LMFDB - Embedded newform 375.3.p.a.14.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,3,Mod(14,375)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("375.14"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([25, 43])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.p (of order $50$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2180099135$
Analytic rank:	$0$
Dimension:	$1960$
Relative dimension:	$98$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			14.10
Character	$\chi$	$=$	375.14
Dual form			375.3.p.a.134.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.43795 - 3.05579i) q^{2} +(-1.66173 + 2.49773i) q^{3} +(-4.72047 + 5.70606i) q^{4} +(3.65114 + 3.41602i) q^{5} +(10.0220 + 1.48631i) q^{6} +(9.55210 + 3.10367i) q^{7} +(11.1399 + 2.86023i) q^{8} +(-3.47729 - 8.30111i) q^{9} +(5.18850 - 16.0692i) q^{10} +(-5.42290 + 2.55182i) q^{11} +(-6.40805 - 21.2724i) q^{12} +(-1.30812 + 10.3548i) q^{13} +(-4.25125 - 33.6521i) q^{14} +(-14.5995 + 3.44304i) q^{15} +(-1.72762 - 9.05649i) q^{16} +(-2.84494 - 3.43894i) q^{17} +(-20.3663 + 22.5624i) q^{18} +(0.605069 + 9.61729i) q^{19} +(-36.7271 + 4.70841i) q^{20} +(-23.6251 + 18.7011i) q^{21} +(15.5957 + 12.9019i) q^{22} +(-35.3563 - 19.4373i) q^{23} +(-25.6556 + 23.0714i) q^{24} +(1.66161 + 24.9447i) q^{25} +(33.5232 - 10.8924i) q^{26} +(26.5122 + 5.10888i) q^{27} +(-62.8001 + 39.8541i) q^{28} +(11.8346 - 7.51046i) q^{29} +(31.5145 + 39.6621i) q^{30} +(13.8737 + 16.7704i) q^{31} +(12.0281 - 8.73896i) q^{32} +(2.63764 - 17.7854i) q^{33} +(-6.41780 + 13.6385i) q^{34} +(24.2739 + 43.9621i) q^{35} +(63.7811 + 19.3434i) q^{36} +(-58.6200 + 11.1824i) q^{37} +(28.5184 - 15.6781i) q^{38} +(-23.6899 - 20.4743i) q^{39} +(30.9026 + 48.4971i) q^{40} +(25.9044 + 47.1199i) q^{41} +(91.1183 + 45.3023i) q^{42} +(11.1497 - 15.3462i) q^{43} +(11.0377 - 42.9892i) q^{44} +(15.6607 - 42.1870i) q^{45} +(-8.55584 + 135.991i) q^{46} +(-51.9878 + 13.3482i) q^{47} +(25.4915 + 10.7343i) q^{48} +(41.9681 + 30.4916i) q^{49} +(73.8365 - 40.9467i) q^{50} +(13.3170 - 1.39129i) q^{51} +(-52.9105 - 56.3439i) q^{52} +(-24.4987 - 9.69972i) q^{53} +(-22.5115 - 88.3621i) q^{54} +(-28.5168 - 9.20768i) q^{55} +(97.5319 + 61.8957i) q^{56} +(-25.0268 - 14.4701i) q^{57} +(-39.9679 - 25.3644i) q^{58} +(-43.9810 + 46.8350i) q^{59} +(49.2702 - 99.5584i) q^{60} +(76.8956 + 42.2737i) q^{61} +(31.2973 - 66.5101i) q^{62} +(-7.45160 - 90.0854i) q^{63} +(-76.3177 - 41.9560i) q^{64} +(-40.1485 + 33.3384i) q^{65} +(-58.1411 + 17.5143i) q^{66} +(19.7463 + 12.5314i) q^{67} +33.0522 q^{68} +(107.302 - 56.0109i) q^{69} +(99.4344 - 137.391i) q^{70} +(-7.57387 - 29.4983i) q^{71} +(-14.9935 - 102.419i) q^{72} +(6.30329 + 6.71233i) q^{73} +(118.463 + 163.051i) q^{74} +(-65.0663 - 37.3012i) q^{75} +(-57.7331 - 41.9455i) q^{76} +(-59.7201 + 7.54440i) q^{77} +(-28.5005 + 101.832i) q^{78} +(-4.09345 + 65.0636i) q^{79} +(24.6294 - 38.9681i) q^{80} +(-56.8168 + 57.7308i) q^{81} +(106.739 - 146.914i) q^{82} +(8.79888 + 139.854i) q^{83} +(4.81207 - 223.084i) q^{84} +(1.36022 - 22.2744i) q^{85} +(-62.9274 - 12.0040i) q^{86} +(-0.906828 + 42.0400i) q^{87} +(-67.7092 + 12.9162i) q^{88} +(-28.4792 - 30.3273i) q^{89} +(-151.434 + 12.8069i) q^{90} +(-44.6333 + 94.8506i) q^{91} +(277.809 - 109.992i) q^{92} +(-64.9424 + 6.78480i) q^{93} +(115.545 + 139.670i) q^{94} +(-30.6437 + 37.1810i) q^{95} +(1.83999 + 44.5649i) q^{96} +(-14.3478 + 9.10536i) q^{97} +(32.8281 - 172.091i) q^{98} +(40.0400 + 36.1426i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1960 q - 20 q^{3} - 40 q^{4} - 20 q^{6} - 50 q^{7} - 20 q^{9} - 40 q^{10} - 180 q^{12} - 40 q^{13} + 20 q^{15} - 140 q^{16} - 25 q^{18} + 10 q^{19} - 65 q^{21} - 15 q^{24} - 350 q^{25} - 125 q^{27} - 320 q^{28}+ \cdots - 15 q^{99}+O(q^{100}) $ 1960 * q - 20 * q^3 - 40 * q^4 - 20 * q^6 - 50 * q^7 - 20 * q^9 - 40 * q^10 - 180 * q^12 - 40 * q^13 + 20 * q^15 - 140 * q^16 - 25 * q^18 + 10 * q^19 - 65 * q^21 - 15 * q^24 - 350 * q^25 - 125 * q^27 - 320 * q^28 - 20 * q^30 + 60 * q^31 - 45 * q^33 - 240 * q^34 - 1000 * q^36 - 160 * q^37 + 180 * q^39 - 120 * q^40 + 150 * q^42 - 50 * q^43 - 820 * q^45 + 160 * q^46 - 175 * q^48 + 2980 * q^49 - 15 * q^51 + 270 * q^52 - 345 * q^54 - 40 * q^55 - 280 * q^58 - 1305 * q^60 - 140 * q^61 - 820 * q^63 - 400 * q^64 + 355 * q^66 + 210 * q^67 - 220 * q^69 - 1250 * q^70 - 240 * q^72 + 100 * q^73 - 225 * q^75 - 30 * q^76 - 830 * q^78 + 60 * q^79 - 620 * q^81 + 1550 * q^82 + 335 * q^84 + 1540 * q^85 + 405 * q^87 + 1660 * q^88 + 705 * q^90 + 70 * q^91 - 25 * q^93 + 660 * q^94 - 595 * q^96 + 100 * q^97 - 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{43}{50}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.43795	−	3.05579i	−0.718973	−	1.52789i	−0.844354	−	0.535786i	$-0.820015\pi$
$2$	−1.43795	−	3.05579i	−0.718973	−	1.52789i	0.125381	−	0.992109i	$-0.459985\pi$
$3$	−1.66173	+	2.49773i	−0.553911	+	0.832576i
$3$	−1.66173	+	2.49773i	−0.553911	+	0.832576i
$4$	−4.72047	+	5.70606i	−1.18012	+	1.42652i
$5$	3.65114	+	3.41602i	0.730228	+	0.683204i
$5$	3.65114	+	3.41602i	0.730228	+	0.683204i
$6$	10.0220	+	1.48631i	1.67034	+	0.247718i
$7$	9.55210	+	3.10367i	1.36459	+	0.443381i	0.897572	−	0.440869i	$-0.145330\pi$
$7$	9.55210	+	3.10367i	1.36459	+	0.443381i	0.467015	+	0.884250i	$0.345330\pi$
$8$	11.1399	+	2.86023i	1.39248	+	0.357529i
$9$	−3.47729	−	8.30111i	−0.386366	−	0.922346i
$10$	5.18850	−	16.0692i	0.518850	−	1.60692i
$11$	−5.42290	+	2.55182i	−0.492991	+	0.231984i	−0.656171	−	0.754612i	$-0.727825\pi$
$11$	−5.42290	+	2.55182i	−0.492991	+	0.231984i	0.163180	+	0.986596i	$0.447825\pi$
$12$	−6.40805	−	21.2724i	−0.534004	−	1.77270i
$13$	−1.30812	+	10.3548i	−0.100625	+	0.796527i	0.858356	+	0.513055i	$0.171486\pi$
$13$	−1.30812	+	10.3548i	−0.100625	+	0.796527i	−0.958981	+	0.283472i	$0.908514\pi$
$14$	−4.25125	−	33.6521i	−0.303661	−	2.40372i
$15$	−14.5995	+	3.44304i	−0.973300	+	0.229536i
$16$	−1.72762	−	9.05649i	−0.107976	−	0.566031i
$17$	−2.84494	−	3.43894i	−0.167349	−	0.202290i	0.680171	−	0.733053i	$-0.261905\pi$
$17$	−2.84494	−	3.43894i	−0.167349	−	0.202290i	−0.847520	+	0.530763i	$0.821905\pi$
$18$	−20.3663	+	22.5624i	−1.13146	+	1.25347i
$19$	0.605069	+	9.61729i	0.0318457	+	0.506173i	0.981327	+	0.192349i	$0.0616104\pi$
$19$	0.605069	+	9.61729i	0.0318457	+	0.506173i	−0.949481	+	0.313825i	$0.898390\pi$
$20$	−36.7271	+	4.70841i	−1.83635	+	0.235421i
$21$	−23.6251	+	18.7011i	−1.12501	+	0.890528i
$22$	15.5957	+	12.9019i	0.708894	+	0.586448i
$23$	−35.3563	−	19.4373i	−1.53723	−	0.845100i	−0.999999	−	0.00166524i	$-0.999470\pi$
$23$	−35.3563	−	19.4373i	−1.53723	−	0.845100i	−0.537232	−	0.843434i	$-0.680530\pi$
$24$	−25.6556	+	23.0714i	−1.06898	+	0.961309i
$25$	1.66161	+	24.9447i	0.0664645	+	0.997789i
$26$	33.5232	−	10.8924i	1.28936	−	0.418937i
$27$	26.5122	+	5.10888i	0.981935	+	0.189218i
$28$	−62.8001	+	39.8541i	−2.24286	+	1.42336i
$29$	11.8346	−	7.51046i	0.408089	−	0.258981i	−0.315900	−	0.948793i	$-0.602306\pi$
$29$	11.8346	−	7.51046i	0.408089	−	0.258981i	0.723989	+	0.689811i	$0.242306\pi$
$30$	31.5145	+	39.6621i	1.05048	+	1.32207i
$31$	13.8737	+	16.7704i	0.447539	+	0.540982i	0.945244	−	0.326365i	$-0.105824\pi$
$31$	13.8737	+	16.7704i	0.447539	+	0.540982i	−0.497705	+	0.867346i	$0.665824\pi$
$32$	12.0281	−	8.73896i	0.375880	−	0.273093i
$33$	2.63764	−	17.7854i	0.0799286	−	0.538951i
$34$	−6.41780	+	13.6385i	−0.188759	+	0.401133i
$35$	24.2739	+	43.9621i	0.693539	+	1.25606i
$36$	63.7811	+	19.3434i	1.77170	+	0.537318i
$37$	−58.6200	+	11.1824i	−1.58432	+	0.302226i	−0.902962	−	0.429720i	$-0.858612\pi$
$37$	−58.6200	+	11.1824i	−1.58432	+	0.302226i	−0.681362	+	0.731946i	$0.738612\pi$
$38$	28.5184	−	15.6781i	0.750483	−	0.412582i
$39$	−23.6899	−	20.4743i	−0.607432	−	0.524982i
$40$	30.9026	+	48.4971i	0.772564	+	1.21243i
$41$	25.9044	+	47.1199i	0.631815	+	1.14927i	0.977504	+	0.210918i	$0.0676452\pi$
$41$	25.9044	+	47.1199i	0.631815	+	1.14927i	−0.345689	+	0.938349i	$0.612355\pi$
$42$	91.1183	+	45.3023i	2.16948	+	1.07863i
$43$	11.1497	−	15.3462i	0.259295	−	0.356888i	−0.659445	−	0.751753i	$-0.729209\pi$
$43$	11.1497	−	15.3462i	0.259295	−	0.356888i	0.918739	+	0.394865i	$0.129209\pi$
$44$	11.0377	−	42.9892i	0.250858	−	0.977027i
$45$	15.6607	−	42.1870i	0.348015	−	0.937489i
$46$	−8.55584	+	135.991i	−0.185997	+	2.95633i
$47$	−51.9878	+	13.3482i	−1.10612	+	0.284004i	−0.757224	−	0.653155i	$-0.773445\pi$
$47$	−51.9878	+	13.3482i	−1.10612	+	0.284004i	−0.348900	+	0.937160i	$0.613445\pi$
$48$	25.4915	+	10.7343i	0.531073	+	0.223632i
$49$	41.9681	+	30.4916i	0.856492	+	0.622278i
$50$	73.8365	−	40.9467i	1.47673	−	0.818934i
$51$	13.3170	−	1.39129i	0.261119	−	0.0272801i
$52$	−52.9105	−	56.3439i	−1.01751	−	1.08354i
$53$	−24.4987	−	9.69972i	−0.462240	−	0.183014i	0.125450	−	0.992100i	$-0.459962\pi$
$53$	−24.4987	−	9.69972i	−0.462240	−	0.183014i	−0.587690	+	0.809086i	$0.699962\pi$
$54$	−22.5115	−	88.3621i	−0.416880	−	1.63634i
$55$	−28.5168	−	9.20768i	−0.518488	−	0.167412i
$56$	97.5319	+	61.8957i	1.74164	+	1.10528i
$57$	−25.0268	−	14.4701i	−0.439067	−	0.253861i
$58$	−39.9679	−	25.3644i	−0.689102	−	0.437317i
$59$	−43.9810	+	46.8350i	−0.745441	+	0.793814i	−0.984161	−	0.177274i	$-0.943272\pi$
$59$	−43.9810	+	46.8350i	−0.745441	+	0.793814i	0.238721	+	0.971088i	$0.423272\pi$
$60$	49.2702	−	99.5584i	0.821171	−	1.65931i
$61$	76.8956	+	42.2737i	1.26058	+	0.693012i	0.964986	−	0.262301i	$-0.0844812\pi$
$61$	76.8956	+	42.2737i	1.26058	+	0.693012i	0.295598	+	0.955313i	$0.404481\pi$
$62$	31.2973	−	66.5101i	0.504795	−	1.07274i
$63$	−7.45160	−	90.0854i	−0.118279	−	1.42993i
$64$	−76.3177	−	41.9560i	−1.19246	−	0.655563i
$65$	−40.1485	+	33.3384i	−0.617669	+	0.512899i
$66$	−58.1411	+	17.5143i	−0.880926	+	0.265368i
$67$	19.7463	+	12.5314i	0.294721	+	0.187036i	0.674964	−	0.737851i	$-0.264159\pi$
$67$	19.7463	+	12.5314i	0.294721	+	0.187036i	−0.380242	+	0.924887i	$0.624159\pi$
$68$	33.0522			0.486062
$69$	107.302	−	56.0109i	1.55510	−	0.811752i
$70$	99.4344	−	137.391i	1.42049	−	1.96273i
$71$	−7.57387	−	29.4983i	−0.106674	−	0.415469i	0.892707	−	0.450637i	$-0.148803\pi$
$71$	−7.57387	−	29.4983i	−0.106674	−	0.415469i	−0.999381	+	0.0351685i	$0.988803\pi$
$72$	−14.9935	−	102.419i	−0.208243	−	1.42249i
$73$	6.30329	+	6.71233i	0.0863465	+	0.0919497i	0.770691	−	0.637209i	$-0.219911\pi$
$73$	6.30329	+	6.71233i	0.0863465	+	0.0919497i	−0.684344	+	0.729159i	$0.739911\pi$
$74$	118.463	+	163.051i	1.60086	+	2.20339i
$75$	−65.0663	−	37.3012i	−0.867551	−	0.497349i
$76$	−57.7331	−	41.9455i	−0.759646	−	0.551915i
$77$	−59.7201	+	7.54440i	−0.775586	+	0.0979793i
$78$	−28.5005	+	101.832i	−0.365391	+	1.30554i
$79$	−4.09345	+	65.0636i	−0.0518159	+	0.823590i	0.883203	+	0.468991i	$0.155382\pi$
$79$	−4.09345	+	65.0636i	−0.0518159	+	0.823590i	−0.935019	+	0.354599i	$0.884618\pi$
$80$	24.6294	−	38.9681i	0.307867	−	0.487101i
$81$	−56.8168	+	57.7308i	−0.701443	+	0.712726i
$82$	106.739	−	146.914i	1.30170	−	1.79164i
$83$	8.79888	+	139.854i	0.106011	+	1.68499i	0.588037	+	0.808834i	$0.299901\pi$
$83$	8.79888	+	139.854i	0.106011	+	1.68499i	−0.482026	+	0.876157i	$0.660099\pi$
$84$	4.81207	−	223.084i	0.0572865	−	2.65577i
$85$	1.36022	−	22.2744i	0.0160026	−	0.262052i
$86$	−62.9274	−	12.0040i	−0.731713	−	0.139582i
$87$	−0.906828	+	42.0400i	−0.0104233	+	0.483218i
$88$	−67.7092	+	12.9162i	−0.769422	+	0.146775i
$89$	−28.4792	−	30.3273i	−0.319991	−	0.340756i	0.548783	−	0.835965i	$-0.315091\pi$
$89$	−28.4792	−	30.3273i	−0.319991	−	0.340756i	−0.868774	+	0.495209i	$0.835091\pi$
$90$	−151.434	+	12.8069i	−1.68260	+	0.142299i
$91$	−44.6333	+	94.8506i	−0.490476	+	1.04231i
$92$	277.809	−	109.992i	3.01966	−	1.19557i
$93$	−64.9424	+	6.78480i	−0.698305	+	0.0729548i
$94$	115.545	+	139.670i	1.22920	+	1.48585i
$95$	−30.6437	+	37.1810i	−0.322565	+	0.391379i
$96$	1.83999	+	44.5649i	0.0191666	+	0.464217i
$97$	−14.3478	+	9.10536i	−0.147915	+	0.0938697i	−0.607725	−	0.794148i	$-0.707918\pi$
$97$	−14.3478	+	9.10536i	−0.147915	+	0.0938697i	0.459810	+	0.888017i	$0.347918\pi$
$98$	32.8281	−	172.091i	0.334981	−	1.75603i
$99$	40.0400	+	36.1426i	0.404444	+	0.365077i
$100$	−150.180	−	108.269i	−1.50180	−	1.08269i
$101$	175.681	+	57.0822i	1.73942	+	0.565170i	0.994756	−	0.102275i	$-0.0326122\pi$
$101$	175.681	+	57.0822i	1.73942	+	0.565170i	0.744659	+	0.667445i	$0.232612\pi$
$102$	−23.4007	−	38.6935i	−0.229418	−	0.379348i
$103$	−64.6686	−	53.4985i	−0.627850	−	0.519403i	0.268195	−	0.963365i	$-0.413573\pi$
$103$	−64.6686	−	53.4985i	−0.627850	−	0.519403i	−0.896046	+	0.443961i	$0.853573\pi$
$104$	−44.1896	+	111.610i	−0.424900	+	1.07317i
$105$	−150.142	−	12.4237i	−1.42992	−	0.118321i
$106$	5.58748	+	88.8105i	0.0527121	+	0.837835i
$107$	−13.4809	−	41.4898i	−0.125989	−	0.387755i	0.868091	−	0.496406i	$-0.165347\pi$
$107$	−13.4809	−	41.4898i	−0.125989	−	0.387755i	−0.994080	+	0.108650i	$0.965347\pi$
$108$	−154.302	+	127.164i	−1.42872	+	1.17745i
$109$	−7.28564	−	38.1927i	−0.0668408	−	0.350392i	0.933117	−	0.359573i	$-0.117078\pi$
$109$	−7.28564	−	38.1927i	−0.0668408	−	0.350392i	−0.999958	+	0.00918108i	$0.997078\pi$
$110$	12.8689	+	100.382i	0.116990	+	0.912560i
$111$	69.4802	−	164.999i	0.625948	−	1.48648i
$112$	11.6059	−	91.8705i	0.103624	−	0.820272i
$113$	119.343	+	112.071i	1.05614	+	0.991777i	0.999978	−	0.00664486i	$-0.00211514\pi$
$113$	119.343	+	112.071i	1.05614	+	0.991777i	0.0561574	+	0.998422i	$0.482115\pi$
$114$	−8.23023	+	97.2839i	−0.0721950	+	0.853368i
$115$	−62.6926	−	191.746i	−0.545153	−	1.66736i
$116$	−13.0096	+	102.982i	−0.112152	+	0.887774i
$117$	90.5055	−	25.1480i	0.773551	−	0.214940i
$118$	206.360	+	67.0505i	1.74882	+	0.568225i
$119$	−16.5018	−	41.6788i	−0.138671	−	0.350242i
$120$	−172.484	−	3.40294i	−1.43737	−	0.0283579i
$121$	−54.2323	+	65.5555i	−0.448201	+	0.541781i
$122$	18.6079	−	295.764i	0.152524	−	2.42430i
$123$	−160.739	−	13.5985i	−1.30682	−	0.110557i
$124$	−161.184			−1.29987
$125$	−79.1449	+	96.7527i	−0.633159	+	0.774022i
$126$	−264.567	+	152.308i	−2.09974	+	1.20880i
$127$	−151.630	+	71.3515i	−1.19393	+	0.561823i	−0.916931	−	0.399046i	$-0.869341\pi$
$127$	−151.630	+	71.3515i	−1.19393	+	0.561823i	−0.277004	+	0.960869i	$0.589341\pi$
$128$	−14.7339	+	234.188i	−0.115108	+	1.82960i
$129$	19.8029	+	53.3501i	0.153511	+	0.413567i
$130$	159.606	+	74.7466i	1.22774	+	0.574974i
$131$	−64.0355	−	161.735i	−0.488821	−	1.23462i	−0.939689	−	0.342030i	$-0.888886\pi$
$131$	−64.0355	−	161.735i	−0.488821	−	1.23462i	0.450868	−	0.892591i	$-0.351114\pi$
$132$	89.0336	+	99.0058i	0.674497	+	0.750044i
$133$	−24.0692	+	93.7433i	−0.180971	+	0.704837i
$134$	9.89918	−	78.3601i	0.0738745	−	0.584777i
$135$	79.3478	+	109.220i	0.587762	+	0.809034i
$136$	−21.8560	−	46.4465i	−0.160706	−	0.341518i
$137$	−84.5050	−	79.3555i	−0.616825	−	0.579237i	0.311850	−	0.950131i	$-0.399051\pi$
$137$	−84.5050	−	79.3555i	−0.616825	−	0.579237i	−0.928675	+	0.370894i	$0.879051\pi$
$138$	−325.452	−	247.351i	−2.35834	−	1.79240i
$139$	217.583	−	27.4872i	1.56535	−	0.197749i	0.705653	−	0.708558i	$-0.250654\pi$
$139$	217.583	−	27.4872i	1.56535	−	0.197749i	0.859695	+	0.510808i	$0.170654\pi$
$140$	−365.434	−	69.0134i	−2.61024	−	0.492953i
$141$	53.0496	−	152.033i	0.376239	−	1.07825i
$142$	−79.2497	+	65.5611i	−0.558097	+	0.461698i
$143$	−19.3299	−	59.4914i	−0.135174	−	0.416024i
$144$	−69.1715	+	45.8332i	−0.480358	+	0.318286i
$145$	68.8656	+	13.0055i	0.474935	+	0.0896930i
$146$	11.4477	−	28.9135i	0.0784087	−	0.198038i
$147$	−145.899	+	54.1560i	−0.992513	+	0.368408i
$148$	212.906	−	387.275i	1.43856	−	2.61672i
$149$	−138.311	−	44.9399i	−0.928260	−	0.301610i	−0.194409	−	0.980921i	$-0.562279\pi$
$149$	−138.311	−	44.9399i	−0.928260	−	0.301610i	−0.733851	+	0.679311i	$0.762279\pi$
$150$	−20.4228	+	252.466i	−0.136152	+	1.68311i
$151$	−18.8945	−	58.1513i	−0.125129	−	0.385108i	0.868795	−	0.495171i	$-0.164895\pi$
$151$	−18.8945	−	58.1513i	−0.125129	−	0.385108i	−0.993925	+	0.110063i	$0.964895\pi$
$152$	−20.7673	+	108.866i	−0.136627	+	0.716223i
$153$	−18.6543	+	35.5743i	−0.121924	+	0.232512i
$154$	108.928	+	171.644i	0.707327	+	1.11457i
$155$	−6.63332	+	108.624i	−0.0427956	+	0.700800i
$156$	228.655	−	38.5275i	1.46574	−	0.246971i
$157$	−117.951	−	162.346i	−0.751282	−	1.03405i	−0.997889	−	0.0649359i	$-0.979316\pi$
$157$	−117.951	−	162.346i	−0.751282	−	1.03405i	0.246607	−	0.969116i	$-0.420684\pi$
$158$	204.707	−	81.0492i	1.29561	−	0.512969i
$159$	64.9375	−	45.0728i	0.408412	−	0.283476i
$160$	73.7689	+	9.18125i	0.461056	+	0.0573828i
$161$	−277.400	−	295.401i	−1.72298	−	1.83479i
$162$	258.113	+	90.6066i	1.59329	+	0.559300i
$163$	−117.807	−	214.290i	−0.722740	−	1.31466i	−0.940879	−	0.338742i	$-0.889999\pi$
$163$	−117.807	−	214.290i	−0.722740	−	1.31466i	0.218139	−	0.975918i	$-0.430001\pi$
$164$	−391.150	−	74.6159i	−2.38506	−	0.454975i
$165$	70.3856	−	55.9266i	0.426579	−	0.338949i
$166$	414.713	−	227.990i	2.49827	−	1.37344i
$167$	7.38292	+	117.348i	0.0442091	+	0.702683i	0.956244	+	0.292571i	$0.0945106\pi$
$167$	7.38292	+	117.348i	0.0442091	+	0.702683i	−0.912035	+	0.410113i	$0.865489\pi$
$168$	−316.670	+	140.754i	−1.88494	+	0.837823i
$169$	58.1788	+	14.9378i	0.344254	+	0.0883893i
$170$	−70.0218	+	27.8728i	−0.411893	+	0.163958i
$171$	77.7302	−	38.4649i	0.454562	−	0.224941i
$172$	34.9348	+	136.062i	0.203109	+	0.791057i
$173$	314.800	−	39.7685i	1.81965	−	0.229876i	0.859850	−	0.510547i	$-0.170557\pi$
$173$	314.800	−	39.7685i	1.81965	−	0.229876i	0.959804	+	0.280671i	$0.0905569\pi$
$174$	129.769	−	57.6801i	0.745800	−	0.331495i
$175$	−61.5482	+	243.432i	−0.351704	+	1.39104i
$176$	32.4793	+	44.7039i	0.184541	+	0.253999i
$177$	−43.8965	−	187.680i	−0.248003	−	1.06034i
$178$	−51.7222	+	130.635i	−0.290574	+	0.733907i
$179$	19.5896	+	76.2965i	0.109439	+	0.426237i	0.999565	−	0.0294765i	$-0.00938403\pi$
$179$	19.5896	+	76.2965i	0.109439	+	0.426237i	−0.890126	+	0.455714i	$0.849384\pi$
$180$	166.796	+	288.503i	0.926644	+	1.60279i
$181$	107.729	−	169.754i	0.595188	−	0.937866i	−0.404539	−	0.914521i	$-0.632568\pi$
$181$	107.729	−	169.754i	0.595188	−	0.937866i	0.999727	−	0.0233458i	$-0.00743186\pi$
$182$	354.024			1.94519
$183$	−233.368	+	121.817i	−1.27524	+	0.665665i
$184$	−338.269	−	317.656i	−1.83842	−	1.72639i
$185$	−252.229	−	159.419i	−1.36340	−	0.861723i
$186$	114.117	+	188.694i	0.613530	+	1.01448i
$187$	24.2034	+	11.3892i	0.129430	+	0.0609050i
$188$	169.241	−	359.656i	0.900218	−	1.91306i
$189$	237.391	+	131.086i	1.25604	+	0.693575i
$190$	157.681	+	40.1764i	0.829901	+	0.211455i
$191$	6.05420	−	6.44707i	0.0316974	−	0.0337543i	−0.712925	−	0.701241i	$-0.752630\pi$
$191$	6.05420	−	6.44707i	0.0316974	−	0.0337543i	0.744622	+	0.667486i	$0.232630\pi$
$192$	231.614	−	120.901i	1.20632	−	0.629694i
$193$		−	345.745i		−	1.79143i	−0.444633	−	0.895713i	$-0.646666\pi$
$193$		−	345.745i		−	1.79143i	0.444633	−	0.895713i	$-0.353334\pi$
$194$	48.4554	+	30.7507i	0.249770	+	0.158509i
$195$	−16.5542	−	155.680i	−0.0848935	−	0.798357i
$196$	−372.096	+	95.5380i	−1.89845	+	0.487439i
$197$	185.769	+	73.5512i	0.942990	+	0.373356i	0.788776	−	0.614681i	$-0.210715\pi$
$197$	185.769	+	73.5512i	0.942990	+	0.373356i	0.154214	+	0.988037i	$0.450715\pi$
$198$	52.8690	−	174.325i	0.267015	−	0.880429i
$199$	−223.735	+	162.553i	−1.12429	+	0.816848i	−0.984854	−	0.173383i	$-0.944530\pi$
$199$	−223.735	+	162.553i	−1.12429	+	0.816848i	−0.139440	+	0.990231i	$0.544530\pi$
$200$	−52.8375	+	282.633i	−0.264188	+	1.41317i
$201$	−64.1132	+	28.4971i	−0.318971	+	0.141777i
$202$	−78.1884	−	618.925i	−0.387071	−	3.06398i
$203$	136.355	−	35.0101i	0.671701	−	0.172463i
$204$	−54.9239	+	82.5554i	−0.269235	+	0.404683i
$205$	−66.3821	+	260.531i	−0.323815	+	1.27088i
$206$	−70.4903	+	274.542i	−0.342186	+	1.33273i
$207$	−38.4068	+	361.086i	−0.185540	+	1.74438i
$208$	96.0385	−	6.04223i	0.461724	−	0.0290492i
$209$	−27.8228	−	50.6096i	−0.133124	−	0.242151i
$210$	177.932	+	476.667i	0.847294	+	2.26984i
$211$	−17.8527	+	93.5872i	−0.0846100	+	0.443541i	0.914620	+	0.404314i	$0.132490\pi$
$211$	−17.8527	+	93.5872i	−0.0846100	+	0.443541i	−0.999230	+	0.0392273i	$0.987510\pi$
$212$	170.992	−	94.0039i	0.806568	−	0.443415i
$213$	86.2644	+	30.1008i	0.404997	+	0.141318i
$214$	−107.399	+	100.855i	−0.501867	+	0.471284i
$215$	93.1319	−	17.9436i	0.433172	−	0.0834586i
$216$	280.730	+	132.743i	1.29968	+	0.614553i
$217$	80.4733	+	203.252i	0.370845	+	0.936647i
$218$	−106.232	+	77.1824i	−0.487305	+	0.354048i
$219$	−27.2400	+	4.58983i	−0.124383	+	0.0209581i
$220$	187.152	−	119.254i	0.850692	−	0.542065i
$221$	39.3312	−	24.9603i	0.177969	−	0.112943i
$222$	−604.111	+	24.9425i	−2.72122	+	0.112354i
$223$	346.932	+	66.1809i	1.55575	+	0.296775i	0.892299	−	0.451444i	$-0.149091\pi$
$223$	346.932	+	66.1809i	1.55575	+	0.296775i	0.663451	+	0.748219i	$0.269091\pi$
$224$	142.017	−	46.1441i	0.634004	−	0.206000i
$225$	201.291	−	100.533i	0.894626	−	0.446815i
$226$	170.856	−	525.840i	0.755998	−	2.32672i
$227$	228.948	+	125.865i	1.00858	+	0.554473i	0.898279	−	0.439425i	$-0.144818\pi$
$227$	228.948	+	125.865i	1.00858	+	0.554473i	0.110303	+	0.993898i	$0.464818\pi$
$228$	200.705	−	74.4993i	0.880287	−	0.326751i
$229$	286.872	+	113.581i	1.25272	+	0.495985i	0.898416	−	0.439146i	$-0.144719\pi$
$229$	286.872	+	113.581i	1.25272	+	0.495985i	0.354301	+	0.935132i	$0.384719\pi$
$230$	−495.787	+	467.296i	−2.15560	+	2.03172i
$231$	80.3949	−	161.701i	0.348030	−	0.700006i
$232$	153.317	−	49.8159i	0.660851	−	0.214724i
$233$	11.9586	+	14.4555i	0.0513245	+	0.0620407i	0.795551	−	0.605887i	$-0.207182\pi$
$233$	11.9586	+	14.4555i	0.0513245	+	0.0620407i	−0.744226	+	0.667928i	$0.767182\pi$
$234$	−206.989	−	240.404i	−0.884568	−	1.02737i
$235$	−235.412	−	128.855i	−1.00176	−	0.548321i
$236$	−59.6327	−	472.041i	−0.252681	−	2.00018i
$237$	−155.709	−	118.343i	−0.657000	−	0.499336i
$238$	−103.633	+	110.358i	−0.435433	+	0.463689i
$239$	−223.552	+	105.195i	−0.935362	+	0.440148i	−0.832175	−	0.554514i	$-0.812904\pi$
$239$	−223.552	+	105.195i	−0.935362	+	0.440148i	−0.103188	+	0.994662i	$0.532904\pi$
$240$	56.4042	+	126.272i	0.235018	+	0.526133i
$241$	428.169	+	54.0903i	1.77664	+	0.224441i	0.944130	−	0.329575i	$-0.106905\pi$
$241$	428.169	+	54.0903i	1.77664	+	0.224441i	0.832506	+	0.554016i	$0.186905\pi$
$242$	278.307	+	71.4571i	1.15003	+	0.295277i
$243$	−49.7815	−	237.846i	−0.204862	−	0.978791i
$244$	−604.200	+	239.220i	−2.47623	+	0.980408i
$245$	49.0713	+	254.693i	0.200291	+	1.03956i
$246$	189.580	+	510.738i	0.770649	+	2.07617i
$247$	−100.377	−	6.31519i	−0.406385	−	0.0255676i
$248$	106.584	+	226.502i	0.429774	+	0.913316i
$249$	−363.939	−	210.423i	−1.46160	−	0.845072i
$250$	409.462	+	102.725i	1.63785	+	0.410900i
$251$			242.238i			0.965091i	0.875871	+	0.482546i	$0.160288\pi$
$251$			242.238i			0.965091i	−0.875871	+	0.482546i	$0.839712\pi$
$252$	549.208	+	382.726i	2.17940	+	1.51875i
$253$	241.334	+	15.1835i	0.953890	+	0.0600137i
$254$	436.070	+	360.749i	1.71681	+	1.42027i
$255$	53.3750	+	40.4115i	0.209314	+	0.158477i
$256$	412.919	−	163.486i	1.61296	−	0.638618i
$257$	107.931	−	332.176i	0.419964	−	1.29251i	−0.487772	−	0.872971i	$-0.662190\pi$
$257$	107.931	−	332.176i	0.419964	−	1.29251i	0.907735	−	0.419544i	$-0.137810\pi$
$258$	134.551	−	137.228i	0.521516	−	0.531891i
$259$	−594.650	−	75.1218i	−2.29595	−	0.290046i
$260$	−0.711412	−	386.463i	−0.00273620	−	1.48639i
$261$	−103.498	−	72.1242i	−0.396542	−	0.276338i
$262$	−402.149	+	428.246i	−1.53492	+	1.63453i
$263$	−77.0127	−	9.72896i	−0.292824	−	0.0369923i	−0.0224510	−	0.999748i	$-0.507147\pi$
$263$	−77.0127	−	9.72896i	−0.292824	−	0.0369923i	−0.270373	+	0.962756i	$0.587147\pi$
$264$	80.2533	−	190.582i	0.303990	−	0.721903i
$265$	−56.3137	−	119.103i	−0.212504	−	0.449445i
$266$	321.070	−	61.2473i	1.20703	−	0.230253i
$267$	123.074	−	20.7375i	0.460952	−	0.0776686i
$268$	−164.717	+	53.5198i	−0.614615	+	0.199701i
$269$	283.119	−	17.8124i	1.05249	−	0.0662170i	0.472892	−	0.881120i	$-0.343210\pi$
$269$	283.119	−	17.8124i	1.05249	−	0.0662170i	0.579597	+	0.814903i	$0.303210\pi$
$270$	219.654	−	399.522i	0.813534	−	1.47971i
$271$	188.567	+	74.6591i	0.695820	+	0.275495i	0.689292	−	0.724484i	$-0.257922\pi$
$271$	188.567	+	74.6591i	0.695820	+	0.275495i	0.00652854	+	0.999979i	$0.497922\pi$
$272$	−26.2297	+	31.7063i	−0.0964329	+	0.116567i
$273$	−162.742	−	269.098i	−0.596126	−	0.985707i
$274$	−120.980	+	372.338i	−0.441533	+	1.35890i
$275$	−72.6653	−	131.033i	−0.264237	−	0.476482i
$276$	−186.913	+	876.668i	−0.677220	+	3.17633i
$277$	173.064	+	33.0138i	0.624781	+	0.119183i	0.490043	−	0.871698i	$-0.336981\pi$
$277$	173.064	+	33.0138i	0.624781	+	0.119183i	0.134737	+	0.990881i	$0.456981\pi$
$278$	−396.868	−	625.364i	−1.42758	−	2.24951i
$279$	90.9703	−	173.483i	0.326058	−	0.621803i
$280$	144.666	+	559.161i	0.516663	+	1.99700i
$281$	135.236	−	111.877i	0.481268	−	0.398139i	−0.364908	−	0.931044i	$-0.618899\pi$
$281$	135.236	−	111.877i	0.481268	−	0.398139i	0.846175	+	0.532904i	$0.178899\pi$
$282$	−540.862	+	56.5061i	−1.91795	+	0.200376i
$283$	22.0231	+	55.6240i	0.0778201	+	0.196551i	0.963478	−	0.267787i	$-0.0862923\pi$
$283$	22.0231	+	55.6240i	0.0778201	+	0.196551i	−0.885658	+	0.464338i	$0.846292\pi$
$284$	204.071	+	96.0286i	0.718561	+	0.338129i
$285$	−41.9464	−	138.324i	−0.147180	−	0.485349i
$286$	−153.998	+	144.614i	−0.538454	+	0.505642i
$287$	101.197	+	530.493i	0.352603	+	1.84841i
$288$	−114.368	−	69.4590i	−0.397113	−	0.241177i
$289$	50.4206	−	264.314i	0.174466	−	0.914581i
$290$	−59.2830	−	229.140i	−0.204424	−	0.790138i
$291$	1.09940	−	50.9675i	0.00377800	−	0.175146i
$292$	−68.0554	+	4.28168i	−0.233067	+	0.0146633i
$293$	−440.349	−	319.932i	−1.50290	−	1.09192i	−0.969209	−	0.246239i	$-0.920805\pi$
$293$	−440.349	−	319.932i	−1.50290	−	1.09192i	−0.533690	−	0.845680i	$-0.679195\pi$
$294$	375.285	+	367.965i	1.27648	+	1.25158i
$295$	−320.570	+	20.7611i	−1.08668	+	0.0703765i
$296$	−685.003	−	43.0967i	−2.31420	−	0.145597i
$297$	−156.810	+	39.9496i	−0.527981	+	0.134510i
$298$	61.5564	+	487.269i	0.206565	+	1.63513i
$299$	247.521	−	340.683i	0.827828	−	1.13941i
$300$	519.986	−	195.193i	1.73329	−	0.650645i
$301$	154.132	−	111.984i	0.512067	−	0.372039i
$302$	−150.529	+	141.356i	−0.498440	+	0.468067i
$303$	−434.510	+	343.948i	−1.43403	+	1.13514i
$304$	86.0536	−	22.0948i	0.283071	−	0.0726803i
$305$	136.349	+	417.024i	0.447045	+	1.36729i
$306$	135.531	+	5.84972i	0.442913	+	0.0191167i
$307$		−	227.903i		−	0.742354i	−0.928562	−	0.371177i	$-0.878954\pi$
$307$		−	227.903i		−	0.742354i	0.928562	−	0.371177i	$-0.121046\pi$
$308$	238.858	−	376.380i	0.775512	−	1.22201i
$309$	241.087	−	72.6244i	0.780216	−	0.235030i
$310$	341.471	−	135.925i	1.10152	−	0.438469i
$311$	118.866	−	216.217i	0.382207	−	0.695231i	−0.613308	−	0.789844i	$-0.710161\pi$
$311$	118.866	−	216.217i	0.382207	−	0.695231i	0.995514	+	0.0946130i	$0.0301614\pi$
$312$	−205.341	−	295.840i	−0.658143	−	0.948204i
$313$	185.384	+	87.2350i	0.592281	+	0.278706i	0.698470	−	0.715640i	$-0.253865\pi$
$313$	185.384	+	87.2350i	0.592281	+	0.278706i	−0.106189	+	0.994346i	$0.533865\pi$
$314$	−326.488	+	593.879i	−1.03977	+	1.89133i
$315$	280.527	−	354.369i	0.890561	−	1.12498i
$316$	−351.934	−	330.488i	−1.11371	−	1.04585i
$317$	60.0648	−	94.6470i	0.189479	−	0.298571i	−0.736286	−	0.676670i	$-0.763422\pi$
$317$	60.0648	−	94.6470i	0.189479	−	0.298571i	0.925765	+	0.378099i	$0.123422\pi$
$318$	−231.109	−	133.623i	−0.726759	−	0.420199i
$319$	−45.0125	+	70.9283i	−0.141105	+	0.222346i
$320$	−135.324	−	413.890i	−0.422887	−	1.29341i
$321$	126.032	+	35.2734i	0.392623	+	0.109886i
$322$	−503.797	+	1272.45i	−1.56459	+	3.95170i
$323$	31.3519	−	29.4414i	0.0970646	−	0.0911497i
$324$	−61.2136	−	596.717i	−0.188931	−	1.84172i
$325$	−260.472	−	15.4250i	−0.801454	−	0.0474615i
$326$	−485.424	+	668.129i	−1.48903	+	2.04948i
$327$	107.502	+	45.2684i	0.328752	+	0.138436i
$328$	153.798	+	599.002i	0.468895	+	1.82623i
$329$	−538.022	−	33.8494i	−1.63532	−	0.102886i
$330$	−272.111	−	134.664i	−0.824577	−	0.408073i
$331$	−414.066	−	106.314i	−1.25096	−	0.321191i	−0.435594	−	0.900143i	$-0.643462\pi$
$331$	−414.066	−	106.314i	−1.25096	−	0.321191i	−0.815361	+	0.578953i	$0.803462\pi$
$332$	−839.552	−	609.970i	−2.52877	−	1.83726i
$333$	296.665	+	447.727i	0.890886	+	1.34452i
$334$	347.975	−	191.301i	1.04184	−	0.572757i
$335$	29.2891	+	113.208i	0.0874300	+	0.337934i
$336$	210.182	+	181.653i	0.625540	+	0.540633i
$337$	133.773	+	243.333i	0.396953	+	0.722055i	0.996958	−	0.0779414i	$-0.0248347\pi$
$337$	133.773	+	243.333i	0.396953	+	0.722055i	−0.600005	+	0.799996i	$0.704835\pi$
$338$	−38.0113	−	199.262i	−0.112459	−	0.589533i
$339$	−478.239	+	111.855i	−1.41073	+	0.329957i
$340$	120.678	+	112.907i	0.354936	+	0.332079i
$341$	−118.031	−	55.5411i	−0.346132	−	0.162877i
$342$	−229.312	−	182.217i	−0.670504	−	0.532797i
$343$	16.9750	+	23.3641i	0.0494899	+	0.0681170i
$344$	168.099	−	139.064i	0.488661	−	0.404256i
$345$	583.108	+	162.042i	1.69017	+	0.469686i
$346$	−574.190	−	904.778i	−1.65951	−	2.61497i
$347$	184.334	+	290.463i	0.531221	+	0.837070i	0.998903	−	0.0468268i	$-0.0149109\pi$
$347$	184.334	+	290.463i	0.531221	+	0.837070i	−0.467682	+	0.883897i	$0.654911\pi$
$348$	−235.602	−	203.623i	−0.677017	−	0.585123i
$349$	19.1832	+	59.0398i	0.0549661	+	0.169168i	0.974771	−	0.223208i	$-0.0716530\pi$
$349$	19.1832	+	59.0398i	0.0549661	+	0.169168i	−0.919805	+	0.392377i	$0.871653\pi$
$350$	832.379	−	161.963i	2.37822	−	0.462751i
$351$	−87.5829	+	267.847i	−0.249524	+	0.763098i
$352$	−42.9272	+	78.0842i	−0.121952	+	0.221830i
$353$	−428.872	+	518.417i	−1.21494	+	1.46860i	−0.374035	+	0.927415i	$0.622026\pi$
$353$	−428.872	+	518.417i	−1.21494	+	1.46860i	−0.840900	+	0.541190i	$0.817974\pi$
$354$	−510.389	+	404.012i	−1.44178	+	1.14128i
$355$	73.1135	−	133.575i	0.205953	−	0.376267i
$356$	307.484	−	19.3453i	0.863720	−	0.0543407i
$357$	131.524	+	28.0420i	0.368414	+	0.0785489i
$358$	204.977	−	169.572i	0.572562	−	0.473664i
$359$	−42.9915	+	8.20107i	−0.119754	+	0.0228442i	−0.246910	−	0.969039i	$-0.579415\pi$
$359$	−42.9915	+	8.20107i	−0.119754	+	0.0228442i	0.127156	+	0.991883i	$0.459415\pi$
$360$	295.122	−	425.164i	0.819785	−	1.18101i
$361$	266.027	−	33.6071i	0.736918	−	0.0930943i
$362$	−673.640	−	85.1006i	−1.86088	−	0.235084i
$363$	−73.6205	−	244.393i	−0.202811	−	0.673260i
$364$	−330.533	−	702.419i	−0.908059	−	1.92972i
$365$	0.0847515	+	46.0398i	0.000232196	+	0.126136i
$366$	707.817	+	537.958i	1.93393	+	1.46983i
$367$	−64.7585	+	252.218i	−0.176454	+	0.687242i	0.817355	+	0.576135i	$0.195440\pi$
$367$	−64.7585	+	252.218i	−0.176454	+	0.687242i	−0.993808	+	0.111107i	$0.964560\pi$
$368$	−114.951	+	353.784i	−0.312368	+	0.961370i
$369$	301.071	−	378.885i	0.815909	−	1.02679i
$370$	−124.459	+	999.994i	−0.336375	+	2.70269i
$371$	−203.909	−	168.689i	−0.549621	−	0.454686i
$372$	267.844	−	402.593i	0.720010	−	1.08224i
$373$	413.350	−	194.508i	1.10818	−	0.521468i	0.217479	−	0.976065i	$-0.430217\pi$
$373$	413.350	−	194.508i	1.10818	−	0.521468i	0.890697	+	0.454597i	$0.150217\pi$
$374$		−	90.3375i		−	0.241544i
$375$	−110.144	−	358.459i	−0.293718	−	0.955892i
$376$	−617.317			−1.64180
$377$	62.2886	+	132.370i	0.165222	+	0.351114i
$378$	59.2144	−	913.912i	0.156652	−	2.41776i
$379$	171.361	−	207.140i	0.452140	−	0.546543i	−0.494356	−	0.869260i	$-0.664596\pi$
$379$	171.361	−	207.140i	0.452140	−	0.546543i	0.946496	+	0.322716i	$0.104596\pi$
$380$	−67.5046	−	350.366i	−0.177644	−	0.922016i
$381$	73.7512	−	497.297i	0.193573	−	1.30524i
$382$	−28.4065	−	9.22983i	−0.0743626	−	0.0241619i
$383$	322.392	+	82.7762i	0.841755	+	0.216126i	0.644862	−	0.764299i	$-0.276915\pi$
$383$	322.392	+	82.7762i	0.841755	+	0.216126i	0.196893	+	0.980425i	$0.436915\pi$
$384$	−560.455	−	425.959i	−1.45952	−	1.10927i
$385$	−243.818	−	176.459i	−0.633294	−	0.458336i
$386$	−1056.52	+	497.162i	−2.73711	+	1.28799i
$387$	−166.161	−	39.1913i	−0.429357	−	0.101270i
$388$	15.7723	−	124.851i	0.0406503	−	0.321780i
$389$	58.7233	+	464.843i	0.150960	+	1.19497i	0.867505	+	0.497429i	$0.165722\pi$
$389$	58.7233	+	464.843i	0.150960	+	1.19497i	−0.716545	+	0.697541i	$0.754278\pi$
$390$	−451.920	+	274.445i	−1.15877	+	0.703705i
$391$	33.7428	+	176.886i	0.0862987	+	0.452394i
$392$	380.306	+	459.711i	0.970168	+	1.17273i
$393$	510.381	+	108.817i	1.29868	+	0.276889i
$394$	−42.3688	−	673.434i	−0.107535	−	1.70922i
$395$	−237.204	+	223.573i	−0.600517	+	0.566007i
$396$	−395.240	+	57.8605i	−0.998080	+	0.146112i
$397$	255.473	+	211.346i	0.643509	+	0.532357i	0.900942	−	0.433939i	$-0.142877\pi$
$397$	255.473	+	211.346i	0.643509	+	0.532357i	−0.257433	+	0.966296i	$0.582877\pi$
$398$	818.445	+	449.944i	2.05639	+	1.13051i
$399$	−194.149	−	215.894i	−0.486588	−	0.541089i
$400$	223.041	−	58.1433i	0.557603	−	0.145358i
$401$	373.356	−	121.311i	0.931061	−	0.302520i	0.196065	−	0.980591i	$-0.437184\pi$
$401$	373.356	−	121.311i	0.931061	−	0.302520i	0.734997	+	0.678071i	$0.237184\pi$
$402$	179.272	+	154.939i	0.445951	+	0.385420i
$403$	−191.804	+	121.722i	−0.475940	+	0.302041i
$404$	−1155.01	+	732.992i	−2.85894	+	1.81434i
$405$	−404.656	+	16.6956i	−0.999150	+	0.0412238i
$406$	−303.055	−	366.330i	−0.746440	−	0.902291i
$407$	289.355	−	210.229i	0.710946	−	0.516532i
$408$	152.330	+	22.5911i	0.373357	+	0.0553703i
$409$	−231.143	+	491.204i	−0.565142	+	1.20099i	0.394274	+	0.918993i	$0.370996\pi$
$409$	−231.143	+	491.204i	−0.565142	+	1.20099i	−0.959416	+	0.281995i	$0.909004\pi$
$410$	891.583	−	171.780i	2.17459	−	0.418976i
$411$	338.633	−	79.2031i	0.823925	−	0.192708i
$412$	610.532	−	116.465i	1.48187	−	0.282682i
$413$	−565.471	+	310.870i	−1.36918	+	0.752713i
$414$	1158.63	−	401.858i	2.79862	−	0.970673i
$415$	−445.619	+	540.684i	−1.07378	+	1.30285i
$416$	74.7563	+	135.981i	0.179703	+	0.326878i
$417$	−292.910	+	589.140i	−0.702421	+	1.41281i
$418$	−114.644	+	157.795i	−0.274269	+	0.377499i
$419$	−69.2363	+	269.658i	−0.165242	+	0.643574i	0.830947	+	0.556351i	$0.187799\pi$
$419$	−69.2363	+	269.658i	−0.165242	+	0.643574i	−0.996189	+	0.0872227i	$0.972201\pi$
$420$	779.630	−	798.074i	1.85626	−	1.90018i
$421$	7.29062	−	115.881i	0.0173174	−	0.275252i	−0.979833	−	0.199817i	$-0.935965\pi$
$421$	7.29062	−	115.881i	0.0173174	−	0.275252i	0.997151	−	0.0754354i	$-0.0240347\pi$
$422$	311.654	−	80.0191i	0.738516	−	0.189619i
$423$	291.582	+	385.141i	0.689319	+	0.910499i
$424$	−245.169	−	178.126i	−0.578228	−	0.420107i
$425$	81.0561	−	76.6803i	0.190720	−	0.180424i
$426$	−32.0620	−	306.889i	−0.0752628	−	0.720397i
$427$	603.311	+	642.461i	1.41291	+	1.50459i
$428$	300.380	+	118.929i	0.701821	+	0.277871i
$429$	180.715	+	50.5778i	0.421246	+	0.117897i
$430$	−188.750	−	258.789i	−0.438954	−	0.601836i
$431$	24.7786	+	15.7250i	0.0574910	+	0.0364849i	0.564262	−	0.825596i	$-0.309161\pi$
$431$	24.7786	+	15.7250i	0.0574910	+	0.0364849i	−0.506771	+	0.862081i	$0.669161\pi$
$432$	0.465493	−	248.934i	0.00107753	−	0.576237i
$433$	−370.275	−	234.984i	−0.855139	−	0.542688i	0.0344723	−	0.999406i	$-0.489025\pi$
$433$	−370.275	−	234.984i	−0.855139	−	0.542688i	−0.889612	+	0.456718i	$0.849025\pi$
$434$	505.380	−	538.175i	1.16447	−	1.24003i
$435$	−146.920	+	150.396i	−0.337748	+	0.345738i
$436$	252.321	+	138.715i	0.578719	+	0.318153i
$437$	165.541	−	351.793i	0.378813	−	0.805018i
$438$	53.1951	+	76.6396i	0.121450	+	0.174976i
$439$	87.8657	+	48.3046i	0.200150	+	0.110033i	0.578677	−	0.815557i	$-0.303569\pi$
$439$	87.8657	+	48.3046i	0.200150	+	0.110033i	−0.378527	+	0.925590i	$0.623569\pi$
$440$	−291.338	−	184.137i	−0.662131	−	0.418493i
$441$	107.179	−	454.410i	0.243036	−	1.03041i
$442$	−132.830	−	84.2962i	−0.300519	−	0.190715i
$443$	−144.139			−0.325370			−0.162685	−	0.986678i	$-0.552015\pi$
$443$	−144.139			−0.325370			−0.162685	+	0.986678i	$0.552015\pi$
$444$	613.515	+	1175.33i	1.38179	+	2.64714i
$445$	−0.382919	−	208.015i	−0.000860493	−	0.467448i
$446$	−296.635	−	1155.32i	−0.665101	−	2.59040i
$447$	342.083	−	270.785i	0.765286	−	0.605782i
$448$	−598.777	−	637.633i	−1.33656	−	1.42329i
$449$	−396.956	−	546.364i	−0.884090	−	1.21685i	−0.975271	−	0.221011i	$-0.929064\pi$
$449$	−396.956	−	546.364i	−0.884090	−	1.21685i	0.0911815	−	0.995834i	$-0.470936\pi$
$450$	−596.654	−	470.541i	−1.32590	−	1.04565i
$451$	−260.719	−	189.423i	−0.578090	−	0.420007i
$452$	−1202.84	+	151.954i	−2.66115	+	0.336181i
$453$	176.644	+	49.4386i	0.389942	+	0.109136i
$454$	55.4030	−	880.605i	0.122033	−	1.93966i
$455$	−486.974	+	193.844i	−1.07027	+	0.426032i
$456$	−237.408	−	232.777i	−0.520631	−	0.510476i
$457$	−3.11057	+	4.28133i	−0.00680649	+	0.00936833i	−0.812407	−	0.583091i	$-0.801843\pi$
$457$	−3.11057	+	4.28133i	−0.00680649	+	0.00936833i	0.805600	+	0.592460i	$0.201843\pi$
$458$	−65.4277	−	1039.94i	−0.142855	−	2.27062i
$459$	−57.8565	−	105.708i	−0.126049	−	0.230301i
$460$	1390.05	+	547.403i	3.02185	+	1.19001i
$461$	281.859	+	53.7674i	0.611407	+	0.116632i	0.483779	−	0.875190i	$-0.339264\pi$
$461$	281.859	+	53.7674i	0.611407	+	0.116632i	0.127628	+	0.991822i	$0.459264\pi$
$462$	−609.729	−	13.1522i	−1.31976	−	0.0284680i
$463$	−171.650	+	32.7440i	−0.370735	+	0.0707214i	−0.369382	−	0.929278i	$-0.620431\pi$
$463$	−171.650	+	32.7440i	−0.370735	+	0.0707214i	−0.00135273	+	0.999999i	$0.500431\pi$
$464$	−88.4641	−	94.2047i	−0.190655	−	0.203027i
$465$	−260.291	−	197.072i	−0.559765	−	0.423811i
$466$	26.9771	−	57.3292i	0.0578907	−	0.123024i
$467$	−126.999	+	50.2824i	−0.271946	+	0.107671i	−0.500140	−	0.865945i	$-0.666718\pi$
$467$	−126.999	+	50.2824i	−0.271946	+	0.107671i	0.228194	+	0.973616i	$0.426718\pi$
$468$	−283.732	+	635.140i	−0.606265	+	1.35714i
$469$	149.726	+	180.987i	0.319245	+	0.385900i
$470$	−55.2445	+	904.658i	−0.117542	+	1.92480i
$471$	601.500	−	24.8347i	1.27707	−	0.0527277i
$472$	−623.902	+	395.940i	−1.32183	+	0.838856i
$473$	−21.3027	+	111.673i	−0.0450375	+	0.236095i
$474$	−137.729	+	645.984i	−0.290568	+	1.36284i
$475$	−238.895	+	31.0735i	−0.502937	+	0.0654178i
$476$	315.718	+	102.583i	0.663273	+	0.215511i
$477$	4.67074	+	237.095i	0.00979192	+	0.497055i
$478$	642.910	+	531.861i	1.34500	+	1.11268i
$479$	−43.5057	+	109.883i	−0.0908261	+	0.229400i	−0.968087	−	0.250612i	$-0.919368\pi$
$479$	−43.5057	+	109.883i	−0.0908261	+	0.229400i	0.877261	+	0.480013i	$0.159368\pi$
$480$	−145.516	+	168.998i	−0.303159	+	0.352079i
$481$	−39.1096	−	621.629i	−0.0813089	−	1.29237i
$482$	−450.395	−	1386.17i	−0.934430	−	2.87588i
$483$	1198.80	−	201.993i	2.48198	−	0.418204i
$484$	−118.063	−	618.905i	−0.243931	−	1.27873i
$485$	−83.4897	−	15.7673i	−0.172144	−	0.0325099i
$486$	−655.225	+	494.132i	−1.34820	+	1.01673i
$487$	5.60738	−	44.3870i	0.0115141	−	0.0911437i	−0.985310	−	0.170773i	$-0.945374\pi$
$487$	5.60738	−	44.3870i	0.0115141	−	0.0911437i	0.996825	+	0.0796291i	$0.0253736\pi$
$488$	735.694	+	690.863i	1.50757	+	1.41570i
$489$	731.000	+	61.8427i	1.49489	+	0.126468i
$490$	707.726	−	516.186i	1.44434	−	1.05344i
$491$	−10.9019	+	86.2975i	−0.0222035	+	0.175759i	−0.999317	−	0.0369612i	$-0.988232\pi$
$491$	−10.9019	+	86.2975i	−0.0222035	+	0.175759i	0.977113	+	0.212720i	$0.0682322\pi$
$492$	836.357	−	852.995i	1.69991	−	1.73373i
$493$	−59.4967	−	19.3316i	−0.120683	−	0.0392122i
$494$	125.039	+	315.812i	0.253115	+	0.639296i
$495$	22.7275	+	268.739i	0.0459141	+	0.542907i
$496$	127.913	−	154.620i	0.257889	−	0.311734i
$497$	19.2064	−	305.277i	0.0386447	−	0.614240i
$498$	−119.684	+	1414.70i	−0.240329	+	2.84076i
$499$	680.848			1.36443			0.682213	−	0.731154i	$-0.261018\pi$
$499$	680.848			1.36443			0.682213	+	0.731154i	$0.261018\pi$
$500$	−178.476	−	908.323i	−0.356952	−	1.81665i
$501$	−305.372	−	176.561i	−0.609525	−	0.352416i
$502$	740.228	−	348.325i	1.47456	−	0.693874i
$503$	27.6071	−	438.803i	0.0548850	−	0.872372i	−0.870221	−	0.492662i	$-0.836024\pi$
$503$	27.6071	−	438.803i	0.0548850	−	0.872372i	0.925106	−	0.379710i	$-0.123976\pi$
$504$	174.655	−	1024.85i	0.346538	−	2.03344i
$505$	446.441	+	808.544i	0.884042	+	1.60108i
$506$	−300.628	−	759.299i	−0.594126	−	1.50059i
$507$	−133.988	+	120.492i	−0.264276	+	0.237658i
$508$	308.627	−	1202.02i	0.607533	−	2.36618i
$509$	−33.0304	+	261.462i	−0.0648927	+	0.513679i	0.925847	+	0.377900i	$0.123354\pi$
$509$	−33.0304	+	261.462i	−0.0648927	+	0.513679i	−0.990739	+	0.135779i	$0.956646\pi$
$510$	46.7387	−	221.212i	0.0916446	−	0.433750i
$511$	39.3769	+	83.6802i	0.0770585	+	0.163758i
$512$	−409.120	−	384.189i	−0.799063	−	0.750370i
$513$	−33.0919	+	258.067i	−0.0645065	+	0.503055i
$514$	−1170.26	+	147.838i	−2.27677	+	0.287623i
$515$	−53.3619	−	416.240i	−0.103615	−	0.808232i
$516$	−397.898	−	138.841i	−0.771120	−	0.269071i
$517$	247.863	−	205.050i	0.479425	−	0.396615i
$518$	625.518	+	1925.15i	1.20756	+	3.71650i
$519$	−423.783	+	852.370i	−0.816537	+	1.64233i
$520$	−542.605	+	256.551i	−1.04347	+	0.493368i
$521$	−28.9327	+	73.0757i	−0.0555331	+	0.140261i	−0.954894	−	0.296946i	$-0.904032\pi$
$521$	−28.9327	+	73.0757i	−0.0555331	+	0.140261i	0.899361	+	0.437206i	$0.144032\pi$
$522$	−71.5725	+	419.977i	−0.137112	+	0.804554i
$523$	207.755	−	377.905i	0.397238	−	0.722572i	−0.599746	−	0.800191i	$-0.704732\pi$
$523$	207.755	−	377.905i	0.397238	−	0.722572i	0.996983	+	0.0776183i	$0.0247316\pi$
$524$	1225.15	+	398.075i	2.33807	+	0.759685i
$525$	−505.749	−	558.249i	−0.963332	−	1.06333i
$526$	81.0104	+	249.324i	0.154012	+	0.474000i
$527$	18.2027	−	95.4216i	0.0345401	−	0.181066i
$528$	−165.630	+	6.83853i	−0.313693	+	0.0129518i
$529$	588.808	+	927.812i	1.11306	+	1.75390i
$530$	−282.978	+	343.346i	−0.533920	+	0.647823i
$531$	541.718	+	202.232i	1.02018	+	0.380851i
$532$	−421.287	−	579.852i	−0.791893	−	1.08995i
$533$	−521.806	+	206.598i	−0.978998	+	0.387613i
$534$	−240.343	−	346.269i	−0.450081	−	0.648444i
$535$	92.5096	−	197.536i	0.172915	−	0.369226i
$536$	184.129	+	196.077i	0.343524	+	0.365816i
$537$	−223.121	−	77.8548i	−0.415495	−	0.144981i
$538$	−461.541	−	839.540i	−0.857883	−	1.56048i
$539$	−305.398	−	58.2578i	−0.566601	−	0.108085i
$540$	−997.773	−	62.8037i	−1.84773	−	0.116303i
$541$	501.264	−	275.572i	0.926551	−	0.509376i	0.0543493	−	0.998522i	$-0.482692\pi$
$541$	501.264	−	275.572i	0.926551	−	0.509376i	0.872202	+	0.489146i	$0.162692\pi$
$542$	−43.0070	−	683.577i	−0.0793488	−	1.26121i
$543$	244.982	+	551.163i	0.451164	+	1.01503i
$544$	−64.2720	−	16.5023i	−0.118147	−	0.0303350i
$545$	103.866	−	164.335i	0.190580	−	0.301531i
$546$	−588.292	+	884.255i	−1.07746	+	1.61951i
$547$	−215.731	−	840.218i	−0.394390	−	1.53605i	−0.787358	−	0.616496i	$-0.788552\pi$
$547$	−215.731	−	840.218i	−0.394390	−	1.53605i	0.392968	−	0.919552i	$-0.371448\pi$
$548$	851.711	−	107.596i	1.55422	−	0.196343i
$549$	83.5301	−	785.317i	0.152150	−	1.43045i
$550$	−295.919	+	410.467i	−0.538035	+	0.746304i
$551$	79.3910	+	109.272i	0.144085	+	0.198316i
$552$	1355.53	−	317.046i	2.45567	−	0.574358i
$553$	−241.037	+	608.789i	−0.435871	+	1.10089i
$554$	−147.974	−	576.320i	−0.267101	−	1.04029i
$555$	817.321	−	365.088i	1.47265	−	0.657816i
$556$	−870.251	+	1371.30i	−1.56520	+	2.46636i
$557$	530.822			0.953003			0.476501	−	0.879174i	$-0.341905\pi$
$557$	530.822			0.953003			0.476501	+	0.879174i	$0.341905\pi$
$558$	−660.938	−	28.5269i	−1.18448	−	0.0511235i
$559$	144.322	+	135.528i	0.258180	+	0.242447i
$560$	356.206	−	295.786i	0.636083	−	0.528189i
$561$	−68.6667	+	41.5276i	−0.122401	+	0.0740242i
$562$	−536.335	−	252.380i	−0.954333	−	0.449075i
$563$	128.734	−	273.574i	0.228657	−	0.485922i	−0.757269	−	0.653104i	$-0.773467\pi$
$563$	128.734	−	273.574i	0.228657	−	0.485922i	0.985926	+	0.167182i	$0.0534666\pi$
$564$	617.089	+	1020.37i	1.09413	+	1.80917i
$565$	52.9026	+	816.865i	0.0936330	+	1.44578i
$566$	138.307	−	147.282i	0.244359	−	0.260216i
$567$	−721.897	+	375.110i	−1.27319	+	0.661570i
$568$		−	350.270i		−	0.616672i
$569$	−460.455	−	292.214i	−0.809236	−	0.513557i	0.0656748	−	0.997841i	$-0.479080\pi$
$569$	−460.455	−	292.214i	−0.809236	−	0.513557i	−0.874911	+	0.484284i	$0.839080\pi$
$570$	−362.373	+	327.082i	−0.635743	+	0.573829i
$571$	−173.167	+	44.4617i	−0.303269	+	0.0778663i	−0.397258	−	0.917707i	$-0.630038\pi$
$571$	−173.167	+	44.4617i	−0.303269	+	0.0778663i	0.0939888	+	0.995573i	$0.470038\pi$
$572$	430.708	+	170.529i	0.752986	+	0.298128i
$573$	6.04257	+	25.8351i	0.0105455	+	0.0450874i
$574$	1475.56	−	1072.06i	2.57066	−	1.86769i
$575$	426.109	−	914.250i	0.741060	−	1.59000i
$576$	−82.9023	+	779.415i	−0.143928	+	1.35315i
$577$	5.26065	+	41.6423i	0.00911725	+	0.0721704i	0.996017	−	0.0891651i	$-0.0284199\pi$
$577$	5.26065	+	41.6423i	0.00911725	+	0.0721704i	−0.986900	+	0.161336i	$0.948420\pi$
$578$	−880.190	+	225.994i	−1.52282	+	0.390994i
$579$	863.577	+	574.536i	1.49150	+	0.992289i
$580$	−399.288	+	331.560i	−0.688427	+	0.571655i
$581$	−350.013	+	1363.21i	−0.602432	+	2.34632i
$582$	−157.327	+	69.9289i	−0.270321	+	0.120153i
$583$	157.606	−	9.91573i	0.270336	−	0.0170081i
$584$	51.0190	+	92.8033i	0.0873614	+	0.158910i
$585$	416.354	+	217.350i	0.711716	+	0.371538i
$586$	−344.448	+	1805.66i	−0.587795	+	3.08133i
$587$	−801.227	+	440.479i	−1.36495	+	0.750389i	−0.984661	−	0.174477i	$-0.944176\pi$
$587$	−801.227	+	440.479i	−1.36495	+	0.750389i	−0.380292	+	0.924867i	$0.624176\pi$
$588$	379.696	−	1088.15i	0.645741	−	1.85060i
$589$	−152.892	+	143.575i	−0.259578	+	0.243760i
$590$	524.404	+	949.741i	0.888820	+	1.60973i
$591$	−492.409	+	341.778i	−0.833180	+	0.578305i
$592$	202.546	+	511.573i	0.342138	+	0.864143i
$593$	−882.691	+	641.313i	−1.48852	+	1.08147i	−0.513833	+	0.857890i	$0.671775\pi$
$593$	−882.691	+	641.313i	−1.48852	+	1.08147i	−0.974685	+	0.223581i	$0.928225\pi$
$594$	347.562	+	421.734i	0.585121	+	0.709989i
$595$	82.1253	−	208.546i	0.138026	−	0.350497i
$596$	909.320	−	577.072i	1.52571	−	0.968242i
$597$	−34.2256	−	828.947i	−0.0573293	−	1.38852i
$598$	−1396.98	−	266.487i	−2.33608	−	0.445631i
$599$	−937.410	+	304.583i	−1.56496	+	0.508486i	−0.958127	−	0.286345i	$-0.907560\pi$
$599$	−937.410	+	304.583i	−1.56496	+	0.508486i	−0.606831	+	0.794831i	$0.707560\pi$
$600$	−618.140	−	601.635i	−1.03023	−	1.00272i
$601$	39.2023	−	120.652i	0.0652285	−	0.200753i	−0.913130	−	0.407667i	$-0.866342\pi$
$601$	39.2023	−	120.652i	0.0652285	−	0.200753i	0.978359	+	0.206915i	$0.0663423\pi$
$602$	−563.832	−	309.969i	−0.936598	−	0.514899i
$603$	35.3607	−	207.492i	0.0586414	−	0.344099i
$604$	421.006	+	166.688i	0.697030	+	0.275974i
$605$	−421.949	+	54.0938i	−0.697436	+	0.0894113i
$606$	1675.83	+	833.194i	2.76540	+	1.37491i
$607$	201.639	−	65.5163i	0.332189	−	0.107935i	−0.138174	−	0.990408i	$-0.544123\pi$
$607$	201.639	−	65.5163i	0.332189	−	0.107935i	0.470362	+	0.882473i	$0.344123\pi$
$608$	91.3230	+	110.391i	0.150202	+	0.181563i
$609$	−139.140	+	398.756i	−0.228473	+	0.654771i
$610$	1078.28	−	1016.31i	1.76767	−	1.66608i
$611$	−70.2123	−	555.787i	−0.114914	−	0.909635i
$612$	−114.932	−	274.370i	−0.187798	−	0.448317i
$613$	−323.748	+	344.756i	−0.528137	+	0.562408i	−0.936615	−	0.350359i	$-0.886059\pi$
$613$	−323.748	+	344.756i	−0.528137	+	0.562408i	0.408479	+	0.912768i	$0.366059\pi$
$614$	−696.422	+	327.711i	−1.13424	+	0.533732i
$615$	−540.427	−	598.738i	−0.878744	−	0.973557i
$616$	−686.853	−	86.7697i	−1.11502	−	0.140860i
$617$	391.578	+	100.540i	0.634648	+	0.162950i	0.552289	−	0.833653i	$-0.313754\pi$
$617$	391.578	+	100.540i	0.634648	+	0.162950i	0.0823594	+	0.996603i	$0.473754\pi$
$618$	−568.594	−	632.280i	−0.920055	−	1.02311i
$619$	−561.849	+	222.452i	−0.907672	+	0.359373i	−0.775128	−	0.631804i	$-0.782315\pi$
$619$	−561.849	+	222.452i	−0.907672	+	0.359373i	−0.132544	+	0.991177i	$0.542315\pi$
$620$	−588.503	−	550.606i	−0.949199	−	0.888075i
$621$	−838.072	−	695.958i	−1.34955	−	1.12070i
$622$	−831.637	−	52.3221i	−1.33704	−	0.0841192i
$623$	−177.911	−	378.079i	−0.285571	−	0.606868i
$624$	−144.498	+	249.919i	−0.231568	+	0.400511i
$625$	−619.478	+	82.8969i	−0.991165	+	0.132635i
$626$		−	691.933i		−	1.10532i
$627$	172.643	+	14.6056i	0.275348	+	0.0232944i
$628$	1483.14	+	93.3114i	2.36169	+	0.148585i
$629$	205.226	+	169.777i	0.326273	+	0.269916i
$630$	−1486.26	−	347.667i	−2.35914	−	0.551853i
$631$	117.402	−	46.4829i	0.186058	−	0.0736654i	−0.273248	−	0.961943i	$-0.588098\pi$
$631$	117.402	−	46.4829i	0.186058	−	0.0736654i	0.459306	+	0.888278i	$0.348098\pi$
$632$	−231.697	+	713.092i	−0.366610	+	1.12831i
$633$	−204.089	−	200.108i	−0.322415	−	0.316126i
$634$	−375.591	−	47.4482i	−0.592415	−	0.0748394i
$635$	−797.359	−	257.456i	−1.25568	−	0.405442i
$636$	−49.3474	+	583.302i	−0.0775902	+	0.917141i
$637$	−370.635	+	394.686i	−0.581845	+	0.619602i
$638$	281.467	+	35.5576i	0.441171	+	0.0557329i
$639$	−218.532	+	165.446i	−0.341990	+	0.258914i
$640$	−853.787	+	804.722i	−1.33404	+	1.25738i
$641$	1123.54	−	214.326i	1.75279	−	0.334362i	0.791762	−	0.610829i	$-0.209164\pi$
$641$	1123.54	−	214.326i	1.75279	−	0.334362i	0.961023	+	0.276468i	$0.0891639\pi$
$642$	−73.4388	−	435.848i	−0.114391	−	0.678891i
$643$	−144.532	+	46.9613i	−0.224777	+	0.0730346i	−0.419240	−	0.907875i	$-0.637704\pi$
$643$	−144.532	+	46.9613i	−0.224777	+	0.0730346i	0.194463	+	0.980910i	$0.437704\pi$
$644$	2995.04	−	188.432i	4.65068	−	0.292596i
$645$	−109.942	+	262.436i	−0.170453	+	0.406877i
$646$	−135.049	−	53.4696i	−0.209054	−	0.0827703i
$647$	41.8292	−	50.5628i	0.0646510	−	0.0781496i	−0.737196	−	0.675679i	$-0.763851\pi$
$647$	41.8292	−	50.5628i	0.0646510	−	0.0781496i	0.801847	+	0.597529i	$0.203851\pi$
$648$	−798.056	+	480.604i	−1.23157	+	0.741673i
$649$	118.990	−	366.213i	0.183343	−	0.564273i
$650$	327.410	+	818.129i	0.503707	+	1.25866i
$651$	−641.394	−	136.750i	−0.985244	−	0.210062i
$652$	1778.85	+	339.334i	2.72830	+	0.520451i
$653$	182.188	+	287.082i	0.279001	+	0.439636i	0.954712	−	0.297531i	$-0.0961631\pi$
$653$	182.188	+	287.082i	0.279001	+	0.439636i	−0.675711	+	0.737167i	$0.736163\pi$
$654$	−16.2508	−	393.596i	−0.0248483	−	0.601829i
$655$	318.689	−	809.265i	0.486547	−	1.23552i
$656$	381.988	−	316.008i	0.582299	−	0.481720i
$657$	33.8013	−	75.6651i	0.0514480	−	0.115168i
$658$	670.209	+	1692.75i	1.01855	+	2.57257i
$659$	1019.95	+	479.954i	1.54773	+	0.728306i	0.994501	−	0.104723i	$-0.0333957\pi$
$659$	1019.95	+	479.954i	1.54773	+	0.728306i	0.553228	+	0.833030i	$0.313396\pi$
$660$	−13.1321	+	665.624i	−0.0198971	+	1.00852i
$661$	38.1205	−	35.7976i	0.0576710	−	0.0541567i	−0.655176	−	0.755476i	$-0.727405\pi$
$661$	38.1205	−	35.7976i	0.0576710	−	0.0541567i	0.712847	+	0.701320i	$0.247405\pi$
$662$	270.531	+	1418.17i	0.408657	+	2.14225i
$663$	−3.01376	+	139.716i	−0.00454564	+	0.210733i
$664$	−301.997	+	1583.12i	−0.454815	+	2.38422i
$665$	−408.109	+	260.049i	−0.613697	+	0.391051i
$666$	941.570	−	1550.35i	1.41377	−	2.32786i
$667$	−564.411	+	35.5097i	−0.846193	+	0.0532379i
$668$	−704.446	−	511.810i	−1.05456	−	0.766183i
$669$	−741.811	+	756.568i	−1.10884	+	1.13089i
$670$	303.823	−	252.288i	0.453467	−	0.376549i
$671$	−524.872	−	33.0222i	−0.782224	−	0.0492134i
$672$	−120.739	+	431.399i	−0.179671	+	0.641962i
$673$	−35.6336	−	282.069i	−0.0529473	−	0.419121i	−0.996203	−	0.0870553i	$-0.972254\pi$
$673$	−35.6336	−	282.069i	−0.0529473	−	0.419121i	0.943256	−	0.332066i	$-0.107746\pi$
$674$	551.214	−	758.681i	0.817825	−	1.12564i
$675$	−83.3865	+	669.830i	−0.123536	+	0.992340i
$676$	−359.867	+	261.459i	−0.532348	+	0.386773i
$677$	504.844	−	474.080i	0.745707	−	0.700266i	−0.215374	−	0.976532i	$-0.569097\pi$
$677$	504.844	−	474.080i	0.745707	−	0.700266i	0.961081	+	0.276266i	$0.0890970\pi$
$678$	1029.49	+	1300.56i	1.51842	+	1.91822i
$679$	−165.311	+	42.4447i	−0.243463	+	0.0625106i
$680$	78.8626	−	244.243i	0.115974	−	0.359181i
$681$	−694.828	+	362.696i	−1.02031	+	0.532593i
$682$			440.543i			0.645957i
$683$	50.9671	−	80.3113i	0.0746224	−	0.117586i	−0.804967	−	0.593319i	$-0.797817\pi$
$683$	50.9671	−	80.3113i	0.0746224	−	0.117586i	0.879590	+	0.475733i	$0.157817\pi$
$684$	−147.440	+	625.105i	−0.215555	+	0.913897i
$685$	−37.4595	−	578.409i	−0.0546854	−	0.844392i
$686$	46.9867	−	85.4685i	0.0684937	−	0.124590i
$687$	−760.398	+	527.788i	−1.10684	+	0.768250i
$688$	−158.245	−	74.4645i	−0.230007	−	0.108233i
$689$	132.486	−	240.992i	0.192288	−	0.349771i
$690$	−343.312	−	2014.86i	−0.497554	−	2.92009i
$691$	−696.133	−	653.713i	−1.00743	−	0.946039i	−0.00888358	−	0.999961i	$-0.502828\pi$
$691$	−696.133	−	653.713i	−1.00743	−	0.946039i	−0.998545	+	0.0539220i	$0.982828\pi$
$692$	−1259.08	+	1984.00i	−1.81948	+	2.86705i
$693$	270.291	+	469.509i	0.390031	+	0.677502i
$694$	622.533	−	980.955i	0.897021	−	1.41348i
$695$	888.323	+	642.910i	1.27816	+	0.925050i
$696$	−130.346	+	465.726i	−0.187279	+	0.669147i
$697$	88.3461	−	223.137i	0.126752	−	0.320139i
$698$	152.829	−	143.516i	0.218952	−	0.205610i
$699$	−55.9779	+	5.84823i	−0.0800828	+	0.00836657i
$700$	−1098.50	−	1500.31i	−1.56929	−	2.14330i
$701$	256.816	−	353.477i	0.366357	−	0.504247i	−0.585549	−	0.810637i	$-0.699121\pi$
$701$	256.816	−	353.477i	0.366357	−	0.504247i	0.951906	+	0.306390i	$0.0991210\pi$
$702$	944.424	−	117.515i	1.34533	−	0.167400i
$703$	−143.013	−	556.999i	−0.203433	−	0.792318i
$704$	520.928	+	32.7740i	0.739954	+	0.0465540i
$705$	713.038	−	373.873i	1.01140	−	0.530317i
$706$	2200.87	+	565.087i	3.11738	+	0.800407i
$707$	1500.96	+	1090.51i	2.12300	+	1.54245i
$708$	1278.12	+	635.460i	1.80526	+	0.897542i
$709$	921.461	−	506.578i	1.29966	−	0.714496i	0.326628	−	0.945153i	$-0.394088\pi$
$709$	921.461	−	506.578i	1.29966	−	0.714496i	0.973035	+	0.230657i	$0.0740876\pi$
$710$	−513.310	−	31.3462i	−0.722971	−	0.0441495i
$711$	554.334	−	192.265i	0.779654	−	0.270415i
$712$	−230.511	−	419.299i	−0.323752	−	0.588903i
$713$	−164.551	−	862.608i	−0.230787	−	1.20983i
$714$	−103.434	−	442.232i	−0.144865	−	0.619373i
$715$	132.648	−	283.243i	0.185521	−	0.396144i
$716$	−527.825	−	248.375i	−0.737185	−	0.346893i
$717$	108.733	−	733.178i	0.151650	−	1.02256i
$718$	86.8802	+	119.580i	0.121003	+	0.166546i
$719$	−87.6887	+	72.5424i	−0.121959	+	0.100893i	−0.696404	−	0.717650i	$-0.745218\pi$
$719$	−87.6887	+	72.5424i	−0.121959	+	0.100893i	0.574445	+	0.818543i	$0.305218\pi$
$720$	−409.122	−	68.9478i	−0.568225	−	0.0957608i
$721$	−451.680	−	711.733i	−0.626463	−	0.987147i
$722$	−485.229	−	764.598i	−0.672062	−	1.05900i
$723$	−846.605	+	979.567i	−1.17096	+	1.35486i
$724$	460.095	+	1416.03i	0.635490	+	1.95584i
$725$	207.011	+	282.731i	0.285532	+	0.389974i
$726$	−640.952	+	576.393i	−0.882854	+	0.793929i
$727$	−116.998	+	212.819i	−0.160933	+	0.292736i	−0.944463	−	0.328618i	$-0.893417\pi$
$727$	−116.998	+	212.819i	−0.160933	+	0.292736i	0.783530	+	0.621354i	$0.213417\pi$
$728$	−768.504	+	928.961i	−1.05564	+	1.27605i
$729$	676.799	+	270.896i	0.928393	+	0.371599i
$730$	140.566	−	66.4617i	0.192556	−	0.0910434i
$731$	−84.4947	+	5.31595i	−0.115588	+	0.00727217i
$732$	406.512	−	1906.65i	0.555345	−	2.60471i
$733$	300.648	−	248.718i	0.410161	−	0.339315i	−0.409351	−	0.912377i	$-0.634245\pi$
$733$	300.648	−	248.718i	0.410161	−	0.339315i	0.819512	+	0.573062i	$0.194245\pi$
$734$	863.843	−	164.787i	1.17690	−	0.224505i
$735$	−717.697	−	300.664i	−0.976458	−	0.409067i
$736$	−595.133	+	75.1827i	−0.808604	+	0.102150i
$737$	−139.060	−	17.5674i	−0.188684	−	0.0238364i
$738$	−1590.72	−	375.192i	−2.15544	−	0.508390i
$739$	141.092	+	299.835i	0.190922	+	0.405730i	0.977253	−	0.212075i	$-0.0680220\pi$
$739$	141.092	+	299.835i	0.190922	+	0.405730i	−0.786331	+	0.617805i	$0.788022\pi$
$740$	2100.29	−	686.703i	2.83823	−	0.927977i
$741$	182.573	−	240.221i	0.246388	−	0.324184i
$742$	−222.266	+	865.669i	−0.299550	+	1.16667i
$743$	55.7920	−	171.710i	0.0750902	−	0.231104i	−0.906466	−	0.422280i	$-0.861230\pi$
$743$	55.7920	−	171.710i	0.0750902	−	0.231104i	0.981556	+	0.191176i	$0.0612300\pi$
$744$	−742.856	−	110.169i	−0.998462	−	0.148076i
$745$	−351.476	−	636.554i	−0.471780	−	0.854435i
$746$	−1188.75	−	983.418i	−1.59350	−	1.31825i
$747$	1130.35	−	559.355i	1.51318	−	0.748802i
$748$	−179.239	+	84.3434i	−0.239624	+	0.112759i
$749$		−	438.155i		−	0.584987i
$750$	−936.995	+	852.023i	−1.24933	+	1.13603i
$751$	387.183			0.515557			0.257778	−	0.966204i	$-0.417010\pi$
$751$	387.183			0.515557			0.257778	+	0.966204i	$0.417010\pi$
$752$	210.703	+	447.767i	0.280190	+	0.595435i
$753$	−605.045	−	402.534i	−0.803512	−	0.534574i
$754$	314.927	−	380.682i	0.417675	−	0.504883i
$755$	129.660	−	276.863i	0.171735	−	0.366705i
$756$	−1868.58	+	735.785i	−2.47167	+	0.973260i
$757$	59.1623	+	19.2230i	0.0781536	+	0.0253936i	0.347833	−	0.937557i	$-0.386918\pi$
$757$	59.1623	+	19.2230i	0.0781536	+	0.0253936i	−0.269679	+	0.962950i	$0.586918\pi$
$758$	−879.384	−	225.787i	−1.16014	−	0.297873i
$759$	−438.957	+	577.557i	−0.578336	+	0.760944i
$760$	−447.713	+	326.543i	−0.589095	+	0.429662i
$761$	13.1676	−	6.19618i	0.0173030	−	0.00814216i	−0.417108	−	0.908857i	$-0.636956\pi$
$761$	13.1676	−	6.19618i	0.0173030	−	0.00814216i	0.434411	+	0.900715i	$0.356956\pi$
$762$	−1625.68	+	489.718i	−2.13344	+	0.642674i
$763$	48.9441	−	387.433i	0.0641470	−	0.507775i
$764$	8.20874	+	64.9788i	0.0107444	+	0.0850508i
$765$	−189.632	+	66.1632i	−0.247885	+	0.0864879i
$766$	−210.636	−	1104.19i	−0.274981	−	1.44150i
$767$	−427.437	−	516.683i	−0.557284	−	0.673641i
$768$	−277.816	+	1303.03i	−0.361740	+	1.69665i
$769$	−41.2391	−	655.477i	−0.0536270	−	0.852376i	−0.929266	−	0.369410i	$-0.879560\pi$
$769$	−41.2391	−	655.477i	−0.0536270	−	0.852376i	0.875639	−	0.482966i	$-0.160440\pi$
$770$	−188.626	+	998.796i	−0.244968	+	1.29714i
$771$	650.335	+	821.569i	0.843495	+	1.06559i
$772$	1972.84	+	1632.08i	2.55550	+	2.11409i
$773$	476.819	+	262.134i	0.616842	+	0.339112i	0.759351	−	0.650682i	$-0.225517\pi$
$773$	476.819	+	262.134i	0.616842	+	0.339112i	−0.142508	+	0.989794i	$0.545517\pi$
$774$	119.170	+	564.108i	0.153967	+	0.728822i
$775$	−395.281	+	373.942i	−0.510040	+	0.482506i
$776$	−185.876	+	60.3946i	−0.239530	+	0.0778281i
$777$	1175.78	−	1360.44i	1.51323	−	1.75089i
$778$	1336.02	−	847.865i	1.71725	−	1.08980i
$779$	−437.492	+	277.641i	−0.561607	+	0.356407i
$780$	966.461	+	640.420i	1.23905	+	0.821052i
$781$	116.347	+	140.639i	0.148971	+	0.180076i
$782$	492.006	−	357.463i	0.629163	−	0.457114i
$783$	352.132	−	138.658i	0.449721	−	0.177085i
$784$	203.642	−	432.761i	0.259748	−	0.551992i
$785$	123.921	−	995.672i	0.157861	−	1.26837i
$786$	−401.377	−	1716.09i	−0.510657	−	2.18332i
$787$	1182.20	−	225.516i	1.50216	−	0.286552i	0.630314	−	0.776340i	$-0.282926\pi$
$787$	1182.20	−	225.516i	1.50216	−	0.286552i	0.871841	+	0.489789i	$0.162926\pi$
$788$	−1296.60	+	712.814i	−1.64544	+	0.904586i
$789$	152.275	−	176.190i	0.192997	−	0.223308i
$790$	1024.28	+	403.361i	1.29655	+	0.510583i
$791$	792.149	+	1440.91i	1.00145	+	1.82164i
$792$	342.664	+	517.148i	0.432656	+	0.652964i
$793$	−538.327	+	740.943i	−0.678848	+	0.934355i
$794$	278.472	−	1084.58i	0.350720	−	1.36596i
$795$	391.065	+	57.2611i	0.491906	+	0.0720265i
$796$	128.596	−	2043.97i	0.161552	−	2.56780i
$797$	−444.980	+	114.251i	−0.558318	+	0.143352i	−0.517296	−	0.855806i	$-0.673061\pi$
$797$	−444.980	+	114.251i	−0.558318	+	0.143352i	−0.0410222	+	0.999158i	$0.513061\pi$
$798$	−380.553	+	903.722i	−0.476883	+	1.13248i
$799$	193.806	+	140.808i	0.242560	+	0.176230i
$800$	237.977	+	285.518i	0.297471	+	0.356897i
$801$	−152.719	+	341.866i	−0.190661	+	0.426799i
$802$	−907.564	−	966.458i	−1.13163	−	1.20506i
$803$	−51.3108	−	20.3154i	−0.0638989	−	0.0252994i
$804$	140.037	−	500.354i	0.174176	−	0.622330i
$805$	−3.72981	−	2026.16i	−0.00463330	−	2.51696i
$806$	647.762	+	411.082i	0.803674	+	0.510027i
$807$	−425.978	+	736.755i	−0.527854	+	0.912955i
$808$	1793.79	+	1138.38i	2.22004	+	1.40888i
$809$	623.255	−	663.699i	0.770402	−	0.820394i	−0.217405	−	0.976082i	$-0.569759\pi$
$809$	623.255	−	663.699i	0.770402	−	0.820394i	0.987806	+	0.155687i	$0.0497592\pi$
$810$	632.891	+	1212.54i	0.781347	+	1.49696i
$811$	445.421	+	244.872i	0.549224	+	0.301938i	0.732100	−	0.681198i	$-0.238541\pi$
$811$	445.421	+	244.872i	0.549224	+	0.301938i	−0.182876	+	0.983136i	$0.558541\pi$
$812$	−443.890	+	943.315i	−0.546663	+	1.16172i
$813$	−499.826	+	346.926i	−0.614792	+	0.426724i
$814$	−1058.49	−	581.910i	−1.30036	−	0.714878i
$815$	301.889	−	1184.83i	0.370416	−	1.45378i
$816$	−35.6070	−	118.202i	−0.0436360	−	0.144856i
$817$	154.335	+	97.9441i	0.188905	+	0.119883i
$818$	1833.39			2.24130
$819$	942.568	+	40.6825i	1.15088	+	0.0496734i
$820$	−1173.25	−	1608.61i	−1.43080	−	1.96172i
$821$	68.3007	+	266.014i	0.0831921	+	0.324012i	0.996534	−	0.0831805i	$-0.0265078\pi$
$821$	68.3007	+	266.014i	0.0831921	+	0.324012i	−0.913342	+	0.407192i	$0.866508\pi$
$822$	−728.964	−	920.902i	−0.886817	−	1.12032i
$823$	63.4062	+	67.5208i	0.0770428	+	0.0820422i	0.766335	−	0.642441i	$-0.222078\pi$
$823$	63.4062	+	67.5208i	0.0770428	+	0.0820422i	−0.689292	+	0.724484i	$0.742078\pi$
$824$	−567.381	−	780.934i	−0.688570	−	0.947735i
$825$	448.034	+	36.2429i	0.543071	+	0.0439308i
$826$	1763.07	+	1280.95i	2.13447	+	1.55078i
$827$	−760.595	+	96.0855i	−0.919704	+	0.116186i	−0.570909	−	0.821013i	$-0.693409\pi$
$827$	−760.595	+	96.0855i	−0.919704	+	0.116186i	−0.348795	+	0.937199i	$0.613409\pi$
$828$	−1879.08	−	1923.64i	−2.26942	−	2.32324i
$829$	85.8490	−	1364.53i	0.103557	−	1.64600i	−0.512785	−	0.858517i	$-0.671386\pi$
$829$	85.8490	−	1364.53i	0.103557	−	1.64600i	0.616342	−	0.787478i	$-0.288614\pi$
$830$	2292.99	+	584.243i	2.76264	+	0.703908i
$831$	−370.046	+	377.408i	−0.445302	+	0.454161i
$832$	534.281	−	735.375i	0.642165	−	0.883864i
$833$	−14.5378	−	231.072i	−0.0174524	−	0.277398i
$834$	2221.48	+	47.9186i	2.66364	+	0.0574564i
$835$	−373.907	+	453.674i	−0.447793	+	0.543323i
$836$	420.118	+	80.1418i	0.502534	+	0.0958634i
$837$	282.145	+	515.501i	0.337091	+	0.615892i
$838$	923.575	−	176.181i	1.10212	−	0.210240i
$839$	−225.233	−	239.849i	−0.268454	−	0.285875i	0.580590	−	0.814196i	$-0.302822\pi$
$839$	−225.233	−	239.849i	−0.268454	−	0.285875i	−0.849045	+	0.528321i	$0.822822\pi$
$840$	−1637.03	−	567.839i	−1.94884	−	0.675999i
$841$	−274.430	+	583.193i	−0.326314	+	0.693452i
$842$	−364.592	+	144.352i	−0.433007	+	0.171440i
$843$	54.7123	+	523.693i	0.0649020	+	0.621225i
$844$	−449.741	−	543.644i	−0.532869	−	0.644128i
$845$	161.391	+	253.280i	0.190995	+	0.299740i
$846$	757.631	−	1444.82i	0.895545	−	1.70783i
$847$	−721.495	+	457.874i	−0.851824	+	0.540584i
$848$	−45.5210	+	238.630i	−0.0536805	+	0.281403i
$849$	−175.530	−	37.4244i	−0.206749	−	0.0440806i
$850$	−350.873	−	137.428i	−0.412792	−	0.161680i
$851$	2289.94	+	744.047i	2.69088	+	0.874321i
$852$	−578.965	+	350.141i	−0.679537	+	0.410963i
$853$	−601.048	−	497.230i	−0.704629	−	0.582919i	0.214572	−	0.976708i	$-0.431164\pi$
$853$	−601.048	−	497.230i	−0.704629	−	0.582919i	−0.919201	+	0.393789i	$0.871164\pi$
$854$	1095.70	−	2767.42i	1.28302	−	3.24053i
$855$	415.200	+	125.087i	0.485615	+	0.146301i
$856$	−31.5045	−	500.750i	−0.0368043	−	0.584988i
$857$	416.696	+	1282.46i	0.486226	+	1.49645i	0.830197	+	0.557470i	$0.188228\pi$
$857$	416.696	+	1282.46i	0.486226	+	1.49645i	−0.343971	+	0.938980i	$0.611772\pi$
$858$	−105.302	−	624.954i	−0.122730	−	0.728384i
$859$	277.793	+	1456.24i	0.323391	+	1.69527i	0.658082	+	0.752946i	$0.271368\pi$
$859$	277.793	+	1456.24i	0.323391	+	1.69527i	−0.334691	+	0.942328i	$0.608632\pi$
$860$	−337.239	+	616.118i	−0.392138	+	0.716417i
$861$	−1493.19	−	628.775i	−1.73425	−	0.730284i
$862$	12.4220	−	98.3300i	0.0144106	−	0.114072i
$863$	−162.054	−	152.179i	−0.187780	−	0.176337i	0.584955	−	0.811066i	$-0.301112\pi$
$863$	−162.054	−	152.179i	−0.187780	−	0.176337i	−0.772735	+	0.634728i	$0.781112\pi$
$864$	363.540	−	170.239i	0.420763	−	0.197036i
$865$	1285.23	+	930.163i	1.48581	+	1.07533i
$866$	−185.626	+	1469.38i	−0.214348	+	1.69674i
$867$	576.399	+	565.156i	0.664820	+	0.651852i
$868$	−1539.64	−	500.260i	−1.77378	−	0.576336i
$869$	−143.832	−	363.279i	−0.165515	−	0.418043i
$870$	670.842	+	232.696i	0.771083	+	0.267467i
$871$	−155.591	+	188.078i	−0.178635	+	0.215933i
$872$	28.0788	−	446.300i	0.0322005	−	0.511812i
$873$	125.476	+	87.4403i	0.143730	+	0.100161i
$874$	−1313.04			−1.50234
$875$	−1056.29	+	678.552i	−1.20719	+	0.775488i
$876$	102.395	−	177.099i	0.116890	−	0.202168i
$877$	−1013.25	+	476.800i	−1.15536	+	0.543672i	−0.905390	−	0.424582i	$-0.860421\pi$
$877$	−1013.25	+	476.800i	−1.15536	+	0.543672i	−0.249971	+	0.968253i	$0.580421\pi$
$878$	21.2625	−	337.958i	0.0242170	−	0.384918i
$879$	1530.85	−	568.231i	1.74158	−	0.646452i
$880$	−34.1231	+	274.170i	−0.0387762	+	0.311557i
$881$	532.937	+	1346.05i	0.604923	+	1.52786i	0.832456	+	0.554091i	$0.186934\pi$
$881$	532.937	+	1346.05i	0.604923	+	1.52786i	−0.227533	+	0.973770i	$0.573066\pi$
$882$	−1542.70	+	325.901i	−1.74909	+	0.369502i
$883$	−166.393	+	648.058i	−0.188441	+	0.733928i	0.802156	+	0.597114i	$0.203686\pi$
$883$	−166.393	+	648.058i	−0.188441	+	0.733928i	−0.990597	+	0.136814i	$0.956314\pi$
$884$	−43.2363	+	342.251i	−0.0489098	+	0.387161i
$885$	480.846	−	835.196i	0.543329	−	0.943725i
$886$	207.264	+	440.458i	0.233932	+	0.497130i
$887$	805.586	+	756.496i	0.908214	+	0.852870i	0.989605	−	0.143812i	$-0.0459362\pi$
$887$	805.586	+	756.496i	0.908214	+	0.852870i	−0.0813908	+	0.996682i	$0.525936\pi$
$888$	1245.94	−	1639.34i	1.40308	−	1.84610i
$889$	−1669.83	+	210.949i	−1.87833	+	0.237288i
$890$	−635.098	+	300.284i	−0.713593	+	0.337397i
$891$	160.793	−	458.055i	0.180464	−	0.514091i
$892$	−2015.31	+	1667.21i	−2.25932	+	1.86907i
$893$	−159.830	−	491.906i	−0.178981	−	0.550846i
$894$	−1319.36	−	655.960i	−1.47579	−	0.733736i
$895$	−189.106	+	345.487i	−0.211292	+	0.386020i
$896$	−867.582	+	2191.26i	−0.968283	+	2.44560i
$897$	439.620	+	1184.36i	0.490101	+	1.32036i
$898$	−1098.77	+	1998.66i	−1.22357	+	2.22567i
$899$	290.144	+	94.2734i	0.322740	+	0.104865i
$900$	−376.537	+	1623.14i	−0.418375	+	1.80349i
$901$	36.3405	+	111.845i	0.0403335	+	0.124134i
$902$	−203.938	+	1069.08i	−0.226096	+	1.18523i
$903$	23.5782	+	571.067i	0.0261110	+	0.632411i
$904$	1008.92	+	1589.80i	1.11606	+	1.75863i
$905$	973.216	−	251.790i	1.07538	−	0.278221i
$906$	−102.930	−	610.876i	−0.113610	−	0.674257i
$907$	248.124	+	341.514i	0.273566	+	0.376531i	0.923589	−	0.383383i	$-0.125241\pi$
$907$	248.124	+	341.514i	0.273566	+	0.376531i	−0.650024	+	0.759914i	$0.725241\pi$
$908$	−1798.94	+	712.250i	−1.98121	+	0.784416i
$909$	−137.049	−	1656.84i	−0.150769	−	1.82270i
$910$	1292.59	+	1209.35i	1.42043	+	1.32896i
$911$	−705.164	−	750.923i	−0.774054	−	0.824284i	0.214250	−	0.976779i	$-0.431269\pi$
$911$	−705.164	−	750.923i	−0.774054	−	0.824284i	−0.988304	+	0.152495i	$0.951269\pi$
$912$	−87.8112	+	251.654i	−0.0962842	+	0.275937i
$913$	−404.599	−	735.962i	−0.443153	−	0.806092i
$914$	17.5557	+	3.34892i	0.0192075	+	0.00366403i
$915$	−1268.19	−	352.421i	−1.38600	−	0.385159i
$916$	−2002.27	+	1100.76i	−2.18588	+	1.20170i
$917$	−109.702	−	1743.66i	−0.119631	−	1.90148i
$918$	−239.828	+	328.800i	−0.261251	+	0.358170i
$919$	−641.483	−	164.705i	−0.698023	−	0.179222i	−0.117027	−	0.993129i	$-0.537337\pi$
$919$	−641.483	−	164.705i	−0.698023	−	0.179222i	−0.580995	+	0.813907i	$0.697337\pi$
$920$	−149.948	−	2315.34i	−0.162987	−	2.51667i
$921$	569.239	+	378.713i	0.618066	+	0.411198i
$922$	−240.995	−	938.615i	−0.261383	−	1.01802i
$923$	315.358	−	39.8390i	0.341666	−	0.0431625i
$924$	543.177	+	1222.04i	0.587853	+	1.32256i
$925$	−376.345	−	1443.68i	−0.406859	−	1.56073i
$926$	346.882	+	477.443i	0.374603	+	0.515597i
$927$	−219.225	+	722.851i	−0.236489	+	0.779775i
$928$	76.7146	−	193.759i	0.0826666	−	0.208792i
$929$	11.5597	+	45.0222i	0.0124432	+	0.0484630i	0.974502	−	0.224381i	$-0.0720359\pi$
$929$	11.5597	+	45.0222i	0.0124432	+	0.0484630i	−0.962058	+	0.272844i	$0.912036\pi$
$930$	−227.928	+	1078.77i	−0.245084	+	1.15997i
$931$	−267.853	+	422.069i	−0.287705	+	0.453350i
$932$	−138.934			−0.149071
$933$	342.527	+	656.190i	0.367125	+	0.703312i
$934$	336.270	+	315.778i	0.360032	+	0.338093i
$935$	49.4639	+	124.263i	0.0529026	+	0.132901i
$936$	1080.15	−	21.2788i	1.15400	−	0.0227337i
$937$	−1112.08	−	523.303i	−1.18685	−	0.558488i	−0.272004	−	0.962296i	$-0.587686\pi$
$937$	−1112.08	−	523.303i	−1.18685	−	0.558488i	−0.914844	+	0.403808i	$0.867686\pi$
$938$	337.762	−	717.780i	0.360087	−	0.765224i
$939$	−525.948	+	318.077i	−0.560115	+	0.338741i
$940$	1846.51	−	735.021i	1.96438	−	0.781937i
$941$	−98.4461	+	104.834i	−0.104619	+	0.111407i	−0.779147	−	0.626842i	$-0.784347\pi$
$941$	−98.4461	+	104.834i	−0.104619	+	0.111407i	0.674528	+	0.738249i	$0.264347\pi$
$942$	−940.814	−	1802.35i	−0.998741	−	1.91332i
$943$		−	2169.50i		−	2.30063i
$944$	500.143	+	317.401i	0.529813	+	0.336229i
$945$	418.957	+	1289.55i	0.443341	+	1.36460i
$946$	371.881	−	95.4828i	0.393109	−	0.100933i
$947$	−584.325	−	231.351i	−0.617027	−	0.244298i	0.0387545	−	0.999249i	$-0.487661\pi$
$947$	−584.325	−	231.351i	−0.617027	−	0.244298i	−0.655782	+	0.754950i	$0.727661\pi$
$948$	1410.29	−	329.853i	1.48765	−	0.347946i
$949$	−77.7506	+	56.4891i	−0.0819290	+	0.0595249i
$950$	438.472	+	685.331i	0.461550	+	0.721402i
$951$	136.591	+	307.303i	0.143629	+	0.323137i
$952$	−64.6169	−	511.495i	−0.0678749	−	0.537285i
$953$	526.169	−	135.097i	0.552118	−	0.141760i	0.0376839	−	0.999290i	$-0.488002\pi$
$953$	526.169	−	135.097i	0.552118	−	0.141760i	0.514434	+	0.857530i	$0.328002\pi$
$954$	717.797	−	355.203i	0.752407	−	0.372330i
$955$	44.1281	−	2.85787i	0.0462074	−	0.00299253i
$956$	455.016	−	1772.17i	0.475958	−	1.85373i
$957$	−102.361	−	230.293i	−0.106960	−	0.240640i
$958$	398.338	−	25.0613i	0.415801	−	0.0261600i
$959$	−560.908	−	1020.29i	−0.584888	−	1.06391i
$960$	1258.66	+	349.772i	1.31110	+	0.364346i
$961$	91.3057	−	478.642i	0.0950112	−	0.498066i
$962$	−1843.33	+	1013.38i	−1.91614	+	1.05341i
$963$	−297.535	+	256.178i	−0.308966	+	0.266021i
$964$	−2329.80	+	2187.83i	−2.41681	+	2.26953i
$965$	1181.07	−	1262.36i	1.22391	−	1.30815i
$966$	−2341.05	−	3372.82i	−2.42345	−	3.49153i
$967$	−370.822	−	936.589i	−0.383476	−	0.968551i	−0.985439	−	0.170027i	$-0.945615\pi$
$967$	−370.822	−	936.589i	−0.383476	−	0.968551i	0.601963	−	0.798524i	$-0.294385\pi$
$968$	−791.644	+	575.163i	−0.817814	+	0.594177i
$969$	21.4381	+	127.232i	0.0221240	+	0.131302i
$970$	71.8721	+	277.800i	0.0740950	+	0.286391i
$971$	712.376	−	452.088i	0.733652	−	0.465590i	−0.115788	−	0.993274i	$-0.536939\pi$
$971$	712.376	−	452.088i	0.733652	−	0.465590i	0.849441	+	0.527684i	$0.176939\pi$
$972$	1592.16	+	838.688i	1.63802	+	0.862848i
$973$	2163.69	+	412.746i	2.22373	+	0.424199i
$974$	−143.700	+	46.6911i	−0.147536	+	0.0479375i
$975$	471.363	−	624.957i	0.483449	−	0.640982i
$976$	250.005	−	769.437i	0.256153	−	0.788358i
$977$	−321.193	−	176.577i	−0.328754	−	0.180734i	0.308825	−	0.951119i	$-0.400064\pi$
$977$	−321.193	−	176.577i	−0.328754	−	0.180734i	−0.637579	+	0.770385i	$0.720064\pi$
$978$	−862.160	−	2322.71i	−0.881554	−	2.37496i
$979$	231.830	+	91.7878i	0.236802	+	0.0937567i
$980$	−1684.93	−	922.265i	−1.71932	−	0.941086i
$981$	−291.707	+	193.286i	−0.297357	+	0.197030i
$982$	279.383	−	90.7772i	0.284504	−	0.0924411i
$983$	−291.111	−	351.893i	−0.296145	−	0.357978i	0.601363	−	0.798976i	$-0.294625\pi$
$983$	−291.111	−	351.893i	−0.296145	−	0.357978i	−0.897508	+	0.440998i	$0.854625\pi$
$984$	−1751.72	−	611.237i	−1.78020	−	0.621175i
$985$	427.016	+	903.136i	0.433519	+	0.916890i
$986$	26.4795	+	209.607i	0.0268555	+	0.212583i
$987$	978.594	−	1287.58i	0.991483	−	1.30454i
$988$	509.861	−	542.947i	0.516054	−	0.549542i
$989$	−692.500	+	325.866i	−0.700202	+	0.329490i
$990$	788.529	−	455.883i	0.796494	−	0.460487i
$991$	546.511	+	69.0404i	0.551474	+	0.0696674i	0.396132	−	0.918193i	$-0.370352\pi$
$991$	546.511	+	69.0404i	0.551474	+	0.0696674i	0.155342	+	0.987861i	$0.450352\pi$
$992$	313.431	+	80.4755i	0.315959	+	0.0811245i
$993$	953.611	−	857.559i	0.960333	−	0.863605i
$994$	−960.481	+	380.281i	−0.966279	+	0.382577i
$995$	−1372.17	−	170.780i	−1.37906	−	0.171638i
$996$	2918.65	−	1083.37i	2.93037	−	1.08772i
$997$	1070.50	+	67.3499i	1.07372	+	0.0675526i	0.589791	−	0.807556i	$-0.299210\pi$
$997$	1070.50	+	67.3499i	1.07372	+	0.0675526i	0.483927	+	0.875109i	$0.339210\pi$
$998$	−979.022	−	2080.53i	−0.980984	−	2.08470i
$999$	−1611.28	−	3.01300i	−1.61289	−	0.00301601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.p.a.14.10	✓	1960
3.2	odd	2	inner	375.3.p.a.14.89	yes	1960
125.9	even	50	inner	375.3.p.a.134.89	yes	1960
375.134	odd	50	inner	375.3.p.a.134.10	yes	1960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
375.3.p.a.14.10	✓	1960	1.1	even	1	trivial
375.3.p.a.14.89	yes	1960	3.2	odd	2	inner
375.3.p.a.134.10	yes	1960	375.134	odd	50	inner
375.3.p.a.134.89	yes	1960	125.9	even	50	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	375.p (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43795 - 3.05579i) q^{2} +(-1.66173 + 2.49773i) q^{3} +(-4.72047 + 5.70606i) q^{4} +(3.65114 + 3.41602i) q^{5} +(10.0220 + 1.48631i) q^{6} +(9.55210 + 3.10367i) q^{7} +(11.1399 + 2.86023i) q^{8} +(-3.47729 - 8.30111i) q^{9} +(5.18850 - 16.0692i) q^{10} +(-5.42290 + 2.55182i) q^{11} +(-6.40805 - 21.2724i) q^{12} +(-1.30812 + 10.3548i) q^{13} +(-4.25125 - 33.6521i) q^{14} +(-14.5995 + 3.44304i) q^{15} +(-1.72762 - 9.05649i) q^{16} +(-2.84494 - 3.43894i) q^{17} +(-20.3663 + 22.5624i) q^{18} +(0.605069 + 9.61729i) q^{19} +(-36.7271 + 4.70841i) q^{20} +(-23.6251 + 18.7011i) q^{21} +(15.5957 + 12.9019i) q^{22} +(-35.3563 - 19.4373i) q^{23} +(-25.6556 + 23.0714i) q^{24} +(1.66161 + 24.9447i) q^{25} +(33.5232 - 10.8924i) q^{26} +(26.5122 + 5.10888i) q^{27} +(-62.8001 + 39.8541i) q^{28} +(11.8346 - 7.51046i) q^{29} +(31.5145 + 39.6621i) q^{30} +(13.8737 + 16.7704i) q^{31} +(12.0281 - 8.73896i) q^{32} +(2.63764 - 17.7854i) q^{33} +(-6.41780 + 13.6385i) q^{34} +(24.2739 + 43.9621i) q^{35} +(63.7811 + 19.3434i) q^{36} +(-58.6200 + 11.1824i) q^{37} +(28.5184 - 15.6781i) q^{38} +(-23.6899 - 20.4743i) q^{39} +(30.9026 + 48.4971i) q^{40} +(25.9044 + 47.1199i) q^{41} +(91.1183 + 45.3023i) q^{42} +(11.1497 - 15.3462i) q^{43} +(11.0377 - 42.9892i) q^{44} +(15.6607 - 42.1870i) q^{45} +(-8.55584 + 135.991i) q^{46} +(-51.9878 + 13.3482i) q^{47} +(25.4915 + 10.7343i) q^{48} +(41.9681 + 30.4916i) q^{49} +(73.8365 - 40.9467i) q^{50} +(13.3170 - 1.39129i) q^{51} +(-52.9105 - 56.3439i) q^{52} +(-24.4987 - 9.69972i) q^{53} +(-22.5115 - 88.3621i) q^{54} +(-28.5168 - 9.20768i) q^{55} +(97.5319 + 61.8957i) q^{56} +(-25.0268 - 14.4701i) q^{57} +(-39.9679 - 25.3644i) q^{58} +(-43.9810 + 46.8350i) q^{59} +(49.2702 - 99.5584i) q^{60} +(76.8956 + 42.2737i) q^{61} +(31.2973 - 66.5101i) q^{62} +(-7.45160 - 90.0854i) q^{63} +(-76.3177 - 41.9560i) q^{64} +(-40.1485 + 33.3384i) q^{65} +(-58.1411 + 17.5143i) q^{66} +(19.7463 + 12.5314i) q^{67} +33.0522 q^{68} +(107.302 - 56.0109i) q^{69} +(99.4344 - 137.391i) q^{70} +(-7.57387 - 29.4983i) q^{71} +(-14.9935 - 102.419i) q^{72} +(6.30329 + 6.71233i) q^{73} +(118.463 + 163.051i) q^{74} +(-65.0663 - 37.3012i) q^{75} +(-57.7331 - 41.9455i) q^{76} +(-59.7201 + 7.54440i) q^{77} +(-28.5005 + 101.832i) q^{78} +(-4.09345 + 65.0636i) q^{79} +(24.6294 - 38.9681i) q^{80} +(-56.8168 + 57.7308i) q^{81} +(106.739 - 146.914i) q^{82} +(8.79888 + 139.854i) q^{83} +(4.81207 - 223.084i) q^{84} +(1.36022 - 22.2744i) q^{85} +(-62.9274 - 12.0040i) q^{86} +(-0.906828 + 42.0400i) q^{87} +(-67.7092 + 12.9162i) q^{88} +(-28.4792 - 30.3273i) q^{89} +(-151.434 + 12.8069i) q^{90} +(-44.6333 + 94.8506i) q^{91} +(277.809 - 109.992i) q^{92} +(-64.9424 + 6.78480i) q^{93} +(115.545 + 139.670i) q^{94} +(-30.6437 + 37.1810i) q^{95} +(1.83999 + 44.5649i) q^{96} +(-14.3478 + 9.10536i) q^{97} +(32.8281 - 172.091i) q^{98} +(40.0400 + 36.1426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1960 q - 20 q^{3} - 40 q^{4} - 20 q^{6} - 50 q^{7} - 20 q^{9} - 40 q^{10} - 180 q^{12} - 40 q^{13} + 20 q^{15} - 140 q^{16} - 25 q^{18} + 10 q^{19} - 65 q^{21} - 15 q^{24} - 350 q^{25} - 125 q^{27} - 320 q^{28}+ \cdots - 15 q^{99}+O(q^{100}) \) 1960 * q - 20 * q^3 - 40 * q^4 - 20 * q^6 - 50 * q^7 - 20 * q^9 - 40 * q^10 - 180 * q^12 - 40 * q^13 + 20 * q^15 - 140 * q^16 - 25 * q^18 + 10 * q^19 - 65 * q^21 - 15 * q^24 - 350 * q^25 - 125 * q^27 - 320 * q^28 - 20 * q^30 + 60 * q^31 - 45 * q^33 - 240 * q^34 - 1000 * q^36 - 160 * q^37 + 180 * q^39 - 120 * q^40 + 150 * q^42 - 50 * q^43 - 820 * q^45 + 160 * q^46 - 175 * q^48 + 2980 * q^49 - 15 * q^51 + 270 * q^52 - 345 * q^54 - 40 * q^55 - 280 * q^58 - 1305 * q^60 - 140 * q^61 - 820 * q^63 - 400 * q^64 + 355 * q^66 + 210 * q^67 - 220 * q^69 - 1250 * q^70 - 240 * q^72 + 100 * q^73 - 225 * q^75 - 30 * q^76 - 830 * q^78 + 60 * q^79 - 620 * q^81 + 1550 * q^82 + 335 * q^84 + 1540 * q^85 + 405 * q^87 + 1660 * q^88 + 705 * q^90 + 70 * q^91 - 25 * q^93 + 660 * q^94 - 595 * q^96 + 100 * q^97 - 15 * q^99

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