LMFDB - Embedded newform 570.2.bf.a.59.14

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			59.14
Character	$\chi$	$=$	570.59
Dual form			570.2.bf.a.29.14

$q$-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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

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

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	−0.974120	−	0.226034i	$-0.927424\pi$
$7$	−3.34801	+	1.93297i	−1.26543	+	0.730595i	−0.291309	+	0.956629i	$0.594091\pi$
$8$	−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	0.922374	−	0.386298i	$-0.126246\pi$
$11$	3.47920	+	2.00872i	1.04902	+	0.605651i	0.126643	+	0.991948i	$0.459580\pi$
$12$	1.36494	−	1.06627i	0.394026	−	0.307805i
$13$	−0.681504	+	0.571849i	−0.189015	+	0.158602i	−0.732385	−	0.680891i	$-0.761593\pi$
$13$	−0.681504	+	0.571849i	−0.189015	+	0.158602i	0.543370	+	0.839494i	$0.317148\pi$
$14$	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	0.835909	+	0.548868i	$0.184941\pi$
$17$	−0.566154	+	3.21082i	−0.137313	+	0.778738i	−0.973221	+	0.229870i	$0.926170\pi$
$18$	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	0.935021	−	0.354592i	$-0.115380\pi$
$23$	6.82620	+	2.48453i	1.42336	+	0.518061i	0.488340	+	0.872653i	$0.337603\pi$
$24$	−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	0.902162	+	0.431397i	$0.141979\pi$
$29$	1.08755	+	6.16782i	0.201953	+	1.14534i	−0.700209	+	0.713938i	$0.746910\pi$
$30$	−3.38627	−	1.87968i	−0.618245	−	0.343182i
$31$	1.50475	−	0.868765i	0.270260	−	0.156035i	−0.358746	−	0.933435i	$-0.616795\pi$
$31$	1.50475	−	0.868765i	0.270260	−	0.156035i	0.629006	+	0.777401i	$0.283462\pi$
$32$	−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	0.226507	−	0.974010i	$-0.427269\pi$
$41$	−4.43975	−	3.72539i	−0.693373	−	0.581809i	−0.919880	+	0.392201i	$0.871714\pi$
$42$	1.39261	−	6.54960i	0.214884	−	1.01063i
$43$	0.819901	+	2.25266i	0.125034	+	0.343527i	0.986378	−	0.164494i	$-0.0525992\pi$
$43$	0.819901	+	2.25266i	0.125034	+	0.343527i	−0.861344	+	0.508022i	$0.830377\pi$
$44$	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	0.873933	+	0.486047i	$0.161562\pi$
$47$	1.50099	+	8.51256i	0.218943	+	1.24168i	−0.654990	+	0.755637i	$0.727327\pi$
$48$	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	−0.321702	−	0.946841i	$-0.604255\pi$
$53$	3.88287	−	10.6681i	0.533354	−	1.46538i	0.855056	−	0.518536i	$-0.173523\pi$
$54$	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	−0.985326	−	0.170681i	$-0.945403\pi$
$59$	−0.00803551	+	0.0455717i	−0.00104613	+	0.00593293i	0.984280	+	0.176614i	$0.0565144\pi$
$60$	3.00842	+	2.43915i	0.388385	+	0.314892i
$61$	−2.60033	−	0.946444i	−0.332939	−	0.121180i	0.170141	−	0.985420i	$-0.445578\pi$
$61$	−2.60033	−	0.946444i	−0.332939	−	0.121180i	−0.503080	+	0.864240i	$0.667800\pi$
$62$	−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	0.998496	+	0.0548318i	$0.0174622\pi$
$67$	0.646399	+	3.66591i	0.0789702	+	0.447862i	−0.919525	+	0.393031i	$0.871427\pi$
$68$	−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	0.484831	−	0.874608i	$-0.338881\pi$
$71$	11.9518	−	4.35011i	1.41842	−	0.516263i	0.933589	+	0.358345i	$0.116659\pi$
$72$	−0.209661	+	2.99266i	−0.0247088	+	0.352689i
$73$	−7.68577	+	9.15955i	−0.899552	+	1.07204i	0.0974943	+	0.995236i	$0.468917\pi$
$73$	−7.68577	+	9.15955i	−0.899552	+	1.07204i	−0.997046	+	0.0768078i	$0.975527\pi$
$74$	−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	−0.121555	−	0.992585i	$-0.538788\pi$
$79$	7.79546	−	9.29027i	0.877058	−	1.04524i	0.998613	−	0.0526520i	$-0.0167674\pi$
$80$	−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	0.936784	−	0.349909i	$-0.113787\pi$
$83$	1.50652	+	2.60937i	0.165362	+	0.286416i	−0.771422	+	0.636324i	$0.780454\pi$
$84$	−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	−0.918785	−	0.394757i	$-0.870829\pi$
$89$	−6.50540	+	5.45868i	−0.689571	+	0.578618i	0.229215	+	0.973376i	$0.426384\pi$
$90$	−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	−0.582806	−	0.812611i	$-0.698045\pi$
$97$	2.39112	−	13.5607i	0.242782	−	1.37688i	0.825588	−	0.564273i	$-0.190843\pi$
$98$	−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	−0.963063	−	0.269275i	$-0.913216\pi$
$101$	−10.6630	−	12.7077i	−1.06101	−	1.26447i	−0.0979496	−	0.995191i	$-0.531228\pi$
$102$	−3.47641	−	4.45020i	−0.344216	−	0.440635i
$103$	−3.57794	+	6.19717i	−0.352545	+	0.610626i	−0.986695	−	0.162585i	$-0.948017\pi$
$103$	−3.57794	+	6.19717i	−0.352545	+	0.610626i	0.634150	+	0.773210i	$0.281350\pi$
$104$	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	−0.291648	−	0.956526i	$-0.594203\pi$
$107$	4.04355	−	2.33454i	0.390904	−	0.225689i	0.682552	+	0.730837i	$0.260870\pi$
$108$	−4.66982	−	2.27876i	−0.449354	−	0.219274i
$109$	2.47142	+	6.79017i	0.236719	+	0.650381i	0.999991	+	0.00430289i	$0.00136966\pi$
$109$	2.47142	+	6.79017i	0.236719	+	0.650381i	−0.763272	+	0.646078i	$0.776408\pi$
$110$	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	$-0.934801\pi$
$113$		−	4.32432i		−	0.406798i	0.979096	−	0.203399i	$-0.0651988\pi$
$114$	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	−0.746090	−	0.665845i	$-0.768071\pi$
$127$	−2.47835	+	2.07958i	−0.219918	+	0.184533i	0.526172	+	0.850378i	$0.323627\pi$
$128$	−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	−0.173756	−	0.984789i	$-0.555590\pi$
$131$	−7.71257	−	1.35993i	−0.673851	−	0.118818i	−0.500095	+	0.865971i	$0.666701\pi$
$132$	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	0.696292	−	0.717758i	$-0.254832\pi$
$137$	8.99292	+	3.27316i	0.768317	+	0.279645i	0.0720248	+	0.997403i	$0.477054\pi$
$138$	−11.1097	+	5.90622i	−0.945724	+	0.502771i
$139$	16.7234	−	14.0326i	1.41846	−	1.19023i	0.466304	−	0.884625i	$-0.345585\pi$
$139$	16.7234	−	14.0326i	1.41846	−	1.19023i	0.952158	−	0.305606i	$-0.0988591\pi$
$140$	−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	0.0757813	−	0.997124i	$-0.475855\pi$
$149$	12.7509	−	15.1960i	1.04460	−	1.24490i	0.968817	−	0.247779i	$-0.0797006\pi$
$150$	2.39649	−	8.32207i	0.195673	−	0.679494i
$151$			6.57645i			0.535184i	0.963532	+	0.267592i	$0.0862280\pi$
$151$			6.57645i			0.535184i	−0.963532	+	0.267592i	$0.913772\pi$
$152$	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	−0.760649	−	0.649163i	$-0.775119\pi$
$157$	−7.45824	−	20.4913i	−0.595232	−	1.63539i	0.165417	−	0.986224i	$-0.447103\pi$
$158$	−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	0.409348	−	0.912378i	$-0.365756\pi$
$163$	−2.24857	−	1.29821i	−0.176121	−	0.101684i	−0.585469	+	0.810695i	$0.699090\pi$
$164$	−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	0.226363	+	0.974043i	$0.427317\pi$
$167$	−7.40665	+	20.3496i	−0.573144	+	1.57470i	−0.799507	+	0.600657i	$0.794906\pi$
$168$	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	0.401609	−	0.915811i	$-0.368451\pi$
$173$	6.12627	+	1.08023i	0.465771	+	0.0821281i	0.0641627	+	0.997939i	$0.479562\pi$
$174$	−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	−0.969739	−	0.244145i	$-0.921493\pi$
$179$	−3.65830	+	6.33636i	−0.273434	+	0.473602i	0.696305	+	0.717746i	$0.254826\pi$
$180$	6.34418	−	2.17977i	0.472867	−	0.162471i
$181$	−11.3503	+	2.00137i	−0.843663	+	0.148760i	−0.578743	−	0.815510i	$-0.696457\pi$
$181$	−11.3503	+	2.00137i	−0.843663	+	0.148760i	−0.264920	+	0.964270i	$0.585345\pi$
$182$	−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	$0.322897\pi$
$191$			23.4715i			1.69834i	−0.528121	+	0.849169i	$0.677103\pi$
$192$	1.73099	+	0.0605610i	0.124924	+	0.00437062i
$193$	−16.7865	−	14.0855i	−1.20832	−	1.01390i	−0.999353	−	0.0359748i	$-0.988546\pi$
$193$	−16.7865	−	14.0855i	−1.20832	−	1.01390i	−0.208964	−	0.977923i	$-0.567009\pi$
$194$	−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	0.997065	−	0.0765605i	$-0.0243938\pi$
$197$	6.06663	+	10.5077i	0.432229	+	0.748643i	−0.564836	+	0.825203i	$0.691060\pi$
$198$	−2.91725	+	11.6939i	−0.207320	+	0.831050i
$199$	−1.61915	−	9.18266i	−0.114779	−	0.650942i	−0.986860	−	0.161580i	$-0.948341\pi$
$199$	−1.61915	−	9.18266i	−0.114779	−	0.650942i	0.872081	−	0.489362i	$-0.162770\pi$
$200$	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	−0.253300	−	0.967388i	$-0.581516\pi$
$211$	−11.9430	−	2.10588i	−0.822191	−	0.144974i	−0.568891	+	0.822413i	$0.692627\pi$
$212$	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	0.283067	−	0.959100i	$-0.408648\pi$
$223$	16.6715	−	6.06793i	1.11641	−	0.406339i	0.833339	+	0.552762i	$0.186426\pi$
$224$	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	$-0.907795\pi$
$227$		−	8.60714i		−	0.571276i	0.958338	−	0.285638i	$-0.0922054\pi$
$228$	−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	−0.291479	−	0.956577i	$-0.594147\pi$
$233$	1.52812	−	0.556189i	0.100110	−	0.0364371i	0.391590	+	0.920140i	$0.371925\pi$
$234$	−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	0.710620	−	0.703576i	$-0.248415\pi$
$239$	7.05910	+	4.07557i	0.456615	+	0.263627i	−0.254005	+	0.967203i	$0.581748\pi$
$240$	1.99275	+	3.32099i	0.128631	+	0.214369i
$241$	−12.5315	−	14.9345i	−0.807225	−	0.962013i	0.192589	−	0.981279i	$-0.438311\pi$
$241$	−12.5315	−	14.9345i	−0.807225	−	0.962013i	−0.999814	+	0.0192662i	$0.993867\pi$
$242$	−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	−0.963545	−	0.267547i	$-0.913787\pi$
$251$	−0.846815	+	2.32661i	−0.0534505	+	0.146854i	0.910094	+	0.414401i	$0.136009\pi$
$252$	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	−0.424043	−	0.905642i	$-0.639389\pi$
$257$	−8.22024	+	1.44945i	−0.512764	+	0.0904142i	−0.0887217	+	0.996056i	$0.528278\pi$
$258$	−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	0.665779	−	0.746149i	$-0.268099\pi$
$263$	0.755363	+	0.633825i	0.0465777	+	0.0390833i	−0.619202	+	0.785232i	$0.712544\pi$
$264$	−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	0.997634	−	0.0687551i	$-0.0219027\pi$
$269$	18.0932	+	15.1820i	1.10316	+	0.925661i	0.105527	+	0.994416i	$0.466347\pi$
$270$	−0.616540	+	11.6026i	−0.0375215	+	0.706111i
$271$	27.8483	−	10.1359i	1.69166	−	0.615714i	0.696828	−	0.717238i	$-0.254594\pi$
$271$	27.8483	−	10.1359i	1.69166	−	0.615714i	0.994833	+	0.101523i	$0.0323717\pi$
$272$	−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	0.180638	−	0.983550i	$-0.442184\pi$
$277$	−9.66682	−	5.58114i	−0.580823	−	0.335338i	−0.761460	+	0.648212i	$0.775517\pi$
$278$	−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	0.830025	−	0.557727i	$-0.188326\pi$
$281$	18.5627	+	6.75629i	1.10736	+	0.403046i	0.277336	+	0.960773i	$0.410548\pi$
$282$	−12.6962	−	7.93459i	−0.756045	−	0.472498i
$283$	−3.30932	−	0.583522i	−0.196719	−	0.0346868i	0.0744206	−	0.997227i	$-0.476289\pi$
$283$	−3.30932	−	0.583522i	−0.196719	−	0.0346868i	−0.271139	+	0.962540i	$0.587400\pi$
$284$	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	0.906850	−	0.421453i	$-0.138480\pi$
$293$	17.0365	+	9.83605i	0.995286	+	0.574628i	0.0884356	+	0.996082i	$0.471813\pi$
$294$	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	0.999623	+	0.0274503i	$0.00873881\pi$
$307$	21.0299	+	17.6462i	1.20024	+	1.00712i	0.200616	+	0.979670i	$0.435706\pi$
$308$	−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	−0.118450	−	0.992960i	$-0.537793\pi$
$311$	12.0317	−	6.94649i	0.682254	−	0.393899i	0.800704	+	0.599061i	$0.204459\pi$
$312$	0.577325	−	1.42866i	0.0326846	−	0.0808820i
$313$	2.56217	−	0.451779i	0.144822	−	0.0255361i	−0.100767	−	0.994910i	$-0.532130\pi$
$313$	2.56217	−	0.451779i	0.144822	−	0.0255361i	0.245589	+	0.969374i	$0.421019\pi$
$314$	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	0.980188	−	0.198072i	$-0.0634679\pi$
$317$	10.9483	+	13.0477i	0.614917	+	0.732830i	−0.365270	+	0.930901i	$0.619023\pi$
$318$	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	0.350450	−	0.936582i	$-0.386029\pi$
$331$	−5.19292	−	2.99813i	−0.285429	−	0.164792i	−0.635878	+	0.771789i	$0.719362\pi$
$332$	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	0.323444	−	0.946247i	$-0.395159\pi$
$337$	21.6519	−	7.88064i	1.17945	−	0.429286i	0.856009	+	0.516962i	$0.172937\pi$
$338$	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	−0.0224354	−	0.999748i	$-0.507142\pi$
$347$	11.2327	−	4.08837i	0.603004	−	0.219475i	0.625439	+	0.780273i	$0.284920\pi$
$348$	8.06099	+	7.25911i	0.432115	+	0.389129i
$349$	11.1495	+	19.3114i	0.596817	+	1.03372i	0.993288	+	0.115670i	$0.0369016\pi$
$349$	11.1495	+	19.3114i	0.596817	+	1.03372i	−0.396470	+	0.918048i	$0.629765\pi$
$350$	−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	−0.204427	−	0.978882i	$-0.565533\pi$
$353$	14.0071	−	24.2610i	0.745523	−	1.29128i	0.949950	−	0.312402i	$-0.101134\pi$
$354$	−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	0.614422	−	0.788978i	$-0.289389\pi$
$359$	17.4683	+	3.08014i	0.921943	+	0.162563i	0.307521	+	0.951541i	$0.400500\pi$
$360$	−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	0.751229	−	0.660042i	$-0.229461\pi$
$367$	−0.560061	−	0.667455i	−0.0292350	−	0.0348409i	−0.780464	+	0.625201i	$0.785017\pi$
$368$	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	0.605506	−	0.795841i	$-0.292971\pi$
$373$	−7.46389	−	12.9278i	−0.386466	−	0.669378i	−0.991971	+	0.126463i	$0.959638\pi$
$374$	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	$0.133951\pi$
$379$			15.9056i			0.817015i	−0.912755	+	0.408507i	$0.866049\pi$
$380$	−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	0.0498995	−	0.998754i	$-0.484110\pi$
$383$	20.0560	−	23.9018i	1.02482	−	1.22133i	0.974916	−	0.222573i	$-0.0714456\pi$
$384$	−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	−0.295260	−	0.955417i	$-0.595406\pi$
$389$	−4.85075	+	0.855317i	−0.245943	+	0.0433663i	0.0493178	+	0.998783i	$0.484295\pi$
$390$	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	0.872629	−	0.488383i	$-0.162413\pi$
$397$	30.3973	+	5.35986i	1.52560	+	0.269004i	0.652966	+	0.757387i	$0.273524\pi$
$398$			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	−0.460411	−	0.887706i	$-0.652298\pi$
$401$	5.52383	−	31.3272i	0.275847	−	1.56441i	0.736258	−	0.676701i	$-0.236591\pi$
$402$	−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	0.420014	−	0.907518i	$-0.362025\pi$
$409$	22.7535	−	4.01205i	1.12509	−	0.198383i	0.705073	+	0.709135i	$0.250914\pi$
$410$	−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	$-0.840653\pi$
$419$		−	19.6488i		−	0.959909i	0.877293	−	0.479954i	$-0.159347\pi$
$420$	−14.7870	−	2.35109i	−0.721532	−	0.114721i
$421$	−7.30361	+	8.70410i	−0.355956	+	0.424212i	−0.914073	−	0.405551i	$-0.867080\pi$
$421$	−7.30361	+	8.70410i	−0.355956	+	0.424212i	0.558117	+	0.829763i	$0.311524\pi$
$422$	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	−0.863882	−	0.503694i	$-0.831974\pi$
$431$	−10.7509	+	9.02106i	−0.517852	+	0.434529i	0.346030	+	0.938223i	$0.387529\pi$
$432$	−3.60882	−	3.73851i	−0.173629	−	0.179869i
$433$	5.13986	+	1.87075i	0.247006	+	0.0899027i	0.462556	−	0.886590i	$-0.346932\pi$
$433$	5.13986	+	1.87075i	0.247006	+	0.0899027i	−0.215550	+	0.976493i	$0.569155\pi$
$434$	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	−0.504143	−	0.863620i	$-0.668191\pi$
$439$	−26.6777	−	4.70400i	−1.27326	−	0.224510i	−0.769115	+	0.639111i	$0.779303\pi$
$440$	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	−0.459448	+	0.888205i	$0.651953\pi$
$443$	−29.7600	+	24.9716i	−1.41394	+	1.18644i	−0.954493	+	0.298232i	$0.903603\pi$
$444$	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	0.595589	−	0.803290i	$-0.296919\pi$
$449$	−8.43082	−	14.6026i	−0.397875	−	0.689140i	−0.993464	+	0.114150i	$0.963586\pi$
$450$	−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	$-0.993581\pi$
$457$		−	0.862202i		−	0.0403321i	0.999797	−	0.0201661i	$-0.00641949\pi$
$458$	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	0.801572	−	0.597898i	$-0.203997\pi$
$461$	−4.22524	−	11.6088i	−0.196789	−	0.540674i	−0.998361	+	0.0572241i	$0.981775\pi$
$462$	18.0015	−	19.9900i	0.837503	−	0.930019i
$463$	30.4784	−	17.5967i	1.41645	−	0.817789i	0.420467	−	0.907308i	$-0.361866\pi$
$463$	30.4784	−	17.5967i	1.41645	−	0.817789i	0.995985	+	0.0895191i	$0.0285330\pi$
$464$	−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	−0.773419	−	0.633895i	$-0.781455\pi$
$467$	3.50646	−	6.07337i	0.162260	−	0.281042i	0.935679	+	0.352853i	$0.114788\pi$
$468$	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	0.260715	+	0.965416i	$0.416042\pi$
$479$	−12.2466	+	33.6473i	−0.559561	+	1.53738i	−0.820277	+	0.571967i	$0.806181\pi$
$480$	−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	0.794713	−	0.606985i	$-0.207621\pi$
$487$	−2.83150	−	4.90431i	−0.128308	−	0.222235i	−0.923021	+	0.384749i	$0.874288\pi$
$488$	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	−0.0144039	−	0.999896i	$-0.504585\pi$
$491$	21.5559	−	25.6893i	0.972803	−	1.15934i	0.987207	−	0.159445i	$-0.0509705\pi$
$492$	−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	−0.956680	−	0.291140i	$-0.905965\pi$
$499$	−33.5611	+	12.2152i	−1.50240	+	0.546829i	−0.545719	+	0.837969i	$0.683743\pi$
$500$	−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	0.997563	−	0.0697704i	$-0.0222267\pi$
$503$	0.814068	+	4.61681i	0.0362975	+	0.205853i	−0.961266	+	0.275624i	$0.911116\pi$
$504$	−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	0.585342	−	0.810787i	$-0.300960\pi$
$509$	11.5642	+	4.20904i	0.512576	+	0.186563i	−0.0727656	+	0.997349i	$0.523183\pi$
$510$	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	−0.917627	−	0.397442i	$-0.869898\pi$
$521$	−2.61622	+	4.53143i	−0.114619	+	0.198526i	0.803009	+	0.595968i	$0.203231\pi$
$522$	−16.8884	+	8.23430i	−0.739187	+	0.360406i
$523$	6.20970	+	35.2170i	0.271531	+	1.53993i	0.749769	+	0.661700i	$0.230165\pi$
$523$	6.20970	+	35.2170i	0.271531	+	1.53993i	−0.478237	+	0.878231i	$0.658724\pi$
$524$	−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	0.724296	+	0.689489i	$0.242165\pi$
$541$	6.50100	+	36.8690i	0.279500	+	1.58512i	−0.444796	+	0.895632i	$0.646724\pi$
$542$	−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	0.284492	−	0.958678i	$-0.408175\pi$
$547$	−2.66159	−	0.968739i	−0.113801	−	0.0414203i	−0.398293	+	0.917258i	$0.630397\pi$
$548$	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	−0.527526	−	0.849539i	$-0.676880\pi$
$557$	5.13324	−	4.30730i	0.217502	−	0.182506i	0.745028	+	0.667033i	$0.232436\pi$
$558$	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	0.222543	−	0.974923i	$-0.428564\pi$
$563$	27.9541	−	16.1393i	1.17812	−	0.680190i	0.955580	+	0.294733i	$0.0952308\pi$
$564$	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	−0.533842	+	0.845585i	$0.679252\pi$
$577$	−36.8254	+	21.2611i	−1.53306	+	0.885113i	−0.999218	+	0.0395281i	$0.987415\pi$
$578$	−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	−0.700785	−	0.713372i	$-0.747167\pi$
$587$	4.88741	−	27.7179i	0.201725	−	1.14404i	0.902510	−	0.430668i	$-0.141722\pi$
$588$	−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	−0.143874	−	0.989596i	$-0.545956\pi$
$593$	−21.6775	−	7.88996i	−0.890188	−	0.324002i	−0.746314	+	0.665594i	$0.768178\pi$
$594$	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	0.926272	+	0.376855i	$0.122995\pi$
$599$	4.52174	+	25.6440i	0.184753	+	1.04779i	−0.741519	+	0.670932i	$0.765894\pi$
$600$	5.09828	−	7.00054i	0.208136	−	0.285796i
$601$	5.09656	−	2.94250i	0.207893	−	0.120027i	−0.392439	−	0.919778i	$-0.628369\pi$
$601$	5.09656	−	2.94250i	0.207893	−	0.120027i	0.600332	+	0.799751i	$0.295035\pi$
$602$	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	0.972476	−	0.233002i	$-0.0748550\pi$
$613$	1.92488	+	5.28856i	0.0777452	+	0.213603i	−0.894731	+	0.446605i	$0.852633\pi$
$614$	−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	0.940146	+	0.340771i	$0.110688\pi$
$617$	4.30340	+	24.4058i	0.173248	+	0.982540i	−0.766898	+	0.641769i	$0.778201\pi$
$618$	−3.82929	−	11.7880i	−0.154037	−	0.474182i
$619$	−10.4425	+	18.0870i	−0.419721	+	0.726978i	−0.995911	−	0.0903379i	$-0.971205\pi$
$619$	−10.4425	+	18.0870i	−0.419721	+	0.726978i	0.576190	+	0.817315i	$0.304539\pi$
$620$	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	0.0108141	−	0.999942i	$-0.496558\pi$
$631$	−15.6660	−	5.70194i	−0.623652	−	0.226991i	−0.634466	+	0.772951i	$0.718780\pi$
$632$	−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	0.704488	−	0.709716i	$-0.251177\pi$
$641$	43.0495	−	15.6687i	1.70035	−	0.618878i	0.995866	+	0.0908379i	$0.0289545\pi$
$642$	−1.68192	+	7.91026i	−0.0663801	+	0.312193i
$643$	−10.2594	+	12.2266i	−0.404590	+	0.482172i	−0.929414	−	0.369039i	$-0.879687\pi$
$643$	−10.2594	+	12.2266i	−0.404590	+	0.482172i	0.524824	+	0.851211i	$0.324131\pi$
$644$	−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	0.844473	−	0.535598i	$-0.179914\pi$
$653$	−1.06318	−	1.84148i	−0.0416053	−	0.0720625i	−0.886078	+	0.463536i	$0.846581\pi$
$654$	−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	−0.512391	−	0.858753i	$-0.671240\pi$
$659$	6.27245	−	5.26321i	0.244340	−	0.205026i	0.756730	+	0.653727i	$0.226796\pi$
$660$	5.56733	+	14.5293i	0.216708	+	0.565553i
$661$	−2.66756	+	7.32905i	−0.103756	+	0.285067i	−0.980698	−	0.195529i	$-0.937358\pi$
$661$	−2.66756	+	7.32905i	−0.103756	+	0.285067i	0.876942	+	0.480596i	$0.159580\pi$
$662$	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	−0.399382	−	0.916785i	$-0.630775\pi$
$673$	15.4166	−	26.7024i	0.594268	−	1.02930i	0.993650	−	0.112517i	$-0.0358913\pi$
$674$	−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	−0.656906	−	0.753972i	$-0.728135\pi$
$677$	−8.64881	+	4.99339i	−0.332401	+	0.191912i	0.324506	+	0.945884i	$0.394802\pi$
$678$	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	$0.0564630\pi$
$683$			9.22304i			0.352910i	−0.984309	+	0.176455i	$0.943537\pi$
$684$	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	0.979187	−	0.202959i	$-0.0650560\pi$
$691$	8.24949	+	14.2885i	0.313826	+	0.543562i	−0.665362	+	0.746521i	$0.731723\pi$
$692$	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	0.292860	−	0.956155i	$-0.405393\pi$
$701$	6.38170	+	1.12527i	0.241033	+	0.0425007i	−0.0518263	+	0.998656i	$0.516504\pi$
$702$	−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	−0.999689	−	0.0249357i	$-0.992062\pi$
$709$	−30.5872	+	25.6657i	−1.14873	+	0.963896i	−0.149037	+	0.988832i	$0.547617\pi$
$710$	−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	−0.164807	−	0.986326i	$-0.552700\pi$
$719$	22.3939	−	26.6880i	0.835152	−	0.995296i	0.999960	−	0.00897016i	$-0.00285533\pi$
$720$	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	−0.666365	−	0.745625i	$-0.732151\pi$
$727$	−17.1263	−	47.0541i	−0.635179	−	1.74514i	0.0311866	−	0.999514i	$-0.490071\pi$
$728$	−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	−0.0558997	−	0.998436i	$-0.517803\pi$
$733$	−25.6802	−	14.8265i	−0.948521	−	0.547629i	−0.892621	+	0.450808i	$0.851136\pi$
$734$	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	−0.957030	−	0.289989i	$-0.906348\pi$
$739$	1.12724	−	6.39289i	0.0414662	−	0.235166i	0.998496	+	0.0548228i	$0.0174594\pi$
$740$	−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	0.313101	−	0.949720i	$-0.398632\pi$
$743$	7.70027	+	1.35777i	0.282496	+	0.0498116i	−0.0306050	+	0.999532i	$0.509743\pi$
$744$	−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	0.185516	−	0.982641i	$-0.440604\pi$
$751$	19.0715	−	3.36281i	0.695928	−	0.122711i	0.510411	+	0.859930i	$0.329493\pi$
$752$	−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	−0.769972	−	0.638078i	$-0.779730\pi$
$757$	−0.216899	+	0.258490i	−0.00788332	+	0.00939498i	0.762088	+	0.647473i	$0.224174\pi$
$758$	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	$0.0199142\pi$
$761$			3.44946i			0.125043i	−0.998044	+	0.0625214i	$0.980086\pi$
$762$	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	−0.999968	−	0.00802243i	$-0.997446\pi$
$769$	−1.74841	−	9.91572i	−0.0630493	−	0.357570i	0.936919	−	0.349548i	$-0.113665\pi$
$770$	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	0.489888	−	0.871785i	$-0.337038\pi$
$773$	−12.6148	−	15.0337i	−0.453721	−	0.540724i	−0.943609	+	0.331061i	$0.892593\pi$
$774$	−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	−0.675631	−	0.737240i	$-0.736129\pi$
$787$	8.43438	−	14.6088i	0.300653	−	0.520747i	0.976284	+	0.216493i	$0.0694620\pi$
$788$	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	$0.172292\pi$
$797$			29.0909i			1.03045i	−0.857054	+	0.515227i	$0.827708\pi$
$798$	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	0.256446	−	0.966559i	$-0.417448\pi$
$809$	−12.8675	−	7.42903i	−0.452396	−	0.261191i	−0.708841	+	0.705368i	$0.750782\pi$
$810$	16.4759	+	11.5561i	0.578906	+	0.406039i
$811$	−4.24280	−	5.05637i	−0.148985	−	0.177553i	0.686391	−	0.727233i	$-0.259194\pi$
$811$	−4.24280	−	5.05637i	−0.148985	−	0.177553i	−0.835375	+	0.549680i	$0.814750\pi$
$812$	−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	−0.0527213	+	0.998609i	$0.516789\pi$
$821$	−18.7457	+	51.5033i	−0.654228	+	1.79748i	−0.601507	+	0.798868i	$0.705433\pi$
$822$	−14.6361	+	7.78093i	−0.510493	+	0.271391i
$823$	−34.2674	−	40.8383i	−1.19449	−	1.42353i	−0.880461	−	0.474119i	$-0.842767\pi$
$823$	−34.2674	−	40.8383i	−1.19449	−	1.42353i	−0.314026	−	0.949415i	$-0.601678\pi$
$824$	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	−0.199158	−	0.979967i	$-0.563821\pi$
$827$	−1.47054	+	0.259297i	−0.0511359	+	0.00901663i	0.148022	+	0.988984i	$0.452709\pi$
$828$	5.27494	−	21.1448i	0.183317	−	0.734834i
$829$	−22.4356	+	12.9532i	−0.779220	+	0.449883i	−0.836154	−	0.548495i	$-0.815201\pi$
$829$	−22.4356	+	12.9532i	−0.779220	+	0.449883i	0.0569335	+	0.998378i	$0.481868\pi$
$830$	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	0.948068	−	0.318067i	$-0.103034\pi$
$839$	23.1568	+	19.4309i	0.799463	+	0.670829i	−0.148605	+	0.988897i	$0.547478\pi$
$840$	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	0.689599	−	0.724191i	$-0.257787\pi$
$853$	31.8325	+	5.61292i	1.08992	+	0.192183i	0.400323	+	0.916374i	$0.368898\pi$
$854$	−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	−0.385001	−	0.922916i	$-0.625799\pi$
$857$	−31.1025	−	5.48420i	−1.06244	−	0.187337i	−0.677439	+	0.735579i	$0.736910\pi$
$858$	3.28079	−	5.24960i	0.112004	−	0.179218i
$859$	16.3134	+	5.93759i	0.556606	+	0.202588i	0.604979	−	0.796241i	$-0.293181\pi$
$859$	16.3134	+	5.93759i	0.556606	+	0.202588i	−0.0483731	+	0.998829i	$0.515404\pi$
$860$	−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	0.0871252	−	0.996197i	$-0.472232\pi$
$863$	−21.5052	−	12.4160i	−0.732044	−	0.422646i	−0.819170	+	0.573551i	$0.805565\pi$
$864$	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	0.528073	−	0.849199i	$-0.322915\pi$
$877$	−6.41225	−	5.38052i	−0.216526	−	0.181687i	−0.744599	+	0.667512i	$0.767359\pi$
$878$	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	−0.691640	−	0.722243i	$-0.743111\pi$
$881$	−12.2282	+	7.05997i	−0.411979	+	0.237856i	0.279660	+	0.960099i	$0.409778\pi$
$882$	23.1278	+	5.76964i	0.778755	+	0.194274i
$883$	3.17975	−	0.560675i	0.107007	−	0.0188682i	−0.119888	−	0.992787i	$-0.538254\pi$
$883$	3.17975	−	0.560675i	0.107007	−	0.0188682i	0.226895	+	0.973919i	$0.427143\pi$
$884$	−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	0.464690	−	0.885473i	$-0.346166\pi$
$887$	−14.5346	−	17.3216i	−0.488024	−	0.581604i	−0.952714	+	0.303869i	$0.901721\pi$
$888$	−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	−0.564394	−	0.825505i	$-0.690890\pi$
$907$	−14.0379	+	5.10938i	−0.466121	+	0.169654i	0.0982735	+	0.995159i	$0.468668\pi$
$908$	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	0.594655	−	0.803981i	$-0.297289\pi$
$919$	−12.0939	−	20.9472i	−0.398941	−	0.690986i	−0.993595	+	0.112996i	$0.963955\pi$
$920$	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	0.0876779	−	0.996149i	$-0.472055\pi$
$929$	−5.20086	−	0.917053i	−0.170635	−	0.0300875i	−0.258313	+	0.966061i	$0.583166\pi$
$930$	−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	0.638467	−	0.769649i	$-0.279569\pi$
$937$	−7.05135	−	8.40347i	−0.230358	−	0.274529i	−0.868825	+	0.495119i	$0.835124\pi$
$938$	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	0.996583	+	0.0825973i	$0.0263215\pi$
$941$	2.71024	+	15.3705i	0.0883513	+	0.501065i	−0.908232	+	0.418468i	$0.862567\pi$
$942$	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	0.555568	−	0.831471i	$-0.312501\pi$
$947$	−5.13292	−	4.30703i	−0.166798	−	0.139960i	−0.722366	+	0.691511i	$0.756945\pi$
$948$	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	−0.950197	−	0.311651i	$-0.899118\pi$
$953$	−14.7648	+	17.5960i	−0.478280	+	0.569992i	0.471917	+	0.881643i	$0.343562\pi$
$954$	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	0.523417	−	0.852076i	$-0.324657\pi$
$967$	22.5090	+	3.96895i	0.723842	+	0.127633i	0.200424	+	0.979709i	$0.435768\pi$
$968$		−	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	−0.883449	−	0.468527i	$-0.844785\pi$
$971$	3.33320	−	18.9035i	0.106967	−	0.606642i	0.990416	−	0.138114i	$-0.0441042\pi$
$972$	−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	−0.00575167	−	0.999983i	$-0.501831\pi$
$977$	−27.3386	−	15.7839i	−0.874639	−	0.504973i	−0.868887	+	0.495011i	$0.835164\pi$
$978$	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	0.997748	+	0.0670780i	$0.0213676\pi$
$983$	8.67049	+	23.8220i	0.276546	+	0.759803i	−0.721202	+	0.692725i	$0.756410\pi$
$984$	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	−0.0710725	+	0.997471i	$0.522642\pi$
$991$	−32.7724	+	39.0566i	−1.04105	+	1.24067i	−0.969976	+	0.243202i	$0.921802\pi$
$992$	−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	0.331342	−	0.943511i	$-0.392499\pi$
$997$	30.4828	−	5.37494i	0.965400	−	0.170226i	0.634059	+	0.773285i	$0.281388\pi$
$998$	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.59.14	yes	240
3.2	odd	2	inner	570.2.bf.a.59.25	yes	240
5.4	even	2	inner	570.2.bf.a.59.27	yes	240
15.14	odd	2	inner	570.2.bf.a.59.16	yes	240
19.10	odd	18	inner	570.2.bf.a.29.16	yes	240
57.29	even	18	inner	570.2.bf.a.29.27	yes	240
95.29	odd	18	inner	570.2.bf.a.29.25	yes	240
285.29	even	18	inner	570.2.bf.a.29.14	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.29.14	✓	240	285.29	even	18	inner
570.2.bf.a.29.16	yes	240	19.10	odd	18	inner
570.2.bf.a.29.25	yes	240	95.29	odd	18	inner
570.2.bf.a.29.27	yes	240	57.29	even	18	inner
570.2.bf.a.59.14	yes	240	1.1	even	1	trivial
570.2.bf.a.59.16	yes	240	15.14	odd	2	inner
570.2.bf.a.59.25	yes	240	3.2	odd	2	inner
570.2.bf.a.59.27	yes	240	5.4	even	2	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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