LMFDB - Embedded newform 507.2.e.k.484.3

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			484.3
Root			$0.900969 + 1.56052i$ of defining polynomial
Character	$\chi$	$=$	507.484
Dual form			507.2.e.k.22.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 + 1.56052i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.623490 + 1.07992i) q^{4} -1.44504 q^{5} +(0.900969 - 1.56052i) q^{6} +(1.72252 - 2.98349i) q^{7} +1.35690 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 6 * q + q^2 - 3 * q^3 + q^4 - 8 * q^5 + q^6 + 10 * q^7 - 3 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$0.0531917\pi$
$2$	0.900969	+	1.56052i	0.637081	+	1.10346i	−0.348989	+	0.937127i	$0.613475\pi$
$3$	−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	$-0.604732\pi$
$5$	−1.44504			−0.646242			−0.323121	+	0.946358i	$0.604732\pi$
$6$	0.900969	−	1.56052i	0.367819	−	0.637081i
$7$	1.72252	−	2.98349i	0.651052	−	1.12765i	−0.331816	−	0.943344i	$-0.607661\pi$
$7$	1.72252	−	2.98349i	0.651052	−	1.12765i	0.982868	−	0.184311i	$-0.0590052\pi$
$8$	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	$-0.880960\pi$
$11$	−2.59299	−	4.49119i	−0.781816	−	1.35415i	0.149067	−	0.988827i	$-0.452373\pi$
$12$	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	$-0.466966\pi$
$19$	3.98039	−	6.89423i	0.913163	−	1.58164i	0.809569	−	0.587025i	$-0.199701\pi$
$20$	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	$-0.354974\pi$
$31$	4.89977			0.880025			0.440013	+	0.897992i	$0.354974\pi$
$32$	−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	$0.00498416\pi$
$37$	3.12349	+	5.41004i	0.513499	+	0.889406i	−0.486379	+	0.873748i	$0.661683\pi$
$38$	14.3448			2.32704
$39$		0			0
$40$	−1.96077			−0.310025
$41$	0.900969	+	1.56052i	0.140708	+	0.243713i	0.927763	−	0.373169i	$-0.121729\pi$
$41$	0.900969	+	1.56052i	0.140708	+	0.243713i	−0.787056	+	0.616882i	$0.788396\pi$
$42$	−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	$-0.779557\pi$
$47$	−10.5526			−1.53925			−0.769625	+	0.638496i	$0.779557\pi$
$48$	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	−0.798406	−	0.602119i	$-0.794323\pi$
$59$	0.939001	−	1.62640i	0.122248	−	0.211739i	0.920654	+	0.390380i	$0.127656\pi$
$60$	−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	0.693263	−	0.720685i	$-0.256173\pi$
$67$	−2.27144	−	3.93425i	−0.277500	−	0.480645i	−0.970763	+	0.240040i	$0.922839\pi$
$68$	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	$0.348677\pi$
$71$	−4.55980	+	7.89781i	−0.541149	+	0.937298i	−0.998838	+	0.0481854i	$0.984656\pi$
$72$	−0.678448	+	1.17511i	−0.0799559	+	0.138488i
$73$	−2.95108			−0.345398			−0.172699	−	0.984975i	$-0.555249\pi$
$73$	−2.95108			−0.345398			−0.172699	+	0.984975i	$0.555249\pi$
$74$	−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	$-0.384511\pi$
$83$	6.46681			0.709825			0.354912	+	0.934900i	$0.384511\pi$
$84$	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	0.895099	−	0.445866i	$-0.147104\pi$
$89$	0.579417	+	1.00358i	0.0614181	+	0.106379i	−0.833681	+	0.552246i	$0.813771\pi$
$90$	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	−0.558103	−	0.829772i	$-0.688471\pi$
$97$	4.32908	−	7.49819i	0.439552	−	0.761326i	0.997655	+	0.0684454i	$0.0218039\pi$
$98$	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	$-0.468300\pi$
$109$	2.07606			0.198851			0.0994255	+	0.995045i	$0.468300\pi$
$110$	−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	$0.364581\pi$
$137$	−6.81767	+	11.8085i	−0.582473	+	1.00887i	−0.995185	+	0.0980109i	$0.968752\pi$
$138$	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	$-0.658597\pi$
$149$	6.36927	−	11.0319i	0.521791	−	0.903769i	0.999679	−	0.0253478i	$-0.00806931\pi$
$150$	−2.62349	+	4.54402i	−0.214207	+	0.371017i
$151$	−15.6407			−1.27282			−0.636412	−	0.771350i	$-0.719582\pi$
$151$	−15.6407			−1.27282			−0.636412	+	0.771350i	$0.719582\pi$
$152$	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	−0.716770	−	0.697310i	$-0.754380\pi$
$163$	3.13437	−	5.42890i	0.245503	−	0.425224i	0.962273	+	0.272086i	$0.0877135\pi$
$164$	−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	0.685130	−	0.728420i	$-0.259745\pi$
$167$	−3.72521	−	6.45225i	−0.288265	−	0.499290i	−0.973396	+	0.229130i	$0.926412\pi$
$168$	−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	0.986523	−	0.163622i	$-0.0523176\pi$
$193$	4.88404	+	8.45941i	0.351561	+	0.608922i	−0.634962	+	0.772543i	$0.718984\pi$
$194$	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	$0.147282\pi$
$197$	11.7056	+	20.2747i	0.833989	+	1.44451i	−0.0608617	+	0.998146i	$0.519385\pi$
$198$	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	0.963366	−	0.268191i	$-0.0864258\pi$
$223$	3.72468	+	6.45133i	0.249423	+	0.432013i	−0.713943	+	0.700204i	$0.753092\pi$
$224$	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	$0.415812\pi$
$227$	−10.6250	+	18.4030i	−0.705205	+	1.22145i	−0.966618	+	0.256223i	$0.917522\pi$
$228$	4.96346	−	8.59696i	0.328713	−	0.569348i
$229$	−9.29590			−0.614290			−0.307145	−	0.951663i	$-0.599374\pi$
$229$	−9.29590			−0.614290			−0.307145	+	0.951663i	$0.599374\pi$
$230$	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	$-0.356072\pi$
$239$	13.5090			0.873826			0.436913	+	0.899504i	$0.356072\pi$
$240$	−3.56853	+	6.18088i	−0.230348	+	0.398974i
$241$	3.13437	−	5.42890i	0.201903	−	0.349706i	−0.747239	−	0.664556i	$-0.768621\pi$
$241$	3.13437	−	5.42890i	0.201903	−	0.349706i	0.949142	+	0.314850i	$0.101954\pi$
$242$	−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	0.853696	−	0.520772i	$-0.174356\pi$
$271$	−0.397616	−	0.688692i	−0.0241535	−	0.0418351i	−0.877849	+	0.478937i	$0.841022\pi$
$272$	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	$-0.689201\pi$
$281$	−18.7748			−1.12001			−0.560005	+	0.828489i	$0.689201\pi$
$282$	−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	−0.753794	−	0.657111i	$-0.771778\pi$
$293$	3.28956	−	5.69769i	0.192178	−	0.332862i	0.945972	+	0.324249i	$0.105112\pi$
$294$	−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	$-0.248895\pi$
$307$	24.8649			1.41911			0.709556	+	0.704649i	$0.248895\pi$
$308$	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	$-0.872310\pi$
$317$	−32.7821			−1.84123			−0.920613	+	0.390477i	$0.872310\pi$
$318$	−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	$0.462599\pi$
$331$	−14.5809	+	25.2549i	−0.801439	+	1.38813i	−0.918669	+	0.395029i	$0.870735\pi$
$332$	−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	0.819529	−	0.573037i	$-0.194235\pi$
$349$	−1.61596	−	2.79892i	−0.0865002	−	0.149823i	−0.906029	+	0.423215i	$0.860902\pi$
$350$	−18.0761			−0.966206
$351$		0			0
$352$	32.0804			1.70989
$353$	4.07338	+	7.05529i	0.216804	+	0.375515i	0.953829	−	0.300350i	$-0.0971034\pi$
$353$	4.07338	+	7.05529i	0.216804	+	0.375515i	−0.737025	+	0.675865i	$0.763770\pi$
$354$	−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	$-0.522200\pi$
$359$	−2.64071			−0.139371			−0.0696857	+	0.997569i	$0.522200\pi$
$360$	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	0.994259	−	0.106998i	$-0.0341240\pi$
$379$	7.87412	+	13.6384i	0.404466	+	0.700556i	−0.589793	+	0.807555i	$0.700791\pi$
$380$	−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	−0.656150	−	0.754631i	$-0.727816\pi$
$383$	6.36927	−	11.0319i	0.325455	−	0.563704i	0.981604	+	0.190927i	$0.0611493\pi$
$384$	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	−0.846712	−	0.532052i	$-0.821421\pi$
$397$	0.745488	−	1.29122i	0.0374150	−	0.0648046i	0.884127	+	0.467248i	$0.154754\pi$
$398$	−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	$-0.963782\pi$
$401$	−11.9167	−	20.6403i	−0.595092	−	1.03073i	0.398442	−	0.917193i	$-0.369551\pi$
$402$	−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	−0.808439	−	0.588580i	$-0.799687\pi$
$409$	2.13371	−	3.69570i	0.105505	−	0.182740i	0.913945	+	0.405839i	$0.133021\pi$
$410$	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	$-0.754217\pi$
$421$	−29.3991			−1.43282			−0.716412	+	0.697677i	$0.754217\pi$
$422$	−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	$-0.873543\pi$
$431$	−16.5281	−	28.6275i	−0.796131	−	1.37894i	0.125988	−	0.992032i	$-0.459790\pi$
$432$	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	−0.977326	−	0.211741i	$-0.932087\pi$
$449$	−6.46897	+	11.2046i	−0.305289	+	0.528777i	0.672036	+	0.740518i	$0.265420\pi$
$450$	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	0.803672	−	0.595073i	$-0.202877\pi$
$457$	−2.42662	−	4.20304i	−0.113513	−	0.196610i	−0.917184	+	0.398463i	$0.869544\pi$
$458$	−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	−0.558978	−	0.829183i	$-0.688806\pi$
$461$	9.41723	−	16.3111i	0.438604	−	0.759685i	0.997582	+	0.0694978i	$0.0221397\pi$
$462$	−16.0966	+	27.8802i	−0.748883	+	1.29710i
$463$	22.8767			1.06317			0.531585	−	0.847005i	$-0.321597\pi$
$463$	22.8767			1.06317			0.531585	+	0.847005i	$0.321597\pi$
$464$	−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	$-0.830663\pi$
$479$	−19.0450	−	32.9870i	−0.870190	−	1.50721i	−0.00838964	−	0.999965i	$-0.502671\pi$
$480$	−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	−0.999774	−	0.0212730i	$-0.993228\pi$
$487$	−10.6250	+	18.4030i	−0.481464	+	0.833920i	0.518310	+	0.855193i	$0.326561\pi$
$488$	−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	$-0.466804\pi$
$499$	4.65087			0.208202			0.104101	+	0.994567i	$0.466804\pi$
$500$	−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	0.544227	−	0.838938i	$-0.316823\pi$
$509$	−10.2524	−	17.7576i	−0.454428	−	0.787092i	−0.998655	+	0.0518459i	$0.983490\pi$
$510$	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	$-0.785829\pi$
$541$	−36.3803			−1.56411			−0.782056	+	0.623208i	$0.785829\pi$
$542$	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	0.991225	−	0.132185i	$-0.0421993\pi$
$557$	8.99516	+	15.5801i	0.381137	+	0.660149i	−0.610088	+	0.792334i	$0.708866\pi$
$558$	−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	$-0.494571\pi$
$577$	0.819396			0.0341119			0.0170560	+	0.999855i	$0.494571\pi$
$578$	−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	$-0.938807\pi$
$587$	−15.8998	−	27.5392i	−0.656254	−	1.13666i	0.325324	−	0.945603i	$-0.394527\pi$
$588$	−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	$-0.472100\pi$
$593$	4.26337			0.175076			0.0875379	+	0.996161i	$0.472100\pi$
$594$	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	$0.0706132\pi$
$613$	16.7937	+	29.0876i	0.678293	+	1.17484i	−0.297202	+	0.954815i	$0.596053\pi$
$614$	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	$0.346421\pi$
$617$	−13.2935	+	23.0250i	−0.535176	+	0.926953i	−0.999155	+	0.0411061i	$0.986912\pi$
$618$	5.08815	−	8.81293i	0.204675	−	0.354508i
$619$	9.17928			0.368946			0.184473	−	0.982838i	$-0.440942\pi$
$619$	9.17928			0.368946			0.184473	+	0.982838i	$0.440942\pi$
$620$	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	−0.645679	−	0.763609i	$-0.723425\pi$
$631$	8.50216	−	14.7262i	0.338465	−	0.586239i	0.984144	+	0.177370i	$0.0567588\pi$
$632$	−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	−0.758925	−	0.651178i	$-0.774275\pi$
$643$	4.67778	−	8.10216i	0.184474	−	0.319518i	0.943399	+	0.331660i	$0.107609\pi$
$644$	−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	0.968687	−	0.248286i	$-0.0798673\pi$
$661$	6.92423	+	11.9931i	0.269321	+	0.466478i	−0.699365	+	0.714764i	$0.746534\pi$
$662$	−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	−0.620705	−	0.784044i	$-0.713154\pi$
$683$	9.63437	−	16.6872i	0.368649	−	0.638519i	0.989355	+	0.145525i	$0.0464871\pi$
$684$	−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	$-0.896988\pi$
$691$	−19.7005	−	34.1223i	−0.749443	−	1.29807i	0.198647	−	0.980071i	$-0.436345\pi$
$692$	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	$0.423494\pi$
$709$	−19.2277	+	33.3033i	−0.722110	+	1.25073i	−0.960153	+	0.279476i	$0.909839\pi$
$710$	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	$-0.650255\pi$
$733$	−24.6213			−0.909410			−0.454705	+	0.890642i	$0.650255\pi$
$734$	−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	$-0.861366\pi$
$739$	−22.2558	−	38.5481i	−0.818692	−	1.41802i	0.0879549	−	0.996124i	$-0.471967\pi$
$740$	11.2567			0.413803
$741$		0			0
$742$	−19.1704			−0.703769
$743$	5.20560	+	9.01636i	0.190975	+	0.330778i	0.945574	−	0.325408i	$-0.105502\pi$
$743$	5.20560	+	9.01636i	0.190975	+	0.330778i	−0.754599	+	0.656186i	$0.772168\pi$
$744$	−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	−0.907973	−	0.419028i	$-0.862371\pi$
$761$	−2.51304	+	4.35271i	−0.0910977	+	0.157786i	0.816876	+	0.576814i	$0.195704\pi$
$762$	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	$0.110750\pi$
$769$	21.2228	+	36.7590i	0.765314	+	1.32556i	−0.174766	+	0.984610i	$0.555917\pi$
$770$	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	−0.525519	−	0.850782i	$-0.676129\pi$
$773$	13.1796	−	22.8278i	0.474039	−	0.821059i	0.999558	+	0.0297223i	$0.00946228\pi$
$774$	−6.39493	+	11.0763i	−0.229861	+	0.398131i

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)

\(f(q)\)	\(=\)	\(q+(0.900969 + 1.56052i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.623490 + 1.07992i) q^{4} -1.44504 q^{5} +(0.900969 - 1.56052i) q^{6} +(1.72252 - 2.98349i) q^{7} +1.35690 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 3 q^{3} + q^{4} - 8 q^{5} + q^{6} + 10 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + q^2 - 3 * q^3 + q^4 - 8 * q^5 + q^6 + 10 * q^7 - 3 * q^9	\( 6 q + q^{2} - 3 q^{3} + q^{4} - 8 q^{5} + q^{6} + 10 q^{7} - 3 q^{9} + q^{10} - q^{11} - 2 q^{12} + 2 q^{14} + 4 q^{15} + 5 q^{16} + 7 q^{17} - 2 q^{18} + 11 q^{19} + q^{20} - 20 q^{21} + 5 q^{22} - 2 q^{23} - 10 q^{25} + 6 q^{27} - q^{28} + 8 q^{29} + q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 18 q^{35} + q^{36} + 14 q^{37} + 40 q^{38} + 14 q^{40} + q^{41} - q^{42} + 3 q^{43} + 32 q^{44} + 4 q^{45} + 3 q^{46} + 18 q^{47} + 5 q^{48} - 17 q^{49} - 11 q^{50} - 14 q^{51} - 26 q^{53} + q^{54} + 13 q^{55} - 7 q^{56} - 22 q^{57} - 12 q^{58} - 14 q^{59} - 2 q^{60} + 13 q^{61} + 16 q^{62} + 10 q^{63} + 8 q^{64} - 10 q^{66} + 5 q^{67} - 7 q^{68} - 2 q^{69} + 16 q^{70} - 6 q^{71} - 36 q^{73} - 7 q^{74} + 5 q^{75} + q^{76} - 30 q^{77} - 18 q^{79} - 16 q^{80} - 3 q^{81} - 5 q^{82} + 32 q^{83} - q^{84} - 7 q^{85} + 30 q^{86} + 8 q^{87} + 7 q^{88} - 5 q^{89} - 2 q^{90} - 34 q^{92} + 8 q^{93} - 32 q^{94} - 3 q^{95} + 8 q^{96} + 5 q^{97} - 13 q^{98} + 2 q^{99}+O(q^{100}) \) 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

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