LMFDB - Embedded newform 315.2.k.c.16.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 2]))

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

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

chi := DirichletCharacter("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.11
Character	$\chi$	$=$	315.16
Dual form			315.2.k.c.256.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.195497 + 0.338610i) q^{2} +(0.811590 + 1.53014i) q^{3} +(0.923562 - 1.59966i) q^{4} +1.00000 q^{5} +(-0.359457 + 0.573950i) q^{6} +(0.0590728 - 2.64509i) q^{7} +1.50420 q^{8} +(-1.68264 + 2.48369i) q^{9} +O(q^{10})$	\(q+(0.195497 + 0.338610i) q^{2} +(0.811590 + 1.53014i) q^{3} +(0.923562 - 1.59966i) q^{4} +1.00000 q^{5} +(-0.359457 + 0.573950i) q^{6} +(0.0590728 - 2.64509i) q^{7} +1.50420 q^{8} +(-1.68264 + 2.48369i) q^{9} +(0.195497 + 0.338610i) q^{10} +3.11514 q^{11} +(3.19725 + 0.114912i) q^{12} +(-1.07656 - 1.86466i) q^{13} +(0.907204 - 0.497104i) q^{14} +(0.811590 + 1.53014i) q^{15} +(-1.55306 - 2.68998i) q^{16} +(-0.0261799 - 0.0453449i) q^{17} +(-1.16995 - 0.0842069i) q^{18} +(-3.73155 + 6.46324i) q^{19} +(0.923562 - 1.59966i) q^{20} +(4.09530 - 2.05634i) q^{21} +(0.609001 + 1.05482i) q^{22} -0.105033 q^{23} +(1.22079 + 2.30163i) q^{24} +1.00000 q^{25} +(0.420929 - 0.729070i) q^{26} +(-5.16600 - 0.558937i) q^{27} +(-4.17668 - 2.53740i) q^{28} +(-2.27483 + 3.94011i) q^{29} +(-0.359457 + 0.573950i) q^{30} +(-3.22356 + 5.58336i) q^{31} +(2.11144 - 3.65711i) q^{32} +(2.52822 + 4.76660i) q^{33} +(0.0102362 - 0.0177296i) q^{34} +(0.0590728 - 2.64509i) q^{35} +(2.41902 + 4.98549i) q^{36} +(-0.298590 + 0.517173i) q^{37} -2.91802 q^{38} +(1.97946 - 3.16063i) q^{39} +1.50420 q^{40} +(4.88281 + 8.45728i) q^{41} +(1.49692 + 0.984702i) q^{42} +(3.29411 - 5.70556i) q^{43} +(2.87703 - 4.98316i) q^{44} +(-1.68264 + 2.48369i) q^{45} +(-0.0205336 - 0.0355652i) q^{46} +(-3.63704 - 6.29953i) q^{47} +(2.85559 - 4.55955i) q^{48} +(-6.99302 - 0.312506i) q^{49} +(0.195497 + 0.338610i) q^{50} +(0.0481366 - 0.0768603i) q^{51} -3.97709 q^{52} +(-2.39011 - 4.13979i) q^{53} +(-0.820675 - 1.85853i) q^{54} +3.11514 q^{55} +(0.0888574 - 3.97875i) q^{56} +(-12.9181 - 0.464288i) q^{57} -1.77888 q^{58} +(-0.625533 + 1.08345i) q^{59} +(3.19725 + 0.114912i) q^{60} +(-3.34004 - 5.78511i) q^{61} -2.52078 q^{62} +(6.47019 + 4.59746i) q^{63} -4.56112 q^{64} +(-1.07656 - 1.86466i) q^{65} +(-1.11976 + 1.78794i) q^{66} +(-1.42345 + 2.46549i) q^{67} -0.0967150 q^{68} +(-0.0852436 - 0.160715i) q^{69} +(0.907204 - 0.497104i) q^{70} +6.22208 q^{71} +(-2.53103 + 3.73597i) q^{72} +(-2.38580 - 4.13233i) q^{73} -0.233493 q^{74} +(0.811590 + 1.53014i) q^{75} +(6.89264 + 11.9384i) q^{76} +(0.184020 - 8.23984i) q^{77} +(1.45720 + 0.0523729i) q^{78} +(-6.00838 - 10.4068i) q^{79} +(-1.55306 - 2.68998i) q^{80} +(-3.33743 - 8.35832i) q^{81} +(-1.90915 + 3.30674i) q^{82} +(-7.38093 + 12.7842i) q^{83} +(0.492823 - 8.45023i) q^{84} +(-0.0261799 - 0.0453449i) q^{85} +2.57595 q^{86} +(-7.87514 - 0.283039i) q^{87} +4.68580 q^{88} +(4.22085 - 7.31072i) q^{89} +(-1.16995 - 0.0842069i) q^{90} +(-4.99580 + 2.73746i) q^{91} +(-0.0970043 + 0.168016i) q^{92} +(-11.1595 - 0.401082i) q^{93} +(1.42206 - 2.46308i) q^{94} +(-3.73155 + 6.46324i) q^{95} +(7.30951 + 0.262710i) q^{96} +(0.575428 - 0.996671i) q^{97} +(-1.26129 - 2.42900i) q^{98} +(-5.24168 + 7.73705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.195497	+	0.338610i	0.138237	+	0.239434i	0.926829	−	0.375483i	$-0.122523\pi$
$2$	0.195497	+	0.338610i	0.138237	+	0.239434i	−0.788592	+	0.614916i	$0.789190\pi$
$3$	0.811590	+	1.53014i	0.468572	+	0.883425i
$3$	0.811590	+	1.53014i	0.468572	+	0.883425i
$4$	0.923562	−	1.59966i	0.461781	−	0.799828i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.359457	+	0.573950i	−0.146748	+	0.234314i
$7$	0.0590728	−	2.64509i	0.0223274	−	0.999751i
$7$	0.0590728	−	2.64509i	0.0223274	−	0.999751i
$8$	1.50420			0.531815
$9$	−1.68264	+	2.48369i	−0.560881	+	0.827896i
$10$	0.195497	+	0.338610i	0.0618215	+	0.107078i
$11$	3.11514			0.939252			0.469626	−	0.882866i	$-0.344389\pi$
$11$	3.11514			0.939252			0.469626	+	0.882866i	$0.344389\pi$
$12$	3.19725	+	0.114912i	0.922966	+	0.0331722i
$13$	−1.07656	−	1.86466i	−0.298585	−	0.517164i	0.677228	−	0.735774i	$-0.263181\pi$
$13$	−1.07656	−	1.86466i	−0.298585	−	0.517164i	−0.975812	+	0.218610i	$0.929848\pi$
$14$	0.907204	−	0.497104i	0.242460	−	0.132857i
$15$	0.811590	+	1.53014i	0.209552	+	0.395080i
$16$	−1.55306	−	2.68998i	−0.388264	−	0.672494i
$17$	−0.0261799	−	0.0453449i	−0.00634955	−	0.0109978i	0.862833	−	0.505489i	$-0.168688\pi$
$17$	−0.0261799	−	0.0453449i	−0.00634955	−	0.0109978i	−0.869183	+	0.494491i	$0.835354\pi$
$18$	−1.16995	−	0.0842069i	−0.275761	−	0.0198478i
$19$	−3.73155	+	6.46324i	−0.856077	+	1.48277i	0.0195660	+	0.999809i	$0.493772\pi$
$19$	−3.73155	+	6.46324i	−0.856077	+	1.48277i	−0.875643	+	0.482960i	$0.839562\pi$
$20$	0.923562	−	1.59966i	0.206515	−	0.357694i
$21$	4.09530	−	2.05634i	0.893667	−	0.448730i
$22$	0.609001	+	1.05482i	0.129839	+	0.224888i
$23$	−0.105033			−0.0219009			−0.0109504	−	0.999940i	$-0.503486\pi$
$23$	−0.105033			−0.0219009			−0.0109504	+	0.999940i	$0.503486\pi$
$24$	1.22079	+	2.30163i	0.249194	+	0.469819i
$25$	1.00000			0.200000
$26$	0.420929	−	0.729070i	0.0825510	−	0.142982i
$27$	−5.16600	−	0.558937i	−0.994198	−	0.107568i
$28$	−4.17668	−	2.53740i	−0.789318	−	0.479524i
$29$	−2.27483	+	3.94011i	−0.422424	+	0.731661i	−0.996176	−	0.0873688i	$-0.972154\pi$
$29$	−2.27483	+	3.94011i	−0.422424	+	0.731661i	0.573752	+	0.819029i	$0.305487\pi$
$30$	−0.359457	+	0.573950i	−0.0656276	+	0.104788i
$31$	−3.22356	+	5.58336i	−0.578968	+	1.00280i	0.416630	+	0.909076i	$0.363211\pi$
$31$	−3.22356	+	5.58336i	−0.578968	+	1.00280i	−0.995598	+	0.0937256i	$0.970122\pi$
$32$	2.11144	−	3.65711i	0.373253	−	0.646492i
$33$	2.52822	+	4.76660i	0.440107	+	0.829759i
$34$	0.0102362	−	0.0177296i	0.00175549	−	0.00304059i
$35$	0.0590728	−	2.64509i	0.00998513	−	0.447102i
$36$	2.41902	+	4.98549i	0.403171	+	0.830915i
$37$	−0.298590	+	0.517173i	−0.0490879	+	0.0850227i	−0.889525	−	0.456886i	$-0.848965\pi$
$37$	−0.298590	+	0.517173i	−0.0490879	+	0.0850227i	0.840437	+	0.541909i	$0.182298\pi$
$38$	−2.91802			−0.473366
$39$	1.97946	−	3.16063i	0.316967	−	0.506106i
$40$	1.50420			0.237835
$41$	4.88281	+	8.45728i	0.762567	+	1.32081i	0.941523	+	0.336948i	$0.109395\pi$
$41$	4.88281	+	8.45728i	0.762567	+	1.32081i	−0.178956	+	0.983857i	$0.557272\pi$
$42$	1.49692	+	0.984702i	0.230979	+	0.151943i
$43$	3.29411	−	5.70556i	0.502347	−	0.870090i	−0.497650	−	0.867378i	$-0.665804\pi$
$43$	3.29411	−	5.70556i	0.502347	−	0.870090i	0.999996	−	0.00271165i	$-0.000863146\pi$
$44$	2.87703	−	4.98316i	0.433729	−	0.751240i
$45$	−1.68264	+	2.48369i	−0.250834	+	0.370247i
$46$	−0.0205336	−	0.0355652i	−0.00302751	−	0.00524380i
$47$	−3.63704	−	6.29953i	−0.530516	−	0.918881i	−0.999366	−	0.0356034i	$-0.988665\pi$
$47$	−3.63704	−	6.29953i	−0.530516	−	0.918881i	0.468850	−	0.883278i	$-0.344669\pi$
$48$	2.85559	−	4.55955i	0.412168	−	0.658114i
$49$	−6.99302	−	0.312506i	−0.999003	−	0.0446437i
$50$	0.195497	+	0.338610i	0.0276474	+	0.0478867i
$51$	0.0481366	−	0.0768603i	0.00674047	−	0.0107626i
$52$	−3.97709			−0.551523
$53$	−2.39011	−	4.13979i	−0.328307	−	0.568644i	0.653869	−	0.756607i	$-0.273145\pi$
$53$	−2.39011	−	4.13979i	−0.328307	−	0.568644i	−0.982176	+	0.187964i	$0.939811\pi$
$54$	−0.820675	−	1.85853i	−0.111680	−	0.252914i
$55$	3.11514			0.420046
$56$	0.0888574	−	3.97875i	0.0118741	−	0.531682i
$57$	−12.9181	−	0.464288i	−1.71105	−	0.0614965i
$58$	−1.77888			−0.233579
$59$	−0.625533	+	1.08345i	−0.0814374	+	0.141054i	−0.903868	−	0.427812i	$-0.859284\pi$
$59$	−0.625533	+	1.08345i	−0.0814374	+	0.141054i	0.822430	+	0.568866i	$0.192618\pi$
$60$	3.19725	+	0.114912i	0.412763	+	0.0148350i
$61$	−3.34004	−	5.78511i	−0.427648	−	0.740708i	0.569016	−	0.822327i	$-0.307324\pi$
$61$	−3.34004	−	5.78511i	−0.427648	−	0.740708i	−0.996664	+	0.0816189i	$0.973991\pi$
$62$	−2.52078			−0.320139
$63$	6.47019	+	4.59746i	0.815167	+	0.579226i
$64$	−4.56112			−0.570140
$65$	−1.07656	−	1.86466i	−0.133531	−	0.231283i
$66$	−1.11976	+	1.78794i	−0.137833	+	0.220080i
$67$	−1.42345	+	2.46549i	−0.173902	+	0.301207i	−0.939781	−	0.341778i	$-0.888971\pi$
$67$	−1.42345	+	2.46549i	−0.173902	+	0.301207i	0.765879	+	0.642985i	$0.222304\pi$
$68$	−0.0967150			−0.0117284
$69$	−0.0852436	−	0.160715i	−0.0102621	−	0.0193478i
$70$	0.907204	−	0.497104i	0.108432	−	0.0594153i
$71$	6.22208			0.738425			0.369212	−	0.929345i	$-0.379628\pi$
$71$	6.22208			0.738425			0.369212	+	0.929345i	$0.379628\pi$
$72$	−2.53103	+	3.73597i	−0.298285	+	0.440288i
$73$	−2.38580	−	4.13233i	−0.279237	−	0.483653i	0.691958	−	0.721938i	$-0.256748\pi$
$73$	−2.38580	−	4.13233i	−0.279237	−	0.483653i	−0.971195	+	0.238285i	$0.923415\pi$
$74$	−0.233493			−0.0271430
$75$	0.811590	+	1.53014i	0.0937144	+	0.176685i
$76$	6.89264	+	11.9384i	0.790640	+	1.36943i
$77$	0.184020	−	8.23984i	0.0209711	−	0.939017i
$78$	1.45720	+	0.0523729i	0.164995	+	0.00593007i
$79$	−6.00838	−	10.4068i	−0.675996	−	1.17086i	−0.976177	−	0.216976i	$-0.930381\pi$
$79$	−6.00838	−	10.4068i	−0.675996	−	1.17086i	0.300181	−	0.953882i	$-0.402953\pi$
$80$	−1.55306	−	2.68998i	−0.173637	−	0.300748i
$81$	−3.33743	−	8.35832i	−0.370825	−	0.928703i
$82$	−1.90915	+	3.30674i	−0.210830	+	0.365169i
$83$	−7.38093	+	12.7842i	−0.810163	+	1.40324i	0.102587	+	0.994724i	$0.467288\pi$
$83$	−7.38093	+	12.7842i	−0.810163	+	1.40324i	−0.912750	+	0.408519i	$0.866045\pi$
$84$	0.492823	−	8.45023i	0.0537713	−	0.921995i
$85$	−0.0261799	−	0.0453449i	−0.00283961	−	0.00491834i
$86$	2.57595			0.277772
$87$	−7.87514	−	0.283039i	−0.844304	−	0.0303450i
$88$	4.68580			0.499508
$89$	4.22085	−	7.31072i	0.447409	−	0.774935i	−0.550807	−	0.834632i	$-0.685680\pi$
$89$	4.22085	−	7.31072i	0.447409	−	0.774935i	0.998217	+	0.0596971i	$0.0190135\pi$
$90$	−1.16995	−	0.0842069i	−0.123324	−	0.00887619i
$91$	−4.99580	+	2.73746i	−0.523702	+	0.286963i
$92$	−0.0970043	+	0.168016i	−0.0101134	+	0.0175169i
$93$	−11.1595	−	0.401082i	−1.15719	−	0.0415903i
$94$	1.42206	−	2.46308i	0.146674	−	0.254047i
$95$	−3.73155	+	6.46324i	−0.382849	+	0.663114i
$96$	7.30951	+	0.262710i	0.746024	+	0.0268127i
$97$	0.575428	−	0.996671i	0.0584259	−	0.101197i	−0.835333	−	0.549744i	$-0.814725\pi$
$97$	0.575428	−	0.996671i	0.0584259	−	0.101197i	0.893759	+	0.448548i	$0.148059\pi$
$98$	−1.26129	−	2.42900i	−0.127410	−	0.245366i
$99$	−5.24168	+	7.73705i	−0.526808	+	0.777603i
$100$	0.923562	−	1.59966i	0.0923562	−	0.159966i
$101$	14.6441			1.45715			0.728573	−	0.684968i	$-0.240184\pi$
$101$	14.6441			1.45715			0.728573	+	0.684968i	$0.240184\pi$
$102$	0.0354362	+	0.00127361i	0.00350871	+	0.000126106i
$103$	12.6387			1.24533			0.622663	−	0.782490i	$-0.286051\pi$
$103$	12.6387			1.24533			0.622663	+	0.782490i	$0.286051\pi$
$104$	−1.61937	−	2.80482i	−0.158792	−	0.275036i
$105$	4.09530	−	2.05634i	0.399660	−	0.200678i
$106$	0.934516	−	1.61863i	0.0907683	−	0.157215i
$107$	−6.58404	+	11.4039i	−0.636503	+	1.10246i	0.349692	+	0.936865i	$0.386286\pi$
$107$	−6.58404	+	11.4039i	−0.636503	+	1.10246i	−0.986195	+	0.165591i	$0.947047\pi$
$108$	−5.66523	+	7.74762i	−0.545137	+	0.745515i
$109$	−7.27924	−	12.6080i	−0.697225	−	1.20763i	−0.969425	−	0.245388i	$-0.921084\pi$
$109$	−7.27924	−	12.6080i	−0.697225	−	1.20763i	0.272200	−	0.962241i	$-0.412249\pi$
$110$	0.609001	+	1.05482i	0.0580659	+	0.100573i
$111$	−1.03368	−	0.0371512i	−0.0981124	−	0.00352624i
$112$	−7.20698	+	3.94908i	−0.680995	+	0.373153i
$113$	2.05008	+	3.55084i	0.192855	+	0.334034i	0.946195	−	0.323596i	$-0.104892\pi$
$113$	2.05008	+	3.55084i	0.192855	+	0.334034i	−0.753340	+	0.657631i	$0.771559\pi$
$114$	−2.36824	−	4.46498i	−0.221806	−	0.418184i
$115$	−0.105033			−0.00979436
$116$	4.20188	+	7.27788i	0.390135	+	0.675734i
$117$	6.44271	+	0.463711i	0.595629	+	0.0428701i
$118$	−0.489158			−0.0450307
$119$	−0.121488	+	0.0665695i	−0.0111368	+	0.00610242i
$120$	1.22079	+	2.30163i	0.111443	+	0.210109i
$121$	−1.29587			−0.117807
$122$	1.30593	−	2.26194i	0.118234	−	0.204786i
$123$	−8.97796	+	14.3352i	−0.809516	+	1.29256i
$124$	5.95431	+	10.3132i	0.534713	+	0.926150i
$125$	1.00000			0.0894427
$126$	−0.291848	+	3.08966i	−0.0259998	+	0.275249i
$127$	−8.15310			−0.723470			−0.361735	−	0.932281i	$-0.617816\pi$
$127$	−8.15310			−0.723470			−0.361735	+	0.932281i	$0.617816\pi$
$128$	−5.11455	−	8.85867i	−0.452067	−	0.783003i
$129$	11.4038	+	0.409860i	1.00404	+	0.0360862i
$130$	0.420929	−	0.729070i	0.0369179	−	0.0639437i
$131$	−6.63780			−0.579947			−0.289973	−	0.957035i	$-0.593646\pi$
$131$	−6.63780			−0.579947			−0.289973	+	0.957035i	$0.593646\pi$
$132$	9.95989	+	0.357967i	0.866897	+	0.0311570i
$133$	16.8754	+	10.2521i	1.46328	+	0.888970i
$134$	−1.11312			−0.0961588
$135$	−5.16600	−	0.558937i	−0.444619	−	0.0481057i
$136$	−0.0393798	−	0.0682078i	−0.00337679	−	0.00584877i
$137$	20.1078			1.71793			0.858964	−	0.512035i	$-0.171108\pi$
$137$	20.1078			1.71793			0.858964	+	0.512035i	$0.171108\pi$
$138$	0.0377548	−	0.0602835i	0.00321390	−	0.00513167i
$139$	8.86312	+	15.3514i	0.751760	+	1.30209i	0.946969	+	0.321325i	$0.104128\pi$
$139$	8.86312	+	15.3514i	0.751760	+	1.30209i	−0.195209	+	0.980762i	$0.562539\pi$
$140$	−4.17668	−	2.53740i	−0.352994	−	0.214450i
$141$	6.68737	−	10.6778i	0.563178	−	0.899234i
$142$	1.21640	+	2.10686i	0.102078	+	0.176804i
$143$	−3.35365	−	5.80869i	−0.280446	−	0.485747i
$144$	9.29431	+	0.668954i	0.774525	+	0.0557462i
$145$	−2.27483	+	3.94011i	−0.188914	+	0.327209i
$146$	0.932834	−	1.61572i	0.0772019	−	0.133718i
$147$	−5.19729	−	10.9539i	−0.428665	−	0.903463i
$148$	0.551532	+	0.955282i	0.0453357	+	0.0785237i
$149$	−18.1125			−1.48383			−0.741916	−	0.670492i	$-0.766083\pi$
$149$	−18.1125			−1.48383			−0.741916	+	0.670492i	$0.766083\pi$
$150$	−0.359457	+	0.573950i	−0.0293495	+	0.0468628i
$151$	9.04349			0.735949			0.367974	−	0.929836i	$-0.380051\pi$
$151$	9.04349			0.735949			0.367974	+	0.929836i	$0.380051\pi$
$152$	−5.61300	+	9.72200i	−0.455274	+	0.788558i
$153$	0.156674	+	0.0112765i	0.0126663	+	0.000911655i
$154$	2.82607	−	1.54855i	0.227731	−	0.124786i
$155$	−3.22356	+	5.58336i	−0.258922	+	0.448467i
$156$	−3.22777	−	6.08550i	−0.258428	−	0.487230i
$157$	1.64435	−	2.84810i	0.131233	−	0.227303i	−0.792919	−	0.609327i	$-0.791440\pi$
$157$	1.64435	−	2.84810i	0.131233	−	0.227303i	0.924152	+	0.382024i	$0.124773\pi$
$158$	2.34924	−	4.06900i	0.186895	−	0.323712i
$159$	4.39466	−	7.01701i	0.348519	−	0.556485i
$160$	2.11144	−	3.65711i	0.166924	−	0.289120i
$161$	−0.00620458	+	0.277821i	−0.000488990	+	0.0218954i
$162$	2.17776	−	2.76411i	0.171101	−	0.217169i
$163$	3.72039	−	6.44390i	0.291403	−	0.504725i	−0.682739	−	0.730663i	$-0.739211\pi$
$163$	3.72039	−	6.44390i	0.291403	−	0.504725i	0.974142	+	0.225938i	$0.0725445\pi$
$164$	18.0383			1.40856
$165$	2.52822	+	4.76660i	0.196822	+	0.371079i
$166$	−5.77179			−0.447978
$167$	8.51412	+	14.7469i	0.658842	+	1.14115i	0.980916	+	0.194433i	$0.0622868\pi$
$167$	8.51412	+	14.7469i	0.658842	+	1.14115i	−0.322074	+	0.946715i	$0.604380\pi$
$168$	6.16015	−	3.09315i	0.475266	−	0.238642i
$169$	4.18203	−	7.24348i	0.321694	−	0.557191i
$170$	0.0102362	−	0.0177296i	0.000785078	−	0.00135979i
$171$	−9.77381	−	20.1433i	−0.747422	−	1.54040i
$172$	−6.08462	−	10.5389i	−0.463948	−	0.803582i
$173$	−9.70551	−	16.8104i	−0.737896	−	1.27807i	−0.953441	−	0.301580i	$-0.902486\pi$
$173$	−9.70551	−	16.8104i	−0.737896	−	1.27807i	0.215545	−	0.976494i	$-0.430847\pi$
$174$	−1.44372	−	2.72194i	−0.109448	−	0.206349i
$175$	0.0590728	−	2.64509i	0.00446549	−	0.199950i
$176$	−4.83800	−	8.37966i	−0.364678	−	0.631641i
$177$	−2.16551	−	0.0778302i	−0.162770	−	0.00585008i
$178$	3.30065			0.247394
$179$	10.8440	+	18.7824i	0.810522	+	1.40387i	0.912499	+	0.409078i	$0.134150\pi$
$179$	10.8440	+	18.7824i	0.810522	+	1.40387i	−0.101977	+	0.994787i	$0.532517\pi$
$180$	2.41902	+	4.98549i	0.180303	+	0.371597i
$181$	15.4159			1.14586			0.572928	−	0.819606i	$-0.305808\pi$
$181$	15.4159			1.14586			0.572928	+	0.819606i	$0.305808\pi$
$182$	−1.90359	−	1.15646i	−0.141104	−	0.0857228i
$183$	6.14128	−	9.80585i	0.453976	−	0.724870i
$184$	−0.157990			−0.0116472
$185$	−0.298590	+	0.517173i	−0.0219528	+	0.0380233i
$186$	−2.04584	−	3.85714i	−0.150008	−	0.282819i
$187$	−0.0815541	−	0.141256i	−0.00596383	−	0.0103297i
$188$	−13.4361			−0.979930
$189$	−1.78361	+	13.6315i	−0.129739	+	0.991548i
$190$	−2.91802			−0.211696
$191$	10.4235	+	18.0541i	0.754220	+	1.30635i	0.945761	+	0.324863i	$0.105318\pi$
$191$	10.4235	+	18.0541i	0.754220	+	1.30635i	−0.191541	+	0.981485i	$0.561348\pi$
$192$	−3.70176	−	6.97914i	−0.267151	−	0.503676i
$193$	10.4529	−	18.1050i	0.752420	−	1.30323i	−0.194227	−	0.980957i	$-0.562220\pi$
$193$	10.4529	−	18.1050i	0.752420	−	1.30323i	0.946647	−	0.322273i	$-0.104447\pi$
$194$	0.449977			0.0323065
$195$	1.97946	−	3.16063i	0.141752	−	0.226337i
$196$	−6.95839	+	10.8978i	−0.497028	+	0.778415i
$197$	6.57881			0.468721			0.234360	−	0.972150i	$-0.424700\pi$
$197$	6.57881			0.468721			0.234360	+	0.972150i	$0.424700\pi$
$198$	−3.64458	−	0.262317i	−0.259009	−	0.0186420i
$199$	9.73940	+	16.8691i	0.690408	+	1.19582i	0.971704	+	0.236201i	$0.0759023\pi$
$199$	9.73940	+	16.8691i	0.690408	+	1.19582i	−0.281296	+	0.959621i	$0.590764\pi$
$200$	1.50420			0.106363
$201$	−4.92779	−	0.177109i	−0.347580	−	0.0124923i
$202$	2.86288	+	4.95865i	0.201432	+	0.348890i
$203$	10.2876	+	6.24987i	0.722046	+	0.438655i
$204$	−0.0784929	−	0.147987i	−0.00549561	−	0.0103612i
$205$	4.88281	+	8.45728i	0.341031	+	0.590682i
$206$	2.47082	+	4.27958i	0.172150	+	0.298173i
$207$	0.176733	−	0.260869i	0.0122838	−	0.0181316i
$208$	−3.34393	+	5.79185i	−0.231860	+	0.401593i
$209$	−11.6243	+	20.1339i	−0.804071	+	1.39269i
$210$	1.49692	+	0.984702i	0.103297	+	0.0679509i
$211$	6.82067	+	11.8137i	0.469554	+	0.813291i	0.999394	−	0.0348062i	$-0.0110814\pi$
$211$	6.82067	+	11.8137i	0.469554	+	0.813291i	−0.529840	+	0.848098i	$0.677748\pi$
$212$	−8.82965			−0.606423
$213$	5.04978	+	9.52063i	0.346005	+	0.652343i
$214$	−5.14863			−0.351953
$215$	3.29411	−	5.70556i	0.224656	−	0.389116i
$216$	−7.77070	−	0.840753i	−0.528729	−	0.0572060i
$217$	14.5781	+	8.85643i	0.989625	+	0.601213i
$218$	2.84614	−	4.92965i	0.192765	−	0.333878i
$219$	4.38674	−	7.00437i	0.296429	−	0.473312i
$220$	2.87703	−	4.98316i	0.193969	−	0.335965i
$221$	−0.0563686	+	0.0976332i	−0.00379176	+	0.00656752i
$222$	−0.189501	−	0.357277i	−0.0127185	−	0.0239789i
$223$	3.76397	−	6.51939i	0.252054	−	0.436570i	−0.712037	−	0.702142i	$-0.752227\pi$
$223$	3.76397	−	6.51939i	0.252054	−	0.436570i	0.964091	+	0.265571i	$0.0855606\pi$
$224$	−9.54867	−	5.80098i	−0.637998	−	0.387594i
$225$	−1.68264	+	2.48369i	−0.112176	+	0.165579i
$226$	−0.801566	+	1.38835i	−0.0533194	+	0.0923519i
$227$	−27.5093			−1.82585			−0.912927	−	0.408124i	$-0.866183\pi$
$227$	−27.5093			−1.82585			−0.912927	+	0.408124i	$0.866183\pi$
$228$	−12.6734	+	20.2358i	−0.839316	+	1.34015i
$229$	1.33543			0.0882478			0.0441239	−	0.999026i	$-0.485950\pi$
$229$	1.33543			0.0882478			0.0441239	+	0.999026i	$0.485950\pi$
$230$	−0.0205336	−	0.0355652i	−0.00135394	−	0.00234510i
$231$	12.7574	−	6.40580i	0.839378	−	0.421471i
$232$	−3.42179	+	5.92672i	−0.224652	+	0.389108i
$233$	−8.28264	+	14.3460i	−0.542614	+	0.939835i	0.456139	+	0.889908i	$0.349232\pi$
$233$	−8.28264	+	14.3460i	−0.542614	+	0.939835i	−0.998753	+	0.0499262i	$0.984101\pi$
$234$	1.10251	+	2.27222i	0.0720734	+	0.148540i
$235$	−3.63704	−	6.29953i	−0.237254	−	0.410936i
$236$	1.15544	+	2.00127i	0.0752125	+	0.130272i
$237$	11.0475	−	17.6397i	0.717614	−	1.14582i
$238$	−0.0462916	−	0.0281229i	−0.00300064	−	0.00182294i
$239$	−7.99809	−	13.8531i	−0.517354	−	0.896083i	−0.999797	−	0.0201556i	$-0.993584\pi$
$239$	−7.99809	−	13.8531i	−0.517354	−	0.896083i	0.482443	−	0.875927i	$-0.339749\pi$
$240$	2.85559	−	4.55955i	0.184327	−	0.294318i
$241$	−21.5179			−1.38609			−0.693046	−	0.720893i	$-0.743732\pi$
$241$	−21.5179			−1.38609			−0.693046	+	0.720893i	$0.743732\pi$
$242$	−0.253339	−	0.438796i	−0.0162852	−	0.0282068i
$243$	10.0808	−	11.8903i	0.646681	−	0.762760i
$244$	−12.3389			−0.789919
$245$	−6.99302	−	0.312506i	−0.446768	−	0.0199653i
$246$	−6.60922	−	0.237541i	−0.421388	−	0.0151450i
$247$	16.0690			1.02245
$248$	−4.84887	+	8.39850i	−0.307904	+	0.533305i
$249$	−25.5518	−	0.918353i	−1.61928	−	0.0581982i
$250$	0.195497	+	0.338610i	0.0123643	+	0.0214156i
$251$	−27.6344			−1.74427			−0.872133	−	0.489269i	$-0.837264\pi$
$251$	−27.6344			−1.74427			−0.872133	+	0.489269i	$0.837264\pi$
$252$	13.3300	−	6.10404i	0.839710	−	0.384518i
$253$	−0.327192			−0.0205704
$254$	−1.59390	−	2.76072i	−0.100010	−	0.173223i
$255$	0.0481366	−	0.0768603i	0.00301443	−	0.00481318i
$256$	−2.56136	+	4.43641i	−0.160085	+	0.277275i
$257$	12.5460			0.782596			0.391298	−	0.920264i	$-0.372026\pi$
$257$	12.5460			0.782596			0.391298	+	0.920264i	$0.372026\pi$
$258$	2.09061	+	3.94155i	0.130156	+	0.245390i
$259$	1.35033	+	0.820348i	0.0839055	+	0.0509740i
$260$	−3.97709			−0.246649
$261$	−5.95830	−	12.2798i	−0.368809	−	0.760098i
$262$	−1.29767	−	2.24763i	−0.0801701	−	0.138859i
$263$	−20.6677			−1.27442			−0.637211	−	0.770689i	$-0.719912\pi$
$263$	−20.6677			−1.27442			−0.637211	+	0.770689i	$0.719912\pi$
$264$	3.80295	+	7.16992i	0.234055	+	0.441278i
$265$	−2.39011	−	4.13979i	−0.146823	−	0.254305i
$266$	−0.172376	+	7.71844i	−0.0105690	+	0.473248i
$267$	14.6120	+	0.525168i	0.894241	+	0.0321397i
$268$	2.62929	+	4.55406i	0.160609	+	0.278183i
$269$	1.78066	+	3.08420i	0.108569	+	0.188047i	0.915191	−	0.403021i	$-0.132040\pi$
$269$	1.78066	+	3.08420i	0.108569	+	0.188047i	−0.806622	+	0.591068i	$0.798707\pi$
$270$	−0.820675	−	1.85853i	−0.0499447	−	0.113107i
$271$	−4.79811	+	8.31057i	−0.291464	+	0.504831i	−0.974156	−	0.225875i	$-0.927476\pi$
$271$	−4.79811	+	8.31057i	−0.291464	+	0.504831i	0.682692	+	0.730706i	$0.260809\pi$
$272$	−0.0813178	+	0.140846i	−0.00493061	+	0.00854007i
$273$	−8.24322	−	5.42256i	−0.498903	−	0.328188i
$274$	3.93102	+	6.80872i	0.237481	+	0.411330i
$275$	3.11514			0.187850
$276$	−0.335816	−	0.0120695i	−0.0202137	−	0.000726498i
$277$	5.08946			0.305796			0.152898	−	0.988242i	$-0.451139\pi$
$277$	5.08946			0.305796			0.152898	+	0.988242i	$0.451139\pi$
$278$	−3.46542	+	6.00228i	−0.207842	+	0.359993i
$279$	−8.44325	−	17.4011i	−0.505484	−	1.04178i
$280$	0.0888574	−	3.97875i	0.00531024	−	0.237776i
$281$	13.4769	−	23.3427i	0.803967	−	1.39251i	−0.113019	−	0.993593i	$-0.536052\pi$
$281$	13.4769	−	23.3427i	0.803967	−	1.39251i	0.916986	−	0.398919i	$-0.130614\pi$
$282$	4.92297	+	0.176936i	0.293159	+	0.0105364i
$283$	6.35298	−	11.0037i	0.377645	−	0.654101i	−0.613074	−	0.790026i	$-0.710067\pi$
$283$	6.35298	−	11.0037i	0.377645	−	0.654101i	0.990719	+	0.135925i	$0.0434006\pi$
$284$	5.74647	−	9.95318i	0.340990	−	0.590613i
$285$	−12.9181	−	0.464288i	−0.765204	−	0.0275021i
$286$	1.31125	−	2.27116i	0.0775361	−	0.134296i
$287$	22.6587	−	12.4159i	1.33750	−	0.732887i
$288$	5.53034	+	11.3978i	0.325879	+	0.671620i
$289$	8.49863	−	14.7201i	0.499919	−	0.865886i
$290$	−1.77888			−0.104460
$291$	1.99206	+	0.0715961i	0.116776	+	0.00419704i
$292$	−8.81375			−0.515786
$293$	−8.79850	−	15.2394i	−0.514014	−	0.890298i	−0.999868	−	0.0162581i	$-0.994825\pi$
$293$	−8.79850	−	15.2394i	−0.514014	−	0.890298i	0.485854	−	0.874040i	$-0.338509\pi$
$294$	2.69305	−	3.90131i	0.157062	−	0.227529i
$295$	−0.625533	+	1.08345i	−0.0364199	+	0.0630811i
$296$	−0.449139	+	0.777931i	−0.0261057	+	0.0452163i
$297$	−16.0928	−	1.74117i	−0.933802	−	0.101033i
$298$	−3.54093	−	6.13307i	−0.205121	−	0.355279i
$299$	0.113074	+	0.195851i	0.00653926	+	0.0113263i
$300$	3.19725	+	0.114912i	0.184593	+	0.00663443i
$301$	−14.8971	−	9.05026i	−0.858657	−	0.521648i
$302$	1.76797	+	3.06222i	0.101735	+	0.176211i
$303$	11.8850	+	22.4075i	0.682777	+	1.28728i
$304$	23.1813			1.32954
$305$	−3.34004	−	5.78511i	−0.191250	−	0.331255i
$306$	0.0268109	+	0.0552560i	0.00153268	+	0.00315877i
$307$	7.58317			0.432795			0.216397	−	0.976305i	$-0.430569\pi$
$307$	7.58317			0.432795			0.216397	+	0.976305i	$0.430569\pi$
$308$	−13.0110	−	7.90438i	−0.741369	−	0.450394i
$309$	10.2574	+	19.3389i	0.583525	+	1.10015i
$310$	−2.52078			−0.143171
$311$	2.53808	−	4.39609i	0.143922	−	0.249279i	−0.785049	−	0.619434i	$-0.787362\pi$
$311$	2.53808	−	4.39609i	0.143922	−	0.249279i	0.928970	+	0.370155i	$0.120695\pi$
$312$	2.97751	−	4.75422i	0.168568	−	0.269155i
$313$	−15.0985	−	26.1513i	−0.853416	−	1.47816i	−0.878107	−	0.478464i	$-0.841194\pi$
$313$	−15.0985	−	26.1513i	−0.853416	−	1.47816i	0.0246912	−	0.999695i	$-0.492140\pi$
$314$	1.28586			0.0725653
$315$	6.47019	+	4.59746i	0.364554	+	0.259038i
$316$	−22.1964			−1.24865
$317$	9.75954	+	16.9040i	0.548151	+	0.949425i	0.998401	+	0.0565224i	$0.0180012\pi$
$317$	9.75954	+	16.9040i	0.548151	+	0.949425i	−0.450251	+	0.892902i	$0.648665\pi$
$318$	3.23517	+	0.116275i	0.181419	+	0.00652036i
$319$	−7.08641	+	12.2740i	−0.396763	+	0.687213i
$320$	−4.56112			−0.254974
$321$	−22.7931	−	0.819201i	−1.27218	−	0.0457233i
$322$	−0.0952861	+	0.0522122i	−0.00531009	+	0.00290967i
$323$	0.390766			0.0217428
$324$	−16.4528	−	2.38070i	−0.914043	−	0.132261i
$325$	−1.07656	−	1.86466i	−0.0597170	−	0.103433i
$326$	2.90929			0.161131
$327$	13.3842	−	21.3708i	0.740150	−	1.18181i
$328$	7.34473	+	12.7214i	0.405545	+	0.702424i
$329$	−16.8777	+	9.24817i	−0.930497	+	0.509868i
$330$	−1.11976	+	1.78794i	−0.0616408	+	0.0984226i
$331$	0.0612040	+	0.106009i	0.00336408	+	0.00582675i	0.867703	−	0.497084i	$-0.165596\pi$
$331$	0.0612040	+	0.106009i	0.00336408	+	0.00582675i	−0.864338	+	0.502911i	$0.832263\pi$
$332$	13.6335	+	23.6139i	0.748236	+	1.29598i
$333$	−0.782076	−	1.61182i	−0.0428575	−	0.0883273i
$334$	−3.32896	+	5.76593i	−0.182153	+	0.315498i
$335$	−1.42345	+	2.46549i	−0.0777713	+	0.134704i
$336$	−11.8917	−	7.82263i	−0.648748	−	0.426760i
$337$	−3.14954	−	5.45516i	−0.171566	−	0.297161i	0.767401	−	0.641167i	$-0.221549\pi$
$337$	−3.14954	−	5.45516i	−0.171566	−	0.297161i	−0.938968	+	0.344006i	$0.888216\pi$
$338$	3.27029			0.177880
$339$	−3.76945	+	6.01872i	−0.204728	+	0.326892i
$340$	−0.0967150			−0.00524511
$341$	−10.0418	+	17.3930i	−0.543796	+	0.941883i
$342$	4.90999	−	7.24747i	0.265502	−	0.391898i
$343$	−1.23970	+	18.4787i	−0.0669378	+	0.997757i
$344$	4.95500	−	8.58230i	0.267155	−	0.462727i
$345$	−0.0852436	−	0.160715i	−0.00458936	−	0.00865259i
$346$	3.79479	−	6.57277i	0.204009	−	0.353354i
$347$	2.80087	−	4.85125i	0.150359	−	0.260429i	−0.781001	−	0.624530i	$-0.785290\pi$
$347$	2.80087	−	4.85125i	0.150359	−	0.260429i	0.931359	+	0.364101i	$0.118624\pi$
$348$	−7.72595	+	12.3361i	−0.414154	+	0.661285i
$349$	−1.32460	+	2.29428i	−0.0709043	+	0.122810i	−0.899298	−	0.437337i	$-0.855922\pi$
$349$	−1.32460	+	2.29428i	−0.0709043	+	0.122810i	0.828394	+	0.560146i	$0.189255\pi$
$350$	0.907204	−	0.497104i	0.0484921	−	0.0265713i
$351$	4.51930	+	10.2346i	0.241222	+	0.546281i
$352$	6.57743	−	11.3924i	0.350578	−	0.607219i
$353$	3.61836			0.192586			0.0962929	−	0.995353i	$-0.469301\pi$
$353$	3.61836			0.192586			0.0962929	+	0.995353i	$0.469301\pi$
$354$	−0.396996	−	0.748480i	−0.0211001	−	0.0397812i
$355$	6.22208			0.330234
$356$	−7.79643	−	13.5038i	−0.413210	−	0.715701i
$357$	−0.200459	−	0.131866i	−0.0106094	−	0.00697909i
$358$	−4.23995	+	7.34381i	−0.224088	+	0.388132i
$359$	14.7465	−	25.5417i	0.778291	−	1.34804i	−0.154634	−	0.987972i	$-0.549420\pi$
$359$	14.7465	−	25.5417i	0.778291	−	1.34804i	0.932926	−	0.360068i	$-0.117247\pi$
$360$	−2.53103	+	3.73597i	−0.133397	+	0.196903i
$361$	−18.3490	−	31.7813i	−0.965734	−	1.67270i
$362$	3.01376	+	5.21998i	0.158400	+	0.274356i
$363$	−1.05172	−	1.98286i	−0.0552008	−	0.104073i
$364$	−0.234938	+	10.5198i	−0.0123141	+	0.551386i
$365$	−2.38580	−	4.13233i	−0.124879	−	0.216296i
$366$	4.52096	+	0.162487i	0.236314	+	0.00849333i
$367$	−31.1245			−1.62469			−0.812343	−	0.583180i	$-0.801808\pi$
$367$	−31.1245			−1.62469			−0.812343	+	0.583180i	$0.801808\pi$
$368$	0.163122	+	0.282536i	0.00850332	+	0.0147282i
$369$	−29.2213	−	2.10319i	−1.52120	−	0.109488i
$370$	−0.233493			−0.0121387
$371$	−11.0913	+	6.07751i	−0.575832	+	0.315528i
$372$	−10.9481	+	17.4810i	−0.567633	+	0.906346i
$373$	24.1371			1.24977			0.624885	−	0.780717i	$-0.285146\pi$
$373$	24.1371			1.24977			0.624885	+	0.780717i	$0.285146\pi$
$374$	0.0318871	−	0.0552301i	0.00164884	−	0.00285588i
$375$	0.811590	+	1.53014i	0.0419103	+	0.0790160i
$376$	−5.47083	−	9.47576i	−0.282137	−	0.488675i
$377$	9.79597			0.504518
$378$	−4.96447	+	2.06097i	−0.255345	+	0.106005i
$379$	15.5639			0.799462			0.399731	−	0.916633i	$-0.369104\pi$
$379$	15.5639			0.799462			0.399731	+	0.916633i	$0.369104\pi$
$380$	6.89264	+	11.9384i	0.353585	+	0.612427i
$381$	−6.61697	−	12.4754i	−0.338998	−	0.639132i
$382$	−4.07553	+	7.05903i	−0.208522	+	0.361171i
$383$	20.0440			1.02420			0.512101	−	0.858925i	$-0.328867\pi$
$383$	20.0440			1.02420			0.512101	+	0.858925i	$0.328867\pi$
$384$	9.40406	−	15.0156i	0.479899	−	0.766261i
$385$	0.184020	−	8.23984i	0.00937855	−	0.419941i
$386$	8.17407			0.416049
$387$	8.62803	+	17.7820i	0.438588	+	0.903908i
$388$	−1.06289	−	1.84098i	−0.0539599	−	0.0934614i
$389$	11.9941			0.608126			0.304063	−	0.952652i	$-0.401657\pi$
$389$	11.9941			0.608126			0.304063	+	0.952652i	$0.401657\pi$
$390$	1.45720	+	0.0523729i	0.0737882	+	0.00265201i
$391$	0.00274975	+	0.00476270i	0.000139061	+	0.000240860i
$392$	−10.5189	−	0.470072i	−0.531285	−	0.0237422i
$393$	−5.38717	−	10.1567i	−0.271747	−	0.512340i
$394$	1.28614	+	2.22765i	0.0647946	+	0.112228i
$395$	−6.00838	−	10.4068i	−0.302314	−	0.523624i
$396$	7.53561	+	15.5305i	0.378679	+	0.780438i
$397$	−9.35248	+	16.1990i	−0.469387	+	0.813003i	−0.999387	−	0.0349949i	$-0.988859\pi$
$397$	−9.35248	+	16.1990i	−0.469387	+	0.813003i	0.530000	+	0.847998i	$0.322192\pi$
$398$	−3.80804	+	6.59572i	−0.190880	+	0.330614i
$399$	−1.99120	+	34.1422i	−0.0996845	+	1.70925i
$400$	−1.55306	−	2.68998i	−0.0776529	−	0.134499i
$401$	22.9933			1.14823			0.574116	−	0.818774i	$-0.305346\pi$
$401$	22.9933			1.14823			0.574116	+	0.818774i	$0.305346\pi$
$402$	−0.903396	−	1.70322i	−0.0450573	−	0.0849491i
$403$	13.8814			0.691484
$404$	13.5248	−	23.4256i	0.672882	−	1.16547i
$405$	−3.33743	−	8.35832i	−0.165838	−	0.415328i
$406$	−0.105084	+	4.70531i	−0.00521521	+	0.233521i
$407$	−0.930150	+	1.61107i	−0.0461058	+	0.0798577i
$408$	0.0724071	−	0.115613i	0.00358468	−	0.00572371i
$409$	5.67651	−	9.83201i	0.280686	−	0.486162i	−0.690868	−	0.722981i	$-0.742772\pi$
$409$	5.67651	−	9.83201i	0.280686	−	0.486162i	0.971554	+	0.236819i	$0.0761049\pi$
$410$	−1.90915	+	3.30674i	−0.0942861	+	0.163308i
$411$	16.3193	+	30.7678i	0.804973	+	1.51766i
$412$	11.6726	−	20.2175i	0.575068	−	0.996047i
$413$	2.82888	+	1.71859i	0.139200	+	0.0845665i
$414$	0.122884	+	0.00884449i	0.00603940	+	0.000434683i
$415$	−7.38093	+	12.7842i	−0.362316	+	0.627549i
$416$	−9.09237			−0.445790
$417$	−16.2965	+	26.0208i	−0.798043	+	1.27424i
$418$	−9.09007			−0.444610
$419$	10.7473	+	18.6148i	0.525038	+	0.909393i	0.999575	+	0.0291571i	$0.00928232\pi$
$419$	10.7473	+	18.6148i	0.525038	+	0.909393i	−0.474537	+	0.880236i	$0.657384\pi$
$420$	0.492823	−	8.45023i	0.0240473	−	0.412329i
$421$	−5.82015	+	10.0808i	−0.283657	+	0.491308i	−0.972283	−	0.233809i	$-0.924881\pi$
$421$	−5.82015	+	10.0808i	−0.283657	+	0.491308i	0.688626	+	0.725117i	$0.258214\pi$
$422$	−2.66684	+	4.61909i	−0.129820	+	0.224854i
$423$	21.7659	+	1.56659i	1.05830	+	0.0761704i
$424$	−3.59520	−	6.22707i	−0.174598	−	0.302413i
$425$	−0.0261799	−	0.0453449i	−0.00126991	−	0.00219955i
$426$	−2.23657	+	3.57116i	−0.108362	+	0.173023i
$427$	−15.4995	+	8.49296i	−0.750071	+	0.411003i
$428$	12.1615	+	21.0644i	0.587850	+	1.01819i
$429$	6.16631	−	9.84582i	0.297712	−	0.475361i
$430$	2.57595			0.124223
$431$	3.29836	+	5.71293i	0.158876	+	0.275182i	0.934464	−	0.356058i	$-0.115880\pi$
$431$	3.29836	+	5.71293i	0.158876	+	0.275182i	−0.775587	+	0.631240i	$0.782546\pi$
$432$	6.51958	+	14.7645i	0.313673	+	0.710357i
$433$	10.1227			0.486468			0.243234	−	0.969968i	$-0.421792\pi$
$433$	10.1227			0.486468			0.243234	+	0.969968i	$0.421792\pi$
$434$	−0.148909	+	6.66769i	−0.00714788	+	0.320059i
$435$	−7.87514	−	0.283039i	−0.377584	−	0.0135707i
$436$	−26.8913			−1.28786
$437$	0.391935	−	0.678852i	0.0187488	−	0.0324739i
$438$	3.22935	+	0.116065i	0.154304	+	0.00554581i
$439$	−10.2470	−	17.7482i	−0.489060	−	0.847077i	0.510861	−	0.859664i	$-0.329327\pi$
$439$	−10.2470	−	17.7482i	−0.489060	−	0.847077i	−0.999921	+	0.0125864i	$0.995994\pi$
$440$	4.68580			0.223387
$441$	12.5429	−	16.8427i	0.597282	−	0.802031i
$442$	−0.0440795			−0.00209665
$443$	−4.31167	−	7.46802i	−0.204853	−	0.354816i	0.745233	−	0.666805i	$-0.232338\pi$
$443$	−4.31167	−	7.46802i	−0.204853	−	0.354816i	−0.950086	+	0.311988i	$0.899005\pi$
$444$	−1.01409	+	1.61922i	−0.0481268	+	0.0768447i
$445$	4.22085	−	7.31072i	0.200087	−	0.346562i
$446$	2.94337			0.139373
$447$	−14.6999	−	27.7146i	−0.695282	−	1.31086i
$448$	−0.269438	+	12.0646i	−0.0127298	+	0.569998i
$449$	−0.0789673			−0.00372670			−0.00186335	−	0.999998i	$-0.500593\pi$
$449$	−0.0789673			−0.00372670			−0.00186335	+	0.999998i	$0.500593\pi$
$450$	−1.16995	−	0.0842069i	−0.0551521	−	0.00396955i
$451$	15.2107	+	26.3457i	0.716243	+	1.24057i
$452$	7.57349			0.356227
$453$	7.33961	+	13.8378i	0.344845	+	0.650156i
$454$	−5.37797	−	9.31491i	−0.252401	−	0.437171i
$455$	−4.99580	+	2.73746i	−0.234207	+	0.128334i
$456$	−19.4315	−	0.698382i	−0.909961	−	0.0327047i
$457$	11.4582	+	19.8463i	0.535994	+	0.928369i	0.999115	+	0.0420736i	$0.0133964\pi$
$457$	11.4582	+	19.8463i	0.535994	+	0.928369i	−0.463120	+	0.886295i	$0.653270\pi$
$458$	0.261072	+	0.452191i	0.0121991	+	0.0211295i
$459$	0.109900	+	0.248885i	0.00512971	+	0.0116169i
$460$	−0.0970043	+	0.168016i	−0.00452285	+	0.00783380i
$461$	12.2509	−	21.2191i	0.570579	−	0.988272i	−0.425927	−	0.904757i	$-0.640052\pi$
$461$	12.2509	−	21.2191i	0.570579	−	0.988272i	0.996507	−	0.0835150i	$-0.0266147\pi$
$462$	4.66311	+	3.06749i	0.216947	+	0.142712i
$463$	−20.3034	−	35.1666i	−0.943581	−	1.63433i	−0.758568	−	0.651594i	$-0.774101\pi$
$463$	−20.3034	−	35.1666i	−0.943581	−	1.63433i	−0.185013	−	0.982736i	$-0.559233\pi$
$464$	14.1317			0.656050
$465$	−11.1595	−	0.401082i	−0.517510	−	0.0185997i
$466$	−6.47692			−0.300037
$467$	18.1554	−	31.4460i	0.840130	−	1.45515i	−0.0496542	−	0.998766i	$-0.515812\pi$
$467$	18.1554	−	31.4460i	0.840130	−	1.45515i	0.889784	−	0.456381i	$-0.150855\pi$
$468$	6.69202	−	9.87786i	0.309339	−	0.456604i
$469$	6.43735	+	3.91080i	0.297249	+	0.180584i
$470$	1.42206	−	2.46308i	0.0655946	−	0.113613i
$471$	5.69252	+	0.204594i	0.262297	+	0.00942718i
$472$	−0.940926	+	1.62973i	−0.0433096	+	0.0750145i
$473$	10.2616	−	17.7736i	0.471830	−	0.817233i
$474$	8.13274	+	0.292297i	0.373549	+	0.0134257i
$475$	−3.73155	+	6.46324i	−0.171215	+	0.296554i
$476$	−0.00571323	+	0.255820i	−0.000261865	+	0.0117255i
$477$	14.3036	+	1.02950i	0.654919	+	0.0471375i
$478$	3.12720	−	5.41647i	0.143035	−	0.247744i
$479$	17.2160			0.786618			0.393309	−	0.919406i	$-0.371330\pi$
$479$	17.2160			0.786618			0.393309	+	0.919406i	$0.371330\pi$
$480$	7.30951	+	0.262710i	0.333632	+	0.0119910i
$481$	1.28580			0.0586275
$482$	−4.20669	−	7.28620i	−0.191609	−	0.331877i
$483$	−0.430141	+	0.215983i	−0.0195721	+	0.00982758i
$484$	−1.19682	+	2.07295i	−0.0544008	+	0.0942250i
$485$	0.575428	−	0.996671i	0.0261289	−	0.0452565i
$486$	5.99692	+	1.08894i	0.272026	+	0.0493955i
$487$	17.9352	+	31.0647i	0.812723	+	1.40768i	0.910951	+	0.412514i	$0.135349\pi$
$487$	17.9352	+	31.0647i	0.812723	+	1.40768i	−0.0982285	+	0.995164i	$0.531318\pi$
$488$	−5.02408	−	8.70197i	−0.227430	−	0.393919i
$489$	12.8795	+	0.462899i	0.582430	+	0.0209330i
$490$	−1.26129	−	2.42900i	−0.0569795	−	0.109731i
$491$	−1.19611	−	2.07173i	−0.0539798	−	0.0934958i	0.837773	−	0.546019i	$-0.183857\pi$
$491$	−1.19611	−	2.07173i	−0.0539798	−	0.0934958i	−0.891753	+	0.452523i	$0.850524\pi$
$492$	14.6397	+	27.6011i	0.660010	+	1.24435i
$493$	0.238219			0.0107288
$494$	3.14144	+	5.44113i	0.141340	+	0.244808i
$495$	−5.24168	+	7.73705i	−0.235596	+	0.347755i
$496$	20.0255			0.899171
$497$	0.367556	−	16.4580i	0.0164871	−	0.738241i
$498$	−4.68433	−	8.83164i	−0.209910	−	0.395755i
$499$	9.19969			0.411835			0.205917	−	0.978569i	$-0.433982\pi$
$499$	9.19969			0.411835			0.205917	+	0.978569i	$0.433982\pi$
$500$	0.923562	−	1.59966i	0.0413030	−	0.0715388i
$501$	−15.6548	+	24.9962i	−0.699404	+	1.11675i
$502$	−5.40243	−	9.35728i	−0.241122	−	0.417636i
$503$	−2.85710			−0.127392			−0.0636959	−	0.997969i	$-0.520289\pi$
$503$	−2.85710			−0.127392			−0.0636959	+	0.997969i	$0.520289\pi$
$504$	9.73246	+	6.91550i	0.433518	+	0.308041i
$505$	14.6441			0.651655
$506$	−0.0639650	−	0.110791i	−0.00284359	−	0.00492525i
$507$	14.4776	+	0.520337i	0.642973	+	0.0231090i
$508$	−7.52989	+	13.0422i	−0.334085	+	0.578652i
$509$	−7.82417			−0.346800			−0.173400	−	0.984851i	$-0.555475\pi$
$509$	−7.82417			−0.346800			−0.173400	+	0.984851i	$0.555475\pi$
$510$	0.0354362	+	0.00127361i	0.00156914	+	5.63963e-5i
$511$	−11.0713	+	6.06656i	−0.489767	+	0.268369i
$512$	−22.4612			−0.992653
$513$	22.8898	−	31.3034i	1.01061	−	1.38208i
$514$	2.45270	+	4.24819i	0.108184	+	0.187380i
$515$	12.6387			0.556927
$516$	11.1877	−	17.8636i	0.492512	−	0.786399i
$517$	−11.3299	−	19.6240i	−0.498288	−	0.863061i
$518$	−0.0137931	+	0.617611i	−0.000606034	+	0.0271363i
$519$	17.8454	−	28.4939i	0.783325	−	1.25075i
$520$	−1.61937	−	2.80482i	−0.0710139	−	0.123000i
$521$	−4.04697	−	7.00956i	−0.177301	−	0.307094i	0.763654	−	0.645626i	$-0.223403\pi$
$521$	−4.04697	−	7.00956i	−0.177301	−	0.307094i	−0.940955	+	0.338531i	$0.890070\pi$
$522$	2.99322	−	4.41819i	0.131010	−	0.193379i
$523$	−6.30363	+	10.9182i	−0.275638	+	0.477420i	−0.970296	−	0.241921i	$-0.922223\pi$
$523$	−6.30363	+	10.9182i	−0.275638	+	0.477420i	0.694658	+	0.719341i	$0.255556\pi$
$524$	−6.13042	+	10.6182i	−0.267808	+	0.463858i
$525$	4.09530	−	2.05634i	0.178733	−	0.0897461i
$526$	−4.04046	−	6.99828i	−0.176172	−	0.305139i
$527$	0.337569			0.0147048
$528$	8.89556	−	14.2037i	0.387130	−	0.618135i
$529$	−22.9890			−0.999520
$530$	0.934516	−	1.61863i	0.0405928	−	0.0703088i
$531$	−1.63842	−	3.37670i	−0.0711012	−	0.146536i
$532$	31.9853	−	17.5264i	1.38674	−	0.759867i
$533$	10.5133	−	18.2096i	0.455382	−	0.788745i
$534$	2.67877	+	5.05045i	0.115922	+	0.218554i
$535$	−6.58404	+	11.4039i	−0.284653	+	0.493033i
$536$	−2.14115	+	3.70858i	−0.0924837	+	0.160186i
$537$	−19.9388	+	31.8365i	−0.860422	+	1.37385i
$538$	−0.696227	+	1.20590i	−0.0300165	+	0.0519901i
$539$	−21.7843	−	0.973502i	−0.938315	−	0.0419317i
$540$	−5.66523	+	7.74762i	−0.243793	+	0.333404i
$541$	−8.97424	+	15.5438i	−0.385833	+	0.668282i	−0.991884	−	0.127143i	$-0.959419\pi$
$541$	−8.97424	+	15.5438i	−0.385833	+	0.668282i	0.606052	+	0.795425i	$0.292753\pi$
$542$	−3.75206			−0.161165
$543$	12.5114	+	23.5885i	0.536915	+	1.01228i
$544$	−0.221109			−0.00947995
$545$	−7.27924	−	12.6080i	−0.311809	−	0.540068i
$546$	0.224612	−	3.85133i	0.00961251	−	0.164822i
$547$	−12.3751	+	21.4343i	−0.529121	+	0.916465i	0.470302	+	0.882506i	$0.344145\pi$
$547$	−12.3751	+	21.4343i	−0.529121	+	0.916465i	−0.999423	+	0.0339594i	$0.989188\pi$
$548$	18.5708	−	32.1656i	0.793307	−	1.37405i
$549$	19.9885	+	1.43866i	0.853089	+	0.0614007i
$550$	0.609001	+	1.05482i	0.0259679	+	0.0449777i
$551$	−16.9773	−	29.4055i	−0.723255	−	1.25271i
$552$	−0.128223	−	0.241747i	−0.00545755	−	0.0102894i
$553$	−27.8819	+	15.2780i	−1.18566	+	0.649685i
$554$	0.994973	+	1.72334i	0.0422723	+	0.0732178i
$555$	−1.03368	−	0.0371512i	−0.0438772	−	0.00157698i
$556$	32.7426			1.38859
$557$	6.53043	+	11.3110i	0.276703	+	0.479264i	0.970563	−	0.240846i	$-0.0774247\pi$
$557$	6.53043	+	11.3110i	0.276703	+	0.479264i	−0.693860	+	0.720110i	$0.744091\pi$
$558$	4.24157	−	6.26083i	0.179560	−	0.265042i
$559$	−14.1852			−0.599972
$560$	−7.20698	+	3.94908i	−0.304550	+	0.166879i
$561$	0.149952	−	0.239431i	0.00633100	−	0.0101088i
$562$	10.5388			0.444552
$563$	6.64889	−	11.5162i	0.280217	−	0.485351i	−0.691221	−	0.722644i	$-0.742927\pi$
$563$	6.64889	−	11.5162i	0.280217	−	0.485351i	0.971438	+	0.237293i	$0.0762601\pi$
$564$	−10.9046	−	20.5591i	−0.459167	−	0.865695i
$565$	2.05008	+	3.55084i	0.0862473	+	0.149385i
$566$	4.96794			0.208818
$567$	−22.3057	+	8.33405i	−0.936751	+	0.349997i
$568$	9.35925			0.392705
$569$	14.1300	+	24.4738i	0.592358	+	1.02599i	0.993914	+	0.110160i	$0.0351364\pi$
$569$	14.1300	+	24.4738i	0.592358	+	1.02599i	−0.401555	+	0.915835i	$0.631530\pi$
$570$	−2.36824	−	4.46498i	−0.0991946	−	0.187017i
$571$	−3.58366	+	6.20709i	−0.149972	+	0.259758i	−0.931217	−	0.364466i	$-0.881252\pi$
$571$	−3.58366	+	6.20709i	−0.149972	+	0.259758i	0.781245	+	0.624224i	$0.214585\pi$
$572$	−12.3892			−0.518019
$573$	−19.1656	+	30.6020i	−0.800655	+	1.27842i
$574$	8.63386	+	5.24521i	0.360370	+	0.218931i
$575$	−0.105033			−0.00438017
$576$	7.67473	−	11.3284i	0.319780	−	0.472017i
$577$	−10.3406	−	17.9104i	−0.430484	−	0.745620i	0.566431	−	0.824109i	$-0.308324\pi$
$577$	−10.3406	−	17.9104i	−0.430484	−	0.745620i	−0.996915	+	0.0784890i	$0.974990\pi$
$578$	6.64582			0.276429
$579$	36.1867	+	1.30058i	1.50387	+	0.0540502i
$580$	4.20188	+	7.27788i	0.174474	+	0.302197i
$581$	33.3792	+	20.2784i	1.38480	+	0.841292i
$582$	0.365197	+	0.688527i	0.0151379	+	0.0285404i
$583$	−7.44553	−	12.8960i	−0.308362	−	0.534099i
$584$	−3.58873	−	6.21586i	−0.148503	−	0.257214i
$585$	6.44271	+	0.463711i	0.266373	+	0.0191721i
$586$	3.44016	−	5.95852i	0.142112	−	0.246144i
$587$	7.32156	−	12.6813i	0.302193	−	0.523414i	−0.674439	−	0.738330i	$-0.735615\pi$
$587$	7.32156	−	12.6813i	0.302193	−	0.523414i	0.976632	+	0.214916i	$0.0689479\pi$
$588$	−22.3225	−	1.80274i	−0.920565	−	0.0743437i
$589$	−24.0577	−	41.6692i	−0.991282	−	1.71695i
$590$	−0.489158			−0.0201383
$591$	5.33930	+	10.0665i	0.219629	+	0.414080i
$592$	1.85491			0.0762363
$593$	−13.5984	+	23.5532i	−0.558421	+	0.967214i	0.439207	+	0.898386i	$0.355259\pi$
$593$	−13.5984	+	23.5532i	−0.558421	+	0.967214i	−0.997629	+	0.0688282i	$0.978074\pi$
$594$	−2.55652	−	5.78960i	−0.104895	−	0.237550i
$595$	−0.121488	+	0.0665695i	−0.00498052	+	0.00272909i
$596$	−16.7280	+	28.9738i	−0.685206	+	1.18681i
$597$	−17.9077	+	28.5935i	−0.732914	+	1.17025i
$598$	−0.0442113	+	0.0765763i	−0.00180794	+	0.00313144i
$599$	−14.4815	+	25.0827i	−0.591699	+	1.02485i	0.402305	+	0.915506i	$0.368209\pi$
$599$	−14.4815	+	25.0827i	−0.591699	+	1.02485i	−0.994004	+	0.109347i	$0.965124\pi$
$600$	1.22079	+	2.30163i	0.0498387	+	0.0939638i
$601$	3.09150	−	5.35463i	0.126105	−	0.218420i	−0.796059	−	0.605218i	$-0.793086\pi$
$601$	3.09150	−	5.35463i	0.126105	−	0.218420i	0.922164	+	0.386798i	$0.126419\pi$
$602$	0.152169	−	6.81362i	0.00620193	−	0.277702i
$603$	−3.72835	−	7.68394i	−0.151830	−	0.312914i
$604$	8.35222	−	14.4665i	0.339847	−	0.588632i
$605$	−1.29587			−0.0526847
$606$	−5.26394	+	8.40499i	−0.213833	+	0.341430i
$607$	−2.25783			−0.0916423			−0.0458211	−	0.998950i	$-0.514590\pi$
$607$	−2.25783			−0.0916423			−0.0458211	+	0.998950i	$0.514590\pi$
$608$	15.7579	+	27.2934i	0.639066	+	1.10689i
$609$	−1.21387	+	20.8137i	−0.0491885	+	0.843416i
$610$	1.30593	−	2.26194i	0.0528756	−	0.0915833i
$611$	−7.83100	+	13.5637i	−0.316808	+	0.548728i
$612$	0.162737	−	0.240210i	0.00657824	−	0.00970991i
$613$	−4.84795	−	8.39689i	−0.195807	−	0.339147i	0.751358	−	0.659895i	$-0.229399\pi$
$613$	−4.84795	−	8.39689i	−0.195807	−	0.339147i	−0.947165	+	0.320748i	$0.896066\pi$
$614$	1.48249	+	2.56774i	0.0598282	+	0.103626i
$615$	−8.97796	+	14.3352i	−0.362026	+	0.578052i
$616$	0.276804	−	12.3944i	0.0111527	−	0.499384i
$617$	3.01551	+	5.22302i	0.121400	+	0.210271i	0.920320	−	0.391166i	$-0.127928\pi$
$617$	3.01551	+	5.22302i	0.121400	+	0.210271i	−0.798920	+	0.601437i	$0.794595\pi$
$618$	−4.54306	+	7.25396i	−0.182749	+	0.291797i
$619$	−26.9709			−1.08405			−0.542026	−	0.840362i	$-0.682343\pi$
$619$	−26.9709			−1.08405			−0.542026	+	0.840362i	$0.682343\pi$
$620$	5.95431	+	10.3132i	0.239131	+	0.414187i
$621$	0.542600	+	0.0587067i	0.0217738	+	0.00235582i
$622$	1.98475			0.0795812
$623$	−19.0882	−	11.5964i	−0.764753	−	0.464600i
$624$	−11.5762	−	0.416059i	−0.463420	−	0.0166557i
$625$	1.00000			0.0400000
$626$	5.90340	−	10.2250i	0.235947	−	0.408673i
$627$	−40.2419	−	1.44632i	−1.60710	−	0.0577607i
$628$	−3.03732	−	5.26079i	−0.121202	−	0.209928i
$629$	0.0312682			0.00124674
$630$	−0.291848	+	3.08966i	−0.0116275	+	0.123095i
$631$	29.4422			1.17208			0.586038	−	0.810283i	$-0.300687\pi$
$631$	29.4422			1.17208			0.586038	+	0.810283i	$0.300687\pi$
$632$	−9.03781	−	15.6539i	−0.359505	−	0.622680i
$633$	−12.5411	+	20.0245i	−0.498463	+	0.795901i
$634$	−3.81592	+	6.60936i	−0.151549	+	0.262491i
$635$	−8.15310			−0.323546
$636$	−7.16606	−	13.5106i	−0.284153	−	0.535729i
$637$	6.94571	+	13.3760i	0.275199	+	0.529978i
$638$	−5.54148			−0.219389
$639$	−10.4695	+	15.4537i	−0.414168	+	0.611339i
$640$	−5.11455	−	8.85867i	−0.202171	−	0.350170i
$641$	−38.9850			−1.53982			−0.769908	−	0.638155i	$-0.779698\pi$
$641$	−38.9850			−1.53982			−0.769908	+	0.638155i	$0.779698\pi$
$642$	−4.17858	−	7.87811i	−0.164915	−	0.310924i
$643$	−4.12119	−	7.13810i	−0.162524	−	0.281499i	0.773249	−	0.634102i	$-0.218630\pi$
$643$	−4.12119	−	7.13810i	−0.162524	−	0.281499i	−0.935773	+	0.352603i	$0.885297\pi$
$644$	0.438688	+	0.266510i	0.0172867	+	0.0105020i
$645$	11.4038	+	0.409860i	0.449022	+	0.0161382i
$646$	0.0763935	+	0.132317i	0.00300566	+	0.00520596i
$647$	−19.8309	−	34.3481i	−0.779633	−	1.35036i	−0.932153	−	0.362064i	$-0.882072\pi$
$647$	−19.8309	−	34.3481i	−0.779633	−	1.35036i	0.152520	−	0.988300i	$-0.451261\pi$
$648$	−5.02016	−	12.5726i	−0.197210	−	0.493898i
$649$	−1.94862	+	3.37512i	−0.0764902	+	0.132485i
$650$	0.420929	−	0.729070i	0.0165102	−	0.0285965i
$651$	−1.72012	+	29.4943i	−0.0674170	+	1.15597i
$652$	−6.87202	−	11.9027i	−0.269129	−	0.466145i
$653$	−9.84429			−0.385237			−0.192618	−	0.981274i	$-0.561698\pi$
$653$	−9.84429			−0.385237			−0.192618	+	0.981274i	$0.561698\pi$
$654$	9.85294	+	0.354123i	0.385281	+	0.0138473i
$655$	−6.63780			−0.259360
$656$	15.1666	−	26.2693i	0.592156	−	1.02564i
$657$	14.2779	+	1.02765i	0.557034	+	0.0400923i
$658$	−6.43106	−	3.90697i	−0.250709	−	0.152310i
$659$	−6.44285	+	11.1593i	−0.250978	+	0.434706i	−0.963795	−	0.266643i	$-0.914085\pi$
$659$	−6.44285	+	11.1593i	−0.250978	+	0.434706i	0.712817	+	0.701350i	$0.247419\pi$
$660$	9.95989	+	0.357967i	0.387688	+	0.0139338i
$661$	8.50793	−	14.7362i	0.330920	−	0.573171i	−0.651772	−	0.758415i	$-0.725974\pi$
$661$	8.50793	−	14.7362i	0.330920	−	0.573171i	0.982693	+	0.185244i	$0.0593076\pi$
$662$	−0.0239304	+	0.0414486i	−0.000930080	+	0.00161095i
$663$	−0.195140	−	0.00701351i	−0.00757863	−	0.000272382i
$664$	−11.1024	+	19.2299i	−0.430857	+	0.746266i
$665$	16.8754	+	10.2521i	0.654401	+	0.397559i
$666$	0.392886	−	0.579925i	0.0152240	−	0.0224716i
$667$	0.238931	−	0.413841i	0.00925145	−	0.0160240i
$668$	31.4533			1.21696
$669$	13.0304	+	0.468322i	0.503783	+	0.0181064i
$670$	−1.11312			−0.0430035
$671$	−10.4047	−	18.0215i	−0.401669	−	0.695711i
$672$	1.12668	−	19.3188i	0.0434628	−	0.745239i
$673$	−18.2152	+	31.5496i	−0.702144	+	1.21615i	0.265569	+	0.964092i	$0.414440\pi$
$673$	−18.2152	+	31.5496i	−0.702144	+	1.21615i	−0.967713	+	0.252057i	$0.918893\pi$
$674$	1.23145	−	2.13293i	0.0474336	−	0.0821574i
$675$	−5.16600	−	0.558937i	−0.198840	−	0.0215135i
$676$	−7.72472	−	13.3796i	−0.297105	−	0.514600i
$677$	19.8026	+	34.2991i	0.761075	+	1.31822i	0.942297	+	0.334778i	$0.108661\pi$
$677$	19.8026	+	34.2991i	0.761075	+	1.31822i	−0.181222	+	0.983442i	$0.558005\pi$
$678$	−2.77491	−	0.0997327i	−0.106570	−	0.00383021i
$679$	−2.60229	−	1.58094i	−0.0998669	−	0.0606708i
$680$	−0.0393798	−	0.0682078i	−0.00151015	−	0.00261565i
$681$	−22.3262	−	42.0929i	−0.855543	−	1.61301i
$682$	−7.85259			−0.300691
$683$	0.225341	+	0.390303i	0.00862245	+	0.0149345i	0.870304	−	0.492514i	$-0.163922\pi$
$683$	0.225341	+	0.390303i	0.00862245	+	0.0149345i	−0.861682	+	0.507449i	$0.830589\pi$
$684$	−41.2491	−	2.96889i	−1.57720	−	0.113518i
$685$	20.1078			0.768281
$686$	−6.49944	+	3.19275i	−0.248150	+	0.121900i
$687$	1.08382	+	2.04339i	0.0413504	+	0.0779603i
$688$	−20.4638			−0.780173
$689$	−5.14620	+	8.91348i	−0.196055	+	0.339577i
$690$	0.0377548	−	0.0602835i	0.00143730	−	0.00229495i
$691$	12.3853	+	21.4520i	0.471160	+	0.816073i	0.999456	−	0.0329873i	$-0.0105021\pi$
$691$	12.3853	+	21.4520i	0.471160	+	0.816073i	−0.528296	+	0.849060i	$0.677169\pi$
$692$	−35.8546			−1.36299
$693$	20.1556	+	14.3218i	0.765647	+	0.544039i
$694$	2.19024			0.0831406
$695$	8.86312	+	15.3514i	0.336197	+	0.582311i
$696$	−11.8458	−	0.425747i	−0.449013	−	0.0161379i
$697$	0.255663	−	0.442821i	0.00968393	−	0.0167731i
$698$	−1.03582			−0.0392064
$699$	−28.6734	−	1.03055i	−1.08453	−	0.0389788i
$700$	−4.17668	−	2.53740i	−0.157864	−	0.0959048i
$701$	3.03950			0.114800			0.0574001	−	0.998351i	$-0.481719\pi$
$701$	3.03950			0.114800			0.0574001	+	0.998351i	$0.481719\pi$
$702$	−2.58202	+	3.53111i	−0.0974522	+	0.133273i
$703$	−2.22841	−	3.85971i	−0.0840459	−	0.145572i
$704$	−14.2085			−0.535505
$705$	6.68737	−	10.6778i	0.251861	−	0.402150i
$706$	0.707377	+	1.22521i	0.0266225	+	0.0461115i
$707$	0.865070	−	38.7351i	0.0325343	−	1.45678i
$708$	−2.12448	+	3.39219i	−0.0798430	+	0.127486i
$709$	1.19656	+	2.07251i	0.0449379	+	0.0778347i	0.887619	−	0.460578i	$-0.152358\pi$
$709$	1.19656	+	2.07251i	0.0449379	+	0.0778347i	−0.842682	+	0.538412i	$0.819024\pi$
$710$	1.21640	+	2.10686i	0.0456505	+	0.0790690i
$711$	35.9573	+	2.58801i	1.34850	+	0.0970579i
$712$	6.34900	−	10.9968i	0.237939	−	0.412122i
$713$	0.338579	−	0.586436i	0.0126799	−	0.0219622i
$714$	0.00546212	−	0.0936568i	0.000204415	−	0.00350502i
$715$	−3.35365	−	5.80869i	−0.125419	−	0.217233i
$716$	40.0606			1.49713
$717$	14.7060	−	23.4812i	0.549205	−	0.876923i
$718$	11.5316			0.430355
$719$	−4.59698	+	7.96220i	−0.171438	+	0.296940i	−0.938923	−	0.344127i	$-0.888175\pi$
$719$	−4.59698	+	7.96220i	−0.171438	+	0.296940i	0.767485	+	0.641067i	$0.221508\pi$
$720$	9.29431	+	0.668954i	0.346378	+	0.0249304i
$721$	0.746602	−	33.4305i	0.0278049	−	1.24502i
$722$	7.17432	−	12.4263i	0.267001	−	0.462459i
$723$	−17.4638	−	32.9254i	−0.649484	−	1.22451i
$724$	14.2375	−	24.6602i	0.529134	−	0.916487i
$725$	−2.27483	+	3.94011i	−0.0844849	+	0.146332i
$726$	0.465810	−	0.743765i	0.0172878	−	0.0276037i
$727$	3.53523	−	6.12320i	0.131114	−	0.227097i	−0.792992	−	0.609232i	$-0.791478\pi$
$727$	3.53523	−	6.12320i	0.131114	−	0.227097i	0.924106	+	0.382135i	$0.124811\pi$
$728$	−7.51468	+	4.11768i	−0.278512	+	0.152611i
$729$	26.3752	+	5.77494i	0.976858	+	0.213887i
$730$	0.932834	−	1.61572i	0.0345257	−	0.0598003i
$731$	−0.344957			−0.0127587
$732$	−10.0141	−	18.8802i	−0.370134	−	0.697834i
$733$	6.25135			0.230899			0.115449	−	0.993313i	$-0.463169\pi$
$733$	6.25135			0.230899			0.115449	+	0.993313i	$0.463169\pi$
$734$	−6.08474	−	10.5391i	−0.224592	−	0.389004i
$735$	−5.19729	−	10.9539i	−0.191705	−	0.404041i
$736$	−0.221770	+	0.384117i	−0.00817455	+	0.0141587i
$737$	−4.43425	+	7.68035i	−0.163338	+	0.282909i
$738$	−5.00050	−	10.3058i	−0.184071	−	0.379362i
$739$	−6.69473	−	11.5956i	−0.246269	−	0.426551i	0.716218	−	0.697876i	$-0.245871\pi$
$739$	−6.69473	−	11.5956i	−0.246269	−	0.426551i	−0.962488	+	0.271325i	$0.912538\pi$
$740$	0.551532	+	0.955282i	0.0202747	+	0.0351169i
$741$	13.0414	+	24.5878i	0.479089	+	0.903255i
$742$	−4.22622	−	2.56750i	−0.155149	−	0.0942558i
$743$	4.39039	+	7.60438i	0.161068	+	0.278978i	0.935252	−	0.353983i	$-0.115173\pi$
$743$	4.39039	+	7.60438i	0.161068	+	0.278978i	−0.774184	+	0.632961i	$0.781840\pi$
$744$	−16.7862	−	0.603308i	−0.615410	−	0.0221183i
$745$	−18.1125			−0.663590
$746$	4.71871	+	8.17305i	0.172764	+	0.299237i
$747$	−19.3324	−	39.8431i	−0.707335	−	1.45778i
$748$	−0.301281			−0.0110159
$749$	29.7754	+	18.0890i	1.08797	+	0.660959i
$750$	−0.359457	+	0.573950i	−0.0131255	+	0.0209577i
$751$	4.57944			0.167106			0.0835531	−	0.996503i	$-0.473373\pi$
$751$	4.57944			0.167106			0.0835531	+	0.996503i	$0.473373\pi$
$752$	−11.2971	+	19.5671i	−0.411961	+	0.713538i
$753$	−22.4278	−	42.2844i	−0.817314	−	1.54093i
$754$	1.91508	+	3.31701i	0.0697431	+	0.120799i
$755$	9.04349			0.329126
$756$	20.1585	+	15.4427i	0.733157	+	0.561647i
$757$	−8.40020			−0.305310			−0.152655	−	0.988280i	$-0.548782\pi$
$757$	−8.40020			−0.305310			−0.152655	+	0.988280i	$0.548782\pi$
$758$	3.04268	+	5.27008i	0.110515	+	0.191418i
$759$	−0.265546	−	0.500649i	−0.00963871	−	0.0181724i
$760$	−5.61300	+	9.72200i	−0.203605	+	0.352654i
$761$	−41.8467			−1.51694			−0.758471	−	0.651707i	$-0.774053\pi$
$761$	−41.8467			−1.51694			−0.758471	+	0.651707i	$0.774053\pi$
$762$	2.93069	−	4.67947i	0.106168	−	0.169519i
$763$	−33.7794	+	18.5095i	−1.22290	+	0.670088i
$764$	38.5071			1.39314
$765$	0.156674	+	0.0112765i	0.00566456	+	0.000407704i
$766$	3.91854	+	6.78712i	0.141583	+	0.245228i
$767$	2.69370			0.0972639
$768$	−8.86709	−	0.318690i	−0.319963	−	0.0114997i
$769$	−1.25915	−	2.18091i	−0.0454061	−	0.0786457i	0.842429	−	0.538807i	$-0.181125\pi$
$769$	−1.25915	−	2.18091i	−0.0454061	−	0.0786457i	−0.887835	+	0.460161i	$0.847792\pi$
$770$	2.82607	−	1.54855i	0.101845	−	0.0558059i
$771$	10.1822	+	19.1971i	0.366702	+	0.691365i
$772$	−19.3079	−	33.4423i	−0.694906	−	1.20361i
$773$	17.6807	+	30.6238i	0.635929	+	1.10146i	0.986317	+	0.164857i	$0.0527163\pi$
$773$	17.6807	+	30.6238i	0.635929	+	1.10146i	−0.350388	+	0.936604i	$0.613950\pi$
$774$	−4.33440	+	6.39785i	−0.155797	+	0.229966i
$775$	−3.22356	+	5.58336i	−0.115794	+	0.200560i
$776$	0.865559	−	1.49919i	0.0310718	−	0.0538179i
$777$	−0.159331	+	2.73198i	−0.00571596	+	0.0980092i
$778$	2.34481	+	4.06133i	0.0840656	+	0.145606i
$779$	−72.8819			−2.61126
$780$	−3.22777	−	6.08550i	−0.115573	−	0.217896i
$781$	19.3827			0.693566
$782$	−0.00107513	+	0.00186218i	−3.84467e−5	+	6.65916e-5i
$783$	13.9540	−	19.0831i	0.498676	−	0.681976i
$784$	10.0199	+	19.2964i	0.357855	+	0.689157i
$785$	1.64435	−	2.84810i	0.0586894	−	0.101653i
$786$	2.38600	−	3.80976i	0.0851059	−	0.135890i
$787$	14.7289	−	25.5112i	0.525029	−	0.909378i	−0.474546	−	0.880231i	$-0.657388\pi$
$787$	14.7289	−	25.5112i	0.525029	−	0.909378i	0.999575	−	0.0291467i	$-0.00927900\pi$
$788$	6.07594	−	10.5238i	0.216446	−	0.374896i
$789$	−16.7737	−	31.6244i	−0.597158	−	1.12586i
$790$	2.34924	−	4.06900i	0.0835821	−	0.144768i
$791$	9.51339	−	5.21288i	0.338257	−	0.185349i
$792$	−7.88453	+	11.6381i	−0.280165	+	0.413541i
$793$	−7.19152	+	12.4561i	−0.255378	+	0.442328i
$794$	−7.31351			−0.259547
$795$	4.39466	−	7.01701i	0.155862	−	0.248868i
$796$	35.9798			1.27527
$797$	17.5902	+	30.4671i	0.623076	+	1.07920i	0.988909	+	0.148519i	$0.0474508\pi$
$797$	17.5902	+	30.4671i	0.623076	+	1.07920i	−0.365833	+	0.930680i	$0.619216\pi$
$798$	−11.9502	+	6.00045i	−0.423032	+	0.212414i
$799$	−0.190434	+	0.329842i	−0.00673709	+	0.0116690i
$800$	2.11144	−	3.65711i	0.0746505	−	0.129298i
$801$	11.0554	+	22.7846i	0.390623	+	0.805055i
$802$	4.49512	+	7.78577i	0.158728	+	0.274925i
$803$	−7.43213	−	12.8728i	−0.262274	−	0.454272i
$804$	−4.83443	+	7.71920i	−0.170497	+	0.272235i
$805$	−0.00620458	+	0.277821i	−0.000218683	+	0.00979192i
$806$	2.71378	+	4.70040i	0.0955887	+	0.165564i
$807$	−3.27408	+	5.22776i	−0.115253	+	0.184026i
$808$	22.0277			0.774932
$809$	−11.4989	−	19.9166i	−0.404278	−	0.700231i	0.589959	−	0.807433i	$-0.299144\pi$
$809$	−11.4989	−	19.9166i	−0.404278	−	0.700231i	−0.994237	+	0.107203i	$0.965811\pi$
$810$	2.17776	−	2.76411i	0.0765186	−	0.0971210i
$811$	20.3449			0.714405			0.357203	−	0.934027i	$-0.383731\pi$
$811$	20.3449			0.714405			0.357203	+	0.934027i	$0.383731\pi$
$812$	19.4989	−	10.6844i	0.684276	−	0.374951i
$813$	−16.6104	−	0.596992i	−0.582553	−	0.0209374i
$814$	−0.727365			−0.0254941
$815$	3.72039	−	6.44390i	0.130319	−	0.225720i
$816$	−0.281511	−	0.0101177i	−0.00985486	−	0.000354192i
$817$	24.5843	+	42.5812i	0.860094	+	1.48973i
$818$	4.43896			0.155205
$819$	1.60715	−	17.0142i	0.0561583	−	0.594523i
$820$	18.0383			0.629926
$821$	−5.39365	−	9.34207i	−0.188240	−	0.326040i	0.756424	−	0.654082i	$-0.226945\pi$
$821$	−5.39365	−	9.34207i	−0.188240	−	0.326040i	−0.944663	+	0.328041i	$0.893611\pi$
$822$	−7.22791	+	11.5409i	−0.252102	+	0.402535i
$823$	−19.0678	+	33.0264i	−0.664661	+	1.15123i	0.314716	+	0.949186i	$0.398091\pi$
$823$	−19.0678	+	33.0264i	−0.664661	+	1.15123i	−0.979377	+	0.202041i	$0.935242\pi$
$824$	19.0111			0.662283
$825$	2.52822	+	4.76660i	0.0880214	+	0.165952i
$826$	−0.0288960	+	1.29387i	−0.00100542	+	0.0450194i
$827$	−40.2684			−1.40027			−0.700135	−	0.714011i	$-0.746877\pi$
$827$	−40.2684			−1.40027			−0.700135	+	0.714011i	$0.746877\pi$
$828$	−0.254077	−	0.523640i	−0.00882978	−	0.0181978i
$829$	−6.36099	−	11.0175i	−0.220926	−	0.382655i	0.734163	−	0.678973i	$-0.237575\pi$
$829$	−6.36099	−	11.0175i	−0.220926	−	0.382655i	−0.955089	+	0.296318i	$0.904241\pi$
$830$	−5.77179			−0.200342
$831$	4.13056	+	7.78758i	0.143287	+	0.270148i
$832$	4.91033	+	8.50494i	0.170235	+	0.294856i
$833$	0.168906	+	0.325279i	0.00585224	+	0.0112703i
$834$	−11.9968	−	0.431175i	−0.415416	−	0.0149304i
$835$	8.51412	+	14.7469i	0.294643	+	0.510337i
$836$	21.4716	+	37.1898i	0.742610	+	1.28624i
$837$	19.7737	−	27.0419i	0.683477	−	0.934705i
$838$	−4.20211	+	7.27827i	−0.145159	+	0.251424i
$839$	−6.43901	+	11.1527i	−0.222299	+	0.385034i	−0.955506	−	0.294972i	$-0.904690\pi$
$839$	−6.43901	+	11.1527i	−0.222299	+	0.385034i	0.733206	+	0.680006i	$0.238023\pi$
$840$	6.16015	−	3.09315i	0.212545	−	0.106724i
$841$	4.15034	+	7.18860i	0.143115	+	0.247883i
$842$	−4.55128			−0.156847
$843$	46.6554	+	1.67683i	1.60690	+	0.0577532i
$844$	25.1972			0.867325
$845$	4.18203	−	7.24348i	0.143866	−	0.249183i
$846$	3.72470	+	7.67643i	0.128058	+	0.263921i
$847$	−0.0765508	+	3.42770i	−0.00263032	+	0.117777i
$848$	−7.42395	+	12.8587i	−0.254940	+	0.441568i
$849$	21.9932	+	0.790452i	0.754803	+	0.0271282i
$850$	0.0102362	−	0.0177296i	0.000351097	−	0.000608119i
$851$	0.0313617	−	0.0543201i	0.00107507	−	0.00186207i
$852$	19.8935	+	0.714989i	0.681541	+	0.0244951i
$853$	−10.1609	+	17.5992i	−0.347903	+	0.602585i	−0.985877	−	0.167473i	$-0.946439\pi$
$853$	−10.1609	+	17.5992i	−0.347903	+	0.602585i	0.637974	+	0.770058i	$0.279773\pi$
$854$	−5.90590	−	3.58793i	−0.202096	−	0.122776i
$855$	−9.77381	−	20.1433i	−0.334257	−	0.688887i
$856$	−9.90371	+	17.1537i	−0.338502	+	0.586302i
$857$	−35.8385			−1.22422			−0.612109	−	0.790773i	$-0.709679\pi$
$857$	−35.8385			−1.22422			−0.612109	+	0.790773i	$0.709679\pi$
$858$	4.53939	+	0.163149i	0.154972	+	0.00556983i
$859$	6.77311			0.231095			0.115548	−	0.993302i	$-0.463138\pi$
$859$	6.77311			0.231095			0.115548	+	0.993302i	$0.463138\pi$
$860$	−6.08462	−	10.5389i	−0.207484	−	0.359373i
$861$	37.3876	+	24.5944i	1.27417	+	0.838173i
$862$	−1.28964	+	2.23372i	−0.0439252	+	0.0760807i
$863$	−22.8677	+	39.6081i	−0.778427	+	1.34828i	0.154421	+	0.988005i	$0.450649\pi$
$863$	−22.8677	+	39.6081i	−0.778427	+	1.34828i	−0.932848	+	0.360270i	$0.882685\pi$
$864$	−12.9518	+	17.7125i	−0.440629	+	0.602592i
$865$	−9.70551	−	16.8104i	−0.329997	−	0.571572i
$866$	1.97896	+	3.42766i	0.0672479	+	0.116477i
$867$	29.4211	+	1.05742i	0.999194	+	0.0359118i
$868$	27.6310	−	15.1405i	0.937857	−	0.513901i
$869$	−18.7170	−	32.4187i	−0.634930	−	1.09973i
$870$	−1.44372	−	2.72194i	−0.0489468	−	0.0922823i
$871$	6.12973			0.207698
$872$	−10.9494	−	18.9650i	−0.370795	−	0.642235i
$873$	1.50718	+	3.10623i	0.0510104	+	0.105130i
$874$	0.306488			0.0103671
$875$	0.0590728	−	2.64509i	0.00199703	−	0.0894204i
$876$	−7.15316	−	13.4863i	−0.241683	−	0.455658i
$877$	31.6672			1.06932			0.534662	−	0.845066i	$-0.320439\pi$
$877$	31.6672			1.06932			0.534662	+	0.845066i	$0.320439\pi$
$878$	4.00649	−	6.93944i	0.135212	−	0.234195i
$879$	16.1777	−	25.8311i	0.545660	−	0.871262i
$880$	−4.83800	−	8.37966i	−0.163089	−	0.282478i
$881$	−17.1461			−0.577667			−0.288833	−	0.957379i	$-0.593267\pi$
$881$	−17.1461			−0.577667			−0.288833	+	0.957379i	$0.593267\pi$
$882$	8.15520	+	0.954479i	0.274600	+	0.0321390i
$883$	29.3139			0.986490			0.493245	−	0.869890i	$-0.335811\pi$
$883$	29.3139			0.986490			0.493245	+	0.869890i	$0.335811\pi$
$884$	0.104120	+	0.180341i	0.00350193	+	0.00606551i
$885$	−2.16551	−	0.0778302i	−0.0727928	−	0.00261623i
$886$	1.68583	−	2.91995i	0.0566367	−	0.0980976i
$887$	−35.5453			−1.19350			−0.596748	−	0.802429i	$-0.703541\pi$
$887$	−35.5453			−1.19350			−0.596748	+	0.802429i	$0.703541\pi$
$888$	−1.55486	−	0.0558829i	−0.0521776	−	0.00187531i
$889$	−0.481627	+	21.5657i	−0.0161532	+	0.723290i
$890$	3.30065			0.110638
$891$	−10.3966	−	26.0374i	−0.348298	−	0.872285i
$892$	−6.95252	−	12.0421i	−0.232788	−	0.403200i
$893$	54.2872			1.81665
$894$	6.51066	−	10.3957i	0.217749	−	0.347683i
$895$	10.8440	+	18.7824i	0.362476	+	0.627828i
$896$	−23.7341	+	13.0052i	−0.792901	+	0.434472i
$897$	−0.207908	+	0.331970i	−0.00694186	+	0.0110841i
$898$	−0.0154378	−	0.0267391i	−0.000515168	−	0.000892296i
$899$	−14.6661	−	25.4023i	−0.489140	−	0.847216i
$900$	2.41902	+	4.98549i	0.0806342	+	0.166183i
$901$	−0.125145	+	0.216758i	−0.00416920	+	0.00722127i
$902$	−5.94727	+	10.3010i	−0.198023	+	0.342985i
$903$	1.75777	−	30.1398i	0.0584949	−	1.00299i
$904$	3.08372	+	5.34117i	0.102563	+	0.177645i
$905$	15.4159			0.512442
$906$	−3.25075	+	5.19051i	−0.107999	+	0.172443i
$907$	57.3561			1.90448			0.952240	−	0.305352i	$-0.0987741\pi$
$907$	57.3561			1.90448			0.952240	+	0.305352i	$0.0987741\pi$
$908$	−25.4065	+	44.0054i	−0.843144	+	1.46037i
$909$	−24.6408	+	36.3715i	−0.817285	+	1.20637i
$910$	−1.90359	−	1.15646i	−0.0631035	−	0.0383364i
$911$	0.121453	−	0.210362i	0.00402390	−	0.00696961i	−0.864006	−	0.503481i	$-0.832052\pi$
$911$	0.121453	−	0.210362i	0.00402390	−	0.00696961i	0.868030	+	0.496511i	$0.165386\pi$
$912$	18.8137	+	35.4705i	0.622983	+	1.17455i
$913$	−22.9927	+	39.8245i	−0.760947	+	1.31800i
$914$	−4.48010	+	7.75976i	−0.148188	+	0.256670i
$915$	6.14128	−	9.80585i	0.203024	−	0.324172i
$916$	1.23335	−	2.13623i	0.0407512	−	0.0705831i
$917$	−0.392113	+	17.5576i	−0.0129487	+	0.579802i
$918$	−0.0627898	+	0.0858696i	−0.00207237	+	0.00283412i
$919$	−2.48697	+	4.30756i	−0.0820376	+	0.142093i	−0.904125	−	0.427268i	$-0.859476\pi$
$919$	−2.48697	+	4.30756i	−0.0820376	+	0.142093i	0.822087	+	0.569361i	$0.192809\pi$
$920$	−0.157990			−0.00520879
$921$	6.15443	+	11.6033i	0.202795	+	0.382342i
$922$	9.58001			0.315501
$923$	−6.69846	−	11.6021i	−0.220482	−	0.381887i
$924$	1.53521	−	26.3237i	0.0505048	−	0.865986i
$925$	−0.298590	+	0.517173i	−0.00981757	+	0.0170045i
$926$	7.93851	−	13.7499i	0.260876	−	0.451850i
$927$	−21.2664	+	31.3905i	−0.698479	+	1.03100i
$928$	9.60629	+	16.6386i	0.315342	+	0.546188i
$929$	1.66412	+	2.88233i	0.0545979	+	0.0945663i	0.892033	−	0.451971i	$-0.149279\pi$
$929$	1.66412	+	2.88233i	0.0545979	+	0.0945663i	−0.837435	+	0.546537i	$0.815946\pi$
$930$	−2.04584	−	3.85714i	−0.0670857	−	0.126481i
$931$	28.1146	−	44.0314i	0.921419	−	1.44307i
$932$	15.2991	+	26.4988i	0.501138	+	0.867996i
$933$	8.78651	+	0.315794i	0.287657	+	0.0103386i
$934$	14.1973			0.464548
$935$	−0.0815541	−	0.141256i	−0.00266711	−	0.00461956i
$936$	9.69113	+	0.697515i	0.316764	+	0.0227990i
$937$	−57.6442			−1.88315			−0.941577	−	0.336797i	$-0.890656\pi$
$937$	−57.6442			−1.88315			−0.941577	+	0.336797i	$0.890656\pi$
$938$	−0.0657550	+	2.94430i	−0.00214698	+	0.0961348i
$939$	27.7613	−	44.3269i	0.905957	−	1.44655i
$940$	−13.4361			−0.438238
$941$	0.00472963	−	0.00819197i	0.000154182	−	0.000267050i	−0.865948	−	0.500134i	$-0.833284\pi$
$941$	0.00472963	−	0.00819197i	0.000154182	−	0.000267050i	0.866102	+	0.499866i	$0.166618\pi$
$942$	1.04359	+	1.96754i	0.0340020	+	0.0641060i
$943$	−0.512856	−	0.888292i	−0.0167009	−	0.0289268i
$944$	3.88595			0.126477
$945$	−1.78361	+	13.6315i	−0.0580209	+	0.443434i
$946$	8.02445			0.260897
$947$	−22.2802	−	38.5905i	−0.724010	−	1.25402i	−0.959380	−	0.282116i	$-0.908964\pi$
$947$	−22.2802	−	38.5905i	−0.724010	−	1.25402i	0.235370	−	0.971906i	$-0.424370\pi$
$948$	−18.0144	−	33.9636i	−0.585081	−	1.10309i
$949$	−5.13694	+	8.89743i	−0.166752	+	0.288823i
$950$	−2.91802			−0.0946732
$951$	−17.9447	+	28.6526i	−0.581898	+	0.929124i
$952$	−0.182742	+	0.100134i	−0.00592271	+	0.00324536i
$953$	−5.51961			−0.178798			−0.0893988	−	0.995996i	$-0.528495\pi$
$953$	−5.51961			−0.178798			−0.0893988	+	0.995996i	$0.528495\pi$
$954$	2.44772	+	5.04462i	0.0792478	+	0.163326i
$955$	10.4235	+	18.0541i	0.337298	+	0.584217i
$956$	−29.5469			−0.955616
$957$	−24.5322	−	0.881707i	−0.793014	−	0.0285015i
$958$	3.36567	+	5.82951i	0.108740	+	0.188343i
$959$	1.18783	−	53.1871i	0.0383569	−	1.71750i
$960$	−3.70176	−	6.97914i	−0.119474	−	0.225251i
$961$	−5.28263	−	9.14978i	−0.170407	−	0.295154i
$962$	0.251370	+	0.435386i	0.00810450	+	0.0140374i
$963$	−17.2451	−	35.5414i	−0.555717	−	1.14530i
$964$	−19.8732	+	34.4213i	−0.640071	+	1.10864i
$965$	10.4529	−	18.1050i	0.336492	−	0.582822i
$966$	−0.157225	−	0.103426i	−0.00505864	−	0.00332768i
$967$	−3.99665	−	6.92240i	−0.128524	−	0.222609i	0.794581	−	0.607158i	$-0.207690\pi$
$967$	−3.99665	−	6.92240i	−0.128524	−	0.222609i	−0.923105	+	0.384549i	$0.874357\pi$
$968$	−1.94925			−0.0626513
$969$	0.317142	+	0.597926i	0.0101881	+	0.0192082i
$970$	0.449977			0.0144479
$971$	−10.4759	+	18.1447i	−0.336187	+	0.582292i	−0.983712	−	0.179752i	$-0.942471\pi$
$971$	−10.4759	+	18.1447i	−0.336187	+	0.582292i	0.647526	+	0.762044i	$0.275804\pi$
$972$	−9.71011	−	27.1071i	−0.311452	−	0.869462i
$973$	41.1293	−	22.5369i	1.31855	−	0.722500i
$974$	−7.01256	+	12.1461i	−0.224697	+	0.389186i
$975$	1.97946	−	3.16063i	0.0633935	−	0.101221i
$976$	−10.3745	+	17.9692i	−0.332081	+	0.575181i
$977$	9.36105	−	16.2138i	0.299487	−	0.518726i	−0.676532	−	0.736413i	$-0.736518\pi$
$977$	9.36105	−	16.2138i	0.299487	−	0.518726i	0.976019	+	0.217687i	$0.0698513\pi$
$978$	2.36115	+	4.45162i	0.0755014	+	0.142347i
$979$	13.1486	−	22.7740i	0.420230	−	0.727859i
$980$	−6.95839	+	10.8978i	−0.222278	+	0.348118i
$981$	43.5628	+	3.13541i	1.39085	+	0.100106i
$982$	0.467672	−	0.810032i	0.0149240	−	0.0258492i
$983$	19.2769			0.614837			0.307418	−	0.951574i	$-0.400535\pi$
$983$	19.2769			0.614837			0.307418	+	0.951574i	$0.400535\pi$
$984$	−13.5047	+	21.5630i	−0.430513	+	0.687405i
$985$	6.57881			0.209618
$986$	0.0465710	+	0.0806633i	0.00148312	+	0.00256884i
$987$	−27.8487	−	18.3195i	−0.886435	−	0.583115i
$988$	14.8407	−	25.7049i	0.472146	−	0.817781i
$989$	−0.345989	+	0.599271i	−0.0110018	+	0.0190557i
$990$	−3.64458	−	0.262317i	−0.115832	−	0.00833698i
$991$	−6.22762	−	10.7866i	−0.197827	−	0.342646i	0.749997	−	0.661442i	$-0.230055\pi$
$991$	−6.22762	−	10.7866i	−0.197827	−	0.342646i	−0.947824	+	0.318795i	$0.896722\pi$
$992$	13.6127	+	23.5778i	0.432202	+	0.748597i
$993$	−0.112535	+	0.179686i	−0.00357119	+	0.00570217i
$994$	5.64469	−	3.09302i	0.179039	−	0.0981046i
$995$	9.73940	+	16.8691i	0.308760	+	0.534788i
$996$	−25.0677	+	40.0260i	−0.794301	+	1.26827i
$997$	−12.3863			−0.392278			−0.196139	−	0.980576i	$-0.562840\pi$
$997$	−12.3863			−0.392278			−0.196139	+	0.980576i	$0.562840\pi$
$998$	1.79851	+	3.11511i	0.0569308	+	0.0986071i
$999$	1.83158	−	2.50482i	0.0579487	−	0.0792491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.c.16.11	✓	36
3.2	odd	2		945.2.k.c.856.8		36
7.4	even	3		315.2.l.c.151.8	yes	36
9.4	even	3		315.2.l.c.121.8	yes	36
9.5	odd	6		945.2.l.c.226.11		36
21.11	odd	6		945.2.l.c.46.11		36
63.4	even	3	inner	315.2.k.c.256.11	yes	36
63.32	odd	6		945.2.k.c.361.8		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.11	✓	36	1.1	even	1	trivial
315.2.k.c.256.11	yes	36	63.4	even	3	inner
315.2.l.c.121.8	yes	36	9.4	even	3
315.2.l.c.151.8	yes	36	7.4	even	3
945.2.k.c.361.8		36	63.32	odd	6
945.2.k.c.856.8		36	3.2	odd	2
945.2.l.c.46.11		36	21.11	odd	6
945.2.l.c.226.11		36	9.5	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.195497 + 0.338610i) q^{2} +(0.811590 + 1.53014i) q^{3} +(0.923562 - 1.59966i) q^{4} +1.00000 q^{5} +(-0.359457 + 0.573950i) q^{6} +(0.0590728 - 2.64509i) q^{7} +1.50420 q^{8} +(-1.68264 + 2.48369i) q^{9} +O(q^{10})\)	\(q+(0.195497 + 0.338610i) q^{2} +(0.811590 + 1.53014i) q^{3} +(0.923562 - 1.59966i) q^{4} +1.00000 q^{5} +(-0.359457 + 0.573950i) q^{6} +(0.0590728 - 2.64509i) q^{7} +1.50420 q^{8} +(-1.68264 + 2.48369i) q^{9} +(0.195497 + 0.338610i) q^{10} +3.11514 q^{11} +(3.19725 + 0.114912i) q^{12} +(-1.07656 - 1.86466i) q^{13} +(0.907204 - 0.497104i) q^{14} +(0.811590 + 1.53014i) q^{15} +(-1.55306 - 2.68998i) q^{16} +(-0.0261799 - 0.0453449i) q^{17} +(-1.16995 - 0.0842069i) q^{18} +(-3.73155 + 6.46324i) q^{19} +(0.923562 - 1.59966i) q^{20} +(4.09530 - 2.05634i) q^{21} +(0.609001 + 1.05482i) q^{22} -0.105033 q^{23} +(1.22079 + 2.30163i) q^{24} +1.00000 q^{25} +(0.420929 - 0.729070i) q^{26} +(-5.16600 - 0.558937i) q^{27} +(-4.17668 - 2.53740i) q^{28} +(-2.27483 + 3.94011i) q^{29} +(-0.359457 + 0.573950i) q^{30} +(-3.22356 + 5.58336i) q^{31} +(2.11144 - 3.65711i) q^{32} +(2.52822 + 4.76660i) q^{33} +(0.0102362 - 0.0177296i) q^{34} +(0.0590728 - 2.64509i) q^{35} +(2.41902 + 4.98549i) q^{36} +(-0.298590 + 0.517173i) q^{37} -2.91802 q^{38} +(1.97946 - 3.16063i) q^{39} +1.50420 q^{40} +(4.88281 + 8.45728i) q^{41} +(1.49692 + 0.984702i) q^{42} +(3.29411 - 5.70556i) q^{43} +(2.87703 - 4.98316i) q^{44} +(-1.68264 + 2.48369i) q^{45} +(-0.0205336 - 0.0355652i) q^{46} +(-3.63704 - 6.29953i) q^{47} +(2.85559 - 4.55955i) q^{48} +(-6.99302 - 0.312506i) q^{49} +(0.195497 + 0.338610i) q^{50} +(0.0481366 - 0.0768603i) q^{51} -3.97709 q^{52} +(-2.39011 - 4.13979i) q^{53} +(-0.820675 - 1.85853i) q^{54} +3.11514 q^{55} +(0.0888574 - 3.97875i) q^{56} +(-12.9181 - 0.464288i) q^{57} -1.77888 q^{58} +(-0.625533 + 1.08345i) q^{59} +(3.19725 + 0.114912i) q^{60} +(-3.34004 - 5.78511i) q^{61} -2.52078 q^{62} +(6.47019 + 4.59746i) q^{63} -4.56112 q^{64} +(-1.07656 - 1.86466i) q^{65} +(-1.11976 + 1.78794i) q^{66} +(-1.42345 + 2.46549i) q^{67} -0.0967150 q^{68} +(-0.0852436 - 0.160715i) q^{69} +(0.907204 - 0.497104i) q^{70} +6.22208 q^{71} +(-2.53103 + 3.73597i) q^{72} +(-2.38580 - 4.13233i) q^{73} -0.233493 q^{74} +(0.811590 + 1.53014i) q^{75} +(6.89264 + 11.9384i) q^{76} +(0.184020 - 8.23984i) q^{77} +(1.45720 + 0.0523729i) q^{78} +(-6.00838 - 10.4068i) q^{79} +(-1.55306 - 2.68998i) q^{80} +(-3.33743 - 8.35832i) q^{81} +(-1.90915 + 3.30674i) q^{82} +(-7.38093 + 12.7842i) q^{83} +(0.492823 - 8.45023i) q^{84} +(-0.0261799 - 0.0453449i) q^{85} +2.57595 q^{86} +(-7.87514 - 0.283039i) q^{87} +4.68580 q^{88} +(4.22085 - 7.31072i) q^{89} +(-1.16995 - 0.0842069i) q^{90} +(-4.99580 + 2.73746i) q^{91} +(-0.0970043 + 0.168016i) q^{92} +(-11.1595 - 0.401082i) q^{93} +(1.42206 - 2.46308i) q^{94} +(-3.73155 + 6.46324i) q^{95} +(7.30951 + 0.262710i) q^{96} +(0.575428 - 0.996671i) q^{97} +(-1.26129 - 2.42900i) q^{98} +(-5.24168 + 7.73705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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