LMFDB - Embedded newform 588.2.n.e.275.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(263,588)]

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

lf = mfeigenbasis(mf)

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")

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

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			275.1
Character	$\chi$	$=$	588.275
Dual form			588.2.n.e.263.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32175 - 0.502962i) q^{2} +(1.72058 - 0.199011i) q^{3} +(1.49406 + 1.32958i) q^{4} +(-1.79791 - 1.03802i) q^{5} +(-2.37428 - 0.602344i) q^{6} +(-1.30604 - 2.50883i) q^{8} +(2.92079 - 0.684828i) q^{9} +(1.85431 + 2.27629i) q^{10} +(1.99399 + 3.45368i) q^{11} +(2.83525 + 1.99032i) q^{12} +1.30998 q^{13} +(-3.30003 - 1.42820i) q^{15} +(0.464417 + 3.97295i) q^{16} +(2.54752 - 1.47081i) q^{17} +(-4.20500 - 0.563873i) 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} +(-2.74644 - 4.05673i) q^{24} +(-0.345008 - 0.597572i) q^{25} +(-1.73147 - 0.658872i) q^{26} +(4.88916 - 1.75957i) q^{27} -0.865568i q^{29} +(3.64349 + 3.54752i) q^{30} +(3.18742 - 1.84026i) q^{31} +(1.38440 - 5.48484i) q^{32} +(4.11813 + 5.54551i) q^{33} +(-4.10695 + 0.662741i) q^{34} +(5.27436 + 2.86026i) q^{36} +(-2.08850 + 3.61738i) q^{37} +(-0.979678 - 1.20262i) q^{38} +(2.25393 - 0.260701i) q^{39} +(-0.256080 + 5.86637i) q^{40} +7.01712i q^{41} -4.27597i q^{43} +(-1.61283 + 7.81117i) q^{44} +(-5.96219 - 1.80059i) q^{45} +(-8.22478 + 6.70004i) q^{46} +(3.75063 - 6.49627i) q^{47} +(1.58973 + 6.74335i) q^{48} +(0.155459 + 0.963368i) q^{50} +(4.09050 - 3.03763i) q^{51} +(1.95719 + 1.74173i) q^{52} +(-4.27909 + 2.47053i) q^{53} +(-7.34726 - 0.133348i) q^{54} -8.27923i q^{55} +(1.74349 + 0.754555i) q^{57} +(-0.435348 + 1.14407i) q^{58} +(2.44458 + 4.23414i) q^{59} +(-3.03152 - 6.52148i) 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} +(-2.65397 - 9.40106i) q^{66} +(2.09778 - 1.21116i) q^{67} +(5.76170 + 1.18966i) q^{68} +(5.16042 - 11.9238i) q^{69} -0.901192 q^{71} +(-5.53280 - 6.43336i) q^{72} +(6.50543 + 11.2677i) q^{73} +(4.57989 - 3.73085i) q^{74} +(-0.712537 - 0.959509i) q^{75} +(0.690016 + 2.08231i) q^{76} +(-3.11026 - 0.789060i) q^{78} +(-8.97336 - 5.18077i) q^{79} +(3.28904 - 7.62509i) q^{80} +(8.06202 - 4.00048i) q^{81} +(3.52935 - 9.27489i) q^{82} +12.4386 q^{83} -6.10695 q^{85} +(-2.15065 + 5.65178i) q^{86} +(-0.172258 - 1.48928i) q^{87} +(6.06049 - 9.51324i) q^{88} +(-7.38393 - 4.26311i) q^{89} +(6.97491 + 5.37869i) q^{90} +(14.2410 - 4.71904i) q^{92} +(5.11797 - 3.80064i) q^{93} +(-8.22478 + 6.70004i) q^{94} +(-1.13854 - 1.97200i) q^{95} +(1.29043 - 9.71261i) 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 $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.32175	−	0.502962i	−0.934620	−	0.355648i
$2$	−1.32175	−	0.502962i	−0.934620	−	0.355648i
$3$	1.72058	−	0.199011i	0.993377	−	0.114899i
$3$	1.72058	−	0.199011i	0.993377	−	0.114899i
$4$	1.49406	+	1.32958i	0.747029	+	0.664792i
$5$	−1.79791	−	1.03802i	−0.804051	−	0.464219i	0.0408349	−	0.999166i	$-0.486998\pi$
$5$	−1.79791	−	1.03802i	−0.804051	−	0.464219i	−0.844886	+	0.534947i	$0.820332\pi$
$6$	−2.37428	−	0.602344i	−0.969294	−	0.245906i
$7$		0			0
$7$		0			0
$8$	−1.30604	−	2.50883i	−0.461756	−	0.887007i
$9$	2.92079	−	0.684828i	0.973596	−	0.228276i
$10$	1.85431	+	2.27629i	0.586383	+	0.719827i
$11$	1.99399	+	3.45368i	0.601209	+	1.04132i	0.992638	+	0.121117i	$0.0386475\pi$
$11$	1.99399	+	3.45368i	0.601209	+	1.04132i	−0.391429	+	0.920208i	$0.628019\pi$
$12$	2.83525	+	1.99032i	0.818465	+	0.574556i
$13$	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
$16$	0.464417	+	3.97295i	0.116104	+	0.993237i
$17$	2.54752	−	1.47081i	0.617863	−	0.356724i	−0.158173	−	0.987411i	$-0.550560\pi$
$17$	2.54752	−	1.47081i	0.617863	−	0.356724i	0.776037	+	0.630688i	$0.217227\pi$
$18$	−4.20500	−	0.563873i	−0.991129	−	0.132906i
$19$	0.949883	+	0.548415i	0.217918	+	0.125815i	0.604986	−	0.796236i	$-0.293179\pi$
$19$	0.949883	+	0.548415i	0.217918	+	0.125815i	−0.387068	+	0.922051i	$0.626512\pi$
$20$	−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	−0.148681	−	0.988885i	$-0.547503\pi$
$23$	3.75063	−	6.49627i	0.782059	−	1.35457i	0.930740	−	0.365681i	$-0.119164\pi$
$24$	−2.74644	−	4.05673i	−0.560614	−	0.828077i
$25$	−0.345008	−	0.597572i	−0.0690016	−	0.119514i
$26$	−1.73147	−	0.658872i	−0.339570	−	0.129216i
$27$	4.88916	−	1.75957i	0.940920	−	0.338630i
$28$		0			0
$29$		−	0.865568i		−	0.160732i	−0.996765	−	0.0803660i	$-0.974391\pi$
$29$		−	0.865568i		−	0.160732i	0.996765	−	0.0803660i	$-0.0256089\pi$
$30$	3.64349	+	3.54752i	0.665207	+	0.647685i
$31$	3.18742	−	1.84026i	0.572477	−	0.330520i	−0.185661	−	0.982614i	$-0.559443\pi$
$31$	3.18742	−	1.84026i	0.572477	−	0.330520i	0.758138	+	0.652094i	$0.226109\pi$
$32$	1.38440	−	5.48484i	0.244729	−	0.969591i
$33$	4.11813	+	5.54551i	0.716875	+	0.965350i
$34$	−4.10695	+	0.662741i	−0.704336	+	0.113659i
$35$		0			0
$36$	5.27436	+	2.86026i	0.879061	+	0.476710i
$37$	−2.08850	+	3.61738i	−0.343347	+	0.594694i	−0.985052	−	0.172257i	$-0.944894\pi$
$37$	−2.08850	+	3.61738i	−0.343347	+	0.594694i	0.641705	+	0.766952i	$0.278227\pi$
$38$	−0.979678	−	1.20262i	−0.158925	−	0.195091i
$39$	2.25393	−	0.260701i	0.360918	−	0.0417456i
$40$	−0.256080	+	5.86637i	−0.0404899	+	0.927554i
$41$			7.01712i			1.09589i	0.836514	+	0.547945i	$0.184590\pi$
$41$			7.01712i			1.09589i	−0.836514	+	0.547945i	$0.815410\pi$
$42$		0			0
$43$		−	4.27597i		−	0.652080i	−0.945356	−	0.326040i	$-0.894286\pi$
$43$		−	4.27597i		−	0.652080i	0.945356	−	0.326040i	$-0.105714\pi$
$44$	−1.61283	+	7.81117i	−0.243143	+	1.17758i
$45$	−5.96219	−	1.80059i	−0.888791	−	0.268416i
$46$	−8.22478	+	6.70004i	−1.21268	+	0.987867i
$47$	3.75063	−	6.49627i	0.547085	−	0.947579i	−0.451388	−	0.892328i	$-0.649071\pi$
$47$	3.75063	−	6.49627i	0.547085	−	0.947579i	0.998473	−	0.0552509i	$-0.0175959\pi$
$48$	1.58973	+	6.74335i	0.229457	+	0.973319i
$49$		0			0
$50$	0.155459	+	0.963368i	0.0219853	+	0.136241i
$51$	4.09050	−	3.03763i	0.572784	−	0.425353i
$52$	1.95719	+	1.74173i	0.271414	+	0.241535i
$53$	−4.27909	+	2.47053i	−0.587778	+	0.339354i	−0.764218	−	0.644957i	$-0.776875\pi$
$53$	−4.27909	+	2.47053i	−0.587778	+	0.339354i	0.176440	+	0.984311i	$0.443542\pi$
$54$	−7.34726	−	0.133348i	−0.999835	−	0.0181463i
$55$		−	8.27923i		−	1.11637i
$56$		0			0
$57$	1.74349	+	0.754555i	0.230931	+	0.0999432i
$58$	−0.435348	+	1.14407i	−0.0571640	+	0.150223i
$59$	2.44458	+	4.23414i	0.318257	+	0.551238i	0.980125	−	0.198383i	$-0.0635691\pi$
$59$	2.44458	+	4.23414i	0.318257	+	0.551238i	−0.661867	+	0.749621i	$0.730236\pi$
$60$	−3.03152	−	6.52148i	−0.391368	−	0.841919i
$61$	2.05347	−	3.55672i	0.262920	−	0.455391i	−0.704096	−	0.710104i	$-0.748648\pi$
$61$	2.05347	−	3.55672i	0.262920	−	0.455391i	0.967017	+	0.254713i	$0.0819810\pi$
$62$	−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
$66$	−2.65397	−	9.40106i	−0.326681	−	1.15719i
$67$	2.09778	−	1.21116i	0.256285	−	0.147966i	−0.366354	−	0.930476i	$-0.619394\pi$
$67$	2.09778	−	1.21116i	0.256285	−	0.147966i	0.622639	+	0.782509i	$0.286061\pi$
$68$	5.76170	+	1.18966i	0.698709	+	0.144268i
$69$	5.16042	−	11.9238i	0.621242	−	1.43545i
$70$		0			0
$71$	−0.901192			−0.106952			−0.0534759	−	0.998569i	$-0.517030\pi$
$71$	−0.901192			−0.106952			−0.0534759	+	0.998569i	$0.517030\pi$
$72$	−5.53280	−	6.43336i	−0.652047	−	0.758179i
$73$	6.50543	+	11.2677i	0.761403	+	1.31879i	0.942128	+	0.335255i	$0.108822\pi$
$73$	6.50543	+	11.2677i	0.761403	+	1.31879i	−0.180725	+	0.983534i	$0.557844\pi$
$74$	4.57989	−	3.73085i	0.532401	−	0.433703i
$75$	−0.712537	−	0.959509i	−0.0822767	−	0.110795i
$76$	0.690016	+	2.08231i	0.0791503	+	0.238858i
$77$		0			0
$78$	−3.11026	−	0.789060i	−0.352168	−	0.0893435i
$79$	−8.97336	−	5.18077i	−1.00958	−	0.582882i	−0.0985123	−	0.995136i	$-0.531408\pi$
$79$	−8.97336	−	5.18077i	−1.00958	−	0.582882i	−0.911069	+	0.412254i	$0.864742\pi$
$80$	3.28904	−	7.62509i	0.367726	−	0.852511i
$81$	8.06202	−	4.00048i	0.895780	−	0.444498i
$82$	3.52935	−	9.27489i	0.389751	−	1.02424i
$83$	12.4386			1.36531			0.682657	−	0.730739i	$-0.260824\pi$
$83$	12.4386			1.36531			0.682657	+	0.730739i	$0.260824\pi$
$84$		0			0
$85$	−6.10695			−0.662391
$86$	−2.15065	+	5.65178i	−0.231911	+	0.609447i
$87$	−0.172258	−	1.48928i	−0.0184680	−	0.159668i
$88$	6.06049	−	9.51324i	0.646050	−	1.01411i
$89$	−7.38393	−	4.26311i	−0.782695	−	0.451889i	0.0546896	−	0.998503i	$-0.482583\pi$
$89$	−7.38393	−	4.26311i	−0.782695	−	0.451889i	−0.837385	+	0.546614i	$0.815916\pi$
$90$	6.97491	+	5.37869i	0.735220	+	0.566964i
$91$		0			0
$92$	14.2410	−	4.71904i	1.48473	−	0.491994i
$93$	5.11797	−	3.80064i	0.530709	−	0.394108i
$94$	−8.22478	+	6.70004i	−0.848321	+	0.691056i
$95$	−1.13854	−	1.97200i	−0.116811	−	0.202323i
$96$	1.29043	−	9.71261i	0.131703	−	0.991289i
$97$	−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
$100$	0.279059	−	1.35152i	0.0279059	−	0.135152i
$101$	−5.28731	+	3.05263i	−0.526107	+	0.303748i	−0.739430	−	0.673234i	$-0.764905\pi$
$101$	−5.28731	+	3.05263i	−0.526107	+	0.303748i	0.213322	+	0.976982i	$0.431572\pi$
$102$	−6.93444	+	1.95763i	−0.686612	+	0.193834i
$103$	−6.17682	−	3.56619i	−0.608620	−	0.351387i	0.163805	−	0.986493i	$-0.447623\pi$
$103$	−6.17682	−	3.56619i	−0.608620	−	0.351387i	−0.772425	+	0.635106i	$0.780956\pi$
$104$	−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	$-0.796064\pi$
$107$	1.20838	−	2.09297i	0.116818	−	0.202335i	0.918505	+	0.395409i	$0.129397\pi$
$108$	9.64419	+	3.87165i	0.928012	+	0.372549i
$109$	3.39848	+	5.88634i	0.325516	+	0.563809i	0.981617	−	0.190864i	$-0.0611288\pi$
$109$	3.39848	+	5.88634i	0.325516	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$110$	−4.16414	+	10.9431i	−0.397035	+	1.04338i
$111$	−2.87353	+	6.63963i	−0.272743	+	0.630206i
$112$		0			0
$113$			3.16365i			0.297611i	0.988867	+	0.148805i	$0.0475428\pi$
$113$			3.16365i			0.297611i	−0.988867	+	0.148805i	$0.952457\pi$
$114$	−1.92495	−	1.87424i	−0.180288	−	0.175539i
$115$	−13.4866	+	7.78649i	−1.25763	+	0.726094i
$116$	1.15085	−	1.29321i	0.106853	−	0.120071i
$117$	3.82619	−	0.897114i	0.353731	−	0.0829382i
$118$	−1.10152	−	6.82601i	−0.101403	−	0.628386i
$119$		0			0
$120$	0.726865	+	10.1445i	0.0663534	+	0.926064i
$121$	−2.45196	+	4.24691i	−0.222905	+	0.386083i
$122$	−4.50308	+	3.66828i	−0.407690	+	0.332111i
$123$	1.39648	+	12.0735i	0.125917	+	1.08863i
$124$	7.20896	+	1.48849i	0.647384	+	0.133670i
$125$			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	$0.766526\pi$
$128$	9.36092	−	6.35399i	0.827396	−	0.561619i
$129$	−0.850965	−	7.35715i	−0.0749233	−	0.647761i
$130$	2.42911	+	2.98191i	0.213047	+	0.261531i
$131$	−3.70488	+	6.41704i	−0.323697	+	0.560660i	−0.981248	−	0.192751i	$-0.938259\pi$
$131$	−3.70488	+	6.41704i	−0.323697	+	0.560660i	0.657551	+	0.753410i	$0.271593\pi$
$132$	−1.22049	+	13.7607i	−0.106230	+	1.19772i
$133$		0			0
$134$	−3.38192	+	0.545742i	−0.292153	+	0.0471449i
$135$	−10.6168	−	1.91152i	−0.913745	−	0.164517i
$136$	−7.01718	−	4.47035i	−0.601719	−	0.383330i
$137$	−13.0764	+	7.54965i	−1.11719	+	0.645010i	−0.940682	−	0.339290i	$-0.889813\pi$
$137$	−13.0764	+	7.54965i	−1.11719	+	0.645010i	−0.176508	+	0.984299i	$0.556480\pi$
$138$	−12.8180	+	13.1648i	−1.09114	+	1.12066i
$139$			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
$142$	1.19115	+	0.453266i	0.0999593	+	0.0380372i
$143$	2.61209	+	4.52427i	0.218434	+	0.378338i
$144$	4.07725	+	11.2861i	0.339771	+	0.940508i
$145$	−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	0.0381428	−	0.999272i	$-0.487856\pi$
$149$	−9.86511	−	5.69562i	−0.808181	−	0.466604i	−0.846324	+	0.532669i	$0.821189\pi$
$150$	0.459201	+	1.62661i	0.0374936	+	0.132812i
$151$	0.795186	−	0.459101i	0.0647113	−	0.0373611i	−0.467295	−	0.884101i	$-0.654771\pi$
$151$	0.795186	−	0.459101i	0.0647113	−	0.0373611i	0.532007	+	0.846740i	$0.321438\pi$
$152$	0.135294	−	3.09935i	0.0109738	−	0.251391i
$153$	6.43351	−	6.04054i	0.520118	−	0.488348i
$154$		0			0
$155$	−7.64093			−0.613734
$156$	3.71413	+	2.60729i	0.297368	+	0.208750i
$157$	−4.36346	−	7.55773i	−0.348242	−	0.603172i	0.637695	−	0.770289i	$-0.279888\pi$
$157$	−4.36346	−	7.55773i	−0.348242	−	0.603172i	−0.985937	+	0.167116i	$0.946555\pi$
$158$	9.25482	+	11.3610i	0.736274	+	0.903829i
$159$	−6.87085	+	5.10234i	−0.544894	+	0.404642i
$160$	−8.18242	+	8.42422i	−0.646877	+	0.665993i
$161$		0			0
$162$	−12.6681	+	1.23275i	−0.995299	+	0.0968540i
$163$	7.78729	+	4.49599i	0.609948	+	0.352153i	0.772945	−	0.634473i	$-0.218783\pi$
$163$	7.78729	+	4.49599i	0.609948	+	0.352153i	−0.162997	+	0.986627i	$0.552116\pi$
$164$	−9.32984	+	10.4840i	−0.728538	+	0.818661i
$165$	−1.64766	−	14.2451i	−0.128270	−	1.10898i
$166$	−16.4408	−	6.25615i	−1.27605	−	0.485571i
$167$	−16.1830			−1.25228			−0.626141	−	0.779710i	$-0.715367\pi$
$167$	−16.1830			−1.25228			−0.626141	+	0.779710i	$0.715367\pi$
$168$		0			0
$169$	−11.2839			−0.867996
$170$	8.07187	+	3.07156i	0.619084	+	0.235578i
$171$	3.14998	+	0.951298i	0.240885	+	0.0727476i
$172$	5.68526	−	6.38855i	0.433497	−	0.487122i
$173$	3.66216	+	2.11435i	0.278429	+	0.160751i	0.632712	−	0.774387i	$-0.281942\pi$
$173$	3.66216	+	2.11435i	0.278429	+	0.160751i	−0.354283	+	0.935138i	$0.615275\pi$
$174$	−0.521370	+	2.05510i	−0.0395249	+	0.155797i
$175$		0			0
$176$	−12.7953	+	9.52595i	−0.964479	+	0.718046i
$177$	5.04874	+	6.79868i	0.379486	+	0.511020i
$178$	7.61554	+	9.34862i	0.570809	+	0.700709i
$179$	−3.27593	−	5.67408i	−0.244855	−	0.424101i	0.717236	−	0.696830i	$-0.245407\pi$
$179$	−3.27593	−	5.67408i	−0.244855	−	0.424101i	−0.962091	+	0.272729i	$0.912074\pi$
$180$	−6.51382	−	10.6174i	−0.485512	−	0.791375i
$181$	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
$184$	−21.1966	−	0.925278i	−1.56263	−	0.0682124i
$185$	7.50987	−	4.33583i	0.552137	−	0.318776i
$186$	−8.67627	+	2.44935i	−0.636175	+	0.179595i
$187$	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	0.0146426	+	0.999893i	$0.495339\pi$
$191$	−11.8662	+	20.5529i	−0.858611	+	1.48716i	−0.873254	+	0.487266i	$0.837994\pi$
$192$	−6.59070	+	12.1886i	−0.475643	+	0.879639i
$193$	1.98698	+	3.44155i	0.143026	+	0.247728i	0.928635	−	0.370995i	$-0.120983\pi$
$193$	1.98698	+	3.44155i	0.143026	+	0.247728i	−0.785609	+	0.618724i	$0.787650\pi$
$194$	20.3429	+	7.74104i	1.46054	+	0.555774i
$195$	−4.32298	−	1.87092i	−0.309575	−	0.133979i
$196$		0			0
$197$			19.7720i			1.40870i	0.709853	+	0.704350i	$0.248761\pi$
$197$			19.7720i			1.40870i	−0.709853	+	0.704350i	$0.751239\pi$
$198$	−6.43727	−	15.6471i	−0.457477	−	1.11199i
$199$	6.63939	−	3.83325i	0.470654	−	0.271732i	−0.245859	−	0.969305i	$-0.579070\pi$
$199$	6.63939	−	3.83325i	0.470654	−	0.271732i	0.716513	+	0.697573i	$0.245737\pi$
$200$	−1.04861	+	1.64602i	−0.0741481	+	0.116391i
$201$	3.36837	−	2.50137i	0.237587	−	0.176433i
$202$	8.52388	−	1.37550i	0.599738	−	0.0967801i
$203$		0			0
$204$	10.1502	+	0.900265i	0.710657	+	0.0630311i
$205$	7.28394	−	12.6162i	0.508733	−	0.881151i
$206$	6.37056	+	7.82032i	0.443858	+	0.544868i
$207$	6.50595	−	21.5428i	0.452195	−	1.49733i
$208$	0.608379	+	5.20450i	0.0421835	+	0.360867i
$209$			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	$-0.132518\pi$
$212$	−9.67799	−	1.99829i	−0.664687	−	0.137243i
$213$	−1.55057	+	0.179347i	−0.106243	+	0.0122887i
$214$	−2.64986	+	2.15862i	−0.181141	+	0.147560i
$215$	−4.43857	+	7.68782i	−0.302708	+	0.524305i
$216$	−10.7999	−	9.96802i	−0.734842	−	0.678238i
$217$		0			0
$218$	−1.53134	−	9.48959i	−0.103716	−	0.642716i
$219$	13.4355	+	18.0924i	0.907888	+	1.22257i
$220$	11.0079	−	12.3696i	0.742154	−	0.833961i
$221$	3.33720	−	1.92674i	0.224485	−	0.129606i
$222$	7.13758	−	7.33067i	0.479043	−	0.492003i
$223$		−	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
$226$	1.59119	−	4.18156i	0.105845	−	0.278153i
$227$	−10.7314	−	18.5874i	−0.712271	−	1.23369i	−0.964003	−	0.265892i	$-0.914333\pi$
$227$	−10.7314	−	18.5874i	−0.712271	−	1.23369i	0.251732	−	0.967797i	$-0.419000\pi$
$228$	1.60163	+	3.44546i	0.106071	+	0.228181i
$229$	−9.81541	+	17.0008i	−0.648621	+	1.12344i	0.334832	+	0.942278i	$0.391320\pi$
$229$	−9.81541	+	17.0008i	−0.648621	+	1.12344i	−0.983453	+	0.181166i	$0.942013\pi$
$230$	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	0.846703	−	0.532065i	$-0.178584\pi$
$233$	12.3530	+	7.13202i	0.809273	+	0.467234i	−0.0374302	+	0.999299i	$0.511917\pi$
$234$	−5.50848	−	0.738665i	−0.360101	−	0.0482880i
$235$	−13.4866	+	7.78649i	−0.879768	+	0.507934i
$236$	−1.97729	+	9.57632i	−0.128711	+	0.623365i
$237$	−16.4704	−	7.12813i	−1.06987	−	0.463022i
$238$		0			0
$239$	15.2819			0.988501			0.494251	−	0.869320i	$-0.335443\pi$
$239$	15.2819			0.988501			0.494251	+	0.869320i	$0.335443\pi$
$240$	4.14158	−	13.7741i	0.267338	−	0.889116i
$241$	−2.95196	−	5.11294i	−0.190152	−	0.329353i	0.755148	−	0.655554i	$-0.227565\pi$
$241$	−2.95196	−	5.11294i	−0.190152	−	0.329353i	−0.945301	+	0.326201i	$0.894231\pi$
$242$	5.37691	−	4.38012i	0.345641	−	0.281565i
$243$	13.0752	−	8.48757i	0.838775	−	0.544478i
$244$	7.79696	−	2.58368i	0.499149	−	0.165403i
$245$		0			0
$246$	4.22672	−	16.6606i	0.269486	−	1.06224i
$247$	1.24433	+	0.718415i	0.0791749	+	0.0457116i
$248$	−8.77981	−	5.59325i	−0.557518	−	0.355171i
$249$	21.4016	−	2.47542i	1.35627	−	0.156873i
$250$	5.94137	−	15.6135i	0.375765	−	0.987487i
$251$	−23.7400			−1.49845			−0.749226	−	0.662314i	$-0.769575\pi$
$251$	−23.7400			−1.49845			−0.749226	+	0.662314i	$0.769575\pi$
$252$		0			0
$253$	29.9148			1.88073
$254$	7.58913	−	19.9437i	0.476184	−	1.25138i
$255$	−10.5075	+	1.21535i	−0.658004	+	0.0761081i
$256$	−15.5686	+	3.69021i	−0.973040	+	0.230638i
$257$	−12.8177	−	7.40033i	−0.799549	−	0.461620i	0.0437643	−	0.999042i	$-0.486065\pi$
$257$	−12.8177	−	7.40033i	−0.799549	−	0.461620i	−0.843314	+	0.537422i	$0.819398\pi$
$258$	−2.57560	+	10.1523i	−0.160350	+	0.632057i
$259$		0			0
$260$	−1.71090	−	5.16309i	−0.106105	−	0.320202i
$261$	−0.592766	−	2.52814i	−0.0366913	−	0.156488i
$262$	8.12447	−	6.61833i	0.501931	−	0.408881i
$263$	−6.95299	−	12.0429i	−0.428740	−	0.742599i	0.568022	−	0.823013i	$-0.307709\pi$
$263$	−6.95299	−	12.0429i	−0.428740	−	0.742599i	−0.996761	+	0.0804148i	$0.974376\pi$
$264$	8.53431	−	17.5744i	0.525251	−	1.08163i
$265$	10.2579			0.630138
$266$		0			0
$267$	−13.5530	−	5.86554i	−0.829433	−	0.358965i
$268$	4.74454	+	0.979641i	0.289819	+	0.0598411i
$269$	7.15156	−	4.12896i	0.436039	−	0.251747i	−0.265877	−	0.964007i	$-0.585662\pi$
$269$	7.15156	−	4.12896i	0.436039	−	0.251747i	0.701916	+	0.712260i	$0.252328\pi$
$270$	13.0713	+	7.86639i	0.795494	+	0.478733i
$271$	−4.59472	−	2.65276i	−0.279109	−	0.161144i	0.353911	−	0.935279i	$-0.384852\pi$
$271$	−4.59472	−	2.65276i	−0.279109	−	0.161144i	−0.633020	+	0.774135i	$0.718185\pi$
$272$	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
$276$	23.5636	−	10.9536i	1.41836	−	0.659329i
$277$	−6.30239	−	10.9161i	−0.378674	−	0.655883i	0.612196	−	0.790706i	$-0.290287\pi$
$277$	−6.30239	−	10.9161i	−0.378674	−	0.655883i	−0.990870	+	0.134824i	$0.956953\pi$
$278$	7.28095	−	19.1339i	0.436683	−	1.14757i
$279$	8.04951	−	7.55783i	0.481912	−	0.452476i
$280$		0			0
$281$		−	2.02977i		−	0.121086i	−0.998166	−	0.0605428i	$-0.980717\pi$
$281$		−	2.02977i		−	0.121086i	0.998166	−	0.0605428i	$-0.0192832\pi$
$282$	−12.8180	+	13.1648i	−0.763301	+	0.783951i
$283$	6.64918	−	3.83891i	0.395253	−	0.228199i	−0.289181	−	0.957274i	$-0.593383\pi$
$283$	6.64918	−	3.83891i	0.395253	−	0.228199i	0.684434	+	0.729075i	$0.260050\pi$
$284$	−1.34643	−	1.19821i	−0.0798961	−	0.0711006i
$285$	−2.35139	−	3.16641i	−0.139285	−	0.187562i
$286$	−1.17700	−	7.29374i	−0.0695972	−	0.431288i
$287$		0			0
$288$	0.287363	−	16.9681i	0.0169331	−	0.999857i
$289$	−4.17344	+	7.22861i	−0.245497	+	0.425212i
$290$	1.97029	−	1.60503i	0.115699	−	0.0942506i
$291$	−26.4813	+	3.06296i	−1.55236	+	0.179554i
$292$	−5.26190	+	25.4842i	−0.307929	+	1.49135i
$293$			1.55539i			0.0908671i	0.998967	+	0.0454336i	$0.0144669\pi$
$293$			1.55539i			0.0908671i	−0.998967	+	0.0454336i	$0.985533\pi$
$294$		0			0
$295$		−	10.1501i		−	0.590964i
$296$	11.8031	+	0.515232i	0.686041	+	0.0299472i
$297$	15.8259	+	13.3771i	0.918313	+	0.776216i
$298$	10.1745	+	12.4900i	0.589395	+	0.723525i
$299$	4.91326	−	8.51001i	0.284141	−	0.492147i
$300$	0.211175	−	2.38094i	0.0121922	−	0.137464i
$301$		0			0
$302$	−1.28195	+	0.206869i	−0.0737679	+	0.0119040i
$303$	−8.48974	+	6.30453i	−0.487723	+	0.362186i
$304$	−1.73768	+	4.02853i	−0.0996629	+	0.231052i
$305$	−7.38393	+	4.26311i	−0.422803	+	0.244105i
$306$	−11.5417	+	4.74828i	−0.659793	+	0.271441i
$307$			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
$310$	10.0994	+	3.84310i	0.573608	+	0.218273i
$311$	−9.13857	−	15.8285i	−0.518201	−	0.897550i	−0.999776	−	0.0211458i	$-0.993269\pi$
$311$	−9.13857	−	15.8285i	−0.518201	−	0.897550i	0.481575	−	0.876405i	$-0.340065\pi$
$312$	−3.59779	−	5.31425i	−0.203685	−	0.300860i
$313$	14.8909	−	25.7918i	0.841683	−	1.45784i	−0.0467882	−	0.998905i	$-0.514899\pi$
$313$	14.8909	−	25.7918i	0.841683	−	1.45784i	0.888471	−	0.458933i	$-0.151768\pi$
$314$	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	0.00351474	−	0.999994i	$-0.498881\pi$
$317$	−15.3252	−	8.84800i	−0.860748	−	0.496953i	−0.864263	+	0.503041i	$0.832215\pi$
$318$	11.6478	−	3.28824i	0.653179	−	0.184396i
$319$	2.98940	−	1.72593i	0.167374	−	0.0966336i
$320$	15.0522	−	7.01927i	0.841444	−	0.392389i
$321$	1.66258	−	3.84160i	0.0927964	−	0.214417i
$322$		0			0
$323$	3.22646			0.179525
$324$	17.3641	+	4.74218i	0.964672	+	0.263454i
$325$	−0.451955	−	0.782809i	−0.0250700	−	0.0434224i
$326$	−8.03155	−	9.85930i	−0.444827	−	0.546056i
$327$	7.01881	+	9.45159i	0.388141	+	0.522674i
$328$	17.6048	−	9.16466i	0.972062	−	0.506034i
$329$		0			0
$330$	−4.98694	+	19.6572i	−0.274522	+	1.08209i
$331$	30.3818	+	17.5410i	1.66994	+	0.964138i	0.967668	+	0.252225i	$0.0811625\pi$
$331$	30.3818	+	17.5410i	1.66994	+	0.964138i	0.702268	+	0.711913i	$0.252171\pi$
$332$	18.5840	+	16.5382i	1.01993	+	0.907649i
$333$	−3.62278	+	11.9959i	−0.198527	+	0.657370i
$334$	21.3900	+	8.13946i	1.17041	+	0.445372i
$335$	−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	$0.501153\pi$
$338$	14.9146	+	5.67540i	0.811246	+	0.308701i
$339$	0.629600	+	5.44330i	0.0341952	+	0.295640i
$340$	−9.12413	−	8.11969i	−0.494826	−	0.440352i
$341$	12.7113	+	7.33889i	0.688357	+	0.397423i
$342$	−3.68502	−	2.84170i	−0.199263	−	0.153662i
$343$		0			0
$344$	−10.7277	+	5.58461i	−0.578399	+	0.301102i
$345$	−21.6552	+	16.0812i	−1.16587	+	0.865785i
$346$	−3.77703	−	4.63658i	−0.203055	−	0.249264i
$347$	−0.0976681	−	0.169166i	−0.00524310	−	0.00908131i	0.863392	−	0.504534i	$-0.168336\pi$
$347$	−0.0976681	−	0.169166i	−0.00524310	−	0.00908131i	−0.868635	+	0.495452i	$0.835002\pi$
$348$	1.72276	−	2.45410i	0.0923495	−	0.131554i
$349$	−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
$352$	21.7034	−	6.15541i	1.15679	−	0.328085i
$353$	−17.3154	+	9.99704i	−0.921604	+	0.532089i	−0.884147	−	0.467210i	$-0.845259\pi$
$353$	−17.3154	+	9.99704i	−0.921604	+	0.532089i	−0.0374578	+	0.999298i	$0.511926\pi$
$354$	−3.25370	−	11.5255i	−0.172932	−	0.612573i
$355$	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	$-0.952936\pi$
$359$	−6.95299	+	12.0429i	−0.366965	+	0.635601i	0.622125	+	0.782918i	$0.286270\pi$
$360$	3.26950	+	17.3098i	0.172318	+	0.912307i
$361$	−8.89848	−	15.4126i	−0.468341	−	0.811191i
$362$	−16.2363	−	6.17836i	−0.853363	−	0.324727i
$363$	−3.37360	+	7.79511i	−0.177068	+	0.409137i
$364$		0			0
$365$		−	27.0112i		−	1.41383i
$366$	−7.01788	+	7.20774i	−0.366830	+	0.376754i
$367$	16.2929	−	9.40672i	0.850483	−	0.491027i	−0.0103306	−	0.999947i	$-0.503288\pi$
$367$	16.2929	−	9.40672i	0.850483	−	0.491027i	0.860814	+	0.508920i	$0.169955\pi$
$368$	27.5512	+	11.8841i	1.43621	+	0.619499i
$369$	4.80552	+	20.4955i	0.250165	+	1.06695i
$370$	−12.1069	+	1.95371i	−0.629410	+	0.101568i
$371$		0			0
$372$	12.6998	+	1.12640i	0.658455	+	0.0584011i
$373$	−2.91150	+	5.04287i	−0.150752	+	0.261110i	−0.931504	−	0.363731i	$-0.881503\pi$
$373$	−2.91150	+	5.04287i	−0.150752	+	0.261110i	0.780752	+	0.624841i	$0.214836\pi$
$374$	−10.4781	−	12.8626i	−0.541809	−	0.665109i
$375$	2.35087	+	20.3248i	0.121398	+	1.04957i
$376$	−21.1966	−	0.925278i	−1.09313	−	0.0477176i
$377$		−	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	$-0.100240\pi$
$380$	0.920903	−	4.46007i	0.0472413	−	0.228797i
$381$	3.00285	+	25.9616i	0.153841	+	1.33005i
$382$	26.0216	−	21.1976i	1.33138	−	1.08456i
$383$	−6.07589	+	10.5237i	−0.310463	+	0.537738i	−0.978463	−	0.206423i	$-0.933818\pi$
$383$	−6.07589	+	10.5237i	−0.310463	+	0.537738i	0.667999	+	0.744162i	$0.267151\pi$
$384$	14.8417	−	12.7955i	0.757387	−	0.652966i
$385$		0			0
$386$	−0.895325	−	5.54825i	−0.0455708	−	0.282399i
$387$	−2.92831	−	12.4892i	−0.148854	−	0.634862i
$388$	−22.9949	−	20.4635i	−1.16739	−	1.03888i
$389$	−1.04831	+	0.605241i	−0.0531513	+	0.0306869i	−0.526340	−	0.850274i	$-0.676436\pi$
$389$	−1.04831	+	0.605241i	−0.0531513	+	0.0306869i	0.473189	+	0.880961i	$0.343103\pi$
$390$	4.77291	+	4.64719i	0.241686	+	0.235320i
$391$		−	22.0658i		−	1.11592i
$392$		0			0
$393$	−5.09748	+	11.7783i	−0.257134	+	0.594139i
$394$	9.94459	−	26.1337i	0.501001	−	1.31660i
$395$	10.7555	+	18.6291i	0.541170	+	0.937334i
$396$	0.638575	+	23.9193i	0.0320896	+	1.20199i
$397$	−4.77851	+	8.27663i	−0.239827	+	0.415392i	−0.960664	−	0.277712i	$-0.910424\pi$
$397$	−4.77851	+	8.27663i	−0.239827	+	0.415392i	0.720838	+	0.693104i	$0.243757\pi$
$398$	−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	0.236709	−	0.971581i	$-0.423931\pi$
$401$	−9.73916	−	5.62291i	−0.486351	−	0.280795i	−0.723059	+	0.690786i	$0.757265\pi$
$402$	−5.71025	+	1.61203i	−0.284801	+	0.0804008i
$403$	4.17546	−	2.41071i	0.207995	−	0.120086i
$404$	−11.9583	−	2.46911i	−0.594947	−	0.122843i
$405$	−18.6474	−	1.17607i	−0.926597	−	0.0584393i
$406$		0			0
$407$	−16.6577			−0.825693
$408$	−12.9633	−	6.29510i	−0.641778	−	0.311654i
$409$	−7.78394	−	13.4822i	−0.384891	−	0.666651i	0.606863	−	0.794807i	$-0.292428\pi$
$409$	−7.78394	−	13.4822i	−0.384891	−	0.666651i	−0.991754	+	0.128155i	$0.959094\pi$
$410$	−15.9730	+	13.0119i	−0.788851	+	0.642611i
$411$	−20.9965	+	15.5921i	−1.03568	+	0.769102i
$412$	−4.48698	−	13.5407i	−0.221058	−	0.667101i
$413$		0			0
$414$	−19.4345	+	25.2020i	−0.955152	+	1.23861i
$415$	−22.3635	−	12.9116i	−1.09778	−	0.633805i
$416$	1.81354	−	7.18505i	0.0889161	−	0.352276i
$417$	2.88091	+	24.9074i	0.141079	+	1.21972i
$418$	2.20002	−	5.78151i	0.107607	−	0.282783i
$419$	18.0336			0.881000			0.440500	−	0.897753i	$-0.354801\pi$
$419$	18.0336			0.881000			0.440500	+	0.897753i	$0.354801\pi$
$420$		0			0
$421$	−12.4978			−0.609107			−0.304554	−	0.952495i	$-0.598507\pi$
$421$	−12.4978			−0.609107			−0.304554	+	0.952495i	$0.598507\pi$
$422$	−5.90898	+	15.5284i	−0.287644	+	0.755911i
$423$	6.50595	−	21.5428i	0.316330	−	1.04745i
$424$	11.7868	+	7.50890i	0.572419	+	0.364664i
$425$	−1.75783	−	1.01488i	−0.0852672	−	0.0492290i
$426$	2.13968	+	0.542827i	0.103668	+	0.0263001i
$427$		0			0
$428$	4.58816	−	1.52038i	0.221777	−	0.0734903i
$429$	5.39468	+	7.26453i	0.260458	+	0.350735i
$430$	9.73337	−	7.92897i	0.469385	−	0.382369i
$431$	6.22304	+	10.7786i	0.299753	+	0.519188i	0.976079	−	0.217415i	$-0.0697624\pi$
$431$	6.22304	+	10.7786i	0.299753	+	0.519188i	−0.676326	+	0.736602i	$0.736429\pi$
$432$	9.26130	+	18.6072i	0.445584	+	0.895240i
$433$	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
$436$	−2.74885	+	13.3131i	−0.131646	+	0.637582i
$437$	7.12531	−	4.11380i	0.340850	−	0.196790i
$438$	−8.65863	−	30.6712i	−0.413725	−	1.46553i
$439$	4.03571	+	2.33002i	0.192614	+	0.111206i	0.593206	−	0.805051i	$-0.297862\pi$
$439$	4.03571	+	2.33002i	0.192614	+	0.111206i	−0.400592	+	0.916257i	$0.631195\pi$
$440$	−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	−0.475317	−	0.879815i	$-0.657667\pi$
$443$	11.0349	−	19.1130i	0.524283	−	0.908086i	0.999600	−	0.0282709i	$-0.00900011\pi$
$444$	−13.1212	+	6.09940i	−0.622703	+	0.289465i
$445$	8.85044	+	15.3294i	0.419551	+	0.726684i
$446$	−7.30312	+	19.1921i	−0.345813	+	0.908773i
$447$	−18.1072	−	7.83651i	−0.856441	−	0.370654i
$448$		0			0
$449$			6.02866i			0.284510i	0.989830	+	0.142255i	$0.0454353\pi$
$449$			6.02866i			0.284510i	−0.989830	+	0.142255i	$0.954565\pi$
$450$	1.11381	+	2.70733i	0.0525053	+	0.127625i
$451$	−24.2349	+	13.9920i	−1.14118	+	0.658859i
$452$	−4.20633	+	4.72667i	−0.197849	+	0.222324i
$453$	1.27681	−	0.948170i	0.0599900	−	0.0445489i
$454$	4.83554	+	29.9654i	0.226943	+	1.40635i
$455$		0			0
$456$	−0.384021	−	5.35961i	−0.0179834	−	0.250987i
$457$	19.1308	−	33.1356i	0.894902	−	1.55002i	0.0609766	−	0.998139i	$-0.480578\pi$
$457$	19.1308	−	33.1356i	0.894902	−	1.55002i	0.833926	−	0.551877i	$-0.186088\pi$
$458$	21.5243	−	17.5341i	1.00576	−	0.819312i
$459$	9.86723	−	11.6736i	0.460563	−	0.544875i
$460$	−30.5025	−	6.29808i	−1.42219	−	0.293650i
$461$		−	12.4563i		−	0.580148i	−0.957004	−	0.290074i	$-0.906320\pi$
$461$		−	12.4563i		−	0.580148i	0.957004	−	0.290074i	$-0.0936799\pi$
$462$		0			0
$463$			28.0609i			1.30410i	0.758176	+	0.652050i	$0.226091\pi$
$463$			28.0609i			1.30410i	−0.758176	+	0.652050i	$0.773909\pi$
$464$	3.43886	−	0.401985i	0.159645	−	0.0186617i
$465$	−13.1468	+	1.52063i	−0.609669	+	0.0705174i
$466$	−12.7405	−	15.6399i	−0.590192	−	0.724503i
$467$	8.54830	−	14.8061i	0.395568	−	0.685144i	−0.597605	−	0.801790i	$-0.703881\pi$
$467$	8.54830	−	14.8061i	0.395568	−	0.685144i	0.993174	+	0.116646i	$0.0372144\pi$
$468$	6.90933	+	3.74689i	0.319384	+	0.173200i
$469$		0			0
$470$	21.7422	−	3.50856i	1.00289	−	0.161838i
$471$	−9.01175	−	12.1353i	−0.415239	−	0.559165i
$472$	7.43002	−	11.6630i	0.341994	−	0.536834i
$473$	14.7679	−	8.52623i	0.679027	−	0.392036i
$474$	18.1846	+	17.7056i	0.835247	+	0.813246i
$475$		−	0.756831i		−	0.0347258i
$476$		0			0
$477$	−10.8064	+	10.1464i	−0.494792	+	0.464569i
$478$	−20.1988	−	7.68620i	−0.923873	−	0.351558i
$479$	8.21329	+	14.2258i	0.375275	+	0.649995i	0.990368	−	0.138459i	$-0.0442151\pi$
$479$	8.21329	+	14.2258i	0.375275	+	0.649995i	−0.615093	+	0.788454i	$0.710882\pi$
$480$	−12.4020	+	16.1229i	−0.566071	+	0.735908i
$481$	−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
$486$	−21.5511	+	4.64213i	−0.977578	+	0.210571i
$487$	27.7018	−	15.9937i	1.25529	−	0.724742i	0.283134	−	0.959080i	$-0.408626\pi$
$487$	27.7018	−	15.9937i	1.25529	−	0.724742i	0.972155	+	0.234339i	$0.0752924\pi$
$488$	−11.6051	−	0.506591i	−0.525340	−	0.0229323i
$489$	14.2934	+	6.18596i	0.646370	+	0.279739i
$490$		0			0
$491$	−2.03844			−0.0919935			−0.0459968	−	0.998942i	$-0.514646\pi$
$491$	−2.03844			−0.0919935			−0.0459968	+	0.998942i	$0.514646\pi$
$492$	−13.9663	+	19.8953i	−0.629650	+	0.896948i
$493$	−1.27309	−	2.20505i	−0.0573369	−	0.0993104i
$494$	−1.28336	−	1.57542i	−0.0577412	−	0.0708814i
$495$	−5.66985	−	24.1819i	−0.254841	−	1.08689i
$496$	8.79153	+	11.8088i	0.394752	+	0.530231i
$497$		0			0
$498$	−29.5327	−	7.49231i	−1.32339	−	0.335739i
$499$	−3.71805	−	2.14662i	−0.166443	−	0.0960957i	0.414465	−	0.910065i	$-0.363969\pi$
$499$	−3.71805	−	2.14662i	−0.166443	−	0.0960957i	−0.580907	+	0.813970i	$0.697302\pi$
$500$	−15.7060	+	17.6489i	−0.702396	+	0.789285i
$501$	−27.8442	+	3.22060i	−1.24399	+	0.143886i
$502$	31.3783	+	11.9403i	1.40048	+	0.532922i
$503$	26.3039			1.17283			0.586415	−	0.810010i	$-0.300539\pi$
$503$	26.3039			1.17283			0.586415	+	0.810010i	$0.300539\pi$
$504$		0			0
$505$	12.6748			0.564023
$506$	−39.5399	−	15.0460i	−1.75776	−	0.668876i
$507$	−19.4149	+	2.24563i	−0.862247	+	0.0997318i
$508$	−20.0619	+	22.5436i	−0.890103	+	1.00021i
$509$	−35.3140	−	20.3886i	−1.56527	−	0.903707i	−0.996709	−	0.0810631i	$-0.974168\pi$
$509$	−35.3140	−	20.3886i	−1.56527	−	0.903707i	−0.568557	−	0.822644i	$-0.692498\pi$
$510$	14.4996	+	3.67848i	0.642052	+	0.162886i
$511$		0			0
$512$	22.4339	+	2.95289i	0.991448	+	0.130500i
$513$	5.60911	+	1.00990i	0.247648	+	0.0445884i
$514$	13.2198	+	16.2282i	0.583100	+	0.715797i
$515$	7.40358	+	12.8234i	0.326241	+	0.565066i
$516$	8.51055	−	12.1234i	0.374656	−	0.533705i
$517$	29.9148			1.31565
$518$		0			0
$519$	6.72182	+	2.90910i	0.295055	+	0.127695i
$520$	−0.335461	+	7.68485i	−0.0147109	+	0.337003i
$521$	6.01740	−	3.47415i	0.263627	−	0.152205i	−0.362361	−	0.932038i	$-0.618029\pi$
$521$	6.01740	−	3.47415i	0.263627	−	0.152205i	0.625988	+	0.779833i	$0.284696\pi$
$522$	−0.488071	+	3.63972i	−0.0213623	+	0.159306i
$523$	6.54296	+	3.77758i	0.286104	+	0.165182i	0.636183	−	0.771538i	$-0.280512\pi$
$523$	6.54296	+	3.77758i	0.286104	+	0.165182i	−0.350080	+	0.936720i	$0.613846\pi$
$524$	−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
$528$	−20.1195	+	18.9366i	−0.875589	+	0.824108i
$529$	−16.6344	−	28.8116i	−0.723234	−	1.25268i
$530$	−13.5584	−	5.15934i	−0.588939	−	0.224107i
$531$	10.0398	+	10.6929i	0.435689	+	0.464033i
$532$		0			0
$533$			9.19231i			0.398163i
$534$	14.9636	+	14.5695i	0.647539	+	0.630482i
$535$	−4.34511	+	2.50865i	−0.187855	+	0.108458i
$536$	−5.77839	−	3.68117i	−0.249588	−	0.159002i
$537$	−6.76571	−	9.11077i	−0.291962	−	0.393159i
$538$	−11.5293	+	1.86049i	−0.497064	+	0.0802115i
$539$		0			0
$540$	−13.3205	−	16.9718i	−0.573224	−	0.730349i
$541$	−5.57548	+	9.65701i	−0.239709	+	0.415187i	−0.960631	−	0.277829i	$-0.910385\pi$
$541$	−5.57548	+	9.65701i	−0.239709	+	0.415187i	0.720922	+	0.693016i	$0.243719\pi$
$542$	4.73884	+	5.81726i	0.203551	+	0.249873i
$543$	21.1355	−	2.44464i	0.907011	−	0.104910i
$544$	−4.54037	−	16.0089i	−0.194667	−	0.686376i
$545$		−	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	$0.682616\pi$
$548$	−29.5747	−	6.10651i	−1.26337	−	0.260857i
$549$	3.56202	−	11.7947i	0.152023	−	0.503386i
$550$	−3.01718	+	2.45785i	−0.128653	+	0.104803i
$551$	0.474691	−	0.822189i	0.0202225	−	0.0350264i
$552$	−36.6545	+	2.62633i	−1.56012	+	0.111784i
$553$		0			0
$554$	2.83983	+	17.5982i	0.120653	+	0.747676i
$555$	12.0585	−	8.95468i	0.511853	−	0.380105i
$556$	−19.2472	+	21.6282i	−0.816264	+	0.917240i
$557$	25.5152	−	14.7312i	1.08112	−	0.624182i	0.149919	−	0.988698i	$-0.452099\pi$
$557$	25.5152	−	14.7312i	1.08112	−	0.624182i	0.931197	+	0.364516i	$0.118766\pi$
$558$	−14.4408	+	5.94098i	−0.611327	+	0.251502i
$559$		−	5.60145i		−	0.236916i
$560$		0			0
$561$	18.6474	+	8.07030i	0.787294	+	0.340728i
$562$	−1.02090	+	2.68285i	−0.0430639	+	0.113169i
$563$	20.3385	+	35.2274i	0.857167	+	1.48466i	0.874620	+	0.484808i	$0.161111\pi$
$563$	20.3385	+	35.2274i	0.857167	+	1.48466i	−0.0174537	+	0.999848i	$0.505556\pi$
$564$	23.5636	−	10.9536i	0.992207	−	0.461230i
$565$	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	0.407033	−	0.913413i	$-0.366563\pi$
$569$	−4.30534	−	2.48569i	−0.180489	−	0.104206i	−0.587523	+	0.809208i	$0.699897\pi$
$570$	1.51538	+	5.36787i	0.0634721	+	0.224835i
$571$	−30.2952	+	17.4909i	−1.26781	+	0.731973i	−0.974574	−	0.224066i	$-0.928067\pi$
$571$	−30.2952	+	17.4909i	−1.26781	+	0.731973i	−0.293240	+	0.956039i	$0.594734\pi$
$572$	−2.11278	+	10.2325i	−0.0883398	+	0.427843i
$573$	−16.3266	+	37.7245i	−0.682052	+	1.57596i
$574$		0			0
$575$	−5.17599			−0.215854
$576$	−8.91415	+	22.2831i	−0.371423	+	0.928464i
$577$	−7.33386	−	12.7026i	−0.305313	−	0.528817i	0.672018	−	0.740535i	$-0.265428\pi$
$577$	−7.33386	−	12.7026i	−0.305313	−	0.528817i	−0.977331	+	0.211718i	$0.932094\pi$
$578$	9.15197	−	7.45535i	0.380672	−	0.310102i
$579$	4.10366	+	5.52603i	0.170542	+	0.229654i
$580$	−3.41150	+	1.13047i	−0.141655	+	0.0469402i
$581$		0			0
$582$	36.5422	+	9.27060i	1.51472	+	0.384279i
$583$	−17.0649	−	9.85242i	−0.706755	−	0.408045i
$584$	19.7725	−	31.0372i	0.818192	−	1.28433i
$585$	−7.81037	−	2.35874i	−0.322919	−	0.0975221i
$586$	0.782305	−	2.05585i	0.0323167	−	0.0849262i
$587$	18.7469			0.773769			0.386885	−	0.922128i	$-0.373551\pi$
$587$	18.7469			0.773769			0.386885	+	0.922128i	$0.373551\pi$
$588$		0			0
$589$	4.03690			0.166337
$590$	−5.10514	+	13.4160i	−0.210175	+	0.552327i
$591$	3.93485	+	34.0194i	0.161858	+	1.39937i
$592$	−15.3416	−	6.61752i	−0.630537	−	0.271978i
$593$	38.8836	+	22.4494i	1.59676	+	0.921888i	0.992107	+	0.125398i	$0.0400207\pi$
$593$	38.8836	+	22.4494i	1.59676	+	0.921888i	0.604651	+	0.796491i	$0.293313\pi$
$594$	−14.1898	−	25.6410i	−0.582214	−	1.05206i
$595$		0			0
$596$	−7.16624	−	21.6261i	−0.293541	−	0.885838i
$597$	10.6607	−	7.91673i	0.436315	−	0.324010i
$598$	−10.7743	+	8.77694i	−0.440595	+	0.358916i
$599$	−0.596454	−	1.03309i	−0.0243704	−	0.0422108i	0.853583	−	0.520957i	$-0.174425\pi$
$599$	−0.596454	−	1.03309i	−0.0243704	−	0.0422108i	−0.877953	+	0.478746i	$0.841091\pi$
$600$	−1.47664	+	3.04080i	−0.0602838	+	0.124140i
$601$	−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
$604$	1.79847	+	0.371343i	0.0731786	+	0.0151097i
$605$	8.81680	−	5.09038i	0.358454	−	0.206953i
$606$	14.3923	−	4.06301i	0.584646	−	0.165048i
$607$	−18.5588	−	10.7149i	−0.753279	−	0.434906i	0.0735982	−	0.997288i	$-0.476552\pi$
$607$	−18.5588	−	10.7149i	−0.753279	−	0.434906i	−0.826878	+	0.562382i	$0.809885\pi$
$608$	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
$612$	17.6434	−	0.471028i	0.713193	−	0.0190402i
$613$	20.2674	+	35.1041i	0.818591	+	1.41784i	0.906720	+	0.421733i	$0.138578\pi$
$613$	20.2674	+	35.1041i	0.818591	+	1.41784i	−0.0881290	+	0.996109i	$0.528089\pi$
$614$	15.8836	−	41.7410i	0.641009	−	1.68453i
$615$	10.0219	−	23.1567i	0.404120	−	0.933768i
$616$		0			0
$617$		−	46.2548i		−	1.86215i	−0.364830	−	0.931074i	$-0.618873\pi$
$617$		−	46.2548i		−	1.86215i	0.364830	−	0.931074i	$-0.381127\pi$
$618$	12.5174	+	12.1877i	0.503523	+	0.490260i
$619$	22.3403	−	12.8982i	0.897932	−	0.518421i	0.0214035	−	0.999771i	$-0.493187\pi$
$619$	22.3403	−	12.8982i	0.897932	−	0.518421i	0.876529	+	0.481349i	$0.159853\pi$
$620$	−11.4160	−	10.1592i	−0.458477	−	0.408005i
$621$	6.90676	−	38.3608i	0.277159	−	1.53937i
$622$	4.11780	+	25.5177i	0.165109	+	1.02317i
$623$		0			0
$624$	2.08252	+	8.83368i	0.0833674	+	0.353630i
$625$	10.5369	−	18.2504i	0.421476	−	0.730018i
$626$	−32.6544	+	26.6008i	−1.30513	+	1.06318i
$627$	0.870499	+	7.52603i	0.0347644	+	0.300561i
$628$	3.52937	−	17.0933i	0.140837	−	0.682095i
$629$			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	$-0.177542\pi$
$632$	−1.27809	+	29.2790i	−0.0508398	+	1.16466i
$633$	−2.33805	−	20.2140i	−0.0929291	−	0.803433i
$634$	15.8059	+	19.4028i	0.627732	+	0.770586i
$635$	15.6626	−	27.1284i	0.621552	−	1.07656i
$636$	−17.0494	−	1.51218i	−0.676054	−	0.0599620i
$637$		0			0
$638$	−4.81932	+	0.777697i	−0.190799	+	0.0307893i
$639$	−2.63219	+	0.617162i	−0.104128	+	0.0244145i
$640$	−23.4257	+	1.70705i	−0.925982	+	0.0674771i
$641$	5.24154	−	3.02620i	0.207028	−	0.119528i	−0.392901	−	0.919581i	$-0.628529\pi$
$641$	5.24154	−	3.02620i	0.207028	−	0.119528i	0.599930	+	0.800053i	$0.295195\pi$
$642$	−4.12970	+	4.24143i	−0.162986	+	0.167396i
$643$			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
$646$	−4.26458	−	1.62279i	−0.167787	−	0.0638477i
$647$	−15.4951	−	26.8383i	−0.609175	−	1.05512i	−0.991377	−	0.131044i	$-0.958167\pi$
$647$	−15.4951	−	26.8383i	−0.609175	−	1.05512i	0.382201	−	0.924079i	$-0.375166\pi$
$648$	−20.5659	−	15.0015i	−0.807905	−	0.589313i
$649$	−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	0.631008	−	0.775776i	$-0.282641\pi$
$653$	7.01889	+	4.05236i	0.274670	+	0.158581i	−0.356338	+	0.934357i	$0.615975\pi$
$654$	−4.52333	−	16.0229i	−0.176876	−	0.626543i
$655$	13.3221	−	7.69152i	0.520538	−	0.300533i
$656$	−27.8786	+	3.25887i	−1.08848	+	0.127238i
$657$	26.7174	+	28.4556i	1.04235	+	1.11016i
$658$		0			0
$659$	38.3085			1.49229			0.746143	−	0.665785i	$-0.231903\pi$
$659$	38.3085			1.49229			0.746143	+	0.665785i	$0.231903\pi$
$660$	16.4783	−	23.4737i	0.641417	−	0.913711i
$661$	3.32843	+	5.76501i	0.129461	+	0.224233i	0.923468	−	0.383676i	$-0.125342\pi$
$661$	3.32843	+	5.76501i	0.129461	+	0.224233i	−0.794007	+	0.607909i	$0.792009\pi$
$662$	−31.3348	−	38.4657i	−1.21786	−	1.49501i
$663$	5.35848	−	3.97924i	0.208106	−	0.154541i
$664$	−16.2454	−	31.2064i	−0.630442	−	1.21104i
$665$		0			0
$666$	10.8219	−	14.0335i	0.419340	−	0.543786i
$667$	−5.62297	−	3.24642i	−0.217722	−	0.125702i
$668$	−24.1784	−	21.5167i	−0.935491	−	0.832506i
$669$	−2.88968	−	24.9832i	−0.111722	−	0.965905i
$670$	6.64688	+	2.52932i	0.256791	+	0.0977160i
$671$	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	$0.639929\pi$
$674$	0.175776	+	0.0668876i	0.00677065	+	0.00257642i
$675$	−2.73827	−	2.31456i	−0.105396	−	0.0890874i
$676$	−16.8589	−	15.0029i	−0.648418	−	0.577036i
$677$	39.0358	+	22.5373i	1.50027	+	0.866180i	1.00000		0.000308342i	$9.81484e-5\pi$
$677$	39.0358	+	22.5373i	1.50027	+	0.866180i	0.500267	+	0.865871i	$0.333235\pi$
$678$	1.90560	−	7.51136i	0.0731842	−	0.288472i
$679$		0			0
$680$	7.97594	+	15.3213i	0.305863	+	0.587546i
$681$	−22.1634	−	29.8454i	−0.849303	−	1.14368i
$682$	−13.1100	−	16.0935i	−0.502009	−	0.616252i
$683$	7.80843	+	13.5246i	0.298781	+	0.517505i	0.975857	−	0.218408i	$-0.0700865\pi$
$683$	7.80843	+	13.5246i	0.298781	+	0.517505i	−0.677076	+	0.735913i	$0.736753\pi$
$684$	3.44142	+	5.60945i	0.131586	+	0.214483i
$685$	31.3469			1.19770
$686$		0			0
$687$	−13.5049	+	31.2046i	−0.515242	+	1.19053i
$688$	16.9882	−	1.98584i	0.647670	−	0.0757093i
$689$	−5.60554	+	3.23636i	−0.213554	+	0.123295i
$690$	36.7110	−	10.3637i	1.39756	−	0.394539i
$691$	−33.1799	−	19.1564i	−1.26222	−	0.728744i	−0.288718	−	0.957414i	$-0.593229\pi$
$691$	−33.1799	−	19.1564i	−1.26222	−	0.728744i	−0.973504	+	0.228670i	$0.926562\pi$
$692$	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
$696$	−3.51138	+	2.37723i	−0.133098	+	0.0901087i
$697$	10.3208	+	17.8762i	0.390930	+	0.677110i
$698$	7.67650	+	2.92111i	0.290560	+	0.110566i
$699$	22.6737	+	9.81282i	0.857598	+	0.371155i
$700$		0			0
$701$			36.6488i			1.38420i	0.721799	+	0.692102i	$0.243315\pi$
$701$			36.6488i			1.38420i	−0.721799	+	0.692102i	$0.756685\pi$
$702$	−9.62479	−	0.174683i	−0.363264	−	0.00659300i
$703$	−3.96766	+	2.29073i	−0.149643	+	0.0863964i
$704$	−31.7824	−	2.78005i	−1.19784	−	0.104777i
$705$	−21.6552	+	16.0812i	−0.815580	+	0.605655i
$706$	27.9148	−	4.50462i	1.05059	−	0.169534i
$707$		0			0
$708$	−1.49630	+	16.8703i	−0.0562344	+	0.634026i
$709$	−18.2674	+	31.6400i	−0.686045	+	1.18827i	0.287062	+	0.957912i	$0.407322\pi$
$709$	−18.2674	+	31.6400i	−0.686045	+	1.18827i	−0.973107	+	0.230353i	$0.926012\pi$
$710$	−1.67109	−	2.05138i	−0.0627147	−	0.0769868i
$711$	−29.7572	−	8.98673i	−1.11598	−	0.337029i
$712$	−1.05171	+	24.0929i	−0.0394144	+	0.902918i
$713$		−	27.6084i		−	1.03394i
$714$		0			0
$715$		−	10.8457i		−	0.405604i
$716$	2.64973	−	12.8330i	0.0990251	−	0.479593i
$717$	26.2937	−	3.04126i	0.981954	−	0.113578i
$718$	15.2473	−	12.4207i	0.569023	−	0.463535i
$719$	−12.2687	+	21.2499i	−0.457543	+	0.792488i	−0.998830	−	0.0483494i	$-0.984604\pi$
$719$	−12.2687	+	21.2499i	−0.457543	+	0.792488i	0.541287	+	0.840838i	$0.317937\pi$
$720$	4.38471	−	24.5237i	0.163408	−	0.913944i
$721$		0			0
$722$	4.00962	+	24.8473i	0.149223	+	0.924720i
$723$	−6.09660	−	8.20974i	−0.226735	−	0.305324i
$724$	18.3529	+	16.3325i	0.682081	+	0.606993i
$725$	−0.517239	+	0.298628i	−0.0192098	+	0.0110908i
$726$	8.37972	−	8.60641i	0.311000	−	0.319414i
$727$			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
$730$	−13.5856	+	35.7021i	−0.502826	+	1.32139i
$731$	−6.28914	−	10.8931i	−0.232612	−	0.402896i
$732$	12.9011	−	5.99711i	0.476839	−	0.221660i
$733$	2.92236	−	5.06167i	0.107940	−	0.186957i	−0.806996	−	0.590557i	$-0.798908\pi$
$733$	2.92236	−	5.06167i	0.107940	−	0.186957i	0.914935	+	0.403600i	$0.132241\pi$
$734$	−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
$738$	3.95677	−	29.5070i	0.145651	−	1.08617i
$739$	−1.22939	+	0.709786i	−0.0452237	+	0.0261099i	−0.522441	−	0.852675i	$-0.674979\pi$
$739$	−1.22939	+	0.709786i	−0.0452237	+	0.0261099i	0.477218	+	0.878785i	$0.341645\pi$
$740$	16.9850	+	3.50702i	0.624382	+	0.128921i
$741$	2.28394	+	0.988455i	0.0839027	+	0.0363118i
$742$		0			0
$743$	1.70600			0.0625872			0.0312936	−	0.999510i	$-0.490037\pi$
$743$	1.70600			0.0625872			0.0312936	+	0.999510i	$0.490037\pi$
$744$	−16.2195	−	7.87635i	−0.594635	−	0.288761i
$745$	11.8244	+	20.4805i	0.433212	+	0.750346i
$746$	6.38466	−	5.20105i	0.233759	−	0.190424i
$747$	36.3305	−	8.51831i	1.32926	−	0.311669i
$748$	7.38003	+	22.2713i	0.269841	+	0.814318i
$749$		0			0
$750$	7.11534	−	28.0467i	0.259815	−	1.02412i
$751$	−23.1969	−	13.3927i	−0.846466	−	0.488707i	0.0129912	−	0.999916i	$-0.495865\pi$
$751$	−23.1969	−	13.3927i	−0.846466	−	0.488707i	−0.859457	+	0.511208i	$0.829198\pi$
$752$	27.5512	+	11.8841i	1.00469	+	0.433367i
$753$	−40.8465	+	4.72451i	−1.48853	+	0.172171i
$754$	−0.570299	+	1.49871i	−0.0207691	+	0.0545798i
$755$	−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	$0.642897\pi$
$758$	−6.06562	+	15.9400i	−0.220313	+	0.578969i
$759$	51.4707	−	5.95337i	1.86827	−	0.216094i
$760$	−3.46045	+	5.43193i	−0.125524	+	0.197037i
$761$	−13.0696	−	7.54576i	−0.473774	−	0.273533i	0.244044	−	0.969764i	$-0.421526\pi$
$761$	−13.0696	−	7.54576i	−0.473774	−	0.273533i	−0.717818	+	0.696231i	$0.754859\pi$
$762$	9.08868	−	35.8251i	0.329248	−	1.29781i
$763$		0			0
$764$	−45.0557	+	14.9301i	−1.63006	+	0.540153i
$765$	−17.8371	+	4.18221i	−0.644902	+	0.151208i
$766$	13.3239	−	10.8538i	0.481411	−	0.392165i
$767$	3.20236	+	5.54665i	0.115631	+	0.200278i
$768$	−26.0527	+	9.44763i	−0.940095	+	0.340912i
$769$	−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
$772$	−1.60716	+	7.78373i	−0.0578431	+	0.280143i
$773$	−33.5367	+	19.3624i	−1.20623	+	0.696417i	−0.961934	−	0.273283i	$-0.911890\pi$
$773$	−33.5367	+	19.3624i	−1.20623	+	0.696417i	−0.244296	+	0.969701i	$0.578557\pi$
$774$	−2.41111	+	17.9805i	−0.0866655	+	0.646295i
$775$	−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
$780$	−3.97125	−	8.54303i	−0.142193	−	0.305889i
$781$	−1.79696	−	3.11243i	−0.0643004	−	0.111372i
$782$	−11.0983	+	29.1655i	−0.396873	+	1.04296i
$783$	−1.52303	−	4.23190i	−0.0544286	−	0.151236i
$784$		0			0
$785$			18.1175i			0.646642i
$786$	12.6617	−	13.0042i	0.451627	−	0.463845i
$787$	−17.6523	+	10.1915i	−0.629235	+	0.363289i	−0.780456	−	0.625211i	$-0.785013\pi$
$787$	−17.6523	+	10.1915i	−0.629235	+	0.363289i	0.151221	+	0.988500i	$0.451680\pi$
$788$	−26.2886	+	29.5406i	−0.936492	+	1.05234i
$789$	−14.3598	−	19.3371i	−0.511224	−	0.688419i
$790$	−4.84640	−	30.0327i	−0.172427	−	1.06852i
$791$		0			0
$792$	11.1865	−	31.9366i	0.397494	−	1.13482i
$793$	2.69002	−	4.65925i	0.0955253	−	0.165455i
$794$	10.4788	−	8.53624i	0.371880	−	0.302940i
$795$	17.6495	−	2.04143i	0.625965	−	0.0724022i
$796$	15.0163	+	3.10052i	0.532237	+	0.109895i
$797$		−	27.9005i		−	0.988287i	−0.869380	−	0.494143i	$-0.835482\pi$
$797$		−	27.9005i		−	0.988287i	0.869380	−	0.494143i	$-0.164518\pi$
$798$		0			0
$799$		−	22.0658i		−	0.780632i
$800$	−3.75521	+	1.06504i	−0.132767	+	0.0376547i
$801$	−24.4864	−	7.39493i	−0.865184	−	0.261287i
$802$	10.0447	+	12.3305i	0.354689	+	0.435406i
$803$	−25.9435	+	44.9354i	−0.915525	+	1.58574i
$804$	8.35832	+	0.741334i	0.294775	+	0.0261448i
$805$		0			0
$806$	−6.73142	+	1.08625i	−0.237104	+	0.0382617i
$807$	11.4831	−	8.52744i	0.404225	−	0.300180i
$808$	14.5640	+	9.27812i	0.512360	+	0.326403i
$809$	−12.3530	+	7.13202i	−0.434309	+	0.250748i	−0.701181	−	0.712984i	$-0.747343\pi$
$809$	−12.3530	+	7.13202i	−0.434309	+	0.250748i	0.266872	+	0.963732i	$0.414010\pi$
$810$	24.0557	+	10.9334i	0.845232	+	0.384161i
$811$		−	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
$814$	22.0174	+	8.37821i	0.771710	+	0.293656i
$815$	−9.33391	−	16.1668i	−0.326953	−	0.566299i
$816$	13.9680	+	14.8406i	0.488979	+	0.519525i
$817$	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	0.992333	+	0.123589i	$0.0394406\pi$
$821$	45.7169	+	26.3947i	1.59553	+	0.921181i	0.603198	+	0.797591i	$0.293893\pi$
$822$	35.5944	−	10.0485i	1.24150	−	0.350481i
$823$	4.96238	−	2.86503i	0.172978	−	0.0998687i	−0.411012	−	0.911630i	$-0.634824\pi$
$823$	4.96238	−	2.86503i	0.172978	−	0.0998687i	0.583989	+	0.811761i	$0.301491\pi$
$824$	−0.879777	+	20.1542i	−0.0306485	+	0.702105i
$825$	1.89305	−	4.37413i	0.0659077	−	0.152288i
$826$		0			0
$827$	−44.5253			−1.54830			−0.774149	−	0.633003i	$-0.781822\pi$
$827$	−44.5253			−1.54830			−0.774149	+	0.633003i	$0.781822\pi$
$828$	38.3632	−	23.5360i	1.33321	−	0.817931i
$829$	13.0293	+	22.5674i	0.452526	+	0.783799i	0.998542	−	0.0539760i	$-0.0171895\pi$
$829$	13.0293	+	22.5674i	0.452526	+	0.783799i	−0.546016	+	0.837775i	$0.683856\pi$
$830$	23.0650	+	28.3139i	0.800597	+	0.982790i
$831$	−13.0162	−	17.5277i	−0.451526	−	0.608030i
$832$	−6.01086	+	8.58471i	−0.208389	+	0.297621i
$833$		0			0
$834$	8.71961	−	34.3703i	0.301935	−	1.19015i
$835$	29.0957	+	16.7984i	1.00690	+	0.581333i
$836$	−5.81577	+	6.53520i	−0.201142	+	0.226025i
$837$	12.3457	−	14.6058i	0.426731	−	0.504850i
$838$	−23.8360	−	9.07023i	−0.823400	−	0.313326i
$839$	−46.0533			−1.58994			−0.794968	−	0.606652i	$-0.792512\pi$
$839$	−46.0533			−1.58994			−0.794968	+	0.606652i	$0.792512\pi$
$840$		0			0
$841$	28.2508			0.974165
$842$	16.5190	+	6.28594i	0.569284	+	0.216628i
$843$	−0.403945	−	3.49237i	−0.0139126	−	0.120284i
$844$	15.6204	−	17.5527i	0.537676	−	0.604189i
$845$	20.2875	+	11.7130i	0.697912	+	0.402940i
$846$	−19.4345	+	25.2020i	−0.668171	+	0.866462i
$847$		0			0
$848$	−11.8026	−	15.8532i	−0.405302	−	0.544403i
$849$	10.6765	−	7.92840i	0.366415	−	0.272102i
$850$	1.81297	+	2.22554i	0.0621842	+	0.0763355i
$851$	15.6663	+	27.1349i	0.537035	+	0.930173i
$852$	−2.55510	−	1.79366i	−0.0875363	−	0.0614498i
$853$	−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
$856$	−6.82910	−	0.298106i	−0.233414	−	0.0101890i
$857$	−35.6333	+	20.5729i	−1.21721	+	0.702756i	−0.964320	−	0.264739i	$-0.914714\pi$
$857$	−35.6333	+	20.5729i	−1.21721	+	0.702756i	−0.252890	+	0.967495i	$0.581381\pi$
$858$	−3.47665	−	12.3152i	−0.118691	−	0.420435i
$859$	49.7193	+	28.7054i	1.69640	+	0.979417i	0.949123	+	0.314905i	$0.101973\pi$
$859$	49.7193	+	28.7054i	1.69640	+	0.979417i	0.747277	+	0.664512i	$0.231361\pi$
$860$	−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	$-0.976157\pi$
$863$	−12.7433	+	22.0721i	−0.433788	+	0.751343i	0.563408	+	0.826179i	$0.309490\pi$
$864$	−2.88241	−	29.2522i	−0.0980616	−	0.995180i
$865$	−4.38950	−	7.60283i	−0.149247	−	0.258504i
$866$	−0.658017	−	0.250393i	−0.0223603	−	0.00850871i
$867$	−5.74216	+	13.2680i	−0.195014	+	0.450604i
$868$		0			0
$869$		−	41.3215i		−	1.40174i
$870$	3.07062	−	3.15369i	0.104104	−	0.106920i
$871$	2.74806	−	1.58659i	0.0931145	−	0.0537597i
$872$	10.3293	−	16.2140i	0.349794	−	0.549077i
$873$	−44.9535	+	10.5401i	−1.52145	+	0.356729i
$874$	−11.4870	+	1.85366i	−0.388553	+	0.0627010i
$875$		0			0
$876$	−3.98189	+	44.8947i	−0.134536	+	1.51685i
$877$	−20.9313	+	36.2541i	−0.706801	+	1.22422i	0.259236	+	0.965814i	$0.416529\pi$
$877$	−20.9313	+	36.2541i	−0.706801	+	1.22422i	−0.966038	+	0.258402i	$0.916804\pi$
$878$	−4.16230	−	5.10952i	−0.140471	−	0.172438i
$879$	0.309541	+	2.67618i	0.0104405	+	0.0902653i
$880$	32.8929	−	3.84502i	1.10882	−	0.129616i
$881$		−	38.5556i		−	1.29897i	−0.760373	−	0.649486i	$-0.774984\pi$
$881$		−	38.5556i		−	1.29897i	0.760373	−	0.649486i	$-0.225016\pi$
$882$		0			0
$883$			4.56420i			0.153597i	0.997047	+	0.0767987i	$0.0244699\pi$
$883$			4.56420i			0.153597i	−0.997047	+	0.0767987i	$0.975530\pi$
$884$	7.54773	+	1.55844i	0.253858	+	0.0524159i
$885$	−2.01999	−	17.4641i	−0.0679012	−	0.587050i
$886$	−24.1985	+	19.7125i	−0.812965	+	0.662255i
$887$	20.2446	−	35.0647i	0.679747	−	1.17736i	−0.295310	−	0.955401i	$-0.595423\pi$
$887$	20.2446	−	35.0647i	0.679747	−	1.17736i	0.975057	−	0.221955i	$-0.0712437\pi$
$888$	20.4107	−	1.46245i	0.684938	−	0.0490765i
$889$		0			0
$890$	−3.98797	−	24.7131i	−0.133677	−	0.828385i
$891$	29.8919	+	19.8668i	1.00142	+	0.665562i
$892$	19.3058	−	21.6940i	0.646407	−	0.726370i
$893$	7.12531	−	4.11380i	0.238439	−	0.137663i
$894$	19.9918	+	19.4652i	0.668624	+	0.651012i
$895$			13.6020i			0.454665i
$896$		0			0
$897$	6.76007	−	15.6199i	0.225712	−	0.521535i
$898$	3.03219	−	7.96840i	0.101185	−	0.265909i
$899$	−1.59287	−	2.75893i	−0.0531251	−	0.0920154i
$900$	−0.110489	−	4.13862i	−0.00368297	−	0.137954i
$901$	−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
$906$	−2.16453	+	0.611056i	−0.0719116	+	0.0203010i
$907$	2.36697	−	1.36657i	0.0785940	−	0.0453763i	−0.460188	−	0.887822i	$-0.652218\pi$
$907$	2.36697	−	1.36657i	0.0785940	−	0.0453763i	0.538782	+	0.842445i	$0.318885\pi$
$908$	8.68010	−	42.0390i	0.288059	−	1.39511i
$909$	−13.3526	+	12.5370i	−0.442878	+	0.415826i
$910$		0			0
$911$	5.16105			0.170993			0.0854966	−	0.996338i	$-0.472752\pi$
$911$	5.16105			0.170993			0.0854966	+	0.996338i	$0.472752\pi$
$912$	−2.18810	+	7.27722i	−0.0724552	+	0.240973i
$913$	24.8024	+	42.9590i	0.820839	+	1.42174i
$914$	−41.9521	+	34.1749i	−1.38765	+	1.13041i
$915$	−11.8562	+	8.80451i	−0.391955	+	0.291068i
$916$	−37.2688	+	12.3498i	−1.23139	+	0.408048i
$917$		0			0
$918$	−18.9134	+	10.4667i	−0.624235	+	0.345453i
$919$	34.5011	+	19.9192i	1.13809	+	0.657074i	0.945956	−	0.324296i	$-0.105127\pi$
$919$	34.5011	+	19.9192i	1.13809	+	0.657074i	0.192130	+	0.981370i	$0.438461\pi$
$920$	37.1491	+	23.6661i	1.22477	+	0.780249i
$921$	6.28477	+	54.3360i	0.207090	+	1.79043i
$922$	−6.26505	+	16.4641i	−0.206328	+	0.542218i
$923$	−1.18055			−0.0388582
$924$		0			0
$925$	2.88220			0.0947660
$926$	14.1136	−	37.0895i	0.463801	−	1.21884i
$927$	−20.4834	−	6.18602i	−0.672763	−	0.203176i
$928$	−4.74750	−	1.19829i	−0.155844	−	0.0393358i
$929$	22.2777	+	12.8621i	0.730909	+	0.421990i	0.818754	−	0.574144i	$-0.194665\pi$
$929$	22.2777	+	12.8621i	0.730909	+	0.421990i	−0.0878459	+	0.996134i	$0.527998\pi$
$930$	18.1417	+	4.60246i	0.594889	+	0.150921i
$931$		0			0
$932$	8.97351	+	27.0800i	0.293937	+	0.887035i
$933$	−18.8737	−	25.4155i	−0.617897	−	0.832065i
$934$	−18.7456	+	15.2705i	−0.613376	+	0.499666i
$935$	−12.1772	−	21.0915i	−0.398236	−	0.689765i
$936$	−7.24788	−	8.42760i	−0.236904	−	0.275465i
$937$	−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
$940$	−30.5025	−	6.29808i	−0.994883	−	0.205421i
$941$	41.4712	−	23.9434i	1.35192	−	0.780533i	0.363403	−	0.931632i	$-0.381615\pi$
$941$	41.4712	−	23.9434i	1.35192	−	0.780533i	0.988519	+	0.151099i	$0.0482813\pi$
$942$	5.80770	+	20.5724i	0.189225	+	0.670286i
$943$	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	$-0.800586\pi$
$947$	3.16035	−	5.47389i	0.102698	−	0.177878i	0.912795	+	0.408418i	$0.133919\pi$
$948$	−15.1303	−	32.5486i	−0.491409	−	1.05713i
$949$	8.52200	+	14.7605i	0.276636	+	0.479148i
$950$	−0.380657	+	1.00034i	−0.0123502	+	0.0324554i
$951$	−28.1290	−	12.1738i	−0.912147	−	0.394763i
$952$		0			0
$953$			3.70027i			0.119863i	0.998202	+	0.0599317i	$0.0190883\pi$
$953$			3.70027i			0.119863i	−0.998202	+	0.0599317i	$0.980912\pi$
$954$	19.3867	−	7.97573i	0.627666	−	0.258224i
$955$	42.6689	−	24.6349i	1.38073	−	0.797167i
$956$	22.8320	+	20.3185i	0.738439	+	0.657147i
$957$	4.80002	−	3.56452i	0.155163	−	0.115225i
$958$	−3.70087	−	22.9340i	−0.119570	−	0.740964i
$959$		0			0
$960$	24.5016	−	15.0728i	0.790786	−	0.486472i
$961$	−8.72691	+	15.1155i	−0.281513	+	0.487595i
$962$	5.99957	−	4.88735i	0.193434	−	0.157575i
$963$	2.09609	−	6.94065i	0.0675455	−	0.223659i
$964$	2.38768	−	11.5639i	0.0769021	−	0.372448i
$965$		−	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	$-0.0754123\pi$
$968$	13.8572	+	0.604896i	0.445386	+	0.0194421i
$969$	5.55138	−	0.642100i	0.178336	−	0.0206272i
$970$	−28.5394	−	35.0342i	−0.916346	−	1.12488i
$971$	−4.10729	+	7.11403i	−0.131809	+	0.228300i	−0.924374	−	0.381488i	$-0.875412\pi$
$971$	−4.10729	+	7.11403i	−0.131809	+	0.228300i	0.792565	+	0.609788i	$0.208745\pi$
$972$	30.8201	+	4.70365i	0.988554	+	0.150870i
$973$		0			0
$974$	−44.6592	+	7.20668i	−1.43097	+	0.230917i
$975$	−0.933412	−	1.25694i	−0.0298931	−	0.0402543i
$976$	15.0843	+	6.50654i	0.482838	+	0.208269i
$977$	30.8426	−	17.8070i	0.986744	−	0.569697i	0.0824443	−	0.996596i	$-0.473727\pi$
$977$	30.8426	−	17.8070i	0.986744	−	0.569697i	0.904299	+	0.426899i	$0.140394\pi$
$978$	−15.7810	−	15.3654i	−0.504622	−	0.491330i
$979$		−	34.0023i		−	1.08672i
$980$		0			0
$981$	13.9574	+	14.8654i	0.445625	+	0.474615i
$982$	2.69431	+	1.02526i	0.0859790	+	0.0327173i
$983$	15.5749	+	26.9764i	0.496761	+	0.860415i	0.999993	−	0.00373618i	$-0.00118926\pi$
$983$	15.5749	+	26.9764i	0.496761	+	0.860415i	−0.503232	+	0.864151i	$0.667856\pi$
$984$	28.4666	−	19.2721i	0.907481	−	0.614371i
$985$	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
$990$	−4.66844	+	34.8142i	−0.148373	+	1.10647i
$991$	−30.1606	+	17.4132i	−0.958083	+	0.553149i	−0.895582	−	0.444896i	$-0.853241\pi$
$991$	−30.1606	+	17.4132i	−0.958083	+	0.553149i	−0.0625004	+	0.998045i	$0.519907\pi$
$992$	−5.68085	−	20.0301i	−0.180367	−	0.635957i
$993$	55.7652	+	24.1343i	1.76966	+	0.765879i
$994$		0			0
$995$	−15.9161			−0.504573
$996$	35.2665	+	24.7568i	1.11746	+	0.784449i
$997$	4.22860	+	7.32414i	0.133921	+	0.231958i	0.925185	−	0.379517i	$-0.123910\pi$
$997$	4.22860	+	7.32414i	0.133921	+	0.231958i	−0.791264	+	0.611475i	$0.790576\pi$
$998$	3.83467	+	4.70733i	0.121384	+	0.149008i
$999$	−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.275.1		24
3.2	odd	2	inner	588.2.n.e.275.12		24
4.3	odd	2	inner	588.2.n.e.275.3		24
7.2	even	3		588.2.e.d.491.8		12
7.3	odd	6		84.2.n.a.11.10	yes	24
7.4	even	3	inner	588.2.n.e.263.10		24
7.5	odd	6		588.2.e.e.491.8		12
7.6	odd	2		84.2.n.a.23.1	yes	24
12.11	even	2	inner	588.2.n.e.275.10		24
21.2	odd	6		588.2.e.d.491.5		12
21.5	even	6		588.2.e.e.491.5		12
21.11	odd	6	inner	588.2.n.e.263.3		24
21.17	even	6		84.2.n.a.11.3	yes	24
21.20	even	2		84.2.n.a.23.12	yes	24
28.3	even	6		84.2.n.a.11.12	yes	24
28.11	odd	6	inner	588.2.n.e.263.12		24
28.19	even	6		588.2.e.e.491.6		12
28.23	odd	6		588.2.e.d.491.6		12
28.27	even	2		84.2.n.a.23.3	yes	24
84.11	even	6	inner	588.2.n.e.263.1		24
84.23	even	6		588.2.e.d.491.7		12
84.47	odd	6		588.2.e.e.491.7		12
84.59	odd	6		84.2.n.a.11.1	✓	24
84.83	odd	2		84.2.n.a.23.10	yes	24

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

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+(-1.32175 - 0.502962i) q^{2} +(1.72058 - 0.199011i) q^{3} +(1.49406 + 1.32958i) q^{4} +(-1.79791 - 1.03802i) q^{5} +(-2.37428 - 0.602344i) q^{6} +(-1.30604 - 2.50883i) q^{8} +(2.92079 - 0.684828i) q^{9} +(1.85431 + 2.27629i) q^{10} +(1.99399 + 3.45368i) q^{11} +(2.83525 + 1.99032i) q^{12} +1.30998 q^{13} +(-3.30003 - 1.42820i) q^{15} +(0.464417 + 3.97295i) q^{16} +(2.54752 - 1.47081i) q^{17} +(-4.20500 - 0.563873i) 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} +(-2.74644 - 4.05673i) q^{24} +(-0.345008 - 0.597572i) q^{25} +(-1.73147 - 0.658872i) q^{26} +(4.88916 - 1.75957i) q^{27} -0.865568i q^{29} +(3.64349 + 3.54752i) q^{30} +(3.18742 - 1.84026i) q^{31} +(1.38440 - 5.48484i) q^{32} +(4.11813 + 5.54551i) q^{33} +(-4.10695 + 0.662741i) q^{34} +(5.27436 + 2.86026i) q^{36} +(-2.08850 + 3.61738i) q^{37} +(-0.979678 - 1.20262i) q^{38} +(2.25393 - 0.260701i) q^{39} +(-0.256080 + 5.86637i) q^{40} +7.01712i q^{41} -4.27597i q^{43} +(-1.61283 + 7.81117i) q^{44} +(-5.96219 - 1.80059i) q^{45} +(-8.22478 + 6.70004i) q^{46} +(3.75063 - 6.49627i) q^{47} +(1.58973 + 6.74335i) q^{48} +(0.155459 + 0.963368i) q^{50} +(4.09050 - 3.03763i) q^{51} +(1.95719 + 1.74173i) q^{52} +(-4.27909 + 2.47053i) q^{53} +(-7.34726 - 0.133348i) q^{54} -8.27923i q^{55} +(1.74349 + 0.754555i) q^{57} +(-0.435348 + 1.14407i) q^{58} +(2.44458 + 4.23414i) q^{59} +(-3.03152 - 6.52148i) 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} +(-2.65397 - 9.40106i) q^{66} +(2.09778 - 1.21116i) q^{67} +(5.76170 + 1.18966i) q^{68} +(5.16042 - 11.9238i) q^{69} -0.901192 q^{71} +(-5.53280 - 6.43336i) q^{72} +(6.50543 + 11.2677i) q^{73} +(4.57989 - 3.73085i) q^{74} +(-0.712537 - 0.959509i) q^{75} +(0.690016 + 2.08231i) q^{76} +(-3.11026 - 0.789060i) q^{78} +(-8.97336 - 5.18077i) q^{79} +(3.28904 - 7.62509i) q^{80} +(8.06202 - 4.00048i) q^{81} +(3.52935 - 9.27489i) q^{82} +12.4386 q^{83} -6.10695 q^{85} +(-2.15065 + 5.65178i) q^{86} +(-0.172258 - 1.48928i) q^{87} +(6.06049 - 9.51324i) q^{88} +(-7.38393 - 4.26311i) q^{89} +(6.97491 + 5.37869i) q^{90} +(14.2410 - 4.71904i) q^{92} +(5.11797 - 3.80064i) q^{93} +(-8.22478 + 6.70004i) q^{94} +(-1.13854 - 1.97200i) q^{95} +(1.29043 - 9.71261i) 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

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