LMFDB - Embedded newform 630.2.i.c.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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.c.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.50000 - 0.866025i) q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(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} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.00000 - 1.73205i) q^{11} +(1.50000 - 0.866025i) q^{12} +(1.00000 - 1.73205i) q^{13} +(-2.50000 - 0.866025i) q^{14} +(-1.50000 - 0.866025i) q^{15} +1.00000 q^{16} +(1.50000 - 2.59808i) q^{18} +(-0.500000 - 0.866025i) q^{20} +(-4.50000 + 0.866025i) q^{21} +(1.00000 - 1.73205i) q^{22} +(2.00000 + 3.46410i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} -5.19615i q^{27} +(-2.50000 - 0.866025i) q^{28} +(0.500000 + 0.866025i) q^{29} +(-1.50000 - 0.866025i) q^{30} +10.0000 q^{31} +1.00000 q^{32} -3.46410i q^{33} +(0.500000 + 2.59808i) q^{35} +(1.50000 - 2.59808i) q^{36} +(-4.00000 + 6.92820i) q^{37} -3.46410i q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(-4.50000 + 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(1.00000 - 1.73205i) q^{44} -3.00000 q^{45} +(2.00000 + 3.46410i) q^{46} -13.0000 q^{47} +(1.50000 - 0.866025i) q^{48} +(5.50000 + 4.33013i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(1.00000 - 1.73205i) q^{52} +(5.00000 + 8.66025i) q^{53} -5.19615i q^{54} -2.00000 q^{55} +(-2.50000 - 0.866025i) q^{56} +(0.500000 + 0.866025i) q^{58} -4.00000 q^{59} +(-1.50000 - 0.866025i) q^{60} -6.00000 q^{61} +10.0000 q^{62} +(-6.00000 + 5.19615i) q^{63} +1.00000 q^{64} -2.00000 q^{65} -3.46410i q^{66} +12.0000 q^{67} +(6.00000 + 3.46410i) q^{69} +(0.500000 + 2.59808i) q^{70} -12.0000 q^{71} +(1.50000 - 2.59808i) q^{72} +(-4.00000 + 6.92820i) q^{74} +1.73205i q^{75} +(-4.00000 + 3.46410i) q^{77} -3.46410i q^{78} +10.0000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-2.50000 + 4.33013i) q^{82} +(2.50000 + 4.33013i) q^{83} +(-4.50000 + 0.866025i) q^{84} +(0.500000 + 0.866025i) q^{86} +(1.50000 + 0.866025i) q^{87} +(1.00000 - 1.73205i) q^{88} +(7.00000 - 12.1244i) q^{89} -3.00000 q^{90} +(-4.00000 + 3.46410i) q^{91} +(2.00000 + 3.46410i) q^{92} +(15.0000 - 8.66025i) q^{93} -13.0000 q^{94} +(1.50000 - 0.866025i) q^{96} +(-1.00000 - 1.73205i) q^{97} +(5.50000 + 4.33013i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} - q^{5} + 3 q^{6} - 5 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 - q^5 + 3 * q^6 - 5 * q^7 + 2 * q^8 + 3 * q^9	$ 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} - q^{5} + 3 q^{6} - 5 q^{7} + 2 q^{8} + 3 q^{9} - q^{10} + 2 q^{11} + 3 q^{12} + 2 q^{13} - 5 q^{14} - 3 q^{15} + 2 q^{16} + 3 q^{18} - q^{20} - 9 q^{21} + 2 q^{22} + 4 q^{23} + 3 q^{24} - q^{25} + 2 q^{26} - 5 q^{28} + q^{29} - 3 q^{30} + 20 q^{31} + 2 q^{32} + q^{35} + 3 q^{36} - 8 q^{37} - q^{40} - 5 q^{41} - 9 q^{42} + q^{43} + 2 q^{44} - 6 q^{45} + 4 q^{46} - 26 q^{47} + 3 q^{48} + 11 q^{49} - q^{50} + 2 q^{52} + 10 q^{53} - 4 q^{55} - 5 q^{56} + q^{58} - 8 q^{59} - 3 q^{60} - 12 q^{61} + 20 q^{62} - 12 q^{63} + 2 q^{64} - 4 q^{65} + 24 q^{67} + 12 q^{69} + q^{70} - 24 q^{71} + 3 q^{72} - 8 q^{74} - 8 q^{77} + 20 q^{79} - q^{80} - 9 q^{81} - 5 q^{82} + 5 q^{83} - 9 q^{84} + q^{86} + 3 q^{87} + 2 q^{88} + 14 q^{89} - 6 q^{90} - 8 q^{91} + 4 q^{92} + 30 q^{93} - 26 q^{94} + 3 q^{96} - 2 q^{97} + 11 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 - q^5 + 3 * q^6 - 5 * q^7 + 2 * q^8 + 3 * q^9 - q^10 + 2 * q^11 + 3 * q^12 + 2 * q^13 - 5 * q^14 - 3 * q^15 + 2 * q^16 + 3 * q^18 - q^20 - 9 * q^21 + 2 * q^22 + 4 * q^23 + 3 * q^24 - q^25 + 2 * q^26 - 5 * q^28 + q^29 - 3 * q^30 + 20 * q^31 + 2 * q^32 + q^35 + 3 * q^36 - 8 * q^37 - q^40 - 5 * q^41 - 9 * q^42 + q^43 + 2 * q^44 - 6 * q^45 + 4 * q^46 - 26 * q^47 + 3 * q^48 + 11 * q^49 - q^50 + 2 * q^52 + 10 * q^53 - 4 * q^55 - 5 * q^56 + q^58 - 8 * q^59 - 3 * q^60 - 12 * q^61 + 20 * q^62 - 12 * q^63 + 2 * q^64 - 4 * q^65 + 24 * q^67 + 12 * q^69 + q^70 - 24 * q^71 + 3 * q^72 - 8 * q^74 - 8 * q^77 + 20 * q^79 - q^80 - 9 * q^81 - 5 * q^82 + 5 * q^83 - 9 * q^84 + q^86 + 3 * q^87 + 2 * q^88 + 14 * q^89 - 6 * q^90 - 8 * q^91 + 4 * q^92 + 30 * q^93 - 26 * q^94 + 3 * q^96 - 2 * q^97 + 11 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$	1.00000			0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	1.50000	−	0.866025i	0.433013	−	0.250000i
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$	−2.50000	−	0.866025i	−0.668153	−	0.231455i
$15$	−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
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−4.50000	+	0.866025i	−0.981981	+	0.188982i
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$	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
$28$	−2.50000	−	0.866025i	−0.472456	−	0.163663i
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$	−1.50000	−	0.866025i	−0.273861	−	0.158114i
$31$	10.0000			1.79605			0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000			1.79605			0.898027	+	0.439941i	$0.145001\pi$
$32$	1.00000			0.176777
$33$		−	3.46410i		−	0.603023i
$34$		0			0
$35$	0.500000	+	2.59808i	0.0845154	+	0.439155i
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$		0			0
$39$		−	3.46410i		−	0.554700i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	−0.992507	−	0.122189i	$-0.961009\pi$
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	0.602072	+	0.798441i	$0.294342\pi$
$42$	−4.50000	+	0.866025i	−0.694365	+	0.133631i
$43$	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	$0.809039\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$	−3.00000			−0.447214
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	−13.0000			−1.89624			−0.948122	−	0.317905i	$-0.897021\pi$
$47$	−13.0000			−1.89624			−0.948122	+	0.317905i	$0.897021\pi$
$48$	1.50000	−	0.866025i	0.216506	−	0.125000i
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	0.972867	+	0.231367i	$0.0743197\pi$
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	−0.286064	+	0.958211i	$0.592347\pi$
$54$		−	5.19615i		−	0.707107i
$55$	−2.00000			−0.269680
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$		0			0
$58$	0.500000	+	0.866025i	0.0656532	+	0.113715i
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$	−1.50000	−	0.866025i	−0.193649	−	0.111803i
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$	10.0000			1.27000
$63$	−6.00000	+	5.19615i	−0.755929	+	0.654654i
$64$	1.00000			0.125000
$65$	−2.00000			−0.248069
$66$		−	3.46410i		−	0.426401i
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$		0			0
$69$	6.00000	+	3.46410i	0.722315	+	0.417029i
$70$	0.500000	+	2.59808i	0.0597614	+	0.310530i
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$73$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$			1.73205i			0.200000i
$76$		0			0
$77$	−4.00000	+	3.46410i	−0.455842	+	0.394771i
$78$		−	3.46410i		−	0.392232i
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−2.50000	+	4.33013i	−0.276079	+	0.478183i
$83$	2.50000	+	4.33013i	0.274411	+	0.475293i	0.969986	−	0.243160i	$-0.0781839\pi$
$83$	2.50000	+	4.33013i	0.274411	+	0.475293i	−0.695576	+	0.718453i	$0.744851\pi$
$84$	−4.50000	+	0.866025i	−0.490990	+	0.0944911i
$85$		0			0
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	1.50000	+	0.866025i	0.160817	+	0.0928477i
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	−0.209585	−	0.977790i	$-0.567211\pi$
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	0.951584	−	0.307389i	$-0.0994552\pi$
$90$	−3.00000			−0.316228
$91$	−4.00000	+	3.46410i	−0.419314	+	0.363137i
$92$	2.00000	+	3.46410i	0.208514	+	0.361158i
$93$	15.0000	−	8.66025i	1.55543	−	0.898027i
$94$	−13.0000			−1.34085
$95$		0			0
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	5.50000	+	4.33013i	0.555584	+	0.437409i
$99$	−3.00000	−	5.19615i	−0.301511	−	0.522233i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$		0			0
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	0.889607	−	0.456727i	$-0.150978\pi$
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	−0.840341	+	0.542059i	$0.817645\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$	3.00000	+	3.46410i	0.292770	+	0.338062i
$106$	5.00000	+	8.66025i	0.485643	+	0.841158i
$107$	−0.500000	+	0.866025i	−0.0483368	+	0.0837218i	−0.889182	−	0.457555i	$-0.848725\pi$
$107$	−0.500000	+	0.866025i	−0.0483368	+	0.0837218i	0.840845	+	0.541276i	$0.182059\pi$
$108$		−	5.19615i		−	0.500000i
$109$	1.50000	+	2.59808i	0.143674	+	0.248851i	0.928877	−	0.370387i	$-0.120775\pi$
$109$	1.50000	+	2.59808i	0.143674	+	0.248851i	−0.785203	+	0.619238i	$0.787442\pi$
$110$	−2.00000			−0.190693
$111$			13.8564i			1.31519i
$112$	−2.50000	−	0.866025i	−0.236228	−	0.0818317i
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$		0			0
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$	0.500000	+	0.866025i	0.0464238	+	0.0804084i
$117$	−3.00000	−	5.19615i	−0.277350	−	0.480384i
$118$	−4.00000			−0.368230
$119$		0			0
$120$	−1.50000	−	0.866025i	−0.136931	−	0.0790569i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−6.00000			−0.543214
$123$			8.66025i			0.780869i
$124$	10.0000			0.898027
$125$	1.00000			0.0894427
$126$	−6.00000	+	5.19615i	−0.534522	+	0.462910i
$127$	−5.00000			−0.443678			−0.221839	−	0.975083i	$-0.571206\pi$
$127$	−5.00000			−0.443678			−0.221839	+	0.975083i	$0.571206\pi$
$128$	1.00000			0.0883883
$129$	1.50000	+	0.866025i	0.132068	+	0.0762493i
$130$	−2.00000			−0.175412
$131$	−10.0000	−	17.3205i	−0.873704	−	1.51330i	−0.858137	−	0.513421i	$-0.828378\pi$
$131$	−10.0000	−	17.3205i	−0.873704	−	1.51330i	−0.0155672	−	0.999879i	$-0.504955\pi$
$132$		−	3.46410i		−	0.301511i
$133$		0			0
$134$	12.0000			1.03664
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$	6.00000	+	3.46410i	0.510754	+	0.294884i
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$	0.500000	+	2.59808i	0.0422577	+	0.219578i
$141$	−19.5000	+	11.2583i	−1.64220	+	0.948122i
$142$	−12.0000			−1.00702
$143$	−2.00000	−	3.46410i	−0.167248	−	0.289683i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	0.500000	−	0.866025i	0.0415227	−	0.0719195i
$146$		0			0
$147$	12.0000	+	1.73205i	0.989743	+	0.142857i
$148$	−4.00000	+	6.92820i	−0.328798	+	0.569495i
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$			1.73205i			0.141421i
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	−0.999909	−	0.0134886i	$-0.995706\pi$
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	0.511636	+	0.859202i	$0.329040\pi$
$152$		0			0
$153$		0			0
$154$	−4.00000	+	3.46410i	−0.322329	+	0.279145i
$155$	−5.00000	−	8.66025i	−0.401610	−	0.695608i
$156$		−	3.46410i		−	0.277350i
$157$	−4.00000			−0.319235			−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000			−0.319235			−0.159617	+	0.987179i	$0.551026\pi$
$158$	10.0000			0.795557
$159$	15.0000	+	8.66025i	1.18958	+	0.686803i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−2.00000	−	10.3923i	−0.157622	−	0.819028i
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	−0.146772	−	0.989170i	$-0.546888\pi$
$163$	10.0000	−	17.3205i	0.783260	−	1.35665i	0.930033	−	0.367477i	$-0.119778\pi$
$164$	−2.50000	+	4.33013i	−0.195217	+	0.338126i
$165$	−3.00000	+	1.73205i	−0.233550	+	0.134840i
$166$	2.50000	+	4.33013i	0.194038	+	0.336083i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$	−4.50000	+	0.866025i	−0.347183	+	0.0668153i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$		0			0
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$	1.50000	+	0.866025i	0.113715	+	0.0656532i
$175$	2.00000	−	1.73205i	0.151186	−	0.130931i
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$	−6.00000	+	3.46410i	−0.450988	+	0.260378i
$178$	7.00000	−	12.1244i	0.524672	−	0.908759i
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	0.781551	−	0.623841i	$-0.214429\pi$
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	−0.931038	+	0.364922i	$0.881096\pi$
$180$	−3.00000			−0.223607
$181$	21.0000			1.56092			0.780459	−	0.625207i	$-0.214986\pi$
$181$	21.0000			1.56092			0.780459	+	0.625207i	$0.214986\pi$
$182$	−4.00000	+	3.46410i	−0.296500	+	0.256776i
$183$	−9.00000	+	5.19615i	−0.665299	+	0.384111i
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	8.00000			0.588172
$186$	15.0000	−	8.66025i	1.09985	−	0.635001i
$187$		0			0
$188$	−13.0000			−0.948122
$189$	−4.50000	+	12.9904i	−0.327327	+	0.944911i
$190$		0			0
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$	1.50000	−	0.866025i	0.108253	−	0.0625000i
$193$	−2.00000			−0.143963			−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000			−0.143963			−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−1.00000	−	1.73205i	−0.0717958	−	0.124354i
$195$	−3.00000	+	1.73205i	−0.214834	+	0.124035i
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$	−26.0000			−1.85242			−0.926212	−	0.377004i	$-0.876954\pi$
$197$	−26.0000			−1.85242			−0.926212	+	0.377004i	$0.876954\pi$
$198$	−3.00000	−	5.19615i	−0.213201	−	0.369274i
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	18.0000	−	10.3923i	1.26962	−	0.733017i
$202$	1.50000	−	2.59808i	0.105540	−	0.182800i
$203$	−0.500000	−	2.59808i	−0.0350931	−	0.182349i
$204$		0			0
$205$	5.00000			0.349215
$206$	0.500000	+	0.866025i	0.0348367	+	0.0603388i
$207$	12.0000			0.834058
$208$	1.00000	−	1.73205i	0.0693375	−	0.120096i
$209$		0			0
$210$	3.00000	+	3.46410i	0.207020	+	0.239046i
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	−0.186966	−	0.982366i	$-0.559865\pi$
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	0.944237	−	0.329266i	$-0.106801\pi$
$212$	5.00000	+	8.66025i	0.343401	+	0.594789i
$213$	−18.0000	+	10.3923i	−1.23334	+	0.712069i
$214$	−0.500000	+	0.866025i	−0.0341793	+	0.0592003i
$215$	0.500000	−	0.866025i	0.0340997	−	0.0590624i
$216$		−	5.19615i		−	0.353553i
$217$	−25.0000	−	8.66025i	−1.69711	−	0.587896i
$218$	1.50000	+	2.59808i	0.101593	+	0.175964i
$219$		0			0
$220$	−2.00000			−0.134840
$221$		0			0
$222$			13.8564i			0.929981i
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	0.675098	−	0.737728i	$-0.264101\pi$
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	−0.976440	+	0.215788i	$0.930768\pi$
$224$	−2.50000	−	0.866025i	−0.167038	−	0.0578638i
$225$	1.50000	+	2.59808i	0.100000	+	0.173205i
$226$	−3.00000	+	5.19615i	−0.199557	+	0.345643i
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	−0.924734	−	0.380615i	$-0.875712\pi$
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	0.791989	+	0.610535i	$0.209046\pi$
$228$		0			0
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	0.882073	−	0.471113i	$-0.156147\pi$
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	−0.849032	+	0.528341i	$0.822814\pi$
$230$	2.00000	−	3.46410i	0.131876	−	0.228416i
$231$	−3.00000	+	8.66025i	−0.197386	+	0.569803i
$232$	0.500000	+	0.866025i	0.0328266	+	0.0568574i
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$	6.50000	+	11.2583i	0.424013	+	0.734412i
$236$	−4.00000			−0.260378
$237$	15.0000	−	8.66025i	0.974355	−	0.562544i
$238$		0			0
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	−0.946590	−	0.322440i	$-0.895497\pi$
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	0.752536	+	0.658551i	$0.228830\pi$
$240$	−1.50000	−	0.866025i	−0.0968246	−	0.0559017i
$241$	−12.5000	+	21.6506i	−0.805196	+	1.39464i	0.110963	+	0.993825i	$0.464606\pi$
$241$	−12.5000	+	21.6506i	−0.805196	+	1.39464i	−0.916159	+	0.400815i	$0.868727\pi$
$242$	3.50000	+	6.06218i	0.224989	+	0.389692i
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	−6.00000			−0.384111
$245$	1.00000	−	6.92820i	0.0638877	−	0.442627i
$246$			8.66025i			0.552158i
$247$		0			0
$248$	10.0000			0.635001
$249$	7.50000	+	4.33013i	0.475293	+	0.274411i
$250$	1.00000			0.0632456
$251$	14.0000			0.883672			0.441836	−	0.897096i	$-0.354327\pi$
$251$	14.0000			0.883672			0.441836	+	0.897096i	$0.354327\pi$
$252$	−6.00000	+	5.19615i	−0.377964	+	0.327327i
$253$	8.00000			0.502956
$254$	−5.00000			−0.313728
$255$		0			0
$256$	1.00000			0.0625000
$257$	−10.0000	−	17.3205i	−0.623783	−	1.08042i	−0.988775	−	0.149413i	$-0.952262\pi$
$257$	−10.0000	−	17.3205i	−0.623783	−	1.08042i	0.364992	−	0.931011i	$-0.381072\pi$
$258$	1.50000	+	0.866025i	0.0933859	+	0.0539164i
$259$	16.0000	−	13.8564i	0.994192	−	0.860995i
$260$	−2.00000			−0.124035
$261$	3.00000			0.185695
$262$	−10.0000	−	17.3205i	−0.617802	−	1.07006i
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	−0.693276	−	0.720672i	$-0.743833\pi$
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	0.970758	+	0.240059i	$0.0771668\pi$
$264$		−	3.46410i		−	0.213201i
$265$	5.00000	−	8.66025i	0.307148	−	0.531995i
$266$		0			0
$267$		−	24.2487i		−	1.48400i
$268$	12.0000			0.733017
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$	−4.50000	+	2.59808i	−0.273861	+	0.158114i
$271$	14.0000	−	24.2487i	0.850439	−	1.47300i	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	14.0000	−	24.2487i	0.850439	−	1.47300i	0.880812	−	0.473466i	$-0.156997\pi$
$272$		0			0
$273$	−3.00000	+	8.66025i	−0.181568	+	0.524142i
$274$	−6.00000	+	10.3923i	−0.362473	+	0.627822i
$275$	1.00000	+	1.73205i	0.0603023	+	0.104447i
$276$	6.00000	+	3.46410i	0.361158	+	0.208514i
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	0.150210	+	0.988654i	$0.452005\pi$
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	8.00000	−	13.8564i	0.479808	−	0.831052i
$279$	15.0000	−	25.9808i	0.898027	−	1.55543i
$280$	0.500000	+	2.59808i	0.0298807	+	0.155265i
$281$	−6.50000	−	11.2583i	−0.387757	−	0.671616i	0.604390	−	0.796689i	$-0.293417\pi$
$281$	−6.50000	−	11.2583i	−0.387757	−	0.671616i	−0.992148	+	0.125073i	$0.960084\pi$
$282$	−19.5000	+	11.2583i	−1.16121	+	0.670424i
$283$	−11.0000			−0.653882			−0.326941	−	0.945045i	$-0.606018\pi$
$283$	−11.0000			−0.653882			−0.326941	+	0.945045i	$0.606018\pi$
$284$	−12.0000			−0.712069
$285$		0			0
$286$	−2.00000	−	3.46410i	−0.118262	−	0.204837i
$287$	10.0000	−	8.66025i	0.590281	−	0.511199i
$288$	1.50000	−	2.59808i	0.0883883	−	0.153093i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	0.500000	−	0.866025i	0.0293610	−	0.0508548i
$291$	−3.00000	−	1.73205i	−0.175863	−	0.101535i
$292$		0			0
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	−0.986341	−	0.164714i	$-0.947330\pi$
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	0.635818	+	0.771839i	$0.280663\pi$
$294$	12.0000	+	1.73205i	0.699854	+	0.101015i
$295$	2.00000	+	3.46410i	0.116445	+	0.201688i
$296$	−4.00000	+	6.92820i	−0.232495	+	0.402694i
$297$	−9.00000	−	5.19615i	−0.522233	−	0.301511i
$298$	9.00000	+	15.5885i	0.521356	+	0.903015i
$299$	8.00000			0.462652
$300$			1.73205i			0.100000i
$301$	−0.500000	−	2.59808i	−0.0288195	−	0.149751i
$302$	−6.00000	+	10.3923i	−0.345261	+	0.598010i
$303$		−	5.19615i		−	0.298511i
$304$		0			0
$305$	3.00000	+	5.19615i	0.171780	+	0.297531i
$306$		0			0
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$	−4.00000	+	3.46410i	−0.227921	+	0.197386i
$309$	1.50000	+	0.866025i	0.0853320	+	0.0492665i
$310$	−5.00000	−	8.66025i	−0.283981	−	0.491869i
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		−	3.46410i		−	0.196116i
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	−4.00000			−0.225733
$315$	7.50000	+	2.59808i	0.422577	+	0.146385i
$316$	10.0000			0.562544
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$	15.0000	+	8.66025i	0.841158	+	0.485643i
$319$	2.00000			0.111979
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$			1.73205i			0.0966736i
$322$	−2.00000	−	10.3923i	−0.111456	−	0.579141i
$323$		0			0
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	1.00000	+	1.73205i	0.0554700	+	0.0960769i
$326$	10.0000	−	17.3205i	0.553849	−	0.959294i
$327$	4.50000	+	2.59808i	0.248851	+	0.143674i
$328$	−2.50000	+	4.33013i	−0.138039	+	0.239091i
$329$	32.5000	+	11.2583i	1.79178	+	0.620692i
$330$	−3.00000	+	1.73205i	−0.165145	+	0.0953463i
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$	2.50000	+	4.33013i	0.137205	+	0.237647i
$333$	12.0000	+	20.7846i	0.657596	+	1.13899i
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	−6.00000	−	10.3923i	−0.327815	−	0.567792i
$336$	−4.50000	+	0.866025i	−0.245495	+	0.0472456i
$337$	−3.00000	+	5.19615i	−0.163420	+	0.283052i	−0.936093	−	0.351752i	$-0.885586\pi$
$337$	−3.00000	+	5.19615i	−0.163420	+	0.283052i	0.772673	+	0.634804i	$0.218919\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$			10.3923i			0.564433i
$340$		0			0
$341$	10.0000	−	17.3205i	0.541530	−	0.937958i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	0.500000	+	0.866025i	0.0269582	+	0.0466930i
$345$		−	6.92820i		−	0.373002i
$346$	−6.00000			−0.322562
$347$	19.0000			1.01997			0.509987	−	0.860182i	$-0.329650\pi$
$347$	19.0000			1.01997			0.509987	+	0.860182i	$0.329650\pi$
$348$	1.50000	+	0.866025i	0.0804084	+	0.0464238i
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	−0.917679	−	0.397324i	$-0.869939\pi$
$349$	−15.0000	−	25.9808i	−0.802932	−	1.39072i	0.114747	−	0.993395i	$-0.463394\pi$
$350$	2.00000	−	1.73205i	0.106904	−	0.0925820i
$351$	−9.00000	−	5.19615i	−0.480384	−	0.277350i
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$	−6.00000	+	3.46410i	−0.318896	+	0.184115i
$355$	6.00000	+	10.3923i	0.318447	+	0.551566i
$356$	7.00000	−	12.1244i	0.370999	−	0.642590i
$357$		0			0
$358$	−2.00000	−	3.46410i	−0.105703	−	0.183083i
$359$	17.0000	−	29.4449i	0.897226	−	1.55404i	0.0662000	−	0.997806i	$-0.478912\pi$
$359$	17.0000	−	29.4449i	0.897226	−	1.55404i	0.831026	−	0.556234i	$-0.187754\pi$
$360$	−3.00000			−0.158114
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	21.0000			1.10374
$363$	10.5000	+	6.06218i	0.551107	+	0.318182i
$364$	−4.00000	+	3.46410i	−0.209657	+	0.181568i
$365$		0			0
$366$	−9.00000	+	5.19615i	−0.470438	+	0.271607i
$367$	8.50000	−	14.7224i	0.443696	−	0.768505i	−0.554264	−	0.832341i	$-0.687000\pi$
$367$	8.50000	−	14.7224i	0.443696	−	0.768505i	0.997960	+	0.0638362i	$0.0203335\pi$
$368$	2.00000	+	3.46410i	0.104257	+	0.180579i
$369$	7.50000	+	12.9904i	0.390434	+	0.676252i
$370$	8.00000			0.415900
$371$	−5.00000	−	25.9808i	−0.259587	−	1.34885i
$372$	15.0000	−	8.66025i	0.777714	−	0.449013i
$373$	−12.0000	−	20.7846i	−0.621336	−	1.07619i	−0.989237	−	0.146321i	$-0.953257\pi$
$373$	−12.0000	−	20.7846i	−0.621336	−	1.07619i	0.367901	−	0.929865i	$-0.380077\pi$
$374$		0			0
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$	−13.0000			−0.670424
$377$	2.00000			0.103005
$378$	−4.50000	+	12.9904i	−0.231455	+	0.668153i
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$		0			0
$381$	−7.50000	+	4.33013i	−0.384237	+	0.221839i
$382$	−18.0000			−0.920960
$383$	−6.50000	−	11.2583i	−0.332134	−	0.575274i	0.650796	−	0.759253i	$-0.274435\pi$
$383$	−6.50000	−	11.2583i	−0.332134	−	0.575274i	−0.982930	+	0.183979i	$0.941102\pi$
$384$	1.50000	−	0.866025i	0.0765466	−	0.0441942i
$385$	5.00000	+	1.73205i	0.254824	+	0.0882735i
$386$	−2.00000			−0.101797
$387$	3.00000			0.152499
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	−2.50000	+	4.33013i	−0.126755	+	0.219546i	−0.922418	−	0.386194i	$-0.873790\pi$
$389$	−2.50000	+	4.33013i	−0.126755	+	0.219546i	0.795663	+	0.605740i	$0.207123\pi$
$390$	−3.00000	+	1.73205i	−0.151911	+	0.0877058i
$391$		0			0
$392$	5.50000	+	4.33013i	0.277792	+	0.218704i
$393$	−30.0000	−	17.3205i	−1.51330	−	0.873704i
$394$	−26.0000			−1.30986
$395$	−5.00000	−	8.66025i	−0.251577	−	0.435745i
$396$	−3.00000	−	5.19615i	−0.150756	−	0.261116i
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	−0.986481	−	0.163876i	$-0.947600\pi$
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	0.635161	+	0.772380i	$0.280934\pi$
$398$		0			0
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	12.5000	+	21.6506i	0.624220	+	1.08118i	0.988691	+	0.149966i	$0.0479165\pi$
$401$	12.5000	+	21.6506i	0.624220	+	1.08118i	−0.364471	+	0.931215i	$0.618750\pi$
$402$	18.0000	−	10.3923i	0.897758	−	0.518321i
$403$	10.0000	−	17.3205i	0.498135	−	0.862796i
$404$	1.50000	−	2.59808i	0.0746278	−	0.129259i
$405$	−4.50000	+	7.79423i	−0.223607	+	0.387298i
$406$	−0.500000	−	2.59808i	−0.0248146	−	0.128940i
$407$	8.00000	+	13.8564i	0.396545	+	0.686837i
$408$		0			0
$409$	−25.0000			−1.23617			−0.618085	−	0.786111i	$-0.712091\pi$
$409$	−25.0000			−1.23617			−0.618085	+	0.786111i	$0.712091\pi$
$410$	5.00000			0.246932
$411$			20.7846i			1.02523i
$412$	0.500000	+	0.866025i	0.0246332	+	0.0426660i
$413$	10.0000	+	3.46410i	0.492068	+	0.170457i
$414$	12.0000			0.589768
$415$	2.50000	−	4.33013i	0.122720	−	0.212558i
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$		−	27.7128i		−	1.35710i
$418$		0			0
$419$	−13.0000	+	22.5167i	−0.635092	+	1.10001i	0.351404	+	0.936224i	$0.385704\pi$
$419$	−13.0000	+	22.5167i	−0.635092	+	1.10001i	−0.986496	+	0.163787i	$0.947629\pi$
$420$	3.00000	+	3.46410i	0.146385	+	0.169031i
$421$	14.5000	+	25.1147i	0.706687	+	1.22402i	0.966079	+	0.258245i	$0.0831443\pi$
$421$	14.5000	+	25.1147i	0.706687	+	1.22402i	−0.259393	+	0.965772i	$0.583522\pi$
$422$	11.0000	−	19.0526i	0.535472	−	0.927464i
$423$	−19.5000	+	33.7750i	−0.948122	+	1.64220i
$424$	5.00000	+	8.66025i	0.242821	+	0.420579i
$425$		0			0
$426$	−18.0000	+	10.3923i	−0.872103	+	0.503509i
$427$	15.0000	+	5.19615i	0.725901	+	0.251459i
$428$	−0.500000	+	0.866025i	−0.0241684	+	0.0418609i
$429$	−6.00000	−	3.46410i	−0.289683	−	0.167248i
$430$	0.500000	−	0.866025i	0.0241121	−	0.0417635i
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	0.563658	−	0.826008i	$-0.309393\pi$
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	−0.997173	+	0.0751385i	$0.976060\pi$
$432$		−	5.19615i		−	0.250000i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	−25.0000	−	8.66025i	−1.20004	−	0.415705i
$435$		−	1.73205i		−	0.0830455i
$436$	1.50000	+	2.59808i	0.0718370	+	0.124425i
$437$		0			0
$438$		0			0
$439$	−34.0000			−1.62273			−0.811366	−	0.584539i	$-0.801275\pi$
$439$	−34.0000			−1.62273			−0.811366	+	0.584539i	$0.801275\pi$
$440$	−2.00000			−0.0953463
$441$	19.5000	−	7.79423i	0.928571	−	0.371154i
$442$		0			0
$443$	17.0000			0.807694			0.403847	−	0.914826i	$-0.367673\pi$
$443$	17.0000			0.807694			0.403847	+	0.914826i	$0.367673\pi$
$444$			13.8564i			0.657596i
$445$	−14.0000			−0.663664
$446$	−4.50000	−	7.79423i	−0.213081	−	0.369067i
$447$	27.0000	+	15.5885i	1.27706	+	0.737309i
$448$	−2.50000	−	0.866025i	−0.118114	−	0.0409159i
$449$	−5.00000			−0.235965			−0.117982	−	0.993016i	$-0.537643\pi$
$449$	−5.00000			−0.235965			−0.117982	+	0.993016i	$0.537643\pi$
$450$	1.50000	+	2.59808i	0.0707107	+	0.122474i
$451$	5.00000	+	8.66025i	0.235441	+	0.407795i
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$			20.7846i			0.976546i
$454$	−2.00000	+	3.46410i	−0.0938647	+	0.162578i
$455$	5.00000	+	1.73205i	0.234404	+	0.0811998i
$456$		0			0
$457$	−18.0000			−0.842004			−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000			−0.842004			−0.421002	+	0.907060i	$0.638322\pi$
$458$	0.500000	+	0.866025i	0.0233635	+	0.0404667i
$459$		0			0
$460$	2.00000	−	3.46410i	0.0932505	−	0.161515i
$461$	−4.50000	−	7.79423i	−0.209586	−	0.363013i	0.741998	−	0.670402i	$-0.233878\pi$
$461$	−4.50000	−	7.79423i	−0.209586	−	0.363013i	−0.951584	+	0.307388i	$0.900545\pi$
$462$	−3.00000	+	8.66025i	−0.139573	+	0.402911i
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	−0.854173	−	0.519989i	$-0.825936\pi$
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	0.877410	+	0.479741i	$0.159269\pi$
$464$	0.500000	+	0.866025i	0.0232119	+	0.0402042i
$465$	−15.0000	−	8.66025i	−0.695608	−	0.401610i
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	10.5000	−	18.1865i	0.485882	−	0.841572i	−0.513986	−	0.857798i	$-0.671832\pi$
$467$	10.5000	−	18.1865i	0.485882	−	0.841572i	0.999868	+	0.0162260i	$0.00516512\pi$
$468$	−3.00000	−	5.19615i	−0.138675	−	0.240192i
$469$	−30.0000	−	10.3923i	−1.38527	−	0.479872i
$470$	6.50000	+	11.2583i	0.299823	+	0.519308i
$471$	−6.00000	+	3.46410i	−0.276465	+	0.159617i
$472$	−4.00000			−0.184115
$473$	2.00000			0.0919601
$474$	15.0000	−	8.66025i	0.688973	−	0.397779i
$475$		0			0
$476$		0			0
$477$	30.0000			1.37361
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$	5.00000	−	8.66025i	0.228456	−	0.395697i	−0.728895	−	0.684626i	$-0.759966\pi$
$479$	5.00000	−	8.66025i	0.228456	−	0.395697i	0.957351	+	0.288929i	$0.0932990\pi$
$480$	−1.50000	−	0.866025i	−0.0684653	−	0.0395285i
$481$	8.00000	+	13.8564i	0.364769	+	0.631798i
$482$	−12.5000	+	21.6506i	−0.569359	+	0.986159i
$483$	−12.0000	−	13.8564i	−0.546019	−	0.630488i
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	−0.958962	−	0.283535i	$-0.908493\pi$
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	0.233933	−	0.972253i	$-0.424840\pi$
$488$	−6.00000			−0.271607
$489$		−	34.6410i		−	1.56652i
$490$	1.00000	−	6.92820i	0.0451754	−	0.312984i
$491$	4.00000	−	6.92820i	0.180517	−	0.312665i	−0.761539	−	0.648119i	$-0.775556\pi$
$491$	4.00000	−	6.92820i	0.180517	−	0.312665i	0.942057	+	0.335453i	$0.108889\pi$
$492$			8.66025i			0.390434i
$493$		0			0
$494$		0			0
$495$	−3.00000	+	5.19615i	−0.134840	+	0.233550i
$496$	10.0000			0.449013
$497$	30.0000	+	10.3923i	1.34568	+	0.466159i
$498$	7.50000	+	4.33013i	0.336083	+	0.194038i
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	0.732137	−	0.681157i	$-0.238523\pi$
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	−0.955968	+	0.293471i	$0.905190\pi$
$500$	1.00000			0.0447214
$501$			20.7846i			0.928588i
$502$	14.0000			0.624851
$503$	−21.0000			−0.936344			−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000			−0.936344			−0.468172	+	0.883637i	$0.655087\pi$
$504$	−6.00000	+	5.19615i	−0.267261	+	0.231455i
$505$	−3.00000			−0.133498
$506$	8.00000			0.355643
$507$	13.5000	+	7.79423i	0.599556	+	0.346154i
$508$	−5.00000			−0.221839
$509$	14.5000	+	25.1147i	0.642701	+	1.11319i	0.984827	+	0.173537i	$0.0555197\pi$
$509$	14.5000	+	25.1147i	0.642701	+	1.11319i	−0.342126	+	0.939654i	$0.611147\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−10.0000	−	17.3205i	−0.441081	−	0.763975i
$515$	0.500000	−	0.866025i	0.0220326	−	0.0381616i
$516$	1.50000	+	0.866025i	0.0660338	+	0.0381246i
$517$	−13.0000	+	22.5167i	−0.571739	+	0.990282i
$518$	16.0000	−	13.8564i	0.703000	−	0.608816i
$519$	−9.00000	+	5.19615i	−0.395056	+	0.228086i
$520$	−2.00000			−0.0877058
$521$	10.5000	+	18.1865i	0.460013	+	0.796766i	0.998961	−	0.0455727i	$-0.0145113\pi$
$521$	10.5000	+	18.1865i	0.460013	+	0.796766i	−0.538948	+	0.842339i	$0.681178\pi$
$522$	3.00000			0.131306
$523$	−17.5000	+	30.3109i	−0.765222	+	1.32540i	0.174908	+	0.984585i	$0.444037\pi$
$523$	−17.5000	+	30.3109i	−0.765222	+	1.32540i	−0.940129	+	0.340818i	$0.889296\pi$
$524$	−10.0000	−	17.3205i	−0.436852	−	0.756650i
$525$	1.50000	−	4.33013i	0.0654654	−	0.188982i
$526$	4.50000	−	7.79423i	0.196209	−	0.339845i
$527$		0			0
$528$		−	3.46410i		−	0.150756i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	5.00000	−	8.66025i	0.217186	−	0.376177i
$531$	−6.00000	+	10.3923i	−0.260378	+	0.450988i
$532$		0			0
$533$	5.00000	+	8.66025i	0.216574	+	0.375117i
$534$		−	24.2487i		−	1.04934i
$535$	1.00000			0.0432338
$536$	12.0000			0.518321
$537$	−6.00000	−	3.46410i	−0.258919	−	0.149487i
$538$	7.00000	+	12.1244i	0.301791	+	0.522718i
$539$	13.0000	−	5.19615i	0.559950	−	0.223814i
$540$	−4.50000	+	2.59808i	−0.193649	+	0.111803i
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	−0.225617	−	0.974216i	$-0.572440\pi$
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	0.956504	−	0.291718i	$-0.0942267\pi$
$542$	14.0000	−	24.2487i	0.601351	−	1.04157i
$543$	31.5000	−	18.1865i	1.35179	−	0.780459i
$544$		0			0
$545$	1.50000	−	2.59808i	0.0642529	−	0.111289i
$546$	−3.00000	+	8.66025i	−0.128388	+	0.370625i
$547$	−6.50000	−	11.2583i	−0.277920	−	0.481371i	0.692948	−	0.720988i	$-0.256312\pi$
$547$	−6.50000	−	11.2583i	−0.277920	−	0.481371i	−0.970868	+	0.239616i	$0.922978\pi$
$548$	−6.00000	+	10.3923i	−0.256307	+	0.443937i
$549$	−9.00000	+	15.5885i	−0.384111	+	0.665299i
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$		0			0
$552$	6.00000	+	3.46410i	0.255377	+	0.147442i
$553$	−25.0000	−	8.66025i	−1.06311	−	0.368271i
$554$	−13.0000	+	22.5167i	−0.552317	+	0.956641i
$555$	12.0000	−	6.92820i	0.509372	−	0.294086i
$556$	8.00000	−	13.8564i	0.339276	−	0.587643i
$557$	12.0000	+	20.7846i	0.508456	+	0.880672i	0.999952	+	0.00979220i	$0.00311700\pi$
$557$	12.0000	+	20.7846i	0.508456	+	0.880672i	−0.491496	+	0.870880i	$0.663550\pi$
$558$	15.0000	−	25.9808i	0.635001	−	1.09985i
$559$	2.00000			0.0845910
$560$	0.500000	+	2.59808i	0.0211289	+	0.109789i
$561$		0			0
$562$	−6.50000	−	11.2583i	−0.274186	−	0.474904i
$563$	−4.00000			−0.168580			−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000			−0.168580			−0.0842900	+	0.996441i	$0.526862\pi$
$564$	−19.5000	+	11.2583i	−0.821098	+	0.474061i
$565$	6.00000			0.252422
$566$	−11.0000			−0.462364
$567$	4.50000	+	23.3827i	0.188982	+	0.981981i
$568$	−12.0000			−0.503509
$569$	−18.0000			−0.754599			−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000			−0.754599			−0.377300	+	0.926091i	$0.623147\pi$
$570$		0			0
$571$	−2.00000			−0.0836974			−0.0418487	−	0.999124i	$-0.513325\pi$
$571$	−2.00000			−0.0836974			−0.0418487	+	0.999124i	$0.513325\pi$
$572$	−2.00000	−	3.46410i	−0.0836242	−	0.144841i
$573$	−27.0000	+	15.5885i	−1.12794	+	0.651217i
$574$	10.0000	−	8.66025i	0.417392	−	0.361472i
$575$	−4.00000			−0.166812
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−14.0000	−	24.2487i	−0.582828	−	1.00949i	−0.995142	−	0.0984456i	$-0.968613\pi$
$577$	−14.0000	−	24.2487i	−0.582828	−	1.00949i	0.412315	−	0.911041i	$-0.364720\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$	−3.00000	+	1.73205i	−0.124676	+	0.0719816i
$580$	0.500000	−	0.866025i	0.0207614	−	0.0359597i
$581$	−2.50000	−	12.9904i	−0.103717	−	0.538932i
$582$	−3.00000	−	1.73205i	−0.124354	−	0.0717958i
$583$	20.0000			0.828315
$584$		0			0
$585$	−3.00000	+	5.19615i	−0.124035	+	0.214834i
$586$	−6.00000	+	10.3923i	−0.247858	+	0.429302i
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	0.974668	+	0.223659i	$0.0718001\pi$
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	−0.293640	+	0.955916i	$0.594867\pi$
$588$	12.0000	+	1.73205i	0.494872	+	0.0714286i
$589$		0			0
$590$	2.00000	+	3.46410i	0.0823387	+	0.142615i
$591$	−39.0000	+	22.5167i	−1.60425	+	0.926212i
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	−7.00000	+	12.1244i	−0.287456	+	0.497888i	−0.973202	−	0.229953i	$-0.926143\pi$
$593$	−7.00000	+	12.1244i	−0.287456	+	0.497888i	0.685746	+	0.727841i	$0.259476\pi$
$594$	−9.00000	−	5.19615i	−0.369274	−	0.213201i
$595$		0			0
$596$	9.00000	+	15.5885i	0.368654	+	0.638528i
$597$		0			0
$598$	8.00000			0.327144
$599$	−44.0000			−1.79779			−0.898896	−	0.438163i	$-0.855629\pi$
$599$	−44.0000			−1.79779			−0.898896	+	0.438163i	$0.855629\pi$
$600$			1.73205i			0.0707107i
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	−0.469095	+	0.883148i	$0.655420\pi$
$602$	−0.500000	−	2.59808i	−0.0203785	−	0.105890i
$603$	18.0000	−	31.1769i	0.733017	−	1.26962i
$604$	−6.00000	+	10.3923i	−0.244137	+	0.422857i
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$		−	5.19615i		−	0.211079i
$607$	21.5000	+	37.2391i	0.872658	+	1.51149i	0.859237	+	0.511578i	$0.170939\pi$
$607$	21.5000	+	37.2391i	0.872658	+	1.51149i	0.0134214	+	0.999910i	$0.495728\pi$
$608$		0			0
$609$	−3.00000	−	3.46410i	−0.121566	−	0.140372i
$610$	3.00000	+	5.19615i	0.121466	+	0.210386i
$611$	−13.0000	+	22.5167i	−0.525924	+	0.910927i
$612$		0			0
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	0.938967	+	0.344008i	$0.111785\pi$
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	−0.171564	+	0.985173i	$0.554882\pi$
$614$	−7.00000			−0.282497
$615$	7.50000	−	4.33013i	0.302429	−	0.174608i
$616$	−4.00000	+	3.46410i	−0.161165	+	0.139573i
$617$	−10.0000	+	17.3205i	−0.402585	+	0.697297i	−0.994037	−	0.109043i	$-0.965221\pi$
$617$	−10.0000	+	17.3205i	−0.402585	+	0.697297i	0.591452	+	0.806340i	$0.298555\pi$
$618$	1.50000	+	0.866025i	0.0603388	+	0.0348367i
$619$	−16.0000	+	27.7128i	−0.643094	+	1.11387i	0.341644	+	0.939829i	$0.389016\pi$
$619$	−16.0000	+	27.7128i	−0.643094	+	1.11387i	−0.984738	+	0.174042i	$0.944317\pi$
$620$	−5.00000	−	8.66025i	−0.200805	−	0.347804i
$621$	18.0000	−	10.3923i	0.722315	−	0.417029i
$622$	24.0000			0.962312
$623$	−28.0000	+	24.2487i	−1.12180	+	0.971504i
$624$		−	3.46410i		−	0.138675i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−6.00000			−0.239808
$627$		0			0
$628$	−4.00000			−0.159617
$629$		0			0
$630$	7.50000	+	2.59808i	0.298807	+	0.103510i
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$	10.0000			0.397779
$633$		−	38.1051i		−	1.51454i
$634$	−18.0000			−0.714871
$635$	2.50000	+	4.33013i	0.0992095	+	0.171836i
$636$	15.0000	+	8.66025i	0.594789	+	0.343401i
$637$	13.0000	−	5.19615i	0.515079	−	0.205879i
$638$	2.00000			0.0791808
$639$	−18.0000	+	31.1769i	−0.712069	+	1.23334i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$			1.73205i			0.0683586i
$643$	−23.5000	+	40.7032i	−0.926750	+	1.60518i	−0.138027	+	0.990429i	$0.544076\pi$
$643$	−23.5000	+	40.7032i	−0.926750	+	1.60518i	−0.788723	+	0.614749i	$0.789257\pi$
$644$	−2.00000	−	10.3923i	−0.0788110	−	0.409514i
$645$		−	1.73205i		−	0.0681994i
$646$		0			0
$647$	3.50000	+	6.06218i	0.137599	+	0.238329i	0.926587	−	0.376080i	$-0.122728\pi$
$647$	3.50000	+	6.06218i	0.137599	+	0.238329i	−0.788988	+	0.614408i	$0.789395\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	−4.00000	+	6.92820i	−0.157014	+	0.271956i
$650$	1.00000	+	1.73205i	0.0392232	+	0.0679366i
$651$	−45.0000	+	8.66025i	−1.76369	+	0.339422i
$652$	10.0000	−	17.3205i	0.391630	−	0.678323i
$653$	2.00000	+	3.46410i	0.0782660	+	0.135561i	0.902502	−	0.430686i	$-0.141728\pi$
$653$	2.00000	+	3.46410i	0.0782660	+	0.135561i	−0.824236	+	0.566247i	$0.808395\pi$
$654$	4.50000	+	2.59808i	0.175964	+	0.101593i
$655$	−10.0000	+	17.3205i	−0.390732	+	0.676768i
$656$	−2.50000	+	4.33013i	−0.0976086	+	0.169063i
$657$		0			0
$658$	32.5000	+	11.2583i	1.26698	+	0.438895i
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$	−3.00000	+	1.73205i	−0.116775	+	0.0674200i
$661$	3.00000			0.116686			0.0583432	−	0.998297i	$-0.481418\pi$
$661$	3.00000			0.116686			0.0583432	+	0.998297i	$0.481418\pi$
$662$	−4.00000			−0.155464
$663$		0			0
$664$	2.50000	+	4.33013i	0.0970188	+	0.168042i
$665$		0			0
$666$	12.0000	+	20.7846i	0.464991	+	0.805387i
$667$	−2.00000	+	3.46410i	−0.0774403	+	0.134131i
$668$	−6.00000	+	10.3923i	−0.232147	+	0.402090i
$669$	−13.5000	−	7.79423i	−0.521940	−	0.301342i
$670$	−6.00000	−	10.3923i	−0.231800	−	0.401490i
$671$	−6.00000	+	10.3923i	−0.231627	+	0.401190i
$672$	−4.50000	+	0.866025i	−0.173591	+	0.0334077i
$673$	4.00000	+	6.92820i	0.154189	+	0.267063i	0.932763	−	0.360489i	$-0.117390\pi$
$673$	4.00000	+	6.92820i	0.154189	+	0.267063i	−0.778575	+	0.627552i	$0.784057\pi$
$674$	−3.00000	+	5.19615i	−0.115556	+	0.200148i
$675$	4.50000	+	2.59808i	0.173205	+	0.100000i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−20.0000			−0.768662			−0.384331	−	0.923195i	$-0.625568\pi$
$677$	−20.0000			−0.768662			−0.384331	+	0.923195i	$0.625568\pi$
$678$			10.3923i			0.399114i
$679$	1.00000	+	5.19615i	0.0383765	+	0.199410i
$680$		0			0
$681$			6.92820i			0.265489i
$682$	10.0000	−	17.3205i	0.382920	−	0.663237i
$683$	−5.50000	−	9.52628i	−0.210452	−	0.364513i	0.741404	−	0.671059i	$-0.234160\pi$
$683$	−5.50000	−	9.52628i	−0.210452	−	0.364513i	−0.951856	+	0.306546i	$0.900827\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$	−10.0000	−	15.5885i	−0.381802	−	0.595170i
$687$	1.50000	+	0.866025i	0.0572286	+	0.0330409i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	20.0000			0.761939
$690$		−	6.92820i		−	0.263752i
$691$	−48.0000			−1.82601			−0.913003	−	0.407953i	$-0.866243\pi$
$691$	−48.0000			−1.82601			−0.913003	+	0.407953i	$0.866243\pi$
$692$	−6.00000			−0.228086
$693$	3.00000	+	15.5885i	0.113961	+	0.592157i
$694$	19.0000			0.721230
$695$	−16.0000			−0.606915
$696$	1.50000	+	0.866025i	0.0568574	+	0.0328266i
$697$		0			0
$698$	−15.0000	−	25.9808i	−0.567758	−	0.983386i
$699$		−	10.3923i		−	0.393073i
$700$	2.00000	−	1.73205i	0.0755929	−	0.0654654i
$701$	−33.0000			−1.24639			−0.623196	−	0.782065i	$-0.714166\pi$
$701$	−33.0000			−1.24639			−0.623196	+	0.782065i	$0.714166\pi$
$702$	−9.00000	−	5.19615i	−0.339683	−	0.196116i
$703$		0			0
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$	19.5000	+	11.2583i	0.734412	+	0.424013i
$706$	12.0000	−	20.7846i	0.451626	−	0.782239i
$707$	−6.00000	+	5.19615i	−0.225653	+	0.195421i
$708$	−6.00000	+	3.46410i	−0.225494	+	0.130189i
$709$	−46.0000			−1.72757			−0.863783	−	0.503864i	$-0.831911\pi$
$709$	−46.0000			−1.72757			−0.863783	+	0.503864i	$0.831911\pi$
$710$	6.00000	+	10.3923i	0.225176	+	0.390016i
$711$	15.0000	−	25.9808i	0.562544	−	0.974355i
$712$	7.00000	−	12.1244i	0.262336	−	0.454379i
$713$	20.0000	+	34.6410i	0.749006	+	1.29732i
$714$		0			0
$715$	−2.00000	+	3.46410i	−0.0747958	+	0.129550i
$716$	−2.00000	−	3.46410i	−0.0747435	−	0.129460i
$717$			10.3923i			0.388108i
$718$	17.0000	−	29.4449i	0.634434	−	1.09887i
$719$	−14.0000	+	24.2487i	−0.522112	+	0.904324i	0.477557	+	0.878601i	$0.341522\pi$
$719$	−14.0000	+	24.2487i	−0.522112	+	0.904324i	−0.999669	+	0.0257237i	$0.991811\pi$
$720$	−3.00000			−0.111803
$721$	−0.500000	−	2.59808i	−0.0186210	−	0.0967574i
$722$	9.50000	+	16.4545i	0.353553	+	0.612372i
$723$			43.3013i			1.61039i
$724$	21.0000			0.780459
$725$	−1.00000			−0.0371391
$726$	10.5000	+	6.06218i	0.389692	+	0.224989i
$727$	20.0000	+	34.6410i	0.741759	+	1.28476i	0.951694	+	0.307049i	$0.0993415\pi$
$727$	20.0000	+	34.6410i	0.741759	+	1.28476i	−0.209935	+	0.977715i	$0.567325\pi$
$728$	−4.00000	+	3.46410i	−0.148250	+	0.128388i
$729$	−27.0000			−1.00000
$730$		0			0
$731$		0			0
$732$	−9.00000	+	5.19615i	−0.332650	+	0.192055i
$733$	−10.0000	−	17.3205i	−0.369358	−	0.639748i	0.620107	−	0.784517i	$-0.287089\pi$
$733$	−10.0000	−	17.3205i	−0.369358	−	0.639748i	−0.989465	+	0.144770i	$0.953756\pi$
$734$	8.50000	−	14.7224i	0.313741	−	0.543415i
$735$	−4.50000	−	11.2583i	−0.165985	−	0.415270i
$736$	2.00000	+	3.46410i	0.0737210	+	0.127688i
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$	7.50000	+	12.9904i	0.276079	+	0.478183i
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	−0.994420	−	0.105493i	$-0.966358\pi$
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	0.405851	−	0.913939i	$-0.366975\pi$
$740$	8.00000			0.294086
$741$		0			0
$742$	−5.00000	−	25.9808i	−0.183556	−	0.953784i
$743$	21.5000	−	37.2391i	0.788759	−	1.36617i	−0.137969	−	0.990437i	$-0.544058\pi$
$743$	21.5000	−	37.2391i	0.788759	−	1.36617i	0.926728	−	0.375733i	$-0.122609\pi$
$744$	15.0000	−	8.66025i	0.549927	−	0.317500i
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$	−12.0000	−	20.7846i	−0.439351	−	0.760979i
$747$	15.0000			0.548821
$748$		0			0
$749$	2.00000	−	1.73205i	0.0730784	−	0.0632878i
$750$	1.50000	−	0.866025i	0.0547723	−	0.0316228i
$751$	23.0000	+	39.8372i	0.839282	+	1.45368i	0.890496	+	0.454991i	$0.150358\pi$
$751$	23.0000	+	39.8372i	0.839282	+	1.45368i	−0.0512140	+	0.998688i	$0.516309\pi$
$752$	−13.0000			−0.474061
$753$	21.0000	−	12.1244i	0.765283	−	0.441836i
$754$	2.00000			0.0728357
$755$	12.0000			0.436725
$756$	−4.50000	+	12.9904i	−0.163663	+	0.472456i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	2.00000			0.0726433
$759$	12.0000	−	6.92820i	0.435572	−	0.251478i
$760$		0			0
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	0.510551	−	0.859848i	$-0.329442\pi$
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	−0.999925	+	0.0122260i	$0.996108\pi$
$762$	−7.50000	+	4.33013i	−0.271696	+	0.156864i
$763$	−1.50000	−	7.79423i	−0.0543036	−	0.282170i
$764$	−18.0000			−0.651217
$765$		0			0
$766$	−6.50000	−	11.2583i	−0.234855	−	0.406780i
$767$	−4.00000	+	6.92820i	−0.144432	+	0.250163i
$768$	1.50000	−	0.866025i	0.0541266	−	0.0312500i
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	−0.580696	−	0.814120i	$-0.697220\pi$
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	0.995397	+	0.0958377i	$0.0305530\pi$
$770$	5.00000	+	1.73205i	0.180187	+	0.0624188i
$771$	−30.0000	−	17.3205i	−1.08042	−	0.623783i
$772$	−2.00000			−0.0719816
$773$	21.0000	+	36.3731i	0.755318	+	1.30825i	0.945216	+	0.326445i	$0.105851\pi$
$773$	21.0000	+	36.3731i	0.755318	+	1.30825i	−0.189899	+	0.981804i	$0.560816\pi$
$774$	3.00000			0.107833
$775$	−5.00000	+	8.66025i	−0.179605	+	0.311086i
$776$	−1.00000	−	1.73205i	−0.0358979	−	0.0621770i
$777$	12.0000	−	34.6410i	0.430498	−	1.24274i
$778$	−2.50000	+	4.33013i	−0.0896293	+	0.155243i
$779$		0			0
$780$	−3.00000	+	1.73205i	−0.107417	+	0.0620174i
$781$	−12.0000	+	20.7846i	−0.429394	+	0.743732i
$782$		0			0
$783$	4.50000	−	2.59808i	0.160817	−	0.0928477i
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	2.00000	+	3.46410i	0.0713831	+	0.123639i
$786$	−30.0000	−	17.3205i	−1.07006	−	0.617802i
$787$	31.0000			1.10503			0.552515	−	0.833503i	$-0.313668\pi$
$787$	31.0000			1.10503			0.552515	+	0.833503i	$0.313668\pi$
$788$	−26.0000			−0.926212
$789$		−	15.5885i		−	0.554964i
$790$	−5.00000	−	8.66025i	−0.177892	−	0.308118i
$791$	12.0000	−	10.3923i	0.426671	−	0.369508i
$792$	−3.00000	−	5.19615i	−0.106600	−	0.184637i
$793$	−6.00000	+	10.3923i	−0.213066	+	0.369042i
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$		−	17.3205i		−	0.614295i
$796$		0			0
$797$	15.0000	−	25.9808i	0.531327	−	0.920286i	−0.468004	−	0.883726i	$-0.655027\pi$
$797$	15.0000	−	25.9808i	0.531327	−	0.920286i	0.999331	−	0.0365596i	$-0.0116399\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−21.0000	−	36.3731i	−0.741999	−	1.28518i
$802$	12.5000	+	21.6506i	0.441390	+	0.764511i
$803$		0			0
$804$	18.0000	−	10.3923i	0.634811	−	0.366508i
$805$	−8.00000	+	6.92820i	−0.281963	+	0.244187i
$806$	10.0000	−	17.3205i	0.352235	−	0.610089i
$807$	21.0000	+	12.1244i	0.739235	+	0.426798i
$808$	1.50000	−	2.59808i	0.0527698	−	0.0914000i
$809$	1.50000	+	2.59808i	0.0527372	+	0.0913435i	0.891189	−	0.453632i	$-0.149872\pi$
$809$	1.50000	+	2.59808i	0.0527372	+	0.0913435i	−0.838452	+	0.544976i	$0.816539\pi$
$810$	−4.50000	+	7.79423i	−0.158114	+	0.273861i
$811$	−42.0000			−1.47482			−0.737410	−	0.675446i	$-0.763951\pi$
$811$	−42.0000			−1.47482			−0.737410	+	0.675446i	$0.763951\pi$
$812$	−0.500000	−	2.59808i	−0.0175466	−	0.0911746i
$813$		−	48.4974i		−	1.70088i
$814$	8.00000	+	13.8564i	0.280400	+	0.485667i
$815$	−20.0000			−0.700569
$816$		0			0
$817$		0			0
$818$	−25.0000			−0.874105
$819$	3.00000	+	15.5885i	0.104828	+	0.544705i
$820$	5.00000			0.174608
$821$	3.00000			0.104701			0.0523504	−	0.998629i	$-0.483329\pi$
$821$	3.00000			0.104701			0.0523504	+	0.998629i	$0.483329\pi$
$822$			20.7846i			0.724947i
$823$	−9.00000			−0.313720			−0.156860	−	0.987621i	$-0.550137\pi$
$823$	−9.00000			−0.313720			−0.156860	+	0.987621i	$0.550137\pi$
$824$	0.500000	+	0.866025i	0.0174183	+	0.0301694i
$825$	3.00000	+	1.73205i	0.104447	+	0.0603023i
$826$	10.0000	+	3.46410i	0.347945	+	0.120532i
$827$	−5.00000			−0.173867			−0.0869335	−	0.996214i	$-0.527707\pi$
$827$	−5.00000			−0.173867			−0.0869335	+	0.996214i	$0.527707\pi$
$828$	12.0000			0.417029
$829$	17.5000	+	30.3109i	0.607800	+	1.05274i	0.991602	+	0.129325i	$0.0412811\pi$
$829$	17.5000	+	30.3109i	0.607800	+	1.05274i	−0.383802	+	0.923415i	$0.625386\pi$
$830$	2.50000	−	4.33013i	0.0867763	−	0.150301i
$831$			45.0333i			1.56219i
$832$	1.00000	−	1.73205i	0.0346688	−	0.0600481i
$833$		0			0
$834$		−	27.7128i		−	0.959616i
$835$	12.0000			0.415277
$836$		0			0
$837$		−	51.9615i		−	1.79605i
$838$	−13.0000	+	22.5167i	−0.449078	+	0.777825i
$839$	−8.00000	−	13.8564i	−0.276191	−	0.478376i	0.694244	−	0.719740i	$-0.255739\pi$
$839$	−8.00000	−	13.8564i	−0.276191	−	0.478376i	−0.970435	+	0.241363i	$0.922405\pi$
$840$	3.00000	+	3.46410i	0.103510	+	0.119523i
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	14.5000	+	25.1147i	0.499703	+	0.865511i
$843$	−19.5000	−	11.2583i	−0.671616	−	0.387757i
$844$	11.0000	−	19.0526i	0.378636	−	0.655816i
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$	−19.5000	+	33.7750i	−0.670424	+	1.16121i
$847$	−3.50000	−	18.1865i	−0.120261	−	0.624897i
$848$	5.00000	+	8.66025i	0.171701	+	0.297394i
$849$	−16.5000	+	9.52628i	−0.566279	+	0.326941i
$850$		0			0
$851$	−32.0000			−1.09695
$852$	−18.0000	+	10.3923i	−0.616670	+	0.356034i
$853$	−8.00000	−	13.8564i	−0.273915	−	0.474434i	0.695946	−	0.718094i	$-0.254985\pi$
$853$	−8.00000	−	13.8564i	−0.273915	−	0.474434i	−0.969861	+	0.243660i	$0.921652\pi$
$854$	15.0000	+	5.19615i	0.513289	+	0.177809i
$855$		0			0
$856$	−0.500000	+	0.866025i	−0.0170896	+	0.0296001i
$857$	5.00000	−	8.66025i	0.170797	−	0.295829i	−0.767902	−	0.640567i	$-0.778699\pi$
$857$	5.00000	−	8.66025i	0.170797	−	0.295829i	0.938699	+	0.344739i	$0.112033\pi$
$858$	−6.00000	−	3.46410i	−0.204837	−	0.118262i
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	0.990533	+	0.137277i	$0.0438352\pi$
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	−0.376381	+	0.926465i	$0.622831\pi$
$860$	0.500000	−	0.866025i	0.0170499	−	0.0295312i
$861$	7.50000	−	21.6506i	0.255599	−	0.737852i
$862$	−9.00000	−	15.5885i	−0.306541	−	0.530945i
$863$	−4.00000	+	6.92820i	−0.136162	+	0.235839i	−0.926041	−	0.377424i	$-0.876810\pi$
$863$	−4.00000	+	6.92820i	−0.136162	+	0.235839i	0.789879	+	0.613263i	$0.210143\pi$
$864$		−	5.19615i		−	0.176777i
$865$	3.00000	+	5.19615i	0.102003	+	0.176674i
$866$	−14.0000			−0.475739
$867$		−	29.4449i		−	1.00000i
$868$	−25.0000	−	8.66025i	−0.848555	−	0.293948i
$869$	10.0000	−	17.3205i	0.339227	−	0.587558i
$870$		−	1.73205i		−	0.0587220i
$871$	12.0000	−	20.7846i	0.406604	−	0.704260i
$872$	1.50000	+	2.59808i	0.0507964	+	0.0879820i
$873$	−6.00000			−0.203069
$874$		0			0
$875$	−2.50000	−	0.866025i	−0.0845154	−	0.0292770i
$876$		0			0
$877$	2.00000	+	3.46410i	0.0675352	+	0.116974i	0.897816	−	0.440371i	$-0.145153\pi$
$877$	2.00000	+	3.46410i	0.0675352	+	0.116974i	−0.830281	+	0.557346i	$0.811820\pi$
$878$	−34.0000			−1.14744
$879$			20.7846i			0.701047i
$880$	−2.00000			−0.0674200
$881$	14.0000			0.471672			0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000			0.471672			0.235836	+	0.971793i	$0.424217\pi$
$882$	19.5000	−	7.79423i	0.656599	−	0.262445i
$883$	51.0000			1.71629			0.858143	−	0.513410i	$-0.171618\pi$
$883$	51.0000			1.71629			0.858143	+	0.513410i	$0.171618\pi$
$884$		0			0
$885$	6.00000	+	3.46410i	0.201688	+	0.116445i
$886$	17.0000			0.571126
$887$	−27.5000	−	47.6314i	−0.923360	−	1.59931i	−0.794178	−	0.607685i	$-0.792098\pi$
$887$	−27.5000	−	47.6314i	−0.923360	−	1.59931i	−0.129181	−	0.991621i	$-0.541235\pi$
$888$			13.8564i			0.464991i
$889$	12.5000	+	4.33013i	0.419237	+	0.145228i
$890$	−14.0000			−0.469281
$891$	−18.0000			−0.603023
$892$	−4.50000	−	7.79423i	−0.150671	−	0.260970i
$893$		0			0
$894$	27.0000	+	15.5885i	0.903015	+	0.521356i
$895$	−2.00000	+	3.46410i	−0.0668526	+	0.115792i
$896$	−2.50000	−	0.866025i	−0.0835191	−	0.0289319i
$897$	12.0000	−	6.92820i	0.400668	−	0.231326i
$898$	−5.00000			−0.166852
$899$	5.00000	+	8.66025i	0.166759	+	0.288836i
$900$	1.50000	+	2.59808i	0.0500000	+	0.0866025i
$901$		0			0
$902$	5.00000	+	8.66025i	0.166482	+	0.288355i
$903$	−3.00000	−	3.46410i	−0.0998337	−	0.115278i
$904$	−3.00000	+	5.19615i	−0.0997785	+	0.172821i
$905$	−10.5000	−	18.1865i	−0.349032	−	0.604541i
$906$			20.7846i			0.690522i
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	−0.376228	−	0.926527i	$-0.622779\pi$
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	0.990510	−	0.137441i	$-0.0438878\pi$
$908$	−2.00000	+	3.46410i	−0.0663723	+	0.114960i
$909$	−4.50000	−	7.79423i	−0.149256	−	0.258518i
$910$	5.00000	+	1.73205i	0.165748	+	0.0574169i
$911$	−10.0000	−	17.3205i	−0.331315	−	0.573854i	0.651455	−	0.758687i	$-0.274159\pi$
$911$	−10.0000	−	17.3205i	−0.331315	−	0.573854i	−0.982770	+	0.184833i	$0.940826\pi$
$912$		0			0
$913$	10.0000			0.330952
$914$	−18.0000			−0.595387
$915$	9.00000	+	5.19615i	0.297531	+	0.171780i
$916$	0.500000	+	0.866025i	0.0165205	+	0.0286143i
$917$	10.0000	+	51.9615i	0.330229	+	1.71592i
$918$		0			0
$919$	24.0000	−	41.5692i	0.791687	−	1.37124i	−0.133235	−	0.991084i	$-0.542536\pi$
$919$	24.0000	−	41.5692i	0.791687	−	1.37124i	0.924922	−	0.380158i	$-0.124130\pi$
$920$	2.00000	−	3.46410i	0.0659380	−	0.114208i
$921$	−10.5000	+	6.06218i	−0.345987	+	0.199756i
$922$	−4.50000	−	7.79423i	−0.148200	−	0.256689i
$923$	−12.0000	+	20.7846i	−0.394985	+	0.684134i
$924$	−3.00000	+	8.66025i	−0.0986928	+	0.284901i
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$	0.500000	−	0.866025i	0.0164310	−	0.0284594i
$927$	3.00000			0.0985329
$928$	0.500000	+	0.866025i	0.0164133	+	0.0284287i
$929$	15.0000			0.492134			0.246067	−	0.969253i	$-0.420862\pi$
$929$	15.0000			0.492134			0.246067	+	0.969253i	$0.420862\pi$
$930$	−15.0000	−	8.66025i	−0.491869	−	0.283981i
$931$		0			0
$932$	3.00000	−	5.19615i	0.0982683	−	0.170206i
$933$	36.0000	−	20.7846i	1.17859	−	0.680458i
$934$	10.5000	−	18.1865i	0.343570	−	0.595082i
$935$		0			0
$936$	−3.00000	−	5.19615i	−0.0980581	−	0.169842i
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	−30.0000	−	10.3923i	−0.979535	−	0.339321i
$939$	−9.00000	+	5.19615i	−0.293704	+	0.169570i
$940$	6.50000	+	11.2583i	0.212007	+	0.367206i
$941$	45.0000			1.46696			0.733479	−	0.679712i	$-0.237895\pi$
$941$	45.0000			1.46696			0.733479	+	0.679712i	$0.237895\pi$
$942$	−6.00000	+	3.46410i	−0.195491	+	0.112867i
$943$	−20.0000			−0.651290
$944$	−4.00000			−0.130189
$945$	13.5000	−	2.59808i	0.439155	−	0.0845154i
$946$	2.00000			0.0650256
$947$	−4.00000			−0.129983			−0.0649913	−	0.997886i	$-0.520702\pi$
$947$	−4.00000			−0.129983			−0.0649913	+	0.997886i	$0.520702\pi$
$948$	15.0000	−	8.66025i	0.487177	−	0.281272i
$949$		0			0
$950$		0			0
$951$	−27.0000	+	15.5885i	−0.875535	+	0.505490i
$952$		0			0
$953$	2.00000			0.0647864			0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000			0.0647864			0.0323932	+	0.999475i	$0.489687\pi$
$954$	30.0000			0.971286
$955$	9.00000	+	15.5885i	0.291233	+	0.504431i
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$	3.00000	−	1.73205i	0.0969762	−	0.0559893i
$958$	5.00000	−	8.66025i	0.161543	−	0.279800i
$959$	24.0000	−	20.7846i	0.775000	−	0.671170i
$960$	−1.50000	−	0.866025i	−0.0484123	−	0.0279508i
$961$	69.0000			2.22581
$962$	8.00000	+	13.8564i	0.257930	+	0.446748i
$963$	1.50000	+	2.59808i	0.0483368	+	0.0837218i
$964$	−12.5000	+	21.6506i	−0.402598	+	0.697320i
$965$	1.00000	+	1.73205i	0.0321911	+	0.0557567i
$966$	−12.0000	−	13.8564i	−0.386094	−	0.445823i
$967$	4.00000	−	6.92820i	0.128631	−	0.222796i	−0.794515	−	0.607244i	$-0.792275\pi$
$967$	4.00000	−	6.92820i	0.128631	−	0.222796i	0.923147	+	0.384448i	$0.125608\pi$
$968$	3.50000	+	6.06218i	0.112494	+	0.194846i
$969$		0			0
$970$	−1.00000	+	1.73205i	−0.0321081	+	0.0556128i
$971$	−21.0000	+	36.3731i	−0.673922	+	1.16727i	0.302861	+	0.953035i	$0.402058\pi$
$971$	−21.0000	+	36.3731i	−0.673922	+	1.16727i	−0.976783	+	0.214232i	$0.931275\pi$
$972$	−13.5000	−	7.79423i	−0.433013	−	0.250000i
$973$	−32.0000	+	27.7128i	−1.02587	+	0.888432i
$974$	−16.0000	−	27.7128i	−0.512673	−	0.887976i
$975$	3.00000	+	1.73205i	0.0960769	+	0.0554700i
$976$	−6.00000			−0.192055
$977$	12.0000			0.383914			0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000			0.383914			0.191957	+	0.981403i	$0.438517\pi$
$978$		−	34.6410i		−	1.10770i
$979$	−14.0000	−	24.2487i	−0.447442	−	0.774992i
$980$	1.00000	−	6.92820i	0.0319438	−	0.221313i
$981$	9.00000			0.287348
$982$	4.00000	−	6.92820i	0.127645	−	0.221088i
$983$	15.5000	−	26.8468i	0.494373	−	0.856280i	−0.505606	−	0.862765i	$-0.668731\pi$
$983$	15.5000	−	26.8468i	0.494373	−	0.856280i	0.999979	+	0.00648510i	$0.00206429\pi$
$984$			8.66025i			0.276079i
$985$	13.0000	+	22.5167i	0.414214	+	0.717440i
$986$		0			0
$987$	58.5000	−	11.2583i	1.86208	−	0.358357i
$988$		0			0
$989$	−2.00000	+	3.46410i	−0.0635963	+	0.110152i
$990$	−3.00000	+	5.19615i	−0.0953463	+	0.165145i
$991$	−23.0000	−	39.8372i	−0.730619	−	1.26547i	−0.956619	−	0.291342i	$-0.905898\pi$
$991$	−23.0000	−	39.8372i	−0.730619	−	1.26547i	0.226000	−	0.974127i	$-0.427435\pi$
$992$	10.0000			0.317500
$993$	−6.00000	+	3.46410i	−0.190404	+	0.109930i
$994$	30.0000	+	10.3923i	0.951542	+	0.329624i
$995$		0			0
$996$	7.50000	+	4.33013i	0.237647	+	0.137205i
$997$	−16.0000	+	27.7128i	−0.506725	+	0.877674i	0.493245	+	0.869891i	$0.335811\pi$
$997$	−16.0000	+	27.7128i	−0.506725	+	0.877674i	−0.999970	+	0.00778294i	$0.997523\pi$
$998$	−5.00000	−	8.66025i	−0.158272	−	0.274136i
$999$	36.0000	+	20.7846i	1.13899	+	0.657596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.c.121.1	✓	2
3.2	odd	2		1890.2.i.b.1171.1		2
7.4	even	3		630.2.l.a.571.1	yes	2
9.2	odd	6		1890.2.l.c.1801.1		2
9.7	even	3		630.2.l.a.331.1	yes	2
21.11	odd	6		1890.2.l.c.361.1		2
63.11	odd	6		1890.2.i.b.991.1		2
63.25	even	3	inner	630.2.i.c.151.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.c.121.1	✓	2	1.1	even	1	trivial
630.2.i.c.151.1	yes	2	63.25	even	3	inner
630.2.l.a.331.1	yes	2	9.7	even	3
630.2.l.a.571.1	yes	2	7.4	even	3
1890.2.i.b.991.1		2	63.11	odd	6
1890.2.i.b.1171.1		2	3.2	odd	2
1890.2.l.c.361.1		2	21.11	odd	6
1890.2.l.c.1801.1		2	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.50000 - 0.866025i) q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(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} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.00000 - 1.73205i) q^{11} +(1.50000 - 0.866025i) q^{12} +(1.00000 - 1.73205i) q^{13} +(-2.50000 - 0.866025i) q^{14} +(-1.50000 - 0.866025i) q^{15} +1.00000 q^{16} +(1.50000 - 2.59808i) q^{18} +(-0.500000 - 0.866025i) q^{20} +(-4.50000 + 0.866025i) q^{21} +(1.00000 - 1.73205i) q^{22} +(2.00000 + 3.46410i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} -5.19615i q^{27} +(-2.50000 - 0.866025i) q^{28} +(0.500000 + 0.866025i) q^{29} +(-1.50000 - 0.866025i) q^{30} +10.0000 q^{31} +1.00000 q^{32} -3.46410i q^{33} +(0.500000 + 2.59808i) q^{35} +(1.50000 - 2.59808i) q^{36} +(-4.00000 + 6.92820i) q^{37} -3.46410i q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(-4.50000 + 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(1.00000 - 1.73205i) q^{44} -3.00000 q^{45} +(2.00000 + 3.46410i) q^{46} -13.0000 q^{47} +(1.50000 - 0.866025i) q^{48} +(5.50000 + 4.33013i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(1.00000 - 1.73205i) q^{52} +(5.00000 + 8.66025i) q^{53} -5.19615i q^{54} -2.00000 q^{55} +(-2.50000 - 0.866025i) q^{56} +(0.500000 + 0.866025i) q^{58} -4.00000 q^{59} +(-1.50000 - 0.866025i) q^{60} -6.00000 q^{61} +10.0000 q^{62} +(-6.00000 + 5.19615i) q^{63} +1.00000 q^{64} -2.00000 q^{65} -3.46410i q^{66} +12.0000 q^{67} +(6.00000 + 3.46410i) q^{69} +(0.500000 + 2.59808i) q^{70} -12.0000 q^{71} +(1.50000 - 2.59808i) q^{72} +(-4.00000 + 6.92820i) q^{74} +1.73205i q^{75} +(-4.00000 + 3.46410i) q^{77} -3.46410i q^{78} +10.0000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-2.50000 + 4.33013i) q^{82} +(2.50000 + 4.33013i) q^{83} +(-4.50000 + 0.866025i) q^{84} +(0.500000 + 0.866025i) q^{86} +(1.50000 + 0.866025i) q^{87} +(1.00000 - 1.73205i) q^{88} +(7.00000 - 12.1244i) q^{89} -3.00000 q^{90} +(-4.00000 + 3.46410i) q^{91} +(2.00000 + 3.46410i) q^{92} +(15.0000 - 8.66025i) q^{93} -13.0000 q^{94} +(1.50000 - 0.866025i) q^{96} +(-1.00000 - 1.73205i) q^{97} +(5.50000 + 4.33013i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} - q^{5} + 3 q^{6} - 5 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 - q^5 + 3 * q^6 - 5 * q^7 + 2 * q^8 + 3 * q^9	\( 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} - q^{5} + 3 q^{6} - 5 q^{7} + 2 q^{8} + 3 q^{9} - q^{10} + 2 q^{11} + 3 q^{12} + 2 q^{13} - 5 q^{14} - 3 q^{15} + 2 q^{16} + 3 q^{18} - q^{20} - 9 q^{21} + 2 q^{22} + 4 q^{23} + 3 q^{24} - q^{25} + 2 q^{26} - 5 q^{28} + q^{29} - 3 q^{30} + 20 q^{31} + 2 q^{32} + q^{35} + 3 q^{36} - 8 q^{37} - q^{40} - 5 q^{41} - 9 q^{42} + q^{43} + 2 q^{44} - 6 q^{45} + 4 q^{46} - 26 q^{47} + 3 q^{48} + 11 q^{49} - q^{50} + 2 q^{52} + 10 q^{53} - 4 q^{55} - 5 q^{56} + q^{58} - 8 q^{59} - 3 q^{60} - 12 q^{61} + 20 q^{62} - 12 q^{63} + 2 q^{64} - 4 q^{65} + 24 q^{67} + 12 q^{69} + q^{70} - 24 q^{71} + 3 q^{72} - 8 q^{74} - 8 q^{77} + 20 q^{79} - q^{80} - 9 q^{81} - 5 q^{82} + 5 q^{83} - 9 q^{84} + q^{86} + 3 q^{87} + 2 q^{88} + 14 q^{89} - 6 q^{90} - 8 q^{91} + 4 q^{92} + 30 q^{93} - 26 q^{94} + 3 q^{96} - 2 q^{97} + 11 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 - q^5 + 3 * q^6 - 5 * q^7 + 2 * q^8 + 3 * q^9 - q^10 + 2 * q^11 + 3 * q^12 + 2 * q^13 - 5 * q^14 - 3 * q^15 + 2 * q^16 + 3 * q^18 - q^20 - 9 * q^21 + 2 * q^22 + 4 * q^23 + 3 * q^24 - q^25 + 2 * q^26 - 5 * q^28 + q^29 - 3 * q^30 + 20 * q^31 + 2 * q^32 + q^35 + 3 * q^36 - 8 * q^37 - q^40 - 5 * q^41 - 9 * q^42 + q^43 + 2 * q^44 - 6 * q^45 + 4 * q^46 - 26 * q^47 + 3 * q^48 + 11 * q^49 - q^50 + 2 * q^52 + 10 * q^53 - 4 * q^55 - 5 * q^56 + q^58 - 8 * q^59 - 3 * q^60 - 12 * q^61 + 20 * q^62 - 12 * q^63 + 2 * q^64 - 4 * q^65 + 24 * q^67 + 12 * q^69 + q^70 - 24 * q^71 + 3 * q^72 - 8 * q^74 - 8 * q^77 + 20 * q^79 - q^80 - 9 * q^81 - 5 * q^82 + 5 * q^83 - 9 * q^84 + q^86 + 3 * q^87 + 2 * q^88 + 14 * q^89 - 6 * q^90 - 8 * q^91 + 4 * q^92 + 30 * q^93 - 26 * q^94 + 3 * q^96 - 2 * q^97 + 11 * q^98 - 6 * q^99

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