LMFDB - Embedded newform 1470.2.n.k.949.6

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			949.6
Root			$-1.46557 + 0.846149i$ of defining polynomial
Character	$\chi$	$=$	1470.949
Dual form			1470.2.n.k.79.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.666969 - 2.13428i) q^{5} +1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.666969 - 2.13428i) q^{5} +1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.64475 - 1.51486i) 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} +(-4.11030 + 2.84700i) q^{25} +(-1.90374 - 3.29738i) q^{26} +1.00000i q^{27} +9.16246 q^{29} +(-0.666969 - 2.13428i) 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} +(-2.13428 + 0.666969i) q^{40} -3.19208 q^{41} -4.90755i q^{43} +(-1.19663 - 2.07263i) q^{44} +(1.51486 - 1.64475i) 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} +(-1.64475 - 1.51486i) q^{60} +(-6.54548 - 11.3371i) q^{61} +1.60673i q^{62} -1.00000 q^{64} +(-8.12624 + 2.53947i) 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} +(-4.98313 + 0.410420i) q^{75} -4.17113 q^{76} -3.80748i q^{78} +(-6.21302 - 10.7613i) q^{79} +(-1.51486 + 1.64475i) 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} +(-6.31867 + 6.86048i) 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
$5$	−0.666969	−	2.13428i	−0.298278	−	0.954479i
$5$	−0.666969	−	2.13428i	−0.298278	−	0.954479i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.64475	−	1.51486i	−0.520116	−	0.479040i
$11$	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	0.521233	−	0.853414i	$-0.325472\pi$
$19$	−2.08557	−	3.61231i	−0.478462	−	0.828720i	−0.999695	+	0.0246940i	$0.992139\pi$
$20$	−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	−0.999619	−	0.0275921i	$-0.991216\pi$
$23$	−7.07641	+	4.08557i	−1.47553	+	0.851900i	−0.475914	+	0.879492i	$0.657883\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−4.11030	+	2.84700i	−0.822061	+	0.569399i
$26$	−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	$0.176171\pi$
$30$	−0.666969	−	2.13428i	−0.121771	−	0.389664i
$31$	−0.803365	+	1.39147i	−0.144289	+	0.249915i	−0.929107	−	0.369810i	$-0.879423\pi$
$31$	−0.803365	+	1.39147i	−0.144289	+	0.249915i	0.784819	+	0.619725i	$0.212756\pi$
$32$	−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	−0.407345	−	0.913274i	$-0.633545\pi$
$37$	1.09430	−	0.631792i	0.179901	−	0.103866i	0.587246	+	0.809408i	$0.300212\pi$
$38$	−3.61231	−	2.08557i	−0.585994	−	0.338324i
$39$	1.90374	−	3.29738i	0.304843	−	0.528003i
$40$	−2.13428	+	0.666969i	−0.337459	+	0.105457i
$41$	−3.19208			−0.498519			−0.249259	−	0.968437i	$-0.580187\pi$
$41$	−3.19208			−0.498519			−0.249259	+	0.968437i	$0.580187\pi$
$42$		0			0
$43$		−	4.90755i		−	0.748394i	−0.927349	−	0.374197i	$-0.877918\pi$
$43$		−	4.90755i		−	0.748394i	0.927349	−	0.374197i	$-0.122082\pi$
$44$	−1.19663	−	2.07263i	−0.180399	−	0.312461i
$45$	1.51486	−	1.64475i	0.225821	−	0.245185i
$46$	−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	0.998353	−	0.0573648i	$-0.0182698\pi$
$53$	10.5405	+	6.08557i	1.44785	+	0.835917i	0.449497	+	0.893282i	$0.351603\pi$
$54$	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	$-0.510583\pi$
$59$	6.52072	−	11.2942i	0.848926	−	1.47038i	0.882168	−	0.470936i	$-0.156084\pi$
$60$	−1.64475	−	1.51486i	−0.212337	−	0.195567i
$61$	−6.54548	−	11.3371i	−0.838062	−	1.45157i	−0.891513	−	0.452996i	$-0.850355\pi$
$61$	−6.54548	−	11.3371i	−0.838062	−	1.45157i	0.0534501	−	0.998571i	$-0.482978\pi$
$62$			1.60673i			0.204055i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−8.12624	+	2.53947i	−1.00794	+	0.314983i
$66$	1.19663	−	2.07263i	0.147296	−	0.255123i
$67$	5.00378	+	2.88893i	0.611309	+	0.352939i	0.773477	−	0.633824i	$-0.218516\pi$
$67$	5.00378	+	2.88893i	0.611309	+	0.352939i	−0.162169	+	0.986763i	$0.551849\pi$
$68$	−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
$75$	−4.98313	+	0.410420i	−0.575402	+	0.0473912i
$76$	−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	$-0.413047\pi$
$80$	−1.51486	+	1.64475i	−0.169366	+	0.183889i
$81$	−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	0.913703	−	0.406383i	$-0.133210\pi$
$89$	0.989747	+	1.71429i	0.104913	+	0.181715i	−0.808790	+	0.588098i	$0.799877\pi$
$90$	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
$95$	−6.31867	+	6.86048i	−0.648282	+	0.703871i
$96$	−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
$100$	0.410420	+	4.98313i	0.0410420	+	0.498313i
$101$	−3.93336	+	6.81278i	−0.391384	+	0.677897i	−0.992632	−	0.121165i	$-0.961337\pi$
$101$	−3.93336	+	6.81278i	−0.391384	+	0.677897i	0.601248	+	0.799062i	$0.294670\pi$
$102$	−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	−0.334369	−	0.942442i	$-0.608523\pi$
$107$	3.25451	−	1.87899i	0.314625	−	0.181649i	0.648994	+	0.760793i	$0.275190\pi$
$108$	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	$0.0555396\pi$
$110$	−5.10791	+	1.59624i	−0.487020	+	0.152195i
$111$	1.26358			0.119934
$112$		0			0
$113$			17.3837i			1.63532i	0.575700	+	0.817661i	$0.304730\pi$
$113$			17.3837i			1.63532i	−0.575700	+	0.817661i	$0.695270\pi$
$114$	−2.08557	−	3.61231i	−0.195331	−	0.338324i
$115$	13.4395	+	12.3781i	1.25324	+	1.15426i
$116$	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	$-0.694921\pi$
$127$		−	18.4434i		−	1.63659i	0.574801	−	0.818293i	$-0.305079\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	2.45377	−	4.25006i	0.216043	−	0.374197i
$130$	−5.76779	+	6.26237i	−0.505869	+	0.549246i
$131$	−0.307703	−	0.532957i	−0.0268841	−	0.0465646i	0.852270	−	0.523102i	$-0.175225\pi$
$131$	−0.307703	−	0.532957i	−0.0268841	−	0.0465646i	−0.879154	+	0.476537i	$0.841892\pi$
$132$		−	2.39327i		−	0.208307i
$133$		0			0
$134$	5.77786			0.499131
$135$	2.13428	−	0.666969i	0.183690	−	0.0574035i
$136$	−0.985191	+	1.70640i	−0.0844794	+	0.146323i
$137$	6.77924	+	3.91399i	0.579189	+	0.334395i	0.760811	−	0.648973i	$-0.224801\pi$
$137$	6.77924	+	3.91399i	0.579189	+	0.334395i	−0.181622	+	0.983368i	$0.558135\pi$
$138$	−7.07641	+	4.08557i	−0.602384	+	0.347787i
$139$	6.15378			0.521957			0.260979	−	0.965345i	$-0.415955\pi$
$139$	6.15378			0.521957			0.260979	+	0.965345i	$0.415955\pi$
$140$		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
$145$	−6.11108	−	19.5553i	−0.507497	−	1.62398i
$146$	−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	$0.933221\pi$
$150$	−4.11030	+	2.84700i	−0.335605	+	0.232456i
$151$	−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	−0.804419	−	0.594063i	$-0.797523\pi$
$163$	−8.83684	+	5.10195i	−0.692155	+	0.399616i	0.112264	+	0.993678i	$0.464190\pi$
$164$	−1.59604	+	2.76442i	−0.124630	+	0.215865i
$165$	−3.93634	−	3.62546i	−0.306443	−	0.282242i
$166$	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
$170$	1.31418	+	4.20535i	0.100793	+	0.322535i
$171$	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	$-0.160726\pi$
$180$	−0.666969	−	2.13428i	−0.0497129	−	0.159080i
$181$	19.6181			1.45820			0.729102	−	0.684405i	$-0.239938\pi$
$181$	19.6181			1.45820			0.729102	+	0.684405i	$0.239938\pi$
$182$		0			0
$183$		−	13.0910i		−	0.967711i
$184$	4.08557	+	7.07641i	0.301192	+	0.521680i
$185$	−2.07828	−	1.91415i	−0.152798	−	0.140731i
$186$	−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	0.343333	−	0.939214i	$-0.388444\pi$
$193$	−4.14526	−	2.39327i	−0.298383	−	0.172271i	−0.641716	+	0.766942i	$0.721777\pi$
$194$	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	$0.209922\pi$
$197$			17.1997i			1.22543i	−0.790305	+	0.612714i	$0.790078\pi$
$198$	2.07263	−	1.19663i	0.147296	−	0.0850411i
$199$	7.75280	−	13.4282i	0.549582	−	0.951903i	−0.448722	−	0.893672i	$-0.648120\pi$
$199$	7.75280	−	13.4282i	0.549582	−	0.951903i	0.998303	−	0.0582316i	$-0.0185462\pi$
$200$	2.84700	+	4.11030i	0.201313	+	0.290642i
$201$	2.88893	+	5.00378i	0.203770	+	0.352939i
$202$			7.86672i			0.553501i
$203$		0			0
$204$	−1.97038			−0.137954
$205$	2.12902	+	6.81279i	0.148697	+	0.475826i
$206$	−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
$215$	−10.4741	+	3.27318i	−0.714327	+	0.223229i
$216$	1.00000			0.0680414
$217$		0			0
$218$		−	7.14257i		−	0.483756i
$219$	−0.253332	−	0.438784i	−0.0171186	−	0.0296503i
$220$	−3.62546	+	3.93634i	−0.244428	+	0.265388i
$221$	−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	$0.125460\pi$
$229$	12.0189	+	20.8174i	0.794233	+	1.37565i	−0.129092	+	0.991633i	$0.541206\pi$
$230$	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	−0.768351	−	0.640029i	$-0.778922\pi$
$233$	−9.13182	+	5.27226i	−0.598246	+	0.345397i	0.170106	+	0.985426i	$0.445589\pi$
$234$	1.90374	−	3.29738i	0.124451	−	0.215556i
$235$	−4.94853	−	4.55771i	−0.322806	−	0.297312i
$236$	−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	$0.458571\pi$
$240$	−2.13428	+	0.666969i	−0.137767	+	0.0430527i
$241$	−0.271949	+	0.471030i	−0.0175178	+	0.0303417i	−0.874651	−	0.484752i	$-0.838910\pi$
$241$	−0.271949	+	0.471030i	−0.0175178	+	0.0303417i	0.857134	+	0.515094i	$0.172243\pi$
$242$	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
$250$	11.0732	+	1.54392i	0.700332	+	0.0976459i
$251$	−4.62829			−0.292135			−0.146068	−	0.989275i	$-0.546662\pi$
$251$	−4.62829			−0.292135			−0.146068	+	0.989275i	$0.546662\pi$
$252$		0			0
$253$			19.5557i			1.22946i
$254$	−9.22170	−	15.9724i	−0.578621	−	1.00220i
$255$	−2.98484	+	3.24079i	−0.186918	+	0.202946i
$256$	−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	0.936200	−	0.351469i	$-0.114318\pi$
$263$	17.8377	+	10.2986i	1.09992	+	0.635038i	0.163719	+	0.986507i	$0.447651\pi$
$264$	−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	−0.898121	−	0.439749i	$-0.855067\pi$
$269$	−1.11899	+	1.93815i	−0.0682263	+	0.118171i	0.829894	+	0.557921i	$0.188401\pi$
$270$	1.51486	−	1.64475i	0.0921912	−	0.100096i
$271$	9.58079	+	16.5944i	0.581992	+	1.00804i	0.995243	+	0.0974221i	$0.0310597\pi$
$271$	9.58079	+	16.5944i	0.581992	+	1.00804i	−0.413252	+	0.910617i	$0.635607\pi$
$272$			1.97038i			0.119472i
$273$		0			0
$274$	7.82799			0.472906
$275$	0.982245	+	11.9260i	0.0592316	+	0.719163i
$276$	−4.08557	+	7.07641i	−0.245922	+	0.425950i
$277$	−3.18415	−	1.83837i	−0.191317	−	0.110457i	0.401282	−	0.915955i	$-0.368565\pi$
$277$	−3.18415	−	1.83837i	−0.191317	−	0.110457i	−0.592599	+	0.805498i	$0.701898\pi$
$278$	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
$285$	−8.90237	+	2.78202i	−0.527331	+	0.164792i
$286$	−9.11233			−0.538824
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−6.55880	−	11.3602i	−0.385812	−	0.668246i
$290$	−15.0700	−	13.8798i	−0.884939	−	0.815051i
$291$	−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
$305$	−19.8309	+	21.5314i	−1.13551	+	1.23288i
$306$	−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
$310$	3.42921	−	1.07164i	0.194766	−	0.0608650i
$311$	−6.99956	+	12.1236i	−0.396909	+	0.687466i	−0.993343	−	0.115196i	$-0.963250\pi$
$311$	−6.99956	+	12.1236i	−0.396909	+	0.687466i	0.596434	+	0.802662i	$0.296584\pi$
$312$	−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	−0.309534	−	0.950888i	$-0.600173\pi$
$317$	6.39525	−	3.69230i	0.359193	−	0.207380i	0.668727	+	0.743508i	$0.266840\pi$
$318$	10.5405	+	6.08557i	0.591083	+	0.341262i
$319$	10.9641	−	18.9904i	0.613873	−	1.06326i
$320$	0.666969	+	2.13428i	0.0372847	+	0.119310i
$321$	3.75798			0.209750
$322$		0			0
$323$			8.21872i			0.457302i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	10.8399	+	15.6499i	0.601289	+	0.868101i
$326$	−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	$-0.792713\pi$
$337$		−	22.2549i		−	1.21230i	0.795350	−	0.606151i	$-0.207287\pi$
$338$	−1.29638	+	0.748465i	−0.0705137	+	0.0407111i
$339$	−8.69186	+	15.0547i	−0.472077	+	0.817661i
$340$	3.24079	+	2.98484i	0.175756	+	0.161876i
$341$	1.92267	+	3.33016i	0.104118	+	0.180338i
$342$		−	4.17113i		−	0.225549i
$343$		0			0
$344$	−4.90755			−0.264597
$345$	5.44989	+	17.4395i	0.293412	+	0.938911i
$346$	6.26739	−	10.8554i	0.336937	−	0.583592i
$347$	1.85407	+	1.07045i	0.0995317	+	0.0574646i	0.548940	−	0.835862i	$-0.315032\pi$
$347$	1.85407	+	1.07045i	0.0995317	+	0.0574646i	−0.449408	+	0.893327i	$0.648365\pi$
$348$	7.93492	−	4.58123i	0.425356	−	0.245580i
$349$	0.906929			0.0485468			0.0242734	−	0.999705i	$-0.492273\pi$
$349$	0.906929			0.0485468			0.0242734	+	0.999705i	$0.492273\pi$
$350$		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
$355$	−4.62898	−	14.8126i	−0.245681	−	0.786171i
$356$	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	$0.667546\pi$
$360$	−1.64475	−	1.51486i	−0.0866861	−	0.0798399i
$361$	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	0.0483362	−	0.998831i	$-0.484608\pi$
$373$	18.1065	−	10.4538i	0.937517	−	0.541276i	0.889181	+	0.457555i	$0.151275\pi$
$374$	−2.35783	+	4.08388i	−0.121920	+	0.211172i
$375$	4.19954	+	10.3617i	0.216863	+	0.535073i
$376$	−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	$0.418805\pi$
$380$	2.78202	+	8.90237i	0.142714	+	0.456682i
$381$	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	$-0.0359518\pi$
$390$	−8.12624	+	2.53947i	−0.411488	+	0.128591i
$391$	16.1002			0.814225
$392$		0			0
$393$		−	0.615405i		−	0.0310431i
$394$	8.59985	+	14.8954i	0.433254	+	0.750418i
$395$	−18.8237	+	20.4378i	−0.947122	+	1.02834i
$396$	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	−0.991302	−	0.131606i	$-0.957987\pi$
$409$	−7.71894	+	13.3696i	−0.381677	+	0.661084i	0.609625	+	0.792690i	$0.291320\pi$
$410$	5.25018	+	4.83554i	0.259288	+	0.238810i
$411$	3.91399	+	6.77924i	0.193063	+	0.334395i
$412$			5.89887i			0.290617i
$413$		0			0
$414$	−8.17113			−0.401589
$415$	4.05273	−	1.26649i	0.198941	−	0.0621696i
$416$	−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	$-0.274594\pi$
$419$	26.6274			1.30083			0.650417	+	0.759577i	$0.274594\pi$
$420$		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
$425$	9.81866	−	0.808683i	0.476275	−	0.0392269i
$426$	6.94032			0.336260
$427$		0			0
$428$		−	3.75798i		−	0.181649i
$429$	−4.55617	−	7.89151i	−0.219974	−	0.381006i
$430$	−7.43423	+	8.07170i	−0.358511	+	0.389252i
$431$	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	$0.0655641\pi$
$439$	13.9658	+	24.1895i	0.666552	+	1.15450i	−0.312309	+	0.949980i	$0.601103\pi$
$440$	−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	−0.704916	−	0.709291i	$-0.749015\pi$
$443$	−9.32639	+	5.38459i	−0.443110	+	0.255830i	0.261806	+	0.965121i	$0.415682\pi$
$444$	0.631792	−	1.09430i	0.0299835	−	0.0519330i
$445$	2.99865	−	3.25578i	0.142150	−	0.154339i
$446$	−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	$0.383804\pi$
$450$	−4.98313	+	0.410420i	−0.234907	+	0.0193474i
$451$	−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	0.00252752	−	0.999997i	$-0.499195\pi$
$457$	18.5945	−	10.7355i	0.869814	−	0.502187i	0.867286	+	0.497810i	$0.165862\pi$
$458$	20.8174	+	12.0189i	0.972733	+	0.561608i
$459$	0.985191	−	1.70640i	0.0459848	−	0.0796479i
$460$	17.4395	−	5.44989i	0.813120	−	0.254103i
$461$	−30.4465			−1.41804			−0.709019	−	0.705190i	$-0.750862\pi$
$461$	−30.4465			−1.41804			−0.709019	+	0.705190i	$0.750862\pi$
$462$		0			0
$463$			40.2005i			1.86828i	0.356913	+	0.934138i	$0.383829\pi$
$463$			40.2005i			1.86828i	−0.356913	+	0.934138i	$0.616171\pi$
$464$	−4.58123	−	7.93492i	−0.212678	−	0.368370i
$465$	2.64267	+	2.43397i	0.122551	+	0.112872i
$466$	−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	$-0.614530\pi$
$479$	13.8872	−	24.0534i	0.634524	−	1.09903i	0.986616	−	0.163062i	$-0.0521370\pi$
$480$	−1.51486	+	1.64475i	−0.0691434	+	0.0750723i
$481$	−2.40554	−	4.16651i	−0.109683	−	0.189977i
$482$			0.543899i			0.0247739i
$483$		0			0
$484$	5.27226			0.239648
$485$	25.7445	−	8.04524i	1.16900	−	0.365316i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−10.8481	−	6.26315i	−0.491574	−	0.283810i	0.233653	−	0.972320i	$-0.424932\pi$
$487$	−10.8481	−	6.26315i	−0.491574	−	0.283810i	−0.725227	+	0.688510i	$0.758265\pi$
$488$	−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
$495$	−1.59624	−	5.10791i	−0.0717455	−	0.229583i
$496$	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	$-0.344285\pi$
$500$	10.3617	−	4.19954i	0.463387	−	0.187809i
$501$	−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	0.893346	−	0.449369i	$-0.148351\pi$
$509$	1.29745	+	2.24725i	0.0575085	+	0.0996076i	−0.835838	+	0.548976i	$0.815018\pi$
$510$	−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
$515$	9.70219	+	8.93595i	0.427529	+	0.393765i
$516$	−2.45377	−	4.25006i	−0.108021	−	0.187099i
$517$		−	7.20057i		−	0.316681i
$518$		0			0
$519$	12.5348			0.550216
$520$	2.53947	+	8.12624i	0.111363	+	0.356359i
$521$	−12.2442	+	21.2076i	−0.536429	+	0.929122i	0.462664	+	0.886534i	$0.346894\pi$
$521$	−12.2442	+	21.2076i	−0.536429	+	0.929122i	−0.999093	+	0.0425883i	$0.986440\pi$
$522$	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
$530$	−8.11777	−	25.9766i	−0.352613	−	1.12835i
$531$	13.0414			0.565951
$532$		0			0
$533$			12.1538i			0.526439i
$534$	0.989747	+	1.71429i	0.0428306	+	0.0741847i
$535$	−6.18095	−	5.69280i	−0.267226	−	0.246121i
$536$	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	$-0.628342\pi$
$547$		−	43.0251i		−	1.83962i	0.392361	−	0.919811i	$-0.371658\pi$
$548$	6.77924	−	3.91399i	0.289595	−	0.167198i
$549$	6.54548	−	11.3371i	0.279354	−	0.483856i
$550$	6.81363	+	9.83707i	0.290534	+	0.419454i
$551$	−19.1089	−	33.0976i	−0.814068	−	1.41001i
$552$			8.17113i			0.347787i
$553$		0			0
$554$	−3.67674			−0.156210
$555$	−0.842772	−	2.69684i	−0.0357737	−	0.114475i
$556$	3.07689	−	5.32933i	0.130489	−	0.226014i
$557$	−9.68419	−	5.59117i	−0.410332	−	0.236906i	0.280600	−	0.959825i	$-0.409467\pi$
$557$	−9.68419	−	5.59117i	−0.410332	−	0.236906i	−0.690933	+	0.722919i	$0.742800\pi$
$558$	−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
$565$	37.1017	−	11.5944i	1.56088	−	0.487780i
$566$	−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	$0.850787\pi$
$570$	−6.31867	+	6.86048i	−0.264660	+	0.287354i
$571$	−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
$585$	−6.26237	−	5.76779i	−0.258917	−	0.238469i
$586$	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
$590$	−27.8341	+	8.69824i	−1.14591	+	0.358101i
$591$	−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	$0.930306\pi$
$600$	0.410420	+	4.98313i	0.0167553	+	0.203435i
$601$	15.2886			0.623633			0.311817	−	0.950142i	$-0.399063\pi$
$601$	15.2886			0.623633			0.311817	+	0.950142i	$0.399063\pi$
$602$		0			0
$603$			5.77786i			0.235293i
$604$	4.52072	+	7.83012i	0.183946	+	0.318603i
$605$	7.98672	−	8.67156i	0.324706	−	0.352549i
$606$	−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	−0.00233921	−	0.999997i	$-0.500745\pi$
$613$	−21.5286	−	12.4295i	−0.869532	−	0.502024i	−0.867193	+	0.497973i	$0.834078\pi$
$614$	−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	$0.151519\pi$
$617$			22.7647i			0.916473i	−0.888830	+	0.458237i	$0.848481\pi$
$618$	−5.10858	+	2.94944i	−0.205497	+	0.118644i
$619$	8.91399	−	15.4395i	0.358284	−	0.620566i	−0.629391	−	0.777089i	$-0.716695\pi$
$619$	8.91399	−	15.4395i	0.358284	−	0.620566i	0.987674	+	0.156524i	$0.0500287\pi$
$620$	2.43397	−	2.64267i	0.0977504	−	0.106132i
$621$	−4.08557	−	7.07641i	−0.163948	−	0.283967i
$622$			13.9991i			0.561314i
$623$		0			0
$624$	−3.80748			−0.152421
$625$	8.78921	−	23.4041i	0.351569	−	0.936162i
$626$	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
$635$	−39.3634	+	12.3012i	−1.56209	+	0.488157i
$636$	12.1711			0.482617
$637$		0			0
$638$		−	21.9282i		−	0.868147i
$639$	3.47016	+	6.01050i	0.137277	+	0.237772i
$640$	1.64475	+	1.51486i	0.0650145	+	0.0598800i
$641$	−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	−0.00996683	−	0.999950i	$-0.503173\pi$
$653$	21.7472	−	12.5557i	0.851032	−	0.491344i	0.860999	+	0.508607i	$0.169839\pi$
$654$	3.57129	−	6.18565i	0.139648	−	0.241878i
$655$	−0.932251	+	1.01219i	−0.0364261	+	0.0395495i
$656$	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	$0.455340\pi$
$660$	−5.10791	+	1.59624i	−0.198825	+	0.0621334i
$661$	12.5165	−	21.6792i	0.486835	−	0.843222i	−0.513051	−	0.858358i	$-0.671485\pi$
$661$	12.5165	−	21.6792i	0.486835	−	0.843222i	0.999885	+	0.0151360i	$0.00481812\pi$
$662$	−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
$670$	−3.85366	−	12.3316i	−0.148880	−	0.476411i
$671$	−31.3302			−1.20949
$672$		0			0
$673$			9.67062i			0.372775i	0.982476	+	0.186388i	$0.0596780\pi$
$673$			9.67062i			0.372775i	−0.982476	+	0.186388i	$0.940322\pi$
$674$	−11.1275	−	19.2733i	−0.428614	−	0.742380i
$675$	−2.84700	−	4.11030i	−0.109581	−	0.158206i
$676$	−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	0.000256275	−	1.00000i	$-0.499918\pi$
$683$	−22.6229	−	13.0613i	−0.865641	−	0.499778i	−0.865897	+	0.500222i	$0.833252\pi$
$684$	−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
$690$	13.4395	+	12.3781i	0.511633	+	0.471226i
$691$	−12.3951	−	21.4689i	−0.471530	−	0.816715i	0.527939	−	0.849282i	$-0.322965\pi$
$691$	−12.3951	−	21.4689i	−0.471530	−	0.816715i	−0.999470	+	0.0325676i	$0.989632\pi$
$692$		−	12.5348i		−	0.476501i
$693$		0			0
$694$	2.14089			0.0812673
$695$	−4.10438	−	13.1339i	−0.155688	−	0.498197i
$696$	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
$705$	−2.00669	−	6.42136i	−0.0755764	−	0.241842i
$706$	−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	$-0.364295\pi$
$710$	−11.4151	−	10.5136i	−0.428402	−	0.394568i
$711$	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	0.667223	−	0.744858i	$-0.267483\pi$
$719$	−8.35138	−	14.4650i	−0.311454	−	0.539454i	−0.978677	+	0.205404i	$0.934149\pi$
$720$	−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
$725$	−37.6605	+	26.0855i	−1.39868	+	0.968791i
$726$	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
$730$	0.337929	+	1.08136i	0.0125073	+	0.0400230i
$731$	−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	$0.982038\pi$
$740$	−2.69684	+	0.842772i	−0.0991379	+	0.0309809i
$741$	−15.8815			−0.583422
$742$		0			0
$743$		−	11.7487i		−	0.431017i	−0.976502	−	0.215509i	$-0.930859\pi$
$743$		−	11.7487i		−	0.431017i	0.976502	−	0.215509i	$-0.0691409\pi$
$744$	0.803365	+	1.39147i	0.0294528	+	0.0510137i
$745$	−11.4157	+	12.3946i	−0.418240	+	0.454103i
$746$	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	$0.103043\pi$
$757$			17.5039i			0.636188i	−0.948059	+	0.318094i	$0.896957\pi$
$758$	8.50818	−	4.91220i	0.309031	−	0.178419i
$759$	−9.77786	+	16.9358i	−0.354914	+	0.614729i
$760$	6.86048	+	6.31867i	0.248856	+	0.229202i
$761$	3.03163	+	5.25095i	0.109897	+	0.190347i	0.915728	−	0.401798i	$-0.131615\pi$
$761$	3.03163	+	5.25095i	0.109897	+	0.190347i	−0.805832	+	0.592145i	$0.798281\pi$
$762$		−	18.4434i		−	0.668134i
$763$		0			0
$764$	19.7269			0.713693
$765$	−4.20535	+	1.31418i	−0.152045	+	0.0475144i
$766$	−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	$-0.460028\pi$
$769$	6.94628			0.250489			0.125245	+	0.992126i	$0.460028\pi$
$770$		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
$775$	−0.659433	−	8.00654i	−0.0236875	−	0.287603i
$776$	12.0624			0.433015
$777$		0			0
$778$		−	23.4476i		−	0.840637i
$779$	6.65729	+	11.5308i	0.238522	+	0.413133i
$780$	−5.76779	+	6.26237i	−0.206520	+	0.224229i
$781$	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
$795$	18.4375	−	20.0185i	0.653912	−	0.709983i
$796$	−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
$800$	4.98313	−	0.410420i	0.176180	−	0.0145105i
$801$	−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	$0.0961383\pi$
$810$	2.13428	−	0.666969i	0.0749910	−	0.0234349i
$811$	−30.4470			−1.06914			−0.534569	−	0.845125i	$-0.679526\pi$
$811$	−30.4470			−1.06914			−0.534569	+	0.845125i	$0.679526\pi$
$812$		0			0
$813$			19.1616i			0.672026i
$814$	−1.51205	−	2.61895i	−0.0529973	−	0.0917940i
$815$	16.7829	+	15.4575i	0.587879	+	0.541451i
$816$	−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	0.812198	−	0.583382i	$-0.198271\pi$
$823$	20.4566	+	11.8106i	0.713073	+	0.411693i	−0.0991247	+	0.995075i	$0.531604\pi$
$824$	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	$-0.794779\pi$
$827$		−	34.5652i		−	1.20195i	0.799268	−	0.600975i	$-0.205221\pi$
$828$	−7.07641	+	4.08557i	−0.245922	+	0.141983i
$829$	−13.6043	+	23.5633i	−0.472496	+	0.818387i	−0.999505	−	0.0314728i	$-0.989980\pi$
$829$	−13.6043	+	23.5633i	−0.472496	+	0.818387i	0.527009	+	0.849860i	$0.323314\pi$
$830$	2.87652	−	3.12318i	0.0998456	−	0.108407i
$831$	−1.83837	−	3.18415i	−0.0637723	−	0.110457i
$832$			3.80748i			0.132001i
$833$		0			0
$834$	6.15378			0.213088
$835$	53.8902	−	16.8408i	1.86495	−	0.582801i
$836$	−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	$-0.491765\pi$
$839$	1.49861			0.0517377			0.0258689	+	0.999665i	$0.491765\pi$
$840$		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
$845$	0.998406	+	3.19487i	0.0343462	+	0.109907i
$846$	3.00868			0.103440
$847$		0			0
$848$		−	12.1711i		−	0.417958i
$849$	−2.14481	−	3.71491i	−0.0736095	−	0.127495i
$850$	8.09887	−	5.60967i	0.277789	−	0.192410i
$851$	−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	0.777910	−	0.628376i	$-0.216280\pi$
$859$	−4.54972	−	7.88035i	−0.155235	−	0.268874i	−0.933144	+	0.359502i	$0.882947\pi$
$860$	−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	−0.646213	−	0.763157i	$-0.723648\pi$
$863$	−9.06003	+	5.23081i	−0.308407	+	0.178059i	0.337806	+	0.941216i	$0.390315\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−20.6166	−	18.9884i	−0.700986	−	0.645625i
$866$	−13.5032	−	23.3881i	−0.458856	−	0.794761i
$867$		−	13.1176i		−	0.445497i
$868$		0			0
$869$	−29.7389			−1.00882
$870$	−6.11108	−	19.5553i	−0.207185	−	0.662985i
$871$	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	−0.575466	−	0.817826i	$-0.695179\pi$
$877$	−4.58845	+	2.64914i	−0.154941	+	0.0894552i	0.420525	+	0.907281i	$0.361846\pi$
$878$	24.1895	+	13.9658i	0.816357	+	0.471324i
$879$	−12.2970	+	21.2990i	−0.414768	+	0.718399i
$880$	1.59624	+	5.10791i	0.0538091	+	0.172188i
$881$	−2.68857			−0.0905802			−0.0452901	−	0.998974i	$-0.514421\pi$
$881$	−2.68857			−0.0905802			−0.0452901	+	0.998974i	$0.514421\pi$
$882$		0			0
$883$			26.4277i			0.889363i	0.895689	+	0.444681i	$0.146683\pi$
$883$			26.4277i			0.889363i	−0.895689	+	0.444681i	$0.853317\pi$
$884$	3.75110	+	6.49709i	0.126163	+	0.218521i
$885$	−21.4500	−	19.7559i	−0.721032	−	0.664088i
$886$	−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
$900$	−4.11030	+	2.84700i	−0.137010	+	0.0948999i
$901$	−11.9909	−	20.7688i	−0.399474	−	0.691910i
$902$			7.63950i			0.254368i
$903$		0			0
$904$	17.3837			0.578174
$905$	−13.0847	−	41.8706i	−0.434949	−	1.39182i
$906$	−4.52072	+	7.83012i	−0.150191	+	0.260138i
$907$	3.29114	+	1.90014i	0.109281	+	0.0630932i	0.553644	−	0.832753i	$-0.313237\pi$
$907$	3.29114	+	1.90014i	0.109281	+	0.0630932i	−0.444364	+	0.895847i	$0.646570\pi$
$908$	−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
$915$	−27.9398	+	8.73126i	−0.923660	+	0.288647i
$916$	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	$0.906674\pi$
$920$	12.3781	−	13.4395i	0.408094	−	0.443087i
$921$	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	0.730317	−	0.683109i	$-0.239373\pi$
$929$	−6.90151	−	11.9538i	−0.226431	−	0.392190i	−0.956748	+	0.290918i	$0.906039\pi$
$930$	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
$935$	7.75608	+	7.14354i	0.253651	+	0.233619i
$936$	−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
$940$	−6.42136	+	2.00669i	−0.209442	+	0.0654511i
$941$	13.4967	−	23.3770i	0.439980	−	0.762068i	−0.557707	−	0.830038i	$-0.688319\pi$
$941$	13.4967	−	23.3770i	0.439980	−	0.762068i	0.997687	+	0.0679699i	$0.0216522\pi$
$942$	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	0.0327127	−	0.999465i	$-0.489585\pi$
$947$	28.1463	−	16.2503i	0.914631	−	0.528062i	0.881918	+	0.471402i	$0.156252\pi$
$948$	−10.7613	−	6.21302i	−0.349510	−	0.201790i
$949$	−0.964557	+	1.67066i	−0.0313108	+	0.0542320i
$950$	20.7853	−	1.71191i	0.674364	−	0.0555419i
$951$	7.38459			0.239462
$952$		0			0
$953$		−	41.4364i		−	1.34226i	−0.741342	−	0.671128i	$-0.765810\pi$
$953$		−	41.4364i		−	1.34226i	0.741342	−	0.671128i	$-0.234190\pi$
$954$	6.08557	+	10.5405i	0.197028	+	0.341262i
$955$	29.8834	−	32.4458i	0.967003	−	1.04992i
$956$	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	$-0.879259\pi$
$967$		−	23.0294i		−	0.740577i	0.928917	−	0.370288i	$-0.120741\pi$
$968$	4.56591	−	2.63613i	0.146754	−	0.0847284i
$969$	−4.10936	+	7.11762i	−0.132012	+	0.228651i
$970$	18.2728	−	19.8396i	0.586704	−	0.637013i
$971$	2.53163	+	4.38491i	0.0812439	+	0.140719i	0.903784	−	0.427988i	$-0.140777\pi$
$971$	2.53163	+	4.38491i	0.0812439	+	0.140719i	−0.822541	+	0.568706i	$0.807444\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$	−12.5263			−0.401368
$975$	1.56267	+	18.9732i	0.0500453	+	0.607628i
$976$	−6.54548	+	11.3371i	−0.209516	+	0.362892i
$977$	25.6528	+	14.8106i	0.820705	+	0.473834i	0.850660	−	0.525717i	$-0.176203\pi$
$977$	25.6528	+	14.8106i	0.820705	+	0.473834i	−0.0299545	+	0.999551i	$0.509536\pi$
$978$	−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
$985$	36.7090	−	11.4717i	1.16964	−	0.365518i
$986$	−18.0535			−0.574942
$987$		0			0
$988$			15.8815i			0.505259i
$989$	20.0501	+	34.7278i	0.637557	+	1.10428i
$990$	−3.93634	−	3.62546i	−0.125105	−	0.115225i
$991$	−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.k.949.6		16
5.4	even	2	inner	1470.2.n.k.949.2		16
7.2	even	3	inner	1470.2.n.k.79.2		16
7.3	odd	6		1470.2.g.j.589.5	yes	8
7.4	even	3		1470.2.g.k.589.8	yes	8
7.5	odd	6		1470.2.n.l.79.3		16
7.6	odd	2		1470.2.n.l.949.7		16
35.3	even	12		7350.2.a.dt.1.2		4
35.4	even	6		1470.2.g.k.589.4	yes	8
35.9	even	6	inner	1470.2.n.k.79.6		16
35.17	even	12		7350.2.a.ds.1.2		4
35.18	odd	12		7350.2.a.du.1.2		4
35.19	odd	6		1470.2.n.l.79.7		16
35.24	odd	6		1470.2.g.j.589.1	✓	8
35.32	odd	12		7350.2.a.dr.1.2		4
35.34	odd	2		1470.2.n.l.949.3		16

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.666969 - 2.13428i) q^{5} +1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.666969 - 2.13428i) q^{5} +1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.64475 - 1.51486i) 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} +(-4.11030 + 2.84700i) q^{25} +(-1.90374 - 3.29738i) q^{26} +1.00000i q^{27} +9.16246 q^{29} +(-0.666969 - 2.13428i) 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} +(-2.13428 + 0.666969i) q^{40} -3.19208 q^{41} -4.90755i q^{43} +(-1.19663 - 2.07263i) q^{44} +(1.51486 - 1.64475i) 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} +(-1.64475 - 1.51486i) q^{60} +(-6.54548 - 11.3371i) q^{61} +1.60673i q^{62} -1.00000 q^{64} +(-8.12624 + 2.53947i) 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} +(-4.98313 + 0.410420i) q^{75} -4.17113 q^{76} -3.80748i q^{78} +(-6.21302 - 10.7613i) q^{79} +(-1.51486 + 1.64475i) 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} +(-6.31867 + 6.86048i) 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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