LMFDB - Embedded newform 350.2.o.c.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(143,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.o (of order $12$, degree $4$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			143.1
Root			$1.45333 - 1.51725i$ of defining polynomial
Character	$\chi$	$=$	350.143
Dual form			350.2.o.c.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.304013 - 1.13459i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.17462i q^{6} +(2.55176 + 0.698943i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.40320 - 0.810140i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.304013 - 1.13459i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.17462i q^{6} +(2.55176 + 0.698943i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.40320 - 0.810140i) q^{9} +(-0.371536 + 0.643519i) q^{11} +(0.304013 - 1.13459i) q^{12} +(-2.05532 + 2.05532i) q^{13} +(-2.28391 - 1.33557i) q^{14} +(0.500000 + 0.866025i) q^{16} +(6.33660 - 1.69789i) q^{17} +(-1.56507 + 0.419359i) q^{18} +(0.946027 + 1.63857i) q^{19} +(0.0172465 - 3.10769i) q^{21} +(0.525431 - 0.525431i) q^{22} +(1.36952 - 5.11112i) q^{23} +(-0.587308 + 1.01725i) q^{24} +(2.51725 - 1.45333i) q^{26} +(-3.83750 - 3.83750i) q^{27} +(1.86042 + 1.88118i) q^{28} -9.69135i q^{29} +(2.96403 + 1.71129i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.843083 + 0.225903i) q^{33} -6.56014 q^{34} +1.62028 q^{36} +(-2.58012 - 0.691342i) q^{37} +(-0.489700 - 1.82758i) q^{38} +(2.95680 + 1.70711i) q^{39} +0.817699i q^{41} +(-0.820989 + 2.99734i) q^{42} +(-1.59589 - 1.59589i) q^{43} +(-0.643519 + 0.371536i) q^{44} +(-2.64571 + 4.58251i) q^{46} +(-1.21894 + 4.54913i) q^{47} +(0.830578 - 0.830578i) q^{48} +(6.02296 + 3.56707i) q^{49} +(-3.85282 - 6.67328i) q^{51} +(-2.80762 + 0.752300i) q^{52} +(4.81583 - 1.29040i) q^{53} +(2.71352 + 4.69996i) q^{54} +(-1.31014 - 2.29859i) q^{56} +(1.57150 - 1.57150i) q^{57} +(-2.50831 + 9.36112i) q^{58} +(-1.27487 + 2.20815i) q^{59} +(5.25989 - 3.03680i) q^{61} +(-2.42012 - 2.42012i) q^{62} +(4.14688 - 1.08652i) q^{63} +1.00000i q^{64} +(-0.755887 - 0.436412i) q^{66} +(3.54358 + 13.2248i) q^{67} +(6.33660 + 1.69789i) q^{68} -6.21538 q^{69} -16.0173 q^{71} +(-1.56507 - 0.419359i) q^{72} +(2.29071 + 8.54906i) q^{73} +(2.31328 + 1.33557i) q^{74} +1.89205i q^{76} +(-1.39785 + 1.38242i) q^{77} +(-2.41421 - 2.41421i) q^{78} +(-5.70091 + 3.29142i) q^{79} +(-0.756928 + 1.31104i) q^{81} +(0.211636 - 0.789836i) q^{82} +(-9.23519 + 9.23519i) q^{83} +(1.56878 - 2.68272i) q^{84} +(1.12846 + 1.95456i) q^{86} +(-10.9957 + 2.94629i) q^{87} +(0.717752 - 0.192321i) q^{88} +(3.01603 + 5.22392i) q^{89} +(-6.68124 + 3.80814i) q^{91} +(3.74160 - 3.74160i) q^{92} +(1.04051 - 3.88322i) q^{93} +(2.35481 - 4.07864i) q^{94} +(-1.01725 + 0.587308i) q^{96} +(-3.16693 - 3.16693i) q^{97} +(-4.89451 - 5.00438i) q^{98} +1.20398i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 12 q^{11} + 8 q^{16} + 36 q^{17} + 8 q^{18} - 28 q^{21} + 8 q^{22} + 4 q^{23} + 12 q^{26} - 4 q^{28} + 24 q^{31} - 48 q^{33} - 8 q^{36} - 4 q^{37} - 24 q^{38} - 36 q^{42} + 8 q^{43} - 8 q^{46} - 12 q^{47} - 16 q^{51} + 28 q^{53} - 4 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{61} + 36 q^{63} - 32 q^{67} + 36 q^{68} + 16 q^{71} + 8 q^{72} + 12 q^{73} - 16 q^{77} - 16 q^{78} + 48 q^{82} + 12 q^{86} + 24 q^{87} + 4 q^{88} - 16 q^{91} - 8 q^{92} - 28 q^{93} + 12 q^{96} - 40 q^{98}+O(q^{100}) $ 16 * q - 8 * q^7 - 12 * q^11 + 8 * q^16 + 36 * q^17 + 8 * q^18 - 28 * q^21 + 8 * q^22 + 4 * q^23 + 12 * q^26 - 4 * q^28 + 24 * q^31 - 48 * q^33 - 8 * q^36 - 4 * q^37 - 24 * q^38 - 36 * q^42 + 8 * q^43 - 8 * q^46 - 12 * q^47 - 16 * q^51 + 28 * q^53 - 4 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^61 + 36 * q^63 - 32 * q^67 + 36 * q^68 + 16 * q^71 + 8 * q^72 + 12 * q^73 - 16 * q^77 - 16 * q^78 + 48 * q^82 + 12 * q^86 + 24 * q^87 + 4 * q^88 - 16 * q^91 - 8 * q^92 - 28 * q^93 + 12 * q^96 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.304013	−	1.13459i	−0.175522	−	0.655056i	−0.996462	−	0.0840425i	$-0.973217\pi$
$3$	−0.304013	−	1.13459i	−0.175522	−	0.655056i	0.820940	−	0.571014i	$-0.193450\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$			1.17462i			0.479535i
$7$	2.55176	+	0.698943i	0.964475	+	0.264175i
$7$	2.55176	+	0.698943i	0.964475	+	0.264175i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.40320	−	0.810140i	0.467734	−	0.270047i
$10$		0			0
$11$	−0.371536	+	0.643519i	−0.112022	+	0.194028i	−0.916586	−	0.399839i	$-0.869066\pi$
$11$	−0.371536	+	0.643519i	−0.112022	+	0.194028i	0.804563	+	0.593867i	$0.202399\pi$
$12$	0.304013	−	1.13459i	0.0877609	−	0.327528i
$13$	−2.05532	+	2.05532i	−0.570044	+	0.570044i	−0.932141	−	0.362097i	$-0.882061\pi$
$13$	−2.05532	+	2.05532i	−0.570044	+	0.570044i	0.362097	+	0.932141i	$0.382061\pi$
$14$	−2.28391	−	1.33557i	−0.610401	−	0.356946i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	6.33660	−	1.69789i	1.53685	−	0.411798i	0.611605	−	0.791163i	$-0.290524\pi$
$17$	6.33660	−	1.69789i	1.53685	−	0.411798i	0.925247	+	0.379365i	$0.123857\pi$
$18$	−1.56507	+	0.419359i	−0.368890	+	0.0988439i
$19$	0.946027	+	1.63857i	0.217033	+	0.375913i	0.953900	−	0.300126i	$-0.0970286\pi$
$19$	0.946027	+	1.63857i	0.217033	+	0.375913i	−0.736866	+	0.676039i	$0.763695\pi$
$20$		0			0
$21$	0.0172465	−	3.10769i	0.00376349	−	0.678154i
$22$	0.525431	−	0.525431i	0.112022	−	0.112022i
$23$	1.36952	−	5.11112i	0.285565	−	1.06574i	−0.662861	−	0.748743i	$-0.730658\pi$
$23$	1.36952	−	5.11112i	0.285565	−	1.06574i	0.948426	−	0.317000i	$-0.102675\pi$
$24$	−0.587308	+	1.01725i	−0.119884	+	0.207645i
$25$		0			0
$26$	2.51725	−	1.45333i	0.493673	−	0.285022i
$27$	−3.83750	−	3.83750i	−0.738528	−	0.738528i
$28$	1.86042	+	1.88118i	0.351586	+	0.355510i
$29$		−	9.69135i		−	1.79964i	−0.436263	−	0.899819i	$-0.643698\pi$
$29$		−	9.69135i		−	1.79964i	0.436263	−	0.899819i	$-0.356302\pi$
$30$		0			0
$31$	2.96403	+	1.71129i	0.532356	+	0.307356i	0.741975	−	0.670427i	$-0.233889\pi$
$31$	2.96403	+	1.71129i	0.532356	+	0.307356i	−0.209619	+	0.977783i	$0.567222\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	0.843083	+	0.225903i	0.146762	+	0.0393247i
$34$	−6.56014			−1.12505
$35$		0			0
$36$	1.62028			0.270047
$37$	−2.58012	−	0.691342i	−0.424170	−	0.113656i	0.0404183	−	0.999183i	$-0.487131\pi$
$37$	−2.58012	−	0.691342i	−0.424170	−	0.113656i	−0.464588	+	0.885527i	$0.653798\pi$
$38$	−0.489700	−	1.82758i	−0.0794398	−	0.296473i
$39$	2.95680	+	1.70711i	0.473466	+	0.273356i
$40$		0			0
$41$			0.817699i			0.127703i	0.997959	+	0.0638515i	$0.0203384\pi$
$41$			0.817699i			0.127703i	−0.997959	+	0.0638515i	$0.979662\pi$
$42$	−0.820989	+	2.99734i	−0.126681	+	0.462499i
$43$	−1.59589	−	1.59589i	−0.243371	−	0.243371i	0.574872	−	0.818243i	$-0.305052\pi$
$43$	−1.59589	−	1.59589i	−0.243371	−	0.243371i	−0.818243	+	0.574872i	$0.805052\pi$
$44$	−0.643519	+	0.371536i	−0.0970142	+	0.0560111i
$45$		0			0
$46$	−2.64571	+	4.58251i	−0.390089	+	0.675654i
$47$	−1.21894	+	4.54913i	−0.177800	+	0.663560i	0.818257	+	0.574852i	$0.194940\pi$
$47$	−1.21894	+	4.54913i	−0.177800	+	0.663560i	−0.996058	+	0.0887076i	$0.971726\pi$
$48$	0.830578	−	0.830578i	0.119884	−	0.119884i
$49$	6.02296	+	3.56707i	0.860423	+	0.509581i
$50$		0			0
$51$	−3.85282	−	6.67328i	−0.539502	−	0.934445i
$52$	−2.80762	+	0.752300i	−0.389347	+	0.104325i
$53$	4.81583	−	1.29040i	0.661505	−	0.177250i	0.0875798	−	0.996158i	$-0.472087\pi$
$53$	4.81583	−	1.29040i	0.661505	−	0.177250i	0.573925	+	0.818908i	$0.305420\pi$
$54$	2.71352	+	4.69996i	0.369264	+	0.639584i
$55$		0			0
$56$	−1.31014	−	2.29859i	−0.175075	−	0.307163i
$57$	1.57150	−	1.57150i	0.208150	−	0.208150i
$58$	−2.50831	+	9.36112i	−0.329357	+	1.22918i
$59$	−1.27487	+	2.20815i	−0.165975	+	0.287476i	−0.937001	−	0.349327i	$-0.886410\pi$
$59$	−1.27487	+	2.20815i	−0.165975	+	0.287476i	0.771026	+	0.636803i	$0.219744\pi$
$60$		0			0
$61$	5.25989	−	3.03680i	0.673460	−	0.388822i	−0.123927	−	0.992291i	$-0.539549\pi$
$61$	5.25989	−	3.03680i	0.673460	−	0.388822i	0.797386	+	0.603469i	$0.206215\pi$
$62$	−2.42012	−	2.42012i	−0.307356	−	0.307356i
$63$	4.14688	−	1.08652i	0.522458	−	0.136889i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−0.755887	−	0.436412i	−0.0930433	−	0.0537186i
$67$	3.54358	+	13.2248i	0.432917	+	1.61567i	0.746002	+	0.665944i	$0.231971\pi$
$67$	3.54358	+	13.2248i	0.432917	+	1.61567i	−0.313084	+	0.949725i	$0.601362\pi$
$68$	6.33660	+	1.69789i	0.768426	+	0.205899i
$69$	−6.21538			−0.748244
$70$		0			0
$71$	−16.0173			−1.90090			−0.950450	−	0.310879i	$-0.899377\pi$
$71$	−16.0173			−1.90090			−0.950450	+	0.310879i	$0.899377\pi$
$72$	−1.56507	−	0.419359i	−0.184445	−	0.0494220i
$73$	2.29071	+	8.54906i	0.268108	+	1.00059i	0.960321	+	0.278898i	$0.0899692\pi$
$73$	2.29071	+	8.54906i	0.268108	+	1.00059i	−0.692213	+	0.721693i	$0.743364\pi$
$74$	2.31328	+	1.33557i	0.268913	+	0.155257i
$75$		0			0
$76$			1.89205i			0.217033i
$77$	−1.39785	+	1.38242i	−0.159300	+	0.157542i
$78$	−2.41421	−	2.41421i	−0.273356	−	0.273356i
$79$	−5.70091	+	3.29142i	−0.641402	+	0.370314i	−0.785155	−	0.619300i	$-0.787417\pi$
$79$	−5.70091	+	3.29142i	−0.641402	+	0.370314i	0.143752	+	0.989614i	$0.454083\pi$
$80$		0			0
$81$	−0.756928	+	1.31104i	−0.0841031	+	0.145671i
$82$	0.211636	−	0.789836i	0.0233713	−	0.0872228i
$83$	−9.23519	+	9.23519i	−1.01369	+	1.01369i	−0.0137887	+	0.999905i	$0.504389\pi$
$83$	−9.23519	+	9.23519i	−1.01369	+	1.01369i	−0.999905	+	0.0137887i	$0.995611\pi$
$84$	1.56878	−	2.68272i	0.171168	−	0.292708i
$85$		0			0
$86$	1.12846	+	1.95456i	0.121685	+	0.210765i
$87$	−10.9957	+	2.94629i	−1.17886	+	0.315876i
$88$	0.717752	−	0.192321i	0.0765127	−	0.0205015i
$89$	3.01603	+	5.22392i	0.319699	+	0.553735i	0.980425	−	0.196892i	$-0.0630849\pi$
$89$	3.01603	+	5.22392i	0.319699	+	0.553735i	−0.660726	+	0.750627i	$0.729752\pi$
$90$		0			0
$91$	−6.68124	+	3.80814i	−0.700385	+	0.399201i
$92$	3.74160	−	3.74160i	0.390089	−	0.390089i
$93$	1.04051	−	3.88322i	0.107895	−	0.402671i
$94$	2.35481	−	4.07864i	0.242880	−	0.420680i
$95$		0			0
$96$	−1.01725	+	0.587308i	−0.103822	+	0.0599418i
$97$	−3.16693	−	3.16693i	−0.321553	−	0.321553i	0.527810	−	0.849363i	$-0.323013\pi$
$97$	−3.16693	−	3.16693i	−0.321553	−	0.321553i	−0.849363	+	0.527810i	$0.823013\pi$
$98$	−4.89451	−	5.00438i	−0.494420	−	0.505519i
$99$			1.20398i			0.121005i
$100$		0			0
$101$	9.68359	+	5.59083i	0.963554	+	0.556308i	0.897265	−	0.441493i	$-0.145551\pi$
$101$	9.68359	+	5.59083i	0.963554	+	0.556308i	0.0662887	+	0.997800i	$0.478884\pi$
$102$	1.99437	+	7.44307i	0.197472	+	0.736974i
$103$	−2.34351	−	0.627940i	−0.230912	−	0.0618728i	0.141507	−	0.989937i	$-0.454805\pi$
$103$	−2.34351	−	0.627940i	−0.230912	−	0.0618728i	−0.372420	+	0.928064i	$0.621472\pi$
$104$	2.90667			0.285022
$105$		0			0
$106$	−4.98571			−0.484255
$107$	−6.41422	−	1.71868i	−0.620086	−	0.166151i	−0.0649189	−	0.997891i	$-0.520679\pi$
$107$	−6.41422	−	1.71868i	−0.620086	−	0.166151i	−0.555167	+	0.831739i	$0.687346\pi$
$108$	−1.40462	−	5.24213i	−0.135160	−	0.504424i
$109$	−7.76000	−	4.48024i	−0.743274	−	0.429129i	0.0799848	−	0.996796i	$-0.474513\pi$
$109$	−7.76000	−	4.48024i	−0.743274	−	0.429129i	−0.823258	+	0.567667i	$0.807846\pi$
$110$		0			0
$111$			3.13756i			0.297804i
$112$	0.670578	+	2.55936i	0.0633637	+	0.241837i
$113$	−0.307790	−	0.307790i	−0.0289545	−	0.0289545i	0.692481	−	0.721436i	$-0.256518\pi$
$113$	−0.307790	−	0.307790i	−0.0289545	−	0.0289545i	−0.721436	+	0.692481i	$0.756518\pi$
$114$	−1.92469	+	1.11122i	−0.180263	+	0.104075i
$115$		0			0
$116$	4.84567	−	8.39295i	0.449910	−	0.779266i
$117$	−1.21894	+	4.54913i	−0.112691	+	0.420568i
$118$	1.80295	−	1.80295i	0.165975	−	0.165975i
$119$	17.3562	+	0.0963204i	1.59104	+	0.00882967i
$120$		0			0
$121$	5.22392	+	9.04810i	0.474902	+	0.822554i
$122$	−5.86664	+	1.57196i	−0.531141	+	0.142319i
$123$	0.927753	−	0.248591i	0.0836527	−	0.0224147i
$124$	1.71129	+	2.96403i	0.153678	+	0.266178i
$125$		0			0
$126$	−4.28679	−	0.0237900i	−0.381898	−	0.00211939i
$127$	11.1823	−	11.1823i	0.992267	−	0.992267i	−0.00770296	−	0.999970i	$-0.502452\pi$
$127$	11.1823	−	11.1823i	0.992267	−	0.992267i	0.999970	+	0.00770296i	$0.00245195\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−1.32551	+	2.29585i	−0.116705	+	0.202139i
$130$		0			0
$131$	−8.30763	+	4.79641i	−0.725841	+	0.419064i	−0.816899	−	0.576781i	$-0.804308\pi$
$131$	−8.30763	+	4.79641i	−0.725841	+	0.419064i	0.0910579	+	0.995846i	$0.470975\pi$
$132$	0.617179	+	0.617179i	0.0537186	+	0.0537186i
$133$	1.26877	+	4.84245i	0.110016	+	0.419893i
$134$		−	13.6913i		−	1.18275i
$135$		0			0
$136$	−5.68124	−	3.28007i	−0.487163	−	0.281264i
$137$	−2.40949	−	8.99233i	−0.205856	−	0.768267i	−0.989187	−	0.146661i	$-0.953147\pi$
$137$	−2.40949	−	8.99233i	−0.205856	−	0.768267i	0.783330	−	0.621606i	$-0.213519\pi$
$138$	6.00360	+	1.60866i	0.511060	+	0.136938i
$139$	−22.1714			−1.88056			−0.940278	−	0.340408i	$-0.889435\pi$
$139$	−22.1714			−1.88056			−0.940278	+	0.340408i	$0.889435\pi$
$140$		0			0
$141$	5.53198			0.465877
$142$	15.4715	+	4.14557i	1.29834	+	0.347889i
$143$	−0.559013	−	2.08627i	−0.0467470	−	0.174462i
$144$	1.40320	+	0.810140i	0.116934	+	0.0675116i
$145$		0			0
$146$		−	8.85064i		−	0.732484i
$147$	2.21611	−	7.91803i	0.182781	−	0.653068i
$148$	−1.88878	−	1.88878i	−0.155257	−	0.155257i
$149$	3.41418	−	1.97118i	0.279701	−	0.161485i	−0.353587	−	0.935402i	$-0.615038\pi$
$149$	3.41418	−	1.97118i	0.279701	−	0.161485i	0.633288	+	0.773916i	$0.281705\pi$
$150$		0			0
$151$	9.97267	−	17.2732i	0.811564	−	1.40567i	−0.100205	−	0.994967i	$-0.531950\pi$
$151$	9.97267	−	17.2732i	0.811564	−	1.40567i	0.911769	−	0.410703i	$-0.134717\pi$
$152$	0.489700	−	1.82758i	0.0397199	−	0.148237i
$153$	7.51602	−	7.51602i	0.607634	−	0.607634i
$154$	1.70802	−	0.973528i	0.137636	−	0.0784491i
$155$		0			0
$156$	1.70711	+	2.95680i	0.136678	+	0.236733i
$157$	7.20903	−	1.93165i	0.575343	−	0.154163i	0.0405972	−	0.999176i	$-0.487074\pi$
$157$	7.20903	−	1.93165i	0.575343	−	0.154163i	0.534746	+	0.845013i	$0.320407\pi$
$158$	6.35854	−	1.70376i	0.505858	−	0.135544i
$159$	−2.92815	−	5.07170i	−0.232217	−	0.402212i
$160$		0			0
$161$	7.06707	−	12.0851i	0.556963	−	0.952442i
$162$	1.07046	−	1.07046i	0.0841031	−	0.0841031i
$163$	−3.14893	+	11.7520i	−0.246644	+	0.920486i	0.725907	+	0.687793i	$0.241420\pi$
$163$	−3.14893	+	11.7520i	−0.246644	+	0.920486i	−0.972550	+	0.232693i	$0.925246\pi$
$164$	−0.408849	+	0.708148i	−0.0319258	+	0.0552970i
$165$		0			0
$166$	11.3107	−	6.53026i	0.877884	−	0.506847i
$167$	−1.45564	−	1.45564i	−0.112641	−	0.112641i	0.648540	−	0.761181i	$-0.275380\pi$
$167$	−1.45564	−	1.45564i	−0.112641	−	0.112641i	−0.761181	+	0.648540i	$0.775380\pi$
$168$	−2.20966	+	2.18527i	−0.170479	+	0.168598i
$169$			4.55129i			0.350099i
$170$		0			0
$171$	2.65494	+	1.53283i	0.203028	+	0.117218i
$172$	−0.584136	−	2.18003i	−0.0445400	−	0.166225i
$173$	−9.08750	−	2.43499i	−0.690910	−	0.185129i	−0.103754	−	0.994603i	$-0.533086\pi$
$173$	−9.08750	−	2.43499i	−0.690910	−	0.185129i	−0.587155	+	0.809474i	$0.699752\pi$
$174$	11.3836			0.862989
$175$		0			0
$176$	−0.743072			−0.0560111
$177$	2.89292	+	0.775156i	0.217445	+	0.0582643i
$178$	−1.56121	−	5.82653i	−0.117018	−	0.436717i
$179$	3.89494	+	2.24874i	0.291121	+	0.168079i	0.638447	−	0.769665i	$-0.279577\pi$
$179$	3.89494	+	2.24874i	0.291121	+	0.168079i	−0.347326	+	0.937744i	$0.612910\pi$
$180$		0			0
$181$			17.8850i			1.32938i	0.747118	+	0.664691i	$0.231437\pi$
$181$			17.8850i			1.32938i	−0.747118	+	0.664691i	$0.768563\pi$
$182$	7.43921	−	1.94915i	0.551431	−	0.144480i
$183$	−5.04460	−	5.04460i	−0.372907	−	0.372907i
$184$	−4.58251	+	2.64571i	−0.337827	+	0.195044i
$185$		0			0
$186$	−2.01010	+	3.48160i	−0.147388	+	0.255283i
$187$	−1.26165	+	4.70855i	−0.0922612	+	0.344323i
$188$	−3.33020	+	3.33020i	−0.242880	+	0.242880i
$189$	−7.11019	−	12.4746i	−0.517190	−	0.907392i
$190$		0			0
$191$	1.38774	+	2.40364i	0.100413	+	0.173921i	0.911855	−	0.410512i	$-0.134650\pi$
$191$	1.38774	+	2.40364i	0.100413	+	0.173921i	−0.811442	+	0.584433i	$0.801317\pi$
$192$	1.13459	−	0.304013i	0.0818821	−	0.0219402i
$193$	−4.96491	+	1.33034i	−0.357382	+	0.0957602i	−0.433043	−	0.901373i	$-0.642560\pi$
$193$	−4.96491	+	1.33034i	−0.357382	+	0.0957602i	0.0756607	+	0.997134i	$0.475893\pi$
$194$	2.23936	+	3.87868i	0.160776	+	0.278473i
$195$		0			0
$196$	3.43250	+	6.10065i	0.245179	+	0.435761i
$197$	−1.34043	+	1.34043i	−0.0955019	+	0.0955019i	−0.753244	−	0.657742i	$-0.771512\pi$
$197$	−1.34043	+	1.34043i	−0.0955019	+	0.0955019i	0.657742	+	0.753244i	$0.271512\pi$
$198$	0.311614	−	1.16296i	0.0221454	−	0.0826479i
$199$	−7.25148	+	12.5599i	−0.514043	+	0.890349i	0.485824	+	0.874057i	$0.338520\pi$
$199$	−7.25148	+	12.5599i	−0.514043	+	0.890349i	−0.999867	+	0.0162926i	$0.994814\pi$
$200$		0			0
$201$	13.9275	−	8.04103i	0.982368	−	0.567171i
$202$	−7.90662	−	7.90662i	−0.556308	−	0.556308i
$203$	6.77370	−	24.7300i	0.475420	−	1.73571i
$204$		−	7.70563i		−	0.539502i
$205$		0			0
$206$	2.10113	+	1.21309i	0.146393	+	0.0845198i
$207$	−2.21901	−	8.28144i	−0.154232	−	0.575600i
$208$	−2.80762	−	0.752300i	−0.194674	−	0.0521627i
$209$	−1.40593			−0.0972504
$210$		0			0
$211$	10.0324			0.690660			0.345330	−	0.938481i	$-0.387767\pi$
$211$	10.0324			0.690660			0.345330	+	0.938481i	$0.387767\pi$
$212$	4.81583	+	1.29040i	0.330752	+	0.0886249i
$213$	4.86945	+	18.1730i	0.333649	+	1.24520i
$214$	5.75083	+	3.32024i	0.393119	+	0.226967i
$215$		0			0
$216$			5.42705i			0.369264i
$217$	6.36741	+	6.43848i	0.432248	+	0.437073i
$218$	6.33602	+	6.33602i	0.429129	+	0.429129i
$219$	9.00328	−	5.19804i	0.608385	−	0.351251i
$220$		0			0
$221$	−9.53406	+	16.5135i	−0.641330	+	1.11082i
$222$	0.812061	−	3.03065i	0.0545020	−	0.203404i
$223$	3.13756	−	3.13756i	0.210107	−	0.210107i	−0.594206	−	0.804313i	$-0.702534\pi$
$223$	3.13756	−	3.13756i	0.210107	−	0.210107i	0.804313	+	0.594206i	$0.202534\pi$
$224$	0.0146827	−	2.64571i	0.000981028	−	0.176774i
$225$		0			0
$226$	0.217641	+	0.376965i	0.0144772	+	0.0250753i
$227$	−0.648012	+	0.173634i	−0.0430101	+	0.0115245i	−0.280260	−	0.959924i	$-0.590421\pi$
$227$	−0.648012	+	0.173634i	−0.0430101	+	0.0115245i	0.237250	+	0.971449i	$0.423754\pi$
$228$	2.14671	−	0.575209i	0.142169	−	0.0380941i
$229$	−6.60166	−	11.4344i	−0.436250	−	0.755608i	0.561146	−	0.827717i	$-0.310360\pi$
$229$	−6.60166	−	11.4344i	−0.436250	−	0.755608i	−0.997397	+	0.0721088i	$0.977027\pi$
$230$		0			0
$231$	1.99345	+	1.16572i	0.131159	+	0.0766986i
$232$	−6.85282	+	6.85282i	−0.449910	+	0.449910i
$233$	2.24110	−	8.36389i	0.146819	−	0.547937i	−0.852849	−	0.522158i	$-0.825127\pi$
$233$	2.24110	−	8.36389i	0.146819	−	0.547937i	0.999668	−	0.0257782i	$-0.00820637\pi$
$234$	2.35481	−	4.07864i	0.153938	−	0.266629i
$235$		0			0
$236$	−2.20815	+	1.27487i	−0.143738	+	0.0829873i
$237$	5.46757	+	5.46757i	0.355157	+	0.355157i
$238$	−16.7399	−	4.58516i	−1.08509	−	0.297212i
$239$		−	4.00294i		−	0.258929i	−0.991584	−	0.129464i	$-0.958674\pi$
$239$		−	4.00294i		−	0.258929i	0.991584	−	0.129464i	$-0.0413258\pi$
$240$		0			0
$241$	−15.0040	−	8.66256i	−0.966493	−	0.558005i	−0.0683274	−	0.997663i	$-0.521766\pi$
$241$	−15.0040	−	8.66256i	−0.966493	−	0.558005i	−0.898165	+	0.439658i	$0.855100\pi$
$242$	−2.70410	−	10.0918i	−0.173826	−	0.648728i
$243$	−14.0088	−	3.75364i	−0.898663	−	0.240796i
$244$	6.07359			0.388822
$245$		0			0
$246$	−0.960481			−0.0612380
$247$	−5.31218	−	1.42339i	−0.338006	−	0.0905683i
$248$	−0.885827	−	3.30595i	−0.0562501	−	0.209928i
$249$	13.2858	+	7.67055i	0.841952	+	0.486101i
$250$		0			0
$251$		−	5.49938i		−	0.347118i	−0.984824	−	0.173559i	$-0.944473\pi$
$251$		−	5.49938i		−	0.347118i	0.984824	−	0.173559i	$-0.0555267\pi$
$252$	4.13456	+	1.13248i	0.260453	+	0.0713397i
$253$	2.78028	+	2.78028i	0.174795	+	0.174795i
$254$	−13.6954	+	7.90707i	−0.859329	+	0.496134i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.27307	+	15.9473i	−0.266547	+	0.994766i	0.694750	+	0.719251i	$0.255515\pi$
$257$	−4.27307	+	15.9473i	−0.266547	+	0.994766i	−0.961297	+	0.275515i	$0.911152\pi$
$258$	1.87456	−	1.87456i	0.116705	−	0.116705i
$259$	−6.10065	−	3.56750i	−0.379076	−	0.221674i
$260$		0			0
$261$	−7.85135	−	13.5989i	−0.485986	−	0.841753i
$262$	9.26595	−	2.48280i	0.572453	−	0.153388i
$263$	−9.52484	+	2.55217i	−0.587327	+	0.157374i	−0.540231	−	0.841517i	$-0.681663\pi$
$263$	−9.52484	+	2.55217i	−0.587327	+	0.157374i	−0.0470956	+	0.998890i	$0.514997\pi$
$264$	−0.436412	−	0.755887i	−0.0268593	−	0.0465216i
$265$		0			0
$266$	0.0277804	−	5.00583i	0.00170333	−	0.306927i
$267$	5.01010	−	5.01010i	0.306613	−	0.306613i
$268$	−3.54358	+	13.2248i	−0.216459	+	0.807835i
$269$	−4.47922	+	7.75824i	−0.273103	+	0.473028i	−0.969655	−	0.244478i	$-0.921383\pi$
$269$	−4.47922	+	7.75824i	−0.273103	+	0.473028i	0.696552	+	0.717506i	$0.254717\pi$
$270$		0			0
$271$	−19.7889	+	11.4251i	−1.20209	+	0.694027i	−0.961020	−	0.276480i	$-0.910832\pi$
$271$	−19.7889	+	11.4251i	−1.20209	+	0.694027i	−0.241071	+	0.970507i	$0.577499\pi$
$272$	4.63872	+	4.63872i	0.281264	+	0.281264i
$273$	6.35186	+	6.42276i	0.384432	+	0.388723i
$274$			9.30954i			0.562410i
$275$		0			0
$276$	−5.38268	−	3.10769i	−0.323999	−	0.187061i
$277$	−5.57320	−	20.7995i	−0.334861	−	1.24972i	−0.904019	−	0.427491i	$-0.859397\pi$
$277$	−5.57320	−	20.7995i	−0.334861	−	1.24972i	0.569158	−	0.822228i	$-0.307269\pi$
$278$	21.4160	+	5.73839i	1.28444	+	0.344166i
$279$	5.54552			0.332002
$280$		0			0
$281$	−5.64885			−0.336982			−0.168491	−	0.985703i	$-0.553889\pi$
$281$	−5.64885			−0.336982			−0.168491	+	0.985703i	$0.553889\pi$
$282$	−5.34348	−	1.43178i	−0.318200	−	0.0852614i
$283$	0.757948	+	2.82870i	0.0450553	+	0.168149i	0.984788	−	0.173762i	$-0.0555925\pi$
$283$	0.757948	+	2.82870i	0.0450553	+	0.168149i	−0.939732	+	0.341911i	$0.888926\pi$
$284$	−13.8714	−	8.00863i	−0.823113	−	0.475225i
$285$		0			0
$286$			2.15986i			0.127715i
$287$	−0.571524	+	2.08657i	−0.0337360	+	0.123166i
$288$	−1.14571	−	1.14571i	−0.0675116	−	0.0675116i
$289$	22.5473	−	13.0177i	1.32631	−	0.765747i
$290$		0			0
$291$	−2.63038	+	4.55596i	−0.154196	+	0.267075i
$292$	−2.29071	+	8.54906i	−0.134054	+	0.500296i
$293$	−10.7875	+	10.7875i	−0.630212	+	0.630212i	−0.948121	−	0.317909i	$-0.897019\pi$
$293$	−10.7875	+	10.7875i	−0.630212	+	0.630212i	0.317909	+	0.948121i	$0.397019\pi$
$294$	−4.18993	+	7.07466i	−0.244362	+	0.412602i
$295$		0			0
$296$	1.33557	+	2.31328i	0.0776285	+	0.134456i
$297$	3.89528	−	1.04374i	0.226027	−	0.0605637i
$298$	−3.80802	+	1.02036i	−0.220593	+	0.0591077i
$299$	7.69020	+	13.3198i	0.444736	+	0.770305i
$300$		0			0
$301$	−2.95689	−	5.18776i	−0.170432	−	0.299018i
$302$	−14.1035	+	14.1035i	−0.811564	+	0.811564i
$303$	3.39936	−	12.6866i	0.195288	−	0.728826i
$304$	−0.946027	+	1.63857i	−0.0542584	+	0.0939783i
$305$		0			0
$306$	−9.20520	+	5.31463i	−0.526226	+	0.303817i
$307$	6.89201	+	6.89201i	0.393348	+	0.393348i	0.875879	−	0.482531i	$-0.160282\pi$
$307$	6.89201	+	6.89201i	0.393348	+	0.393348i	−0.482531	+	0.875879i	$0.660282\pi$
$308$	−1.90179	+	0.498288i	−0.108364	+	0.0283926i
$309$			2.84982i			0.162121i
$310$		0			0
$311$	−0.109136	−	0.0630096i	−0.00618852	−	0.00357294i	0.496903	−	0.867806i	$-0.334471\pi$
$311$	−0.109136	−	0.0630096i	−0.00618852	−	0.00357294i	−0.503091	+	0.864233i	$0.667804\pi$
$312$	−0.883663	−	3.29788i	−0.0500276	−	0.186706i
$313$	11.2955	+	3.02662i	0.638459	+	0.171075i	0.563505	−	0.826112i	$-0.309452\pi$
$313$	11.2955	+	3.02662i	0.638459	+	0.171075i	0.0749536	+	0.997187i	$0.476119\pi$
$314$	−7.46334			−0.421181
$315$		0			0
$316$	−6.58284			−0.370314
$317$	−10.5732	−	2.83308i	−0.593851	−	0.159122i	−0.0506382	−	0.998717i	$-0.516126\pi$
$317$	−10.5732	−	2.83308i	−0.593851	−	0.159122i	−0.543212	+	0.839595i	$0.682792\pi$
$318$	1.51572	+	5.65674i	0.0849974	+	0.317214i
$319$	6.23657	+	3.60068i	0.349181	+	0.201600i
$320$		0			0
$321$			7.80001i			0.435354i
$322$	−9.95413	+	9.84425i	−0.554722	+	0.548599i
$323$	8.77670	+	8.77670i	0.488349	+	0.488349i
$324$	−1.31104	+	0.756928i	−0.0728354	+	0.0420516i
$325$		0			0
$326$	6.08327	−	10.5365i	0.336921	−	0.583565i
$327$	−2.72410	+	10.1665i	−0.150643	+	0.562208i
$328$	0.578200	−	0.578200i	0.0319258	−	0.0319258i
$329$	−6.29002	+	10.7563i	−0.346780	+	0.593016i
$330$		0			0
$331$	2.73019	+	4.72883i	0.150065	+	0.259920i	0.931251	−	0.364378i	$-0.118718\pi$
$331$	2.73019	+	4.72883i	0.150065	+	0.259920i	−0.781186	+	0.624298i	$0.785385\pi$
$332$	−12.6155	+	3.38031i	−0.692366	+	0.185519i
$333$	−4.18052	+	1.12017i	−0.229091	+	0.0613848i
$334$	1.02929	+	1.78279i	0.0563205	+	0.0975500i
$335$		0			0
$336$	2.69996	−	1.53891i	0.147295	−	0.0839544i
$337$	−20.4823	+	20.4823i	−1.11574	+	1.11574i	−0.123385	+	0.992359i	$0.539375\pi$
$337$	−20.4823	+	20.4823i	−1.11574	+	1.11574i	−0.992359	+	0.123385i	$0.960625\pi$
$338$	1.17796	−	4.39621i	0.0640727	−	0.239122i
$339$	−0.255644	+	0.442788i	−0.0138847	+	0.0240490i
$340$		0			0
$341$	−2.20249	+	1.27161i	−0.119272	+	0.0688615i
$342$	−2.16775	−	2.16775i	−0.117218	−	0.117218i
$343$	12.8760	+	13.3120i	0.695237	+	0.718781i
$344$			2.25693i			0.121685i
$345$		0			0
$346$	8.14763	+	4.70404i	0.438019	+	0.252891i
$347$	5.57442	+	20.8040i	0.299250	+	1.11682i	0.937783	+	0.347223i	$0.112875\pi$
$347$	5.57442	+	20.8040i	0.299250	+	1.11682i	−0.638532	+	0.769595i	$0.720458\pi$
$348$	−10.9957	−	2.94629i	−0.589432	−	0.157938i
$349$	12.5744			0.673093			0.336546	−	0.941667i	$-0.390741\pi$
$349$	12.5744			0.673093			0.336546	+	0.941667i	$0.390741\pi$
$350$		0			0
$351$	15.7746			0.841987
$352$	0.717752	+	0.192321i	0.0382563	+	0.0102508i
$353$	−0.178457	−	0.666012i	−0.00949832	−	0.0354482i	0.961014	−	0.276500i	$-0.0891744\pi$
$353$	−0.178457	−	0.666012i	−0.00949832	−	0.0354482i	−0.970512	+	0.241051i	$0.922508\pi$
$354$	−2.59372	−	1.49749i	−0.137855	−	0.0795905i
$355$		0			0
$356$			6.03207i			0.319699i
$357$	−5.16723	−	19.7215i	−0.273479	−	1.04377i
$358$	−3.18020	−	3.18020i	−0.168079	−	0.168079i
$359$	−19.1381	+	11.0494i	−1.01007	+	0.583165i	−0.911212	−	0.411937i	$-0.864852\pi$
$359$	−19.1381	+	11.0494i	−1.01007	+	0.583165i	−0.0988582	+	0.995102i	$0.531519\pi$
$360$		0			0
$361$	7.71007	−	13.3542i	0.405793	−	0.702854i
$362$	4.62898	−	17.2756i	0.243294	−	0.907985i
$363$	8.67775	−	8.67775i	0.455464	−	0.455464i
$364$	−7.69020	−	0.0426776i	−0.403076	−	0.00223692i
$365$		0			0
$366$	3.56707	+	6.17834i	0.186454	+	0.322947i
$367$	−12.9539	+	3.47100i	−0.676191	+	0.181185i	−0.580542	−	0.814230i	$-0.697159\pi$
$367$	−12.9539	+	3.47100i	−0.676191	+	0.181185i	−0.0956487	+	0.995415i	$0.530493\pi$
$368$	5.11112	−	1.36952i	0.266436	−	0.0713912i
$369$	0.662450	+	1.14740i	0.0344858	+	0.0597311i
$370$		0			0
$371$	13.1908	+	0.0732036i	0.684830	+	0.00380054i
$372$	2.84271	−	2.84271i	0.147388	−	0.147388i
$373$	3.87359	−	14.4564i	0.200567	−	0.748526i	−0.790188	−	0.612864i	$-0.790017\pi$
$373$	3.87359	−	14.4564i	0.200567	−	0.748526i	0.990755	−	0.135662i	$-0.0433160\pi$
$374$	2.43733	−	4.22157i	0.126031	−	0.218292i
$375$		0			0
$376$	4.07864	−	2.35481i	0.210340	−	0.121440i
$377$	19.9189	+	19.9189i	1.02587	+	1.02587i
$378$	3.63926	+	13.8898i	0.187183	+	0.714413i
$379$		−	1.71784i		−	0.0882395i	−0.999026	−	0.0441198i	$-0.985952\pi$
$379$		−	1.71784i		−	0.0882395i	0.999026	−	0.0441198i	$-0.0140483\pi$
$380$		0			0
$381$	−16.0869	−	9.28776i	−0.824156	−	0.475827i
$382$	−0.718348	−	2.68091i	−0.0367539	−	0.137167i
$383$	10.1017	+	2.70676i	0.516175	+	0.138309i	0.507497	−	0.861654i	$-0.330571\pi$
$383$	10.1017	+	2.70676i	0.516175	+	0.138309i	0.00867837	+	0.999962i	$0.497238\pi$
$384$	−1.17462			−0.0599418
$385$		0			0
$386$	5.14005			0.261622
$387$	−3.53225	−	0.946464i	−0.179554	−	0.0481114i
$388$	−1.15918	−	4.32611i	−0.0588483	−	0.219625i
$389$	−18.8548	−	10.8858i	−0.955978	−	0.551934i	−0.0610449	−	0.998135i	$-0.519443\pi$
$389$	−18.8548	−	10.8858i	−0.955978	−	0.551934i	−0.894933	+	0.446201i	$0.852777\pi$
$390$		0			0
$391$		−	34.7124i		−	1.75548i
$392$	−1.73658	−	6.78117i	−0.0877104	−	0.342501i
$393$	7.96759	+	7.96759i	0.401912	+	0.401912i
$394$	1.64169	−	0.947829i	0.0827071	−	0.0477510i
$395$		0			0
$396$	−0.601992	+	1.04268i	−0.0302512	+	0.0523967i
$397$	8.20427	−	30.6188i	0.411761	−	1.53671i	−0.379476	−	0.925202i	$-0.623896\pi$
$397$	8.20427	−	30.6188i	0.411761	−	1.53671i	0.791237	−	0.611510i	$-0.209438\pi$
$398$	10.2551	−	10.2551i	0.514043	−	0.514043i
$399$	5.10848	−	2.91170i	0.255744	−	0.145767i
$400$		0			0
$401$	−6.98528	−	12.0989i	−0.348828	−	0.604188i	0.637213	−	0.770687i	$-0.280087\pi$
$401$	−6.98528	−	12.0989i	−0.348828	−	0.604188i	−0.986042	+	0.166499i	$0.946754\pi$
$402$	−15.5341	+	4.16234i	−0.774769	+	0.207599i
$403$	−9.60930	+	2.57480i	−0.478673	+	0.128260i
$404$	5.59083	+	9.68359i	0.278154	+	0.481777i
$405$		0			0
$406$	−12.9435	+	22.1342i	−0.642374	+	1.09850i
$407$	1.40350	−	1.40350i	0.0695690	−	0.0695690i
$408$	−1.99437	+	7.44307i	−0.0987358	+	0.368487i
$409$	9.36960	−	16.2286i	0.463297	−	0.802454i	−0.535826	−	0.844328i	$-0.680000\pi$
$409$	9.36960	−	16.2286i	0.463297	−	0.802454i	0.999123	+	0.0418748i	$0.0133330\pi$
$410$		0			0
$411$	−9.47010	+	5.46757i	−0.467126	+	0.269695i
$412$	−1.71557	−	1.71557i	−0.0845198	−	0.0845198i
$413$	−4.79654	+	4.74360i	−0.236022	+	0.233417i
$414$			8.57358i			0.421369i
$415$		0			0
$416$	2.51725	+	1.45333i	0.123418	+	0.0712555i
$417$	6.74040	+	25.1555i	0.330079	+	1.23187i
$418$	1.35803	+	0.363882i	0.0664232	+	0.0177981i
$419$	31.5744			1.54251			0.771255	−	0.636526i	$-0.219629\pi$
$419$	31.5744			1.54251			0.771255	+	0.636526i	$0.219629\pi$
$420$		0			0
$421$	−13.5569			−0.660722			−0.330361	−	0.943855i	$-0.607171\pi$
$421$	−13.5569			−0.660722			−0.330361	+	0.943855i	$0.607171\pi$
$422$	−9.69057	−	2.59658i	−0.471729	−	0.126399i
$423$	1.97502	+	7.37087i	0.0960287	+	0.358384i
$424$	−4.31775	−	2.49286i	−0.209689	−	0.121064i
$425$		0			0
$426$		−	18.8141i		−	0.911547i
$427$	15.5445	−	4.07282i	0.752252	−	0.197097i
$428$	−4.69553	−	4.69553i	−0.226967	−	0.226967i
$429$	−2.19711	+	1.26850i	−0.106078	+	0.0612439i
$430$		0			0
$431$	−6.63518	+	11.4925i	−0.319605	+	0.553572i	−0.980406	−	0.196989i	$-0.936884\pi$
$431$	−6.63518	+	11.4925i	−0.319605	+	0.553572i	0.660800	+	0.750562i	$0.270217\pi$
$432$	1.40462	−	5.24213i	0.0675800	−	0.252212i
$433$	12.0535	−	12.0535i	0.579252	−	0.579252i	−0.355445	−	0.934697i	$-0.615671\pi$
$433$	12.0535	−	12.0535i	0.579252	−	0.579252i	0.934697	+	0.355445i	$0.115671\pi$
$434$	−4.48405	−	7.86710i	−0.215241	−	0.377633i
$435$		0			0
$436$	−4.48024	−	7.76000i	−0.214565	−	0.371637i
$437$	9.67052	−	2.59121i	0.462604	−	0.123954i
$438$	−10.0419	+	2.69071i	−0.479818	+	0.128567i
$439$	−17.5238	−	30.3521i	−0.836366	−	1.44863i	−0.892913	−	0.450228i	$-0.851343\pi$
$439$	−17.5238	−	30.3521i	−0.836366	−	1.44863i	0.0565475	−	0.998400i	$-0.481991\pi$
$440$		0			0
$441$	11.3413	+	0.125883i	0.540060	+	0.00599443i
$442$	13.4832	−	13.4832i	0.641330	−	0.641330i
$443$	0.0163232	−	0.0609189i	0.000775538	−	0.00289435i	−0.965537	−	0.260266i	$-0.916190\pi$
$443$	0.0163232	−	0.0609189i	0.000775538	−	0.00289435i	0.966313	+	0.257372i	$0.0828564\pi$
$444$	−1.56878	+	2.71721i	−0.0744511	+	0.128953i
$445$		0			0
$446$	−3.84271	+	2.21859i	−0.181958	+	0.105053i
$447$	−3.27444	−	3.27444i	−0.154876	−	0.154876i
$448$	−0.698943	+	2.55176i	−0.0330219	+	0.120559i
$449$			24.5207i			1.15720i	0.815611	+	0.578601i	$0.196401\pi$
$449$			24.5207i			1.15720i	−0.815611	+	0.578601i	$0.803599\pi$
$450$		0			0
$451$	−0.526205	−	0.303804i	−0.0247780	−	0.0143056i
$452$	−0.112659	−	0.420450i	−0.00529904	−	0.0197763i
$453$	−22.6298	−	6.06364i	−1.06324	−	0.284894i
$454$	0.670872			0.0314856
$455$		0			0
$456$	−2.22244			−0.104075
$457$	19.3892	+	5.19531i	0.906987	+	0.243027i	0.682015	−	0.731339i	$-0.261104\pi$
$457$	19.3892	+	5.19531i	0.906987	+	0.243027i	0.224973	+	0.974365i	$0.427771\pi$
$458$	3.41727	+	12.7534i	0.159679	+	0.595929i
$459$	−30.8324	−	17.8011i	−1.43913	−	0.830884i
$460$		0			0
$461$			11.6940i			0.544642i	0.962207	+	0.272321i	$0.0877912\pi$
$461$			11.6940i			0.544642i	−0.962207	+	0.272321i	$0.912209\pi$
$462$	−1.62382	−	1.64194i	−0.0755468	−	0.0763900i
$463$	−2.77226	−	2.77226i	−0.128838	−	0.128838i	0.639747	−	0.768585i	$-0.279039\pi$
$463$	−2.77226	−	2.77226i	−0.128838	−	0.128838i	−0.768585	+	0.639747i	$0.779039\pi$
$464$	8.39295	−	4.84567i	0.389633	−	0.224955i
$465$		0			0
$466$	−4.32947	+	7.49886i	−0.200559	+	0.347378i
$467$	5.41472	−	20.2080i	0.250563	−	0.935116i	−0.719942	−	0.694035i	$-0.755831\pi$
$467$	5.41472	−	20.2080i	0.250563	−	0.935116i	0.970505	−	0.241081i	$-0.0775019\pi$
$468$	−3.33020	+	3.33020i	−0.153938	+	0.153938i
$469$	−0.201026	+	36.2233i	−0.00928250	+	1.67264i
$470$		0			0
$471$	−4.38327	−	7.59205i	−0.201971	−	0.349823i
$472$	2.46287	−	0.659924i	0.113363	−	0.0303754i
$473$	1.61992	−	0.434055i	0.0744838	−	0.0199579i
$474$	−3.86615	−	6.69637i	−0.177578	−	0.307575i
$475$		0			0
$476$	14.9828	+	8.76153i	0.686734	+	0.401584i
$477$	5.71218	−	5.71218i	0.261543	−	0.261543i
$478$	−1.03604	+	3.86655i	−0.0473873	+	0.176852i
$479$	12.1419	−	21.0303i	0.554775	−	0.960899i	−0.443145	−	0.896450i	$-0.646137\pi$
$479$	12.1419	−	21.0303i	0.554775	−	0.960899i	0.997921	−	0.0644496i	$-0.0205292\pi$
$480$		0			0
$481$	6.72392	−	3.88206i	0.306584	−	0.177007i
$482$	12.2507	+	12.2507i	0.558005	+	0.558005i
$483$	−15.8602	−	4.34420i	−0.721663	−	0.197668i
$484$			10.4478i			0.474902i
$485$		0			0
$486$	12.5599	+	7.25148i	0.569730	+	0.328934i
$487$	−0.661539	−	2.46890i	−0.0299772	−	0.111876i	0.949316	−	0.314323i	$-0.101777\pi$
$487$	−0.661539	−	2.46890i	−0.0299772	−	0.111876i	−0.979293	+	0.202446i	$0.935111\pi$
$488$	−5.86664	−	1.57196i	−0.265570	−	0.0711594i
$489$	14.2910			0.646262
$490$		0			0
$491$	14.5668			0.657391			0.328695	−	0.944436i	$-0.393391\pi$
$491$	14.5668			0.657391			0.328695	+	0.944436i	$0.393391\pi$
$492$	0.927753	+	0.248591i	0.0418264	+	0.0112073i
$493$	−16.4548	−	61.4102i	−0.741088	−	2.76578i
$494$	4.76277	+	2.74978i	0.214287	+	0.123719i
$495$		0			0
$496$			3.42257i			0.153678i
$497$	−40.8722	−	11.1951i	−1.83337	−	0.502171i
$498$	−10.8478	−	10.8478i	−0.486101	−	0.486101i
$499$	26.0565	−	15.0437i	1.16645	−	0.673450i	0.213608	−	0.976919i	$-0.431478\pi$
$499$	26.0565	−	15.0437i	1.16645	−	0.673450i	0.952841	+	0.303469i	$0.0981450\pi$
$500$		0			0
$501$	−1.20902	+	2.09409i	−0.0540152	+	0.0935572i
$502$	−1.42334	+	5.31199i	−0.0635269	+	0.237086i
$503$	−24.6819	+	24.6819i	−1.10051	+	1.10051i	−0.106161	+	0.994349i	$0.533856\pi$
$503$	−24.6819	+	24.6819i	−1.10051	+	1.10051i	−0.994349	+	0.106161i	$0.966144\pi$
$504$	−3.70057	−	2.16400i	−0.164837	−	0.0963921i
$505$		0			0
$506$	−1.96595	−	3.40513i	−0.0873973	−	0.151377i
$507$	5.16386	−	1.38365i	0.229335	−	0.0614501i
$508$	15.2753	−	4.09300i	0.677731	−	0.181598i
$509$	−6.22521	−	10.7824i	−0.275927	−	0.477920i	0.694441	−	0.719549i	$-0.255652\pi$
$509$	−6.22521	−	10.7824i	−0.275927	−	0.477920i	−0.970369	+	0.241629i	$0.922318\pi$
$510$		0			0
$511$	−0.129951	+	23.4162i	−0.00574869	+	1.03587i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	2.65762	−	9.91839i	0.117337	−	0.437908i
$514$	8.25494	−	14.2980i	0.364110	−	0.630656i
$515$		0			0
$516$	−2.29585	+	1.32551i	−0.101069	+	0.0583524i
$517$	−2.47458	−	2.47458i	−0.108832	−	0.108832i
$518$	4.96944	+	5.02490i	0.218345	+	0.220782i
$519$			11.0509i			0.485079i
$520$		0			0
$521$	30.6011	+	17.6676i	1.34066	+	0.774030i	0.986904	−	0.161308i	$-0.0515711\pi$
$521$	30.6011	+	17.6676i	1.34066	+	0.774030i	0.353756	+	0.935338i	$0.384904\pi$
$522$	4.06416	+	15.1676i	0.177883	+	0.663869i
$523$	15.8804	+	4.25513i	0.694400	+	0.186064i	0.588721	−	0.808336i	$-0.299632\pi$
$523$	15.8804	+	4.25513i	0.694400	+	0.186064i	0.105679	+	0.994400i	$0.466298\pi$
$524$	−9.59282			−0.419064
$525$		0			0
$526$	9.86084			0.429953
$527$	21.6875	+	5.81115i	0.944722	+	0.253137i
$528$	0.225903	+	0.843083i	0.00983118	+	0.0366905i
$529$	−4.32938	−	2.49957i	−0.188234	−	0.108677i
$530$		0			0
$531$			4.13131i			0.179283i
$532$	−1.32244	+	4.82807i	−0.0573349	+	0.209323i
$533$	−1.68063	−	1.68063i	−0.0727964	−	0.0727964i
$534$	−6.13610	+	3.54268i	−0.265535	+	0.153307i
$535$		0			0
$536$	6.84567	−	11.8571i	0.295688	−	0.512147i
$537$	1.36729	−	5.10281i	0.0590031	−	0.220202i
$538$	6.33457	−	6.33457i	0.273103	−	0.273103i
$539$	−4.53322	+	2.55059i	−0.195260	+	0.109862i
$540$		0			0
$541$	13.2572	+	22.9621i	0.569970	+	0.987218i	0.996568	+	0.0827763i	$0.0263787\pi$
$541$	13.2572	+	22.9621i	0.569970	+	0.987218i	−0.426598	+	0.904441i	$0.640288\pi$
$542$	22.0717	−	5.91408i	0.948059	−	0.254032i
$543$	20.2922	−	5.43727i	0.870820	−	0.233336i
$544$	−3.28007	−	5.68124i	−0.140632	−	0.243581i
$545$		0			0
$546$	−4.47310	−	7.84789i	−0.191431	−	0.335859i
$547$	1.07403	−	1.07403i	0.0459223	−	0.0459223i	−0.683773	−	0.729695i	$-0.739662\pi$
$547$	1.07403	−	1.07403i	0.0459223	−	0.0459223i	0.729695	+	0.683773i	$0.239662\pi$
$548$	2.40949	−	8.99233i	0.102928	−	0.384133i
$549$	4.92046	−	8.52249i	0.210000	−	0.363731i
$550$		0			0
$551$	15.8799	−	9.16828i	0.676507	−	0.390582i
$552$	4.39494	+	4.39494i	0.187061	+	0.187061i
$553$	−16.8479	+	4.41431i	−0.716444	+	0.187715i
$554$			21.5332i			0.914858i
$555$		0			0
$556$	−19.2010	−	11.0857i	−0.814305	−	0.470139i
$557$	−4.02313	−	15.0145i	−0.170466	−	0.636186i	−0.997280	−	0.0737108i	$-0.976516\pi$
$557$	−4.02313	−	15.0145i	−0.170466	−	0.636186i	0.826814	−	0.562475i	$-0.190151\pi$
$558$	−5.35657	−	1.43529i	−0.226761	−	0.0607606i
$559$	6.56014			0.277464
$560$		0			0
$561$	5.72584			0.241745
$562$	5.45637	+	1.46203i	0.230163	+	0.0616721i
$563$	7.10355	+	26.5108i	0.299379	+	1.11730i	0.937677	+	0.347508i	$0.112972\pi$
$563$	7.10355	+	26.5108i	0.299379	+	1.11730i	−0.638298	+	0.769789i	$0.720361\pi$
$564$	4.79084	+	2.76599i	0.201731	+	0.116469i
$565$		0			0
$566$		−	2.92849i		−	0.123093i
$567$	−2.84784	+	2.81641i	−0.119598	+	0.118278i
$568$	11.3259	+	11.3259i	0.475225	+	0.475225i
$569$	−5.85207	+	3.37869i	−0.245332	+	0.141642i	−0.617625	−	0.786473i	$-0.711905\pi$
$569$	−5.85207	+	3.37869i	−0.245332	+	0.141642i	0.372293	+	0.928115i	$0.378572\pi$
$570$		0			0
$571$	−5.87721	+	10.1796i	−0.245953	+	0.426004i	−0.962399	−	0.271639i	$-0.912434\pi$
$571$	−5.87721	+	10.1796i	−0.245953	+	0.426004i	0.716446	+	0.697643i	$0.245768\pi$
$572$	0.559013	−	2.08627i	0.0233735	−	0.0872312i
$573$	2.30526	−	2.30526i	0.0963034	−	0.0963034i
$574$	1.09209	−	1.86755i	0.0455831	−	0.0779501i
$575$		0			0
$576$	0.810140	+	1.40320i	0.0337558	+	0.0584668i
$577$	−2.17865	+	0.583767i	−0.0906983	+	0.0243025i	−0.303883	−	0.952709i	$-0.598283\pi$
$577$	−2.17865	+	0.583767i	−0.0906983	+	0.0243025i	0.213184	+	0.977012i	$0.431616\pi$
$578$	−25.1483	+	6.73845i	−1.04603	+	0.280283i
$579$	3.01879	+	5.22870i	0.125457	+	0.217297i
$580$		0			0
$581$	−30.0209	+	17.1111i	−1.24547	+	0.709889i
$582$	3.71992	−	3.71992i	0.154196	−	0.154196i
$583$	−0.958858	+	3.57851i	−0.0397118	+	0.148207i
$584$	4.42532	−	7.66488i	0.183121	−	0.317175i
$585$		0			0
$586$	13.2119	−	7.62790i	0.545779	−	0.315106i
$587$	−12.8372	−	12.8372i	−0.529847	−	0.529847i	0.390680	−	0.920527i	$-0.372240\pi$
$587$	−12.8372	−	12.8372i	−0.529847	−	0.529847i	−0.920527	+	0.390680i	$0.872240\pi$
$588$	5.87822	−	5.74916i	0.242414	−	0.237091i
$589$			6.47569i			0.266826i
$590$		0			0
$591$	1.92835	+	1.11333i	0.0793218	+	0.0457965i
$592$	−0.691342	−	2.58012i	−0.0284140	−	0.106042i
$593$	−35.1170	−	9.40957i	−1.44208	−	0.386405i	−0.548820	−	0.835940i	$-0.684923\pi$
$593$	−35.1170	−	9.40957i	−1.44208	−	0.386405i	−0.893262	+	0.449535i	$0.851590\pi$
$594$	−4.03269			−0.165463
$595$		0			0
$596$	3.94236			0.161485
$597$	16.4549	+	4.40908i	0.673455	+	0.180452i
$598$	−3.98074	−	14.8563i	−0.162785	−	0.607520i
$599$	30.9792	+	17.8858i	1.26578	+	0.730796i	0.974186	−	0.225748i	$-0.0724826\pi$
$599$	30.9792	+	17.8858i	1.26578	+	0.730796i	0.291589	+	0.956544i	$0.405816\pi$
$600$		0			0
$601$		−	45.6631i		−	1.86264i	−0.364204	−	0.931319i	$-0.618659\pi$
$601$		−	45.6631i		−	1.86264i	0.364204	−	0.931319i	$-0.381341\pi$
$602$	1.51345	+	5.77629i	0.0616835	+	0.235424i
$603$	15.6863	+	15.6863i	0.638796	+	0.638796i
$604$	17.2732	−	9.97267i	0.702835	−	0.405782i
$605$		0			0
$606$	−6.56707	+	11.3745i	−0.266769	+	0.462057i
$607$	0.303188	−	1.13151i	0.0123060	−	0.0459267i	−0.959500	−	0.281709i	$-0.909099\pi$
$607$	0.303188	−	1.13151i	0.0123060	−	0.0459267i	0.971806	+	0.235783i	$0.0757653\pi$
$608$	1.33788	−	1.33788i	0.0542584	−	0.0542584i
$609$	−30.1177	−	0.167142i	−1.22043	−	0.00677293i
$610$		0			0
$611$	−6.84463	−	11.8553i	−0.276904	−	0.479612i
$612$	10.2671	−	2.75105i	0.415022	−	0.111205i
$613$	−13.4629	+	3.60737i	−0.543760	+	0.145700i	−0.520235	−	0.854023i	$-0.674156\pi$
$613$	−13.4629	+	3.60737i	−0.543760	+	0.145700i	−0.0235253	+	0.999723i	$0.507489\pi$
$614$	−4.87339	−	8.44095i	−0.196674	−	0.340649i
$615$		0			0
$616$	1.96595	+	0.0109103i	0.0792105	+	0.000439588i
$617$	−22.7725	+	22.7725i	−0.916788	+	0.916788i	−0.996794	−	0.0800065i	$-0.974506\pi$
$617$	−22.7725	+	22.7725i	−0.916788	+	0.916788i	0.0800065	+	0.996794i	$0.474506\pi$
$618$	0.737588	−	2.75272i	0.0296702	−	0.110731i
$619$	−11.3386	+	19.6391i	−0.455738	+	0.789361i	−0.998730	−	0.0503763i	$-0.983958\pi$
$619$	−11.3386	+	19.6391i	−0.455738	+	0.789361i	0.542992	+	0.839738i	$0.317291\pi$
$620$		0			0
$621$	−24.8695	+	14.3584i	−0.997978	+	0.576183i
$622$	0.0891090	+	0.0891090i	0.00357294	+	0.00357294i
$623$	4.04497	+	15.4382i	0.162058	+	0.618520i
$624$			3.41421i			0.136678i
$625$		0			0
$626$	−10.1273	−	5.84698i	−0.404767	−	0.233692i
$627$	0.427421	+	1.59516i	0.0170696	+	0.0637045i
$628$	7.20903	+	1.93165i	0.287672	+	0.0770814i
$629$	−17.5231			−0.698690
$630$		0			0
$631$	32.4210			1.29066			0.645330	−	0.763904i	$-0.276720\pi$
$631$	32.4210			1.29066			0.645330	+	0.763904i	$0.276720\pi$
$632$	6.35854	+	1.70376i	0.252929	+	0.0677721i
$633$	−3.04998	−	11.3827i	−0.121226	−	0.452421i
$634$	9.47968	+	5.47310i	0.376486	+	0.217364i
$635$		0			0
$636$		−	5.85629i		−	0.232217i
$637$	−19.7106	+	5.04765i	−0.780963	+	0.199995i
$638$	−5.09214	−	5.09214i	−0.201600	−	0.201600i
$639$	−22.4755	+	12.9762i	−0.889116	+	0.513331i
$640$		0			0
$641$	0.428070	−	0.741439i	0.0169077	−	0.0292851i	−0.857448	−	0.514571i	$-0.827951\pi$
$641$	0.428070	−	0.741439i	0.0169077	−	0.0292851i	0.874355	+	0.485286i	$0.161285\pi$
$642$	2.01879	−	7.53423i	0.0796754	−	0.297353i
$643$	16.4254	−	16.4254i	0.647754	−	0.647754i	−0.304696	−	0.952450i	$-0.598555\pi$
$643$	16.4254	−	16.4254i	0.647754	−	0.647754i	0.952450	+	0.304696i	$0.0985548\pi$
$644$	12.1628	−	6.93250i	0.479283	−	0.273179i
$645$		0			0
$646$	−6.20607	−	10.7492i	−0.244174	−	0.422922i
$647$	45.8316	−	12.2805i	1.80183	−	0.482798i	0.807564	−	0.589779i	$-0.200785\pi$
$647$	45.8316	−	12.2805i	1.80183	−	0.482798i	0.994261	+	0.106982i	$0.0341186\pi$
$648$	1.46227	−	0.391815i	0.0574435	−	0.0153919i
$649$	−0.947323	−	1.64081i	−0.0371857	−	0.0644075i
$650$		0			0
$651$	5.36927	−	9.18179i	0.210438	−	0.359863i
$652$	−8.60305	+	8.60305i	−0.336921	+	0.336921i
$653$	−6.80004	+	25.3781i	−0.266106	+	0.993121i	0.695464	+	0.718561i	$0.255199\pi$
$653$	−6.80004	+	25.3781i	−0.266106	+	0.993121i	−0.961570	+	0.274560i	$0.911468\pi$
$654$	5.26256	−	9.11502i	0.205782	−	0.356425i
$655$		0			0
$656$	−0.708148	+	0.408849i	−0.0276485	+	0.0159629i
$657$	10.1403	+	10.1403i	0.395609	+	0.395609i
$658$	8.85964	−	8.76184i	0.345385	−	0.341572i
$659$		−	26.2355i		−	1.02199i	−0.859583	−	0.510996i	$-0.829277\pi$
$659$		−	26.2355i		−	1.02199i	0.859583	−	0.510996i	$-0.170723\pi$
$660$		0			0
$661$	−12.6197	−	7.28597i	−0.490848	−	0.283391i	0.234078	−	0.972218i	$-0.424793\pi$
$661$	−12.6197	−	7.28597i	−0.490848	−	0.283391i	−0.724926	+	0.688827i	$0.758126\pi$
$662$	−1.41325	−	5.27432i	−0.0549275	−	0.204992i
$663$	21.6345	+	5.79695i	0.840215	+	0.225135i
$664$	13.0605			0.506847
$665$		0			0
$666$	4.32800			0.167706
$667$	−49.5336	−	13.2725i	−1.91795	−	0.513913i
$668$	−0.532802	−	1.98844i	−0.0206147	−	0.0769352i
$669$	−4.51371	−	2.60599i	−0.174510	−	0.100753i
$670$		0			0
$671$			4.51312i			0.174227i
$672$	−3.00626	+	0.787671i	−0.115969	+	0.0303851i
$673$	16.4201	+	16.4201i	0.632950	+	0.632950i	0.948807	−	0.315857i	$-0.102292\pi$
$673$	16.4201	+	16.4201i	0.632950	+	0.632950i	−0.315857	+	0.948807i	$0.602292\pi$
$674$	25.0856	−	14.4832i	0.966263	−	0.557872i
$675$		0			0
$676$	−2.27565	+	3.94154i	−0.0875249	+	0.151598i
$677$	5.89172	−	21.9882i	0.226437	−	0.845075i	−0.755386	−	0.655280i	$-0.772551\pi$
$677$	5.89172	−	21.9882i	0.226437	−	0.845075i	0.981824	−	0.189796i	$-0.0607825\pi$
$678$	0.361535	−	0.361535i	0.0138847	−	0.0138847i
$679$	−5.86774	−	10.2947i	−0.225183	−	0.395076i
$680$		0			0
$681$	0.394008	+	0.682442i	0.0150984	+	0.0261512i
$682$	2.45656	−	0.658233i	0.0940665	−	0.0252050i
$683$	29.5964	−	7.93034i	1.13248	−	0.303446i	0.356554	−	0.934275i	$-0.383952\pi$
$683$	29.5964	−	7.93034i	1.13248	−	0.303446i	0.775922	+	0.630829i	$0.217285\pi$
$684$	1.53283	+	2.65494i	0.0586091	+	0.101514i
$685$		0			0
$686$	−8.99183	−	16.1910i	−0.343310	−	0.618173i
$687$	−10.9664	+	10.9664i	−0.418394	+	0.418394i
$688$	0.584136	−	2.18003i	0.0222700	−	0.0831127i
$689$	−7.24590	+	12.5503i	−0.276047	+	0.478127i
$690$		0			0
$691$	27.7284	−	16.0090i	1.05484	−	0.609012i	0.130839	−	0.991404i	$-0.458233\pi$
$691$	27.7284	−	16.0090i	1.05484	−	0.609012i	0.924000	+	0.382392i	$0.124900\pi$
$692$	−6.65251	−	6.65251i	−0.252891	−	0.252891i
$693$	−0.841516	+	3.07228i	−0.0319665	+	0.116706i
$694$		−	21.5379i		−	0.817567i
$695$		0			0
$696$	9.85849	+	5.69180i	0.373685	+	0.215747i
$697$	1.38836	+	5.18143i	0.0525879	+	0.196261i
$698$	−12.1459	−	3.25450i	−0.459731	−	0.123184i
$699$	−10.1709			−0.384699
$700$		0			0
$701$	−18.5294			−0.699844			−0.349922	−	0.936779i	$-0.613792\pi$
$701$	−18.5294			−0.699844			−0.349922	+	0.936779i	$0.613792\pi$
$702$	−15.2371	−	4.08277i	−0.575088	−	0.154094i
$703$	−1.30806	−	4.88174i	−0.0493343	−	0.184118i
$704$	−0.643519	−	0.371536i	−0.0242535	−	0.0140028i
$705$		0			0
$706$			0.689506i			0.0259499i
$707$	20.8025	+	21.0347i	0.782360	+	0.791092i
$708$	2.11777	+	2.11777i	0.0795905	+	0.0795905i
$709$	−23.1074	+	13.3411i	−0.867818	+	0.501035i	−0.866622	−	0.498965i	$-0.833714\pi$
$709$	−23.1074	+	13.3411i	−0.867818	+	0.501035i	−0.00119522	+	0.999999i	$0.500380\pi$
$710$		0			0
$711$	−5.33302	+	9.23706i	−0.200004	+	0.346417i
$712$	1.56121	−	5.82653i	0.0585089	−	0.218358i
$713$	12.8059	−	12.8059i	0.479585	−	0.479585i
$714$	−0.113139	+	20.3869i	−0.00423413	+	0.762960i
$715$		0			0
$716$	2.24874	+	3.89494i	0.0840395	+	0.145561i
$717$	−4.54170	+	1.21695i	−0.169613	+	0.0454477i
$718$	21.3458	−	5.71959i	0.796618	−	0.213453i
$719$	−15.9890	−	27.6937i	−0.596288	−	1.03280i	−0.993364	−	0.115015i	$-0.963308\pi$
$719$	−15.9890	−	27.6937i	−0.596288	−	1.03280i	0.397076	−	0.917786i	$-0.370025\pi$
$720$		0			0
$721$	−5.54117	−	3.24033i	−0.206364	−	0.120676i
$722$	−10.9037	+	10.9037i	−0.405793	+	0.405793i
$723$	−5.26706	+	19.6569i	−0.195884	+	0.731049i
$724$	−8.94250	+	15.4889i	−0.332346	+	0.575639i
$725$		0			0
$726$	−10.6280	+	6.13610i	−0.394443	+	0.227732i
$727$	−21.4539	−	21.4539i	−0.795683	−	0.795683i	0.186729	−	0.982412i	$-0.440211\pi$
$727$	−21.4539	−	21.4539i	−0.795683	−	0.795683i	−0.982412	+	0.186729i	$0.940211\pi$
$728$	7.41711	+	2.03159i	0.274897	+	0.0752958i
$729$			21.5770i			0.799146i
$730$		0			0
$731$	−12.8222	−	7.40288i	−0.474245	−	0.273805i
$732$	−1.84645	−	6.89105i	−0.0682468	−	0.254700i
$733$	12.5691	+	3.36789i	0.464252	+	0.124396i	0.483360	−	0.875422i	$-0.339416\pi$
$733$	12.5691	+	3.36789i	0.464252	+	0.124396i	−0.0191085	+	0.999817i	$0.506083\pi$
$734$	13.4109			0.495006
$735$		0			0
$736$	−5.29142			−0.195044
$737$	−9.82700	−	2.63314i	−0.361982	−	0.0969928i
$738$	−0.342909	−	1.27976i	−0.0126227	−	0.0471084i
$739$	−3.12136	−	1.80212i	−0.114821	−	0.0662920i	0.441490	−	0.897266i	$-0.354450\pi$
$739$	−3.12136	−	1.80212i	−0.114821	−	0.0662920i	−0.556311	+	0.830974i	$0.687784\pi$
$740$		0			0
$741$			6.45988i			0.237309i
$742$	−12.7223	−	3.48473i	−0.467052	−	0.127928i
$743$	−31.1070	−	31.1070i	−1.14121	−	1.14121i	−0.988230	−	0.152977i	$-0.951114\pi$
$743$	−31.1070	−	31.1070i	−1.14121	−	1.14121i	−0.152977	−	0.988230i	$-0.548886\pi$
$744$	−3.48160	+	2.01010i	−0.127642	+	0.0736939i
$745$		0			0
$746$	−7.48320	+	12.9613i	−0.273979	+	0.474546i
$747$	−5.47705	+	20.4406i	−0.200395	+	0.747884i
$748$	−3.44690	+	3.44690i	−0.126031	+	0.126031i
$749$	−15.1663	−	8.86884i	−0.554164	−	0.324060i
$750$		0			0
$751$	25.5141	+	44.1917i	0.931023	+	1.61258i	0.781576	+	0.623810i	$0.214416\pi$
$751$	25.5141	+	44.1917i	0.931023	+	1.61258i	0.149447	+	0.988770i	$0.452251\pi$
$752$	−4.54913	+	1.21894i	−0.165890	+	0.0444501i
$753$	−6.23954	+	1.67188i	−0.227382	+	0.0609267i
$754$	−14.0848	−	24.3955i	−0.512936	−	0.888432i
$755$		0			0
$756$	0.0796836	−	14.3584i	0.00289807	−	0.522210i
$757$	−26.8141	+	26.8141i	−0.974576	+	0.974576i	−0.999685	−	0.0251083i	$-0.992007\pi$
$757$	−26.8141	+	26.8141i	−0.974576	+	0.974576i	0.0251083	+	0.999685i	$0.492007\pi$
$758$	−0.444610	+	1.65931i	−0.0161490	+	0.0602687i
$759$	2.30924	−	3.99972i	0.0838200	−	0.145181i
$760$		0			0
$761$	−25.8753	+	14.9391i	−0.937980	+	0.541543i	−0.889326	−	0.457273i	$-0.848826\pi$
$761$	−25.8753	+	14.9391i	−0.937980	+	0.541543i	−0.0486532	+	0.998816i	$0.515493\pi$
$762$	13.1349	+	13.1349i	0.475827	+	0.475827i
$763$	−16.6702	−	16.8563i	−0.603503	−	0.610239i
$764$			2.77548i			0.100413i
$765$		0			0
$766$	−9.05698	−	5.22905i	−0.327242	−	0.188933i
$767$	−1.91818	−	7.15874i	−0.0692614	−	0.258487i
$768$	1.13459	+	0.304013i	0.0409410	+	0.0109701i
$769$	44.7341			1.61315			0.806576	−	0.591130i	$-0.201318\pi$
$769$	44.7341			1.61315			0.806576	+	0.591130i	$0.201318\pi$
$770$		0			0
$771$	19.3927			0.698413
$772$	−4.96491	−	1.33034i	−0.178691	−	0.0478801i
$773$	6.25202	+	23.3328i	0.224869	+	0.839224i	0.982457	+	0.186490i	$0.0597113\pi$
$773$	6.25202	+	23.3328i	0.224869	+	0.839224i	−0.757587	+	0.652734i	$0.773622\pi$
$774$	3.16693	+	1.82843i	0.113833	+	0.0657215i
$775$		0			0
$776$			4.47871i			0.160776i
$777$	−2.19298	+	8.00631i	−0.0786726	+	0.287225i
$778$	15.3949	+	15.3949i	0.551934	+	0.551934i
$779$	−1.33985	+	0.773565i	−0.0480052	+	0.0277158i
$780$		0			0
$781$	5.95099	−	10.3074i	0.212943	−	0.368828i
$782$	−8.98424	+	33.5296i	−0.321276	+	1.19902i
$783$	−37.1906	+	37.1906i	−1.32908	+	1.32908i
$784$	−0.0776922	+	6.99957i	−0.00277472	+	0.249985i
$785$		0			0
$786$	−5.63394	−	9.75826i	−0.200956	−	0.348066i
$787$	−12.2669	+	3.28689i	−0.437266	+	0.117165i	−0.470735	−	0.882275i	$-0.656011\pi$
$787$	−12.2669	+	3.28689i	−0.437266	+	0.117165i	0.0334688	+	0.999440i	$0.489345\pi$
$788$	−1.83107	+	0.490633i	−0.0652290	+	0.0174781i
$789$	5.79134	+	10.0309i	0.206177	+	0.357110i
$790$		0			0
$791$	−0.570279	−	1.00054i	−0.0202768	−	0.0355749i
$792$	0.851345	−	0.851345i	0.0302512	−	0.0302512i
$793$	−4.56917	+	17.0524i	−0.162256	+	0.605547i
$794$	−15.8494	+	27.4520i	−0.562475	+	0.974236i
$795$		0			0
$796$	−12.5599	+	7.25148i	−0.445175	+	0.257022i
$797$	8.99183	+	8.99183i	0.318507	+	0.318507i	0.848193	−	0.529687i	$-0.177690\pi$
$797$	8.99183	+	8.99183i	0.318507	+	0.318507i	−0.529687	+	0.848193i	$0.677690\pi$
$798$	−5.68801	+	1.49032i	−0.201353	+	0.0527566i
$799$			30.8957i			1.09301i
$800$		0			0
$801$	8.46421	+	4.88682i	0.299068	+	0.172667i
$802$	3.61585	+	13.4945i	0.127680	+	0.476508i
$803$	−6.35256	−	1.70216i	−0.224177	−	0.0600681i
$804$	16.0821			0.567171
$805$		0			0
$806$	9.94828			0.350413
$807$	10.1642	+	2.72348i	0.357796	+	0.0958710i
$808$	−2.89402	−	10.8006i	−0.101811	−	0.379965i
$809$	23.7782	+	13.7284i	0.835997	+	0.482663i	0.855902	−	0.517139i	$-0.173003\pi$
$809$	23.7782	+	13.7284i	0.835997	+	0.482663i	−0.0199044	+	0.999802i	$0.506336\pi$
$810$		0			0
$811$		−	12.7335i		−	0.447132i	−0.974689	−	0.223566i	$-0.928230\pi$
$811$		−	12.7335i		−	0.447132i	0.974689	−	0.223566i	$-0.0717699\pi$
$812$	18.2312	−	18.0300i	0.639789	−	0.632727i
$813$	18.9789	+	18.9789i	0.665620	+	0.665620i
$814$	−1.71893	+	0.992425i	−0.0602485	+	0.0347845i
$815$		0			0
$816$	3.85282	−	6.67328i	0.134876	−	0.233611i
$817$	1.10522	−	4.12473i	0.0386666	−	0.144306i
$818$	−13.2506	+	13.2506i	−0.463297	+	0.463297i
$819$	−6.29002	+	10.7563i	−0.219791	+	0.375857i
$820$		0			0
$821$	−15.1707	−	26.2764i	−0.529461	−	0.917054i	−0.999410	−	0.0343601i	$-0.989061\pi$
$821$	−15.1707	−	26.2764i	−0.529461	−	0.917054i	0.469948	−	0.882694i	$-0.344273\pi$
$822$	10.5625	−	2.83022i	0.368410	−	0.0987153i
$823$	9.82702	−	2.63314i	0.342549	−	0.0917856i	−0.0834435	−	0.996513i	$-0.526592\pi$
$823$	9.82702	−	2.63314i	0.342549	−	0.0917856i	0.425992	+	0.904727i	$0.359925\pi$
$824$	1.21309	+	2.10113i	0.0422599	+	0.0731963i
$825$		0			0
$826$	5.86084	−	3.34053i	0.203925	−	0.116232i
$827$	15.9794	−	15.9794i	0.555660	−	0.555660i	−0.372409	−	0.928069i	$-0.621468\pi$
$827$	15.9794	−	15.9794i	0.555660	−	0.555660i	0.928069	+	0.372409i	$0.121468\pi$
$828$	2.21901	−	8.28144i	0.0771158	−	0.287800i
$829$	3.17447	−	5.49835i	0.110254	−	0.190966i	−0.805619	−	0.592435i	$-0.798167\pi$
$829$	3.17447	−	5.49835i	0.110254	−	0.190966i	0.915873	+	0.401469i	$0.131500\pi$
$830$		0			0
$831$	−21.9046	+	12.6466i	−0.759861	+	0.438706i
$832$	−2.05532	−	2.05532i	−0.0712555	−	0.0712555i
$833$	44.2216	+	12.3768i	1.53219	+	0.428830i
$834$		−	26.0429i		−	0.901792i
$835$		0			0
$836$	−1.21757	−	0.702966i	−0.0421106	−	0.0243126i
$837$	−4.80743	−	17.9416i	−0.166169	−	0.620151i
$838$	−30.4985	−	8.17206i	−1.05355	−	0.282299i
$839$	−39.7411			−1.37202			−0.686008	−	0.727594i	$-0.740638\pi$
$839$	−39.7411			−1.37202			−0.686008	+	0.727594i	$0.740638\pi$
$840$		0			0
$841$	−64.9222			−2.23870
$842$	13.0949	+	3.50878i	0.451282	+	0.120921i
$843$	1.71732	+	6.40914i	0.0591478	+	0.220742i
$844$	8.68832	+	5.01621i	0.299064	+	0.172665i
$845$		0			0
$846$		−	7.63089i		−	0.262355i
$847$	7.00609	+	26.7398i	0.240732	+	0.918790i
$848$	3.52543	+	3.52543i	0.121064	+	0.121064i
$849$	2.97899	−	1.71992i	0.102239	−	0.0590276i
$850$		0			0
$851$	−7.06707	+	12.2405i	−0.242256	+	0.419600i
$852$	−4.86945	+	18.1730i	−0.166825	+	0.622598i
$853$	17.1451	−	17.1451i	0.587036	−	0.587036i	−0.349791	−	0.936828i	$-0.613748\pi$
$853$	17.1451	−	17.1451i	0.587036	−	0.587036i	0.936828	+	0.349791i	$0.113748\pi$
$854$	−16.0690	−	0.0891766i	−0.549869	−	0.00305156i
$855$		0			0
$856$	3.32024	+	5.75083i	0.113484	+	0.196559i
$857$	−16.2677	+	4.35890i	−0.555692	+	0.148897i	−0.525727	−	0.850654i	$-0.676206\pi$
$857$	−16.2677	+	4.35890i	−0.555692	+	0.148897i	−0.0299658	+	0.999551i	$0.509540\pi$
$858$	2.45056	−	0.656625i	0.0836607	−	0.0224168i
$859$	15.4345	+	26.7333i	0.526619	+	0.912130i	0.999519	+	0.0310142i	$0.00987370\pi$
$859$	15.4345	+	26.7333i	0.526619	+	0.912130i	−0.472900	+	0.881116i	$0.656793\pi$
$860$		0			0
$861$	2.54115	+	0.0141024i	0.0866023	+	0.000480610i
$862$	9.38356	−	9.38356i	0.319605	−	0.319605i
$863$	0.334691	−	1.24908i	0.0113930	−	0.0425193i	−0.959995	−	0.280016i	$-0.909660\pi$
$863$	0.334691	−	1.24908i	0.0113930	−	0.0425193i	0.971388	+	0.237497i	$0.0763269\pi$
$864$	−2.71352	+	4.69996i	−0.0923160	+	0.159896i
$865$		0			0
$866$	−14.7624	+	8.52308i	−0.501647	+	0.289626i
$867$	−21.6244	−	21.6244i	−0.734404	−	0.734404i
$868$	2.29510	+	8.75960i	0.0779008	+	0.297320i
$869$		−	4.89152i		−	0.165934i
$870$		0			0
$871$	−34.4645	−	19.8981i	−1.16778	−	0.674221i
$872$	2.31914	+	8.65516i	0.0785361	+	0.293101i
$873$	−7.00950	−	1.87819i	−0.237236	−	0.0635671i
$874$	−10.0117			−0.338649
$875$		0			0
$876$	10.3961			0.351251
$877$	9.37406	+	2.51177i	0.316540	+	0.0848165i	0.413591	−	0.910463i	$-0.364274\pi$
$877$	9.37406	+	2.51177i	0.316540	+	0.0848165i	−0.0970513	+	0.995279i	$0.530941\pi$
$878$	9.07099	+	33.8534i	0.306131	+	1.14250i
$879$	15.5189	+	8.95985i	0.523440	+	0.302208i
$880$		0			0
$881$			18.3500i			0.618227i	0.951025	+	0.309113i	$0.100032\pi$
$881$			18.3500i			0.618227i	−0.951025	+	0.309113i	$0.899968\pi$
$882$	−10.9222	−	3.05693i	−0.367771	−	0.102932i
$883$	−23.7527	−	23.7527i	−0.799342	−	0.799342i	0.183650	−	0.982992i	$-0.441209\pi$
$883$	−23.7527	−	23.7527i	−0.799342	−	0.799342i	−0.982992	+	0.183650i	$0.941209\pi$
$884$	−16.5135	+	9.53406i	−0.555408	+	0.320665i
$885$		0			0
$886$	−0.0315340	+	0.0546184i	−0.00105940	+	0.00183494i
$887$	−10.0547	+	37.5247i	−0.337604	+	1.25996i	0.563414	+	0.826175i	$0.309488\pi$
$887$	−10.0547	+	37.5247i	−0.337604	+	1.25996i	−0.901018	+	0.433781i	$0.857179\pi$
$888$	2.21859	−	2.21859i	0.0744511	−	0.0744511i
$889$	36.3503	−	20.7187i	1.21915	−	0.694884i
$890$		0			0
$891$	−0.562452	−	0.974195i	−0.0188429	−	0.0326368i
$892$	4.28599	−	1.14843i	0.143506	−	0.0384522i
$893$	−8.60721	+	2.30629i	−0.288029	+	0.0771772i
$894$	2.31538	+	4.01035i	0.0774378	+	0.134126i
$895$		0			0
$896$	1.33557	−	2.28391i	0.0446183	−	0.0763001i
$897$	12.7746	−	12.7746i	0.426532	−	0.426532i
$898$	6.34642	−	23.6851i	0.211783	−	0.790384i
$899$	16.5847	−	28.7255i	0.553130	−	0.958049i
$900$		0			0
$901$	28.3251	−	16.3535i	0.943644	−	0.544813i
$902$	0.429644	+	0.429644i	0.0143056	+	0.0143056i
$903$	−4.98705	+	4.93201i	−0.165959	+	0.164127i
$904$			0.435281i			0.0144772i
$905$		0			0
$906$	20.2893	+	11.7140i	0.674067	+	0.389173i
$907$	−8.97748	−	33.5044i	−0.298092	−	1.11250i	−0.938730	−	0.344653i	$-0.887997\pi$
$907$	−8.97748	−	33.5044i	−0.298092	−	1.11250i	0.640638	−	0.767843i	$-0.278670\pi$
$908$	−0.648012	−	0.173634i	−0.0215050	−	0.00576226i
$909$	18.1174			0.600916
$910$		0			0
$911$	48.1523			1.59536			0.797678	−	0.603083i	$-0.206061\pi$
$911$	48.1523			1.59536			0.797678	+	0.603083i	$0.206061\pi$
$912$	2.14671	+	0.575209i	0.0710846	+	0.0190471i
$913$	−2.51182	−	9.37422i	−0.0831290	−	0.310242i
$914$	−17.3839	−	10.0366i	−0.575007	−	0.331980i
$915$		0			0
$916$		−	13.2033i		−	0.436250i
$917$	−24.5515	+	6.43273i	−0.810761	+	0.212428i
$918$	25.1745	+	25.1745i	0.830884	+	0.830884i
$919$	15.4242	−	8.90515i	0.508797	−	0.293754i	−0.223542	−	0.974694i	$-0.571762\pi$
$919$	15.4242	−	8.90515i	0.508797	−	0.293754i	0.732339	+	0.680940i	$0.238429\pi$
$920$		0			0
$921$	5.72435	−	9.91487i	0.188624	−	0.326706i
$922$	3.02662	−	11.2955i	0.0996763	−	0.371997i
$923$	32.9206	−	32.9206i	1.08360	−	1.08360i
$924$	1.14352	+	2.00627i	0.0376191	+	0.0660013i
$925$		0			0
$926$	1.96028	+	3.39531i	0.0644188	+	0.111577i
$927$	−3.79713	+	1.01744i	−0.124714	+	0.0334171i
$928$	−9.36112	+	2.50831i	−0.307294	+	0.0823392i
$929$	16.1326	+	27.9424i	0.529292	+	0.916761i	0.999416	+	0.0341607i	$0.0108758\pi$
$929$	16.1326	+	27.9424i	0.529292	+	0.916761i	−0.470124	+	0.882600i	$0.655791\pi$
$930$		0			0
$931$	−0.146998	+	13.2436i	−0.00481766	+	0.434040i
$932$	6.12279	−	6.12279i	0.200559	−	0.200559i
$933$	−0.0383114	+	0.142980i	−0.00125426	+	0.00468096i
$934$	−10.4604	+	18.1180i	−0.342276	+	0.592839i
$935$		0			0
$936$	4.07864	−	2.35481i	0.133315	−	0.0769692i
$937$	28.9650	+	28.9650i	0.946244	+	0.946244i	0.998627	−	0.0523829i	$-0.0166816\pi$
$937$	28.9650	+	28.9650i	0.946244	+	0.946244i	−0.0523829	+	0.998627i	$0.516682\pi$
$938$	9.56947	−	34.9370i	0.312454	−	1.14073i
$939$		−	13.7359i		−	0.448254i
$940$		0			0
$941$	30.8629	+	17.8187i	1.00610	+	0.580874i	0.910048	−	0.414502i	$-0.136044\pi$
$941$	30.8629	+	17.8187i	1.00610	+	0.580874i	0.0960550	+	0.995376i	$0.469378\pi$
$942$	2.26895	+	8.46784i	0.0739264	+	0.275897i
$943$	4.17936	+	1.11985i	0.136099	+	0.0364675i
$944$	−2.54975			−0.0829873
$945$		0			0
$946$	−1.67706			−0.0545259
$947$	13.4783	+	3.61149i	0.437985	+	0.117358i	0.471072	−	0.882095i	$-0.343867\pi$
$947$	13.4783	+	3.61149i	0.437985	+	0.117358i	−0.0330871	+	0.999452i	$0.510534\pi$
$948$	2.00127	+	7.46883i	0.0649982	+	0.242576i
$949$	−22.2792	−	12.8629i	−0.723214	−	0.417548i
$950$		0			0
$951$			12.8576i			0.416935i
$952$	−12.2046	−	12.3408i	−0.395553	−	0.399968i
$953$	−25.4475	−	25.4475i	−0.824326	−	0.824326i	0.162399	−	0.986725i	$-0.448077\pi$
$953$	−25.4475	−	25.4475i	−0.824326	−	0.824326i	−0.986725	+	0.162399i	$0.948077\pi$
$954$	−6.99597	+	4.03912i	−0.226503	+	0.130771i
$955$		0			0
$956$	2.00147	−	3.46665i	0.0647322	−	0.112120i
$957$	2.18931	−	8.17061i	0.0707703	−	0.264118i
$958$	−17.1712	+	17.1712i	−0.554775	+	0.554775i
$959$	0.136689	−	24.6304i	0.00441392	−	0.795356i
$960$		0			0
$961$	−9.64300	−	16.7022i	−0.311064	−	0.538779i
$962$	−7.49956	+	2.00950i	−0.241796	+	0.0647889i
$963$	−10.3928	+	2.78475i	−0.334904	+	0.0897373i
$964$	−8.66256	−	15.0040i	−0.279002	−	0.483246i
$965$		0			0
$966$	14.1954	+	8.30108i	0.456729	+	0.267083i
$967$	34.0735	−	34.0735i	1.09573	−	1.09573i	0.100827	−	0.994904i	$-0.467851\pi$
$967$	34.0735	−	34.0735i	1.09573	−	1.09573i	0.994904	−	0.100827i	$-0.0321488\pi$
$968$	2.70410	−	10.0918i	0.0869131	−	0.324364i
$969$	7.28974	−	12.6262i	0.234180	−	0.405612i
$970$		0			0
$971$	4.07547	−	2.35297i	0.130788	−	0.0755105i	−0.433179	−	0.901308i	$-0.642608\pi$
$971$	4.07547	−	2.35297i	0.130788	−	0.0755105i	0.563966	+	0.825798i	$0.309275\pi$
$972$	−10.2551	−	10.2551i	−0.328934	−	0.328934i
$973$	−56.5762	−	15.4966i	−1.81375	−	0.496797i
$974$			2.55599i			0.0818993i
$975$		0			0
$976$	5.25989	+	3.03680i	0.168365	+	0.0972055i
$977$	7.12351	+	26.5853i	0.227901	+	0.850540i	0.981221	+	0.192885i	$0.0617846\pi$
$977$	7.12351	+	26.5853i	0.227901	+	0.850540i	−0.753320	+	0.657654i	$0.771549\pi$
$978$	−13.8041	−	3.69879i	−0.441405	−	0.118274i
$979$	−4.48226			−0.143254
$980$		0			0
$981$	−14.5185			−0.463539
$982$	−14.0704	−	3.77017i	−0.449006	−	0.120311i
$983$	−11.6256	−	43.3874i	−0.370799	−	1.38384i	−0.859386	−	0.511327i	$-0.829154\pi$
$983$	−11.6256	−	43.3874i	−0.370799	−	1.38384i	0.488587	−	0.872515i	$-0.337513\pi$
$984$	−0.831801	−	0.480241i	−0.0265168	−	0.0153095i
$985$		0			0
$986$			63.5766i			2.02469i
$987$	14.1163	+	3.86654i	0.449326	+	0.123073i
$988$	−3.88878	−	3.88878i	−0.123719	−	0.123719i
$989$	−10.3424	+	5.97118i	−0.328869	+	0.189872i
$990$		0			0
$991$	3.08498	−	5.34334i	0.0979975	−	0.169737i	−0.812858	−	0.582462i	$-0.802090\pi$
$991$	3.08498	−	5.34334i	0.0979975	−	0.169737i	0.910856	+	0.412725i	$0.135423\pi$
$992$	0.885827	−	3.30595i	0.0281250	−	0.104964i
$993$	4.53527	−	4.53527i	0.143922	−	0.143922i
$994$	36.5820	+	21.3922i	1.16031	+	0.678519i
$995$		0			0
$996$	7.67055	+	13.2858i	0.243051	+	0.420976i
$997$	−18.1820	+	4.87184i	−0.575829	+	0.154293i	−0.534968	−	0.844872i	$-0.679676\pi$
$997$	−18.1820	+	4.87184i	−0.575829	+	0.154293i	−0.0408602	+	0.999165i	$0.513010\pi$
$998$	−29.0623	+	7.78721i	−0.919950	+	0.246500i
$999$	7.24821	+	12.5543i	0.229323	+	0.397199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.o.c.143.1		16
5.2	odd	4	inner	350.2.o.c.157.3		16
5.3	odd	4		70.2.k.a.17.2	yes	16
5.4	even	2		70.2.k.a.3.4	✓	16
7.5	odd	6	inner	350.2.o.c.243.3		16
15.8	even	4		630.2.bv.c.577.3		16
15.14	odd	2		630.2.bv.c.73.2		16
20.3	even	4		560.2.ci.c.17.2		16
20.19	odd	2		560.2.ci.c.353.2		16
35.3	even	12		490.2.g.c.97.3		16
35.4	even	6		490.2.g.c.293.3		16
35.9	even	6		490.2.l.c.313.1		16
35.12	even	12	inner	350.2.o.c.257.1		16
35.13	even	4		490.2.l.c.227.1		16
35.18	odd	12		490.2.g.c.97.2		16
35.19	odd	6		70.2.k.a.33.2	yes	16
35.23	odd	12		490.2.l.c.117.3		16
35.24	odd	6		490.2.g.c.293.2		16
35.33	even	12		70.2.k.a.47.4	yes	16
35.34	odd	2		490.2.l.c.423.3		16
105.68	odd	12		630.2.bv.c.397.2		16
105.89	even	6		630.2.bv.c.523.3		16
140.19	even	6		560.2.ci.c.33.2		16
140.103	odd	12		560.2.ci.c.257.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.4	✓	16	5.4	even	2
70.2.k.a.17.2	yes	16	5.3	odd	4
70.2.k.a.33.2	yes	16	35.19	odd	6
70.2.k.a.47.4	yes	16	35.33	even	12
350.2.o.c.143.1		16	1.1	even	1	trivial
350.2.o.c.157.3		16	5.2	odd	4	inner
350.2.o.c.243.3		16	7.5	odd	6	inner
350.2.o.c.257.1		16	35.12	even	12	inner
490.2.g.c.97.2		16	35.18	odd	12
490.2.g.c.97.3		16	35.3	even	12
490.2.g.c.293.2		16	35.24	odd	6
490.2.g.c.293.3		16	35.4	even	6
490.2.l.c.117.3		16	35.23	odd	12
490.2.l.c.227.1		16	35.13	even	4
490.2.l.c.313.1		16	35.9	even	6
490.2.l.c.423.3		16	35.34	odd	2
560.2.ci.c.17.2		16	20.3	even	4
560.2.ci.c.33.2		16	140.19	even	6
560.2.ci.c.257.2		16	140.103	odd	12
560.2.ci.c.353.2		16	20.19	odd	2
630.2.bv.c.73.2		16	15.14	odd	2
630.2.bv.c.397.2		16	105.68	odd	12
630.2.bv.c.523.3		16	105.89	even	6
630.2.bv.c.577.3		16	15.8	even	4

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.304013 - 1.13459i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.17462i q^{6} +(2.55176 + 0.698943i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.40320 - 0.810140i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.304013 - 1.13459i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.17462i q^{6} +(2.55176 + 0.698943i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.40320 - 0.810140i) q^{9} +(-0.371536 + 0.643519i) q^{11} +(0.304013 - 1.13459i) q^{12} +(-2.05532 + 2.05532i) q^{13} +(-2.28391 - 1.33557i) q^{14} +(0.500000 + 0.866025i) q^{16} +(6.33660 - 1.69789i) q^{17} +(-1.56507 + 0.419359i) q^{18} +(0.946027 + 1.63857i) q^{19} +(0.0172465 - 3.10769i) q^{21} +(0.525431 - 0.525431i) q^{22} +(1.36952 - 5.11112i) q^{23} +(-0.587308 + 1.01725i) q^{24} +(2.51725 - 1.45333i) q^{26} +(-3.83750 - 3.83750i) q^{27} +(1.86042 + 1.88118i) q^{28} -9.69135i q^{29} +(2.96403 + 1.71129i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.843083 + 0.225903i) q^{33} -6.56014 q^{34} +1.62028 q^{36} +(-2.58012 - 0.691342i) q^{37} +(-0.489700 - 1.82758i) q^{38} +(2.95680 + 1.70711i) q^{39} +0.817699i q^{41} +(-0.820989 + 2.99734i) q^{42} +(-1.59589 - 1.59589i) q^{43} +(-0.643519 + 0.371536i) q^{44} +(-2.64571 + 4.58251i) q^{46} +(-1.21894 + 4.54913i) q^{47} +(0.830578 - 0.830578i) q^{48} +(6.02296 + 3.56707i) q^{49} +(-3.85282 - 6.67328i) q^{51} +(-2.80762 + 0.752300i) q^{52} +(4.81583 - 1.29040i) q^{53} +(2.71352 + 4.69996i) q^{54} +(-1.31014 - 2.29859i) q^{56} +(1.57150 - 1.57150i) q^{57} +(-2.50831 + 9.36112i) q^{58} +(-1.27487 + 2.20815i) q^{59} +(5.25989 - 3.03680i) q^{61} +(-2.42012 - 2.42012i) q^{62} +(4.14688 - 1.08652i) q^{63} +1.00000i q^{64} +(-0.755887 - 0.436412i) q^{66} +(3.54358 + 13.2248i) q^{67} +(6.33660 + 1.69789i) q^{68} -6.21538 q^{69} -16.0173 q^{71} +(-1.56507 - 0.419359i) q^{72} +(2.29071 + 8.54906i) q^{73} +(2.31328 + 1.33557i) q^{74} +1.89205i q^{76} +(-1.39785 + 1.38242i) q^{77} +(-2.41421 - 2.41421i) q^{78} +(-5.70091 + 3.29142i) q^{79} +(-0.756928 + 1.31104i) q^{81} +(0.211636 - 0.789836i) q^{82} +(-9.23519 + 9.23519i) q^{83} +(1.56878 - 2.68272i) q^{84} +(1.12846 + 1.95456i) q^{86} +(-10.9957 + 2.94629i) q^{87} +(0.717752 - 0.192321i) q^{88} +(3.01603 + 5.22392i) q^{89} +(-6.68124 + 3.80814i) q^{91} +(3.74160 - 3.74160i) q^{92} +(1.04051 - 3.88322i) q^{93} +(2.35481 - 4.07864i) q^{94} +(-1.01725 + 0.587308i) q^{96} +(-3.16693 - 3.16693i) q^{97} +(-4.89451 - 5.00438i) q^{98} +1.20398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 12 q^{11} + 8 q^{16} + 36 q^{17} + 8 q^{18} - 28 q^{21} + 8 q^{22} + 4 q^{23} + 12 q^{26} - 4 q^{28} + 24 q^{31} - 48 q^{33} - 8 q^{36} - 4 q^{37} - 24 q^{38} - 36 q^{42} + 8 q^{43} - 8 q^{46} - 12 q^{47} - 16 q^{51} + 28 q^{53} - 4 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{61} + 36 q^{63} - 32 q^{67} + 36 q^{68} + 16 q^{71} + 8 q^{72} + 12 q^{73} - 16 q^{77} - 16 q^{78} + 48 q^{82} + 12 q^{86} + 24 q^{87} + 4 q^{88} - 16 q^{91} - 8 q^{92} - 28 q^{93} + 12 q^{96} - 40 q^{98}+O(q^{100}) \) 16 * q - 8 * q^7 - 12 * q^11 + 8 * q^16 + 36 * q^17 + 8 * q^18 - 28 * q^21 + 8 * q^22 + 4 * q^23 + 12 * q^26 - 4 * q^28 + 24 * q^31 - 48 * q^33 - 8 * q^36 - 4 * q^37 - 24 * q^38 - 36 * q^42 + 8 * q^43 - 8 * q^46 - 12 * q^47 - 16 * q^51 + 28 * q^53 - 4 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^61 + 36 * q^63 - 32 * q^67 + 36 * q^68 + 16 * q^71 + 8 * q^72 + 12 * q^73 - 16 * q^77 - 16 * q^78 + 48 * q^82 + 12 * q^86 + 24 * q^87 + 4 * q^88 - 16 * q^91 - 8 * q^92 - 28 * q^93 + 12 * q^96 - 40 * q^98

Introduction

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