LMFDB - Embedded newform 490.2.l.c.313.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(117,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("490.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.l (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:	$3.91266969904$
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			313.1
Root			$1.45333 + 1.51725i$ of defining polynomial
Character	$\chi$	$=$	490.313
Dual form			490.2.l.c.227.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-1.13459 - 0.304013i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.264946 + 2.22032i) q^{5} +1.17462i q^{6} +(0.707107 + 0.707107i) q^{8} +(-1.40320 - 0.810140i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.13459 - 0.304013i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.264946 + 2.22032i) q^{5} +1.17462i q^{6} +(0.707107 + 0.707107i) q^{8} +(-1.40320 - 0.810140i) q^{9} +(2.21323 - 0.318742i) q^{10} +(-0.371536 - 0.643519i) q^{11} +(1.13459 - 0.304013i) q^{12} +(2.05532 - 2.05532i) q^{13} +(0.975610 - 2.43860i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.69789 - 6.33660i) q^{17} +(-0.419359 + 1.56507i) q^{18} +(0.946027 - 1.63857i) q^{19} +(-0.880708 - 2.05532i) q^{20} +(-0.525431 + 0.525431i) q^{22} +(5.11112 - 1.36952i) q^{23} +(-0.587308 - 1.01725i) q^{24} +(-4.85961 - 1.17653i) q^{25} +(-2.51725 - 1.45333i) q^{26} +(3.83750 + 3.83750i) q^{27} -9.69135i q^{29} +(-2.60802 - 0.311210i) q^{30} +(-2.96403 + 1.71129i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.225903 + 0.843083i) q^{33} -6.56014 q^{34} +1.62028 q^{36} +(-0.691342 - 2.58012i) q^{37} +(-1.82758 - 0.489700i) q^{38} +(-2.95680 + 1.70711i) q^{39} +(-1.75735 + 1.38266i) q^{40} +0.817699i q^{41} +(1.59589 + 1.59589i) q^{43} +(0.643519 + 0.371536i) q^{44} +(2.17054 - 2.90091i) q^{45} +(-2.64571 - 4.58251i) q^{46} +(-4.54913 + 1.21894i) q^{47} +(-0.830578 + 0.830578i) q^{48} +(0.121320 + 4.99853i) q^{50} +(-3.85282 + 6.67328i) q^{51} +(-0.752300 + 2.80762i) q^{52} +(1.29040 - 4.81583i) q^{53} +(2.71352 - 4.69996i) q^{54} +(1.52725 - 0.654429i) q^{55} +(-1.57150 + 1.57150i) q^{57} +(-9.36112 + 2.50831i) q^{58} +(-1.27487 - 2.20815i) q^{59} +(0.374399 + 2.59970i) q^{60} +(-5.25989 - 3.03680i) q^{61} +(2.42012 + 2.42012i) q^{62} +1.00000i q^{64} +(4.01892 + 5.10802i) q^{65} +(0.755887 - 0.436412i) q^{66} +(13.2248 + 3.54358i) q^{67} +(1.69789 + 6.33660i) q^{68} -6.21538 q^{69} -16.0173 q^{71} +(-0.419359 - 1.56507i) q^{72} +(8.54906 + 2.29071i) q^{73} +(-2.31328 + 1.33557i) q^{74} +(5.15599 + 2.81226i) q^{75} +1.89205i q^{76} +(2.41421 + 2.41421i) q^{78} +(5.70091 + 3.29142i) q^{79} +(1.79038 + 1.33961i) q^{80} +(-0.756928 - 1.31104i) q^{81} +(0.789836 - 0.211636i) q^{82} +(9.23519 - 9.23519i) q^{83} +(13.6194 + 5.44871i) q^{85} +(1.12846 - 1.95456i) q^{86} +(-2.94629 + 10.9957i) q^{87} +(0.192321 - 0.717752i) q^{88} +(3.01603 - 5.22392i) q^{89} +(-3.36384 - 1.34577i) q^{90} +(-3.74160 + 3.74160i) q^{92} +(3.88322 - 1.04051i) q^{93} +(2.35481 + 4.07864i) q^{94} +(3.38749 + 2.53461i) q^{95} +(1.01725 + 0.587308i) q^{96} +(3.16693 + 3.16693i) q^{97} +1.20398i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5}+O(q^{10}) $ 16 * q + 12 * q^5	$ 16 q + 12 q^{5} + 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} + 36 q^{17} - 8 q^{18} - 8 q^{22} - 4 q^{23} + 12 q^{25} - 12 q^{26} + 20 q^{30} - 24 q^{31} - 48 q^{33} - 8 q^{36} + 4 q^{37} - 24 q^{38} - 8 q^{43} + 12 q^{45} - 8 q^{46} - 12 q^{47} - 32 q^{50} - 16 q^{51} - 28 q^{53} + 8 q^{57} - 32 q^{58} + 8 q^{60} + 12 q^{61} - 8 q^{65} + 32 q^{67} + 36 q^{68} + 16 q^{71} - 8 q^{72} + 12 q^{73} + 48 q^{75} + 16 q^{78} + 12 q^{80} + 48 q^{82} + 24 q^{85} + 12 q^{86} + 24 q^{87} - 4 q^{88} + 8 q^{92} + 28 q^{93} + 20 q^{95} - 12 q^{96}+O(q^{100}) $ 16 * q + 12 * q^5 + 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 + 36 * q^17 - 8 * q^18 - 8 * q^22 - 4 * q^23 + 12 * q^25 - 12 * q^26 + 20 * q^30 - 24 * q^31 - 48 * q^33 - 8 * q^36 + 4 * q^37 - 24 * q^38 - 8 * q^43 + 12 * q^45 - 8 * q^46 - 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 + 8 * q^57 - 32 * q^58 + 8 * q^60 + 12 * q^61 - 8 * q^65 + 32 * q^67 + 36 * q^68 + 16 * q^71 - 8 * q^72 + 12 * q^73 + 48 * q^75 + 16 * q^78 + 12 * q^80 + 48 * q^82 + 24 * q^85 + 12 * q^86 + 24 * q^87 - 4 * q^88 + 8 * q^92 + 28 * q^93 + 20 * q^95 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−1.13459	−	0.304013i	−0.655056	−	0.175522i	−0.0840425	−	0.996462i	$-0.526783\pi$
$3$	−1.13459	−	0.304013i	−0.655056	−	0.175522i	−0.571014	+	0.820940i	$0.693450\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.264946	+	2.22032i	−0.118487	+	0.992956i
$5$	−0.264946	+	2.22032i	−0.118487	+	0.992956i
$6$			1.17462i			0.479535i
$7$		0			0
$7$		0			0
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.40320	−	0.810140i	−0.467734	−	0.270047i
$10$	2.21323	−	0.318742i	0.699886	−	0.100795i
$11$	−0.371536	−	0.643519i	−0.112022	−	0.194028i	0.804563	−	0.593867i	$-0.202399\pi$
$11$	−0.371536	−	0.643519i	−0.112022	−	0.194028i	−0.916586	+	0.399839i	$0.869066\pi$
$12$	1.13459	−	0.304013i	0.327528	−	0.0877609i
$13$	2.05532	−	2.05532i	0.570044	−	0.570044i	−0.362097	−	0.932141i	$-0.617939\pi$
$13$	2.05532	−	2.05532i	0.570044	−	0.570044i	0.932141	+	0.362097i	$0.117939\pi$
$14$		0			0
$15$	0.975610	−	2.43860i	0.251901	−	0.629645i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.69789	−	6.33660i	0.411798	−	1.53685i	−0.379365	−	0.925247i	$-0.623857\pi$
$17$	1.69789	−	6.33660i	0.411798	−	1.53685i	0.791163	−	0.611605i	$-0.209476\pi$
$18$	−0.419359	+	1.56507i	−0.0988439	+	0.368890i
$19$	0.946027	−	1.63857i	0.217033	−	0.375913i	−0.736866	−	0.676039i	$-0.763695\pi$
$19$	0.946027	−	1.63857i	0.217033	−	0.375913i	0.953900	+	0.300126i	$0.0970286\pi$
$20$	−0.880708	−	2.05532i	−0.196932	−	0.459584i
$21$		0			0
$22$	−0.525431	+	0.525431i	−0.112022	+	0.112022i
$23$	5.11112	−	1.36952i	1.06574	−	0.285565i	0.317000	−	0.948426i	$-0.397325\pi$
$23$	5.11112	−	1.36952i	1.06574	−	0.285565i	0.748743	+	0.662861i	$0.230658\pi$
$24$	−0.587308	−	1.01725i	−0.119884	−	0.207645i
$25$	−4.85961	−	1.17653i	−0.971921	−	0.235306i
$26$	−2.51725	−	1.45333i	−0.493673	−	0.285022i
$27$	3.83750	+	3.83750i	0.738528	+	0.738528i
$28$		0			0
$29$		−	9.69135i		−	1.79964i	−0.436263	−	0.899819i	$-0.643698\pi$
$29$		−	9.69135i		−	1.79964i	0.436263	−	0.899819i	$-0.356302\pi$
$30$	−2.60802	−	0.311210i	−0.476157	−	0.0568188i
$31$	−2.96403	+	1.71129i	−0.532356	+	0.307356i	−0.741975	−	0.670427i	$-0.766111\pi$
$31$	−2.96403	+	1.71129i	−0.532356	+	0.307356i	0.209619	+	0.977783i	$0.432778\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	0.225903	+	0.843083i	0.0393247	+	0.146762i
$34$	−6.56014			−1.12505
$35$		0			0
$36$	1.62028			0.270047
$37$	−0.691342	−	2.58012i	−0.113656	−	0.424170i	0.885527	−	0.464588i	$-0.153798\pi$
$37$	−0.691342	−	2.58012i	−0.113656	−	0.424170i	−0.999183	+	0.0404183i	$0.987131\pi$
$38$	−1.82758	−	0.489700i	−0.296473	−	0.0794398i
$39$	−2.95680	+	1.70711i	−0.473466	+	0.273356i
$40$	−1.75735	+	1.38266i	−0.277861	+	0.218617i
$41$			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			0
$43$	1.59589	+	1.59589i	0.243371	+	0.243371i	0.818243	−	0.574872i	$-0.194948\pi$
$43$	1.59589	+	1.59589i	0.243371	+	0.243371i	−0.574872	+	0.818243i	$0.694948\pi$
$44$	0.643519	+	0.371536i	0.0970142	+	0.0560111i
$45$	2.17054	−	2.90091i	0.323565	−	0.432442i
$46$	−2.64571	−	4.58251i	−0.390089	−	0.675654i
$47$	−4.54913	+	1.21894i	−0.663560	+	0.177800i	−0.574852	−	0.818257i	$-0.694940\pi$
$47$	−4.54913	+	1.21894i	−0.663560	+	0.177800i	−0.0887076	+	0.996058i	$0.528274\pi$
$48$	−0.830578	+	0.830578i	−0.119884	+	0.119884i
$49$		0			0
$50$	0.121320	+	4.99853i	0.0171573	+	0.706899i
$51$	−3.85282	+	6.67328i	−0.539502	+	0.934445i
$52$	−0.752300	+	2.80762i	−0.104325	+	0.389347i
$53$	1.29040	−	4.81583i	0.177250	−	0.661505i	−0.818908	−	0.573925i	$-0.805420\pi$
$53$	1.29040	−	4.81583i	0.177250	−	0.661505i	0.996158	−	0.0875798i	$-0.0279133\pi$
$54$	2.71352	−	4.69996i	0.369264	−	0.639584i
$55$	1.52725	−	0.654429i	0.205935	−	0.0882432i
$56$		0			0
$57$	−1.57150	+	1.57150i	−0.208150	+	0.208150i
$58$	−9.36112	+	2.50831i	−1.22918	+	0.329357i
$59$	−1.27487	−	2.20815i	−0.165975	−	0.287476i	0.771026	−	0.636803i	$-0.219744\pi$
$59$	−1.27487	−	2.20815i	−0.165975	−	0.287476i	−0.937001	+	0.349327i	$0.886410\pi$
$60$	0.374399	+	2.59970i	0.0483347	+	0.335620i
$61$	−5.25989	−	3.03680i	−0.673460	−	0.388822i	0.123927	−	0.992291i	$-0.460451\pi$
$61$	−5.25989	−	3.03680i	−0.673460	−	0.388822i	−0.797386	+	0.603469i	$0.793785\pi$
$62$	2.42012	+	2.42012i	0.307356	+	0.307356i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	4.01892	+	5.10802i	0.498485	+	0.633572i
$66$	0.755887	−	0.436412i	0.0930433	−	0.0537186i
$67$	13.2248	+	3.54358i	1.61567	+	0.432917i	0.949725	−	0.313084i	$-0.101362\pi$
$67$	13.2248	+	3.54358i	1.61567	+	0.432917i	0.665944	+	0.746002i	$0.268029\pi$
$68$	1.69789	+	6.33660i	0.205899	+	0.768426i
$69$	−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	$0.899377\pi$
$72$	−0.419359	−	1.56507i	−0.0494220	−	0.184445i
$73$	8.54906	+	2.29071i	1.00059	+	0.268108i	0.721693	−	0.692213i	$-0.243364\pi$
$73$	8.54906	+	2.29071i	1.00059	+	0.268108i	0.278898	+	0.960321i	$0.410031\pi$
$74$	−2.31328	+	1.33557i	−0.268913	+	0.155257i
$75$	5.15599	+	2.81226i	0.595362	+	0.324732i
$76$			1.89205i			0.217033i
$77$		0			0
$78$	2.41421	+	2.41421i	0.273356	+	0.273356i
$79$	5.70091	+	3.29142i	0.641402	+	0.370314i	0.785155	−	0.619300i	$-0.212583\pi$
$79$	5.70091	+	3.29142i	0.641402	+	0.370314i	−0.143752	+	0.989614i	$0.545917\pi$
$80$	1.79038	+	1.33961i	0.200170	+	0.149773i
$81$	−0.756928	−	1.31104i	−0.0841031	−	0.145671i
$82$	0.789836	−	0.211636i	0.0872228	−	0.0233713i
$83$	9.23519	−	9.23519i	1.01369	−	1.01369i	0.0137887	−	0.999905i	$-0.495611\pi$
$83$	9.23519	−	9.23519i	1.01369	−	1.01369i	0.999905	−	0.0137887i	$-0.00438921\pi$
$84$		0			0
$85$	13.6194	+	5.44871i	1.47723	+	0.590995i
$86$	1.12846	−	1.95456i	0.121685	−	0.210765i
$87$	−2.94629	+	10.9957i	−0.315876	+	1.17886i
$88$	0.192321	−	0.717752i	0.0205015	−	0.0765127i
$89$	3.01603	−	5.22392i	0.319699	−	0.553735i	−0.660726	−	0.750627i	$-0.729752\pi$
$89$	3.01603	−	5.22392i	0.319699	−	0.553735i	0.980425	+	0.196892i	$0.0630849\pi$
$90$	−3.36384	−	1.34577i	−0.354580	−	0.141856i
$91$		0			0
$92$	−3.74160	+	3.74160i	−0.390089	+	0.390089i
$93$	3.88322	−	1.04051i	0.402671	−	0.107895i
$94$	2.35481	+	4.07864i	0.242880	+	0.420680i
$95$	3.38749	+	2.53461i	0.347549	+	0.260046i
$96$	1.01725	+	0.587308i	0.103822	+	0.0599418i
$97$	3.16693	+	3.16693i	0.321553	+	0.321553i	0.849363	−	0.527810i	$-0.176987\pi$
$97$	3.16693	+	3.16693i	0.321553	+	0.321553i	−0.527810	+	0.849363i	$0.676987\pi$
$98$		0			0
$99$			1.20398i			0.121005i
$100$	4.79681	−	1.41090i	0.479681	−	0.141090i
$101$	−9.68359	+	5.59083i	−0.963554	+	0.556308i	−0.897265	−	0.441493i	$-0.854449\pi$
$101$	−9.68359	+	5.59083i	−0.963554	+	0.556308i	−0.0662887	+	0.997800i	$0.521116\pi$
$102$	7.44307	+	1.99437i	0.736974	+	0.197472i
$103$	−0.627940	−	2.34351i	−0.0618728	−	0.230912i	0.928064	−	0.372420i	$-0.121472\pi$
$103$	−0.627940	−	2.34351i	−0.0618728	−	0.230912i	−0.989937	+	0.141507i	$0.954805\pi$
$104$	2.90667			0.285022
$105$		0			0
$106$	−4.98571			−0.484255
$107$	−1.71868	−	6.41422i	−0.166151	−	0.620086i	−0.997891	−	0.0649189i	$-0.979321\pi$
$107$	−1.71868	−	6.41422i	−0.166151	−	0.620086i	0.831739	−	0.555167i	$-0.187346\pi$
$108$	−5.24213	−	1.40462i	−0.504424	−	0.135160i
$109$	7.76000	−	4.48024i	0.743274	−	0.429129i	−0.0799848	−	0.996796i	$-0.525487\pi$
$109$	7.76000	−	4.48024i	0.743274	−	0.429129i	0.823258	+	0.567667i	$0.192154\pi$
$110$	−1.02741	−	1.30583i	−0.0979599	−	0.124506i
$111$			3.13756i			0.297804i
$112$		0			0
$113$	0.307790	+	0.307790i	0.0289545	+	0.0289545i	0.721436	−	0.692481i	$-0.243482\pi$
$113$	0.307790	+	0.307790i	0.0289545	+	0.0289545i	−0.692481	+	0.721436i	$0.743482\pi$
$114$	1.92469	+	1.11122i	0.180263	+	0.104075i
$115$	1.68660	+	11.7112i	0.157276	+	1.09207i
$116$	4.84567	+	8.39295i	0.449910	+	0.779266i
$117$	−4.54913	+	1.21894i	−0.420568	+	0.112691i
$118$	−1.80295	+	1.80295i	−0.165975	+	0.165975i
$119$		0			0
$120$	2.41421	−	1.03449i	0.220387	−	0.0944359i
$121$	5.22392	−	9.04810i	0.474902	−	0.822554i
$122$	−1.57196	+	5.86664i	−0.142319	+	0.531141i
$123$	0.248591	−	0.927753i	0.0224147	−	0.0836527i
$124$	1.71129	−	2.96403i	0.153678	−	0.266178i
$125$	3.89980	−	10.4781i	0.348808	−	0.937194i
$126$		0			0
$127$	−11.1823	+	11.1823i	−0.992267	+	0.992267i	−0.999970	−	0.00770296i	$-0.997548\pi$
$127$	−11.1823	+	11.1823i	−0.992267	+	0.992267i	0.00770296	+	0.999970i	$0.497548\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−1.32551	−	2.29585i	−0.116705	−	0.202139i
$130$	3.89379	−	5.20403i	0.341508	−	0.456423i
$131$	8.30763	+	4.79641i	0.725841	+	0.419064i	0.816899	−	0.576781i	$-0.195692\pi$
$131$	8.30763	+	4.79641i	0.725841	+	0.419064i	−0.0910579	+	0.995846i	$0.529025\pi$
$132$	−0.617179	−	0.617179i	−0.0537186	−	0.0537186i
$133$		0			0
$134$		−	13.6913i		−	1.18275i
$135$	−9.53720	+	7.50374i	−0.820832	+	0.645819i
$136$	5.68124	−	3.28007i	0.487163	−	0.281264i
$137$	−8.99233	−	2.40949i	−0.768267	−	0.205856i	−0.146661	−	0.989187i	$-0.546853\pi$
$137$	−8.99233	−	2.40949i	−0.768267	−	0.205856i	−0.621606	+	0.783330i	$0.713519\pi$
$138$	1.60866	+	6.00360i	0.136938	+	0.511060i
$139$	−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
$142$	4.14557	+	15.4715i	0.347889	+	1.29834i
$143$	−2.08627	−	0.559013i	−0.174462	−	0.0467470i
$144$	−1.40320	+	0.810140i	−0.116934	+	0.0675116i
$145$	21.5179	+	2.56768i	1.78696	+	0.213235i
$146$		−	8.85064i		−	0.732484i
$147$		0			0
$148$	1.88878	+	1.88878i	0.155257	+	0.155257i
$149$	−3.41418	−	1.97118i	−0.279701	−	0.161485i	0.353587	−	0.935402i	$-0.384962\pi$
$149$	−3.41418	−	1.97118i	−0.279701	−	0.161485i	−0.633288	+	0.773916i	$0.718295\pi$
$150$	1.38197	−	5.70817i	0.112837	−	0.466070i
$151$	9.97267	+	17.2732i	0.811564	+	1.40567i	0.911769	+	0.410703i	$0.134717\pi$
$151$	9.97267	+	17.2732i	0.811564	+	1.40567i	−0.100205	+	0.994967i	$0.531950\pi$
$152$	1.82758	−	0.489700i	0.148237	−	0.0397199i
$153$	−7.51602	+	7.51602i	−0.607634	+	0.607634i
$154$		0			0
$155$	−3.01429	−	7.03449i	−0.242113	−	0.565024i
$156$	1.70711	−	2.95680i	0.136678	−	0.236733i
$157$	1.93165	−	7.20903i	0.154163	−	0.575343i	−0.845013	−	0.534746i	$-0.820407\pi$
$157$	1.93165	−	7.20903i	0.154163	−	0.575343i	0.999176	−	0.0405972i	$-0.0129261\pi$
$158$	1.70376	−	6.35854i	0.135544	−	0.505858i
$159$	−2.92815	+	5.07170i	−0.232217	+	0.402212i
$160$	0.830578	−	2.07609i	0.0656630	−	0.164129i
$161$		0			0
$162$	−1.07046	+	1.07046i	−0.0841031	+	0.0841031i
$163$	−11.7520	+	3.14893i	−0.920486	+	0.246644i	−0.687793	−	0.725907i	$-0.741420\pi$
$163$	−11.7520	+	3.14893i	−0.920486	+	0.246644i	−0.232693	+	0.972550i	$0.574754\pi$
$164$	−0.408849	−	0.708148i	−0.0319258	−	0.0552970i
$165$	−1.93176	+	0.278205i	−0.150387	+	0.0216583i
$166$	−11.3107	−	6.53026i	−0.877884	−	0.506847i
$167$	1.45564	+	1.45564i	0.112641	+	0.112641i	0.761181	−	0.648540i	$-0.224620\pi$
$167$	1.45564	+	1.45564i	0.112641	+	0.112641i	−0.648540	+	0.761181i	$0.724620\pi$
$168$		0			0
$169$			4.55129i			0.350099i
$170$	1.73808	−	14.5656i	0.133305	−	1.11713i
$171$	−2.65494	+	1.53283i	−0.203028	+	0.117218i
$172$	−2.18003	−	0.584136i	−0.166225	−	0.0445400i
$173$	−2.43499	−	9.08750i	−0.185129	−	0.690910i	−0.994603	−	0.103754i	$-0.966914\pi$
$173$	−2.43499	−	9.08750i	−0.185129	−	0.690910i	0.809474	−	0.587155i	$-0.199752\pi$
$174$	11.3836			0.862989
$175$		0			0
$176$	−0.743072			−0.0560111
$177$	0.775156	+	2.89292i	0.0582643	+	0.217445i
$178$	−5.82653	−	1.56121i	−0.436717	−	0.117018i
$179$	−3.89494	+	2.24874i	−0.291121	+	0.168079i	−0.638447	−	0.769665i	$-0.720423\pi$
$179$	−3.89494	+	2.24874i	−0.291121	+	0.168079i	0.347326	+	0.937744i	$0.387090\pi$
$180$	−0.429287	+	3.59753i	−0.0319971	+	0.268144i
$181$			17.8850i			1.32938i	0.747118	+	0.664691i	$0.231437\pi$
$181$			17.8850i			1.32938i	−0.747118	+	0.664691i	$0.768563\pi$
$182$		0			0
$183$	5.04460	+	5.04460i	0.372907	+	0.372907i
$184$	4.58251	+	2.64571i	0.337827	+	0.195044i
$185$	5.91186	−	0.851405i	0.434649	−	0.0625965i
$186$	−2.01010	−	3.48160i	−0.147388	−	0.255283i
$187$	−4.70855	+	1.26165i	−0.344323	+	0.0922612i
$188$	3.33020	−	3.33020i	0.242880	−	0.242880i
$189$		0			0
$190$	1.57150	−	3.92807i	0.114009	−	0.284972i
$191$	1.38774	−	2.40364i	0.100413	−	0.173921i	−0.811442	−	0.584433i	$-0.801317\pi$
$191$	1.38774	−	2.40364i	0.100413	−	0.173921i	0.911855	+	0.410512i	$0.134650\pi$
$192$	0.304013	−	1.13459i	0.0219402	−	0.0818821i
$193$	−1.33034	+	4.96491i	−0.0957602	+	0.357382i	−0.997134	−	0.0756607i	$-0.975893\pi$
$193$	−1.33034	+	4.96491i	−0.0957602	+	0.357382i	0.901373	+	0.433043i	$0.142560\pi$
$194$	2.23936	−	3.87868i	0.160776	−	0.278473i
$195$	−3.00693	−	7.01731i	−0.215330	−	0.502520i
$196$		0			0
$197$	1.34043	−	1.34043i	0.0955019	−	0.0955019i	−0.657742	−	0.753244i	$-0.728488\pi$
$197$	1.34043	−	1.34043i	0.0955019	−	0.0955019i	0.753244	+	0.657742i	$0.228488\pi$
$198$	1.16296	−	0.311614i	0.0826479	−	0.0221454i
$199$	−7.25148	−	12.5599i	−0.514043	−	0.890349i	−0.999867	−	0.0162926i	$-0.994814\pi$
$199$	−7.25148	−	12.5599i	−0.514043	−	0.890349i	0.485824	−	0.874057i	$-0.338520\pi$
$200$	−2.60433	−	4.26819i	−0.184154	−	0.301807i
$201$	−13.9275	−	8.04103i	−0.982368	−	0.567171i
$202$	7.90662	+	7.90662i	0.556308	+	0.556308i
$203$		0			0
$204$		−	7.70563i		−	0.539502i
$205$	−1.81555	−	0.216646i	−0.126803	−	0.0151312i
$206$	−2.10113	+	1.21309i	−0.146393	+	0.0845198i
$207$	−8.28144	−	2.21901i	−0.575600	−	0.154232i
$208$	−0.752300	−	2.80762i	−0.0521627	−	0.194674i
$209$	−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	$0.387767\pi$
$212$	1.29040	+	4.81583i	0.0886249	+	0.330752i
$213$	18.1730	+	4.86945i	1.24520	+	0.333649i
$214$	−5.75083	+	3.32024i	−0.393119	+	0.226967i
$215$	−3.96620	+	3.12055i	−0.270493	+	0.212820i
$216$			5.42705i			0.369264i
$217$		0			0
$218$	−6.33602	−	6.33602i	−0.429129	−	0.429129i
$219$	−9.00328	−	5.19804i	−0.608385	−	0.351251i
$220$	−0.995425	+	1.33038i	−0.0671115	+	0.0896941i
$221$	−9.53406	−	16.5135i	−0.641330	−	1.11082i
$222$	3.03065	−	0.812061i	0.203404	−	0.0545020i
$223$	−3.13756	+	3.13756i	−0.210107	+	0.210107i	−0.804313	−	0.594206i	$-0.797466\pi$
$223$	−3.13756	+	3.13756i	−0.210107	+	0.210107i	0.594206	+	0.804313i	$0.297466\pi$
$224$		0			0
$225$	5.86586	+	5.58787i	0.391058	+	0.372525i
$226$	0.217641	−	0.376965i	0.0144772	−	0.0250753i
$227$	−0.173634	+	0.648012i	−0.0115245	+	0.0430101i	−0.971449	−	0.237250i	$-0.923754\pi$
$227$	−0.173634	+	0.648012i	−0.0115245	+	0.0430101i	0.959924	+	0.280260i	$0.0904207\pi$
$228$	0.575209	−	2.14671i	0.0380941	−	0.142169i
$229$	−6.60166	+	11.4344i	−0.436250	+	0.755608i	−0.997397	−	0.0721088i	$-0.977027\pi$
$229$	−6.60166	+	11.4344i	−0.436250	+	0.755608i	0.561146	+	0.827717i	$0.310360\pi$
$230$	10.8756	−	4.66020i	0.717115	−	0.307284i
$231$		0			0
$232$	6.85282	−	6.85282i	0.449910	−	0.449910i
$233$	8.36389	−	2.24110i	0.547937	−	0.146819i	0.0257782	−	0.999668i	$-0.491794\pi$
$233$	8.36389	−	2.24110i	0.547937	−	0.146819i	0.522158	+	0.852849i	$0.325127\pi$
$234$	2.35481	+	4.07864i	0.153938	+	0.266629i
$235$	−1.50115	−	10.4235i	−0.0979243	−	0.679952i
$236$	2.20815	+	1.27487i	0.143738	+	0.0829873i
$237$	−5.46757	−	5.46757i	−0.355157	−	0.355157i
$238$		0			0
$239$		−	4.00294i		−	0.258929i	−0.991584	−	0.129464i	$-0.958674\pi$
$239$		−	4.00294i		−	0.258929i	0.991584	−	0.129464i	$-0.0413258\pi$
$240$	−1.62409	−	2.06420i	−0.104834	−	0.133244i
$241$	15.0040	−	8.66256i	0.966493	−	0.558005i	0.0683274	−	0.997663i	$-0.478234\pi$
$241$	15.0040	−	8.66256i	0.966493	−	0.558005i	0.898165	+	0.439658i	$0.144900\pi$
$242$	−10.0918	−	2.70410i	−0.648728	−	0.173826i
$243$	−3.75364	−	14.0088i	−0.240796	−	0.898663i
$244$	6.07359			0.388822
$245$		0			0
$246$	−0.960481			−0.0612380
$247$	−1.42339	−	5.31218i	−0.0905683	−	0.338006i
$248$	−3.30595	−	0.885827i	−0.209928	−	0.0562501i
$249$	−13.2858	+	7.67055i	−0.841952	+	0.486101i
$250$	−11.1305	−	1.05497i	−0.703952	−	0.0667222i
$251$		−	5.49938i		−	0.347118i	−0.984824	−	0.173559i	$-0.944473\pi$
$251$		−	5.49938i		−	0.347118i	0.984824	−	0.173559i	$-0.0555267\pi$
$252$		0			0
$253$	−2.78028	−	2.78028i	−0.174795	−	0.174795i
$254$	13.6954	+	7.90707i	0.859329	+	0.496134i
$255$	−13.7960	−	10.3225i	−0.863939	−	0.646422i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.9473	+	4.27307i	−0.994766	+	0.266547i	−0.719251	−	0.694750i	$-0.755515\pi$
$257$	−15.9473	+	4.27307i	−0.994766	+	0.266547i	−0.275515	+	0.961297i	$0.588848\pi$
$258$	−1.87456	+	1.87456i	−0.116705	+	0.116705i
$259$		0			0
$260$	−6.03449	−	2.41421i	−0.374243	−	0.149723i
$261$	−7.85135	+	13.5989i	−0.485986	+	0.841753i
$262$	2.48280	−	9.26595i	0.153388	−	0.572453i
$263$	−2.55217	+	9.52484i	−0.157374	+	0.587327i	0.841517	+	0.540231i	$0.181663\pi$
$263$	−2.55217	+	9.52484i	−0.157374	+	0.587327i	−0.998890	+	0.0470956i	$0.985003\pi$
$264$	−0.436412	+	0.755887i	−0.0268593	+	0.0465216i
$265$	10.3508	+	4.14102i	0.635843	+	0.254381i
$266$		0			0
$267$	−5.01010	+	5.01010i	−0.306613	+	0.306613i
$268$	−13.2248	+	3.54358i	−0.807835	+	0.216459i
$269$	−4.47922	−	7.75824i	−0.273103	−	0.473028i	0.696552	−	0.717506i	$-0.254717\pi$
$269$	−4.47922	−	7.75824i	−0.273103	−	0.473028i	−0.969655	+	0.244478i	$0.921383\pi$
$270$	9.71647	+	7.27012i	0.591325	+	0.442445i
$271$	19.7889	+	11.4251i	1.20209	+	0.694027i	0.961020	−	0.276480i	$-0.0891680\pi$
$271$	19.7889	+	11.4251i	1.20209	+	0.694027i	0.241071	+	0.970507i	$0.422501\pi$
$272$	−4.63872	−	4.63872i	−0.281264	−	0.281264i
$273$		0			0
$274$			9.30954i			0.562410i
$275$	1.04840	+	3.56437i	0.0632209	+	0.214940i
$276$	5.38268	−	3.10769i	0.323999	−	0.187061i
$277$	−20.7995	−	5.57320i	−1.24972	−	0.334861i	−0.427491	−	0.904019i	$-0.640603\pi$
$277$	−20.7995	−	5.57320i	−1.24972	−	0.334861i	−0.822228	+	0.569158i	$0.807269\pi$
$278$	5.73839	+	21.4160i	0.344166	+	1.28444i
$279$	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	$0.553889\pi$
$282$	−1.43178	−	5.34348i	−0.0852614	−	0.318200i
$283$	2.82870	+	0.757948i	0.168149	+	0.0450553i	0.341911	−	0.939732i	$-0.388926\pi$
$283$	2.82870	+	0.757948i	0.168149	+	0.0450553i	−0.173762	+	0.984788i	$0.555592\pi$
$284$	13.8714	−	8.00863i	0.823113	−	0.475225i
$285$	−3.07286	−	3.90559i	−0.182021	−	0.231347i
$286$			2.15986i			0.127715i
$287$		0			0
$288$	1.14571	+	1.14571i	0.0675116	+	0.0675116i
$289$	−22.5473	−	13.0177i	−1.32631	−	0.765747i
$290$	−3.08904	−	21.4492i	−0.181395	−	1.25954i
$291$	−2.63038	−	4.55596i	−0.154196	−	0.267075i
$292$	−8.54906	+	2.29071i	−0.500296	+	0.134054i
$293$	10.7875	−	10.7875i	0.630212	−	0.630212i	−0.317909	−	0.948121i	$-0.602981\pi$
$293$	10.7875	−	10.7875i	0.630212	−	0.630212i	0.948121	+	0.317909i	$0.102981\pi$
$294$		0			0
$295$	5.24056	−	2.24558i	0.305117	−	0.130743i
$296$	1.33557	−	2.31328i	0.0776285	−	0.134456i
$297$	1.04374	−	3.89528i	0.0605637	−	0.226027i
$298$	−1.02036	+	3.80802i	−0.0591077	+	0.220593i
$299$	7.69020	−	13.3198i	0.444736	−	0.770305i
$300$	−5.87135	+	0.142505i	−0.338982	+	0.00822751i
$301$		0			0
$302$	14.1035	−	14.1035i	0.811564	−	0.811564i
$303$	12.6866	−	3.39936i	0.728826	−	0.195288i
$304$	−0.946027	−	1.63857i	−0.0542584	−	0.0939783i
$305$	8.13624	−	10.8740i	0.465880	−	0.622645i
$306$	9.20520	+	5.31463i	0.526226	+	0.303817i
$307$	−6.89201	−	6.89201i	−0.393348	−	0.393348i	0.482531	−	0.875879i	$-0.339718\pi$
$307$	−6.89201	−	6.89201i	−0.393348	−	0.393348i	−0.875879	+	0.482531i	$0.839718\pi$
$308$		0			0
$309$			2.84982i			0.162121i
$310$	−6.01464	+	4.73224i	−0.341609	+	0.268773i
$311$	0.109136	−	0.0630096i	0.00618852	−	0.00357294i	−0.496903	−	0.867806i	$-0.665529\pi$
$311$	0.109136	−	0.0630096i	0.00618852	−	0.00357294i	0.503091	+	0.864233i	$0.332196\pi$
$312$	−3.29788	−	0.883663i	−0.186706	−	0.0500276i
$313$	3.02662	+	11.2955i	0.171075	+	0.638459i	0.997187	+	0.0749536i	$0.0238809\pi$
$313$	3.02662	+	11.2955i	0.171075	+	0.638459i	−0.826112	+	0.563505i	$0.809452\pi$
$314$	−7.46334			−0.421181
$315$		0			0
$316$	−6.58284			−0.370314
$317$	−2.83308	−	10.5732i	−0.159122	−	0.593851i	−0.998717	−	0.0506382i	$-0.983874\pi$
$317$	−2.83308	−	10.5732i	−0.159122	−	0.593851i	0.839595	−	0.543212i	$-0.182792\pi$
$318$	5.65674	+	1.51572i	0.317214	+	0.0849974i
$319$	−6.23657	+	3.60068i	−0.349181	+	0.201600i
$320$	−2.22032	−	0.264946i	−0.124119	−	0.0148109i
$321$			7.80001i			0.435354i
$322$		0			0
$323$	−8.77670	−	8.77670i	−0.488349	−	0.488349i
$324$	1.31104	+	0.756928i	0.0728354	+	0.0420516i
$325$	−12.4062	+	7.56992i	−0.688173	+	0.419904i
$326$	6.08327	+	10.5365i	0.336921	+	0.583565i
$327$	−10.1665	+	2.72410i	−0.562208	+	0.150643i
$328$	−0.578200	+	0.578200i	−0.0319258	+	0.0319258i
$329$		0			0
$330$	0.768703	+	1.79393i	0.0423157	+	0.0987528i
$331$	2.73019	−	4.72883i	0.150065	−	0.259920i	−0.781186	−	0.624298i	$-0.785385\pi$
$331$	2.73019	−	4.72883i	0.150065	−	0.259920i	0.931251	+	0.364378i	$0.118718\pi$
$332$	−3.38031	+	12.6155i	−0.185519	+	0.692366i
$333$	−1.12017	+	4.18052i	−0.0613848	+	0.229091i
$334$	1.02929	−	1.78279i	0.0563205	−	0.0975500i
$335$	−11.3717	+	28.4244i	−0.621304	+	1.55299i
$336$		0			0
$337$	20.4823	−	20.4823i	1.11574	−	1.11574i	0.123385	−	0.992359i	$-0.460625\pi$
$337$	20.4823	−	20.4823i	1.11574	−	1.11574i	0.992359	−	0.123385i	$-0.0393751\pi$
$338$	4.39621	−	1.17796i	0.239122	−	0.0640727i
$339$	−0.255644	−	0.442788i	−0.0138847	−	0.0240490i
$340$	−14.5191	+	2.09099i	−0.787410	+	0.113400i
$341$	2.20249	+	1.27161i	0.119272	+	0.0688615i
$342$	2.16775	+	2.16775i	0.117218	+	0.117218i
$343$		0			0
$344$			2.25693i			0.121685i
$345$	1.64674	−	13.8001i	0.0886576	−	0.742973i
$346$	−8.14763	+	4.70404i	−0.438019	+	0.252891i
$347$	20.8040	+	5.57442i	1.11682	+	0.299250i	0.769595	−	0.638532i	$-0.220458\pi$
$347$	20.8040	+	5.57442i	1.11682	+	0.299250i	0.347223	+	0.937783i	$0.387125\pi$
$348$	−2.94629	−	10.9957i	−0.157938	−	0.589432i
$349$	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
$352$	0.192321	+	0.717752i	0.0102508	+	0.0382563i
$353$	−0.666012	−	0.178457i	−0.0354482	−	0.00949832i	0.241051	−	0.970512i	$-0.422508\pi$
$353$	−0.666012	−	0.178457i	−0.0354482	−	0.00949832i	−0.276500	+	0.961014i	$0.589174\pi$
$354$	2.59372	−	1.49749i	0.137855	−	0.0795905i
$355$	4.24371	−	35.5634i	0.225233	−	1.88751i
$356$			6.03207i			0.319699i
$357$		0			0
$358$	3.18020	+	3.18020i	0.168079	+	0.168079i
$359$	19.1381	+	11.0494i	1.01007	+	0.583165i	0.911212	−	0.411937i	$-0.135148\pi$
$359$	19.1381	+	11.0494i	1.01007	+	0.583165i	0.0988582	+	0.995102i	$0.468481\pi$
$360$	3.58606	−	0.516451i	0.189002	−	0.0272194i
$361$	7.71007	+	13.3542i	0.405793	+	0.702854i
$362$	17.2756	−	4.62898i	0.907985	−	0.243294i
$363$	−8.67775	+	8.67775i	−0.455464	+	0.455464i
$364$		0			0
$365$	−7.35115	+	18.3747i	−0.384777	+	0.961775i
$366$	3.56707	−	6.17834i	0.186454	−	0.322947i
$367$	−3.47100	+	12.9539i	−0.181185	+	0.676191i	0.814230	+	0.580542i	$0.197159\pi$
$367$	−3.47100	+	12.9539i	−0.181185	+	0.676191i	−0.995415	+	0.0956487i	$0.969507\pi$
$368$	1.36952	−	5.11112i	0.0713912	−	0.266436i
$369$	0.662450	−	1.14740i	0.0344858	−	0.0597311i
$370$	−2.35250	−	5.49006i	−0.122300	−	0.285415i
$371$		0			0
$372$	−2.84271	+	2.84271i	−0.147388	+	0.147388i
$373$	14.4564	−	3.87359i	0.748526	−	0.200567i	0.135662	−	0.990755i	$-0.456684\pi$
$373$	14.4564	−	3.87359i	0.748526	−	0.200567i	0.612864	+	0.790188i	$0.290017\pi$
$374$	2.43733	+	4.22157i	0.126031	+	0.218292i
$375$	−7.61017	+	10.7028i	−0.392987	+	0.552691i
$376$	−4.07864	−	2.35481i	−0.210340	−	0.121440i
$377$	−19.9189	−	19.9189i	−1.02587	−	1.02587i
$378$		0			0
$379$		−	1.71784i		−	0.0882395i	−0.999026	−	0.0441198i	$-0.985952\pi$
$379$		−	1.71784i		−	0.0882395i	0.999026	−	0.0441198i	$-0.0140483\pi$
$380$	−4.20096	−	0.501292i	−0.215505	−	0.0257157i
$381$	16.0869	−	9.28776i	0.824156	−	0.475827i
$382$	−2.68091	−	0.718348i	−0.137167	−	0.0367539i
$383$	2.70676	+	10.1017i	0.138309	+	0.516175i	0.999962	+	0.00867837i	$0.00276245\pi$
$383$	2.70676	+	10.1017i	0.138309	+	0.516175i	−0.861654	+	0.507497i	$0.830571\pi$
$384$	−1.17462			−0.0599418
$385$		0			0
$386$	5.14005			0.261622
$387$	−0.946464	−	3.53225i	−0.0481114	−	0.179554i
$388$	−4.32611	−	1.15918i	−0.219625	−	0.0588483i
$389$	18.8548	−	10.8858i	0.955978	−	0.551934i	0.0610449	−	0.998135i	$-0.480557\pi$
$389$	18.8548	−	10.8858i	0.955978	−	0.551934i	0.894933	+	0.446201i	$0.147223\pi$
$390$	−5.99995	+	4.72068i	−0.303819	+	0.239041i
$391$		−	34.7124i		−	1.75548i
$392$		0			0
$393$	−7.96759	−	7.96759i	−0.401912	−	0.401912i
$394$	−1.64169	−	0.947829i	−0.0827071	−	0.0477510i
$395$	−8.81843	+	11.7858i	−0.443703	+	0.593006i
$396$	−0.601992	−	1.04268i	−0.0302512	−	0.0523967i
$397$	30.6188	−	8.20427i	1.53671	−	0.411761i	0.611510	−	0.791237i	$-0.290562\pi$
$397$	30.6188	−	8.20427i	1.53671	−	0.411761i	0.925202	+	0.379476i	$0.123896\pi$
$398$	−10.2551	+	10.2551i	−0.514043	+	0.514043i
$399$		0			0
$400$	−3.44871	+	3.62028i	−0.172435	+	0.181014i
$401$	−6.98528	+	12.0989i	−0.348828	+	0.604188i	−0.986042	−	0.166499i	$-0.946754\pi$
$401$	−6.98528	+	12.0989i	−0.348828	+	0.604188i	0.637213	+	0.770687i	$0.280087\pi$
$402$	−4.16234	+	15.5341i	−0.207599	+	0.774769i
$403$	−2.57480	+	9.60930i	−0.128260	+	0.478673i
$404$	5.59083	−	9.68359i	0.278154	−	0.481777i
$405$	3.11146	−	1.33327i	0.154610	−	0.0662505i
$406$		0			0
$407$	−1.40350	+	1.40350i	−0.0695690	+	0.0695690i
$408$	−7.44307	+	1.99437i	−0.368487	+	0.0987358i
$409$	9.36960	+	16.2286i	0.463297	+	0.802454i	0.999123	−	0.0418748i	$-0.0133330\pi$
$409$	9.36960	+	16.2286i	0.463297	+	0.802454i	−0.535826	+	0.844328i	$0.680000\pi$
$410$	0.260635	+	1.80976i	0.0128718	+	0.0893776i
$411$	9.47010	+	5.46757i	0.467126	+	0.269695i
$412$	1.71557	+	1.71557i	0.0845198	+	0.0845198i
$413$		0			0
$414$			8.57358i			0.421369i
$415$	18.0582	+	22.9519i	0.886443	+	1.12666i
$416$	−2.51725	+	1.45333i	−0.123418	+	0.0712555i
$417$	25.1555	+	6.74040i	1.23187	+	0.330079i
$418$	0.363882	+	1.35803i	0.0177981	+	0.0664232i
$419$	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	$0.607171\pi$
$422$	−2.59658	−	9.69057i	−0.126399	−	0.471729i
$423$	7.37087	+	1.97502i	0.358384	+	0.0960287i
$424$	4.31775	−	2.49286i	0.209689	−	0.121064i
$425$	−15.7063	+	28.7958i	−0.761866	+	1.39680i
$426$		−	18.8141i		−	0.911547i
$427$		0			0
$428$	4.69553	+	4.69553i	0.226967	+	0.226967i
$429$	2.19711	+	1.26850i	0.106078	+	0.0612439i
$430$	4.04075	+	3.02340i	0.194862	+	0.145801i
$431$	−6.63518	−	11.4925i	−0.319605	−	0.553572i	0.660800	−	0.750562i	$-0.270217\pi$
$431$	−6.63518	−	11.4925i	−0.319605	−	0.553572i	−0.980406	+	0.196989i	$0.936884\pi$
$432$	5.24213	−	1.40462i	0.252212	−	0.0675800i
$433$	−12.0535	+	12.0535i	−0.579252	+	0.579252i	−0.934697	−	0.355445i	$-0.884329\pi$
$433$	−12.0535	+	12.0535i	−0.579252	+	0.579252i	0.355445	+	0.934697i	$0.384329\pi$
$434$		0			0
$435$	−23.6334	−	9.45497i	−1.13313	−	0.453331i
$436$	−4.48024	+	7.76000i	−0.214565	+	0.371637i
$437$	2.59121	−	9.67052i	0.123954	−	0.462604i
$438$	−2.69071	+	10.0419i	−0.128567	+	0.479818i
$439$	−17.5238	+	30.3521i	−0.836366	+	1.44863i	0.0565475	+	0.998400i	$0.481991\pi$
$439$	−17.5238	+	30.3521i	−0.836366	+	1.44863i	−0.892913	+	0.450228i	$0.851343\pi$
$440$	1.54268	+	0.617179i	0.0735445	+	0.0294229i
$441$		0			0
$442$	−13.4832	+	13.4832i	−0.641330	+	0.641330i
$443$	0.0609189	−	0.0163232i	0.00289435	−	0.000775538i	−0.257372	−	0.966313i	$-0.582856\pi$
$443$	0.0609189	−	0.0163232i	0.00289435	−	0.000775538i	0.260266	+	0.965537i	$0.416190\pi$
$444$	−1.56878	−	2.71721i	−0.0744511	−	0.128953i
$445$	10.7997	+	8.08060i	0.511954	+	0.383057i
$446$	3.84271	+	2.21859i	0.181958	+	0.105053i
$447$	3.27444	+	3.27444i	0.154876	+	0.154876i
$448$		0			0
$449$			24.5207i			1.15720i	0.815611	+	0.578601i	$0.196401\pi$
$449$			24.5207i			1.15720i	−0.815611	+	0.578601i	$0.803599\pi$
$450$	3.87927	−	7.11224i	0.182870	−	0.335274i
$451$	0.526205	−	0.303804i	0.0247780	−	0.0143056i
$452$	−0.420450	−	0.112659i	−0.0197763	−	0.00529904i
$453$	−6.06364	−	22.6298i	−0.284894	−	1.06324i
$454$	0.670872			0.0314856
$455$		0			0
$456$	−2.22244			−0.104075
$457$	5.19531	+	19.3892i	0.243027	+	0.906987i	0.974365	+	0.224973i	$0.0722293\pi$
$457$	5.19531	+	19.3892i	0.243027	+	0.906987i	−0.731339	+	0.682015i	$0.761104\pi$
$458$	12.7534	+	3.41727i	0.595929	+	0.159679i
$459$	30.8324	−	17.8011i	1.43913	−	0.830884i
$460$	−7.31621	−	9.29886i	−0.341120	−	0.433561i
$461$			11.6940i			0.544642i	0.962207	+	0.272321i	$0.0877912\pi$
$461$			11.6940i			0.544642i	−0.962207	+	0.272321i	$0.912209\pi$
$462$		0			0
$463$	2.77226	+	2.77226i	0.128838	+	0.128838i	0.768585	−	0.639747i	$-0.220961\pi$
$463$	2.77226	+	2.77226i	0.128838	+	0.128838i	−0.639747	+	0.768585i	$0.720961\pi$
$464$	−8.39295	−	4.84567i	−0.389633	−	0.224955i
$465$	1.28141	+	8.89765i	0.0594239	+	0.412619i
$466$	−4.32947	−	7.49886i	−0.200559	−	0.347378i
$467$	20.2080	−	5.41472i	0.935116	−	0.250563i	0.241081	−	0.970505i	$-0.422498\pi$
$467$	20.2080	−	5.41472i	0.935116	−	0.250563i	0.694035	+	0.719942i	$0.255831\pi$
$468$	3.33020	−	3.33020i	0.153938	−	0.153938i
$469$		0			0
$470$	−9.67977	+	4.14779i	−0.446495	+	0.191323i
$471$	−4.38327	+	7.59205i	−0.201971	+	0.349823i
$472$	0.659924	−	2.46287i	0.0303754	−	0.113363i
$473$	0.434055	−	1.61992i	0.0199579	−	0.0744838i
$474$	−3.86615	+	6.69637i	−0.177578	+	0.307575i
$475$	−6.52514	+	6.84976i	−0.299394	+	0.314289i
$476$		0			0
$477$	−5.71218	+	5.71218i	−0.261543	+	0.261543i
$478$	−3.86655	+	1.03604i	−0.176852	+	0.0473873i
$479$	12.1419	+	21.0303i	0.554775	+	0.960899i	0.997921	+	0.0644496i	$0.0205292\pi$
$479$	12.1419	+	21.0303i	0.554775	+	0.960899i	−0.443145	+	0.896450i	$0.646137\pi$
$480$	−1.57352	+	2.10300i	−0.0718212	+	0.0959886i
$481$	−6.72392	−	3.88206i	−0.306584	−	0.177007i
$482$	−12.2507	−	12.2507i	−0.558005	−	0.558005i
$483$		0			0
$484$			10.4478i			0.474902i
$485$	−7.87065	+	6.19252i	−0.357388	+	0.281188i
$486$	−12.5599	+	7.25148i	−0.569730	+	0.328934i
$487$	−2.46890	−	0.661539i	−0.111876	−	0.0299772i	0.202446	−	0.979293i	$-0.435111\pi$
$487$	−2.46890	−	0.661539i	−0.111876	−	0.0299772i	−0.314323	+	0.949316i	$0.601777\pi$
$488$	−1.57196	−	5.86664i	−0.0711594	−	0.265570i
$489$	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	$0.393391\pi$
$492$	0.248591	+	0.927753i	0.0112073	+	0.0418264i
$493$	−61.4102	−	16.4548i	−2.76578	−	0.741088i
$494$	−4.76277	+	2.74978i	−0.214287	+	0.123719i
$495$	−2.67323	−	0.318991i	−0.120153	−	0.0143376i
$496$			3.42257i			0.153678i
$497$		0			0
$498$	10.8478	+	10.8478i	0.486101	+	0.486101i
$499$	−26.0565	−	15.0437i	−1.16645	−	0.673450i	−0.213608	−	0.976919i	$-0.568522\pi$
$499$	−26.0565	−	15.0437i	−1.16645	−	0.673450i	−0.952841	+	0.303469i	$0.901855\pi$
$500$	1.86175	+	11.0242i	0.0832600	+	0.493019i
$501$	−1.20902	−	2.09409i	−0.0540152	−	0.0935572i
$502$	−5.31199	+	1.42334i	−0.237086	+	0.0635269i
$503$	24.6819	−	24.6819i	1.10051	−	1.10051i	0.106161	−	0.994349i	$-0.466144\pi$
$503$	24.6819	−	24.6819i	1.10051	−	1.10051i	0.994349	−	0.106161i	$-0.0338558\pi$
$504$		0			0
$505$	−9.84777	−	22.9819i	−0.438220	−	1.02268i
$506$	−1.96595	+	3.40513i	−0.0873973	+	0.151377i
$507$	1.38365	−	5.16386i	0.0614501	−	0.229335i
$508$	4.09300	−	15.2753i	0.181598	−	0.677731i
$509$	−6.22521	+	10.7824i	−0.275927	+	0.477920i	−0.970369	−	0.241629i	$-0.922318\pi$
$509$	−6.22521	+	10.7824i	−0.275927	+	0.477920i	0.694441	+	0.719549i	$0.255652\pi$
$510$	−6.40013	+	15.9976i	−0.283403	+	0.708384i
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	9.91839	−	2.65762i	0.437908	−	0.117337i
$514$	8.25494	+	14.2980i	0.364110	+	0.630656i
$515$	5.36969	−	0.773324i	0.236617	−	0.0340767i
$516$	2.29585	+	1.32551i	0.101069	+	0.0583524i
$517$	2.47458	+	2.47458i	0.108832	+	0.108832i
$518$		0			0
$519$			11.0509i			0.485079i
$520$	−0.770110	+	6.45372i	−0.0337715	+	0.283014i
$521$	−30.6011	+	17.6676i	−1.34066	+	0.774030i	−0.986904	−	0.161308i	$-0.948429\pi$
$521$	−30.6011	+	17.6676i	−1.34066	+	0.774030i	−0.353756	+	0.935338i	$0.615096\pi$
$522$	15.1676	+	4.06416i	0.663869	+	0.177883i
$523$	4.25513	+	15.8804i	0.186064	+	0.694400i	0.994400	+	0.105679i	$0.0337016\pi$
$523$	4.25513	+	15.8804i	0.186064	+	0.694400i	−0.808336	+	0.588721i	$0.799632\pi$
$524$	−9.59282			−0.419064
$525$		0			0
$526$	9.86084			0.429953
$527$	5.81115	+	21.6875i	0.253137	+	0.944722i
$528$	0.843083	+	0.225903i	0.0366905	+	0.00983118i
$529$	4.32938	−	2.49957i	0.188234	−	0.108677i
$530$	1.32094	−	11.0699i	0.0573782	−	0.480844i
$531$			4.13131i			0.179283i
$532$		0			0
$533$	1.68063	+	1.68063i	0.0727964	+	0.0727964i
$534$	6.13610	+	3.54268i	0.265535	+	0.153307i
$535$	14.6969	−	2.11660i	0.635404	−	0.0915086i
$536$	6.84567	+	11.8571i	0.295688	+	0.512147i
$537$	5.10281	−	1.36729i	0.220202	−	0.0590031i
$538$	−6.33457	+	6.33457i	−0.273103	+	0.273103i
$539$		0			0
$540$	4.50759	−	11.2670i	0.193976	−	0.484856i
$541$	13.2572	−	22.9621i	0.569970	−	0.987218i	−0.426598	−	0.904441i	$-0.640288\pi$
$541$	13.2572	−	22.9621i	0.569970	−	0.987218i	0.996568	−	0.0827763i	$-0.0263787\pi$
$542$	5.91408	−	22.0717i	0.254032	−	0.948059i
$543$	5.43727	−	20.2922i	0.233336	−	0.870820i
$544$	−3.28007	+	5.68124i	−0.140632	+	0.243581i
$545$	7.89157	+	18.4167i	0.338038	+	0.788884i
$546$		0			0
$547$	−1.07403	+	1.07403i	−0.0459223	+	0.0459223i	−0.729695	−	0.683773i	$-0.760338\pi$
$547$	−1.07403	+	1.07403i	−0.0459223	+	0.0459223i	0.683773	+	0.729695i	$0.260338\pi$
$548$	8.99233	−	2.40949i	0.384133	−	0.102928i
$549$	4.92046	+	8.52249i	0.210000	+	0.363731i
$550$	3.17157	−	1.93520i	0.135236	−	0.0825174i
$551$	−15.8799	−	9.16828i	−0.676507	−	0.390582i
$552$	−4.39494	−	4.39494i	−0.187061	−	0.187061i
$553$		0			0
$554$			21.5332i			0.914858i
$555$	−6.96638	−	0.831285i	−0.295706	−	0.0352861i
$556$	19.2010	−	11.0857i	0.814305	−	0.470139i
$557$	−15.0145	−	4.02313i	−0.636186	−	0.170466i	−0.0737108	−	0.997280i	$-0.523484\pi$
$557$	−15.0145	−	4.02313i	−0.636186	−	0.170466i	−0.562475	+	0.826814i	$0.690151\pi$
$558$	−1.43529	−	5.35657i	−0.0607606	−	0.226761i
$559$	6.56014			0.277464
$560$		0			0
$561$	5.72584			0.241745
$562$	1.46203	+	5.45637i	0.0616721	+	0.230163i
$563$	26.5108	+	7.10355i	1.11730	+	0.299379i	0.769789	−	0.638298i	$-0.220361\pi$
$563$	26.5108	+	7.10355i	1.11730	+	0.299379i	0.347508	+	0.937677i	$0.387028\pi$
$564$	−4.79084	+	2.76599i	−0.201731	+	0.116469i
$565$	−0.764940	+	0.601844i	−0.0321813	+	0.0253198i
$566$		−	2.92849i		−	0.123093i
$567$		0			0
$568$	−11.3259	−	11.3259i	−0.475225	−	0.475225i
$569$	5.85207	+	3.37869i	0.245332	+	0.141642i	0.617625	−	0.786473i	$-0.288095\pi$
$569$	5.85207	+	3.37869i	0.245332	+	0.141642i	−0.372293	+	0.928115i	$0.621428\pi$
$570$	−2.97719	+	3.97900i	−0.124701	+	0.166662i
$571$	−5.87721	−	10.1796i	−0.245953	−	0.426004i	0.716446	−	0.697643i	$-0.245768\pi$
$571$	−5.87721	−	10.1796i	−0.245953	−	0.426004i	−0.962399	+	0.271639i	$0.912434\pi$
$572$	2.08627	−	0.559013i	0.0872312	−	0.0233735i
$573$	−2.30526	+	2.30526i	−0.0963034	+	0.0963034i
$574$		0			0
$575$	−26.4493	+	0.641957i	−1.10301	+	0.0267715i
$576$	0.810140	−	1.40320i	0.0337558	−	0.0584668i
$577$	−0.583767	+	2.17865i	−0.0243025	+	0.0906983i	−0.977012	−	0.213184i	$-0.931616\pi$
$577$	−0.583767	+	2.17865i	−0.0243025	+	0.0906983i	0.952709	+	0.303883i	$0.0982831\pi$
$578$	−6.73845	+	25.1483i	−0.280283	+	1.04603i
$579$	3.01879	−	5.22870i	0.125457	−	0.217297i
$580$	−19.9189	+	8.53525i	−0.827085	+	0.354407i
$581$		0			0
$582$	−3.71992	+	3.71992i	−0.154196	+	0.154196i
$583$	−3.57851	+	0.958858i	−0.148207	+	0.0397118i
$584$	4.42532	+	7.66488i	0.183121	+	0.317175i
$585$	−1.50115	−	10.4235i	−0.0620649	−	0.430957i
$586$	−13.2119	−	7.62790i	−0.545779	−	0.315106i
$587$	12.8372	+	12.8372i	0.529847	+	0.529847i	0.920527	−	0.390680i	$-0.127760\pi$
$587$	12.8372	+	12.8372i	0.529847	+	0.529847i	−0.390680	+	0.920527i	$0.627760\pi$
$588$		0			0
$589$			6.47569i			0.266826i
$590$	−3.52542	−	4.48079i	−0.145139	−	0.184471i
$591$	−1.92835	+	1.11333i	−0.0793218	+	0.0457965i
$592$	−2.58012	−	0.691342i	−0.106042	−	0.0284140i
$593$	−9.40957	−	35.1170i	−0.386405	−	1.44208i	−0.835940	−	0.548820i	$-0.815077\pi$
$593$	−9.40957	−	35.1170i	−0.386405	−	1.44208i	0.449535	−	0.893262i	$-0.351590\pi$
$594$	−4.03269			−0.165463
$595$		0			0
$596$	3.94236			0.161485
$597$	4.40908	+	16.4549i	0.180452	+	0.673455i
$598$	−14.8563	−	3.98074i	−0.607520	−	0.162785i
$599$	−30.9792	+	17.8858i	−1.26578	+	0.730796i	−0.974186	−	0.225748i	$-0.927517\pi$
$599$	−30.9792	+	17.8858i	−1.26578	+	0.730796i	−0.291589	+	0.956544i	$0.594184\pi$
$600$	1.65727	+	5.63440i	0.0676576	+	0.230024i
$601$		−	45.6631i		−	1.86264i	−0.364204	−	0.931319i	$-0.618659\pi$
$601$		−	45.6631i		−	1.86264i	0.364204	−	0.931319i	$-0.381341\pi$
$602$		0			0
$603$	−15.6863	−	15.6863i	−0.638796	−	0.638796i
$604$	−17.2732	−	9.97267i	−0.702835	−	0.405782i
$605$	18.7056	+	13.9960i	0.760490	+	0.569019i
$606$	−6.56707	−	11.3745i	−0.266769	−	0.462057i
$607$	1.13151	−	0.303188i	0.0459267	−	0.0123060i	−0.235783	−	0.971806i	$-0.575765\pi$
$607$	1.13151	−	0.303188i	0.0459267	−	0.0123060i	0.281709	+	0.959500i	$0.409099\pi$
$608$	−1.33788	+	1.33788i	−0.0542584	+	0.0542584i
$609$		0			0
$610$	−12.6093	−	5.04460i	−0.510536	−	0.204250i
$611$	−6.84463	+	11.8553i	−0.276904	+	0.479612i
$612$	2.75105	−	10.2671i	0.111205	−	0.415022i
$613$	−3.60737	+	13.4629i	−0.145700	+	0.543760i	0.854023	+	0.520235i	$0.174156\pi$
$613$	−3.60737	+	13.4629i	−0.145700	+	0.543760i	−0.999723	+	0.0235253i	$0.992511\pi$
$614$	−4.87339	+	8.44095i	−0.196674	+	0.340649i
$615$	1.99404	+	0.797755i	0.0804076	+	0.0321686i
$616$		0			0
$617$	22.7725	−	22.7725i	0.916788	−	0.916788i	−0.0800065	−	0.996794i	$-0.525494\pi$
$617$	22.7725	−	22.7725i	0.916788	−	0.916788i	0.996794	+	0.0800065i	$0.0254941\pi$
$618$	2.75272	−	0.737588i	0.110731	−	0.0296702i
$619$	−11.3386	−	19.6391i	−0.455738	−	0.789361i	0.542992	−	0.839738i	$-0.317291\pi$
$619$	−11.3386	−	19.6391i	−0.455738	−	0.789361i	−0.998730	+	0.0503763i	$0.983958\pi$
$620$	6.12770	+	4.58491i	0.246094	+	0.184134i
$621$	24.8695	+	14.3584i	0.997978	+	0.576183i
$622$	−0.0891090	−	0.0891090i	−0.00357294	−	0.00357294i
$623$		0			0
$624$			3.41421i			0.136678i
$625$	22.2316	+	11.4349i	0.889263	+	0.457397i
$626$	10.1273	−	5.84698i	0.404767	−	0.233692i
$627$	1.59516	+	0.427421i	0.0637045	+	0.0170696i
$628$	1.93165	+	7.20903i	0.0770814	+	0.287672i
$629$	−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	$0.276720\pi$
$632$	1.70376	+	6.35854i	0.0677721	+	0.252929i
$633$	−11.3827	−	3.04998i	−0.452421	−	0.121226i
$634$	−9.47968	+	5.47310i	−0.376486	+	0.217364i
$635$	−21.8655	−	27.7909i	−0.867706	−	1.10285i
$636$		−	5.85629i		−	0.232217i
$637$		0			0
$638$	5.09214	+	5.09214i	0.201600	+	0.201600i
$639$	22.4755	+	12.9762i	0.889116	+	0.513331i
$640$	0.318742	+	2.21323i	0.0125994	+	0.0874857i
$641$	0.428070	+	0.741439i	0.0169077	+	0.0292851i	0.874355	−	0.485286i	$-0.161285\pi$
$641$	0.428070	+	0.741439i	0.0169077	+	0.0292851i	−0.857448	+	0.514571i	$0.827951\pi$
$642$	7.53423	−	2.01879i	0.297353	−	0.0796754i
$643$	−16.4254	+	16.4254i	−0.647754	+	0.647754i	−0.952450	−	0.304696i	$-0.901445\pi$
$643$	−16.4254	+	16.4254i	−0.647754	+	0.647754i	0.304696	+	0.952450i	$0.401445\pi$
$644$		0			0
$645$	5.44871	−	2.33478i	0.214543	−	0.0919317i
$646$	−6.20607	+	10.7492i	−0.244174	+	0.422922i
$647$	12.2805	−	45.8316i	0.482798	−	1.80183i	−0.106982	−	0.994261i	$-0.534119\pi$
$647$	12.2805	−	45.8316i	0.482798	−	1.80183i	0.589779	−	0.807564i	$-0.299215\pi$
$648$	0.391815	−	1.46227i	0.0153919	−	0.0574435i
$649$	−0.947323	+	1.64081i	−0.0371857	+	0.0644075i
$650$	10.5229	+	10.0242i	0.412744	+	0.393183i
$651$		0			0
$652$	8.60305	−	8.60305i	0.336921	−	0.336921i
$653$	−25.3781	+	6.80004i	−0.993121	+	0.266106i	−0.718561	−	0.695464i	$-0.755199\pi$
$653$	−25.3781	+	6.80004i	−0.993121	+	0.266106i	−0.274560	+	0.961570i	$0.588532\pi$
$654$	5.26256	+	9.11502i	0.205782	+	0.356425i
$655$	−12.8506	+	17.1748i	−0.502115	+	0.671074i
$656$	0.708148	+	0.408849i	0.0276485	+	0.0159629i
$657$	−10.1403	−	10.1403i	−0.395609	−	0.395609i
$658$		0			0
$659$		−	26.2355i		−	1.02199i	−0.859583	−	0.510996i	$-0.829277\pi$
$659$		−	26.2355i		−	1.02199i	0.859583	−	0.510996i	$-0.170723\pi$
$660$	1.53385	−	1.20681i	0.0597051	−	0.0469752i
$661$	12.6197	−	7.28597i	0.490848	−	0.283391i	−0.234078	−	0.972218i	$-0.575207\pi$
$661$	12.6197	−	7.28597i	0.490848	−	0.283391i	0.724926	+	0.688827i	$0.241874\pi$
$662$	−5.27432	−	1.41325i	−0.204992	−	0.0549275i
$663$	5.79695	+	21.6345i	0.225135	+	0.840215i
$664$	13.0605			0.506847
$665$		0			0
$666$	4.32800			0.167706
$667$	−13.2725	−	49.5336i	−0.513913	−	1.91795i
$668$	−1.98844	−	0.532802i	−0.0769352	−	0.0206147i
$669$	4.51371	−	2.60599i	0.174510	−	0.100753i
$670$	30.3991	+	3.62747i	1.17442	+	0.140141i
$671$			4.51312i			0.174227i
$672$		0			0
$673$	−16.4201	−	16.4201i	−0.632950	−	0.632950i	0.315857	−	0.948807i	$-0.397708\pi$
$673$	−16.4201	−	16.4201i	−0.632950	−	0.632950i	−0.948807	+	0.315857i	$0.897708\pi$
$674$	−25.0856	−	14.4832i	−0.966263	−	0.557872i
$675$	−14.1338	−	23.1637i	−0.544011	−	0.891571i
$676$	−2.27565	−	3.94154i	−0.0875249	−	0.151598i
$677$	21.9882	−	5.89172i	0.845075	−	0.226437i	0.189796	−	0.981824i	$-0.439217\pi$
$677$	21.9882	−	5.89172i	0.845075	−	0.226437i	0.655280	+	0.755386i	$0.272551\pi$
$678$	−0.361535	+	0.361535i	−0.0138847	+	0.0138847i
$679$		0			0
$680$	5.77756	+	13.4832i	0.221559	+	0.517057i
$681$	0.394008	−	0.682442i	0.0150984	−	0.0261512i
$682$	0.658233	−	2.45656i	0.0252050	−	0.0940665i
$683$	7.93034	−	29.5964i	0.303446	−	1.13248i	−0.630829	−	0.775922i	$-0.717285\pi$
$683$	7.93034	−	29.5964i	0.303446	−	1.13248i	0.934275	−	0.356554i	$-0.116048\pi$
$684$	1.53283	−	2.65494i	0.0586091	−	0.101514i
$685$	7.73231	−	19.3274i	0.295436	−	0.738463i
$686$		0			0
$687$	10.9664	−	10.9664i	0.418394	−	0.418394i
$688$	2.18003	−	0.584136i	0.0831127	−	0.0222700i
$689$	−7.24590	−	12.5503i	−0.276047	−	0.478127i
$690$	−13.7561	+	1.98110i	−0.523686	+	0.0754193i
$691$	−27.7284	−	16.0090i	−1.05484	−	0.609012i	−0.130839	−	0.991404i	$-0.541767\pi$
$691$	−27.7284	−	16.0090i	−1.05484	−	0.609012i	−0.924000	+	0.382392i	$0.875100\pi$
$692$	6.65251	+	6.65251i	0.252891	+	0.252891i
$693$		0			0
$694$		−	21.5379i		−	0.817567i
$695$	5.87423	−	49.2276i	0.222822	−	1.86731i
$696$	−9.85849	+	5.69180i	−0.373685	+	0.215747i
$697$	5.18143	+	1.38836i	0.196261	+	0.0525879i
$698$	−3.25450	−	12.1459i	−0.123184	−	0.459731i
$699$	−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	$0.613792\pi$
$702$	−4.08277	−	15.2371i	−0.154094	−	0.575088i
$703$	−4.88174	−	1.30806i	−0.184118	−	0.0493343i
$704$	0.643519	−	0.371536i	0.0242535	−	0.0140028i
$705$	−1.46568	+	12.2827i	−0.0552006	+	0.462595i
$706$			0.689506i			0.0259499i
$707$		0			0
$708$	−2.11777	−	2.11777i	−0.0795905	−	0.0795905i
$709$	23.1074	+	13.3411i	0.867818	+	0.501035i	0.866622	−	0.498965i	$-0.166286\pi$
$709$	23.1074	+	13.3411i	0.867818	+	0.501035i	0.00119522	+	0.999999i	$0.499620\pi$
$710$	−35.4499	+	5.10537i	−1.33041	+	0.191601i
$711$	−5.33302	−	9.23706i	−0.200004	−	0.346417i
$712$	5.82653	−	1.56121i	0.218358	−	0.0585089i
$713$	−12.8059	+	12.8059i	−0.479585	+	0.479585i
$714$		0			0
$715$	1.79393	−	4.48406i	0.0670893	−	0.167694i
$716$	2.24874	−	3.89494i	0.0840395	−	0.145561i
$717$	−1.21695	+	4.54170i	−0.0454477	+	0.169613i
$718$	5.71959	−	21.3458i	0.213453	−	0.796618i
$719$	−15.9890	+	27.6937i	−0.596288	+	1.03280i	0.397076	+	0.917786i	$0.370025\pi$
$719$	−15.9890	+	27.6937i	−0.596288	+	1.03280i	−0.993364	+	0.115015i	$0.963308\pi$
$720$	−1.42699	−	3.33020i	−0.0531809	−	0.124109i
$721$		0			0
$722$	10.9037	−	10.9037i	0.405793	−	0.405793i
$723$	−19.6569	+	5.26706i	−0.731049	+	0.195884i
$724$	−8.94250	−	15.4889i	−0.332346	−	0.575639i
$725$	−11.4021	+	47.0961i	−0.423465	+	1.74911i
$726$	10.6280	+	6.13610i	0.394443	+	0.227732i
$727$	21.4539	+	21.4539i	0.795683	+	0.795683i	0.982412	−	0.186729i	$-0.0597885\pi$
$727$	21.4539	+	21.4539i	0.795683	+	0.795683i	−0.186729	+	0.982412i	$0.559789\pi$
$728$		0			0
$729$			21.5770i			0.799146i
$730$	19.6512	+	2.34494i	0.727324	+	0.0867901i
$731$	12.8222	−	7.40288i	0.474245	−	0.273805i
$732$	−6.89105	−	1.84645i	−0.254700	−	0.0682468i
$733$	3.36789	+	12.5691i	0.124396	+	0.464252i	0.999817	−	0.0191085i	$-0.00608281\pi$
$733$	3.36789	+	12.5691i	0.124396	+	0.464252i	−0.875422	+	0.483360i	$0.839416\pi$
$734$	13.4109			0.495006
$735$		0			0
$736$	−5.29142			−0.195044
$737$	−2.63314	−	9.82700i	−0.0969928	−	0.361982i
$738$	−1.27976	−	0.342909i	−0.0471084	−	0.0126227i
$739$	3.12136	−	1.80212i	0.114821	−	0.0662920i	−0.441490	−	0.897266i	$-0.645550\pi$
$739$	3.12136	−	1.80212i	0.114821	−	0.0662920i	0.556311	+	0.830974i	$0.312216\pi$
$740$	−4.69412	+	3.69327i	−0.172559	+	0.135767i
$741$			6.45988i			0.237309i
$742$		0			0
$743$	31.1070	+	31.1070i	1.14121	+	1.14121i	0.988230	+	0.152977i	$0.0488859\pi$
$743$	31.1070	+	31.1070i	1.14121	+	1.14121i	0.152977	+	0.988230i	$0.451114\pi$
$744$	3.48160	+	2.01010i	0.127642	+	0.0736939i
$745$	5.28121	−	7.05831i	0.193489	−	0.258596i
$746$	−7.48320	−	12.9613i	−0.273979	−	0.474546i
$747$	−20.4406	+	5.47705i	−0.747884	+	0.200395i
$748$	3.44690	−	3.44690i	0.126031	−	0.126031i
$749$		0			0
$750$	12.3078	+	4.58076i	0.449417	+	0.167266i
$751$	25.5141	−	44.1917i	0.931023	−	1.61258i	0.149447	−	0.988770i	$-0.452251\pi$
$751$	25.5141	−	44.1917i	0.931023	−	1.61258i	0.781576	−	0.623810i	$-0.214416\pi$
$752$	−1.21894	+	4.54913i	−0.0444501	+	0.165890i
$753$	−1.67188	+	6.23954i	−0.0609267	+	0.227382i
$754$	−14.0848	+	24.3955i	−0.512936	+	0.888432i
$755$	−40.9941	+	17.5660i	−1.49193	+	0.639293i
$756$		0			0
$757$	26.8141	−	26.8141i	0.974576	−	0.974576i	−0.0251083	−	0.999685i	$-0.507993\pi$
$757$	26.8141	−	26.8141i	0.974576	−	0.974576i	0.999685	+	0.0251083i	$0.00799305\pi$
$758$	−1.65931	+	0.444610i	−0.0602687	+	0.0161490i
$759$	2.30924	+	3.99972i	0.0838200	+	0.145181i
$760$	0.603077	+	4.18756i	0.0218759	+	0.151899i
$761$	25.8753	+	14.9391i	0.937980	+	0.541543i	0.889326	−	0.457273i	$-0.151174\pi$
$761$	25.8753	+	14.9391i	0.937980	+	0.541543i	0.0486532	+	0.998816i	$0.484507\pi$
$762$	−13.1349	−	13.1349i	−0.475827	−	0.475827i
$763$		0			0
$764$			2.77548i			0.100413i
$765$	−14.6966	−	18.6793i	−0.531357	−	0.675351i
$766$	9.05698	−	5.22905i	0.327242	−	0.188933i
$767$	−7.15874	−	1.91818i	−0.258487	−	0.0692614i
$768$	0.304013	+	1.13459i	0.0109701	+	0.0409410i
$769$	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
$772$	−1.33034	−	4.96491i	−0.0478801	−	0.178691i
$773$	23.3328	+	6.25202i	0.839224	+	0.224869i	0.652734	−	0.757587i	$-0.273622\pi$
$773$	23.3328	+	6.25202i	0.839224	+	0.224869i	0.186490	+	0.982457i	$0.440289\pi$
$774$	−3.16693	+	1.82843i	−0.113833	+	0.0657215i
$775$	16.4174	−	4.82891i	0.589731	−	0.173460i
$776$			4.47871i			0.160776i
$777$		0			0
$778$	−15.3949	−	15.3949i	−0.551934	−	0.551934i
$779$	1.33985	+	0.773565i	0.0480052	+	0.0277158i
$780$	6.11273	+	4.57371i	0.218871	+	0.163765i
$781$	5.95099	+	10.3074i	0.212943	+	0.368828i
$782$	−33.5296	+	8.98424i	−1.19902	+	0.321276i
$783$	37.1906	−	37.1906i	1.32908	−	1.32908i
$784$		0			0
$785$	15.4945	+	6.19889i	0.553024	+	0.221248i
$786$	−5.63394	+	9.75826i	−0.200956	+	0.348066i
$787$	−3.28689	+	12.2669i	−0.117165	+	0.437266i	−0.999440	−	0.0334688i	$-0.989345\pi$
$787$	−3.28689	+	12.2669i	−0.117165	+	0.437266i	0.882275	+	0.470735i	$0.156011\pi$
$788$	−0.490633	+	1.83107i	−0.0174781	+	0.0652290i
$789$	5.79134	−	10.0309i	0.206177	−	0.357110i
$790$	13.6666	+	5.46757i	0.486234	+	0.194527i
$791$		0			0
$792$	−0.851345	+	0.851345i	−0.0302512	+	0.0302512i
$793$	−17.0524	+	4.56917i	−0.605547	+	0.162256i
$794$	−15.8494	−	27.4520i	−0.562475	−	0.974236i
$795$	−10.4850	−	7.84514i	−0.371864	−	0.278238i
$796$	12.5599	+	7.25148i	0.445175	+	0.257022i
$797$	−8.99183	−	8.99183i	−0.318507	−	0.318507i	0.529687	−	0.848193i	$-0.322310\pi$
$797$	−8.99183	−	8.99183i	−0.318507	−	0.318507i	−0.848193	+	0.529687i	$0.822310\pi$
$798$		0			0
$799$			30.8957i			1.09301i
$800$	4.38951	+	2.39420i	0.155193	+	0.0846477i
$801$	−8.46421	+	4.88682i	−0.299068	+	0.172667i
$802$	13.4945	+	3.61585i	0.476508	+	0.127680i
$803$	−1.70216	−	6.35256i	−0.0600681	−	0.224177i
$804$	16.0821			0.567171
$805$		0			0
$806$	9.94828			0.350413
$807$	2.72348	+	10.1642i	0.0958710	+	0.357796i
$808$	−10.8006	−	2.89402i	−0.379965	−	0.101811i
$809$	−23.7782	+	13.7284i	−0.835997	+	0.482663i	−0.855902	−	0.517139i	$-0.826997\pi$
$809$	−23.7782	+	13.7284i	−0.835997	+	0.482663i	0.0199044	+	0.999802i	$0.493664\pi$
$810$	−2.09314	−	2.66037i	−0.0735455	−	0.0934758i
$811$		−	12.7335i		−	0.447132i	−0.974689	−	0.223566i	$-0.928230\pi$
$811$		−	12.7335i		−	0.447132i	0.974689	−	0.223566i	$-0.0717699\pi$
$812$		0			0
$813$	−18.9789	−	18.9789i	−0.665620	−	0.665620i
$814$	1.71893	+	0.992425i	0.0602485	+	0.0347845i
$815$	−3.87799	−	26.9274i	−0.135840	−	0.943226i
$816$	3.85282	+	6.67328i	0.134876	+	0.233611i
$817$	4.12473	−	1.10522i	0.144306	−	0.0386666i
$818$	13.2506	−	13.2506i	0.463297	−	0.463297i
$819$		0			0
$820$	1.68063	−	0.720154i	0.0586903	−	0.0251489i
$821$	−15.1707	+	26.2764i	−0.529461	+	0.917054i	0.469948	+	0.882694i	$0.344273\pi$
$821$	−15.1707	+	26.2764i	−0.529461	+	0.917054i	−0.999410	+	0.0343601i	$0.989061\pi$
$822$	2.83022	−	10.5625i	0.0987153	−	0.368410i
$823$	2.63314	−	9.82702i	0.0917856	−	0.342549i	−0.904727	−	0.425992i	$-0.859925\pi$
$823$	2.63314	−	9.82702i	0.0917856	−	0.342549i	0.996513	+	0.0834435i	$0.0265918\pi$
$824$	1.21309	−	2.10113i	0.0422599	−	0.0731963i
$825$	−0.105891	−	4.36283i	−0.00368666	−	0.151894i
$826$		0			0
$827$	−15.9794	+	15.9794i	−0.555660	+	0.555660i	−0.928069	−	0.372409i	$-0.878532\pi$
$827$	−15.9794	+	15.9794i	−0.555660	+	0.555660i	0.372409	+	0.928069i	$0.378532\pi$
$828$	8.28144	−	2.21901i	0.287800	−	0.0771158i
$829$	3.17447	+	5.49835i	0.110254	+	0.190966i	0.915873	−	0.401469i	$-0.131500\pi$
$829$	3.17447	+	5.49835i	0.110254	+	0.190966i	−0.805619	+	0.592435i	$0.798167\pi$
$830$	17.4960	−	23.3833i	0.607295	−	0.811645i
$831$	21.9046	+	12.6466i	0.759861	+	0.438706i
$832$	2.05532	+	2.05532i	0.0712555	+	0.0712555i
$833$		0			0
$834$		−	26.0429i		−	0.901792i
$835$	−3.61765	+	2.84632i	−0.125194	+	0.0985009i
$836$	1.21757	−	0.702966i	0.0421106	−	0.0243126i
$837$	−17.9416	−	4.80743i	−0.620151	−	0.166169i
$838$	−8.17206	−	30.4985i	−0.282299	−	1.05355i
$839$	−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
$842$	3.50878	+	13.0949i	0.120921	+	0.451282i
$843$	6.40914	+	1.71732i	0.220742	+	0.0591478i
$844$	−8.68832	+	5.01621i	−0.299064	+	0.172665i
$845$	−10.1053	−	1.20585i	−0.347633	−	0.0414824i
$846$		−	7.63089i		−	0.262355i
$847$		0			0
$848$	−3.52543	−	3.52543i	−0.121064	−	0.121064i
$849$	−2.97899	−	1.71992i	−0.102239	−	0.0590276i
$850$	31.8797	+	7.71818i	1.09346	+	0.264731i
$851$	−7.06707	−	12.2405i	−0.242256	−	0.419600i
$852$	−18.1730	+	4.86945i	−0.622598	+	0.166825i
$853$	−17.1451	+	17.1451i	−0.587036	+	0.587036i	−0.936828	−	0.349791i	$-0.886252\pi$
$853$	−17.1451	+	17.1451i	−0.587036	+	0.587036i	0.349791	+	0.936828i	$0.386252\pi$
$854$		0			0
$855$	−2.69995	−	6.30091i	−0.0923363	−	0.215487i
$856$	3.32024	−	5.75083i	0.113484	−	0.196559i
$857$	−4.35890	+	16.2677i	−0.148897	+	0.555692i	0.850654	+	0.525727i	$0.176206\pi$
$857$	−4.35890	+	16.2677i	−0.148897	+	0.555692i	−0.999551	+	0.0299658i	$0.990460\pi$
$858$	0.656625	−	2.45056i	0.0224168	−	0.0836607i
$859$	15.4345	−	26.7333i	0.526619	−	0.912130i	−0.472900	−	0.881116i	$-0.656793\pi$
$859$	15.4345	−	26.7333i	0.526619	−	0.912130i	0.999519	−	0.0310142i	$-0.00987370\pi$
$860$	1.87456	−	4.68558i	0.0639218	−	0.159777i
$861$		0			0
$862$	−9.38356	+	9.38356i	−0.319605	+	0.319605i
$863$	1.24908	−	0.334691i	0.0425193	−	0.0113930i	−0.237497	−	0.971388i	$-0.576327\pi$
$863$	1.24908	−	0.334691i	0.0425193	−	0.0113930i	0.280016	+	0.959995i	$0.409660\pi$
$864$	−2.71352	−	4.69996i	−0.0923160	−	0.159896i
$865$	20.8223	−	2.99875i	0.707978	−	0.101960i
$866$	14.7624	+	8.52308i	0.501647	+	0.289626i
$867$	21.6244	+	21.6244i	0.734404	+	0.734404i
$868$		0			0
$869$		−	4.89152i		−	0.165934i
$870$	−3.01604	+	25.2752i	−0.102253	+	0.856909i
$871$	34.4645	−	19.8981i	1.16778	−	0.674221i
$872$	8.65516	+	2.31914i	0.293101	+	0.0785361i
$873$	−1.87819	−	7.00950i	−0.0635671	−	0.237236i
$874$	−10.0117			−0.338649
$875$		0			0
$876$	10.3961			0.351251
$877$	2.51177	+	9.37406i	0.0848165	+	0.316540i	0.995279	−	0.0970513i	$-0.0309411\pi$
$877$	2.51177	+	9.37406i	0.0848165	+	0.316540i	−0.910463	+	0.413591i	$0.864274\pi$
$878$	33.8534	+	9.07099i	1.14250	+	0.306131i
$879$	−15.5189	+	8.95985i	−0.523440	+	0.302208i
$880$	0.196874	−	1.64985i	0.00663662	−	0.0556166i
$881$			18.3500i			0.618227i	0.951025	+	0.309113i	$0.100032\pi$
$881$			18.3500i			0.618227i	−0.951025	+	0.309113i	$0.899968\pi$
$882$		0			0
$883$	23.7527	+	23.7527i	0.799342	+	0.799342i	0.982992	−	0.183650i	$-0.0587913\pi$
$883$	23.7527	+	23.7527i	0.799342	+	0.799342i	−0.183650	+	0.982992i	$0.558791\pi$
$884$	16.5135	+	9.53406i	0.555408	+	0.320665i
$885$	−6.62858	+	0.954624i	−0.222817	+	0.0320893i
$886$	−0.0315340	−	0.0546184i	−0.00105940	−	0.00183494i
$887$	−37.5247	+	10.0547i	−1.25996	+	0.337604i	−0.826175	−	0.563414i	$-0.809488\pi$
$887$	−37.5247	+	10.0547i	−1.25996	+	0.337604i	−0.433781	+	0.901018i	$0.642821\pi$
$888$	−2.21859	+	2.21859i	−0.0744511	+	0.0744511i
$889$		0			0
$890$	5.01010	−	12.5231i	0.167939	−	0.419775i
$891$	−0.562452	+	0.974195i	−0.0188429	+	0.0326368i
$892$	1.14843	−	4.28599i	0.0384522	−	0.143506i
$893$	−2.30629	+	8.60721i	−0.0771772	+	0.288029i
$894$	2.31538	−	4.01035i	0.0774378	−	0.134126i
$895$	−3.96097	−	9.24379i	−0.132401	−	0.308986i
$896$		0			0
$897$	−12.7746	+	12.7746i	−0.426532	+	0.426532i
$898$	23.6851	−	6.34642i	0.790384	−	0.211783i
$899$	16.5847	+	28.7255i	0.553130	+	0.958049i
$900$	−7.87392	−	1.90630i	−0.262464	−	0.0635435i
$901$	−28.3251	−	16.3535i	−0.943644	−	0.544813i
$902$	−0.429644	−	0.429644i	−0.0143056	−	0.0143056i
$903$		0			0
$904$			0.435281i			0.0144772i
$905$	−39.7104	−	4.73856i	−1.32002	−	0.157515i
$906$	−20.2893	+	11.7140i	−0.674067	+	0.389173i
$907$	−33.5044	−	8.97748i	−1.11250	−	0.298092i	−0.344653	−	0.938730i	$-0.612003\pi$
$907$	−33.5044	−	8.97748i	−1.11250	−	0.298092i	−0.767843	+	0.640638i	$0.778670\pi$
$908$	−0.173634	−	0.648012i	−0.00576226	−	0.0215050i
$909$	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	$0.206061\pi$
$912$	0.575209	+	2.14671i	0.0190471	+	0.0710846i
$913$	−9.37422	−	2.51182i	−0.310242	−	0.0831290i
$914$	17.3839	−	10.0366i	0.575007	−	0.331980i
$915$	−12.5371	+	9.86405i	−0.414465	+	0.326095i
$916$		−	13.2033i		−	0.436250i
$917$		0			0
$918$	−25.1745	−	25.1745i	−0.830884	−	0.830884i
$919$	−15.4242	−	8.90515i	−0.508797	−	0.293754i	0.223542	−	0.974694i	$-0.428238\pi$
$919$	−15.4242	−	8.90515i	−0.508797	−	0.293754i	−0.732339	+	0.680940i	$0.761571\pi$
$920$	−7.08843	+	9.47364i	−0.233699	+	0.312337i
$921$	5.72435	+	9.91487i	0.188624	+	0.326706i
$922$	11.2955	−	3.02662i	0.371997	−	0.0996763i
$923$	−32.9206	+	32.9206i	−1.08360	+	1.08360i
$924$		0			0
$925$	0.324064	+	13.3518i	0.0106552	+	0.439004i
$926$	1.96028	−	3.39531i	0.0644188	−	0.111577i
$927$	−1.01744	+	3.79713i	−0.0334171	+	0.124714i
$928$	−2.50831	+	9.36112i	−0.0823392	+	0.307294i
$929$	16.1326	−	27.9424i	0.529292	−	0.916761i	−0.470124	−	0.882600i	$-0.655791\pi$
$929$	16.1326	−	27.9424i	0.529292	−	0.916761i	0.999416	−	0.0341607i	$-0.0108758\pi$
$930$	8.26282	−	3.54063i	0.270949	−	0.116102i
$931$		0			0
$932$	−6.12279	+	6.12279i	−0.200559	+	0.200559i
$933$	−0.142980	+	0.0383114i	−0.00468096	+	0.00125426i
$934$	−10.4604	−	18.1180i	−0.342276	−	0.592839i
$935$	−1.55376	−	10.7887i	−0.0508133	−	0.352830i
$936$	−4.07864	−	2.35481i	−0.133315	−	0.0769692i
$937$	−28.9650	−	28.9650i	−0.946244	−	0.946244i	0.0523829	−	0.998627i	$-0.483318\pi$
$937$	−28.9650	−	28.9650i	−0.946244	−	0.946244i	−0.998627	+	0.0523829i	$0.983318\pi$
$938$		0			0
$939$		−	13.7359i		−	0.448254i
$940$	6.51177	+	8.27641i	0.212390	+	0.269947i
$941$	−30.8629	+	17.8187i	−1.00610	+	0.580874i	−0.910048	−	0.414502i	$-0.863956\pi$
$941$	−30.8629	+	17.8187i	−1.00610	+	0.580874i	−0.0960550	+	0.995376i	$0.530622\pi$
$942$	8.46784	+	2.26895i	0.275897	+	0.0739264i
$943$	1.11985	+	4.17936i	0.0364675	+	0.136099i
$944$	−2.54975			−0.0829873
$945$		0			0
$946$	−1.67706			−0.0545259
$947$	3.61149	+	13.4783i	0.117358	+	0.437985i	0.999452	−	0.0330871i	$-0.0105339\pi$
$947$	3.61149	+	13.4783i	0.117358	+	0.437985i	−0.882095	+	0.471072i	$0.843867\pi$
$948$	7.46883	+	2.00127i	0.242576	+	0.0649982i
$949$	22.2792	−	12.8629i	0.723214	−	0.417548i
$950$	8.30519	+	4.52995i	0.269456	+	0.146971i
$951$			12.8576i			0.416935i
$952$		0			0
$953$	25.4475	+	25.4475i	0.824326	+	0.824326i	0.986725	−	0.162399i	$-0.0519232\pi$
$953$	25.4475	+	25.4475i	0.824326	+	0.824326i	−0.162399	+	0.986725i	$0.551923\pi$
$954$	6.99597	+	4.03912i	0.226503	+	0.130771i
$955$	4.96916	+	3.71806i	0.160798	+	0.120314i
$956$	2.00147	+	3.46665i	0.0647322	+	0.112120i
$957$	8.17061	−	2.18931i	0.264118	−	0.0707703i
$958$	17.1712	−	17.1712i	0.554775	−	0.554775i
$959$		0			0
$960$	2.43860	+	0.975610i	0.0787056	+	0.0314877i
$961$	−9.64300	+	16.7022i	−0.311064	+	0.538779i
$962$	−2.00950	+	7.49956i	−0.0647889	+	0.241796i
$963$	−2.78475	+	10.3928i	−0.0897373	+	0.334904i
$964$	−8.66256	+	15.0040i	−0.279002	+	0.483246i
$965$	−10.6712	−	4.26922i	−0.343518	−	0.137431i
$966$		0			0
$967$	−34.0735	+	34.0735i	−1.09573	+	1.09573i	−0.100827	+	0.994904i	$0.532149\pi$
$967$	−34.0735	+	34.0735i	−1.09573	+	1.09573i	−0.994904	+	0.100827i	$0.967851\pi$
$968$	10.0918	−	2.70410i	0.324364	−	0.0869131i
$969$	7.28974	+	12.6262i	0.234180	+	0.405612i
$970$	8.01859	+	5.99972i	0.257461	+	0.192639i
$971$	−4.07547	−	2.35297i	−0.130788	−	0.0755105i	0.433179	−	0.901308i	$-0.357392\pi$
$971$	−4.07547	−	2.35297i	−0.130788	−	0.0755105i	−0.563966	+	0.825798i	$0.690725\pi$
$972$	10.2551	+	10.2551i	0.328934	+	0.328934i
$973$		0			0
$974$			2.55599i			0.0818993i
$975$	16.3773	−	4.81712i	0.524494	−	0.154271i
$976$	−5.25989	+	3.03680i	−0.168365	+	0.0972055i
$977$	26.5853	+	7.12351i	0.850540	+	0.227901i	0.657654	−	0.753320i	$-0.271549\pi$
$977$	26.5853	+	7.12351i	0.850540	+	0.227901i	0.192885	+	0.981221i	$0.438215\pi$
$978$	−3.69879	−	13.8041i	−0.118274	−	0.441405i
$979$	−4.48226			−0.143254
$980$		0			0
$981$	−14.5185			−0.463539
$982$	−3.77017	−	14.0704i	−0.120311	−	0.449006i
$983$	−43.3874	−	11.6256i	−1.38384	−	0.370799i	−0.511327	−	0.859386i	$-0.670846\pi$
$983$	−43.3874	−	11.6256i	−1.38384	−	0.370799i	−0.872515	+	0.488587i	$0.837513\pi$
$984$	0.831801	−	0.480241i	0.0265168	−	0.0153095i
$985$	2.62104	+	3.33133i	0.0835134	+	0.106145i
$986$			63.5766i			2.02469i
$987$		0			0
$988$	3.88878	+	3.88878i	0.123719	+	0.123719i
$989$	10.3424	+	5.97118i	0.328869	+	0.189872i
$990$	0.383760	+	2.66470i	0.0121967	+	0.0846897i
$991$	3.08498	+	5.34334i	0.0979975	+	0.169737i	0.910856	−	0.412725i	$-0.135423\pi$
$991$	3.08498	+	5.34334i	0.0979975	+	0.169737i	−0.812858	+	0.582462i	$0.802090\pi$
$992$	3.30595	−	0.885827i	0.104964	−	0.0281250i
$993$	−4.53527	+	4.53527i	−0.143922	+	0.143922i
$994$		0			0
$995$	29.8083	−	12.7729i	0.944985	−	0.404927i
$996$	7.67055	−	13.2858i	0.243051	−	0.420976i
$997$	−4.87184	+	18.1820i	−0.154293	+	0.575829i	0.844872	+	0.534968i	$0.179676\pi$
$997$	−4.87184	+	18.1820i	−0.154293	+	0.575829i	−0.999165	+	0.0408602i	$0.986990\pi$
$998$	−7.78721	+	29.0623i	−0.246500	+	0.919950i
$999$	7.24821	−	12.5543i	0.229323	−	0.397199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.l.c.313.1		16
5.2	odd	4	inner	490.2.l.c.117.3		16
7.2	even	3		490.2.g.c.293.3		16
7.3	odd	6	inner	490.2.l.c.423.3		16
7.4	even	3		70.2.k.a.3.4	✓	16
7.5	odd	6		490.2.g.c.293.2		16
7.6	odd	2		70.2.k.a.33.2	yes	16
21.11	odd	6		630.2.bv.c.73.2		16
21.20	even	2		630.2.bv.c.523.3		16
28.11	odd	6		560.2.ci.c.353.2		16
28.27	even	2		560.2.ci.c.33.2		16
35.2	odd	12		490.2.g.c.97.2		16
35.4	even	6		350.2.o.c.143.1		16
35.12	even	12		490.2.g.c.97.3		16
35.13	even	4		350.2.o.c.257.1		16
35.17	even	12	inner	490.2.l.c.227.1		16
35.18	odd	12		350.2.o.c.157.3		16
35.27	even	4		70.2.k.a.47.4	yes	16
35.32	odd	12		70.2.k.a.17.2	yes	16
35.34	odd	2		350.2.o.c.243.3		16
105.32	even	12		630.2.bv.c.577.3		16
105.62	odd	4		630.2.bv.c.397.2		16
140.27	odd	4		560.2.ci.c.257.2		16
140.67	even	12		560.2.ci.c.17.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.4	✓	16	7.4	even	3
70.2.k.a.17.2	yes	16	35.32	odd	12
70.2.k.a.33.2	yes	16	7.6	odd	2
70.2.k.a.47.4	yes	16	35.27	even	4
350.2.o.c.143.1		16	35.4	even	6
350.2.o.c.157.3		16	35.18	odd	12
350.2.o.c.243.3		16	35.34	odd	2
350.2.o.c.257.1		16	35.13	even	4
490.2.g.c.97.2		16	35.2	odd	12
490.2.g.c.97.3		16	35.12	even	12
490.2.g.c.293.2		16	7.5	odd	6
490.2.g.c.293.3		16	7.2	even	3
490.2.l.c.117.3		16	5.2	odd	4	inner
490.2.l.c.227.1		16	35.17	even	12	inner
490.2.l.c.313.1		16	1.1	even	1	trivial
490.2.l.c.423.3		16	7.3	odd	6	inner
560.2.ci.c.17.2		16	140.67	even	12
560.2.ci.c.33.2		16	28.27	even	2
560.2.ci.c.257.2		16	140.27	odd	4
560.2.ci.c.353.2		16	28.11	odd	6
630.2.bv.c.73.2		16	21.11	odd	6
630.2.bv.c.397.2		16	105.62	odd	4
630.2.bv.c.523.3		16	21.20	even	2
630.2.bv.c.577.3		16	105.32	even	12

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.13459 - 0.304013i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.264946 + 2.22032i) q^{5} +1.17462i q^{6} +(0.707107 + 0.707107i) q^{8} +(-1.40320 - 0.810140i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.13459 - 0.304013i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.264946 + 2.22032i) q^{5} +1.17462i q^{6} +(0.707107 + 0.707107i) q^{8} +(-1.40320 - 0.810140i) q^{9} +(2.21323 - 0.318742i) q^{10} +(-0.371536 - 0.643519i) q^{11} +(1.13459 - 0.304013i) q^{12} +(2.05532 - 2.05532i) q^{13} +(0.975610 - 2.43860i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.69789 - 6.33660i) q^{17} +(-0.419359 + 1.56507i) q^{18} +(0.946027 - 1.63857i) q^{19} +(-0.880708 - 2.05532i) q^{20} +(-0.525431 + 0.525431i) q^{22} +(5.11112 - 1.36952i) q^{23} +(-0.587308 - 1.01725i) q^{24} +(-4.85961 - 1.17653i) q^{25} +(-2.51725 - 1.45333i) q^{26} +(3.83750 + 3.83750i) q^{27} -9.69135i q^{29} +(-2.60802 - 0.311210i) q^{30} +(-2.96403 + 1.71129i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.225903 + 0.843083i) q^{33} -6.56014 q^{34} +1.62028 q^{36} +(-0.691342 - 2.58012i) q^{37} +(-1.82758 - 0.489700i) q^{38} +(-2.95680 + 1.70711i) q^{39} +(-1.75735 + 1.38266i) q^{40} +0.817699i q^{41} +(1.59589 + 1.59589i) q^{43} +(0.643519 + 0.371536i) q^{44} +(2.17054 - 2.90091i) q^{45} +(-2.64571 - 4.58251i) q^{46} +(-4.54913 + 1.21894i) q^{47} +(-0.830578 + 0.830578i) q^{48} +(0.121320 + 4.99853i) q^{50} +(-3.85282 + 6.67328i) q^{51} +(-0.752300 + 2.80762i) q^{52} +(1.29040 - 4.81583i) q^{53} +(2.71352 - 4.69996i) q^{54} +(1.52725 - 0.654429i) q^{55} +(-1.57150 + 1.57150i) q^{57} +(-9.36112 + 2.50831i) q^{58} +(-1.27487 - 2.20815i) q^{59} +(0.374399 + 2.59970i) q^{60} +(-5.25989 - 3.03680i) q^{61} +(2.42012 + 2.42012i) q^{62} +1.00000i q^{64} +(4.01892 + 5.10802i) q^{65} +(0.755887 - 0.436412i) q^{66} +(13.2248 + 3.54358i) q^{67} +(1.69789 + 6.33660i) q^{68} -6.21538 q^{69} -16.0173 q^{71} +(-0.419359 - 1.56507i) q^{72} +(8.54906 + 2.29071i) q^{73} +(-2.31328 + 1.33557i) q^{74} +(5.15599 + 2.81226i) q^{75} +1.89205i q^{76} +(2.41421 + 2.41421i) q^{78} +(5.70091 + 3.29142i) q^{79} +(1.79038 + 1.33961i) q^{80} +(-0.756928 - 1.31104i) q^{81} +(0.789836 - 0.211636i) q^{82} +(9.23519 - 9.23519i) q^{83} +(13.6194 + 5.44871i) q^{85} +(1.12846 - 1.95456i) q^{86} +(-2.94629 + 10.9957i) q^{87} +(0.192321 - 0.717752i) q^{88} +(3.01603 - 5.22392i) q^{89} +(-3.36384 - 1.34577i) q^{90} +(-3.74160 + 3.74160i) q^{92} +(3.88322 - 1.04051i) q^{93} +(2.35481 + 4.07864i) q^{94} +(3.38749 + 2.53461i) q^{95} +(1.01725 + 0.587308i) q^{96} +(3.16693 + 3.16693i) q^{97} +1.20398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5}+O(q^{10}) \) 16 * q + 12 * q^5	\( 16 q + 12 q^{5} + 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} + 36 q^{17} - 8 q^{18} - 8 q^{22} - 4 q^{23} + 12 q^{25} - 12 q^{26} + 20 q^{30} - 24 q^{31} - 48 q^{33} - 8 q^{36} + 4 q^{37} - 24 q^{38} - 8 q^{43} + 12 q^{45} - 8 q^{46} - 12 q^{47} - 32 q^{50} - 16 q^{51} - 28 q^{53} + 8 q^{57} - 32 q^{58} + 8 q^{60} + 12 q^{61} - 8 q^{65} + 32 q^{67} + 36 q^{68} + 16 q^{71} - 8 q^{72} + 12 q^{73} + 48 q^{75} + 16 q^{78} + 12 q^{80} + 48 q^{82} + 24 q^{85} + 12 q^{86} + 24 q^{87} - 4 q^{88} + 8 q^{92} + 28 q^{93} + 20 q^{95} - 12 q^{96}+O(q^{100}) \) 16 * q + 12 * q^5 + 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 + 36 * q^17 - 8 * q^18 - 8 * q^22 - 4 * q^23 + 12 * q^25 - 12 * q^26 + 20 * q^30 - 24 * q^31 - 48 * q^33 - 8 * q^36 + 4 * q^37 - 24 * q^38 - 8 * q^43 + 12 * q^45 - 8 * q^46 - 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 + 8 * q^57 - 32 * q^58 + 8 * q^60 + 12 * q^61 - 8 * q^65 + 32 * q^67 + 36 * q^68 + 16 * q^71 - 8 * q^72 + 12 * q^73 + 48 * q^75 + 16 * q^78 + 12 * q^80 + 48 * q^82 + 24 * q^85 + 12 * q^86 + 24 * q^87 - 4 * q^88 + 8 * q^92 + 28 * q^93 + 20 * q^95 - 12 * q^96

Introduction

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