LMFDB - Embedded newform 75.3.k.a.22.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(13,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			22.3
Character	$\chi$	$=$	75.22
Dual form			75.3.k.a.58.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.16137 + 1.10127i) q^{2} +(1.71073 - 0.270952i) q^{3} +(1.10757 - 1.52445i) q^{4} +(2.52133 - 4.31774i) q^{5} +(-3.39912 + 2.46960i) q^{6} +(6.20191 + 6.20191i) q^{7} +(0.802843 - 5.06895i) q^{8} +(2.85317 - 0.927051i) q^{9} +O(q^{10})$	\(q+(-2.16137 + 1.10127i) q^{2} +(1.71073 - 0.270952i) q^{3} +(1.10757 - 1.52445i) q^{4} +(2.52133 - 4.31774i) q^{5} +(-3.39912 + 2.46960i) q^{6} +(6.20191 + 6.20191i) q^{7} +(0.802843 - 5.06895i) q^{8} +(2.85317 - 0.927051i) q^{9} +(-0.694505 + 12.1089i) q^{10} +(-2.91866 + 8.98272i) q^{11} +(1.48171 - 2.90801i) q^{12} +(19.3727 + 9.87087i) q^{13} +(-20.2346 - 6.57463i) q^{14} +(3.14340 - 8.06964i) q^{15} +(6.17620 + 19.0084i) q^{16} +(7.79733 + 1.23498i) q^{17} +(-5.14582 + 5.14582i) q^{18} +(-18.8393 - 25.9301i) q^{19} +(-3.78961 - 8.62585i) q^{20} +(12.2902 + 8.92935i) q^{21} +(-3.58412 - 22.6292i) q^{22} +(-9.95365 - 19.5351i) q^{23} -8.88912i q^{24} +(-12.2858 - 21.7729i) q^{25} -52.7420 q^{26} +(4.62981 - 2.35900i) q^{27} +(16.3236 - 2.58540i) q^{28} +(-8.82827 + 12.1511i) q^{29} +(2.09283 + 20.9032i) q^{30} +(-17.8806 + 12.9910i) q^{31} +(-19.7666 - 19.7666i) q^{32} +(-2.55914 + 16.1578i) q^{33} +(-18.2130 + 5.91775i) q^{34} +(42.4153 - 11.1412i) q^{35} +(1.74686 - 5.37628i) q^{36} +(17.2521 - 33.8591i) q^{37} +(69.2749 + 35.2973i) q^{38} +(35.8159 + 11.6373i) q^{39} +(-19.8622 - 16.2470i) q^{40} +(-5.26285 - 16.1974i) q^{41} +(-36.3973 - 5.76477i) q^{42} +(-27.9207 + 27.9207i) q^{43} +(10.4610 + 14.3984i) q^{44} +(3.19100 - 14.6567i) q^{45} +(43.0270 + 31.2610i) q^{46} +(9.41591 + 59.4497i) q^{47} +(15.7162 + 30.8447i) q^{48} +27.9275i q^{49} +(50.5321 + 33.5292i) q^{50} +13.6737 q^{51} +(36.5043 - 18.5999i) q^{52} +(-61.1373 + 9.68320i) q^{53} +(-7.40881 + 10.1974i) q^{54} +(31.4262 + 35.2504i) q^{55} +(36.4164 - 26.4580i) q^{56} +(-39.2548 - 39.2548i) q^{57} +(5.69951 - 35.9853i) q^{58} +(-60.6852 + 19.7178i) q^{59} +(-8.82018 - 13.7297i) q^{60} +(2.03033 - 6.24871i) q^{61} +(24.3399 - 47.7698i) q^{62} +(23.4446 + 11.9456i) q^{63} +(-11.5422 - 3.75029i) q^{64} +(91.4648 - 58.7586i) q^{65} +(-12.2629 - 37.7413i) q^{66} +(-23.4900 - 3.72046i) q^{67} +(10.5188 - 10.5188i) q^{68} +(-22.3211 - 30.7223i) q^{69} +(-79.4057 + 70.7911i) q^{70} +(-35.4335 - 25.7440i) q^{71} +(-2.40853 - 15.2069i) q^{72} +(-34.5264 - 67.7618i) q^{73} +92.1812i q^{74} +(-26.9171 - 33.9186i) q^{75} -60.3951 q^{76} +(-73.8113 + 37.6087i) q^{77} +(-90.2272 + 14.2906i) q^{78} +(52.4271 - 72.1598i) q^{79} +(97.6456 + 21.2591i) q^{80} +(7.28115 - 5.29007i) q^{81} +(29.2127 + 29.2127i) q^{82} +(-2.22048 + 14.0196i) q^{83} +(27.2246 - 8.84582i) q^{84} +(24.9919 - 30.5531i) q^{85} +(29.5986 - 91.0953i) q^{86} +(-11.8104 + 23.1792i) q^{87} +(43.1897 + 22.0063i) q^{88} +(118.011 + 38.3441i) q^{89} +(9.24403 + 35.1926i) q^{90} +(58.9294 + 181.366i) q^{91} +(-40.8047 - 6.46283i) q^{92} +(-27.0689 + 27.0689i) q^{93} +(-85.8216 - 118.123i) q^{94} +(-159.460 + 15.9651i) q^{95} +(-39.1711 - 28.4595i) q^{96} +(3.30251 + 20.8512i) q^{97} +(-30.7557 - 60.3615i) q^{98} +28.3350i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−2.16137	+	1.10127i	−1.08068	+	0.550636i	−0.901323	−	0.433147i	$-0.857403\pi$
$2$	−2.16137	+	1.10127i	−1.08068	+	0.550636i	−0.179361	+	0.983783i	$0.557403\pi$
$3$	1.71073	−	0.270952i	0.570242	−	0.0903175i
$3$	1.71073	−	0.270952i	0.570242	−	0.0903175i
$4$	1.10757	−	1.52445i	0.276894	−	0.381112i
$5$	2.52133	−	4.31774i	0.504265	−	0.863549i
$5$	2.52133	−	4.31774i	0.504265	−	0.863549i
$6$	−3.39912	+	2.46960i	−0.566520	+	0.411601i
$7$	6.20191	+	6.20191i	0.885988	+	0.885988i	0.994135	−	0.108147i	$-0.0344918\pi$
$7$	6.20191	+	6.20191i	0.885988	+	0.885988i	−0.108147	+	0.994135i	$0.534492\pi$
$8$	0.802843	−	5.06895i	0.100355	−	0.633619i
$9$	2.85317	−	0.927051i	0.317019	−	0.103006i
$10$	−0.694505	+	12.1089i	−0.0694505	+	1.21089i
$11$	−2.91866	+	8.98272i	−0.265333	+	0.816611i	0.726284	+	0.687395i	$0.241246\pi$
$11$	−2.91866	+	8.98272i	−0.265333	+	0.816611i	−0.991617	+	0.129216i	$0.958754\pi$
$12$	1.48171	−	2.90801i	0.123475	−	0.242334i
$13$	19.3727	+	9.87087i	1.49021	+	0.759298i	0.994049	−	0.108935i	$-0.0347439\pi$
$13$	19.3727	+	9.87087i	1.49021	+	0.759298i	0.496157	+	0.868233i	$0.334744\pi$
$14$	−20.2346	−	6.57463i	−1.44533	−	0.469616i
$15$	3.14340	−	8.06964i	0.209560	−	0.537976i
$16$	6.17620	+	19.0084i	0.386013	+	1.18803i
$17$	7.79733	+	1.23498i	0.458666	+	0.0726456i	0.381492	−	0.924372i	$-0.375410\pi$
$17$	7.79733	+	1.23498i	0.458666	+	0.0726456i	0.0771741	+	0.997018i	$0.475410\pi$
$18$	−5.14582	+	5.14582i	−0.285879	+	0.285879i
$19$	−18.8393	−	25.9301i	−0.991545	−	1.36474i	−0.930372	−	0.366617i	$-0.880516\pi$
$19$	−18.8393	−	25.9301i	−0.991545	−	1.36474i	−0.0611727	−	0.998127i	$-0.519484\pi$
$20$	−3.78961	−	8.62585i	−0.189480	−	0.431293i
$21$	12.2902	+	8.92935i	0.585248	+	0.425207i
$22$	−3.58412	−	22.6292i	−0.162914	−	1.02860i
$23$	−9.95365	−	19.5351i	−0.432767	−	0.849354i	−0.999673	−	0.0255711i	$-0.991860\pi$
$23$	−9.95365	−	19.5351i	−0.432767	−	0.849354i	0.566906	−	0.823783i	$-0.308140\pi$
$24$		−	8.88912i		−	0.370380i
$25$	−12.2858	−	21.7729i	−0.491433	−	0.870915i
$26$	−52.7420			−2.02854
$27$	4.62981	−	2.35900i	0.171474	−	0.0873705i
$28$	16.3236	−	2.58540i	0.582985	−	0.0923357i
$29$	−8.82827	+	12.1511i	−0.304423	+	0.419003i	−0.933632	−	0.358234i	$-0.883379\pi$
$29$	−8.82827	+	12.1511i	−0.304423	+	0.419003i	0.629209	+	0.777236i	$0.283379\pi$
$30$	2.09283	+	20.9032i	0.0697610	+	0.696774i
$31$	−17.8806	+	12.9910i	−0.576793	+	0.419065i	−0.837567	−	0.546335i	$-0.816022\pi$
$31$	−17.8806	+	12.9910i	−0.576793	+	0.419065i	0.260773	+	0.965400i	$0.416022\pi$
$32$	−19.7666	−	19.7666i	−0.617707	−	0.617707i
$33$	−2.55914	+	16.1578i	−0.0775498	+	0.489630i
$34$	−18.2130	+	5.91775i	−0.535675	+	0.174051i
$35$	42.4153	−	11.1412i	1.21187	−	0.318321i
$36$	1.74686	−	5.37628i	0.0485239	−	0.149341i
$37$	17.2521	−	33.8591i	0.466272	−	0.915110i	−0.531414	−	0.847112i	$-0.678339\pi$
$37$	17.2521	−	33.8591i	0.466272	−	0.915110i	0.997685	−	0.0679974i	$-0.0216610\pi$
$38$	69.2749	+	35.2973i	1.82302	+	0.928878i
$39$	35.8159	+	11.6373i	0.918356	+	0.298392i
$40$	−19.8622	−	16.2470i	−0.496555	−	0.406174i
$41$	−5.26285	−	16.1974i	−0.128362	−	0.395058i	0.866137	−	0.499808i	$-0.166596\pi$
$41$	−5.26285	−	16.1974i	−0.128362	−	0.395058i	−0.994499	+	0.104750i	$0.966596\pi$
$42$	−36.3973	−	5.76477i	−0.866603	−	0.137256i
$43$	−27.9207	+	27.9207i	−0.649319	+	0.649319i	−0.952828	−	0.303510i	$-0.901842\pi$
$43$	−27.9207	+	27.9207i	−0.649319	+	0.649319i	0.303510	+	0.952828i	$0.401842\pi$
$44$	10.4610	+	14.3984i	0.237751	+	0.327236i
$45$	3.19100	−	14.6567i	0.0709112	−	0.325703i
$46$	43.0270	+	31.2610i	0.935370	+	0.679586i
$47$	9.41591	+	59.4497i	0.200339	+	1.26489i	0.858815	+	0.512286i	$0.171201\pi$
$47$	9.41591	+	59.4497i	0.200339	+	1.26489i	−0.658476	+	0.752601i	$0.728799\pi$
$48$	15.7162	+	30.8447i	0.327420	+	0.642598i
$49$			27.9275i			0.569948i
$50$	50.5321	+	33.5292i	1.01064	+	0.670584i
$51$	13.6737			0.268112
$52$	36.5043	−	18.5999i	0.702006	−	0.357690i
$53$	−61.1373	+	9.68320i	−1.15353	+	0.182702i	−0.703758	−	0.710439i	$-0.748496\pi$
$53$	−61.1373	+	9.68320i	−1.15353	+	0.182702i	−0.449776	+	0.893141i	$0.648496\pi$
$54$	−7.40881	+	10.1974i	−0.137200	+	0.188840i
$55$	31.4262	+	35.2504i	0.571385	+	0.640916i
$56$	36.4164	−	26.4580i	0.650292	−	0.472465i
$57$	−39.2548	−	39.2548i	−0.688681	−	0.688681i
$58$	5.69951	−	35.9853i	0.0982674	−	0.620436i
$59$	−60.6852	+	19.7178i	−1.02856	+	0.334200i	−0.774222	−	0.632915i	$-0.781858\pi$
$59$	−60.6852	+	19.7178i	−1.02856	+	0.334200i	−0.254341	+	0.967115i	$0.581858\pi$
$60$	−8.82018	−	13.7297i	−0.147003	−	0.228828i
$61$	2.03033	−	6.24871i	0.0332841	−	0.102438i	−0.933034	−	0.359787i	$-0.882849\pi$
$61$	2.03033	−	6.24871i	0.0332841	−	0.102438i	0.966318	+	0.257350i	$0.0828492\pi$
$62$	24.3399	−	47.7698i	0.392579	−	0.770480i
$63$	23.4446	+	11.9456i	0.372137	+	0.189613i
$64$	−11.5422	−	3.75029i	−0.180347	−	0.0585983i
$65$	91.4648	−	58.7586i	1.40715	−	0.903978i
$66$	−12.2629	−	37.7413i	−0.185801	−	0.571837i
$67$	−23.4900	−	3.72046i	−0.350598	−	0.0555292i	−0.0213479	−	0.999772i	$-0.506796\pi$
$67$	−23.4900	−	3.72046i	−0.350598	−	0.0555292i	−0.329250	+	0.944243i	$0.606796\pi$
$68$	10.5188	−	10.5188i	0.154688	−	0.154688i
$69$	−22.3211	−	30.7223i	−0.323494	−	0.445251i
$70$	−79.4057	+	70.7911i	−1.13437	+	1.01130i
$71$	−35.4335	−	25.7440i	−0.499064	−	0.362591i	0.309596	−	0.950868i	$-0.399806\pi$
$71$	−35.4335	−	25.7440i	−0.499064	−	0.362591i	−0.808659	+	0.588277i	$0.799806\pi$
$72$	−2.40853	−	15.2069i	−0.0334518	−	0.211206i
$73$	−34.5264	−	67.7618i	−0.472964	−	0.928244i	−0.997063	−	0.0765866i	$-0.975598\pi$
$73$	−34.5264	−	67.7618i	−0.472964	−	0.928244i	0.524099	−	0.851657i	$-0.324402\pi$
$74$			92.1812i			1.24569i
$75$	−26.9171	−	33.9186i	−0.358895	−	0.452248i
$76$	−60.3951			−0.794672
$77$	−73.8113	+	37.6087i	−0.958589	+	0.488425i
$78$	−90.2272	+	14.2906i	−1.15676	+	0.183213i
$79$	52.4271	−	72.1598i	0.663635	−	0.913415i	−0.335960	−	0.941876i	$-0.609061\pi$
$79$	52.4271	−	72.1598i	0.663635	−	0.913415i	0.999595	+	0.0284614i	$0.00906076\pi$
$80$	97.6456	+	21.2591i	1.22057	+	0.265739i
$81$	7.28115	−	5.29007i	0.0898908	−	0.0653095i
$82$	29.2127	+	29.2127i	0.356252	+	0.356252i
$83$	−2.22048	+	14.0196i	−0.0267528	+	0.168910i	−0.997447	−	0.0714064i	$-0.977251\pi$
$83$	−2.22048	+	14.0196i	−0.0267528	+	0.168910i	0.970695	+	0.240317i	$0.0772513\pi$
$84$	27.2246	−	8.84582i	0.324103	−	0.105307i
$85$	24.9919	−	30.5531i	0.294023	−	0.359448i
$86$	29.5986	−	91.0953i	0.344170	−	1.05925i
$87$	−11.8104	+	23.1792i	−0.135752	+	0.266428i
$88$	43.1897	+	22.0063i	0.490793	+	0.250071i
$89$	118.011	+	38.3441i	1.32597	+	0.430833i	0.884540	−	0.466465i	$-0.154473\pi$
$89$	118.011	+	38.3441i	1.32597	+	0.430833i	0.441427	+	0.897297i	$0.354473\pi$
$90$	9.24403	+	35.1926i	0.102711	+	0.391029i
$91$	58.9294	+	181.366i	0.647576	+	1.99303i
$92$	−40.8047	−	6.46283i	−0.443529	−	0.0702481i
$93$	−27.0689	+	27.0689i	−0.291063	+	0.291063i
$94$	−85.8216	−	118.123i	−0.912996	−	1.25663i
$95$	−159.460	+	15.9651i	−1.67852	+	0.168054i
$96$	−39.1711	−	28.4595i	−0.408032	−	0.296453i
$97$	3.30251	+	20.8512i	0.0340465	+	0.214961i	0.998846	−	0.0480251i	$-0.0152927\pi$
$97$	3.30251	+	20.8512i	0.0340465	+	0.214961i	−0.964800	+	0.262986i	$0.915293\pi$
$98$	−30.7557	−	60.3615i	−0.313834	−	0.615934i
$99$			28.3350i			0.286212i
$100$	−46.7991	−	5.38603i	−0.467991	−	0.0538603i
$101$	−27.4933			−0.272211			−0.136105	−	0.990694i	$-0.543459\pi$
$101$	−27.4933			−0.272211			−0.136105	+	0.990694i	$0.543459\pi$
$102$	−29.5540	+	15.0585i	−0.289745	+	0.147632i
$103$	−81.2396	+	12.8671i	−0.788734	+	0.124923i	−0.537791	−	0.843078i	$-0.680741\pi$
$103$	−81.2396	+	12.8671i	−0.788734	+	0.124923i	−0.250944	+	0.968002i	$0.580741\pi$
$104$	65.5882	−	90.2744i	0.630656	−	0.868023i
$105$	69.5423	−	30.5521i	0.662307	−	0.290973i
$106$	121.476	−	88.2578i	1.14600	−	0.832621i
$107$	112.084	+	112.084i	1.04751	+	1.04751i	0.998814	+	0.0486959i	$0.0155065\pi$
$107$	112.084	+	112.084i	1.04751	+	1.04751i	0.0486959	+	0.998814i	$0.484493\pi$
$108$	1.53168	−	9.67066i	0.0141822	−	0.0895432i
$109$	−14.9277	+	4.85031i	−0.136951	+	0.0444982i	−0.376691	−	0.926339i	$-0.622938\pi$
$109$	−14.9277	+	4.85031i	−0.136951	+	0.0444982i	0.239739	+	0.970837i	$0.422938\pi$
$110$	−106.744	−	41.5803i	−0.970399	−	0.378003i
$111$	20.3393	−	62.5981i	0.183237	−	0.563947i
$112$	−79.5842	+	156.193i	−0.710573	+	1.39458i
$113$	−50.5741	−	25.7688i	−0.447558	−	0.228042i	0.215660	−	0.976469i	$-0.430810\pi$
$113$	−50.5741	−	25.7688i	−0.447558	−	0.228042i	−0.663218	+	0.748426i	$0.730810\pi$
$114$	128.074	+	41.6139i	1.12346	+	0.365034i
$115$	−109.444	−	6.27715i	−0.951688	−	0.0545839i
$116$	8.74569	+	26.9165i	0.0753938	+	0.232038i
$117$	64.4243	+	10.2038i	0.550635	+	0.0872121i
$118$	109.448	−	109.448i	0.927529	−	0.927529i
$119$	40.6991	+	56.0176i	0.342010	+	0.470736i
$120$	−38.3810	−	22.4124i	−0.319841	−	0.186770i
$121$	25.7204	+	18.6870i	0.212565	+	0.154438i
$122$	2.49324	+	15.7417i	0.0204364	+	0.129030i
$123$	−13.3920	−	26.2833i	−0.108878	−	0.213685i
$124$			41.6465i			0.335859i
$125$	−124.986	−	1.84951i	−0.999891	−	0.0147961i
$126$	−63.8278			−0.506570
$127$	207.311	−	105.630i	1.63237	−	0.831734i	0.634081	−	0.773267i	$-0.281379\pi$
$127$	207.311	−	105.630i	1.63237	−	0.831734i	0.998289	−	0.0584677i	$-0.0186215\pi$
$128$	139.517	−	22.0974i	1.08998	−	0.172636i
$129$	−40.1995	+	55.3299i	−0.311624	+	0.428914i
$130$	−132.980	+	227.727i	−1.02292	+	1.75174i
$131$	−31.5128	+	22.8954i	−0.240556	+	0.174774i	−0.701531	−	0.712639i	$-0.747500\pi$
$131$	−31.5128	+	22.8954i	−0.240556	+	0.174774i	0.460975	+	0.887413i	$0.347500\pi$
$132$	21.7972	+	21.7972i	0.165131	+	0.165131i
$133$	43.9765	−	277.656i	0.330650	−	2.08764i
$134$	54.8679	−	17.8277i	0.409462	−	0.133042i
$135$	1.48768	−	25.9381i	0.0110198	−	0.192134i
$136$	12.5201	−	38.5328i	0.0920593	−	0.283329i
$137$	24.4313	−	47.9491i	0.178331	−	0.349994i	−0.784487	−	0.620145i	$-0.787074\pi$
$137$	24.4313	−	47.9491i	0.178331	−	0.349994i	0.962818	+	0.270151i	$0.0870738\pi$
$138$	82.0777	+	41.8207i	0.594766	+	0.303048i
$139$	−130.562	−	42.4223i	−0.939298	−	0.305196i	−0.200939	−	0.979604i	$-0.564399\pi$
$139$	−130.562	−	42.4223i	−0.939298	−	0.305196i	−0.738359	+	0.674407i	$0.764399\pi$
$140$	29.9940	−	76.9996i	0.214243	−	0.549997i
$141$	32.2161	+	99.1509i	0.228483	+	0.703198i
$142$	104.936	+	16.6202i	0.738986	+	0.117044i
$143$	−145.210	+	145.210i	−1.01545	+	1.01545i
$144$	35.2435	+	48.5085i	0.244747	+	0.336865i
$145$	30.2063	+	68.7551i	0.208319	+	0.474173i
$146$	149.248	+	108.435i	1.02225	+	0.742708i
$147$	7.56701	+	47.7762i	0.0514763	+	0.325008i
$148$	−32.5084	−	63.8013i	−0.219651	−	0.431090i
$149$		−	208.760i		−	1.40107i	−0.713617	−	0.700536i	$-0.752944\pi$
$149$		−	208.760i		−	1.40107i	0.713617	−	0.700536i	$-0.247056\pi$
$150$	95.5314	+	43.6675i	0.636876	+	0.291117i
$151$	−168.361			−1.11497			−0.557486	−	0.830186i	$-0.688234\pi$
$151$	−168.361			−1.11497			−0.557486	+	0.830186i	$0.688234\pi$
$152$	−146.564	+	74.6779i	−0.964235	+	0.491302i
$153$	23.3920	−	3.70493i	0.152889	−	0.0242152i
$154$	118.116	−	162.573i	0.766987	−	1.05567i
$155$	11.0090	+	109.958i	0.0710261	+	0.709409i
$156$	57.4092	−	41.7102i	0.368008	−	0.267373i
$157$	108.790	+	108.790i	0.692930	+	0.692930i	0.962875	−	0.269946i	$-0.0870058\pi$
$157$	108.790	+	108.790i	0.692930	+	0.692930i	−0.269946	+	0.962875i	$0.587006\pi$
$158$	−33.8468	+	213.701i	−0.214220	+	1.35253i
$159$	−101.966	+	33.1306i	−0.641293	+	0.208369i
$160$	−135.185	+	35.5091i	−0.844908	+	0.221932i
$161$	59.4236	−	182.887i	0.369090	−	1.13594i
$162$	−9.91145	+	19.4523i	−0.0611818	+	0.120076i
$163$	202.149	+	103.000i	1.24018	+	0.631901i	0.946098	−	0.323881i	$-0.104988\pi$
$163$	202.149	+	103.000i	1.24018	+	0.631901i	0.294077	+	0.955782i	$0.404988\pi$
$164$	−30.5210	−	9.91688i	−0.186104	−	0.0604688i
$165$	63.3128	+	51.7888i	0.383714	+	0.313871i
$166$	−10.6401	−	32.7468i	−0.0640969	−	0.197270i
$167$	88.3954	+	14.0005i	0.529314	+	0.0838350i	0.415371	−	0.909652i	$-0.363652\pi$
$167$	88.3954	+	14.0005i	0.529314	+	0.0838350i	0.113943	+	0.993487i	$0.463652\pi$
$168$	55.1296	−	55.1296i	0.328152	−	0.328152i
$169$	178.531	+	245.727i	1.05640	+	1.45400i
$170$	−20.3695	+	93.5594i	−0.119821	+	0.550350i
$171$	−77.7904	−	56.5180i	−0.454915	−	0.330515i
$172$	11.6393	+	73.4879i	0.0676706	+	0.427255i
$173$	−94.5352	−	185.536i	−0.546446	−	1.07246i	−0.984805	−	0.173661i	$-0.944440\pi$
$173$	−94.5352	−	185.536i	−0.546446	−	1.07246i	0.438359	−	0.898800i	$-0.355560\pi$
$174$		−	63.1053i		−	0.362674i
$175$	58.8379	−	211.229i	0.336217	−	1.20702i
$176$	−188.773			−1.07258
$177$	−98.4731	+	50.1746i	−0.556345	+	0.283472i
$178$	−297.293	+	47.0865i	−1.67018	+	0.264531i
$179$	−92.2871	+	127.022i	−0.515571	+	0.709622i	−0.984846	−	0.173430i	$-0.944515\pi$
$179$	−92.2871	+	127.022i	−0.515571	+	0.709622i	0.469276	+	0.883052i	$0.344515\pi$
$180$	−18.8090	−	21.0979i	−0.104494	−	0.117210i
$181$	−99.1597	+	72.0437i	−0.547844	+	0.398032i	−0.826990	−	0.562217i	$-0.809949\pi$
$181$	−99.1597	+	72.0437i	−0.547844	+	0.398032i	0.279146	+	0.960249i	$0.409949\pi$
$182$	−327.102	−	327.102i	−1.79726	−	1.79726i
$183$	1.78023	−	11.2400i	0.00972806	−	0.0614205i
$184$	−107.014	+	34.7709i	−0.581597	+	0.188972i
$185$	−102.697	−	159.860i	−0.555117	−	0.864107i
$186$	28.6956	−	88.3160i	0.154277	−	0.474817i
$187$	−33.8512	+	66.4367i	−0.181022	+	0.355277i
$188$	101.057	+	51.4910i	0.537536	+	0.273888i
$189$	43.3440	+	14.0833i	0.229333	+	0.0745149i
$190$	327.070	−	210.115i	1.72142	−	1.10587i
$191$	4.10624	+	12.6377i	0.0214987	+	0.0661661i	0.961230	−	0.275747i	$-0.0889252\pi$
$191$	4.10624	+	12.6377i	0.0214987	+	0.0661661i	−0.939732	+	0.341913i	$0.888925\pi$
$192$	−20.7617	−	3.28833i	−0.108134	−	0.0171267i
$193$	162.042	−	162.042i	0.839598	−	0.839598i	−0.149207	−	0.988806i	$-0.547672\pi$
$193$	162.042	−	162.042i	0.839598	−	0.839598i	0.988806	+	0.149207i	$0.0476722\pi$
$194$	−30.1008	−	41.4302i	−0.155159	−	0.213558i
$195$	140.550	−	125.302i	0.720771	−	0.642577i
$196$	42.5739	+	30.9317i	0.217214	+	0.157815i
$197$	−51.5909	−	325.732i	−0.261883	−	1.65346i	−0.671351	−	0.741139i	$-0.734286\pi$
$197$	−51.5909	−	325.732i	−0.261883	−	1.65346i	0.409468	−	0.912324i	$-0.365714\pi$
$198$	−31.2045	−	61.2423i	−0.157599	−	0.309305i
$199$			275.624i			1.38505i	0.721396	+	0.692523i	$0.243501\pi$
$199$			275.624i			1.38505i	−0.721396	+	0.692523i	$0.756499\pi$
$200$	−120.229	+	44.7960i	−0.601147	+	0.223980i
$201$	−41.1931			−0.204941
$202$	59.4232	−	30.2776i	0.294174	−	0.149889i
$203$	−130.112	+	20.6077i	−0.640946	+	0.101516i
$204$	15.1447	−	20.8448i	0.0742386	−	0.102181i
$205$	−83.2055	−	18.1153i	−0.405880	−	0.0883671i
$206$	161.419	−	117.278i	0.783586	−	0.569308i
$207$	−46.5095	−	46.5095i	−0.224684	−	0.224684i
$208$	−67.9799	+	429.208i	−0.326826	+	2.06350i
$209$	287.909	−	93.5472i	1.37755	−	0.447594i
$210$	−116.660	+	142.619i	−0.555525	+	0.679140i
$211$	40.2638	−	123.919i	0.190824	−	0.587296i	−0.809176	−	0.587566i	$-0.800086\pi$
$211$	40.2638	−	123.919i	0.190824	−	0.587296i	1.00000		0.000270670i	$8.61568e-5\pi$
$212$	−52.9526	+	103.925i	−0.249777	+	0.490214i
$213$	−67.5924	−	34.4401i	−0.317335	−	0.161690i
$214$	−365.688	−	118.819i	−1.70882	−	0.555231i
$215$	50.1572	+	190.952i	0.233289	+	0.888147i
$216$	−8.24067	−	25.3622i	−0.0381513	−	0.117417i
$217$	−191.463	−	30.3248i	−0.882318	−	0.139745i
$218$	26.9228	−	26.9228i	0.123499	−	0.123499i
$219$	−77.4254	−	106.567i	−0.353541	−	0.486607i
$220$	88.5442	−	8.86505i	0.402474	−	0.0402957i
$221$	138.865	+	100.891i	0.628348	+	0.456521i
$222$	24.9767	+	157.697i	0.112508	+	0.710346i
$223$	−27.8674	−	54.6928i	−0.124966	−	0.245259i	0.820045	−	0.572300i	$-0.193949\pi$
$223$	−27.8674	−	54.6928i	−0.124966	−	0.245259i	−0.945010	+	0.327041i	$0.893949\pi$
$224$		−	245.182i		−	1.09456i
$225$	−55.2381	−	50.7321i	−0.245503	−	0.225476i
$226$	137.688			0.609238
$227$	101.656	−	51.7965i	0.447826	−	0.228179i	−0.215508	−	0.976502i	$-0.569141\pi$
$227$	101.656	−	51.7965i	0.447826	−	0.228179i	0.663334	+	0.748323i	$0.269141\pi$
$228$	−103.319	+	16.3642i	−0.453156	+	0.0717728i
$229$	−88.4521	+	121.744i	−0.386254	+	0.531633i	−0.957228	−	0.289336i	$-0.906566\pi$
$229$	−88.4521	+	121.744i	−0.386254	+	0.531633i	0.570974	+	0.820968i	$0.306566\pi$
$230$	243.462	−	106.961i	1.05853	−	0.465046i
$231$	−116.081	+	84.3376i	−0.502514	+	0.365098i
$232$	54.5055	+	54.5055i	0.234938	+	0.234938i
$233$	−57.5364	+	363.271i	−0.246937	+	1.55910i	0.483020	+	0.875609i	$0.339540\pi$
$233$	−57.5364	+	363.271i	−0.246937	+	1.55910i	−0.729957	+	0.683493i	$0.760460\pi$
$234$	−150.482	+	48.8946i	−0.643085	+	0.208951i
$235$	280.429	+	109.237i	1.19332	+	0.464837i
$236$	−37.1546	+	114.350i	−0.157435	+	0.484535i
$237$	70.1366	−	137.651i	0.295935	−	0.580805i
$238$	−149.657	−	76.2538i	−0.628809	−	0.320394i
$239$	186.249	+	60.5160i	0.779285	+	0.253205i	0.671535	−	0.740973i	$-0.265635\pi$
$239$	186.249	+	60.5160i	0.779285	+	0.253205i	0.107750	+	0.994178i	$0.465635\pi$
$240$	172.805	+	9.91122i	0.720022	+	0.0412967i
$241$	43.2319	+	133.054i	0.179385	+	0.552091i	0.999807	−	0.0196682i	$-0.00626100\pi$
$241$	43.2319	+	133.054i	0.179385	+	0.552091i	−0.820421	+	0.571760i	$0.806261\pi$
$242$	−76.1708	−	12.0643i	−0.314755	−	0.0498523i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$	−7.27708	−	10.0160i	−0.0298241	−	0.0410494i
$245$	120.584	+	70.4142i	0.492178	+	0.287405i
$246$	57.8902	+	42.0597i	0.235326	+	0.170974i
$247$	−109.016	−	688.297i	−0.441359	−	2.78663i
$248$	51.4955	+	101.066i	0.207643	+	0.407523i
$249$			24.5853i			0.0987360i
$250$	272.178	−	133.647i	1.08871	−	0.534586i
$251$	85.1890			0.339399			0.169699	−	0.985496i	$-0.445720\pi$
$251$	85.1890			0.339399			0.169699	+	0.985496i	$0.445720\pi$
$252$	44.1771	−	22.5094i	0.175306	−	0.0893229i
$253$	204.530	−	32.3944i	0.808419	−	0.128041i
$254$	−331.748	+	456.612i	−1.30609	+	1.79768i
$255$	34.4759	−	59.0396i	0.135200	−	0.231528i
$256$	−237.940	+	172.873i	−0.929452	+	0.675286i
$257$	197.944	+	197.944i	0.770209	+	0.770209i	0.978143	−	0.207934i	$-0.0666738\pi$
$257$	197.944	+	197.944i	0.770209	+	0.770209i	−0.207934	+	0.978143i	$0.566674\pi$
$258$	25.9527	−	163.859i	0.100592	−	0.635112i
$259$	316.987	−	102.995i	1.22389	−	0.397665i
$260$	11.7298	−	204.513i	0.0451146	−	0.786587i
$261$	−13.9239	+	42.8533i	−0.0533483	+	0.164189i
$262$	42.8968	−	84.1897i	0.163728	−	0.321335i
$263$	98.3791	+	50.1266i	0.374065	+	0.190596i	0.630908	−	0.775857i	$-0.282682\pi$
$263$	98.3791	+	50.1266i	0.374065	+	0.190596i	−0.256843	+	0.966453i	$0.582682\pi$
$264$	79.8485	+	25.9443i	0.302456	+	0.0982740i
$265$	−112.338	+	288.390i	−0.423915	+	1.08826i
$266$	210.726	+	648.548i	0.792203	+	2.43815i
$267$	212.274	+	33.6209i	0.795034	+	0.125921i
$268$	−31.6886	+	31.6886i	−0.118241	+	0.118241i
$269$	−11.5678	−	15.9218i	−0.0430031	−	0.0591887i	0.786974	−	0.616986i	$-0.211647\pi$
$269$	−11.5678	−	15.9218i	−0.0430031	−	0.0591887i	−0.829977	+	0.557797i	$0.811647\pi$
$270$	25.3495	+	57.7002i	0.0938872	+	0.213705i
$271$	−258.416	−	187.750i	−0.953566	−	0.692806i	−0.00191814	−	0.999998i	$-0.500611\pi$
$271$	−258.416	−	187.750i	−0.953566	−	0.692806i	−0.951648	+	0.307192i	$0.900611\pi$
$272$	24.6830	+	155.842i	0.0907463	+	0.572949i
$273$	149.954	+	294.301i	0.549281	+	1.07802i
$274$			130.541i			0.476428i
$275$	231.438	−	46.8124i	0.841592	−	0.170227i
$276$	−71.5568			−0.259264
$277$	−416.032	+	211.979i	−1.50192	+	0.765267i	−0.995294	−	0.0968987i	$-0.969108\pi$
$277$	−416.032	+	211.979i	−1.50192	+	0.765267i	−0.506627	+	0.862166i	$0.669108\pi$
$278$	328.912	−	52.0946i	1.18314	−	0.187391i
$279$	−38.9730	+	53.6418i	−0.139688	+	0.192264i
$280$	−22.4215	−	223.946i	−0.0800767	−	0.799807i
$281$	−116.131	+	84.3741i	−0.413278	+	0.300264i	−0.774927	−	0.632050i	$-0.782214\pi$
$281$	−116.131	+	84.3741i	−0.413278	+	0.300264i	0.361650	+	0.932314i	$0.382214\pi$
$282$	−178.823	−	178.823i	−0.634124	−	0.634124i
$283$	−45.7749	+	289.011i	−0.161749	+	1.02124i	0.764581	+	0.644527i	$0.222946\pi$
$283$	−45.7749	+	289.011i	−0.161749	+	1.02124i	−0.926330	+	0.376713i	$0.877054\pi$
$284$	−78.4906	+	25.5031i	−0.276375	+	0.0897997i
$285$	−268.466	+	70.5180i	−0.941987	+	0.247432i
$286$	153.936	−	473.767i	0.538238	−	1.65653i
$287$	67.8150	−	133.094i	0.236289	−	0.463744i
$288$	−74.7222	−	38.0728i	−0.259452	−	0.132197i
$289$	−215.582	−	70.0469i	−0.745959	−	0.242377i
$290$	−141.005	−	115.340i	−0.486224	−	0.397723i
$291$	11.2994	+	34.7759i	0.0388294	+	0.119505i
$292$	−141.540	−	22.4177i	−0.484725	−	0.0767729i
$293$	372.027	−	372.027i	1.26972	−	1.26972i	0.323480	−	0.946235i	$-0.395147\pi$
$293$	372.027	−	372.027i	1.26972	−	1.26972i	0.946235	−	0.323480i	$-0.104853\pi$
$294$	−68.9698	−	94.9287i	−0.234591	−	0.322887i
$295$	−67.8707	+	311.738i	−0.230070	+	1.05674i
$296$	−157.779	−	114.633i	−0.533038	−	0.387275i
$297$	7.67743	+	48.4734i	0.0258499	+	0.163210i
$298$	229.901	+	451.207i	0.771481	+	1.51412i
$299$		−	476.699i		−	1.59431i
$300$	−81.5197	+	3.46630i	−0.271732	+	0.0115543i
$301$	−346.324			−1.15058
$302$	363.890	−	185.411i	1.20493	−	0.613944i
$303$	−47.0335	+	7.44937i	−0.155226	+	0.0245854i
$304$	376.535	−	518.256i	1.23860	−	1.70479i
$305$	−21.8612	−	24.5215i	−0.0716761	−	0.0803983i
$306$	−46.4786	+	33.7687i	−0.151891	+	0.110355i
$307$	−175.096	−	175.096i	−0.570344	−	0.570344i	0.361880	−	0.932225i	$-0.382135\pi$
$307$	−175.096	−	175.096i	−0.570344	−	0.570344i	−0.932225	+	0.361880i	$0.882135\pi$
$308$	−24.4191	+	154.176i	−0.0792827	+	0.500571i
$309$	−135.492	+	44.0241i	−0.438487	+	0.142473i
$310$	−144.889	−	225.537i	−0.467383	−	0.727538i
$311$	21.2700	−	65.4624i	0.0683923	−	0.210490i	−0.911019	−	0.412364i	$-0.864703\pi$
$311$	21.2700	−	65.4624i	0.0683923	−	0.210490i	0.979411	+	0.201874i	$0.0647032\pi$
$312$	87.7434	−	172.206i	0.281229	−	0.551943i
$313$	−168.493	−	85.8514i	−0.538316	−	0.274286i	0.163623	−	0.986523i	$-0.447682\pi$
$313$	−168.493	−	85.8514i	−0.538316	−	0.274286i	−0.701939	+	0.712237i	$0.747682\pi$
$314$	−354.943	−	115.328i	−1.13039	−	0.367286i
$315$	110.690	−	71.1090i	0.351396	−	0.225743i
$316$	−51.9367	−	159.845i	−0.164357	−	0.505838i
$317$	172.144	+	27.2649i	0.543041	+	0.0860093i	0.421928	−	0.906629i	$-0.361354\pi$
$317$	172.144	+	27.2649i	0.543041	+	0.0860093i	0.121113	+	0.992639i	$0.461354\pi$
$318$	183.899	−	183.899i	0.578300	−	0.578300i
$319$	−83.3829	−	114.767i	−0.261389	−	0.359770i
$320$	−45.2945	+	40.3806i	−0.141545	+	0.126189i
$321$	222.114	+	161.375i	0.691943	+	0.502726i
$322$	72.9721	+	460.728i	0.226621	+	1.43083i
$323$	−114.874	−	225.452i	−0.355646	−	0.697994i
$324$		−	16.9589i		−	0.0523422i
$325$	−23.0919	−	543.071i	−0.0710521	−	1.67099i
$326$	−550.349			−1.68819
$327$	−24.2230	+	12.3422i	−0.0740765	+	0.0377439i
$328$	−86.3290	+	13.6732i	−0.263198	+	0.0416865i
$329$	−310.305	+	427.099i	−0.943177	+	1.29817i
$330$	−193.876	−	42.2101i	−0.587503	−	0.127909i
$331$	173.131	−	125.787i	0.523056	−	0.380022i	−0.294698	−	0.955590i	$-0.595219\pi$
$331$	173.131	−	125.787i	0.523056	−	0.380022i	0.817754	+	0.575568i	$0.195219\pi$
$332$	18.9127	+	18.9127i	0.0569660	+	0.0569660i
$333$	17.8340	−	112.599i	0.0535554	−	0.338136i
$334$	−206.473	+	67.0873i	−0.618184	+	0.200860i
$335$	−75.2900	+	92.0435i	−0.224746	+	0.274757i
$336$	−93.8260	+	288.767i	−0.279244	+	0.859424i
$337$	−110.173	+	216.227i	−0.326924	+	0.641624i	−0.994709	−	0.102730i	$-0.967242\pi$
$337$	−110.173	+	216.227i	−0.326924	+	0.641624i	0.667786	+	0.744354i	$0.267242\pi$
$338$	−656.483	−	334.495i	−1.94226	−	0.989630i
$339$	−93.5005	−	30.3802i	−0.275813	−	0.0896170i
$340$	−18.8961	−	71.9387i	−0.0555768	−	0.211584i
$341$	−64.5072	−	198.533i	−0.189171	−	0.582207i
$342$	230.376	+	36.4879i	0.673613	+	0.106690i
$343$	130.690	−	130.690i	0.381021	−	0.381021i
$344$	119.113	+	163.945i	0.346258	+	0.476583i
$345$	−188.930	+	18.9157i	−0.547622	+	0.0548280i
$346$	408.651	+	296.902i	1.18107	+	0.858099i
$347$	73.1006	+	461.539i	0.210665	+	1.33008i	0.835570	+	0.549384i	$0.185138\pi$
$347$	73.1006	+	461.539i	0.210665	+	1.33008i	−0.624905	+	0.780700i	$0.714862\pi$
$348$	22.2546	+	43.6770i	0.0639499	+	0.125509i
$349$			308.020i			0.882579i	0.897365	+	0.441289i	$0.145479\pi$
$349$			308.020i			0.882579i	−0.897365	+	0.441289i	$0.854521\pi$
$350$	105.450	+	521.341i	0.301287	+	1.48955i
$351$	112.977			0.321872
$352$	235.250	−	119.866i	0.668324	−	0.340528i
$353$	564.102	−	89.3451i	1.59802	−	0.253102i	0.707052	−	0.707161i	$-0.250024\pi$
$353$	564.102	−	89.3451i	1.59802	−	0.253102i	0.890972	+	0.454059i	$0.150024\pi$
$354$	157.581	−	216.892i	0.445144	−	0.612688i
$355$	−200.495	+	88.0839i	−0.564775	+	0.248124i
$356$	189.160	−	137.432i	0.531347	−	0.386046i
$357$	84.8032	+	84.8032i	0.237544	+	0.237544i
$358$	59.5803	−	376.175i	0.166426	−	1.05077i
$359$	15.2963	−	4.97008i	0.0426081	−	0.0138442i	−0.287635	−	0.957740i	$-0.592869\pi$
$359$	15.2963	−	4.97008i	0.0426081	−	0.0138442i	0.330244	+	0.943896i	$0.392869\pi$
$360$	−71.7320	−	27.9420i	−0.199256	−	0.0776168i
$361$	−205.896	+	633.683i	−0.570349	+	1.75535i
$362$	134.981	−	264.915i	0.372876	−	0.731809i
$363$	49.0639	+	24.9993i	0.135162	+	0.0688686i
$364$	341.751	+	111.042i	0.938877	+	0.305060i
$365$	−379.630	−	21.7736i	−1.04008	−	0.0596538i
$366$	8.53051	+	26.2542i	0.0233074	+	0.0717328i
$367$	−172.731	−	27.3579i	−0.470657	−	0.0745447i	−0.0833991	−	0.996516i	$-0.526578\pi$
$367$	−172.731	−	27.3579i	−0.470657	−	0.0745447i	−0.387258	+	0.921971i	$0.626578\pi$
$368$	309.856	−	309.856i	0.842000	−	0.842000i
$369$	−30.0316	−	41.3349i	−0.0813864	−	0.112019i
$370$	398.015	+	232.419i	1.07572	+	0.628159i
$371$	−439.223	−	319.114i	−1.18389	−	0.860146i
$372$	11.2842	+	71.2458i	0.0303339	+	0.191521i
$373$	195.249	+	383.197i	0.523455	+	1.02734i	0.989764	+	0.142716i	$0.0455837\pi$
$373$	195.249	+	383.197i	0.523455	+	1.02734i	−0.466308	+	0.884622i	$0.654416\pi$
$374$		−	180.874i		−	0.483620i
$375$	−214.319	+	30.7013i	−0.571516	+	0.0818702i
$376$	308.907			0.821562
$377$	−290.969	+	148.256i	−0.771801	+	0.393252i
$378$	−109.192	+	17.2943i	−0.288868	+	0.0457521i
$379$	159.304	−	219.263i	0.420327	−	0.578530i	−0.545373	−	0.838194i	$-0.683612\pi$
$379$	159.304	−	219.263i	0.420327	−	0.578530i	0.965699	+	0.259664i	$0.0836118\pi$
$380$	−152.276	+	260.771i	−0.400726	+	0.686238i
$381$	326.032	−	236.876i	0.855726	−	0.621722i
$382$	−22.7927	−	22.7927i	−0.0596667	−	0.0596667i
$383$	−48.8228	+	308.255i	−0.127475	+	0.804844i	0.838252	+	0.545283i	$0.183578\pi$
$383$	−48.8228	+	308.255i	−0.127475	+	0.804844i	−0.965727	+	0.259561i	$0.916422\pi$
$384$	232.689	−	75.6051i	0.605960	−	0.196888i
$385$	−23.7175	+	413.522i	−0.0616039	+	1.07408i
$386$	−171.781	+	528.687i	−0.445028	+	1.36965i
$387$	−53.7786	+	105.546i	−0.138963	+	0.272730i
$388$	35.4443	+	18.0598i	0.0913513	+	0.0465458i
$389$	−206.128	−	66.9751i	−0.529892	−	0.172172i	0.0318378	−	0.999493i	$-0.489864\pi$
$389$	−206.128	−	66.9751i	−0.529892	−	0.172172i	−0.561730	+	0.827321i	$0.689864\pi$
$390$	−165.789	+	425.609i	−0.425100	+	1.09131i
$391$	−53.4865	−	164.614i	−0.136794	−	0.421009i
$392$	141.563	+	22.4214i	0.361130	+	0.0571974i
$393$	−47.7063	+	47.7063i	−0.121390	+	0.121390i
$394$	470.227	+	647.212i	1.19347	+	1.64267i
$395$	−179.381	−	408.305i	−0.454130	−	1.03368i
$396$	43.1951	+	31.3831i	0.109079	+	0.0792502i
$397$	−56.9367	−	359.484i	−0.143417	−	0.905501i	−0.949516	−	0.313720i	$-0.898425\pi$
$397$	−56.9367	−	359.484i	−0.143417	−	0.905501i	0.806098	−	0.591782i	$-0.201575\pi$
$398$	−303.537	−	595.726i	−0.762657	−	1.49680i
$399$		−	486.910i		−	1.22033i
$400$	337.988	−	368.008i	0.844970	−	0.920019i
$401$	753.085			1.87802			0.939008	−	0.343895i	$-0.111746\pi$
$401$	753.085			1.87802			0.939008	+	0.343895i	$0.111746\pi$
$402$	89.0335	−	45.3648i	0.221476	−	0.112848i
$403$	−474.628	+	75.1736i	−1.17774	+	0.186535i
$404$	−30.4509	+	41.9120i	−0.0753735	+	0.103743i
$405$	−4.48299	−	44.7761i	−0.0110691	−	0.110558i
$406$	258.526	−	187.830i	0.636762	−	0.462635i
$407$	253.794	+	253.794i	0.623571	+	0.623571i
$408$	10.9779	−	69.3114i	0.0269065	−	0.169881i
$409$	554.763	−	180.254i	1.35639	−	0.440718i	0.461554	−	0.887112i	$-0.347292\pi$
$409$	554.763	−	180.254i	1.35639	−	0.440718i	0.894836	+	0.446394i	$0.147292\pi$
$410$	199.788	−	52.4782i	0.487287	−	0.127996i
$411$	28.8033	−	88.6475i	0.0700811	−	0.215687i
$412$	−70.3638	+	138.097i	−0.170786	+	0.335186i
$413$	−498.652	−	254.076i	−1.20739	−	0.615196i
$414$	151.744	+	49.3046i	0.366531	+	0.119093i
$415$	54.9343	+	44.9353i	0.132372	+	0.108278i
$416$	−187.819	−	578.046i	−0.451487	−	1.38953i
$417$	−234.851	−	37.1967i	−0.563192	−	0.0892008i
$418$	−519.256	+	519.256i	−1.24224	+	1.24224i
$419$	−347.628	−	478.468i	−0.829660	−	1.14193i	−0.987986	−	0.154542i	$-0.950610\pi$
$419$	−347.628	−	478.468i	−0.829660	−	1.14193i	0.158326	−	0.987387i	$-0.449390\pi$
$420$	30.4482	−	139.852i	0.0724957	−	0.332981i
$421$	−290.899	−	211.350i	−0.690971	−	0.502020i	0.186008	−	0.982548i	$-0.440445\pi$
$421$	−290.899	−	211.350i	−0.690971	−	0.502020i	−0.876979	+	0.480528i	$0.840445\pi$
$422$	49.4440	+	312.177i	0.117166	+	0.739756i
$423$	81.9781	+	160.891i	0.193802	+	0.380357i
$424$			317.676i			0.749236i
$425$	−68.9076	−	184.943i	−0.162136	−	0.435160i
$426$	184.020			0.431972
$427$	51.3459	−	26.1620i	0.120248	−	0.0612694i
$428$	295.006	−	46.7244i	0.689267	−	0.109169i
$429$	−209.069	+	287.759i	−0.487340	+	0.670766i
$430$	−318.698	−	357.480i	−0.741158	−	0.831349i
$431$	−301.141	+	218.792i	−0.698703	+	0.507637i	−0.879509	−	0.475881i	$-0.842129\pi$
$431$	−301.141	+	218.792i	−0.698703	+	0.507637i	0.180807	+	0.983519i	$0.442129\pi$
$432$	73.4355	+	73.4355i	0.169990	+	0.169990i
$433$	−30.5498	+	192.884i	−0.0705539	+	0.445460i	0.926970	+	0.375135i	$0.122404\pi$
$433$	−30.5498	+	192.884i	−0.0705539	+	0.445460i	−0.997524	+	0.0703248i	$0.977596\pi$
$434$	447.218	−	145.310i	1.03046	−	0.334816i
$435$	70.3040	+	109.437i	0.161618	+	0.251578i
$436$	−9.13952	+	28.1286i	−0.0209622	+	0.0645150i
$437$	−319.029	+	626.129i	−0.730042	+	1.43279i
$438$	284.704	+	145.064i	0.650009	+	0.331196i
$439$	686.534	+	223.068i	1.56386	+	0.508128i	0.957835	−	0.287319i	$-0.0927639\pi$
$439$	686.534	+	223.068i	1.56386	+	0.508128i	0.606023	+	0.795447i	$0.292764\pi$
$440$	203.913	−	130.997i	0.463438	−	0.297721i
$441$	25.8902	+	79.6818i	0.0587079	+	0.180684i
$442$	−411.247	−	65.1351i	−0.930423	−	0.147365i
$443$	−465.679	+	465.679i	−1.05119	+	1.05119i	−0.0525781	+	0.998617i	$0.516744\pi$
$443$	−465.679	+	465.679i	−1.05119	+	1.05119i	−0.998617	+	0.0525781i	$0.983256\pi$
$444$	−72.9000	−	100.338i	−0.164189	−	0.225987i
$445$	463.104	−	412.863i	1.04068	−	0.927783i
$446$	120.463	+	87.5217i	0.270097	+	0.196237i
$447$	−56.5640	−	357.131i	−0.126541	−	0.798951i
$448$	−48.3248	−	94.8428i	−0.107868	−	0.211703i
$449$			294.622i			0.656173i	0.944648	+	0.328087i	$0.106404\pi$
$449$			294.622i			0.656173i	−0.944648	+	0.328087i	$0.893596\pi$
$450$	175.260	+	48.8187i	0.389466	+	0.108486i
$451$	160.857			0.356667
$452$	−95.2977	+	48.5566i	−0.210836	+	0.107426i
$453$	−288.019	+	45.6178i	−0.635804	+	0.100701i
$454$	−162.675	+	223.903i	−0.358315	+	0.493178i
$455$	931.672	+	202.841i	2.04763	+	0.445804i
$456$	−230.496	+	167.465i	−0.505474	+	0.367248i
$457$	341.319	+	341.319i	0.746868	+	0.746868i	0.973890	−	0.227022i	$-0.0728989\pi$
$457$	341.319	+	341.319i	0.746868	+	0.746868i	−0.227022	+	0.973890i	$0.572899\pi$
$458$	57.1044	−	360.543i	0.124682	−	0.787212i
$459$	39.0134	−	12.6762i	0.0849966	−	0.0276171i
$460$	−130.787	+	159.889i	−0.284319	+	0.347585i
$461$	224.457	−	690.807i	0.486891	−	1.49850i	−0.342332	−	0.939579i	$-0.611217\pi$
$461$	224.457	−	690.807i	0.486891	−	1.49850i	0.829223	−	0.558918i	$-0.188783\pi$
$462$	158.015	−	310.121i	0.342023	−	0.671258i
$463$	7.46164	+	3.80190i	0.0161159	+	0.00821144i	0.462030	−	0.886864i	$-0.347121\pi$
$463$	7.46164	+	3.80190i	0.0161159	+	0.00821144i	−0.445914	+	0.895076i	$0.647121\pi$
$464$	−285.498	−	92.7638i	−0.615297	−	0.199922i
$465$	48.6270	+	185.126i	0.104574	+	0.398120i
$466$	−275.703	−	848.526i	−0.591637	−	1.82087i
$467$	−65.0396	−	10.3013i	−0.139271	−	0.0220584i	0.0864096	−	0.996260i	$-0.472461\pi$
$467$	−65.0396	−	10.3013i	−0.139271	−	0.0220584i	−0.225681	+	0.974201i	$0.572461\pi$
$468$	86.9100	−	86.9100i	0.185705	−	0.185705i
$469$	−122.609	−	168.757i	−0.261427	−	0.359823i
$470$	−726.410	+	72.7283i	−1.54555	+	0.154741i
$471$	215.587	+	156.633i	0.457721	+	0.332554i
$472$	51.2279	+	323.441i	0.108534	+	0.685255i
$473$	−169.313	−	332.295i	−0.357955	−	0.702526i
$474$			374.754i			0.790620i
$475$	−333.117	+	728.760i	−0.701299	+	1.53423i
$476$	130.473			0.274103
$477$	−165.458	+	84.3052i	−0.346873	+	0.176741i
$478$	−469.198	+	74.3137i	−0.981586	+	0.155468i
$479$	−126.522	+	174.142i	−0.264137	+	0.363553i	−0.920399	−	0.390979i	$-0.872136\pi$
$479$	−126.522	+	174.142i	−0.264137	+	0.363553i	0.656262	+	0.754533i	$0.272136\pi$
$480$	−221.644	+	97.3751i	−0.461758	+	0.202865i
$481$	668.437	−	485.648i	1.38968	−	1.00966i
$482$	−239.969	−	239.969i	−0.497861	−	0.497861i
$483$	52.1038	−	328.970i	0.107875	−	0.681098i
$484$	56.9746	−	18.5122i	0.117716	−	0.0382483i
$485$	98.3568	+	38.3133i	0.202798	+	0.0789965i
$486$	−11.6851	+	35.9631i	−0.0240435	+	0.0739982i
$487$	66.7333	−	130.971i	0.137029	−	0.268935i	−0.812287	−	0.583258i	$-0.801778\pi$
$487$	66.7333	−	130.971i	0.137029	−	0.268935i	0.949316	+	0.314323i	$0.101778\pi$
$488$	−30.0444	−	15.3084i	−0.0615664	−	0.0313696i
$489$	373.729	+	121.432i	0.764272	+	0.248327i
$490$	−338.171	−	19.3957i	−0.690145	−	0.0395832i
$491$	−49.9056	−	153.594i	−0.101641	−	0.312818i	0.887287	−	0.461218i	$-0.152588\pi$
$491$	−49.9056	−	153.594i	−0.101641	−	0.312818i	−0.988927	+	0.148401i	$0.952588\pi$
$492$	−54.9001	−	8.69533i	−0.111586	−	0.0176734i
$493$	−83.8432	+	83.8432i	−0.170067	+	0.170067i
$494$	993.626	+	1367.61i	2.01139	+	2.76844i
$495$	122.343	+	71.4417i	0.247158	+	0.144327i
$496$	−357.373	−	259.646i	−0.720509	−	0.523481i
$497$	−60.0938	−	379.417i	−0.120913	−	0.763415i
$498$	−27.0751	−	53.1379i	−0.0543676	−	0.106703i
$499$		−	358.490i		−	0.718417i	−0.933257	−	0.359209i	$-0.883047\pi$
$499$		−	358.490i		−	0.718417i	0.933257	−	0.359209i	$-0.116953\pi$
$500$	−141.251	+	188.486i	−0.282502	+	0.376973i
$501$	155.014			0.309409
$502$	−184.125	+	93.8163i	−0.366783	+	0.186885i
$503$	658.799	−	104.344i	1.30974	−	0.207442i	0.537765	−	0.843095i	$-0.319269\pi$
$503$	658.799	−	104.344i	1.30974	−	0.207442i	0.771975	+	0.635652i	$0.219269\pi$
$504$	79.3741	−	109.249i	0.157488	−	0.216764i
$505$	−69.3196	+	118.709i	−0.137266	+	0.235067i
$506$	−406.390	+	295.259i	−0.803142	+	0.583517i
$507$	371.998	+	371.998i	0.733723	+	0.733723i
$508$	68.5849	−	433.028i	0.135010	−	0.852417i
$509$	−139.383	+	45.2884i	−0.273838	+	0.0889753i	−0.442717	−	0.896661i	$-0.645985\pi$
$509$	−139.383	+	45.2884i	−0.273838	+	0.0889753i	0.168879	+	0.985637i	$0.445985\pi$
$510$	−9.49646	+	165.574i	−0.0186205	+	0.324654i
$511$	206.123	−	634.382i	0.403372	−	1.24145i
$512$	67.3785	−	132.238i	0.131599	−	0.258277i
$513$	−148.392	−	75.6094i	−0.289263	−	0.147387i
$514$	−645.820	−	209.840i	−1.25646	−	0.408248i
$515$	−149.275	+	383.214i	−0.289854	+	0.744105i
$516$	39.8234	+	122.564i	0.0771772	+	0.237527i
$517$	−561.502	−	88.9332i	−1.08608	−	0.172018i
$518$	−571.700	+	571.700i	−1.10367	+	1.10367i
$519$	−211.995	−	291.786i	−0.408469	−	0.562209i
$520$	−224.413	−	510.804i	−0.431563	−	0.982316i
$521$	684.075	+	497.010i	1.31300	+	0.953953i	0.999991	+	0.00420404i	$0.00133819\pi$
$521$	684.075	+	497.010i	1.31300	+	0.953953i	0.313013	+	0.949749i	$0.398662\pi$
$522$	−17.0985	−	107.956i	−0.0327558	−	0.206812i
$523$	−93.9501	−	184.387i	−0.179637	−	0.352557i	0.783576	−	0.621296i	$-0.213393\pi$
$523$	−93.9501	−	184.387i	−0.179637	−	0.352557i	−0.963213	+	0.268738i	$0.913393\pi$
$524$			73.3980i			0.140073i
$525$	43.4225	−	377.298i	0.0827096	−	0.718662i
$526$	−267.837			−0.509195
$527$	−155.464	+	79.2131i	−0.294999	+	0.150309i
$528$	−322.940	+	51.1486i	−0.611628	+	0.0968724i
$529$	28.3919	−	39.0782i	0.0536710	−	0.0738717i
$530$	−74.7928	−	747.031i	−0.141119	−	1.40949i
$531$	−154.866	+	112.516i	−0.291649	+	0.211895i
$532$	−374.565	−	374.565i	−0.704070	−	0.704070i
$533$	57.9268	−	365.736i	0.108681	−	0.686183i
$534$	−495.828	+	161.104i	−0.928517	+	0.301694i
$535$	766.547	−	201.349i	1.43280	−	0.376353i
$536$	−37.7176	+	116.083i	−0.0703687	+	0.216573i
$537$	−123.461	+	242.306i	−0.229909	+	0.451221i
$538$	42.5366	+	21.6735i	0.0790643	+	0.0402852i
$539$	−250.864	−	81.5108i	−0.465426	−	0.151226i
$540$	−37.8936	−	30.9963i	−0.0701733	−	0.0574006i
$541$	91.8733	+	282.757i	0.169821	+	0.522656i	0.999359	−	0.0357942i	$-0.0113961\pi$
$541$	91.8733	+	282.757i	0.169821	+	0.522656i	−0.829538	+	0.558451i	$0.811396\pi$
$542$	765.297	+	121.211i	1.41199	+	0.223637i
$543$	−150.115	+	150.115i	−0.276454	+	0.276454i
$544$	−129.716	−	178.538i	−0.238448	−	0.328195i
$545$	−16.6952	+	76.6832i	−0.0306335	+	0.140703i
$546$	−648.210	−	470.952i	−1.18720	−	0.862550i
$547$	−10.3402	−	65.2853i	−0.0189034	−	0.119352i	0.976432	−	0.215824i	$-0.0692439\pi$
$547$	−10.3402	−	65.2853i	−0.0189034	−	0.119352i	−0.995336	+	0.0964729i	$0.969244\pi$
$548$	−46.0363	−	90.3514i	−0.0840079	−	0.164875i
$549$		−	19.7109i		−	0.0359032i
$550$	−448.669	+	356.055i	−0.815763	+	0.647373i
$551$	481.398			0.873681
$552$	−173.650	+	88.4792i	−0.314584	+	0.160288i
$553$	772.677	−	122.380i	1.39725	−	0.221302i
$554$	665.752	−	916.330i	1.20172	−	1.65402i
$555$	−219.000	−	245.650i	−0.394595	−	0.442613i
$556$	−209.278	+	152.049i	−0.376400	+	0.273470i
$557$	−280.628	−	280.628i	−0.503821	−	0.503821i	0.408802	−	0.912623i	$-0.365947\pi$
$557$	−280.628	−	280.628i	−0.503821	−	0.503821i	−0.912623	+	0.408802i	$0.865947\pi$
$558$	25.1609	−	158.860i	0.0450912	−	0.284695i
$559$	−816.501	+	265.297i	−1.46065	+	0.474592i
$560$	473.743	+	737.437i	0.845969	+	1.31685i
$561$	−39.9090	+	122.827i	−0.0711390	+	0.218943i
$562$	158.083	−	310.256i	0.281287	−	0.552056i
$563$	460.383	+	234.577i	0.817732	+	0.416655i	0.812236	−	0.583329i	$-0.198250\pi$
$563$	460.383	+	234.577i	0.817732	+	0.416655i	0.00549667	+	0.999985i	$0.498250\pi$
$564$	186.832	+	60.7054i	0.331262	+	0.107634i
$565$	−238.777	+	153.394i	−0.422614	+	0.271494i
$566$	−219.344	−	675.070i	−0.387533	−	1.19270i
$567$	77.9656	+	12.3485i	0.137505	+	0.0217787i
$568$	−158.942	+	158.942i	−0.279828	+	0.279828i
$569$	42.2942	+	58.2129i	0.0743307	+	0.102307i	0.844564	−	0.535455i	$-0.179860\pi$
$569$	42.2942	+	58.2129i	0.0743307	+	0.102307i	−0.770233	+	0.637763i	$0.779860\pi$
$570$	502.595	−	448.070i	0.881746	−	0.786088i
$571$	19.8568	+	14.4268i	0.0347755	+	0.0252659i	0.605037	−	0.796197i	$-0.293158\pi$
$571$	19.8568	+	14.4268i	0.0347755	+	0.0252659i	−0.570262	+	0.821463i	$0.693158\pi$
$572$	60.5337	+	382.195i	0.105828	+	0.668172i
$573$	10.4489	+	20.5071i	0.0182354	+	0.0357890i
$574$			362.349i			0.631270i
$575$	−303.048	+	456.725i	−0.527039	+	0.794304i
$576$	−36.4086			−0.0632094
$577$	217.794	−	110.971i	0.377459	−	0.192325i	−0.254960	−	0.966952i	$-0.582062\pi$
$577$	217.794	−	110.971i	0.377459	−	0.192325i	0.632419	+	0.774627i	$0.282062\pi$
$578$	543.093	−	86.0175i	0.939608	−	0.148819i
$579$	233.305	−	321.116i	0.402944	−	0.554605i
$580$	138.269	+	30.1035i	0.238395	+	0.0519027i
$581$	−100.719	+	73.1769i	−0.173355	+	0.125950i
$582$	−62.7198	−	62.7198i	−0.107766	−	0.107766i
$583$	91.4577	−	577.441i	0.156874	−	0.990465i
$584$	−371.201	+	120.610i	−0.635618	+	0.206525i
$585$	206.492	−	252.441i	0.352978	−	0.431523i
$586$	−394.384	+	1213.79i	−0.673010	+	2.07131i
$587$	294.222	−	577.444i	0.501231	−	0.983721i	−0.492329	−	0.870409i	$-0.663854\pi$
$587$	294.222	−	577.444i	0.501231	−	0.983721i	0.993560	−	0.113311i	$-0.0361458\pi$
$588$	81.2133	+	41.3803i	0.138118	+	0.0703746i
$589$	673.717	+	218.904i	1.14383	+	0.371654i
$590$	−196.615	−	748.525i	−0.333246	−	1.26869i
$591$	−176.516	−	543.260i	−0.298673	−	0.919222i
$592$	750.159	+	118.814i	1.26716	+	0.200698i
$593$	−493.428	+	493.428i	−0.832088	+	0.832088i	−0.987802	−	0.155714i	$-0.950232\pi$
$593$	−493.428	+	493.428i	−0.832088	+	0.832088i	0.155714	+	0.987802i	$0.450232\pi$
$594$	−69.9762	−	96.3139i	−0.117805	−	0.162145i
$595$	344.485	−	34.4899i	0.578967	−	0.0579662i
$596$	−318.243	−	231.217i	−0.533965	−	0.387948i
$597$	74.6811	+	471.518i	0.125094	+	0.789812i
$598$	524.976	+	1030.32i	0.877886	+	1.72295i
$599$		−	530.606i		−	0.885820i	−0.896566	−	0.442910i	$-0.853946\pi$
$599$		−	530.606i		−	0.885820i	0.896566	−	0.442910i	$-0.146054\pi$
$600$	−193.542	+	109.210i	−0.322570	+	0.182017i
$601$	348.728			0.580246			0.290123	−	0.956989i	$-0.406304\pi$
$601$	348.728			0.580246			0.290123	+	0.956989i	$0.406304\pi$
$602$	748.533	−	381.397i	1.24341	−	0.633549i
$603$	−70.4701	+	11.1614i	−0.116866	+	0.0185097i
$604$	−186.472	+	256.657i	−0.308729	+	0.424929i
$605$	145.535	−	63.9382i	0.240554	−	0.105683i
$606$	93.4530	−	67.8975i	0.154213	−	0.112042i
$607$	331.155	+	331.155i	0.545561	+	0.545561i	0.925154	−	0.379593i	$-0.123936\pi$
$607$	331.155	+	331.155i	0.545561	+	0.545561i	−0.379593	+	0.925154i	$0.623936\pi$
$608$	−140.161	+	884.941i	−0.230528	+	1.45550i
$609$	−217.002	+	70.5084i	−0.356326	+	0.115777i
$610$	74.2550	+	28.9248i	0.121729	+	0.0474178i
$611$	−404.409	+	1244.64i	−0.661881	+	2.03706i
$612$	20.2604	−	39.7633i	0.0331053	−	0.0649727i
$613$	636.130	+	324.124i	1.03773	+	0.528751i	0.887937	−	0.459966i	$-0.152138\pi$
$613$	636.130	+	324.124i	1.03773	+	0.528751i	0.149796	+	0.988717i	$0.452138\pi$
$614$	571.274	+	185.618i	0.930414	+	0.302310i
$615$	−147.250	−	8.44551i	−0.239431	−	0.0137325i
$616$	131.378	+	404.340i	0.213276	+	0.656396i
$617$	−559.390	−	88.5987i	−0.906629	−	0.143596i	−0.314330	−	0.949314i	$-0.601780\pi$
$617$	−559.390	−	88.5987i	−0.906629	−	0.143596i	−0.592299	+	0.805718i	$0.701780\pi$
$618$	244.367	−	244.367i	0.395415	−	0.395415i
$619$	−627.651	−	863.888i	−1.01398	−	1.39562i	−0.916342	−	0.400396i	$-0.868873\pi$
$619$	−627.651	−	863.888i	−1.01398	−	1.39562i	−0.0976339	−	0.995222i	$-0.531127\pi$
$620$	179.819	+	105.004i	0.290031	+	0.169362i
$621$	−92.1669	−	66.9632i	−0.148417	−	0.107831i
$622$	26.1196	+	164.912i	0.0419929	+	0.265133i
$623$	494.087	+	969.701i	0.793078	+	1.55650i
$624$			752.677i			1.20621i
$625$	−323.117	+	534.996i	−0.516987	+	0.855993i
$626$	458.721			0.732781
$627$	467.186	−	238.043i	0.745114	−	0.379654i
$628$	286.337	−	45.3514i	0.455951	−	0.0722156i
$629$	176.335	−	242.704i	0.280342	−	0.385858i
$630$	−160.931	+	275.592i	−0.255446	+	0.437448i
$631$	−958.129	+	696.122i	−1.51843	+	1.10320i	−0.556172	+	0.831067i	$0.687730\pi$
$631$	−958.129	+	696.122i	−1.51843	+	1.10320i	−0.962259	+	0.272137i	$0.912270\pi$
$632$	−323.684	−	323.684i	−0.512158	−	0.512158i
$633$	35.3042	−	222.902i	0.0557728	−	0.352135i
$634$	−402.093	+	130.648i	−0.634216	+	0.206069i
$635$	66.6145	−	1161.44i	0.104905	−	1.82905i
$636$	−62.4286	+	192.136i	−0.0981582	+	0.302100i
$637$	−275.668	+	541.030i	−0.432760	+	0.849340i
$638$	306.611	+	156.226i	0.480581	+	0.244868i
$639$	−124.964	−	40.6032i	−0.195562	−	0.0635418i
$640$	256.358	−	658.115i	0.400559	−	1.02830i
$641$	226.669	+	697.615i	0.353618	+	1.08832i	0.956807	+	0.290725i	$0.0938965\pi$
$641$	226.669	+	697.615i	0.353618	+	1.08832i	−0.603189	+	0.797598i	$0.706104\pi$
$642$	−657.787	−	104.183i	−1.02459	−	0.162279i
$643$	474.928	−	474.928i	0.738613	−	0.738613i	−0.233697	−	0.972310i	$-0.575082\pi$
$643$	474.928	−	474.928i	0.738613	−	0.738613i	0.972310	+	0.233697i	$0.0750823\pi$
$644$	−212.985	−	293.149i	−0.330722	−	0.455200i
$645$	137.544	+	313.076i	0.213247	+	0.485389i
$646$	496.568	+	360.778i	0.768681	+	0.558480i
$647$	−18.7843	−	118.599i	−0.0290329	−	0.183306i	0.968910	−	0.247413i	$-0.0795804\pi$
$647$	−18.7843	−	118.599i	−0.0290329	−	0.183306i	−0.997943	+	0.0641062i	$0.979580\pi$
$648$	−20.9695	−	41.1549i	−0.0323603	−	0.0635107i
$649$		−	602.667i		−	0.928609i
$650$	647.979	+	1148.35i	0.996891	+	1.76669i
$651$	−335.757			−0.515756
$652$	380.912	−	194.085i	0.584221	−	0.297676i
$653$	−679.332	+	107.596i	−1.04033	+	0.164771i	−0.653145	−	0.757233i	$-0.726551\pi$
$653$	−679.332	+	107.596i	−1.04033	+	0.164771i	−0.387180	+	0.922004i	$0.626551\pi$
$654$	38.7627	−	53.3523i	0.0592702	−	0.0815784i
$655$	19.4024	+	193.791i	0.0296220	+	0.295864i
$656$	275.382	−	200.077i	0.419789	−	0.304995i
$657$	−161.328	−	161.328i	−0.245553	−	0.245553i
$658$	200.332	−	1264.85i	0.304456	−	1.92226i
$659$	395.364	−	128.462i	0.599946	−	0.194934i	0.00672938	−	0.999977i	$-0.497858\pi$
$659$	395.364	−	128.462i	0.599946	−	0.194934i	0.593216	+	0.805043i	$0.297858\pi$
$660$	149.073	−	39.1569i	0.225868	−	0.0593287i
$661$	−13.8891	+	42.7463i	−0.0210123	+	0.0646692i	−0.961013	−	0.276504i	$-0.910824\pi$
$661$	−13.8891	+	42.7463i	−0.0210123	+	0.0646692i	0.940001	+	0.341173i	$0.110824\pi$
$662$	−235.675	+	462.538i	−0.356004	+	0.698698i
$663$	264.897	+	134.972i	0.399542	+	0.203577i
$664$	69.2818	+	22.5110i	0.104340	+	0.0339021i
$665$	−1087.97	−	889.942i	−1.63605	−	1.33826i
$666$	85.4566	+	263.008i	0.128313	+	0.394908i
$667$	325.246	+	51.5140i	0.487626	+	0.0772324i
$668$	119.247	−	119.247i	0.178514	−	0.178514i
$669$	−62.4926	−	86.0137i	−0.0934119	−	0.128570i
$670$	61.3646	−	281.855i	0.0915889	−	0.420679i
$671$	50.2046	+	36.4758i	0.0748205	+	0.0543603i
$672$	−66.4326	−	419.439i	−0.0988580	−	0.624165i
$673$	−116.930	−	229.489i	−0.173745	−	0.340994i	0.787669	−	0.616098i	$-0.211288\pi$
$673$	−116.930	−	229.489i	−0.173745	−	0.340994i	−0.961414	+	0.275105i	$0.911288\pi$
$674$		−	588.678i		−	0.873409i
$675$	−108.243	−	71.8219i	−0.160360	−	0.106403i
$676$	572.333			0.846647
$677$	53.7661	−	27.3952i	0.0794181	−	0.0404656i	−0.413830	−	0.910354i	$-0.635809\pi$
$677$	53.7661	−	27.3952i	0.0794181	−	0.0404656i	0.493248	+	0.869888i	$0.335809\pi$
$678$	235.546	−	37.3068i	0.347413	−	0.0550248i
$679$	−108.835	+	149.799i	−0.160288	+	0.220617i
$680$	−134.808	−	151.212i	−0.198246	−	0.222371i
$681$	159.872	−	116.154i	0.234761	−	0.170564i
$682$	358.062	+	358.062i	0.525018	+	0.525018i
$683$	12.9251	−	81.6059i	0.0189240	−	0.119482i	−0.976418	−	0.215889i	$-0.930735\pi$
$683$	12.9251	−	81.6059i	0.0189240	−	0.119482i	0.995342	+	0.0964073i	$0.0307351\pi$
$684$	−172.317	+	55.9893i	−0.251926	+	0.0818557i
$685$	−145.433	−	226.383i	−0.212311	−	0.330487i
$686$	−138.544	+	426.395i	−0.201959	+	0.621567i
$687$	−118.331	+	232.237i	−0.172242	+	0.338045i
$688$	−703.172	−	358.284i	−1.02205	−	0.520762i
$689$	−1279.98	−	415.889i	−1.85773	−	0.603613i
$690$	387.516	−	248.947i	0.561617	−	0.360793i
$691$	21.5662	+	66.3741i	0.0312102	+	0.0960551i	0.965448	−	0.260595i	$-0.0839188\pi$
$691$	21.5662	+	66.3741i	0.0312102	+	0.0960551i	−0.934238	+	0.356650i	$0.883919\pi$
$692$	−387.544	−	61.3810i	−0.560035	−	0.0887008i
$693$	−175.731	+	175.731i	−0.253580	+	0.253580i
$694$	−666.278	−	917.053i	−0.960055	−	1.32140i
$695$	−512.359	+	456.775i	−0.737207	+	0.657230i
$696$	108.012	+	78.4756i	0.155190	+	0.112752i
$697$	−21.0328	−	132.796i	−0.0301762	−	0.190525i
$698$	−339.214	−	665.745i	−0.485980	−	0.953789i
$699$			637.047i			0.911368i
$700$	−256.840	−	323.647i	−0.366914	−	0.462353i
$701$	426.864			0.608936			0.304468	−	0.952523i	$-0.401521\pi$
$701$	426.864			0.608936			0.304468	+	0.952523i	$0.401521\pi$
$702$	−244.185	+	124.419i	−0.347842	+	0.177235i
$703$	−1202.99	+	190.535i	−1.71122	+	0.271031i
$704$	67.3757	−	92.7346i	0.0957040	−	0.131725i
$705$	509.336	+	110.891i	0.722462	+	0.157292i
$706$	−1120.84	+	814.338i	−1.58759	+	1.15345i
$707$	−170.511	−	170.511i	−0.241175	−	0.241175i
$708$	−32.5779	+	205.689i	−0.0460140	+	0.290521i
$709$	−701.962	+	228.081i	−0.990074	+	0.321694i	−0.758892	−	0.651216i	$-0.774259\pi$
$709$	−701.962	+	228.081i	−0.990074	+	0.321694i	−0.231181	+	0.972911i	$0.574259\pi$
$710$	336.340	−	411.182i	0.473718	−	0.579129i
$711$	82.6877	−	254.487i	0.116298	−	0.357928i
$712$	289.109	−	567.408i	0.406052	−	0.796921i
$713$	431.758	+	219.992i	0.605552	+	0.308544i
$714$	−276.682	−	89.8996i	−0.387510	−	0.125910i
$715$	260.857	+	993.099i	0.364835	+	1.38895i
$716$	91.4238	+	281.374i	0.127687	+	0.392980i
$717$	335.018	+	53.0617i	0.467250	+	0.0740052i
$718$	−27.5876	+	27.5876i	−0.0384228	+	0.0384228i
$719$	−384.793	−	529.623i	−0.535178	−	0.736610i	0.452730	−	0.891648i	$-0.350450\pi$
$719$	−384.793	−	529.623i	−0.535178	−	0.736610i	−0.987909	+	0.155038i	$0.950450\pi$
$720$	298.308	−	29.8666i	0.414316	−	0.0414814i
$721$	−583.642	−	424.040i	−0.809489	−	0.588128i
$722$	−252.840	−	1596.37i	−0.350194	−	2.21104i
$723$	110.009	+	215.905i	0.152157	+	0.298624i
$724$			230.957i			0.319002i
$725$	373.027	+	42.9310i	0.514519	+	0.0592152i
$726$	−133.576			−0.183989
$727$	−117.812	+	60.0280i	−0.162052	+	0.0825695i	−0.533135	−	0.846030i	$-0.678986\pi$
$727$	−117.812	+	60.0280i	−0.162052	+	0.0825695i	0.371084	+	0.928599i	$0.378986\pi$
$728$	966.647	−	153.102i	1.32781	−	0.210305i
$729$	15.8702	−	21.8435i	0.0217698	−	0.0299636i
$730$	844.500	−	371.016i	1.15685	−	0.508241i
$731$	−252.188	+	183.226i	−0.344991	+	0.250651i
$732$	−15.1630	−	15.1630i	−0.0207144	−	0.0207144i
$733$	165.068	−	1042.20i	0.225194	−	1.42182i	−0.573066	−	0.819509i	$-0.694246\pi$
$733$	165.068	−	1042.20i	0.225194	−	1.42182i	0.798260	−	0.602313i	$-0.205754\pi$
$734$	403.464	−	131.093i	0.549679	−	0.178601i
$735$	225.364	+	87.7871i	0.306618	+	0.119438i
$736$	−189.394	+	582.894i	−0.257328	+	0.791975i
$737$	101.979	−	200.146i	0.138371	−	0.271568i
$738$	110.430	+	56.2671i	0.149635	+	0.0762427i
$739$	704.368	+	228.863i	0.953136	+	0.309693i	0.743989	−	0.668192i	$-0.232931\pi$
$739$	704.368	+	228.863i	0.953136	+	0.309693i	0.209147	+	0.977884i	$0.432931\pi$
$740$	−357.442	−	20.5010i	−0.483029	−	0.0277041i
$741$	−372.992	−	1147.95i	−0.503362	−	1.54919i
$742$	1300.75	+	206.019i	1.75304	+	0.277654i
$743$	−688.904	+	688.904i	−0.927192	+	0.927192i	−0.997524	−	0.0703312i	$-0.977594\pi$
$743$	−688.904	+	688.904i	−0.927192	+	0.927192i	0.0703312	+	0.997524i	$0.477594\pi$
$744$	115.479	+	158.943i	0.155213	+	0.213633i
$745$	−901.371	−	526.352i	−1.20989	−	0.706512i
$746$	−844.009	−	613.209i	−1.13138	−	0.821996i
$747$	6.66144	+	42.0587i	0.00891759	+	0.0563034i
$748$	63.7865	+	125.188i	0.0852760	+	0.167364i
$749$			1390.26i			1.85616i
$750$	429.411	−	302.380i	0.572548	−	0.403173i
$751$	317.101			0.422238			0.211119	−	0.977460i	$-0.432289\pi$
$751$	317.101			0.422238			0.211119	+	0.977460i	$0.432289\pi$
$752$	−1071.89	+	546.155i	−1.42539	+	0.726270i
$753$	145.735	−	23.0822i	0.193539	−	0.0306536i
$754$	465.621	−	640.873i	0.617535	−	0.849964i
$755$	−424.492	+	726.939i	−0.562242	+	0.962833i
$756$	69.4760	−	50.4772i	0.0918994	−	0.0667688i
$757$	−459.155	−	459.155i	−0.606545	−	0.606545i	0.335496	−	0.942042i	$-0.391096\pi$
$757$	−459.155	−	459.155i	−0.606545	−	0.606545i	−0.942042	+	0.335496i	$0.891096\pi$
$758$	−102.846	+	649.345i	−0.135681	+	0.856655i
$759$	341.117	−	110.836i	0.449430	−	0.146029i
$760$	−47.0948	+	821.112i	−0.0619668	+	1.08041i
$761$	232.926	−	716.872i	0.306078	−	0.942013i	−0.673194	−	0.739466i	$-0.735078\pi$
$761$	232.926	−	716.872i	0.306078	−	0.942013i	0.979273	−	0.202547i	$-0.0649218\pi$
$762$	−443.810	+	871.026i	−0.582428	+	1.14308i
$763$	−122.662	−	62.4992i	−0.160762	−	0.0819124i
$764$	23.8135	+	7.73748i	0.0311695	+	0.0101276i
$765$	42.9819	−	110.342i	0.0561855	−	0.144238i
$766$	−233.949	−	720.020i	−0.305416	−	0.939974i
$767$	−1370.27	−	217.029i	−1.78653	−	0.282958i
$768$	−360.209	+	360.209i	−0.469022	+	0.469022i
$769$	−51.4380	−	70.7983i	−0.0668894	−	0.0920654i	0.774262	−	0.632866i	$-0.218121\pi$
$769$	−51.4380	−	70.7983i	−0.0668894	−	0.0920654i	−0.841151	+	0.540800i	$0.818121\pi$
$770$	−404.139	−	919.894i	−0.524855	−	1.19467i
$771$	392.261	+	284.994i	0.508769	+	0.369642i
$772$	−67.5508	−	426.499i	−0.0875011	−	0.552460i
$773$	368.858	+	723.925i	0.477178	+	0.936514i	0.996631	+	0.0820150i	$0.0261355\pi$
$773$	368.858	+	723.925i	0.477178	+	0.936514i	−0.519454	+	0.854499i	$0.673864\pi$
$774$		−	287.350i		−	0.371253i
$775$	502.530	+	229.707i	0.648425	+	0.296396i
$776$	108.345			0.139620
$777$	514.371	−	262.085i	0.661996	−	0.337304i
$778$	519.277	−	82.2453i	0.667451	−	0.105714i
$779$	−320.852	+	441.614i	−0.411876	+	0.566899i
$780$	−35.3467	−	353.043i	−0.0453163	−	0.452620i
$781$	334.669	−	243.151i	0.428514	−	0.311333i
$782$	296.889	+	296.889i	0.379654	+	0.379654i
$783$	−12.2088	+	77.0830i	−0.0155923	+	0.0984458i
$784$	−530.856	+	172.486i	−0.677113	+	0.220007i
$785$	744.022	−	195.432i	0.947799	−	0.248958i
$786$	50.5733	−	155.648i	0.0643426	−	0.198026i
$787$	186.760	−	366.536i	0.237306	−	0.465739i	−0.741385	−	0.671080i	$-0.765831\pi$
$787$	186.760	−	366.536i	0.237306	−	0.465739i	0.978690	+	0.205342i	$0.0658305\pi$
$788$	−553.702	−	282.125i	−0.702668	−	0.358027i
$789$	181.882	+	59.0969i	0.230522	+	0.0749010i
$790$	837.365	+	684.951i	1.05996	+	0.867026i
$791$	−153.840	−	473.472i	−0.194488	−	0.598574i
$792$	143.629	+	22.7485i	0.181349	+	0.0287229i
$793$	101.013	−	101.013i	0.127381	−	0.127381i
$794$	518.951	+	714.275i	0.653591	+	0.899591i
$795$	−114.039	+	523.794i	−0.143445	+	0.658861i
$796$	420.174	+	305.275i	0.527857	+	0.383511i
$797$	−10.7588	−	67.9284i	−0.0134991	−	0.0852301i	0.980019	−	0.198904i	$-0.0637381\pi$
$797$	−10.7588	−	67.9284i	−0.0134991	−	0.0852301i	−0.993518	+	0.113674i	$0.963738\pi$
$798$	536.220	+	1052.39i	0.671955	+	1.31879i
$799$			475.177i			0.594715i
$800$	−187.527	+	673.225i	−0.234409	+	0.841532i
$801$	372.252			0.464735
$802$	−1627.69	+	829.352i	−2.02954	+	1.03410i
$803$	709.456	−	112.367i	0.883507	−	0.139934i
$804$	−45.6244	+	62.7966i	−0.0567468	+	0.0781053i
$805$	−639.833	−	717.693i	−0.794823	−	0.891544i
$806$	943.059	−	685.172i	1.17005	−	0.850090i
$807$	−24.1034	−	24.1034i	−0.0298680	−	0.0298680i
$808$	−22.0728	+	139.362i	−0.0273178	+	0.172478i
$809$	308.187	−	100.136i	0.380948	−	0.123778i	−0.112282	−	0.993676i	$-0.535816\pi$
$809$	308.187	−	100.136i	0.380948	−	0.123778i	0.493230	+	0.869899i	$0.335816\pi$
$810$	59.0001	+	91.8408i	0.0728397	+	0.113384i
$811$	−316.407	+	973.802i	−0.390145	+	1.20074i	0.542534	+	0.840034i	$0.317465\pi$
$811$	−316.407	+	973.802i	−0.390145	+	1.20074i	−0.932679	+	0.360708i	$0.882535\pi$
$812$	−112.694	+	221.173i	−0.138785	+	0.272381i
$813$	−492.951	−	251.171i	−0.606336	−	0.308944i
$814$	−828.037	−	269.046i	−1.01724	−	0.330523i
$815$	954.409	−	613.129i	1.17105	−	0.752306i
$816$	84.4517	+	259.916i	0.103495	+	0.318524i
$817$	1250.00	+	197.980i	1.52998	+	0.242325i
$818$	−1000.54	+	1000.54i	−1.22315	+	1.22315i
$819$	336.271	+	462.837i	0.410587	+	0.565125i
$820$	−119.772	+	106.778i	−0.146063	+	0.130217i
$821$	−830.389	−	603.313i	−1.01144	−	0.734851i	−0.0469261	−	0.998898i	$-0.514943\pi$
$821$	−830.389	−	603.313i	−1.01144	−	0.734851i	−0.964510	+	0.264047i	$0.914943\pi$
$822$	35.3705	+	223.320i	0.0430298	+	0.271679i
$823$	−91.9972	−	180.555i	−0.111783	−	0.219386i	0.828337	−	0.560230i	$-0.189287\pi$
$823$	−91.9972	−	180.555i	−0.111783	−	0.219386i	−0.940120	+	0.340844i	$0.889287\pi$
$824$			422.130i			0.512294i
$825$	383.243	−	142.792i	0.464537	−	0.173081i
$826$	1357.58			1.64356
$827$	413.894	−	210.889i	0.500476	−	0.255005i	−0.185480	−	0.982648i	$-0.559384\pi$
$827$	413.894	−	210.889i	0.500476	−	0.255005i	0.685956	+	0.727643i	$0.259384\pi$
$828$	−122.414	+	19.3885i	−0.147843	+	0.0234160i
$829$	−696.257	+	958.316i	−0.839876	+	1.15599i	0.146128	+	0.989266i	$0.453319\pi$
$829$	−696.257	+	958.316i	−0.839876	+	1.15599i	−0.986004	+	0.166724i	$0.946681\pi$
$830$	−168.219	−	36.6242i	−0.202674	−	0.0441256i
$831$	−654.281	+	475.363i	−0.787342	+	0.572037i
$832$	−186.585	−	186.585i	−0.224261	−	0.224261i
$833$	−34.4897	+	217.760i	−0.0414042	+	0.261416i
$834$	548.563	−	178.239i	0.657750	−	0.213716i
$835$	283.324	−	346.369i	0.339310	−	0.414813i
$836$	176.273	−	542.512i	0.210853	−	0.648938i
$837$	−52.1378	+	102.326i	−0.0622913	+	0.122254i
$838$	1278.28	+	651.314i	1.52539	+	0.777224i
$839$	1294.81	+	420.710i	1.54328	+	0.501442i	0.952279	−	0.305228i	$-0.0987327\pi$
$839$	1294.81	+	420.710i	1.54328	+	0.501442i	0.591002	+	0.806670i	$0.298733\pi$
$840$	−99.0357	−	377.035i	−0.117900	−	0.448851i
$841$	190.173	+	585.293i	0.226127	+	0.695948i
$842$	861.494	+	136.447i	1.02315	+	0.162051i
$843$	−175.807	+	175.807i	−0.208549	+	0.208549i
$844$	−144.313	−	198.630i	−0.170987	−	0.235344i
$845$	1511.12	−	151.293i	1.78831	−	0.179045i
$846$	−354.370	−	257.465i	−0.418877	−	0.304332i
$847$	43.6208	+	275.411i	0.0515003	+	0.325160i
$848$	−561.659	−	1102.32i	−0.662333	−	1.29990i
$849$			506.822i			0.596963i
$850$	352.608	+	323.844i	0.414832	+	0.380993i
$851$	−833.162			−0.979039
$852$	−127.366	+	64.8961i	−0.149490	+	0.0761691i
$853$	353.979	−	56.0648i	0.414981	−	0.0657266i	0.0545470	−	0.998511i	$-0.482629\pi$
$853$	353.979	−	56.0648i	0.414981	−	0.0657266i	0.360434	+	0.932785i	$0.382629\pi$
$854$	−82.1659	+	113.092i	−0.0962130	+	0.132426i
$855$	−440.166	+	193.379i	−0.514813	+	0.226174i
$856$	658.132	−	478.161i	0.768845	−	0.558599i
$857$	240.045	+	240.045i	0.280099	+	0.280099i	0.833149	−	0.553049i	$-0.186536\pi$
$857$	240.045	+	240.045i	0.280099	+	0.280099i	−0.553049	+	0.833149i	$0.686536\pi$
$858$	134.974	−	852.195i	0.157313	−	0.993234i
$859$	125.784	−	40.8697i	0.146431	−	0.0475782i	−0.234885	−	0.972023i	$-0.575471\pi$
$859$	125.784	−	40.8697i	0.146431	−	0.0475782i	0.381315	+	0.924445i	$0.375471\pi$
$860$	346.648	+	135.031i	0.403080	+	0.157013i
$861$	79.9507	−	246.063i	0.0928579	−	0.285787i
$862$	409.927	−	804.528i	0.475554	−	0.933327i
$863$	−988.227	−	503.527i	−1.14511	−	0.583461i	−0.224701	−	0.974428i	$-0.572141\pi$
$863$	−988.227	−	503.527i	−1.14511	−	0.583461i	−0.920405	+	0.390967i	$0.872141\pi$
$864$	−138.145	−	44.8861i	−0.159890	−	0.0519515i
$865$	−1039.45	−	59.6175i	−1.20168	−	0.0689220i
$866$	−146.388	−	450.537i	−0.169040	−	0.520251i
$867$	−387.781	−	61.4185i	−0.447268	−	0.0708403i
$868$	−258.288	+	258.288i	−0.297567	+	0.297567i
$869$	495.174	+	681.548i	0.569820	+	0.784290i
$870$	−272.473	−	159.109i	−0.313187	−	0.182884i
$871$	−418.341	−	303.942i	−0.480299	−	0.348958i
$872$	12.6014	+	79.5619i	0.0144511	+	0.0912407i
$873$	28.7527	+	56.4304i	0.0329356	+	0.0646397i
$874$		−	1704.63i		−	1.95038i
$875$	−763.684	−	786.625i	−0.872781	−	0.899000i
$876$	−248.210			−0.283345
$877$	326.651	−	166.437i	0.372464	−	0.189780i	−0.257731	−	0.966217i	$-0.582975\pi$
$877$	326.651	−	166.437i	0.372464	−	0.189780i	0.630195	+	0.776437i	$0.282975\pi$
$878$	−1729.51	+	273.928i	−1.96983	+	0.311991i
$879$	535.634	−	737.237i	0.609368	−	0.838722i
$880$	−475.959	+	815.075i	−0.540863	+	0.926222i
$881$	57.8294	−	42.0155i	0.0656406	−	0.0476907i	−0.554481	−	0.832196i	$-0.687083\pi$
$881$	57.8294	−	42.0155i	0.0656406	−	0.0476907i	0.620122	+	0.784506i	$0.287083\pi$
$882$	−143.710	−	143.710i	−0.162936	−	0.162936i
$883$	−138.173	+	872.388i	−0.156481	+	0.987982i	0.777038	+	0.629454i	$0.216721\pi$
$883$	−138.173	+	872.388i	−0.156481	+	0.987982i	−0.933519	+	0.358528i	$0.883279\pi$
$884$	307.607	−	99.9474i	0.347971	−	0.113063i
$885$	−31.6420	+	551.688i	−0.0357537	+	0.623376i
$886$	493.665	−	1519.35i	0.557184	−	1.71484i
$887$	146.991	−	288.487i	0.165717	−	0.325239i	−0.793182	−	0.608984i	$-0.791577\pi$
$887$	146.991	−	288.487i	0.165717	−	0.325239i	0.958900	+	0.283746i	$0.0915772\pi$
$888$	−300.977	−	153.356i	−0.338938	−	0.172698i
$889$	1940.83	+	630.615i	2.18317	+	0.709354i
$890$	−546.264	+	1402.35i	−0.613780	+	1.57568i
$891$	26.2680	+	80.8445i	0.0294814	+	0.0907345i
$892$	−114.241	−	18.0941i	−0.128073	−	0.0202848i
$893$	1364.15	−	1364.15i	1.52760	−	1.52760i
$894$	515.554	+	709.599i	0.576682	+	0.793735i
$895$	315.764	+	718.737i	0.352809	+	0.803058i
$896$	1002.32	+	728.228i	1.11866	+	0.812755i
$897$	−129.163	−	815.502i	−0.143994	−	0.909144i
$898$	−324.459	−	636.786i	−0.361313	−	0.709116i
$899$		−	331.957i		−	0.369251i
$900$	−138.519	+	28.0179i	−0.153910	+	0.0311310i
$901$	−488.666			−0.542360
$902$	−347.671	+	177.147i	−0.385445	+	0.196394i
$903$	−592.465	+	93.8372i	−0.656107	+	0.103917i
$904$	−171.224	+	235.669i	−0.189407	+	0.260696i
$905$	61.0524	+	609.792i	0.0674612	+	0.673803i
$906$	572.278	−	415.784i	0.631654	−	0.458923i
$907$	−626.393	−	626.393i	−0.690621	−	0.690621i	0.271747	−	0.962369i	$-0.412398\pi$
$907$	−626.393	−	626.393i	−0.690621	−	0.690621i	−0.962369	+	0.271747i	$0.912398\pi$
$908$	33.6311	−	212.338i	0.0370386	−	0.233853i
$909$	−78.4430	+	25.4877i	−0.0862959	+	0.0280393i
$910$	−2237.07	+	587.611i	−2.45832	+	0.645726i
$911$	−75.5340	+	232.470i	−0.0829132	+	0.255181i	−0.983916	−	0.178633i	$-0.942832\pi$
$911$	−75.5340	+	232.470i	−0.0829132	+	0.255181i	0.901003	+	0.433814i	$0.142832\pi$
$912$	503.725	−	988.617i	0.552331	−	1.08401i
$913$	−119.453	−	60.8643i	−0.130836	−	0.0666641i
$914$	−1113.60	−	361.831i	−1.21838	−	0.395876i
$915$	−44.0427	−	36.0262i	−0.0481341	−	0.0393729i
$916$	87.6246	+	269.681i	0.0956601	+	0.294411i
$917$	−337.435	−	53.4445i	−0.367977	−	0.0582819i
$918$	−70.3624	+	70.3624i	−0.0766475	+	0.0766475i
$919$	420.585	+	578.885i	0.457655	+	0.629908i	0.974020	−	0.226461i	$-0.0727154\pi$
$919$	420.585	+	578.885i	0.457655	+	0.629908i	−0.516366	+	0.856368i	$0.672715\pi$
$920$	−119.685	+	549.727i	−0.130092	+	0.597530i
$921$	−346.983	−	252.098i	−0.376746	−	0.273722i
$922$	275.633	+	1740.28i	0.298951	+	1.88750i
$923$	−432.327	−	848.489i	−0.468393	−	0.919273i
$924$			270.369i			0.292607i
$925$	−949.165	+	40.3595i	−1.02612	+	0.0436319i
$926$	−20.3143			−0.0219377
$927$	−219.862	+	112.025i	−0.237176	+	0.120847i
$928$	414.691	−	65.6806i	0.446865	−	0.0707765i
$929$	−542.177	+	746.243i	−0.583614	+	0.803276i	−0.994086	−	0.108597i	$-0.965364\pi$
$929$	−542.177	+	746.243i	−0.583614	+	0.803276i	0.410472	+	0.911873i	$0.365364\pi$
$930$	−308.975	−	346.574i	−0.332231	−	0.372660i
$931$	724.163	−	526.135i	0.777833	−	0.565129i
$932$	490.061	+	490.061i	0.525816	+	0.525816i
$933$	18.6500	−	117.751i	0.0199893	−	0.126207i
$934$	151.919	−	49.3615i	0.162654	−	0.0528496i
$935$	201.507	+	313.670i	0.215515	+	0.335475i
$936$	103.445	−	318.372i	0.110518	−	0.340141i
$937$	−347.841	+	682.677i	−0.371229	+	0.728578i	−0.998748	−	0.0500235i	$-0.984070\pi$
$937$	−347.841	+	682.677i	−0.371229	+	0.728578i	0.627519	+	0.778601i	$0.284070\pi$
$938$	450.851	+	229.720i	0.480652	+	0.244904i
$939$	−311.507	−	101.215i	−0.331743	−	0.107790i
$940$	477.122	−	306.511i	0.507576	−	0.326076i
$941$	188.275	+	579.450i	0.200080	+	0.615781i	0.999880	+	0.0155150i	$0.00493878\pi$
$941$	188.275	+	579.450i	0.200080	+	0.615781i	−0.799800	+	0.600266i	$0.795061\pi$
$942$	−638.458	−	101.122i	−0.677769	−	0.107348i
$943$	−264.033	+	264.033i	−0.279993	+	0.279993i
$944$	−749.608	−	1031.75i	−0.794076	−	1.09295i
$945$	170.093	−	151.640i	0.179992	−	0.160465i
$946$	731.895	+	531.753i	0.773673	+	0.562106i
$947$	99.1835	+	626.220i	0.104734	+	0.661267i	0.983071	+	0.183225i	$0.0586535\pi$
$947$	99.1835	+	626.220i	0.104734	+	0.661267i	−0.878337	+	0.478043i	$0.841346\pi$
$948$	−132.160	−	259.378i	−0.139409	−	0.273606i
$949$		−	1653.53i		−	1.74240i
$950$	−82.5747	−	1941.97i	−0.0869207	−	2.04418i
$951$	301.879			0.317433
$952$	316.625	−	161.329i	0.332590	−	0.169463i
$953$	1054.38	−	166.998i	1.10638	−	0.175234i	0.423595	−	0.905852i	$-0.360768\pi$
$953$	1054.38	−	166.998i	1.10638	−	0.175234i	0.682786	+	0.730618i	$0.260768\pi$
$954$	264.774	−	364.429i	0.277540	−	0.382002i
$955$	64.9196	+	14.1341i	0.0679787	+	0.0148001i
$956$	298.538	−	216.901i	0.312279	−	0.226884i
$957$	−173.742	−	173.742i	−0.181548	−	0.181548i
$958$	81.6820	−	515.720i	0.0852631	−	0.538330i
$959$	448.897	−	145.855i	0.468089	−	0.152091i
$960$	−66.5453	+	81.3528i	−0.0693180	+	0.0847425i
$961$	−146.016	+	449.391i	−0.151942	+	0.467629i
$962$	−909.909	+	1785.80i	−0.945851	+	1.85634i
$963$	423.700	+	215.886i	0.439980	+	0.224181i
$964$	250.716	+	81.4626i	0.260079	+	0.0845048i
$965$	−291.096	−	1108.22i	−0.301654	−	1.14841i
$966$	249.671	+	768.407i	0.258458	+	0.795452i
$967$	90.3676	+	14.3128i	0.0934515	+	0.0148013i	0.202985	−	0.979182i	$-0.434936\pi$
$967$	90.3676	+	14.3128i	0.0934515	+	0.0148013i	−0.109534	+	0.993983i	$0.534936\pi$
$968$	115.373	−	115.373i	0.119187	−	0.119187i
$969$	−257.604	−	354.561i	−0.265845	−	0.365904i
$970$	−254.779	+	25.5085i	−0.262659	+	0.0262974i
$971$	−355.467	−	258.262i	−0.366084	−	0.265975i	0.389501	−	0.921026i	$-0.372647\pi$
$971$	−355.467	−	258.262i	−0.366084	−	0.265975i	−0.755585	+	0.655050i	$0.772647\pi$
$972$	−4.59505	−	29.0120i	−0.00472742	−	0.0298477i
$973$	−546.637	−	1072.84i	−0.561806	−	1.10261i
$974$			356.569i			0.366088i
$975$	−186.650	−	922.789i	−0.191436	−	0.946450i
$976$	131.318			0.134547
$977$	670.255	−	341.512i	0.686034	−	0.349552i	−0.0759826	−	0.997109i	$-0.524209\pi$
$977$	670.255	−	341.512i	0.686034	−	0.349552i	0.762017	+	0.647557i	$0.224209\pi$
$978$	−941.496	+	149.118i	−0.962675	+	0.152473i
$979$	−688.869	+	948.146i	−0.703645	+	0.968484i
$980$	240.898	−	105.834i	0.245814	−	0.107994i
$981$	−38.0948	+	27.6775i	−0.0388326	+	0.0282135i
$982$	277.013	+	277.013i	0.282090	+	0.282090i
$983$	24.0730	−	151.991i	0.0244893	−	0.154619i	−0.972413	−	0.233264i	$-0.925059\pi$
$983$	24.0730	−	151.991i	0.0244893	−	0.154619i	0.996903	+	0.0786448i	$0.0250593\pi$
$984$	−143.980	+	46.7821i	−0.146322	+	0.0475428i
$985$	−1536.51	−	598.521i	−1.55990	−	0.607636i
$986$	88.8819	−	273.550i	0.0901439	−	0.277435i
$987$	−415.124	+	814.727i	−0.420592	+	0.825458i
$988$	−1170.01	−	596.152i	−1.18423	−	0.603393i
$989$	823.348	+	267.522i	0.832505	+	0.270497i
$990$	−343.105	−	19.6788i	−0.346571	−	0.0198775i
$991$	−380.144	−	1169.96i	−0.383597	−	1.18059i	−0.937493	−	0.348003i	$-0.886860\pi$
$991$	−380.144	−	1169.96i	−0.383597	−	1.18059i	0.553897	−	0.832585i	$-0.313140\pi$
$992$	610.227	+	96.6505i	0.615148	+	0.0974299i
$993$	262.098	−	262.098i	0.263946	−	0.263946i
$994$	547.727	+	753.881i	0.551033	+	0.758432i
$995$	1190.07	+	694.939i	1.19606	+	0.698431i
$996$	37.4789	+	27.2300i	0.0376294	+	0.0273394i
$997$	234.255	+	1479.03i	0.234960	+	1.48348i	0.769671	+	0.638441i	$0.220420\pi$
$997$	234.255	+	1479.03i	0.234960	+	1.48348i	−0.534711	+	0.845035i	$0.679580\pi$
$998$	394.795	+	774.830i	0.395587	+	0.776382i
$999$		−	197.459i		−	0.197656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.22.3	✓	80
3.2	odd	2		225.3.r.b.172.8		80
5.2	odd	4		375.3.k.b.118.3		80
5.3	odd	4		375.3.k.c.118.8		80
5.4	even	2		375.3.k.a.7.8		80
25.6	even	5		375.3.k.c.232.8		80
25.8	odd	20	inner	75.3.k.a.58.3	yes	80
25.17	odd	20		375.3.k.a.268.8		80
25.19	even	10		375.3.k.b.232.3		80
75.8	even	20		225.3.r.b.208.8		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.22.3	✓	80	1.1	even	1	trivial
75.3.k.a.58.3	yes	80	25.8	odd	20	inner
225.3.r.b.172.8		80	3.2	odd	2
225.3.r.b.208.8		80	75.8	even	20
375.3.k.a.7.8		80	5.4	even	2
375.3.k.a.268.8		80	25.17	odd	20
375.3.k.b.118.3		80	5.2	odd	4
375.3.k.b.232.3		80	25.19	even	10
375.3.k.c.118.8		80	5.3	odd	4
375.3.k.c.232.8		80	25.6	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.16137 + 1.10127i) q^{2} +(1.71073 - 0.270952i) q^{3} +(1.10757 - 1.52445i) q^{4} +(2.52133 - 4.31774i) q^{5} +(-3.39912 + 2.46960i) q^{6} +(6.20191 + 6.20191i) q^{7} +(0.802843 - 5.06895i) q^{8} +(2.85317 - 0.927051i) q^{9} +O(q^{10})\)	\(q+(-2.16137 + 1.10127i) q^{2} +(1.71073 - 0.270952i) q^{3} +(1.10757 - 1.52445i) q^{4} +(2.52133 - 4.31774i) q^{5} +(-3.39912 + 2.46960i) q^{6} +(6.20191 + 6.20191i) q^{7} +(0.802843 - 5.06895i) q^{8} +(2.85317 - 0.927051i) q^{9} +(-0.694505 + 12.1089i) q^{10} +(-2.91866 + 8.98272i) q^{11} +(1.48171 - 2.90801i) q^{12} +(19.3727 + 9.87087i) q^{13} +(-20.2346 - 6.57463i) q^{14} +(3.14340 - 8.06964i) q^{15} +(6.17620 + 19.0084i) q^{16} +(7.79733 + 1.23498i) q^{17} +(-5.14582 + 5.14582i) q^{18} +(-18.8393 - 25.9301i) q^{19} +(-3.78961 - 8.62585i) q^{20} +(12.2902 + 8.92935i) q^{21} +(-3.58412 - 22.6292i) q^{22} +(-9.95365 - 19.5351i) q^{23} -8.88912i q^{24} +(-12.2858 - 21.7729i) q^{25} -52.7420 q^{26} +(4.62981 - 2.35900i) q^{27} +(16.3236 - 2.58540i) q^{28} +(-8.82827 + 12.1511i) q^{29} +(2.09283 + 20.9032i) q^{30} +(-17.8806 + 12.9910i) q^{31} +(-19.7666 - 19.7666i) q^{32} +(-2.55914 + 16.1578i) q^{33} +(-18.2130 + 5.91775i) q^{34} +(42.4153 - 11.1412i) q^{35} +(1.74686 - 5.37628i) q^{36} +(17.2521 - 33.8591i) q^{37} +(69.2749 + 35.2973i) q^{38} +(35.8159 + 11.6373i) q^{39} +(-19.8622 - 16.2470i) q^{40} +(-5.26285 - 16.1974i) q^{41} +(-36.3973 - 5.76477i) q^{42} +(-27.9207 + 27.9207i) q^{43} +(10.4610 + 14.3984i) q^{44} +(3.19100 - 14.6567i) q^{45} +(43.0270 + 31.2610i) q^{46} +(9.41591 + 59.4497i) q^{47} +(15.7162 + 30.8447i) q^{48} +27.9275i q^{49} +(50.5321 + 33.5292i) q^{50} +13.6737 q^{51} +(36.5043 - 18.5999i) q^{52} +(-61.1373 + 9.68320i) q^{53} +(-7.40881 + 10.1974i) q^{54} +(31.4262 + 35.2504i) q^{55} +(36.4164 - 26.4580i) q^{56} +(-39.2548 - 39.2548i) q^{57} +(5.69951 - 35.9853i) q^{58} +(-60.6852 + 19.7178i) q^{59} +(-8.82018 - 13.7297i) q^{60} +(2.03033 - 6.24871i) q^{61} +(24.3399 - 47.7698i) q^{62} +(23.4446 + 11.9456i) q^{63} +(-11.5422 - 3.75029i) q^{64} +(91.4648 - 58.7586i) q^{65} +(-12.2629 - 37.7413i) q^{66} +(-23.4900 - 3.72046i) q^{67} +(10.5188 - 10.5188i) q^{68} +(-22.3211 - 30.7223i) q^{69} +(-79.4057 + 70.7911i) q^{70} +(-35.4335 - 25.7440i) q^{71} +(-2.40853 - 15.2069i) q^{72} +(-34.5264 - 67.7618i) q^{73} +92.1812i q^{74} +(-26.9171 - 33.9186i) q^{75} -60.3951 q^{76} +(-73.8113 + 37.6087i) q^{77} +(-90.2272 + 14.2906i) q^{78} +(52.4271 - 72.1598i) q^{79} +(97.6456 + 21.2591i) q^{80} +(7.28115 - 5.29007i) q^{81} +(29.2127 + 29.2127i) q^{82} +(-2.22048 + 14.0196i) q^{83} +(27.2246 - 8.84582i) q^{84} +(24.9919 - 30.5531i) q^{85} +(29.5986 - 91.0953i) q^{86} +(-11.8104 + 23.1792i) q^{87} +(43.1897 + 22.0063i) q^{88} +(118.011 + 38.3441i) q^{89} +(9.24403 + 35.1926i) q^{90} +(58.9294 + 181.366i) q^{91} +(-40.8047 - 6.46283i) q^{92} +(-27.0689 + 27.0689i) q^{93} +(-85.8216 - 118.123i) q^{94} +(-159.460 + 15.9651i) q^{95} +(-39.1711 - 28.4595i) q^{96} +(3.30251 + 20.8512i) q^{97} +(-30.7557 - 60.3615i) q^{98} +28.3350i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

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