LMFDB - Embedded newform 507.2.q.a.16.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, 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 $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.8
Character	$\chi$	$=$	507.16
Dual form			507.2.q.a.412.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.164145 - 0.0132511i) q^{2} +(0.845190 + 0.534466i) q^{3} +(-1.94733 - 0.316472i) q^{4} +(2.22303 + 1.96943i) q^{5} +(-0.131651 - 0.0989295i) q^{6} +(-0.158039 + 0.164536i) q^{7} +(0.635238 + 0.156572i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-0.338802 - 0.352730i) q^{10} +(-2.22412 + 4.68723i) q^{11} +(-1.47672 - 1.30826i) q^{12} +(-3.60200 - 0.160034i) q^{13} +(0.0281215 - 0.0249135i) q^{14} +(0.826289 + 2.85268i) q^{15} +(3.64050 + 1.21538i) q^{16} +(-1.50394 + 1.56577i) q^{17} +(-0.0583959 - 0.153977i) q^{18} +(2.38525 - 4.13137i) q^{19} +(-3.70571 - 4.53867i) q^{20} +(-0.221511 + 0.0545977i) q^{21} +(0.427188 - 0.739912i) q^{22} +(1.04711 + 1.81364i) q^{23} +(0.453214 + 0.471846i) q^{24} +(0.460516 + 3.79269i) q^{25} +(0.589128 + 0.0739994i) q^{26} +(-0.120537 + 0.992709i) q^{27} +(0.359825 - 0.270391i) q^{28} +(5.67697 + 0.458292i) q^{29} +(-0.0978298 - 0.479202i) q^{30} +(-0.846498 + 6.97154i) q^{31} +(-1.78526 - 0.760626i) q^{32} +(-4.38496 + 2.77288i) q^{33} +(0.267612 - 0.237084i) q^{34} +(-0.675368 + 0.0545213i) q^{35} +(-0.548890 - 1.89499i) q^{36} +(-10.5266 + 4.48495i) q^{37} +(-0.446271 + 0.646536i) q^{38} +(-2.95884 - 2.06040i) q^{39} +(1.10380 + 1.59912i) q^{40} +(-0.450107 - 0.284630i) q^{41} +(0.0370834 - 0.00602664i) q^{42} +(3.19123 + 1.35966i) q^{43} +(5.81447 - 8.42372i) q^{44} +(-0.826289 + 2.85268i) q^{45} +(-0.147844 - 0.311575i) q^{46} +(0.481360 - 1.26924i) q^{47} +(2.42734 + 2.97295i) q^{48} +(0.279766 + 6.94232i) q^{49} +(-0.0253338 - 0.628652i) q^{50} +(-2.10797 + 0.519567i) q^{51} +(6.96364 + 1.45157i) q^{52} +(7.73573 + 1.90669i) q^{53} +(0.0329400 - 0.161351i) q^{54} +(-14.1755 + 6.03960i) q^{55} +(-0.126154 + 0.0797749i) q^{56} +(4.22407 - 2.21696i) q^{57} +(-0.925771 - 0.150453i) q^{58} +(8.17603 - 2.72956i) q^{59} +(-0.706265 - 5.81662i) q^{60} +(0.807216 - 2.78683i) q^{61} +(0.231329 - 1.13312i) q^{62} +(-0.216400 - 0.0722449i) q^{63} +(-6.51384 - 3.41873i) q^{64} +(-7.69218 - 7.44966i) q^{65} +(0.756513 - 0.397048i) q^{66} +(14.6335 - 2.37817i) q^{67} +(3.42420 - 2.57312i) q^{68} +(-0.0843254 + 2.09251i) q^{69} +0.111581 q^{70} +(0.600339 - 14.8973i) q^{71} +(0.130867 + 0.641027i) q^{72} +(-4.24371 - 6.14808i) q^{73} +(1.78731 - 0.596692i) q^{74} +(-1.63784 + 3.45167i) q^{75} +(-5.95234 + 7.29029i) q^{76} +(-0.419720 - 1.10671i) q^{77} +(0.458375 + 0.377413i) q^{78} +(3.43630 - 9.06078i) q^{79} +(5.69935 + 9.87156i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(0.0701110 + 0.0526850i) q^{82} +(-13.0810 - 6.86545i) q^{83} +(0.448635 - 0.0362176i) q^{84} +(-6.42699 + 0.518840i) q^{85} +(-0.505806 - 0.265468i) q^{86} +(4.55318 + 3.42149i) q^{87} +(-2.14673 + 2.62927i) q^{88} +(3.64596 + 6.31499i) q^{89} +(0.173432 - 0.457303i) q^{90} +(0.595587 - 0.567366i) q^{91} +(-1.46510 - 3.86314i) q^{92} +(-4.44150 + 5.43985i) q^{93} +(-0.0958316 + 0.201961i) q^{94} +(13.4390 - 4.48658i) q^{95} +(-1.10235 - 1.59703i) q^{96} +(2.65909 + 13.0251i) q^{97} +(0.0460715 - 1.14325i) q^{98} -5.18814 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21}+ \cdots + 30 q^{99}+O(q^{100}) $ 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

Coefficient data

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

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

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

$2$	−0.164145	−	0.0132511i	−0.116068	−	0.00936997i	0.0222961	−	0.999751i	$-0.492902\pi$
$2$	−0.164145	−	0.0132511i	−0.116068	−	0.00936997i	−0.138364	+	0.990381i	$0.544184\pi$
$3$	0.845190	+	0.534466i	0.487971	+	0.308574i
$3$	0.845190	+	0.534466i	0.487971	+	0.308574i
$4$	−1.94733	−	0.316472i	−0.973666	−	0.158236i
$5$	2.22303	+	1.96943i	0.994170	+	0.880758i	0.992865	−	0.119241i	$-0.0380462\pi$
$5$	2.22303	+	1.96943i	0.994170	+	0.880758i	0.00130491	+	0.999999i	$0.499585\pi$
$6$	−0.131651	−	0.0989295i	−0.0537464	−	0.0403878i
$7$	−0.158039	+	0.164536i	−0.0597330	+	0.0621887i	−0.750398	−	0.660986i	$-0.770138\pi$
$7$	−0.158039	+	0.164536i	−0.0597330	+	0.0621887i	0.690665	+	0.723175i	$0.257318\pi$
$8$	0.635238	+	0.156572i	0.224590	+	0.0553566i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−0.338802	−	0.352730i	−0.107139	−	0.111543i
$11$	−2.22412	+	4.68723i	−0.670596	+	1.41325i	0.227643	+	0.973745i	$0.426898\pi$
$11$	−2.22412	+	4.68723i	−0.670596	+	1.41325i	−0.898239	+	0.439507i	$0.855153\pi$
$12$	−1.47672	−	1.30826i	−0.426293	−	0.377663i
$13$	−3.60200	−	0.160034i	−0.999014	−	0.0443856i
$13$	−3.60200	−	0.160034i	−0.999014	−	0.0443856i
$14$	0.0281215	−	0.0249135i	0.00751579	−	0.00665841i
$15$	0.826289	+	2.85268i	0.213347	+	0.736559i
$16$	3.64050	+	1.21538i	0.910126	+	0.303845i
$17$	−1.50394	+	1.56577i	−0.364759	+	0.379755i	−0.878138	−	0.478407i	$-0.841214\pi$
$17$	−1.50394	+	1.56577i	−0.364759	+	0.379755i	0.513379	+	0.858162i	$0.328394\pi$
$18$	−0.0583959	−	0.153977i	−0.0137640	−	0.0362928i
$19$	2.38525	−	4.13137i	0.547214	−	0.947802i	−0.451250	−	0.892397i	$-0.649022\pi$
$19$	2.38525	−	4.13137i	0.547214	−	0.947802i	0.998464	−	0.0554043i	$-0.0176448\pi$
$20$	−3.70571	−	4.53867i	−0.828622	−	1.01488i
$21$	−0.221511	+	0.0545977i	−0.0483378	+	0.0119142i
$22$	0.427188	−	0.739912i	0.0910768	−	0.157750i
$23$	1.04711	+	1.81364i	0.218337	+	0.378170i	0.954300	−	0.298852i	$-0.0966036\pi$
$23$	1.04711	+	1.81364i	0.218337	+	0.378170i	−0.735963	+	0.677022i	$0.763270\pi$
$24$	0.453214	+	0.471846i	0.0925120	+	0.0963152i
$25$	0.460516	+	3.79269i	0.0921032	+	0.758538i
$26$	0.589128	+	0.0739994i	0.115538	+	0.0145125i
$27$	−0.120537	+	0.992709i	−0.0231973	+	0.191047i
$28$	0.359825	−	0.270391i	0.0680005	−	0.0510991i
$29$	5.67697	+	0.458292i	1.05419	+	0.0851027i	0.595389	−	0.803438i	$-0.296998\pi$
$29$	5.67697	+	0.458292i	1.05419	+	0.0851027i	0.458798	+	0.888541i	$0.348280\pi$
$30$	−0.0978298	−	0.479202i	−0.0178612	−	0.0874899i
$31$	−0.846498	+	6.97154i	−0.152036	+	1.25213i	0.694382	+	0.719606i	$0.255678\pi$
$31$	−0.846498	+	6.97154i	−0.152036	+	1.25213i	−0.846418	+	0.532519i	$0.821245\pi$
$32$	−1.78526	−	0.760626i	−0.315592	−	0.134461i
$33$	−4.38496	+	2.77288i	−0.763324	+	0.482697i
$34$	0.267612	−	0.237084i	0.0458951	−	0.0406595i
$35$	−0.675368	+	0.0545213i	−0.114158	+	0.00921578i
$36$	−0.548890	−	1.89499i	−0.0914817	−	0.315831i
$37$	−10.5266	+	4.48495i	−1.73056	+	0.737321i	−0.732135	+	0.681159i	$0.761476\pi$
$37$	−10.5266	+	4.48495i	−1.73056	+	0.737321i	−0.998422	+	0.0561624i	$0.982114\pi$
$38$	−0.446271	+	0.646536i	−0.0723948	+	0.104882i
$39$	−2.95884	−	2.06040i	−0.473794	−	0.329929i
$40$	1.10380	+	1.59912i	0.174525	+	0.252844i
$41$	−0.450107	−	0.284630i	−0.0702949	−	0.0444518i	0.498856	−	0.866685i	$-0.333754\pi$
$41$	−0.450107	−	0.284630i	−0.0702949	−	0.0444518i	−0.569151	+	0.822233i	$0.692728\pi$
$42$	0.0370834	−	0.00602664i	0.00572210	−	0.000929931i
$43$	3.19123	+	1.35966i	0.486658	+	0.207346i	0.621337	−	0.783544i	$-0.286590\pi$
$43$	3.19123	+	1.35966i	0.486658	+	0.207346i	−0.134679	+	0.990889i	$0.543000\pi$
$44$	5.81447	−	8.42372i	0.876565	−	1.26992i
$45$	−0.826289	+	2.85268i	−0.123176	+	0.425253i
$46$	−0.147844	−	0.311575i	−0.0217984	−	0.0459392i
$47$	0.481360	−	1.26924i	0.0702136	−	0.185138i	−0.895316	−	0.445432i	$-0.853050\pi$
$47$	0.481360	−	1.26924i	0.0702136	−	0.185138i	0.965529	+	0.260294i	$0.0838194\pi$
$48$	2.42734	+	2.97295i	0.350356	+	0.429108i
$49$	0.279766	+	6.94232i	0.0399665	+	0.991760i
$50$	−0.0253338	−	0.628652i	−0.00358274	−	0.0889049i
$51$	−2.10797	+	0.519567i	−0.295174	+	0.0727540i
$52$	6.96364	+	1.45157i	0.965683	+	0.201297i
$53$	7.73573	+	1.90669i	1.06258	+	0.261903i	0.731601	−	0.681733i	$-0.238774\pi$
$53$	7.73573	+	1.90669i	1.06258	+	0.261903i	0.330983	+	0.943637i	$0.392620\pi$
$54$	0.0329400	−	0.161351i	0.00448256	−	0.0219570i
$55$	−14.1755	+	6.03960i	−1.91142	+	0.814380i
$56$	−0.126154	+	0.0797749i	−0.0168580	+	0.0106604i
$57$	4.22407	−	2.21696i	0.559491	−	0.293644i
$58$	−0.925771	−	0.150453i	−0.121560	−	0.0197554i
$59$	8.17603	−	2.72956i	1.06443	−	0.355359i	0.270091	−	0.962835i	$-0.412946\pi$
$59$	8.17603	−	2.72956i	1.06443	−	0.355359i	0.794338	+	0.607476i	$0.207818\pi$
$60$	−0.706265	−	5.81662i	−0.0911784	−	0.750922i
$61$	0.807216	−	2.78683i	0.103353	−	0.356817i	−0.892127	−	0.451785i	$-0.850787\pi$
$61$	0.807216	−	2.78683i	0.103353	−	0.356817i	0.995480	+	0.0949674i	$0.0302747\pi$
$62$	0.231329	−	1.13312i	0.0293788	−	0.143907i
$63$	−0.216400	−	0.0722449i	−0.0272638	−	0.00910200i
$64$	−6.51384	−	3.41873i	−0.814230	−	0.427341i
$65$	−7.69218	−	7.44966i	−0.954097	−	0.924017i
$66$	0.756513	−	0.397048i	0.0931203	−	0.0488733i
$67$	14.6335	−	2.37817i	1.78776	−	0.290540i	0.825850	−	0.563890i	$-0.190696\pi$
$67$	14.6335	−	2.37817i	1.78776	−	0.290540i	0.961915	+	0.273350i	$0.0881317\pi$
$68$	3.42420	−	2.57312i	0.415245	−	0.312036i
$69$	−0.0843254	+	2.09251i	−0.0101516	+	0.251909i
$70$	0.111581			0.0133364
$71$	0.600339	−	14.8973i	0.0712471	−	1.76798i	−0.430146	−	0.902759i	$-0.641538\pi$
$71$	0.600339	−	14.8973i	0.0712471	−	1.76798i	0.501393	−	0.865220i	$-0.332821\pi$
$72$	0.130867	+	0.641027i	0.0154228	+	0.0755458i
$73$	−4.24371	−	6.14808i	−0.496689	−	0.719578i	0.491827	−	0.870693i	$-0.336329\pi$
$73$	−4.24371	−	6.14808i	−0.496689	−	0.719578i	−0.988516	+	0.151115i	$0.951714\pi$
$74$	1.78731	−	0.596692i	0.207771	−	0.0693641i
$75$	−1.63784	+	3.45167i	−0.189121	+	0.398565i
$76$	−5.95234	+	7.29029i	−0.682780	+	0.836254i
$77$	−0.419720	−	1.10671i	−0.0478315	−	0.126121i
$78$	0.458375	+	0.377413i	0.0519008	+	0.0427336i
$79$	3.43630	−	9.06078i	0.386614	−	1.01942i	−0.590563	−	0.806992i	$-0.701094\pi$
$79$	3.43630	−	9.06078i	0.386614	−	1.01942i	0.977177	−	0.212426i	$-0.0681365\pi$
$80$	5.69935	+	9.87156i	0.637206	+	1.10367i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	0.0701110	+	0.0526850i	0.00774246	+	0.00581808i
$83$	−13.0810	−	6.86545i	−1.43583	−	0.753581i	−0.445891	−	0.895087i	$-0.647113\pi$
$83$	−13.0810	−	6.86545i	−1.43583	−	0.753581i	−0.989937	+	0.141507i	$0.954805\pi$
$84$	0.448635	−	0.0362176i	0.0489501	−	0.00395166i
$85$	−6.42699	+	0.518840i	−0.697105	+	0.0562761i
$86$	−0.505806	−	0.265468i	−0.0545425	−	0.0286261i
$87$	4.55318	+	3.42149i	0.488152	+	0.366822i
$88$	−2.14673	+	2.62927i	−0.228842	+	0.280281i
$89$	3.64596	+	6.31499i	0.386471	+	0.669387i	0.991972	−	0.126457i	$-0.0403606\pi$
$89$	3.64596	+	6.31499i	0.386471	+	0.669387i	−0.605501	+	0.795844i	$0.707027\pi$
$90$	0.173432	−	0.457303i	0.0182814	−	0.0482040i
$91$	0.595587	−	0.567366i	0.0624344	−	0.0594761i
$92$	−1.46510	−	3.86314i	−0.152747	−	0.402760i
$93$	−4.44150	+	5.43985i	−0.460562	+	0.564086i
$94$	−0.0958316	+	0.201961i	−0.00988427	+	0.0208307i
$95$	13.4390	−	4.48658i	1.37881	−	0.460313i
$96$	−1.10235	−	1.59703i	−0.112508	−	0.162996i
$97$	2.65909	+	13.0251i	0.269990	+	1.32250i	0.858003	+	0.513645i	$0.171705\pi$
$97$	2.65909	+	13.0251i	0.269990	+	1.32250i	−0.588013	+	0.808851i	$0.700090\pi$
$98$	0.0460715	−	1.14325i	0.00465392	−	0.115486i
$99$	−5.18814			−0.521428
$100$	0.303504	−	7.53137i	0.0303504	−	0.753137i
$101$	4.60040	−	3.45698i	0.457757	−	0.343982i	−0.346717	−	0.937970i	$-0.612704\pi$
$101$	4.60040	−	3.45698i	0.457757	−	0.343982i	0.804474	+	0.593988i	$0.202447\pi$
$102$	0.352897	−	0.0573513i	0.0349420	−	0.00567862i
$103$	7.01938	−	3.68406i	0.691640	−	0.363001i	−0.0819944	−	0.996633i	$-0.526129\pi$
$103$	7.01938	−	3.68406i	0.691640	−	0.363001i	0.773635	+	0.633632i	$0.218437\pi$
$104$	−2.26307	−	0.665632i	−0.221912	−	0.0652706i
$105$	−0.599954	−	0.314880i	−0.0585495	−	0.0307291i
$106$	−1.24451	−	0.415480i	−0.120878	−	0.0403549i
$107$	2.84771	−	13.9490i	0.275298	−	1.34850i	−0.573250	−	0.819381i	$-0.694318\pi$
$107$	2.84771	−	13.9490i	0.275298	−	1.34850i	0.848548	−	0.529118i	$-0.177477\pi$
$108$	0.548890	−	1.89499i	0.0528170	−	0.182345i
$109$	1.00309	+	8.26117i	0.0960784	+	0.791277i	0.958501	+	0.285088i	$0.0920229\pi$
$109$	1.00309	+	8.26117i	0.0960784	+	0.791277i	−0.862423	+	0.506188i	$0.831054\pi$
$110$	2.40686	−	0.803528i	0.229485	−	0.0766134i
$111$	−11.2940	−	1.83545i	−1.07198	−	0.174214i
$112$	−0.775314	+	0.406916i	−0.0732602	+	0.0384499i
$113$	9.35339	−	5.91472i	0.879893	−	0.556410i	−0.0164040	−	0.999865i	$-0.505222\pi$
$113$	9.35339	−	5.91472i	0.879893	−	0.556410i	0.896297	+	0.443455i	$0.146247\pi$
$114$	−0.722735	+	0.307929i	−0.0676904	+	0.0288402i
$115$	−1.24410	+	6.09399i	−0.116013	+	0.568267i
$116$	−10.9099	−	2.68905i	−1.01296	−	0.249672i
$117$	−1.39957	−	3.32283i	−0.129390	−	0.307196i
$118$	−1.37822	+	0.339701i	−0.126876	+	0.0312720i
$119$	−0.0199440	−	0.494904i	−0.00182826	−	0.0453678i
$120$	0.0782400	+	1.94150i	0.00714230	+	0.177234i
$121$	−10.0665	−	12.3292i	−0.915136	−	1.12084i
$122$	−0.169429	+	0.446747i	−0.0153394	+	0.0404466i
$123$	−0.228301	−	0.481133i	−0.0205852	−	0.0433823i
$124$	3.85471	−	13.3080i	0.346163	−	1.19509i
$125$	1.98988	−	2.88284i	0.177980	−	0.257849i
$126$	0.0345636	+	0.0147262i	0.00307917	+	0.00131191i
$127$	−1.82224	+	0.296143i	−0.161698	+	0.0262785i	−0.240721	−	0.970594i	$-0.577384\pi$
$127$	−1.82224	+	0.296143i	−0.161698	+	0.0262785i	0.0790233	+	0.996873i	$0.474820\pi$
$128$	4.30416	+	2.72178i	0.380437	+	0.240574i
$129$	1.97051	+	2.85477i	0.173493	+	0.251348i
$130$	1.16391	+	1.32475i	0.102082	+	0.116189i
$131$	−9.05618	+	13.1201i	−0.791242	+	1.14631i	0.194967	+	0.980810i	$0.437540\pi$
$131$	−9.05618	+	13.1201i	−0.791242	+	1.14631i	−0.986209	+	0.165503i	$0.947075\pi$
$132$	9.41652	−	4.01201i	0.819603	−	0.349200i
$133$	0.302797	+	1.04538i	0.0262558	+	0.0906455i
$134$	−2.43352	+	0.196454i	−0.210224	+	0.0169711i
$135$	−2.22303	+	1.96943i	−0.191328	+	0.169502i
$136$	−1.20052	+	0.759161i	−0.102943	+	0.0650975i
$137$	−5.98592	−	2.55036i	−0.511412	−	0.217892i	0.120816	−	0.992675i	$-0.461449\pi$
$137$	−5.98592	−	2.55036i	−0.511412	−	0.217892i	−0.632228	+	0.774783i	$0.717859\pi$
$138$	0.0415697	−	0.342358i	0.00353865	−	0.0291434i
$139$	−3.79838	−	18.6057i	−0.322175	−	1.57812i	−0.741929	−	0.670478i	$-0.766089\pi$
$139$	−3.79838	−	18.6057i	−0.322175	−	1.57812i	0.419755	−	0.907637i	$-0.362116\pi$
$140$	1.33242	+	0.107564i	0.112610	+	0.00909082i
$141$	1.08521	−	0.815480i	0.0913909	−	0.0686758i
$142$	−0.295948	+	2.43735i	−0.0248354	+	0.204538i
$143$	8.76138	−	16.5274i	0.732663	−	1.38209i
$144$	0.462622	+	3.81004i	0.0385519	+	0.317503i
$145$	11.7175	+	12.1992i	0.973086	+	1.01309i
$146$	0.615114	+	1.06541i	0.0509072	+	0.0881738i
$147$	−3.47398	+	6.01710i	−0.286529	+	0.496282i
$148$	21.9181	−	5.40232i	1.80166	−	0.444068i
$149$	7.79502	+	9.54716i	0.638593	+	0.782134i	0.987936	−	0.154861i	$-0.0494928\pi$
$149$	7.79502	+	9.54716i	0.638593	+	0.782134i	−0.349344	+	0.936995i	$0.613595\pi$
$150$	0.314581	−	0.544871i	0.0256855	−	0.0444885i
$151$	−1.24873	−	3.29263i	−0.101620	−	0.267951i	0.874558	−	0.484921i	$-0.161152\pi$
$151$	−1.24873	−	3.29263i	−0.101620	−	0.267951i	−0.976178	+	0.216970i	$0.930382\pi$
$152$	2.16206	−	2.25094i	0.175366	−	0.182575i
$153$	−2.05932	−	0.687503i	−0.166486	−	0.0555813i
$154$	0.0542296	+	0.187222i	0.00436995	+	0.0150868i
$155$	−15.6118	+	13.8308i	−1.25397	+	1.11092i
$156$	5.10978	+	4.94868i	0.409110	+	0.396212i
$157$	3.25944	+	2.88761i	0.260131	+	0.230456i	0.783100	−	0.621895i	$-0.213637\pi$
$157$	3.25944	+	2.88761i	0.260131	+	0.230456i	−0.522969	+	0.852352i	$0.675176\pi$
$158$	−0.684117	+	1.44175i	−0.0544254	+	0.114699i
$159$	5.51910	+	5.74599i	0.437693	+	0.455687i
$160$	−2.47068	−	5.20684i	−0.195324	−	0.411637i
$161$	−0.463892	−	0.114339i	−0.0365598	−	0.00901118i
$162$	0.114077	−	0.118767i	0.00896273	−	0.00933119i
$163$	−2.21150	−	1.66183i	−0.173218	−	0.130165i	0.510598	−	0.859820i	$-0.329424\pi$
$163$	−2.21150	−	1.66183i	−0.173218	−	0.130165i	−0.683815	+	0.729655i	$0.739681\pi$
$164$	0.786430	+	0.696716i	0.0614099	+	0.0544044i
$165$	−15.2089	−	2.47169i	−1.18401	−	0.192421i
$166$	2.05621	+	1.30027i	0.159592	+	0.100920i
$167$	6.43114	+	0.519175i	0.497656	+	0.0401750i	0.326747	−	0.945112i	$-0.394047\pi$
$167$	6.43114	+	0.519175i	0.497656	+	0.0401750i	0.170909	+	0.985287i	$0.445330\pi$
$168$	−0.149261			−0.0115157
$169$	12.9488	+	1.15289i	0.996060	+	0.0886837i
$170$	1.06183			0.0814388
$171$	4.75503	+	0.383866i	0.363626	+	0.0293549i
$172$	−5.78409	−	3.65764i	−0.441033	−	0.278892i
$173$	6.48539	+	1.05398i	0.493075	+	0.0801325i	0.401865	−	0.915699i	$-0.368362\pi$
$173$	6.48539	+	1.05398i	0.493075	+	0.0801325i	0.0912106	+	0.995832i	$0.470926\pi$
$174$	−0.702041	−	0.621954i	−0.0532216	−	0.0471502i
$175$	−0.696812	−	0.523620i	−0.0526741	−	0.0395820i
$176$	−13.7937	+	14.3607i	−1.03974	+	1.08248i
$177$	8.36916	+	2.06281i	0.629065	+	0.155050i
$178$	−0.514784	−	1.08489i	−0.0385847	−	0.0813156i
$179$	8.80802	+	9.17012i	0.658342	+	0.685407i	0.963748	−	0.266816i	$-0.0859715\pi$
$179$	8.80802	+	9.17012i	0.658342	+	0.685407i	−0.305405	+	0.952222i	$0.598792\pi$
$180$	2.51185	−	5.29362i	0.187223	−	0.394563i
$181$	−13.0567	−	11.5673i	−0.970499	−	0.859787i	0.0196494	−	0.999807i	$-0.493745\pi$
$181$	−13.0567	−	11.5673i	−0.970499	−	0.859787i	−0.990149	+	0.140020i	$0.955283\pi$
$182$	−0.105281	+	0.0852379i	−0.00780392	+	0.00631825i
$183$	2.17172	−	1.92397i	0.160538	−	0.142224i
$184$	0.381196	+	1.31604i	0.0281021	+	0.0970198i
$185$	−32.2337	−	10.7612i	−2.36987	−	0.791179i
$186$	0.801133	−	0.834068i	0.0587419	−	0.0611568i
$187$	−3.99417	−	10.5318i	−0.292083	−	0.770159i
$188$	−1.33905	+	2.31930i	−0.0976601	+	0.169152i
$189$	−0.144287	−	0.176719i	−0.0104953	−	0.0128544i
$190$	−2.26539	+	0.558367i	−0.164348	+	0.0405082i
$191$	1.15011	−	1.99204i	0.0832188	−	0.144139i	−0.821412	−	0.570335i	$-0.806813\pi$
$191$	1.15011	−	1.99204i	0.0832188	−	0.144139i	0.904631	+	0.426196i	$0.140147\pi$
$192$	−3.67824	−	6.37090i	−0.265454	−	0.459780i
$193$	−7.47154	−	7.77869i	−0.537813	−	0.559923i	0.395740	−	0.918363i	$-0.370488\pi$
$193$	−7.47154	−	7.77869i	−0.537813	−	0.559923i	−0.933553	+	0.358440i	$0.883309\pi$
$194$	−0.263878	−	2.17323i	−0.0189454	−	0.156029i
$195$	−2.51976	−	10.4076i	−0.180444	−	0.745303i
$196$	1.65225	−	13.6075i	0.118018	−	0.971967i
$197$	−18.3302	+	13.7743i	−1.30597	+	0.981375i	−0.306408	+	0.951900i	$0.599127\pi$
$197$	−18.3302	+	13.7743i	−1.30597	+	0.981375i	−0.999566	+	0.0294749i	$0.990616\pi$
$198$	0.851606	+	0.0687487i	0.0605210	+	0.00488576i
$199$	−1.18316	−	5.79551i	−0.0838721	−	0.410833i	−0.999952	−	0.00983598i	$-0.996869\pi$
$199$	−1.18316	−	5.79551i	−0.0838721	−	0.410833i	0.916080	−	0.400997i	$-0.131336\pi$
$200$	−0.301292	+	2.48136i	−0.0213046	+	0.175459i
$201$	13.6391	+	5.81109i	0.962030	+	0.409883i
$202$	−0.800940	+	0.506484i	−0.0563540	+	0.0356361i
$203$	−0.972586	+	0.861636i	−0.0682622	+	0.0604750i
$204$	4.26934	−	0.344657i	0.298914	−	0.0241308i
$205$	−0.440041	−	1.51920i	−0.0307338	−	0.106105i
$206$	−1.20101	+	0.511704i	−0.0836785	+	0.0356521i
$207$	−1.18965	+	1.72350i	−0.0826862	+	0.119792i
$208$	−12.9186	−	4.96040i	−0.895742	−	0.343942i
$209$	14.0596	+	20.3689i	0.972523	+	1.40894i
$210$	0.0943067	+	0.0596360i	0.00650778	+	0.00411527i
$211$	−5.99206	+	0.973805i	−0.412511	+	0.0670395i	−0.363125	−	0.931740i	$-0.618290\pi$
$211$	−5.99206	+	0.973805i	−0.412511	+	0.0670395i	−0.0493853	+	0.998780i	$0.515726\pi$
$212$	−14.4606	−	6.16109i	−0.993159	−	0.423146i
$213$	8.46948	−	12.2702i	0.580319	−	0.840737i
$214$	−0.652276	+	2.25192i	−0.0445886	+	0.153938i
$215$	4.41645	+	9.30747i	0.301199	+	0.634764i
$216$	−0.232000	+	0.611733i	−0.0157856	+	0.0416232i
$217$	−1.01329	−	1.24105i	−0.0687865	−	0.0842481i
$218$	−0.0551817	−	1.36932i	−0.00373738	−	0.0927420i
$219$	−0.300806	−	7.46441i	−0.0203266	−	0.504398i
$220$	29.5157	−	7.27497i	1.98995	−	0.490478i
$221$	5.66777	−	5.39922i	0.381256	−	0.363191i
$222$	1.82953	+	0.450939i	0.122790	+	0.0302650i
$223$	−4.70132	+	23.0286i	−0.314824	+	1.54211i	0.447126	+	0.894471i	$0.352448\pi$
$223$	−4.70132	+	23.0286i	−0.314824	+	1.54211i	−0.761949	+	0.647637i	$0.775757\pi$
$224$	0.407290	−	0.173530i	0.0272132	−	0.0115945i
$225$	−3.22909	+	2.04195i	−0.215272	+	0.136130i
$226$	−1.61369	+	0.846928i	−0.107341	+	0.0563368i
$227$	18.3582	+	2.98349i	1.21847	+	0.198021i	0.735446	−	0.677583i	$-0.236973\pi$
$227$	18.3582	+	2.98349i	1.21847	+	0.198021i	0.483028	+	0.875605i	$0.339537\pi$
$228$	−8.92727	+	2.98036i	−0.591223	+	0.197379i
$229$	1.57068	+	12.9357i	0.103793	+	0.854816i	0.947884	+	0.318616i	$0.103218\pi$
$229$	1.57068	+	12.9357i	0.103793	+	0.854816i	−0.844091	+	0.536201i	$0.819859\pi$
$230$	0.284964	−	0.983810i	0.0187900	−	0.0648705i
$231$	0.236756	−	1.15971i	0.0155774	−	0.0763031i
$232$	3.53447	+	1.17998i	0.232049	+	0.0774694i
$233$	−2.02515	−	1.06288i	−0.132672	−	0.0696316i	0.397081	−	0.917783i	$-0.370023\pi$
$233$	−2.02515	−	1.06288i	−0.132672	−	0.0696316i	−0.529753	+	0.848152i	$0.677715\pi$
$234$	0.185700	+	0.563971i	0.0121396	+	0.0368680i
$235$	3.56977	−	1.87356i	0.232866	−	0.122217i
$236$	−16.7853	+	2.72787i	−1.09263	+	0.177570i
$237$	7.74701	−	5.82150i	0.503222	−	0.378147i
$238$	−0.00328435	+	0.0815002i	−0.000212893	+	0.00528288i
$239$	28.3034			1.83079			0.915397	−	0.402553i	$-0.131877\pi$
$239$	28.3034			1.83079			0.915397	+	0.402553i	$0.131877\pi$
$240$	−0.458979	+	11.3894i	−0.0296270	+	0.735186i
$241$	5.32754	+	26.0960i	0.343177	+	1.68099i	0.675132	+	0.737697i	$0.264087\pi$
$241$	5.32754	+	26.0960i	0.343177	+	1.68099i	−0.331955	+	0.943295i	$0.607708\pi$
$242$	1.48899	+	2.15717i	0.0957157	+	0.138668i
$243$	−0.948536	+	0.316668i	−0.0608486	+	0.0203143i
$244$	−2.45387	+	5.17143i	−0.157093	+	0.331067i
$245$	−13.0505	+	15.9840i	−0.833767	+	1.02118i
$246$	0.0310988	+	0.0820008i	0.00198279	+	0.00522818i
$247$	−9.25282	+	14.4995i	−0.588743	+	0.922579i
$248$	−1.62928	+	4.29605i	−0.103459	+	0.272799i
$249$	−7.38660	−	12.7940i	−0.468107	−	0.810785i
$250$	−0.364829	+	0.446835i	−0.0230738	+	0.0282603i
$251$	−11.3405	−	8.52181i	−0.715804	−	0.537892i	0.179275	−	0.983799i	$-0.442625\pi$
$251$	−11.3405	−	8.52181i	−0.715804	−	0.537892i	−0.895079	+	0.445907i	$0.852881\pi$
$252$	0.398539	+	0.209169i	0.0251056	+	0.0131764i
$253$	−10.8298	+	0.874274i	−0.680865	+	0.0549651i
$254$	0.303036	−	0.0244636i	0.0190142	−	0.00153498i
$255$	−5.70933	−	2.99649i	−0.357532	−	0.187647i
$256$	11.0917	+	8.33489i	0.693233	+	0.520931i
$257$	11.6848	−	14.3113i	0.728879	−	0.892715i	−0.268631	−	0.963243i	$-0.586571\pi$
$257$	11.6848	−	14.3113i	0.728879	−	0.892715i	0.997510	+	0.0705285i	$0.0224686\pi$
$258$	−0.285619	−	0.494707i	−0.0177819	−	0.0307991i
$259$	0.925671	−	2.44079i	0.0575184	−	0.151663i
$260$	12.6216	+	16.9413i	0.782760	+	1.05066i
$261$	2.01963	+	5.32533i	0.125012	+	0.329629i
$262$	1.66038	−	2.03360i	0.102579	−	0.125636i
$263$	−8.16148	+	17.2000i	−0.503258	+	1.06059i	0.479813	+	0.877371i	$0.340705\pi$
$263$	−8.16148	+	17.2000i	−0.503258	+	1.06059i	−0.983071	+	0.183224i	$0.941347\pi$
$264$	−3.21965	+	1.07488i	−0.198156	+	0.0661541i
$265$	13.4417	+	19.4736i	0.825716	+	1.19626i
$266$	−0.0358501	−	0.175605i	−0.00219811	−	0.0107670i
$267$	−0.293616	+	7.28601i	−0.0179690	+	0.445896i
$268$	−29.2489			−1.78666
$269$	−0.244423	+	6.06528i	−0.0149027	+	0.369807i	0.974480	+	0.224474i	$0.0720664\pi$
$269$	−0.244423	+	6.06528i	−0.0149027	+	0.369807i	−0.989383	+	0.145333i	$0.953575\pi$
$270$	0.390996	−	0.293815i	0.0237953	−	0.0178810i
$271$	−4.05828	+	0.659534i	−0.246523	+	0.0400639i	−0.282417	−	0.959292i	$-0.591136\pi$
$271$	−4.05828	+	0.659534i	−0.246523	+	0.0400639i	0.0358942	+	0.999356i	$0.488572\pi$
$272$	−7.37811	+	3.87233i	−0.447363	+	0.234794i
$273$	0.806621	−	0.161211i	0.0488189	−	0.00975695i
$274$	0.948762	+	0.497949i	0.0573168	+	0.0300822i
$275$	−18.8014	−	6.27684i	−1.13377	−	0.378508i
$276$	0.826432	−	4.04813i	0.0497454	−	0.243669i
$277$	2.17014	−	7.49218i	0.130391	−	0.450161i	−0.868579	−	0.495552i	$-0.834966\pi$
$277$	2.17014	−	7.49218i	0.130391	−	0.450161i	0.998969	+	0.0453903i	$0.0144531\pi$
$278$	0.376938	+	3.10436i	0.0226072	+	0.186187i
$279$	−6.66133	+	2.22388i	−0.398803	+	0.133140i
$280$	−0.437555	−	0.0711097i	−0.0261489	−	0.00424962i
$281$	−6.55558	+	3.44063i	−0.391073	+	0.205251i	−0.648787	−	0.760970i	$-0.724723\pi$
$281$	−6.55558	+	3.44063i	−0.391073	+	0.205251i	0.257714	+	0.966221i	$0.417031\pi$
$282$	−0.188937	+	0.119477i	−0.0112510	+	0.00711473i
$283$	25.2368	−	10.7524i	1.50017	−	0.639164i	0.523138	−	0.852248i	$-0.324761\pi$
$283$	25.2368	−	10.7524i	1.50017	−	0.639164i	0.977034	+	0.213084i	$0.0683508\pi$
$284$	−5.88363	+	28.8199i	−0.349129	+	1.71015i
$285$	13.7564	+	3.39065i	0.814858	+	0.200845i
$286$	−1.65714	+	2.59679i	−0.0979889	+	0.153552i
$287$	0.117966	−	0.0290760i	0.00696332	−	0.00171630i
$288$	−0.0781376	−	1.93896i	−0.00460430	−	0.114255i
$289$	0.494728	+	12.2766i	0.0291017	+	0.722151i
$290$	−1.76171	−	2.15771i	−0.103451	−	0.126705i
$291$	−4.71402	+	12.4299i	−0.276341	+	0.728651i
$292$	6.31822	+	13.3154i	0.369746	+	0.779223i
$293$	0.491004	−	1.69514i	0.0286847	−	0.0990312i	−0.944899	−	0.327363i	$-0.893840\pi$
$293$	0.491004	−	1.69514i	0.0286847	−	0.0990312i	0.973583	+	0.228332i	$0.0733271\pi$
$294$	0.649968	−	0.941642i	0.0379069	−	0.0549177i
$295$	23.5513	+	10.0343i	1.37121	+	0.584217i
$296$	−7.38909	+	1.20084i	−0.429482	+	0.0697977i
$297$	−4.38496	−	2.77288i	−0.254441	−	0.160899i
$298$	−1.15300	−	1.67041i	−0.0667915	−	0.0967642i
$299$	−3.48143	−	6.70030i	−0.201336	−	0.387488i
$300$	4.28178	−	6.20322i	0.247209	−	0.358143i
$301$	−0.728050	+	0.310193i	−0.0419641	+	0.0178792i
$302$	0.161342	+	0.557016i	0.00928417	+	0.0320527i
$303$	5.73585	−	0.463045i	0.329516	−	0.0266013i
$304$	13.7047	−	12.1413i	0.786017	−	0.696351i
$305$	7.28295	−	4.60546i	0.417021	−	0.263708i
$306$	0.328917	+	0.140138i	0.0188029	+	0.00801118i
$307$	−0.522561	+	4.30368i	−0.0298241	+	0.245624i	0.970171	+	0.242423i	$0.0779420\pi$
$307$	−0.522561	+	4.30368i	−0.0298241	+	0.245624i	−0.999995	+	0.00320115i	$0.998981\pi$
$308$	0.467091	+	2.28796i	0.0266150	+	0.130369i
$309$	7.90171	+	0.637892i	0.449513	+	0.0362884i
$310$	2.74587	−	2.06338i	0.155955	−	0.117192i
$311$	−0.0280627	+	0.231117i	−0.00159129	+	0.0131054i	−0.993483	−	0.113981i	$-0.963640\pi$
$311$	−0.0280627	+	0.231117i	−0.00159129	+	0.0131054i	0.991892	+	0.127087i	$0.0405627\pi$
$312$	−1.55697	−	1.77212i	−0.0881458	−	0.100326i
$313$	0.517871	+	4.26505i	0.0292718	+	0.241075i	1.00000		0.000892548i	$0.000284107\pi$
$313$	0.517871	+	4.26505i	0.0292718	+	0.241075i	−0.970728	+	0.240182i	$0.922793\pi$
$314$	−0.496755	−	0.517177i	−0.0280335	−	0.0291860i
$315$	−0.338782	−	0.586788i	−0.0190882	−	0.0330618i
$316$	−9.55911	+	16.5569i	−0.537742	+	0.931396i
$317$	−23.3085	+	5.74502i	−1.30913	+	0.322673i	−0.831323	−	0.555790i	$-0.812416\pi$
$317$	−23.3085	+	5.74502i	−1.30913	+	0.322673i	−0.477812	+	0.878462i	$0.658570\pi$
$318$	−0.829791	−	1.01631i	−0.0465323	−	0.0569918i
$319$	−14.7744	+	25.5899i	−0.827205	+	1.43276i
$320$	−7.74751	−	20.4285i	−0.433099	−	1.14199i
$321$	9.86211	−	10.2675i	0.550449	−	0.573078i
$322$	0.0746303	+	0.0249152i	0.00415898	+	0.00138847i
$323$	2.88150	+	9.94809i	0.160331	+	0.553527i
$324$	1.47672	−	1.30826i	0.0820401	−	0.0726812i
$325$	−1.05182	−	13.7350i	−0.0583443	−	0.761878i
$326$	0.340984	+	0.302086i	0.0188854	+	0.0167310i
$327$	−3.56751	+	7.51838i	−0.197284	+	0.415767i
$328$	−0.241360	−	0.251282i	−0.0133269	−	0.0138747i
$329$	0.132762	+	0.279790i	0.00731941	+	0.0154253i
$330$	2.46371	+	0.607251i	0.135623	+	0.0334280i
$331$	−10.7661	+	11.2087i	−0.591757	+	0.616084i	−0.947985	−	0.318315i	$-0.896883\pi$
$331$	−10.7661	+	11.2087i	−0.591757	+	0.616084i	0.356228	+	0.934399i	$0.384063\pi$
$332$	23.3004	+	17.5091i	1.27877	+	0.960936i
$333$	−8.56459	−	7.58757i	−0.469337	−	0.415796i
$334$	−1.04876	−	0.170440i	−0.0573855	−	0.00932604i
$335$	37.2144	+	23.5329i	2.03324	+	1.28574i
$336$	−0.872770	−	0.0704573i	−0.0476135	−	0.00384376i
$337$	3.04045			0.165624			0.0828120	−	0.996565i	$-0.473610\pi$
$337$	3.04045			0.165624			0.0828120	+	0.996565i	$0.473610\pi$
$338$	−2.11020	−	0.360826i	−0.114780	−	0.0196264i
$339$	11.0666			0.601056
$340$	12.6797	+	1.02361i	0.687653	+	0.0555131i
$341$	−30.7945	−	19.4732i	−1.66761	−	1.05454i
$342$	−0.775426	−	0.126019i	−0.0419302	−	0.00681433i
$343$	−2.38183	−	2.11012i	−0.128607	−	0.113936i
$344$	1.81430	+	1.36336i	0.0978208	+	0.0735075i
$345$	−4.30852	+	4.48565i	−0.231963	+	0.241499i
$346$	−1.05058	−	0.258944i	−0.0564793	−	0.0139209i
$347$	−4.56894	−	9.62884i	−0.245274	−	0.516903i	0.743057	−	0.669228i	$-0.233375\pi$
$347$	−4.56894	−	9.62884i	−0.245274	−	0.516903i	−0.988330	+	0.152325i	$0.951324\pi$
$348$	−7.78374	−	8.10373i	−0.417252	−	0.434406i
$349$	11.3138	−	23.8434i	0.605616	−	1.27631i	−0.336709	−	0.941609i	$-0.609314\pi$
$349$	11.3138	−	23.8434i	0.605616	−	1.27631i	0.942325	−	0.334699i	$-0.108635\pi$
$350$	0.107439	+	0.0951831i	0.00574288	+	0.00508775i
$351$	0.593041	−	3.55645i	0.0316542	−	0.189829i
$352$	7.53584	−	6.67618i	0.401662	−	0.355841i
$353$	−4.58557	−	15.8312i	−0.244065	−	0.842611i	−0.985222	−	0.171280i	$-0.945210\pi$
$353$	−4.58557	−	15.8312i	−0.244065	−	0.842611i	0.741157	−	0.671332i	$-0.234277\pi$
$354$	−1.34642	−	0.449501i	−0.0715614	−	0.0238907i
$355$	30.6737	−	31.9348i	1.62799	−	1.69492i
$356$	−5.10138	−	13.4512i	−0.270372	−	0.712914i
$357$	0.247653	−	0.428948i	0.0131072	−	0.0227023i
$358$	−1.32428	−	1.62194i	−0.0699901	−	0.0857224i
$359$	−2.19905	+	0.542017i	−0.116061	+	0.0286066i	−0.296919	−	0.954903i	$-0.595959\pi$
$359$	−2.19905	+	0.542017i	−0.116061	+	0.0286066i	0.180857	+	0.983509i	$0.442113\pi$
$360$	−0.971540	+	1.68276i	−0.0512047	+	0.0886891i
$361$	−1.87882	−	3.25421i	−0.0988853	−	0.171274i
$362$	1.98991	+	2.07172i	0.104588	+	0.108887i
$363$	−1.91856	−	15.8007i	−0.100698	−	0.829323i
$364$	−1.33936	+	0.916363i	−0.0702016	+	0.0480305i
$365$	2.67433	−	22.0251i	0.139981	−	1.15285i
$366$	−0.381971	+	0.287033i	−0.0199659	+	0.0150034i
$367$	−5.88774	−	0.475308i	−0.307338	−	0.0248109i	−0.0741642	−	0.997246i	$-0.523629\pi$
$367$	−5.88774	−	0.475308i	−0.307338	−	0.0248109i	−0.233173	+	0.972435i	$0.574911\pi$
$368$	1.60773	+	7.87519i	0.0838088	+	0.410523i
$369$	0.0641919	−	0.528668i	0.00334170	−	0.0275214i
$370$	5.14840	+	2.19353i	0.267652	+	0.114036i
$371$	−1.53626	+	0.971473i	−0.0797588	+	0.0504364i
$372$	10.3706	−	9.18759i	0.537693	−	0.476354i
$373$	−24.8039	+	2.00238i	−1.28430	+	0.103679i	−0.703692	−	0.710505i	$-0.748466\pi$
$373$	−24.8039	+	2.00238i	−1.28430	+	0.103679i	−0.580606	+	0.814185i	$0.697184\pi$
$374$	0.516065	+	1.78166i	0.0266851	+	0.0921275i
$375$	3.22261	−	1.37302i	0.166415	−	0.0709027i
$376$	0.504506	−	0.730903i	0.0260179	−	0.0376934i
$377$	−20.3751	−	2.55928i	−1.04937	−	0.131810i
$378$	0.0213422	+	0.0309195i	0.00109772	+	0.00159033i
$379$	−15.3320	−	9.69538i	−0.787553	−	0.498018i	0.0791381	−	0.996864i	$-0.474783\pi$
$379$	−15.3320	−	9.69538i	−0.787553	−	0.498018i	−0.866691	+	0.498845i	$0.833758\pi$
$380$	−27.5900	+	4.48381i	−1.41534	+	0.230015i
$381$	−1.69842	−	0.723629i	−0.0870127	−	0.0370726i
$382$	−0.215181	+	0.311743i	−0.0110096	+	0.0159502i
$383$	−2.99757	+	10.3488i	−0.153168	+	0.528799i	−0.999995	−	0.00306984i	$-0.999023\pi$
$383$	−2.99757	+	10.3488i	−0.153168	+	0.528799i	0.846827	+	0.531869i	$0.178510\pi$
$384$	2.18313	+	4.60085i	0.111407	+	0.234786i
$385$	1.24654	−	3.28686i	0.0635297	−	0.167514i
$386$	1.12334	+	1.37584i	0.0571763	+	0.0700283i
$387$	0.139675	+	3.46599i	0.00710006	+	0.176186i
$388$	−1.05605	−	26.2057i	−0.0536130	−	1.33039i
$389$	3.82002	−	0.941549i	0.193682	−	0.0477384i	−0.141281	−	0.989970i	$-0.545122\pi$
$389$	3.82002	−	0.941549i	0.193682	−	0.0477384i	0.334964	+	0.942231i	$0.391276\pi$
$390$	0.275694	+	1.74174i	0.0139603	+	0.0881965i
$391$	−4.41453	−	1.08808i	−0.223252	−	0.0550267i
$392$	−0.909255	+	4.45383i	−0.0459243	+	0.224952i
$393$	−14.6665	+	6.24880i	−0.739825	+	0.315210i
$394$	3.19133	−	2.01808i	0.160777	−	0.101669i
$395$	25.4836	−	13.3748i	1.28222	−	0.672961i
$396$	10.1030	+	1.64190i	0.507696	+	0.0825087i
$397$	−19.0545	+	6.36132i	−0.956317	+	0.319265i	−0.751647	−	0.659566i	$-0.770740\pi$
$397$	−19.0545	+	6.36132i	−0.956317	+	0.319265i	−0.204670	+	0.978831i	$0.565612\pi$
$398$	0.117413	+	0.966980i	0.00588536	+	0.0484703i
$399$	−0.302797	+	1.04538i	−0.0151588	+	0.0523342i
$400$	−2.93304	+	14.3670i	−0.146652	+	0.718350i
$401$	18.6429	+	6.22393i	0.930984	+	0.310808i	0.741406	−	0.671057i	$-0.234160\pi$
$401$	18.6429	+	6.22393i	0.930984	+	0.310808i	0.189579	+	0.981866i	$0.439288\pi$
$402$	−2.16179	−	1.13459i	−0.107820	−	0.0565884i
$403$	4.16477	−	24.9760i	0.207462	−	1.24414i
$404$	−10.0525	+	5.27598i	−0.500133	+	0.262490i
$405$	−2.93148	+	0.476412i	−0.145666	+	0.0236731i
$406$	0.171063	−	0.128545i	0.00848969	−	0.00637959i
$407$	2.39033	−	59.3155i	0.118484	−	2.94016i
$408$	−1.42041			−0.0703208
$409$	0.187481	−	4.65231i	0.00927036	−	0.230042i	−0.987911	−	0.155019i	$-0.950456\pi$
$409$	0.187481	−	4.65231i	0.00927036	−	0.230042i	0.997182	−	0.0750226i	$-0.0239029\pi$
$410$	0.0520993	+	0.255199i	0.00257300	+	0.0126034i
$411$	−3.69616	−	5.35481i	−0.182318	−	0.264133i
$412$	−14.8350	+	4.95264i	−0.730867	+	0.243999i
$413$	−0.843020	+	1.77663i	−0.0414823	+	0.0874221i
$414$	0.218113	−	0.267140i	0.0107197	−	0.0131292i
$415$	−15.5585	−	41.0243i	−0.763735	−	2.01380i
$416$	6.30876	+	3.02548i	0.309312	+	0.148336i
$417$	6.73376	−	17.7555i	0.329754	−	0.869489i
$418$	−2.03790	−	3.52975i	−0.0996769	−	0.172645i
$419$	20.3410	−	24.9132i	0.993725	−	1.21709i	0.0176081	−	0.999845i	$-0.494395\pi$
$419$	20.3410	−	24.9132i	0.993725	−	1.21709i	0.976117	−	0.217247i	$-0.0697077\pi$
$420$	1.06866	+	0.803045i	0.0521452	+	0.0391846i
$421$	−10.1136	−	5.30804i	−0.492908	−	0.258698i	0.199905	−	0.979815i	$-0.435937\pi$
$421$	−10.1136	−	5.30804i	−0.492908	−	0.258698i	−0.692813	+	0.721117i	$0.743629\pi$
$422$	0.996470	−	0.0804434i	0.0485074	−	0.00391592i
$423$	1.35305	−	0.109230i	0.0657877	−	0.00531093i
$424$	4.61549	+	2.42240i	0.224148	+	0.117642i
$425$	−6.63107	−	4.98292i	−0.321654	−	0.241707i
$426$	−1.55281	+	1.90185i	−0.0752341	+	0.0921450i
$427$	0.330962	+	0.573243i	0.0160164	+	0.0277412i
$428$	−9.95990	+	26.2621i	−0.481430	+	1.26943i
$429$	16.2384	−	9.28617i	0.783997	−	0.448341i
$430$	−0.601603	−	1.58630i	−0.0290119	−	0.0764980i
$431$	−8.39232	+	10.2787i	−0.404244	+	0.495109i	−0.936104	−	0.351724i	$-0.885596\pi$
$431$	−8.39232	+	10.2787i	−0.404244	+	0.495109i	0.531860	+	0.846832i	$0.321493\pi$
$432$	−1.64533	+	3.46746i	−0.0791610	+	0.166828i
$433$	−26.7699	+	8.93709i	−1.28648	+	0.429489i	−0.875969	−	0.482367i	$-0.839777\pi$
$433$	−26.7699	+	8.93709i	−1.28648	+	0.429489i	−0.410509	+	0.911857i	$0.634649\pi$
$434$	0.149881	+	0.217139i	0.00719449	+	0.0104230i
$435$	3.38346	+	16.5733i	0.162224	+	0.794627i
$436$	0.661087	−	16.4047i	0.0316603	−	0.785643i
$437$	9.99043			0.477907
$438$	−0.0495363	+	1.22923i	−0.00236693	+	0.0587349i
$439$	30.7489	−	23.1063i	1.46757	−	1.10280i	0.495358	−	0.868689i	$-0.335037\pi$
$439$	30.7489	−	23.1063i	1.46757	−	1.10280i	0.972209	−	0.234116i	$-0.0752194\pi$
$440$	−9.95043	+	1.61710i	−0.474368	+	0.0770923i
$441$	−6.15211	+	3.22887i	−0.292957	+	0.153756i
$442$	−1.00188	+	0.811148i	−0.0476546	+	0.0385824i
$443$	14.6134	+	7.66973i	0.694306	+	0.364400i	0.774670	−	0.632366i	$-0.217916\pi$
$443$	14.6134	+	7.66973i	0.694306	+	0.364400i	−0.0803642	+	0.996766i	$0.525608\pi$
$444$	21.4123	+	7.14848i	1.01618	+	0.339252i
$445$	−4.33187	+	21.2189i	−0.205350	+	1.00587i
$446$	1.07685	−	3.71772i	0.0509904	−	0.176039i
$447$	1.48564	+	12.2353i	0.0702683	+	0.578712i
$448$	1.59194	−	0.531468i	0.0752121	−	0.0251095i
$449$	15.4465	+	2.51029i	0.728964	+	0.118468i	0.513556	−	0.858056i	$-0.328328\pi$
$449$	15.4465	+	2.51029i	0.728964	+	0.118468i	0.215408	+	0.976524i	$0.430892\pi$
$450$	0.557096	−	0.292386i	0.0262617	−	0.0137832i
$451$	2.33522	−	1.47670i	0.109961	−	0.0695352i
$452$	−20.0860	+	8.55784i	−0.944766	+	0.402527i
$453$	0.704385	−	3.45031i	0.0330949	−	0.162110i
$454$	−2.97386	−	0.732991i	−0.139570	−	0.0344010i
$455$	2.44140	−	0.0883035i	0.114454	−	0.00413973i
$456$	3.03040	−	0.746926i	0.141911	−	0.0349780i
$457$	0.105153	+	2.60935i	0.00491885	+	0.122060i	0.999783	+	0.0208393i	$0.00663383\pi$
$457$	0.105153	+	2.60935i	0.00491885	+	0.122060i	−0.994864	+	0.101221i	$0.967725\pi$
$458$	−0.0864060	−	2.14414i	−0.00403749	−	0.100189i
$459$	−1.37307	−	1.68171i	−0.0640896	−	0.0784955i
$460$	4.35125	−	11.4733i	0.202878	−	0.534945i
$461$	6.50415	+	13.7072i	0.302928	+	0.638408i	0.996646	−	0.0818395i	$-0.0260795\pi$
$461$	6.50415	+	13.7072i	0.302928	+	0.638408i	−0.693717	+	0.720248i	$0.744028\pi$
$462$	−0.0542296	+	0.187222i	−0.00252299	+	0.00871037i
$463$	0.613987	−	0.889514i	0.0285344	−	0.0413392i	−0.808457	−	0.588555i	$-0.799697\pi$
$463$	0.613987	−	0.889514i	0.0285344	−	0.0413392i	0.836991	+	0.547216i	$0.184312\pi$
$464$	20.1100	+	8.56808i	0.933584	+	0.397763i
$465$	−20.5870	+	3.34572i	−0.954701	+	0.155154i
$466$	0.318333	+	0.201302i	0.0147465	+	0.00932512i
$467$	−16.9342	−	24.5335i	−0.783622	−	1.13527i	−0.987707	−	0.156320i	$-0.950037\pi$
$467$	−16.9342	−	24.5335i	−0.783622	−	1.13527i	0.204084	−	0.978953i	$-0.434578\pi$
$468$	1.67384	+	6.91358i	0.0773731	+	0.319581i
$469$	−1.92136	+	2.78357i	−0.0887203	+	0.128534i
$470$	−0.610785	+	0.260231i	−0.0281734	+	0.0120036i
$471$	1.21152	+	4.18264i	0.0558237	+	0.192726i
$472$	5.62110	−	0.453782i	0.258732	−	0.0208870i
$473$	−13.4707	+	11.9340i	−0.619382	+	0.548725i
$474$	−1.34877	+	0.852912i	−0.0619511	+	0.0391755i
$475$	16.7675	+	7.14394i	0.769343	+	0.327787i
$476$	−0.117786	+	0.970055i	−0.00539871	+	0.0444624i
$477$	1.59365	+	7.80623i	0.0729683	+	0.357423i
$478$	−4.64585	−	0.375052i	−0.212496	−	0.0171545i
$479$	13.2997	−	9.99405i	0.607677	−	0.456640i	−0.251824	−	0.967773i	$-0.581031\pi$
$479$	13.2997	−	9.99405i	0.607677	−	0.456640i	0.859502	+	0.511133i	$0.170774\pi$
$480$	0.694687	−	5.72126i	0.0317080	−	0.261139i
$481$	38.6344	−	14.4702i	1.76158	−	0.659783i
$482$	−0.528686	−	4.35412i	−0.0240810	−	0.198325i
$483$	−0.330966	−	0.344573i	−0.0150595	−	0.0156786i
$484$	15.7010	+	27.1949i	0.713680	+	1.23613i
$485$	−19.7408	+	34.1921i	−0.896384	+	1.55258i
$486$	0.159893	−	0.0394102i	0.00725292	−	0.00178768i
$487$	−4.31871	−	5.28946i	−0.195699	−	0.239688i	0.667428	−	0.744674i	$-0.267395\pi$
$487$	−4.31871	−	5.28946i	−0.195699	−	0.239688i	−0.863128	+	0.504986i	$0.831498\pi$
$488$	0.949114	−	1.64391i	0.0429644	−	0.0744165i
$489$	−0.980942	−	2.58653i	−0.0443597	−	0.116967i
$490$	2.35398	−	2.45075i	0.106342	−	0.110714i
$491$	34.4374	+	11.4969i	1.55414	+	0.518848i	0.958668	−	0.284528i	$-0.0918370\pi$
$491$	34.4374	+	11.4969i	1.55414	+	0.518848i	0.595472	+	0.803376i	$0.296965\pi$
$492$	0.292312	+	1.00918i	0.0131784	+	0.0454972i
$493$	−9.25541	+	8.19958i	−0.416843	+	0.369290i
$494$	1.71094	−	2.25740i	0.0769787	−	0.101565i
$495$	−11.5334	−	10.2177i	−0.518388	−	0.459251i
$496$	−11.5547	+	24.3511i	−0.518823	+	1.09340i
$497$	2.35625	+	2.45312i	0.105692	+	0.110038i
$498$	1.04294	+	2.19794i	0.0467351	+	0.0984922i
$499$	−8.33655	−	2.05478i	−0.373195	−	0.0919844i	0.0482570	−	0.998835i	$-0.484633\pi$
$499$	−8.33655	−	2.05478i	−0.373195	−	0.0919844i	−0.421452	+	0.906851i	$0.638480\pi$
$500$	−4.78730	+	4.98410i	−0.214094	+	0.222896i
$501$	5.15805	+	3.87602i	0.230445	+	0.173168i
$502$	1.74856	+	1.54909i	0.0780419	+	0.0691391i
$503$	7.87630	+	1.28002i	0.351187	+	0.0570734i	0.333446	−	0.942769i	$-0.391789\pi$
$503$	7.87630	+	1.28002i	0.351187	+	0.0570734i	0.0177409	+	0.999843i	$0.494353\pi$
$504$	−0.126154	−	0.0797749i	−0.00561934	−	0.00355345i
$505$	17.0351	+	1.37522i	0.758053	+	0.0611964i
$506$	1.78924			0.0795416
$507$	10.3280	+	7.89509i	0.458683	+	0.350633i
$508$	3.64223			0.161598
$509$	−29.3127	−	2.36637i	−1.29926	−	0.104887i	−0.588603	−	0.808422i	$-0.700322\pi$
$509$	−29.3127	−	2.36637i	−1.29926	−	0.104887i	−0.710661	+	0.703534i	$0.751604\pi$
$510$	0.897450	+	0.567513i	0.0397398	+	0.0251299i
$511$	1.68225	+	0.273392i	0.0744183	+	0.0120942i
$512$	−9.33383	−	8.26905i	−0.412501	−	0.365444i
$513$	3.81374	+	2.86584i	0.168381	+	0.126530i
$514$	−2.10764	+	2.19429i	−0.0929641	+	0.0967859i
$515$	22.8598	+	5.63444i	1.00732	+	0.248283i
$516$	−2.93377	−	6.18280i	−0.129152	−	0.272182i
$517$	4.87862	+	5.07918i	0.214562	+	0.223382i
$518$	−0.184287	+	0.388377i	−0.00809712	+	0.0170643i
$519$	4.91807	+	4.35703i	0.215879	+	0.191252i
$520$	−3.71995	−	5.93669i	−0.163131	−	0.260341i
$521$	−5.60723	+	4.96758i	−0.245657	+	0.217633i	−0.776962	−	0.629547i	$-0.783240\pi$
$521$	−5.60723	+	4.96758i	−0.245657	+	0.217633i	0.531305	+	0.847181i	$0.321702\pi$
$522$	−0.260945	−	0.900887i	−0.0114213	−	0.0394307i
$523$	−17.1844	−	5.73699i	−0.751421	−	0.250861i	−0.0849427	−	0.996386i	$-0.527071\pi$
$523$	−17.1844	−	5.73699i	−0.751421	−	0.250861i	−0.666478	+	0.745525i	$0.732199\pi$
$524$	21.7876	−	22.6833i	0.951794	−	0.990923i
$525$	−0.309082	−	0.814981i	−0.0134894	−	0.0355687i
$526$	1.56758	−	2.71513i	0.0683499	−	0.118385i
$527$	−9.64274	−	11.8102i	−0.420044	−	0.514461i
$528$	−19.3336	+	4.76530i	−0.841386	+	0.207383i
$529$	9.30714	−	16.1204i	0.404658	−	0.700889i
$530$	−1.94833	−	3.37461i	−0.0846302	−	0.146584i
$531$	5.97103	+	6.21650i	0.259121	+	0.269773i
$532$	−0.258813	−	2.13152i	−0.0112210	−	0.0924131i
$533$	1.57573	+	1.09727i	0.0682526	+	0.0475281i
$534$	0.144743	−	1.19207i	0.00626366	−	0.0515859i
$535$	33.8021	−	25.4007i	1.46139	−	1.09817i
$536$	9.66810	+	0.780489i	0.417598	+	0.0337120i
$537$	2.54333	+	12.4581i	0.109753	+	0.537606i
$538$	0.120493	−	0.992346i	0.00519480	−	0.0427831i
$539$	−33.1624	−	14.1292i	−1.42841	−	0.608588i
$540$	4.95225	−	3.13162i	0.213111	−	0.134763i
$541$	12.0956	−	10.7158i	0.520030	−	0.460707i	−0.361812	−	0.932251i	$-0.617842\pi$
$541$	12.0956	−	10.7158i	0.520030	−	0.460707i	0.881842	+	0.471544i	$0.156303\pi$
$542$	0.674885	−	0.0544823i	0.0289888	−	0.00234022i
$543$	−4.85312	−	16.7549i	−0.208267	−	0.719022i
$544$	3.87589	−	1.65136i	0.166177	−	0.0708015i
$545$	−14.0399	+	20.3404i	−0.601405	+	0.871285i
$546$	−0.134539	+	0.0157733i	−0.00575773	+	0.000675036i
$547$	−0.603081	−	0.873714i	−0.0257859	−	0.0373573i	0.809879	−	0.586597i	$-0.199533\pi$
$547$	−0.603081	−	0.873714i	−0.0257859	−	0.0373573i	−0.835665	+	0.549240i	$0.814917\pi$
$548$	10.8495	+	6.86078i	0.463466	+	0.293078i
$549$	2.86381	−	0.465415i	0.122225	−	0.0198634i
$550$	3.00298	+	1.27945i	0.128048	+	0.0545560i
$551$	15.4344	−	22.3605i	0.657526	−	0.952590i
$552$	−0.381196	+	1.31604i	−0.0162248	+	0.0560144i
$553$	0.947754	+	1.99735i	0.0403026	+	0.0849359i
$554$	−0.455496	+	1.20104i	−0.0193522	+	0.0510275i
$555$	−21.4921	−	26.3231i	−0.912290	−	1.11735i
$556$	1.50852	+	37.4336i	0.0639756	+	1.58754i
$557$	0.735373	+	18.2481i	0.0311588	+	0.773197i	0.936948	+	0.349468i	$0.113638\pi$
$557$	0.735373	+	18.2481i	0.0311588	+	0.773197i	−0.905789	+	0.423728i	$0.860721\pi$
$558$	1.12289	−	0.276768i	0.0475358	−	0.0117165i
$559$	−11.2772	−	5.40818i	−0.476975	−	0.228742i
$560$	−2.52494	−	0.622342i	−0.106698	−	0.0262988i
$561$	2.25304	−	11.0361i	0.0951232	−	0.465944i
$562$	1.12166	−	0.477893i	0.0473142	−	0.0201587i
$563$	−29.1131	+	18.4100i	−1.22697	+	0.775889i	−0.981117	−	0.193417i	$-0.938043\pi$
$563$	−29.1131	+	18.4100i	−1.22697	+	0.775889i	−0.245854	+	0.969307i	$0.579069\pi$
$564$	−2.37134	+	1.24457i	−0.0998512	+	0.0524060i
$565$	32.4415	+	5.27226i	1.36483	+	0.221806i
$566$	−4.28497	+	1.43053i	−0.180111	+	0.0601298i
$567$	−0.0274993	−	0.226477i	−0.00115486	−	0.00951116i
$568$	2.71385	−	9.36930i	0.113871	−	0.393127i
$569$	−3.36822	+	16.4986i	−0.141203	+	0.691658i	0.846127	+	0.532981i	$0.178928\pi$
$569$	−3.36822	+	16.4986i	−0.141203	+	0.691658i	−0.987330	+	0.158678i	$0.949277\pi$
$570$	−2.21311	−	0.738845i	−0.0926970	−	0.0309468i
$571$	−27.7308	−	14.5542i	−1.16050	−	0.609076i	−0.229216	−	0.973376i	$-0.573616\pi$
$571$	−27.7308	−	14.5542i	−1.16050	−	0.609076i	−0.931282	+	0.364299i	$0.881309\pi$
$572$	−22.2918	+	29.4117i	−0.932067	+	1.22976i
$573$	2.03674	−	1.06896i	0.0850860	−	0.0446566i
$574$	−0.0197488	+	0.00320949i	−0.000824300	+	0.000133962i
$575$	−6.39636	+	4.80656i	−0.266747	+	0.200447i
$576$	0.296215	−	7.35051i	0.0123423	−	0.306271i
$577$	12.2558			0.510215			0.255108	−	0.966913i	$-0.417889\pi$
$577$	12.2558			0.510215			0.255108	+	0.966913i	$0.417889\pi$
$578$	0.0814713	−	2.02169i	0.00338876	−	0.0840912i
$579$	−2.15742	−	10.5678i	−0.0896594	−	0.439181i
$580$	−18.9572	−	27.4642i	−0.787153	−	1.14039i
$581$	3.19692	−	1.06729i	0.132631	−	0.0442786i
$582$	0.938492	−	1.97783i	0.0389017	−	0.0819837i
$583$	−26.1422	+	32.0184i	−1.08270	+	1.32607i
$584$	−1.73315	−	4.56994i	−0.0717182	−	0.189105i
$585$	3.43282	−	10.1431i	0.141930	−	0.419366i
$586$	−0.103058	+	0.271742i	−0.00425730	+	0.0112256i
$587$	2.89224	+	5.00951i	0.119375	+	0.206764i	0.919520	−	0.393042i	$-0.128577\pi$
$587$	2.89224	+	5.00951i	0.119375	+	0.206764i	−0.800145	+	0.599807i	$0.795244\pi$
$588$	8.66923	−	10.6179i	0.357513	−	0.437874i
$589$	26.7829	+	20.1260i	1.10357	+	0.829279i
$590$	−3.73285	−	1.95915i	−0.153679	−	0.0806570i
$591$	−22.8544	+	1.84500i	−0.940104	+	0.0758930i
$592$	−43.7729	+	3.53371i	−1.79906	+	0.145235i
$593$	3.85744	+	2.02454i	0.158406	+	0.0831379i	0.542063	−	0.840338i	$-0.317643\pi$
$593$	3.85744	+	2.02454i	0.158406	+	0.0831379i	−0.383657	+	0.923476i	$0.625336\pi$
$594$	0.683025	+	0.513260i	0.0280249	+	0.0210593i
$595$	0.930346	−	1.13947i	0.0381405	−	0.0467136i
$596$	−12.1581	−	21.0584i	−0.498014	−	0.862586i
$597$	2.09750	−	5.53066i	0.0858451	−	0.226355i
$598$	0.482671	+	1.14595i	0.0197379	+	0.0468615i
$599$	−1.73562	−	4.57644i	−0.0709153	−	0.186988i	0.894872	−	0.446322i	$-0.147266\pi$
$599$	−1.73562	−	4.57644i	−0.0709153	−	0.186988i	−0.965788	+	0.259334i	$0.916497\pi$
$600$	−1.58085	+	1.93619i	−0.0645380	+	0.0790448i
$601$	13.7684	−	29.0164i	0.561626	−	1.18360i	−0.401825	−	0.915717i	$-0.631624\pi$
$601$	13.7684	−	29.0164i	0.561626	−	1.18360i	0.963451	−	0.267885i	$-0.0863249\pi$
$602$	0.123616	−	0.0412691i	0.00503821	−	0.00168200i
$603$	8.42183	+	12.2011i	0.342963	+	0.496868i
$604$	1.38967	+	6.80704i	0.0565448	+	0.276975i
$605$	1.90345	−	47.2336i	0.0773861	−	1.92032i
$606$	−0.947645			−0.0384955
$607$	−0.743652	+	18.4535i	−0.0301839	+	0.749006i	0.911259	+	0.411834i	$0.135112\pi$
$607$	−0.743652	+	18.4535i	−0.0301839	+	0.749006i	−0.941443	+	0.337172i	$0.890529\pi$
$608$	−7.40071	+	5.56127i	−0.300138	+	0.225539i
$609$	−1.28254	+	0.208432i	−0.0519709	+	0.00844610i
$610$	−1.25649	+	0.659455i	−0.0508736	+	0.0267005i
$611$	−1.93698	+	4.49477i	−0.0783618	+	0.181839i
$612$	3.79261	+	1.99052i	0.153307	+	0.0804619i
$613$	2.26360	+	0.755702i	0.0914261	+	0.0305225i	0.362013	−	0.932173i	$-0.382090\pi$
$613$	2.26360	+	0.755702i	0.0914261	+	0.0305225i	−0.270587	+	0.962696i	$0.587218\pi$
$614$	0.142804	−	0.699501i	0.00576311	−	0.0282296i
$615$	0.440041	−	1.51920i	0.0177442	−	0.0612600i
$616$	−0.0933420	−	0.768740i	−0.00376086	−	0.0309734i
$617$	12.0399	−	4.01952i	0.484709	−	0.161820i	−0.0638027	−	0.997963i	$-0.520323\pi$
$617$	12.0399	−	4.01952i	0.484709	−	0.161820i	0.548512	+	0.836143i	$0.315195\pi$
$618$	−1.28857	−	0.209413i	−0.0518340	−	0.00842384i
$619$	3.54766	−	1.86195i	0.142592	−	0.0748383i	−0.391918	−	0.920000i	$-0.628188\pi$
$619$	3.54766	−	1.86195i	0.142592	−	0.0748383i	0.534510	+	0.845162i	$0.320496\pi$
$620$	34.7784	−	21.9925i	1.39673	−	0.883241i
$621$	−1.92663	+	0.820861i	−0.0773130	+	0.0329400i
$622$	0.00766890	−	0.0375648i	0.000307495	−	0.00150621i
$623$	−1.61524	−	0.398122i	−0.0647134	−	0.0159504i
$624$	−8.26749	−	11.0970i	−0.330965	−	0.444236i
$625$	28.6488	−	7.06129i	1.14595	−	0.282451i
$626$	−0.0284890	−	0.706947i	−0.00113865	−	0.0282553i
$627$	0.996582	+	24.7299i	0.0397997	+	0.987618i
$628$	−5.43336	−	6.65466i	−0.216815	−	0.265550i
$629$	8.80895	−	23.2273i	0.351236	−	0.926132i
$630$	0.0478337	+	0.100807i	0.00190574	+	0.00401627i
$631$	9.09242	−	31.3907i	0.361963	−	1.24964i	−0.548534	−	0.836128i	$-0.684814\pi$
$631$	9.09242	−	31.3907i	0.361963	−	1.24964i	0.910498	−	0.413514i	$-0.135699\pi$
$632$	3.60153	−	5.21772i	0.143261	−	0.207550i
$633$	−5.58490	−	2.37950i	−0.221980	−	0.0945768i
$634$	3.90209	−	0.634152i	0.154972	−	0.0251854i
$635$	−4.63414	−	2.93045i	−0.183900	−	0.116291i
$636$	−8.92908	−	12.9360i	−0.354061	−	0.512946i
$637$	0.103294	−	25.0510i	0.00409267	−	0.992556i
$638$	2.76423	−	4.00468i	0.109437	−	0.158547i
$639$	13.7163	−	5.84397i	0.542608	−	0.231184i
$640$	4.20790	+	14.5274i	0.166332	+	0.574245i
$641$	25.2110	−	2.03524i	0.995775	−	0.0803872i	0.428178	−	0.903694i	$-0.359156\pi$
$641$	25.2110	−	2.03524i	0.995775	−	0.0803872i	0.567596	+	0.823307i	$0.307873\pi$
$642$	−1.75487	+	1.55468i	−0.0692592	+	0.0613583i
$643$	−36.0587	+	22.8021i	−1.42201	+	0.899228i	−0.999973	−	0.00734874i	$-0.997661\pi$
$643$	−36.0587	+	22.8021i	−1.42201	+	0.899228i	−0.422042	+	0.906576i	$0.638686\pi$
$644$	0.867166	+	0.369465i	0.0341711	+	0.0145590i
$645$	−1.24179	+	10.2270i	−0.0488953	+	0.402689i
$646$	−0.341160	−	1.67111i	−0.0134227	−	0.0657489i
$647$	−5.60113	−	0.452170i	−0.220203	−	0.0177766i	−0.0301273	−	0.999546i	$-0.509591\pi$
$647$	−5.60113	−	0.452170i	−0.220203	−	0.0177766i	−0.190076	+	0.981769i	$0.560873\pi$
$648$	−0.523035	+	0.393035i	−0.0205467	+	0.0154399i
$649$	−5.39038	+	44.3938i	−0.211591	+	1.74261i
$650$	−0.00935367	+	2.26846i	−0.000366881	+	0.0889763i
$651$	−0.193121	−	1.59049i	−0.00756900	−	0.0623363i
$652$	3.78059	+	3.93601i	0.148059	+	0.154146i
$653$	9.92438	+	17.1895i	0.388371	+	0.672678i	0.992231	−	0.124412i	$-0.0397045\pi$
$653$	9.92438	+	17.1895i	0.388371	+	0.672678i	−0.603860	+	0.797091i	$0.706371\pi$
$654$	0.685216	−	1.18683i	0.0267941	−	0.0464087i
$655$	−45.9714	+	11.3309i	−1.79625	+	0.442737i
$656$	−1.29268	−	1.58325i	−0.0504707	−	0.0618154i
$657$	3.73524	−	6.46962i	0.145725	−	0.252404i
$658$	−0.0180847	−	0.0476853i	−0.000705014	−	0.00185897i
$659$	27.2216	−	28.3407i	1.06040	−	1.10400i	0.0660549	−	0.997816i	$-0.478959\pi$
$659$	27.2216	−	28.3407i	1.06040	−	1.10400i	0.994347	−	0.106179i	$-0.0338618\pi$
$660$	28.8346	+	9.62641i	1.12239	+	0.374707i
$661$	2.43269	+	8.39862i	0.0946206	+	0.326668i	0.993839	−	0.110831i	$-0.0353513\pi$
$661$	2.43269	+	8.39862i	0.0946206	+	0.326668i	−0.899219	+	0.437500i	$0.855864\pi$
$662$	1.91572	−	1.69718i	0.0744567	−	0.0659629i
$663$	7.67604	−	1.53413i	0.298113	−	0.0595808i
$664$	−7.23462	−	6.40931i	−0.280758	−	0.248730i
$665$	−1.38567	+	2.92024i	−0.0537340	+	0.113242i
$666$	1.30529	+	1.35895i	0.0505789	+	0.0526582i
$667$	5.11321	+	10.7759i	0.197984	+	0.417243i
$668$	−12.3593	−	3.04628i	−0.478194	−	0.117864i
$669$	−16.2815	+	16.9508i	−0.629479	+	0.655357i
$670$	−5.79670	−	4.35594i	−0.223946	−	0.168285i
$671$	11.2672	+	9.98185i	0.434964	+	0.385345i
$672$	0.436983	+	0.0710167i	0.0168570	+	0.00273953i
$673$	−40.9222	−	25.8776i	−1.57743	−	0.997508i	−0.980805	−	0.194991i	$-0.937532\pi$
$673$	−40.9222	−	25.8776i	−1.57743	−	0.997508i	−0.596628	−	0.802518i	$-0.703493\pi$
$674$	−0.499074	−	0.0402894i	−0.0192236	−	0.00155189i
$675$	−3.82055			−0.147053
$676$	−24.8507	−	6.34299i	−0.955797	−	0.243961i
$677$	−27.0764			−1.04063			−0.520316	−	0.853974i	$-0.674186\pi$
$677$	−27.0764			−1.04063			−0.520316	+	0.853974i	$0.674186\pi$
$678$	−1.81653	−	0.146645i	−0.0697632	−	0.00563187i
$679$	−2.56333	−	1.62095i	−0.0983716	−	0.0622064i
$680$	−4.16390	−	0.676700i	−0.159678	−	0.0259503i
$681$	13.9216	+	12.3334i	0.533475	+	0.472618i
$682$	4.79671	+	3.60449i	0.183675	+	0.138023i
$683$	31.8687	−	33.1788i	1.21942	−	1.26955i	0.267377	−	0.963592i	$-0.413843\pi$
$683$	31.8687	−	33.1788i	1.21942	−	1.26955i	0.952044	−	0.305960i	$-0.0989775\pi$
$684$	−9.13814	−	2.25235i	−0.349405	−	0.0861207i
$685$	−8.28412	−	17.4584i	−0.316520	−	0.667052i
$686$	0.363004	+	0.377927i	0.0138596	+	0.0144293i
$687$	−5.58618	+	11.7726i	−0.213126	+	0.449153i
$688$	9.96518	+	8.82838i	0.379919	+	0.336579i
$689$	−27.5589	−	8.10586i	−1.04991	−	0.308809i
$690$	0.766662	−	0.679203i	0.0291863	−	0.0258568i
$691$	4.50643	+	15.5580i	0.171433	+	0.591854i	0.999512	+	0.0312431i	$0.00994661\pi$
$691$	4.50643	+	15.5580i	0.171433	+	0.591854i	−0.828079	+	0.560611i	$0.810566\pi$
$692$	−12.2957	−	4.10489i	−0.467411	−	0.156045i
$693$	0.819927	−	0.853634i	0.0311464	−	0.0324269i
$694$	0.622375	+	1.64107i	0.0236250	+	0.0622941i
$695$	28.1988	−	48.8417i	1.06964	−	1.85267i
$696$	2.35664	+	2.88636i	0.0893282	+	0.109407i
$697$	1.12260	−	0.276696i	0.0425215	−	0.0104806i
$698$	−2.17306	+	3.76385i	−0.0822515	+	0.142464i
$699$	−1.14356	−	1.98071i	−0.0432535	−	0.0749173i
$700$	1.19121	+	1.24018i	0.0450236	+	0.0468746i
$701$	4.58560	+	37.7658i	0.173196	+	1.42640i	0.777119	+	0.629353i	$0.216680\pi$
$701$	4.58560	+	37.7658i	0.173196	+	1.42640i	−0.603923	+	0.797042i	$0.706397\pi$
$702$	−0.144471	+	0.575913i	−0.00545272	+	0.0217364i
$703$	−6.57948	+	54.1869i	−0.248150	+	2.04370i
$704$	30.5119	−	22.9282i	1.14996	−	0.864138i
$705$	4.01848	+	0.324406i	0.151345	+	0.0122178i
$706$	0.542916	+	2.65938i	0.0204329	+	0.100087i
$707$	−0.158245	+	1.30327i	−0.00595142	+	0.0490144i
$708$	−15.6447	−	6.66559i	−0.587964	−	0.250508i
$709$	−16.8885	+	10.6796i	−0.634260	+	0.401082i	−0.812546	−	0.582897i	$-0.801919\pi$
$709$	−16.8885	+	10.6796i	−0.634260	+	0.401082i	0.178286	+	0.983979i	$0.442945\pi$
$710$	−5.45811	+	4.83546i	−0.204839	+	0.181472i
$711$	9.65909	−	0.779762i	0.362244	−	0.0292434i
$712$	1.32730	+	4.58237i	0.0497427	+	0.171732i
$713$	−13.5302	+	5.76469i	−0.506711	+	0.215889i
$714$	−0.0463350	+	0.0671278i	−0.00173404	+	0.00251220i
$715$	52.0266	−	19.4861i	1.94568	−	0.728738i
$716$	−14.2501	−	20.6448i	−0.532549	−	0.771531i
$717$	23.9217	+	15.1272i	0.893374	+	0.564935i
$718$	0.368145	−	0.0598293i	0.0137390	−	0.00223281i
$719$	−32.0603	−	13.6596i	−1.19565	−	0.509418i	−0.299896	−	0.953972i	$-0.596952\pi$
$719$	−32.0603	−	13.6596i	−1.19565	−	0.509418i	−0.895752	+	0.444554i	$0.853362\pi$
$720$	−6.47520	+	9.38094i	−0.241316	+	0.349607i
$721$	−0.503175	+	1.73716i	−0.0187392	+	0.0646953i
$722$	0.265276	+	0.559058i	0.00987257	+	0.0208060i
$723$	−9.44465	+	24.9035i	−0.351250	+	0.926171i
$724$	21.7651	+	26.6574i	0.808893	+	0.990714i
$725$	0.876174	+	21.7420i	0.0325403	+	0.807478i
$726$	0.105543	+	2.61903i	0.00391708	+	0.0972013i
$727$	−25.8960	+	6.38279i	−0.960430	+	0.236725i	−0.688211	−	0.725511i	$-0.741604\pi$
$727$	−25.8960	+	6.38279i	−0.960430	+	0.236725i	−0.272219	+	0.962235i	$0.587758\pi$
$728$	0.467173	−	0.267160i	0.0173146	−	0.00990161i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−0.730834	+	3.57986i	−0.0270494	+	0.132497i
$731$	−6.92833	+	2.95189i	−0.256254	+	0.109179i
$732$	−4.83794	+	3.05933i	−0.178815	+	0.113076i
$733$	−24.1867	+	12.6942i	−0.893356	+	0.468869i	−0.847936	−	0.530099i	$-0.822155\pi$
$733$	−24.1867	+	12.6942i	−0.893356	+	0.468869i	−0.0454199	+	0.998968i	$0.514463\pi$
$734$	0.960143	+	0.156038i	0.0354395	+	0.00575949i
$735$	−19.5731	+	6.53444i	−0.721963	+	0.241027i
$736$	−0.489849	−	4.03427i	−0.0180561	−	0.148705i
$737$	−21.3995	+	73.8798i	−0.788262	+	2.72140i
$738$	−0.0175422	+	0.0859275i	−0.000645738	+	0.00316303i
$739$	−34.2442	−	11.4324i	−1.25969	−	0.420547i	−0.393069	−	0.919509i	$-0.628587\pi$
$739$	−34.2442	−	11.4324i	−1.25969	−	0.420547i	−0.866624	+	0.498961i	$0.833715\pi$
$740$	59.3641	+	31.1567i	2.18227	+	1.14534i
$741$	−15.5699	+	7.30949i	−0.571973	+	0.268521i
$742$	0.265042	−	0.139105i	0.00973002	−	0.00510671i
$743$	26.5892	−	4.32117i	0.975465	−	0.158528i	0.348273	−	0.937393i	$-0.386768\pi$
$743$	26.5892	−	4.32117i	0.975465	−	0.158528i	0.627192	+	0.778865i	$0.284204\pi$
$744$	−3.67314	+	2.76018i	−0.134664	+	0.101193i
$745$	−1.47394	+	36.5754i	−0.0540010	+	1.34002i
$746$	4.09796			0.150037
$747$	0.594857	−	14.7612i	0.0217647	−	0.540085i
$748$	4.44497	+	21.7729i	0.162524	+	0.796096i
$749$	1.84506	+	2.67303i	0.0674170	+	0.0976703i
$750$	−0.547168	+	0.182671i	−0.0199797	+	0.00667022i
$751$	−9.32594	+	19.6540i	−0.340309	+	0.717185i	−0.999391	−	0.0348854i	$-0.988893\pi$
$751$	−9.32594	+	19.6540i	−0.340309	+	0.717185i	0.659083	+	0.752070i	$0.270945\pi$
$752$	3.29500	−	4.03564i	0.120156	−	0.147165i
$753$	−5.03024	−	13.2636i	−0.183312	−	0.483354i
$754$	3.31055	+	0.690085i	0.120563	+	0.0251314i
$755$	3.70866	−	9.77893i	0.134972	−	0.355892i
$756$	0.225047	+	0.389793i	0.00818489	+	0.0141767i
$757$	21.4741	−	26.3010i	0.780491	−	0.955928i	−0.219314	−	0.975654i	$-0.570382\pi$
$757$	21.4741	−	26.3010i	0.780491	−	0.955928i	0.999805	+	0.0197263i	$0.00627950\pi$
$758$	2.38820	+	1.79461i	0.0867432	+	0.0651833i
$759$	−9.62053	−	5.04924i	−0.349203	−	0.183276i
$760$	9.23940	−	0.745882i	0.335148	−	0.0270560i
$761$	34.4139	−	2.77818i	1.24750	−	0.100709i	0.560988	−	0.827824i	$-0.310421\pi$
$761$	34.4139	−	2.77818i	1.24750	−	0.100709i	0.686516	+	0.727115i	$0.259139\pi$
$762$	0.269198	+	0.141286i	0.00975201	+	0.00511825i
$763$	−1.51778	−	1.14054i	−0.0549475	−	0.0412904i
$764$	−2.87007	+	3.51519i	−0.103835	+	0.127175i
$765$	−3.22395	−	5.58405i	−0.116562	−	0.201892i
$766$	0.629168	−	1.65898i	0.0227328	−	0.0599414i
$767$	−29.8869	+	8.52343i	−1.07915	+	0.307763i
$768$	4.91990	+	12.9727i	0.177532	+	0.468113i
$769$	−17.1465	+	21.0006i	−0.618317	+	0.757301i	−0.984908	−	0.173081i	$-0.944628\pi$
$769$	−17.1465	+	21.0006i	−0.618317	+	0.757301i	0.366590	+	0.930382i	$0.380525\pi$
$770$	−0.248168	+	0.523003i	−0.00894336	+	0.0188477i
$771$	17.5248	−	5.85064i	0.631140	−	0.210706i
$772$	12.0878	+	17.5122i	0.435050	+	0.630279i
$773$	−2.69703	−	13.2109i	−0.0970056	−	0.475165i	−0.999052	−	0.0435263i	$-0.986141\pi$
$773$	−2.69703	−	13.2109i	−0.0970056	−	0.475165i	0.902047	−	0.431638i	$-0.142064\pi$
$774$	0.0230014	−	0.570775i	0.000826770	−	0.0205161i
$775$	−26.8307			−0.963787
$776$	−0.350210	+	8.69036i	−0.0125718	+	0.311966i
$777$	2.08689	−	1.56819i	0.0748667	−	0.0562587i
$778$	−0.639512	+	0.103931i	−0.0229276	+	0.00372610i
$779$	−2.24953	+	1.18064i	−0.0805978	+	0.0423010i
$780$	1.61311	+	21.0645i	0.0577585	+	0.754229i
$781$	68.4916	+	35.9472i	2.45082	+	1.28629i
$782$	0.710203	+	0.237101i	0.0253968	+	0.00847870i
$783$	−1.13923	+	5.58033i	−0.0407129	+	0.199425i
$784$	−7.41905	+	25.6135i	−0.264966	+	0.914769i
$785$	1.55888	+	12.8385i	0.0556387	+	0.458226i
$786$	2.49023	−	0.831360i	0.0888234	−	0.0296536i
$787$	12.0447	+	1.95746i	0.429348	+	0.0697758i	0.371245	−	0.928535i	$-0.378931\pi$
$787$	12.0447	+	1.95746i	0.429348	+	0.0697758i	0.0581024	+	0.998311i	$0.481495\pi$
$788$	40.0542	−	21.0221i	1.42687	−	0.748880i
$789$	−16.0908	+	10.1752i	−0.572847	+	0.362247i
$790$	−4.36024	+	1.85772i	−0.155130	+	0.0660948i
$791$	−0.505014	+	2.47372i	−0.0179562	+	0.0879554i
$792$	−3.29570	−	0.812318i	−0.117108	−	0.0288644i
$793$	−3.35358	+	9.90898i	−0.119089	+	0.351878i
$794$	3.21199	−	0.791683i	0.113989	−	0.0280958i
$795$	0.952782	+	23.6430i	0.0337917	+	0.838532i
$796$	0.469891	+	11.6602i	0.0166548	+	0.413285i
$797$	18.0048	+	22.0519i	0.637763	+	0.781118i	0.987818	−	0.155611i	$-0.0497347\pi$
$797$	18.0048	+	22.0519i	0.637763	+	0.781118i	−0.350056	+	0.936729i	$0.613837\pi$
$798$	0.0635549	−	0.167580i	0.00224982	−	0.00593228i
$799$	1.26340	+	2.66256i	0.0446960	+	0.0941948i
$800$	2.06268	−	7.12120i	0.0729268	−	0.251772i
$801$	−4.14228	+	6.00113i	−0.146360	+	0.212040i
$802$	−2.97767	−	1.26867i	−0.105145	−	0.0447981i
$803$	38.2559	−	6.21719i	1.35002	−	0.219400i
$804$	−24.7209	−	15.6325i	−0.871838	−	0.551317i
$805$	−0.806063	−	1.16778i	−0.0284100	−	0.0411590i
$806$	−1.01459	+	4.04449i	−0.0357373	+	0.142461i
$807$	−3.44827	+	4.99568i	−0.121385	+	0.175856i
$808$	3.46361	−	1.47571i	0.121849	−	0.0519152i
$809$	3.83066	+	13.2250i	0.134679	+	0.464966i	0.999298	−	0.0374623i	$-0.0119274\pi$
$809$	3.83066	+	13.2250i	0.134679	+	0.464966i	−0.864619	+	0.502428i	$0.832440\pi$
$810$	0.487500	−	0.0393551i	0.0171290	−	0.00138280i
$811$	20.4974	−	18.1591i	0.719760	−	0.637652i	−0.221568	−	0.975145i	$-0.571117\pi$
$811$	20.4974	−	18.1591i	0.719760	−	0.637652i	0.941328	+	0.337493i	$0.109579\pi$
$812$	2.16663	−	1.37010i	0.0760339	−	0.0480809i
$813$	−3.78251	−	1.61158i	−0.132659	−	0.0565205i
$814$	−1.17836	+	9.70465i	−0.0413014	+	0.340148i
$815$	−1.64336	−	8.04970i	−0.0575643	−	0.281969i
$816$	−8.30553	−	0.670492i	−0.290752	−	0.0234719i
$817$	13.2291	−	9.94103i	0.462828	−	0.347793i
$818$	−0.0924224	+	0.761167i	−0.00323147	+	0.0266136i
$819$	0.767910	+	0.294857i	0.0268330	+	0.0103032i
$820$	0.376122	+	3.09765i	0.0131348	+	0.108174i
$821$	−29.6482	−	30.8670i	−1.03473	−	1.07727i	−0.996955	−	0.0779801i	$-0.975153\pi$
$821$	−29.6482	−	30.8670i	−1.03473	−	1.07727i	−0.0377735	−	0.999286i	$-0.512027\pi$
$822$	0.535748	+	0.927943i	0.0186864	+	0.0323657i
$823$	−4.53825	+	7.86048i	−0.158194	+	0.273999i	−0.934217	−	0.356704i	$-0.883900\pi$
$823$	−4.53825	+	7.86048i	−0.158194	+	0.273999i	0.776024	+	0.630704i	$0.217234\pi$
$824$	5.03580	−	1.24121i	0.175430	−	0.0432397i
$825$	−12.5360	−	15.3538i	−0.436448	−	0.534552i
$826$	0.161920	−	0.280453i	0.00563390	−	0.00975820i
$827$	−8.84633	−	23.3259i	−0.307617	−	0.811120i	−0.996291	−	0.0860483i	$-0.972576\pi$
$827$	−8.84633	−	23.3259i	−0.307617	−	0.811120i	0.688674	−	0.725071i	$-0.258193\pi$
$828$	2.86208	−	2.97974i	0.0994642	−	0.103553i
$829$	−40.9597	−	13.6744i	−1.42259	−	0.474930i	−0.501798	−	0.864985i	$-0.667328\pi$
$829$	−40.9597	−	13.6744i	−1.42259	−	0.474930i	−0.920792	+	0.390055i	$0.872456\pi$
$830$	2.01022	+	6.94009i	0.0697758	+	0.240894i
$831$	5.83849	−	5.17245i	0.202535	−	0.179430i
$832$	22.9157	+	13.3567i	0.794459	+	0.463060i
$833$	−11.2908	−	10.0028i	−0.391204	−	0.346576i
$834$	−1.34059	+	2.82524i	−0.0464209	+	0.0978299i
$835$	13.2741	+	13.8198i	0.459371	+	0.478255i
$836$	−20.9325	−	44.1144i	−0.723967	−	1.52573i
$837$	−6.81867	−	1.68065i	−0.235688	−	0.0580918i
$838$	−3.66900	+	3.81984i	−0.126744	+	0.131954i
$839$	26.3135	+	19.7733i	0.908442	+	0.682650i	0.948578	−	0.316544i	$-0.102523\pi$
$839$	26.3135	+	19.7733i	0.908442	+	0.682650i	−0.0401358	+	0.999194i	$0.512779\pi$
$840$	−0.331812	−	0.293960i	−0.0114486	−	0.0101426i
$841$	3.39347	+	0.551492i	0.117016	+	0.0190170i
$842$	1.58976	+	1.00530i	0.0547868	+	0.0346451i
$843$	−7.37961	−	0.595744i	−0.254167	−	0.0205185i
$844$	11.9767			0.412256
$845$	26.5150	+	28.0647i	0.912144	+	0.965454i
$846$	−0.223544			−0.00768560
$847$	3.61949	+	0.292196i	0.124367	+	0.0100400i
$848$	25.8446	+	16.3431i	0.887507	+	0.561225i
$849$	27.0767	+	4.40039i	0.929269	+	0.151021i
$850$	1.02243	+	0.905790i	0.0350689	+	0.0310683i
$851$	−19.1565	−	14.3952i	−0.656677	−	0.493461i
$852$	−20.3761	+	21.2137i	−0.698072	+	0.726770i
$853$	−19.3287	−	4.76410i	−0.661802	−	0.163120i	−0.105912	−	0.994375i	$-0.533776\pi$
$853$	−19.3287	−	4.76410i	−0.661802	−	0.163120i	−0.555890	+	0.831256i	$0.687622\pi$
$854$	−0.0467296	−	0.0984805i	−0.00159905	−	0.00336993i
$855$	9.81458	+	10.2181i	0.335652	+	0.349450i
$856$	3.99299	−	8.41505i	0.136478	−	0.287620i
$857$	−14.1687	−	12.5523i	−0.483992	−	0.428779i	0.385514	−	0.922702i	$-0.374024\pi$
$857$	−14.1687	−	12.5523i	−0.483992	−	0.428779i	−0.869506	+	0.493923i	$0.835563\pi$
$858$	−2.78850	+	1.30910i	−0.0951978	+	0.0446919i
$859$	39.8701	−	35.3218i	1.36035	−	1.20517i	0.403363	−	0.915040i	$-0.367841\pi$
$859$	39.8701	−	35.3218i	1.36035	−	1.20517i	0.956989	−	0.290126i	$-0.0936971\pi$
$860$	−5.65474	−	19.5224i	−0.192825	−	0.665709i
$861$	0.115244	+	0.0384741i	0.00392750	+	0.00131119i
$862$	1.51376	−	1.57599i	0.0515588	−	0.0536784i
$863$	−7.54408	−	19.8921i	−0.256803	−	0.677135i	−0.999968	−	0.00802598i	$-0.997445\pi$
$863$	−7.54408	−	19.8921i	−0.256803	−	0.677135i	0.743164	−	0.669109i	$-0.233324\pi$
$864$	0.970269	−	1.68056i	0.0330092	−	0.0571737i
$865$	12.3415	+	15.1156i	0.419623	+	0.513945i
$866$	4.51256	−	1.11225i	0.153343	−	0.0377957i
$867$	−6.14326	+	10.6404i	−0.208636	+	0.361368i
$868$	1.58045	+	2.73742i	0.0536440	+	0.0929141i
$869$	34.8272	+	36.2590i	1.18143	+	1.23000i
$870$	−0.335762	−	2.76525i	−0.0113834	−	0.0937507i
$871$	−53.0904	+	6.22431i	−1.79890	+	0.210903i
$872$	−0.656269	+	5.40486i	−0.0222241	+	0.183032i
$873$	−10.6276	+	7.98611i	−0.359689	+	0.270289i
$874$	−1.63988	−	0.132384i	−0.0554696	−	0.00447797i
$875$	0.159852	+	0.783007i	0.00540398	+	0.0264705i
$876$	−1.77651	+	14.6309i	−0.0600228	+	0.494332i
$877$	−40.6660	−	17.3262i	−1.37319	−	0.585063i	−0.425708	−	0.904861i	$-0.639975\pi$
$877$	−40.6660	−	17.3262i	−1.37319	−	0.585063i	−0.947486	+	0.319797i	$0.896385\pi$
$878$	−5.35346	+	3.38532i	−0.180671	+	0.114249i
$879$	1.32099	−	1.17029i	0.0445558	−	0.0394730i
$880$	−58.9462	+	4.75863i	−1.98708	+	0.160413i
$881$	−3.01702	−	10.4160i	−0.101646	−	0.350922i	0.893533	−	0.448997i	$-0.148219\pi$
$881$	−3.01702	−	10.4160i	−0.101646	−	0.350922i	−0.995179	+	0.0980749i	$0.968732\pi$
$882$	1.05262	−	0.448480i	0.0354436	−	0.0151011i
$883$	1.81598	−	2.63090i	0.0611125	−	0.0885367i	−0.791236	−	0.611511i	$-0.790562\pi$
$883$	1.81598	−	2.63090i	0.0611125	−	0.0885367i	0.852349	+	0.522974i	$0.175178\pi$
$884$	−12.7457	+	8.72037i	−0.428686	+	0.293298i
$885$	14.5423	+	21.0682i	0.488835	+	0.708200i
$886$	−2.29709	−	1.45259i	−0.0771722	−	0.0488007i
$887$	−35.1048	+	5.70508i	−1.17870	+	0.191558i	−0.718030	−	0.696012i	$-0.754956\pi$
$887$	−35.1048	+	5.70508i	−1.17870	+	0.191558i	−0.460673	+	0.887570i	$0.652392\pi$
$888$	−6.88700	−	2.93428i	−0.231112	−	0.0984678i
$889$	0.239259	−	0.346626i	0.00802448	−	0.0116255i
$890$	0.992228	−	3.42557i	0.0332596	−	0.114825i
$891$	−2.22412	−	4.68723i	−0.0745107	−	0.157028i
$892$	16.4429	−	43.3565i	0.550550	−	1.45168i
$893$	−4.09555	−	5.01613i	−0.137052	−	0.167859i
$894$	−0.0817277	−	2.02805i	−0.00273338	−	0.0678282i
$895$	1.52056	+	37.7323i	0.0508267	+	1.26125i
$896$	−1.12805	+	0.278040i	−0.0376857	+	0.00928868i
$897$	0.638614	−	7.52373i	0.0213227	−	0.251210i
$898$	−2.50219	−	0.616735i	−0.0834992	−	0.0205807i
$899$	−8.00054	+	39.1893i	−0.266833	+	1.30703i
$900$	6.93433	−	2.95444i	0.231144	−	0.0984814i
$901$	−14.6195	+	9.24482i	−0.487047	+	0.307990i
$902$	−0.402882	+	0.211449i	−0.0134145	+	0.00704047i
$903$	−0.781128	−	0.126946i	−0.0259943	−	0.00422449i
$904$	6.86770	−	2.29278i	0.228416	−	0.0762566i
$905$	−6.24458	−	51.4288i	−0.207577	−	1.70955i
$906$	−0.161342	+	0.557016i	−0.00536022	+	0.0185056i
$907$	8.37898	−	41.0429i	0.278219	−	1.36281i	−0.564934	−	0.825136i	$-0.691098\pi$
$907$	8.37898	−	41.0429i	0.278219	−	1.36281i	0.843154	−	0.537673i	$-0.180696\pi$
$908$	−34.8053	−	11.6197i	−1.15505	−	0.385613i
$909$	5.09536	+	2.67425i	0.169003	+	0.0886994i
$910$	−0.401913	−	0.0178567i	−0.0133233	−	0.000591945i
$911$	−28.1111	+	14.7538i	−0.931363	+	0.488817i	−0.860943	−	0.508701i	$-0.830126\pi$
$911$	−28.1111	+	14.7538i	−0.931363	+	0.488817i	−0.0704192	+	0.997517i	$0.522434\pi$
$912$	18.0722	−	2.93701i	0.598429	−	0.0972542i
$913$	61.2736	−	46.0441i	2.02786	−	1.52384i
$914$	0.0173165	−	0.429704i	0.000572778	−	0.0142133i
$915$	8.61694			0.284867
$916$	1.03516	−	25.6872i	0.0342026	−	0.848730i
$917$	−0.727505	−	3.56356i	−0.0240243	−	0.117679i
$918$	0.203098	+	0.294238i	0.00670324	+	0.00971132i
$919$	−0.942137	+	0.314532i	−0.0310782	+	0.0103754i	−0.332165	−	0.943221i	$-0.607779\pi$
$919$	−0.942137	+	0.314532i	−0.0310782	+	0.0103754i	0.301086	+	0.953597i	$0.402651\pi$
$920$	−1.74444	+	3.67634i	−0.0575126	+	0.121205i
$921$	−2.74183	+	3.35813i	−0.0903464	+	0.110654i
$922$	−0.885986	−	2.33615i	−0.0291784	−	0.0769371i
$923$	−4.54649	+	53.5638i	−0.149650	+	1.76307i
$924$	−0.828057	+	2.18341i	−0.0272411	+	0.0718288i
$925$	−21.8577	−	37.8586i	−0.718676	−	1.24478i
$926$	−0.112570	+	0.137873i	−0.00369927	+	0.00453079i
$927$	6.33752	+	4.76234i	0.208151	+	0.156416i
$928$	−9.78625	−	5.13622i	−0.321249	−	0.168605i
$929$	−1.30252	+	0.105150i	−0.0427342	+	0.00344986i	−0.101815	−	0.994803i	$-0.532465\pi$
$929$	−1.30252	+	0.105150i	−0.0427342	+	0.00344986i	0.0590810	+	0.998253i	$0.481183\pi$
$930$	3.42359	−	0.276381i	0.112264	−	0.00906288i
$931$	29.3486	+	15.4033i	0.961862	+	0.504824i
$932$	3.60727	+	2.71068i	0.118160	+	0.0887914i
$933$	−0.147242	+	0.180339i	−0.00482050	+	0.00590404i
$934$	2.45457	+	4.25144i	0.0803159	+	0.139111i
$935$	11.8625	−	31.2787i	0.387944	−	1.02292i
$936$	−0.368795	−	2.32992i	−0.0120544	−	0.0761559i
$937$	−14.9489	−	39.4170i	−0.488360	−	1.28770i	−0.922201	−	0.386710i	$-0.873612\pi$
$937$	−14.9489	−	39.4170i	−0.488360	−	1.28770i	0.433842	−	0.900989i	$-0.357158\pi$
$938$	0.352267	−	0.431449i	0.0115019	−	0.0140873i
$939$	−1.84182	+	3.88156i	−0.0601056	+	0.126670i
$940$	−7.54445	+	2.51871i	−0.246073	+	0.0821512i
$941$	13.3730	+	19.3741i	0.435947	+	0.631579i	0.977960	−	0.208792i	$-0.0669530\pi$
$941$	13.3730	+	19.3741i	0.435947	+	0.631579i	−0.542013	+	0.840370i	$0.682338\pi$
$942$	−0.143439	−	0.702612i	−0.00467350	−	0.0228923i
$943$	0.0449076	−	1.11437i	0.00146239	−	0.0362889i
$944$	33.0823			1.07674
$945$	0.0272828	−	0.677015i	0.000887509	−	0.0220233i
$946$	2.36928	−	1.78040i	0.0770319	−	0.0578857i
$947$	13.6793	−	2.22311i	0.444518	−	0.0722413i	0.0659676	−	0.997822i	$-0.478987\pi$
$947$	13.6793	−	2.22311i	0.444518	−	0.0722413i	0.378551	+	0.925580i	$0.376423\pi$
$948$	−16.9283	+	8.88468i	−0.549807	+	0.288561i
$949$	14.3019	+	22.8245i	0.464260	+	0.740915i
$950$	−2.65762	−	1.39483i	−0.0862247	−	0.0452542i
$951$	−22.7706	−	7.60195i	−0.738388	−	0.246510i
$952$	0.0648190	−	0.317505i	0.00210080	−	0.0102904i
$953$	14.2035	−	49.0361i	0.460095	−	1.58843i	−0.310151	−	0.950687i	$-0.600380\pi$
$953$	14.2035	−	49.0361i	0.460095	−	1.58843i	0.770246	−	0.637746i	$-0.220133\pi$
$954$	−0.158148	−	1.30247i	−0.00512024	−	0.0421690i
$955$	6.47992	−	2.16332i	0.209685	−	0.0700033i
$956$	−55.1161	−	8.95724i	−1.78258	−	0.289698i
$957$	−26.1641	+	13.7320i	−0.845765	+	0.443892i
$958$	−2.31550	+	1.46424i	−0.0748105	+	0.0473073i
$959$	1.36563	−	0.581842i	0.0440986	−	0.0187887i
$960$	4.37022	−	21.4068i	0.141048	−	0.690900i
$961$	−17.7866	−	4.38400i	−0.573761	−	0.141419i
$962$	−6.53338	+	1.86325i	−0.210645	+	0.0600737i
$963$	13.8230	−	3.40706i	0.445440	−	0.109791i
$964$	−2.11582	−	52.5037i	−0.0681461	−	1.69103i
$965$	−1.28984	−	32.0070i	−0.0415213	−	1.03034i
$966$	0.0497604	+	0.0609455i	0.00160102	+	0.00196089i
$967$	5.20919	−	13.7355i	0.167516	−	0.441704i	−0.824801	−	0.565423i	$-0.808713\pi$
$967$	5.20919	−	13.7355i	0.167516	−	0.441704i	0.992317	+	0.123719i	$0.0394821\pi$
$968$	−4.46421	−	9.40812i	−0.143485	−	0.302388i
$969$	−2.88150	+	9.94809i	−0.0925671	+	0.319579i
$970$	3.69343	−	5.35086i	0.118589	−	0.171806i
$971$	9.68356	+	4.12578i	0.310760	+	0.132403i	0.541716	−	0.840562i	$-0.317775\pi$
$971$	9.68356	+	4.12578i	0.310760	+	0.132403i	−0.230956	+	0.972964i	$0.574185\pi$
$972$	1.94733	−	0.316472i	0.0624607	−	0.0101509i
$973$	3.66159	+	2.31545i	0.117385	+	0.0742300i
$974$	0.638802	+	0.925465i	0.0204685	+	0.0296538i
$975$	6.45188	−	12.1708i	0.206626	−	0.389778i
$976$	6.32573	−	9.16440i	0.202482	−	0.293345i
$977$	47.6912	−	20.3193i	1.52578	−	0.650072i	0.543823	−	0.839200i	$-0.316976\pi$
$977$	47.6912	−	20.3193i	1.52578	−	0.650072i	0.981953	+	0.189128i	$0.0605660\pi$
$978$	0.126742	+	0.437564i	0.00405276	+	0.0139918i
$979$	−37.7088	+	3.04417i	−1.20518	+	0.0972921i
$980$	30.4722	−	26.9960i	0.973398	−	0.862355i
$981$	−7.03354	+	4.44774i	−0.224564	+	0.142005i
$982$	−5.50038	−	2.34349i	−0.175524	−	0.0747838i
$983$	−1.81248	+	14.9271i	−0.0578091	+	0.476101i	0.934840	+	0.355070i	$0.115543\pi$
$983$	−1.81248	+	14.9271i	−0.0578091	+	0.476101i	−0.992649	+	0.121031i	$0.961380\pi$
$984$	−0.0696931	−	0.341380i	−0.00222174	−	0.0108828i
$985$	−67.8761	−	5.47953i	−2.16271	−	0.174592i
$986$	1.62788	−	1.22327i	0.0518423	−	0.0389569i
$987$	−0.0373291	+	0.307433i	−0.00118820	+	0.00978569i
$988$	22.6070	−	25.3070i	0.719225	−	0.805124i
$989$	0.875628	+	7.21144i	0.0278433	+	0.229311i
$990$	1.75775	+	1.83001i	0.0558650	+	0.0581616i
$991$	18.7818	+	32.5310i	0.596622	+	1.03338i	0.993316	+	0.115429i	$0.0368243\pi$
$991$	18.7818	+	32.5310i	0.596622	+	1.03338i	−0.396693	+	0.917951i	$0.629842\pi$
$992$	6.81395	−	11.8021i	0.216343	−	0.374717i
$993$	−15.0900	+	3.71936i	−0.478868	+	0.118030i
$994$	−0.354260	−	0.433890i	−0.0112364	−	0.0137622i
$995$	8.78367	−	15.2138i	0.278461	−	0.482308i
$996$	10.3352	+	27.2518i	0.327484	+	0.863505i
$997$	−24.5338	+	25.5424i	−0.776992	+	0.808934i	−0.985605	−	0.169064i	$-0.945926\pi$
$997$	−24.5338	+	25.5424i	−0.776992	+	0.808934i	0.208613	+	0.977998i	$0.433105\pi$
$998$	1.34117	+	0.447749i	0.0424541	+	0.0141733i
$999$	−3.18341	−	10.9904i	−0.100719	−	0.347721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.a.16.8	✓	360
169.74	even	39	inner	507.2.q.a.412.8	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.a.16.8	✓	360	1.1	even	1	trivial
507.2.q.a.412.8	yes	360	169.74	even	39	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.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.164145 - 0.0132511i) q^{2} +(0.845190 + 0.534466i) q^{3} +(-1.94733 - 0.316472i) q^{4} +(2.22303 + 1.96943i) q^{5} +(-0.131651 - 0.0989295i) q^{6} +(-0.158039 + 0.164536i) q^{7} +(0.635238 + 0.156572i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-0.338802 - 0.352730i) q^{10} +(-2.22412 + 4.68723i) q^{11} +(-1.47672 - 1.30826i) q^{12} +(-3.60200 - 0.160034i) q^{13} +(0.0281215 - 0.0249135i) q^{14} +(0.826289 + 2.85268i) q^{15} +(3.64050 + 1.21538i) q^{16} +(-1.50394 + 1.56577i) q^{17} +(-0.0583959 - 0.153977i) q^{18} +(2.38525 - 4.13137i) q^{19} +(-3.70571 - 4.53867i) q^{20} +(-0.221511 + 0.0545977i) q^{21} +(0.427188 - 0.739912i) q^{22} +(1.04711 + 1.81364i) q^{23} +(0.453214 + 0.471846i) q^{24} +(0.460516 + 3.79269i) q^{25} +(0.589128 + 0.0739994i) q^{26} +(-0.120537 + 0.992709i) q^{27} +(0.359825 - 0.270391i) q^{28} +(5.67697 + 0.458292i) q^{29} +(-0.0978298 - 0.479202i) q^{30} +(-0.846498 + 6.97154i) q^{31} +(-1.78526 - 0.760626i) q^{32} +(-4.38496 + 2.77288i) q^{33} +(0.267612 - 0.237084i) q^{34} +(-0.675368 + 0.0545213i) q^{35} +(-0.548890 - 1.89499i) q^{36} +(-10.5266 + 4.48495i) q^{37} +(-0.446271 + 0.646536i) q^{38} +(-2.95884 - 2.06040i) q^{39} +(1.10380 + 1.59912i) q^{40} +(-0.450107 - 0.284630i) q^{41} +(0.0370834 - 0.00602664i) q^{42} +(3.19123 + 1.35966i) q^{43} +(5.81447 - 8.42372i) q^{44} +(-0.826289 + 2.85268i) q^{45} +(-0.147844 - 0.311575i) q^{46} +(0.481360 - 1.26924i) q^{47} +(2.42734 + 2.97295i) q^{48} +(0.279766 + 6.94232i) q^{49} +(-0.0253338 - 0.628652i) q^{50} +(-2.10797 + 0.519567i) q^{51} +(6.96364 + 1.45157i) q^{52} +(7.73573 + 1.90669i) q^{53} +(0.0329400 - 0.161351i) q^{54} +(-14.1755 + 6.03960i) q^{55} +(-0.126154 + 0.0797749i) q^{56} +(4.22407 - 2.21696i) q^{57} +(-0.925771 - 0.150453i) q^{58} +(8.17603 - 2.72956i) q^{59} +(-0.706265 - 5.81662i) q^{60} +(0.807216 - 2.78683i) q^{61} +(0.231329 - 1.13312i) q^{62} +(-0.216400 - 0.0722449i) q^{63} +(-6.51384 - 3.41873i) q^{64} +(-7.69218 - 7.44966i) q^{65} +(0.756513 - 0.397048i) q^{66} +(14.6335 - 2.37817i) q^{67} +(3.42420 - 2.57312i) q^{68} +(-0.0843254 + 2.09251i) q^{69} +0.111581 q^{70} +(0.600339 - 14.8973i) q^{71} +(0.130867 + 0.641027i) q^{72} +(-4.24371 - 6.14808i) q^{73} +(1.78731 - 0.596692i) q^{74} +(-1.63784 + 3.45167i) q^{75} +(-5.95234 + 7.29029i) q^{76} +(-0.419720 - 1.10671i) q^{77} +(0.458375 + 0.377413i) q^{78} +(3.43630 - 9.06078i) q^{79} +(5.69935 + 9.87156i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(0.0701110 + 0.0526850i) q^{82} +(-13.0810 - 6.86545i) q^{83} +(0.448635 - 0.0362176i) q^{84} +(-6.42699 + 0.518840i) q^{85} +(-0.505806 - 0.265468i) q^{86} +(4.55318 + 3.42149i) q^{87} +(-2.14673 + 2.62927i) q^{88} +(3.64596 + 6.31499i) q^{89} +(0.173432 - 0.457303i) q^{90} +(0.595587 - 0.567366i) q^{91} +(-1.46510 - 3.86314i) q^{92} +(-4.44150 + 5.43985i) q^{93} +(-0.0958316 + 0.201961i) q^{94} +(13.4390 - 4.48658i) q^{95} +(-1.10235 - 1.59703i) q^{96} +(2.65909 + 13.0251i) q^{97} +(0.0460715 - 1.14325i) q^{98} -5.18814 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21}+ \cdots + 30 q^{99}+O(q^{100}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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