LMFDB - Embedded newform 630.2.t.a.311.2

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			311.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	630.311
Dual form			630.2.t.a.551.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(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} -1.26795i 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} +(4.09808 - 2.36603i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.46410 - 3.00000i) q^{21} +(0.633975 - 1.09808i) q^{22} -9.46410i 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} +(-0.401924 + 0.232051i) q^{29} +(-1.50000 + 0.866025i) q^{30} +(-1.90192 + 1.09808i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.90192 - 1.09808i) q^{33} +(-0.500000 + 2.59808i) q^{35} +(1.50000 - 2.59808i) q^{36} +(2.09808 + 3.63397i) q^{37} +4.73205 q^{38} +(5.19615 - 3.00000i) q^{39} -1.00000i q^{40} +(-4.50000 + 7.79423i) q^{41} +(-1.50000 - 4.33013i) q^{42} +(3.59808 + 6.23205i) q^{43} +(1.09808 - 0.633975i) q^{44} +(1.50000 + 2.59808i) q^{45} +(4.73205 - 8.19615i) 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} +(9.29423 + 5.36603i) q^{53} +(-4.50000 - 2.59808i) q^{54} +1.26795i q^{55} +(2.59808 + 0.500000i) q^{56} -8.19615i q^{57} -0.464102 q^{58} +(-4.09808 - 7.09808i) q^{59} -1.73205 q^{60} +(0.803848 + 0.464102i) q^{61} -2.19615 q^{62} +(-7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(-3.00000 - 1.73205i) q^{65} +(-1.09808 - 1.90192i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-14.1962 - 8.19615i) q^{69} +(-1.73205 + 2.00000i) q^{70} +1.26795i q^{71} +(2.59808 - 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +4.19615i q^{74} +(0.866025 - 1.50000i) q^{75} +(4.09808 + 2.36603i) q^{76} +(-3.29423 - 0.633975i) q^{77} +6.00000 q^{78} +(8.29423 - 14.3660i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-7.79423 + 4.50000i) q^{82} +(0.401924 + 0.696152i) q^{83} +(0.866025 - 4.50000i) q^{84} +7.19615i q^{86} +0.803848i q^{87} +1.26795 q^{88} +(8.19615 + 14.1962i) q^{89} +3.00000i q^{90} +(6.00000 - 6.92820i) q^{91} +(8.19615 - 4.73205i) q^{92} +3.80385i q^{93} +(-7.79423 + 4.50000i) q^{94} +(-4.09808 + 2.36603i) q^{95} +1.73205i q^{96} +(-13.3923 + 7.73205i) q^{97} +(-4.33013 - 5.50000i) q^{98} +(-3.29423 + 1.90192i) 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$	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
$11$		−	1.26795i		−	0.382301i	−0.981561	−	0.191151i	$-0.938778\pi$
$11$		−	1.26795i		−	0.382301i	0.981561	−	0.191151i	$-0.0612219\pi$
$12$	1.73205			0.500000
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	0.854554	−	0.519362i	$-0.173830\pi$
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	−0.0225039	+	0.999747i	$0.507164\pi$
$14$	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	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		−	3.00000i		−	0.707107i
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.0501517	−	0.998742i	$-0.484030\pi$
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.890011	+	0.455938i	$0.150696\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−3.46410	−	3.00000i	−0.755929	−	0.654654i
$22$	0.633975	−	1.09808i	0.135164	−	0.234111i
$23$		−	9.46410i		−	1.97340i	−0.162547	−	0.986701i	$-0.551971\pi$
$23$		−	9.46410i		−	1.97340i	0.162547	−	0.986701i	$-0.448029\pi$
$24$	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
$29$	−0.401924	+	0.232051i	−0.0746354	+	0.0430908i	−0.536853	−	0.843676i	$-0.680387\pi$
$29$	−0.401924	+	0.232051i	−0.0746354	+	0.0430908i	0.462218	+	0.886766i	$0.347054\pi$
$30$	−1.50000	+	0.866025i	−0.273861	+	0.158114i
$31$	−1.90192	+	1.09808i	−0.341596	+	0.197220i	−0.660977	−	0.750406i	$-0.729858\pi$
$31$	−1.90192	+	1.09808i	−0.341596	+	0.197220i	0.319382	+	0.947626i	$0.396525\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−1.90192	−	1.09808i	−0.331082	−	0.191151i
$34$		0			0
$35$	−0.500000	+	2.59808i	−0.0845154	+	0.439155i
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	2.09808	+	3.63397i	0.344922	+	0.597422i	0.985340	−	0.170605i	$-0.0545722\pi$
$37$	2.09808	+	3.63397i	0.344922	+	0.597422i	−0.640418	+	0.768027i	$0.721239\pi$
$38$	4.73205			0.767640
$39$	5.19615	−	3.00000i	0.832050	−	0.480384i
$40$		−	1.00000i		−	0.158114i
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	0.264704	+	0.964330i	$0.414726\pi$
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	−0.967486	+	0.252924i	$0.918608\pi$
$42$	−1.50000	−	4.33013i	−0.231455	−	0.668153i
$43$	3.59808	+	6.23205i	0.548701	+	0.950379i	0.998364	+	0.0571802i	$0.0182110\pi$
$43$	3.59808	+	6.23205i	0.548701	+	0.950379i	−0.449662	+	0.893199i	$0.648456\pi$
$44$	1.09808	−	0.633975i	0.165541	−	0.0955753i
$45$	1.50000	+	2.59808i	0.223607	+	0.387298i
$46$	4.73205	−	8.19615i	0.697703	−	1.20846i
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	0.325150	+	0.945662i	$0.394585\pi$
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	−0.981543	+	0.191243i	$0.938748\pi$
$48$	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
$53$	9.29423	+	5.36603i	1.27666	+	0.737080i	0.976233	−	0.216724i	$-0.0695373\pi$
$53$	9.29423	+	5.36603i	1.27666	+	0.737080i	0.300428	+	0.953805i	$0.402871\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$			1.26795i			0.170970i
$56$	2.59808	+	0.500000i	0.347183	+	0.0668153i
$57$		−	8.19615i		−	1.08561i
$58$	−0.464102			−0.0609395
$59$	−4.09808	−	7.09808i	−0.533524	−	0.924091i	−0.999233	−	0.0391530i	$-0.987534\pi$
$59$	−4.09808	−	7.09808i	−0.533524	−	0.924091i	0.465709	−	0.884938i	$-0.345799\pi$
$60$	−1.73205			−0.223607
$61$	0.803848	+	0.464102i	0.102922	+	0.0594221i	0.550578	−	0.834784i	$-0.314408\pi$
$61$	0.803848	+	0.464102i	0.102922	+	0.0594221i	−0.447655	+	0.894206i	$0.647741\pi$
$62$	−2.19615			−0.278912
$63$	−7.50000	+	2.59808i	−0.944911	+	0.327327i
$64$	−1.00000			−0.125000
$65$	−3.00000	−	1.73205i	−0.372104	−	0.214834i
$66$	−1.09808	−	1.90192i	−0.135164	−	0.234111i
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$		0			0
$69$	−14.1962	−	8.19615i	−1.70902	−	0.986701i
$70$	−1.73205	+	2.00000i	−0.207020	+	0.239046i
$71$			1.26795i			0.150478i	0.997166	+	0.0752389i	$0.0239720\pi$
$71$			1.26795i			0.150478i	−0.997166	+	0.0752389i	$0.976028\pi$
$72$	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	$0.533784\pi$
$74$			4.19615i			0.487793i
$75$	0.866025	−	1.50000i	0.100000	−	0.173205i
$76$	4.09808	+	2.36603i	0.470082	+	0.271402i
$77$	−3.29423	−	0.633975i	−0.375412	−	0.0722481i
$78$	6.00000			0.679366
$79$	8.29423	−	14.3660i	0.933174	−	1.61630i	0.155315	−	0.987865i	$-0.450361\pi$
$79$	8.29423	−	14.3660i	0.933174	−	1.61630i	0.777859	−	0.628439i	$-0.216306\pi$
$80$	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
$83$	0.401924	+	0.696152i	0.0441169	+	0.0764127i	0.887241	−	0.461307i	$-0.152619\pi$
$83$	0.401924	+	0.696152i	0.0441169	+	0.0764127i	−0.843124	+	0.537720i	$0.819286\pi$
$84$	0.866025	−	4.50000i	0.0944911	−	0.490990i
$85$		0			0
$86$			7.19615i			0.775981i
$87$			0.803848i			0.0861815i
$88$	1.26795			0.135164
$89$	8.19615	+	14.1962i	0.868790	+	1.50479i	0.863234	+	0.504805i	$0.168435\pi$
$89$	8.19615	+	14.1962i	0.868790	+	1.50479i	0.00555677	+	0.999985i	$0.498231\pi$
$90$			3.00000i			0.316228i
$91$	6.00000	−	6.92820i	0.628971	−	0.726273i
$92$	8.19615	−	4.73205i	0.854508	−	0.493350i
$93$			3.80385i			0.394441i
$94$	−7.79423	+	4.50000i	−0.803913	+	0.464140i
$95$	−4.09808	+	2.36603i	−0.420454	+	0.242749i
$96$			1.73205i			0.176777i
$97$	−13.3923	+	7.73205i	−1.35978	+	0.785071i	−0.989594	−	0.143886i	$-0.954040\pi$
$97$	−13.3923	+	7.73205i	−1.35978	+	0.785071i	−0.370188	+	0.928957i	$0.620707\pi$
$98$	−4.33013	−	5.50000i	−0.437409	−	0.555584i
$99$	−3.29423	+	1.90192i	−0.331082	+	0.191151i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−0.803848			−0.0799858			−0.0399929	−	0.999200i	$-0.512734\pi$
$101$	−0.803848			−0.0799858			−0.0399929	+	0.999200i	$0.512734\pi$
$102$		0			0
$103$			12.1244i			1.19465i	0.802000	+	0.597324i	$0.203769\pi$
$103$			12.1244i			1.19465i	−0.802000	+	0.597324i	$0.796231\pi$
$104$	−1.73205	+	3.00000i	−0.169842	+	0.294174i
$105$	3.46410	+	3.00000i	0.338062	+	0.292770i
$106$	5.36603	+	9.29423i	0.521194	+	0.902735i
$107$	−1.79423	+	1.03590i	−0.173455	+	0.100144i	−0.584214	−	0.811600i	$-0.698597\pi$
$107$	−1.79423	+	1.03590i	−0.173455	+	0.100144i	0.410759	+	0.911744i	$0.365264\pi$
$108$	−2.59808	−	4.50000i	−0.250000	−	0.433013i
$109$	−1.59808	+	2.76795i	−0.153068	+	0.265121i	−0.932354	−	0.361547i	$-0.882249\pi$
$109$	−1.59808	+	2.76795i	−0.153068	+	0.265121i	0.779286	+	0.626669i	$0.215582\pi$
$110$	−0.633975	+	1.09808i	−0.0604471	+	0.104697i
$111$	7.26795			0.689843
$112$	2.00000	+	1.73205i	0.188982	+	0.163663i
$113$	−16.0981	−	9.29423i	−1.51438	−	0.874327i	−0.999858	−	0.0168501i	$-0.994636\pi$
$113$	−16.0981	−	9.29423i	−1.51438	−	0.874327i	−0.514522	−	0.857477i	$-0.672030\pi$
$114$	4.09808	−	7.09808i	0.383820	−	0.664796i
$115$			9.46410i			0.882532i
$116$	−0.401924	−	0.232051i	−0.0373177	−	0.0215454i
$117$		−	10.3923i		−	0.960769i
$118$		−	8.19615i		−	0.754517i
$119$		0			0
$120$	−1.50000	−	0.866025i	−0.136931	−	0.0790569i
$121$	9.39230			0.853846
$122$	0.464102	+	0.803848i	0.0420178	+	0.0727769i
$123$	7.79423	+	13.5000i	0.702782	+	1.21725i
$124$	−1.90192	−	1.09808i	−0.170798	−	0.0986102i
$125$	−1.00000			−0.0894427
$126$	−7.79423	−	1.50000i	−0.694365	−	0.133631i
$127$	9.39230			0.833432			0.416716	−	0.909037i	$-0.363181\pi$
$127$	9.39230			0.833432			0.416716	+	0.909037i	$0.363181\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	12.4641			1.09740
$130$	−1.73205	−	3.00000i	−0.151911	−	0.263117i
$131$	−16.3923			−1.43220			−0.716101	−	0.697997i	$-0.754075\pi$
$131$	−16.3923			−1.43220			−0.716101	+	0.697997i	$0.754075\pi$
$132$		−	2.19615i		−	0.191151i
$133$	−4.09808	−	11.8301i	−0.355348	−	1.02580i
$134$			4.00000i			0.345547i
$135$	5.19615			0.447214
$136$		0			0
$137$			10.7321i			0.916901i	0.888720	+	0.458450i	$0.151595\pi$
$137$			10.7321i			0.916901i	−0.888720	+	0.458450i	$0.848405\pi$
$138$	−8.19615	−	14.1962i	−0.697703	−	1.20846i
$139$	13.9019	+	8.02628i	1.17915	+	0.680780i	0.955817	−	0.293963i	$-0.0949742\pi$
$139$	13.9019	+	8.02628i	1.17915	+	0.680780i	0.223329	+	0.974743i	$0.428308\pi$
$140$	−2.50000	+	0.866025i	−0.211289	+	0.0731925i
$141$	7.79423	+	13.5000i	0.656392	+	1.13691i
$142$	−0.633975	+	1.09808i	−0.0532020	+	0.0921485i
$143$	2.19615	−	3.80385i	0.183651	−	0.318094i
$144$	3.00000			0.250000
$145$	0.401924	−	0.232051i	0.0333780	−	0.0192708i
$146$	3.46410	+	6.00000i	0.286691	+	0.496564i
$147$	−9.52628	+	7.50000i	−0.785714	+	0.618590i
$148$	−2.09808	+	3.63397i	−0.172461	+	0.298711i
$149$		−	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
$151$	6.19615			0.504236			0.252118	−	0.967697i	$-0.418873\pi$
$151$	6.19615			0.504236			0.252118	+	0.967697i	$0.418873\pi$
$152$	2.36603	+	4.09808i	0.191910	+	0.332398i
$153$		0			0
$154$	−2.53590	−	2.19615i	−0.204349	−	0.176971i
$155$	1.90192	−	1.09808i	0.152766	−	0.0881996i
$156$	5.19615	+	3.00000i	0.416025	+	0.240192i
$157$	0.294229	−	0.169873i	0.0234820	−	0.0135573i	−0.488213	−	0.872724i	$-0.662351\pi$
$157$	0.294229	−	0.169873i	0.0234820	−	0.0135573i	0.511695	+	0.859167i	$0.329018\pi$
$158$	14.3660	−	8.29423i	1.14290	−	0.659853i
$159$	16.0981	−	9.29423i	1.27666	−	0.737080i
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	−24.5885	−	4.73205i	−1.93784	−	0.372938i
$162$	−7.79423	+	4.50000i	−0.612372	+	0.353553i
$163$	−6.19615	−	10.7321i	−0.485320	−	0.840599i	0.514538	−	0.857468i	$-0.327964\pi$
$163$	−6.19615	−	10.7321i	−0.485320	−	0.840599i	−0.999858	+	0.0168687i	$0.994630\pi$
$164$	−9.00000			−0.702782
$165$	1.90192	+	1.09808i	0.148065	+	0.0854851i
$166$			0.803848i			0.0623907i
$167$	−5.19615	+	9.00000i	−0.402090	+	0.696441i	−0.993978	−	0.109580i	$-0.965050\pi$
$167$	−5.19615	+	9.00000i	−0.402090	+	0.696441i	0.591888	+	0.806020i	$0.298383\pi$
$168$	3.00000	−	3.46410i	0.231455	−	0.267261i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		0			0
$171$	−12.2942	−	7.09808i	−0.940163	−	0.542803i
$172$	−3.59808	+	6.23205i	−0.274351	+	0.475189i
$173$	−1.09808	+	1.90192i	−0.0834852	+	0.144601i	−0.904745	−	0.425954i	$-0.859938\pi$
$173$	−1.09808	+	1.90192i	−0.0834852	+	0.144601i	0.821260	+	0.570555i	$0.193272\pi$
$174$	−0.401924	+	0.696152i	−0.0304698	+	0.0527752i
$175$	0.500000	−	2.59808i	0.0377964	−	0.196396i
$176$	1.09808	+	0.633975i	0.0827706	+	0.0477876i
$177$	−14.1962			−1.06705
$178$			16.3923i			1.22866i
$179$	5.70577	+	3.29423i	0.426469	+	0.246222i	0.697841	−	0.716252i	$-0.254144\pi$
$179$	5.70577	+	3.29423i	0.426469	+	0.246222i	−0.271372	+	0.962475i	$0.587477\pi$
$180$	−1.50000	+	2.59808i	−0.111803	+	0.193649i
$181$		−	7.39230i		−	0.549466i	−0.961521	−	0.274733i	$-0.911411\pi$
$181$		−	7.39230i		−	0.549466i	0.961521	−	0.274733i	$-0.0885894\pi$
$182$	8.66025	−	3.00000i	0.641941	−	0.222375i
$183$	1.39230	−	0.803848i	0.102922	−	0.0594221i
$184$	9.46410			0.697703
$185$	−2.09808	−	3.63397i	−0.154254	−	0.267175i
$186$	−1.90192	+	3.29423i	−0.139456	+	0.241545i
$187$		0			0
$188$	−9.00000			−0.656392
$189$	−2.59808	+	13.5000i	−0.188982	+	0.981981i
$190$	−4.73205			−0.343299
$191$	3.00000	+	1.73205i	0.217072	+	0.125327i	0.604594	−	0.796534i	$-0.293335\pi$
$191$	3.00000	+	1.73205i	0.217072	+	0.125327i	−0.387522	+	0.921861i	$0.626669\pi$
$192$	−0.866025	+	1.50000i	−0.0625000	+	0.108253i
$193$	−12.0981	−	20.9545i	−0.870839	−	1.50834i	−0.861131	−	0.508384i	$-0.830243\pi$
$193$	−12.0981	−	20.9545i	−0.870839	−	1.50834i	−0.00970797	−	0.999953i	$-0.503090\pi$
$194$	−15.4641			−1.11026
$195$	−5.19615	+	3.00000i	−0.372104	+	0.214834i
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$			6.33975i			0.451688i	0.974163	+	0.225844i	$0.0725140\pi$
$197$			6.33975i			0.451688i	−0.974163	+	0.225844i	$0.927486\pi$
$198$	−3.80385			−0.270328
$199$	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	$0.587694\pi$
$200$			1.00000i			0.0707107i
$201$	6.92820			0.488678
$202$	−0.696152	−	0.401924i	−0.0489811	−	0.0282793i
$203$	0.401924	+	1.16025i	0.0282095	+	0.0814339i
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	−6.06218	+	10.5000i	−0.422372	+	0.731570i
$207$	−24.5885	+	14.1962i	−1.70902	+	0.986701i
$208$	−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
$211$	−5.29423	+	9.16987i	−0.364470	+	0.631280i	−0.988691	−	0.149968i	$-0.952083\pi$
$211$	−5.29423	+	9.16987i	−0.364470	+	0.631280i	0.624221	+	0.781248i	$0.285416\pi$
$212$			10.7321i			0.737080i
$213$	1.90192	+	1.09808i	0.130318	+	0.0752389i
$214$	−2.07180			−0.141625
$215$	−3.59808	−	6.23205i	−0.245387	−	0.425022i
$216$		−	5.19615i		−	0.353553i
$217$	1.90192	+	5.49038i	0.129111	+	0.372711i
$218$	−2.76795	+	1.59808i	−0.187469	+	0.108235i
$219$	10.3923	−	6.00000i	0.702247	−	0.405442i
$220$	−1.09808	+	0.633975i	−0.0740323	+	0.0427426i
$221$		0			0
$222$	6.29423	+	3.63397i	0.422441	+	0.243896i
$223$	−8.89230	+	5.13397i	−0.595473	+	0.343796i	−0.767259	−	0.641338i	$-0.778380\pi$
$223$	−8.89230	+	5.13397i	−0.595473	+	0.343796i	0.171786	+	0.985134i	$0.445046\pi$
$224$	0.866025	+	2.50000i	0.0578638	+	0.167038i
$225$	−1.50000	−	2.59808i	−0.100000	−	0.173205i
$226$	−9.29423	−	16.0981i	−0.618243	−	1.07083i
$227$	4.39230			0.291528			0.145764	−	0.989319i	$-0.453436\pi$
$227$	4.39230			0.291528			0.145764	+	0.989319i	$0.453436\pi$
$228$	7.09808	−	4.09808i	0.470082	−	0.271402i
$229$		−	27.9282i		−	1.84555i	−0.385342	−	0.922774i	$-0.625917\pi$
$229$		−	27.9282i		−	1.84555i	0.385342	−	0.922774i	$-0.374083\pi$
$230$	−4.73205	+	8.19615i	−0.312022	+	0.540438i
$231$	−3.80385	+	4.39230i	−0.250275	+	0.288992i
$232$	−0.232051	−	0.401924i	−0.0152349	−	0.0263876i
$233$	−4.09808	+	2.36603i	−0.268474	+	0.155003i	−0.628194	−	0.778057i	$-0.716206\pi$
$233$	−4.09808	+	2.36603i	−0.268474	+	0.155003i	0.359720	+	0.933060i	$0.382872\pi$
$234$	5.19615	−	9.00000i	0.339683	−	0.588348i
$235$	4.50000	−	7.79423i	0.293548	−	0.508439i
$236$	4.09808	−	7.09808i	0.266762	−	0.462045i
$237$	−14.3660	−	24.8827i	−0.933174	−	1.61630i
$238$		0			0
$239$	18.2942	+	10.5622i	1.18336	+	0.683210i	0.956788	−	0.290785i	$-0.0939165\pi$
$239$	18.2942	+	10.5622i	1.18336	+	0.683210i	0.226567	+	0.973996i	$0.427250\pi$
$240$	−0.866025	−	1.50000i	−0.0559017	−	0.0968246i
$241$		−	20.6603i		−	1.33084i	−0.746467	−	0.665422i	$-0.768252\pi$
$241$		−	20.6603i		−	1.33084i	0.746467	−	0.665422i	$-0.231748\pi$
$242$	8.13397	+	4.69615i	0.522872	+	0.301880i
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$			0.928203i			0.0594221i
$245$	6.50000	+	2.59808i	0.415270	+	0.165985i
$246$			15.5885i			0.993884i
$247$	16.3923			1.04302
$248$	−1.09808	−	1.90192i	−0.0697279	−	0.120772i
$249$	1.39230			0.0882337
$250$	−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
$254$	8.13397	+	4.69615i	0.510371	+	0.294663i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.60770			0.474555			0.237277	−	0.971442i	$-0.423745\pi$
$257$	7.60770			0.474555			0.237277	+	0.971442i	$0.423745\pi$
$258$	10.7942	+	6.23205i	0.672019	+	0.387991i
$259$	10.4904	−	3.63397i	0.651841	−	0.225804i
$260$		−	3.46410i		−	0.214834i
$261$	1.20577	+	0.696152i	0.0746354	+	0.0430908i
$262$	−14.1962	−	8.19615i	−0.877041	−	0.506360i
$263$		−	10.2679i		−	0.633149i	−0.948568	−	0.316574i	$-0.897467\pi$
$263$		−	10.2679i		−	0.633149i	0.948568	−	0.316574i	$-0.102533\pi$
$264$	1.09808	−	1.90192i	0.0675819	−	0.117055i
$265$	−9.29423	−	5.36603i	−0.570940	−	0.329632i
$266$	2.36603	−	12.2942i	0.145070	−	0.753808i
$267$	28.3923			1.73758
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$	4.50000	+	2.59808i	0.273861	+	0.158114i
$271$	21.2942	−	12.2942i	1.29353	−	0.746821i	0.314254	−	0.949339i	$-0.398246\pi$
$271$	21.2942	−	12.2942i	1.29353	−	0.746821i	0.979279	+	0.202518i	$0.0649124\pi$
$272$		0			0
$273$	−5.19615	−	15.0000i	−0.314485	−	0.907841i
$274$	−5.36603	+	9.29423i	−0.324173	+	0.561485i
$275$		−	1.26795i		−	0.0764602i
$276$		−	16.3923i		−	0.986701i
$277$	−13.8038			−0.829393			−0.414696	−	0.909960i	$-0.636112\pi$
$277$	−13.8038			−0.829393			−0.414696	+	0.909960i	$0.636112\pi$
$278$	8.02628	+	13.9019i	0.481384	+	0.833782i
$279$	5.70577	+	3.29423i	0.341596	+	0.197220i
$280$	−2.59808	−	0.500000i	−0.155265	−	0.0298807i
$281$	2.30385	−	1.33013i	0.137436	−	0.0793487i	−0.429705	−	0.902969i	$-0.641383\pi$
$281$	2.30385	−	1.33013i	0.137436	−	0.0793487i	0.567141	+	0.823620i	$0.308049\pi$
$282$			15.5885i			0.928279i
$283$	−9.40192	+	5.42820i	−0.558886	+	0.322673i	−0.752698	−	0.658365i	$-0.771248\pi$
$283$	−9.40192	+	5.42820i	−0.558886	+	0.322673i	0.193812	+	0.981039i	$0.437915\pi$
$284$	−1.09808	+	0.633975i	−0.0651588	+	0.0376195i
$285$			8.19615i			0.485498i
$286$	3.80385	−	2.19615i	0.224926	−	0.129861i
$287$	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
$290$	0.464102			0.0272530
$291$			26.7846i			1.57014i
$292$			6.92820i			0.405442i
$293$	2.19615	−	3.80385i	0.128301	−	0.222223i	−0.794718	−	0.606979i	$-0.792381\pi$
$293$	2.19615	−	3.80385i	0.128301	−	0.222223i	0.923018	+	0.384756i	$0.125714\pi$
$294$	−12.0000	+	1.73205i	−0.699854	+	0.101015i
$295$	4.09808	+	7.09808i	0.238599	+	0.413266i
$296$	−3.63397	+	2.09808i	−0.211220	+	0.121948i
$297$			6.58846i			0.382301i
$298$	6.00000	−	10.3923i	0.347571	−	0.602010i
$299$	16.3923	−	28.3923i	0.947991	−	1.64197i
$300$	1.73205			0.100000
$301$	17.9904	−	6.23205i	1.03695	−	0.359209i
$302$	5.36603	+	3.09808i	0.308780	+	0.178274i
$303$	−0.696152	+	1.20577i	−0.0399929	+	0.0692698i
$304$			4.73205i			0.271402i
$305$	−0.803848	−	0.464102i	−0.0460282	−	0.0265744i
$306$		0			0
$307$			17.7846i			1.01502i	0.861645	+	0.507511i	$0.169434\pi$
$307$			17.7846i			1.01502i	−0.861645	+	0.507511i	$0.830566\pi$
$308$	−1.09808	−	3.16987i	−0.0625687	−	0.180620i
$309$	18.1865	+	10.5000i	1.03460	+	0.597324i
$310$	2.19615			0.124733
$311$	−13.0981	−	22.6865i	−0.742724	−	1.28644i	−0.951251	−	0.308419i	$-0.900200\pi$
$311$	−13.0981	−	22.6865i	−0.742724	−	1.28644i	0.208527	−	0.978017i	$-0.433133\pi$
$312$	3.00000	+	5.19615i	0.169842	+	0.294174i
$313$	8.49038	+	4.90192i	0.479905	+	0.277073i	0.720377	−	0.693583i	$-0.243969\pi$
$313$	8.49038	+	4.90192i	0.479905	+	0.277073i	−0.240472	+	0.970656i	$0.577302\pi$
$314$	0.339746			0.0191730
$315$	7.50000	−	2.59808i	0.422577	−	0.146385i
$316$	16.5885			0.933174
$317$	−23.7846	−	13.7321i	−1.33588	−	0.771269i	−0.349684	−	0.936868i	$-0.613711\pi$
$317$	−23.7846	−	13.7321i	−1.33588	−	0.771269i	−0.986193	+	0.165599i	$0.947044\pi$
$318$	18.5885			1.04239
$319$	0.294229	+	0.509619i	0.0164736	+	0.0285332i
$320$	1.00000			0.0559017
$321$			3.58846i			0.200288i
$322$	−18.9282	−	16.3923i	−1.05483	−	0.913507i
$323$		0			0
$324$	−9.00000			−0.500000
$325$	3.00000	+	1.73205i	0.166410	+	0.0960769i
$326$		−	12.3923i		−	0.686346i
$327$	2.76795	+	4.79423i	0.153068	+	0.265121i
$328$	−7.79423	−	4.50000i	−0.430364	−	0.248471i
$329$	18.0000	+	15.5885i	0.992372	+	0.859419i
$330$	1.09808	+	1.90192i	0.0604471	+	0.104697i
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$	−0.401924	+	0.696152i	−0.0220584	+	0.0382063i
$333$	6.29423	−	10.9019i	0.344922	−	0.597422i
$334$	−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	−0.969468	−	0.245220i	$-0.921140\pi$
$337$	−5.00000	+	8.66025i	−0.272367	+	0.471754i	0.697100	+	0.716974i	$0.254473\pi$
$338$		−	1.00000i		−	0.0543928i
$339$	−27.8827	+	16.0981i	−1.51438	+	0.874327i
$340$		0			0
$341$	1.39230	+	2.41154i	0.0753975	+	0.130592i
$342$	−7.09808	−	12.2942i	−0.383820	−	0.664796i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−6.23205	+	3.59808i	−0.336010	+	0.193995i
$345$	14.1962	+	8.19615i	0.764295	+	0.441266i
$346$	−1.90192	+	1.09808i	−0.102248	+	0.0590329i
$347$	23.5981	−	13.6244i	1.26681	−	0.731394i	0.292428	−	0.956288i	$-0.405537\pi$
$347$	23.5981	−	13.6244i	1.26681	−	0.731394i	0.974383	+	0.224894i	$0.0722035\pi$
$348$	−0.696152	+	0.401924i	−0.0373177	+	0.0215454i
$349$	3.80385	−	2.19615i	0.203615	−	0.117557i	−0.394725	−	0.918799i	$-0.629160\pi$
$349$	3.80385	−	2.19615i	0.203615	−	0.117557i	0.598341	+	0.801242i	$0.295827\pi$
$350$	1.73205	−	2.00000i	0.0925820	−	0.106904i
$351$	−15.5885	−	9.00000i	−0.832050	−	0.480384i
$352$	0.633975	+	1.09808i	0.0337910	+	0.0585277i
$353$	30.5885			1.62806			0.814030	−	0.580823i	$-0.197269\pi$
$353$	30.5885			1.62806			0.814030	+	0.580823i	$0.197269\pi$
$354$	−12.2942	−	7.09808i	−0.653431	−	0.377258i
$355$		−	1.26795i		−	0.0672958i
$356$	−8.19615	+	14.1962i	−0.434395	+	0.752395i
$357$		0			0
$358$	3.29423	+	5.70577i	0.174105	+	0.301559i
$359$	22.6865	−	13.0981i	1.19735	−	0.691290i	0.237386	−	0.971415i	$-0.423709\pi$
$359$	22.6865	−	13.0981i	1.19735	−	0.691290i	0.959963	+	0.280125i	$0.0903760\pi$
$360$	−2.59808	+	1.50000i	−0.136931	+	0.0790569i
$361$	1.69615	−	2.93782i	0.0892712	−	0.154622i
$362$	3.69615	−	6.40192i	0.194265	−	0.336478i
$363$	8.13397	−	14.0885i	0.426923	−	0.739452i
$364$	9.00000	+	1.73205i	0.471728	+	0.0907841i
$365$	−6.00000	−	3.46410i	−0.314054	−	0.181319i
$366$	1.60770			0.0840356
$367$			18.8038i			0.981553i	0.871286	+	0.490776i	$0.163287\pi$
$367$			18.8038i			0.981553i	−0.871286	+	0.490776i	$0.836713\pi$
$368$	8.19615	+	4.73205i	0.427254	+	0.246675i
$369$	27.0000			1.40556
$370$		−	4.19615i		−	0.218148i
$371$	18.5885	−	21.4641i	0.965065	−	1.11436i
$372$	−3.29423	+	1.90192i	−0.170798	+	0.0986102i
$373$	−0.196152			−0.0101564			−0.00507819	−	0.999987i	$-0.501616\pi$
$373$	−0.196152			−0.0101564			−0.00507819	+	0.999987i	$0.501616\pi$
$374$		0			0
$375$	−0.866025	+	1.50000i	−0.0447214	+	0.0774597i
$376$	−7.79423	−	4.50000i	−0.401957	−	0.232070i
$377$	−1.60770			−0.0828005
$378$	−9.00000	+	10.3923i	−0.462910	+	0.534522i
$379$	−30.3923			−1.56115			−0.780574	−	0.625063i	$-0.785073\pi$
$379$	−30.3923			−1.56115			−0.780574	+	0.625063i	$0.785073\pi$
$380$	−4.09808	−	2.36603i	−0.210227	−	0.121375i
$381$	8.13397	−	14.0885i	0.416716	−	0.721774i
$382$	1.73205	+	3.00000i	0.0886194	+	0.153493i
$383$	−1.39230			−0.0711435			−0.0355717	−	0.999367i	$-0.511325\pi$
$383$	−1.39230			−0.0711435			−0.0355717	+	0.999367i	$0.511325\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$	3.29423	+	0.633975i	0.167889	+	0.0323103i
$386$		−	24.1962i		−	1.23155i
$387$	10.7942	−	18.6962i	0.548701	−	0.950379i
$388$	−13.3923	−	7.73205i	−0.679891	−	0.392535i
$389$		−	30.7128i		−	1.55720i	−0.627520	−	0.778601i	$-0.715930\pi$
$389$		−	30.7128i		−	1.55720i	0.627520	−	0.778601i	$-0.284070\pi$
$390$	−6.00000			−0.303822
$391$		0			0
$392$	2.59808	−	6.50000i	0.131223	−	0.328300i
$393$	−14.1962	+	24.5885i	−0.716101	+	1.24032i
$394$	−3.16987	+	5.49038i	−0.159696	+	0.276601i
$395$	−8.29423	+	14.3660i	−0.417328	+	0.722833i
$396$	−3.29423	−	1.90192i	−0.165541	−	0.0955753i
$397$	−0.509619	+	0.294229i	−0.0255770	+	0.0147669i	−0.512734	−	0.858548i	$-0.671367\pi$
$397$	−0.509619	+	0.294229i	−0.0255770	+	0.0147669i	0.487157	+	0.873314i	$0.338034\pi$
$398$	3.46410	+	6.00000i	0.173640	+	0.300753i
$399$	−21.2942	−	4.09808i	−1.06604	−	0.205160i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$			27.5885i			1.37770i	0.724903	+	0.688851i	$0.241885\pi$
$401$			27.5885i			1.37770i	−0.724903	+	0.688851i	$0.758115\pi$
$402$	6.00000	+	3.46410i	0.299253	+	0.172774i
$403$	−7.60770			−0.378966
$404$	−0.401924	−	0.696152i	−0.0199965	−	0.0346349i
$405$	4.50000	−	7.79423i	0.223607	−	0.387298i
$406$	−0.232051	+	1.20577i	−0.0115165	+	0.0598414i
$407$	4.60770	−	2.66025i	0.228395	−	0.131864i
$408$		0			0
$409$	−29.8923	+	17.2583i	−1.47808	+	0.853370i	−0.999693	−	0.0247799i	$-0.992111\pi$
$409$	−29.8923	+	17.2583i	−1.47808	+	0.853370i	−0.478386	+	0.878149i	$0.658778\pi$
$410$	7.79423	−	4.50000i	0.384930	−	0.222239i
$411$	16.0981	+	9.29423i	0.794060	+	0.458450i
$412$	−10.5000	+	6.06218i	−0.517298	+	0.298662i
$413$	−20.4904	+	7.09808i	−1.00827	+	0.349273i
$414$	−28.3923			−1.39541
$415$	−0.401924	−	0.696152i	−0.0197297	−	0.0341728i
$416$	−3.46410			−0.169842
$417$	24.0788	−	13.9019i	1.17915	−	0.680780i
$418$		−	6.00000i		−	0.293470i
$419$	−5.19615	+	9.00000i	−0.253849	+	0.439679i	−0.964582	−	0.263783i	$-0.915030\pi$
$419$	−5.19615	+	9.00000i	−0.253849	+	0.439679i	0.710734	+	0.703461i	$0.248363\pi$
$420$	−0.866025	+	4.50000i	−0.0422577	+	0.219578i
$421$	−10.9904	−	19.0359i	−0.535638	−	0.927753i	−0.999132	−	0.0416527i	$-0.986738\pi$
$421$	−10.9904	−	19.0359i	−0.535638	−	0.927753i	0.463494	−	0.886100i	$-0.346596\pi$
$422$	−9.16987	+	5.29423i	−0.446382	+	0.257719i
$423$	27.0000			1.31278
$424$	−5.36603	+	9.29423i	−0.260597	+	0.451368i
$425$		0			0
$426$	1.09808	+	1.90192i	0.0532020	+	0.0921485i
$427$	1.60770	−	1.85641i	0.0778018	−	0.0898378i
$428$	−1.79423	−	1.03590i	−0.0867273	−	0.0500720i
$429$	−3.80385	−	6.58846i	−0.183651	−	0.318094i
$430$		−	7.19615i		−	0.347029i
$431$	−2.41154	−	1.39230i	−0.116160	−	0.0670650i	0.440794	−	0.897608i	$-0.354697\pi$
$431$	−2.41154	−	1.39230i	−0.116160	−	0.0670650i	−0.556954	+	0.830543i	$0.688030\pi$
$432$	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	$0.857627\pi$
$434$	−1.09808	+	5.70577i	−0.0527093	+	0.273886i
$435$		−	0.803848i		−	0.0385415i
$436$	−3.19615			−0.153068
$437$	−22.3923	−	38.7846i	−1.07117	−	1.85532i
$438$	12.0000			0.573382
$439$	−10.6865	−	6.16987i	−0.510040	−	0.294472i	0.222810	−	0.974862i	$-0.428477\pi$
$439$	−10.6865	−	6.16987i	−0.510040	−	0.294472i	−0.732850	+	0.680390i	$0.761810\pi$
$440$	−1.26795			−0.0604471
$441$	3.00000	+	20.7846i	0.142857	+	0.989743i
$442$		0			0
$443$	−7.79423	−	4.50000i	−0.370315	−	0.213801i	0.303281	−	0.952901i	$-0.401918\pi$
$443$	−7.79423	−	4.50000i	−0.370315	−	0.213801i	−0.673596	+	0.739100i	$0.735251\pi$
$444$	3.63397	+	6.29423i	0.172461	+	0.298711i
$445$	−8.19615	−	14.1962i	−0.388535	−	0.672962i
$446$	−10.2679			−0.486201
$447$	−18.0000	−	10.3923i	−0.851371	−	0.491539i
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$			21.5885i			1.01882i	0.860523	+	0.509411i	$0.170137\pi$
$449$			21.5885i			1.01882i	−0.860523	+	0.509411i	$0.829863\pi$
$450$		−	3.00000i		−	0.141421i
$451$	9.88269	+	5.70577i	0.465358	+	0.268674i
$452$		−	18.5885i		−	0.874327i
$453$	5.36603	−	9.29423i	0.252118	−	0.436681i
$454$	3.80385	+	2.19615i	0.178523	+	0.103071i
$455$	−6.00000	+	6.92820i	−0.281284	+	0.324799i
$456$	8.19615			0.383820
$457$	9.19615	−	15.9282i	0.430178	−	0.745090i	−0.566710	−	0.823917i	$-0.691784\pi$
$457$	9.19615	−	15.9282i	0.430178	−	0.745090i	0.996888	+	0.0788271i	$0.0251175\pi$
$458$	13.9641	−	24.1865i	0.652500	−	1.13016i
$459$		0			0
$460$	−8.19615	+	4.73205i	−0.382148	+	0.220633i
$461$	2.59808	+	4.50000i	0.121004	+	0.209586i	0.920164	−	0.391533i	$-0.128055\pi$
$461$	2.59808	+	4.50000i	0.121004	+	0.209586i	−0.799160	+	0.601119i	$0.794722\pi$
$462$	−5.49038	+	1.90192i	−0.255436	+	0.0884855i
$463$	11.6962	−	20.2583i	0.543566	−	0.941484i	−0.455129	−	0.890425i	$-0.650407\pi$
$463$	11.6962	−	20.2583i	0.543566	−	0.941484i	0.998696	−	0.0510591i	$-0.0162597\pi$
$464$		−	0.464102i		−	0.0215454i
$465$		−	3.80385i		−	0.176399i
$466$	−4.73205			−0.219208
$467$	8.59808	+	14.8923i	0.397872	+	0.689134i	0.993463	−	0.114154i	$-0.0364156\pi$
$467$	8.59808	+	14.8923i	0.397872	+	0.689134i	−0.595592	+	0.803287i	$0.703082\pi$
$468$	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
$471$		−	0.588457i		−	0.0271147i
$472$	7.09808	−	4.09808i	0.326715	−	0.188629i
$473$	7.90192	−	4.56218i	0.363331	−	0.209769i
$474$		−	28.7321i		−	1.31971i
$475$	4.09808	−	2.36603i	0.188033	−	0.108561i
$476$		0			0
$477$		−	32.1962i		−	1.47416i
$478$	10.5622	+	18.2942i	0.483103	+	0.836759i
$479$	10.3923			0.474837			0.237418	−	0.971408i	$-0.423699\pi$
$479$	10.3923			0.474837			0.237418	+	0.971408i	$0.423699\pi$
$480$		−	1.73205i		−	0.0790569i
$481$			14.5359i			0.662780i
$482$	10.3301	−	17.8923i	0.470524	−	0.814972i
$483$	−28.3923	+	32.7846i	−1.29189	+	1.49175i
$484$	4.69615	+	8.13397i	0.213461	+	0.369726i
$485$	13.3923	−	7.73205i	0.608113	−	0.351094i
$486$			15.5885i			0.707107i
$487$	−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	$0.886751\pi$
$488$	−0.464102	+	0.803848i	−0.0210089	+	0.0363885i
$489$	−21.4641			−0.970640
$490$	4.33013	+	5.50000i	0.195615	+	0.248465i
$491$	2.49038	+	1.43782i	0.112389	+	0.0648880i	0.555141	−	0.831756i	$-0.312664\pi$
$491$	2.49038	+	1.43782i	0.112389	+	0.0648880i	−0.442752	+	0.896644i	$0.645998\pi$
$492$	−7.79423	+	13.5000i	−0.351391	+	0.608627i
$493$		0			0
$494$	14.1962	+	8.19615i	0.638715	+	0.368762i
$495$	3.29423	−	1.90192i	0.148065	−	0.0854851i
$496$		−	2.19615i		−	0.0986102i
$497$	3.29423	+	0.633975i	0.147766	+	0.0284376i
$498$	1.20577	+	0.696152i	0.0540319	+	0.0311953i
$499$	−5.80385			−0.259816			−0.129908	−	0.991526i	$-0.541468\pi$
$499$	−5.80385			−0.259816			−0.129908	+	0.991526i	$0.541468\pi$
$500$	−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
$503$	13.3923			0.597133			0.298567	−	0.954389i	$-0.403491\pi$
$503$	13.3923			0.597133			0.298567	+	0.954389i	$0.403491\pi$
$504$	−2.59808	−	7.50000i	−0.115728	−	0.334077i
$505$	0.803848			0.0357707
$506$	−10.3923	−	6.00000i	−0.461994	−	0.266733i
$507$	−1.73205			−0.0769231
$508$	4.69615	+	8.13397i	0.208358	+	0.360887i
$509$	−21.5885			−0.956892			−0.478446	−	0.878117i	$-0.658800\pi$
$509$	−21.5885			−0.956892			−0.478446	+	0.878117i	$0.658800\pi$
$510$		0			0
$511$	12.0000	−	13.8564i	0.530849	−	0.612971i
$512$		−	1.00000i		−	0.0441942i
$513$	−21.2942	+	12.2942i	−0.940163	+	0.542803i
$514$	6.58846	+	3.80385i	0.290604	+	0.167781i
$515$		−	12.1244i		−	0.534263i
$516$	6.23205	+	10.7942i	0.274351	+	0.475189i
$517$	9.88269	+	5.70577i	0.434640	+	0.250940i
$518$	10.9019	+	2.09808i	0.479003	+	0.0921842i
$519$	1.90192	+	3.29423i	0.0834852	+	0.144601i
$520$	1.73205	−	3.00000i	0.0759555	−	0.131559i
$521$	10.5000	−	18.1865i	0.460013	−	0.796766i	−0.538948	−	0.842339i	$-0.681178\pi$
$521$	10.5000	−	18.1865i	0.460013	−	0.796766i	0.998961	+	0.0455727i	$0.0145113\pi$
$522$	0.696152	+	1.20577i	0.0304698	+	0.0527752i
$523$	−28.5788	+	16.5000i	−1.24967	+	0.721495i	−0.971043	−	0.238906i	$-0.923211\pi$
$523$	−28.5788	+	16.5000i	−1.24967	+	0.721495i	−0.278623	+	0.960401i	$0.589878\pi$
$524$	−8.19615	−	14.1962i	−0.358051	−	0.620162i
$525$	−3.46410	−	3.00000i	−0.151186	−	0.130931i
$526$	5.13397	−	8.89230i	0.223852	−	0.387723i
$527$		0			0
$528$	1.90192	−	1.09808i	0.0827706	−	0.0477876i
$529$	−66.5692			−2.89431
$530$	−5.36603	−	9.29423i	−0.233085	−	0.403715i
$531$	−12.2942	+	21.2942i	−0.533524	+	0.924091i
$532$	8.19615	−	9.46410i	0.355348	−	0.410321i
$533$	−27.0000	+	15.5885i	−1.16950	+	0.675211i
$534$	24.5885	+	14.1962i	1.06405	+	0.614328i
$535$	1.79423	−	1.03590i	0.0775713	−	0.0447858i
$536$	−3.46410	+	2.00000i	−0.149626	+	0.0863868i
$537$	9.88269	−	5.70577i	0.426469	−	0.246222i
$538$	15.5885	−	9.00000i	0.672066	−	0.388018i
$539$	−3.29423	+	8.24167i	−0.141892	+	0.354994i
$540$	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	$0.888348\pi$
$542$	24.5885			1.05616
$543$	−11.0885	−	6.40192i	−0.475851	−	0.274733i
$544$		0			0
$545$	1.59808	−	2.76795i	0.0684541	−	0.118566i
$546$	3.00000	−	15.5885i	0.128388	−	0.667124i
$547$	12.7942	+	22.1603i	0.547042	+	0.947504i	0.998475	+	0.0551993i	$0.0175794\pi$
$547$	12.7942	+	22.1603i	0.547042	+	0.947504i	−0.451434	+	0.892305i	$0.649087\pi$
$548$	−9.29423	+	5.36603i	−0.397030	+	0.229225i
$549$		−	2.78461i		−	0.118844i
$550$	0.633975	−	1.09808i	0.0270328	−	0.0468221i
$551$	−1.09808	+	1.90192i	−0.0467796	+	0.0810247i
$552$	8.19615	−	14.1962i	0.348851	−	0.604228i
$553$	−33.1769	−	28.7321i	−1.41083	−	1.22181i
$554$	−11.9545	−	6.90192i	−0.507897	−	0.293235i
$555$	−7.26795			−0.308507
$556$			16.0526i			0.680780i
$557$	7.60770	+	4.39230i	0.322348	+	0.186108i	0.652439	−	0.757841i	$-0.273746\pi$
$557$	7.60770	+	4.39230i	0.322348	+	0.186108i	−0.330090	+	0.943949i	$0.607079\pi$
$558$	3.29423	+	5.70577i	0.139456	+	0.241545i
$559$			24.9282i			1.05435i
$560$	−2.00000	−	1.73205i	−0.0845154	−	0.0731925i
$561$		0			0
$562$	2.66025			0.112216
$563$	−17.1962	−	29.7846i	−0.724731	−	1.25527i	−0.959084	−	0.283120i	$-0.908631\pi$
$563$	−17.1962	−	29.7846i	−0.724731	−	1.25527i	0.234353	−	0.972152i	$-0.424703\pi$
$564$	−7.79423	+	13.5000i	−0.328196	+	0.568453i
$565$	16.0981	+	9.29423i	0.677251	+	0.391011i
$566$	−10.8564			−0.456329
$567$	18.0000	+	15.5885i	0.755929	+	0.654654i
$568$	−1.26795			−0.0532020
$569$	5.19615	+	3.00000i	0.217834	+	0.125767i	0.604947	−	0.796266i	$-0.293194\pi$
$569$	5.19615	+	3.00000i	0.217834	+	0.125767i	−0.387113	+	0.922032i	$0.626528\pi$
$570$	−4.09808	+	7.09808i	−0.171650	+	0.297306i
$571$	−21.1962	−	36.7128i	−0.887031	−	1.53638i	−0.843368	−	0.537337i	$-0.819430\pi$
$571$	−21.1962	−	36.7128i	−0.887031	−	1.53638i	−0.0436638	−	0.999046i	$-0.513903\pi$
$572$	4.39230			0.183651
$573$	5.19615	−	3.00000i	0.217072	−	0.125327i
$574$	7.79423	+	22.5000i	0.325325	+	0.939132i
$575$		−	9.46410i		−	0.394680i
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−20.7846	−	12.0000i	−0.865275	−	0.499567i	0.000500448	−	1.00000i	$-0.499841\pi$
$577$	−20.7846	−	12.0000i	−0.865275	−	0.499567i	−0.865775	+	0.500433i	$0.833174\pi$
$578$			17.0000i			0.707107i
$579$	−41.9090			−1.74168
$580$	0.401924	+	0.232051i	0.0166890	+	0.00963539i
$581$	2.00962	−	0.696152i	0.0833730	−	0.0288813i
$582$	−13.3923	+	23.1962i	−0.555129	+	0.961511i
$583$	6.80385	−	11.7846i	0.281787	−	0.488069i
$584$	−3.46410	+	6.00000i	−0.143346	+	0.248282i
$585$			10.3923i			0.429669i
$586$	3.80385	−	2.19615i	0.157135	−	0.0907222i
$587$	20.5981	+	35.6769i	0.850174	+	1.47254i	0.881051	+	0.473021i	$0.156836\pi$
$587$	20.5981	+	35.6769i	0.850174	+	1.47254i	−0.0308777	+	0.999523i	$0.509830\pi$
$588$	−11.2583	−	4.50000i	−0.464286	−	0.185577i
$589$	−5.19615	+	9.00000i	−0.214104	+	0.370839i
$590$			8.19615i			0.337430i
$591$	9.50962	+	5.49038i	0.391173	+	0.225844i
$592$	−4.19615			−0.172461
$593$	7.39230	+	12.8038i	0.303566	+	0.525791i	0.976941	−	0.213510i	$-0.0684895\pi$
$593$	7.39230	+	12.8038i	0.303566	+	0.525791i	−0.673375	+	0.739301i	$0.735156\pi$
$594$	−3.29423	+	5.70577i	−0.135164	+	0.234111i
$595$		0			0
$596$	10.3923	−	6.00000i	0.425685	−	0.245770i
$597$	10.3923	−	6.00000i	0.425329	−	0.245564i
$598$	28.3923	−	16.3923i	1.16105	−	0.670331i
$599$	14.1962	−	8.19615i	0.580039	−	0.334886i	−0.181110	−	0.983463i	$-0.557969\pi$
$599$	14.1962	−	8.19615i	0.580039	−	0.334886i	0.761149	+	0.648577i	$0.224636\pi$
$600$	1.50000	+	0.866025i	0.0612372	+	0.0353553i
$601$	−3.58846	+	2.07180i	−0.146376	+	0.0845104i	−0.571399	−	0.820672i	$-0.693599\pi$
$601$	−3.58846	+	2.07180i	−0.146376	+	0.0845104i	0.425023	+	0.905182i	$0.360266\pi$
$602$	18.6962	+	3.59808i	0.761998	+	0.146647i
$603$	6.00000	−	10.3923i	0.244339	−	0.423207i
$604$	3.09808	+	5.36603i	0.126059	+	0.218340i
$605$	−9.39230			−0.381851
$606$	−1.20577	+	0.696152i	−0.0489811	+	0.0282793i
$607$			18.1244i			0.735645i	0.929896	+	0.367822i	$0.119897\pi$
$607$			18.1244i			0.735645i	−0.929896	+	0.367822i	$0.880103\pi$
$608$	−2.36603	+	4.09808i	−0.0959550	+	0.166199i
$609$	2.08846	+	0.401924i	0.0846286	+	0.0162868i
$610$	−0.464102	−	0.803848i	−0.0187909	−	0.0325468i
$611$	−27.0000	+	15.5885i	−1.09230	+	0.630641i
$612$		0			0
$613$	−17.3923	+	30.1244i	−0.702469	+	1.21671i	0.265129	+	0.964213i	$0.414586\pi$
$613$	−17.3923	+	30.1244i	−0.702469	+	1.21671i	−0.967597	+	0.252498i	$0.918748\pi$
$614$	−8.89230	+	15.4019i	−0.358864	+	0.621571i
$615$	−7.79423	−	13.5000i	−0.314294	−	0.544373i
$616$	0.633975	−	3.29423i	0.0255436	−	0.132728i
$617$	26.1962	+	15.1244i	1.05462	+	0.608884i	0.923938	−	0.382541i	$-0.124951\pi$
$617$	26.1962	+	15.1244i	1.05462	+	0.608884i	0.130679	+	0.991425i	$0.458284\pi$
$618$	10.5000	+	18.1865i	0.422372	+	0.731570i
$619$			4.39230i			0.176542i	0.996097	+	0.0882708i	$0.0281341\pi$
$619$			4.39230i			0.176542i	−0.996097	+	0.0882708i	$0.971866\pi$
$620$	1.90192	+	1.09808i	0.0763831	+	0.0440998i
$621$			49.1769i			1.97340i
$622$		−	26.1962i		−	1.05037i
$623$	40.9808	−	14.1962i	1.64186	−	0.568757i
$624$			6.00000i			0.240192i
$625$	1.00000			0.0400000
$626$	4.90192	+	8.49038i	0.195920	+	0.339344i
$627$	−10.3923			−0.415029
$628$	0.294229	+	0.169873i	0.0117410	+	0.00677867i
$629$		0			0
$630$	7.79423	+	1.50000i	0.310530	+	0.0597614i
$631$	−8.39230			−0.334092			−0.167046	−	0.985949i	$-0.553423\pi$
$631$	−8.39230			−0.334092			−0.167046	+	0.985949i	$0.553423\pi$
$632$	14.3660	+	8.29423i	0.571450	+	0.329927i
$633$	9.16987	+	15.8827i	0.364470	+	0.631280i
$634$	−13.7321	−	23.7846i	−0.545369	−	0.944608i
$635$	−9.39230			−0.372722
$636$	16.0981	+	9.29423i	0.638330	+	0.368540i
$637$	−15.0000	−	19.0526i	−0.594322	−	0.754890i
$638$			0.588457i			0.0232972i
$639$	3.29423	−	1.90192i	0.130318	−	0.0752389i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$			44.7846i			1.76889i	0.466648	+	0.884443i	$0.345461\pi$
$641$			44.7846i			1.76889i	−0.466648	+	0.884443i	$0.654539\pi$
$642$	−1.79423	+	3.10770i	−0.0708126	+	0.122651i
$643$	31.7942	+	18.3564i	1.25384	+	0.723906i	0.971870	−	0.235517i	$-0.0756782\pi$
$643$	31.7942	+	18.3564i	1.25384	+	0.723906i	0.281972	+	0.959423i	$0.409012\pi$
$644$	−8.19615	−	23.6603i	−0.322974	−	0.932345i
$645$	−12.4641			−0.490774
$646$		0			0
$647$	12.6962	−	21.9904i	0.499137	−	0.864531i	−0.500862	−	0.865527i	$-0.666984\pi$
$647$	12.6962	−	21.9904i	0.499137	−	0.864531i	1.00000		0.000995924i	$0.000317013\pi$
$648$	−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
$651$	9.88269	+	1.90192i	0.387333	+	0.0745423i
$652$	6.19615	−	10.7321i	0.242660	−	0.420300i
$653$			22.1436i			0.866546i	0.901263	+	0.433273i	$0.142641\pi$
$653$			22.1436i			0.866546i	−0.901263	+	0.433273i	$0.857359\pi$
$654$			5.53590i			0.216471i
$655$	16.3923			0.640500
$656$	−4.50000	−	7.79423i	−0.175695	−	0.304314i
$657$		−	20.7846i		−	0.810885i
$658$	7.79423	+	22.5000i	0.303851	+	0.877141i
$659$	−17.7058	+	10.2224i	−0.689719	+	0.398209i	−0.803507	−	0.595296i	$-0.797035\pi$
$659$	−17.7058	+	10.2224i	−0.689719	+	0.398209i	0.113788	+	0.993505i	$0.463702\pi$
$660$			2.19615i			0.0854851i
$661$	−35.3827	+	20.4282i	−1.37623	+	0.794565i	−0.991703	−	0.128550i	$-0.958968\pi$
$661$	−35.3827	+	20.4282i	−1.37623	+	0.794565i	−0.384524	+	0.923115i	$0.625634\pi$
$662$	6.92820	−	4.00000i	0.269272	−	0.155464i
$663$		0			0
$664$	−0.696152	+	0.401924i	−0.0270160	+	0.0155977i
$665$	4.09808	+	11.8301i	0.158917	+	0.458753i
$666$	10.9019	−	6.29423i	0.422441	−	0.243896i
$667$	2.19615	+	3.80385i	0.0850354	+	0.147286i
$668$	−10.3923			−0.402090
$669$			17.7846i			0.687593i
$670$		−	4.00000i		−	0.154533i
$671$	0.588457	−	1.01924i	0.0227171	−	0.0393472i
$672$	4.50000	+	0.866025i	0.173591	+	0.0334077i
$673$	−13.4904	−	23.3660i	−0.520016	−	0.900694i	−0.999729	−	0.0232688i	$-0.992593\pi$
$673$	−13.4904	−	23.3660i	−0.520016	−	0.900694i	0.479713	−	0.877425i	$-0.340741\pi$
$674$	−8.66025	+	5.00000i	−0.333581	+	0.192593i
$675$	−5.19615			−0.200000
$676$	0.500000	−	0.866025i	0.0192308	−	0.0333087i
$677$	−14.4904	+	25.0981i	−0.556911	+	0.964597i	0.440842	+	0.897585i	$0.354680\pi$
$677$	−14.4904	+	25.0981i	−0.556911	+	0.964597i	−0.997752	+	0.0670125i	$0.978653\pi$
$678$	−32.1962			−1.23649
$679$	13.3923	+	38.6603i	0.513949	+	1.48364i
$680$		0			0
$681$	3.80385	−	6.58846i	0.145764	−	0.252470i
$682$			2.78461i			0.106628i
$683$	−36.7750	−	21.2321i	−1.40716	−	0.812422i	−0.412043	−	0.911164i	$-0.635185\pi$
$683$	−36.7750	−	21.2321i	−1.40716	−	0.812422i	−0.995113	+	0.0987426i	$0.968518\pi$
$684$		−	14.1962i		−	0.542803i
$685$		−	10.7321i		−	0.410051i
$686$	−16.4545	+	8.50000i	−0.628235	+	0.324532i
$687$	−41.8923	−	24.1865i	−1.59829	−	0.922774i
$688$	−7.19615			−0.274351
$689$	18.5885	+	32.1962i	0.708164	+	1.22658i
$690$	8.19615	+	14.1962i	0.312022	+	0.540438i
$691$	16.3923	+	9.46410i	0.623593	+	0.360031i	0.778266	−	0.627934i	$-0.216099\pi$
$691$	16.3923	+	9.46410i	0.623593	+	0.360031i	−0.154674	+	0.987966i	$0.549433\pi$
$692$	−2.19615			−0.0834852
$693$	3.29423	+	9.50962i	0.125137	+	0.361241i
$694$	27.2487			1.03435
$695$	−13.9019	−	8.02628i	−0.527330	−	0.304454i
$696$	−0.803848			−0.0304698
$697$		0			0
$698$	4.39230			0.166251
$699$			8.19615i			0.310007i
$700$	2.50000	−	0.866025i	0.0944911	−	0.0327327i
$701$		−	9.67949i		−	0.365589i	−0.983151	−	0.182795i	$-0.941486\pi$
$701$		−	9.67949i		−	0.365589i	0.983151	−	0.182795i	$-0.0585144\pi$
$702$	−9.00000	−	15.5885i	−0.339683	−	0.588348i
$703$	17.1962	+	9.92820i	0.648565	+	0.374449i
$704$			1.26795i			0.0477876i
$705$	−7.79423	−	13.5000i	−0.293548	−	0.508439i
$706$	26.4904	+	15.2942i	0.996979	+	0.575606i
$707$	−0.401924	+	2.08846i	−0.0151159	+	0.0785445i
$708$	−7.09808	−	12.2942i	−0.266762	−	0.462045i
$709$	2.60770	−	4.51666i	0.0979340	−	0.169627i	−0.812895	−	0.582410i	$-0.802110\pi$
$709$	2.60770	−	4.51666i	0.0979340	−	0.169627i	0.910829	+	0.412783i	$0.135443\pi$
$710$	0.633975	−	1.09808i	0.0237926	−	0.0412101i
$711$	−49.7654			−1.86635
$712$	−14.1962	+	8.19615i	−0.532023	+	0.307164i
$713$	10.3923	+	18.0000i	0.389195	+	0.674105i
$714$		0			0
$715$	−2.19615	+	3.80385i	−0.0821314	+	0.142256i
$716$			6.58846i			0.246222i
$717$	31.6865	−	18.2942i	1.18336	−	0.683210i
$718$	26.1962			0.977632
$719$	−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
$722$	2.93782	−	1.69615i	0.109334	−	0.0631243i
$723$	−30.9904	−	17.8923i	−1.15254	−	0.665422i
$724$	6.40192	−	3.69615i	0.237926	−	0.137366i
$725$	−0.401924	+	0.232051i	−0.0149271	+	0.00861815i
$726$	14.0885	−	8.13397i	0.522872	−	0.301880i
$727$	−0.215390	+	0.124356i	−0.00798838	+	0.00461210i	−0.503989	−	0.863710i	$-0.668135\pi$
$727$	−0.215390	+	0.124356i	−0.00798838	+	0.00461210i	0.496000	+	0.868322i	$0.334801\pi$
$728$	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
$732$	1.39230	+	0.803848i	0.0514611	+	0.0297111i
$733$			4.05256i			0.149685i	0.997195	+	0.0748423i	$0.0238454\pi$
$733$			4.05256i			0.149685i	−0.997195	+	0.0748423i	$0.976155\pi$
$734$	−9.40192	+	16.2846i	−0.347031	+	0.601076i
$735$	9.52628	−	7.50000i	0.351382	−	0.276642i
$736$	4.73205	+	8.19615i	0.174426	+	0.302114i
$737$	4.39230	−	2.53590i	0.161793	−	0.0934110i
$738$	23.3827	+	13.5000i	0.860729	+	0.496942i
$739$	14.5885	−	25.2679i	0.536645	−	0.929497i	−0.462437	−	0.886652i	$-0.653025\pi$
$739$	14.5885	−	25.2679i	0.536645	−	0.929497i	0.999082	−	0.0428442i	$-0.0136419\pi$
$740$	2.09808	−	3.63397i	0.0771268	−	0.133588i
$741$	14.1962	−	24.5885i	0.521509	−	0.903280i
$742$	26.8301	−	9.29423i	0.984965	−	0.341202i
$743$	38.6769	+	22.3301i	1.41892	+	0.819213i	0.996204	−	0.0870500i	$-0.0277440\pi$
$743$	38.6769	+	22.3301i	1.41892	+	0.819213i	0.422714	+	0.906263i	$0.361077\pi$
$744$	−3.80385			−0.139456
$745$			12.0000i			0.439646i
$746$	−0.169873	−	0.0980762i	−0.00621949	−	0.00359083i
$747$	1.20577	−	2.08846i	0.0441169	−	0.0764127i
$748$		0			0
$749$	1.79423	+	5.17949i	0.0655597	+	0.189255i
$750$	−1.50000	+	0.866025i	−0.0547723	+	0.0316228i
$751$	−42.3923			−1.54692			−0.773459	−	0.633847i	$-0.781475\pi$
$751$	−42.3923			−1.54692			−0.773459	+	0.633847i	$0.781475\pi$
$752$	−4.50000	−	7.79423i	−0.164098	−	0.284226i
$753$	−15.5885	+	27.0000i	−0.568075	+	0.983935i
$754$	−1.39230	−	0.803848i	−0.0507048	−	0.0292744i
$755$	−6.19615			−0.225501
$756$	−12.9904	+	4.50000i	−0.472456	+	0.163663i
$757$	22.5885			0.820991			0.410496	−	0.911863i	$-0.365356\pi$
$757$	22.5885			0.820991			0.410496	+	0.911863i	$0.365356\pi$
$758$	−26.3205	−	15.1962i	−0.956004	−	0.551949i
$759$	−10.3923	+	18.0000i	−0.377217	+	0.653359i
$760$	−2.36603	−	4.09808i	−0.0858248	−	0.148653i
$761$	−33.0000			−1.19625			−0.598125	−	0.801403i	$-0.704087\pi$
$761$	−33.0000			−1.19625			−0.598125	+	0.801403i	$0.704087\pi$
$762$	14.0885	−	8.13397i	0.510371	−	0.294663i
$763$	6.39230	+	5.53590i	0.231417	+	0.200413i
$764$			3.46410i			0.125327i
$765$		0			0
$766$	−1.20577	−	0.696152i	−0.0435663	−	0.0251530i
$767$		−	28.3923i		−	1.02519i
$768$	−1.73205			−0.0625000
$769$	13.5000	+	7.79423i	0.486822	+	0.281067i	0.723255	−	0.690581i	$-0.242645\pi$
$769$	13.5000	+	7.79423i	0.486822	+	0.281067i	−0.236433	+	0.971648i	$0.575978\pi$
$770$	2.53590	+	2.19615i	0.0913874	+	0.0791438i
$771$	6.58846	−	11.4115i	0.237277	−	0.410977i
$772$	12.0981	−	20.9545i	0.435419	−	0.754168i
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	−0.981250	−	0.192740i	$-0.938263\pi$
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	0.657542	+	0.753418i	$0.271596\pi$
$774$	18.6962	−	10.7942i	0.672019	−	0.387991i
$775$	−1.90192	+	1.09808i	−0.0683191	+	0.0394441i
$776$	−7.73205	−	13.3923i	−0.277564	−	0.480756i
$777$	3.63397	−	18.8827i	0.130368	−	0.677413i
$778$	15.3564	−	26.5981i	0.550554	−	0.953587i
$779$			42.5885i			1.52589i
$780$	−5.19615	−	3.00000i	−0.186052	−	0.107417i
$781$	1.60770			0.0575279
$782$		0			0
$783$	2.08846	−	1.20577i	0.0746354	−	0.0430908i
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	−0.294229	+	0.169873i	−0.0105015	+	0.00606303i
$786$	−24.5885	+	14.1962i	−0.877041	+	0.506360i
$787$	−33.9904	+	19.6244i	−1.21163	+	0.699533i	−0.963113	−	0.269096i	$-0.913275\pi$
$787$	−33.9904	+	19.6244i	−1.21163	+	0.699533i	−0.248513	+	0.968629i	$0.579942\pi$
$788$	−5.49038	+	3.16987i	−0.195587	+	0.112922i
$789$	−15.4019	−	8.89230i	−0.548323	−	0.316574i
$790$	−14.3660	+	8.29423i	−0.511120	+	0.295095i
$791$	−32.1962	+	37.1769i	−1.14476	+	1.32186i
$792$	−1.90192	−	3.29423i	−0.0675819	−	0.117055i
$793$	1.60770	+	2.78461i	0.0570909	+	0.0988844i
$794$	−0.588457			−0.0208836
$795$	−16.0981	+	9.29423i	−0.570940	+	0.329632i
$796$			6.92820i			0.245564i
$797$	21.5885	−	37.3923i	0.764702	−	1.32450i	−0.175701	−	0.984444i	$-0.556219\pi$
$797$	21.5885	−	37.3923i	0.764702	−	1.32450i	0.940404	−	0.340060i	$-0.110447\pi$
$798$	−16.3923	−	14.1962i	−0.580281	−	0.502538i
$799$		0			0
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	24.5885	−	42.5885i	0.868790	−	1.50479i
$802$	−13.7942	+	23.8923i	−0.487091	+	0.843667i
$803$	4.39230	−	7.60770i	0.155001	−	0.268470i
$804$	3.46410	+	6.00000i	0.122169	+	0.211604i
$805$	24.5885	+	4.73205i	0.866629	+	0.166783i
$806$	−6.58846	−	3.80385i	−0.232069	−	0.133985i
$807$	−15.5885	−	27.0000i	−0.548740	−	0.950445i
$808$		−	0.803848i		−	0.0282793i
$809$	−6.48076	−	3.74167i	−0.227851	−	0.131550i	0.381729	−	0.924274i	$-0.375329\pi$
$809$	−6.48076	−	3.74167i	−0.227851	−	0.131550i	−0.609580	+	0.792724i	$0.708662\pi$
$810$	7.79423	−	4.50000i	0.273861	−	0.158114i
$811$		−	51.4641i		−	1.80715i	−0.428431	−	0.903575i	$-0.640933\pi$
$811$		−	51.4641i		−	1.80715i	0.428431	−	0.903575i	$-0.359067\pi$
$812$	−0.803848	+	0.928203i	−0.0282095	+	0.0325735i
$813$		−	42.5885i		−	1.49364i
$814$	5.32051			0.186484
$815$	6.19615	+	10.7321i	0.217042	+	0.375927i
$816$		0			0
$817$	29.4904	+	17.0263i	1.03174	+	0.595674i
$818$	−34.5167			−1.20685
$819$	−27.0000	−	5.19615i	−0.943456	−	0.181568i
$820$	9.00000			0.314294
$821$	16.2058	+	9.35641i	0.565585	+	0.326541i	0.755384	−	0.655282i	$-0.227450\pi$
$821$	16.2058	+	9.35641i	0.565585	+	0.326541i	−0.189799	+	0.981823i	$0.560784\pi$
$822$	9.29423	+	16.0981i	0.324173	+	0.561485i
$823$	−25.6962	−	44.5070i	−0.895712	−	1.55142i	−0.832921	−	0.553391i	$-0.813333\pi$
$823$	−25.6962	−	44.5070i	−0.895712	−	1.55142i	−0.0627901	−	0.998027i	$-0.520000\pi$
$824$	−12.1244			−0.422372
$825$	−1.90192	−	1.09808i	−0.0662165	−	0.0382301i
$826$	−21.2942	−	4.09808i	−0.740921	−	0.142590i
$827$		−	37.6410i		−	1.30891i	−0.756103	−	0.654453i	$-0.772899\pi$
$827$		−	37.6410i		−	1.30891i	0.756103	−	0.654453i	$-0.227101\pi$
$828$	−24.5885	−	14.1962i	−0.854508	−	0.493350i
$829$	−6.18653	−	3.57180i	−0.214867	−	0.124054i	0.388704	−	0.921363i	$-0.372923\pi$
$829$	−6.18653	−	3.57180i	−0.214867	−	0.124054i	−0.603571	+	0.797309i	$0.706256\pi$
$830$		−	0.803848i		−	0.0279020i
$831$	−11.9545	+	20.7058i	−0.414696	+	0.718275i
$832$	−3.00000	−	1.73205i	−0.104006	−	0.0600481i
$833$		0			0
$834$	27.8038			0.962769
$835$	5.19615	−	9.00000i	0.179820	−	0.311458i
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$	9.88269	−	5.70577i	0.341596	−	0.197220i
$838$	−9.00000	+	5.19615i	−0.310900	+	0.179498i
$839$	7.09808	+	12.2942i	0.245053	+	0.424444i	0.962146	−	0.272533i	$-0.0878614\pi$
$839$	7.09808	+	12.2942i	0.245053	+	0.424444i	−0.717094	+	0.696977i	$0.754528\pi$
$840$	−3.00000	+	3.46410i	−0.103510	+	0.119523i
$841$	−14.3923	+	24.9282i	−0.496286	+	0.859593i
$842$		−	21.9808i		−	0.757507i
$843$		−	4.60770i		−	0.158697i
$844$	−10.5885			−0.364470
$845$	0.500000	+	0.866025i	0.0172005	+	0.0297922i
$846$	23.3827	+	13.5000i	0.803913	+	0.464140i
$847$	4.69615	−	24.4019i	0.161362	−	0.838460i
$848$	−9.29423	+	5.36603i	−0.319165	+	0.184270i
$849$			18.8038i			0.645346i
$850$		0			0
$851$	34.3923	−	19.8564i	1.17895	−	0.680669i
$852$			2.19615i			0.0752389i
$853$	38.7846	−	22.3923i	1.32796	−	0.766698i	0.342976	−	0.939344i	$-0.388565\pi$
$853$	38.7846	−	22.3923i	1.32796	−	0.766698i	0.984984	+	0.172646i	$0.0552318\pi$
$854$	2.32051	−	0.803848i	0.0794062	−	0.0275071i
$855$	12.2942	+	7.09808i	0.420454	+	0.242749i
$856$	−1.03590	−	1.79423i	−0.0354063	−	0.0613255i
$857$	−48.5885			−1.65975			−0.829875	−	0.557949i	$-0.811588\pi$
$857$	−48.5885			−1.65975			−0.829875	+	0.557949i	$0.811588\pi$
$858$		−	7.60770i		−	0.259722i
$859$		−	26.1962i		−	0.893801i	−0.894584	−	0.446901i	$-0.852528\pi$
$859$		−	26.1962i		−	0.893801i	0.894584	−	0.446901i	$-0.147472\pi$
$860$	3.59808	−	6.23205i	0.122693	−	0.212511i
$861$	38.9711	−	13.5000i	1.32813	−	0.460079i
$862$	−1.39230	−	2.41154i	−0.0474221	−	0.0821375i
$863$	4.60770	−	2.66025i	0.156848	−	0.0905561i	−0.419522	−	0.907745i	$-0.637802\pi$
$863$	4.60770	−	2.66025i	0.156848	−	0.0905561i	0.576370	+	0.817189i	$0.304469\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$	1.09808	−	1.90192i	0.0373357	−	0.0646673i
$866$	−9.00000	+	15.5885i	−0.305832	+	0.529717i
$867$	29.4449			1.00000
$868$	−3.80385	+	4.39230i	−0.129111	+	0.149085i
$869$	−18.2154	−	10.5167i	−0.617915	−	0.356753i
$870$	0.401924	−	0.696152i	0.0136265	−	0.0236018i
$871$			13.8564i			0.469506i
$872$	−2.76795	−	1.59808i	−0.0937346	−	0.0541177i
$873$	40.1769	+	23.1962i	1.35978	+	0.785071i
$874$		−	44.7846i		−	1.51486i
$875$	−0.500000	+	2.59808i	−0.0169031	+	0.0878310i
$876$	10.3923	+	6.00000i	0.351123	+	0.202721i
$877$	−41.7654			−1.41032			−0.705158	−	0.709050i	$-0.749124\pi$
$877$	−41.7654			−1.41032			−0.705158	+	0.709050i	$0.749124\pi$
$878$	−6.16987	−	10.6865i	−0.208223	−	0.360653i
$879$	−3.80385	−	6.58846i	−0.128301	−	0.222223i
$880$	−1.09808	−	0.633975i	−0.0370161	−	0.0213713i
$881$	4.39230			0.147981			0.0739903	−	0.997259i	$-0.476427\pi$
$881$	4.39230			0.147981			0.0739903	+	0.997259i	$0.476427\pi$
$882$	−7.79423	+	19.5000i	−0.262445	+	0.656599i
$883$	−44.3731			−1.49327			−0.746636	−	0.665232i	$-0.768332\pi$
$883$	−44.3731			−1.49327			−0.746636	+	0.665232i	$0.768332\pi$
$884$		0			0
$885$	14.1962			0.477198
$886$	−4.50000	−	7.79423i	−0.151180	−	0.261852i
$887$	−28.6077			−0.960552			−0.480276	−	0.877117i	$-0.659464\pi$
$887$	−28.6077			−0.960552			−0.480276	+	0.877117i	$0.659464\pi$
$888$			7.26795i			0.243896i
$889$	4.69615	−	24.4019i	0.157504	−	0.818414i
$890$		−	16.3923i		−	0.549471i
$891$	9.88269	+	5.70577i	0.331082	+	0.191151i
$892$	−8.89230	−	5.13397i	−0.297736	−	0.171898i
$893$			42.5885i			1.42517i
$894$	−10.3923	−	18.0000i	−0.347571	−	0.602010i
$895$	−5.70577	−	3.29423i	−0.190723	−	0.110114i
$896$	−1.73205	+	2.00000i	−0.0578638	+	0.0668153i
$897$	−28.3923	−	49.1769i	−0.947991	−	1.64197i
$898$	−10.7942	+	18.6962i	−0.360208	+	0.623899i
$899$	0.509619	−	0.882686i	0.0169967	−	0.0294392i
$900$	1.50000	−	2.59808i	0.0500000	−	0.0866025i
$901$		0			0
$902$	5.70577	+	9.88269i	0.189981	+	0.329057i
$903$	6.23205	−	32.3827i	0.207390	−	1.07763i
$904$	9.29423	−	16.0981i	0.309121	−	0.535414i
$905$			7.39230i			0.245729i
$906$	9.29423	−	5.36603i	0.308780	−	0.178274i
$907$	33.1962			1.10226			0.551130	−	0.834419i	$-0.314197\pi$
$907$	33.1962			1.10226			0.551130	+	0.834419i	$0.314197\pi$
$908$	2.19615	+	3.80385i	0.0728819	+	0.126235i
$909$	1.20577	+	2.08846i	0.0399929	+	0.0692698i
$910$	−8.66025	+	3.00000i	−0.287085	+	0.0994490i
$911$	4.90192	−	2.83013i	0.162408	−	0.0937663i	−0.416593	−	0.909093i	$-0.636776\pi$
$911$	4.90192	−	2.83013i	0.162408	−	0.0937663i	0.579001	+	0.815327i	$0.303443\pi$
$912$	7.09808	+	4.09808i	0.235041	+	0.135701i
$913$	0.882686	−	0.509619i	0.0292126	−	0.0168659i
$914$	15.9282	−	9.19615i	0.526858	−	0.304182i
$915$	−1.39230	+	0.803848i	−0.0460282	+	0.0265744i
$916$	24.1865	−	13.9641i	0.799146	−	0.461387i
$917$	−8.19615	+	42.5885i	−0.270661	+	1.40639i
$918$		0			0
$919$	13.2942	+	23.0263i	0.438536	+	0.759567i	0.997577	−	0.0695733i	$-0.0221638\pi$
$919$	13.2942	+	23.0263i	0.438536	+	0.759567i	−0.559041	+	0.829140i	$0.688830\pi$
$920$	−9.46410			−0.312022
$921$	26.6769	+	15.4019i	0.879034	+	0.507511i
$922$			5.19615i			0.171126i
$923$	−2.19615	+	3.80385i	−0.0722872	+	0.125205i
$924$	−5.70577	−	1.09808i	−0.187706	−	0.0361241i
$925$	2.09808	+	3.63397i	0.0689843	+	0.119484i
$926$	20.2583	−	11.6962i	0.665730	−	0.384359i
$927$	31.5000	−	18.1865i	1.03460	−	0.597324i
$928$	0.232051	−	0.401924i	0.00761744	−	0.0131938i
$929$	16.2846	−	28.2058i	0.534281	−	0.925401i	−0.464917	−	0.885354i	$-0.653916\pi$
$929$	16.2846	−	28.2058i	0.534281	−	0.925401i	0.999198	−	0.0400471i	$-0.0127508\pi$
$930$	1.90192	−	3.29423i	0.0623665	−	0.108022i
$931$	−32.7846	+	4.73205i	−1.07447	+	0.155087i
$932$	−4.09808	−	2.36603i	−0.134237	−	0.0775017i
$933$	−45.3731			−1.48545
$934$			17.1962i			0.562675i
$935$		0			0
$936$	10.3923			0.339683
$937$			11.4115i			0.372799i	0.982474	+	0.186399i	$0.0596818\pi$
$937$			11.4115i			0.372799i	−0.982474	+	0.186399i	$0.940318\pi$
$938$	10.3923	+	2.00000i	0.339321	+	0.0653023i
$939$	14.7058	−	8.49038i	0.479905	−	0.277073i
$940$	9.00000			0.293548
$941$	12.9904	+	22.5000i	0.423474	+	0.733479i	0.996277	−	0.0862145i	$-0.0274771\pi$
$941$	12.9904	+	22.5000i	0.423474	+	0.733479i	−0.572802	+	0.819694i	$0.694144\pi$
$942$	0.294229	−	0.509619i	0.00958649	−	0.0166043i
$943$	73.7654	+	42.5885i	2.40213	+	1.38687i
$944$	8.19615			0.266762
$945$	2.59808	−	13.5000i	0.0845154	−	0.439155i
$946$	9.12436			0.296658
$947$	−51.5885	−	29.7846i	−1.67640	−	0.967870i	−0.963926	−	0.266171i	$-0.914241\pi$
$947$	−51.5885	−	29.7846i	−1.67640	−	0.967870i	−0.712474	−	0.701699i	$-0.752425\pi$
$948$	14.3660	−	24.8827i	0.466587	−	0.808152i
$949$	12.0000	+	20.7846i	0.389536	+	0.674697i
$950$	4.73205			0.153528
$951$	−41.1962	+	23.7846i	−1.33588	+	0.771269i
$952$		0			0
$953$			4.73205i			0.153286i	0.997059	+	0.0766431i	$0.0244202\pi$
$953$			4.73205i			0.153286i	−0.997059	+	0.0766431i	$0.975580\pi$
$954$	16.0981	−	27.8827i	0.521194	−	0.902735i
$955$	−3.00000	−	1.73205i	−0.0970777	−	0.0560478i
$956$			21.1244i			0.683210i
$957$	1.01924			0.0329473
$958$	9.00000	+	5.19615i	0.290777	+	0.167880i
$959$	27.8827	+	5.36603i	0.900379	+	0.173278i
$960$	0.866025	−	1.50000i	0.0279508	−	0.0484123i
$961$	−13.0885	+	22.6699i	−0.422208	+	0.731286i
$962$	−7.26795	+	12.5885i	−0.234328	+	0.405868i
$963$	5.38269	+	3.10770i	0.173455	+	0.100144i
$964$	17.8923	−	10.3301i	0.576272	−	0.332711i
$965$	12.0981	+	20.9545i	0.389451	+	0.674549i
$966$	−40.9808	+	14.1962i	−1.31853	+	0.456754i
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	−0.708245	−	0.705967i	$-0.750513\pi$
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	0.965508	+	0.260375i	$0.0838461\pi$
$968$			9.39230i			0.301880i
$969$		0			0
$970$	15.4641			0.496522
$971$	−13.3923	−	23.1962i	−0.429780	−	0.744400i	0.567074	−	0.823667i	$-0.308075\pi$
$971$	−13.3923	−	23.1962i	−0.429780	−	0.744400i	−0.996853	+	0.0792670i	$0.974742\pi$
$972$	−7.79423	+	13.5000i	−0.250000	+	0.433013i
$973$	27.8038	−	32.1051i	0.891350	−	1.02924i
$974$	−29.4449	+	17.0000i	−0.943474	+	0.544715i
$975$	5.19615	−	3.00000i	0.166410	−	0.0960769i
$976$	−0.803848	+	0.464102i	−0.0257305	+	0.0148555i
$977$	−16.3923	+	9.46410i	−0.524436	+	0.302783i	−0.738748	−	0.673982i	$-0.764583\pi$
$977$	−16.3923	+	9.46410i	−0.524436	+	0.302783i	0.214312	+	0.976765i	$0.431249\pi$
$978$	−18.5885	−	10.7321i	−0.594393	−	0.343173i
$979$	18.0000	−	10.3923i	0.575282	−	0.332140i
$980$	1.00000	+	6.92820i	0.0319438	+	0.221313i
$981$	9.58846			0.306136
$982$	1.43782	+	2.49038i	0.0458827	+	0.0794713i
$983$	−10.6077			−0.338333			−0.169166	−	0.985587i	$-0.554108\pi$
$983$	−10.6077			−0.338333			−0.169166	+	0.985587i	$0.554108\pi$
$984$	−13.5000	+	7.79423i	−0.430364	+	0.248471i
$985$		−	6.33975i		−	0.202001i
$986$		0			0
$987$	38.9711	−	13.5000i	1.24047	−	0.429710i
$988$	8.19615	+	14.1962i	0.260754	+	0.451640i
$989$	58.9808	−	34.0526i	1.87548	−	1.08281i
$990$	3.80385			0.120894
$991$	22.2942	−	38.6147i	0.708200	−	1.22664i	−0.257325	−	0.966325i	$-0.582841\pi$
$991$	22.2942	−	38.6147i	0.708200	−	1.22664i	0.965524	−	0.260313i	$-0.0838256\pi$
$992$	1.09808	−	1.90192i	0.0348640	−	0.0603861i
$993$	−6.92820	−	12.0000i	−0.219860	−	0.380808i
$994$	2.53590	+	2.19615i	0.0804338	+	0.0696577i
$995$	−6.00000	−	3.46410i	−0.190213	−	0.109819i
$996$	0.696152	+	1.20577i	0.0220584	+	0.0382063i
$997$		−	13.5167i		−	0.428077i	−0.976825	−	0.214038i	$-0.931338\pi$
$997$		−	13.5167i		−	0.428077i	0.976825	−	0.214038i	$-0.0686618\pi$
$998$	−5.02628	−	2.90192i	−0.159104	−	0.0918588i
$999$	−10.9019	−	18.8827i	−0.344922	−	0.597422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.a.311.2	✓	4
3.2	odd	2		1890.2.t.a.1151.1		4
7.5	odd	6		630.2.bk.a.131.1	yes	4
9.2	odd	6		630.2.bk.a.101.2	yes	4
9.7	even	3		1890.2.bk.a.521.1		4
21.5	even	6		1890.2.bk.a.341.2		4
63.47	even	6	inner	630.2.t.a.551.2	yes	4
63.61	odd	6		1890.2.t.a.1601.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.a.311.2	✓	4	1.1	even	1	trivial
630.2.t.a.551.2	yes	4	63.47	even	6	inner
630.2.bk.a.101.2	yes	4	9.2	odd	6
630.2.bk.a.131.1	yes	4	7.5	odd	6
1890.2.t.a.1151.1		4	3.2	odd	2
1890.2.t.a.1601.1		4	63.61	odd	6
1890.2.bk.a.341.2		4	21.5	even	6
1890.2.bk.a.521.1		4	9.7	even	3

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} -1.26795i 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} +(4.09808 - 2.36603i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.46410 - 3.00000i) q^{21} +(0.633975 - 1.09808i) q^{22} -9.46410i 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} +(-0.401924 + 0.232051i) q^{29} +(-1.50000 + 0.866025i) q^{30} +(-1.90192 + 1.09808i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.90192 - 1.09808i) q^{33} +(-0.500000 + 2.59808i) q^{35} +(1.50000 - 2.59808i) q^{36} +(2.09808 + 3.63397i) q^{37} +4.73205 q^{38} +(5.19615 - 3.00000i) q^{39} -1.00000i q^{40} +(-4.50000 + 7.79423i) q^{41} +(-1.50000 - 4.33013i) q^{42} +(3.59808 + 6.23205i) q^{43} +(1.09808 - 0.633975i) q^{44} +(1.50000 + 2.59808i) q^{45} +(4.73205 - 8.19615i) 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} +(9.29423 + 5.36603i) q^{53} +(-4.50000 - 2.59808i) q^{54} +1.26795i q^{55} +(2.59808 + 0.500000i) q^{56} -8.19615i q^{57} -0.464102 q^{58} +(-4.09808 - 7.09808i) q^{59} -1.73205 q^{60} +(0.803848 + 0.464102i) q^{61} -2.19615 q^{62} +(-7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(-3.00000 - 1.73205i) q^{65} +(-1.09808 - 1.90192i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-14.1962 - 8.19615i) q^{69} +(-1.73205 + 2.00000i) q^{70} +1.26795i q^{71} +(2.59808 - 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +4.19615i q^{74} +(0.866025 - 1.50000i) q^{75} +(4.09808 + 2.36603i) q^{76} +(-3.29423 - 0.633975i) q^{77} +6.00000 q^{78} +(8.29423 - 14.3660i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-7.79423 + 4.50000i) q^{82} +(0.401924 + 0.696152i) q^{83} +(0.866025 - 4.50000i) q^{84} +7.19615i q^{86} +0.803848i q^{87} +1.26795 q^{88} +(8.19615 + 14.1962i) q^{89} +3.00000i q^{90} +(6.00000 - 6.92820i) q^{91} +(8.19615 - 4.73205i) q^{92} +3.80385i q^{93} +(-7.79423 + 4.50000i) q^{94} +(-4.09808 + 2.36603i) q^{95} +1.73205i q^{96} +(-13.3923 + 7.73205i) q^{97} +(-4.33013 - 5.50000i) q^{98} +(-3.29423 + 1.90192i) 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

Groups

Database

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