LMFDB - Embedded newform 630.2.bk.a.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(101,630)]

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([1, 0, 1]))

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

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

chi := DirichletCharacter("630.101");

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.bk (of order $6$, 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:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.a.131.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.866025 - 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.866025 - 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-4.09808 + 2.36603i) q^{11} +(-0.866025 + 1.50000i) q^{12} +(-3.00000 + 1.73205i) q^{13} +(0.866025 + 2.50000i) q^{14} +(0.866025 + 1.50000i) q^{15} +1.00000 q^{16} +(-2.59808 + 1.50000i) q^{18} +(-1.09808 + 0.633975i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.866025 + 4.50000i) q^{21} +(2.36603 + 4.09808i) q^{22} +(2.19615 + 1.26795i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.73205 + 3.00000i) q^{26} -5.19615 q^{27} +(2.50000 - 0.866025i) q^{28} +(-5.59808 - 3.23205i) q^{29} +(1.50000 - 0.866025i) q^{30} -8.19615i q^{31} -1.00000i q^{32} +8.19615i q^{33} +(0.500000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-3.09808 - 5.36603i) q^{37} +(0.633975 + 1.09808i) q^{38} +6.00000i q^{39} +(-0.866025 - 0.500000i) q^{40} +(4.50000 + 7.79423i) q^{41} +(4.50000 + 0.866025i) q^{42} +(-1.59808 + 2.76795i) q^{43} +(4.09808 - 2.36603i) q^{44} +3.00000 q^{45} +(1.26795 - 2.19615i) q^{46} -9.00000 q^{47} +(0.866025 - 1.50000i) q^{48} +(5.50000 - 4.33013i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.00000 - 1.73205i) q^{52} +(6.29423 + 3.63397i) q^{53} +5.19615i q^{54} -4.73205i q^{55} +(-0.866025 - 2.50000i) q^{56} +2.19615i q^{57} +(-3.23205 + 5.59808i) q^{58} +2.19615 q^{59} +(-0.866025 - 1.50000i) q^{60} -12.9282i q^{61} -8.19615 q^{62} +(6.00000 + 5.19615i) q^{63} -1.00000 q^{64} -3.46410i q^{65} +8.19615 q^{66} -4.00000 q^{67} +(3.80385 - 2.19615i) q^{69} +(-2.59808 - 0.500000i) q^{70} +4.73205i q^{71} +(2.59808 - 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +(-5.36603 + 3.09808i) q^{74} -1.73205 q^{75} +(1.09808 - 0.633975i) q^{76} +(8.19615 - 9.46410i) q^{77} +6.00000 q^{78} +14.5885 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(7.79423 - 4.50000i) q^{82} +(-5.59808 + 9.69615i) q^{83} +(0.866025 - 4.50000i) q^{84} +(2.76795 + 1.59808i) q^{86} +(-9.69615 + 5.59808i) q^{87} +(-2.36603 - 4.09808i) q^{88} +(2.19615 + 3.80385i) q^{89} -3.00000i q^{90} +(6.00000 - 6.92820i) q^{91} +(-2.19615 - 1.26795i) q^{92} +(-12.2942 - 7.09808i) q^{93} +9.00000i q^{94} -1.26795i q^{95} +(-1.50000 - 0.866025i) q^{96} +(-7.39230 - 4.26795i) q^{97} +(-4.33013 - 5.50000i) q^{98} +(12.2942 + 7.09808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 2 q^{5} - 6 q^{6} - 10 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 2 * q^5 - 6 * q^6 - 10 * q^7 - 6 * q^9	$ 4 q - 4 q^{4} - 2 q^{5} - 6 q^{6} - 10 q^{7} - 6 q^{9} - 6 q^{11} - 12 q^{13} + 4 q^{16} + 6 q^{19} + 2 q^{20} + 6 q^{22} - 12 q^{23} + 6 q^{24} - 2 q^{25} + 10 q^{28} - 12 q^{29} + 6 q^{30} + 2 q^{35} + 6 q^{36} - 2 q^{37} + 6 q^{38} + 18 q^{41} + 18 q^{42} + 4 q^{43} + 6 q^{44} + 12 q^{45} + 12 q^{46} - 36 q^{47} + 22 q^{49} + 12 q^{52} - 6 q^{53} - 6 q^{58} - 12 q^{59} - 12 q^{62} + 24 q^{63} - 4 q^{64} + 12 q^{66} - 16 q^{67} + 36 q^{69} + 24 q^{73} - 18 q^{74} - 6 q^{76} + 12 q^{77} + 24 q^{78} - 4 q^{79} - 2 q^{80} - 18 q^{81} - 12 q^{83} + 18 q^{86} - 18 q^{87} - 6 q^{88} - 12 q^{89} + 24 q^{91} + 12 q^{92} - 18 q^{93} - 6 q^{96} + 12 q^{97} + 18 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 2 * q^5 - 6 * q^6 - 10 * q^7 - 6 * q^9 - 6 * q^11 - 12 * q^13 + 4 * q^16 + 6 * q^19 + 2 * q^20 + 6 * q^22 - 12 * q^23 + 6 * q^24 - 2 * q^25 + 10 * q^28 - 12 * q^29 + 6 * q^30 + 2 * q^35 + 6 * q^36 - 2 * q^37 + 6 * q^38 + 18 * q^41 + 18 * q^42 + 4 * q^43 + 6 * q^44 + 12 * q^45 + 12 * q^46 - 36 * q^47 + 22 * q^49 + 12 * q^52 - 6 * q^53 - 6 * q^58 - 12 * q^59 - 12 * q^62 + 24 * q^63 - 4 * q^64 + 12 * q^66 - 16 * q^67 + 36 * q^69 + 24 * q^73 - 18 * q^74 - 6 * q^76 + 12 * q^77 + 24 * q^78 - 4 * q^79 - 2 * q^80 - 18 * q^81 - 12 * q^83 + 18 * q^86 - 18 * q^87 - 6 * q^88 - 12 * q^89 + 24 * q^91 + 12 * q^92 - 18 * q^93 - 6 * q^96 + 12 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$4$	−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
$8$			1.00000i			0.353553i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	−4.09808	+	2.36603i	−1.23562	+	0.713384i	−0.968195	−	0.250196i	$-0.919505\pi$
$11$	−4.09808	+	2.36603i	−1.23562	+	0.713384i	−0.267421	+	0.963580i	$0.586172\pi$
$12$	−0.866025	+	1.50000i	−0.250000	+	0.433013i
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	−0.854554	−	0.519362i	$-0.826170\pi$
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	0.0225039	+	0.999747i	$0.492836\pi$
$14$	0.866025	+	2.50000i	0.231455	+	0.668153i
$15$	0.866025	+	1.50000i	0.223607	+	0.387298i
$16$	1.00000			0.250000
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−2.59808	+	1.50000i	−0.612372	+	0.353553i
$19$	−1.09808	+	0.633975i	−0.251916	+	0.145444i	−0.620641	−	0.784095i	$-0.713128\pi$
$19$	−1.09808	+	0.633975i	−0.251916	+	0.145444i	0.368725	+	0.929538i	$0.379794\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−0.866025	+	4.50000i	−0.188982	+	0.981981i
$22$	2.36603	+	4.09808i	0.504438	+	0.873713i
$23$	2.19615	+	1.26795i	0.457929	+	0.264386i	0.711173	−	0.703017i	$-0.248164\pi$
$23$	2.19615	+	1.26795i	0.457929	+	0.264386i	−0.253244	+	0.967402i	$0.581497\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.73205	+	3.00000i	0.339683	+	0.588348i
$27$	−5.19615			−1.00000
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	−5.59808	−	3.23205i	−1.03954	−	0.600177i	−0.119835	−	0.992794i	$-0.538236\pi$
$29$	−5.59808	−	3.23205i	−1.03954	−	0.600177i	−0.919702	+	0.392617i	$0.871570\pi$
$30$	1.50000	−	0.866025i	0.273861	−	0.158114i
$31$		−	8.19615i		−	1.47207i	−0.676942	−	0.736036i	$-0.736695\pi$
$31$		−	8.19615i		−	1.47207i	0.676942	−	0.736036i	$-0.263305\pi$
$32$		−	1.00000i		−	0.176777i
$33$			8.19615i			1.42677i
$34$		0			0
$35$	0.500000	−	2.59808i	0.0845154	−	0.439155i
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	−3.09808	−	5.36603i	−0.509321	−	0.882169i	−0.999942	−	0.0107961i	$-0.996563\pi$
$37$	−3.09808	−	5.36603i	−0.509321	−	0.882169i	0.490621	−	0.871373i	$-0.336770\pi$
$38$	0.633975	+	1.09808i	0.102844	+	0.178131i
$39$			6.00000i			0.960769i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$	4.50000	+	0.866025i	0.694365	+	0.133631i
$43$	−1.59808	+	2.76795i	−0.243704	+	0.422108i	−0.961767	−	0.273871i	$-0.911696\pi$
$43$	−1.59808	+	2.76795i	−0.243704	+	0.422108i	0.718062	+	0.695979i	$0.245029\pi$
$44$	4.09808	−	2.36603i	0.617808	−	0.356692i
$45$	3.00000			0.447214
$46$	1.26795	−	2.19615i	0.186949	−	0.323805i
$47$	−9.00000			−1.31278			−0.656392	−	0.754420i	$-0.727918\pi$
$47$	−9.00000			−1.31278			−0.656392	+	0.754420i	$0.727918\pi$
$48$	0.866025	−	1.50000i	0.125000	−	0.216506i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$	3.00000	−	1.73205i	0.416025	−	0.240192i
$53$	6.29423	+	3.63397i	0.864579	+	0.499165i	0.865543	−	0.500835i	$-0.166974\pi$
$53$	6.29423	+	3.63397i	0.864579	+	0.499165i	−0.000964138		1.00000i	$0.500307\pi$
$54$			5.19615i			0.707107i
$55$		−	4.73205i		−	0.638070i
$56$	−0.866025	−	2.50000i	−0.115728	−	0.334077i
$57$			2.19615i			0.290887i
$58$	−3.23205	+	5.59808i	−0.424389	+	0.735063i
$59$	2.19615			0.285915			0.142957	−	0.989729i	$-0.454339\pi$
$59$	2.19615			0.285915			0.142957	+	0.989729i	$0.454339\pi$
$60$	−0.866025	−	1.50000i	−0.111803	−	0.193649i
$61$		−	12.9282i		−	1.65529i	−0.561254	−	0.827643i	$-0.689681\pi$
$61$		−	12.9282i		−	1.65529i	0.561254	−	0.827643i	$-0.310319\pi$
$62$	−8.19615			−1.04091
$63$	6.00000	+	5.19615i	0.755929	+	0.654654i
$64$	−1.00000			−0.125000
$65$		−	3.46410i		−	0.429669i
$66$	8.19615			1.00888
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	3.80385	−	2.19615i	0.457929	−	0.264386i
$70$	−2.59808	−	0.500000i	−0.310530	−	0.0597614i
$71$			4.73205i			0.561591i	0.959768	+	0.280796i	$0.0905983\pi$
$71$			4.73205i			0.561591i	−0.959768	+	0.280796i	$0.909402\pi$
$72$	2.59808	−	1.50000i	0.306186	−	0.176777i
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	0.808184	−	0.588930i	$-0.200451\pi$
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	−0.105937	+	0.994373i	$0.533784\pi$
$74$	−5.36603	+	3.09808i	−0.623788	+	0.360144i
$75$	−1.73205			−0.200000
$76$	1.09808	−	0.633975i	0.125958	−	0.0727219i
$77$	8.19615	−	9.46410i	0.934038	−	1.07853i
$78$	6.00000			0.679366
$79$	14.5885			1.64133			0.820665	−	0.571410i	$-0.193603\pi$
$79$	14.5885			1.64133			0.820665	+	0.571410i	$0.193603\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	7.79423	−	4.50000i	0.860729	−	0.496942i
$83$	−5.59808	+	9.69615i	−0.614469	+	1.06429i	0.376009	+	0.926616i	$0.377296\pi$
$83$	−5.59808	+	9.69615i	−0.614469	+	1.06429i	−0.990477	+	0.137675i	$0.956037\pi$
$84$	0.866025	−	4.50000i	0.0944911	−	0.490990i
$85$		0			0
$86$	2.76795	+	1.59808i	0.298476	+	0.172325i
$87$	−9.69615	+	5.59808i	−1.03954	+	0.600177i
$88$	−2.36603	−	4.09808i	−0.252219	−	0.436856i
$89$	2.19615	+	3.80385i	0.232792	+	0.403207i	0.958629	−	0.284660i	$-0.0918806\pi$
$89$	2.19615	+	3.80385i	0.232792	+	0.403207i	−0.725837	+	0.687867i	$0.758547\pi$
$90$		−	3.00000i		−	0.316228i
$91$	6.00000	−	6.92820i	0.628971	−	0.726273i
$92$	−2.19615	−	1.26795i	−0.228965	−	0.132193i
$93$	−12.2942	−	7.09808i	−1.27485	−	0.736036i
$94$			9.00000i			0.928279i
$95$		−	1.26795i		−	0.130089i
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	−7.39230	−	4.26795i	−0.750575	−	0.433345i	0.0753267	−	0.997159i	$-0.476000\pi$
$97$	−7.39230	−	4.26795i	−0.750575	−	0.433345i	−0.825902	+	0.563814i	$0.809333\pi$
$98$	−4.33013	−	5.50000i	−0.437409	−	0.555584i
$99$	12.2942	+	7.09808i	1.23562	+	0.713384i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−5.59808	−	9.69615i	−0.557029	−	0.964803i	−0.997743	−	0.0671552i	$-0.978608\pi$
$101$	−5.59808	−	9.69615i	−0.557029	−	0.964803i	0.440713	−	0.897648i	$-0.354726\pi$
$102$		0			0
$103$	−10.5000	−	6.06218i	−1.03460	−	0.597324i	−0.116298	−	0.993214i	$-0.537103\pi$
$103$	−10.5000	−	6.06218i	−1.03460	−	0.597324i	−0.918298	+	0.395890i	$0.870436\pi$
$104$	−1.73205	−	3.00000i	−0.169842	−	0.294174i
$105$	−3.46410	−	3.00000i	−0.338062	−	0.292770i
$106$	3.63397	−	6.29423i	0.352963	−	0.611350i
$107$	−13.7942	+	7.96410i	−1.33354	+	0.769919i	−0.985840	−	0.167688i	$-0.946370\pi$
$107$	−13.7942	+	7.96410i	−1.33354	+	0.769919i	−0.347698	+	0.937606i	$0.613037\pi$
$108$	5.19615			0.500000
$109$	3.59808	−	6.23205i	0.344633	−	0.596922i	−0.640654	−	0.767830i	$-0.721337\pi$
$109$	3.59808	−	6.23205i	0.344633	−	0.596922i	0.985287	+	0.170908i	$0.0546700\pi$
$110$	−4.73205			−0.451183
$111$	−10.7321			−1.01864
$112$	−2.50000	+	0.866025i	−0.236228	+	0.0818317i
$113$	−10.9019	+	6.29423i	−1.02557	+	0.592111i	−0.915711	−	0.401836i	$-0.868372\pi$
$113$	−10.9019	+	6.29423i	−1.02557	+	0.592111i	−0.109855	+	0.993948i	$0.535039\pi$
$114$	2.19615			0.205689
$115$	−2.19615	+	1.26795i	−0.204792	+	0.118237i
$116$	5.59808	+	3.23205i	0.519768	+	0.300088i
$117$	9.00000	+	5.19615i	0.832050	+	0.480384i
$118$		−	2.19615i		−	0.202172i
$119$		0			0
$120$	−1.50000	+	0.866025i	−0.136931	+	0.0790569i
$121$	5.69615	−	9.86603i	0.517832	−	0.896911i
$122$	−12.9282			−1.17046
$123$	15.5885			1.40556
$124$			8.19615i			0.736036i
$125$	1.00000			0.0894427
$126$	5.19615	−	6.00000i	0.462910	−	0.534522i
$127$	−11.3923			−1.01090			−0.505452	−	0.862855i	$-0.668674\pi$
$127$	−11.3923			−1.01090			−0.505452	+	0.862855i	$0.668674\pi$
$128$			1.00000i			0.0883883i
$129$	2.76795	+	4.79423i	0.243704	+	0.422108i
$130$	−3.46410			−0.303822
$131$	2.19615	−	3.80385i	0.191879	−	0.332344i	−0.753994	−	0.656881i	$-0.771875\pi$
$131$	2.19615	−	3.80385i	0.191879	−	0.332344i	0.945873	+	0.324537i	$0.105209\pi$
$132$		−	8.19615i		−	0.713384i
$133$	2.19615	−	2.53590i	0.190431	−	0.219890i
$134$			4.00000i			0.345547i
$135$	2.59808	−	4.50000i	0.223607	−	0.387298i
$136$		0			0
$137$	6.29423	−	3.63397i	0.537752	−	0.310471i	−0.206415	−	0.978464i	$-0.566180\pi$
$137$	6.29423	−	3.63397i	0.537752	−	0.310471i	0.744167	+	0.667993i	$0.232846\pi$
$138$	−2.19615	−	3.80385i	−0.186949	−	0.323805i
$139$	−19.0981	+	11.0263i	−1.61988	+	0.935237i	−0.632927	+	0.774211i	$0.718147\pi$
$139$	−19.0981	+	11.0263i	−1.61988	+	0.935237i	−0.986950	+	0.161026i	$0.948520\pi$
$140$	−0.500000	+	2.59808i	−0.0422577	+	0.219578i
$141$	−7.79423	+	13.5000i	−0.656392	+	1.13691i
$142$	4.73205			0.397105
$143$	8.19615	−	14.1962i	0.685397	−	1.18714i
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	5.59808	−	3.23205i	0.464895	−	0.268407i
$146$	3.46410	−	6.00000i	0.286691	−	0.496564i
$147$	−1.73205	−	12.0000i	−0.142857	−	0.989743i
$148$	3.09808	+	5.36603i	0.254660	+	0.441085i
$149$	10.3923	+	6.00000i	0.851371	+	0.491539i	0.861113	−	0.508413i	$-0.169768\pi$
$149$	10.3923	+	6.00000i	0.851371	+	0.491539i	−0.00974235	+	0.999953i	$0.503101\pi$
$150$			1.73205i			0.141421i
$151$	2.09808	+	3.63397i	0.170739	+	0.295729i	0.938678	−	0.344794i	$-0.112051\pi$
$151$	2.09808	+	3.63397i	0.170739	+	0.295729i	−0.767939	+	0.640522i	$0.778718\pi$
$152$	−0.633975	−	1.09808i	−0.0514221	−	0.0890657i
$153$		0			0
$154$	−9.46410	−	8.19615i	−0.762639	−	0.660465i
$155$	7.09808	+	4.09808i	0.570131	+	0.329165i
$156$		−	6.00000i		−	0.480384i
$157$		−	17.6603i		−	1.40944i	−0.709485	−	0.704721i	$-0.751072\pi$
$157$		−	17.6603i		−	1.40944i	0.709485	−	0.704721i	$-0.248928\pi$
$158$		−	14.5885i		−	1.16060i
$159$	10.9019	−	6.29423i	0.864579	−	0.499165i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	−6.58846	−	1.26795i	−0.519243	−	0.0999284i
$162$	7.79423	+	4.50000i	0.612372	+	0.353553i
$163$	4.19615	+	7.26795i	0.328668	+	0.569270i	0.982248	−	0.187588i	$-0.0600669\pi$
$163$	4.19615	+	7.26795i	0.328668	+	0.569270i	−0.653580	+	0.756858i	$0.726734\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$	−7.09808	−	4.09808i	−0.552584	−	0.319035i
$166$	9.69615	+	5.59808i	0.752567	+	0.434495i
$167$	−5.19615	−	9.00000i	−0.402090	−	0.696441i	0.591888	−	0.806020i	$-0.298383\pi$
$167$	−5.19615	−	9.00000i	−0.402090	−	0.696441i	−0.993978	+	0.109580i	$0.965050\pi$
$168$	−4.50000	−	0.866025i	−0.347183	−	0.0668153i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$	3.29423	+	1.90192i	0.251916	+	0.145444i
$172$	1.59808	−	2.76795i	0.121852	−	0.211054i
$173$	8.19615			0.623142			0.311571	−	0.950223i	$-0.399145\pi$
$173$	8.19615			0.623142			0.311571	+	0.950223i	$0.399145\pi$
$174$	5.59808	+	9.69615i	0.424389	+	0.735063i
$175$	2.00000	+	1.73205i	0.151186	+	0.130931i
$176$	−4.09808	+	2.36603i	−0.308904	+	0.178346i
$177$	1.90192	−	3.29423i	0.142957	−	0.247609i
$178$	3.80385	−	2.19615i	0.285110	−	0.164609i
$179$	−21.2942	−	12.2942i	−1.59161	−	0.918914i	−0.993032	−	0.117846i	$-0.962401\pi$
$179$	−21.2942	−	12.2942i	−1.59161	−	0.918914i	−0.598573	−	0.801068i	$-0.704266\pi$
$180$	−3.00000			−0.223607
$181$		−	13.3923i		−	0.995442i	−0.867337	−	0.497721i	$-0.834170\pi$
$181$		−	13.3923i		−	0.995442i	0.867337	−	0.497721i	$-0.165830\pi$
$182$	−6.92820	−	6.00000i	−0.513553	−	0.444750i
$183$	−19.3923	−	11.1962i	−1.43352	−	0.827643i
$184$	−1.26795	+	2.19615i	−0.0934745	+	0.161903i
$185$	6.19615			0.455550
$186$	−7.09808	+	12.2942i	−0.520456	+	0.901457i
$187$		0			0
$188$	9.00000			0.656392
$189$	12.9904	−	4.50000i	0.944911	−	0.327327i
$190$	−1.26795			−0.0919867
$191$			3.46410i			0.250654i	0.992116	+	0.125327i	$0.0399979\pi$
$191$			3.46410i			0.250654i	−0.992116	+	0.125327i	$0.960002\pi$
$192$	−0.866025	+	1.50000i	−0.0625000	+	0.108253i
$193$	13.8038			0.993623			0.496811	−	0.867859i	$-0.334504\pi$
$193$	13.8038			0.993623			0.496811	+	0.867859i	$0.334504\pi$
$194$	−4.26795	+	7.39230i	−0.306421	+	0.530737i
$195$	−5.19615	−	3.00000i	−0.372104	−	0.214834i
$196$	−5.50000	+	4.33013i	−0.392857	+	0.309295i
$197$			23.6603i			1.68572i	0.538130	+	0.842862i	$0.319131\pi$
$197$			23.6603i			1.68572i	−0.538130	+	0.842862i	$0.680869\pi$
$198$	7.09808	−	12.2942i	0.504438	−	0.873713i
$199$	6.00000	+	3.46410i	0.425329	+	0.245564i	0.697355	−	0.716726i	$-0.254360\pi$
$199$	6.00000	+	3.46410i	0.425329	+	0.245564i	−0.272026	+	0.962290i	$0.587694\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	−3.46410	+	6.00000i	−0.244339	+	0.423207i
$202$	−9.69615	+	5.59808i	−0.682219	+	0.393879i
$203$	16.7942	+	3.23205i	1.17872	+	0.226845i
$204$		0			0
$205$	−9.00000			−0.628587
$206$	−6.06218	+	10.5000i	−0.422372	+	0.731570i
$207$		−	7.60770i		−	0.528771i
$208$	−3.00000	+	1.73205i	−0.208013	+	0.120096i
$209$	3.00000	−	5.19615i	0.207514	−	0.359425i
$210$	−3.00000	+	3.46410i	−0.207020	+	0.239046i
$211$	10.2942	+	17.8301i	0.708684	+	1.22748i	0.965345	+	0.260975i	$0.0840441\pi$
$211$	10.2942	+	17.8301i	0.708684	+	1.22748i	−0.256662	+	0.966501i	$0.582623\pi$
$212$	−6.29423	−	3.63397i	−0.432289	−	0.249582i
$213$	7.09808	+	4.09808i	0.486352	+	0.280796i
$214$	7.96410	+	13.7942i	0.544415	+	0.942954i
$215$	−1.59808	−	2.76795i	−0.108988	−	0.188773i
$216$		−	5.19615i		−	0.353553i
$217$	7.09808	+	20.4904i	0.481849	+	1.39098i
$218$	−6.23205	−	3.59808i	−0.422088	−	0.243692i
$219$	10.3923	−	6.00000i	0.702247	−	0.405442i
$220$			4.73205i			0.319035i
$221$		0			0
$222$			10.7321i			0.720288i
$223$	−11.8923	−	6.86603i	−0.796368	−	0.459783i	0.0458318	−	0.998949i	$-0.485406\pi$
$223$	−11.8923	−	6.86603i	−0.796368	−	0.459783i	−0.842199	+	0.539166i	$0.818740\pi$
$224$	0.866025	+	2.50000i	0.0578638	+	0.167038i
$225$	−1.50000	+	2.59808i	−0.100000	+	0.173205i
$226$	6.29423	+	10.9019i	0.418686	+	0.725185i
$227$	−8.19615	−	14.1962i	−0.543998	−	0.942232i	−0.998669	−	0.0515725i	$-0.983577\pi$
$227$	−8.19615	−	14.1962i	−0.543998	−	0.942232i	0.454672	−	0.890659i	$-0.349757\pi$
$228$		−	2.19615i		−	0.145444i
$229$	−12.1865	−	7.03590i	−0.805309	−	0.464945i	0.0400153	−	0.999199i	$-0.487259\pi$
$229$	−12.1865	−	7.03590i	−0.805309	−	0.464945i	−0.845324	+	0.534254i	$0.820593\pi$
$230$	1.26795	+	2.19615i	0.0836061	+	0.144810i
$231$	−7.09808	−	20.4904i	−0.467019	−	1.34817i
$232$	3.23205	−	5.59808i	0.212195	−	0.367532i
$233$	−1.09808	+	0.633975i	−0.0719374	+	0.0415331i	−0.535537	−	0.844512i	$-0.679891\pi$
$233$	−1.09808	+	0.633975i	−0.0719374	+	0.0415331i	0.463600	+	0.886045i	$0.346558\pi$
$234$	5.19615	−	9.00000i	0.339683	−	0.588348i
$235$	4.50000	−	7.79423i	0.293548	−	0.508439i
$236$	−2.19615			−0.142957
$237$	12.6340	−	21.8827i	0.820665	−	1.42143i
$238$		0			0
$239$	2.70577	−	1.56218i	0.175022	−	0.101049i	−0.409930	−	0.912117i	$-0.634447\pi$
$239$	2.70577	−	1.56218i	0.175022	−	0.101049i	0.584952	+	0.811068i	$0.301113\pi$
$240$	0.866025	+	1.50000i	0.0559017	+	0.0968246i
$241$	2.89230	−	1.66987i	0.186310	−	0.107566i	−0.403944	−	0.914784i	$-0.632361\pi$
$241$	2.89230	−	1.66987i	0.186310	−	0.107566i	0.590254	+	0.807218i	$0.299028\pi$
$242$	−9.86603	−	5.69615i	−0.634212	−	0.366163i
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$			12.9282i			0.827643i
$245$	1.00000	+	6.92820i	0.0638877	+	0.442627i
$246$		−	15.5885i		−	0.993884i
$247$	2.19615	−	3.80385i	0.139738	−	0.242033i
$248$	8.19615			0.520456
$249$	9.69615	+	16.7942i	0.614469	+	1.06429i
$250$		−	1.00000i		−	0.0632456i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$	−6.00000	−	5.19615i	−0.377964	−	0.327327i
$253$	−12.0000			−0.754434
$254$			11.3923i			0.714817i
$255$		0			0
$256$	1.00000			0.0625000
$257$	14.1962	−	24.5885i	0.885532	−	1.53379i	0.0404286	−	0.999182i	$-0.487128\pi$
$257$	14.1962	−	24.5885i	0.885532	−	1.53379i	0.845103	−	0.534603i	$-0.179539\pi$
$258$	4.79423	−	2.76795i	0.298476	−	0.172325i
$259$	12.3923	+	10.7321i	0.770020	+	0.666857i
$260$			3.46410i			0.214834i
$261$			19.3923i			1.20035i
$262$	−3.80385	−	2.19615i	−0.235002	−	0.135679i
$263$	−11.8923	+	6.86603i	−0.733311	+	0.423377i	−0.819632	−	0.572890i	$-0.805822\pi$
$263$	−11.8923	+	6.86603i	−0.733311	+	0.423377i	0.0863213	+	0.996267i	$0.472489\pi$
$264$	−8.19615			−0.504438
$265$	−6.29423	+	3.63397i	−0.386651	+	0.223233i
$266$	−2.53590	−	2.19615i	−0.155486	−	0.134655i
$267$	7.60770			0.465583
$268$	4.00000			0.244339
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	−4.50000	−	2.59808i	−0.273861	−	0.158114i
$271$	5.70577	−	3.29423i	0.346601	−	0.200110i	−0.316586	−	0.948564i	$-0.602537\pi$
$271$	5.70577	−	3.29423i	0.346601	−	0.200110i	0.663187	+	0.748454i	$0.269203\pi$
$272$		0			0
$273$	−5.19615	−	15.0000i	−0.314485	−	0.907841i
$274$	−3.63397	−	6.29423i	−0.219536	−	0.380248i
$275$	4.09808	+	2.36603i	0.247123	+	0.142677i
$276$	−3.80385	+	2.19615i	−0.228965	+	0.132193i
$277$	12.0981	+	20.9545i	0.726903	+	1.25903i	0.958186	+	0.286146i	$0.0923743\pi$
$277$	12.0981	+	20.9545i	0.726903	+	1.25903i	−0.231283	+	0.972887i	$0.574292\pi$
$278$	11.0263	+	19.0981i	0.661312	+	1.14543i
$279$	−21.2942	+	12.2942i	−1.27485	+	0.736036i
$280$	2.59808	+	0.500000i	0.155265	+	0.0298807i
$281$	12.6962	+	7.33013i	0.757389	+	0.437279i	0.828357	−	0.560200i	$-0.189276\pi$
$281$	12.6962	+	7.33013i	0.757389	+	0.437279i	−0.0709685	+	0.997479i	$0.522609\pi$
$282$	13.5000	+	7.79423i	0.803913	+	0.464140i
$283$		−	16.8564i		−	1.00201i	−0.865445	−	0.501005i	$-0.832964\pi$
$283$		−	16.8564i		−	1.00201i	0.865445	−	0.501005i	$-0.167036\pi$
$284$		−	4.73205i		−	0.280796i
$285$	−1.90192	−	1.09808i	−0.112660	−	0.0650444i
$286$	−14.1962	−	8.19615i	−0.839436	−	0.484649i
$287$	−18.0000	−	15.5885i	−1.06251	−	0.920158i
$288$	−2.59808	+	1.50000i	−0.153093	+	0.0883883i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−3.23205	−	5.59808i	−0.189793	−	0.328730i
$291$	−12.8038	+	7.39230i	−0.750575	+	0.433345i
$292$	−6.00000	−	3.46410i	−0.351123	−	0.202721i
$293$	8.19615	+	14.1962i	0.478824	+	0.829348i	0.999705	−	0.0242813i	$-0.00772975\pi$
$293$	8.19615	+	14.1962i	0.478824	+	0.829348i	−0.520881	+	0.853629i	$0.674396\pi$
$294$	−12.0000	+	1.73205i	−0.699854	+	0.101015i
$295$	−1.09808	+	1.90192i	−0.0639325	+	0.110734i
$296$	5.36603	−	3.09808i	0.311894	−	0.180072i
$297$	21.2942	−	12.2942i	1.23562	−	0.713384i
$298$	6.00000	−	10.3923i	0.347571	−	0.602010i
$299$	−8.78461			−0.508027
$300$	1.73205			0.100000
$301$	1.59808	−	8.30385i	0.0921116	−	0.478626i
$302$	3.63397	−	2.09808i	0.209112	−	0.120731i
$303$	−19.3923			−1.11406
$304$	−1.09808	+	0.633975i	−0.0629790	+	0.0363609i
$305$	11.1962	+	6.46410i	0.641090	+	0.370133i
$306$		0			0
$307$			23.7846i			1.35746i	0.734388	+	0.678730i	$0.237469\pi$
$307$			23.7846i			1.35746i	−0.734388	+	0.678730i	$0.762531\pi$
$308$	−8.19615	+	9.46410i	−0.467019	+	0.539267i
$309$	−18.1865	+	10.5000i	−1.03460	+	0.597324i
$310$	4.09808	−	7.09808i	0.232755	−	0.403144i
$311$	−15.8038			−0.896154			−0.448077	−	0.893995i	$-0.647891\pi$
$311$	−15.8038			−0.896154			−0.448077	+	0.893995i	$0.647891\pi$
$312$	−6.00000			−0.339683
$313$			20.1962i			1.14155i	0.821105	+	0.570777i	$0.193358\pi$
$313$			20.1962i			1.14155i	−0.821105	+	0.570777i	$0.806642\pi$
$314$	−17.6603			−0.996626
$315$	−7.50000	+	2.59808i	−0.422577	+	0.146385i
$316$	−14.5885			−0.820665
$317$			20.5359i			1.15341i	0.816952	+	0.576705i	$0.195662\pi$
$317$			20.5359i			1.15341i	−0.816952	+	0.576705i	$0.804338\pi$
$318$	−6.29423	−	10.9019i	−0.352963	−	0.611350i
$319$	30.5885			1.71262
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$			27.5885i			1.53984i
$322$	−1.26795	+	6.58846i	−0.0706600	+	0.367160i
$323$		0			0
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	3.00000	+	1.73205i	0.166410	+	0.0960769i
$326$	7.26795	−	4.19615i	0.402534	−	0.232403i
$327$	−6.23205	−	10.7942i	−0.344633	−	0.596922i
$328$	−7.79423	+	4.50000i	−0.430364	+	0.248471i
$329$	22.5000	−	7.79423i	1.24047	−	0.429710i
$330$	−4.09808	+	7.09808i	−0.225592	+	0.390736i
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$	5.59808	−	9.69615i	0.307234	−	0.532145i
$333$	−9.29423	+	16.0981i	−0.509321	+	0.882169i
$334$	−9.00000	+	5.19615i	−0.492458	+	0.284321i
$335$	2.00000	−	3.46410i	0.109272	−	0.189264i
$336$	−0.866025	+	4.50000i	−0.0472456	+	0.245495i
$337$	−5.00000	−	8.66025i	−0.272367	−	0.471754i	0.697100	−	0.716974i	$-0.254473\pi$
$337$	−5.00000	−	8.66025i	−0.272367	−	0.471754i	−0.969468	+	0.245220i	$0.921140\pi$
$338$	0.866025	+	0.500000i	0.0471056	+	0.0271964i
$339$			21.8038i			1.18422i
$340$		0			0
$341$	19.3923	+	33.5885i	1.05015	+	1.81892i
$342$	1.90192	−	3.29423i	0.102844	−	0.178131i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−2.76795	−	1.59808i	−0.149238	−	0.0861625i
$345$			4.39230i			0.236474i
$346$		−	8.19615i		−	0.440628i
$347$		−	21.2487i		−	1.14069i	−0.821405	−	0.570345i	$-0.806809\pi$
$347$		−	21.2487i		−	1.14069i	0.821405	−	0.570345i	$-0.193191\pi$
$348$	9.69615	−	5.59808i	0.519768	−	0.300088i
$349$	−14.1962	−	8.19615i	−0.759903	−	0.438730i	0.0693582	−	0.997592i	$-0.477905\pi$
$349$	−14.1962	−	8.19615i	−0.759903	−	0.438730i	−0.829261	+	0.558862i	$0.811238\pi$
$350$	1.73205	−	2.00000i	0.0925820	−	0.106904i
$351$	15.5885	−	9.00000i	0.832050	−	0.480384i
$352$	2.36603	+	4.09808i	0.126110	+	0.218428i
$353$	−0.294229	−	0.509619i	−0.0156602	−	0.0271243i	0.858089	−	0.513501i	$-0.171652\pi$
$353$	−0.294229	−	0.509619i	−0.0156602	−	0.0271243i	−0.873749	+	0.486377i	$0.838318\pi$
$354$	−3.29423	−	1.90192i	−0.175086	−	0.101086i
$355$	−4.09808	−	2.36603i	−0.217503	−	0.125576i
$356$	−2.19615	−	3.80385i	−0.116396	−	0.201604i
$357$		0			0
$358$	−12.2942	+	21.2942i	−0.649770	+	1.12543i
$359$	13.6865	−	7.90192i	0.722348	−	0.417048i	−0.0932685	−	0.995641i	$-0.529732\pi$
$359$	13.6865	−	7.90192i	0.722348	−	0.417048i	0.815616	+	0.578593i	$0.196398\pi$
$360$			3.00000i			0.158114i
$361$	−8.69615	+	15.0622i	−0.457692	+	0.792746i
$362$	−13.3923			−0.703884
$363$	−9.86603	−	17.0885i	−0.517832	−	0.896911i
$364$	−6.00000	+	6.92820i	−0.314485	+	0.363137i
$365$	−6.00000	+	3.46410i	−0.314054	+	0.181319i
$366$	−11.1962	+	19.3923i	−0.585232	+	1.01365i
$367$	−25.2846	+	14.5981i	−1.31985	+	0.762013i	−0.983704	−	0.179798i	$-0.942456\pi$
$367$	−25.2846	+	14.5981i	−1.31985	+	0.762013i	−0.336142	+	0.941811i	$0.609122\pi$
$368$	2.19615	+	1.26795i	0.114482	+	0.0660964i
$369$	13.5000	−	23.3827i	0.702782	−	1.21725i
$370$		−	6.19615i		−	0.322123i
$371$	−18.8827	−	3.63397i	−0.980340	−	0.188667i
$372$	12.2942	+	7.09808i	0.637426	+	0.368018i
$373$	−5.09808	+	8.83013i	−0.263968	+	0.457207i	−0.967293	−	0.253662i	$-0.918365\pi$
$373$	−5.09808	+	8.83013i	−0.263968	+	0.457207i	0.703324	+	0.710869i	$0.251698\pi$
$374$		0			0
$375$	0.866025	−	1.50000i	0.0447214	−	0.0774597i
$376$		−	9.00000i		−	0.464140i
$377$	22.3923			1.15326
$378$	−4.50000	−	12.9904i	−0.231455	−	0.668153i
$379$	−9.60770			−0.493514			−0.246757	−	0.969077i	$-0.579365\pi$
$379$	−9.60770			−0.493514			−0.246757	+	0.969077i	$0.579365\pi$
$380$			1.26795i			0.0650444i
$381$	−9.86603	+	17.0885i	−0.505452	+	0.875468i
$382$	3.46410			0.177239
$383$	9.69615	−	16.7942i	0.495450	−	0.858145i	−0.504536	−	0.863391i	$-0.668336\pi$
$383$	9.69615	−	16.7942i	0.495450	−	0.858145i	0.999986	+	0.00524566i	$0.00166975\pi$
$384$	1.50000	+	0.866025i	0.0765466	+	0.0441942i
$385$	4.09808	+	11.8301i	0.208857	+	0.602919i
$386$		−	13.8038i		−	0.702597i
$387$	9.58846			0.487409
$388$	7.39230	+	4.26795i	0.375287	+	0.216672i
$389$	21.4019	−	12.3564i	1.08512	−	0.626495i	0.152847	−	0.988250i	$-0.451156\pi$
$389$	21.4019	−	12.3564i	1.08512	−	0.626495i	0.932273	+	0.361755i	$0.117822\pi$
$390$	−3.00000	+	5.19615i	−0.151911	+	0.263117i
$391$		0			0
$392$	4.33013	+	5.50000i	0.218704	+	0.277792i
$393$	−3.80385	−	6.58846i	−0.191879	−	0.332344i
$394$	23.6603			1.19199
$395$	−7.29423	+	12.6340i	−0.367012	+	0.635684i
$396$	−12.2942	−	7.09808i	−0.617808	−	0.356692i
$397$	−26.4904	+	15.2942i	−1.32951	+	0.767595i	−0.985224	−	0.171268i	$-0.945214\pi$
$397$	−26.4904	+	15.2942i	−1.32951	+	0.767595i	−0.344290	+	0.938863i	$0.611880\pi$
$398$	3.46410	−	6.00000i	0.173640	−	0.300753i
$399$	−1.90192	−	5.49038i	−0.0952153	−	0.274863i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	3.10770	+	1.79423i	0.155191	+	0.0895995i	0.575584	−	0.817742i	$-0.304775\pi$
$401$	3.10770	+	1.79423i	0.155191	+	0.0895995i	−0.420393	+	0.907342i	$0.638108\pi$
$402$	6.00000	+	3.46410i	0.299253	+	0.172774i
$403$	14.1962	+	24.5885i	0.707161	+	1.22484i
$404$	5.59808	+	9.69615i	0.278515	+	0.482402i
$405$	−4.50000	−	7.79423i	−0.223607	−	0.387298i
$406$	3.23205	−	16.7942i	0.160404	−	0.833484i
$407$	25.3923	+	14.6603i	1.25865	+	0.726682i
$408$		0			0
$409$		−	10.5167i		−	0.520015i	−0.965607	−	0.260008i	$-0.916275\pi$
$409$		−	10.5167i		−	0.520015i	0.965607	−	0.260008i	$-0.0837251\pi$
$410$			9.00000i			0.444478i
$411$		−	12.5885i		−	0.620943i
$412$	10.5000	+	6.06218i	0.517298	+	0.298662i
$413$	−5.49038	+	1.90192i	−0.270164	+	0.0935876i
$414$	−7.60770			−0.373898
$415$	−5.59808	−	9.69615i	−0.274799	−	0.475965i
$416$	1.73205	+	3.00000i	0.0849208	+	0.147087i
$417$			38.1962i			1.87047i
$418$	−5.19615	−	3.00000i	−0.254152	−	0.146735i
$419$	−5.19615	−	9.00000i	−0.253849	−	0.439679i	0.710734	−	0.703461i	$-0.248363\pi$
$419$	−5.19615	−	9.00000i	−0.253849	−	0.439679i	−0.964582	+	0.263783i	$0.915030\pi$
$420$	3.46410	+	3.00000i	0.169031	+	0.146385i
$421$	14.9904	−	25.9641i	0.730586	−	1.26541i	−0.226046	−	0.974117i	$-0.572580\pi$
$421$	14.9904	−	25.9641i	0.730586	−	1.26541i	0.956633	−	0.291296i	$-0.0940866\pi$
$422$	17.8301	−	10.2942i	0.867957	−	0.501115i
$423$	13.5000	+	23.3827i	0.656392	+	1.13691i
$424$	−3.63397	+	6.29423i	−0.176481	+	0.305675i
$425$		0			0
$426$	4.09808	−	7.09808i	0.198552	−	0.343903i
$427$	11.1962	+	32.3205i	0.541820	+	1.56410i
$428$	13.7942	−	7.96410i	0.666769	−	0.384959i
$429$	−14.1962	−	24.5885i	−0.685397	−	1.18714i
$430$	−2.76795	+	1.59808i	−0.133482	+	0.0770661i
$431$	33.5885	+	19.3923i	1.61790	+	0.934094i	0.987463	+	0.157854i	$0.0504574\pi$
$431$	33.5885	+	19.3923i	1.61790	+	0.934094i	0.630437	+	0.776241i	$0.282876\pi$
$432$	−5.19615			−0.250000
$433$		−	18.0000i		−	0.865025i	−0.901628	−	0.432512i	$-0.857627\pi$
$433$		−	18.0000i		−	0.865025i	0.901628	−	0.432512i	$-0.142373\pi$
$434$	20.4904	−	7.09808i	0.983570	−	0.340719i
$435$		−	11.1962i		−	0.536814i
$436$	−3.59808	+	6.23205i	−0.172317	+	0.298461i
$437$	−3.21539			−0.153813
$438$	−6.00000	−	10.3923i	−0.286691	−	0.496564i
$439$		−	29.6603i		−	1.41561i	−0.706410	−	0.707803i	$-0.749686\pi$
$439$		−	29.6603i		−	1.41561i	0.706410	−	0.707803i	$-0.250314\pi$
$440$	4.73205			0.225592
$441$	−19.5000	−	7.79423i	−0.928571	−	0.371154i
$442$		0			0
$443$			9.00000i			0.427603i	0.976877	+	0.213801i	$0.0685846\pi$
$443$			9.00000i			0.427603i	−0.976877	+	0.213801i	$0.931415\pi$
$444$	10.7321			0.509321
$445$	−4.39230			−0.208215
$446$	−6.86603	+	11.8923i	−0.325116	+	0.563117i
$447$	18.0000	−	10.3923i	0.851371	−	0.491539i
$448$	2.50000	−	0.866025i	0.118114	−	0.0409159i
$449$		−	9.58846i		−	0.452507i	−0.974068	−	0.226254i	$-0.927352\pi$
$449$		−	9.58846i		−	0.452507i	0.974068	−	0.226254i	$-0.0726478\pi$
$450$	2.59808	+	1.50000i	0.122474	+	0.0707107i
$451$	−36.8827	−	21.2942i	−1.73674	−	1.00271i
$452$	10.9019	−	6.29423i	0.512783	−	0.296056i
$453$	7.26795			0.341478
$454$	−14.1962	+	8.19615i	−0.666258	+	0.384664i
$455$	3.00000	+	8.66025i	0.140642	+	0.405999i
$456$	−2.19615			−0.102844
$457$	2.39230			0.111907			0.0559537	−	0.998433i	$-0.482180\pi$
$457$	2.39230			0.111907			0.0559537	+	0.998433i	$0.482180\pi$
$458$	−7.03590	+	12.1865i	−0.328766	+	0.569439i
$459$		0			0
$460$	2.19615	−	1.26795i	0.102396	−	0.0591184i
$461$	2.59808	−	4.50000i	0.121004	−	0.209586i	−0.799160	−	0.601119i	$-0.794722\pi$
$461$	2.59808	−	4.50000i	0.121004	−	0.209586i	0.920164	+	0.391533i	$0.128055\pi$
$462$	−20.4904	+	7.09808i	−0.953299	+	0.330232i
$463$	1.30385	+	2.25833i	0.0605949	+	0.104954i	0.894731	−	0.446604i	$-0.147367\pi$
$463$	1.30385	+	2.25833i	0.0605949	+	0.104954i	−0.834137	+	0.551558i	$0.814034\pi$
$464$	−5.59808	−	3.23205i	−0.259884	−	0.150044i
$465$	12.2942	−	7.09808i	0.570131	−	0.329165i
$466$	0.633975	+	1.09808i	0.0293683	+	0.0508674i
$467$	−3.40192	−	5.89230i	−0.157422	−	0.272663i	0.776516	−	0.630097i	$-0.216985\pi$
$467$	−3.40192	−	5.89230i	−0.157422	−	0.272663i	−0.933938	+	0.357434i	$0.883652\pi$
$468$	−9.00000	−	5.19615i	−0.416025	−	0.240192i
$469$	10.0000	−	3.46410i	0.461757	−	0.159957i
$470$	−7.79423	−	4.50000i	−0.359521	−	0.207570i
$471$	−26.4904	−	15.2942i	−1.22061	−	0.704721i
$472$			2.19615i			0.101086i
$473$		−	15.1244i		−	0.695419i
$474$	−21.8827	−	12.6340i	−1.00511	−	0.580298i
$475$	1.09808	+	0.633975i	0.0503832	+	0.0290887i
$476$		0			0
$477$		−	21.8038i		−	0.998330i
$478$	−1.56218	−	2.70577i	−0.0714524	−	0.123759i
$479$	−5.19615	−	9.00000i	−0.237418	−	0.411220i	0.722554	−	0.691314i	$-0.242968\pi$
$479$	−5.19615	−	9.00000i	−0.237418	−	0.411220i	−0.959973	+	0.280094i	$0.909635\pi$
$480$	1.50000	−	0.866025i	0.0684653	−	0.0395285i
$481$	18.5885	+	10.7321i	0.847561	+	0.489339i
$482$	−1.66987	−	2.89230i	−0.0760606	−	0.131741i
$483$	−7.60770	+	8.78461i	−0.346162	+	0.399714i
$484$	−5.69615	+	9.86603i	−0.258916	+	0.448456i
$485$	7.39230	−	4.26795i	0.335667	−	0.193798i
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$	−17.0000	+	29.4449i	−0.770344	+	1.33427i	0.167031	+	0.985952i	$0.446582\pi$
$487$	−17.0000	+	29.4449i	−0.770344	+	1.33427i	−0.937375	+	0.348323i	$0.886751\pi$
$488$	12.9282			0.585232
$489$	14.5359			0.657336
$490$	6.92820	−	1.00000i	0.312984	−	0.0451754i
$491$	−23.4904	+	13.5622i	−1.06011	+	0.612053i	−0.925462	−	0.378841i	$-0.876323\pi$
$491$	−23.4904	+	13.5622i	−1.06011	+	0.612053i	−0.134644	+	0.990894i	$0.542989\pi$
$492$	−15.5885			−0.702782
$493$		0			0
$494$	−3.80385	−	2.19615i	−0.171143	−	0.0988096i
$495$	−12.2942	+	7.09808i	−0.552584	+	0.319035i
$496$		−	8.19615i		−	0.368018i
$497$	−4.09808	−	11.8301i	−0.183824	−	0.530654i
$498$	16.7942	−	9.69615i	0.752567	−	0.434495i
$499$	8.09808	−	14.0263i	0.362520	−	0.627903i	−0.625855	−	0.779939i	$-0.715250\pi$
$499$	8.09808	−	14.0263i	0.362520	−	0.627903i	0.988375	+	0.152037i	$0.0485832\pi$
$500$	−1.00000			−0.0447214
$501$	−18.0000			−0.804181
$502$		−	18.0000i		−	0.803379i
$503$	7.39230			0.329607			0.164803	−	0.986326i	$-0.447301\pi$
$503$	7.39230			0.329607			0.164803	+	0.986326i	$0.447301\pi$
$504$	−5.19615	+	6.00000i	−0.231455	+	0.267261i
$505$	11.1962			0.498222
$506$			12.0000i			0.533465i
$507$	0.866025	+	1.50000i	0.0384615	+	0.0666173i
$508$	11.3923			0.505452
$509$	4.79423	−	8.30385i	0.212500	−	0.368062i	−0.739996	−	0.672611i	$-0.765173\pi$
$509$	4.79423	−	8.30385i	0.212500	−	0.368062i	0.952496	+	0.304550i	$0.0985060\pi$
$510$		0			0
$511$	−18.0000	−	3.46410i	−0.796273	−	0.153243i
$512$		−	1.00000i		−	0.0441942i
$513$	5.70577	−	3.29423i	0.251916	−	0.145444i
$514$	−24.5885	−	14.1962i	−1.08455	−	0.626165i
$515$	10.5000	−	6.06218i	0.462685	−	0.267131i
$516$	−2.76795	−	4.79423i	−0.121852	−	0.211054i
$517$	36.8827	−	21.2942i	1.62210	−	0.936519i
$518$	10.7321	−	12.3923i	0.471539	−	0.544487i
$519$	7.09808	−	12.2942i	0.311571	−	0.539657i
$520$	3.46410			0.151911
$521$	−10.5000	+	18.1865i	−0.460013	+	0.796766i	−0.998961	−	0.0455727i	$-0.985489\pi$
$521$	−10.5000	+	18.1865i	−0.460013	+	0.796766i	0.538948	+	0.842339i	$0.318822\pi$
$522$	19.3923			0.848778
$523$	28.5788	−	16.5000i	1.24967	−	0.721495i	0.278623	−	0.960401i	$-0.410122\pi$
$523$	28.5788	−	16.5000i	1.24967	−	0.721495i	0.971043	+	0.238906i	$0.0767888\pi$
$524$	−2.19615	+	3.80385i	−0.0959394	+	0.166172i
$525$	4.33013	−	1.50000i	0.188982	−	0.0654654i
$526$	6.86603	+	11.8923i	0.299373	+	0.518529i
$527$		0			0
$528$			8.19615i			0.356692i
$529$	−8.28461	−	14.3494i	−0.360200	−	0.623885i
$530$	3.63397	+	6.29423i	0.157850	+	0.273404i
$531$	−3.29423	−	5.70577i	−0.142957	−	0.247609i
$532$	−2.19615	+	2.53590i	−0.0952153	+	0.109945i
$533$	−27.0000	−	15.5885i	−1.16950	−	0.675211i
$534$		−	7.60770i		−	0.329217i
$535$		−	15.9282i		−	0.688636i
$536$		−	4.00000i		−	0.172774i
$537$	−36.8827	+	21.2942i	−1.59161	+	0.918914i
$538$	15.5885	+	9.00000i	0.672066	+	0.388018i
$539$	−12.2942	+	30.7583i	−0.529550	+	1.32486i
$540$	−2.59808	+	4.50000i	−0.111803	+	0.193649i
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	−3.29423	−	5.70577i	−0.141499	−	0.245084i
$543$	−20.0885	−	11.5981i	−0.862078	−	0.497721i
$544$		0			0
$545$	3.59808	+	6.23205i	0.154125	+	0.266952i
$546$	−15.0000	+	5.19615i	−0.641941	+	0.222375i
$547$	−2.79423	+	4.83975i	−0.119473	+	0.206933i	−0.919559	−	0.392952i	$-0.871454\pi$
$547$	−2.79423	+	4.83975i	−0.119473	+	0.206933i	0.800086	+	0.599885i	$0.204787\pi$
$548$	−6.29423	+	3.63397i	−0.268876	+	0.155236i
$549$	−33.5885	+	19.3923i	−1.43352	+	0.827643i
$550$	2.36603	−	4.09808i	0.100888	−	0.174743i
$551$	8.19615			0.349168
$552$	2.19615	+	3.80385i	0.0934745	+	0.161903i
$553$	−36.4711	+	12.6340i	−1.55091	+	0.537251i
$554$	20.9545	−	12.0981i	0.890271	−	0.513998i
$555$	5.36603	−	9.29423i	0.227775	−	0.394518i
$556$	19.0981	−	11.0263i	0.809939	−	0.467618i
$557$	−28.3923	−	16.3923i	−1.20302	−	0.694564i	−0.241795	−	0.970327i	$-0.577736\pi$
$557$	−28.3923	−	16.3923i	−1.20302	−	0.694564i	−0.961226	+	0.275763i	$0.911069\pi$
$558$	12.2942	+	21.2942i	0.520456	+	0.901457i
$559$		−	11.0718i		−	0.468287i
$560$	0.500000	−	2.59808i	0.0211289	−	0.109789i
$561$		0			0
$562$	7.33013	−	12.6962i	0.309203	−	0.535555i
$563$	−13.6077			−0.573496			−0.286748	−	0.958006i	$-0.592574\pi$
$563$	−13.6077			−0.573496			−0.286748	+	0.958006i	$0.592574\pi$
$564$	7.79423	−	13.5000i	0.328196	−	0.568453i
$565$		−	12.5885i		−	0.529600i
$566$	−16.8564			−0.708528
$567$	4.50000	−	23.3827i	0.188982	−	0.981981i
$568$	−4.73205			−0.198552
$569$		−	6.00000i		−	0.251533i	−0.992060	−	0.125767i	$-0.959861\pi$
$569$		−	6.00000i		−	0.251533i	0.992060	−	0.125767i	$-0.0401390\pi$
$570$	−1.09808	+	1.90192i	−0.0459934	+	0.0796628i
$571$	21.6077			0.904254			0.452127	−	0.891954i	$-0.350665\pi$
$571$	21.6077			0.904254			0.452127	+	0.891954i	$0.350665\pi$
$572$	−8.19615	+	14.1962i	−0.342698	+	0.593571i
$573$	5.19615	+	3.00000i	0.217072	+	0.125327i
$574$	−15.5885	+	18.0000i	−0.650650	+	0.751305i
$575$		−	2.53590i		−	0.105754i
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	20.7846	+	12.0000i	0.865275	+	0.499567i	0.865775	−	0.500433i	$-0.166826\pi$
$577$	20.7846	+	12.0000i	0.865275	+	0.499567i	−0.000500448		1.00000i	$0.500159\pi$
$578$	14.7224	−	8.50000i	0.612372	−	0.353553i
$579$	11.9545	−	20.7058i	0.496811	−	0.860502i
$580$	−5.59808	+	3.23205i	−0.232447	+	0.134204i
$581$	5.59808	−	29.0885i	0.232247	−	1.20679i
$582$	7.39230	+	12.8038i	0.306421	+	0.530737i
$583$	−34.3923			−1.42438
$584$	−3.46410	+	6.00000i	−0.143346	+	0.248282i
$585$	−9.00000	+	5.19615i	−0.372104	+	0.214834i
$586$	14.1962	−	8.19615i	0.586438	−	0.338580i
$587$	−15.4019	+	26.6769i	−0.635705	+	1.10107i	0.350660	+	0.936503i	$0.385957\pi$
$587$	−15.4019	+	26.6769i	−0.635705	+	1.10107i	−0.986365	+	0.164571i	$0.947376\pi$
$588$	1.73205	+	12.0000i	0.0714286	+	0.494872i
$589$	5.19615	+	9.00000i	0.214104	+	0.370839i
$590$	1.90192	+	1.09808i	0.0783010	+	0.0452071i
$591$	35.4904	+	20.4904i	1.45988	+	0.842862i
$592$	−3.09808	−	5.36603i	−0.127330	−	0.220542i
$593$	13.3923	+	23.1962i	0.549956	+	0.952552i	0.998277	+	0.0586791i	$0.0186889\pi$
$593$	13.3923	+	23.1962i	0.549956	+	0.952552i	−0.448321	+	0.893873i	$0.647978\pi$
$594$	−12.2942	−	21.2942i	−0.504438	−	0.873713i
$595$		0			0
$596$	−10.3923	−	6.00000i	−0.425685	−	0.245770i
$597$	10.3923	−	6.00000i	0.425329	−	0.245564i
$598$			8.78461i			0.359229i
$599$		−	4.39230i		−	0.179465i	−0.995966	−	0.0897324i	$-0.971399\pi$
$599$		−	4.39230i		−	0.179465i	0.995966	−	0.0897324i	$-0.0286012\pi$
$600$		−	1.73205i		−	0.0707107i
$601$	−27.5885	−	15.9282i	−1.12536	−	0.649725i	−0.182594	−	0.983188i	$-0.558449\pi$
$601$	−27.5885	−	15.9282i	−1.12536	−	0.649725i	−0.942763	+	0.333464i	$0.891783\pi$
$602$	−8.30385	−	1.59808i	−0.338440	−	0.0651327i
$603$	6.00000	+	10.3923i	0.244339	+	0.423207i
$604$	−2.09808	−	3.63397i	−0.0853695	−	0.147864i
$605$	5.69615	+	9.86603i	0.231582	+	0.401111i
$606$			19.3923i			0.787759i
$607$	−5.30385	−	3.06218i	−0.215277	−	0.124290i	0.388485	−	0.921455i	$-0.372999\pi$
$607$	−5.30385	−	3.06218i	−0.215277	−	0.124290i	−0.603761	+	0.797165i	$0.706332\pi$
$608$	0.633975	+	1.09808i	0.0257111	+	0.0445329i
$609$	19.3923	−	22.3923i	0.785816	−	0.907382i
$610$	6.46410	−	11.1962i	0.261724	−	0.453319i
$611$	27.0000	−	15.5885i	1.09230	−	0.630641i
$612$		0			0
$613$	3.39230	−	5.87564i	0.137014	−	0.237315i	−0.789351	−	0.613942i	$-0.789583\pi$
$613$	3.39230	−	5.87564i	0.137014	−	0.237315i	0.926365	+	0.376627i	$0.122916\pi$
$614$	23.7846			0.959869
$615$	−7.79423	+	13.5000i	−0.314294	+	0.544373i
$616$	9.46410	+	8.19615i	0.381320	+	0.330232i
$617$	15.8038	−	9.12436i	0.636239	−	0.367333i	−0.146925	−	0.989148i	$-0.546938\pi$
$617$	15.8038	−	9.12436i	0.636239	−	0.367333i	0.783164	+	0.621815i	$0.213604\pi$
$618$	10.5000	+	18.1865i	0.422372	+	0.731570i
$619$	14.1962	−	8.19615i	0.570592	−	0.329431i	−0.186794	−	0.982399i	$-0.559810\pi$
$619$	14.1962	−	8.19615i	0.570592	−	0.329431i	0.757386	+	0.652968i	$0.226476\pi$
$620$	−7.09808	−	4.09808i	−0.285066	−	0.164583i
$621$	−11.4115	−	6.58846i	−0.457929	−	0.264386i
$622$			15.8038i			0.633677i
$623$	−8.78461	−	7.60770i	−0.351948	−	0.304796i
$624$			6.00000i			0.240192i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	20.1962			0.807201
$627$	−5.19615	−	9.00000i	−0.207514	−	0.359425i
$628$			17.6603i			0.704721i
$629$		0			0
$630$	2.59808	+	7.50000i	0.103510	+	0.298807i
$631$	12.3923			0.493330			0.246665	−	0.969101i	$-0.420665\pi$
$631$	12.3923			0.493330			0.246665	+	0.969101i	$0.420665\pi$
$632$			14.5885i			0.580298i
$633$	35.6603			1.41737
$634$	20.5359			0.815585
$635$	5.69615	−	9.86603i	0.226045	−	0.391521i
$636$	−10.9019	+	6.29423i	−0.432289	+	0.249582i
$637$	−9.00000	+	22.5167i	−0.356593	+	0.892143i
$638$		−	30.5885i		−	1.21101i
$639$	12.2942	−	7.09808i	0.486352	−	0.280796i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	2.78461	−	1.60770i	0.109985	−	0.0635001i	−0.443998	−	0.896028i	$-0.646440\pi$
$641$	2.78461	−	1.60770i	0.109985	−	0.0635001i	0.553984	+	0.832528i	$0.313107\pi$
$642$	27.5885			1.08883
$643$	−16.2058	+	9.35641i	−0.639093	+	0.368981i	−0.784265	−	0.620426i	$-0.786960\pi$
$643$	−16.2058	+	9.35641i	−0.639093	+	0.368981i	0.145172	+	0.989406i	$0.453626\pi$
$644$	6.58846	+	1.26795i	0.259622	+	0.0499642i
$645$	−5.53590			−0.217976
$646$		0			0
$647$	−2.30385	+	3.99038i	−0.0905736	+	0.156878i	−0.907753	−	0.419506i	$-0.862203\pi$
$647$	−2.30385	+	3.99038i	−0.0905736	+	0.156878i	0.817179	+	0.576384i	$0.195537\pi$
$648$	−7.79423	−	4.50000i	−0.306186	−	0.176777i
$649$	−9.00000	+	5.19615i	−0.353281	+	0.203967i
$650$	1.73205	−	3.00000i	0.0679366	−	0.117670i
$651$	36.8827	+	7.09808i	1.44555	+	0.278196i
$652$	−4.19615	−	7.26795i	−0.164334	−	0.284635i
$653$	−43.1769	−	24.9282i	−1.68964	−	0.975516i	−0.954786	−	0.297294i	$-0.903916\pi$
$653$	−43.1769	−	24.9282i	−1.68964	−	0.975516i	−0.734857	−	0.678222i	$-0.762751\pi$
$654$	−10.7942	+	6.23205i	−0.422088	+	0.243692i
$655$	2.19615	+	3.80385i	0.0858108	+	0.148629i
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$		−	20.7846i		−	0.810885i
$658$	−7.79423	−	22.5000i	−0.303851	−	0.877141i
$659$	−33.2942	−	19.2224i	−1.29696	−	0.748800i	−0.317081	−	0.948398i	$-0.602703\pi$
$659$	−33.2942	−	19.2224i	−1.29696	−	0.748800i	−0.979878	+	0.199599i	$0.936036\pi$
$660$	7.09808	+	4.09808i	0.276292	+	0.159517i
$661$			13.1436i			0.511227i	0.966779	+	0.255613i	$0.0822774\pi$
$661$			13.1436i			0.511227i	−0.966779	+	0.255613i	$0.917723\pi$
$662$			8.00000i			0.310929i
$663$		0			0
$664$	−9.69615	−	5.59808i	−0.376284	−	0.217247i
$665$	1.09808	+	3.16987i	0.0425816	+	0.122922i
$666$	16.0981	+	9.29423i	0.623788	+	0.360144i
$667$	−8.19615	−	14.1962i	−0.317356	−	0.549677i
$668$	5.19615	+	9.00000i	0.201045	+	0.348220i
$669$	−20.5981	+	11.8923i	−0.796368	+	0.459783i
$670$	−3.46410	−	2.00000i	−0.133830	−	0.0772667i
$671$	30.5885	+	52.9808i	1.18085	+	2.04530i
$672$	4.50000	+	0.866025i	0.173591	+	0.0334077i
$673$	12.4904	−	21.6340i	0.481469	−	0.833928i	−0.518305	−	0.855196i	$-0.673437\pi$
$673$	12.4904	−	21.6340i	0.481469	−	0.833928i	0.999774	+	0.0212674i	$0.00677013\pi$
$674$	−8.66025	+	5.00000i	−0.333581	+	0.192593i
$675$	2.59808	+	4.50000i	0.100000	+	0.173205i
$676$	0.500000	−	0.866025i	0.0192308	−	0.0333087i
$677$	22.9808			0.883222			0.441611	−	0.897207i	$-0.354407\pi$
$677$	22.9808			0.883222			0.441611	+	0.897207i	$0.354407\pi$
$678$	21.8038			0.837372
$679$	22.1769	+	4.26795i	0.851072	+	0.163789i
$680$		0			0
$681$	−28.3923			−1.08800
$682$	33.5885	−	19.3923i	1.28617	−	0.742570i
$683$	−30.7750	−	17.7679i	−1.17757	−	0.679872i	−0.222121	−	0.975019i	$-0.571298\pi$
$683$	−30.7750	−	17.7679i	−1.17757	−	0.679872i	−0.955452	+	0.295148i	$0.904631\pi$
$684$	−3.29423	−	1.90192i	−0.125958	−	0.0727219i
$685$			7.26795i			0.277694i
$686$	15.5885	+	10.0000i	0.595170	+	0.381802i
$687$	−21.1077	+	12.1865i	−0.805309	+	0.464945i
$688$	−1.59808	+	2.76795i	−0.0609261	+	0.105527i
$689$	−25.1769			−0.959164
$690$	4.39230			0.167212
$691$			5.07180i			0.192940i	0.995336	+	0.0964701i	$0.0307552\pi$
$691$			5.07180i			0.192940i	−0.995336	+	0.0964701i	$0.969245\pi$
$692$	−8.19615			−0.311571
$693$	−36.8827	−	7.09808i	−1.40106	−	0.269634i
$694$	−21.2487			−0.806590
$695$		−	22.0526i		−	0.836501i
$696$	−5.59808	−	9.69615i	−0.212195	−	0.367532i
$697$		0			0
$698$	−8.19615	+	14.1962i	−0.310229	+	0.537332i
$699$			2.19615i			0.0830661i
$700$	−2.00000	−	1.73205i	−0.0755929	−	0.0654654i
$701$		−	44.3205i		−	1.67396i	−0.547232	−	0.836981i	$-0.684318\pi$
$701$		−	44.3205i		−	1.67396i	0.547232	−	0.836981i	$-0.315682\pi$
$702$	−9.00000	−	15.5885i	−0.339683	−	0.588348i
$703$	6.80385	+	3.92820i	0.256612	+	0.148155i
$704$	4.09808	−	2.36603i	0.154452	−	0.0891729i
$705$	−7.79423	−	13.5000i	−0.293548	−	0.508439i
$706$	−0.509619	+	0.294229i	−0.0191798	+	0.0110734i
$707$	22.3923	+	19.3923i	0.842149	+	0.729323i
$708$	−1.90192	+	3.29423i	−0.0714787	+	0.123805i
$709$	−46.7846			−1.75703			−0.878516	−	0.477712i	$-0.841466\pi$
$709$	−46.7846			−1.75703			−0.878516	+	0.477712i	$0.841466\pi$
$710$	−2.36603	+	4.09808i	−0.0887954	+	0.153798i
$711$	−21.8827	−	37.9019i	−0.820665	−	1.42143i
$712$	−3.80385	+	2.19615i	−0.142555	+	0.0823043i
$713$	10.3923	−	18.0000i	0.389195	−	0.674105i
$714$		0			0
$715$	8.19615	+	14.1962i	0.306519	+	0.530906i
$716$	21.2942	+	12.2942i	0.795803	+	0.459457i
$717$		−	5.41154i		−	0.202098i
$718$	−7.90192	−	13.6865i	−0.294897	−	0.510777i
$719$	−20.7846	−	36.0000i	−0.775135	−	1.34257i	−0.934718	−	0.355389i	$-0.884348\pi$
$719$	−20.7846	−	36.0000i	−0.775135	−	1.34257i	0.159583	−	0.987184i	$-0.448985\pi$
$720$	3.00000			0.111803
$721$	31.5000	+	6.06218i	1.17312	+	0.225767i
$722$	15.0622	+	8.69615i	0.560556	+	0.323637i
$723$		−	5.78461i		−	0.215132i
$724$			13.3923i			0.497721i
$725$			6.46410i			0.240071i
$726$	−17.0885	+	9.86603i	−0.634212	+	0.366163i
$727$	41.7846	+	24.1244i	1.54971	+	0.894723i	0.998164	+	0.0605756i	$0.0192936\pi$
$727$	41.7846	+	24.1244i	1.54971	+	0.894723i	0.551542	+	0.834147i	$0.314040\pi$
$728$	6.92820	+	6.00000i	0.256776	+	0.222375i
$729$	27.0000			1.00000
$730$	3.46410	+	6.00000i	0.128212	+	0.222070i
$731$		0			0
$732$	19.3923	+	11.1962i	0.716760	+	0.413822i
$733$	−29.4904	−	17.0263i	−1.08925	−	0.628880i	−0.155875	−	0.987777i	$-0.549820\pi$
$733$	−29.4904	−	17.0263i	−1.08925	−	0.628880i	−0.933377	+	0.358897i	$0.883153\pi$
$734$	14.5981	+	25.2846i	0.538825	+	0.933272i
$735$	11.2583	+	4.50000i	0.415270	+	0.165985i
$736$	1.26795	−	2.19615i	0.0467372	−	0.0809513i
$737$	16.3923	−	9.46410i	0.603818	−	0.348615i
$738$	−23.3827	−	13.5000i	−0.860729	−	0.496942i
$739$	−16.5885	+	28.7321i	−0.610216	+	1.05693i	0.380987	+	0.924580i	$0.375584\pi$
$739$	−16.5885	+	28.7321i	−0.610216	+	1.05693i	−0.991204	+	0.132345i	$0.957749\pi$
$740$	−6.19615			−0.227775
$741$	−3.80385	−	6.58846i	−0.139738	−	0.242033i
$742$	−3.63397	+	18.8827i	−0.133407	+	0.693205i
$743$	−23.6769	+	13.6699i	−0.868622	+	0.501499i	−0.866890	−	0.498499i	$-0.833885\pi$
$743$	−23.6769	+	13.6699i	−0.868622	+	0.501499i	−0.00173176	+	0.999999i	$0.500551\pi$
$744$	7.09808	−	12.2942i	0.260228	−	0.450728i
$745$	−10.3923	+	6.00000i	−0.380745	+	0.219823i
$746$	8.83013	+	5.09808i	0.323294	+	0.186654i
$747$	33.5885			1.22894
$748$		0			0
$749$	27.5885	−	31.8564i	1.00806	−	1.16401i
$750$	−1.50000	−	0.866025i	−0.0547723	−	0.0316228i
$751$	10.8038	−	18.7128i	0.394238	−	0.682840i	−0.598766	−	0.800924i	$-0.704342\pi$
$751$	10.8038	−	18.7128i	0.394238	−	0.682840i	0.993004	+	0.118084i	$0.0376752\pi$
$752$	−9.00000			−0.328196
$753$	15.5885	−	27.0000i	0.568075	−	0.983935i
$754$		−	22.3923i		−	0.815480i
$755$	−4.19615			−0.152714
$756$	−12.9904	+	4.50000i	−0.472456	+	0.163663i
$757$	−8.58846			−0.312153			−0.156076	−	0.987745i	$-0.549885\pi$
$757$	−8.58846			−0.312153			−0.156076	+	0.987745i	$0.549885\pi$
$758$			9.60770i			0.348967i
$759$	−10.3923	+	18.0000i	−0.377217	+	0.653359i
$760$	1.26795			0.0459934
$761$	−16.5000	+	28.5788i	−0.598125	+	1.03598i	0.394973	+	0.918693i	$0.370754\pi$
$761$	−16.5000	+	28.5788i	−0.598125	+	1.03598i	−0.993098	+	0.117289i	$0.962579\pi$
$762$	17.0885	+	9.86603i	0.619049	+	0.357408i
$763$	−3.59808	+	18.6962i	−0.130259	+	0.676846i
$764$		−	3.46410i		−	0.125327i
$765$		0			0
$766$	−16.7942	−	9.69615i	−0.606800	−	0.350336i
$767$	−6.58846	+	3.80385i	−0.237895	+	0.137349i
$768$	0.866025	−	1.50000i	0.0312500	−	0.0541266i
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	−0.723255	−	0.690581i	$-0.757355\pi$
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	0.236433	+	0.971648i	$0.424022\pi$
$770$	11.8301	−	4.09808i	0.426328	−	0.147684i
$771$	−24.5885	−	42.5885i	−0.885532	−	1.53379i
$772$	−13.8038			−0.496811
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$		−	9.58846i		−	0.344650i
$775$	−7.09808	+	4.09808i	−0.254970	+	0.147207i
$776$	4.26795	−	7.39230i	0.153210	−	0.265368i
$777$	26.8301	−	9.29423i	0.962525	−	0.333429i
$778$	−12.3564	−	21.4019i	−0.442999	−	0.767296i
$779$	−9.88269	−	5.70577i	−0.354084	−	0.204430i
$780$	5.19615	+	3.00000i	0.186052	+	0.107417i
$781$	−11.1962	−	19.3923i	−0.400630	−	0.693911i
$782$		0			0
$783$	29.0885	+	16.7942i	1.03954	+	0.600177i
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	15.2942	+	8.83013i	0.545874	+	0.315161i
$786$	−6.58846	+	3.80385i	−0.235002	+	0.135679i
$787$		−	9.24871i		−	0.329681i	−0.986320	−	0.164840i	$-0.947289\pi$
$787$		−	9.24871i		−	0.329681i	0.986320	−	0.164840i	$-0.0527109\pi$
$788$		−	23.6603i		−	0.842862i
$789$			23.7846i			0.846755i
$790$	12.6340	+	7.29423i	0.449497	+	0.259517i
$791$	21.8038	−	25.1769i	0.775256	−	0.895188i
$792$	−7.09808	+	12.2942i	−0.252219	+	0.436856i
$793$	22.3923	+	38.7846i	0.795174	+	1.37728i
$794$	15.2942	+	26.4904i	0.542772	+	0.940108i
$795$			12.5885i			0.446467i
$796$	−6.00000	−	3.46410i	−0.212664	−	0.122782i
$797$	9.58846	+	16.6077i	0.339641	+	0.588275i	0.984365	−	0.176140i	$-0.0563612\pi$
$797$	9.58846	+	16.6077i	0.339641	+	0.588275i	−0.644724	+	0.764415i	$0.723028\pi$
$798$	−5.49038	+	1.90192i	−0.194357	+	0.0673274i
$799$		0			0
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	6.58846	−	11.4115i	0.232792	−	0.403207i
$802$	1.79423	−	3.10770i	0.0633564	−	0.109737i
$803$	−32.7846			−1.15694
$804$	3.46410	−	6.00000i	0.122169	−	0.211604i
$805$	4.39230	−	5.07180i	0.154808	−	0.178757i
$806$	24.5885	−	14.1962i	0.866091	−	0.500038i
$807$	15.5885	+	27.0000i	0.548740	+	0.950445i
$808$	9.69615	−	5.59808i	0.341109	−	0.196940i
$809$	−45.4808	−	26.2583i	−1.59902	−	0.923194i	−0.991677	−	0.128753i	$-0.958903\pi$
$809$	−45.4808	−	26.2583i	−1.59902	−	0.923194i	−0.607342	−	0.794441i	$-0.707764\pi$
$810$	−7.79423	+	4.50000i	−0.273861	+	0.158114i
$811$			44.5359i			1.56387i	0.623362	+	0.781933i	$0.285766\pi$
$811$			44.5359i			1.56387i	−0.623362	+	0.781933i	$0.714234\pi$
$812$	−16.7942	−	3.23205i	−0.589362	−	0.113423i
$813$		−	11.4115i		−	0.400220i
$814$	14.6603	−	25.3923i	0.513842	−	0.890000i
$815$	−8.39230			−0.293970
$816$		0			0
$817$		−	4.05256i		−	0.141781i
$818$	−10.5167			−0.367706
$819$	−27.0000	−	5.19615i	−0.943456	−	0.181568i
$820$	9.00000			0.314294
$821$			36.7128i			1.28129i	0.767839	+	0.640643i	$0.221332\pi$
$821$			36.7128i			1.28129i	−0.767839	+	0.640643i	$0.778668\pi$
$822$	−12.5885			−0.439073
$823$	30.6077			1.06692			0.533459	−	0.845826i	$-0.320892\pi$
$823$	30.6077			1.06692			0.533459	+	0.845826i	$0.320892\pi$
$824$	6.06218	−	10.5000i	0.211186	−	0.365785i
$825$	7.09808	−	4.09808i	0.247123	−	0.142677i
$826$	1.90192	+	5.49038i	0.0661764	+	0.191035i
$827$			31.6410i			1.10027i	0.835077	+	0.550133i	$0.185423\pi$
$827$			31.6410i			1.10027i	−0.835077	+	0.550133i	$0.814577\pi$
$828$			7.60770i			0.264386i
$829$	30.1865	+	17.4282i	1.04842	+	0.605307i	0.922207	−	0.386696i	$-0.126384\pi$
$829$	30.1865	+	17.4282i	1.04842	+	0.605307i	0.126215	+	0.992003i	$0.459717\pi$
$830$	−9.69615	+	5.59808i	−0.336558	+	0.194312i
$831$	41.9090			1.45381
$832$	3.00000	−	1.73205i	0.104006	−	0.0600481i
$833$		0			0
$834$	38.1962			1.32262
$835$	10.3923			0.359641
$836$	−3.00000	+	5.19615i	−0.103757	+	0.179713i
$837$			42.5885i			1.47207i
$838$	−9.00000	+	5.19615i	−0.310900	+	0.179498i
$839$	−1.90192	+	3.29423i	−0.0656617	+	0.113729i	−0.896987	−	0.442056i	$-0.854249\pi$
$839$	−1.90192	+	3.29423i	−0.0656617	+	0.113729i	0.831326	+	0.555786i	$0.187582\pi$
$840$	3.00000	−	3.46410i	0.103510	−	0.119523i
$841$	6.39230	+	11.0718i	0.220424	+	0.381786i
$842$	−25.9641	−	14.9904i	−0.894782	−	0.516603i
$843$	21.9904	−	12.6962i	0.757389	−	0.437279i
$844$	−10.2942	−	17.8301i	−0.354342	−	0.613738i
$845$	−0.500000	−	0.866025i	−0.0172005	−	0.0297922i
$846$	23.3827	−	13.5000i	0.803913	−	0.464140i
$847$	−5.69615	+	29.5981i	−0.195722	+	1.01700i
$848$	6.29423	+	3.63397i	0.216145	+	0.124791i
$849$	−25.2846	−	14.5981i	−0.867766	−	0.501005i
$850$		0			0
$851$		−	15.7128i		−	0.538628i
$852$	−7.09808	−	4.09808i	−0.243176	−	0.140398i
$853$	2.78461	+	1.60770i	0.0953432	+	0.0550464i	0.546914	−	0.837189i	$-0.315803\pi$
$853$	2.78461	+	1.60770i	0.0953432	+	0.0550464i	−0.451570	+	0.892236i	$0.649136\pi$
$854$	32.3205	−	11.1962i	1.10599	−	0.383124i
$855$	−3.29423	+	1.90192i	−0.112660	+	0.0650444i
$856$	−7.96410	−	13.7942i	−0.272207	−	0.471477i
$857$	−8.70577	−	15.0788i	−0.297383	−	0.515083i	0.678153	−	0.734921i	$-0.262781\pi$
$857$	−8.70577	−	15.0788i	−0.297383	−	0.515083i	−0.975537	+	0.219837i	$0.929447\pi$
$858$	−24.5885	+	14.1962i	−0.839436	+	0.484649i
$859$	−13.6865	−	7.90192i	−0.466978	−	0.269610i	0.247996	−	0.968761i	$-0.420228\pi$
$859$	−13.6865	−	7.90192i	−0.466978	−	0.269610i	−0.714974	+	0.699151i	$0.753562\pi$
$860$	1.59808	+	2.76795i	0.0544939	+	0.0943863i
$861$	−38.9711	+	13.5000i	−1.32813	+	0.460079i
$862$	19.3923	−	33.5885i	0.660505	−	1.14403i
$863$	−25.3923	+	14.6603i	−0.864364	+	0.499041i	−0.865471	−	0.500959i	$-0.832981\pi$
$863$	−25.3923	+	14.6603i	−0.864364	+	0.499041i	0.00110718	+	0.999999i	$0.499648\pi$
$864$			5.19615i			0.176777i
$865$	−4.09808	+	7.09808i	−0.139339	+	0.241342i
$866$	−18.0000			−0.611665
$867$	29.4449			1.00000
$868$	−7.09808	−	20.4904i	−0.240924	−	0.695489i
$869$	−59.7846	+	34.5167i	−2.02805	+	1.17090i
$870$	−11.1962			−0.379585
$871$	12.0000	−	6.92820i	0.406604	−	0.234753i
$872$	6.23205	+	3.59808i	0.211044	+	0.121846i
$873$			25.6077i			0.866689i
$874$			3.21539i			0.108762i
$875$	−2.50000	+	0.866025i	−0.0845154	+	0.0292770i
$876$	−10.3923	+	6.00000i	−0.351123	+	0.202721i
$877$	−25.8827	+	44.8301i	−0.873996	+	1.51381i	−0.0161680	+	0.999869i	$0.505147\pi$
$877$	−25.8827	+	44.8301i	−0.873996	+	1.51381i	−0.857828	+	0.513937i	$0.828187\pi$
$878$	−29.6603			−1.00099
$879$	28.3923			0.957649
$880$		−	4.73205i		−	0.159517i
$881$	16.3923			0.552271			0.276135	−	0.961119i	$-0.410946\pi$
$881$	16.3923			0.552271			0.276135	+	0.961119i	$0.410946\pi$
$882$	−7.79423	+	19.5000i	−0.262445	+	0.656599i
$883$	28.3731			0.954830			0.477415	−	0.878678i	$-0.341574\pi$
$883$	28.3731			0.954830			0.477415	+	0.878678i	$0.341574\pi$
$884$		0			0
$885$	1.90192	+	3.29423i	0.0639325	+	0.110734i
$886$	9.00000			0.302361
$887$	−24.6962	+	42.7750i	−0.829216	+	1.43624i	0.0694387	+	0.997586i	$0.477879\pi$
$887$	−24.6962	+	42.7750i	−0.829216	+	1.43624i	−0.898654	+	0.438657i	$0.855454\pi$
$888$		−	10.7321i		−	0.360144i
$889$	28.4808	−	9.86603i	0.955214	−	0.330896i
$890$			4.39230i			0.147230i
$891$		−	42.5885i		−	1.42677i
$892$	11.8923	+	6.86603i	0.398184	+	0.229892i
$893$	9.88269	−	5.70577i	0.330711	−	0.190936i
$894$	−10.3923	−	18.0000i	−0.347571	−	0.602010i
$895$	21.2942	−	12.2942i	0.711788	−	0.410951i
$896$	−0.866025	−	2.50000i	−0.0289319	−	0.0835191i
$897$	−7.60770	+	13.1769i	−0.254014	+	0.439964i
$898$	−9.58846			−0.319971
$899$	−26.4904	+	45.8827i	−0.883504	+	1.53027i
$900$	1.50000	−	2.59808i	0.0500000	−	0.0866025i
$901$		0			0
$902$	−21.2942	+	36.8827i	−0.709020	+	1.22806i
$903$	−11.0718	−	9.58846i	−0.368446	−	0.319084i
$904$	−6.29423	−	10.9019i	−0.209343	−	0.362593i
$905$	11.5981	+	6.69615i	0.385533	+	0.222588i
$906$		−	7.26795i		−	0.241461i
$907$	−11.4019	−	19.7487i	−0.378595	−	0.655745i	0.612263	−	0.790654i	$-0.290259\pi$
$907$	−11.4019	−	19.7487i	−0.378595	−	0.655745i	−0.990858	+	0.134909i	$0.956926\pi$
$908$	8.19615	+	14.1962i	0.271999	+	0.471116i
$909$	−16.7942	+	29.0885i	−0.557029	+	0.964803i
$910$	8.66025	−	3.00000i	0.287085	−	0.0994490i
$911$	10.0981	+	5.83013i	0.334564	+	0.193161i	0.657866	−	0.753135i	$-0.271459\pi$
$911$	10.0981	+	5.83013i	0.334564	+	0.193161i	−0.323301	+	0.946296i	$0.604793\pi$
$912$			2.19615i			0.0727219i
$913$		−	52.9808i		−	1.75341i
$914$		−	2.39230i		−	0.0791304i
$915$	19.3923	−	11.1962i	0.641090	−	0.370133i
$916$	12.1865	+	7.03590i	0.402654	+	0.232473i
$917$	−2.19615	+	11.4115i	−0.0725233	+	0.376842i
$918$		0			0
$919$	−2.29423	−	3.97372i	−0.0756796	−	0.131081i	0.825702	−	0.564107i	$-0.190779\pi$
$919$	−2.29423	−	3.97372i	−0.0756796	−	0.131081i	−0.901382	+	0.433026i	$0.857446\pi$
$920$	−1.26795	−	2.19615i	−0.0418030	−	0.0724050i
$921$	35.6769	+	20.5981i	1.17559	+	0.678730i
$922$	−4.50000	−	2.59808i	−0.148200	−	0.0855631i
$923$	−8.19615	−	14.1962i	−0.269780	−	0.467272i
$924$	7.09808	+	20.4904i	0.233510	+	0.674084i
$925$	−3.09808	+	5.36603i	−0.101864	+	0.176434i
$926$	2.25833	−	1.30385i	0.0742133	−	0.0428471i
$927$			36.3731i			1.19465i
$928$	−3.23205	+	5.59808i	−0.106097	+	0.183766i
$929$	−50.5692			−1.65912			−0.829561	−	0.558416i	$-0.811409\pi$
$929$	−50.5692			−1.65912			−0.829561	+	0.558416i	$0.811409\pi$
$930$	−7.09808	−	12.2942i	−0.232755	−	0.403144i
$931$	−3.29423	+	8.24167i	−0.107964	+	0.270110i
$932$	1.09808	−	0.633975i	0.0359687	−	0.0207665i
$933$	−13.6865	+	23.7058i	−0.448077	+	0.776092i
$934$	−5.89230	+	3.40192i	−0.192802	+	0.111314i
$935$		0			0
$936$	−5.19615	+	9.00000i	−0.169842	+	0.294174i
$937$		−	42.5885i		−	1.39130i	−0.718379	−	0.695652i	$-0.755116\pi$
$937$		−	42.5885i		−	1.39130i	0.718379	−	0.695652i	$-0.244884\pi$
$938$	−3.46410	−	10.0000i	−0.113107	−	0.326512i
$939$	30.2942	+	17.4904i	0.988615	+	0.570777i
$940$	−4.50000	+	7.79423i	−0.146774	+	0.254220i
$941$	−25.9808			−0.846949			−0.423474	−	0.905908i	$-0.639190\pi$
$941$	−25.9808			−0.846949			−0.423474	+	0.905908i	$0.639190\pi$
$942$	−15.2942	+	26.4904i	−0.498313	+	0.863103i
$943$			22.8231i			0.743222i
$944$	2.19615			0.0714787
$945$	−2.59808	+	13.5000i	−0.0845154	+	0.439155i
$946$	−15.1244			−0.491735
$947$		−	23.5692i		−	0.765897i	−0.923770	−	0.382948i	$-0.874909\pi$
$947$		−	23.5692i		−	0.765897i	0.923770	−	0.382948i	$-0.125091\pi$
$948$	−12.6340	+	21.8827i	−0.410332	+	0.710717i
$949$	−24.0000			−0.779073
$950$	0.633975	−	1.09808i	0.0205689	−	0.0356263i
$951$	30.8038	+	17.7846i	0.998883	+	0.576705i
$952$		0			0
$953$			1.26795i			0.0410729i	0.999789	+	0.0205365i	$0.00653742\pi$
$953$			1.26795i			0.0410729i	−0.999789	+	0.0205365i	$0.993463\pi$
$954$	−21.8038			−0.705926
$955$	−3.00000	−	1.73205i	−0.0970777	−	0.0560478i
$956$	−2.70577	+	1.56218i	−0.0875109	+	0.0505244i
$957$	26.4904	−	45.8827i	0.856312	−	1.48318i
$958$	−9.00000	+	5.19615i	−0.290777	+	0.167880i
$959$	−12.5885	+	14.5359i	−0.406502	+	0.469389i
$960$	−0.866025	−	1.50000i	−0.0279508	−	0.0484123i
$961$	−36.1769			−1.16700
$962$	10.7321	−	18.5885i	0.346015	−	0.599316i
$963$	41.3827	+	23.8923i	1.33354	+	0.769919i
$964$	−2.89230	+	1.66987i	−0.0931549	+	0.0537830i
$965$	−6.90192	+	11.9545i	−0.222181	+	0.384828i
$966$	8.78461	+	7.60770i	0.282640	+	0.244774i
$967$	8.00000	+	13.8564i	0.257263	+	0.445592i	0.965508	−	0.260375i	$-0.0838461\pi$
$967$	8.00000	+	13.8564i	0.257263	+	0.445592i	−0.708245	+	0.705967i	$0.750513\pi$
$968$	9.86603	+	5.69615i	0.317106	+	0.183081i
$969$		0			0
$970$	−4.26795	−	7.39230i	−0.137036	−	0.237353i
$971$	−7.39230	−	12.8038i	−0.237230	−	0.410895i	0.722688	−	0.691174i	$-0.242906\pi$
$971$	−7.39230	−	12.8038i	−0.237230	−	0.410895i	−0.959919	+	0.280279i	$0.909573\pi$
$972$	−7.79423	−	13.5000i	−0.250000	−	0.433013i
$973$	38.1962	−	44.1051i	1.22451	−	1.41395i
$974$	29.4449	+	17.0000i	0.943474	+	0.544715i
$975$	5.19615	−	3.00000i	0.166410	−	0.0960769i
$976$		−	12.9282i		−	0.413822i
$977$		−	5.07180i		−	0.162261i	−0.996703	−	0.0811306i	$-0.974147\pi$
$977$		−	5.07180i		−	0.162261i	0.996703	−	0.0811306i	$-0.0258531\pi$
$978$		−	14.5359i		−	0.464807i
$979$	−18.0000	−	10.3923i	−0.575282	−	0.332140i
$980$	−1.00000	−	6.92820i	−0.0319438	−	0.221313i
$981$	−21.5885			−0.689266
$982$	13.5622	+	23.4904i	0.432786	+	0.749608i
$983$	−15.6962	−	27.1865i	−0.500630	−	0.867116i	−1.00000		0.000727052i	$-0.999769\pi$
$983$	−15.6962	−	27.1865i	−0.500630	−	0.867116i	0.499370	−	0.866389i	$-0.333565\pi$
$984$			15.5885i			0.496942i
$985$	−20.4904	−	11.8301i	−0.652878	−	0.376939i
$986$		0			0
$987$	7.79423	−	40.5000i	0.248093	−	1.28913i
$988$	−2.19615	+	3.80385i	−0.0698689	+	0.121017i
$989$	−7.01924	+	4.05256i	−0.223199	+	0.128864i
$990$	7.09808	+	12.2942i	0.225592	+	0.390736i
$991$	6.70577	−	11.6147i	0.213016	−	0.368954i	−0.739641	−	0.673002i	$-0.765005\pi$
$991$	6.70577	−	11.6147i	0.213016	−	0.368954i	0.952657	+	0.304047i	$0.0983381\pi$
$992$	−8.19615			−0.260228
$993$	−6.92820	+	12.0000i	−0.219860	+	0.380808i
$994$	−11.8301	+	4.09808i	−0.375229	+	0.129983i
$995$	−6.00000	+	3.46410i	−0.190213	+	0.109819i
$996$	−9.69615	−	16.7942i	−0.307234	−	0.532145i
$997$	−27.2942	+	15.7583i	−0.864417	+	0.499071i	−0.865489	−	0.500928i	$-0.832992\pi$
$997$	−27.2942	+	15.7583i	−0.864417	+	0.499071i	0.00107201	+	0.999999i	$0.499659\pi$
$998$	−14.0263	−	8.09808i	−0.443994	−	0.256340i
$999$	16.0981	+	27.8827i	0.509321	+	0.882169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.a.101.1	yes	4
3.2	odd	2		1890.2.bk.a.521.2		4
7.5	odd	6		630.2.t.a.551.1	yes	4
9.4	even	3		1890.2.t.a.1151.2		4
9.5	odd	6		630.2.t.a.311.1	✓	4
21.5	even	6		1890.2.t.a.1601.2		4
63.5	even	6	inner	630.2.bk.a.131.2	yes	4
63.40	odd	6		1890.2.bk.a.341.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.a.311.1	✓	4	9.5	odd	6
630.2.t.a.551.1	yes	4	7.5	odd	6
630.2.bk.a.101.1	yes	4	1.1	even	1	trivial
630.2.bk.a.131.2	yes	4	63.5	even	6	inner
1890.2.t.a.1151.2		4	9.4	even	3
1890.2.t.a.1601.2		4	21.5	even	6
1890.2.bk.a.341.1		4	63.40	odd	6
1890.2.bk.a.521.2		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.866025 - 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.866025 - 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-4.09808 + 2.36603i) q^{11} +(-0.866025 + 1.50000i) q^{12} +(-3.00000 + 1.73205i) q^{13} +(0.866025 + 2.50000i) q^{14} +(0.866025 + 1.50000i) q^{15} +1.00000 q^{16} +(-2.59808 + 1.50000i) q^{18} +(-1.09808 + 0.633975i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.866025 + 4.50000i) q^{21} +(2.36603 + 4.09808i) q^{22} +(2.19615 + 1.26795i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.73205 + 3.00000i) q^{26} -5.19615 q^{27} +(2.50000 - 0.866025i) q^{28} +(-5.59808 - 3.23205i) q^{29} +(1.50000 - 0.866025i) q^{30} -8.19615i q^{31} -1.00000i q^{32} +8.19615i q^{33} +(0.500000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-3.09808 - 5.36603i) q^{37} +(0.633975 + 1.09808i) q^{38} +6.00000i q^{39} +(-0.866025 - 0.500000i) q^{40} +(4.50000 + 7.79423i) q^{41} +(4.50000 + 0.866025i) q^{42} +(-1.59808 + 2.76795i) q^{43} +(4.09808 - 2.36603i) q^{44} +3.00000 q^{45} +(1.26795 - 2.19615i) q^{46} -9.00000 q^{47} +(0.866025 - 1.50000i) q^{48} +(5.50000 - 4.33013i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.00000 - 1.73205i) q^{52} +(6.29423 + 3.63397i) q^{53} +5.19615i q^{54} -4.73205i q^{55} +(-0.866025 - 2.50000i) q^{56} +2.19615i q^{57} +(-3.23205 + 5.59808i) q^{58} +2.19615 q^{59} +(-0.866025 - 1.50000i) q^{60} -12.9282i q^{61} -8.19615 q^{62} +(6.00000 + 5.19615i) q^{63} -1.00000 q^{64} -3.46410i q^{65} +8.19615 q^{66} -4.00000 q^{67} +(3.80385 - 2.19615i) q^{69} +(-2.59808 - 0.500000i) q^{70} +4.73205i q^{71} +(2.59808 - 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +(-5.36603 + 3.09808i) q^{74} -1.73205 q^{75} +(1.09808 - 0.633975i) q^{76} +(8.19615 - 9.46410i) q^{77} +6.00000 q^{78} +14.5885 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(7.79423 - 4.50000i) q^{82} +(-5.59808 + 9.69615i) q^{83} +(0.866025 - 4.50000i) q^{84} +(2.76795 + 1.59808i) q^{86} +(-9.69615 + 5.59808i) q^{87} +(-2.36603 - 4.09808i) q^{88} +(2.19615 + 3.80385i) q^{89} -3.00000i q^{90} +(6.00000 - 6.92820i) q^{91} +(-2.19615 - 1.26795i) q^{92} +(-12.2942 - 7.09808i) q^{93} +9.00000i q^{94} -1.26795i q^{95} +(-1.50000 - 0.866025i) q^{96} +(-7.39230 - 4.26795i) q^{97} +(-4.33013 - 5.50000i) q^{98} +(12.2942 + 7.09808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 2 q^{5} - 6 q^{6} - 10 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 2 * q^5 - 6 * q^6 - 10 * q^7 - 6 * q^9	\( 4 q - 4 q^{4} - 2 q^{5} - 6 q^{6} - 10 q^{7} - 6 q^{9} - 6 q^{11} - 12 q^{13} + 4 q^{16} + 6 q^{19} + 2 q^{20} + 6 q^{22} - 12 q^{23} + 6 q^{24} - 2 q^{25} + 10 q^{28} - 12 q^{29} + 6 q^{30} + 2 q^{35} + 6 q^{36} - 2 q^{37} + 6 q^{38} + 18 q^{41} + 18 q^{42} + 4 q^{43} + 6 q^{44} + 12 q^{45} + 12 q^{46} - 36 q^{47} + 22 q^{49} + 12 q^{52} - 6 q^{53} - 6 q^{58} - 12 q^{59} - 12 q^{62} + 24 q^{63} - 4 q^{64} + 12 q^{66} - 16 q^{67} + 36 q^{69} + 24 q^{73} - 18 q^{74} - 6 q^{76} + 12 q^{77} + 24 q^{78} - 4 q^{79} - 2 q^{80} - 18 q^{81} - 12 q^{83} + 18 q^{86} - 18 q^{87} - 6 q^{88} - 12 q^{89} + 24 q^{91} + 12 q^{92} - 18 q^{93} - 6 q^{96} + 12 q^{97} + 18 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 2 * q^5 - 6 * q^6 - 10 * q^7 - 6 * q^9 - 6 * q^11 - 12 * q^13 + 4 * q^16 + 6 * q^19 + 2 * q^20 + 6 * q^22 - 12 * q^23 + 6 * q^24 - 2 * q^25 + 10 * q^28 - 12 * q^29 + 6 * q^30 + 2 * q^35 + 6 * q^36 - 2 * q^37 + 6 * q^38 + 18 * q^41 + 18 * q^42 + 4 * q^43 + 6 * q^44 + 12 * q^45 + 12 * q^46 - 36 * q^47 + 22 * q^49 + 12 * q^52 - 6 * q^53 - 6 * q^58 - 12 * q^59 - 12 * q^62 + 24 * q^63 - 4 * q^64 + 12 * q^66 - 16 * q^67 + 36 * q^69 + 24 * q^73 - 18 * q^74 - 6 * q^76 + 12 * q^77 + 24 * q^78 - 4 * q^79 - 2 * q^80 - 18 * q^81 - 12 * q^83 + 18 * q^86 - 18 * q^87 - 6 * q^88 - 12 * q^89 + 24 * q^91 + 12 * q^92 - 18 * q^93 - 6 * q^96 + 12 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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