LMFDB - Embedded newform 220.3.w.a.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(7,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 14]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("220.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.w (of order $20$, degree $8$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96237 - 0.386136i) q^{2} +(0.676076 - 0.344478i) q^{3} +(3.70180 + 1.51549i) q^{4} +(3.50937 + 3.56150i) q^{5} +(-1.45973 + 0.414936i) q^{6} +(-3.62504 + 7.11454i) q^{7} +(-6.67911 - 4.40334i) q^{8} +(-4.95165 + 6.81537i) q^{9} +(-5.51146 - 8.34409i) q^{10} +(-8.53099 + 6.94422i) q^{11} +(3.02475 - 0.250604i) q^{12} +(-2.75214 - 17.3763i) q^{13} +(9.86085 - 12.5616i) q^{14} +(3.59946 + 1.19895i) q^{15} +(11.4066 + 11.2200i) q^{16} +(0.282319 - 1.78249i) q^{17} +(12.3486 - 11.4623i) q^{18} +(-29.4107 - 9.55611i) q^{19} +(7.59357 + 18.5024i) q^{20} +6.05871i q^{21} +(19.4224 - 10.3330i) q^{22} +(-10.0993 - 10.0993i) q^{23} +(-6.03244 - 0.676187i) q^{24} +(-0.368626 + 24.9973i) q^{25} +(-1.30891 + 35.1614i) q^{26} +(-2.06824 + 13.0584i) q^{27} +(-24.2011 + 20.8429i) q^{28} +(11.6683 + 35.9113i) q^{29} +(-6.60052 - 3.74266i) q^{30} +(-9.77073 + 13.4483i) q^{31} +(-18.0515 - 26.4224i) q^{32} +(-3.37546 + 7.63356i) q^{33} +(-1.24230 + 3.38889i) q^{34} +(-38.0601 + 12.0570i) q^{35} +(-28.6586 + 17.7249i) q^{36} +(4.52256 - 8.87603i) q^{37} +(54.0247 + 30.1092i) q^{38} +(-7.84640 - 10.7996i) q^{39} +(-7.75696 - 39.2407i) q^{40} +(70.5782 + 22.9322i) q^{41} +(2.33949 - 11.8894i) q^{42} +(-1.92568 + 1.92568i) q^{43} +(-42.1039 + 12.7775i) q^{44} +(-41.6501 + 6.28232i) q^{45} +(15.9188 + 23.7182i) q^{46} +(17.7547 + 34.8455i) q^{47} +(11.5768 + 3.65628i) q^{48} +(-8.67429 - 11.9391i) q^{49} +(10.3757 - 48.9116i) q^{50} +(-0.423159 - 1.30235i) q^{51} +(16.1457 - 68.4943i) q^{52} +(-14.3061 + 2.26586i) q^{53} +(9.10096 - 24.8267i) q^{54} +(-54.6703 - 6.01330i) q^{55} +(55.5398 - 31.5565i) q^{56} +(-23.1757 + 3.67067i) q^{57} +(-9.03085 - 74.9769i) q^{58} +(8.73280 + 26.8768i) q^{59} +(11.5075 + 9.89319i) q^{60} +(1.41349 + 1.94550i) q^{61} +(24.3667 - 22.6176i) q^{62} +(-30.5383 - 59.9347i) q^{63} +(25.2211 + 58.8209i) q^{64} +(52.2275 - 70.7816i) q^{65} +(9.57151 - 13.6765i) q^{66} +(53.1731 - 53.1731i) q^{67} +(3.74642 - 6.17057i) q^{68} +(-10.3068 - 3.34889i) q^{69} +(79.3436 - 8.96386i) q^{70} +(48.5363 + 66.8045i) q^{71} +(63.0831 - 23.7168i) q^{72} +(9.19257 - 18.0414i) q^{73} +(-12.3023 + 15.6717i) q^{74} +(8.36179 + 17.0270i) q^{75} +(-94.3902 - 79.9462i) q^{76} +(-18.4798 - 85.8671i) q^{77} +(11.2274 + 24.2227i) q^{78} +(27.3454 - 37.6377i) q^{79} +(0.0697902 + 80.0000i) q^{80} +(-20.3291 - 62.5666i) q^{81} +(-129.646 - 72.2544i) q^{82} +(-22.6709 + 143.139i) q^{83} +(-9.18189 + 22.4281i) q^{84} +(7.33911 - 5.24994i) q^{85} +(4.52248 - 3.03533i) q^{86} +(20.2593 + 20.2593i) q^{87} +(87.5572 - 8.81638i) q^{88} -5.61342i q^{89} +(84.1589 + 3.75441i) q^{90} +(133.601 + 43.4096i) q^{91} +(-22.0801 - 52.6907i) q^{92} +(-1.97313 + 12.4578i) q^{93} +(-21.3861 - 75.2355i) q^{94} +(-69.1789 - 138.282i) q^{95} +(-21.3061 - 11.6452i) q^{96} +(-1.56473 - 9.87934i) q^{97} +(12.4120 + 26.7785i) q^{98} +(-5.08492 - 92.5272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) $ 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.96237	−	0.386136i	−0.981185	−	0.193068i
$2$	−1.96237	−	0.386136i	−0.981185	−	0.193068i
$3$	0.676076	−	0.344478i	0.225359	−	0.114826i	−0.337666	−	0.941266i	$-0.609638\pi$
$3$	0.676076	−	0.344478i	0.225359	−	0.114826i	0.563025	+	0.826440i	$0.309638\pi$
$4$	3.70180	+	1.51549i	0.925449	+	0.378871i
$5$	3.50937	+	3.56150i	0.701874	+	0.712301i
$5$	3.50937	+	3.56150i	0.701874	+	0.712301i
$6$	−1.45973	+	0.414936i	−0.243288	+	0.0691559i
$7$	−3.62504	+	7.11454i	−0.517863	+	1.01636i	0.472946	+	0.881091i	$0.343191\pi$
$7$	−3.62504	+	7.11454i	−0.517863	+	1.01636i	−0.990809	+	0.135271i	$0.956809\pi$
$8$	−6.67911	−	4.40334i	−0.834889	−	0.550418i
$9$	−4.95165	+	6.81537i	−0.550184	+	0.757263i
$10$	−5.51146	−	8.34409i	−0.551146	−	0.834409i
$11$	−8.53099	+	6.94422i	−0.775544	+	0.631293i
$11$	−8.53099	+	6.94422i	−0.775544	+	0.631293i
$12$	3.02475	−	0.250604i	0.252062	−	0.0208837i
$13$	−2.75214	−	17.3763i	−0.211703	−	1.33664i	−0.833091	−	0.553136i	$-0.813431\pi$
$13$	−2.75214	−	17.3763i	−0.211703	−	1.33664i	0.621389	−	0.783503i	$-0.286569\pi$
$14$	9.86085	−	12.5616i	0.704347	−	0.897257i
$15$	3.59946	+	1.19895i	0.239964	+	0.0799297i
$16$	11.4066	+	11.2200i	0.712913	+	0.701253i
$17$	0.282319	−	1.78249i	0.0166070	−	0.104852i	−0.977992	−	0.208640i	$-0.933096\pi$
$17$	0.282319	−	1.78249i	0.0166070	−	0.104852i	0.994599	+	0.103788i	$0.0330963\pi$
$18$	12.3486	−	11.4623i	0.686036	−	0.636792i
$19$	−29.4107	−	9.55611i	−1.54793	−	0.502953i	−0.594379	−	0.804185i	$-0.702602\pi$
$19$	−29.4107	−	9.55611i	−1.54793	−	0.502953i	−0.953551	+	0.301232i	$0.902602\pi$
$20$	7.59357	+	18.5024i	0.379679	+	0.925118i
$21$			6.05871i			0.288510i
$22$	19.4224	−	10.3330i	0.882835	−	0.469682i
$23$	−10.0993	−	10.0993i	−0.439098	−	0.439098i	0.452610	−	0.891708i	$-0.350493\pi$
$23$	−10.0993	−	10.0993i	−0.439098	−	0.439098i	−0.891708	+	0.452610i	$0.850493\pi$
$24$	−6.03244	−	0.676187i	−0.251352	−	0.0281745i
$25$	−0.368626	+	24.9973i	−0.0147450	+	0.999891i
$26$	−1.30891	+	35.1614i	−0.0503428	+	1.35236i
$27$	−2.06824	+	13.0584i	−0.0766015	+	0.483643i
$28$	−24.2011	+	20.8429i	−0.864327	+	0.744389i
$29$	11.6683	+	35.9113i	0.402355	+	1.23832i	0.923084	+	0.384599i	$0.125660\pi$
$29$	11.6683	+	35.9113i	0.402355	+	1.23832i	−0.520729	+	0.853722i	$0.674340\pi$
$30$	−6.60052	−	3.74266i	−0.220017	−	0.124755i
$31$	−9.77073	+	13.4483i	−0.315185	+	0.433815i	−0.936989	−	0.349358i	$-0.886400\pi$
$31$	−9.77073	+	13.4483i	−0.315185	+	0.433815i	0.621805	+	0.783172i	$0.286400\pi$
$32$	−18.0515	−	26.4224i	−0.564110	−	0.825700i
$33$	−3.37546	+	7.63356i	−0.102287	+	0.231320i
$34$	−1.24230	+	3.38889i	−0.0365382	+	0.0996733i
$35$	−38.0601	+	12.0570i	−1.08743	+	0.344485i
$36$	−28.6586	+	17.7249i	−0.796072	+	0.492360i
$37$	4.52256	−	8.87603i	0.122231	−	0.239893i	−0.821780	−	0.569804i	$-0.807019\pi$
$37$	4.52256	−	8.87603i	0.122231	−	0.239893i	0.944012	+	0.329912i	$0.107019\pi$
$38$	54.0247	+	30.1092i	1.42170	+	0.792346i
$39$	−7.84640	−	10.7996i	−0.201190	−	0.276914i
$40$	−7.75696	−	39.2407i	−0.193924	−	0.981017i
$41$	70.5782	+	22.9322i	1.72142	+	0.559323i	0.992167	−	0.124922i	$-0.0398680\pi$
$41$	70.5782	+	22.9322i	1.72142	+	0.559323i	0.729252	+	0.684245i	$0.239868\pi$
$42$	2.33949	−	11.8894i	0.0557021	−	0.283082i
$43$	−1.92568	+	1.92568i	−0.0447834	+	0.0447834i	−0.729144	−	0.684360i	$-0.760081\pi$
$43$	−1.92568	+	1.92568i	−0.0447834	+	0.0447834i	0.684360	+	0.729144i	$0.260081\pi$
$44$	−42.1039	+	12.7775i	−0.956906	+	0.290398i
$45$	−41.6501	+	6.28232i	−0.925559	+	0.139607i
$46$	15.9188	+	23.7182i	0.346061	+	0.515612i
$47$	17.7547	+	34.8455i	0.377759	+	0.741394i	0.999112	−	0.0421373i	$-0.0134167\pi$
$47$	17.7547	+	34.8455i	0.377759	+	0.741394i	−0.621353	+	0.783531i	$0.713417\pi$
$48$	11.5768	+	3.65628i	0.241183	+	0.0761724i
$49$	−8.67429	−	11.9391i	−0.177026	−	0.243656i
$50$	10.3757	−	48.9116i	0.207515	−	0.978232i
$51$	−0.423159	−	1.30235i	−0.00829724	−	0.0255363i
$52$	16.1457	−	68.4943i	0.310494	−	1.31720i
$53$	−14.3061	+	2.26586i	−0.269926	+	0.0427521i	−0.289930	−	0.957048i	$-0.593632\pi$
$53$	−14.3061	+	2.26586i	−0.269926	+	0.0427521i	0.0200041	+	0.999800i	$0.493632\pi$
$54$	9.10096	−	24.8267i	0.168536	−	0.459754i
$55$	−54.6703	−	6.01330i	−0.994005	−	0.109333i
$56$	55.5398	−	31.5565i	0.991782	−	0.563509i
$57$	−23.1757	+	3.67067i	−0.406591	+	0.0643978i
$58$	−9.03085	−	74.9769i	−0.155704	−	1.29270i
$59$	8.73280	+	26.8768i	0.148014	+	0.455539i	0.997386	−	0.0722546i	$-0.0230194\pi$
$59$	8.73280	+	26.8768i	0.148014	+	0.455539i	−0.849373	+	0.527794i	$0.823019\pi$
$60$	11.5075	+	9.89319i	0.191791	+	0.164886i
$61$	1.41349	+	1.94550i	0.0231719	+	0.0318934i	0.820446	−	0.571724i	$-0.193725\pi$
$61$	1.41349	+	1.94550i	0.0231719	+	0.0318934i	−0.797274	+	0.603618i	$0.793725\pi$
$62$	24.3667	−	22.6176i	0.393011	−	0.364800i
$63$	−30.5383	−	59.9347i	−0.484734	−	0.951345i
$64$	25.2211	+	58.8209i	0.394080	+	0.919076i
$65$	52.2275	−	70.7816i	0.803500	−	1.08895i
$66$	9.57151	−	13.6765i	0.145023	−	0.207219i
$67$	53.1731	−	53.1731i	0.793628	−	0.793628i	−0.188454	−	0.982082i	$-0.560348\pi$
$67$	53.1731	−	53.1731i	0.793628	−	0.793628i	0.982082	+	0.188454i	$0.0603475\pi$
$68$	3.74642	−	6.17057i	0.0550945	−	0.0907436i
$69$	−10.3068	−	3.34889i	−0.149374	−	0.0485347i
$70$	79.3436	−	8.96386i	1.13348	−	0.128055i
$71$	48.5363	+	66.8045i	0.683610	+	0.940908i	0.999970	−	0.00773106i	$-0.00246090\pi$
$71$	48.5363	+	66.8045i	0.683610	+	0.940908i	−0.316360	+	0.948639i	$0.602461\pi$
$72$	63.0831	−	23.7168i	0.876154	−	0.329400i
$73$	9.19257	−	18.0414i	0.125926	−	0.247143i	−0.819433	−	0.573175i	$-0.805712\pi$
$73$	9.19257	−	18.0414i	0.125926	−	0.247143i	0.945359	+	0.326032i	$0.105712\pi$
$74$	−12.3023	+	15.6717i	−0.166247	+	0.211780i
$75$	8.36179	+	17.0270i	0.111491	+	0.227027i
$76$	−94.3902	−	79.9462i	−1.24198	−	1.05192i
$77$	−18.4798	−	85.8671i	−0.239997	−	1.11516i
$78$	11.2274	+	24.2227i	0.143941	+	0.310547i
$79$	27.3454	−	37.6377i	0.346144	−	0.476426i	−0.600079	−	0.799940i	$-0.704864\pi$
$79$	27.3454	−	37.6377i	0.346144	−	0.476426i	0.946223	+	0.323514i	$0.104864\pi$
$80$	0.0697902	+	80.0000i	0.000872378	+	1.00000i
$81$	−20.3291	−	62.5666i	−0.250977	−	0.772427i
$82$	−129.646	−	72.2544i	−1.58104	−	0.881151i
$83$	−22.6709	+	143.139i	−0.273144	+	1.72456i	0.345092	+	0.938569i	$0.387848\pi$
$83$	−22.6709	+	143.139i	−0.273144	+	1.72456i	−0.618236	+	0.785993i	$0.712152\pi$
$84$	−9.18189	+	22.4281i	−0.109308	+	0.267002i
$85$	7.33911	−	5.24994i	0.0863424	−	0.0617640i
$86$	4.52248	−	3.03533i	0.0525870	−	0.0352945i
$87$	20.2593	+	20.2593i	0.232866	+	0.232866i
$88$	87.5572	−	8.81638i	0.994969	−	0.100186i
$89$		−	5.61342i		−	0.0630721i	−0.999503	−	0.0315360i	$-0.989960\pi$
$89$		−	5.61342i		−	0.0630721i	0.999503	−	0.0315360i	$-0.0100399\pi$
$90$	84.1589	+	3.75441i	0.935098	+	0.0417156i
$91$	133.601	+	43.4096i	1.46814	+	0.477028i
$92$	−22.0801	−	52.6907i	−0.240001	−	0.572725i
$93$	−1.97313	+	12.4578i	−0.0212164	+	0.133955i
$94$	−21.3861	−	75.2355i	−0.227512	−	0.800378i
$95$	−69.1789	−	138.282i	−0.728198	−	1.45560i
$96$	−21.3061	−	11.6452i	−0.221939	−	0.121304i
$97$	−1.56473	−	9.87934i	−0.0161313	−	0.101849i	0.978309	−	0.207151i	$-0.0664191\pi$
$97$	−1.56473	−	9.87934i	−0.0161313	−	0.101849i	−0.994440	+	0.105302i	$0.966419\pi$
$98$	12.4120	+	26.7785i	0.126653	+	0.273250i
$99$	−5.08492	−	92.5272i	−0.0513629	−	0.934618i
$100$	−39.2476	+	91.9762i	−0.392476	+	0.919762i
$101$	−56.4692	+	77.7232i	−0.559101	+	0.769536i	−0.991212	−	0.132284i	$-0.957769\pi$
$101$	−56.4692	+	77.7232i	−0.559101	+	0.769536i	0.432111	+	0.901820i	$0.357769\pi$
$102$	0.327510	+	2.71909i	0.00321089	+	0.0266578i
$103$	13.7955	−	27.0751i	0.133937	−	0.262865i	−0.814291	−	0.580457i	$-0.802874\pi$
$103$	13.7955	−	27.0751i	0.133937	−	0.262865i	0.948228	+	0.317591i	$0.102874\pi$
$104$	−58.1320	+	128.177i	−0.558961	+	1.23247i
$105$	−21.5781	+	21.2623i	−0.205506	+	0.202498i
$106$	28.9488	+	1.07764i	0.273102	+	0.0101664i
$107$	143.834	−	73.2873i	1.34425	−	0.684928i	0.374087	−	0.927394i	$-0.377956\pi$
$107$	143.834	−	73.2873i	1.34425	−	0.684928i	0.970160	+	0.242466i	$0.0779561\pi$
$108$	−27.4460	+	45.2050i	−0.254129	+	0.418565i
$109$	−157.535			−1.44527			−0.722636	−	0.691229i	$-0.757069\pi$
$109$	−157.535			−1.44527			−0.722636	+	0.691229i	$0.757069\pi$
$110$	104.961	+	32.9105i	0.954195	+	0.299186i
$111$		−	7.55879i		−	0.0680972i
$112$	−121.175	+	40.4797i	−1.08192	+	0.361426i
$113$	73.5546	+	144.359i	0.650926	+	1.27751i	0.946657	+	0.322243i	$0.104437\pi$
$113$	73.5546	+	144.359i	0.650926	+	1.27751i	−0.295731	+	0.955271i	$0.595563\pi$
$114$	46.8967	+	1.74577i	0.411375	+	0.0153138i
$115$	0.526504	−	71.4106i	0.00457830	−	0.620962i
$116$	−11.2294	+	150.620i	−0.0968054	+	1.29844i
$117$	132.053	+	67.2846i	1.12866	+	0.575082i
$118$	−6.75888	−	56.1143i	−0.0572787	−	0.475545i
$119$	11.6582	+	8.47016i	0.0979679	+	0.0711778i
$120$	−18.7618	−	23.8576i	−0.156349	−	0.198813i
$121$	24.5555	−	118.482i	0.202938	−	0.979192i
$122$	−2.02256	−	4.36359i	−0.0165783	−	0.0357671i
$123$	55.6158	−	8.80868i	0.452161	−	0.0716153i
$124$	−56.5499	+	34.9753i	−0.456048	+	0.282059i
$125$	−90.3216	+	86.4119i	−0.722573	+	0.691295i
$126$	36.7844	+	129.406i	0.291940	+	1.02703i
$127$	−166.030	−	26.2966i	−1.30732	−	0.207060i	−0.536388	−	0.843972i	$-0.680211\pi$
$127$	−166.030	−	26.2966i	−1.30732	−	0.207060i	−0.770937	+	0.636912i	$0.780211\pi$
$128$	−26.7803	−	125.167i	−0.209221	−	0.977868i
$129$	−0.638553	+	1.96526i	−0.00495002	+	0.0152346i
$130$	−129.821	+	118.733i	−0.998624	+	0.913329i
$131$	−165.619			−1.26427			−0.632135	−	0.774858i	$-0.717821\pi$
$131$	−165.619			−1.26427			−0.632135	+	0.774858i	$0.717821\pi$
$132$	−24.0638	+	23.1424i	−0.182302	+	0.175321i
$133$	174.602	−	174.602i	1.31280	−	1.31280i
$134$	−124.877	+	83.8133i	−0.931921	+	0.625472i
$135$	−53.7656	+	38.4606i	−0.398264	+	0.284893i
$136$	−9.73455	+	10.6623i	−0.0715776	+	0.0783993i
$137$	−113.597	−	17.9920i	−0.829177	−	0.131329i	−0.272603	−	0.962127i	$-0.587884\pi$
$137$	−113.597	−	17.9920i	−0.829177	−	0.131329i	−0.556574	+	0.830798i	$0.687884\pi$
$138$	18.9327	+	10.5516i	0.137193	+	0.0764610i
$139$	194.379	−	63.1577i	1.39841	−	0.454372i	0.489735	−	0.871871i	$-0.337093\pi$
$139$	194.379	−	63.1577i	1.39841	−	0.454372i	0.908677	+	0.417499i	$0.137093\pi$
$140$	−159.163	−	13.0470i	−1.13688	−	0.0931931i
$141$	24.0070	+	17.4421i	0.170262	+	0.123703i
$142$	−69.4505	−	149.837i	−0.489088	−	1.05519i
$143$	144.143	+	129.126i	1.00800	+	0.902976i
$144$	−132.950	+	22.1824i	−0.923266	+	0.154045i
$145$	−86.9499	+	167.583i	−0.599655	+	1.15574i
$146$	−25.0057	+	31.8544i	−0.171272	+	0.218181i
$147$	−9.97725	−	5.08366i	−0.0678724	−	0.0345827i
$148$	30.1931	−	26.0034i	0.204007	−	0.175698i
$149$	128.941	−	93.6811i	0.865376	−	0.628732i	−0.0639665	−	0.997952i	$-0.520375\pi$
$149$	128.941	−	93.6811i	0.865376	−	0.628732i	0.929342	+	0.369220i	$0.120375\pi$
$150$	−9.83417	−	36.6422i	−0.0655611	−	0.244281i
$151$	−82.2950	+	253.278i	−0.545000	+	1.67734i	0.175989	+	0.984392i	$0.443688\pi$
$151$	−82.2950	+	253.278i	−0.545000	+	1.67734i	−0.720990	+	0.692946i	$0.756312\pi$
$152$	154.358	+	193.332i	1.01552	+	1.27192i
$153$	10.7504	+	10.7504i	0.0702639	+	0.0702639i
$154$	3.10775	+	175.639i	0.0201802	+	1.14051i
$155$	−82.1851	+	12.3964i	−0.530227	+	0.0799770i
$156$	−12.6791	−	51.8692i	−0.0812761	−	0.332495i
$157$	−20.0924	+	10.2376i	−0.127977	+	0.0652075i	−0.516807	−	0.856102i	$-0.672879\pi$
$157$	−20.0924	+	10.2376i	−0.127977	+	0.0652075i	0.388830	+	0.921310i	$0.372879\pi$
$158$	−68.1950	+	63.3000i	−0.431614	+	0.400633i
$159$	−8.89146	+	6.46002i	−0.0559211	+	0.0406291i
$160$	30.7540	−	157.017i	0.192212	−	0.981353i
$161$	108.462	−	35.2414i	0.673676	−	0.218890i
$162$	15.7340	+	130.629i	0.0971236	+	0.806350i
$163$	2.06309	+	13.0259i	0.0126570	+	0.0799133i	0.993208	−	0.116350i	$-0.0371194\pi$
$163$	2.06309	+	13.0259i	0.0126570	+	0.0799133i	−0.980551	+	0.196263i	$0.937119\pi$
$164$	226.513	+	191.851i	1.38117	+	1.16982i
$165$	−39.0327	+	14.7673i	−0.236562	+	0.0894985i
$166$	99.7598	−	272.137i	0.600963	−	1.63938i
$167$	36.5443	+	230.731i	0.218828	+	1.38162i	0.815322	+	0.579008i	$0.196560\pi$
$167$	36.5443	+	230.731i	0.218828	+	1.38162i	−0.596494	+	0.802617i	$0.703440\pi$
$168$	26.6786	−	40.4668i	0.158801	−	0.240874i
$169$	−133.633	+	43.4200i	−0.790727	+	0.256923i
$170$	−16.4292	+	7.46843i	−0.0966426	+	0.0439319i
$171$	210.760	−	153.126i	1.23251	−	0.895474i
$172$	−10.0468	+	4.21015i	−0.0584119	+	0.0244776i
$173$	−19.1647	+	9.76490i	−0.110779	+	0.0564445i	−0.508502	−	0.861061i	$-0.669800\pi$
$173$	−19.1647	+	9.76490i	−0.110779	+	0.0564445i	0.397723	+	0.917505i	$0.369800\pi$
$174$	−31.9334	−	47.5791i	−0.183525	−	0.273443i
$175$	−176.508	−	93.2387i	−1.00862	−	0.532793i
$176$	−175.224	−	16.5080i	−0.995591	−	0.0937956i
$177$	15.1625	+	15.1625i	0.0856638	+	0.0856638i
$178$	−2.16754	+	11.0156i	−0.0121772	+	0.0618854i
$179$	106.579	−	328.015i	0.595411	−	1.83249i	0.0427440	−	0.999086i	$-0.486390\pi$
$179$	106.579	−	328.015i	0.595411	−	1.83249i	0.552667	−	0.833402i	$-0.313610\pi$
$180$	−163.701	−	39.8643i	−0.909451	−	0.221469i
$181$	44.7076	−	32.4820i	0.247004	−	0.179459i	−0.457394	−	0.889264i	$-0.651217\pi$
$181$	44.7076	−	32.4820i	0.247004	−	0.179459i	0.704398	+	0.709805i	$0.251217\pi$
$182$	−245.413	−	136.774i	−1.34842	−	0.751505i
$183$	1.62581	+	0.828389i	0.00888418	+	0.00452672i
$184$	22.9836	+	111.925i	0.124911	+	0.608286i
$185$	47.4834	−	15.0422i	0.256667	−	0.0813089i
$186$	8.68243	−	23.6850i	0.0466798	−	0.127339i
$187$	9.96955	+	17.1669i	0.0533131	+	0.0918015i
$188$	12.9163	+	155.898i	0.0687039	+	0.829244i
$189$	−85.4068	−	62.0517i	−0.451888	−	0.328316i
$190$	82.3588	+	298.073i	0.433467	+	1.56881i
$191$	122.340	−	39.7508i	0.640526	−	0.208120i	0.0292939	−	0.999571i	$-0.490674\pi$
$191$	122.340	−	39.7508i	0.640526	−	0.208120i	0.611232	+	0.791451i	$0.290674\pi$
$192$	37.3139	+	31.0792i	0.194343	+	0.161871i
$193$	−304.922	−	48.2950i	−1.57991	−	0.250233i	−0.696052	−	0.717991i	$-0.745062\pi$
$193$	−304.922	−	48.2950i	−1.57991	−	0.250233i	−0.883857	+	0.467758i	$0.845062\pi$
$194$	−0.744186	+	19.9911i	−0.00383601	+	0.103047i
$195$	10.9270	−	65.8449i	0.0560361	−	0.337666i
$196$	−14.0169	−	57.3420i	−0.0715147	−	0.292561i
$197$	78.9040	−	78.9040i	0.400528	−	0.400528i	−0.477891	−	0.878419i	$-0.658599\pi$
$197$	78.9040	−	78.9040i	0.400528	−	0.400528i	0.878419	+	0.477891i	$0.158599\pi$
$198$	−25.7496	+	183.536i	−0.130049	+	0.926950i
$199$	145.371			0.730508			0.365254	−	0.930908i	$-0.380982\pi$
$199$	145.371			0.730508			0.365254	+	0.930908i	$0.380982\pi$
$200$	112.534	−	165.337i	0.562669	−	0.826683i
$201$	17.6321	−	54.2660i	0.0877218	−	0.269980i
$202$	140.825	−	130.717i	0.697155	−	0.647113i
$203$	−297.790	−	47.1654i	−1.46695	−	0.232342i
$204$	0.407244	−	5.46233i	0.00199629	−	0.0267761i
$205$	166.012	+	331.842i	0.809814	+	1.61874i
$206$	−37.5265	+	47.8045i	−0.182168	+	0.232061i
$207$	118.838	−	18.8221i	0.574097	−	0.0909281i
$208$	163.570	−	229.084i	0.786395	−	1.10136i
$209$	317.262	−	122.711i	1.51800	−	0.587135i
$210$	50.5544	−	33.3924i	0.240735	−	0.159011i
$211$	111.627	+	81.1020i	0.529039	+	0.384370i	0.819998	−	0.572366i	$-0.193974\pi$
$211$	111.627	+	81.1020i	0.529039	+	0.384370i	−0.290959	+	0.956736i	$0.593974\pi$
$212$	−56.3921	−	13.2929i	−0.266000	−	0.0627024i
$213$	55.8269	+	28.4452i	0.262098	+	0.133546i
$214$	−310.555	+	88.2771i	−1.45119	+	0.412510i
$215$	−13.6163	−	0.100392i	−0.0633315	−	0.000466938i
$216$	71.3145	−	78.1111i	0.330160	−	0.361625i
$217$	−60.2589	−	118.265i	−0.277691	−	0.544999i
$218$	309.141	+	60.8298i	1.41808	+	0.279036i
$219$		−	15.3640i		−	0.0701553i
$220$	−193.265	−	105.112i	−0.878478	−	0.477782i
$221$	−31.7501			−0.143665
$222$	−2.91872	+	14.8331i	−0.0131474	+	0.0668160i
$223$	−77.6090	+	39.5438i	−0.348022	+	0.177326i	−0.619260	−	0.785186i	$-0.712567\pi$
$223$	−77.6090	+	39.5438i	−0.348022	+	0.177326i	0.271237	+	0.962513i	$0.412567\pi$
$224$	253.421	−	32.6461i	1.13134	−	0.145741i
$225$	−168.540	−	126.290i	−0.749068	−	0.561290i
$226$	−88.5991	−	311.688i	−0.392032	−	1.37915i
$227$	123.293	−	241.977i	0.543143	−	1.06598i	−0.442442	−	0.896797i	$-0.645888\pi$
$227$	123.293	−	241.977i	0.543143	−	1.06598i	0.985585	−	0.169181i	$-0.0541122\pi$
$228$	−91.3546	−	21.5344i	−0.400678	−	0.0944490i
$229$	−23.4994	+	32.3442i	−0.102617	+	0.141241i	−0.857238	−	0.514921i	$-0.827821\pi$
$229$	−23.4994	+	32.3442i	−0.102617	+	0.141241i	0.754620	+	0.656162i	$0.227821\pi$
$230$	−28.6074	+	139.931i	−0.124380	+	0.608394i
$231$	−42.0731	−	51.6868i	−0.182134	−	0.223752i
$232$	80.1960	−	291.235i	0.345672	−	1.25532i
$233$	−21.4341	−	135.330i	−0.0919920	−	0.580814i	−0.990026	−	0.140888i	$-0.955004\pi$
$233$	−21.4341	−	135.330i	−0.0919920	−	0.580814i	0.898034	−	0.439927i	$-0.144996\pi$
$234$	−233.157	−	183.028i	−0.996397	−	0.782171i
$235$	−61.7947	+	185.519i	−0.262956	+	0.789443i
$236$	−8.40435	+	112.727i	−0.0356116	+	0.477656i
$237$	5.52220	−	34.8658i	0.0233004	−	0.147113i
$238$	−19.6070	−	21.1232i	−0.0823825	−	0.0887531i
$239$	43.3398	+	14.0819i	0.181338	+	0.0589203i	0.398278	−	0.917265i	$-0.369608\pi$
$239$	43.3398	+	14.0819i	0.181338	+	0.0589203i	−0.216941	+	0.976185i	$0.569608\pi$
$240$	27.6054	+	54.0620i	0.115022	+	0.225258i
$241$			46.1322i			0.191420i	0.995409	+	0.0957100i	$0.0305121\pi$
$241$			46.1322i			0.191420i	−0.995409	+	0.0957100i	$0.969488\pi$
$242$	−93.9373	+	223.024i	−0.388171	+	0.921587i
$243$	−119.436	−	119.436i	−0.491505	−	0.491505i
$244$	2.28407	+	9.34396i	0.00936093	+	0.0382949i
$245$	12.0800	−	72.7924i	0.0493061	−	0.297112i
$246$	−112.540	−	4.18940i	−0.457481	−	0.0170301i
$247$	−85.1076	+	537.348i	−0.344565	+	2.17550i
$248$	124.477	−	46.7986i	0.501924	−	0.188704i
$249$	33.9808	+	104.582i	0.136469	+	0.420009i
$250$	210.611	−	134.696i	0.842445	−	0.538783i
$251$	192.816	−	265.388i	0.768191	−	1.05732i	−0.228297	−	0.973592i	$-0.573316\pi$
$251$	192.816	−	265.388i	0.768191	−	1.05732i	0.996488	−	0.0837328i	$-0.0266842\pi$
$252$	−22.2163	−	268.146i	−0.0881597	−	1.06407i
$253$	156.288	+	16.0252i	0.617740	+	0.0633405i
$254$	315.659	+	115.714i	1.24275	+	0.455567i
$255$	3.15330	−	6.07752i	0.0123659	−	0.0238334i
$256$	4.22133	+	255.965i	0.0164896	+	0.999864i
$257$	−135.201	+	265.347i	−0.526074	+	1.03248i	0.463179	+	0.886265i	$0.346709\pi$
$257$	−135.201	+	265.347i	−0.526074	+	1.03248i	−0.989253	+	0.146214i	$0.953291\pi$
$258$	2.01194	−	3.61001i	0.00779821	−	0.0139923i
$259$	46.7544	+	64.3519i	0.180519	+	0.248463i
$260$	300.604	−	182.869i	1.15617	−	0.703343i
$261$	−302.526	−	98.2967i	−1.15910	−	0.376616i
$262$	325.007	+	63.9517i	1.24048	+	0.244090i
$263$	−55.4741	+	55.4741i	−0.210928	+	0.210928i	−0.804662	−	0.593733i	$-0.797653\pi$
$263$	−55.4741	+	55.4741i	−0.210928	+	0.210928i	0.593733	+	0.804662i	$0.297653\pi$
$264$	56.1583	−	36.1221i	0.212721	−	0.136826i
$265$	−58.2752	−	42.9994i	−0.219907	−	0.162262i
$266$	−410.054	+	275.214i	−1.54156	+	1.03464i
$267$	−1.93370	−	3.79509i	−0.00724231	−	0.0142138i
$268$	277.419	−	116.253i	1.03515	−	0.433780i
$269$	−152.271	−	209.584i	−0.566065	−	0.779122i	0.426017	−	0.904715i	$-0.359916\pi$
$269$	−152.271	−	209.584i	−0.566065	−	0.779122i	−0.992082	+	0.125594i	$0.959916\pi$
$270$	120.359	−	54.7131i	0.445775	−	0.202641i
$271$	90.2497	+	277.760i	0.333025	+	1.02495i	0.967687	+	0.252155i	$0.0811394\pi$
$271$	90.2497	+	277.760i	0.333025	+	1.02495i	−0.634662	+	0.772790i	$0.718861\pi$
$272$	23.2199	−	17.1645i	0.0853673	−	0.0631049i
$273$	105.278	−	16.6744i	0.385634	−	0.0610784i
$274$	215.973	+	79.1711i	0.788221	+	0.288946i
$275$	−170.442	−	215.811i	−0.619789	−	0.784769i
$276$	−33.0786	−	28.0168i	−0.119850	−	0.101510i
$277$	144.821	−	22.9374i	0.522821	−	0.0828067i	0.110554	−	0.993870i	$-0.464737\pi$
$277$	144.821	−	22.9374i	0.522821	−	0.0828067i	0.412266	+	0.911063i	$0.364737\pi$
$278$	−405.832	+	48.8818i	−1.45983	+	0.175834i
$279$	−43.2735	−	133.182i	−0.155102	−	0.477356i
$280$	307.299	+	87.0617i	1.09749	+	0.310935i
$281$	4.99155	+	6.87029i	0.0177635	+	0.0244494i	0.817806	−	0.575493i	$-0.195190\pi$
$281$	4.99155	+	6.87029i	0.0177635	+	0.0244494i	−0.800043	+	0.599943i	$0.795190\pi$
$282$	−40.3756	−	43.4979i	−0.143176	−	0.154248i
$283$	−42.0181	−	82.4651i	−0.148474	−	0.291396i	0.804777	−	0.593578i	$-0.202285\pi$
$283$	−42.0181	−	82.4651i	−0.148474	−	0.291396i	−0.953250	+	0.302182i	$0.902285\pi$
$284$	78.4303	+	320.853i	0.276163	+	1.12976i
$285$	−94.4053	−	69.6586i	−0.331247	−	0.244416i
$286$	−233.003	−	309.051i	−0.814694	−	1.08060i
$287$	−419.001	+	419.001i	−1.45993	+	1.45993i
$288$	269.463	+	7.80677i	0.935636	+	0.0271068i
$289$	271.758	+	88.2995i	0.940338	+	0.305534i
$290$	235.338	−	295.285i	0.811510	−	1.01822i
$291$	−4.46109	−	6.14017i	−0.0153302	−	0.0211002i
$292$	61.3706	−	52.8545i	0.210173	−	0.181009i
$293$	−235.210	+	461.626i	−0.802766	+	1.57552i	0.0149458	+	0.999888i	$0.495242\pi$
$293$	−235.210	+	461.626i	−0.802766	+	1.57552i	−0.817712	+	0.575628i	$0.804758\pi$
$294$	17.6161	+	13.8286i	0.0599186	+	0.0470361i
$295$	−65.0752	+	125.423i	−0.220594	+	0.425161i
$296$	−69.2909	+	39.3696i	−0.234091	+	0.133005i
$297$	−73.0360	−	125.763i	−0.245913	−	0.423445i
$298$	−289.204	+	134.048i	−0.970482	+	0.449826i
$299$	−147.693	+	203.282i	−0.493957	+	0.679874i
$300$	5.14942	+	75.7028i	0.0171647	+	0.252343i
$301$	−6.71968	−	20.6810i	−0.0223245	−	0.0687078i
$302$	259.293	−	465.248i	0.858587	−	1.54056i
$303$	−11.4035	+	71.9991i	−0.0376355	+	0.237621i
$304$	−228.256	−	438.992i	−0.750842	−	1.44405i
$305$	−1.96845	+	11.8616i	−0.00645393	+	0.0388905i
$306$	−16.9451	−	25.2473i	−0.0553762	−	0.0825076i
$307$	170.671	+	170.671i	0.555933	+	0.555933i	0.928147	−	0.372214i	$-0.121401\pi$
$307$	170.671	+	170.671i	0.555933	+	0.555933i	−0.372214	+	0.928147i	$0.621401\pi$
$308$	61.7220	−	345.869i	0.200396	−	1.12295i
$309$		−	23.0571i		−	0.0746184i
$310$	166.064	+	7.40829i	0.535692	+	0.0238977i
$311$	−282.646	−	91.8372i	−0.908829	−	0.295296i	−0.182953	−	0.983122i	$-0.558565\pi$
$311$	−282.646	−	91.8372i	−0.908829	−	0.295296i	−0.725876	+	0.687825i	$0.758565\pi$
$312$	4.85246	+	106.682i	0.0155528	+	0.341931i
$313$	−44.7144	+	282.315i	−0.142857	+	0.901966i	0.807288	+	0.590158i	$0.200935\pi$
$313$	−44.7144	+	282.315i	−0.142857	+	0.901966i	−0.950145	+	0.311808i	$0.899065\pi$
$314$	43.3818	−	12.3315i	0.138159	−	0.0392724i
$315$	106.288	−	319.095i	0.337421	−	1.01300i
$316$	158.266	−	97.8855i	0.500843	−	0.309764i
$317$	53.9840	+	340.841i	0.170296	+	1.07521i	0.913707	+	0.406374i	$0.133207\pi$
$317$	53.9840	+	340.841i	0.170296	+	1.07521i	−0.743410	+	0.668836i	$0.766793\pi$
$318$	19.9428	−	9.24364i	0.0627132	−	0.0290681i
$319$	−348.918	−	225.332i	−1.09379	−	0.706369i
$320$	−120.980	+	296.249i	−0.378064	+	0.925779i
$321$	71.9971	−	99.0955i	0.224290	−	0.308709i
$322$	−226.450	+	27.2756i	−0.703261	+	0.0847068i
$323$	−25.3368	+	49.7264i	−0.0784422	+	0.153952i
$324$	19.5645	−	262.417i	0.0603843	−	0.809930i
$325$	435.375	−	62.3905i	1.33961	−	0.191971i
$326$	0.981206	−	26.3582i	0.00300983	−	0.0808534i
$327$	−106.505	+	54.2672i	−0.325704	+	0.165955i
$328$	−370.421	−	463.947i	−1.12933	−	1.41447i
$329$	−312.271			−0.949152
$330$	82.2988	−	13.9069i	0.249390	−	0.0421421i
$331$			15.9005i			0.0480377i	0.999712	+	0.0240188i	$0.00764617\pi$
$331$			15.9005i			0.0480377i	−0.999712	+	0.0240188i	$0.992354\pi$
$332$	−300.848	+	495.513i	−0.906168	+	1.49251i
$333$	38.0992	+	74.7739i	0.114412	+	0.224546i
$334$	17.3804	−	466.892i	0.0520372	−	1.39788i
$335$	375.980	+	2.77207i	1.12233	+	0.00827484i
$336$	−67.9790	+	69.1094i	−0.202319	+	0.205683i
$337$	555.102	+	282.838i	1.64719	+	0.839283i	0.996822	+	0.0796602i	$0.0253835\pi$
$337$	555.102	+	282.838i	1.64719	+	0.839283i	0.650364	+	0.759623i	$0.274616\pi$
$338$	279.003	−	33.6055i	0.825454	−	0.0994246i
$339$	99.4570	+	72.2597i	0.293384	+	0.213156i
$340$	35.1241	−	8.31190i	0.103306	−	0.0244468i
$341$	−10.0337	−	182.577i	−0.0294243	−	0.535417i
$342$	−472.716	+	219.108i	−1.38221	+	0.640666i
$343$	−270.054	+	42.7723i	−0.787329	+	0.124701i
$344$	21.3413	−	4.38242i	0.0620387	−	0.0127396i
$345$	−24.2434	−	48.4603i	−0.0702707	−	0.140465i
$346$	41.3788	−	11.7622i	0.119592	−	0.0339947i
$347$	−302.641	−	47.9336i	−0.872164	−	0.138137i	−0.295721	−	0.955274i	$-0.595560\pi$
$347$	−302.641	−	47.9336i	−0.872164	−	0.138137i	−0.576443	+	0.817137i	$0.695560\pi$
$348$	44.2931	+	105.698i	0.127279	+	0.303731i
$349$	107.776	−	331.701i	0.308814	−	0.950431i	−0.669413	−	0.742891i	$-0.733454\pi$
$349$	107.776	−	331.701i	0.308814	−	0.950431i	0.978226	−	0.207540i	$-0.0665459\pi$
$350$	310.371	+	251.125i	0.886774	+	0.717500i
$351$	232.598			0.662672
$352$	337.480	+	100.055i	0.958751	+	0.284248i
$353$	−7.94999	+	7.94999i	−0.0225212	+	0.0225212i	−0.718278	−	0.695757i	$-0.755069\pi$
$353$	−7.94999	+	7.94999i	−0.0225212	+	0.0225212i	0.695757	+	0.718278i	$0.255069\pi$
$354$	−23.8996	−	35.6092i	−0.0675131	−	0.100591i
$355$	−67.5925	+	407.304i	−0.190402	+	1.14733i
$356$	8.50705	−	20.7797i	0.0238962	−	0.0583700i
$357$	10.7996	+	1.71049i	0.0302510	+	0.00479128i
$358$	−335.805	+	602.534i	−0.938004	+	1.68306i
$359$	−279.395	+	90.7810i	−0.778259	+	0.252872i	−0.671097	−	0.741370i	$-0.734177\pi$
$359$	−279.395	+	90.7810i	−0.778259	+	0.252872i	−0.107163	+	0.994242i	$0.534177\pi$
$360$	305.849	+	141.440i	0.849581	+	0.392888i
$361$	481.613	+	349.913i	1.33411	+	0.969287i
$362$	−100.275	+	46.4785i	−0.277004	+	0.128394i
$363$	−24.2131	−	88.5618i	−0.0667027	−	0.243972i
$364$	428.777	+	363.164i	1.17796	+	0.997703i
$365$	96.5148	−	30.5747i	0.264424	−	0.0837664i
$366$	−2.87056	−	2.25339i	−0.00784306	−	0.00615680i
$367$	7.96681	+	4.05929i	0.0217079	+	0.0110607i	0.464811	−	0.885410i	$-0.346122\pi$
$367$	7.96681	+	4.05929i	0.0217079	+	0.0110607i	−0.443103	+	0.896471i	$0.646122\pi$
$368$	−1.88416	−	228.512i	−0.00512001	−	0.620957i
$369$	−505.770	+	367.464i	−1.37065	+	0.995837i
$370$	−98.9883	+	11.1832i	−0.267536	+	0.0302249i
$371$	35.7396	−	109.995i	0.0963330	−	0.296483i
$372$	−26.1838	+	43.1262i	−0.0703866	+	0.115931i
$373$	−177.519	−	177.519i	−0.475923	−	0.475923i	0.427902	−	0.903825i	$-0.359253\pi$
$373$	−177.519	−	177.519i	−0.475923	−	0.475923i	−0.903825	+	0.427902i	$0.859253\pi$
$374$	−12.9352	−	37.5374i	−0.0345861	−	0.100367i
$375$	−31.2972	+	89.5348i	−0.0834593	+	0.238759i
$376$	34.8512	−	310.917i	0.0926895	−	0.826907i
$377$	591.893	−	301.584i	1.57001	−	0.799959i
$378$	143.639	+	154.747i	0.379998	+	0.409384i
$379$	197.872	−	143.762i	0.522089	−	0.379320i	−0.295301	−	0.955404i	$-0.595420\pi$
$379$	197.872	−	143.762i	0.522089	−	0.379320i	0.817390	+	0.576084i	$0.195420\pi$
$380$	−46.5215	−	616.732i	−0.122425	−	1.62298i
$381$	−121.308	+	39.4152i	−0.318393	+	0.103452i
$382$	−255.427	+	30.7658i	−0.668656	+	0.0805386i
$383$	−106.222	−	670.661i	−0.277343	−	1.75107i	−0.595798	−	0.803135i	$-0.703164\pi$
$383$	−106.222	−	670.661i	−0.277343	−	1.75107i	0.318455	−	0.947938i	$-0.396836\pi$
$384$	−61.2228	−	75.3972i	−0.159434	−	0.196347i
$385$	240.964	−	367.156i	0.625880	−	0.953651i
$386$	579.722	+	212.514i	1.50187	+	0.550555i
$387$	−3.58892	−	22.6596i	−0.00927370	−	0.0585519i
$388$	9.17968	−	38.9427i	0.0236590	−	0.100368i
$389$	−648.297	+	210.645i	−1.66657	+	0.541503i	−0.982234	−	0.187661i	$-0.939909\pi$
$389$	−648.297	+	210.645i	−1.66657	+	0.541503i	−0.684340	+	0.729163i	$0.739909\pi$
$390$	−46.8680	+	124.993i	−0.120174	+	0.320495i
$391$	−20.8530	+	15.1506i	−0.0533326	+	0.0387484i
$392$	5.36446	+	117.939i	0.0136848	+	0.300864i
$393$	−111.971	+	57.0522i	−0.284914	+	0.145171i
$394$	−185.306	+	124.371i	−0.470321	+	0.315663i
$395$	230.012	−	34.6939i	0.582308	−	0.0878327i
$396$	121.400	−	350.223i	0.306566	−	0.884402i
$397$	−418.619	−	418.619i	−1.05446	−	1.05446i	−0.998429	−	0.0560277i	$-0.982156\pi$
$397$	−418.619	−	418.619i	−1.05446	−	1.05446i	−0.0560277	−	0.998429i	$-0.517844\pi$
$398$	−285.272	−	56.1331i	−0.716764	−	0.141038i
$399$	57.8977	−	178.191i	0.145107	−	0.446594i
$400$	−284.675	+	280.998i	−0.711688	+	0.702495i
$401$	−485.852	+	352.992i	−1.21160	+	0.880280i	−0.995375	−	0.0960629i	$-0.969375\pi$
$401$	−485.852	+	352.992i	−1.21160	+	0.880280i	−0.216227	+	0.976343i	$0.569375\pi$
$402$	−55.5548	+	99.6816i	−0.138196	+	0.247964i
$403$	260.571	+	132.768i	0.646579	+	0.329448i
$404$	−326.826	+	202.137i	−0.808975	+	0.500340i
$405$	151.489	−	291.972i	0.374046	−	0.720918i
$406$	566.163	+	207.544i	1.39449	+	0.511191i
$407$	23.0552	+	107.127i	0.0566467	+	0.263211i
$408$	−2.90837	+	10.5619i	−0.00712835	+	0.0258869i
$409$	−58.5866	−	42.5657i	−0.143244	−	0.104073i	0.513856	−	0.857877i	$-0.328217\pi$
$409$	−58.5866	−	42.5657i	−0.143244	−	0.104073i	−0.657099	+	0.753804i	$0.728217\pi$
$410$	−197.640	−	715.301i	−0.482049	−	1.74464i
$411$	−82.9982	+	26.9677i	−0.201942	+	0.0656150i
$412$	92.1000	−	79.3198i	0.223544	−	0.192524i
$413$	−222.873	−	35.2996i	−0.539644	−	0.0854712i
$414$	−240.472	−	8.95178i	−0.580851	−	0.0216227i
$415$	−589.349	+	421.584i	−1.42012	+	1.01586i
$416$	−409.443	+	386.387i	−0.984238	+	0.928814i
$417$	109.659	−	109.659i	0.262971	−	0.262971i
$418$	−669.969	+	118.299i	−1.60280	+	0.283011i
$419$	540.520			1.29002			0.645012	−	0.764172i	$-0.276852\pi$
$419$	540.520			1.29002			0.645012	+	0.764172i	$0.276852\pi$
$420$	−112.101	+	46.0073i	−0.266906	+	0.109541i
$421$	4.20919	−	12.9546i	0.00999808	−	0.0307709i	−0.945933	−	0.324362i	$-0.894850\pi$
$421$	4.20919	−	12.9546i	0.00999808	−	0.0307709i	0.955931	+	0.293591i	$0.0948504\pi$
$422$	−187.738	−	202.256i	−0.444876	−	0.479278i
$423$	−325.400	−	51.5383i	−0.769267	−	0.121840i
$424$	105.529	+	47.8607i	0.248890	+	0.112879i
$425$	44.4533	+	7.71427i	0.104596	+	0.0181512i
$426$	−98.5693	−	77.3768i	−0.231383	−	0.181636i
$427$	−18.9653	+	3.00380i	−0.0444152	+	0.00703467i
$428$	643.512	−	53.3157i	1.50353	−	0.124569i
$429$	141.933	+	37.6445i	0.330845	+	0.0877494i
$430$	26.6814	+	5.45475i	0.0620498	+	0.0126855i
$431$	−108.092	−	78.5333i	−0.250793	−	0.182212i	0.455285	−	0.890346i	$-0.349537\pi$
$431$	−108.092	−	78.5333i	−0.250793	−	0.182212i	−0.706078	+	0.708134i	$0.749537\pi$
$432$	−170.107	+	125.746i	−0.393766	+	0.291078i
$433$	−103.112	−	52.5382i	−0.238134	−	0.121335i	0.330852	−	0.943683i	$-0.392664\pi$
$433$	−103.112	−	52.5382i	−0.238134	−	0.121335i	−0.568986	+	0.822347i	$0.692664\pi$
$434$	72.5839	+	255.347i	0.167244	+	0.588358i
$435$	−1.05618	+	143.251i	−0.00242799	+	0.329313i
$436$	−583.161	−	238.741i	−1.33753	−	0.547572i
$437$	200.516	+	393.535i	0.458847	+	0.900539i
$438$	−5.93261	+	30.1499i	−0.0135448	+	0.0688354i
$439$		−	18.3830i		−	0.0418747i	−0.999781	−	0.0209374i	$-0.993335\pi$
$439$		−	18.3830i		−	0.0418747i	0.999781	−	0.0209374i	$-0.00666505\pi$
$440$	338.670	+	280.896i	0.769706	+	0.638399i
$441$	124.322			0.281909
$442$	62.3054	+	12.2599i	0.140962	+	0.0277372i
$443$	478.256	−	243.684i	1.07958	−	0.550076i	0.178598	−	0.983922i	$-0.442844\pi$
$443$	478.256	−	243.684i	1.07958	−	0.550076i	0.900987	+	0.433846i	$0.142844\pi$
$444$	11.4552	−	27.9811i	0.0258001	−	0.0630205i
$445$	19.9922	−	19.6996i	0.0449263	−	0.0442687i
$446$	167.567	−	47.6319i	0.375711	−	0.106798i
$447$	54.9028	−	107.753i	0.122825	−	0.241058i
$448$	−509.911	−	33.7912i	−1.13819	−	0.0754268i
$449$	514.918	−	708.724i	1.14681	−	1.57845i	0.395551	−	0.918444i	$-0.370554\pi$
$449$	514.918	−	708.724i	1.14681	−	1.57845i	0.751260	−	0.660006i	$-0.229446\pi$
$450$	281.973	+	312.908i	0.626607	+	0.695351i
$451$	−761.348	+	294.476i	−1.68813	+	0.652940i
$452$	53.5102	+	645.859i	0.118385	+	1.42889i
$453$	31.6110	+	199.584i	0.0697814	+	0.440583i
$454$	−335.384	+	427.240i	−0.738730	+	0.941058i
$455$	314.252	+	628.161i	0.690664	+	1.38057i
$456$	170.956	+	77.5338i	0.374904	+	0.170030i
$457$	−83.1112	+	524.743i	−0.181863	+	1.14823i	0.712759	+	0.701409i	$0.247446\pi$
$457$	−83.1112	+	524.743i	−0.181863	+	1.14823i	−0.894621	+	0.446825i	$0.852554\pi$
$458$	58.6038	−	54.3973i	0.127956	−	0.118771i
$459$	22.6925	+	7.37324i	0.0494390	+	0.0160637i
$460$	110.171	−	263.550i	0.239502	−	0.572934i
$461$			660.717i			1.43322i	0.697472	+	0.716612i	$0.254308\pi$
$461$			660.717i			1.43322i	−0.697472	+	0.716612i	$0.745692\pi$
$462$	62.6048	+	117.675i	0.135508	+	0.254707i
$463$	66.4704	+	66.4704i	0.143564	+	0.143564i	0.775236	−	0.631672i	$-0.217631\pi$
$463$	66.4704	+	66.4704i	0.143564	+	0.143564i	−0.631672	+	0.775236i	$0.717631\pi$
$464$	−269.831	+	540.545i	−0.581532	+	1.16497i
$465$	−51.2931	+	36.6919i	−0.110308	+	0.0789073i
$466$	−10.1940	+	273.844i	−0.0218756	+	0.587647i
$467$	80.4077	−	507.674i	0.172179	−	1.08710i	−0.738582	−	0.674164i	$-0.764504\pi$
$467$	80.4077	−	507.674i	0.172179	−	1.08710i	0.910761	−	0.412933i	$-0.135496\pi$
$468$	386.866	+	449.199i	0.826637	+	0.959827i
$469$	185.548	+	571.057i	0.395624	+	1.21760i
$470$	192.900	−	340.196i	0.410425	−	0.723821i
$471$	−10.0574	+	13.8428i	−0.0213532	+	0.0293901i
$472$	60.0204	−	217.967i	0.127162	−	0.461794i
$473$	3.05561	−	29.8004i	0.00646006	−	0.0630029i
$474$	−24.2995	+	66.2873i	−0.0512649	+	0.139847i
$475$	249.718	−	731.664i	0.525723	−	1.54035i
$476$	30.3198	+	49.0226i	0.0636971	+	0.102989i
$477$	55.3961	−	108.721i	0.116134	−	0.227927i
$478$	−79.6111	−	44.3691i	−0.166551	−	0.0928223i
$479$	83.5926	+	115.055i	0.174515	+	0.240199i	0.887310	−	0.461173i	$-0.152571\pi$
$479$	83.5926	+	115.055i	0.174515	+	0.240199i	−0.712795	+	0.701372i	$0.752571\pi$
$480$	−33.2967	−	116.749i	−0.0693682	−	0.243227i
$481$	−166.679	−	54.1573i	−0.346526	−	0.112593i
$482$	17.8133	−	90.5285i	0.0369571	−	0.187818i
$483$	61.1885	−	61.1885i	0.126684	−	0.126684i
$484$	270.458	−	401.383i	0.558797	−	0.829305i
$485$	29.6941	−	40.2431i	0.0612249	−	0.0829755i
$486$	188.258	+	280.495i	0.387363	+	0.577151i
$487$	−128.182	−	251.571i	−0.263207	−	0.516573i	0.721145	−	0.692784i	$-0.243616\pi$
$487$	−128.182	−	251.571i	−0.263207	−	0.516573i	−0.984352	+	0.176211i	$0.943616\pi$
$488$	−0.874145	−	19.2183i	−0.00179128	−	0.0393817i
$489$	5.88193	+	8.09578i	0.0120285	+	0.0165558i
$490$	−51.8132	+	138.181i	−0.105741	+	0.282002i
$491$	−11.5819	−	35.6453i	−0.0235883	−	0.0725974i	0.938569	−	0.345091i	$-0.112152\pi$
$491$	−11.5819	−	35.6453i	−0.0235883	−	0.0725974i	−0.962158	+	0.272493i	$0.912152\pi$
$492$	219.228	+	51.6771i	0.445585	+	0.105035i
$493$	67.3057	−	10.6602i	0.136523	−	0.0216231i
$494$	374.502	−	1021.61i	0.758102	−	2.06804i
$495$	311.691	−	342.822i	0.629679	−	0.692570i
$496$	−262.341	+	43.7710i	−0.528913	+	0.0882479i
$497$	−651.229	+	103.145i	−1.31032	+	0.207534i
$498$	−26.3000	−	218.350i	−0.0528111	−	0.438454i
$499$	81.6809	+	251.388i	0.163689	+	0.503784i	0.998937	−	0.0460896i	$-0.0146760\pi$
$499$	81.6809	+	251.388i	0.163689	+	0.503784i	−0.835248	+	0.549873i	$0.814676\pi$
$500$	−465.308	+	182.998i	−0.930616	+	0.365996i
$501$	104.189	+	143.403i	0.207961	+	0.286234i
$502$	−480.853	+	446.337i	−0.957874	+	0.889118i
$503$	252.204	+	494.978i	0.501399	+	0.984052i	0.993534	+	0.113533i	$0.0362167\pi$
$503$	252.204	+	494.978i	0.501399	+	0.984052i	−0.492135	+	0.870519i	$0.663783\pi$
$504$	−59.9446	+	534.781i	−0.118938	+	1.06107i
$505$	−474.983	+	71.6442i	−0.940560	+	0.141870i
$506$	−300.507	−	91.7958i	−0.593888	−	0.181415i
$507$	−75.3887	+	75.3887i	−0.148696	+	0.148696i
$508$	−574.758	−	348.961i	−1.13141	−	0.686931i
$509$	758.576	+	246.476i	1.49033	+	0.484236i	0.937180	−	0.348847i	$-0.113427\pi$
$509$	758.576	+	246.476i	1.49033	+	0.484236i	0.553147	+	0.833084i	$0.313427\pi$
$510$	−8.53470	+	10.7087i	−0.0167347	+	0.0209975i
$511$	95.0331	+	130.802i	0.185975	+	0.255972i
$512$	90.5537	−	503.929i	0.176863	−	0.984236i
$513$	185.615	−	364.291i	0.361823	−	0.710119i
$514$	367.775	−	468.503i	0.715515	−	0.911485i
$515$	144.842	−	45.8841i	0.281246	−	0.0890953i
$516$	−5.34212	+	6.30729i	−0.0103530	+	0.0122234i
$517$	−393.440	−	173.974i	−0.761005	−	0.336507i
$518$	−66.9008	−	144.336i	−0.129152	−	0.278641i
$519$	−9.59300	+	13.2036i	−0.0184836	+	0.0254405i
$520$	−660.509	+	242.783i	−1.27021	+	0.466890i
$521$	−154.319	−	474.944i	−0.296197	−	0.911601i	−0.982817	−	0.184584i	$-0.940906\pi$
$521$	−154.319	−	474.944i	−0.296197	−	0.911601i	0.686619	−	0.727017i	$-0.259094\pi$
$522$	555.712	+	309.711i	1.06458	+	0.593316i
$523$	−27.1497	+	171.416i	−0.0519114	+	0.327756i	0.948042	+	0.318144i	$0.103060\pi$
$523$	−27.1497	+	171.416i	−0.0519114	+	0.327756i	−0.999954	+	0.00961166i	$0.996940\pi$
$524$	−613.089	−	250.994i	−1.17002	−	0.478996i
$525$	−151.451	−	2.23340i	−0.288479	−	0.00425409i
$526$	130.281	−	87.4402i	0.247683	−	0.166236i
$527$	21.2129	+	21.2129i	0.0402522	+	0.0402522i
$528$	−124.151	+	49.2001i	−0.235135	+	0.0931821i
$529$		−	325.010i		−	0.614386i
$530$	97.7540	+	106.883i	0.184441	+	0.201666i
$531$	−226.417	−	73.5674i	−0.426398	−	0.138545i
$532$	910.949	−	381.735i	1.71231	−	0.717546i
$533$	204.237	−	1289.50i	0.383183	−	2.41932i
$534$	2.32921	+	8.19405i	0.00436181	+	0.0153447i
$535$	765.781	+	255.075i	1.43137	+	0.476775i
$536$	−589.289	+	121.010i	−1.09942	+	0.225765i
$537$	−40.9388	−	258.477i	−0.0762361	−	0.481336i
$538$	217.885	+	470.078i	0.404991	+	0.873752i
$539$	156.908	+	41.6164i	0.291110	+	0.0772105i
$540$	−257.316	+	60.8922i	−0.476511	+	0.112763i
$541$	410.296	−	564.723i	0.758402	−	1.04385i	−0.238943	−	0.971034i	$-0.576801\pi$
$541$	410.296	−	564.723i	0.758402	−	1.04385i	0.997345	−	0.0728175i	$-0.0231991\pi$
$542$	−69.8501	−	579.917i	−0.128875	−	1.06996i
$543$	19.0364	−	37.3611i	0.0350579	−	0.0688050i
$544$	−52.1939	+	24.7171i	−0.0959447	+	0.0454359i
$545$	−552.847	−	561.060i	−1.01440	−	1.02947i
$546$	−213.033	−	7.93033i	−0.390170	−	0.0145244i
$547$	588.929	−	300.074i	1.07665	−	0.548582i	0.176564	−	0.984289i	$-0.443502\pi$
$547$	588.929	−	300.074i	1.07665	−	0.548582i	0.900088	+	0.435708i	$0.143502\pi$
$548$	−393.247	−	238.758i	−0.717605	−	0.435690i
$549$	−20.2584			−0.0369005
$550$	251.138	+	489.316i	0.456614	+	0.889665i
$551$		−	1167.68i		−	2.11920i
$552$	54.0942	+	67.7522i	0.0979967	+	0.122739i
$553$	168.647	+	330.988i	0.304967	+	0.598531i
$554$	−293.050	−	10.9090i	−0.528971	−	0.0196914i
$555$	26.9207	−	26.5266i	0.0485057	−	0.0477957i
$556$	815.267	+	60.7822i	1.46631	+	0.109320i
$557$	−23.0631	−	11.7512i	−0.0414059	−	0.0210974i	0.433165	−	0.901315i	$-0.357397\pi$
$557$	−23.0631	−	11.7512i	−0.0414059	−	0.0210974i	−0.474571	+	0.880217i	$0.657397\pi$
$558$	33.4922	+	278.062i	0.0600218	+	0.498320i
$559$	38.7610	+	28.1615i	0.0693399	+	0.0503784i
$560$	−569.416	−	289.507i	−1.01681	−	0.516976i
$561$	12.6538	+	8.17183i	0.0225558	+	0.0145665i
$562$	−7.14241	−	15.4095i	−0.0127089	−	0.0274190i
$563$	568.005	−	89.9632i	1.00889	−	0.159793i	0.369952	−	0.929051i	$-0.379374\pi$
$563$	568.005	−	89.9632i	1.00889	−	0.159793i	0.638938	+	0.769258i	$0.279374\pi$
$564$	62.4358	+	100.949i	0.110702	+	0.178988i
$565$	−256.005	+	768.575i	−0.453106	+	1.36031i
$566$	50.6122	+	178.052i	0.0894209	+	0.314579i
$567$	518.826	+	82.1740i	0.915038	+	0.144928i
$568$	−30.0164	−	659.917i	−0.0528457	−	1.16183i
$569$	−58.4701	+	179.953i	−0.102759	+	0.316261i	−0.989198	−	0.146585i	$-0.953172\pi$
$569$	−58.4701	+	179.953i	−0.102759	+	0.316261i	0.886439	+	0.462846i	$0.153172\pi$
$570$	158.360	+	173.149i	0.277825	+	0.303771i
$571$	668.647			1.17101			0.585505	−	0.810669i	$-0.300896\pi$
$571$	668.647			1.17101			0.585505	+	0.810669i	$0.300896\pi$
$572$	337.901	+	696.444i	0.590737	+	1.21756i
$573$	69.0182	−	69.0182i	0.120451	−	0.120451i
$574$	984.027	−	660.444i	1.71433	−	1.15060i
$575$	256.177	−	248.731i	0.445525	−	0.432576i
$576$	−525.772	−	119.369i	−0.912799	−	0.207238i
$577$	217.368	+	34.4277i	0.376721	+	0.0596668i	0.341924	−	0.939728i	$-0.388921\pi$
$577$	217.368	+	34.4277i	0.376721	+	0.0596668i	0.0347972	+	0.999394i	$0.488921\pi$
$578$	−499.194	−	278.212i	−0.863657	−	0.481335i
$579$	−222.787	+	72.3879i	−0.384779	+	0.125022i
$580$	−575.840	+	488.586i	−0.992828	+	0.842390i
$581$	−936.182	−	680.176i	−1.61133	−	1.17070i
$582$	6.38338	+	13.7719i	0.0109680	+	0.0236630i
$583$	106.310	−	118.675i	0.182351	−	0.203559i
$584$	−140.841	+	80.0228i	−0.241166	+	0.137025i
$585$	223.790	+	706.436i	0.382547	+	1.20758i
$586$	639.821	−	815.059i	1.09184	−	1.39089i
$587$	−50.1379	−	25.5466i	−0.0854138	−	0.0435205i	0.410762	−	0.911743i	$-0.365263\pi$
$587$	−50.1379	−	25.5466i	−0.0854138	−	0.0435205i	−0.496176	+	0.868222i	$0.665263\pi$
$588$	−29.2295	−	33.9391i	−0.0497101	−	0.0577195i
$589$	415.877	−	302.152i	0.706073	−	0.512992i
$590$	176.132	−	220.998i	0.298529	−	0.374572i
$591$	26.1644	−	80.5257i	0.0442714	−	0.136253i
$592$	151.176	−	50.5020i	0.255366	−	0.0853075i
$593$	70.5152	+	70.5152i	0.118913	+	0.118913i	0.764059	−	0.645146i	$-0.223204\pi$
$593$	70.5152	+	70.5152i	0.118913	+	0.118913i	−0.645146	+	0.764059i	$0.723204\pi$
$594$	94.7621	+	274.996i	0.159532	+	0.462956i
$595$	10.7464	+	71.2456i	0.0180611	+	0.119741i
$596$	619.286	−	151.380i	1.03907	−	0.253994i
$597$	98.2819	−	50.0771i	0.164626	−	0.0838813i
$598$	368.323	−	341.885i	0.615925	−	0.571715i
$599$	7.99488	−	5.80862i	0.0133470	−	0.00969719i	−0.581092	−	0.813838i	$-0.697374\pi$
$599$	7.99488	−	5.80862i	0.0133470	−	0.00969719i	0.594439	+	0.804141i	$0.297374\pi$
$600$	19.1266	−	150.545i	0.0318776	−	0.250909i
$601$	−318.990	+	103.646i	−0.530765	+	0.172456i	−0.562125	−	0.827052i	$-0.690016\pi$
$601$	−318.990	+	103.646i	−0.530765	+	0.172456i	0.0313600	+	0.999508i	$0.490016\pi$
$602$	5.20079	+	43.1786i	0.00863919	+	0.0717252i
$603$	99.0994	+	625.689i	0.164344	+	1.03763i
$604$	−688.479	+	812.867i	−1.13987	+	1.34581i
$605$	508.149	−	328.343i	0.839916	−	0.542716i
$606$	50.1795	−	136.886i	0.0828044	−	0.225884i
$607$	−111.473	−	703.812i	−0.183646	−	1.15949i	−0.891462	−	0.453096i	$-0.850320\pi$
$607$	−111.473	−	703.812i	−0.183646	−	1.15949i	0.707816	−	0.706397i	$-0.249680\pi$
$608$	278.412	+	949.602i	0.457915	+	1.56185i
$609$	−217.576	+	70.6948i	−0.357268	+	0.116083i
$610$	8.44303	−	22.5168i	0.0138410	−	0.0369128i
$611$	556.622	−	404.410i	0.911002	−	0.661882i
$612$	23.5037	+	56.0878i	0.0384047	+	0.0916467i
$613$	125.605	−	63.9988i	0.204902	−	0.104403i	−0.348528	−	0.937298i	$-0.613319\pi$
$613$	125.605	−	63.9988i	0.204902	−	0.104403i	0.553430	+	0.832896i	$0.313319\pi$
$614$	−269.018	−	400.823i	−0.438140	−	0.652806i
$615$	226.549	+	167.163i	0.368372	+	0.271810i
$616$	−254.674	+	654.889i	−0.413432	+	1.06313i
$617$	−837.199	−	837.199i	−1.35689	−	1.35689i	−0.877729	−	0.479157i	$-0.840942\pi$
$617$	−837.199	−	837.199i	−1.35689	−	1.35689i	−0.479157	−	0.877729i	$-0.659058\pi$
$618$	−8.90318	+	45.2465i	−0.0144064	+	0.0732144i
$619$	−218.469	+	672.380i	−0.352939	+	1.08624i	0.604255	+	0.796791i	$0.293471\pi$
$619$	−218.469	+	672.380i	−0.352939	+	1.08624i	−0.957195	+	0.289445i	$0.906529\pi$
$620$	−323.019	−	78.6614i	−0.520999	−	0.126873i
$621$	152.767	−	110.992i	0.246002	−	0.178731i
$622$	519.194	+	289.358i	0.834717	+	0.465206i
$623$	39.9369	+	20.3489i	0.0641041	+	0.0326627i
$624$	31.6717	−	211.224i	0.0507559	−	0.338500i
$625$	−624.728	−	18.4293i	−0.999565	−	0.0294868i
$626$	196.758	−	536.742i	0.314311	−	0.857415i
$627$	172.222	−	192.252i	0.274676	−	0.306622i
$628$	−89.8928	+	7.44773i	−0.143141	+	0.0118594i
$629$	−14.5446	−	10.5673i	−0.0231234	−	0.0168001i
$630$	−331.790	+	585.142i	−0.526651	+	0.928796i
$631$	−373.554	+	121.375i	−0.592003	+	0.192353i	−0.589671	−	0.807644i	$-0.700742\pi$
$631$	−373.554	+	121.375i	−0.592003	+	0.192353i	−0.00233239	+	0.999997i	$0.500742\pi$
$632$	−348.374	+	130.975i	−0.551225	+	0.207239i
$633$	103.406	+	16.3780i	0.163359	+	0.0258735i
$634$	25.6747	−	689.703i	0.0404964	−	1.08786i
$635$	−489.006	−	683.602i	−0.770088	−	1.07654i
$636$	−42.7044	+	10.4388i	−0.0671454	+	0.0164132i
$637$	−183.585	+	183.585i	−0.288203	+	0.288203i
$638$	597.698	+	576.914i	0.936831	+	0.904255i
$639$	−695.632			−1.08863
$640$	351.801	−	534.636i	0.549689	−	0.835369i
$641$	−114.059	+	351.038i	−0.177939	+	0.547641i	−0.999756	−	0.0221119i	$-0.992961\pi$
$641$	−114.059	+	351.038i	−0.177939	+	0.547641i	0.821816	+	0.569753i	$0.192961\pi$
$642$	−179.549	+	166.661i	−0.279672	+	0.259597i
$643$	−248.142	−	39.3018i	−0.385913	−	0.0611226i	−0.0395362	−	0.999218i	$-0.512588\pi$
$643$	−248.142	−	39.3018i	−0.385913	−	0.0611226i	−0.346377	+	0.938096i	$0.612588\pi$
$644$	454.911	+	33.9159i	0.706384	+	0.0526644i
$645$	−9.24022	+	4.62263i	−0.0143259	+	0.00716687i
$646$	68.9214	−	87.7981i	0.106690	−	0.135910i
$647$	−675.080	+	106.922i	−1.04340	+	0.165258i	−0.654531	−	0.756035i	$-0.727134\pi$
$647$	−675.080	+	106.922i	−1.04340	+	0.165258i	−0.388869	+	0.921293i	$0.627134\pi$
$648$	−139.722	+	507.406i	−0.215620	+	0.783033i
$649$	−261.138	−	168.643i	−0.402370	−	0.259851i
$650$	−878.458	−	45.6807i	−1.35147	−	0.0702779i
$651$	−81.4791	−	59.1981i	−0.125160	−	0.0909340i
$652$	−12.1034	+	51.3457i	−0.0185634	+	0.0787511i
$653$	−167.996	−	85.5984i	−0.257269	−	0.131085i	0.320600	−	0.947215i	$-0.396115\pi$
$653$	−167.996	−	85.5984i	−0.257269	−	0.131085i	−0.577869	+	0.816130i	$0.696115\pi$
$654$	229.957	−	65.3667i	0.351617	−	0.0999491i
$655$	−581.220	−	589.854i	−0.887359	−	0.900541i
$656$	547.757	+	1053.47i	0.834995	+	1.60590i
$657$	77.4406	+	151.986i	0.117870	+	0.231333i
$658$	612.792	+	120.579i	0.931294	+	0.183251i
$659$			943.001i			1.43096i	0.698635	+	0.715479i	$0.253791\pi$
$659$			943.001i			1.43096i	−0.698635	+	0.715479i	$0.746209\pi$
$660$	−166.871	−	4.48811i	−0.252834	−	0.00680017i
$661$	788.731			1.19324			0.596619	−	0.802524i	$-0.296510\pi$
$661$	788.731			1.19324			0.596619	+	0.802524i	$0.296510\pi$
$662$	6.13975	−	31.2026i	0.00927455	−	0.0471339i
$663$	−21.4654	+	10.9372i	−0.0323762	+	0.0164965i
$664$	781.710	−	856.211i	1.17727	−	1.28947i
$665$	1234.59	+	9.10253i	1.85653	+	0.0136880i
$666$	−45.8919	−	161.446i	−0.0689067	−	0.242411i
$667$	244.836	−	480.519i	0.367071	−	0.720418i
$668$	−214.391	+	909.503i	−0.320944	+	1.36153i
$669$	−38.8476	+	53.4692i	−0.0580682	+	0.0799240i
$670$	−736.742	−	150.620i	−1.09962	−	0.224805i
$671$	−25.5684	−	6.78145i	−0.0381049	−	0.0101065i
$672$	160.086	−	109.369i	0.238223	−	0.162751i
$673$	60.8690	+	384.311i	0.0904442	+	0.571042i	0.990741	+	0.135766i	$0.0433494\pi$
$673$	60.8690	+	384.311i	0.0904442	+	0.571042i	−0.900297	+	0.435277i	$0.856651\pi$
$674$	−980.101	−	769.379i	−1.45416	−	1.14151i
$675$	−325.661	−	56.5141i	−0.482461	−	0.0837245i
$676$	−560.484	−	41.7869i	−0.829119	−	0.0618149i
$677$	−141.049	+	890.546i	−0.208344	+	1.31543i	0.632672	+	0.774420i	$0.281958\pi$
$677$	−141.049	+	890.546i	−0.208344	+	1.31543i	−0.841016	+	0.541010i	$0.818042\pi$
$678$	−167.269	−	180.204i	−0.246710	−	0.265788i
$679$	75.9592	+	24.6806i	0.111869	+	0.0363485i
$680$	−72.1360	+	2.74834i	−0.106082	+	0.00404168i
$681$		−	206.067i		−	0.302594i
$682$	−50.8098	+	362.158i	−0.0745012	+	0.531024i
$683$	165.942	+	165.942i	0.242960	+	0.242960i	0.818074	−	0.575113i	$-0.195042\pi$
$683$	165.942	+	165.942i	0.242960	+	0.242960i	−0.575113	+	0.818074i	$0.695042\pi$
$684$	1012.25	−	247.438i	1.47990	−	0.361751i
$685$	−334.576	−	467.718i	−0.488432	−	0.682800i
$686$	546.461	+	20.3425i	0.796591	+	0.0296537i
$687$	−4.74553	+	29.9621i	−0.00690762	+	0.0436130i
$688$	−43.5718	+	0.359264i	−0.0633311	+	0.000522187i
$689$	78.7446	+	242.351i	0.114288	+	0.351743i
$690$	28.8622	+	104.458i	0.0418293	+	0.151389i
$691$	−745.651	+	1026.30i	−1.07909	+	1.48524i	−0.218569	+	0.975821i	$0.570139\pi$
$691$	−745.651	+	1026.30i	−1.07909	+	1.48524i	−0.860520	+	0.509417i	$0.829861\pi$
$692$	−85.7424	+	7.10386i	−0.123905	+	0.0102657i
$693$	676.722	+	299.238i	0.976510	+	0.431801i
$694$	575.385	+	210.924i	0.829085	+	0.303925i
$695$	907.086	+	470.639i	1.30516	+	0.677179i
$696$	−46.1055	−	224.523i	−0.0662436	−	0.322590i
$697$	60.8020	−	119.331i	0.0872339	−	0.171206i
$698$	−339.578	+	609.303i	−0.486502	+	0.872927i
$699$	−61.1092	−	84.1096i	−0.0874237	−	0.120328i
$700$	−512.094	−	612.646i	−0.731563	−	0.875209i
$701$	745.778	+	242.318i	1.06388	+	0.345675i	0.788100	−	0.615547i	$-0.211065\pi$
$701$	745.778	+	242.318i	1.06388	+	0.345675i	0.275777	+	0.961222i	$0.411065\pi$
$702$	−456.444	−	89.8146i	−0.650204	−	0.127941i
$703$	−217.832	+	217.832i	−0.309860	+	0.309860i
$704$	−623.626	−	326.659i	−0.885833	−	0.464004i
$705$	22.1293	+	146.712i	0.0313891	+	0.208102i
$706$	18.6706	−	12.5310i	0.0264456	−	0.0177494i
$707$	−348.262	−	683.502i	−0.492591	−	0.966764i
$708$	33.1499	+	79.1070i	0.0468220	+	0.111733i
$709$	−9.63426	−	13.2604i	−0.0135885	−	0.0187030i	0.802169	−	0.597097i	$-0.203679\pi$
$709$	−9.63426	−	13.2604i	−0.0135885	−	0.0187030i	−0.815757	+	0.578394i	$0.803679\pi$
$710$	289.917	−	773.181i	0.408333	−	1.08899i
$711$	121.110	+	372.737i	0.170337	+	0.524244i
$712$	−24.7178	+	37.4926i	−0.0347160	+	0.0526582i
$713$	234.495	−	37.1403i	0.328884	−	0.0520902i
$714$	−20.5323	−	7.52673i	−0.0287568	−	0.0105416i
$715$	45.9712	+	966.517i	0.0642954	+	1.35177i
$716$	891.635	−	1052.73i	1.24530	−	1.47029i
$717$	34.1519	−	5.40913i	0.0476316	−	0.00754411i
$718$	583.331	−	70.2613i	0.812438	−	0.0978569i
$719$	92.3775	+	284.309i	0.128481	+	0.395422i	0.994519	−	0.104555i	$-0.0333417\pi$
$719$	92.3775	+	284.309i	0.128481	+	0.395422i	−0.866039	+	0.499977i	$0.833342\pi$
$720$	−545.575	−	395.657i	−0.757743	−	0.549523i
$721$	142.618	+	196.297i	0.197806	+	0.272256i
$722$	−809.990	−	872.627i	−1.12187	−	1.20862i
$723$	15.8915	+	31.1889i	0.0219800	+	0.0431381i
$724$	214.725	−	52.4880i	0.296581	−	0.0724972i
$725$	−901.986	+	278.438i	−1.24412	+	0.384052i
$726$	13.3181	+	183.141i	0.0183445	+	0.252260i
$727$	−555.190	+	555.190i	−0.763673	+	0.763673i	−0.976984	−	0.213311i	$-0.931575\pi$
$727$	−555.190	+	555.190i	−0.763673	+	0.763673i	0.213311	+	0.976984i	$0.431575\pi$
$728$	−701.189	−	878.228i	−0.963171	−	1.20636i
$729$	441.209	+	143.357i	0.605225	+	0.196649i
$730$	−201.204	+	22.7311i	−0.275622	+	0.0311384i
$731$	2.88886	+	3.97617i	0.00395192	+	0.00543936i
$732$	4.76299	+	5.53041i	0.00650682	+	0.00755521i
$733$	−374.514	+	735.026i	−0.510934	+	1.00276i	0.481085	+	0.876674i	$0.340243\pi$
$733$	−374.514	+	735.026i	−0.510934	+	1.00276i	−0.992019	+	0.126090i	$0.959757\pi$
$734$	−14.0664	−	11.0421i	−0.0191640	−	0.0150437i
$735$	−16.9084	−	53.3745i	−0.0230046	−	0.0726183i
$736$	−84.5395	+	449.153i	−0.114863	+	0.610263i
$737$	−84.3733	+	822.865i	−0.114482	+	1.11651i
$738$	1134.40	−	525.804i	1.53713	−	0.712471i
$739$	−646.145	+	889.342i	−0.874350	+	1.20344i	0.103604	+	0.994619i	$0.466963\pi$
$739$	−646.145	+	889.342i	−0.874350	+	1.20344i	−0.977954	+	0.208821i	$0.933037\pi$
$740$	198.570	+	16.2774i	0.268338	+	0.0219964i
$741$	127.565	+	392.606i	0.172153	+	0.529832i
$742$	−112.607	+	202.051i	−0.151762	+	0.272306i
$743$	−36.4471	+	230.118i	−0.0490540	+	0.309715i	0.950946	+	0.309357i	$0.100114\pi$
$743$	−36.4471	+	230.118i	−0.0490540	+	0.309715i	−1.00000		0.000357556i	$0.999886\pi$
$744$	68.0349	−	74.5190i	0.0914448	−	0.100160i
$745$	786.147	+	130.462i	1.05523	+	0.175117i
$746$	279.812	+	416.906i	0.375083	+	0.558855i
$747$	−863.284	−	863.284i	−1.15567	−	1.15567i
$748$	10.8891	+	78.6570i	0.0145576	+	0.105156i
$749$			1288.99i			1.72094i
$750$	95.9894	−	163.615i	0.127986	−	0.218154i
$751$	214.087	+	69.5612i	0.285070	+	0.0926247i	0.448062	−	0.894003i	$-0.352115\pi$
$751$	214.087	+	69.5612i	0.285070	+	0.0926247i	−0.162992	+	0.986627i	$0.552115\pi$
$752$	−188.447	+	596.677i	−0.250595	+	0.793453i
$753$	38.9378	−	245.843i	0.0517102	−	0.326485i
$754$	−1277.97	+	363.269i	−1.69492	+	0.481789i
$755$	−1190.85	+	595.753i	−1.57729	+	0.789076i
$756$	−222.120	−	359.135i	−0.293810	−	0.475047i
$757$	−161.749	−	1021.25i	−0.213672	−	1.34907i	−0.828314	−	0.560264i	$-0.810700\pi$
$757$	−161.749	−	1021.25i	−0.213672	−	1.34907i	0.614643	−	0.788806i	$-0.289300\pi$
$758$	−443.810	+	205.709i	−0.585501	+	0.271385i
$759$	111.183	−	43.0036i	0.146486	−	0.0566582i
$760$	−146.850	+	1228.22i	−0.193224	+	1.61608i
$761$	144.314	−	198.631i	0.189637	−	0.261013i	−0.703603	−	0.710593i	$-0.748427\pi$
$761$	144.314	−	198.631i	0.189637	−	0.261013i	0.893240	+	0.449581i	$0.148427\pi$
$762$	253.270	−	30.5060i	0.332375	−	0.0400341i
$763$	571.069	−	1120.79i	0.748452	−	1.46892i
$764$	513.122	+	38.2557i	0.671625	+	0.0500729i
$765$	−0.560449	+	76.0146i	−0.000732613	+	0.0993655i
$766$	−50.5192	+	1357.10i	−0.0659519	+	1.77167i
$767$	442.985	−	225.712i	0.577556	−	0.294280i
$768$	91.0283	+	171.598i	0.118526	+	0.223435i
$769$	−140.854			−0.183165			−0.0915823	−	0.995798i	$-0.529192\pi$
$769$	−140.854			−0.183165			−0.0915823

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96237 - 0.386136i) q^{2} +(0.676076 - 0.344478i) q^{3} +(3.70180 + 1.51549i) q^{4} +(3.50937 + 3.56150i) q^{5} +(-1.45973 + 0.414936i) q^{6} +(-3.62504 + 7.11454i) q^{7} +(-6.67911 - 4.40334i) q^{8} +(-4.95165 + 6.81537i) q^{9} +(-5.51146 - 8.34409i) q^{10} +(-8.53099 + 6.94422i) q^{11} +(3.02475 - 0.250604i) q^{12} +(-2.75214 - 17.3763i) q^{13} +(9.86085 - 12.5616i) q^{14} +(3.59946 + 1.19895i) q^{15} +(11.4066 + 11.2200i) q^{16} +(0.282319 - 1.78249i) q^{17} +(12.3486 - 11.4623i) q^{18} +(-29.4107 - 9.55611i) q^{19} +(7.59357 + 18.5024i) q^{20} +6.05871i q^{21} +(19.4224 - 10.3330i) q^{22} +(-10.0993 - 10.0993i) q^{23} +(-6.03244 - 0.676187i) q^{24} +(-0.368626 + 24.9973i) q^{25} +(-1.30891 + 35.1614i) q^{26} +(-2.06824 + 13.0584i) q^{27} +(-24.2011 + 20.8429i) q^{28} +(11.6683 + 35.9113i) q^{29} +(-6.60052 - 3.74266i) q^{30} +(-9.77073 + 13.4483i) q^{31} +(-18.0515 - 26.4224i) q^{32} +(-3.37546 + 7.63356i) q^{33} +(-1.24230 + 3.38889i) q^{34} +(-38.0601 + 12.0570i) q^{35} +(-28.6586 + 17.7249i) q^{36} +(4.52256 - 8.87603i) q^{37} +(54.0247 + 30.1092i) q^{38} +(-7.84640 - 10.7996i) q^{39} +(-7.75696 - 39.2407i) q^{40} +(70.5782 + 22.9322i) q^{41} +(2.33949 - 11.8894i) q^{42} +(-1.92568 + 1.92568i) q^{43} +(-42.1039 + 12.7775i) q^{44} +(-41.6501 + 6.28232i) q^{45} +(15.9188 + 23.7182i) q^{46} +(17.7547 + 34.8455i) q^{47} +(11.5768 + 3.65628i) q^{48} +(-8.67429 - 11.9391i) q^{49} +(10.3757 - 48.9116i) q^{50} +(-0.423159 - 1.30235i) q^{51} +(16.1457 - 68.4943i) q^{52} +(-14.3061 + 2.26586i) q^{53} +(9.10096 - 24.8267i) q^{54} +(-54.6703 - 6.01330i) q^{55} +(55.5398 - 31.5565i) q^{56} +(-23.1757 + 3.67067i) q^{57} +(-9.03085 - 74.9769i) q^{58} +(8.73280 + 26.8768i) q^{59} +(11.5075 + 9.89319i) q^{60} +(1.41349 + 1.94550i) q^{61} +(24.3667 - 22.6176i) q^{62} +(-30.5383 - 59.9347i) q^{63} +(25.2211 + 58.8209i) q^{64} +(52.2275 - 70.7816i) q^{65} +(9.57151 - 13.6765i) q^{66} +(53.1731 - 53.1731i) q^{67} +(3.74642 - 6.17057i) q^{68} +(-10.3068 - 3.34889i) q^{69} +(79.3436 - 8.96386i) q^{70} +(48.5363 + 66.8045i) q^{71} +(63.0831 - 23.7168i) q^{72} +(9.19257 - 18.0414i) q^{73} +(-12.3023 + 15.6717i) q^{74} +(8.36179 + 17.0270i) q^{75} +(-94.3902 - 79.9462i) q^{76} +(-18.4798 - 85.8671i) q^{77} +(11.2274 + 24.2227i) q^{78} +(27.3454 - 37.6377i) q^{79} +(0.0697902 + 80.0000i) q^{80} +(-20.3291 - 62.5666i) q^{81} +(-129.646 - 72.2544i) q^{82} +(-22.6709 + 143.139i) q^{83} +(-9.18189 + 22.4281i) q^{84} +(7.33911 - 5.24994i) q^{85} +(4.52248 - 3.03533i) q^{86} +(20.2593 + 20.2593i) q^{87} +(87.5572 - 8.81638i) q^{88} -5.61342i q^{89} +(84.1589 + 3.75441i) q^{90} +(133.601 + 43.4096i) q^{91} +(-22.0801 - 52.6907i) q^{92} +(-1.97313 + 12.4578i) q^{93} +(-21.3861 - 75.2355i) q^{94} +(-69.1789 - 138.282i) q^{95} +(-21.3061 - 11.6452i) q^{96} +(-1.56473 - 9.87934i) q^{97} +(12.4120 + 26.7785i) q^{98} +(-5.08492 - 92.5272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) \) 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Introduction

L-functions

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