LMFDB - Embedded newform 507.2.t.b.4.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			4.15
Character	$\chi$	$=$	507.4
Dual form			507.2.t.b.127.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.56929 + 0.103539i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(4.59701 + 0.371109i) q^{4} +(1.84810 + 0.700893i) q^{5} +(-0.814272 + 2.43904i) q^{6} +(-1.21279 - 2.84653i) q^{7} +(6.66737 + 0.809566i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})$	\(q+(2.56929 + 0.103539i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(4.59701 + 0.371109i) q^{4} +(1.84810 + 0.700893i) q^{5} +(-0.814272 + 2.43904i) q^{6} +(-1.21279 - 2.84653i) q^{7} +(6.66737 + 0.809566i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(4.67574 + 1.99215i) q^{10} +(-2.30769 - 3.64932i) q^{11} +(-1.63543 + 4.31226i) q^{12} +(1.98415 + 3.01051i) q^{13} +(-2.82129 - 7.43912i) q^{14} +(-1.18739 + 1.58013i) q^{15} +(7.94210 + 1.29072i) q^{16} +(-0.883687 + 0.376504i) q^{17} +(-2.11620 - 1.46071i) q^{18} +(-5.15303 + 2.97510i) q^{19} +(8.23564 + 3.90786i) q^{20} +(3.07156 - 0.372955i) q^{21} +(-5.55127 - 9.61508i) q^{22} +(-3.68294 + 6.37904i) q^{23} +(-2.63258 + 6.17890i) q^{24} +(-0.818324 - 0.724971i) q^{25} +(4.78614 + 7.94030i) q^{26} +(0.748511 - 0.663123i) q^{27} +(-4.51884 - 13.5356i) q^{28} +(-0.109222 + 2.71032i) q^{29} +(-3.21436 + 3.93688i) q^{30} +(-1.82438 - 2.05929i) q^{31} +(7.11070 + 1.45166i) q^{32} +(4.14727 - 1.20127i) q^{33} +(-2.30943 + 0.875851i) q^{34} +(-0.246253 - 6.11071i) q^{35} +(-3.68700 - 2.77060i) q^{36} +(0.170182 - 0.0347430i) q^{37} +(-13.5477 + 7.11036i) q^{38} +(-3.44367 + 1.06823i) q^{39} +(11.7546 + 6.16927i) q^{40} +(8.35089 + 2.41886i) q^{41} +(7.93034 - 0.640203i) q^{42} +(1.09751 - 5.37597i) q^{43} +(-9.25417 - 17.6324i) q^{44} +(-1.18739 - 1.58013i) q^{45} +(-10.1230 + 16.0083i) q^{46} +(0.0305345 - 0.0210764i) q^{47} +(-3.44939 + 7.26944i) q^{48} +(-1.78278 + 1.85607i) q^{49} +(-2.02745 - 1.94739i) q^{50} +(-0.115782 - 0.953547i) q^{51} +(8.00392 + 14.5757i) q^{52} +(1.35362 - 11.1481i) q^{53} +(1.99180 - 1.62625i) q^{54} +(-1.70706 - 8.36175i) q^{55} +(-5.78168 - 19.9607i) q^{56} +(-1.42398 - 5.77731i) q^{57} +(-0.561247 + 6.95229i) q^{58} +(0.0265754 + 0.163525i) q^{59} +(-6.04487 + 6.82324i) q^{60} +(-0.00409345 + 0.00307603i) q^{61} +(-4.47413 - 5.47982i) q^{62} +(-0.496332 + 3.05405i) q^{63} +(2.49416 + 0.614756i) q^{64} +(1.55686 + 6.95440i) q^{65} +(10.7799 - 2.65701i) q^{66} +(0.885913 + 10.9740i) q^{67} +(-4.20204 + 1.40285i) q^{68} +(-5.10253 - 5.31229i) q^{69} -15.7257i q^{70} +(9.67205 - 9.29013i) q^{71} +(-5.20251 - 4.24772i) q^{72} +(7.47313 - 14.2389i) q^{73} +(0.440845 - 0.0716443i) q^{74} +(0.924020 - 0.584315i) q^{75} +(-24.7926 + 11.7643i) q^{76} +(-7.58913 + 10.9948i) q^{77} +(-8.95839 + 2.38804i) q^{78} +(5.90211 + 8.55068i) q^{79} +(13.7732 + 7.95194i) q^{80} +(0.428693 + 0.903450i) q^{81} +(21.2054 + 7.07940i) q^{82} +(-1.04882 + 4.25521i) q^{83} +(14.2584 - 0.574594i) q^{84} +(-1.89703 + 0.0764478i) q^{85} +(3.37645 - 13.6988i) q^{86} +(-2.57292 - 0.858968i) q^{87} +(-12.4319 - 26.1996i) q^{88} +(11.1145 + 6.41695i) q^{89} +(-2.88715 - 4.18276i) q^{90} +(6.16313 - 9.29904i) q^{91} +(-19.2979 + 27.9578i) q^{92} +(2.48556 - 1.17941i) q^{93} +(0.0806342 - 0.0509900i) q^{94} +(-11.6086 + 1.88657i) q^{95} +(-3.37267 + 6.42608i) q^{96} +(3.66773 + 2.99461i) q^{97} +(-4.77264 + 4.58418i) q^{98} +4.31775i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{78}\right)$

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 $

$2$	2.56929	+	0.103539i	1.81676	+	0.0732130i	0.925153	−	0.379594i	$-0.123936\pi$
$2$	2.56929	+	0.103539i	1.81676	+	0.0732130i	0.891609	+	0.452807i	$0.149577\pi$
$3$	−0.278217	+	0.960518i	−0.160629	+	0.554555i
$3$	−0.278217	+	0.960518i	−0.160629	+	0.554555i
$4$	4.59701	+	0.371109i	2.29851	+	0.185555i
$5$	1.84810	+	0.700893i	0.826496	+	0.313449i	0.731339	−	0.682014i	$-0.238896\pi$
$5$	1.84810	+	0.700893i	0.826496	+	0.313449i	0.0951568	+	0.995462i	$0.469665\pi$
$6$	−0.814272	+	2.43904i	−0.332425	+	0.995735i
$7$	−1.21279	−	2.84653i	−0.458392	−	1.07589i	−0.975507	−	0.219970i	$-0.929404\pi$
$7$	−1.21279	−	2.84653i	−0.458392	−	1.07589i	0.517115	−	0.855916i	$-0.327006\pi$
$8$	6.66737	+	0.809566i	2.35727	+	0.286225i
$9$	−0.845190	−	0.534466i	−0.281730	−	0.178155i
$10$	4.67574	+	1.99215i	1.47860	+	0.629972i
$11$	−2.30769	−	3.64932i	−0.695794	−	1.10031i	−0.989517	−	0.144420i	$-0.953868\pi$
$11$	−2.30769	−	3.64932i	−0.695794	−	1.10031i	0.293722	−	0.955891i	$-0.405106\pi$
$12$	−1.63543	+	4.31226i	−0.472107	+	1.24484i
$13$	1.98415	+	3.01051i	0.550303	+	0.834965i
$13$	1.98415	+	3.01051i	0.550303	+	0.834965i
$14$	−2.82129	−	7.43912i	−0.754020	−	1.98819i
$15$	−1.18739	+	1.58013i	−0.306584	+	0.407989i
$16$	7.94210	+	1.29072i	1.98553	+	0.322679i
$17$	−0.883687	+	0.376504i	−0.214326	+	0.0913156i	−0.496461	−	0.868059i	$-0.665367\pi$
$17$	−0.883687	+	0.376504i	−0.214326	+	0.0913156i	0.282136	+	0.959375i	$0.408957\pi$
$18$	−2.11620	−	1.46071i	−0.498793	−	0.344292i
$19$	−5.15303	+	2.97510i	−1.18219	+	0.682536i	−0.956519	−	0.291669i	$-0.905790\pi$
$19$	−5.15303	+	2.97510i	−1.18219	+	0.682536i	−0.225667	+	0.974204i	$0.572456\pi$
$20$	8.23564	+	3.90786i	1.84154	+	0.873824i
$21$	3.07156	−	0.372955i	0.670269	−	0.0813854i
$22$	−5.55127	−	9.61508i	−1.18354	−	2.04994i
$23$	−3.68294	+	6.37904i	−0.767947	+	1.33012i	0.170728	+	0.985318i	$0.445388\pi$
$23$	−3.68294	+	6.37904i	−0.767947	+	1.33012i	−0.938675	+	0.344804i	$0.887945\pi$
$24$	−2.63258	+	6.17890i	−0.537374	+	1.26126i
$25$	−0.818324	−	0.724971i	−0.163665	−	0.144994i
$26$	4.78614	+	7.94030i	0.938640	+	1.55722i
$27$	0.748511	−	0.663123i	0.144051	−	0.127618i
$28$	−4.51884	−	13.5356i	−0.853981	−	2.55799i
$29$	−0.109222	+	2.71032i	−0.0202820	+	0.503294i	0.956840	+	0.290615i	$0.0938598\pi$
$29$	−0.109222	+	2.71032i	−0.0202820	+	0.503294i	−0.977122	+	0.212679i	$0.931781\pi$
$30$	−3.21436	+	3.93688i	−0.586860	+	0.718773i
$31$	−1.82438	−	2.05929i	−0.327667	−	0.369860i	0.561473	−	0.827495i	$-0.310235\pi$
$31$	−1.82438	−	2.05929i	−0.327667	−	0.369860i	−0.889140	+	0.457635i	$0.848697\pi$
$32$	7.11070	+	1.45166i	1.25701	+	0.256620i
$33$	4.14727	−	1.20127i	0.721948	−	0.209115i
$34$	−2.30943	+	0.875851i	−0.396064	+	0.150207i
$35$	−0.246253	−	6.11071i	−0.0416244	−	1.03290i
$36$	−3.68700	−	2.77060i	−0.614501	−	0.461767i
$37$	0.170182	−	0.0347430i	0.0279778	−	0.00571171i	−0.186016	−	0.982547i	$-0.559558\pi$
$37$	0.170182	−	0.0347430i	0.0279778	−	0.00571171i	0.213994	+	0.976835i	$0.431353\pi$
$38$	−13.5477	+	7.11036i	−2.19772	+	1.15345i
$39$	−3.44367	+	1.06823i	−0.551429	+	0.171054i
$40$	11.7546	+	6.16927i	1.85856	+	0.975448i
$41$	8.35089	+	2.41886i	1.30419	+	0.377763i	0.856371	−	0.516362i	$-0.172714\pi$
$41$	8.35089	+	2.41886i	1.30419	+	0.377763i	0.447818	+	0.894125i	$0.352201\pi$
$42$	7.93034	−	0.640203i	1.22368	−	0.0987855i
$43$	1.09751	−	5.37597i	0.167369	−	0.819828i	−0.806237	−	0.591593i	$-0.798499\pi$
$43$	1.09751	−	5.37597i	0.167369	−	0.819828i	0.973606	−	0.228235i	$-0.0732956\pi$
$44$	−9.25417	−	17.6324i	−1.39512	−	2.65818i
$45$	−1.18739	−	1.58013i	−0.177006	−	0.235553i
$46$	−10.1230	+	16.0083i	−1.49256	+	2.36029i
$47$	0.0305345	−	0.0210764i	0.00445391	−	0.00307431i	−0.565836	−	0.824518i	$-0.691446\pi$
$47$	0.0305345	−	0.0210764i	0.00445391	−	0.00307431i	0.570290	+	0.821444i	$0.306831\pi$
$48$	−3.44939	+	7.26944i	−0.497877	+	1.04925i
$49$	−1.78278	+	1.85607i	−0.254682	+	0.265152i
$50$	−2.02745	−	1.94739i	−0.286724	−	0.275402i
$51$	−0.115782	−	0.953547i	−0.0162127	−	0.133523i
$52$	8.00392	+	14.5757i	1.10994	+	2.02128i
$53$	1.35362	−	11.1481i	0.185934	−	1.53130i	−0.538895	−	0.842373i	$-0.681158\pi$
$53$	1.35362	−	11.1481i	0.185934	−	1.53130i	0.724828	−	0.688930i	$-0.241919\pi$
$54$	1.99180	−	1.62625i	0.271050	−	0.221305i
$55$	−1.70706	−	8.36175i	−0.230180	−	1.12750i
$56$	−5.78168	−	19.9607i	−0.772610	−	2.66736i
$57$	−1.42398	−	5.77731i	−0.188610	−	0.765223i
$58$	−0.561247	+	6.95229i	−0.0736953	+	0.912880i
$59$	0.0265754	+	0.163525i	0.00345982	+	0.0212891i	0.988723	−	0.149757i	$-0.0478493\pi$
$59$	0.0265754	+	0.163525i	0.00345982	+	0.0212891i	−0.985263	+	0.171047i	$0.945285\pi$
$60$	−6.04487	+	6.82324i	−0.780389	+	0.880877i
$61$	−0.00409345	+	0.00307603i	−0.000524113	+	0.000393845i	−0.601004	−	0.799246i	$-0.705233\pi$
$61$	−0.00409345	+	0.00307603i	−0.000524113	+	0.000393845i	0.600480	+	0.799640i	$0.294976\pi$
$62$	−4.47413	−	5.47982i	−0.568215	−	0.695937i
$63$	−0.496332	+	3.05405i	−0.0625319	+	0.384774i
$64$	2.49416	+	0.614756i	0.311770	+	0.0768444i
$65$	1.55686	+	6.95440i	0.193105	+	0.862587i
$66$	10.7799	−	2.65701i	1.32692	−	0.327056i
$67$	0.885913	+	10.9740i	0.108231	+	1.34069i	0.791791	+	0.610792i	$0.209149\pi$
$67$	0.885913	+	10.9740i	0.108231	+	1.34069i	−0.683559	+	0.729895i	$0.739569\pi$
$68$	−4.20204	+	1.40285i	−0.509573	+	0.170120i
$69$	−5.10253	−	5.31229i	−0.614272	−	0.639525i
$70$		−	15.7257i		−	1.87958i
$71$	9.67205	−	9.29013i	1.14786	−	1.10254i	0.154442	−	0.988002i	$-0.450642\pi$
$71$	9.67205	−	9.29013i	1.14786	−	1.10254i	0.993419	−	0.114534i	$-0.0365376\pi$
$72$	−5.20251	−	4.24772i	−0.613122	−	0.500599i
$73$	7.47313	−	14.2389i	0.874663	−	1.66653i	0.137831	−	0.990456i	$-0.455987\pi$
$73$	7.47313	−	14.2389i	0.874663	−	1.66653i	0.736832	−	0.676076i	$-0.236321\pi$
$74$	0.440845	−	0.0716443i	0.0512472	−	0.00832848i
$75$	0.924020	−	0.584315i	0.106697	−	0.0674709i
$76$	−24.7926	+	11.7643i	−2.84391	+	1.34945i
$77$	−7.58913	+	10.9948i	−0.864862	+	1.25297i
$78$	−8.95839	+	2.38804i	−1.01434	+	0.270393i
$79$	5.90211	+	8.55068i	0.664039	+	0.962027i	0.999798	+	0.0200788i	$0.00639172\pi$
$79$	5.90211	+	8.55068i	0.664039	+	0.962027i	−0.335759	+	0.941948i	$0.608993\pi$
$80$	13.7732	+	7.95194i	1.53989	+	0.889054i
$81$	0.428693	+	0.903450i	0.0476325	+	0.100383i
$82$	21.2054	+	7.07940i	2.34174	+	0.781789i
$83$	−1.04882	+	4.25521i	−0.115122	+	0.467070i	0.884877	+	0.465825i	$0.154242\pi$
$83$	−1.04882	+	4.25521i	−0.115122	+	0.467070i	−0.999999	+	0.00124493i	$0.999604\pi$
$84$	14.2584	−	0.574594i	1.55572	−	0.0626933i
$85$	−1.89703	+	0.0764478i	−0.205762	+	0.00829193i
$86$	3.37645	−	13.6988i	0.364092	−	1.47718i
$87$	−2.57292	−	0.858968i	−0.275846	−	0.0920911i
$88$	−12.4319	−	26.1996i	−1.32524	−	2.79289i
$89$	11.1145	+	6.41695i	1.17813	+	0.680195i	0.955582	−	0.294726i	$-0.0952284\pi$
$89$	11.1145	+	6.41695i	1.17813	+	0.680195i	0.222551	+	0.974921i	$0.428562\pi$
$90$	−2.88715	−	4.18276i	−0.304333	−	0.440902i
$91$	6.16313	−	9.29904i	0.646072	−	0.974805i
$92$	−19.2979	+	27.9578i	−2.01194	+	2.91480i
$93$	2.48556	−	1.17941i	0.257741	−	0.122300i
$94$	0.0806342	−	0.0509900i	0.00831678	−	0.00525921i
$95$	−11.6086	+	1.88657i	−1.19101	+	0.193558i
$96$	−3.37267	+	6.42608i	−0.344221	+	0.655859i
$97$	3.66773	+	2.99461i	0.372401	+	0.304056i	0.800102	−	0.599864i	$-0.204779\pi$
$97$	3.66773	+	2.99461i	0.372401	+	0.304056i	−0.427701	+	0.903921i	$0.640676\pi$
$98$	−4.77264	+	4.58418i	−0.482110	+	0.463072i
$99$			4.31775i			0.433950i
$100$	−3.49280	−	3.63639i	−0.349280	−	0.363639i
$101$	3.31496	−	1.10670i	0.329851	−	0.110120i	−0.146919	−	0.989149i	$-0.546936\pi$
$101$	3.31496	−	1.10670i	0.329851	−	0.110120i	0.476770	+	0.879028i	$0.341807\pi$
$102$	−0.198747	−	2.46193i	−0.0196789	−	0.243767i
$103$	−14.9692	+	3.68957i	−1.47496	+	0.363544i	−0.893141	−	0.449776i	$-0.851504\pi$
$103$	−14.9692	+	3.68957i	−1.47496	+	0.363544i	−0.581816	+	0.813320i	$0.697658\pi$
$104$	10.7918	+	21.6785i	1.05823	+	2.12575i
$105$	5.93796	+	1.46357i	0.579485	+	0.142830i
$106$	4.63209	−	28.5024i	0.449909	−	2.76840i
$107$	−6.53415	−	8.00288i	−0.631680	−	0.773668i	0.355258	−	0.934768i	$-0.384393\pi$
$107$	−6.53415	−	8.00288i	−0.631680	−	0.773668i	−0.986938	+	0.161101i	$0.948496\pi$
$108$	3.68700	−	2.77060i	0.354782	−	0.266601i
$109$	−10.5073	+	11.8602i	−1.00641	+	1.13600i	−0.0157213	+	0.999876i	$0.505004\pi$
$109$	−10.5073	+	11.8602i	−1.00641	+	1.13600i	−0.990691	+	0.136128i	$0.956534\pi$
$110$	−3.52017	−	21.6605i	−0.335635	−	2.06525i
$111$	−0.0139764	+	0.173129i	−0.00132659	+	0.0164327i
$112$	−5.95805	−	24.1728i	−0.562983	−	2.28411i
$113$	0.0535349	+	0.184824i	0.00503614	+	0.0173868i	0.962997	−	0.269513i	$-0.0868626\pi$
$113$	0.0535349	+	0.184824i	0.00503614	+	0.0173868i	−0.957961	+	0.286899i	$0.907375\pi$
$114$	−3.06044	−	14.9910i	−0.286636	−	1.40404i
$115$	−11.2775	+	9.20778i	−1.05163	+	0.858630i
$116$	−1.50792	+	12.4188i	−0.140007	+	1.15306i
$117$	−0.0679670	−	3.60491i	−0.00628355	−	0.333274i
$118$	0.0513486	+	0.422894i	0.00472702	+	0.0389305i
$119$	2.14346	+	2.05882i	0.196490	+	0.188731i
$120$	−9.19602	+	9.57408i	−0.839478	+	0.873990i
$121$	−3.27647	+	6.90501i	−0.297861	+	0.627729i
$122$	−0.0108358	+	0.00747938i	−0.000981023	+	0.000677151i
$123$	−4.64672	+	7.34821i	−0.418981	+	0.662565i
$124$	−7.62245	−	10.1436i	−0.684516	−	0.910926i
$125$	−5.59695	−	10.6641i	−0.500606	−	0.953826i
$126$	−1.59143	+	7.79535i	−0.141776	+	0.694465i
$127$	−15.5006	+	1.25134i	−1.37546	+	0.111038i	−0.745974	−	0.665975i	$-0.768016\pi$
$127$	−15.5006	+	1.25134i	−1.37546	+	0.111038i	−0.629484	+	0.777013i	$0.716734\pi$
$128$	−7.59710	−	2.20053i	−0.671495	−	0.194501i
$129$	4.85837	+	2.54987i	0.427756	+	0.224504i
$130$	3.27998	+	18.0291i	0.287673	+	1.58125i
$131$	10.9112	−	5.72664i	0.953315	−	0.500339i	0.0850163	−	0.996380i	$-0.472906\pi$
$131$	10.9112	−	5.72664i	0.953315	−	0.500339i	0.868299	+	0.496041i	$0.165213\pi$
$132$	19.5109	−	3.98317i	1.69820	−	0.346691i
$133$	14.7183	+	11.0601i	1.27624	+	0.959029i
$134$	1.13993	+	28.2871i	0.0984751	+	2.44363i
$135$	1.84810	−	0.700893i	0.159059	−	0.0603232i
$136$	−6.19668	+	1.79489i	−0.531361	+	0.153910i
$137$	−3.65278	−	0.745721i	−0.312078	−	0.0637112i	0.0414337	−	0.999141i	$-0.486807\pi$
$137$	−3.65278	−	0.745721i	−0.312078	−	0.0637112i	−0.353512	+	0.935430i	$0.615013\pi$
$138$	−12.5598	−	14.1771i	−1.06916	−	1.20684i
$139$	7.77296	−	9.52014i	0.659294	−	0.807488i	−0.331416	−	0.943485i	$-0.607526\pi$
$139$	7.77296	−	9.52014i	0.659294	−	0.807488i	0.990709	+	0.135997i	$0.0434237\pi$
$140$	1.13571	−	28.1824i	0.0959851	−	2.38185i
$141$	0.0117491	+	0.0351928i	0.000989450	+	0.00296377i
$142$	25.8122	−	22.8676i	2.16611	−	1.91901i
$143$	6.40751	−	14.1881i	0.535823	−	1.18647i
$144$	−6.02274	−	5.33569i	−0.501895	−	0.444640i
$145$	−2.10150	+	4.93239i	−0.174520	+	0.409613i
$146$	20.6749	−	35.8100i	1.71107	−	2.96365i
$147$	−1.28679	−	2.22878i	−0.106132	−	0.183827i
$148$	0.795224	−	0.0965576i	0.0653670	−	0.00793699i
$149$	−8.44286	−	4.00619i	−0.691666	−	0.328200i	0.0502081	−	0.998739i	$-0.484012\pi$
$149$	−8.44286	−	4.00619i	−0.691666	−	0.328200i	−0.741874	+	0.670539i	$0.766063\pi$
$150$	2.43457	−	1.40560i	0.198782	−	0.114767i
$151$	8.73967	+	6.03256i	0.711224	+	0.490923i	0.867907	−	0.496726i	$-0.165465\pi$
$151$	8.73967	+	6.03256i	0.711224	+	0.490923i	−0.156683	+	0.987649i	$0.550080\pi$
$152$	−36.7657	+	15.6644i	−2.98209	+	1.27055i
$153$	0.948112	+	0.154083i	0.0766503	+	0.0124569i
$154$	−20.6371	+	27.4629i	−1.66298	+	2.21303i
$155$	−1.92829	−	5.08448i	−0.154884	−	0.408395i
$156$	−16.2270	+	3.63270i	−1.29920	+	0.290849i
$157$	−8.34993	+	22.0170i	−0.666397	+	1.75715i	−0.0132526	+	0.999912i	$0.504219\pi$
$157$	−8.34993	+	22.0170i	−0.666397	+	1.75715i	−0.653145	+	0.757233i	$0.726551\pi$
$158$	14.2789	+	22.5803i	1.13597	+	1.79639i
$159$	10.3313	+	4.40176i	0.819326	+	0.349082i
$160$	12.1238	+	7.66665i	0.958474	+	0.606102i
$161$	22.6248	+	2.74714i	1.78308	+	0.216505i
$162$	1.00789	+	2.36561i	0.0791875	+	0.185860i
$163$	−3.05574	+	9.15305i	−0.239344	+	0.716922i	0.758523	+	0.651646i	$0.225921\pi$
$163$	−3.05574	+	9.15305i	−0.239344	+	0.716922i	−0.997867	+	0.0652763i	$0.979207\pi$
$164$	37.4915	+	14.2186i	2.92759	+	1.11029i
$165$	8.50655	+	0.686720i	0.662234	+	0.0534610i
$166$	−3.13529	+	10.8243i	−0.243346	+	0.840127i
$167$	23.6670	+	0.953748i	1.83141	+	0.0738032i	0.931817	−	0.362929i	$-0.118223\pi$
$167$	23.6670	+	0.953748i	1.83141	+	0.0738032i	0.899591	+	0.436732i	$0.143864\pi$
$168$	20.7812			1.60330
$169$	−5.12633	+	11.9466i	−0.394333	+	0.918968i
$170$	−4.88194			−0.374428
$171$	5.94538	+	0.239591i	0.454655	+	0.0183220i
$172$	7.04035	−	24.3061i	0.536822	−	1.85332i
$173$	−0.377935	−	0.0305101i	−0.0287339	−	0.00231964i	0.0660913	−	0.997814i	$-0.478947\pi$
$173$	−0.377935	−	0.0305101i	−0.0287339	−	0.00231964i	−0.0948251	+	0.995494i	$0.530229\pi$
$174$	−6.52165	−	2.47333i	−0.494405	−	0.187503i
$175$	−1.07119	+	3.20862i	−0.0809747	+	0.242549i
$176$	−13.6177	−	31.9618i	−1.02647	−	2.40921i
$177$	−0.164462	−	0.0199693i	−0.0123617	−	0.00150099i
$178$	27.8919	+	17.6378i	2.09059	+	1.32201i
$179$	17.6924	+	7.53804i	1.32239	+	0.563419i	0.933736	−	0.357963i	$-0.116528\pi$
$179$	17.6924	+	7.53804i	1.32239	+	0.563419i	0.388658	+	0.921382i	$0.372939\pi$
$180$	−4.87206	−	7.70455i	−0.363142	−	0.574263i
$181$	−3.47727	+	9.16882i	−0.258464	+	0.681513i	0.741481	+	0.670974i	$0.234124\pi$
$181$	−3.47727	+	9.16882i	−0.258464	+	0.681513i	−0.999944	+	0.0105387i	$0.996645\pi$
$182$	16.7977	−	23.2538i	1.24513	−	1.72369i
$183$	−0.00181571	−	0.00478764i	−0.000134221	−	0.000353913i
$184$	−29.7198	+	39.5499i	−2.19097	+	2.91566i
$185$	0.338865	+	0.0550710i	0.0249139	+	0.00404890i
$186$	6.50824	−	2.77290i	0.477208	−	0.203319i
$187$	3.41326	+	2.35600i	0.249602	+	0.172288i
$188$	0.148189	−	0.0855570i	0.0108078	−	0.00623989i
$189$	−2.79538	−	1.32643i	−0.203334	−	0.0964833i
$190$	−30.0211	+	3.64522i	−2.17796	+	0.264452i
$191$	−9.32535	−	16.1520i	−0.674759	−	1.16872i	−0.976539	−	0.215339i	$-0.930914\pi$
$191$	−9.32535	−	16.1520i	−0.674759	−	1.16872i	0.301781	−	0.953377i	$-0.402419\pi$
$192$	−1.28440	+	2.22465i	−0.0926938	+	0.160550i
$193$	−0.341854	+	0.802360i	−0.0246072	+	0.0577552i	−0.931830	−	0.362896i	$-0.881788\pi$
$193$	−0.341854	+	0.802360i	−0.0246072	+	0.0577552i	0.907223	+	0.420651i	$0.138198\pi$
$194$	9.11339	+	8.07376i	0.654303	+	0.579662i
$195$	−7.11297	−	0.439442i	−0.509371	−	0.0314691i
$196$	−8.88424	+	7.87075i	−0.634589	+	0.562197i
$197$	2.79892	+	8.38380i	0.199415	+	0.597321i	0.999998	−	0.00190082i	$-0.000605051\pi$
$197$	2.79892	+	8.38380i	0.199415	+	0.597321i	−0.800583	+	0.599222i	$0.795477\pi$
$198$	−0.447054	+	11.0935i	−0.0317708	+	0.788384i
$199$	9.94296	−	12.1779i	0.704838	−	0.863269i	−0.290780	−	0.956790i	$-0.593915\pi$
$199$	9.94296	−	12.1779i	0.704838	−	0.863269i	0.995617	+	0.0935207i	$0.0298121\pi$
$200$	−4.86916	−	5.49614i	−0.344301	−	0.388636i
$201$	−10.7872	−	2.20222i	−0.760870	−	0.155333i
$202$	8.63168	−	2.50020i	0.607323	−	0.175913i
$203$	7.84746	−	2.97615i	0.550784	−	0.208885i
$204$	−0.178379	−	4.42644i	−0.0124890	−	0.309912i
$205$	13.7379	+	10.3234i	0.959498	+	0.721016i
$206$	−38.8422	+	7.92969i	−2.70626	+	0.552487i
$207$	6.52217	−	3.42310i	0.453322	−	0.237922i
$208$	11.8726	+	26.4707i	0.823216	+	1.83542i
$209$	22.7487	+	11.9394i	1.57356	+	0.825868i
$210$	15.1048	+	4.37516i	1.04233	+	0.301914i
$211$	−19.1071	+	1.54248i	−1.31539	+	0.106189i	−0.718157	−	0.695882i	$-0.755014\pi$
$211$	−19.1071	+	1.54248i	−1.31539	+	0.106189i	−0.597229	+	0.802070i	$0.703732\pi$
$212$	10.3597	−	50.7454i	0.711510	−	3.48521i
$213$	6.23241	+	11.8749i	0.427038	+	0.813652i
$214$	−15.9595	−	21.2382i	−1.09097	−	1.45182i
$215$	5.79630	−	9.16611i	0.395304	−	0.625123i
$216$	5.52744	−	3.81532i	0.376095	−	0.259600i
$217$	−3.64925	+	7.69063i	−0.247727	+	0.522074i
$218$	−28.2242	+	29.3845i	−1.91158	+	1.99017i
$219$	11.5975	+	11.1396i	0.783688	+	0.752742i
$220$	−4.74427	−	39.0726i	−0.319859	−	2.63427i
$221$	−2.88683	−	1.91331i	−0.194189	−	0.128703i
$222$	−0.0538351	+	0.443372i	−0.00361318	+	0.0297572i
$223$	21.6372	−	17.6662i	1.44894	−	1.18302i	0.500630	−	0.865662i	$-0.333102\pi$
$223$	21.6372	−	17.6662i	1.44894	−	1.18302i	0.948306	−	0.317358i	$-0.102796\pi$
$224$	−4.49161	−	22.0014i	−0.300108	−	1.47003i
$225$	0.304167	+	1.05010i	0.0202778	+	0.0700070i
$226$	0.118410	+	0.480409i	0.00787653	+	0.0319563i
$227$	0.924494	−	11.4519i	0.0613608	−	0.760090i	−0.890781	−	0.454433i	$-0.849842\pi$
$227$	0.924494	−	11.4519i	0.0613608	−	0.760090i	0.952142	−	0.305657i	$-0.0988762\pi$
$228$	−4.40203	−	27.0868i	−0.291532	−	1.79387i
$229$	−4.29201	+	4.84467i	−0.283624	+	0.320145i	−0.873006	−	0.487709i	$-0.837833\pi$
$229$	−4.29201	+	4.84467i	−0.283624	+	0.320145i	0.589382	+	0.807854i	$0.299371\pi$
$230$	−29.9285	+	22.4898i	−1.97342	+	1.48293i
$231$	−8.44923	−	10.3484i	−0.555919	−	0.680877i
$232$	−2.92241	+	17.9823i	−0.191865	+	1.18060i
$233$	13.7136	+	3.38010i	0.898409	+	0.221438i	0.661368	−	0.750062i	$-0.269976\pi$
$233$	13.7136	+	3.38010i	0.898409	+	0.221438i	0.237041	+	0.971500i	$0.423822\pi$
$234$	0.198621	−	9.26909i	0.0129843	−	0.605940i
$235$	0.0712032	−	0.0175500i	0.00464478	−	0.00114484i
$236$	0.0614817	+	0.761587i	0.00400212	+	0.0495751i
$237$	−9.85515	+	3.29013i	−0.640161	+	0.213717i
$238$	5.29399	+	5.51163i	0.343158	+	0.357266i
$239$		−	9.53842i		−	0.616989i	−0.951226	−	0.308495i	$-0.900175\pi$
$239$		−	9.53842i		−	0.616989i	0.951226	−	0.308495i	$-0.0998251\pi$
$240$	−11.4699	+	11.0170i	−0.740380	+	0.711145i
$241$	−18.1956	−	14.8562i	−1.17208	−	0.956973i	−0.172472	−	0.985014i	$-0.555175\pi$
$241$	−18.1956	−	14.8562i	−1.17208	−	0.956973i	−0.999607	+	0.0280418i	$0.991073\pi$
$242$	−9.13314	+	17.4017i	−0.587100	+	1.11863i
$243$	−0.987050	+	0.160411i	−0.0633193	+	0.0102904i
$244$	−0.0199592	+	0.0126214i	−0.00127776	+	0.000808004i
$245$	−4.59565	+	2.18066i	−0.293606	+	0.139318i
$246$	−12.6996	+	18.3986i	−0.809697	+	1.17305i
$247$	−19.1809	−	9.61020i	−1.22045	−	0.611483i
$248$	−10.4967	−	15.2070i	−0.666539	−	0.965648i
$249$	−3.79541	−	2.19128i	−0.240524	−	0.138867i
$250$	−13.2760	−	27.9787i	−0.839650	−	1.76953i
$251$	−12.9410	−	4.32034i	−0.816828	−	0.272697i	−0.122604	−	0.992456i	$-0.539124\pi$
$251$	−12.9410	−	4.32034i	−0.816828	−	0.272697i	−0.694225	+	0.719758i	$0.744253\pi$
$252$	−3.41503	+	13.8553i	−0.215127	+	0.872803i
$253$	31.7782	−	1.28062i	1.99788	−	0.0805118i
$254$	−39.9552	+	1.61014i	−2.50701	+	0.101029i
$255$	0.454358	−	1.84340i	0.0284530	−	0.115438i
$256$	−24.1645	−	8.06730i	−1.51028	−	0.504206i
$257$	1.62244	+	3.41923i	0.101205	+	0.213286i	0.947737	−	0.319053i	$-0.103365\pi$
$257$	1.62244	+	3.41923i	0.101205	+	0.213286i	−0.846532	+	0.532338i	$0.821313\pi$
$258$	12.2186	+	7.05439i	0.760694	+	0.439187i
$259$	−0.305292	−	0.442292i	−0.0189699	−	0.0274827i
$260$	4.57607	+	32.5472i	0.283796	+	2.01849i
$261$	1.54089	−	2.23236i	0.0953785	−	0.138180i
$262$	28.6269	−	13.5837i	1.76858	−	0.839201i
$263$	−7.93564	+	5.01819i	−0.489332	+	0.309435i	−0.756248	−	0.654285i	$-0.772970\pi$
$263$	−7.93564	+	5.01819i	−0.489332	+	0.309435i	0.266916	+	0.963720i	$0.413995\pi$
$264$	28.6239	−	4.65184i	1.76168	−	0.286301i
$265$	10.3152	−	19.6540i	0.633658	−	1.20734i
$266$	36.6703	+	29.9404i	2.24840	+	1.83576i
$267$	−9.25584	+	8.89035i	−0.566448	+	0.544081i
$268$			50.7764i			3.10166i
$269$	−13.9836	−	14.5585i	−0.852596	−	0.887647i	0.142168	−	0.989843i	$-0.454593\pi$
$269$	−13.9836	−	14.5585i	−0.852596	−	0.887647i	−0.994764	+	0.102196i	$0.967413\pi$
$270$	4.82088	−	1.60945i	0.293389	−	0.0979477i
$271$	1.31455	+	16.2836i	0.0798533	+	0.989160i	0.905326	+	0.424718i	$0.139627\pi$
$271$	1.31455	+	16.2836i	0.0798533	+	0.989160i	−0.825472	+	0.564442i	$0.809091\pi$
$272$	−7.50430	+	1.84964i	−0.455015	+	0.112151i
$273$	7.21721	+	8.50696i	0.436805	+	0.514865i
$274$	−9.30784	−	2.29418i	−0.562307	−	0.138596i
$275$	−0.757215	+	4.65933i	−0.0456618	+	0.280968i
$276$	−21.4849	−	26.3143i	−1.29324	−	1.58393i
$277$	1.42424	−	1.07025i	0.0855746	−	0.0643051i	−0.557094	−	0.830449i	$-0.688084\pi$
$277$	1.42424	−	1.07025i	0.0855746	−	0.0643051i	0.642669	+	0.766144i	$0.277827\pi$
$278$	20.9567	−	23.6552i	1.25690	−	1.41874i
$279$	0.441322	+	2.71556i	0.0264212	+	0.162576i
$280$	3.30516	−	40.9417i	0.197521	−	2.44674i
$281$	−0.658602	−	2.67205i	−0.0392889	−	0.159401i	0.948021	−	0.318209i	$-0.103081\pi$
$281$	−0.658602	−	2.67205i	−0.0392889	−	0.159401i	−0.987310	+	0.158807i	$0.949235\pi$
$282$	0.0265429	+	0.0916369i	0.00158061	+	0.00545690i
$283$	4.51758	+	22.1285i	0.268542	+	1.31541i	0.860506	+	0.509441i	$0.170148\pi$
$283$	4.51758	+	22.1285i	0.268542	+	1.31541i	−0.591964	+	0.805965i	$0.701647\pi$
$284$	47.9102	−	39.1175i	2.84295	−	2.32119i
$285$	1.41761	−	11.6751i	0.0839722	−	0.691574i
$286$	17.9318	−	35.7899i	1.06033	−	2.11630i
$287$	−3.24252	−	26.7046i	−0.191400	−	1.57632i
$288$	−5.23403	−	5.02736i	−0.308418	−	0.296240i
$289$	−11.1372	+	11.5950i	−0.655127	+	0.682060i
$290$	−5.91005	+	12.4552i	−0.347050	+	0.731392i
$291$	−3.89680	+	2.68977i	−0.228434	+	0.157677i
$292$	39.6382	−	62.6828i	2.31965	−	3.66823i
$293$	8.31677	+	11.0676i	0.485871	+	0.646577i	0.974094	−	0.226142i	$-0.0726112\pi$
$293$	8.31677	+	11.0676i	0.485871	+	0.646577i	−0.488223	+	0.872719i	$0.662355\pi$
$294$	−3.07536	−	5.85961i	−0.179359	−	0.341739i
$295$	−0.0654993	+	0.320837i	−0.00381352	+	0.0186798i
$296$	1.16280	−	0.0938706i	0.0675861	−	0.00545612i
$297$	−4.14727	−	1.20127i	−0.240649	−	0.0697049i
$298$	−21.2774	−	11.1672i	−1.23256	−	0.646899i
$299$	−26.5117	+	1.56943i	−1.53321	+	0.0907623i
$300$	4.46458	−	2.34319i	0.257762	−	0.135284i
$301$	−16.6339	+	3.39584i	−0.958762	+	0.195733i
$302$	21.8301	+	16.4043i	1.25618	+	0.943960i
$303$	0.140722	+	3.49198i	0.00808427	+	0.200609i
$304$	−44.7659	+	16.9775i	−2.56750	+	0.973725i
$305$	−0.00972109	+	0.00281575i	−0.000556628	+	0.000161229i
$306$	2.42002	+	0.494051i	0.138343	+	0.0282430i
$307$	−10.3923	−	11.7305i	−0.593119	−	0.669493i	0.372928	−	0.927860i	$-0.378354\pi$
$307$	−10.3923	−	11.7305i	−0.593119	−	0.669493i	−0.966047	+	0.258367i	$0.916816\pi$
$308$	−38.9676	+	47.7266i	−2.22038	+	2.71948i
$309$	0.620787	−	15.4047i	0.0353153	−	0.876341i
$310$	−4.42789	−	13.2631i	−0.251487	−	0.753296i
$311$	10.2706	−	9.09894i	0.582391	−	0.515953i	−0.319689	−	0.947523i	$-0.603578\pi$
$311$	10.2706	−	9.09894i	0.582391	−	0.515953i	0.902080	+	0.431569i	$0.142040\pi$
$312$	−23.8251	+	4.33443i	−1.34883	+	0.245389i
$313$	−6.65227	−	5.89340i	−0.376009	−	0.333115i	0.453860	−	0.891073i	$-0.350047\pi$
$313$	−6.65227	−	5.89340i	−0.376009	−	0.333115i	−0.829869	+	0.557958i	$0.811585\pi$
$314$	−23.7330	+	55.7034i	−1.33933	+	3.14353i
$315$	−3.05783	+	5.29632i	−0.172289	+	0.298414i
$316$	23.9588	+	41.4979i	1.34779	+	2.33444i
$317$	15.6683	−	1.90247i	0.880017	−	0.106853i	0.331959	−	0.943294i	$-0.392290\pi$
$317$	15.6683	−	1.90247i	0.880017	−	0.106853i	0.548058	+	0.836440i	$0.315367\pi$
$318$	26.0884	+	12.3791i	1.46296	+	0.694184i
$319$	10.1429	−	5.85599i	0.567891	−	0.327872i
$320$	4.17859	+	2.88427i	0.233590	+	0.161236i
$321$	9.50482	−	4.04963i	0.530508	−	0.226028i
$322$	57.8451	+	9.40074i	3.22358	+	0.523883i
$323$	3.43353	−	4.56920i	0.191047	−	0.254237i
$324$	1.63543	+	4.31226i	0.0908570	+	0.239570i
$325$	0.558859	−	3.90202i	0.0309999	−	0.216445i
$326$	−8.79877	+	23.2004i	−0.487319	+	1.28495i
$327$	−8.46867	−	13.3921i	−0.468319	−	0.740587i
$328$	53.7202	+	22.8881i	2.96620	+	1.26378i
$329$	−0.0970266	−	0.0613559i	−0.00534925	−	0.00338266i
$330$	21.7847	+	2.64514i	1.19921	+	0.145610i
$331$	3.32772	+	7.81045i	0.182908	+	0.429301i	0.986042	−	0.166498i	$-0.0532458\pi$
$331$	3.32772	+	7.81045i	0.182908	+	0.429301i	−0.803134	+	0.595799i	$0.796836\pi$
$332$	−6.40056	+	19.1720i	−0.351277	+	1.05220i
$333$	−0.162405	−	0.0615922i	−0.00889976	−	0.00337523i
$334$	60.7086	+	4.90091i	3.32183	+	0.268166i
$335$	−6.05434	+	20.9020i	−0.330784	+	1.14200i
$336$	24.8760	+	1.00247i	1.35710	+	0.0546892i
$337$	−6.51659			−0.354981			−0.177491	−	0.984123i	$-0.556798\pi$
$337$	−6.51659			−0.354981			−0.177491	+	0.984123i	$0.556798\pi$
$338$	−14.4079	+	30.1634i	−0.783689	+	1.64068i
$339$	−0.192421			−0.0104509
$340$	−8.74905	−	0.352575i	−0.474484	−	0.0191210i
$341$	−3.30493	+	11.4099i	−0.178972	+	0.617882i
$342$	15.2506	+	1.23116i	0.824658	+	0.0665733i
$343$	−12.8059	−	4.85663i	−0.691453	−	0.262233i
$344$	11.6697	−	34.9551i	0.629190	−	1.88465i
$345$	−5.70664	−	13.3940i	−0.307235	−	0.721108i
$346$	−0.967866	−	0.117520i	−0.0520328	−	0.00631792i
$347$	14.4862	+	9.16049i	0.777657	+	0.491761i	0.863378	−	0.504558i	$-0.168345\pi$
$347$	14.4862	+	9.16049i	0.777657	+	0.491761i	−0.0857200	+	0.996319i	$0.527319\pi$
$348$	−11.5090	−	4.90352i	−0.616947	−	0.262856i
$349$	0.276097	+	0.436612i	0.0147791	+	0.0233713i	0.852499	−	0.522729i	$-0.175086\pi$
$349$	0.276097	+	0.436612i	0.0147791	+	0.0233713i	−0.837720	+	0.546100i	$0.816112\pi$
$350$	−3.08442	+	8.13296i	−0.164869	+	0.434725i
$351$	3.48149	+	0.937666i	0.185828	+	0.0500489i
$352$	−11.1117	−	29.2992i	−0.592256	−	1.56165i
$353$	−16.8469	+	22.4192i	−0.896672	+	1.19325i	0.0837774	+	0.996484i	$0.473302\pi$
$353$	−16.8469	+	22.4192i	−0.896672	+	1.19325i	−0.980450	+	0.196770i	$0.936955\pi$
$354$	−0.420483	−	0.0683352i	−0.0223484	−	0.00363197i
$355$	24.3863	−	10.3900i	1.29429	−	0.551446i
$356$	48.7120	+	33.6235i	2.58173	+	1.78204i
$357$	−2.57388	+	1.48603i	−0.136224	+	0.0786490i
$358$	44.6765	+	21.1993i	2.36123	+	1.12042i
$359$	−15.2900	+	1.85654i	−0.806975	+	0.0979845i	−0.513618	−	0.858019i	$-0.671695\pi$
$359$	−15.2900	+	1.85654i	−0.806975	+	0.0979845i	−0.293356	+	0.956003i	$0.594772\pi$
$360$	−6.63758	−	11.4966i	−0.349831	−	0.605925i
$361$	8.20249	−	14.2071i	0.431710	−	0.747744i
$362$	−9.88345	+	23.1973i	−0.519463	+	1.21922i
$363$	−5.72082	−	5.06820i	−0.300265	−	0.266012i
$364$	31.7830	−	40.4606i	1.66588	−	2.12071i
$365$	23.7910	−	21.0770i	1.24528	−	1.10322i
$366$	−0.00416939	−	0.0124888i	−0.000217937	−	0.000652802i
$367$	−0.693578	+	17.2110i	−0.0362045	+	0.898405i	0.874420	+	0.485170i	$0.161242\pi$
$367$	−0.693578	+	17.2110i	−0.0362045	+	0.898405i	−0.910624	+	0.413235i	$0.864399\pi$
$368$	−37.4839	+	45.9094i	−1.95398	+	2.39319i
$369$	−5.76529	−	6.50766i	−0.300129	−	0.338775i
$370$	0.864941	+	0.176579i	0.0449662	+	0.00917991i
$371$	−33.3749	+	9.66715i	−1.73274	+	0.501893i
$372$	11.8638	−	4.49936i	0.615112	−	0.233281i
$373$	0.0109238	+	0.271071i	0.000565612	+	0.0140355i	0.999447	−	0.0332472i	$-0.0105849\pi$
$373$	0.0109238	+	0.271071i	0.000565612	+	0.0140355i	−0.998882	+	0.0472827i	$0.984944\pi$
$374$	8.52570	+	6.40665i	0.440854	+	0.331280i
$375$	11.8002	−	2.40903i	0.609361	−	0.124402i
$376$	0.220648	−	0.115805i	0.0113790	−	0.00597218i
$377$	−8.37615	+	5.04886i	−0.431394	+	0.260029i
$378$	−7.04481	−	3.69740i	−0.362346	−	0.190174i
$379$	−35.2055	−	10.1974i	−1.80839	−	0.523805i	−0.810320	−	0.585987i	$-0.800707\pi$
$379$	−35.2055	−	10.1974i	−1.80839	−	0.523805i	−0.998065	+	0.0621821i	$0.980194\pi$
$380$	−54.0648	+	4.36456i	−2.77347	+	0.223897i
$381$	3.11061	−	15.2368i	0.159361	−	0.780604i
$382$	−22.2872	−	42.4646i	−1.14031	−	2.17268i
$383$	4.12280	+	5.48646i	0.210665	+	0.280345i	0.892391	−	0.451263i	$-0.149027\pi$
$383$	4.12280	+	5.48646i	0.210665	+	0.280345i	−0.681725	+	0.731608i	$0.738770\pi$
$384$	4.22729	−	6.68492i	0.215723	−	0.341139i
$385$	−21.7316	+	15.0003i	−1.10755	+	0.764484i
$386$	−0.961396	+	2.02610i	−0.0489338	+	0.103126i
$387$	−3.80088	+	3.95714i	−0.193210	+	0.201153i
$388$	15.7493	+	15.1274i	0.799547	+	0.767976i
$389$	−0.880473	−	7.25135i	−0.0446418	−	0.367658i	−0.997861	−	0.0653771i	$-0.979175\pi$
$389$	−0.880473	−	7.25135i	−0.0446418	−	0.367658i	0.953219	−	0.302281i	$-0.0977481\pi$
$390$	−18.2298	−	1.86552i	−0.923101	−	0.0944644i
$391$	0.852834	−	7.02372i	0.0431297	−	0.355205i
$392$	−13.3890	+	10.9318i	−0.676249	+	0.552140i
$393$	2.46485	+	12.0736i	0.124335	+	0.609035i
$394$	6.32319	+	21.8302i	0.318558	+	1.09979i
$395$	4.91459	+	19.9393i	0.247280	+	1.00325i
$396$	−1.60236	+	19.8487i	−0.0805214	+	0.997436i
$397$	2.37559	+	14.6176i	0.119227	+	0.733634i	0.975972	+	0.217894i	$0.0699188\pi$
$397$	2.37559	+	14.6176i	0.119227	+	0.733634i	−0.856745	+	0.515740i	$0.827517\pi$
$398$	26.8072	−	30.2591i	1.34372	−	1.51675i
$399$	−14.7183	+	11.0601i	−0.736835	+	0.553695i
$400$	−5.56348	−	6.81402i	−0.278174	−	0.340701i
$401$	4.95977	−	30.5187i	0.247679	−	1.52403i	−0.503537	−	0.863974i	$-0.667968\pi$
$401$	4.95977	−	30.5187i	0.247679	−	1.52403i	0.751216	−	0.660056i	$-0.229468\pi$
$402$	−27.4874	−	6.77504i	−1.37095	−	0.337908i
$403$	2.57969	−	9.57824i	0.128504	−	0.477126i
$404$	15.6496	−	3.85728i	0.778597	−	0.191907i
$405$	0.159046	+	1.97014i	0.00790305	+	0.0978968i
$406$	20.4705	−	6.83407i	1.01594	−	0.339169i
$407$	−0.519516	−	0.540873i	−0.0257514	−	0.0268101i
$408$		−	6.45139i		−	0.319391i
$409$	20.1134	−	19.3191i	0.994542	−	0.955270i	−0.00445793	−	0.999990i	$-0.501419\pi$
$409$	20.1134	−	19.3191i	0.994542	−	0.955270i	0.999000	+	0.0447199i	$0.0142395\pi$
$410$	34.2278	+	27.9462i	1.69039	+	1.38016i
$411$	1.73255	−	3.30109i	0.0854602	−	0.162831i
$412$	−70.1827	+	11.4058i	−3.45766	+	0.561924i
$413$	0.433247	−	0.273969i	0.0213187	−	0.0134811i
$414$	17.1118	−	8.11963i	0.840997	−	0.399058i
$415$	−4.92076	+	7.12896i	−0.241551	+	0.349947i
$416$	9.73844	+	24.2871i	0.477466	+	1.19077i
$417$	6.98170	+	10.1147i	0.341895	+	0.495321i
$418$	57.2118	+	33.0312i	2.79832	+	1.61561i
$419$	−2.52689	−	5.32532i	−0.123447	−	0.260159i	0.832314	−	0.554305i	$-0.187016\pi$
$419$	−2.52689	−	5.32532i	−0.123447	−	0.260159i	−0.955760	+	0.294146i	$0.904965\pi$
$420$	26.7537	+	8.93170i	1.30545	+	0.435822i
$421$	5.45639	−	22.1374i	0.265928	−	1.07891i	−0.674324	−	0.738435i	$-0.735565\pi$
$421$	5.45639	−	22.1374i	0.265928	−	1.07891i	0.940253	−	0.340478i	$-0.110589\pi$
$422$	−49.2513	+	1.98476i	−2.39752	+	0.0966166i
$423$	−0.0370721	+	0.00149395i	−0.00180251	+	7.26385e-5i
$424$	18.0502	−	73.2324i	0.876593	−	3.55648i
$425$	0.996097	+	0.332546i	0.0483178	+	0.0161308i
$426$	14.7833	+	31.1552i	0.716256	+	1.50948i
$427$	0.0137205	+	0.00792154i	0.000663982	+	0.000383350i
$428$	−27.0676	−	39.2142i	−1.30836	−	1.89549i
$429$	11.8452	+	10.1019i	0.571894	+	0.487724i
$430$	15.8414	−	22.9502i	0.763940	−	1.10676i
$431$	29.9507	−	14.2118i	1.44267	−	0.684558i	0.463224	−	0.886241i	$-0.346693\pi$
$431$	29.9507	−	14.2118i	1.44267	−	0.684558i	0.979451	+	0.201684i	$0.0646413\pi$
$432$	6.80065	−	4.30047i	0.327197	−	0.206907i
$433$	2.67646	−	0.434968i	0.128623	−	0.0209032i	−0.0957591	−	0.995405i	$-0.530528\pi$
$433$	2.67646	−	0.434968i	0.128623	−	0.0209032i	0.224382	+	0.974501i	$0.427964\pi$
$434$	−10.1722	+	19.3816i	−0.488284	+	0.930347i
$435$	−4.15298	−	3.39080i	−0.199120	−	0.162577i
$436$	−52.7034	+	50.6223i	−2.52404	+	2.42437i
$437$		−	43.8286i		−	2.09660i
$438$	28.6440	+	29.8216i	1.36866	+	1.42493i
$439$	−9.85360	+	3.28962i	−0.470287	+	0.157005i	−0.541927	−	0.840426i	$-0.682305\pi$
$439$	−9.85360	+	3.28962i	−0.470287	+	0.157005i	0.0716399	+	0.997431i	$0.477177\pi$
$440$	−4.61224	−	57.1329i	−0.219880	−	2.72370i
$441$	2.49879	−	0.615896i	0.118990	−	0.0293284i
$442$	−7.21901	−	5.21474i	−0.343373	−	0.248040i
$443$	−20.2706	−	4.99625i	−0.963084	−	0.237379i	−0.273732	−	0.961806i	$-0.588258\pi$
$443$	−20.2706	−	4.99625i	−0.963084	−	0.237379i	−0.689351	+	0.724427i	$0.742104\pi$
$444$	−0.128500	+	0.790691i	−0.00609833	+	0.0375245i
$445$	16.0431	+	19.6492i	0.760516	+	0.931463i
$446$	57.4214	−	43.1494i	2.71898	−	2.04318i
$447$	6.19697	−	6.99493i	0.293106	−	0.330849i
$448$	−1.27498	−	7.84526i	−0.0602371	−	0.370654i
$449$	0.696327	−	8.62556i	0.0328617	−	0.407065i	−0.959325	−	0.282304i	$-0.908901\pi$
$449$	0.696327	−	8.62556i	0.0328617	−	0.407065i	0.992187	−	0.124762i	$-0.0398166\pi$
$450$	0.672765	+	2.72952i	0.0317145	+	0.128671i
$451$	−10.4440	−	36.0570i	−0.491791	−	1.69786i
$452$	0.177511	+	0.869505i	0.00834940	+	0.0408981i
$453$	−8.22591	+	6.71625i	−0.386487	+	0.315557i
$454$	3.56101	−	29.3276i	0.167127	−	1.37641i
$455$	17.9077	−	12.8659i	0.839527	−	0.603162i
$456$	−4.81709	−	39.6723i	−0.225581	−	1.85782i
$457$	−12.3909	−	11.9016i	−0.579620	−	0.556732i	0.344524	−	0.938778i	$-0.388040\pi$
$457$	−12.3909	−	11.9016i	−0.579620	−	0.556732i	−0.924144	+	0.382045i	$0.875220\pi$
$458$	−11.5290	+	12.0030i	−0.538716	+	0.560862i
$459$	−0.411781	+	0.867810i	−0.0192203	+	0.0405059i
$460$	−55.2598	+	38.1431i	−2.57650	+	1.77843i
$461$	−11.8236	+	18.6975i	−0.550679	+	0.870829i	−0.999743	−	0.0226709i	$-0.992783\pi$
$461$	−11.8236	+	18.6975i	−0.550679	+	0.870829i	0.449064	+	0.893499i	$0.351757\pi$
$462$	−20.6371	−	27.4629i	−0.960123	−	1.27769i
$463$	13.2026	+	25.1554i	0.613577	+	1.16907i	0.971882	+	0.235468i	$0.0756624\pi$
$463$	13.2026	+	25.1554i	0.613577	+	1.16907i	−0.358305	+	0.933604i	$0.616645\pi$
$464$	−4.36571	+	21.3847i	−0.202673	+	0.992758i
$465$	5.42021	−	0.437565i	0.251356	−	0.0202916i
$466$	34.8843	+	10.1044i	1.61598	+	0.468075i
$467$	−7.44657	−	3.90826i	−0.344586	−	0.180853i	0.283548	−	0.958958i	$-0.408489\pi$
$467$	−7.44657	−	3.90826i	−0.344586	−	0.180853i	−0.628134	+	0.778105i	$0.716181\pi$
$468$	1.02537	−	16.5970i	0.0473978	−	0.767198i
$469$	30.1633	−	15.8309i	1.39281	−	0.731005i
$470$	0.184759	−	0.0377188i	0.00852228	−	0.00173984i
$471$	−18.8246	−	14.1458i	−0.867392	−	0.651803i
$472$	0.0448038	+	1.11179i	0.00206226	+	0.0511745i
$473$	−22.1513	+	8.40090i	−1.01852	+	0.386274i
$474$	−25.6614	+	7.43291i	−1.17867	+	0.341405i
$475$	6.37371	+	1.30120i	0.292446	+	0.0597033i
$476$	9.08945	+	10.2599i	0.416614	+	0.470260i
$477$	−7.10232	+	8.69876i	−0.325193	+	0.398289i
$478$	0.987597	−	24.5070i	0.0451716	−	1.12092i
$479$	13.0517	+	39.0945i	0.596345	+	1.78627i	0.617593	+	0.786498i	$0.288108\pi$
$479$	13.0517	+	39.0945i	0.596345	+	1.78627i	−0.0212483	+	0.999774i	$0.506764\pi$
$480$	−10.7370	+	9.51217i	−0.490076	+	0.434169i
$481$	0.442261	+	0.443400i	0.0201654	+	0.0202173i
$482$	−45.2114	−	40.0538i	−2.05932	−	1.82440i
$483$	−8.93328	+	20.9672i	−0.406478	+	0.954040i
$484$	−17.6245	+	30.5265i	−0.801113	+	1.38757i
$485$	4.67944	+	8.10502i	0.212482	+	0.368030i
$486$	−2.55263	+	0.309945i	−0.115789	+	0.0140594i
$487$	0.778090	+	0.369208i	0.0352586	+	0.0167304i	0.446240	−	0.894913i	$-0.352763\pi$
$487$	0.778090	+	0.369208i	0.0352586	+	0.0167304i	−0.410982	+	0.911644i	$0.634814\pi$
$488$	−0.0297828	+	0.0171951i	−0.00134821	+	0.000778387i
$489$	−7.94151	−	5.48163i	−0.359127	−	0.247888i
$490$	−12.0333	+	5.12693i	−0.543611	+	0.231611i
$491$	12.1778	+	1.97908i	0.549575	+	0.0893146i	0.428857	−	0.903372i	$-0.358916\pi$
$491$	12.1778	+	1.97908i	0.549575	+	0.0893146i	0.120718	+	0.992687i	$0.461480\pi$
$492$	−24.0880	+	32.0553i	−1.08597	+	1.44517i
$493$	−0.923928	−	2.43620i	−0.0416116	−	0.109721i
$494$	−48.2864	−	26.6774i	−2.17251	−	1.20027i
$495$	−3.02628	+	7.97964i	−0.136021	+	0.358658i
$496$	−11.8314	−	18.7099i	−0.531246	−	0.840099i
$497$	−38.1748	−	16.2648i	−1.71237	−	0.729574i
$498$	−9.52462	−	6.02300i	−0.426808	−	0.269897i
$499$	18.0030	+	2.18595i	0.805923	+	0.0978567i	0.513121	−	0.858316i	$-0.328489\pi$
$499$	18.0030	+	2.18595i	0.805923	+	0.0978567i	0.292802	+	0.956173i	$0.405412\pi$
$500$	−21.7717	−	51.1001i	−0.973660	−	2.28526i
$501$	−7.50067	+	22.4672i	−0.335105	+	1.00376i
$502$	−32.8018	−	12.4401i	−1.46402	−	0.555229i
$503$	9.03832	+	0.729649i	0.402999	+	0.0325334i	0.280305	−	0.959911i	$-0.409565\pi$
$503$	9.03832	+	0.729649i	0.402999	+	0.0325334i	0.122694	+	0.992445i	$0.460847\pi$
$504$	−5.78168	+	19.9607i	−0.257537	+	0.889120i
$505$	6.90206	+	0.278143i	0.307138	+	0.0123772i
$506$	81.7801			3.63557
$507$	−10.0487	−	8.24768i	−0.446277	−	0.366292i
$508$	−71.7209			−3.18210
$509$	−32.9095	−	1.32621i	−1.45869	−	0.0587831i	−0.701822	−	0.712353i	$-0.747630\pi$
$509$	−32.9095	−	1.32621i	−1.45869	−	0.0587831i	−0.756867	+	0.653569i	$0.773271\pi$
$510$	1.35824	−	4.68919i	0.0601439	−	0.207641i
$511$	−49.5946	−	4.00369i	−2.19394	−	0.177113i
$512$	−46.4595	−	17.6198i	−2.05324	−	0.778692i
$513$	−1.88424	+	5.64399i	−0.0831913	+	0.249188i
$514$	3.81450	+	8.95297i	0.168251	+	0.394899i
$515$	−30.2506	−	3.67308i	−1.33300	−	0.161855i
$516$	21.3877	+	13.5248i	0.941542	+	0.595395i
$517$	−0.147379	−	0.0627922i	−0.00648171	−	0.00276160i
$518$	−0.738590	−	1.16799i	−0.0324518	−	0.0513184i
$519$	0.134454	−	0.354525i	0.00590186	−	0.0155619i
$520$	4.75014	+	47.6280i	0.208307	+	2.08862i
$521$	2.44706	+	6.45238i	0.107208	+	0.282684i	0.977875	−	0.209188i	$-0.0670821\pi$
$521$	2.44706	+	6.45238i	0.107208	+	0.282684i	−0.870668	+	0.491872i	$0.836313\pi$
$522$	4.19012	−	5.57604i	0.183397	−	0.244056i
$523$	−7.90061	−	1.28397i	−0.345470	−	0.0561443i	−0.0147989	−	0.999890i	$-0.504711\pi$
$523$	−7.90061	−	1.28397i	−0.345470	−	0.0561443i	−0.330671	+	0.943746i	$0.607275\pi$
$524$	52.2841	−	22.2762i	2.28404	−	0.973139i
$525$	−2.78391	−	1.92160i	−0.121500	−	0.0838653i
$526$	−20.9085	+	12.0715i	−0.911655	+	0.526344i
$527$	2.38751	+	1.13289i	0.104002	+	0.0493493i
$528$	34.4886	−	4.18767i	1.50092	−	0.182245i
$529$	−15.6281	−	27.0687i	−0.679484	−	1.17690i
$530$	28.5377	−	49.4288i	1.23960	−	2.14705i
$531$	0.0649371	−	0.152413i	0.00281803	−	0.00661416i
$532$	63.5555	+	56.3053i	2.75548	+	2.44114i
$533$	9.28737	+	29.9398i	0.402281	+	1.29684i
$534$	−24.7014	+	21.8835i	−1.06893	+	0.946993i
$535$	−6.46661	−	19.3699i	−0.279576	−	0.837433i
$536$	−2.97746	+	73.8850i	−0.128607	+	3.19134i
$537$	−12.1628	+	14.8967i	−0.524862	+	0.642839i
$538$	−34.4206	−	38.8528i	−1.48398	−	1.67506i
$539$	10.8875	+	2.22269i	0.468956	+	0.0957381i
$540$	8.75585	−	2.53616i	0.376792	−	0.109139i
$541$	−17.6943	+	6.71056i	−0.760737	+	0.288509i	−0.704305	−	0.709897i	$-0.748741\pi$
$541$	−17.6943	+	6.71056i	−0.760737	+	0.288509i	−0.0564312	+	0.998406i	$0.517972\pi$
$542$	1.69147	+	41.9735i	0.0726550	+	1.80291i
$543$	−7.83938	−	5.89091i	−0.336420	−	0.252803i
$544$	−6.83019	+	1.39439i	−0.292842	+	0.0597841i
$545$	−27.7312	+	14.5545i	−1.18788	+	0.623445i
$546$	17.6623	+	22.6041i	0.755876	+	0.967366i
$547$	−10.6065	−	5.56673i	−0.453502	−	0.238016i	0.222476	−	0.974938i	$-0.428586\pi$
$547$	−10.6065	−	5.56673i	−0.453502	−	0.238016i	−0.675978	+	0.736922i	$0.736279\pi$
$548$	−16.5151	−	4.78367i	−0.705492	−	0.204348i
$549$	0.00510378		0.000412020i	0.000217824		1.75846e-5i
$550$	−2.42793	+	11.8928i	−0.103527	+	0.507109i
$551$	−7.50066	−	14.2913i	−0.319539	−	0.608830i
$552$	−29.7198	−	39.5499i	−1.26496	−	1.68336i
$553$	17.1817	−	27.1707i	0.730640	−	1.15542i
$554$	3.77011	−	2.60232i	0.160177	−	0.110562i
$555$	−0.147175	+	0.310165i	−0.00624723	+	0.0131658i
$556$	39.2654	−	40.8796i	1.66522	−	1.73368i
$557$	5.44988	+	5.23468i	0.230919	+	0.221801i	0.799249	−	0.601000i	$-0.205231\pi$
$557$	5.44988	+	5.23468i	0.230919	+	0.221801i	−0.568330	+	0.822801i	$0.692410\pi$
$558$	0.852717	+	7.02276i	0.0360984	+	0.297297i
$559$	18.3620	−	7.36265i	0.776632	−	0.311407i
$560$	5.93143	−	48.8497i	0.250649	−	2.06428i
$561$	−3.21261	+	2.62301i	−0.135636	+	0.110744i
$562$	−1.41548	−	6.93346i	−0.0597083	−	0.292471i
$563$	−0.184268	−	0.636166i	−0.00776596	−	0.0268112i	0.956542	−	0.291596i	$-0.0941863\pi$
$563$	−0.184268	−	0.636166i	−0.00776596	−	0.0268112i	−0.964308	+	0.264785i	$0.914699\pi$
$564$	0.0409503	+	0.166142i	0.00172432	+	0.00699583i
$565$	−0.0306038	+	0.379096i	−0.00128751	+	0.0159487i
$566$	9.31579	+	57.3224i	0.391572	+	2.40944i
$567$	2.05178	−	2.31598i	0.0861667	−	0.0972621i
$568$	72.0082	−	54.1106i	3.02140	−	2.27043i
$569$	−15.7182	−	19.2513i	−0.658941	−	0.807056i	0.331724	−	0.943376i	$-0.392370\pi$
$569$	−15.7182	−	19.2513i	−0.658941	−	0.807056i	−0.990665	+	0.136320i	$0.956472\pi$
$570$	4.85109	−	29.8499i	0.203190	−	1.25028i
$571$	−38.0958	−	9.38977i	−1.59426	−	0.392950i	−0.660493	−	0.750832i	$-0.729653\pi$
$571$	−38.0958	−	9.38977i	−1.59426	−	0.392950i	−0.933767	+	0.357883i	$0.883499\pi$
$572$	34.7207	−	62.8449i	1.45175	−	2.62768i
$573$	18.1087	−	4.46340i	0.756504	−	0.186461i
$574$	−5.56602	−	68.9475i	−0.232321	−	2.87781i
$575$	7.63846	−	2.55009i	0.318546	−	0.106346i
$576$	−1.77947	−	1.85263i	−0.0741448	−	0.0771929i
$577$		−	13.2724i		−	0.552539i	−0.961080	−	0.276270i	$-0.910902\pi$
$577$		−	13.2724i		−	0.552539i	0.961080	−	0.276270i	$-0.0890983\pi$
$578$	−29.8151	+	28.6378i	−1.24015	+	1.19118i
$579$	−0.675572	−	0.551587i	−0.0280758	−	0.0229232i
$580$	−11.4911	+	21.8944i	−0.477140	+	0.909115i
$581$	13.3846	−	2.17520i	0.555285	−	0.0902426i
$582$	−10.2905	+	6.50732i	−0.426555	+	0.269737i
$583$	−43.8065	+	20.7864i	−1.81428	+	0.860887i
$584$	61.3534	−	88.8858i	2.53882	−	3.67812i
$585$	2.40105	−	6.70988i	0.0992710	−	0.277419i
$586$	20.2223	+	29.2970i	0.835374	+	1.21025i
$587$	7.10854	+	4.10412i	0.293401	+	0.169395i	0.639475	−	0.768812i	$-0.279152\pi$
$587$	7.10854	+	4.10412i	0.293401	+	0.169395i	−0.346074	+	0.938207i	$0.612485\pi$
$588$	−5.08825	−	10.7233i	−0.209836	−	0.442220i
$589$	15.5277	+	5.18390i	0.639807	+	0.213599i
$590$	−0.201506	+	0.817541i	−0.00829586	+	0.0336576i
$591$	−8.83150	+	0.355897i	−0.363279	+	0.0146397i
$592$	1.39645	−	0.0562750i	0.0573937	−	0.00231289i
$593$	−10.6066	+	43.0328i	−0.435562	+	1.76714i	0.184746	+	0.982786i	$0.440854\pi$
$593$	−10.6066	+	43.0328i	−0.435562	+	1.76714i	−0.620308	+	0.784358i	$0.712993\pi$
$594$	−10.5312	−	3.51582i	−0.432099	−	0.144256i
$595$	2.51832	+	5.30724i	0.103241	+	0.217575i
$596$	−37.3252	−	21.5497i	−1.52890	−	0.882710i
$597$	8.93080	+	12.9385i	0.365513	+	0.529538i
$598$	−68.2786	+	1.28733i	−2.79212	+	0.0526426i
$599$	−21.6078	+	31.3042i	−0.882869	+	1.27906i	0.0765482	+	0.997066i	$0.475610\pi$
$599$	−21.6078	+	31.3042i	−0.882869	+	1.27906i	−0.959417	+	0.281991i	$0.909005\pi$
$600$	6.63383	−	3.14779i	0.270825	−	0.128508i
$601$	13.7304	−	8.68255i	0.560073	−	0.354169i	−0.224240	−	0.974534i	$-0.571990\pi$
$601$	13.7304	−	8.68255i	0.560073	−	0.354169i	0.784313	+	0.620365i	$0.213016\pi$
$602$	−43.0889	+	7.00263i	−1.75617	+	0.285406i
$603$	5.11646	−	9.74861i	0.208358	−	0.396994i
$604$	37.9376	+	30.9751i	1.54366	+	1.26036i
$605$	−10.8949	+	10.4647i	−0.442942	+	0.425451i
$606$			8.98648i			0.365051i
$607$	−0.893522	−	0.930255i	−0.0362670	−	0.0377579i	0.702822	−	0.711366i	$-0.251923\pi$
$607$	−0.893522	−	0.930255i	−0.0362670	−	0.0377579i	−0.739089	+	0.673608i	$0.764744\pi$
$608$	−40.9605	+	13.6746i	−1.66117	+	0.554579i
$609$	0.675344	+	8.36564i	0.0273663	+	0.338993i
$610$	−0.0252678	+	0.00622796i	−0.00102306	+	0.000252163i
$611$	0.124036	+	0.0501056i	0.00501795	+	0.00202706i
$612$	4.30130	+	1.06018i	0.173870	+	0.0428550i
$613$	−2.55562	+	15.7254i	−0.103221	+	0.635142i	0.882957	+	0.469453i	$0.155549\pi$
$613$	−2.55562	+	15.7254i	−0.103221	+	0.635142i	−0.986178	+	0.165689i	$0.947015\pi$
$614$	−25.4862	−	31.2150i	−1.02854	−	1.25973i
$615$	−13.7379	+	10.3234i	−0.553967	+	0.416279i
$616$	−59.5005	+	67.1622i	−2.39735	+	2.70604i
$617$	1.23126	+	7.57625i	0.0495687	+	0.305008i	0.999982	−	0.00598092i	$-0.00190380\pi$
$617$	1.23126	+	7.57625i	0.0495687	+	0.305008i	−0.950413	+	0.310989i	$0.899340\pi$
$618$	3.18996	−	39.5148i	0.128319	−	1.58952i
$619$	3.96871	+	16.1017i	0.159516	+	0.647181i	0.995191	+	0.0979567i	$0.0312307\pi$
$619$	3.96871	+	16.1017i	0.159516	+	0.647181i	−0.835675	+	0.549225i	$0.814923\pi$
$620$	−6.97746	−	24.0890i	−0.280222	−	0.967438i
$621$	1.47337	+	7.21703i	0.0591242	+	0.289609i
$622$	27.3302	−	22.3144i	1.09584	−	0.894726i
$623$	4.78646	−	39.4201i	0.191766	−	1.57933i
$624$	−28.7288	+	4.03921i	−1.15007	+	0.161698i
$625$	−2.21045	−	18.2047i	−0.0884181	−	0.728188i
$626$	−16.4814	−	15.8306i	−0.658730	−	0.632719i
$627$	−17.7971	+	18.5288i	−0.710749	+	0.739968i
$628$	−46.5554	+	98.1135i	−1.85776	+	3.91516i
$629$	−0.137307	+	0.0947762i	−0.00547479	+	0.00377898i
$630$	−8.40483	+	13.2912i	−0.334857	+	0.529533i
$631$	10.0749	+	13.4072i	0.401074	+	0.533732i	0.954122	−	0.299417i	$-0.0967921\pi$
$631$	10.0749	+	13.4072i	0.401074	+	0.533732i	−0.553049	+	0.833149i	$0.686536\pi$
$632$	32.4292	+	61.7887i	1.28997	+	2.45782i
$633$	3.83434	−	18.7818i	0.152401	−	0.746511i
$634$	40.4533	−	3.26573i	1.60660	−	0.129699i
$635$	−29.5238	−	8.55167i	−1.17162	−	0.339363i
$636$	45.8596	+	24.0690i	1.81845	+	0.954397i
$637$	−9.12499	−	1.68435i	−0.361545	−	0.0667366i
$638$	26.6663	−	13.9955i	1.05573	−	0.554089i
$639$	−13.1400	+	2.68255i	−0.519810	+	0.106120i
$640$	−12.4979	−	9.39154i	−0.494022	−	0.371233i
$641$	−1.17889	−	29.2538i	−0.0465632	−	1.15545i	−0.838518	−	0.544874i	$-0.816577\pi$
$641$	−1.17889	−	29.2538i	−0.0465632	−	1.15545i	0.791955	−	0.610580i	$-0.209064\pi$
$642$	24.8399	−	9.42054i	0.980354	−	0.371799i
$643$	32.3784	−	9.37850i	1.27688	−	0.369852i	0.430575	−	0.902555i	$-0.358311\pi$
$643$	32.3784	−	9.37850i	1.27688	−	0.369852i	0.846303	+	0.532703i	$0.178824\pi$
$644$	102.987	+	21.0249i	4.05825	+	0.828497i
$645$	7.19158	+	8.11762i	0.283168	+	0.319631i
$646$	9.29482	−	11.3841i	0.365700	−	0.447901i
$647$	1.33258	−	33.0677i	0.0523892	−	1.30003i	−0.732661	−	0.680594i	$-0.761722\pi$
$647$	1.33258	−	33.0677i	0.0523892	−	1.30003i	0.785050	−	0.619432i	$-0.212637\pi$
$648$	2.12685	+	6.37070i	0.0835506	+	0.250265i
$649$	0.535426	−	0.474346i	0.0210173	−	0.0186197i
$650$	1.83988	−	9.96755i	0.0721661	−	0.390960i
$651$	−6.37170	−	5.64483i	−0.249727	−	0.221238i
$652$	−17.4440	+	40.9427i	−0.683161	+	1.60344i
$653$	−4.42062	+	7.65674i	−0.172992	+	0.299631i	−0.939465	−	0.342646i	$-0.888677\pi$
$653$	−4.42062	+	7.65674i	−0.172992	+	0.299631i	0.766472	+	0.642277i	$0.222010\pi$
$654$	−20.3719	−	35.2851i	−0.796603	−	1.37976i
$655$	24.1788	−	2.93583i	0.944742	−	0.114712i
$656$	63.2015	+	29.9895i	2.46761	+	1.17089i
$657$	−13.9264	+	8.04041i	−0.543320	+	0.313686i
$658$	−0.242937	−	0.167687i	−0.00947066	−	0.00653712i
$659$	42.6120	−	18.1553i	1.65993	−	0.707229i	0.660865	−	0.750505i	$-0.270190\pi$
$659$	42.6120	−	18.1553i	1.65993	−	0.707229i	0.999063	+	0.0432760i	$0.0137795\pi$
$660$	38.8498	+	6.31371i	1.51223	+	0.245761i
$661$	14.1261	−	18.7985i	0.549443	−	0.731176i	−0.436231	−	0.899835i	$-0.643687\pi$
$661$	14.1261	−	18.7985i	0.549443	−	0.731176i	0.985675	+	0.168658i	$0.0539434\pi$
$662$	7.74120	+	20.4119i	0.300870	+	0.793330i
$663$	2.64093	−	2.24054i	0.102565	−	0.0870153i
$664$	−10.4377	+	27.5220i	−0.405062	+	1.06806i
$665$	19.4489	+	30.7560i	0.754197	+	1.19267i
$666$	−0.410889	−	0.175063i	−0.0159216	−	0.00678357i
$667$	−16.8870	−	10.6787i	−0.653867	−	0.413480i
$668$	108.444	+	13.1674i	4.19581	+	0.509463i
$669$	10.9489	+	25.6980i	0.423309	+	0.993542i
$670$	−17.7195	+	53.0764i	−0.684564	+	2.05052i
$671$	0.0206718	+	0.00783979i	0.000798027	+	0.000302652i
$672$	22.3823	+	1.80689i	0.863418	+	0.0697023i
$673$	6.70801	−	23.1587i	0.258575	−	0.892703i	−0.721221	−	0.692705i	$-0.756419\pi$
$673$	6.70801	−	23.1587i	0.258575	−	0.892703i	0.979796	−	0.199999i	$-0.0640938\pi$
$674$	−16.7430	−	0.674719i	−0.644916	−	0.0259892i
$675$	−1.09327			−0.0420799
$676$	−27.9993	+	53.0161i	−1.07689	+	2.03908i
$677$	33.6620			1.29373			0.646867	−	0.762603i	$-0.276079\pi$
$677$	33.6620			1.29373			0.646867	+	0.762603i	$0.276079\pi$
$678$	−0.494386	−	0.0199231i	−0.0189868	−	0.000765140i
$679$	4.07604	−	14.0721i	0.156424	−	0.540038i
$680$	−12.7101	−	1.02607i	−0.487411	−	0.0393479i
$681$	10.7426	+	4.07412i	0.411656	+	0.156121i
$682$	−9.67268	+	28.9732i	−0.370386	+	1.10944i
$683$	2.48211	+	5.82574i	0.0949755	+	0.222916i	0.960691	−	0.277622i	$-0.0895461\pi$
$683$	2.48211	+	5.82574i	0.0949755	+	0.222916i	−0.865715	+	0.500537i	$0.833136\pi$
$684$	27.2421	+	3.30779i	1.04163	+	0.126476i
$685$	−6.22804	−	3.93838i	−0.237961	−	0.150478i
$686$	−32.3992	−	13.8040i	−1.23701	−	0.527039i
$687$	−3.45929	−	5.47042i	−0.131980	−	0.208710i
$688$	15.6554	−	41.2800i	0.596858	−	1.57378i
$689$	36.2471	−	18.0443i	1.38090	−	0.687433i
$690$	−13.2752	−	35.0039i	−0.505379	−	1.33258i
$691$	−21.9980	+	29.2740i	−0.836842	+	1.11363i	0.155219	+	0.987880i	$0.450392\pi$
$691$	−21.9980	+	29.2740i	−0.836842	+	1.11363i	−0.992061	+	0.125755i	$0.959865\pi$
$692$	−1.72605	−	0.280510i	−0.0656146	−	0.0106634i
$693$	12.2906	−	5.23653i	0.466880	−	0.198919i
$694$	36.2707	+	25.0358i	1.37682	+	0.950347i
$695$	21.0378	−	12.1462i	0.798010	−	0.460731i
$696$	−16.4593	−	7.81001i	−0.623886	−	0.296038i
$697$	−8.29028	+	1.00662i	−0.314017	+	0.0381285i
$698$	0.664166	+	1.15037i	0.0251390	+	0.0435421i
$699$	−7.06202	+	12.2318i	−0.267110	+	0.462648i
$700$	−6.11504	+	14.3525i	−0.231127	+	0.542474i
$701$	−7.31887	−	6.48395i	−0.276430	−	0.244896i	0.513504	−	0.858087i	$-0.328347\pi$
$701$	−7.31887	−	6.48395i	−0.276430	−	0.244896i	−0.789934	+	0.613191i	$0.789885\pi$
$702$	8.84787	+	2.76960i	0.333941	+	0.104532i
$703$	−0.773591	+	0.685342i	−0.0291765	+	0.0258482i
$704$	−3.51231	−	10.5206i	−0.132375	−	0.396512i
$705$	−0.00295287	+	0.0732747i	−0.000111211	+	0.00275968i
$706$	−45.6059	+	55.8571i	−1.71640	+	2.10221i
$707$	−7.17059	−	8.09393i	−0.269678	−	0.304403i
$708$	−0.748624	−	0.152833i	−0.0281350	−	0.00574380i
$709$	21.7841	−	6.30985i	0.818120	−	0.236971i	0.157334	−	0.987546i	$-0.449710\pi$
$709$	21.7841	−	6.30985i	0.818120	−	0.236971i	0.660786	+	0.750574i	$0.270223\pi$
$710$	63.7313	−	24.1701i	2.39179	−	0.907087i
$711$	−0.418357	−	10.3814i	−0.0156896	−	0.389334i
$712$	68.9094	+	51.7821i	2.58249	+	1.94062i
$713$	19.8554	−	4.05351i	0.743591	−	0.151805i
$714$	−6.76690	+	3.55154i	−0.253245	+	0.132913i
$715$	21.7861	−	21.7301i	0.814752	−	0.812658i
$716$	78.5348	+	41.2183i	2.93498	+	1.54040i
$717$	9.16182	+	2.65375i	0.342155	+	0.0991063i
$718$	−39.4766	+	3.18688i	−1.47325	+	0.118933i
$719$	6.66348	−	32.6399i	0.248506	−	1.21726i	−0.643574	−	0.765384i	$-0.722549\pi$
$719$	6.66348	−	32.6399i	0.248506	−	1.21726i	0.892080	−	0.451878i	$-0.149246\pi$
$720$	−7.39090	−	14.0822i	−0.275443	−	0.524812i
$721$	28.6570	+	38.1355i	1.06724	+	1.42024i
$722$	22.5456	−	35.6529i	0.839059	−	1.32687i
$723$	19.3320	−	13.3439i	0.718964	−	0.496265i
$724$	−19.3877	+	40.8587i	−0.720538	+	1.51850i
$725$	2.05428	−	2.13874i	0.0762942	−	0.0794307i
$726$	−14.1737	−	13.6140i	−0.526035	−	0.505263i
$727$	−0.565871	−	4.66037i	−0.0209870	−	0.172843i	0.978446	−	0.206501i	$-0.0662076\pi$
$727$	−0.565871	−	4.66037i	−0.0209870	−	0.172843i	−0.999433	+	0.0336573i	$0.989285\pi$
$728$	48.6201	−	57.0107i	1.80198	−	2.11296i
$729$	0.120537	−	0.992709i	0.00446432	−	0.0367670i
$730$	63.3083	−	51.6896i	2.34314	−	1.91312i
$731$	1.05422	+	5.16390i	0.0389916	+	0.190994i
$732$	−0.00657012	−	0.0226827i	−0.000242839	−	0.000838376i
$733$	−4.30556	−	17.4684i	−0.159030	−	0.645208i	−0.995296	−	0.0968845i	$-0.969112\pi$
$733$	−4.30556	−	17.4684i	−0.159030	−	0.645208i	0.836266	−	0.548324i	$-0.184734\pi$
$734$	−3.56401	+	44.1481i	−0.131550	+	1.62954i
$735$	−0.815977	−	5.02091i	−0.0300978	−	0.185199i
$736$	−35.4485	+	40.0131i	−1.30665	+	1.47490i
$737$	38.0032	−	28.5575i	1.39987	−	1.05193i
$738$	−14.1389	−	17.3170i	−0.520460	−	0.637447i
$739$	−2.50519	+	15.4150i	−0.0921548	+	0.567051i	0.899376	+	0.437177i	$0.144022\pi$
$739$	−2.50519	+	15.4150i	−0.0921548	+	0.567051i	−0.991530	+	0.129875i	$0.958543\pi$
$740$	1.53733	+	0.378918i	0.0565134	+	0.0139293i
$741$	14.5672	−	15.7499i	0.535141	−	0.578588i
$742$	−86.7506	+	21.3821i	−3.18472	+	0.784962i
$743$	1.73201	+	21.4547i	0.0635411	+	0.787098i	0.947546	+	0.319620i	$0.103555\pi$
$743$	1.73201	+	21.4547i	0.0635411	+	0.787098i	−0.884005	+	0.467478i	$0.845163\pi$
$744$	17.5270	−	5.85137i	0.642571	−	0.214522i
$745$	−12.7954	−	13.3214i	−0.468786	−	0.488058i
$746$			0.697590i			0.0255406i
$747$	3.16071	−	3.03591i	0.115644	−	0.111078i
$748$	14.8164	+	12.0973i	0.541743	+	0.442319i
$749$	−14.8558	+	28.3054i	−0.542821	+	1.03426i
$750$	30.5676	−	4.96772i	1.11617	−	0.181396i
$751$	7.53045	−	4.76197i	0.274790	−	0.173767i	−0.389962	−	0.920831i	$-0.627512\pi$
$751$	7.53045	−	4.76197i	0.274790	−	0.173767i	0.664752	+	0.747064i	$0.268537\pi$
$752$	0.269712	−	0.127980i	0.00983538	−	0.00466695i
$753$	7.75017	−	11.2281i	0.282432	−	0.409173i
$754$	−22.0435	+	12.1047i	−0.802777	+	0.440828i
$755$	11.9236	+	17.2743i	0.433945	+	0.628678i
$756$	−12.3582	−	7.13499i	−0.449462	−	0.259497i
$757$	−15.2388	−	32.1152i	−0.553865	−	1.16725i	−0.966575	−	0.256384i	$-0.917469\pi$
$757$	−15.2388	−	32.1152i	−0.553865	−	1.16725i	0.412710	−	0.910863i	$-0.364582\pi$
$758$	−89.3973	−	29.8452i	−3.24706	−	1.08403i
$759$	−7.61120	+	30.8799i	−0.276269	+	1.12087i
$760$	−78.9259	+	3.18060i	−2.86294	+	0.115373i
$761$	−45.6977	+	1.84155i	−1.65654	+	0.0667563i	−0.850792	−	0.525503i	$-0.823877\pi$
$761$	−45.6977	+	1.84155i	−1.65654	+	0.0667563i	−0.805748	+	0.592259i	$0.798236\pi$
$762$	9.56966	−	38.8256i	0.346672	−	1.40650i
$763$	46.5036	+	15.5252i	1.68354	+	0.562049i
$764$	−36.8746	−	77.7115i	−1.33408	−	2.81151i
$765$	1.64421	+	0.949286i	0.0594466	+	0.0343215i
$766$	10.0246	+	14.5232i	0.362204	+	0.524743i
$767$	−0.439563	+	0.404462i	−0.0158717	+	0.0146043i
$768$	14.4718	−	20.9660i	0.522205	−	0.756545i
$769$	−3.21407	+	1.52509i	−0.115902	+	0.0549963i	−0.485761	−	0.874092i	$-0.661457\pi$
$769$	−3.21407	+	1.52509i	−0.115902	+	0.0549963i	0.369859	+	0.929088i	$0.379406\pi$
$770$	−57.3879	+	36.2899i	−2.06812	+	1.30780i
$771$	−3.73562	+	0.607098i	−0.134535	+	0.0218641i
$772$	−1.86927	+	3.56159i	−0.0672765	+	0.128185i
$773$	11.2489	+	9.18442i	0.404594	+	0.330341i	0.812793	−	0.582552i	$-0.197946\pi$
$773$	11.2489	+	9.18442i	0.404594	+	0.330341i	−0.408200	+	0.912893i	$0.633843\pi$
$774$	−10.1753	+	9.77349i	−0.365743	+	0.351301i
$775$			3.00779i			0.108043i
$776$	22.0298	+	22.9354i	0.790823	+	0.823334i
$777$	0.509768	−	0.170185i	0.0182878	−	0.00610537i
$778$	−1.51139	−	18.7220i	−0.0541861	−	0.671216i
$779$	−50.2287	+	12.3803i	−1.79963	+	0.443569i
$780$	−32.5353	−	4.65981i	−1.16495	−	0.166848i
$781$	−56.2227	−	13.8577i	−2.01181	−	0.495866i
$782$	2.91841	−	17.9577i	0.104362	−	0.642165i
$783$	1.71552	+	2.10113i	0.0613077	+	0.0750883i
$784$	−16.5546	+	12.4400i	−0.591237	+	0.444286i
$785$	−30.8631	+	34.8372i	−1.10155	+	1.24339i
$786$	5.08283	+	31.2759i	0.181299	+	1.11557i
$787$	−4.15177	+	51.4289i	−0.147995	+	1.83324i	0.317577	+	0.948232i	$0.397131\pi$
$787$	−4.15177	+	51.4289i	−0.147995	+	1.83324i	−0.465572	+	0.885010i	$0.654151\pi$
$788$	9.75538	+	39.5791i	0.347521	+	1.40995i
$789$	−2.61223	−	9.01847i	−0.0929979	−	0.321066i
$790$	10.5625	+	51.7386i	0.375797	+	1.84078i
$791$	0.461180	−	0.376541i	0.0163977	−	0.0133883i
$792$	−3.49550	+	28.7880i	−0.124207	+	1.02294i
$793$	−0.0173824	−	0.00622008i	−0.000617268	−	0.000220882i
$794$	4.59008	+	37.8027i	0.162896	+	1.34157i
$795$	16.0081	+	15.3760i	0.567750	+	0.545332i
$796$	50.2272	−	52.2921i	1.78026	−	1.85344i
$797$	−9.56255	+	20.1526i	−0.338723	+	0.713843i	−0.999319	−	0.0368980i	$-0.988252\pi$
$797$	−9.56255	+	20.1526i	−0.338723	+	0.713843i	0.660596	+	0.750741i	$0.270304\pi$
$798$	−38.9606	+	26.8926i	−1.37919	+	0.951987i
$799$	−0.0190476	+	0.0301213i	−0.000673855	+	0.00106562i
$800$	−4.76644	−	6.34298i	−0.168519	−	0.224258i
$801$	−5.96421	−	11.3638i	−0.210735	−	0.401522i
$802$	15.9029	−	77.8978i	0.561552	−	2.75067i
$803$	−69.2077	+	5.58703i	−2.44229	+	0.197162i
$804$	−48.7716	−	14.1269i	−1.72004	−	0.498216i
$805$	39.8874	+	20.9345i	1.40585	+	0.737845i
$806$	7.61970	−	24.3422i	0.268393	−	0.857416i
$807$	17.8742	−	9.38109i	0.629201	−	0.330230i
$808$	22.9980	−	4.69508i	0.809068	−	0.165172i
$809$	−33.5824	−	25.2356i	−1.18070	−	0.887235i	−0.185262	−	0.982689i	$-0.559313\pi$
$809$	−33.5824	−	25.2356i	−1.18070	−	0.887235i	−0.995434	+	0.0954537i	$0.969570\pi$
$810$	0.204649	+	5.07832i	0.00719064	+	0.178434i
$811$	12.3144	−	4.67024i	0.432417	−	0.163994i	−0.128786	−	0.991672i	$-0.541108\pi$
$811$	12.3144	−	4.67024i	0.432417	−	0.163994i	0.561203	+	0.827678i	$0.310339\pi$
$812$	37.1793	−	10.7691i	1.30474	−	0.377922i
$813$	−16.0065	−	3.26774i	−0.561371	−	0.114605i
$814$	−1.27879	−	1.44345i	−0.0448214	−	0.0505929i
$815$	−12.0626	+	14.7740i	−0.422535	+	0.517511i
$816$	0.311211	−	7.72261i	0.0108946	−	0.270346i
$817$	10.3386	+	30.9678i	0.361701	+	1.08343i
$818$	53.6773	−	47.5540i	1.87678	−	1.66268i
$819$	−10.1790	+	4.56547i	−0.355684	+	0.159531i
$820$	59.3223	+	52.5550i	2.07162	+	1.83530i
$821$	19.0770	−	44.7754i	0.665793	−	1.56267i	−0.152774	−	0.988261i	$-0.548821\pi$
$821$	19.0770	−	44.7754i	0.665793	−	1.56267i	0.818567	−	0.574412i	$-0.194769\pi$
$822$	4.79320	−	8.30207i	0.167182	−	0.289568i
$823$	−20.3328	−	35.2174i	−0.708756	−	1.22760i	−0.965319	−	0.261074i	$-0.915923\pi$
$823$	−20.3328	−	35.2174i	−0.708756	−	1.22760i	0.256562	−	0.966528i	$-0.417410\pi$
$824$	−102.792	+	12.4812i	−3.58093	+	0.434804i
$825$	−4.26470	−	2.02363i	−0.148478	−	0.0704536i
$826$	1.14150	−	0.659047i	0.0397180	−	0.0229312i
$827$	27.9590	+	19.2987i	0.972229	+	0.671081i	0.944492	−	0.328534i	$-0.106554\pi$
$827$	27.9590	+	19.2987i	0.972229	+	0.671081i	0.0277371	+	0.999615i	$0.491170\pi$
$828$	31.2528	−	13.3156i	1.08611	−	0.462749i
$829$	36.8031	+	5.98109i	1.27823	+	0.207732i	0.761357	−	0.648333i	$-0.224534\pi$
$829$	36.8031	+	5.98109i	1.27823	+	0.207732i	0.516868	+	0.856065i	$0.327098\pi$
$830$	−13.3810	+	17.8069i	−0.464461	+	0.618085i
$831$	0.631745	+	1.66578i	0.0219150	+	0.0577851i
$832$	3.09805	+	8.72846i	0.107406	+	0.302605i
$833$	0.876600	−	2.31140i	0.0303724	−	0.0800854i
$834$	16.8907	+	26.7106i	0.584878	+	0.924911i
$835$	43.0706	+	18.3507i	1.49052	+	0.635051i
$836$	100.145	+	63.3279i	3.46359	+	2.19024i
$837$	−2.73113	−	0.331619i	−0.0944016	−	0.0114624i
$838$	−5.94094	−	13.9439i	−0.205226	−	0.481684i
$839$	4.54294	−	13.6078i	0.156840	−	0.469793i	−0.840571	−	0.541701i	$-0.817781\pi$
$839$	4.54294	−	13.6078i	0.156840	−	0.469793i	0.997411	+	0.0719081i	$0.0229088\pi$
$840$	38.4057	+	14.5654i	1.32512	+	0.502553i
$841$	21.5721	+	1.74148i	0.743864	+	0.0600509i
$842$	16.3111	−	56.3125i	0.562119	−	1.94066i
$843$	2.74979	+	0.110813i	0.0947077	+	0.00381659i
$844$	−88.4079			−3.04313
$845$	−17.8472	+	18.4855i	−0.613964	+	0.635920i
$846$	−0.0954036			−0.00328004
$847$	23.6290	+	0.952215i	0.811901	+	0.0327185i
$848$	25.1396	−	86.7919i	0.863296	−	2.98044i
$849$	−22.5117	−	1.81734i	−0.772601	−	0.0623708i
$850$	2.52483	+	0.957541i	0.0866009	+	0.0328434i
$851$	−0.405145	+	1.21356i	−0.0138882	+	0.0416002i
$852$	24.2436	+	56.9018i	0.830571	+	1.94942i
$853$	−13.1697	−	1.59909i	−0.450922	−	0.0547518i	−0.108074	−	0.994143i	$-0.534468\pi$
$853$	−13.1697	−	1.59909i	−0.450922	−	0.0547518i	−0.342848	+	0.939391i	$0.611391\pi$
$854$	0.0344318	+	0.0217733i	0.00117823	+	0.000745068i
$855$	10.8197	+	4.60986i	0.370027	+	0.157654i
$856$	−37.0868	−	58.6480i	−1.26760	−	2.00455i
$857$	−15.1270	+	39.8867i	−0.516729	+	1.36250i	0.382066	+	0.924135i	$0.375213\pi$
$857$	−15.1270	+	39.8867i	−0.516729	+	1.36250i	−0.898795	+	0.438368i	$0.855556\pi$
$858$	29.3879	+	27.1812i	1.00329	+	0.927949i
$859$	−11.3646	−	29.9661i	−0.387756	−	1.02243i	−0.976767	−	0.214304i	$-0.931252\pi$
$859$	−11.3646	−	29.9661i	−0.387756	−	1.02243i	0.589011	−	0.808125i	$-0.299518\pi$
$860$	30.0473	−	39.9856i	1.02460	−	1.36350i
$861$	26.5524	+	4.31518i	0.904902	+	0.147061i
$862$	78.4235	−	33.4131i	2.67111	−	1.13806i
$863$	−14.9536	−	10.3217i	−0.509027	−	0.351356i	0.285704	−	0.958318i	$-0.407773\pi$
$863$	−14.9536	−	10.3217i	−0.509027	−	0.351356i	−0.794731	+	0.606962i	$0.792388\pi$
$864$	6.28507	−	3.62868i	0.213822	−	0.123450i
$865$	−0.677078	−	0.321278i	−0.0230214	−	0.0109238i
$866$	6.92165	−	0.840440i	0.235207	−	0.0285593i
$867$	−8.03867	−	13.9234i	−0.273008	−	0.472863i
$868$	−19.6297	+	33.9996i	−0.666275	+	1.15402i
$869$	17.5839	−	41.2710i	0.596493	−	1.40002i
$870$	−10.3191	−	9.14195i	−0.349851	−	0.309941i
$871$	−31.2795	+	24.4411i	−1.05987	+	0.828154i
$872$	−79.6574	+	70.5703i	−2.69754	+	2.38981i
$873$	−1.49941	−	4.49129i	−0.0507474	−	0.152007i
$874$	4.53796	−	112.608i	0.153499	−	3.80903i
$875$	−23.5677	+	28.8652i	−0.796734	+	0.975821i
$876$	49.1799	+	55.5127i	1.66164	+	1.87560i
$877$	37.0501	+	7.56383i	1.25109	+	0.255412i	0.779499	−	0.626404i	$-0.215474\pi$
$877$	37.0501	+	7.56383i	1.25109	+	0.255412i	0.471594	+	0.881816i	$0.343679\pi$
$878$	−25.6574	+	7.43174i	−0.865894	+	0.250809i
$879$	−12.9445	+	4.90921i	−0.436608	+	0.165583i
$880$	−2.76502	−	68.6132i	−0.0932088	−	2.31295i
$881$	36.7472	+	27.6137i	1.23804	+	0.930329i	0.999171	−	0.0407216i	$-0.0129657\pi$
$881$	36.7472	+	27.6137i	1.23804	+	0.930329i	0.238873	+	0.971051i	$0.423222\pi$
$882$	6.48388	−	1.32369i	0.218324	−	0.0445711i
$883$	−14.5520	+	7.63748i	−0.489714	+	0.257022i	−0.691458	−	0.722416i	$-0.743031\pi$
$883$	−14.5520	+	7.63748i	−0.489714	+	0.257022i	0.201744	+	0.979438i	$0.435339\pi$
$884$	−12.5608	−	9.86683i	−0.422464	−	0.331857i
$885$	−0.289946	−	0.152176i	−0.00974644	−	0.00511533i
$886$	−51.5636	−	14.9356i	−1.73231	−	0.501771i
$887$	42.5300	−	3.43338i	1.42802	−	0.115281i	0.657862	−	0.753138i	$-0.271461\pi$
$887$	42.5300	−	3.43338i	1.42802	−	0.115281i	0.770155	+	0.637857i	$0.220179\pi$
$888$	−0.233346	+	1.14300i	−0.00783057	+	0.0383567i
$889$	22.3610	+	42.6053i	0.749964	+	1.42894i
$890$	39.1849	+	52.1456i	1.31348	+	1.74793i
$891$	2.30769	−	3.64932i	0.0773105	−	0.122257i
$892$	106.023	−	73.1822i	3.54990	−	2.45032i
$893$	−0.0946406	+	0.199451i	−0.00316703	+	0.00667437i
$894$	16.6460	−	17.3304i	0.556727	−	0.579614i
$895$	27.4140	+	26.3316i	0.916351	+	0.880167i
$896$	2.94984	+	24.2941i	0.0985472	+	0.811609i
$897$	5.86855	−	25.9016i	0.195945	−	0.864829i
$898$	2.68215	−	22.0895i	0.0895044	−	0.737135i
$899$	5.78061	−	4.71972i	0.192794	−	0.157411i
$900$	1.00855	+	4.94022i	0.0336185	+	0.164674i
$901$	3.00111	+	10.3610i	0.0999815	+	0.345176i
$902$	−23.1005	−	93.7222i	−0.769161	−	3.12061i
$903$	1.36608	−	16.9219i	0.0454603	−	0.563127i
$904$	0.207310	+	1.27563i	0.00689503	+	0.0424268i
$905$	−12.8527	+	14.5077i	−0.427239	+	0.482253i
$906$	−21.8301	+	16.4043i	−0.725257	+	0.544996i
$907$	−0.625527	−	0.766131i	−0.0207703	−	0.0254390i	0.764115	−	0.645080i	$-0.223176\pi$
$907$	−0.625527	−	0.766131i	−0.0207703	−	0.0254390i	−0.784886	+	0.619641i	$0.787278\pi$
$908$	8.49982	−	52.3015i	0.282077	−	1.73569i
$909$	−3.39326	−	0.836364i	−0.112547	−	0.0277404i
$910$	47.3423	−	31.2020i	1.56938	−	1.03434i
$911$	5.28235	−	1.30198i	0.175012	−	0.0431366i	−0.150836	−	0.988559i	$-0.548196\pi$
$911$	5.28235	−	1.30198i	0.175012	−	0.0431366i	0.325848	+	0.945422i	$0.394350\pi$
$912$	−3.85251	−	47.7219i	−0.127569	−	1.58023i
$913$	17.9490	−	5.99224i	0.594024	−	0.198314i
$914$	−30.6034	−	31.8615i	−1.01227	−	1.05389i
$915$		−	0.0101207i		−	0.000334579i
$916$	−21.5283	+	20.6782i	−0.711315	+	0.683228i
$917$	−29.5340	−	24.1138i	−0.975299	−	0.796307i
$918$	−1.14784	+	2.18702i	−0.0378842	+	0.0721824i
$919$	−15.3055	+	2.48738i	−0.504882	+	0.0820512i	−0.407517	−	0.913198i	$-0.633605\pi$
$919$	−15.3055	+	2.48738i	−0.504882	+	0.0820512i	−0.0973644	+	0.995249i	$0.531041\pi$
$920$	−82.6455	+	52.2618i	−2.72474	+	1.72302i
$921$	14.1586	−	6.71836i	0.466543	−	0.221377i
$922$	−32.3141	+	46.8150i	−1.06421	+	1.54177i
$923$	47.1588	+	10.6848i	1.55225	+	0.351695i
$924$	−35.0008	−	50.7074i	−1.15144	−	1.66815i
$925$	−0.164452	−	0.0949463i	−0.00540714	−	0.00312182i
$926$	31.3167	+	65.9986i	1.02913	+	2.16885i
$927$	14.6238	+	4.88213i	0.480307	+	0.160350i
$928$	−4.71111	+	19.1137i	−0.154650	+	0.627439i
$929$	−12.8882	+	0.519377i	−0.422849	+	0.0170402i	−0.250779	−	0.968044i	$-0.580687\pi$
$929$	−12.8882	+	0.519377i	−0.422849	+	0.0170402i	−0.172070	+	0.985085i	$0.555046\pi$
$930$	13.9714	−	0.563028i	0.458140	−	0.0184624i
$931$	3.66471	−	14.8683i	0.120106	−	0.487289i
$932$	61.7873	+	20.6276i	2.02391	+	0.675680i
$933$	5.88224	+	12.3966i	0.192576	+	0.405845i
$934$	−18.7277	−	10.8125i	−0.612790	−	0.353795i
$935$	4.65674	+	6.74645i	0.152292	+	0.220633i
$936$	2.46525	−	24.0903i	0.0805793	−	0.787416i
$937$	26.8359	−	38.8785i	0.876691	−	1.27011i	−0.0851139	−	0.996371i	$-0.527125\pi$
$937$	26.8359	−	38.8785i	0.876691	−	1.27011i	0.961805	−	0.273735i	$-0.0882592\pi$
$938$	79.1375	−	37.5512i	2.58393	−	1.22609i
$939$	7.51150	−	4.74998i	0.245128	−	0.155010i
$940$	0.333835	−	0.0542534i	0.0108885	−	0.00176955i
$941$	−13.3971	+	25.5261i	−0.436735	+	0.832128i	0.563248	+	0.826288i	$0.309551\pi$
$941$	−13.3971	+	25.5261i	−0.436735	+	0.832128i	−0.999983	+	0.00584059i	$0.998141\pi$
$942$	−46.9012	−	38.2936i	−1.52812	−	1.24767i
$943$	−46.1859	+	44.3621i	−1.50402	+	1.44463i
$944$			1.33303i			0.0433865i
$945$	−4.23647	−	4.41063i	−0.137812	−	0.143478i
$946$	−57.7830	+	19.2908i	−1.87869	+	0.627198i
$947$	0.691644	+	8.56754i	0.0224754	+	0.278408i	0.998227	+	0.0595259i	$0.0189589\pi$
$947$	0.691644	+	8.56754i	0.0224754	+	0.278408i	−0.975751	+	0.218882i	$0.929759\pi$
$948$	−46.5252	+	11.4674i	−1.51107	+	0.372445i
$949$	57.6940	−	5.75406i	1.87283	−	0.186785i
$950$	16.2412	+	4.00309i	0.526934	+	0.129877i
$951$	−2.53183	+	15.5790i	−0.0821001	+	0.505182i
$952$	12.6245	+	15.4622i	0.409162	+	0.501132i
$953$	−39.8921	+	29.9770i	−1.29223	+	0.971049i	−0.292340	+	0.956314i	$0.594434\pi$
$953$	−39.8921	+	29.9770i	−1.29223	+	0.971049i	−0.999891	+	0.0147343i	$0.995310\pi$
$954$	−19.1486	+	21.6143i	−0.619958	+	0.699788i
$955$	−5.91339	−	36.3866i	−0.191353	−	1.17744i
$956$	3.53979	−	43.8482i	0.114485	−	1.41815i
$957$	2.80286	+	11.3716i	0.0906035	+	0.367593i
$958$	29.4857	+	101.796i	0.952639	+	3.28889i
$959$	2.30735	+	11.3021i	0.0745082	+	0.364965i
$960$	−3.93295	+	3.21115i	−0.126935	+	0.103640i
$961$	2.82429	−	23.2601i	0.0911061	−	0.750327i
$962$	1.09039	+	1.18501i	0.0351555	+	0.0382064i
$963$	1.24533	+	10.2562i	0.0401303	+	0.330502i
$964$	−78.1319	−	75.0467i	−2.51646	−	2.41709i
$965$	−1.19415	+	1.24324i	−0.0384410	+	0.0400213i
$966$	−25.1231	+	52.9458i	−0.808323	+	1.70350i
$967$	−29.1284	+	20.1059i	−0.936706	+	0.646561i	−0.935458	−	0.353438i	$-0.885013\pi$
$967$	−29.1284	+	20.1059i	−0.936706	+	0.646561i	−0.00124766	+	0.999999i	$0.500397\pi$
$968$	−27.4355	+	43.3858i	−0.881811	+	1.39447i
$969$	3.43353	+	4.56920i	0.110301	+	0.146784i
$970$	11.1836	+	21.3086i	0.359085	+	0.684179i
$971$	1.88964	−	9.25606i	0.0606414	−	0.297041i	−0.938148	−	0.346235i	$-0.887460\pi$
$971$	1.88964	−	9.25606i	0.0606414	−	0.297041i	0.998789	+	0.0491938i	$0.0156652\pi$
$972$	−4.59701	+	0.371109i	−0.147449	+	0.0119033i
$973$	−36.5263	−	10.5800i	−1.17098	−	0.339178i
$974$	1.96091	+	1.02917i	0.0628317	+	0.0329766i
$975$	3.59248	+	1.62240i	0.115051	+	0.0519585i
$976$	−0.0364809	+	0.0191467i	−0.00116773	+	0.000612870i
$977$	−38.8469	+	7.93065i	−1.24282	+	0.253724i	−0.776060	−	0.630659i	$-0.782785\pi$
$977$	−38.8469	+	7.93065i	−1.24282	+	0.253724i	−0.466762	+	0.884383i	$0.654580\pi$
$978$	−19.8365	−	14.9061i	−0.634300	−	0.476646i
$979$	−2.23128	−	55.3686i	−0.0713119	−	1.76959i
$980$	−21.9355	+	8.31905i	−0.700705	+	0.265742i
$981$	15.2195	−	4.40839i	0.485922	−	0.140749i
$982$	31.0833	+	6.34570i	0.991908	+	0.202499i
$983$	2.56553	+	2.89589i	0.0818278	+	0.0923645i	0.787999	−	0.615677i	$-0.211117\pi$
$983$	2.56553	+	2.89589i	0.0818278	+	0.0923645i	−0.706171	+	0.708042i	$0.749579\pi$
$984$	−36.9303	+	45.2314i	−1.17730	+	1.44192i
$985$	−0.703447	+	17.4559i	−0.0224137	+	0.556190i
$986$	−2.12160	−	6.35496i	−0.0675654	−	0.202383i
$987$	0.0859280	−	0.0761255i	0.00273512	−	0.00242310i
$988$	−84.6086	−	51.2964i	−2.69176	−	1.63196i
$989$	30.2515	+	26.8005i	0.961942	+	0.852206i
$990$	−8.60158	+	20.1887i	−0.273376	+	0.641638i
$991$	15.3867	−	26.6506i	0.488776	−	0.846584i	−0.511141	−	0.859497i	$-0.670777\pi$
$991$	15.3867	−	26.6506i	0.488776	−	0.846584i	0.999917	+	0.0129126i	$0.00411032\pi$
$992$	−9.98319	−	17.2914i	−0.316967	−	0.549002i
$993$	−8.42791	+	1.02333i	−0.267452	+	0.0324745i
$994$	−96.3980	−	45.7414i	−3.05756	−	1.45083i
$995$	26.9110	−	15.5371i	0.853136	−	0.492558i
$996$	−16.6343	−	11.4819i	−0.527079	−	0.363816i
$997$	9.12401	−	3.88738i	0.288960	−	0.123115i	−0.242623	−	0.970121i	$-0.578008\pi$
$997$	9.12401	−	3.88738i	0.288960	−	0.123115i	0.531583	+	0.847006i	$0.321597\pi$
$998$	46.0285	+	7.48035i	1.45701	+	0.236786i
$999$	0.104344	−	0.138857i	0.00330131	−	0.00439325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.4.15	✓	360
169.127	even	78	inner	507.2.t.b.127.15	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.4.15	✓	360	1.1	even	1	trivial
507.2.t.b.127.15	yes	360	169.127	even	78	inner

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.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(2.56929 + 0.103539i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(4.59701 + 0.371109i) q^{4} +(1.84810 + 0.700893i) q^{5} +(-0.814272 + 2.43904i) q^{6} +(-1.21279 - 2.84653i) q^{7} +(6.66737 + 0.809566i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})\)	\(q+(2.56929 + 0.103539i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(4.59701 + 0.371109i) q^{4} +(1.84810 + 0.700893i) q^{5} +(-0.814272 + 2.43904i) q^{6} +(-1.21279 - 2.84653i) q^{7} +(6.66737 + 0.809566i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(4.67574 + 1.99215i) q^{10} +(-2.30769 - 3.64932i) q^{11} +(-1.63543 + 4.31226i) q^{12} +(1.98415 + 3.01051i) q^{13} +(-2.82129 - 7.43912i) q^{14} +(-1.18739 + 1.58013i) q^{15} +(7.94210 + 1.29072i) q^{16} +(-0.883687 + 0.376504i) q^{17} +(-2.11620 - 1.46071i) q^{18} +(-5.15303 + 2.97510i) q^{19} +(8.23564 + 3.90786i) q^{20} +(3.07156 - 0.372955i) q^{21} +(-5.55127 - 9.61508i) q^{22} +(-3.68294 + 6.37904i) q^{23} +(-2.63258 + 6.17890i) q^{24} +(-0.818324 - 0.724971i) q^{25} +(4.78614 + 7.94030i) q^{26} +(0.748511 - 0.663123i) q^{27} +(-4.51884 - 13.5356i) q^{28} +(-0.109222 + 2.71032i) q^{29} +(-3.21436 + 3.93688i) q^{30} +(-1.82438 - 2.05929i) q^{31} +(7.11070 + 1.45166i) q^{32} +(4.14727 - 1.20127i) q^{33} +(-2.30943 + 0.875851i) q^{34} +(-0.246253 - 6.11071i) q^{35} +(-3.68700 - 2.77060i) q^{36} +(0.170182 - 0.0347430i) q^{37} +(-13.5477 + 7.11036i) q^{38} +(-3.44367 + 1.06823i) q^{39} +(11.7546 + 6.16927i) q^{40} +(8.35089 + 2.41886i) q^{41} +(7.93034 - 0.640203i) q^{42} +(1.09751 - 5.37597i) q^{43} +(-9.25417 - 17.6324i) q^{44} +(-1.18739 - 1.58013i) q^{45} +(-10.1230 + 16.0083i) q^{46} +(0.0305345 - 0.0210764i) q^{47} +(-3.44939 + 7.26944i) q^{48} +(-1.78278 + 1.85607i) q^{49} +(-2.02745 - 1.94739i) q^{50} +(-0.115782 - 0.953547i) q^{51} +(8.00392 + 14.5757i) q^{52} +(1.35362 - 11.1481i) q^{53} +(1.99180 - 1.62625i) q^{54} +(-1.70706 - 8.36175i) q^{55} +(-5.78168 - 19.9607i) q^{56} +(-1.42398 - 5.77731i) q^{57} +(-0.561247 + 6.95229i) q^{58} +(0.0265754 + 0.163525i) q^{59} +(-6.04487 + 6.82324i) q^{60} +(-0.00409345 + 0.00307603i) q^{61} +(-4.47413 - 5.47982i) q^{62} +(-0.496332 + 3.05405i) q^{63} +(2.49416 + 0.614756i) q^{64} +(1.55686 + 6.95440i) q^{65} +(10.7799 - 2.65701i) q^{66} +(0.885913 + 10.9740i) q^{67} +(-4.20204 + 1.40285i) q^{68} +(-5.10253 - 5.31229i) q^{69} -15.7257i q^{70} +(9.67205 - 9.29013i) q^{71} +(-5.20251 - 4.24772i) q^{72} +(7.47313 - 14.2389i) q^{73} +(0.440845 - 0.0716443i) q^{74} +(0.924020 - 0.584315i) q^{75} +(-24.7926 + 11.7643i) q^{76} +(-7.58913 + 10.9948i) q^{77} +(-8.95839 + 2.38804i) q^{78} +(5.90211 + 8.55068i) q^{79} +(13.7732 + 7.95194i) q^{80} +(0.428693 + 0.903450i) q^{81} +(21.2054 + 7.07940i) q^{82} +(-1.04882 + 4.25521i) q^{83} +(14.2584 - 0.574594i) q^{84} +(-1.89703 + 0.0764478i) q^{85} +(3.37645 - 13.6988i) q^{86} +(-2.57292 - 0.858968i) q^{87} +(-12.4319 - 26.1996i) q^{88} +(11.1145 + 6.41695i) q^{89} +(-2.88715 - 4.18276i) q^{90} +(6.16313 - 9.29904i) q^{91} +(-19.2979 + 27.9578i) q^{92} +(2.48556 - 1.17941i) q^{93} +(0.0806342 - 0.0509900i) q^{94} +(-11.6086 + 1.88657i) q^{95} +(-3.37267 + 6.42608i) q^{96} +(3.66773 + 2.99461i) q^{97} +(-4.77264 + 4.58418i) q^{98} +4.31775i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

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