LMFDB - Embedded newform 784.2.x.p.557.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.12
Character	$\chi$	$=$	784.557
Dual form			784.2.x.p.373.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.561091 - 1.29814i) q^{2} +(0.614599 - 0.164681i) q^{3} +(-1.37035 + 1.45675i) q^{4} +(1.45338 + 0.389432i) q^{5} +(-0.558626 - 0.705436i) q^{6} +(2.65997 + 0.961542i) q^{8} +(-2.24746 + 1.29757i) q^{9} +O(q^{10})$	\(q+(-0.561091 - 1.29814i) q^{2} +(0.614599 - 0.164681i) q^{3} +(-1.37035 + 1.45675i) q^{4} +(1.45338 + 0.389432i) q^{5} +(-0.558626 - 0.705436i) q^{6} +(2.65997 + 0.961542i) q^{8} +(-2.24746 + 1.29757i) q^{9} +(-0.309941 - 2.10520i) q^{10} +(0.899678 + 3.35764i) q^{11} +(-0.602317 + 1.12099i) q^{12} +(0.433866 + 0.433866i) q^{13} +0.957378 q^{15} +(-0.244266 - 3.99253i) q^{16} +(-3.24640 + 5.62292i) q^{17} +(2.94547 + 2.18947i) q^{18} +(-0.341695 + 1.27522i) q^{19} +(-2.55895 + 1.58356i) q^{20} +(3.85390 - 3.05186i) q^{22} +(1.18252 - 0.682730i) q^{23} +(1.79316 + 0.152916i) q^{24} +(-2.36947 - 1.36801i) q^{25} +(0.319782 - 0.806658i) q^{26} +(-2.51736 + 2.51736i) q^{27} +(2.40449 + 2.40449i) q^{29} +(-0.537177 - 1.24281i) q^{30} +(-3.56343 + 6.17204i) q^{31} +(-5.04583 + 2.55727i) q^{32} +(1.10588 + 1.91544i) q^{33} +(9.12089 + 1.05931i) q^{34} +(1.18957 - 5.05214i) q^{36} +(4.87836 + 1.30715i) q^{37} +(1.84714 - 0.271947i) q^{38} +(0.338103 + 0.195204i) q^{39} +(3.49149 + 2.43336i) q^{40} -7.83707i q^{41} +(0.978094 - 0.978094i) q^{43} +(-6.12414 - 3.29055i) q^{44} +(-3.77174 + 1.01063i) q^{45} +(-1.54978 - 1.15201i) q^{46} +(6.31769 + 10.9426i) q^{47} +(-0.807621 - 2.41358i) q^{48} +(-0.446389 + 3.84349i) q^{50} +(-1.06924 + 3.99046i) q^{51} +(-1.22658 + 0.0374866i) q^{52} +(-2.34860 - 8.76508i) q^{53} +(4.68036 + 1.85542i) q^{54} +5.23030i q^{55} +0.840021i q^{57} +(1.77223 - 4.47051i) q^{58} +(1.92480 + 7.18346i) q^{59} +(-1.31195 + 1.39467i) q^{60} +(-1.57583 + 5.88108i) q^{61} +(10.0116 + 1.16276i) q^{62} +(6.15087 + 5.11535i) q^{64} +(0.461611 + 0.799533i) q^{65} +(1.86602 - 2.51033i) q^{66} +(15.4719 - 4.14569i) q^{67} +(-3.74251 - 12.4346i) q^{68} +(0.614344 - 0.614344i) q^{69} -8.41138i q^{71} +(-7.22586 + 1.29048i) q^{72} +(-0.483999 - 0.279437i) q^{73} +(-1.04033 - 7.06624i) q^{74} +(-1.68156 - 0.450572i) q^{75} +(-1.38944 - 2.24527i) q^{76} +(0.0636959 - 0.548433i) q^{78} +(0.458833 + 0.794722i) q^{79} +(1.19981 - 5.89780i) q^{80} +(2.76012 - 4.78067i) q^{81} +(-10.1736 + 4.39731i) q^{82} +(-2.41581 - 2.41581i) q^{83} +(-6.90800 + 6.90800i) q^{85} +(-1.81851 - 0.720906i) q^{86} +(1.87377 + 1.08182i) q^{87} +(-0.835401 + 9.79631i) q^{88} +(13.9976 - 8.08152i) q^{89} +(3.42824 + 4.32920i) q^{90} +(-0.625904 + 2.65823i) q^{92} +(-1.17366 + 4.38016i) q^{93} +(10.6602 - 14.3410i) q^{94} +(-0.993225 + 1.72032i) q^{95} +(-2.68003 + 2.40265i) q^{96} +5.39436 q^{97} +(-6.37879 - 6.37879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{4}+O(q^{10}) $ 96 * q + 4 * q^4	$ 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) $ 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.561091	−	1.29814i	−0.396752	−	0.917926i
$2$	−0.561091	−	1.29814i	−0.396752	−	0.917926i
$3$	0.614599	−	0.164681i	0.354839	−	0.0950788i	−0.0769962	−	0.997031i	$-0.524533\pi$
$3$	0.614599	−	0.164681i	0.354839	−	0.0950788i	0.431835	+	0.901953i	$0.357866\pi$
$4$	−1.37035	+	1.45675i	−0.685176	+	0.728377i
$5$	1.45338	+	0.389432i	0.649972	+	0.174159i	0.568716	−	0.822534i	$-0.307440\pi$
$5$	1.45338	+	0.389432i	0.649972	+	0.174159i	0.0812556	+	0.996693i	$0.474107\pi$
$6$	−0.558626	−	0.705436i	−0.228058	−	0.287993i
$7$		0			0
$7$		0			0
$8$	2.65997	+	0.961542i	0.940441	+	0.339957i
$9$	−2.24746	+	1.29757i	−0.749155	+	0.432525i
$10$	−0.309941	−	2.10520i	−0.0980118	−	0.665724i
$11$	0.899678	+	3.35764i	0.271263	+	1.01237i	0.958304	+	0.285750i	$0.0922425\pi$
$11$	0.899678	+	3.35764i	0.271263	+	1.01237i	−0.687041	+	0.726619i	$0.741091\pi$
$12$	−0.602317	+	1.12099i	−0.173874	+	0.323602i
$13$	0.433866	+	0.433866i	0.120333	+	0.120333i	0.764709	−	0.644376i	$-0.222883\pi$
$13$	0.433866	+	0.433866i	0.120333	+	0.120333i	−0.644376	+	0.764709i	$0.722883\pi$
$14$		0			0
$15$	0.957378			0.247194
$16$	−0.244266	−	3.99253i	−0.0610665	−	0.998134i
$17$	−3.24640	+	5.62292i	−0.787367	+	1.36376i	0.140208	+	0.990122i	$0.455223\pi$
$17$	−3.24640	+	5.62292i	−0.787367	+	1.36376i	−0.927575	+	0.373637i	$0.878110\pi$
$18$	2.94547	+	2.18947i	0.694254	+	0.516064i
$19$	−0.341695	+	1.27522i	−0.0783902	+	0.292556i	−0.993981	−	0.109556i	$-0.965057\pi$
$19$	−0.341695	+	1.27522i	−0.0783902	+	0.292556i	0.915590	+	0.402112i	$0.131724\pi$
$20$	−2.55895	+	1.58356i	−0.572199	+	0.354095i
$21$		0			0
$22$	3.85390	−	3.05186i	0.821655	−	0.650658i
$23$	1.18252	−	0.682730i	0.246573	−	0.142359i	−0.371621	−	0.928385i	$-0.621198\pi$
$23$	1.18252	−	0.682730i	0.246573	−	0.142359i	0.618194	+	0.786026i	$0.287865\pi$
$24$	1.79316	+	0.152916i	0.366028	+	0.0312138i
$25$	−2.36947	−	1.36801i	−0.473894	−	0.273603i
$26$	0.319782	−	0.806658i	0.0627143	−	0.158199i
$27$	−2.51736	+	2.51736i	−0.484465	+	0.484465i
$28$		0			0
$29$	2.40449	+	2.40449i	0.446503	+	0.446503i	0.894190	−	0.447687i	$-0.147752\pi$
$29$	2.40449	+	2.40449i	0.446503	+	0.446503i	−0.447687	+	0.894190i	$0.647752\pi$
$30$	−0.537177	−	1.24281i	−0.0980746	−	0.226906i
$31$	−3.56343	+	6.17204i	−0.640011	+	1.10853i	0.345419	+	0.938449i	$0.387737\pi$
$31$	−3.56343	+	6.17204i	−0.640011	+	1.10853i	−0.985430	+	0.170083i	$0.945596\pi$
$32$	−5.04583	+	2.55727i	−0.891985	+	0.452066i
$33$	1.10588	+	1.91544i	0.192509	+	0.333436i
$34$	9.12089	+	1.05931i	1.56422	+	0.181671i
$35$		0			0
$36$	1.18957	−	5.05214i	0.198262	−	0.842023i
$37$	4.87836	+	1.30715i	0.801997	+	0.214895i	0.636461	−	0.771309i	$-0.280398\pi$
$37$	4.87836	+	1.30715i	0.801997	+	0.214895i	0.165537	+	0.986204i	$0.447064\pi$
$38$	1.84714	−	0.271947i	0.299646	−	0.0441157i
$39$	0.338103	+	0.195204i	0.0541398	+	0.0312576i
$40$	3.49149	+	2.43336i	0.552053	+	0.384749i
$41$		−	7.83707i		−	1.22395i	−0.790879	−	0.611973i	$-0.790376\pi$
$41$		−	7.83707i		−	1.22395i	0.790879	−	0.611973i	$-0.209624\pi$
$42$		0			0
$43$	0.978094	−	0.978094i	0.149158	−	0.149158i	−0.628584	−	0.777742i	$-0.716365\pi$
$43$	0.978094	−	0.978094i	0.149158	−	0.149158i	0.777742	+	0.628584i	$0.216365\pi$
$44$	−6.12414	−	3.29055i	−0.923249	−	0.496069i
$45$	−3.77174	+	1.01063i	−0.562258	+	0.150656i
$46$	−1.54978	−	1.15201i	−0.228503	−	0.169855i
$47$	6.31769	+	10.9426i	0.921530	+	1.59614i	0.797049	+	0.603915i	$0.206393\pi$
$47$	6.31769	+	10.9426i	0.921530	+	1.59614i	0.124481	+	0.992222i	$0.460273\pi$
$48$	−0.807621	−	2.41358i	−0.116570	−	0.348370i
$49$		0			0
$50$	−0.446389	+	3.84349i	−0.0631290	+	0.543552i
$51$	−1.06924	+	3.99046i	−0.149724	+	0.558777i
$52$	−1.22658	+	0.0374866i	−0.170097	+	0.00519846i
$53$	−2.34860	−	8.76508i	−0.322604	−	1.20398i	−0.916698	−	0.399580i	$-0.869156\pi$
$53$	−2.34860	−	8.76508i	−0.322604	−	1.20398i	0.594094	−	0.804396i	$-0.297511\pi$
$54$	4.68036	+	1.85542i	0.636916	+	0.252491i
$55$			5.23030i			0.705254i
$56$		0			0
$57$			0.840021i			0.111264i
$58$	1.77223	−	4.47051i	0.232706	−	0.587007i
$59$	1.92480	+	7.18346i	0.250588	+	0.935206i	0.970492	+	0.241133i	$0.0775190\pi$
$59$	1.92480	+	7.18346i	0.250588	+	0.935206i	−0.719904	+	0.694073i	$0.755814\pi$
$60$	−1.31195	+	1.39467i	−0.169372	+	0.180050i
$61$	−1.57583	+	5.88108i	−0.201764	+	0.752995i	0.788647	+	0.614846i	$0.210782\pi$
$61$	−1.57583	+	5.88108i	−0.201764	+	0.752995i	−0.990411	+	0.138149i	$0.955885\pi$
$62$	10.0116	+	1.16276i	1.27148	+	0.147671i
$63$		0			0
$64$	6.15087	+	5.11535i	0.768859	+	0.639418i
$65$	0.461611	+	0.799533i	0.0572558	+	0.0991699i
$66$	1.86602	−	2.51033i	0.229691	−	0.309001i
$67$	15.4719	−	4.14569i	1.89019	−	0.506476i	0.891640	−	0.452746i	$-0.149556\pi$
$67$	15.4719	−	4.14569i	1.89019	−	0.506476i	0.998555	−	0.0537302i	$-0.0171111\pi$
$68$	−3.74251	−	12.4346i	−0.453846	−	1.50792i
$69$	0.614344	−	0.614344i	0.0739584	−	0.0739584i
$70$		0			0
$71$		−	8.41138i		−	0.998247i	−0.866531	−	0.499123i	$-0.833655\pi$
$71$		−	8.41138i		−	0.998247i	0.866531	−	0.499123i	$-0.166345\pi$
$72$	−7.22586	+	1.29048i	−0.851576	+	0.152084i
$73$	−0.483999	−	0.279437i	−0.0566478	−	0.0327056i	0.471409	−	0.881915i	$-0.343746\pi$
$73$	−0.483999	−	0.279437i	−0.0566478	−	0.0327056i	−0.528056	+	0.849209i	$0.677079\pi$
$74$	−1.04033	−	7.06624i	−0.120936	−	0.821434i
$75$	−1.68156	−	0.450572i	−0.194170	−	0.0520276i
$76$	−1.38944	−	2.24527i	−0.159380	−	0.257550i
$77$		0			0
$78$	0.0636959	−	0.548433i	0.00721214	−	0.0620978i
$79$	0.458833	+	0.794722i	0.0516227	+	0.0894132i	0.890682	−	0.454627i	$-0.150227\pi$
$79$	0.458833	+	0.794722i	0.0516227	+	0.0894132i	−0.839059	+	0.544040i	$0.816894\pi$
$80$	1.19981	−	5.89780i	0.134143	−	0.659394i
$81$	2.76012	−	4.78067i	0.306680	−	0.531185i
$82$	−10.1736	+	4.39731i	−1.12349	+	0.485602i
$83$	−2.41581	−	2.41581i	−0.265170	−	0.265170i	0.561981	−	0.827150i	$-0.310040\pi$
$83$	−2.41581	−	2.41581i	−0.265170	−	0.265170i	−0.827150	+	0.561981i	$0.810040\pi$
$84$		0			0
$85$	−6.90800	+	6.90800i	−0.749278	+	0.749278i
$86$	−1.81851	−	0.720906i	−0.196095	−	0.0777373i
$87$	1.87377	+	1.08182i	0.200889	+	0.115984i
$88$	−0.835401	+	9.79631i	−0.0890541	+	1.04429i
$89$	13.9976	−	8.08152i	1.48374	−	0.856639i	0.483913	−	0.875116i	$-0.339215\pi$
$89$	13.9976	−	8.08152i	1.48374	−	0.856639i	0.999829	+	0.0184769i	$0.00588172\pi$
$90$	3.42824	+	4.32920i	0.361368	+	0.456338i
$91$		0			0
$92$	−0.625904	+	2.65823i	−0.0652550	+	0.277139i
$93$	−1.17366	+	4.38016i	−0.121703	+	0.454201i
$94$	10.6602	−	14.3410i	1.09952	−	1.47917i
$95$	−0.993225	+	1.72032i	−0.101903	+	0.176501i
$96$	−2.68003	+	2.40265i	−0.273529	+	0.245219i
$97$	5.39436			0.547714			0.273857	−	0.961770i	$-0.411700\pi$
$97$	5.39436			0.547714			0.273857	+	0.961770i	$0.411700\pi$
$98$		0			0
$99$	−6.37879	−	6.37879i	−0.641092	−	0.641092i
$100$	5.23987	−	1.57707i	0.523987	−	0.157707i
$101$	−3.20128	−	11.9473i	−0.318539	−	1.18881i	−0.920649	−	0.390392i	$-0.872340\pi$
$101$	−3.20128	−	11.9473i	−0.318539	−	1.18881i	0.602109	−	0.798414i	$-0.294327\pi$
$102$	5.78014	−	0.850986i	0.572319	−	0.0842602i
$103$	−13.6924	+	7.90533i	−1.34916	+	0.778935i	−0.988130	−	0.153621i	$-0.950907\pi$
$103$	−13.6924	+	7.90533i	−1.34916	+	0.778935i	−0.361025	+	0.932556i	$0.617573\pi$
$104$	0.736889	+	1.57125i	0.0722579	+	0.154074i
$105$		0			0
$106$	−10.0606	+	7.96682i	−0.977167	+	0.773806i
$107$	8.44147	+	2.26189i	0.816068	+	0.218665i	0.642627	−	0.766179i	$-0.277845\pi$
$107$	8.44147	+	2.26189i	0.816068	+	0.218665i	0.173441	+	0.984844i	$0.444511\pi$
$108$	−0.217503	−	7.11683i	−0.0209292	−	0.684818i
$109$	−6.38616	+	1.71117i	−0.611684	+	0.163900i	−0.551344	−	0.834278i	$-0.685885\pi$
$109$	−6.38616	+	1.71117i	−0.611684	+	0.163900i	−0.0603393	+	0.998178i	$0.519218\pi$
$110$	6.78968	−	2.93468i	0.647371	−	0.279810i
$111$	3.21350			0.305012
$112$		0			0
$113$	−4.06000			−0.381932			−0.190966	−	0.981597i	$-0.561162\pi$
$113$	−4.06000			−0.381932			−0.190966	+	0.981597i	$0.561162\pi$
$114$	1.09047	−	0.471329i	0.102132	−	0.0441440i
$115$	1.98453	−	0.531754i	0.185059	−	0.0495863i
$116$	−6.79775	+	0.207751i	−0.631155	+	0.0192892i
$117$	−1.53807	−	0.412125i	−0.142195	−	0.0381009i
$118$	8.24517	−	6.52924i	0.759029	−	0.601066i
$119$		0			0
$120$	2.54660	+	0.920560i	0.232471	+	0.0840352i
$121$	−0.938079	+	0.541600i	−0.0852799	+	0.0492364i
$122$	8.51867	−	1.25417i	0.771244	−	0.113547i
$123$	−1.29062	−	4.81666i	−0.116371	−	0.434303i
$124$	−4.10799	−	13.6489i	−0.368909	−	1.22571i
$125$	−8.23073	−	8.23073i	−0.736179	−	0.736179i
$126$		0			0
$127$	9.00650			0.799197			0.399599	−	0.916690i	$-0.369149\pi$
$127$	9.00650			0.799197			0.399599	+	0.916690i	$0.369149\pi$
$128$	3.18925	−	10.8549i	0.281893	−	0.959446i
$129$	0.440062	−	0.762209i	0.0387453	−	0.0671088i
$130$	0.778903	−	1.04785i	0.0683143	−	0.0919024i
$131$	4.03161	−	15.0462i	0.352243	−	1.31459i	−0.531675	−	0.846948i	$-0.678437\pi$
$131$	4.03161	−	15.0462i	0.352243	−	1.31459i	0.883918	−	0.467641i	$-0.154896\pi$
$132$	−4.30578	−	1.01384i	−0.374770	−	0.0882431i
$133$		0			0
$134$	−14.0629	−	17.7587i	−1.21485	−	1.53411i
$135$	−4.63902	+	2.67834i	−0.399263	+	0.230515i
$136$	−14.0420	+	11.8353i	−1.20409	+	1.01487i
$137$	−7.78255	−	4.49326i	−0.664908	−	0.383885i	0.129237	−	0.991614i	$-0.458747\pi$
$137$	−7.78255	−	4.49326i	−0.664908	−	0.383885i	−0.794144	+	0.607729i	$0.792081\pi$
$138$	−1.14221	−	0.452804i	−0.0972314	−	0.0385452i
$139$	−13.0941	+	13.0941i	−1.11063	+	1.11063i	−0.117562	+	0.993066i	$0.537508\pi$
$139$	−13.0941	+	13.0941i	−1.11063	+	1.11063i	−0.993066	+	0.117562i	$0.962492\pi$
$140$		0			0
$141$	5.68488	+	5.68488i	0.478753	+	0.478753i
$142$	−10.9192	+	4.71955i	−0.916317	+	0.396056i
$143$	−1.06643	+	1.84711i	−0.0891791	+	0.154463i
$144$	5.72959	+	8.65613i	0.477466	+	0.721344i
$145$	2.55825	+	4.43103i	0.212451	+	0.367977i
$146$	−0.0911816	+	0.785090i	−0.00754625	+	0.0649745i
$147$		0			0
$148$	−8.58927	+	5.31531i	−0.706034	+	0.436916i
$149$	17.1013	+	4.58227i	1.40099	+	0.375394i	0.878700	−	0.477374i	$-0.158411\pi$
$149$	17.1013	+	4.58227i	1.40099	+	0.375394i	0.522289	+	0.852768i	$0.325078\pi$
$150$	0.358601	+	2.43572i	0.0292796	+	0.198875i
$151$	11.1788	+	6.45409i	0.909718	+	0.525226i	0.880341	−	0.474342i	$-0.157314\pi$
$151$	11.1788	+	6.45409i	0.909718	+	0.525226i	0.0293779	+	0.999568i	$0.490647\pi$
$152$	−2.13508	+	3.06350i	−0.173178	+	0.248483i
$153$		−	16.8498i		−	1.36222i
$154$		0			0
$155$	−7.58261	+	7.58261i	−0.609050	+	0.609050i
$156$	−0.747684	+	0.225035i	−0.0598626	+	0.0180172i
$157$	−16.5925	+	4.44594i	−1.32422	+	0.354824i	−0.850558	−	0.525881i	$-0.823736\pi$
$157$	−16.5925	+	4.44594i	−1.32422	+	0.354824i	−0.473665	+	0.880705i	$0.657069\pi$
$158$	0.774216	−	1.04154i	0.0615933	−	0.0828607i
$159$	−2.88689	−	5.00024i	−0.228945	−	0.396545i
$160$	−8.32939	+	1.75168i	−0.658496	+	0.138482i
$161$		0			0
$162$	−7.75467	−	0.900640i	−0.609265	−	0.0707610i
$163$	−3.88545	+	14.5007i	−0.304332	+	1.13578i	0.629187	+	0.777254i	$0.283388\pi$
$163$	−3.88545	+	14.5007i	−0.304332	+	1.13578i	−0.933519	+	0.358528i	$0.883279\pi$
$164$	11.4167	+	10.7396i	0.891494	+	0.838618i
$165$	0.861332	+	3.21454i	0.0670546	+	0.250251i
$166$	−1.78058	+	4.49156i	−0.138200	+	0.348613i
$167$			24.1537i			1.86907i	0.355872	+	0.934535i	$0.384184\pi$
$167$			24.1537i			1.86907i	−0.355872	+	0.934535i	$0.615816\pi$
$168$		0			0
$169$		−	12.6235i		−	0.971040i
$170$	12.8436	+	5.09155i	0.985059	+	0.390504i
$171$	−0.886749	−	3.30939i	−0.0678114	−	0.253076i
$172$	0.0845087	+	2.76518i	0.00644373	+	0.210843i
$173$	0.524598	−	1.95782i	0.0398844	−	0.148851i	−0.943112	−	0.332475i	$-0.892116\pi$
$173$	0.524598	−	1.95782i	0.0398844	−	0.148851i	0.982997	+	0.183624i	$0.0587830\pi$
$174$	0.353004	−	3.03943i	0.0267611	−	0.230418i
$175$		0			0
$176$	13.1858	−	4.41216i	0.993914	−	0.332579i
$177$	2.36596	+	4.09797i	0.177837	+	0.308022i
$178$	−18.3449	−	13.6364i	−1.37501	−	1.02209i
$179$	−8.27206	+	2.21649i	−0.618283	+	0.165668i	−0.554347	−	0.832286i	$-0.687032\pi$
$179$	−8.27206	+	2.21649i	−0.618283	+	0.165668i	−0.0639358	+	0.997954i	$0.520365\pi$
$180$	3.69637	−	6.87942i	0.275511	−	0.512762i
$181$	−5.02152	+	5.02152i	−0.373247	+	0.373247i	−0.868658	−	0.495412i	$-0.835017\pi$
$181$	−5.02152	+	5.02152i	−0.373247	+	0.373247i	0.495412	+	0.868658i	$0.335017\pi$
$182$		0			0
$183$			3.87402i			0.286375i
$184$	3.80195	−	0.678995i	0.280283	−	0.0500562i
$185$	6.58107	+	3.79958i	0.483850	+	0.279351i
$186$	6.34461	−	0.934091i	0.465209	−	0.0684909i
$187$	−21.8005	−	5.84143i	−1.59421	−	0.427167i
$188$	−24.5981	−	5.79185i	−1.79400	−	0.422414i
$189$		0			0
$190$	2.79051	+	0.324094i	0.202445	+	0.0235123i
$191$	−6.96812	−	12.0691i	−0.504196	−	0.873292i	−0.999988	−	0.00485148i	$-0.998456\pi$
$191$	−6.96812	−	12.0691i	−0.504196	−	0.873292i	0.495793	−	0.868441i	$-0.334878\pi$
$192$	4.62272	+	2.13095i	0.333616	+	0.153788i
$193$	1.59321	−	2.75953i	0.114682	−	0.198635i	−0.802971	−	0.596019i	$-0.796748\pi$
$193$	1.59321	−	2.75953i	0.114682	−	0.198635i	0.917653	+	0.397384i	$0.130082\pi$
$194$	−3.02673	−	7.00266i	−0.217307	−	0.502761i
$195$	0.415374	+	0.415374i	0.0297455	+	0.0297455i
$196$		0			0
$197$	−18.6310	+	18.6310i	−1.32740	+	1.32740i	−0.419772	+	0.907630i	$0.637890\pi$
$197$	−18.6310	+	18.6310i	−1.32740	+	1.32740i	−0.907630	+	0.419772i	$0.862110\pi$
$198$	−4.70150	+	11.8597i	−0.334121	+	0.842830i
$199$	9.10258	+	5.25538i	0.645265	+	0.372544i	0.786640	−	0.617412i	$-0.211819\pi$
$199$	9.10258	+	5.25538i	0.645265	+	0.372544i	−0.141375	+	0.989956i	$0.545152\pi$
$200$	−4.98731	−	5.91722i	−0.352656	−	0.418411i
$201$	8.82630	−	5.09587i	0.622559	−	0.359435i
$202$	−13.7132	+	10.8593i	−0.964854	+	0.764056i
$203$		0			0
$204$	−4.34789	−	7.02597i	−0.304413	−	0.491916i
$205$	3.05201	−	11.3903i	0.213162	−	0.795530i
$206$	17.9450	+	13.3391i	1.25028	+	0.929381i
$207$	−1.77178	+	3.06882i	−0.123148	+	0.213298i
$208$	1.62625	−	1.83820i	0.112760	−	0.127456i
$209$	−4.58916			−0.317439
$210$		0			0
$211$	−15.8537	−	15.8537i	−1.09142	−	1.09142i	−0.995378	−	0.0960391i	$-0.969383\pi$
$211$	−15.8537	−	15.8537i	−1.09142	−	1.09142i	−0.0960391	−	0.995378i	$-0.530617\pi$
$212$	15.9870	+	8.58992i	1.09799	+	0.589958i
$213$	−1.38520	−	5.16962i	−0.0949121	−	0.354217i
$214$	−1.80019	−	12.2274i	−0.123058	−	0.835846i
$215$	1.80244	−	1.04064i	0.122926	−	0.0709712i
$216$	−9.11663	+	4.27554i	−0.620308	+	0.290914i
$217$		0			0
$218$	5.80456	+	7.33004i	0.393135	+	0.496453i
$219$	−0.343483	−	0.0920361i	−0.0232105	−	0.00621922i
$220$	−7.61926	−	7.16736i	−0.513691	−	0.483223i
$221$	−3.84809	+	1.03109i	−0.258851	+	0.0693589i
$222$	−1.80307	−	4.17158i	−0.121014	−	0.279978i
$223$	1.50291			0.100642			0.0503211	−	0.998733i	$-0.483976\pi$
$223$	1.50291			0.100642			0.0503211	+	0.998733i	$0.483976\pi$
$224$		0			0
$225$	7.10040			0.473360
$226$	2.27803	+	5.27046i	0.151532	+	0.350586i
$227$	15.5373	−	4.16320i	1.03124	−	0.276321i	0.296764	−	0.954951i	$-0.404093\pi$
$227$	15.5373	−	4.16320i	1.03124	−	0.276321i	0.734481	+	0.678630i	$0.237426\pi$
$228$	−1.22370	−	1.15113i	−0.0810418	−	0.0762351i
$229$	−21.6115	−	5.79079i	−1.42813	−	0.382666i	−0.539770	−	0.841813i	$-0.681489\pi$
$229$	−21.6115	−	5.79079i	−1.42813	−	0.382666i	−0.888361	+	0.459146i	$0.848155\pi$
$230$	−1.80380	−	2.27785i	−0.118939	−	0.150197i
$231$		0			0
$232$	4.08385	+	8.70789i	0.268118	+	0.571701i
$233$	−10.4572	+	6.03746i	−0.685074	+	0.395527i	−0.801764	−	0.597641i	$-0.796105\pi$
$233$	−10.4572	+	6.03746i	−0.685074	+	0.395527i	0.116690	+	0.993168i	$0.462772\pi$
$234$	0.328001	+	2.22788i	0.0214421	+	0.145641i
$235$	4.92063	+	18.3640i	0.320986	+	1.19794i
$236$	−13.1022	−	7.03991i	−0.852880	−	0.458259i
$237$	0.412874	+	0.412874i	0.0268190	+	0.0268190i
$238$		0			0
$239$	23.3681			1.51156			0.755778	−	0.654828i	$-0.227259\pi$
$239$	23.3681			1.51156			0.755778	+	0.654828i	$0.227259\pi$
$240$	−0.233855	−	3.82237i	−0.0150953	−	0.246733i
$241$	4.69064	−	8.12443i	0.302151	−	0.523341i	−0.674472	−	0.738300i	$-0.735629\pi$
$241$	4.69064	−	8.12443i	0.302151	−	0.523341i	0.976623	+	0.214960i	$0.0689620\pi$
$242$	1.22942	+	0.913874i	0.0790303	+	0.0587460i
$243$	3.67333	−	13.7090i	0.235644	−	0.879436i
$244$	−6.40784	−	10.3548i	−0.410220	−	0.662895i
$245$		0			0
$246$	−5.52856	+	4.37799i	−0.352488	+	0.279131i
$247$	−0.701525	+	0.405026i	−0.0446370	+	0.0257712i
$248$	−15.4133	+	12.9911i	−0.978745	+	0.824933i
$249$	−1.88259	−	1.08692i	−0.119305	−	0.0688805i
$250$	−6.06648	+	15.3029i	−0.383678	+	0.967838i
$251$	2.22827	−	2.22827i	0.140647	−	0.140647i	−0.633278	−	0.773925i	$-0.718291\pi$
$251$	2.22827	−	2.22827i	0.140647	−	0.140647i	0.773925	+	0.633278i	$0.218291\pi$
$252$		0			0
$253$	3.35625	+	3.35625i	0.211006	+	0.211006i
$254$	−5.05347	−	11.6917i	−0.317083	−	0.733604i
$255$	−3.10803	+	5.38327i	−0.194632	+	0.337113i
$256$	−15.8807	+	1.95048i	−0.992542	+	0.121905i
$257$	−4.88188	−	8.45566i	−0.304523	−	0.527450i	0.672632	−	0.739977i	$-0.265164\pi$
$257$	−4.88188	−	8.45566i	−0.304523	−	0.527450i	−0.977155	+	0.212528i	$0.931830\pi$
$258$	−1.23637	−	0.143594i	−0.0769731	−	0.00893978i
$259$		0			0
$260$	−1.79729	−	0.423189i	−0.111463	−	0.0262451i
$261$	−8.52401	−	2.28400i	−0.527623	−	0.141376i
$262$	−21.7942	+	3.20867i	−1.34645	+	0.198232i
$263$	0.887606	+	0.512459i	0.0547321	+	0.0315996i	0.527116	−	0.849793i	$-0.323273\pi$
$263$	0.887606	+	0.512459i	0.0547321	+	0.0315996i	−0.472384	+	0.881393i	$0.656607\pi$
$264$	1.09983	+	6.15838i	0.0676900	+	0.379022i
$265$		−	13.6536i		−	0.838735i
$266$		0			0
$267$	7.27203	−	7.27203i	0.445041	−	0.445041i
$268$	−15.1627	+	28.2198i	−0.926211	+	1.72380i
$269$	21.0485	−	5.63993i	1.28335	−	0.343872i	0.448218	−	0.893924i	$-0.352059\pi$
$269$	21.0485	−	5.63993i	1.28335	−	0.343872i	0.835131	+	0.550052i	$0.185392\pi$
$270$	6.07978	+	4.51932i	0.370003	+	0.275037i
$271$	12.5358	+	21.7126i	0.761495	+	1.31895i	0.942080	+	0.335388i	$0.108868\pi$
$271$	12.5358	+	21.7126i	0.761495	+	1.31895i	−0.180585	+	0.983559i	$0.557799\pi$
$272$	23.2427	+	11.5879i	1.40930	+	0.702617i
$273$		0			0
$274$	−1.46617	+	12.6240i	−0.0885746	+	0.762643i
$275$	2.46154	−	9.18661i	0.148437	−	0.553973i
$276$	0.0530802	+	1.73682i	0.00319505	+	0.104544i
$277$	−1.74009	−	6.49409i	−0.104552	−	0.390192i	0.893742	−	0.448581i	$-0.148070\pi$
$277$	−1.74009	−	6.49409i	−0.104552	−	0.390192i	−0.998294	+	0.0583888i	$0.981404\pi$
$278$	24.3450	+	9.65104i	1.46012	+	0.578831i
$279$		−	18.4953i		−	1.10728i
$280$		0			0
$281$		−	12.0895i		−	0.721197i	−0.932721	−	0.360599i	$-0.882572\pi$
$281$		−	12.0895i		−	0.721197i	0.932721	−	0.360599i	$-0.117428\pi$
$282$	4.19005	−	10.5695i	0.249514	−	0.629406i
$283$	−4.43421	−	16.5487i	−0.263587	−	0.983719i	−0.963110	−	0.269109i	$-0.913271\pi$
$283$	−4.43421	−	16.5487i	−0.263587	−	0.983719i	0.699523	−	0.714610i	$-0.253396\pi$
$284$	12.2533	+	11.5266i	0.727100	+	0.683975i
$285$	−0.327131	+	1.22087i	−0.0193776	+	0.0723181i
$286$	2.99617	+	0.347980i	0.177167	+	0.0205765i
$287$		0			0
$288$	8.02207	−	12.2947i	0.472705	−	0.724473i
$289$	−12.5782	−	21.7861i	−0.739893	−	1.28153i
$290$	4.31669	−	5.80719i	0.253485	−	0.341010i
$291$	3.31537	−	0.888350i	0.194350	−	0.0520760i
$292$	1.07032	−	0.322141i	0.0626358	−	0.0188519i
$293$	7.66847	−	7.66847i	0.447997	−	0.447997i	−0.446691	−	0.894688i	$-0.647398\pi$
$293$	7.66847	−	7.66847i	0.447997	−	0.447997i	0.894688	+	0.446691i	$0.147398\pi$
$294$		0			0
$295$			11.1899i			0.651500i
$296$	11.7194	+	8.16774i	0.681177	+	0.474740i
$297$	−10.7172	−	6.18758i	−0.621875	−	0.359040i
$298$	−3.64693	−	24.7710i	−0.211261	−	1.43494i
$299$	0.809269	+	0.216843i	0.0468012	+	0.0125404i
$300$	2.96070	−	1.83218i	0.170936	−	0.105781i
$301$		0			0
$302$	2.10600	−	18.1330i	0.121187	−	1.04344i
$303$	−3.93501	−	6.81563i	−0.226060	−	0.391548i
$304$	5.17483	+	1.05273i	0.296797	+	0.0603785i
$305$	−4.58056	+	7.93377i	−0.262282	+	0.454286i
$306$	−21.8734	+	9.45426i	−1.25042	+	0.540464i
$307$	3.93313	+	3.93313i	0.224476	+	0.224476i	0.810380	−	0.585905i	$-0.199261\pi$
$307$	3.93313	+	3.93313i	0.224476	+	0.224476i	−0.585905	+	0.810380i	$0.699261\pi$
$308$		0			0
$309$	−7.11349	+	7.11349i	−0.404672	+	0.404672i
$310$	14.0979	+	5.58878i	0.800705	+	0.317421i
$311$	2.05948	+	1.18904i	0.116782	+	0.0674243i	0.557253	−	0.830343i	$-0.311855\pi$
$311$	2.05948	+	1.18904i	0.116782	+	0.0674243i	−0.440471	+	0.897767i	$0.645189\pi$
$312$	0.711647	+	0.844336i	0.0402891	+	0.0478011i
$313$	13.2786	−	7.66638i	0.750548	−	0.433329i	−0.0753437	−	0.997158i	$-0.524005\pi$
$313$	13.2786	−	7.66638i	0.750548	−	0.433329i	0.825892	+	0.563828i	$0.190672\pi$
$314$	15.0814	+	19.0448i	0.851090	+	1.07476i
$315$		0			0
$316$	−1.78648	−	0.420642i	−0.100497	−	0.0236630i
$317$	6.87589	−	25.6612i	0.386188	−	1.44127i	−0.450097	−	0.892980i	$-0.648610\pi$
$317$	6.87589	−	25.6612i	0.386188	−	1.44127i	0.836285	−	0.548295i	$-0.184723\pi$
$318$	−4.87122	+	6.55319i	−0.273164	+	0.367484i
$319$	−5.91016	+	10.2367i	−0.330905	+	0.573145i
$320$	6.94748	+	9.82989i	0.388376	+	0.549508i
$321$	5.56061			0.310363
$322$		0			0
$323$	−6.06120	−	6.06120i	−0.337254	−	0.337254i
$324$	3.18192	+	10.5720i	0.176773	+	0.587334i
$325$	−0.434497	−	1.62157i	−0.0241016	−	0.0899483i
$326$	21.0041	−	3.09234i	1.16331	−	0.171269i
$327$	−3.64313	+	2.10336i	−0.201466	+	0.116316i
$328$	7.53568	−	20.8464i	0.416088	−	1.15105i
$329$		0			0
$330$	3.68964	−	2.92178i	0.203108	−	0.160839i
$331$	−16.1131	−	4.31749i	−0.885655	−	0.237310i	−0.212809	−	0.977094i	$-0.568261\pi$
$331$	−16.1131	−	4.31749i	−0.885655	−	0.237310i	−0.672845	+	0.739783i	$0.734928\pi$
$332$	6.82976	−	0.208730i	0.374832	−	0.0114555i
$333$	−12.6601	+	3.39225i	−0.693767	+	0.185894i
$334$	31.3550	−	13.5524i	1.71567	−	0.741556i
$335$	24.1010			1.31678
$336$		0			0
$337$	16.0461			0.874089			0.437044	−	0.899440i	$-0.356025\pi$
$337$	16.0461			0.874089			0.437044	+	0.899440i	$0.356025\pi$
$338$	−16.3871	+	7.08295i	−0.891343	+	0.385262i
$339$	−2.49527	+	0.668605i	−0.135524	+	0.0363137i
$340$	−0.596861	−	19.5297i	−0.0323693	−	1.05914i
$341$	−23.9295	−	6.41188i	−1.29585	−	0.347223i
$342$	−3.79852	+	3.00800i	−0.205400	+	0.162654i
$343$		0			0
$344$	3.54218	−	1.66122i	0.190981	−	0.0895670i
$345$	1.13212	−	0.653631i	0.0609514	−	0.0351903i
$346$	−2.83588	+	0.417516i	−0.152458	+	0.0224458i
$347$	0.0523108	+	0.195227i	0.00280819	+	0.0104803i	0.967316	−	0.253575i	$-0.0816065\pi$
$347$	0.0523108	+	0.195227i	0.00280819	+	0.0104803i	−0.964508	+	0.264055i	$0.914940\pi$
$348$	−4.14368	+	1.24715i	−0.222124	+	0.0668540i
$349$	22.4847	+	22.4847i	1.20358	+	1.20358i	0.973070	+	0.230509i	$0.0740390\pi$
$349$	22.4847	+	22.4847i	1.20358	+	1.20358i	0.230509	+	0.973070i	$0.425961\pi$
$350$		0			0
$351$	−2.18439			−0.116594
$352$	−13.1260	−	14.6414i	−0.699619	−	0.780388i
$353$	4.81244	−	8.33539i	0.256140	−	0.443648i	−0.709064	−	0.705144i	$-0.750882\pi$
$353$	4.81244	−	8.33539i	0.256140	−	0.443648i	0.965205	+	0.261496i	$0.0842157\pi$
$354$	3.99223	−	5.37069i	0.212184	−	0.285449i
$355$	3.27566	−	12.2249i	0.173854	−	0.648832i
$356$	−7.40886	+	31.4656i	−0.392669	+	1.66767i
$357$		0			0
$358$	7.51871	+	9.49467i	0.397376	+	0.501809i
$359$	14.8625	−	8.58090i	0.784415	−	0.452882i	−0.0535775	−	0.998564i	$-0.517062\pi$
$359$	14.8625	−	8.58090i	0.784415	−	0.452882i	0.837993	+	0.545681i	$0.183729\pi$
$360$	−11.0045	−	0.938430i	−0.579987	−	0.0494596i
$361$	14.9450	+	8.62853i	0.786581	+	0.454133i
$362$	9.33618	+	3.70112i	0.490699	+	0.194527i
$363$	−0.487351	+	0.487351i	−0.0255793	+	0.0255793i
$364$		0			0
$365$	−0.594613	−	0.594613i	−0.0311235	−	0.0311235i
$366$	5.02903	−	2.17368i	0.262871	−	0.113620i
$367$	7.22745	−	12.5183i	0.377270	−	0.653451i	−0.613394	−	0.789777i	$-0.710196\pi$
$367$	7.22745	−	12.5183i	0.377270	−	0.653451i	0.990664	+	0.136326i	$0.0435295\pi$
$368$	−3.01467	−	4.55450i	−0.157151	−	0.237419i
$369$	10.1692	+	17.6135i	0.529387	+	0.916925i
$370$	1.23982	−	10.6751i	0.0644552	−	0.554971i
$371$		0			0
$372$	−4.77249	−	7.71210i	−0.247442	−	0.399854i
$373$	−11.6214	−	3.11394i	−0.601733	−	0.161234i	−0.0549228	−	0.998491i	$-0.517491\pi$
$373$	−11.6214	−	3.11394i	−0.601733	−	0.161234i	−0.546810	+	0.837257i	$0.684158\pi$
$374$	4.64906	+	31.5777i	0.240397	+	1.63285i
$375$	−6.41405	−	3.70315i	−0.331220	−	0.191230i
$376$	6.28313	+	35.1816i	0.324028	+	1.81435i
$377$			2.08645i			0.107458i
$378$		0			0
$379$	−13.5029	+	13.5029i	−0.693598	+	0.693598i	−0.963022	−	0.269424i	$-0.913167\pi$
$379$	−13.5029	+	13.5029i	−0.693598	+	0.693598i	0.269424	+	0.963022i	$0.413167\pi$
$380$	−1.14501	−	3.80433i	−0.0587378	−	0.195158i
$381$	5.53538	−	1.48320i	0.283586	−	0.0759867i
$382$	−11.7577	+	15.8175i	−0.601577	+	0.809294i
$383$	12.1233	+	20.9982i	0.619472	+	1.07296i	0.989582	+	0.143969i	$0.0459866\pi$
$383$	12.1233	+	20.9982i	0.619472	+	1.07296i	−0.370110	+	0.928988i	$0.620680\pi$
$384$	0.172513	−	7.19661i	0.00880349	−	0.367251i
$385$		0			0
$386$	−4.47620	−	0.519873i	−0.227833	−	0.0264608i
$387$	−0.929082	+	3.46738i	−0.0472279	+	0.176257i
$388$	−7.39218	+	7.85826i	−0.375281	+	0.398943i
$389$	−2.93716	−	10.9616i	−0.148920	−	0.555777i	−0.999550	−	0.0300114i	$-0.990446\pi$
$389$	−2.93716	−	10.9616i	−0.148920	−	0.555777i	0.850630	−	0.525765i	$-0.176221\pi$
$390$	0.306152	−	0.772277i	0.0155026	−	0.0391058i
$391$			8.86565i			0.448355i
$392$		0			0
$393$		−	9.91129i		−	0.499958i
$394$	34.6393	+	13.7320i	1.74510	+	0.691808i
$395$	0.357368	+	1.33372i	0.0179812	+	0.0671066i
$396$	18.0335	−	0.551136i	0.906218	−	0.0276956i
$397$	−6.17957	+	23.0625i	−0.310144	+	1.15747i	0.618283	+	0.785956i	$0.287829\pi$
$397$	−6.17957	+	23.0625i	−0.310144	+	1.15747i	−0.928427	+	0.371516i	$0.878838\pi$
$398$	1.71485	−	14.7652i	0.0859579	−	0.740113i
$399$		0			0
$400$	−4.88306	+	9.79435i	−0.244153	+	0.489717i
$401$	2.56161	+	4.43683i	0.127921	+	0.221565i	0.922871	−	0.385110i	$-0.125836\pi$
$401$	2.56161	+	4.43683i	0.127921	+	0.221565i	−0.794950	+	0.606675i	$0.792503\pi$
$402$	−11.5675	−	8.59856i	−0.576936	−	0.428857i
$403$	−4.22389	+	1.13179i	−0.210407	+	0.0563783i
$404$	21.7912	+	11.7086i	1.08415	+	0.582525i
$405$	5.87325	−	5.87325i	0.291844	−	0.291844i
$406$		0			0
$407$			17.5558i			0.870210i
$408$	−6.68115	+	9.58639i	−0.330766	+	0.474597i
$409$	12.2891	+	7.09510i	0.607655	+	0.350830i	0.772047	−	0.635565i	$-0.219233\pi$
$409$	12.2891	+	7.09510i	0.607655	+	0.350830i	−0.164392	+	0.986395i	$0.552566\pi$
$410$	−16.4986	+	2.42903i	−0.814810	+	0.119961i
$411$	−5.52310	−	1.47991i	−0.272434	−	0.0729986i
$412$	7.24734	−	30.7796i	0.357051	−	1.51640i
$413$		0			0
$414$	4.97790	+	0.578142i	0.244651	+	0.0284141i
$415$	−2.57030	−	4.45189i	−0.126171	−	0.218535i
$416$	−3.29872	−	1.07970i	−0.161733	−	0.0529366i
$417$	−5.89127	+	10.2040i	−0.288497	+	0.499691i
$418$	2.57494	+	5.95739i	0.125944	+	0.291385i
$419$	−4.24793	−	4.24793i	−0.207525	−	0.207525i	0.595690	−	0.803215i	$-0.296879\pi$
$419$	−4.24793	−	4.24793i	−0.207525	−	0.207525i	−0.803215	+	0.595690i	$0.796879\pi$
$420$		0			0
$421$	12.2505	−	12.2505i	0.597051	−	0.597051i	−0.342475	−	0.939527i	$-0.611265\pi$
$421$	12.2505	−	12.2505i	0.597051	−	0.597051i	0.939527	+	0.342475i	$0.111265\pi$
$422$	−11.6850	+	29.4758i	−0.568819	+	1.43486i
$423$	−28.3976	−	16.3953i	−1.38074	−	0.797169i
$424$	2.18080	−	25.5731i	0.105909	−	1.24194i
$425$	15.3845	−	8.88223i	0.746257	−	0.430851i
$426$	−5.93369	+	4.69881i	−0.287488	+	0.227658i
$427$		0			0
$428$	−14.8628	+	9.19757i	−0.718421	+	0.444581i
$429$	−0.351241	+	1.31085i	−0.0169581	+	0.0632884i
$430$	−2.36224	−	1.75594i	−0.113917	−	0.0846788i
$431$	3.25246	−	5.63343i	0.156666	−	0.271353i	−0.776999	−	0.629502i	$-0.783259\pi$
$431$	3.25246	−	5.63343i	0.156666	−	0.271353i	0.933664	+	0.358149i	$0.116592\pi$
$432$	10.6655	+	9.43573i	0.513146	+	0.453977i
$433$	12.3043			0.591305			0.295653	−	0.955296i	$-0.404463\pi$
$433$	12.3043			0.591305			0.295653	+	0.955296i	$0.404463\pi$
$434$		0			0
$435$	2.30201	+	2.30201i	0.110373	+	0.110373i
$436$	6.25855	−	11.6480i	0.299730	−	0.557837i
$437$	0.466570	+	1.74126i	0.0223191	+	0.0832960i
$438$	0.0732495	+	0.497532i	0.00350000	+	0.0237730i
$439$	14.0697	−	8.12313i	0.671509	−	0.387696i	−0.125139	−	0.992139i	$-0.539938\pi$
$439$	14.0697	−	8.12313i	0.671509	−	0.387696i	0.796648	+	0.604443i	$0.206604\pi$
$440$	−5.02915	+	13.9124i	−0.239756	+	0.663249i
$441$		0			0
$442$	3.49764	+	4.41684i	0.166366	+	0.210088i
$443$	13.8662	+	3.71543i	0.658801	+	0.176525i	0.572705	−	0.819762i	$-0.305894\pi$
$443$	13.8662	+	3.71543i	0.658801	+	0.176525i	0.0860962	+	0.996287i	$0.472561\pi$
$444$	−4.40363	+	4.68128i	−0.208987	+	0.222164i
$445$	23.4910	−	6.29441i	1.11358	−	0.298383i
$446$	−0.843270	−	1.95099i	−0.0399300	−	0.0923822i
$447$	11.2650			0.532818
$448$		0			0
$449$	9.89895			0.467160			0.233580	−	0.972338i	$-0.424956\pi$
$449$	9.89895			0.467160			0.233580	+	0.972338i	$0.424956\pi$
$450$	−3.98397	−	9.21733i	−0.187806	−	0.434509i
$451$	26.3141	−	7.05085i	1.23908	−	0.332011i
$452$	5.56363	−	5.91442i	0.261691	−	0.278191i
$453$	7.93335	+	2.12573i	0.372741	+	0.0998757i
$454$	−14.1223	−	17.8337i	−0.662790	−	0.836975i
$455$		0			0
$456$	−0.807716	+	2.23443i	−0.0378248	+	0.104637i
$457$	−11.1211	+	6.42079i	−0.520224	+	0.300352i	−0.737026	−	0.675864i	$-0.763771\pi$
$457$	−11.1211	+	6.42079i	−0.520224	+	0.300352i	0.216802	+	0.976216i	$0.430437\pi$
$458$	4.60877	+	31.3040i	0.215353	+	1.46274i
$459$	−5.98257	−	22.3272i	−0.279242	−	1.04215i
$460$	−1.94488	+	3.61967i	−0.0906803	+	0.168768i
$461$	7.50371	+	7.50371i	0.349482	+	0.349482i	0.859917	−	0.510434i	$-0.170515\pi$
$461$	7.50371	+	7.50371i	0.349482	+	0.349482i	−0.510434	+	0.859917i	$0.670515\pi$
$462$		0			0
$463$	30.2985			1.40809			0.704044	−	0.710156i	$-0.251376\pi$
$463$	30.2985			1.40809			0.704044	+	0.710156i	$0.251376\pi$
$464$	9.01267	−	10.1873i	0.418403	−	0.472936i
$465$	−3.41155	+	5.90898i	−0.158207	+	0.274022i
$466$	13.7049	+	10.1874i	0.634869	+	0.471921i
$467$	−1.82145	+	6.79774i	−0.0842867	+	0.314562i	−0.995178	−	0.0980839i	$-0.968729\pi$
$467$	−1.82145	+	6.79774i	−0.0842867	+	0.314562i	0.910892	+	0.412646i	$0.135395\pi$
$468$	2.70806	−	1.67583i	0.125180	−	0.0774655i
$469$		0			0
$470$	21.0782	−	16.6916i	0.972266	−	0.769925i
$471$	−9.46555	+	5.46494i	−0.436149	+	0.251811i
$472$	−1.78728	+	20.9586i	−0.0822664	+	0.964696i
$473$	4.16406	+	2.40412i	0.191464	+	0.110542i
$474$	0.304310	−	0.767629i	0.0139774	−	0.0352584i
$475$	2.55416	−	2.55416i	0.117193	−	0.117193i
$476$		0			0
$477$	16.6517	+	16.6517i	0.762430	+	0.762430i
$478$	−13.1116	−	30.3351i	−0.599712	−	1.38750i
$479$	−1.31897	+	2.28452i	−0.0602653	+	0.104382i	−0.894584	−	0.446900i	$-0.852528\pi$
$479$	−1.31897	+	2.28452i	−0.0602653	+	0.104382i	0.834319	+	0.551282i	$0.185861\pi$
$480$	−4.83077	+	2.44827i	−0.220493	+	0.111748i
$481$	1.54942	+	2.68368i	0.0706477	+	0.122365i
$482$	−13.1786	−	1.53058i	−0.600267	−	0.0697159i
$483$		0			0
$484$	0.496521	−	2.10873i	0.0225691	−	0.0958515i
$485$	7.84006	+	2.10074i	0.355999	+	0.0953896i
$486$	−19.8574	+	2.92352i	−0.900749	+	0.132614i
$487$	−2.41546	−	1.39457i	−0.109455	−	0.0631938i	0.444273	−	0.895891i	$-0.353462\pi$
$487$	−2.41546	−	1.39457i	−0.109455	−	0.0631938i	−0.553728	+	0.832698i	$0.686795\pi$
$488$	−9.84657	+	14.1283i	−0.445733	+	0.639556i
$489$			9.55197i			0.431955i
$490$		0			0
$491$	15.8794	−	15.8794i	0.716629	−	0.716629i	−0.251284	−	0.967913i	$-0.580853\pi$
$491$	15.8794	−	15.8794i	0.716629	−	0.716629i	0.967913	+	0.251284i	$0.0808529\pi$
$492$	8.78529	+	4.72040i	0.396071	+	0.212812i
$493$	−21.3262	+	5.71434i	−0.960484	+	0.257361i
$494$	0.919401	+	0.683424i	0.0413658	+	0.0307487i
$495$	−6.78670	−	11.7549i	−0.305040	−	0.528344i
$496$	25.5125	+	12.7195i	1.14555	+	0.571122i
$497$		0			0
$498$	−0.354666	+	3.05374i	−0.0158930	+	0.136841i
$499$	−0.777511	+	2.90171i	−0.0348062	+	0.129898i	−0.981143	−	0.193284i	$-0.938086\pi$
$499$	−0.777511	+	2.90171i	−0.0348062	+	0.129898i	0.946337	+	0.323182i	$0.104753\pi$
$500$	23.2692	−	0.711147i	1.04063	−	0.0318035i
$501$	3.97766	+	14.8448i	0.177709	+	0.663218i
$502$	−4.14287	−	1.64235i	−0.184906	−	0.0733017i
$503$		−	26.5444i		−	1.18356i	−0.806101	−	0.591778i	$-0.798426\pi$
$503$		−	26.5444i		−	1.18356i	0.806101	−	0.591778i	$-0.201574\pi$
$504$		0			0
$505$		−	18.6107i		−	0.828166i
$506$	2.47373	−	6.24006i	0.109971	−	0.277405i
$507$	−2.07886	−	7.75840i	−0.0923253	−	0.344563i
$508$	−12.3421	+	13.1203i	−0.547591	+	0.582117i
$509$	2.96258	−	11.0565i	0.131314	−	0.490071i	−0.868672	−	0.495388i	$-0.835026\pi$
$509$	2.96258	−	11.0565i	0.131314	−	0.490071i	0.999986	+	0.00531724i	$0.00169254\pi$
$510$	8.73214	+	1.01416i	0.386666	+	0.0449080i
$511$		0			0
$512$	11.4425	+	19.5210i	0.505692	+	0.862714i
$513$	−2.35002	−	4.07036i	−0.103756	−	0.179711i
$514$	−8.23748	+	11.0818i	−0.363340	+	0.488796i
$515$	−22.9789	+	6.15718i	−1.01257	+	0.271318i
$516$	0.507312	+	1.68556i	0.0223332	+	0.0742025i
$517$	−31.0574	+	31.0574i	−1.36590	+	1.36590i
$518$		0			0
$519$		−	1.28967i		−	0.0566102i
$520$	0.459085	+	2.57059i	0.0201322	+	0.112728i
$521$	27.8708	+	16.0912i	1.22104	+	0.704970i	0.965140	−	0.261733i	$-0.0842939\pi$
$521$	27.8708	+	16.0912i	1.22104	+	0.704970i	0.255903	+	0.966702i	$0.417627\pi$
$522$	1.81779	+	12.3469i	0.0795624	+	0.540410i
$523$	3.27851	+	0.878475i	0.143359	+	0.0384130i	0.329785	−	0.944056i	$-0.393024\pi$
$523$	3.27851	+	0.878475i	0.143359	+	0.0384130i	−0.186426	+	0.982469i	$0.559690\pi$
$524$	16.3938	+	26.4916i	0.716168	+	1.15729i
$525$		0			0
$526$	0.167218	−	1.43978i	0.00729105	−	0.0627772i
$527$	−23.1366	−	40.0738i	−1.00785	−	1.74564i
$528$	7.37735	−	4.88315i	0.321058	−	0.212512i
$529$	−10.5678	+	18.3039i	−0.459468	+	0.795822i
$530$	−17.7244	+	7.66093i	−0.769897	+	0.332769i
$531$	−13.6470	−	13.6470i	−0.592229	−	0.592229i
$532$		0			0
$533$	3.40024	−	3.40024i	0.147281	−	0.147281i
$534$	−13.5204	−	5.35987i	−0.585086	−	0.231944i
$535$	11.3878	+	6.57476i	0.492338	+	0.284252i
$536$	45.1411	+	3.84950i	1.94980	+	0.166273i
$537$	−4.71898	+	2.72451i	−0.203639	+	0.117571i
$538$	−19.1316	−	24.1594i	−0.824820	−	1.04159i
$539$		0			0
$540$	2.45541	−	10.4282i	0.105664	−	0.448757i
$541$	−9.27902	+	34.6298i	−0.398936	+	1.48885i	0.416035	+	0.909348i	$0.363419\pi$
$541$	−9.27902	+	34.6298i	−0.398936	+	1.48885i	−0.814971	+	0.579501i	$0.803247\pi$
$542$	21.1524	−	28.4560i	0.908572	−	1.22229i
$543$	−2.25927	+	3.91317i	−0.0969545	+	0.167930i
$544$	2.00143	−	36.6742i	0.0858104	−	1.57239i
$545$	−9.94791			−0.426122
$546$		0			0
$547$	−8.63409	−	8.63409i	−0.369167	−	0.369167i	0.498006	−	0.867173i	$-0.334066\pi$
$547$	−8.63409	−	8.63409i	−0.369167	−	0.369167i	−0.867173	+	0.498006i	$0.834066\pi$
$548$	17.2104	−	5.17991i	0.735192	−	0.221275i
$549$	−4.08951	−	15.2623i	−0.174536	−	0.651378i
$550$	−13.3067	+	1.95909i	−0.567399	+	0.0835358i
$551$	−3.88786	+	2.24466i	−0.165628	+	0.0956256i
$552$	2.22485	−	1.04342i	0.0946961	−	0.0444109i
$553$		0			0
$554$	−7.45391	+	5.90266i	−0.316686	+	0.250780i
$555$	4.67044	+	1.25144i	0.198249	+	0.0531207i
$556$	−1.13135	−	37.0184i	−0.0479799	−	1.56993i
$557$	0.537087	−	0.143912i	0.0227571	−	0.00609774i	−0.247423	−	0.968908i	$-0.579584\pi$
$557$	0.537087	−	0.143912i	0.0227571	−	0.00609774i	0.270180	+	0.962810i	$0.412917\pi$
$558$	−24.0095	+	10.3775i	−1.01640	+	0.439316i
$559$	0.848723			0.0358971
$560$		0			0
$561$	−14.3605			−0.606302
$562$	−15.6939	+	6.78330i	−0.662006	+	0.286136i
$563$	−24.0714	+	6.44992i	−1.01449	+	0.271832i	−0.727504	−	0.686103i	$-0.759320\pi$
$563$	−24.0714	+	6.44992i	−1.01449	+	0.271832i	−0.286986	+	0.957935i	$0.592653\pi$
$564$	−16.0718	+	0.491182i	−0.676744	+	0.0206825i
$565$	−5.90072	−	1.58109i	−0.248245	−	0.0665171i
$566$	−18.9946	+	15.0416i	−0.798403	+	0.632245i
$567$		0			0
$568$	8.08789	−	22.3740i	0.339361	−	0.938792i
$569$	−3.78183	+	2.18344i	−0.158543	+	0.0915346i	−0.577172	−	0.816622i	$-0.695844\pi$
$569$	−3.78183	+	2.18344i	−0.158543	+	0.0915346i	0.418630	+	0.908157i	$0.362511\pi$
$570$	1.76842	−	0.260357i	0.0740708	−	0.0109051i
$571$	1.33744	+	4.99139i	0.0559701	+	0.208883i	0.988248	−	0.152860i	$-0.0488484\pi$
$571$	1.33744	+	4.99139i	0.0559701	+	0.208883i	−0.932278	+	0.361743i	$0.882182\pi$
$572$	−1.22940	−	4.08471i	−0.0514037	−	0.170790i
$573$	−6.27016	−	6.27016i	−0.261940	−	0.261940i
$574$		0			0
$575$	−3.73593			−0.155799
$576$	−20.4614	−	3.51534i	−0.852559	−	0.146473i
$577$	−3.62493	+	6.27856i	−0.150908	+	0.261380i	−0.931561	−	0.363584i	$-0.881553\pi$
$577$	−3.62493	+	6.27856i	−0.150908	+	0.261380i	0.780654	+	0.624964i	$0.214886\pi$
$578$	−21.2239	+	28.5523i	−0.882799	+	1.18762i
$579$	0.524745	−	1.95838i	0.0218077	−	0.0813873i
$580$	−9.96063	−	2.34532i	−0.413592	−	0.0973842i
$581$		0			0
$582$	−3.01343	−	3.80538i	−0.124911	−	0.157738i
$583$	27.3170	−	15.7715i	1.13136	−	0.653189i
$584$	−1.01873	−	1.20868i	−0.0421555	−	0.0500155i
$585$	−2.07491	−	1.19795i	−0.0857869	−	0.0495291i
$586$	−14.2575	−	5.65206i	−0.588972	−	0.233485i
$587$	21.0987	−	21.0987i	0.870837	−	0.870837i	−0.121727	−	0.992564i	$-0.538843\pi$
$587$	21.0987	−	21.0987i	0.870837	−	0.870837i	0.992564	+	0.121727i	$0.0388432\pi$
$588$		0			0
$589$	−6.65312	−	6.65312i	−0.274137	−	0.274137i
$590$	14.5261	−	6.27854i	0.598029	−	0.258484i
$591$	−8.38240	+	14.5187i	−0.344806	+	0.597221i
$592$	4.02723	−	19.7963i	0.165518	−	0.813624i
$593$	−7.89073	−	13.6672i	−0.324034	−	0.561243i	0.657283	−	0.753644i	$-0.271706\pi$
$593$	−7.89073	−	13.6672i	−0.324034	−	0.561243i	−0.981316	+	0.192401i	$0.938372\pi$
$594$	−2.01903	+	17.3843i	−0.0828420	+	0.713285i
$595$		0			0
$596$	−30.1100	+	18.6330i	−1.23335	+	0.763238i
$597$	6.45990	+	1.73092i	0.264386	+	0.0708420i
$598$	−0.172581	−	1.17222i	−0.00705735	−	0.0479355i
$599$	−16.1332	−	9.31450i	−0.659184	−	0.380580i	0.132782	−	0.991145i	$-0.457609\pi$
$599$	−16.1332	−	9.31450i	−0.659184	−	0.380580i	−0.791966	+	0.610565i	$0.790942\pi$
$600$	−4.03965	−	2.81540i	−0.164918	−	0.114938i
$601$			34.5975i			1.41126i	0.708580	+	0.705631i	$0.249336\pi$
$601$			34.5975i			1.41126i	−0.708580	+	0.705631i	$0.750664\pi$
$602$		0			0
$603$	−29.3932	+	29.3932i	−1.19699	+	1.19699i
$604$	−24.7209	+	7.44040i	−1.00588	+	0.302746i
$605$	−1.57430	+	0.421833i	−0.0640045	+	0.0171500i
$606$	−6.63977	+	8.93240i	−0.269722	+	0.362854i
$607$	−16.4752	−	28.5359i	−0.668708	−	1.15824i	−0.978266	−	0.207355i	$-0.933515\pi$
$607$	−16.4752	−	28.5359i	−0.668708	−	1.15824i	0.309558	−	0.950880i	$-0.399819\pi$
$608$	−1.53695	−	7.30836i	−0.0623317	−	0.296393i
$609$		0			0
$610$	12.8693	+	1.49466i	0.521062	+	0.0605170i
$611$	−2.00657	+	7.48863i	−0.0811773	+	0.302958i
$612$	24.5460	+	23.0901i	0.992212	+	0.933363i
$613$	8.28898	+	30.9349i	0.334789	+	1.24945i	0.904098	+	0.427325i	$0.140544\pi$
$613$	8.28898	+	30.9349i	0.334789	+	1.24945i	−0.569309	+	0.822124i	$0.692789\pi$
$614$	2.89892	−	7.31261i	0.116991	−	0.295113i
$615$		−	7.50305i		−	0.302552i
$616$		0			0
$617$			10.5533i			0.424862i	0.977176	+	0.212431i	$0.0681380\pi$
$617$			10.5533i			0.424862i	−0.977176	+	0.212431i	$0.931862\pi$
$618$	13.2257	+	5.24301i	0.532014	+	0.210905i
$619$	1.26876	+	4.73508i	0.0509958	+	0.190319i	0.986725	−	0.162401i	$-0.0519237\pi$
$619$	1.26876	+	4.73508i	0.0509958	+	0.190319i	−0.935729	+	0.352720i	$0.885257\pi$
$620$	−0.655149	−	21.4369i	−0.0263114	−	0.860925i
$621$	−1.25816	+	4.69550i	−0.0504881	+	0.188424i
$622$	0.387989	−	3.34066i	0.0155569	−	0.133948i
$623$		0			0
$624$	0.696771	−	1.39757i	0.0278932	−	0.0559475i
$625$	−1.91701	−	3.32036i	−0.0766804	−	0.132814i
$626$	−17.4025	−	12.9359i	−0.695545	−	0.517024i
$627$	−2.82049	+	0.755749i	−0.112640	+	0.0301817i
$628$	16.2609	−	30.2636i	0.648880	−	1.20765i
$629$	−23.1871	+	23.1871i	−0.924531	+	0.924531i
$630$		0			0
$631$		−	34.6105i		−	1.37782i	−0.724846	−	0.688911i	$-0.758089\pi$
$631$		−	34.6105i		−	1.37782i	0.724846	−	0.688911i	$-0.241911\pi$
$632$	0.456323	+	2.55512i	0.0181515	+	0.101637i
$633$	−12.3545	−	7.13288i	−0.491048	−	0.283506i
$634$	−37.1699	+	5.47237i	−1.47620	+	0.217336i
$635$	13.0899	+	3.50742i	0.519456	+	0.139188i
$636$	11.2402	+	2.64660i	0.445702	+	0.104945i
$637$		0			0
$638$	16.6048	+	1.92851i	0.657392	+	0.0763505i
$639$	10.9144	+	18.9043i	0.431766	+	0.747841i
$640$	8.86244	−	14.5343i	0.350319	−	0.574518i
$641$	11.0592	−	19.1551i	0.436811	−	0.756580i	−0.560630	−	0.828066i	$-0.689441\pi$
$641$	11.0592	−	19.1551i	0.436811	−	0.756580i	0.997442	+	0.0714868i	$0.0227744\pi$
$642$	−3.12001	−	7.21847i	−0.123137	−	0.284890i
$643$	−35.2632	−	35.2632i	−1.39064	−	1.39064i	−0.823883	−	0.566761i	$-0.808196\pi$
$643$	−35.2632	−	35.2632i	−1.39064	−	1.39064i	−0.566761	−	0.823883i	$-0.691804\pi$
$644$		0			0
$645$	0.936406	−	0.936406i	0.0368709	−	0.0368709i
$646$	−4.46742	+	11.2692i	−0.175768	+	0.443381i
$647$	−27.3950	−	15.8165i	−1.07701	−	0.621810i	−0.146920	−	0.989148i	$-0.546936\pi$
$647$	−27.3950	−	15.8165i	−1.07701	−	0.621810i	−0.930087	+	0.367338i	$0.880269\pi$
$648$	11.9386	−	10.0625i	0.468994	−	0.395291i
$649$	−22.3878	+	12.9256i	−0.878798	+	0.507374i
$650$	−1.86123	+	1.47389i	−0.0730035	+	0.0578106i
$651$		0			0
$652$	−15.7995	−	25.5312i	−0.618757	−	0.999880i
$653$	0.370901	−	1.38422i	0.0145145	−	0.0541687i	−0.958289	−	0.285802i	$-0.907740\pi$
$653$	0.370901	−	1.38422i	0.0145145	−	0.0541687i	0.972803	+	0.231633i	$0.0744068\pi$
$654$	4.77460	+	3.54913i	0.186702	+	0.138782i
$655$	11.7189	−	20.2978i	0.457896	−	0.793100i
$656$	−31.2898	+	1.91433i	−1.22166	+	0.0747421i
$657$	1.45036			0.0565840
$658$		0			0
$659$	29.1346	+	29.1346i	1.13492	+	1.13492i	0.989347	+	0.145577i	$0.0465038\pi$
$659$	29.1346	+	29.1346i	1.13492	+	1.13492i	0.145577	+	0.989347i	$0.453496\pi$
$660$	−5.86312	−	3.15030i	−0.228222	−	0.122625i
$661$	6.02209	+	22.4747i	0.234232	+	0.874166i	0.978494	+	0.206278i	$0.0661350\pi$
$661$	6.02209	+	22.4747i	0.234232	+	0.874166i	−0.744261	+	0.667888i	$0.767198\pi$
$662$	3.43619	+	23.3396i	0.133551	+	0.907119i
$663$	−2.19523	+	1.26742i	−0.0852558	+	0.0492224i
$664$	−4.10308	−	8.74889i	−0.159230	−	0.339523i
$665$		0			0
$666$	11.5071	+	14.5312i	0.445891	+	0.563073i
$667$	4.48498	+	1.20175i	0.173659	+	0.0465318i
$668$	−35.1860	−	33.0991i	−1.36139	−	1.28064i
$669$	0.923687	−	0.247501i	0.0357118	−	0.00956895i
$670$	−13.5229	−	31.2866i	−0.522435	−	1.20871i
$671$	−21.1643			−0.817040
$672$		0			0
$673$	−19.8511			−0.765204			−0.382602	−	0.923913i	$-0.624972\pi$
$673$	−19.8511			−0.765204			−0.382602	+	0.923913i	$0.624972\pi$
$674$	−9.00335	−	20.8302i	−0.346796	−	0.802349i
$675$	9.40857	−	2.52102i	0.362136	−	0.0970341i
$676$	18.3894	+	17.2987i	0.707283	+	0.665334i
$677$	−20.2320	−	5.42114i	−0.777578	−	0.208352i	−0.151862	−	0.988402i	$-0.548527\pi$
$677$	−20.2320	−	5.42114i	−0.777578	−	0.208352i	−0.625717	+	0.780050i	$0.715193\pi$
$678$	2.26802	+	2.86407i	0.0871028	+	0.109994i
$679$		0			0
$680$	−25.0174	+	11.7327i	−0.959373	+	0.449930i
$681$	8.86358	−	5.11739i	0.339653	−	0.196099i
$682$	5.10308	+	34.6615i	0.195407	+	1.32726i
$683$	−12.9333	−	48.2678i	−0.494879	−	1.84692i	−0.530704	−	0.847557i	$-0.678073\pi$
$683$	−12.9333	−	48.2678i	−0.494879	−	1.84692i	0.0358249	−	0.999358i	$-0.488594\pi$
$684$	6.03613	+	3.24326i	0.230797	+	0.124009i
$685$	−9.56118	−	9.56118i	−0.365314	−	0.365314i
$686$		0			0
$687$	−14.2361			−0.543139
$688$	−4.14399	−	3.66616i	−0.157988	−	0.139771i
$689$	2.78389	−	4.82184i	0.106058	−	0.183698i
$690$	−1.48373	−	1.10291i	−0.0564846	−	0.0419871i
$691$	−0.215771	+	0.805269i	−0.00820833	+	0.0306339i	−0.969909	−	0.243470i	$-0.921714\pi$
$691$	−0.215771	+	0.805269i	−0.00820833	+	0.0306339i	0.961700	+	0.274103i	$0.0883811\pi$
$692$	2.13319	+	3.44712i	0.0810916	+	0.131040i
$693$		0			0
$694$	0.224081	−	0.177447i	0.00850600	−	0.00673579i
$695$	−24.1300	+	13.9315i	−0.915302	+	0.528450i
$696$	3.94396	+	4.67932i	0.149495	+	0.177369i
$697$	44.0673	+	25.4423i	1.66917	+	0.963694i
$698$	16.5724	−	41.8044i	0.627275	−	1.58232i
$699$	−5.43272	+	5.43272i	−0.205484	+	0.205484i
$700$		0			0
$701$	−26.8122	−	26.8122i	−1.01268	−	1.01268i	−0.999919	−	0.0127630i	$-0.995937\pi$
$701$	−26.8122	−	26.8122i	−1.01268	−	1.01268i	−0.0127630	−	0.999919i	$-0.504063\pi$
$702$	1.22564	+	2.83565i	0.0462589	+	0.107025i
$703$	−3.33382	+	5.77435i	−0.125737	+	0.217784i
$704$	−11.6417	+	25.2546i	−0.438763	+	0.951819i
$705$	6.04842	+	10.4762i	0.227797	+	0.394556i
$706$	−13.5208	−	1.57032i	−0.508860	−	0.0590998i
$707$		0			0
$708$	−9.21193	−	2.16903i	−0.346206	−	0.0815173i
$709$	22.0409	+	5.90585i	0.827764	+	0.221799i	0.647738	−	0.761863i	$-0.275715\pi$
$709$	22.0409	+	5.90585i	0.827764	+	0.221799i	0.180026	+	0.983662i	$0.442382\pi$
$710$	−17.7077	+	2.60703i	−0.664557	+	0.0978400i
$711$	−2.06242	−	1.19074i	−0.0773468	−	0.0446562i
$712$	45.0039	−	8.03730i	1.68659	−	0.301211i
$713$			9.73144i			0.364445i
$714$		0			0
$715$	−2.26925	+	2.26925i	−0.0848651	+	0.0848651i
$716$	8.10676	−	15.0877i	0.302964	−	0.563855i
$717$	14.3620	−	3.84829i	0.536359	−	0.143717i
$718$	−19.4785	−	14.4791i	−0.726930	−	0.540353i
$719$	18.9649	+	32.8482i	0.707273	+	1.22503i	0.965865	+	0.259046i	$0.0834080\pi$
$719$	18.9649	+	32.8482i	0.707273	+	1.22503i	−0.258592	+	0.965987i	$0.583259\pi$
$720$	4.95630	+	14.8119i	0.184710	+	0.552008i
$721$		0			0
$722$	2.81553	−	24.2422i	0.104783	−	0.902201i
$723$	1.54492	−	5.76573i	0.0574563	−	0.214430i
$724$	−0.433866	−	14.1964i	−0.0161245	−	0.527604i
$725$	−2.40799	−	8.98674i	−0.0894305	−	0.333759i
$726$	0.906100	+	0.359203i	0.0336285	+	0.0133313i
$727$			13.6332i			0.505628i	0.967515	+	0.252814i	$0.0813560\pi$
$727$			13.6332i			0.505628i	−0.967515	+	0.252814i	$0.918644\pi$
$728$		0			0
$729$			7.53022i			0.278897i
$730$	−0.438261	+	1.10553i	−0.0162208	+	0.0409174i
$731$	2.32447	+	8.67503i	0.0859735	+	0.320858i
$732$	−5.64349	−	5.30877i	−0.208589	−	0.196218i
$733$	−1.60496	+	5.98979i	−0.0592806	+	0.221238i	−0.989211	−	0.146497i	$-0.953200\pi$
$733$	−1.60496	+	5.98979i	−0.0592806	+	0.221238i	0.929931	+	0.367735i	$0.119867\pi$
$734$	−20.3058	−	2.35835i	−0.749502	−	0.0870483i
$735$		0			0
$736$	−4.22088	+	6.46897i	−0.155584	+	0.238449i
$737$	27.8395	+	48.2194i	1.02548	+	1.77618i
$738$	17.1591	−	23.0839i	0.631634	−	0.849729i
$739$	23.9383	−	6.41426i	0.880586	−	0.235952i	0.209926	−	0.977717i	$-0.432678\pi$
$739$	23.9383	−	6.41426i	0.880586	−	0.235952i	0.670660	+	0.741765i	$0.266011\pi$
$740$	−14.5534	+	4.38023i	−0.534995	+	0.161021i
$741$	−0.364456	+	0.364456i	−0.0133886	+	0.0133886i
$742$		0			0
$743$			39.9129i			1.46426i	0.681164	+	0.732131i	$0.261474\pi$
$743$			39.9129i			1.46426i	−0.681164	+	0.732131i	$0.738526\pi$
$744$	−7.33361	+	10.5226i	−0.268863	+	0.385776i
$745$	23.0702	+	13.3196i	0.845225	+	0.487991i
$746$	2.47832	+	16.8334i	0.0907377	+	0.616316i
$747$	8.56415	+	2.29476i	0.313346	+	0.0839607i
$748$	38.3839	−	23.7532i	1.40345	−	0.868501i
$749$		0			0
$750$	−1.20836	+	10.4042i	−0.0441229	+	0.379906i
$751$	24.5357	+	42.4971i	0.895321	+	1.55074i	0.833407	+	0.552660i	$0.186387\pi$
$751$	24.5357	+	42.4971i	0.895321	+	1.55074i	0.0619145	+	0.998081i	$0.480279\pi$
$752$	42.1454	−	27.8965i	1.53688	−	1.01728i
$753$	1.00254	−	1.73645i	0.0365345	−	0.0632796i
$754$	2.70851	−	1.17069i	0.0986382	−	0.0426340i
$755$	13.7336	+	13.7336i	0.499818	+	0.499818i
$756$		0			0
$757$	17.7514	−	17.7514i	0.645185	−	0.645185i	−0.306641	−	0.951825i	$-0.599205\pi$
$757$	17.7514	−	17.7514i	0.645185	−	0.645185i	0.951825	+	0.306641i	$0.0992050\pi$
$758$	25.1051	+	9.95235i	0.911858	+	0.361486i
$759$	2.61546	+	1.51004i	0.0949353	+	0.0548109i
$760$	−4.29611	+	3.62096i	−0.155836	+	0.131346i
$761$	−0.912216	+	0.526668i	−0.0330678	+	0.0190917i	−0.516443	−	0.856322i	$-0.672744\pi$
$761$	−0.912216	+	0.526668i	−0.0330678	+	0.0190917i	0.483375	+	0.875413i	$0.339411\pi$
$762$	−5.03126	−	6.35351i	−0.182263	−	0.230163i
$763$		0			0
$764$	27.1306	+	6.38814i	0.981549	+	0.231115i
$765$	6.56184	−	24.4891i	0.237244	−	0.885406i
$766$	20.4564	−	27.5197i	0.739119	−	0.994327i
$767$	−2.28155	+	3.95176i	−0.0823820	+	0.142690i
$768$	−9.43903	+	3.81401i	−0.340602	+	0.137626i
$769$	−0.951932			−0.0343276			−0.0171638	−	0.999853i	$-0.505464\pi$
$769$	−0.951932			−0.0343276			−0.0171638	+	0.999853i	$0.505464\pi$
$770$		0			0
$771$	−4.39289	−	4.39289i	−0.158206	−	0.158206i
$772$	1.83669	+	6.10245i	0.0661039	+	0.219632i
$773$	4.91119	+	18.3288i	0.176643	+	0.659241i	0.996266	+	0.0863375i	$0.0275163\pi$
$773$	4.91119	+	18.3288i	0.176643	+	0.659241i	−0.819623	+	0.572903i	$0.805817\pi$
$774$	5.02246	−	0.739436i	0.180529	−	0.0265785i
$775$	16.8869	−	9.74964i	0.606594	−	0.350217i
$776$	14.3488	+	5.18691i	0.515093	+	0.186199i
$777$		0			0
$778$	−12.5818	+	9.96333i	−0.451078	+	0.357203i
$779$	9.99401	+	2.67789i	0.358073	+	0.0959453i
$780$	−1.17431	+	0.0358889i	−0.0420469	+	0.00128503i
$781$	28.2424	−	7.56753i	1.01059	−	0.270788i
$782$	11.5089	−	4.97444i	0.411557	−	0.177886i
$783$	−12.1059			−0.432630
$784$		0			0
$785$	−25.8466			−0.922503
$786$	−12.8663	+	5.56114i	−0.458925	+	0.198359i
$787$	−30.0147	+	8.04240i	−1.06991	+	0.286681i	−0.750455	−	0.660922i	$-0.770166\pi$
$787$	−30.0147	+	8.04240i	−1.06991	+	0.286681i	−0.319452	+	0.947602i	$0.603499\pi$
$788$	−1.60974	−	52.6717i	−0.0573447	−	1.87635i
$789$	0.629914	+	0.168785i	0.0224255	+	0.00600890i
$790$	1.53084	−	1.21225i	0.0544648	−	0.0431300i
$791$		0			0
$792$	−10.8339	−	23.1009i	−0.384966	−	0.820853i
$793$	−3.23530	+	1.86790i	−0.114889	+	0.0663311i
$794$	33.4057	−	4.91818i	1.18552	−	0.174540i
$795$	−2.24849	−	8.39150i	−0.0797459	−	0.297616i
$796$	−20.1295	+	6.05850i	−0.713473	+	0.214738i
$797$	−2.25830	−	2.25830i	−0.0799929	−	0.0799929i	0.665978	−	0.745971i	$-0.268014\pi$
$797$	−2.25830	−	2.25830i	−0.0799929	−	0.0799929i	−0.745971	+	0.665978i	$0.768014\pi$
$798$		0			0
$799$	−82.0390			−2.90233
$800$	15.4543	+	0.843390i	0.546392	+	0.0298183i
$801$	−20.9727	+	36.3258i	−0.741035	+	1.28351i
$802$	4.32235	−	5.81480i	0.152628	−	0.205328i
$803$	0.502807	−	1.87650i	0.0177437	−	0.0662203i
$804$	−4.67172	+	19.8409i	−0.164759	+	0.699734i
$805$		0			0
$806$	3.83921	+	4.84818i	0.135230	+	0.170770i
$807$	12.0076	−	6.93258i	0.422687	−	0.244039i
$808$	2.97257	−	34.8577i	0.104575	−	1.22629i
$809$	0.992787	+	0.573186i	0.0349045	+	0.0201521i	0.517351	−	0.855773i	$-0.326918\pi$
$809$	0.992787	+	0.573186i	0.0349045	+	0.0201521i	−0.482446	+	0.875926i	$0.660252\pi$
$810$	−10.9198	−	4.32889i	−0.383681	−	0.152102i
$811$	18.0272	−	18.0272i	0.633019	−	0.633019i	−0.315805	−	0.948824i	$-0.602275\pi$
$811$	18.0272	−	18.0272i	0.633019	−	0.633019i	0.948824	+	0.315805i	$0.102275\pi$
$812$		0			0
$813$	11.2801	+	11.2801i	0.395612	+	0.395612i
$814$	22.7900	−	9.85042i	0.798788	−	0.345257i
$815$	−11.2941	+	19.5619i	−0.395614	+	0.685224i
$816$	16.1932	+	3.29425i	0.566877	+	0.115322i
$817$	0.913078	+	1.58150i	0.0319445	+	0.0553296i
$818$	2.31516	−	19.9340i	0.0809478	−	0.696975i
$819$		0			0
$820$	12.4105	+	20.0547i	0.433392	+	0.700340i
$821$	−25.5160	−	6.83700i	−0.890516	−	0.238613i	−0.215577	−	0.976487i	$-0.569163\pi$
$821$	−25.5160	−	6.83700i	−0.890516	−	0.238613i	−0.674939	+	0.737874i	$0.735830\pi$
$822$	1.17783	+	8.00014i	0.0410815	+	0.279037i
$823$	−11.4579	−	6.61523i	−0.399398	−	0.230593i	0.286826	−	0.957983i	$-0.407400\pi$
$823$	−11.4579	−	6.61523i	−0.399398	−	0.230593i	−0.686224	+	0.727390i	$0.740733\pi$
$824$	−44.0227	+	7.86208i	−1.53361	+	0.273888i
$825$		−	6.05145i		−	0.210684i
$826$		0			0
$827$	−11.8854	+	11.8854i	−0.413297	+	0.413297i	−0.882885	−	0.469589i	$-0.844402\pi$
$827$	−11.8854	+	11.8854i	−0.413297	+	0.413297i	0.469589	+	0.882885i	$0.344402\pi$
$828$	−2.04255	−	6.78642i	−0.0709835	−	0.235845i
$829$	18.4216	−	4.93604i	0.639807	−	0.171436i	0.0756912	−	0.997131i	$-0.475884\pi$
$829$	18.4216	−	4.93604i	0.639807	−	0.171436i	0.564116	+	0.825695i	$0.309217\pi$
$830$	−4.33702	+	5.83453i	−0.150540	+	0.202520i
$831$	−2.13891	−	3.70470i	−0.0741979	−	0.128515i
$832$	0.449280	+	4.88803i	0.0155760	+	0.169462i
$833$		0			0
$834$	16.5518	+	1.92235i	0.573141	+	0.0665655i
$835$	−9.40623	+	35.1045i	−0.325516	+	1.21484i
$836$	6.28877	−	6.68528i	0.217502	−	0.231215i
$837$	−6.56680	−	24.5076i	−0.226982	−	0.847108i
$838$	−3.13095	+	7.89791i	−0.108157	+	0.272829i
$839$		−	33.0983i		−	1.14268i	−0.820714	−	0.571339i	$-0.806424\pi$
$839$		−	33.0983i		−	1.14268i	0.820714	−	0.571339i	$-0.193576\pi$
$840$		0			0
$841$		−	17.4369i		−	0.601271i
$842$	−22.7765	−	9.02923i	−0.784930	−	0.311168i
$843$	−1.99091	−	7.43018i	−0.0685706	−	0.255909i
$844$	44.8202	−	1.36979i	1.54278	−	0.0471500i
$845$	4.91601	−	18.3468i	0.169116	−	0.631149i
$846$	−5.34988	+	46.0634i	−0.183933	+	1.58369i
$847$		0			0
$848$	−34.4212	+	11.5179i	−1.18203	+	0.395525i
$849$	−5.45053	−	9.44059i	−0.187062	−	0.324000i
$850$	−20.1625	−	14.9875i	−0.691568	−	0.514067i
$851$	6.66120	−	1.78486i	0.228343	−	0.0611844i
$852$	9.42908	+	5.06632i	0.323035	+	0.173569i
$853$	10.7030	−	10.7030i	0.366463	−	0.366463i	−0.499723	−	0.866185i	$-0.666565\pi$
$853$	10.7030	−	10.7030i	0.366463	−	0.366463i	0.866185	+	0.499723i	$0.166565\pi$
$854$		0			0
$855$		−	5.15513i		−	0.176302i
$856$	20.2792	+	14.1334i	0.693127	+	0.483069i
$857$	−30.0916	−	17.3734i	−1.02791	−	0.593464i	−0.111524	−	0.993762i	$-0.535573\pi$
$857$	−30.0916	−	17.3734i	−1.02791	−	0.593464i	−0.916385	+	0.400298i	$0.868907\pi$
$858$	1.89875	−	0.279545i	0.0648223	−	0.00954352i
$859$	−25.0048	−	6.70000i	−0.853151	−	0.228601i	−0.194363	−	0.980930i	$-0.562264\pi$
$859$	−25.0048	−	6.70000i	−0.853151	−	0.228601i	−0.658788	+	0.752328i	$0.728931\pi$
$860$	−0.954025	+	4.05176i	−0.0325320	+	0.138164i
$861$		0			0
$862$	−9.13793	−	1.06129i	−0.311239	−	0.0361478i
$863$	22.1159	+	38.3058i	0.752832	+	1.30394i	0.946445	+	0.322866i	$0.104646\pi$
$863$	22.1159	+	38.3058i	0.752832	+	1.30394i	−0.193612	+	0.981078i	$0.562020\pi$
$864$	6.26459	−	19.1397i	0.213126	−	0.651146i
$865$	1.52488	−	2.64117i	0.0518475	−	0.0898025i
$866$	−6.90382	−	15.9727i	−0.234601	−	0.542774i
$867$	−11.3183	−	11.3183i	−0.384390	−	0.384390i
$868$		0			0
$869$	−2.25559	+	2.25559i	−0.0765157	+	0.0765157i
$870$	1.69670	−	4.27997i	0.0575235	−	0.145105i
$871$	8.51140	+	4.91406i	0.288398	+	0.166507i
$872$	−18.6324	−	1.58891i	−0.630971	−	0.0538074i
$873$	−12.1236	+	6.99958i	−0.410323	+	0.236900i
$874$	1.99862	−	1.58268i	0.0676044	−	0.0535351i
$875$		0			0
$876$	0.604768	−	0.374249i	0.0204332	−	0.0126447i
$877$	−13.4169	+	50.0727i	−0.453057	+	1.69083i	0.240679	+	0.970605i	$0.422630\pi$
$877$	−13.4169	+	50.0727i	−0.453057	+	1.69083i	−0.693737	+	0.720229i	$0.744037\pi$
$878$	−18.4394	−	13.7066i	−0.622298	−	0.462576i
$879$	3.45018	−	5.97589i	0.116372	−	0.201562i
$880$	20.8822	−	1.27758i	0.703937	−	0.0430674i
$881$	−22.9696			−0.773865			−0.386932	−	0.922108i	$-0.626465\pi$
$881$	−22.9696			−0.773865			−0.386932	+	0.922108i	$0.626465\pi$
$882$		0			0
$883$	6.89740	+	6.89740i	0.232116	+	0.232116i	0.813575	−	0.581459i	$-0.197518\pi$
$883$	6.89740	+	6.89740i	0.232116	+	0.232116i	−0.581459	+	0.813575i	$0.697518\pi$
$884$	3.77120	−	7.01869i	0.126839	−	0.236064i
$885$	1.84276	+	6.87729i	0.0619438	+	0.231177i
$886$	−2.95703	−	20.0850i	−0.0993433	−	0.674767i
$887$	10.6280	−	6.13605i	0.356852	−	0.206028i	−0.310847	−	0.950460i	$-0.600613\pi$
$887$	10.6280	−	6.13605i	0.356852	−	0.206028i	0.667699	+	0.744431i	$0.267279\pi$
$888$	8.54781	+	3.08991i	0.286846	+	0.103691i
$889$		0			0
$890$	−21.3517	−	26.9630i	−0.715709	−	0.903802i
$891$	18.5350	+	4.96644i	0.620946	+	0.166382i
$892$	−2.05952	+	2.18937i	−0.0689577	+	0.0733055i
$893$	−16.1129	+	4.31745i	−0.539199	+	0.144478i
$894$	−6.32071	−	14.6236i	−0.211396	−	0.489087i
$895$	−12.8856			−0.430719
$896$		0			0
$897$	0.533086			0.0177992
$898$	−5.55422	−	12.8503i	−0.185347	−	0.428819i
$899$	−23.4088	+	6.27238i	−0.780729	+	0.209196i
$900$	−9.73005	+	10.3435i	−0.324335	+	0.344784i
$901$	56.9099	+	15.2489i	1.89594	+	0.508016i
$902$	−23.9176	−	30.2033i	−0.796370	−	1.00566i
$903$		0			0
$904$	−10.7995	−	3.90386i	−0.359185	−	0.129840i
$905$	−9.25372	+	5.34264i	−0.307604	+	0.177595i
$906$	−1.69183	−	11.4914i	−0.0562072	−	0.381775i
$907$	6.10163	+	22.7716i	0.202601	+	0.756119i	0.990167	+	0.139888i	$0.0446743\pi$
$907$	6.10163	+	22.7716i	0.202601	+	0.756119i	−0.787566	+	0.616230i	$0.788659\pi$
$908$	−15.2268	+	28.3390i	−0.505318	+	0.940464i
$909$	22.6973	+	22.6973i	0.752823	+	0.752823i
$910$		0			0
$911$	30.0024			0.994023			0.497012	−	0.867744i	$-0.334431\pi$
$911$	30.0024			0.994023			0.497012	+	0.867744i	$0.334431\pi$
$912$	3.35381	−	0.205189i	0.111056	−	0.00679448i
$913$	5.93798	−	10.2849i	0.196519	−	0.340380i
$914$	14.5751	+	10.8342i	0.482101	+	0.358363i
$915$	−1.50867	+	5.63042i	−0.0498750	+	0.186136i
$916$	38.0512	−	23.5473i	1.25725	−	0.778023i
$917$		0			0
$918$	−25.6272	+	20.2938i	−0.845823	+	0.669797i
$919$	6.99945	−	4.04114i	0.230891	−	0.133305i	−0.380092	−	0.924949i	$-0.624108\pi$
$919$	6.99945	−	4.04114i	0.230891	−	0.133305i	0.610983	+	0.791644i	$0.290774\pi$
$920$	5.79010	+	0.493763i	0.190894	+	0.0162789i
$921$	3.06501	+	1.76958i	0.100995	+	0.0583098i
$922$	5.53062	−	13.9512i	0.182141	−	0.459457i
$923$	3.64941	−	3.64941i	0.120122	−	0.120122i
$924$		0			0
$925$	−9.77092	−	9.77092i	−0.321266	−	0.321266i
$926$	−17.0002	−	39.3317i	−0.558661	−	1.29252i
$927$	20.5155	−	35.5339i	0.673817	−	1.16709i
$928$	−18.2816	−	5.98371i	−0.600122	−	0.196425i
$929$	−10.7324	−	18.5891i	−0.352120	−	0.609889i	0.634501	−	0.772922i	$-0.281206\pi$
$929$	−10.7324	−	18.5891i	−0.352120	−	0.609889i	−0.986621	+	0.163033i	$0.947872\pi$
$930$	9.58490	+	1.11320i	0.314301	+	0.0365034i
$931$		0			0
$932$	5.53495	−	23.5070i	0.181303	−	0.769998i
$933$	1.46157	+	0.391625i	0.0478495	+	0.0128212i
$934$	9.84645	−	1.44965i	0.322186	−	0.0474341i
$935$	−29.4096	−	16.9796i	−0.961796	−	0.555293i
$936$	−3.69494	−	2.57516i	−0.120773	−	0.0841717i
$937$			27.1581i			0.887216i	0.896221	+	0.443608i	$0.146302\pi$
$937$			27.1581i			0.887216i	−0.896221	+	0.443608i	$0.853698\pi$
$938$		0			0
$939$	6.89848	−	6.89848i	0.225123	−	0.225123i
$940$	−33.4949	−	17.9971i	−1.09248	−	0.586999i
$941$	−11.6132	+	3.11176i	−0.378581	+	0.101440i	−0.443091	−	0.896477i	$-0.646118\pi$
$941$	−11.6132	+	3.11176i	−0.378581	+	0.101440i	0.0645102	+	0.997917i	$0.479452\pi$
$942$	12.4053	+	9.22131i	0.404187	+	0.300446i
$943$	−5.35060	−	9.26752i	−0.174240	−	0.301792i
$944$	28.2100	−	9.43951i	0.918158	−	0.307230i
$945$		0			0
$946$	0.784476	−	6.75448i	0.0255055	−	0.219607i
$947$	11.3673	−	42.4234i	0.369388	−	1.37858i	−0.491985	−	0.870604i	$-0.663728\pi$
$947$	11.3673	−	42.4234i	0.369388	−	1.37858i	0.861373	−	0.507973i	$-0.169605\pi$
$948$	−1.16724	+	0.0356729i	−0.0379101	+	0.00115860i
$949$	−0.0887525	−	0.331229i	−0.00288103	−	0.0107521i
$950$	−4.74878	−	1.88255i	−0.154071	−	0.0610779i
$951$		−	16.9037i		−	0.548139i
$952$		0			0
$953$			32.0416i			1.03793i	0.854796	+	0.518964i	$0.173682\pi$
$953$			32.0416i			1.03793i	−0.854796	+	0.518964i	$0.826318\pi$
$954$	12.2732	−	30.9595i	0.397359	−	1.00235i
$955$	−5.42722	−	20.2547i	−0.175621	−	0.655426i
$956$	−32.0225	+	34.0416i	−1.03568	+	1.10098i
$957$	−1.94658	+	7.26475i	−0.0629241	+	0.234836i
$958$	3.70570	+	0.430386i	0.119726	+	0.0139051i
$959$		0			0
$960$	5.88871	+	4.89732i	0.190057	+	0.158060i
$961$	−9.89607	−	17.1405i	−0.319228	−	0.552919i
$962$	2.61444	−	3.51717i	0.0842928	−	0.113398i
$963$	−21.9069	+	5.86993i	−0.705939	+	0.189156i
$964$	5.40746	+	17.9665i	0.174163	+	0.578660i
$965$	3.39020	−	3.39020i	0.109134	−	0.109134i
$966$		0			0
$967$			5.86480i			0.188599i	0.995544	+	0.0942997i	$0.0300612\pi$
$967$			5.86480i			0.188599i	−0.995544	+	0.0942997i	$0.969939\pi$
$968$	−3.01603	+	0.538637i	−0.0969390	+	0.0173125i
$969$	−4.72338	−	2.72704i	−0.151737	−	0.0876052i
$970$	−1.67193	−	11.3562i	−0.0536825	−	0.364627i
$971$	59.2479	+	15.8754i	1.90136	+	0.509467i	0.996484	+	0.0837830i	$0.0267003\pi$
$971$	59.2479	+	15.8754i	1.90136	+	0.509467i	0.904872	+	0.425684i	$0.139966\pi$
$972$	14.9370	+	24.1374i	0.479103	+	0.774207i
$973$		0			0
$974$	−0.455053	+	3.91809i	−0.0145809	+	0.125544i
$975$	−0.534083	−	0.925059i	−0.0171043	−	0.0296256i
$976$	23.8653	+	4.85501i	0.763911	+	0.155405i
$977$	22.4338	−	38.8564i	0.717719	−	1.24313i	−0.244182	−	0.969729i	$-0.578519\pi$
$977$	22.4338	−	38.8564i	0.717719	−	1.24313i	0.961901	−	0.273397i	$-0.0881473\pi$
$978$	12.3998	−	5.35953i	0.396503	−	0.171379i
$979$	39.7282	+	39.7282i	1.26972	+	1.26972i
$980$		0			0
$981$	12.1323	−	12.1323i	0.387355	−	0.387355i
$982$	−29.5236	−	11.7040i	−0.942136	−	0.373489i
$983$	−4.60693	−	2.65981i	−0.146938	−	0.0848349i	0.424728	−	0.905321i	$-0.360370\pi$
$983$	−4.60693	−	2.65981i	−0.146938	−	0.0848349i	−0.571667	+	0.820486i	$0.693703\pi$
$984$	1.19841	−	14.0531i	0.0382040	−	0.447998i
$985$	−34.3334	+	19.8224i	−1.09395	+	0.631594i
$986$	19.3840	+	24.4782i	0.617312	+	0.779545i
$987$		0			0
$988$	0.371314	−	1.57698i	0.0118131	−	0.0501703i
$989$	0.488844	−	1.82439i	0.0155443	−	0.0580123i
$990$	−11.4516	+	15.4057i	−0.363956	+	0.489625i
$991$	11.0623	−	19.1605i	0.351407	−	0.608654i	−0.635090	−	0.772438i	$-0.719037\pi$
$991$	11.0623	−	19.1605i	0.351407	−	0.608654i	0.986496	+	0.163784i	$0.0523702\pi$
$992$	2.19688	−	40.2557i	0.0697510	−	1.27812i
$993$	−10.6141			−0.336828
$994$		0			0
$995$	11.1829	+	11.1829i	0.354522	+	0.354522i
$996$	4.16319	−	1.25302i	0.131916	−	0.0397034i
$997$	11.7163	+	43.7258i	0.371059	+	1.38481i	0.859019	+	0.511944i	$0.171075\pi$
$997$	11.7163	+	43.7258i	0.371059	+	1.38481i	−0.487960	+	0.872866i	$0.662259\pi$
$998$	4.20309	−	0.618804i	0.133046	−	0.0195879i
$999$	−15.5711	+	8.99000i	−0.492649	+	0.284431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.p.557.12		96
7.2	even	3	inner	784.2.x.p.765.7		96
7.3	odd	6		784.2.m.l.589.22	yes	48
7.4	even	3		784.2.m.l.589.21	yes	48
7.5	odd	6	inner	784.2.x.p.765.8		96
7.6	odd	2	inner	784.2.x.p.557.11		96
16.5	even	4	inner	784.2.x.p.165.7		96
112.5	odd	12	inner	784.2.x.p.373.11		96
112.37	even	12	inner	784.2.x.p.373.12		96
112.53	even	12		784.2.m.l.197.21	✓	48
112.69	odd	4	inner	784.2.x.p.165.8		96
112.101	odd	12		784.2.m.l.197.22	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.l.197.21	✓	48	112.53	even	12
784.2.m.l.197.22	yes	48	112.101	odd	12
784.2.m.l.589.21	yes	48	7.4	even	3
784.2.m.l.589.22	yes	48	7.3	odd	6
784.2.x.p.165.7		96	16.5	even	4	inner
784.2.x.p.165.8		96	112.69	odd	4	inner
784.2.x.p.373.11		96	112.5	odd	12	inner
784.2.x.p.373.12		96	112.37	even	12	inner
784.2.x.p.557.11		96	7.6	odd	2	inner
784.2.x.p.557.12		96	1.1	even	1	trivial
784.2.x.p.765.7		96	7.2	even	3	inner
784.2.x.p.765.8		96	7.5	odd	6	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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.561091 - 1.29814i) q^{2} +(0.614599 - 0.164681i) q^{3} +(-1.37035 + 1.45675i) q^{4} +(1.45338 + 0.389432i) q^{5} +(-0.558626 - 0.705436i) q^{6} +(2.65997 + 0.961542i) q^{8} +(-2.24746 + 1.29757i) q^{9} +O(q^{10})\)	\(q+(-0.561091 - 1.29814i) q^{2} +(0.614599 - 0.164681i) q^{3} +(-1.37035 + 1.45675i) q^{4} +(1.45338 + 0.389432i) q^{5} +(-0.558626 - 0.705436i) q^{6} +(2.65997 + 0.961542i) q^{8} +(-2.24746 + 1.29757i) q^{9} +(-0.309941 - 2.10520i) q^{10} +(0.899678 + 3.35764i) q^{11} +(-0.602317 + 1.12099i) q^{12} +(0.433866 + 0.433866i) q^{13} +0.957378 q^{15} +(-0.244266 - 3.99253i) q^{16} +(-3.24640 + 5.62292i) q^{17} +(2.94547 + 2.18947i) q^{18} +(-0.341695 + 1.27522i) q^{19} +(-2.55895 + 1.58356i) q^{20} +(3.85390 - 3.05186i) q^{22} +(1.18252 - 0.682730i) q^{23} +(1.79316 + 0.152916i) q^{24} +(-2.36947 - 1.36801i) q^{25} +(0.319782 - 0.806658i) q^{26} +(-2.51736 + 2.51736i) q^{27} +(2.40449 + 2.40449i) q^{29} +(-0.537177 - 1.24281i) q^{30} +(-3.56343 + 6.17204i) q^{31} +(-5.04583 + 2.55727i) q^{32} +(1.10588 + 1.91544i) q^{33} +(9.12089 + 1.05931i) q^{34} +(1.18957 - 5.05214i) q^{36} +(4.87836 + 1.30715i) q^{37} +(1.84714 - 0.271947i) q^{38} +(0.338103 + 0.195204i) q^{39} +(3.49149 + 2.43336i) q^{40} -7.83707i q^{41} +(0.978094 - 0.978094i) q^{43} +(-6.12414 - 3.29055i) q^{44} +(-3.77174 + 1.01063i) q^{45} +(-1.54978 - 1.15201i) q^{46} +(6.31769 + 10.9426i) q^{47} +(-0.807621 - 2.41358i) q^{48} +(-0.446389 + 3.84349i) q^{50} +(-1.06924 + 3.99046i) q^{51} +(-1.22658 + 0.0374866i) q^{52} +(-2.34860 - 8.76508i) q^{53} +(4.68036 + 1.85542i) q^{54} +5.23030i q^{55} +0.840021i q^{57} +(1.77223 - 4.47051i) q^{58} +(1.92480 + 7.18346i) q^{59} +(-1.31195 + 1.39467i) q^{60} +(-1.57583 + 5.88108i) q^{61} +(10.0116 + 1.16276i) q^{62} +(6.15087 + 5.11535i) q^{64} +(0.461611 + 0.799533i) q^{65} +(1.86602 - 2.51033i) q^{66} +(15.4719 - 4.14569i) q^{67} +(-3.74251 - 12.4346i) q^{68} +(0.614344 - 0.614344i) q^{69} -8.41138i q^{71} +(-7.22586 + 1.29048i) q^{72} +(-0.483999 - 0.279437i) q^{73} +(-1.04033 - 7.06624i) q^{74} +(-1.68156 - 0.450572i) q^{75} +(-1.38944 - 2.24527i) q^{76} +(0.0636959 - 0.548433i) q^{78} +(0.458833 + 0.794722i) q^{79} +(1.19981 - 5.89780i) q^{80} +(2.76012 - 4.78067i) q^{81} +(-10.1736 + 4.39731i) q^{82} +(-2.41581 - 2.41581i) q^{83} +(-6.90800 + 6.90800i) q^{85} +(-1.81851 - 0.720906i) q^{86} +(1.87377 + 1.08182i) q^{87} +(-0.835401 + 9.79631i) q^{88} +(13.9976 - 8.08152i) q^{89} +(3.42824 + 4.32920i) q^{90} +(-0.625904 + 2.65823i) q^{92} +(-1.17366 + 4.38016i) q^{93} +(10.6602 - 14.3410i) q^{94} +(-0.993225 + 1.72032i) q^{95} +(-2.68003 + 2.40265i) q^{96} +5.39436 q^{97} +(-6.37879 - 6.37879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{4}+O(q^{10}) \) 96 * q + 4 * q^4	\( 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) \) 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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