LMFDB - Embedded newform 570.2.bf.a.29.16

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			29.16
Character	$\chi$	$=$	570.29
Dual form			570.2.bf.a.59.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(1.28709 + 1.15905i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.01621 + 1.99181i) q^{5} +(-1.46880 - 0.917943i) q^{6} +(3.34801 + 1.93297i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.313195 + 2.98361i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(1.28709 + 1.15905i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.01621 + 1.99181i) q^{5} +(-1.46880 - 0.917943i) q^{6} +(3.34801 + 1.93297i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.313195 + 2.98361i) q^{9} +(0.654901 - 2.13801i) q^{10} +(-3.47920 + 2.00872i) q^{11} +(1.60589 + 0.648943i) q^{12} +(0.681504 + 0.571849i) q^{13} +(-3.63280 - 1.32223i) q^{14} +(-3.61657 + 1.38579i) 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} +(2.06877 + 6.36843i) q^{21} +(3.07753 - 2.58236i) q^{22} +(6.82620 - 2.48453i) q^{23} +(-1.69418 - 0.360225i) q^{24} +(-2.93462 - 4.04821i) q^{25} +(-0.770451 - 0.444820i) q^{26} +(-3.05505 + 4.20318i) q^{27} +(3.80722 + 0.671315i) q^{28} +(-1.08755 + 6.16782i) q^{29} +(3.32099 - 1.99275i) q^{30} +(1.50475 + 0.868765i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-6.80624 - 1.44718i) q^{33} +(1.11511 + 3.06373i) q^{34} +(-7.25241 + 4.70429i) q^{35} +(1.31476 + 2.69655i) q^{36} -2.85084 q^{37} +(3.84038 + 2.06191i) q^{38} +(0.214352 + 1.52592i) q^{39} +(-0.115839 - 2.23307i) q^{40} +(4.43975 - 3.72539i) q^{41} +(-3.14320 - 5.91244i) q^{42} +(-0.819901 + 2.25266i) q^{43} +(-2.58236 + 3.07753i) q^{44} +(-6.26105 - 2.40816i) q^{45} +(-6.29106 + 3.63214i) q^{46} +(1.50099 - 8.51256i) q^{47} +(1.73099 + 0.0605610i) q^{48} +(3.97278 + 6.88105i) q^{49} +(3.59300 + 3.47712i) q^{50} +(2.99282 - 4.78881i) q^{51} +(0.835988 + 0.304275i) q^{52} +(3.88287 + 10.6681i) q^{53} +(2.27876 - 4.66982i) q^{54} +(-0.465374 - 8.97119i) q^{55} -3.86595 q^{56} +(-1.28048 - 7.44045i) q^{57} -6.26297i q^{58} +(0.00803551 + 0.0455717i) q^{59} +(-2.92450 + 2.53916i) q^{60} +(-2.60033 + 0.946444i) q^{61} +(-1.63274 - 0.594270i) q^{62} +(-4.71865 + 10.5945i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-1.83157 + 0.776305i) q^{65} +(6.95414 + 0.243300i) q^{66} +(-0.646399 + 3.66591i) q^{67} +(-1.63018 - 2.82355i) q^{68} +(11.6656 + 4.71411i) q^{69} +(6.32534 - 5.89219i) q^{70} +(-11.9518 - 4.35011i) q^{71} +(-1.76304 - 2.42728i) 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} +(-0.476069 - 1.46552i) q^{78} +(7.79546 + 9.29027i) q^{79} +(0.501847 + 2.17902i) q^{80} +(-8.80382 + 1.86890i) q^{81} +(-3.72539 + 4.43975i) q^{82} +(1.50652 - 2.60937i) q^{83} +(4.12213 + 5.27680i) q^{84} +(6.97068 + 2.13521i) q^{85} +(0.416275 - 2.36081i) q^{86} +(-8.54860 + 6.67800i) q^{87} +(2.00872 - 3.47920i) q^{88} +(6.50540 + 5.45868i) q^{89} +(6.58411 + 1.28435i) q^{90} +(1.17631 + 3.23189i) q^{91} +(5.56477 - 4.66940i) q^{92} +(0.929796 + 2.86226i) q^{93} +8.64388i q^{94} +(8.85233 - 4.07875i) q^{95} +(-1.71521 + 0.240943i) q^{96} +(-2.39112 - 13.5607i) q^{97} +(-5.10730 - 6.08665i) q^{98} +(-7.08288 - 9.75144i) 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
$3$	1.28709	+	1.15905i	0.743101	+	0.669179i
$3$	1.28709	+	1.15905i	0.743101	+	0.669179i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	−1.01621	+	1.99181i	−0.454464	+	0.890765i
$5$	−1.01621	+	1.99181i	−0.454464	+	0.890765i
$6$	−1.46880	−	0.917943i	−0.599636	−	0.374749i
$7$	3.34801	+	1.93297i	1.26543	+	0.730595i	0.974120	−	0.226034i	$-0.0725759\pi$
$7$	3.34801	+	1.93297i	1.26543	+	0.730595i	0.291309	+	0.956629i	$0.405909\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	0.313195	+	2.98361i	0.104398	+	0.994536i
$10$	0.654901	−	2.13801i	0.207098	−	0.676099i
$11$	−3.47920	+	2.00872i	−1.04902	+	0.605651i	−0.922374	−	0.386298i	$-0.873754\pi$
$11$	−3.47920	+	2.00872i	−1.04902	+	0.605651i	−0.126643	+	0.991948i	$0.540420\pi$
$12$	1.60589	+	0.648943i	0.463580	+	0.187334i
$13$	0.681504	+	0.571849i	0.189015	+	0.158602i	0.732385	−	0.680891i	$-0.238407\pi$
$13$	0.681504	+	0.571849i	0.189015	+	0.158602i	−0.543370	+	0.839494i	$0.682852\pi$
$14$	−3.63280	−	1.32223i	−0.970907	−	0.353381i
$15$	−3.61657	+	1.38579i	−0.933794	+	0.357810i
$16$	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
$21$	2.06877	+	6.36843i	0.451442	+	1.38970i
$22$	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	$0.115380\pi$
$24$	−1.69418	−	0.360225i	−0.345823	−	0.0735305i
$25$	−2.93462	−	4.04821i	−0.586924	−	0.809642i
$26$	−0.770451	−	0.444820i	−0.151098	−	0.0872364i
$27$	−3.05505	+	4.20318i	−0.587944	+	0.808902i
$28$	3.80722	+	0.671315i	0.719496	+	0.126867i
$29$	−1.08755	+	6.16782i	−0.201953	+	1.14534i	0.700209	+	0.713938i	$0.253090\pi$
$29$	−1.08755	+	6.16782i	−0.201953	+	1.14534i	−0.902162	+	0.431397i	$0.858021\pi$
$30$	3.32099	−	1.99275i	0.606326	−	0.363825i
$31$	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
$33$	−6.80624	−	1.44718i	−1.18481	−	0.251921i
$34$	1.11511	+	3.06373i	0.191239	+	0.525425i
$35$	−7.25241	+	4.70429i	−1.22588	+	0.795170i
$36$	1.31476	+	2.69655i	0.219127	+	0.449426i
$37$	−2.85084			−0.468674			−0.234337	−	0.972155i	$-0.575292\pi$
$37$	−2.85084			−0.468674			−0.234337	+	0.972155i	$0.575292\pi$
$38$	3.84038	+	2.06191i	0.622992	+	0.334486i
$39$	0.214352	+	1.52592i	0.0343238	+	0.244343i
$40$	−0.115839	−	2.23307i	−0.0183157	−	0.353079i
$41$	4.43975	−	3.72539i	0.693373	−	0.581809i	−0.226507	−	0.974010i	$-0.572731\pi$
$41$	4.43975	−	3.72539i	0.693373	−	0.581809i	0.919880	+	0.392201i	$0.128286\pi$
$42$	−3.14320	−	5.91244i	−0.485007	−	0.912309i
$43$	−0.819901	+	2.25266i	−0.125034	+	0.343527i	−0.986378	−	0.164494i	$-0.947401\pi$
$43$	−0.819901	+	2.25266i	−0.125034	+	0.343527i	0.861344	+	0.508022i	$0.169623\pi$
$44$	−2.58236	+	3.07753i	−0.389305	+	0.463955i
$45$	−6.26105	−	2.40816i	−0.933343	−	0.358987i
$46$	−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	$-0.161562\pi$
$48$	1.73099	+	0.0605610i	0.249847	+	0.00874123i
$49$	3.97278	+	6.88105i	0.567539	+	0.983007i
$50$	3.59300	+	3.47712i	0.508127	+	0.491739i
$51$	2.99282	−	4.78881i	0.419078	−	0.670568i
$52$	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	$0.604255\pi$
$54$	2.27876	−	4.66982i	0.310100	−	0.635482i
$55$	−0.465374	−	8.97119i	−0.0627510	−	1.20967i
$56$	−3.86595			−0.516609
$57$	−1.28048	−	7.44045i	−0.169604	−	0.985512i
$58$		−	6.26297i		−	0.822368i
$59$	0.00803551	+	0.0455717i	0.00104613	+	0.00593293i	0.985326	−	0.170681i	$-0.0545967\pi$
$59$	0.00803551	+	0.0455717i	0.00104613	+	0.00593293i	−0.984280	+	0.176614i	$0.943486\pi$
$60$	−2.92450	+	2.53916i	−0.377551	+	0.327804i
$61$	−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
$63$	−4.71865	+	10.5945i	−0.594495	+	1.33479i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−1.83157	+	0.776305i	−0.227178	+	0.0962888i
$66$	6.95414	+	0.243300i	0.855996	+	0.0299481i
$67$	−0.646399	+	3.66591i	−0.0789702	+	0.447862i	0.919525	+	0.393031i	$0.128573\pi$
$67$	−0.646399	+	3.66591i	−0.0789702	+	0.447862i	−0.998496	+	0.0548318i	$0.982538\pi$
$68$	−1.63018	−	2.82355i	−0.197688	−	0.342405i
$69$	11.6656	+	4.71411i	1.40438	+	0.567512i
$70$	6.32534	−	5.89219i	0.756023	−	0.704251i
$71$	−11.9518	−	4.35011i	−1.41842	−	0.516263i	−0.484831	−	0.874608i	$-0.661119\pi$
$71$	−11.9518	−	4.35011i	−1.41842	−	0.516263i	−0.933589	+	0.358345i	$0.883341\pi$
$72$	−1.76304	−	2.42728i	−0.207776	−	0.286058i
$73$	7.68577	+	9.15955i	0.899552	+	1.07204i	0.997046	+	0.0768078i	$0.0244728\pi$
$73$	7.68577	+	9.15955i	0.899552	+	1.07204i	−0.0974943	+	0.995236i	$0.531083\pi$
$74$	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
$78$	−0.476069	−	1.46552i	−0.0539042	−	0.165937i
$79$	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	$0.538788\pi$
$80$	0.501847	+	2.17902i	0.0561082	+	0.243622i
$81$	−8.80382	+	1.86890i	−0.978202	+	0.207656i
$82$	−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	$0.113787\pi$
$84$	4.12213	+	5.27680i	0.449762	+	0.575747i
$85$	6.97068	+	2.13521i	0.756076	+	0.231596i
$86$	0.416275	−	2.36081i	0.0448881	−	0.254573i
$87$	−8.54860	+	6.67800i	−0.916506	+	0.715957i
$88$	2.00872	−	3.47920i	0.214130	−	0.370884i
$89$	6.50540	+	5.45868i	0.689571	+	0.578618i	0.918785	−	0.394757i	$-0.129171\pi$
$89$	6.50540	+	5.45868i	0.689571	+	0.578618i	−0.229215	+	0.973376i	$0.573616\pi$
$90$	6.58411	+	1.28435i	0.694026	+	0.135382i
$91$	1.17631	+	3.23189i	0.123311	+	0.338794i
$92$	5.56477	−	4.66940i	0.580167	−	0.486818i
$93$	0.929796	+	2.86226i	0.0964154	+	0.296802i
$94$			8.64388i			0.891548i
$95$	8.85233	−	4.07875i	0.908230	−	0.418471i
$96$	−1.71521	+	0.240943i	−0.175058	+	0.0245911i
$97$	−2.39112	−	13.5607i	−0.242782	−	1.37688i	−0.825588	−	0.564273i	$-0.809157\pi$
$97$	−2.39112	−	13.5607i	−0.242782	−	1.37688i	0.582806	−	0.812611i	$-0.301955\pi$
$98$	−5.10730	−	6.08665i	−0.515915	−	0.614844i
$99$	−7.08288	−	9.75144i	−0.711857	−	0.980056i
$100$	−4.14221	−	2.80037i	−0.414221	−	0.280037i
$101$	10.6630	−	12.7077i	1.06101	−	1.26447i	0.0979496	−	0.995191i	$-0.468772\pi$
$101$	10.6630	−	12.7077i	1.06101	−	1.26447i	0.963063	−	0.269275i	$-0.0867840\pi$
$102$	−2.11578	+	5.23576i	−0.209494	+	0.518417i
$103$	3.57794	+	6.19717i	0.352545	+	0.610626i	0.986695	−	0.162585i	$-0.0519830\pi$
$103$	3.57794	+	6.19717i	0.352545	+	0.610626i	−0.634150	+	0.773210i	$0.718650\pi$
$104$	−0.876124	−	0.154484i	−0.0859110	−	0.0151484i
$105$	−14.7870	−	2.35109i	−1.44306	−	0.229443i
$106$	−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	$0.594203\pi$
$108$	−1.43323	+	4.99458i	−0.137913	+	0.480604i
$109$	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	$-0.00136966\pi$
$110$	2.01613	+	8.75408i	0.192231	+	0.834669i
$111$	−3.66928	−	3.30427i	−0.348272	−	0.313627i
$112$	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	$0.934801\pi$
$114$	2.55305	+	7.10506i	0.239115	+	0.665450i
$115$	−1.98816	+	16.1213i	−0.185396	+	1.50332i
$116$	1.08755	+	6.16782i	0.100977	+	0.572668i
$117$	−1.49273	+	2.21244i	−0.138003	+	0.204540i
$118$	−0.0158269	−	0.0434840i	−0.00145698	−	0.00400302i
$119$	4.31094	−	11.8442i	0.395183	−	1.08576i
$120$	2.43915	−	3.00842i	0.222662	−	0.274630i
$121$	2.56988	−	4.45116i	0.233625	−	0.404651i
$122$	2.39648	−	1.38361i	0.216967	−	0.125266i
$123$	10.0323	+	0.350992i	0.904580	+	0.0316479i
$124$	1.71113	+	0.301719i	0.153664	+	0.0270952i
$125$	11.0455	−	1.73136i	0.987937	−	0.154858i
$126$	2.80725	−	11.2530i	0.250089	−	1.00249i
$127$	2.47835	+	2.07958i	0.219918	+	0.184533i	0.746090	−	0.665845i	$-0.231929\pi$
$127$	2.47835	+	2.07958i	0.219918	+	0.184533i	−0.526172	+	0.850378i	$0.676373\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	−3.66624	+	1.94906i	−0.322794	+	0.171606i
$130$	1.66894	−	1.08256i	0.146376	−	0.0949468i
$131$	7.71257	−	1.35993i	0.673851	−	0.118818i	0.173756	−	0.984789i	$-0.444410\pi$
$131$	7.71257	−	1.35993i	0.673851	−	0.118818i	0.500095	+	0.865971i	$0.333299\pi$
$132$	−6.89074	+	0.967970i	−0.599762	+	0.0842510i
$133$	−6.24943	−	15.6496i	−0.541894	−	1.35699i
$134$		−	3.72246i		−	0.321572i
$135$	−5.26735	−	10.3564i	−0.453341	−	0.891337i
$136$	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	$0.254832\pi$
$138$	−12.3070	−	2.61678i	−1.04764	−	0.222755i
$139$	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	$0.345585\pi$
$140$	−5.20608	+	6.90105i	−0.439994	+	0.583245i
$141$	11.7984	−	9.21669i	0.993606	−	0.776185i
$142$	12.5256	+	2.20861i	1.05113	+	0.185342i
$143$	−3.51977	−	0.620630i	−0.294338	−	0.0518997i
$144$	2.15775	+	2.08426i	0.179812	+	0.173688i
$145$	−11.1799	−	8.43402i	−0.928444	−	0.700407i
$146$	−9.15955	−	7.68577i	−0.758049	−	0.636079i
$147$	−2.86218	+	13.4612i	−0.236069	+	1.11026i
$148$	−2.67891	+	0.975043i	−0.220205	+	0.0801480i
$149$	−12.7509	−	15.1960i	−1.04460	−	1.24490i	−0.968817	−	0.247779i	$-0.920299\pi$
$149$	−12.7509	−	15.1960i	−1.04460	−	1.24490i	−0.0757813	−	0.997124i	$-0.524145\pi$
$150$	0.594350	+	8.63983i	0.0485285	+	0.705440i
$151$		−	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
$155$	−3.25956	+	2.11432i	−0.261814	+	0.169826i
$156$	0.723320	+	1.36058i	0.0579120	+	0.108934i
$157$	7.45824	−	20.4913i	0.595232	−	1.63539i	−0.165417	−	0.986224i	$-0.552897\pi$
$157$	7.45824	−	20.4913i	0.595232	−	1.63539i	0.760649	−	0.649163i	$-0.224881\pi$
$158$	−9.29027	−	7.79546i	−0.739094	−	0.620173i
$159$	−7.36729	+	18.2313i	−0.584264	+	1.44583i
$160$	−0.872606	−	2.05878i	−0.0689856	−	0.162761i
$161$	27.6567	+	4.87662i	2.17965	+	0.384332i
$162$	8.34554	−	3.36927i	0.655687	−	0.264715i
$163$	2.24857	−	1.29821i	0.176121	−	0.101684i	−0.409348	−	0.912378i	$-0.634244\pi$
$163$	2.24857	−	1.29821i	0.176121	−	0.101684i	0.585469	+	0.810695i	$0.300910\pi$
$164$	2.89784	−	5.01921i	0.226283	−	0.391934i
$165$	9.79910	−	12.0861i	0.762859	−	0.940902i
$166$	−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	$-0.427317\pi$
$168$	−4.97582	−	4.48084i	−0.383893	−	0.345704i
$169$	−2.11999	−	12.0231i	−0.163076	−	0.924851i
$170$	−7.23555	−	0.892322i	−0.554942	−	0.0684380i
$171$	6.97578	−	11.0607i	0.533452	−	0.845831i
$172$			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	$0.368451\pi$
$174$	7.25911	−	8.06099i	0.550312	−	0.611102i
$175$	−2.00005	−	19.2260i	−0.151190	−	1.45335i
$176$	−1.37404	+	3.77515i	−0.103572	+	0.284563i
$177$	−0.0424775	+	0.0679684i	−0.00319281	+	0.00510882i
$178$	−7.35445	−	4.24610i	−0.551240	−	0.318258i
$179$	3.65830	+	6.33636i	0.273434	+	0.473602i	0.969739	−	0.244145i	$-0.0785071\pi$
$179$	3.65830	+	6.33636i	0.273434	+	0.473602i	−0.696305	+	0.717746i	$0.745174\pi$
$180$	−6.70710	−	0.121521i	−0.499918	−	0.00905762i
$181$	−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
$183$	−4.44384	−	1.79577i	−0.328498	−	0.132747i
$184$	−4.66940	+	5.56477i	−0.344232	+	0.410240i
$185$	2.89706	−	5.67832i	0.212996	−	0.417479i
$186$	−1.41270	−	2.65731i	−0.103584	−	0.194844i
$187$	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
$190$	−8.00958	+	5.55397i	−0.581076	+	0.402928i
$191$			23.4715i			1.69834i	0.528121	+	0.849169i	$0.322897\pi$
$191$			23.4715i			1.69834i	−0.528121	+	0.849169i	$0.677103\pi$
$192$	1.64731	−	0.535125i	0.118885	−	0.0386193i
$193$	16.7865	−	14.0855i	1.20832	−	1.01390i	0.208964	−	0.977923i	$-0.432991\pi$
$193$	16.7865	−	14.0855i	1.20832	−	1.01390i	0.999353	−	0.0359748i	$-0.0114536\pi$
$194$	4.70959	+	12.9395i	0.338129	+	0.929002i
$195$	−3.25717	−	1.12371i	−0.233251	−	0.0804706i
$196$	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	$0.0243938\pi$
$198$	8.66860	+	8.37336i	0.616051	+	0.595069i
$199$	−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	$0.948341\pi$
$200$	4.56556	+	2.03854i	0.322834	+	0.144147i
$201$	−5.08096	+	3.96914i	−0.358383	+	0.279962i
$202$	−8.29438	+	14.3663i	−0.583591	+	1.01081i
$203$	−15.5634	+	18.5477i	−1.09233	+	1.30179i
$204$	1.17446	−	5.52361i	0.0822285	−	0.386730i
$205$	2.90854	+	12.6289i	0.203142	+	0.882043i
$206$	−4.59971	−	5.48172i	−0.320477	−	0.381930i
$207$	9.55080	+	19.5886i	0.663826	+	1.36150i
$208$	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
$213$	−10.3410	−	19.4518i	−0.708557	−	1.33281i
$214$	−4.38751	−	1.59692i	−0.299924	−	0.109163i
$215$	−3.65368	−	3.92227i	−0.249179	−	0.267497i
$216$	0.544161	−	5.16758i	0.0370254	−	0.351609i
$217$	3.35860	+	5.81727i	0.227997	+	0.394902i
$218$	−1.25477	+	7.11617i	−0.0849840	+	0.481968i
$219$	−0.724124	+	20.6974i	−0.0489318	+	1.39860i
$220$	−3.50564	−	8.27099i	−0.236350	−	0.557630i
$221$	1.45027	−	2.51194i	0.0975557	−	0.168971i
$222$	4.18731	+	2.61690i	0.281034	+	0.175635i
$223$	−16.6715	−	6.06793i	−1.11641	−	0.406339i	−0.283067	−	0.959100i	$-0.591352\pi$
$223$	−16.6715	−	6.06793i	−1.11641	−	0.406339i	−0.833339	+	0.552762i	$0.813574\pi$
$224$	−3.63280	+	1.32223i	−0.242727	+	0.0883453i
$225$	11.1592	−	10.0236i	0.743944	−	0.668242i
$226$	−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	$0.907795\pi$
$228$	−3.74804	−	6.55379i	−0.248220	−	0.434035i
$229$	−0.547836			−0.0362020			−0.0181010	−	0.999836i	$-0.505762\pi$
$229$	−0.547836			−0.0362020			−0.0181010	+	0.999836i	$0.505762\pi$
$230$	−0.841486	−	16.2216i	−0.0554860	−	1.06962i
$231$	−19.9900	−	18.0015i	−1.31525	−	1.18441i
$232$	−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	$0.594147\pi$
$234$	1.08587	−	2.43804i	0.0709853	−	0.159379i
$235$	15.4301	+	11.6403i	1.00655	+	0.759328i
$236$	0.0231373	+	0.0400751i	0.00150611	+	0.00260866i
$237$	−0.734459	+	20.9927i	−0.0477082	+	1.36363i
$238$	−2.18872	+	12.4129i	−0.141874	+	0.804606i
$239$	−7.05910	+	4.07557i	−0.456615	+	0.263627i	−0.710620	−	0.703576i	$-0.751585\pi$
$239$	−7.05910	+	4.07557i	−0.456615	+	0.263627i	0.254005	+	0.967203i	$0.418252\pi$
$240$	−1.87968	+	3.38627i	−0.121333	+	0.218582i
$241$	−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
$243$	−13.4974	−	7.79865i	−0.865862	−	0.500283i
$244$	−2.11981	+	1.77873i	−0.135707	+	0.113872i
$245$	−17.7429	+	0.920403i	−1.13355	+	0.0588024i
$246$	−9.94082	+	1.39643i	−0.633803	+	0.0890329i
$247$	−0.790921	−	3.79634i	−0.0503251	−	0.241555i
$248$	−1.73753			−0.110333
$249$	4.96343	−	1.61236i	0.314544	−	0.102179i
$250$	−10.5770	+	3.62309i	−0.668949	+	0.229144i
$251$	0.846815	+	2.32661i	0.0534505	+	0.146854i	0.963545	−	0.267547i	$-0.0862132\pi$
$251$	0.846815	+	2.32661i	0.0534505	+	0.146854i	−0.910094	+	0.414401i	$0.863991\pi$
$252$	−0.810539	+	11.5695i	−0.0510592	+	0.728809i
$253$	−18.7590	+	22.3561i	−1.17937	+	1.40551i
$254$	−2.80181	−	1.61763i	−0.175801	−	0.101499i
$255$	6.49707	+	10.8276i	0.406862	+	0.678049i
$256$	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	$0.639389\pi$
$258$	3.27209	−	2.55609i	0.203711	−	0.159135i
$259$	−9.54462	−	5.51059i	−0.593074	−	0.342411i
$260$	−1.45560	+	1.35592i	−0.0902725	+	0.0840907i
$261$	−18.7430	−	1.31310i	−1.16016	−	0.0812789i
$262$	−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	$0.268099\pi$
$264$	6.61797	−	2.14983i	0.407308	−	0.132313i
$265$	−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	$-0.978097\pi$
$269$	−18.0932	+	15.1820i	−1.10316	+	0.925661i	−0.105527	+	0.994416i	$0.533653\pi$
$270$	6.98570	+	9.28440i	0.425136	+	0.565030i
$271$	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
$273$	−2.23191	+	5.52313i	−0.135081	+	0.334275i
$274$	−8.28792	+	4.78503i	−0.500692	+	0.289074i
$275$	18.3418	+	8.18970i	1.10605	+	0.493858i
$276$	12.5744	+	0.439933i	0.756891	+	0.0264808i
$277$	9.66682	−	5.58114i	0.580823	−	0.335338i	−0.180638	−	0.983550i	$-0.557816\pi$
$277$	9.66682	−	5.58114i	0.580823	−	0.335338i	0.761460	+	0.648212i	$0.224483\pi$
$278$	−18.9061	−	10.9154i	−1.13391	−	0.654664i
$279$	−2.12078	+	4.76166i	−0.126967	+	0.285073i
$280$	3.92863	−	7.70024i	0.234780	−	0.460177i
$281$	−18.5627	+	6.75629i	−1.10736	+	0.403046i	−0.830025	−	0.557727i	$-0.811674\pi$
$281$	−18.5627	+	6.75629i	−1.10736	+	0.403046i	−0.277336	+	0.960773i	$0.589452\pi$
$282$	−10.0187	+	11.1254i	−0.596606	+	0.662510i
$283$	3.30932	−	0.583522i	0.196719	−	0.0346868i	−0.0744206	−	0.997227i	$-0.523711\pi$
$283$	3.30932	−	0.583522i	0.196719	−	0.0346868i	0.271139	+	0.962540i	$0.412600\pi$
$284$	−12.7189			−0.754725
$285$	16.1212	+	5.01061i	0.954939	+	0.296803i
$286$	3.57407			0.211339
$287$	22.0654	−	3.89073i	1.30248	−	0.229662i
$288$	−2.48689	−	1.67790i	−0.146542	−	0.0988715i
$289$	5.98594	−	2.17871i	0.352114	−	0.128159i
$290$	12.4746	+	6.36451i	0.732536	+	0.373737i
$291$	12.6400	−	20.2253i	0.740971	−	1.18563i
$292$	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	$0.138480\pi$
$294$	0.481191	−	13.7537i	0.0280636	−	0.802131i
$295$	−0.0989359	−	0.0303053i	−0.00576027	−	0.00176444i
$296$	2.46890	−	1.42542i	0.143502	−	0.0828507i
$297$	2.18613	−	20.7604i	0.126852	−	1.20464i
$298$	15.1960	+	12.7509i	0.880280	+	0.738642i
$299$	6.07286	+	2.21034i	0.351202	+	0.127827i
$300$	−2.08561	−	8.40537i	−0.120413	−	0.485284i
$301$	−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
$306$	−8.79171	+	4.28658i	−0.502589	+	0.245048i
$307$	−21.0299	+	17.6462i	−1.20024	+	1.00712i	−0.200616	+	0.979670i	$0.564294\pi$
$307$	−21.0299	+	17.6462i	−1.20024	+	1.00712i	−0.999623	+	0.0274503i	$0.991261\pi$
$308$	−14.5945	+	5.31198i	−0.831601	+	0.302678i
$309$	−2.57772	+	12.1233i	−0.146642	+	0.689672i
$310$	2.84289	−	2.64821i	0.161465	−	0.150408i
$311$	−12.0317	−	6.94649i	−0.682254	−	0.393899i	0.118450	−	0.992960i	$-0.462207\pi$
$311$	−12.0317	−	6.94649i	−0.682254	−	0.393899i	−0.800704	+	0.599061i	$0.795541\pi$
$312$	−0.948594	−	1.21431i	−0.0537036	−	0.0687467i
$313$	−2.56217	−	0.451779i	−0.144822	−	0.0255361i	0.100767	−	0.994910i	$-0.467870\pi$
$313$	−2.56217	−	0.451779i	−0.144822	−	0.0255361i	−0.245589	+	0.969374i	$0.578981\pi$
$314$	−3.78665	+	21.4751i	−0.213693	+	1.21191i
$315$	−16.3072	−	20.1650i	−0.918804	−	1.13617i
$316$	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	$0.0634679\pi$
$318$	4.08954	−	19.2336i	0.229330	−	1.07857i
$319$	−8.60558	−	23.6436i	−0.481820	−	1.32379i
$320$	1.21685	+	1.87597i	0.0680241	+	0.104870i
$321$	2.49855	+	7.69145i	0.139455	+	0.429295i
$322$	−28.0834			−1.56502
$323$	−6.72255	+	12.5210i	−0.374053	+	0.696687i
$324$	−7.63368	+	4.76727i	−0.424093	+	0.264849i
$325$	0.315012	−	4.43703i	0.0174737	−	0.246122i
$326$	−1.98897	+	1.66895i	−0.110159	+	0.0924344i
$327$	11.0511	−	5.87505i	0.611128	−	0.324891i
$328$	−1.98224	+	5.44616i	−0.109451	+	0.300714i
$329$	21.4799	−	25.5987i	1.18423	−	1.41130i
$330$	−7.55150	+	13.6041i	−0.415696	+	0.748880i
$331$	−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
$333$	−0.892867	−	8.50577i	−0.0489288	−	0.466113i
$334$	10.8278	+	18.7543i	0.592471	+	1.02619i
$335$	−6.64492	−	5.01285i	−0.363051	−	0.273881i
$336$	5.67831	+	3.54872i	0.309777	+	0.193599i
$337$	−21.6519	−	7.88064i	−1.17945	−	0.429286i	−0.323444	−	0.946247i	$-0.604841\pi$
$337$	−21.6519	−	7.88064i	−1.17945	−	0.429286i	−0.856009	+	0.516962i	$0.827063\pi$
$338$	4.17557	+	11.4723i	0.227121	+	0.624010i
$339$	−5.01211	+	5.56578i	−0.272221	+	0.302292i
$340$	7.28058	−	0.377675i	0.394845	−	0.0204823i
$341$	−6.98041			−0.378010
$342$	−4.94914	+	12.1040i	−0.267619	+	0.654508i
$343$			3.65545i			0.197376i
$344$	−0.416275	−	2.36081i	−0.0224440	−	0.127286i
$345$	−21.2444	+	18.4452i	−1.14376	+	0.993055i
$346$	−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	$0.507142\pi$
$348$	−5.74905	+	9.19906i	−0.308181	+	0.493121i
$349$	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	$-0.0369016\pi$
$350$	5.30822	+	18.5866i	0.283737	+	0.993495i
$351$	−4.48561	+	1.11745i	−0.239424	+	0.0596452i
$352$	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	$0.565533\pi$
$354$	0.0300296	−	0.0743119i	0.00159606	−	0.00394963i
$355$	20.8102	−	19.3851i	1.10449	−	1.02886i
$356$	7.98005	+	2.90450i	0.422942	+	0.153938i
$357$	19.2766	−	10.2479i	1.02023	−	0.542379i
$358$	−4.70302	−	5.60484i	−0.248562	−	0.296225i
$359$	−17.4683	+	3.08014i	−0.921943	+	0.162563i	−0.614422	−	0.788978i	$-0.710611\pi$
$359$	−17.4683	+	3.08014i	−0.921943	+	0.162563i	−0.307521	+	0.951541i	$0.599500\pi$
$360$	6.62631	−	1.04500i	0.349237	−	0.0550764i
$361$	4.44742	+	18.4722i	0.234075	+	0.972219i
$362$	11.5254			0.605762
$363$	8.46679	−	2.75041i	0.444391	−	0.144359i
$364$	2.21074	+	2.63466i	0.115874	+	0.138094i
$365$	−26.0545	+	6.00055i	−1.36375	+	0.314083i
$366$	4.68816	+	0.996819i	0.245054	+	0.0521046i
$367$	0.560061	−	0.667455i	0.0292350	−	0.0348409i	−0.751229	−	0.660042i	$-0.770539\pi$
$367$	0.560061	−	0.667455i	0.0292350	−	0.0348409i	0.780464	+	0.625201i	$0.214983\pi$
$368$	3.63214	−	6.29106i	0.189339	−	0.327944i
$369$	12.5056	+	12.0797i	0.651016	+	0.628844i
$370$	−1.86701	+	6.09513i	−0.0970614	+	0.316871i
$371$	−7.62128	+	43.2224i	−0.395677	+	2.24400i
$372$	1.85267	+	2.37163i	0.0960566	+	0.122963i
$373$	7.46389	−	12.9278i	0.386466	−	0.669378i	−0.605506	−	0.795841i	$-0.707029\pi$
$373$	7.46389	−	12.9278i	0.386466	−	0.669378i	0.991971	+	0.126463i	$0.0403624\pi$
$374$	−10.0338	−	8.41939i	−0.518837	−	0.435356i
$375$	16.2232	+	10.5739i	0.837764	+	0.546032i
$376$	2.95638	+	8.12259i	0.152464	+	0.418891i
$377$	−4.26823	+	3.58147i	−0.219825	+	0.184455i
$378$	16.6560	−	11.2298i	0.856690	−	0.577600i
$379$		−	15.9056i		−	0.817015i	−0.912755	−	0.408507i	$-0.866049\pi$
$379$		−	15.9056i		−	0.817015i	0.912755	−	0.408507i	$-0.133951\pi$
$380$	6.92346	−	6.86044i	0.355166	−	0.351933i
$381$	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	$0.484110\pi$
$384$	−1.52936	+	0.813048i	−0.0780450	+	0.0414907i
$385$	15.7830	−	30.9352i	0.804376	−	1.57660i
$386$	−14.0855	+	16.7865i	−0.716934	+	0.854409i
$387$	−6.97784	−	1.74074i	−0.354703	−	0.0884868i
$388$	−6.88497	−	11.9251i	−0.349531	−	0.605406i
$389$	4.85075	+	0.855317i	0.245943	+	0.0433663i	0.295260	−	0.955417i	$-0.404594\pi$
$389$	4.85075	+	0.855317i	0.245943	+	0.0433663i	−0.0493178	+	0.998783i	$0.515705\pi$
$390$	3.40282	+	0.541038i	0.172308	+	0.0273965i
$391$	−11.8421	−	20.5111i	−0.598879	−	1.03729i
$392$	−6.88105	−	3.97278i	−0.347545	−	0.200655i
$393$	11.5030	+	7.18892i	0.580250	+	0.362633i
$394$	−4.14982	+	11.4015i	−0.209065	+	0.574401i
$395$	−26.4263	+	6.08619i	−1.32965	+	0.306229i
$396$	−9.99092	−	6.74087i	−0.502063	−	0.338741i
$397$	−30.3973	+	5.35986i	−1.52560	+	0.269004i	−0.872629	−	0.488383i	$-0.837587\pi$
$397$	−30.3973	+	5.35986i	−1.52560	+	0.269004i	−0.652966	+	0.757387i	$0.726476\pi$
$398$		−	9.32432i		−	0.467386i
$399$	10.0951	−	27.3858i	0.505389	−	1.37101i
$400$	−4.85019	−	1.21477i	−0.242509	−	0.0607385i
$401$	−5.52383	−	31.3272i	−0.275847	−	1.56441i	−0.736258	−	0.676701i	$-0.763409\pi$
$401$	−5.52383	−	31.3272i	−0.275847	−	1.56441i	0.460411	−	0.887706i	$-0.347702\pi$
$402$	4.31453	−	4.79114i	0.215189	−	0.238960i
$403$	0.528686	+	1.45255i	0.0263358	+	0.0723569i
$404$	5.67369	−	15.5883i	0.282277	−	0.775549i
$405$	5.22406	−	19.4347i	0.259586	−	0.965720i
$406$	12.1062	−	20.9685i	0.600818	−	1.04065i
$407$	9.91862	−	5.72652i	0.491648	−	0.283853i
$408$	−0.197450	+	5.64364i	−0.00977524	+	0.279402i
$409$	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	$0.362025\pi$
$410$	−5.05735	−	11.9320i	−0.249765	−	0.589280i
$411$	15.3684	+	6.21043i	0.758070	+	0.306338i
$412$	5.48172	+	4.59971i	0.270065	+	0.226611i
$413$	−0.0611859	+	0.168107i	−0.00301076	+	0.00827199i
$414$	−12.8072	−	17.6325i	−0.629440	−	0.866589i
$415$	3.66643	+	5.65238i	0.179978	+	0.277465i
$416$	−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	$-0.159347\pi$
$420$	−14.6994	+	2.84815i	−0.717256	+	0.138976i
$421$	−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
$423$	25.8682	+	1.81229i	1.25776	+	0.0881164i
$424$	−8.69672	−	7.29742i	−0.422350	−	0.354394i
$425$	−11.3366	+	11.7144i	−0.549907	+	0.568234i
$426$	13.5617	+	17.3605i	0.657067	+	0.841121i
$427$	−10.5354	−	1.85767i	−0.509843	−	0.0898991i
$428$	4.59815	+	0.810778i	0.222260	+	0.0391904i
$429$	−3.81091	−	4.87840i	−0.183993	−	0.235532i
$430$	4.27926	+	3.22823i	0.206364	+	0.155679i
$431$	10.7509	+	9.02106i	0.517852	+	0.434529i	0.863882	−	0.503694i	$-0.168026\pi$
$431$	10.7509	+	9.02106i	0.517852	+	0.434529i	−0.346030	+	0.938223i	$0.612471\pi$
$432$	0.361447	+	5.18357i	0.0173901	+	0.249394i
$433$	−5.13986	+	1.87075i	−0.247006	+	0.0899027i	−0.462556	−	0.886590i	$-0.653068\pi$
$433$	−5.13986	+	1.87075i	−0.247006	+	0.0899027i	0.215550	+	0.976493i	$0.430845\pi$
$434$	−4.31773	−	5.14567i	−0.207258	−	0.247000i
$435$	−4.61411	−	23.8135i	−0.221229	−	1.14177i
$436$		−	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	$0.668191\pi$
$440$	4.88862	+	7.53659i	0.233056	+	0.359293i
$441$	−19.2861	+	14.0083i	−0.918385	+	0.667062i
$442$	−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	$-0.651953\pi$
$444$	−4.57812	−	1.85003i	−0.217268	−	0.0877985i
$445$	−17.4835	+	7.41034i	−0.828798	+	0.351284i
$446$	17.4719	+	3.08077i	0.827319	+	0.145879i
$447$	1.20135	−	34.3376i	0.0568217	−	1.62411i
$448$	3.34801	−	1.93297i	0.158179	−	0.0913244i
$449$	8.43082	−	14.6026i	0.397875	−	0.689140i	−0.595589	−	0.803290i	$-0.703081\pi$
$449$	8.43082	−	14.6026i	0.397875	−	0.689140i	0.993464	+	0.114150i	$0.0364145\pi$
$450$	−9.24904	+	11.8091i	−0.436004	+	0.556687i
$451$	−7.96352	+	21.8796i	−0.374987	+	1.03027i
$452$	1.47900	+	4.06353i	0.0695665	+	0.191132i
$453$	7.62246	−	8.46448i	0.358134	−	0.397696i
$454$	−1.49461	−	8.47638i	−0.0701457	−	0.397816i
$455$	−7.63269	−	0.941298i	−0.357826	−	0.0441287i
$456$	4.82916	+	5.80338i	0.226146	+	0.271768i
$457$		−	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
$459$	15.2253	+	7.42956i	0.710655	+	0.346782i
$460$	3.64556	+	15.8291i	0.169975	+	0.738034i
$461$	4.22524	−	11.6088i	0.196789	−	0.540674i	−0.801572	−	0.597898i	$-0.796003\pi$
$461$	4.22524	−	11.6088i	0.196789	−	0.540674i	0.998361	+	0.0572241i	$0.0182249\pi$
$462$	22.8122	+	14.2567i	1.06132	+	0.663284i
$463$	−30.4784	−	17.5967i	−1.41645	−	0.817789i	−0.420467	−	0.907308i	$-0.638134\pi$
$463$	−30.4784	−	17.5967i	−1.41645	−	0.817789i	−0.995985	+	0.0895191i	$0.971467\pi$
$464$	3.13148	+	5.42389i	0.145375	+	0.251798i
$465$	−6.64595	−	1.05669i	−0.308198	−	0.0490026i
$466$	−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	$0.781455\pi$
$468$	−0.646009	+	2.58956i	−0.0298618	+	0.119702i
$469$	−9.25026	+	11.0240i	−0.427137	+	0.509042i
$470$	−17.2170	−	8.78403i	−0.794160	−	0.405177i
$471$	33.3499	−	17.7297i	1.53668	−	0.816941i
$472$	−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
$475$	−0.871771	+	21.7771i	−0.0399996	+	0.999200i
$476$		−	12.6043i		−	0.577719i
$477$	−30.6133	+	14.9262i	−1.40169	+	0.683422i
$478$	6.24414	−	5.23946i	0.285600	−	0.239647i
$479$	12.2466	+	33.6473i	0.559561	+	1.53738i	0.820277	+	0.571967i	$0.193819\pi$
$479$	12.2466	+	33.6473i	0.559561	+	1.53738i	−0.260715	+	0.965416i	$0.583958\pi$
$480$	1.26311	−	3.66122i	0.0576527	−	0.167111i
$481$	−1.94285	−	1.63025i	−0.0885865	−	0.0743329i
$482$	9.74778	−	16.8836i	0.443999	−	0.769029i
$483$	29.9444	+	38.3322i	1.36252	+	1.74418i
$484$	0.892510	−	5.06167i	0.0405686	−	0.230076i
$485$	29.4403	+	9.01794i	1.33682	+	0.409483i
$486$	14.6466	+	5.33636i	0.664384	+	0.242062i
$487$	2.83150	−	4.90431i	0.128308	−	0.222235i	−0.794713	−	0.606985i	$-0.792379\pi$
$487$	2.83150	−	4.90431i	0.128308	−	0.222235i	0.923021	+	0.384749i	$0.125712\pi$
$488$	1.77873	−	2.11981i	0.0805194	−	0.0959593i
$489$	4.39880	+	0.935294i	0.198920	+	0.0422955i
$490$	17.3136	−	3.98745i	0.782147	−	0.180135i
$491$	−21.5559	−	25.6893i	−0.972803	−	1.15934i	−0.987207	−	0.159445i	$-0.949030\pi$
$491$	−21.5559	−	25.6893i	−0.972803	−	1.15934i	0.0144039	−	0.999896i	$-0.495415\pi$
$492$	9.54731	−	3.10142i	0.430426	−	0.139823i
$493$	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
$498$	−4.60804	+	2.44975i	−0.206491	+	0.109776i
$499$	−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	$0.905965\pi$
$500$	9.78718	−	5.40472i	0.437696	−	0.241707i
$501$	14.0532	−	34.7765i	0.627853	−	1.55370i
$502$	−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	$0.0222267\pi$
$504$	−1.21079	−	11.5345i	−0.0539331	−	0.513786i
$505$	14.4755	+	34.1525i	0.644149	+	1.51977i
$506$	14.5919	−	25.2739i	0.648689	−	1.12356i
$507$	11.2067	−	17.9319i	0.497709	−	0.796385i
$508$	3.04014	+	1.10652i	0.134885	+	0.0490940i
$509$	−11.5642	+	4.20904i	−0.512576	+	0.186563i	−0.585342	−	0.810787i	$-0.699040\pi$
$509$	−11.5642	+	4.20904i	−0.512576	+	0.186563i	0.0727656	+	0.997349i	$0.476817\pi$
$510$	−8.27855	−	9.53488i	−0.366580	−	0.422212i
$511$	8.02687	+	45.5226i	0.355088	+	2.01380i
$512$			1.00000i			0.0441942i
$513$	21.7984	−	6.15077i	0.962421	−	0.271563i
$514$	8.34705			0.368172
$515$	−15.9795	+	0.828928i	−0.704143	+	0.0365269i
$516$	−2.77852	+	3.08545i	−0.122317	+	0.135829i
$517$	11.8771	+	32.6320i	0.522353	+	1.43515i
$518$	10.3565	+	3.76947i	0.455039	+	0.165621i
$519$	9.13709	+	5.71032i	0.401074	+	0.250655i
$520$	1.19803	−	1.58808i	0.0525372	−	0.0696421i
$521$	2.61622	+	4.53143i	0.114619	+	0.198526i	0.917627	−	0.397442i	$-0.130102\pi$
$521$	2.61622	+	4.53143i	0.114619	+	0.198526i	−0.803009	+	0.595968i	$0.796769\pi$
$522$	18.6862	−	1.96153i	0.817874	−	0.0858538i
$523$	−6.20970	+	35.2170i	−0.271531	+	1.53993i	0.478237	+	0.878231i	$0.341276\pi$
$523$	−6.20970	+	35.2170i	−0.271531	+	1.53993i	−0.749769	+	0.661700i	$0.769835\pi$
$524$	6.78232	−	3.91578i	0.296287	−	0.171061i
$525$	19.7097	−	27.0637i	0.860201	−	1.18116i
$526$	−0.633825	+	0.755363i	−0.0276361	+	0.0329354i
$527$	1.93753	−	5.32332i	0.0844001	−	0.231887i
$528$	−6.14411	+	3.26637i	−0.267388	+	0.142150i
$529$	22.8051	−	19.1357i	0.991525	−	0.831988i
$530$	25.3515	−	1.31509i	1.10120	−	0.0571238i
$531$	−0.133451	+	0.0382476i	−0.00579129	+	0.00165981i
$532$	−11.2250	−	12.5684i	−0.486666	−	0.544909i
$533$	5.15607			0.223334
$534$	−4.54439	−	13.9893i	−0.196655	−	0.605376i
$535$	−8.75907	+	5.68159i	−0.378688	+	0.245636i
$536$	−1.27316	−	3.49797i	−0.0549920	−	0.151089i
$537$	−2.63562	+	12.3956i	−0.113735	+	0.534910i
$538$	15.1820	−	18.0932i	0.654541	−	0.780052i
$539$	−27.6441	−	15.9604i	−1.19072	−	0.687461i
$540$	−8.49179	−	7.93029i	−0.365428	−	0.341265i
$541$	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
$543$	−12.2892	−	15.7316i	−0.527379	−	0.675106i
$544$	2.82355	+	1.63018i	0.121059	+	0.0698932i
$545$	11.0133	+	11.8229i	0.471756	+	0.506436i
$546$	1.23892	−	5.82679i	0.0530209	−	0.249363i
$547$	2.66159	−	0.968739i	0.113801	−	0.0414203i	−0.284492	−	0.958678i	$-0.591825\pi$
$547$	2.66159	−	0.968739i	0.113801	−	0.0414203i	0.398293	+	0.917258i	$0.369603\pi$
$548$	7.33110	−	6.15152i	0.313169	−	0.262780i
$549$	−3.63823	−	7.46195i	−0.155276	−	0.318468i
$550$	−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
$555$	10.3102	−	3.95067i	0.437646	−	0.167696i
$556$	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	$0.676880\pi$
$558$	1.26170	−	5.05759i	0.0534121	−	0.214105i
$559$	−1.84695	+	1.06634i	−0.0781176	+	0.0451012i
$560$	−2.53181	+	8.26545i	−0.106989	+	0.349279i
$561$	−0.793243	+	22.6729i	−0.0334907	+	0.957252i
$562$	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	$0.428564\pi$
$564$	7.93459	−	12.6962i	0.334107	−	0.534604i
$565$	−8.61323	−	4.39443i	−0.362361	−	0.184875i
$566$	−3.15771	+	1.14931i	−0.132729	+	0.0483093i
$567$	−33.0878	−	10.7605i	−1.38956	−	0.451897i
$568$	12.5256	−	2.20861i	0.525564	−	0.0926711i
$569$	39.3716			1.65054			0.825272	−	0.564735i	$-0.191022\pi$
$569$	39.3716			1.65054			0.825272	+	0.564735i	$0.191022\pi$
$570$	−16.7464	−	2.13507i	−0.701429	−	0.0894282i
$571$	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
$573$	−27.2047	+	30.2099i	−1.13649	+	1.26204i
$574$	−21.0546	+	7.66324i	−0.878801	+	0.319857i
$575$	−30.0902	−	20.3427i	−1.25485	−	0.848350i
$576$	2.74048	+	1.22057i	0.114187	+	0.0508570i
$577$	36.8254	+	21.2611i	1.53306	+	0.885113i	0.999218	+	0.0395281i	$0.0125855\pi$
$577$	36.8254	+	21.2611i	1.53306	+	0.885113i	0.533842	+	0.845585i	$0.320748\pi$
$578$	−5.51668	+	3.18505i	−0.229463	+	0.132481i
$579$	37.9315	+	1.32708i	1.57638	+	0.0551518i
$580$	−13.3903	−	4.10162i	−0.556002	−	0.170311i
$581$	10.0877	−	5.82413i	0.418508	−	0.241626i
$582$	−8.93590	+	22.1130i	−0.370405	+	0.916612i
$583$	−34.9385	−	29.3169i	−1.44700	−	1.21418i
$584$	−11.2358	−	4.08951i	−0.464943	−	0.169225i
$585$	−2.88983	−	5.22155i	−0.119480	−	0.215884i
$586$	−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
$591$	19.9873	−	6.49281i	0.822166	−	0.267078i
$592$	−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	$0.545956\pi$
$594$	1.45209	+	20.8246i	0.0595800	+	0.854445i
$595$	19.2106	+	20.6228i	0.787558	+	0.845453i
$596$	−17.1793	−	9.91847i	−0.703691	−	0.406276i
$597$	−12.7272	+	9.94222i	−0.520889	+	0.406908i
$598$	−6.36442	−	1.12222i	−0.260260	−	0.0458909i
$599$	−4.52174	+	25.6440i	−0.184753	+	1.04779i	0.741519	+	0.670932i	$0.234106\pi$
$599$	−4.52174	+	25.6440i	−0.184753	+	1.04779i	−0.926272	+	0.376855i	$0.877005\pi$
$600$	3.51350	+	7.91551i	0.143438	+	0.323149i
$601$	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
$603$	−11.1401	−	0.780456i	−0.453659	−	0.0317826i
$604$	−2.24928	−	6.17985i	−0.0915219	−	0.251454i
$605$	6.25432	+	9.64204i	0.254274	+	0.392005i
$606$	−27.3269	+	8.87706i	−1.11008	+	0.360606i
$607$	13.9107			0.564620			0.282310	−	0.959323i	$-0.408899\pi$
$607$	13.9107			0.564620			0.282310	+	0.959323i	$0.408899\pi$
$608$	4.26727	−	0.889035i	0.173061	−	0.0360551i
$609$	−41.5292	+	5.83378i	−1.68285	+	0.236396i
$610$	0.320551	+	6.17938i	0.0129787	+	0.250196i
$611$	5.89084	−	4.94300i	0.238318	−	0.199972i
$612$	7.91379	−	5.74812i	0.319896	−	0.232354i
$613$	−1.92488	+	5.28856i	−0.0777452	+	0.213603i	−0.972476	−	0.233002i	$-0.925145\pi$
$613$	−1.92488	+	5.28856i	−0.0777452	+	0.213603i	0.894731	+	0.446605i	$0.147367\pi$
$614$	17.6462	−	21.0299i	0.712142	−	0.848697i
$615$	−10.8940	+	19.6257i	−0.439290	+	0.791385i
$616$	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	$-0.110688\pi$
$618$	0.433367	−	12.3868i	0.0174326	−	0.498269i
$619$	−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	$0.971205\pi$
$620$	−2.33984	+	3.10164i	−0.0939704	+	0.124565i
$621$	−10.4114	+	36.2821i	−0.417796	+	1.45595i
$622$	13.0551	+	4.75168i	0.523463	+	0.190525i
$623$	11.2286	+	30.8505i	0.449866	+	1.23600i
$624$	1.14505	+	1.03114i	0.0458385	+	0.0412786i
$625$	−7.77601	+	23.7599i	−0.311040	+	0.950397i
$626$	2.60169			0.103985
$627$	19.4008	+	23.3147i	0.774794	+	0.931099i
$628$		−	21.8064i		−	0.870171i
$629$	1.61401	+	9.15352i	0.0643549	+	0.364975i
$630$	19.5610	+	17.0269i	0.779330	+	0.678369i
$631$	−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
$633$	−17.8125	−	11.1321i	−0.707985	−	0.442463i
$634$	−8.51626	+	14.7506i	−0.338224	+	0.585821i
$635$	−6.66066	+	2.82310i	−0.264320	+	0.112031i
$636$	−0.687535	+	19.6515i	−0.0272625	+	0.779234i
$637$	−1.22746	+	6.96129i	−0.0486339	+	0.275816i
$638$	12.5805	+	21.7901i	0.498068	+	0.862678i
$639$	9.23576	−	37.0220i	0.365361	−	1.46457i
$640$	−1.52412	−	1.63617i	−0.0602463	−	0.0646752i
$641$	−43.0495	−	15.6687i	−1.70035	−	0.618878i	−0.704488	−	0.709716i	$-0.748823\pi$
$641$	−43.0495	−	15.6687i	−1.70035	−	0.618878i	−0.995866	+	0.0908379i	$0.971045\pi$
$642$	−3.79619	−	7.14073i	−0.149824	−	0.281822i
$643$	10.2594	+	12.2266i	0.404590	+	0.482172i	0.929414	−	0.369039i	$-0.120313\pi$
$643$	10.2594	+	12.2266i	0.404590	+	0.482172i	−0.524824	+	0.851211i	$0.675869\pi$
$644$	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	$0.578487\pi$
$648$	6.68988	−	6.02042i	0.262803	−	0.236505i
$649$	−0.119498	−	0.142412i	−0.00469069	−	0.00559015i
$650$	0.460256	+	4.42432i	0.0180527	+	0.173536i
$651$	−2.41970	+	11.3801i	−0.0948355	+	0.446023i
$652$	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	$0.179914\pi$
$654$	−9.86302	+	7.70480i	−0.385675	+	0.301281i
$655$	−5.12889	+	16.7440i	−0.200402	+	0.654241i
$656$	1.00641	−	5.70763i	0.0392937	−	0.222846i
$657$	−24.9213	+	25.8000i	−0.972274	+	1.00656i
$658$	−16.7084	+	28.9398i	−0.651361	+	1.12819i
$659$	−6.27245	−	5.26321i	−0.244340	−	0.205026i	0.512391	−	0.858753i	$-0.328760\pi$
$659$	−6.27245	−	5.26321i	−0.244340	−	0.205026i	−0.756730	+	0.653727i	$0.773204\pi$
$660$	5.07445	−	14.7087i	0.197523	−	0.572536i
$661$	−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
$663$	4.77809	−	1.55215i	0.185566	−	0.0602806i
$664$			3.01304i			0.116929i
$665$	37.5218	+	3.45565i	1.45503	+	0.134004i
$666$	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
$669$	−14.4246	−	27.1331i	−0.557689	−	1.04903i
$670$	7.41444	+	3.78282i	0.286445	+	0.146143i
$671$	7.14594	−	8.51620i	0.275866	−	0.328764i
$672$	−6.20828	−	2.50878i	−0.239489	−	0.0967782i
$673$	−15.4166	−	26.7024i	−0.594268	−	1.02930i	−0.993650	−	0.112517i	$-0.964109\pi$
$673$	−15.4166	−	26.7024i	−0.594268	−	1.02930i	0.399382	−	0.916785i	$-0.369225\pi$
$674$	22.6914	+	4.00110i	0.874040	+	0.154117i
$675$	25.9807	+	0.0327469i	0.999999	+	0.00126043i
$676$	−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	$0.728135\pi$
$678$	3.96948	−	6.35157i	0.152447	−	0.243931i
$679$	18.2070	−	50.0234i	0.698722	−	1.91972i
$680$	−7.10439	+	1.63620i	−0.272441	+	0.0627453i
$681$	−9.97612	+	11.0781i	−0.382286	+	0.424516i
$682$	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	$-0.0564630\pi$
$684$	2.77212	−	12.7795i	0.105995	−	0.488636i
$685$	−2.61922	+	21.2384i	−0.100075	+	0.811478i
$686$	−0.634763	−	3.59992i	−0.0242353	−	0.137445i
$687$	−0.705114	−	0.634971i	−0.0269018	−	0.0242256i
$688$	0.819901	+	2.25266i	0.0312584	+	0.0858818i
$689$	−3.45436	+	9.49077i	−0.131601	+	0.361570i
$690$	17.7187	−	21.8540i	0.674538	−	0.831968i
$691$	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
$693$	−4.86428	−	46.3389i	−0.184779	−	1.76027i
$694$	−11.7720	−	2.07572i	−0.446859	−	0.0787933i
$695$	−44.9449	+	19.0498i	−1.70486	+	0.722598i
$696$	4.06431	−	10.0576i	0.154057	−	0.381233i
$697$	−14.4751	−	12.1461i	−0.548285	−	0.460066i
$698$	−7.62668	+	20.9541i	−0.288674	+	0.793126i
$699$	1.32217	+	2.48703i	0.0500090	+	0.0940682i
$700$	−8.45511	−	17.3825i	−0.319573	−	0.656995i
$701$	−6.38170	+	1.12527i	−0.241033	+	0.0425007i	−0.292860	−	0.956155i	$-0.594607\pi$
$701$	−6.38170	+	1.12527i	−0.241033	+	0.0425007i	0.0518263	+	0.998656i	$0.483496\pi$
$702$	4.22342	−	1.87939i	0.159403	−	0.0709331i
$703$	9.76123	+	7.69001i	0.368152	+	0.290034i
$704$			4.01743i			0.151413i
$705$	6.36819	+	32.8663i	0.239840	+	1.23782i
$706$	−18.0072	−	21.4601i	−0.677710	−	0.807663i
$707$	60.2637	−	21.9342i	2.26645	−	0.824920i
$708$	−0.0166693	+	0.0783975i	−0.000626470	+	0.00294636i
$709$	−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	$0.992062\pi$
$710$	−17.1278	+	22.7043i	−0.642796	+	0.852076i
$711$	−25.2770	+	26.1682i	−0.947962	+	0.981386i
$712$	−8.36318	−	1.47465i	−0.313423	−	0.0552650i
$713$	12.4302	+	2.19177i	0.465513	+	0.0820826i
$714$	−17.2042	+	13.4396i	−0.643852	+	0.502965i
$715$	4.81301	−	6.38002i	0.179997	−	0.238599i
$716$	5.60484	+	4.70302i	0.209463	+	0.175760i
$717$	−13.8095	−	2.93624i	−0.515725	−	0.109656i
$718$	16.6681	−	6.06669i	0.622048	−	0.226407i
$719$	−22.3939	−	26.6880i	−0.835152	−	0.995296i	−0.999960	−	0.00897016i	$-0.997145\pi$
$719$	−22.3939	−	26.6880i	−0.835152	−	0.995296i	0.164807	−	0.986326i	$-0.447300\pi$
$720$	−6.34418	+	2.17977i	−0.236434	+	0.0812353i
$721$			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
$725$	28.1602	−	13.6976i	1.04584	−	0.508715i
$726$	−7.86056	+	4.17887i	−0.291733	+	0.155092i
$727$	17.1263	−	47.0541i	0.635179	−	1.74514i	−0.0311866	−	0.999514i	$-0.509929\pi$
$727$	17.1263	−	47.0541i	0.635179	−	1.74514i	0.666365	−	0.745625i	$-0.267849\pi$
$728$	−2.63466	−	2.21074i	−0.0976469	−	0.0819355i
$729$	−8.33337	−	25.6818i	−0.308643	−	0.951178i
$730$	24.6167	−	10.4337i	0.911103	−	0.386169i
$731$	7.69707	+	1.35720i	0.284687	+	0.0501979i
$732$	−4.79003	−	0.167585i	−0.177045	−	0.00619414i
$733$	25.6802	−	14.8265i	0.948521	−	0.547629i	0.0558997	−	0.998436i	$-0.482197\pi$
$733$	25.6802	−	14.8265i	0.948521	−	0.547629i	0.892621	+	0.450808i	$0.148864\pi$
$734$	−0.435650	+	0.754569i	−0.0160801	+	0.0278516i
$735$	−23.9035	−	19.3804i	−0.881695	−	0.714855i
$736$	−2.48453	+	6.82620i	−0.0915811	+	0.251617i
$737$	−5.11482	−	14.0529i	−0.188407	−	0.517644i
$738$	−14.4132	−	9.72460i	−0.530559	−	0.357968i
$739$	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
$741$	3.38217	−	5.80294i	0.124247	−	0.213176i
$742$		−	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	$0.398632\pi$
$744$	−2.23636	−	2.01389i	−0.0819888	−	0.0738327i
$745$	43.2252	−	9.95510i	1.58365	−	0.364727i
$746$	−5.10560	+	14.0275i	−0.186929	+	0.513584i
$747$	8.25717	+	3.67763i	0.302114	+	0.134557i
$748$	11.3434	+	6.54912i	0.414756	+	0.239460i
$749$	9.02522	+	15.6321i	0.329774	+	0.571186i
$750$	−17.8129	−	7.59608i	−0.650435	−	0.277370i
$751$	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
$753$	−1.60673	+	3.97605i	−0.0585526	+	0.144895i
$754$	3.58147	−	4.26823i	0.130430	−	0.155440i
$755$	13.0991	+	6.68308i	0.476723	+	0.243222i
$756$	−14.4529	+	13.9515i	−0.525646	+	0.507411i
$757$	0.216899	+	0.258490i	0.00788332	+	0.00939498i	0.769972	−	0.638078i	$-0.220270\pi$
$757$	0.216899	+	0.258490i	0.00788332	+	0.00939498i	−0.762088	+	0.647473i	$0.775826\pi$
$758$	2.76198	+	15.6639i	0.100319	+	0.568940i
$759$	−50.0563	+	7.03162i	−1.81693	+	0.255232i
$760$	−5.62697	+	7.95847i	−0.204112	+	0.288684i
$761$			3.44946i			0.125043i	0.998044	+	0.0625214i	$0.0199142\pi$
$761$			3.44946i			0.125043i	−0.998044	+	0.0625214i	$0.980086\pi$
$762$	−1.73127	−	5.32948i	−0.0627172	−	0.193067i
$763$	21.3996	−	17.9564i	0.774716	−	0.650064i
$764$	8.02773	+	22.0560i	0.290433	+	0.797958i
$765$	−4.18744	+	21.4665i	−0.151397	+	0.776123i
$766$	−23.9018	−	20.0560i	−0.863609	−	0.724654i
$767$	−0.0205839	+	0.0356524i	−0.000743242	+	0.00128733i
$768$	1.36494	−	1.06627i	0.0492532	−	0.0384756i
$769$	−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	$0.997446\pi$
$770$	−10.1714	+	33.2059i	−0.366551	+	1.19666i
$771$	−8.90019	−	11.3933i	−0.320532	−	0.410318i
$772$	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	$0.337038\pi$
$774$	7.17411	+	0.502606i	0.257868	+	0.0180658i
$775$	−0.898913	−	8.64102i	−0.0322899	−	0.310395i
$776$	8.85114	+	10.5484i	0.317737	+	0.378665i
$777$	−5.89771	−	18.1553i	−0.211579	−	0.651319i
$778$	−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
$783$	−22.6019	−	23.4142i	−0.807726	−	0.836754i
$784$	7.46638	+	2.71754i	0.266656	+	0.0970550i
$785$	33.2357	+	35.6790i	1.18623	+	1.27344i
$786$	−12.5766	−	5.08223i	−0.448592	−	0.181277i
$787$	−8.43438	−	14.6088i	−0.300653	−	0.520747i	0.675631	−	0.737240i	$-0.263871\pi$
$787$	−8.43438	−	14.6088i	−0.300653	−	0.520747i	−0.976284	+	0.216493i	$0.930538\pi$
$788$	2.10692	−	11.9489i	0.0750558	−	0.425663i
$789$	1.70686	+	0.0597166i	0.0607657	+	0.00212597i
$790$	24.9680	−	10.5826i	0.888321	−	0.376512i
$791$	−8.35880	+	14.4779i	−0.297205	+	0.514774i
$792$	11.0097	+	4.90355i	0.391212	+	0.174240i
$793$	−2.31336	−	0.841994i	−0.0821498	−	0.0299001i
$794$	29.0047	−	10.5569i	1.02934	−	0.374649i
$795$	−28.8265	−	33.2011i	−1.02237	−	1.17752i
$796$	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	$-0.172292\pi$
$798$	−5.18627	+	28.7228i	−0.183592	+	1.01678i
$799$	−28.1821			−0.997011
$800$	4.98745	+	0.354089i	0.176333	+	0.0125190i
$801$	−14.2491	+	21.1192i	−0.503467	+	0.746209i
$802$	10.8798	+	29.8921i	0.384180	+	1.05553i
$803$	−45.1392	−	16.4293i	−1.59293	−	0.579779i
$804$	−3.41701	+	5.46756i	−0.120509	+	0.192826i
$805$	−37.8184	+	50.1312i	−1.33292	+	1.76689i
$806$	−0.772888	−	1.33868i	−0.0272238	−	0.0471530i
$807$	−40.8842	−	1.43039i	−1.43919	−	0.0503521i
$808$	−2.88061	+	16.3367i	−0.101339	+	0.574724i
$809$	12.8675	−	7.42903i	0.452396	−	0.261191i	−0.256446	−	0.966559i	$-0.582552\pi$
$809$	12.8675	−	7.42903i	0.452396	−	0.261191i	0.708841	+	0.705368i	$0.249218\pi$
$810$	−1.76989	+	20.0466i	−0.0621876	+	0.704367i
$811$	−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
$813$	24.0951	+	45.3235i	0.845052	+	1.58956i
$814$	−8.77353	+	7.36187i	−0.307512	+	0.258033i
$815$	0.300766	+	5.79797i	0.0105354	+	0.203094i
$816$	−0.785558	−	5.59219i	−0.0275000	−	0.195766i
$817$	8.88379	−	5.50143i	0.310805	−	0.192471i
$818$	−23.1045			−0.807829
$819$	−9.27426	+	4.52186i	−0.324069	+	0.158006i
$820$	7.05249	+	10.8725i	0.246284	+	0.379686i
$821$	18.7457	+	51.5033i	0.654228	+	1.79748i	0.601507	+	0.798868i	$0.294567\pi$
$821$	18.7457	+	51.5033i	0.654228	+	1.79748i	0.0527213	+	0.998609i	$0.483211\pi$
$822$	−16.2134	−	3.44737i	−0.565507	−	0.120241i
$823$	34.2674	−	40.8383i	1.19449	−	1.42353i	0.314026	−	0.949415i	$-0.398322\pi$
$823$	34.2674	−	40.8383i	1.19449	−	1.42353i	0.880461	−	0.474119i	$-0.157233\pi$
$824$	−6.19717	−	3.57794i	−0.215889	−	0.124643i
$825$	14.1153	+	31.8000i	0.491430	+	1.10713i
$826$	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	$0.563821\pi$
$828$	15.6745	+	15.1407i	0.544726	+	0.526174i
$829$	−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	$0.815201\pi$
$830$	−4.59225	−	4.92984i	−0.159399	−	0.171117i
$831$	18.9109	+	4.02093i	0.656011	+	0.139484i
$832$	0.835988	−	0.304275i	0.0289827	−	0.0105488i
$833$	19.8446	−	16.6516i	0.687575	−	0.576944i
$834$	−11.6823	−	35.9623i	−0.404523	−	1.24527i
$835$	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	$-0.896966\pi$
$839$	−23.1568	+	19.4309i	−0.799463	+	0.670829i	0.148605	+	0.988897i	$0.452522\pi$
$840$	13.9815	−	5.35740i	0.482407	−	0.184848i
$841$	−9.60813	−	3.49707i	−0.331315	−	0.120589i
$842$	8.70410	+	7.30361i	0.299963	+	0.251699i
$843$	−31.7228	−	12.8193i	−1.09259	−	0.441519i
$844$	−10.5025	+	6.06363i	−0.361511	+	0.208719i
$845$	26.1020	+	7.99538i	0.897937	+	0.275049i
$846$	−25.7899	+	2.70722i	−0.886676	+	0.0930761i
$847$	17.2080	−	9.93502i	0.591272	−	0.341371i
$848$	9.83178	+	5.67638i	0.337625	+	0.194928i
$849$	4.93572	+	3.08463i	0.169393	+	0.105864i
$850$	9.13020	−	13.5051i	0.313163	−	0.463220i
$851$	−19.4604	+	7.08300i	−0.667093	+	0.242802i
$852$	−16.3703	−	14.7418i	−0.560837	−	0.505047i
$853$	−31.8325	+	5.61292i	−1.08992	+	0.192183i	−0.689599	−	0.724191i	$-0.742213\pi$
$853$	−31.8325	+	5.61292i	−1.08992	+	0.192183i	−0.400323	+	0.916374i	$0.631102\pi$
$854$	10.6979			0.366075
$855$	14.9419	+	25.1344i	0.511001	+	0.859580i
$856$	−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	$0.625799\pi$
$858$	4.60014	+	4.14253i	0.157046	+	0.141424i
$859$	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	$0.293181\pi$
$860$	−4.77483	−	2.43610i	−0.162820	−	0.0830702i
$861$	32.9097	+	20.5673i	1.12156	+	0.700930i
$862$	−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	$0.472232\pi$
$864$	−1.25607	−	5.04205i	−0.0427325	−	0.171534i
$865$	−4.07399	+	13.3001i	−0.138520	+	0.452217i
$866$	4.73692	−	2.73486i	0.160967	−	0.0929343i
$867$	10.2297	+	4.13384i	0.347418	+	0.140392i
$868$	5.14567	+	4.31773i	0.174656	+	0.146553i
$869$	−45.7835	−	16.6638i	−1.55310	−	0.565281i
$870$	8.67917	+	22.6505i	0.294252	+	0.767922i
$871$	−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
$876$	6.39846	+	19.6968i	0.216184	+	0.665494i
$877$	6.41225	−	5.38052i	0.216526	−	0.181687i	−0.528073	−	0.849199i	$-0.677085\pi$
$877$	6.41225	−	5.38052i	0.216526	−	0.181687i	0.744599	+	0.667512i	$0.232641\pi$
$878$	25.4556	−	9.26507i	0.859084	−	0.312681i
$879$	33.3280	+	7.08638i	1.12413	+	0.239018i
$880$	−6.12307	−	6.57319i	−0.206409	−	0.221582i
$881$	12.2282	+	7.05997i	0.411979	+	0.237856i	0.691640	−	0.722243i	$-0.256889\pi$
$881$	12.2282	+	7.05997i	0.411979	+	0.237856i	−0.279660	+	0.960099i	$0.590222\pi$
$882$	16.5606	−	17.1445i	0.557624	−	0.577285i
$883$	−3.17975	−	0.560675i	−0.107007	−	0.0188682i	0.119888	−	0.992787i	$-0.461746\pi$
$883$	−3.17975	−	0.560675i	−0.107007	−	0.0188682i	−0.226895	+	0.973919i	$0.572857\pi$
$884$	0.503673	−	2.85647i	0.0169404	−	0.0960736i
$885$	−0.0922139	−	0.153678i	−0.00309974	−	0.00516582i
$886$	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	$0.346166\pi$
$888$	4.82982	+	1.02694i	0.162078	+	0.0344619i
$889$	4.27776	+	11.7530i	0.143471	+	0.394184i
$890$	15.9311	−	10.3337i	0.534012	−	0.346388i
$891$	26.8761	−	24.1866i	0.900384	−	0.810283i
$892$	−17.7414			−0.594027
$893$	−28.1017	+	25.0981i	−0.940387	+	0.839874i
$894$	4.77957	+	34.0245i	0.159853	+	1.13795i
$895$	−16.3384	+	0.847545i	−0.546134	+	0.0283303i
$896$	−2.96149	+	2.48498i	−0.0989364	+	0.0830175i
$897$	5.25441	+	9.88366i	0.175440	+	0.330006i
$898$	−5.76702	+	15.8448i	−0.192448	+	0.528746i
$899$	−6.99488	+	8.33617i	−0.233292	+	0.278027i
$900$	7.05789	−	13.2358i	0.235263	−	0.441193i
$901$	32.0551	−	18.5070i	1.06791	−	0.616557i
$902$	4.04318	−	22.9300i	0.134623	−	0.763486i
$903$	−16.0421	−	0.561253i	−0.533847	−	0.0186773i
$904$	−2.16216	−	3.74497i	−0.0719124	−	0.124556i
$905$	15.5207	−	20.5739i	0.515925	−	0.683899i
$906$	−6.03681	+	9.65951i	−0.200560	+	0.320916i
$907$	14.0379	+	5.10938i	0.466121	+	0.169654i	0.564394	−	0.825505i	$-0.309110\pi$
$907$	14.0379	+	5.10938i	0.466121	+	0.169654i	−0.0982735	+	0.995159i	$0.531332\pi$
$908$	2.94381	+	8.08806i	0.0976939	+	0.268412i
$909$	41.2545	+	27.8344i	1.36832	+	0.923207i
$910$	7.68018	−	0.398404i	0.254596	−	0.0132070i
$911$	−34.6078			−1.14661			−0.573304	−	0.819343i	$-0.694339\pi$
$911$	−34.6078			−1.14661			−0.573304	+	0.819343i	$0.694339\pi$
$912$	−5.76354	−	4.87664i	−0.190850	−	0.161482i
$913$			12.1047i			0.400607i
$914$	0.149720	+	0.849104i	0.00495229	+	0.0280859i
$915$	8.09271	−	7.02640i	0.267537	−	0.232286i
$916$	−0.514798	+	0.187371i	−0.0170094	+	0.00619091i
$917$	28.4505	+	10.3551i	0.939518	+	0.341956i
$918$	−16.2841	−	4.67285i	−0.537455	−	0.154227i
$919$	−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	$0.297289\pi$
$920$	−6.33886	−	14.9555i	−0.208986	−	0.493070i
$921$	−47.5202	−	1.66256i	−1.56584	−	0.0547831i
$922$	−2.14521	+	12.1661i	−0.0706488	+	0.400669i
$923$	−5.65760	−	9.79925i	−0.186222	−	0.322546i
$924$	−24.9413	−	10.0788i	−0.820509	−	0.331570i
$925$	8.36612	+	11.5408i	0.275076	+	0.379458i
$926$	33.0710	+	12.0369i	1.08678	+	0.395556i
$927$	−17.3693	+	12.6161i	−0.570484	+	0.414367i
$928$	−4.02576	−	4.79771i	−0.132152	−	0.157493i
$929$	5.20086	−	0.917053i	0.170635	−	0.0300875i	−0.0876779	−	0.996149i	$-0.527945\pi$
$929$	5.20086	−	0.917053i	0.170635	−	0.0300875i	0.258313	+	0.966061i	$0.416834\pi$
$930$	6.72847	−	0.113425i	0.220635	−	0.00371934i
$931$	4.95861	−	34.2770i	0.162512	−	1.12338i
$932$	1.62619			0.0532675
$933$	−7.43449	−	22.8861i	−0.243394	−	0.749257i
$934$	−4.50782	−	5.37221i	−0.147500	−	0.175784i
$935$	−28.5414	+	6.57331i	−0.933403	+	0.214970i
$936$	0.186523	−	2.66239i	0.00609669	−	0.0870231i
$937$	7.05135	−	8.40347i	0.230358	−	0.274529i	−0.638467	−	0.769649i	$-0.720431\pi$
$937$	7.05135	−	8.40347i	0.230358	−	0.274529i	0.868825	+	0.495119i	$0.164876\pi$
$938$	7.19543	−	12.4628i	0.234939	−	0.406926i
$939$	−2.77410	−	3.55117i	−0.0905294	−	0.115888i
$940$	18.4807	+	5.66088i	0.602775	+	0.184638i
$941$	−2.71024	+	15.3705i	−0.0883513	+	0.501065i	0.908232	+	0.418468i	$0.137433\pi$
$941$	−2.71024	+	15.3705i	−0.0883513	+	0.501065i	−0.996583	+	0.0825973i	$0.973678\pi$
$942$	−29.7646	+	23.2515i	−0.969782	+	0.757574i
$943$	21.0508	−	36.4610i	0.685507	−	1.18733i
$944$	0.0354485	+	0.0297448i	0.00115375	+	0.000968111i
$945$	2.38351	−	44.8550i	0.0775357	−	1.45913i
$946$	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	$0.312501\pi$
$948$	6.48978	+	19.9779i	0.210778	+	0.648853i
$949$			10.6374i			0.345304i
$950$	−2.92302	−	21.5976i	−0.0948352	−	0.700718i
$951$	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	$0.899118\pi$
$954$	27.5564	−	20.0154i	0.892170	−	0.648021i
$955$	−46.7508	−	23.8521i	−1.51282	−	0.771834i
$956$	−5.23946	+	6.24414i	−0.169456	+	0.201950i
$957$	16.3281	−	40.4058i	0.527812	−	1.30613i
$958$	−17.9033	−	31.0095i	−0.578430	−	1.00187i
$959$	36.4353	+	6.42453i	1.17656	+	0.207459i
$960$	−0.608154	+	3.82494i	−0.0196281	+	0.123449i
$961$	−13.9905	−	24.2322i	−0.451306	−	0.781685i
$962$	2.19643	+	1.26811i	0.0708157	+	0.0408854i
$963$	−5.69894	+	12.7955i	−0.183646	+	0.412330i
$964$	−6.66787	+	18.3198i	−0.214758	+	0.590042i
$965$	10.9971	+	47.7494i	0.354008	+	1.53711i
$966$	−36.1458	−	32.5501i	−1.16297	−	1.04728i
$967$	−22.5090	+	3.96895i	−0.723842	+	0.127633i	−0.523417	−	0.852076i	$-0.675343\pi$
$967$	−22.5090	+	3.96895i	−0.723842	+	0.127633i	−0.200424	+	0.979709i	$0.564232\pi$
$968$			5.13976i			0.165198i
$969$	−23.1650	+	8.32384i	−0.744167	+	0.267400i
$970$	−30.5590	−	3.76868i	−0.981190	−	0.121005i
$971$	−3.33320	−	18.9035i	−0.106967	−	0.606642i	−0.990416	−	0.138114i	$-0.955896\pi$
$971$	−3.33320	−	18.9035i	−0.106967	−	0.606642i	0.883449	−	0.468527i	$-0.155215\pi$
$972$	−15.3507	−	2.71193i	−0.492375	−	0.0869853i
$973$	28.8655	+	79.3073i	0.925385	+	2.54247i
$974$	−1.93686	+	5.32149i	−0.0620611	+	0.170511i
$975$	5.54820	−	5.34574i	0.177685	−	0.171201i
$976$	−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	$0.501831\pi$
$978$	−4.49438	−	0.157242i	−0.143714	−	0.00502804i
$979$	−33.5985	−	5.92432i	−1.07381	−	0.189342i
$980$	−16.3581	+	6.93334i	−0.522541	+	0.221477i
$981$	21.0332	+	5.24710i	0.671540	+	0.167527i
$982$	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	$-0.0213676\pi$
$984$	−8.86371	+	4.71217i	−0.282565	+	0.150219i
$985$	14.7644	+	22.7616i	0.470432	+	0.725246i
$986$	−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
$990$	−25.4873	+	8.75709i	−0.810040	+	0.278318i
$991$	−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
$993$	−10.1587	−	2.16000i	−0.322378	−	0.0685456i
$994$	37.6667	+	31.6062i	1.19472	+	1.00249i
$995$	−16.6447	−	12.5566i	−0.527673	−	0.398071i
$996$	4.11264	−	3.21271i	0.130314	−	0.101799i
$997$	−30.4828	−	5.37494i	−0.965400	−	0.170226i	−0.331342	−	0.943511i	$-0.607501\pi$
$997$	−30.4828	−	5.37494i	−0.965400	−	0.170226i	−0.634059	+	0.773285i	$0.718612\pi$
$998$	35.1723	+	6.20183i	1.11336	+	0.196316i
$999$	8.70944	−	11.9826i	0.275554	−	0.379111i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(1.28709 + 1.15905i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.01621 + 1.99181i) q^{5} +(-1.46880 - 0.917943i) q^{6} +(3.34801 + 1.93297i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.313195 + 2.98361i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(1.28709 + 1.15905i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.01621 + 1.99181i) q^{5} +(-1.46880 - 0.917943i) q^{6} +(3.34801 + 1.93297i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.313195 + 2.98361i) q^{9} +(0.654901 - 2.13801i) q^{10} +(-3.47920 + 2.00872i) q^{11} +(1.60589 + 0.648943i) q^{12} +(0.681504 + 0.571849i) q^{13} +(-3.63280 - 1.32223i) q^{14} +(-3.61657 + 1.38579i) 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} +(2.06877 + 6.36843i) q^{21} +(3.07753 - 2.58236i) q^{22} +(6.82620 - 2.48453i) q^{23} +(-1.69418 - 0.360225i) q^{24} +(-2.93462 - 4.04821i) q^{25} +(-0.770451 - 0.444820i) q^{26} +(-3.05505 + 4.20318i) q^{27} +(3.80722 + 0.671315i) q^{28} +(-1.08755 + 6.16782i) q^{29} +(3.32099 - 1.99275i) q^{30} +(1.50475 + 0.868765i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-6.80624 - 1.44718i) q^{33} +(1.11511 + 3.06373i) q^{34} +(-7.25241 + 4.70429i) q^{35} +(1.31476 + 2.69655i) q^{36} -2.85084 q^{37} +(3.84038 + 2.06191i) q^{38} +(0.214352 + 1.52592i) q^{39} +(-0.115839 - 2.23307i) q^{40} +(4.43975 - 3.72539i) q^{41} +(-3.14320 - 5.91244i) q^{42} +(-0.819901 + 2.25266i) q^{43} +(-2.58236 + 3.07753i) q^{44} +(-6.26105 - 2.40816i) q^{45} +(-6.29106 + 3.63214i) q^{46} +(1.50099 - 8.51256i) q^{47} +(1.73099 + 0.0605610i) q^{48} +(3.97278 + 6.88105i) q^{49} +(3.59300 + 3.47712i) q^{50} +(2.99282 - 4.78881i) q^{51} +(0.835988 + 0.304275i) q^{52} +(3.88287 + 10.6681i) q^{53} +(2.27876 - 4.66982i) q^{54} +(-0.465374 - 8.97119i) q^{55} -3.86595 q^{56} +(-1.28048 - 7.44045i) q^{57} -6.26297i q^{58} +(0.00803551 + 0.0455717i) q^{59} +(-2.92450 + 2.53916i) q^{60} +(-2.60033 + 0.946444i) q^{61} +(-1.63274 - 0.594270i) q^{62} +(-4.71865 + 10.5945i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-1.83157 + 0.776305i) q^{65} +(6.95414 + 0.243300i) q^{66} +(-0.646399 + 3.66591i) q^{67} +(-1.63018 - 2.82355i) q^{68} +(11.6656 + 4.71411i) q^{69} +(6.32534 - 5.89219i) q^{70} +(-11.9518 - 4.35011i) q^{71} +(-1.76304 - 2.42728i) 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} +(-0.476069 - 1.46552i) q^{78} +(7.79546 + 9.29027i) q^{79} +(0.501847 + 2.17902i) q^{80} +(-8.80382 + 1.86890i) q^{81} +(-3.72539 + 4.43975i) q^{82} +(1.50652 - 2.60937i) q^{83} +(4.12213 + 5.27680i) q^{84} +(6.97068 + 2.13521i) q^{85} +(0.416275 - 2.36081i) q^{86} +(-8.54860 + 6.67800i) q^{87} +(2.00872 - 3.47920i) q^{88} +(6.50540 + 5.45868i) q^{89} +(6.58411 + 1.28435i) q^{90} +(1.17631 + 3.23189i) q^{91} +(5.56477 - 4.66940i) q^{92} +(0.929796 + 2.86226i) q^{93} +8.64388i q^{94} +(8.85233 - 4.07875i) q^{95} +(-1.71521 + 0.240943i) q^{96} +(-2.39112 - 13.5607i) q^{97} +(-5.10730 - 6.08665i) q^{98} +(-7.08288 - 9.75144i) 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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