LMFDB - Embedded newform 630.2.t.a.551.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

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([5, 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("630.311");

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.t (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:	$0$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	630.551
Dual form			630.2.t.a.311.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 + 0.866025i) q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 + 0.866025i) q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(0.866025 - 0.500000i) q^{10} -4.73205i q^{11} -1.73205 q^{12} +(3.00000 - 1.73205i) q^{13} +(-1.73205 - 2.00000i) q^{14} +(0.866025 + 1.50000i) q^{15} +(-0.500000 - 0.866025i) q^{16} -3.00000i q^{18} +(-1.09808 - 0.633975i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(3.46410 - 3.00000i) q^{21} +(2.36603 + 4.09808i) q^{22} -2.53590i q^{23} +(1.50000 - 0.866025i) q^{24} +1.00000 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} +(-7.09808 - 4.09808i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-7.09808 + 4.09808i) q^{33} +(-0.500000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-3.09808 + 5.36603i) q^{37} +1.26795 q^{38} +(-5.19615 - 3.00000i) q^{39} -1.00000i q^{40} +(-4.50000 - 7.79423i) q^{41} +(-1.50000 + 4.33013i) q^{42} +(-1.59808 + 2.76795i) q^{43} +(-4.09808 - 2.36603i) q^{44} +(1.50000 - 2.59808i) q^{45} +(1.26795 + 2.19615i) q^{46} +(-4.50000 - 7.79423i) q^{47} +(-0.866025 + 1.50000i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(-0.866025 + 0.500000i) q^{50} -3.46410i q^{52} +(-6.29423 + 3.63397i) q^{53} +(-4.50000 + 2.59808i) q^{54} +4.73205i q^{55} +(-2.59808 + 0.500000i) q^{56} +2.19615i q^{57} +6.46410 q^{58} +(1.09808 - 1.90192i) q^{59} +1.73205 q^{60} +(11.1962 - 6.46410i) q^{61} +8.19615 q^{62} +(-7.50000 - 2.59808i) q^{63} -1.00000 q^{64} +(-3.00000 + 1.73205i) q^{65} +(4.09808 - 7.09808i) q^{66} +(2.00000 - 3.46410i) q^{67} +(-3.80385 + 2.19615i) q^{69} +(1.73205 + 2.00000i) q^{70} +4.73205i q^{71} +(-2.59808 - 1.50000i) q^{72} +(6.00000 - 3.46410i) q^{73} -6.19615i q^{74} +(-0.866025 - 1.50000i) q^{75} +(-1.09808 + 0.633975i) q^{76} +(12.2942 - 2.36603i) q^{77} +6.00000 q^{78} +(-7.29423 - 12.6340i) 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} -3.19615i q^{86} +11.1962i q^{87} +4.73205 q^{88} +(-2.19615 + 3.80385i) q^{89} +3.00000i q^{90} +(6.00000 + 6.92820i) q^{91} +(-2.19615 - 1.26795i) q^{92} +14.1962i q^{93} +(7.79423 + 4.50000i) q^{94} +(1.09808 + 0.633975i) q^{95} -1.73205i 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 + 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 6 * q^9	$ 4 q + 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 6 q^{9} + 12 q^{13} - 2 q^{16} + 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{24} + 4 q^{25} + 10 q^{28} - 12 q^{29} - 6 q^{30} - 18 q^{31} - 18 q^{33} - 2 q^{35} + 6 q^{36} - 2 q^{37} + 12 q^{38} - 18 q^{41} - 6 q^{42} + 4 q^{43} - 6 q^{44} + 6 q^{45} + 12 q^{46} - 18 q^{47} - 26 q^{49} + 6 q^{53} - 18 q^{54} + 12 q^{58} - 6 q^{59} + 24 q^{61} + 12 q^{62} - 30 q^{63} - 4 q^{64} - 12 q^{65} + 6 q^{66} + 8 q^{67} - 36 q^{69} + 24 q^{73} + 6 q^{76} + 18 q^{77} + 24 q^{78} + 2 q^{79} + 2 q^{80} - 18 q^{81} + 12 q^{83} + 12 q^{88} + 12 q^{89} + 24 q^{91} + 12 q^{92} - 6 q^{95} - 12 q^{97} + 18 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 6 * q^9 + 12 * q^13 - 2 * q^16 + 6 * q^19 - 2 * q^20 + 6 * q^22 + 6 * q^24 + 4 * q^25 + 10 * q^28 - 12 * q^29 - 6 * q^30 - 18 * q^31 - 18 * q^33 - 2 * q^35 + 6 * q^36 - 2 * q^37 + 12 * q^38 - 18 * q^41 - 6 * q^42 + 4 * q^43 - 6 * q^44 + 6 * q^45 + 12 * q^46 - 18 * q^47 - 26 * q^49 + 6 * q^53 - 18 * q^54 + 12 * q^58 - 6 * q^59 + 24 * q^61 + 12 * q^62 - 30 * q^63 - 4 * q^64 - 12 * q^65 + 6 * q^66 + 8 * q^67 - 36 * q^69 + 24 * q^73 + 6 * q^76 + 18 * q^77 + 24 * q^78 + 2 * q^79 + 2 * q^80 - 18 * q^81 + 12 * q^83 + 12 * q^88 + 12 * q^89 + 24 * q^91 + 12 * q^92 - 6 * q^95 - 12 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.50000	+	0.866025i	0.612372	+	0.353553i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$			1.00000i			0.353553i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$		−	4.73205i		−	1.42677i	−0.700774	−	0.713384i	$-0.747162\pi$
$11$		−	4.73205i		−	1.42677i	0.700774	−	0.713384i	$-0.252838\pi$
$12$	−1.73205			−0.500000
$13$	3.00000	−	1.73205i	0.832050	−	0.480384i	−0.0225039	−	0.999747i	$-0.507164\pi$
$13$	3.00000	−	1.73205i	0.832050	−	0.480384i	0.854554	+	0.519362i	$0.173830\pi$
$14$	−1.73205	−	2.00000i	−0.462910	−	0.534522i
$15$	0.866025	+	1.50000i	0.223607	+	0.387298i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		−	3.00000i		−	0.707107i
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	0.368725	−	0.929538i	$-0.379794\pi$
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	−0.620641	+	0.784095i	$0.713128\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	3.46410	−	3.00000i	0.755929	−	0.654654i
$22$	2.36603	+	4.09808i	0.504438	+	0.873713i
$23$		−	2.53590i		−	0.528771i	−0.964417	−	0.264386i	$-0.914831\pi$
$23$		−	2.53590i		−	0.528771i	0.964417	−	0.264386i	$-0.0851692\pi$
$24$	1.50000	−	0.866025i	0.306186	−	0.176777i
$25$	1.00000			0.200000
$26$	−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
$31$	−7.09808	−	4.09808i	−1.27485	−	0.736036i	−0.298955	−	0.954267i	$-0.596638\pi$
$31$	−7.09808	−	4.09808i	−1.27485	−	0.736036i	−0.975897	+	0.218231i	$0.929971\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−7.09808	+	4.09808i	−1.23562	+	0.713384i
$34$		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	0.490621	+	0.871373i	$0.336770\pi$
$37$	−3.09808	+	5.36603i	−0.509321	+	0.882169i	−0.999942	+	0.0107961i	$0.996563\pi$
$38$	1.26795			0.205689
$39$	−5.19615	−	3.00000i	−0.832050	−	0.480384i
$40$		−	1.00000i		−	0.158114i
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$	−1.50000	+	4.33013i	−0.231455	+	0.668153i
$43$	−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
$45$	1.50000	−	2.59808i	0.223607	−	0.387298i
$46$	1.26795	+	2.19615i	0.186949	+	0.323805i
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	−0.981543	−	0.191243i	$-0.938748\pi$
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	0.325150	−	0.945662i	$-0.394585\pi$
$48$	−0.866025	+	1.50000i	−0.125000	+	0.216506i
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$		−	3.46410i		−	0.480384i
$53$	−6.29423	+	3.63397i	−0.864579	+	0.499165i	−0.865543	−	0.500835i	$-0.833026\pi$
$53$	−6.29423	+	3.63397i	−0.864579	+	0.499165i	0.000964138		1.00000i	$0.499693\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$			4.73205i			0.638070i
$56$	−2.59808	+	0.500000i	−0.347183	+	0.0668153i
$57$			2.19615i			0.290887i
$58$	6.46410			0.848778
$59$	1.09808	−	1.90192i	0.142957	−	0.247609i	−0.785652	−	0.618669i	$-0.787672\pi$
$59$	1.09808	−	1.90192i	0.142957	−	0.247609i	0.928609	+	0.371060i	$0.121005\pi$
$60$	1.73205			0.223607
$61$	11.1962	−	6.46410i	1.43352	−	0.827643i	0.436133	−	0.899882i	$-0.356348\pi$
$61$	11.1962	−	6.46410i	1.43352	−	0.827643i	0.997387	+	0.0722388i	$0.0230144\pi$
$62$	8.19615			1.04091
$63$	−7.50000	−	2.59808i	−0.944911	−	0.327327i
$64$	−1.00000			−0.125000
$65$	−3.00000	+	1.73205i	−0.372104	+	0.214834i
$66$	4.09808	−	7.09808i	0.504438	−	0.873713i
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$		0			0
$69$	−3.80385	+	2.19615i	−0.457929	+	0.264386i
$70$	1.73205	+	2.00000i	0.207020	+	0.239046i
$71$			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	−0.105937	−	0.994373i	$-0.533784\pi$
$73$	6.00000	−	3.46410i	0.702247	−	0.405442i	0.808184	+	0.588930i	$0.200451\pi$
$74$		−	6.19615i		−	0.720288i
$75$	−0.866025	−	1.50000i	−0.100000	−	0.173205i
$76$	−1.09808	+	0.633975i	−0.125958	+	0.0727219i
$77$	12.2942	−	2.36603i	1.40106	−	0.269634i
$78$	6.00000			0.679366
$79$	−7.29423	−	12.6340i	−0.820665	−	1.42143i	−0.905188	−	0.425012i	$-0.860270\pi$
$79$	−7.29423	−	12.6340i	−0.820665	−	1.42143i	0.0845230	−	0.996422i	$-0.473063\pi$
$80$	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	$-0.622704\pi$
$83$	5.59808	−	9.69615i	0.614469	−	1.06429i	0.990477	−	0.137675i	$-0.0439629\pi$
$84$	−0.866025	−	4.50000i	−0.0944911	−	0.490990i
$85$		0			0
$86$		−	3.19615i		−	0.344650i
$87$			11.1962i			1.20035i
$88$	4.73205			0.504438
$89$	−2.19615	+	3.80385i	−0.232792	+	0.403207i	−0.958629	−	0.284660i	$-0.908119\pi$
$89$	−2.19615	+	3.80385i	−0.232792	+	0.403207i	0.725837	+	0.687867i	$0.241453\pi$
$90$			3.00000i			0.316228i
$91$	6.00000	+	6.92820i	0.628971	+	0.726273i
$92$	−2.19615	−	1.26795i	−0.228965	−	0.132193i
$93$			14.1962i			1.47207i
$94$	7.79423	+	4.50000i	0.803913	+	0.464140i
$95$	1.09808	+	0.633975i	0.112660	+	0.0650444i
$96$		−	1.73205i		−	0.176777i
$97$	7.39230	+	4.26795i	0.750575	+	0.433345i	0.825902	−	0.563814i	$-0.190667\pi$
$97$	7.39230	+	4.26795i	0.750575	+	0.433345i	−0.0753267	+	0.997159i	$0.524000\pi$
$98$	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
$101$	−11.1962			−1.11406			−0.557029	−	0.830493i	$-0.688059\pi$
$101$	−11.1962			−1.11406			−0.557029	+	0.830493i	$0.688059\pi$
$102$		0			0
$103$		−	12.1244i		−	1.19465i	−0.802000	−	0.597324i	$-0.796231\pi$
$103$		−	12.1244i		−	1.19465i	0.802000	−	0.597324i	$-0.203769\pi$
$104$	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	$-0.0536300\pi$
$107$	13.7942	+	7.96410i	1.33354	+	0.769919i	0.347698	+	0.937606i	$0.386963\pi$
$108$	2.59808	−	4.50000i	0.250000	−	0.433013i
$109$	3.59808	+	6.23205i	0.344633	+	0.596922i	0.985287	−	0.170908i	$-0.0546700\pi$
$109$	3.59808	+	6.23205i	0.344633	+	0.596922i	−0.640654	+	0.767830i	$0.721337\pi$
$110$	−2.36603	−	4.09808i	−0.225592	−	0.390736i
$111$	10.7321			1.01864
$112$	2.00000	−	1.73205i	0.188982	−	0.163663i
$113$	−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	$0.535039\pi$
$114$	−1.09808	−	1.90192i	−0.102844	−	0.178131i
$115$			2.53590i			0.236474i
$116$	−5.59808	+	3.23205i	−0.519768	+	0.300088i
$117$			10.3923i			0.960769i
$118$			2.19615i			0.202172i
$119$		0			0
$120$	−1.50000	+	0.866025i	−0.136931	+	0.0790569i
$121$	−11.3923			−1.03566
$122$	−6.46410	+	11.1962i	−0.585232	+	1.01365i
$123$	−7.79423	+	13.5000i	−0.702782	+	1.21725i
$124$	−7.09808	+	4.09808i	−0.637426	+	0.368018i
$125$	−1.00000			−0.0894427
$126$	7.79423	−	1.50000i	0.694365	−	0.133631i
$127$	−11.3923			−1.01090			−0.505452	−	0.862855i	$-0.668674\pi$
$127$	−11.3923			−1.01090			−0.505452	+	0.862855i	$0.668674\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	5.53590			0.487409
$130$	1.73205	−	3.00000i	0.151911	−	0.263117i
$131$	4.39230			0.383757			0.191879	−	0.981419i	$-0.438542\pi$
$131$	4.39230			0.383757			0.191879	+	0.981419i	$0.438542\pi$
$132$			8.19615i			0.713384i
$133$	1.09808	−	3.16987i	0.0952153	−	0.274863i
$134$			4.00000i			0.345547i
$135$	−5.19615			−0.447214
$136$		0			0
$137$			7.26795i			0.620943i	0.950583	+	0.310471i	$0.100487\pi$
$137$			7.26795i			0.620943i	−0.950583	+	0.310471i	$0.899513\pi$
$138$	2.19615	−	3.80385i	0.186949	−	0.323805i
$139$	19.0981	−	11.0263i	1.61988	−	0.935237i	0.632927	−	0.774211i	$-0.281853\pi$
$139$	19.0981	−	11.0263i	1.61988	−	0.935237i	0.986950	−	0.161026i	$-0.0514802\pi$
$140$	−2.50000	−	0.866025i	−0.211289	−	0.0731925i
$141$	−7.79423	+	13.5000i	−0.656392	+	1.13691i
$142$	−2.36603	−	4.09808i	−0.198552	−	0.343903i
$143$	−8.19615	−	14.1962i	−0.685397	−	1.18714i
$144$	3.00000			0.250000
$145$	5.59808	+	3.23205i	0.464895	+	0.268407i
$146$	−3.46410	+	6.00000i	−0.286691	+	0.496564i
$147$	9.52628	+	7.50000i	0.785714	+	0.618590i
$148$	3.09808	+	5.36603i	0.254660	+	0.441085i
$149$		−	12.0000i		−	0.983078i	−0.870855	−	0.491539i	$-0.836434\pi$
$149$		−	12.0000i		−	0.983078i	0.870855	−	0.491539i	$-0.163566\pi$
$150$	1.50000	+	0.866025i	0.122474	+	0.0707107i
$151$	−4.19615			−0.341478			−0.170739	−	0.985316i	$-0.554616\pi$
$151$	−4.19615			−0.341478			−0.170739	+	0.985316i	$0.554616\pi$
$152$	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
$156$	−5.19615	+	3.00000i	−0.416025	+	0.240192i
$157$	−15.2942	−	8.83013i	−1.22061	−	0.704721i	−0.255564	−	0.966792i	$-0.582261\pi$
$157$	−15.2942	−	8.83013i	−1.22061	−	0.704721i	−0.965049	+	0.262071i	$0.915594\pi$
$158$	12.6340	+	7.29423i	1.00511	+	0.580298i
$159$	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	−0.653580	−	0.756858i	$-0.726734\pi$
$163$	4.19615	−	7.26795i	0.328668	−	0.569270i	0.982248	+	0.187588i	$0.0600669\pi$
$164$	−9.00000			−0.702782
$165$	7.09808	−	4.09808i	0.552584	−	0.319035i
$166$			11.1962i			0.868990i
$167$	5.19615	+	9.00000i	0.402090	+	0.696441i	0.993978	−	0.109580i	$-0.0349504\pi$
$167$	5.19615	+	9.00000i	0.402090	+	0.696441i	−0.591888	+	0.806020i	$0.701617\pi$
$168$	3.00000	+	3.46410i	0.231455	+	0.267261i
$169$	−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
$173$	4.09808	+	7.09808i	0.311571	+	0.539657i	0.978703	−	0.205283i	$-0.0658115\pi$
$173$	4.09808	+	7.09808i	0.311571	+	0.539657i	−0.667132	+	0.744940i	$0.732478\pi$
$174$	−5.59808	−	9.69615i	−0.424389	−	0.735063i
$175$	0.500000	+	2.59808i	0.0377964	+	0.196396i
$176$	−4.09808	+	2.36603i	−0.308904	+	0.178346i
$177$	−3.80385			−0.285915
$178$		−	4.39230i		−	0.329217i
$179$	21.2942	−	12.2942i	1.59161	−	0.918914i	0.598573	−	0.801068i	$-0.295734\pi$
$179$	21.2942	−	12.2942i	1.59161	−	0.918914i	0.993032	−	0.117846i	$-0.0375989\pi$
$180$	−1.50000	−	2.59808i	−0.111803	−	0.193649i
$181$			13.3923i			0.995442i	0.867337	+	0.497721i	$0.165830\pi$
$181$			13.3923i			0.995442i	−0.867337	+	0.497721i	$0.834170\pi$
$182$	−8.66025	−	3.00000i	−0.641941	−	0.222375i
$183$	−19.3923	−	11.1962i	−1.43352	−	0.827643i
$184$	2.53590			0.186949
$185$	3.09808	−	5.36603i	0.227775	−	0.394518i
$186$	−7.09808	−	12.2942i	−0.520456	−	0.901457i
$187$		0			0
$188$	−9.00000			−0.656392
$189$	2.59808	+	13.5000i	0.188982	+	0.981981i
$190$	−1.26795			−0.0919867
$191$	3.00000	−	1.73205i	0.217072	−	0.125327i	−0.387522	−	0.921861i	$-0.626669\pi$
$191$	3.00000	−	1.73205i	0.217072	−	0.125327i	0.604594	+	0.796534i	$0.293335\pi$
$192$	0.866025	+	1.50000i	0.0625000	+	0.108253i
$193$	−6.90192	+	11.9545i	−0.496811	+	0.860502i	−0.999993	−	0.00367804i	$-0.998829\pi$
$193$	−6.90192	+	11.9545i	−0.496811	+	0.860502i	0.503182	+	0.864181i	$0.332163\pi$
$194$	−8.53590			−0.612842
$195$	5.19615	+	3.00000i	0.372104	+	0.214834i
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$			23.6603i			1.68572i	0.538130	+	0.842862i	$0.319131\pi$
$197$			23.6603i			1.68572i	−0.538130	+	0.842862i	$0.680869\pi$
$198$	−14.1962			−1.00888
$199$	6.00000	−	3.46410i	0.425329	−	0.245564i	−0.272026	−	0.962290i	$-0.587694\pi$
$199$	6.00000	−	3.46410i	0.425329	−	0.245564i	0.697355	+	0.716726i	$0.254360\pi$
$200$			1.00000i			0.0707107i
$201$	−6.92820			−0.488678
$202$	9.69615	−	5.59808i	0.682219	−	0.393879i
$203$	5.59808	−	16.1603i	0.392908	−	1.13423i
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	6.06218	+	10.5000i	0.422372	+	0.731570i
$207$	6.58846	+	3.80385i	0.457929	+	0.264386i
$208$	−3.00000	−	1.73205i	−0.208013	−	0.120096i
$209$	−3.00000	+	5.19615i	−0.207514	+	0.359425i
$210$	1.50000	−	4.33013i	0.103510	−	0.298807i
$211$	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	$0.582623\pi$
$212$			7.26795i			0.499165i
$213$	7.09808	−	4.09808i	0.486352	−	0.280796i
$214$	−15.9282			−1.08883
$215$	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
$220$	4.09808	+	2.36603i	0.276292	+	0.159517i
$221$		0			0
$222$	−9.29423	+	5.36603i	−0.623788	+	0.360144i
$223$	11.8923	+	6.86603i	0.796368	+	0.459783i	0.842199	−	0.539166i	$-0.181260\pi$
$223$	11.8923	+	6.86603i	0.796368	+	0.459783i	−0.0458318	+	0.998949i	$0.514594\pi$
$224$	−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
$227$	−16.3923			−1.08800			−0.543998	−	0.839087i	$-0.683090\pi$
$227$	−16.3923			−1.08800			−0.543998	+	0.839087i	$0.683090\pi$
$228$	1.90192	+	1.09808i	0.125958	+	0.0727219i
$229$		−	14.0718i		−	0.929891i	−0.885339	−	0.464945i	$-0.846074\pi$
$229$		−	14.0718i		−	0.929891i	0.885339	−	0.464945i	$-0.153926\pi$
$230$	−1.26795	−	2.19615i	−0.0836061	−	0.144810i
$231$	−14.1962	−	16.3923i	−0.934038	−	1.07853i
$232$	3.23205	−	5.59808i	0.212195	−	0.367532i
$233$	1.09808	+	0.633975i	0.0719374	+	0.0415331i	0.535537	−	0.844512i	$-0.320109\pi$
$233$	1.09808	+	0.633975i	0.0719374	+	0.0415331i	−0.463600	+	0.886045i	$0.653442\pi$
$234$	−5.19615	−	9.00000i	−0.339683	−	0.588348i
$235$	4.50000	+	7.79423i	0.293548	+	0.508439i
$236$	−1.09808	−	1.90192i	−0.0714787	−	0.123805i
$237$	−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
$241$		−	3.33975i		−	0.215132i	−0.994198	−	0.107566i	$-0.965694\pi$
$241$		−	3.33975i		−	0.215132i	0.994198	−	0.107566i	$-0.0343057\pi$
$242$	9.86603	−	5.69615i	0.634212	−	0.366163i
$243$	−7.79423	+	13.5000i	−0.500000	+	0.866025i
$244$		−	12.9282i		−	0.827643i
$245$	6.50000	−	2.59808i	0.415270	−	0.165985i
$246$		−	15.5885i		−	0.993884i
$247$	−4.39230			−0.279476
$248$	4.09808	−	7.09808i	0.260228	−	0.450728i
$249$	−19.3923			−1.22894
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$	−6.00000	+	5.19615i	−0.377964	+	0.327327i
$253$	−12.0000			−0.754434
$254$	9.86603	−	5.69615i	0.619049	−	0.357408i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	28.3923			1.77106			0.885532	−	0.464579i	$-0.153794\pi$
$257$	28.3923			1.77106			0.885532	+	0.464579i	$0.153794\pi$
$258$	−4.79423	+	2.76795i	−0.298476	+	0.172325i
$259$	−15.4904	−	5.36603i	−0.962525	−	0.333429i
$260$			3.46410i			0.214834i
$261$	16.7942	−	9.69615i	1.03954	−	0.600177i
$262$	−3.80385	+	2.19615i	−0.235002	+	0.135679i
$263$		−	13.7321i		−	0.846755i	−0.905953	−	0.423377i	$-0.860844\pi$
$263$		−	13.7321i		−	0.846755i	0.905953	−	0.423377i	$-0.139156\pi$
$264$	−4.09808	−	7.09808i	−0.252219	−	0.436856i
$265$	6.29423	−	3.63397i	0.386651	−	0.223233i
$266$	0.633975	+	3.29423i	0.0388715	+	0.201982i
$267$	7.60770			0.465583
$268$	−2.00000	−	3.46410i	−0.122169	−	0.211604i
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$	4.50000	−	2.59808i	0.273861	−	0.158114i
$271$	5.70577	+	3.29423i	0.346601	+	0.200110i	0.663187	−	0.748454i	$-0.269203\pi$
$271$	5.70577	+	3.29423i	0.346601	+	0.200110i	−0.316586	+	0.948564i	$0.602537\pi$
$272$		0			0
$273$	5.19615	−	15.0000i	0.314485	−	0.907841i
$274$	−3.63397	−	6.29423i	−0.219536	−	0.380248i
$275$		−	4.73205i		−	0.285353i
$276$			4.39230i			0.264386i
$277$	−24.1962			−1.45381			−0.726903	−	0.686740i	$-0.759041\pi$
$277$	−24.1962			−1.45381			−0.726903	+	0.686740i	$0.759041\pi$
$278$	−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	$0.522609\pi$
$282$		−	15.5885i		−	0.928279i
$283$	−14.5981	−	8.42820i	−0.867766	−	0.501005i	−0.00116049	−	0.999999i	$-0.500369\pi$
$283$	−14.5981	−	8.42820i	−0.867766	−	0.501005i	−0.866605	+	0.498995i	$0.833703\pi$
$284$	4.09808	+	2.36603i	0.243176	+	0.140398i
$285$		−	2.19615i		−	0.130089i
$286$	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
$290$	−6.46410			−0.379585
$291$		−	14.7846i		−	0.866689i
$292$		−	6.92820i		−	0.405442i
$293$	−8.19615	−	14.1962i	−0.478824	−	0.829348i	0.520881	−	0.853629i	$-0.325604\pi$
$293$	−8.19615	−	14.1962i	−0.478824	−	0.829348i	−0.999705	+	0.0242813i	$0.992270\pi$
$294$	−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
$297$		−	24.5885i		−	1.42677i
$298$	6.00000	+	10.3923i	0.347571	+	0.602010i
$299$	−4.39230	−	7.60770i	−0.254014	−	0.439964i
$300$	−1.73205			−0.100000
$301$	−7.99038	−	2.76795i	−0.460558	−	0.159542i
$302$	3.63397	−	2.09808i	0.209112	−	0.120731i
$303$	9.69615	+	16.7942i	0.557029	+	0.964803i
$304$			1.26795i			0.0727219i
$305$	−11.1962	+	6.46410i	−0.641090	+	0.370133i
$306$		0			0
$307$		−	23.7846i		−	1.35746i	−0.734388	−	0.678730i	$-0.762531\pi$
$307$		−	23.7846i		−	1.35746i	0.734388	−	0.678730i	$-0.237469\pi$
$308$	4.09808	−	11.8301i	0.233510	−	0.674084i
$309$	−18.1865	+	10.5000i	−1.03460	+	0.597324i
$310$	−8.19615			−0.465510
$311$	−7.90192	+	13.6865i	−0.448077	+	0.776092i	−0.998261	−	0.0589514i	$-0.981224\pi$
$311$	−7.90192	+	13.6865i	−0.448077	+	0.776092i	0.550184	+	0.835044i	$0.314558\pi$
$312$	3.00000	−	5.19615i	0.169842	−	0.294174i
$313$	−17.4904	+	10.0981i	−0.988615	+	0.570777i	−0.904860	−	0.425709i	$-0.860025\pi$
$313$	−17.4904	+	10.0981i	−0.988615	+	0.570777i	−0.0837548	+	0.996486i	$0.526691\pi$
$314$	17.6603			0.996626
$315$	7.50000	+	2.59808i	0.422577	+	0.146385i
$316$	−14.5885			−0.820665
$317$	17.7846	−	10.2679i	0.998883	−	0.576705i	0.0909655	−	0.995854i	$-0.471005\pi$
$317$	17.7846	−	10.2679i	0.998883	−	0.576705i	0.907918	+	0.419149i	$0.137671\pi$
$318$	−12.5885			−0.705926
$319$	−15.2942	+	26.4904i	−0.856312	+	1.48318i
$320$	1.00000			0.0559017
$321$		−	27.5885i		−	1.53984i
$322$	−5.07180	+	4.39230i	−0.282640	+	0.244774i
$323$		0			0
$324$	−9.00000			−0.500000
$325$	3.00000	−	1.73205i	0.166410	−	0.0960769i
$326$			8.39230i			0.464807i
$327$	6.23205	−	10.7942i	0.344633	−	0.596922i
$328$	7.79423	−	4.50000i	0.430364	−	0.248471i
$329$	18.0000	−	15.5885i	0.992372	−	0.859419i
$330$	−4.09808	+	7.09808i	−0.225592	+	0.390736i
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$	−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
$336$	−4.33013	−	1.50000i	−0.236228	−	0.0818317i
$337$	−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	$0.921140\pi$
$338$		−	1.00000i		−	0.0543928i
$339$	18.8827	+	10.9019i	1.02557	+	0.592111i
$340$		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
$345$	3.80385	−	2.19615i	0.204792	−	0.118237i
$346$	−7.09808	−	4.09808i	−0.381595	−	0.220314i
$347$	18.4019	+	10.6244i	0.987867	+	0.570345i	0.904636	−	0.426185i	$-0.140143\pi$
$347$	18.4019	+	10.6244i	0.987867	+	0.570345i	0.0832310	+	0.996530i	$0.473476\pi$
$348$	9.69615	+	5.59808i	0.519768	+	0.300088i
$349$	14.1962	+	8.19615i	0.759903	+	0.438730i	0.829261	−	0.558862i	$-0.188762\pi$
$349$	14.1962	+	8.19615i	0.759903	+	0.438730i	−0.0693582	+	0.997592i	$0.522095\pi$
$350$	−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
$353$	−0.588457			−0.0313204			−0.0156602	−	0.999877i	$-0.504985\pi$
$353$	−0.588457			−0.0313204			−0.0156602	+	0.999877i	$0.504985\pi$
$354$	3.29423	−	1.90192i	0.175086	−	0.101086i
$355$		−	4.73205i		−	0.251151i
$356$	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	$-0.470268\pi$
$359$	−13.6865	−	7.90192i	−0.722348	−	0.417048i	−0.815616	+	0.578593i	$0.803602\pi$
$360$	2.59808	+	1.50000i	0.136931	+	0.0790569i
$361$	−8.69615	−	15.0622i	−0.457692	−	0.792746i
$362$	−6.69615	−	11.5981i	−0.351942	−	0.609581i
$363$	9.86603	+	17.0885i	0.517832	+	0.896911i
$364$	9.00000	−	1.73205i	0.471728	−	0.0907841i
$365$	−6.00000	+	3.46410i	−0.314054	+	0.181319i
$366$	22.3923			1.17046
$367$			29.1962i			1.52403i	0.647561	+	0.762013i	$0.275789\pi$
$367$			29.1962i			1.52403i	−0.647561	+	0.762013i	$0.724211\pi$
$368$	−2.19615	+	1.26795i	−0.114482	+	0.0660964i
$369$	27.0000			1.40556
$370$			6.19615i			0.322123i
$371$	−12.5885	−	14.5359i	−0.653560	−	0.754666i
$372$	12.2942	+	7.09808i	0.637426	+	0.368018i
$373$	10.1962			0.527937			0.263968	−	0.964531i	$-0.414969\pi$
$373$	10.1962			0.527937			0.263968	+	0.964531i	$0.414969\pi$
$374$		0			0
$375$	0.866025	+	1.50000i	0.0447214	+	0.0774597i
$376$	7.79423	−	4.50000i	0.401957	−	0.232070i
$377$	−22.3923			−1.15326
$378$	−9.00000	−	10.3923i	−0.462910	−	0.534522i
$379$	−9.60770			−0.493514			−0.246757	−	0.969077i	$-0.579365\pi$
$379$	−9.60770			−0.493514			−0.246757	+	0.969077i	$0.579365\pi$
$380$	1.09808	−	0.633975i	0.0563301	−	0.0325222i
$381$	9.86603	+	17.0885i	0.505452	+	0.875468i
$382$	−1.73205	+	3.00000i	−0.0886194	+	0.153493i
$383$	19.3923			0.990900			0.495450	−	0.868636i	$-0.335003\pi$
$383$	19.3923			0.990900			0.495450	+	0.868636i	$0.335003\pi$
$384$	−1.50000	−	0.866025i	−0.0765466	−	0.0441942i
$385$	−12.2942	+	2.36603i	−0.626572	+	0.120584i
$386$		−	13.8038i		−	0.702597i
$387$	−4.79423	−	8.30385i	−0.243704	−	0.422108i
$388$	7.39230	−	4.26795i	0.375287	−	0.216672i
$389$			24.7128i			1.25299i	0.779426	+	0.626495i	$0.215511\pi$
$389$			24.7128i			1.25299i	−0.779426	+	0.626495i	$0.784489\pi$
$390$	−6.00000			−0.303822
$391$		0			0
$392$	−2.59808	−	6.50000i	−0.131223	−	0.328300i
$393$	−3.80385	−	6.58846i	−0.191879	−	0.332344i
$394$	−11.8301	−	20.4904i	−0.595993	−	1.03229i
$395$	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	−0.344290	−	0.938863i	$-0.611880\pi$
$397$	−26.4904	−	15.2942i	−1.32951	−	0.767595i	−0.985224	+	0.171268i	$0.945214\pi$
$398$	−3.46410	+	6.00000i	−0.173640	+	0.300753i
$399$	−5.70577	+	1.09808i	−0.285646	+	0.0549726i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$		−	3.58846i		−	0.179199i	−0.995978	−	0.0895995i	$-0.971441\pi$
$401$		−	3.58846i		−	0.179199i	0.995978	−	0.0895995i	$-0.0285587\pi$
$402$	6.00000	−	3.46410i	0.299253	−	0.172774i
$403$	−28.3923			−1.41432
$404$	−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
$409$	−9.10770	−	5.25833i	−0.450347	−	0.260008i	0.257630	−	0.966244i	$-0.417058\pi$
$409$	−9.10770	−	5.25833i	−0.450347	−	0.260008i	−0.707977	+	0.706236i	$0.750392\pi$
$410$	−7.79423	−	4.50000i	−0.384930	−	0.222239i
$411$	10.9019	−	6.29423i	0.537752	−	0.310471i
$412$	−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
$416$	3.46410			0.169842
$417$	−33.0788	−	19.0981i	−1.61988	−	0.935237i
$418$		−	6.00000i		−	0.293470i
$419$	5.19615	+	9.00000i	0.253849	+	0.439679i	0.964582	−	0.263783i	$-0.0849701\pi$
$419$	5.19615	+	9.00000i	0.253849	+	0.439679i	−0.710734	+	0.703461i	$0.751637\pi$
$420$	0.866025	+	4.50000i	0.0422577	+	0.219578i
$421$	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
$423$	27.0000			1.31278
$424$	−3.63397	−	6.29423i	−0.176481	−	0.305675i
$425$		0			0
$426$	−4.09808	+	7.09808i	−0.198552	+	0.343903i
$427$	22.3923	+	25.8564i	1.08364	+	1.25128i
$428$	13.7942	−	7.96410i	0.666769	−	0.384959i
$429$	−14.1962	+	24.5885i	−0.685397	+	1.18714i
$430$			3.19615i			0.154132i
$431$	−33.5885	+	19.3923i	−1.61790	+	0.934094i	−0.630437	+	0.776241i	$0.717124\pi$
$431$	−33.5885	+	19.3923i	−1.61790	+	0.934094i	−0.987463	+	0.157854i	$0.949543\pi$
$432$	−2.59808	−	4.50000i	−0.125000	−	0.216506i
$433$			18.0000i			0.865025i	0.901628	+	0.432512i	$0.142373\pi$
$433$			18.0000i			0.865025i	−0.901628	+	0.432512i	$0.857627\pi$
$434$	4.09808	+	21.2942i	0.196714	+	1.02216i
$435$		−	11.1962i		−	0.536814i
$436$	7.19615			0.344633
$437$	−1.60770	+	2.78461i	−0.0769065	+	0.133206i
$438$	12.0000			0.573382
$439$	25.6865	−	14.8301i	1.22595	−	0.707803i	0.259771	−	0.965670i	$-0.416353\pi$
$439$	25.6865	−	14.8301i	1.22595	−	0.707803i	0.966180	+	0.257867i	$0.0830196\pi$
$440$	−4.73205			−0.225592
$441$	3.00000	−	20.7846i	0.142857	−	0.989743i
$442$		0			0
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	−0.303281	−	0.952901i	$-0.598082\pi$
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	0.673596	+	0.739100i	$0.264749\pi$
$444$	5.36603	−	9.29423i	0.254660	−	0.441085i
$445$	2.19615	−	3.80385i	0.104108	−	0.180320i
$446$	−13.7321			−0.650231
$447$	−18.0000	+	10.3923i	−0.851371	+	0.491539i
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$		−	9.58846i		−	0.452507i	−0.974068	−	0.226254i	$-0.927352\pi$
$449$		−	9.58846i		−	0.452507i	0.974068	−	0.226254i	$-0.0726478\pi$
$450$		−	3.00000i		−	0.141421i
$451$	−36.8827	+	21.2942i	−1.73674	+	1.00271i
$452$			12.5885i			0.592111i
$453$	3.63397	+	6.29423i	0.170739	+	0.295729i
$454$	14.1962	−	8.19615i	0.666258	−	0.384664i
$455$	−6.00000	−	6.92820i	−0.281284	−	0.324799i
$456$	−2.19615			−0.102844
$457$	−1.19615	−	2.07180i	−0.0559537	−	0.0969146i	0.836692	−	0.547674i	$-0.184487\pi$
$457$	−1.19615	−	2.07180i	−0.0559537	−	0.0969146i	−0.892645	+	0.450759i	$0.851153\pi$
$458$	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	−0.920164	−	0.391533i	$-0.871945\pi$
$461$	−2.59808	+	4.50000i	−0.121004	+	0.209586i	0.799160	+	0.601119i	$0.205278\pi$
$462$	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	$0.814034\pi$
$464$			6.46410i			0.300088i
$465$		−	14.1962i		−	0.658331i
$466$	−1.26795			−0.0587366
$467$	3.40192	−	5.89230i	0.157422	−	0.272663i	−0.776516	−	0.630097i	$-0.783015\pi$
$467$	3.40192	−	5.89230i	0.157422	−	0.272663i	0.933938	+	0.357434i	$0.116348\pi$
$468$	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
$471$			30.5885i			1.40944i
$472$	1.90192	+	1.09808i	0.0875431	+	0.0505431i
$473$	13.0981	+	7.56218i	0.602250	+	0.347709i
$474$		−	25.2679i		−	1.16060i
$475$	−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
$479$	−10.3923			−0.474837			−0.237418	−	0.971408i	$-0.576301\pi$
$479$	−10.3923			−0.474837			−0.237418	+	0.971408i	$0.576301\pi$
$480$			1.73205i			0.0790569i
$481$			21.4641i			0.978679i
$482$	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
$486$		−	15.5885i		−	0.707107i
$487$	−17.0000	−	29.4449i	−0.770344	−	1.33427i	−0.937375	−	0.348323i	$-0.886751\pi$
$487$	−17.0000	−	29.4449i	−0.770344	−	1.33427i	0.167031	−	0.985952i	$-0.446582\pi$
$488$	6.46410	+	11.1962i	0.292616	+	0.506826i
$489$	−14.5359			−0.657336
$490$	−4.33013	+	5.50000i	−0.195615	+	0.248465i
$491$	−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	$0.542989\pi$
$492$	7.79423	+	13.5000i	0.351391	+	0.608627i
$493$		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
$497$	−12.2942	+	2.36603i	−0.551472	+	0.106131i
$498$	16.7942	−	9.69615i	0.752567	−	0.434495i
$499$	−16.1962			−0.725039			−0.362520	−	0.931976i	$-0.618083\pi$
$499$	−16.1962			−0.725039			−0.362520	+	0.931976i	$0.618083\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	9.00000	−	15.5885i	0.402090	−	0.696441i
$502$	15.5885	−	9.00000i	0.695747	−	0.401690i
$503$	−7.39230			−0.329607			−0.164803	−	0.986326i	$-0.552699\pi$
$503$	−7.39230			−0.329607			−0.164803	+	0.986326i	$0.552699\pi$
$504$	2.59808	−	7.50000i	0.115728	−	0.334077i
$505$	11.1962			0.498222
$506$	10.3923	−	6.00000i	0.461994	−	0.266733i
$507$	1.73205			0.0769231
$508$	−5.69615	+	9.86603i	−0.252726	+	0.437734i
$509$	9.58846			0.425001			0.212500	−	0.977161i	$-0.431839\pi$
$509$	9.58846			0.425001			0.212500	+	0.977161i	$0.431839\pi$
$510$		0			0
$511$	12.0000	+	13.8564i	0.530849	+	0.612971i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.70577	−	3.29423i	−0.251916	−	0.145444i
$514$	−24.5885	+	14.1962i	−1.08455	+	0.626165i
$515$			12.1244i			0.534263i
$516$	2.76795	−	4.79423i	0.121852	−	0.211054i
$517$	−36.8827	+	21.2942i	−1.62210	+	0.936519i
$518$	16.0981	−	3.09808i	0.707309	−	0.136122i
$519$	7.09808	−	12.2942i	0.311571	−	0.539657i
$520$	−1.73205	−	3.00000i	−0.0759555	−	0.131559i
$521$	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	$0.681178\pi$
$522$	−9.69615	+	16.7942i	−0.424389	+	0.735063i
$523$	28.5788	+	16.5000i	1.24967	+	0.721495i	0.971043	−	0.238906i	$-0.0767888\pi$
$523$	28.5788	+	16.5000i	1.24967	+	0.721495i	0.278623	+	0.960401i	$0.410122\pi$
$524$	2.19615	−	3.80385i	0.0959394	−	0.166172i
$525$	3.46410	−	3.00000i	0.151186	−	0.130931i
$526$	6.86603	+	11.8923i	0.299373	+	0.518529i
$527$		0			0
$528$	7.09808	+	4.09808i	0.308904	+	0.178346i
$529$	16.5692			0.720401
$530$	−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
$534$	−6.58846	+	3.80385i	−0.285110	+	0.164609i
$535$	−13.7942	−	7.96410i	−0.596377	−	0.344318i
$536$	3.46410	+	2.00000i	0.149626	+	0.0863868i
$537$	−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	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$	−6.58846			−0.282998
$543$	20.0885	−	11.5981i	0.862078	−	0.497721i
$544$		0			0
$545$	−3.59808	−	6.23205i	−0.154125	−	0.266952i
$546$	3.00000	+	15.5885i	0.128388	+	0.667124i
$547$	−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
$549$			38.7846i			1.65529i
$550$	2.36603	+	4.09808i	0.100888	+	0.174743i
$551$	4.09808	+	7.09808i	0.174584	+	0.302388i
$552$	−2.19615	−	3.80385i	−0.0934745	−	0.161903i
$553$	29.1769	−	25.2679i	1.24073	−	1.07450i
$554$	20.9545	−	12.0981i	0.890271	−	0.513998i
$555$	−10.7321			−0.455550
$556$		−	22.0526i		−	0.935237i
$557$	28.3923	−	16.3923i	1.20302	−	0.694564i	0.241795	−	0.970327i	$-0.422264\pi$
$557$	28.3923	−	16.3923i	1.20302	−	0.694564i	0.961226	+	0.275763i	$0.0889305\pi$
$558$	−12.2942	+	21.2942i	−0.520456	+	0.901457i
$559$			11.0718i			0.468287i
$560$	−2.00000	+	1.73205i	−0.0845154	+	0.0731925i
$561$		0			0
$562$	−14.6603			−0.618405
$563$	−6.80385	+	11.7846i	−0.286748	+	0.496662i	−0.973032	−	0.230672i	$-0.925908\pi$
$563$	−6.80385	+	11.7846i	−0.286748	+	0.496662i	0.686284	+	0.727334i	$0.259241\pi$
$564$	7.79423	+	13.5000i	0.328196	+	0.568453i
$565$	10.9019	−	6.29423i	0.458647	−	0.264800i
$566$	16.8564			0.708528
$567$	18.0000	−	15.5885i	0.755929	−	0.654654i
$568$	−4.73205			−0.198552
$569$	−5.19615	+	3.00000i	−0.217834	+	0.125767i	−0.604947	−	0.796266i	$-0.706806\pi$
$569$	−5.19615	+	3.00000i	−0.217834	+	0.125767i	0.387113	+	0.922032i	$0.373472\pi$
$570$	1.09808	+	1.90192i	0.0459934	+	0.0796628i
$571$	−10.8038	+	18.7128i	−0.452127	+	0.783107i	−0.998518	−	0.0544234i	$-0.982668\pi$
$571$	−10.8038	+	18.7128i	−0.452127	+	0.783107i	0.546391	+	0.837530i	$0.316001\pi$
$572$	−16.3923			−0.685397
$573$	−5.19615	−	3.00000i	−0.217072	−	0.125327i
$574$	−7.79423	+	22.5000i	−0.325325	+	0.939132i
$575$		−	2.53590i		−	0.105754i
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	20.7846	−	12.0000i	0.865275	−	0.499567i	−0.000500448	−	1.00000i	$-0.500159\pi$
$577$	20.7846	−	12.0000i	0.865275	−	0.499567i	0.865775	+	0.500433i	$0.166826\pi$
$578$			17.0000i			0.707107i
$579$	23.9090			0.993623
$580$	5.59808	−	3.23205i	0.232447	−	0.134204i
$581$	27.9904	+	9.69615i	1.16124	+	0.402264i
$582$	7.39230	+	12.8038i	0.306421	+	0.530737i
$583$	17.1962	+	29.7846i	0.712192	+	1.23355i
$584$	3.46410	+	6.00000i	0.143346	+	0.248282i
$585$		−	10.3923i		−	0.429669i
$586$	14.1962	+	8.19615i	0.586438	+	0.338580i
$587$	15.4019	−	26.6769i	0.635705	−	1.10107i	−0.350660	−	0.936503i	$-0.614043\pi$
$587$	15.4019	−	26.6769i	0.635705	−	1.10107i	0.986365	−	0.164571i	$-0.0526240\pi$
$588$	11.2583	−	4.50000i	0.464286	−	0.185577i
$589$	5.19615	+	9.00000i	0.214104	+	0.370839i
$590$		−	2.19615i		−	0.0904142i
$591$	35.4904	−	20.4904i	1.45988	−	0.842862i
$592$	6.19615			0.254660
$593$	−13.3923	+	23.1962i	−0.549956	+	0.952552i	0.448321	+	0.893873i	$0.352022\pi$
$593$	−13.3923	+	23.1962i	−0.549956	+	0.952552i	−0.998277	+	0.0586791i	$0.981311\pi$
$594$	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
$598$	7.60770	+	4.39230i	0.311102	+	0.179615i
$599$	3.80385	+	2.19615i	0.155421	+	0.0897324i	0.575693	−	0.817666i	$-0.304732\pi$
$599$	3.80385	+	2.19615i	0.155421	+	0.0897324i	−0.420272	+	0.907398i	$0.638066\pi$
$600$	1.50000	−	0.866025i	0.0612372	−	0.0353553i
$601$	27.5885	+	15.9282i	1.12536	+	0.649725i	0.942763	−	0.333464i	$-0.108217\pi$
$601$	27.5885	+	15.9282i	1.12536	+	0.649725i	0.182594	+	0.983188i	$0.441551\pi$
$602$	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
$605$	11.3923			0.463163
$606$	−16.7942	−	9.69615i	−0.682219	−	0.393879i
$607$		−	6.12436i		−	0.248580i	−0.992246	−	0.124290i	$-0.960335\pi$
$607$		−	6.12436i		−	0.248580i	0.992246	−	0.124290i	$-0.0396653\pi$
$608$	−0.633975	−	1.09808i	−0.0257111	−	0.0445329i
$609$	−29.0885	+	5.59808i	−1.17872	+	0.226845i
$610$	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	0.926365	−	0.376627i	$-0.122916\pi$
$613$	3.39230	+	5.87564i	0.137014	+	0.237315i	−0.789351	+	0.613942i	$0.789583\pi$
$614$	11.8923	+	20.5981i	0.479934	+	0.831271i
$615$	7.79423	−	13.5000i	0.314294	−	0.544373i
$616$	2.36603	+	12.2942i	0.0953299	+	0.495349i
$617$	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
$619$		−	16.3923i		−	0.658862i	−0.944180	−	0.329431i	$-0.893143\pi$
$619$		−	16.3923i		−	0.658862i	0.944180	−	0.329431i	$-0.106857\pi$
$620$	7.09808	−	4.09808i	0.285066	−	0.164583i
$621$		−	13.1769i		−	0.528771i
$622$		−	15.8038i		−	0.633677i
$623$	−10.9808	−	3.80385i	−0.439935	−	0.152398i
$624$			6.00000i			0.240192i
$625$	1.00000			0.0400000
$626$	10.0981	−	17.4904i	0.403600	−	0.699056i
$627$	10.3923			0.415029
$628$	−15.2942	+	8.83013i	−0.610306	+	0.352360i
$629$		0			0
$630$	−7.79423	+	1.50000i	−0.310530	+	0.0597614i
$631$	12.3923			0.493330			0.246665	−	0.969101i	$-0.420665\pi$
$631$	12.3923			0.493330			0.246665	+	0.969101i	$0.420665\pi$
$632$	12.6340	−	7.29423i	0.502553	−	0.290149i
$633$	17.8301	−	30.8827i	0.708684	−	1.22748i
$634$	−10.2679	+	17.7846i	−0.407792	+	0.706317i
$635$	11.3923			0.452090
$636$	10.9019	−	6.29423i	0.432289	−	0.249582i
$637$	−15.0000	+	19.0526i	−0.594322	+	0.754890i
$638$		−	30.5885i		−	1.21101i
$639$	−12.2942	−	7.09808i	−0.486352	−	0.280796i
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$			3.21539i			0.127000i	0.997982	+	0.0635001i	$0.0202263\pi$
$641$			3.21539i			0.127000i	−0.997982	+	0.0635001i	$0.979774\pi$
$642$	13.7942	+	23.8923i	0.544415	+	0.942954i
$643$	16.2058	−	9.35641i	0.639093	−	0.368981i	−0.145172	−	0.989406i	$-0.546374\pi$
$643$	16.2058	−	9.35641i	0.639093	−	0.368981i	0.784265	+	0.620426i	$0.213040\pi$
$644$	2.19615	−	6.33975i	0.0865405	−	0.249821i
$645$	−5.53590			−0.217976
$646$		0			0
$647$	2.30385	+	3.99038i	0.0905736	+	0.156878i	0.907753	−	0.419506i	$-0.137797\pi$
$647$	2.30385	+	3.99038i	0.0905736	+	0.156878i	−0.817179	+	0.576384i	$0.804463\pi$
$648$	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
$653$			49.8564i			1.95103i	0.219929	+	0.975516i	$0.429418\pi$
$653$			49.8564i			1.95103i	−0.219929	+	0.975516i	$0.570582\pi$
$654$			12.4641i			0.487385i
$655$	−4.39230			−0.171622
$656$	−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	$0.936036\pi$
$660$		−	8.19615i		−	0.319035i
$661$	11.3827	+	6.57180i	0.442735	+	0.255613i	0.704757	−	0.709449i	$-0.251056\pi$
$661$	11.3827	+	6.57180i	0.442735	+	0.255613i	−0.262022	+	0.965062i	$0.584389\pi$
$662$	−6.92820	−	4.00000i	−0.269272	−	0.155464i
$663$		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
$668$	10.3923			0.402090
$669$		−	23.7846i		−	0.919566i
$670$		−	4.00000i		−	0.154533i
$671$	−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
$675$	5.19615			0.200000
$676$	0.500000	+	0.866025i	0.0192308	+	0.0333087i
$677$	11.4904	+	19.9019i	0.441611	+	0.764893i	0.997809	−	0.0661567i	$-0.0210737\pi$
$677$	11.4904	+	19.9019i	0.441611	+	0.764893i	−0.556198	+	0.831050i	$0.687740\pi$
$678$	−21.8038			−0.837372
$679$	−7.39230	+	21.3397i	−0.283691	+	0.818944i
$680$		0			0
$681$	14.1962	+	24.5885i	0.543998	+	0.942232i
$682$		−	38.7846i		−	1.48514i
$683$	30.7750	−	17.7679i	1.17757	−	0.679872i	0.222121	−	0.975019i	$-0.428702\pi$
$683$	30.7750	−	17.7679i	1.17757	−	0.679872i	0.955452	+	0.295148i	$0.0953688\pi$
$684$		−	3.80385i		−	0.145444i
$685$		−	7.26795i		−	0.277694i
$686$	16.4545	+	8.50000i	0.628235	+	0.324532i
$687$	−21.1077	+	12.1865i	−0.805309	+	0.464945i
$688$	3.19615			0.121852
$689$	−12.5885	+	21.8038i	−0.479582	+	0.830660i
$690$	−2.19615	+	3.80385i	−0.0836061	+	0.144810i
$691$	−4.39230	+	2.53590i	−0.167091	+	0.0964701i	−0.581214	−	0.813751i	$-0.697422\pi$
$691$	−4.39230	+	2.53590i	−0.167091	+	0.0964701i	0.414122	+	0.910221i	$0.364089\pi$
$692$	8.19615			0.311571
$693$	−12.2942	+	35.4904i	−0.467019	+	1.34817i
$694$	−21.2487			−0.806590
$695$	−19.0981	+	11.0263i	−0.724431	+	0.418251i
$696$	−11.1962			−0.424389
$697$		0			0
$698$	−16.3923			−0.620458
$699$		−	2.19615i		−	0.0830661i
$700$	2.50000	+	0.866025i	0.0944911	+	0.0327327i
$701$		−	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
$704$			4.73205i			0.178346i
$705$	7.79423	−	13.5000i	0.293548	−	0.508439i
$706$	0.509619	−	0.294229i	0.0191798	−	0.0110734i
$707$	−5.59808	−	29.0885i	−0.210537	−	1.09398i
$708$	−1.90192	+	3.29423i	−0.0714787	+	0.123805i
$709$	23.3923	+	40.5167i	0.878516	+	1.52164i	0.852969	+	0.521962i	$0.174800\pi$
$709$	23.3923	+	40.5167i	0.878516	+	1.52164i	0.0255474	+	0.999674i	$0.491867\pi$
$710$	2.36603	+	4.09808i	0.0887954	+	0.153798i
$711$	43.7654			1.64133
$712$	−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
$716$		−	24.5885i		−	0.918914i
$717$	−4.68653	−	2.70577i	−0.175022	−	0.101049i
$718$	15.8038			0.589794
$719$	20.7846	−	36.0000i	0.775135	−	1.34257i	−0.159583	−	0.987184i	$-0.551015\pi$
$719$	20.7846	−	36.0000i	0.775135	−	1.34257i	0.934718	−	0.355389i	$-0.115652\pi$
$720$	−3.00000			−0.111803
$721$	31.5000	−	6.06218i	1.17312	−	0.225767i
$722$	15.0622	+	8.69615i	0.560556	+	0.323637i
$723$	−5.00962	+	2.89230i	−0.186310	+	0.107566i
$724$	11.5981	+	6.69615i	0.431039	+	0.248861i
$725$	−5.59808	−	3.23205i	−0.207907	−	0.120035i
$726$	−17.0885	−	9.86603i	−0.634212	−	0.366163i
$727$	−41.7846	−	24.1244i	−1.54971	−	0.894723i	−0.998164	−	0.0605756i	$-0.980706\pi$
$727$	−41.7846	−	24.1244i	−1.54971	−	0.894723i	−0.551542	−	0.834147i	$-0.685960\pi$
$728$	−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
$733$		−	34.0526i		−	1.25776i	−0.777502	−	0.628880i	$-0.783514\pi$
$733$		−	34.0526i		−	1.25776i	0.777502	−	0.628880i	$-0.216486\pi$
$734$	−14.5981	−	25.2846i	−0.538825	−	0.933272i
$735$	−9.52628	−	7.50000i	−0.351382	−	0.276642i
$736$	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	−0.991204	−	0.132345i	$-0.957749\pi$
$739$	−16.5885	−	28.7321i	−0.610216	−	1.05693i	0.380987	−	0.924580i	$-0.375584\pi$
$740$	−3.09808	−	5.36603i	−0.113888	−	0.197259i
$741$	3.80385	+	6.58846i	0.139738	+	0.242033i
$742$	18.1699	+	6.29423i	0.667037	+	0.231068i
$743$	−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	$0.500551\pi$
$744$	−14.1962			−0.520456
$745$			12.0000i			0.439646i
$746$	−8.83013	+	5.09808i	−0.323294	+	0.186654i
$747$	16.7942	+	29.0885i	0.614469	+	1.06429i
$748$		0			0
$749$	−13.7942	+	39.8205i	−0.504030	+	1.45501i
$750$	−1.50000	−	0.866025i	−0.0547723	−	0.0316228i
$751$	−21.6077			−0.788476			−0.394238	−	0.919008i	$-0.628991\pi$
$751$	−21.6077			−0.788476			−0.394238	+	0.919008i	$0.628991\pi$
$752$	−4.50000	+	7.79423i	−0.164098	+	0.284226i
$753$	15.5885	+	27.0000i	0.568075	+	0.983935i
$754$	19.3923	−	11.1962i	0.706226	−	0.407740i
$755$	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	$0.549885\pi$
$758$	8.32051	−	4.80385i	0.302214	−	0.174484i
$759$	10.3923	+	18.0000i	0.377217	+	0.653359i
$760$	−0.633975	+	1.09808i	−0.0229967	+	0.0398314i
$761$	−33.0000			−1.19625			−0.598125	−	0.801403i	$-0.704087\pi$
$761$	−33.0000			−1.19625			−0.598125	+	0.801403i	$0.704087\pi$
$762$	−17.0885	−	9.86603i	−0.619049	−	0.357408i
$763$	−14.3923	+	12.4641i	−0.521036	+	0.451231i
$764$		−	3.46410i		−	0.125327i
$765$		0			0
$766$	−16.7942	+	9.69615i	−0.606800	+	0.350336i
$767$		−	7.60770i		−	0.274698i
$768$	1.73205			0.0625000
$769$	13.5000	−	7.79423i	0.486822	−	0.281067i	−0.236433	−	0.971648i	$-0.575978\pi$
$769$	13.5000	−	7.79423i	0.486822	−	0.281067i	0.723255	+	0.690581i	$0.242645\pi$
$770$	9.46410	−	8.19615i	0.341063	−	0.295369i
$771$	−24.5885	−	42.5885i	−0.885532	−	1.53379i
$772$	6.90192	+	11.9545i	0.248406	+	0.430251i
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	0.657542	−	0.753418i	$-0.271596\pi$
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	−0.981250	+	0.192740i	$0.938263\pi$
$774$	8.30385	+	4.79423i	0.298476	+	0.172325i
$775$	−7.09808	−	4.09808i	−0.254970	−	0.147207i
$776$	−4.26795	+	7.39230i	−0.153210	+	0.265368i
$777$	5.36603	+	27.8827i	0.192505	+	1.00029i
$778$	−12.3564	−	21.4019i	−0.442999	−	0.767296i
$779$			11.4115i			0.408861i
$780$	5.19615	−	3.00000i	0.186052	−	0.107417i
$781$	22.3923			0.801260
$782$		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
$787$	−8.00962	−	4.62436i	−0.285512	−	0.164840i	0.350404	−	0.936599i	$-0.386044\pi$
$787$	−8.00962	−	4.62436i	−0.285512	−	0.164840i	−0.635916	+	0.771758i	$0.719378\pi$
$788$	20.4904	+	11.8301i	0.729940	+	0.421431i
$789$	−20.5981	+	11.8923i	−0.733311	+	0.423377i
$790$	−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
$794$	30.5885			1.08554
$795$	−10.9019	−	6.29423i	−0.386651	−	0.223233i
$796$		−	6.92820i		−	0.245564i
$797$	−9.58846	−	16.6077i	−0.339641	−	0.588275i	0.644724	−	0.764415i	$-0.276972\pi$
$797$	−9.58846	−	16.6077i	−0.339641	−	0.588275i	−0.984365	+	0.176140i	$0.943639\pi$
$798$	4.39230	−	3.80385i	0.155486	−	0.134655i
$799$		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
$803$	−16.3923	−	28.3923i	−0.578472	−	1.00194i
$804$	−3.46410	+	6.00000i	−0.122169	+	0.211604i
$805$	−6.58846	+	1.26795i	−0.232213	+	0.0446893i
$806$	24.5885	−	14.1962i	0.866091	−	0.500038i
$807$	15.5885	−	27.0000i	0.548740	−	0.950445i
$808$		−	11.1962i		−	0.393879i
$809$	45.4808	−	26.2583i	1.59902	−	0.923194i	0.607342	−	0.794441i	$-0.292236\pi$
$809$	45.4808	−	26.2583i	1.59902	−	0.923194i	0.991677	−	0.128753i	$-0.0410975\pi$
$810$	−7.79423	−	4.50000i	−0.273861	−	0.158114i
$811$		−	44.5359i		−	1.56387i	−0.623362	−	0.781933i	$-0.714234\pi$
$811$		−	44.5359i		−	1.56387i	0.623362	−	0.781933i	$-0.285766\pi$
$812$	−11.1962	−	12.9282i	−0.392908	−	0.453691i
$813$		−	11.4115i		−	0.400220i
$814$	−29.3205			−1.02768
$815$	−4.19615	+	7.26795i	−0.146985	+	0.254585i
$816$		0			0
$817$	3.50962	−	2.02628i	0.122786	−	0.0708905i
$818$	10.5167			0.367706
$819$	−27.0000	+	5.19615i	−0.943456	+	0.181568i
$820$	9.00000			0.314294
$821$	31.7942	−	18.3564i	1.10963	−	0.640643i	0.170894	−	0.985289i	$-0.445335\pi$
$821$	31.7942	−	18.3564i	1.10963	−	0.640643i	0.938733	+	0.344646i	$0.112001\pi$
$822$	−6.29423	+	10.9019i	−0.219536	+	0.380248i
$823$	−15.3038	+	26.5070i	−0.533459	+	0.923977i	0.465778	+	0.884902i	$0.345775\pi$
$823$	−15.3038	+	26.5070i	−0.533459	+	0.923977i	−0.999236	+	0.0390756i	$0.987559\pi$
$824$	12.1244			0.422372
$825$	−7.09808	+	4.09808i	−0.247123	+	0.142677i
$826$	−5.70577	+	1.09808i	−0.198529	+	0.0382070i
$827$			31.6410i			1.10027i	0.835077	+	0.550133i	$0.185423\pi$
$827$			31.6410i			1.10027i	−0.835077	+	0.550133i	$0.814577\pi$
$828$	6.58846	−	3.80385i	0.228965	−	0.132193i
$829$	30.1865	−	17.4282i	1.04842	−	0.605307i	0.126215	−	0.992003i	$-0.459717\pi$
$829$	30.1865	−	17.4282i	1.04842	−	0.605307i	0.922207	+	0.386696i	$0.126384\pi$
$830$		−	11.1962i		−	0.388624i
$831$	20.9545	+	36.2942i	0.726903	+	1.25903i
$832$	−3.00000	+	1.73205i	−0.104006	+	0.0600481i
$833$		0			0
$834$	38.1962			1.32262
$835$	−5.19615	−	9.00000i	−0.179820	−	0.311458i
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$	−36.8827	−	21.2942i	−1.27485	−	0.736036i
$838$	−9.00000	−	5.19615i	−0.310900	−	0.179498i
$839$	1.90192	−	3.29423i	0.0656617	−	0.113729i	−0.831326	−	0.555786i	$-0.812418\pi$
$839$	1.90192	−	3.29423i	0.0656617	−	0.113729i	0.896987	+	0.442056i	$0.145751\pi$
$840$	−3.00000	−	3.46410i	−0.103510	−	0.119523i
$841$	6.39230	+	11.0718i	0.220424	+	0.381786i
$842$			29.9808i			1.03321i
$843$		−	25.3923i		−	0.874557i
$844$	20.5885			0.708684
$845$	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
$849$			29.1962i			1.00201i
$850$		0			0
$851$	13.6077	+	7.85641i	0.466466	+	0.269314i
$852$		−	8.19615i		−	0.280796i
$853$	−2.78461	−	1.60770i	−0.0953432	−	0.0550464i	0.451570	−	0.892236i	$-0.350864\pi$
$853$	−2.78461	−	1.60770i	−0.0953432	−	0.0550464i	−0.546914	+	0.837189i	$0.684197\pi$
$854$	−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
$857$	−17.4115			−0.594767			−0.297383	−	0.954758i	$-0.596114\pi$
$857$	−17.4115			−0.594767			−0.297383	+	0.954758i	$0.596114\pi$
$858$		−	28.3923i		−	0.969297i
$859$		−	15.8038i		−	0.539220i	−0.962970	−	0.269610i	$-0.913105\pi$
$859$		−	15.8038i		−	0.539220i	0.962970	−	0.269610i	$-0.0868948\pi$
$860$	−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	$-0.167019\pi$
$863$	25.3923	+	14.6603i	0.864364	+	0.499041i	−0.00110718	+	0.999999i	$0.500352\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$	−4.09808	−	7.09808i	−0.139339	−	0.241342i
$866$	−9.00000	−	15.5885i	−0.305832	−	0.529717i
$867$	−29.4449			−1.00000
$868$	−14.1962	−	16.3923i	−0.481849	−	0.556391i
$869$	−59.7846	+	34.5167i	−2.02805	+	1.17090i
$870$	5.59808	+	9.69615i	0.189793	+	0.328730i
$871$		−	13.8564i		−	0.469506i
$872$	−6.23205	+	3.59808i	−0.211044	+	0.121846i
$873$	−22.1769	+	12.8038i	−0.750575	+	0.433345i
$874$		−	3.21539i		−	0.108762i
$875$	−0.500000	−	2.59808i	−0.0169031	−	0.0878310i
$876$	−10.3923	+	6.00000i	−0.351123	+	0.202721i
$877$	51.7654			1.74799			0.873996	−	0.485933i	$-0.161520\pi$
$877$	51.7654			1.74799			0.873996	+	0.485933i	$0.161520\pi$
$878$	−14.8301	+	25.6865i	−0.500493	+	0.866879i
$879$	−14.1962	+	24.5885i	−0.478824	+	0.829348i
$880$	4.09808	−	2.36603i	0.138146	−	0.0797587i
$881$	−16.3923			−0.552271			−0.276135	−	0.961119i	$-0.589054\pi$
$881$	−16.3923			−0.552271			−0.276135	+	0.961119i	$0.589054\pi$
$882$	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
$885$	3.80385			0.127865
$886$	−4.50000	+	7.79423i	−0.151180	+	0.261852i
$887$	−49.3923			−1.65843			−0.829216	−	0.558929i	$-0.811212\pi$
$887$	−49.3923			−1.65843			−0.829216	+	0.558929i	$0.811212\pi$
$888$			10.7321i			0.360144i
$889$	−5.69615	−	29.5981i	−0.191043	−	0.992688i
$890$			4.39230i			0.147230i
$891$	−36.8827	+	21.2942i	−1.23562	+	0.713384i
$892$	11.8923	−	6.86603i	0.398184	−	0.229892i
$893$			11.4115i			0.381873i
$894$	10.3923	−	18.0000i	0.347571	−	0.602010i
$895$	−21.2942	+	12.2942i	−0.711788	+	0.410951i
$896$	1.73205	+	2.00000i	0.0578638	+	0.0668153i
$897$	−7.60770	+	13.1769i	−0.254014	+	0.439964i
$898$	4.79423	+	8.30385i	0.159985	+	0.277103i
$899$	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
$903$	2.76795	+	14.3827i	0.0921116	+	0.478626i
$904$	−6.29423	−	10.9019i	−0.209343	−	0.362593i
$905$		−	13.3923i		−	0.445175i
$906$	−6.29423	−	3.63397i	−0.209112	−	0.120731i
$907$	22.8038			0.757189			0.378595	−	0.925563i	$-0.376407\pi$
$907$	22.8038			0.757189			0.378595	+	0.925563i	$0.376407\pi$
$908$	−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	$0.604793\pi$
$912$	1.90192	−	1.09808i	0.0629790	−	0.0363609i
$913$	−45.8827	−	26.4904i	−1.51850	−	0.876704i
$914$	2.07180	+	1.19615i	0.0685289	+	0.0395652i
$915$	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	−0.901382	−	0.433026i	$-0.857446\pi$
$919$	−2.29423	+	3.97372i	−0.0756796	+	0.131081i	0.825702	+	0.564107i	$0.190779\pi$
$920$	−2.53590			−0.0836061
$921$	−35.6769	+	20.5981i	−1.17559	+	0.678730i
$922$		−	5.19615i		−	0.171126i
$923$	8.19615	+	14.1962i	0.269780	+	0.467272i
$924$	−21.2942	+	4.09808i	−0.700529	+	0.134817i
$925$	−3.09808	+	5.36603i	−0.101864	+	0.176434i
$926$	−2.25833	−	1.30385i	−0.0742133	−	0.0428471i
$927$	31.5000	+	18.1865i	1.03460	+	0.597324i
$928$	−3.23205	−	5.59808i	−0.106097	−	0.183766i
$929$	−25.2846	−	43.7942i	−0.829561	−	1.43684i	−0.898383	−	0.439213i	$-0.855257\pi$
$929$	−25.2846	−	43.7942i	−0.829561	−	1.43684i	0.0688218	−	0.997629i	$-0.478076\pi$
$930$	7.09808	+	12.2942i	0.232755	+	0.403144i
$931$	8.78461	+	1.26795i	0.287904	+	0.0415554i
$932$	1.09808	−	0.633975i	0.0359687	−	0.0207665i
$933$	27.3731			0.896154
$934$			6.80385i			0.222629i
$935$		0			0
$936$	−10.3923			−0.339683
$937$			42.5885i			1.39130i	0.718379	+	0.695652i	$0.244884\pi$
$937$			42.5885i			1.39130i	−0.718379	+	0.695652i	$0.755116\pi$
$938$	−10.3923	+	2.00000i	−0.339321	+	0.0653023i
$939$	30.2942	+	17.4904i	0.988615	+	0.570777i
$940$	9.00000			0.293548
$941$	−12.9904	+	22.5000i	−0.423474	+	0.733479i	−0.996277	−	0.0862145i	$-0.972523\pi$
$941$	−12.9904	+	22.5000i	−0.423474	+	0.733479i	0.572802	+	0.819694i	$0.305856\pi$
$942$	−15.2942	−	26.4904i	−0.498313	−	0.863103i
$943$	−19.7654	+	11.4115i	−0.643649	+	0.371611i
$944$	−2.19615			−0.0714787
$945$	−2.59808	−	13.5000i	−0.0845154	−	0.439155i
$946$	−15.1244			−0.491735
$947$	−20.4115	+	11.7846i	−0.663286	+	0.382948i	−0.793528	−	0.608534i	$-0.791758\pi$
$947$	−20.4115	+	11.7846i	−0.663286	+	0.382948i	0.130242	+	0.991482i	$0.458425\pi$
$948$	12.6340	+	21.8827i	0.410332	+	0.710717i
$949$	12.0000	−	20.7846i	0.389536	−	0.674697i
$950$	1.26795			0.0411377
$951$	−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	$0.993463\pi$
$954$	10.9019	+	18.8827i	0.352963	+	0.611350i
$955$	−3.00000	+	1.73205i	−0.0970777	+	0.0560478i
$956$		−	3.12436i		−	0.101049i
$957$	52.9808			1.71262
$958$	9.00000	−	5.19615i	0.290777	−	0.167880i
$959$	−18.8827	+	3.63397i	−0.609754	+	0.117347i
$960$	−0.866025	−	1.50000i	−0.0279508	−	0.0484123i
$961$	18.0885	+	31.3301i	0.583499	+	1.01065i
$962$	−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
$966$	10.9808	+	3.80385i	0.353300	+	0.122387i
$967$	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	$0.750513\pi$
$968$		−	11.3923i		−	0.366163i
$969$		0			0
$970$	8.53590			0.274071
$971$	7.39230	−	12.8038i	0.237230	−	0.410895i	−0.722688	−	0.691174i	$-0.757094\pi$
$971$	7.39230	−	12.8038i	0.237230	−	0.410895i	0.959919	+	0.280279i	$0.0904271\pi$
$972$	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
$976$	−11.1962	−	6.46410i	−0.358380	−	0.206911i
$977$	4.39230	+	2.53590i	0.140522	+	0.0811306i	0.568613	−	0.822605i	$-0.307480\pi$
$977$	4.39230	+	2.53590i	0.140522	+	0.0811306i	−0.428091	+	0.903736i	$0.640814\pi$
$978$	12.5885	−	7.26795i	0.402534	−	0.232403i
$979$	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
$983$	−31.3923			−1.00126			−0.500630	−	0.865662i	$-0.666898\pi$
$983$	−31.3923			−1.00126			−0.500630	+	0.865662i	$0.666898\pi$
$984$	−13.5000	−	7.79423i	−0.430364	−	0.248471i
$985$		−	23.6603i		−	0.753878i
$986$		0			0
$987$	−38.9711	−	13.5000i	−1.24047	−	0.429710i
$988$	−2.19615	+	3.80385i	−0.0698689	+	0.121017i
$989$	7.01924	+	4.05256i	0.223199	+	0.128864i
$990$	14.1962			0.451183
$991$	6.70577	+	11.6147i	0.213016	+	0.368954i	0.952657	−	0.304047i	$-0.0983381\pi$
$991$	6.70577	+	11.6147i	0.213016	+	0.368954i	−0.739641	+	0.673002i	$0.765005\pi$
$992$	−4.09808	−	7.09808i	−0.130114	−	0.225364i
$993$	6.92820	−	12.0000i	0.219860	−	0.380808i
$994$	9.46410	−	8.19615i	0.300183	−	0.259966i
$995$	−6.00000	+	3.46410i	−0.190213	+	0.109819i
$996$	−9.69615	+	16.7942i	−0.307234	+	0.532145i
$997$			31.5167i			0.998143i	0.866561	+	0.499071i	$0.166325\pi$
$997$			31.5167i			0.998143i	−0.866561	+	0.499071i	$0.833675\pi$
$998$	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.t.a.551.1	yes	4
3.2	odd	2		1890.2.t.a.1601.2		4
7.3	odd	6		630.2.bk.a.101.1	yes	4
9.4	even	3		1890.2.bk.a.341.1		4
9.5	odd	6		630.2.bk.a.131.2	yes	4
21.17	even	6		1890.2.bk.a.521.2		4
63.31	odd	6		1890.2.t.a.1151.2		4
63.59	even	6	inner	630.2.t.a.311.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.a.311.1	✓	4	63.59	even	6	inner
630.2.t.a.551.1	yes	4	1.1	even	1	trivial
630.2.bk.a.101.1	yes	4	7.3	odd	6
630.2.bk.a.131.2	yes	4	9.5	odd	6
1890.2.t.a.1151.2		4	63.31	odd	6
1890.2.t.a.1601.2		4	3.2	odd	2
1890.2.bk.a.341.1		4	9.4	even	3
1890.2.bk.a.521.2		4	21.17	even	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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 + 0.866025i) q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 + 0.866025i) q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(0.866025 - 0.500000i) q^{10} -4.73205i q^{11} -1.73205 q^{12} +(3.00000 - 1.73205i) q^{13} +(-1.73205 - 2.00000i) q^{14} +(0.866025 + 1.50000i) q^{15} +(-0.500000 - 0.866025i) q^{16} -3.00000i q^{18} +(-1.09808 - 0.633975i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(3.46410 - 3.00000i) q^{21} +(2.36603 + 4.09808i) q^{22} -2.53590i q^{23} +(1.50000 - 0.866025i) q^{24} +1.00000 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} +(-7.09808 - 4.09808i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-7.09808 + 4.09808i) q^{33} +(-0.500000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-3.09808 + 5.36603i) q^{37} +1.26795 q^{38} +(-5.19615 - 3.00000i) q^{39} -1.00000i q^{40} +(-4.50000 - 7.79423i) q^{41} +(-1.50000 + 4.33013i) q^{42} +(-1.59808 + 2.76795i) q^{43} +(-4.09808 - 2.36603i) q^{44} +(1.50000 - 2.59808i) q^{45} +(1.26795 + 2.19615i) q^{46} +(-4.50000 - 7.79423i) q^{47} +(-0.866025 + 1.50000i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(-0.866025 + 0.500000i) q^{50} -3.46410i q^{52} +(-6.29423 + 3.63397i) q^{53} +(-4.50000 + 2.59808i) q^{54} +4.73205i q^{55} +(-2.59808 + 0.500000i) q^{56} +2.19615i q^{57} +6.46410 q^{58} +(1.09808 - 1.90192i) q^{59} +1.73205 q^{60} +(11.1962 - 6.46410i) q^{61} +8.19615 q^{62} +(-7.50000 - 2.59808i) q^{63} -1.00000 q^{64} +(-3.00000 + 1.73205i) q^{65} +(4.09808 - 7.09808i) q^{66} +(2.00000 - 3.46410i) q^{67} +(-3.80385 + 2.19615i) q^{69} +(1.73205 + 2.00000i) q^{70} +4.73205i q^{71} +(-2.59808 - 1.50000i) q^{72} +(6.00000 - 3.46410i) q^{73} -6.19615i q^{74} +(-0.866025 - 1.50000i) q^{75} +(-1.09808 + 0.633975i) q^{76} +(12.2942 - 2.36603i) q^{77} +6.00000 q^{78} +(-7.29423 - 12.6340i) 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} -3.19615i q^{86} +11.1962i q^{87} +4.73205 q^{88} +(-2.19615 + 3.80385i) q^{89} +3.00000i q^{90} +(6.00000 + 6.92820i) q^{91} +(-2.19615 - 1.26795i) q^{92} +14.1962i q^{93} +(7.79423 + 4.50000i) q^{94} +(1.09808 + 0.633975i) q^{95} -1.73205i q^{96} +(7.39230 + 4.26795i) q^{97} +(4.33013 - 5.50000i) q^{98} +(12.2942 + 7.09808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 6 * q^9	\( 4 q + 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 6 q^{9} + 12 q^{13} - 2 q^{16} + 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{24} + 4 q^{25} + 10 q^{28} - 12 q^{29} - 6 q^{30} - 18 q^{31} - 18 q^{33} - 2 q^{35} + 6 q^{36} - 2 q^{37} + 12 q^{38} - 18 q^{41} - 6 q^{42} + 4 q^{43} - 6 q^{44} + 6 q^{45} + 12 q^{46} - 18 q^{47} - 26 q^{49} + 6 q^{53} - 18 q^{54} + 12 q^{58} - 6 q^{59} + 24 q^{61} + 12 q^{62} - 30 q^{63} - 4 q^{64} - 12 q^{65} + 6 q^{66} + 8 q^{67} - 36 q^{69} + 24 q^{73} + 6 q^{76} + 18 q^{77} + 24 q^{78} + 2 q^{79} + 2 q^{80} - 18 q^{81} + 12 q^{83} + 12 q^{88} + 12 q^{89} + 24 q^{91} + 12 q^{92} - 6 q^{95} - 12 q^{97} + 18 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 6 * q^9 + 12 * q^13 - 2 * q^16 + 6 * q^19 - 2 * q^20 + 6 * q^22 + 6 * q^24 + 4 * q^25 + 10 * q^28 - 12 * q^29 - 6 * q^30 - 18 * q^31 - 18 * q^33 - 2 * q^35 + 6 * q^36 - 2 * q^37 + 12 * q^38 - 18 * q^41 - 6 * q^42 + 4 * q^43 - 6 * q^44 + 6 * q^45 + 12 * q^46 - 18 * q^47 - 26 * q^49 + 6 * q^53 - 18 * q^54 + 12 * q^58 - 6 * q^59 + 24 * q^61 + 12 * q^62 - 30 * q^63 - 4 * q^64 - 12 * q^65 + 6 * q^66 + 8 * q^67 - 36 * q^69 + 24 * q^73 + 6 * q^76 + 18 * q^77 + 24 * q^78 + 2 * q^79 + 2 * q^80 - 18 * q^81 + 12 * q^83 + 12 * q^88 + 12 * q^89 + 24 * q^91 + 12 * q^92 - 6 * q^95 - 12 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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