307056	−	0.177279i
$931$	11.2132	+	10.9867i	0.367498	+	0.360073i
$932$	−9.87868	+	17.1104i	−0.323587	+	0.560469i
$933$		−	42.8300i		−	1.40219i
$934$	1.97056			0.0644788
$935$		0			0
$936$	−6.00000			−0.196116
$937$	−2.24264			−0.0732639			−0.0366319	−	0.999329i	$-0.511663\pi$
$937$	−2.24264			−0.0732639			−0.0366319	+	0.999329i	$0.511663\pi$
$938$	17.0000	−	2.32640i	0.555070	−	0.0759595i
$939$	−25.8198	+	14.9071i	−0.842597	+	0.486474i
$940$	−1.24264			−0.0405305
$941$	−6.62132	−	11.4685i	−0.215849	−	0.373861i	0.737686	−	0.675144i	$-0.235919\pi$
$941$	−6.62132	−	11.4685i	−0.215849	−	0.373861i	−0.953535	+	0.301283i	$0.902585\pi$
$942$	−25.0919	−	14.4868i	−0.817538	−	0.472006i
$943$	38.1838	−	66.1362i	1.24343	−	2.15369i
$944$	1.75736			0.0571972
$945$	1.86396	+	13.6208i	0.0606347	+	0.443084i
$946$	4.24264			0.137940
$947$	−7.24264	+	12.5446i	−0.235354	+	0.407645i	−0.959376	−	0.282132i	$-0.908958\pi$
$947$	−7.24264	+	12.5446i	−0.235354	+	0.407645i	0.724021	+	0.689778i	$0.242292\pi$
$948$	−16.0919	−	9.29065i	−0.522640	−	0.301746i
$949$	−4.48528	−	7.76874i	−0.145598	−	0.252184i
$950$	−2.24264			−0.0727609
$951$	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	$0.197939\pi$
$954$	2.63604	−	4.56575i	0.0853449	−	0.147822i
$955$	7.24264	−	12.5446i	0.234366	−	0.405934i
$956$	22.2426			0.719378
$957$			9.13151i			0.295180i
$958$	−7.24264	+	12.5446i	−0.233999	+	0.405298i
$959$	−49.0919	+	6.71807i	−1.58526	+	0.216938i
$960$	−1.50000	−	0.866025i	−0.0484123	−	0.0279508i
$961$	−3.98528	+	6.90271i	−0.128557	+	0.222668i
$962$	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
$966$	−30.7279	+	23.8284i	−0.988655	+	0.766668i
$967$	−21.4853	+	37.2136i	−0.690920	+	1.19671i	0.280617	+	0.959820i	$0.409461\pi$
$967$	−21.4853	+	37.2136i	−0.690920	+	1.19671i	−0.971537	+	0.236889i	$0.923872\pi$
$968$	7.00000			0.224989
$969$		0			0
$970$	6.48528			0.208230
$971$	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
$976$	6.24264	+	10.8126i	0.199822	+	0.346102i
$977$	19.7574	+	34.2208i	0.632094	+	1.09482i	0.987123	+	0.159964i	$0.0511377\pi$
$977$	19.7574	+	34.2208i	0.632094	+	1.09482i	−0.355029	+	0.934855i	$0.615529\pi$
$978$	−22.4558	−	12.9649i	−0.718059	−	0.414571i
$979$		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
$983$	−3.72792			−0.118902			−0.0594511	−	0.998231i	$-0.518935\pi$
$983$	−3.72792			−0.118902			−0.0594511	+	0.998231i	$0.518935\pi$
$984$	−13.5000	+	7.79423i	−0.430364	+	0.248471i
$985$	−27.2132			−0.867085
$986$		0			0
$987$	4.50000	−	3.48960i	0.143237	−	0.111075i
$988$	2.24264	+	3.88437i	0.0713479	+	0.123578i
$989$	−4.24264	−	7.34847i	−0.134908	−	0.233668i
$990$	−12.7279			−0.404520
$991$	−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	$0.198280\pi$
$992$	−3.12132	+	5.40629i	−0.0991020	+	0.171650i
$993$	6.00000	−	3.46410i	0.190404	−	0.109930i
$994$	4.24264	−	10.3923i	0.134568	−	0.329624i
$995$	2.24264	−	3.88437i	0.0710965	−	0.123143i
$996$	13.5000	−	7.79423i	0.427764	−	0.246970i
$997$	44.7279			1.41655			0.708274	−	0.705938i	$-0.249474\pi$
$997$	44.7279			1.41655			0.708274	+	0.705938i	$0.249474\pi$
$998$	−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.l.e.571.1	yes	4
3.2	odd	2		1890.2.l.e.361.1		4
7.2	even	3		630.2.i.e.121.2	✓	4
9.2	odd	6		1890.2.i.e.991.2		4
9.7	even	3		630.2.i.e.151.2	yes	4
21.2	odd	6		1890.2.i.e.1171.2		4
63.2	odd	6		1890.2.l.e.1801.1		4
63.16	even	3	inner	630.2.l.e.331.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.e.121.2	✓	4	7.2	even	3
630.2.i.e.151.2	yes	4	9.7	even	3
630.2.l.e.331.1	yes	4	63.16	even	3	inner
630.2.l.e.571.1	yes	4	1.1	even	1	trivial
1890.2.i.e.991.2		4	9.2	odd	6
1890.2.i.e.1171.2		4	21.2	odd	6
1890.2.l.e.361.1		4	3.2	odd	2
1890.2.l.e.1801.1		4	63.2	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.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.50000 + 0.866025i) q^{6} +(-2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 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} -4.24264 q^{11} -1.73205i q^{12} +(-1.00000 + 1.73205i) q^{13} +(1.00000 - 2.44949i) q^{14} +(-1.50000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{18} +(1.12132 + 1.94218i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.24264 - 1.73205i) q^{21} +(2.12132 - 3.67423i) q^{22} -8.48528 q^{23} +(1.50000 + 0.866025i) q^{24} +1.00000 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} +(-3.12132 - 5.40629i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-6.36396 - 3.67423i) q^{33} +(2.62132 - 0.358719i) q^{35} +(1.50000 - 2.59808i) q^{36} +(4.12132 + 7.13834i) q^{37} -2.24264 q^{38} +(-3.00000 + 1.73205i) q^{39} -1.00000 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} +(-1.50000 - 2.59808i) q^{45} +(4.24264 - 7.34847i) q^{46} +(-0.621320 + 1.07616i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(6.74264 - 1.88064i) q^{49} +(-0.500000 + 0.866025i) q^{50} +2.00000 q^{52} +(-0.878680 + 1.52192i) q^{53} +(-4.50000 - 2.59808i) q^{54} +4.24264 q^{55} +(-2.62132 + 0.358719i) q^{56} +3.88437i q^{57} +1.24264 q^{58} +(-0.878680 - 1.52192i) q^{59} +1.73205i q^{60} +(6.24264 - 10.8126i) q^{61} +6.24264 q^{62} +(-4.86396 - 6.27231i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(6.36396 - 3.67423i) q^{66} +(3.24264 + 5.61642i) q^{67} +(-12.7279 - 7.34847i) q^{69} +(-1.00000 + 2.44949i) q^{70} +4.24264 q^{71} +(1.50000 + 2.59808i) q^{72} +(-2.24264 + 3.88437i) q^{73} -8.24264 q^{74} +(1.50000 + 0.866025i) q^{75} +(1.12132 - 1.94218i) q^{76} +(11.1213 - 1.52192i) q^{77} -3.46410i q^{78} +(5.36396 - 9.29065i) 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} -1.00000 q^{86} -2.15232i q^{87} -4.24264 q^{88} +3.00000 q^{90} +(2.00000 - 4.89898i) q^{91} +(4.24264 + 7.34847i) q^{92} -10.8126i q^{93} +(-0.621320 - 1.07616i) q^{94} +(-1.12132 - 1.94218i) q^{95} -1.73205i q^{96} +(3.24264 + 5.61642i) q^{97} +(-1.74264 + 6.77962i) q^{98} +(-6.36396 - 11.0227i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 4 q^{5} - 6 q^{6} - 2 q^{7} + 4 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 4 * q^5 - 6 * q^6 - 2 * q^7 + 4 * q^8 + 6 * q^9	\( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 4 q^{5} - 6 q^{6} - 2 q^{7} + 4 q^{8} + 6 q^{9} + 2 q^{10} - 4 q^{13} + 4 q^{14} - 6 q^{15} - 2 q^{16} - 12 q^{18} - 4 q^{19} + 2 q^{20} + 6 q^{24} + 4 q^{25} - 4 q^{26} - 2 q^{28} + 6 q^{29} + 6 q^{30} - 4 q^{31} - 2 q^{32} + 2 q^{35} + 6 q^{36} + 8 q^{37} + 8 q^{38} - 12 q^{39} - 4 q^{40} - 18 q^{41} + 6 q^{42} + 2 q^{43} - 6 q^{45} + 6 q^{47} - 6 q^{48} + 10 q^{49} - 2 q^{50} + 8 q^{52} - 12 q^{53} - 18 q^{54} - 2 q^{56} - 12 q^{58} - 12 q^{59} + 8 q^{61} + 8 q^{62} + 6 q^{63} + 4 q^{64} + 4 q^{65} - 4 q^{67} - 4 q^{70} + 6 q^{72} + 8 q^{73} - 16 q^{74} + 6 q^{75} - 4 q^{76} + 36 q^{77} - 4 q^{79} + 2 q^{80} - 18 q^{81} - 18 q^{82} + 18 q^{83} - 6 q^{84} - 4 q^{86} + 12 q^{90} + 8 q^{91} + 6 q^{94} + 4 q^{95} - 4 q^{97} + 10 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 4 * q^5 - 6 * q^6 - 2 * q^7 + 4 * q^8 + 6 * q^9 + 2 * q^10 - 4 * q^13 + 4 * q^14 - 6 * q^15 - 2 * q^16 - 12 * q^18 - 4 * q^19 + 2 * q^20 + 6 * q^24 + 4 * q^25 - 4 * q^26 - 2 * q^28 + 6 * q^29 + 6 * q^30 - 4 * q^31 - 2 * q^32 + 2 * q^35 + 6 * q^36 + 8 * q^37 + 8 * q^38 - 12 * q^39 - 4 * q^40 - 18 * q^41 + 6 * q^42 + 2 * q^43 - 6 * q^45 + 6 * q^47 - 6 * q^48 + 10 * q^49 - 2 * q^50 + 8 * q^52 - 12 * q^53 - 18 * q^54 - 2 * q^56 - 12 * q^58 - 12 * q^59 + 8 * q^61 + 8 * q^62 + 6 * q^63 + 4 * q^64 + 4 * q^65 - 4 * q^67 - 4 * q^70 + 6 * q^72 + 8 * q^73 - 16 * q^74 + 6 * q^75 - 4 * q^76 + 36 * q^77 - 4 * q^79 + 2 * q^80 - 18 * q^81 - 18 * q^82 + 18 * q^83 - 6 * q^84 - 4 * q^86 + 12 * q^90 + 8 * q^91 + 6 * q^94 + 4 * q^95 - 4 * q^97 + 10 * q^98

Introduction

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