LMFDB - Embedded newform 507.2.p.a.493.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			493.9
Character	$\chi$	$=$	507.493
Dual form			507.2.p.a.181.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.620957 + 0.428616i) q^{2} +(0.885456 - 0.464723i) q^{3} +(-0.507334 - 1.33773i) q^{4} +(0.0551559 - 0.0622582i) q^{5} +(0.749018 + 0.0909472i) q^{6} +(0.872920 - 3.54157i) q^{7} +(0.619476 - 2.51331i) q^{8} +(0.568065 - 0.822984i) q^{9} +O(q^{10})$	\(q+(0.620957 + 0.428616i) q^{2} +(0.885456 - 0.464723i) q^{3} +(-0.507334 - 1.33773i) q^{4} +(0.0551559 - 0.0622582i) q^{5} +(0.749018 + 0.0909472i) q^{6} +(0.872920 - 3.54157i) q^{7} +(0.619476 - 2.51331i) q^{8} +(0.568065 - 0.822984i) q^{9} +(0.0609343 - 0.0150189i) q^{10} +(-4.91596 + 3.39324i) q^{11} +(-1.07090 - 0.948730i) q^{12} +(3.60532 - 0.0405680i) q^{13} +(2.06002 - 1.82502i) q^{14} +(0.0199053 - 0.0807591i) q^{15} +(-0.679878 + 0.602320i) q^{16} +(-5.60683 - 1.38196i) q^{17} +(0.705487 - 0.267556i) q^{18} -4.48545i q^{19} +(-0.111267 - 0.0421980i) q^{20} +(-0.872920 - 3.54157i) q^{21} -4.50700 q^{22} +1.33359 q^{23} +(-0.619476 - 2.51331i) q^{24} +(0.601849 + 4.95668i) q^{25} +(2.25614 + 1.52011i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-5.18053 + 0.629030i) q^{28} +(4.93183 - 7.14499i) q^{29} +(0.0469750 - 0.0416162i) q^{30} +(8.90724 + 1.08153i) q^{31} +(-5.81965 + 0.706633i) q^{32} +(-2.77595 + 5.28913i) q^{33} +(-2.88927 - 3.26131i) q^{34} +(-0.172345 - 0.249685i) q^{35} +(-1.38913 - 0.342389i) q^{36} +(8.97250 + 1.08946i) q^{37} +(1.92253 - 2.78527i) q^{38} +(3.17350 - 1.71140i) q^{39} +(-0.122306 - 0.177191i) q^{40} +(2.55755 + 4.87301i) q^{41} +(0.975928 - 2.57331i) q^{42} +(0.160517 + 1.32198i) q^{43} +(7.03328 + 4.85472i) q^{44} +(-0.0199053 - 0.0807591i) q^{45} +(0.828101 + 0.571597i) q^{46} +(-1.11086 - 0.421292i) q^{47} +(-0.322091 + 0.849283i) q^{48} +(-5.58257 - 2.92996i) q^{49} +(-1.75079 + 3.33584i) q^{50} +(-5.60683 + 1.38196i) q^{51} +(-1.88337 - 4.80236i) q^{52} +(10.3880 + 2.56042i) q^{53} +(0.500339 - 0.564766i) q^{54} +(-0.0598873 + 0.493216i) q^{55} +(-8.36033 - 4.38784i) q^{56} +(-2.08449 - 3.97167i) q^{57} +(6.12491 - 2.32287i) q^{58} +(-7.98914 + 9.01788i) q^{59} +(-0.118132 + 0.0143439i) q^{60} +(0.174489 - 0.0430077i) q^{61} +(5.06745 + 4.48937i) q^{62} +(-2.41878 - 2.73024i) q^{63} +(-2.30809 - 1.21138i) q^{64} +(0.196329 - 0.226698i) q^{65} +(-3.99075 + 2.09451i) q^{66} +(-4.98335 - 1.88993i) q^{67} +(0.995847 + 8.20154i) q^{68} +(1.18083 - 0.619750i) q^{69} -0.228914i q^{70} +(0.697105 + 1.32822i) q^{71} +(-1.71651 - 1.93754i) q^{72} +(-8.39873 + 5.79723i) q^{73} +(5.10458 + 4.52226i) q^{74} +(2.83639 + 4.10923i) q^{75} +(-6.00031 + 2.27562i) q^{76} +(7.72619 + 20.3723i) q^{77} +(2.70414 + 0.297508i) q^{78} +(2.59921 - 6.85356i) q^{79} +0.0755495i q^{80} +(-0.354605 - 0.935016i) q^{81} +(-0.500518 + 4.12213i) q^{82} +(0.872339 - 1.66210i) q^{83} +(-4.29480 + 2.96449i) q^{84} +(-0.395288 + 0.272848i) q^{85} +(-0.466946 + 0.889691i) q^{86} +(1.04648 - 8.61851i) q^{87} +(5.48296 + 14.4574i) q^{88} -9.41292i q^{89} +(0.0222543 - 0.0586796i) q^{90} +(3.00348 - 12.8039i) q^{91} +(-0.676574 - 1.78398i) q^{92} +(8.38958 - 3.18175i) q^{93} +(-0.509222 - 0.737735i) q^{94} +(-0.279256 - 0.247399i) q^{95} +(-4.82466 + 3.33022i) q^{96} +(7.31268 + 8.25431i) q^{97} +(-2.21071 - 4.21215i) q^{98} +5.97334i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{26}\right)$

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 $

$2$	0.620957	+	0.428616i	0.439083	+	0.303077i	0.767021	−	0.641622i	$-0.221738\pi$
$2$	0.620957	+	0.428616i	0.439083	+	0.303077i	−0.327938	+	0.944699i	$0.606354\pi$
$3$	0.885456	−	0.464723i	0.511218	−	0.268308i
$3$	0.885456	−	0.464723i	0.511218	−	0.268308i
$4$	−0.507334	−	1.33773i	−0.253667	−	0.668864i
$5$	0.0551559	−	0.0622582i	0.0246665	−	0.0278427i	−0.736048	−	0.676929i	$-0.763310\pi$
$5$	0.0551559	−	0.0622582i	0.0246665	−	0.0278427i	0.760715	+	0.649087i	$0.224849\pi$
$6$	0.749018	+	0.0909472i	0.305785	+	0.0371290i
$7$	0.872920	−	3.54157i	0.329933	−	1.33859i	−0.538435	−	0.842667i	$-0.680984\pi$
$7$	0.872920	−	3.54157i	0.329933	−	1.33859i	0.868367	−	0.495922i	$-0.165170\pi$
$8$	0.619476	−	2.51331i	0.219018	−	0.888590i
$9$	0.568065	−	0.822984i	0.189355	−	0.274328i
$10$	0.0609343	−	0.0150189i	0.0192691	−	0.00474941i
$11$	−4.91596	+	3.39324i	−1.48222	+	1.02310i	−0.494101	+	0.869405i	$0.664503\pi$
$11$	−4.91596	+	3.39324i	−1.48222	+	1.02310i	−0.988118	+	0.153697i	$0.950882\pi$
$12$	−1.07090	−	0.948730i	−0.309141	−	0.273875i
$13$	3.60532	−	0.0405680i	0.999937	−	0.0112515i
$13$	3.60532	−	0.0405680i	0.999937	−	0.0112515i
$14$	2.06002	−	1.82502i	0.550563	−	0.487757i
$15$	0.0199053	−	0.0807591i	0.00513953	−	0.0208519i
$16$	−0.679878	+	0.602320i	−0.169970	+	0.150580i
$17$	−5.60683	−	1.38196i	−1.35986	−	0.335175i	−0.509088	−	0.860714i	$-0.670017\pi$
$17$	−5.60683	−	1.38196i	−1.35986	−	0.335175i	−0.850769	+	0.525540i	$0.823863\pi$
$18$	0.705487	−	0.267556i	0.166285	−	0.0630636i
$19$		−	4.48545i		−	1.02903i	−0.857481	−	0.514516i	$-0.827972\pi$
$19$		−	4.48545i		−	1.02903i	0.857481	−	0.514516i	$-0.172028\pi$
$20$	−0.111267	−	0.0421980i	−0.0248801	−	0.00943576i
$21$	−0.872920	−	3.54157i	−0.190487	−	0.772835i
$22$	−4.50700			−0.960895
$23$	1.33359			0.278072			0.139036	−	0.990287i	$-0.455600\pi$
$23$	1.33359			0.278072			0.139036	+	0.990287i	$0.455600\pi$
$24$	−0.619476	−	2.51331i	−0.126450	−	0.513027i
$25$	0.601849	+	4.95668i	0.120370	+	0.991335i
$26$	2.25614	+	1.52011i	0.442465	+	0.298117i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	−5.18053	+	0.629030i	−0.979028	+	0.118875i
$29$	4.93183	−	7.14499i	0.915818	−	1.32679i	−0.0291323	−	0.999576i	$-0.509274\pi$
$29$	4.93183	−	7.14499i	0.915818	−	1.32679i	0.944950	−	0.327215i	$-0.106110\pi$
$30$	0.0469750	−	0.0416162i	0.00857641	−	0.00759804i
$31$	8.90724	+	1.08153i	1.59979	+	0.194249i	0.871279	−	0.490788i	$-0.163291\pi$
$31$	8.90724	+	1.08153i	1.59979	+	0.194249i	0.728508	+	0.685037i	$0.240214\pi$
$32$	−5.81965	+	0.706633i	−1.02878	+	0.124916i
$33$	−2.77595	+	5.28913i	−0.483231	+	0.920720i
$34$	−2.88927	−	3.26131i	−0.495506	−	0.559311i
$35$	−0.172345	−	0.249685i	−0.0291317	−	0.0422045i
$36$	−1.38913	−	0.342389i	−0.231521	−	0.0570649i
$37$	8.97250	+	1.08946i	1.47507	+	0.179106i	0.818216	−	0.574911i	$-0.194963\pi$
$37$	8.97250	+	1.08946i	1.47507	+	0.179106i	0.656855	+	0.754017i	$0.271886\pi$
$38$	1.92253	−	2.78527i	0.311876	−	0.451830i
$39$	3.17350	−	1.71140i	0.508167	−	0.274043i
$40$	−0.122306	−	0.177191i	−0.0193383	−	0.0280164i
$41$	2.55755	+	4.87301i	0.399422	+	0.761036i	0.999235	−	0.0391046i	$-0.0124506\pi$
$41$	2.55755	+	4.87301i	0.399422	+	0.761036i	−0.599813	+	0.800140i	$0.704758\pi$
$42$	0.975928	−	2.57331i	0.150589	−	0.397071i
$43$	0.160517	+	1.32198i	0.0244786	+	0.201600i	0.999817	−	0.0191138i	$-0.00608449\pi$
$43$	0.160517	+	1.32198i	0.0244786	+	0.201600i	−0.975339	+	0.220714i	$0.929161\pi$
$44$	7.03328	+	4.85472i	1.06031	+	0.731876i
$45$	−0.0199053	−	0.0807591i	−0.00296731	−	0.0120389i
$46$	0.828101	+	0.571597i	0.122097	+	0.0842774i
$47$	−1.11086	−	0.421292i	−0.162035	−	0.0614518i	0.272254	−	0.962226i	$-0.412231\pi$
$47$	−1.11086	−	0.421292i	−0.162035	−	0.0614518i	−0.434289	+	0.900774i	$0.643000\pi$
$48$	−0.322091	+	0.849283i	−0.0464898	+	0.122583i
$49$	−5.58257	−	2.92996i	−0.797510	−	0.418565i
$50$	−1.75079	+	3.33584i	−0.247599	+	0.471760i
$51$	−5.60683	+	1.38196i	−0.785114	+	0.193513i
$52$	−1.88337	−	4.80236i	−0.261177	−	0.665968i
$53$	10.3880	+	2.56042i	1.42690	+	0.351700i	0.875775	−	0.482719i	$-0.160351\pi$
$53$	10.3880	+	2.56042i	1.42690	+	0.351700i	0.551130	+	0.834420i	$0.314197\pi$
$54$	0.500339	−	0.564766i	0.0680875	−	0.0768549i
$55$	−0.0598873	+	0.493216i	−0.00807520	+	0.0665053i
$56$	−8.36033	−	4.38784i	−1.11720	−	0.586349i
$57$	−2.08449	−	3.97167i	−0.276098	−	0.526060i
$58$	6.12491	−	2.32287i	0.804240	−	0.305008i
$59$	−7.98914	+	9.01788i	−1.04010	+	1.17403i	−0.0556320	+	0.998451i	$0.517717\pi$
$59$	−7.98914	+	9.01788i	−1.04010	+	1.17403i	−0.984466	+	0.175576i	$0.943821\pi$
$60$	−0.118132	+	0.0143439i	−0.0152508	+	0.00185179i
$61$	0.174489	−	0.0430077i	0.0223411	−	0.00550658i	−0.228129	−	0.973631i	$-0.573261\pi$
$61$	0.174489	−	0.0430077i	0.0223411	−	0.00550658i	0.250470	+	0.968124i	$0.419415\pi$
$62$	5.06745	+	4.48937i	0.643566	+	0.570150i
$63$	−2.41878	−	2.73024i	−0.304738	−	0.343978i
$64$	−2.30809	−	1.21138i	−0.288512	−	0.151423i
$65$	0.196329	−	0.226698i	0.0243516	−	0.0281185i
$66$	−3.99075	+	2.09451i	−0.491227	+	0.257816i
$67$	−4.98335	−	1.88993i	−0.608813	−	0.230892i	0.0308797	−	0.999523i	$-0.490169\pi$
$67$	−4.98335	−	1.88993i	−0.608813	−	0.230892i	−0.639693	+	0.768631i	$0.720938\pi$
$68$	0.995847	+	8.20154i	0.120764	+	0.994583i
$69$	1.18083	−	0.619750i	0.142156	−	0.0746091i
$70$		−	0.228914i		−	0.0273604i
$71$	0.697105	+	1.32822i	0.0827312	+	0.157631i	0.923307	−	0.384063i	$-0.125475\pi$
$71$	0.697105	+	1.32822i	0.0827312	+	0.157631i	−0.840576	+	0.541694i	$0.817783\pi$
$72$	−1.71651	−	1.93754i	−0.202293	−	0.228341i
$73$	−8.39873	+	5.79723i	−0.982997	+	0.678514i	−0.947132	−	0.320843i	$-0.896034\pi$
$73$	−8.39873	+	5.79723i	−0.982997	+	0.678514i	−0.0358647	+	0.999357i	$0.511419\pi$
$74$	5.10458	+	4.52226i	0.593395	+	0.525702i
$75$	2.83639	+	4.10923i	0.327519	+	0.474493i
$76$	−6.00031	+	2.27562i	−0.688283	+	0.261031i
$77$	7.72619	+	20.3723i	0.880481	+	2.32164i
$78$	2.70414	+	0.297508i	0.306184	+	0.0336861i
$79$	2.59921	−	6.85356i	0.292434	−	0.771086i	−0.705611	−	0.708599i	$-0.749328\pi$
$79$	2.59921	−	6.85356i	0.292434	−	0.771086i	0.998046	−	0.0624869i	$-0.0199032\pi$
$80$			0.0755495i			0.00844669i
$81$	−0.354605	−	0.935016i	−0.0394005	−	0.103891i
$82$	−0.500518	+	4.12213i	−0.0552729	+	0.455214i
$83$	0.872339	−	1.66210i	0.0957516	−	0.182439i	−0.832869	−	0.553470i	$-0.813303\pi$
$83$	0.872339	−	1.66210i	0.0957516	−	0.182439i	0.928621	+	0.371031i	$0.120996\pi$
$84$	−4.29480	+	2.96449i	−0.468602	+	0.323452i
$85$	−0.395288	+	0.272848i	−0.0428750	+	0.0295945i
$86$	−0.466946	+	0.889691i	−0.0503521	+	0.0959379i
$87$	1.04648	−	8.61851i	0.112194	−	0.924001i
$88$	5.48296	+	14.4574i	0.584486	+	1.54116i
$89$		−	9.41292i		−	0.997768i	−0.866669	−	0.498884i	$-0.833743\pi$
$89$		−	9.41292i		−	0.997768i	0.866669	−	0.498884i	$-0.166257\pi$
$90$	0.0222543	−	0.0586796i	0.00234580	−	0.00618538i
$91$	3.00348	−	12.8039i	0.314851	−	1.34222i
$92$	−0.676574	−	1.78398i	−0.0705378	−	0.185993i
$93$	8.38958	−	3.18175i	0.869959	−	0.329932i
$94$	−0.509222	−	0.737735i	−0.0525222	−	0.0760916i
$95$	−0.279256	−	0.247399i	−0.0286510	−	0.0253826i
$96$	−4.82466	+	3.33022i	−0.492414	+	0.339889i
$97$	7.31268	+	8.25431i	0.742490	+	0.838098i	0.991460	−	0.130413i	$-0.0416305\pi$
$97$	7.31268	+	8.25431i	0.742490	+	0.838098i	−0.248970	+	0.968511i	$0.580092\pi$
$98$	−2.21071	−	4.21215i	−0.223315	−	0.425492i
$99$			5.97334i			0.600343i
$100$	6.32535	−	3.31980i	0.632535	−	0.331980i
$101$	−0.352596	−	2.90389i	−0.0350846	−	0.288948i	−0.999682	−	0.0252204i	$-0.991971\pi$
$101$	−0.352596	−	2.90389i	−0.0350846	−	0.288948i	0.964597	−	0.263727i	$-0.0849518\pi$
$102$	−4.07393	−	1.54504i	−0.403379	−	0.152982i
$103$	3.44011	−	1.80551i	0.338964	−	0.177902i	−0.286649	−	0.958036i	$-0.592541\pi$
$103$	3.44011	−	1.80551i	0.338964	−	0.177902i	0.625613	+	0.780134i	$0.284849\pi$
$104$	2.13145	−	9.08643i	0.209006	−	0.890998i
$105$	−0.268639	−	0.140992i	−0.0262164	−	0.0137594i
$106$	5.35308	+	6.04238i	0.519937	+	0.586888i
$107$	2.91265	+	2.58039i	0.281577	+	0.249455i	0.792075	−	0.610423i	$-0.209001\pi$
$107$	2.91265	+	2.58039i	0.281577	+	0.249455i	−0.510498	+	0.859879i	$0.670539\pi$
$108$	−1.38913	+	0.342389i	−0.133669	+	0.0329464i
$109$	−17.7870	+	2.15973i	−1.70368	+	0.206865i	−0.913736	−	0.406309i	$-0.866816\pi$
$109$	−17.7870	+	2.15973i	−1.70368	+	0.206865i	−0.789948	+	0.613173i	$0.789893\pi$
$110$	−0.248588	+	0.280597i	−0.0237019	+	0.0267539i
$111$	8.45105	−	3.20506i	0.802139	−	0.304211i
$112$	1.53968	+	2.93362i	0.145486	+	0.277201i
$113$	5.78286	+	3.03508i	0.544006	+	0.285516i	0.714256	−	0.699885i	$-0.246765\pi$
$113$	5.78286	+	3.03508i	0.544006	+	0.285516i	−0.170250	+	0.985401i	$0.554458\pi$
$114$	0.407939	−	3.35968i	0.0382070	−	0.314663i
$115$	0.0735553	−	0.0830268i	0.00685907	−	0.00774229i
$116$	−12.0601	−	2.97256i	−1.11976	−	0.275995i
$117$	2.01467	−	2.99017i	0.186256	−	0.276441i
$118$	−8.82612	+	2.17544i	−0.812510	+	0.200266i
$119$	−9.78863	+	18.6507i	−0.897322	+	1.70971i
$120$	−0.190642	−	0.100057i	−0.0174031	−	0.00913387i
$121$	8.75194	−	23.0770i	0.795630	−	2.09791i
$122$	0.126784	+	0.0480829i	0.0114785	+	0.00435322i
$123$	4.52920	+	3.12628i	0.408384	+	0.281887i
$124$	−3.07214	−	12.4642i	−0.275886	−	1.11932i
$125$	0.684052	+	0.472167i	0.0611834	+	0.0422319i
$126$	−0.331736	−	2.73209i	−0.0295534	−	0.243394i
$127$	−2.68184	+	7.07144i	−0.237975	+	0.627489i	−0.999794	−	0.0203015i	$-0.993537\pi$
$127$	−2.68184	+	7.07144i	−0.237975	+	0.627489i	0.761819	+	0.647790i	$0.224307\pi$
$128$	4.53477	+	8.64028i	0.400821	+	0.763700i
$129$	0.756485	+	1.09596i	0.0666048	+	0.0964936i
$130$	0.219078	−	0.0566201i	0.0192144	−	0.00496591i
$131$	−5.83152	+	8.44842i	−0.509503	+	0.738142i	−0.990339	−	0.138669i	$-0.955718\pi$
$131$	−5.83152	+	8.44842i	−0.509503	+	0.738142i	0.480836	+	0.876810i	$0.340333\pi$
$132$	8.48376	+	1.03011i	0.738416	+	0.0896600i
$133$	−15.8855	−	3.91543i	−1.37745	−	0.339511i
$134$	−2.28439	−	3.30951i	−0.197341	−	0.285898i
$135$	−0.0551559	−	0.0622582i	−0.00474706	−	0.00535833i
$136$	−6.94659	+	13.2356i	−0.595666	+	1.13495i
$137$	7.56201	−	0.918195i	0.646066	−	0.0784467i	0.209057	−	0.977903i	$-0.432961\pi$
$137$	7.56201	−	0.918195i	0.646066	−	0.0784467i	0.437010	+	0.899457i	$0.356038\pi$
$138$	0.998881	+	0.121286i	0.0850304	+	0.0103246i
$139$	−0.218659	+	0.193715i	−0.0185464	+	0.0164307i	−0.672345	−	0.740238i	$-0.734713\pi$
$139$	−0.218659	+	0.193715i	−0.0185464	+	0.0164307i	0.653799	+	0.756669i	$0.273174\pi$
$140$	−0.246574	+	0.357225i	−0.0208393	+	0.0301910i
$141$	−1.17940	+	0.143205i	−0.0993233	+	0.0120600i
$142$	−0.136425	+	1.12356i	−0.0114485	+	0.0942870i
$143$	−17.5860	+	12.4332i	−1.47061	+	1.03971i
$144$	0.109484	+	0.901686i	0.00912371	+	0.0751405i
$145$	−0.172814	−	0.701135i	−0.0143514	−	0.0582261i
$146$	−7.70003			−0.637259
$147$	−6.30474			−0.520006
$148$	−3.09465	−	12.5555i	−0.254379	−	1.03206i
$149$	−0.802994	−	0.304535i	−0.0657838	−	0.0249485i	0.321494	−	0.946912i	$-0.395815\pi$
$149$	−0.802994	−	0.304535i	−0.0657838	−	0.0249485i	−0.387277	+	0.921963i	$0.626584\pi$
$150$			3.76737i			0.307605i
$151$	−21.4728	+	8.14356i	−1.74743	+	0.662713i	−0.999999	−	0.00162467i	$-0.999483\pi$
$151$	−21.4728	+	8.14356i	−1.74743	+	0.662713i	−0.747432	+	0.664338i	$0.768714\pi$
$152$	−11.2733	−	2.77862i	−0.914387	−	0.225376i
$153$	−4.32238	+	3.82929i	−0.349443	+	0.309580i
$154$	−3.93425	+	15.9619i	−0.317031	+	1.28624i
$155$	0.558621	−	0.494895i	0.0448695	−	0.0397509i
$156$	−3.89941	−	3.37704i	−0.312203	−	0.270379i
$157$	14.0007	+	12.4035i	1.11738	+	0.989909i	0.999995	−	0.00317843i	$-0.00101173\pi$
$157$	14.0007	+	12.4035i	1.11738	+	0.989909i	0.117381	+	0.993087i	$0.462550\pi$
$158$	4.55154	−	3.14170i	0.362101	−	0.249940i
$159$	10.3880	−	2.56042i	0.823824	−	0.203054i
$160$	−0.276994	+	0.401296i	−0.0218983	+	0.0317252i
$161$	1.16412	−	4.72300i	0.0917452	−	0.372225i
$162$	0.180568	−	0.732594i	0.0141868	−	0.0575580i
$163$	−19.6649	−	2.38775i	−1.54028	−	0.187023i	−0.694081	−	0.719897i	$-0.744189\pi$
$163$	−19.6649	−	2.38775i	−1.54028	−	0.187023i	−0.846195	+	0.532874i	$0.821112\pi$
$164$	5.22123	−	5.89355i	0.407710	−	0.460209i
$165$	0.176181	+	0.464552i	0.0137157	+	0.0361654i
$166$	1.25409	−	0.658196i	0.0973361	−	0.0510859i
$167$	5.79514	+	4.00010i	0.448441	+	0.309537i	0.770796	−	0.637082i	$-0.219859\pi$
$167$	5.79514	+	4.00010i	0.448441	+	0.309537i	−0.322354	+	0.946619i	$0.604474\pi$
$168$	−9.44183			−0.728453
$169$	12.9967	−	0.292521i	0.999747	−	0.0225016i
$170$	−0.362404			−0.0277951
$171$	−3.69145	−	2.54802i	−0.282292	−	0.194852i
$172$	1.68701	−	0.885412i	0.128633	−	0.0675120i
$173$	−1.05778	−	2.78915i	−0.0804218	−	0.212055i	0.888774	−	0.458345i	$-0.151558\pi$
$173$	−1.05778	−	2.78915i	−0.0804218	−	0.212055i	−0.969196	+	0.246290i	$0.920788\pi$
$174$	4.34384	−	4.90319i	0.329306	−	0.371710i
$175$	18.0798	+	2.19529i	1.36670	+	0.165948i
$176$	1.29844	−	5.26798i	0.0978736	−	0.397089i
$177$	−2.88322	+	11.6977i	−0.216716	+	0.879251i
$178$	4.03452	−	5.84502i	0.302400	−	0.438103i
$179$	17.6028	−	4.33869i	1.31569	−	0.324289i	0.481831	−	0.876264i	$-0.339972\pi$
$179$	17.6028	−	4.33869i	1.31569	−	0.324289i	0.833861	+	0.551975i	$0.186126\pi$
$180$	−0.0979351	+	0.0675997i	−0.00729965	+	0.00503859i
$181$	−9.34195	−	8.27625i	−0.694382	−	0.615169i	0.240281	−	0.970703i	$-0.422760\pi$
$181$	−9.34195	−	8.27625i	−0.694382	−	0.615169i	−0.934663	+	0.355535i	$0.884299\pi$
$182$	7.35300	−	6.66335i	0.545040	−	0.493920i
$183$	0.134516	−	0.119171i	0.00994370	−	0.00880935i
$184$	0.826126	−	3.35172i	0.0609028	−	0.247092i
$185$	0.562714	−	0.498521i	0.0413716	−	0.0366520i
$186$	6.57331	+	1.62018i	0.481979	+	0.118797i
$187$	32.2523	−	12.2317i	2.35852	−	0.894470i
$188$			1.69976i			0.123968i
$189$	−3.41053	−	1.29344i	−0.248080	−	0.0940843i
$190$	−0.0673667	−	0.273317i	−0.00488729	−	0.0198285i
$191$	21.2783			1.53964			0.769821	−	0.638260i	$-0.220346\pi$
$191$	21.2783			1.53964			0.769821	+	0.638260i	$0.220346\pi$
$192$	−2.60667			−0.188120
$193$	1.12831	+	4.57775i	0.0812178	+	0.329514i	0.997470	−	0.0710883i	$-0.0226472\pi$
$193$	1.12831	+	4.57775i	0.0812178	+	0.329514i	−0.916252	+	0.400602i	$0.868801\pi$
$194$	1.00293	+	8.25990i	0.0720064	+	0.593026i
$195$	0.0684889	−	0.291970i	0.00490459	−	0.0209084i
$196$	−1.08726	+	8.95443i	−0.0776617	+	0.639602i
$197$	−11.4066	+	1.38501i	−0.812686	+	0.0986779i	−0.516319	−	0.856396i	$-0.672698\pi$
$197$	−11.4066	+	1.38501i	−0.812686	+	0.0986779i	−0.296367	+	0.955074i	$0.595775\pi$
$198$	−2.56027	+	3.70919i	−0.181950	+	0.263600i
$199$	8.28454	−	7.33947i	0.587276	−	0.520281i	−0.316328	−	0.948650i	$-0.602450\pi$
$199$	8.28454	−	7.33947i	0.587276	−	0.520281i	0.903604	+	0.428369i	$0.140912\pi$
$200$	12.8305	+	1.55790i	0.907253	+	0.110161i
$201$	−5.29083	+	0.642423i	−0.373187	+	0.0453131i
$202$	1.02570	−	1.95432i	0.0721683	−	0.137505i
$203$	−20.9994	−	23.7034i	−1.47387	−	1.66366i
$204$	4.69322	+	6.79931i	0.328591	+	0.476047i
$205$	0.444448	+	0.109547i	0.0310416	+	0.00765107i
$206$	2.91003	+	0.353341i	0.202751	+	0.0246184i
$207$	0.757565	−	1.09752i	0.0526544	−	0.0762830i
$208$	−2.42675	+	2.19914i	−0.168265	+	0.152483i
$209$	15.2202	+	22.0503i	1.05280	+	1.52525i
$210$	−0.106381	−	0.202693i	−0.00734102	−	0.0139871i
$211$	−6.21468	+	16.3868i	−0.427836	+	1.12811i	0.531800	+	0.846870i	$0.321516\pi$
$211$	−6.21468	+	16.3868i	−0.427836	+	1.12811i	−0.959637	+	0.281242i	$0.909254\pi$
$212$	−1.84505	−	15.1953i	−0.126718	−	1.04362i
$213$	1.23451	+	0.852122i	0.0845874	+	0.0583865i
$214$	0.702639	+	2.85072i	0.0480314	+	0.194871i
$215$	0.0911574	+	0.0629214i	0.00621688	+	0.00429120i
$216$	−2.42032	−	0.917905i	−0.164682	−	0.0624555i
$217$	11.6056	−	30.6015i	0.787842	−	2.07737i
$218$	−11.9706	−	6.28268i	−0.810754	−	0.425517i
$219$	−4.74260	+	9.03627i	−0.320475	+	0.610615i
$220$	0.690173	−	0.170112i	0.0465314	−	0.0114690i
$221$	−20.2705	−	4.75496i	−1.36354	−	0.319853i
$222$	6.62148	+	1.63205i	0.444405	+	0.109536i
$223$	0.0609164	−	0.0687605i	0.00407927	−	0.00460454i	−0.746468	−	0.665422i	$-0.768252\pi$
$223$	0.0609164	−	0.0687605i	0.00407927	−	0.00460454i	0.750547	+	0.660817i	$0.229790\pi$
$224$	−2.57749	+	21.2276i	−0.172216	+	1.41833i
$225$	4.42115	+	2.32040i	0.294744	+	0.154693i
$226$	2.29003	+	4.36328i	0.152330	+	0.290241i
$227$	−13.7393	+	5.21062i	−0.911907	+	0.345841i	−0.765539	−	0.643389i	$-0.777528\pi$
$227$	−13.7393	+	5.21062i	−0.911907	+	0.345841i	−0.146368	+	0.989230i	$0.546758\pi$
$228$	−4.25548	+	4.80344i	−0.281826	+	0.318116i
$229$	2.07938	−	0.252482i	0.137409	−	0.0166845i	−0.0515431	−	0.998671i	$-0.516414\pi$
$229$	2.07938	−	0.252482i	0.137409	−	0.0166845i	0.188952	+	0.981986i	$0.439491\pi$
$230$	0.0812612	−	0.0200291i	0.00535821	−	0.00132068i
$231$	16.3087	+	14.4482i	1.07303	+	0.950623i
$232$	−14.9024	−	16.8214i	−0.978392	−	1.10438i
$233$	−13.1362	−	6.89440i	−0.860580	−	0.451667i	−0.0241291	−	0.999709i	$-0.507681\pi$
$233$	−13.1362	−	6.89440i	−0.860580	−	0.451667i	−0.836451	+	0.548042i	$0.815374\pi$
$234$	2.53266	−	0.993246i	0.165565	−	0.0649305i
$235$	−0.0874992	+	0.0459231i	−0.00570782	+	0.00299569i
$236$	16.1166	+	6.11223i	1.04910	+	0.397873i
$237$	−0.883520	−	7.27644i	−0.0573908	−	0.472656i
$238$	−14.0723	+	7.38571i	−0.912171	+	0.478744i
$239$		−	4.88502i		−	0.315986i	−0.987440	−	0.157993i	$-0.949498\pi$
$239$		−	4.88502i		−	0.315986i	0.987440	−	0.157993i	$-0.0505023\pi$
$240$	0.0351096	+	0.0668957i	0.00226631	+	0.00431810i
$241$	15.4212	+	17.4069i	0.993366	+	1.12128i	0.992619	+	0.121278i	$0.0386994\pi$
$241$	15.4212	+	17.4069i	0.993366	+	1.12128i	0.000747276		1.00000i	$0.499762\pi$
$242$	15.3257	−	10.5786i	0.985175	−	0.680017i
$243$	−0.748511	−	0.663123i	−0.0480170	−	0.0425393i
$244$	−0.146057	−	0.211600i	−0.00935034	−	0.0135463i
$245$	−0.490325	+	0.185956i	−0.0313257	+	0.0118803i
$246$	1.47246	+	3.88257i	0.0938809	+	0.247544i
$247$	−0.181965	−	16.1715i	−0.0115782	−	1.02897i
$248$	8.23605	−	21.7167i	0.522990	−	1.37901i
$249$		−	1.87711i		−	0.118957i
$250$	0.222389	+	0.586390i	0.0140651	+	0.0370866i
$251$	2.84387	−	23.4214i	0.179503	−	1.47834i	−0.572892	−	0.819631i	$-0.694179\pi$
$251$	2.84387	−	23.4214i	0.179503	−	1.47834i	0.752395	−	0.658712i	$-0.228898\pi$
$252$	−2.42519	+	4.62082i	−0.152773	+	0.291084i
$253$	−6.55587	+	4.52519i	−0.412164	+	0.284496i
$254$	−4.69624	+	3.24158i	−0.294668	+	0.203395i
$255$	−0.223212	+	0.425294i	−0.0139781	+	0.0266330i
$256$	−1.51586	+	12.4842i	−0.0947414	+	0.780266i
$257$	2.68898	+	7.09027i	0.167734	+	0.442279i	0.992356	−	0.123405i	$-0.0393815\pi$
$257$	2.68898	+	7.09027i	0.167734	+	0.442279i	−0.824622	+	0.565684i	$0.808612\pi$
$258$			1.00478i			0.0625551i
$259$	11.6907	−	30.8258i	0.726423	−	1.91542i
$260$	−0.402865	−	0.147624i	−0.0249846	−	0.00915522i
$261$	−3.07861	−	8.11763i	−0.190561	−	0.502469i
$262$	−7.24225	+	2.74662i	−0.447428	+	0.169687i
$263$	−7.07954	−	10.2565i	−0.436543	−	0.632442i	0.541535	−	0.840678i	$-0.317843\pi$
$263$	−7.07954	−	10.2565i	−0.436543	−	0.632442i	−0.978079	+	0.208236i	$0.933228\pi$
$264$	11.5736	+	10.2533i	0.712306	+	0.631048i
$265$	0.732368	−	0.505517i	0.0449890	−	0.0310537i
$266$	−8.18602	−	9.24011i	−0.501917	−	0.566547i
$267$	−4.37440	−	8.33473i	−0.267709	−	0.510077i
$268$			7.62520i			0.465783i
$269$	7.70111	−	4.04185i	0.469545	−	0.246436i	−0.213318	−	0.976983i	$-0.568427\pi$
$269$	7.70111	−	4.04185i	0.469545	−	0.246436i	0.682863	+	0.730547i	$0.260735\pi$
$270$	−0.00756463	−	0.0623003i	−0.000460369	−	0.00379148i
$271$	−22.2933	−	8.45474i	−1.35422	−	0.513589i	−0.432568	−	0.901601i	$-0.642393\pi$
$271$	−22.2933	−	8.45474i	−1.35422	−	0.513589i	−0.921654	+	0.388012i	$0.873162\pi$
$272$	4.64435	−	2.43754i	0.281605	−	0.147798i
$273$	−3.29083	−	12.7331i	−0.199170	−	0.770643i
$274$	5.08924	+	2.67104i	0.307452	+	0.161363i
$275$	−19.7779	−	22.3246i	−1.19265	−	1.34623i
$276$	−1.42813	−	1.26522i	−0.0859635	−	0.0761571i
$277$	5.50856	−	1.35774i	0.330978	−	0.0815786i	−0.0703252	−	0.997524i	$-0.522404\pi$
$277$	5.50856	−	1.35774i	0.330978	−	0.0815786i	0.401303	+	0.915945i	$0.368558\pi$
$278$	−0.218807	+	0.0265680i	−0.0131232	+	0.00159344i
$279$	5.94997	−	6.71613i	0.356216	−	0.402084i
$280$	−0.734300	+	0.278483i	−0.0438828	+	0.0166426i
$281$	3.39916	+	6.47657i	0.202777	+	0.386360i	0.965515	−	0.260349i	$-0.0838375\pi$
$281$	3.39916	+	6.47657i	0.202777	+	0.386360i	−0.762738	+	0.646708i	$0.776145\pi$
$282$	−0.793736	−	0.416585i	−0.0472663	−	0.0248073i
$283$	1.36961	−	11.2798i	0.0814150	−	0.670513i	−0.893677	−	0.448711i	$-0.851883\pi$
$283$	1.36961	−	11.2798i	0.0814150	−	0.670513i	0.975092	−	0.221802i	$-0.0711938\pi$
$284$	1.42314	−	1.60639i	0.0844477	−	0.0953217i
$285$	−0.362241	−	0.0892843i	−0.0214573	−	0.00528874i
$286$	−16.2492	+	0.182840i	−0.960835	+	0.0108115i
$287$	19.4907	−	4.80401i	1.15050	−	0.283572i
$288$	−2.72439	+	5.19089i	−0.160536	+	0.305876i
$289$	14.4740	+	7.59656i	0.851413	+	0.446856i
$290$	0.193207	−	0.509445i	0.0113455	−	0.0299157i
$291$	10.3110	+	3.91045i	0.604443	+	0.229235i
$292$	12.0161	+	8.29410i	0.703188	+	0.485375i
$293$	−4.28387	−	17.3803i	−0.250266	−	1.01537i	−0.952771	−	0.303690i	$-0.901781\pi$
$293$	−4.28387	−	17.3803i	−0.250266	−	1.01537i	0.702505	−	0.711679i	$-0.252065\pi$
$294$	−3.91497	−	2.70231i	−0.228326	−	0.157602i
$295$	0.120788	+	0.994779i	0.00703255	+	0.0579182i
$296$	8.29640	−	21.8758i	0.482218	−	1.27151i
$297$	2.77595	+	5.28913i	0.161077	+	0.306907i
$298$	−0.368096	−	0.533279i	−0.0213232	−	0.0308920i
$299$	4.80802	−	0.0541010i	0.278055	−	0.00312874i
$300$	4.05803	−	5.87907i	0.234291	−	0.339429i
$301$	4.82200	+	0.585497i	0.277935	+	0.0337475i
$302$	−16.8241	−	4.14678i	−0.968120	−	0.238620i
$303$	−1.66171	−	2.40740i	−0.0954628	−	0.138302i
$304$	2.70167	+	3.04956i	0.154952	+	0.174904i
$305$	0.00694653	−	0.0132355i	0.000397757	−	0.000757863i
$306$	−4.32530	+	0.525187i	−0.247261	+	0.0300229i
$307$	−24.5849	−	2.98515i	−1.40314	−	0.170372i	−0.616289	−	0.787520i	$-0.711365\pi$
$307$	−24.5849	−	2.98515i	−1.40314	−	0.170372i	−0.786847	+	0.617149i	$0.788288\pi$
$308$	23.3328	−	20.6711i	1.32951	−	1.17784i
$309$	2.20700	−	3.19739i	0.125552	−	0.181893i
$310$	0.558999	−	0.0678748i	0.0317490	−	0.00385503i
$311$	2.08203	−	17.1470i	0.118061	−	0.972319i	−0.806487	−	0.591252i	$-0.798634\pi$
$311$	2.08203	−	17.1470i	0.118061	−	0.972319i	0.924548	−	0.381067i	$-0.124443\pi$
$312$	−2.33537	−	9.03617i	−0.132214	−	0.511572i
$313$	1.25012	+	10.2957i	0.0706611	+	0.581947i	0.984438	+	0.175731i	$0.0562288\pi$
$313$	1.25012	+	10.2957i	0.0706611	+	0.581947i	−0.913777	+	0.406216i	$0.866848\pi$
$314$	3.37748	+	13.7030i	0.190602	+	0.773303i
$315$	−0.303390			−0.0170941
$316$	−10.4869			−0.589933
$317$	1.96983	+	7.99193i	0.110637	+	0.448871i	0.999965	−	0.00839865i	$-0.00267340\pi$
$317$	1.96983	+	7.99193i	0.110637	+	0.448871i	−0.889328	+	0.457270i	$0.848827\pi$
$318$	7.54795	+	2.86256i	0.423268	+	0.160524i
$319$			51.8594i			2.90357i
$320$	−0.202723	+	0.0768828i	−0.0113326	+	0.00429788i
$321$	3.77819	+	0.931241i	0.210878	+	0.0519768i
$322$	2.74722	−	2.43382i	0.153097	−	0.135632i
$323$	−6.19871	+	25.1492i	−0.344906	+	1.39934i
$324$	−1.07090	+	0.948730i	−0.0594942	+	0.0527072i
$325$	2.37094	+	17.8460i	0.131516	+	0.989918i
$326$	−11.1876	−	9.91139i	−0.619626	−	0.548941i
$327$	−14.7459	+	10.1784i	−0.815451	+	0.562865i
$328$	13.8317	−	3.40921i	0.763729	−	0.188242i
$329$	−2.46173	+	3.56643i	−0.135719	+	0.196624i
$330$	−0.0897133	+	0.363981i	−0.00493855	+	0.0200365i
$331$	−1.05433	+	4.27757i	−0.0579510	+	0.235117i	−0.992774	−	0.119997i	$-0.961712\pi$
$331$	−1.05433	+	4.27757i	−0.0579510	+	0.235117i	0.934823	+	0.355113i	$0.115558\pi$
$332$	−2.66601	−	0.323712i	−0.146316	−	0.0177660i
$333$	5.99357	−	6.76534i	0.328446	−	0.370738i
$334$	1.88403	+	4.96778i	0.103089	+	0.271825i
$335$	−0.392525	+	0.206013i	−0.0214459	+	0.0112557i
$336$	2.72664	+	1.88206i	0.148750	+	0.102675i
$337$	−17.9837			−0.979635			−0.489817	−	0.871825i	$-0.662937\pi$
$337$	−17.9837			−0.979635			−0.489817	+	0.871825i	$0.662937\pi$
$338$	8.19578	+	5.38895i	0.445791	+	0.293120i
$339$	6.53094			0.354712
$340$	0.565540	+	0.390364i	0.0306707	+	0.0211704i
$341$	−47.4576	+	24.9076i	−2.56997	+	1.34882i
$342$	−1.20011	−	3.16443i	−0.0648944	−	0.171113i
$343$	1.68169	−	1.89824i	0.0908029	−	0.102495i
$344$	3.42198	+	0.415503i	0.184501	+	0.0224024i
$345$	0.0265455	−	0.107699i	0.00142916	−	0.00579834i
$346$	0.538633	−	2.18532i	0.0289571	−	0.117484i
$347$	−7.19964	+	10.4305i	−0.386497	+	0.559937i	−0.967148	−	0.254215i	$-0.918183\pi$
$347$	−7.19964	+	10.4305i	−0.386497	+	0.559937i	0.580651	+	0.814153i	$0.302798\pi$
$348$	−12.0601	+	2.97256i	−0.646491	+	0.159346i
$349$	6.09140	−	4.20459i	0.326065	−	0.225067i	−0.393774	−	0.919207i	$-0.628831\pi$
$349$	6.09140	−	4.20459i	0.326065	−	0.225067i	0.719839	+	0.694141i	$0.244215\pi$
$350$	10.2858	+	9.11246i	0.549802	+	0.487082i
$351$	0.394302	−	3.58393i	0.0210463	−	0.191296i
$352$	26.2114	−	23.2213i	1.39707	−	1.23770i
$353$	−4.03871	+	16.3857i	−0.214959	+	0.872123i	0.760033	+	0.649884i	$0.225183\pi$
$353$	−4.03871	+	16.3857i	−0.214959	+	0.872123i	−0.974992	+	0.222239i	$0.928663\pi$
$354$	−6.80416	+	6.02796i	−0.361637	+	0.320382i
$355$	0.121142	+	0.0298589i	0.00642956	+	0.00158474i
$356$	−12.5919	+	4.77549i	−0.667371	+	0.253101i
$357$			21.0634i			1.11479i
$358$	12.7902	+	4.85068i	0.675982	+	0.256366i
$359$	−6.48685	−	26.3182i	−0.342363	−	1.38902i	−0.849697	−	0.527271i	$-0.823215\pi$
$359$	−6.48685	−	26.3182i	−0.342363	−	1.38902i	0.507335	−	0.861749i	$-0.330631\pi$
$360$	−0.215304			−0.0113475
$361$	−1.11924			−0.0589071
$362$	−2.25362	−	9.14330i	−0.118448	−	0.480561i
$363$	−2.97494	−	24.5009i	−0.156144	−	1.28596i
$364$	−18.6520	+	2.47802i	−0.977628	+	0.129884i
$365$	−0.102315	+	0.842641i	−0.00535542	+	0.0441058i
$366$	0.134607	−	0.0163442i	0.00703602	−	0.000854327i
$367$	16.4433	−	23.8223i	0.858335	−	1.24351i	−0.110018	−	0.993930i	$-0.535091\pi$
$367$	16.4433	−	23.8223i	0.858335	−	1.24351i	0.968353	−	0.249584i	$-0.0802939\pi$
$368$	−0.906678	+	0.803247i	−0.0472639	+	0.0418721i
$369$	5.46326	+	0.663360i	0.284406	+	0.0345331i
$370$	0.563095	−	0.0683722i	0.0292739	−	0.00355450i
$371$	18.1358	−	34.5549i	0.941565	−	1.79400i
$372$	−8.51263	−	9.60878i	−0.441359	−	0.498192i
$373$	4.33354	+	6.27821i	0.224382	+	0.325073i	0.918965	−	0.394339i	$-0.129026\pi$
$373$	4.33354	+	6.27821i	0.224382	+	0.325073i	−0.694583	+	0.719413i	$0.744411\pi$
$374$	25.2700	+	6.22850i	1.30668	+	0.322068i
$375$	0.825125	+	0.100188i	0.0426092	+	0.00517370i
$376$	−1.74699	+	2.53095i	−0.0900940	+	0.130524i
$377$	17.4910	−	25.9601i	0.900831	−	1.33701i
$378$	−1.56340	−	2.26498i	−0.0804128	−	0.116498i
$379$	0.643613	+	1.22630i	0.0330602	+	0.0629909i	0.901426	−	0.432934i	$-0.142522\pi$
$379$	0.643613	+	1.22630i	0.0330602	+	0.0629909i	−0.868366	+	0.495925i	$0.834829\pi$
$380$	−0.189277	+	0.499082i	−0.00970970	+	0.0256024i
$381$	0.911607	+	7.50776i	0.0467031	+	0.384634i
$382$	13.2129	+	9.12020i	0.676030	+	0.466630i
$383$	−4.66857	−	18.9411i	−0.238553	−	0.967847i	−0.961028	−	0.276450i	$-0.910842\pi$
$383$	−4.66857	−	18.9411i	−0.238553	−	0.967847i	0.722475	−	0.691397i	$-0.243004\pi$
$384$	8.03068	+	5.54318i	0.409814	+	0.282874i
$385$	1.69449	+	0.642634i	0.0863590	+	0.0327516i
$386$	−1.26146	+	3.32620i	−0.0642066	+	0.169299i
$387$	1.17915	+	0.618866i	0.0599396	+	0.0314587i
$388$	7.33206	−	13.9701i	0.372229	−	0.709223i
$389$	−10.4307	+	2.57095i	−0.528860	+	0.130352i	−0.494699	−	0.869064i	$-0.664722\pi$
$389$	−10.4307	+	2.57095i	−0.528860	+	0.130352i	−0.0341604	+	0.999416i	$0.510876\pi$
$390$	0.167672	−	0.151945i	0.00849038	−	0.00769406i
$391$	−7.47721	−	1.84297i	−0.378139	−	0.0932028i
$392$	−10.8222	+	12.2157i	−0.546601	+	0.616985i
$393$	−1.23738	+	10.1907i	−0.0624176	+	0.514055i
$394$	−7.67664	−	4.02901i	−0.386743	−	0.202979i
$395$	−0.283328	−	0.539837i	−0.0142558	−	0.0271621i
$396$	7.99071	−	3.03048i	0.401548	−	0.152287i
$397$	−23.1228	+	26.1003i	−1.16050	+	1.30994i	−0.217917	+	0.975967i	$0.569926\pi$
$397$	−23.1228	+	26.1003i	−1.16050	+	1.30994i	−0.942584	+	0.333968i	$0.891612\pi$
$398$	8.29015	−	1.00661i	0.415548	−	0.0504566i
$399$	−15.8855	+	3.91543i	−0.795272	+	0.196017i
$400$	−3.39469	−	3.00743i	−0.169734	−	0.150372i
$401$	17.5209	+	19.7770i	0.874953	+	0.987618i	0.999990	−	0.00453449i	$-0.00144338\pi$
$401$	17.5209	+	19.7770i	0.874953	+	0.987618i	−0.125037	+	0.992152i	$0.539905\pi$
$402$	−3.56073	−	1.86882i	−0.177593	−	0.0932081i
$403$	32.1573	+	3.53793i	1.60187	+	0.176237i
$404$	−3.70573	+	1.94492i	−0.184367	+	0.0967632i
$405$	−0.0777709	−	0.0294946i	−0.00386447	−	0.00146560i
$406$	−2.88007	−	23.7195i	−0.142935	−	1.17718i
$407$	−47.8053	+	25.0902i	−2.36962	+	1.24367i
$408$			14.9478i			0.740027i
$409$	12.3520	+	23.5348i	0.610769	+	1.16372i	0.972820	+	0.231564i	$0.0743843\pi$
$409$	12.3520	+	23.5348i	0.610769	+	1.16372i	−0.362051	+	0.932158i	$0.617923\pi$
$410$	0.229030	+	0.258521i	0.0113110	+	0.0127675i
$411$	6.26912	−	4.32726i	0.309233	−	0.213448i
$412$	−4.16056	−	3.68594i	−0.204976	−	0.181593i
$413$	24.9636	+	36.1660i	1.22838	+	1.77961i
$414$	0.940830	−	0.356810i	0.0462393	−	0.0175362i
$415$	−0.0553648	−	0.145985i	−0.00271775	−	0.00716612i
$416$	−20.9531	+	2.78373i	−1.02731	+	0.136484i
$417$	−0.103589	+	0.273142i	−0.00507279	+	0.0133758i
$418$			20.2159i			0.988792i
$419$	−6.35414	−	16.7545i	−0.310420	−	0.818510i	−0.995904	−	0.0904222i	$-0.971178\pi$
$419$	−6.35414	−	16.7545i	−0.310420	−	0.818510i	0.685483	−	0.728088i	$-0.259591\pi$
$420$	−0.0523202	+	0.430896i	−0.00255296	+	0.0210256i
$421$	−4.14433	+	7.89636i	−0.201982	+	0.384845i	−0.965286	−	0.261194i	$-0.915884\pi$
$421$	−4.14433	+	7.89636i	−0.201982	+	0.384845i	0.763304	+	0.646040i	$0.223576\pi$
$422$	−10.8827	+	7.51177i	−0.529760	+	0.365667i
$423$	−0.977756	+	0.674896i	−0.0475401	+	0.0328146i
$424$	12.8703	−	24.5222i	0.625035	−	1.19090i
$425$	3.47546	−	28.6230i	0.168585	−	1.38842i
$426$	0.401346	+	1.05826i	0.0194453	+	0.0512730i
$427$		−	0.655509i		−	0.0317223i
$428$	1.97417	−	5.20546i	0.0954251	−	0.251615i
$429$	−9.79363	+	19.1816i	−0.472841	+	0.926098i
$430$	0.0296357	+	0.0781429i	0.00142916	+	0.00376839i
$431$	8.41064	−	3.18973i	0.405126	−	0.153644i	−0.143620	−	0.989633i	$-0.545874\pi$
$431$	8.41064	−	3.18973i	0.405126	−	0.153644i	0.548747	+	0.835989i	$0.315105\pi$
$432$	0.515978	+	0.747523i	0.0248250	+	0.0359652i
$433$	−15.3840	−	13.6290i	−0.739306	−	0.654968i	0.206963	−	0.978349i	$-0.433642\pi$
$433$	−15.3840	−	13.6290i	−0.739306	−	0.654968i	−0.946269	+	0.323381i	$0.895181\pi$
$434$	20.3229	−	14.0279i	0.975530	−	0.673360i
$435$	−0.478853	−	0.540513i	−0.0229592	−	0.0259156i
$436$	11.9131	+	22.6985i	0.570533	+	1.08706i
$437$		−	5.98174i		−	0.286145i
$438$	−6.81804	+	3.57838i	−0.325779	+	0.170982i
$439$	−0.0166760	−	0.137339i	−0.000795900	−	0.00655483i	0.992306	−	0.123813i	$-0.0395124\pi$
$439$	−0.0166760	−	0.137339i	−0.000795900	−	0.00655483i	−0.993101	+	0.117259i	$0.962589\pi$
$440$	1.20251	+	0.456051i	0.0573273	+	0.0217414i
$441$	−5.58257	+	2.92996i	−0.265837	+	0.139522i
$442$	−10.5491	−	11.6409i	−0.501768	−	0.553700i
$443$	−27.9486	−	14.6685i	−1.32788	−	0.696923i	−0.356461	−	0.934310i	$-0.616017\pi$
$443$	−27.9486	−	14.6685i	−1.32788	−	0.696923i	−0.971415	+	0.237387i	$0.923709\pi$
$444$	−8.57501	−	9.67918i	−0.406952	−	0.459354i
$445$	−0.586031	−	0.519178i	−0.0277805	−	0.0246114i
$446$	0.0672983	−	0.0165875i	0.00318667	−	0.000785443i
$447$	−0.852540	+	0.103517i	−0.0403238	+	0.00489619i
$448$	−6.30497	+	7.11684i	−0.297882	+	0.336239i
$449$	−21.6670	+	8.21722i	−1.02253	+	0.387795i	−0.808163	−	0.588959i	$-0.799538\pi$
$449$	−21.6670	+	8.21722i	−1.02253	+	0.387795i	−0.214367	+	0.976753i	$0.568769\pi$
$450$	1.75079	+	3.33584i	0.0825329	+	0.157253i
$451$	−29.1081	−	15.2771i	−1.37065	−	0.719372i
$452$	1.12627	−	9.27570i	0.0529755	−	0.436292i
$453$	−15.2287	+	17.1897i	−0.715507	+	0.807641i
$454$	−10.7648	−	2.65330i	−0.505219	−	0.124525i
$455$	−0.631489	−	0.893204i	−0.0296047	−	0.0418740i
$456$	−11.2733	+	2.77862i	−0.527922	+	0.130121i
$457$	8.44986	−	16.0999i	0.395268	−	0.753120i	−0.603762	−	0.797165i	$-0.706332\pi$
$457$	8.44986	−	16.0999i	0.395268	−	0.753120i	0.999030	+	0.0440448i	$0.0140244\pi$
$458$	1.39942	+	0.734473i	0.0653907	+	0.0343197i
$459$	−2.04771	+	5.39938i	−0.0955791	+	0.252021i
$460$	−0.148384	−	0.0562748i	−0.00691846	−	0.00262382i
$461$	11.6539	+	8.04413i	0.542778	+	0.374653i	0.807678	−	0.589623i	$-0.200724\pi$
$461$	11.6539	+	8.04413i	0.542778	+	0.374653i	−0.264900	+	0.964276i	$0.585339\pi$
$462$	3.93425	+	15.9619i	0.183038	+	0.742613i
$463$	21.4587	+	14.8119i	0.997271	+	0.688367i	0.950560	−	0.310542i	$-0.100510\pi$
$463$	21.4587	+	14.8119i	0.997271	+	0.688367i	0.0467115	+	0.998908i	$0.485126\pi$
$464$	0.950523	+	7.82826i	0.0441269	+	0.363418i
$465$	0.264645	−	0.697812i	0.0122726	−	0.0323603i
$466$	−5.20196	−	9.91150i	−0.240976	−	0.459141i
$467$	11.2430	+	16.2883i	0.520263	+	0.753732i	0.991756	−	0.128138i	$-0.0409001\pi$
$467$	11.2430	+	16.2883i	0.520263	+	0.753732i	−0.471493	+	0.881870i	$0.656285\pi$
$468$	−5.02214	−	1.17807i	−0.232149	−	0.0544563i
$469$	−11.0434	+	15.9991i	−0.509937	+	0.738772i
$470$	−0.0740166	−	0.00898724i	−0.00341413	−	0.000414551i
$471$	18.1612	+	4.47633i	0.836823	+	0.206258i
$472$	17.7157	+	25.6656i	0.815429	+	1.18135i
$473$	−5.27489	−	5.95412i	−0.242540	−	0.273771i
$474$	2.57017	−	4.89705i	0.118052	−	0.224929i
$475$	22.2329	−	2.69956i	1.02012	−	0.123864i
$476$	29.9157	+	3.63242i	1.37118	+	0.166492i
$477$	8.00825	−	7.09469i	0.366673	−	0.324844i
$478$	2.09380	−	3.03339i	0.0957680	−	0.138744i
$479$	22.6096	−	2.74530i	1.03306	−	0.125436i	0.413595	−	0.910461i	$-0.364273\pi$
$479$	22.6096	−	2.74530i	1.03306	−	0.125436i	0.619464	+	0.785025i	$0.287350\pi$
$480$	−0.0587750	+	0.484055i	−0.00268270	+	0.0220940i
$481$	32.3930	+	3.56386i	1.47699	+	0.162498i
$482$	2.11501	+	17.4187i	0.0963362	+	0.793400i
$483$	−1.16412	−	4.72300i	−0.0529691	−	0.214904i
$484$	−35.3109			−1.60504
$485$	0.917235			0.0416495
$486$	−0.180568	−	0.732594i	−0.00819074	−	0.0332311i
$487$	−24.3277	−	9.22628i	−1.10239	−	0.418083i	−0.264759	−	0.964315i	$-0.585292\pi$
$487$	−24.3277	−	9.22628i	−1.10239	−	0.418083i	−0.837634	+	0.546232i	$0.816062\pi$
$488$		−	0.465188i		−	0.0210581i
$489$	−18.5221	+	7.02449i	−0.837597	+	0.317659i
$490$	−0.384174	−	0.0946905i	−0.0173552	−	0.00427768i
$491$	−32.5694	+	28.8540i	−1.46984	+	1.30216i	−0.609122	+	0.793077i	$0.708478\pi$
$491$	−32.5694	+	28.8540i	−1.46984	+	1.30216i	−0.860716	+	0.509086i	$0.829984\pi$
$492$	1.88430	−	7.64491i	0.0849508	−	0.344659i
$493$	−37.5260	+	33.2452i	−1.69009	+	1.49729i
$494$	6.81836	−	10.1198i	0.306772	−	0.455311i
$495$	0.371889	+	0.329465i	0.0167152	+	0.0148084i
$496$	−6.70727	+	4.62969i	−0.301165	+	0.207879i
$497$	5.31252	−	1.30942i	0.238299	−	0.0587354i
$498$	0.804561	−	1.16561i	0.0360532	−	0.0522321i
$499$	−2.24379	+	9.10340i	−0.100446	+	0.407524i	−0.999543	−	0.0302243i	$-0.990378\pi$
$499$	−2.24379	+	9.10340i	−0.100446	+	0.407524i	0.899097	+	0.437749i	$0.144224\pi$
$500$	0.284589	−	1.15462i	0.0127272	−	0.0516363i
$501$	6.99028	+	0.848774i	0.312303	+	0.0379204i
$502$	11.8047	−	13.3247i	0.526868	−	0.594712i
$503$	−9.78468	−	25.8001i	−0.436277	−	1.15037i	−0.955308	−	0.295613i	$-0.904476\pi$
$503$	−9.78468	−	25.8001i	−0.436277	−	1.15037i	0.519031	−	0.854756i	$-0.326293\pi$
$504$	−8.36033	+	4.38784i	−0.372398	+	0.195450i
$505$	−0.200238	−	0.138215i	−0.00891049	−	0.00615047i
$506$	−6.01048			−0.267199
$507$	11.3721	−	6.29889i	0.505051	−	0.279743i
$508$	10.8203			0.480071
$509$	12.1503	+	8.38674i	0.538552	+	0.371736i	0.806073	−	0.591816i	$-0.201589\pi$
$509$	12.1503	+	8.38674i	0.538552	+	0.371736i	−0.267521	+	0.963552i	$0.586204\pi$
$510$	−0.320893	+	0.168417i	−0.0142094	+	0.00745765i
$511$	13.1999	+	34.8052i	0.583929	+	1.53969i
$512$	6.64928	−	7.50549i	0.293859	−	0.331699i
$513$	−4.45274	−	0.540661i	−0.196593	−	0.0238708i
$514$	−1.36926	+	5.55529i	−0.0603953	+	0.245033i
$515$	0.0773347	−	0.313759i	0.00340777	−	0.0138259i
$516$	1.08230	−	1.56799i	0.0476457	−	0.0690268i
$517$	6.89048	−	1.69835i	0.303043	−	0.0746934i
$518$	20.4718	−	14.1307i	0.899480	−	0.620866i
$519$	−2.23280	−	1.97809i	−0.0980091	−	0.0868285i
$520$	−0.448142	−	0.633870i	−0.0196523	−	0.0277971i
$521$	−3.25831	+	2.88661i	−0.142749	+	0.126465i	−0.731476	−	0.681868i	$-0.761168\pi$
$521$	−3.25831	+	2.88661i	−0.142749	+	0.126465i	0.588727	+	0.808332i	$0.299630\pi$
$522$	1.56766	−	6.36024i	0.0686145	−	0.278380i
$523$	−29.5811	+	26.2066i	−1.29349	+	1.14593i	−0.312920	+	0.949780i	$0.601307\pi$
$523$	−29.5811	+	26.2066i	−1.29349	+	1.14593i	−0.980573	+	0.196155i	$0.937154\pi$
$524$	14.2602	+	3.51483i	0.622961	+	0.153546i
$525$	17.0291	−	6.45827i	0.743210	−	0.281862i
$526$		−	9.40324i		−	0.410001i
$527$	−48.4468	−	18.3734i	−2.11037	−	0.800359i
$528$	−1.29844	−	5.26798i	−0.0565073	−	0.229259i
$529$	−21.2215			−0.922676
$530$	0.671441			0.0291655
$531$	2.88322	+	11.6977i	0.125121	+	0.507636i
$532$	2.82148	+	23.2370i	0.122327	+	1.00745i
$533$	9.41849	+	17.4650i	0.407960	+	0.756494i
$534$	0.856079	−	7.05044i	0.0370462	−	0.305103i
$535$	0.321300	−	0.0390129i	0.0138910	−	0.00168668i
$536$	−7.83706	+	11.3539i	−0.338509	+	0.490415i
$537$	13.5702	−	12.0221i	0.585597	−	0.518793i
$538$	6.51446	+	0.790998i	0.280858	+	0.0341024i
$539$	37.3858	−	4.53945i	1.61032	−	0.195528i
$540$	−0.0553021	+	0.105369i	−0.00237982	+	0.00453437i
$541$	26.0956	+	29.4559i	1.12194	+	1.26641i	0.960120	+	0.279587i	$0.0901975\pi$
$541$	26.0956	+	29.4559i	1.12194	+	1.26641i	0.161819	+	0.986821i	$0.448264\pi$
$542$	−10.2194	−	14.8053i	−0.438959	−	0.635942i
$543$	−12.1180	−	2.98683i	−0.520035	−	0.128177i
$544$	33.6064	+	4.08055i	1.44086	+	0.174952i
$545$	−0.846596	+	1.22651i	−0.0362642	+	0.0525378i
$546$	3.41414	−	9.31721i	0.146112	−	0.398740i
$547$	9.99494	+	14.4802i	0.427353	+	0.619128i	0.976220	−	0.216782i	$-0.0695561\pi$
$547$	9.99494	+	14.4802i	0.427353	+	0.619128i	−0.548867	+	0.835910i	$0.684941\pi$
$548$	−5.06476	−	9.65009i	−0.216356	−	0.412232i
$549$	0.0637265	−	0.168033i	0.00271978	−	0.00717147i
$550$	−2.71254	−	22.3397i	−0.115663	−	0.952570i
$551$	−32.0485	−	22.1215i	−1.36531	−	0.942406i
$552$	−0.826126	−	3.35172i	−0.0351622	−	0.142659i
$553$	−22.0035	−	15.1879i	−0.935684	−	0.645856i
$554$	4.00253	+	1.51796i	0.170051	+	0.0644919i
$555$	0.266584	−	0.702925i	0.0113159	−	0.0298375i
$556$	0.370072	+	0.194229i	0.0156945	+	0.00823713i
$557$	−4.35501	+	8.29778i	−0.184528	+	0.351588i	−0.960094	−	0.279678i	$-0.909772\pi$
$557$	−4.35501	+	8.29778i	−0.184528	+	0.351588i	0.775566	+	0.631266i	$0.217465\pi$
$558$	6.57331	−	1.62018i	0.278271	−	0.0685875i
$559$	0.632346	+	4.75964i	0.0267454	+	0.201312i
$560$	0.267564	+	0.0659486i	0.0113066	+	0.00278684i
$561$	22.8737	−	25.8190i	0.965727	−	1.09008i
$562$	−0.665223	+	5.47860i	−0.0280607	+	0.231101i
$563$	4.18358	+	2.19571i	0.176317	+	0.0925382i	0.550572	−	0.834787i	$-0.314409\pi$
$563$	4.18358	+	2.19571i	0.176317	+	0.0925382i	−0.374256	+	0.927326i	$0.622102\pi$
$564$	0.789918	+	1.50506i	0.0332616	+	0.0633746i
$565$	0.507918	−	0.192628i	0.0213683	−	0.00810391i
$566$	5.68516	−	6.41722i	0.238965	−	0.269736i
$567$	−3.62097	+	0.439665i	−0.152066	+	0.0184642i
$568$	3.77008	−	0.929241i	0.158189	−	0.0389901i
$569$	−1.31535	−	1.16530i	−0.0551423	−	0.0488518i	0.635101	−	0.772429i	$-0.280958\pi$
$569$	−1.31535	−	1.16530i	−0.0551423	−	0.0488518i	−0.690244	+	0.723577i	$0.742497\pi$
$570$	−0.186667	−	0.210704i	−0.00781863	−	0.00882541i
$571$	−10.4537	−	5.48654i	−0.437475	−	0.229605i	0.231582	−	0.972815i	$-0.425610\pi$
$571$	−10.4537	−	5.48654i	−0.437475	−	0.229605i	−0.669058	+	0.743211i	$0.733302\pi$
$572$	25.5542	+	17.2175i	1.06847	+	0.719900i
$573$	18.8410	−	9.88850i	0.787093	−	0.413098i
$574$	14.1619	+	5.37091i	0.591108	+	0.224178i
$575$	0.802620	+	6.61017i	0.0334716	+	0.275663i
$576$	−2.30809	+	1.21138i	−0.0961705	+	0.0504742i
$577$		−	0.877682i		−	0.0365384i	−0.999833	−	0.0182692i	$-0.994184\pi$
$577$		−	0.877682i		−	0.0365384i	0.999833	−	0.0182692i	$-0.00581558\pi$
$578$	5.73175	+	10.9209i	0.238409	+	0.454251i
$579$	3.12646	+	3.52904i	0.129931	+	0.146662i
$580$	−0.850254	+	0.586888i	−0.0353049	+	0.0243692i
$581$	−5.12498	−	4.54033i	−0.212620	−	0.188365i
$582$	4.72662	+	6.84769i	0.195925	+	0.283846i
$583$	−59.7553	+	22.6622i	−2.47481	+	0.938572i
$584$	9.36742	+	24.6999i	0.387627	+	1.02209i
$585$	−0.0750414	−	0.290355i	−0.00310258	−	0.0120047i
$586$	4.78938	−	12.6286i	0.197848	−	0.521681i
$587$			29.3120i			1.20984i	0.796287	+	0.604919i	$0.206794\pi$
$587$			29.3120i			1.20984i	−0.796287	+	0.604919i	$0.793206\pi$
$588$	3.19860	+	8.43403i	0.131908	+	0.347813i
$589$	4.85116	−	39.9529i	0.199889	−	1.64623i
$590$	−0.351373	+	0.669486i	−0.0144658	+	0.0275623i
$591$	−9.45638	+	6.52727i	−0.388984	+	0.268496i
$592$	−6.75642	+	4.66362i	−0.277687	+	0.191673i
$593$	−3.90043	+	7.43165i	−0.160172	+	0.305181i	−0.952295	−	0.305180i	$-0.901283\pi$
$593$	−3.90043	+	7.43165i	−0.160172	+	0.305181i	0.792123	+	0.610361i	$0.208976\pi$
$594$	−0.543259	+	4.47414i	−0.0222902	+	0.183576i
$595$	0.621256	+	1.63812i	0.0254690	+	0.0671563i
$596$			1.22869i			0.0503291i
$597$	3.92478	−	10.3488i	0.160631	−	0.423548i
$598$	3.00876	+	2.02720i	0.123037	+	0.0828983i
$599$	10.9680	+	28.9203i	0.448141	+	1.18165i	0.948764	+	0.315985i	$0.102335\pi$
$599$	10.9680	+	28.9203i	0.448141	+	1.18165i	−0.500623	+	0.865665i	$0.666896\pi$
$600$	12.0848	−	4.58317i	0.493361	−	0.187107i
$601$	−16.7172	−	24.2191i	−0.681911	−	0.987918i	−0.999216	−	0.0395947i	$-0.987393\pi$
$601$	−16.7172	−	24.2191i	−0.681911	−	0.987918i	0.317305	−	0.948323i	$-0.397222\pi$
$602$	2.74330	+	2.43035i	0.111809	+	0.0990538i
$603$	−4.38625	+	3.02761i	−0.178622	+	0.123294i
$604$	21.7877	+	24.5933i	0.886531	+	1.00069i
$605$	−0.954008	−	1.81771i	−0.0387859	−	0.0739004i
$606$		−	2.20713i		−	0.0896585i
$607$	−8.61891	+	4.52355i	−0.349831	+	0.183605i	−0.630481	−	0.776205i	$-0.717142\pi$
$607$	−8.61891	+	4.52355i	−0.349831	+	0.183605i	0.280650	+	0.959810i	$0.409450\pi$
$608$	3.16957	+	26.1037i	0.128543	+	1.05865i
$609$	−29.6096	−	11.2294i	−1.19984	−	0.455040i
$610$	0.00998644	−	0.00524129i	0.000404339	−	0.000212214i
$611$	−4.02209	−	1.47383i	−0.162716	−	0.0596248i
$612$	7.31544	+	3.83944i	0.295709	+	0.155200i
$613$	11.8654	+	13.3932i	0.479237	+	0.540947i	0.937553	−	0.347842i	$-0.113086\pi$
$613$	11.8654	+	13.3932i	0.479237	+	0.540947i	−0.458316	+	0.888789i	$0.651547\pi$
$614$	−13.9867	−	12.3911i	−0.564457	−	0.500065i
$615$	0.444448	−	0.109547i	0.0179219	−	0.00441735i
$616$	55.9881	−	6.79818i	2.25582	−	0.273907i
$617$	−0.575411	+	0.649504i	−0.0231652	+	0.0261481i	−0.759979	−	0.649947i	$-0.774791\pi$
$617$	−0.575411	+	0.649504i	−0.0231652	+	0.0261481i	0.736814	+	0.676096i	$0.236329\pi$
$618$	2.74091	−	1.03949i	0.110255	−	0.0418144i
$619$	−13.0786	−	24.9191i	−0.525672	−	1.00158i	−0.993069	−	0.117536i	$-0.962500\pi$
$619$	−13.0786	−	24.9191i	−0.525672	−	1.00158i	0.467397	−	0.884048i	$-0.345192\pi$
$620$	−0.945443	−	0.496207i	−0.0379699	−	0.0199281i
$621$	0.160746	−	1.32387i	0.00645053	−	0.0531249i
$622$	8.64233	−	9.75518i	0.346526	−	0.391147i
$623$	−33.3366	−	8.21672i	−1.33560	−	0.329196i
$624$	−1.12679	+	3.07501i	−0.0451076	+	0.123099i
$625$	−24.1728	+	5.95807i	−0.966913	+	0.238323i
$626$	−3.63662	+	6.92900i	−0.145349	+	0.276939i
$627$	23.7241	+	12.4514i	0.947450	+	0.497260i
$628$	9.48953	−	25.0218i	0.378673	−	0.998480i
$629$	−48.8018	−	18.5081i	−1.94585	−	0.737965i
$630$	−0.188392	−	0.130038i	−0.00750572	−	0.00518083i
$631$	1.61044	+	6.53382i	0.0641107	+	0.260107i	0.994248	−	0.107106i	$-0.0341583\pi$
$631$	1.61044	+	6.53382i	0.0641107	+	0.260107i	−0.930137	+	0.367213i	$0.880312\pi$
$632$	−15.6150	−	10.7782i	−0.621131	−	0.428736i
$633$	2.11248	+	17.3979i	0.0839637	+	0.691503i
$634$	−2.20228	+	5.80695i	−0.0874639	+	0.230623i
$635$	0.292335	+	0.556998i	0.0116010	+	0.0221038i
$636$	−8.69534	−	12.5974i	−0.344793	−	0.499518i
$637$	−20.2458	−	10.3370i	−0.802169	−	0.409566i
$638$	−22.2277	+	32.2025i	−0.880005	+	1.27491i
$639$	1.48911	+	0.180810i	0.0589082	+	0.00715275i
$640$	0.788048	+	0.194236i	0.0311503	+	0.00767786i
$641$	26.1840	+	37.9340i	1.03421	+	1.49830i	0.857798	+	0.513988i	$0.171832\pi$
$641$	26.1840	+	37.9340i	1.03421	+	1.49830i	0.176407	+	0.984317i	$0.443552\pi$
$642$	1.94695	+	2.19765i	0.0768400	+	0.0867344i
$643$	18.0148	−	34.3243i	0.710434	−	1.35362i	−0.215713	−	0.976457i	$-0.569208\pi$
$643$	18.0148	−	34.3243i	0.710434	−	1.35362i	0.926147	−	0.377162i	$-0.123100\pi$
$644$	−6.90869	+	0.838867i	−0.272241	+	0.0330560i
$645$	0.109957	+	0.0133512i	0.00432955	+	0.000525702i
$646$	−14.6285	+	12.9597i	−0.575549	+	0.509892i
$647$	−1.18918	+	1.72283i	−0.0467516	+	0.0677313i	−0.845663	−	0.533718i	$-0.820794\pi$
$647$	−1.18918	+	1.72283i	−0.0467516	+	0.0677313i	0.798911	+	0.601449i	$0.205410\pi$
$648$	−2.56966	+	0.312013i	−0.100946	+	0.0122570i
$649$	8.67447	−	71.4407i	0.340503	−	2.80429i
$650$	−6.17682	+	12.0978i	−0.242275	+	0.474516i
$651$	−3.94497	−	32.4897i	−0.154615	−	1.27337i
$652$	6.78251	+	27.5177i	0.265624	+	1.07768i
$653$	0.744787			0.0291458			0.0145729	−	0.999894i	$-0.495361\pi$
$653$	0.744787			0.0291458			0.0145729	+	0.999894i	$0.495361\pi$
$654$	−13.5192			−0.528642
$655$	0.204340	+	0.829040i	0.00798423	+	0.0323933i
$656$	−4.67393	−	1.77259i	−0.182486	−	0.0692080i
$657$			10.2052i			0.398144i
$658$	−3.05725	+	1.15946i	−0.119184	+	0.0452006i
$659$	32.5931	+	8.03348i	1.26965	+	0.312940i	0.815901	−	0.578191i	$-0.196241\pi$
$659$	32.5931	+	8.03348i	1.26965	+	0.312940i	0.453746	+	0.891131i	$0.350087\pi$
$660$	0.532062	−	0.471366i	0.0207105	−	0.0183479i
$661$	−4.69394	+	19.0440i	−0.182573	+	0.740727i	0.806243	+	0.591585i	$0.201498\pi$
$661$	−4.69394	+	19.0440i	−0.182573	+	0.740727i	−0.988816	+	0.149143i	$0.952349\pi$
$662$	−2.48812	+	2.20429i	−0.0967037	+	0.0856720i
$663$	−20.1584	+	5.20987i	−0.782887	+	0.202335i
$664$	−3.63699	−	3.22209i	−0.141143	−	0.125041i
$665$	−1.11995	+	0.773045i	−0.0434298	+	0.0299774i
$666$	6.62148	−	1.63205i	0.256577	−	0.0632406i
$667$	6.57703	−	9.52847i	0.254664	−	0.368944i
$668$	2.41097	−	9.78171i	0.0932834	−	0.378466i
$669$	0.0219843	−	0.0891936i	0.000849961	−	0.00344843i
$670$	−0.332041	−	0.0403171i	−0.0128279	−	0.00155759i
$671$	−0.711847	+	0.803509i	−0.0274806	+	0.0310191i
$672$	7.58268	+	19.9939i	0.292508	+	0.771281i
$673$	29.2501	−	15.3516i	1.12751	−	0.591761i	0.205393	−	0.978680i	$-0.434153\pi$
$673$	29.2501	−	15.3516i	1.12751	−	0.591761i	0.922114	+	0.386918i	$0.126461\pi$
$674$	−11.1671	−	7.70810i	−0.430141	−	0.296905i
$675$	4.99308			0.192184
$676$	−6.98498	−	17.2377i	−0.268653	−	0.662987i
$677$	15.5618			0.598090			0.299045	−	0.954239i	$-0.403332\pi$
$677$	15.5618			0.598090			0.299045	+	0.954239i	$0.403332\pi$
$678$	4.05543	+	2.79926i	0.155748	+	0.107505i
$679$	35.6166	−	18.6930i	1.36684	−	0.717373i
$680$	0.440880	+	1.16251i	0.0169070	+	0.0445800i
$681$	−9.74402	+	10.9987i	−0.373392	+	0.421472i
$682$	−40.1449	−	4.87447i	−1.53723	−	0.186653i
$683$	−6.12220	+	24.8388i	−0.234260	+	0.950429i	0.729569	+	0.683907i	$0.239721\pi$
$683$	−6.12220	+	24.8388i	−0.234260	+	0.950429i	−0.963829	+	0.266522i	$0.914126\pi$
$684$	−1.53577	+	6.23086i	−0.0587216	+	0.238243i
$685$	0.359925	−	0.521441i	0.0137520	−	0.0199232i
$686$	1.85787	−	0.457925i	0.0709339	−	0.0174836i
$687$	1.72386	−	1.18990i	0.0657695	−	0.0453974i
$688$	−0.905385	−	0.802102i	−0.0345175	−	0.0305798i
$689$	37.5561	+	8.80971i	1.43077	+	0.335623i
$690$	0.0626453	−	0.0554989i	0.00238486	−	0.00211281i
$691$	2.35297	−	9.54637i	0.0895112	−	0.363161i	−0.909056	−	0.416674i	$-0.863196\pi$
$691$	2.35297	−	9.54637i	0.0895112	−	0.363161i	0.998567	+	0.0535129i	$0.0170418\pi$
$692$	−3.19447	+	2.83006i	−0.121436	+	0.107583i
$693$	21.1550	+	5.21425i	0.803613	+	0.198073i
$694$	−8.94133	+	3.39100i	−0.339408	+	0.128721i
$695$			0.0242979i			0.000921671i
$696$	−21.0127	−	7.96907i	−0.796485	−	0.302067i
$697$	−7.60546	−	30.8566i	−0.288077	−	1.16878i
$698$	5.58465			0.211382
$699$	−14.8355			−0.561130
$700$	−6.23580	−	25.2996i	−0.235691	−	0.956236i
$701$	2.07318	+	17.0742i	0.0783030	+	0.644883i	0.978035	+	0.208440i	$0.0668387\pi$
$701$	2.07318	+	17.0742i	0.0783030	+	0.644883i	−0.899732	+	0.436443i	$0.856238\pi$
$702$	1.78097	−	2.05646i	0.0672184	−	0.0776161i
$703$	4.88671	−	40.2457i	0.184306	−	1.51790i
$704$	15.4570	−	1.87682i	0.582558	−	0.0707353i
$705$	−0.0561352	+	0.0813258i	−0.00211417	+	0.00306291i
$706$	−9.53104	+	8.44376i	−0.358705	+	0.317785i
$707$	−10.5921	−	1.28612i	−0.398358	−	0.0483694i
$708$	17.1111	−	2.07766i	0.643073	−	0.0780832i
$709$	−1.08583	+	2.06887i	−0.0407791	+	0.0776980i	−0.904993	−	0.425427i	$-0.860124\pi$
$709$	−1.08583	+	2.06887i	−0.0407791	+	0.0776980i	0.864214	+	0.503125i	$0.167816\pi$
$710$	0.0624261	+	0.0704645i	0.00234281	+	0.00264449i
$711$	−4.16385	−	6.03238i	−0.156157	−	0.226232i
$712$	−23.6576	−	5.83107i	−0.886606	−	0.218529i
$713$	11.8786	+	1.44232i	0.444857	+	0.0540154i
$714$	−9.02809	+	13.0794i	−0.337868	+	0.489486i
$715$	−0.195904	+	1.78063i	−0.00732641	+	0.0665919i
$716$	−14.7345	−	21.3466i	−0.550653	−	0.797758i
$717$	−2.27018	−	4.32547i	−0.0847815	−	0.161538i
$718$	7.25233	−	19.1228i	0.270654	−	0.713657i
$719$	−3.14191	−	25.8759i	−0.117173	−	0.965009i	−0.926147	−	0.377164i	$-0.876899\pi$
$719$	−3.14191	−	25.8759i	−0.117173	−	0.965009i	0.808973	−	0.587845i	$-0.200024\pi$
$720$	0.0621760	+	0.0429170i	0.00231716	+	0.00159942i
$721$	−3.39140	−	13.7595i	−0.126302	−	0.512429i
$722$	−0.694997	−	0.479722i	−0.0258651	−	0.0178534i
$723$	21.7442	+	8.24648i	0.808675	+	0.306690i
$724$	−6.33189	+	16.6958i	−0.235323	+	0.620495i
$725$	38.3836	+	20.1453i	1.42553	+	0.748177i
$726$	8.65414	−	16.4891i	0.321185	−	0.611967i
$727$	20.3443	−	5.01443i	0.754529	−	0.185975i	0.156753	−	0.987638i	$-0.449897\pi$
$727$	20.3443	−	5.01443i	0.754529	−	0.185975i	0.597776	+	0.801663i	$0.296051\pi$
$728$	−30.3197	−	15.4804i	−1.12372	−	0.573742i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−0.424702	+	0.479390i	−0.0157189	+	0.0177430i
$731$	0.926928	−	7.63394i	0.0342837	−	0.282351i
$732$	−0.227662	−	0.119486i	−0.00841465	−	0.00441635i
$733$	−20.5378	−	39.1316i	−0.758582	−	1.44536i	−0.890924	−	0.454153i	$-0.849942\pi$
$733$	−20.5378	−	39.1316i	−0.758582	−	1.44536i	0.132342	−	0.991204i	$-0.457750\pi$
$734$	20.4212	−	7.74474i	0.753761	−	0.285864i
$735$	−0.347743	+	0.392521i	−0.0128267	+	0.0144784i
$736$	−7.76102	+	0.942358i	−0.286075	+	0.0347358i
$737$	30.9110	−	7.61887i	1.13862	−	0.280645i
$738$	3.10812	+	2.75356i	0.114412	+	0.101360i
$739$	26.3752	+	29.7715i	0.970228	+	1.09516i	0.995431	+	0.0954788i	$0.0304382\pi$
$739$	26.3752	+	29.7715i	0.970228	+	1.09516i	−0.0252034	+	0.999682i	$0.508023\pi$
$740$	−0.952370	−	0.499843i	−0.0350098	−	0.0183746i
$741$	−7.67639	−	14.2346i	−0.281999	−	0.522920i
$742$	26.0723	−	13.6838i	0.957146	−	0.502349i
$743$	−22.2636	−	8.44346i	−0.816772	−	0.309761i	−0.0893926	−	0.995996i	$-0.528493\pi$
$743$	−22.2636	−	8.44346i	−0.816772	−	0.309761i	−0.727379	+	0.686236i	$0.759262\pi$
$744$	−2.79958	−	23.0566i	−0.102638	−	0.845297i
$745$	−0.0632497	+	0.0331960i	−0.00231729	+	0.00121621i
$746$			5.75592i			0.210739i
$747$	−0.872339	−	1.66210i	−0.0319172	−	0.0608132i
$748$	−32.7254	−	36.9393i	−1.19656	−	1.35064i
$749$	11.6811	−	8.06291i	0.426820	−	0.294612i
$750$	0.469425	+	0.415874i	0.0171410	+	0.0151856i
$751$	2.45403	+	3.55528i	0.0895489	+	0.129734i	0.865198	−	0.501430i	$-0.167193\pi$
$751$	2.45403	+	3.55528i	0.0895489	+	0.129734i	−0.775649	+	0.631164i	$0.782577\pi$
$752$	1.00900	−	0.382663i	0.0367945	−	0.0139543i
$753$	−8.36633	−	22.0602i	−0.304886	−	0.803918i
$754$	21.9880	−	8.62317i	0.800757	−	0.314037i
$755$	−0.677349	+	1.78602i	−0.0246512	+	0.0650000i
$756$			5.21858i			0.189798i
$757$	0.0795509	+	0.209758i	0.00289133	+	0.00762380i	0.936454	−	0.350790i	$-0.114087\pi$
$757$	0.0795509	+	0.209758i	0.00289133	+	0.00762380i	−0.933563	+	0.358414i	$0.883318\pi$
$758$	−0.125956	+	1.03734i	−0.00457494	+	0.0376780i
$759$	−3.70198	+	7.05353i	−0.134373	+	0.256027i
$760$	−0.794782	+	0.548599i	−0.0288298	+	0.0198998i
$761$	29.2402	−	20.1830i	1.05996	−	0.731635i	0.0953804	−	0.995441i	$-0.469593\pi$
$761$	29.2402	−	20.1830i	1.05996	−	0.731635i	0.964576	+	0.263806i	$0.0849779\pi$
$762$	−2.65187	+	5.05273i	−0.0960673	+	0.183041i
$763$	−7.87776	+	64.8792i	−0.285194	+	2.34878i
$764$	−10.7952	−	28.4645i	−0.390556	−	1.02981i
$765$			0.480311i			0.0173657i
$766$	5.21949	−	13.7627i	0.188588	−	0.497265i
$767$	−28.4376	+	32.8365i	−1.02682	+	1.18566i
$768$	4.45949	+	11.7587i	0.160918	+	0.424306i
$769$	−5.18933	+	1.96805i	−0.187132	+	0.0709698i	−0.446391	−	0.894838i	$-0.647291\pi$
$769$	−5.18933	+	1.96805i	−0.187132	+	0.0709698i	0.259259	+	0.965808i	$0.416522\pi$
$770$	0.776760	+	1.12533i	0.0279925	+	0.0405541i
$771$	5.67599	+	5.02849i	0.204416	+	0.181096i
$772$	5.55135	−	3.83182i	0.199798	−	0.137910i
$773$	−25.7226	−	29.0348i	−0.925177	−	1.04431i	−0.998893	−	0.0470300i	$-0.985024\pi$
$773$	−25.7226	−	29.0348i	−0.925177	−	1.04431i	0.0737162	−	0.997279i	$-0.476514\pi$
$774$	0.466946	+	0.889691i	0.0167840	+	0.0319793i
$775$			44.8012i			1.60931i
$776$	25.2757	−	13.2657i	0.907343	−	0.476211i
$777$	−3.97387	−	32.7278i	−0.142562	−	1.17410i
$778$	−7.57899	−	2.87433i	−0.271720	−	0.103050i
$779$	21.8576	−	11.4718i	0.783130	−	0.411018i
$780$	−0.425324	+	0.0565067i	−0.0152290	+	0.00202326i
$781$	−7.93393	−	4.16405i	−0.283898	−	0.149001i
$782$	−3.85310	−	4.34925i	−0.137787	−	0.155529i
$783$	−6.49843	−	5.75710i	−0.232235	−	0.205742i
$784$	5.56024	−	1.37048i	0.198580	−	0.0489456i
$785$	1.54444	−	0.187529i	0.0551234	−	0.00669320i
$786$	−5.13627	+	5.79765i	−0.183205	+	0.206795i
$787$	22.6780	−	8.60064i	0.808384	−	0.306580i	0.0844313	−	0.996429i	$-0.473093\pi$
$787$	22.6780	−	8.60064i	0.808384	−	0.306580i	0.723953	+	0.689850i	$0.242323\pi$
$788$	7.63971	+	14.5563i	0.272154	+	0.518545i
$789$	−11.0351	−	5.79164i	−0.392858	−	0.206188i
$790$	0.0554478	−	0.456654i	0.00197275	−	0.0162470i
$791$	15.7969	−	17.8311i	0.561674	−	0.633999i
$792$	15.0129	+	3.70034i	0.533459	+	0.131486i
$793$	0.627345	−	0.162135i	0.0222777	−	0.00575760i
$794$	−25.5453	+	6.29634i	−0.906568	+	0.223449i
$795$	0.413554	−	0.787961i	0.0146672	−	0.0279461i
$796$	−14.0212	−	7.35892i	−0.496970	−	0.260830i
$797$	−9.80467	+	25.8528i	−0.347299	+	0.915753i	0.641583	+	0.767054i	$0.278278\pi$
$797$	−9.80467	+	25.8528i	−0.347299	+	0.915753i	−0.988882	+	0.148700i	$0.952491\pi$
$798$	−11.5425	−	4.37748i	−0.408598	−	0.154961i
$799$	5.64618	+	3.89728i	0.199748	+	0.137876i
$800$	−7.00511	−	28.4208i	−0.247668	−	1.00483i
$801$	−7.74668	−	5.34715i	−0.273716	−	0.188932i
$802$	2.40299	+	19.7904i	0.0848526	+	0.698824i
$803$	21.6165	−	56.9979i	0.762828	−	2.01141i
$804$	3.54361	+	6.75178i	0.124973	+	0.238117i
$805$	−0.229838	−	0.332977i	−0.00810071	−	0.0117359i
$806$	18.4519	+	15.9800i	0.649941	+	0.562873i
$807$	4.94065	−	7.15777i	0.173919	−	0.251965i
$808$	−7.51679	−	0.912704i	−0.264440	−	0.0321088i
$809$	−1.36723	−	0.336993i	−0.0480693	−	0.0118480i	0.215208	−	0.976568i	$-0.430957\pi$
$809$	−1.36723	−	0.336993i	−0.0480693	−	0.0118480i	−0.263277	+	0.964720i	$0.584803\pi$
$810$	−0.0356505	−	0.0516487i	−0.00125263	−	0.00181475i
$811$	2.61380	+	2.95037i	0.0917830	+	0.103602i	0.792608	−	0.609732i	$-0.208723\pi$
$811$	2.61380	+	2.95037i	0.0917830	+	0.103602i	−0.700825	+	0.713334i	$0.747184\pi$
$812$	−21.0551	+	40.1171i	−0.738888	+	1.40783i
$813$	−23.6689	+	2.87392i	−0.830103	+	0.100793i
$814$	−40.4391	−	4.91019i	−1.41739	−	0.172102i
$815$	−1.23329	+	1.09260i	−0.0432004	+	0.0382722i
$816$	2.97958	−	4.31667i	0.104306	−	0.151114i
$817$	5.92966	−	0.719991i	0.207453	−	0.0251893i
$818$	−2.41732	+	19.9084i	−0.0845195	+	0.696080i
$819$	−8.83126	−	9.74528i	−0.308589	−	0.340528i
$820$	−0.0789399	−	0.650128i	−0.00275670	−	0.0227035i
$821$	5.74033	+	23.2894i	0.200339	+	0.812807i	0.981965	+	0.189060i	$0.0605442\pi$
$821$	5.74033	+	23.2894i	0.200339	+	0.812807i	−0.781626	+	0.623747i	$0.785610\pi$
$822$	5.74759			0.200470
$823$	35.3917			1.23368			0.616838	−	0.787090i	$-0.288413\pi$
$823$	35.3917			1.23368			0.616838	+	0.787090i	$0.288413\pi$
$824$	−2.40674	−	9.76452i	−0.0838427	−	0.340163i
$825$	−27.8872	−	10.5762i	−0.970908	−	0.368217i
$826$			33.1573i			1.15369i
$827$	3.33930	−	1.26643i	0.116119	−	0.0440380i	−0.295861	−	0.955231i	$-0.595607\pi$
$827$	3.33930	−	1.26643i	0.116119	−	0.0440380i	0.411980	+	0.911193i	$0.364837\pi$
$828$	−1.85252	−	0.456606i	−0.0643797	−	0.0158682i
$829$	−11.8480	+	10.4964i	−0.411498	+	0.364556i	−0.843328	−	0.537400i	$-0.819407\pi$
$829$	−11.8480	+	10.4964i	−0.411498	+	0.364556i	0.431829	+	0.901955i	$0.357868\pi$
$830$	0.0281923	−	0.114381i	0.000978569	−	0.00397021i
$831$	4.24662	−	3.76218i	0.147314	−	0.130508i
$832$	−8.37056	−	4.27378i	−0.290197	−	0.148167i
$833$	27.2514	+	24.1427i	0.944207	+	0.836494i
$834$	−0.181398	+	0.125210i	−0.00628128	+	0.00433566i
$835$	0.568675	−	0.140166i	0.0196798	−	0.00485064i
$836$	21.7756	−	31.5474i	0.753124	−	1.09109i
$837$	2.14730	−	8.71193i	0.0742215	−	0.301128i
$838$	3.23559	−	13.1273i	0.111772	−	0.453475i
$839$	20.2548	+	2.45938i	0.699275	+	0.0849073i	0.462450	−	0.886645i	$-0.346970\pi$
$839$	20.2548	+	2.45938i	0.699275	+	0.0849073i	0.236824	+	0.971552i	$0.423893\pi$
$840$	−0.520773	+	0.587831i	−0.0179684	+	0.0202821i
$841$	−16.4444	−	43.3602i	−0.567047	−	1.49518i
$842$	−5.95796	+	3.12698i	−0.205325	+	0.107763i
$843$	6.01962	+	4.15504i	0.207327	+	0.143107i
$844$	25.0740			0.863082
$845$	0.698633	−	0.825285i	0.0240337	−	0.0283907i
$846$	−0.896415			−0.0308194
$847$	−74.0890	−	51.1400i	−2.54573	−	1.75719i
$848$	−8.60478	+	4.51614i	−0.295490	+	0.155085i
$849$	−4.02924	−	10.6242i	−0.138283	−	0.364623i
$850$	14.4264	−	16.2840i	0.494821	−	0.558537i
$851$	11.9656	+	1.45289i	0.410177	+	0.0498044i
$852$	0.513599	−	2.08375i	0.0175956	−	0.0713882i
$853$	3.96982	−	16.1062i	0.135924	−	0.551466i	−0.863005	−	0.505196i	$-0.831420\pi$
$853$	3.96982	−	16.1062i	0.135924	−	0.551466i	0.998929	−	0.0462703i	$-0.0147336\pi$
$854$	0.280961	−	0.407043i	0.00961430	−	0.0139287i
$855$	−0.362241	+	0.0892843i	−0.0123884	+	0.00305346i
$856$	8.28963	−	5.72192i	0.283334	−	0.195571i
$857$	−4.52445	−	4.00831i	−0.154552	−	0.136921i	0.582303	−	0.812972i	$-0.302152\pi$
$857$	−4.52445	−	4.00831i	−0.154552	−	0.136921i	−0.736855	+	0.676050i	$0.763690\pi$
$858$	−14.3030	+	7.71327i	−0.488295	+	0.263327i
$859$	−9.65169	+	8.55065i	−0.329311	+	0.291744i	−0.811535	−	0.584304i	$-0.801368\pi$
$859$	−9.65169	+	8.55065i	−0.329311	+	0.291744i	0.482224	+	0.876048i	$0.339829\pi$
$860$	0.0379246	−	0.153866i	0.00129322	−	0.00524679i
$861$	15.0256	−	13.3115i	0.512070	−	0.453655i
$862$	6.58981	+	1.62424i	0.224450	+	0.0553219i
$863$	−36.8142	+	13.9618i	−1.25317	+	0.475265i	−0.889788	−	0.456375i	$-0.849148\pi$
$863$	−36.8142	+	13.9618i	−1.25317	+	0.475265i	−0.363383	+	0.931640i	$0.618378\pi$
$864$			5.86239i			0.199443i
$865$	−0.231990	−	0.0879822i	−0.00788790	−	0.00299149i
$866$	−3.71118	−	15.0568i	−0.126111	−	0.511652i
$867$	16.3464			0.555153
$868$	−46.8245			−1.58933
$869$	10.4782	+	42.5116i	0.355448	+	1.44211i
$870$	−0.0656746	−	0.540879i	−0.00222658	−	0.0183375i
$871$	−18.0433	−	6.61166i	−0.611372	−	0.224028i
$872$	−5.59053	+	46.0421i	−0.189319	+	1.55918i
$873$	10.9472	−	1.32924i	0.370508	−	0.0449878i
$874$	2.56387	−	3.71440i	0.0867241	−	0.125642i
$875$	2.26934	−	2.01046i	0.0767176	−	0.0679658i
$876$	14.4942	+	1.75991i	0.489712	+	0.0594619i
$877$	34.6795	−	4.21085i	1.17104	−	0.142190i	0.488184	−	0.872741i	$-0.337660\pi$
$877$	34.6795	−	4.21085i	1.17104	−	0.142190i	0.682859	+	0.730551i	$0.260736\pi$
$878$	0.0485105	−	0.0924291i	0.00163715	−	0.00311933i
$879$	−11.8702	−	13.3987i	−0.400372	−	0.451927i
$880$	−0.256358	−	0.371398i	−0.00864182	−	0.0125198i
$881$	39.2426	+	9.67243i	1.32212	+	0.325872i	0.836340	−	0.548211i	$-0.184691\pi$
$881$	39.2426	+	9.67243i	1.32212	+	0.325872i	0.485776	+	0.874083i	$0.338537\pi$
$882$	−4.72236	−	0.573398i	−0.159010	−	0.0193073i
$883$	3.23406	−	4.68534i	0.108835	−	0.157674i	−0.764782	−	0.644289i	$-0.777153\pi$
$883$	3.23406	−	4.68534i	0.108835	−	0.157674i	0.873616	+	0.486615i	$0.161769\pi$
$884$	3.92307	+	29.5288i	0.131947	+	0.993161i
$885$	0.569249	+	0.824700i	0.0191351	+	0.0277220i
$886$	−11.0677	−	21.0877i	−0.371826	−	0.708456i
$887$	0.687826	−	1.81365i	0.0230949	−	0.0608964i	−0.922973	−	0.384865i	$-0.874248\pi$
$887$	0.687826	−	1.81365i	0.0230949	−	0.0608964i	0.946068	+	0.323969i	$0.105017\pi$
$888$	−2.82010	−	23.2256i	−0.0946363	−	0.779400i
$889$	22.7030	+	15.6707i	0.761434	+	0.525580i
$890$	−0.141372	−	0.573569i	−0.00473880	−	0.0192261i
$891$	4.91596	+	3.39324i	0.164691	+	0.113678i
$892$	−0.122888	−	0.0466052i	−0.00411459	−	0.00156046i
$893$	−1.88968	+	4.98269i	−0.0632359	+	0.166739i
$894$	−0.573760	−	0.301132i	−0.0191894	−	0.0100714i
$895$	0.700777	−	1.33522i	0.0234244	−	0.0446315i
$896$	34.5587	−	8.51795i	1.15453	−	0.284565i
$897$	4.23215	−	2.28230i	0.141307	−	0.0762038i
$898$	−16.9763	−	4.18429i	−0.566507	−	0.139631i
$899$	51.6565	−	58.3081i	1.72284	−	1.94469i
$900$	0.861067	−	7.09152i	0.0287022	−	0.236384i
$901$	−54.7055	−	28.7117i	−1.82251	−	0.956525i
$902$	−11.5269	−	21.9626i	−0.383803	−	0.731276i
$903$	4.54176	−	1.72246i	0.151140	−	0.0573200i
$904$	11.2104	−	12.6540i	0.372854	−	0.420865i
$905$	−1.03053	+	0.125129i	−0.0342559	+	0.00415942i
$906$	−16.8241	+	4.14678i	−0.558944	+	0.137767i
$907$	−11.8254	−	10.4764i	−0.392657	−	0.347864i	0.443577	−	0.896236i	$-0.353709\pi$
$907$	−11.8254	−	10.4764i	−0.392657	−	0.347864i	−0.836234	+	0.548372i	$0.815248\pi$
$908$	13.9408	+	15.7359i	0.462641	+	0.522214i
$909$	−2.59015	−	1.35942i	−0.0859098	−	0.0450890i
$910$	−0.00928655	−	0.825307i	−0.000307846	−	0.0273587i
$911$	21.3107	−	11.1847i	0.706057	−	0.370567i	−0.0731614	−	0.997320i	$-0.523309\pi$
$911$	21.3107	−	11.1847i	0.706057	−	0.370567i	0.779218	+	0.626753i	$0.215617\pi$
$912$	3.80941	+	1.44472i	0.126142	+	0.0478395i
$913$	1.35154	+	11.1309i	0.0447293	+	0.368379i
$914$	12.1477	−	6.37558i	0.401809	−	0.210885i
$915$		−	0.0149477i		−	0.000494155i
$916$	−1.39269	−	2.65355i	−0.0460158	−	0.0876758i
$917$	24.8303	+	28.0276i	0.819967	+	0.925552i
$918$	−3.58580	+	2.47510i	−0.118349	+	0.0816904i
$919$	10.7870	+	9.55641i	0.355829	+	0.315237i	0.822033	−	0.569441i	$-0.192840\pi$
$919$	10.7870	+	9.55641i	0.355829	+	0.315237i	−0.466204	+	0.884677i	$0.654379\pi$
$920$	−0.163106	−	0.236300i	−0.00537746	−	0.00779059i
$921$	−23.1561	+	8.78196i	−0.763021	+	0.289376i
$922$	3.78875	+	9.99012i	0.124776	+	0.329007i
$923$	2.56717	+	4.76039i	0.0844996	+	0.156690i
$924$	11.0539	−	29.1466i	0.363645	−	0.958854i
$925$			45.1295i			1.48385i
$926$	6.97633	+	18.3951i	0.229257	+	0.604500i
$927$	0.468300	−	3.85680i	0.0153810	−	0.126674i
$928$	−23.6526	+	45.0663i	−0.776436	+	1.47937i
$929$	5.60977	−	3.87214i	0.184051	−	0.127041i	−0.472477	−	0.881343i	$-0.656640\pi$
$929$	5.60977	−	3.87214i	0.184051	−	0.127041i	0.656527	+	0.754302i	$0.272025\pi$
$930$	0.463426	−	0.319880i	0.0151963	−	0.0104893i
$931$	−13.1422	+	25.0403i	−0.430717	+	0.820663i
$932$	−2.55841	+	21.0704i	−0.0838036	+	0.690184i
$933$	−6.12508	−	16.1505i	−0.200526	−	0.528744i
$934$			14.9332i			0.488630i
$935$	1.01738	−	2.68262i	0.0332720	−	0.0877311i
$936$	−6.26718	−	6.91583i	−0.204849	−	0.226051i
$937$	0.471099	+	1.24219i	0.0153901	+	0.0405804i	0.942491	−	0.334231i	$-0.108477\pi$
$937$	0.471099	+	1.24219i	0.0153901	+	0.0405804i	−0.927101	+	0.374812i	$0.877707\pi$
$938$	−13.7150	+	5.20140i	−0.447809	+	0.169832i
$939$	5.89157	+	8.53542i	0.192264	+	0.278543i
$940$	0.105824	+	0.0937519i	0.00345160	+	0.00305785i
$941$	−6.17373	+	4.26141i	−0.201258	+	0.138918i	−0.664431	−	0.747350i	$-0.731326\pi$
$941$	−6.17373	+	4.26141i	−0.201258	+	0.138918i	0.463173	+	0.886268i	$0.346711\pi$
$942$	9.35869	+	10.5638i	0.304923	+	0.344186i
$943$	3.41072	+	6.49859i	0.111068	+	0.211623i
$944$		−	10.9431i		−	0.356167i
$945$	−0.268639	+	0.140992i	−0.00873881	+	0.00458648i
$946$	−0.723451	−	5.95815i	−0.0235214	−	0.193716i
$947$	5.98280	+	2.26898i	0.194415	+	0.0737318i	0.449891	−	0.893084i	$-0.351463\pi$
$947$	5.98280	+	2.26898i	0.194415	+	0.0737318i	−0.255476	+	0.966815i	$0.582232\pi$
$948$	−9.28567	+	4.87349i	−0.301584	+	0.158284i
$949$	−30.0450	+	21.2416i	−0.975301	+	0.689531i
$950$	14.9628	+	7.85306i	0.485456	+	0.254787i
$951$	5.45824	+	6.16108i	0.176995	+	0.199787i
$952$	40.8111	+	36.1555i	1.32270	+	1.17181i
$953$	−29.2345	+	7.20566i	−0.946998	+	0.233414i	−0.682428	−	0.730952i	$-0.739076\pi$
$953$	−29.2345	+	7.20566i	−0.946998	+	0.233414i	−0.264570	+	0.964367i	$0.585230\pi$
$954$	8.01368	−	0.973036i	0.259452	−	0.0315032i
$955$	1.17362	−	1.32475i	0.0379775	−	0.0428678i
$956$	−6.53483	+	2.47833i	−0.211352	+	0.0801551i
$957$	24.1003	+	45.9192i	0.779051	+	1.48436i
$958$	15.2163	+	7.98611i	0.491615	+	0.258020i
$959$	3.34918	−	27.5829i	0.108151	−	0.890700i
$960$	−0.143773	+	0.162286i	−0.00464026	+	0.00523777i
$961$	48.0699	+	11.8482i	1.55064	+	0.382199i
$962$	18.5871	+	16.0971i	0.599273	+	0.518992i
$963$	3.77819	−	0.931241i	0.121751	−	0.0300088i
$964$	15.4621	−	29.4605i	0.497999	−	0.948858i
$965$	0.347235	+	0.182243i	0.0111779	+	0.00586661i
$966$	1.30149	−	3.43174i	0.0418747	−	0.110414i
$967$	−17.1038	−	6.48663i	−0.550022	−	0.208596i	0.0639087	−	0.997956i	$-0.479643\pi$
$967$	−17.1038	−	6.48663i	−0.550022	−	0.208596i	−0.613931	+	0.789360i	$0.710413\pi$
$968$	−52.5780	−	36.2919i	−1.68992	−	1.16647i
$969$	6.19871	+	25.1492i	0.199131	+	0.807907i
$970$	0.569564	+	0.393141i	0.0182876	+	0.0126230i
$971$	1.99621	+	16.4403i	0.0640614	+	0.527593i	0.989048	+	0.147594i	$0.0471528\pi$
$971$	1.99621	+	16.4403i	0.0640614	+	0.527593i	−0.924987	+	0.380000i	$0.875924\pi$
$972$	−0.507334	+	1.33773i	−0.0162727	+	0.0429077i
$973$	0.495185	+	0.943496i	0.0158749	+	0.0302471i
$974$	−11.1519	−	16.1564i	−0.357331	−	0.517683i
$975$	10.3928	+	14.7000i	0.332837	+	0.470777i
$976$	−0.0927271	+	0.134338i	−0.00296812	+	0.00430007i
$977$	−18.7033	−	2.27099i	−0.598370	−	0.0726553i	−0.184253	−	0.982879i	$-0.558987\pi$
$977$	−18.7033	−	2.27099i	−0.598370	−	0.0726553i	−0.414117	+	0.910224i	$0.635910\pi$
$978$	−14.5122	−	3.57694i	−0.464049	−	0.114378i
$979$	31.9403	+	46.2736i	1.02082	+	1.47891i
$980$	0.497517	+	0.561581i	0.0158926	+	0.0179390i
$981$	−8.32674	+	15.8653i	−0.265852	+	0.506539i
$982$	−32.5915	+	3.95732i	−1.04004	+	0.126283i
$983$	23.8191	+	2.89217i	0.759713	+	0.0922458i	0.491220	−	0.871036i	$-0.336551\pi$
$983$	23.8191	+	2.89217i	0.759713	+	0.0922458i	0.268493	+	0.963282i	$0.413474\pi$
$984$	10.6630	−	9.44663i	0.339925	−	0.301148i
$985$	−0.542912	+	0.786545i	−0.0172986	+	0.0250614i
$986$	−37.5515	+	4.55957i	−1.19588	+	0.145206i
$987$	−0.522350	+	4.30194i	−0.0166266	+	0.136932i
$988$	−21.5407	+	8.44776i	−0.685302	+	0.268759i
$989$	0.214064	+	1.76297i	0.00680683	+	0.0560593i
$990$	0.0897133	+	0.363981i	0.00285128	+	0.0115681i
$991$	3.95597			0.125666			0.0628328	−	0.998024i	$-0.479987\pi$
$991$	3.95597			0.125666			0.0628328	+	0.998024i	$0.479987\pi$
$992$	−52.6012			−1.67009
$993$	1.05433	+	4.27757i	0.0334580	+	0.135745i
$994$	3.86008	+	1.46394i	0.122434	+	0.0464332i
$995$		−	0.920595i		−	0.0291848i
$996$	−2.51107	+	0.952324i	−0.0795663	+	0.0301755i
$997$	34.3109	+	8.45688i	1.08664	+	0.267832i	0.741658	−	0.670778i	$-0.234040\pi$
$997$	34.3109	+	8.45688i	1.08664	+	0.267832i	0.344980	+	0.938610i	$0.387886\pi$
$998$	−5.29515	+	4.69110i	−0.167615	+	0.148494i
$999$	2.16303	−	8.77576i	0.0684353	−	0.277653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.a.493.9	yes	168
169.12	even	26	inner	507.2.p.a.181.9	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.a.181.9	✓	168	169.12	even	26	inner
507.2.p.a.493.9	yes	168	1.1	even	1	trivial

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.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.620957 + 0.428616i) q^{2} +(0.885456 - 0.464723i) q^{3} +(-0.507334 - 1.33773i) q^{4} +(0.0551559 - 0.0622582i) q^{5} +(0.749018 + 0.0909472i) q^{6} +(0.872920 - 3.54157i) q^{7} +(0.619476 - 2.51331i) q^{8} +(0.568065 - 0.822984i) q^{9} +O(q^{10})\)	\(q+(0.620957 + 0.428616i) q^{2} +(0.885456 - 0.464723i) q^{3} +(-0.507334 - 1.33773i) q^{4} +(0.0551559 - 0.0622582i) q^{5} +(0.749018 + 0.0909472i) q^{6} +(0.872920 - 3.54157i) q^{7} +(0.619476 - 2.51331i) q^{8} +(0.568065 - 0.822984i) q^{9} +(0.0609343 - 0.0150189i) q^{10} +(-4.91596 + 3.39324i) q^{11} +(-1.07090 - 0.948730i) q^{12} +(3.60532 - 0.0405680i) q^{13} +(2.06002 - 1.82502i) q^{14} +(0.0199053 - 0.0807591i) q^{15} +(-0.679878 + 0.602320i) q^{16} +(-5.60683 - 1.38196i) q^{17} +(0.705487 - 0.267556i) q^{18} -4.48545i q^{19} +(-0.111267 - 0.0421980i) q^{20} +(-0.872920 - 3.54157i) q^{21} -4.50700 q^{22} +1.33359 q^{23} +(-0.619476 - 2.51331i) q^{24} +(0.601849 + 4.95668i) q^{25} +(2.25614 + 1.52011i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-5.18053 + 0.629030i) q^{28} +(4.93183 - 7.14499i) q^{29} +(0.0469750 - 0.0416162i) q^{30} +(8.90724 + 1.08153i) q^{31} +(-5.81965 + 0.706633i) q^{32} +(-2.77595 + 5.28913i) q^{33} +(-2.88927 - 3.26131i) q^{34} +(-0.172345 - 0.249685i) q^{35} +(-1.38913 - 0.342389i) q^{36} +(8.97250 + 1.08946i) q^{37} +(1.92253 - 2.78527i) q^{38} +(3.17350 - 1.71140i) q^{39} +(-0.122306 - 0.177191i) q^{40} +(2.55755 + 4.87301i) q^{41} +(0.975928 - 2.57331i) q^{42} +(0.160517 + 1.32198i) q^{43} +(7.03328 + 4.85472i) q^{44} +(-0.0199053 - 0.0807591i) q^{45} +(0.828101 + 0.571597i) q^{46} +(-1.11086 - 0.421292i) q^{47} +(-0.322091 + 0.849283i) q^{48} +(-5.58257 - 2.92996i) q^{49} +(-1.75079 + 3.33584i) q^{50} +(-5.60683 + 1.38196i) q^{51} +(-1.88337 - 4.80236i) q^{52} +(10.3880 + 2.56042i) q^{53} +(0.500339 - 0.564766i) q^{54} +(-0.0598873 + 0.493216i) q^{55} +(-8.36033 - 4.38784i) q^{56} +(-2.08449 - 3.97167i) q^{57} +(6.12491 - 2.32287i) q^{58} +(-7.98914 + 9.01788i) q^{59} +(-0.118132 + 0.0143439i) q^{60} +(0.174489 - 0.0430077i) q^{61} +(5.06745 + 4.48937i) q^{62} +(-2.41878 - 2.73024i) q^{63} +(-2.30809 - 1.21138i) q^{64} +(0.196329 - 0.226698i) q^{65} +(-3.99075 + 2.09451i) q^{66} +(-4.98335 - 1.88993i) q^{67} +(0.995847 + 8.20154i) q^{68} +(1.18083 - 0.619750i) q^{69} -0.228914i q^{70} +(0.697105 + 1.32822i) q^{71} +(-1.71651 - 1.93754i) q^{72} +(-8.39873 + 5.79723i) q^{73} +(5.10458 + 4.52226i) q^{74} +(2.83639 + 4.10923i) q^{75} +(-6.00031 + 2.27562i) q^{76} +(7.72619 + 20.3723i) q^{77} +(2.70414 + 0.297508i) q^{78} +(2.59921 - 6.85356i) q^{79} +0.0755495i q^{80} +(-0.354605 - 0.935016i) q^{81} +(-0.500518 + 4.12213i) q^{82} +(0.872339 - 1.66210i) q^{83} +(-4.29480 + 2.96449i) q^{84} +(-0.395288 + 0.272848i) q^{85} +(-0.466946 + 0.889691i) q^{86} +(1.04648 - 8.61851i) q^{87} +(5.48296 + 14.4574i) q^{88} -9.41292i q^{89} +(0.0222543 - 0.0586796i) q^{90} +(3.00348 - 12.8039i) q^{91} +(-0.676574 - 1.78398i) q^{92} +(8.38958 - 3.18175i) q^{93} +(-0.509222 - 0.737735i) q^{94} +(-0.279256 - 0.247399i) q^{95} +(-4.82466 + 3.33022i) q^{96} +(7.31268 + 8.25431i) q^{97} +(-2.21071 - 4.21215i) q^{98} +5.97334i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

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