LMFDB - Embedded newform 130.3.r.a.23.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,3,Mod(17,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.17"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	130.r (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.54224343668$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.7
Character	$\chi$	$=$	130.23
Dual form			130.3.r.a.17.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.366025 - 1.36603i) q^{2} +(1.39661 - 5.21223i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-4.51108 + 2.15642i) q^{5} +(-6.60884 - 3.81562i) q^{6} +(2.83686 - 0.760135i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-17.4226 - 10.0589i) q^{9} +(1.29455 + 6.95156i) q^{10} +(16.9545 - 9.78866i) q^{11} +(-7.63124 + 7.63124i) q^{12} +(-10.6279 + 7.48647i) q^{13} -4.15345i q^{14} +(4.93952 + 26.5245i) q^{15} +(2.00000 + 3.46410i) q^{16} +(2.15948 + 8.05929i) q^{17} +(-20.1179 + 20.1179i) q^{18} +(5.74201 - 9.94544i) q^{19} +(9.96984 + 0.776053i) q^{20} -15.8480i q^{21} +(-7.16580 - 26.7431i) q^{22} +(1.68113 - 6.27406i) q^{23} +(7.63124 + 13.2177i) q^{24} +(15.6997 - 19.4556i) q^{25} +(6.33661 + 17.2583i) q^{26} +(-42.4216 + 42.4216i) q^{27} +(-5.67372 - 1.52027i) q^{28} +(12.7363 - 7.35328i) q^{29} +(38.0411 + 2.96112i) q^{30} -42.7672i q^{31} +(5.46410 - 1.46410i) q^{32} +(-27.3420 - 102.042i) q^{33} +11.7996 q^{34} +(-11.1581 + 9.54649i) q^{35} +(20.1179 + 34.8452i) q^{36} +(-3.93798 + 14.6967i) q^{37} +(-11.4840 - 11.4840i) q^{38} +(24.1781 + 65.8509i) q^{39} +(4.70932 - 13.3350i) q^{40} +(22.3968 - 12.9308i) q^{41} +(-21.6488 - 5.80077i) q^{42} +(10.8222 - 2.89981i) q^{43} -39.1547 q^{44} +(100.286 + 7.80628i) q^{45} +(-7.95519 - 4.59293i) q^{46} +(28.0345 + 28.0345i) q^{47} +(20.8489 - 5.58645i) q^{48} +(-34.9653 + 20.1872i) q^{49} +(-20.8303 - 28.5674i) q^{50} +45.0228 q^{51} +(25.8946 - 2.33902i) q^{52} +(71.4142 + 71.4142i) q^{53} +(42.4216 + 73.4764i) q^{54} +(-55.3745 + 80.7184i) q^{55} +(-4.15345 + 7.19399i) q^{56} +(-43.8186 - 43.8186i) q^{57} +(-5.38297 - 20.0895i) q^{58} +(44.7209 - 77.4589i) q^{59} +(17.9690 - 50.8813i) q^{60} +(-42.5801 + 73.7509i) q^{61} +(-58.4211 - 15.6539i) q^{62} +(-57.0716 - 15.2923i) q^{63} -8.00000i q^{64} +(31.7995 - 56.6903i) q^{65} -149.399 q^{66} +(-15.6648 + 58.4618i) q^{67} +(4.31896 - 16.1186i) q^{68} +(-30.3540 - 17.5249i) q^{69} +(8.95659 + 18.7366i) q^{70} +(-5.25780 - 3.03559i) q^{71} +(54.9631 - 14.7273i) q^{72} +(62.8256 - 62.8256i) q^{73} +(18.6347 + 10.7588i) q^{74} +(-79.4805 - 109.002i) q^{75} +(-19.8909 + 11.4840i) q^{76} +(40.6567 - 40.6567i) q^{77} +(98.8038 - 8.92480i) q^{78} +34.9015i q^{79} +(-16.4922 - 11.3140i) q^{80} +(71.3342 + 123.554i) q^{81} +(-9.46599 - 35.3275i) q^{82} +(-46.8941 + 46.8941i) q^{83} +(-15.8480 + 27.4495i) q^{84} +(-27.1208 - 31.6994i) q^{85} -15.8449i q^{86} +(-20.5394 - 76.6540i) q^{87} +(-14.3316 + 53.4862i) q^{88} +(71.5926 + 124.002i) q^{89} +(47.3708 - 134.136i) q^{90} +(-24.4592 + 29.3167i) q^{91} +(-9.18586 + 9.18586i) q^{92} +(-222.913 - 59.7293i) q^{93} +(48.5572 - 28.0345i) q^{94} +(-4.45610 + 57.2469i) q^{95} -30.5249i q^{96} +(-173.724 + 46.5493i) q^{97} +(14.7781 + 55.1525i) q^{98} -393.854 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 14 q^{2} + 8 q^{5} + 4 q^{7} - 56 q^{8} - 48 q^{9} - 12 q^{10} - 12 q^{11} - 24 q^{13} + 10 q^{15} + 56 q^{16} + 50 q^{17} - 92 q^{18} - 36 q^{19} + 8 q^{20} + 12 q^{22} + 68 q^{23} - 6 q^{25} + 42 q^{26}+ \cdots + 16 q^{99}+O(q^{100}) $ 28 * q - 14 * q^2 + 8 * q^5 + 4 * q^7 - 56 * q^8 - 48 * q^9 - 12 * q^10 - 12 * q^11 - 24 * q^13 + 10 * q^15 + 56 * q^16 + 50 * q^17 - 92 * q^18 - 36 * q^19 + 8 * q^20 + 12 * q^22 + 68 * q^23 - 6 * q^25 + 42 * q^26 - 24 * q^27 - 8 * q^28 + 186 * q^29 + 12 * q^30 + 56 * q^32 - 164 * q^33 - 20 * q^34 - 18 * q^35 + 92 * q^36 + 24 * q^37 + 72 * q^38 + 156 * q^39 - 20 * q^40 + 48 * q^41 - 204 * q^42 + 80 * q^43 + 26 * q^45 - 96 * q^46 + 104 * q^47 + 96 * q^49 + 18 * q^50 - 336 * q^51 - 96 * q^52 + 126 * q^53 + 24 * q^54 - 502 * q^55 - 16 * q^56 + 160 * q^57 - 130 * q^58 + 80 * q^59 + 136 * q^60 - 336 * q^61 - 108 * q^62 + 396 * q^63 + 160 * q^65 - 64 * q^66 - 32 * q^67 + 100 * q^68 + 264 * q^69 + 200 * q^70 - 60 * q^71 + 188 * q^72 - 286 * q^73 + 6 * q^74 - 684 * q^75 + 24 * q^76 + 424 * q^77 + 128 * q^78 + 40 * q^80 + 86 * q^81 + 42 * q^82 - 64 * q^83 - 96 * q^84 + 356 * q^85 + 384 * q^87 + 24 * q^88 - 348 * q^89 - 294 * q^90 + 192 * q^91 + 80 * q^92 - 336 * q^93 + 432 * q^94 - 446 * q^95 - 86 * q^97 - 82 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$3$	1.39661	−	5.21223i	0.465538	−	1.73741i	−0.189563	−	0.981869i	$-0.560707\pi$
$3$	1.39661	−	5.21223i	0.465538	−	1.73741i	0.655100	−	0.755542i	$-0.272626\pi$
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$	−4.51108	+	2.15642i	−0.902216	+	0.431284i
$5$	−4.51108	+	2.15642i	−0.902216	+	0.431284i
$6$	−6.60884	−	3.81562i	−1.10147	−	0.635936i
$7$	2.83686	−	0.760135i	0.405266	−	0.108591i	−0.0504270	−	0.998728i	$-0.516058\pi$
$7$	2.83686	−	0.760135i	0.405266	−	0.108591i	0.455693	+	0.890137i	$0.349392\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	−17.4226	−	10.0589i	−1.93584	−	1.11766i
$10$	1.29455	+	6.95156i	0.129455	+	0.695156i
$11$	16.9545	−	9.78866i	1.54131	−	0.889878i	0.542558	−	0.840018i	$-0.317456\pi$
$11$	16.9545	−	9.78866i	1.54131	−	0.889878i	0.998756	−	0.0498604i	$-0.0158777\pi$
$12$	−7.63124	+	7.63124i	−0.635936	+	0.635936i
$13$	−10.6279	+	7.48647i	−0.817533	+	0.575882i
$13$	−10.6279	+	7.48647i	−0.817533	+	0.575882i
$14$		−	4.15345i		−	0.296675i
$15$	4.93952	+	26.5245i	0.329301	+	1.76830i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	2.15948	+	8.05929i	0.127028	+	0.474076i	0.999904	−	0.0138670i	$-0.00441413\pi$
$17$	2.15948	+	8.05929i	0.127028	+	0.474076i	−0.872876	+	0.487943i	$0.837747\pi$
$18$	−20.1179	+	20.1179i	−1.11766	+	1.11766i
$19$	5.74201	−	9.94544i	0.302211	−	0.523444i	−0.674426	−	0.738343i	$-0.735609\pi$
$19$	5.74201	−	9.94544i	0.302211	−	0.523444i	0.976636	+	0.214898i	$0.0689420\pi$
$20$	9.96984	+	0.776053i	0.498492	+	0.0388027i
$21$		−	15.8480i		−	0.754666i
$22$	−7.16580	−	26.7431i	−0.325718	−	1.21560i
$23$	1.68113	−	6.27406i	0.0730926	−	0.272785i	−0.919701	−	0.392618i	$-0.871569\pi$
$23$	1.68113	−	6.27406i	0.0730926	−	0.272785i	0.992794	+	0.119833i	$0.0382360\pi$
$24$	7.63124	+	13.2177i	0.317968	+	0.550737i
$25$	15.6997	−	19.4556i	0.627988	−	0.778223i
$26$	6.33661	+	17.2583i	0.243716	+	0.663779i
$27$	−42.4216	+	42.4216i	−1.57117	+	1.57117i
$28$	−5.67372	−	1.52027i	−0.202633	−	0.0542953i
$29$	12.7363	−	7.35328i	0.439181	−	0.253561i	−0.264069	−	0.964504i	$-0.585065\pi$
$29$	12.7363	−	7.35328i	0.439181	−	0.253561i	0.703250	+	0.710942i	$0.251731\pi$
$30$	38.0411	+	2.96112i	1.26804	+	0.0987041i
$31$		−	42.7672i		−	1.37959i	−0.724006	−	0.689794i	$-0.757701\pi$
$31$		−	42.7672i		−	1.37959i	0.724006	−	0.689794i	$-0.242299\pi$
$32$	5.46410	−	1.46410i	0.170753	−	0.0457532i
$33$	−27.3420	−	102.042i	−0.828544	−	3.09217i
$34$	11.7996			0.347048
$35$	−11.1581	+	9.54649i	−0.318804	+	0.272757i
$36$	20.1179	+	34.8452i	0.558830	+	0.967922i
$37$	−3.93798	+	14.6967i	−0.106432	+	0.397209i	−0.998504	−	0.0546845i	$-0.982585\pi$
$37$	−3.93798	+	14.6967i	−0.106432	+	0.397209i	0.892072	+	0.451894i	$0.149251\pi$
$38$	−11.4840	−	11.4840i	−0.302211	−	0.302211i
$39$	24.1781	+	65.8509i	0.619951	+	1.68848i
$40$	4.70932	−	13.3350i	0.117733	−	0.333375i
$41$	22.3968	−	12.9308i	0.546263	−	0.315385i	−0.201351	−	0.979519i	$-0.564533\pi$
$41$	22.3968	−	12.9308i	0.546263	−	0.315385i	0.747613	+	0.664134i	$0.231200\pi$
$42$	−21.6488	−	5.80077i	−0.515447	−	0.138114i
$43$	10.8222	−	2.89981i	0.251680	−	0.0674375i	−0.130773	−	0.991412i	$-0.541746\pi$
$43$	10.8222	−	2.89981i	0.251680	−	0.0674375i	0.382453	+	0.923975i	$0.375079\pi$
$44$	−39.1547			−0.889878
$45$	100.286	+	7.80628i	2.22858	+	0.173473i
$46$	−7.95519	−	4.59293i	−0.172939	−	0.0998463i
$47$	28.0345	+	28.0345i	0.596479	+	0.596479i	0.939374	−	0.342895i	$-0.111407\pi$
$47$	28.0345	+	28.0345i	0.596479	+	0.596479i	−0.342895	+	0.939374i	$0.611407\pi$
$48$	20.8489	−	5.58645i	0.434353	−	0.116384i
$49$	−34.9653	+	20.1872i	−0.713577	+	0.411984i
$50$	−20.8303	−	28.5674i	−0.416606	−	0.571349i
$51$	45.0228			0.882801
$52$	25.8946	−	2.33902i	0.497973	−	0.0449811i
$53$	71.4142	+	71.4142i	1.34744	+	1.34744i	0.888434	+	0.459005i	$0.151794\pi$
$53$	71.4142	+	71.4142i	1.34744	+	1.34744i	0.459005	+	0.888434i	$0.348206\pi$
$54$	42.4216	+	73.4764i	0.785586	+	1.36067i
$55$	−55.3745	+	80.7184i	−1.00681	+	1.46761i
$56$	−4.15345	+	7.19399i	−0.0741688	+	0.128464i
$57$	−43.8186	−	43.8186i	−0.768747	−	0.768747i
$58$	−5.38297	−	20.0895i	−0.0928099	−	0.346371i
$59$	44.7209	−	77.4589i	0.757982	−	1.31286i	−0.185897	−	0.982569i	$-0.559519\pi$
$59$	44.7209	−	77.4589i	0.757982	−	1.31286i	0.943878	−	0.330294i	$-0.107148\pi$
$60$	17.9690	−	50.8813i	0.299483	−	0.848021i
$61$	−42.5801	+	73.7509i	−0.698034	+	1.20903i	0.271112	+	0.962548i	$0.412608\pi$
$61$	−42.5801	+	73.7509i	−0.698034	+	1.20903i	−0.969147	+	0.246484i	$0.920725\pi$
$62$	−58.4211	−	15.6539i	−0.942276	−	0.252482i
$63$	−57.0716	−	15.2923i	−0.905899	−	0.242735i
$64$		−	8.00000i		−	0.125000i
$65$	31.7995	−	56.6903i	0.489223	−	0.872159i
$66$	−149.399			−2.26362
$67$	−15.6648	+	58.4618i	−0.233803	+	0.872564i	0.744882	+	0.667196i	$0.232506\pi$
$67$	−15.6648	+	58.4618i	−0.233803	+	0.872564i	−0.978685	+	0.205368i	$0.934161\pi$
$68$	4.31896	−	16.1186i	0.0635141	−	0.237038i
$69$	−30.3540	−	17.5249i	−0.439913	−	0.253984i
$70$	8.95659	+	18.7366i	0.127951	+	0.267665i
$71$	−5.25780	−	3.03559i	−0.0740536	−	0.0427549i	0.462516	−	0.886611i	$-0.346947\pi$
$71$	−5.25780	−	3.03559i	−0.0740536	−	0.0427549i	−0.536570	+	0.843856i	$0.680280\pi$
$72$	54.9631	−	14.7273i	0.763376	−	0.204546i
$73$	62.8256	−	62.8256i	0.860624	−	0.860624i	−0.130786	−	0.991411i	$-0.541750\pi$
$73$	62.8256	−	62.8256i	0.860624	−	0.860624i	0.991411	+	0.130786i	$0.0417502\pi$
$74$	18.6347	+	10.7588i	0.251821	+	0.145389i
$75$	−79.4805	−	109.002i	−1.05974	−	1.45337i
$76$	−19.8909	+	11.4840i	−0.261722	+	0.151105i
$77$	40.6567	−	40.6567i	0.528010	−	0.528010i
$78$	98.8038	−	8.92480i	1.26672	−	0.114420i
$79$			34.9015i			0.441791i	0.975297	+	0.220895i	$0.0708980\pi$
$79$			34.9015i			0.441791i	−0.975297	+	0.220895i	$0.929102\pi$
$80$	−16.4922	−	11.3140i	−0.206153	−	0.141425i
$81$	71.3342	+	123.554i	0.880669	+	1.52536i
$82$	−9.46599	−	35.3275i	−0.115439	−	0.430824i
$83$	−46.8941	+	46.8941i	−0.564990	+	0.564990i	−0.930721	−	0.365731i	$-0.880819\pi$
$83$	−46.8941	+	46.8941i	−0.564990	+	0.564990i	0.365731	+	0.930721i	$0.380819\pi$
$84$	−15.8480	+	27.4495i	−0.188667	+	0.326780i
$85$	−27.1208	−	31.6994i	−0.319068	−	0.372934i
$86$		−	15.8449i		−	0.184243i
$87$	−20.5394	−	76.6540i	−0.236085	−	0.881080i
$88$	−14.3316	+	53.4862i	−0.162859	+	0.607798i
$89$	71.5926	+	124.002i	0.804411	+	1.39328i	0.916688	+	0.399603i	$0.130852\pi$
$89$	71.5926	+	124.002i	0.804411	+	1.39328i	−0.112277	+	0.993677i	$0.535815\pi$
$90$	47.3708	−	134.136i	0.526342	−	1.49040i
$91$	−24.4592	+	29.3167i	−0.268783	+	0.322162i
$92$	−9.18586	+	9.18586i	−0.0998463	+	0.0998463i
$93$	−222.913	−	59.7293i	−2.39691	−	0.642250i
$94$	48.5572	−	28.0345i	0.516566	−	0.298239i
$95$	−4.45610	+	57.2469i	−0.0469063	+	0.602599i
$96$		−	30.5249i		−	0.317968i
$97$	−173.724	+	46.5493i	−1.79097	+	0.479890i	−0.992511	−	0.122157i	$-0.961019\pi$
$97$	−173.724	+	46.5493i	−1.79097	+	0.479890i	−0.798461	+	0.602046i	$0.794352\pi$
$98$	14.7781	+	55.1525i	0.150797	+	0.562780i
$99$	−393.854			−3.97833
$100$	−46.6483	+	17.9983i	−0.466483	+	0.179983i
$101$	43.5544	+	75.4384i	0.431231	+	0.746915i	0.996980	−	0.0776634i	$-0.0247459\pi$
$101$	43.5544	+	75.4384i	0.431231	+	0.746915i	−0.565748	+	0.824578i	$0.691413\pi$
$102$	16.4795	−	61.5023i	0.161564	−	0.602964i
$103$	−32.6979	−	32.6979i	−0.317455	−	0.317455i	0.530334	−	0.847789i	$-0.322067\pi$
$103$	−32.6979	−	32.6979i	−0.317455	−	0.317455i	−0.847789	+	0.530334i	$0.822067\pi$
$104$	6.28292	−	36.2288i	0.0604127	−	0.348354i
$105$	34.1749	+	71.4916i	0.325475	+	0.680872i
$106$	123.693	−	71.4142i	1.16692	−	0.673719i
$107$	12.3595	+	3.31173i	0.115510	+	0.0309507i	0.316111	−	0.948722i	$-0.397623\pi$
$107$	12.3595	+	3.31173i	0.115510	+	0.0309507i	−0.200601	+	0.979673i	$0.564290\pi$
$108$	115.898	−	31.0548i	1.07313	−	0.287544i
$109$	41.2744			0.378664			0.189332	−	0.981913i	$-0.439368\pi$
$109$	41.2744			0.378664			0.189332	+	0.981913i	$0.439368\pi$
$110$	89.9949	+	105.188i	0.818135	+	0.956254i
$111$	71.1030	+	41.0513i	0.640567	+	0.369832i
$112$	8.30691	+	8.30691i	0.0741688	+	0.0741688i
$113$	83.3640	−	22.3373i	0.737734	−	0.197675i	0.129663	−	0.991558i	$-0.458610\pi$
$113$	83.3640	−	22.3373i	0.737734	−	0.197675i	0.608071	+	0.793883i	$0.291944\pi$
$114$	−75.8960	+	43.8186i	−0.665755	+	0.384374i
$115$	5.94579	+	31.9280i	0.0517026	+	0.277635i
$116$	−29.4131			−0.253561
$117$	260.472	−	23.5280i	2.22626	−	0.201094i
$118$	−89.4418	−	89.4418i	−0.757982	−	0.757982i
$119$	12.2523	+	21.2216i	0.102960	+	0.178333i
$120$	−62.9280	−	43.1699i	−0.524400	−	0.359749i
$121$	131.136	−	227.134i	1.08377	−	1.87714i
$122$	85.1602	+	85.1602i	0.698034	+	0.698034i
$123$	−36.1186	−	134.796i	−0.293647	−	1.09591i
$124$	−42.7672	+	74.0750i	−0.344897	+	0.597379i
$125$	−28.8683	+	121.621i	−0.230946	+	0.972966i
$126$	−41.7793	+	72.3640i	−0.331582	+	0.574317i
$127$	−13.5080	−	3.61947i	−0.106363	−	0.0284998i	0.205245	−	0.978711i	$-0.434201\pi$
$127$	−13.5080	−	3.61947i	−0.106363	−	0.0284998i	−0.311608	+	0.950211i	$0.600867\pi$
$128$	−10.9282	−	2.92820i	−0.0853766	−	0.0228766i
$129$		−	60.4579i		−	0.468666i
$130$	−65.8010	−	64.1890i	−0.506162	−	0.493761i
$131$	−125.831			−0.960541			−0.480270	−	0.877121i	$-0.659461\pi$
$131$	−125.831			−0.960541			−0.480270	+	0.877121i	$0.659461\pi$
$132$	−54.6839	+	204.083i	−0.414272	+	1.54608i
$133$	8.72939	−	32.5785i	0.0656345	−	0.244951i
$134$	74.1266	+	42.7970i	0.553183	+	0.319380i
$135$	99.8886	−	282.846i	0.739915	−	2.09516i
$136$	−20.4375	−	11.7996i	−0.150276	−	0.0867619i
$137$	68.1350	−	18.2567i	0.497336	−	0.133261i	−0.00142747	−	0.999999i	$-0.500454\pi$
$137$	68.1350	−	18.2567i	0.497336	−	0.133261i	0.498763	+	0.866738i	$0.333788\pi$
$138$	−35.0497	+	35.0497i	−0.253984	+	0.253984i
$139$	19.5435	+	11.2835i	0.140601	+	0.0811759i	0.568650	−	0.822579i	$-0.307466\pi$
$139$	19.5435	+	11.2835i	0.140601	+	0.0811759i	−0.428049	+	0.903755i	$0.640799\pi$
$140$	28.8730	−	5.37687i	0.206235	−	0.0384062i
$141$	185.276	−	106.969i	1.31401	−	0.758645i
$142$	−6.07119	+	6.07119i	−0.0427549	+	0.0427549i
$143$	−106.908	+	230.962i	−0.747610	+	1.61512i
$144$		−	80.4716i		−	0.558830i
$145$	−41.5975	+	60.6360i	−0.286879	+	0.418179i
$146$	−62.8256	−	108.817i	−0.430312	−	0.745322i
$147$	56.3874	+	210.441i	0.383588	+	1.43157i
$148$	21.5175	−	21.5175i	0.145389	−	0.145389i
$149$	5.09106	−	8.81797i	0.0341682	−	0.0591810i	−0.848436	−	0.529299i	$-0.822455\pi$
$149$	5.09106	−	8.81797i	0.0341682	−	0.0591810i	0.882604	+	0.470118i	$0.155788\pi$
$150$	−177.992	+	68.6747i	−1.18661	+	0.457832i
$151$		−	110.398i		−	0.731109i	−0.930790	−	0.365555i	$-0.880879\pi$
$151$		−	110.398i		−	0.731109i	0.930790	−	0.365555i	$-0.119121\pi$
$152$	8.40688	+	31.3749i	0.0553084	+	0.206414i
$153$	43.4442	−	162.136i	0.283949	−	1.05971i
$154$	−40.6567	−	70.4196i	−0.264005	−	0.457270i
$155$	92.2240	+	192.926i	0.594994	+	1.24469i
$156$	23.9732	−	138.235i	0.153674	−	0.886123i
$157$	−204.980	+	204.980i	−1.30561	+	1.30561i	−0.381052	+	0.924553i	$0.624438\pi$
$157$	−204.980	+	204.980i	−1.30561	+	1.30561i	−0.924553	+	0.381052i	$0.875562\pi$
$158$	47.6763	+	12.7748i	0.301749	+	0.0808533i
$159$	471.966	−	272.490i	2.96834	−	1.71377i
$160$	−21.4918	+	18.3876i	−0.134324	+	0.114922i
$161$		−	19.0765i		−	0.118488i
$162$	194.889	−	52.2203i	1.20302	−	0.322347i
$163$	43.4187	+	162.041i	0.266372	+	0.994115i	0.961405	+	0.275137i	$0.0887232\pi$
$163$	43.4187	+	162.041i	0.266372	+	0.994115i	−0.695033	+	0.718978i	$0.744610\pi$
$164$	−51.7231			−0.315385
$165$	343.386	+	401.357i	2.08113	+	2.43247i
$166$	46.8941	+	81.2230i	0.282495	+	0.489295i
$167$	61.1025	−	228.038i	0.365883	−	1.36550i	−0.500336	−	0.865831i	$-0.666790\pi$
$167$	61.1025	−	228.038i	0.365883	−	1.36550i	0.866219	−	0.499664i	$-0.166543\pi$
$168$	31.6960	+	31.6960i	0.188667	+	0.188667i
$169$	56.9056	−	159.131i	0.336720	−	0.941605i
$170$	−53.2290	+	25.4449i	−0.313112	+	0.149676i
$171$	−200.081	+	115.517i	−1.17007	+	0.675538i
$172$	−21.6445	−	5.79962i	−0.125840	−	0.0337187i
$173$	−194.105	+	52.0104i	−1.12200	+	0.300638i	−0.771691	−	0.635997i	$-0.780589\pi$
$173$	−194.105	+	52.0104i	−1.12200	+	0.300638i	−0.350305	+	0.936636i	$0.613922\pi$
$174$	−112.229			−0.644996
$175$	29.7490	−	67.1266i	0.169995	−	0.383581i
$176$	67.8178	+	39.1547i	0.385329	+	0.222470i
$177$	−341.276	−	341.276i	−1.92811	−	1.92811i
$178$	195.595	−	52.4094i	1.09885	−	0.294435i
$179$	85.8392	−	49.5593i	0.479549	−	0.276868i	−0.240680	−	0.970605i	$-0.577370\pi$
$179$	85.8392	−	49.5593i	0.479549	−	0.276868i	0.720228	+	0.693737i	$0.244037\pi$
$180$	−165.894	−	113.807i	−0.921635	−	0.632261i
$181$	28.9450			0.159917			0.0799586	−	0.996798i	$-0.474521\pi$
$181$	28.9450			0.159917			0.0799586	+	0.996798i	$0.474521\pi$
$182$	31.0947	+	44.1426i	0.170850	+	0.242542i
$183$	324.939	+	324.939i	1.77562	+	1.77562i
$184$	9.18586	+	15.9104i	0.0499232	+	0.0864694i
$185$	−13.9278	−	74.7901i	−0.0752854	−	0.404271i
$186$	−163.183	+	282.642i	−0.877330	+	1.51958i
$187$	115.502	+	115.502i	0.617660	+	0.617660i
$188$	−20.5227	−	76.5917i	−0.109163	−	0.407403i
$189$	−88.0981	+	152.590i	−0.466127	+	0.807356i
$190$	76.5696	+	27.0410i	0.402998	+	0.142321i
$191$	−66.8559	+	115.798i	−0.350031	+	0.606271i	−0.986254	−	0.165233i	$-0.947162\pi$
$191$	−66.8559	+	115.798i	−0.350031	+	0.606271i	0.636224	+	0.771505i	$0.280496\pi$
$192$	−41.6979	−	11.1729i	−0.217176	−	0.0581922i
$193$	−137.565	−	36.8605i	−0.712773	−	0.190987i	−0.115828	−	0.993269i	$-0.536952\pi$
$193$	−137.565	−	36.8605i	−0.712773	−	0.190987i	−0.596945	+	0.802282i	$0.703619\pi$
$194$			254.350i			1.31108i
$195$	−251.072	−	244.921i	−1.28755	−	1.25600i
$196$	80.7488			0.411984
$197$	57.5288	−	214.700i	0.292024	−	1.08985i	−0.651528	−	0.758625i	$-0.725872\pi$
$197$	57.5288	−	214.700i	0.292024	−	1.08985i	0.943552	−	0.331224i	$-0.107462\pi$
$198$	−144.161	+	538.015i	−0.728085	+	2.71725i
$199$	−12.8522	−	7.42020i	−0.0645837	−	0.0372874i	0.467360	−	0.884067i	$-0.345205\pi$
$199$	−12.8522	−	7.42020i	−0.0645837	−	0.0372874i	−0.531944	+	0.846779i	$0.678538\pi$
$200$	7.51172	+	70.3106i	0.0375586	+	0.351553i
$201$	282.839	+	163.297i	1.40716	+	0.812423i
$202$	118.993	−	31.8840i	0.589073	−	0.157842i
$203$	30.5415	−	30.5415i	0.150451	−	0.150451i
$204$	−77.9818	−	45.0228i	−0.382264	−	0.220700i
$205$	−73.1494	+	106.629i	−0.356827	+	0.520140i
$206$	−56.6344	+	32.6979i	−0.274924	+	0.158728i
$207$	−92.4001	+	92.4001i	−0.446377	+	0.446377i
$208$	−47.1897	−	21.8433i	−0.226874	−	0.105016i
$209$		−	224.826i		−	1.07572i
$210$	110.168	−	20.5161i	0.524610	−	0.0976956i
$211$	−103.424	−	179.136i	−0.490161	−	0.848985i	0.509774	−	0.860308i	$-0.329729\pi$
$211$	−103.424	−	179.136i	−0.490161	−	0.848985i	−0.999936	+	0.0113235i	$0.996396\pi$
$212$	−52.2789	−	195.107i	−0.246598	−	0.920318i
$213$	−23.1653	+	23.1653i	−0.108757	+	0.108757i
$214$	9.04780	−	15.6713i	0.0422795	−	0.0732302i
$215$	−42.5668	+	36.4186i	−0.197985	+	0.169389i
$216$		−	169.686i		−	0.785586i
$217$	−32.5088	−	121.325i	−0.149810	−	0.559100i
$218$	15.1075	−	56.3819i	0.0693004	−	0.258633i
$219$	−239.718	−	415.204i	−1.09460	−	1.89591i
$220$	176.630	−	84.4339i	0.802863	−	0.383790i
$221$	−83.2864	−	69.4866i	−0.376862	−	0.314419i
$222$	82.1027	−	82.1027i	0.369832	−	0.369832i
$223$	125.352	+	33.5881i	0.562119	+	0.150619i	0.528680	−	0.848822i	$-0.322687\pi$
$223$	125.352	+	33.5881i	0.562119	+	0.150619i	0.0334391	+	0.999441i	$0.489354\pi$
$224$	14.3880	−	8.30691i	0.0642321	−	0.0370844i
$225$	−469.232	+	181.044i	−2.08548	+	0.804640i
$226$		−	122.053i		−	0.540059i
$227$	−93.7496	+	25.1201i	−0.412994	+	0.110661i	−0.459332	−	0.888264i	$-0.651911\pi$
$227$	−93.7496	+	25.1201i	−0.412994	+	0.110661i	0.0463386	+	0.998926i	$0.485245\pi$
$228$	32.0774	+	119.715i	0.140691	+	0.525064i
$229$	18.5166			0.0808587			0.0404293	−	0.999182i	$-0.487127\pi$
$229$	18.5166			0.0808587			0.0404293	+	0.999182i	$0.487127\pi$
$230$	45.7908	+	3.56436i	0.199090	+	0.0154972i
$231$	−155.131	−	268.694i	−0.671561	−	1.16318i
$232$	−10.7659	+	40.1791i	−0.0464050	+	0.173186i
$233$	−24.7654	−	24.7654i	−0.106289	−	0.106289i	0.651962	−	0.758251i	$-0.273946\pi$
$233$	−24.7654	−	24.7654i	−0.106289	−	0.106289i	−0.758251	+	0.651962i	$0.773946\pi$
$234$	63.1995	−	364.423i	0.270083	−	1.55736i
$235$	−186.920	−	66.0118i	−0.795405	−	0.280901i
$236$	−154.918	+	89.4418i	−0.656431	+	0.378991i
$237$	181.915	+	48.7439i	0.767572	+	0.205670i
$238$	33.4739	−	8.96930i	0.140647	−	0.0376861i
$239$	124.625			0.521443			0.260721	−	0.965414i	$-0.416040\pi$
$239$	124.625			0.521443			0.260721	+	0.965414i	$0.416040\pi$
$240$	−82.0045	+	70.1600i	−0.341685	+	0.292333i
$241$	−307.605	−	177.596i	−1.27637	−	0.736912i	−0.300191	−	0.953879i	$-0.597050\pi$
$241$	−307.605	−	177.596i	−1.27637	−	0.736912i	−0.976179	+	0.216967i	$0.930384\pi$
$242$	−262.272	−	262.272i	−1.08377	−	1.08377i
$243$	222.080	−	59.5061i	0.913909	−	0.244881i
$244$	147.502	−	85.1602i	0.604516	−	0.349017i
$245$	114.199	−	166.466i	0.466119	−	0.679453i
$246$	−197.356			−0.802259
$247$	13.4306	+	148.687i	0.0543751	+	0.601971i
$248$	85.5344	+	85.5344i	0.344897	+	0.344897i
$249$	178.930	+	309.916i	0.718595	+	1.24464i
$250$	155.571	+	83.9511i	0.622282	+	0.335805i
$251$	−121.468	+	210.389i	−0.483937	+	0.838204i	−0.999830	−	0.0184492i	$-0.994127\pi$
$251$	−121.468	+	210.389i	−0.483937	+	0.838204i	0.515892	+	0.856653i	$0.327460\pi$
$252$	83.5587	+	83.5587i	0.331582	+	0.331582i
$253$	−32.9120	−	122.829i	−0.130087	−	0.485491i
$254$	−9.88858	+	17.1275i	−0.0389314	+	0.0674312i
$255$	−203.102	+	97.0881i	−0.796477	+	0.380738i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	161.836	+	43.3638i	0.629712	+	0.168731i	0.559539	−	0.828804i	$-0.310978\pi$
$257$	161.836	+	43.3638i	0.629712	+	0.168731i	0.0701728	+	0.997535i	$0.477645\pi$
$258$	−82.5871	−	22.1291i	−0.320105	−	0.0857719i
$259$			44.6860i			0.172533i
$260$	−111.769	+	66.3911i	−0.429879	+	0.255350i
$261$	−295.865			−1.13358
$262$	−46.0573	+	171.888i	−0.175791	+	0.656061i
$263$	−1.22549	+	4.57361i	−0.00465968	+	0.0173901i	−0.968217	−	0.250113i	$-0.919532\pi$
$263$	−1.22549	+	4.57361i	−0.00465968	+	0.0173901i	0.963557	+	0.267504i	$0.0861987\pi$
$264$	258.767	+	149.399i	0.980178	+	0.565906i
$265$	−476.155	−	168.156i	−1.79681	−	0.634552i
$266$	−41.3079	−	23.8491i	−0.155293	−	0.0896584i
$267$	746.314	−	199.974i	2.79518	−	0.748967i
$268$	85.5940	−	85.5940i	0.319380	−	0.319380i
$269$	−91.3836	−	52.7604i	−0.339716	−	0.196135i	0.320430	−	0.947272i	$-0.396172\pi$
$269$	−91.3836	−	52.7604i	−0.339716	−	0.196135i	−0.660147	+	0.751137i	$0.729506\pi$
$270$	−349.813	−	239.979i	−1.29560	−	0.888812i
$271$	396.469	−	228.901i	1.46298	−	0.844654i	0.463836	−	0.885921i	$-0.346473\pi$
$271$	396.469	−	228.901i	1.46298	−	0.844654i	0.999148	+	0.0412665i	$0.0131393\pi$
$272$	−23.5992	+	23.5992i	−0.0867619	+	0.0867619i
$273$	118.645	+	168.431i	0.434599	+	0.616964i
$274$		−	99.7566i		−	0.364075i
$275$	75.7361	−	483.538i	0.275404	−	1.75832i
$276$	35.0497	+	60.7079i	0.126992	+	0.219956i
$277$	−93.3927	−	348.546i	−0.337158	−	1.25829i	−0.901511	−	0.432757i	$-0.857541\pi$
$277$	−93.3927	−	348.546i	−0.337158	−	1.25829i	0.564353	−	0.825534i	$-0.309126\pi$
$278$	22.5669	−	22.5669i	0.0811759	−	0.0811759i
$279$	−430.193	+	745.116i	−1.54191	+	2.67067i
$280$	3.22330	−	41.4093i	0.0115118	−	0.147890i
$281$			114.357i			0.406966i	0.979079	+	0.203483i	$0.0652261\pi$
$281$			114.357i			0.406966i	−0.979079	+	0.203483i	$0.934774\pi$
$282$	−78.3067	−	292.245i	−0.277683	−	1.03633i
$283$	−101.683	+	379.486i	−0.359303	+	1.34094i	0.515678	+	0.856782i	$0.327540\pi$
$283$	−101.683	+	379.486i	−0.359303	+	1.34094i	−0.874982	+	0.484156i	$0.839127\pi$
$284$	6.07119	+	10.5156i	0.0213774	+	0.0370268i
$285$	292.161	+	103.178i	1.02512	+	0.362028i
$286$	276.369	+	230.577i	0.966326	+	0.806215i
$287$	53.7074	−	53.7074i	0.187134	−	0.187134i
$288$	−109.926	−	29.4546i	−0.381688	−	0.102273i
$289$	189.993	−	109.692i	0.657414	−	0.379558i
$290$	67.6045	+	79.0176i	0.233119	+	0.272474i
$291$			970.503i			3.33506i
$292$	−171.643	+	45.9915i	−0.587817	+	0.157505i
$293$	30.1952	+	112.690i	0.103055	+	0.384608i	0.998117	−	0.0613340i	$-0.0195355\pi$
$293$	30.1952	+	112.690i	0.103055	+	0.384608i	−0.895062	+	0.445942i	$0.852869\pi$
$294$	308.107			1.04798
$295$	−34.7058	+	445.861i	−0.117647	+	1.51139i
$296$	−21.5175	−	37.2694i	−0.0726943	−	0.125910i
$297$	−303.985	+	1134.49i	−1.02352	+	3.81982i
$298$	−10.1821	−	10.1821i	−0.0341682	−	0.0341682i
$299$	29.1036	+	79.2660i	0.0973366	+	0.265104i
$300$	28.6618	+	268.278i	0.0955395	+	0.894261i
$301$	28.4969	−	16.4527i	0.0946742	−	0.0546602i
$302$	−150.806	−	40.4083i	−0.499357	−	0.133802i
$303$	454.031	−	121.657i	1.49845	−	0.401509i
$304$	45.9360			0.151105
$305$	33.0444	−	424.517i	0.108342	−	1.39186i
$306$	−205.580	−	118.692i	−0.671830	−	0.387881i
$307$	194.511	+	194.511i	0.633586	+	0.633586i	0.948966	−	0.315380i	$-0.102132\pi$
$307$	194.511	+	194.511i	0.633586	+	0.633586i	−0.315380	+	0.948966i	$0.602132\pi$
$308$	−111.076	+	29.7628i	−0.360637	+	0.0966325i
$309$	−216.095	+	124.763i	−0.699337	+	0.403763i
$310$	297.299	−	55.3644i	0.959028	−	0.178595i
$311$	−101.693			−0.326988			−0.163494	−	0.986544i	$-0.552276\pi$
$311$	−101.693			−0.326988			−0.163494	+	0.986544i	$0.552276\pi$
$312$	−180.058	−	83.3456i	−0.577109	−	0.267133i
$313$	93.9325	+	93.9325i	0.300104	+	0.300104i	0.841054	−	0.540951i	$-0.181935\pi$
$313$	93.9325	+	93.9325i	0.300104	+	0.300104i	−0.540951	+	0.841054i	$0.681935\pi$
$314$	204.980	+	355.036i	0.652803	+	1.13069i
$315$	290.431	−	54.0856i	0.922005	−	0.171700i
$316$	34.9015	−	60.4511i	0.110448	−	0.191301i
$317$	−256.146	−	256.146i	−0.808030	−	0.808030i	0.176305	−	0.984336i	$-0.443585\pi$
$317$	−256.146	−	256.146i	−0.808030	−	0.808030i	−0.984336	+	0.176305i	$0.943585\pi$
$318$	−199.476	−	744.455i	−0.627284	−	2.34105i
$319$	143.958	−	249.342i	0.451278	−	0.781636i
$320$	17.2514	+	36.0887i	0.0539105	+	0.112777i
$321$	34.5230	−	59.7955i	0.107548	−	0.186279i
$322$	−26.0590	−	6.98249i	−0.0809286	−	0.0216848i
$323$	92.5530	+	24.7995i	0.286542	+	0.0767786i
$324$		−	285.337i		−	0.880669i
$325$	−21.2019	+	324.308i	−0.0652365	+	0.997870i
$326$	237.244			0.727743
$327$	57.6444	−	215.132i	0.176283	−	0.657895i
$328$	−18.9320	+	70.6551i	−0.0577194	+	0.215412i
$329$	100.840	+	58.2200i	0.306505	+	0.176960i
$330$	673.952	−	322.167i	2.04228	−	0.976265i
$331$	276.997	+	159.924i	0.836849	+	0.483155i	0.856192	−	0.516658i	$-0.172824\pi$
$331$	276.997	+	159.924i	0.836849	+	0.483155i	−0.0193432	+	0.999813i	$0.506158\pi$
$332$	128.117	−	34.3289i	0.385895	−	0.103400i
$333$	216.444	−	216.444i	0.649981	−	0.649981i
$334$	−289.140	−	166.935i	−0.865689	−	0.499806i
$335$	−55.4030	−	297.506i	−0.165382	−	0.888077i
$336$	54.8990	−	31.6960i	0.163390	−	0.0943333i
$337$	−16.1158	+	16.1158i	−0.0478214	+	0.0478214i	−0.730613	−	0.682792i	$-0.760766\pi$
$337$	−16.1158	+	16.1158i	−0.0478214	+	0.0478214i	0.682792	+	0.730613i	$0.260766\pi$
$338$	−196.548	−	135.981i	−0.581504	−	0.402309i
$339$		−	465.709i		−	1.37377i
$340$	15.2752	+	82.0257i	0.0449272	+	0.241252i
$341$	−418.634	−	725.095i	−1.22767	−	2.12638i
$342$	84.5643	+	315.598i	0.247264	+	0.922802i
$343$	−185.606	+	185.606i	−0.541126	+	0.541126i
$344$	−15.8449	+	27.4441i	−0.0460606	+	0.0797794i
$345$	174.720	+	13.6002i	0.506435	+	0.0394210i
$346$			284.190i			0.821358i
$347$	−18.9752	−	70.8164i	−0.0546835	−	0.204082i	0.933179	−	0.359412i	$-0.117023\pi$
$347$	−18.9752	−	70.8164i	−0.0546835	−	0.204082i	−0.987863	+	0.155330i	$0.950356\pi$
$348$	−41.0788	+	153.308i	−0.118042	+	0.440540i
$349$	119.707	+	207.339i	0.343001	+	0.594095i	0.984989	−	0.172620i	$-0.0552232\pi$
$349$	119.707	+	207.339i	0.343001	+	0.594095i	−0.641987	+	0.766715i	$0.721890\pi$
$350$	−80.8078	−	65.2080i	−0.230879	−	0.186309i
$351$	133.266	−	768.442i	0.379674	−	2.18929i
$352$	78.3093	−	78.3093i	0.222470	−	0.222470i
$353$	412.735	+	110.592i	1.16922	+	0.313291i	0.790642	−	0.612278i	$-0.209747\pi$
$353$	412.735	+	110.592i	1.16922	+	0.313291i	0.378577	+	0.925570i	$0.376413\pi$
$354$	−591.107	+	341.276i	−1.66979	+	0.964056i
$355$	30.2644	+	2.35578i	0.0852518	+	0.00663601i
$356$		−	286.370i		−	0.804411i
$357$	127.724	−	34.2234i	0.357769	−	0.0958639i
$358$	−36.2799	−	135.399i	−0.101341	−	0.378208i
$359$	194.173			0.540871			0.270435	−	0.962738i	$-0.412832\pi$
$359$	194.173			0.540871			0.270435	+	0.962738i	$0.412832\pi$
$360$	−216.185	+	184.960i	−0.600513	+	0.513777i
$361$	114.559	+	198.422i	0.317337	+	0.549644i
$362$	10.5946	−	39.5396i	0.0292669	−	0.109225i
$363$	−1000.73	−	1000.73i	−2.75683	−	2.75683i
$364$	71.6813	−	26.3188i	0.196927	−	0.0723045i
$365$	−147.933	+	418.890i	−0.405296	+	1.14764i
$366$	562.811	−	324.939i	1.53773	−	0.887811i
$367$	−86.0380	−	23.0538i	−0.234436	−	0.0628169i	0.139688	−	0.990196i	$-0.455390\pi$
$367$	−86.0380	−	23.0538i	−0.234436	−	0.0628169i	−0.374124	+	0.927379i	$0.622057\pi$
$368$	25.0962	−	6.72452i	0.0681963	−	0.0182731i
$369$	−520.280			−1.40997
$370$	−107.263	−	8.34937i	−0.289900	−	0.0225659i
$371$	256.877	+	148.308i	0.692390	+	0.399752i
$372$	326.367	+	326.367i	0.877330	+	0.877330i
$373$	−52.5461	+	14.0797i	−0.140874	+	0.0377471i	−0.328567	−	0.944481i	$-0.606566\pi$
$373$	−52.5461	+	14.0797i	−0.140874	+	0.0377471i	0.187693	+	0.982228i	$0.439899\pi$
$374$	200.056	−	115.502i	0.534910	−	0.308830i
$375$	593.598	+	320.326i	1.58293	+	0.854201i
$376$	−112.138			−0.298239
$377$	−80.3099	+	173.500i	−0.213024	+	0.460211i
$378$	176.196	+	176.196i	0.466127	+	0.466127i
$379$	−225.706	−	390.934i	−0.595530	−	1.03149i	−0.993472	−	0.114077i	$-0.963609\pi$
$379$	−225.706	−	390.934i	−0.595530	−	1.03149i	0.397942	−	0.917411i	$-0.369725\pi$
$380$	64.9651	−	94.6984i	0.170961	−	0.249206i
$381$	−37.7310	+	65.3521i	−0.0990316	+	0.171528i
$382$	133.712	+	133.712i	0.350031	+	0.350031i
$383$	−67.1898	−	250.756i	−0.175430	−	0.654715i	−0.996478	−	0.0838550i	$-0.973277\pi$
$383$	−67.1898	−	250.756i	−0.175430	−	0.654715i	0.821048	−	0.570860i	$-0.193390\pi$
$384$	−30.5249	+	52.8708i	−0.0794921	+	0.137684i
$385$	−95.7329	+	271.079i	−0.248657	+	0.704101i
$386$	−100.705	+	174.426i	−0.260893	+	0.451880i
$387$	−217.721	−	58.3381i	−0.562586	−	0.150744i
$388$	347.449	+	93.0986i	0.895486	+	0.239945i
$389$			224.650i			0.577507i	0.957403	+	0.288754i	$0.0932409\pi$
$389$			224.650i			0.577507i	−0.957403	+	0.288754i	$0.906759\pi$
$390$	−426.466	+	253.323i	−1.09350	+	0.649546i
$391$	54.1948			0.138606
$392$	29.5561	−	110.305i	0.0753983	−	0.281390i
$393$	−175.737	+	655.859i	−0.447168	+	1.66885i
$394$	−272.229	−	157.172i	−0.690937	−	0.398912i
$395$	−75.2622	−	157.443i	−0.190537	−	0.398591i
$396$	682.176	+	393.854i	1.72267	+	0.994582i
$397$	94.3771	−	25.2883i	0.237726	−	0.0636984i	−0.137989	−	0.990434i	$-0.544064\pi$
$397$	94.3771	−	25.2883i	0.237726	−	0.0636984i	0.375715	+	0.926735i	$0.377397\pi$
$398$	−14.8404	+	14.8404i	−0.0372874	+	0.0372874i
$399$	−157.615	−	90.9992i	−0.395026	−	0.228068i
$400$	98.7955	+	15.4743i	0.246989	+	0.0386856i
$401$	−139.287	+	80.4173i	−0.347349	+	0.200542i	−0.663517	−	0.748161i	$-0.730937\pi$
$401$	−139.287	+	80.4173i	−0.347349	+	0.200542i	0.316168	+	0.948703i	$0.397604\pi$
$402$	326.594	−	326.594i	0.812423	−	0.812423i
$403$	320.175	+	454.527i	0.794480	+	1.12786i
$404$		−	174.217i		−	0.431231i
$405$	−588.230	−	403.538i	−1.45242	−	0.996390i
$406$	−30.5415	−	52.8994i	−0.0752254	−	0.130294i
$407$	77.0951	+	287.723i	0.189423	+	0.706936i
$408$	−90.0457	+	90.0457i	−0.220700	+	0.220700i
$409$	−12.4032	+	21.4830i	−0.0303258	+	0.0525258i	−0.880790	−	0.473507i	$-0.842988\pi$
$409$	−12.4032	+	21.4830i	−0.0303258	+	0.0525258i	0.850464	+	0.526033i	$0.176321\pi$
$410$	118.883	+	138.953i	0.289958	+	0.338909i
$411$		−	380.633i		−	0.926114i
$412$	23.9365	+	89.3323i	0.0580983	+	0.216826i
$413$	67.9878	−	253.734i	0.164619	−	0.614368i
$414$	92.4001	+	160.042i	0.223189	+	0.386574i
$415$	110.420	−	312.667i	0.266072	−	0.753414i
$416$	−47.1111	+	56.4672i	−0.113248	+	0.135738i
$417$	86.1067	−	86.1067i	0.206491	−	0.206491i
$418$	−307.118	−	82.2921i	−0.734733	−	0.196871i
$419$	−324.941	+	187.605i	−0.775515	+	0.447744i	−0.834839	−	0.550495i	$-0.814439\pi$
$419$	−324.941	+	187.605i	−0.775515	+	0.447744i	0.0593232	+	0.998239i	$0.481106\pi$
$420$	12.2989	−	158.002i	0.0292831	−	0.376195i
$421$			529.467i			1.25764i	0.777550	+	0.628821i	$0.216462\pi$
$421$			529.467i			1.25764i	−0.777550	+	0.628821i	$0.783538\pi$
$422$	−282.560	+	75.7117i	−0.669573	+	0.179412i
$423$	−206.437	−	770.432i	−0.488030	−	1.82135i
$424$	−285.657			−0.673719
$425$	190.701	+	84.5146i	0.448709	+	0.198858i
$426$	23.1653	+	40.1235i	0.0543787	+	0.0941867i
$427$	−64.7332	+	241.588i	−0.151600	+	0.565779i
$428$	−18.0956	−	18.0956i	−0.0422795	−	0.0422795i
$429$	1054.52	+	879.795i	2.45809	+	2.05081i
$430$	34.1682	+	71.4775i	0.0794609	+	0.166227i
$431$	−397.988	+	229.779i	−0.923407	+	0.533129i	−0.884720	−	0.466122i	$-0.845651\pi$
$431$	−397.988	+	229.779i	−0.923407	+	0.533129i	−0.0386864	+	0.999251i	$0.512317\pi$
$432$	−231.796	−	62.1096i	−0.536565	−	0.143772i
$433$	−226.153	+	60.5975i	−0.522293	+	0.139948i	−0.510327	−	0.859980i	$-0.670476\pi$
$433$	−226.153	+	60.5975i	−0.522293	+	0.139948i	−0.0119660	+	0.999928i	$0.503809\pi$
$434$	−177.632			−0.409289
$435$	257.953	+	301.501i	0.592995	+	0.693106i
$436$	−71.4894	−	41.2744i	−0.163966	−	0.0946661i
$437$	−52.7453	−	52.7453i	−0.120699	−	0.120699i
$438$	−654.923	+	175.486i	−1.49526	+	0.400653i
$439$	−701.861	+	405.220i	−1.59877	+	0.923052i	−0.607048	+	0.794665i	$0.707647\pi$
$439$	−701.861	+	405.220i	−1.59877	+	0.923052i	−0.991724	+	0.128387i	$0.959020\pi$
$440$	−50.6878	−	272.186i	−0.115200	−	0.618604i
$441$	812.248			1.84183
$442$	−125.405	+	88.3375i	−0.283723	+	0.199859i
$443$	−323.330	−	323.330i	−0.729865	−	0.729865i	0.240727	−	0.970593i	$-0.422614\pi$
$443$	−323.330	−	323.330i	−0.729865	−	0.729865i	−0.970593	+	0.240727i	$0.922614\pi$
$444$	−82.1027	−	142.206i	−0.184916	−	0.320284i
$445$	−590.360	−	404.999i	−1.32665	−	0.910111i
$446$	91.7644	−	158.941i	0.205750	−	0.356369i
$447$	−38.8511	−	38.8511i	−0.0869151	−	0.0869151i
$448$	−6.08108	−	22.6949i	−0.0135738	−	0.0506582i
$449$	−263.178	+	455.838i	−0.586143	+	1.01523i	0.408589	+	0.912718i	$0.366021\pi$
$449$	−263.178	+	455.838i	−0.586143	+	1.01523i	−0.994732	+	0.102511i	$0.967312\pi$
$450$	75.5599	+	707.250i	0.167911	+	1.57167i
$451$	253.150	−	438.469i	0.561308	−	0.972215i
$452$	−166.728	−	44.6746i	−0.368867	−	0.0988376i
$453$	−575.417	−	154.183i	−1.27024	−	0.340359i
$454$			137.259i			0.302332i
$455$	47.1184	−	184.994i	0.103557	−	0.406581i
$456$	175.274			0.384374
$457$	−79.6259	+	297.168i	−0.174236	+	0.650258i	0.822444	+	0.568845i	$0.192610\pi$
$457$	−79.6259	+	297.168i	−0.174236	+	0.650258i	−0.996681	+	0.0814124i	$0.974057\pi$
$458$	6.77756	−	25.2942i	0.0147982	−	0.0552275i
$459$	−433.497	−	250.279i	−0.944437	−	0.545271i
$460$	21.6296	−	61.2467i	0.0470209	−	0.133145i
$461$	−535.212	−	309.005i	−1.16098	−	0.670292i	−0.209441	−	0.977821i	$-0.567164\pi$
$461$	−535.212	−	309.005i	−1.16098	−	0.670292i	−0.951539	+	0.307530i	$0.900498\pi$
$462$	−423.825	+	113.564i	−0.917370	+	0.245808i
$463$	168.921	−	168.921i	0.364841	−	0.364841i	−0.500751	−	0.865591i	$-0.666943\pi$
$463$	168.921	−	168.921i	0.364841	−	0.364841i	0.865591	+	0.500751i	$0.166943\pi$
$464$	50.9450	+	29.4131i	0.109795	+	0.0633903i
$465$	1134.38	−	211.250i	2.43952	−	0.454300i
$466$	−42.8949	+	24.7654i	−0.0920491	+	0.0531446i
$467$	−438.000	+	438.000i	−0.937901	+	0.937901i	−0.998182	−	0.0602800i	$-0.980801\pi$
$467$	−438.000	+	438.000i	−0.937901	+	0.937901i	0.0602800	+	0.998182i	$0.480801\pi$
$468$	−474.679	−	219.720i	−1.01427	−	0.469488i
$469$			177.755i			0.379009i
$470$	−158.591	+	231.176i	−0.337428	+	0.491863i
$471$	782.126	+	1354.68i	1.66056	+	2.87618i
$472$	65.4760	+	244.360i	0.138720	+	0.517711i
$473$	155.100	−	155.100i	0.327907	−	0.327907i
$474$	133.171	−	230.658i	0.280951	−	0.486621i
$475$	−103.346	−	267.855i	−0.217571	−	0.563904i
$476$		−	49.0092i		−	0.102960i
$477$	−525.870	−	1962.57i	−1.10245	−	4.11441i
$478$	45.6159	−	170.241i	0.0954307	−	0.356152i
$479$	−384.379	−	665.763i	−0.802461	−	1.38990i	−0.917992	−	0.396599i	$-0.870190\pi$
$479$	−384.379	−	665.763i	−0.802461	−	1.38990i	0.115532	−	0.993304i	$-0.463143\pi$
$480$	65.8246	+	137.701i	0.137135	+	0.286876i
$481$	−68.1741	−	185.677i	−0.141734	−	0.386024i
$482$	−355.192	+	355.192i	−0.736912	+	0.736912i
$483$	−99.4312	−	26.6425i	−0.205862	−	0.0551605i
$484$	−454.268	+	262.272i	−0.938570	+	0.541884i
$485$	683.305	−	584.610i	1.40888	−	1.20538i
$486$		−	325.147i		−	0.669028i
$487$	347.181	−	93.0269i	0.712898	−	0.191020i	0.115897	−	0.993261i	$-0.463026\pi$
$487$	347.181	−	93.0269i	0.712898	−	0.191020i	0.597001	+	0.802241i	$0.296359\pi$
$488$	−62.3416	−	232.662i	−0.127749	−	0.476766i
$489$	905.233			1.85119
$490$	−185.597	−	216.930i	−0.378769	−	0.442713i
$491$	402.964	+	697.954i	0.820701	+	1.42150i	0.905161	+	0.425069i	$0.139750\pi$
$491$	402.964	+	697.954i	0.820701	+	1.42150i	−0.0844603	+	0.996427i	$0.526917\pi$
$492$	−72.2372	+	269.593i	−0.146824	+	0.547953i
$493$	86.7659	+	86.7659i	0.175996	+	0.175996i
$494$	208.026	+	36.0765i	0.421105	+	0.0730294i
$495$	1776.71	−	849.315i	3.58931	−	1.71579i
$496$	148.150	−	85.5344i	0.298689	−	0.172448i
$497$	−17.2231	−	4.61492i	−0.0346542	−	0.00928556i
$498$	488.846	−	130.986i	0.981619	−	0.263024i
$499$	466.152			0.934173			0.467086	−	0.884212i	$-0.345304\pi$
$499$	466.152			0.934173			0.467086	+	0.884212i	$0.345304\pi$
$500$	171.622	−	181.785i	0.343244	−	0.363570i
$501$	−1103.25	−	636.961i	−2.20209	−	1.27138i
$502$	242.937	+	242.937i	0.483937	+	0.483937i
$503$	378.476	−	101.412i	0.752438	−	0.201615i	0.137839	−	0.990455i	$-0.455984\pi$
$503$	378.476	−	101.412i	0.752438	−	0.201615i	0.614599	+	0.788840i	$0.289318\pi$
$504$	144.728	−	83.5587i	0.287159	−	0.165791i
$505$	−359.154	−	246.387i	−0.711196	−	0.487895i
$506$	−179.835			−0.355404
$507$	−749.954	−	518.850i	−1.47920	−	1.02337i
$508$	19.7772	+	19.7772i	0.0389314	+	0.0389314i
$509$	53.0124	+	91.8201i	0.104150	+	0.180393i	0.913391	−	0.407084i	$-0.133454\pi$
$509$	53.0124	+	91.8201i	0.104150	+	0.180393i	−0.809241	+	0.587477i	$0.800121\pi$
$510$	58.2845	+	312.979i	0.114283	+	0.613684i
$511$	130.472	−	225.983i	0.255326	−	0.442237i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	178.317	+	665.487i	0.347596	+	1.29725i
$514$	118.472	−	205.200i	0.230490	−	0.399221i
$515$	218.013	+	76.9925i	0.423327	+	0.149500i
$516$	−60.4579	+	104.716i	−0.117167	+	0.202938i
$517$	749.730	+	200.890i	1.45016	+	0.388568i
$518$	61.0422	+	16.3562i	0.117842	+	0.0315757i
$519$			1084.36i			2.08933i
$520$	49.7817	+	176.980i	0.0957341	+	0.340345i
$521$	−439.897			−0.844331			−0.422166	−	0.906519i	$-0.638730\pi$
$521$	−439.897			−0.844331			−0.422166	+	0.906519i	$0.638730\pi$
$522$	−108.294	+	404.159i	−0.207460	+	0.774251i
$523$	187.040	−	698.042i	0.357629	−	1.33469i	−0.519515	−	0.854461i	$-0.673887\pi$
$523$	187.040	−	698.042i	0.357629	−	1.33469i	0.877144	−	0.480228i	$-0.159446\pi$
$524$	217.945	+	125.831i	0.415926	+	0.240135i
$525$	−308.332	−	248.809i	−0.587298	−	0.473922i
$526$	5.79910	+	3.34811i	0.0110249	+	0.00636523i
$527$	344.673	−	92.3549i	0.654029	−	0.175247i
$528$	298.798	−	298.798i	0.565906	−	0.565906i
$529$	421.590	+	243.405i	0.796956	+	0.460123i
$530$	−403.991	+	588.890i	−0.762246	+	1.11111i
$531$	−1558.31	+	899.690i	−2.93467	+	1.69433i
$532$	−47.6983	+	47.6983i	−0.0896584	+	0.0896584i
$533$	−141.225	+	305.100i	−0.264963	+	0.572420i
$534$		−	1092.68i		−	2.04622i
$535$	−62.8963	+	11.7129i	−0.117563	+	0.0218932i
$536$	−85.5940	−	148.253i	−0.159690	−	0.276592i
$537$	−138.430	−	516.629i	−0.257785	−	0.962066i
$538$	−105.521	+	105.521i	−0.196135	+	0.196135i
$539$	−395.212	+	684.526i	−0.733231	+	1.26999i
$540$	−455.858	+	390.015i	−0.844182	+	0.722251i
$541$			366.398i			0.677261i	0.940919	+	0.338630i	$0.109964\pi$
$541$			366.398i			0.677261i	−0.940919	+	0.338630i	$0.890036\pi$
$542$	−167.567	−	625.370i	−0.309165	−	1.15382i
$543$	40.4250	−	150.868i	0.0744475	−	0.277842i
$544$	23.5992	+	40.8751i	0.0433810	+	0.0751380i
$545$	−186.192	+	89.0050i	−0.341637	+	0.163312i
$546$	273.509	−	100.423i	0.500932	−	0.183924i
$547$	−632.879	+	632.879i	−1.15700	+	1.15700i	−0.171883	+	0.985117i	$0.554985\pi$
$547$	−632.879	+	632.879i	−1.15700	+	1.15700i	−0.985117	+	0.171883i	$0.945015\pi$
$548$	−136.270	−	36.5134i	−0.248668	−	0.0666304i
$549$	1483.71	−	856.622i	2.70257	−	1.56033i
$550$	−632.804	−	280.445i	−1.15055	−	0.509899i
$551$		−	168.890i		−	0.306516i
$552$	95.7577	−	25.6582i	0.173474	−	0.0464822i
$553$	26.5298	+	99.0106i	0.0479744	+	0.179043i
$554$	−510.307			−0.921133
$555$	−409.275	−	31.8580i	−0.737433	−	0.0574018i
$556$	−22.5669	−	39.0870i	−0.0405880	−	0.0703004i
$557$	−49.5183	+	184.805i	−0.0889018	+	0.331786i	−0.996024	−	0.0890802i	$-0.971607\pi$
$557$	−49.5183	+	184.805i	−0.0889018	+	0.331786i	0.907123	+	0.420866i	$0.138274\pi$
$558$	860.386	+	860.386i	1.54191	+	1.54191i
$559$	−93.3086	+	111.839i	−0.166921	+	0.200070i
$560$	−55.3863	−	19.5600i	−0.0989041	−	0.0349285i
$561$	763.338	−	440.713i	1.36067	−	0.785585i
$562$	156.215	+	41.8577i	0.277963	+	0.0744799i
$563$	−541.955	+	145.216i	−0.962620	+	0.257933i	−0.705709	−	0.708502i	$-0.749371\pi$
$563$	−541.955	+	145.216i	−0.962620	+	0.257933i	−0.256911	+	0.966435i	$0.582705\pi$
$564$	−427.876			−0.758645
$565$	−327.893	+	280.533i	−0.580342	+	0.496519i
$566$	481.168	+	277.803i	0.850121	+	0.490818i
$567$	296.283	+	296.283i	0.522545	+	0.522545i
$568$	16.5868	−	4.44442i	0.0292021	−	0.00782468i
$569$	340.790	−	196.755i	0.598928	−	0.345791i	−0.169692	−	0.985497i	$-0.554277\pi$
$569$	340.790	−	196.755i	0.598928	−	0.345791i	0.768620	+	0.639706i	$0.220944\pi$
$570$	247.882	−	361.333i	0.434881	−	0.633918i
$571$	−84.7190			−0.148369			−0.0741847	−	0.997245i	$-0.523635\pi$
$571$	−84.7190			−0.148369			−0.0741847	+	0.997245i	$0.523635\pi$
$572$	416.133	−	293.130i	0.727505	−	0.512465i
$573$	510.193	+	510.193i	0.890389	+	0.890389i
$574$	−53.7074	−	93.0239i	−0.0935669	−	0.162063i
$575$	−95.6722	−	131.208i	−0.166386	−	0.228188i
$576$	−80.4716	+	139.381i	−0.139708	+	0.241981i
$577$	195.275	+	195.275i	0.338431	+	0.338431i	0.855777	−	0.517345i	$-0.173080\pi$
$577$	195.275	+	195.275i	0.338431	+	0.338431i	−0.517345	+	0.855777i	$0.673080\pi$
$578$	−80.3003	−	299.685i	−0.138928	−	0.518486i
$579$	−384.251	+	665.541i	−0.663645	+	1.14947i
$580$	132.685	−	63.4270i	0.228767	−	0.109357i
$581$	−97.3863	+	168.678i	−0.167618	+	0.290324i
$582$	1325.73	+	355.229i	2.27789	+	0.610358i
$583$	1909.84	+	511.740i	3.27588	+	0.877770i
$584$			251.302i			0.430312i
$585$	−1124.27	+	667.824i	−1.92184	+	1.14158i
$586$	164.990			0.281552
$587$	156.282	−	583.254i	0.266239	−	0.993618i	−0.695248	−	0.718769i	$-0.744706\pi$
$587$	156.282	−	583.254i	0.266239	−	0.993618i	0.961488	−	0.274848i	$-0.0886277\pi$
$588$	112.775	−	420.882i	0.191794	−	0.715785i
$589$	−425.339	−	245.570i	−0.722137	−	0.416926i
$590$	596.354	+	210.605i	1.01077	+	0.356958i
$591$	−1038.72	−	599.706i	−1.75757	−	1.01473i
$592$	−58.7870	+	15.7519i	−0.0993023	+	0.0266080i
$593$	−411.061	+	411.061i	−0.693189	+	0.693189i	−0.962932	−	0.269744i	$-0.913061\pi$
$593$	−411.061	+	411.061i	−0.693189	+	0.693189i	0.269744	+	0.962932i	$0.413061\pi$
$594$	1438.47	+	830.502i	2.42167	+	1.39815i
$595$	−101.034	−	69.3112i	−0.169805	−	0.116489i
$596$	−17.6359	+	10.1821i	−0.0295905	+	0.0170841i
$597$	−56.6253	+	56.6253i	−0.0948497	+	0.0948497i
$598$	118.932	−	10.7429i	0.198883	−	0.0179648i
$599$		−	724.726i		−	1.20989i	−0.796266	−	0.604947i	$-0.793194\pi$
$599$		−	724.726i		−	1.20989i	0.796266	−	0.604947i	$-0.206806\pi$
$600$	376.966	+	59.0439i	0.628276	+	0.0984064i
$601$	−7.90031	−	13.6837i	−0.0131453	−	0.0227683i	0.859378	−	0.511341i	$-0.170851\pi$
$601$	−7.90031	−	13.6837i	−0.0131453	−	0.0227683i	−0.872523	+	0.488573i	$0.837518\pi$
$602$	−12.0442	−	44.9497i	−0.0200070	−	0.0746672i
$603$	860.985	−	860.985i	1.42784	−	1.42784i
$604$	−110.398	+	191.214i	−0.182777	+	0.316580i
$605$	−101.768	+	1307.40i	−0.168212	+	2.16100i
$606$		−	664.747i		−	1.09694i
$607$	303.639	+	1133.19i	0.500228	+	1.86688i	0.498519	+	0.866879i	$0.333877\pi$
$607$	303.639	+	1133.19i	0.500228	+	1.86688i	0.00170908	+	0.999999i	$0.499456\pi$
$608$	16.8138	−	62.7498i	0.0276542	−	0.103207i
$609$	−116.535	−	201.844i	−0.191354	−	0.331435i
$610$	−567.806	−	200.523i	−0.930829	−	0.328727i
$611$	−507.828	−	88.0692i	−0.831142	−	0.144139i
$612$	−237.383	+	237.383i	−0.387881	+	0.387881i
$613$	−599.986	−	160.766i	−0.978770	−	0.262260i	−0.266243	−	0.963906i	$-0.585782\pi$
$613$	−599.986	−	160.766i	−0.978770	−	0.262260i	−0.712526	+	0.701645i	$0.752449\pi$
$614$	336.903	−	194.511i	0.548701	−	0.316793i
$615$	453.612	+	530.191i	0.737580	+	0.862099i
$616$			162.627i			0.264005i
$617$	1135.59	−	304.281i	1.84051	−	0.493162i	0.841608	−	0.540089i	$-0.181609\pi$
$617$	1135.59	−	304.281i	1.84051	−	0.493162i	0.998898	+	0.0469263i	$0.0149426\pi$
$618$	91.3326	+	340.858i	0.147787	+	0.551550i
$619$	564.525			0.911995			0.455997	−	0.889981i	$-0.349283\pi$
$619$	564.525			0.911995			0.455997	+	0.889981i	$0.349283\pi$
$620$	33.1896	−	426.382i	0.0535317	−	0.687713i
$621$	194.840	+	337.472i	0.313751	+	0.543433i
$622$	−37.2223	+	138.915i	−0.0598429	+	0.223337i
$623$	297.356	+	297.356i	0.477297	+	0.477297i
$624$	−179.758	+	215.457i	−0.288074	+	0.345284i
$625$	−132.038	−	610.894i	−0.211261	−	0.977430i
$626$	162.696	−	93.9325i	0.259897	−	0.150052i
$627$	−1171.85	−	313.995i	−1.86897	−	0.500790i
$628$	560.016	−	150.056i	0.891745	−	0.238942i
$629$	−126.949			−0.201827
$630$	32.4230	−	416.533i	0.0514651	−	0.661164i
$631$	115.091	+	66.4477i	0.182394	+	0.105305i	0.588417	−	0.808558i	$-0.299751\pi$
$631$	115.091	+	66.4477i	0.182394	+	0.105305i	−0.406023	+	0.913863i	$0.633085\pi$
$632$	−69.8030	−	69.8030i	−0.110448	−	0.110448i
$633$	−1078.14	+	288.887i	−1.70322	+	0.456377i
$634$	−443.657	+	256.146i	−0.699775	+	0.404015i
$635$	68.7410	−	12.8013i	0.108254	−	0.0201595i
$636$	−1089.96			−1.71377
$637$	220.477	−	476.315i	0.346118	−	0.747746i
$638$	−287.915	−	287.915i	−0.451278	−	0.451278i
$639$	61.0698	+	105.776i	0.0955708	+	0.165534i
$640$	55.6124	−	10.3564i	0.0868945	−	0.0161819i
$641$	490.757	−	850.015i	0.765611	−	1.32608i	−0.174312	−	0.984690i	$-0.555770\pi$
$641$	490.757	−	850.015i	0.765611	−	1.32608i	0.939923	−	0.341387i	$-0.110897\pi$
$642$	−69.0459	−	69.0459i	−0.107548	−	0.107548i
$643$	2.74709	+	10.2523i	0.00427230	+	0.0159444i	0.968029	−	0.250838i	$-0.0807061\pi$
$643$	2.74709	+	10.2523i	0.00427230	+	0.0159444i	−0.963757	+	0.266782i	$0.914039\pi$
$644$	−19.0765	+	33.0415i	−0.0296219	+	0.0513067i
$645$	130.373	+	272.731i	0.202128	+	0.422838i
$646$	67.7535	−	117.352i	0.104882	−	0.181660i
$647$	−316.134	−	84.7079i	−0.488615	−	0.130924i	0.00609613	−	0.999981i	$-0.498060\pi$
$647$	−316.134	−	84.7079i	−0.488615	−	0.130924i	−0.494711	+	0.869057i	$0.664726\pi$
$648$	−389.777	−	104.441i	−0.601508	−	0.161174i
$649$		−	1751.03i		−	2.69805i
$650$	435.252	+	147.667i	0.669619	+	0.227180i
$651$	−677.774			−1.04113
$652$	86.8374	−	324.082i	0.133186	−	0.497058i
$653$	151.210	−	564.324i	0.231562	−	0.864202i	−0.748106	−	0.663579i	$-0.769037\pi$
$653$	151.210	−	564.324i	0.231562	−	0.864202i	0.979669	−	0.200623i	$-0.0642966\pi$
$654$	−272.776	−	157.487i	−0.417089	−	0.240806i
$655$	567.633	−	271.344i	0.866615	−	0.414266i
$656$	89.5871	+	51.7231i	0.136566	+	0.0788462i
$657$	−1726.54	+	462.626i	−2.62792	+	0.704149i
$658$	116.440	−	116.440i	0.176960	−	0.176960i
$659$	847.322	+	489.202i	1.28577	+	0.742340i	0.977897	−	0.209088i	$-0.0670495\pi$
$659$	847.322	+	489.202i	1.28577	+	0.742340i	0.307873	+	0.951427i	$0.400383\pi$
$660$	−193.405	−	1038.56i	−0.293038	−	1.57357i
$661$	585.618	−	338.107i	0.885958	−	0.511508i	0.0133400	−	0.999911i	$-0.495754\pi$
$661$	585.618	−	338.107i	0.885958	−	0.511508i	0.872618	+	0.488403i	$0.162420\pi$
$662$	319.848	−	319.848i	0.483155	−	0.483155i
$663$	−478.499	+	337.062i	−0.721719	+	0.508389i
$664$		−	187.577i		−	0.282495i
$665$	30.8740	+	165.789i	0.0464271	+	0.249306i
$666$	−216.444	−	374.891i	−0.324990	−	0.562900i
$667$	−24.7236	−	92.2698i	−0.0370669	−	0.138336i
$668$	−333.870	+	333.870i	−0.499806	+	0.499806i
$669$	350.138	−	606.456i	0.523375	−	0.906512i
$670$	−426.679	−	33.2127i	−0.636835	−	0.0495713i
$671$			1667.21i			2.48466i
$672$	−23.2031	−	86.5950i	−0.0345284	−	0.128862i
$673$	−2.63439	+	9.83169i	−0.00391441	+	0.0146088i	−0.967855	−	0.251507i	$-0.919074\pi$
$673$	−2.63439	+	9.83169i	−0.00391441	+	0.0146088i	0.963941	+	0.266116i	$0.0857404\pi$
$674$	16.1158	+	27.9134i	0.0239107	+	0.0414146i
$675$	159.330	+	1491.34i	0.236044	+	2.20940i
$676$	−257.695	+	218.718i	−0.381205	+	0.323547i
$677$	694.271	−	694.271i	1.02551	−	1.02551i	0.0258444	−	0.999666i	$-0.491773\pi$
$677$	694.271	−	694.271i	1.02551	−	1.02551i	0.999666	−	0.0258444i	$-0.00822746\pi$
$678$	−636.170	−	170.461i	−0.938304	−	0.251418i
$679$	−457.448	+	264.108i	−0.673708	+	0.388966i
$680$	117.640	+	9.15713i	0.173000	+	0.0134664i
$681$			523.728i			0.769057i
$682$	−1143.73	+	306.461i	−1.67702	+	0.449357i
$683$	105.339	+	393.130i	0.154230	+	0.575593i	0.999170	+	0.0407323i	$0.0129691\pi$
$683$	105.339	+	393.130i	0.154230	+	0.575593i	−0.844941	+	0.534860i	$0.820364\pi$
$684$	462.068			0.675538
$685$	−267.993	+	229.285i	−0.391231	+	0.334723i
$686$	185.606	+	321.479i	0.270563	+	0.468629i
$687$	25.8606	−	96.5130i	0.0376428	−	0.140485i
$688$	31.6897	+	31.6897i	0.0460606	+	0.0460606i
$689$	−1293.63	−	224.345i	−1.87754	−	0.325609i
$690$	82.5303	−	233.694i	0.119609	−	0.338687i
$691$	1074.25	−	620.218i	1.55463	−	0.897566i	0.556874	−	0.830597i	$-0.312000\pi$
$691$	1074.25	−	620.218i	1.55463	−	0.897566i	0.997755	−	0.0669691i	$-0.0213329\pi$
$692$	388.211	+	104.021i	0.560998	+	0.150319i
$693$	−1117.31	+	299.382i	−1.61228	+	0.432009i
$694$	−103.682			−0.149398
$695$	−112.494	−	8.75656i	−0.161862	−	0.0125994i
$696$	194.387	+	112.229i	0.279291	+	0.161249i
$697$	152.578	+	152.578i	0.218907	+	0.218907i
$698$	327.047	−	87.6319i	0.468548	−	0.125547i
$699$	−163.671	+	94.4952i	−0.234150	+	0.135186i
$700$	−118.653	+	86.5177i	−0.169505	+	0.123597i
$701$	1137.98			1.62337			0.811683	−	0.584098i	$-0.198552\pi$
$701$	1137.98			1.62337			0.811683	+	0.584098i	$0.198552\pi$
$702$	−1000.93	−	463.314i	−1.42583	−	0.659991i
$703$	123.554	+	123.554i	0.175752	+	0.175752i
$704$	−78.3093	−	135.636i	−0.111235	−	0.192664i
$705$	−605.124	+	882.078i	−0.858332	+	1.25117i
$706$	302.143	−	523.326i	0.427964	−	0.741256i
$707$	180.901	+	180.901i	0.255871	+	0.255871i
$708$	249.831	+	932.383i	0.352869	+	1.31693i
$709$	−40.3782	+	69.9371i	−0.0569510	+	0.0986420i	−0.893095	−	0.449868i	$-0.851471\pi$
$709$	−40.3782	+	69.9371i	−0.0569510	+	0.0986420i	0.836144	+	0.548509i	$0.184805\pi$
$710$	14.2956	−	40.4797i	0.0201346	−	0.0570136i
$711$	351.072	−	608.075i	0.493772	−	0.855239i
$712$	−391.189	−	104.819i	−0.549423	−	0.147217i
$713$	−268.324	−	71.8972i	−0.376331	−	0.100838i
$714$		−	187.000i		−	0.261905i
$715$	−15.7796	−	1272.43i	−0.0220694	−	1.77962i
$716$	−198.237			−0.276868
$717$	174.053	−	649.574i	0.242751	−	0.905961i
$718$	71.0721	−	265.245i	0.0989862	−	0.369421i
$719$	−1010.54	−	583.435i	−1.40548	−	0.811453i	−0.410530	−	0.911847i	$-0.634656\pi$
$719$	−1010.54	−	583.435i	−1.40548	−	0.811453i	−0.994948	+	0.100394i	$0.967990\pi$
$720$	173.530	+	363.014i	0.241014	+	0.504186i
$721$	−117.614	−	67.9046i	−0.163126	−	0.0941811i
$722$	312.980	−	83.8628i	0.433491	−	0.116153i
$723$	−1355.28	+	1355.28i	−1.87452	+	1.87452i
$724$	−50.1342	−	28.9450i	−0.0692462	−	0.0399793i
$725$	56.8933	−	363.235i	0.0784735	−	0.501014i
$726$	−1733.31	+	1000.73i	−2.38748	+	1.37841i
$727$	−391.411	+	391.411i	−0.538392	+	0.538392i	−0.923056	−	0.384665i	$-0.874317\pi$
$727$	−391.411	+	391.411i	−0.538392	+	0.538392i	0.384665	+	0.923056i	$0.374317\pi$
$728$	−9.71500	−	107.552i	−0.0133448	−	0.147736i
$729$			43.3774i			0.0595026i
$730$	518.066	+	355.404i	0.709680	+	0.486855i
$731$	46.7408	+	80.9575i	0.0639409	+	0.110749i
$732$	−237.872	−	887.749i	−0.324961	−	1.21277i
$733$	218.569	−	218.569i	0.298184	−	0.298184i	−0.542118	−	0.840302i	$-0.682378\pi$
$733$	218.569	−	218.569i	0.298184	−	0.298184i	0.840302	+	0.542118i	$0.182378\pi$
$734$	−62.9842	+	109.092i	−0.0858095	+	0.148626i
$735$	−708.167	−	827.721i	−0.963493	−	1.12615i
$736$		−	36.7434i		−	0.0499232i
$737$	306.675	+	1144.53i	0.416112	+	1.55295i
$738$	−190.436	+	710.716i	−0.258043	+	0.963029i
$739$	−368.379	−	638.051i	−0.498483	−	0.863398i	0.501515	−	0.865149i	$-0.332776\pi$
$739$	−368.379	−	638.051i	−0.498483	−	0.863398i	−0.999998	+	0.00175039i	$0.999443\pi$
$740$	−50.6665	+	143.468i	−0.0684682	+	0.193876i
$741$	793.747	+	137.654i	1.07118	+	0.185768i
$742$	296.616	−	296.616i	0.399752	−	0.399752i
$743$	−353.572	−	94.7393i	−0.475871	−	0.127509i	0.0129085	−	0.999917i	$-0.495891\pi$
$743$	−353.572	−	94.7393i	−0.475871	−	0.127509i	−0.488779	+	0.872407i	$0.662558\pi$
$744$	565.284	−	326.367i	0.759790	−	0.438665i
$745$	−3.95093	+	50.7570i	−0.00530326	+	0.0681302i
$746$			76.9328i			0.103127i
$747$	1288.72	−	345.312i	1.72520	−	0.462266i
$748$	−84.5537	−	315.559i	−0.113040	−	0.421870i
$749$	37.5796			0.0501731
$750$	654.845	−	693.623i	0.873126	−	0.924830i
$751$	−361.945	−	626.907i	−0.481950	−	0.834763i	0.517835	−	0.855481i	$-0.326738\pi$
$751$	−361.945	−	626.907i	−0.481950	−	0.834763i	−0.999785	+	0.0207179i	$0.993405\pi$
$752$	−41.0454	+	153.183i	−0.0545816	+	0.203701i
$753$	926.953	+	926.953i	1.23101	+	1.23101i
$754$	207.610	+	173.211i	0.275344	+	0.229722i
$755$	238.063	+	498.012i	0.315316	+	0.659619i
$756$	305.181	−	176.196i	0.403678	−	0.233064i
$757$	55.5216	+	14.8770i	0.0733443	+	0.0196525i	0.295305	−	0.955403i	$-0.404579\pi$
$757$	55.5216	+	14.8770i	0.0733443	+	0.0196525i	−0.221960	+	0.975056i	$0.571246\pi$
$758$	−616.640	+	165.228i	−0.813509	+	0.217979i
$759$	−686.180			−0.904058
$760$	−105.582	−	123.406i	−0.138923	−	0.162376i
$761$	784.111	+	452.706i	1.03037	+	0.594884i	0.917090	−	0.398680i	$-0.130531\pi$
$761$	784.111	+	452.706i	1.03037	+	0.594884i	0.113278	+	0.993563i	$0.463865\pi$
$762$	75.4621	+	75.4621i	0.0990316	+	0.0990316i
$763$	117.090	−	31.3741i	0.153460	−	0.0411194i
$764$	231.596	−	133.712i	0.303136	−	0.175015i
$765$	153.653	+	825.092i	0.200853	+	1.07855i
$766$	−367.132			−0.479284
$767$	104.603	+	1158.03i	0.136379	+	1.50982i
$768$	61.0499	+	61.0499i	0.0794921	+	0.0794921i
$769$	−399.094	−	691.250i	−0.518977	−	0.898895i	−0.999757	−	0.0220535i	$-0.992980\pi$
$769$	−399.094	−	691.250i	−0.518977	−	0.898895i	0.480779	−	0.876842i	$-0.340354\pi$
$770$	335.260	+	229.995i	0.435403	+	0.298695i
$771$	452.044	−	782.964i	0.586309	−	1.01552i
$772$	201.409	+	201.409i	0.260893	+	0.260893i
$773$	319.664	+	1193.00i	0.413537	+	1.54334i	0.787748	+	0.615998i	$0.211247\pi$
$773$	319.664	+	1193.00i	0.413537	+	1.54334i	−0.374210	+	0.927344i	$0.622086\pi$
$774$	−159.383	+	276.059i	−0.205921	+	0.356665i
$775$	−832.060	−	671.433i	−1.07363	−	0.866365i
$776$	254.350	−	440.547i	0.327771	−	0.567715i
$777$	232.914	+	62.4091i	0.299760	+	0.0803205i
$778$	306.878	+	82.2277i	0.394445	+	0.105691i
$779$		−	296.994i		−	0.381251i
$780$	189.948	+	675.287i	0.243523	+	0.865752i
$781$	−118.858			−0.152186
$782$	19.8367	−	74.0315i	0.0253666	−	0.0946695i
$783$	−228.354	+	852.231i	−0.291640	+	1.08842i
$784$	−139.861	−	80.7488i	−0.178394	−	0.102996i
$785$	482.659	−	1366.71i	0.614852	−	1.74103i
$786$	831.596	+	480.122i	1.05801	+	0.610843i
$787$	658.007	−	176.312i	0.836095	−	0.224031i	0.184724	−	0.982790i	$-0.440861\pi$
$787$	658.007	−	176.312i	0.836095	−	0.224031i	0.651371	+	0.758760i	$0.274194\pi$
$788$	−314.343	+	314.343i	−0.398912	+	0.398912i
$789$	22.1272	+	12.7751i	0.0280446	+	0.0161915i
$790$	−242.620	+	45.1818i	−0.307113	+	0.0571922i
$791$	219.513	−	126.736i	0.277513	−	0.160222i
$792$	787.709	−	787.709i	0.994582	−	0.994582i
$793$	−99.5956	−	1102.59i	−0.125593	−	1.39041i
$794$		−	138.178i		−	0.174027i
$795$	−1541.47	+	2246.98i	−1.93896	+	2.82639i
$796$	14.8404	+	25.7043i	0.0186437	+	0.0322919i
$797$	111.400	+	415.752i	0.139775	+	0.521646i	0.999933	+	0.0116183i	$0.00369831\pi$
$797$	111.400	+	415.752i	0.139775	+	0.521646i	−0.860158	+	0.510028i	$0.829635\pi$
$798$	−181.998	+	181.998i	−0.228068	+	0.228068i
$799$	−165.398	+	286.478i	−0.207007	+	0.358546i
$800$	57.2999	−	129.293i	0.0716249	−	0.161616i
$801$		−	2880.58i		−	3.59623i
$802$	58.8695	+	219.704i	0.0734034	+	0.273945i
$803$	450.195	−	1680.15i	0.560642	−	2.09234i
$804$	−326.594	−	565.677i	−0.406211	−	0.703579i
$805$	41.1370	+	86.0557i	0.0511018	+	0.106902i
$806$	738.087	−	270.999i	0.915741	−	0.336227i
$807$	−402.627	+	402.627i	−0.498918	+	0.498918i
$808$	−237.985	−	63.7680i	−0.294536	−	0.0789208i
$809$	56.8706	−	32.8342i	0.0702974	−	0.0405862i	−0.464439	−	0.885605i	$-0.653744\pi$
$809$	56.8706	−	32.8342i	0.0702974	−	0.0405862i	0.534737	+	0.845019i	$0.320411\pi$
$810$	−766.550	+	655.832i	−0.946358	+	0.809669i
$811$		−	122.348i		−	0.150860i	−0.997151	−	0.0754301i	$-0.975967\pi$
$811$		−	122.348i		−	0.150860i	0.997151	−	0.0754301i	$-0.0240330\pi$
$812$	−83.4409	+	22.3579i	−0.102760	+	0.0275344i
$813$	−639.373	−	2386.17i	−0.786437	−	2.93502i
$814$	421.256			0.517513
$815$	−545.293	−	637.350i	−0.669071	−	0.782025i
$816$	90.0457	+	155.964i	0.110350	+	0.191132i
$817$	33.3015	−	124.283i	0.0407607	−	0.152121i
$818$	24.8065	+	24.8065i	0.0303258	+	0.0303258i
$819$	721.039	−	264.740i	0.880389	−	0.323247i
$820$	233.327	−	111.537i	0.284545	−	0.136020i
$821$	−1188.33	+	686.084i	−1.44742	+	0.835668i	−0.998327	−	0.0578166i	$-0.981586\pi$
$821$	−1188.33	+	686.084i	−1.44742	+	0.835668i	−0.449093	+	0.893485i	$0.648253\pi$
$822$	−519.954	−	139.321i	−0.632548	−	0.169491i
$823$	524.623	−	140.572i	0.637453	−	0.170805i	0.0744033	−	0.997228i	$-0.476295\pi$
$823$	524.623	−	140.572i	0.637453	−	0.170805i	0.563049	+	0.826423i	$0.309628\pi$
$824$	130.792			0.158728
$825$	−2414.54	−	1070.07i	−2.92671	−	1.29705i
$826$	−321.722	−	185.746i	−0.389494	−	0.224874i
$827$	413.053	+	413.053i	0.499459	+	0.499459i	0.911270	−	0.411810i	$-0.135103\pi$
$827$	413.053	+	413.053i	0.499459	+	0.499459i	−0.411810	+	0.911270i	$0.635103\pi$
$828$	252.442	−	67.6415i	0.304881	−	0.0816927i
$829$	−640.051	+	369.534i	−0.772076	+	0.445759i	−0.833615	−	0.552346i	$-0.813733\pi$
$829$	−640.051	+	369.534i	−0.772076	+	0.445759i	0.0615384	+	0.998105i	$0.480399\pi$
$830$	−386.694	−	265.280i	−0.465897	−	0.319615i
$831$	−1947.14			−2.34313
$832$	59.8917	+	85.0234i	0.0719853	+	0.102192i
$833$	−238.201	−	238.201i	−0.285956	−	0.285956i
$834$	−86.1067	−	149.141i	−0.103245	−	0.178826i
$835$	216.107	+	1160.46i	0.258810	+	1.38977i
$836$	−224.826	+	389.410i	−0.268931	+	0.465802i
$837$	1814.25	+	1814.25i	2.16757	+	2.16757i
$838$	137.336	+	512.546i	0.163886	+	0.611630i
$839$	−620.501	+	1074.74i	−0.739572	+	1.28098i	0.213116	+	0.977027i	$0.431639\pi$
$839$	−620.501	+	1074.74i	−0.739572	+	1.28098i	−0.952688	+	0.303950i	$0.901694\pi$
$840$	−211.333	−	74.6333i	−0.251587	−	0.0888492i
$841$	−312.359	+	541.021i	−0.371413	+	0.643307i
$842$	723.266	+	193.798i	0.858985	+	0.230164i
$843$	596.057	+	159.713i	0.707066	+	0.189458i
$844$			413.696i			0.490161i
$845$	86.4479	+	840.566i	0.102305	+	0.994753i
$846$	−1127.99			−1.33332
$847$	199.362	−	744.028i	0.235374	−	0.878428i
$848$	−104.558	+	390.215i	−0.123299	+	0.460159i
$849$	1835.96	+	1059.99i	2.16249	+	1.24851i
$850$	185.251	−	229.568i	0.217942	−	0.270080i
$851$	85.5880	+	49.4142i	0.100573	+	0.0580661i
$852$	63.2889	−	16.9582i	0.0742827	−	0.0199040i
$853$	76.7120	−	76.7120i	0.0899321	−	0.0899321i	−0.660710	−	0.750642i	$-0.729745\pi$
$853$	76.7120	−	76.7120i	0.0899321	−	0.0899321i	0.750642	+	0.660710i	$0.229745\pi$
$854$	306.321	+	176.854i	0.358690	+	0.207090i
$855$	653.480	−	952.566i	0.764304	−	1.11411i
$856$	−31.3425	+	18.0956i	−0.0366151	+	0.0211397i
$857$	133.544	−	133.544i	0.155827	−	0.155827i	−0.624888	−	0.780715i	$-0.714855\pi$
$857$	133.544	−	133.544i	0.155827	−	0.155827i	0.780715	+	0.624888i	$0.214855\pi$
$858$	1587.80	−	1118.47i	1.85059	−	1.30358i
$859$		−	574.099i		−	0.668334i	−0.942514	−	0.334167i	$-0.891545\pi$
$859$		−	574.099i		−	0.668334i	0.942514	−	0.334167i	$-0.108455\pi$
$860$	110.146	−	20.5120i	0.128077	−	0.0238512i
$861$	−204.927	−	354.944i	−0.238010	−	0.412246i
$862$	168.210	+	627.767i	0.195139	+	0.728268i
$863$	425.311	−	425.311i	0.492828	−	0.492828i	−0.416368	−	0.909196i	$-0.636697\pi$
$863$	425.311	−	425.311i	0.492828	−	0.492828i	0.909196	+	0.416368i	$0.136697\pi$
$864$	−169.686	+	293.906i	−0.196396	+	0.340169i
$865$	763.469	−	653.196i	0.882623	−	0.755140i
$866$			331.111i			0.382345i
$867$	−306.395	−	1143.48i	−0.353397	−	1.31890i
$868$	−65.0177	+	242.649i	−0.0749051	+	0.279550i
$869$	341.639	+	591.736i	0.393140	+	0.680939i
$870$	506.275	−	242.013i	0.581926	−	0.278176i
$871$	−271.188	−	738.601i	−0.311352	−	0.847992i
$872$	−82.5488	+	82.5488i	−0.0946661	+	0.0946661i
$873$	3494.97	+	936.473i	4.00340	+	1.07271i
$874$	−91.3575	+	52.7453i	−0.104528	+	0.0603493i
$875$	10.5528	+	366.965i	0.0120604	+	0.419389i
$876$			958.874i			1.09460i
$877$	−145.490	+	38.9839i	−0.165895	+	0.0444514i	−0.340810	−	0.940132i	$-0.610701\pi$
$877$	−145.490	+	38.9839i	−0.165895	+	0.0444514i	0.174916	+	0.984583i	$0.444035\pi$
$878$	296.641	+	1107.08i	0.337860	+	1.26091i
$879$	629.538			0.716198
$880$	−390.366	−	30.3861i	−0.443597	−	0.0345297i
$881$	82.4836	+	142.866i	0.0936249	+	0.162163i	0.909034	−	0.416722i	$-0.136821\pi$
$881$	82.4836	+	142.866i	0.0936249	+	0.162163i	−0.815409	+	0.578885i	$0.803488\pi$
$882$	297.303	−	1109.55i	0.337079	−	1.25799i
$883$	−737.915	−	737.915i	−0.835691	−	0.835691i	0.152597	−	0.988288i	$-0.451236\pi$
$883$	−737.915	−	737.915i	−0.835691	−	0.835691i	−0.988288	+	0.152597i	$0.951236\pi$
$884$	74.7696	+	203.641i	0.0845810	+	0.230363i
$885$	2275.46	+	803.589i	2.57114	+	0.908011i
$886$	−560.025	+	323.330i	−0.632082	+	0.364933i
$887$	−895.341	−	239.906i	−1.00940	−	0.270469i	−0.284024	−	0.958817i	$-0.591669\pi$
$887$	−895.341	−	239.906i	−1.00940	−	0.270469i	−0.725380	+	0.688348i	$0.758336\pi$
$888$	−224.309	+	60.1033i	−0.252600	+	0.0676839i
$889$	−41.0717			−0.0461999
$890$	−769.326	+	658.207i	−0.864411	+	0.739558i
$891$	2418.87	+	1396.53i	2.71478	+	1.56738i
$892$	−183.529	−	183.529i	−0.205750	−	0.205750i
$893$	439.790	−	117.841i	0.492486	−	0.131961i
$894$	−67.2920	+	38.8511i	−0.0752707	+	0.0434576i
$895$	−280.357	+	408.672i	−0.313248	+	0.456616i
$896$	−33.2276			−0.0370844
$897$	453.799	−	40.9910i	0.505908	−	0.0456978i
$898$	526.356	+	526.356i	0.586143	+	0.586143i
$899$	−314.479	−	544.694i	−0.349810	−	0.605889i
$900$	993.778	+	155.655i	1.10420	+	0.172950i
$901$	−421.330	+	729.766i	−0.467625	+	0.809951i
$902$	−506.300	−	506.300i	−0.561308	−	0.561308i
$903$	−45.9562	−	171.511i	−0.0508928	−	0.189934i
$904$	−122.053	+	211.403i	−0.135015	+	0.233852i
$905$	−130.573	+	62.4176i	−0.144280	+	0.0689697i
$906$	−421.235	+	729.600i	−0.464939	+	0.805298i
$907$	−481.560	−	129.034i	−0.530937	−	0.142264i	−0.0166162	−	0.999862i	$-0.505289\pi$
$907$	−481.560	−	129.034i	−0.530937	−	0.142264i	−0.514321	+	0.857598i	$0.671956\pi$
$908$	187.499	+	50.2403i	0.206497	+	0.0553307i
$909$		−	1752.44i		−	1.92788i
$910$	−235.461	−	132.078i	−0.258748	−	0.145140i
$911$	1203.93			1.32155			0.660776	−	0.750583i	$-0.270227\pi$
$911$	1203.93			1.32155			0.660776	+	0.750583i	$0.270227\pi$
$912$	64.1549	−	239.429i	0.0703453	−	0.262532i
$913$	−336.034	+	1254.10i	−0.368055	+	1.37360i
$914$	376.794	+	217.542i	0.412247	+	0.238011i
$915$	−2166.53	−	765.121i	−2.36779	−	0.836198i
$916$	−32.0718	−	18.5166i	−0.0350128	−	0.0202147i
$917$	−356.965	+	95.6484i	−0.389274	+	0.104306i
$918$	−500.559	+	500.559i	−0.545271	+	0.545271i
$919$	−478.714	−	276.385i	−0.520907	−	0.300746i	0.216399	−	0.976305i	$-0.430569\pi$
$919$	−478.714	−	276.385i	−0.520907	−	0.300746i	−0.737306	+	0.675559i	$0.763902\pi$
$920$	−75.7476	−	51.9644i	−0.0823344	−	0.0564831i
$921$	1285.49	−	742.179i	1.39576	−	0.805841i
$922$	−618.009	+	618.009i	−0.670292	+	0.670292i
$923$	78.6054	−	7.10031i	0.0851630	−	0.00769264i
$924$			620.523i			0.671561i
$925$	224.108	+	307.350i	0.242279	+	0.332270i
$926$	−168.921	−	292.580i	−0.182420	−	0.315961i
$927$	240.776	+	898.589i	0.259737	+	0.969351i
$928$	58.8262	−	58.8262i	0.0633903	−	0.0633903i
$929$	192.343	−	333.148i	0.207043	−	0.358610i	−0.743738	−	0.668471i	$-0.766949\pi$
$929$	192.343	−	333.148i	0.207043	−	0.358610i	0.950782	+	0.309861i	$0.100283\pi$
$930$	126.639	−	1626.91i	0.136171	−	1.74937i
$931$			463.660i			0.498024i
$932$	18.1295	+	67.6603i	0.0194523	+	0.0725969i
$933$	−142.026	+	530.048i	−0.152225	+	0.568112i
$934$	438.000	+	758.638i	0.468951	+	0.812246i
$935$	−770.113	−	271.969i	−0.823650	−	0.290876i
$936$	−473.888	+	568.000i	−0.506291	+	0.606838i
$937$	−414.800	+	414.800i	−0.442689	+	0.442689i	−0.892915	−	0.450225i	$-0.851344\pi$
$937$	−414.800	+	414.800i	−0.442689	+	0.442689i	0.450225	+	0.892915i	$0.351344\pi$
$938$	242.818	+	65.0629i	0.258868	+	0.0693635i
$939$	620.785	−	358.410i	0.661113	−	0.381694i
$940$	257.743	+	301.256i	0.274195	+	0.320485i
$941$			1399.54i			1.48729i	0.668572	+	0.743647i	$0.266906\pi$
$941$			1399.54i			1.48729i	−0.668572	+	0.743647i	$0.733094\pi$
$942$	2136.81	−	572.556i	2.26837	−	0.607809i
$943$	−43.4766	−	162.257i	−0.0461046	−	0.172065i
$944$	357.767			0.378991
$945$	68.3688	−	878.324i	0.0723479	−	0.929443i
$946$	−155.100	−	268.641i	−0.163953	−	0.283976i
$947$	174.525	−	651.335i	0.184292	−	0.687788i	−0.810489	−	0.585754i	$-0.800798\pi$
$947$	174.525	−	651.335i	0.184292	−	0.687788i	0.994781	−	0.102034i	$-0.0325350\pi$
$948$	−266.341	−	266.341i	−0.280951	−	0.280951i
$949$	−197.364	+	1138.05i	−0.207970	+	1.19921i
$950$	−403.724	+	43.1323i	−0.424972	+	0.0454024i
$951$	−1692.83	+	977.354i	−1.78005	+	1.02771i
$952$	−66.9478	−	17.9386i	−0.0703233	−	0.0188431i
$953$	−699.293	+	187.375i	−0.733781	+	0.196616i	−0.606312	−	0.795227i	$-0.707352\pi$
$953$	−699.293	+	187.375i	−0.733781	+	0.196616i	−0.127468	+	0.991843i	$0.540685\pi$
$954$	−2873.41			−3.01196
$955$	51.8837	−	666.543i	0.0543285	−	0.697950i
$956$	−215.857	−	124.625i	−0.225791	−	0.130361i
$957$	−1098.57	−	1098.57i	−1.14794	−	1.14794i
$958$	−1050.14	+	281.385i	−1.09618	+	0.293721i
$959$	179.412	−	103.584i	0.187082	−	0.108012i
$960$	212.196	−	39.5162i	0.221037	−	0.0411627i
$961$	−868.034			−0.903261
$962$	−278.594	+	25.1649i	−0.289598	+	0.0261590i
$963$	−182.023	−	182.023i	−0.189016	−	0.189016i
$964$	355.192	+	615.210i	0.368456	+	0.638185i
$965$	700.054	−	130.368i	0.725445	−	0.135096i
$966$	−72.7887	+	126.074i	−0.0753506	+	0.130511i
$967$	−817.829	−	817.829i	−0.845738	−	0.845738i	0.143860	−	0.989598i	$-0.454048\pi$
$967$	−817.829	−	817.829i	−0.845738	−	0.845738i	−0.989598	+	0.143860i	$0.954048\pi$
$968$	191.996	+	716.540i	0.198343	+	0.740227i
$969$	258.521	−	447.772i	0.266792	−	0.462097i
$970$	−548.485	−	1147.39i	−0.565449	−	1.18288i
$971$	681.090	−	1179.68i	0.701432	−	1.21492i	−0.266532	−	0.963826i	$-0.585878\pi$
$971$	681.090	−	1179.68i	0.701432	−	1.21492i	0.967964	−	0.251090i	$-0.0807889\pi$
$972$	−444.160	−	119.012i	−0.456954	−	0.122441i
$973$	64.0192	+	17.1539i	0.0657957	+	0.0176299i
$974$		−	508.309i		−	0.521877i
$975$	1660.76	+	563.441i	1.70334	+	0.577889i
$976$	−340.641			−0.349017
$977$	146.241	−	545.780i	0.149684	−	0.558628i	−0.849818	−	0.527076i	$-0.823288\pi$
$977$	146.241	−	545.780i	0.149684	−	0.558628i	0.999502	−	0.0315521i	$-0.0100450\pi$
$978$	331.338	−	1236.57i	0.338792	−	1.26439i
$979$	2427.63	+	1401.59i	2.47970	+	1.43166i
$980$	−364.265	+	174.128i	−0.371699	+	0.177682i
$981$	−719.108	−	415.177i	−0.733035	−	0.423218i
$982$	1100.92	−	294.990i	1.12110	−	0.300397i
$983$	−172.937	+	172.937i	−0.175928	+	0.175928i	−0.789578	−	0.613650i	$-0.789701\pi$
$983$	−172.937	+	172.937i	−0.175928	+	0.175928i	0.613650	+	0.789578i	$0.289701\pi$
$984$	341.830	+	197.356i	0.347388	+	0.200565i
$985$	203.467	+	1092.59i	0.206565	+	1.10922i
$986$	150.283	−	86.7659i	0.152417	−	0.0879979i
$987$	444.291	−	444.291i	0.450142	−	0.450142i
$988$	125.424	−	270.964i	0.126948	−	0.274255i
$989$		−	72.7744i		−	0.0735838i
$990$	−509.866	−	2737.90i	−0.515016	−	2.76556i
$991$	−281.275	−	487.183i	−0.283830	−	0.491607i	0.688495	−	0.725241i	$-0.258272\pi$
$991$	−281.275	−	487.183i	−0.283830	−	0.491607i	−0.972325	+	0.233634i	$0.924938\pi$
$992$	−62.6155	−	233.684i	−0.0631205	−	0.235569i
$993$	1220.42	−	1220.42i	1.22902	−	1.22902i
$994$	−12.6082	+	21.8380i	−0.0126843	+	0.0219699i
$995$	73.9782	+	5.75847i	0.0743499	+	0.00578740i
$996$		−	715.721i		−	0.718595i
$997$	200.356	+	747.738i	0.200959	+	0.749988i	0.990643	+	0.136475i	$0.0435774\pi$
$997$	200.356	+	747.738i	0.200959	+	0.749988i	−0.789685	+	0.613513i	$0.789756\pi$
$998$	170.624	−	636.776i	0.170966	−	0.638052i
$999$	−456.404	−	790.515i	−0.456861	−	0.791306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.3.r.a.23.7	yes	28
5.2	odd	4		130.3.r.b.127.1	yes	28
13.4	even	6		130.3.r.b.43.1	yes	28
65.17	odd	12	inner	130.3.r.a.17.7	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.3.r.a.17.7	✓	28	65.17	odd	12	inner
130.3.r.a.23.7	yes	28	1.1	even	1	trivial
130.3.r.b.43.1	yes	28	13.4	even	6
130.3.r.b.127.1	yes	28	5.2	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	130.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(1.39661 - 5.21223i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-4.51108 + 2.15642i) q^{5} +(-6.60884 - 3.81562i) q^{6} +(2.83686 - 0.760135i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-17.4226 - 10.0589i) q^{9} +(1.29455 + 6.95156i) q^{10} +(16.9545 - 9.78866i) q^{11} +(-7.63124 + 7.63124i) q^{12} +(-10.6279 + 7.48647i) q^{13} -4.15345i q^{14} +(4.93952 + 26.5245i) q^{15} +(2.00000 + 3.46410i) q^{16} +(2.15948 + 8.05929i) q^{17} +(-20.1179 + 20.1179i) q^{18} +(5.74201 - 9.94544i) q^{19} +(9.96984 + 0.776053i) q^{20} -15.8480i q^{21} +(-7.16580 - 26.7431i) q^{22} +(1.68113 - 6.27406i) q^{23} +(7.63124 + 13.2177i) q^{24} +(15.6997 - 19.4556i) q^{25} +(6.33661 + 17.2583i) q^{26} +(-42.4216 + 42.4216i) q^{27} +(-5.67372 - 1.52027i) q^{28} +(12.7363 - 7.35328i) q^{29} +(38.0411 + 2.96112i) q^{30} -42.7672i q^{31} +(5.46410 - 1.46410i) q^{32} +(-27.3420 - 102.042i) q^{33} +11.7996 q^{34} +(-11.1581 + 9.54649i) q^{35} +(20.1179 + 34.8452i) q^{36} +(-3.93798 + 14.6967i) q^{37} +(-11.4840 - 11.4840i) q^{38} +(24.1781 + 65.8509i) q^{39} +(4.70932 - 13.3350i) q^{40} +(22.3968 - 12.9308i) q^{41} +(-21.6488 - 5.80077i) q^{42} +(10.8222 - 2.89981i) q^{43} -39.1547 q^{44} +(100.286 + 7.80628i) q^{45} +(-7.95519 - 4.59293i) q^{46} +(28.0345 + 28.0345i) q^{47} +(20.8489 - 5.58645i) q^{48} +(-34.9653 + 20.1872i) q^{49} +(-20.8303 - 28.5674i) q^{50} +45.0228 q^{51} +(25.8946 - 2.33902i) q^{52} +(71.4142 + 71.4142i) q^{53} +(42.4216 + 73.4764i) q^{54} +(-55.3745 + 80.7184i) q^{55} +(-4.15345 + 7.19399i) q^{56} +(-43.8186 - 43.8186i) q^{57} +(-5.38297 - 20.0895i) q^{58} +(44.7209 - 77.4589i) q^{59} +(17.9690 - 50.8813i) q^{60} +(-42.5801 + 73.7509i) q^{61} +(-58.4211 - 15.6539i) q^{62} +(-57.0716 - 15.2923i) q^{63} -8.00000i q^{64} +(31.7995 - 56.6903i) q^{65} -149.399 q^{66} +(-15.6648 + 58.4618i) q^{67} +(4.31896 - 16.1186i) q^{68} +(-30.3540 - 17.5249i) q^{69} +(8.95659 + 18.7366i) q^{70} +(-5.25780 - 3.03559i) q^{71} +(54.9631 - 14.7273i) q^{72} +(62.8256 - 62.8256i) q^{73} +(18.6347 + 10.7588i) q^{74} +(-79.4805 - 109.002i) q^{75} +(-19.8909 + 11.4840i) q^{76} +(40.6567 - 40.6567i) q^{77} +(98.8038 - 8.92480i) q^{78} +34.9015i q^{79} +(-16.4922 - 11.3140i) q^{80} +(71.3342 + 123.554i) q^{81} +(-9.46599 - 35.3275i) q^{82} +(-46.8941 + 46.8941i) q^{83} +(-15.8480 + 27.4495i) q^{84} +(-27.1208 - 31.6994i) q^{85} -15.8449i q^{86} +(-20.5394 - 76.6540i) q^{87} +(-14.3316 + 53.4862i) q^{88} +(71.5926 + 124.002i) q^{89} +(47.3708 - 134.136i) q^{90} +(-24.4592 + 29.3167i) q^{91} +(-9.18586 + 9.18586i) q^{92} +(-222.913 - 59.7293i) q^{93} +(48.5572 - 28.0345i) q^{94} +(-4.45610 + 57.2469i) q^{95} -30.5249i q^{96} +(-173.724 + 46.5493i) q^{97} +(14.7781 + 55.1525i) q^{98} -393.854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 14 q^{2} + 8 q^{5} + 4 q^{7} - 56 q^{8} - 48 q^{9} - 12 q^{10} - 12 q^{11} - 24 q^{13} + 10 q^{15} + 56 q^{16} + 50 q^{17} - 92 q^{18} - 36 q^{19} + 8 q^{20} + 12 q^{22} + 68 q^{23} - 6 q^{25} + 42 q^{26}+ \cdots + 16 q^{99}+O(q^{100}) \) 28 * q - 14 * q^2 + 8 * q^5 + 4 * q^7 - 56 * q^8 - 48 * q^9 - 12 * q^10 - 12 * q^11 - 24 * q^13 + 10 * q^15 + 56 * q^16 + 50 * q^17 - 92 * q^18 - 36 * q^19 + 8 * q^20 + 12 * q^22 + 68 * q^23 - 6 * q^25 + 42 * q^26 - 24 * q^27 - 8 * q^28 + 186 * q^29 + 12 * q^30 + 56 * q^32 - 164 * q^33 - 20 * q^34 - 18 * q^35 + 92 * q^36 + 24 * q^37 + 72 * q^38 + 156 * q^39 - 20 * q^40 + 48 * q^41 - 204 * q^42 + 80 * q^43 + 26 * q^45 - 96 * q^46 + 104 * q^47 + 96 * q^49 + 18 * q^50 - 336 * q^51 - 96 * q^52 + 126 * q^53 + 24 * q^54 - 502 * q^55 - 16 * q^56 + 160 * q^57 - 130 * q^58 + 80 * q^59 + 136 * q^60 - 336 * q^61 - 108 * q^62 + 396 * q^63 + 160 * q^65 - 64 * q^66 - 32 * q^67 + 100 * q^68 + 264 * q^69 + 200 * q^70 - 60 * q^71 + 188 * q^72 - 286 * q^73 + 6 * q^74 - 684 * q^75 + 24 * q^76 + 424 * q^77 + 128 * q^78 + 40 * q^80 + 86 * q^81 + 42 * q^82 - 64 * q^83 - 96 * q^84 + 356 * q^85 + 384 * q^87 + 24 * q^88 - 348 * q^89 - 294 * q^90 + 192 * q^91 + 80 * q^92 - 336 * q^93 + 432 * q^94 - 446 * q^95 - 86 * q^97 - 82 * q^98 + 16 * q^99

Introduction

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