LMFDB - Embedded newform 1470.2.n.l.949.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(79,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1470.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.n (of order $6$, degree $2$, not 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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 18x^{14} + 227x^{12} - 1394x^{10} + 6177x^{8} - 14768x^{6} + 24768x^{4} - 11264x^{2} + 4096 $ x^16 - 18x^14 + 227x^12 - 1394x^10 + 6177x^8 - 14768x^6 + 24768x^4 - 11264*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			949.3
Root			$-1.46557 + 0.846149i$ of defining polynomial
Character	$\chi$	$=$	1470.949
Dual form			1470.2.n.l.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.51486 + 1.64475i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.51486 + 1.64475i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.13428 - 0.666969i) q^{10} +(1.19663 - 2.07263i) q^{11} +(0.866025 - 0.500000i) q^{12} -3.80748i q^{13} +(0.489528 + 2.18183i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.70640 - 0.985191i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(2.08557 + 3.61231i) q^{19} +(2.18183 - 0.489528i) q^{20} +2.39327i q^{22} +(7.07641 - 4.08557i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.410420 + 4.98313i) q^{25} +(1.90374 + 3.29738i) q^{26} +1.00000i q^{27} +9.16246 q^{29} +(-1.51486 - 1.64475i) q^{30} +(0.803365 - 1.39147i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.07263 - 1.19663i) q^{33} +1.97038 q^{34} +1.00000 q^{36} +(-1.09430 + 0.631792i) q^{37} +(-3.61231 - 2.08557i) q^{38} +(1.90374 - 3.29738i) q^{39} +(-1.64475 + 1.51486i) q^{40} +3.19208 q^{41} +4.90755i q^{43} +(-1.19663 - 2.07263i) q^{44} +(-0.666969 + 2.13428i) q^{45} +(-4.08557 + 7.07641i) q^{46} +(2.60559 - 1.50434i) q^{47} -1.00000i q^{48} +(-2.13613 - 4.52072i) q^{50} +(-0.985191 - 1.70640i) q^{51} +(-3.29738 - 1.90374i) q^{52} +(-10.5405 - 6.08557i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(5.22170 - 1.17157i) q^{55} +4.17113i q^{57} +(-7.93492 + 4.58123i) q^{58} +(-6.52072 + 11.2942i) q^{59} +(2.13428 + 0.666969i) q^{60} +(6.54548 + 11.3371i) q^{61} +1.60673i q^{62} -1.00000 q^{64} +(6.26237 - 5.76779i) q^{65} +(-1.19663 + 2.07263i) q^{66} +(-5.00378 - 2.88893i) q^{67} +(-1.70640 + 0.985191i) q^{68} +8.17113 q^{69} +6.94032 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-0.438784 - 0.253332i) q^{73} +(0.631792 - 1.09430i) q^{74} +(-2.84700 + 4.11030i) q^{75} +4.17113 q^{76} +3.80748i q^{78} +(-6.21302 - 10.7613i) q^{79} +(0.666969 - 2.13428i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.76442 + 1.59604i) q^{82} +1.89887i q^{83} +(-0.964557 - 4.29903i) q^{85} +(-2.45377 - 4.25006i) q^{86} +(7.93492 + 4.58123i) q^{87} +(2.07263 + 1.19663i) q^{88} +(-0.989747 - 1.71429i) q^{89} +(-0.489528 - 2.18183i) q^{90} -8.17113i q^{92} +(1.39147 - 0.803365i) q^{93} +(-1.50434 + 2.60559i) q^{94} +(-2.78202 + 8.90237i) q^{95} +(0.500000 + 0.866025i) q^{96} +12.0624i q^{97} +2.39327 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9	$ 16 q + 8 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9} - 8 q^{16} - 24 q^{19} + 8 q^{20} - 8 q^{24} - 4 q^{25} + 32 q^{29} - 4 q^{30} + 32 q^{31} + 16 q^{34} + 16 q^{36} - 48 q^{41} - 4 q^{45} - 8 q^{46} - 8 q^{50} - 8 q^{51} - 8 q^{54} - 40 q^{59} + 24 q^{61} - 16 q^{64} - 28 q^{65} + 16 q^{69} - 80 q^{71} - 16 q^{74} + 4 q^{75} - 48 q^{76} - 16 q^{79} + 4 q^{80} - 8 q^{81} + 56 q^{85} - 8 q^{86} - 88 q^{89} - 24 q^{94} - 24 q^{95} + 8 q^{96}+O(q^{100}) $ 16 * q + 8 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9 - 8 * q^16 - 24 * q^19 + 8 * q^20 - 8 * q^24 - 4 * q^25 + 32 * q^29 - 4 * q^30 + 32 * q^31 + 16 * q^34 + 16 * q^36 - 48 * q^41 - 4 * q^45 - 8 * q^46 - 8 * q^50 - 8 * q^51 - 8 * q^54 - 40 * q^59 + 24 * q^61 - 16 * q^64 - 28 * q^65 + 16 * q^69 - 80 * q^71 - 16 * q^74 + 4 * q^75 - 48 * q^76 - 16 * q^79 + 4 * q^80 - 8 * q^81 + 56 * q^85 - 8 * q^86 - 88 * q^89 - 24 * q^94 - 24 * q^95 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.51486	+	1.64475i	0.677464	+	0.735556i
$5$	1.51486	+	1.64475i	0.677464	+	0.735556i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.13428	−	0.666969i	−0.674919	−	0.210914i
$11$	1.19663	−	2.07263i	0.360799	−	0.624922i	−0.627294	−	0.778783i	$-0.715837\pi$
$11$	1.19663	−	2.07263i	0.360799	−	0.624922i	0.988093	+	0.153861i	$0.0491707\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$		−	3.80748i		−	1.05601i	−0.849243	−	0.528003i	$-0.822941\pi$
$13$		−	3.80748i		−	1.05601i	0.849243	−	0.528003i	$-0.177059\pi$
$14$		0			0
$15$	0.489528	+	2.18183i	0.126396	+	0.563345i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.70640	−	0.985191i	−0.413863	−	0.238944i	0.278585	−	0.960411i	$-0.410135\pi$
$17$	−1.70640	−	0.985191i	−0.413863	−	0.238944i	−0.692448	+	0.721468i	$0.743468\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	2.08557	+	3.61231i	0.478462	+	0.828720i	0.999695	−	0.0246940i	$-0.00786114\pi$
$19$	2.08557	+	3.61231i	0.478462	+	0.828720i	−0.521233	+	0.853414i	$0.674528\pi$
$20$	2.18183	−	0.489528i	0.487871	−	0.109462i
$21$		0			0
$22$			2.39327i			0.510247i
$23$	7.07641	−	4.08557i	1.47553	−	0.851900i	0.475914	−	0.879492i	$-0.342117\pi$
$23$	7.07641	−	4.08557i	1.47553	−	0.851900i	0.999619	+	0.0275921i	$0.00878395\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−0.410420	+	4.98313i	−0.0820839	+	0.996625i
$26$	1.90374	+	3.29738i	0.373354	+	0.646669i
$27$			1.00000i			0.192450i
$28$		0			0
$29$	9.16246			1.70143			0.850713	−	0.525631i	$-0.176171\pi$
$29$	9.16246			1.70143			0.850713	+	0.525631i	$0.176171\pi$
$30$	−1.51486	−	1.64475i	−0.276574	−	0.300289i
$31$	0.803365	−	1.39147i	0.144289	−	0.249915i	−0.784819	−	0.619725i	$-0.787244\pi$
$31$	0.803365	−	1.39147i	0.144289	−	0.249915i	0.929107	+	0.369810i	$0.120577\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	2.07263	−	1.19663i	0.360799	−	0.208307i
$34$	1.97038			0.337918
$35$		0			0
$36$	1.00000			0.166667
$37$	−1.09430	+	0.631792i	−0.179901	+	0.103866i	−0.587246	−	0.809408i	$-0.699788\pi$
$37$	−1.09430	+	0.631792i	−0.179901	+	0.103866i	0.407345	+	0.913274i	$0.366455\pi$
$38$	−3.61231	−	2.08557i	−0.585994	−	0.338324i
$39$	1.90374	−	3.29738i	0.304843	−	0.528003i
$40$	−1.64475	+	1.51486i	−0.260058	+	0.239520i
$41$	3.19208			0.498519			0.249259	−	0.968437i	$-0.419813\pi$
$41$	3.19208			0.498519			0.249259	+	0.968437i	$0.419813\pi$
$42$		0			0
$43$			4.90755i			0.748394i	0.927349	+	0.374197i	$0.122082\pi$
$43$			4.90755i			0.748394i	−0.927349	+	0.374197i	$0.877918\pi$
$44$	−1.19663	−	2.07263i	−0.180399	−	0.312461i
$45$	−0.666969	+	2.13428i	−0.0994259	+	0.318160i
$46$	−4.08557	+	7.07641i	−0.602384	+	1.04336i
$47$	2.60559	−	1.50434i	0.380064	−	0.219430i	−0.297782	−	0.954634i	$-0.596247\pi$
$47$	2.60559	−	1.50434i	0.380064	−	0.219430i	0.677846	+	0.735204i	$0.262914\pi$
$48$		−	1.00000i		−	0.144338i
$49$		0			0
$50$	−2.13613	−	4.52072i	−0.302094	−	0.639327i
$51$	−0.985191	−	1.70640i	−0.137954	−	0.238944i
$52$	−3.29738	−	1.90374i	−0.457264	−	0.264001i
$53$	−10.5405	−	6.08557i	−1.44785	−	0.835917i	−0.449497	−	0.893282i	$-0.648397\pi$
$53$	−10.5405	−	6.08557i	−1.44785	−	0.835917i	−0.998353	+	0.0573648i	$0.981730\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	5.22170	−	1.17157i	0.704093	−	0.157975i
$56$		0			0
$57$			4.17113i			0.552480i
$58$	−7.93492	+	4.58123i	−1.04191	+	0.601545i
$59$	−6.52072	+	11.2942i	−0.848926	+	1.47038i	0.0332416	+	0.999447i	$0.489417\pi$
$59$	−6.52072	+	11.2942i	−0.848926	+	1.47038i	−0.882168	+	0.470936i	$0.843916\pi$
$60$	2.13428	+	0.666969i	0.275534	+	0.0861053i
$61$	6.54548	+	11.3371i	0.838062	+	1.45157i	0.891513	+	0.452996i	$0.149645\pi$
$61$	6.54548	+	11.3371i	0.838062	+	1.45157i	−0.0534501	+	0.998571i	$0.517022\pi$
$62$			1.60673i			0.204055i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	6.26237	−	5.76779i	0.776751	−	0.715406i
$66$	−1.19663	+	2.07263i	−0.147296	+	0.255123i
$67$	−5.00378	−	2.88893i	−0.611309	−	0.352939i	0.162169	−	0.986763i	$-0.448151\pi$
$67$	−5.00378	−	2.88893i	−0.611309	−	0.352939i	−0.773477	+	0.633824i	$0.781484\pi$
$68$	−1.70640	+	0.985191i	−0.206931	+	0.119472i
$69$	8.17113			0.983689
$70$		0			0
$71$	6.94032			0.823665			0.411832	−	0.911260i	$-0.364889\pi$
$71$	6.94032			0.823665			0.411832	+	0.911260i	$0.364889\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−0.438784	−	0.253332i	−0.0513557	−	0.0296503i	0.474102	−	0.880470i	$-0.342773\pi$
$73$	−0.438784	−	0.253332i	−0.0513557	−	0.0296503i	−0.525458	+	0.850820i	$0.676106\pi$
$74$	0.631792	−	1.09430i	0.0734444	−	0.127209i
$75$	−2.84700	+	4.11030i	−0.328743	+	0.474617i
$76$	4.17113			0.478462
$77$		0			0
$78$			3.80748i			0.431113i
$79$	−6.21302	−	10.7613i	−0.699020	−	1.21074i	−0.968807	−	0.247817i	$-0.920287\pi$
$79$	−6.21302	−	10.7613i	−0.699020	−	1.21074i	0.269787	−	0.962920i	$-0.413047\pi$
$80$	0.666969	−	2.13428i	0.0745694	−	0.238620i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.76442	+	1.59604i	−0.305279	+	0.176253i
$83$			1.89887i			0.208429i	0.994555	+	0.104214i	$0.0332328\pi$
$83$			1.89887i			0.208429i	−0.994555	+	0.104214i	$0.966767\pi$
$84$		0			0
$85$	−0.964557	−	4.29903i	−0.104621	−	0.466295i
$86$	−2.45377	−	4.25006i	−0.264597	−	0.458296i
$87$	7.93492	+	4.58123i	0.850713	+	0.491159i
$88$	2.07263	+	1.19663i	0.220943	+	0.127562i
$89$	−0.989747	−	1.71429i	−0.104913	−	0.181715i	0.808790	−	0.588098i	$-0.200123\pi$
$89$	−0.989747	−	1.71429i	−0.104913	−	0.181715i	−0.913703	+	0.406383i	$0.866790\pi$
$90$	−0.489528	−	2.18183i	−0.0516008	−	0.229985i
$91$		0			0
$92$		−	8.17113i		−	0.851900i
$93$	1.39147	−	0.803365i	0.144289	−	0.0833051i
$94$	−1.50434	+	2.60559i	−0.155161	+	0.268746i
$95$	−2.78202	+	8.90237i	−0.285429	+	0.913364i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$			12.0624i			1.22475i	0.790567	+	0.612375i	$0.209786\pi$
$97$			12.0624i			1.22475i	−0.790567	+	0.612375i	$0.790214\pi$
$98$		0			0
$99$	2.39327			0.240533
$100$	4.11030	+	2.84700i	0.411030	+	0.284700i
$101$	3.93336	−	6.81278i	0.391384	−	0.677897i	−0.601248	−	0.799062i	$-0.705330\pi$
$101$	3.93336	−	6.81278i	0.391384	−	0.677897i	0.992632	+	0.121165i	$0.0386631\pi$
$102$	1.70640	+	0.985191i	0.168959	+	0.0975484i
$103$	−5.10858	+	2.94944i	−0.503363	+	0.290617i	−0.730101	−	0.683339i	$-0.760527\pi$
$103$	−5.10858	+	2.94944i	−0.503363	+	0.290617i	0.226738	+	0.973956i	$0.427194\pi$
$104$	3.80748			0.373354
$105$		0			0
$106$	12.1711			1.18217
$107$	−3.25451	+	1.87899i	−0.314625	+	0.181649i	−0.648994	−	0.760793i	$-0.724810\pi$
$107$	−3.25451	+	1.87899i	−0.314625	+	0.181649i	0.334369	+	0.942442i	$0.391477\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	3.57129	−	6.18565i	0.342067	−	0.592478i	−0.642749	−	0.766077i	$-0.722206\pi$
$109$	3.57129	−	6.18565i	0.342067	−	0.592478i	0.984816	+	0.173599i	$0.0555396\pi$
$110$	−3.93634	+	3.62546i	−0.375315	+	0.345674i
$111$	−1.26358			−0.119934
$112$		0			0
$113$		−	17.3837i		−	1.63532i	−0.575700	−	0.817661i	$-0.695270\pi$
$113$		−	17.3837i		−	1.63532i	0.575700	−	0.817661i	$-0.304730\pi$
$114$	−2.08557	−	3.61231i	−0.195331	−	0.338324i
$115$	17.4395	+	5.44989i	1.62624	+	0.508205i
$116$	4.58123	−	7.93492i	0.425356	−	0.736739i
$117$	3.29738	−	1.90374i	0.304843	−	0.176001i
$118$		−	13.0414i		−	1.20056i
$119$		0			0
$120$	−2.18183	+	0.489528i	−0.199173	+	0.0446876i
$121$	2.63613	+	4.56591i	0.239648	+	0.415083i
$122$	−11.3371	−	6.54548i	−1.02641	−	0.592600i
$123$	2.76442	+	1.59604i	0.249259	+	0.143910i
$124$	−0.803365	−	1.39147i	−0.0721443	−	0.124958i
$125$	−8.81774	+	6.87368i	−0.788682	+	0.614801i
$126$		0			0
$127$			18.4434i			1.63659i	0.574801	+	0.818293i	$0.305079\pi$
$127$			18.4434i			1.63659i	−0.574801	+	0.818293i	$0.694921\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.45377	+	4.25006i	−0.216043	+	0.374197i
$130$	−2.53947	+	8.12624i	−0.222727	+	0.712718i
$131$	0.307703	+	0.532957i	0.0268841	+	0.0465646i	0.879154	−	0.476537i	$-0.158108\pi$
$131$	0.307703	+	0.532957i	0.0268841	+	0.0465646i	−0.852270	+	0.523102i	$0.824775\pi$
$132$		−	2.39327i		−	0.208307i
$133$		0			0
$134$	5.77786			0.499131
$135$	−1.64475	+	1.51486i	−0.141558	+	0.130378i
$136$	0.985191	−	1.70640i	0.0844794	−	0.146323i
$137$	−6.77924	−	3.91399i	−0.579189	−	0.334395i	0.181622	−	0.983368i	$-0.441865\pi$
$137$	−6.77924	−	3.91399i	−0.579189	−	0.334395i	−0.760811	+	0.648973i	$0.775199\pi$
$138$	−7.07641	+	4.08557i	−0.602384	+	0.347787i
$139$	−6.15378			−0.521957			−0.260979	−	0.965345i	$-0.584045\pi$
$139$	−6.15378			−0.521957			−0.260979	+	0.965345i	$0.584045\pi$
$140$		0			0
$141$	3.00868			0.253376
$142$	−6.01050	+	3.47016i	−0.504390	+	0.291210i
$143$	−7.89151	−	4.55617i	−0.659922	−	0.381006i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	13.8798	+	15.0700i	1.15266	+	1.25149i
$146$	0.506664			0.0419318
$147$		0			0
$148$			1.26358i			0.103866i
$149$	−3.76792	−	6.52623i	−0.308680	−	0.534650i	0.669394	−	0.742908i	$-0.266554\pi$
$149$	−3.76792	−	6.52623i	−0.308680	−	0.534650i	−0.978074	+	0.208258i	$0.933221\pi$
$150$	0.410420	−	4.98313i	0.0335106	−	0.406871i
$151$	−4.52072	+	7.83012i	−0.367891	+	0.637206i	−0.989236	−	0.146331i	$-0.953253\pi$
$151$	−4.52072	+	7.83012i	−0.367891	+	0.637206i	0.621344	+	0.783538i	$0.286587\pi$
$152$	−3.61231	+	2.08557i	−0.292997	+	0.169162i
$153$		−	1.97038i		−	0.159296i
$154$		0			0
$155$	3.50560	−	0.786540i	0.281577	−	0.0631764i
$156$	−1.90374	−	3.29738i	−0.152421	−	0.264001i
$157$	19.6276	+	11.3320i	1.56646	+	0.904393i	0.996577	+	0.0826638i	$0.0263428\pi$
$157$	19.6276	+	11.3320i	1.56646	+	0.904393i	0.569878	+	0.821730i	$0.306991\pi$
$158$	10.7613	+	6.21302i	0.856121	+	0.494281i
$159$	−6.08557	−	10.5405i	−0.482617	−	0.835917i
$160$	0.489528	+	2.18183i	0.0387006	+	0.172488i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	8.83684	−	5.10195i	0.692155	−	0.399616i	−0.112264	−	0.993678i	$-0.535810\pi$
$163$	8.83684	−	5.10195i	0.692155	−	0.399616i	0.804419	+	0.594063i	$0.202477\pi$
$164$	1.59604	−	2.76442i	0.124630	−	0.215865i
$165$	5.10791	+	1.59624i	0.397650	+	0.124267i
$166$	−0.949437	−	1.64447i	−0.0736906	−	0.127636i
$167$			25.2498i			1.95389i	0.213492	+	0.976945i	$0.431516\pi$
$167$			25.2498i			1.95389i	−0.213492	+	0.976945i	$0.568484\pi$
$168$		0			0
$169$	−1.49693			−0.115148
$170$	2.98484	+	3.24079i	0.228927	+	0.248557i
$171$	−2.08557	+	3.61231i	−0.159487	+	0.276240i
$172$	4.25006	+	2.45377i	0.324064	+	0.187099i
$173$	10.8554	−	6.26739i	0.825324	−	0.476501i	−0.0269250	−	0.999637i	$-0.508572\pi$
$173$	10.8554	−	6.26739i	0.825324	−	0.476501i	0.852249	+	0.523136i	$0.175238\pi$
$174$	−9.16246			−0.694604
$175$		0			0
$176$	−2.39327			−0.180399
$177$	−11.2942	+	6.52072i	−0.848926	+	0.490128i
$178$	1.71429	+	0.989747i	0.128492	+	0.0741847i
$179$	11.4598	−	19.8489i	0.856544	−	1.48358i	−0.0186608	−	0.999826i	$-0.505940\pi$
$179$	11.4598	−	19.8489i	0.856544	−	1.48358i	0.875205	−	0.483752i	$-0.160726\pi$
$180$	1.51486	+	1.64475i	0.112911	+	0.122593i
$181$	−19.6181			−1.45820			−0.729102	−	0.684405i	$-0.760062\pi$
$181$	−19.6181			−1.45820			−0.729102	+	0.684405i	$0.760062\pi$
$182$		0			0
$183$			13.0910i			0.967711i
$184$	4.08557	+	7.07641i	0.301192	+	0.521680i
$185$	−2.69684	−	0.842772i	−0.198276	−	0.0619618i
$186$	−0.803365	+	1.39147i	−0.0589056	+	0.102027i
$187$	−4.08388	+	2.35783i	−0.298643	+	0.172421i
$188$		−	3.00868i		−	0.219430i
$189$		0			0
$190$	−2.04189	−	9.10069i	−0.148134	−	0.660233i
$191$	9.86343	+	17.0840i	0.713693	+	1.23615i	0.963462	+	0.267847i	$0.0863121\pi$
$191$	9.86343	+	17.0840i	0.713693	+	1.23615i	−0.249769	+	0.968306i	$0.580355\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	4.14526	+	2.39327i	0.298383	+	0.172271i	0.641716	−	0.766942i	$-0.278223\pi$
$193$	4.14526	+	2.39327i	0.298383	+	0.172271i	−0.343333	+	0.939214i	$0.611556\pi$
$194$	−6.03120	−	10.4463i	−0.433015	−	0.750003i
$195$	8.30726	−	1.86387i	0.594896	−	0.133475i
$196$		0			0
$197$		−	17.1997i		−	1.22543i	−0.790305	−	0.612714i	$-0.790078\pi$
$197$		−	17.1997i		−	1.22543i	0.790305	−	0.612714i	$-0.209922\pi$
$198$	−2.07263	+	1.19663i	−0.147296	+	0.0850411i
$199$	−7.75280	+	13.4282i	−0.549582	+	0.951903i	0.448722	+	0.893672i	$0.351880\pi$
$199$	−7.75280	+	13.4282i	−0.549582	+	0.951903i	−0.998303	+	0.0582316i	$0.981454\pi$
$200$	−4.98313	−	0.410420i	−0.352360	−	0.0290210i
$201$	−2.88893	−	5.00378i	−0.203770	−	0.352939i
$202$			7.86672i			0.553501i
$203$		0			0
$204$	−1.97038			−0.137954
$205$	4.83554	+	5.25018i	0.337729	+	0.366688i
$206$	2.94944	−	5.10858i	0.205497	−	0.355931i
$207$	7.07641	+	4.08557i	0.491844	+	0.283967i
$208$	−3.29738	+	1.90374i	−0.228632	+	0.132001i
$209$	9.98265			0.690514
$210$		0			0
$211$	−23.8980			−1.64521			−0.822603	−	0.568616i	$-0.807479\pi$
$211$	−23.8980			−1.64521			−0.822603	+	0.568616i	$0.807479\pi$
$212$	−10.5405	+	6.08557i	−0.723925	+	0.417958i
$213$	6.01050	+	3.47016i	0.411832	+	0.237772i
$214$	1.87899	−	3.25451i	0.128445	−	0.222473i
$215$	−8.07170	+	7.43423i	−0.550486	+	0.507011i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$			7.14257i			0.483756i
$219$	−0.253332	−	0.438784i	−0.0171186	−	0.0296503i
$220$	1.59624	−	5.10791i	0.107618	−	0.344375i
$221$	−3.75110	+	6.49709i	−0.252326	+	0.437042i
$222$	1.09430	−	0.631792i	0.0734444	−	0.0424031i
$223$		−	0.870315i		−	0.0582806i	−0.999575	−	0.0291403i	$-0.990723\pi$
$223$		−	0.870315i		−	0.0582806i	0.999575	−	0.0291403i	$-0.00927696\pi$
$224$		0			0
$225$	−4.52072	+	2.13613i	−0.301382	+	0.142409i
$226$	8.69186	+	15.0547i	0.578174	+	1.00143i
$227$	−12.7179	−	7.34271i	−0.844119	−	0.487353i	0.0145429	−	0.999894i	$-0.495371\pi$
$227$	−12.7179	−	7.34271i	−0.844119	−	0.487353i	−0.858662	+	0.512542i	$0.828704\pi$
$228$	3.61231	+	2.08557i	0.239231	+	0.138120i
$229$	−12.0189	−	20.8174i	−0.794233	−	1.37565i	−0.923325	−	0.384019i	$-0.874540\pi$
$229$	−12.0189	−	20.8174i	−0.794233	−	1.37565i	0.129092	−	0.991633i	$-0.458794\pi$
$230$	−17.8280	+	4.00000i	−1.17554	+	0.263752i
$231$		0			0
$232$			9.16246i			0.601545i
$233$	9.13182	−	5.27226i	0.598246	−	0.345397i	−0.170106	−	0.985426i	$-0.554411\pi$
$233$	9.13182	−	5.27226i	0.598246	−	0.345397i	0.768351	+	0.640029i	$0.221078\pi$
$234$	−1.90374	+	3.29738i	−0.124451	+	0.215556i
$235$	6.42136	+	2.00669i	0.418883	+	0.130902i
$236$	6.52072	+	11.2942i	0.424463	+	0.735191i
$237$		−	12.4260i		−	0.807158i
$238$		0			0
$239$	4.01289			0.259572			0.129786	−	0.991542i	$-0.458571\pi$
$239$	4.01289			0.259572			0.129786	+	0.991542i	$0.458571\pi$
$240$	1.64475	−	1.51486i	0.106168	−	0.0977836i
$241$	0.271949	−	0.471030i	0.0175178	−	0.0303417i	−0.857134	−	0.515094i	$-0.827757\pi$
$241$	0.271949	−	0.471030i	0.0175178	−	0.0303417i	0.874651	+	0.484752i	$0.161090\pi$
$242$	−4.56591	−	2.63613i	−0.293508	−	0.169457i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	13.0910			0.838062
$245$		0			0
$246$	−3.19208			−0.203519
$247$	13.7538	−	7.94076i	0.875134	−	0.505259i
$248$	1.39147	+	0.803365i	0.0883584	+	0.0510137i
$249$	−0.949437	+	1.64447i	−0.0601681	+	0.104214i
$250$	4.19954	−	10.3617i	0.265602	−	0.655328i
$251$	4.62829			0.292135			0.146068	−	0.989275i	$-0.453338\pi$
$251$	4.62829			0.292135			0.146068	+	0.989275i	$0.453338\pi$
$252$		0			0
$253$		−	19.5557i		−	1.22946i
$254$	−9.22170	−	15.9724i	−0.578621	−	1.00220i
$255$	1.31418	−	4.20535i	0.0822973	−	0.263349i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	22.1418	−	12.7836i	1.38117	−	0.797417i	0.388868	−	0.921293i	$-0.372866\pi$
$257$	22.1418	−	12.7836i	1.38117	−	0.797417i	0.992298	+	0.123877i	$0.0395327\pi$
$258$		−	4.90755i		−	0.305531i
$259$		0			0
$260$	−1.86387	−	8.30726i	−0.115592	−	0.515195i
$261$	4.58123	+	7.93492i	0.283571	+	0.491159i
$262$	−0.532957	−	0.307703i	−0.0329262	−	0.0190099i
$263$	−17.8377	−	10.2986i	−1.09992	−	0.635038i	−0.163719	−	0.986507i	$-0.552349\pi$
$263$	−17.8377	−	10.2986i	−1.09992	−	0.635038i	−0.936200	+	0.351469i	$0.885682\pi$
$264$	1.19663	+	2.07263i	0.0736478	+	0.127562i
$265$	−5.95811	−	26.5553i	−0.366004	−	1.63128i
$266$		0			0
$267$		−	1.97949i		−	0.121143i
$268$	−5.00378	+	2.88893i	−0.305654	+	0.176470i
$269$	1.11899	−	1.93815i	0.0682263	−	0.118171i	−0.829894	−	0.557921i	$-0.811599\pi$
$269$	1.11899	−	1.93815i	0.0682263	−	0.118171i	0.898121	+	0.439749i	$0.144933\pi$
$270$	0.666969	−	2.13428i	0.0405904	−	0.129888i
$271$	−9.58079	−	16.5944i	−0.581992	−	1.00804i	−0.995243	−	0.0974221i	$-0.968940\pi$
$271$	−9.58079	−	16.5944i	−0.581992	−	1.00804i	0.413252	−	0.910617i	$-0.364393\pi$
$272$			1.97038i			0.119472i
$273$		0			0
$274$	7.82799			0.472906
$275$	9.83707	+	6.81363i	0.593198	+	0.410878i
$276$	4.08557	−	7.07641i	0.245922	−	0.425950i
$277$	3.18415	+	1.83837i	0.191317	+	0.110457i	0.592599	−	0.805498i	$-0.298102\pi$
$277$	3.18415	+	1.83837i	0.191317	+	0.110457i	−0.401282	+	0.915955i	$0.631435\pi$
$278$	5.32933	−	3.07689i	0.319632	−	0.184540i
$279$	1.60673			0.0961924
$280$		0			0
$281$	−29.8280			−1.77939			−0.889694	−	0.456557i	$-0.849083\pi$
$281$	−29.8280			−1.77939			−0.889694	+	0.456557i	$0.849083\pi$
$282$	−2.60559	+	1.50434i	−0.155161	+	0.0895820i
$283$	−3.71491	−	2.14481i	−0.220829	−	0.127495i	0.385505	−	0.922706i	$-0.374027\pi$
$283$	−3.71491	−	2.14481i	−0.220829	−	0.127495i	−0.606334	+	0.795210i	$0.707360\pi$
$284$	3.47016	−	6.01050i	0.205916	−	0.356657i
$285$	−6.86048	+	6.31867i	−0.406380	+	0.374286i
$286$	9.11233			0.538824
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	−6.55880	−	11.3602i	−0.385812	−	0.668246i
$290$	−19.5553	−	6.11108i	−1.14832	−	0.358855i
$291$	−6.03120	+	10.4463i	−0.353555	+	0.612375i
$292$	−0.438784	+	0.253332i	−0.0256779	+	0.0148251i
$293$			24.5940i			1.43680i	0.695631	+	0.718399i	$0.255125\pi$
$293$			24.5940i			1.43680i	−0.695631	+	0.718399i	$0.744875\pi$
$294$		0			0
$295$	−28.4542	+	6.38416i	−1.65667	+	0.371700i
$296$	−0.631792	−	1.09430i	−0.0367222	−	0.0636047i
$297$	2.07263	+	1.19663i	0.120266	+	0.0694358i
$298$	6.52623	+	3.76792i	0.378054	+	0.218270i
$299$	−15.5557	−	26.9433i	−0.899611	−	1.55817i
$300$	2.13613	+	4.52072i	0.123330	+	0.261004i
$301$		0			0
$302$		−	9.04145i		−	0.520277i
$303$	6.81278	−	3.93336i	0.391384	−	0.225966i
$304$	2.08557	−	3.61231i	0.119615	−	0.207180i
$305$	−8.73126	+	27.9398i	−0.499950	+	1.59983i
$306$	0.985191	+	1.70640i	0.0563196	+	0.0975484i
$307$		−	2.14089i		−	0.122187i	−0.998132	−	0.0610937i	$-0.980541\pi$
$307$		−	2.14089i		−	0.122187i	0.998132	−	0.0610937i	$-0.0194588\pi$
$308$		0			0
$309$	−5.89887			−0.335575
$310$	−2.64267	+	2.43397i	−0.150094	+	0.138240i
$311$	6.99956	−	12.1236i	0.396909	−	0.687466i	−0.596434	−	0.802662i	$-0.703416\pi$
$311$	6.99956	−	12.1236i	0.396909	−	0.687466i	0.993343	+	0.115196i	$0.0367496\pi$
$312$	3.29738	+	1.90374i	0.186677	+	0.107778i
$313$	28.6418	−	16.5364i	1.61893	−	0.934690i	0.631734	−	0.775185i	$-0.282343\pi$
$313$	28.6418	−	16.5364i	1.61893	−	0.934690i	0.987197	−	0.159506i	$-0.0509900\pi$
$314$	−22.6640			−1.27901
$315$		0			0
$316$	−12.4260			−0.699020
$317$	−6.39525	+	3.69230i	−0.359193	+	0.207380i	−0.668727	−	0.743508i	$-0.733160\pi$
$317$	−6.39525	+	3.69230i	−0.359193	+	0.207380i	0.309534	+	0.950888i	$0.399827\pi$
$318$	10.5405	+	6.08557i	0.591083	+	0.341262i
$319$	10.9641	−	18.9904i	0.613873	−	1.06326i
$320$	−1.51486	−	1.64475i	−0.0846831	−	0.0919444i
$321$	−3.75798			−0.209750
$322$		0			0
$323$		−	8.21872i		−	0.457302i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	18.9732	+	1.56267i	1.05244	+	0.0866811i
$326$	−5.10195	+	8.83684i	−0.282571	+	0.489427i
$327$	6.18565	−	3.57129i	0.342067	−	0.197493i
$328$			3.19208i			0.176253i
$329$		0			0
$330$	−5.22170	+	1.17157i	−0.287445	+	0.0644930i
$331$	−10.7774	−	18.6670i	−0.592381	−	1.02603i	−0.993911	−	0.110188i	$-0.964855\pi$
$331$	−10.7774	−	18.6670i	−0.592381	−	1.02603i	0.401530	−	0.915846i	$-0.368479\pi$
$332$	1.64447	+	0.949437i	0.0902522	+	0.0521071i
$333$	−1.09430	−	0.631792i	−0.0599671	−	0.0346220i
$334$	−12.6249	−	21.8670i	−0.690804	−	1.19651i
$335$	−2.82843	−	12.6063i	−0.154533	−	0.688755i
$336$		0			0
$337$			22.2549i			1.21230i	0.795350	+	0.606151i	$0.207287\pi$
$337$			22.2549i			1.21230i	−0.795350	+	0.606151i	$0.792713\pi$
$338$	1.29638	−	0.748465i	0.0705137	−	0.0407111i
$339$	8.69186	−	15.0547i	0.472077	−	0.817661i
$340$	−4.20535	−	1.31418i	−0.228067	−	0.0712716i
$341$	−1.92267	−	3.33016i	−0.104118	−	0.180338i
$342$		−	4.17113i		−	0.225549i
$343$		0			0
$344$	−4.90755			−0.264597
$345$	12.3781	+	13.4395i	0.666414	+	0.723558i
$346$	−6.26739	+	10.8554i	−0.336937	+	0.583592i
$347$	−1.85407	−	1.07045i	−0.0995317	−	0.0574646i	0.449408	−	0.893327i	$-0.351635\pi$
$347$	−1.85407	−	1.07045i	−0.0995317	−	0.0574646i	−0.548940	+	0.835862i	$0.684968\pi$
$348$	7.93492	−	4.58123i	0.425356	−	0.245580i
$349$	−0.906929			−0.0485468			−0.0242734	−	0.999705i	$-0.507727\pi$
$349$	−0.906929			−0.0485468			−0.0242734	+	0.999705i	$0.507727\pi$
$350$		0			0
$351$	3.80748			0.203228
$352$	2.07263	−	1.19663i	0.110472	−	0.0637809i
$353$	−12.0262	−	6.94330i	−0.640088	−	0.369555i	0.144561	−	0.989496i	$-0.453823\pi$
$353$	−12.0262	−	6.94330i	−0.640088	−	0.369555i	−0.784648	+	0.619941i	$0.787156\pi$
$354$	6.52072	−	11.2942i	0.346573	−	0.600281i
$355$	10.5136	+	11.4151i	0.558004	+	0.605851i
$356$	−1.97949			−0.104913
$357$		0			0
$358$			22.9196i			1.21134i
$359$	9.42827	+	16.3302i	0.497605	+	0.861878i	0.999996	−	0.00276298i	$-0.000879485\pi$
$359$	9.42827	+	16.3302i	0.497605	+	0.861878i	−0.502391	+	0.864641i	$0.667546\pi$
$360$	−2.13428	−	0.666969i	−0.112486	−	0.0351523i
$361$	0.800820	−	1.38706i	0.0421484	−	0.0730032i
$362$	16.9898	−	9.80906i	0.892964	−	0.515553i
$363$			5.27226i			0.276722i
$364$		0			0
$365$	−0.248026	−	1.10545i	−0.0129823	−	0.0578620i
$366$	−6.54548	−	11.3371i	−0.342138	−	0.592600i
$367$	−27.3423	−	15.7861i	−1.42726	−	0.824028i	−0.430354	−	0.902660i	$-0.641611\pi$
$367$	−27.3423	−	15.7861i	−1.42726	−	0.824028i	−0.996904	+	0.0786323i	$0.974945\pi$
$368$	−7.07641	−	4.08557i	−0.368883	−	0.212975i
$369$	1.59604	+	2.76442i	0.0830865	+	0.143910i
$370$	2.75692	−	0.618560i	0.143325	−	0.0321574i
$371$		0			0
$372$		−	1.60673i		−	0.0833051i
$373$	−18.1065	+	10.4538i	−0.937517	+	0.541276i	−0.889181	−	0.457555i	$-0.848725\pi$
$373$	−18.1065	+	10.4538i	−0.937517	+	0.541276i	−0.0483362	+	0.998831i	$0.515392\pi$
$374$	2.35783	−	4.08388i	0.121920	−	0.211172i
$375$	−11.0732	+	1.54392i	−0.571819	+	0.0797275i
$376$	1.50434	+	2.60559i	0.0775803	+	0.134373i
$377$		−	34.8859i		−	1.79672i
$378$		0			0
$379$	9.82440			0.504646			0.252323	−	0.967643i	$-0.418805\pi$
$379$	9.82440			0.504646			0.252323	+	0.967643i	$0.418805\pi$
$380$	6.31867	+	6.86048i	0.324141	+	0.351935i
$381$	−9.22170	+	15.9724i	−0.472442	+	0.818293i
$382$	−17.0840	−	9.86343i	−0.874092	−	0.504657i
$383$	−26.5564	+	15.3323i	−1.35697	+	0.783445i	−0.989214	−	0.146478i	$-0.953206\pi$
$383$	−26.5564	+	15.3323i	−1.35697	+	0.783445i	−0.367753	+	0.929923i	$0.619873\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−4.78654			−0.243628
$387$	−4.25006	+	2.45377i	−0.216043	+	0.124732i
$388$	10.4463	+	6.03120i	0.530332	+	0.306188i
$389$	11.7238	−	20.3062i	0.594420	−	1.02957i	−0.399208	−	0.916860i	$-0.630715\pi$
$389$	11.7238	−	20.3062i	0.594420	−	1.02957i	0.993628	−	0.112706i	$-0.0359518\pi$
$390$	−6.26237	+	5.76779i	−0.317107	+	0.292063i
$391$	−16.1002			−0.814225
$392$		0			0
$393$			0.615405i			0.0310431i
$394$	8.59985	+	14.8954i	0.433254	+	0.750418i
$395$	8.28778	−	26.5207i	0.417004	−	1.33440i
$396$	1.19663	−	2.07263i	0.0601332	−	0.104154i
$397$	−30.6366	+	17.6881i	−1.53761	+	0.887738i	−0.538629	+	0.842543i	$0.681057\pi$
$397$	−30.6366	+	17.6881i	−1.53761	+	0.887738i	−0.998978	+	0.0451946i	$0.985609\pi$
$398$		−	15.5056i		−	0.777226i
$399$		0			0
$400$	4.52072	−	2.13613i	0.226036	−	0.106806i
$401$	4.52072	+	7.83012i	0.225754	+	0.391018i	0.956545	−	0.291583i	$-0.0941820\pi$
$401$	4.52072	+	7.83012i	0.225754	+	0.391018i	−0.730791	+	0.682601i	$0.760849\pi$
$402$	5.00378	+	2.88893i	0.249566	+	0.144087i
$403$	−5.29800	−	3.05880i	−0.263912	−	0.152370i
$404$	−3.93336	−	6.81278i	−0.195692	−	0.338948i
$405$	−2.18183	+	0.489528i	−0.108416	+	0.0243248i
$406$		0			0
$407$			3.02410i			0.149899i
$408$	1.70640	−	0.985191i	0.0844794	−	0.0487742i
$409$	7.71894	−	13.3696i	0.381677	−	0.661084i	−0.609625	−	0.792690i	$-0.708680\pi$
$409$	7.71894	−	13.3696i	0.381677	−	0.661084i	0.991302	+	0.131606i	$0.0420134\pi$
$410$	−6.81279	−	2.12902i	−0.336460	−	0.105145i
$411$	−3.91399	−	6.77924i	−0.193063	−	0.334395i
$412$			5.89887i			0.290617i
$413$		0			0
$414$	−8.17113			−0.401589
$415$	−3.12318	+	2.87652i	−0.153311	+	0.141203i
$416$	1.90374	−	3.29738i	0.0933386	−	0.161667i
$417$	−5.32933	−	3.07689i	−0.260979	−	0.150676i
$418$	−8.64523	+	4.99132i	−0.422852	+	0.244134i
$419$	−26.6274			−1.30083			−0.650417	−	0.759577i	$-0.725406\pi$
$419$	−26.6274			−1.30083			−0.650417	+	0.759577i	$0.725406\pi$
$420$		0			0
$421$	5.04591			0.245923			0.122961	−	0.992411i	$-0.460761\pi$
$421$	5.04591			0.245923			0.122961	+	0.992411i	$0.460761\pi$
$422$	20.6963	−	11.9490i	1.00748	−	0.581668i
$423$	2.60559	+	1.50434i	0.126688	+	0.0731434i
$424$	6.08557	−	10.5405i	0.295541	−	0.511892i
$425$	5.60967	−	8.09887i	0.272109	−	0.392853i
$426$	−6.94032			−0.336260
$427$		0			0
$428$			3.75798i			0.181649i
$429$	−4.55617	−	7.89151i	−0.219974	−	0.381006i
$430$	3.27318	−	10.4741i	0.157847	−	0.505105i
$431$	12.6417	−	21.8961i	0.608931	−	1.05470i	−0.382486	−	0.923961i	$-0.624932\pi$
$431$	12.6417	−	21.8961i	0.608931	−	1.05470i	0.991417	−	0.130738i	$-0.0417347\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$		−	27.0063i		−	1.29784i	−0.760857	−	0.648920i	$-0.775221\pi$
$433$		−	27.0063i		−	1.29784i	0.760857	−	0.648920i	$-0.224779\pi$
$434$		0			0
$435$	4.48528	+	19.9909i	0.215053	+	0.958490i
$436$	−3.57129	−	6.18565i	−0.171034	−	0.296239i
$437$	29.5167	+	17.0414i	1.41197	+	0.815203i
$438$	0.438784	+	0.253332i	0.0209659	+	0.0121047i
$439$	−13.9658	−	24.1895i	−0.666552	−	1.15450i	−0.978862	−	0.204522i	$-0.934436\pi$
$439$	−13.9658	−	24.1895i	−0.666552	−	1.15450i	0.312309	−	0.949980i	$-0.398897\pi$
$440$	1.17157	+	5.22170i	0.0558525	+	0.248935i
$441$		0			0
$442$		−	7.50219i		−	0.356843i
$443$	9.32639	−	5.38459i	0.443110	−	0.255830i	−0.261806	−	0.965121i	$-0.584318\pi$
$443$	9.32639	−	5.38459i	0.443110	−	0.255830i	0.704916	+	0.709291i	$0.250985\pi$
$444$	−0.631792	+	1.09430i	−0.0299835	+	0.0519330i
$445$	1.32026	−	4.22480i	0.0625864	−	0.200275i
$446$	0.435157	+	0.753715i	0.0206053	+	0.0356894i
$447$		−	7.53584i		−	0.356433i
$448$		0			0
$449$	15.1288			0.713973			0.356986	−	0.934110i	$-0.383804\pi$
$449$	15.1288			0.713973			0.356986	+	0.934110i	$0.383804\pi$
$450$	2.84700	−	4.11030i	0.134209	−	0.193762i
$451$	3.81975	−	6.61600i	0.179865	−	0.311535i
$452$	−15.0547	−	8.69186i	−0.708115	−	0.408831i
$453$	−7.83012	+	4.52072i	−0.367891	+	0.212402i
$454$	14.6854			0.689221
$455$		0			0
$456$	−4.17113			−0.195331
$457$	−18.5945	+	10.7355i	−0.869814	+	0.502187i	−0.867286	−	0.497810i	$-0.834138\pi$
$457$	−18.5945	+	10.7355i	−0.869814	+	0.502187i	−0.00252752	+	0.999997i	$0.500805\pi$
$458$	20.8174	+	12.0189i	0.972733	+	0.561608i
$459$	0.985191	−	1.70640i	0.0459848	−	0.0796479i
$460$	13.4395	−	12.3781i	0.626619	−	0.577132i
$461$	30.4465			1.41804			0.709019	−	0.705190i	$-0.249138\pi$
$461$	30.4465			1.41804			0.709019	+	0.705190i	$0.249138\pi$
$462$		0			0
$463$		−	40.2005i		−	1.86828i	−0.356913	−	0.934138i	$-0.616171\pi$
$463$		−	40.2005i		−	1.86828i	0.356913	−	0.934138i	$-0.383829\pi$
$464$	−4.58123	−	7.93492i	−0.212678	−	0.368370i
$465$	3.42921	+	1.07164i	0.159026	+	0.0496961i
$466$	−5.27226	+	9.13182i	−0.244233	+	0.423023i
$467$	6.79116	−	3.92088i	0.314257	−	0.181437i	−0.334573	−	0.942370i	$-0.608592\pi$
$467$	6.79116	−	3.92088i	0.314257	−	0.181437i	0.648830	+	0.760933i	$0.275259\pi$
$468$		−	3.80748i		−	0.176001i
$469$		0			0
$470$	−6.56440	+	1.47283i	−0.302793	+	0.0679366i
$471$	11.3320	+	19.6276i	0.522152	+	0.904393i
$472$	−11.2942	−	6.52072i	−0.519859	−	0.300141i
$473$	10.1715	+	5.87255i	0.467688	+	0.270020i
$474$	6.21302	+	10.7613i	0.285374	+	0.494281i
$475$	−18.8565	+	8.91008i	−0.865198	+	0.408823i
$476$		0			0
$477$		−	12.1711i		−	0.557278i
$478$	−3.47526	+	2.00644i	−0.158955	+	0.0917726i
$479$	−13.8872	+	24.0534i	−0.634524	+	1.09903i	0.352092	+	0.935965i	$0.385470\pi$
$479$	−13.8872	+	24.0534i	−0.634524	+	1.09903i	−0.986616	+	0.163062i	$0.947863\pi$
$480$	−0.666969	+	2.13428i	−0.0304428	+	0.0974161i
$481$	2.40554	+	4.16651i	0.109683	+	0.189977i
$482$			0.543899i			0.0247739i
$483$		0			0
$484$	5.27226			0.239648
$485$	−19.8396	+	18.2728i	−0.900872	+	0.829725i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	10.8481	+	6.26315i	0.491574	+	0.283810i	0.725227	−	0.688510i	$-0.241735\pi$
$487$	10.8481	+	6.26315i	0.491574	+	0.283810i	−0.233653	+	0.972320i	$0.575068\pi$
$488$	−11.3371	+	6.54548i	−0.513206	+	0.296300i
$489$	10.2039			0.461437
$490$		0			0
$491$	−24.3924			−1.10081			−0.550407	−	0.834897i	$-0.685527\pi$
$491$	−24.3924			−1.10081			−0.550407	+	0.834897i	$0.685527\pi$
$492$	2.76442	−	1.59604i	0.124630	−	0.0719550i
$493$	−15.6348	−	9.02677i	−0.704157	−	0.406545i
$494$	−7.94076	+	13.7538i	−0.357272	+	0.618813i
$495$	3.62546	+	3.93634i	0.162952	+	0.176925i
$496$	−1.60673			−0.0721443
$497$		0			0
$498$		−	1.89887i		−	0.0850906i
$499$	−11.8280	−	20.4867i	−0.529493	−	0.917110i	−0.999408	−	0.0343978i	$-0.989049\pi$
$499$	−11.8280	−	20.4867i	−0.529493	−	0.917110i	0.469915	−	0.882712i	$-0.344285\pi$
$500$	1.54392	+	11.0732i	0.0690461	+	0.495210i
$501$	−12.6249	+	21.8670i	−0.564039	+	0.976945i
$502$	−4.00822	+	2.31415i	−0.178896	+	0.103285i
$503$			20.8496i			0.929636i	0.885406	+	0.464818i	$0.153880\pi$
$503$			20.8496i			0.929636i	−0.885406	+	0.464818i	$0.846120\pi$
$504$		0			0
$505$	17.1638	−	3.85098i	0.763780	−	0.171366i
$506$	9.77786	+	16.9358i	0.434679	+	0.752886i
$507$	−1.29638	−	0.748465i	−0.0575742	−	0.0332405i
$508$	15.9724	+	9.22170i	0.708663	+	0.409147i
$509$	−1.29745	−	2.24725i	−0.0575085	−	0.0996076i	0.835838	−	0.548976i	$-0.184982\pi$
$509$	−1.29745	−	2.24725i	−0.0575085	−	0.0996076i	−0.893346	+	0.449369i	$0.851649\pi$
$510$	0.964557	+	4.29903i	0.0427113	+	0.190364i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−3.61231	+	2.08557i	−0.159487	+	0.0920800i
$514$	−12.7836	+	22.1418i	−0.563859	+	0.976632i
$515$	−12.5899	−	3.93437i	−0.554775	−	0.173369i
$516$	2.45377	+	4.25006i	0.108021	+	0.187099i
$517$		−	7.20057i		−	0.316681i
$518$		0			0
$519$	12.5348			0.550216
$520$	5.76779	+	6.26237i	0.252934	+	0.274623i
$521$	12.2442	−	21.2076i	0.536429	−	0.929122i	−0.462664	−	0.886534i	$-0.653106\pi$
$521$	12.2442	−	21.2076i	0.536429	−	0.929122i	0.999093	−	0.0425883i	$-0.0135604\pi$
$522$	−7.93492	−	4.58123i	−0.347302	−	0.200515i
$523$	−18.7284	+	10.8129i	−0.818937	+	0.472814i	−0.850050	−	0.526702i	$-0.823428\pi$
$523$	−18.7284	+	10.8129i	−0.818937	+	0.472814i	0.0311125	+	0.999516i	$0.490095\pi$
$524$	0.615405			0.0268841
$525$		0			0
$526$	20.5972			0.898080
$527$	−2.74172	+	1.58294i	−0.119431	+	0.0689537i
$528$	−2.07263	−	1.19663i	−0.0901997	−	0.0520768i
$529$	21.8837	−	37.9037i	0.951466	−	1.64799i
$530$	18.4375	+	20.0185i	0.800875	+	0.869548i
$531$	−13.0414			−0.565951
$532$		0			0
$533$		−	12.1538i		−	0.526439i
$534$	0.989747	+	1.71429i	0.0428306	+	0.0741847i
$535$	−8.02058	−	2.50646i	−0.346760	−	0.108364i
$536$	2.88893	−	5.00378i	0.124783	−	0.216130i
$537$	19.8489	−	11.4598i	0.856544	−	0.494526i
$538$			2.23799i			0.0964865i
$539$		0			0
$540$	0.489528	+	2.18183i	0.0210659	+	0.0938908i
$541$	−4.00868	−	6.94323i	−0.172346	−	0.298513i	0.766893	−	0.641775i	$-0.221802\pi$
$541$	−4.00868	−	6.94323i	−0.172346	−	0.298513i	−0.939240	+	0.343262i	$0.888468\pi$
$542$	16.5944	+	9.58079i	0.712791	+	0.411530i
$543$	−16.9898	−	9.80906i	−0.729102	−	0.420947i
$544$	−0.985191	−	1.70640i	−0.0422397	−	0.0731613i
$545$	15.5839	−	3.49649i	0.667539	−	0.149773i
$546$		0			0
$547$			43.0251i			1.83962i	0.392361	+	0.919811i	$0.371658\pi$
$547$			43.0251i			1.83962i	−0.392361	+	0.919811i	$0.628342\pi$
$548$	−6.77924	+	3.91399i	−0.289595	+	0.167198i
$549$	−6.54548	+	11.3371i	−0.279354	+	0.483856i
$550$	−11.9260	−	0.982245i	−0.508525	−	0.0418831i
$551$	19.1089	+	33.0976i	0.814068	+	1.41001i
$552$			8.17113i			0.347787i
$553$		0			0
$554$	−3.67674			−0.156210
$555$	−1.91415	−	2.07828i	−0.0812511	−	0.0882182i
$556$	−3.07689	+	5.32933i	−0.130489	+	0.226014i
$557$	9.68419	+	5.59117i	0.410332	+	0.236906i	0.690933	−	0.722919i	$-0.257200\pi$
$557$	9.68419	+	5.59117i	0.410332	+	0.236906i	−0.280600	+	0.959825i	$0.590533\pi$
$558$	−1.39147	+	0.803365i	−0.0589056	+	0.0340092i
$559$	18.6854			0.790309
$560$		0			0
$561$	−4.71565			−0.199095
$562$	25.8318	−	14.9140i	1.08965	−	0.629109i
$563$	−23.2696	−	13.4347i	−0.980697	−	0.566206i	−0.0782168	−	0.996936i	$-0.524923\pi$
$563$	−23.2696	−	13.4347i	−0.980697	−	0.566206i	−0.902481	+	0.430730i	$0.858256\pi$
$564$	1.50434	−	2.60559i	0.0633440	−	0.109715i
$565$	28.5919	−	26.3338i	1.20287	−	1.10787i
$566$	4.28961			0.180306
$567$		0			0
$568$			6.94032i			0.291210i
$569$	−1.30726	−	2.26425i	−0.0548034	−	0.0949222i	0.837322	−	0.546710i	$-0.184120\pi$
$569$	−1.30726	−	2.26425i	−0.0548034	−	0.0949222i	−0.892126	+	0.451787i	$0.850787\pi$
$570$	2.78202	−	8.90237i	0.116526	−	0.372879i
$571$	−6.23037	+	10.7913i	−0.260733	+	0.451603i	−0.966437	−	0.256904i	$-0.917298\pi$
$571$	−6.23037	+	10.7913i	−0.260733	+	0.451603i	0.705704	+	0.708507i	$0.250631\pi$
$572$	−7.89151	+	4.55617i	−0.329961	+	0.190503i
$573$			19.7269i			0.824102i
$574$		0			0
$575$	17.4546	+	36.9394i	0.727907	+	1.54048i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−15.4321	−	8.90975i	−0.642448	−	0.370918i	0.143109	−	0.989707i	$-0.454290\pi$
$577$	−15.4321	−	8.90975i	−0.642448	−	0.370918i	−0.785557	+	0.618789i	$0.787623\pi$
$578$	11.3602	+	6.55880i	0.472521	+	0.272810i
$579$	2.39327	+	4.14526i	0.0994609	+	0.172271i
$580$	19.9909	−	4.48528i	0.830076	−	0.186241i
$581$		0			0
$582$		−	12.0624i		−	0.500002i
$583$	−25.2263	+	14.5644i	−1.04477	+	0.603196i
$584$	0.253332	−	0.438784i	0.0104829	−	0.0181570i
$585$	8.12624	+	2.53947i	0.335979	+	0.104994i
$586$	−12.2970	−	21.2990i	−0.507985	−	0.879856i
$587$		−	9.55661i		−	0.394443i	−0.980359	−	0.197222i	$-0.936808\pi$
$587$		−	9.55661i		−	0.394443i	0.980359	−	0.197222i	$-0.0631919\pi$
$588$		0			0
$589$	6.70189			0.276146
$590$	21.4500	−	19.7559i	0.883081	−	0.813339i
$591$	8.59985	−	14.8954i	0.353750	−	0.612714i
$592$	1.09430	+	0.631792i	0.0449753	+	0.0259665i
$593$	10.0995	−	5.83097i	0.414738	−	0.239449i	−0.278085	−	0.960556i	$-0.589700\pi$
$593$	10.0995	−	5.83097i	0.414738	−	0.239449i	0.692824	+	0.721107i	$0.256366\pi$
$594$	−2.39327			−0.0981970
$595$		0			0
$596$	−7.53584			−0.308680
$597$	−13.4282	+	7.75280i	−0.549582	+	0.317301i
$598$	26.9433	+	15.5557i	1.10179	+	0.636121i
$599$	−16.5488	+	28.6634i	−0.676168	+	1.17116i	0.299959	+	0.953952i	$0.403027\pi$
$599$	−16.5488	+	28.6634i	−0.676168	+	1.17116i	−0.976126	+	0.217204i	$0.930306\pi$
$600$	−4.11030	−	2.84700i	−0.167802	−	0.116228i
$601$	−15.2886			−0.623633			−0.311817	−	0.950142i	$-0.600937\pi$
$601$	−15.2886			−0.623633			−0.311817	+	0.950142i	$0.600937\pi$
$602$		0			0
$603$		−	5.77786i		−	0.235293i
$604$	4.52072	+	7.83012i	0.183946	+	0.318603i
$605$	−3.51643	+	11.2525i	−0.142963	+	0.457478i
$606$	−3.93336	+	6.81278i	−0.159782	+	0.276750i
$607$	−34.7989	+	20.0911i	−1.41244	+	0.815474i	−0.995618	−	0.0935131i	$-0.970190\pi$
$607$	−34.7989	+	20.0911i	−1.41244	+	0.815474i	−0.416824	+	0.908987i	$0.636857\pi$
$608$			4.17113i			0.169162i
$609$		0			0
$610$	−6.40839	−	28.5622i	−0.259468	−	1.15645i
$611$	−5.72774	−	9.92074i	−0.231720	−	0.401350i
$612$	−1.70640	−	0.985191i	−0.0689771	−	0.0398240i
$613$	21.5286	+	12.4295i	0.869532	+	0.502024i	0.867193	−	0.497973i	$-0.165922\pi$
$613$	21.5286	+	12.4295i	0.869532	+	0.502024i	0.00233921	+	0.999997i	$0.499255\pi$
$614$	1.07045	+	1.85407i	0.0431997	+	0.0748242i
$615$	1.56261	+	6.96456i	0.0630106	+	0.280838i
$616$		0			0
$617$		−	22.7647i		−	0.916473i	−0.888830	−	0.458237i	$-0.848481\pi$
$617$		−	22.7647i		−	0.916473i	0.888830	−	0.458237i	$-0.151519\pi$
$618$	5.10858	−	2.94944i	0.205497	−	0.118644i
$619$	−8.91399	+	15.4395i	−0.358284	+	0.620566i	−0.987674	−	0.156524i	$-0.949971\pi$
$619$	−8.91399	+	15.4395i	−0.358284	+	0.620566i	0.629391	+	0.777089i	$0.283305\pi$
$620$	1.07164	−	3.42921i	0.0430381	−	0.137720i
$621$	4.08557	+	7.07641i	0.163948	+	0.283967i
$622$			13.9991i			0.561314i
$623$		0			0
$624$	−3.80748			−0.152421
$625$	−24.6631	−	4.09035i	−0.986524	−	0.163614i
$626$	−16.5364	+	28.6418i	−0.660926	+	1.14476i
$627$	8.64523	+	4.99132i	0.345257	+	0.199334i
$628$	19.6276	−	11.3320i	0.783228	−	0.452197i
$629$	2.48974			0.0992725
$630$		0			0
$631$	0.580705			0.0231175			0.0115587	−	0.999933i	$-0.496321\pi$
$631$	0.580705			0.0231175			0.0115587	+	0.999933i	$0.496321\pi$
$632$	10.7613	−	6.21302i	0.428060	−	0.247141i
$633$	−20.6963	−	11.9490i	−0.822603	−	0.474930i
$634$	3.69230	−	6.39525i	0.146640	−	0.253988i
$635$	−30.3348	+	27.9391i	−1.20380	+	1.10873i
$636$	−12.1711			−0.482617
$637$		0			0
$638$			21.9282i			0.868147i
$639$	3.47016	+	6.01050i	0.137277	+	0.237772i
$640$	2.13428	+	0.666969i	0.0843648	+	0.0263643i
$641$	−9.01765	+	15.6190i	−0.356176	+	0.616915i	−0.987318	−	0.158752i	$-0.949253\pi$
$641$	−9.01765	+	15.6190i	−0.356176	+	0.616915i	0.631143	+	0.775667i	$0.282586\pi$
$642$	3.25451	−	1.87899i	0.128445	−	0.0741578i
$643$			39.3664i			1.55246i	0.630451	+	0.776229i	$0.282870\pi$
$643$			39.3664i			1.55246i	−0.630451	+	0.776229i	$0.717130\pi$
$644$		0			0
$645$	−10.7074	+	2.40238i	−0.421604	+	0.0945938i
$646$	4.10936	+	7.11762i	0.161681	+	0.280039i
$647$	2.06147	+	1.19019i	0.0810448	+	0.0467912i	0.539975	−	0.841681i	$-0.318434\pi$
$647$	2.06147	+	1.19019i	0.0810448	+	0.0467912i	−0.458930	+	0.888472i	$0.651767\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	15.6059	+	27.0301i	0.612583	+	1.06103i
$650$	−17.2126	+	8.13328i	−0.675133	+	0.319013i
$651$		0			0
$652$		−	10.2039i		−	0.399616i
$653$	−21.7472	+	12.5557i	−0.851032	+	0.491344i	−0.860999	−	0.508607i	$-0.830161\pi$
$653$	−21.7472	+	12.5557i	−0.851032	+	0.491344i	0.00996683	+	0.999950i	$0.496827\pi$
$654$	−3.57129	+	6.18565i	−0.139648	+	0.241878i
$655$	−0.410456	+	1.31345i	−0.0160379	+	0.0513206i
$656$	−1.59604	−	2.76442i	−0.0623149	−	0.107932i
$657$		−	0.506664i		−	0.0197668i
$658$		0			0
$659$	7.17981			0.279686			0.139843	−	0.990174i	$-0.455340\pi$
$659$	7.17981			0.279686			0.139843	+	0.990174i	$0.455340\pi$
$660$	3.93634	−	3.62546i	0.153222	−	0.141121i
$661$	−12.5165	+	21.6792i	−0.486835	+	0.843222i	−0.999885	−	0.0151360i	$-0.995182\pi$
$661$	−12.5165	+	21.6792i	−0.486835	+	0.843222i	0.513051	+	0.858358i	$0.328515\pi$
$662$	18.6670	+	10.7774i	0.725515	+	0.418877i
$663$	−6.49709	+	3.75110i	−0.252326	+	0.145681i
$664$	−1.89887			−0.0736906
$665$		0			0
$666$	1.26358			0.0489629
$667$	64.8373	−	37.4338i	2.51051	−	1.44944i
$668$	21.8670	+	12.6249i	0.846059	+	0.488472i
$669$	0.435157	−	0.753715i	0.0168242	−	0.0291403i
$670$	8.75264	+	9.50316i	0.338144	+	0.367139i
$671$	31.3302			1.20949
$672$		0			0
$673$		−	9.67062i		−	0.372775i	−0.982476	−	0.186388i	$-0.940322\pi$
$673$		−	9.67062i		−	0.372775i	0.982476	−	0.186388i	$-0.0596780\pi$
$674$	−11.1275	−	19.2733i	−0.428614	−	0.742380i
$675$	−4.98313	−	0.410420i	−0.191801	−	0.0157971i
$676$	−0.748465	+	1.29638i	−0.0287871	+	0.0498607i
$677$	−23.9794	+	13.8445i	−0.921603	+	0.532088i	−0.884146	−	0.467211i	$-0.845259\pi$
$677$	−23.9794	+	13.8445i	−0.921603	+	0.532088i	−0.0374566	+	0.999298i	$0.511926\pi$
$678$			17.3837i			0.667618i
$679$		0			0
$680$	4.29903	−	0.964557i	0.164860	−	0.0369891i
$681$	−7.34271	−	12.7179i	−0.281373	−	0.487353i
$682$	3.33016	+	1.92267i	0.127518	+	0.0736228i
$683$	22.6229	+	13.0613i	0.865641	+	0.499778i	0.865897	−	0.500222i	$-0.166748\pi$
$683$	22.6229	+	13.0613i	0.865641	+	0.499778i	−0.000256275		1.00000i	$0.500082\pi$
$684$	2.08557	+	3.61231i	0.0797437	+	0.138120i
$685$	−3.83202	−	17.0793i	−0.146414	−	0.652567i
$686$		0			0
$687$		−	24.0379i		−	0.917101i
$688$	4.25006	−	2.45377i	0.162032	−	0.0935493i
$689$	−23.1707	+	40.1328i	−0.882733	+	1.52894i
$690$	−17.4395	−	5.44989i	−0.663910	−	0.207474i
$691$	12.3951	+	21.4689i	0.471530	+	0.816715i	0.999470	−	0.0325676i	$-0.0103684\pi$
$691$	12.3951	+	21.4689i	0.471530	+	0.816715i	−0.527939	+	0.849282i	$0.677035\pi$
$692$		−	12.5348i		−	0.476501i
$693$		0			0
$694$	2.14089			0.0812673
$695$	−9.32210	−	10.1214i	−0.353607	−	0.383928i
$696$	−4.58123	+	7.93492i	−0.173651	+	0.300772i
$697$	−5.44696	−	3.14481i	−0.206318	−	0.119118i
$698$	0.785424	−	0.453465i	0.0297287	−	0.0171639i
$699$	10.5445			0.398830
$700$		0			0
$701$	37.8817			1.43077			0.715386	−	0.698730i	$-0.246251\pi$
$701$	37.8817			1.43077			0.715386	+	0.698730i	$0.246251\pi$
$702$	−3.29738	+	1.90374i	−0.124451	+	0.0718521i
$703$	−4.56446	−	2.63529i	−0.172152	−	0.0993919i
$704$	−1.19663	+	2.07263i	−0.0450999	+	0.0781153i
$705$	4.55771	+	4.94853i	0.171653	+	0.186372i
$706$	13.8866			0.522629
$707$		0			0
$708$			13.0414i			0.490128i
$709$	−15.4900	−	26.8295i	−0.581741	−	1.00760i	−0.995273	−	0.0971153i	$-0.969038\pi$
$709$	−15.4900	−	26.8295i	−0.581741	−	1.00760i	0.413532	−	0.910489i	$-0.364295\pi$
$710$	−14.8126	−	4.62898i	−0.555907	−	0.173723i
$711$	6.21302	−	10.7613i	0.233007	−	0.403579i
$712$	1.71429	−	0.989747i	0.0642458	−	0.0370924i
$713$		−	13.1288i		−	0.491678i
$714$		0			0
$715$	−4.46074	−	19.8815i	−0.166822	−	0.743527i
$716$	−11.4598	−	19.8489i	−0.428272	−	0.741789i
$717$	3.47526	+	2.00644i	0.129786	+	0.0749320i
$718$	−16.3302	−	9.42827i	−0.609440	−	0.351860i
$719$	8.35138	+	14.4650i	0.311454	+	0.539454i	0.978677	−	0.205404i	$-0.0658507\pi$
$719$	8.35138	+	14.4650i	0.311454	+	0.539454i	−0.667223	+	0.744858i	$0.732517\pi$
$720$	2.18183	−	0.489528i	0.0813118	−	0.0182436i
$721$		0			0
$722$			1.60164i			0.0596068i
$723$	0.471030	−	0.271949i	0.0175178	−	0.0101139i
$724$	−9.80906	+	16.9898i	−0.364551	+	0.631421i
$725$	−3.76045	+	45.6577i	−0.139660	+	1.69568i
$726$	−2.63613	−	4.56591i	−0.0978360	−	0.169457i
$727$			36.1218i			1.33968i	0.742504	+	0.669842i	$0.233638\pi$
$727$			36.1218i			1.33968i	−0.742504	+	0.669842i	$0.766362\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	0.767523	+	0.833336i	0.0284073	+	0.0308432i
$731$	4.83487	−	8.37424i	0.178824	−	0.309733i
$732$	11.3371	+	6.54548i	0.419031	+	0.241928i
$733$	6.78843	−	3.91930i	0.250736	−	0.144763i	−0.369365	−	0.929284i	$-0.620425\pi$
$733$	6.78843	−	3.91930i	0.250736	−	0.144763i	0.620101	+	0.784522i	$0.287091\pi$
$734$	31.5722			1.16535
$735$		0			0
$736$	8.17113			0.301192
$737$	−11.9754	+	6.91399i	−0.441119	+	0.254680i
$738$	−2.76442	−	1.59604i	−0.101760	−	0.0587510i
$739$	−14.8984	+	25.8048i	−0.548048	+	0.949247i	0.450360	+	0.892847i	$0.351295\pi$
$739$	−14.8984	+	25.8048i	−0.548048	+	0.949247i	−0.998408	+	0.0563998i	$0.982038\pi$
$740$	−2.07828	+	1.91415i	−0.0763992	+	0.0703655i
$741$	15.8815			0.583422
$742$		0			0
$743$			11.7487i			0.431017i	0.976502	+	0.215509i	$0.0691409\pi$
$743$			11.7487i			0.431017i	−0.976502	+	0.215509i	$0.930859\pi$
$744$	0.803365	+	1.39147i	0.0294528	+	0.0510137i
$745$	5.02617	−	16.0836i	0.184145	−	0.589258i
$746$	10.4538	−	18.1065i	0.382740	−	0.662925i
$747$	−1.64447	+	0.949437i	−0.0601681	+	0.0347381i
$748$			4.71565i			0.172421i
$749$		0			0
$750$	8.81774	−	6.87368i	0.321978	−	0.250991i
$751$	1.21990	+	2.11294i	0.0445150	+	0.0771022i	0.887424	−	0.460953i	$-0.152492\pi$
$751$	1.21990	+	2.11294i	0.0445150	+	0.0771022i	−0.842909	+	0.538055i	$0.819159\pi$
$752$	−2.60559	−	1.50434i	−0.0950161	−	0.0548575i
$753$	4.00822	+	2.31415i	0.146068	+	0.0843322i
$754$	17.4430	+	30.2121i	0.635235	+	1.10026i
$755$	−19.7269	+	4.42604i	−0.717934	+	0.161080i
$756$		0			0
$757$		−	17.5039i		−	0.636188i	−0.948059	−	0.318094i	$-0.896957\pi$
$757$		−	17.5039i		−	0.636188i	0.948059	−	0.318094i	$-0.103043\pi$
$758$	−8.50818	+	4.91220i	−0.309031	+	0.178419i
$759$	9.77786	−	16.9358i	0.354914	−	0.614729i
$760$	−8.90237	−	2.78202i	−0.322923	−	0.100914i
$761$	−3.03163	−	5.25095i	−0.109897	−	0.190347i	0.805832	−	0.592145i	$-0.201719\pi$
$761$	−3.03163	−	5.25095i	−0.109897	−	0.190347i	−0.915728	+	0.401798i	$0.868385\pi$
$762$		−	18.4434i		−	0.668134i
$763$		0			0
$764$	19.7269			0.713693
$765$	3.24079	−	2.98484i	0.117171	−	0.107917i
$766$	15.3323	−	26.5564i	0.553979	−	0.959521i
$767$	43.0026	+	24.8275i	1.55273	+	0.896471i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−6.94628			−0.250489			−0.125245	−	0.992126i	$-0.539972\pi$
$769$	−6.94628			−0.250489			−0.125245	+	0.992126i	$0.539972\pi$
$770$		0			0
$771$	25.5671			0.920777
$772$	4.14526	−	2.39327i	0.149191	−	0.0861357i
$773$	12.8689	+	7.42985i	0.462861	+	0.267233i	0.713247	−	0.700913i	$-0.247224\pi$
$773$	12.8689	+	7.42985i	0.462861	+	0.267233i	−0.250385	+	0.968146i	$0.580557\pi$
$774$	2.45377	−	4.25006i	0.0881991	−	0.152765i
$775$	6.60415	+	4.57436i	0.237228	+	0.164316i
$776$	−12.0624			−0.433015
$777$		0			0
$778$			23.4476i			0.840637i
$779$	6.65729	+	11.5308i	0.238522	+	0.413133i
$780$	2.53947	−	8.12624i	0.0909277	−	0.290966i
$781$	8.30503	−	14.3847i	0.297177	−	0.514726i
$782$	13.9432	−	8.05012i	0.498609	−	0.287872i
$783$			9.16246i			0.327440i
$784$		0			0
$785$	11.0947	+	49.4490i	0.395986	+	1.76491i
$786$	−0.307703	−	0.532957i	−0.0109754	−	0.0190099i
$787$	−14.5218	−	8.38416i	−0.517646	−	0.298863i	0.218325	−	0.975876i	$-0.429941\pi$
$787$	−14.5218	−	8.38416i	−0.517646	−	0.298863i	−0.735971	+	0.677013i	$0.763274\pi$
$788$	−14.8954	−	8.59985i	−0.530626	−	0.306357i
$789$	−10.2986	−	17.8377i	−0.366639	−	0.635038i
$790$	6.08290	+	27.1115i	0.216420	+	0.964582i
$791$		0			0
$792$			2.39327i			0.0850411i
$793$	43.1658	−	24.9218i	1.53286	−	0.884999i
$794$	17.6881	−	30.6366i	0.627725	−	1.08725i
$795$	8.11777	−	25.9766i	0.287908	−	0.921295i
$796$	7.75280	+	13.4282i	0.274791	+	0.475952i
$797$		−	37.5481i		−	1.33002i	−0.746833	−	0.665011i	$-0.768427\pi$
$797$		−	37.5481i		−	1.33002i	0.746833	−	0.665011i	$-0.231573\pi$
$798$		0			0
$799$	−5.92824			−0.209726
$800$	−2.84700	+	4.11030i	−0.100657	+	0.145321i
$801$	0.989747	−	1.71429i	0.0349710	−	0.0605716i
$802$	−7.83012	−	4.52072i	−0.276491	−	0.159632i
$803$	−1.05013	+	0.606292i	−0.0370582	+	0.0213956i
$804$	−5.77786			−0.203770
$805$		0			0
$806$	6.11760			0.215483
$807$	1.93815	−	1.11899i	0.0682263	−	0.0393905i
$808$	6.81278	+	3.93336i	0.239673	+	0.138375i
$809$	6.25070	−	10.8265i	0.219763	−	0.380640i	−0.734973	−	0.678097i	$-0.762805\pi$
$809$	6.25070	−	10.8265i	0.219763	−	0.380640i	0.954735	+	0.297457i	$0.0961383\pi$
$810$	1.64475	−	1.51486i	0.0577907	−	0.0532266i
$811$	30.4470			1.06914			0.534569	−	0.845125i	$-0.320474\pi$
$811$	30.4470			1.06914			0.534569	+	0.845125i	$0.320474\pi$
$812$		0			0
$813$		−	19.1616i		−	0.672026i
$814$	−1.51205	−	2.61895i	−0.0529973	−	0.0917940i
$815$	21.7780	+	6.80569i	0.762850	+	0.238393i
$816$	−0.985191	+	1.70640i	−0.0344886	+	0.0597360i
$817$	−17.7276	+	10.2350i	−0.620210	+	0.358078i
$818$			15.4379i			0.539773i
$819$		0			0
$820$	6.96456	−	1.56261i	0.243213	−	0.0545688i
$821$	−19.1388	−	33.1493i	−0.667947	−	1.15692i	−0.978477	−	0.206355i	$-0.933840\pi$
$821$	−19.1388	−	33.1493i	−0.667947	−	1.15692i	0.310530	−	0.950563i	$-0.399493\pi$
$822$	6.77924	+	3.91399i	0.236453	+	0.136516i
$823$	−20.4566	−	11.8106i	−0.713073	−	0.411693i	0.0991247	−	0.995075i	$-0.468396\pi$
$823$	−20.4566	−	11.8106i	−0.713073	−	0.411693i	−0.812198	+	0.583382i	$0.801729\pi$
$824$	−2.94944	−	5.10858i	−0.102749	−	0.177966i
$825$	5.11233	+	10.8193i	0.177989	+	0.376680i
$826$		0			0
$827$			34.5652i			1.20195i	0.799268	+	0.600975i	$0.205221\pi$
$827$			34.5652i			1.20195i	−0.799268	+	0.600975i	$0.794779\pi$
$828$	7.07641	−	4.08557i	0.245922	−	0.141983i
$829$	13.6043	−	23.5633i	0.472496	−	0.818387i	−0.527009	−	0.849860i	$-0.676686\pi$
$829$	13.6043	−	23.5633i	0.472496	−	0.818387i	0.999505	+	0.0314728i	$0.0100198\pi$
$830$	1.26649	−	4.05273i	0.0439605	−	0.140672i
$831$	1.83837	+	3.18415i	0.0637723	+	0.110457i
$832$			3.80748i			0.132001i
$833$		0			0
$834$	6.15378			0.213088
$835$	−41.5297	+	38.2499i	−1.43719	+	1.32369i
$836$	4.99132	−	8.64523i	0.172629	−	0.299001i
$837$	1.39147	+	0.803365i	0.0480962	+	0.0277684i
$838$	23.0600	−	13.3137i	0.796595	−	0.459914i
$839$	−1.49861			−0.0517377			−0.0258689	−	0.999665i	$-0.508235\pi$
$839$	−1.49861			−0.0517377			−0.0258689	+	0.999665i	$0.508235\pi$
$840$		0			0
$841$	54.9507			1.89485
$842$	−4.36989	+	2.52296i	−0.150596	+	0.0869468i
$843$	−25.8318	−	14.9140i	−0.889694	−	0.513665i
$844$	−11.9490	+	20.6963i	−0.411301	+	0.712395i
$845$	−2.26763	−	2.46208i	−0.0780090	−	0.0846981i
$846$	−3.00868			−0.103440
$847$		0			0
$848$			12.1711i			0.417958i
$849$	−2.14481	−	3.71491i	−0.0736095	−	0.127495i
$850$	−0.808683	+	9.81866i	−0.0277376	+	0.336777i
$851$	−5.16246	+	8.94164i	−0.176967	+	0.306516i
$852$	6.01050	−	3.47016i	0.205916	−	0.118886i
$853$			38.9306i			1.33296i	0.745524	+	0.666479i	$0.232199\pi$
$853$			38.9306i			1.33296i	−0.745524	+	0.666479i	$0.767801\pi$
$854$		0			0
$855$	−9.10069	+	2.04189i	−0.311237	+	0.0698311i
$856$	−1.87899	−	3.25451i	−0.0642225	−	0.111237i
$857$	16.1069	+	9.29934i	0.550202	+	0.317659i	0.749203	−	0.662340i	$-0.230437\pi$
$857$	16.1069	+	9.29934i	0.550202	+	0.317659i	−0.199001	+	0.979999i	$0.563770\pi$
$858$	7.89151	+	4.55617i	0.269412	+	0.155545i
$859$	4.54972	+	7.88035i	0.155235	+	0.268874i	0.933144	−	0.359502i	$-0.117053\pi$
$859$	4.54972	+	7.88035i	0.155235	+	0.268874i	−0.777910	+	0.628376i	$0.783720\pi$
$860$	2.40238	+	10.7074i	0.0819206	+	0.365120i
$861$		0			0
$862$			25.2835i			0.861158i
$863$	9.06003	−	5.23081i	0.308407	−	0.178059i	−0.337806	−	0.941216i	$-0.609685\pi$
$863$	9.06003	−	5.23081i	0.308407	−	0.178059i	0.646213	+	0.763157i	$0.276352\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	26.7527	+	8.36031i	0.909621	+	0.284259i
$866$	13.5032	+	23.3881i	0.458856	+	0.794761i
$867$		−	13.1176i		−	0.445497i
$868$		0			0
$869$	−29.7389			−1.00882
$870$	−13.8798	−	15.0700i	−0.470570	−	0.510920i
$871$	−10.9996	+	19.0518i	−0.372706	+	0.645546i
$872$	6.18565	+	3.57129i	0.209473	+	0.120939i
$873$	−10.4463	+	6.03120i	−0.353555	+	0.204125i
$874$	−34.0829			−1.15287
$875$		0			0
$876$	−0.506664			−0.0171186
$877$	4.58845	−	2.64914i	0.154941	−	0.0894552i	−0.420525	−	0.907281i	$-0.638154\pi$
$877$	4.58845	−	2.64914i	0.154941	−	0.0894552i	0.575466	+	0.817826i	$0.304821\pi$
$878$	24.1895	+	13.9658i	0.816357	+	0.471324i
$879$	−12.2970	+	21.2990i	−0.414768	+	0.718399i
$880$	−3.62546	−	3.93634i	−0.122214	−	0.132694i
$881$	2.68857			0.0905802			0.0452901	−	0.998974i	$-0.485579\pi$
$881$	2.68857			0.0905802			0.0452901	+	0.998974i	$0.485579\pi$
$882$		0			0
$883$		−	26.4277i		−	0.889363i	−0.895689	−	0.444681i	$-0.853317\pi$
$883$		−	26.4277i		−	0.889363i	0.895689	−	0.444681i	$-0.146683\pi$
$884$	3.75110	+	6.49709i	0.126163	+	0.218521i
$885$	−27.8341	−	8.69824i	−0.935633	−	0.292388i
$886$	−5.38459	+	9.32639i	−0.180899	+	0.313326i
$887$	7.08538	−	4.09074i	0.237904	−	0.137354i	−0.376309	−	0.926494i	$-0.622807\pi$
$887$	7.08538	−	4.09074i	0.237904	−	0.137354i	0.614213	+	0.789140i	$0.289474\pi$
$888$		−	1.26358i		−	0.0424031i
$889$		0			0
$890$	0.969018	+	4.31891i	0.0324816	+	0.144770i
$891$	1.19663	+	2.07263i	0.0400888	+	0.0694358i
$892$	−0.753715	−	0.435157i	−0.0252362	−	0.0145701i
$893$	10.8683	+	6.27479i	0.363693	+	0.209978i
$894$	3.76792	+	6.52623i	0.126018	+	0.218270i
$895$	50.0065	−	11.2198i	1.67153	−	0.375036i
$896$		0			0
$897$		−	31.1115i		−	1.03878i
$898$	−13.1019	+	7.56440i	−0.437217	+	0.252427i
$899$	7.36080	−	12.7493i	0.245496	−	0.425212i
$900$	−0.410420	+	4.98313i	−0.0136807	+	0.166104i
$901$	11.9909	+	20.7688i	0.399474	+	0.691910i
$902$			7.63950i			0.254368i
$903$		0			0
$904$	17.3837			0.578174
$905$	−29.7186	−	32.2669i	−0.987881	−	1.07259i
$906$	4.52072	−	7.83012i	0.150191	−	0.260138i
$907$	−3.29114	−	1.90014i	−0.109281	−	0.0630932i	0.444364	−	0.895847i	$-0.353430\pi$
$907$	−3.29114	−	1.90014i	−0.109281	−	0.0630932i	−0.553644	+	0.832753i	$0.686763\pi$
$908$	−12.7179	+	7.34271i	−0.422060	+	0.243676i
$909$	7.86672			0.260923
$910$		0			0
$911$	39.1590			1.29740			0.648699	−	0.761045i	$-0.275314\pi$
$911$	39.1590			1.29740			0.648699	+	0.761045i	$0.275314\pi$
$912$	3.61231	−	2.08557i	0.119615	−	0.0690600i
$913$	3.93567	+	2.27226i	0.130252	+	0.0752008i
$914$	10.7355	−	18.5945i	0.355100	−	0.615051i
$915$	−21.5314	+	19.8309i	−0.711805	+	0.655590i
$916$	−24.0379			−0.794233
$917$		0			0
$918$			1.97038i			0.0650323i
$919$	−6.92311	−	11.9912i	−0.228372	−	0.395552i	0.728954	−	0.684563i	$-0.240007\pi$
$919$	−6.92311	−	11.9912i	−0.228372	−	0.395552i	−0.957326	+	0.289011i	$0.906674\pi$
$920$	−5.44989	+	17.4395i	−0.179678	+	0.574963i
$921$	1.07045	−	1.85407i	0.0352724	−	0.0610937i
$922$	−26.3675	+	15.2233i	−0.868367	+	0.501352i
$923$		−	26.4252i		−	0.869795i
$924$		0			0
$925$	−2.69918	−	5.71232i	−0.0887485	−	0.187820i
$926$	20.1002	+	34.8147i	0.660535	+	1.14408i
$927$	−5.10858	−	2.94944i	−0.167788	−	0.0968722i
$928$	7.93492	+	4.58123i	0.260477	+	0.150386i
$929$	6.90151	+	11.9538i	0.226431	+	0.392190i	0.956748	−	0.290918i	$-0.0939608\pi$
$929$	6.90151	+	11.9538i	0.226431	+	0.392190i	−0.730317	+	0.683109i	$0.760627\pi$
$930$	−3.50560	+	0.786540i	−0.114953	+	0.0257917i
$931$		0			0
$932$		−	10.5445i		−	0.345397i
$933$	12.1236	−	6.99956i	0.396909	−	0.229155i
$934$	−3.92088	+	6.79116i	−0.128295	+	0.222214i
$935$	−10.0645	−	3.14519i	−0.329145	−	0.102859i
$936$	1.90374	+	3.29738i	0.0622257	+	0.107778i
$937$		−	29.1062i		−	0.950858i	−0.879754	−	0.475429i	$-0.842293\pi$
$937$		−	29.1062i		−	0.950858i	0.879754	−	0.475429i	$-0.157707\pi$
$938$		0			0
$939$	33.0727			1.07929
$940$	4.94853	−	4.55771i	0.161403	−	0.148656i
$941$	−13.4967	+	23.3770i	−0.439980	+	0.762068i	−0.997687	−	0.0679699i	$-0.978348\pi$
$941$	−13.4967	+	23.3770i	−0.439980	+	0.762068i	0.557707	+	0.830038i	$0.311681\pi$
$942$	−19.6276	−	11.3320i	−0.639503	−	0.369217i
$943$	22.5885	−	13.0414i	0.735581	−	0.424688i
$944$	13.0414			0.424463
$945$		0			0
$946$	−11.7451			−0.381866
$947$	−28.1463	+	16.2503i	−0.914631	+	0.528062i	−0.881918	−	0.471402i	$-0.843748\pi$
$947$	−28.1463	+	16.2503i	−0.914631	+	0.528062i	−0.0327127	+	0.999465i	$0.510415\pi$
$948$	−10.7613	−	6.21302i	−0.349510	−	0.201790i
$949$	−0.964557	+	1.67066i	−0.0313108	+	0.0542320i
$950$	11.8752	−	17.1446i	0.385283	−	0.556245i
$951$	−7.38459			−0.239462
$952$		0			0
$953$			41.4364i			1.34226i	0.741342	+	0.671128i	$0.234190\pi$
$953$			41.4364i			1.34226i	−0.741342	+	0.671128i	$0.765810\pi$
$954$	6.08557	+	10.5405i	0.197028	+	0.341262i
$955$	−13.1572	+	42.1027i	−0.425757	+	1.36241i
$956$	2.00644	−	3.47526i	0.0648931	−	0.112398i
$957$	18.9904	−	10.9641i	0.613873	−	0.354420i
$958$		−	27.7745i		−	0.897352i
$959$		0			0
$960$	−0.489528	−	2.18183i	−0.0157995	−	0.0704181i
$961$	14.2092	+	24.6111i	0.458362	+	0.793906i
$962$	−4.16651	−	2.40554i	−0.134334	−	0.0775577i
$963$	−3.25451	−	1.87899i	−0.104875	−	0.0605496i
$964$	−0.271949	−	0.471030i	−0.00875890	−	0.0151709i
$965$	2.34315	+	10.4434i	0.0754285	+	0.336185i
$966$		0			0
$967$			23.0294i			0.740577i	0.928917	+	0.370288i	$0.120741\pi$
$967$			23.0294i			0.740577i	−0.928917	+	0.370288i	$0.879259\pi$
$968$	−4.56591	+	2.63613i	−0.146754	+	0.0847284i
$969$	4.10936	−	7.11762i	0.132012	−	0.228651i
$970$	8.04524	−	25.7445i	0.258317	−	0.826607i
$971$	−2.53163	−	4.38491i	−0.0812439	−	0.140719i	0.822541	−	0.568706i	$-0.192556\pi$
$971$	−2.53163	−	4.38491i	−0.0812439	−	0.140719i	−0.903784	+	0.427988i	$0.859223\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$	−12.5263			−0.401368
$975$	15.6499	+	10.8399i	0.501198	+	0.347154i
$976$	6.54548	−	11.3371i	0.209516	−	0.362892i
$977$	−25.6528	−	14.8106i	−0.820705	−	0.473834i	0.0299545	−	0.999551i	$-0.490464\pi$
$977$	−25.6528	−	14.8106i	−0.820705	−	0.473834i	−0.850660	+	0.525717i	$0.823797\pi$
$978$	−8.83684	+	5.10195i	−0.282571	+	0.163142i
$979$	−4.73747			−0.151410
$980$		0			0
$981$	7.14257			0.228045
$982$	21.1244	−	12.1962i	0.674108	−	0.389196i
$983$	−7.08538	−	4.09074i	−0.225988	−	0.130474i	0.382732	−	0.923860i	$-0.374983\pi$
$983$	−7.08538	−	4.09074i	−0.225988	−	0.130474i	−0.608720	+	0.793385i	$0.708317\pi$
$984$	−1.59604	+	2.76442i	−0.0508799	+	0.0881265i
$985$	28.2892	−	26.0551i	0.901370	−	0.830184i
$986$	18.0535			0.574942
$987$		0			0
$988$		−	15.8815i		−	0.505259i
$989$	20.0501	+	34.7278i	0.637557	+	1.10428i
$990$	−5.10791	−	1.59624i	−0.162340	−	0.0507317i
$991$	−8.37771	+	14.5106i	−0.266127	+	0.460945i	−0.967858	−	0.251496i	$-0.919077\pi$
$991$	−8.37771	+	14.5106i	−0.266127	+	0.460945i	0.701731	+	0.712442i	$0.252411\pi$
$992$	1.39147	−	0.803365i	0.0441792	−	0.0255069i
$993$		−	21.5549i		−	0.684023i
$994$		0			0
$995$	−33.8305	+	7.59043i	−1.07250	+	0.240633i
$996$	0.949437	+	1.64447i	0.0300841	+	0.0521071i
$997$	4.00441	+	2.31195i	0.126821	+	0.0732202i	0.562068	−	0.827091i	$-0.310006\pi$
$997$	4.00441	+	2.31195i	0.126821	+	0.0732202i	−0.435247	+	0.900311i	$0.643339\pi$
$998$	20.4867	+	11.8280i	0.648494	+	0.374408i
$999$	−0.631792	−	1.09430i	−0.0199890	−	0.0346220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.n.l.949.3		16
5.4	even	2	inner	1470.2.n.l.949.7		16
7.2	even	3	inner	1470.2.n.l.79.7		16
7.3	odd	6		1470.2.g.k.589.4	yes	8
7.4	even	3		1470.2.g.j.589.1	✓	8
7.5	odd	6		1470.2.n.k.79.6		16
7.6	odd	2		1470.2.n.k.949.2		16
35.3	even	12		7350.2.a.dr.1.2		4
35.4	even	6		1470.2.g.j.589.5	yes	8
35.9	even	6	inner	1470.2.n.l.79.3		16
35.17	even	12		7350.2.a.du.1.2		4
35.18	odd	12		7350.2.a.ds.1.2		4
35.19	odd	6		1470.2.n.k.79.2		16
35.24	odd	6		1470.2.g.k.589.8	yes	8
35.32	odd	12		7350.2.a.dt.1.2		4
35.34	odd	2		1470.2.n.k.949.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.g.j.589.1	✓	8	7.4	even	3
1470.2.g.j.589.5	yes	8	35.4	even	6
1470.2.g.k.589.4	yes	8	7.3	odd	6
1470.2.g.k.589.8	yes	8	35.24	odd	6
1470.2.n.k.79.2		16	35.19	odd	6
1470.2.n.k.79.6		16	7.5	odd	6
1470.2.n.k.949.2		16	7.6	odd	2
1470.2.n.k.949.6		16	35.34	odd	2
1470.2.n.l.79.3		16	35.9	even	6	inner
1470.2.n.l.79.7		16	7.2	even	3	inner
1470.2.n.l.949.3		16	1.1	even	1	trivial
1470.2.n.l.949.7		16	5.4	even	2	inner
7350.2.a.dr.1.2		4	35.3	even	12
7350.2.a.ds.1.2		4	35.18	odd	12
7350.2.a.dt.1.2		4	35.32	odd	12
7350.2.a.du.1.2		4	35.17	even	12

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.51486 + 1.64475i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.51486 + 1.64475i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.13428 - 0.666969i) q^{10} +(1.19663 - 2.07263i) q^{11} +(0.866025 - 0.500000i) q^{12} -3.80748i q^{13} +(0.489528 + 2.18183i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.70640 - 0.985191i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(2.08557 + 3.61231i) q^{19} +(2.18183 - 0.489528i) q^{20} +2.39327i q^{22} +(7.07641 - 4.08557i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.410420 + 4.98313i) q^{25} +(1.90374 + 3.29738i) q^{26} +1.00000i q^{27} +9.16246 q^{29} +(-1.51486 - 1.64475i) q^{30} +(0.803365 - 1.39147i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.07263 - 1.19663i) q^{33} +1.97038 q^{34} +1.00000 q^{36} +(-1.09430 + 0.631792i) q^{37} +(-3.61231 - 2.08557i) q^{38} +(1.90374 - 3.29738i) q^{39} +(-1.64475 + 1.51486i) q^{40} +3.19208 q^{41} +4.90755i q^{43} +(-1.19663 - 2.07263i) q^{44} +(-0.666969 + 2.13428i) q^{45} +(-4.08557 + 7.07641i) q^{46} +(2.60559 - 1.50434i) q^{47} -1.00000i q^{48} +(-2.13613 - 4.52072i) q^{50} +(-0.985191 - 1.70640i) q^{51} +(-3.29738 - 1.90374i) q^{52} +(-10.5405 - 6.08557i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(5.22170 - 1.17157i) q^{55} +4.17113i q^{57} +(-7.93492 + 4.58123i) q^{58} +(-6.52072 + 11.2942i) q^{59} +(2.13428 + 0.666969i) q^{60} +(6.54548 + 11.3371i) q^{61} +1.60673i q^{62} -1.00000 q^{64} +(6.26237 - 5.76779i) q^{65} +(-1.19663 + 2.07263i) q^{66} +(-5.00378 - 2.88893i) q^{67} +(-1.70640 + 0.985191i) q^{68} +8.17113 q^{69} +6.94032 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-0.438784 - 0.253332i) q^{73} +(0.631792 - 1.09430i) q^{74} +(-2.84700 + 4.11030i) q^{75} +4.17113 q^{76} +3.80748i q^{78} +(-6.21302 - 10.7613i) q^{79} +(0.666969 - 2.13428i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.76442 + 1.59604i) q^{82} +1.89887i q^{83} +(-0.964557 - 4.29903i) q^{85} +(-2.45377 - 4.25006i) q^{86} +(7.93492 + 4.58123i) q^{87} +(2.07263 + 1.19663i) q^{88} +(-0.989747 - 1.71429i) q^{89} +(-0.489528 - 2.18183i) q^{90} -8.17113i q^{92} +(1.39147 - 0.803365i) q^{93} +(-1.50434 + 2.60559i) q^{94} +(-2.78202 + 8.90237i) q^{95} +(0.500000 + 0.866025i) q^{96} +12.0624i q^{97} +2.39327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9	\( 16 q + 8 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9} - 8 q^{16} - 24 q^{19} + 8 q^{20} - 8 q^{24} - 4 q^{25} + 32 q^{29} - 4 q^{30} + 32 q^{31} + 16 q^{34} + 16 q^{36} - 48 q^{41} - 4 q^{45} - 8 q^{46} - 8 q^{50} - 8 q^{51} - 8 q^{54} - 40 q^{59} + 24 q^{61} - 16 q^{64} - 28 q^{65} + 16 q^{69} - 80 q^{71} - 16 q^{74} + 4 q^{75} - 48 q^{76} - 16 q^{79} + 4 q^{80} - 8 q^{81} + 56 q^{85} - 8 q^{86} - 88 q^{89} - 24 q^{94} - 24 q^{95} + 8 q^{96}+O(q^{100}) \) 16 * q + 8 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9 - 8 * q^16 - 24 * q^19 + 8 * q^20 - 8 * q^24 - 4 * q^25 + 32 * q^29 - 4 * q^30 + 32 * q^31 + 16 * q^34 + 16 * q^36 - 48 * q^41 - 4 * q^45 - 8 * q^46 - 8 * q^50 - 8 * q^51 - 8 * q^54 - 40 * q^59 + 24 * q^61 - 16 * q^64 - 28 * q^65 + 16 * q^69 - 80 * q^71 - 16 * q^74 + 4 * q^75 - 48 * q^76 - 16 * q^79 + 4 * q^80 - 8 * q^81 + 56 * q^85 - 8 * q^86 - 88 * q^89 - 24 * q^94 - 24 * q^95 + 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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