LMFDB - Embedded newform 507.2.e.j.484.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(22,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("507.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			484.1
Root			$0.900969 + 1.56052i$ of defining polynomial
Character	$\chi$	$=$	507.484
Dual form			507.2.e.j.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.900969 - 1.56052i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.623490 + 1.07992i) q^{4} +1.44504 q^{5} +(-0.900969 + 1.56052i) q^{6} +(-1.72252 + 2.98349i) q^{7} -1.35690 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.30194 - 2.25502i) q^{10} +(2.59299 + 4.49119i) q^{11} +1.24698 q^{12} +6.20775 q^{14} +(-0.722521 - 1.25144i) q^{15} +(2.46950 + 4.27730i) q^{16} +(0.376510 - 0.652135i) q^{17} +1.80194 q^{18} +(-3.98039 + 6.89423i) q^{19} +(-0.900969 + 1.56052i) q^{20} +3.44504 q^{21} +(4.67241 - 8.09285i) q^{22} +(1.41454 + 2.45006i) q^{23} +(0.678448 + 1.17511i) q^{24} -2.91185 q^{25} +1.00000 q^{27} +(-2.14795 - 3.72036i) q^{28} +(1.95593 + 3.38776i) q^{29} +(-1.30194 + 2.25502i) q^{30} -4.89977 q^{31} +(3.09299 - 5.35722i) q^{32} +(2.59299 - 4.49119i) q^{33} -1.35690 q^{34} +(-2.48911 + 4.31127i) q^{35} +(-0.623490 - 1.07992i) q^{36} +(-3.12349 - 5.41004i) q^{37} +14.3448 q^{38} -1.96077 q^{40} +(-0.900969 - 1.56052i) q^{41} +(-3.10388 - 5.37607i) q^{42} +(3.54892 - 6.14691i) q^{43} -6.46681 q^{44} +(-0.722521 + 1.25144i) q^{45} +(2.54892 - 4.41485i) q^{46} +10.5526 q^{47} +(2.46950 - 4.27730i) q^{48} +(-2.43416 - 4.21608i) q^{49} +(2.62349 + 4.54402i) q^{50} -0.753020 q^{51} -3.08815 q^{53} +(-0.900969 - 1.56052i) q^{54} +(3.74698 + 6.48996i) q^{55} +(2.33728 - 4.04829i) q^{56} +7.96077 q^{57} +(3.52446 - 6.10454i) q^{58} +(-0.939001 + 1.62640i) q^{59} +1.80194 q^{60} +(-1.67241 + 2.89669i) q^{61} +(4.41454 + 7.64621i) q^{62} +(-1.72252 - 2.98349i) q^{63} -1.26875 q^{64} -9.34481 q^{66} +(2.27144 + 3.93425i) q^{67} +(0.469501 + 0.813199i) q^{68} +(1.41454 - 2.45006i) q^{69} +8.97046 q^{70} +(4.55980 - 7.89781i) q^{71} +(0.678448 - 1.17511i) q^{72} +2.95108 q^{73} +(-5.62833 + 9.74856i) q^{74} +(1.45593 + 2.52174i) q^{75} +(-4.96346 - 8.59696i) q^{76} -17.8659 q^{77} -9.43296 q^{79} +(3.56853 + 6.18088i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.62349 + 2.81197i) q^{82} -6.46681 q^{83} +(-2.14795 + 3.72036i) q^{84} +(0.544073 - 0.942362i) q^{85} -12.7899 q^{86} +(1.95593 - 3.38776i) q^{87} +(-3.51842 - 6.09408i) q^{88} +(-0.579417 - 1.00358i) q^{89} +2.60388 q^{90} -3.52781 q^{92} +(2.44989 + 4.24333i) q^{93} +(-9.50753 - 16.4675i) q^{94} +(-5.75182 + 9.96245i) q^{95} -6.18598 q^{96} +(-4.32908 + 7.49819i) q^{97} +(-4.38620 + 7.59712i) q^{98} -5.18598 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 3 q^{3} + q^{4} + 8 q^{5} - q^{6} - 10 q^{7} - 3 q^{9} + q^{10} + q^{11} - 2 q^{12} + 2 q^{14} - 4 q^{15} + 5 q^{16} + 7 q^{17} + 2 q^{18} - 11 q^{19} - q^{20} + 20 q^{21} + 5 q^{22}+ \cdots - 2 q^{99}+O(q^{100}) $ 6 * q - q^2 - 3 * q^3 + q^4 + 8 * q^5 - q^6 - 10 * q^7 - 3 * q^9 + q^10 + q^11 - 2 * q^12 + 2 * q^14 - 4 * q^15 + 5 * q^16 + 7 * q^17 + 2 * q^18 - 11 * q^19 - q^20 + 20 * q^21 + 5 * q^22 - 2 * q^23 - 10 * q^25 + 6 * q^27 + q^28 + 8 * q^29 + q^30 + 16 * q^31 + 4 * q^32 + q^33 - 18 * q^35 + q^36 - 14 * q^37 + 40 * q^38 + 14 * q^40 - q^41 - q^42 + 3 * q^43 - 32 * q^44 - 4 * q^45 - 3 * q^46 - 18 * q^47 + 5 * q^48 - 17 * q^49 + 11 * q^50 - 14 * q^51 - 26 * q^53 - q^54 + 13 * q^55 - 7 * q^56 + 22 * q^57 + 12 * q^58 + 14 * q^59 + 2 * q^60 + 13 * q^61 + 16 * q^62 - 10 * q^63 + 8 * q^64 - 10 * q^66 - 5 * q^67 - 7 * q^68 - 2 * q^69 - 16 * q^70 + 6 * q^71 + 36 * q^73 - 7 * q^74 + 5 * q^75 - q^76 - 30 * q^77 - 18 * q^79 + 16 * q^80 - 3 * q^81 - 5 * q^82 - 32 * q^83 + q^84 + 7 * q^85 - 30 * q^86 + 8 * q^87 + 7 * q^88 + 5 * q^89 - 2 * q^90 - 34 * q^92 - 8 * q^93 - 32 * q^94 - 3 * q^95 - 8 * q^96 - 5 * q^97 + 13 * q^98 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.900969	−	1.56052i	−0.637081	−	1.10346i	−0.986070	−	0.166330i	$-0.946808\pi$
$2$	−0.900969	−	1.56052i	−0.637081	−	1.10346i	0.348989	−	0.937127i	$-0.386525\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.623490	+	1.07992i	−0.311745	+	0.539958i
$5$	1.44504			0.646242			0.323121	−	0.946358i	$-0.395268\pi$
$5$	1.44504			0.646242			0.323121	+	0.946358i	$0.395268\pi$
$6$	−0.900969	+	1.56052i	−0.367819	+	0.637081i
$7$	−1.72252	+	2.98349i	−0.651052	+	1.12765i	0.331816	+	0.943344i	$0.392339\pi$
$7$	−1.72252	+	2.98349i	−0.651052	+	1.12765i	−0.982868	+	0.184311i	$0.940995\pi$
$8$	−1.35690			−0.479735
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.30194	−	2.25502i	−0.411709	−	0.713101i
$11$	2.59299	+	4.49119i	0.781816	+	1.35415i	0.930883	+	0.365318i	$0.119040\pi$
$11$	2.59299	+	4.49119i	0.781816	+	1.35415i	−0.149067	+	0.988827i	$0.547627\pi$
$12$	1.24698			0.359972
$13$		0			0
$13$		0			0
$14$	6.20775			1.65909
$15$	−0.722521	−	1.25144i	−0.186554	−	0.323121i
$16$	2.46950	+	4.27730i	0.617375	+	1.06933i
$17$	0.376510	−	0.652135i	0.0913171	−	0.158166i	−0.816748	−	0.576994i	$-0.804226\pi$
$17$	0.376510	−	0.652135i	0.0913171	−	0.158166i	0.908066	+	0.418828i	$0.137559\pi$
$18$	1.80194			0.424721
$19$	−3.98039	+	6.89423i	−0.913163	+	1.58164i	−0.103594	+	0.994620i	$0.533034\pi$
$19$	−3.98039	+	6.89423i	−0.913163	+	1.58164i	−0.809569	+	0.587025i	$0.800299\pi$
$20$	−0.900969	+	1.56052i	−0.201463	+	0.348944i
$21$	3.44504			0.751770
$22$	4.67241	−	8.09285i	0.996161	−	1.72540i
$23$	1.41454	+	2.45006i	0.294952	+	0.510873i	0.974974	−	0.222320i	$-0.0713628\pi$
$23$	1.41454	+	2.45006i	0.294952	+	0.510873i	−0.680021	+	0.733192i	$0.738030\pi$
$24$	0.678448	+	1.17511i	0.138488	+	0.239868i
$25$	−2.91185			−0.582371
$26$		0			0
$27$	1.00000			0.192450
$28$	−2.14795	−	3.72036i	−0.405924	−	0.703081i
$29$	1.95593	+	3.38776i	0.363207	+	0.629092i	0.988487	−	0.151308i	$-0.0483486\pi$
$29$	1.95593	+	3.38776i	0.363207	+	0.629092i	−0.625280	+	0.780400i	$0.715015\pi$
$30$	−1.30194	+	2.25502i	−0.237700	+	0.411709i
$31$	−4.89977			−0.880025			−0.440013	−	0.897992i	$-0.645026\pi$
$31$	−4.89977			−0.880025			−0.440013	+	0.897992i	$0.645026\pi$
$32$	3.09299	−	5.35722i	0.546769	−	0.947031i
$33$	2.59299	−	4.49119i	0.451382	−	0.781816i
$34$	−1.35690			−0.232706
$35$	−2.48911	+	4.31127i	−0.420737	+	0.728738i
$36$	−0.623490	−	1.07992i	−0.103915	−	0.179986i
$37$	−3.12349	−	5.41004i	−0.513499	−	0.889406i	−0.999877	−	0.0156576i	$-0.995016\pi$
$37$	−3.12349	−	5.41004i	−0.513499	−	0.889406i	0.486379	−	0.873748i	$-0.338317\pi$
$38$	14.3448			2.32704
$39$		0			0
$40$	−1.96077			−0.310025
$41$	−0.900969	−	1.56052i	−0.140708	−	0.243713i	0.787056	−	0.616882i	$-0.211604\pi$
$41$	−0.900969	−	1.56052i	−0.140708	−	0.243713i	−0.927763	+	0.373169i	$0.878271\pi$
$42$	−3.10388	−	5.37607i	−0.478938	−	0.829546i
$43$	3.54892	−	6.14691i	0.541205	−	0.937394i	−0.457630	−	0.889143i	$-0.651302\pi$
$43$	3.54892	−	6.14691i	0.541205	−	0.937394i	0.998835	−	0.0482517i	$-0.0153650\pi$
$44$	−6.46681			−0.974909
$45$	−0.722521	+	1.25144i	−0.107707	+	0.186554i
$46$	2.54892	−	4.41485i	0.375817	−	0.650935i
$47$	10.5526			1.53925			0.769625	−	0.638496i	$-0.220443\pi$
$47$	10.5526			1.53925			0.769625	+	0.638496i	$0.220443\pi$
$48$	2.46950	−	4.27730i	0.356442	−	0.617375i
$49$	−2.43416	−	4.21608i	−0.347737	−	0.602298i
$50$	2.62349	+	4.54402i	0.371017	+	0.642621i
$51$	−0.753020			−0.105444
$52$		0			0
$53$	−3.08815			−0.424189			−0.212095	−	0.977249i	$-0.568029\pi$
$53$	−3.08815			−0.424189			−0.212095	+	0.977249i	$0.568029\pi$
$54$	−0.900969	−	1.56052i	−0.122606	−	0.212360i
$55$	3.74698	+	6.48996i	0.505243	+	0.875106i
$56$	2.33728	−	4.04829i	0.312332	−	0.540976i
$57$	7.96077			1.05443
$58$	3.52446	−	6.10454i	0.462784	−	0.801566i
$59$	−0.939001	+	1.62640i	−0.122248	+	0.211739i	−0.920654	−	0.390380i	$-0.872344\pi$
$59$	−0.939001	+	1.62640i	−0.122248	+	0.211739i	0.798406	+	0.602119i	$0.205677\pi$
$60$	1.80194			0.232629
$61$	−1.67241	+	2.89669i	−0.214130	+	0.370884i	−0.953003	−	0.302961i	$-0.902025\pi$
$61$	−1.67241	+	2.89669i	−0.214130	+	0.370884i	0.738873	+	0.673844i	$0.235358\pi$
$62$	4.41454	+	7.64621i	0.560647	+	0.971070i
$63$	−1.72252	−	2.98349i	−0.217017	−	0.375885i
$64$	−1.26875			−0.158594
$65$		0			0
$66$	−9.34481			−1.15027
$67$	2.27144	+	3.93425i	0.277500	+	0.480645i	0.970763	−	0.240040i	$-0.0771607\pi$
$67$	2.27144	+	3.93425i	0.277500	+	0.480645i	−0.693263	+	0.720685i	$0.743827\pi$
$68$	0.469501	+	0.813199i	0.0569353	+	0.0986148i
$69$	1.41454	−	2.45006i	0.170291	−	0.294952i
$70$	8.97046			1.07218
$71$	4.55980	−	7.89781i	0.541149	−	0.937298i	−0.457689	−	0.889112i	$-0.651323\pi$
$71$	4.55980	−	7.89781i	0.541149	−	0.937298i	0.998838	−	0.0481854i	$-0.0153438\pi$
$72$	0.678448	−	1.17511i	0.0799559	−	0.138488i
$73$	2.95108			0.345398			0.172699	−	0.984975i	$-0.444751\pi$
$73$	2.95108			0.345398			0.172699	+	0.984975i	$0.444751\pi$
$74$	−5.62833	+	9.74856i	−0.654281	+	1.13325i
$75$	1.45593	+	2.52174i	0.168116	+	0.291185i
$76$	−4.96346	−	8.59696i	−0.569348	−	0.986139i
$77$	−17.8659			−2.03601
$78$		0			0
$79$	−9.43296			−1.06129			−0.530645	−	0.847594i	$-0.678050\pi$
$79$	−9.43296			−1.06129			−0.530645	+	0.847594i	$0.678050\pi$
$80$	3.56853	+	6.18088i	0.398974	+	0.691043i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.62349	+	2.81197i	−0.179284	+	0.310530i
$83$	−6.46681			−0.709825			−0.354912	−	0.934900i	$-0.615489\pi$
$83$	−6.46681			−0.709825			−0.354912	+	0.934900i	$0.615489\pi$
$84$	−2.14795	+	3.72036i	−0.234360	+	0.405924i
$85$	0.544073	−	0.942362i	0.0590130	−	0.102214i
$86$	−12.7899			−1.37917
$87$	1.95593	−	3.38776i	0.209697	−	0.363207i
$88$	−3.51842	−	6.09408i	−0.375065	−	0.649631i
$89$	−0.579417	−	1.00358i	−0.0614181	−	0.106379i	0.833681	−	0.552246i	$-0.186229\pi$
$89$	−0.579417	−	1.00358i	−0.0614181	−	0.106379i	−0.895099	+	0.445866i	$0.852896\pi$
$90$	2.60388			0.274473
$91$		0			0
$92$	−3.52781			−0.367800
$93$	2.44989	+	4.24333i	0.254041	+	0.440013i
$94$	−9.50753	−	16.4675i	−0.980627	−	1.69850i
$95$	−5.75182	+	9.96245i	−0.590125	+	1.02213i
$96$	−6.18598			−0.631354
$97$	−4.32908	+	7.49819i	−0.439552	+	0.761326i	−0.997655	−	0.0684454i	$-0.978196\pi$
$97$	−4.32908	+	7.49819i	−0.439552	+	0.761326i	0.558103	+	0.829772i	$0.311529\pi$
$98$	−4.38620	+	7.59712i	−0.443073	+	0.767425i
$99$	−5.18598			−0.521211
$100$	1.81551	−	3.14456i	0.181551	−	0.314456i
$101$	4.23825	+	7.34087i	0.421722	+	0.730443i	0.996108	−	0.0881410i	$-0.0280926\pi$
$101$	4.23825	+	7.34087i	0.421722	+	0.730443i	−0.574386	+	0.818584i	$0.694759\pi$
$102$	0.678448	+	1.17511i	0.0671764	+	0.116353i
$103$	5.64742			0.556456			0.278228	−	0.960515i	$-0.410253\pi$
$103$	5.64742			0.556456			0.278228	+	0.960515i	$0.410253\pi$
$104$		0			0
$105$	4.97823			0.485825
$106$	2.78232	+	4.81913i	0.270243	+	0.468075i
$107$	3.36778	+	5.83317i	0.325576	+	0.563914i	0.981629	−	0.190801i	$-0.0611086\pi$
$107$	3.36778	+	5.83317i	0.325576	+	0.563914i	−0.656053	+	0.754715i	$0.727775\pi$
$108$	−0.623490	+	1.07992i	−0.0599953	+	0.103915i
$109$	−2.07606			−0.198851			−0.0994255	−	0.995045i	$-0.531700\pi$
$109$	−2.07606			−0.198851			−0.0994255	+	0.995045i	$0.531700\pi$
$110$	6.75182	−	11.6945i	0.643761	−	1.11503i
$111$	−3.12349	+	5.41004i	−0.296469	+	0.513499i
$112$	−17.0151			−1.60777
$113$	−3.08426	+	5.34210i	−0.290143	+	0.502542i	−0.973843	−	0.227221i	$-0.927036\pi$
$113$	−3.08426	+	5.34210i	−0.290143	+	0.502542i	0.683700	+	0.729763i	$0.260370\pi$
$114$	−7.17241	−	12.4230i	−0.671757	−	1.16352i
$115$	2.04407	+	3.54044i	0.190611	+	0.330148i
$116$	−4.87800			−0.452911
$117$		0			0
$118$	3.38404			0.311526
$119$	1.29709	+	2.24663i	0.118904	+	0.205948i
$120$	0.980386	+	1.69808i	0.0894966	+	0.155013i
$121$	−7.94720	+	13.7650i	−0.722473	+	1.25136i
$122$	6.02715			0.545672
$123$	−0.900969	+	1.56052i	−0.0812376	+	0.140708i
$124$	3.05496	−	5.29134i	0.274343	−	0.475177i
$125$	−11.4330			−1.02260
$126$	−3.10388	+	5.37607i	−0.276515	+	0.478938i
$127$	7.13102	+	12.3513i	0.632776	+	1.09600i	0.986982	+	0.160833i	$0.0514179\pi$
$127$	7.13102	+	12.3513i	0.632776	+	1.09600i	−0.354206	+	0.935168i	$0.615249\pi$
$128$	−5.04288	−	8.73452i	−0.445732	−	0.772030i
$129$	−7.09783			−0.624929
$130$		0			0
$131$	22.6015			1.97470			0.987350	−	0.158554i	$-0.0506831\pi$
$131$	22.6015			1.97470			0.987350	+	0.158554i	$0.0506831\pi$
$132$	3.23341	+	5.60042i	0.281432	+	0.487454i
$133$	−13.7126	−	23.7509i	−1.18903	−	2.05947i
$134$	4.09299	−	7.08927i	0.353581	−	0.612419i
$135$	1.44504			0.124369
$136$	−0.510885	+	0.884879i	−0.0438080	+	0.0758777i
$137$	6.81767	−	11.8085i	0.582473	−	1.00887i	−0.412713	−	0.910861i	$-0.635419\pi$
$137$	6.81767	−	11.8085i	0.582473	−	1.00887i	0.995185	−	0.0980109i	$-0.0312480\pi$
$138$	−5.09783			−0.433957
$139$	−8.80074	+	15.2433i	−0.746469	+	1.29292i	0.203036	+	0.979171i	$0.434919\pi$
$139$	−8.80074	+	15.2433i	−0.746469	+	1.29292i	−0.949505	+	0.313751i	$0.898414\pi$
$140$	−3.10388	−	5.37607i	−0.262325	−	0.454361i
$141$	−5.27628	−	9.13879i	−0.444343	−	0.769625i
$142$	−16.4330			−1.37902
$143$		0			0
$144$	−4.93900			−0.411583
$145$	2.82640	+	4.89546i	0.234719	+	0.406546i
$146$	−2.65883	−	4.60523i	−0.220047	−	0.381132i
$147$	−2.43416	+	4.21608i	−0.200766	+	0.347737i
$148$	7.78986			0.640322
$149$	−6.36927	+	11.0319i	−0.521791	+	0.903769i	0.477888	+	0.878421i	$0.341403\pi$
$149$	−6.36927	+	11.0319i	−0.521791	+	0.903769i	−0.999679	+	0.0253478i	$0.991931\pi$
$150$	2.62349	−	4.54402i	0.214207	−	0.371017i
$151$	15.6407			1.27282			0.636412	−	0.771350i	$-0.280418\pi$
$151$	15.6407			1.27282			0.636412	+	0.771350i	$0.280418\pi$
$152$	5.40097	−	9.35475i	0.438076	−	0.758771i
$153$	0.376510	+	0.652135i	0.0304390	+	0.0527220i
$154$	16.0966	+	27.8802i	1.29710	+	2.24665i
$155$	−7.08038			−0.568710
$156$		0			0
$157$	−0.823708			−0.0657391			−0.0328695	−	0.999460i	$-0.510465\pi$
$157$	−0.823708			−0.0657391			−0.0328695	+	0.999460i	$0.510465\pi$
$158$	8.49880	+	14.7204i	0.676129	+	1.17109i
$159$	1.54407	+	2.67441i	0.122453	+	0.212095i
$160$	4.46950	−	7.74140i	0.353345	−	0.612012i
$161$	−9.74632			−0.768117
$162$	−0.900969	+	1.56052i	−0.0707868	+	0.122606i
$163$	−3.13437	+	5.42890i	−0.245503	+	0.425224i	−0.962273	−	0.272086i	$-0.912287\pi$
$163$	−3.13437	+	5.42890i	−0.245503	+	0.425224i	0.716770	+	0.697310i	$0.245620\pi$
$164$	2.24698			0.175460
$165$	3.74698	−	6.48996i	0.291702	−	0.505243i
$166$	5.82640	+	10.0916i	0.452216	+	0.783261i
$167$	3.72521	+	6.45225i	0.288265	+	0.499290i	0.973396	−	0.229130i	$-0.0735881\pi$
$167$	3.72521	+	6.45225i	0.288265	+	0.499290i	−0.685130	+	0.728420i	$0.740255\pi$
$168$	−4.67456			−0.360650
$169$		0			0
$170$	−1.96077			−0.150384
$171$	−3.98039	−	6.89423i	−0.304388	−	0.527215i
$172$	4.42543	+	7.66507i	0.337436	+	0.584456i
$173$	1.00484	−	1.74044i	0.0763969	−	0.132323i	−0.825296	−	0.564700i	$-0.808992\pi$
$173$	1.00484	−	1.74044i	0.0763969	−	0.132323i	0.901693	+	0.432377i	$0.142325\pi$
$174$	−7.04892			−0.534377
$175$	5.01573	−	8.68750i	0.379154	−	0.656713i
$176$	−12.8068	+	22.1820i	−0.965348	+	1.67203i
$177$	1.87800			0.141159
$178$	−1.04407	+	1.80839i	−0.0782566	+	0.135544i
$179$	−10.0184	−	17.3524i	−0.748812	−	1.29698i	−0.948393	−	0.317099i	$-0.897291\pi$
$179$	−10.0184	−	17.3524i	−0.748812	−	1.29698i	0.199581	−	0.979881i	$-0.436042\pi$
$180$	−0.900969	−	1.56052i	−0.0671543	−	0.116315i
$181$	24.1226			1.79302			0.896509	−	0.443026i	$-0.146095\pi$
$181$	24.1226			1.79302			0.896509	+	0.443026i	$0.146095\pi$
$182$		0			0
$183$	3.34481			0.247256
$184$	−1.91939	−	3.32448i	−0.141499	−	0.245084i
$185$	−4.51357	−	7.81774i	−0.331845	−	0.574772i
$186$	4.41454	−	7.64621i	0.323690	−	0.560647i
$187$	3.90515			0.285573
$188$	−6.57942	+	11.3959i	−0.479853	+	0.831130i
$189$	−1.72252	+	2.98349i	−0.125295	+	0.217017i
$190$	20.7289			1.50383
$191$	3.54019	−	6.13179i	0.256159	−	0.443680i	−0.709051	−	0.705158i	$-0.750876\pi$
$191$	3.54019	−	6.13179i	0.256159	−	0.443680i	0.965210	+	0.261477i	$0.0842096\pi$
$192$	0.634375	+	1.09877i	0.0457821	+	0.0792969i
$193$	−4.88404	−	8.45941i	−0.351561	−	0.608922i	0.634962	−	0.772543i	$-0.281016\pi$
$193$	−4.88404	−	8.45941i	−0.351561	−	0.608922i	−0.986523	+	0.163622i	$0.947682\pi$
$194$	15.6015			1.12012
$195$		0			0
$196$	6.07069			0.433621
$197$	−11.7056	−	20.2747i	−0.833989	−	1.44451i	−0.894851	−	0.446365i	$-0.852718\pi$
$197$	−11.7056	−	20.2747i	−0.833989	−	1.44451i	0.0608617	−	0.998146i	$-0.480615\pi$
$198$	4.67241	+	8.09285i	0.332054	+	0.575134i
$199$	−2.01238	+	3.48554i	−0.142654	+	0.247083i	−0.928495	−	0.371345i	$-0.878897\pi$
$199$	−2.01238	+	3.48554i	−0.142654	+	0.247083i	0.785841	+	0.618428i	$0.212230\pi$
$200$	3.95108			0.279384
$201$	2.27144	−	3.93425i	0.160215	−	0.277500i
$202$	7.63706	−	13.2278i	0.537342	−	0.930703i
$203$	−13.4765			−0.945865
$204$	0.469501	−	0.813199i	0.0328716	−	0.0569353i
$205$	−1.30194	−	2.25502i	−0.0909313	−	0.157498i
$206$	−5.08815	−	8.81293i	−0.354508	−	0.614026i
$207$	−2.82908			−0.196635
$208$		0			0
$209$	−41.2844			−2.85570
$210$	−4.48523	−	7.76865i	−0.309510	−	0.536088i
$211$	1.95593	+	3.38776i	0.134652	+	0.233223i	0.925464	−	0.378835i	$-0.123675\pi$
$211$	1.95593	+	3.38776i	0.134652	+	0.233223i	−0.790813	+	0.612058i	$0.790342\pi$
$212$	1.92543	−	3.33494i	0.132239	−	0.229045i
$213$	−9.11960			−0.624865
$214$	6.06853	−	10.5110i	0.414836	−	0.718518i
$215$	5.12833	−	8.88254i	0.349749	−	0.605784i
$216$	−1.35690			−0.0923251
$217$	8.43996	−	14.6184i	0.572942	−	0.992364i
$218$	1.87047	+	3.23975i	0.126684	+	0.219423i
$219$	−1.47554	−	2.55571i	−0.0997078	−	0.172699i
$220$	−9.34481			−0.630027
$221$		0			0
$222$	11.2567			0.755498
$223$	−3.72468	−	6.45133i	−0.249423	−	0.432013i	0.713943	−	0.700204i	$-0.246908\pi$
$223$	−3.72468	−	6.45133i	−0.249423	−	0.432013i	−0.963366	+	0.268191i	$0.913574\pi$
$224$	10.6555	+	18.4558i	0.711949	+	1.23313i
$225$	1.45593	−	2.52174i	0.0970618	−	0.168116i
$226$	11.1153			0.739378
$227$	10.6250	−	18.4030i	0.705205	−	1.22145i	−0.261413	−	0.965227i	$-0.584188\pi$
$227$	10.6250	−	18.4030i	0.705205	−	1.22145i	0.966618	−	0.256223i	$-0.0824783\pi$
$228$	−4.96346	+	8.59696i	−0.328713	+	0.569348i
$229$	9.29590			0.614290			0.307145	−	0.951663i	$-0.400626\pi$
$229$	9.29590			0.614290			0.307145	+	0.951663i	$0.400626\pi$
$230$	3.68329	−	6.37965i	0.242869	−	0.420662i
$231$	8.93296	+	15.4723i	0.587746	+	1.01801i
$232$	−2.65399	−	4.59684i	−0.174243	−	0.301798i
$233$	16.2107			1.06200			0.531000	−	0.847372i	$-0.321816\pi$
$233$	16.2107			1.06200			0.531000	+	0.847372i	$0.321816\pi$
$234$		0			0
$235$	15.2489			0.994728
$236$	−1.17092	−	2.02808i	−0.0762201	−	0.132017i
$237$	4.71648	+	8.16918i	0.306368	+	0.530645i
$238$	2.33728	−	4.04829i	0.151503	−	0.262412i
$239$	−13.5090			−0.873826			−0.436913	−	0.899504i	$-0.643928\pi$
$239$	−13.5090			−0.873826			−0.436913	+	0.899504i	$0.643928\pi$
$240$	3.56853	−	6.18088i	0.230348	−	0.398974i
$241$	−3.13437	+	5.42890i	−0.201903	+	0.349706i	−0.949142	−	0.314850i	$-0.898046\pi$
$241$	−3.13437	+	5.42890i	−0.201903	+	0.349706i	0.747239	+	0.664556i	$0.231379\pi$
$242$	28.6407			1.84109
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.08546	−	3.61212i	−0.133508	−	0.231242i
$245$	−3.51746	−	6.09242i	−0.224722	−	0.389230i
$246$	3.24698			0.207020
$247$		0			0
$248$	6.64848			0.422179
$249$	3.23341	+	5.60042i	0.204909	+	0.354912i
$250$	10.3007	+	17.8414i	0.651476	+	1.12839i
$251$	0.376510	−	0.652135i	0.0237651	−	0.0411624i	−0.853898	−	0.520440i	$-0.825768\pi$
$251$	0.376510	−	0.652135i	0.0237651	−	0.0411624i	0.877663	+	0.479278i	$0.159101\pi$
$252$	4.29590			0.270616
$253$	−7.33579	+	12.7060i	−0.461197	+	0.798817i
$254$	12.8497	−	22.2563i	0.806259	−	1.39648i
$255$	−1.08815			−0.0681423
$256$	−10.3557	+	17.9366i	−0.647231	+	1.12104i
$257$	−9.86323	−	17.0836i	−0.615252	−	1.06565i	−0.990340	−	0.138658i	$-0.955721\pi$
$257$	−9.86323	−	17.0836i	−0.615252	−	1.06565i	0.375089	−	0.926989i	$-0.377612\pi$
$258$	6.39493	+	11.0763i	0.398131	+	0.689583i
$259$	21.5211			1.33726
$260$		0			0
$261$	−3.91185			−0.242138
$262$	−20.3632	−	35.2702i	−1.25804	−	2.17900i
$263$	8.80463	+	15.2501i	0.542917	+	0.940359i	0.998735	+	0.0502861i	$0.0160133\pi$
$263$	8.80463	+	15.2501i	0.542917	+	0.940359i	−0.455818	+	0.890073i	$0.650653\pi$
$264$	−3.51842	+	6.09408i	−0.216544	+	0.375065i
$265$	−4.46250			−0.274129
$266$	−24.7092	+	42.7977i	−1.51502	+	2.62409i
$267$	−0.579417	+	1.00358i	−0.0354597	+	0.0614181i
$268$	−5.66487			−0.346037
$269$	8.19351	−	14.1916i	0.499567	−	0.865276i	−0.500433	−	0.865776i	$-0.666826\pi$
$269$	8.19351	−	14.1916i	0.499567	−	0.865276i	1.00000		0.000499532i	$0.000159006\pi$
$270$	−1.30194	−	2.25502i	−0.0792334	−	0.137236i
$271$	0.397616	+	0.688692i	0.0241535	+	0.0418351i	0.877849	−	0.478937i	$-0.158978\pi$
$271$	0.397616	+	0.688692i	0.0241535	+	0.0418351i	−0.853696	+	0.520772i	$0.825644\pi$
$272$	3.71917			0.225508
$273$		0			0
$274$	−24.5700			−1.48433
$275$	−7.55041	−	13.0777i	−0.455307	−	0.788615i
$276$	1.76391	+	3.05517i	0.106175	+	0.183900i
$277$	2.41670	−	4.18584i	0.145205	−	0.251503i	−0.784244	−	0.620452i	$-0.786949\pi$
$277$	2.41670	−	4.18584i	0.145205	−	0.251503i	0.929450	+	0.368949i	$0.120282\pi$
$278$	31.7168			1.90225
$279$	2.44989	−	4.24333i	0.146671	−	0.254041i
$280$	3.37747	−	5.84995i	0.201842	−	0.349601i
$281$	18.7748			1.12001			0.560005	−	0.828489i	$-0.310799\pi$
$281$	18.7748			1.12001			0.560005	+	0.828489i	$0.310799\pi$
$282$	−9.50753	+	16.4675i	−0.566165	+	0.980627i
$283$	3.95862	+	6.85652i	0.235315	+	0.407578i	0.959364	−	0.282171i	$-0.0910544\pi$
$283$	3.95862	+	6.85652i	0.235315	+	0.407578i	−0.724049	+	0.689749i	$0.757721\pi$
$284$	5.68598	+	9.84841i	0.337401	+	0.584395i
$285$	11.5036			0.681417
$286$		0			0
$287$	6.20775			0.366432
$288$	3.09299	+	5.35722i	0.182256	+	0.315677i
$289$	8.21648	+	14.2314i	0.483322	+	0.837139i
$290$	5.09299	−	8.82132i	0.299071	−	0.518006i
$291$	8.65817			0.507551
$292$	−1.83997	+	3.18692i	−0.107676	+	0.186500i
$293$	−3.28956	+	5.69769i	−0.192178	+	0.332862i	−0.945972	−	0.324249i	$-0.894888\pi$
$293$	−3.28956	+	5.69769i	−0.192178	+	0.332862i	0.753794	+	0.657111i	$0.228222\pi$
$294$	8.77240			0.511617
$295$	−1.35690	+	2.35021i	−0.0790015	+	0.136835i
$296$	4.23825	+	7.34087i	0.246343	+	0.426679i
$297$	2.59299	+	4.49119i	0.150461	+	0.260605i
$298$	22.9541			1.32969
$299$		0			0
$300$	−3.63102			−0.209637
$301$	12.2262	+	21.1763i	0.704705	+	1.22058i
$302$	−14.0918	−	24.4077i	−0.810892	−	1.40451i
$303$	4.23825	−	7.34087i	0.243481	−	0.421722i
$304$	−39.3183			−2.25506
$305$	−2.41670	+	4.18584i	−0.138380	+	0.239681i
$306$	0.678448	−	1.17511i	0.0387843	−	0.0671764i
$307$	−24.8649			−1.41911			−0.709556	−	0.704649i	$-0.751105\pi$
$307$	−24.8649			−1.41911			−0.709556	+	0.704649i	$0.751105\pi$
$308$	11.1392	−	19.2937i	0.634716	−	1.09936i
$309$	−2.82371	−	4.89081i	−0.160635	−	0.278228i
$310$	6.37920	+	11.0491i	0.362314	+	0.627546i
$311$	−17.0804			−0.968539			−0.484270	−	0.874919i	$-0.660915\pi$
$311$	−17.0804			−0.968539			−0.484270	+	0.874919i	$0.660915\pi$
$312$		0			0
$313$	15.6974			0.887269			0.443635	−	0.896208i	$-0.353689\pi$
$313$	15.6974			0.887269			0.443635	+	0.896208i	$0.353689\pi$
$314$	0.742135	+	1.28542i	0.0418811	+	0.0725402i
$315$	−2.48911	−	4.31127i	−0.140246	−	0.242913i
$316$	5.88135	−	10.1868i	0.330852	−	0.573053i
$317$	32.7821			1.84123			0.920613	−	0.390477i	$-0.127690\pi$
$317$	32.7821			1.84123			0.920613	+	0.390477i	$0.127690\pi$
$318$	2.78232	−	4.81913i	0.156025	−	0.270243i
$319$	−10.1434	+	17.5689i	−0.567921	+	0.983669i
$320$	−1.83340			−0.102490
$321$	3.36778	−	5.83317i	0.187971	−	0.325576i
$322$	8.78113	+	15.2094i	0.489353	+	0.847584i
$323$	2.99731	+	5.19150i	0.166775	+	0.288863i
$324$	1.24698			0.0692766
$325$		0			0
$326$	11.2959			0.625622
$327$	1.03803	+	1.79792i	0.0574033	+	0.0994255i
$328$	1.22252	+	2.11747i	0.0675024	+	0.116918i
$329$	−18.1770	+	31.4835i	−1.00213	+	1.73574i
$330$	−13.5036			−0.743351
$331$	14.5809	−	25.2549i	0.801439	−	1.38813i	−0.117230	−	0.993105i	$-0.537401\pi$
$331$	14.5809	−	25.2549i	0.801439	−	1.38813i	0.918669	−	0.395029i	$-0.129265\pi$
$332$	4.03199	−	6.98361i	0.221284	−	0.383276i
$333$	6.24698			0.342332
$334$	6.71260	−	11.6266i	0.367297	−	0.636177i
$335$	3.28232	+	5.68515i	0.179332	+	0.310613i
$336$	8.50753	+	14.7355i	0.464124	+	0.803886i
$337$	−33.2911			−1.81348			−0.906741	−	0.421688i	$-0.861438\pi$
$337$	−33.2911			−1.81348			−0.906741	+	0.421688i	$0.861438\pi$
$338$		0			0
$339$	6.16852			0.335028
$340$	0.678448	+	1.17511i	0.0367940	+	0.0637291i
$341$	−12.7051	−	22.0058i	−0.688018	−	1.19168i
$342$	−7.17241	+	12.4230i	−0.387839	+	0.671757i
$343$	−7.34375			−0.396525
$344$	−4.81551	+	8.34071i	−0.259635	+	0.449701i
$345$	2.04407	−	3.54044i	0.110049	−	0.190611i
$346$	−3.62133			−0.194684
$347$	0.436845	−	0.756638i	0.0234511	−	0.0406185i	−0.854062	−	0.520172i	$-0.825868\pi$
$347$	0.436845	−	0.756638i	0.0234511	−	0.0406185i	0.877513	+	0.479553i	$0.159201\pi$
$348$	2.43900	+	4.22447i	0.130744	+	0.226456i
$349$	1.61596	+	2.79892i	0.0865002	+	0.149823i	0.906029	−	0.423215i	$-0.139098\pi$
$349$	1.61596	+	2.79892i	0.0865002	+	0.149823i	−0.819529	+	0.573037i	$0.805765\pi$
$350$	−18.0761			−0.966206
$351$		0			0
$352$	32.0804			1.70989
$353$	−4.07338	−	7.05529i	−0.216804	−	0.375515i	0.737025	−	0.675865i	$-0.236230\pi$
$353$	−4.07338	−	7.05529i	−0.216804	−	0.375515i	−0.953829	+	0.300350i	$0.902897\pi$
$354$	−1.69202	−	2.93067i	−0.0899299	−	0.155763i
$355$	6.58911	−	11.4127i	0.349713	−	0.605721i
$356$	1.44504			0.0765871
$357$	1.29709	−	2.24663i	0.0686495	−	0.118904i
$358$	−18.0526	+	31.2680i	−0.954108	+	1.65256i
$359$	2.64071			0.139371			0.0696857	−	0.997569i	$-0.477800\pi$
$359$	2.64071			0.139371			0.0696857	+	0.997569i	$0.477800\pi$
$360$	0.980386	−	1.69808i	0.0516709	−	0.0894966i
$361$	−22.1869	−	38.4289i	−1.16773	−	2.02257i
$362$	−21.7337	−	37.6439i	−1.14230	−	1.97852i
$363$	15.8944			0.834239
$364$		0			0
$365$	4.26444			0.223211
$366$	−3.01357	−	5.21966i	−0.157522	−	0.272836i
$367$	1.45204	+	2.51501i	0.0757960	+	0.131282i	0.901432	−	0.432920i	$-0.142517\pi$
$367$	1.45204	+	2.51501i	0.0757960	+	0.131282i	−0.825636	+	0.564203i	$0.809184\pi$
$368$	−6.98643	+	12.1008i	−0.364193	+	0.630800i
$369$	1.80194			0.0938051
$370$	−8.13318	+	14.0871i	−0.422824	+	0.732352i
$371$	5.31940	−	9.21346i	0.276169	−	0.478339i
$372$	−6.10992			−0.316784
$373$	4.19926	−	7.27333i	0.217429	−	0.376599i	−0.736592	−	0.676337i	$-0.763566\pi$
$373$	4.19926	−	7.27333i	0.217429	−	0.376599i	0.954021	+	0.299739i	$0.0968995\pi$
$374$	−3.51842	−	6.09408i	−0.181933	−	0.315117i
$375$	5.71648	+	9.90123i	0.295198	+	0.511298i
$376$	−14.3187			−0.738432
$377$		0			0
$378$	6.20775			0.319292
$379$	−7.87412	−	13.6384i	−0.404466	−	0.700556i	0.589793	−	0.807555i	$-0.299209\pi$
$379$	−7.87412	−	13.6384i	−0.404466	−	0.700556i	−0.994259	+	0.106998i	$0.965876\pi$
$380$	−7.17241	−	12.4230i	−0.367937	−	0.637285i
$381$	7.13102	−	12.3513i	0.365333	−	0.632776i
$382$	−12.7584			−0.652776
$383$	−6.36927	+	11.0319i	−0.325455	+	0.563704i	−0.981604	−	0.190927i	$-0.938851\pi$
$383$	−6.36927	+	11.0319i	−0.325455	+	0.563704i	0.656150	+	0.754631i	$0.272184\pi$
$384$	−5.04288	+	8.73452i	−0.257343	+	0.445732i
$385$	−25.8170			−1.31576
$386$	−8.80074	+	15.2433i	−0.447946	+	0.775865i
$387$	3.54892	+	6.14691i	0.180402	+	0.312465i
$388$	−5.39828	−	9.35010i	−0.274056	−	0.474679i
$389$	−0.310371			−0.0157365			−0.00786823	−	0.999969i	$-0.502505\pi$
$389$	−0.310371			−0.0157365			−0.00786823	+	0.999969i	$0.502505\pi$
$390$		0			0
$391$	2.13036			0.107737
$392$	3.30290	+	5.72079i	0.166822	+	0.288943i
$393$	−11.3007	−	19.5735i	−0.570047	−	0.987350i
$394$	−21.0928	+	36.5337i	−1.06264	+	1.84054i
$395$	−13.6310			−0.685851
$396$	3.23341	−	5.60042i	0.162485	−	0.281432i
$397$	−0.745488	+	1.29122i	−0.0374150	+	0.0648046i	−0.884127	−	0.467248i	$-0.845246\pi$
$397$	−0.745488	+	1.29122i	−0.0374150	+	0.0648046i	0.846712	+	0.532052i	$0.178579\pi$
$398$	7.25236			0.363528
$399$	−13.7126	+	23.7509i	−0.686488	+	1.18903i
$400$	−7.19083	−	12.4549i	−0.359541	−	0.622744i
$401$	11.9167	+	20.6403i	0.595092	+	1.03073i	0.993534	+	0.113535i	$0.0362175\pi$
$401$	11.9167	+	20.6403i	0.595092	+	1.03073i	−0.398442	+	0.917193i	$0.630449\pi$
$402$	−8.18598			−0.408280
$403$		0			0
$404$	−10.5700			−0.525878
$405$	−0.722521	−	1.25144i	−0.0359024	−	0.0621847i
$406$	12.1419	+	21.0304i	0.602593	+	1.04372i
$407$	16.1984	−	28.0564i	0.802923	−	1.39070i
$408$	1.02177			0.0505852
$409$	−2.13371	+	3.69570i	−0.105505	+	0.182740i	−0.913945	−	0.405839i	$-0.866979\pi$
$409$	−2.13371	+	3.69570i	−0.105505	+	0.182740i	0.808439	+	0.588580i	$0.200313\pi$
$410$	−2.34601	+	4.06341i	−0.115861	+	0.200678i
$411$	−13.6353			−0.672581
$412$	−3.52111	+	6.09873i	−0.173472	+	0.300463i
$413$	−3.23490	−	5.60301i	−0.159179	−	0.275706i
$414$	2.54892	+	4.41485i	0.125272	+	0.216978i
$415$	−9.34481			−0.458719
$416$		0			0
$417$	17.6015			0.861948
$418$	37.1960	+	64.4253i	1.81931	+	3.15114i
$419$	−14.8448	−	25.7120i	−0.725217	−	1.25611i	−0.958885	−	0.283796i	$-0.908406\pi$
$419$	−14.8448	−	25.7120i	−0.725217	−	1.25611i	0.233668	−	0.972316i	$-0.424927\pi$
$420$	−3.10388	+	5.37607i	−0.151454	+	0.262325i
$421$	29.3991			1.43282			0.716412	−	0.697677i	$-0.245783\pi$
$421$	29.3991			1.43282			0.716412	+	0.697677i	$0.245783\pi$
$422$	3.52446	−	6.10454i	0.171568	−	0.297164i
$423$	−5.27628	+	9.13879i	−0.256542	+	0.444343i
$424$	4.19029			0.203499
$425$	−1.09634	+	1.89892i	−0.0531804	+	0.0921112i
$426$	8.21648	+	14.2314i	0.398090	+	0.689512i
$427$	−5.76151	−	9.97923i	−0.278819	−	0.482929i
$428$	−8.39911			−0.405986
$429$		0			0
$430$	−18.4819			−0.891275
$431$	16.5281	+	28.6275i	0.796131	+	1.37894i	0.922119	+	0.386907i	$0.126457\pi$
$431$	16.5281	+	28.6275i	0.796131	+	1.37894i	−0.125988	+	0.992032i	$0.540210\pi$
$432$	2.46950	+	4.27730i	0.118814	+	0.205792i
$433$	14.6332	−	25.3454i	0.703226	−	1.21802i	−0.264102	−	0.964495i	$-0.585076\pi$
$433$	14.6332	−	25.3454i	0.703226	−	1.21802i	0.967328	−	0.253528i	$-0.0815910\pi$
$434$	−30.4166			−1.46004
$435$	2.82640	−	4.89546i	0.135515	−	0.234719i
$436$	1.29440	−	2.24198i	0.0619908	−	0.107371i
$437$	−22.5217			−1.07736
$438$	−2.65883	+	4.60523i	−0.127044	+	0.220047i
$439$	1.06584	+	1.84609i	0.0508699	+	0.0881093i	0.890339	−	0.455298i	$-0.150467\pi$
$439$	1.06584	+	1.84609i	0.0508699	+	0.0881093i	−0.839469	+	0.543407i	$0.817134\pi$
$440$	−5.08426	−	8.80620i	−0.242383	−	0.419819i
$441$	4.86831			0.231824
$442$		0			0
$443$	−22.9922			−1.09239			−0.546197	−	0.837657i	$-0.683925\pi$
$443$	−22.9922			−1.09239			−0.546197	+	0.837657i	$0.683925\pi$
$444$	−3.89493	−	6.74621i	−0.184845	−	0.320161i
$445$	−0.837282	−	1.45021i	−0.0396910	−	0.0687467i
$446$	−6.71164	+	11.6249i	−0.317805	+	0.550455i
$447$	12.7385			0.602513
$448$	2.18545	−	3.78531i	0.103253	−	0.178839i
$449$	6.46897	−	11.2046i	0.305289	−	0.528777i	−0.672036	−	0.740518i	$-0.734580\pi$
$449$	6.46897	−	11.2046i	0.305289	−	0.528777i	0.977326	+	0.211741i	$0.0679134\pi$
$450$	−5.24698			−0.247345
$451$	4.67241	−	8.09285i	0.220015	−	0.381077i
$452$	−3.84601	−	6.66149i	−0.180901	−	0.313330i
$453$	−7.82036	−	13.5453i	−0.367432	−	0.636412i
$454$	−38.2911			−1.79709
$455$		0			0
$456$	−10.8019			−0.505847
$457$	2.42662	+	4.20304i	0.113513	+	0.196610i	0.917184	−	0.398463i	$-0.130456\pi$
$457$	2.42662	+	4.20304i	0.113513	+	0.196610i	−0.803672	+	0.595073i	$0.797123\pi$
$458$	−8.37531	−	14.5065i	−0.391353	−	0.677843i
$459$	0.376510	−	0.652135i	0.0175740	−	0.0304390i
$460$	−5.09783			−0.237688
$461$	−9.41723	+	16.3111i	−0.438604	+	0.759685i	−0.997582	−	0.0694978i	$-0.977860\pi$
$461$	−9.41723	+	16.3111i	−0.438604	+	0.759685i	0.558978	+	0.829183i	$0.311194\pi$
$462$	16.0966	−	27.8802i	0.748883	−	1.29710i
$463$	−22.8767			−1.06317			−0.531585	−	0.847005i	$-0.678403\pi$
$463$	−22.8767			−1.06317			−0.531585	+	0.847005i	$0.678403\pi$
$464$	−9.66033	+	16.7322i	−0.448469	+	0.776772i
$465$	3.54019	+	6.13179i	0.164172	+	0.284355i
$466$	−14.6054	−	25.2972i	−0.676581	−	1.17187i
$467$	13.0000			0.601568			0.300784	−	0.953692i	$-0.402752\pi$
$467$	13.0000			0.601568			0.300784	+	0.953692i	$0.402752\pi$
$468$		0			0
$469$	−15.6504			−0.722668
$470$	−13.7388	−	23.7963i	−0.633723	−	1.09764i
$471$	0.411854	+	0.713352i	0.0189772	+	0.0328695i
$472$	1.27413	−	2.20685i	0.0586464	−	0.101579i
$473$	36.8092			1.69249
$474$	8.49880	−	14.7204i	0.390363	−	0.676129i
$475$	11.5903	−	20.0750i	0.531800	−	0.921104i
$476$	−3.23490			−0.148271
$477$	1.54407	−	2.67441i	0.0706982	−	0.122453i
$478$	12.1712	+	21.0812i	0.556698	+	0.964230i
$479$	19.0450	+	32.9870i	0.870190	+	1.50721i	0.861800	+	0.507248i	$0.169337\pi$
$479$	19.0450	+	32.9870i	0.870190	+	1.50721i	0.00838964	+	0.999965i	$0.497329\pi$
$480$	−8.93900			−0.408008
$481$		0			0
$482$	11.2959			0.514514
$483$	4.87316	+	8.44056i	0.221736	+	0.384059i
$484$	−9.90999	−	17.1646i	−0.450454	−	0.780210i
$485$	−6.25571	+	10.8352i	−0.284057	+	0.492001i
$486$	1.80194			0.0817376
$487$	10.6250	−	18.4030i	0.481464	−	0.833920i	−0.518310	−	0.855193i	$-0.673439\pi$
$487$	10.6250	−	18.4030i	0.481464	−	0.833920i	0.999774	+	0.0212730i	$0.00677192\pi$
$488$	2.26928	−	3.93051i	0.102726	−	0.177926i
$489$	6.26875			0.283483
$490$	−6.33824	+	10.9782i	−0.286333	+	0.495943i
$491$	3.17510	+	5.49943i	0.143290	+	0.248186i	0.928734	−	0.370748i	$-0.120898\pi$
$491$	3.17510	+	5.49943i	0.143290	+	0.248186i	−0.785444	+	0.618933i	$0.787565\pi$
$492$	−1.12349	−	1.94594i	−0.0506508	−	0.0877298i
$493$	2.94571			0.132668
$494$		0			0
$495$	−7.49396			−0.336828
$496$	−12.1000	−	20.9578i	−0.543306	−	0.941033i
$497$	15.7087	+	27.2083i	0.704632	+	1.22046i
$498$	5.82640	−	10.0916i	0.261087	−	0.452216i
$499$	−4.65087			−0.208202			−0.104101	−	0.994567i	$-0.533196\pi$
$499$	−4.65087			−0.208202			−0.104101	+	0.994567i	$0.533196\pi$
$500$	7.12833	−	12.3466i	0.318789	−	0.552158i
$501$	3.72521	−	6.45225i	0.166430	−	0.288265i
$502$	−1.35690			−0.0605612
$503$	−7.73759	+	13.4019i	−0.345002	+	0.597561i	−0.985354	−	0.170521i	$-0.945455\pi$
$503$	−7.73759	+	13.4019i	−0.345002	+	0.597561i	0.640352	+	0.768081i	$0.278788\pi$
$504$	2.33728	+	4.04829i	0.104111	+	0.180325i
$505$	6.12445	+	10.6079i	0.272534	+	0.472043i
$506$	26.4373			1.17528
$507$		0			0
$508$	−17.7845			−0.789059
$509$	10.2524	+	17.7576i	0.454428	+	0.787092i	0.998655	−	0.0518459i	$-0.0165105\pi$
$509$	10.2524	+	17.7576i	0.454428	+	0.787092i	−0.544227	+	0.838938i	$0.683177\pi$
$510$	0.980386	+	1.69808i	0.0434122	+	0.0751921i
$511$	−5.08330	+	8.80454i	−0.224872	+	0.389490i
$512$	17.1491			0.757892
$513$	−3.98039	+	6.89423i	−0.175738	+	0.304388i
$514$	−17.7729	+	30.7836i	−0.783930	+	1.35781i
$515$	8.16075			0.359606
$516$	4.42543	−	7.66507i	0.194819	−	0.337436i
$517$	27.3627	+	47.3936i	1.20341	+	2.08437i
$518$	−19.3898	−	33.5842i	−0.851941	−	1.47561i
$519$	−2.00969			−0.0882155
$520$		0			0
$521$	−42.0267			−1.84122			−0.920611	−	0.390481i	$-0.872309\pi$
$521$	−42.0267			−1.84122			−0.920611	+	0.390481i	$0.872309\pi$
$522$	3.52446	+	6.10454i	0.154261	+	0.267189i
$523$	14.9943	+	25.9708i	0.655653	+	1.13562i	0.981730	+	0.190281i	$0.0609399\pi$
$523$	14.9943	+	25.9708i	0.655653	+	1.13562i	−0.326077	+	0.945343i	$0.605727\pi$
$524$	−14.0918	+	24.4077i	−0.615603	+	1.06626i
$525$	−10.0315			−0.437809
$526$	15.8654	−	27.4797i	0.691764	−	1.19817i
$527$	−1.84481	+	3.19531i	−0.0803614	+	0.139190i
$528$	25.6136			1.11469
$529$	7.49814	−	12.9872i	0.326006	−	0.564659i
$530$	4.02057	+	6.96384i	0.174643	+	0.302490i
$531$	−0.939001	−	1.62640i	−0.0407492	−	0.0705796i
$532$	34.1987			1.48270
$533$		0			0
$534$	2.08815			0.0903629
$535$	4.86658	+	8.42917i	0.210401	+	0.364425i
$536$	−3.08211	−	5.33836i	−0.133127	−	0.230582i
$537$	−10.0184	+	17.3524i	−0.432327	+	0.748812i
$538$	−29.5284			−1.27306
$539$	12.6235	−	21.8645i	0.543732	−	0.941772i
$540$	−0.900969	+	1.56052i	−0.0387715	+	0.0671543i
$541$	36.3803			1.56411			0.782056	−	0.623208i	$-0.214171\pi$
$541$	36.3803			1.56411			0.782056	+	0.623208i	$0.214171\pi$
$542$	0.716480	−	1.24098i	0.0307755	−	0.0533047i
$543$	−12.0613	−	20.8908i	−0.517600	−	0.896509i
$544$	−2.32908	−	4.03409i	−0.0998587	−	0.172960i
$545$	−3.00000			−0.128506
$546$		0			0
$547$	−25.8159			−1.10381			−0.551905	−	0.833907i	$-0.686099\pi$
$547$	−25.8159			−1.10381			−0.551905	+	0.833907i	$0.686099\pi$
$548$	8.50149	+	14.7250i	0.363166	+	0.629022i
$549$	−1.67241	−	2.89669i	−0.0713766	−	0.123628i
$550$	−13.6054	+	23.5652i	−0.580135	+	1.00482i
$551$	−31.1414			−1.32667
$552$	−1.91939	+	3.32448i	−0.0816945	+	0.141499i
$553$	16.2485	−	28.1432i	0.690955	−	1.19677i
$554$	−8.70948			−0.370030
$555$	−4.51357	+	7.81774i	−0.191591	+	0.331845i
$556$	−10.9743	−	19.0081i	−0.465416	−	0.806124i
$557$	−8.99516	−	15.5801i	−0.381137	−	0.660149i	0.610088	−	0.792334i	$-0.291134\pi$
$557$	−8.99516	−	15.5801i	−0.381137	−	0.660149i	−0.991225	+	0.132185i	$0.957801\pi$
$558$	−8.82908			−0.373765
$559$		0			0
$560$	−24.5875			−1.03901
$561$	−1.95257	−	3.38196i	−0.0824378	−	0.142786i
$562$	−16.9155	−	29.2985i	−0.713537	−	1.23588i
$563$	19.5661	−	33.8895i	0.824614	−	1.42827i	−0.0775992	−	0.996985i	$-0.524725\pi$
$563$	19.5661	−	33.8895i	0.824614	−	1.42827i	0.902214	−	0.431289i	$-0.141941\pi$
$564$	13.1588			0.554087
$565$	−4.45689	+	7.71955i	−0.187503	+	0.324764i
$566$	7.13318	−	12.3550i	0.299830	−	0.519321i
$567$	3.44504			0.144678
$568$	−6.18718	+	10.7165i	−0.259608	+	0.449655i
$569$	−15.3001	−	26.5005i	−0.641413	−	1.11096i	−0.985118	−	0.171882i	$-0.945015\pi$
$569$	−15.3001	−	26.5005i	−0.641413	−	1.11096i	0.343705	−	0.939078i	$-0.388318\pi$
$570$	−10.3644	−	17.9517i	−0.434118	−	0.751915i
$571$	−2.96184			−0.123949			−0.0619745	−	0.998078i	$-0.519740\pi$
$571$	−2.96184			−0.123949			−0.0619745	+	0.998078i	$0.519740\pi$
$572$		0			0
$573$	−7.08038			−0.295787
$574$	−5.59299	−	9.68734i	−0.233447	−	0.404342i
$575$	−4.11894	−	7.13422i	−0.171772	−	0.297517i
$576$	0.634375	−	1.09877i	0.0264323	−	0.0457821i
$577$	−0.819396			−0.0341119			−0.0170560	−	0.999855i	$-0.505429\pi$
$577$	−0.819396			−0.0341119			−0.0170560	+	0.999855i	$0.505429\pi$
$578$	14.8056	−	25.6440i	0.615831	−	1.06665i
$579$	−4.88404	+	8.45941i	−0.202974	+	0.351561i
$580$	−7.04892			−0.292690
$581$	11.1392	−	19.2937i	0.462133	−	0.800437i
$582$	−7.80074	−	13.5113i	−0.323351	−	0.560061i
$583$	−8.00753	−	13.8695i	−0.331638	−	0.574414i
$584$	−4.00431			−0.165700
$585$		0			0
$586$	11.8552			0.489732
$587$	15.8998	+	27.5392i	0.656254	+	1.13666i	0.981578	+	0.191062i	$0.0611933\pi$
$587$	15.8998	+	27.5392i	0.656254	+	1.13666i	−0.325324	+	0.945603i	$0.605473\pi$
$588$	−3.03534	−	5.25737i	−0.125175	−	0.216810i
$589$	19.5030	−	33.7802i	0.803606	−	1.39189i
$590$	4.89008			0.201322
$591$	−11.7056	+	20.2747i	−0.481504	+	0.833989i
$592$	15.4269	−	26.7202i	0.634042	−	1.09819i
$593$	−4.26337			−0.175076			−0.0875379	−	0.996161i	$-0.527900\pi$
$593$	−4.26337			−0.175076			−0.0875379	+	0.996161i	$0.527900\pi$
$594$	4.67241	−	8.09285i	0.191711	−	0.332054i
$595$	1.87435	+	3.24648i	0.0768410	+	0.133093i
$596$	−7.94235	−	13.7566i	−0.325331	−	0.563491i
$597$	4.02475			0.164722
$598$		0			0
$599$	24.7278			1.01035			0.505175	−	0.863017i	$-0.331428\pi$
$599$	24.7278			1.01035			0.505175	+	0.863017i	$0.331428\pi$
$600$	−1.97554	−	3.42174i	−0.0806511	−	0.139692i
$601$	−3.41185	−	5.90950i	−0.139172	−	0.241054i	0.788011	−	0.615661i	$-0.211111\pi$
$601$	−3.41185	−	5.90950i	−0.139172	−	0.241054i	−0.927184	+	0.374607i	$0.877778\pi$
$602$	22.0308	−	38.1585i	0.897908	−	1.55522i
$603$	−4.54288			−0.185000
$604$	−9.75182	+	16.8907i	−0.396796	+	0.687271i
$605$	−11.4840	+	19.8909i	−0.466892	+	0.808681i
$606$	−15.2741			−0.620469
$607$	−15.9981	+	27.7096i	−0.649344	+	1.12470i	0.333935	+	0.942596i	$0.391623\pi$
$607$	−15.9981	+	27.7096i	−0.649344	+	1.12470i	−0.983280	+	0.182102i	$0.941710\pi$
$608$	24.6226	+	42.6476i	0.998578	+	1.72959i
$609$	6.73825	+	11.6710i	0.273048	+	0.472932i
$610$	8.70948			0.352637
$611$		0			0
$612$	−0.939001			−0.0379569
$613$	−16.7937	−	29.0876i	−0.678293	−	1.17484i	−0.975495	−	0.220023i	$-0.929387\pi$
$613$	−16.7937	−	29.0876i	−0.678293	−	1.17484i	0.297202	−	0.954815i	$-0.403947\pi$
$614$	22.4025	+	38.8022i	0.904090	+	1.56593i
$615$	−1.30194	+	2.25502i	−0.0524992	+	0.0909313i
$616$	24.2422			0.976746
$617$	13.2935	−	23.0250i	0.535176	−	0.926953i	−0.463978	−	0.885846i	$-0.653579\pi$
$617$	13.2935	−	23.0250i	0.535176	−	0.926953i	0.999155	−	0.0411061i	$-0.0130882\pi$
$618$	−5.08815	+	8.81293i	−0.204675	+	0.354508i
$619$	−9.17928			−0.368946			−0.184473	−	0.982838i	$-0.559058\pi$
$619$	−9.17928			−0.368946			−0.184473	+	0.982838i	$0.559058\pi$
$620$	4.41454	−	7.64621i	0.177292	−	0.307079i
$621$	1.41454	+	2.45006i	0.0567636	+	0.0983175i
$622$	15.3889	+	26.6543i	0.617038	+	1.06874i
$623$	3.99223			0.159945
$624$		0			0
$625$	−1.96184			−0.0784735
$626$	−14.1429	−	24.4962i	−0.565263	−	0.979064i
$627$	20.6422	+	35.7533i	0.824370	+	1.42785i
$628$	0.513574	−	0.889535i	0.0204938	−	0.0354963i
$629$	−4.70410			−0.187565
$630$	−4.48523	+	7.76865i	−0.178696	+	0.309510i
$631$	−8.50216	+	14.7262i	−0.338465	+	0.586239i	−0.984144	−	0.177370i	$-0.943241\pi$
$631$	−8.50216	+	14.7262i	−0.338465	+	0.586239i	0.645679	+	0.763609i	$0.276575\pi$
$632$	12.7995			0.509139
$633$	1.95593	−	3.38776i	0.0777411	−	0.134652i
$634$	−29.5356	−	51.1572i	−1.17301	−	2.03171i
$635$	10.3046	+	17.8481i	0.408927	+	0.708282i
$636$	−3.85086			−0.152696
$637$		0			0
$638$	36.5555			1.44725
$639$	4.55980	+	7.89781i	0.180383	+	0.312433i
$640$	−7.28717	−	12.6217i	−0.288051	−	0.498918i
$641$	10.8324	−	18.7623i	0.427856	−	0.741068i	−0.568827	−	0.822457i	$-0.692603\pi$
$641$	10.8324	−	18.7623i	0.427856	−	0.741068i	0.996682	+	0.0813898i	$0.0259359\pi$
$642$	−12.1371			−0.479012
$643$	−4.67778	+	8.10216i	−0.184474	+	0.319518i	−0.943399	−	0.331660i	$-0.892391\pi$
$643$	−4.67778	+	8.10216i	−0.184474	+	0.319518i	0.758925	+	0.651178i	$0.225725\pi$
$644$	6.07673	−	10.5252i	0.239457	−	0.414751i
$645$	−10.2567			−0.403856
$646$	5.40097	−	9.35475i	0.212498	−	0.368058i
$647$	0.351388	+	0.608621i	0.0138145	+	0.0239274i	0.872850	−	0.487989i	$-0.162269\pi$
$647$	0.351388	+	0.608621i	0.0138145	+	0.0239274i	−0.859036	+	0.511916i	$0.828936\pi$
$648$	0.678448	+	1.17511i	0.0266520	+	0.0461625i
$649$	−9.73928			−0.382300
$650$		0			0
$651$	−16.8799			−0.661576
$652$	−3.90850	−	6.76972i	−0.153069	−	0.265123i
$653$	18.6705	+	32.3383i	0.730635	+	1.26550i	0.956612	+	0.291364i	$0.0941092\pi$
$653$	18.6705	+	32.3383i	0.730635	+	1.26550i	−0.225977	+	0.974133i	$0.572557\pi$
$654$	1.87047	−	3.23975i	0.0731411	−	0.126684i
$655$	32.6601			1.27614
$656$	4.44989	−	7.70743i	0.173739	−	0.300925i
$657$	−1.47554	+	2.55571i	−0.0575664	+	0.0997078i
$658$	65.5077			2.55376
$659$	0.367781	−	0.637015i	0.0143267	−	0.0248146i	−0.858773	−	0.512356i	$-0.828773\pi$
$659$	0.367781	−	0.637015i	0.0143267	−	0.0248146i	0.873100	+	0.487541i	$0.162106\pi$
$660$	4.67241	+	8.09285i	0.181873	+	0.315014i
$661$	−6.92423	−	11.9931i	−0.269321	−	0.466478i	0.699365	−	0.714764i	$-0.253466\pi$
$661$	−6.92423	−	11.9931i	−0.269321	−	0.466478i	−0.968687	+	0.248286i	$0.920133\pi$
$662$	−52.5478			−2.04233
$663$		0			0
$664$	8.77479			0.340528
$665$	−19.8153	−	34.3211i	−0.768403	−	1.33091i
$666$	−5.62833	−	9.74856i	−0.218094	−	0.377749i
$667$	−5.53348	+	9.58427i	−0.214257	+	0.371105i
$668$	−9.29052			−0.359461
$669$	−3.72468	+	6.45133i	−0.144004	+	0.249423i
$670$	5.91454	−	10.2443i	0.228499	−	0.395771i
$671$	−17.3461			−0.669640
$672$	10.6555	−	18.4558i	0.411044	−	0.711949i
$673$	3.17510	+	5.49943i	0.122391	+	0.211987i	0.920710	−	0.390247i	$-0.127610\pi$
$673$	3.17510	+	5.49943i	0.122391	+	0.211987i	−0.798319	+	0.602235i	$0.794277\pi$
$674$	29.9943	+	51.9516i	1.15534	+	2.00110i
$675$	−2.91185			−0.112077
$676$		0			0
$677$	33.7241			1.29612			0.648061	−	0.761589i	$-0.275580\pi$
$677$	33.7241			1.29612			0.648061	+	0.761589i	$0.275580\pi$
$678$	−5.55765	−	9.62613i	−0.213440	−	0.369689i
$679$	−14.9139	−	25.8316i	−0.572342	−	0.991326i
$680$	−0.738250	+	1.27869i	−0.0283106	+	0.0490354i
$681$	−21.2500			−0.814300
$682$	−22.8937	+	39.6531i	−0.876646	+	1.51840i
$683$	−9.63437	+	16.6872i	−0.368649	+	0.638519i	−0.989355	−	0.145525i	$-0.953513\pi$
$683$	−9.63437	+	16.6872i	−0.368649	+	0.638519i	0.620705	+	0.784044i	$0.286846\pi$
$684$	9.92692			0.379565
$685$	9.85181	−	17.0638i	0.376418	−	0.651976i
$686$	6.61649	+	11.4601i	0.252619	+	0.437548i
$687$	−4.64795	−	8.05048i	−0.177330	−	0.307145i
$688$	35.0562			1.33651
$689$		0			0
$690$	−7.36658			−0.280441
$691$	19.7005	+	34.1223i	0.749443	+	1.29807i	0.948090	+	0.318002i	$0.103012\pi$
$691$	19.7005	+	34.1223i	0.749443	+	1.29807i	−0.198647	+	0.980071i	$0.563655\pi$
$692$	1.25302	+	2.17029i	0.0476327	+	0.0825022i
$693$	8.93296	−	15.4723i	0.339335	−	0.587746i
$694$	−1.57434			−0.0597610
$695$	−12.7174	+	22.0273i	−0.482400	+	0.835541i
$696$	−2.65399	+	4.59684i	−0.100599	+	0.174243i
$697$	−1.35690			−0.0513961
$698$	2.91185	−	5.04348i	0.110215	−	0.190898i
$699$	−8.10537	−	14.0389i	−0.306573	−	0.531000i
$700$	6.25451	+	10.8331i	0.236398	+	0.409454i
$701$	18.3985			0.694902			0.347451	−	0.937698i	$-0.387047\pi$
$701$	18.3985			0.694902			0.347451	+	0.937698i	$0.387047\pi$
$702$		0			0
$703$	49.7308			1.87563
$704$	−3.28986	−	5.69820i	−0.123991	−	0.214759i
$705$	−7.62445	−	13.2059i	−0.287153	−	0.497364i
$706$	−7.33997	+	12.7132i	−0.276243	+	0.478468i
$707$	−29.2019			−1.09825
$708$	−1.17092	+	2.02808i	−0.0440057	+	0.0762201i
$709$	19.2277	−	33.3033i	0.722110	−	1.25073i	−0.238043	−	0.971255i	$-0.576506\pi$
$709$	19.2277	−	33.3033i	0.722110	−	1.25073i	0.960153	−	0.279476i	$-0.0901609\pi$
$710$	−23.7463			−0.891183
$711$	4.71648	−	8.16918i	0.176882	−	0.306368i
$712$	0.786208	+	1.36175i	0.0294644	+	0.0510338i
$713$	−6.93094	−	12.0047i	−0.259566	−	0.449581i
$714$	−4.67456			−0.174941
$715$		0			0
$716$	24.9855			0.933753
$717$	6.75451	+	11.6992i	0.252252	+	0.436913i
$718$	−2.37920	−	4.12089i	−0.0887909	−	0.153790i
$719$	−24.2500	+	42.0022i	−0.904371	+	1.56642i	−0.0826117	+	0.996582i	$0.526326\pi$
$719$	−24.2500	+	42.0022i	−0.904371	+	1.56642i	−0.821759	+	0.569835i	$0.807007\pi$
$720$	−7.13706			−0.265983
$721$	−9.72779	+	16.8490i	−0.362282	+	0.627491i
$722$	−39.9795	+	69.2465i	−1.48788	+	2.57709i
$723$	6.26875			0.233137
$724$	−15.0402	+	26.0504i	−0.558964	+	0.968154i
$725$	−5.69537	−	9.86468i	−0.211521	−	0.366365i
$726$	−14.3204	−	24.8036i	−0.531478	−	0.920547i
$727$	19.0344			0.705948			0.352974	−	0.935633i	$-0.385170\pi$
$727$	19.0344			0.705948			0.352974	+	0.935633i	$0.385170\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−3.84213	−	6.65476i	−0.142203	−	0.246304i
$731$	−2.67241	−	4.62874i	−0.0988425	−	0.171200i
$732$	−2.08546	+	3.61212i	−0.0770807	+	0.133508i
$733$	24.6213			0.909410			0.454705	−	0.890642i	$-0.349745\pi$
$733$	24.6213			0.909410			0.454705	+	0.890642i	$0.349745\pi$
$734$	2.61649	−	4.53189i	0.0965764	−	0.167275i
$735$	−3.51746	+	6.09242i	−0.129743	+	0.224722i
$736$	17.5007			0.645083
$737$	−11.7796	+	20.4029i	−0.433908	+	0.751551i
$738$	−1.62349	−	2.81197i	−0.0597615	−	0.103510i
$739$	22.2558	+	38.5481i	0.818692	+	1.41802i	0.906647	+	0.421891i	$0.138634\pi$
$739$	22.2558	+	38.5481i	0.818692	+	1.41802i	−0.0879549	+	0.996124i	$0.528033\pi$
$740$	11.2567			0.413803
$741$		0			0
$742$	−19.1704			−0.703769
$743$	−5.20560	−	9.01636i	−0.190975	−	0.330778i	0.754599	−	0.656186i	$-0.227832\pi$
$743$	−5.20560	−	9.01636i	−0.190975	−	0.330778i	−0.945574	+	0.325408i	$0.894498\pi$
$744$	−3.32424	−	5.75775i	−0.121873	−	0.211089i
$745$	−9.20387	+	15.9416i	−0.337204	+	0.584054i
$746$	−15.1336			−0.554081
$747$	3.23341	−	5.60042i	0.118304	−	0.204909i
$748$	−2.43482	+	4.21723i	−0.0890259	+	0.154197i
$749$	−23.2043			−0.847866
$750$	10.3007	−	17.8414i	0.376130	−	0.651476i
$751$	−0.849896	−	1.47206i	−0.0310131	−	0.0537163i	0.850102	−	0.526618i	$-0.176540\pi$
$751$	−0.849896	−	1.47206i	−0.0310131	−	0.0537163i	−0.881115	+	0.472901i	$0.843207\pi$
$752$	26.0596	+	45.1365i	0.950295	+	1.64596i
$753$	−0.753020			−0.0274416
$754$		0			0
$755$	22.6015			0.822552
$756$	−2.14795	−	3.72036i	−0.0781201	−	0.135308i
$757$	−13.7126	−	23.7509i	−0.498393	−	0.863242i	0.501606	−	0.865096i	$-0.332743\pi$
$757$	−13.7126	−	23.7509i	−0.498393	−	0.863242i	−0.999998	+	0.00185490i	$0.999410\pi$
$758$	−14.1887	+	24.5755i	−0.515356	+	0.892622i
$759$	14.6716			0.532545
$760$	7.80463	−	13.5180i	0.283104	−	0.490350i
$761$	2.51304	−	4.35271i	0.0910977	−	0.157786i	−0.816876	−	0.576814i	$-0.804296\pi$
$761$	2.51304	−	4.35271i	0.0910977	−	0.157786i	0.907973	+	0.419028i	$0.137629\pi$
$762$	−25.6993			−0.930988
$763$	3.57606	−	6.19393i	0.129462	−	0.224235i
$764$	4.41454	+	7.64621i	0.159713	+	0.276630i
$765$	0.544073	+	0.942362i	0.0196710	+	0.0340712i
$766$	22.9541			0.829364
$767$		0			0
$768$	20.7114			0.747358
$769$	−21.2228	−	36.7590i	−0.765314	−	1.32556i	−0.940080	−	0.340953i	$-0.889250\pi$
$769$	−21.2228	−	36.7590i	−0.765314	−	1.32556i	0.174766	−	0.984610i	$-0.444083\pi$
$770$	23.2603	+	40.2880i	0.838244	+	1.45188i
$771$	−9.86323	+	17.0836i	−0.355216	+	0.615252i
$772$	12.1806			0.438390
$773$	−13.1796	+	22.8278i	−0.474039	+	0.821059i	−0.999558	−	0.0297223i	$-0.990538\pi$
$773$	−13.1796	+	22.8278i	−0.474039	+	0.821059i	0.525519	+	0.850782i	$0.323871\pi$
$774$	6.39493	−	11.0763i	0.229861	−	0.398131i
$775$	14.2674			0.512501
$776$	5.87412	−	10.1743i	0.210869	−	0.365235i
$777$	−10.7606	−	18.6378i	−0.386033	−	0.668628i
$778$	0.279635	+	0.484342i	0.0100254	+	0.0173645i
$779$	14.3448			0.513956
$780$		0			0
$781$	47.2941			1.69232
$782$	−1.91939	−	3.32448i	−0.0686371	−	0.118883i
$783$	1.95593	+	3.38776i	0.0698991	+	0.121069i
$784$	12.0223	−	20.8232i	0.429368	−	0.743687i
$785$	−1.19029			−0.0424834
$786$	−20.3632	+	35.2702i	−0.726332	+	1.25804i
$787$	−8.57122	+	14.8458i	−0.305531	+	0.529195i	−0.977379	−	0.211493i	$-0.932167\pi$
$787$	−8.57122	+	14.8458i	−0.305531	+	0.529195i	0.671848	+	0.740689i	$0.265501\pi$
$788$	29.1933			1.03997
$789$	8.80463	−	15.2501i	0.313453	−	0.542917i
$790$	12.2811	+	21.2715i	0.436943	+	0.756807i
$791$	−10.6254	−	18.4037i	−0.377796	−	0.654362i
$792$	7.03684			0.250043
$793$		0			0
$794$	2.68664			0.0953455
$795$	2.23125	+	3.86464i	0.0791343	+	0.137065i
$796$	−2.50939	−	4.34640i	−0.0889431	−	0.154054i
$797$	−15.0814	+	26.1218i	−0.534212	+	0.925282i	0.464989	+	0.885316i	$0.346058\pi$
$797$	−15.0814	+	26.1218i	−0.534212	+	0.925282i	−0.999201	+	0.0399660i	$0.987275\pi$
$798$	49.4185			1.74940
$799$	3.97315	−	6.88169i	0.140560	−	0.243457i
$800$	−9.00634	+	15.5994i	−0.318422	+	0.551523i
$801$	1.15883			0.0409454
$802$	21.4731	−	37.1926i	0.758243	−	1.31332i
$803$	7.65213	+	13.2539i	0.270038	+	0.467719i
$804$	2.83244	+	4.90593i	0.0998924	+	0.173019i
$805$	−14.0838			−0.496390
$806$		0			0
$807$	−16.3870			−0.576851
$808$	−5.75086	−	9.96079i	−0.202315	−	0.350419i
$809$	14.9252	+	25.8512i	0.524742	+	0.908879i	0.999585	+	0.0288090i	$0.00917144\pi$
$809$	14.9252	+	25.8512i	0.524742	+	0.908879i	−0.474843	+	0.880070i	$0.657495\pi$
$810$	−1.30194	+	2.25502i	−0.0457454	+	0.0792334i
$811$	47.7362			1.67624			0.838122	−	0.545484i	$-0.183654\pi$
$811$	47.7362			1.67624			0.838122	+	0.545484i	$0.183654\pi$
$812$	8.40246	−	14.5535i	0.294869	−	0.510727i
$813$	0.397616	−	0.688692i	0.0139450	−	0.0241535i
$814$	−58.3769			−2.04611
$815$	−4.52930	+	7.84498i	−0.158655	+	0.274798i
$816$	−1.85958	−	3.22089i	−0.0650985	−	0.112754i
$817$	28.2521	+	48.9341i	0.988417	+	1.71199i
$818$	7.68963			0.268862
$819$		0			0
$820$	3.24698			0.113389
$821$	8.96495	+	15.5278i	0.312879	+	0.541922i	0.978984	−	0.203935i	$-0.0653732\pi$
$821$	8.96495	+	15.5278i	0.312879	+	0.541922i	−0.666105	+	0.745858i	$0.732040\pi$
$822$	12.2850	+	21.2783i	0.428489	+	0.742165i
$823$	−27.1598	+	47.0421i	−0.946731	+	1.63979i	−0.194483	+	0.980906i	$0.562303\pi$
$823$	−27.1598	+	47.0421i	−0.946731	+	1.63979i	−0.752248	+	0.658880i	$0.771030\pi$
$824$	−7.66296			−0.266952
$825$	−7.55041	+	13.0777i	−0.262872	+	0.455307i
$826$	−5.82908	+	10.0963i	−0.202820	+	0.351294i
$827$	49.1041			1.70752			0.853758	−	0.520670i	$-0.174318\pi$
$827$	49.1041			1.70752			0.853758	+	0.520670i	$0.174318\pi$
$828$	1.76391	−	3.05517i	0.0613000	−	0.106175i
$829$	3.67898	+	6.37218i	0.127776	+	0.221315i	0.922815	−	0.385244i	$-0.125883\pi$
$829$	3.67898	+	6.37218i	0.127776	+	0.221315i	−0.795038	+	0.606559i	$0.792549\pi$
$830$	8.41939	+	14.5828i	0.292241	+	0.506177i
$831$	−4.83340			−0.167669
$832$		0			0
$833$	−3.66594			−0.127017
$834$	−15.8584	−	27.4675i	−0.549131	−	0.951123i
$835$	5.38308	+	9.32377i	0.186289	+	0.322663i
$836$	25.7404	−	44.5837i	0.890251	−	1.54196i
$837$	−4.89977			−0.169361
$838$	−26.7494	+	46.3314i	−0.924044	+	1.60049i
$839$	18.2506	−	31.6110i	0.630082	−	1.09133i	−0.357453	−	0.933931i	$-0.616355\pi$
$839$	18.2506	−	31.6110i	0.630082	−	1.09133i	0.987535	−	0.157402i	$-0.0503119\pi$
$840$	−6.75494			−0.233068
$841$	6.84870	−	11.8623i	0.236162	−	0.409045i
$842$	−26.4877	−	45.8780i	−0.912826	−	1.58106i
$843$	−9.38740	−	16.2594i	−0.323319	−	0.560005i
$844$	−4.87800			−0.167908
$845$		0			0
$846$	19.0151			0.653751
$847$	−27.3784	−	47.4208i	−0.940734	−	1.62940i
$848$	−7.62618	−	13.2089i	−0.261884	−	0.453596i
$849$	3.95862	−	6.85652i	0.135859	−	0.235315i
$850$	3.95108			0.135521
$851$	8.83662	−	15.3055i	0.302915	−	0.524665i
$852$	5.68598	−	9.84841i	0.194798	−	0.337401i
$853$	−9.73855			−0.333441			−0.166721	−	0.986004i	$-0.553318\pi$
$853$	−9.73855			−0.333441			−0.166721	+	0.986004i	$0.553318\pi$
$854$	−10.3819	+	17.9820i	−0.355261	+	0.615330i
$855$	−5.75182	−	9.96245i	−0.196708	−	0.340709i
$856$	−4.56973	−	7.91500i	−0.156190	−	0.270529i
$857$	−15.2030			−0.519323			−0.259662	−	0.965700i	$-0.583611\pi$
$857$	−15.2030			−0.519323			−0.259662	+	0.965700i	$0.583611\pi$
$858$		0			0
$859$	−31.9885			−1.09143			−0.545717	−	0.837970i	$-0.683743\pi$
$859$	−31.9885			−1.09143			−0.545717	+	0.837970i	$0.683743\pi$
$860$	6.39493	+	11.0763i	0.218065	+	0.377700i
$861$	−3.10388	−	5.37607i	−0.105780	−	0.183216i
$862$	29.7826	−	51.5850i	1.01440	−	1.75699i
$863$	−35.2905			−1.20130			−0.600652	−	0.799511i	$-0.705092\pi$
$863$	−35.2905			−1.20130			−0.600652	+	0.799511i	$0.705092\pi$
$864$	3.09299	−	5.35722i	0.105226	−	0.182256i
$865$	1.45204	−	2.51501i	0.0493709	−	0.0855129i
$866$	−52.7362			−1.79205
$867$	8.21648	−	14.2314i	0.279046	−	0.483322i
$868$	10.5245	+	18.2289i	0.357223	+	0.618729i
$869$	−24.4596	−	42.3652i	−0.829734	−	1.43714i
$870$	−10.1860			−0.345337
$871$		0			0
$872$	2.81700			0.0953958
$873$	−4.32908	−	7.49819i	−0.146517	−	0.253775i
$874$	20.2913	+	35.1456i	0.686365	+	1.18882i
$875$	19.6935	−	34.1102i	0.665762	−	1.15313i
$876$	3.67994			0.124334
$877$	7.66315	−	13.2730i	0.258766	−	0.448196i	−0.707146	−	0.707068i	$-0.750017\pi$
$877$	7.66315	−	13.2730i	0.258766	−	0.448196i	0.965912	+	0.258872i	$0.0833508\pi$
$878$	1.92058	−	3.32655i	0.0648165	−	0.112266i
$879$	6.57912			0.221908
$880$	−18.5063	+	32.0539i	−0.623848	+	1.08054i
$881$	18.2153	+	31.5498i	0.613689	+	1.06294i	0.990613	+	0.136696i	$0.0436483\pi$
$881$	18.2153	+	31.5498i	0.613689	+	1.06294i	−0.376925	+	0.926244i	$0.623018\pi$
$882$	−4.38620	−	7.59712i	−0.147691	−	0.255808i
$883$	−37.6819			−1.26810			−0.634048	−	0.773294i	$-0.718608\pi$
$883$	−37.6819			−1.26810			−0.634048	+	0.773294i	$0.718608\pi$
$884$		0			0
$885$	2.71379			0.0912231
$886$	20.7153	+	35.8799i	0.695944	+	1.20541i
$887$	−2.12445	−	3.67965i	−0.0713320	−	0.123551i	0.828153	−	0.560502i	$-0.189392\pi$
$887$	−2.12445	−	3.67965i	−0.0713320	−	0.123551i	−0.899485	+	0.436951i	$0.856058\pi$
$888$	4.23825	−	7.34087i	0.142226	−	0.246343i
$889$	−49.1333			−1.64788
$890$	−1.50873	+	2.61320i	−0.0505727	+	0.0875945i
$891$	2.59299	−	4.49119i	0.0868684	−	0.150461i
$892$	9.28919			0.311025
$893$	−42.0033	+	72.7518i	−1.40559	+	2.43455i
$894$	−11.4770	−	19.8788i	−0.383849	−	0.664847i
$895$	−14.4770	−	25.0750i	−0.483914	−	0.838163i
$896$	34.7458			1.16078
$897$		0			0
$898$	−23.3134			−0.777977
$899$	−9.58360	−	16.5993i	−0.319631	−	0.553617i
$900$	1.81551	+	3.14456i	0.0605170	+	0.104819i
$901$	−1.16272	+	2.01389i	−0.0387358	+	0.0670923i
$902$	−16.8388			−0.560670
$903$	12.2262	−	21.1763i	0.406861	−	0.704705i
$904$	4.18502	−	7.24867i	0.139192	−	0.241087i
$905$	34.8582			1.15872
$906$	−14.0918	+	24.4077i	−0.468168	+	0.810892i
$907$	6.30917	+	10.9278i	0.209493	+	0.362852i	0.951555	−	0.307479i	$-0.0994854\pi$
$907$	6.30917	+	10.9278i	0.209493	+	0.362852i	−0.742062	+	0.670331i	$0.766152\pi$
$908$	13.2491	+	22.9482i	0.439688	+	0.761562i
$909$	−8.47650			−0.281148
$910$		0			0
$911$	6.77777			0.224558			0.112279	−	0.993677i	$-0.464185\pi$
$911$	6.77777			0.224558			0.112279	+	0.993677i	$0.464185\pi$
$912$	19.6591	+	34.0506i	0.650979	+	1.12753i
$913$	−16.7684	−	29.0437i	−0.554952	−	0.961206i
$914$	4.37263	−	7.57361i	0.144634	−	0.250513i
$915$	4.83340			0.159787
$916$	−5.79590	+	10.0388i	−0.191502	+	0.331691i
$917$	−38.9315	+	67.4314i	−1.28563	+	2.22678i
$918$	−1.35690			−0.0447842
$919$	10.2337	−	17.7253i	0.337579	−	0.584703i	−0.646398	−	0.763000i	$-0.723725\pi$
$919$	10.2337	−	17.7253i	0.337579	−	0.584703i	0.983977	+	0.178297i	$0.0570588\pi$
$920$	−2.77359	−	4.80401i	−0.0914427	−	0.158383i
$921$	12.4324	+	21.5336i	0.409662	+	0.709556i
$922$	33.9385			1.11771
$923$		0			0
$924$	−22.2784			−0.732907
$925$	9.09515	+	15.7533i	0.299047	+	0.517964i
$926$	20.6112	+	35.6996i	0.677325	+	1.17316i
$927$	−2.82371	+	4.89081i	−0.0927427	+	0.160635i
$928$	24.1987			0.794360
$929$	2.32610	−	4.02892i	0.0763169	−	0.132185i	−0.825341	−	0.564634i	$-0.809017\pi$
$929$	2.32610	−	4.02892i	0.0763169	−	0.132185i	0.901658	+	0.432449i	$0.142351\pi$
$930$	6.37920	−	11.0491i	0.209182	−	0.362314i
$931$	38.7555			1.27016
$932$	−10.1072	+	17.5062i	−0.331073	+	0.573436i
$933$	8.54019	+	14.7920i	0.279593	+	0.484270i
$934$	−11.7126	−	20.2868i	−0.383248	−	0.663805i
$935$	5.64310			0.184549
$936$		0			0
$937$	−41.8544			−1.36732			−0.683662	−	0.729798i	$-0.739614\pi$
$937$	−41.8544			−1.36732			−0.683662	+	0.729798i	$0.739614\pi$
$938$	14.1005	+	24.4228i	0.460398	+	0.797433i
$939$	−7.84870	−	13.5943i	−0.256133	−	0.443635i
$940$	−9.50753	+	16.4675i	−0.310102	+	0.537112i
$941$	30.3454			0.989232			0.494616	−	0.869112i	$-0.335309\pi$
$941$	30.3454			0.989232			0.494616	+	0.869112i	$0.335309\pi$
$942$	0.742135	−	1.28542i	0.0241801	−	0.0418811i
$943$	2.54892	−	4.41485i	0.0830042	−	0.143767i
$944$	−9.27545			−0.301890
$945$	−2.48911	+	4.31127i	−0.0809709	+	0.140246i
$946$	−33.1640	−	57.4417i	−1.07825	−	1.86759i
$947$	−6.01626	−	10.4205i	−0.195502	−	0.338620i	0.751563	−	0.659662i	$-0.229300\pi$
$947$	−6.01626	−	10.4205i	−0.195502	−	0.338620i	−0.947065	+	0.321042i	$0.895967\pi$
$948$	−11.7627			−0.382035
$949$		0			0
$950$	−41.7700			−1.35520
$951$	−16.3910	−	28.3901i	−0.531516	−	0.920613i
$952$	−1.76002	−	3.04845i	−0.0570426	−	0.0988007i
$953$	−11.4913	+	19.9035i	−0.372239	+	0.644736i	−0.989910	−	0.141700i	$-0.954743\pi$
$953$	−11.4913	+	19.9035i	−0.372239	+	0.644736i	0.617671	+	0.786437i	$0.288076\pi$
$954$	−5.56465			−0.180162
$955$	5.11572	−	8.86069i	0.165541	−	0.286725i
$956$	8.42274	−	14.5886i	0.272411	−	0.471829i
$957$	20.2868			0.655779
$958$	34.3180	−	59.4405i	1.10876	−	1.92043i
$959$	23.4871	+	40.6809i	0.758440	+	1.31366i
$960$	0.916698	+	1.58777i	0.0295863	+	0.0512450i
$961$	−6.99223			−0.225556
$962$		0			0
$963$	−6.73556			−0.217050
$964$	−3.90850	−	6.76972i	−0.125884	−	0.218038i
$965$	−7.05765	−	12.2242i	−0.227194	−	0.393511i
$966$	8.78113	−	15.2094i	0.282528	−	0.489353i
$967$	−38.8883			−1.25056			−0.625281	−	0.780399i	$-0.715016\pi$
$967$	−38.8883			−1.25056			−0.625281	+	0.780399i	$0.715016\pi$
$968$	10.7835	−	18.6776i	0.346595	−	0.600321i
$969$	2.99731	−	5.19150i	0.0962875	−	0.166775i
$970$	22.5448			0.723870
$971$	28.7567	−	49.8080i	0.922845	−	1.59842i	0.127855	−	0.991793i	$-0.459191\pi$
$971$	28.7567	−	49.8080i	0.922845	−	1.59842i	0.794990	−	0.606622i	$-0.207476\pi$
$972$	−0.623490	−	1.07992i	−0.0199984	−	0.0346383i
$973$	−30.3189	−	52.5139i	−0.971980	−	1.68352i
$974$	−38.2911			−1.22693
$975$		0			0
$976$	−16.5200			−0.528794
$977$	−8.18449	−	14.1760i	−0.261845	−	0.453529i	0.704887	−	0.709319i	$-0.250998\pi$
$977$	−8.18449	−	14.1760i	−0.261845	−	0.453529i	−0.966732	+	0.255791i	$0.917664\pi$
$978$	−5.64795	−	9.78253i	−0.180601	−	0.312811i
$979$	3.00484	−	5.20454i	0.0960352	−	0.166338i
$980$	8.77240			0.280224
$981$	1.03803	−	1.79792i	0.0331418	−	0.0574033i
$982$	5.72132	−	9.90962i	0.182575	−	0.316229i
$983$	−15.6963			−0.500635			−0.250318	−	0.968164i	$-0.580535\pi$
$983$	−15.6963			−0.500635			−0.250318	+	0.968164i	$0.580535\pi$
$984$	1.22252	−	2.11747i	0.0389725	−	0.0675024i
$985$	−16.9151	−	29.2978i	−0.538959	−	0.933505i
$986$	−2.65399	−	4.59684i	−0.0845202	−	0.146393i
$987$	36.3540			1.15716
$988$		0			0
$989$	20.0804			0.638519
$990$	6.75182	+	11.6945i	0.214587	+	0.371676i
$991$	5.63222	+	9.75529i	0.178913	+	0.309887i	0.941509	−	0.336989i	$-0.109408\pi$
$991$	5.63222	+	9.75529i	0.178913	+	0.309887i	−0.762595	+	0.646876i	$0.776075\pi$
$992$	−15.1549	+	26.2491i	−0.481170	+	0.833411i
$993$	−29.1618			−0.925422
$994$	28.3061	−	49.0276i	0.897816	−	1.55506i
$995$	−2.90797	+	5.03675i	−0.0921888	+	0.159676i
$996$	−8.06398			−0.255517
$997$	3.85056	−	6.66936i	0.121948	−	0.211221i	−0.798588	−	0.601879i	$-0.794419\pi$
$997$	3.85056	−	6.66936i	0.121948	−	0.211221i	0.920536	+	0.390658i	$0.127752\pi$
$998$	4.19029	+	7.25780i	0.132641	+	0.229742i
$999$	−3.12349	−	5.41004i	−0.0988228	−	0.171166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.e.j.484.1		6
13.2	odd	12		507.2.b.g.337.1		6
13.3	even	3		507.2.a.k.1.3	yes	3
13.4	even	6		507.2.e.k.22.3		6
13.5	odd	4		507.2.j.h.361.1		12
13.6	odd	12		507.2.j.h.316.6		12
13.7	odd	12		507.2.j.h.316.1		12
13.8	odd	4		507.2.j.h.361.6		12
13.9	even	3	inner	507.2.e.j.22.1		6
13.10	even	6		507.2.a.j.1.1	✓	3
13.11	odd	12		507.2.b.g.337.6		6
13.12	even	2		507.2.e.k.484.3		6
39.2	even	12		1521.2.b.m.1351.6		6
39.11	even	12		1521.2.b.m.1351.1		6
39.23	odd	6		1521.2.a.q.1.3		3
39.29	odd	6		1521.2.a.p.1.1		3
52.3	odd	6		8112.2.a.cf.1.2		3
52.23	odd	6		8112.2.a.by.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.j.1.1	✓	3	13.10	even	6
507.2.a.k.1.3	yes	3	13.3	even	3
507.2.b.g.337.1		6	13.2	odd	12
507.2.b.g.337.6		6	13.11	odd	12
507.2.e.j.22.1		6	13.9	even	3	inner
507.2.e.j.484.1		6	1.1	even	1	trivial
507.2.e.k.22.3		6	13.4	even	6
507.2.e.k.484.3		6	13.12	even	2
507.2.j.h.316.1		12	13.7	odd	12
507.2.j.h.316.6		12	13.6	odd	12
507.2.j.h.361.1		12	13.5	odd	4
507.2.j.h.361.6		12	13.8	odd	4
1521.2.a.p.1.1		3	39.29	odd	6
1521.2.a.q.1.3		3	39.23	odd	6
1521.2.b.m.1351.1		6	39.11	even	12
1521.2.b.m.1351.6		6	39.2	even	12
8112.2.a.by.1.2		3	52.23	odd	6
8112.2.a.cf.1.2		3	52.3	odd	6

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.900969 - 1.56052i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.623490 + 1.07992i) q^{4} +1.44504 q^{5} +(-0.900969 + 1.56052i) q^{6} +(-1.72252 + 2.98349i) q^{7} -1.35690 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.30194 - 2.25502i) q^{10} +(2.59299 + 4.49119i) q^{11} +1.24698 q^{12} +6.20775 q^{14} +(-0.722521 - 1.25144i) q^{15} +(2.46950 + 4.27730i) q^{16} +(0.376510 - 0.652135i) q^{17} +1.80194 q^{18} +(-3.98039 + 6.89423i) q^{19} +(-0.900969 + 1.56052i) q^{20} +3.44504 q^{21} +(4.67241 - 8.09285i) q^{22} +(1.41454 + 2.45006i) q^{23} +(0.678448 + 1.17511i) q^{24} -2.91185 q^{25} +1.00000 q^{27} +(-2.14795 - 3.72036i) q^{28} +(1.95593 + 3.38776i) q^{29} +(-1.30194 + 2.25502i) q^{30} -4.89977 q^{31} +(3.09299 - 5.35722i) q^{32} +(2.59299 - 4.49119i) q^{33} -1.35690 q^{34} +(-2.48911 + 4.31127i) q^{35} +(-0.623490 - 1.07992i) q^{36} +(-3.12349 - 5.41004i) q^{37} +14.3448 q^{38} -1.96077 q^{40} +(-0.900969 - 1.56052i) q^{41} +(-3.10388 - 5.37607i) q^{42} +(3.54892 - 6.14691i) q^{43} -6.46681 q^{44} +(-0.722521 + 1.25144i) q^{45} +(2.54892 - 4.41485i) q^{46} +10.5526 q^{47} +(2.46950 - 4.27730i) q^{48} +(-2.43416 - 4.21608i) q^{49} +(2.62349 + 4.54402i) q^{50} -0.753020 q^{51} -3.08815 q^{53} +(-0.900969 - 1.56052i) q^{54} +(3.74698 + 6.48996i) q^{55} +(2.33728 - 4.04829i) q^{56} +7.96077 q^{57} +(3.52446 - 6.10454i) q^{58} +(-0.939001 + 1.62640i) q^{59} +1.80194 q^{60} +(-1.67241 + 2.89669i) q^{61} +(4.41454 + 7.64621i) q^{62} +(-1.72252 - 2.98349i) q^{63} -1.26875 q^{64} -9.34481 q^{66} +(2.27144 + 3.93425i) q^{67} +(0.469501 + 0.813199i) q^{68} +(1.41454 - 2.45006i) q^{69} +8.97046 q^{70} +(4.55980 - 7.89781i) q^{71} +(0.678448 - 1.17511i) q^{72} +2.95108 q^{73} +(-5.62833 + 9.74856i) q^{74} +(1.45593 + 2.52174i) q^{75} +(-4.96346 - 8.59696i) q^{76} -17.8659 q^{77} -9.43296 q^{79} +(3.56853 + 6.18088i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.62349 + 2.81197i) q^{82} -6.46681 q^{83} +(-2.14795 + 3.72036i) q^{84} +(0.544073 - 0.942362i) q^{85} -12.7899 q^{86} +(1.95593 - 3.38776i) q^{87} +(-3.51842 - 6.09408i) q^{88} +(-0.579417 - 1.00358i) q^{89} +2.60388 q^{90} -3.52781 q^{92} +(2.44989 + 4.24333i) q^{93} +(-9.50753 - 16.4675i) q^{94} +(-5.75182 + 9.96245i) q^{95} -6.18598 q^{96} +(-4.32908 + 7.49819i) q^{97} +(-4.38620 + 7.59712i) q^{98} -5.18598 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 3 q^{3} + q^{4} + 8 q^{5} - q^{6} - 10 q^{7} - 3 q^{9} + q^{10} + q^{11} - 2 q^{12} + 2 q^{14} - 4 q^{15} + 5 q^{16} + 7 q^{17} + 2 q^{18} - 11 q^{19} - q^{20} + 20 q^{21} + 5 q^{22}+ \cdots - 2 q^{99}+O(q^{100}) \) 6 * q - q^2 - 3 * q^3 + q^4 + 8 * q^5 - q^6 - 10 * q^7 - 3 * q^9 + q^10 + q^11 - 2 * q^12 + 2 * q^14 - 4 * q^15 + 5 * q^16 + 7 * q^17 + 2 * q^18 - 11 * q^19 - q^20 + 20 * q^21 + 5 * q^22 - 2 * q^23 - 10 * q^25 + 6 * q^27 + q^28 + 8 * q^29 + q^30 + 16 * q^31 + 4 * q^32 + q^33 - 18 * q^35 + q^36 - 14 * q^37 + 40 * q^38 + 14 * q^40 - q^41 - q^42 + 3 * q^43 - 32 * q^44 - 4 * q^45 - 3 * q^46 - 18 * q^47 + 5 * q^48 - 17 * q^49 + 11 * q^50 - 14 * q^51 - 26 * q^53 - q^54 + 13 * q^55 - 7 * q^56 + 22 * q^57 + 12 * q^58 + 14 * q^59 + 2 * q^60 + 13 * q^61 + 16 * q^62 - 10 * q^63 + 8 * q^64 - 10 * q^66 - 5 * q^67 - 7 * q^68 - 2 * q^69 - 16 * q^70 + 6 * q^71 + 36 * q^73 - 7 * q^74 + 5 * q^75 - q^76 - 30 * q^77 - 18 * q^79 + 16 * q^80 - 3 * q^81 - 5 * q^82 - 32 * q^83 + q^84 + 7 * q^85 - 30 * q^86 + 8 * q^87 + 7 * q^88 + 5 * q^89 - 2 * q^90 - 34 * q^92 - 8 * q^93 - 32 * q^94 - 3 * q^95 - 8 * q^96 - 5 * q^97 + 13 * q^98 - 2 * q^99

Introduction

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