LMFDB - Embedded newform 784.2.x.p.765.7

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			765.7
Character	$\chi$	$=$	784.765
Dual form			784.2.x.p.165.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.843680 + 1.13499i) q^{2} +(-0.164681 + 0.614599i) q^{3} +(-0.576410 - 1.91514i) q^{4} +(-0.389432 - 1.45338i) q^{5} +(-0.558626 - 0.705436i) q^{6} +(2.65997 + 0.961542i) q^{8} +(2.24746 + 1.29757i) q^{9} +O(q^{10})$	\(q+(-0.843680 + 1.13499i) q^{2} +(-0.164681 + 0.614599i) q^{3} +(-0.576410 - 1.91514i) q^{4} +(-0.389432 - 1.45338i) q^{5} +(-0.558626 - 0.705436i) q^{6} +(2.65997 + 0.961542i) q^{8} +(2.24746 + 1.29757i) q^{9} +(1.97813 + 0.784185i) q^{10} +(-3.35764 - 0.899678i) q^{11} +(1.27197 - 0.0388735i) q^{12} +(0.433866 + 0.433866i) q^{13} +0.957378 q^{15} +(-3.33550 + 2.20781i) q^{16} +(-3.24640 - 5.62292i) q^{17} +(-3.36887 + 1.45612i) q^{18} +(1.27522 - 0.341695i) q^{19} +(-2.55895 + 1.58356i) q^{20} +(3.85390 - 3.05186i) q^{22} +(-1.18252 - 0.682730i) q^{23} +(-1.02901 + 1.47647i) q^{24} +(2.36947 - 1.36801i) q^{25} +(-0.858477 + 0.126390i) q^{26} +(-2.51736 + 2.51736i) q^{27} +(2.40449 + 2.40449i) q^{29} +(-0.807720 + 1.08662i) q^{30} +(-3.56343 - 6.17204i) q^{31} +(0.308253 - 5.64845i) q^{32} +(1.10588 - 1.91544i) q^{33} +(9.12089 + 1.05931i) q^{34} +(1.18957 - 5.05214i) q^{36} +(-1.30715 - 4.87836i) q^{37} +(-0.688059 + 1.73565i) q^{38} +(-0.338103 + 0.195204i) q^{39} +(0.361609 - 4.24040i) q^{40} -7.83707i q^{41} +(0.978094 - 0.978094i) q^{43} +(0.212372 + 6.94894i) q^{44} +(1.01063 - 3.77174i) q^{45} +(1.77256 - 0.766148i) q^{46} +(6.31769 - 10.9426i) q^{47} +(-0.807621 - 2.41358i) q^{48} +(-0.446389 + 3.84349i) q^{50} +(3.99046 - 1.06924i) q^{51} +(0.580828 - 1.08100i) q^{52} +(8.76508 + 2.34860i) q^{53} +(-0.733335 - 4.98102i) q^{54} +5.23030i q^{55} +0.840021i q^{57} +(-4.75769 + 0.700456i) q^{58} +(-7.18346 - 1.92480i) q^{59} +(-0.551842 - 1.83351i) q^{60} +(5.88108 - 1.57583i) q^{61} +(10.0116 + 1.16276i) q^{62} +(6.15087 + 5.11535i) q^{64} +(0.461611 - 0.799533i) q^{65} +(1.24100 + 2.87119i) q^{66} +(-4.14569 + 15.4719i) q^{67} +(-8.89742 + 9.45841i) q^{68} +(0.614344 - 0.614344i) q^{69} -8.41138i q^{71} +(4.73051 + 5.61254i) q^{72} +(0.483999 - 0.279437i) q^{73} +(6.63971 + 2.63217i) q^{74} +(0.450572 + 1.68156i) q^{75} +(-1.38944 - 2.24527i) q^{76} +(0.0636959 - 0.548433i) q^{78} +(0.458833 - 0.794722i) q^{79} +(4.50774 + 3.98797i) q^{80} +(2.76012 + 4.78067i) q^{81} +(8.89501 + 6.61198i) q^{82} +(-2.41581 - 2.41581i) q^{83} +(-6.90800 + 6.90800i) q^{85} +(0.284930 + 1.93533i) q^{86} +(-1.87377 + 1.08182i) q^{87} +(-8.06615 - 5.62163i) q^{88} +(-13.9976 - 8.08152i) q^{89} +(3.42824 + 4.32920i) q^{90} +(-0.625904 + 2.65823i) q^{92} +(4.38016 - 1.17366i) q^{93} +(7.08961 + 16.4025i) q^{94} +(-0.993225 - 1.72032i) q^{95} +(3.42077 + 1.11965i) 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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.843680	+	1.13499i	−0.596571	+	0.802560i
$2$	−0.843680	+	1.13499i	−0.596571	+	0.802560i
$3$	−0.164681	+	0.614599i	−0.0950788	+	0.354839i	−0.997031	−	0.0769962i	$-0.975467\pi$
$3$	−0.164681	+	0.614599i	−0.0950788	+	0.354839i	0.901953	+	0.431835i	$0.142134\pi$
$4$	−0.576410	−	1.91514i	−0.288205	−	0.957569i
$5$	−0.389432	−	1.45338i	−0.174159	−	0.649972i	−0.996693	−	0.0812556i	$-0.974107\pi$
$5$	−0.389432	−	1.45338i	−0.174159	−	0.649972i	0.822534	−	0.568716i	$-0.192560\pi$
$6$	−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
$10$	1.97813	+	0.784185i	0.625540	+	0.247981i
$11$	−3.35764	−	0.899678i	−1.01237	−	0.271263i	−0.285750	−	0.958304i	$-0.592243\pi$
$11$	−3.35764	−	0.899678i	−1.01237	−	0.271263i	−0.726619	+	0.687041i	$0.758909\pi$
$12$	1.27197	−	0.0388735i	0.367185	−	0.0112218i
$13$	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
$16$	−3.33550	+	2.20781i	−0.833876	+	0.551952i
$17$	−3.24640	−	5.62292i	−0.787367	−	1.36376i	−0.927575	−	0.373637i	$-0.878110\pi$
$17$	−3.24640	−	5.62292i	−0.787367	−	1.36376i	0.140208	−	0.990122i	$-0.455223\pi$
$18$	−3.36887	+	1.45612i	−0.794051	+	0.343210i
$19$	1.27522	−	0.341695i	0.292556	−	0.0783902i	−0.109556	−	0.993981i	$-0.534943\pi$
$19$	1.27522	−	0.341695i	0.292556	−	0.0783902i	0.402112	+	0.915590i	$0.368276\pi$
$20$	−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	$-0.378802\pi$
$23$	−1.18252	−	0.682730i	−0.246573	−	0.142359i	−0.618194	+	0.786026i	$0.712135\pi$
$24$	−1.02901	+	1.47647i	−0.210046	+	0.301382i
$25$	2.36947	−	1.36801i	0.473894	−	0.273603i
$26$	−0.858477	+	0.126390i	−0.168361	+	0.0247871i
$27$	−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	$0.647752\pi$
$30$	−0.807720	+	1.08662i	−0.147469	+	0.198388i
$31$	−3.56343	−	6.17204i	−0.640011	−	1.10853i	−0.985430	−	0.170083i	$-0.945596\pi$
$31$	−3.56343	−	6.17204i	−0.640011	−	1.10853i	0.345419	−	0.938449i	$-0.387737\pi$
$32$	0.308253	−	5.64845i	0.0544920	−	0.998514i
$33$	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
$37$	−1.30715	−	4.87836i	−0.214895	−	0.801997i	−0.986204	−	0.165537i	$-0.947064\pi$
$37$	−1.30715	−	4.87836i	−0.214895	−	0.801997i	0.771309	−	0.636461i	$-0.219602\pi$
$38$	−0.688059	+	1.73565i	−0.111618	+	0.281559i
$39$	−0.338103	+	0.195204i	−0.0541398	+	0.0312576i
$40$	0.361609	−	4.24040i	0.0571755	−	0.670467i
$41$		−	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	$0.216365\pi$
$44$	0.212372	+	6.94894i	0.0320163	+	1.04759i
$45$	1.01063	−	3.77174i	0.150656	−	0.562258i
$46$	1.77256	−	0.766148i	0.261350	−	0.112962i
$47$	6.31769	−	10.9426i	0.921530	−	1.59614i	0.124481	−	0.992222i	$-0.460273\pi$
$47$	6.31769	−	10.9426i	0.921530	−	1.59614i	0.797049	−	0.603915i	$-0.206393\pi$
$48$	−0.807621	−	2.41358i	−0.116570	−	0.348370i
$49$		0			0
$50$	−0.446389	+	3.84349i	−0.0631290	+	0.543552i
$51$	3.99046	−	1.06924i	0.558777	−	0.149724i
$52$	0.580828	−	1.08100i	0.0805464	−	0.149907i
$53$	8.76508	+	2.34860i	1.20398	+	0.322604i	0.804396	−	0.594094i	$-0.202489\pi$
$53$	8.76508	+	2.34860i	1.20398	+	0.322604i	0.399580	+	0.916698i	$0.369156\pi$
$54$	−0.733335	−	4.98102i	−0.0997943	−	0.677831i
$55$			5.23030i			0.705254i
$56$		0			0
$57$			0.840021i			0.111264i
$58$	−4.75769	+	0.700456i	−0.624716	+	0.0919744i
$59$	−7.18346	−	1.92480i	−0.935206	−	0.250588i	−0.241133	−	0.970492i	$-0.577519\pi$
$59$	−7.18346	−	1.92480i	−0.935206	−	0.250588i	−0.694073	+	0.719904i	$0.744186\pi$
$60$	−0.551842	−	1.83351i	−0.0712425	−	0.236705i
$61$	5.88108	−	1.57583i	0.752995	−	0.201764i	0.138149	−	0.990411i	$-0.455885\pi$
$61$	5.88108	−	1.57583i	0.752995	−	0.201764i	0.614846	+	0.788647i	$0.289218\pi$
$62$	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
$66$	1.24100	+	2.87119i	0.152757	+	0.353419i
$67$	−4.14569	+	15.4719i	−0.506476	+	1.89019i	−0.0537302	+	0.998555i	$0.517111\pi$
$67$	−4.14569	+	15.4719i	−0.506476	+	1.89019i	−0.452746	+	0.891640i	$0.649556\pi$
$68$	−8.89742	+	9.45841i	−1.07897	+	1.14700i
$69$	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	$-0.166345\pi$
$72$	4.73051	+	5.61254i	0.557496	+	0.661444i
$73$	0.483999	−	0.279437i	0.0566478	−	0.0327056i	−0.471409	−	0.881915i	$-0.656254\pi$
$73$	0.483999	−	0.279437i	0.0566478	−	0.0327056i	0.528056	+	0.849209i	$0.322921\pi$
$74$	6.63971	+	2.63217i	0.771851	+	0.305983i
$75$	0.450572	+	1.68156i	0.0520276	+	0.194170i
$76$	−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	−0.839059	−	0.544040i	$-0.816894\pi$
$79$	0.458833	−	0.794722i	0.0516227	−	0.0894132i	0.890682	+	0.454627i	$0.150227\pi$
$80$	4.50774	+	3.98797i	0.503980	+	0.445868i
$81$	2.76012	+	4.78067i	0.306680	+	0.531185i
$82$	8.89501	+	6.61198i	0.982289	+	0.730171i
$83$	−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
$86$	0.284930	+	1.93533i	0.0307248	+	0.208692i
$87$	−1.87377	+	1.08182i	−0.200889	+	0.115984i
$88$	−8.06615	−	5.62163i	−0.859855	−	0.599268i
$89$	−13.9976	−	8.08152i	−1.48374	−	0.856639i	−0.483913	−	0.875116i	$-0.660785\pi$
$89$	−13.9976	−	8.08152i	−1.48374	−	0.856639i	−0.999829	+	0.0184769i	$0.994118\pi$
$90$	3.42824	+	4.32920i	0.361368	+	0.456338i
$91$		0			0
$92$	−0.625904	+	2.65823i	−0.0652550	+	0.277139i
$93$	4.38016	−	1.17366i	0.454201	−	0.121703i
$94$	7.08961	+	16.4025i	0.731237	+	1.69179i
$95$	−0.993225	−	1.72032i	−0.101903	−	0.176501i
$96$	3.42077	+	1.11965i	0.349131	+	0.114273i
$97$	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
$100$	−3.98572	−	3.74932i	−0.398572	−	0.374932i
$101$	11.9473	+	3.20128i	1.18881	+	0.318539i	0.798414	−	0.602109i	$-0.205673\pi$
$101$	11.9473	+	3.20128i	1.18881	+	0.318539i	0.390392	+	0.920649i	$0.372340\pi$
$102$	−2.15309	+	5.43124i	−0.213188	+	0.537773i
$103$	13.6924	+	7.90533i	1.34916	+	0.778935i	0.988130	−	0.153621i	$-0.0490935\pi$
$103$	13.6924	+	7.90533i	1.34916	+	0.778935i	0.361025	+	0.932556i	$0.382427\pi$
$104$	0.736889	+	1.57125i	0.0722579	+	0.154074i
$105$		0			0
$106$	−10.0606	+	7.96682i	−0.977167	+	0.773806i
$107$	−2.26189	−	8.44147i	−0.218665	−	0.816068i	−0.984844	−	0.173441i	$-0.944511\pi$
$107$	−2.26189	−	8.44147i	−0.218665	−	0.816068i	0.766179	−	0.642627i	$-0.222155\pi$
$108$	6.27211	+	3.37005i	0.603534	+	0.324284i
$109$	1.71117	−	6.38616i	0.163900	−	0.611684i	−0.834278	−	0.551344i	$-0.814115\pi$
$109$	1.71117	−	6.38616i	0.163900	−	0.611684i	0.998178	−	0.0603393i	$-0.0192183\pi$
$110$	−5.93634	−	4.41270i	−0.566008	−	0.420734i
$111$	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	$0.561162\pi$
$114$	−0.953416	−	0.708709i	−0.0892956	−	0.0663766i
$115$	−0.531754	+	1.98453i	−0.0495863	+	0.185059i
$116$	3.21896	−	5.99090i	0.298873	−	0.556241i
$117$	0.412125	+	1.53807i	0.0381009	+	0.142195i
$118$	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
$122$	−3.17319	+	8.00447i	−0.287287	+	0.724691i
$123$	4.81666	+	1.29062i	0.434303	+	0.116371i
$124$	−9.76631	+	10.3821i	−0.877041	+	0.932339i
$125$	−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	$0.369149\pi$
$128$	−10.9952	+	2.66547i	−0.971851	+	0.235597i
$129$	0.440062	+	0.762209i	0.0387453	+	0.0671088i
$130$	0.518012	+	1.19847i	0.0454326	+	0.105113i
$131$	−15.0462	+	4.03161i	−1.31459	+	0.352243i	−0.846948	−	0.531675i	$-0.821563\pi$
$131$	−15.0462	+	4.03161i	−1.31459	+	0.352243i	−0.467641	+	0.883918i	$0.654896\pi$
$132$	−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
$136$	−3.22864	−	18.0784i	−0.276853	−	1.55021i
$137$	7.78255	−	4.49326i	0.664908	−	0.383885i	−0.129237	−	0.991614i	$-0.541253\pi$
$137$	7.78255	−	4.49326i	0.664908	−	0.383885i	0.794144	+	0.607729i	$0.207919\pi$
$138$	0.178966	+	1.21558i	0.0152346	+	0.103477i
$139$	−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
$142$	9.54684	+	7.09651i	0.801153	+	0.595526i
$143$	−1.06643	−	1.84711i	−0.0891791	−	0.154463i
$144$	−10.3612	+	0.633907i	−0.863435	+	0.0528256i
$145$	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
$149$	−4.58227	−	17.1013i	−0.375394	−	1.40099i	−0.852768	−	0.522289i	$-0.825078\pi$
$149$	−4.58227	−	17.1013i	−0.375394	−	1.40099i	0.477374	−	0.878700i	$-0.341589\pi$
$150$	−2.28869	−	0.907301i	−0.186871	−	0.0740808i
$151$	−11.1788	+	6.45409i	−0.909718	+	0.525226i	−0.880341	−	0.474342i	$-0.842686\pi$
$151$	−11.1788	+	6.45409i	−0.909718	+	0.525226i	−0.0293779	+	0.999568i	$0.509353\pi$
$152$	3.72061	+	0.317283i	0.301781	+	0.0257350i
$153$		−	16.8498i		−	1.36222i
$154$		0			0
$155$	−7.58261	+	7.58261i	−0.609050	+	0.609050i
$156$	0.568728	+	0.534996i	0.0455347	+	0.0428340i
$157$	4.44594	−	16.5925i	0.354824	−	1.32422i	−0.525881	−	0.850558i	$-0.676264\pi$
$157$	4.44594	−	16.5925i	0.354824	−	1.32422i	0.880705	−	0.473665i	$-0.157069\pi$
$158$	0.514894	+	1.19126i	0.0409628	+	0.0947717i
$159$	−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
$163$	14.5007	−	3.88545i	1.13578	−	0.304332i	0.358528	−	0.933519i	$-0.383279\pi$
$163$	14.5007	−	3.88545i	1.13578	−	0.304332i	0.777254	+	0.629187i	$0.216612\pi$
$164$	−15.0091	+	4.51737i	−1.17201	+	0.352747i
$165$	−3.21454	−	0.861332i	−0.250251	−	0.0670546i
$166$	4.78010	−	0.703754i	0.371007	−	0.0546219i
$167$			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
$170$	−2.01238	−	13.6687i	−0.154343	−	1.04834i
$171$	3.30939	+	0.886749i	0.253076	+	0.0678114i
$172$	−2.43697	−	1.30940i	−0.185817	−	0.0998409i
$173$	−1.95782	+	0.524598i	−0.148851	+	0.0398844i	−0.332475	−	0.943112i	$-0.607884\pi$
$173$	−1.95782	+	0.524598i	−0.148851	+	0.0398844i	0.183624	+	0.982997i	$0.441217\pi$
$174$	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
$178$	20.9819	−	9.06894i	1.57266	−	0.679746i
$179$	2.21649	−	8.27206i	0.165668	−	0.618283i	−0.832286	−	0.554347i	$-0.812968\pi$
$179$	2.21649	−	8.27206i	0.165668	−	0.618283i	0.997954	−	0.0639358i	$-0.0203653\pi$
$180$	−7.80594	+	0.238563i	−0.581820	+	0.0177815i
$181$	−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
$184$	−2.48900	−	2.95309i	−0.183492	−	0.217704i
$185$	−6.58107	+	3.79958i	−0.483850	+	0.279351i
$186$	−2.36336	+	5.96164i	−0.173290	+	0.437128i
$187$	5.84143	+	21.8005i	0.427167	+	1.59421i
$188$	−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	0.495793	+	0.868441i	$0.334878\pi$
$191$	−6.96812	+	12.0691i	−0.504196	+	0.873292i	−0.999988	+	0.00485148i	$0.998456\pi$
$192$	−4.15682	+	2.93792i	−0.299993	+	0.212026i
$193$	1.59321	+	2.75953i	0.114682	+	0.198635i	0.917653	−	0.397384i	$-0.130082\pi$
$193$	1.59321	+	2.75953i	0.114682	+	0.198635i	−0.802971	+	0.596019i	$0.796748\pi$
$194$	−4.55111	+	6.12255i	−0.326751	+	0.439574i
$195$	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	$0.862110\pi$
$198$	12.6215	−	1.85822i	0.896972	−	0.132058i
$199$	−9.10258	+	5.25538i	−0.645265	+	0.372544i	−0.786640	−	0.617412i	$-0.788181\pi$
$199$	−9.10258	+	5.25538i	−0.645265	+	0.372544i	0.141375	+	0.989956i	$0.454848\pi$
$200$	7.61812	−	1.36053i	0.538682	−	0.0962040i
$201$	−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
$205$	−11.3903	+	3.05201i	−0.795530	+	0.213162i
$206$	−20.5245	+	8.87122i	−1.43001	+	0.618087i
$207$	−1.77178	−	3.06882i	−0.123148	−	0.213298i
$208$	−2.40505	−	0.489268i	−0.166760	−	0.0339247i
$209$	−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	$-0.530617\pi$
$212$	−0.554393	−	18.1401i	−0.0380759	−	1.24587i
$213$	5.16962	+	1.38520i	0.354217	+	0.0949121i
$214$	11.4893	+	4.55468i	0.785393	+	0.311351i
$215$	−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
$219$	0.0920361	+	0.343483i	0.00621922	+	0.0232105i
$220$	10.0167	−	3.01480i	0.675329	−	0.203258i
$221$	1.03109	−	3.84809i	0.0693589	−	0.258851i
$222$	−2.71116	+	3.64729i	−0.181961	+	0.244790i
$223$	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
$226$	3.42534	−	4.60806i	0.227850	−	0.306524i
$227$	−4.16320	+	15.5373i	−0.276321	+	1.03124i	0.678630	+	0.734481i	$0.262574\pi$
$227$	−4.16320	+	15.5373i	−0.276321	+	1.03124i	−0.954951	+	0.296764i	$0.904093\pi$
$228$	1.60876	−	0.484196i	0.106542	−	0.0320667i
$229$	5.79079	+	21.6115i	0.382666	+	1.42813i	0.841813	+	0.539770i	$0.181489\pi$
$229$	5.79079	+	21.6115i	0.382666	+	1.42813i	−0.459146	+	0.888361i	$0.651845\pi$
$230$	−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	$-0.203895\pi$
$233$	10.4572	+	6.03746i	0.685074	+	0.395527i	−0.116690	+	0.993168i	$0.537228\pi$
$234$	−2.09340	−	0.829881i	−0.136850	−	0.0542510i
$235$	−18.3640	−	4.92063i	−1.19794	−	0.320986i
$236$	0.454355	+	14.8668i	0.0295760	+	0.967745i
$237$	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	$0.227259\pi$
$240$	−3.19334	+	2.11371i	−0.206129	+	0.136439i
$241$	4.69064	+	8.12443i	0.302151	+	0.523341i	0.976623	−	0.214960i	$-0.0689620\pi$
$241$	4.69064	+	8.12443i	0.302151	+	0.523341i	−0.674472	+	0.738300i	$0.735629\pi$
$242$	−1.40615	+	0.607774i	−0.0903907	+	0.0390692i
$243$	−13.7090	+	3.67333i	−0.879436	+	0.235644i
$244$	−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
$248$	−3.54394	−	19.8438i	−0.225040	−	1.26008i
$249$	1.88259	−	1.08692i	0.119305	−	0.0688805i
$250$	16.2859	−	2.39771i	1.03001	−	0.151644i
$251$	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
$254$	−7.59860	+	10.2223i	−0.476778	+	0.641404i
$255$	−3.10803	−	5.38327i	−0.194632	−	0.337113i
$256$	6.25117	−	14.7283i	0.390698	−	0.920519i
$257$	−4.88188	+	8.45566i	−0.304523	+	0.527450i	−0.977155	−	0.212528i	$-0.931830\pi$
$257$	−4.88188	+	8.45566i	−0.304523	+	0.527450i	0.672632	+	0.739977i	$0.265164\pi$
$258$	−1.23637	−	0.143594i	−0.0769731	−	0.00893978i
$259$		0			0
$260$	−1.79729	−	0.423189i	−0.111463	−	0.0262451i
$261$	2.28400	+	8.52401i	0.141376	+	0.527623i
$262$	8.11830	−	20.4787i	0.501550	−	1.26518i
$263$	−0.887606	+	0.512459i	−0.0547321	+	0.0315996i	−0.527116	−	0.849793i	$-0.676727\pi$
$263$	−0.887606	+	0.512459i	−0.0547321	+	0.0315996i	0.472384	+	0.881393i	$0.343393\pi$
$264$	4.78339	−	4.03167i	0.294398	−	0.248132i
$265$		−	13.6536i		−	0.838735i
$266$		0			0
$267$	7.27203	−	7.27203i	0.445041	−	0.445041i
$268$	32.0205	−	0.978602i	1.95596	−	0.0597776i
$269$	−5.63993	+	21.0485i	−0.343872	+	1.28335i	0.550052	+	0.835131i	$0.314608\pi$
$269$	−5.63993	+	21.0485i	−0.343872	+	1.28335i	−0.893924	+	0.448218i	$0.852059\pi$
$270$	−6.95373	+	3.00558i	−0.423191	+	0.182914i
$271$	12.5358	−	21.7126i	0.761495	−	1.31895i	−0.180585	−	0.983559i	$-0.557799\pi$
$271$	12.5358	−	21.7126i	0.761495	−	1.31895i	0.942080	−	0.335388i	$-0.108868\pi$
$272$	23.2427	+	11.5879i	1.40930	+	0.702617i
$273$		0			0
$274$	−1.46617	+	12.6240i	−0.0885746	+	0.762643i
$275$	−9.18661	+	2.46154i	−0.553973	+	0.148437i
$276$	−1.53067	−	0.822440i	−0.0921354	−	0.0495051i
$277$	6.49409	+	1.74009i	0.390192	+	0.104552i	0.448581	−	0.893742i	$-0.351930\pi$
$277$	6.49409	+	1.74009i	0.390192	+	0.104552i	−0.0583888	+	0.998294i	$0.518596\pi$
$278$	−3.81446	−	25.9089i	−0.228776	−	1.55391i
$279$		−	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	$-0.117428\pi$
$282$	−11.2485	+	1.65607i	−0.669839	+	0.0986177i
$283$	16.5487	+	4.43421i	0.983719	+	0.263587i	0.714610	−	0.699523i	$-0.246604\pi$
$283$	16.5487	+	4.43421i	0.983719	+	0.263587i	0.269109	+	0.963110i	$0.413271\pi$
$284$	−16.1089	+	4.84840i	−0.955890	+	0.287700i
$285$	1.22087	−	0.327131i	0.0723181	−	0.0193776i
$286$	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
$290$	2.87083	+	6.64196i	0.168581	+	0.390029i
$291$	−0.888350	+	3.31537i	−0.0520760	+	0.194350i
$292$	−0.814142	−	0.765855i	−0.0476441	−	0.0448183i
$293$	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
$296$	1.21376	−	14.2332i	0.0705486	−	0.827286i
$297$	10.7172	−	6.18758i	0.621875	−	0.359040i
$298$	23.2757	+	9.22715i	1.34833	+	0.534514i
$299$	−0.216843	−	0.809269i	−0.0125404	−	0.0468012i
$300$	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
$304$	−3.49911	+	3.95517i	−0.200688	+	0.226845i
$305$	−4.58056	−	7.93377i	−0.262282	−	0.454286i
$306$	19.1243	+	14.2158i	1.09327	+	0.812663i
$307$	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
$310$	−2.20890	−	15.0035i	−0.125457	−	0.852141i
$311$	−2.05948	+	1.18904i	−0.116782	+	0.0674243i	−0.557253	−	0.830343i	$-0.688145\pi$
$311$	−2.05948	+	1.18904i	−0.116782	+	0.0674243i	0.440471	+	0.897767i	$0.354811\pi$
$312$	−1.08704	+	0.194136i	−0.0615415	+	0.0109908i
$313$	−13.2786	−	7.66638i	−0.750548	−	0.433329i	0.0753437	−	0.997158i	$-0.475995\pi$
$313$	−13.2786	−	7.66638i	−0.750548	−	0.433329i	−0.825892	+	0.563828i	$0.809328\pi$
$314$	15.0814	+	19.0448i	0.851090	+	1.07476i
$315$		0			0
$316$	−1.78648	−	0.420642i	−0.100497	−	0.0236630i
$317$	−25.6612	+	6.87589i	−1.44127	+	0.386188i	−0.892980	−	0.450097i	$-0.851390\pi$
$317$	−25.6612	+	6.87589i	−1.44127	+	0.386188i	−0.548295	+	0.836285i	$0.684723\pi$
$318$	−3.23962	−	7.49519i	−0.181669	−	0.420309i
$319$	−5.91016	−	10.2367i	−0.330905	−	0.573145i
$320$	5.03920	−	10.9316i	0.281700	−	0.611097i
$321$	5.56061			0.310363
$322$		0			0
$323$	−6.06120	−	6.06120i	−0.337254	−	0.337254i
$324$	7.56468	−	8.04163i	0.420260	−	0.446757i
$325$	1.62157	+	0.434497i	0.0899483	+	0.0241016i
$326$	−7.82399	+	19.7362i	−0.433331	+	1.09309i
$327$	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
$331$	4.31749	+	16.1131i	0.237310	+	0.885655i	0.977094	+	0.212809i	$0.0682614\pi$
$331$	4.31749	+	16.1131i	0.237310	+	0.885655i	−0.739783	+	0.672845i	$0.765072\pi$
$332$	−3.23411	+	6.01911i	−0.177495	+	0.330342i
$333$	3.39225	−	12.6601i	0.185894	−	0.693767i
$334$	−27.4142	−	20.3780i	−1.50004	−	1.11503i
$335$	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	$0.356025\pi$
$338$	14.3276	+	10.6502i	0.779318	+	0.579295i
$339$	0.668605	−	2.49527i	0.0363137	−	0.135524i
$340$	17.2116	+	9.24793i	0.933430	+	0.501539i
$341$	6.41188	+	23.9295i	0.347223	+	1.29585i
$342$	−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
$346$	1.05636	−	2.66471i	0.0567904	−	0.143255i
$347$	−0.195227	−	0.0523108i	−0.0104803	−	0.00280819i	0.253575	−	0.967316i	$-0.418394\pi$
$347$	−0.195227	−	0.0523108i	−0.0104803	−	0.00280819i	−0.264055	+	0.964508i	$0.585060\pi$
$348$	3.15190	+	2.96496i	0.168960	+	0.158938i
$349$	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
$352$	−6.11679	+	18.6882i	−0.326026	+	0.996082i
$353$	4.81244	+	8.33539i	0.256140	+	0.443648i	0.965205	−	0.261496i	$-0.0842157\pi$
$353$	4.81244	+	8.33539i	0.256140	+	0.443648i	−0.709064	+	0.705144i	$0.750882\pi$
$354$	2.65504	+	6.14272i	0.141114	+	0.326482i
$355$	−12.2249	+	3.27566i	−0.648832	+	0.173854i
$356$	−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	$-0.482938\pi$
$359$	−14.8625	−	8.58090i	−0.784415	−	0.452882i	−0.837993	+	0.545681i	$0.816271\pi$
$360$	6.31494	−	9.06094i	0.332827	−	0.477554i
$361$	−14.9450	+	8.62853i	−0.786581	+	0.454133i
$362$	−1.46283	−	9.93593i	−0.0768845	−	0.522221i
$363$	−0.487351	+	0.487351i	−0.0255793	+	0.0255793i
$364$		0			0
$365$	−0.594613	−	0.594613i	−0.0311235	−	0.0311235i
$366$	−4.39697	−	3.26843i	−0.229833	−	0.170843i
$367$	7.22745	+	12.5183i	0.377270	+	0.653451i	0.990664	−	0.136326i	$-0.0435295\pi$
$367$	7.22745	+	12.5183i	0.377270	+	0.653451i	−0.613394	+	0.789777i	$0.710196\pi$
$368$	5.45164	−	0.333535i	0.284187	−	0.0173867i
$369$	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
$373$	3.11394	+	11.6214i	0.161234	+	0.601733i	0.998491	+	0.0549228i	$0.0174913\pi$
$373$	3.11394	+	11.6214i	0.161234	+	0.601733i	−0.837257	+	0.546810i	$0.815842\pi$
$374$	−29.6717	−	11.7627i	−1.53429	−	0.608233i
$375$	6.41405	−	3.70315i	0.331220	−	0.191230i
$376$	27.3266	−	23.0322i	1.40926	−	1.18779i
$377$			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	$0.413167\pi$
$380$	−2.72214	+	2.89377i	−0.139643	+	0.148447i
$381$	−1.48320	+	5.53538i	−0.0759867	+	0.283586i
$382$	−7.81951	−	18.0912i	−0.400081	−	0.925629i
$383$	12.1233	−	20.9982i	0.619472	−	1.07296i	−0.370110	−	0.928988i	$-0.620680\pi$
$383$	12.1233	−	20.9982i	0.619472	−	1.07296i	0.989582	−	0.143969i	$-0.0459866\pi$
$384$	0.172513	−	7.19661i	0.00880349	−	0.367251i
$385$		0			0
$386$	−4.47620	−	0.519873i	−0.227833	−	0.0264608i
$387$	3.46738	−	0.929082i	0.176257	−	0.0472279i
$388$	−3.10936	−	10.3309i	−0.157854	−	0.524474i
$389$	10.9616	+	2.93716i	0.555777	+	0.148920i	0.525765	−	0.850630i	$-0.323779\pi$
$389$	10.9616	+	2.93716i	0.555777	+	0.148920i	0.0300114	+	0.999550i	$0.490446\pi$
$390$	−0.821888	+	0.121003i	−0.0416179	+	0.00612723i
$391$			8.86565i			0.448355i
$392$		0			0
$393$		−	9.91129i		−	0.499958i
$394$	−5.42742	−	36.8645i	−0.273429	−	1.85721i
$395$	−1.33372	−	0.357368i	−0.0671066	−	0.0179812i
$396$	−8.53946	+	15.8931i	−0.429124	+	0.798656i
$397$	23.0625	−	6.17957i	1.15747	−	0.310144i	0.371516	−	0.928427i	$-0.378838\pi$
$397$	23.0625	−	6.17957i	1.15747	−	0.310144i	0.785956	+	0.618283i	$0.212171\pi$
$398$	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	−0.794950	−	0.606675i	$-0.792503\pi$
$401$	2.56161	−	4.43683i	0.127921	−	0.221565i	0.922871	+	0.385110i	$0.125836\pi$
$402$	13.2303	−	5.71850i	0.659869	−	0.285213i
$403$	1.13179	−	4.22389i	0.0563783	−	0.210407i
$404$	−0.755672	−	24.7261i	−0.0375961	−	1.23017i
$405$	5.87325	−	5.87325i	0.291844	−	0.291844i
$406$		0			0
$407$			17.5558i			0.870210i
$408$	11.6426	+	0.992850i	0.576396	+	0.0491534i
$409$	−12.2891	+	7.09510i	−0.607655	+	0.350830i	−0.772047	−	0.635565i	$-0.780767\pi$
$409$	−12.2891	+	7.09510i	−0.607655	+	0.350830i	0.164392	+	0.986395i	$0.447434\pi$
$410$	6.14572	−	15.5028i	0.303515	−	0.765626i
$411$	1.47991	+	5.52310i	0.0729986	+	0.272434i
$412$	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
$416$	2.58441	−	2.31693i	0.126711	−	0.113597i
$417$	−5.89127	−	10.2040i	−0.288497	−	0.499691i
$418$	3.87178	−	5.20866i	0.189375	−	0.254764i
$419$	−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	$0.111265\pi$
$422$	31.3693	−	4.61838i	1.52704	−	0.224819i
$423$	28.3976	−	16.3953i	1.38074	−	0.797169i
$424$	21.0566	+	14.6752i	1.02260	+	0.712690i
$425$	−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
$429$	1.31085	−	0.351241i	0.0632884	−	0.0169581i
$430$	2.70180	−	1.16779i	0.130293	−	0.0563158i
$431$	3.25246	+	5.63343i	0.156666	+	0.271353i	0.933664	−	0.358149i	$-0.116592\pi$
$431$	3.25246	+	5.63343i	0.156666	+	0.271353i	−0.776999	+	0.629502i	$0.783259\pi$
$432$	2.83881	−	13.9545i	0.136582	−	0.671386i
$433$	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
$436$	−13.2167	+	0.403926i	−0.632966	+	0.0193446i
$437$	−1.74126	−	0.466570i	−0.0832960	−	0.0223191i
$438$	−0.467500	−	0.185330i	−0.0223380	−	0.00885540i
$439$	−14.0697	−	8.12313i	−0.671509	−	0.387696i	0.125139	−	0.992139i	$-0.460062\pi$
$439$	−14.0697	−	8.12313i	−0.671509	−	0.387696i	−0.796648	+	0.604443i	$0.793396\pi$
$440$	−5.02915	+	13.9124i	−0.239756	+	0.663249i
$441$		0			0
$442$	3.49764	+	4.41684i	0.166366	+	0.210088i
$443$	−3.71543	−	13.8662i	−0.176525	−	0.658801i	−0.996287	−	0.0860962i	$-0.972561\pi$
$443$	−3.71543	−	13.8662i	−0.176525	−	0.658801i	0.819762	−	0.572705i	$-0.194106\pi$
$444$	−1.85229	−	6.15429i	−0.0879059	−	0.292070i
$445$	−6.29441	+	23.4910i	−0.298383	+	1.11358i
$446$	−1.26797	+	1.70579i	−0.0600403	+	0.0807715i
$447$	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	$0.424956\pi$
$450$	−5.99046	+	8.05889i	−0.282393	+	0.379900i
$451$	−7.05085	+	26.3141i	−0.332011	+	1.23908i
$452$	2.34022	+	7.77545i	0.110075	+	0.365726i
$453$	−2.12573	−	7.93335i	−0.0998757	−	0.372741i
$454$	−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	$-0.236229\pi$
$457$	11.1211	+	6.42079i	0.520224	+	0.300352i	−0.216802	+	0.976216i	$0.569563\pi$
$458$	−29.4145	−	11.6607i	−1.37445	−	0.544869i
$459$	22.3272	+	5.98257i	1.04215	+	0.279242i
$460$	4.10716	−	0.125522i	0.191497	−	0.00585250i
$461$	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	$0.251376\pi$
$464$	−13.3288	−	2.71153i	−0.618776	−	0.125880i
$465$	−3.41155	−	5.90898i	−0.158207	−	0.274022i
$466$	−15.6750	+	6.77514i	−0.726130	+	0.313852i
$467$	6.79774	−	1.82145i	0.314562	−	0.0842867i	−0.0980839	−	0.995178i	$-0.531271\pi$
$467$	6.79774	−	1.82145i	0.314562	−	0.0842867i	0.412646	+	0.910892i	$0.364605\pi$
$468$	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
$472$	−17.2570	−	12.0271i	−0.794318	−	0.553593i
$473$	−4.16406	+	2.40412i	−0.191464	+	0.110542i
$474$	−0.816941	+	0.120275i	−0.0375234	+	0.00552441i
$475$	2.55416	−	2.55416i	0.117193	−	0.117193i
$476$		0			0
$477$	16.6517	+	16.6517i	0.762430	+	0.762430i
$478$	−19.7152	+	26.5226i	−0.901751	+	1.21311i
$479$	−1.31897	−	2.28452i	−0.0602653	−	0.104382i	0.834319	−	0.551282i	$-0.185861\pi$
$479$	−1.31897	−	2.28452i	−0.0602653	−	0.104382i	−0.894584	+	0.446900i	$0.852528\pi$
$480$	0.295115	−	5.40770i	0.0134701	−	0.246827i
$481$	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
$485$	−2.10074	−	7.84006i	−0.0953896	−	0.355999i
$486$	7.39685	−	18.6588i	0.335528	−	0.846379i
$487$	2.41546	−	1.39457i	0.109455	−	0.0631938i	−0.444273	−	0.895891i	$-0.646538\pi$
$487$	2.41546	−	1.39457i	0.109455	−	0.0631938i	0.553728	+	0.832698i	$0.313205\pi$
$488$	17.1587	+	1.46325i	0.776739	+	0.0662380i
$489$			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	$0.0808529\pi$
$492$	−0.304655	−	9.96849i	−0.0137349	−	0.449414i
$493$	5.71434	−	21.3262i	0.257361	−	0.960484i
$494$	−1.05156	+	0.454513i	−0.0473120	+	0.0204495i
$495$	−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
$499$	2.90171	−	0.777511i	0.129898	−	0.0348062i	−0.193284	−	0.981143i	$-0.561914\pi$
$499$	2.90171	−	0.777511i	0.129898	−	0.0348062i	0.323182	+	0.946337i	$0.395247\pi$
$500$	−11.0187	+	20.5073i	−0.492772	+	0.917113i
$501$	−14.8448	−	3.97766i	−0.663218	−	0.177709i
$502$	0.649120	+	4.40901i	0.0289717	+	0.196784i
$503$		−	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
$506$	−6.64092	+	0.977716i	−0.295225	+	0.0434648i
$507$	7.75840	+	2.07886i	0.344563	+	0.0923253i
$508$	−5.19143	−	17.2487i	−0.230333	−	0.765286i
$509$	−11.0565	+	2.96258i	−0.490071	+	0.131314i	−0.495388	−	0.868672i	$-0.664974\pi$
$509$	−11.0565	+	2.96258i	−0.490071	+	0.131314i	0.00531724	+	0.999986i	$0.498307\pi$
$510$	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
$514$	−5.47836	−	12.6748i	−0.241640	−	0.559060i
$515$	6.15718	−	22.9789i	0.271318	−	1.01257i
$516$	1.20608	−	1.28212i	0.0530947	−	0.0564423i
$517$	−31.0574	+	31.0574i	−1.36590	+	1.36590i
$518$		0			0
$519$		−	1.28967i		−	0.0566102i
$520$	1.99666	−	1.68288i	0.0875591	−	0.0737990i
$521$	−27.8708	+	16.0912i	−1.22104	+	0.704970i	−0.965140	−	0.261733i	$-0.915706\pi$
$521$	−27.8708	+	16.0912i	−1.22104	+	0.704970i	−0.255903	+	0.966702i	$0.582373\pi$
$522$	−11.6016	−	4.59921i	−0.507790	−	0.201302i
$523$	−0.878475	−	3.27851i	−0.0384130	−	0.143359i	0.944056	−	0.329785i	$-0.106976\pi$
$523$	−0.878475	−	3.27851i	−0.0384130	−	0.143359i	−0.982469	+	0.186426i	$0.940310\pi$
$524$	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
$528$	0.540259	+	8.83055i	0.0235118	+	0.384300i
$529$	−10.5678	−	18.3039i	−0.459468	−	0.795822i
$530$	15.4967	+	11.5193i	0.673135	+	0.500365i
$531$	−13.6470	−	13.6470i	−0.592229	−	0.592229i
$532$		0			0
$533$	3.40024	−	3.40024i	0.147281	−	0.147281i
$534$	2.11843	+	14.3890i	0.0916733	+	0.622671i
$535$	−11.3878	+	6.57476i	−0.492338	+	0.284252i
$536$	−25.9043	+	37.1686i	−1.11890	+	1.60544i
$537$	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
$541$	34.6298	−	9.27902i	1.48885	−	0.398936i	0.579501	−	0.814971i	$-0.303247\pi$
$541$	34.6298	−	9.27902i	1.48885	−	0.398936i	0.909348	+	0.416035i	$0.136581\pi$
$542$	14.0674	+	32.5465i	0.604248	+	1.39799i
$543$	−2.25927	−	3.91317i	−0.0969545	−	0.167930i
$544$	−32.7615	+	16.6038i	−1.40464	+	0.711883i
$545$	−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	$0.834066\pi$
$548$	−13.0911	−	12.3147i	−0.559226	−	0.526057i
$549$	15.2623	+	4.08951i	0.651378	+	0.174536i
$550$	4.95672	−	12.5035i	0.211355	−	0.533150i
$551$	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
$555$	−1.25144	−	4.67044i	−0.0531207	−	0.198249i
$556$	32.6246	+	17.5294i	1.38359	+	0.743414i
$557$	−0.143912	+	0.537087i	−0.00609774	+	0.0227571i	−0.968908	−	0.247423i	$-0.920416\pi$
$557$	−0.143912	+	0.537087i	−0.00609774	+	0.0227571i	0.962810	+	0.270180i	$0.0870831\pi$
$558$	20.9920	+	15.6041i	0.888660	+	0.660573i
$559$	0.848723			0.0358971
$560$		0			0
$561$	−14.3605			−0.606302
$562$	13.7214	+	10.1996i	0.578804	+	0.430246i
$563$	6.44992	−	24.0714i	0.271832	−	1.01449i	−0.686103	−	0.727504i	$-0.740680\pi$
$563$	6.44992	−	24.0714i	0.271832	−	1.01449i	0.957935	−	0.286986i	$-0.0926532\pi$
$564$	7.61051	−	14.1642i	0.320460	−	0.596418i
$565$	1.58109	+	5.90072i	0.0665171	+	0.248245i
$566$	−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	$-0.304156\pi$
$569$	3.78183	+	2.18344i	0.158543	+	0.0915346i	−0.418630	+	0.908157i	$0.637489\pi$
$570$	−0.658732	+	1.66167i	−0.0275913	+	0.0695997i
$571$	−4.99139	−	1.33744i	−0.208883	−	0.0559701i	0.152860	−	0.988248i	$-0.451152\pi$
$571$	−4.99139	−	1.33744i	−0.208883	−	0.0559701i	−0.361743	+	0.932278i	$0.617818\pi$
$572$	−2.92276	+	3.10705i	−0.122207	+	0.129912i
$573$	−6.27016	−	6.27016i	−0.261940	−	0.261940i
$574$		0			0
$575$	−3.73593			−0.155799
$576$	7.18633	+	19.4778i	0.299430	+	0.811574i
$577$	−3.62493	−	6.27856i	−0.150908	−	0.261380i	0.780654	−	0.624964i	$-0.214886\pi$
$577$	−3.62493	−	6.27856i	−0.150908	−	0.261380i	−0.931561	+	0.363584i	$0.881553\pi$
$578$	−14.1150	−	32.6566i	−0.587108	−	1.35833i
$579$	−1.95838	+	0.524745i	−0.0813873	+	0.0218077i
$580$	−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
$584$	1.55611	−	0.277908i	0.0643925	−	0.0114999i
$585$	2.07491	−	1.19795i	0.0857869	−	0.0495291i
$586$	2.23392	+	15.1734i	0.0922822	+	0.626807i
$587$	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
$590$	−12.7004	−	9.44067i	−0.522868	−	0.388666i
$591$	−8.38240	−	14.5187i	−0.344806	−	0.597221i
$592$	15.1305	+	13.3858i	0.621860	+	0.550155i
$593$	−7.89073	+	13.6672i	−0.324034	+	0.561243i	−0.981316	−	0.192401i	$-0.938372\pi$
$593$	−7.89073	+	13.6672i	−0.324034	+	0.561243i	0.657283	+	0.753644i	$0.271706\pi$
$594$	−2.01903	+	17.3843i	−0.0828420	+	0.713285i
$595$		0			0
$596$	−30.1100	+	18.6330i	−1.23335	+	0.763238i
$597$	−1.73092	−	6.45990i	−0.0708420	−	0.264386i
$598$	1.10146	+	0.436649i	0.0450420	+	0.0178559i
$599$	16.1332	−	9.31450i	0.659184	−	0.380580i	−0.132782	−	0.991145i	$-0.542391\pi$
$599$	16.1332	−	9.31450i	0.659184	−	0.380580i	0.791966	+	0.610565i	$0.209058\pi$
$600$	−0.418381	+	4.90614i	−0.0170804	+	0.200292i
$601$			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
$604$	18.8040	+	17.6888i	0.765126	+	0.719745i
$605$	0.421833	−	1.57430i	0.0171500	−	0.0640045i
$606$	−4.41580	−	10.2164i	−0.179380	−	0.415013i
$607$	−16.4752	+	28.5359i	−0.668708	+	1.15824i	0.309558	+	0.950880i	$0.399819\pi$
$607$	−16.4752	+	28.5359i	−0.668708	+	1.15824i	−0.978266	+	0.207355i	$0.933515\pi$
$608$	−1.53695	−	7.30836i	−0.0623317	−	0.296393i
$609$		0			0
$610$	12.8693	+	1.49466i	0.521062	+	0.0605170i
$611$	7.48863	−	2.00657i	0.302958	−	0.0811773i
$612$	−32.2696	+	9.71237i	−1.30442	+	0.392599i
$613$	−30.9349	−	8.28898i	−1.24945	−	0.334789i	−0.427325	−	0.904098i	$-0.640544\pi$
$613$	−30.9349	−	8.28898i	−1.24945	−	0.334789i	−0.822124	+	0.569309i	$0.807211\pi$
$614$	−7.78237	+	1.14577i	−0.314071	+	0.0462394i
$615$		−	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	$0.931862\pi$
$618$	−2.07224	−	14.0753i	−0.0833578	−	0.566190i
$619$	−4.73508	−	1.26876i	−0.190319	−	0.0509958i	0.162401	−	0.986725i	$-0.448076\pi$
$619$	−4.73508	−	1.26876i	−0.190319	−	0.0509958i	−0.352720	+	0.935729i	$0.614743\pi$
$620$	18.8924	+	10.1511i	0.758739	+	0.407676i
$621$	4.69550	−	1.25816i	0.188424	−	0.0504881i
$622$	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
$626$	19.9041	−	8.60308i	0.795528	−	0.343848i
$627$	0.755749	−	2.82049i	0.0301817	−	0.112640i
$628$	−34.3395	+	1.04948i	−1.37030	+	0.0418787i
$629$	−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	$-0.241911\pi$
$632$	1.98464	−	1.67275i	0.0789447	−	0.0665383i
$633$	12.3545	−	7.13288i	0.491048	−	0.283506i
$634$	13.8457	−	34.9262i	0.549884	−	1.38710i
$635$	−3.50742	−	13.0899i	−0.139188	−	0.519456i
$636$	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
$640$	8.15585	+	14.9422i	0.322388	+	0.590644i
$641$	11.0592	+	19.1551i	0.436811	+	0.756580i	0.997442	−	0.0714868i	$-0.0227744\pi$
$641$	11.0592	+	19.1551i	0.436811	+	0.756580i	−0.560630	+	0.828066i	$0.689441\pi$
$642$	−4.69137	+	6.31124i	−0.185154	+	0.249085i
$643$	−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
$646$	11.9931	−	1.76570i	0.471863	−	0.0694705i
$647$	27.3950	−	15.8165i	1.07701	−	0.621810i	0.146920	−	0.989148i	$-0.453064\pi$
$647$	27.3950	−	15.8165i	1.07701	−	0.621810i	0.930087	+	0.367338i	$0.119731\pi$
$648$	2.74502	+	15.3704i	0.107835	+	0.603806i
$649$	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
$653$	−1.38422	+	0.370901i	−0.0541687	+	0.0145145i	−0.285802	−	0.958289i	$-0.592260\pi$
$653$	−1.38422	+	0.370901i	−0.0541687	+	0.0145145i	0.231633	+	0.972803i	$0.425593\pi$
$654$	−5.46093	+	2.36036i	−0.213539	+	0.0922973i
$655$	11.7189	+	20.2978i	0.457896	+	0.793100i
$656$	17.3028	+	26.1406i	0.675559	+	1.02062i
$657$	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	$0.453496\pi$
$660$	0.203320	+	6.65276i	0.00791423	+	0.258958i
$661$	−22.4747	−	6.02209i	−0.874166	−	0.234232i	−0.206278	−	0.978494i	$-0.566135\pi$
$661$	−22.4747	−	6.02209i	−0.874166	−	0.234232i	−0.667888	+	0.744261i	$0.732802\pi$
$662$	−21.9308	−	8.69396i	−0.852364	−	0.337901i
$663$	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
$667$	−1.20175	−	4.48498i	−0.0465318	−	0.173659i
$668$	46.2577	−	13.9224i	1.78976	−	0.538675i
$669$	−0.247501	+	0.923687i	−0.00956895	+	0.0357118i
$670$	−20.3336	+	27.3545i	−0.785554	+	1.05680i
$671$	−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	$0.624972\pi$
$674$	−13.5378	+	18.2122i	−0.521456	+	0.701508i
$675$	−2.52102	+	9.40857i	−0.0970341	+	0.362136i
$676$	−24.1758	+	7.27632i	−0.929838	+	0.279859i
$677$	5.42114	+	20.2320i	0.208352	+	0.777578i	0.988402	+	0.151862i	$0.0485268\pi$
$677$	5.42114	+	20.2320i	0.208352	+	0.777578i	−0.780050	+	0.625717i	$0.784807\pi$
$678$	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
$682$	−32.5693	−	12.9114i	−1.24714	−	0.494402i
$683$	48.2678	+	12.9333i	1.84692	+	0.494879i	0.999358	−	0.0358249i	$-0.0114059\pi$
$683$	48.2678	+	12.9333i	1.84692	+	0.494879i	0.847557	+	0.530704i	$0.178073\pi$
$684$	−0.209320	−	6.84907i	−0.00800354	−	0.261881i
$685$	−9.56118	−	9.56118i	−0.365314	−	0.365314i
$686$		0			0
$687$	−14.2361			−0.543139
$688$	−1.10299	+	5.42188i	−0.0420512	+	0.206707i
$689$	2.78389	+	4.82184i	0.106058	+	0.183698i
$690$	1.69701	−	0.733493i	0.0646042	−	0.0279236i
$691$	0.805269	−	0.215771i	0.0306339	−	0.00820833i	−0.243470	−	0.969909i	$-0.578286\pi$
$691$	0.805269	−	0.215771i	0.0306339	−	0.00820833i	0.274103	+	0.961700i	$0.411619\pi$
$692$	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
$696$	−6.02439	+	1.07590i	−0.228354	+	0.0407820i
$697$	−44.0673	+	25.4423i	−1.66917	+	0.963694i
$698$	−44.4898	+	6.55006i	−1.68397	+	0.247923i
$699$	−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	$-0.504063\pi$
$702$	1.84292	−	2.47926i	0.0695567	−	0.0935737i
$703$	−3.33382	−	5.77435i	−0.125737	−	0.217784i
$704$	−16.0503	−	22.7093i	−0.604918	−	0.855890i
$705$	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
$709$	−5.90585	−	22.0409i	−0.221799	−	0.827764i	−0.983662	−	0.180026i	$-0.942382\pi$
$709$	−5.90585	−	22.0409i	−0.221799	−	0.827764i	0.761863	−	0.647738i	$-0.224285\pi$
$710$	6.59608	−	16.6388i	0.247546	−	0.624443i
$711$	2.06242	−	1.19074i	0.0773468	−	0.0446562i
$712$	−29.4625	−	34.9559i	−1.10415	−	1.31003i
$713$			9.73144i			0.364445i
$714$		0			0
$715$	−2.26925	+	2.26925i	−0.0848651	+	0.0848651i
$716$	−17.1197	+	0.523210i	−0.639795	+	0.0195533i
$717$	−3.84829	+	14.3620i	−0.143717	+	0.536359i
$718$	22.2785	−	9.62933i	0.831425	−	0.359364i
$719$	18.9649	−	32.8482i	0.707273	−	1.22503i	−0.258592	−	0.965987i	$-0.583259\pi$
$719$	18.9649	−	32.8482i	0.707273	−	1.22503i	0.965865	−	0.259046i	$-0.0834080\pi$
$720$	4.95630	+	14.8119i	0.184710	+	0.552008i
$721$		0			0
$722$	2.81553	−	24.2422i	0.104783	−	0.902201i
$723$	−5.76573	+	1.54492i	−0.214430	+	0.0574563i
$724$	12.5114	+	6.72245i	0.464981	+	0.249838i
$725$	8.98674	+	2.40799i	0.333759	+	0.0894305i
$726$	−0.141971	−	0.964307i	−0.00526904	−	0.0357888i
$727$			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
$730$	1.17654	−	0.173218i	0.0435459	−	0.00641108i
$731$	−8.67503	−	2.32447i	−0.320858	−	0.0859735i
$732$	7.41927	−	2.23302i	0.274224	−	0.0825348i
$733$	5.98979	−	1.60496i	0.221238	−	0.0592806i	−0.146497	−	0.989211i	$-0.546800\pi$
$733$	5.98979	−	1.60496i	0.221238	−	0.0592806i	0.367735	+	0.929931i	$0.380133\pi$
$734$	−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
$738$	11.4117	+	26.4021i	0.420070	+	0.971876i
$739$	−6.41426	+	23.9383i	−0.235952	+	0.880586i	0.741765	+	0.670660i	$0.233989\pi$
$739$	−6.41426	+	23.9383i	−0.235952	+	0.880586i	−0.977717	+	0.209926i	$0.932678\pi$
$740$	11.0701	+	10.4135i	0.406945	+	0.382809i
$741$	−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	$0.738526\pi$
$744$	12.7796	+	1.08981i	0.468523	+	0.0399543i
$745$	−23.0702	+	13.3196i	−0.845225	+	0.487991i
$746$	−15.8173	−	6.27043i	−0.579114	−	0.229577i
$747$	−2.29476	−	8.56415i	−0.0839607	−	0.313346i
$748$	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	0.0619145	−	0.998081i	$-0.480279\pi$
$751$	24.5357	−	42.4971i	0.895321	−	1.55074i	0.833407	−	0.552660i	$-0.186387\pi$
$752$	3.08640	+	50.4472i	0.112549	+	1.83962i
$753$	1.00254	+	1.73645i	0.0365345	+	0.0632796i
$754$	−2.36810	−	1.76030i	−0.0862413	−	0.0641062i
$755$	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	$0.0992050\pi$
$758$	−3.93355	−	26.7178i	−0.142873	−	0.970435i
$759$	−2.61546	+	1.51004i	−0.0949353	+	0.0548109i
$760$	−0.987792	−	5.53102i	−0.0358310	−	0.200631i
$761$	0.912216	+	0.526668i	0.0330678	+	0.0190917i	0.516443	−	0.856322i	$-0.327256\pi$
$761$	0.912216	+	0.526668i	0.0330678	+	0.0190917i	−0.483375	+	0.875413i	$0.660589\pi$
$762$	−5.03126	−	6.35351i	−0.182263	−	0.230163i
$763$		0			0
$764$	27.1306	+	6.38814i	0.981549	+	0.231115i
$765$	−24.4891	+	6.56184i	−0.885406	+	0.237244i
$766$	13.6046	+	31.4756i	0.491553	+	1.13726i
$767$	−2.28155	−	3.95176i	−0.0823820	−	0.142690i
$768$	8.02255	+	6.26744i	0.289489	+	0.226157i
$769$	−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
$772$	4.36653	−	4.64184i	0.157155	−	0.167064i
$773$	−18.3288	−	4.91119i	−0.659241	−	0.176643i	−0.0863375	−	0.996266i	$-0.527516\pi$
$773$	−18.3288	−	4.91119i	−0.659241	−	0.176643i	−0.572903	+	0.819623i	$0.694183\pi$
$774$	−1.87086	+	4.71929i	−0.0672466	+	0.169632i
$775$	−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
$779$	−2.67789	−	9.99401i	−0.0959453	−	0.358073i
$780$	0.556072	−	1.03492i	0.0199106	−	0.0370562i
$781$	−7.56753	+	28.2424i	−0.270788	+	1.01059i
$782$	−10.0624	−	7.47977i	−0.359832	−	0.267476i
$783$	−12.1059			−0.432630
$784$		0			0
$785$	−25.8466			−0.922503
$786$	11.2492	+	8.36195i	0.401247	+	0.298261i
$787$	8.04240	−	30.0147i	0.286681	−	1.06991i	−0.660922	−	0.750455i	$-0.729834\pi$
$787$	8.04240	−	30.0147i	0.286681	−	1.06991i	0.947602	−	0.319452i	$-0.103499\pi$
$788$	46.4199	+	24.9418i	1.65364	+	0.888514i
$789$	−0.168785	−	0.629914i	−0.00600890	−	0.0224255i
$790$	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
$794$	−12.4436	+	31.3893i	−0.441606	+	1.11396i
$795$	8.39150	+	2.24849i	0.297616	+	0.0797459i
$796$	15.3116	+	14.4034i	0.542705	+	0.510517i
$797$	−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
$800$	−6.99676	−	13.8055i	−0.247373	−	0.488099i
$801$	−20.9727	−	36.3258i	−0.741035	−	1.28351i
$802$	2.87459	+	6.65067i	0.101505	+	0.234843i
$803$	−1.87650	+	0.502807i	−0.0662203	+	0.0177437i
$804$	−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
$808$	28.7014	+	20.0032i	1.00971	+	0.703710i
$809$	−0.992787	+	0.573186i	−0.0349045	+	0.0201521i	−0.517351	−	0.855773i	$-0.673082\pi$
$809$	−0.992787	+	0.573186i	−0.0349045	+	0.0201521i	0.482446	+	0.875926i	$0.339748\pi$
$810$	1.71095	+	11.6212i	0.0601165	+	0.408328i
$811$	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
$814$	−19.9257	−	14.8115i	−0.698395	−	0.519142i
$815$	−11.2941	−	19.5619i	−0.395614	−	0.685224i
$816$	−10.9495	+	12.3766i	−0.383310	+	0.433269i
$817$	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
$821$	6.83700	+	25.5160i	0.238613	+	0.890516i	0.976487	+	0.215577i	$0.0691633\pi$
$821$	6.83700	+	25.5160i	0.238613	+	0.890516i	−0.737874	+	0.674939i	$0.764170\pi$
$822$	−7.51724	−	2.98004i	−0.262194	−	0.103941i
$823$	11.4579	−	6.61523i	0.399398	−	0.230593i	−0.286826	−	0.957983i	$-0.592600\pi$
$823$	11.4579	−	6.61523i	0.399398	−	0.230593i	0.686224	+	0.727390i	$0.259267\pi$
$824$	28.8201	+	34.1938i	1.00400	+	1.19120i
$825$		−	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	$0.344402\pi$
$828$	−4.85594	+	5.16211i	−0.168756	+	0.179396i
$829$	−4.93604	+	18.4216i	−0.171436	+	0.639807i	0.825695	+	0.564116i	$0.190783\pi$
$829$	−4.93604	+	18.4216i	−0.171436	+	0.639807i	−0.997131	+	0.0756912i	$0.975884\pi$
$830$	−2.88435	−	6.67323i	−0.100117	−	0.231631i
$831$	−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
$835$	35.1045	−	9.40623i	1.21484	−	0.325516i
$836$	2.64524	+	8.78887i	0.0914874	+	0.303970i
$837$	24.5076	+	6.56680i	0.847108	+	0.226982i
$838$	8.40526	−	1.23747i	0.290355	−	0.0427478i
$839$		−	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
$842$	3.56870	+	24.2396i	0.122986	+	0.835353i
$843$	7.43018	+	1.99091i	0.255909	+	0.0685706i
$844$	−21.2238	+	39.5004i	−0.730555	+	1.35966i
$845$	−18.3468	+	4.91601i	−0.631149	+	0.169116i
$846$	−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
$850$	23.0608	−	9.96749i	0.790980	−	0.341882i
$851$	−1.78486	+	6.66120i	−0.0611844	+	0.228343i
$852$	−0.326980	−	10.6990i	−0.0112021	−	0.366541i
$853$	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
$856$	2.10029	−	24.6290i	0.0717863	−	0.841800i
$857$	30.0916	−	17.3734i	1.02791	−	0.593464i	0.111524	−	0.993762i	$-0.464427\pi$
$857$	30.0916	−	17.3734i	1.02791	−	0.593464i	0.916385	+	0.400298i	$0.131093\pi$
$858$	−0.707282	+	1.78414i	−0.0241462	+	0.0609095i
$859$	6.70000	+	25.0048i	0.228601	+	0.853151i	0.980930	+	0.194363i	$0.0622640\pi$
$859$	6.70000	+	25.0048i	0.228601	+	0.853151i	−0.752328	+	0.658788i	$0.771069\pi$
$860$	−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	−0.193612	−	0.981078i	$-0.562020\pi$
$863$	22.1159	−	38.3058i	0.752832	−	1.30394i	0.946445	−	0.322866i	$-0.104646\pi$
$864$	13.4432	+	14.9951i	0.457346	+	0.510145i
$865$	1.52488	+	2.64117i	0.0518475	+	0.0898025i
$866$	−10.3809	+	13.9652i	−0.352756	+	0.474558i
$867$	−11.3183	−	11.3183i	−0.384390	−	0.384390i
$868$		0			0
$869$	−2.25559	+	2.25559i	−0.0765157	+	0.0765157i
$870$	−4.55491	+	0.670601i	−0.154426	+	0.0227355i
$871$	−8.51140	+	4.91406i	−0.288398	+	0.166507i
$872$	10.6922	−	15.3416i	0.362084	−	0.519533i
$873$	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
$877$	50.0727	−	13.4169i	1.69083	−	0.453057i	0.720229	−	0.693737i	$-0.244037\pi$
$877$	50.0727	−	13.4169i	1.69083	−	0.453057i	0.970605	+	0.240679i	$0.0773702\pi$
$878$	21.0900	−	9.11563i	0.711752	−	0.307638i
$879$	3.45018	+	5.97589i	0.116372	+	0.201562i
$880$	−11.5475	−	17.4457i	−0.389266	−	0.588094i
$881$	−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	$0.697518\pi$
$884$	−7.96396	+	0.243393i	−0.267857	+	0.00818619i
$885$	−6.87729	−	1.84276i	−0.231177	−	0.0619438i
$886$	18.8726	+	7.48162i	0.634037	+	0.251350i
$887$	−10.6280	−	6.13605i	−0.356852	−	0.206028i	0.310847	−	0.950460i	$-0.399387\pi$
$887$	−10.6280	−	6.13605i	−0.356852	−	0.206028i	−0.667699	+	0.744431i	$0.732721\pi$
$888$	8.54781	+	3.08991i	0.286846	+	0.103691i
$889$		0			0
$890$	−21.3517	−	26.9630i	−0.715709	−	0.903802i
$891$	−4.96644	−	18.5350i	−0.166382	−	0.620946i
$892$	−0.866292	−	2.87828i	−0.0290056	−	0.0963719i
$893$	4.31745	−	16.1129i	0.144478	−	0.539199i
$894$	−9.50407	+	12.7857i	−0.317864	+	0.427618i
$895$	−12.8856			−0.430719
$896$		0			0
$897$	0.533086			0.0177992
$898$	−8.35154	+	11.2352i	−0.278695	+	0.374924i
$899$	6.27238	−	23.4088i	0.209196	−	0.780729i
$900$	−4.09274	−	13.5982i	−0.136425	−	0.453274i
$901$	−15.2489	−	56.9099i	−0.508016	−	1.89594i
$902$	−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
$906$	10.7977	+	4.28051i	0.358730	+	0.142211i
$907$	−22.7716	−	6.10163i	−0.756119	−	0.202601i	−0.139888	−	0.990167i	$-0.544674\pi$
$907$	−22.7716	−	6.10163i	−0.756119	−	0.202601i	−0.616230	+	0.787566i	$0.711341\pi$
$908$	32.1557	−	0.982735i	1.06712	−	0.0326132i
$909$	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	$0.334431\pi$
$912$	−1.85461	−	2.80189i	−0.0614121	−	0.0927800i
$913$	5.93798	+	10.2849i	0.196519	+	0.340380i
$914$	−16.6702	+	7.20530i	−0.551401	+	0.238330i
$915$	5.63042	−	1.50867i	0.186136	−	0.0498750i
$916$	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	$-0.375892\pi$
$919$	−6.99945	−	4.04114i	−0.230891	−	0.133305i	−0.610983	+	0.791644i	$0.709226\pi$
$920$	−3.32266	+	4.76749i	−0.109545	+	0.157180i
$921$	−3.06501	+	1.76958i	−0.100995	+	0.0583098i
$922$	−14.8474	+	2.18592i	−0.488972	+	0.0719893i
$923$	3.64941	−	3.64941i	0.120122	−	0.120122i
$924$		0			0
$925$	−9.77092	−	9.77092i	−0.321266	−	0.321266i
$926$	−25.5622	+	34.3885i	−0.840026	+	1.13008i
$927$	20.5155	+	35.5339i	0.673817	+	1.16709i
$928$	14.3228	−	12.8404i	0.470170	−	0.421508i
$929$	−10.7324	+	18.5891i	−0.352120	+	0.609889i	−0.986621	−	0.163033i	$-0.947872\pi$
$929$	−10.7324	+	18.5891i	−0.352120	+	0.609889i	0.634501	+	0.772922i	$0.281206\pi$
$930$	9.58490	+	1.11320i	0.314301	+	0.0365034i
$931$		0			0
$932$	5.53495	−	23.5070i	0.181303	−	0.769998i
$933$	−0.391625	−	1.46157i	−0.0128212	−	0.0478495i
$934$	−3.66779	+	9.25210i	−0.120014	+	0.302738i
$935$	29.4096	−	16.9796i	0.961796	−	0.555293i
$936$	−0.382681	+	4.48750i	−0.0125083	+	0.146678i
$937$			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
$940$	1.16153	+	38.0059i	0.0378849	+	1.23962i
$941$	3.11176	−	11.6132i	0.101440	−	0.378581i	−0.896477	−	0.443091i	$-0.853882\pi$
$941$	3.11176	−	11.6132i	0.101440	−	0.378581i	0.997917	+	0.0645102i	$0.0205485\pi$
$942$	−14.1885	+	6.13266i	−0.462288	+	0.199813i
$943$	−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
$947$	−42.4234	+	11.3673i	−1.37858	+	0.369388i	−0.870604	−	0.491985i	$-0.836272\pi$
$947$	−42.4234	+	11.3673i	−1.37858	+	0.369388i	−0.507973	+	0.861373i	$0.669605\pi$
$948$	0.552726	−	1.02869i	0.0179517	−	0.0334105i
$949$	0.331229	+	0.0887525i	0.0107521	+	0.00288103i
$950$	0.744056	+	5.05384i	0.0241404	+	0.163968i
$951$		−	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	$0.826318\pi$
$954$	−32.9483	+	4.85084i	−1.06674	+	0.157052i
$955$	20.2547	+	5.42722i	0.655426	+	0.175621i
$956$	−13.4696	−	44.7531i	−0.435638	−	1.44742i
$957$	7.26475	−	1.94658i	0.234836	−	0.0629241i
$958$	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
$962$	1.73874	+	4.02275i	0.0560591	+	0.129699i
$963$	5.86993	−	21.9069i	0.189156	−	0.705939i
$964$	12.8557	−	13.6662i	0.414053	−	0.440160i
$965$	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	$0.969939\pi$
$968$	1.97449	+	2.34264i	0.0634625	+	0.0752954i
$969$	4.72338	−	2.72704i	0.151737	−	0.0876052i
$970$	10.6708	+	4.23018i	0.342617	+	0.135823i
$971$	−15.8754	−	59.2479i	−0.509467	−	1.90136i	−0.425684	−	0.904872i	$-0.639966\pi$
$971$	−15.8754	−	59.2479i	−0.509467	−	1.90136i	−0.0837830	−	0.996484i	$-0.526700\pi$
$972$	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
$976$	−16.1372	+	18.2405i	−0.516540	+	0.583864i
$977$	22.4338	+	38.8564i	0.717719	+	1.24313i	0.961901	+	0.273397i	$0.0881473\pi$
$977$	22.4338	+	38.8564i	0.717719	+	1.24313i	−0.244182	+	0.969729i	$0.578519\pi$
$978$	−10.8414	−	8.05880i	−0.346670	−	0.257692i
$979$	39.7282	+	39.7282i	1.26972	+	1.26972i
$980$		0			0
$981$	12.1323	−	12.1323i	0.387355	−	0.387355i
$982$	4.62587	+	31.4202i	0.147617	+	1.00266i
$983$	4.60693	−	2.65981i	0.146938	−	0.0848349i	−0.424728	−	0.905321i	$-0.639630\pi$
$983$	4.60693	−	2.65981i	0.146938	−	0.0848349i	0.571667	+	0.820486i	$0.306297\pi$
$984$	11.5712	+	8.06443i	0.368876	+	0.257085i
$985$	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
$989$	−1.82439	+	0.488844i	−0.0580123	+	0.0155443i
$990$	−7.61592	−	17.6202i	−0.242050	−	0.560008i
$991$	11.0623	+	19.1605i	0.351407	+	0.608654i	0.986496	−	0.163784i	$-0.0523702\pi$
$991$	11.0623	+	19.1605i	0.351407	+	0.608654i	−0.635090	+	0.772438i	$0.719037\pi$
$992$	−35.9609	+	18.2253i	−1.14176	+	0.578654i
$993$	−10.6141			−0.336828
$994$		0			0
$995$	11.1829	+	11.1829i	0.354522	+	0.354522i
$996$	−3.16674	−	2.97892i	−0.100342	−	0.0943906i
$997$	−43.7258	−	11.7163i	−1.38481	−	0.371059i	−0.511944	−	0.859019i	$-0.671075\pi$
$997$	−43.7258	−	11.7163i	−1.38481	−	0.371059i	−0.872866	+	0.487960i	$0.837741\pi$
$998$	−1.56564	+	3.94938i	−0.0495596	+	0.125016i
$999$	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.765.7		96
7.2	even	3		784.2.m.l.589.21	yes	48
7.3	odd	6	inner	784.2.x.p.557.11		96
7.4	even	3	inner	784.2.x.p.557.12		96
7.5	odd	6		784.2.m.l.589.22	yes	48
7.6	odd	2	inner	784.2.x.p.765.8		96
16.5	even	4	inner	784.2.x.p.373.12		96
112.5	odd	12		784.2.m.l.197.22	yes	48
112.37	even	12		784.2.m.l.197.21	✓	48
112.53	even	12	inner	784.2.x.p.165.7		96
112.69	odd	4	inner	784.2.x.p.373.11		96
112.101	odd	12	inner	784.2.x.p.165.8		96

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

\(f(q)\)	\(=\)	\(q+(-0.843680 + 1.13499i) q^{2} +(-0.164681 + 0.614599i) q^{3} +(-0.576410 - 1.91514i) q^{4} +(-0.389432 - 1.45338i) q^{5} +(-0.558626 - 0.705436i) q^{6} +(2.65997 + 0.961542i) q^{8} +(2.24746 + 1.29757i) q^{9} +O(q^{10})\)	\(q+(-0.843680 + 1.13499i) q^{2} +(-0.164681 + 0.614599i) q^{3} +(-0.576410 - 1.91514i) q^{4} +(-0.389432 - 1.45338i) q^{5} +(-0.558626 - 0.705436i) q^{6} +(2.65997 + 0.961542i) q^{8} +(2.24746 + 1.29757i) q^{9} +(1.97813 + 0.784185i) q^{10} +(-3.35764 - 0.899678i) q^{11} +(1.27197 - 0.0388735i) q^{12} +(0.433866 + 0.433866i) q^{13} +0.957378 q^{15} +(-3.33550 + 2.20781i) q^{16} +(-3.24640 - 5.62292i) q^{17} +(-3.36887 + 1.45612i) q^{18} +(1.27522 - 0.341695i) q^{19} +(-2.55895 + 1.58356i) q^{20} +(3.85390 - 3.05186i) q^{22} +(-1.18252 - 0.682730i) q^{23} +(-1.02901 + 1.47647i) q^{24} +(2.36947 - 1.36801i) q^{25} +(-0.858477 + 0.126390i) q^{26} +(-2.51736 + 2.51736i) q^{27} +(2.40449 + 2.40449i) q^{29} +(-0.807720 + 1.08662i) q^{30} +(-3.56343 - 6.17204i) q^{31} +(0.308253 - 5.64845i) q^{32} +(1.10588 - 1.91544i) q^{33} +(9.12089 + 1.05931i) q^{34} +(1.18957 - 5.05214i) q^{36} +(-1.30715 - 4.87836i) q^{37} +(-0.688059 + 1.73565i) q^{38} +(-0.338103 + 0.195204i) q^{39} +(0.361609 - 4.24040i) q^{40} -7.83707i q^{41} +(0.978094 - 0.978094i) q^{43} +(0.212372 + 6.94894i) q^{44} +(1.01063 - 3.77174i) q^{45} +(1.77256 - 0.766148i) q^{46} +(6.31769 - 10.9426i) q^{47} +(-0.807621 - 2.41358i) q^{48} +(-0.446389 + 3.84349i) q^{50} +(3.99046 - 1.06924i) q^{51} +(0.580828 - 1.08100i) q^{52} +(8.76508 + 2.34860i) q^{53} +(-0.733335 - 4.98102i) q^{54} +5.23030i q^{55} +0.840021i q^{57} +(-4.75769 + 0.700456i) q^{58} +(-7.18346 - 1.92480i) q^{59} +(-0.551842 - 1.83351i) q^{60} +(5.88108 - 1.57583i) q^{61} +(10.0116 + 1.16276i) q^{62} +(6.15087 + 5.11535i) q^{64} +(0.461611 - 0.799533i) q^{65} +(1.24100 + 2.87119i) q^{66} +(-4.14569 + 15.4719i) q^{67} +(-8.89742 + 9.45841i) q^{68} +(0.614344 - 0.614344i) q^{69} -8.41138i q^{71} +(4.73051 + 5.61254i) q^{72} +(0.483999 - 0.279437i) q^{73} +(6.63971 + 2.63217i) q^{74} +(0.450572 + 1.68156i) q^{75} +(-1.38944 - 2.24527i) q^{76} +(0.0636959 - 0.548433i) q^{78} +(0.458833 - 0.794722i) q^{79} +(4.50774 + 3.98797i) q^{80} +(2.76012 + 4.78067i) q^{81} +(8.89501 + 6.61198i) q^{82} +(-2.41581 - 2.41581i) q^{83} +(-6.90800 + 6.90800i) q^{85} +(0.284930 + 1.93533i) q^{86} +(-1.87377 + 1.08182i) q^{87} +(-8.06615 - 5.62163i) q^{88} +(-13.9976 - 8.08152i) q^{89} +(3.42824 + 4.32920i) q^{90} +(-0.625904 + 2.65823i) q^{92} +(4.38016 - 1.17366i) q^{93} +(7.08961 + 16.4025i) q^{94} +(-0.993225 - 1.72032i) q^{95} +(3.42077 + 1.11965i) 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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