LMFDB - Embedded newform 570.2.bf.a.29.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(29,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 17]))

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

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

chi := DirichletCharacter("570.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bf (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.14
Character	$\chi$	$=$	570.29
Dual form			570.2.bf.a.59.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(0.917943 + 1.46880i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.501847 - 2.17902i) q^{5} +(-1.15905 - 1.28709i) q^{6} +(-3.34801 - 1.93297i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.31476 + 2.69655i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(0.917943 + 1.46880i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.501847 - 2.17902i) q^{5} +(-1.15905 - 1.28709i) q^{6} +(-3.34801 - 1.93297i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.31476 + 2.69655i) q^{9} +(-0.115839 + 2.23307i) q^{10} +(3.47920 - 2.00872i) q^{11} +(1.36494 + 1.06627i) q^{12} +(-0.681504 - 0.571849i) q^{13} +(3.63280 + 1.32223i) q^{14} +(3.66122 - 1.26311i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.566154 - 3.21082i) q^{17} +(0.826534 - 2.88389i) q^{18} +(-3.42399 - 2.69746i) q^{19} +(-0.273689 - 2.21926i) q^{20} +(-0.234126 - 6.69192i) q^{21} +(-3.07753 + 2.58236i) q^{22} +(6.82620 - 2.48453i) q^{23} +(-1.52936 - 0.813048i) q^{24} +(-4.49630 - 2.18707i) q^{25} +(0.770451 + 0.444820i) q^{26} +(-5.16758 + 0.544161i) q^{27} +(-3.80722 - 0.671315i) q^{28} +(1.08755 - 6.16782i) q^{29} +(-3.38627 + 1.87968i) q^{30} +(1.50475 + 0.868765i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(6.14411 + 3.26637i) q^{33} +(1.11511 + 3.06373i) q^{34} +(-5.89219 + 6.32534i) q^{35} +(-0.313195 + 2.98361i) q^{36} +2.85084 q^{37} +(3.84038 + 2.06191i) q^{38} +(0.214352 - 1.52592i) q^{39} +(0.654901 + 2.13801i) q^{40} +(-4.43975 + 3.72539i) q^{41} +(1.39261 + 6.54960i) q^{42} +(0.819901 - 2.25266i) q^{43} +(2.58236 - 3.07753i) q^{44} +(5.21605 + 4.21815i) q^{45} +(-6.29106 + 3.63214i) q^{46} +(1.50099 - 8.51256i) q^{47} +(1.64731 + 0.535125i) q^{48} +(3.97278 + 6.88105i) q^{49} +(4.80777 + 1.37307i) q^{50} +(4.19636 - 3.77892i) q^{51} +(-0.835988 - 0.304275i) q^{52} +(3.88287 + 10.6681i) q^{53} +(4.99458 - 1.43323i) q^{54} +(-2.63102 - 8.58933i) q^{55} +3.86595 q^{56} +(0.819006 - 7.50528i) q^{57} +6.26297i q^{58} +(-0.00803551 - 0.0455717i) q^{59} +(3.00842 - 2.43915i) q^{60} +(-2.60033 + 0.946444i) q^{61} +(-1.63274 - 0.594270i) q^{62} +(9.61420 - 6.48669i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-1.58808 + 1.19803i) q^{65} +(-6.61797 - 2.14983i) q^{66} +(0.646399 - 3.66591i) q^{67} +(-1.63018 - 2.82355i) q^{68} +(9.91535 + 7.74568i) q^{69} +(4.70429 - 7.25241i) q^{70} +(11.9518 + 4.35011i) q^{71} +(-0.209661 - 2.99266i) q^{72} +(-7.68577 - 9.15955i) q^{73} +(-2.80752 + 0.495042i) q^{74} +(-0.914971 - 8.61178i) q^{75} +(-4.14008 - 1.36371i) q^{76} -15.5312 q^{77} +(0.0538775 + 1.53996i) q^{78} +(7.79546 + 9.29027i) q^{79} +(-1.01621 - 1.99181i) q^{80} +(-5.54281 - 7.09065i) q^{81} +(3.72539 - 4.43975i) q^{82} +(1.50652 - 2.60937i) q^{83} +(-2.50878 - 6.20828i) q^{84} +(-7.28058 - 0.377675i) q^{85} +(-0.416275 + 2.36081i) q^{86} +(10.0576 - 4.06431i) q^{87} +(-2.00872 + 3.47920i) q^{88} +(-6.50540 - 5.45868i) q^{89} +(-5.86928 - 3.24831i) q^{90} +(1.17631 + 3.23189i) q^{91} +(5.56477 - 4.66940i) q^{92} +(0.105227 + 3.00765i) q^{93} +8.64388i q^{94} +(-7.59615 + 6.10725i) q^{95} +(-1.71521 - 0.240943i) q^{96} +(2.39112 + 13.5607i) q^{97} +(-5.10730 - 6.08665i) q^{98} +(0.842300 + 12.0228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) $ 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	0.917943	+	1.46880i	0.529975	+	0.848013i
$3$	0.917943	+	1.46880i	0.529975	+	0.848013i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	0.501847	−	2.17902i	0.224433	−	0.974490i
$5$	0.501847	−	2.17902i	0.224433	−	0.974490i
$6$	−1.15905	−	1.28709i	−0.473181	−	0.525452i
$7$	−3.34801	−	1.93297i	−1.26543	−	0.730595i	−0.291309	−	0.956629i	$-0.594091\pi$
$7$	−3.34801	−	1.93297i	−1.26543	−	0.730595i	−0.974120	+	0.226034i	$0.927424\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−1.31476	+	2.69655i	−0.438253	+	0.898851i
$10$	−0.115839	+	2.23307i	−0.0366314	+	0.706157i
$11$	3.47920	−	2.00872i	1.04902	−	0.605651i	0.126643	−	0.991948i	$-0.459580\pi$
$11$	3.47920	−	2.00872i	1.04902	−	0.605651i	0.922374	+	0.386298i	$0.126246\pi$
$12$	1.36494	+	1.06627i	0.394026	+	0.307805i
$13$	−0.681504	−	0.571849i	−0.189015	−	0.158602i	0.543370	−	0.839494i	$-0.317148\pi$
$13$	−0.681504	−	0.571849i	−0.189015	−	0.158602i	−0.732385	+	0.680891i	$0.761593\pi$
$14$	3.63280	+	1.32223i	0.970907	+	0.353381i
$15$	3.66122	−	1.26311i	0.945324	−	0.326133i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.566154	−	3.21082i	−0.137313	−	0.778738i	−0.973221	−	0.229870i	$-0.926170\pi$
$17$	−0.566154	−	3.21082i	−0.137313	−	0.778738i	0.835909	−	0.548868i	$-0.184941\pi$
$18$	0.826534	−	2.88389i	0.194816	−	0.679740i
$19$	−3.42399	−	2.69746i	−0.785517	−	0.618840i
$19$	−3.42399	−	2.69746i	−0.785517	−	0.618840i
$20$	−0.273689	−	2.21926i	−0.0611987	−	0.496241i
$21$	−0.234126	−	6.69192i	−0.0510904	−	1.46030i
$22$	−3.07753	+	2.58236i	−0.656132	+	0.550560i
$23$	6.82620	−	2.48453i	1.42336	−	0.518061i	0.488340	−	0.872653i	$-0.337603\pi$
$23$	6.82620	−	2.48453i	1.42336	−	0.518061i	0.935021	+	0.354592i	$0.115380\pi$
$24$	−1.52936	−	0.813048i	−0.312180	−	0.165963i
$25$	−4.49630	−	2.18707i	−0.899260	−	0.437415i
$26$	0.770451	+	0.444820i	0.151098	+	0.0872364i
$27$	−5.16758	+	0.544161i	−0.994501	+	0.104724i
$28$	−3.80722	−	0.671315i	−0.719496	−	0.126867i
$29$	1.08755	−	6.16782i	0.201953	−	1.14534i	−0.700209	−	0.713938i	$-0.746910\pi$
$29$	1.08755	−	6.16782i	0.201953	−	1.14534i	0.902162	−	0.431397i	$-0.141979\pi$
$30$	−3.38627	+	1.87968i	−0.618245	+	0.343182i
$31$	1.50475	+	0.868765i	0.270260	+	0.156035i	0.629006	−	0.777401i	$-0.283462\pi$
$31$	1.50475	+	0.868765i	0.270260	+	0.156035i	−0.358746	+	0.933435i	$0.616795\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	6.14411	+	3.26637i	1.06955	+	0.568601i
$34$	1.11511	+	3.06373i	0.191239	+	0.525425i
$35$	−5.89219	+	6.32534i	−0.995961	+	1.06918i
$36$	−0.313195	+	2.98361i	−0.0521991	+	0.497268i
$37$	2.85084			0.468674			0.234337	−	0.972155i	$-0.424708\pi$
$37$	2.85084			0.468674			0.234337	+	0.972155i	$0.424708\pi$
$38$	3.84038	+	2.06191i	0.622992	+	0.334486i
$39$	0.214352	−	1.52592i	0.0343238	−	0.244343i
$40$	0.654901	+	2.13801i	0.103549	+	0.338050i
$41$	−4.43975	+	3.72539i	−0.693373	+	0.581809i	−0.919880	−	0.392201i	$-0.871714\pi$
$41$	−4.43975	+	3.72539i	−0.693373	+	0.581809i	0.226507	+	0.974010i	$0.427269\pi$
$42$	1.39261	+	6.54960i	0.214884	+	1.01063i
$43$	0.819901	−	2.25266i	0.125034	−	0.343527i	−0.861344	−	0.508022i	$-0.830377\pi$
$43$	0.819901	−	2.25266i	0.125034	−	0.343527i	0.986378	+	0.164494i	$0.0525992\pi$
$44$	2.58236	−	3.07753i	0.389305	−	0.463955i
$45$	5.21605	+	4.21815i	0.777563	+	0.628805i
$46$	−6.29106	+	3.63214i	−0.927566	+	0.535531i
$47$	1.50099	−	8.51256i	0.218943	−	1.24168i	−0.654990	−	0.755637i	$-0.727327\pi$
$47$	1.50099	−	8.51256i	0.218943	−	1.24168i	0.873933	−	0.486047i	$-0.161562\pi$
$48$	1.64731	+	0.535125i	0.237769	+	0.0772387i
$49$	3.97278	+	6.88105i	0.567539	+	0.983007i
$50$	4.80777	+	1.37307i	0.679922	+	0.194182i
$51$	4.19636	−	3.77892i	0.587608	−	0.529154i
$52$	−0.835988	−	0.304275i	−0.115931	−	0.0421953i
$53$	3.88287	+	10.6681i	0.533354	+	1.46538i	0.855056	+	0.518536i	$0.173523\pi$
$53$	3.88287	+	10.6681i	0.533354	+	1.46538i	−0.321702	+	0.946841i	$0.604255\pi$
$54$	4.99458	−	1.43323i	0.679676	−	0.195039i
$55$	−2.63102	−	8.58933i	−0.354766	−	1.15818i
$56$	3.86595			0.516609
$57$	0.819006	−	7.50528i	0.108480	−	0.994099i
$58$			6.26297i			0.822368i
$59$	−0.00803551	−	0.0455717i	−0.00104613	−	0.00593293i	0.984280	−	0.176614i	$-0.0565144\pi$
$59$	−0.00803551	−	0.0455717i	−0.00104613	−	0.00593293i	−0.985326	+	0.170681i	$0.945403\pi$
$60$	3.00842	−	2.43915i	0.388385	−	0.314892i
$61$	−2.60033	+	0.946444i	−0.332939	+	0.121180i	−0.503080	−	0.864240i	$-0.667800\pi$
$61$	−2.60033	+	0.946444i	−0.332939	+	0.121180i	0.170141	+	0.985420i	$0.445578\pi$
$62$	−1.63274	−	0.594270i	−0.207359	−	0.0754724i
$63$	9.61420	−	6.48669i	1.21128	−	0.817246i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−1.58808	+	1.19803i	−0.196978	+	0.148598i
$66$	−6.61797	−	2.14983i	−0.814616	−	0.264626i
$67$	0.646399	−	3.66591i	0.0789702	−	0.447862i	−0.919525	−	0.393031i	$-0.871427\pi$
$67$	0.646399	−	3.66591i	0.0789702	−	0.447862i	0.998496	−	0.0548318i	$-0.0174622\pi$
$68$	−1.63018	−	2.82355i	−0.197688	−	0.342405i
$69$	9.91535	+	7.74568i	1.19367	+	0.932470i
$70$	4.70429	−	7.25241i	0.562270	−	0.866829i
$71$	11.9518	+	4.35011i	1.41842	+	0.516263i	0.933589	−	0.358345i	$-0.116659\pi$
$71$	11.9518	+	4.35011i	1.41842	+	0.516263i	0.484831	+	0.874608i	$0.338881\pi$
$72$	−0.209661	−	2.99266i	−0.0247088	−	0.352689i
$73$	−7.68577	−	9.15955i	−0.899552	−	1.07204i	−0.997046	−	0.0768078i	$-0.975527\pi$
$73$	−7.68577	−	9.15955i	−0.899552	−	1.07204i	0.0974943	−	0.995236i	$-0.468917\pi$
$74$	−2.80752	+	0.495042i	−0.326368	+	0.0575475i
$75$	−0.914971	−	8.61178i	−0.105652	−	0.994403i
$76$	−4.14008	−	1.36371i	−0.474900	−	0.156428i
$77$	−15.5312			−1.76994
$78$	0.0538775	+	1.53996i	0.00610042	+	0.174366i
$79$	7.79546	+	9.29027i	0.877058	+	1.04524i	0.998613	+	0.0526520i	$0.0167674\pi$
$79$	7.79546	+	9.29027i	0.877058	+	1.04524i	−0.121555	+	0.992585i	$0.538788\pi$
$80$	−1.01621	−	1.99181i	−0.113616	−	0.222691i
$81$	−5.54281	−	7.09065i	−0.615868	−	0.787850i
$82$	3.72539	−	4.43975i	0.411401	−	0.490288i
$83$	1.50652	−	2.60937i	0.165362	−	0.286416i	−0.771422	−	0.636324i	$-0.780454\pi$
$83$	1.50652	−	2.60937i	0.165362	−	0.286416i	0.936784	+	0.349909i	$0.113787\pi$
$84$	−2.50878	−	6.20828i	−0.273730	−	0.677378i
$85$	−7.28058	−	0.377675i	−0.789690	−	0.0409646i
$86$	−0.416275	+	2.36081i	−0.0448881	+	0.254573i
$87$	10.0576	−	4.06431i	1.07829	−	0.435739i
$88$	−2.00872	+	3.47920i	−0.214130	+	0.370884i
$89$	−6.50540	−	5.45868i	−0.689571	−	0.578618i	0.229215	−	0.973376i	$-0.426384\pi$
$89$	−6.50540	−	5.45868i	−0.689571	−	0.578618i	−0.918785	+	0.394757i	$0.870829\pi$
$90$	−5.86928	−	3.24831i	−0.618677	−	0.342402i
$91$	1.17631	+	3.23189i	0.123311	+	0.338794i
$92$	5.56477	−	4.66940i	0.580167	−	0.486818i
$93$	0.105227	+	3.00765i	0.0109115	+	0.311879i
$94$			8.64388i			0.891548i
$95$	−7.59615	+	6.10725i	−0.779349	+	0.626591i
$96$	−1.71521	−	0.240943i	−0.175058	−	0.0245911i
$97$	2.39112	+	13.5607i	0.242782	+	1.37688i	0.825588	+	0.564273i	$0.190843\pi$
$97$	2.39112	+	13.5607i	0.242782	+	1.37688i	−0.582806	+	0.812611i	$0.698045\pi$
$98$	−5.10730	−	6.08665i	−0.515915	−	0.614844i
$99$	0.842300	+	12.0228i	0.0846543	+	1.20834i
$100$	−4.97316	−	0.517351i	−0.497316	−	0.0517351i
$101$	−10.6630	+	12.7077i	−1.06101	+	1.26447i	−0.0979496	+	0.995191i	$0.531228\pi$
$101$	−10.6630	+	12.7077i	−1.06101	+	1.26447i	−0.963063	+	0.269275i	$0.913216\pi$
$102$	−3.47641	+	4.45020i	−0.344216	+	0.440635i
$103$	−3.57794	−	6.19717i	−0.352545	−	0.610626i	0.634150	−	0.773210i	$-0.281350\pi$
$103$	−3.57794	−	6.19717i	−0.352545	−	0.610626i	−0.986695	+	0.162585i	$0.948017\pi$
$104$	0.876124	+	0.154484i	0.0859110	+	0.0151484i
$105$	−14.6994	−	2.84815i	−1.43451	−	0.277951i
$106$	−5.67638	−	9.83178i	−0.551339	−	0.954947i
$107$	4.04355	+	2.33454i	0.390904	+	0.225689i	0.682552	−	0.730837i	$-0.260870\pi$
$107$	4.04355	+	2.33454i	0.390904	+	0.225689i	−0.291648	+	0.956526i	$0.594203\pi$
$108$	−4.66982	+	2.27876i	−0.449354	+	0.219274i
$109$	2.47142	−	6.79017i	0.236719	−	0.650381i	−0.763272	−	0.646078i	$-0.776408\pi$
$109$	2.47142	−	6.79017i	0.236719	−	0.650381i	0.999991	−	0.00430289i	$-0.00136966\pi$
$110$	4.08257	+	8.00196i	0.389258	+	0.762957i
$111$	2.61690	+	4.18731i	0.248386	+	0.397442i
$112$	−3.80722	+	0.671315i	−0.359748	+	0.0634333i
$113$			4.32432i			0.406798i	0.979096	+	0.203399i	$0.0651988\pi$
$113$			4.32432i			0.406798i	−0.979096	+	0.203399i	$0.934801\pi$
$114$	0.496714	+	7.53348i	0.0465216	+	0.705575i
$115$	−1.98816	−	16.1213i	−0.185396	−	1.50332i
$116$	−1.08755	−	6.16782i	−0.100977	−	0.572668i
$117$	2.43804	−	1.08587i	0.225397	−	0.100388i
$118$	0.0158269	+	0.0434840i	0.00145698	+	0.00400302i
$119$	−4.31094	+	11.8442i	−0.395183	+	1.08576i
$120$	−2.53916	+	2.92450i	−0.231792	+	0.266969i
$121$	2.56988	−	4.45116i	0.233625	−	0.404651i
$122$	2.39648	−	1.38361i	0.216967	−	0.125266i
$123$	−9.54731	−	3.10142i	−0.860852	−	0.279645i
$124$	1.71113	+	0.301719i	0.153664	+	0.0270952i
$125$	−7.02214	+	8.69997i	−0.628079	+	0.778149i
$126$	−8.34174	+	8.05763i	−0.743141	+	0.717831i
$127$	−2.47835	−	2.07958i	−0.219918	−	0.184533i	0.526172	−	0.850378i	$-0.323627\pi$
$127$	−2.47835	−	2.07958i	−0.219918	−	0.184533i	−0.746090	+	0.665845i	$0.768071\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	4.06133	−	0.863541i	0.357581	−	0.0760306i
$130$	1.35592	−	1.45560i	0.118922	−	0.127665i
$131$	−7.71257	+	1.35993i	−0.673851	+	0.118818i	−0.500095	−	0.865971i	$-0.666701\pi$
$131$	−7.71257	+	1.35993i	−0.673851	+	0.118818i	−0.173756	+	0.984789i	$0.555590\pi$
$132$	6.89074	+	0.967970i	0.599762	+	0.0842510i
$133$	6.24943	+	15.6496i	0.541894	+	1.35699i
$134$			3.72246i			0.321572i
$135$	−1.40759	+	11.5334i	−0.121146	+	0.992635i
$136$	2.09571	+	2.49757i	0.179706	+	0.214165i
$137$	8.99292	−	3.27316i	0.768317	−	0.279645i	0.0720248	−	0.997403i	$-0.477054\pi$
$137$	8.99292	−	3.27316i	0.768317	−	0.279645i	0.696292	+	0.717758i	$0.254832\pi$
$138$	−11.1097	−	5.90622i	−0.945724	−	0.502771i
$139$	16.7234	+	14.0326i	1.41846	+	1.19023i	0.952158	+	0.305606i	$0.0988591\pi$
$139$	16.7234	+	14.0326i	1.41846	+	1.19023i	0.466304	+	0.884625i	$0.345585\pi$
$140$	−3.37345	+	7.95912i	−0.285109	+	0.672668i
$141$	13.8811	−	5.60938i	1.16900	−	0.472395i
$142$	−12.5256	−	2.20861i	−1.05113	−	0.185342i
$143$	−3.51977	−	0.620630i	−0.294338	−	0.0518997i
$144$	0.726147	+	2.91079i	0.0605122	+	0.242566i
$145$	−12.8940	−	5.46510i	−1.07079	−	0.453852i
$146$	9.15955	+	7.68577i	0.758049	+	0.636079i
$147$	−6.46012	+	12.1516i	−0.532822	+	1.00225i
$148$	2.67891	−	0.975043i	0.220205	−	0.0801480i
$149$	12.7509	+	15.1960i	1.04460	+	1.24490i	0.968817	+	0.247779i	$0.0797006\pi$
$149$	12.7509	+	15.1960i	1.04460	+	1.24490i	0.0757813	+	0.997124i	$0.475855\pi$
$150$	2.39649	+	8.32207i	0.195673	+	0.679494i
$151$		−	6.57645i		−	0.535184i	−0.963532	−	0.267592i	$-0.913772\pi$
$151$		−	6.57645i		−	0.535184i	0.963532	−	0.267592i	$-0.0862280\pi$
$152$	4.31399	+	0.624074i	0.349911	+	0.0506191i
$153$	9.40251	+	2.69479i	0.760148	+	0.217861i
$154$	15.2952	−	2.69696i	1.23252	−	0.217327i
$155$	2.64821	−	2.84289i	0.212710	−	0.228346i
$156$	−0.320470	−	1.50721i	−0.0256581	−	0.120673i
$157$	−7.45824	+	20.4913i	−0.595232	+	1.63539i	0.165417	+	0.986224i	$0.447103\pi$
$157$	−7.45824	+	20.4913i	−0.595232	+	1.63539i	−0.760649	+	0.649163i	$0.775119\pi$
$158$	−9.29027	−	7.79546i	−0.739094	−	0.620173i
$159$	−12.1051	+	15.4959i	−0.959996	+	1.22890i
$160$	1.34665	+	1.78509i	0.106462	+	0.141124i
$161$	−27.6567	−	4.87662i	−2.17965	−	0.384332i
$162$	6.68988	+	6.02042i	0.525607	+	0.473009i
$163$	−2.24857	+	1.29821i	−0.176121	+	0.101684i	−0.585469	−	0.810695i	$-0.699090\pi$
$163$	−2.24857	+	1.29821i	−0.176121	+	0.101684i	0.409348	+	0.912378i	$0.365756\pi$
$164$	−2.89784	+	5.01921i	−0.226283	+	0.391934i
$165$	10.2009	−	11.7490i	0.794139	−	0.914655i
$166$	−1.03052	+	2.83133i	−0.0799840	+	0.219754i
$167$	−7.40665	−	20.3496i	−0.573144	−	1.57470i	−0.799507	−	0.600657i	$-0.794906\pi$
$167$	−7.40665	−	20.3496i	−0.573144	−	1.57470i	0.226363	−	0.974043i	$-0.427317\pi$
$168$	3.54872	+	5.67831i	0.273790	+	0.438091i
$169$	−2.11999	−	12.0231i	−0.163076	−	0.924851i
$170$	7.23555	−	0.892322i	0.554942	−	0.0684380i
$171$	11.7756	−	5.68646i	0.900501	−	0.434855i
$172$		−	2.39723i		−	0.182787i
$173$	6.12627	−	1.08023i	0.465771	−	0.0821281i	0.0641627	−	0.997939i	$-0.479562\pi$
$173$	6.12627	−	1.08023i	0.465771	−	0.0821281i	0.401609	+	0.915811i	$0.368451\pi$
$174$	−9.19906	+	5.74905i	−0.697379	+	0.435834i
$175$	10.8261	+	16.0136i	0.818376	+	1.21051i
$176$	1.37404	−	3.77515i	0.103572	−	0.284563i
$177$	0.0595596	−	0.0536348i	0.00447678	−	0.00403144i
$178$	7.35445	+	4.24610i	0.551240	+	0.318258i
$179$	−3.65830	−	6.33636i	−0.273434	−	0.473602i	0.696305	−	0.717746i	$-0.254826\pi$
$179$	−3.65830	−	6.33636i	−0.273434	−	0.473602i	−0.969739	+	0.244145i	$0.921493\pi$
$180$	6.34418	+	2.17977i	0.472867	+	0.162471i
$181$	−11.3503	−	2.00137i	−0.843663	−	0.148760i	−0.264920	−	0.964270i	$-0.585345\pi$
$181$	−11.3503	−	2.00137i	−0.843663	−	0.148760i	−0.578743	+	0.815510i	$0.696457\pi$
$182$	−1.71965	−	2.97852i	−0.127469	−	0.220783i
$183$	−3.77710	−	2.95059i	−0.279211	−	0.218114i
$184$	−4.66940	+	5.56477i	−0.344232	+	0.410240i
$185$	1.43068	−	6.21204i	0.105186	−	0.456718i
$186$	−0.625901	−	2.94369i	−0.0458933	−	0.215841i
$187$	−8.41939	−	10.0338i	−0.615686	−	0.733747i
$188$	−1.50099	−	8.51256i	−0.109471	−	0.620842i
$189$	18.3530	+	8.16694i	1.33498	+	0.594058i
$190$	6.42024	−	7.33352i	0.465773	−	0.532030i
$191$		−	23.4715i		−	1.69834i	−0.528121	−	0.849169i	$-0.677103\pi$
$191$		−	23.4715i		−	1.69834i	0.528121	−	0.849169i	$-0.322897\pi$
$192$	1.73099	−	0.0605610i	0.124924	−	0.00437062i
$193$	−16.7865	+	14.0855i	−1.20832	+	1.01390i	−0.208964	+	0.977923i	$0.567009\pi$
$193$	−16.7865	+	14.0855i	−1.20832	+	1.01390i	−0.999353	+	0.0359748i	$0.988546\pi$
$194$	−4.70959	−	12.9395i	−0.338129	−	0.929002i
$195$	−3.21744	−	1.23286i	−0.230406	−	0.0882867i
$196$	6.08665	+	5.10730i	0.434760	+	0.364807i
$197$	6.06663	−	10.5077i	0.432229	−	0.748643i	−0.564836	−	0.825203i	$-0.691060\pi$
$197$	6.06663	−	10.5077i	0.432229	−	0.748643i	0.997065	+	0.0765605i	$0.0243938\pi$
$198$	−2.91725	−	11.6939i	−0.207320	−	0.831050i
$199$	−1.61915	+	9.18266i	−0.114779	+	0.650942i	0.872081	+	0.489362i	$0.162770\pi$
$199$	−1.61915	+	9.18266i	−0.114779	+	0.650942i	−0.986860	+	0.161580i	$0.948341\pi$
$200$	4.98745	−	0.354089i	0.352666	−	0.0250379i
$201$	5.97786	−	2.41567i	0.421646	−	0.170388i
$202$	8.29438	−	14.3663i	0.583591	−	1.01081i
$203$	−15.5634	+	18.5477i	−1.09233	+	1.30179i
$204$	2.65082	−	4.98626i	0.185595	−	0.349108i
$205$	5.88965	+	11.5439i	0.411351	+	0.806261i
$206$	4.59971	+	5.48172i	0.320477	+	0.381930i
$207$	−2.27514	+	21.6738i	−0.158133	+	1.50643i
$208$	−0.889640			−0.0616854
$209$	−17.3312	−	2.50717i	−1.19882	−	0.173425i
$210$	14.9706	+	0.252366i	1.03307	+	0.0174149i
$211$	−11.9430	+	2.10588i	−0.822191	+	0.144974i	−0.568891	−	0.822413i	$-0.692627\pi$
$211$	−11.9430	+	2.10588i	−0.822191	+	0.144974i	−0.253300	+	0.967388i	$0.581516\pi$
$212$	7.29742	+	8.69672i	0.501189	+	0.597293i
$213$	4.58165	+	21.5480i	0.313929	+	1.47645i
$214$	−4.38751	−	1.59692i	−0.299924	−	0.109163i
$215$	−4.49714	−	2.91707i	−0.306702	−	0.198943i
$216$	4.20318	−	3.05505i	0.285990	−	0.207870i
$217$	−3.35860	−	5.81727i	−0.227997	−	0.394902i
$218$	−1.25477	+	7.11617i	−0.0849840	+	0.481968i
$219$	6.39846	−	19.6968i	0.432368	−	1.33099i
$220$	−5.41007	−	7.17147i	−0.364747	−	0.483500i
$221$	−1.45027	+	2.51194i	−0.0975557	+	0.168971i
$222$	−3.30427	−	3.66928i	−0.221768	−	0.246266i
$223$	16.6715	+	6.06793i	1.11641	+	0.406339i	0.833339	−	0.552762i	$-0.186426\pi$
$223$	16.6715	+	6.06793i	1.11641	+	0.406339i	0.283067	+	0.959100i	$0.408648\pi$
$224$	3.63280	−	1.32223i	0.242727	−	0.0883453i
$225$	11.8091	−	9.24904i	0.787274	−	0.616603i
$226$	−0.750910	−	4.25862i	−0.0499498	−	0.283279i
$227$			8.60714i			0.571276i	0.958338	+	0.285638i	$0.0922054\pi$
$227$			8.60714i			0.571276i	−0.958338	+	0.285638i	$0.907795\pi$
$228$	−1.79734	−	7.33277i	−0.119032	−	0.485625i
$229$	−0.547836			−0.0362020			−0.0181010	−	0.999836i	$-0.505762\pi$
$229$	−0.547836			−0.0362020			−0.0181010	+	0.999836i	$0.505762\pi$
$230$	4.75739	+	15.5312i	0.313693	+	1.02409i
$231$	−14.2567	−	22.8122i	−0.938025	−	1.50093i
$232$	2.14206	+	5.88526i	0.140633	+	0.386387i
$233$	1.52812	+	0.556189i	0.100110	+	0.0364371i	0.391590	−	0.920140i	$-0.371925\pi$
$233$	1.52812	+	0.556189i	0.100110	+	0.0364371i	−0.291479	+	0.956577i	$0.594147\pi$
$234$	−2.21244	+	1.49273i	−0.144632	+	0.0975828i
$235$	−17.7958	−	7.54270i	−1.16087	−	0.492032i
$236$	−0.0231373	−	0.0400751i	−0.00150611	−	0.00260866i
$237$	−6.48978	+	19.9779i	−0.421556	+	1.29771i
$238$	2.18872	−	12.4129i	0.141874	−	0.804606i
$239$	7.05910	−	4.07557i	0.456615	−	0.263627i	−0.254005	−	0.967203i	$-0.581748\pi$
$239$	7.05910	−	4.07557i	0.456615	−	0.263627i	0.710620	+	0.703576i	$0.248415\pi$
$240$	1.99275	−	3.32099i	0.128631	−	0.214369i
$241$	−12.5315	+	14.9345i	−0.807225	+	0.962013i	−0.999814	−	0.0192662i	$-0.993867\pi$
$241$	−12.5315	+	14.9345i	−0.807225	+	0.962013i	0.192589	+	0.981279i	$0.438311\pi$
$242$	−1.75790	+	4.82979i	−0.113002	+	0.310471i
$243$	5.32677	−	14.6501i	0.341713	−	0.939805i
$244$	−2.11981	+	1.77873i	−0.135707	+	0.113872i
$245$	16.9877	−	5.20355i	1.08530	−	0.332442i
$246$	9.94082	+	1.39643i	0.633803	+	0.0890329i
$247$	0.790921	+	3.79634i	0.0503251	+	0.241555i
$248$	−1.73753			−0.110333
$249$	5.21555	−	0.182473i	0.330522	−	0.0115638i
$250$	5.40472	−	9.78718i	0.341825	−	0.618996i
$251$	−0.846815	−	2.32661i	−0.0534505	−	0.146854i	0.910094	−	0.414401i	$-0.136009\pi$
$251$	−0.846815	−	2.32661i	−0.0534505	−	0.146854i	−0.963545	+	0.267547i	$0.913787\pi$
$252$	6.81581	−	9.38374i	0.429356	−	0.591120i
$253$	18.7590	−	22.3561i	1.17937	−	1.40551i
$254$	2.80181	+	1.61763i	0.175801	+	0.101499i
$255$	−6.12843	−	11.0404i	−0.383777	−	0.691378i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−8.22024	−	1.44945i	−0.512764	−	0.0904142i	−0.0887217	−	0.996056i	$-0.528278\pi$
$257$	−8.22024	−	1.44945i	−0.512764	−	0.0904142i	−0.424043	+	0.905642i	$0.639389\pi$
$258$	−3.84968	+	1.55567i	−0.239671	+	0.0968515i
$259$	−9.54462	−	5.51059i	−0.593074	−	0.342411i
$260$	−1.08256	+	1.66894i	−0.0671375	+	0.103503i
$261$	15.2020	+	11.0418i	0.940979	+	0.683473i
$262$	7.35925	−	2.67855i	0.454656	−	0.165481i
$263$	0.755363	−	0.633825i	0.0465777	−	0.0390833i	−0.619202	−	0.785232i	$-0.712544\pi$
$263$	0.755363	−	0.633825i	0.0465777	−	0.0390833i	0.665779	+	0.746149i	$0.268099\pi$
$264$	−6.95414	+	0.243300i	−0.427998	+	0.0149741i
$265$	25.1947	−	3.10712i	1.54770	−	0.190869i
$266$	−8.87201	−	14.3266i	−0.543978	−	0.878423i
$267$	2.04613	−	14.5659i	0.125221	−	0.891418i
$268$	−0.646399	−	3.66591i	−0.0394851	−	0.223931i
$269$	18.0932	−	15.1820i	1.10316	−	0.925661i	0.105527	−	0.994416i	$-0.466347\pi$
$269$	18.0932	−	15.1820i	1.10316	−	0.925661i	0.997634	+	0.0687551i	$0.0219027\pi$
$270$	−0.616540	−	11.6026i	−0.0375215	−	0.706111i
$271$	27.8483	+	10.1359i	1.69166	+	0.615714i	0.994833	−	0.101523i	$-0.0323717\pi$
$271$	27.8483	+	10.1359i	1.69166	+	0.615714i	0.696828	+	0.717238i	$0.254594\pi$
$272$	−2.49757	−	2.09571i	−0.151438	−	0.127071i
$273$	−3.66721	+	4.69445i	−0.221950	+	0.284121i
$274$	−8.28792	+	4.78503i	−0.500692	+	0.289074i
$275$	−20.0367	+	1.42253i	−1.20826	+	0.0857818i
$276$	11.9666	+	3.88730i	0.720302	+	0.233988i
$277$	−9.66682	+	5.58114i	−0.580823	+	0.335338i	−0.761460	−	0.648212i	$-0.775517\pi$
$277$	−9.66682	+	5.58114i	−0.580823	+	0.335338i	0.180638	+	0.983550i	$0.442184\pi$
$278$	−18.9061	−	10.9154i	−1.13391	−	0.654664i
$279$	−4.32105	+	2.91541i	−0.258695	+	0.174541i
$280$	1.94011	−	8.42400i	0.115944	−	0.503430i
$281$	18.5627	−	6.75629i	1.10736	−	0.403046i	0.277336	−	0.960773i	$-0.410548\pi$
$281$	18.5627	−	6.75629i	1.10736	−	0.403046i	0.830025	+	0.557727i	$0.188326\pi$
$282$	−12.6962	+	7.93459i	−0.756045	+	0.472498i
$283$	−3.30932	+	0.583522i	−0.196719	+	0.0346868i	−0.271139	−	0.962540i	$-0.587400\pi$
$283$	−3.30932	+	0.583522i	−0.196719	+	0.0346868i	0.0744206	+	0.997227i	$0.476289\pi$
$284$	12.7189			0.754725
$285$	−15.9432	−	5.55114i	−0.944392	−	0.328821i
$286$	3.57407			0.211339
$287$	22.0654	−	3.89073i	1.30248	−	0.229662i
$288$	−1.22057	−	2.74048i	−0.0719227	−	0.161484i
$289$	5.98594	−	2.17871i	0.352114	−	0.128159i
$290$	13.6472	+	3.14305i	0.801389	+	0.184566i
$291$	−17.7231	+	15.9601i	−1.03895	+	0.935596i
$292$	−10.3550	−	5.97847i	−0.605981	−	0.349863i
$293$	17.0365	−	9.83605i	0.995286	−	0.574628i	0.0884356	−	0.996082i	$-0.471813\pi$
$293$	17.0365	−	9.83605i	0.995286	−	0.574628i	0.906850	+	0.421453i	$0.138480\pi$
$294$	4.25187	−	13.0888i	0.247974	−	0.763355i
$295$	−0.103334	−	0.00536040i	−0.00601636	−	0.000312095i
$296$	−2.46890	+	1.42542i	−0.143502	+	0.0828507i
$297$	−16.8860	+	12.2734i	−0.979823	+	0.712177i
$298$	−15.1960	−	12.7509i	−0.880280	−	0.738642i
$299$	−6.07286	−	2.21034i	−0.351202	−	0.127827i
$300$	−3.80519	−	7.77949i	−0.219693	−	0.449149i
$301$	−7.09937	+	5.95708i	−0.409201	+	0.343360i
$302$	1.14199	+	6.47654i	0.0657141	+	0.372683i
$303$	−28.4532	−	3.99694i	−1.63459	−	0.229618i
$304$	−4.35682	+	0.134524i	−0.249881	+	0.00771551i
$305$	0.757356	+	6.14116i	0.0433661	+	0.351642i
$306$	−9.72761	−	1.02112i	−0.556090	−	0.0583738i
$307$	21.0299	−	17.6462i	1.20024	−	1.00712i	0.200616	−	0.979670i	$-0.435706\pi$
$307$	21.0299	−	17.6462i	1.20024	−	1.00712i	0.999623	−	0.0274503i	$-0.00873881\pi$
$308$	−14.5945	+	5.31198i	−0.831601	+	0.302678i
$309$	5.81808	−	10.9439i	0.330979	−	0.622579i
$310$	−2.11432	+	3.25956i	−0.120085	+	0.185130i
$311$	12.0317	+	6.94649i	0.682254	+	0.393899i	0.800704	−	0.599061i	$-0.204459\pi$
$311$	12.0317	+	6.94649i	0.682254	+	0.393899i	−0.118450	+	0.992960i	$0.537793\pi$
$312$	0.577325	+	1.42866i	0.0326846	+	0.0808820i
$313$	2.56217	+	0.451779i	0.144822	+	0.0255361i	0.245589	−	0.969374i	$-0.421019\pi$
$313$	2.56217	+	0.451779i	0.144822	+	0.0255361i	−0.100767	+	0.994910i	$0.532130\pi$
$314$	3.78665	−	21.4751i	0.213693	−	1.21191i
$315$	−9.30981	−	24.2049i	−0.524548	−	1.36379i
$316$	10.5028	+	6.06379i	0.590828	+	0.341115i
$317$	10.9483	−	13.0477i	0.614917	−	0.732830i	−0.365270	−	0.930901i	$-0.619023\pi$
$317$	10.9483	−	13.0477i	0.614917	−	0.732830i	0.980188	+	0.198072i	$0.0634679\pi$
$318$	9.23035	−	17.3625i	0.517612	−	0.973641i
$319$	−8.60558	−	23.6436i	−0.481820	−	1.32379i
$320$	−1.63617	−	1.52412i	−0.0914646	−	0.0852011i
$321$	0.282765	+	8.08215i	0.0157824	+	0.451102i
$322$	28.0834			1.56502
$323$	−6.72255	+	12.5210i	−0.374053	+	0.696687i
$324$	−7.63368	−	4.76727i	−0.424093	−	0.264849i
$325$	1.81357	+	4.06170i	0.100599	+	0.225303i
$326$	1.98897	−	1.66895i	0.110159	−	0.0924344i
$327$	12.2420	−	2.60297i	0.676987	−	0.143944i
$328$	1.98224	−	5.44616i	0.109451	−	0.300714i
$329$	−21.4799	+	25.5987i	−1.18423	+	1.41130i
$330$	−8.00574	+	13.3418i	−0.440701	+	0.734444i
$331$	−5.19292	+	2.99813i	−0.285429	+	0.164792i	−0.635878	−	0.771789i	$-0.719362\pi$
$331$	−5.19292	+	2.99813i	−0.285429	+	0.164792i	0.350450	+	0.936582i	$0.386029\pi$
$332$	0.523209	−	2.96727i	0.0287148	−	0.162850i
$333$	−3.74817	+	7.68743i	−0.205398	+	0.421269i
$334$	10.8278	+	18.7543i	0.592471	+	1.02619i
$335$	−7.66372	−	3.24825i	−0.418714	−	0.177471i
$336$	−4.48084	−	4.97582i	−0.244450	−	0.271453i
$337$	21.6519	+	7.88064i	1.17945	+	0.429286i	0.856009	−	0.516962i	$-0.172937\pi$
$337$	21.6519	+	7.88064i	1.17945	+	0.429286i	0.323444	+	0.946247i	$0.395159\pi$
$338$	4.17557	+	11.4723i	0.227121	+	0.624010i
$339$	−6.35157	+	3.96948i	−0.344970	+	0.215593i
$340$	−6.97068	+	2.13521i	−0.378038	+	0.115798i
$341$	6.98041			0.378010
$342$	−10.6092	+	7.64488i	−0.573682	+	0.413388i
$343$		−	3.65545i		−	0.197376i
$344$	0.416275	+	2.36081i	0.0224440	+	0.127286i
$345$	21.8540	−	17.7187i	1.17658	−	0.953940i
$346$	−5.84561	+	2.12763i	−0.314262	+	0.114382i
$347$	11.2327	+	4.08837i	0.603004	+	0.219475i	0.625439	−	0.780273i	$-0.284920\pi$
$347$	11.2327	+	4.08837i	0.603004	+	0.219475i	−0.0224354	+	0.999748i	$0.507142\pi$
$348$	8.06099	−	7.25911i	0.432115	−	0.389129i
$349$	11.1495	−	19.3114i	0.596817	−	1.03372i	−0.396470	−	0.918048i	$-0.629765\pi$
$349$	11.1495	−	19.3114i	0.596817	−	1.03372i	0.993288	−	0.115670i	$-0.0369016\pi$
$350$	−13.4424	−	13.8904i	−0.718524	−	0.742471i
$351$	3.83290	+	2.58423i	0.204585	+	0.137936i
$352$	−0.697620	+	3.95640i	−0.0371833	+	0.210877i
$353$	14.0071	+	24.2610i	0.745523	+	1.29128i	0.949950	+	0.312402i	$0.101134\pi$
$353$	14.0071	+	24.2610i	0.745523	+	1.29128i	−0.204427	+	0.978882i	$0.565533\pi$
$354$	−0.0493412	+	0.0631624i	−0.00262246	+	0.00335704i
$355$	15.4770	−	23.8602i	0.821432	−	1.26637i
$356$	−7.98005	−	2.90450i	−0.422942	−	0.153938i
$357$	−21.3540	+	4.54040i	−1.13017	+	0.240303i
$358$	4.70302	+	5.60484i	0.248562	+	0.296225i
$359$	17.4683	−	3.08014i	0.921943	−	0.162563i	0.307521	−	0.951541i	$-0.400500\pi$
$359$	17.4683	−	3.08014i	0.921943	−	0.162563i	0.614422	+	0.788978i	$0.289389\pi$
$360$	−6.62631	−	1.04500i	−0.349237	−	0.0550764i
$361$	4.44742	+	18.4722i	0.234075	+	0.972219i
$362$	11.5254			0.605762
$363$	8.89688	−	0.311269i	0.466965	−	0.0163374i
$364$	2.21074	+	2.63466i	0.115874	+	0.138094i
$365$	−23.8160	+	12.1508i	−1.24658	+	0.636002i
$366$	4.23208	+	2.24988i	0.221214	+	0.117603i
$367$	−0.560061	+	0.667455i	−0.0292350	+	0.0348409i	−0.780464	−	0.625201i	$-0.785017\pi$
$367$	−0.560061	+	0.667455i	−0.0292350	+	0.0348409i	0.751229	+	0.660042i	$0.229461\pi$
$368$	3.63214	−	6.29106i	0.189339	−	0.327944i
$369$	−4.20852	−	16.8700i	−0.219087	−	0.878219i
$370$	−0.330237	+	6.36610i	−0.0171682	+	0.330958i
$371$	7.62128	−	43.2224i	0.395677	−	2.24400i
$372$	1.12756	+	2.79028i	0.0584611	+	0.144669i
$373$	−7.46389	+	12.9278i	−0.386466	+	0.669378i	−0.991971	−	0.126463i	$-0.959638\pi$
$373$	−7.46389	+	12.9278i	−0.386466	+	0.669378i	0.605506	+	0.795841i	$0.292971\pi$
$374$	10.0338	+	8.41939i	0.518837	+	0.435356i
$375$	−19.2245	−	2.32805i	−0.992747	−	0.120220i
$376$	2.95638	+	8.12259i	0.152464	+	0.418891i
$377$	−4.26823	+	3.58147i	−0.219825	+	0.184455i
$378$	−19.4923	−	4.85591i	−1.00258	−	0.249761i
$379$		−	15.9056i		−	0.817015i	−0.912755	−	0.408507i	$-0.866049\pi$
$379$		−	15.9056i		−	0.817015i	0.912755	−	0.408507i	$-0.133951\pi$
$380$	−5.04924	+	8.33697i	−0.259021	+	0.427678i
$381$	0.779510	−	5.54914i	0.0399355	−	0.284291i
$382$	4.07578	+	23.1149i	0.208535	+	1.18266i
$383$	20.0560	+	23.9018i	1.02482	+	1.22133i	0.974916	+	0.222573i	$0.0714456\pi$
$383$	20.0560	+	23.9018i	1.02482	+	1.22133i	0.0498995	+	0.998754i	$0.484110\pi$
$384$	−1.69418	+	0.360225i	−0.0864556	+	0.0183826i
$385$	−7.79427	+	33.8428i	−0.397233	+	1.72479i
$386$	14.0855	−	16.7865i	0.716934	−	0.854409i
$387$	4.99645	+	5.17262i	0.253984	+	0.262939i
$388$	6.88497	+	11.9251i	0.349531	+	0.605406i
$389$	−4.85075	−	0.855317i	−0.245943	−	0.0433663i	0.0493178	−	0.998783i	$-0.484295\pi$
$389$	−4.85075	−	0.855317i	−0.245943	−	0.0433663i	−0.295260	+	0.955417i	$0.595406\pi$
$390$	3.38265	+	0.655423i	0.171287	+	0.0331886i
$391$	−11.8421	−	20.5111i	−0.598879	−	1.03729i
$392$	−6.88105	−	3.97278i	−0.347545	−	0.200655i
$393$	−9.07718	−	10.0799i	−0.457883	−	0.508464i
$394$	−4.14982	+	11.4015i	−0.209065	+	0.574401i
$395$	24.1558	−	12.3242i	1.21541	−	0.620098i
$396$	4.90355	+	11.0097i	0.246413	+	0.553257i
$397$	30.3973	−	5.35986i	1.52560	−	0.269004i	0.652966	−	0.757387i	$-0.273524\pi$
$397$	30.3973	−	5.35986i	1.52560	−	0.269004i	0.872629	+	0.488383i	$0.162413\pi$
$398$		−	9.32432i		−	0.467386i
$399$	−17.2496	+	23.5446i	−0.863558	+	1.17871i
$400$	−4.85019	+	1.21477i	−0.242509	+	0.0607385i
$401$	5.52383	+	31.3272i	0.275847	+	1.56441i	0.736258	+	0.676701i	$0.236591\pi$
$401$	5.52383	+	31.3272i	0.275847	+	1.56441i	−0.460411	+	0.887706i	$0.652298\pi$
$402$	−5.46756	+	3.41701i	−0.272697	+	0.170425i
$403$	−0.528686	−	1.45255i	−0.0263358	−	0.0723569i
$404$	−5.67369	+	15.5883i	−0.282277	+	0.775549i
$405$	−18.2323	+	8.51951i	−0.905972	+	0.423338i
$406$	12.1062	−	20.9685i	0.600818	−	1.04065i
$407$	9.91862	−	5.72652i	0.491648	−	0.283853i
$408$	−1.74470	+	5.37082i	−0.0863753	+	0.265895i
$409$	22.7535	+	4.01205i	1.12509	+	0.198383i	0.705073	−	0.709135i	$-0.250914\pi$
$409$	22.7535	+	4.01205i	1.12509	+	0.198383i	0.420014	+	0.907518i	$0.362025\pi$
$410$	−7.80475	−	10.3458i	−0.385449	−	0.510943i
$411$	13.0626	+	10.2043i	0.644331	+	0.503339i
$412$	−5.48172	−	4.59971i	−0.270065	−	0.226611i
$413$	−0.0611859	+	0.168107i	−0.00301076	+	0.00827199i
$414$	−1.52304	−	21.7396i	−0.0748533	−	1.06844i
$415$	−4.92984	−	4.59225i	−0.241996	−	0.225425i
$416$	0.876124	−	0.154484i	0.0429555	−	0.00757422i
$417$	−5.25999	+	37.4445i	−0.257583	+	1.83367i
$418$	17.5032	−	0.540443i	0.856111	−	0.0264339i
$419$			19.6488i			0.959909i	0.877293	+	0.479954i	$0.159347\pi$
$419$			19.6488i			0.959909i	−0.877293	+	0.479954i	$0.840653\pi$
$420$	−14.7870	+	2.35109i	−0.721532	+	0.114721i
$421$	−7.30361	−	8.70410i	−0.355956	−	0.424212i	0.558117	−	0.829763i	$-0.311524\pi$
$421$	−7.30361	−	8.70410i	−0.355956	−	0.424212i	−0.914073	+	0.405551i	$0.867080\pi$
$422$	11.3959	−	4.14777i	0.554743	−	0.201910i
$423$	20.9811	+	15.2395i	1.02014	+	0.740969i
$424$	−8.69672	−	7.29742i	−0.422350	−	0.354394i
$425$	−4.47670	+	15.6750i	−0.217152	+	0.760350i
$426$	−8.25381	−	20.4251i	−0.399899	−	0.989597i
$427$	10.5354	+	1.85767i	0.509843	+	0.0898991i
$428$	4.59815	+	0.810778i	0.222260	+	0.0391904i
$429$	−2.31936	−	5.73955i	−0.111980	−	0.277108i
$430$	4.93536	+	2.09184i	0.238004	+	0.100877i
$431$	−10.7509	−	9.02106i	−0.517852	−	0.434529i	0.346030	−	0.938223i	$-0.387529\pi$
$431$	−10.7509	−	9.02106i	−0.517852	−	0.434529i	−0.863882	+	0.503694i	$0.831974\pi$
$432$	−3.60882	+	3.73851i	−0.173629	+	0.179869i
$433$	5.13986	−	1.87075i	0.247006	−	0.0899027i	−0.215550	−	0.976493i	$-0.569155\pi$
$433$	5.13986	−	1.87075i	0.247006	−	0.0899027i	0.462556	+	0.886590i	$0.346932\pi$
$434$	4.31773	+	5.14567i	0.207258	+	0.247000i
$435$	−3.80885	−	23.9555i	−0.182620	−	1.14858i
$436$		−	7.22595i		−	0.346060i
$437$	−30.0748	−	9.90638i	−1.43867	−	0.473886i
$438$	−2.88094	+	20.5087i	−0.137656	+	0.979942i
$439$	−26.6777	+	4.70400i	−1.27326	+	0.224510i	−0.769115	−	0.639111i	$-0.779303\pi$
$439$	−26.6777	+	4.70400i	−1.27326	+	0.224510i	−0.504143	+	0.863620i	$0.668191\pi$
$440$	6.57319	+	6.12307i	0.313365	+	0.291906i
$441$	−23.7784	+	1.66587i	−1.13230	+	0.0793273i
$442$	0.992042	−	2.72561i	0.0471866	−	0.129644i
$443$	−29.7600	−	24.9716i	−1.41394	−	1.18644i	−0.954493	−	0.298232i	$-0.903603\pi$
$443$	−29.7600	−	24.9716i	−1.41394	−	1.18644i	−0.459448	−	0.888205i	$-0.651953\pi$
$444$	3.89123	+	3.03975i	0.184670	+	0.144260i
$445$	−15.1593	+	11.4360i	−0.718620	+	0.542118i
$446$	−17.4719	−	3.08077i	−0.827319	−	0.145879i
$447$	−10.6153	+	32.6777i	−0.502084	+	1.54560i
$448$	−3.34801	+	1.93297i	−0.158179	+	0.0913244i
$449$	−8.43082	+	14.6026i	−0.397875	+	0.689140i	−0.993464	−	0.114150i	$-0.963586\pi$
$449$	−8.43082	+	14.6026i	−0.397875	+	0.689140i	0.595589	+	0.803290i	$0.296919\pi$
$450$	−10.0236	+	11.1592i	−0.472519	+	0.526048i
$451$	−7.96352	+	21.8796i	−0.374987	+	1.03027i
$452$	1.47900	+	4.06353i	0.0695665	+	0.191132i
$453$	9.65951	−	6.03681i	0.453843	−	0.283634i
$454$	−1.49461	−	8.47638i	−0.0701457	−	0.397816i
$455$	7.63269	−	0.941298i	0.357826	−	0.0441287i
$456$	3.04336	+	6.90927i	0.142518	+	0.323556i
$457$			0.862202i			0.0403321i	0.999797	+	0.0201661i	$0.00641949\pi$
$457$			0.862202i			0.0403321i	−0.999797	+	0.0201661i	$0.993581\pi$
$458$	0.539513	−	0.0951308i	0.0252098	−	0.00444517i
$459$	4.67285	+	16.2841i	0.218110	+	0.760076i
$460$	−7.38207	−	14.4691i	−0.344191	−	0.674625i
$461$	−4.22524	+	11.6088i	−0.196789	+	0.540674i	−0.998361	−	0.0572241i	$-0.981775\pi$
$461$	−4.22524	+	11.6088i	−0.196789	+	0.540674i	0.801572	+	0.597898i	$0.203997\pi$
$462$	18.0015	+	19.9900i	0.837503	+	0.930019i
$463$	30.4784	+	17.5967i	1.41645	+	0.817789i	0.995985	−	0.0895191i	$-0.0285330\pi$
$463$	30.4784	+	17.5967i	1.41645	+	0.817789i	0.420467	+	0.907308i	$0.361866\pi$
$464$	−3.13148	−	5.42389i	−0.145375	−	0.251798i
$465$	6.60655	+	1.28009i	0.306372	+	0.0593627i
$466$	−1.60148	−	0.282385i	−0.0741872	−	0.0130812i
$467$	3.50646	+	6.07337i	0.162260	+	0.281042i	0.935679	−	0.352853i	$-0.114788\pi$
$467$	3.50646	+	6.07337i	0.162260	+	0.281042i	−0.773419	+	0.633895i	$0.781455\pi$
$468$	1.91962	−	1.85424i	0.0887343	−	0.0857122i
$469$	−9.25026	+	11.0240i	−0.427137	+	0.509042i
$470$	18.8352	+	4.33790i	0.868805	+	0.200093i
$471$	−36.9440	+	7.85521i	−1.70229	+	0.361949i
$472$	0.0297448	+	0.0354485i	0.00136912	+	0.00163165i
$473$	−1.67235	−	9.48440i	−0.0768950	−	0.436093i
$474$	2.92205	−	20.8014i	0.134214	−	0.955438i
$475$	9.49575	+	19.6171i	0.435695	+	0.900094i
$476$			12.6043i			0.577719i
$477$	−33.8722	−	3.55563i	−1.55090	−	0.162801i
$478$	−6.24414	+	5.23946i	−0.285600	+	0.239647i
$479$	−12.2466	−	33.6473i	−0.559561	−	1.53738i	−0.820277	−	0.571967i	$-0.806181\pi$
$479$	−12.2466	−	33.6473i	−0.559561	−	1.53738i	0.260715	−	0.965416i	$-0.416042\pi$
$480$	−1.38579	+	3.61657i	−0.0632525	+	0.165073i
$481$	−1.94285	−	1.63025i	−0.0885865	−	0.0743329i
$482$	9.74778	−	16.8836i	0.443999	−	0.769029i
$483$	−18.2245	−	45.0987i	−0.829243	−	2.05206i
$484$	0.892510	−	5.06167i	0.0405686	−	0.230076i
$485$	30.7492	+	1.59509i	1.39625	+	0.0724294i
$486$	−2.70188	+	15.3525i	−0.122560	+	0.696404i
$487$	−2.83150	+	4.90431i	−0.128308	+	0.222235i	−0.923021	−	0.384749i	$-0.874288\pi$
$487$	−2.83150	+	4.90431i	−0.128308	+	0.222235i	0.794713	+	0.606985i	$0.207621\pi$
$488$	1.77873	−	2.11981i	0.0805194	−	0.0959593i
$489$	−3.97087	−	2.11101i	−0.179569	−	0.0954634i
$490$	−15.8260	+	8.07438i	−0.714947	+	0.364763i
$491$	21.5559	+	25.6893i	0.972803	+	1.15934i	0.987207	+	0.159445i	$0.0509705\pi$
$491$	21.5559	+	25.6893i	0.972803	+	1.15934i	−0.0144039	+	0.999896i	$0.504585\pi$
$492$	−10.0323	+	0.350992i	−0.452290	+	0.0158240i
$493$	−20.4195			−0.919647
$494$	−1.43813	−	3.60132i	−0.0647046	−	0.162031i
$495$	26.6207	+	4.19822i	1.19651	+	0.188696i
$496$	1.71113	−	0.301719i	0.0768322	−	0.0135476i
$497$	−31.6062	−	37.6667i	−1.41773	−	1.68958i
$498$	−5.10463	+	1.08537i	−0.228744	+	0.0486367i
$499$	−33.5611	−	12.2152i	−1.50240	−	0.546829i	−0.545719	−	0.837969i	$-0.683743\pi$
$499$	−33.5611	−	12.2152i	−1.50240	−	0.546829i	−0.956680	+	0.291140i	$0.905965\pi$
$500$	−3.62309	+	10.5770i	−0.162029	+	0.473018i
$501$	23.0907	−	29.5587i	1.03162	−	1.32059i
$502$	1.23796	+	2.14421i	0.0552529	+	0.0957008i
$503$	0.814068	−	4.61681i	0.0362975	−	0.205853i	−0.961266	−	0.275624i	$-0.911116\pi$
$503$	0.814068	−	4.61681i	0.0362975	−	0.205853i	0.997563	+	0.0697704i	$0.0222267\pi$
$504$	−5.08279	+	10.4247i	−0.226406	+	0.464355i
$505$	22.3392	+	29.6124i	0.994083	+	1.31773i
$506$	−14.5919	+	25.2739i	−0.648689	+	1.12356i
$507$	15.7135	−	14.1503i	0.697860	−	0.628439i
$508$	−3.04014	−	1.10652i	−0.134885	−	0.0490940i
$509$	11.5642	−	4.20904i	0.512576	−	0.186563i	−0.0727656	−	0.997349i	$-0.523183\pi$
$509$	11.5642	−	4.20904i	0.512576	−	0.186563i	0.585342	+	0.810787i	$0.300960\pi$
$510$	7.95247	+	9.80849i	0.352141	+	0.434327i
$511$	8.02687	+	45.5226i	0.355088	+	2.01380i
$512$			1.00000i			0.0441942i
$513$	19.1616	+	12.0761i	0.846005	+	0.533175i
$514$	8.34705			0.368172
$515$	−15.2994	+	4.68639i	−0.674171	+	0.206507i
$516$	3.52106	−	2.20052i	0.155006	−	0.0968725i
$517$	−11.8771	−	32.6320i	−0.522353	−	1.43515i
$518$	10.3565	+	3.76947i	0.455039	+	0.165621i
$519$	7.21020	+	8.00669i	0.316493	+	0.351455i
$520$	0.776305	−	1.83157i	0.0340432	−	0.0803196i
$521$	−2.61622	−	4.53143i	−0.114619	−	0.198526i	0.803009	−	0.595968i	$-0.203231\pi$
$521$	−2.61622	−	4.53143i	−0.114619	−	0.198526i	−0.917627	+	0.397442i	$0.869898\pi$
$522$	−16.8884	−	8.23430i	−0.739187	−	0.360406i
$523$	6.20970	−	35.2170i	0.271531	−	1.53993i	−0.478237	−	0.878231i	$-0.658724\pi$
$523$	6.20970	−	35.2170i	0.271531	−	1.53993i	0.749769	−	0.661700i	$-0.230165\pi$
$524$	−6.78232	+	3.91578i	−0.296287	+	0.171061i
$525$	−13.5830	+	30.6009i	−0.592812	+	1.33553i
$526$	−0.633825	+	0.755363i	−0.0276361	+	0.0329354i
$527$	1.93753	−	5.32332i	0.0844001	−	0.231887i
$528$	6.80624	−	1.44718i	0.296204	−	0.0629803i
$529$	22.8051	−	19.1357i	0.991525	−	0.831988i
$530$	−24.2724	+	7.43493i	−1.05432	+	0.322953i
$531$	0.133451	+	0.0382476i	0.00579129	+	0.00165981i
$532$	11.2250	+	12.5684i	0.486666	+	0.544909i
$533$	5.15607			0.223334
$534$	0.514296	+	14.6999i	0.0222558	+	0.636127i
$535$	7.11627	−	7.63941i	0.307663	−	0.330280i
$536$	1.27316	+	3.49797i	0.0549920	+	0.151089i
$537$	5.94875	−	11.1897i	0.256707	−	0.482873i
$538$	−15.1820	+	18.0932i	−0.654541	+	0.780052i
$539$	27.6441	+	15.9604i	1.19072	+	0.687461i
$540$	2.62194	+	11.3193i	0.112830	+	0.487103i
$541$	6.50100	−	36.8690i	0.279500	−	1.58512i	−0.444796	−	0.895632i	$-0.646724\pi$
$541$	6.50100	−	36.8690i	0.279500	−	1.58512i	0.724296	−	0.689489i	$-0.242165\pi$
$542$	−29.1853	−	5.14615i	−1.25361	−	0.221046i
$543$	−7.47934	−	18.5085i	−0.320969	−	0.794276i
$544$	2.82355	+	1.63018i	0.121059	+	0.0698932i
$545$	−13.5557	−	8.79292i	−0.580662	−	0.376647i
$546$	2.79632	−	5.25994i	0.119671	−	0.225105i
$547$	−2.66159	+	0.968739i	−0.113801	+	0.0414203i	−0.398293	−	0.917258i	$-0.630397\pi$
$547$	−2.66159	+	0.968739i	−0.113801	+	0.0414203i	0.284492	+	0.958678i	$0.408175\pi$
$548$	7.33110	−	6.15152i	0.313169	−	0.262780i
$549$	0.866678	−	8.25629i	0.0369889	−	0.352370i
$550$	19.4853	−	4.88026i	0.830856	−	0.208095i
$551$	−20.3612	+	18.1849i	−0.867417	+	0.774704i
$552$	−12.4598	−	1.75028i	−0.530324	−	0.0744967i
$553$	−8.14143	−	46.1723i	−0.346209	−	1.96345i
$554$	8.55080	−	7.17497i	0.363289	−	0.304835i
$555$	10.4375	−	3.60091i	0.443049	−	0.152850i
$556$	20.5143	+	7.46660i	0.870001	+	0.316654i
$557$	5.13324	+	4.30730i	0.217502	+	0.182506i	0.745028	−	0.667033i	$-0.232436\pi$
$557$	5.13324	+	4.30730i	0.217502	+	0.182506i	−0.527526	+	0.849539i	$0.676880\pi$
$558$	3.74915	−	3.62146i	0.158714	−	0.153309i
$559$	−1.84695	+	1.06634i	−0.0781176	+	0.0451012i
$560$	−0.447827	+	8.63291i	−0.0189241	+	0.364807i
$561$	7.00920	−	21.5769i	0.295929	−	0.910978i
$562$	−17.1075	+	9.87703i	−0.721637	+	0.416637i
$563$	27.9541	+	16.1393i	1.17812	+	0.680190i	0.955580	−	0.294733i	$-0.0952308\pi$
$563$	27.9541	+	16.1393i	1.17812	+	0.680190i	0.222543	+	0.974923i	$0.428564\pi$
$564$	11.1254	−	10.0187i	0.468466	−	0.421864i
$565$	9.42280	+	2.17015i	0.396420	+	0.0912987i
$566$	3.15771	−	1.14931i	0.132729	−	0.0483093i
$567$	4.85135	+	34.4537i	0.203737	+	1.44692i
$568$	−12.5256	+	2.20861i	−0.525564	+	0.0926711i
$569$	−39.3716			−1.65054			−0.825272	−	0.564735i	$-0.808978\pi$
$569$	−39.3716			−1.65054			−0.825272	+	0.564735i	$0.808978\pi$
$570$	16.6649	+	2.69830i	0.698016	+	0.113019i
$571$	21.6060			0.904184			0.452092	−	0.891971i	$-0.350678\pi$
$571$	21.6060			0.904184			0.452092	+	0.891971i	$0.350678\pi$
$572$	−3.51977	+	0.620630i	−0.147169	+	0.0259499i
$573$	34.4750	−	21.5455i	1.44021	−	0.900076i
$574$	−21.0546	+	7.66324i	−0.878801	+	0.319857i
$575$	−36.1265	−	3.75819i	−1.50658	−	0.156727i
$576$	1.67790	+	2.48689i	0.0699127	+	0.103621i
$577$	−36.8254	−	21.2611i	−1.53306	−	0.885113i	−0.999218	−	0.0395281i	$-0.987415\pi$
$577$	−36.8254	−	21.2611i	−1.53306	−	0.885113i	−0.533842	−	0.845585i	$-0.679252\pi$
$578$	−5.51668	+	3.18505i	−0.229463	+	0.132481i
$579$	−36.0979	−	11.7263i	−1.50018	−	0.487328i
$580$	−13.9856	−	0.725494i	−0.580721	−	0.0301245i
$581$	−10.0877	+	5.82413i	−0.418508	+	0.241626i
$582$	14.6824	−	18.7952i	0.608606	−	0.779086i
$583$	34.9385	+	29.3169i	1.44700	+	1.21418i
$584$	11.2358	+	4.08951i	0.464943	+	0.169225i
$585$	−1.14261	−	5.85748i	−0.0472411	−	0.242177i
$586$	−15.0697	+	12.6450i	−0.622524	+	0.522360i
$587$	4.88741	+	27.7179i	0.201725	+	1.14404i	0.902510	+	0.430668i	$0.141722\pi$
$587$	4.88741	+	27.7179i	0.201725	+	1.14404i	−0.700785	+	0.713372i	$0.747167\pi$
$588$	−1.91442	+	13.6283i	−0.0789494	+	0.562021i
$589$	−2.80877	−	7.03363i	−0.115734	−	0.289816i
$590$	0.102695	−	0.0126649i	0.00422790	−	0.000521404i
$591$	21.0026	−	0.734802i	0.863930	−	0.0302257i
$592$	2.18387	−	1.83248i	0.0897564	−	0.0753145i
$593$	−21.6775	+	7.88996i	−0.890188	+	0.324002i	−0.746314	−	0.665594i	$-0.768178\pi$
$593$	−21.6775	+	7.88996i	−0.890188	+	0.324002i	−0.143874	+	0.989596i	$0.545956\pi$
$594$	14.4982	−	15.0192i	0.594867	−	0.616245i
$595$	23.6454	+	15.3376i	0.969367	+	0.628781i
$596$	17.1793	+	9.91847i	0.703691	+	0.406276i
$597$	−14.9738	+	6.05095i	−0.612837	+	0.247649i
$598$	6.36442	+	1.12222i	0.260260	+	0.0458909i
$599$	4.52174	−	25.6440i	0.184753	−	1.04779i	−0.741519	−	0.670932i	$-0.765894\pi$
$599$	4.52174	−	25.6440i	0.184753	−	1.04779i	0.926272	−	0.376855i	$-0.122995\pi$
$600$	5.09828	+	7.00054i	0.208136	+	0.285796i
$601$	5.09656	+	2.94250i	0.207893	+	0.120027i	0.600332	−	0.799751i	$-0.295035\pi$
$601$	5.09656	+	2.94250i	0.207893	+	0.120027i	−0.392439	+	0.919778i	$0.628369\pi$
$602$	5.95708	−	7.09937i	0.242792	−	0.289349i
$603$	9.03547	+	6.56285i	0.367953	+	0.267260i
$604$	−2.24928	−	6.17985i	−0.0915219	−	0.251454i
$605$	−8.40951	−	7.83363i	−0.341895	−	0.318482i
$606$	28.7150	−	1.00463i	1.16647	−	0.0408104i
$607$	−13.9107			−0.564620			−0.282310	−	0.959323i	$-0.591101\pi$
$607$	−13.9107			−0.564620			−0.282310	+	0.959323i	$0.591101\pi$
$608$	4.26727	−	0.889035i	0.173061	−	0.0360551i
$609$	−41.5292	−	5.83378i	−1.68285	−	0.236396i
$610$	−1.81225	−	5.91635i	−0.0733759	−	0.239546i
$611$	−5.89084	+	4.94300i	−0.238318	+	0.199972i
$612$	9.75714	−	0.683569i	0.394409	−	0.0276317i
$613$	1.92488	−	5.28856i	0.0777452	−	0.213603i	−0.894731	−	0.446605i	$-0.852633\pi$
$613$	1.92488	−	5.28856i	0.0777452	−	0.213603i	0.972476	+	0.233002i	$0.0748550\pi$
$614$	−17.6462	+	21.0299i	−0.712142	+	0.848697i
$615$	−11.5493	+	19.2474i	−0.465715	+	0.776129i
$616$	13.4504	−	7.76559i	0.541932	−	0.312885i
$617$	4.30340	−	24.4058i	0.173248	−	0.982540i	−0.766898	−	0.641769i	$-0.778201\pi$
$617$	4.30340	−	24.4058i	0.173248	−	0.982540i	0.940146	−	0.340771i	$-0.110688\pi$
$618$	−3.82929	+	11.7880i	−0.154037	+	0.474182i
$619$	−10.4425	−	18.0870i	−0.419721	−	0.726978i	0.576190	−	0.817315i	$-0.304539\pi$
$619$	−10.4425	−	18.0870i	−0.419721	−	0.726978i	−0.995911	+	0.0903379i	$0.971205\pi$
$620$	1.51618	−	3.57719i	0.0608912	−	0.143663i
$621$	−33.9229	+	16.5536i	−1.36128	+	0.664272i
$622$	−13.0551	−	4.75168i	−0.523463	−	0.190525i
$623$	11.2286	+	30.8505i	0.449866	+	1.23600i
$624$	−0.816639	−	1.30670i	−0.0326917	−	0.0523101i
$625$	15.4334	+	19.6675i	0.617337	+	0.786699i
$626$	−2.60169			−0.103985
$627$	−12.2265	−	27.7575i	−0.488279	−	1.10853i
$628$			21.8064i			0.870171i
$629$	−1.61401	−	9.15352i	−0.0643549	−	0.364975i
$630$	13.3715	+	22.2205i	0.532734	+	0.885288i
$631$	−15.6660	+	5.70194i	−0.623652	+	0.226991i	−0.634466	−	0.772951i	$-0.718780\pi$
$631$	−15.6660	+	5.70194i	−0.623652	+	0.226991i	0.0108141	+	0.999942i	$0.496558\pi$
$632$	−11.3962	−	4.14788i	−0.453316	−	0.164994i
$633$	−14.0561	−	15.6089i	−0.558681	−	0.620396i
$634$	−8.51626	+	14.7506i	−0.338224	+	0.585821i
$635$	−5.77521	+	4.35675i	−0.229182	+	0.172892i
$636$	−6.07515	+	18.7016i	−0.240895	+	0.741565i
$637$	1.22746	−	6.96129i	0.0486339	−	0.275816i
$638$	12.5805	+	21.7901i	0.498068	+	0.862678i
$639$	−27.4441	+	26.5094i	−1.08567	+	1.04869i
$640$	1.87597	+	1.21685i	0.0741543	+	0.0481003i
$641$	43.0495	+	15.6687i	1.70035	+	0.618878i	0.995866	−	0.0908379i	$-0.0289545\pi$
$641$	43.0495	+	15.6687i	1.70035	+	0.618878i	0.704488	+	0.709716i	$0.251177\pi$
$642$	−1.68192	−	7.91026i	−0.0663801	−	0.312193i
$643$	−10.2594	−	12.2266i	−0.404590	−	0.482172i	0.524824	−	0.851211i	$-0.324131\pi$
$643$	−10.2594	−	12.2266i	−0.404590	−	0.482172i	−0.929414	+	0.369039i	$0.879687\pi$
$644$	−27.6567	+	4.87662i	−1.08983	+	0.192166i
$645$	0.156489	−	9.28311i	0.00616176	−	0.365522i
$646$	4.44617	−	13.4981i	0.174932	−	0.531077i
$647$	−12.4171			−0.488168			−0.244084	−	0.969754i	$-0.578487\pi$
$647$	−12.4171			−0.488168			−0.244084	+	0.969754i	$0.578487\pi$
$648$	8.34554	+	3.36927i	0.327844	+	0.132358i
$649$	−0.119498	−	0.142412i	−0.00469069	−	0.00559015i
$650$	−2.49132	−	3.68508i	−0.0977177	−	0.144541i
$651$	5.46141	−	10.2730i	0.214050	−	0.402632i
$652$	−1.66895	+	1.98897i	−0.0653610	+	0.0778942i
$653$	−1.06318	+	1.84148i	−0.0416053	+	0.0720625i	−0.886078	−	0.463536i	$-0.846581\pi$
$653$	−1.06318	+	1.84148i	−0.0416053	+	0.0720625i	0.844473	+	0.535598i	$0.179914\pi$
$654$	−11.6041	+	4.68923i	−0.453755	+	0.183363i
$655$	−0.907197	+	17.4884i	−0.0354471	+	0.683327i
$656$	−1.00641	+	5.70763i	−0.0392937	+	0.222846i
$657$	34.8042	−	8.68249i	1.35784	−	0.338736i
$658$	16.7084	−	28.9398i	0.651361	−	1.12819i
$659$	6.27245	+	5.26321i	0.244340	+	0.205026i	0.756730	−	0.653727i	$-0.226796\pi$
$659$	6.27245	+	5.26321i	0.244340	+	0.205026i	−0.512391	+	0.858753i	$0.671240\pi$
$660$	5.56733	−	14.5293i	0.216708	−	0.565553i
$661$	−2.66756	−	7.32905i	−0.103756	−	0.285067i	0.876942	−	0.480596i	$-0.159580\pi$
$661$	−2.66756	−	7.32905i	−0.103756	−	0.285067i	−0.980698	+	0.195529i	$0.937358\pi$
$662$	4.59341	−	3.85433i	0.178528	−	0.149803i
$663$	−5.02081	+	0.175660i	−0.194992	+	0.00682205i
$664$			3.01304i			0.116929i
$665$	37.2371	−	5.76397i	1.44399	−	0.223517i
$666$	2.35631	−	8.22150i	0.0913053	−	0.318577i
$667$	−7.90030	−	44.8048i	−0.305901	−	1.73485i
$668$	−13.9200	−	16.5892i	−0.538579	−	0.641854i
$669$	6.39090	+	30.0571i	0.247087	+	1.16208i
$670$	8.11134	+	1.86811i	0.313368	+	0.0721712i
$671$	−7.14594	+	8.51620i	−0.275866	+	0.328764i
$672$	5.27680	+	4.12213i	0.203557	+	0.159015i
$673$	15.4166	+	26.7024i	0.594268	+	1.02930i	0.993650	+	0.112517i	$0.0358913\pi$
$673$	15.4166	+	26.7024i	0.594268	+	1.02930i	−0.399382	+	0.916785i	$0.630775\pi$
$674$	−22.6914	−	4.00110i	−0.874040	−	0.154117i
$675$	24.4251	+	8.85516i	0.940123	+	0.340835i
$676$	−6.10427	−	10.5729i	−0.234780	−	0.406650i
$677$	−8.64881	−	4.99339i	−0.332401	−	0.191912i	0.324506	−	0.945884i	$-0.394802\pi$
$677$	−8.64881	−	4.99339i	−0.332401	−	0.191912i	−0.656906	+	0.753972i	$0.728135\pi$
$678$	5.56578	−	5.01211i	0.213753	−	0.192489i
$679$	18.2070	−	50.0234i	0.698722	−	1.91972i
$680$	6.49400	−	3.31321i	0.249034	−	0.127056i
$681$	−12.6422	+	7.90086i	−0.484449	+	0.302762i
$682$	−6.87436	+	1.21214i	−0.263233	+	0.0464151i
$683$		−	9.22304i		−	0.352910i	−0.984309	−	0.176455i	$-0.943537\pi$
$683$		−	9.22304i		−	0.352910i	0.984309	−	0.176455i	$-0.0564630\pi$
$684$	9.12054	−	9.37101i	0.348732	−	0.358310i
$685$	−2.61922	−	21.2384i	−0.100075	−	0.811478i
$686$	0.634763	+	3.59992i	0.0242353	+	0.137445i
$687$	−0.502883	−	0.804663i	−0.0191862	−	0.0306998i
$688$	−0.819901	−	2.25266i	−0.0312584	−	0.0858818i
$689$	3.45436	−	9.49077i	0.131601	−	0.361570i
$690$	−18.4452	+	21.2444i	−0.702196	+	0.808760i
$691$	8.24949	−	14.2885i	0.313826	−	0.543562i	−0.665362	−	0.746521i	$-0.731723\pi$
$691$	8.24949	−	14.2885i	0.313826	−	0.543562i	0.979187	+	0.202959i	$0.0650560\pi$
$692$	5.38735	−	3.11039i	0.204796	−	0.118239i
$693$	20.4198	−	41.8807i	0.775683	−	1.59092i
$694$	−11.7720	−	2.07572i	−0.446859	−	0.0787933i
$695$	38.9700	−	29.3985i	1.47822	−	1.11515i
$696$	−6.67800	+	8.54860i	−0.253129	+	0.324034i
$697$	14.4751	+	12.1461i	0.548285	+	0.460066i
$698$	−7.62668	+	20.9541i	−0.288674	+	0.793126i
$699$	0.585793	+	2.75505i	0.0221567	+	0.104206i
$700$	15.6502	+	11.3451i	0.591521	+	0.428804i
$701$	6.38170	−	1.12527i	0.241033	−	0.0425007i	−0.0518263	−	0.998656i	$-0.516504\pi$
$701$	6.38170	−	1.12527i	0.241033	−	0.0425007i	0.292860	+	0.956155i	$0.405393\pi$
$702$	−4.22342	−	1.87939i	−0.159403	−	0.0709331i
$703$	−9.76123	−	7.69001i	−0.368152	−	0.290034i
$704$		−	4.01743i		−	0.151413i
$705$	−5.25681	−	33.0623i	−0.197983	−	1.24520i
$706$	−18.0072	−	21.4601i	−0.677710	−	0.807663i
$707$	60.2637	−	21.9342i	2.26645	−	0.824920i
$708$	0.0376236	−	0.0707708i	0.00141398	−	0.00265973i
$709$	−30.5872	−	25.6657i	−1.14873	−	0.963896i	−0.149037	−	0.988832i	$-0.547617\pi$
$709$	−30.5872	−	25.6657i	−1.14873	−	0.963896i	−0.999689	+	0.0249357i	$0.992062\pi$
$710$	−11.0986	+	26.1853i	−0.416521	+	0.982716i
$711$	−35.3009	+	8.80641i	−1.32389	+	0.330266i
$712$	8.36318	+	1.47465i	0.313423	+	0.0552650i
$713$	12.4302	+	2.19177i	0.465513	+	0.0820826i
$714$	20.2412	−	8.17950i	0.757506	−	0.306110i
$715$	−3.11875	+	7.35820i	−0.116635	+	0.275181i
$716$	−5.60484	−	4.70302i	−0.209463	−	0.175760i
$717$	12.4661	+	6.62728i	0.465554	+	0.247500i
$718$	−16.6681	+	6.06669i	−0.622048	+	0.226407i
$719$	22.3939	+	26.6880i	0.835152	+	0.995296i	0.999960	+	0.00897016i	$0.00285533\pi$
$719$	22.3939	+	26.6880i	0.835152	+	0.995296i	−0.164807	+	0.986326i	$0.552700\pi$
$720$	6.70710	−	0.121521i	0.249959	−	0.00452881i
$721$			27.6643i			1.03027i
$722$	−7.58751	−	17.4192i	−0.282378	−	0.648277i
$723$	−33.4390	−	4.69731i	−1.24361	−	0.174695i
$724$	−11.3503	+	2.00137i	−0.421831	+	0.0743802i
$725$	−18.3794	+	25.3538i	−0.682595	+	0.941617i
$726$	−8.70766	+	1.85147i	−0.323172	+	0.0687144i
$727$	−17.1263	+	47.0541i	−0.635179	+	1.74514i	0.0311866	+	0.999514i	$0.490071\pi$
$727$	−17.1263	+	47.0541i	−0.635179	+	1.74514i	−0.666365	+	0.745625i	$0.732151\pi$
$728$	−2.63466	−	2.21074i	−0.0976469	−	0.0819355i
$729$	26.4078	−	5.62399i	0.978066	−	0.208296i
$730$	21.3442	−	16.1018i	0.789983	−	0.595954i
$731$	−7.69707	−	1.35720i	−0.284687	−	0.0501979i
$732$	−4.55847	−	1.48081i	−0.168486	−	0.0547322i
$733$	−25.6802	+	14.8265i	−0.948521	+	0.547629i	−0.892621	−	0.450808i	$-0.851136\pi$
$733$	−25.6802	+	14.8265i	−0.948521	+	0.547629i	−0.0558997	+	0.998436i	$0.517803\pi$
$734$	0.435650	−	0.754569i	0.0160801	−	0.0278516i
$735$	23.2367	+	20.1750i	0.857100	+	0.744167i
$736$	−2.48453	+	6.82620i	−0.0915811	+	0.251617i
$737$	−5.11482	−	14.0529i	−0.188407	−	0.517644i
$738$	7.07403	+	15.8829i	0.260399	+	0.584659i
$739$	1.12724	+	6.39289i	0.0414662	+	0.235166i	0.998496	−	0.0548228i	$-0.0174594\pi$
$739$	1.12724	+	6.39289i	0.0414662	+	0.235166i	−0.957030	+	0.289989i	$0.906348\pi$
$740$	−0.780242	−	6.32673i	−0.0286823	−	0.232575i
$741$	−4.85005	+	4.64653i	−0.178171	+	0.170694i
$742$			43.8892i			1.61122i
$743$	7.70027	−	1.35777i	0.282496	−	0.0498116i	−0.0306050	−	0.999532i	$-0.509743\pi$
$743$	7.70027	−	1.35777i	0.282496	−	0.0498116i	0.313101	+	0.949720i	$0.398632\pi$
$744$	−1.59495	−	2.55209i	−0.0584739	−	0.0935641i
$745$	39.5114	−	20.1586i	1.44759	−	0.738553i
$746$	5.10560	−	14.0275i	0.186929	−	0.513584i
$747$	5.05560	+	7.49312i	0.184975	+	0.274159i
$748$	−11.3434	−	6.54912i	−0.414756	−	0.239460i
$749$	−9.02522	−	15.6321i	−0.329774	−	0.571186i
$750$	19.3367	−	1.04561i	0.706075	−	0.0381803i
$751$	19.0715	+	3.36281i	0.695928	+	0.122711i	0.510411	−	0.859930i	$-0.329493\pi$
$751$	19.0715	+	3.36281i	0.695928	+	0.122711i	0.185516	+	0.982641i	$0.440604\pi$
$752$	−4.32194	−	7.48582i	−0.157605	−	0.272980i
$753$	2.64000	−	3.37950i	0.0962068	−	0.123156i
$754$	3.58147	−	4.26823i	0.130430	−	0.155440i
$755$	−14.3303	−	3.30037i	−0.521532	−	0.120113i
$756$	20.0394	+	1.39734i	0.728826	+	0.0508206i
$757$	−0.216899	−	0.258490i	−0.00788332	−	0.00939498i	0.762088	−	0.647473i	$-0.224174\pi$
$757$	−0.216899	−	0.258490i	−0.00788332	−	0.00939498i	−0.769972	+	0.638078i	$0.779730\pi$
$758$	2.76198	+	15.6639i	0.100319	+	0.568940i
$759$	50.0563	+	7.03162i	1.81693	+	0.255232i
$760$	3.52483	−	9.08711i	0.127859	−	0.329624i
$761$		−	3.44946i		−	0.125043i	−0.998044	−	0.0625214i	$-0.980086\pi$
$761$		−	3.44946i		−	0.125043i	0.998044	−	0.0625214i	$-0.0199142\pi$
$762$	0.195930	+	5.60020i	0.00709781	+	0.202874i
$763$	−21.3996	+	17.9564i	−0.774716	+	0.650064i
$764$	−8.02773	−	22.0560i	−0.290433	−	0.797958i
$765$	10.5906	−	19.1359i	0.382905	−	0.691861i
$766$	−23.9018	−	20.0560i	−0.863609	−	0.724654i
$767$	−0.0205839	+	0.0356524i	−0.000743242	+	0.00128733i
$768$	1.60589	−	0.648943i	0.0579475	−	0.0234167i
$769$	−1.74841	+	9.91572i	−0.0630493	+	0.357570i	0.936919	+	0.349548i	$0.113665\pi$
$769$	−1.74841	+	9.91572i	−0.0630493	+	0.357570i	−0.999968	+	0.00802243i	$0.997446\pi$
$770$	1.79911	−	34.6821i	0.0648355	−	1.24986i
$771$	−5.41676	−	13.4044i	−0.195080	−	0.482748i
$772$	−10.9566	+	18.9774i	−0.394336	+	0.683011i
$773$	−12.6148	+	15.0337i	−0.453721	+	0.540724i	−0.943609	−	0.331061i	$-0.892593\pi$
$773$	−12.6148	+	15.0337i	−0.453721	+	0.540724i	0.489888	+	0.871785i	$0.337038\pi$
$774$	−5.81875	−	4.22641i	−0.209151	−	0.151915i
$775$	−4.86573	−	7.19722i	−0.174782	−	0.258532i
$776$	−8.85114	−	10.5484i	−0.317737	−	0.378665i
$777$	−0.667454	−	19.0776i	−0.0239448	−	0.684404i
$778$	4.92558			0.176590
$779$	25.2508	−	0.779661i	0.904703	−	0.0279343i
$780$	−3.44507	−	0.0580750i	−0.123353	−	0.00207942i
$781$	50.3209	−	8.87293i	1.80062	−	0.317498i
$782$	15.2239	+	18.1431i	0.544404	+	0.648796i
$783$	−2.26373	+	32.4645i	−0.0808992	+	1.16019i
$784$	7.46638	+	2.71754i	0.266656	+	0.0970550i
$785$	40.9082	+	26.5352i	1.46008	+	0.947082i
$786$	10.6896	+	8.35053i	0.381287	+	0.297854i
$787$	8.43438	+	14.6088i	0.300653	+	0.520747i	0.976284	−	0.216493i	$-0.0694620\pi$
$787$	8.43438	+	14.6088i	0.300653	+	0.520747i	−0.675631	+	0.737240i	$0.736129\pi$
$788$	2.10692	−	11.9489i	0.0750558	−	0.425663i
$789$	1.62434	+	0.527664i	0.0578282	+	0.0187853i
$790$	−21.6488	+	16.3316i	−0.770229	+	0.581052i
$791$	8.35880	−	14.4779i	0.297205	−	0.514774i
$792$	−6.74087	−	9.99092i	−0.239526	−	0.355012i
$793$	2.31336	+	0.841994i	0.0821498	+	0.0299001i
$794$	−29.0047	+	10.5569i	−1.02934	+	0.374649i
$795$	27.6910	+	34.1538i	0.982100	+	1.21131i
$796$	1.61915	+	9.18266i	0.0573893	+	0.325471i
$797$		−	29.0909i		−	1.03045i	−0.857054	−	0.515227i	$-0.827708\pi$
$797$		−	29.0909i		−	1.03045i	0.857054	−	0.515227i	$-0.172292\pi$
$798$	12.8990	−	26.1823i	0.456620	−	0.926843i
$799$	−28.1821			−0.997011
$800$	4.56556	−	2.03854i	0.161417	−	0.0720734i
$801$	23.2727	−	10.3653i	0.822299	−	0.366240i
$802$	−10.8798	−	29.8921i	−0.384180	−	1.05553i
$803$	−45.1392	−	16.4293i	−1.59293	−	0.579779i
$804$	4.79114	−	4.31453i	0.168971	−	0.152162i
$805$	−24.5057	+	57.8174i	−0.863713	+	2.03779i
$806$	0.772888	+	1.33868i	0.0272238	+	0.0471530i
$807$	38.9078	+	12.6391i	1.36962	+	0.444918i
$808$	2.88061	−	16.3367i	0.101339	−	0.574724i
$809$	−12.8675	+	7.42903i	−0.452396	+	0.261191i	−0.708841	−	0.705368i	$-0.750782\pi$
$809$	−12.8675	+	7.42903i	−0.452396	+	0.261191i	0.256446	+	0.966559i	$0.417448\pi$
$810$	16.4759	−	11.5561i	0.578906	−	0.406039i
$811$	−4.24280	+	5.05637i	−0.148985	+	0.177553i	−0.835375	−	0.549680i	$-0.814750\pi$
$811$	−4.24280	+	5.05637i	−0.148985	+	0.177553i	0.686391	+	0.727233i	$0.259194\pi$
$812$	−8.28110	+	22.7521i	−0.290609	+	0.798443i
$813$	10.6754	+	50.2078i	0.374404	+	1.76086i
$814$	−8.77353	+	7.36187i	−0.307512	+	0.258033i
$815$	1.70040	+	5.55118i	0.0595623	+	0.194449i
$816$	0.785558	−	5.59219i	0.0275000	−	0.195766i
$817$	−8.88379	+	5.50143i	−0.310805	+	0.192471i
$818$	−23.1045			−0.807829
$819$	−10.2615	−	1.07717i	−0.358567	−	0.0376394i
$820$	9.48271	+	8.83334i	0.331151	+	0.308474i
$821$	−18.7457	−	51.5033i	−0.654228	−	1.79748i	−0.601507	−	0.798868i	$-0.705433\pi$
$821$	−18.7457	−	51.5033i	−0.654228	−	1.79748i	−0.0527213	−	0.998609i	$-0.516789\pi$
$822$	−14.6361	−	7.78093i	−0.510493	−	0.271391i
$823$	−34.2674	+	40.8383i	−1.19449	+	1.42353i	−0.314026	+	0.949415i	$0.601678\pi$
$823$	−34.2674	+	40.8383i	−1.19449	+	1.42353i	−0.880461	+	0.474119i	$0.842767\pi$
$824$	6.19717	+	3.57794i	0.215889	+	0.124643i
$825$	−20.4820	−	28.1242i	−0.713091	−	0.979158i
$826$	0.0310649	−	0.176178i	0.00108089	−	0.00613001i
$827$	−1.47054	−	0.259297i	−0.0511359	−	0.00901663i	0.148022	−	0.988984i	$-0.452709\pi$
$827$	−1.47054	−	0.259297i	−0.0511359	−	0.00901663i	−0.199158	+	0.979967i	$0.563821\pi$
$828$	5.27494	+	21.1448i	0.183317	+	0.734834i
$829$	−22.4356	−	12.9532i	−0.779220	−	0.449883i	0.0569335	−	0.998378i	$-0.481868\pi$
$829$	−22.4356	−	12.9532i	−0.779220	−	0.449883i	−0.836154	+	0.548495i	$0.815201\pi$
$830$	5.65238	+	3.66643i	0.196197	+	0.127264i
$831$	−17.0712	−	9.07547i	−0.592193	−	0.314825i
$832$	−0.835988	+	0.304275i	−0.0289827	+	0.0105488i
$833$	19.8446	−	16.6516i	0.687575	−	0.576944i
$834$	−1.32210	−	37.7891i	−0.0457806	−	1.30853i
$835$	−48.0593	+	5.92690i	−1.66316	+	0.205109i
$836$	−17.1435	+	3.57164i	−0.592920	+	0.123528i
$837$	−8.24864	−	3.67059i	−0.285115	−	0.126874i
$838$	−3.41199	−	19.3503i	−0.117865	−	0.668446i
$839$	23.1568	−	19.4309i	0.799463	−	0.670829i	−0.148605	−	0.988897i	$-0.547478\pi$
$839$	23.1568	−	19.4309i	0.799463	−	0.670829i	0.948068	+	0.318067i	$0.103034\pi$
$840$	14.1541	−	4.88311i	0.488363	−	0.168483i
$841$	−9.60813	−	3.49707i	−0.331315	−	0.120589i
$842$	8.70410	+	7.30361i	0.299963	+	0.251699i
$843$	26.9632	+	21.0631i	0.928662	+	0.725452i
$844$	−10.5025	+	6.06363i	−0.361511	+	0.208719i
$845$	−27.2625	−	1.41422i	−0.937858	−	0.0486507i
$846$	−23.3087	−	11.3646i	−0.801369	−	0.390724i
$847$	−17.2080	+	9.93502i	−0.591272	+	0.341371i
$848$	9.83178	+	5.67638i	0.337625	+	0.194928i
$849$	−3.89485	−	4.32509i	−0.133671	−	0.148437i
$850$	1.68675	−	16.2143i	0.0578549	−	0.556144i
$851$	19.4604	−	7.08300i	0.667093	−	0.242802i
$852$	11.6752	+	18.6815i	0.399985	+	0.640017i
$853$	31.8325	−	5.61292i	1.08992	−	0.192183i	0.400323	−	0.916374i	$-0.368898\pi$
$853$	31.8325	−	5.61292i	1.08992	−	0.192183i	0.689599	+	0.724191i	$0.257787\pi$
$854$	−10.6979			−0.366075
$855$	−6.48141	−	28.5130i	−0.221660	−	0.975124i
$856$	−4.66909			−0.159586
$857$	−31.1025	+	5.48420i	−1.06244	+	0.187337i	−0.677439	−	0.735579i	$-0.736910\pi$
$857$	−31.1025	+	5.48420i	−1.06244	+	0.187337i	−0.385001	+	0.922916i	$0.625799\pi$
$858$	3.28079	+	5.24960i	0.112004	+	0.179218i
$859$	16.3134	−	5.93759i	0.556606	−	0.202588i	−0.0483731	−	0.998829i	$-0.515404\pi$
$859$	16.3134	−	5.93759i	0.556606	−	0.202588i	0.604979	+	0.796241i	$0.293181\pi$
$860$	−5.22362	−	1.20304i	−0.178124	−	0.0410234i
$861$	25.9695	+	28.8383i	0.885038	+	0.982805i
$862$	12.1540	+	7.01714i	0.413968	+	0.239005i
$863$	−21.5052	+	12.4160i	−0.732044	+	0.422646i	−0.819170	−	0.573551i	$-0.805565\pi$
$863$	−21.5052	+	12.4160i	−0.732044	+	0.422646i	0.0871252	+	0.996197i	$0.472232\pi$
$864$	2.90481	−	4.30838i	0.0988235	−	0.146574i
$865$	0.720607	−	13.8914i	0.0245014	−	0.472322i
$866$	−4.73692	+	2.73486i	−0.160967	+	0.0929343i
$867$	8.69485	+	6.79224i	0.295292	+	0.230677i
$868$	−5.14567	−	4.31773i	−0.174656	−	0.146553i
$869$	45.7835	+	16.6638i	1.55310	+	0.565281i
$870$	7.91080	+	22.9301i	0.268201	+	0.777404i
$871$	−2.53687	+	2.12869i	−0.0859586	+	0.0721279i
$872$	1.25477	+	7.11617i	0.0424920	+	0.240984i
$873$	−39.7110	−	11.3813i	−1.34401	−	0.385199i
$874$	31.3381	+	4.53345i	1.06003	+	0.153346i
$875$	40.3270	−	15.5540i	1.36330	−	0.525821i
$876$	−0.724124	−	20.6974i	−0.0244659	−	0.699299i
$877$	−6.41225	+	5.38052i	−0.216526	+	0.181687i	−0.744599	−	0.667512i	$-0.767359\pi$
$877$	−6.41225	+	5.38052i	−0.216526	+	0.181687i	0.528073	+	0.849199i	$0.322915\pi$
$878$	25.4556	−	9.26507i	0.859084	−	0.312681i
$879$	30.0858	+	15.9944i	1.01477	+	0.539477i
$880$	−7.53659	−	4.88862i	−0.254058	−	0.164795i
$881$	−12.2282	−	7.05997i	−0.411979	−	0.237856i	0.279660	−	0.960099i	$-0.409778\pi$
$881$	−12.2282	−	7.05997i	−0.411979	−	0.237856i	−0.691640	+	0.722243i	$0.743111\pi$
$882$	23.1278	−	5.76964i	0.778755	−	0.194274i
$883$	3.17975	+	0.560675i	0.107007	+	0.0188682i	0.226895	−	0.973919i	$-0.427143\pi$
$883$	3.17975	+	0.560675i	0.107007	+	0.0188682i	−0.119888	+	0.992787i	$0.538254\pi$
$884$	−0.503673	+	2.85647i	−0.0169404	+	0.0960736i
$885$	−0.0869817	−	0.156698i	−0.00292386	−	0.00526736i
$886$	33.6442	+	19.4245i	1.13030	+	0.652578i
$887$	−14.5346	+	17.3216i	−0.488024	+	0.581604i	−0.952714	−	0.303869i	$-0.901721\pi$
$887$	−14.5346	+	17.3216i	−0.488024	+	0.581604i	0.464690	+	0.885473i	$0.346166\pi$
$888$	−4.35996	−	2.31787i	−0.146311	−	0.0777825i
$889$	4.27776	+	11.7530i	0.143471	+	0.394184i
$890$	12.9432	−	13.8946i	0.433856	−	0.465750i
$891$	−33.5276	−	13.5358i	−1.12322	−	0.453467i
$892$	17.7414			0.594027
$893$	−28.1017	+	25.0981i	−0.940387	+	0.839874i
$894$	4.77957	−	34.0245i	0.159853	−	1.13795i
$895$	−15.6430	+	4.79164i	−0.522887	+	0.160167i
$896$	2.96149	−	2.48498i	0.0989364	−	0.0830175i
$897$	−2.32799	−	10.9488i	−0.0777292	−	0.365570i
$898$	5.76702	−	15.8448i	0.192448	−	0.528746i
$899$	6.99488	−	8.33617i	0.233292	−	0.278027i
$900$	7.93358	−	12.7302i	0.264453	−	0.424340i
$901$	32.0551	−	18.5070i	1.06791	−	0.616557i
$902$	4.04318	−	22.9300i	0.134623	−	0.763486i
$903$	−15.2666	−	4.95931i	−0.508040	−	0.165035i
$904$	−2.16216	−	3.74497i	−0.0719124	−	0.124556i
$905$	−10.0571	+	23.7282i	−0.334311	+	0.788754i
$906$	−8.46448	+	7.62246i	−0.281214	+	0.253239i
$907$	−14.0379	−	5.10938i	−0.466121	−	0.169654i	0.0982735	−	0.995159i	$-0.468668\pi$
$907$	−14.0379	−	5.10938i	−0.466121	−	0.169654i	−0.564394	+	0.825505i	$0.690890\pi$
$908$	2.94381	+	8.08806i	0.0976939	+	0.268412i
$909$	−20.2477	−	45.4611i	−0.671575	−	1.50785i
$910$	−7.35327	+	2.25240i	−0.243759	+	0.0746663i
$911$	34.6078			1.14661			0.573304	−	0.819343i	$-0.305661\pi$
$911$	34.6078			1.14661			0.573304	+	0.819343i	$0.305661\pi$
$912$	−4.19691	−	6.27583i	−0.138973	−	0.207813i
$913$		−	12.1047i		−	0.400607i
$914$	−0.149720	−	0.849104i	−0.00495229	−	0.0280859i
$915$	−8.32494	+	6.74964i	−0.275214	+	0.223136i
$916$	−0.514798	+	0.187371i	−0.0170094	+	0.00619091i
$917$	28.4505	+	10.3551i	0.939518	+	0.341956i
$918$	−7.42956	−	15.2253i	−0.245212	−	0.502509i
$919$	−12.0939	+	20.9472i	−0.398941	+	0.690986i	−0.993595	−	0.112996i	$-0.963955\pi$
$919$	−12.0939	+	20.9472i	−0.398941	+	0.690986i	0.594655	+	0.803981i	$0.297289\pi$
$920$	9.78245	+	12.9674i	0.322518	+	0.427522i
$921$	45.2230	+	14.6906i	1.49015	+	0.484071i
$922$	2.14521	−	12.1661i	0.0706488	−	0.400669i
$923$	−5.65760	−	9.79925i	−0.186222	−	0.322546i
$924$	−21.1992	−	16.5604i	−0.697402	−	0.544797i
$925$	−12.8182	−	6.23498i	−0.421460	−	0.205005i
$926$	−33.0710	−	12.0369i	−1.08678	−	0.395556i
$927$	21.4151	−	1.50031i	0.703366	−	0.0492767i
$928$	4.02576	+	4.79771i	0.132152	+	0.157493i
$929$	−5.20086	+	0.917053i	−0.170635	+	0.0300875i	−0.258313	−	0.966061i	$-0.583166\pi$
$929$	−5.20086	+	0.917053i	−0.170635	+	0.0300875i	0.0876779	+	0.996149i	$0.472055\pi$
$930$	−6.72847	−	0.113425i	−0.220635	−	0.00371934i
$931$	4.95861	−	34.2770i	0.162512	−	1.12338i
$932$	1.62619			0.0532675
$933$	0.841373	+	24.0486i	0.0275453	+	0.787317i
$934$	−4.50782	−	5.37221i	−0.147500	−	0.175784i
$935$	−26.0892	+	13.3106i	−0.853209	+	0.435303i
$936$	−1.56847	+	2.15941i	−0.0512670	+	0.0705824i
$937$	−7.05135	+	8.40347i	−0.230358	+	0.274529i	−0.868825	−	0.495119i	$-0.835124\pi$
$937$	−7.05135	+	8.40347i	−0.230358	+	0.274529i	0.638467	+	0.769649i	$0.279569\pi$
$938$	7.19543	−	12.4628i	0.234939	−	0.406926i
$939$	1.68835	+	4.17803i	0.0550972	+	0.136345i
$940$	−19.3024	−	1.00130i	−0.629573	−	0.0326587i
$941$	2.71024	−	15.3705i	0.0883513	−	0.501065i	−0.908232	−	0.418468i	$-0.862567\pi$
$941$	2.71024	−	15.3705i	0.0883513	−	0.501065i	0.996583	−	0.0825973i	$-0.0263215\pi$
$942$	35.0187	−	14.1511i	1.14097	−	0.461068i
$943$	−21.0508	+	36.4610i	−0.685507	+	1.18733i
$944$	−0.0354485	−	0.0297448i	−0.00115375	−	0.000968111i
$945$	27.0063	−	35.8930i	0.878516	−	1.16760i
$946$	3.29390	+	9.04991i	0.107094	+	0.294238i
$947$	−5.13292	+	4.30703i	−0.166798	+	0.139960i	−0.722366	−	0.691511i	$-0.756945\pi$
$947$	−5.13292	+	4.30703i	−0.166798	+	0.139960i	0.555568	+	0.831471i	$0.312501\pi$
$948$	0.734459	+	20.9927i	0.0238541	+	0.681813i
$949$			10.6374i			0.345304i
$950$	−12.7580	−	17.6702i	−0.413923	−	0.573296i
$951$	29.2143	+	4.10386i	0.947340	+	0.133077i
$952$	−2.18872	−	12.4129i	−0.0709369	−	0.402303i
$953$	−14.7648	−	17.5960i	−0.478280	−	0.569992i	0.471917	−	0.881643i	$-0.343562\pi$
$953$	−14.7648	−	17.5960i	−0.478280	−	0.569992i	−0.950197	+	0.311651i	$0.899118\pi$
$954$	33.9750	−	2.38023i	1.09998	−	0.0770629i
$955$	−51.1450	−	11.7791i	−1.65501	−	0.381163i
$956$	5.23946	−	6.24414i	0.169456	−	0.201950i
$957$	26.8284	−	34.3434i	0.867239	−	1.11017i
$958$	17.9033	+	31.0095i	0.578430	+	1.00187i
$959$	−36.4353	−	6.42453i	−1.17656	−	0.207459i
$960$	0.736728	−	3.80227i	0.0237778	−	0.122718i
$961$	−13.9905	−	24.2322i	−0.451306	−	0.781685i
$962$	2.19643	+	1.26811i	0.0708157	+	0.0408854i
$963$	−11.6115	+	7.83428i	−0.374176	+	0.252456i
$964$	−6.66787	+	18.3198i	−0.214758	+	0.590042i
$965$	22.2685	+	43.6469i	0.716847	+	1.40504i
$966$	25.7789	+	41.2489i	0.829424	+	1.32716i
$967$	22.5090	−	3.96895i	0.723842	−	0.127633i	0.200424	−	0.979709i	$-0.435768\pi$
$967$	22.5090	−	3.96895i	0.723842	−	0.127633i	0.523417	+	0.852076i	$0.324657\pi$
$968$			5.13976i			0.165198i
$969$	−24.5618	+	1.61946i	−0.789038	+	0.0520247i
$970$	−30.5590	+	3.76868i	−0.981190	+	0.121005i
$971$	3.33320	+	18.9035i	0.106967	+	0.606642i	0.990416	+	0.138114i	$0.0441042\pi$
$971$	3.33320	+	18.9035i	0.106967	+	0.606642i	−0.883449	+	0.468527i	$0.844785\pi$
$972$	−0.00510251	−	15.5885i	−0.000163663	−	0.500000i
$973$	−28.8655	−	79.3073i	−0.925385	−	2.54247i
$974$	1.93686	−	5.32149i	0.0620611	−	0.170511i
$975$	−4.30109	+	6.39219i	−0.137745	+	0.204714i
$976$	−1.38361	+	2.39648i	−0.0442882	+	0.0767094i
$977$	−27.3386	+	15.7839i	−0.874639	+	0.504973i	−0.868887	−	0.495011i	$-0.835164\pi$
$977$	−27.3386	+	15.7839i	−0.874639	+	0.504973i	−0.00575167	+	0.999983i	$0.501831\pi$
$978$	4.27712	+	1.38941i	0.136767	+	0.0444284i
$979$	−33.5985	−	5.92432i	−1.07381	−	0.189342i
$980$	14.1835	−	10.6999i	0.453075	−	0.341795i
$981$	15.0607	+	15.5918i	0.480853	+	0.497807i
$982$	−25.6893	−	21.5559i	−0.819778	−	0.687876i
$983$	8.67049	−	23.8220i	0.276546	−	0.759803i	−0.721202	−	0.692725i	$-0.756410\pi$
$983$	8.67049	−	23.8220i	0.276546	−	0.759803i	0.997748	−	0.0670780i	$-0.0213676\pi$
$984$	9.81892	−	2.08775i	0.313016	−	0.0665550i
$985$	−19.8520	−	18.4926i	−0.632538	−	0.589223i
$986$	20.1093	−	3.54580i	0.640409	−	0.112921i
$987$	−57.3168	−	8.05153i	−1.82441	−	0.256283i
$988$	2.04165	+	3.29688i	0.0649534	+	0.104888i
$989$		−	17.4142i		−	0.553739i
$990$	−26.9453	+	0.488201i	−0.856379	+	0.0155161i
$991$	−32.7724	−	39.0566i	−1.04105	−	1.24067i	−0.969976	−	0.243202i	$-0.921802\pi$
$991$	−32.7724	−	39.0566i	−1.04105	−	1.24067i	−0.0710725	−	0.997471i	$-0.522642\pi$
$992$	−1.63274	+	0.594270i	−0.0518397	+	0.0188681i
$993$	−9.17047	−	4.87526i	−0.291016	−	0.154712i
$994$	37.6667	+	31.6062i	1.19472	+	1.00249i
$995$	19.1967	+	8.13646i	0.608576	+	0.257943i
$996$	4.83861	−	1.95529i	0.153317	−	0.0619558i
$997$	30.4828	+	5.37494i	0.965400	+	0.170226i	0.634059	−	0.773285i	$-0.281388\pi$
$997$	30.4828	+	5.37494i	0.965400	+	0.170226i	0.331342	+	0.943511i	$0.392499\pi$
$998$	35.1723	+	6.20183i	1.11336	+	0.196316i
$999$	−14.7319	+	1.55131i	−0.466097	+	0.0490814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.29.14	✓	240
3.2	odd	2	inner	570.2.bf.a.29.25	yes	240
5.4	even	2	inner	570.2.bf.a.29.27	yes	240
15.14	odd	2	inner	570.2.bf.a.29.16	yes	240
19.2	odd	18	inner	570.2.bf.a.59.16	yes	240
57.2	even	18	inner	570.2.bf.a.59.27	yes	240
95.59	odd	18	inner	570.2.bf.a.59.25	yes	240
285.59	even	18	inner	570.2.bf.a.59.14	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.29.14	✓	240	1.1	even	1	trivial
570.2.bf.a.29.16	yes	240	15.14	odd	2	inner
570.2.bf.a.29.25	yes	240	3.2	odd	2	inner
570.2.bf.a.29.27	yes	240	5.4	even	2	inner
570.2.bf.a.59.14	yes	240	285.59	even	18	inner
570.2.bf.a.59.16	yes	240	19.2	odd	18	inner
570.2.bf.a.59.25	yes	240	95.59	odd	18	inner
570.2.bf.a.59.27	yes	240	57.2	even	18	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(0.917943 + 1.46880i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.501847 - 2.17902i) q^{5} +(-1.15905 - 1.28709i) q^{6} +(-3.34801 - 1.93297i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.31476 + 2.69655i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(0.917943 + 1.46880i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.501847 - 2.17902i) q^{5} +(-1.15905 - 1.28709i) q^{6} +(-3.34801 - 1.93297i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.31476 + 2.69655i) q^{9} +(-0.115839 + 2.23307i) q^{10} +(3.47920 - 2.00872i) q^{11} +(1.36494 + 1.06627i) q^{12} +(-0.681504 - 0.571849i) q^{13} +(3.63280 + 1.32223i) q^{14} +(3.66122 - 1.26311i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.566154 - 3.21082i) q^{17} +(0.826534 - 2.88389i) q^{18} +(-3.42399 - 2.69746i) q^{19} +(-0.273689 - 2.21926i) q^{20} +(-0.234126 - 6.69192i) q^{21} +(-3.07753 + 2.58236i) q^{22} +(6.82620 - 2.48453i) q^{23} +(-1.52936 - 0.813048i) q^{24} +(-4.49630 - 2.18707i) q^{25} +(0.770451 + 0.444820i) q^{26} +(-5.16758 + 0.544161i) q^{27} +(-3.80722 - 0.671315i) q^{28} +(1.08755 - 6.16782i) q^{29} +(-3.38627 + 1.87968i) q^{30} +(1.50475 + 0.868765i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(6.14411 + 3.26637i) q^{33} +(1.11511 + 3.06373i) q^{34} +(-5.89219 + 6.32534i) q^{35} +(-0.313195 + 2.98361i) q^{36} +2.85084 q^{37} +(3.84038 + 2.06191i) q^{38} +(0.214352 - 1.52592i) q^{39} +(0.654901 + 2.13801i) q^{40} +(-4.43975 + 3.72539i) q^{41} +(1.39261 + 6.54960i) q^{42} +(0.819901 - 2.25266i) q^{43} +(2.58236 - 3.07753i) q^{44} +(5.21605 + 4.21815i) q^{45} +(-6.29106 + 3.63214i) q^{46} +(1.50099 - 8.51256i) q^{47} +(1.64731 + 0.535125i) q^{48} +(3.97278 + 6.88105i) q^{49} +(4.80777 + 1.37307i) q^{50} +(4.19636 - 3.77892i) q^{51} +(-0.835988 - 0.304275i) q^{52} +(3.88287 + 10.6681i) q^{53} +(4.99458 - 1.43323i) q^{54} +(-2.63102 - 8.58933i) q^{55} +3.86595 q^{56} +(0.819006 - 7.50528i) q^{57} +6.26297i q^{58} +(-0.00803551 - 0.0455717i) q^{59} +(3.00842 - 2.43915i) q^{60} +(-2.60033 + 0.946444i) q^{61} +(-1.63274 - 0.594270i) q^{62} +(9.61420 - 6.48669i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-1.58808 + 1.19803i) q^{65} +(-6.61797 - 2.14983i) q^{66} +(0.646399 - 3.66591i) q^{67} +(-1.63018 - 2.82355i) q^{68} +(9.91535 + 7.74568i) q^{69} +(4.70429 - 7.25241i) q^{70} +(11.9518 + 4.35011i) q^{71} +(-0.209661 - 2.99266i) q^{72} +(-7.68577 - 9.15955i) q^{73} +(-2.80752 + 0.495042i) q^{74} +(-0.914971 - 8.61178i) q^{75} +(-4.14008 - 1.36371i) q^{76} -15.5312 q^{77} +(0.0538775 + 1.53996i) q^{78} +(7.79546 + 9.29027i) q^{79} +(-1.01621 - 1.99181i) q^{80} +(-5.54281 - 7.09065i) q^{81} +(3.72539 - 4.43975i) q^{82} +(1.50652 - 2.60937i) q^{83} +(-2.50878 - 6.20828i) q^{84} +(-7.28058 - 0.377675i) q^{85} +(-0.416275 + 2.36081i) q^{86} +(10.0576 - 4.06431i) q^{87} +(-2.00872 + 3.47920i) q^{88} +(-6.50540 - 5.45868i) q^{89} +(-5.86928 - 3.24831i) q^{90} +(1.17631 + 3.23189i) q^{91} +(5.56477 - 4.66940i) q^{92} +(0.105227 + 3.00765i) q^{93} +8.64388i q^{94} +(-7.59615 + 6.10725i) q^{95} +(-1.71521 - 0.240943i) q^{96} +(2.39112 + 13.5607i) q^{97} +(-5.10730 - 6.08665i) q^{98} +(0.842300 + 12.0228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) \) 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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