LMFDB - Embedded newform 588.2.n.e.263.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(263,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.263"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.3
Character	$\chi$	$=$	588.263
Dual form			588.2.n.e.275.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09645 + 0.893190i) q^{2} +(-1.72058 - 0.199011i) q^{3} +(0.404424 - 1.95868i) q^{4} +(-1.79791 + 1.03802i) q^{5} +(2.06429 - 1.31860i) q^{6} +(1.30604 + 2.50883i) q^{8} +(2.92079 + 0.684828i) q^{9} +(1.04417 - 2.74402i) q^{10} +(-1.99399 + 3.45368i) q^{11} +(-1.08564 + 3.28959i) q^{12} +1.30998 q^{13} +(3.30003 - 1.42820i) q^{15} +(-3.67288 - 1.58428i) q^{16} +(2.54752 + 1.47081i) q^{17} +(-3.81419 + 1.85794i) q^{18} +(-0.949883 + 0.548415i) q^{19} +(1.30604 + 3.94134i) q^{20} +(-0.898482 - 5.56781i) q^{22} +(-3.75063 - 6.49627i) q^{23} +(-1.74787 - 4.57657i) q^{24} +(-0.345008 + 0.597572i) q^{25} +(-1.43634 + 1.17006i) q^{26} +(-4.88916 - 1.75957i) q^{27} +0.865568i q^{29} +(-2.34268 + 4.51351i) q^{30} +(-3.18742 - 1.84026i) q^{31} +(5.44221 - 1.54349i) q^{32} +(4.11813 - 5.54551i) q^{33} +(-4.10695 + 0.662741i) q^{34} +(2.52260 - 5.44394i) q^{36} +(-2.08850 - 3.61738i) q^{37} +(0.551664 - 1.44974i) q^{38} +(-2.25393 - 0.260701i) q^{39} +(-4.95238 - 3.15496i) q^{40} -7.01712i q^{41} -4.27597i q^{43} +(5.95826 + 5.30234i) q^{44} +(-5.96219 + 1.80059i) q^{45} +(9.91479 + 3.77285i) q^{46} +(-3.75063 - 6.49627i) q^{47} +(6.00420 + 3.45682i) q^{48} +(-0.155459 - 0.963368i) q^{50} +(-4.09050 - 3.03763i) q^{51} +(0.529789 - 2.56584i) q^{52} +(-4.27909 - 2.47053i) q^{53} +(6.93237 - 2.43766i) q^{54} -8.27923i q^{55} +(1.74349 - 0.754555i) q^{57} +(-0.773117 - 0.949056i) q^{58} +(-2.44458 + 4.23414i) q^{59} +(-1.46278 - 7.04131i) q^{60} +(2.05347 + 3.55672i) q^{61} +(5.13856 - 0.829212i) q^{62} +(-4.58850 + 6.55330i) q^{64} +(-2.35524 + 1.35980i) q^{65} +(0.437853 + 9.75868i) q^{66} +(-2.09778 - 1.21116i) q^{67} +(3.91113 - 4.39495i) q^{68} +(5.16042 + 11.9238i) q^{69} +0.901192 q^{71} +(2.09656 + 8.22219i) q^{72} +(6.50543 - 11.2677i) q^{73} +(5.52095 + 2.10087i) q^{74} +(0.712537 - 0.959509i) q^{75} +(0.690016 + 2.08231i) q^{76} +(2.70419 - 1.72734i) q^{78} +(8.97336 - 5.18077i) q^{79} +(8.24804 - 0.964154i) q^{80} +(8.06202 + 4.00048i) q^{81} +(6.26762 + 7.69395i) q^{82} -12.4386 q^{83} -6.10695 q^{85} +(3.81926 + 4.68841i) q^{86} +(0.172258 - 1.48928i) q^{87} +(-11.2690 - 0.491915i) q^{88} +(-7.38393 + 4.26311i) q^{89} +(4.92900 - 7.29963i) q^{90} +(-14.2410 + 4.71904i) q^{92} +(5.11797 + 3.80064i) q^{93} +(9.91479 + 3.77285i) q^{94} +(1.13854 - 1.97200i) q^{95} +(-9.67092 + 1.57265i) q^{96} -15.3909 q^{97} +(-8.18919 + 8.72195i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} - 2 q^{9} + 10 q^{10} + 12 q^{12} + 24 q^{13} - 10 q^{16} - 10 q^{18} + 28 q^{22} + 14 q^{24} - 12 q^{25} - 14 q^{30} - 10 q^{33} + 8 q^{34} + 44 q^{36} - 8 q^{37} - 34 q^{40} + 18 q^{45}+ \cdots - 72 q^{97}+O(q^{100}) $ 24 * q - 2 * q^4 - 2 * q^9 + 10 * q^10 + 12 * q^12 + 24 * q^13 - 10 * q^16 - 10 * q^18 + 28 * q^22 + 14 * q^24 - 12 * q^25 - 14 * q^30 - 10 * q^33 + 8 * q^34 + 44 * q^36 - 8 * q^37 - 34 * q^40 + 18 * q^45 + 24 * q^46 - 8 * q^48 - 16 * q^52 - 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 - 4 * q^61 - 68 * q^64 - 30 * q^66 - 36 * q^69 + 20 * q^72 + 24 * q^76 - 104 * q^78 + 26 * q^81 + 68 * q^82 - 40 * q^85 - 34 * q^88 + 40 * q^90 - 6 * q^93 + 24 * q^94 + 62 * q^96 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.09645	+	0.893190i	−0.775310	+	0.631581i
$2$	−1.09645	+	0.893190i	−0.775310	+	0.631581i
$3$	−1.72058	−	0.199011i	−0.993377	−	0.114899i
$3$	−1.72058	−	0.199011i	−0.993377	−	0.114899i
$4$	0.404424	−	1.95868i	0.202212	−	0.979342i
$5$	−1.79791	+	1.03802i	−0.804051	+	0.464219i	−0.844886	−	0.534947i	$-0.820332\pi$
$5$	−1.79791	+	1.03802i	−0.804051	+	0.464219i	0.0408349	+	0.999166i	$0.486998\pi$
$6$	2.06429	−	1.31860i	0.842743	−	0.538315i
$7$		0			0
$7$		0			0
$8$	1.30604	+	2.50883i	0.461756	+	0.887007i
$9$	2.92079	+	0.684828i	0.973596	+	0.228276i
$10$	1.04417	−	2.74402i	0.330197	−	0.867736i
$11$	−1.99399	+	3.45368i	−0.601209	+	1.04132i	0.391429	+	0.920208i	$0.371981\pi$
$11$	−1.99399	+	3.45368i	−0.601209	+	1.04132i	−0.992638	+	0.121117i	$0.961353\pi$
$12$	−1.08564	+	3.28959i	−0.313398	+	0.949622i
$13$	1.30998			0.363324			0.181662	−	0.983361i	$-0.441852\pi$
$13$	1.30998			0.363324			0.181662	+	0.983361i	$0.441852\pi$
$14$		0			0
$15$	3.30003	−	1.42820i	0.852064	−	0.368760i
$16$	−3.67288	−	1.58428i	−0.918221	−	0.396069i
$17$	2.54752	+	1.47081i	0.617863	+	0.356724i	0.776037	−	0.630688i	$-0.217227\pi$
$17$	2.54752	+	1.47081i	0.617863	+	0.356724i	−0.158173	+	0.987411i	$0.550560\pi$
$18$	−3.81419	+	1.85794i	−0.899014	+	0.437920i
$19$	−0.949883	+	0.548415i	−0.217918	+	0.125815i	−0.604986	−	0.796236i	$-0.706821\pi$
$19$	−0.949883	+	0.548415i	−0.217918	+	0.125815i	0.387068	+	0.922051i	$0.373488\pi$
$20$	1.30604	+	3.94134i	0.292040	+	0.881311i
$21$		0			0
$22$	−0.898482	−	5.56781i	−0.191557	−	1.18706i
$23$	−3.75063	−	6.49627i	−0.782059	−	1.35457i	−0.930740	−	0.365681i	$-0.880836\pi$
$23$	−3.75063	−	6.49627i	−0.782059	−	1.35457i	0.148681	−	0.988885i	$-0.452497\pi$
$24$	−1.74787	−	4.57657i	−0.356782	−	0.934188i
$25$	−0.345008	+	0.597572i	−0.0690016	+	0.119514i
$26$	−1.43634	+	1.17006i	−0.281689	+	0.229468i
$27$	−4.88916	−	1.75957i	−0.940920	−	0.338630i
$28$		0			0
$29$			0.865568i			0.160732i	0.996765	+	0.0803660i	$0.0256089\pi$
$29$			0.865568i			0.160732i	−0.996765	+	0.0803660i	$0.974391\pi$
$30$	−2.34268	+	4.51351i	−0.427712	+	0.824050i
$31$	−3.18742	−	1.84026i	−0.572477	−	0.330520i	0.185661	−	0.982614i	$-0.440557\pi$
$31$	−3.18742	−	1.84026i	−0.572477	−	0.330520i	−0.758138	+	0.652094i	$0.773891\pi$
$32$	5.44221	−	1.54349i	0.962055	−	0.272854i
$33$	4.11813	−	5.54551i	0.716875	−	0.965350i
$34$	−4.10695	+	0.662741i	−0.704336	+	0.113659i
$35$		0			0
$36$	2.52260	−	5.44394i	0.420433	−	0.907324i
$37$	−2.08850	−	3.61738i	−0.343347	−	0.594694i	0.641705	−	0.766952i	$-0.278227\pi$
$37$	−2.08850	−	3.61738i	−0.343347	−	0.594694i	−0.985052	+	0.172257i	$0.944894\pi$
$38$	0.551664	−	1.44974i	0.0894918	−	0.235179i
$39$	−2.25393	−	0.260701i	−0.360918	−	0.0417456i
$40$	−4.95238	−	3.15496i	−0.783041	−	0.498842i
$41$		−	7.01712i		−	1.09589i	−0.836514	−	0.547945i	$-0.815410\pi$
$41$		−	7.01712i		−	1.09589i	0.836514	−	0.547945i	$-0.184590\pi$
$42$		0			0
$43$		−	4.27597i		−	0.652080i	−0.945356	−	0.326040i	$-0.894286\pi$
$43$		−	4.27597i		−	0.652080i	0.945356	−	0.326040i	$-0.105714\pi$
$44$	5.95826	+	5.30234i	0.898241	+	0.799358i
$45$	−5.96219	+	1.80059i	−0.888791	+	0.268416i
$46$	9.91479	+	3.77285i	1.46186	+	0.556276i
$47$	−3.75063	−	6.49627i	−0.547085	−	0.947579i	−0.998473	−	0.0552509i	$-0.982404\pi$
$47$	−3.75063	−	6.49627i	−0.547085	−	0.947579i	0.451388	−	0.892328i	$-0.350929\pi$
$48$	6.00420	+	3.45682i	0.866632	+	0.498949i
$49$		0			0
$50$	−0.155459	−	0.963368i	−0.0219853	−	0.136241i
$51$	−4.09050	−	3.03763i	−0.572784	−	0.425353i
$52$	0.529789	−	2.56584i	0.0734685	−	0.355818i
$53$	−4.27909	−	2.47053i	−0.587778	−	0.339354i	0.176440	−	0.984311i	$-0.443542\pi$
$53$	−4.27909	−	2.47053i	−0.587778	−	0.339354i	−0.764218	+	0.644957i	$0.776875\pi$
$54$	6.93237	−	2.43766i	0.943377	−	0.331724i
$55$		−	8.27923i		−	1.11637i
$56$		0			0
$57$	1.74349	−	0.754555i	0.230931	−	0.0999432i
$58$	−0.773117	−	0.949056i	−0.101515	−	0.124617i
$59$	−2.44458	+	4.23414i	−0.318257	+	0.551238i	−0.980125	−	0.198383i	$-0.936431\pi$
$59$	−2.44458	+	4.23414i	−0.318257	+	0.551238i	0.661867	+	0.749621i	$0.269764\pi$
$60$	−1.46278	−	7.04131i	−0.188844	−	0.909029i
$61$	2.05347	+	3.55672i	0.262920	+	0.455391i	0.967017	−	0.254713i	$-0.0819810\pi$
$61$	2.05347	+	3.55672i	0.262920	+	0.455391i	−0.704096	+	0.710104i	$0.748648\pi$
$62$	5.13856	−	0.829212i	0.652597	−	0.105310i
$63$		0			0
$64$	−4.58850	+	6.55330i	−0.573562	+	0.819162i
$65$	−2.35524	+	1.35980i	−0.292131	+	0.168662i
$66$	0.437853	+	9.75868i	0.0538960	+	1.20121i
$67$	−2.09778	−	1.21116i	−0.256285	−	0.147966i	0.366354	−	0.930476i	$-0.380606\pi$
$67$	−2.09778	−	1.21116i	−0.256285	−	0.147966i	−0.622639	+	0.782509i	$0.713939\pi$
$68$	3.91113	−	4.39495i	0.474294	−	0.532966i
$69$	5.16042	+	11.9238i	0.621242	+	1.43545i
$70$		0			0
$71$	0.901192			0.106952			0.0534759	−	0.998569i	$-0.482970\pi$
$71$	0.901192			0.106952			0.0534759	+	0.998569i	$0.482970\pi$
$72$	2.09656	+	8.22219i	0.247082	+	0.968995i
$73$	6.50543	−	11.2677i	0.761403	−	1.31879i	−0.180725	−	0.983534i	$-0.557844\pi$
$73$	6.50543	−	11.2677i	0.761403	−	1.31879i	0.942128	−	0.335255i	$-0.108822\pi$
$74$	5.52095	+	2.10087i	0.641798	+	0.244221i
$75$	0.712537	−	0.959509i	0.0822767	−	0.110795i
$76$	0.690016	+	2.08231i	0.0791503	+	0.238858i
$77$		0			0
$78$	2.70419	−	1.72734i	0.306189	−	0.195583i
$79$	8.97336	−	5.18077i	1.00958	−	0.582882i	0.0985123	−	0.995136i	$-0.468592\pi$
$79$	8.97336	−	5.18077i	1.00958	−	0.582882i	0.911069	+	0.412254i	$0.135258\pi$
$80$	8.24804	−	0.964154i	0.922159	−	0.107796i
$81$	8.06202	+	4.00048i	0.895780	+	0.444498i
$82$	6.26762	+	7.69395i	0.692143	+	0.849654i
$83$	−12.4386			−1.36531			−0.682657	−	0.730739i	$-0.739176\pi$
$83$	−12.4386			−1.36531			−0.682657	+	0.730739i	$0.739176\pi$
$84$		0			0
$85$	−6.10695			−0.662391
$86$	3.81926	+	4.68841i	0.411841	+	0.505564i
$87$	0.172258	−	1.48928i	0.0184680	−	0.159668i
$88$	−11.2690	−	0.491915i	−1.20127	−	0.0524384i
$89$	−7.38393	+	4.26311i	−0.782695	+	0.451889i	−0.837385	−	0.546614i	$-0.815916\pi$
$89$	−7.38393	+	4.26311i	−0.782695	+	0.451889i	0.0546896	+	0.998503i	$0.482583\pi$
$90$	4.92900	−	7.29963i	0.519562	−	0.769449i
$91$		0			0
$92$	−14.2410	+	4.71904i	−1.48473	+	0.491994i
$93$	5.11797	+	3.80064i	0.530709	+	0.394108i
$94$	9.91479	+	3.77285i	1.02263	+	0.389139i
$95$	1.13854	−	1.97200i	0.116811	−	0.202323i
$96$	−9.67092	+	1.57265i	−0.987035	+	0.160508i
$97$	−15.3909			−1.56271			−0.781354	−	0.624088i	$-0.785471\pi$
$97$	−15.3909			−1.56271			−0.781354	+	0.624088i	$0.785471\pi$
$98$		0			0
$99$	−8.18919	+	8.72195i	−0.823045	+	0.876588i
$100$	1.03092	+	0.917434i	0.103092	+	0.0917434i
$101$	−5.28731	−	3.05263i	−0.526107	−	0.303748i	0.213322	−	0.976982i	$-0.431572\pi$
$101$	−5.28731	−	3.05263i	−0.526107	−	0.303748i	−0.739430	+	0.673234i	$0.764905\pi$
$102$	7.19822	−	0.322971i	0.712730	−	0.0319789i
$103$	6.17682	−	3.56619i	0.608620	−	0.351387i	−0.163805	−	0.986493i	$-0.552377\pi$
$103$	6.17682	−	3.56619i	0.608620	−	0.351387i	0.772425	+	0.635106i	$0.219044\pi$
$104$	1.71090	+	3.28653i	0.167767	+	0.322271i
$105$		0			0
$106$	6.89848	−	1.11321i	0.670040	−	0.108125i
$107$	−1.20838	−	2.09297i	−0.116818	−	0.202335i	0.801687	−	0.597744i	$-0.203936\pi$
$107$	−1.20838	−	2.09297i	−0.116818	−	0.202335i	−0.918505	+	0.395409i	$0.870603\pi$
$108$	−5.42374	+	8.86471i	−0.521899	+	0.853007i
$109$	3.39848	−	5.88634i	0.325516	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$109$	3.39848	−	5.88634i	0.325516	−	0.563809i	0.981617	+	0.190864i	$0.0611288\pi$
$110$	7.39492	+	9.07779i	0.705078	+	0.865534i
$111$	2.87353	+	6.63963i	0.272743	+	0.630206i
$112$		0			0
$113$		−	3.16365i		−	0.297611i	−0.988867	−	0.148805i	$-0.952457\pi$
$113$		−	3.16365i		−	0.297611i	0.988867	−	0.148805i	$-0.0475428\pi$
$114$	−1.23770	+	2.38460i	−0.115921	+	0.223338i
$115$	13.4866	+	7.78649i	1.25763	+	0.726094i
$116$	1.69537	+	0.350057i	0.157412	+	0.0325019i
$117$	3.82619	+	0.897114i	0.353731	+	0.0829382i
$118$	−1.10152	−	6.82601i	−0.101403	−	0.628386i
$119$		0			0
$120$	7.89310	+	6.41393i	0.720538	+	0.585509i
$121$	−2.45196	−	4.24691i	−0.222905	−	0.386083i
$122$	−5.42837	−	2.06564i	−0.491461	−	0.187014i
$123$	−1.39648	+	12.0735i	−0.125917	+	1.08863i
$124$	−4.89355	+	5.49890i	−0.439454	+	0.493816i
$125$		−	11.8128i		−	1.05657i
$126$		0			0
$127$			15.0889i			1.33892i	0.742848	+	0.669460i	$0.233474\pi$
$127$			15.0889i			1.33892i	−0.742848	+	0.669460i	$0.766526\pi$
$128$	−0.822259	−	11.2838i	−0.0726781	−	0.997355i
$129$	−0.850965	+	7.35715i	−0.0749233	+	0.647761i
$130$	1.36785	−	3.59463i	0.119969	−	0.315270i
$131$	3.70488	+	6.41704i	0.323697	+	0.560660i	0.981248	−	0.192751i	$-0.0617408\pi$
$131$	3.70488	+	6.41704i	0.323697	+	0.560660i	−0.657551	+	0.753410i	$0.728407\pi$
$132$	−9.19644	−	10.3089i	−0.800447	−	0.897271i
$133$		0			0
$134$	3.38192	−	0.545742i	0.292153	−	0.0471449i
$135$	10.6168	−	1.91152i	0.913745	−	0.164517i
$136$	−0.362848	+	8.31224i	−0.0311140	+	0.712768i
$137$	−13.0764	−	7.54965i	−1.11719	−	0.645010i	−0.176508	−	0.984299i	$-0.556480\pi$
$137$	−13.0764	−	7.54965i	−1.11719	−	0.645010i	−0.940682	+	0.339290i	$0.889813\pi$
$138$	−16.3084	−	8.46464i	−1.38826	−	0.720558i
$139$			14.4761i			1.22785i	0.789364	+	0.613925i	$0.210410\pi$
$139$			14.4761i			1.22785i	−0.789364	+	0.613925i	$0.789590\pi$
$140$		0			0
$141$	5.16042	+	11.9238i	0.434586	+	1.00416i
$142$	−0.988116	+	0.804935i	−0.0829208	+	0.0675487i
$143$	−2.61209	+	4.52427i	−0.218434	+	0.378338i
$144$	−9.64276	−	7.14263i	−0.803563	−	0.595219i
$145$	−0.898482	−	1.55622i	−0.0746148	−	0.129237i
$146$	2.93132	+	18.1651i	0.242598	+	1.50336i
$147$		0			0
$148$	−7.92995	+	2.62775i	−0.651838	+	0.216000i
$149$	−9.86511	+	5.69562i	−0.808181	+	0.466604i	−0.846324	−	0.532669i	$-0.821189\pi$
$149$	−9.86511	+	5.69562i	−0.808181	+	0.466604i	0.0381428	+	0.999272i	$0.487856\pi$
$150$	0.0757594	+	1.68849i	0.00618573	+	0.137865i
$151$	−0.795186	−	0.459101i	−0.0647113	−	0.0373611i	0.467295	−	0.884101i	$-0.345229\pi$
$151$	−0.795186	−	0.459101i	−0.0647113	−	0.0373611i	−0.532007	+	0.846740i	$0.678562\pi$
$152$	−2.61647	−	1.66684i	−0.212224	−	0.135199i
$153$	6.43351	+	6.04054i	0.520118	+	0.488348i
$154$		0			0
$155$	7.64093			0.613734
$156$	−1.42217	+	4.30930i	−0.113865	+	0.345020i
$157$	−4.36346	+	7.55773i	−0.348242	+	0.603172i	−0.985937	−	0.167116i	$-0.946555\pi$
$157$	−4.36346	+	7.55773i	−0.348242	+	0.603172i	0.637695	+	0.770289i	$0.279888\pi$
$158$	−5.21146	+	13.6954i	−0.414602	+	1.08955i
$159$	6.87085	+	5.10234i	0.544894	+	0.404642i
$160$	−8.18242	+	8.42422i	−0.646877	+	0.665993i
$161$		0			0
$162$	−12.4128	+	2.81457i	−0.975244	+	0.221134i
$163$	−7.78729	+	4.49599i	−0.609948	+	0.352153i	−0.772945	−	0.634473i	$-0.781217\pi$
$163$	−7.78729	+	4.49599i	−0.609948	+	0.352153i	0.162997	+	0.986627i	$0.447884\pi$
$164$	−13.7443	−	2.83789i	−1.07325	−	0.221602i
$165$	−1.64766	+	14.2451i	−0.128270	+	1.10898i
$166$	13.6384	−	11.1100i	1.05854	−	0.862306i
$167$	16.1830			1.25228			0.626141	−	0.779710i	$-0.284633\pi$
$167$	16.1830			1.25228			0.626141	+	0.779710i	$0.284633\pi$
$168$		0			0
$169$	−11.2839			−0.867996
$170$	6.69599	−	5.45466i	0.513559	−	0.418354i
$171$	−3.14998	+	0.951298i	−0.240885	+	0.0727476i
$172$	−8.37528	−	1.72931i	−0.638609	−	0.131858i
$173$	3.66216	−	2.11435i	0.278429	−	0.160751i	−0.354283	−	0.935138i	$-0.615275\pi$
$173$	3.66216	−	2.11435i	0.278429	−	0.160751i	0.632712	+	0.774387i	$0.281942\pi$
$174$	1.14134	+	1.78679i	0.0865245	+	0.135456i
$175$		0			0
$176$	12.7953	−	9.52595i	0.964479	−	0.718046i
$177$	5.04874	−	6.79868i	0.379486	−	0.511020i
$178$	4.28837	−	11.2696i	0.321427	−	0.844689i
$179$	3.27593	−	5.67408i	0.244855	−	0.424101i	−0.717236	−	0.696830i	$-0.754593\pi$
$179$	3.27593	−	5.67408i	0.244855	−	0.424101i	0.962091	+	0.272729i	$0.0879264\pi$
$180$	1.11554	+	12.4062i	0.0831471	+	0.924707i
$181$	12.2839			0.913058			0.456529	−	0.889708i	$-0.349092\pi$
$181$	12.2839			0.913058			0.456529	+	0.889708i	$0.349092\pi$
$182$		0			0
$183$	−2.82534	−	6.52828i	−0.208855	−	0.482585i
$184$	11.3996	−	17.8941i	0.840389	−	1.31917i
$185$	7.50987	+	4.33583i	0.552137	+	0.318776i
$186$	−9.00632	+	0.404097i	−0.660375	+	0.0296298i
$187$	−10.1594	+	5.86554i	−0.742930	+	0.428931i
$188$	−14.2410	+	4.71904i	−1.03863	+	0.344171i
$189$		0			0
$190$	0.513020	+	3.17914i	0.0372184	+	0.230639i
$191$	11.8662	+	20.5529i	0.858611	+	1.48716i	0.873254	+	0.487266i	$0.162006\pi$
$191$	11.8662	+	20.5529i	0.858611	+	1.48716i	−0.0146426	+	0.999893i	$0.504661\pi$
$192$	9.19905	−	10.3623i	0.663885	−	0.747835i
$193$	1.98698	−	3.44155i	0.143026	−	0.247728i	−0.785609	−	0.618724i	$-0.787650\pi$
$193$	1.98698	−	3.44155i	0.143026	−	0.247728i	0.928635	+	0.370995i	$0.120983\pi$
$194$	16.8754	−	13.7470i	1.21158	−	0.986976i
$195$	4.32298	−	1.87092i	0.309575	−	0.133979i
$196$		0			0
$197$		−	19.7720i		−	1.40870i	−0.709853	−	0.704350i	$-0.751239\pi$
$197$		−	19.7720i		−	1.40870i	0.709853	−	0.704350i	$-0.248761\pi$
$198$	1.18872	−	16.8777i	0.0844788	−	1.19945i
$199$	−6.63939	−	3.83325i	−0.470654	−	0.271732i	0.245859	−	0.969305i	$-0.420930\pi$
$199$	−6.63939	−	3.83325i	−0.470654	−	0.271732i	−0.716513	+	0.697573i	$0.754263\pi$
$200$	−1.94980	−	0.0851134i	−0.137872	−	0.00601843i
$201$	3.36837	+	2.50137i	0.237587	+	0.176433i
$202$	8.52388	−	1.37550i	0.599738	−	0.0967801i
$203$		0			0
$204$	−7.60405	+	6.78350i	−0.532390	+	0.474940i
$205$	7.28394	+	12.6162i	0.508733	+	0.881151i
$206$	−3.58732	+	9.42723i	−0.249940	+	0.656826i
$207$	−6.50595	−	21.5428i	−0.452195	−	1.49733i
$208$	−4.81142	−	2.07538i	−0.333612	−	0.143901i
$209$		−	4.37413i		−	0.302565i
$210$		0			0
$211$		−	11.7483i		−	0.808789i	−0.914585	−	0.404395i	$-0.867482\pi$
$211$		−	11.7483i		−	0.808789i	0.914585	−	0.404395i	$-0.132518\pi$
$212$	−6.56956	+	7.38224i	−0.451199	+	0.507014i
$213$	−1.55057	−	0.179347i	−0.106243	−	0.0122887i
$214$	3.19435	+	1.21554i	0.218361	+	0.0830923i
$215$	4.43857	+	7.68782i	0.302708	+	0.524305i
$216$	−1.97099	−	14.5642i	−0.134109	−	0.990967i
$217$		0			0
$218$	1.53134	+	9.48959i	0.103716	+	0.642716i
$219$	−13.4355	+	18.0924i	−0.907888	+	1.22257i
$220$	−16.2164	−	3.34832i	−1.09331	−	0.225743i
$221$	3.33720	+	1.92674i	0.224485	+	0.129606i
$222$	−9.08115	−	4.71345i	−0.609487	−	0.316346i
$223$		−	14.5202i		−	0.972345i	−0.873863	−	0.486173i	$-0.838393\pi$
$223$		−	14.5202i		−	0.972345i	0.873863	−	0.486173i	$-0.161607\pi$
$224$		0			0
$225$	−1.41693	+	1.50911i	−0.0944620	+	0.100607i
$226$	2.82574	+	3.46879i	0.187965	+	0.230741i
$227$	10.7314	−	18.5874i	0.712271	−	1.23369i	−0.251732	−	0.967797i	$-0.581000\pi$
$227$	10.7314	−	18.5874i	0.712271	−	1.23369i	0.964003	−	0.265892i	$-0.0856665\pi$
$228$	−0.772825	−	3.72010i	−0.0511816	−	0.246370i
$229$	−9.81541	−	17.0008i	−0.648621	−	1.12344i	−0.983453	−	0.181166i	$-0.942013\pi$
$229$	−9.81541	−	17.0008i	−0.648621	−	1.12344i	0.334832	−	0.942278i	$-0.391320\pi$
$230$	−21.7422	+	3.50856i	−1.43364	+	0.231348i
$231$		0			0
$232$	−2.17157	+	1.13047i	−0.142570	+	0.0742190i
$233$	12.3530	−	7.13202i	0.809273	−	0.467234i	−0.0374302	−	0.999299i	$-0.511917\pi$
$233$	12.3530	−	7.13202i	0.809273	−	0.467234i	0.846703	+	0.532065i	$0.178584\pi$
$234$	−4.99653	+	2.43387i	−0.326633	+	0.159107i
$235$	13.4866	+	7.78649i	0.879768	+	0.507934i
$236$	7.30469	+	6.50055i	0.475495	+	0.423150i
$237$	−16.4704	+	7.12813i	−1.06987	+	0.463022i
$238$		0			0
$239$	−15.2819			−0.988501			−0.494251	−	0.869320i	$-0.664557\pi$
$239$	−15.2819			−0.988501			−0.494251	+	0.869320i	$0.664557\pi$
$240$	−14.3833	+	0.0174537i	−0.928437	+	0.00112663i
$241$	−2.95196	+	5.11294i	−0.190152	+	0.329353i	−0.945301	−	0.326201i	$-0.894231\pi$
$241$	−2.95196	+	5.11294i	−0.190152	+	0.329353i	0.755148	+	0.655554i	$0.227565\pi$
$242$	6.48175	+	2.46648i	0.416663	+	0.158551i
$243$	−13.0752	−	8.48757i	−0.838775	−	0.544478i
$244$	7.79696	−	2.58368i	0.499149	−	0.165403i
$245$		0			0
$246$	−9.25276	−	14.4854i	−0.589934	−	0.923554i
$247$	−1.24433	+	0.718415i	−0.0791749	+	0.0457116i
$248$	0.453991	−	10.4002i	0.0288284	−	0.660411i
$249$	21.4016	+	2.47542i	1.35627	+	0.156873i
$250$	10.5510	+	12.9521i	0.667306	+	0.819166i
$251$	23.7400			1.49845			0.749226	−	0.662314i	$-0.230425\pi$
$251$	23.7400			1.49845			0.749226	+	0.662314i	$0.230425\pi$
$252$		0			0
$253$	29.9148			1.88073
$254$	−13.4772	−	16.5442i	−0.845636	−	1.03808i
$255$	10.5075	+	1.21535i	0.658004	+	0.0761081i
$256$	10.9801	+	11.6377i	0.686258	+	0.727358i
$257$	−12.8177	+	7.40033i	−0.799549	+	0.461620i	−0.843314	−	0.537422i	$-0.819398\pi$
$257$	−12.8177	+	7.40033i	−0.799549	+	0.461620i	0.0437643	+	0.999042i	$0.486065\pi$
$258$	−5.63829	−	8.82685i	−0.351025	−	0.549536i
$259$		0			0
$260$	1.71090	+	5.16309i	0.106105	+	0.320202i
$261$	−0.592766	+	2.52814i	−0.0366913	+	0.156488i
$262$	−9.79387	−	3.72683i	−0.605067	−	0.230244i
$263$	6.95299	−	12.0429i	0.428740	−	0.742599i	−0.568022	−	0.823013i	$-0.692291\pi$
$263$	6.95299	−	12.0429i	0.428740	−	0.742599i	0.996761	+	0.0804148i	$0.0256245\pi$
$264$	19.2912	+	3.08902i	1.18729	+	0.190116i
$265$	10.2579			0.630138
$266$		0			0
$267$	13.5530	−	5.86554i	0.829433	−	0.358965i
$268$	−3.22066	+	3.61907i	−0.196733	+	0.221070i
$269$	7.15156	+	4.12896i	0.436039	+	0.251747i	0.701916	−	0.712260i	$-0.252328\pi$
$269$	7.15156	+	4.12896i	0.436039	+	0.251747i	−0.265877	+	0.964007i	$0.585662\pi$
$270$	−9.93345	+	11.5787i	−0.604530	+	0.704656i
$271$	4.59472	−	2.65276i	0.279109	−	0.161144i	−0.353911	−	0.935279i	$-0.615148\pi$
$271$	4.59472	−	2.65276i	0.279109	−	0.161144i	0.633020	+	0.774135i	$0.281815\pi$
$272$	−7.02656	−	9.43808i	−0.426048	−	0.572268i
$273$		0			0
$274$	21.0809	−	3.40184i	1.27354	−	0.205513i
$275$	−1.37588	−	2.38310i	−0.0829688	−	0.143706i
$276$	25.4419	−	5.28537i	1.53142	−	0.318142i
$277$	−6.30239	+	10.9161i	−0.378674	+	0.655883i	−0.990870	−	0.134824i	$-0.956953\pi$
$277$	−6.30239	+	10.9161i	−0.378674	+	0.655883i	0.612196	+	0.790706i	$0.290287\pi$
$278$	−12.9299	−	15.8724i	−0.775486	−	0.951965i
$279$	−8.04951	−	7.55783i	−0.481912	−	0.452476i
$280$		0			0
$281$			2.02977i			0.121086i	0.998166	+	0.0605428i	$0.0192832\pi$
$281$			2.02977i			0.121086i	−0.998166	+	0.0605428i	$0.980717\pi$
$282$	−16.3084	−	8.46464i	−0.971149	−	0.504062i
$283$	−6.64918	−	3.83891i	−0.395253	−	0.228199i	0.289181	−	0.957274i	$-0.406617\pi$
$283$	−6.64918	−	3.83891i	−0.395253	−	0.228199i	−0.684434	+	0.729075i	$0.739950\pi$
$284$	0.364463	−	1.76515i	0.0216269	−	0.104742i
$285$	−2.35139	+	3.16641i	−0.139285	+	0.187562i
$286$	−1.17700	−	7.29374i	−0.0695972	−	0.431288i
$287$		0			0
$288$	16.9526	−	0.781244i	0.998940	−	0.0460352i
$289$	−4.17344	−	7.22861i	−0.245497	−	0.425212i
$290$	2.37514	+	0.903805i	0.139473	+	0.0530732i
$291$	26.4813	+	3.06296i	1.55236	+	0.179554i
$292$	−19.4390	−	17.2990i	−1.13758	−	1.01235i
$293$		−	1.55539i		−	0.0908671i	−0.998967	−	0.0454336i	$-0.985533\pi$
$293$		−	1.55539i		−	0.0908671i	0.998967	−	0.0454336i	$-0.0144669\pi$
$294$		0			0
$295$		−	10.1501i		−	0.590964i
$296$	6.34775	−	9.96416i	0.368955	−	0.579155i
$297$	15.8259	−	13.3771i	0.918313	−	0.776216i
$298$	5.72937	−	15.0564i	0.331893	−	0.872194i
$299$	−4.91326	−	8.51001i	−0.284141	−	0.492147i
$300$	−1.59121	−	1.78368i	−0.0918685	−	0.102981i
$301$		0			0
$302$	1.28195	−	0.206869i	0.0737679	−	0.0119040i
$303$	8.48974	+	6.30453i	0.487723	+	0.362186i
$304$	4.35765	−	0.509387i	0.249928	−	0.0292154i
$305$	−7.38393	−	4.26311i	−0.422803	−	0.244105i
$306$	−12.4494	−	0.876828i	−0.711684	−	0.0501249i
$307$			31.5800i			1.80237i	0.433437	+	0.901184i	$0.357301\pi$
$307$			31.5800i			1.80237i	−0.433437	+	0.901184i	$0.642699\pi$
$308$		0			0
$309$	−11.3374	+	4.90665i	−0.644963	+	0.279130i
$310$	−8.37793	+	6.82480i	−0.475834	+	0.387623i
$311$	9.13857	−	15.8285i	0.518201	−	0.897550i	−0.481575	−	0.876405i	$-0.659935\pi$
$311$	9.13857	−	15.8285i	0.518201	−	0.897550i	0.999776	−	0.0211458i	$-0.00673141\pi$
$312$	−2.28968	−	5.99523i	−0.129627	−	0.339413i
$313$	14.8909	+	25.7918i	0.841683	+	1.45784i	0.888471	+	0.458933i	$0.151768\pi$
$313$	14.8909	+	25.7918i	0.841683	+	1.45784i	−0.0467882	+	0.998905i	$0.514899\pi$
$314$	−1.96616	−	12.1841i	−0.110957	−	0.687589i
$315$		0			0
$316$	−6.51845	−	19.6712i	−0.366691	−	1.10659i
$317$	−15.3252	+	8.84800i	−0.860748	+	0.496953i	−0.864263	−	0.503041i	$-0.832215\pi$
$317$	−15.3252	+	8.84800i	−0.860748	+	0.496953i	0.00351474	+	0.999994i	$0.498881\pi$
$318$	−12.0909	+	0.542497i	−0.678026	+	0.0304217i
$319$	−2.98940	−	1.72593i	−0.167374	−	0.0966336i
$320$	1.44723	−	16.5452i	0.0809027	−	0.924906i
$321$	1.66258	+	3.84160i	0.0927964	+	0.214417i
$322$		0			0
$323$	−3.22646			−0.179525
$324$	11.0961	−	14.1731i	0.616453	−	0.787392i
$325$	−0.451955	+	0.782809i	−0.0250700	+	0.0434224i
$326$	4.52263	−	11.8852i	0.250485	−	0.658259i
$327$	−7.01881	+	9.45159i	−0.388141	+	0.522674i
$328$	17.6048	−	9.16466i	0.972062	−	0.506034i
$329$		0			0
$330$	−10.9170	−	17.0907i	−0.600959	−	0.940814i
$331$	−30.3818	+	17.5410i	−1.66994	+	0.964138i	−0.702268	+	0.711913i	$0.747829\pi$
$331$	−30.3818	+	17.5410i	−1.66994	+	0.964138i	−0.967668	+	0.252225i	$0.918838\pi$
$332$	−5.03047	+	24.3633i	−0.276083	+	1.33711i
$333$	−3.62278	−	11.9959i	−0.198527	−	0.657370i
$334$	−17.7440	+	14.4545i	−0.970907	+	0.790917i
$335$	5.02884			0.274755
$336$		0			0
$337$	−0.132987			−0.00724428			−0.00362214	−	0.999993i	$-0.501153\pi$
$337$	−0.132987			−0.00724428			−0.00362214	+	0.999993i	$0.501153\pi$
$338$	12.3723	−	10.0787i	0.672966	−	0.548209i
$339$	−0.629600	+	5.44330i	−0.0341952	+	0.295640i
$340$	−2.46979	+	11.9616i	−0.133943	+	0.648708i
$341$	12.7113	−	7.33889i	0.688357	−	0.397423i
$342$	2.60412	−	3.85658i	0.140815	−	0.208540i
$343$		0			0
$344$	10.7277	−	5.58461i	0.578399	−	0.301102i
$345$	−21.6552	−	16.0812i	−1.16587	−	0.865785i
$346$	−2.12688	+	5.58930i	−0.114342	+	0.300482i
$347$	0.0976681	−	0.169166i	0.00524310	−	0.00908131i	−0.863392	−	0.504534i	$-0.831664\pi$
$347$	0.0976681	−	0.169166i	0.00524310	−	0.00908131i	0.868635	+	0.495452i	$0.164998\pi$
$348$	−2.84736	−	0.939698i	−0.152635	−	0.0503731i
$349$	−5.80782			−0.310885			−0.155443	−	0.987845i	$-0.549680\pi$
$349$	−5.80782			−0.310885			−0.155443	+	0.987845i	$0.549680\pi$
$350$		0			0
$351$	−6.40472	−	2.30501i	−0.341859	−	0.123032i
$352$	−5.52094	+	21.8734i	−0.294267	+	1.16585i
$353$	−17.3154	−	9.99704i	−0.921604	−	0.532089i	−0.0374578	−	0.999298i	$-0.511926\pi$
$353$	−17.3154	−	9.99704i	−0.921604	−	0.532089i	−0.884147	+	0.467210i	$0.845259\pi$
$354$	0.536798	+	11.9639i	0.0285305	+	0.635875i
$355$	−1.62026	+	0.935460i	−0.0859947	+	0.0496490i
$356$	5.36385	+	16.1869i	0.284284	+	0.857903i
$357$		0			0
$358$	1.47612	+	9.14741i	0.0780155	+	0.483455i
$359$	6.95299	+	12.0429i	0.366965	+	0.635601i	0.989089	−	0.147317i	$-0.0470637\pi$
$359$	6.95299	+	12.0429i	0.366965	+	0.635601i	−0.622125	+	0.782918i	$0.713730\pi$
$360$	−12.3043	−	12.6065i	−0.648492	−	0.664421i
$361$	−8.89848	+	15.4126i	−0.468341	+	0.811191i
$362$	−13.4688	+	10.9719i	−0.707903	+	0.576670i
$363$	3.37360	+	7.79511i	0.177068	+	0.409137i
$364$		0			0
$365$			27.0112i			1.41383i
$366$	8.92885	+	4.63440i	0.466719	+	0.242244i
$367$	−16.2929	−	9.40672i	−0.850483	−	0.491027i	0.0103306	−	0.999947i	$-0.496712\pi$
$367$	−16.2929	−	9.40672i	−0.850483	−	0.491027i	−0.860814	+	0.508920i	$0.830045\pi$
$368$	3.48371	+	29.8021i	0.181601	+	1.55354i
$369$	4.80552	−	20.4955i	0.250165	−	1.06695i
$370$	−12.1069	+	1.95371i	−0.629410	+	0.101568i
$371$		0			0
$372$	9.51408	−	8.48742i	0.493282	−	0.440052i
$373$	−2.91150	−	5.04287i	−0.150752	−	0.261110i	0.780752	−	0.624841i	$-0.214836\pi$
$373$	−2.91150	−	5.04287i	−0.150752	−	0.261110i	−0.931504	+	0.363731i	$0.881503\pi$
$374$	5.90030	−	15.5056i	0.305097	−	0.801775i
$375$	−2.35087	+	20.3248i	−0.121398	+	1.04957i
$376$	11.3996	−	17.8941i	0.587889	−	0.922819i
$377$			1.13388i			0.0583978i
$378$		0			0
$379$		−	12.0598i		−	0.619469i	−0.950823	−	0.309735i	$-0.899760\pi$
$379$		−	12.0598i		−	0.619469i	0.950823	−	0.309735i	$-0.100240\pi$
$380$	−3.40208	−	3.02756i	−0.174523	−	0.155311i
$381$	3.00285	−	25.9616i	0.153841	−	1.33005i
$382$	−31.3685	−	11.9365i	−1.60495	−	0.610727i
$383$	6.07589	+	10.5237i	0.310463	+	0.537738i	0.978463	−	0.206423i	$-0.0661824\pi$
$383$	6.07589	+	10.5237i	0.310463	+	0.537738i	−0.667999	+	0.744162i	$0.732849\pi$
$384$	−0.830836	+	19.5783i	−0.0423984	+	0.999101i
$385$		0			0
$386$	0.895325	+	5.54825i	0.0455708	+	0.282399i
$387$	2.92831	−	12.4892i	0.148854	−	0.634862i
$388$	−6.22444	+	30.1459i	−0.315998	+	1.53043i
$389$	−1.04831	−	0.605241i	−0.0531513	−	0.0306869i	0.473189	−	0.880961i	$-0.343103\pi$
$389$	−1.04831	−	0.605241i	−0.0531513	−	0.0306869i	−0.526340	+	0.850274i	$0.676436\pi$
$390$	−3.06887	+	5.91262i	−0.155398	+	0.299397i
$391$		−	22.0658i		−	1.11592i
$392$		0			0
$393$	−5.09748	−	11.7783i	−0.257134	−	0.594139i
$394$	17.6602	+	21.6791i	0.889708	+	1.09218i
$395$	−10.7555	+	18.6291i	−0.541170	+	0.937334i
$396$	13.7716	+	19.5674i	0.692050	+	0.983299i
$397$	−4.77851	−	8.27663i	−0.239827	−	0.415392i	0.720838	−	0.693104i	$-0.243757\pi$
$397$	−4.77851	−	8.27663i	−0.239827	−	0.415392i	−0.960664	+	0.277712i	$0.910424\pi$
$398$	10.7036	−	1.72725i	0.536524	−	0.0865792i
$399$		0			0
$400$	2.21389	−	1.64822i	0.110695	−	0.0824111i
$401$	−9.73916	+	5.62291i	−0.486351	+	0.280795i	−0.723059	−	0.690786i	$-0.757265\pi$
$401$	−9.73916	+	5.62291i	−0.486351	+	0.280795i	0.236709	+	0.971581i	$0.423931\pi$
$402$	−5.92746	+	0.265954i	−0.295635	+	0.0132646i
$403$	−4.17546	−	2.41071i	−0.207995	−	0.120086i
$404$	−8.11746	+	9.12162i	−0.403859	+	0.453817i
$405$	−18.6474	+	1.17607i	−0.926597	+	0.0584393i
$406$		0			0
$407$	16.6577			0.825693
$408$	2.27854	−	14.2297i	0.112804	−	0.704473i
$409$	−7.78394	+	13.4822i	−0.384891	+	0.666651i	−0.991754	−	0.128155i	$-0.959094\pi$
$409$	−7.78394	+	13.4822i	−0.384891	+	0.666651i	0.606863	+	0.794807i	$0.292428\pi$
$410$	−19.2551	−	7.32710i	−0.950943	−	0.361860i
$411$	20.9965	+	15.5921i	1.03568	+	0.769102i
$412$	−4.48698	−	13.5407i	−0.221058	−	0.667101i
$413$		0			0
$414$	26.3753	+	17.8096i	1.29627	+	0.875295i
$415$	22.3635	−	12.9116i	1.09778	−	0.633805i
$416$	7.12920	−	2.02195i	0.349538	−	0.0991344i
$417$	2.88091	−	24.9074i	0.141079	−	1.21972i
$418$	3.90693	+	4.79603i	0.191094	+	0.234582i
$419$	−18.0336			−0.881000			−0.440500	−	0.897753i	$-0.645199\pi$
$419$	−18.0336			−0.881000			−0.440500	+	0.897753i	$0.645199\pi$
$420$		0			0
$421$	−12.4978			−0.609107			−0.304554	−	0.952495i	$-0.598507\pi$
$421$	−12.4978			−0.609107			−0.304554	+	0.952495i	$0.598507\pi$
$422$	10.4935	+	12.8815i	0.510816	+	0.627063i
$423$	−6.50595	−	21.5428i	−0.316330	−	1.04745i
$424$	0.609480	−	13.9622i	0.0295990	−	0.678062i
$425$	−1.75783	+	1.01488i	−0.0852672	+	0.0492290i
$426$	1.86032	−	1.18831i	0.0901329	−	0.0575738i
$427$		0			0
$428$	−4.58816	+	1.52038i	−0.221777	+	0.0734903i
$429$	5.39468	−	7.26453i	0.260458	−	0.350735i
$430$	−11.7334	−	4.46486i	−0.565833	−	0.215315i
$431$	−6.22304	+	10.7786i	−0.299753	+	0.519188i	−0.976079	−	0.217415i	$-0.930238\pi$
$431$	−6.22304	+	10.7786i	−0.299753	+	0.519188i	0.676326	+	0.736602i	$0.263571\pi$
$432$	15.1697	+	14.2085i	0.729851	+	0.683606i
$433$	0.497837			0.0239245			0.0119623	−	0.999928i	$-0.496192\pi$
$433$	0.497837			0.0239245			0.0119623	+	0.999928i	$0.496192\pi$
$434$		0			0
$435$	1.23621	+	2.85640i	0.0592715	+	0.136954i
$436$	−10.1551	−	9.03713i	−0.486339	−	0.432800i
$437$	7.12531	+	4.11380i	0.340850	+	0.196790i
$438$	−1.42851	−	31.8379i	−0.0682568	−	1.52128i
$439$	−4.03571	+	2.33002i	−0.192614	+	0.111206i	−0.593206	−	0.805051i	$-0.702138\pi$
$439$	−4.03571	+	2.33002i	−0.192614	+	0.111206i	0.400592	+	0.916257i	$0.368805\pi$
$440$	20.7712	−	10.8130i	0.990228	−	0.515491i
$441$		0			0
$442$	−5.38003	+	0.868179i	−0.255902	+	0.0412951i
$443$	−11.0349	−	19.1130i	−0.524283	−	0.908086i	−0.999600	−	0.0282709i	$-0.991000\pi$
$443$	−11.0349	−	19.1130i	−0.524283	−	0.908086i	0.475317	−	0.879815i	$-0.342333\pi$
$444$	14.1671	−	2.94311i	0.672339	−	0.139674i
$445$	8.85044	−	15.3294i	0.419551	−	0.726684i
$446$	12.9693	+	15.9207i	0.614114	+	0.753869i
$447$	18.1072	−	7.83651i	0.856441	−	0.370654i
$448$		0			0
$449$		−	6.02866i		−	0.284510i	−0.989830	−	0.142255i	$-0.954565\pi$
$449$		−	6.02866i		−	0.284510i	0.989830	−	0.142255i	$-0.0454353\pi$
$450$	0.205678	−	2.92026i	0.00969575	−	0.137662i
$451$	24.2349	+	13.9920i	1.14118	+	0.658859i
$452$	−6.19658	−	1.27945i	−0.291463	−	0.0601804i
$453$	1.27681	+	0.948170i	0.0599900	+	0.0445489i
$454$	4.83554	+	29.9654i	0.226943	+	1.40635i
$455$		0			0
$456$	4.17013	+	3.38865i	0.195284	+	0.158688i
$457$	19.1308	+	33.1356i	0.894902	+	1.55002i	0.833926	+	0.551877i	$0.186088\pi$
$457$	19.1308	+	33.1356i	0.894902	+	1.55002i	0.0609766	+	0.998139i	$0.480578\pi$
$458$	25.9471	+	9.87356i	1.21243	+	0.461361i
$459$	−9.86723	−	11.6736i	−0.460563	−	0.544875i
$460$	20.7056	−	23.2669i	0.965402	−	1.08483i
$461$			12.4563i			0.580148i	0.957004	+	0.290074i	$0.0936799\pi$
$461$			12.4563i			0.580148i	−0.957004	+	0.290074i	$0.906320\pi$
$462$		0			0
$463$			28.0609i			1.30410i	0.758176	+	0.652050i	$0.226091\pi$
$463$			28.0609i			1.30410i	−0.758176	+	0.652050i	$0.773909\pi$
$464$	1.37130	−	3.17913i	0.0636610	−	0.147587i
$465$	−13.1468	−	1.52063i	−0.609669	−	0.0705174i
$466$	−7.17427	+	18.8535i	−0.332342	+	0.873373i
$467$	−8.54830	−	14.8061i	−0.395568	−	0.685144i	0.597605	−	0.801790i	$-0.296119\pi$
$467$	−8.54830	−	14.8061i	−0.395568	−	0.685144i	−0.993174	+	0.116646i	$0.962786\pi$
$468$	3.30456	−	7.13147i	0.152753	−	0.329652i
$469$		0			0
$470$	−21.7422	+	3.50856i	−1.00289	+	0.161838i
$471$	9.01175	−	12.1353i	0.415239	−	0.559165i
$472$	−13.8155	−	0.603077i	−0.635909	−	0.0277589i
$473$	14.7679	+	8.52623i	0.679027	+	0.392036i
$474$	11.6923	−	22.5269i	0.537044	−	1.03469i
$475$		−	0.756831i		−	0.0347258i
$476$		0			0
$477$	−10.8064	−	10.1464i	−0.494792	−	0.464569i
$478$	16.7559	−	13.6496i	0.766395	−	0.624318i
$479$	−8.21329	+	14.2258i	−0.375275	+	0.649995i	−0.990368	−	0.138459i	$-0.955785\pi$
$479$	−8.21329	+	14.2258i	−0.375275	+	0.649995i	0.615093	+	0.788454i	$0.289118\pi$
$480$	15.7550	−	12.8661i	0.719115	−	0.587256i
$481$	−2.73590	−	4.73871i	−0.124746	−	0.216067i
$482$	−1.33014	−	8.24276i	−0.0605862	−	0.375447i
$483$		0			0
$484$	−9.30998	+	3.08505i	−0.423181	+	0.140230i
$485$	27.6715	−	15.9761i	1.25650	−	0.725439i
$486$	21.9174	−	2.37241i	0.994193	−	0.107615i
$487$	−27.7018	−	15.9937i	−1.25529	−	0.724742i	−0.283134	−	0.959080i	$-0.591374\pi$
$487$	−27.7018	−	15.9937i	−1.25529	−	0.724742i	−0.972155	+	0.234339i	$0.924708\pi$
$488$	−6.24129	+	9.79706i	−0.282530	+	0.443492i
$489$	14.2934	−	6.18596i	0.646370	−	0.279739i
$490$		0			0
$491$	2.03844			0.0919935			0.0459968	−	0.998942i	$-0.485354\pi$
$491$	2.03844			0.0919935			0.0459968	+	0.998942i	$0.485354\pi$
$492$	23.0834	+	7.61808i	1.04068	+	0.343450i
$493$	−1.27309	+	2.20505i	−0.0573369	+	0.0993104i
$494$	0.722671	−	1.89913i	0.0325145	−	0.0854460i
$495$	5.66985	−	24.1819i	0.254841	−	1.08689i
$496$	8.79153	+	11.8088i	0.394752	+	0.530231i
$497$		0			0
$498$	−25.6769	+	16.4015i	−1.15061	+	0.734970i
$499$	3.71805	−	2.14662i	0.166443	−	0.0960957i	−0.414465	−	0.910065i	$-0.636031\pi$
$499$	3.71805	−	2.14662i	0.166443	−	0.0960957i	0.580907	+	0.813970i	$0.302698\pi$
$500$	−23.1375	−	4.77736i	−1.03474	−	0.213650i
$501$	−27.8442	−	3.22060i	−1.24399	−	0.143886i
$502$	−26.0298	+	21.2043i	−1.16177	+	0.946394i
$503$	−26.3039			−1.17283			−0.586415	−	0.810010i	$-0.699461\pi$
$503$	−26.3039			−1.17283			−0.586415	+	0.810010i	$0.699461\pi$
$504$		0			0
$505$	12.6748			0.564023
$506$	−32.8002	+	26.7196i	−1.45815	+	1.18783i
$507$	19.4149	+	2.24563i	0.862247	+	0.0997318i
$508$	29.5543	+	6.10229i	1.31126	+	0.270746i
$509$	−35.3140	+	20.3886i	−1.56527	+	0.903707i	−0.568557	+	0.822644i	$0.692498\pi$
$509$	−35.3140	+	20.3886i	−1.56527	+	0.903707i	−0.996709	+	0.0810631i	$0.974168\pi$
$510$	−12.6065	+	8.05261i	−0.558226	+	0.356575i
$511$		0			0
$512$	−22.4339	−	2.95289i	−0.991448	−	0.130500i
$513$	5.60911	−	1.00990i	0.247648	−	0.0445884i
$514$	7.44418	−	19.5628i	0.328348	−	0.862878i
$515$	−7.40358	+	12.8234i	−0.326241	+	0.565066i
$516$	14.0662	+	4.64218i	0.619229	+	0.204361i
$517$	29.9148			1.31565
$518$		0			0
$519$	−6.72182	+	2.90910i	−0.295055	+	0.127695i
$520$	−6.48754	−	4.13294i	−0.284498	−	0.181241i
$521$	6.01740	+	3.47415i	0.263627	+	0.152205i	0.625988	−	0.779833i	$-0.284696\pi$
$521$	6.01740	+	3.47415i	0.263627	+	0.152205i	−0.362361	+	0.932038i	$0.618029\pi$
$522$	−1.60817	−	3.30145i	−0.0703877	−	0.144500i
$523$	−6.54296	+	3.77758i	−0.286104	+	0.165182i	−0.636183	−	0.771538i	$-0.719488\pi$
$523$	−6.54296	+	3.77758i	−0.286104	+	0.165182i	0.350080	+	0.936720i	$0.386154\pi$
$524$	14.0673	−	4.66149i	0.614533	−	0.203638i
$525$		0			0
$526$	3.13299	+	19.4149i	0.136605	+	0.846528i
$527$	−5.41333	−	9.37617i	−0.235808	−	0.408432i
$528$	−23.9110	+	13.8438i	−1.04059	+	0.602472i
$529$	−16.6344	+	28.8116i	−0.723234	+	1.25268i
$530$	−11.2473	+	9.16225i	−0.488552	+	0.397983i
$531$	−10.0398	+	10.6929i	−0.435689	+	0.464033i
$532$		0			0
$533$		−	9.19231i		−	0.398163i
$534$	−9.62125	+	18.5367i	−0.416352	+	0.802163i
$535$	4.34511	+	2.50865i	0.187855	+	0.108458i
$536$	0.298792	−	6.84481i	0.0129058	−	0.295651i
$537$	−6.76571	+	9.11077i	−0.291962	+	0.393159i
$538$	−11.5293	+	1.86049i	−0.497064	+	0.0802115i
$539$		0			0
$540$	0.549611	−	21.5679i	0.0236515	−	0.928136i
$541$	−5.57548	−	9.65701i	−0.239709	−	0.415187i	0.720922	−	0.693016i	$-0.243719\pi$
$541$	−5.57548	−	9.65701i	−0.239709	−	0.415187i	−0.960631	+	0.277829i	$0.910385\pi$
$542$	−2.66848	+	7.01259i	−0.114621	+	0.301216i
$543$	−21.1355	−	2.44464i	−0.907011	−	0.104910i
$544$	16.1343	+	4.07237i	0.691752	+	0.174601i
$545$			14.1108i			0.604442i
$546$		0			0
$547$			39.2870i			1.67979i	0.542748	+	0.839896i	$0.317384\pi$
$547$			39.2870i			1.67979i	−0.542748	+	0.839896i	$0.682616\pi$
$548$	−20.0758	+	22.5592i	−0.857594	+	0.963682i
$549$	3.56202	+	11.7947i	0.152023	+	0.503386i
$550$	3.63715	+	1.38403i	0.155089	+	0.0590154i
$551$	−0.474691	−	0.822189i	−0.0202225	−	0.0350264i
$552$	−23.1750	+	28.5196i	−0.986395	+	1.21388i
$553$		0			0
$554$	−2.83983	−	17.5982i	−0.120653	−	0.747676i
$555$	−12.0585	−	8.95468i	−0.511853	−	0.380105i
$556$	28.3542	+	5.85450i	1.20249	+	0.248286i
$557$	25.5152	+	14.7312i	1.08112	+	0.624182i	0.931197	−	0.364516i	$-0.118766\pi$
$557$	25.5152	+	14.7312i	1.08112	+	0.624182i	0.149919	+	0.988698i	$0.452099\pi$
$558$	15.5765	+	1.09708i	0.659406	+	0.0464429i
$559$		−	5.60145i		−	0.236916i
$560$		0			0
$561$	18.6474	−	8.07030i	0.787294	−	0.340728i
$562$	−1.81297	−	2.22554i	−0.0764753	−	0.0938789i
$563$	−20.3385	+	35.2274i	−0.857167	+	1.48466i	0.0174537	+	0.999848i	$0.494444\pi$
$563$	−20.3385	+	35.2274i	−0.857167	+	1.48466i	−0.874620	+	0.484808i	$0.838889\pi$
$564$	25.4419	−	5.28537i	1.07130	−	0.222554i
$565$	3.28394	+	5.68796i	0.138157	+	0.239294i
$566$	10.7194	−	1.72980i	0.450570	−	0.0727087i
$567$		0			0
$568$	1.17700	+	2.26094i	0.0493857	+	0.0948670i
$569$	−4.30534	+	2.48569i	−0.180489	+	0.104206i	−0.587523	−	0.809208i	$-0.699897\pi$
$569$	−4.30534	+	2.48569i	−0.180489	+	0.104206i	0.407033	+	0.913413i	$0.366563\pi$
$570$	−0.250008	−	5.57206i	−0.0104717	−	0.233388i
$571$	30.2952	+	17.4909i	1.26781	+	0.731973i	0.974574	−	0.224066i	$-0.0719331\pi$
$571$	30.2952	+	17.4909i	1.26781	+	0.731973i	0.293240	+	0.956039i	$0.405266\pi$
$572$	7.80522	+	6.94598i	0.326353	+	0.290426i
$573$	−16.3266	−	37.7245i	−0.682052	−	1.57596i
$574$		0			0
$575$	5.17599			0.215854
$576$	−17.8899	+	15.9985i	−0.745413	+	0.666603i
$577$	−7.33386	+	12.7026i	−0.305313	+	0.528817i	−0.977331	−	0.211718i	$-0.932094\pi$
$577$	−7.33386	+	12.7026i	−0.305313	+	0.528817i	0.672018	+	0.740535i	$0.265428\pi$
$578$	11.0325	+	4.19817i	0.458892	+	0.174621i
$579$	−4.10366	+	5.52603i	−0.170542	+	0.229654i
$580$	−3.41150	+	1.13047i	−0.141655	+	0.0469402i
$581$		0			0
$582$	−31.7713	+	20.2944i	−1.31696	+	0.841230i
$583$	17.0649	−	9.85242i	0.706755	−	0.408045i
$584$	36.7652	+	1.60489i	1.52136	+	0.0664107i
$585$	−7.81037	+	2.35874i	−0.322919	+	0.0975221i
$586$	1.38926	+	1.70542i	0.0573899	+	0.0704502i
$587$	−18.7469			−0.773769			−0.386885	−	0.922128i	$-0.626449\pi$
$587$	−18.7469			−0.773769			−0.386885	+	0.922128i	$0.626449\pi$
$588$		0			0
$589$	4.03690			0.166337
$590$	9.06601	+	11.1292i	0.373242	+	0.458181i
$591$	−3.93485	+	34.0194i	−0.161858	+	1.39937i
$592$	1.93987	+	16.5950i	0.0797282	+	0.682050i
$593$	38.8836	−	22.4494i	1.59676	−	0.921888i	0.604651	−	0.796491i	$-0.293313\pi$
$593$	38.8836	−	22.4494i	1.59676	−	0.921888i	0.992107	−	0.125398i	$-0.0400207\pi$
$594$	−5.40414	+	28.8029i	−0.221735	+	1.18180i
$595$		0			0
$596$	7.16624	+	21.6261i	0.293541	+	0.885838i
$597$	10.6607	+	7.91673i	0.436315	+	0.324010i
$598$	12.9882	+	4.94237i	0.531128	+	0.202108i
$599$	0.596454	−	1.03309i	0.0243704	−	0.0422108i	−0.853583	−	0.520957i	$-0.825575\pi$
$599$	0.596454	−	1.03309i	0.0243704	−	0.0422108i	0.877953	+	0.478746i	$0.158909\pi$
$600$	3.33786	+	0.534477i	0.136267	+	0.0218199i
$601$	−37.4089			−1.52594			−0.762970	−	0.646434i	$-0.776259\pi$
$601$	−37.4089			−1.52594			−0.762970	+	0.646434i	$0.776259\pi$
$602$		0			0
$603$	−5.29775	−	4.97415i	−0.215741	−	0.202563i
$604$	−1.22083	+	1.37185i	−0.0496747	+	0.0558196i
$605$	8.81680	+	5.09038i	0.358454	+	0.206953i
$606$	−14.9398	+	0.670319i	−0.606886	+	0.0272298i
$607$	18.5588	−	10.7149i	0.753279	−	0.434906i	−0.0735982	−	0.997288i	$-0.523448\pi$
$607$	18.5588	−	10.7149i	0.753279	−	0.434906i	0.826878	+	0.562382i	$0.190115\pi$
$608$	−4.32298	+	4.45073i	−0.175320	+	0.180501i
$609$		0			0
$610$	11.9039	−	1.92094i	0.481975	−	0.0777766i
$611$	−4.91326	−	8.51001i	−0.198769	−	0.344278i
$612$	14.4334	−	10.1583i	0.583434	−	0.410624i
$613$	20.2674	−	35.1041i	0.818591	−	1.41784i	−0.0881290	−	0.996109i	$-0.528089\pi$
$613$	20.2674	−	35.1041i	0.818591	−	1.41784i	0.906720	−	0.421733i	$-0.138578\pi$
$614$	−28.2070	−	34.6261i	−1.13834	−	1.39739i
$615$	−10.0219	−	23.1567i	−0.404120	−	0.933768i
$616$		0			0
$617$			46.2548i			1.86215i	0.364830	+	0.931074i	$0.381127\pi$
$617$			46.2548i			1.86215i	−0.364830	+	0.931074i	$0.618873\pi$
$618$	8.04838	−	15.5064i	0.323753	−	0.623758i
$619$	−22.3403	−	12.8982i	−0.897932	−	0.518421i	−0.0214035	−	0.999771i	$-0.506813\pi$
$619$	−22.3403	−	12.8982i	−0.897932	−	0.518421i	−0.876529	+	0.481349i	$0.840147\pi$
$620$	3.09017	−	14.9662i	0.124104	−	0.601055i
$621$	6.90676	+	38.3608i	0.277159	+	1.53937i
$622$	4.11780	+	25.5177i	0.165109	+	1.02317i
$623$		0			0
$624$	7.86540	+	4.52838i	0.314868	+	0.181280i
$625$	10.5369	+	18.2504i	0.421476	+	0.730018i
$626$	−39.3641	−	14.9791i	−1.57331	−	0.598686i
$627$	−0.870499	+	7.52603i	−0.0347644	+	0.300561i
$628$	13.0385	+	11.6032i	0.520293	+	0.463016i
$629$		−	12.2871i		−	0.489920i
$630$		0			0
$631$		−	26.5913i		−	1.05858i	−0.848440	−	0.529291i	$-0.822458\pi$
$631$		−	26.5913i		−	1.05858i	0.848440	−	0.529291i	$-0.177542\pi$
$632$	24.7173	+	15.7463i	0.983201	+	0.626356i
$633$	−2.33805	+	20.2140i	−0.0929291	+	0.803433i
$634$	8.90042	−	23.3897i	0.353481	−	0.928924i
$635$	−15.6626	−	27.1284i	−0.621552	−	1.07656i
$636$	12.7726	−	11.3943i	0.506466	−	0.451814i
$637$		0			0
$638$	4.81932	−	0.777697i	0.190799	−	0.0307893i
$639$	2.63219	+	0.617162i	0.104128	+	0.0244145i
$640$	13.1912	+	19.4337i	0.521428	+	0.768186i
$641$	5.24154	+	3.02620i	0.207028	+	0.119528i	0.599930	−	0.800053i	$-0.295195\pi$
$641$	5.24154	+	3.02620i	0.207028	+	0.119528i	−0.392901	+	0.919581i	$0.628529\pi$
$642$	−5.25422	−	2.72714i	−0.207368	−	0.107631i
$643$			9.95426i			0.392558i	0.980548	+	0.196279i	$0.0628858\pi$
$643$			9.95426i			0.392558i	−0.980548	+	0.196279i	$0.937114\pi$
$644$		0			0
$645$	−6.10695	−	14.1108i	−0.240461	−	0.555614i
$646$	3.53766	−	2.88184i	0.139187	−	0.113384i
$647$	15.4951	−	26.8383i	0.609175	−	1.05512i	−0.382201	−	0.924079i	$-0.624834\pi$
$647$	15.4951	−	26.8383i	0.609175	−	1.05512i	0.991377	−	0.131044i	$-0.0418328\pi$
$648$	0.492815	+	25.4511i	0.0193596	+	0.999813i
$649$	−9.74892	−	16.8856i	−0.382679	−	0.662819i
$650$	−0.203649	−	1.26200i	−0.00798778	−	0.0494996i
$651$		0			0
$652$	5.65686	+	17.0711i	0.221540	+	0.668557i
$653$	7.01889	−	4.05236i	0.274670	−	0.158581i	−0.356338	−	0.934357i	$-0.615975\pi$
$653$	7.01889	−	4.05236i	0.274670	−	0.158581i	0.631008	+	0.775776i	$0.282641\pi$
$654$	−0.746263	−	16.6324i	−0.0291812	−	0.650377i
$655$	−13.3221	−	7.69152i	−0.520538	−	0.300533i
$656$	−11.1171	+	25.7730i	−0.434048	+	1.00627i
$657$	26.7174	−	28.4556i	1.04235	−	1.11016i
$658$		0			0
$659$	−38.3085			−1.49229			−0.746143	−	0.665785i	$-0.768097\pi$
$659$	−38.3085			−1.49229			−0.746143	+	0.665785i	$0.768097\pi$
$660$	27.2352	+	8.98828i	1.06013	+	0.349868i
$661$	3.32843	−	5.76501i	0.129461	−	0.224233i	−0.794007	−	0.607909i	$-0.792009\pi$
$661$	3.32843	−	5.76501i	0.129461	−	0.224233i	0.923468	+	0.383676i	$0.125342\pi$
$662$	17.6449	−	46.3696i	0.685788	−	1.80221i
$663$	−5.35848	−	3.97924i	−0.208106	−	0.154541i
$664$	−16.2454	−	31.2064i	−0.630442	−	1.21104i
$665$		0			0
$666$	14.6868	+	9.91711i	0.569102	+	0.384280i
$667$	5.62297	−	3.24642i	0.217722	−	0.125702i
$668$	6.54481	−	31.6975i	0.253226	−	1.22641i
$669$	−2.88968	+	24.9832i	−0.111722	+	0.965905i
$670$	−5.51389	+	4.49171i	−0.213020	+	0.173530i
$671$	−16.3784			−0.632280
$672$		0			0
$673$	−22.0809			−0.851156			−0.425578	−	0.904922i	$-0.639929\pi$
$673$	−22.0809			−0.851156			−0.425578	+	0.904922i	$0.639929\pi$
$674$	0.145815	−	0.118783i	0.00561657	−	0.00457535i
$675$	2.73827	−	2.31456i	0.105396	−	0.0890874i
$676$	−4.56350	+	22.1017i	−0.175519	+	0.850064i
$677$	39.0358	−	22.5373i	1.50027	−	0.866180i	0.500267	−	0.865871i	$-0.333235\pi$
$677$	39.0358	−	22.5373i	1.50027	−	0.866180i	1.00000		0.000308342i	$-9.81484e-5\pi$
$678$	−4.17158	−	6.53069i	−0.160208	−	0.250810i
$679$		0			0
$680$	−7.97594	−	15.3213i	−0.305863	−	0.587546i
$681$	−22.1634	+	29.8454i	−0.849303	+	1.14368i
$682$	−7.38237	+	19.4004i	−0.282685	+	0.742879i
$683$	−7.80843	+	13.5246i	−0.298781	+	0.517505i	−0.975857	−	0.218408i	$-0.929913\pi$
$683$	−7.80843	+	13.5246i	−0.298781	+	0.517505i	0.677076	+	0.735913i	$0.263247\pi$
$684$	0.589366	+	6.55454i	0.0225350	+	0.250619i
$685$	31.3469			1.19770
$686$		0			0
$687$	13.5049	+	31.2046i	0.515242	+	1.19053i
$688$	−6.77432	+	15.7051i	−0.258269	+	0.598753i
$689$	−5.60554	−	3.23636i	−0.213554	−	0.123295i
$690$	38.1075	−	1.70981i	1.45073	−	0.0650914i
$691$	33.1799	−	19.1564i	1.26222	−	0.728744i	0.288718	−	0.957414i	$-0.406771\pi$
$691$	33.1799	−	19.1564i	1.26222	−	0.728744i	0.973504	+	0.228670i	$0.0734376\pi$
$692$	−2.66028	−	8.02811i	−0.101129	−	0.305183i
$693$		0			0
$694$	0.0440088	+	0.272719i	0.00167055	+	0.0103523i
$695$	−15.0266	−	26.0268i	−0.569991	−	0.987254i
$696$	3.96133	−	1.51290i	0.150154	−	0.0573463i
$697$	10.3208	−	17.8762i	0.390930	−	0.677110i
$698$	6.36801	−	5.18749i	0.241033	−	0.196349i
$699$	−22.6737	+	9.81282i	−0.857598	+	0.371155i
$700$		0			0
$701$		−	36.6488i		−	1.38420i	−0.721799	−	0.692102i	$-0.756685\pi$
$701$		−	36.6488i		−	1.38420i	0.721799	−	0.692102i	$-0.243315\pi$
$702$	9.08130	−	3.19330i	0.342751	−	0.120523i
$703$	3.96766	+	2.29073i	0.149643	+	0.0863964i
$704$	−13.4836	−	28.9144i	−0.508183	−	1.08975i
$705$	−21.6552	−	16.0812i	−0.815580	−	0.605655i
$706$	27.9148	−	4.50462i	1.05059	−	0.169534i
$707$		0			0
$708$	−11.2746	−	12.6384i	−0.423726	−	0.474981i
$709$	−18.2674	−	31.6400i	−0.686045	−	1.18827i	−0.973107	−	0.230353i	$-0.926012\pi$
$709$	−18.2674	−	31.6400i	−0.686045	−	1.18827i	0.287062	−	0.957912i	$-0.407322\pi$
$710$	0.941002	−	2.47289i	0.0353152	−	0.0928060i
$711$	29.7572	−	8.98673i	1.11598	−	0.337029i
$712$	−20.3392	−	12.9572i	−0.762243	−	0.485593i
$713$			27.6084i			1.03394i
$714$		0			0
$715$		−	10.8457i		−	0.405604i
$716$	−9.78887	−	8.71125i	−0.365827	−	0.325555i
$717$	26.2937	+	3.04126i	0.981954	+	0.113578i
$718$	−18.3803	−	6.99418i	−0.685945	−	0.261020i
$719$	12.2687	+	21.2499i	0.457543	+	0.792488i	0.998830	−	0.0483494i	$-0.0153961\pi$
$719$	12.2687	+	21.2499i	0.457543	+	0.792488i	−0.541287	+	0.840838i	$0.682063\pi$
$720$	24.7511	+	2.83240i	0.922418	+	0.105557i
$721$		0			0
$722$	−4.00962	−	24.8473i	−0.149223	−	0.924720i
$723$	6.09660	−	8.20974i	0.226735	−	0.305324i
$724$	4.96792	−	24.0604i	0.184631	−	0.894196i
$725$	−0.517239	−	0.298628i	−0.0192098	−	0.0110908i
$726$	−10.6615	−	5.53372i	−0.395686	−	0.205376i
$727$			7.89691i			0.292880i	0.989220	+	0.146440i	$0.0467816\pi$
$727$			7.89691i			0.292880i	−0.989220	+	0.146440i	$0.953218\pi$
$728$		0			0
$729$	20.8078	+	17.2057i	0.770660	+	0.637247i
$730$	−24.1261	−	29.6165i	−0.892948	−	1.09616i
$731$	6.28914	−	10.8931i	0.232612	−	0.402896i
$732$	−13.9295	+	2.89375i	−0.514848	+	0.106956i
$733$	2.92236	+	5.06167i	0.107940	+	0.186957i	0.914935	−	0.403600i	$-0.132241\pi$
$733$	2.92236	+	5.06167i	0.107940	+	0.186957i	−0.806996	+	0.590557i	$0.798908\pi$
$734$	26.2664	−	4.23863i	0.969511	−	0.156451i
$735$		0			0
$736$	−30.4386	−	29.5650i	−1.12198	−	1.08978i
$737$	8.36590	−	4.83005i	0.308162	−	0.177917i
$738$	13.0374	+	26.7646i	0.479912	+	0.985220i
$739$	1.22939	+	0.709786i	0.0452237	+	0.0261099i	0.522441	−	0.852675i	$-0.325021\pi$
$739$	1.22939	+	0.709786i	0.0452237	+	0.0261099i	−0.477218	+	0.878785i	$0.658355\pi$
$740$	11.5297	−	12.9560i	0.423840	−	0.476270i
$741$	2.28394	−	0.988455i	0.0839027	−	0.0363118i
$742$		0			0
$743$	−1.70600			−0.0625872			−0.0312936	−	0.999510i	$-0.509963\pi$
$743$	−1.70600			−0.0625872			−0.0312936	+	0.999510i	$0.509963\pi$
$744$	−2.85087	+	17.8040i	−0.104518	+	0.652724i
$745$	11.8244	−	20.4805i	0.433212	−	0.750346i
$746$	7.69657	+	2.92875i	0.281791	+	0.107229i
$747$	−36.3305	−	8.51831i	−1.32926	−	0.311669i
$748$	7.38003	+	22.2713i	0.269841	+	0.814318i
$749$		0			0
$750$	−15.5763	−	24.3850i	−0.568765	−	0.890413i
$751$	23.1969	−	13.3927i	0.846466	−	0.488707i	−0.0129912	−	0.999916i	$-0.504135\pi$
$751$	23.1969	−	13.3927i	0.846466	−	0.488707i	0.859457	+	0.511208i	$0.170802\pi$
$752$	3.48371	+	29.8021i	0.127038	+	1.08677i
$753$	−40.8465	−	4.72451i	−1.48853	−	0.172171i
$754$	−1.01277	−	1.24325i	−0.0368829	−	0.0452764i
$755$	1.90623			0.0693749
$756$		0			0
$757$	−23.8816			−0.867992			−0.433996	−	0.900915i	$-0.642897\pi$
$757$	−23.8816			−0.867992			−0.433996	+	0.900915i	$0.642897\pi$
$758$	10.7717	+	13.2230i	0.391245	+	0.480281i
$759$	−51.4707	−	5.95337i	−1.86827	−	0.216094i
$760$	6.43441	+	0.280877i	0.233401	+	0.0101885i
$761$	−13.0696	+	7.54576i	−0.473774	+	0.273533i	−0.717818	−	0.696231i	$-0.754859\pi$
$761$	−13.0696	+	7.54576i	−0.473774	+	0.273533i	0.244044	+	0.969764i	$0.421526\pi$
$762$	19.8961	+	31.1478i	0.720761	+	1.12837i
$763$		0			0
$764$	45.0557	−	14.9301i	1.63006	−	0.540153i
$765$	−17.8371	−	4.18221i	−0.644902	−	0.151208i
$766$	−16.0616	−	6.11189i	−0.580331	−	0.220831i
$767$	−3.20236	+	5.54665i	−0.115631	+	0.200278i
$768$	−16.5762	−	22.2088i	−0.598141	−	0.801391i
$769$	−12.6792			−0.457222			−0.228611	−	0.973518i	$-0.573418\pi$
$769$	−12.6792			−0.457222			−0.228611	+	0.973518i	$0.573418\pi$
$770$		0			0
$771$	23.5267	−	10.1820i	0.847294	−	0.366695i
$772$	−5.93733	−	5.28371i	−0.213689	−	0.190165i
$773$	−33.5367	−	19.3624i	−1.20623	−	0.696417i	−0.244296	−	0.969701i	$-0.578557\pi$
$773$	−33.5367	−	19.3624i	−1.20623	−	0.696417i	−0.961934	+	0.273283i	$0.911890\pi$
$774$	7.94448	+	16.3094i	0.285559	+	0.586229i
$775$	2.19937	−	1.26981i	0.0790037	−	0.0456128i
$776$	−20.1012	−	38.6132i	−0.721590	−	1.38613i
$777$		0			0
$778$	1.69002	−	0.272719i	0.0605900	−	0.00977745i
$779$	3.84829	+	6.66544i	0.137879	+	0.238814i
$780$	−1.91622	−	9.22400i	−0.0686117	−	0.330272i
$781$	−1.79696	+	3.11243i	−0.0643004	+	0.111372i
$782$	19.7090	+	24.1942i	0.704791	+	0.865181i
$783$	1.52303	−	4.23190i	0.0544286	−	0.151236i
$784$		0			0
$785$		−	18.1175i		−	0.646642i
$786$	16.1095	+	8.36140i	0.574605	+	0.298241i
$787$	17.6523	+	10.1915i	0.629235	+	0.363289i	0.780456	−	0.625211i	$-0.214987\pi$
$787$	17.6523	+	10.1915i	0.629235	+	0.363289i	−0.151221	+	0.988500i	$0.548320\pi$
$788$	−38.7272	−	7.99629i	−1.37960	−	0.284856i
$789$	−14.3598	+	19.3371i	−0.511224	+	0.688419i
$790$	−4.84640	−	30.0327i	−0.172427	−	1.06852i
$791$		0			0
$792$	−32.5774	−	9.15408i	−1.15759	−	0.325276i
$793$	2.69002	+	4.65925i	0.0955253	+	0.165455i
$794$	12.6320	+	4.80683i	0.448294	+	0.170588i
$795$	−17.6495	−	2.04143i	−0.625965	−	0.0724022i
$796$	−10.1933	+	11.4542i	−0.361291	+	0.405984i
$797$			27.9005i			0.988287i	0.869380	+	0.494143i	$0.164518\pi$
$797$			27.9005i			0.988287i	−0.869380	+	0.494143i	$0.835482\pi$
$798$		0			0
$799$		−	22.0658i		−	0.780632i
$800$	−0.955258	+	3.78463i	−0.0337735	+	0.133807i
$801$	−24.4864	+	7.39493i	−0.865184	+	0.261287i
$802$	5.65622	−	14.8642i	0.199728	−	0.524873i
$803$	25.9435	+	44.9354i	0.915525	+	1.58574i
$804$	6.26165	−	5.58596i	0.220831	−	0.197002i
$805$		0			0
$806$	6.73142	−	1.08625i	0.237104	−	0.0382617i
$807$	−11.4831	−	8.52744i	−0.404225	−	0.300180i
$808$	0.753083	−	17.2519i	0.0264934	−	0.606918i
$809$	−12.3530	−	7.13202i	−0.434309	−	0.250748i	0.266872	−	0.963732i	$-0.414010\pi$
$809$	−12.3530	−	7.13202i	−0.434309	−	0.250748i	−0.701181	+	0.712984i	$0.747343\pi$
$810$	19.3956	−	17.9452i	0.681491	−	0.630529i
$811$		−	38.4069i		−	1.34865i	−0.738435	−	0.674325i	$-0.764435\pi$
$811$		−	38.4069i		−	1.34865i	0.738435	−	0.674325i	$-0.235565\pi$
$812$		0			0
$813$	−8.43351	+	3.64989i	−0.295776	+	0.128007i
$814$	−18.2644	+	14.8785i	−0.640169	+	0.521492i
$815$	9.33391	−	16.1668i	0.326953	−	0.566299i
$816$	10.2115	+	17.6373i	0.357473	+	0.617430i
$817$	2.34501	+	4.06167i	0.0820415	+	0.142100i
$818$	−3.50741	−	21.7351i	−0.122634	−	0.759951i
$819$		0			0
$820$	27.6569	−	9.16466i	0.965820	−	0.320044i
$821$	45.7169	−	26.3947i	1.59553	−	0.921181i	0.603198	−	0.797591i	$-0.293893\pi$
$821$	45.7169	−	26.3947i	1.59553	−	0.921181i	0.992333	−	0.123589i	$-0.0394406\pi$
$822$	−36.9484	+	1.65780i	−1.28872	+	0.0578226i
$823$	−4.96238	−	2.86503i	−0.172978	−	0.0998687i	0.411012	−	0.911630i	$-0.365176\pi$
$823$	−4.96238	−	2.86503i	−0.172978	−	0.0998687i	−0.583989	+	0.811761i	$0.698509\pi$
$824$	17.0142	+	10.8390i	0.592717	+	0.377595i
$825$	1.89305	+	4.37413i	0.0659077	+	0.152288i
$826$		0			0
$827$	44.5253			1.54830			0.774149	−	0.633003i	$-0.218178\pi$
$827$	44.5253			1.54830			0.774149	+	0.633003i	$0.218178\pi$
$828$	−44.8267	+	4.03069i	−1.55783	+	0.140076i
$829$	13.0293	−	22.5674i	0.452526	−	0.783799i	−0.546016	−	0.837775i	$-0.683856\pi$
$829$	13.0293	−	22.5674i	0.452526	−	0.783799i	0.998542	+	0.0539760i	$0.0171895\pi$
$830$	−12.9881	+	34.1318i	−0.450823	+	1.18473i
$831$	13.0162	−	17.5277i	0.451526	−	0.608030i
$832$	−6.01086	+	8.58471i	−0.208389	+	0.297621i
$833$		0			0
$834$	19.0882	+	29.8830i	0.660971	+	1.03476i
$835$	−29.0957	+	16.7984i	−1.00690	+	0.581333i
$836$	−8.56753	−	1.76900i	−0.296314	−	0.0611822i
$837$	12.3457	+	14.6058i	0.426731	+	0.504850i
$838$	19.7730	−	16.1074i	0.683048	−	0.556423i
$839$	46.0533			1.58994			0.794968	−	0.606652i	$-0.207488\pi$
$839$	46.0533			1.58994			0.794968	+	0.606652i	$0.207488\pi$
$840$		0			0
$841$	28.2508			0.974165
$842$	13.7033	−	11.1629i	0.472247	−	0.384700i
$843$	0.403945	−	3.49237i	0.0139126	−	0.120284i
$844$	−23.0113	−	4.75131i	−0.792081	−	0.163547i
$845$	20.2875	−	11.7130i	0.697912	−	0.402940i
$846$	26.3753	+	17.8096i	0.906801	+	0.612307i
$847$		0			0
$848$	11.8026	+	15.8532i	0.405302	+	0.544403i
$849$	10.6765	+	7.92840i	0.366415	+	0.272102i
$850$	1.02090	−	2.68285i	0.0350164	−	0.0920209i
$851$	−15.6663	+	27.1349i	−0.537035	+	0.930173i
$852$	−0.978373	+	2.96455i	−0.0335185	+	0.101564i
$853$	−46.3274			−1.58622			−0.793109	−	0.609079i	$-0.791539\pi$
$853$	−46.3274			−1.58622			−0.793109	+	0.609079i	$0.791539\pi$
$854$		0			0
$855$	4.67591	−	4.98011i	0.159913	−	0.170316i
$856$	3.67272	−	5.76512i	0.125531	−	0.197048i
$857$	−35.6333	−	20.5729i	−1.21721	−	0.702756i	−0.252890	−	0.967495i	$-0.581381\pi$
$857$	−35.6333	−	20.5729i	−1.21721	−	0.702756i	−0.964320	+	0.264739i	$0.914714\pi$
$858$	0.573581	+	12.7837i	0.0195817	+	0.436428i
$859$	−49.7193	+	28.7054i	−1.69640	+	0.979417i	−0.747277	+	0.664512i	$0.768639\pi$
$859$	−49.7193	+	28.7054i	−1.69640	+	0.979417i	−0.949123	+	0.314905i	$0.898027\pi$
$860$	16.8531	−	5.58461i	0.574685	−	0.190434i
$861$		0			0
$862$	−2.80407	−	17.3766i	−0.0955072	−	0.591850i
$863$	12.7433	+	22.0721i	0.433788	+	0.751343i	0.997196	−	0.0748356i	$-0.0238432\pi$
$863$	12.7433	+	22.0721i	0.433788	+	0.751343i	−0.563408	+	0.826179i	$0.690510\pi$
$864$	−29.3237	−	2.02955i	−0.997613	−	0.0690468i
$865$	−4.38950	+	7.60283i	−0.149247	+	0.258504i
$866$	−0.545855	+	0.444663i	−0.0185489	+	0.0151103i
$867$	5.74216	+	13.2680i	0.195014	+	0.450604i
$868$		0			0
$869$			41.3215i			1.40174i
$870$	−3.90675	−	2.02775i	−0.132451	−	0.0687471i
$871$	−2.74806	−	1.58659i	−0.0931145	−	0.0537597i
$872$	19.2064	+	0.838404i	0.650412	+	0.0283919i
$873$	−44.9535	−	10.5401i	−1.52145	−	0.356729i
$874$	−11.4870	+	1.85366i	−0.388553	+	0.0627010i
$875$		0			0
$876$	30.0036	+	33.6329i	1.01373	+	1.13635i
$877$	−20.9313	−	36.2541i	−0.706801	−	1.22422i	−0.966038	−	0.258402i	$-0.916804\pi$
$877$	−20.9313	−	36.2541i	−0.706801	−	1.22422i	0.259236	−	0.965814i	$-0.416529\pi$
$878$	2.34382	−	6.15942i	0.0791002	−	0.207870i
$879$	−0.309541	+	2.67618i	−0.0104405	+	0.0902653i
$880$	−13.1166	+	30.4086i	−0.442160	+	1.02507i
$881$			38.5556i			1.29897i	0.760373	+	0.649486i	$0.225016\pi$
$881$			38.5556i			1.29897i	−0.760373	+	0.649486i	$0.774984\pi$
$882$		0			0
$883$			4.56420i			0.153597i	0.997047	+	0.0767987i	$0.0244699\pi$
$883$			4.56420i			0.153597i	−0.997047	+	0.0767987i	$0.975530\pi$
$884$	5.12351	−	5.75731i	0.172322	−	0.193639i
$885$	−2.01999	+	17.4641i	−0.0679012	+	0.587050i
$886$	29.1708	+	11.1003i	0.980012	+	0.372921i
$887$	−20.2446	−	35.0647i	−0.679747	−	1.17736i	−0.975057	−	0.221955i	$-0.928756\pi$
$887$	−20.2446	−	35.0647i	−0.679747	−	1.17736i	0.295310	−	0.955401i	$-0.404577\pi$
$888$	−12.9048	+	15.8809i	−0.433056	+	0.532927i
$889$		0			0
$890$	3.98797	+	24.7131i	0.133677	+	0.828385i
$891$	−29.8919	+	19.8668i	−1.00142	+	0.665562i
$892$	−28.4405	−	5.87232i	−0.952258	−	0.196620i
$893$	7.12531	+	4.11380i	0.238439	+	0.137663i
$894$	−12.8542	+	24.7655i	−0.429909	+	0.828283i
$895$			13.6020i			0.454665i
$896$		0			0
$897$	6.76007	+	15.6199i	0.225712	+	0.521535i
$898$	5.38474	+	6.61015i	0.179691	+	0.220584i
$899$	1.59287	−	2.75893i	0.0531251	−	0.0920154i
$900$	2.38283	+	3.38564i	0.0794276	+	0.112855i
$901$	−7.26737	−	12.5874i	−0.242111	−	0.419349i
$902$	−39.0700	+	6.30475i	−1.30089	+	0.209925i
$903$		0			0
$904$	7.93706	−	4.13186i	0.263983	−	0.137424i
$905$	−22.0854	+	12.7510i	−0.734145	+	0.423859i
$906$	−2.24686	+	0.100813i	−0.0746471	+	0.00334927i
$907$	−2.36697	−	1.36657i	−0.0785940	−	0.0453763i	0.460188	−	0.887822i	$-0.347782\pi$
$907$	−2.36697	−	1.36657i	−0.0785940	−	0.0453763i	−0.538782	+	0.842445i	$0.681115\pi$
$908$	−32.0668	−	28.5367i	−1.06417	−	0.947023i
$909$	−13.3526	−	12.5370i	−0.442878	−	0.415826i
$910$		0			0
$911$	−5.16105			−0.170993			−0.0854966	−	0.996338i	$-0.527248\pi$
$911$	−5.16105			−0.170993			−0.0854966	+	0.996338i	$0.527248\pi$
$912$	−7.59906	+	0.00922123i	−0.251630	+	0.000305345i
$913$	24.8024	−	42.9590i	0.820839	−	1.42174i
$914$	−50.5724	−	19.2442i	−1.67279	−	0.636540i
$915$	11.8562	+	8.80451i	0.391955	+	0.291068i
$916$	−37.2688	+	12.3498i	−1.23139	+	0.408048i
$917$		0			0
$918$	21.2457	+	3.98622i	0.701212	+	0.131565i
$919$	−34.5011	+	19.9192i	−1.13809	+	0.657074i	−0.945956	−	0.324296i	$-0.894873\pi$
$919$	−34.5011	+	19.9192i	−1.13809	+	0.657074i	−0.192130	+	0.981370i	$0.561539\pi$
$920$	−1.92092	+	44.0051i	−0.0633310	+	1.45081i
$921$	6.28477	−	54.3360i	0.207090	−	1.79043i
$922$	−11.1258	−	13.6578i	−0.366410	−	0.449794i
$923$	1.18055			0.0388582
$924$		0			0
$925$	2.88220			0.0947660
$926$	−25.0637	−	30.7675i	−0.823644	−	1.01108i
$927$	20.4834	−	6.18602i	0.672763	−	0.203176i
$928$	1.33600	+	4.71060i	0.0438564	+	0.154633i
$929$	22.2777	−	12.8621i	0.730909	−	0.421990i	−0.0878459	−	0.996134i	$-0.527998\pi$
$929$	22.2777	−	12.8621i	0.730909	−	0.421990i	0.818754	+	0.574144i	$0.194665\pi$
$930$	15.7731	−	10.0753i	0.517220	−	0.330382i
$931$		0			0
$932$	−8.97351	−	27.0800i	−0.293937	−	0.887035i
$933$	−18.8737	+	25.4155i	−0.617897	+	0.832065i
$934$	22.5975	+	8.59895i	0.739412	+	0.281366i
$935$	12.1772	−	21.0915i	0.398236	−	0.689765i
$936$	2.74646	+	10.7709i	0.0897708	+	0.352059i
$937$	−20.2068			−0.660127			−0.330063	−	0.943959i	$-0.607070\pi$
$937$	−20.2068			−0.660127			−0.330063	+	0.943959i	$0.607070\pi$
$938$		0			0
$939$	−20.4881	−	47.3403i	−0.668604	−	1.54489i
$940$	20.7056	−	23.2669i	0.675341	−	0.758883i
$941$	41.4712	+	23.9434i	1.35192	+	0.780533i	0.988519	−	0.151099i	$-0.0482813\pi$
$941$	41.4712	+	23.9434i	1.35192	+	0.780533i	0.363403	+	0.931632i	$0.381615\pi$
$942$	0.958159	+	21.3550i	0.0312185	+	0.695784i
$943$	−45.5851	+	26.3186i	−1.48446	+	0.857051i
$944$	15.6867	−	11.6786i	0.510559	−	0.380106i
$945$		0			0
$946$	−23.8078	+	3.84188i	−0.774059	+	0.124910i
$947$	−3.16035	−	5.47389i	−0.102698	−	0.177878i	0.810098	−	0.586295i	$-0.199414\pi$
$947$	−3.16035	−	5.47389i	−0.102698	−	0.177878i	−0.912795	+	0.408418i	$0.866081\pi$
$948$	7.30073	+	35.1431i	0.237117	+	1.14139i
$949$	8.52200	−	14.7605i	0.276636	−	0.479148i
$950$	0.675994	+	0.829830i	0.0219321	+	0.0269233i
$951$	28.1290	−	12.1738i	0.912147	−	0.394763i
$952$		0			0
$953$		−	3.70027i		−	0.119863i	−0.998202	−	0.0599317i	$-0.980912\pi$
$953$		−	3.70027i		−	0.119863i	0.998202	−	0.0599317i	$-0.0190883\pi$
$954$	20.9114	+	1.47282i	0.677031	+	0.0476842i
$955$	−42.6689	−	24.6349i	−1.38073	−	0.797167i
$956$	−6.18035	+	29.9323i	−0.199887	+	0.968080i
$957$	4.80002	+	3.56452i	0.155163	+	0.115225i
$958$	−3.70087	−	22.9340i	−0.119570	−	0.740964i
$959$		0			0
$960$	−5.78276	+	28.1794i	−0.186638	+	0.909485i
$961$	−8.72691	−	15.1155i	−0.281513	−	0.487595i
$962$	7.23236	+	2.75211i	0.233181	+	0.0887315i
$963$	−2.09609	−	6.94065i	−0.0675455	−	0.223659i
$964$	8.82078	+	7.84974i	0.284098	+	0.252823i
$965$			8.25014i			0.265581i
$966$		0			0
$967$		−	14.5970i		−	0.469409i	−0.972067	−	0.234705i	$-0.924588\pi$
$967$		−	14.5970i		−	0.469409i	0.972067	−	0.234705i	$-0.0754123\pi$
$968$	7.45243	−	11.6982i	0.239530	−	0.375994i
$969$	5.55138	+	0.642100i	0.178336	+	0.0206272i
$970$	−16.0708	+	42.2330i	−0.516002	+	1.35602i
$971$	4.10729	+	7.11403i	0.131809	+	0.228300i	0.924374	−	0.381488i	$-0.124588\pi$
$971$	4.10729	+	7.11403i	0.131809	+	0.228300i	−0.792565	+	0.609788i	$0.791255\pi$
$972$	−21.9124	+	22.1776i	−0.702840	+	0.711348i
$973$		0			0
$974$	44.6592	−	7.20668i	1.43097	−	0.230917i
$975$	0.933412	−	1.25694i	0.0298931	−	0.0402543i
$976$	−1.90734	−	16.3167i	−0.0610524	−	0.522284i
$977$	30.8426	+	17.8070i	0.986744	+	0.569697i	0.904299	−	0.426899i	$-0.140394\pi$
$977$	30.8426	+	17.8070i	0.986744	+	0.569697i	0.0824443	+	0.996596i	$0.473727\pi$
$978$	−10.1468	+	19.5493i	−0.324460	+	0.625119i
$979$		−	34.0023i		−	1.08672i
$980$		0			0
$981$	13.9574	−	14.8654i	0.445625	−	0.474615i
$982$	−2.23506	+	1.82071i	−0.0713235	+	0.0581013i
$983$	−15.5749	+	26.9764i	−0.496761	+	0.860415i	−0.999993	−	0.00373618i	$-0.998811\pi$
$983$	−15.5749	+	26.9764i	−0.496761	+	0.860415i	0.503232	+	0.864151i	$0.332144\pi$
$984$	−32.1143	+	12.2650i	−1.02377	+	0.390994i
$985$	20.5239	+	35.5484i	0.653945	+	1.13267i
$986$	−0.573647	−	3.55484i	−0.0182687	−	0.113209i
$987$		0			0
$988$	0.903910	+	2.72779i	0.0287572	+	0.0867827i
$989$	−27.7779	+	16.0376i	−0.883285	+	0.509965i
$990$	15.3823	+	31.5786i	0.488881	+	1.00363i
$991$	30.1606	+	17.4132i	0.958083	+	0.553149i	0.895582	−	0.444896i	$-0.146759\pi$
$991$	30.1606	+	17.4132i	0.958083	+	0.553149i	0.0625004	+	0.998045i	$0.480093\pi$
$992$	−20.1870	−	5.09530i	−0.640938	−	0.161776i
$993$	55.7652	−	24.1343i	1.76966	−	0.765879i
$994$		0			0
$995$	15.9161			0.504573
$996$	13.5039	−	40.9179i	0.427887	−	1.29653i
$997$	4.22860	−	7.32414i	0.133921	−	0.231958i	−0.791264	−	0.611475i	$-0.790576\pi$
$997$	4.22860	−	7.32414i	0.133921	−	0.231958i	0.925185	+	0.379517i	$0.123910\pi$
$998$	−2.15933	+	5.67459i	−0.0683525	+	0.179626i
$999$	3.84596	+	21.3608i	0.121681	+	0.675827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.e.263.3		24
3.2	odd	2	inner	588.2.n.e.263.10		24
4.3	odd	2	inner	588.2.n.e.263.1		24
7.2	even	3	inner	588.2.n.e.275.12		24
7.3	odd	6		588.2.e.e.491.5		12
7.4	even	3		588.2.e.d.491.5		12
7.5	odd	6		84.2.n.a.23.12	yes	24
7.6	odd	2		84.2.n.a.11.3	yes	24
12.11	even	2	inner	588.2.n.e.263.12		24
21.2	odd	6	inner	588.2.n.e.275.1		24
21.5	even	6		84.2.n.a.23.1	yes	24
21.11	odd	6		588.2.e.d.491.8		12
21.17	even	6		588.2.e.e.491.8		12
21.20	even	2		84.2.n.a.11.10	yes	24
28.3	even	6		588.2.e.e.491.7		12
28.11	odd	6		588.2.e.d.491.7		12
28.19	even	6		84.2.n.a.23.10	yes	24
28.23	odd	6	inner	588.2.n.e.275.10		24
28.27	even	2		84.2.n.a.11.1	✓	24
84.11	even	6		588.2.e.d.491.6		12
84.23	even	6	inner	588.2.n.e.275.3		24
84.47	odd	6		84.2.n.a.23.3	yes	24
84.59	odd	6		588.2.e.e.491.6		12
84.83	odd	2		84.2.n.a.11.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.n.a.11.1	✓	24	28.27	even	2
84.2.n.a.11.3	yes	24	7.6	odd	2
84.2.n.a.11.10	yes	24	21.20	even	2
84.2.n.a.11.12	yes	24	84.83	odd	2
84.2.n.a.23.1	yes	24	21.5	even	6
84.2.n.a.23.3	yes	24	84.47	odd	6
84.2.n.a.23.10	yes	24	28.19	even	6
84.2.n.a.23.12	yes	24	7.5	odd	6
588.2.e.d.491.5		12	7.4	even	3
588.2.e.d.491.6		12	84.11	even	6
588.2.e.d.491.7		12	28.11	odd	6
588.2.e.d.491.8		12	21.11	odd	6
588.2.e.e.491.5		12	7.3	odd	6
588.2.e.e.491.6		12	84.59	odd	6
588.2.e.e.491.7		12	28.3	even	6
588.2.e.e.491.8		12	21.17	even	6
588.2.n.e.263.1		24	4.3	odd	2	inner
588.2.n.e.263.3		24	1.1	even	1	trivial
588.2.n.e.263.10		24	3.2	odd	2	inner
588.2.n.e.263.12		24	12.11	even	2	inner
588.2.n.e.275.1		24	21.2	odd	6	inner
588.2.n.e.275.3		24	84.23	even	6	inner
588.2.n.e.275.10		24	28.23	odd	6	inner
588.2.n.e.275.12		24	7.2	even	3	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09645 + 0.893190i) q^{2} +(-1.72058 - 0.199011i) q^{3} +(0.404424 - 1.95868i) q^{4} +(-1.79791 + 1.03802i) q^{5} +(2.06429 - 1.31860i) q^{6} +(1.30604 + 2.50883i) q^{8} +(2.92079 + 0.684828i) q^{9} +(1.04417 - 2.74402i) q^{10} +(-1.99399 + 3.45368i) q^{11} +(-1.08564 + 3.28959i) q^{12} +1.30998 q^{13} +(3.30003 - 1.42820i) q^{15} +(-3.67288 - 1.58428i) q^{16} +(2.54752 + 1.47081i) q^{17} +(-3.81419 + 1.85794i) q^{18} +(-0.949883 + 0.548415i) q^{19} +(1.30604 + 3.94134i) q^{20} +(-0.898482 - 5.56781i) q^{22} +(-3.75063 - 6.49627i) q^{23} +(-1.74787 - 4.57657i) q^{24} +(-0.345008 + 0.597572i) q^{25} +(-1.43634 + 1.17006i) q^{26} +(-4.88916 - 1.75957i) q^{27} +0.865568i q^{29} +(-2.34268 + 4.51351i) q^{30} +(-3.18742 - 1.84026i) q^{31} +(5.44221 - 1.54349i) q^{32} +(4.11813 - 5.54551i) q^{33} +(-4.10695 + 0.662741i) q^{34} +(2.52260 - 5.44394i) q^{36} +(-2.08850 - 3.61738i) q^{37} +(0.551664 - 1.44974i) q^{38} +(-2.25393 - 0.260701i) q^{39} +(-4.95238 - 3.15496i) q^{40} -7.01712i q^{41} -4.27597i q^{43} +(5.95826 + 5.30234i) q^{44} +(-5.96219 + 1.80059i) q^{45} +(9.91479 + 3.77285i) q^{46} +(-3.75063 - 6.49627i) q^{47} +(6.00420 + 3.45682i) q^{48} +(-0.155459 - 0.963368i) q^{50} +(-4.09050 - 3.03763i) q^{51} +(0.529789 - 2.56584i) q^{52} +(-4.27909 - 2.47053i) q^{53} +(6.93237 - 2.43766i) q^{54} -8.27923i q^{55} +(1.74349 - 0.754555i) q^{57} +(-0.773117 - 0.949056i) q^{58} +(-2.44458 + 4.23414i) q^{59} +(-1.46278 - 7.04131i) q^{60} +(2.05347 + 3.55672i) q^{61} +(5.13856 - 0.829212i) q^{62} +(-4.58850 + 6.55330i) q^{64} +(-2.35524 + 1.35980i) q^{65} +(0.437853 + 9.75868i) q^{66} +(-2.09778 - 1.21116i) q^{67} +(3.91113 - 4.39495i) q^{68} +(5.16042 + 11.9238i) q^{69} +0.901192 q^{71} +(2.09656 + 8.22219i) q^{72} +(6.50543 - 11.2677i) q^{73} +(5.52095 + 2.10087i) q^{74} +(0.712537 - 0.959509i) q^{75} +(0.690016 + 2.08231i) q^{76} +(2.70419 - 1.72734i) q^{78} +(8.97336 - 5.18077i) q^{79} +(8.24804 - 0.964154i) q^{80} +(8.06202 + 4.00048i) q^{81} +(6.26762 + 7.69395i) q^{82} -12.4386 q^{83} -6.10695 q^{85} +(3.81926 + 4.68841i) q^{86} +(0.172258 - 1.48928i) q^{87} +(-11.2690 - 0.491915i) q^{88} +(-7.38393 + 4.26311i) q^{89} +(4.92900 - 7.29963i) q^{90} +(-14.2410 + 4.71904i) q^{92} +(5.11797 + 3.80064i) q^{93} +(9.91479 + 3.77285i) q^{94} +(1.13854 - 1.97200i) q^{95} +(-9.67092 + 1.57265i) q^{96} -15.3909 q^{97} +(-8.18919 + 8.72195i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} - 2 q^{9} + 10 q^{10} + 12 q^{12} + 24 q^{13} - 10 q^{16} - 10 q^{18} + 28 q^{22} + 14 q^{24} - 12 q^{25} - 14 q^{30} - 10 q^{33} + 8 q^{34} + 44 q^{36} - 8 q^{37} - 34 q^{40} + 18 q^{45}+ \cdots - 72 q^{97}+O(q^{100}) \) 24 * q - 2 * q^4 - 2 * q^9 + 10 * q^10 + 12 * q^12 + 24 * q^13 - 10 * q^16 - 10 * q^18 + 28 * q^22 + 14 * q^24 - 12 * q^25 - 14 * q^30 - 10 * q^33 + 8 * q^34 + 44 * q^36 - 8 * q^37 - 34 * q^40 + 18 * q^45 + 24 * q^46 - 8 * q^48 - 16 * q^52 - 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 - 4 * q^61 - 68 * q^64 - 30 * q^66 - 36 * q^69 + 20 * q^72 + 24 * q^76 - 104 * q^78 + 26 * q^81 + 68 * q^82 - 40 * q^85 - 34 * q^88 + 40 * q^90 - 6 * q^93 + 24 * q^94 + 62 * q^96 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more