LMFDB - Embedded newform 507.2.t.b.127.15

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			127.15
Character	$\chi$	$=$	507.127
Dual form			507.2.t.b.4.15

$q$-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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{77}{78}\right)$

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	0.891609	−	0.452807i	$-0.149577\pi$
$2$	2.56929	−	0.103539i	1.81676	−	0.0732130i	0.925153	+	0.379594i	$0.123936\pi$
$3$	−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	0.0951568	−	0.995462i	$-0.469665\pi$
$5$	1.84810	−	0.700893i	0.826496	−	0.313449i	0.731339	+	0.682014i	$0.238896\pi$
$6$	−0.814272	−	2.43904i	−0.332425	−	0.995735i
$7$	−1.21279	+	2.84653i	−0.458392	+	1.07589i	0.517115	+	0.855916i	$0.327006\pi$
$7$	−1.21279	+	2.84653i	−0.458392	+	1.07589i	−0.975507	+	0.219970i	$0.929404\pi$
$8$	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	0.293722	+	0.955891i	$0.405106\pi$
$11$	−2.30769	+	3.64932i	−0.695794	+	1.10031i	−0.989517	+	0.144420i	$0.953868\pi$
$12$	−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	0.282136	−	0.959375i	$-0.408957\pi$
$17$	−0.883687	−	0.376504i	−0.214326	−	0.0913156i	−0.496461	+	0.868059i	$0.665367\pi$
$18$	−2.11620	+	1.46071i	−0.498793	+	0.344292i
$19$	−5.15303	−	2.97510i	−1.18219	−	0.682536i	−0.225667	−	0.974204i	$-0.572456\pi$
$19$	−5.15303	−	2.97510i	−1.18219	−	0.682536i	−0.956519	+	0.291669i	$0.905790\pi$
$20$	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	−0.938675	−	0.344804i	$-0.887945\pi$
$23$	−3.68294	−	6.37904i	−0.767947	−	1.33012i	0.170728	−	0.985318i	$-0.445388\pi$
$24$	−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	−0.977122	−	0.212679i	$-0.931781\pi$
$29$	−0.109222	−	2.71032i	−0.0202820	−	0.503294i	0.956840	−	0.290615i	$-0.0938598\pi$
$30$	−3.21436	−	3.93688i	−0.586860	−	0.718773i
$31$	−1.82438	+	2.05929i	−0.327667	+	0.369860i	−0.889140	−	0.457635i	$-0.848697\pi$
$31$	−1.82438	+	2.05929i	−0.327667	+	0.369860i	0.561473	+	0.827495i	$0.310235\pi$
$32$	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	0.213994	−	0.976835i	$-0.431353\pi$
$37$	0.170182	+	0.0347430i	0.0279778	+	0.00571171i	−0.186016	+	0.982547i	$0.559558\pi$
$38$	−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	0.447818	−	0.894125i	$-0.352201\pi$
$41$	8.35089	−	2.41886i	1.30419	−	0.377763i	0.856371	+	0.516362i	$0.172714\pi$
$42$	7.93034	+	0.640203i	1.22368	+	0.0987855i
$43$	1.09751	+	5.37597i	0.167369	+	0.819828i	0.973606	+	0.228235i	$0.0732956\pi$
$43$	1.09751	+	5.37597i	0.167369	+	0.819828i	−0.806237	+	0.591593i	$0.798499\pi$
$44$	−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	0.570290	−	0.821444i	$-0.306831\pi$
$47$	0.0305345	+	0.0210764i	0.00445391	+	0.00307431i	−0.565836	+	0.824518i	$0.691446\pi$
$48$	−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	0.724828	+	0.688930i	$0.241919\pi$
$53$	1.35362	+	11.1481i	0.185934	+	1.53130i	−0.538895	+	0.842373i	$0.681158\pi$
$54$	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	−0.985263	−	0.171047i	$-0.945285\pi$
$59$	0.0265754	−	0.163525i	0.00345982	−	0.0212891i	0.988723	+	0.149757i	$0.0478493\pi$
$60$	−6.04487	−	6.82324i	−0.780389	−	0.880877i
$61$	−0.00409345	−	0.00307603i	−0.000524113	−	0.000393845i	0.600480	−	0.799640i	$-0.294976\pi$
$61$	−0.00409345	−	0.00307603i	−0.000524113	−	0.000393845i	−0.601004	+	0.799246i	$0.705233\pi$
$62$	−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	−0.683559	−	0.729895i	$-0.739569\pi$
$67$	0.885913	−	10.9740i	0.108231	−	1.34069i	0.791791	−	0.610792i	$-0.209149\pi$
$68$	−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	0.993419	+	0.114534i	$0.0365376\pi$
$71$	9.67205	+	9.29013i	1.14786	+	1.10254i	0.154442	+	0.988002i	$0.450642\pi$
$72$	−5.20251	+	4.24772i	−0.613122	+	0.500599i
$73$	7.47313	+	14.2389i	0.874663	+	1.66653i	0.736832	+	0.676076i	$0.236321\pi$
$73$	7.47313	+	14.2389i	0.874663	+	1.66653i	0.137831	+	0.990456i	$0.455987\pi$
$74$	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	−0.335759	−	0.941948i	$-0.608993\pi$
$79$	5.90211	−	8.55068i	0.664039	−	0.962027i	0.999798	−	0.0200788i	$-0.00639172\pi$
$80$	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	−0.999999	−	0.00124493i	$-0.999604\pi$
$83$	−1.04882	−	4.25521i	−0.115122	−	0.467070i	0.884877	−	0.465825i	$-0.154242\pi$
$84$	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	0.222551	−	0.974921i	$-0.428562\pi$
$89$	11.1145	−	6.41695i	1.17813	−	0.680195i	0.955582	+	0.294726i	$0.0952284\pi$
$90$	−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	−0.427701	−	0.903921i	$-0.640676\pi$
$97$	3.66773	−	2.99461i	0.372401	−	0.304056i	0.800102	+	0.599864i	$0.204779\pi$
$98$	−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	0.476770	−	0.879028i	$-0.341807\pi$
$101$	3.31496	+	1.10670i	0.329851	+	0.110120i	−0.146919	+	0.989149i	$0.546936\pi$
$102$	−0.198747	+	2.46193i	−0.0196789	+	0.243767i
$103$	−14.9692	−	3.68957i	−1.47496	−	0.363544i	−0.581816	−	0.813320i	$-0.697658\pi$
$103$	−14.9692	−	3.68957i	−1.47496	−	0.363544i	−0.893141	+	0.449776i	$0.851504\pi$
$104$	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	−0.986938	−	0.161101i	$-0.948496\pi$
$107$	−6.53415	+	8.00288i	−0.631680	+	0.773668i	0.355258	+	0.934768i	$0.384393\pi$
$108$	3.68700	+	2.77060i	0.354782	+	0.266601i
$109$	−10.5073	−	11.8602i	−1.00641	−	1.13600i	−0.990691	−	0.136128i	$-0.956534\pi$
$109$	−10.5073	−	11.8602i	−1.00641	−	1.13600i	−0.0157213	−	0.999876i	$-0.505004\pi$
$110$	−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	−0.957961	−	0.286899i	$-0.907375\pi$
$113$	0.0535349	−	0.184824i	0.00503614	−	0.0173868i	0.962997	+	0.269513i	$0.0868626\pi$
$114$	−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	−0.629484	−	0.777013i	$-0.716734\pi$
$127$	−15.5006	−	1.25134i	−1.37546	−	0.111038i	−0.745974	+	0.665975i	$0.768016\pi$
$128$	−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	0.868299	−	0.496041i	$-0.165213\pi$
$131$	10.9112	+	5.72664i	0.953315	+	0.500339i	0.0850163	+	0.996380i	$0.472906\pi$
$132$	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	−0.353512	−	0.935430i	$-0.615013\pi$
$137$	−3.65278	+	0.745721i	−0.312078	+	0.0637112i	0.0414337	+	0.999141i	$0.486807\pi$
$138$	−12.5598	+	14.1771i	−1.06916	+	1.20684i
$139$	7.77296	+	9.52014i	0.659294	+	0.807488i	0.990709	−	0.135997i	$-0.0434237\pi$
$139$	7.77296	+	9.52014i	0.659294	+	0.807488i	−0.331416	+	0.943485i	$0.607526\pi$
$140$	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	−0.741874	−	0.670539i	$-0.766063\pi$
$149$	−8.44286	+	4.00619i	−0.691666	+	0.328200i	0.0502081	+	0.998739i	$0.484012\pi$
$150$	2.43457	+	1.40560i	0.198782	+	0.114767i
$151$	8.73967	−	6.03256i	0.711224	−	0.490923i	−0.156683	−	0.987649i	$-0.550080\pi$
$151$	8.73967	−	6.03256i	0.711224	−	0.490923i	0.867907	+	0.496726i	$0.165465\pi$
$152$	−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	−0.653145	−	0.757233i	$-0.726551\pi$
$157$	−8.34993	−	22.0170i	−0.666397	−	1.75715i	−0.0132526	−	0.999912i	$-0.504219\pi$
$158$	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	−0.997867	−	0.0652763i	$-0.979207\pi$
$163$	−3.05574	−	9.15305i	−0.239344	−	0.716922i	0.758523	−	0.651646i	$-0.225921\pi$
$164$	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	0.899591	−	0.436732i	$-0.143864\pi$
$167$	23.6670	−	0.953748i	1.83141	−	0.0738032i	0.931817	+	0.362929i	$0.118223\pi$
$168$	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	−0.0948251	−	0.995494i	$-0.530229\pi$
$173$	−0.377935	+	0.0305101i	−0.0287339	+	0.00231964i	0.0660913	+	0.997814i	$0.478947\pi$
$174$	−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	0.388658	−	0.921382i	$-0.372939\pi$
$179$	17.6924	−	7.53804i	1.32239	−	0.563419i	0.933736	+	0.357963i	$0.116528\pi$
$180$	−4.87206	+	7.70455i	−0.363142	+	0.574263i
$181$	−3.47727	−	9.16882i	−0.258464	−	0.681513i	−0.999944	−	0.0105387i	$-0.996645\pi$
$181$	−3.47727	−	9.16882i	−0.258464	−	0.681513i	0.741481	−	0.670974i	$-0.234124\pi$
$182$	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	0.301781	+	0.953377i	$0.402419\pi$
$191$	−9.32535	+	16.1520i	−0.674759	+	1.16872i	−0.976539	+	0.215339i	$0.930914\pi$
$192$	−1.28440	−	2.22465i	−0.0926938	−	0.160550i
$193$	−0.341854	−	0.802360i	−0.0246072	−	0.0577552i	0.907223	−	0.420651i	$-0.138198\pi$
$193$	−0.341854	−	0.802360i	−0.0246072	−	0.0577552i	−0.931830	+	0.362896i	$0.881788\pi$
$194$	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	−0.800583	−	0.599222i	$-0.795477\pi$
$197$	2.79892	−	8.38380i	0.199415	−	0.597321i	0.999998	+	0.00190082i	$0.000605051\pi$
$198$	−0.447054	−	11.0935i	−0.0317708	−	0.788384i
$199$	9.94296	+	12.1779i	0.704838	+	0.863269i	0.995617	−	0.0935207i	$-0.0298121\pi$
$199$	9.94296	+	12.1779i	0.704838	+	0.863269i	−0.290780	+	0.956790i	$0.593915\pi$
$200$	−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	−0.597229	−	0.802070i	$-0.703732\pi$
$211$	−19.1071	−	1.54248i	−1.31539	−	0.106189i	−0.718157	+	0.695882i	$0.755014\pi$
$212$	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	0.948306	+	0.317358i	$0.102796\pi$
$223$	21.6372	+	17.6662i	1.44894	+	1.18302i	0.500630	+	0.865662i	$0.333102\pi$
$224$	−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	0.952142	+	0.305657i	$0.0988762\pi$
$227$	0.924494	+	11.4519i	0.0613608	+	0.760090i	−0.890781	+	0.454433i	$0.849842\pi$
$228$	−4.40203	+	27.0868i	−0.291532	+	1.79387i
$229$	−4.29201	−	4.84467i	−0.283624	−	0.320145i	0.589382	−	0.807854i	$-0.299371\pi$
$229$	−4.29201	−	4.84467i	−0.283624	−	0.320145i	−0.873006	+	0.487709i	$0.837833\pi$
$230$	−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	0.237041	−	0.971500i	$-0.423822\pi$
$233$	13.7136	−	3.38010i	0.898409	−	0.221438i	0.661368	+	0.750062i	$0.269976\pi$
$234$	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	$0.0998251\pi$
$239$			9.53842i			0.616989i	−0.951226	+	0.308495i	$0.900175\pi$
$240$	−11.4699	−	11.0170i	−0.740380	−	0.711145i
$241$	−18.1956	+	14.8562i	−1.17208	+	0.956973i	−0.999607	−	0.0280418i	$-0.991073\pi$
$241$	−18.1956	+	14.8562i	−1.17208	+	0.956973i	−0.172472	+	0.985014i	$0.555175\pi$
$242$	−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	−0.694225	−	0.719758i	$-0.744253\pi$
$251$	−12.9410	+	4.32034i	−0.816828	+	0.272697i	−0.122604	+	0.992456i	$0.539124\pi$
$252$	−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	−0.846532	−	0.532338i	$-0.821313\pi$
$257$	1.62244	−	3.41923i	0.101205	−	0.213286i	0.947737	+	0.319053i	$0.103365\pi$
$258$	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	0.266916	−	0.963720i	$-0.413995\pi$
$263$	−7.93564	−	5.01819i	−0.489332	−	0.309435i	−0.756248	+	0.654285i	$0.772970\pi$
$264$	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	−0.994764	−	0.102196i	$-0.967413\pi$
$269$	−13.9836	+	14.5585i	−0.852596	+	0.887647i	0.142168	+	0.989843i	$0.454593\pi$
$270$	4.82088	+	1.60945i	0.293389	+	0.0979477i
$271$	1.31455	−	16.2836i	0.0798533	−	0.989160i	−0.825472	−	0.564442i	$-0.809091\pi$
$271$	1.31455	−	16.2836i	0.0798533	−	0.989160i	0.905326	−	0.424718i	$-0.139627\pi$
$272$	−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	0.642669	−	0.766144i	$-0.277827\pi$
$277$	1.42424	+	1.07025i	0.0855746	+	0.0643051i	−0.557094	+	0.830449i	$0.688084\pi$
$278$	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	−0.987310	−	0.158807i	$-0.949235\pi$
$281$	−0.658602	+	2.67205i	−0.0392889	+	0.159401i	0.948021	+	0.318209i	$0.103081\pi$
$282$	0.0265429	−	0.0916369i	0.00158061	−	0.00545690i
$283$	4.51758	−	22.1285i	0.268542	−	1.31541i	−0.591964	−	0.805965i	$-0.701647\pi$
$283$	4.51758	−	22.1285i	0.268542	−	1.31541i	0.860506	−	0.509441i	$-0.170148\pi$
$284$	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	−0.488223	−	0.872719i	$-0.662355\pi$
$293$	8.31677	−	11.0676i	0.485871	−	0.646577i	0.974094	+	0.226142i	$0.0726112\pi$
$294$	−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	−0.966047	−	0.258367i	$-0.916816\pi$
$307$	−10.3923	+	11.7305i	−0.593119	+	0.669493i	0.372928	+	0.927860i	$0.378354\pi$
$308$	−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	0.902080	−	0.431569i	$-0.142040\pi$
$311$	10.2706	+	9.09894i	0.582391	+	0.515953i	−0.319689	+	0.947523i	$0.603578\pi$
$312$	−23.8251	−	4.33443i	−1.34883	−	0.245389i
$313$	−6.65227	+	5.89340i	−0.376009	+	0.333115i	−0.829869	−	0.557958i	$-0.811585\pi$
$313$	−6.65227	+	5.89340i	−0.376009	+	0.333115i	0.453860	+	0.891073i	$0.350047\pi$
$314$	−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	0.548058	−	0.836440i	$-0.315367\pi$
$317$	15.6683	+	1.90247i	0.880017	+	0.106853i	0.331959	+	0.943294i	$0.392290\pi$
$318$	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	−0.803134	−	0.595799i	$-0.796836\pi$
$331$	3.32772	−	7.81045i	0.182908	−	0.429301i	0.986042	+	0.166498i	$0.0532458\pi$
$332$	−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	−0.0857200	−	0.996319i	$-0.527319\pi$
$347$	14.4862	−	9.16049i	0.777657	−	0.491761i	0.863378	+	0.504558i	$0.168345\pi$
$348$	−11.5090	+	4.90352i	−0.616947	+	0.262856i
$349$	0.276097	−	0.436612i	0.0147791	−	0.0233713i	−0.837720	−	0.546100i	$-0.816112\pi$
$349$	0.276097	−	0.436612i	0.0147791	−	0.0233713i	0.852499	+	0.522729i	$0.175086\pi$
$350$	−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	−0.980450	−	0.196770i	$-0.936955\pi$
$353$	−16.8469	−	22.4192i	−0.896672	−	1.19325i	0.0837774	−	0.996484i	$-0.473302\pi$
$354$	−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	−0.293356	−	0.956003i	$-0.594772\pi$
$359$	−15.2900	−	1.85654i	−0.806975	−	0.0979845i	−0.513618	+	0.858019i	$0.671695\pi$
$360$	−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	−0.910624	−	0.413235i	$-0.864399\pi$
$367$	−0.693578	−	17.2110i	−0.0362045	−	0.898405i	0.874420	−	0.485170i	$-0.161242\pi$
$368$	−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	−0.998882	−	0.0472827i	$-0.984944\pi$
$373$	0.0109238	−	0.271071i	0.000565612	−	0.0140355i	0.999447	+	0.0332472i	$0.0105849\pi$
$374$	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	−0.998065	−	0.0621821i	$-0.980194\pi$
$379$	−35.2055	+	10.1974i	−1.80839	+	0.523805i	−0.810320	+	0.585987i	$0.800707\pi$
$380$	−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	−0.681725	−	0.731608i	$-0.738770\pi$
$383$	4.12280	−	5.48646i	0.210665	−	0.280345i	0.892391	+	0.451263i	$0.149027\pi$
$384$	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	0.953219	+	0.302281i	$0.0977481\pi$
$389$	−0.880473	+	7.25135i	−0.0446418	+	0.367658i	−0.997861	+	0.0653771i	$0.979175\pi$
$390$	−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	−0.856745	−	0.515740i	$-0.827517\pi$
$397$	2.37559	−	14.6176i	0.119227	−	0.733634i	0.975972	−	0.217894i	$-0.0699188\pi$
$398$	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	0.751216	+	0.660056i	$0.229468\pi$
$401$	4.95977	+	30.5187i	0.247679	+	1.52403i	−0.503537	+	0.863974i	$0.667968\pi$
$402$	−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	0.999000	−	0.0447199i	$-0.0142395\pi$
$409$	20.1134	+	19.3191i	0.994542	+	0.955270i	−0.00445793	+	0.999990i	$0.501419\pi$
$410$	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	−0.955760	−	0.294146i	$-0.904965\pi$
$419$	−2.52689	+	5.32532i	−0.123447	+	0.260159i	0.832314	+	0.554305i	$0.187016\pi$
$420$	26.7537	−	8.93170i	1.30545	−	0.435822i
$421$	5.45639	+	22.1374i	0.265928	+	1.07891i	0.940253	+	0.340478i	$0.110589\pi$
$421$	5.45639	+	22.1374i	0.265928	+	1.07891i	−0.674324	+	0.738435i	$0.735565\pi$
$422$	−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	0.979451	−	0.201684i	$-0.0646413\pi$
$431$	29.9507	+	14.2118i	1.44267	+	0.684558i	0.463224	+	0.886241i	$0.346693\pi$
$432$	6.80065	+	4.30047i	0.327197	+	0.206907i
$433$	2.67646	+	0.434968i	0.128623	+	0.0209032i	0.224382	−	0.974501i	$-0.427964\pi$
$433$	2.67646	+	0.434968i	0.128623	+	0.0209032i	−0.0957591	+	0.995405i	$0.530528\pi$
$434$	−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	0.0716399	−	0.997431i	$-0.477177\pi$
$439$	−9.85360	−	3.28962i	−0.470287	−	0.157005i	−0.541927	+	0.840426i	$0.682305\pi$
$440$	−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	−0.689351	−	0.724427i	$-0.742104\pi$
$443$	−20.2706	+	4.99625i	−0.963084	+	0.237379i	−0.273732	+	0.961806i	$0.588258\pi$
$444$	−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	0.992187	+	0.124762i	$0.0398166\pi$
$449$	0.696327	+	8.62556i	0.0328617	+	0.407065i	−0.959325	+	0.282304i	$0.908901\pi$
$450$	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	−0.924144	−	0.382045i	$-0.875220\pi$
$457$	−12.3909	+	11.9016i	−0.579620	+	0.556732i	0.344524	+	0.938778i	$0.388040\pi$
$458$	−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	0.449064	−	0.893499i	$-0.351757\pi$
$461$	−11.8236	−	18.6975i	−0.550679	−	0.870829i	−0.999743	+	0.0226709i	$0.992783\pi$
$462$	−20.6371	+	27.4629i	−0.960123	+	1.27769i
$463$	13.2026	−	25.1554i	0.613577	−	1.16907i	−0.358305	−	0.933604i	$-0.616645\pi$
$463$	13.2026	−	25.1554i	0.613577	−	1.16907i	0.971882	−	0.235468i	$-0.0756624\pi$
$464$	−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	−0.628134	−	0.778105i	$-0.716181\pi$
$467$	−7.44657	+	3.90826i	−0.344586	+	0.180853i	0.283548	+	0.958958i	$0.408489\pi$
$468$	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	−0.0212483	−	0.999774i	$-0.506764\pi$
$479$	13.0517	−	39.0945i	0.596345	−	1.78627i	0.617593	−	0.786498i	$-0.288108\pi$
$480$	−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	−0.410982	−	0.911644i	$-0.634814\pi$
$487$	0.778090	−	0.369208i	0.0352586	−	0.0167304i	0.446240	+	0.894913i	$0.352763\pi$
$488$	−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	0.120718	−	0.992687i	$-0.461480\pi$
$491$	12.1778	−	1.97908i	0.549575	−	0.0893146i	0.428857	+	0.903372i	$0.358916\pi$
$492$	−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	0.292802	−	0.956173i	$-0.405412\pi$
$499$	18.0030	−	2.18595i	0.805923	−	0.0978567i	0.513121	+	0.858316i	$0.328489\pi$
$500$	−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	0.122694	−	0.992445i	$-0.460847\pi$
$503$	9.03832	−	0.729649i	0.402999	−	0.0325334i	0.280305	+	0.959911i	$0.409565\pi$
$504$	−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	−0.756867	−	0.653569i	$-0.773271\pi$
$509$	−32.9095	+	1.32621i	−1.45869	+	0.0587831i	−0.701822	+	0.712353i	$0.747630\pi$
$510$	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	−0.870668	−	0.491872i	$-0.836313\pi$
$521$	2.44706	−	6.45238i	0.107208	−	0.282684i	0.977875	+	0.209188i	$0.0670821\pi$
$522$	4.19012	+	5.57604i	0.183397	+	0.244056i
$523$	−7.90061	+	1.28397i	−0.345470	+	0.0561443i	−0.330671	−	0.943746i	$-0.607275\pi$
$523$	−7.90061	+	1.28397i	−0.345470	+	0.0561443i	−0.0147989	+	0.999890i	$0.504711\pi$
$524$	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	−0.0564312	−	0.998406i	$-0.517972\pi$
$541$	−17.6943	−	6.71056i	−0.760737	−	0.288509i	−0.704305	+	0.709897i	$0.748741\pi$
$542$	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	−0.675978	−	0.736922i	$-0.736279\pi$
$547$	−10.6065	+	5.56673i	−0.453502	+	0.238016i	0.222476	+	0.974938i	$0.428586\pi$
$548$	−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	−0.568330	−	0.822801i	$-0.692410\pi$
$557$	5.44988	−	5.23468i	0.230919	−	0.221801i	0.799249	+	0.601000i	$0.205231\pi$
$558$	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	−0.964308	−	0.264785i	$-0.914699\pi$
$563$	−0.184268	+	0.636166i	−0.00776596	+	0.0268112i	0.956542	+	0.291596i	$0.0941863\pi$
$564$	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	−0.990665	−	0.136320i	$-0.956472\pi$
$569$	−15.7182	+	19.2513i	−0.658941	+	0.807056i	0.331724	+	0.943376i	$0.392370\pi$
$570$	4.85109	+	29.8499i	0.203190	+	1.25028i
$571$	−38.0958	+	9.38977i	−1.59426	+	0.392950i	−0.933767	−	0.357883i	$-0.883499\pi$
$571$	−38.0958	+	9.38977i	−1.59426	+	0.392950i	−0.660493	+	0.750832i	$0.729653\pi$
$572$	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	$0.0890983\pi$
$577$			13.2724i			0.552539i	−0.961080	+	0.276270i	$0.910902\pi$
$578$	−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	−0.346074	−	0.938207i	$-0.612485\pi$
$587$	7.10854	−	4.10412i	0.293401	−	0.169395i	0.639475	+	0.768812i	$0.279152\pi$
$588$	−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	−0.620308	−	0.784358i	$-0.712993\pi$
$593$	−10.6066	−	43.0328i	−0.435562	−	1.76714i	0.184746	−	0.982786i	$-0.440854\pi$
$594$	−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	−0.959417	−	0.281991i	$-0.909005\pi$
$599$	−21.6078	−	31.3042i	−0.882869	−	1.27906i	0.0765482	−	0.997066i	$-0.475610\pi$
$600$	6.63383	+	3.14779i	0.270825	+	0.128508i
$601$	13.7304	+	8.68255i	0.560073	+	0.354169i	0.784313	−	0.620365i	$-0.213016\pi$
$601$	13.7304	+	8.68255i	0.560073	+	0.354169i	−0.224240	+	0.974534i	$0.571990\pi$
$602$	−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	−0.739089	−	0.673608i	$-0.764744\pi$
$607$	−0.893522	+	0.930255i	−0.0362670	+	0.0377579i	0.702822	+	0.711366i	$0.251923\pi$
$608$	−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	−0.986178	−	0.165689i	$-0.947015\pi$
$613$	−2.55562	−	15.7254i	−0.103221	−	0.635142i	0.882957	−	0.469453i	$-0.155549\pi$
$614$	−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	−0.950413	−	0.310989i	$-0.899340\pi$
$617$	1.23126	−	7.57625i	0.0495687	−	0.305008i	0.999982	+	0.00598092i	$0.00190380\pi$
$618$	3.18996	+	39.5148i	0.128319	+	1.58952i
$619$	3.96871	−	16.1017i	0.159516	−	0.647181i	−0.835675	−	0.549225i	$-0.814923\pi$
$619$	3.96871	−	16.1017i	0.159516	−	0.647181i	0.995191	−	0.0979567i	$-0.0312307\pi$
$620$	−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	−0.553049	−	0.833149i	$-0.686536\pi$
$631$	10.0749	−	13.4072i	0.401074	−	0.533732i	0.954122	+	0.299417i	$0.0967921\pi$
$632$	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	0.791955	+	0.610580i	$0.209064\pi$
$641$	−1.17889	+	29.2538i	−0.0465632	+	1.15545i	−0.838518	+	0.544874i	$0.816577\pi$
$642$	24.8399	+	9.42054i	0.980354	+	0.371799i
$643$	32.3784	+	9.37850i	1.27688	+	0.369852i	0.846303	−	0.532703i	$-0.178824\pi$
$643$	32.3784	+	9.37850i	1.27688	+	0.369852i	0.430575	+	0.902555i	$0.358311\pi$
$644$	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	0.785050	+	0.619432i	$0.212637\pi$
$647$	1.33258	+	33.0677i	0.0523892	+	1.30003i	−0.732661	+	0.680594i	$0.761722\pi$
$648$	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	0.766472	−	0.642277i	$-0.222010\pi$
$653$	−4.42062	−	7.65674i	−0.172992	−	0.299631i	−0.939465	+	0.342646i	$0.888677\pi$
$654$	−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	0.999063	−	0.0432760i	$-0.0137795\pi$
$659$	42.6120	+	18.1553i	1.65993	+	0.707229i	0.660865	+	0.750505i	$0.270190\pi$
$660$	38.8498	−	6.31371i	1.51223	−	0.245761i
$661$	14.1261	+	18.7985i	0.549443	+	0.731176i	0.985675	−	0.168658i	$-0.0539434\pi$
$661$	14.1261	+	18.7985i	0.549443	+	0.731176i	−0.436231	+	0.899835i	$0.643687\pi$
$662$	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	0.979796	+	0.199999i	$0.0640938\pi$
$673$	6.70801	+	23.1587i	0.258575	+	0.892703i	−0.721221	+	0.692705i	$0.756419\pi$
$674$	−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	−0.865715	−	0.500537i	$-0.833136\pi$
$683$	2.48211	−	5.82574i	0.0949755	−	0.222916i	0.960691	+	0.277622i	$0.0895461\pi$
$684$	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	−0.992061	−	0.125755i	$-0.959865\pi$
$691$	−21.9980	−	29.2740i	−0.836842	−	1.11363i	0.155219	−	0.987880i	$-0.450392\pi$
$692$	−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	−0.789934	−	0.613191i	$-0.789885\pi$
$701$	−7.31887	+	6.48395i	−0.276430	+	0.244896i	0.513504	+	0.858087i	$0.328347\pi$
$702$	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	0.660786	−	0.750574i	$-0.270223\pi$
$709$	21.7841	+	6.30985i	0.818120	+	0.236971i	0.157334	+	0.987546i	$0.449710\pi$
$710$	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	0.892080	+	0.451878i	$0.149246\pi$
$719$	6.66348	+	32.6399i	0.248506	+	1.21726i	−0.643574	+	0.765384i	$0.722549\pi$
$720$	−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	−0.999433	−	0.0336573i	$-0.989285\pi$
$727$	−0.565871	+	4.66037i	−0.0209870	+	0.172843i	0.978446	+	0.206501i	$0.0662076\pi$
$728$	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	0.836266	+	0.548324i	$0.184734\pi$
$733$	−4.30556	+	17.4684i	−0.159030	+	0.645208i	−0.995296	+	0.0968845i	$0.969112\pi$
$734$	−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	−0.991530	−	0.129875i	$-0.958543\pi$
$739$	−2.50519	−	15.4150i	−0.0921548	−	0.567051i	0.899376	−	0.437177i	$-0.144022\pi$
$740$	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	−0.884005	−	0.467478i	$-0.845163\pi$
$743$	1.73201	−	21.4547i	0.0635411	−	0.787098i	0.947546	−	0.319620i	$-0.103555\pi$
$744$	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	0.664752	−	0.747064i	$-0.268537\pi$
$751$	7.53045	+	4.76197i	0.274790	+	0.173767i	−0.389962	+	0.920831i	$0.627512\pi$
$752$	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	0.412710	+	0.910863i	$0.364582\pi$
$757$	−15.2388	+	32.1152i	−0.553865	+	1.16725i	−0.966575	+	0.256384i	$0.917469\pi$
$758$	−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	−0.805748	−	0.592259i	$-0.798236\pi$
$761$	−45.6977	−	1.84155i	−1.65654	−	0.0667563i	−0.850792	+	0.525503i	$0.823877\pi$
$762$	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	0.369859	−	0.929088i	$-0.379406\pi$
$769$	−3.21407	−	1.52509i	−0.115902	−	0.0549963i	−0.485761	+	0.874092i	$0.661457\pi$
$770$	−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	−0.408200	−	0.912893i	$-0.633843\pi$
$773$	11.2489	−	9.18442i	0.404594	−	0.330341i	0.812793	+	0.582552i	$0.197946\pi$
$774$	−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	−0.465572	−	0.885010i	$-0.654151\pi$
$787$	−4.15177	−	51.4289i	−0.147995	−	1.83324i	0.317577	−	0.948232i	$-0.397131\pi$
$788$	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	0.660596	−	0.750741i	$-0.270304\pi$
$797$	−9.56255	−	20.1526i	−0.338723	−	0.713843i	−0.999319	+	0.0368980i	$0.988252\pi$
$798$	−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	−0.995434	−	0.0954537i	$-0.969570\pi$
$809$	−33.5824	+	25.2356i	−1.18070	+	0.887235i	−0.185262	+	0.982689i	$0.559313\pi$
$810$	0.204649	−	5.07832i	0.00719064	−	0.178434i
$811$	12.3144	+	4.67024i	0.432417	+	0.163994i	0.561203	−	0.827678i	$-0.310339\pi$
$811$	12.3144	+	4.67024i	0.432417	+	0.163994i	−0.128786	+	0.991672i	$0.541108\pi$
$812$	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	0.818567	+	0.574412i	$0.194769\pi$
$821$	19.0770	+	44.7754i	0.665793	+	1.56267i	−0.152774	+	0.988261i	$0.548821\pi$
$822$	4.79320	+	8.30207i	0.167182	+	0.289568i
$823$	−20.3328	+	35.2174i	−0.708756	+	1.22760i	0.256562	+	0.966528i	$0.417410\pi$
$823$	−20.3328	+	35.2174i	−0.708756	+	1.22760i	−0.965319	+	0.261074i	$0.915923\pi$
$824$	−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	0.0277371	−	0.999615i	$-0.491170\pi$
$827$	27.9590	−	19.2987i	0.972229	−	0.671081i	0.944492	+	0.328534i	$0.106554\pi$
$828$	31.2528	+	13.3156i	1.08611	+	0.462749i
$829$	36.8031	−	5.98109i	1.27823	−	0.207732i	0.516868	−	0.856065i	$-0.327098\pi$
$829$	36.8031	−	5.98109i	1.27823	−	0.207732i	0.761357	+	0.648333i	$0.224534\pi$
$830$	−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	0.997411	−	0.0719081i	$-0.0229088\pi$
$839$	4.54294	+	13.6078i	0.156840	+	0.469793i	−0.840571	+	0.541701i	$0.817781\pi$
$840$	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	−0.342848	−	0.939391i	$-0.611391\pi$
$853$	−13.1697	+	1.59909i	−0.450922	+	0.0547518i	−0.108074	+	0.994143i	$0.534468\pi$
$854$	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	−0.898795	−	0.438368i	$-0.855556\pi$
$857$	−15.1270	−	39.8867i	−0.516729	−	1.36250i	0.382066	−	0.924135i	$-0.375213\pi$
$858$	29.3879	−	27.1812i	1.00329	−	0.927949i
$859$	−11.3646	+	29.9661i	−0.387756	+	1.02243i	0.589011	+	0.808125i	$0.299518\pi$
$859$	−11.3646	+	29.9661i	−0.387756	+	1.02243i	−0.976767	+	0.214304i	$0.931252\pi$
$860$	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	−0.794731	−	0.606962i	$-0.792388\pi$
$863$	−14.9536	+	10.3217i	−0.509027	+	0.351356i	0.285704	+	0.958318i	$0.407773\pi$
$864$	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	0.471594	−	0.881816i	$-0.343679\pi$
$877$	37.0501	−	7.56383i	1.25109	−	0.255412i	0.779499	+	0.626404i	$0.215474\pi$
$878$	−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	0.238873	−	0.971051i	$-0.423222\pi$
$881$	36.7472	−	27.6137i	1.23804	−	0.930329i	0.999171	+	0.0407216i	$0.0129657\pi$
$882$	6.48388	+	1.32369i	0.218324	+	0.0445711i
$883$	−14.5520	−	7.63748i	−0.489714	−	0.257022i	0.201744	−	0.979438i	$-0.435339\pi$
$883$	−14.5520	−	7.63748i	−0.489714	−	0.257022i	−0.691458	+	0.722416i	$0.743031\pi$
$884$	−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	0.770155	−	0.637857i	$-0.220179\pi$
$887$	42.5300	+	3.43338i	1.42802	+	0.115281i	0.657862	+	0.753138i	$0.271461\pi$
$888$	−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	−0.784886	−	0.619641i	$-0.787278\pi$
$907$	−0.625527	+	0.766131i	−0.0207703	+	0.0254390i	0.764115	+	0.645080i	$0.223176\pi$
$908$	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	0.325848	−	0.945422i	$-0.394350\pi$
$911$	5.28235	+	1.30198i	0.175012	+	0.0431366i	−0.150836	+	0.988559i	$0.548196\pi$
$912$	−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	−0.0973644	−	0.995249i	$-0.531041\pi$
$919$	−15.3055	−	2.48738i	−0.504882	−	0.0820512i	−0.407517	+	0.913198i	$0.633605\pi$
$920$	−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	−0.172070	−	0.985085i	$-0.555046\pi$
$929$	−12.8882	−	0.519377i	−0.422849	−	0.0170402i	−0.250779	+	0.968044i	$0.580687\pi$
$930$	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	0.961805	+	0.273735i	$0.0882592\pi$
$937$	26.8359	+	38.8785i	0.876691	+	1.27011i	−0.0851139	+	0.996371i	$0.527125\pi$
$938$	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	−0.999983	−	0.00584059i	$-0.998141\pi$
$941$	−13.3971	−	25.5261i	−0.436735	−	0.832128i	0.563248	−	0.826288i	$-0.309551\pi$
$942$	−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	−0.975751	−	0.218882i	$-0.929759\pi$
$947$	0.691644	−	8.56754i	0.0224754	−	0.278408i	0.998227	−	0.0595259i	$-0.0189589\pi$
$948$	−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	−0.999891	−	0.0147343i	$-0.995310\pi$
$953$	−39.8921	−	29.9770i	−1.29223	−	0.971049i	−0.292340	−	0.956314i	$-0.594434\pi$
$954$	−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	−0.00124766	−	0.999999i	$-0.500397\pi$
$967$	−29.1284	−	20.1059i	−0.936706	−	0.646561i	−0.935458	+	0.353438i	$0.885013\pi$
$968$	−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	0.998789	−	0.0491938i	$-0.0156652\pi$
$971$	1.88964	+	9.25606i	0.0606414	+	0.297041i	−0.938148	+	0.346235i	$0.887460\pi$
$972$	−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	−0.466762	−	0.884383i	$-0.654580\pi$
$977$	−38.8469	−	7.93065i	−1.24282	−	0.253724i	−0.776060	+	0.630659i	$0.782785\pi$
$978$	−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	−0.706171	−	0.708042i	$-0.749579\pi$
$983$	2.56553	−	2.89589i	0.0818278	−	0.0923645i	0.787999	+	0.615677i	$0.211117\pi$
$984$	−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	0.999917	−	0.0129126i	$-0.00411032\pi$
$991$	15.3867	+	26.6506i	0.488776	+	0.846584i	−0.511141	+	0.859497i	$0.670777\pi$
$992$	−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	0.531583	−	0.847006i	$-0.321597\pi$
$997$	9.12401	+	3.88738i	0.288960	+	0.123115i	−0.242623	+	0.970121i	$0.578008\pi$
$998$	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.127.15	yes	360
169.4	even	78	inner	507.2.t.b.4.15	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.4.15	✓	360	169.4	even	78	inner
507.2.t.b.127.15	yes	360	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.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

Varieties

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Representations

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