LMFDB - Embedded newform 409.3.p.a.21.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [409,3,Mod(21,409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(409, base_ring=CyclotomicField(408)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("409.21"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 409 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	409.p (of order $408$, degree $128$, 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:	$11.1444428123$
Analytic rank:	$0$
Dimension:	$8576$
Relative dimension:	$67$ over $\Q(\zeta_{408})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{408}]$

Embedding invariants

Embedding label			21.4
Character	$\chi$	$=$	409.21
Dual form			409.3.p.a.39.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.97290 - 2.17396i) q^{2} +(-1.71585 - 1.33773i) q^{3} +(2.89942 + 9.11414i) q^{4} +(3.00382 + 0.561512i) q^{5} +(2.19287 + 7.70713i) q^{6} +(-8.04167 + 6.17059i) q^{7} +(6.51243 - 19.4305i) q^{8} +(-1.04062 - 4.13748i) q^{9} +(-7.70936 - 8.19950i) q^{10} +(-2.12909 - 18.3516i) q^{11} +(7.21733 - 19.5171i) q^{12} +(-5.54020 + 4.38833i) q^{13} +(37.3217 - 0.862282i) q^{14} +(-4.40295 - 4.98178i) q^{15} +(-30.3767 + 21.5032i) q^{16} +(10.6963 - 16.1424i) q^{17} +(-5.90105 + 14.5626i) q^{18} +(-4.20160 + 4.01184i) q^{19} +(3.59164 + 29.0053i) q^{20} +(22.0529 + 0.169810i) q^{21} +(-33.5661 + 59.1861i) q^{22} +(-1.32532 - 6.53134i) q^{23} +(-37.1671 + 24.6278i) q^{24} +(-14.6041 - 5.65768i) q^{25} +(26.0105 - 1.00190i) q^{26} +(-11.6586 + 26.4042i) q^{27} +(-79.5558 - 55.4018i) q^{28} +(-34.9798 + 42.7907i) q^{29} +(2.25934 + 24.3822i) q^{30} +(41.5015 + 17.1905i) q^{31} +(55.0923 + 0.848487i) q^{32} +(-20.8964 + 34.3368i) q^{33} +(-66.8920 + 24.7363i) q^{34} +(-27.6206 + 14.0199i) q^{35} +(34.6924 - 21.4806i) q^{36} +(25.2434 + 23.3709i) q^{37} +(21.2125 - 2.79268i) q^{38} +(15.3766 - 0.118402i) q^{39} +(30.4726 - 54.7089i) q^{40} +(50.9293 - 54.1673i) q^{41} +(-65.1918 - 48.4469i) q^{42} +(-7.47233 + 7.82577i) q^{43} +(161.086 - 72.6138i) q^{44} +(-0.802588 - 13.0126i) q^{45} +(-10.2588 + 22.2982i) q^{46} +(-16.2349 + 71.4924i) q^{47} +(80.8873 + 3.73964i) q^{48} +(13.9101 - 51.9133i) q^{49} +(31.1171 + 48.5685i) q^{50} +(-39.9475 + 13.3891i) q^{51} +(-56.0592 - 37.7706i) q^{52} +(-13.5673 + 23.4993i) q^{53} +(92.0614 - 53.1517i) q^{54} +(3.90927 - 56.3206i) q^{55} +(67.5265 + 196.439i) q^{56} +(12.5761 - 1.26308i) q^{57} +(197.016 - 51.1678i) q^{58} +(-22.1453 + 61.3330i) q^{59} +(32.6387 - 54.5734i) q^{60} +(58.9307 - 34.6314i) q^{61} +(-86.0084 - 141.328i) q^{62} +(33.8990 + 26.8510i) q^{63} +(-43.1390 - 32.5771i) q^{64} +(-19.1059 + 10.0709i) q^{65} +(136.770 - 56.6518i) q^{66} +(-115.779 + 45.8813i) q^{67} +(178.137 + 50.6844i) q^{68} +(-6.46313 + 12.9797i) q^{69} +(112.592 + 18.3664i) q^{70} +(-68.8549 - 80.3677i) q^{71} +(-87.1700 - 6.72537i) q^{72} +(52.4579 + 75.3284i) q^{73} +(-24.2389 - 124.357i) q^{74} +(17.4900 + 29.2442i) q^{75} +(-48.7466 - 26.6620i) q^{76} +(130.362 + 134.440i) q^{77} +(-45.9703 - 33.0760i) q^{78} +(-1.48568 - 7.04289i) q^{79} +(-103.320 + 47.5350i) q^{80} +(21.4979 - 11.5441i) q^{81} +(-269.165 + 50.3156i) q^{82} +(21.6637 + 43.5066i) q^{83} +(62.3928 + 201.485i) q^{84} +(41.1941 - 42.4828i) q^{85} +(39.2274 - 7.02070i) q^{86} +(117.262 - 26.6287i) q^{87} +(-370.446 - 78.1447i) q^{88} +(-0.362165 + 0.330157i) q^{89} +(-25.9028 + 40.4298i) q^{90} +(17.4739 - 69.4758i) q^{91} +(55.6849 - 31.0163i) q^{92} +(-48.2140 - 85.0142i) q^{93} +(203.686 - 177.245i) q^{94} +(-14.8736 + 9.69160i) q^{95} +(-93.3950 - 75.1547i) q^{96} +(-27.3239 - 8.92460i) q^{97} +(-154.211 + 124.093i) q^{98} +(-73.7140 + 27.9061i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8576 q - 124 q^{2} - 112 q^{3} - 124 q^{4} - 120 q^{5} - 120 q^{6} - 144 q^{7} + 8 q^{8} - 292 q^{9} - 96 q^{10} - 160 q^{11} + 36 q^{12} - 164 q^{13} - 16 q^{14} - 80 q^{15} - 204 q^{16} - 148 q^{17} - 148 q^{18}+ \cdots + 1180 q^{99}+O(q^{100}) $ 8576 * q - 124 * q^2 - 112 * q^3 - 124 * q^4 - 120 * q^5 - 120 * q^6 - 144 * q^7 + 8 * q^8 - 292 * q^9 - 96 * q^10 - 160 * q^11 + 36 * q^12 - 164 * q^13 - 16 * q^14 - 80 * q^15 - 204 * q^16 - 148 * q^17 - 148 * q^18 - 96 * q^19 + 68 * q^20 - 144 * q^21 - 256 * q^22 - 128 * q^23 - 1156 * q^24 - 2496 * q^25 - 280 * q^26 - 100 * q^27 - 92 * q^28 - 80 * q^29 + 672 * q^30 - 168 * q^31 + 2112 * q^32 - 96 * q^33 + 92 * q^34 + 64 * q^35 - 2344 * q^36 - 152 * q^37 - 2972 * q^39 + 112 * q^40 - 196 * q^41 + 488 * q^42 - 452 * q^43 + 92 * q^44 - 244 * q^45 - 124 * q^46 + 16 * q^47 - 188 * q^48 + 16 * q^49 + 96 * q^50 + 8 * q^51 - 828 * q^52 - 256 * q^53 + 240 * q^54 - 1016 * q^55 + 76 * q^56 - 92 * q^57 - 800 * q^58 + 48 * q^59 - 64 * q^60 + 428 * q^61 - 52 * q^62 + 1604 * q^63 - 136 * q^64 + 136 * q^65 + 224 * q^66 + 600 * q^67 - 136 * q^68 + 2808 * q^69 - 20 * q^70 - 188 * q^71 + 560 * q^72 + 144 * q^73 - 996 * q^74 + 1152 * q^75 + 992 * q^76 - 3084 * q^77 - 4900 * q^78 - 560 * q^79 - 292 * q^80 - 3128 * q^81 + 1488 * q^82 + 120 * q^83 + 6560 * q^84 + 288 * q^85 + 3248 * q^86 - 632 * q^87 + 144 * q^88 + 608 * q^89 + 268 * q^90 + 404 * q^91 - 5128 * q^92 - 104 * q^93 - 624 * q^94 + 84 * q^95 + 140 * q^96 - 840 * q^97 - 72 * q^98 + 1180 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{408}\right)$

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 $

$2$	−2.97290	−	2.17396i	−1.48645	−	1.08698i	−0.973535	−	0.228539i	$-0.926605\pi$
$2$	−2.97290	−	2.17396i	−1.48645	−	1.08698i	−0.512914	−	0.858440i	$-0.671434\pi$
$3$	−1.71585	−	1.33773i	−0.571949	−	0.445911i	0.287030	−	0.957922i	$-0.407332\pi$
$3$	−1.71585	−	1.33773i	−0.571949	−	0.445911i	−0.858979	+	0.512011i	$0.828901\pi$
$4$	2.89942	+	9.11414i	0.724854	+	2.27854i
$5$	3.00382	+	0.561512i	0.600765	+	0.112302i	0.475342	−	0.879801i	$-0.342324\pi$
$5$	3.00382	+	0.561512i	0.600765	+	0.112302i	0.125423	+	0.992103i	$0.459971\pi$
$6$	2.19287	+	7.70713i	0.365478	+	1.28452i
$7$	−8.04167	+	6.17059i	−1.14881	+	0.881513i	−0.994315	−	0.106481i	$-0.966042\pi$
$7$	−8.04167	+	6.17059i	−1.14881	+	0.881513i	−0.154495	+	0.987994i	$0.549375\pi$
$8$	6.51243	−	19.4305i	0.814054	−	2.42881i
$9$	−1.04062	−	4.13748i	−0.115624	−	0.459720i
$10$	−7.70936	−	8.19950i	−0.770936	−	0.819950i
$11$	−2.12909	−	18.3516i	−0.193553	−	1.66833i	−0.636116	−	0.771594i	$-0.719460\pi$
$11$	−2.12909	−	18.3516i	−0.193553	−	1.66833i	0.442563	−	0.896738i	$-0.354069\pi$
$12$	7.21733	−	19.5171i	0.601444	−	1.62643i
$13$	−5.54020	+	4.38833i	−0.426169	+	0.337564i	−0.810611	−	0.585585i	$-0.800865\pi$
$13$	−5.54020	+	4.38833i	−0.426169	+	0.337564i	0.384441	+	0.923149i	$0.374394\pi$
$14$	37.3217	−	0.862282i	2.66583	−	0.0615915i
$15$	−4.40295	−	4.98178i	−0.293530	−	0.332119i
$16$	−30.3767	+	21.5032i	−1.89854	+	1.34395i
$17$	10.6963	−	16.1424i	0.629196	−	0.949552i	−0.370588	−	0.928797i	$-0.620844\pi$
$17$	10.6963	−	16.1424i	0.629196	−	0.949552i	0.999785	−	0.0207552i	$-0.00660705\pi$
$18$	−5.90105	+	14.5626i	−0.327836	+	0.809031i
$19$	−4.20160	+	4.01184i	−0.221137	+	0.211149i	−0.793036	−	0.609174i	$-0.791501\pi$
$19$	−4.20160	+	4.01184i	−0.221137	+	0.211149i	0.571899	+	0.820324i	$0.306207\pi$
$20$	3.59164	+	29.0053i	0.179582	+	1.45027i
$21$	22.0529	+	0.169810i	1.05014	+	0.00808620i
$22$	−33.5661	+	59.1861i	−1.52573	+	2.69028i
$23$	−1.32532	−	6.53134i	−0.0576228	−	0.283971i	0.940876	−	0.338752i	$-0.110005\pi$
$23$	−1.32532	−	6.53134i	−0.0576228	−	0.283971i	−0.998498	+	0.0547812i	$0.982554\pi$
$24$	−37.1671	+	24.6278i	−1.54863	+	1.02616i
$25$	−14.6041	−	5.65768i	−0.584166	−	0.226307i
$26$	26.0105	−	1.00190i	1.00040	−	0.0385345i
$27$	−11.6586	+	26.4042i	−0.431800	+	0.977933i
$28$	−79.5558	−	55.4018i	−2.84128	−	1.97864i
$29$	−34.9798	+	42.7907i	−1.20620	+	1.47554i	−0.368307	+	0.929704i	$0.620062\pi$
$29$	−34.9798	+	42.7907i	−1.20620	+	1.47554i	−0.837892	+	0.545836i	$0.816212\pi$
$30$	2.25934	+	24.3822i	0.0753114	+	0.812739i
$31$	41.5015	+	17.1905i	1.33876	+	0.554532i	0.933141	−	0.359511i	$-0.117056\pi$
$31$	41.5015	+	17.1905i	1.33876	+	0.554532i	0.405618	+	0.914043i	$0.367056\pi$
$32$	55.0923	+	0.848487i	1.72164	+	0.0265152i
$33$	−20.8964	+	34.3368i	−0.633225	+	1.04051i
$34$	−66.8920	+	24.7363i	−1.96741	+	0.727538i
$35$	−27.6206	+	14.0199i	−0.789160	+	0.400568i
$36$	34.6924	−	21.4806i	0.963677	−	0.596684i
$37$	25.2434	+	23.3709i	0.682255	+	0.631645i	0.942621	−	0.333865i	$-0.108353\pi$
$37$	25.2434	+	23.3709i	0.682255	+	0.631645i	−0.260366	+	0.965510i	$0.583843\pi$
$38$	21.2125	−	2.79268i	0.558224	−	0.0734915i
$39$	15.3766	−	0.118402i	0.394271	−	0.00303594i
$40$	30.4726	−	54.7089i	0.761816	−	1.36772i
$41$	50.9293	−	54.1673i	1.24218	−	1.32115i	0.313811	−	0.949485i	$-0.398394\pi$
$41$	50.9293	−	54.1673i	1.24218	−	1.32115i	0.928366	−	0.371667i	$-0.121214\pi$
$42$	−65.1918	−	48.4469i	−1.55219	−	1.15350i
$43$	−7.47233	+	7.82577i	−0.173775	+	0.181995i	−0.804391	−	0.594100i	$-0.797508\pi$
$43$	−7.47233	+	7.82577i	−0.173775	+	0.181995i	0.630616	+	0.776095i	$0.282802\pi$
$44$	161.086	−	72.6138i	3.66105	−	1.65031i
$45$	−0.802588	−	13.0126i	−0.0178353	−	0.289168i
$46$	−10.2588	+	22.2982i	−0.223017	+	0.484743i
$47$	−16.2349	+	71.4924i	−0.345424	+	1.52111i	0.437627	+	0.899157i	$0.355819\pi$
$47$	−16.2349	+	71.4924i	−0.345424	+	1.52111i	−0.783051	+	0.621957i	$0.786338\pi$
$48$	80.8873	+	3.73964i	1.68515	+	0.0779093i
$49$	13.9101	−	51.9133i	0.283880	−	1.05945i
$50$	31.1171	+	48.5685i	0.622342	+	0.971370i
$51$	−39.9475	+	13.3891i	−0.783284	+	0.262530i
$52$	−56.0592	−	37.7706i	−1.07806	−	0.726357i
$53$	−13.5673	+	23.4993i	−0.255987	+	0.443383i	−0.965163	−	0.261649i	$-0.915734\pi$
$53$	−13.5673	+	23.4993i	−0.255987	+	0.443383i	0.709176	+	0.705031i	$0.249067\pi$
$54$	92.0614	−	53.1517i	1.70484	−	0.984290i
$55$	3.90927	−	56.3206i	0.0710776	−	1.02401i
$56$	67.5265	+	196.439i	1.20583	+	3.50784i
$57$	12.5761	−	1.26308i	0.220633	−	0.0221594i
$58$	197.016	−	51.1678i	3.39683	−	0.882203i
$59$	−22.1453	+	61.3330i	−0.375343	+	1.03954i	0.596232	+	0.802812i	$0.296664\pi$
$59$	−22.1453	+	61.3330i	−0.375343	+	1.03954i	−0.971576	+	0.236730i	$0.923924\pi$
$60$	32.6387	−	54.5734i	0.543978	−	0.909557i
$61$	58.9307	−	34.6314i	0.966076	−	0.567727i	0.0633726	−	0.997990i	$-0.479814\pi$
$61$	58.9307	−	34.6314i	0.966076	−	0.567727i	0.902704	+	0.430263i	$0.141579\pi$
$62$	−86.0084	−	141.328i	−1.38723	−	2.27949i
$63$	33.8990	+	26.8510i	0.538079	+	0.426206i
$64$	−43.1390	−	32.5771i	−0.674047	−	0.509016i
$65$	−19.1059	+	10.0709i	−0.293937	+	0.154937i
$66$	136.770	−	56.6518i	2.07227	−	0.858361i
$67$	−115.779	+	45.8813i	−1.72804	+	0.684795i	−1.00000		0.000739993i	$-0.999764\pi$
$67$	−115.779	+	45.8813i	−1.72804	+	0.684795i	−0.728040	+	0.685535i	$0.759568\pi$
$68$	178.137	+	50.6844i	2.61966	+	0.745359i
$69$	−6.46313	+	12.9797i	−0.0936685	+	0.188112i
$70$	112.592	+	18.3664i	1.60846	+	0.262377i
$71$	−68.8549	−	80.3677i	−0.969787	−	1.13194i	−0.991227	−	0.132170i	$-0.957806\pi$
$71$	−68.8549	−	80.3677i	−0.969787	−	1.13194i	0.0214402	−	0.999770i	$-0.493175\pi$
$72$	−87.1700	−	6.72537i	−1.21070	−	0.0934080i
$73$	52.4579	+	75.3284i	0.718601	+	1.03190i	0.997437	+	0.0715570i	$0.0227968\pi$
$73$	52.4579	+	75.3284i	0.718601	+	1.03190i	−0.278835	+	0.960339i	$0.589948\pi$
$74$	−24.2389	−	124.357i	−0.327552	−	1.68050i
$75$	17.4900	+	29.2442i	0.233200	+	0.389922i
$76$	−48.7466	−	26.6620i	−0.641403	−	0.350816i
$77$	130.362	+	134.440i	1.69301	+	1.74598i
$78$	−45.9703	−	33.0760i	−0.589363	−	0.424051i
$79$	−1.48568	−	7.04289i	−0.0188061	−	0.0891505i	0.968048	−	0.250766i	$-0.0806825\pi$
$79$	−1.48568	−	7.04289i	−0.0188061	−	0.0891505i	−0.986854	+	0.161616i	$0.948330\pi$
$80$	−103.320	+	47.5350i	−1.29151	+	0.594187i
$81$	21.4979	−	11.5441i	0.265406	−	0.142520i
$82$	−269.165	+	50.3156i	−3.28250	+	0.613605i
$83$	21.6637	+	43.5066i	0.261009	+	0.524176i	0.986441	−	0.164117i	$-0.0524776\pi$
$83$	21.6637	+	43.5066i	0.261009	+	0.524176i	−0.725432	+	0.688294i	$0.758360\pi$
$84$	62.3928	+	201.485i	0.742772	+	2.39864i
$85$	41.1941	−	42.4828i	0.484636	−	0.499797i
$86$	39.2274	−	7.02070i	0.456132	−	0.0816361i
$87$	117.262	−	26.6287i	1.34784	−	0.306077i
$88$	−370.446	−	78.1447i	−4.20962	−	0.888008i
$89$	−0.362165	+	0.330157i	−0.00406927	+	0.00370963i	−0.675728	−	0.737151i	$-0.736170\pi$
$89$	−0.362165	+	0.330157i	−0.00406927	+	0.00370963i	0.671658	+	0.740861i	$0.265582\pi$
$90$	−25.9028	+	40.4298i	−0.287809	+	0.449221i
$91$	17.4739	−	69.4758i	0.192020	−	0.763470i
$92$	55.6849	−	31.0163i	0.605270	−	0.337133i
$93$	−48.2140	−	85.0142i	−0.518430	−	0.914132i
$94$	203.686	−	177.245i	2.16687	−	1.88559i
$95$	−14.8736	+	9.69160i	−0.156564	+	0.102017i
$96$	−93.3950	−	75.1547i	−0.972865	−	0.782861i
$97$	−27.3239	−	8.92460i	−0.281689	−	0.0920062i	0.166210	−	0.986090i	$-0.446847\pi$
$97$	−27.3239	−	8.92460i	−0.281689	−	0.0920062i	−0.447899	+	0.894084i	$0.647828\pi$
$98$	−154.211	+	124.093i	−1.57358	+	1.26625i
$99$	−73.7140	+	27.9061i	−0.744585	+	0.281880i
$100$	9.22135	−	149.508i	0.0922135	−	1.49508i
$101$	63.2079	+	33.9419i	0.625821	+	0.336059i	0.755159	−	0.655542i	$-0.227560\pi$
$101$	63.2079	+	33.9419i	0.625821	+	0.336059i	−0.129338	+	0.991601i	$0.541285\pi$
$102$	147.867	+	47.0399i	1.44968	+	0.461175i
$103$	−57.1609	+	39.1562i	−0.554961	+	0.380157i	−0.809692	−	0.586855i	$-0.800366\pi$
$103$	−57.1609	+	39.1562i	−0.554961	+	0.380157i	0.254731	+	0.967012i	$0.418013\pi$
$104$	49.1871	+	136.227i	0.472953	+	1.30988i
$105$	66.1476	+	12.8930i	0.629977	+	0.122791i
$106$	91.4207	−	40.3662i	0.862460	−	0.380813i
$107$	37.6929	+	77.1812i	0.352270	+	0.721320i	0.999148	−	0.0412735i	$-0.0131415\pi$
$107$	37.6929	+	77.1812i	0.352270	+	0.721320i	−0.646878	+	0.762593i	$0.723926\pi$
$108$	−274.455	−	29.7013i	−2.54125	−	0.275012i
$109$	131.460	+	116.186i	1.20605	+	1.06592i	0.996102	+	0.0882107i	$0.0281149\pi$
$109$	131.460	+	116.186i	1.20605	+	1.06592i	0.209951	+	0.977712i	$0.432669\pi$
$110$	−134.060	+	158.937i	−1.21873	+	1.44488i
$111$	−12.0499	−	73.8698i	−0.108558	−	0.665494i
$112$	111.592	−	360.363i	0.996354	−	3.21753i
$113$	79.3886	+	145.148i	0.702554	+	1.28449i	0.948982	+	0.315332i	$0.102116\pi$
$113$	79.3886	+	145.148i	0.702554	+	1.28449i	−0.246428	+	0.969161i	$0.579257\pi$
$114$	−40.1333	−	23.5848i	−0.352046	−	0.206885i
$115$	−0.313617	−	20.3632i	−0.00272710	−	0.177071i
$116$	−491.421	−	194.742i	−4.23639	−	1.67881i
$117$	23.9219	+	18.3559i	0.204460	+	0.156888i
$118$	199.171	−	134.194i	1.68789	−	1.13723i
$119$	13.5917	+	195.814i	0.114216	+	1.64550i
$120$	−125.472	+	53.1079i	−1.04560	+	0.442565i
$121$	−214.464	+	50.4414i	−1.77243	+	0.416871i
$122$	−250.482	−	25.1573i	−2.05313	−	0.206207i
$123$	−159.848	+	24.8130i	−1.29958	+	0.201732i
$124$	−36.3464	+	428.093i	−0.293116	+	3.45236i
$125$	−105.645	−	65.4126i	−0.845160	−	0.523301i
$126$	−42.4052	−	153.520i	−0.336550	−	1.21841i
$127$	−4.23443	−	78.4850i	−0.0333420	−	0.617992i	−0.966207	−	0.257766i	$-0.917014\pi$
$127$	−4.23443	−	78.4850i	−0.0333420	−	0.617992i	0.932865	−	0.360225i	$-0.117300\pi$
$128$	−6.14464	−	20.3974i	−0.0480050	−	0.159355i
$129$	23.2902	−	3.43186i	0.180544	−	0.0266036i
$130$	78.6935	+	11.5957i	0.605335	+	0.0891976i
$131$	58.7919	+	17.7108i	0.448793	+	0.135197i	0.504806	−	0.863233i	$-0.331564\pi$
$131$	58.7919	+	17.7108i	0.448793	+	0.135197i	−0.0560123	+	0.998430i	$0.517839\pi$
$132$	−373.538	−	90.8962i	−2.82983	−	0.688607i
$133$	9.03248	−	58.1882i	0.0679134	−	0.437505i
$134$	443.942	+	115.298i	3.31300	+	0.860430i
$135$	−49.8466	+	72.7671i	−0.369234	+	0.539016i
$136$	−243.995	−	312.961i	−1.79408	−	2.30118i
$137$	−91.7308	+	2.82620i	−0.669568	+	0.0206292i	−0.363800	−	0.931477i	$-0.618521\pi$
$137$	−91.7308	+	2.82620i	−0.669568	+	0.0206292i	−0.305768	+	0.952106i	$0.598913\pi$
$138$	47.4316	−	24.5368i	0.343707	−	0.177803i
$139$	−41.3189	−	117.254i	−0.297258	−	0.843557i	−0.992218	−	0.124509i	$-0.960264\pi$
$139$	−41.3189	−	117.254i	−0.297258	−	0.843557i	0.694960	−	0.719048i	$-0.255422\pi$
$140$	−207.863	−	211.089i	−1.48473	−	1.50778i
$141$	123.494	−	100.952i	0.875847	−	0.715972i
$142$	29.9824	+	388.613i	0.211144	+	2.73671i
$143$	92.3286	+	92.3286i	0.645655	+	0.645655i
$144$	120.580	+	103.306i	0.837358	+	0.717404i
$145$	−129.101	+	108.894i	−0.890348	+	0.750994i
$146$	7.80882	−	337.985i	0.0534851	−	2.31497i
$147$	−93.3138	+	70.4673i	−0.634788	+	0.479369i
$148$	−139.814	+	297.834i	−0.944689	+	2.01239i
$149$	−13.2596	+	13.4654i	−0.0889906	+	0.0903717i	−0.755592	−	0.655043i	$-0.772650\pi$
$149$	−13.2596	+	13.4654i	−0.0889906	+	0.0903717i	0.666601	+	0.745415i	$0.267749\pi$
$150$	11.5795	−	124.962i	0.0771965	−	0.833083i
$151$	−66.7013	+	126.542i	−0.441731	+	0.838025i	0.558235	+	0.829683i	$0.311479\pi$
$151$	−66.7013	+	126.542i	−0.441731	+	0.838025i	−0.999965	+	0.00834198i	$0.997345\pi$
$152$	50.5892	+	107.766i	0.332824	+	0.708986i
$153$	−77.9196	−	27.4578i	−0.509278	−	0.179463i
$154$	−95.2853	−	683.078i	−0.618736	−	4.43557i
$155$	115.011	+	74.9408i	0.742004	+	0.483489i
$156$	45.6622	+	139.801i	0.292706	+	0.896159i
$157$	47.7827	+	18.0892i	0.304349	+	0.115218i	0.501507	−	0.865154i	$-0.332779\pi$
$157$	47.7827	+	18.0892i	0.304349	+	0.115218i	−0.197158	+	0.980372i	$0.563171\pi$
$158$	−10.8942	+	24.1676i	−0.0689504	+	0.152959i
$159$	54.7152	−	22.1718i	0.344121	−	0.139445i
$160$	165.011	+	33.4837i	1.03132	+	0.209273i
$161$	50.9600	+	44.3448i	0.316522	+	0.275434i
$162$	−89.0075	−	12.4160i	−0.549429	−	0.0766421i
$163$	−93.6614	+	181.055i	−0.574610	+	1.11077i	0.405830	+	0.913949i	$0.366983\pi$
$163$	−93.6614	+	181.055i	−0.574610	+	1.11077i	−0.980440	+	0.196818i	$0.936939\pi$
$164$	641.353	+	307.123i	3.91069	+	1.87270i
$165$	−82.0497	+	91.4081i	−0.497271	+	0.553988i
$166$	30.1775	−	176.437i	0.181792	−	1.06287i
$167$	22.1478	−	52.3261i	0.132621	−	0.313330i	−0.841171	−	0.540769i	$-0.818133\pi$
$167$	22.1478	−	52.3261i	0.132621	−	0.313330i	0.973792	+	0.227439i	$0.0730352\pi$
$168$	146.917	−	427.392i	0.874508	−	2.54400i
$169$	−27.2563	+	115.887i	−0.161280	+	0.685719i
$170$	−214.821	+	36.7428i	−1.26366	+	0.216134i
$171$	20.9712	+	13.2092i	0.122638	+	0.0772470i
$172$	−92.9906	−	45.4137i	−0.540643	−	0.264033i
$173$	0.822267	−	21.3471i	0.00475299	−	0.123394i	−0.994976	−	0.100114i	$-0.968079\pi$
$173$	0.822267	−	21.3471i	0.00475299	−	0.123394i	0.999729	−	0.0232798i	$-0.00741086\pi$
$174$	−406.499	−	175.759i	−2.33620	−	1.01011i
$175$	152.353	−	44.6190i	0.870588	−	0.254966i
$176$	459.293	+	511.680i	2.60962	+	2.90727i
$177$	120.045	−	75.6136i	0.678220	−	0.427195i
$178$	1.79443	−	0.194192i	0.0100811	−	0.00109096i
$179$	91.7229	+	64.9293i	0.512418	+	0.362733i	0.804779	−	0.593575i	$-0.202284\pi$
$179$	91.7229	+	64.9293i	0.512418	+	0.362733i	−0.292361	+	0.956308i	$0.594441\pi$
$180$	116.271	−	45.0438i	0.645952	−	0.250243i
$181$	187.998	−	81.2854i	1.03867	−	0.449091i	0.192100	−	0.981375i	$-0.438470\pi$
$181$	187.998	−	81.2854i	1.03867	−	0.449091i	0.846566	+	0.532285i	$0.178666\pi$
$182$	−202.985	+	168.557i	−1.11530	+	0.926137i
$183$	−147.444	−	19.4113i	−0.805703	−	0.106073i
$184$	−135.538	−	16.7832i	−0.736619	−	0.0912132i
$185$	62.7038	+	84.3764i	0.338939	+	0.456089i
$186$	−41.4820	+	357.554i	−0.223022	+	1.92233i
$187$	−319.013	−	161.927i	−1.70595	−	0.865919i
$188$	−698.663	+	59.3186i	−3.71629	+	0.315524i
$189$	−69.1749	−	284.274i	−0.366005	−	1.50410i
$190$	65.2867	+	3.52236i	0.343614	+	0.0185387i
$191$	−33.9227	+	7.42918i	−0.177606	+	0.0388962i	−0.301850	−	0.953355i	$-0.597604\pi$
$191$	−33.9227	+	7.42918i	−0.177606	+	0.0388962i	0.124244	+	0.992252i	$0.460349\pi$
$192$	30.4406	+	113.606i	0.158545	+	0.591697i
$193$	164.822	−	180.801i	0.853999	−	0.936792i	−0.144612	−	0.989488i	$-0.546193\pi$
$193$	164.822	−	180.801i	0.853999	−	0.936792i	0.998611	+	0.0526966i	$0.0167816\pi$
$194$	61.8293	+	85.9328i	0.318708	+	0.442953i
$195$	46.2550	+	8.27846i	0.237205	+	0.0424537i
$196$	513.476	−	23.7394i	2.61978	−	0.121120i
$197$	54.5400	−	249.037i	0.276853	−	1.26415i	−0.606366	−	0.795186i	$-0.707373\pi$
$197$	54.5400	−	249.037i	0.276853	−	1.26415i	0.883218	−	0.468962i	$-0.155372\pi$
$198$	279.811	+	77.2891i	1.41319	+	0.390349i
$199$	−42.1332	+	39.0077i	−0.211725	+	0.196019i	−0.778121	−	0.628114i	$-0.783827\pi$
$199$	−42.1332	+	39.0077i	−0.211725	+	0.196019i	0.566397	+	0.824133i	$0.308337\pi$
$200$	−205.040	+	246.920i	−1.02520	+	1.23460i
$201$	260.035	+	76.1556i	1.29371	+	0.378884i
$202$	−114.122	−	238.317i	−0.564962	−	1.17979i
$203$	17.2520	−	559.954i	0.0849852	−	2.75839i
$204$	−237.854	−	325.267i	−1.16595	−	1.59444i
$205$	183.398	−	134.111i	0.894625	−	0.654202i
$206$	255.057	+	7.85824i	1.23814	+	0.0381468i
$207$	−25.6441	+	12.2801i	−0.123885	+	0.0593243i
$208$	73.9297	−	252.435i	0.355431	−	1.21363i
$209$	82.5694	+	68.5647i	0.395069	+	0.328061i
$210$	−168.621	−	182.132i	−0.802958	−	0.867294i
$211$	−34.3621	+	124.402i	−0.162854	+	0.589581i	0.836293	+	0.548282i	$0.184718\pi$
$211$	−34.3621	+	124.402i	−0.162854	+	0.589581i	−0.999147	+	0.0412985i	$0.986851\pi$
$212$	−253.513	−	55.5202i	−1.19582	−	0.261888i
$213$	10.6339	+	230.008i	0.0499245	+	1.07985i
$214$	55.7317	−	311.395i	0.260429	−	1.45511i
$215$	−26.8398	+	19.3114i	−0.124836	+	0.0898207i
$216$	437.120	+	398.487i	2.02370	+	1.84485i
$217$	−439.817	+	117.849i	−2.02681	+	0.543081i
$218$	−138.234	−	631.196i	−0.634101	−	2.89539i
$219$	10.7595	−	199.427i	0.0491301	−	0.910625i
$220$	524.649	−	127.667i	2.38477	−	0.580306i
$221$	11.5783	+	136.371i	0.0523905	+	0.617064i
$222$	−124.767	+	245.803i	−0.562012	+	1.10722i
$223$	−109.486	−	12.7021i	−0.490967	−	0.0569600i	−0.133815	−	0.991006i	$-0.542723\pi$
$223$	−109.486	−	12.7021i	−0.490967	−	0.0569600i	−0.357152	+	0.934046i	$0.616252\pi$
$224$	−448.270	+	333.129i	−2.00120	+	1.48718i
$225$	−8.21118	+	66.3118i	−0.0364941	+	0.294719i
$226$	79.5308	−	604.097i	0.351906	−	2.67299i
$227$	75.3938	+	90.7933i	0.332131	+	0.399970i	0.908952	−	0.416900i	$-0.136884\pi$
$227$	75.3938	+	90.7933i	0.332131	+	0.399970i	−0.576821	+	0.816870i	$0.695707\pi$
$228$	47.9752	+	110.958i	0.210418	+	0.486658i
$229$	−81.1627	−	209.505i	−0.354422	−	0.914869i	−0.989774	−	0.142646i	$-0.954439\pi$
$229$	−81.1627	−	209.505i	−0.354422	−	0.914869i	0.635351	−	0.772223i	$-0.280855\pi$
$230$	−43.3363	+	61.2194i	−0.188419	+	0.266171i
$231$	−43.8362	−	405.068i	−0.189767	−	1.75354i
$232$	603.639	+	958.344i	2.60189	+	4.13079i
$233$	−86.2492	+	77.4190i	−0.370168	+	0.332270i	−0.832080	−	0.554656i	$-0.812850\pi$
$233$	−86.2492	+	77.4190i	−0.370168	+	0.332270i	0.461912	+	0.886926i	$0.347164\pi$
$234$	−31.2123	−	106.575i	−0.133386	−	0.455450i
$235$	−88.9108	+	205.634i	−0.378344	+	0.875040i
$236$	−623.205	−	24.0052i	−2.64070	−	0.101717i
$237$	−6.87230	+	14.0720i	−0.0289971	+	0.0593754i
$238$	385.286	−	611.684i	1.61885	−	2.57010i
$239$	14.6783	+	85.8185i	0.0614155	+	0.359073i	0.999905	+	0.0137663i	$0.00438207\pi$
$239$	14.6783	+	85.8185i	0.0614155	+	0.359073i	−0.938490	+	0.345307i	$0.887775\pi$
$240$	240.871	+	56.6524i	1.00363	+	0.236052i
$241$	348.678	+	119.859i	1.44680	+	0.497341i	0.932782	−	0.360440i	$-0.117374\pi$
$241$	348.678	+	119.859i	1.44680	+	0.497341i	0.514014	+	0.857782i	$0.328158\pi$
$242$	747.236	+	316.278i	3.08775	+	1.30693i
$243$	203.723	+	34.8446i	0.838368	+	0.143394i
$244$	486.500	+	436.692i	1.99385	+	1.78972i
$245$	70.9335	−	148.128i	0.289525	−	0.604603i
$246$	529.155	+	273.737i	2.15104	+	1.11275i
$247$	5.67244	−	40.6644i	0.0229653	−	0.164633i
$248$	604.295	−	694.442i	2.43667	−	2.80017i
$249$	21.0286	−	103.631i	0.0844522	−	0.416189i
$250$	171.867	+	424.133i	0.687470	+	1.69653i
$251$	−143.612	−	64.7367i	−0.572158	−	0.257915i	0.104116	−	0.994565i	$-0.466799\pi$
$251$	−143.612	−	64.7367i	−0.572158	−	0.257915i	−0.676274	+	0.736650i	$0.736407\pi$
$252$	−146.437	+	386.812i	−0.581097	+	1.53497i
$253$	−117.039	+	38.2277i	−0.462605	+	0.151097i
$254$	−158.034	+	242.533i	−0.622183	+	0.954855i
$255$	−127.513	+	17.7874i	−0.500052	+	0.0697543i
$256$	−97.9411	+	277.937i	−0.382583	+	1.08569i
$257$	−97.3401	+	45.6950i	−0.378755	+	0.177801i	−0.604917	−	0.796288i	$-0.706794\pi$
$257$	−97.3401	+	45.6950i	−0.378755	+	0.177801i	0.226162	+	0.974090i	$0.427382\pi$
$258$	−76.7000	−	40.4293i	−0.297287	−	0.156703i
$259$	−347.211	−	32.1738i	−1.34058	−	0.124223i
$260$	−147.183	−	144.934i	−0.566090	−	0.557439i
$261$	213.446	+	100.199i	0.817801	+	0.383905i
$262$	−136.280	−	180.464i	−0.520152	−	0.688793i
$263$	−343.827	−	7.94379i	−1.30733	−	0.0302045i	−0.636186	−	0.771536i	$-0.719489\pi$
$263$	−343.827	−	7.94379i	−1.30733	−	0.0302045i	−0.671139	+	0.741331i	$0.734195\pi$
$264$	531.093	+	629.643i	2.01172	+	2.38501i
$265$	−53.9490	+	62.9695i	−0.203581	+	0.237621i
$266$	−153.351	+	153.351i	−0.576509	+	0.576509i
$267$	1.06308	−	0.0820193i	0.00398158	−	0.000307189i
$268$	−753.859	−	922.194i	−2.81291	−	3.44102i
$269$	−60.9650	+	60.0333i	−0.226636	+	0.223172i	−0.806029	−	0.591876i	$-0.798388\pi$
$269$	−60.9650	+	60.0333i	−0.226636	+	0.223172i	0.579393	+	0.815048i	$0.303289\pi$
$270$	306.382	−	107.965i	1.13475	−	0.399869i
$271$	−70.0482	−	135.409i	−0.258480	−	0.499663i	0.723093	−	0.690751i	$-0.242720\pi$
$271$	−70.0482	−	135.409i	−0.258480	−	0.499663i	−0.981573	+	0.191088i	$0.938798\pi$
$272$	22.1940	+	720.357i	0.0815955	+	2.64837i
$273$	−122.923	+	95.8346i	−0.450266	+	0.351042i
$274$	278.850	+	191.017i	1.01770	+	0.697142i
$275$	−72.7342	+	280.056i	−0.264488	+	1.01838i
$276$	−137.038	−	21.2723i	−0.496515	−	0.0770734i
$277$	−10.9311	+	44.9214i	−0.0394625	+	0.162171i	−0.987988	−	0.154529i	$-0.950614\pi$
$277$	−10.9311	+	44.9214i	−0.0394625	+	0.162171i	0.948526	+	0.316700i	$0.102575\pi$
$278$	−132.069	+	438.411i	−0.475070	+	1.57702i
$279$	27.9381	−	189.600i	0.100137	−	0.679571i
$280$	92.5351	+	627.985i	0.330482	+	2.24280i
$281$	−444.175	+	133.806i	−1.58070	+	0.476178i	−0.953174	−	0.302422i	$-0.902205\pi$
$281$	−444.175	+	133.806i	−1.58070	+	0.476178i	−0.627521	+	0.778600i	$0.715930\pi$
$282$	−586.602	+	31.6484i	−2.08015	+	0.112228i
$283$	−333.673	+	92.1668i	−1.17906	+	0.325678i	−0.800174	−	0.599767i	$-0.795260\pi$
$283$	−333.673	+	92.1668i	−1.17906	+	0.325678i	−0.378881	+	0.925445i	$0.623691\pi$
$284$	532.844	−	860.573i	1.87621	−	3.03018i
$285$	38.4856	+	3.26754i	0.135037	+	0.0114650i
$286$	−73.7650	−	475.202i	−0.257920	−	1.66155i
$287$	−75.3124	+	749.859i	−0.262412	+	2.61275i
$288$	−53.8194	−	228.826i	−0.186873	−	0.794536i
$289$	−33.5171	−	79.1872i	−0.115976	−	0.274004i
$290$	620.534	−	43.0719i	2.13977	−	0.148524i
$291$	34.9449	+	51.8653i	0.120085	+	0.178231i
$292$	−534.456	+	696.517i	−1.83033	+	2.38533i
$293$	96.6590	−	243.913i	0.329894	−	0.832469i	−0.666330	−	0.745657i	$-0.732136\pi$
$293$	96.6590	−	243.913i	0.329894	−	0.832469i	0.996225	−	0.0868121i	$-0.0276680\pi$
$294$	430.605	−	6.63183i	1.46464	−	0.0225572i
$295$	−100.960	+	171.799i	−0.342236	+	0.582368i
$296$	618.502	−	338.290i	2.08954	−	1.14287i
$297$	509.383	+	157.738i	1.71509	+	0.531103i
$298$	68.6926	−	11.2054i	0.230512	−	0.0376020i
$299$	36.0042	+	30.3689i	0.120415	+	0.101568i
$300$	−215.824	+	244.198i	−0.719415	+	0.813992i
$301$	11.8003	−	109.041i	0.0392038	−	0.362262i
$302$	473.393	−	231.190i	1.56753	−	0.765530i
$303$	−63.0500	−	142.795i	−0.208086	−	0.471269i
$304$	41.3633	−	212.214i	0.136063	−	0.698073i
$305$	196.463	−	70.9362i	0.644142	−	0.232578i
$306$	171.955	+	251.023i	0.561944	+	0.820337i
$307$	−2.08986	+	6.56936i	−0.00680737	+	0.0213986i	−0.956286	−	0.292434i	$-0.905535\pi$
$307$	−2.08986	+	6.56936i	−0.00680737	+	0.0213986i	0.949478	+	0.313833i	$0.101613\pi$
$308$	−847.333	+	1577.93i	−2.75108	+	5.12316i
$309$	150.460	+	9.28006i	0.486926	+	0.0300325i
$310$	−178.997	−	472.820i	−0.577408	−	1.52522i
$311$	−82.8497	−	102.958i	−0.266398	−	0.331053i	0.628094	−	0.778137i	$-0.283835\pi$
$311$	−82.8497	−	102.958i	−0.266398	−	0.331053i	−0.894492	+	0.447084i	$0.852463\pi$
$312$	97.8382	−	299.545i	0.313584	−	0.960079i
$313$	−134.065	+	166.603i	−0.428322	+	0.532277i	−0.946375	−	0.323072i	$-0.895285\pi$
$313$	−134.065	+	166.603i	−0.428322	+	0.532277i	0.518053	+	0.855349i	$0.326657\pi$
$314$	−102.728	−	157.655i	−0.327159	−	0.502086i
$315$	86.7494	+	99.6904i	0.275395	+	0.316477i
$316$	59.8823	−	33.9610i	0.189501	−	0.107471i
$317$	19.1897	+	34.4521i	0.0605353	+	0.108682i	0.902198	−	0.431321i	$-0.141952\pi$
$317$	19.1897	+	34.4521i	0.0605353	+	0.108682i	−0.841663	+	0.540003i	$0.818423\pi$
$318$	−210.863	−	53.0342i	−0.663092	−	0.166774i
$319$	859.754	+	550.831i	2.69515	+	1.72674i
$320$	−111.290	−	122.079i	−0.347780	−	0.381496i
$321$	38.5727	−	182.854i	0.120164	−	0.569639i
$322$	−55.0951	−	242.617i	−0.171103	−	0.753470i
$323$	19.8189	+	110.736i	0.0613588	+	0.342835i
$324$	167.546	+	162.464i	0.517118	+	0.501431i
$325$	105.738	−	32.7432i	0.325347	−	0.100748i
$326$	672.052	−	334.642i	2.06151	−	1.02651i
$327$	−70.1398	−	375.215i	−0.214495	−	1.14745i
$328$	−720.821	−	1342.34i	−2.19763	−	4.09250i
$329$	−310.594	−	675.097i	−0.944055	−	2.05197i
$330$	442.642	−	93.3743i	1.34134	−	0.282953i
$331$	−125.365	+	174.237i	−0.378745	+	0.526395i	−0.957242	−	0.289290i	$-0.906581\pi$
$331$	−125.365	+	174.237i	−0.378745	+	0.526395i	0.578496	+	0.815685i	$0.303640\pi$
$332$	−333.713	+	323.590i	−1.00516	+	0.974669i
$333$	70.4276	−	128.764i	0.211494	−	0.386679i
$334$	−179.598	+	107.412i	−0.537718	+	0.321593i
$335$	−373.542	+	72.8081i	−1.11505	+	0.217338i
$336$	−673.545	+	469.049i	−2.00460	+	1.39598i
$337$	35.5272	−	460.481i	0.105422	−	1.36641i	−0.673451	−	0.739232i	$-0.735189\pi$
$337$	35.5272	−	460.481i	0.105422	−	1.36641i	0.778873	−	0.627181i	$-0.215791\pi$
$338$	332.963	−	285.265i	0.985097	−	0.843979i
$339$	57.9501	−	355.252i	0.170944	−	1.04794i
$340$	506.633	+	252.273i	1.49010	+	0.741980i
$341$	227.114	−	798.221i	0.666022	−	2.34082i
$342$	−33.6287	−	84.8601i	−0.0983297	−	0.248129i
$343$	18.4043	+	44.4318i	0.0536568	+	0.129539i
$344$	103.395	+	196.156i	0.300568	+	0.570220i
$345$	−26.7024	+	35.3596i	−0.0773982	+	0.102492i
$346$	−48.8522	+	61.6751i	−0.141191	+	0.178252i
$347$	132.541	−	80.6610i	0.381964	−	0.232452i	−0.315729	−	0.948849i	$-0.602249\pi$
$347$	132.541	−	80.6610i	0.381964	−	0.232452i	0.697693	+	0.716397i	$0.254210\pi$
$348$	582.691	+	991.539i	1.67440	+	2.84925i
$349$	−452.619	−	270.698i	−1.29690	−	0.775638i	−0.312223	−	0.950009i	$-0.601073\pi$
$349$	−452.619	−	270.698i	−1.29690	−	0.775638i	−0.984680	+	0.174371i	$0.944211\pi$
$350$	−549.929	−	198.561i	−1.57123	−	0.567317i
$351$	−51.2794	−	197.446i	−0.146095	−	0.562525i
$352$	−101.725	−	1012.84i	−0.288992	−	2.87739i
$353$	−314.431	+	108.087i	−0.890738	+	0.306194i	−0.732144	−	0.681150i	$-0.761480\pi$
$353$	−314.431	+	108.087i	−0.890738	+	0.306194i	−0.158594	+	0.987344i	$0.550696\pi$
$354$	−521.262	−	36.1813i	−1.47249	−	0.102207i
$355$	−161.700	−	280.073i	−0.455494	−	0.788939i
$356$	−4.05917	−	2.34356i	−0.0114022	−	0.00658304i
$357$	238.626	−	354.170i	0.668421	−	0.992073i
$358$	−131.529	−	392.430i	−0.367400	−	1.09617i
$359$	299.140	−	191.655i	0.833260	−	0.533857i	−0.0521655	−	0.998638i	$-0.516612\pi$
$359$	299.140	−	191.655i	0.833260	−	0.533857i	0.885425	+	0.464782i	$0.153867\pi$
$360$	−258.067	−	69.1489i	−0.716853	−	0.192080i
$361$	−15.1136	+	326.903i	−0.0418660	+	0.905547i
$362$	−735.611	−	167.047i	−2.03208	−	0.461457i
$363$	435.464	+	200.345i	1.19963	+	0.551916i
$364$	683.876	−	42.1800i	1.87878	−	0.115879i
$365$	115.276	+	255.729i	0.315826	+	0.700627i
$366$	396.135	+	378.244i	1.08234	+	1.03345i
$367$	−84.8915	+	114.233i	−0.231312	+	0.311261i	−0.903057	−	0.429521i	$-0.858682\pi$
$367$	−84.8915	+	114.233i	−0.231312	+	0.311261i	0.671745	+	0.740783i	$0.265545\pi$
$368$	180.704	+	169.902i	0.491042	+	0.461689i
$369$	−277.114	−	154.351i	−0.750986	−	0.418296i
$370$	−2.98117	−	387.158i	−0.00805721	−	1.04637i
$371$	−35.9006	−	272.692i	−0.0967670	−	0.735018i
$372$	635.039	−	685.921i	1.70709	−	1.84387i
$373$	−162.837	−	262.990i	−0.436560	−	0.705068i	0.555405	−	0.831580i	$-0.312563\pi$
$373$	−162.837	−	262.990i	−0.436560	−	0.705068i	−0.991965	+	0.126512i	$0.959622\pi$
$374$	596.370	+	1174.91i	1.59457	+	3.14148i
$375$	93.7661	+	253.563i	0.250043	+	0.676167i
$376$	1283.40	+	781.042i	3.41330	+	2.07724i
$377$	6.01527	−	390.572i	0.0159556	−	1.03600i
$378$	−412.350	+	995.501i	−1.09087	+	2.63360i
$379$	399.165	−	36.9881i	1.05321	−	0.0975939i	0.448294	−	0.893886i	$-0.352032\pi$
$379$	399.165	−	36.9881i	1.05321	−	0.0975939i	0.604912	+	0.796292i	$0.293208\pi$
$380$	−131.455	−	107.460i	−0.345935	−	0.282789i
$381$	−97.7263	+	140.333i	−0.256499	+	0.368328i
$382$	116.999	+	51.6603i	0.306281	+	0.135236i
$383$	−12.2887	−	319.029i	−0.0320853	−	0.832975i	−0.924369	−	0.381500i	$-0.875408\pi$
$383$	−12.2887	−	319.029i	−0.0320853	−	0.832975i	0.892284	−	0.451475i	$-0.149102\pi$
$384$	−16.7430	+	43.2188i	−0.0436017	+	0.112549i
$385$	316.094	+	477.034i	0.821024	+	1.23905i
$386$	−883.052	+	179.187i	−2.28770	+	0.464215i
$387$	40.1548	+	22.7730i	0.103759	+	0.0588448i
$388$	2.11684	−	274.910i	0.00545578	−	0.708530i
$389$	171.170	−	21.1954i	0.440025	−	0.0544869i	0.100182	−	0.994969i	$-0.468057\pi$
$389$	171.170	−	21.1954i	0.440025	−	0.0544869i	0.339843	+	0.940482i	$0.389626\pi$
$390$	−119.514	−	125.167i	−0.306447	−	0.320942i
$391$	−119.607	−	48.4675i	−0.305902	−	0.123958i
$392$	−918.110	−	608.362i	−2.34212	−	1.55194i
$393$	−77.1857	−	109.037i	−0.196401	−	0.277448i
$394$	−703.538	+	621.794i	−1.78563	+	1.57816i
$395$	−0.508054	−	21.9898i	−0.00128621	−	0.0556704i
$396$	−468.068	−	590.928i	−1.18199	−	1.49224i
$397$	233.675	+	86.4119i	0.588603	+	0.217662i	0.623624	−	0.781724i	$-0.285660\pi$
$397$	233.675	+	86.4119i	0.588603	+	0.217662i	−0.0350209	+	0.999387i	$0.511150\pi$
$398$	210.059	−	24.3702i	0.527786	−	0.0612317i
$399$	−93.3387	+	87.7591i	−0.233932	+	0.219948i
$400$	565.283	−	142.174i	1.41321	−	0.355436i
$401$	−596.565	−	199.948i	−1.48769	−	0.498624i	−0.546781	−	0.837276i	$-0.684147\pi$
$401$	−596.565	−	199.948i	−1.48769	−	0.498624i	−0.940912	+	0.338651i	$0.890029\pi$
$402$	−607.500	−	791.709i	−1.51119	−	1.96943i
$403$	−305.364	+	86.8836i	−0.757728	+	0.215592i
$404$	−126.085	+	674.498i	−0.312093	+	1.66955i
$405$	71.0581	−	22.6052i	0.175452	−	0.0558153i
$406$	−1268.61	+	1627.18i	−3.12464	+	4.00784i
$407$	375.148	−	513.017i	0.921740	−	1.26048i
$408$			863.393i			2.11616i
$409$	−326.946	+	245.738i	−0.799380	+	0.600826i
$409$	−326.946	+	245.738i	−0.799380	+	0.600826i
$410$	−836.777			−2.04092
$411$	161.177	+	117.862i	0.392158	+	0.286769i
$412$	−522.608	−	407.443i	−1.26847	−	0.988939i
$413$	−200.376	−	629.869i	−0.485171	−	1.52511i
$414$	102.934	+	19.2417i	0.248632	+	0.0464774i
$415$	40.6445	+	142.851i	0.0979386	+	0.344219i
$416$	−308.946	+	237.063i	−0.742658	+	0.569862i
$417$	−85.9582	+	256.464i	−0.206135	+	0.615023i
$418$	−96.4134	−	383.338i	−0.230654	−	0.917077i
$419$	377.304	+	401.292i	0.900487	+	0.957738i	0.999302	−	0.0373676i	$-0.0118972\pi$
$419$	377.304	+	401.292i	0.900487	+	0.957738i	−0.0988146	+	0.995106i	$0.531505\pi$
$420$	74.2806	+	640.261i	0.176859	+	1.52443i
$421$	−108.390	+	293.110i	−0.257459	+	0.696223i	0.742201	+	0.670177i	$0.233782\pi$
$421$	−108.390	+	293.110i	−0.257459	+	0.696223i	−0.999661	+	0.0260459i	$0.991708\pi$
$422$	372.599	−	295.131i	0.882935	−	0.699363i
$423$	312.693	−	7.22447i	0.739226	−	0.0170791i
$424$	368.246	+	416.657i	0.868504	+	0.982681i
$425$	−247.539	+	175.229i	−0.582445	+	0.412304i
$426$	468.415	−	706.909i	1.09957	−	1.65941i
$427$	−260.205	+	642.131i	−0.609379	+	1.50382i
$428$	−594.153	+	567.319i	−1.38821	+	1.32551i
$429$	−34.9109	−	281.933i	−0.0813773	−	0.657187i
$430$	121.774	+	0.937679i	0.283196	+	0.00218065i
$431$	356.190	−	628.059i	0.826428	−	1.45721i	−0.0619394	−	0.998080i	$-0.519729\pi$
$431$	356.190	−	628.059i	0.826428	−	1.45721i	0.888367	−	0.459134i	$-0.151840\pi$
$432$	−213.625	−	1052.77i	−0.494503	−	2.43696i
$433$	−254.703	+	168.772i	−0.588228	+	0.389774i	−0.810956	−	0.585107i	$-0.801053\pi$
$433$	−254.703	+	168.772i	−0.588228	+	0.389774i	0.222729	+	0.974880i	$0.428504\pi$
$434$	1563.73	+	605.792i	3.60306	+	1.39583i
$435$	367.188	−	14.1437i	0.844111	−	0.0325142i
$436$	−677.775	+	1535.01i	−1.55453	+	3.52067i
$437$	31.7711	+	22.1251i	0.0727028	+	0.0506295i
$438$	−465.532	+	569.485i	−1.06286	+	1.30019i
$439$	71.8661	+	775.558i	0.163704	+	1.76665i	0.541445	+	0.840736i	$0.317878\pi$
$439$	71.8661	+	775.558i	0.163704	+	1.76665i	−0.377740	+	0.925912i	$0.623299\pi$
$440$	−1068.88	−	442.743i	−2.42926	−	1.00623i
$441$	−229.265	−	3.53096i	−0.519876	−	0.00800670i
$442$	262.044	−	430.588i	0.592860	−	0.974181i
$443$	728.912	−	269.548i	1.64540	−	0.608460i	0.656141	−	0.754638i	$-0.272188\pi$
$443$	728.912	−	269.548i	1.64540	−	0.608460i	0.989258	+	0.146179i	$0.0466975\pi$
$444$	638.322	−	324.004i	1.43766	−	0.729739i
$445$	−1.27327	+	0.788374i	−0.00286128	+	0.00177163i
$446$	297.876	+	275.779i	0.667883	+	0.618339i
$447$	40.7646	−	5.36676i	0.0911959	−	0.0120062i
$448$	547.929	−	4.21913i	1.22306	−	0.00941770i
$449$	119.936	−	215.326i	0.267118	−	0.479568i	−0.706512	−	0.707701i	$-0.749733\pi$
$449$	119.936	−	215.326i	0.267118	−	0.479568i	0.973630	+	0.228133i	$0.0732620\pi$
$450$	168.570	−	179.287i	0.374600	−	0.398417i
$451$	−1102.49	−	819.309i	−2.44455	−	1.81665i
$452$	−1092.72	+	1144.40i	−2.41751	+	2.53186i
$453$	283.728	−	127.898i	0.626332	−	0.282335i
$454$	−26.7572	−	433.822i	−0.0589366	−	0.955555i
$455$	91.4999	−	198.881i	0.201099	−	0.437102i
$456$	57.3586	−	252.585i	0.125786	−	0.553914i
$457$	−402.593	−	18.6130i	−0.880948	−	0.0407287i	−0.399023	−	0.916941i	$-0.630650\pi$
$457$	−402.593	−	18.6130i	−0.880948	−	0.0407287i	−0.481925	+	0.876212i	$0.660062\pi$
$458$	−214.167	+	799.282i	−0.467613	+	1.74516i
$459$	301.523	+	470.626i	0.656912	+	1.02533i
$460$	184.683	−	61.8997i	0.401486	−	0.134564i
$461$	395.396	+	266.403i	0.857692	+	0.577880i	0.907108	−	0.420898i	$-0.138285\pi$
$461$	395.396	+	266.403i	0.857692	+	0.577880i	−0.0494158	+	0.998778i	$0.515736\pi$
$462$	−750.281	+	1299.52i	−1.62398	+	2.81282i
$463$	−463.989	+	267.884i	−1.00214	+	0.578584i	−0.908880	−	0.417058i	$-0.863061\pi$
$463$	−463.989	+	267.884i	−1.00214	+	0.578584i	−0.0932571	+	0.995642i	$0.529728\pi$
$464$	142.432	−	2052.01i	0.306966	−	4.42245i
$465$	−97.0899	−	282.441i	−0.208796	−	0.607399i
$466$	424.716	−	42.6565i	0.911407	−	0.0915376i
$467$	−283.666	+	73.6718i	−0.607422	+	0.157755i	−0.542389	−	0.840128i	$-0.682480\pi$
$467$	−283.666	+	73.6718i	−0.607422	+	0.157755i	−0.0650331	+	0.997883i	$0.520715\pi$
$468$	−97.9387	+	271.249i	−0.209271	+	0.579591i
$469$	647.939	−	1083.38i	1.38153	−	2.30999i
$470$	711.363	−	418.042i	1.51354	−	0.889450i
$471$	−57.7893	−	94.9589i	−0.122695	−	0.201611i
$472$	1047.51	+	829.719i	2.21930	+	1.75788i
$473$	159.525	+	120.468i	0.337262	+	0.254689i
$474$	51.0225	−	26.8944i	0.107642	−	0.0567393i
$475$	84.0585	−	34.8182i	0.176965	−	0.0733014i
$476$	−1745.27	+	691.624i	−3.66654	+	1.45299i
$477$	111.346	+	31.6807i	0.233430	+	0.0664166i
$478$	142.929	−	287.040i	0.299014	−	0.600501i
$479$	−550.245	−	89.7581i	−1.14874	−	0.187386i	−0.443444	−	0.896302i	$-0.646244\pi$
$479$	−550.245	−	89.7581i	−1.14874	−	0.187386i	−0.705293	+	0.708916i	$0.749185\pi$
$480$	−238.342	−	278.194i	−0.496546	−	0.579571i
$481$	−242.413	−	18.7027i	−0.503976	−	0.0388830i
$482$	−776.015	−	1114.34i	−1.60999	−	2.31191i
$483$	−28.1181	−	144.260i	−0.0582156	−	0.298675i
$484$	−1081.55	−	1808.40i	−2.23461	−	3.73637i
$485$	−77.0648	−	42.1506i	−0.158896	−	0.0869085i
$486$	−529.898	−	546.476i	−1.09033	−	1.12444i
$487$	−28.0607	−	20.1899i	−0.0576194	−	0.0414576i	0.554864	−	0.831941i	$-0.312770\pi$
$487$	−28.0607	−	20.1899i	−0.0576194	−	0.0414576i	−0.612483	+	0.790484i	$0.709829\pi$
$488$	−289.121	−	1370.58i	−0.592462	−	2.80857i
$489$	402.912	−	185.369i	0.823951	−	0.379078i
$490$	−532.901	+	286.162i	−1.08755	+	0.584004i
$491$	−383.984	+	71.7790i	−0.782044	+	0.146189i	−0.559608	−	0.828758i	$-0.689048\pi$
$491$	−383.984	+	71.7790i	−0.782044	+	0.146189i	−0.222437	+	0.974947i	$0.571401\pi$
$492$	−689.616	−	1384.94i	−1.40166	−	2.81491i
$493$	316.588	+	1022.36i	0.642167	+	2.07375i
$494$	−105.266	+	108.559i	−0.213090	+	0.219756i
$495$	−237.093	+	42.4337i	−0.478976	+	0.0857246i
$496$	−1630.33	+	370.226i	−3.28695	+	0.746422i
$497$	1049.62	+	221.416i	2.11192	+	0.445504i
$498$	−287.805	+	262.369i	−0.577923	+	0.526846i
$499$	−137.726	+	214.967i	−0.276004	+	0.430795i	−0.951994	−	0.306115i	$-0.900971\pi$
$499$	−137.726	+	214.967i	−0.276004	+	0.430795i	0.675991	+	0.736910i	$0.263716\pi$
$500$	289.871	−	1152.52i	0.579741	−	2.30504i
$501$	−108.001	+	60.1559i	−0.215570	+	0.120072i
$502$	286.208	+	504.661i	0.570136	+	1.00530i
$503$	0.490145	−	0.426519i	0.000974444	−	0.000847950i	−0.655959	−	0.754797i	$-0.727736\pi$
$503$	0.490145	−	0.426519i	0.000974444	−	0.000847950i	0.656933	+	0.753949i	$0.271853\pi$
$504$	742.492	−	483.807i	1.47320	−	0.959935i
$505$	170.807	+	137.448i	0.338231	+	0.272174i
$506$	431.050	+	140.791i	0.851878	+	0.278243i
$507$	201.793	−	162.382i	0.398014	−	0.320280i
$508$	703.046	−	266.154i	1.38395	−	0.523925i
$509$	−31.5469	+	511.478i	−0.0619782	+	1.00487i	0.831432	+	0.555627i	$0.187522\pi$
$509$	−31.5469	+	511.478i	−0.0619782	+	1.00487i	−0.893410	+	0.449242i	$0.851694\pi$
$510$	417.753	+	224.329i	0.819124	+	0.439860i
$511$	−886.670	−	282.070i	−1.73517	−	0.551996i
$512$	825.093	−	565.202i	1.61151	−	1.10391i
$513$	−56.9446	−	157.712i	−0.111003	−	0.307431i
$514$	388.721	+	75.7668i	0.756267	+	0.147406i
$515$	−193.688	+	85.5216i	−0.376093	+	0.166061i
$516$	98.8064	+	202.320i	0.191485	+	0.392092i
$517$	1346.57	+	145.725i	2.60458	+	0.281866i
$518$	962.279	+	850.472i	1.85768	+	1.64184i
$519$	−29.9676	+	35.5284i	−0.0577410	+	0.0684555i
$520$	71.2561	+	436.822i	0.137031	+	0.840042i
$521$	−42.7122	+	137.931i	−0.0819813	+	0.264742i	−0.987023	−	0.160581i	$-0.948663\pi$
$521$	−42.7122	+	137.931i	−0.0819813	+	0.264742i	0.905041	+	0.425324i	$0.139840\pi$
$522$	−416.724	−	761.905i	−0.798322	−	1.45959i
$523$	273.801	+	160.903i	0.523520	+	0.307653i	0.744497	−	0.667626i	$-0.232689\pi$
$523$	273.801	+	160.903i	0.523520	+	0.307653i	−0.220977	+	0.975279i	$0.570925\pi$
$524$	9.04341	+	587.189i	0.0172584	+	1.12059i
$525$	−321.103	−	127.248i	−0.611624	−	0.242377i
$526$	1004.89	+	771.080i	1.91044	+	1.46593i
$527$	721.410	−	486.059i	1.36890	−	0.922312i
$528$	−103.587	−	1492.38i	−0.196188	−	2.82647i
$529$	446.257	−	188.884i	0.843586	−	0.357059i
$530$	297.278	−	69.9191i	0.560902	−	0.131923i
$531$	276.809	+	27.8014i	0.521297	+	0.0523567i
$532$	556.525	−	86.3886i	1.04610	−	0.162385i
$533$	−44.4545	+	523.592i	−0.0834043	+	0.982349i
$534$	−3.33874	−	2.06726i	−0.00625233	−	0.00387128i
$535$	69.8845	+	253.004i	0.130625	+	0.472904i
$536$	137.493	+	2548.43i	0.256517	+	4.75453i
$537$	−70.5245	−	234.110i	−0.131331	−	0.435958i
$538$	311.752	−	45.9375i	0.579466	−	0.0853857i
$539$	−982.310	−	144.746i	−1.82247	−	0.268545i
$540$	−807.736	−	243.327i	−1.49581	−	0.450606i
$541$	312.935	+	76.1492i	0.578438	+	0.140756i	0.514941	−	0.857226i	$-0.327814\pi$
$541$	312.935	+	76.1492i	0.578438	+	0.140756i	0.0634973	+	0.997982i	$0.479775\pi$
$542$	−86.1268	+	554.838i	−0.158906	+	1.02369i
$543$	−431.315	−	112.018i	−0.794319	−	0.206295i
$544$	602.983	−	880.246i	1.10842	−	1.61810i
$545$	329.642	+	422.817i	0.604849	+	0.775811i
$546$	573.777	−	17.6779i	1.05087	−	0.0323770i
$547$	21.5260	−	11.1356i	0.0393529	−	0.0203576i	−0.439681	−	0.898154i	$-0.644909\pi$
$547$	21.5260	−	11.1356i	0.0393529	−	0.0203576i	0.479034	+	0.877796i	$0.340987\pi$
$548$	−291.724	−	827.853i	−0.532344	−	1.51068i
$549$	−204.611	−	207.786i	−0.372697	−	0.378481i
$550$	825.061	−	674.456i	1.50011	−	1.22628i
$551$	−24.6982	−	320.122i	−0.0448243	−	0.580984i
$552$	210.111	+	210.111i	0.380636	+	0.380636i
$553$	55.4061	+	47.4691i	0.100192	+	0.0858392i
$554$	130.154	−	109.783i	0.234936	−	0.198164i
$555$	5.28293	−	228.658i	0.00951879	−	0.411996i
$556$	948.873	−	716.555i	1.70661	−	1.28877i
$557$	−417.155	+	888.629i	−0.748931	+	1.59538i	0.0534482	+	0.998571i	$0.482979\pi$
$557$	−417.155	+	888.629i	−0.748931	+	1.59538i	−0.802380	+	0.596814i	$0.796433\pi$
$558$	−495.240	+	502.926i	−0.887528	+	0.901302i
$559$	7.05610	−	76.1474i	0.0126227	−	0.136221i
$560$	537.550	−	1019.81i	0.959911	−	1.82109i
$561$	330.763	+	704.596i	0.589595	+	1.25596i
$562$	1611.38	+	567.827i	2.86722	+	1.01037i
$563$	−79.2332	−	568.004i	−0.140734	−	1.00889i	−0.922687	−	0.385551i	$-0.874012\pi$
$563$	−79.2332	−	568.004i	−0.140734	−	1.00889i	0.781953	−	0.623338i	$-0.214224\pi$
$564$	1278.15	+	832.843i	2.26623	+	1.47667i
$565$	156.967	+	480.576i	0.277818	+	0.850577i
$566$	1192.34	+	451.388i	2.10661	+	0.797505i
$567$	−101.645	+	225.489i	−0.179268	+	0.397688i
$568$	−2009.99	+	814.492i	−3.53872	+	1.43396i
$569$	−399.234	−	81.0116i	−0.701641	−	0.142375i	−0.165134	−	0.986271i	$-0.552806\pi$
$569$	−399.234	−	81.0116i	−0.701641	−	0.142375i	−0.536507	+	0.843896i	$0.680257\pi$
$570$	−107.310	−	93.3800i	−0.188263	−	0.163825i
$571$	−396.019	−	55.2422i	−0.693553	−	0.0967465i	−0.217365	−	0.976090i	$-0.569746\pi$
$571$	−396.019	−	55.2422i	−0.693553	−	0.0967465i	−0.476187	+	0.879344i	$0.657982\pi$
$572$	−573.797	+	1109.20i	−1.00314	+	1.93915i
$573$	68.1444	+	32.6321i	0.118926	+	0.0569496i
$574$	1854.06	−	2065.53i	3.23006	−	3.59848i
$575$	−17.5970	+	102.883i	−0.0306034	+	0.178927i
$576$	−89.8957	+	212.387i	−0.156069	+	0.368727i
$577$	279.483	−	813.033i	0.484373	−	1.40907i	−0.388648	−	0.921386i	$-0.627058\pi$
$577$	279.483	−	813.033i	0.484373	−	1.40907i	0.873021	−	0.487683i	$-0.162158\pi$
$578$	−72.5068	+	308.280i	−0.125444	+	0.533356i
$579$	−524.672	+	89.7393i	−0.906170	+	0.154990i
$580$	−1366.79	−	860.911i	−2.35654	−	1.48433i
$581$	−442.674	−	216.188i	−0.761918	−	0.372096i
$582$	8.86547	−	230.159i	0.0152328	−	0.395462i
$583$	460.137	+	198.951i	0.789256	+	0.341253i
$584$	1805.29	−	528.710i	3.09126	−	0.905325i
$585$	61.5500	+	68.5703i	0.105214	+	0.117214i
$586$	−817.615	+	514.997i	−1.39525	+	0.878834i
$587$	422.786	−	45.7536i	0.720249	−	0.0779448i	0.259840	−	0.965652i	$-0.416330\pi$
$587$	422.786	−	45.7536i	0.720249	−	0.0779448i	0.460409	+	0.887707i	$0.347703\pi$
$588$	−912.805	−	646.161i	−1.55239	−	1.09891i
$589$	−243.338	+	94.2698i	−0.413138	+	0.160051i
$590$	673.626	−	291.258i	1.14174	−	0.493657i
$591$	−426.727	+	354.350i	−0.722043	+	0.599577i
$592$	−1269.36	−	167.114i	−2.14419	−	0.282288i
$593$	771.554	+	95.5391i	1.30110	+	0.161112i	0.743354	−	0.668898i	$-0.233234\pi$
$593$	771.554	+	95.5391i	1.30110	+	0.161112i	0.557749	+	0.830009i	$0.311665\pi$
$594$	−1171.43	−	1576.31i	−1.97210	−	2.65373i
$595$	−69.1252	+	595.824i	−0.116177	+	1.00138i
$596$	−161.171	−	81.8081i	−0.270420	−	0.137262i
$597$	124.476	−	10.5684i	0.208503	−	0.0177025i
$598$	−41.0161	−	168.555i	−0.0685887	−	0.281865i
$599$	700.381	+	37.7870i	1.16925	+	0.0630835i	0.628300	−	0.777971i	$-0.283751\pi$
$599$	700.381	+	37.7870i	1.16925	+	0.0630835i	0.540950	+	0.841055i	$0.318065\pi$
$600$	682.130	−	149.389i	1.13688	−	0.248981i
$601$	170.834	+	637.560i	0.284249	+	1.06083i	0.949386	+	0.314111i	$0.101706\pi$
$601$	170.834	+	637.560i	0.284249	+	1.06083i	−0.665137	+	0.746721i	$0.731627\pi$
$602$	−272.132	+	298.514i	−0.452046	+	0.495871i
$603$	310.314	+	431.287i	0.514617	+	0.715235i
$604$	−1346.71	−	241.028i	−2.22966	−	0.399053i
$605$	−672.535	+	31.0932i	−1.11163	+	0.0513937i
$606$	−122.988	+	561.582i	−0.202951	+	0.926702i
$607$	11.1711	+	3.08568i	0.0184038	+	0.00508350i	0.275439	−	0.961319i	$-0.411177\pi$
$607$	11.1711	+	3.08568i	0.0184038	+	0.00508350i	−0.257035	+	0.966402i	$0.582746\pi$
$608$	−234.880	+	217.456i	−0.386316	+	0.357659i
$609$	−778.671	+	937.718i	−1.27861	+	1.53977i
$610$	−738.278	−	216.217i	−1.21029	−	0.354453i
$611$	−223.787	−	467.326i	−0.366264	−	0.764855i
$612$	24.3329	−	789.782i	0.0397597	−	1.29049i
$613$	439.523	+	601.049i	0.717003	+	0.980505i	0.999773	+	0.0213169i	$0.00678589\pi$
$613$	439.523	+	601.049i	0.717003	+	0.980505i	−0.282770	+	0.959188i	$0.591253\pi$
$614$	20.4945	−	14.9868i	0.0333786	−	0.0244084i
$615$	−494.089	−	15.2227i	−0.803396	−	0.0247524i
$616$	3461.21	−	1657.46i	5.61884	−	2.69068i
$617$	56.1377	−	191.684i	0.0909849	−	0.310670i	−0.901543	−	0.432690i	$-0.857565\pi$
$617$	56.1377	−	191.684i	0.0909849	−	0.310670i	0.992528	+	0.122020i	$0.0389371\pi$
$618$	−427.128	−	354.682i	−0.691145	−	0.573920i
$619$	−443.331	−	478.853i	−0.716205	−	0.773591i	0.265477	−	0.964117i	$-0.414471\pi$
$619$	−443.331	−	478.853i	−0.716205	−	0.773591i	−0.981682	+	0.190527i	$0.938980\pi$
$620$	−349.558	+	1265.51i	−0.563802	+	2.04114i
$621$	187.906	+	41.1521i	0.302586	+	0.0662674i
$622$	22.4781	+	486.194i	0.0361385	+	0.781663i
$623$	0.875148	−	4.88979i	0.00140473	−	0.00784878i
$624$	−464.543	+	334.242i	−0.744459	+	0.535644i
$625$	8.74540	+	7.97249i	0.0139926	+	0.0127560i
$626$	760.748	−	203.842i	1.21525	−	0.325626i
$627$	−49.9552	−	228.102i	−0.0796734	−	0.363800i
$628$	−26.3258	+	487.947i	−0.0419200	+	0.776985i
$629$	647.274	−	157.507i	1.02905	−	0.250408i
$630$	−41.1744	−	484.959i	−0.0653562	−	0.769776i
$631$	−71.4004	+	140.666i	−0.113154	+	0.222926i	−0.941288	−	0.337605i	$-0.890383\pi$
$631$	−71.4004	+	140.666i	−0.113154	+	0.222926i	0.828134	+	0.560531i	$0.189403\pi$
$632$	−146.522	−	16.9989i	−0.231838	−	0.0268970i
$633$	225.376	−	167.487i	0.356045	−	0.264592i
$634$	17.8484	−	144.140i	0.0281521	−	0.227350i
$635$	31.3508	−	238.133i	0.0493713	−	0.375012i
$636$	360.719	+	434.397i	0.567168	+	0.683014i
$637$	150.748	+	348.652i	0.236653	+	0.547335i
$638$	−1358.48	−	3506.63i	−2.12927	−	5.49629i
$639$	−260.868	+	368.518i	−0.408244	+	0.576710i
$640$	−7.00401	−	64.7206i	−0.0109438	−	0.101126i
$641$	−134.933	−	214.222i	−0.210504	−	0.334199i	0.724222	−	0.689567i	$-0.242199\pi$
$641$	−134.933	−	214.222i	−0.210504	−	0.334199i	−0.934727	+	0.355367i	$0.884356\pi$
$642$	−512.190	+	459.752i	−0.797804	+	0.716124i
$643$	−231.617	−	790.862i	−0.360213	−	1.22996i	−0.916860	−	0.399208i	$-0.869285\pi$
$643$	−231.617	−	790.862i	−0.360213	−	1.22996i	0.556647	−	0.830749i	$-0.312087\pi$
$644$	−256.411	+	593.031i	−0.398153	+	0.920855i
$645$	71.8866	+	2.76900i	0.111452	+	0.00429302i
$646$	181.815	−	372.292i	0.281448	−	0.576303i
$647$	−536.993	+	852.537i	−0.829974	+	1.31768i	0.115939	+	0.993256i	$0.463012\pi$
$647$	−536.993	+	852.537i	−0.829974	+	1.31768i	−0.945913	+	0.324421i	$0.894831\pi$
$648$	−84.3041	−	492.895i	−0.130099	−	0.760640i
$649$	1172.71	+	275.819i	1.80695	+	0.424990i
$650$	−385.529	−	132.527i	−0.593122	−	0.203888i
$651$	912.309	+	386.147i	1.40140	+	0.593160i
$652$	−1921.72	−	328.689i	−2.94743	−	0.504125i
$653$	45.5485	+	40.8852i	0.0697526	+	0.0626113i	0.702128	−	0.712051i	$-0.252234\pi$
$653$	45.5485	+	40.8852i	0.0697526	+	0.0626113i	−0.632375	+	0.774662i	$0.717920\pi$
$654$	−607.183	+	1267.96i	−0.928414	+	1.93877i
$655$	166.656	+	86.2126i	0.254436	+	0.131622i
$656$	−382.292	+	2740.56i	−0.582762	+	4.17769i
$657$	257.081	−	295.431i	0.391295	−	0.449667i
$658$	−544.269	+	2682.21i	−0.827156	+	4.07631i
$659$	−281.938	−	695.764i	−0.427827	−	1.05579i	−0.975677	−	0.219211i	$-0.929652\pi$
$659$	−281.938	−	695.764i	−0.427827	−	1.05579i	0.547850	−	0.836577i	$-0.315446\pi$
$660$	−1071.00	−	482.782i	−1.62273	−	0.731488i
$661$	136.373	−	360.229i	0.206313	−	0.544975i	−0.791493	−	0.611178i	$-0.790696\pi$
$661$	136.373	−	360.229i	0.206313	−	0.544975i	0.997806	+	0.0662022i	$0.0210882\pi$
$662$	751.480	−	245.451i	1.13517	−	0.370772i
$663$	162.562	−	249.481i	0.245191	−	0.376291i
$664$	986.438	−	137.602i	1.48560	−	0.207232i
$665$	59.8054	−	169.715i	0.0899329	−	0.255211i
$666$	−489.302	+	229.696i	−0.734688	+	0.344889i
$667$	325.840	+	171.753i	0.488515	+	0.257501i
$668$	541.123	+	50.1425i	0.810065	+	0.0750636i
$669$	170.869	+	168.257i	0.255409	+	0.251506i
$670$	1268.78	+	595.612i	1.89371	+	0.888974i
$671$	−761.011	−	1007.74i	−1.13414	−	1.50185i
$672$	1214.80	+	28.0668i	1.80774	+	0.0417661i
$673$	−267.083	−	316.644i	−0.396855	−	0.470496i	0.528865	−	0.848706i	$-0.322618\pi$
$673$	−267.083	−	316.644i	−0.396855	−	0.470496i	−0.925720	+	0.378211i	$0.876540\pi$
$674$	−1106.69	+	1291.73i	−1.64197	+	1.91651i
$675$	319.650	−	319.650i	0.473556	−	0.473556i
$676$	−1135.23	+	87.5860i	−1.67934	+	0.129565i
$677$	828.707	+	1013.76i	1.22409	+	1.49742i	0.809180	+	0.587560i	$0.199912\pi$
$677$	828.707	+	1013.76i	1.22409	+	1.49742i	0.414907	+	0.909864i	$0.363814\pi$
$678$	−944.583	+	930.147i	−1.39319	+	1.37190i
$679$	274.799	−	96.8356i	0.404712	−	0.142615i
$680$	−557.186	−	1077.09i	−0.819392	−	1.58395i
$681$	−7.90712	−	256.644i	−0.0116110	−	0.376864i
$682$	−2410.48	+	1879.29i	−3.53443	+	2.75556i
$683$	363.047	+	248.693i	0.531547	+	0.364118i	0.800782	−	0.598956i	$-0.204418\pi$
$683$	363.047	+	248.693i	0.531547	+	0.364118i	−0.269234	+	0.963075i	$0.586771\pi$
$684$	−59.5868	+	229.433i	−0.0871152	+	0.335429i
$685$	−277.130	−	43.0186i	−0.404570	−	0.0628008i
$686$	41.8789	−	172.101i	0.0610480	−	0.250877i
$687$	−140.999	+	468.053i	−0.205239	+	0.681300i
$688$	58.7052	−	398.400i	0.0853273	−	0.579070i
$689$	−27.9570	−	189.729i	−0.0405762	−	0.275368i
$690$	156.254	−	47.0708i	0.226455	−	0.0682185i
$691$	−344.232	+	18.5721i	−0.498166	+	0.0268771i	−0.301254	−	0.953544i	$-0.597405\pi$
$691$	−344.232	+	18.5721i	−0.498166	+	0.0268771i	−0.196912	+	0.980421i	$0.563091\pi$
$692$	196.944	−	54.3998i	0.284602	−	0.0786125i
$693$	420.586	−	679.270i	0.606907	−	0.980188i
$694$	−569.386	−	48.3425i	−0.820440	−	0.0696578i
$695$	−58.2748	−	375.413i	−0.0838487	−	0.540162i
$696$	246.256	−	2451.88i	0.353816	−	3.52282i
$697$	−329.632	−	1401.51i	−0.472930	−	2.01078i
$698$	757.105	+	1788.73i	1.08468	+	2.56265i
$699$	251.557	−	17.4608i	0.359881	−	0.0249797i
$700$	848.399	+	1259.20i	1.21200	+	1.79885i
$701$	−361.931	+	471.677i	−0.516306	+	0.672864i	−0.976640	−	0.214882i	$-0.931063\pi$
$701$	−361.931	+	471.677i	−0.516306	+	0.672864i	0.460333	+	0.887746i	$0.347730\pi$
$702$	−276.792	+	698.467i	−0.394290	+	0.994967i
$703$	−199.823	+	3.07751i	−0.284243	+	0.00437768i
$704$	−505.996	+	861.031i	−0.718744	+	1.22305i
$705$	427.641	−	233.899i	0.606583	−	0.331771i
$706$	1169.75	+	362.228i	1.65686	+	0.513071i
$707$	−717.739	+	117.080i	−1.01519	+	0.165602i
$708$	1037.21	+	874.872i	1.46499	+	1.23569i
$709$	−748.177	+	846.535i	−1.05526	+	1.19398i	−0.0748102	+	0.997198i	$0.523835\pi$
$709$	−748.177	+	846.535i	−1.05526	+	1.19398i	−0.980446	+	0.196787i	$0.936949\pi$
$710$	−128.149	+	1184.16i	−0.180491	+	1.66783i
$711$	−27.5938	+	13.4759i	−0.0388098	+	0.0189535i
$712$	4.05653	+	9.18716i	0.00569737	+	0.0129033i
$713$	57.2739	−	293.843i	0.0803281	−	0.412123i
$714$	−1479.36	+	534.148i	−2.07194	+	0.748106i
$715$	225.495	+	329.183i	0.315378	+	0.460395i
$716$	−325.832	+	1024.23i	−0.455072	+	1.43049i
$717$	89.6165	−	166.887i	0.124988	−	0.232758i
$718$	−1305.96	−	80.5490i	−1.81889	−	0.112185i
$719$	461.522	+	1219.11i	0.641894	+	1.69556i	0.715806	+	0.698299i	$0.246059\pi$
$719$	461.522	+	1219.11i	0.641894	+	1.69556i	−0.0739121	+	0.997265i	$0.523548\pi$
$720$	304.192	+	378.020i	0.422489	+	0.525028i
$721$	218.053	−	667.598i	0.302431	−	0.925933i
$722$	755.604	−	938.991i	1.04654	−	1.30054i
$723$	−437.939	−	672.098i	−0.605724	−	0.929597i
$724$	1285.93	+	1477.76i	1.77615	+	2.04111i
$725$	752.945	−	427.017i	1.03855	−	0.588989i
$726$	−859.049	−	1542.29i	−1.18326	−	2.12436i
$727$	714.995	+	179.828i	0.983486	+	0.247357i	0.701975	−	0.712201i	$-0.252302\pi$
$727$	714.995	+	179.828i	0.983486	+	0.247357i	0.281511	+	0.959558i	$0.409164\pi$
$728$	−1236.15	−	791.982i	−1.69801	−	1.08789i
$729$	−450.898	−	494.611i	−0.618515	−	0.678479i
$730$	213.239	−	1010.86i	0.292108	−	1.38474i
$731$	46.4002	+	204.328i	0.0634750	+	0.279519i
$732$	−250.583	−	1400.10i	−0.342326	−	1.91271i
$733$	133.109	+	129.071i	0.181594	+	0.176086i	0.781341	−	0.624104i	$-0.214536\pi$
$733$	133.109	+	129.071i	0.181594	+	0.176086i	−0.599747	+	0.800190i	$0.704732\pi$
$734$	500.711	−	155.052i	0.682168	−	0.211243i
$735$	−319.866	+	159.275i	−0.435192	+	0.216700i
$736$	−67.4734	−	360.951i	−0.0916759	−	0.490423i
$737$	1088.50	+	2027.04i	1.47693	+	2.75040i
$738$	488.277	+	1061.30i	0.661623	+	1.43808i
$739$	938.363	−	197.945i	1.26977	−	0.267856i	0.477832	−	0.878451i	$-0.341423\pi$
$739$	938.363	−	197.945i	1.26977	−	0.267856i	0.791943	+	0.610596i	$0.209070\pi$
$740$	−587.214	+	816.133i	−0.793532	+	1.10288i
$741$	−64.1312	+	62.1857i	−0.0865468	+	0.0839214i
$742$	−486.092	+	888.731i	−0.655110	+	1.19775i
$743$	−49.9571	+	29.8778i	−0.0672370	+	0.0402124i	−0.546502	−	0.837458i	$-0.684041\pi$
$743$	−49.9571	+	29.8778i	−0.0672370	+	0.0402124i	0.479264	+	0.877671i	$0.340903\pi$
$744$	−1965.86	+	383.171i	−2.64228	+	0.515015i
$745$	−47.3905	+	33.0022i	−0.0636114	+	0.0442983i
$746$	−87.6330	+	1135.84i	−0.117471	+	1.52258i
$747$	157.464	−	134.907i	0.210795	−	0.180598i
$748$	550.873	−	3377.02i	0.736461	−	4.51473i
$749$	−779.367	−	388.079i	−1.04054	−	0.518129i
$750$	272.478	−	957.660i	0.363304	−	1.27688i
$751$	−186.316	−	470.157i	−0.248091	−	0.626042i	0.751335	−	0.659921i	$-0.229410\pi$
$751$	−186.316	−	470.157i	−0.248091	−	0.626042i	−0.999426	+	0.0338788i	$0.989214\pi$
$752$	−1044.15	−	2520.80i	−1.38850	−	3.35213i
$753$	159.816	+	303.193i	0.212238	+	0.402646i
$754$	−866.969	+	1148.05i	−1.14983	+	1.52262i
$755$	−271.414	+	342.656i	−0.359488	+	0.453849i
$756$	2390.35	−	1454.70i	3.16184	−	1.92421i
$757$	39.1944	+	66.6953i	0.0517759	+	0.0881048i	0.886912	−	0.461939i	$-0.152846\pi$
$757$	39.1944	+	66.6953i	0.0517759	+	0.0881048i	−0.835136	+	0.550044i	$0.814611\pi$
$758$	−1267.09	−	757.806i	−1.67162	−	0.999744i
$759$	251.960	+	90.9741i	0.331963	+	0.119860i
$760$	91.4492	+	352.116i	0.120328	+	0.463311i
$761$	72.4074	+	720.935i	0.0951477	+	0.947352i	0.922585	+	0.385794i	$0.126072\pi$
$761$	72.4074	+	720.935i	0.0951477	+	0.947352i	−0.827437	+	0.561558i	$0.810202\pi$
$762$	595.608	−	204.742i	0.781638	−	0.268691i
$763$	−1774.09	−	123.141i	−2.32515	−	0.161391i
$764$	−166.067	−	287.636i	−0.217365	−	0.376487i
$765$	−218.639	−	126.231i	−0.285802	−	0.165008i
$766$	−657.024	+	975.157i	−0.857733	+	1.27305i
$767$	−146.460	−	436.978i	−0.190952	−	0.569723i
$768$	539.857	−	345.878i	0.702939	−	0.450362i
$769$	−1089.87	−	292.031i	−1.41726	−	0.379754i	−0.532749	−	0.846273i	$-0.678841\pi$
$769$	−1089.87	−	292.031i	−1.41726	−	0.379754i	−0.884511	+	0.466519i	$0.845508\pi$
$770$	97.3362	−	2105.35i	0.126411	−	2.73422i
$771$	228.149	+	51.8094i	0.295912	+	0.0671977i
$772$	2125.73	+	977.991i	2.75354	+	1.26683i
$773$	−178.452	+	11.0066i	−0.230857	+	0.0142388i	−0.176576	−	0.984287i	$-0.556502\pi$
$773$	−178.452	+	11.0066i	−0.230857	+	0.0142388i	−0.0542805	+	0.998526i	$0.517287\pi$
$774$	−69.8687	−	154.997i	−0.0902696	−	0.200254i
$775$	−508.836	−	485.855i	−0.656563	−	0.626909i
$776$	−351.354	+	472.794i	−0.452776	+	0.609271i
$777$	552.722	+	519.681i	0.711353	+	0.668830i
$778$	−554.948	−	309.104i	−0.713301	−	0.397306i
$779$	3.32576	+	431.909i	0.00426927	+	0.554440i
$780$	58.6613	+	445.577i	0.0752068	+	0.571252i
$781$	−1328.28	+	1434.71i	−1.70075	+	1.83702i
$782$	250.215	+	404.110i	0.319968	+	0.516765i
$783$	−722.038	−	1422.49i	−0.922144	−	1.81672i
$784$	693.759	+	1876.06i	0.884896	+	2.39294i
$785$	133.374	+	81.1674i	0.169903	+	0.103398i
$786$	−7.57668	+	491.954i	−0.00963954	+	0.625896i
$787$	197.207	−	476.100i	0.250581	−	0.604956i	−0.747670	−	0.664070i	$-0.768828\pi$
$787$	197.207	−	476.100i	0.250581	−	0.604956i	0.998251	+	0.0591141i	$0.0188276\pi$
$788$	2427.89	−	224.977i	3.08108	−	0.285504i
$789$	579.328	+	473.578i	0.734255	+	0.600226i
$790$	−46.2946	+	66.4780i	−0.0586007	+	0.0841493i
$791$	−1534.06	−	677.355i	−1.93940	−	0.856328i
$792$	62.1708	+	1614.03i	0.0784985	+	2.03792i
$793$	−174.514	+	450.472i	−0.220068	+	0.568060i
$794$	−506.837	−	764.894i	−0.638334	−	0.963343i
$795$	176.805	−	35.8768i	0.222396	−	0.0451281i
$796$	−477.684	−	270.908i	−0.600105	−	0.340337i
$797$	−3.65594	+	474.790i	−0.00458713	+	0.595721i	0.952285	+	0.305211i	$0.0987269\pi$
$797$	−3.65594	+	474.790i	−0.00458713	+	0.595721i	−0.956872	+	0.290510i	$0.906175\pi$
$798$	468.271	−	57.9845i	0.586806	−	0.0726623i
$799$	980.403	+	1026.78i	1.22704	+	1.28508i
$800$	−799.776	−	324.086i	−0.999720	−	0.405107i
$801$	1.74289	+	1.15488i	0.00217590	+	0.00144180i
$802$	1338.85	+	1891.33i	1.66939	+	2.35827i
$803$	1270.71	−	1123.07i	1.58246	−	1.39859i
$804$	59.8581	+	2590.81i	0.0744504	+	3.22240i
$805$	128.175	+	161.819i	0.159223	+	0.201017i
$806$	1096.70	+	405.553i	1.36067	+	0.503168i
$807$	184.915	−	21.4531i	0.229139	−	0.0265838i
$808$	1071.14	−	1007.11i	1.32567	−	1.24643i
$809$	−151.417	+	38.0829i	−0.187166	+	0.0470741i	−0.336358	−	0.941734i	$-0.609195\pi$
$809$	−151.417	+	38.0829i	−0.187166	+	0.0470741i	0.149193	+	0.988808i	$0.452333\pi$
$810$	−260.391	−	87.2743i	−0.321471	−	0.107746i
$811$	427.391	+	556.987i	0.526992	+	0.686790i	0.978681	−	0.205386i	$-0.0658449\pi$
$811$	427.391	+	556.987i	0.526992	+	0.686790i	−0.451689	+	0.892176i	$0.649178\pi$
$812$	5153.52	−	1466.30i	6.34670	−	1.80579i
$813$	−60.9487	+	326.047i	−0.0749676	+	0.401041i
$814$	−2230.55	+	709.590i	−2.74024	+	0.871732i
$815$	−383.007	+	491.265i	−0.469947	+	0.602780i
$816$	925.564	−	1265.71i	1.13427	−	1.55112i
$817$		−	62.8585i		−	0.0769382i
$818$	1506.20	−	19.7858i	1.84132	−	0.0241880i
$819$	−305.638			−0.373185
$820$	1754.06	+	1282.67i	2.13910	+	1.56423i
$821$	−764.726	−	596.206i	−0.931457	−	0.726195i	0.0304603	−	0.999536i	$-0.490303\pi$
$821$	−764.726	−	596.206i	−0.931457	−	0.726195i	−0.961917	+	0.273341i	$0.911871\pi$
$822$	−222.935	−	700.784i	−0.271211	−	0.852535i
$823$	−183.615	−	34.3236i	−0.223104	−	0.0417054i	0.0710103	−	0.997476i	$-0.477378\pi$
$823$	−183.615	−	34.3236i	−0.223104	−	0.0417054i	−0.294115	+	0.955770i	$0.595025\pi$
$824$	388.565	+	1365.67i	0.471560	+	1.65736i
$825$	499.441	−	383.234i	0.605382	−	0.464526i
$826$	−773.612	+	2308.14i	−0.936576	+	2.79436i
$827$	−335.892	−	1335.50i	−0.406157	−	1.61487i	−0.740248	−	0.672333i	$-0.765292\pi$
$827$	−335.892	−	1335.50i	−0.406157	−	1.61487i	0.334091	−	0.942541i	$-0.391571\pi$
$828$	−186.276	−	198.119i	−0.224971	−	0.239274i
$829$	−103.425	−	891.475i	−0.124759	−	1.07536i	−0.897615	−	0.440780i	$-0.854702\pi$
$829$	−103.425	−	891.475i	−0.124759	−	1.07536i	0.772856	−	0.634581i	$-0.218827\pi$
$830$	189.719	−	513.040i	0.228578	−	0.618121i
$831$	78.8490	−	62.4554i	0.0948844	−	0.0751569i
$832$	381.958	−	8.82477i	0.459084	−	0.0106067i
$833$	−689.217	−	779.825i	−0.827392	−	0.936164i
$834$	813.088	−	575.573i	0.974926	−	0.690135i
$835$	95.9097	−	144.742i	0.114862	−	0.173344i
$836$	−385.506	+	951.347i	−0.461131	+	1.13797i
$837$	−937.751	+	895.398i	−1.12037	+	1.06977i
$838$	−249.294	−	2013.24i	−0.297486	−	2.40244i
$839$	14.4247	+	0.111072i	0.0171927	+	0.000132386i	0.0162960	−	0.999867i	$-0.494813\pi$
$839$	14.4247	+	0.111072i	0.0171927	+	0.000132386i	0.000896722		1.00000i	$0.499715\pi$
$840$	681.300	−	1201.31i	0.811071	−	1.43014i
$841$	−440.212	−	2169.41i	−0.523439	−	2.57956i
$842$	959.442	−	635.749i	1.13948	−	0.755047i
$843$	941.134	+	364.597i	1.11641	+	0.432500i
$844$	−1233.44	+	47.5109i	−1.46143	+	0.0562926i
$845$	−146.945	+	332.798i	−0.173899	+	0.393844i
$846$	−945.309	−	658.303i	−1.11739	−	0.778136i
$847$	1413.39	−	1729.00i	1.66871	−	2.04132i
$848$	−93.1799	−	1005.57i	−0.109882	−	1.18581i
$849$	695.826	+	288.221i	0.819584	+	0.339483i
$850$	1116.85	+	17.2008i	1.31394	+	0.0202362i
$851$	119.187	−	195.847i	0.140055	−	0.230138i
$852$	−2065.50	+	763.809i	−2.42429	+	0.896489i
$853$	63.2341	−	32.0968i	0.0741314	−	0.0376282i	−0.415161	−	0.909748i	$-0.636275\pi$
$853$	63.2341	−	32.0968i	0.0741314	−	0.0376282i	0.489292	+	0.872120i	$0.337255\pi$
$854$	2169.53	−	1343.31i	2.54043	−	1.57297i
$855$	55.5765	+	51.4538i	0.0650017	+	0.0601799i
$856$	1745.14	−	229.752i	2.03871	−	0.268402i
$857$	1392.12	−	10.7195i	1.62441	−	0.0125081i	0.807711	−	0.589578i	$-0.200706\pi$
$857$	1392.12	−	10.7195i	1.62441	−	0.0125081i	0.816694	+	0.577070i	$0.195804\pi$
$858$	−509.124	+	914.053i	−0.593385	+	1.06533i
$859$	−727.604	+	773.864i	−0.847036	+	0.900889i	−0.996126	−	0.0879344i	$-0.971973\pi$
$859$	−727.604	+	773.864i	−0.847036	+	0.900889i	0.149090	+	0.988824i	$0.452366\pi$
$860$	−253.827	−	188.630i	−0.295148	−	0.219337i
$861$	1132.34	−	1185.90i	1.31514	−	1.37735i
$862$	−2424.29	+	1092.81i	−2.81240	+	1.26776i
$863$	−86.0963	−	1395.90i	−0.0997640	−	1.61750i	−0.634804	−	0.772673i	$-0.718919\pi$
$863$	−86.0963	−	1395.90i	−0.0997640	−	1.61750i	0.535040	−	0.844827i	$-0.320296\pi$
$864$	−664.703	+	1444.78i	−0.769332	+	1.67219i
$865$	14.4566	−	63.6612i	0.0167128	−	0.0735967i
$866$	1124.11	+	51.9707i	1.29805	+	0.0600123i
$867$	−48.4211	+	180.710i	−0.0558490	+	0.208431i
$868$	−2349.30	−	3666.86i	−2.70657	−	4.22450i
$869$	−126.085	+	42.2596i	−0.145093	+	0.0486301i
$870$	−1122.36	−	756.204i	−1.29007	−	0.869200i
$871$	440.095	−	762.266i	0.505275	−	0.875162i
$872$	3113.66	−	1797.67i	3.57071	−	2.06155i
$873$	−8.49167	+	122.339i	−0.00972700	+	0.140136i
$874$	−46.3534	−	134.845i	−0.0530359	−	0.154285i
$875$	1253.20	−	125.865i	1.43222	−	0.143846i
$876$	1848.80	−	480.158i	2.11050	−	0.548125i
$877$	−152.721	+	422.973i	−0.174141	+	0.482295i	−0.996199	−	0.0871080i	$-0.972237\pi$
$877$	−152.721	+	422.973i	−0.174141	+	0.482295i	0.822058	+	0.569403i	$0.192826\pi$
$878$	1472.38	−	2461.89i	1.67697	−	2.80397i
$879$	−492.143	+	289.214i	−0.559890	+	0.329027i
$880$	1092.32	+	1794.89i	1.24128	+	2.03965i
$881$	−830.389	−	657.742i	−0.942553	−	0.746586i	0.0248859	−	0.999690i	$-0.492078\pi$
$881$	−830.389	−	657.742i	−0.942553	−	0.746586i	−0.967439	+	0.253105i	$0.918548\pi$
$882$	673.906	+	508.910i	0.764066	+	0.576996i
$883$	−1017.62	+	536.397i	−1.15246	+	0.607471i	−0.930032	−	0.367478i	$-0.880221\pi$
$883$	−1017.62	+	536.397i	−1.15246	+	0.607471i	−0.222427	+	0.974949i	$0.571398\pi$
$884$	−1209.34	+	500.923i	−1.36803	+	0.566655i
$885$	403.052	−	159.723i	0.455426	−	0.180478i
$886$	−2752.97	−	783.286i	−3.10718	−	0.884070i
$887$	−755.723	+	1517.70i	−0.851998	+	1.71104i	−0.162561	+	0.986699i	$0.551975\pi$
$887$	−755.723	+	1517.70i	−0.851998	+	1.71104i	−0.689438	+	0.724345i	$0.742142\pi$
$888$	−1513.80	−	246.937i	−1.70473	−	0.278082i
$889$	518.350	+	605.021i	0.583071	+	0.680564i
$890$	5.49919	+	0.424275i	0.00617886	+	0.000476714i
$891$	−257.625	−	369.943i	−0.289141	−	0.415200i
$892$	−201.676	−	1034.70i	−0.226094	−	1.15997i
$893$	−218.603	−	365.514i	−0.244796	−	0.409311i
$894$	−132.856	−	72.6656i	−0.148608	−	0.0812815i
$895$	239.061	+	246.540i	0.267107	+	0.275463i
$896$	175.277	+	126.113i	0.195622	+	0.140751i
$897$	−21.1522	−	100.273i	−0.0235811	−	0.111787i
$898$	−824.667	+	379.407i	−0.918337	+	0.422502i
$899$	−2187.31	+	1174.56i	−2.43304	+	1.30652i
$900$	−628.183	+	117.428i	−0.697981	+	0.130475i
$901$	234.214	+	470.365i	0.259949	+	0.522048i
$902$	1496.45	+	4832.49i	1.65903	+	5.35753i
$903$	−166.115	+	171.312i	−0.183959	+	0.189714i
$904$	3337.30	−	597.292i	3.69170	−	0.660721i
$905$	610.357	−	138.604i	0.674428	−	0.153153i
$906$	−1121.54	−	236.586i	−1.23790	−	0.261133i
$907$	−392.957	+	358.228i	−0.433250	+	0.394959i	−0.860727	−	0.509067i	$-0.829991\pi$
$907$	−392.957	+	358.228i	−0.433250	+	0.394959i	0.427477	+	0.904026i	$0.359402\pi$
$908$	−608.905	+	950.397i	−0.670600	+	1.04669i
$909$	74.6588	−	296.842i	0.0821329	−	0.326559i
$910$	−704.379	+	392.337i	−0.774043	+	0.431139i
$911$	459.836	+	810.815i	0.504760	+	0.890027i	0.999776	+	0.0211434i	$0.00673064\pi$
$911$	459.836	+	810.815i	0.504760	+	0.890027i	−0.495016	+	0.868884i	$0.664838\pi$
$912$	−354.859	+	308.794i	−0.389100	+	0.338590i
$913$	752.294	−	490.194i	0.823981	−	0.536905i
$914$	1156.40	+	930.555i	1.26521	+	1.01811i
$915$	−431.995	−	141.100i	−0.472126	−	0.154207i
$916$	1674.13	−	1347.17i	1.82766	−	1.47071i
$917$	−582.071	+	220.356i	−0.634756	+	0.240301i
$918$	126.725	−	2054.62i	0.138044	−	2.23815i
$919$	−237.579	−	127.577i	−0.258519	−	0.138822i	0.338714	−	0.940889i	$-0.390008\pi$
$919$	−237.579	−	127.577i	−0.258519	−	0.138822i	−0.597234	+	0.802067i	$0.703733\pi$
$920$	−397.708	−	126.520i	−0.432291	−	0.137522i
$921$	12.3739	−	8.47634i	0.0134353	−	0.00920341i
$922$	−596.324	−	1651.56i	−0.646772	−	1.79128i
$923$	734.150	+	143.095i	0.795395	+	0.155033i
$924$	3564.75	−	1573.99i	3.85795	−	1.70345i
$925$	−236.434	−	484.130i	−0.255604	−	0.523384i
$926$	1961.76	+	212.301i	2.11853	+	0.229266i
$927$	221.490	+	195.756i	0.238933	+	0.211171i
$928$	−1963.42	+	2327.76i	−2.11576	+	2.50836i
$929$	−284.873	−	1746.36i	−0.306644	−	1.87983i	−0.454394	−	0.890801i	$-0.650144\pi$
$929$	−284.873	−	1746.36i	−0.306644	−	1.87983i	0.147750	−	0.989025i	$-0.452797\pi$
$930$	−325.375	+	1050.74i	−0.349866	+	1.12982i
$931$	149.823	+	273.924i	0.160927	+	0.294226i
$932$	−955.680	−	561.618i	−1.02541	−	0.602594i
$933$	4.42769	+	287.490i	0.00474565	+	0.308136i
$934$	1003.47	+	397.659i	1.07438	+	0.425759i
$935$	−867.334	−	665.529i	−0.927630	−	0.711796i
$936$	512.453	−	345.271i	0.547492	−	0.368879i
$937$	87.4978	+	1260.58i	0.0933808	+	1.34533i	0.783390	+	0.621531i	$0.213489\pi$
$937$	87.4978	+	1260.58i	0.0933808	+	1.34533i	−0.690009	+	0.723801i	$0.742393\pi$
$938$	−4281.49	+	1812.20i	−4.56449	+	1.93198i
$939$	452.905	−	106.522i	0.482327	−	0.113442i
$940$	−2131.97	−	214.125i	−2.26805	−	0.227793i
$941$	−703.977	+	109.277i	−0.748116	+	0.116129i	−0.516035	−	0.856568i	$-0.672593\pi$
$941$	−703.977	+	109.277i	−0.748116	+	0.116129i	−0.232081	+	0.972697i	$0.574553\pi$
$942$	−34.6349	+	407.935i	−0.0367674	+	0.433052i
$943$	−421.282	−	260.847i	−0.446747	−	0.276614i
$944$	−646.155	−	2339.28i	−0.684487	−	2.47806i
$945$	−48.1659	−	892.752i	−0.0509692	−	0.944711i
$946$	−212.360	−	704.939i	−0.224482	−	0.745179i
$947$	−1124.34	+	165.675i	−1.18727	+	0.174947i	−0.710252	−	0.703947i	$-0.751419\pi$
$947$	−1124.34	+	165.675i	−1.18727	+	0.174947i	−0.477017	+	0.878894i	$0.658282\pi$
$948$	−148.180	−	21.8346i	−0.156308	−	0.0230323i
$949$	−621.193	−	187.132i	−0.654577	−	0.197188i
$950$	−325.590	−	79.2287i	−0.342727	−	0.0833987i
$951$	13.1611	−	84.7852i	0.0138392	−	0.0891537i
$952$	3893.28	+	1011.14i	4.08958	+	1.06212i
$953$	262.713	−	383.514i	0.275669	−	0.402428i	−0.662249	−	0.749284i	$-0.730398\pi$
$953$	262.713	−	383.514i	0.275669	−	0.402428i	0.937918	+	0.346856i	$0.112751\pi$
$954$	−262.148	−	336.245i	−0.274789	−	0.352459i
$955$	−106.069	+	3.26796i	−0.111067	+	0.00342195i
$956$	−739.603	+	382.604i	−0.773644	+	0.400213i
$957$	−738.343	−	2095.26i	−0.771518	−	2.18941i
$958$	1440.69	+	1463.05i	1.50385	+	1.52719i
$959$	720.230	−	588.761i	0.751021	−	0.613932i
$960$	27.6471	+	358.344i	0.0287991	+	0.373275i
$961$	747.334	+	747.334i	0.777663	+	0.777663i
$962$	680.009	+	582.596i	0.706870	+	0.605609i
$963$	280.112	−	236.270i	0.290874	−	0.245347i
$964$	−81.4515	+	3525.42i	−0.0844933	+	3.65708i
$965$	596.617	−	450.544i	0.618256	−	0.466885i
$966$	−230.023	+	489.997i	−0.238119	+	0.507244i
$967$	775.611	−	787.648i	0.802079	−	0.814527i	−0.183628	−	0.982996i	$-0.558784\pi$
$967$	775.611	−	787.648i	0.802079	−	0.814527i	0.985707	+	0.168469i	$0.0538822\pi$
$968$	−416.581	+	4495.63i	−0.430352	+	4.64424i
$969$	114.129	−	216.518i	0.117780	−	0.223445i
$970$	137.472	+	292.845i	0.141724	+	0.301902i
$971$	1295.03	+	456.352i	1.33371	+	0.469981i	0.901885	−	0.431977i	$-0.142184\pi$
$971$	1295.03	+	456.352i	1.33371	+	0.469981i	0.431825	+	0.901958i	$0.357870\pi$
$972$	273.101	+	1957.79i	0.280968	+	2.01419i
$973$	1055.80	+	687.960i	1.08510	+	0.707050i
$974$	39.5296	+	121.025i	0.0405848	+	0.124256i
$975$	−225.231	−	85.2664i	−0.231007	−	0.0874527i
$976$	−1045.43	+	2319.18i	−1.07114	+	2.37621i
$977$	−1205.96	+	488.679i	−1.23435	+	0.500183i	−0.897348	−	0.441323i	$-0.854509\pi$
$977$	−1205.96	+	488.679i	−1.23435	+	0.500183i	−0.336997	+	0.941506i	$0.609411\pi$
$978$	−1600.80	−	324.831i	−1.63681	−	0.332138i
$979$	6.83001	+	5.94339i	0.00697651	+	0.00607088i
$980$	1555.72	+	217.014i	1.58747	+	0.221443i
$981$	343.916	−	664.817i	0.350577	−	0.677693i
$982$	1297.59	+	621.373i	1.32137	+	0.632763i
$983$	−592.875	+	660.497i	−0.603128	+	0.671919i	−0.965587	−	0.260080i	$-0.916251\pi$
$983$	−592.875	+	660.497i	−0.603128	+	0.671919i	0.362459	+	0.932000i	$0.381937\pi$
$984$	−558.872	+	3267.52i	−0.567960	+	3.32065i
$985$	303.666	−	717.439i	0.308290	−	0.728364i
$986$	1281.38	−	3727.62i	1.29958	−	3.78055i
$987$	−370.168	+	1573.86i	−0.375043	+	1.59459i
$988$	387.068	−	66.2036i	0.391769	−	0.0670077i
$989$	61.0160	+	38.4326i	0.0616947	+	0.0388601i
$990$	797.103	+	389.280i	0.805155	+	0.393212i
$991$	−70.6502	+	1834.17i	−0.0712918	+	1.85082i	0.341357	+	0.939934i	$0.389114\pi$
$991$	−70.6502	+	1834.17i	−0.0712918	+	1.85082i	−0.412649	+	0.910890i	$0.635396\pi$
$992$	2271.83	+	982.278i	2.29015	+	0.990199i
$993$	448.189	−	131.260i	0.451349	−	0.132185i
$994$	−2639.08	−	2940.09i	−2.65501	−	2.95783i
$995$	−148.464	+	93.5140i	−0.149210	+	0.0939840i
$996$	1005.48	−	108.812i	1.00952	−	0.109249i
$997$	−240.004	−	169.895i	−0.240726	−	0.170406i	0.451094	−	0.892476i	$-0.351034\pi$
$997$	−240.004	−	169.895i	−0.240726	−	0.170406i	−0.691820	+	0.722070i	$0.743191\pi$
$998$	876.773	−	339.664i	0.878530	−	0.340344i
$999$	−911.391	+	394.061i	−0.912304	+	0.394455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.3.p.a.21.4	✓	8576
409.39	odd	408	inner	409.3.p.a.39.4	yes	8576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.3.p.a.21.4	✓	8576	1.1	even	1	trivial
409.3.p.a.39.4	yes	8576	409.39	odd	408	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:	\( N \)	\(=\)	\( 409 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	409.p (of order \(408\), degree \(128\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.97290 - 2.17396i) q^{2} +(-1.71585 - 1.33773i) q^{3} +(2.89942 + 9.11414i) q^{4} +(3.00382 + 0.561512i) q^{5} +(2.19287 + 7.70713i) q^{6} +(-8.04167 + 6.17059i) q^{7} +(6.51243 - 19.4305i) q^{8} +(-1.04062 - 4.13748i) q^{9} +(-7.70936 - 8.19950i) q^{10} +(-2.12909 - 18.3516i) q^{11} +(7.21733 - 19.5171i) q^{12} +(-5.54020 + 4.38833i) q^{13} +(37.3217 - 0.862282i) q^{14} +(-4.40295 - 4.98178i) q^{15} +(-30.3767 + 21.5032i) q^{16} +(10.6963 - 16.1424i) q^{17} +(-5.90105 + 14.5626i) q^{18} +(-4.20160 + 4.01184i) q^{19} +(3.59164 + 29.0053i) q^{20} +(22.0529 + 0.169810i) q^{21} +(-33.5661 + 59.1861i) q^{22} +(-1.32532 - 6.53134i) q^{23} +(-37.1671 + 24.6278i) q^{24} +(-14.6041 - 5.65768i) q^{25} +(26.0105 - 1.00190i) q^{26} +(-11.6586 + 26.4042i) q^{27} +(-79.5558 - 55.4018i) q^{28} +(-34.9798 + 42.7907i) q^{29} +(2.25934 + 24.3822i) q^{30} +(41.5015 + 17.1905i) q^{31} +(55.0923 + 0.848487i) q^{32} +(-20.8964 + 34.3368i) q^{33} +(-66.8920 + 24.7363i) q^{34} +(-27.6206 + 14.0199i) q^{35} +(34.6924 - 21.4806i) q^{36} +(25.2434 + 23.3709i) q^{37} +(21.2125 - 2.79268i) q^{38} +(15.3766 - 0.118402i) q^{39} +(30.4726 - 54.7089i) q^{40} +(50.9293 - 54.1673i) q^{41} +(-65.1918 - 48.4469i) q^{42} +(-7.47233 + 7.82577i) q^{43} +(161.086 - 72.6138i) q^{44} +(-0.802588 - 13.0126i) q^{45} +(-10.2588 + 22.2982i) q^{46} +(-16.2349 + 71.4924i) q^{47} +(80.8873 + 3.73964i) q^{48} +(13.9101 - 51.9133i) q^{49} +(31.1171 + 48.5685i) q^{50} +(-39.9475 + 13.3891i) q^{51} +(-56.0592 - 37.7706i) q^{52} +(-13.5673 + 23.4993i) q^{53} +(92.0614 - 53.1517i) q^{54} +(3.90927 - 56.3206i) q^{55} +(67.5265 + 196.439i) q^{56} +(12.5761 - 1.26308i) q^{57} +(197.016 - 51.1678i) q^{58} +(-22.1453 + 61.3330i) q^{59} +(32.6387 - 54.5734i) q^{60} +(58.9307 - 34.6314i) q^{61} +(-86.0084 - 141.328i) q^{62} +(33.8990 + 26.8510i) q^{63} +(-43.1390 - 32.5771i) q^{64} +(-19.1059 + 10.0709i) q^{65} +(136.770 - 56.6518i) q^{66} +(-115.779 + 45.8813i) q^{67} +(178.137 + 50.6844i) q^{68} +(-6.46313 + 12.9797i) q^{69} +(112.592 + 18.3664i) q^{70} +(-68.8549 - 80.3677i) q^{71} +(-87.1700 - 6.72537i) q^{72} +(52.4579 + 75.3284i) q^{73} +(-24.2389 - 124.357i) q^{74} +(17.4900 + 29.2442i) q^{75} +(-48.7466 - 26.6620i) q^{76} +(130.362 + 134.440i) q^{77} +(-45.9703 - 33.0760i) q^{78} +(-1.48568 - 7.04289i) q^{79} +(-103.320 + 47.5350i) q^{80} +(21.4979 - 11.5441i) q^{81} +(-269.165 + 50.3156i) q^{82} +(21.6637 + 43.5066i) q^{83} +(62.3928 + 201.485i) q^{84} +(41.1941 - 42.4828i) q^{85} +(39.2274 - 7.02070i) q^{86} +(117.262 - 26.6287i) q^{87} +(-370.446 - 78.1447i) q^{88} +(-0.362165 + 0.330157i) q^{89} +(-25.9028 + 40.4298i) q^{90} +(17.4739 - 69.4758i) q^{91} +(55.6849 - 31.0163i) q^{92} +(-48.2140 - 85.0142i) q^{93} +(203.686 - 177.245i) q^{94} +(-14.8736 + 9.69160i) q^{95} +(-93.3950 - 75.1547i) q^{96} +(-27.3239 - 8.92460i) q^{97} +(-154.211 + 124.093i) q^{98} +(-73.7140 + 27.9061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8576 q - 124 q^{2} - 112 q^{3} - 124 q^{4} - 120 q^{5} - 120 q^{6} - 144 q^{7} + 8 q^{8} - 292 q^{9} - 96 q^{10} - 160 q^{11} + 36 q^{12} - 164 q^{13} - 16 q^{14} - 80 q^{15} - 204 q^{16} - 148 q^{17} - 148 q^{18}+ \cdots + 1180 q^{99}+O(q^{100}) \) 8576 * q - 124 * q^2 - 112 * q^3 - 124 * q^4 - 120 * q^5 - 120 * q^6 - 144 * q^7 + 8 * q^8 - 292 * q^9 - 96 * q^10 - 160 * q^11 + 36 * q^12 - 164 * q^13 - 16 * q^14 - 80 * q^15 - 204 * q^16 - 148 * q^17 - 148 * q^18 - 96 * q^19 + 68 * q^20 - 144 * q^21 - 256 * q^22 - 128 * q^23 - 1156 * q^24 - 2496 * q^25 - 280 * q^26 - 100 * q^27 - 92 * q^28 - 80 * q^29 + 672 * q^30 - 168 * q^31 + 2112 * q^32 - 96 * q^33 + 92 * q^34 + 64 * q^35 - 2344 * q^36 - 152 * q^37 - 2972 * q^39 + 112 * q^40 - 196 * q^41 + 488 * q^42 - 452 * q^43 + 92 * q^44 - 244 * q^45 - 124 * q^46 + 16 * q^47 - 188 * q^48 + 16 * q^49 + 96 * q^50 + 8 * q^51 - 828 * q^52 - 256 * q^53 + 240 * q^54 - 1016 * q^55 + 76 * q^56 - 92 * q^57 - 800 * q^58 + 48 * q^59 - 64 * q^60 + 428 * q^61 - 52 * q^62 + 1604 * q^63 - 136 * q^64 + 136 * q^65 + 224 * q^66 + 600 * q^67 - 136 * q^68 + 2808 * q^69 - 20 * q^70 - 188 * q^71 + 560 * q^72 + 144 * q^73 - 996 * q^74 + 1152 * q^75 + 992 * q^76 - 3084 * q^77 - 4900 * q^78 - 560 * q^79 - 292 * q^80 - 3128 * q^81 + 1488 * q^82 + 120 * q^83 + 6560 * q^84 + 288 * q^85 + 3248 * q^86 - 632 * q^87 + 144 * q^88 + 608 * q^89 + 268 * q^90 + 404 * q^91 - 5128 * q^92 - 104 * q^93 - 624 * q^94 + 84 * q^95 + 140 * q^96 - 840 * q^97 - 72 * q^98 + 1180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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