LMFDB - Embedded newform 56.2.m.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,2,Mod(3,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("56.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	56.m (of order $6$, degree $2$, 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:	$0.447162251319$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.144054149089536.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 $ x^12 - 3x^11 + x^9 + 48x^8 - 189x^7 + 431x^6 - 654x^5 + 624x^4 - 340x^3 + 96x^2 - 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.1
Root			$0.186445 + 1.54034i$ of defining polynomial
Character	$\chi$	$=$	56.3
Dual form			56.2.m.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30084 - 0.554812i) q^{2} +(1.18878 + 0.686340i) q^{3} +(1.38437 + 1.44344i) q^{4} +(-0.345107 - 0.597743i) q^{5} +(-1.16562 - 1.55237i) q^{6} +(2.63639 + 0.222310i) q^{7} +(-1.00000 - 2.64575i) q^{8} +(-0.557875 - 0.966267i) q^{9} +O(q^{10})$	\(q+(-1.30084 - 0.554812i) q^{2} +(1.18878 + 0.686340i) q^{3} +(1.38437 + 1.44344i) q^{4} +(-0.345107 - 0.597743i) q^{5} +(-1.16562 - 1.55237i) q^{6} +(2.63639 + 0.222310i) q^{7} +(-1.00000 - 2.64575i) q^{8} +(-0.557875 - 0.966267i) q^{9} +(0.117294 + 0.969037i) q^{10} +(-1.63090 + 2.82480i) q^{11} +(0.655009 + 2.66608i) q^{12} -5.27279 q^{13} +(-3.30619 - 1.75189i) q^{14} -0.947443i q^{15} +(-0.167055 + 3.99651i) q^{16} +(-2.20393 - 1.27244i) q^{17} +(0.189609 + 1.56647i) q^{18} +(-0.484848 + 0.279927i) q^{19} +(0.385053 - 1.32564i) q^{20} +(2.98150 + 2.07374i) q^{21} +(3.68878 - 2.76977i) q^{22} +(2.50610 - 1.44690i) q^{23} +(0.627109 - 3.83155i) q^{24} +(2.26180 - 3.91756i) q^{25} +(6.85905 + 2.92541i) q^{26} -5.64961i q^{27} +(3.32885 + 4.11324i) q^{28} +0.444621i q^{29} +(-0.525653 + 1.23247i) q^{30} +(-4.45228 + 7.71158i) q^{31} +(2.43462 - 5.10613i) q^{32} +(-3.87755 + 2.23871i) q^{33} +(2.16099 + 2.87800i) q^{34} +(-0.776954 - 1.65261i) q^{35} +(0.622448 - 2.14293i) q^{36} +(6.00295 - 3.46580i) q^{37} +(0.786017 - 0.0951408i) q^{38} +(-6.26817 - 3.61893i) q^{39} +(-1.23637 + 1.51081i) q^{40} +9.76765i q^{41} +(-2.72792 - 4.35178i) q^{42} +(-6.33521 + 1.55645i) q^{44} +(-0.385053 + 0.666931i) q^{45} +(-4.06279 + 0.491767i) q^{46} +(-2.20094 - 3.81214i) q^{47} +(-2.94156 + 4.63630i) q^{48} +(6.90116 + 1.17220i) q^{49} +(-5.11575 + 3.84124i) q^{50} +(-1.74665 - 3.02529i) q^{51} +(-7.29948 - 7.61097i) q^{52} +(8.17440 + 4.71949i) q^{53} +(-3.13447 + 7.34923i) q^{54} +2.25134 q^{55} +(-2.04822 - 7.19756i) q^{56} -0.768501 q^{57} +(0.246681 - 0.578380i) q^{58} +(8.59663 + 4.96327i) q^{59} +(1.36758 - 1.31161i) q^{60} +(-5.23284 - 9.06355i) q^{61} +(10.0702 - 7.56134i) q^{62} +(-1.25597 - 2.67148i) q^{63} +(-6.00000 + 5.29150i) q^{64} +(1.81968 + 3.15177i) q^{65} +(6.28613 - 0.760884i) q^{66} +(-1.45058 + 2.51247i) q^{67} +(-1.21435 - 4.94277i) q^{68} +3.97225 q^{69} +(0.0938060 + 2.58084i) q^{70} +5.29150i q^{71} +(-1.99863 + 2.44227i) q^{72} +(-5.28541 - 3.05153i) q^{73} +(-9.73174 + 1.17795i) q^{74} +(5.37755 - 3.10473i) q^{75} +(-1.07527 - 0.312329i) q^{76} +(-4.92768 + 7.08473i) q^{77} +(6.14605 + 8.18530i) q^{78} +(5.01803 - 2.89716i) q^{79} +(2.44654 - 1.27937i) q^{80} +(2.20393 - 3.81731i) q^{81} +(5.41921 - 12.7061i) q^{82} +1.83845i q^{83} +(1.13417 + 7.17445i) q^{84} +1.75651i q^{85} +(-0.305161 + 0.528555i) q^{87} +(9.10463 + 1.49016i) q^{88} +(1.50000 - 0.866025i) q^{89} +(0.870914 - 0.653939i) q^{90} +(-13.9012 - 1.17220i) q^{91} +(5.55787 + 1.61437i) q^{92} +(-10.5855 + 6.11156i) q^{93} +(0.748048 + 6.18008i) q^{94} +(0.334649 + 0.193210i) q^{95} +(6.39877 - 4.39907i) q^{96} -7.42325i q^{97} +(-8.32695 - 5.35368i) q^{98} +3.63935 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 12 q^{8}+O(q^{10}) $ 12 * q - 6 * q^3 - 12 * q^8	$ 12 q - 6 q^{3} - 12 q^{8} + 6 q^{10} - 6 q^{11} - 18 q^{12} + 6 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 24 q^{22} + 6 q^{24} + 6 q^{26} + 6 q^{28} - 12 q^{30} - 6 q^{33} + 18 q^{35} + 48 q^{36} - 24 q^{38} + 42 q^{40} - 30 q^{42} + 6 q^{44} - 18 q^{46} - 12 q^{49} - 48 q^{50} + 6 q^{51} - 24 q^{52} - 36 q^{54} - 36 q^{57} + 18 q^{58} + 42 q^{59} - 6 q^{60} - 72 q^{64} - 12 q^{65} + 12 q^{66} + 30 q^{67} - 36 q^{68} + 30 q^{70} + 18 q^{73} + 12 q^{74} + 24 q^{75} + 60 q^{78} + 36 q^{80} + 6 q^{81} + 54 q^{82} + 12 q^{84} + 6 q^{88} + 18 q^{89} - 72 q^{91} + 60 q^{92} - 12 q^{94} + 60 q^{96} - 6 q^{98} - 24 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 - 12 * q^8 + 6 * q^10 - 6 * q^11 - 18 * q^12 + 6 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 24 * q^22 + 6 * q^24 + 6 * q^26 + 6 * q^28 - 12 * q^30 - 6 * q^33 + 18 * q^35 + 48 * q^36 - 24 * q^38 + 42 * q^40 - 30 * q^42 + 6 * q^44 - 18 * q^46 - 12 * q^49 - 48 * q^50 + 6 * q^51 - 24 * q^52 - 36 * q^54 - 36 * q^57 + 18 * q^58 + 42 * q^59 - 6 * q^60 - 72 * q^64 - 12 * q^65 + 12 * q^66 + 30 * q^67 - 36 * q^68 + 30 * q^70 + 18 * q^73 + 12 * q^74 + 24 * q^75 + 60 * q^78 + 36 * q^80 + 6 * q^81 + 54 * q^82 + 12 * q^84 + 6 * q^88 + 18 * q^89 - 72 * q^91 + 60 * q^92 - 12 * q^94 + 60 * q^96 - 6 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.30084	−	0.554812i	−0.919832	−	0.392311i
$2$	−1.30084	−	0.554812i	−0.919832	−	0.392311i
$3$	1.18878	+	0.686340i	0.686340	+	0.396259i	0.802239	−	0.597002i	$-0.203642\pi$
$3$	1.18878	+	0.686340i	0.686340	+	0.396259i	−0.115899	+	0.993261i	$0.536975\pi$
$4$	1.38437	+	1.44344i	0.692184	+	0.721721i
$5$	−0.345107	−	0.597743i	−0.154337	−	0.267319i	0.778481	−	0.627669i	$-0.215991\pi$
$5$	−0.345107	−	0.597743i	−0.154337	−	0.267319i	−0.932817	+	0.360350i	$0.882657\pi$
$6$	−1.16562	−	1.55237i	−0.475861	−	0.633751i
$7$	2.63639	+	0.222310i	0.996464	+	0.0840255i
$7$	2.63639	+	0.222310i	0.996464	+	0.0840255i
$8$	−1.00000	−	2.64575i	−0.353553	−	0.935414i
$9$	−0.557875	−	0.966267i	−0.185958	−	0.322089i
$10$	0.117294	+	0.969037i	0.0370916	+	0.306436i
$11$	−1.63090	+	2.82480i	−0.491735	+	0.851710i	−0.999955	−	0.00951723i	$-0.996971\pi$
$11$	−1.63090	+	2.82480i	−0.491735	+	0.851710i	0.508220	+	0.861228i	$0.330304\pi$
$12$	0.655009	+	2.66608i	0.189085	+	0.769630i
$13$	−5.27279			−1.46241			−0.731204	−	0.682158i	$-0.761041\pi$
$13$	−5.27279			−1.46241			−0.731204	+	0.682158i	$0.761041\pi$
$14$	−3.30619	−	1.75189i	−0.883615	−	0.468213i
$15$		−	0.947443i		−	0.244629i
$16$	−0.167055	+	3.99651i	−0.0417638	+	0.999128i
$17$	−2.20393	−	1.27244i	−0.534531	−	0.308612i	0.208329	−	0.978059i	$-0.433198\pi$
$17$	−2.20393	−	1.27244i	−0.534531	−	0.308612i	−0.742860	+	0.669447i	$0.766531\pi$
$18$	0.189609	+	1.56647i	0.0446912	+	0.369222i
$19$	−0.484848	+	0.279927i	−0.111232	+	0.0642197i	−0.554584	−	0.832128i	$-0.687123\pi$
$19$	−0.484848	+	0.279927i	−0.111232	+	0.0642197i	0.443352	+	0.896348i	$0.353789\pi$
$20$	0.385053	−	1.32564i	0.0861005	−	0.296422i
$21$	2.98150	+	2.07374i	0.650617	+	0.452527i
$22$	3.68878	−	2.76977i	0.786450	−	0.590518i
$23$	2.50610	−	1.44690i	0.522558	−	0.301699i	−0.215423	−	0.976521i	$-0.569113\pi$
$23$	2.50610	−	1.44690i	0.522558	−	0.301699i	0.737981	+	0.674822i	$0.235780\pi$
$24$	0.627109	−	3.83155i	0.128008	−	0.782111i
$25$	2.26180	−	3.91756i	0.452360	−	0.783511i
$26$	6.85905	+	2.92541i	1.34517	+	0.573720i
$27$		−	5.64961i		−	1.08727i
$28$	3.32885	+	4.11324i	0.629093	+	0.777330i
$29$			0.444621i			0.0825640i	0.999148	+	0.0412820i	$0.0131442\pi$
$29$			0.444621i			0.0825640i	−0.999148	+	0.0412820i	$0.986856\pi$
$30$	−0.525653	+	1.23247i	−0.0959706	+	0.225017i
$31$	−4.45228	+	7.71158i	−0.799653	+	1.38504i	0.120189	+	0.992751i	$0.461650\pi$
$31$	−4.45228	+	7.71158i	−0.799653	+	1.38504i	−0.919842	+	0.392289i	$0.871683\pi$
$32$	2.43462	−	5.10613i	0.430385	−	0.902646i
$33$	−3.87755	+	2.23871i	−0.674995	+	0.389709i
$34$	2.16099	+	2.87800i	0.370607	+	0.493574i
$35$	−0.776954	−	1.65261i	−0.131329	−	0.279342i
$36$	0.622448	−	2.14293i	0.103741	−	0.357155i
$37$	6.00295	−	3.46580i	0.986879	−	0.569775i	0.0825390	−	0.996588i	$-0.473697\pi$
$37$	6.00295	−	3.46580i	0.986879	−	0.569775i	0.904340	+	0.426813i	$0.140364\pi$
$38$	0.786017	−	0.0951408i	0.127509	−	0.0154339i
$39$	−6.26817	−	3.61893i	−1.00371	−	0.579492i
$40$	−1.23637	+	1.51081i	−0.195488	+	0.238880i
$41$			9.76765i			1.52545i	0.646723	+	0.762725i	$0.276139\pi$
$41$			9.76765i			1.52545i	−0.646723	+	0.762725i	$0.723861\pi$
$42$	−2.72792	−	4.35178i	−0.420927	−	0.671494i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	−6.33521	+	1.55645i	−0.955069	+	0.234644i
$45$	−0.385053	+	0.666931i	−0.0574003	+	0.0994203i
$46$	−4.06279	+	0.491767i	−0.599026	+	0.0725071i
$47$	−2.20094	−	3.81214i	−0.321040	−	0.556057i	0.659663	−	0.751561i	$-0.270699\pi$
$47$	−2.20094	−	3.81214i	−0.321040	−	0.556057i	−0.980703	+	0.195504i	$0.937366\pi$
$48$	−2.94156	+	4.63630i	−0.424577	+	0.669192i
$49$	6.90116	+	1.17220i	0.985879	+	0.167457i
$50$	−5.11575	+	3.84124i	−0.723476	+	0.543233i
$51$	−1.74665	−	3.02529i	−0.244580	−	0.423625i
$52$	−7.29948	−	7.61097i	−1.01226	−	1.05545i
$53$	8.17440	+	4.71949i	1.12284	+	0.648272i	0.942124	−	0.335263i	$-0.108825\pi$
$53$	8.17440	+	4.71949i	1.12284	+	0.648272i	0.180716	+	0.983535i	$0.442159\pi$
$54$	−3.13447	+	7.34923i	−0.426547	+	1.00010i
$55$	2.25134			0.303571
$56$	−2.04822	−	7.19756i	−0.273704	−	0.961814i
$57$	−0.768501			−0.101790
$58$	0.246681	−	0.578380i	0.0323908	−	0.0759451i
$59$	8.59663	+	4.96327i	1.11919	+	0.646162i	0.941193	−	0.337869i	$-0.109706\pi$
$59$	8.59663	+	4.96327i	1.11919	+	0.646162i	0.177993	+	0.984032i	$0.443040\pi$
$60$	1.36758	−	1.31161i	0.176554	−	0.169328i
$61$	−5.23284	−	9.06355i	−0.669997	−	1.16047i	−0.977904	−	0.209053i	$-0.932962\pi$
$61$	−5.23284	−	9.06355i	−0.669997	−	1.16047i	0.307907	−	0.951416i	$-0.400371\pi$
$62$	10.0702	−	7.56134i	1.27891	−	0.960292i
$63$	−1.25597	−	2.67148i	−0.158237	−	0.336575i
$64$	−6.00000	+	5.29150i	−0.750000	+	0.661438i
$65$	1.81968	+	3.15177i	0.225703	+	0.390929i
$66$	6.28613	−	0.760884i	0.773770	−	0.0936584i
$67$	−1.45058	+	2.51247i	−0.177216	+	0.306948i	−0.940926	−	0.338612i	$-0.890043\pi$
$67$	−1.45058	+	2.51247i	−0.177216	+	0.306948i	0.763710	+	0.645560i	$0.223376\pi$
$68$	−1.21435	−	4.94277i	−0.147262	−	0.599398i
$69$	3.97225			0.478203
$70$	0.0938060	+	2.58084i	0.0112120	+	0.308469i
$71$			5.29150i			0.627986i	0.949425	+	0.313993i	$0.101667\pi$
$71$			5.29150i			0.627986i	−0.949425	+	0.313993i	$0.898333\pi$
$72$	−1.99863	+	2.44227i	−0.235541	+	0.287824i
$73$	−5.28541	−	3.05153i	−0.618610	−	0.357155i	0.157718	−	0.987484i	$-0.449586\pi$
$73$	−5.28541	−	3.05153i	−0.618610	−	0.357155i	−0.776328	+	0.630330i	$0.782920\pi$
$74$	−9.73174	+	1.17795i	−1.13129	+	0.136934i
$75$	5.37755	−	3.10473i	0.620946	−	0.358503i
$76$	−1.07527	−	0.312329i	−0.123342	−	0.0358266i
$77$	−4.92768	+	7.08473i	−0.561562	+	0.807380i
$78$	6.14605	+	8.18530i	0.695903	+	0.926802i
$79$	5.01803	−	2.89716i	0.564573	−	0.325956i	−0.190406	−	0.981705i	$-0.560980\pi$
$79$	5.01803	−	2.89716i	0.564573	−	0.325956i	0.754979	+	0.655749i	$0.227647\pi$
$80$	2.44654	−	1.27937i	0.273531	−	0.143038i
$81$	2.20393	−	3.81731i	0.244881	−	0.424146i
$82$	5.41921	−	12.7061i	0.598451	−	1.40316i
$83$			1.83845i			0.201796i	0.994897	+	0.100898i	$0.0321716\pi$
$83$			1.83845i			0.201796i	−0.994897	+	0.100898i	$0.967828\pi$
$84$	1.13417	+	7.17445i	0.123748	+	0.782796i
$85$			1.75651i			0.190520i
$86$		0			0
$87$	−0.305161	+	0.528555i	−0.0327167	+	0.0566670i
$88$	9.10463	+	1.49016i	0.970557	+	0.158851i
$89$	1.50000	−	0.866025i	0.159000	−	0.0917985i	−0.418389	−	0.908268i	$-0.637405\pi$
$89$	1.50000	−	0.866025i	0.159000	−	0.0917985i	0.577389	+	0.816469i	$0.304072\pi$
$90$	0.870914	−	0.653939i	0.0918024	−	0.0689312i
$91$	−13.9012	−	1.17220i	−1.45724	−	0.122880i
$92$	5.55787	+	1.61437i	0.579448	+	0.168310i
$93$	−10.5855	+	6.11156i	−1.09767	+	0.633739i
$94$	0.748048	+	6.18008i	0.0771553	+	0.637427i
$95$	0.334649	+	0.193210i	0.0343343	+	0.0198229i
$96$	6.39877	−	4.39907i	0.653071	−	0.448978i
$97$		−	7.42325i		−	0.753717i	−0.926271	−	0.376859i	$-0.877004\pi$
$97$		−	7.42325i		−	0.753717i	0.926271	−	0.376859i	$-0.122996\pi$
$98$	−8.32695	−	5.35368i	−0.841149	−	0.540804i
$99$	3.63935			0.365769
$100$	8.78593	−	2.15855i	0.878593	−	0.215855i
$101$	6.30811	−	10.9260i	0.627681	−	1.08717i	−0.360335	−	0.932823i	$-0.617338\pi$
$101$	6.30811	−	10.9260i	0.627681	−	1.08717i	0.988016	−	0.154352i	$-0.0493289\pi$
$102$	0.593646	+	4.90448i	0.0587797	+	0.485616i
$103$	3.19631	+	5.53618i	0.314942	+	0.545496i	0.979425	−	0.201808i	$-0.0646816\pi$
$103$	3.19631	+	5.53618i	0.314942	+	0.545496i	−0.664483	+	0.747303i	$0.731348\pi$
$104$	5.27279	+	13.9505i	0.517040	+	1.36796i
$105$	0.210627	−	2.49783i	0.0205550	−	0.243764i
$106$	−8.01515	−	10.6746i	−0.778500	−	1.03680i
$107$	−1.51515	−	2.62432i	−0.146475	−	0.253703i	0.783447	−	0.621458i	$-0.213460\pi$
$107$	−1.51515	−	2.62432i	−0.146475	−	0.253703i	−0.929922	+	0.367756i	$0.880126\pi$
$108$	8.15489	−	7.82113i	0.784704	−	0.752589i
$109$	−7.25892	−	4.19094i	−0.695278	−	0.401419i	0.110308	−	0.993897i	$-0.464816\pi$
$109$	−7.25892	−	4.19094i	−0.695278	−	0.401419i	−0.805586	+	0.592478i	$0.798150\pi$
$110$	−2.92863	−	1.24907i	−0.279234	−	0.119094i
$111$	9.51488			0.903113
$112$	−1.32889	+	10.4992i	−0.125568	+	0.992085i
$113$	−12.6260			−1.18775			−0.593875	−	0.804557i	$-0.702403\pi$
$113$	−12.6260			−1.18775			−0.593875	+	0.804557i	$0.702403\pi$
$114$	0.999697	+	0.426374i	0.0936302	+	0.0399336i
$115$	−1.72974	−	0.998669i	−0.161300	−	0.0931263i
$116$	−0.641785	+	0.615519i	−0.0595882	+	0.0571495i
$117$	2.94156	+	5.09492i	0.271947	+	0.471026i
$118$	−8.42916	−	11.2259i	−0.775967	−	1.03343i
$119$	−5.52755	−	3.84461i	−0.506709	−	0.352434i
$120$	−2.50670	+	0.947443i	−0.228829	+	0.0864893i
$121$	0.180323	+	0.312329i	0.0163930	+	0.0283935i
$122$	1.77852	+	14.6935i	0.161020	+	1.33028i
$123$	−6.70393	+	11.6115i	−0.604473	+	1.04698i
$124$	−17.2948	+	4.24904i	−1.55312	+	0.381575i
$125$	−6.57333			−0.587936
$126$	0.151640	+	4.17200i	0.0135092	+	0.371671i
$127$			6.18074i			0.548452i	0.961665	+	0.274226i	$0.0884217\pi$
$127$			6.18074i			0.548452i	−0.961665	+	0.274226i	$0.911578\pi$
$128$	10.7408	−	3.55452i	0.949364	−	0.314178i
$129$		0			0
$130$	−0.618466	−	5.10953i	−0.0542431	−	0.448135i
$131$	−1.81122	+	1.04571i	−0.158247	+	0.0913642i	−0.577032	−	0.816721i	$-0.695789\pi$
$131$	−1.81122	+	1.04571i	−0.158247	+	0.0913642i	0.418785	+	0.908085i	$0.362456\pi$
$132$	−8.59940	−	2.49783i	−0.748482	−	0.217409i
$133$	−1.34048	+	0.630212i	−0.116235	+	0.0546463i
$134$	3.28092	−	2.46353i	0.283428	−	0.212816i
$135$	−3.37701	+	1.94972i	−0.290647	+	0.167805i
$136$	−1.16263	+	7.10348i	−0.0996945	+	0.609119i
$137$	2.43543	−	4.21828i	0.208073	−	0.360392i	−0.743035	−	0.669253i	$-0.766614\pi$
$137$	2.43543	−	4.21828i	0.208073	−	0.360392i	0.951107	+	0.308861i	$0.0999477\pi$
$138$	−5.16726	−	2.20385i	−0.439867	−	0.187605i
$139$		−	1.83845i		−	0.155935i	−0.996956	−	0.0779677i	$-0.975157\pi$
$139$		−	1.83845i		−	0.155935i	0.996956	−	0.0779677i	$-0.0248431\pi$
$140$	1.30985	−	3.40930i	0.110703	−	0.288139i
$141$		−	6.04237i		−	0.508859i
$142$	2.93579	−	6.88340i	0.246366	−	0.577642i
$143$	8.59940	−	14.8946i	0.719118	−	1.24555i
$144$	3.95489	−	2.06813i	0.329574	−	0.172344i
$145$	0.265769	−	0.153442i	0.0220709	−	0.0127426i
$146$	5.18244	+	6.90196i	0.428902	+	0.571210i
$147$	7.39940	+	6.13002i	0.610292	+	0.505595i
$148$	13.3130	+	3.86697i	1.09432	+	0.317863i
$149$	−7.68854	+	4.43898i	−0.629870	+	0.363655i	−0.780702	−	0.624904i	$-0.785138\pi$
$149$	−7.68854	+	4.43898i	−0.629870	+	0.363655i	0.150832	+	0.988559i	$0.451805\pi$
$150$	−8.71787	+	1.05523i	−0.711811	+	0.0861589i
$151$	1.69142	+	0.976544i	0.137646	+	0.0794700i	0.567242	−	0.823551i	$-0.308011\pi$
$151$	1.69142	+	0.976544i	0.137646	+	0.0794700i	−0.429596	+	0.903021i	$0.641344\pi$
$152$	1.22547	+	1.00286i	0.0993984	+	0.0813427i
$153$			2.83944i			0.229555i
$154$	10.3408	−	6.48216i	0.833287	−	0.522347i
$155$	6.14605			0.493663
$156$	−3.45373	−	14.0577i	−0.276519	−	1.12551i
$157$	0.650268	−	1.12630i	0.0518970	−	0.0898883i	−0.838910	−	0.544270i	$-0.816807\pi$
$157$	0.650268	−	1.12630i	0.0518970	−	0.0898883i	0.890807	+	0.454382i	$0.150140\pi$
$158$	−8.13504	+	0.984679i	−0.647189	+	0.0783368i
$159$	6.47835	+	11.2208i	0.513767	+	0.889870i
$160$	−3.89236	+	0.306884i	−0.307718	+	0.0242613i
$161$	6.92873	−	3.25746i	0.546060	−	0.256724i
$162$	−4.98485	+	3.74295i	−0.391647	+	0.294074i
$163$	4.30453	+	7.45566i	0.337156	+	0.583972i	0.983897	−	0.178738i	$-0.0572015\pi$
$163$	4.30453	+	7.45566i	0.337156	+	0.583972i	−0.646740	+	0.762710i	$0.723868\pi$
$164$	−14.0990	+	13.5220i	−1.10095	+	1.05589i
$165$	2.67634	+	1.54519i	0.208353	+	0.120293i
$166$	1.01999	−	2.39153i	0.0791669	−	0.185619i
$167$	−5.27279			−0.408021			−0.204010	−	0.978969i	$-0.565398\pi$
$167$	−5.27279			−0.408021			−0.204010	+	0.978969i	$0.565398\pi$
$168$	2.50510	−	9.96205i	0.193273	−	0.768589i
$169$	14.8023			1.13864
$170$	0.974533	−	2.28494i	0.0747432	−	0.175247i
$171$	0.540969	+	0.312329i	0.0413689	+	0.0238844i
$172$		0			0
$173$	8.25429	+	14.2969i	0.627562	+	1.08697i	0.988039	+	0.154202i	$0.0492805\pi$
$173$	8.25429	+	14.2969i	0.627562	+	1.08697i	−0.360477	+	0.932768i	$0.617386\pi$
$174$	0.690214	−	0.518258i	0.0523250	−	0.0392890i
$175$	6.83392	−	9.82540i	0.516596	−	0.742731i
$176$	−11.0169	−	6.98981i	−0.830430	−	0.526877i
$177$	6.81298	+	11.8004i	0.512095	+	0.886974i
$178$	−2.43174	+	0.294342i	−0.182267	+	0.0220619i
$179$	11.1242	−	19.2677i	0.831462	−	1.44013i	−0.0654170	−	0.997858i	$-0.520838\pi$
$179$	11.1242	−	19.2677i	0.831462	−	1.44013i	0.896879	−	0.442276i	$-0.145829\pi$
$180$	−1.49573	+	0.367476i	−0.111485	+	0.0273900i
$181$	10.0244			0.745108			0.372554	−	0.928011i	$-0.378482\pi$
$181$	10.0244			0.745108			0.372554	+	0.928011i	$0.378482\pi$
$182$	17.4328	+	9.23737i	1.29221	+	0.684719i
$183$		−	14.3660i		−	1.06197i
$184$	−6.33423	−	5.18362i	−0.466966	−	0.382141i
$185$	−4.14332	−	2.39215i	−0.304623	−	0.175874i
$186$	17.1608	−	2.07718i	1.25829	−	0.152306i
$187$	7.18878	−	4.15044i	0.525695	−	0.303510i
$188$	2.45570	−	8.45433i	0.179100	−	0.616595i
$189$	1.25597	−	14.8946i	0.0913581	−	1.08342i
$190$	−0.328130	−	0.437002i	−0.0238050	−	0.0317035i
$191$	−21.6511	+	12.5003i	−1.56662	+	0.904487i	−0.570058	+	0.821605i	$0.693079\pi$
$191$	−21.6511	+	12.5003i	−1.56662	+	0.904487i	−0.996559	+	0.0828820i	$0.973588\pi$
$192$	−10.7644	+	2.17237i	−0.776855	+	0.156777i
$193$	−5.69723	+	9.86789i	−0.410095	+	0.710306i	−0.994900	−	0.100868i	$-0.967838\pi$
$193$	−5.69723	+	9.86789i	−0.410095	+	0.710306i	0.584804	+	0.811174i	$0.301171\pi$
$194$	−4.11851	+	9.65646i	−0.295692	+	0.693294i
$195$			4.99567i			0.357747i
$196$	7.86174	+	11.5842i	0.561553	+	0.827441i
$197$		−	10.1384i		−	0.722330i	−0.932502	−	0.361165i	$-0.882379\pi$
$197$		−	10.1384i		−	0.722330i	0.932502	−	0.361165i	$-0.117621\pi$
$198$	−4.73422	−	2.01916i	−0.336446	−	0.143495i
$199$	−5.40309	+	9.35842i	−0.383015	+	0.663401i	−0.991492	−	0.130171i	$-0.958447\pi$
$199$	−5.40309	+	9.35842i	−0.383015	+	0.663401i	0.608477	+	0.793572i	$0.291781\pi$
$200$	−12.6267	−	2.06661i	−0.892841	−	0.146131i
$201$	−3.44882	+	1.99118i	−0.243261	+	0.140447i
$202$	−14.2677	+	10.7131i	−1.00387	+	0.753772i
$203$	−0.0988439	+	1.17220i	−0.00693748	+	0.0822720i
$204$	1.94882	−	6.70930i	0.136445	−	0.469745i
$205$	5.83854	−	3.37088i	0.407781	−	0.235433i
$206$	−1.08635	−	8.97503i	−0.0756898	−	0.625320i
$207$	−2.79618	−	1.61437i	−0.194348	−	0.112207i
$208$	0.880847	−	21.0728i	0.0610757	−	1.46113i
$209$		−	1.82613i		−	0.126316i
$210$	−1.65982	+	3.13242i	−0.114538	+	0.216158i
$211$	−15.8023			−1.08788			−0.543938	−	0.839125i	$-0.683067\pi$
$211$	−15.8023			−1.08788			−0.543938	+	0.839125i	$0.683067\pi$
$212$	4.50405	+	18.3328i	0.309340	+	1.25910i
$213$	−3.63177	+	6.29041i	−0.248845	+	0.431012i
$214$	0.514965	+	4.25444i	0.0352023	+	0.290828i
$215$		0			0
$216$	−14.9475	+	5.64961i	−1.01705	+	0.384407i
$217$	−13.4523	+	19.3410i	−0.913204	+	1.31295i
$218$	7.11750	+	9.47907i	0.482058	+	0.642004i
$219$	−4.18878	−	7.25517i	−0.283051	−	0.490259i
$220$	3.11668	+	3.24968i	0.210127	+	0.219094i
$221$	11.6208	+	6.70930i	0.781703	+	0.451316i
$222$	−12.3773	−	5.27897i	−0.830712	−	0.354301i
$223$	−14.8885			−0.997006			−0.498503	−	0.866888i	$-0.666117\pi$
$223$	−14.8885			−0.997006			−0.498503	+	0.866888i	$0.666117\pi$
$224$	7.55378	−	12.9205i	0.504708	−	0.863290i
$225$	−5.04721			−0.336481
$226$	16.4243	+	7.00503i	1.09253	+	0.465968i
$227$	−24.3726	−	14.0715i	−1.61767	−	0.933960i	−0.987522	−	0.157483i	$-0.949662\pi$
$227$	−24.3726	−	14.0715i	−1.61767	−	0.933960i	−0.630145	−	0.776477i	$-0.717005\pi$
$228$	−1.06389	−	1.10929i	−0.0704577	−	0.0734644i
$229$	3.36655	+	5.83104i	0.222468	+	0.385326i	0.955557	−	0.294807i	$-0.0952553\pi$
$229$	3.36655	+	5.83104i	0.222468	+	0.385326i	−0.733089	+	0.680133i	$0.761922\pi$
$230$	1.69605	+	2.25879i	0.111834	+	0.148940i
$231$	−10.7204	+	5.04009i	−0.705353	+	0.331614i
$232$	1.17636	−	0.444621i	0.0772316	−	0.0291908i
$233$	−8.58148	−	14.8636i	−0.562191	−	0.973744i	−0.997305	−	0.0733685i	$-0.976625\pi$
$233$	−8.58148	−	14.8636i	−0.562191	−	0.973744i	0.435114	−	0.900376i	$-0.356708\pi$
$234$	−0.999767	−	8.25969i	−0.0653568	−	0.539953i
$235$	−1.51912	+	2.63119i	−0.0990964	+	0.171640i
$236$	4.73670	+	19.2797i	0.308333	+	1.25500i
$237$	7.95375			0.516652
$238$	5.05742	+	8.06796i	0.327824	+	0.522968i
$239$		−	11.9169i		−	0.770838i	−0.922742	−	0.385419i	$-0.874057\pi$
$239$		−	11.9169i		−	0.770838i	0.922742	−	0.385419i	$-0.125943\pi$
$240$	3.78647	+	0.158275i	0.244415	+	0.0102166i
$241$	7.66296	+	4.42421i	0.493615	+	0.284988i	0.726073	−	0.687618i	$-0.241344\pi$
$241$	7.66296	+	4.42421i	0.493615	+	0.284988i	−0.232458	+	0.972606i	$0.574677\pi$
$242$	−0.0612876	−	0.506335i	−0.00393972	−	0.0325484i
$243$	−9.43816	+	5.44912i	−0.605458	+	0.349561i
$244$	5.83854	−	20.1006i	0.373774	−	1.28681i
$245$	−1.68097	−	4.52965i	−0.107393	−	0.289389i
$246$	15.1630	−	11.3853i	0.966755	−	0.725902i
$247$	2.55650	−	1.47600i	0.162666	−	0.0939155i
$248$	24.8552	+	4.06805i	1.57831	+	0.258321i
$249$	−1.26180	+	2.18551i	−0.0799635	+	0.138501i
$250$	8.55084	+	3.64696i	0.540803	+	0.230654i
$251$		−	18.1333i		−	1.14457i	−0.820056	−	0.572283i	$-0.806058\pi$
$251$		−	18.1333i		−	1.14457i	0.820056	−	0.572283i	$-0.193942\pi$
$252$	2.11742	−	5.51123i	0.133385	−	0.347175i
$253$			9.43898i			0.593424i
$254$	3.42915	−	8.04016i	0.215164	−	0.504484i
$255$	−1.20556	+	2.08810i	−0.0754953	+	0.130762i
$256$	−15.9442	−	1.33528i	−0.996512	−	0.0834547i
$257$	8.01964	−	4.63014i	0.500251	−	0.288820i	−0.228566	−	0.973528i	$-0.573404\pi$
$257$	8.01964	−	4.63014i	0.500251	−	0.288820i	0.728817	+	0.684708i	$0.240070\pi$
$258$		0			0
$259$	16.5966	−	7.80271i	1.03126	−	0.484837i
$260$	−2.03030	+	6.98981i	−0.125914	+	0.433490i
$261$	0.429623	−	0.248043i	0.0265930	−	0.0153535i
$262$	2.93629	−	0.355413i	0.181404	−	0.0219575i
$263$	20.3951	+	11.7751i	1.25762	+	0.726085i	0.972611	−	0.232441i	$-0.0746711\pi$
$263$	20.3951	+	11.7751i	1.25762	+	0.726085i	0.285006	+	0.958526i	$0.408004\pi$
$264$	9.80061	+	8.02033i	0.603186	+	0.493617i
$265$		−	6.51492i		−	0.400208i
$266$	2.09340	−	0.0760890i	0.128355	−	0.00466532i
$267$	2.37755			0.145504
$268$	−5.63475	+	1.38436i	−0.344197	+	0.0845633i
$269$	0.810052	−	1.40305i	0.0493897	−	0.0855455i	−0.840274	−	0.542163i	$-0.817606\pi$
$269$	0.810052	−	1.40305i	0.0493897	−	0.0855455i	0.889663	+	0.456617i	$0.150939\pi$
$270$	5.47468	−	0.662665i	0.333178	−	0.0403285i
$271$	−4.22701	−	7.32140i	−0.256773	−	0.444743i	0.708603	−	0.705608i	$-0.249326\pi$
$271$	−4.22701	−	7.32140i	−0.256773	−	0.444743i	−0.965375	+	0.260864i	$0.915992\pi$
$272$	5.45349	−	8.59545i	0.330666	−	0.521176i
$273$	−15.7208	−	10.9344i	−0.951468	−	0.661780i
$274$	−5.50845	+	4.13610i	−0.332778	+	0.249871i
$275$	7.37755	+	12.7783i	0.444883	+	0.770560i
$276$	5.49906	+	5.73372i	0.331004	+	0.345129i
$277$	−16.1282	−	9.31159i	−0.969047	−	0.559479i	−0.0701013	−	0.997540i	$-0.522332\pi$
$277$	−16.1282	−	9.31159i	−0.969047	−	0.559479i	−0.898946	+	0.438060i	$0.855666\pi$
$278$	−1.01999	+	2.39153i	−0.0611752	+	0.143434i
$279$	9.93526			0.594808
$280$	−3.59543	+	3.70823i	−0.214868	+	0.221609i
$281$	12.6260			0.753201			0.376601	−	0.926376i	$-0.377093\pi$
$281$	12.6260			0.753201			0.376601	+	0.926376i	$0.377093\pi$
$282$	−3.35238	+	7.86015i	−0.199631	+	0.468065i
$283$	21.2096	+	12.2454i	1.26078	+	0.727913i	0.973226	−	0.229850i	$-0.0738237\pi$
$283$	21.2096	+	12.2454i	1.26078	+	0.727913i	0.287557	+	0.957764i	$0.407157\pi$
$284$	−7.63798	+	7.32538i	−0.453231	+	0.434681i
$285$	0.265215	+	0.459366i	0.0157100	+	0.0272105i
$286$	−19.4501	+	14.6044i	−1.15011	+	0.863578i
$287$	−2.17145	+	25.7514i	−0.128177	+	1.52006i
$288$	−6.29211	+	0.496085i	−0.370766	+	0.0292321i
$289$	−5.26180	−	9.11371i	−0.309518	−	0.536101i
$290$	−0.430854	+	0.0521513i	−0.0253006	+	0.00306243i
$291$	5.09488	−	8.82459i	0.298667	−	0.517306i
$292$	−2.91223	−	11.8536i	−0.170426	−	0.693681i
$293$	−26.7727			−1.56408			−0.782038	−	0.623231i	$-0.785820\pi$
$293$	−26.7727			−1.56408			−0.782038	+	0.623231i	$0.785820\pi$
$294$	−6.22443	−	12.0794i	−0.363016	−	0.704488i
$295$		−	6.85143i		−	0.398906i
$296$	−15.1726	−	12.4165i	−0.881890	−	0.721695i
$297$	15.9590	+	9.21395i	0.926037	+	0.534648i
$298$	12.4644	−	1.50871i	0.722041	−	0.0873970i
$299$	−13.2141	+	7.62918i	−0.764193	+	0.441207i
$300$	11.9260	+	3.46410i	0.688548	+	0.200000i
$301$		0			0
$302$	−1.65847	−	2.20875i	−0.0954344	−	0.127099i
$303$	14.9979	−	8.65902i	0.861605	−	0.497448i
$304$	−1.03774	−	1.98446i	−0.0595182	−	0.113817i
$305$	−3.61178	+	6.25579i	−0.206810	+	0.358206i
$306$	1.57536	−	3.69366i	0.0900572	−	0.211153i
$307$			28.4069i			1.62127i	0.585553	+	0.810634i	$0.300878\pi$
$307$			28.4069i			1.62127i	−0.585553	+	0.810634i	$0.699122\pi$
$308$	−17.0481	+	2.69504i	−0.971407	+	0.153564i
$309$			8.77503i			0.499194i
$310$	−7.99503	−	3.40990i	−0.454087	−	0.193670i
$311$	12.2816	−	21.2723i	0.696424	−	1.20624i	−0.273274	−	0.961936i	$-0.588107\pi$
$311$	12.2816	−	21.2723i	0.696424	−	1.20624i	0.969698	−	0.244306i	$-0.0785600\pi$
$312$	−3.30662	+	20.2029i	−0.187200	+	1.14377i
$313$	8.12245	−	4.68950i	0.459108	−	0.265066i	−0.252561	−	0.967581i	$-0.581273\pi$
$313$	8.12245	−	4.68950i	0.459108	−	0.265066i	0.711669	+	0.702515i	$0.247940\pi$
$314$	−1.47078	+	1.10436i	−0.0830008	+	0.0623224i
$315$	−1.16342	+	1.67269i	−0.0655512	+	0.0942456i
$316$	11.1287	+	3.23251i	0.626038	+	0.181843i
$317$	10.4847	−	6.05335i	0.588880	−	0.339990i	−0.175774	−	0.984430i	$-0.556243\pi$
$317$	10.4847	−	6.05335i	0.588880	−	0.339990i	0.764655	+	0.644440i	$0.222910\pi$
$318$	−2.20184	−	18.1908i	−0.123473	−	1.02009i
$319$	−1.25597	−	0.725133i	−0.0703206	−	0.0405996i
$320$	5.23360	+	1.76032i	0.292567	+	0.0984050i
$321$		−	4.15964i		−	0.232168i
$322$	−10.8204	+	0.393291i	−0.603000	+	0.0219173i
$323$	1.42476			0.0792758
$324$	8.56112	−	2.10332i	0.475618	−	0.116851i
$325$	−11.9260	+	20.6565i	−0.661536	+	1.14581i
$326$	−1.46301	−	12.0868i	−0.0810286	−	0.669427i
$327$	−5.75282	−	9.96417i	−0.318131	−	0.551020i
$328$	25.8428	−	9.76765i	1.42693	−	0.539328i
$329$	−4.95506	−	10.5396i	−0.273182	−	0.581066i
$330$	−2.62420	−	3.49491i	−0.144458	−	0.192388i
$331$	4.62693	+	8.01409i	0.254319	+	0.440494i	0.964710	−	0.263313i	$-0.0848152\pi$
$331$	4.62693	+	8.01409i	0.254319	+	0.440494i	−0.710391	+	0.703807i	$0.751482\pi$
$332$	−2.65370	+	2.54509i	−0.145641	+	0.139680i
$333$	−6.69779	−	3.86697i	−0.367037	−	0.211909i
$334$	6.85905	+	2.92541i	0.375311	+	0.160071i
$335$	2.00242			0.109404
$336$	−8.78580	+	11.5692i	−0.479305	+	0.631150i
$337$	−0.823644			−0.0448667			−0.0224334	−	0.999748i	$-0.507141\pi$
$337$	−0.823644			−0.0448667			−0.0224334	+	0.999748i	$0.507141\pi$
$338$	−19.2554	−	8.21250i	−1.04736	−	0.446701i
$339$	−15.0094	−	8.66570i	−0.815200	−	0.470656i
$340$	−2.53542	+	2.43165i	−0.137503	+	0.131875i
$341$	−14.5225	−	25.1536i	−0.786435	−	1.36215i
$342$	−0.530430	−	0.706426i	−0.0286824	−	0.0381991i
$343$	17.9336	+	4.62457i	0.968322	+	0.249703i
$344$		0			0
$345$	−1.37085	−	2.37439i	−0.0738042	−	0.127833i
$346$	−2.80544	−	23.1775i	−0.150822	−	1.24603i
$347$	−6.43367	+	11.1434i	−0.345378	+	0.598212i	−0.985422	−	0.170126i	$-0.945582\pi$
$347$	−6.43367	+	11.1434i	−0.345378	+	0.598212i	0.640045	+	0.768338i	$0.278916\pi$
$348$	−1.18539	+	0.291231i	−0.0635438	+	0.0156116i
$349$	30.7068			1.64370			0.821850	−	0.569704i	$-0.192942\pi$
$349$	30.7068			1.64370			0.821850	+	0.569704i	$0.192942\pi$
$350$	−14.3411	+	8.98973i	−0.766563	+	0.480521i
$351$			29.7892i			1.59003i
$352$	10.4532	+	15.2049i	0.557157	+	0.810426i
$353$	11.9893	+	6.92205i	0.638128	+	0.368423i	0.783893	−	0.620896i	$-0.213231\pi$
$353$	11.9893	+	6.92205i	0.638128	+	0.368423i	−0.145765	+	0.989319i	$0.546564\pi$
$354$	−2.31557	−	19.1304i	−0.123071	−	1.01677i
$355$	3.16296	−	1.82613i	0.167872	−	0.0969212i
$356$	3.32661	+	0.966267i	0.176310	+	0.0512121i
$357$	−3.93231	−	8.36415i	−0.208120	−	0.442678i
$358$	−25.1607	+	18.8923i	−1.32979	+	0.998490i
$359$	3.76207	−	2.17203i	0.198554	−	0.114635i	−0.397427	−	0.917634i	$-0.630097\pi$
$359$	3.76207	−	2.17203i	0.198554	−	0.114635i	0.595981	+	0.802999i	$0.296763\pi$
$360$	2.14959	+	0.351823i	0.113293	+	0.0185427i
$361$	−9.34328	+	16.1830i	−0.491752	+	0.851739i
$362$	−13.0401	−	5.56166i	−0.685374	−	0.292314i
$363$			0.495052i			0.0259835i
$364$	−17.5523	−	21.6883i	−0.919991	−	1.13677i
$365$			4.21242i			0.220488i
$366$	−7.97045	+	18.6879i	−0.416622	+	0.976833i
$367$	2.07648	−	3.59656i	0.108391	−	0.187739i	−0.806727	−	0.590924i	$-0.798763\pi$
$367$	2.07648	−	3.59656i	0.108391	−	0.187739i	0.915119	+	0.403185i	$0.132097\pi$
$368$	5.36388	+	10.2574i	0.279612	+	0.534702i
$369$	9.43816	−	5.44912i	0.491331	−	0.283670i
$370$	4.06260	+	5.41056i	0.211205	+	0.281282i
$371$	20.5018	+	14.2597i	1.06440	+	0.740327i
$372$	−23.4759	−	6.81896i	−1.21717	−	0.353547i
$373$	1.52118	−	0.878255i	0.0787638	−	0.0454743i	−0.460101	−	0.887867i	$-0.652187\pi$
$373$	1.52118	−	0.878255i	0.0787638	−	0.0454743i	0.538865	+	0.842392i	$0.318853\pi$
$374$	−11.6542	+	1.41064i	−0.602622	+	0.0729424i
$375$	−7.81421	−	4.51154i	−0.403524	−	0.232975i
$376$	−7.88503	+	9.63527i	−0.406639	+	0.496901i
$377$		−	2.34439i		−	0.120742i
$378$	−9.89751	+	18.6787i	−0.509073	+	0.960726i
$379$	−14.9787			−0.769403			−0.384701	−	0.923041i	$-0.625696\pi$
$379$	−14.9787			−0.769403			−0.384701	+	0.923041i	$0.625696\pi$
$380$	0.184390	+	0.750520i	0.00945901	+	0.0385009i
$381$	−4.24209	+	7.34752i	−0.217329	+	0.376425i
$382$	35.0999	−	4.24855i	1.79587	−	0.217375i
$383$	−8.26475	−	14.3150i	−0.422309	−	0.731461i	0.573856	−	0.818956i	$-0.305447\pi$
$383$	−8.26475	−	14.3150i	−0.422309	−	0.731461i	−0.996165	+	0.0874957i	$0.972114\pi$
$384$	15.2080	+	3.14633i	0.776082	+	0.160560i
$385$	5.93543	+	0.500497i	0.302497	+	0.0255077i
$386$	12.8860	−	9.67565i	0.655880	−	0.492478i
$387$		0			0
$388$	10.7150	−	10.2765i	0.543974	−	0.521711i
$389$	−21.8776	−	12.6310i	−1.10924	−	0.640418i	−0.170605	−	0.985340i	$-0.554572\pi$
$389$	−21.8776	−	12.6310i	−1.10924	−	0.640418i	−0.938631	+	0.344922i	$0.887905\pi$
$390$	2.77166	−	6.49856i	0.140348	−	0.329068i
$391$	−7.36435			−0.372431
$392$	−3.79982	−	19.4309i	−0.191920	−	0.981411i
$393$	−2.87085			−0.144815
$394$	−5.62490	+	13.1884i	−0.283378	+	0.664423i
$395$	−3.46352	−	1.99966i	−0.174268	−	0.100614i
$396$	5.03820	+	5.25320i	0.253179	+	0.263983i
$397$	−4.05677	−	7.02653i	−0.203603	−	0.352651i	0.746083	−	0.665852i	$-0.231932\pi$
$397$	−4.05677	−	7.02653i	−0.203603	−	0.352651i	−0.949687	+	0.313201i	$0.898599\pi$
$398$	12.2207	−	9.17610i	0.612569	−	0.459957i
$399$	−2.02607	−	0.170846i	−0.101431	−	0.00855299i
$400$	15.2787	+	9.69376i	0.763935	+	0.484688i
$401$	0.564574	+	0.977870i	0.0281935	+	0.0488325i	0.879778	−	0.475385i	$-0.157691\pi$
$401$	0.564574	+	0.977870i	0.0281935	+	0.0488325i	−0.851584	+	0.524217i	$0.824358\pi$
$402$	5.59110	−	0.676756i	0.278859	−	0.0337535i
$403$	23.4759	−	40.6615i	1.16942	−	2.02549i
$404$	24.5038	−	6.02015i	1.21911	−	0.299514i
$405$	−3.04236			−0.151176
$406$	0.778929	−	1.47000i	0.0386576	−	0.0729548i
$407$			22.6095i			1.12071i
$408$	−6.25751	+	7.64649i	−0.309793	+	0.378558i
$409$	−10.8567	−	6.26811i	−0.536828	−	0.309938i	0.206964	−	0.978349i	$-0.433642\pi$
$409$	−10.8567	−	6.26811i	−0.536828	−	0.309938i	−0.743793	+	0.668411i	$0.766975\pi$
$410$	−9.46521	+	1.14569i	−0.467454	+	0.0565814i
$411$	5.79035	−	3.34306i	0.285617	−	0.164901i
$412$	−3.56628	+	12.2778i	−0.175698	+	0.604884i
$413$	21.5607	+	14.9963i	1.06093	+	0.737917i
$414$	2.74171	+	3.65140i	0.134747	+	0.179456i
$415$	1.09892	−	0.634462i	0.0539439	−	0.0311445i
$416$	−12.8373	+	26.9236i	−0.629398	+	1.32004i
$417$	1.26180	−	2.18551i	0.0617907	−	0.107025i
$418$	−1.01316	+	2.37551i	−0.0495554	+	0.116190i
$419$			27.3950i			1.33834i	0.743111	+	0.669168i	$0.233349\pi$
$419$			27.3950i			1.33834i	−0.743111	+	0.669168i	$0.766651\pi$
$420$	3.89707	−	3.15389i	0.190157	−	0.153894i
$421$			30.7814i			1.50019i	0.661329	+	0.750096i	$0.269993\pi$
$421$			30.7814i			1.50019i	−0.661329	+	0.750096i	$0.730007\pi$
$422$	20.5563	+	8.76731i	1.00066	+	0.426786i
$423$	−2.45570	+	4.25339i	−0.119400	+	0.206807i
$424$	4.31220	−	26.3469i	0.209419	−	1.27952i
$425$	−9.96970	+	5.75601i	−0.483601	+	0.279207i
$426$	8.21435	−	6.16786i	0.397986	−	0.298834i
$427$	−11.7809	−	25.0584i	−0.570119	−	1.21266i
$428$	1.69053	−	5.82006i	0.0817148	−	0.281323i
$429$	20.4455	−	11.8042i	0.987119	−	0.569913i
$430$		0			0
$431$	13.0280	+	7.52173i	0.627538	+	0.362309i	0.779798	−	0.626031i	$-0.215322\pi$
$431$	13.0280	+	7.52173i	0.627538	+	0.362309i	−0.152260	+	0.988340i	$0.548655\pi$
$432$	22.5787	+	0.943796i	1.08632	+	0.0454084i
$433$		−	16.8008i		−	0.807396i	−0.914892	−	0.403698i	$-0.867725\pi$
$433$		−	16.8008i		−	0.807396i	0.914892	−	0.403698i	$-0.132275\pi$
$434$	28.2299	−	17.6960i	1.35508	−	0.849434i
$435$	0.421253			0.0201975
$436$	−3.99963	−	16.2796i	−0.191547	−	0.779653i
$437$	−0.810052	+	1.40305i	−0.0387500	+	0.0671170i
$438$	1.42367	+	11.7618i	0.0680255	+	0.562000i
$439$	−5.91260	−	10.2409i	−0.282193	−	0.488773i	0.689732	−	0.724065i	$-0.257729\pi$
$439$	−5.91260	−	10.2409i	−0.282193	−	0.488773i	−0.971925	+	0.235293i	$0.924395\pi$
$440$	−2.25134	−	5.95649i	−0.107329	−	0.283965i
$441$	−2.71733	−	7.32230i	−0.129396	−	0.348681i
$442$	−11.3945	−	15.1751i	−0.541979	−	0.721806i
$443$	−9.12420	−	15.8036i	−0.433504	−	0.750851i	0.563668	−	0.826001i	$-0.309390\pi$
$443$	−9.12420	−	15.8036i	−0.433504	−	0.750851i	−0.997172	+	0.0751504i	$0.976056\pi$
$444$	13.1721	+	13.7342i	0.625120	+	0.651796i
$445$	−1.03532	−	0.597743i	−0.0490789	−	0.0283357i
$446$	19.3675	+	8.26031i	0.917079	+	0.391137i
$447$	−12.1866			−0.576406
$448$	−16.9947	+	12.6166i	−0.802925	+	0.596080i
$449$	−3.17636			−0.149902			−0.0749508	−	0.997187i	$-0.523880\pi$
$449$	−3.17636			−0.149902			−0.0749508	+	0.997187i	$0.523880\pi$
$450$	6.56561	+	2.80025i	0.309506	+	0.132005i
$451$	−27.5917	−	15.9301i	−1.29924	−	0.750118i
$452$	−17.4790	−	18.2248i	−0.822141	−	0.857225i
$453$	1.34048	+	2.32178i	0.0629814	+	0.109087i
$454$	23.8978	+	31.8270i	1.12158	+	1.49372i
$455$	4.09671	+	8.71385i	0.192057	+	0.408512i
$456$	0.768501	+	2.03326i	0.0359884	+	0.0952163i
$457$	−0.714593	−	1.23771i	−0.0334273	−	0.0578977i	0.848828	−	0.528669i	$-0.177309\pi$
$457$	−0.714593	−	1.23771i	−0.0334273	−	0.0578977i	−0.882255	+	0.470772i	$0.843976\pi$
$458$	−1.14421	−	9.45306i	−0.0534656	−	0.441712i
$459$	−7.18878	+	12.4513i	−0.335543	+	0.581178i
$460$	−0.953081	−	3.87931i	−0.0444376	−	0.180874i
$461$	11.4755			0.534466			0.267233	−	0.963632i	$-0.413891\pi$
$461$	11.4755			0.534466			0.267233	+	0.963632i	$0.413891\pi$
$462$	16.7419	−	0.608518i	0.778903	−	0.0283108i
$463$		−	35.6282i		−	1.65578i	−0.560887	−	0.827892i	$-0.689540\pi$
$463$		−	35.6282i		−	1.65578i	0.560887	−	0.827892i	$-0.310460\pi$
$464$	−1.77693	−	0.0742762i	−0.0824920	−	0.00344819i
$465$	7.30628	+	4.21828i	0.338821	+	0.195618i
$466$	2.91665	+	24.0962i	0.135111	+	1.11624i
$467$	−21.4541	+	12.3865i	−0.992777	+	0.573180i	−0.906103	−	0.423057i	$-0.860957\pi$
$467$	−21.4541	+	12.3865i	−0.992777	+	0.573180i	−0.0866736	+	0.996237i	$0.527624\pi$
$468$	−3.28204	+	11.2992i	−0.151712	+	0.522306i
$469$	−4.38285	+	6.30140i	−0.202381	+	0.290971i
$470$	3.43595	−	2.57993i	0.158488	−	0.119003i
$471$	1.54605	−	0.892610i	0.0712380	−	0.0411293i
$472$	4.53494	−	27.7078i	0.208738	−	1.27536i
$473$		0			0
$474$	−10.3466	−	4.41284i	−0.475233	−	0.202688i
$475$			2.53256i			0.116202i
$476$	−2.10269	−	13.3010i	−0.0963764	−	0.609652i
$477$		−	10.5315i		−	0.482206i
$478$	−6.61162	+	15.5019i	−0.302409	+	0.709042i
$479$	−11.9318	+	20.6666i	−0.545180	+	0.944279i	0.453416	+	0.891299i	$0.350205\pi$
$479$	−11.9318	+	20.6666i	−0.545180	+	0.944279i	−0.998596	+	0.0529800i	$0.983128\pi$
$480$	−4.83777	−	2.30667i	−0.220813	−	0.105284i
$481$	−31.6523	+	18.2745i	−1.44322	+	0.833244i
$482$	−7.51367	−	10.0067i	−0.342238	−	0.455792i
$483$	10.4724	+	0.883073i	0.476512	+	0.0401812i
$484$	−0.201195	+	0.692664i	−0.00914524	+	0.0314847i
$485$	−4.43720	+	2.56182i	−0.201483	+	0.116326i
$486$	15.3008	−	1.85203i	0.694057	−	0.0840098i
$487$	−15.3829	−	8.88133i	−0.697066	−	0.402451i	0.109188	−	0.994021i	$-0.465175\pi$
$487$	−15.3829	−	8.88133i	−0.697066	−	0.402451i	−0.806254	+	0.591570i	$0.798508\pi$
$488$	−18.7471	+	22.9084i	−0.848639	+	1.03701i
$489$			11.8175i			0.534405i
$490$	−0.326438	+	6.82497i	−0.0147470	+	0.308321i
$491$	24.6260			1.11135			0.555677	−	0.831398i	$-0.312459\pi$
$491$	24.6260			1.11135			0.555677	+	0.831398i	$0.312459\pi$
$492$	−26.0413	+	6.39790i	−1.17403	+	0.288440i
$493$	0.565753	−	0.979912i	0.0254802	−	0.0441330i
$494$	−4.14450	+	0.501658i	−0.186470	+	0.0225706i
$495$	−1.25597	−	2.17540i	−0.0564515	−	0.0977769i
$496$	−30.0756	−	19.0818i	−1.35043	−	0.856800i
$497$	−1.17636	+	13.9505i	−0.0527668	+	0.625765i
$498$	2.85395	−	2.14293i	0.127888	−	0.0960269i
$499$	−7.20568	−	12.4806i	−0.322571	−	0.558709i	0.658447	−	0.752627i	$-0.271214\pi$
$499$	−7.20568	−	12.4806i	−0.322571	−	0.558709i	−0.981018	+	0.193918i	$0.937880\pi$
$500$	−9.09990	−	9.48822i	−0.406960	−	0.424326i
$501$	−6.26817	−	3.61893i	−0.280041	−	0.161682i
$502$	−10.0606	+	23.5886i	−0.449026	+	1.05281i
$503$	−27.2938			−1.21697			−0.608486	−	0.793565i	$-0.708223\pi$
$503$	−27.2938			−1.21697			−0.608486	+	0.793565i	$0.708223\pi$
$504$	−5.81211	+	5.99446i	−0.258892	+	0.267014i
$505$	−8.70789			−0.387496
$506$	5.23686	−	12.2786i	0.232807	−	0.545851i
$507$	17.5966	+	10.1594i	0.781494	+	0.451196i
$508$	−8.92155	+	8.55642i	−0.395830	+	0.379630i
$509$	9.43037	+	16.3339i	0.417994	+	0.723986i	0.995738	−	0.0922319i	$-0.0294001\pi$
$509$	9.43037	+	16.3339i	0.417994	+	0.723986i	−0.577744	+	0.816218i	$0.696067\pi$
$510$	2.72674	−	2.04742i	0.120742	−	0.0906612i
$511$	−13.2560	−	9.22004i	−0.586412	−	0.407871i
$512$	20.0000	+	10.5830i	0.883883	+	0.467707i
$513$	1.58148	+	2.73920i	0.0698240	+	0.120939i
$514$	−13.0011	+	1.57368i	−0.573455	+	0.0694119i
$515$	2.20614	−	3.82115i	0.0972142	−	0.168380i
$516$		0			0
$517$	14.3580			0.631466
$518$	−25.9186	+	0.942065i	−1.13880	+	0.0413919i
$519$			22.6610i			0.994708i
$520$	6.51913	−	7.96619i	0.285883	−	0.349340i
$521$	23.7236	+	13.6968i	1.03935	+	0.600068i	0.919649	−	0.392742i	$-0.128474\pi$
$521$	23.7236	+	13.6968i	1.03935	+	0.600068i	0.119700	+	0.992810i	$0.461807\pi$
$522$	−0.696487	+	0.0843040i	−0.0304844	+	0.00368989i
$523$	25.7805	−	14.8844i	1.12730	−	0.650847i	0.184046	−	0.982918i	$-0.441080\pi$
$523$	25.7805	−	14.8844i	1.12730	−	0.650847i	0.943255	+	0.332070i	$0.107747\pi$
$524$	−4.01682	−	1.16675i	−0.175476	−	0.0509698i
$525$	14.8676	−	6.98981i	0.648874	−	0.305060i
$526$	−19.9978	−	26.6330i	−0.871945	−	1.16125i
$527$	19.6250	−	11.3305i	0.854879	−	0.493564i
$528$	−8.29924	−	15.8707i	−0.361178	−	0.690682i
$529$	−7.31298	+	12.6664i	−0.317956	+	0.550715i
$530$	−3.61456	+	8.47487i	−0.157006	+	0.368125i
$531$		−	11.0755i		−	0.480637i
$532$	−2.76539	−	1.06246i	−0.119895	−	0.0460637i
$533$		−	51.5028i		−	2.23083i
$534$	−3.09281	−	1.31909i	−0.133839	−	0.0570828i
$535$	−1.04578	+	1.81134i	−0.0452130	+	0.0783112i
$536$	8.09796	+	1.32539i	0.349779	+	0.0572483i
$537$	26.4484	−	15.2700i	1.14133	−	0.658948i
$538$	−1.83218	+	1.37572i	−0.0789908	+	0.0593114i
$539$	−14.5663	+	17.5827i	−0.627416	+	0.757339i
$540$	−7.48933	−	2.17540i	−0.322290	−	0.0936142i
$541$	8.21897	−	4.74522i	0.353361	−	0.204013i	−0.312804	−	0.949818i	$-0.601268\pi$
$541$	8.21897	−	4.74522i	0.353361	−	0.204013i	0.666165	+	0.745805i	$0.267935\pi$
$542$	1.43666	+	11.8692i	0.0617100	+	0.509824i
$543$	11.9168	+	6.88014i	0.511397	+	0.295255i
$544$	−11.8630	+	8.15564i	−0.508621	+	0.349670i
$545$			5.78529i			0.247815i
$546$	14.3837	+	22.9460i	0.615567	+	0.981998i
$547$	10.2732			0.439252			0.219626	−	0.975584i	$-0.429516\pi$
$547$	10.2732			0.439252			0.219626	+	0.975584i	$0.429516\pi$
$548$	9.46037	−	2.32425i	0.404127	−	0.0992871i
$549$	−5.83854	+	10.1127i	−0.249183	+	0.431597i
$550$	−2.50746	−	20.7157i	−0.106918	−	0.883319i
$551$	−0.124462	−	0.215574i	−0.00530224	−	0.00918375i
$552$	−3.97225	−	10.5096i	−0.169070	−	0.447318i
$553$	13.8736	−	6.52250i	0.589965	−	0.277365i
$554$	15.8140	+	21.0610i	0.671871	+	0.894795i
$555$	−3.28365	−	5.68745i	−0.139383	−	0.241419i
$556$	2.65370	−	2.54509i	0.112542	−	0.107936i
$557$	31.8011	+	18.3604i	1.34746	+	0.777955i	0.987889	−	0.155163i	$-0.0495904\pi$
$557$	31.8011	+	18.3604i	1.34746	+	0.777955i	0.359569	+	0.933119i	$0.382924\pi$
$558$	−12.9242	−	5.51220i	−0.547124	−	0.233350i
$559$		0			0
$560$	6.73446	−	2.82903i	0.284583	−	0.119548i
$561$	11.3945			0.481074
$562$	−16.4243	−	7.00503i	−0.692819	−	0.295489i
$563$	5.48439	+	3.16641i	0.231139	+	0.133448i	0.611098	−	0.791555i	$-0.290728\pi$
$563$	5.48439	+	3.16641i	0.231139	+	0.133448i	−0.379958	+	0.925004i	$0.624062\pi$
$564$	8.72181	−	8.36486i	0.367255	−	0.352224i
$565$	4.35731	+	7.54708i	0.183313	+	0.317508i
$566$	−20.7965	−	27.6967i	−0.874140	−	1.16418i
$567$	6.65905	−	9.57399i	0.279654	−	0.402070i
$568$	14.0000	−	5.29150i	0.587427	−	0.222027i
$569$	19.7484	+	34.2052i	0.827896	+	1.43396i	0.899686	+	0.436538i	$0.143796\pi$
$569$	19.7484	+	34.2052i	0.827896	+	1.43396i	−0.0717894	+	0.997420i	$0.522871\pi$
$570$	−0.0901405	−	0.744706i	−0.00377557	−	0.0311923i
$571$	−6.22305	+	10.7786i	−0.260426	+	0.451072i	−0.966355	−	0.257211i	$-0.917196\pi$
$571$	−6.22305	+	10.7786i	−0.260426	+	0.451072i	0.705929	+	0.708283i	$0.250530\pi$
$572$	33.4042	−	8.20685i	1.39670	−	0.343146i
$573$	−34.3177			−1.43364
$574$	17.1119	−	32.2937i	0.714236	−	1.34791i
$575$		−	13.0904i		−	0.545907i
$576$	8.46025	+	2.84561i	0.352511	+	0.118567i
$577$	−10.8259	−	6.25035i	−0.450689	−	0.260205i	0.257432	−	0.966296i	$-0.417124\pi$
$577$	−10.8259	−	6.25035i	−0.450689	−	0.260205i	−0.708121	+	0.706091i	$0.750457\pi$
$578$	1.78836	+	14.7748i	0.0743862	+	0.614550i
$579$	−13.5455	+	7.82047i	−0.562930	+	0.325008i
$580$	0.589406	+	0.171203i	0.0244738	+	0.00710880i
$581$	−0.408707	+	4.84688i	−0.0169560	+	0.201083i
$582$	−11.5236	+	8.65267i	−0.477669	+	0.358665i
$583$	−26.6633	+	15.3940i	−1.10428	+	0.637556i
$584$	−2.78819	+	17.0354i	−0.115376	+	0.704930i
$585$	2.03030	−	3.51659i	0.0839427	−	0.145393i
$586$	34.8269	+	14.8538i	1.43869	+	0.613605i
$587$		−	32.0838i		−	1.32424i	−0.749397	−	0.662121i	$-0.769657\pi$
$587$		−	32.0838i		−	1.32424i	0.749397	−	0.662121i	$-0.230343\pi$
$588$	1.39516	+	19.1668i	0.0575353	+	0.790426i
$589$		−	4.98526i		−	0.205414i
$590$	−3.80126	+	8.91262i	−0.156495	+	0.366927i
$591$	6.95838	−	12.0523i	0.286229	−	0.495764i
$592$	12.8483	+	24.5698i	0.528062	+	1.00981i
$593$	17.2760	−	9.97429i	0.709439	−	0.409595i	−0.101414	−	0.994844i	$-0.532337\pi$
$593$	17.2760	−	9.97429i	0.709439	−	0.409595i	0.810853	+	0.585249i	$0.199003\pi$
$594$	−15.6481	−	20.8401i	−0.642050	−	0.855081i
$595$	−0.390490	+	4.63085i	−0.0160085	+	0.189846i
$596$	−17.0512	−	4.95279i	−0.698443	−	0.202874i
$597$	−12.8461	+	7.41671i	−0.525756	+	0.303546i
$598$	21.4222	−	2.59298i	0.876020	−	0.106035i
$599$	9.05851	+	5.22993i	0.370121	+	0.213689i	0.673511	−	0.739177i	$-0.264785\pi$
$599$	9.05851	+	5.22993i	0.370121	+	0.213689i	−0.303391	+	0.952866i	$0.598119\pi$
$600$	−13.5919	−	11.1229i	−0.554887	−	0.454092i
$601$		−	30.6355i		−	1.24965i	−0.780766	−	0.624823i	$-0.785171\pi$
$601$		−	30.6355i		−	1.24965i	0.780766	−	0.624823i	$-0.214829\pi$
$602$		0			0
$603$	3.23696			0.131819
$604$	0.931966	+	3.79337i	0.0379212	+	0.154350i
$605$	0.124462	−	0.215574i	0.00506008	−	0.00876432i
$606$	−24.3139	+	2.94300i	−0.987686	+	0.119551i
$607$	18.7095	+	32.4058i	0.759396	+	1.31531i	0.943159	+	0.332342i	$0.107839\pi$
$607$	18.7095	+	32.4058i	0.759396	+	1.31531i	−0.183763	+	0.982971i	$0.558828\pi$
$608$	0.248923	+	3.15722i	0.0100952	+	0.128042i
$609$	−0.922028	+	1.32564i	−0.0373625	+	0.0537176i
$610$	8.16914	−	6.13392i	0.330759	−	0.248355i
$611$	11.6051	+	20.1006i	0.469491	+	0.813183i
$612$	−4.09858	+	3.93083i	−0.165675	+	0.158895i
$613$	23.6077	+	13.6299i	0.953507	+	0.550507i	0.894169	−	0.447731i	$-0.147768\pi$
$613$	23.6077	+	13.6299i	0.953507	+	0.550507i	0.0593382	+	0.998238i	$0.481101\pi$
$614$	15.7605	−	36.9528i	0.636042	−	1.49130i
$615$	9.25429			0.373169
$616$	23.6721	+	5.95269i	0.953777	+	0.239841i
$617$	−26.7810			−1.07816			−0.539081	−	0.842254i	$-0.681228\pi$
$617$	−26.7810			−1.07816			−0.539081	+	0.842254i	$0.681228\pi$
$618$	4.86849	−	11.4149i	0.195840	−	0.459175i
$619$	31.4426	+	18.1534i	1.26379	+	0.729648i	0.973805	−	0.227385i	$-0.0730175\pi$
$619$	31.4426	+	18.1534i	1.26379	+	0.729648i	0.289982	+	0.957032i	$0.406351\pi$
$620$	8.50839	+	8.87148i	0.341705	+	0.356287i
$621$	−8.17440	−	14.1585i	−0.328027	−	0.568160i
$622$	−27.7785	+	20.8579i	−1.11382	+	0.836325i
$623$	4.14712	−	1.94972i	0.166151	−	0.0781139i
$624$	15.5102	−	24.4462i	0.620905	−	0.978632i
$625$	−9.04051	−	15.6586i	−0.361620	−	0.626345i
$626$	−13.1678	+	1.59385i	−0.526291	+	0.0637031i
$627$	1.25335	−	2.17086i	0.0500540	−	0.0866960i
$628$	2.52596	−	0.620584i	0.100797	−	0.0247640i
$629$	−17.6401			−0.703356
$630$	2.44145	−	1.53043i	0.0972697	−	0.0609737i
$631$		−	25.5683i		−	1.01786i	−0.860809	−	0.508928i	$-0.830042\pi$
$631$		−	25.5683i		−	1.01786i	0.860809	−	0.508928i	$-0.169958\pi$
$632$	−12.6832	−	10.3793i	−0.504511	−	0.412867i
$633$	−18.7854	−	10.8458i	−0.746653	−	0.431080i
$634$	−16.9974	+	2.05740i	−0.675053	+	0.0817096i
$635$	3.69450	−	2.13302i	0.146612	−	0.0846463i
$636$	−7.22822	+	24.8849i	−0.286617	+	0.986750i
$637$	−36.3883	−	6.18074i	−1.44176	−	0.244890i
$638$	1.23150	+	1.64011i	0.0487555	+	0.0649324i
$639$	5.11301	−	2.95200i	0.202267	−	0.116779i
$640$	−5.83143	−	5.19356i	−0.230507	−	0.205294i
$641$	8.66296	−	15.0047i	0.342166	−	0.592649i	−0.642668	−	0.766144i	$-0.722173\pi$
$641$	8.66296	−	15.0047i	0.342166	−	0.592649i	0.984835	+	0.173495i	$0.0555061\pi$
$642$	−2.30782	+	5.41102i	−0.0910823	+	0.213556i
$643$			19.0294i			0.750444i	0.926935	+	0.375222i	$0.122434\pi$
$643$			19.0294i			0.750444i	−0.926935	+	0.375222i	$0.877566\pi$
$644$	14.2939	+	5.49170i	0.563257	+	0.216403i
$645$		0			0
$646$	−1.85338	−	0.790474i	−0.0729205	−	0.0311008i
$647$	1.28545	−	2.22647i	0.0505364	−	0.0875317i	−0.839651	−	0.543127i	$-0.817240\pi$
$647$	1.28545	−	2.22647i	0.0505364	−	0.0875317i	0.890187	+	0.455595i	$0.150574\pi$
$648$	−12.3036	−	2.01373i	−0.483331	−	0.0791068i
$649$	−28.0405	+	16.1892i	−1.10069	+	0.635482i
$650$	26.9743	−	20.2540i	1.05802	−	0.794429i
$651$	−29.2663	+	13.7592i	−1.14704	+	0.539266i
$652$	−4.80277	+	16.5347i	−0.188091	+	0.647549i
$653$	−37.8296	+	21.8410i	−1.48039	+	0.854702i	−0.999753	−	0.0222184i	$-0.992927\pi$
$653$	−37.8296	+	21.8410i	−1.48039	+	0.854702i	−0.480635	+	0.876921i	$0.659594\pi$
$654$	1.95525	+	16.1535i	0.0764563	+	0.631653i
$655$	1.25013	+	0.721764i	0.0488467	+	0.0282017i
$656$	−39.0365	−	1.63174i	−1.52412	−	0.0637086i
$657$			6.80949i			0.265663i
$658$	0.598252	+	16.4594i	0.0233223	+	0.641656i
$659$	−25.4496			−0.991376			−0.495688	−	0.868501i	$-0.665084\pi$
$659$	−25.4496			−0.991376			−0.495688	+	0.868501i	$0.665084\pi$
$660$	1.47465	+	6.00225i	0.0574007	+	0.233637i
$661$	11.9660	−	20.7256i	0.465422	−	0.806134i	−0.533799	−	0.845612i	$-0.679236\pi$
$661$	11.9660	−	20.7256i	0.465422	−	0.806134i	0.999220	+	0.0394776i	$0.0125694\pi$
$662$	−1.57259	−	12.9921i	−0.0611204	−	0.504953i
$663$	9.20972	+	15.9517i	0.357676	+	0.619513i
$664$	4.86408	−	1.83845i	0.188763	−	0.0713457i
$665$	0.839315	+	0.583773i	0.0325472	+	0.0226378i
$666$	6.56731	+	8.74632i	0.254478	+	0.338913i
$667$	0.643321	+	1.11426i	0.0249095	+	0.0431445i
$668$	−7.29948	−	7.61097i	−0.282425	−	0.294477i
$669$	−17.6991	−	10.2186i	−0.684285	−	0.395072i
$670$	−2.60483	−	1.11097i	−0.100633	−	0.0429204i
$671$	34.1370			1.31784
$672$	17.8476	−	10.1752i	0.688487	−	0.392516i
$673$	42.7810			1.64909			0.824543	−	0.565800i	$-0.191432\pi$
$673$	42.7810			1.64909			0.824543	+	0.565800i	$0.191432\pi$
$674$	1.07143	+	0.456967i	0.0412699	+	0.0176017i
$675$	−22.1327	−	12.7783i	−0.851886	−	0.491837i
$676$	20.4918	+	21.3663i	0.788147	+	0.821781i
$677$	−0.685590	−	1.18748i	−0.0263494	−	0.0456385i	0.852550	−	0.522646i	$-0.175055\pi$
$677$	−0.685590	−	1.18748i	−0.0263494	−	0.0456385i	−0.878899	+	0.477007i	$0.841722\pi$
$678$	14.7170	+	19.6001i	0.565204	+	0.752737i
$679$	1.65027	−	19.5706i	0.0633314	−	0.751052i
$680$	4.64729	−	1.75651i	0.178215	−	0.0673591i
$681$	−19.3157	−	33.4558i	−0.740180	−	1.28203i
$682$	4.93585	+	40.7781i	0.189003	+	1.56147i
$683$	−22.9399	+	39.7331i	−0.877771	+	1.52034i	−0.0239904	+	0.999712i	$0.507637\pi$
$683$	−22.9399	+	39.7331i	−0.877771	+	1.52034i	−0.853781	+	0.520632i	$0.825696\pi$
$684$	0.298071	+	1.21324i	0.0113970	+	0.0463892i
$685$	−3.36193			−0.128453
$686$	−20.7629	−	15.9656i	−0.792733	−	0.609569i
$687$			9.24241i			0.352620i
$688$		0			0
$689$	−43.1019	−	24.8849i	−1.64205	−	0.948039i
$690$	0.465921	+	3.84926i	0.0177373	+	0.146539i
$691$	8.57530	−	4.95095i	0.326220	−	0.188343i	−0.327942	−	0.944698i	$-0.606355\pi$
$691$	8.57530	−	4.95095i	0.326220	−	0.188343i	0.654162	+	0.756355i	$0.273022\pi$
$692$	−9.20972	+	31.7067i	−0.350101	+	1.20531i
$693$	9.59477	+	0.809066i	0.364475	+	0.0307339i
$694$	14.5517	−	10.9264i	0.552375	−	0.414759i
$695$	−1.09892	+	0.634462i	−0.0416844	+	0.0240665i
$696$	1.70359	+	0.278826i	0.0645742	+	0.0105689i
$697$	12.4287	−	21.5272i	0.470772	−	0.815400i
$698$	−39.9447	−	17.0365i	−1.51193	−	0.644842i
$699$		−	23.5593i		−	0.891093i
$700$	23.6431	−	3.73760i	0.893624	−	0.141268i
$701$			22.9445i			0.866602i	0.901249	+	0.433301i	$0.142651\pi$
$701$			22.9445i			0.866602i	−0.901249	+	0.433301i	$0.857349\pi$
$702$	16.5274	−	38.7510i	0.623787	−	1.46256i
$703$	−1.94035	+	3.36078i	−0.0731816	+	0.126754i
$704$	−5.16205	−	25.5787i	−0.194552	−	0.964035i
$705$	−3.61178	+	2.08526i	−0.136028	+	0.0785356i
$706$	−11.7558	−	15.6563i	−0.442434	−	0.589233i
$707$	19.0596	−	27.4028i	0.716811	−	1.03059i
$708$	−7.60158	+	26.1703i	−0.285685	+	0.983539i
$709$	−17.4404	+	10.0692i	−0.654986	+	0.378157i	−0.790364	−	0.612637i	$-0.790109\pi$
$709$	−17.4404	+	10.0692i	−0.654986	+	0.378157i	0.135378	+	0.990794i	$0.456775\pi$
$710$	−5.12766	+	0.620661i	−0.192438	+	0.0232930i
$711$	−5.59887	−	3.23251i	−0.209974	−	0.121228i
$712$	−3.79129	−	3.10260i	−0.142085	−	0.116275i
$713$			25.7680i			0.965018i
$714$	0.474769	+	13.0621i	0.0177678	+	0.488837i
$715$	−11.8709			−0.443945
$716$	43.2118	−	10.6164i	1.61490	−	0.396753i
$717$	8.17902	−	14.1665i	0.305451	−	0.529057i
$718$	−6.09891	+	0.738223i	−0.227609	+	0.0275502i
$719$	3.19631	+	5.53618i	0.119202	+	0.206465i	0.919452	−	0.393203i	$-0.128633\pi$
$719$	3.19631	+	5.53618i	0.119202	+	0.206465i	−0.800249	+	0.599667i	$0.795300\pi$
$720$	−2.60107	−	1.65028i	−0.0969363	−	0.0615024i
$721$	7.19599	+	15.3061i	0.267993	+	0.570030i
$722$	21.1327	−	15.8678i	0.786476	−	0.590537i
$723$	6.07303	+	10.5188i	0.225858	+	0.391198i
$724$	13.8774	+	14.4696i	0.515751	+	0.537760i
$725$	1.74183	+	1.00564i	0.0646898	+	0.0373487i
$726$	0.274661	−	0.643983i	0.0101936	−	0.0239004i
$727$	27.2938			1.01227			0.506136	−	0.862454i	$-0.331073\pi$
$727$	27.2938			1.01227			0.506136	+	0.862454i	$0.331073\pi$
$728$	10.7998	+	37.9512i	0.400268	+	1.40656i
$729$	−28.1834			−1.04383
$730$	2.33710	−	5.47968i	0.0865000	−	0.202812i
$731$		0			0
$732$	20.7366	−	19.8879i	0.766445	−	0.735077i
$733$	5.90214	+	10.2228i	0.218001	+	0.377588i	0.954197	−	0.299180i	$-0.0967132\pi$
$733$	5.90214	+	10.2228i	0.218001	+	0.377588i	−0.736196	+	0.676768i	$0.763380\pi$
$734$	−4.69658	+	3.52650i	−0.173354	+	0.130165i
$735$	1.11059	−	6.53845i	0.0409647	−	0.241174i
$736$	−1.28664	−	16.3191i	−0.0474262	−	0.601531i
$737$	−4.73150	−	8.19520i	−0.174287	−	0.301874i
$738$	−15.3008	+	1.85203i	−0.563229	+	0.0681742i
$739$	−5.17141	+	8.95715i	−0.190233	+	0.329494i	−0.945328	−	0.326122i	$-0.894258\pi$
$739$	−5.17141	+	8.95715i	−0.190233	+	0.329494i	0.755094	+	0.655616i	$0.227591\pi$
$740$	−2.28295	−	9.29226i	−0.0839229	−	0.341590i
$741$	4.05215			0.148859
$742$	−18.7580	−	29.9242i	−0.688629	−	1.09855i
$743$		−	7.06999i		−	0.259373i	−0.991555	−	0.129686i	$-0.958603\pi$
$743$		−	7.06999i		−	0.259373i	0.991555	−	0.129686i	$-0.0413970\pi$
$744$	26.7552	+	21.8951i	0.980893	+	0.802714i
$745$	5.30674	+	3.06385i	0.194424	+	0.112251i
$746$	−2.46608	+	0.298498i	−0.0902896	+	0.0109288i
$747$	1.77643	−	1.02563i	0.0649963	−	0.0375257i
$748$	15.9428	+	4.63085i	0.582928	+	0.169321i
$749$	−3.41112	−	7.25558i	−0.124640	−	0.265113i
$750$	7.66198	+	10.2042i	0.279776	+	0.372605i
$751$	−24.1630	+	13.9505i	−0.881721	+	0.509062i	−0.871225	−	0.490883i	$-0.836674\pi$
$751$	−24.1630	+	13.9505i	−0.881721	+	0.509062i	−0.0104954	+	0.999945i	$0.503341\pi$
$752$	15.6029	−	8.15923i	0.568980	−	0.297537i
$753$	12.4456	−	21.5565i	0.453544	−	0.785561i
$754$	−1.30070	+	3.04968i	−0.0473686	+	0.111063i
$755$		−	1.34805i		−	0.0490605i
$756$	23.2382	−	18.8067i	0.845166	−	0.683992i
$757$			18.9429i			0.688492i	0.938880	+	0.344246i	$0.111865\pi$
$757$			18.9429i			0.688492i	−0.938880	+	0.344246i	$0.888135\pi$
$758$	19.4848	+	8.31035i	0.707721	+	0.301845i
$759$	−6.47835	+	11.2208i	−0.235149	+	0.407291i
$760$	0.176536	−	1.07861i	0.00640363	−	0.0391252i
$761$	10.8780	−	6.28042i	0.394328	−	0.227665i	−0.289706	−	0.957116i	$-0.593558\pi$
$761$	10.8780	−	6.28042i	0.394328	−	0.227665i	0.684034	+	0.729451i	$0.260224\pi$
$762$	9.59477	−	7.20438i	0.347582	−	0.260987i
$763$	−18.2057	−	12.6627i	−0.659090	−	0.458420i
$764$	−48.0164	−	13.9472i	−1.73717	−	0.504590i
$765$	1.69726	−	0.979912i	0.0613645	−	0.0354288i
$766$	2.80900	+	23.2069i	0.101493	+	0.838498i
$767$	−45.3282	−	26.1703i	−1.63671	−	0.944953i
$768$	−18.0376	−	12.5305i	−0.650876	−	0.452155i
$769$			32.9798i			1.18928i	0.803991	+	0.594642i	$0.202706\pi$
$769$			32.9798i			1.18928i	−0.803991	+	0.594642i	$0.797294\pi$
$770$	−7.44336	−	3.94411i	−0.268240	−	0.142136i
$771$	12.7114			0.457790
$772$	−22.1308	+	5.43716i	−0.796505	+	0.195688i
$773$	19.3656	−	33.5422i	0.696533	−	1.20643i	−0.273128	−	0.961978i	$-0.588058\pi$
$773$	19.3656	−	33.5422i	0.696533	−	1.20643i	0.969661	−	0.244453i	$-0.0786084\pi$
$774$		0			0
$775$	20.1404	+	34.8841i	0.723463	+	1.25307i
$776$	−19.6401	+	7.42325i	−0.705038	+	0.266479i
$777$	25.0850	+	2.11526i	0.899919	+	0.0758844i
$778$	21.4514	+	28.5689i	0.769068	+	1.02424i
$779$	−2.73423	−	4.73583i	−0.0979640	−	0.169679i
$780$	−7.21096	+	6.91584i	−0.258194	+	0.247627i
$781$	−14.9475	−	8.62992i	−0.534862	−	0.308803i
$782$	9.57984	+	4.08583i	0.342574	+	0.146109i
$783$	2.51193			0.0897692
$784$	−5.83757	+	27.3847i	−0.208485	+	0.978026i
$785$	−0.897649			−0.0320384
$786$	3.73452	+	1.59278i	0.133206	+	0.0568127i
$787$	25.8406	+	14.9191i	0.921118	+	0.531808i	0.883992	−	0.467503i	$-0.154846\pi$
$787$	25.8406	+	14.9191i	0.921118	+	0.531808i	0.0371266	+	0.999311i	$0.488180\pi$
$788$	14.6342	−	14.0352i	0.521321	−	0.499985i
$789$	16.1635	+	27.9960i	0.575435	+	0.996683i
$790$	3.39604	+	4.52284i	0.120826	+	0.160915i
$791$	−33.2870	−	2.80688i	−1.18355	−	0.0998012i
$792$	−3.63935	−	9.62883i	−0.129319	−	0.342145i
$793$	27.5917	+	47.7902i	0.979809	+	1.69708i
$794$	1.37880	+	11.3911i	0.0489319	+	0.404256i
$795$	4.47145	−	7.74478i	0.158586	−	0.274679i
$796$	−20.9882	+	5.15644i	−0.743907	+	0.182765i
$797$	0.929890			0.0329384			0.0164692	−	0.999864i	$-0.494757\pi$
$797$	0.929890			0.0329384			0.0164692	+	0.999864i	$0.494757\pi$
$798$	2.54081	+	1.34633i	0.0899436	+	0.0476597i
$799$			11.2022i			0.396306i
$800$	−14.4969	−	21.0868i	−0.512544	−	0.745532i
$801$	−1.67362	−	0.966267i	−0.0591346	−	0.0341414i
$802$	−0.191886	−	1.58528i	−0.00677571	−	0.0559783i
$803$	17.2400	−	9.95349i	0.608385	−	0.351251i
$804$	−7.64859	−	2.22166i	−0.269745	−	0.0783518i
$805$	−4.33828	−	3.01743i	−0.152904	−	0.106350i
$806$	−53.0979	+	39.8694i	−1.87029	+	1.40434i
$807$	1.92594	−	1.11194i	0.0677963	−	0.0391422i
$808$	−35.2155	−	5.76372i	−1.23888	−	0.202767i
$809$	8.69326	−	15.0572i	0.305639	−	0.529382i	−0.671765	−	0.740765i	$-0.734463\pi$
$809$	8.69326	−	15.0572i	0.305639	−	0.529382i	0.977403	+	0.211383i	$0.0677967\pi$
$810$	3.95763	+	1.68794i	0.139057	+	0.0593082i
$811$		−	19.0294i		−	0.668211i	−0.942536	−	0.334105i	$-0.891566\pi$
$811$		−	19.0294i		−	0.668211i	0.942536	−	0.334105i	$-0.108434\pi$
$812$	−1.82883	+	1.48007i	−0.0641795	+	0.0519404i
$813$		−	11.6047i		−	0.406993i
$814$	12.5440	−	29.4114i	0.439669	−	1.03087i
$815$	2.97104	−	5.14600i	0.104071	−	0.180256i
$816$	12.3824	−	6.47512i	0.433470	−	0.226674i
$817$		0			0
$818$	10.6452	+	14.1772i	0.372200	+	0.495695i
$819$	6.62245	+	14.0862i	0.231407	+	0.492211i
$820$	12.9484	+	3.76106i	0.452177	+	0.131342i
$821$	38.6560	−	22.3180i	1.34910	−	0.778905i	0.360981	−	0.932573i	$-0.382442\pi$
$821$	38.6560	−	22.3180i	1.34910	−	0.778905i	0.988122	+	0.153668i	$0.0491087\pi$
$822$	−9.38709	+	1.13623i	−0.327412	+	0.0396305i
$823$	−0.764272	−	0.441253i	−0.0266408	−	0.0153811i	0.486620	−	0.873614i	$-0.338229\pi$
$823$	−0.764272	−	0.441253i	−0.0266408	−	0.0153811i	−0.513261	+	0.858232i	$0.671563\pi$
$824$	11.4510	−	13.9928i	0.398916	−	0.487463i
$825$			20.2540i			0.705155i
$826$	−19.7269	−	31.4699i	−0.686388	−	1.09498i
$827$	18.3527			0.638186			0.319093	−	0.947723i	$-0.396622\pi$
$827$	18.3527			0.638186			0.319093	+	0.947723i	$0.396622\pi$
$828$	−1.54068	−	6.27101i	−0.0535423	−	0.217933i
$829$	18.2550	−	31.6186i	0.634024	−	1.09816i	−0.352698	−	0.935737i	$-0.614736\pi$
$829$	18.2550	−	31.6186i	0.634024	−	1.09816i	0.986721	−	0.162424i	$-0.0519311\pi$
$830$	−1.78153	+	0.215639i	−0.0618377	+	0.00748494i
$831$	−12.7818	−	22.1388i	−0.443397	−	0.767986i
$832$	31.6367	−	27.9010i	1.09681	−	0.967292i
$833$	−13.7181	−	11.3647i	−0.475304	−	0.393765i
$834$	−2.85395	+	2.14293i	−0.0988241	+	0.0742036i
$835$	1.81968	+	3.15177i	0.0629725	+	0.109072i
$836$	2.63592	−	2.52804i	0.0911653	−	0.0874341i
$837$	43.5674	+	25.1536i	1.50591	+	0.869437i
$838$	15.1991	−	35.6366i	0.525044	−	1.23104i
$839$	31.6367			1.09222			0.546111	−	0.837713i	$-0.316108\pi$
$839$	31.6367			1.09222			0.546111	+	0.837713i	$0.316108\pi$
$840$	−6.81927	+	1.94057i	−0.235287	+	0.0669560i
$841$	28.8023			0.993183
$842$	17.0779	−	40.0416i	0.588542	−	1.37993i
$843$	15.0094	+	8.66570i	0.516952	+	0.298463i
$844$	−21.8762	−	22.8097i	−0.753010	−	0.785144i
$845$	−5.10838	−	8.84798i	−0.175734	−	0.304380i
$846$	5.55430	−	4.17053i	0.190961	−	0.143386i
$847$	0.405969	+	0.863509i	0.0139493	+	0.0296705i
$848$	−20.2271	+	31.8807i	−0.694601	+	1.09479i
$849$	16.8090	+	29.1141i	0.576884	+	0.999192i
$850$	16.1625	−	1.95633i	0.554368	−	0.0671017i
$851$	10.0293	−	17.3713i	0.343801	−	0.595481i
$852$	−14.1076	+	3.46598i	−0.483317	+	0.118743i
$853$	26.3639			0.902684			0.451342	−	0.892351i	$-0.350945\pi$
$853$	26.3639			0.902684			0.451342	+	0.892351i	$0.350945\pi$
$854$	1.42238	+	39.1332i	0.0486727	+	1.33911i
$855$		−	0.431147i		−	0.0147449i
$856$	−5.42815	+	6.63303i	−0.185530	+	0.226712i
$857$	−22.5909	−	13.0429i	−0.771691	−	0.445536i	0.0617866	−	0.998089i	$-0.480320\pi$
$857$	−22.5909	−	13.0429i	−0.771691	−	0.445536i	−0.833477	+	0.552553i	$0.813653\pi$
$858$	−33.1455	+	4.01198i	−1.13157	+	0.136967i
$859$	6.13760	−	3.54355i	0.209412	−	0.120904i	−0.391626	−	0.920124i	$-0.628087\pi$
$859$	6.13760	−	3.54355i	0.209412	−	0.120904i	0.601038	+	0.799220i	$0.294754\pi$
$860$		0			0
$861$	−20.2556	+	29.1223i	−0.690308	+	0.992484i
$862$	−12.7742	−	17.0127i	−0.435092	−	0.579454i
$863$	−13.4014	+	7.73731i	−0.456189	+	0.263381i	−0.710441	−	0.703757i	$-0.751504\pi$
$863$	−13.4014	+	7.73731i	−0.456189	+	0.263381i	0.254251	+	0.967138i	$0.418171\pi$
$864$	−28.8477	−	13.7547i	−0.981417	−	0.467943i
$865$	5.69723	−	9.86789i	0.193712	−	0.335518i
$866$	−9.32130	+	21.8552i	−0.316751	+	0.742669i
$867$		−	14.4455i		−	0.490596i
$868$	−46.5406	+	7.35733i	−1.57969	+	0.249724i
$869$			18.8999i			0.641137i
$870$	−0.547983	−	0.233716i	−0.0185783	−	0.00792372i
$871$	7.64859	−	13.2478i	0.259163	−	0.448883i
$872$	−3.82926	+	23.3962i	−0.129675	+	0.792296i
$873$	−7.17285	+	4.14125i	−0.242764	+	0.140160i
$874$	1.83218	−	1.37572i	0.0619743	−	0.0465343i
$875$	−17.3299	−	1.46132i	−0.585857	−	0.0494016i
$876$	4.67362	−	16.0901i	0.157907	−	0.543633i
$877$	−40.0954	+	23.1491i	−1.35392	+	0.781689i	−0.988797	−	0.149268i	$-0.952308\pi$
$877$	−40.0954	+	23.1491i	−1.35392	+	0.781689i	−0.365128	+	0.930957i	$0.618975\pi$
$878$	2.00956	+	16.6022i	0.0678192	+	0.560296i
$879$	−31.8267	−	18.3751i	−1.07349	−	0.619778i
$880$	−0.376098	+	8.99751i	−0.0126783	+	0.303306i
$881$			37.7381i			1.27143i	0.771925	+	0.635714i	$0.219294\pi$
$881$			37.7381i			1.27143i	−0.771925	+	0.635714i	$0.780706\pi$
$882$	−0.527696	+	11.0327i	−0.0177684	+	0.371492i
$883$	−37.0542			−1.24697			−0.623487	−	0.781834i	$-0.714285\pi$
$883$	−37.0542			−1.24697			−0.623487	+	0.781834i	$0.714285\pi$
$884$	6.40303	+	26.0622i	0.215357	+	0.876565i
$885$	4.70241	−	8.14482i	0.158070	−	0.273785i
$886$	3.10111	+	25.6201i	0.104184	+	0.860725i
$887$	−21.7519	−	37.6754i	−0.730357	−	1.26502i	−0.956731	−	0.290975i	$-0.906020\pi$
$887$	−21.7519	−	37.6754i	−0.730357	−	1.26502i	0.226374	−	0.974040i	$-0.427313\pi$
$888$	−9.51488	−	25.1740i	−0.319299	−	0.844785i
$889$	−1.37404	+	16.2949i	−0.0460840	+	0.546513i
$890$	1.01515	+	1.35198i	0.0340280	+	0.0453183i
$891$	7.18878	+	12.4513i	0.240833	+	0.417135i
$892$	−20.6111	−	21.4907i	−0.690111	−	0.719561i
$893$	2.13424	+	1.23221i	0.0714197	+	0.0412342i
$894$	15.8528	+	6.76127i	0.530197	+	0.226131i
$895$	−15.3562			−0.513300
$896$	29.1073	−	6.98333i	0.972406	−	0.233297i
$897$	−20.9449			−0.699328
$898$	4.13193	+	1.76228i	0.137884	+	0.0588081i
$899$	−3.42873	−	1.97958i	−0.114354	−	0.0660226i
$900$	−6.98719	−	7.28536i	−0.232906	−	0.242845i
$901$	−12.0105	−	20.8028i	−0.400129	−	0.693043i
$902$	27.0542	+	36.0307i	0.900805	+	1.19969i
$903$		0			0
$904$	12.6260	+	33.4051i	0.419933	+	1.11104i
$905$	−3.45949	−	5.99201i	−0.114997	−	0.199181i
$906$	−0.455599	−	3.76398i	−0.0151363	−	0.125050i
$907$	−26.6304	+	46.1253i	−0.884249	+	1.53156i	−0.0376777	+	0.999290i	$0.511996\pi$
$907$	−26.6304	+	46.1253i	−0.884249	+	1.53156i	−0.846572	+	0.532275i	$0.821337\pi$
$908$	−13.4292	−	54.6606i	−0.445663	−	1.81398i
$909$	−14.0765			−0.466889
$910$	−0.494619	−	13.6082i	−0.0163965	−	0.451108i
$911$			46.2112i			1.53105i	0.643408	+	0.765523i	$0.277520\pi$
$911$			46.2112i			1.53105i	−0.643408	+	0.765523i	$0.722480\pi$
$912$	0.128382	−	3.07132i	0.00425116	−	0.101702i
$913$	−5.19326	−	2.99833i	−0.171872	−	0.0992303i
$914$	0.242874	+	2.00653i	0.00803355	+	0.0663701i
$915$	−8.58720	+	4.95782i	−0.283884	+	0.163901i
$916$	−3.75623	+	12.9317i	−0.124109	+	0.427277i
$917$	−5.00757	+	2.35425i	−0.165365	+	0.0777443i
$918$	16.2596	−	12.2088i	0.536646	−	0.402949i
$919$	12.7256	−	7.34713i	0.419779	−	0.242359i	−0.275204	−	0.961386i	$-0.588745\pi$
$919$	12.7256	−	7.34713i	0.419779	−	0.242359i	0.694983	+	0.719026i	$0.255412\pi$
$920$	−0.912484	+	5.57514i	−0.0300837	+	0.183807i
$921$	−19.4968	+	33.7695i	−0.642442	+	1.11274i
$922$	−14.9277	−	6.36673i	−0.491619	−	0.209677i
$923$		−	27.9010i		−	0.918372i
$924$	−22.1161	−	8.49701i	−0.727567	−	0.279531i
$925$		−	31.3559i		−	1.03097i
$926$	−19.7670	+	46.3466i	−0.649583	+	1.52304i
$927$	3.56628	−	6.17699i	0.117132	−	0.202879i
$928$	2.27029	+	1.08248i	0.0745260	+	0.0355343i
$929$	10.5507	−	6.09146i	0.346158	−	0.199854i	−0.316834	−	0.948481i	$-0.602620\pi$
$929$	10.5507	−	6.09146i	0.346158	−	0.199854i	0.662992	+	0.748627i	$0.269286\pi$
$930$	−7.16394	−	9.54092i	−0.234915	−	0.312859i
$931$	−3.67414	+	1.36348i	−0.120415	+	0.0446864i
$932$	9.57478	−	32.9635i	0.313632	−	1.07976i
$933$	29.2001	−	16.8587i	0.955967	−	0.551928i
$934$	34.7805	−	4.20989i	1.13805	−	0.137752i
$935$	−4.96179	−	2.86469i	−0.162268	−	0.0936855i
$936$	10.5383	−	12.8776i	0.344457	−	0.420916i
$937$		−	30.7049i		−	1.00309i	−0.865133	−	0.501543i	$-0.832766\pi$
$937$		−	30.7049i		−	1.00309i	0.865133	−	0.501543i	$-0.167234\pi$
$938$	9.19747	−	5.76545i	0.300308	−	0.188249i
$939$	12.8744			0.420139
$940$	−5.90099	+	1.44977i	−0.192469	+	0.0472864i
$941$	−20.8705	+	36.1488i	−0.680359	+	1.17842i	0.294512	+	0.955648i	$0.404843\pi$
$941$	−20.8705	+	36.1488i	−0.680359	+	1.17842i	−0.974871	+	0.222769i	$0.928490\pi$
$942$	−2.50639	+	0.303378i	−0.0816626	+	0.00988458i
$943$	14.1328	+	24.4787i	0.460227	+	0.797136i
$944$	−21.2719	+	33.5274i	−0.692340	+	1.09122i
$945$	−9.33658	+	4.38948i	−0.303719	+	0.142790i
$946$		0			0
$947$	−24.1540	−	41.8360i	−0.784901	−	1.35949i	−0.929058	−	0.369934i	$-0.879380\pi$
$947$	−24.1540	−	41.8360i	−0.784901	−	1.35949i	0.144157	−	0.989555i	$-0.453953\pi$
$948$	11.0109	+	11.4808i	0.357618	+	0.372879i
$949$	27.8688	+	16.0901i	0.904661	+	0.522306i
$950$	1.40510	−	3.29446i	0.0455873	−	0.106886i
$951$	16.6186			0.538896
$952$	−4.64432	+	18.4691i	−0.150523	+	0.598588i
$953$	−26.2732			−0.851074			−0.425537	−	0.904941i	$-0.639915\pi$
$953$	−26.2732			−0.851074			−0.425537	+	0.904941i	$0.639915\pi$
$954$	−5.84303	+	13.6998i	−0.189175	+	0.443549i
$955$	14.9439	+	8.62785i	0.483573	+	0.279191i
$956$	17.2013	−	16.4973i	0.556330	−	0.533561i
$957$	−0.995375	−	1.72404i	−0.0321759	−	0.0557303i
$958$	26.9875	−	20.2639i	0.871925	−	0.654698i
$959$	7.35851	−	10.5796i	0.237619	−	0.341634i
$960$	5.01340	+	5.68466i	0.161807	+	0.183472i
$961$	−24.1456	−	41.8214i	−0.778890	−	1.34908i
$962$	51.3134	−	6.21107i	1.65441	−	0.200253i
$963$	−1.69053	+	2.92808i	−0.0544766	+	0.0943562i
$964$	4.22225	+	17.1858i	0.135990	+	0.553517i
$965$	7.86462			0.253171
$966$	−13.1330	−	6.95897i	−0.422548	−	0.223901i
$967$		−	3.51302i		−	0.112971i	−0.998403	−	0.0564855i	$-0.982011\pi$
$967$		−	3.51302i		−	0.112971i	0.998403	−	0.0564855i	$-0.0179895\pi$
$968$	0.646021	−	0.789419i	0.0207639	−	0.0253729i
$969$	1.69372	+	0.977870i	0.0544102	+	0.0314137i
$970$	7.19341	−	0.870703i	0.230966	−	0.0279566i
$971$	37.4934	−	21.6468i	1.20322	−	0.694679i	0.241950	−	0.970289i	$-0.422213\pi$
$971$	37.4934	−	21.6468i	1.20322	−	0.694679i	0.961270	+	0.275610i	$0.0888798\pi$
$972$	−20.9314	−	6.07986i	−0.671374	−	0.195011i
$973$	0.408707	−	4.84688i	0.0131025	−	0.155384i
$974$	15.0832	+	20.0878i	0.483298	+	0.643655i
$975$	−28.3547	+	16.3706i	−0.908077	+	0.524279i
$976$	37.0967	−	19.3990i	1.18744	−	0.620947i
$977$	11.4106	−	19.7637i	0.365057	−	0.632297i	−0.623728	−	0.781641i	$-0.714383\pi$
$977$	11.4106	−	19.7637i	0.365057	−	0.632297i	0.988785	+	0.149344i	$0.0477162\pi$
$978$	6.55648	−	15.3726i	0.209653	−	0.491563i
$979$			5.64961i			0.180562i
$980$	4.21122	−	8.69708i	0.134522	−	0.277818i
$981$			9.35207i			0.298589i
$982$	−32.0344	−	13.6628i	−1.02226	−	0.435997i
$983$	−26.9239	+	46.6335i	−0.858738	+	1.48738i	0.0143953	+	0.999896i	$0.495418\pi$
$983$	−26.9239	+	46.6335i	−0.858738	+	1.48738i	−0.873133	+	0.487481i	$0.837916\pi$
$984$	37.4252	+	6.12538i	1.19307	+	0.195270i
$985$	−6.06015	+	3.49883i	−0.193092	+	0.111482i
$986$	−1.27962	+	0.960822i	−0.0407514	+	0.0305988i
$987$	1.34328	−	15.9301i	0.0427571	−	0.507060i
$988$	5.66966	+	1.64684i	0.180376	+	0.0523931i
$989$		0			0
$990$	0.426874	+	3.52667i	0.0135669	+	0.112085i
$991$	33.3611	+	19.2610i	1.05975	+	0.611846i	0.925363	−	0.379083i	$-0.123760\pi$
$991$	33.3611	+	19.2610i	1.05975	+	0.611846i	0.134386	+	0.990929i	$0.457094\pi$
$992$	28.5367	+	41.5087i	0.906041	+	1.31790i
$993$			12.7026i			0.403105i
$994$	9.27015	−	17.4947i	0.294031	−	0.554898i
$995$	7.45857			0.236453
$996$	−4.90145	+	1.20420i	−0.155308	+	0.0381566i
$997$	10.0643	−	17.4320i	0.318741	−	0.552075i	−0.661485	−	0.749959i	$-0.730073\pi$
$997$	10.0643	−	17.4320i	0.318741	−	0.552075i	0.980226	+	0.197883i	$0.0634067\pi$
$998$	2.44904	+	20.2331i	0.0775232	+	0.640466i
$999$	−19.5804	−	33.9143i	−0.619498	−	1.07300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.2.m.a.3.1	✓	12
3.2	odd	2		504.2.bk.a.451.6		12
4.3	odd	2		224.2.q.a.143.1		12
7.2	even	3		392.2.m.g.19.4		12
7.3	odd	6		392.2.e.e.195.10		12
7.4	even	3		392.2.e.e.195.9		12
7.5	odd	6	inner	56.2.m.a.19.4	yes	12
7.6	odd	2		392.2.m.g.227.1		12
8.3	odd	2	inner	56.2.m.a.3.3	yes	12
8.5	even	2		224.2.q.a.143.2		12
12.11	even	2		2016.2.bs.a.1711.4		12
21.5	even	6		504.2.bk.a.19.3		12
24.5	odd	2		2016.2.bs.a.1711.3		12
24.11	even	2		504.2.bk.a.451.4		12
28.3	even	6		1568.2.e.e.783.3		12
28.11	odd	6		1568.2.e.e.783.10		12
28.19	even	6		224.2.q.a.47.2		12
28.23	odd	6		1568.2.q.g.1391.5		12
28.27	even	2		1568.2.q.g.815.6		12
56.3	even	6		392.2.e.e.195.12		12
56.5	odd	6		224.2.q.a.47.1		12
56.11	odd	6		392.2.e.e.195.11		12
56.13	odd	2		1568.2.q.g.815.5		12
56.19	even	6	inner	56.2.m.a.19.2	yes	12
56.27	even	2		392.2.m.g.227.3		12
56.37	even	6		1568.2.q.g.1391.6		12
56.45	odd	6		1568.2.e.e.783.4		12
56.51	odd	6		392.2.m.g.19.2		12
56.53	even	6		1568.2.e.e.783.9		12
84.47	odd	6		2016.2.bs.a.271.3		12
168.5	even	6		2016.2.bs.a.271.4		12
168.131	odd	6		504.2.bk.a.19.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.1	✓	12	1.1	even	1	trivial
56.2.m.a.3.3	yes	12	8.3	odd	2	inner
56.2.m.a.19.2	yes	12	56.19	even	6	inner
56.2.m.a.19.4	yes	12	7.5	odd	6	inner
224.2.q.a.47.1		12	56.5	odd	6
224.2.q.a.47.2		12	28.19	even	6
224.2.q.a.143.1		12	4.3	odd	2
224.2.q.a.143.2		12	8.5	even	2
392.2.e.e.195.9		12	7.4	even	3
392.2.e.e.195.10		12	7.3	odd	6
392.2.e.e.195.11		12	56.11	odd	6
392.2.e.e.195.12		12	56.3	even	6
392.2.m.g.19.2		12	56.51	odd	6
392.2.m.g.19.4		12	7.2	even	3
392.2.m.g.227.1		12	7.6	odd	2
392.2.m.g.227.3		12	56.27	even	2
504.2.bk.a.19.3		12	21.5	even	6
504.2.bk.a.19.5		12	168.131	odd	6
504.2.bk.a.451.4		12	24.11	even	2
504.2.bk.a.451.6		12	3.2	odd	2
1568.2.e.e.783.3		12	28.3	even	6
1568.2.e.e.783.4		12	56.45	odd	6
1568.2.e.e.783.9		12	56.53	even	6
1568.2.e.e.783.10		12	28.11	odd	6
1568.2.q.g.815.5		12	56.13	odd	2
1568.2.q.g.815.6		12	28.27	even	2
1568.2.q.g.1391.5		12	28.23	odd	6
1568.2.q.g.1391.6		12	56.37	even	6
2016.2.bs.a.271.3		12	84.47	odd	6
2016.2.bs.a.271.4		12	168.5	even	6
2016.2.bs.a.1711.3		12	24.5	odd	2
2016.2.bs.a.1711.4		12	12.11	even	2

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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	56.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30084 - 0.554812i) q^{2} +(1.18878 + 0.686340i) q^{3} +(1.38437 + 1.44344i) q^{4} +(-0.345107 - 0.597743i) q^{5} +(-1.16562 - 1.55237i) q^{6} +(2.63639 + 0.222310i) q^{7} +(-1.00000 - 2.64575i) q^{8} +(-0.557875 - 0.966267i) q^{9} +O(q^{10})\)	\(q+(-1.30084 - 0.554812i) q^{2} +(1.18878 + 0.686340i) q^{3} +(1.38437 + 1.44344i) q^{4} +(-0.345107 - 0.597743i) q^{5} +(-1.16562 - 1.55237i) q^{6} +(2.63639 + 0.222310i) q^{7} +(-1.00000 - 2.64575i) q^{8} +(-0.557875 - 0.966267i) q^{9} +(0.117294 + 0.969037i) q^{10} +(-1.63090 + 2.82480i) q^{11} +(0.655009 + 2.66608i) q^{12} -5.27279 q^{13} +(-3.30619 - 1.75189i) q^{14} -0.947443i q^{15} +(-0.167055 + 3.99651i) q^{16} +(-2.20393 - 1.27244i) q^{17} +(0.189609 + 1.56647i) q^{18} +(-0.484848 + 0.279927i) q^{19} +(0.385053 - 1.32564i) q^{20} +(2.98150 + 2.07374i) q^{21} +(3.68878 - 2.76977i) q^{22} +(2.50610 - 1.44690i) q^{23} +(0.627109 - 3.83155i) q^{24} +(2.26180 - 3.91756i) q^{25} +(6.85905 + 2.92541i) q^{26} -5.64961i q^{27} +(3.32885 + 4.11324i) q^{28} +0.444621i q^{29} +(-0.525653 + 1.23247i) q^{30} +(-4.45228 + 7.71158i) q^{31} +(2.43462 - 5.10613i) q^{32} +(-3.87755 + 2.23871i) q^{33} +(2.16099 + 2.87800i) q^{34} +(-0.776954 - 1.65261i) q^{35} +(0.622448 - 2.14293i) q^{36} +(6.00295 - 3.46580i) q^{37} +(0.786017 - 0.0951408i) q^{38} +(-6.26817 - 3.61893i) q^{39} +(-1.23637 + 1.51081i) q^{40} +9.76765i q^{41} +(-2.72792 - 4.35178i) q^{42} +(-6.33521 + 1.55645i) q^{44} +(-0.385053 + 0.666931i) q^{45} +(-4.06279 + 0.491767i) q^{46} +(-2.20094 - 3.81214i) q^{47} +(-2.94156 + 4.63630i) q^{48} +(6.90116 + 1.17220i) q^{49} +(-5.11575 + 3.84124i) q^{50} +(-1.74665 - 3.02529i) q^{51} +(-7.29948 - 7.61097i) q^{52} +(8.17440 + 4.71949i) q^{53} +(-3.13447 + 7.34923i) q^{54} +2.25134 q^{55} +(-2.04822 - 7.19756i) q^{56} -0.768501 q^{57} +(0.246681 - 0.578380i) q^{58} +(8.59663 + 4.96327i) q^{59} +(1.36758 - 1.31161i) q^{60} +(-5.23284 - 9.06355i) q^{61} +(10.0702 - 7.56134i) q^{62} +(-1.25597 - 2.67148i) q^{63} +(-6.00000 + 5.29150i) q^{64} +(1.81968 + 3.15177i) q^{65} +(6.28613 - 0.760884i) q^{66} +(-1.45058 + 2.51247i) q^{67} +(-1.21435 - 4.94277i) q^{68} +3.97225 q^{69} +(0.0938060 + 2.58084i) q^{70} +5.29150i q^{71} +(-1.99863 + 2.44227i) q^{72} +(-5.28541 - 3.05153i) q^{73} +(-9.73174 + 1.17795i) q^{74} +(5.37755 - 3.10473i) q^{75} +(-1.07527 - 0.312329i) q^{76} +(-4.92768 + 7.08473i) q^{77} +(6.14605 + 8.18530i) q^{78} +(5.01803 - 2.89716i) q^{79} +(2.44654 - 1.27937i) q^{80} +(2.20393 - 3.81731i) q^{81} +(5.41921 - 12.7061i) q^{82} +1.83845i q^{83} +(1.13417 + 7.17445i) q^{84} +1.75651i q^{85} +(-0.305161 + 0.528555i) q^{87} +(9.10463 + 1.49016i) q^{88} +(1.50000 - 0.866025i) q^{89} +(0.870914 - 0.653939i) q^{90} +(-13.9012 - 1.17220i) q^{91} +(5.55787 + 1.61437i) q^{92} +(-10.5855 + 6.11156i) q^{93} +(0.748048 + 6.18008i) q^{94} +(0.334649 + 0.193210i) q^{95} +(6.39877 - 4.39907i) q^{96} -7.42325i q^{97} +(-8.32695 - 5.35368i) q^{98} +3.63935 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 12 q^{8}+O(q^{10}) \) 12 * q - 6 * q^3 - 12 * q^8	\( 12 q - 6 q^{3} - 12 q^{8} + 6 q^{10} - 6 q^{11} - 18 q^{12} + 6 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 24 q^{22} + 6 q^{24} + 6 q^{26} + 6 q^{28} - 12 q^{30} - 6 q^{33} + 18 q^{35} + 48 q^{36} - 24 q^{38} + 42 q^{40} - 30 q^{42} + 6 q^{44} - 18 q^{46} - 12 q^{49} - 48 q^{50} + 6 q^{51} - 24 q^{52} - 36 q^{54} - 36 q^{57} + 18 q^{58} + 42 q^{59} - 6 q^{60} - 72 q^{64} - 12 q^{65} + 12 q^{66} + 30 q^{67} - 36 q^{68} + 30 q^{70} + 18 q^{73} + 12 q^{74} + 24 q^{75} + 60 q^{78} + 36 q^{80} + 6 q^{81} + 54 q^{82} + 12 q^{84} + 6 q^{88} + 18 q^{89} - 72 q^{91} + 60 q^{92} - 12 q^{94} + 60 q^{96} - 6 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 - 12 * q^8 + 6 * q^10 - 6 * q^11 - 18 * q^12 + 6 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 24 * q^22 + 6 * q^24 + 6 * q^26 + 6 * q^28 - 12 * q^30 - 6 * q^33 + 18 * q^35 + 48 * q^36 - 24 * q^38 + 42 * q^40 - 30 * q^42 + 6 * q^44 - 18 * q^46 - 12 * q^49 - 48 * q^50 + 6 * q^51 - 24 * q^52 - 36 * q^54 - 36 * q^57 + 18 * q^58 + 42 * q^59 - 6 * q^60 - 72 * q^64 - 12 * q^65 + 12 * q^66 + 30 * q^67 - 36 * q^68 + 30 * q^70 + 18 * q^73 + 12 * q^74 + 24 * q^75 + 60 * q^78 + 36 * q^80 + 6 * q^81 + 54 * q^82 + 12 * q^84 + 6 * q^88 + 18 * q^89 - 72 * q^91 + 60 * q^92 - 12 * q^94 + 60 * q^96 - 6 * q^98 - 24 * q^99

Introduction

L-functions

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