LMFDB - Embedded newform 375.3.p.a.14.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			14.1
Character	$\chi$	$=$	375.14
Dual form			375.3.p.a.134.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.68926 - 3.58987i) q^{2} +(-2.97064 - 0.418686i) q^{3} +(-7.48385 + 9.04642i) q^{4} +(-1.07499 + 4.88307i) q^{5} +(3.51517 + 11.3715i) q^{6} +(-5.06561 - 1.64592i) q^{7} +(29.7464 + 7.63757i) q^{8} +(8.64940 + 2.48753i) q^{9} +(19.3455 - 4.38973i) q^{10} +(-9.43777 + 4.44108i) q^{11} +(26.0194 - 23.7403i) q^{12} +(0.469255 - 3.71454i) q^{13} +(2.64853 + 20.9652i) q^{14} +(5.23788 - 14.0558i) q^{15} +(-14.0316 - 73.5562i) q^{16} +(7.75199 + 9.37054i) q^{17} +(-5.68121 - 35.2523i) q^{18} +(1.46576 + 23.2976i) q^{19} +(-36.1293 - 46.2690i) q^{20} +(14.3590 + 7.01032i) q^{21} +(31.8858 + 26.3782i) q^{22} +(7.15803 + 3.93516i) q^{23} +(-85.1680 - 35.1429i) q^{24} +(-22.6888 - 10.4985i) q^{25} +(-14.1274 + 4.59027i) q^{26} +(-24.6528 - 11.0109i) q^{27} +(52.7999 - 33.5078i) q^{28} +(-25.3050 + 16.0590i) q^{29} +(-59.3065 + 4.94060i) q^{30} +(-27.8995 - 33.7247i) q^{31} +(-140.970 + 102.421i) q^{32} +(29.8956 - 9.24138i) q^{33} +(20.5439 - 43.6579i) q^{34} +(13.4826 - 22.9664i) q^{35} +(-87.2341 + 59.6298i) q^{36} +(23.1239 - 4.41112i) q^{37} +(81.1591 - 44.6176i) q^{38} +(-2.94921 + 10.8381i) q^{39} +(-69.2718 + 137.043i) q^{40} +(14.3813 + 26.1595i) q^{41} +(0.910040 - 63.3891i) q^{42} +(27.4718 - 37.8117i) q^{43} +(30.4550 - 118.614i) q^{44} +(-21.4448 + 39.5616i) q^{45} +(2.03491 - 32.3439i) q^{46} +(28.6043 - 7.34435i) q^{47} +(10.8859 + 224.384i) q^{48} +(-16.6905 - 12.1264i) q^{49} +(0.639142 + 99.1845i) q^{50} +(-19.1050 - 31.0822i) q^{51} +(30.0914 + 32.0441i) q^{52} +(7.71921 + 3.05625i) q^{53} +(2.11718 + 107.101i) q^{54} +(-11.5406 - 50.8594i) q^{55} +(-138.113 - 87.6489i) q^{56} +(5.40012 - 69.8223i) q^{57} +(100.397 + 63.7136i) q^{58} +(1.54071 - 1.64069i) q^{59} +(87.9549 + 152.575i) q^{60} +(47.9420 + 26.3563i) q^{61} +(-73.9377 + 157.126i) q^{62} +(-39.7202 - 26.8370i) q^{63} +(343.334 + 188.749i) q^{64} +(17.6339 + 6.28449i) q^{65} +(-83.6769 - 91.7103i) q^{66} +(-89.3967 - 56.7328i) q^{67} -142.785 q^{68} +(-19.6163 - 14.6869i) q^{69} +(-105.222 - 9.60446i) q^{70} +(-29.4025 - 114.515i) q^{71} +(238.290 + 140.055i) q^{72} +(-87.2666 - 92.9295i) q^{73} +(-54.8977 - 75.5603i) q^{74} +(63.0047 + 40.6867i) q^{75} +(-221.729 - 161.095i) q^{76} +(55.1177 - 6.96298i) q^{77} +(43.8893 - 7.72109i) q^{78} +(-1.76126 + 27.9944i) q^{79} +(374.264 + 10.5548i) q^{80} +(68.6244 + 43.0313i) q^{81} +(69.6154 - 95.8173i) q^{82} +(4.23946 + 67.3843i) q^{83} +(-170.879 + 77.4331i) q^{84} +(-54.0903 + 27.7803i) q^{85} +(-182.146 - 34.7463i) q^{86} +(81.8957 - 37.1107i) q^{87} +(-314.658 + 60.0243i) q^{88} +(4.18659 + 4.45827i) q^{89} +(178.247 + 10.1541i) q^{90} +(-8.49087 + 18.0440i) q^{91} +(-89.1687 + 35.3044i) q^{92} +(68.7593 + 111.865i) q^{93} +(-74.6855 - 90.2793i) q^{94} +(-115.339 - 17.8872i) q^{95} +(461.655 - 245.234i) q^{96} +(62.3290 - 39.5552i) q^{97} +(-15.3374 + 80.4013i) q^{98} +(-92.6784 + 14.9359i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1960 q - 20 q^{3} - 40 q^{4} - 20 q^{6} - 50 q^{7} - 20 q^{9} - 40 q^{10} - 180 q^{12} - 40 q^{13} + 20 q^{15} - 140 q^{16} - 25 q^{18} + 10 q^{19} - 65 q^{21} - 15 q^{24} - 350 q^{25} - 125 q^{27} - 320 q^{28}+ \cdots - 15 q^{99}+O(q^{100}) $ 1960 * q - 20 * q^3 - 40 * q^4 - 20 * q^6 - 50 * q^7 - 20 * q^9 - 40 * q^10 - 180 * q^12 - 40 * q^13 + 20 * q^15 - 140 * q^16 - 25 * q^18 + 10 * q^19 - 65 * q^21 - 15 * q^24 - 350 * q^25 - 125 * q^27 - 320 * q^28 - 20 * q^30 + 60 * q^31 - 45 * q^33 - 240 * q^34 - 1000 * q^36 - 160 * q^37 + 180 * q^39 - 120 * q^40 + 150 * q^42 - 50 * q^43 - 820 * q^45 + 160 * q^46 - 175 * q^48 + 2980 * q^49 - 15 * q^51 + 270 * q^52 - 345 * q^54 - 40 * q^55 - 280 * q^58 - 1305 * q^60 - 140 * q^61 - 820 * q^63 - 400 * q^64 + 355 * q^66 + 210 * q^67 - 220 * q^69 - 1250 * q^70 - 240 * q^72 + 100 * q^73 - 225 * q^75 - 30 * q^76 - 830 * q^78 + 60 * q^79 - 620 * q^81 + 1550 * q^82 + 335 * q^84 + 1540 * q^85 + 405 * q^87 + 1660 * q^88 + 705 * q^90 + 70 * q^91 - 25 * q^93 + 660 * q^94 - 595 * q^96 + 100 * q^97 - 15 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−1.68926	−	3.58987i	−0.844632	−	1.79493i	−0.537489	−	0.843271i	$-0.680627\pi$
$2$	−1.68926	−	3.58987i	−0.844632	−	1.79493i	−0.307143	−	0.951663i	$-0.599373\pi$
$3$	−2.97064	−	0.418686i	−0.990213	−	0.139562i
$3$	−2.97064	−	0.418686i	−0.990213	−	0.139562i
$4$	−7.48385	+	9.04642i	−1.87096	+	2.26160i
$5$	−1.07499	+	4.88307i	−0.214998	+	0.976615i
$5$	−1.07499	+	4.88307i	−0.214998	+	0.976615i
$6$	3.51517	+	11.3715i	0.585861	+	1.89525i
$7$	−5.06561	−	1.64592i	−0.723658	−	0.235131i	−0.0760496	−	0.997104i	$-0.524231\pi$
$7$	−5.06561	−	1.64592i	−0.723658	−	0.235131i	−0.647608	+	0.761973i	$0.724231\pi$
$8$	29.7464	+	7.63757i	3.71830	+	0.954696i
$9$	8.64940	+	2.48753i	0.961045	+	0.276392i
$10$	19.3455	−	4.38973i	1.93455	−	0.438973i
$11$	−9.43777	+	4.44108i	−0.857979	+	0.403734i	−0.803873	−	0.594801i	$-0.797231\pi$
$11$	−9.43777	+	4.44108i	−0.857979	+	0.403734i	−0.0541060	+	0.998535i	$0.517231\pi$
$12$	26.0194	−	23.7403i	2.16829	−	1.97836i
$13$	0.469255	−	3.71454i	0.0360965	−	0.285734i	−0.963726	−	0.266894i	$-0.914003\pi$
$13$	0.469255	−	3.71454i	0.0360965	−	0.285734i	0.999823	−	0.0188399i	$-0.00599727\pi$
$14$	2.64853	+	20.9652i	0.189180	+	1.49752i
$15$	5.23788	−	14.0558i	0.349192	−	0.937051i
$16$	−14.0316	−	73.5562i	−0.876975	−	4.59726i
$17$	7.75199	+	9.37054i	0.455999	+	0.551208i	0.947536	−	0.319648i	$-0.103565\pi$
$17$	7.75199	+	9.37054i	0.455999	+	0.551208i	−0.491537	+	0.870857i	$0.663565\pi$
$18$	−5.68121	−	35.2523i	−0.315623	−	1.95846i
$19$	1.46576	+	23.2976i	0.0771451	+	1.22619i	0.826084	+	0.563547i	$0.190564\pi$
$19$	1.46576	+	23.2976i	0.0771451	+	1.22619i	−0.748939	+	0.662639i	$0.769436\pi$
$20$	−36.1293	−	46.2690i	−1.80646	−	2.31345i
$21$	14.3590	+	7.01032i	0.683760	+	0.333825i
$22$	31.8858	+	26.3782i	1.44935	+	1.19901i
$23$	7.15803	+	3.93516i	0.311219	+	0.171094i	0.629707	−	0.776833i	$-0.283175\pi$
$23$	7.15803	+	3.93516i	0.311219	+	0.171094i	−0.318488	+	0.947927i	$0.603175\pi$
$24$	−85.1680	−	35.1429i	−3.54867	−	1.46429i
$25$	−22.6888	−	10.4985i	−0.907552	−	0.419940i
$26$	−14.1274	+	4.59027i	−0.543361	+	0.176549i
$27$	−24.6528	−	11.0109i	−0.913066	−	0.407813i
$28$	52.7999	−	33.5078i	1.88571	−	1.19671i
$29$	−25.3050	+	16.0590i	−0.872585	+	0.553759i	−0.895039	−	0.445988i	$-0.852852\pi$
$29$	−25.3050	+	16.0590i	−0.872585	+	0.553759i	0.0224535	+	0.999748i	$0.492852\pi$
$30$	−59.3065	+	4.94060i	−1.97688	+	0.164687i
$31$	−27.8995	−	33.7247i	−0.899984	−	1.08789i	−0.995714	−	0.0924866i	$-0.970518\pi$
$31$	−27.8995	−	33.7247i	−0.899984	−	1.08789i	0.0957298	−	0.995407i	$-0.469482\pi$
$32$	−140.970	+	102.421i	−4.40533	+	3.20066i
$33$	29.8956	−	9.24138i	0.905928	−	0.280042i
$34$	20.5439	−	43.6579i	0.604231	−	1.28406i
$35$	13.4826	−	22.9664i	0.385217	−	0.656182i
$36$	−87.2341	+	59.6298i	−2.42317	+	1.65638i
$37$	23.1239	−	4.41112i	0.624971	−	0.119220i	0.134838	−	0.990868i	$-0.456948\pi$
$37$	23.1239	−	4.41112i	0.624971	−	0.119220i	0.490132	+	0.871648i	$0.336948\pi$
$38$	81.1591	−	44.6176i	2.13577	−	1.17415i
$39$	−2.94921	+	10.8381i	−0.0756208	+	0.277899i
$40$	−69.2718	+	137.043i	−1.73180	+	3.42608i
$41$	14.3813	+	26.1595i	0.350764	+	0.638037i	0.991556	−	0.129677i	$-0.0413941\pi$
$41$	14.3813	+	26.1595i	0.350764	+	0.638037i	−0.640793	+	0.767714i	$0.721394\pi$
$42$	0.910040	−	63.3891i	0.0216676	−	1.50926i
$43$	27.4718	−	37.8117i	0.638879	−	0.879342i	−0.359676	−	0.933077i	$-0.617113\pi$
$43$	27.4718	−	37.8117i	0.638879	−	0.879342i	0.998555	+	0.0537352i	$0.0171127\pi$
$44$	30.4550	−	118.614i	0.692159	−	2.69578i
$45$	−21.4448	+	39.5616i	−0.476551	+	0.879147i
$46$	2.03491	−	32.3439i	0.0442371	−	0.703129i
$47$	28.6043	−	7.34435i	0.608603	−	0.156263i	0.0682038	−	0.997671i	$-0.478273\pi$
$47$	28.6043	−	7.34435i	0.608603	−	0.156263i	0.540399	+	0.841409i	$0.318273\pi$
$48$	10.8859	+	224.384i	0.226789	+	4.67466i
$49$	−16.6905	−	12.1264i	−0.340623	−	0.247477i
$50$	0.639142	+	99.1845i	0.0127828	+	1.98369i
$51$	−19.1050	−	31.0822i	−0.374609	−	0.609454i
$52$	30.0914	+	32.0441i	0.578681	+	0.616233i
$53$	7.71921	+	3.05625i	0.145645	+	0.0576651i	0.439816	−	0.898088i	$-0.355044\pi$
$53$	7.71921	+	3.05625i	0.145645	+	0.0576651i	−0.294171	+	0.955753i	$0.595044\pi$
$54$	2.11718	+	107.101i	0.0392070	+	1.98334i
$55$	−11.5406	−	50.8594i	−0.209829	−	0.924717i
$56$	−138.113	−	87.6489i	−2.46630	−	1.56516i
$57$	5.40012	−	69.8223i	0.0947390	−	1.22495i
$58$	100.397	+	63.7136i	1.73098	+	1.09851i
$59$	1.54071	−	1.64069i	0.0261137	−	0.0278083i	−0.715779	−	0.698327i	$-0.753928\pi$
$59$	1.54071	−	1.64069i	0.0261137	−	0.0278083i	0.741893	+	0.670518i	$0.233928\pi$
$60$	87.9549	+	152.575i	1.46591	+	2.54292i
$61$	47.9420	+	26.3563i	0.785934	+	0.432071i	0.823566	−	0.567221i	$-0.191981\pi$
$61$	47.9420	+	26.3563i	0.785934	+	0.432071i	−0.0376315	+	0.999292i	$0.511981\pi$
$62$	−73.9377	+	157.126i	−1.19254	+	2.53428i
$63$	−39.7202	−	26.8370i	−0.630479	−	0.425985i
$64$	343.334	+	188.749i	5.36459	+	2.94921i
$65$	17.6339	+	6.28449i	0.271291	+	0.0966845i
$66$	−83.6769	−	91.7103i	−1.26783	−	1.38955i
$67$	−89.3967	−	56.7328i	−1.33428	−	0.846759i	−0.338719	−	0.940888i	$-0.609993\pi$
$67$	−89.3967	−	56.7328i	−1.33428	−	0.846759i	−0.995560	+	0.0941288i	$0.969993\pi$
$68$	−142.785			−2.09977
$69$	−19.6163	−	14.6869i	−0.284295	−	0.212854i
$70$	−105.222	−	9.60446i	−1.50317	−	0.137207i
$71$	−29.4025	−	114.515i	−0.414120	−	1.61289i	−0.743528	−	0.668704i	$-0.766849\pi$
$71$	−29.4025	−	114.515i	−0.414120	−	1.61289i	0.329408	−	0.944188i	$-0.393151\pi$
$72$	238.290	+	140.055i	3.30958	+	1.94521i
$73$	−87.2666	−	92.9295i	−1.19543	−	1.27301i	−0.953045	−	0.302828i	$-0.902069\pi$
$73$	−87.2666	−	92.9295i	−1.19543	−	1.27301i	−0.242388	−	0.970179i	$-0.577931\pi$
$74$	−54.8977	−	75.5603i	−0.741861	−	1.02108i
$75$	63.0047	+	40.6867i	0.840062	+	0.542490i
$76$	−221.729	−	161.095i	−2.91749	−	2.11968i
$77$	55.1177	−	6.96298i	0.715814	−	0.0904283i
$78$	43.8893	−	7.72109i	0.562683	−	0.0989883i
$79$	−1.76126	+	27.9944i	−0.0222944	+	0.354359i	0.971026	+	0.238973i	$0.0768107\pi$
$79$	−1.76126	+	27.9944i	−0.0222944	+	0.354359i	−0.993321	+	0.115387i	$0.963189\pi$
$80$	374.264	+	10.5548i	4.67830	+	0.131935i
$81$	68.6244	+	43.0313i	0.847214	+	0.531251i
$82$	69.6154	−	95.8173i	0.848968	−	1.16850i
$83$	4.23946	+	67.3843i	0.0510779	+	0.811860i	0.937284	+	0.348568i	$0.113332\pi$
$83$	4.23946	+	67.3843i	0.0510779	+	0.811860i	−0.886206	+	0.463292i	$0.846668\pi$
$84$	−170.879	+	77.4331i	−2.03427	+	0.921822i
$85$	−54.0903	+	27.7803i	−0.636357	+	0.326827i
$86$	−182.146	−	34.7463i	−2.11798	−	0.404026i
$87$	81.8957	−	37.1107i	0.941329	−	0.426560i
$88$	−314.658	+	60.0243i	−3.57566	+	0.682094i
$89$	4.18659	+	4.45827i	0.0470404	+	0.0500929i	0.752058	−	0.659096i	$-0.229061\pi$
$89$	4.18659	+	4.45827i	0.0470404	+	0.0500929i	−0.705018	+	0.709189i	$0.749061\pi$
$90$	178.247	+	10.1541i	1.98052	+	0.112823i
$91$	−8.49087	+	18.0440i	−0.0933063	+	0.198286i
$92$	−89.1687	+	35.3044i	−0.969225	+	0.383743i
$93$	68.7593	+	111.865i	0.739348	+	1.20285i
$94$	−74.6855	−	90.2793i	−0.794527	−	0.960418i
$95$	−115.339	−	17.8872i	−1.21410	−	0.188286i
$96$	461.655	−	245.234i	4.80890	−	2.55452i
$97$	62.3290	−	39.5552i	0.642567	−	0.407786i	−0.174234	−	0.984704i	$-0.555745\pi$
$97$	62.3290	−	39.5552i	0.642567	−	0.407786i	0.816802	+	0.576919i	$0.195745\pi$
$98$	−15.3374	+	80.4013i	−0.156504	+	0.820422i
$99$	−92.6784	+	14.9359i	−0.936145	+	0.150868i
$100$	264.773	−	126.683i	2.64773	−	1.26683i
$101$	38.9826	+	12.6662i	0.385966	+	0.125408i	0.495572	−	0.868567i	$-0.334959\pi$
$101$	38.9826	+	12.6662i	0.385966	+	0.125408i	−0.109605	+	0.993975i	$0.534959\pi$
$102$	−79.3074	+	121.091i	−0.777524	+	1.18716i
$103$	−80.3954	−	66.5089i	−0.780538	−	0.645717i	0.159341	−	0.987224i	$-0.449063\pi$
$103$	−80.3954	−	66.5089i	−0.780538	−	0.645717i	−0.939880	+	0.341506i	$0.889063\pi$
$104$	42.3287	−	106.910i	0.407006	−	1.02798i
$105$	−49.6676	+	62.5799i	−0.473025	+	0.595999i
$106$	−2.06824	−	32.8737i	−0.0195117	−	0.310130i
$107$	−50.9768	−	156.891i	−0.476419	−	1.46627i	−0.844035	−	0.536289i	$-0.819826\pi$
$107$	−50.9768	−	156.891i	−0.476419	−	1.46627i	0.367616	−	0.929978i	$-0.380174\pi$
$108$	284.107	−	140.615i	2.63062	−	1.30199i
$109$	−30.9405	−	162.196i	−0.283858	−	1.48804i	−0.783275	−	0.621675i	$-0.786453\pi$
$109$	−30.9405	−	162.196i	−0.283858	−	1.48804i	0.499417	−	0.866362i	$-0.333547\pi$
$110$	−163.084	+	127.344i	−1.48258	+	1.15767i
$111$	−70.5397	+	3.42219i	−0.635493	+	0.0308306i
$112$	−49.9887	+	395.702i	−0.446328	+	3.53305i
$113$	130.250	+	122.312i	1.15265	+	1.08241i	0.995493	+	0.0948376i	$0.0302332\pi$
$113$	130.250	+	122.312i	1.15265	+	1.08241i	0.157158	+	0.987573i	$0.449767\pi$
$114$	−259.775	+	98.5626i	−2.27873	+	0.864584i
$115$	−26.9105	+	30.7229i	−0.234004	+	0.267156i
$116$	44.1019	−	349.103i	0.380189	−	3.00951i
$117$	13.2988	−	30.9612i	0.113665	−	0.264626i
$118$	−8.49252	−	2.75939i	−0.0719705	−	0.0233846i
$119$	−23.8454	−	60.2266i	−0.200381	−	0.506106i
$120$	263.160	−	378.103i	2.19300	−	3.15086i
$121$	−7.77999	+	9.40439i	−0.0642974	+	0.0777222i
$122$	13.6291	−	216.628i	0.111714	−	1.77564i
$123$	−31.7691	−	83.7317i	−0.258285	−	0.680746i
$124$	513.884			4.14422
$125$	75.6551	−	99.5053i	0.605241	−	0.796042i
$126$	−29.2435	+	187.925i	−0.232092	+	1.49147i
$127$	36.5736	−	17.2102i	0.287981	−	0.135514i	−0.276363	−	0.961053i	$-0.589129\pi$
$127$	36.5736	−	17.2102i	0.287981	−	0.135514i	0.564344	+	0.825540i	$0.309129\pi$
$128$	53.8392	−	855.750i	0.420619	−	6.68555i
$129$	−97.4401	+	100.823i	−0.755350	+	0.781573i
$130$	−7.22782	−	73.9196i	−0.0555986	−	0.568612i
$131$	16.8533	+	42.5665i	0.128651	+	0.324935i	0.979797	−	0.199994i	$-0.0640921\pi$
$131$	16.8533	+	42.5665i	0.128651	+	0.324935i	−0.851146	+	0.524928i	$0.824092\pi$
$132$	−140.133	+	339.609i	−1.06161	+	2.57280i
$133$	30.9208	−	120.429i	0.232488	−	0.905479i
$134$	−52.6489	+	416.759i	−0.392902	+	3.11014i
$135$	80.2687	−	108.545i	0.594583	−	0.804034i
$136$	159.025	+	337.946i	1.16930	+	2.48490i
$137$	−120.809	−	113.447i	−0.881816	−	0.828080i	0.104230	−	0.994553i	$-0.466762\pi$
$137$	−120.809	−	113.447i	−0.881816	−	0.828080i	−0.986046	+	0.166473i	$0.946762\pi$
$138$	−19.5869	+	95.2301i	−0.141934	+	0.690073i
$139$	10.4303	−	1.31766i	0.0750385	−	0.00947956i	−0.0877243	−	0.996145i	$-0.527959\pi$
$139$	10.4303	−	1.31766i	0.0750385	−	0.00947956i	0.162763	+	0.986665i	$0.447959\pi$
$140$	106.862	+	293.846i	0.763299	+	2.09890i
$141$	−88.0482	+	9.84117i	−0.624455	+	0.0697955i
$142$	−361.426	+	298.998i	−2.54526	+	2.10562i
$143$	12.0678	+	37.1409i	0.0843904	+	0.259727i
$144$	61.6084	−	671.121i	0.427836	−	4.66056i
$145$	−51.2148	−	140.829i	−0.353206	−	0.971236i
$146$	−186.188	+	470.258i	−1.27526	+	3.22095i
$147$	44.5043	+	43.0111i	0.302751	+	0.292593i
$148$	−133.151	+	242.201i	−0.899669	+	1.63649i
$149$	236.326	+	76.7868i	1.58608	+	0.515348i	0.963613	−	0.267300i	$-0.0861316\pi$
$149$	236.326	+	76.7868i	1.58608	+	0.515348i	0.622464	+	0.782648i	$0.286132\pi$
$150$	39.6285	−	294.909i	0.264190	−	1.96606i
$151$	3.35615	+	10.3292i	0.0222261	+	0.0684050i	0.961554	−	0.274615i	$-0.0885503\pi$
$151$	3.35615	+	10.3292i	0.0222261	+	0.0684050i	−0.939328	+	0.343020i	$0.888550\pi$
$152$	−134.336	+	704.212i	−0.883787	+	4.63298i
$153$	43.7405	+	100.333i	0.285886	+	0.655771i
$154$	−118.104	−	186.103i	−0.766912	−	1.20846i
$155$	194.672	−	99.9816i	1.25595	−	0.645043i
$156$	−75.9743	−	107.790i	−0.487015	−	0.690964i
$157$	12.9525	+	17.8276i	0.0824999	+	0.113551i	0.848272	−	0.529560i	$-0.177643\pi$
$157$	12.9525	+	17.8276i	0.0824999	+	0.113551i	−0.765772	+	0.643112i	$0.777643\pi$
$158$	103.471	−	40.9672i	0.654882	−	0.259286i
$159$	−21.6514	−	12.3109i	−0.136172	−	0.0774273i
$160$	−348.588	−	798.470i	−2.17867	−	4.99044i
$161$	−29.7828	−	31.7155i	−0.184986	−	0.196991i
$162$	38.5522	−	319.044i	0.237976	−	1.96941i
$163$	72.1437	+	131.229i	0.442599	+	0.805085i	0.999678	−	0.0253748i	$-0.00807791\pi$
$163$	72.1437	+	131.229i	0.442599	+	0.805085i	−0.557079	+	0.830460i	$0.688078\pi$
$164$	−344.277	−	65.6744i	−2.09925	−	0.400454i
$165$	12.9888	+	155.917i	0.0787203	+	0.944951i
$166$	234.739	−	129.049i	1.41409	−	0.777404i
$167$	−19.0113	−	302.175i	−0.113840	−	1.80943i	−0.478281	−	0.878207i	$-0.658740\pi$
$167$	−19.0113	−	302.175i	−0.113840	−	1.80943i	0.364441	−	0.931227i	$-0.381260\pi$
$168$	373.585	+	318.199i	2.22372	+	1.89404i
$169$	150.113	+	38.5425i	0.888242	+	0.228062i
$170$	191.100	+	147.249i	1.12412	+	0.866170i
$171$	−45.2755	+	205.156i	−0.264769	+	1.19974i
$172$	136.466	+	531.499i	0.793405	+	3.09011i
$173$	184.157	−	23.2644i	1.06449	−	0.134476i	0.426474	−	0.904500i	$-0.359755\pi$
$173$	184.157	−	23.2644i	1.06449	−	0.134476i	0.638016	+	0.770023i	$0.279755\pi$
$174$	−271.566	−	231.305i	−1.56072	−	1.32934i
$175$	97.6529	+	90.5251i	0.558016	+	0.517286i
$176$	459.096	+	631.891i	2.60850	+	3.59029i
$177$	−5.26382	+	4.22882i	−0.0297391	+	0.0238916i
$178$	8.93234	−	22.5605i	0.0501817	−	0.126744i
$179$	4.91462	+	19.1412i	0.0274560	+	0.106934i	0.980834	−	0.194844i	$-0.0624200\pi$
$179$	4.91462	+	19.1412i	0.0274560	+	0.106934i	−0.953378	+	0.301778i	$0.902420\pi$
$180$	−197.401	−	490.072i	−1.09667	−	2.72262i
$181$	26.7198	−	42.1037i	0.147623	−	0.232617i	−0.762467	−	0.647027i	$-0.776012\pi$
$181$	26.7198	−	42.1037i	0.147623	−	0.232617i	0.910090	+	0.414410i	$0.136012\pi$
$182$	79.1190			0.434720
$183$	−131.383	−	98.3678i	−0.717942	−	0.537529i
$184$	182.870	+	171.727i	0.993861	+	0.933297i
$185$	−3.31812	+	117.658i	−0.0179358	+	0.635987i
$186$	285.428	−	435.807i	1.53456	−	2.34305i
$187$	−114.777	−	54.0098i	−0.613780	−	0.288823i
$188$	−147.631	+	313.731i	−0.785269	+	1.66878i
$189$	106.758	+	96.3535i	0.564858	+	0.509807i
$190$	130.626	+	444.269i	0.687504	+	2.33826i
$191$	125.712	−	133.870i	0.658180	−	0.700891i	−0.310115	−	0.950699i	$-0.600368\pi$
$191$	125.712	−	133.870i	0.658180	−	0.700891i	0.968295	+	0.249808i	$0.0803676\pi$
$192$	−940.894	−	704.455i	−4.90049	−	3.66904i
$193$		−	26.4429i		−	0.137010i	−0.997651	−	0.0685050i	$-0.978177\pi$
$193$		−	26.4429i		−	0.137010i	0.997651	−	0.0685050i	$-0.0218229\pi$
$194$	−247.288	−	156.934i	−1.27468	−	0.808937i
$195$	−49.7528	−	26.0520i	−0.255142	−	0.133600i
$196$	234.609	−	60.2374i	1.19699	−	0.307334i
$197$	2.99804	+	1.18701i	0.0152185	+	0.00602542i	0.375721	−	0.926733i	$-0.377395\pi$
$197$	2.99804	+	1.18701i	0.0152185	+	0.00602542i	−0.360503	+	0.932758i	$0.617395\pi$
$198$	210.176	+	307.473i	1.06150	+	1.55289i
$199$	90.2974	−	65.6049i	0.453756	−	0.329673i	−0.337321	−	0.941390i	$-0.609521\pi$
$199$	90.2974	−	65.6049i	0.453756	−	0.329673i	0.791077	+	0.611717i	$0.209521\pi$
$200$	−594.726	−	485.579i	−2.97363	−	2.42790i
$201$	241.812	+	205.962i	1.20304	+	1.02469i
$202$	−20.3819	−	161.339i	−0.100900	−	0.798708i
$203$	154.617	−	39.6988i	0.761659	−	0.195561i
$204$	424.161	+	59.7819i	2.07922	+	0.293049i
$205$	−143.199	+	42.1038i	−0.698529	+	0.205384i
$206$	−102.949	+	400.960i	−0.499753	+	1.94641i
$207$	52.1239	+	51.8426i	0.251806	+	0.250447i
$208$	−279.812	+	17.6043i	−1.34525	+	0.0846358i
$209$	−117.300	−	213.367i	−0.561243	−	1.02090i
$210$	308.555	+	72.5864i	1.46931	+	0.345649i
$211$	−43.5348	+	228.217i	−0.206326	+	1.08160i	0.716852	+	0.697225i	$0.245582\pi$
$211$	−43.5348	+	228.217i	−0.206326	+	1.08160i	−0.923178	+	0.384373i	$0.874418\pi$
$212$	−85.4175	+	46.9587i	−0.402913	+	0.221503i
$213$	39.3984	+	352.494i	0.184969	+	1.65490i
$214$	−477.103	+	448.030i	−2.22945	+	2.09360i
$215$	155.105	+	174.794i	0.721421	+	0.812996i
$216$	−649.234	−	515.823i	−3.00571	−	2.38807i
$217$	85.8199	+	216.756i	0.395483	+	0.998877i
$218$	−529.996	+	385.064i	−2.43117	+	1.76635i
$219$	220.329	+	312.597i	1.00607	+	1.42739i
$220$	546.464	+	276.223i	2.48393	+	1.25556i
$221$	38.4449	−	24.3979i	0.173959	−	0.110398i
$222$	131.445	+	247.447i	0.592096	+	1.11463i
$223$	−82.2275	−	15.6857i	−0.368733	−	0.0703396i	−0.000315361	−	1.00000i	$-0.500100\pi$
$223$	−82.2275	−	15.6857i	−0.368733	−	0.0703396i	−0.368418	+	0.929660i	$0.620100\pi$
$224$	882.677	−	286.799i	3.94052	−	1.28035i
$225$	−170.129	−	147.245i	−0.756130	−	0.654422i
$226$	219.060	−	674.197i	0.969291	−	2.98317i
$227$	50.3205	+	27.6639i	0.221676	+	0.121867i	0.588723	−	0.808335i	$-0.299631\pi$
$227$	50.3205	+	27.6639i	0.221676	+	0.121867i	−0.367047	+	0.930203i	$0.619631\pi$
$228$	591.228	+	571.391i	2.59311	+	2.50610i
$229$	18.4077	+	7.28812i	0.0803829	+	0.0318258i	0.407972	−	0.912994i	$-0.366236\pi$
$229$	18.4077	+	7.28812i	0.0803829	+	0.0318258i	−0.327589	+	0.944820i	$0.606236\pi$
$230$	155.750	+	44.7059i	0.677175	+	0.194374i
$231$	−166.650	−	2.39250i	−0.721429	−	0.0103571i
$232$	−875.383	+	284.429i	−3.77320	+	1.22599i
$233$	−158.193	−	191.223i	−0.678941	−	0.820699i	0.312683	−	0.949858i	$-0.398772\pi$
$233$	−158.193	−	191.223i	−0.678941	−	0.820699i	−0.991624	+	0.129159i	$0.958772\pi$
$234$	−133.612	+	4.56074i	−0.570991	+	0.0194904i
$235$	5.11363	+	147.572i	0.0217601	+	0.627967i
$236$	3.31192	+	26.2166i	0.0140336	+	0.111087i
$237$	16.9529	−	82.4239i	0.0715313	−	0.347780i
$238$	−175.924	+	187.340i	−0.739178	+	0.787145i
$239$	5.71600	−	2.68975i	0.0239163	−	0.0112542i	−0.413784	−	0.910375i	$-0.635793\pi$
$239$	5.71600	−	2.68975i	0.0239163	−	0.0112542i	0.437700	+	0.899121i	$0.355793\pi$
$240$	−1107.38	−	188.054i	−4.61410	−	0.783557i
$241$	18.1602	+	2.29416i	0.0753534	+	0.00951935i	0.162920	−	0.986639i	$-0.447909\pi$
$241$	18.1602	+	2.29416i	0.0753534	+	0.00951935i	−0.0875661	+	0.996159i	$0.527909\pi$
$242$	46.9030	+	12.0426i	0.193814	+	0.0497630i
$243$	−185.842	−	156.563i	−0.764781	−	0.644291i
$244$	−597.221	+	236.457i	−2.44763	+	0.969084i
$245$	77.1560	−	68.4652i	0.314923	−	0.279450i
$246$	−246.920	+	255.492i	−1.00374	+	1.03858i
$247$	87.2274	+	5.48788i	0.353147	+	0.0222182i
$248$	−572.334	−	1216.27i	−2.30780	−	4.90432i
$249$	15.6190	−	201.950i	0.0627268	−	0.811043i
$250$	−485.012	−	103.501i	−1.94005	−	0.414005i
$251$			31.0503i			0.123706i	0.998085	+	0.0618531i	$0.0197010\pi$
$251$			31.0503i			0.123706i	−0.998085	+	0.0618531i	$0.980299\pi$
$252$	540.039	−	158.481i	2.14301	−	0.628894i
$253$	−85.0322	−	5.34977i	−0.336096	−	0.0211453i
$254$	−123.565	−	102.222i	−0.486476	−	0.402448i
$255$	172.314	−	59.8784i	0.675742	−	0.234817i
$256$	−1705.85	+	675.392i	−6.66346	+	2.63825i
$257$	49.5047	−	152.360i	0.192625	−	0.592840i	−0.807371	−	0.590045i	$-0.799110\pi$
$257$	49.5047	−	152.360i	0.192625	−	0.592840i	0.999996	−	0.00279555i	$-0.000889853\pi$
$258$	526.543	+	179.481i	2.04086	+	0.695662i
$259$	−124.397	−	15.7150i	−0.480297	−	0.0606756i
$260$	−188.822	+	112.492i	−0.726237	+	0.432660i
$261$	−258.820	+	75.9541i	−0.991648	+	0.291012i
$262$	124.338	−	132.407i	0.474574	−	0.505370i
$263$	−82.7605	−	10.4551i	−0.314679	−	0.0397531i	−0.0335922	−	0.999436i	$-0.510695\pi$
$263$	−82.7605	−	10.4551i	−0.314679	−	0.0397531i	−0.281086	+	0.959682i	$0.590695\pi$
$264$	959.868	−	46.5675i	3.63586	−	0.176392i
$265$	−23.2219	+	34.4080i	−0.0876300	+	0.129842i
$266$	−484.557	+	92.4341i	−1.82164	+	0.347497i
$267$	−10.5702	−	14.9968i	−0.0395889	−	0.0561677i
$268$	1182.26	−	384.140i	4.41142	−	1.43336i
$269$	−357.121	+	22.4681i	−1.32759	+	0.0835247i	−0.710682	−	0.703513i	$-0.751614\pi$
$269$	−357.121	+	22.4681i	−1.32759	+	0.0835247i	−0.616904	+	0.787038i	$0.711614\pi$
$270$	−525.256	−	104.794i	−1.94539	−	0.388124i
$271$	−179.804	−	71.1893i	−0.663482	−	0.262691i	0.0121544	−	0.999926i	$-0.496131\pi$
$271$	−179.804	−	71.1893i	−0.663482	−	0.262691i	−0.675636	+	0.737235i	$0.736131\pi$
$272$	580.489	−	701.690i	2.13415	−	2.57974i
$273$	32.7781	−	50.0473i	0.120066	−	0.183323i
$274$	−203.182	+	625.330i	−0.741540	+	2.28222i
$275$	260.756	−	1.68031i	0.948205	−	0.00611020i
$276$	279.670	−	67.5429i	1.01330	−	0.244721i
$277$	−126.022	−	24.0400i	−0.454954	−	0.0867871i	−0.0451893	−	0.998978i	$-0.514389\pi$
$277$	−126.022	−	24.0400i	−0.454954	−	0.0867871i	−0.409764	+	0.912191i	$0.634389\pi$
$278$	−22.3498	−	35.2177i	−0.0803951	−	0.126682i
$279$	−157.423	−	361.100i	−0.564239	−	1.29426i
$280$	576.466	−	580.192i	2.05881	−	2.07212i
$281$	−275.661	+	228.047i	−0.981000	+	0.811554i	−0.982084	−	0.188445i	$-0.939655\pi$
$281$	−275.661	+	228.047i	−0.981000	+	0.811554i	0.00108342	+	0.999999i	$0.499655\pi$
$282$	184.065	+	299.457i	0.652713	+	1.06190i
$283$	−71.4835	−	180.547i	−0.252592	−	0.637975i	0.747049	−	0.664769i	$-0.231470\pi$
$283$	−71.4835	−	180.547i	−0.252592	−	0.637975i	−0.999641	+	0.0267944i	$0.991470\pi$
$284$	1256.00	+	591.028i	4.42253	+	2.08108i
$285$	335.142	+	101.427i	1.17594	+	0.355886i
$286$	112.945	−	106.063i	0.394914	−	0.370849i
$287$	−29.7937	−	156.184i	−0.103811	−	0.544196i
$288$	−1474.09	+	535.212i	−5.11835	+	1.85838i
$289$	26.4394	−	138.600i	0.0914859	−	0.479586i
$290$	−419.043	+	421.752i	−1.44498	+	1.45432i
$291$	−201.718	+	91.4080i	−0.693190	+	0.314117i
$292$	1493.77	−	93.9800i	5.11565	−	0.321849i
$293$	252.469	+	183.429i	0.861667	+	0.626038i	0.928338	−	0.371737i	$-0.121238\pi$
$293$	252.469	+	183.429i	0.861667	+	0.626038i	−0.0666708	+	0.997775i	$0.521238\pi$
$294$	79.2248	−	232.422i	0.269472	−	0.790551i
$295$	6.35535	+	9.28711i	0.0215436	+	0.0314817i
$296$	721.543	+	45.3956i	2.43764	+	0.153364i
$297$	281.568	−	5.56607i	0.948039	−	0.0187410i
$298$	−123.562	−	978.091i	−0.414636	−	3.28218i
$299$	17.9762	−	24.7422i	0.0601212	−	0.0827497i
$300$	−839.587	+	265.473i	−2.79862	+	0.884911i
$301$	−201.396	+	146.323i	−0.669091	+	0.486123i
$302$	31.4109	−	29.4968i	0.104010	−	0.0976715i
$303$	−110.500	−	53.9483i	−0.364687	−	0.178047i
$304$	1693.11	−	434.717i	5.56945	−	1.42999i
$305$	−180.237	+	205.771i	−0.590941	+	0.674661i
$306$	286.293	−	326.512i	0.935597	−	1.06703i
$307$		−	332.311i		−	1.08245i	−0.840879	−	0.541223i	$-0.817962\pi$
$307$		−	332.311i		−	1.08245i	0.840879	−	0.541223i	$-0.182038\pi$
$308$	−349.502	+	550.727i	−1.13475	+	1.78808i
$309$	210.980	+	231.234i	0.682782	+	0.748332i
$310$	−687.773	−	529.951i	−2.21862	−	1.70952i
$311$	−171.802	+	312.507i	−0.552419	+	1.00485i	0.441763	+	0.897132i	$0.354353\pi$
$311$	−171.802	+	312.507i	−0.552419	+	1.00485i	−0.994182	+	0.107715i	$0.965647\pi$
$312$	−170.505	+	299.869i	−0.546490	+	0.961118i
$313$	510.214	+	240.088i	1.63008	+	0.767056i	0.999955	−	0.00944157i	$-0.00300539\pi$
$313$	510.214	+	240.088i	1.63008	+	0.767056i	0.630121	+	0.776497i	$0.283005\pi$
$314$	42.1185	−	76.6132i	0.134135	−	0.243991i
$315$	173.746	−	165.107i	0.551575	−	0.524150i
$316$	−240.068	−	225.439i	−0.759709	−	0.713414i
$317$	−29.1136	+	45.8758i	−0.0918412	+	0.144719i	−0.887142	−	0.461496i	$-0.847313\pi$
$317$	−29.1136	+	45.8758i	−0.0918412	+	0.144719i	0.795301	+	0.606215i	$0.207313\pi$
$318$	−7.61978	+	98.5220i	−0.0239616	+	0.309818i
$319$	167.503	−	263.943i	0.525088	−	0.827407i
$320$	−1290.76	+	1473.62i	−4.03361	+	4.60506i
$321$	85.7459	+	487.409i	0.267121	+	1.51841i
$322$	−63.5434	+	160.492i	−0.197340	+	0.498423i
$323$	−206.948	+	194.337i	−0.640706	+	0.601663i
$324$	−902.854	+	298.765i	−2.78659	+	0.922114i
$325$	−49.6439	+	79.3519i	−0.152750	+	0.244160i
$326$	349.225	−	480.666i	1.07124	−	1.47444i
$327$	24.0040	+	494.780i	0.0734067	+	1.51309i
$328$	227.997	+	887.989i	0.695112	+	2.70728i
$329$	−156.987	−	9.87675i	−0.477163	−	0.0300205i
$330$	537.780	−	310.013i	1.62964	−	0.939434i
$331$	397.103	+	101.959i	1.19971	+	0.308032i	0.795112	−	0.606463i	$-0.207412\pi$
$331$	397.103	+	101.959i	1.19971	+	0.308032i	0.404596	+	0.914496i	$0.367412\pi$
$332$	−641.314	−	465.942i	−1.93167	−	1.40344i
$333$	210.981	+	19.3679i	0.633576	+	0.0581618i
$334$	−1052.65	+	578.702i	−3.15166	+	1.73264i
$335$	373.131	−	375.543i	1.11382	−	1.12102i
$336$	314.173	−	1154.56i	0.935039	−	3.43618i
$337$	−212.465	−	386.472i	−0.630460	−	1.14680i	−0.977895	−	0.209098i	$-0.932947\pi$
$337$	−212.465	−	386.472i	−0.630460	−	1.14680i	0.347435	−	0.937704i	$-0.387053\pi$
$338$	−115.218	−	603.994i	−0.340882	−	1.78697i
$339$	−335.714	−	417.880i	−0.990307	−	1.23268i
$340$	153.492	−	697.227i	0.451446	−	2.05067i
$341$	413.083	+	194.382i	1.21139	+	0.570036i
$342$	812.965	−	184.030i	2.37709	−	0.538099i
$343$	217.994	+	300.043i	0.635550	+	0.874760i
$344$	1105.98	−	914.943i	3.21505	−	2.65972i
$345$	92.8046	−	79.9997i	0.268999	−	0.231883i
$346$	−394.606	−	621.799i	−1.14048	−	1.79711i
$347$	−180.087	−	283.772i	−0.518983	−	0.817787i	0.479221	−	0.877694i	$-0.340919\pi$
$347$	−180.087	−	283.772i	−0.518983	−	0.817787i	−0.998204	+	0.0599078i	$0.980919\pi$
$348$	−277.175	+	1018.59i	−0.796481	+	2.92699i
$349$	110.019	+	338.604i	0.315241	+	0.970213i	0.975655	+	0.219311i	$0.0703809\pi$
$349$	110.019	+	338.604i	0.315241	+	0.970213i	−0.660414	+	0.750902i	$0.729619\pi$
$350$	160.012	−	503.482i	0.457176	−	1.43852i
$351$	−52.4690	+	86.4067i	−0.149484	+	0.246173i
$352$	875.587	−	1592.69i	2.48746	−	4.52468i
$353$	−250.056	+	302.266i	−0.708375	+	0.856279i	−0.994802	−	0.101823i	$-0.967532\pi$
$353$	−250.056	+	302.266i	−0.708375	+	0.856279i	0.286427	+	0.958102i	$0.407532\pi$
$354$	24.0729	+	11.7528i	0.0680025	+	0.0332001i
$355$	590.794	−	20.4720i	1.66421	−	0.0576677i
$356$	−71.6632	+	4.50866i	−0.201301	+	0.0126648i
$357$	45.6200	+	188.895i	0.127787	+	0.529118i
$358$	60.4122	−	49.9773i	0.168749	−	0.139601i
$359$	−435.687	+	83.1118i	−1.21361	+	0.231509i	−0.754159	−	0.656692i	$-0.771955\pi$
$359$	−435.687	+	83.1118i	−1.21361	+	0.231509i	−0.459455	+	0.888201i	$0.651955\pi$
$360$	−940.060	+	1013.03i	−2.61128	+	2.81397i
$361$	−182.474	+	23.0518i	−0.505468	+	0.0638555i
$362$	−196.284	−	24.7964i	−0.542220	−	0.0684983i
$363$	27.0490	−	24.6797i	0.0745152	−	0.0679881i
$364$	−99.6894	−	211.851i	−0.273872	−	0.582007i
$365$	547.592	−	326.231i	1.50025	−	0.893784i
$366$	−131.186	+	637.818i	−0.358433	+	1.74267i
$367$	25.3478	−	98.7233i	0.0690677	−	0.269001i	−0.924665	−	0.380781i	$-0.875655\pi$
$367$	25.3478	−	98.7233i	0.0690677	−	0.269001i	0.993733	+	0.111780i	$0.0356552\pi$
$368$	189.017	−	581.734i	0.513633	−	1.58080i
$369$	59.3172	+	262.038i	0.160751	+	0.710130i
$370$	427.981	−	186.843i	1.15670	−	0.504982i
$371$	−34.0721	−	28.1869i	−0.0918386	−	0.0759755i
$372$	−1526.56	−	215.156i	−4.10366	−	0.578376i
$373$	−338.315	+	159.199i	−0.907011	+	0.426807i	−0.821944	−	0.569568i	$-0.807110\pi$
$373$	−338.315	+	159.199i	−0.907011	+	0.426807i	−0.0850668	+	0.996375i	$0.527110\pi$
$374$			503.270i			1.34564i
$375$	−266.406	+	263.919i	−0.710415	+	0.703783i
$376$	906.968			2.41215
$377$	47.7773	+	101.532i	0.126730	+	0.269316i
$378$	165.554	−	546.014i	0.437973	−	1.44448i
$379$	276.150	−	333.808i	0.728628	−	0.880760i	−0.267949	−	0.963433i	$-0.586346\pi$
$379$	276.150	−	333.808i	0.728628	−	0.880760i	0.996577	+	0.0826731i	$0.0263457\pi$
$380$	1025.00	−	909.542i	2.69736	−	2.39353i
$381$	−115.853	+	35.8125i	−0.304075	+	0.0939961i
$382$	−692.938	−	225.149i	−1.81397	−	0.589395i
$383$	207.943	+	53.3906i	0.542931	+	0.139401i	0.510188	−	0.860063i	$-0.329576\pi$
$383$	207.943	+	53.3906i	0.542931	+	0.139401i	0.0327429	+	0.999464i	$0.489576\pi$
$384$	−518.228	+	2519.58i	−1.34955	+	6.56141i
$385$	−25.2501	+	276.629i	−0.0655848	+	0.718516i
$386$	−94.9266	+	44.6691i	−0.245924	+	0.115723i
$387$	331.673	−	258.712i	0.857035	−	0.668506i
$388$	−108.628	+	859.880i	−0.279969	+	2.21618i
$389$	14.3179	+	113.337i	0.0368068	+	0.291356i	0.999764	+	0.0217032i	$0.00690890\pi$
$389$	14.3179	+	113.337i	0.0368068	+	0.291356i	−0.962958	+	0.269653i	$0.913091\pi$
$390$	−9.47784	+	222.615i	−0.0243022	+	0.570807i
$391$	18.6144	+	97.5800i	0.0476071	+	0.249565i
$392$	−403.866	−	488.190i	−1.03027	−	1.24538i
$393$	−32.2430	−	133.506i	−0.0820432	−	0.339710i
$394$	−0.803278	−	12.7677i	−0.00203878	−	0.0324054i
$395$	−134.805	−	38.6940i	−0.341279	−	0.0979595i
$396$	558.474	−	950.186i	1.41029	−	2.39946i
$397$	−106.434	−	88.0503i	−0.268097	−	0.221789i	0.493655	−	0.869658i	$-0.335661\pi$
$397$	−106.434	−	88.0503i	−0.268097	−	0.221789i	−0.761752	+	0.647869i	$0.775661\pi$
$398$	−388.049	−	213.332i	−0.974998	−	0.536009i
$399$	−142.277	+	344.804i	−0.356583	+	0.864171i
$400$	−453.870	+	1816.21i	−1.13467	+	4.54053i
$401$	−659.241	+	214.200i	−1.64399	+	0.534165i	−0.977426	−	0.211280i	$-0.932237\pi$
$401$	−659.241	+	214.200i	−1.64399	+	0.534165i	−0.666567	+	0.745445i	$0.732237\pi$
$402$	330.892	−	1216.00i	0.823115	−	3.02487i
$403$	−138.364	+	87.8082i	−0.343334	+	0.217886i
$404$	−406.324	+	257.861i	−1.00575	+	0.638270i
$405$	−283.896	+	288.840i	−0.700977	+	0.713184i
$406$	−403.702	−	487.992i	−0.994340	−	1.20195i
$407$	−198.648	+	144.326i	−0.488079	+	0.354610i
$408$	−330.914	−	1070.50i	−0.811063	−	2.62377i
$409$	89.7798	−	190.792i	0.219510	−	0.466484i	−0.764493	−	0.644632i	$-0.777011\pi$
$409$	89.7798	−	190.792i	0.219510	−	0.466484i	0.984004	+	0.178148i	$0.0570107\pi$
$410$	393.047	+	442.939i	0.958652	+	1.08034i
$411$	311.381	+	387.591i	0.757617	+	0.943044i
$412$	1203.33	−	229.548i	2.92071	−	0.557156i
$413$	−10.5051	+	5.77520i	−0.0254360	+	0.0139835i
$414$	98.0572	−	274.694i	0.236853	−	0.663511i
$415$	−333.600	−	51.7358i	−0.803856	−	0.124665i
$416$	314.295	+	571.701i	0.755518	+	1.37428i
$417$	−31.5365	−	0.452751i	−0.0756271	−	0.00108573i
$418$	−567.811	+	781.524i	−1.35840	+	1.86968i
$419$	69.2257	−	269.616i	0.165217	−	0.643476i	−0.830977	−	0.556307i	$-0.812218\pi$
$419$	69.2257	−	269.616i	0.165217	−	0.643476i	0.996194	−	0.0871691i	$-0.0277820\pi$
$420$	−194.419	−	917.652i	−0.462902	−	2.18489i
$421$	0.128801	−	2.04723i	0.000305940	−	0.00486277i	−0.997871	−	0.0652217i	$-0.979225\pi$
$421$	0.128801	−	2.04723i	0.000305940	−	0.00486277i	0.998177	+	0.0603589i	$0.0192245\pi$
$422$	892.812	−	229.235i	2.11567	−	0.543211i
$423$	265.680	+	7.62999i	0.628085	+	0.0180378i
$424$	206.276	+	149.868i	0.486500	+	0.353463i
$425$	−77.5067	−	293.991i	−0.182369	−	0.691743i
$426$	1198.85	−	736.891i	2.81421	−	1.72979i
$427$	−199.475	−	212.419i	−0.467155	−	0.497469i
$428$	1800.80	+	712.987i	4.20748	+	1.66586i
$429$	−20.2988	−	115.385i	−0.0473164	−	0.268963i
$430$	365.474	−	852.081i	0.849939	−	1.98158i
$431$	161.111	+	102.244i	0.373806	+	0.237225i	0.709437	−	0.704769i	$-0.248949\pi$
$431$	161.111	+	102.244i	0.373806	+	0.237225i	−0.335630	+	0.941994i	$0.608949\pi$
$432$	−464.006	+	1967.87i	−1.07409	+	4.55524i
$433$	−275.754	−	174.999i	−0.636845	−	0.404154i	0.177839	−	0.984060i	$-0.443089\pi$
$433$	−275.754	−	174.999i	−0.636845	−	0.404154i	−0.814684	+	0.579906i	$0.803089\pi$
$434$	633.154	−	674.241i	1.45888	−	1.55355i
$435$	93.1775	+	439.796i	0.214201	+	1.01103i
$436$	1698.85	+	933.949i	3.89644	+	2.14208i
$437$	−81.1877	+	172.533i	−0.185784	+	0.394811i
$438$	749.989	−	1319.01i	1.71230	−	3.01145i
$439$	−153.296	−	84.2753i	−0.349194	−	0.191971i	0.297498	−	0.954723i	$-0.403848\pi$
$439$	−153.296	−	84.2753i	−0.349194	−	0.191971i	−0.646692	+	0.762752i	$0.723848\pi$
$440$	45.1512	−	1601.03i	0.102616	−	3.63869i
$441$	−114.198	−	146.404i	−0.258953	−	0.331982i
$442$	−152.529	−	96.7976i	−0.345088	−	0.218999i
$443$	−527.600			−1.19097			−0.595485	−	0.803366i	$-0.703040\pi$
$443$	−527.600			−1.19097			−0.595485	+	0.803366i	$0.703040\pi$
$444$	496.950	−	663.743i	1.11926	−	1.49492i
$445$	−26.2706	+	15.6508i	−0.0590350	+	0.0351704i
$446$	82.5942	+	321.683i	0.185189	+	0.721263i
$447$	−669.889	−	327.052i	−1.49863	−	0.731661i
$448$	−1428.53	−	1521.23i	−3.18868	−	3.39560i
$449$	−409.917	−	564.202i	−0.912955	−	1.25657i	−0.966147	−	0.257991i	$-0.916940\pi$
$449$	−409.917	−	564.202i	−0.912955	−	1.25657i	0.0531924	−	0.998584i	$-0.483060\pi$
$450$	−241.196	+	859.477i	−0.535992	+	1.90995i
$451$	−251.904	−	183.019i	−0.558545	−	0.405807i
$452$	−2081.26	+	262.924i	−4.60455	+	0.581690i
$453$	−5.64523	−	32.0894i	−0.0124619	−	0.0708375i
$454$	14.3053	−	227.376i	0.0315094	−	0.500827i
$455$	−78.9827	−	60.8587i	−0.173588	−	0.133755i
$456$	693.907	−	2035.72i	1.52173	−	4.46429i
$457$	−58.9581	+	81.1489i	−0.129011	+	0.177569i	−0.868636	−	0.495451i	$-0.835003\pi$
$457$	−58.9581	+	81.1489i	−0.129011	+	0.177569i	0.739625	+	0.673019i	$0.235003\pi$
$458$	−4.93205	−	78.3927i	−0.0107687	−	0.171163i
$459$	−87.9294	−	316.367i	−0.191567	−	0.689252i
$460$	−76.5385	−	473.369i	−0.166388	−	1.02906i
$461$	83.9184	+	16.0083i	0.182036	+	0.0347251i	0.277593	−	0.960699i	$-0.410463\pi$
$461$	83.9184	+	16.0083i	0.182036	+	0.0347251i	−0.0955574	+	0.995424i	$0.530463\pi$
$462$	272.927	+	602.293i	0.590751	+	1.30366i
$463$	540.335	−	103.074i	1.16703	−	0.222623i	0.432779	−	0.901500i	$-0.357533\pi$
$463$	540.335	−	103.074i	1.16703	−	0.222623i	0.734252	+	0.678877i	$0.237533\pi$
$464$	1536.31	+	1636.00i	3.31101	+	3.52587i
$465$	−620.161	+	215.503i	−1.33368	+	0.463447i
$466$	−419.235	+	890.919i	−0.899645	+	1.91184i
$467$	−105.409	+	41.7343i	−0.225715	+	0.0893668i	−0.478260	−	0.878218i	$-0.658732\pi$
$467$	−105.409	+	41.7343i	−0.225715	+	0.0893668i	0.252545	+	0.967585i	$0.418732\pi$
$468$	180.562	+	352.016i	0.385816	+	0.752170i
$469$	359.471	+	434.526i	0.766462	+	0.926494i
$470$	521.127	−	267.646i	1.10878	−	0.569459i
$471$	−31.0130	−	58.3823i	−0.0658451	−	0.123954i
$472$	58.3614	−	37.0372i	0.123647	−	0.0784687i
$473$	−91.3479	+	478.863i	−0.193125	+	1.01239i
$474$	−324.529	+	78.3769i	−0.684660	+	0.165352i
$475$	211.333	−	543.982i	0.444912	−	1.14522i
$476$	723.290	+	235.011i	1.51952	+	0.493721i
$477$	59.1640	+	45.6365i	0.124034	+	0.0956740i
$478$	−19.3117	−	15.9760i	−0.0404010	−	0.0334226i
$479$	9.96765	−	25.1754i	0.0208093	−	0.0525583i	−0.919000	−	0.394257i	$-0.871002\pi$
$479$	9.96765	−	25.1754i	0.0208093	−	0.0525583i	0.939810	+	0.341698i	$0.111002\pi$
$480$	701.220	+	2517.92i	1.46087	+	5.24566i
$481$	−5.53426	−	87.9646i	−0.0115057	−	0.182878i
$482$	−22.4416	−	69.0681i	−0.0465593	−	0.143295i
$483$	75.1952	+	106.685i	0.155684	+	0.220880i
$484$	−26.8518	−	140.762i	−0.0554789	−	0.290831i
$485$	126.148	+	346.879i	0.260099	+	0.715214i
$486$	−248.104	+	931.623i	−0.510502	+	1.91692i
$487$	−15.4537	+	122.329i	−0.0317325	+	0.251189i	0.968267	+	0.249919i	$0.0804041\pi$
$487$	−15.4537	+	122.329i	−0.0317325	+	0.251189i	−0.999999	+	0.00126939i	$0.999596\pi$
$488$	1224.80	+	1150.17i	2.50984	+	2.35690i
$489$	−159.369	−	420.039i	−0.325908	−	0.858976i
$490$	−376.118	−	161.324i	−0.767588	−	0.329233i
$491$	−23.2666	+	184.174i	−0.0473861	+	0.375100i	0.950533	+	0.310623i	$0.100538\pi$
$491$	−23.2666	+	184.174i	−0.0473861	+	0.375100i	−0.997919	+	0.0644766i	$0.979462\pi$
$492$	995.227	+	339.239i	2.02282	+	0.689511i
$493$	−346.646	−	112.632i	−0.703135	−	0.228462i
$494$	−127.649	−	322.405i	−0.258399	−	0.652643i
$495$	26.6951	−	468.611i	0.0539294	−	0.946689i
$496$	−2089.19	+	2525.39i	−4.21207	+	5.09152i
$497$	−39.5408	+	628.484i	−0.0795590	+	1.26455i
$498$	−751.357	+	285.076i	−1.50875	+	0.572442i
$499$	−864.448			−1.73236			−0.866181	−	0.499731i	$-0.833432\pi$
$499$	−864.448			−1.73236			−0.866181	+	0.499731i	$0.833432\pi$
$500$	333.975	+	1429.09i	0.667950	+	2.85818i
$501$	−70.0410	+	905.614i	−0.139802	+	1.80761i
$502$	111.466	−	52.4521i	0.222044	−	0.104486i
$503$	−19.0384	+	302.607i	−0.0378497	+	0.601604i	0.932692	+	0.360673i	$0.117453\pi$
$503$	−19.0384	+	302.607i	−0.0378497	+	0.601604i	−0.970542	+	0.240931i	$0.922547\pi$
$504$	−976.562	−	1101.67i	−1.93762	−	2.18585i
$505$	−103.756	+	176.739i	−0.205457	+	0.349978i
$506$	124.437	+	314.292i	0.245923	+	0.621130i
$507$	−429.794	−	177.346i	−0.847721	−	0.349795i
$508$	−118.020	+	459.659i	−0.232323	+	0.904840i
$509$	−26.5557	+	210.210i	−0.0521722	+	0.412986i	0.944302	+	0.329081i	$0.106739\pi$
$509$	−26.5557	+	210.210i	−0.0521722	+	0.412986i	−0.996474	+	0.0839044i	$0.973261\pi$
$510$	−506.040	−	517.435i	−0.992234	−	1.01458i
$511$	289.104	+	614.378i	0.565762	+	1.20230i
$512$	2806.00	+	2635.01i	5.48047	+	5.14650i
$513$	220.393	−	590.489i	0.429616	−	1.15105i
$514$	−630.579	+	79.6606i	−1.22681	+	0.154982i
$515$	411.192	−	321.080i	0.798431	−	0.623457i
$516$	−182.859	−	1636.03i	−0.354378	−	3.17060i
$517$	−237.344	+	196.348i	−0.459080	+	0.379784i
$518$	153.725	+	473.115i	0.296766	+	0.913350i
$519$	−556.804	−	7.99371i	−1.07284	−	0.0154021i
$520$	476.546	+	321.621i	0.916436	+	0.618502i
$521$	245.807	−	620.838i	0.471799	−	1.19163i	−0.477886	−	0.878422i	$-0.658597\pi$
$521$	245.807	−	620.838i	0.471799	−	1.19163i	0.949685	−	0.313206i	$-0.101403\pi$
$522$	709.881	+	800.824i	1.35992	+	1.53415i
$523$	331.187	−	602.427i	0.633245	−	1.15187i	−0.343841	−	0.939028i	$-0.611728\pi$
$523$	331.187	−	602.427i	0.633245	−	1.15187i	0.977087	−	0.212841i	$-0.0682717\pi$
$524$	−511.201	−	166.099i	−0.975575	−	0.316983i
$525$	−252.190	−	309.803i	−0.480362	−	0.590102i
$526$	102.272	+	314.761i	0.194433	+	0.598404i
$527$	99.7422	−	522.867i	0.189264	−	0.992158i
$528$	−1099.24	−	2069.34i	−2.08190	−	3.91920i
$529$	−247.700	−	390.313i	−0.468243	−	0.737833i
$530$	162.748	+	25.2395i	0.307072	+	0.0476218i
$531$	17.4075	−	10.3584i	0.0327824	−	0.0195074i
$532$	858.042	+	1180.99i	1.61286	+	2.21991i
$533$	103.919	−	41.1444i	0.194970	−	0.0771940i
$534$	−35.9805	+	63.2793i	−0.0673793	+	0.118501i
$535$	820.907	−	80.2680i	1.53441	−	0.150034i
$536$	−2225.93	−	2370.37i	−4.15285	−	4.42233i
$537$	−6.58541	−	58.9192i	−0.0122633	−	0.109719i
$538$	683.929	+	1244.06i	1.27124	+	2.31238i
$539$	211.375	+	40.3220i	0.392162	+	0.0748089i
$540$	381.221	+	1538.48i	0.705965	+	2.84903i
$541$	−223.179	+	122.694i	−0.412531	+	0.226791i	−0.674484	−	0.738290i	$-0.735634\pi$
$541$	−223.179	+	122.694i	−0.412531	+	0.226791i	0.261952	+	0.965081i	$0.415634\pi$
$542$	48.1756	+	765.729i	0.0888848	+	1.41278i
$543$	−97.0033	+	113.888i	−0.178643	+	0.209738i
$544$	−2052.54	−	527.003i	−3.77305	−	0.968756i
$545$	825.276	+	23.2740i	1.51427	+	0.0427045i
$546$	−235.034	−	33.1260i	−0.430465	−	0.0606704i
$547$	28.4067	+	110.637i	0.0519318	+	0.202261i	0.989255	−	0.146200i	$-0.0467043\pi$
$547$	28.4067	+	110.637i	0.0519318	+	0.202261i	−0.937323	+	0.348461i	$0.886704\pi$
$548$	1930.40	−	243.867i	3.52263	−	0.445012i
$549$	349.107	+	347.224i	0.635897	+	0.632466i
$550$	−446.518	−	933.242i	−0.811851	−	1.69680i
$551$	−411.227	−	566.005i	−0.746328	−	1.02723i
$552$	−471.342	−	586.704i	−0.853881	−	1.06287i
$553$	54.9982	−	138.910i	0.0994543	−	0.251193i
$554$	126.584	+	493.013i	0.228491	+	0.889915i
$555$	59.1186	−	348.129i	0.106520	−	0.627260i
$556$	−66.1390	+	104.218i	−0.118955	+	0.187443i
$557$	−77.8608			−0.139786			−0.0698930	−	0.997554i	$-0.522266\pi$
$557$	−77.8608			−0.139786			−0.0698930	+	0.997554i	$0.522266\pi$
$558$	−1030.37	+	1175.12i	−1.84654	+	2.10595i
$559$	−127.562	−	119.788i	−0.228196	−	0.214291i
$560$	−1878.50	−	669.473i	−3.35447	−	1.19549i
$561$	318.347	+	208.499i	0.567464	+	0.371656i
$562$	1284.32	+	604.356i	2.28527	+	1.07537i
$563$	−89.4326	+	190.054i	−0.158850	+	0.337574i	−0.968370	−	0.249519i	$-0.919728\pi$
$563$	−89.4326	+	190.054i	−0.158850	+	0.337574i	0.809520	+	0.587093i	$0.199728\pi$
$564$	569.912	−	870.171i	1.01048	−	1.54286i
$565$	−737.277	+	504.533i	−1.30492	+	0.892979i
$566$	−527.385	+	561.608i	−0.931775	+	0.992240i
$567$	−276.798	−	330.930i	−0.488180	−	0.583650i
$568$		−	3630.98i		−	6.39257i
$569$	626.903	+	397.845i	1.10176	+	0.699200i	0.956948	−	0.290259i	$-0.0937416\pi$
$569$	626.903	+	397.845i	1.10176	+	0.699200i	0.144814	+	0.989459i	$0.453742\pi$
$570$	−202.033	−	1374.45i	−0.354444	−	2.41132i
$571$	−160.590	+	41.2326i	−0.281244	+	0.0722112i	−0.386677	−	0.922215i	$-0.626377\pi$
$571$	−160.590	+	41.2326i	−0.281244	+	0.0722112i	0.105433	+	0.994426i	$0.466377\pi$
$572$	−426.306	−	168.787i	−0.745290	−	0.295081i
$573$	−429.496	+	345.046i	−0.749557	+	0.602174i
$574$	−510.351	+	370.792i	−0.889114	+	0.645979i
$575$	−121.094	−	164.433i	−0.210598	−	0.285970i
$576$	2500.11	+	2486.62i	4.34047	+	4.31705i
$577$	39.1697	+	310.060i	0.0678850	+	0.537365i	0.988982	+	0.148033i	$0.0472942\pi$
$577$	39.1697	+	310.060i	0.0678850	+	0.537365i	−0.921097	+	0.389332i	$0.872706\pi$
$578$	−542.220	+	139.218i	−0.938097	+	0.240862i
$579$	−11.0713	+	78.5524i	−0.0191214	+	0.135669i
$580$	1657.28	+	590.634i	2.85739	+	1.01833i
$581$	89.4335	−	348.320i	0.153930	−	0.599519i
$582$	668.898	+	569.730i	1.14931	+	0.978918i
$583$	−86.4251	+	5.43741i	−0.148242	+	0.00932660i
$584$	−1886.11	−	3430.82i	−3.22964	−	5.87469i
$585$	136.890	+	98.2220i	0.234000	+	0.167901i
$586$	232.000	−	1216.19i	0.395905	−	2.07541i
$587$	522.932	−	287.485i	0.890856	−	0.489752i	0.0305518	−	0.999533i	$-0.490274\pi$
$587$	522.932	−	287.485i	0.890856	−	0.489752i	0.860304	+	0.509781i	$0.170274\pi$
$588$	−722.160	+	80.7161i	−1.22816	+	0.137272i
$589$	744.809	−	699.422i	1.26453	−	1.18747i
$590$	22.6036	−	38.5033i	0.0383113	−	0.0652598i
$591$	−8.40911	−	4.78141i	−0.0142286	−	0.00809037i
$592$	−648.931	−	1639.01i	−1.09617	−	2.76860i
$593$	58.9030	−	42.7956i	0.0993306	−	0.0721679i	−0.537011	−	0.843575i	$-0.680447\pi$
$593$	58.9030	−	42.7956i	0.0993306	−	0.0721679i	0.636342	+	0.771407i	$0.280447\pi$
$594$	−495.623	−	1001.39i	−0.834383	−	1.68584i
$595$	319.724	−	51.6959i	0.537352	−	0.0868838i
$596$	−2463.27	+	1563.24i	−4.13300	+	2.62288i
$597$	−295.709	+	157.082i	−0.495325	+	0.263119i
$598$	−119.188	−	22.7363i	−0.199311	−	0.0380205i
$599$	610.742	−	198.442i	1.01960	−	0.331289i	0.248931	−	0.968521i	$-0.419921\pi$
$599$	610.742	−	198.442i	1.01960	−	0.331289i	0.770672	+	0.637232i	$0.219921\pi$
$600$	1563.41	+	1691.49i	2.60569	+	2.81914i
$601$	306.301	−	942.698i	0.509653	−	1.56855i	−0.283153	−	0.959075i	$-0.591380\pi$
$601$	306.301	−	942.698i	0.509653	−	1.56855i	0.792805	−	0.609475i	$-0.208620\pi$
$602$	865.492	+	475.808i	1.43769	+	0.790379i
$603$	−632.103	−	713.082i	−1.04826	−	1.18256i
$604$	−118.559	−	46.9407i	−0.196289	−	0.0777164i
$605$	−37.5589	−	48.0999i	−0.0620808	−	0.0795039i
$606$	−7.00326	+	487.814i	−0.0115565	+	0.804973i
$607$	−912.832	+	296.597i	−1.50384	+	0.488628i	−0.941136	−	0.338029i	$-0.890240\pi$
$607$	−912.832	+	296.597i	−1.50384	+	0.488628i	−0.562707	+	0.826657i	$0.690240\pi$
$608$	−2592.79	−	3134.14i	−4.26445	−	5.15484i
$609$	−475.932	+	53.1951i	−0.781498	+	0.0873482i
$610$	1043.16	+	299.425i	1.71010	+	0.490860i
$611$	−13.8581	−	109.698i	−0.0226810	−	0.179539i
$612$	−1235.00	−	355.181i	−2.01798	−	0.580361i
$613$	7.07108	−	7.52993i	0.0115352	−	0.0122837i	−0.723175	−	0.690665i	$-0.757318\pi$
$613$	7.07108	−	7.52993i	0.0115352	−	0.0122837i	0.734710	+	0.678381i	$0.237318\pi$
$614$	−1192.95	+	561.361i	−1.94292	+	0.914268i
$615$	443.020	−	65.1200i	0.720357	−	0.105886i
$616$	1692.73	+	213.842i	2.74794	+	0.347145i
$617$	−860.106	−	220.838i	−1.39401	−	0.357922i	−0.524323	−	0.851519i	$-0.675682\pi$
$617$	−860.106	−	220.838i	−1.39401	−	0.357922i	−0.869691	+	0.493597i	$0.835682\pi$
$618$	473.701	−	1148.00i	0.766507	−	1.85761i
$619$	512.886	−	203.066i	0.828572	−	0.328055i	0.0847249	−	0.996404i	$-0.472999\pi$
$619$	512.886	−	203.066i	0.828572	−	0.328055i	0.743848	+	0.668349i	$0.232999\pi$
$620$	−552.419	+	2509.33i	−0.890998	+	4.04731i
$621$	−133.135	−	175.829i	−0.214389	−	0.283139i
$622$	1412.08	+	88.8405i	2.27022	+	0.142830i
$623$	−13.8697	−	29.4746i	−0.0222628	−	0.0473108i
$624$	838.590	+	64.8573i	1.34389	+	0.103938i
$625$	404.563	+	476.397i	0.647301	+	0.762235i
$626$		−	2237.17i		−	3.57376i
$627$	259.121	+	682.949i	0.413271	+	1.08923i
$628$	−258.210	−	16.2452i	−0.411163	−	0.0258682i
$629$	220.591	+	182.489i	0.350701	+	0.290125i
$630$	−886.216	−	344.816i	−1.40669	−	0.547327i
$631$	93.3697	−	36.9677i	0.147971	−	0.0585858i	−0.292972	−	0.956121i	$-0.594644\pi$
$631$	93.3697	−	36.9677i	0.147971	−	0.0585858i	0.440943	+	0.897535i	$0.354644\pi$
$632$	−266.200	+	819.280i	−0.421203	+	1.29633i
$633$	224.878	−	659.724i	0.355257	−	1.04222i
$634$	213.869	+	27.0179i	0.337332	+	0.0426150i
$635$	44.7226	+	197.092i	0.0704293	+	0.310382i
$636$	273.405	−	103.734i	0.429883	−	0.163104i
$637$	−52.8759	+	56.3071i	−0.0830077	+	0.0883942i
$638$	−1230.48	−	155.445i	−1.92865	−	0.243645i
$639$	30.5461	−	1063.63i	0.0478030	−	1.66452i
$640$	4120.81	+	1182.82i	6.43877	+	1.84816i
$641$	174.976	−	33.3785i	0.272974	−	0.0520725i	−0.0490769	−	0.998795i	$-0.515628\pi$
$641$	174.976	−	33.3785i	0.272974	−	0.0520725i	0.322050	+	0.946723i	$0.395628\pi$
$642$	1604.89	−	1131.18i	2.49982	−	1.76196i
$643$	−564.504	+	183.418i	−0.877922	+	0.285254i	−0.713094	−	0.701068i	$-0.752707\pi$
$643$	−564.504	+	183.418i	−0.877922	+	0.285254i	−0.164828	+	0.986322i	$0.552707\pi$
$644$	509.802	−	32.0740i	0.791617	−	0.0498043i
$645$	−387.579	−	584.191i	−0.600897	−	0.905722i
$646$	1047.24	+	414.630i	1.62111	+	0.641842i
$647$	−74.7632	+	90.3732i	−0.115554	+	0.139680i	−0.825118	−	0.564960i	$-0.808892\pi$
$647$	−74.7632	+	90.3732i	−0.115554	+	0.139680i	0.709565	+	0.704640i	$0.248892\pi$
$648$	1712.67	+	1804.15i	2.64301	+	2.78418i
$649$	−7.25443	+	22.3268i	−0.0111779	+	0.0344019i
$650$	368.724	+	44.1687i	0.567268	+	0.0679519i
$651$	−164.187	−	679.837i	−0.252208	−	1.04430i
$652$	−1727.06	−	329.455i	−2.64887	−	0.505299i
$653$	−240.229	−	378.541i	−0.367886	−	0.579695i	0.609075	−	0.793112i	$-0.291541\pi$
$653$	−240.229	−	378.541i	−0.367886	−	0.579695i	−0.976961	+	0.213417i	$0.931541\pi$
$654$	1735.65	−	921.986i	2.65389	−	1.40976i
$655$	−225.972	+	36.5372i	−0.344996	+	0.0557820i
$656$	1722.40	−	1424.89i	2.62561	−	2.17209i
$657$	−523.639	−	1020.86i	−0.797015	−	1.55383i
$658$	229.735	+	580.245i	0.349142	+	0.881832i
$659$	272.029	+	128.007i	0.412791	+	0.194245i	0.620950	−	0.783850i	$-0.286747\pi$
$659$	272.029	+	128.007i	0.412791	+	0.194245i	−0.208159	+	0.978095i	$0.566747\pi$
$660$	−1507.70	−	1049.36i	−2.28439	−	1.58993i
$661$	−132.084	+	124.035i	−0.199824	+	0.187647i	−0.777999	−	0.628266i	$-0.783765\pi$
$661$	−132.084	+	124.035i	−0.199824	+	0.187647i	0.578175	+	0.815913i	$0.303765\pi$
$662$	−304.793	−	1597.78i	−0.460413	−	2.41357i
$663$	−124.421	+	56.3809i	−0.187664	+	0.0850391i
$664$	−388.544	+	2036.82i	−0.585157	+	3.06750i
$665$	554.823	+	280.448i	0.834320	+	0.421727i
$666$	−286.874	−	790.111i	−0.430742	−	1.18635i
$667$	−244.329	+	15.3719i	−0.366310	+	0.0230463i
$668$	2875.88	+	2089.45i	4.30521	+	3.12792i
$669$	237.701	+	81.0242i	0.355308	+	0.121112i
$670$	−1978.47	−	705.100i	−2.95294	−	1.05239i
$671$	−569.516	−	35.8309i	−0.848757	−	0.0533993i
$672$	−2742.19	+	482.412i	−4.08065	+	0.717875i
$673$	−7.62391	−	60.3494i	−0.0113282	−	0.0896723i	0.985437	−	0.170041i	$-0.0543901\pi$
$673$	−7.62391	−	60.3494i	−0.0113282	−	0.0896723i	−0.996765	+	0.0803691i	$0.974390\pi$
$674$	−1028.48	+	1415.57i	−1.52593	+	2.10026i
$675$	443.743	+	508.642i	0.657397	+	0.753544i
$676$	−1472.09	+	1069.54i	−2.17765	+	1.58216i
$677$	421.966	−	396.253i	0.623288	−	0.585307i	−0.307192	−	0.951647i	$-0.599390\pi$
$677$	421.966	−	396.253i	0.623288	−	0.585307i	0.930481	+	0.366341i	$0.119390\pi$
$678$	−933.025	+	1911.08i	−1.37614	+	2.81870i
$679$	−380.839	+	97.7828i	−0.560882	+	0.144010i
$680$	−1821.17	+	413.244i	−2.67818	+	0.607712i
$681$	−137.902	−	103.248i	−0.202499	−	0.151612i
$682$		−	1811.28i		−	2.65583i
$683$	−215.315	+	339.281i	−0.315248	+	0.496752i	−0.964593	−	0.263742i	$-0.915043\pi$
$683$	−215.315	+	339.281i	−0.315248	+	0.496752i	0.649345	+	0.760494i	$0.275043\pi$
$684$	−1517.09	−	1944.94i	−2.21797	−	2.84348i
$685$	683.838	−	467.964i	0.998304	−	0.683159i
$686$	708.864	−	1289.42i	1.03333	−	1.87962i
$687$	−51.6312	−	29.3574i	−0.0751545	−	0.0427328i
$688$	−3166.76	−	1490.16i	−4.60285	−	2.16594i
$689$	14.9748	−	27.2391i	0.0217341	−	0.0395343i
$690$	−443.960	−	198.016i	−0.643420	−	0.286979i
$691$	−690.334	−	648.267i	−0.999036	−	0.938157i	−0.000950272	−	1.00000i	$-0.500302\pi$
$691$	−690.334	−	648.267i	−0.999036	−	0.938157i	−0.998086	+	0.0618421i	$0.980302\pi$
$692$	−1167.74	+	1840.07i	−1.68749	+	2.65906i
$693$	494.055	+	76.8813i	0.712923	+	0.110940i
$694$	−714.489	+	1125.85i	−1.02952	+	1.62227i
$695$	−4.77828	+	52.3486i	−0.00687522	+	0.0753217i
$696$	2719.53	−	478.426i	3.90738	−	0.687394i
$697$	−133.645	+	337.549i	−0.191743	+	0.484288i
$698$	1029.69	−	966.946i	1.47521	−	1.38531i
$699$	389.873	+	634.287i	0.557758	+	0.907421i
$700$	−1549.75	+	205.933i	−2.21392	+	0.294190i
$701$	−564.218	+	776.579i	−0.804876	+	1.10782i	0.187218	+	0.982318i	$0.440053\pi$
$701$	−564.218	+	776.579i	−0.804876	+	1.10782i	−0.992094	+	0.125498i	$0.959947\pi$
$702$	398.823	+	42.3932i	0.568123	+	0.0603891i
$703$	136.662	+	532.265i	0.194399	+	0.757133i
$704$	−4078.56	−	256.601i	−5.79340	−	0.364490i
$705$	46.5957	−	440.525i	0.0660932	−	0.624858i
$706$	1507.51	+	387.062i	2.13528	+	0.548247i
$707$	−176.623	−	128.324i	−0.249820	−	0.181505i
$708$	1.13798	−	79.2666i	0.00160732	−	0.111958i
$709$	288.342	−	158.517i	0.406688	−	0.223579i	−0.265260	−	0.964177i	$-0.585458\pi$
$709$	288.342	−	158.517i	0.406688	−	0.223579i	0.671948	+	0.740598i	$0.265458\pi$
$710$	−1071.50	−	2086.29i	−1.50915	−	2.93844i
$711$	−84.8708	+	237.754i	−0.119368	+	0.334393i
$712$	90.4856	+	164.593i	0.127086	+	0.231169i
$713$	−66.9934	−	351.192i	−0.0939599	−	0.492555i
$714$	601.045	−	482.864i	0.841800	−	0.676280i
$715$	−194.335	+	19.0020i	−0.271797	+	0.0265762i
$716$	−209.939	−	98.7899i	−0.293211	−	0.137975i
$717$	−18.1063	+	5.59706i	−0.0252529	+	0.00780621i
$718$	1034.35	+	1423.66i	1.44060	+	1.98282i
$719$	−737.419	+	610.046i	−1.02562	+	0.848464i	−0.988557	−	0.150849i	$-0.951799\pi$
$719$	−737.419	+	610.046i	−1.02562	+	0.848464i	−0.0370603	+	0.999313i	$0.511799\pi$
$720$	3210.91	+	1022.29i	4.45959	+	1.41984i
$721$	297.784	+	469.232i	0.413015	+	0.650807i
$722$	391.000	+	616.117i	0.541551	+	0.853348i
$723$	−52.9868	−	14.4185i	−0.0732874	−	0.0199427i
$724$	180.921	+	556.817i	0.249890	+	0.769084i
$725$	742.735	−	98.6958i	1.02446	−	0.136132i
$726$	−134.290	−	55.4120i	−0.184972	−	0.0763250i
$727$	−226.819	+	412.581i	−0.311992	+	0.567512i	−0.985090	−	0.172042i	$-0.944964\pi$
$727$	−226.819	+	412.581i	−0.311992	+	0.567512i	0.673097	+	0.739554i	$0.264964\pi$
$728$	−390.385	+	471.895i	−0.536243	+	0.648207i
$729$	486.518	+	542.901i	0.667377	+	0.744720i
$730$	−2096.15	−	1414.69i	−2.87144	−	1.93794i
$731$	567.277	−	35.6901i	0.776029	−	0.0488236i
$732$	1873.13	−	452.379i	2.55892	−	0.618004i
$733$	970.458	−	802.832i	1.32395	−	1.09527i	0.335778	−	0.941941i	$-0.391001\pi$
$733$	970.458	−	802.832i	1.32395	−	1.09527i	0.988175	−	0.153328i	$-0.0489991\pi$
$734$	−397.223	+	75.7743i	−0.541176	+	0.103235i
$735$	−257.868	+	171.081i	−0.350841	+	0.232764i
$736$	−1412.11	+	178.391i	−1.91863	+	0.242380i
$737$	1095.66	+	138.414i	1.48665	+	0.187807i
$738$	840.480	−	655.592i	1.13886	−	0.888336i
$739$	483.651	+	1027.81i	0.654466	+	1.39081i	0.906131	+	0.422997i	$0.139022\pi$
$739$	483.651	+	1027.81i	0.654466	+	1.39081i	−0.251665	+	0.967815i	$0.580978\pi$
$740$	−1039.55	−	910.549i	−1.40479	−	1.23047i
$741$	−256.824	−	52.8234i	−0.346590	−	0.0712867i
$742$	−43.6305	+	169.930i	−0.0588012	+	0.229016i
$743$	141.676	−	436.035i	0.190682	−	0.586858i	−0.809318	−	0.587370i	$-0.800163\pi$
$743$	141.676	−	436.035i	0.190682	−	0.586858i	1.00000		0.000512716i	$0.000163203\pi$
$744$	1190.96	+	3852.74i	1.60076	+	5.17841i
$745$	−629.003	+	1071.45i	−0.844299	+	1.43819i
$746$	1143.01	+	945.577i	1.53218	+	1.26753i
$747$	−130.952	+	593.380i	−0.175304	+	0.794351i
$748$	1347.57	−	634.117i	1.80156	−	0.847750i
$749$			878.649i			1.17310i
$750$	1397.46	+	510.533i	1.86328	+	0.680711i
$751$	−1421.84			−1.89327			−0.946634	−	0.322310i	$-0.895541\pi$
$751$	−1421.84			−1.89327			−0.946634	+	0.322310i	$0.895541\pi$
$752$	−941.587	−	2000.97i	−1.25211	−	2.66087i
$753$	13.0003	−	92.2391i	0.0172647	−	0.122496i
$754$	283.778	−	343.029i	0.376363	−	0.454945i
$755$	−54.0458	+	5.28458i	−0.0715839	+	0.00699944i
$756$	−1670.62	+	244.684i	−2.20981	+	0.323656i
$757$	−501.675	−	163.004i	−0.662714	−	0.215329i	−0.0417025	−	0.999130i	$-0.513278\pi$
$757$	−501.675	−	163.004i	−0.662714	−	0.215329i	−0.621012	+	0.783801i	$0.713278\pi$
$758$	−1664.82	−	427.452i	−2.19633	−	0.563921i
$759$	250.360	+	51.4941i	0.329855	+	0.0678446i
$760$	−3294.31	−	1412.99i	−4.33462	−	1.85920i
$761$	566.305	−	266.483i	0.744158	−	0.350174i	−0.0160348	−	0.999871i	$-0.505104\pi$
$761$	566.305	−	266.483i	0.744158	−	0.350174i	0.760193	+	0.649697i	$0.225104\pi$
$762$	324.268	+	355.399i	0.425549	+	0.466403i
$763$	−110.228	+	872.546i	−0.144467	+	1.14357i
$764$	270.233	+	2139.11i	0.353707	+	2.79988i
$765$	−536.954	+	105.731i	−0.701900	+	0.138211i
$766$	−159.605	−	836.678i	−0.208361	−	1.09227i
$767$	−5.37141	−	6.49292i	−0.00700314	−	0.00846534i
$768$	5350.23	−	1292.13i	6.96645	−	1.68246i
$769$	−46.1314	−	733.238i	−0.0599889	−	0.953496i	−0.906789	−	0.421585i	$-0.861474\pi$
$769$	−46.1314	−	733.238i	−0.0599889	−	0.953496i	0.846800	−	0.531911i	$-0.178526\pi$
$770$	1035.71	−	376.654i	1.34508	−	0.489161i
$771$	−210.852	+	431.880i	−0.273478	+	0.560155i
$772$	239.214	+	197.895i	0.309862	+	0.256340i
$773$	−757.878	−	416.647i	−0.980437	−	0.539000i	−0.0908986	−	0.995860i	$-0.528974\pi$
$773$	−757.878	−	416.647i	−0.980437	−	0.539000i	−0.889538	+	0.456860i	$0.848974\pi$
$774$	−1489.02	−	753.629i	−1.92380	−	0.973681i
$775$	278.948	+	1058.08i	0.359932	+	1.36526i
$776$	2156.17	−	700.581i	2.77857	−	0.902811i
$777$	362.959	+	98.7669i	0.467129	+	0.127113i
$778$	382.680	−	242.856i	0.491877	−	0.312154i
$779$	−588.373	+	373.393i	−0.755293	+	0.479323i
$780$	608.020	−	255.115i	0.779512	−	0.327070i
$781$	786.066	+	950.190i	1.00649	+	1.21663i
$782$	318.855	−	231.661i	0.407742	−	0.296242i
$783$	800.663	−	117.268i	1.02256	−	0.149767i
$784$	−657.775	+	1397.84i	−0.838998	+	1.78296i
$785$	−100.977	+	44.0835i	−0.128633	+	0.0561573i
$786$	−424.802	+	341.275i	−0.540460	+	0.434192i
$787$	1253.51	−	239.119i	1.59277	−	0.303836i	0.686689	−	0.726951i	$-0.259063\pi$
$787$	1253.51	−	239.119i	1.59277	−	0.303836i	0.906076	+	0.423115i	$0.139063\pi$
$788$	−33.1750	+	18.2381i	−0.0421003	+	0.0231448i
$789$	241.474	+	65.7089i	0.306051	+	0.0832813i
$790$	88.8154	+	549.298i	0.112425	+	0.695314i
$791$	−458.477	−	833.966i	−0.579617	−	1.05432i
$792$	−2870.92	−	263.548i	−3.62490	−	0.332763i
$793$	120.399	−	165.714i	0.151827	−	0.208972i
$794$	−136.293	+	530.826i	−0.171654	+	0.668547i
$795$	83.3902	−	92.4911i	0.104893	−	0.116341i
$796$	−82.2826	+	1307.84i	−0.103370	+	1.64302i
$797$	−703.535	+	180.637i	−0.882729	+	0.226646i	−0.662734	−	0.748855i	$-0.730604\pi$
$797$	−703.535	+	180.637i	−0.882729	+	0.226646i	−0.219995	+	0.975501i	$0.570604\pi$
$798$	1478.14	−	71.7113i	1.85231	−	0.0898638i
$799$	290.561	+	211.105i	0.363656	+	0.264211i
$800$	4273.72	−	843.832i	5.34214	−	1.05479i
$801$	25.1214	+	48.9756i	0.0313626	+	0.0611431i
$802$	1882.58	+	2004.75i	2.34736	+	2.49968i
$803$	1236.31	+	489.490i	1.53961	+	0.609576i
$804$	−3672.90	+	646.144i	−4.56829	+	0.803662i
$805$	186.885	−	111.338i	0.232156	−	0.138308i
$806$	548.953	+	348.376i	0.681083	+	0.432228i
$807$	1070.28	+	82.7768i	1.32625	+	0.102573i
$808$	1062.85	+	674.506i	1.31541	+	0.834785i
$809$	190.965	−	203.357i	0.236050	−	0.251368i	−0.600027	−	0.799980i	$-0.704843\pi$
$809$	190.965	−	203.357i	0.236050	−	0.251368i	0.836077	+	0.548612i	$0.184843\pi$
$810$	1516.47	+	531.221i	1.87219	+	0.655829i
$811$	−509.770	−	280.248i	−0.628570	−	0.345559i	0.135419	−	0.990788i	$-0.456762\pi$
$811$	−509.770	−	280.248i	−0.628570	−	0.345559i	−0.763989	+	0.645229i	$0.776762\pi$
$812$	−797.996	+	1695.83i	−0.982754	+	2.08846i
$813$	504.326	+	286.759i	0.620327	+	0.352717i
$814$	853.681	+	469.315i	1.04875	+	0.576554i
$815$	−718.353	+	211.213i	−0.881415	+	0.259157i
$816$	−2018.21	+	1841.43i	−2.47330	+	2.25665i
$817$	921.187	+	584.603i	1.12752	+	0.715549i
$818$	−836.579			−1.02271
$819$	−118.326	+	134.949i	−0.144476	+	0.164773i
$820$	690.787	−	1610.53i	0.842424	−	1.96406i
$821$	−177.149	−	689.951i	−0.215773	−	0.840379i	−0.980580	−	0.196120i	$-0.937166\pi$
$821$	−177.149	−	689.951i	−0.215773	−	0.840379i	0.764807	−	0.644259i	$-0.222834\pi$
$822$	865.397	−	1772.56i	1.05279	−	2.15640i
$823$	726.883	+	774.052i	0.883212	+	0.940525i	0.998605	−	0.0527950i	$-0.0168130\pi$
$823$	726.883	+	774.052i	0.883212	+	0.940525i	−0.115394	+	0.993320i	$0.536813\pi$
$824$	−1883.51	−	2592.42i	−2.28581	−	3.14615i
$825$	−775.317	−	104.183i	−0.939778	−	0.126283i
$826$	38.4780	+	27.9559i	0.0465836	+	0.0338449i
$827$	−544.824	+	68.8272i	−0.658795	+	0.0832252i	−0.447621	−	0.894223i	$-0.647729\pi$
$827$	−544.824	+	68.8272i	−0.658795	+	0.0832252i	−0.211174	+	0.977448i	$0.567729\pi$
$828$	−859.077	+	83.5519i	−1.03753	+	0.100908i
$829$	18.7291	−	297.691i	0.0225925	−	0.359097i	−0.970447	−	0.241314i	$-0.922421\pi$
$829$	18.7291	−	297.691i	0.0225925	−	0.359097i	0.993039	−	0.117782i	$-0.0375785\pi$
$830$	377.814	+	1284.98i	0.455197	+	1.54816i
$831$	364.301	+	124.178i	0.438389	+	0.149432i
$832$	862.227	−	1186.75i	1.03633	−	1.42639i
$833$	−15.7540	−	250.403i	−0.0189124	−	0.300603i
$834$	51.6481	+	113.977i	0.0619282	+	0.136663i
$835$	1495.98	+	232.002i	1.79159	+	0.277846i
$836$	2808.06	+	535.667i	3.35893	+	0.640750i
$837$	316.459	+	1138.61i	0.378087	+	1.36034i
$838$	−1084.83	+	206.942i	−1.29454	+	0.246947i
$839$	374.376	+	398.670i	0.446217	+	0.475173i	0.912273	−	0.409582i	$-0.134325\pi$
$839$	374.376	+	398.670i	0.446217	+	0.475173i	−0.466056	+	0.884755i	$0.654325\pi$
$840$	−1955.39	+	1482.18i	−2.32785	+	1.76450i
$841$	24.3690	−	51.7867i	0.0289762	−	0.0615775i
$842$	−7.56686	+	2.99593i	−0.00898677	+	0.00355811i
$843$	914.370	−	562.029i	1.08466	−	0.666701i
$844$	−1738.74	−	2101.78i	−2.06012	−	2.49026i
$845$	−349.575	+	691.580i	−0.413699	+	0.818438i
$846$	−421.413	−	966.645i	−0.498124	−	1.14261i
$847$	54.8892	−	34.8337i	0.0648042	−	0.0411260i
$848$	116.493	−	610.679i	0.137374	−	0.720141i
$849$	136.759	+	566.269i	0.161083	+	0.666983i
$850$	−924.458	+	774.866i	−1.08760	+	0.911607i
$851$	182.880	+	59.4214i	0.214900	+	0.0698253i
$852$	−3483.66	−	2281.60i	−4.08880	−	2.67793i
$853$	75.3491	+	62.3342i	0.0883343	+	0.0730765i	0.680543	−	0.732708i	$-0.261744\pi$
$853$	75.3491	+	62.3342i	0.0883343	+	0.0730765i	−0.592209	+	0.805785i	$0.701744\pi$
$854$	−425.591	+	1074.92i	−0.498351	+	1.25869i
$855$	−953.121	−	441.624i	−1.11476	−	0.516519i
$856$	−318.113	−	5056.26i	−0.371627	−	5.90685i
$857$	−407.471	−	1254.07i	−0.475462	−	1.46332i	−0.845333	−	0.534240i	$-0.820598\pi$
$857$	−407.471	−	1254.07i	−0.475462	−	1.46332i	0.369871	−	0.929083i	$-0.379402\pi$
$858$	−379.927	+	267.786i	−0.442805	+	0.312104i
$859$	171.303	+	898.004i	0.199422	+	1.04541i	0.931378	+	0.364054i	$0.118608\pi$
$859$	171.303	+	898.004i	0.199422	+	1.04541i	−0.731956	+	0.681352i	$0.761392\pi$
$860$	−2742.05	+	95.0166i	−3.18842	+	0.110484i
$861$	23.1143	+	476.441i	0.0268458	+	0.553358i
$862$	94.8838	−	751.083i	0.110074	−	0.871326i
$863$	425.441	+	399.516i	0.492980	+	0.462939i	0.890715	−	0.454561i	$-0.150204\pi$
$863$	425.441	+	399.516i	0.492980	+	0.462939i	−0.397736	+	0.917500i	$0.630204\pi$
$864$	4603.06	−	972.744i	5.32762	−	1.12586i
$865$	−84.3647	+	924.260i	−0.0975314	+	1.06851i
$866$	−162.401	+	1285.54i	−0.187530	+	1.48446i
$867$	−136.572	+	400.662i	−0.157523	+	0.462124i
$868$	−2603.13	−	845.809i	−2.99900	−	0.974434i
$869$	−107.703	−	272.027i	−0.123939	−	0.313034i
$870$	1421.41	−	1077.43i	1.63380	−	1.23842i
$871$	−252.686	+	305.445i	−0.290110	+	0.350683i
$872$	318.414	−	5061.05i	0.365154	−	5.80396i
$873$	637.504	−	187.084i	0.730245	−	0.214300i
$874$	756.517			0.865580
$875$	−547.016	+	379.533i	−0.625162	+	0.433752i
$876$	−4476.80	−	346.240i	−5.11050	−	0.395251i
$877$	−1415.75	+	666.202i	−1.61431	+	0.759637i	−0.999577	−	0.0290961i	$-0.990737\pi$
$877$	−1415.75	+	666.202i	−1.61431	+	0.759637i	−0.614735	+	0.788734i	$0.710737\pi$
$878$	−43.5795	+	692.676i	−0.0496350	+	0.788925i
$879$	−673.194	−	650.607i	−0.765863	−	0.740167i
$880$	−3579.09	+	1562.52i	−4.06715	+	1.77559i
$881$	−486.353	−	1228.39i	−0.552047	−	1.39431i	−0.891213	−	0.453585i	$-0.850145\pi$
$881$	−486.353	−	1228.39i	−0.552047	−	1.39431i	0.339166	−	0.940726i	$-0.389855\pi$
$882$	−332.660	+	657.272i	−0.377166	+	0.745206i
$883$	64.8333	−	252.509i	0.0734239	−	0.285967i	−0.921259	−	0.388949i	$-0.872838\pi$
$883$	64.8333	−	252.509i	0.0734239	−	0.285967i	0.994683	+	0.102982i	$0.0328383\pi$
$884$	−67.0024	+	530.378i	−0.0757945	+	0.599976i
$885$	−14.9911	−	30.2496i	−0.0169391	−	0.0341803i
$886$	891.256	+	1894.02i	1.00593	+	2.13771i
$887$	−61.1549	−	57.4282i	−0.0689457	−	0.0647444i	0.649308	−	0.760525i	$-0.275058\pi$
$887$	−61.1549	−	57.4282i	−0.0689457	−	0.0647444i	−0.718254	+	0.695781i	$0.755058\pi$
$888$	−2124.44	−	436.954i	−2.39238	−	0.492065i
$889$	−213.594	+	26.9832i	−0.240263	+	0.0303523i
$890$	100.562	+	67.8695i	0.112991	+	0.0762579i
$891$	−838.766	−	101.354i	−0.941376	−	0.113753i
$892$	757.278	−	626.475i	0.848966	−	0.702326i
$893$	213.032	+	655.646i	0.238558	+	0.734206i
$894$	−42.4561	+	2957.29i	−0.0474900	+	3.30793i
$895$	−98.7509	+	3.42189i	−0.110336	+	0.00382334i
$896$	−1681.22	+	4246.28i	−1.87636	+	4.73915i
$897$	−63.7601	+	65.9737i	−0.0710815	+	0.0735493i
$898$	−1332.95	+	2424.63i	−1.48436	+	2.70004i
$899$	1247.58	+	405.364i	1.38774	+	0.450905i
$900$	2605.26	−	437.102i	2.89473	−	0.485669i
$901$	31.2005	+	96.0252i	0.0346287	+	0.106576i
$902$	−231.482	+	1213.47i	−0.256631	+	1.34531i
$903$	659.539	−	350.351i	0.730387	−	0.387986i
$904$	2940.28	+	4633.14i	3.25252	+	5.12516i
$905$	176.872	+	175.736i	0.195439	+	0.194183i
$906$	−105.660	+	74.4730i	−0.116623	+	0.0821998i
$907$	−266.329	−	366.571i	−0.293638	−	0.404157i	0.636554	−	0.771232i	$-0.280359\pi$
$907$	−266.329	−	366.571i	−0.293638	−	0.404157i	−0.930191	+	0.367075i	$0.880359\pi$
$908$	−626.850	+	248.188i	−0.690364	+	0.273334i
$909$	305.669	+	206.526i	0.336269	+	0.227201i
$910$	−85.0520	+	386.344i	−0.0934638	+	0.424554i
$911$	112.161	+	119.440i	0.123119	+	0.131108i	0.787575	−	0.616219i	$-0.211337\pi$
$911$	112.161	+	119.440i	0.123119	+	0.131108i	−0.664456	+	0.747328i	$0.731337\pi$
$912$	−5211.64	+	582.506i	−5.71451	+	0.638713i
$913$	−339.270	−	617.130i	−0.371599	−	0.675937i
$914$	390.910	+	74.5700i	0.427691	+	0.0815864i
$915$	621.573	−	535.810i	0.679315	−	0.585585i
$916$	−203.692	+	111.980i	−0.222371	+	0.122249i
$917$	−15.3112	−	243.364i	−0.0166970	−	0.265391i
$918$	−987.178	+	850.082i	−1.07536	+	0.926015i
$919$	314.922	+	80.8583i	0.342679	+	0.0879851i	0.416108	−	0.909315i	$-0.363394\pi$
$919$	314.922	+	80.8583i	0.342679	+	0.0879851i	−0.0734282	+	0.997301i	$0.523394\pi$
$920$	−1035.14	+	708.365i	−1.12515	+	0.769962i
$921$	−139.134	+	987.176i	−0.151068	+	1.07185i
$922$	−84.2927	−	328.298i	−0.0914237	−	0.356072i
$923$	−439.169	+	55.4799i	−0.475806	+	0.0601082i
$924$	1268.83	−	1489.68i	1.37319	−	1.61221i
$925$	−570.964	−	142.683i	−0.617258	−	0.154252i
$926$	−1282.79	−	1765.61i	−1.38530	−	1.90671i
$927$	−529.930	−	775.248i	−0.571661	−	0.836298i
$928$	1922.47	−	4855.61i	2.07163	−	5.23234i
$929$	−126.303	−	491.917i	−0.135956	−	0.529512i	−0.999674	−	0.0255370i	$-0.991870\pi$
$929$	−126.303	−	491.917i	−0.135956	−	0.529512i	0.863718	−	0.503975i	$-0.168130\pi$
$930$	1821.24	+	1862.25i	1.95833	+	2.00242i
$931$	258.050	−	406.622i	0.277175	−	0.436759i
$932$	2913.78			3.12637
$933$	641.205	−	856.415i	0.687251	−	0.917916i
$934$	327.884	+	307.903i	0.351053	+	0.329661i
$935$	387.118	−	502.403i	0.414030	−	0.537330i
$936$	632.060	−	819.414i	0.675277	−	0.875442i
$937$	1275.99	+	600.433i	1.36178	+	0.640804i	0.961300	−	0.275503i	$-0.0888443\pi$
$937$	1275.99	+	600.433i	1.36178	+	0.640804i	0.400477	+	0.916307i	$0.368844\pi$
$938$	952.649	−	2024.48i	1.01562	−	2.15830i
$939$	−1415.14	−	926.836i	−1.50707	−	0.987045i
$940$	−1373.27	−	1058.15i	−1.46092	−	1.12569i
$941$	780.989	−	831.669i	0.829956	−	0.883814i	−0.164775	−	0.986331i	$-0.552690\pi$
$941$	780.989	−	831.669i	0.829956	−	0.883814i	0.994731	+	0.102517i	$0.0326897\pi$
$942$	−157.196	+	209.956i	−0.166874	+	0.222883i
$943$			243.843i			0.258583i
$944$	−142.301	−	90.3072i	−0.150743	−	0.0956644i
$945$	−585.265	+	417.729i	−0.619328	+	0.442041i
$946$	1873.36	−	480.998i	1.98030	−	0.508455i
$947$	457.857	+	181.278i	0.483481	+	0.191424i	0.597205	−	0.802089i	$-0.296278\pi$
$947$	457.857	+	181.278i	0.483481	+	0.191424i	−0.113724	+	0.993512i	$0.536278\pi$
$948$	618.767	+	770.211i	0.652708	+	0.812459i
$949$	−386.140	+	280.547i	−0.406892	+	0.295624i
$950$	−2309.82	+	160.271i	−2.43139	+	0.168706i
$951$	105.694	−	124.091i	0.111140	−	0.130485i
$952$	−249.329	−	1973.64i	−0.261900	−	2.07315i
$953$	−1353.85	+	347.610i	−1.42062	+	0.364753i	−0.879382	−	0.476116i	$-0.842044\pi$
$953$	−1353.85	+	347.610i	−1.42062	+	0.364753i	−0.541238	+	0.840870i	$0.682044\pi$
$954$	63.8854	−	289.483i	0.0669659	−	0.303441i
$955$	518.558	+	757.772i	0.542993	+	0.793478i
$956$	−18.4451	+	71.8390i	−0.0192941	+	0.0751454i
$957$	−608.101	+	713.947i	−0.635424	+	0.746027i
$958$	−107.214	+	6.74536i	−0.111915	+	0.00704109i
$959$	425.246	+	773.519i	0.443426	+	0.806589i
$960$	4451.36	−	3837.17i	4.63683	−	3.99706i
$961$	−178.900	+	937.828i	−0.186160	+	0.975887i
$962$	−306.432	+	168.463i	−0.318537	+	0.175117i
$963$	−50.6489	−	1483.82i	−0.0525950	−	1.54083i
$964$	−156.662	+	147.115i	−0.162512	+	0.152609i
$965$	129.123	+	28.4258i	0.133806	+	0.0294568i
$966$	255.960	−	450.160i	0.264969	−	0.466004i
$967$	−590.559	−	1491.58i	−0.610713	−	1.54248i	−0.824654	−	0.565638i	$-0.808630\pi$
$967$	−590.559	−	1491.58i	−0.610713	−	1.54248i	0.213941	−	0.976847i	$-0.431370\pi$
$968$	−303.253	+	220.326i	−0.313278	+	0.227610i
$969$	696.135	−	490.660i	0.718405	−	0.506357i
$970$	1032.15	−	1038.82i	1.06407	−	1.07095i
$971$	818.432	−	519.393i	0.842876	−	0.534905i	−0.0428676	−	0.999081i	$-0.513649\pi$
$971$	818.432	−	519.393i	0.842876	−	0.534905i	0.885743	+	0.464176i	$0.153649\pi$
$972$	2807.14	−	509.510i	2.88801	−	0.524187i
$973$	−55.0048	−	10.4927i	−0.0565311	−	0.0107839i
$974$	465.250	−	151.169i	0.477669	−	0.155204i
$975$	180.698	−	214.941i	0.185331	−	0.220452i
$976$	1265.97	−	3896.25i	1.29710	−	3.99206i
$977$	172.630	+	94.9043i	0.176694	+	0.0971385i	0.567646	−	0.823273i	$-0.307854\pi$
$977$	172.630	+	94.9043i	0.176694	+	0.0971385i	−0.390952	+	0.920411i	$0.627854\pi$
$978$	−1238.67	+	1281.67i	−1.26653	+	1.31050i
$979$	−59.3116	−	23.4831i	−0.0605839	−	0.0239868i
$980$	41.9414	+	1210.37i	0.0427973	+	1.23507i
$981$	135.850	−	1479.86i	0.138482	−	1.50853i
$982$	700.464	−	227.595i	0.713304	−	0.231766i
$983$	−308.962	−	373.471i	−0.314305	−	0.379930i	0.589576	−	0.807713i	$-0.299295\pi$
$983$	−308.962	−	373.471i	−0.314305	−	0.379930i	−0.903882	+	0.427783i	$0.859295\pi$
$984$	−305.508	−	2733.35i	−0.310475	−	2.77780i
$985$	−9.01910	+	13.3636i	−0.00915645	+	0.0135671i
$986$	181.242	+	1434.68i	0.183815	+	1.45505i
$987$	462.215	+	95.0684i	0.468303	+	0.0963205i
$988$	−702.442	+	748.025i	−0.710974	+	0.757110i
$989$	345.439	−	162.551i	0.349281	−	0.164359i
$990$	−1727.35	+	695.776i	−1.74480	+	0.702804i
$991$	448.437	+	56.6507i	0.452509	+	0.0571652i	0.348285	−	0.937389i	$-0.386764\pi$
$991$	448.437	+	56.6507i	0.452509	+	0.0571652i	0.104224	+	0.994554i	$0.466764\pi$
$992$	7387.12	+	1896.69i	7.44670	+	1.91199i
$993$	−1136.96	−	469.144i	−1.14498	−	0.472452i
$994$	2322.97	−	919.728i	2.33699	−	0.925280i
$995$	223.285	+	511.453i	0.224407	+	0.514023i
$996$	1710.03	+	1652.66i	1.71690	+	1.65929i
$997$	603.832	+	37.9899i	0.605649	+	0.0381042i	0.362655	−	0.931924i	$-0.381870\pi$
$997$	603.832	+	37.9899i	0.605649	+	0.0381042i	0.242994	+	0.970028i	$0.421870\pi$
$998$	1460.28	+	3103.26i	1.46321	+	3.10947i
$999$	−618.639	−	145.870i	−0.619258	−	0.146016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.p.a.14.1	✓	1960
3.2	odd	2	inner	375.3.p.a.14.98	yes	1960
125.9	even	50	inner	375.3.p.a.134.98	yes	1960
375.134	odd	50	inner	375.3.p.a.134.1	yes	1960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
375.3.p.a.14.1	✓	1960	1.1	even	1	trivial
375.3.p.a.14.98	yes	1960	3.2	odd	2	inner
375.3.p.a.134.1	yes	1960	375.134	odd	50	inner
375.3.p.a.134.98	yes	1960	125.9	even	50	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.68926 - 3.58987i) q^{2} +(-2.97064 - 0.418686i) q^{3} +(-7.48385 + 9.04642i) q^{4} +(-1.07499 + 4.88307i) q^{5} +(3.51517 + 11.3715i) q^{6} +(-5.06561 - 1.64592i) q^{7} +(29.7464 + 7.63757i) q^{8} +(8.64940 + 2.48753i) q^{9} +(19.3455 - 4.38973i) q^{10} +(-9.43777 + 4.44108i) q^{11} +(26.0194 - 23.7403i) q^{12} +(0.469255 - 3.71454i) q^{13} +(2.64853 + 20.9652i) q^{14} +(5.23788 - 14.0558i) q^{15} +(-14.0316 - 73.5562i) q^{16} +(7.75199 + 9.37054i) q^{17} +(-5.68121 - 35.2523i) q^{18} +(1.46576 + 23.2976i) q^{19} +(-36.1293 - 46.2690i) q^{20} +(14.3590 + 7.01032i) q^{21} +(31.8858 + 26.3782i) q^{22} +(7.15803 + 3.93516i) q^{23} +(-85.1680 - 35.1429i) q^{24} +(-22.6888 - 10.4985i) q^{25} +(-14.1274 + 4.59027i) q^{26} +(-24.6528 - 11.0109i) q^{27} +(52.7999 - 33.5078i) q^{28} +(-25.3050 + 16.0590i) q^{29} +(-59.3065 + 4.94060i) q^{30} +(-27.8995 - 33.7247i) q^{31} +(-140.970 + 102.421i) q^{32} +(29.8956 - 9.24138i) q^{33} +(20.5439 - 43.6579i) q^{34} +(13.4826 - 22.9664i) q^{35} +(-87.2341 + 59.6298i) q^{36} +(23.1239 - 4.41112i) q^{37} +(81.1591 - 44.6176i) q^{38} +(-2.94921 + 10.8381i) q^{39} +(-69.2718 + 137.043i) q^{40} +(14.3813 + 26.1595i) q^{41} +(0.910040 - 63.3891i) q^{42} +(27.4718 - 37.8117i) q^{43} +(30.4550 - 118.614i) q^{44} +(-21.4448 + 39.5616i) q^{45} +(2.03491 - 32.3439i) q^{46} +(28.6043 - 7.34435i) q^{47} +(10.8859 + 224.384i) q^{48} +(-16.6905 - 12.1264i) q^{49} +(0.639142 + 99.1845i) q^{50} +(-19.1050 - 31.0822i) q^{51} +(30.0914 + 32.0441i) q^{52} +(7.71921 + 3.05625i) q^{53} +(2.11718 + 107.101i) q^{54} +(-11.5406 - 50.8594i) q^{55} +(-138.113 - 87.6489i) q^{56} +(5.40012 - 69.8223i) q^{57} +(100.397 + 63.7136i) q^{58} +(1.54071 - 1.64069i) q^{59} +(87.9549 + 152.575i) q^{60} +(47.9420 + 26.3563i) q^{61} +(-73.9377 + 157.126i) q^{62} +(-39.7202 - 26.8370i) q^{63} +(343.334 + 188.749i) q^{64} +(17.6339 + 6.28449i) q^{65} +(-83.6769 - 91.7103i) q^{66} +(-89.3967 - 56.7328i) q^{67} -142.785 q^{68} +(-19.6163 - 14.6869i) q^{69} +(-105.222 - 9.60446i) q^{70} +(-29.4025 - 114.515i) q^{71} +(238.290 + 140.055i) q^{72} +(-87.2666 - 92.9295i) q^{73} +(-54.8977 - 75.5603i) q^{74} +(63.0047 + 40.6867i) q^{75} +(-221.729 - 161.095i) q^{76} +(55.1177 - 6.96298i) q^{77} +(43.8893 - 7.72109i) q^{78} +(-1.76126 + 27.9944i) q^{79} +(374.264 + 10.5548i) q^{80} +(68.6244 + 43.0313i) q^{81} +(69.6154 - 95.8173i) q^{82} +(4.23946 + 67.3843i) q^{83} +(-170.879 + 77.4331i) q^{84} +(-54.0903 + 27.7803i) q^{85} +(-182.146 - 34.7463i) q^{86} +(81.8957 - 37.1107i) q^{87} +(-314.658 + 60.0243i) q^{88} +(4.18659 + 4.45827i) q^{89} +(178.247 + 10.1541i) q^{90} +(-8.49087 + 18.0440i) q^{91} +(-89.1687 + 35.3044i) q^{92} +(68.7593 + 111.865i) q^{93} +(-74.6855 - 90.2793i) q^{94} +(-115.339 - 17.8872i) q^{95} +(461.655 - 245.234i) q^{96} +(62.3290 - 39.5552i) q^{97} +(-15.3374 + 80.4013i) q^{98} +(-92.6784 + 14.9359i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1960 q - 20 q^{3} - 40 q^{4} - 20 q^{6} - 50 q^{7} - 20 q^{9} - 40 q^{10} - 180 q^{12} - 40 q^{13} + 20 q^{15} - 140 q^{16} - 25 q^{18} + 10 q^{19} - 65 q^{21} - 15 q^{24} - 350 q^{25} - 125 q^{27} - 320 q^{28}+ \cdots - 15 q^{99}+O(q^{100}) \) 1960 * q - 20 * q^3 - 40 * q^4 - 20 * q^6 - 50 * q^7 - 20 * q^9 - 40 * q^10 - 180 * q^12 - 40 * q^13 + 20 * q^15 - 140 * q^16 - 25 * q^18 + 10 * q^19 - 65 * q^21 - 15 * q^24 - 350 * q^25 - 125 * q^27 - 320 * q^28 - 20 * q^30 + 60 * q^31 - 45 * q^33 - 240 * q^34 - 1000 * q^36 - 160 * q^37 + 180 * q^39 - 120 * q^40 + 150 * q^42 - 50 * q^43 - 820 * q^45 + 160 * q^46 - 175 * q^48 + 2980 * q^49 - 15 * q^51 + 270 * q^52 - 345 * q^54 - 40 * q^55 - 280 * q^58 - 1305 * q^60 - 140 * q^61 - 820 * q^63 - 400 * q^64 + 355 * q^66 + 210 * q^67 - 220 * q^69 - 1250 * q^70 - 240 * q^72 + 100 * q^73 - 225 * q^75 - 30 * q^76 - 830 * q^78 + 60 * q^79 - 620 * q^81 + 1550 * q^82 + 335 * q^84 + 1540 * q^85 + 405 * q^87 + 1660 * q^88 + 705 * q^90 + 70 * q^91 - 25 * q^93 + 660 * q^94 - 595 * q^96 + 100 * q^97 - 15 * q^99

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