LMFDB - Embedded newform 630.2.bk.a.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("630.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.a.131.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(1.09808 - 0.633975i) q^{11} +(0.866025 - 1.50000i) q^{12} +(-3.00000 + 1.73205i) q^{13} +(-0.866025 - 2.50000i) q^{14} +(-0.866025 - 1.50000i) q^{15} +1.00000 q^{16} +(2.59808 - 1.50000i) q^{18} +(4.09808 - 2.36603i) q^{19} +(0.500000 - 0.866025i) q^{20} +(0.866025 - 4.50000i) q^{21} +(0.633975 + 1.09808i) q^{22} +(-8.19615 - 4.73205i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.73205 - 3.00000i) q^{26} +5.19615 q^{27} +(2.50000 - 0.866025i) q^{28} +(-0.401924 - 0.232051i) q^{29} +(1.50000 - 0.866025i) q^{30} -2.19615i q^{31} +1.00000i q^{32} +2.19615i q^{33} +(0.500000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{36} +(2.09808 + 3.63397i) q^{37} +(2.36603 + 4.09808i) q^{38} -6.00000i q^{39} +(0.866025 + 0.500000i) q^{40} +(4.50000 + 7.79423i) q^{41} +(4.50000 + 0.866025i) q^{42} +(3.59808 - 6.23205i) q^{43} +(-1.09808 + 0.633975i) q^{44} +3.00000 q^{45} +(4.73205 - 8.19615i) q^{46} -9.00000 q^{47} +(-0.866025 + 1.50000i) q^{48} +(5.50000 - 4.33013i) q^{49} +(0.866025 - 0.500000i) q^{50} +(3.00000 - 1.73205i) q^{52} +(-9.29423 - 5.36603i) q^{53} +5.19615i q^{54} +1.26795i q^{55} +(0.866025 + 2.50000i) q^{56} +8.19615i q^{57} +(0.232051 - 0.401924i) q^{58} -8.19615 q^{59} +(0.866025 + 1.50000i) q^{60} -0.928203i q^{61} +2.19615 q^{62} +(6.00000 + 5.19615i) q^{63} -1.00000 q^{64} -3.46410i q^{65} -2.19615 q^{66} -4.00000 q^{67} +(14.1962 - 8.19615i) q^{69} +(2.59808 + 0.500000i) q^{70} -1.26795i q^{71} +(-2.59808 + 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +(-3.63397 + 2.09808i) q^{74} +1.73205 q^{75} +(-4.09808 + 2.36603i) q^{76} +(-2.19615 + 2.53590i) q^{77} +6.00000 q^{78} -16.5885 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} +(6.23205 + 3.59808i) q^{86} +(0.696152 - 0.401924i) q^{87} +(-0.633975 - 1.09808i) q^{88} +(-8.19615 - 14.1962i) q^{89} +3.00000i q^{90} +(6.00000 - 6.92820i) q^{91} +(8.19615 + 4.73205i) q^{92} +(3.29423 + 1.90192i) q^{93} -9.00000i q^{94} +4.73205i q^{95} +(-1.50000 - 0.866025i) 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 - 4 q^{4} - 2 q^{5} - 6 q^{6} - 10 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 2 * q^5 - 6 * q^6 - 10 * q^7 - 6 * q^9	$ 4 q - 4 q^{4} - 2 q^{5} - 6 q^{6} - 10 q^{7} - 6 q^{9} - 6 q^{11} - 12 q^{13} + 4 q^{16} + 6 q^{19} + 2 q^{20} + 6 q^{22} - 12 q^{23} + 6 q^{24} - 2 q^{25} + 10 q^{28} - 12 q^{29} + 6 q^{30} + 2 q^{35} + 6 q^{36} - 2 q^{37} + 6 q^{38} + 18 q^{41} + 18 q^{42} + 4 q^{43} + 6 q^{44} + 12 q^{45} + 12 q^{46} - 36 q^{47} + 22 q^{49} + 12 q^{52} - 6 q^{53} - 6 q^{58} - 12 q^{59} - 12 q^{62} + 24 q^{63} - 4 q^{64} + 12 q^{66} - 16 q^{67} + 36 q^{69} + 24 q^{73} - 18 q^{74} - 6 q^{76} + 12 q^{77} + 24 q^{78} - 4 q^{79} - 2 q^{80} - 18 q^{81} - 12 q^{83} + 18 q^{86} - 18 q^{87} - 6 q^{88} - 12 q^{89} + 24 q^{91} + 12 q^{92} - 18 q^{93} - 6 q^{96} + 12 q^{97} + 18 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 2 * q^5 - 6 * q^6 - 10 * q^7 - 6 * q^9 - 6 * q^11 - 12 * q^13 + 4 * q^16 + 6 * q^19 + 2 * q^20 + 6 * q^22 - 12 * q^23 + 6 * q^24 - 2 * q^25 + 10 * q^28 - 12 * q^29 + 6 * q^30 + 2 * q^35 + 6 * q^36 - 2 * q^37 + 6 * q^38 + 18 * q^41 + 18 * q^42 + 4 * q^43 + 6 * q^44 + 12 * q^45 + 12 * q^46 - 36 * q^47 + 22 * q^49 + 12 * q^52 - 6 * q^53 - 6 * q^58 - 12 * q^59 - 12 * q^62 + 24 * q^63 - 4 * q^64 + 12 * q^66 - 16 * q^67 + 36 * q^69 + 24 * q^73 - 18 * q^74 - 6 * q^76 + 12 * q^77 + 24 * q^78 - 4 * q^79 - 2 * q^80 - 18 * q^81 - 12 * q^83 + 18 * q^86 - 18 * q^87 - 6 * q^88 - 12 * q^89 + 24 * q^91 + 12 * q^92 - 18 * q^93 - 6 * q^96 + 12 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$4$	−1.00000			−0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$		−	1.00000i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	1.09808	−	0.633975i	0.331082	−	0.191151i	−0.325239	−	0.945632i	$-0.605445\pi$
$11$	1.09808	−	0.633975i	0.331082	−	0.191151i	0.656322	+	0.754481i	$0.272111\pi$
$12$	0.866025	−	1.50000i	0.250000	−	0.433013i
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	−0.854554	−	0.519362i	$-0.826170\pi$
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	0.0225039	+	0.999747i	$0.492836\pi$
$14$	−0.866025	−	2.50000i	−0.231455	−	0.668153i
$15$	−0.866025	−	1.50000i	−0.223607	−	0.387298i
$16$	1.00000			0.250000
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	2.59808	−	1.50000i	0.612372	−	0.353553i
$19$	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
$21$	0.866025	−	4.50000i	0.188982	−	0.981981i
$22$	0.633975	+	1.09808i	0.135164	+	0.234111i
$23$	−8.19615	−	4.73205i	−1.70902	−	0.986701i	−0.935781	−	0.352581i	$-0.885304\pi$
$23$	−8.19615	−	4.73205i	−1.70902	−	0.986701i	−0.773234	−	0.634120i	$-0.781362\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.73205	−	3.00000i	−0.339683	−	0.588348i
$27$	5.19615			1.00000
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	−0.401924	−	0.232051i	−0.0746354	−	0.0430908i	0.462218	−	0.886766i	$-0.347054\pi$
$29$	−0.401924	−	0.232051i	−0.0746354	−	0.0430908i	−0.536853	+	0.843676i	$0.680387\pi$
$30$	1.50000	−	0.866025i	0.273861	−	0.158114i
$31$		−	2.19615i		−	0.394441i	−0.980359	−	0.197220i	$-0.936809\pi$
$31$		−	2.19615i		−	0.394441i	0.980359	−	0.197220i	$-0.0631914\pi$
$32$			1.00000i			0.176777i
$33$			2.19615i			0.382301i
$34$		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	$0.721239\pi$
$38$	2.36603	+	4.09808i	0.383820	+	0.664796i
$39$		−	6.00000i		−	0.960769i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$	4.50000	+	0.866025i	0.694365	+	0.133631i
$43$	3.59808	−	6.23205i	0.548701	−	0.950379i	−0.449662	−	0.893199i	$-0.648456\pi$
$43$	3.59808	−	6.23205i	0.548701	−	0.950379i	0.998364	−	0.0571802i	$-0.0182110\pi$
$44$	−1.09808	+	0.633975i	−0.165541	+	0.0955753i
$45$	3.00000			0.447214
$46$	4.73205	−	8.19615i	0.697703	−	1.20846i
$47$	−9.00000			−1.31278			−0.656392	−	0.754420i	$-0.727918\pi$
$47$	−9.00000			−1.31278			−0.656392	+	0.754420i	$0.727918\pi$
$48$	−0.866025	+	1.50000i	−0.125000	+	0.216506i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		0			0
$52$	3.00000	−	1.73205i	0.416025	−	0.240192i
$53$	−9.29423	−	5.36603i	−1.27666	−	0.737080i	−0.300428	−	0.953805i	$-0.597129\pi$
$53$	−9.29423	−	5.36603i	−1.27666	−	0.737080i	−0.976233	+	0.216724i	$0.930463\pi$
$54$			5.19615i			0.707107i
$55$			1.26795i			0.170970i
$56$	0.866025	+	2.50000i	0.115728	+	0.334077i
$57$			8.19615i			1.08561i
$58$	0.232051	−	0.401924i	0.0304698	−	0.0527752i
$59$	−8.19615			−1.06705			−0.533524	−	0.845785i	$-0.679133\pi$
$59$	−8.19615			−1.06705			−0.533524	+	0.845785i	$0.679133\pi$
$60$	0.866025	+	1.50000i	0.111803	+	0.193649i
$61$		−	0.928203i		−	0.118844i	−0.998233	−	0.0594221i	$-0.981074\pi$
$61$		−	0.928203i		−	0.118844i	0.998233	−	0.0594221i	$-0.0189258\pi$
$62$	2.19615			0.278912
$63$	6.00000	+	5.19615i	0.755929	+	0.654654i
$64$	−1.00000			−0.125000
$65$		−	3.46410i		−	0.429669i
$66$	−2.19615			−0.270328
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	14.1962	−	8.19615i	1.70902	−	0.986701i
$70$	2.59808	+	0.500000i	0.310530	+	0.0597614i
$71$		−	1.26795i		−	0.150478i	−0.997166	−	0.0752389i	$-0.976028\pi$
$71$		−	1.26795i		−	0.150478i	0.997166	−	0.0752389i	$-0.0239720\pi$
$72$	−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	$0.533784\pi$
$74$	−3.63397	+	2.09808i	−0.422441	+	0.243896i
$75$	1.73205			0.200000
$76$	−4.09808	+	2.36603i	−0.470082	+	0.271402i
$77$	−2.19615	+	2.53590i	−0.250275	+	0.288992i
$78$	6.00000			0.679366
$79$	−16.5885			−1.86635			−0.933174	−	0.359426i	$-0.882973\pi$
$79$	−16.5885			−1.86635			−0.933174	+	0.359426i	$0.882973\pi$
$80$	−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	$-0.847381\pi$
$83$	−0.401924	+	0.696152i	−0.0441169	+	0.0764127i	0.843124	+	0.537720i	$0.180714\pi$
$84$	−0.866025	+	4.50000i	−0.0944911	+	0.490990i
$85$		0			0
$86$	6.23205	+	3.59808i	0.672019	+	0.387991i
$87$	0.696152	−	0.401924i	0.0746354	−	0.0430908i
$88$	−0.633975	−	1.09808i	−0.0675819	−	0.117055i
$89$	−8.19615	−	14.1962i	−0.868790	−	1.50479i	−0.863234	−	0.504805i	$-0.831565\pi$
$89$	−8.19615	−	14.1962i	−0.868790	−	1.50479i	−0.00555677	−	0.999985i	$-0.501769\pi$
$90$			3.00000i			0.316228i
$91$	6.00000	−	6.92820i	0.628971	−	0.726273i
$92$	8.19615	+	4.73205i	0.854508	+	0.493350i
$93$	3.29423	+	1.90192i	0.341596	+	0.197220i
$94$		−	9.00000i		−	0.928279i
$95$			4.73205i			0.485498i
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	13.3923	+	7.73205i	1.35978	+	0.785071i	0.989594	−	0.143886i	$-0.0459598\pi$
$97$	13.3923	+	7.73205i	1.35978	+	0.785071i	0.370188	+	0.928957i	$0.379293\pi$
$98$	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
$101$	−0.401924	−	0.696152i	−0.0399929	−	0.0692698i	0.845336	−	0.534235i	$-0.179400\pi$
$101$	−0.401924	−	0.696152i	−0.0399929	−	0.0692698i	−0.885329	+	0.464965i	$0.846067\pi$
$102$		0			0
$103$	−10.5000	−	6.06218i	−1.03460	−	0.597324i	−0.116298	−	0.993214i	$-0.537103\pi$
$103$	−10.5000	−	6.06218i	−1.03460	−	0.597324i	−0.918298	+	0.395890i	$0.870436\pi$
$104$	1.73205	+	3.00000i	0.169842	+	0.294174i
$105$	3.46410	+	3.00000i	0.338062	+	0.292770i
$106$	5.36603	−	9.29423i	0.521194	−	0.902735i
$107$	1.79423	−	1.03590i	0.173455	−	0.100144i	−0.410759	−	0.911744i	$-0.634736\pi$
$107$	1.79423	−	1.03590i	0.173455	−	0.100144i	0.584214	+	0.811600i	$0.301403\pi$
$108$	−5.19615			−0.500000
$109$	−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	$0.215582\pi$
$110$	−1.26795			−0.120894
$111$	−7.26795			−0.689843
$112$	−2.50000	+	0.866025i	−0.236228	+	0.0818317i
$113$	−16.0981	+	9.29423i	−1.51438	+	0.874327i	−0.514522	+	0.857477i	$0.672030\pi$
$113$	−16.0981	+	9.29423i	−1.51438	+	0.874327i	−0.999858	+	0.0168501i	$0.994636\pi$
$114$	−8.19615			−0.767640
$115$	8.19615	−	4.73205i	0.764295	−	0.441266i
$116$	0.401924	+	0.232051i	0.0373177	+	0.0215454i
$117$	9.00000	+	5.19615i	0.832050	+	0.480384i
$118$		−	8.19615i		−	0.754517i
$119$		0			0
$120$	−1.50000	+	0.866025i	−0.136931	+	0.0790569i
$121$	−4.69615	+	8.13397i	−0.426923	+	0.739452i
$122$	0.928203			0.0840356
$123$	−15.5885			−1.40556
$124$			2.19615i			0.197220i
$125$	1.00000			0.0894427
$126$	−5.19615	+	6.00000i	−0.462910	+	0.534522i
$127$	9.39230			0.833432			0.416716	−	0.909037i	$-0.363181\pi$
$127$	9.39230			0.833432			0.416716	+	0.909037i	$0.363181\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	6.23205	+	10.7942i	0.548701	+	0.950379i
$130$	3.46410			0.303822
$131$	−8.19615	+	14.1962i	−0.716101	+	1.24032i	0.246432	+	0.969160i	$0.420742\pi$
$131$	−8.19615	+	14.1962i	−0.716101	+	1.24032i	−0.962533	+	0.271164i	$0.912592\pi$
$132$		−	2.19615i		−	0.191151i
$133$	−8.19615	+	9.46410i	−0.710697	+	0.820642i
$134$		−	4.00000i		−	0.345547i
$135$	−2.59808	+	4.50000i	−0.223607	+	0.387298i
$136$		0			0
$137$	−9.29423	+	5.36603i	−0.794060	+	0.458450i	−0.841390	−	0.540429i	$-0.818262\pi$
$137$	−9.29423	+	5.36603i	−0.794060	+	0.458450i	0.0473302	+	0.998879i	$0.484929\pi$
$138$	8.19615	+	14.1962i	0.697703	+	1.20846i
$139$	−13.9019	+	8.02628i	−1.17915	+	0.680780i	−0.955817	−	0.293963i	$-0.905026\pi$
$139$	−13.9019	+	8.02628i	−1.17915	+	0.680780i	−0.223329	+	0.974743i	$0.571692\pi$
$140$	−0.500000	+	2.59808i	−0.0422577	+	0.219578i
$141$	7.79423	−	13.5000i	0.656392	−	1.13691i
$142$	1.26795			0.106404
$143$	−2.19615	+	3.80385i	−0.183651	+	0.318094i
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	0.401924	−	0.232051i	0.0333780	−	0.0192708i
$146$	−3.46410	+	6.00000i	−0.286691	+	0.496564i
$147$	1.73205	+	12.0000i	0.142857	+	0.989743i
$148$	−2.09808	−	3.63397i	−0.172461	−	0.298711i
$149$	−10.3923	−	6.00000i	−0.851371	−	0.491539i	0.00974235	−	0.999953i	$-0.496899\pi$
$149$	−10.3923	−	6.00000i	−0.851371	−	0.491539i	−0.861113	+	0.508413i	$0.830232\pi$
$150$			1.73205i			0.141421i
$151$	−3.09808	−	5.36603i	−0.252118	−	0.436681i	0.711991	−	0.702189i	$-0.247794\pi$
$151$	−3.09808	−	5.36603i	−0.252118	−	0.436681i	−0.964109	+	0.265508i	$0.914460\pi$
$152$	−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
$156$			6.00000i			0.480384i
$157$			0.339746i			0.0271147i	0.999908	+	0.0135573i	$0.00431557\pi$
$157$			0.339746i			0.0271147i	−0.999908	+	0.0135573i	$0.995684\pi$
$158$		−	16.5885i		−	1.31971i
$159$	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	$0.994630\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$	−1.90192	−	1.09808i	−0.148065	−	0.0854851i
$166$	−0.696152	−	0.401924i	−0.0540319	−	0.0311953i
$167$	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	$0.701617\pi$
$168$	−4.50000	−	0.866025i	−0.347183	−	0.0668153i
$169$	−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
$173$	−2.19615			−0.166970			−0.0834852	−	0.996509i	$-0.526605\pi$
$173$	−2.19615			−0.166970			−0.0834852	+	0.996509i	$0.526605\pi$
$174$	0.401924	+	0.696152i	0.0304698	+	0.0527752i
$175$	2.00000	+	1.73205i	0.151186	+	0.130931i
$176$	1.09808	−	0.633975i	0.0827706	−	0.0477876i
$177$	7.09808	−	12.2942i	0.533524	−	0.924091i
$178$	14.1962	−	8.19615i	1.06405	−	0.614328i
$179$	−5.70577	−	3.29423i	−0.426469	−	0.246222i	0.271372	−	0.962475i	$-0.412523\pi$
$179$	−5.70577	−	3.29423i	−0.426469	−	0.246222i	−0.697841	+	0.716252i	$0.745856\pi$
$180$	−3.00000			−0.223607
$181$		−	7.39230i		−	0.549466i	−0.961521	−	0.274733i	$-0.911411\pi$
$181$		−	7.39230i		−	0.549466i	0.961521	−	0.274733i	$-0.0885894\pi$
$182$	6.92820	+	6.00000i	0.513553	+	0.444750i
$183$	1.39230	+	0.803848i	0.102922	+	0.0594221i
$184$	−4.73205	+	8.19615i	−0.348851	+	0.604228i
$185$	−4.19615			−0.308507
$186$	−1.90192	+	3.29423i	−0.139456	+	0.241545i
$187$		0			0
$188$	9.00000			0.656392
$189$	−12.9904	+	4.50000i	−0.944911	+	0.327327i
$190$	−4.73205			−0.343299
$191$			3.46410i			0.250654i	0.992116	+	0.125327i	$0.0399979\pi$
$191$			3.46410i			0.250654i	−0.992116	+	0.125327i	$0.960002\pi$
$192$	0.866025	−	1.50000i	0.0625000	−	0.108253i
$193$	24.1962			1.74168			0.870839	−	0.491569i	$-0.163576\pi$
$193$	24.1962			1.74168			0.870839	+	0.491569i	$0.163576\pi$
$194$	−7.73205	+	13.3923i	−0.555129	+	0.961511i
$195$	5.19615	+	3.00000i	0.372104	+	0.214834i
$196$	−5.50000	+	4.33013i	−0.392857	+	0.309295i
$197$		−	6.33975i		−	0.451688i	−0.974163	−	0.225844i	$-0.927486\pi$
$197$		−	6.33975i		−	0.451688i	0.974163	−	0.225844i	$-0.0725140\pi$
$198$	1.90192	−	3.29423i	0.135164	−	0.234111i
$199$	6.00000	+	3.46410i	0.425329	+	0.245564i	0.697355	−	0.716726i	$-0.254360\pi$
$199$	6.00000	+	3.46410i	0.425329	+	0.245564i	−0.272026	+	0.962290i	$0.587694\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	3.46410	−	6.00000i	0.244339	−	0.423207i
$202$	0.696152	−	0.401924i	0.0489811	−	0.0282793i
$203$	1.20577	+	0.232051i	0.0846286	+	0.0162868i
$204$		0			0
$205$	−9.00000			−0.628587
$206$	6.06218	−	10.5000i	0.422372	−	0.731570i
$207$			28.3923i			1.97340i
$208$	−3.00000	+	1.73205i	−0.208013	+	0.120096i
$209$	3.00000	−	5.19615i	0.207514	−	0.359425i
$210$	−3.00000	+	3.46410i	−0.207020	+	0.239046i
$211$	−5.29423	−	9.16987i	−0.364470	−	0.631280i	0.624221	−	0.781248i	$-0.285416\pi$
$211$	−5.29423	−	9.16987i	−0.364470	−	0.631280i	−0.988691	+	0.149968i	$0.952083\pi$
$212$	9.29423	+	5.36603i	0.638330	+	0.368540i
$213$	1.90192	+	1.09808i	0.130318	+	0.0752389i
$214$	1.03590	+	1.79423i	0.0708126	+	0.122651i
$215$	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
$220$		−	1.26795i		−	0.0854851i
$221$		0			0
$222$		−	7.26795i		−	0.487793i
$223$	8.89230	+	5.13397i	0.595473	+	0.343796i	0.767259	−	0.641338i	$-0.221620\pi$
$223$	8.89230	+	5.13397i	0.595473	+	0.343796i	−0.171786	+	0.985134i	$0.554954\pi$
$224$	−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
$227$	2.19615	+	3.80385i	0.145764	+	0.252470i	0.929658	−	0.368425i	$-0.120103\pi$
$227$	2.19615	+	3.80385i	0.145764	+	0.252470i	−0.783894	+	0.620895i	$0.786769\pi$
$228$		−	8.19615i		−	0.542803i
$229$	24.1865	+	13.9641i	1.59829	+	0.922774i	0.991817	+	0.127671i	$0.0407501\pi$
$229$	24.1865	+	13.9641i	1.59829	+	0.922774i	0.606475	+	0.795103i	$0.292583\pi$
$230$	4.73205	+	8.19615i	0.312022	+	0.540438i
$231$	−1.90192	−	5.49038i	−0.125137	−	0.361241i
$232$	−0.232051	+	0.401924i	−0.0152349	+	0.0263876i
$233$	4.09808	−	2.36603i	0.268474	−	0.155003i	−0.359720	−	0.933060i	$-0.617128\pi$
$233$	4.09808	−	2.36603i	0.268474	−	0.155003i	0.628194	+	0.778057i	$0.283794\pi$
$234$	−5.19615	+	9.00000i	−0.339683	+	0.588348i
$235$	4.50000	−	7.79423i	0.293548	−	0.508439i
$236$	8.19615			0.533524
$237$	14.3660	−	24.8827i	0.933174	−	1.61630i
$238$		0			0
$239$	18.2942	−	10.5622i	1.18336	−	0.683210i	0.226567	−	0.973996i	$-0.427250\pi$
$239$	18.2942	−	10.5622i	1.18336	−	0.683210i	0.956788	+	0.290785i	$0.0939165\pi$
$240$	−0.866025	−	1.50000i	−0.0559017	−	0.0968246i
$241$	−17.8923	+	10.3301i	−1.15254	+	0.665422i	−0.949506	−	0.313749i	$-0.898415\pi$
$241$	−17.8923	+	10.3301i	−1.15254	+	0.665422i	−0.203039	+	0.979171i	$0.565082\pi$
$242$	−8.13397	−	4.69615i	−0.522872	−	0.301880i
$243$	−7.79423	−	13.5000i	−0.500000	−	0.866025i
$244$			0.928203i			0.0594221i
$245$	1.00000	+	6.92820i	0.0638877	+	0.442627i
$246$		−	15.5885i		−	0.993884i
$247$	−8.19615	+	14.1962i	−0.521509	+	0.903280i
$248$	−2.19615			−0.139456
$249$	−0.696152	−	1.20577i	−0.0441169	−	0.0764127i
$250$			1.00000i			0.0632456i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$	−6.00000	−	5.19615i	−0.377964	−	0.327327i
$253$	−12.0000			−0.754434
$254$			9.39230i			0.589326i
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.80385	−	6.58846i	0.237277	−	0.410977i	−0.722655	−	0.691209i	$-0.757078\pi$
$257$	3.80385	−	6.58846i	0.237277	−	0.410977i	0.959932	+	0.280233i	$0.0904116\pi$
$258$	−10.7942	+	6.23205i	−0.672019	+	0.387991i
$259$	−8.39230	−	7.26795i	−0.521472	−	0.451608i
$260$			3.46410i			0.214834i
$261$			1.39230i			0.0861815i
$262$	−14.1962	−	8.19615i	−0.877041	−	0.506360i
$263$	8.89230	−	5.13397i	0.548323	−	0.316574i	−0.200122	−	0.979771i	$-0.564134\pi$
$263$	8.89230	−	5.13397i	0.548323	−	0.316574i	0.748445	+	0.663196i	$0.230801\pi$
$264$	2.19615			0.135164
$265$	9.29423	−	5.36603i	0.570940	−	0.329632i
$266$	−9.46410	−	8.19615i	−0.580281	−	0.502538i
$267$	28.3923			1.73758
$268$	4.00000			0.244339
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	−4.50000	−	2.59808i	−0.273861	−	0.158114i
$271$	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
$275$	−1.09808	−	0.633975i	−0.0662165	−	0.0382301i
$276$	−14.1962	+	8.19615i	−0.854508	+	0.493350i
$277$	6.90192	+	11.9545i	0.414696	+	0.718275i	0.995397	−	0.0958423i	$-0.0305544\pi$
$277$	6.90192	+	11.9545i	0.414696	+	0.718275i	−0.580700	+	0.814118i	$0.697221\pi$
$278$	−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	0.567141	−	0.823620i	$-0.308049\pi$
$281$	2.30385	+	1.33013i	0.137436	+	0.0793487i	−0.429705	+	0.902969i	$0.641383\pi$
$282$	13.5000	+	7.79423i	0.803913	+	0.464140i
$283$		−	10.8564i		−	0.645346i	−0.946510	−	0.322673i	$-0.895419\pi$
$283$		−	10.8564i		−	0.645346i	0.946510	−	0.322673i	$-0.104581\pi$
$284$			1.26795i			0.0752389i
$285$	−7.09808	−	4.09808i	−0.420454	−	0.242749i
$286$	−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
$290$	0.232051	+	0.401924i	0.0136265	+	0.0236018i
$291$	−23.1962	+	13.3923i	−1.35978	+	0.785071i
$292$	−6.00000	−	3.46410i	−0.351123	−	0.202721i
$293$	−2.19615	−	3.80385i	−0.128301	−	0.222223i	0.794718	−	0.606979i	$-0.207619\pi$
$293$	−2.19615	−	3.80385i	−0.128301	−	0.222223i	−0.923018	+	0.384756i	$0.874286\pi$
$294$	−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
$297$	5.70577	−	3.29423i	0.331082	−	0.191151i
$298$	6.00000	−	10.3923i	0.347571	−	0.602010i
$299$	32.7846			1.89598
$300$	−1.73205			−0.100000
$301$	−3.59808	+	18.6962i	−0.207390	+	1.07763i
$302$	5.36603	−	3.09808i	0.308780	−	0.178274i
$303$	1.39230			0.0799858
$304$	4.09808	−	2.36603i	0.235041	−	0.135701i
$305$	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	$0.830566\pi$
$308$	2.19615	−	2.53590i	0.125137	−	0.144496i
$309$	18.1865	−	10.5000i	1.03460	−	0.597324i
$310$	−1.09808	+	1.90192i	−0.0623665	+	0.108022i
$311$	−26.1962			−1.48545			−0.742724	−	0.669598i	$-0.766466\pi$
$311$	−26.1962			−1.48545			−0.742724	+	0.669598i	$0.766466\pi$
$312$	−6.00000			−0.339683
$313$		−	9.80385i		−	0.554146i	−0.960849	−	0.277073i	$-0.910636\pi$
$313$		−	9.80385i		−	0.554146i	0.960849	−	0.277073i	$-0.0893644\pi$
$314$	−0.339746			−0.0191730
$315$	−7.50000	+	2.59808i	−0.422577	+	0.146385i
$316$	16.5885			0.933174
$317$		−	27.4641i		−	1.54254i	−0.636510	−	0.771269i	$-0.719622\pi$
$317$		−	27.4641i		−	1.54254i	0.636510	−	0.771269i	$-0.280378\pi$
$318$	9.29423	+	16.0981i	0.521194	+	0.902735i
$319$	−0.588457			−0.0329473
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$			3.58846i			0.200288i
$322$	−4.73205	+	24.5885i	−0.263707	+	1.37026i
$323$		0			0
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	3.00000	+	1.73205i	0.166410	+	0.0960769i
$326$	10.7321	−	6.19615i	0.594393	−	0.343173i
$327$	−2.76795	−	4.79423i	−0.153068	−	0.265121i
$328$	7.79423	−	4.50000i	0.430364	−	0.248471i
$329$	22.5000	−	7.79423i	1.24047	−	0.429710i
$330$	1.09808	−	1.90192i	0.0604471	−	0.104697i
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$	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
$336$	0.866025	−	4.50000i	0.0472456	−	0.245495i
$337$	−5.00000	−	8.66025i	−0.272367	−	0.471754i	0.697100	−	0.716974i	$-0.254473\pi$
$337$	−5.00000	−	8.66025i	−0.272367	−	0.471754i	−0.969468	+	0.245220i	$0.921140\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$		−	32.1962i		−	1.74865i
$340$		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
$345$			16.3923i			0.882532i
$346$		−	2.19615i		−	0.118066i
$347$		−	27.2487i		−	1.46279i	−0.681955	−	0.731394i	$-0.738870\pi$
$347$		−	27.2487i		−	1.46279i	0.681955	−	0.731394i	$-0.261130\pi$
$348$	−0.696152	+	0.401924i	−0.0373177	+	0.0215454i
$349$	−3.80385	−	2.19615i	−0.203615	−	0.117557i	0.394725	−	0.918799i	$-0.370840\pi$
$349$	−3.80385	−	2.19615i	−0.203615	−	0.117557i	−0.598341	+	0.801242i	$0.704173\pi$
$350$	−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
$353$	15.2942	+	26.4904i	0.814030	+	1.40994i	0.910023	+	0.414559i	$0.136064\pi$
$353$	15.2942	+	26.4904i	0.814030	+	1.40994i	−0.0959929	+	0.995382i	$0.530603\pi$
$354$	12.2942	+	7.09808i	0.653431	+	0.377258i
$355$	1.09808	+	0.633975i	0.0582798	+	0.0336479i
$356$	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	−0.959963	−	0.280125i	$-0.909624\pi$
$359$	−22.6865	+	13.0981i	−1.19735	+	0.691290i	−0.237386	+	0.971415i	$0.576291\pi$
$360$		−	3.00000i		−	0.158114i
$361$	1.69615	−	2.93782i	0.0892712	−	0.154622i
$362$	7.39230			0.388531
$363$	−8.13397	−	14.0885i	−0.426923	−	0.739452i
$364$	−6.00000	+	6.92820i	−0.314485	+	0.363137i
$365$	−6.00000	+	3.46410i	−0.314054	+	0.181319i
$366$	−0.803848	+	1.39230i	−0.0420178	+	0.0727769i
$367$	16.2846	−	9.40192i	0.850050	−	0.490776i	−0.0106179	−	0.999944i	$-0.503380\pi$
$367$	16.2846	−	9.40192i	0.850050	−	0.490776i	0.860668	+	0.509167i	$0.170047\pi$
$368$	−8.19615	−	4.73205i	−0.427254	−	0.246675i
$369$	13.5000	−	23.3827i	0.702782	−	1.21725i
$370$		−	4.19615i		−	0.218148i
$371$	27.8827	+	5.36603i	1.44760	+	0.278590i
$372$	−3.29423	−	1.90192i	−0.170798	−	0.0986102i
$373$	0.0980762	−	0.169873i	0.00507819	−	0.00879569i	−0.863475	−	0.504391i	$-0.831717\pi$
$373$	0.0980762	−	0.169873i	0.00507819	−	0.00879569i	0.868553	+	0.495596i	$0.165050\pi$
$374$		0			0
$375$	−0.866025	+	1.50000i	−0.0447214	+	0.0774597i
$376$			9.00000i			0.464140i
$377$	1.60770			0.0828005
$378$	−4.50000	−	12.9904i	−0.231455	−	0.668153i
$379$	−30.3923			−1.56115			−0.780574	−	0.625063i	$-0.785073\pi$
$379$	−30.3923			−1.56115			−0.780574	+	0.625063i	$0.785073\pi$
$380$		−	4.73205i		−	0.242749i
$381$	−8.13397	+	14.0885i	−0.416716	+	0.721774i
$382$	−3.46410			−0.177239
$383$	−0.696152	+	1.20577i	−0.0355717	+	0.0616120i	−0.883263	−	0.468878i	$-0.844659\pi$
$383$	−0.696152	+	1.20577i	−0.0355717	+	0.0616120i	0.847691	+	0.530490i	$0.177992\pi$
$384$	1.50000	+	0.866025i	0.0765466	+	0.0441942i
$385$	−1.09808	−	3.16987i	−0.0559631	−	0.161552i
$386$			24.1962i			1.23155i
$387$	−21.5885			−1.09740
$388$	−13.3923	−	7.73205i	−0.679891	−	0.392535i
$389$	26.5981	−	15.3564i	1.34858	−	0.778601i	0.360528	−	0.932748i	$-0.382596\pi$
$389$	26.5981	−	15.3564i	1.34858	−	0.778601i	0.988048	+	0.154148i	$0.0492631\pi$
$390$	−3.00000	+	5.19615i	−0.151911	+	0.263117i
$391$		0			0
$392$	−4.33013	−	5.50000i	−0.218704	−	0.277792i
$393$	−14.1962	−	24.5885i	−0.716101	−	1.24032i
$394$	6.33975			0.319392
$395$	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
$399$	−7.09808	−	20.4904i	−0.355348	−	1.02580i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	23.8923	+	13.7942i	1.19312	+	0.688851i	0.959014	−	0.283359i	$-0.0914488\pi$
$401$	23.8923	+	13.7942i	1.19312	+	0.688851i	0.234111	+	0.972210i	$0.424782\pi$
$402$	6.00000	+	3.46410i	0.299253	+	0.172774i
$403$	3.80385	+	6.58846i	0.189483	+	0.328194i
$404$	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
$409$		−	34.5167i		−	1.70674i	−0.521307	−	0.853370i	$-0.674555\pi$
$409$		−	34.5167i		−	1.70674i	0.521307	−	0.853370i	$-0.325445\pi$
$410$		−	9.00000i		−	0.444478i
$411$		−	18.5885i		−	0.916901i
$412$	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
$416$	−1.73205	−	3.00000i	−0.0849208	−	0.147087i
$417$		−	27.8038i		−	1.36156i
$418$	5.19615	+	3.00000i	0.254152	+	0.146735i
$419$	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	$0.751637\pi$
$420$	−3.46410	−	3.00000i	−0.169031	−	0.146385i
$421$	−10.9904	+	19.0359i	−0.535638	+	0.927753i	0.463494	+	0.886100i	$0.346596\pi$
$421$	−10.9904	+	19.0359i	−0.535638	+	0.927753i	−0.999132	+	0.0416527i	$0.986738\pi$
$422$	9.16987	−	5.29423i	0.446382	−	0.257719i
$423$	13.5000	+	23.3827i	0.656392	+	1.13691i
$424$	−5.36603	+	9.29423i	−0.260597	+	0.451368i
$425$		0			0
$426$	−1.09808	+	1.90192i	−0.0532020	+	0.0921485i
$427$	0.803848	+	2.32051i	0.0389009	+	0.112297i
$428$	−1.79423	+	1.03590i	−0.0867273	+	0.0500720i
$429$	−3.80385	−	6.58846i	−0.183651	−	0.318094i
$430$	−6.23205	+	3.59808i	−0.300536	+	0.173515i
$431$	2.41154	+	1.39230i	0.116160	+	0.0670650i	0.556954	−	0.830543i	$-0.311970\pi$
$431$	2.41154	+	1.39230i	0.116160	+	0.0670650i	−0.440794	+	0.897608i	$0.645303\pi$
$432$	5.19615			0.250000
$433$			18.0000i			0.865025i	0.901628	+	0.432512i	$0.142373\pi$
$433$			18.0000i			0.865025i	−0.901628	+	0.432512i	$0.857627\pi$
$434$	−5.49038	+	1.90192i	−0.263547	+	0.0912953i
$435$			0.803848i			0.0385415i
$436$	1.59808	−	2.76795i	0.0765340	−	0.132561i
$437$	−44.7846			−2.14234
$438$	−6.00000	−	10.3923i	−0.286691	−	0.496564i
$439$			12.3397i			0.588944i	0.955660	+	0.294472i	$0.0951438\pi$
$439$			12.3397i			0.588944i	−0.955660	+	0.294472i	$0.904856\pi$
$440$	1.26795			0.0604471
$441$	−19.5000	−	7.79423i	−0.928571	−	0.371154i
$442$		0			0
$443$		−	9.00000i		−	0.427603i	−0.976877	−	0.213801i	$-0.931415\pi$
$443$		−	9.00000i		−	0.427603i	0.976877	−	0.213801i	$-0.0685846\pi$
$444$	7.26795			0.344922
$445$	16.3923			0.777070
$446$	−5.13397	+	8.89230i	−0.243101	+	0.421063i
$447$	18.0000	−	10.3923i	0.851371	−	0.491539i
$448$	2.50000	−	0.866025i	0.118114	−	0.0409159i
$449$		−	21.5885i		−	1.01882i	−0.860523	−	0.509411i	$-0.829863\pi$
$449$		−	21.5885i		−	1.01882i	0.860523	−	0.509411i	$-0.170137\pi$
$450$	−2.59808	−	1.50000i	−0.122474	−	0.0707107i
$451$	9.88269	+	5.70577i	0.465358	+	0.268674i
$452$	16.0981	−	9.29423i	0.757190	−	0.437164i
$453$	10.7321			0.504236
$454$	−3.80385	+	2.19615i	−0.178523	+	0.103071i
$455$	3.00000	+	8.66025i	0.140642	+	0.405999i
$456$	8.19615			0.383820
$457$	−18.3923			−0.860356			−0.430178	−	0.902744i	$-0.641549\pi$
$457$	−18.3923			−0.860356			−0.430178	+	0.902744i	$0.641549\pi$
$458$	−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	$-0.871945\pi$
$461$	−2.59808	+	4.50000i	−0.121004	+	0.209586i	0.799160	+	0.601119i	$0.205278\pi$
$462$	5.49038	−	1.90192i	0.255436	−	0.0884855i
$463$	11.6962	+	20.2583i	0.543566	+	0.941484i	0.998696	+	0.0510591i	$0.0162597\pi$
$463$	11.6962	+	20.2583i	0.543566	+	0.941484i	−0.455129	+	0.890425i	$0.650407\pi$
$464$	−0.401924	−	0.232051i	−0.0186588	−	0.0107727i
$465$	−3.29423	+	1.90192i	−0.152766	+	0.0881996i
$466$	2.36603	+	4.09808i	0.109604	+	0.189840i
$467$	−8.59808	−	14.8923i	−0.397872	−	0.689134i	0.595592	−	0.803287i	$-0.296918\pi$
$467$	−8.59808	−	14.8923i	−0.397872	−	0.689134i	−0.993463	+	0.114154i	$0.963584\pi$
$468$	−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
$471$	−0.509619	−	0.294229i	−0.0234820	−	0.0135573i
$472$			8.19615i			0.377258i
$473$		−	9.12436i		−	0.419538i
$474$	24.8827	+	14.3660i	1.14290	+	0.659853i
$475$	−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
$479$	5.19615	+	9.00000i	0.237418	+	0.411220i	0.959973	−	0.280094i	$-0.0903655\pi$
$479$	5.19615	+	9.00000i	0.237418	+	0.411220i	−0.722554	+	0.691314i	$0.757032\pi$
$480$	1.50000	−	0.866025i	0.0684653	−	0.0395285i
$481$	−12.5885	−	7.26795i	−0.573984	−	0.331390i
$482$	−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
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$	−17.0000	+	29.4449i	−0.770344	+	1.33427i	0.167031	+	0.985952i	$0.446582\pi$
$487$	−17.0000	+	29.4449i	−0.770344	+	1.33427i	−0.937375	+	0.348323i	$0.886751\pi$
$488$	−0.928203			−0.0420178
$489$	21.4641			0.970640
$490$	−6.92820	+	1.00000i	−0.312984	+	0.0451754i
$491$	2.49038	−	1.43782i	0.112389	−	0.0648880i	−0.442752	−	0.896644i	$-0.645998\pi$
$491$	2.49038	−	1.43782i	0.112389	−	0.0648880i	0.555141	+	0.831756i	$0.312664\pi$
$492$	15.5885			0.702782
$493$		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
$497$	1.09808	+	3.16987i	0.0492554	+	0.142188i
$498$	1.20577	−	0.696152i	0.0540319	−	0.0311953i
$499$	2.90192	−	5.02628i	0.129908	−	0.225007i	−0.793733	−	0.608267i	$-0.791865\pi$
$499$	2.90192	−	5.02628i	0.129908	−	0.225007i	0.923641	+	0.383259i	$0.125198\pi$
$500$	−1.00000			−0.0447214
$501$	−18.0000			−0.804181
$502$			18.0000i			0.803379i
$503$	−13.3923			−0.597133			−0.298567	−	0.954389i	$-0.596509\pi$
$503$	−13.3923			−0.597133			−0.298567	+	0.954389i	$0.596509\pi$
$504$	5.19615	−	6.00000i	0.231455	−	0.267261i
$505$	0.803848			0.0357707
$506$		−	12.0000i		−	0.533465i
$507$	−0.866025	−	1.50000i	−0.0384615	−	0.0666173i
$508$	−9.39230			−0.416716
$509$	−10.7942	+	18.6962i	−0.478446	+	0.828692i	−0.999695	−	0.0247124i	$-0.992133\pi$
$509$	−10.7942	+	18.6962i	−0.478446	+	0.828692i	0.521249	+	0.853405i	$0.325466\pi$
$510$		0			0
$511$	−18.0000	−	3.46410i	−0.796273	−	0.153243i
$512$			1.00000i			0.0441942i
$513$	21.2942	−	12.2942i	0.940163	−	0.542803i
$514$	6.58846	+	3.80385i	0.290604	+	0.167781i
$515$	10.5000	−	6.06218i	0.462685	−	0.267131i
$516$	−6.23205	−	10.7942i	−0.274351	−	0.475189i
$517$	−9.88269	+	5.70577i	−0.434640	+	0.250940i
$518$	7.26795	−	8.39230i	0.319335	−	0.368737i
$519$	1.90192	−	3.29423i	0.0834852	−	0.144601i
$520$	−3.46410			−0.151911
$521$	−10.5000	+	18.1865i	−0.460013	+	0.796766i	−0.998961	−	0.0455727i	$-0.985489\pi$
$521$	−10.5000	+	18.1865i	−0.460013	+	0.796766i	0.538948	+	0.842339i	$0.318822\pi$
$522$	−1.39230			−0.0609395
$523$	−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
$525$	−4.33013	+	1.50000i	−0.188982	+	0.0654654i
$526$	5.13397	+	8.89230i	0.223852	+	0.387723i
$527$		0			0
$528$			2.19615i			0.0955753i
$529$	33.2846	+	57.6506i	1.44716	+	2.50655i
$530$	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
$534$			28.3923i			1.22866i
$535$			2.07180i			0.0895716i
$536$			4.00000i			0.172774i
$537$	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	$0.888348\pi$
$542$	12.2942	+	21.2942i	0.528082	+	0.914665i
$543$	11.0885	+	6.40192i	0.475851	+	0.274733i
$544$		0			0
$545$	−1.59808	−	2.76795i	−0.0684541	−	0.118566i
$546$	−15.0000	+	5.19615i	−0.641941	+	0.222375i
$547$	12.7942	−	22.1603i	0.547042	−	0.947504i	−0.451434	−	0.892305i	$-0.649087\pi$
$547$	12.7942	−	22.1603i	0.547042	−	0.947504i	0.998475	−	0.0551993i	$-0.0175794\pi$
$548$	9.29423	−	5.36603i	0.397030	−	0.229225i
$549$	−2.41154	+	1.39230i	−0.102922	+	0.0594221i
$550$	0.633975	−	1.09808i	0.0270328	−	0.0468221i
$551$	−2.19615			−0.0935592
$552$	−8.19615	−	14.1962i	−0.348851	−	0.604228i
$553$	41.4711	−	14.3660i	1.76353	−	0.610906i
$554$	−11.9545	+	6.90192i	−0.507897	+	0.293235i
$555$	3.63397	−	6.29423i	0.154254	−	0.267175i
$556$	13.9019	−	8.02628i	0.589573	−	0.340390i
$557$	−7.60770	−	4.39230i	−0.322348	−	0.186108i	0.330090	−	0.943949i	$-0.392921\pi$
$557$	−7.60770	−	4.39230i	−0.322348	−	0.186108i	−0.652439	+	0.757841i	$0.726254\pi$
$558$	−3.29423	−	5.70577i	−0.139456	−	0.241545i
$559$			24.9282i			1.05435i
$560$	0.500000	−	2.59808i	0.0211289	−	0.109789i
$561$		0			0
$562$	−1.33013	+	2.30385i	−0.0561080	+	0.0971819i
$563$	−34.3923			−1.44946			−0.724731	−	0.689031i	$-0.758036\pi$
$563$	−34.3923			−1.44946			−0.724731	+	0.689031i	$0.758036\pi$
$564$	−7.79423	+	13.5000i	−0.328196	+	0.568453i
$565$		−	18.5885i		−	0.782022i
$566$	10.8564			0.456329
$567$	4.50000	−	23.3827i	0.188982	−	0.981981i
$568$	−1.26795			−0.0532020
$569$			6.00000i			0.251533i	0.992060	+	0.125767i	$0.0401390\pi$
$569$			6.00000i			0.251533i	−0.992060	+	0.125767i	$0.959861\pi$
$570$	4.09808	−	7.09808i	0.171650	−	0.297306i
$571$	42.3923			1.77406			0.887031	−	0.461709i	$-0.152764\pi$
$571$	42.3923			1.77406			0.887031	+	0.461709i	$0.152764\pi$
$572$	2.19615	−	3.80385i	0.0918257	−	0.159047i
$573$	−5.19615	−	3.00000i	−0.217072	−	0.125327i
$574$	15.5885	−	18.0000i	0.650650	−	0.751305i
$575$			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	$0.833174\pi$
$578$	−14.7224	+	8.50000i	−0.612372	+	0.353553i
$579$	−20.9545	+	36.2942i	−0.870839	+	1.50834i
$580$	−0.401924	+	0.232051i	−0.0166890	+	0.00963539i
$581$	0.401924	−	2.08846i	0.0166746	−	0.0866438i
$582$	−13.3923	−	23.1962i	−0.555129	−	0.961511i
$583$	−13.6077			−0.563573
$584$	3.46410	−	6.00000i	0.143346	−	0.248282i
$585$	−9.00000	+	5.19615i	−0.372104	+	0.214834i
$586$	3.80385	−	2.19615i	0.157135	−	0.0907222i
$587$	−20.5981	+	35.6769i	−0.850174	+	1.47254i	0.0308777	+	0.999523i	$0.490170\pi$
$587$	−20.5981	+	35.6769i	−0.850174	+	1.47254i	−0.881051	+	0.473021i	$0.843164\pi$
$588$	−1.73205	−	12.0000i	−0.0714286	−	0.494872i
$589$	−5.19615	−	9.00000i	−0.214104	−	0.370839i
$590$	7.09808	+	4.09808i	0.292223	+	0.168715i
$591$	9.50962	+	5.49038i	0.391173	+	0.225844i
$592$	2.09808	+	3.63397i	0.0862304	+	0.149355i
$593$	−7.39230	−	12.8038i	−0.303566	−	0.525791i	0.673375	−	0.739301i	$-0.264844\pi$
$593$	−7.39230	−	12.8038i	−0.303566	−	0.525791i	−0.976941	+	0.213510i	$0.931510\pi$
$594$	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
$598$			32.7846i			1.34066i
$599$		−	16.3923i		−	0.669771i	−0.942259	−	0.334886i	$-0.891302\pi$
$599$		−	16.3923i		−	0.669771i	0.942259	−	0.334886i	$-0.108698\pi$
$600$		−	1.73205i		−	0.0707107i
$601$	3.58846	+	2.07180i	0.146376	+	0.0845104i	0.571399	−	0.820672i	$-0.306401\pi$
$601$	3.58846	+	2.07180i	0.146376	+	0.0845104i	−0.425023	+	0.905182i	$0.639734\pi$
$602$	−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
$605$	−4.69615	−	8.13397i	−0.190926	−	0.330693i
$606$			1.39230i			0.0565585i
$607$	−15.6962	−	9.06218i	−0.637087	−	0.367822i	0.146404	−	0.989225i	$-0.453230\pi$
$607$	−15.6962	−	9.06218i	−0.637087	−	0.367822i	−0.783492	+	0.621402i	$0.786563\pi$
$608$	2.36603	+	4.09808i	0.0959550	+	0.166199i
$609$	−1.39230	+	1.60770i	−0.0564190	+	0.0651471i
$610$	−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	$0.918748\pi$
$614$	−17.7846			−0.717728
$615$	7.79423	−	13.5000i	0.314294	−	0.544373i
$616$	2.53590	+	2.19615i	0.102174	+	0.0884855i
$617$	26.1962	−	15.1244i	1.05462	−	0.608884i	0.130679	−	0.991425i	$-0.458284\pi$
$617$	26.1962	−	15.1244i	1.05462	−	0.608884i	0.923938	+	0.382541i	$0.124951\pi$
$618$	10.5000	+	18.1865i	0.422372	+	0.731570i
$619$	3.80385	−	2.19615i	0.152890	−	0.0882708i	−0.421603	−	0.906780i	$-0.638533\pi$
$619$	3.80385	−	2.19615i	0.152890	−	0.0882708i	0.574493	+	0.818509i	$0.305199\pi$
$620$	−1.90192	−	1.09808i	−0.0763831	−	0.0440998i
$621$	−42.5885	−	24.5885i	−1.70902	−	0.986701i
$622$		−	26.1962i		−	1.05037i
$623$	32.7846	+	28.3923i	1.31349	+	1.13751i
$624$		−	6.00000i		−	0.240192i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	9.80385			0.391841
$627$	5.19615	+	9.00000i	0.207514	+	0.359425i
$628$		−	0.339746i		−	0.0135573i
$629$		0			0
$630$	−2.59808	−	7.50000i	−0.103510	−	0.298807i
$631$	−8.39230			−0.334092			−0.167046	−	0.985949i	$-0.553423\pi$
$631$	−8.39230			−0.334092			−0.167046	+	0.985949i	$0.553423\pi$
$632$			16.5885i			0.659853i
$633$	18.3397			0.728939
$634$	27.4641			1.09074
$635$	−4.69615	+	8.13397i	−0.186361	+	0.322787i
$636$	−16.0981	+	9.29423i	−0.638330	+	0.368540i
$637$	−9.00000	+	22.5167i	−0.356593	+	0.892143i
$638$		−	0.588457i		−	0.0232972i
$639$	−3.29423	+	1.90192i	−0.130318	+	0.0752389i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	−38.7846	+	22.3923i	−1.53190	+	0.884443i	−0.532626	+	0.846351i	$0.678795\pi$
$641$	−38.7846	+	22.3923i	−1.53190	+	0.884443i	−0.999274	+	0.0380920i	$0.987872\pi$
$642$	−3.58846			−0.141625
$643$	−31.7942	+	18.3564i	−1.25384	+	0.723906i	−0.971870	−	0.235517i	$-0.924322\pi$
$643$	−31.7942	+	18.3564i	−1.25384	+	0.723906i	−0.281972	+	0.959423i	$0.590988\pi$
$644$	−24.5885	−	4.73205i	−0.968921	−	0.186469i
$645$	−12.4641			−0.490774
$646$		0			0
$647$	−12.6962	+	21.9904i	−0.499137	+	0.864531i	−1.00000		0.000995924i	$-0.999683\pi$
$647$	−12.6962	+	21.9904i	−0.499137	+	0.864531i	0.500862	+	0.865527i	$0.333016\pi$
$648$	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
$653$	19.1769	+	11.0718i	0.750451	+	0.433273i	0.825857	−	0.563880i	$-0.190692\pi$
$653$	19.1769	+	11.0718i	0.750451	+	0.433273i	−0.0754061	+	0.997153i	$0.524025\pi$
$654$	4.79423	−	2.76795i	0.187469	−	0.108235i
$655$	−8.19615	−	14.1962i	−0.320250	−	0.554690i
$656$	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	0.113788	−	0.993505i	$-0.463702\pi$
$659$	−17.7058	−	10.2224i	−0.689719	−	0.398209i	−0.803507	+	0.595296i	$0.797035\pi$
$660$	1.90192	+	1.09808i	0.0740323	+	0.0427426i
$661$		−	40.8564i		−	1.58913i	−0.607179	−	0.794565i	$-0.707699\pi$
$661$		−	40.8564i		−	1.58913i	0.607179	−	0.794565i	$-0.292301\pi$
$662$		−	8.00000i		−	0.310929i
$663$		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
$668$	−5.19615	−	9.00000i	−0.201045	−	0.348220i
$669$	−15.4019	+	8.89230i	−0.595473	+	0.343796i
$670$	3.46410	+	2.00000i	0.133830	+	0.0772667i
$671$	−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	0.479713	+	0.877425i	$0.340741\pi$
$673$	−13.4904	+	23.3660i	−0.520016	+	0.900694i	−0.999729	+	0.0232688i	$0.992593\pi$
$674$	8.66025	−	5.00000i	0.333581	−	0.192593i
$675$	−2.59808	−	4.50000i	−0.100000	−	0.173205i
$676$	0.500000	−	0.866025i	0.0192308	−	0.0333087i
$677$	−28.9808			−1.11382			−0.556911	−	0.830572i	$-0.688013\pi$
$677$	−28.9808			−1.11382			−0.556911	+	0.830572i	$0.688013\pi$
$678$	32.1962			1.23649
$679$	−40.1769	−	7.73205i	−1.54185	−	0.296729i
$680$		0			0
$681$	−7.60770			−0.291528
$682$	2.41154	−	1.39230i	0.0923427	−	0.0533141i
$683$	36.7750	+	21.2321i	1.40716	+	0.812422i	0.995113	−	0.0987426i	$-0.0314820\pi$
$683$	36.7750	+	21.2321i	1.40716	+	0.812422i	0.412043	+	0.911164i	$0.364815\pi$
$684$	12.2942	+	7.09808i	0.470082	+	0.271402i
$685$		−	10.7321i		−	0.410051i
$686$	−15.5885	−	10.0000i	−0.595170	−	0.381802i
$687$	−41.8923	+	24.1865i	−1.59829	+	0.922774i
$688$	3.59808	−	6.23205i	0.137175	−	0.237595i
$689$	37.1769			1.41633
$690$	−16.3923			−0.624044
$691$		−	18.9282i		−	0.720063i	−0.932940	−	0.360031i	$-0.882766\pi$
$691$		−	18.9282i		−	0.720063i	0.932940	−	0.360031i	$-0.117234\pi$
$692$	2.19615			0.0834852
$693$	9.88269	+	1.90192i	0.375412	+	0.0722481i
$694$	27.2487			1.03435
$695$		−	16.0526i		−	0.608908i
$696$	−0.401924	−	0.696152i	−0.0152349	−	0.0263876i
$697$		0			0
$698$	2.19615	−	3.80385i	0.0831256	−	0.143978i
$699$			8.19615i			0.310007i
$700$	−2.00000	−	1.73205i	−0.0755929	−	0.0654654i
$701$			9.67949i			0.365589i	0.983151	+	0.182795i	$0.0585144\pi$
$701$			9.67949i			0.365589i	−0.983151	+	0.182795i	$0.941486\pi$
$702$	−9.00000	−	15.5885i	−0.339683	−	0.588348i
$703$	17.1962	+	9.92820i	0.648565	+	0.374449i
$704$	−1.09808	+	0.633975i	−0.0413853	+	0.0238938i
$705$	7.79423	+	13.5000i	0.293548	+	0.508439i
$706$	−26.4904	+	15.2942i	−0.996979	+	0.575606i
$707$	1.60770	+	1.39230i	0.0604636	+	0.0523630i
$708$	−7.09808	+	12.2942i	−0.266762	+	0.462045i
$709$	−5.21539			−0.195868			−0.0979340	−	0.995193i	$-0.531223\pi$
$709$	−5.21539			−0.195868			−0.0979340	+	0.995193i	$0.531223\pi$
$710$	−0.633975	+	1.09808i	−0.0237926	+	0.0412101i
$711$	24.8827	+	43.0981i	0.933174	+	1.61630i
$712$	−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
$716$	5.70577	+	3.29423i	0.213235	+	0.123111i
$717$			36.5885i			1.36642i
$718$	−13.0981	−	22.6865i	−0.488816	−	0.846654i
$719$	20.7846	+	36.0000i	0.775135	+	1.34257i	0.934718	+	0.355389i	$0.115652\pi$
$719$	20.7846	+	36.0000i	0.775135	+	1.34257i	−0.159583	+	0.987184i	$0.551015\pi$
$720$	3.00000			0.111803
$721$	31.5000	+	6.06218i	1.17312	+	0.225767i
$722$	2.93782	+	1.69615i	0.109334	+	0.0631243i
$723$		−	35.7846i		−	1.33084i
$724$			7.39230i			0.274733i
$725$			0.464102i			0.0172363i
$726$	14.0885	−	8.13397i	0.522872	−	0.301880i
$727$	0.215390	+	0.124356i	0.00798838	+	0.00461210i	0.503989	−	0.863710i	$-0.331865\pi$
$727$	0.215390	+	0.124356i	0.00798838	+	0.00461210i	−0.496000	+	0.868322i	$0.665199\pi$
$728$	−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
$733$	−3.50962	−	2.02628i	−0.129631	−	0.0748423i	0.433782	−	0.901018i	$-0.357179\pi$
$733$	−3.50962	−	2.02628i	−0.129631	−	0.0748423i	−0.563413	+	0.826175i	$0.690512\pi$
$734$	9.40192	+	16.2846i	0.347031	+	0.601076i
$735$	−11.2583	−	4.50000i	−0.415270	−	0.165985i
$736$	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	$-0.0136419\pi$
$740$	4.19615			0.154254
$741$	−14.1962	−	24.5885i	−0.521509	−	0.903280i
$742$	−5.36603	+	27.8827i	−0.196993	+	1.02361i
$743$	38.6769	−	22.3301i	1.41892	−	0.819213i	0.422714	−	0.906263i	$-0.361077\pi$
$743$	38.6769	−	22.3301i	1.41892	−	0.819213i	0.996204	+	0.0870500i	$0.0277440\pi$
$744$	1.90192	−	3.29423i	0.0697279	−	0.120772i
$745$	10.3923	−	6.00000i	0.380745	−	0.219823i
$746$	0.169873	+	0.0980762i	0.00621949	+	0.00359083i
$747$	2.41154			0.0882337
$748$		0			0
$749$	−3.58846	+	4.14359i	−0.131119	+	0.151404i
$750$	−1.50000	−	0.866025i	−0.0547723	−	0.0316228i
$751$	21.1962	−	36.7128i	0.773459	−	1.33967i	−0.162198	−	0.986758i	$-0.551858\pi$
$751$	21.1962	−	36.7128i	0.773459	−	1.33967i	0.935657	−	0.352911i	$-0.114808\pi$
$752$	−9.00000			−0.328196
$753$	−15.5885	+	27.0000i	−0.568075	+	0.983935i
$754$			1.60770i			0.0585488i
$755$	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	$0.365356\pi$
$758$		−	30.3923i		−	1.10390i
$759$	10.3923	−	18.0000i	0.377217	−	0.653359i
$760$	4.73205			0.171650
$761$	−16.5000	+	28.5788i	−0.598125	+	1.03598i	0.394973	+	0.918693i	$0.370754\pi$
$761$	−16.5000	+	28.5788i	−0.598125	+	1.03598i	−0.993098	+	0.117289i	$0.962579\pi$
$762$	−14.0885	−	8.13397i	−0.510371	−	0.294663i
$763$	1.59808	−	8.30385i	0.0578542	−	0.300619i
$764$		−	3.46410i		−	0.125327i
$765$		0			0
$766$	−1.20577	−	0.696152i	−0.0435663	−	0.0251530i
$767$	24.5885	−	14.1962i	0.887838	−	0.512593i
$768$	−0.866025	+	1.50000i	−0.0312500	+	0.0541266i
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	−0.723255	−	0.690581i	$-0.757355\pi$
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	0.236433	+	0.971648i	$0.424022\pi$
$770$	3.16987	−	1.09808i	0.114234	−	0.0395719i
$771$	6.58846	+	11.4115i	0.237277	+	0.410977i
$772$	−24.1962			−0.870839
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$		−	21.5885i		−	0.775981i
$775$	−1.90192	+	1.09808i	−0.0683191	+	0.0394441i
$776$	7.73205	−	13.3923i	0.277564	−	0.480756i
$777$	18.1699	−	6.29423i	0.651841	−	0.225804i
$778$	15.3564	+	26.5981i	0.550554	+	0.953587i
$779$	36.8827	+	21.2942i	1.32146	+	0.762945i
$780$	−5.19615	−	3.00000i	−0.186052	−	0.107417i
$781$	−0.803848	−	1.39230i	−0.0287639	−	0.0498206i
$782$		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
$787$		−	39.2487i		−	1.39907i	−0.714601	−	0.699533i	$-0.753392\pi$
$787$		−	39.2487i		−	1.39907i	0.714601	−	0.699533i	$-0.246608\pi$
$788$			6.33975i			0.225844i
$789$			17.7846i			0.633149i
$790$	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
$794$	−0.294229	−	0.509619i	−0.0104418	−	0.0180857i
$795$			18.5885i			0.659265i
$796$	−6.00000	−	3.46410i	−0.212664	−	0.122782i
$797$	−21.5885	−	37.3923i	−0.764702	−	1.32450i	−0.940404	−	0.340060i	$-0.889553\pi$
$797$	−21.5885	−	37.3923i	−0.764702	−	1.32450i	0.175701	−	0.984444i	$-0.443781\pi$
$798$	20.4904	−	7.09808i	0.725352	−	0.251269i
$799$		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
$803$	8.78461			0.310002
$804$	−3.46410	+	6.00000i	−0.122169	+	0.211604i
$805$	−16.3923	+	18.9282i	−0.577753	+	0.667132i
$806$	−6.58846	+	3.80385i	−0.232069	+	0.133985i
$807$	−15.5885	−	27.0000i	−0.548740	−	0.950445i
$808$	−0.696152	+	0.401924i	−0.0244906	+	0.0141396i
$809$	6.48076	+	3.74167i	0.227851	+	0.131550i	0.609580	−	0.792724i	$-0.291338\pi$
$809$	6.48076	+	3.74167i	0.227851	+	0.131550i	−0.381729	+	0.924274i	$0.624671\pi$
$810$	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	$-0.359067\pi$
$812$	−1.20577	−	0.232051i	−0.0423143	−	0.00814339i
$813$			42.5885i			1.49364i
$814$	−2.66025	+	4.60770i	−0.0932419	+	0.161500i
$815$	12.3923			0.434084
$816$		0			0
$817$		−	34.0526i		−	1.19135i
$818$	34.5167			1.20685
$819$	−27.0000	−	5.19615i	−0.943456	−	0.181568i
$820$	9.00000			0.314294
$821$			18.7128i			0.653082i	0.945183	+	0.326541i	$0.105883\pi$
$821$			18.7128i			0.653082i	−0.945183	+	0.326541i	$0.894117\pi$
$822$	18.5885			0.648347
$823$	51.3923			1.79142			0.895712	−	0.444636i	$-0.146667\pi$
$823$	51.3923			1.79142			0.895712	+	0.444636i	$0.146667\pi$
$824$	−6.06218	+	10.5000i	−0.211186	+	0.365785i
$825$	1.90192	−	1.09808i	0.0662165	−	0.0382301i
$826$	7.09808	+	20.4904i	0.246974	+	0.712952i
$827$			37.6410i			1.30891i	0.756103	+	0.654453i	$0.227101\pi$
$827$			37.6410i			1.30891i	−0.756103	+	0.654453i	$0.772899\pi$
$828$		−	28.3923i		−	0.986701i
$829$	−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	$0.706256\pi$
$830$	0.696152	−	0.401924i	0.0241638	−	0.0139510i
$831$	−23.9090			−0.829393
$832$	3.00000	−	1.73205i	0.104006	−	0.0600481i
$833$		0			0
$834$	27.8038			0.962769
$835$	−10.3923			−0.359641
$836$	−3.00000	+	5.19615i	−0.103757	+	0.179713i
$837$		−	11.4115i		−	0.394441i
$838$	−9.00000	+	5.19615i	−0.310900	+	0.179498i
$839$	−7.09808	+	12.2942i	−0.245053	+	0.424444i	−0.962146	−	0.272533i	$-0.912139\pi$
$839$	−7.09808	+	12.2942i	−0.245053	+	0.424444i	0.717094	+	0.696977i	$0.245472\pi$
$840$	3.00000	−	3.46410i	0.103510	−	0.119523i
$841$	−14.3923	−	24.9282i	−0.496286	−	0.859593i
$842$	−19.0359	−	10.9904i	−0.656020	−	0.378754i
$843$	−3.99038	+	2.30385i	−0.137436	+	0.0793487i
$844$	5.29423	+	9.16987i	0.182235	+	0.315640i
$845$	−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
$849$	16.2846	+	9.40192i	0.558886	+	0.322673i
$850$		0			0
$851$		−	39.7128i		−	1.36134i
$852$	−1.90192	−	1.09808i	−0.0651588	−	0.0376195i
$853$	−38.7846	−	22.3923i	−1.32796	−	0.766698i	−0.342976	−	0.939344i	$-0.611435\pi$
$853$	−38.7846	−	22.3923i	−1.32796	−	0.766698i	−0.984984	+	0.172646i	$0.944768\pi$
$854$	−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
$857$	−24.2942	−	42.0788i	−0.829875	−	1.43739i	−0.898136	−	0.439718i	$-0.855078\pi$
$857$	−24.2942	−	42.0788i	−0.829875	−	1.43739i	0.0682607	−	0.997668i	$-0.478255\pi$
$858$	6.58846	−	3.80385i	0.224926	−	0.129861i
$859$	22.6865	+	13.0981i	0.774055	+	0.446901i	0.834319	−	0.551282i	$-0.185861\pi$
$859$	22.6865	+	13.0981i	0.774055	+	0.446901i	−0.0602645	+	0.998182i	$0.519194\pi$
$860$	−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	−0.576370	−	0.817189i	$-0.695531\pi$
$863$	−4.60770	+	2.66025i	−0.156848	+	0.0905561i	0.419522	+	0.907745i	$0.362198\pi$
$864$			5.19615i			0.176777i
$865$	1.09808	−	1.90192i	0.0373357	−	0.0646673i
$866$	−18.0000			−0.611665
$867$	−29.4449			−1.00000
$868$	−1.90192	−	5.49038i	−0.0645555	−	0.186356i
$869$	−18.2154	+	10.5167i	−0.617915	+	0.356753i
$870$	−0.803848			−0.0272530
$871$	12.0000	−	6.92820i	0.406604	−	0.234753i
$872$	2.76795	+	1.59808i	0.0937346	+	0.0541177i
$873$		−	46.3923i		−	1.57014i
$874$		−	44.7846i		−	1.51486i
$875$	−2.50000	+	0.866025i	−0.0845154	+	0.0292770i
$876$	10.3923	−	6.00000i	0.351123	−	0.202721i
$877$	20.8827	−	36.1699i	0.705158	−	1.22137i	−0.261476	−	0.965210i	$-0.584209\pi$
$877$	20.8827	−	36.1699i	0.705158	−	1.22137i	0.966634	−	0.256160i	$-0.0824574\pi$
$878$	−12.3397			−0.416446
$879$	7.60770			0.256601
$880$			1.26795i			0.0427426i
$881$	−4.39230			−0.147981			−0.0739903	−	0.997259i	$-0.523573\pi$
$881$	−4.39230			−0.147981			−0.0739903	+	0.997259i	$0.523573\pi$
$882$	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
$885$	7.09808	+	12.2942i	0.238599	+	0.413266i
$886$	9.00000			0.302361
$887$	−14.3038	+	24.7750i	−0.480276	+	0.831863i	−0.999744	−	0.0226273i	$-0.992797\pi$
$887$	−14.3038	+	24.7750i	−0.480276	+	0.831863i	0.519468	+	0.854490i	$0.326130\pi$
$888$			7.26795i			0.243896i
$889$	−23.4808	+	8.13397i	−0.787519	+	0.272805i
$890$			16.3923i			0.549471i
$891$			11.4115i			0.382301i
$892$	−8.89230	−	5.13397i	−0.297736	−	0.171898i
$893$	−36.8827	+	21.2942i	−1.23423	+	0.712584i
$894$	10.3923	+	18.0000i	0.347571	+	0.602010i
$895$	5.70577	−	3.29423i	0.190723	−	0.110114i
$896$	0.866025	+	2.50000i	0.0289319	+	0.0835191i
$897$	−28.3923	+	49.1769i	−0.947991	+	1.64197i
$898$	21.5885			0.720416
$899$	−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
$903$	−24.9282	−	21.5885i	−0.829559	−	0.718419i
$904$	9.29423	+	16.0981i	0.309121	+	0.535414i
$905$	6.40192	+	3.69615i	0.212807	+	0.122864i
$906$			10.7321i			0.356549i
$907$	−16.5981	−	28.7487i	−0.551130	−	0.954585i	−0.998193	−	0.0600830i	$-0.980863\pi$
$907$	−16.5981	−	28.7487i	−0.551130	−	0.954585i	0.447063	−	0.894502i	$-0.352470\pi$
$908$	−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	0.579001	−	0.815327i	$-0.303443\pi$
$911$	4.90192	+	2.83013i	0.162408	+	0.0937663i	−0.416593	+	0.909093i	$0.636776\pi$
$912$			8.19615i			0.271402i
$913$			1.01924i			0.0337319i
$914$		−	18.3923i		−	0.608363i
$915$	−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	$0.688830\pi$
$920$	−4.73205	−	8.19615i	−0.156011	−	0.270219i
$921$	−26.6769	−	15.4019i	−0.879034	−	0.507511i
$922$	−4.50000	−	2.59808i	−0.148200	−	0.0855631i
$923$	2.19615	+	3.80385i	0.0722872	+	0.125205i
$924$	1.90192	+	5.49038i	0.0625687	+	0.180620i
$925$	2.09808	−	3.63397i	0.0689843	−	0.119484i
$926$	−20.2583	+	11.6962i	−0.665730	+	0.384359i
$927$			36.3731i			1.19465i
$928$	0.232051	−	0.401924i	0.00761744	−	0.0131938i
$929$	32.5692			1.06856			0.534281	−	0.845307i	$-0.320583\pi$
$929$	32.5692			1.06856			0.534281	+	0.845307i	$0.320583\pi$
$930$	−1.90192	−	3.29423i	−0.0623665	−	0.108022i
$931$	12.2942	−	30.7583i	0.402927	−	1.00806i
$932$	−4.09808	+	2.36603i	−0.134237	+	0.0775017i
$933$	22.6865	−	39.2942i	0.742724	−	1.28644i
$934$	14.8923	−	8.59808i	0.487291	−	0.281338i
$935$		0			0
$936$	5.19615	−	9.00000i	0.169842	−	0.294174i
$937$			11.4115i			0.372799i	0.982474	+	0.186399i	$0.0596818\pi$
$937$			11.4115i			0.372799i	−0.982474	+	0.186399i	$0.940318\pi$
$938$	3.46410	+	10.0000i	0.113107	+	0.326512i
$939$	14.7058	+	8.49038i	0.479905	+	0.277073i
$940$	−4.50000	+	7.79423i	−0.146774	+	0.254220i
$941$	25.9808			0.846949			0.423474	−	0.905908i	$-0.360810\pi$
$941$	25.9808			0.846949			0.423474	+	0.905908i	$0.360810\pi$
$942$	0.294229	−	0.509619i	0.00958649	−	0.0166043i
$943$		−	85.1769i		−	2.77374i
$944$	−8.19615			−0.266762
$945$	2.59808	−	13.5000i	0.0845154	−	0.439155i
$946$	9.12436			0.296658
$947$		−	59.5692i		−	1.93574i	−0.251452	−	0.967870i	$-0.580908\pi$
$947$		−	59.5692i		−	1.93574i	0.251452	−	0.967870i	$-0.419092\pi$
$948$	−14.3660	+	24.8827i	−0.466587	+	0.808152i
$949$	−24.0000			−0.779073
$950$	2.36603	−	4.09808i	0.0767640	−	0.132959i
$951$	41.1962	+	23.7846i	1.33588	+	0.771269i
$952$		0			0
$953$		−	4.73205i		−	0.153286i	−0.997059	−	0.0766431i	$-0.975580\pi$
$953$		−	4.73205i		−	0.153286i	0.997059	−	0.0766431i	$-0.0244202\pi$
$954$	−32.1962			−1.04239
$955$	−3.00000	−	1.73205i	−0.0970777	−	0.0560478i
$956$	−18.2942	+	10.5622i	−0.591678	+	0.341605i
$957$	0.509619	−	0.882686i	0.0164736	−	0.0285332i
$958$	−9.00000	+	5.19615i	−0.290777	+	0.167880i
$959$	18.5885	−	21.4641i	0.600253	−	0.693112i
$960$	0.866025	+	1.50000i	0.0279508	+	0.0484123i
$961$	26.1769			0.844417
$962$	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
$966$	−32.7846	−	28.3923i	−1.05483	−	0.913507i
$967$	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	$0.750513\pi$
$968$	8.13397	+	4.69615i	0.261436	+	0.150940i
$969$		0			0
$970$	−7.73205	−	13.3923i	−0.248261	−	0.430001i
$971$	13.3923	+	23.1962i	0.429780	+	0.744400i	0.996853	−	0.0792670i	$-0.0252580\pi$
$971$	13.3923	+	23.1962i	0.429780	+	0.744400i	−0.567074	+	0.823667i	$0.691925\pi$
$972$	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
$976$		−	0.928203i		−	0.0297111i
$977$			18.9282i			0.605567i	0.953059	+	0.302783i	$0.0979159\pi$
$977$			18.9282i			0.605567i	−0.953059	+	0.302783i	$0.902084\pi$
$978$			21.4641i			0.686346i
$979$	−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
$983$	−5.30385	−	9.18653i	−0.169166	−	0.293005i	0.768961	−	0.639296i	$-0.220774\pi$
$983$	−5.30385	−	9.18653i	−0.169166	−	0.293005i	−0.938127	+	0.346291i	$0.887441\pi$
$984$			15.5885i			0.496942i
$985$	5.49038	+	3.16987i	0.174938	+	0.101001i
$986$		0			0
$987$	−7.79423	+	40.5000i	−0.248093	+	1.28913i
$988$	8.19615	−	14.1962i	0.260754	−	0.451640i
$989$	−58.9808	+	34.0526i	−1.87548	+	1.08281i
$990$	1.90192	+	3.29423i	0.0604471	+	0.104697i
$991$	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	$-0.0838256\pi$
$992$	2.19615			0.0697279
$993$	6.92820	−	12.0000i	0.219860	−	0.380808i
$994$	−3.16987	+	1.09808i	−0.100542	+	0.0348289i
$995$	−6.00000	+	3.46410i	−0.190213	+	0.109819i
$996$	0.696152	+	1.20577i	0.0220584	+	0.0382063i
$997$	−11.7058	+	6.75833i	−0.370725	+	0.214038i	−0.673775	−	0.738936i	$-0.735328\pi$
$997$	−11.7058	+	6.75833i	−0.370725	+	0.214038i	0.303050	+	0.952975i	$0.401995\pi$
$998$	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.bk.a.101.2	yes	4
3.2	odd	2		1890.2.bk.a.521.1		4
7.5	odd	6		630.2.t.a.551.2	yes	4
9.4	even	3		1890.2.t.a.1151.1		4
9.5	odd	6		630.2.t.a.311.2	✓	4
21.5	even	6		1890.2.t.a.1601.1		4
63.5	even	6	inner	630.2.bk.a.131.1	yes	4
63.40	odd	6		1890.2.bk.a.341.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.a.311.2	✓	4	9.5	odd	6
630.2.t.a.551.2	yes	4	7.5	odd	6
630.2.bk.a.101.2	yes	4	1.1	even	1	trivial
630.2.bk.a.131.1	yes	4	63.5	even	6	inner
1890.2.t.a.1151.1		4	9.4	even	3
1890.2.t.a.1601.1		4	21.5	even	6
1890.2.bk.a.341.2		4	63.40	odd	6
1890.2.bk.a.521.1		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(1.09808 - 0.633975i) q^{11} +(0.866025 - 1.50000i) q^{12} +(-3.00000 + 1.73205i) q^{13} +(-0.866025 - 2.50000i) q^{14} +(-0.866025 - 1.50000i) q^{15} +1.00000 q^{16} +(2.59808 - 1.50000i) q^{18} +(4.09808 - 2.36603i) q^{19} +(0.500000 - 0.866025i) q^{20} +(0.866025 - 4.50000i) q^{21} +(0.633975 + 1.09808i) q^{22} +(-8.19615 - 4.73205i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.73205 - 3.00000i) q^{26} +5.19615 q^{27} +(2.50000 - 0.866025i) q^{28} +(-0.401924 - 0.232051i) q^{29} +(1.50000 - 0.866025i) q^{30} -2.19615i q^{31} +1.00000i q^{32} +2.19615i q^{33} +(0.500000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{36} +(2.09808 + 3.63397i) q^{37} +(2.36603 + 4.09808i) q^{38} -6.00000i q^{39} +(0.866025 + 0.500000i) q^{40} +(4.50000 + 7.79423i) q^{41} +(4.50000 + 0.866025i) q^{42} +(3.59808 - 6.23205i) q^{43} +(-1.09808 + 0.633975i) q^{44} +3.00000 q^{45} +(4.73205 - 8.19615i) q^{46} -9.00000 q^{47} +(-0.866025 + 1.50000i) q^{48} +(5.50000 - 4.33013i) q^{49} +(0.866025 - 0.500000i) q^{50} +(3.00000 - 1.73205i) q^{52} +(-9.29423 - 5.36603i) q^{53} +5.19615i q^{54} +1.26795i q^{55} +(0.866025 + 2.50000i) q^{56} +8.19615i q^{57} +(0.232051 - 0.401924i) q^{58} -8.19615 q^{59} +(0.866025 + 1.50000i) q^{60} -0.928203i q^{61} +2.19615 q^{62} +(6.00000 + 5.19615i) q^{63} -1.00000 q^{64} -3.46410i q^{65} -2.19615 q^{66} -4.00000 q^{67} +(14.1962 - 8.19615i) q^{69} +(2.59808 + 0.500000i) q^{70} -1.26795i q^{71} +(-2.59808 + 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +(-3.63397 + 2.09808i) q^{74} +1.73205 q^{75} +(-4.09808 + 2.36603i) q^{76} +(-2.19615 + 2.53590i) q^{77} +6.00000 q^{78} -16.5885 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} +(6.23205 + 3.59808i) q^{86} +(0.696152 - 0.401924i) q^{87} +(-0.633975 - 1.09808i) q^{88} +(-8.19615 - 14.1962i) q^{89} +3.00000i q^{90} +(6.00000 - 6.92820i) q^{91} +(8.19615 + 4.73205i) q^{92} +(3.29423 + 1.90192i) q^{93} -9.00000i q^{94} +4.73205i q^{95} +(-1.50000 - 0.866025i) q^{96} +(13.3923 + 7.73205i) q^{97} +(4.33013 + 5.50000i) q^{98} +(-3.29423 - 1.90192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 2 q^{5} - 6 q^{6} - 10 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 2 * q^5 - 6 * q^6 - 10 * q^7 - 6 * q^9	\( 4 q - 4 q^{4} - 2 q^{5} - 6 q^{6} - 10 q^{7} - 6 q^{9} - 6 q^{11} - 12 q^{13} + 4 q^{16} + 6 q^{19} + 2 q^{20} + 6 q^{22} - 12 q^{23} + 6 q^{24} - 2 q^{25} + 10 q^{28} - 12 q^{29} + 6 q^{30} + 2 q^{35} + 6 q^{36} - 2 q^{37} + 6 q^{38} + 18 q^{41} + 18 q^{42} + 4 q^{43} + 6 q^{44} + 12 q^{45} + 12 q^{46} - 36 q^{47} + 22 q^{49} + 12 q^{52} - 6 q^{53} - 6 q^{58} - 12 q^{59} - 12 q^{62} + 24 q^{63} - 4 q^{64} + 12 q^{66} - 16 q^{67} + 36 q^{69} + 24 q^{73} - 18 q^{74} - 6 q^{76} + 12 q^{77} + 24 q^{78} - 4 q^{79} - 2 q^{80} - 18 q^{81} - 12 q^{83} + 18 q^{86} - 18 q^{87} - 6 q^{88} - 12 q^{89} + 24 q^{91} + 12 q^{92} - 18 q^{93} - 6 q^{96} + 12 q^{97} + 18 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 2 * q^5 - 6 * q^6 - 10 * q^7 - 6 * q^9 - 6 * q^11 - 12 * q^13 + 4 * q^16 + 6 * q^19 + 2 * q^20 + 6 * q^22 - 12 * q^23 + 6 * q^24 - 2 * q^25 + 10 * q^28 - 12 * q^29 + 6 * q^30 + 2 * q^35 + 6 * q^36 - 2 * q^37 + 6 * q^38 + 18 * q^41 + 18 * q^42 + 4 * q^43 + 6 * q^44 + 12 * q^45 + 12 * q^46 - 36 * q^47 + 22 * q^49 + 12 * q^52 - 6 * q^53 - 6 * q^58 - 12 * q^59 - 12 * q^62 + 24 * q^63 - 4 * q^64 + 12 * q^66 - 16 * q^67 + 36 * q^69 + 24 * q^73 - 18 * q^74 - 6 * q^76 + 12 * q^77 + 24 * q^78 - 4 * q^79 - 2 * q^80 - 18 * q^81 - 12 * q^83 + 18 * q^86 - 18 * q^87 - 6 * q^88 - 12 * q^89 + 24 * q^91 + 12 * q^92 - 18 * q^93 - 6 * q^96 + 12 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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