LMFDB - Embedded newform 180.3.v.a.167.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,3,Mod(23,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 10, 9]))

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

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

chi := DirichletCharacter("180.23");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	180.v (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.90464475849$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			167.21
Character	$\chi$	$=$	180.167
Dual form			180.3.v.a.83.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17726 - 1.61680i) q^{2} +(2.98295 + 0.319431i) q^{3} +(-1.22810 + 3.80680i) q^{4} +(-2.35124 + 4.41267i) q^{5} +(-2.99525 - 5.19889i) q^{6} +(-7.09282 - 1.90052i) q^{7} +(7.60065 - 2.49601i) q^{8} +(8.79593 + 1.90569i) q^{9} +O(q^{10})$	\(q+(-1.17726 - 1.61680i) q^{2} +(2.98295 + 0.319431i) q^{3} +(-1.22810 + 3.80680i) q^{4} +(-2.35124 + 4.41267i) q^{5} +(-2.99525 - 5.19889i) q^{6} +(-7.09282 - 1.90052i) q^{7} +(7.60065 - 2.49601i) q^{8} +(8.79593 + 1.90569i) q^{9} +(9.90245 - 1.39338i) q^{10} +(6.90992 + 11.9683i) q^{11} +(-4.87938 + 10.9632i) q^{12} +(2.19933 + 8.20800i) q^{13} +(5.27736 + 13.7051i) q^{14} +(-8.42317 + 12.4117i) q^{15} +(-12.9835 - 9.35031i) q^{16} +(-19.5704 + 19.5704i) q^{17} +(-7.27399 - 16.4648i) q^{18} +27.8736 q^{19} +(-13.9106 - 14.3699i) q^{20} +(-20.5504 - 7.93481i) q^{21} +(11.2156 - 25.2618i) q^{22} +(6.28869 + 23.4697i) q^{23} +(23.4696 - 5.01757i) q^{24} +(-13.9433 - 20.7505i) q^{25} +(10.6815 - 13.2188i) q^{26} +(25.6290 + 8.49426i) q^{27} +(15.9456 - 24.6670i) q^{28} +(-1.37932 - 2.38905i) q^{29} +(29.9836 - 0.993217i) q^{30} +(1.95683 + 1.12978i) q^{31} +(0.167407 + 31.9996i) q^{32} +(16.7888 + 37.9081i) q^{33} +(54.6811 + 8.60199i) q^{34} +(25.0633 - 26.8297i) q^{35} +(-18.0569 + 31.1440i) q^{36} +(-39.3205 - 39.3205i) q^{37} +(-32.8146 - 45.0662i) q^{38} +(3.93858 + 25.1865i) q^{39} +(-6.85693 + 39.4079i) q^{40} +(28.6563 + 16.5447i) q^{41} +(11.3642 + 42.5673i) q^{42} +(16.4101 - 61.2432i) q^{43} +(-54.0472 + 11.6063i) q^{44} +(-29.0905 + 34.3328i) q^{45} +(30.5425 - 37.7976i) q^{46} +(9.46501 - 35.3239i) q^{47} +(-35.7424 - 32.0388i) q^{48} +(4.26096 + 2.46006i) q^{49} +(-17.1346 + 46.9724i) q^{50} +(-64.6289 + 52.1261i) q^{51} +(-33.9472 - 1.70787i) q^{52} +(-31.2552 - 31.2552i) q^{53} +(-16.4386 - 51.4371i) q^{54} +(-69.0592 + 2.35074i) q^{55} +(-58.6538 + 3.25856i) q^{56} +(83.1455 + 8.90370i) q^{57} +(-2.23880 + 5.04263i) q^{58} +(7.02941 + 4.05843i) q^{59} +(-36.9044 - 47.3082i) q^{60} +(20.9812 + 36.3405i) q^{61} +(-0.477078 - 4.49386i) q^{62} +(-58.7662 - 30.2335i) q^{63} +(51.5399 - 37.9426i) q^{64} +(-41.3903 - 9.59409i) q^{65} +(41.5250 - 71.7721i) q^{66} +(12.0139 + 44.8365i) q^{67} +(-50.4663 - 98.5353i) q^{68} +(11.2619 + 72.0177i) q^{69} +(-72.8845 - 8.93680i) q^{70} -3.29546 q^{71} +(71.6114 - 7.47019i) q^{72} +(-9.77104 + 9.77104i) q^{73} +(-17.2829 + 109.864i) q^{74} +(-34.9638 - 66.3516i) q^{75} +(-34.2317 + 106.109i) q^{76} +(-26.2648 - 98.0216i) q^{77} +(36.0849 - 36.0191i) q^{78} +(-5.14562 - 8.91247i) q^{79} +(71.7872 - 35.3071i) q^{80} +(73.7367 + 33.5246i) q^{81} +(-6.98645 - 65.8092i) q^{82} +(32.7794 + 8.78320i) q^{83} +(55.4443 - 68.4867i) q^{84} +(-40.3430 - 132.373i) q^{85} +(-118.337 + 45.5675i) q^{86} +(-3.35130 - 7.56701i) q^{87} +(82.3929 + 73.7199i) q^{88} -100.456 q^{89} +(89.7566 + 6.61496i) q^{90} -62.3977i q^{91} +(-97.0678 - 4.88345i) q^{92} +(5.47624 + 3.99514i) q^{93} +(-68.2546 + 26.2824i) q^{94} +(-65.5376 + 122.997i) q^{95} +(-9.72228 + 95.5064i) q^{96} +(2.09127 - 7.80472i) q^{97} +(-1.03883 - 9.78527i) q^{98} +(37.9712 + 118.441i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 6 q^{2} - 12 q^{5} - 8 q^{6}+O(q^{10}) $ 272 * q - 6 * q^2 - 12 * q^5 - 8 * q^6	$ 272 q - 6 q^{2} - 12 q^{5} - 8 q^{6} - 8 q^{10} + 14 q^{12} - 4 q^{13} - 4 q^{16} - 24 q^{18} - 6 q^{20} + 14 q^{22} - 4 q^{25} + 56 q^{28} - 74 q^{30} - 186 q^{32} + 28 q^{33} - 184 q^{36} - 16 q^{37} - 30 q^{38} - 2 q^{40} - 24 q^{41} + 178 q^{42} + 92 q^{45} + 152 q^{46} - 202 q^{48} - 6 q^{50} - 66 q^{52} - 264 q^{56} - 48 q^{57} + 14 q^{58} - 382 q^{60} - 8 q^{61} - 300 q^{65} - 84 q^{66} - 102 q^{68} + 98 q^{70} + 210 q^{72} - 16 q^{73} + 88 q^{76} - 12 q^{77} - 510 q^{78} - 96 q^{81} - 24 q^{82} - 4 q^{85} - 336 q^{86} - 106 q^{88} + 66 q^{90} + 336 q^{92} + 628 q^{93} - 140 q^{96} - 4 q^{97}+O(q^{100}) $ 272 * q - 6 * q^2 - 12 * q^5 - 8 * q^6 - 8 * q^10 + 14 * q^12 - 4 * q^13 - 4 * q^16 - 24 * q^18 - 6 * q^20 + 14 * q^22 - 4 * q^25 + 56 * q^28 - 74 * q^30 - 186 * q^32 + 28 * q^33 - 184 * q^36 - 16 * q^37 - 30 * q^38 - 2 * q^40 - 24 * q^41 + 178 * q^42 + 92 * q^45 + 152 * q^46 - 202 * q^48 - 6 * q^50 - 66 * q^52 - 264 * q^56 - 48 * q^57 + 14 * q^58 - 382 * q^60 - 8 * q^61 - 300 * q^65 - 84 * q^66 - 102 * q^68 + 98 * q^70 + 210 * q^72 - 16 * q^73 + 88 * q^76 - 12 * q^77 - 510 * q^78 - 96 * q^81 - 24 * q^82 - 4 * q^85 - 336 * q^86 - 106 * q^88 + 66 * q^90 + 336 * q^92 + 628 * q^93 - 140 * q^96 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.17726	−	1.61680i	−0.588631	−	0.808402i
$2$	−1.17726	−	1.61680i	−0.588631	−	0.808402i
$3$	2.98295	+	0.319431i	0.994315	+	0.106477i
$3$	2.98295	+	0.319431i	0.994315	+	0.106477i
$4$	−1.22810	+	3.80680i	−0.307026	+	0.951701i
$5$	−2.35124	+	4.41267i	−0.470249	+	0.882534i
$5$	−2.35124	+	4.41267i	−0.470249	+	0.882534i
$6$	−2.99525	−	5.19889i	−0.499209	−	0.866482i
$7$	−7.09282	−	1.90052i	−1.01326	−	0.271502i	−0.286269	−	0.958149i	$-0.592415\pi$
$7$	−7.09282	−	1.90052i	−1.01326	−	0.271502i	−0.726991	+	0.686647i	$0.759082\pi$
$8$	7.60065	−	2.49601i	0.950082	−	0.312001i
$9$	8.79593	+	1.90569i	0.977325	+	0.211743i
$10$	9.90245	−	1.39338i	0.990245	−	0.139338i
$11$	6.90992	+	11.9683i	0.628174	+	1.08803i	0.987918	+	0.154978i	$0.0495308\pi$
$11$	6.90992	+	11.9683i	0.628174	+	1.08803i	−0.359744	+	0.933051i	$0.617136\pi$
$12$	−4.87938	+	10.9632i	−0.406615	+	0.913600i
$13$	2.19933	+	8.20800i	0.169179	+	0.631384i	0.997470	+	0.0710866i	$0.0226467\pi$
$13$	2.19933	+	8.20800i	0.169179	+	0.631384i	−0.828291	+	0.560298i	$0.810687\pi$
$14$	5.27736	+	13.7051i	0.376954	+	0.978936i
$15$	−8.42317	+	12.4117i	−0.561545	+	0.827446i
$16$	−12.9835	−	9.35031i	−0.811470	−	0.584394i
$17$	−19.5704	+	19.5704i	−1.15120	+	1.15120i	−0.164890	+	0.986312i	$0.552727\pi$
$17$	−19.5704	+	19.5704i	−1.15120	+	1.15120i	−0.986312	+	0.164890i	$0.947273\pi$
$18$	−7.27399	−	16.4648i	−0.404111	−	0.914710i
$19$	27.8736			1.46703			0.733516	−	0.679672i	$-0.237878\pi$
$19$	27.8736			1.46703			0.733516	+	0.679672i	$0.237878\pi$
$20$	−13.9106	−	14.3699i	−0.695530	−	0.718497i
$21$	−20.5504	−	7.93481i	−0.978592	−	0.377848i
$22$	11.2156	−	25.2618i	0.509802	−	1.14827i
$23$	6.28869	+	23.4697i	0.273421	+	1.02042i	0.956892	+	0.290444i	$0.0938031\pi$
$23$	6.28869	+	23.4697i	0.273421	+	1.02042i	−0.683471	+	0.729978i	$0.739530\pi$
$24$	23.4696	−	5.01757i	0.977902	−	0.209065i
$25$	−13.9433	−	20.7505i	−0.557733	−	0.830021i
$26$	10.6815	−	13.2188i	0.410828	−	0.508417i
$27$	25.6290	+	8.49426i	0.949224	+	0.314602i
$28$	15.9456	−	24.6670i	0.569487	−	0.880963i
$29$	−1.37932	−	2.38905i	−0.0475627	−	0.0823811i	0.841264	−	0.540625i	$-0.181812\pi$
$29$	−1.37932	−	2.38905i	−0.0475627	−	0.0823811i	−0.888827	+	0.458244i	$0.848479\pi$
$30$	29.9836	−	0.993217i	0.999452	−	0.0331072i
$31$	1.95683	+	1.12978i	0.0631236	+	0.0364445i	0.531230	−	0.847228i	$-0.321730\pi$
$31$	1.95683	+	1.12978i	0.0631236	+	0.0364445i	−0.468106	+	0.883672i	$0.655063\pi$
$32$	0.167407	+	31.9996i	0.00523148	+	0.999986i
$33$	16.7888	+	37.9081i	0.508753	+	1.14873i
$34$	54.6811	+	8.60199i	1.60827	+	0.253000i
$35$	25.0633	−	26.8297i	0.716094	−	0.766563i
$36$	−18.0569	+	31.1440i	−0.501581	+	0.865111i
$37$	−39.3205	−	39.3205i	−1.06272	−	1.06272i	−0.997897	−	0.0648192i	$-0.979353\pi$
$37$	−39.3205	−	39.3205i	−1.06272	−	1.06272i	−0.0648192	−	0.997897i	$-0.520647\pi$
$38$	−32.8146	−	45.0662i	−0.863542	−	1.18595i
$39$	3.93858	+	25.1865i	0.100989	+	0.645809i
$40$	−6.85693	+	39.4079i	−0.171423	+	0.985197i
$41$	28.6563	+	16.5447i	0.698935	+	0.403530i	0.806951	−	0.590619i	$-0.201116\pi$
$41$	28.6563	+	16.5447i	0.698935	+	0.403530i	−0.108015	+	0.994149i	$0.534450\pi$
$42$	11.3642	+	42.5673i	0.270577	+	1.01351i
$43$	16.4101	−	61.2432i	0.381629	−	1.42426i	−0.461783	−	0.886993i	$-0.652790\pi$
$43$	16.4101	−	61.2432i	0.381629	−	1.42426i	0.843412	−	0.537267i	$-0.180543\pi$
$44$	−54.0472	+	11.6063i	−1.22834	+	0.263780i
$45$	−29.0905	+	34.3328i	−0.646456	+	0.762951i
$46$	30.5425	−	37.7976i	0.663967	−	0.821687i
$47$	9.46501	−	35.3239i	0.201383	−	0.751572i	−0.789138	−	0.614215i	$-0.789473\pi$
$47$	9.46501	−	35.3239i	0.201383	−	0.751572i	0.990522	−	0.137357i	$-0.0438607\pi$
$48$	−35.7424	−	32.0388i	−0.744632	−	0.667475i
$49$	4.26096	+	2.46006i	0.0869583	+	0.0502054i
$50$	−17.1346	+	46.9724i	−0.342691	+	0.939448i
$51$	−64.6289	+	52.1261i	−1.26723	+	1.02208i
$52$	−33.9472	−	1.70787i	−0.652832	−	0.0328437i
$53$	−31.2552	−	31.2552i	−0.589721	−	0.589721i	0.347835	−	0.937556i	$-0.386917\pi$
$53$	−31.2552	−	31.2552i	−0.589721	−	0.589721i	−0.937556	+	0.347835i	$0.886917\pi$
$54$	−16.4386	−	51.4371i	−0.304418	−	0.952539i
$55$	−69.0592	+	2.35074i	−1.25562	+	0.0427408i
$56$	−58.6538	+	3.25856i	−1.04739	+	0.0581886i
$57$	83.1455	+	8.90370i	1.45869	+	0.156205i
$58$	−2.23880	+	5.04263i	−0.0386001	+	0.0869419i
$59$	7.02941	+	4.05843i	0.119143	+	0.0687870i	0.558387	−	0.829581i	$-0.311420\pi$
$59$	7.02941	+	4.05843i	0.119143	+	0.0687870i	−0.439244	+	0.898368i	$0.644754\pi$
$60$	−36.9044	−	47.3082i	−0.615073	−	0.788470i
$61$	20.9812	+	36.3405i	0.343954	+	0.595746i	0.985163	−	0.171620i	$-0.0549002\pi$
$61$	20.9812	+	36.3405i	0.343954	+	0.595746i	−0.641209	+	0.767366i	$0.721567\pi$
$62$	−0.477078	−	4.49386i	−0.00769481	−	0.0724816i
$63$	−58.7662	−	30.2335i	−0.932797	−	0.479897i
$64$	51.5399	−	37.9426i	0.805311	−	0.592852i
$65$	−41.3903	−	9.59409i	−0.636774	−	0.147601i
$66$	41.5250	−	71.7721i	0.629167	−	1.08746i
$67$	12.0139	+	44.8365i	0.179312	+	0.669202i	0.995777	+	0.0918066i	$0.0292641\pi$
$67$	12.0139	+	44.8365i	0.179312	+	0.669202i	−0.816465	+	0.577395i	$0.804069\pi$
$68$	−50.4663	−	98.5353i	−0.742151	−	1.44905i
$69$	11.2619	+	72.0177i	0.163215	+	1.04373i
$70$	−72.8845	−	8.93680i	−1.04121	−	0.127669i
$71$	−3.29546			−0.0464149			−0.0232075	−	0.999731i	$-0.507388\pi$
$71$	−3.29546			−0.0464149			−0.0232075	+	0.999731i	$0.507388\pi$
$72$	71.6114	−	7.47019i	0.994603	−	0.103753i
$73$	−9.77104	+	9.77104i	−0.133850	+	0.133850i	−0.770858	−	0.637008i	$-0.780172\pi$
$73$	−9.77104	+	9.77104i	−0.133850	+	0.133850i	0.637008	+	0.770858i	$0.280172\pi$
$74$	−17.2829	+	109.864i	−0.233553	+	1.48465i
$75$	−34.9638	−	66.3516i	−0.466184	−	0.884688i
$76$	−34.2317	+	106.109i	−0.450417	+	1.39618i
$77$	−26.2648	−	98.0216i	−0.341102	−	1.27301i
$78$	36.0849	−	36.0191i	0.462627	−	0.461783i
$79$	−5.14562	−	8.91247i	−0.0651344	−	0.112816i	0.831619	−	0.555346i	$-0.187414\pi$
$79$	−5.14562	−	8.91247i	−0.0651344	−	0.112816i	−0.896754	+	0.442530i	$0.854081\pi$
$80$	71.7872	−	35.3071i	0.897340	−	0.441339i
$81$	73.7367	+	33.5246i	0.910330	+	0.413884i
$82$	−6.98645	−	65.8092i	−0.0852006	−	0.802551i
$83$	32.7794	+	8.78320i	0.394932	+	0.105822i	0.450819	−	0.892615i	$-0.351132\pi$
$83$	32.7794	+	8.78320i	0.394932	+	0.105822i	−0.0558870	+	0.998437i	$0.517799\pi$
$84$	55.4443	−	68.4867i	0.660051	−	0.815318i
$85$	−40.3430	−	132.373i	−0.474624	−	1.55733i
$86$	−118.337	+	45.5675i	−1.37601	+	0.529854i
$87$	−3.35130	−	7.56701i	−0.0385207	−	0.0869771i
$88$	82.3929	+	73.7199i	0.936283	+	0.837726i
$89$	−100.456			−1.12872			−0.564359	−	0.825529i	$-0.690877\pi$
$89$	−100.456			−1.12872			−0.564359	+	0.825529i	$0.690877\pi$
$90$	89.7566	+	6.61496i	0.997295	+	0.0734996i
$91$		−	62.3977i		−	0.685690i
$92$	−97.0678	−	4.88345i	−1.05508	−	0.0530809i
$93$	5.47624	+	3.99514i	0.0588843	+	0.0429585i
$94$	−68.2546	+	26.2824i	−0.726113	+	0.279601i
$95$	−65.5376	+	122.997i	−0.689870	+	1.29471i
$96$	−9.72228	+	95.5064i	−0.101274	+	0.994859i
$97$	2.09127	−	7.80472i	0.0215595	−	0.0804610i	−0.954308	−	0.298825i	$-0.903405\pi$
$97$	2.09127	−	7.80472i	0.0215595	−	0.0804610i	0.975867	+	0.218364i	$0.0700720\pi$
$98$	−1.03883	−	9.78527i	−0.0106003	−	0.0998497i
$99$	37.9712	+	118.441i	0.383547	+	1.19637i
$100$	96.1170	−	27.5957i	0.961170	−	0.275957i
$101$	127.484	−	73.6028i	1.26222	−	0.728741i	0.288713	−	0.957416i	$-0.406773\pi$
$101$	127.484	−	73.6028i	1.26222	−	0.728741i	0.973503	+	0.228675i	$0.0734394\pi$
$102$	160.363	+	43.1261i	1.57219	+	0.422805i
$103$	52.8927	−	14.1725i	0.513521	−	0.137598i	0.00725290	−	0.999974i	$-0.497691\pi$
$103$	52.8927	−	14.1725i	0.513521	−	0.137598i	0.506268	+	0.862376i	$0.331025\pi$
$104$	37.2035	+	56.8966i	0.357726	+	0.547083i
$105$	83.3327	−	72.0256i	0.793645	−	0.685958i
$106$	−13.7379	+	87.3292i	−0.129603	+	0.823860i
$107$	64.8320	+	64.8320i	0.605906	+	0.605906i	0.941874	−	0.335967i	$-0.109063\pi$
$107$	64.8320	+	64.8320i	0.605906	+	0.605906i	−0.335967	+	0.941874i	$0.609063\pi$
$108$	−63.8111	+	87.1329i	−0.590844	+	0.806786i
$109$			186.892i			1.71461i	0.514812	+	0.857303i	$0.327862\pi$
$109$			186.892i			1.71461i	−0.514812	+	0.857303i	$0.672138\pi$
$110$	85.1015	+	108.888i	0.773650	+	0.989887i
$111$	−104.731	−	129.851i	−0.943520	−	1.16983i
$112$	74.3194	+	90.9955i	0.663566	+	0.812460i
$113$	170.201	−	45.6052i	1.50620	−	0.403586i	0.591030	−	0.806649i	$-0.298721\pi$
$113$	170.201	−	45.6052i	1.50620	−	0.403586i	0.915172	+	0.403064i	$0.132055\pi$
$114$	−83.4886	−	144.912i	−0.732356	−	1.27116i
$115$	−118.350	−	27.4331i	−1.02913	−	0.238548i
$116$	10.7886	−	2.31679i	0.0930051	−	0.0199724i
$117$	3.70322	+	76.3882i	0.0316514	+	0.652891i
$118$	−1.71378	−	16.1430i	−0.0145235	−	0.136805i
$119$	176.004	−	101.616i	1.47902	−	0.853913i
$120$	−33.0420	+	115.361i	−0.275350	+	0.961344i
$121$	−34.9939	+	60.6111i	−0.289205	+	0.500919i
$122$	34.0551	−	76.7048i	0.279140	−	0.628728i
$123$	80.1954	+	58.5058i	0.651995	+	0.475657i
$124$	−6.70404	+	6.06180i	−0.0540648	+	0.0488854i
$125$	124.349	−	12.7378i	0.994794	−	0.101902i
$126$	20.3016	+	130.606i	0.161124	+	1.03656i
$127$	117.896	−	117.896i	0.928318	−	0.928318i	−0.0692793	−	0.997597i	$-0.522070\pi$
$127$	117.896	−	117.896i	0.928318	−	0.928318i	0.997597	+	0.0692793i	$0.0220700\pi$
$128$	−122.022	−	38.6615i	−0.953294	−	0.302043i
$129$	68.5133	−	177.443i	0.531111	−	1.37553i
$130$	33.2155	+	78.2148i	0.255504	+	0.601652i
$131$	51.7777	−	89.6815i	0.395249	−	0.684592i	−0.597884	−	0.801583i	$-0.703992\pi$
$131$	51.7777	−	89.6815i	0.395249	−	0.684592i	0.993133	+	0.116991i	$0.0373249\pi$
$132$	−164.927	+	17.3567i	−1.24945	+	0.131491i
$133$	−197.703	−	52.9743i	−1.48649	−	0.398303i
$134$	58.3483	−	72.2085i	0.435435	−	0.538869i
$135$	−97.7425	+	93.1204i	−0.724018	+	0.689781i
$136$	−99.9002	+	197.596i	−0.734560	+	1.45291i
$137$	−20.4804	−	5.48770i	−0.149492	−	0.0400562i	0.183297	−	0.983058i	$-0.441323\pi$
$137$	−20.4804	−	5.48770i	−0.149492	−	0.0400562i	−0.332789	+	0.943001i	$0.607990\pi$
$138$	103.180	−	102.992i	0.747683	−	0.746319i
$139$	17.4393	−	30.2057i	0.125462	−	0.217307i	−0.796451	−	0.604703i	$-0.793292\pi$
$139$	17.4393	−	30.2057i	0.125462	−	0.217307i	0.921914	+	0.387396i	$0.126625\pi$
$140$	71.3551	+	128.361i	0.509680	+	0.916863i
$141$	39.5171	−	102.346i	0.280263	−	0.725857i
$142$	3.87962	+	5.32811i	0.0273213	+	0.0375219i
$143$	−83.0388	+	83.0388i	−0.580691	+	0.580691i
$144$	−96.3833	−	106.987i	−0.669328	−	0.742967i
$145$	13.7852	−	0.469242i	0.0950704	−	0.00323615i
$146$	27.3009	+	4.29477i	0.186993	+	0.0294162i
$147$	11.9244	+	8.69932i	0.0811182	+	0.0591791i
$148$	197.975	−	101.396i	1.33767	−	0.685107i
$149$	−42.0868	+	72.8964i	−0.282461	+	0.489238i	−0.971990	−	0.235020i	$-0.924484\pi$
$149$	−42.0868	+	72.8964i	−0.282461	+	0.489238i	0.689529	+	0.724258i	$0.257818\pi$
$150$	−66.1159	+	134.643i	−0.440772	+	0.897619i
$151$	86.3008	−	49.8258i	0.571529	−	0.329972i	−0.186231	−	0.982506i	$-0.559627\pi$
$151$	86.3008	−	49.8258i	0.571529	−	0.329972i	0.757760	+	0.652534i	$0.226294\pi$
$152$	211.858	−	69.5727i	1.39380	−	0.457715i
$153$	−209.435	+	134.845i	−1.36886	+	0.881339i
$154$	−127.561	+	157.862i	−0.828319	+	1.02508i
$155$	−9.58633	+	5.97848i	−0.0618473	+	0.0385708i
$156$	−100.717	−	15.9383i	−0.645623	−	0.102169i
$157$	−27.3934	+	7.34004i	−0.174480	+	0.0467518i	−0.345001	−	0.938602i	$-0.612122\pi$
$157$	−27.3934	+	7.34004i	−0.174480	+	0.0467518i	0.170521	+	0.985354i	$0.445455\pi$
$158$	−8.35197	+	18.8118i	−0.0528606	+	0.119062i
$159$	−83.2488	−	103.217i	−0.523577	−	0.649161i
$160$	−141.597	−	74.5000i	−0.884982	−	0.465625i
$161$		−	178.418i		−	1.10819i
$162$	−32.6047	−	158.685i	−0.201264	−	0.979537i
$163$	−159.023	−	159.023i	−0.975603	−	0.975603i	0.0241065	−	0.999709i	$-0.492326\pi$
$163$	−159.023	−	159.023i	−0.975603	−	0.975603i	−0.999709	+	0.0241065i	$0.992326\pi$
$164$	−98.1756	+	88.7704i	−0.598632	+	0.541283i
$165$	−206.751	−	15.0475i	−1.25303	−	0.0911969i
$166$	−24.3892	−	63.3379i	−0.146923	−	0.381554i
$167$	−128.301	+	34.3782i	−0.768271	+	0.205857i	−0.621607	−	0.783329i	$-0.713520\pi$
$167$	−128.301	+	34.3782i	−0.768271	+	0.205857i	−0.146663	+	0.989186i	$0.546853\pi$
$168$	−176.002	−	9.01573i	−1.04763	−	0.0536651i
$169$	83.8241	−	48.3959i	0.496001	−	0.286366i
$170$	−166.526	+	221.064i	−0.979566	+	1.30038i
$171$	245.174	+	53.1185i	1.43377	+	0.310634i
$172$	212.987	+	137.683i	1.23830	+	0.800482i
$173$	−8.58522	+	32.0405i	−0.0496256	+	0.185205i	−0.986289	−	0.165024i	$-0.947230\pi$
$173$	−8.58522	+	32.0405i	−0.0496256	+	0.185205i	0.936664	+	0.350229i	$0.113896\pi$
$174$	−8.28900	+	14.3267i	−0.0476379	+	0.0823376i
$175$	59.4608	+	173.679i	0.339776	+	0.992453i
$176$	22.1925	−	220.001i	0.126094	−	1.25000i
$177$	19.6720	+	14.3515i	0.111141	+	0.0810819i
$178$	118.263	+	162.418i	0.664399	+	0.912458i
$179$		−	36.8511i		−	0.205872i	−0.994688	−	0.102936i	$-0.967176\pi$
$179$		−	36.8511i		−	0.205872i	0.994688	−	0.102936i	$-0.0328237\pi$
$180$	−94.9720	−	152.906i	−0.527622	−	0.849479i
$181$	221.518			1.22386			0.611929	−	0.790913i	$-0.290394\pi$
$181$	221.518			1.22386			0.611929	+	0.790913i	$0.290394\pi$
$182$	−100.885	+	73.4585i	−0.554312	+	0.403618i
$183$	50.9775	+	115.104i	0.278566	+	0.628982i
$184$	106.379	+	162.689i	0.578145	+	0.884177i
$185$	265.960	−	81.0564i	1.43762	−	0.438143i
$186$	0.0123799	−	13.5573i	6.65585e−5	−	0.0728889i
$187$	−369.455	−	98.9952i	−1.97570	−	0.529386i
$188$	122.847	+	79.4129i	0.653442	+	0.422409i
$189$	−165.639	−	108.957i	−0.876396	−	0.576491i
$190$	276.017	−	38.8384i	1.45272	−	0.204413i
$191$	−53.7944	−	93.1747i	−0.281646	−	0.487826i	0.690144	−	0.723672i	$-0.257547\pi$
$191$	−53.7944	−	93.1747i	−0.281646	−	0.487826i	−0.971790	+	0.235846i	$0.924214\pi$
$192$	165.861	−	96.7171i	0.863858	−	0.503735i
$193$	17.9766	+	67.0896i	0.0931431	+	0.347615i	0.996731	−	0.0807872i	$-0.0257434\pi$
$193$	17.9766	+	67.0896i	0.0931431	+	0.347615i	−0.903588	+	0.428402i	$0.859077\pi$
$194$	−15.0807	+	5.80704i	−0.0777354	+	0.0299332i
$195$	−120.400	−	41.8400i	−0.617438	−	0.214564i
$196$	−14.5979	+	13.1994i	−0.0744790	+	0.0673439i
$197$	−152.887	+	152.887i	−0.776078	+	0.776078i	−0.979161	−	0.203083i	$-0.934904\pi$
$197$	−152.887	+	152.887i	−0.776078	+	0.776078i	0.203083	+	0.979161i	$0.434904\pi$
$198$	146.793	−	200.828i	0.741380	−	1.01428i
$199$	26.6313			0.133826			0.0669129	−	0.997759i	$-0.478685\pi$
$199$	26.6313			0.133826			0.0669129	+	0.997759i	$0.478685\pi$
$200$	−157.772	−	122.915i	−0.788859	−	0.614575i
$201$	21.5147	+	137.583i	0.107038	+	0.684490i
$202$	−269.083	−	119.466i	−1.33209	−	0.591418i
$203$	5.24284	+	19.5665i	0.0258268	+	0.0963869i
$204$	−119.063	−	310.046i	−0.583641	−	1.51983i
$205$	−140.385	+	87.5503i	−0.684803	+	0.427075i
$206$	−85.1828	−	68.8322i	−0.413509	−	0.334137i
$207$	10.5889	+	218.422i	0.0511539	+	1.05518i
$208$	48.1923	−	127.133i	0.231694	−	0.611217i
$209$	192.604	+	333.601i	0.921552	+	1.59617i
$210$	−214.556	−	49.9395i	−1.02169	−	0.237807i
$211$	−40.5195	−	23.3939i	−0.192035	−	0.110872i	0.400900	−	0.916122i	$-0.368698\pi$
$211$	−40.5195	−	23.3939i	−0.192035	−	0.110872i	−0.592935	+	0.805250i	$0.702031\pi$
$212$	157.367	−	80.5979i	0.742298	−	0.380179i
$213$	−9.83018	−	1.05267i	−0.0461511	−	0.00494212i
$214$	28.4963	−	181.145i	0.133160	−	0.846471i
$215$	231.662	+	216.410i	1.07750	+	1.00656i
$216$	215.999	+	0.591720i	0.999996	+	0.00273945i
$217$	−11.7323	−	11.7323i	−0.0540660	−	0.0540660i
$218$	302.168	−	220.021i	1.38609	−	1.00927i
$219$	−32.2677	+	26.0253i	−0.147341	+	0.118837i
$220$	75.8630	−	265.782i	0.344832	−	1.20810i
$221$	−203.676	−	117.592i	−0.921610	−	0.532092i
$222$	−86.6481	+	322.198i	−0.390307	+	1.45134i
$223$	−6.41007	+	23.9227i	−0.0287447	+	0.107277i	−0.978808	−	0.204781i	$-0.934352\pi$
$223$	−6.41007	+	23.9227i	−0.0287447	+	0.107277i	0.950063	+	0.312058i	$0.101018\pi$
$224$	59.6283	−	227.285i	0.266198	−	1.01467i
$225$	−83.1004	−	209.092i	−0.369335	−	0.929296i
$226$	−274.106	−	221.492i	−1.21286	−	0.980053i
$227$	−16.8801	+	62.9973i	−0.0743616	+	0.277521i	−0.993088	−	0.117374i	$-0.962552\pi$
$227$	−16.8801	+	62.9973i	−0.0743616	+	0.277521i	0.918726	+	0.394895i	$0.129219\pi$
$228$	−136.006	+	305.584i	−0.596518	+	1.34028i
$229$	153.672	+	88.7223i	0.671055	+	0.387434i	0.796476	−	0.604670i	$-0.206695\pi$
$229$	153.672	+	88.7223i	0.671055	+	0.387434i	−0.125421	+	0.992104i	$0.540028\pi$
$230$	94.9756	+	223.645i	0.412937	+	0.972370i
$231$	−47.0354	−	300.783i	−0.203616	−	1.30209i
$232$	−16.4468	−	14.7156i	−0.0708914	−	0.0634291i
$233$	292.500	+	292.500i	1.25536	+	1.25536i	0.953282	+	0.302082i	$0.0976816\pi$
$233$	292.500	+	292.500i	1.25536	+	1.25536i	0.302082	+	0.953282i	$0.402318\pi$
$234$	119.145	−	95.9163i	0.509167	−	0.409899i
$235$	133.618	+	124.821i	0.568588	+	0.531153i
$236$	−24.0825	+	21.7754i	−0.102045	+	0.0922687i
$237$	−12.5022	−	28.2291i	−0.0527518	−	0.119110i
$238$	−371.495	−	164.935i	−1.56090	−	0.693003i
$239$	−153.767	−	88.7775i	−0.643377	−	0.371454i	0.142537	−	0.989789i	$-0.454474\pi$
$239$	−153.767	−	88.7775i	−0.643377	−	0.371454i	−0.785914	+	0.618335i	$0.787807\pi$
$240$	225.416	−	82.3882i	0.939232	−	0.343284i
$241$	3.58801	+	6.21461i	0.0148880	+	0.0257868i	0.873373	−	0.487051i	$-0.161927\pi$
$241$	3.58801	+	6.21461i	0.0148880	+	0.0257868i	−0.858485	+	0.512838i	$0.828594\pi$
$242$	139.193	−	14.7771i	0.575179	−	0.0610622i
$243$	209.244	+	123.556i	0.861085	+	0.508461i
$244$	−164.108	+	35.2414i	−0.672575	+	0.144432i
$245$	−20.8740	+	13.0180i	−0.0852000	+	0.0531347i
$246$	0.181294	−	198.537i	0.000736968	−	0.807061i
$247$	61.3032	+	228.787i	0.248191	+	0.926262i
$248$	17.6931	+	3.70279i	0.0713433	+	0.0149306i
$249$	94.9734	+	36.6705i	0.381419	+	0.147271i
$250$	−166.986	−	186.053i	−0.667945	−	0.744211i
$251$	7.10374			0.0283017			0.0141509	−	0.999900i	$-0.495495\pi$
$251$	7.10374			0.0283017			0.0141509	+	0.999900i	$0.495495\pi$
$252$	187.264	−	186.581i	0.743112	−	0.740402i
$253$	−237.439	+	237.439i	−0.938493	+	0.938493i
$254$	−329.410	−	51.8202i	−1.29689	−	0.204017i
$255$	−78.0571	−	407.747i	−0.306106	−	1.59901i
$256$	81.1435	+	242.800i	0.316967	+	0.948437i
$257$	−127.609	−	476.241i	−0.496531	−	1.85308i	−0.521280	−	0.853386i	$-0.674545\pi$
$257$	−127.609	−	476.241i	−0.496531	−	1.85308i	0.0247487	−	0.999694i	$-0.492121\pi$
$258$	−367.549	+	98.1247i	−1.42461	+	0.380328i
$259$	204.164	+	353.623i	0.788279	+	1.36534i
$260$	87.3545	−	145.782i	0.335979	−	0.560701i
$261$	−7.57960	−	23.6425i	−0.0290406	−	0.0905842i
$262$	−205.953	+	21.8645i	−0.786081	+	0.0834521i
$263$	317.946	+	85.1934i	1.20892	+	0.323929i	0.806338	−	0.591455i	$-0.201446\pi$
$263$	317.946	+	85.1934i	1.20892	+	0.323929i	0.402582	+	0.915384i	$0.368113\pi$
$264$	222.225	+	246.221i	0.841762	+	0.932657i
$265$	211.408	−	64.4304i	0.797765	−	0.243134i
$266$	147.099	+	382.011i	0.553004	+	1.43613i
$267$	−299.655	−	32.0887i	−1.12230	−	0.120183i
$268$	−185.438	−	9.32933i	−0.691934	−	0.0348109i
$269$	−467.847			−1.73921			−0.869604	−	0.493750i	$-0.835626\pi$
$269$	−467.847			−1.73921			−0.869604	+	0.493750i	$0.835626\pi$
$270$	265.626	+	48.4031i	0.983800	+	0.179271i
$271$			258.025i			0.952122i	0.879412	+	0.476061i	$0.157936\pi$
$271$			258.025i			0.952122i	−0.879412	+	0.476061i	$0.842064\pi$
$272$	437.082	−	71.1035i	1.60692	−	0.261410i
$273$	19.9318	−	186.129i	0.0730101	−	0.681792i
$274$	15.2383	+	39.5732i	0.0556141	+	0.144428i
$275$	152.002	−	310.262i	0.552734	−	1.12823i
$276$	−287.988	−	45.5735i	−1.04343	−	0.165121i
$277$	7.22910	−	26.9794i	0.0260978	−	0.0973985i	−0.951648	−	0.307189i	$-0.900612\pi$
$277$	7.22910	−	26.9794i	0.0260978	−	0.0973985i	0.977746	+	0.209791i	$0.0672782\pi$
$278$	−69.3673	+	7.36418i	−0.249523	+	0.0264899i
$279$	15.0592	+	13.6666i	0.0539755	+	0.0489841i
$280$	123.530	−	266.482i	0.441180	−	0.951720i
$281$	−85.5669	+	49.4021i	−0.304509	+	0.175808i	−0.644467	−	0.764633i	$-0.722920\pi$
$281$	−85.5669	+	49.4021i	−0.304509	+	0.175808i	0.339958	+	0.940441i	$0.389587\pi$
$282$	−211.995	+	56.5965i	−0.751756	+	0.200697i
$283$	97.3247	−	26.0781i	0.343903	−	0.0921487i	−0.0827333	−	0.996572i	$-0.526365\pi$
$283$	97.3247	−	26.0781i	0.343903	−	0.0921487i	0.426637	+	0.904423i	$0.359698\pi$
$284$	4.04717	−	12.5452i	0.0142506	−	0.0441731i
$285$	−234.784	+	345.959i	−0.823805	+	1.21389i
$286$	232.016	+	36.4989i	0.811245	+	0.127619i
$287$	−171.811	−	171.811i	−0.598644	−	0.598644i
$288$	−59.5087	+	281.785i	−0.206628	+	0.978420i
$289$		−	477.003i		−	1.65053i
$290$	−16.9875	−	21.7355i	−0.0585775	−	0.0749502i
$291$	8.73121	−	22.6130i	0.0300042	−	0.0777080i
$292$	−25.1966	−	49.1963i	−0.0862897	−	0.168480i
$293$	−266.879	+	71.5100i	−0.910849	+	0.244061i	−0.683670	−	0.729792i	$-0.739617\pi$
$293$	−266.879	+	71.5100i	−0.910849	+	0.244061i	−0.227180	+	0.973853i	$0.572950\pi$
$294$	0.0269569	−	29.5208i	9.16901e−5	−	0.100411i
$295$	−34.4364	+	21.4761i	−0.116734	+	0.0728004i
$296$	−397.006	−	200.717i	−1.34124	−	0.678099i
$297$	75.4324	+	365.431i	0.253981	+	1.23041i
$298$	167.406	−	17.7722i	0.561766	−	0.0596383i
$299$	−178.808	+	103.235i	−0.598022	+	0.345268i
$300$	295.527	−	51.6136i	0.985089	−	0.172045i
$301$	−232.787	+	403.199i	−0.773380	+	1.33953i
$302$	−182.157	−	80.8734i	−0.603170	−	0.267793i
$303$	403.788	−	178.831i	1.33263	−	0.590201i
$304$	−361.898	−	260.627i	−1.19045	−	0.857325i
$305$	−209.691	+	7.13777i	−0.687510	+	0.0234025i
$306$	464.578	+	179.868i	1.51823	+	0.587803i
$307$	249.868	−	249.868i	0.813901	−	0.813901i	−0.171315	−	0.985216i	$-0.554802\pi$
$307$	249.868	−	249.868i	0.813901	−	0.813901i	0.985216	+	0.171315i	$0.0548016\pi$
$308$	405.405	+	20.3958i	1.31625	+	0.0662201i
$309$	162.303	−	25.3804i	0.525253	−	0.0821371i
$310$	20.9516	+	8.46097i	0.0675860	+	0.0272934i
$311$	131.337	−	227.482i	0.422305	−	0.731454i	−0.573859	−	0.818954i	$-0.694554\pi$
$311$	131.337	−	227.482i	0.422305	−	0.731454i	0.996165	+	0.0874997i	$0.0278877\pi$
$312$	92.8016	+	181.603i	0.297441	+	0.582062i
$313$	195.084	+	52.2726i	0.623272	+	0.167005i	0.556615	−	0.830771i	$-0.312100\pi$
$313$	195.084	+	52.2726i	0.623272	+	0.167005i	0.0666572	+	0.997776i	$0.478767\pi$
$314$	44.1166	+	35.6486i	0.140499	+	0.113530i
$315$	271.584	−	188.229i	0.862172	−	0.597554i
$316$	40.2474	−	8.64292i	0.127365	−	0.0273510i
$317$	275.271	+	73.7587i	0.868363	+	0.232677i	0.665380	−	0.746505i	$-0.268270\pi$
$317$	275.271	+	73.7587i	0.868363	+	0.232677i	0.202983	+	0.979182i	$0.434936\pi$
$318$	−68.8751	+	256.110i	−0.216589	+	0.805377i
$319$	19.0620	−	33.0163i	0.0597554	−	0.103499i
$320$	46.2452	+	316.641i	0.144516	+	0.989502i
$321$	172.681	+	214.100i	0.537947	+	0.666977i
$322$	−288.467	+	210.045i	−0.895861	+	0.652314i
$323$	−545.499	+	545.499i	−1.68885	+	1.68885i
$324$	−218.178	+	239.529i	−0.673389	+	0.739288i
$325$	139.654	−	160.084i	0.429705	−	0.492566i
$326$	−69.8971	+	444.322i	−0.214408	+	1.36295i
$327$	−59.6991	+	557.489i	−0.182566	+	1.70486i
$328$	259.103	+	54.2245i	0.789947	+	0.165319i
$329$	−134.267	+	232.558i	−0.408107	+	0.706863i
$330$	219.071	+	351.990i	0.663851	+	1.06664i
$331$	−169.665	+	97.9562i	−0.512584	+	0.295940i	−0.733895	−	0.679263i	$-0.762300\pi$
$331$	−169.665	+	97.9562i	−0.512584	+	0.295940i	0.221311	+	0.975203i	$0.428966\pi$
$332$	−73.6924	+	113.998i	−0.221965	+	0.343367i
$333$	−270.928	−	420.793i	−0.813596	−	1.26364i
$334$	206.627	+	166.966i	0.618644	+	0.499897i
$335$	−226.096	−	52.4081i	−0.674915	−	0.156442i
$336$	192.624	+	295.174i	0.573286	+	0.878496i
$337$	−433.451	+	116.143i	−1.28621	+	0.344638i	−0.836218	−	0.548397i	$-0.815238\pi$
$337$	−433.451	+	116.143i	−1.28621	+	0.344638i	−0.449987	+	0.893035i	$0.648571\pi$
$338$	−176.930	−	78.5524i	−0.523460	−	0.232404i
$339$	522.268	−	81.6703i	1.54061	−	0.240915i
$340$	553.462	+	8.98949i	1.62783	+	0.0264397i
$341$			31.2267i			0.0915739i
$342$	−202.753	−	458.933i	−0.592844	−	1.34191i
$343$	228.876	+	228.876i	0.667278	+	0.667278i
$344$	−28.1361	−	506.448i	−0.0817911	−	1.47223i
$345$	−344.270	−	119.636i	−0.997883	−	0.346771i
$346$	61.9102	−	23.8395i	0.178931	−	0.0689002i
$347$	−496.922	+	133.150i	−1.43205	+	0.383717i	−0.889743	−	0.456461i	$-0.849117\pi$
$347$	−496.922	+	133.150i	−1.43205	+	0.383717i	−0.542310	+	0.840179i	$0.682450\pi$
$348$	32.9219	−	3.46466i	0.0946030	−	0.00995591i
$349$	377.599	−	218.007i	1.08195	−	0.624662i	0.150525	−	0.988606i	$-0.451904\pi$
$349$	377.599	−	218.007i	1.08195	−	0.624662i	0.931421	+	0.363944i	$0.118570\pi$
$350$	210.804	−	300.603i	0.602298	−	0.858864i
$351$	−13.3543	+	229.045i	−0.0380463	+	0.652549i
$352$	−381.824	+	223.118i	−1.08473	+	0.633858i
$353$	−69.0885	+	257.842i	−0.195718	+	0.730430i	0.796362	+	0.604821i	$0.206755\pi$
$353$	−69.0885	+	257.842i	−0.195718	+	0.730430i	−0.992080	+	0.125609i	$0.959912\pi$
$354$	0.0444715	−	48.7012i	0.000125626	−	0.137574i
$355$	7.74843	−	14.5418i	0.0218266	−	0.0409628i
$356$	123.370	−	382.416i	0.346546	−	1.07420i
$357$	557.468	−	246.893i	1.56154	−	0.691577i
$358$	−59.5810	+	43.3834i	−0.166427	+	0.121183i
$359$		−	301.913i		−	0.840983i	−0.907297	−	0.420491i	$-0.861858\pi$
$359$		−	301.913i		−	0.840983i	0.907297	−	0.420491i	$-0.138142\pi$
$360$	−135.412	+	333.562i	−0.376145	+	0.926561i
$361$	415.939			1.15219
$362$	−260.785	−	358.151i	−0.720401	−	0.989369i
$363$	−123.746	+	169.622i	−0.340898	+	0.467277i
$364$	237.536	+	76.6310i	0.652571	+	0.210525i
$365$	−20.1423	−	66.0905i	−0.0551844	−	0.181070i
$366$	126.086	−	217.928i	0.344498	−	0.595432i
$367$	516.474	+	138.389i	1.40729	+	0.377081i	0.880956	−	0.473199i	$-0.156901\pi$
$367$	516.474	+	138.389i	1.40729	+	0.377081i	0.526331	+	0.850280i	$0.323567\pi$
$368$	137.800	−	363.521i	0.374456	−	0.987828i
$369$	220.530	+	200.137i	0.597642	+	0.542375i
$370$	−444.158	−	334.581i	−1.20043	−	0.904273i
$371$	162.287	+	281.089i	0.437431	+	0.757652i
$372$	−21.9341	+	15.9405i	−0.0589627	+	0.0428509i
$373$	−134.654	−	502.535i	−0.361003	−	1.34728i	−0.872760	−	0.488150i	$-0.837672\pi$
$373$	−134.654	−	502.535i	−0.361003	−	1.34728i	0.511757	−	0.859130i	$-0.328995\pi$
$374$	274.890	+	713.880i	0.735000	+	1.90877i
$375$	374.996	+	1.72497i	0.999989	+	0.00459992i
$376$	−16.2284	−	292.109i	−0.0431606	−	0.776887i
$377$	16.5758	−	16.5758i	0.0439675	−	0.0439675i
$378$	18.8388	+	396.076i	0.0498381	+	1.04782i
$379$	−273.266			−0.721017			−0.360509	−	0.932756i	$-0.617397\pi$
$379$	−273.266			−0.721017			−0.360509	+	0.932756i	$0.617397\pi$
$380$	−387.739	−	400.542i	−1.02037	−	1.05406i
$381$	389.338	−	314.019i	1.02189	−	0.824196i
$382$	−87.3149	+	196.666i	−0.228573	+	0.514833i
$383$	−58.7442	−	219.236i	−0.153379	−	0.572419i	−0.999239	−	0.0390132i	$-0.987579\pi$
$383$	−58.7442	−	219.236i	−0.153379	−	0.572419i	0.845859	−	0.533406i	$-0.179088\pi$
$384$	−351.634	−	154.303i	−0.915714	−	0.401830i
$385$	494.292	+	114.575i	1.28388	+	0.297597i
$386$	87.3075	−	108.047i	0.226185	−	0.279914i
$387$	261.052	−	507.418i	0.674553	−	1.31116i
$388$	27.1427	+	17.5461i	0.0699555	+	0.0452218i
$389$	−45.3539	−	78.5553i	−0.116591	−	0.201942i	0.801824	−	0.597561i	$-0.203863\pi$
$389$	−45.3539	−	78.5553i	−0.116591	−	0.201942i	−0.918415	+	0.395619i	$0.870530\pi$
$390$	74.0959	+	243.921i	0.189990	+	0.625437i
$391$	−582.385	−	336.240i	−1.48947	−	0.859949i
$392$	38.5264	+	8.06273i	0.0982816	+	0.0205682i
$393$	183.097	−	250.976i	0.465896	−	0.638615i
$394$	427.177	+	67.2002i	1.08421	+	0.170559i
$395$	51.4264	−	1.75053i	0.130193	−	0.00443173i
$396$	−497.513	−	0.908609i	−1.25635	−	0.00229447i
$397$	−410.228	−	410.228i	−1.03332	−	1.03332i	−0.999425	−	0.0338954i	$-0.989209\pi$
$397$	−410.228	−	410.228i	−1.03332	−	1.03332i	−0.0338954	−	0.999425i	$-0.510791\pi$
$398$	−31.3521	−	43.0576i	−0.0787741	−	0.108185i
$399$	−572.815	−	221.172i	−1.43563	−	0.554315i
$400$	−12.9904	+	399.789i	−0.0324760	+	0.999473i
$401$	1.65687	+	0.956596i	0.00413185	+	0.00238553i	0.502065	−	0.864830i	$-0.332574\pi$
$401$	1.65687	+	0.956596i	0.00413185	+	0.00238553i	−0.497933	+	0.867216i	$0.665907\pi$
$402$	197.115	−	196.756i	0.490337	−	0.489442i
$403$	−4.96950	+	18.5464i	−0.0123313	+	0.0460209i
$404$	123.628	+	575.698i	0.306010	+	1.42499i
$405$	−321.306	+	246.551i	−0.793348	+	0.608768i
$406$	25.4630	−	31.5116i	0.0627169	−	0.0776148i
$407$	198.899	−	742.302i	0.488696	−	1.82384i
$408$	−361.115	+	557.507i	−0.885086	+	1.36644i
$409$	299.641	+	172.998i	0.732619	+	0.422978i	0.819380	−	0.573251i	$-0.194318\pi$
$409$	299.641	+	172.998i	0.732619	+	0.422978i	−0.0867603	+	0.996229i	$0.527651\pi$
$410$	306.821	+	123.904i	0.748344	+	0.302206i
$411$	−59.3389	−	22.9116i	−0.144377	−	0.0557460i
$412$	−11.0056	+	218.757i	−0.0267126	+	0.530964i
$413$	−42.1453	−	42.1453i	−0.102047	−	0.102047i
$414$	340.680	−	274.260i	0.822898	−	0.662465i
$415$	−115.830	+	123.993i	−0.279107	+	0.298778i
$416$	−262.284	+	71.7516i	−0.630491	+	0.172480i
$417$	61.6690	−	84.5313i	0.147887	−	0.202713i
$418$	312.620	−	704.139i	0.747896	−	1.68454i
$419$	−622.189	−	359.221i	−1.48494	−	0.857329i	−0.485084	−	0.874467i	$-0.661211\pi$
$419$	−622.189	−	359.221i	−1.48494	−	0.857329i	−0.999853	+	0.0171385i	$0.994544\pi$
$420$	171.846	+	405.686i	0.409157	+	0.965920i
$421$	−85.1812	−	147.538i	−0.202331	−	0.350447i	0.746948	−	0.664882i	$-0.231518\pi$
$421$	−85.1812	−	147.538i	−0.202331	−	0.350447i	−0.949279	+	0.314435i	$0.898185\pi$
$422$	9.87869	+	93.0528i	0.0234092	+	0.220504i
$423$	150.570	−	292.669i	0.355957	−	0.691889i
$424$	−315.573	−	159.547i	−0.744277	−	0.376290i
$425$	678.973	+	133.220i	1.59758	+	0.313458i
$426$	9.87074	+	17.1327i	0.0231707	+	0.0402177i
$427$	−79.7502	−	297.632i	−0.186769	−	0.697030i
$428$	−326.423	+	167.182i	−0.762671	+	0.390613i
$429$	−274.225	+	221.175i	−0.639220	+	0.515560i
$430$	77.1650	−	629.323i	0.179453	−	1.46354i
$431$	209.773			0.486713			0.243356	−	0.969937i	$-0.421752\pi$
$431$	209.773			0.486713			0.243356	+	0.969937i	$0.421752\pi$
$432$	−253.331	−	349.925i	−0.586415	−	0.810011i
$433$	−39.6453	+	39.6453i	−0.0915595	+	0.0915595i	−0.751403	−	0.659844i	$-0.770623\pi$
$433$	−39.6453	+	39.6453i	−0.0915595	+	0.0915595i	0.659844	+	0.751403i	$0.270623\pi$
$434$	−5.15682	+	32.7809i	−0.0118821	+	0.0755319i
$435$	41.2704	+	3.00370i	0.0948745	+	0.00690505i
$436$	−711.461	−	229.523i	−1.63179	−	0.526429i
$437$	175.289	+	654.186i	0.401118	+	1.49699i
$438$	80.0653	+	21.5318i	0.182798	+	0.0491594i
$439$	379.156	+	656.718i	0.863682	+	1.49594i	0.868350	+	0.495952i	$0.165181\pi$
$439$	379.156	+	656.718i	0.863682	+	1.49594i	−0.00466802	+	0.999989i	$0.501486\pi$
$440$	−519.027	+	190.239i	−1.17961	+	0.432362i
$441$	32.7909	+	29.7586i	0.0743559	+	0.0674799i
$442$	49.6564	+	467.741i	0.112345	+	1.05824i
$443$	−718.882	−	192.624i	−1.62276	−	0.434817i	−0.670948	−	0.741505i	$-0.734113\pi$
$443$	−718.882	−	192.624i	−1.62276	−	0.434817i	−0.951810	+	0.306688i	$0.900779\pi$
$444$	622.938	−	239.219i	1.40301	−	0.538781i
$445$	236.196	−	443.279i	0.530778	−	0.996133i
$446$	46.2246	−	17.7995i	0.103643	−	0.0399091i
$447$	−148.828	+	204.002i	−0.332948	+	0.456381i
$448$	−437.674	+	171.167i	−0.976951	+	0.382070i
$449$	−754.075			−1.67945			−0.839727	−	0.543008i	$-0.817285\pi$
$449$	−754.075			−1.67945			−0.839727	+	0.543008i	$0.817285\pi$
$450$	−240.229	+	380.513i	−0.533843	+	0.845584i
$451$			457.291i			1.01395i
$452$	−35.4144	+	703.929i	−0.0783505	+	1.55737i
$453$	273.347	−	121.061i	0.603414	−	0.267242i
$454$	121.727	−	46.8726i	0.268120	−	0.103244i
$455$	275.341	+	146.712i	0.605144	+	0.322444i
$456$	654.184	−	139.858i	1.43461	−	0.306706i
$457$	−29.8287	+	111.322i	−0.0652706	+	0.243593i	−0.990852	−	0.134957i	$-0.956911\pi$
$457$	−29.8287	+	111.322i	−0.0652706	+	0.243593i	0.925581	+	0.378550i	$0.123577\pi$
$458$	−37.4653	−	352.906i	−0.0818020	−	0.770538i
$459$	−667.807	+	335.335i	−1.45492	+	0.730577i
$460$	249.779	−	416.846i	0.542998	−	0.906187i
$461$	−398.622	+	230.145i	−0.864690	+	0.499229i	−0.865580	−	0.500771i	$-0.833050\pi$
$461$	−398.622	+	230.145i	−0.864690	+	0.499229i	0.000890032		1.00000i	$0.499717\pi$
$462$	−430.934	+	430.148i	−0.932757	+	0.931055i
$463$	−675.274	+	180.939i	−1.45847	+	0.390797i	−0.898963	−	0.438026i	$-0.855678\pi$
$463$	−675.274	+	180.939i	−1.45847	+	0.390797i	−0.559512	+	0.828823i	$0.689011\pi$
$464$	−4.42994	+	43.9153i	−0.00954729	+	0.0946451i
$465$	−30.5052	+	14.7713i	−0.0656026	+	0.0317662i
$466$	128.565	−	817.264i	0.275892	−	1.75378i
$467$	487.701	+	487.701i	1.04433	+	1.04433i	0.998971	+	0.0453559i	$0.0144422\pi$
$467$	487.701	+	487.701i	1.04433	+	1.04433i	0.0453559	+	0.998971i	$0.485558\pi$
$468$	−295.343	−	79.7153i	−0.631074	−	0.170332i
$469$		−	340.850i		−	0.726760i
$470$	44.5073	−	362.981i	0.0946964	−	0.772301i
$471$	−84.0576	+	13.1446i	−0.178466	+	0.0279079i
$472$	63.5580	+	13.3013i	0.134657	+	0.0281807i
$473$	846.370	−	226.784i	1.78937	−	0.479459i
$474$	−30.9225	+	53.4466i	−0.0652374	+	0.112757i
$475$	−388.651	−	578.392i	−0.818212	−	1.21767i
$476$	170.680	+	794.806i	0.358572	+	1.66976i
$477$	−215.356	−	334.482i	−0.451480	−	0.701219i
$478$	37.4886	+	353.126i	0.0784280	+	0.738757i
$479$	34.4778	−	19.9058i	0.0719787	−	0.0415569i	−0.463579	−	0.886056i	$-0.653435\pi$
$479$	34.4778	−	19.9058i	0.0719787	−	0.0415569i	0.535557	+	0.844499i	$0.320102\pi$
$480$	−398.579	−	267.460i	−0.830373	−	0.557208i
$481$	236.264	−	409.221i	0.491193	−	0.850772i
$482$	5.82377	−	13.1173i	0.0120825	−	0.0272144i
$483$	56.9923	−	532.212i	0.117997	−	1.10189i
$484$	−187.759	−	207.652i	−0.387931	−	0.429032i
$485$	29.5226	+	27.5789i	0.0608713	+	0.0568636i
$486$	−46.5693	−	483.764i	−0.0958216	−	0.995399i
$487$	−26.8873	+	26.8873i	−0.0552100	+	0.0552100i	−0.734173	−	0.678963i	$-0.762430\pi$
$487$	−26.8873	+	26.8873i	−0.0552100	+	0.0552100i	0.678963	+	0.734173i	$0.262430\pi$
$488$	250.177	+	223.842i	0.512658	+	0.458694i
$489$	−423.561	−	525.155i	−0.866178	−	1.07394i
$490$	45.6217	+	18.4235i	0.0931055	+	0.0375991i
$491$	22.1072	−	38.2908i	0.0450248	−	0.0779853i	−0.842635	−	0.538486i	$-0.818997\pi$
$491$	22.1072	−	38.2908i	0.0450248	−	0.0779853i	0.887660	+	0.460500i	$0.152330\pi$
$492$	−321.208	+	233.437i	−0.652863	+	0.474465i
$493$	73.7486	+	19.7609i	0.149591	+	0.0400829i
$494$	297.733	−	368.457i	0.602698	−	0.745865i
$495$	−611.919	−	110.928i	−1.23620	−	0.224098i
$496$	−14.8428	−	32.9655i	−0.0299250	−	0.0664627i
$497$	23.3741	+	6.26308i	0.0470304	+	0.0126018i
$498$	−52.5196	−	196.724i	−0.105461	−	0.395028i
$499$	448.438	−	776.718i	0.898674	−	1.55655i	0.0694839	−	0.997583i	$-0.477865\pi$
$499$	448.438	−	776.718i	0.898674	−	1.55655i	0.829190	−	0.558966i	$-0.188802\pi$
$500$	−104.224	+	489.017i	−0.208448	+	0.978034i
$501$	−393.697	+	61.5649i	−0.785822	+	0.122884i
$502$	−8.36297	−	11.4853i	−0.0166593	−	0.0228792i
$503$	−134.585	+	134.585i	−0.267565	+	0.267565i	−0.828118	−	0.560553i	$-0.810589\pi$
$503$	−134.585	+	134.585i	−0.267565	+	0.267565i	0.560553	+	0.828118i	$0.310589\pi$
$504$	−522.125	−	83.1139i	−1.03596	−	0.164909i
$505$	25.0396	+	735.602i	0.0495833	+	1.45664i
$506$	663.420	+	104.364i	1.31111	+	0.206253i
$507$	265.502	−	117.586i	0.523672	−	0.231925i
$508$	304.019	+	593.598i	0.598463	+	1.16850i
$509$	131.338	−	227.484i	0.258031	−	0.446922i	−0.707684	−	0.706530i	$-0.750260\pi$
$509$	131.338	−	227.484i	0.258031	−	0.446922i	0.965714	+	0.259607i	$0.0835931\pi$
$510$	−567.353	+	606.229i	−1.11246	+	1.18868i
$511$	87.8743	−	50.7343i	0.171965	−	0.0992843i
$512$	297.032	−	417.032i	0.580141	−	0.814516i
$513$	714.374	+	236.766i	1.39254	+	0.461532i
$514$	−619.760	+	766.979i	−1.20576	+	1.49218i
$515$	−61.8247	+	266.721i	−0.120048	+	0.517905i
$516$	591.350	+	478.735i	1.14603	+	0.927782i
$517$	488.170	−	130.805i	0.944236	−	0.253007i
$518$	331.383	−	746.400i	0.639736	−	1.44093i
$519$	−35.8440	+	92.8326i	−0.0690635	+	0.178868i
$520$	−338.541	+	30.3891i	−0.651040	+	0.0584407i
$521$		−	262.661i		−	0.504148i	−0.967708	−	0.252074i	$-0.918887\pi$
$521$		−	262.661i		−	0.504148i	0.967708	−	0.252074i	$-0.0811126\pi$
$522$	−29.3020	+	40.0881i	−0.0561342	+	0.0767972i
$523$	−603.390	−	603.390i	−1.15371	−	1.15371i	−0.985803	−	0.167906i	$-0.946300\pi$
$523$	−603.390	−	603.390i	−1.15371	−	1.15371i	−0.167906	−	0.985803i	$-0.553700\pi$
$524$	277.812	+	307.246i	0.530175	+	0.586347i
$525$	121.890	+	537.069i	0.232171	+	1.02299i
$526$	−236.565	−	614.351i	−0.449743	−	1.16797i
$527$	−60.4063	+	16.1858i	−0.114623	+	0.0307131i
$528$	136.474	−	649.161i	0.258474	−	1.22947i
$529$	−53.1523	+	30.6875i	−0.100477	+	0.0580104i
$530$	−353.054	−	265.953i	−0.666139	−	0.501798i
$531$	54.0961	+	49.0936i	0.101876	+	0.0924549i
$532$	444.462	−	687.558i	0.835456	−	1.29240i
$533$	−72.7746	+	271.599i	−0.136538	+	0.509566i
$534$	300.891	+	522.260i	0.563467	+	0.978014i
$535$	−438.518	+	133.646i	−0.819659	+	0.249806i
$536$	203.226	+	310.800i	0.379153	+	0.579851i
$537$	11.7714	−	109.925i	0.0219206	−	0.204702i
$538$	550.779	+	756.416i	1.02375	+	1.40598i
$539$			67.9954i			0.126151i
$540$	−234.453	−	486.448i	−0.434173	−	0.900830i
$541$	−509.824			−0.942374			−0.471187	−	0.882033i	$-0.656174\pi$
$541$	−509.824			−0.942374			−0.471187	+	0.882033i	$0.656174\pi$
$542$	417.176	−	303.763i	0.769697	−	0.560449i
$543$	660.777	+	70.7598i	1.21690	+	0.130313i
$544$	−629.521	−	622.969i	−1.15721	−	1.14516i
$545$	−824.693	−	439.429i	−1.51320	−	0.806291i
$546$	−324.399	+	186.897i	−0.594137	+	0.342302i
$547$	614.842	+	164.746i	1.12402	+	0.301182i	0.772511	−	0.635001i	$-0.219000\pi$
$547$	614.842	+	164.746i	1.12402	+	0.301182i	0.351514	+	0.936183i	$0.385667\pi$
$548$	46.0427	−	71.2254i	0.0840195	−	0.129973i
$549$	115.295	+	359.632i	0.210010	+	0.655068i
$550$	−680.579	+	119.504i	−1.23742	+	0.217279i
$551$	−38.4466	−	66.5915i	−0.0697761	−	0.120856i
$552$	265.354	+	519.272i	0.480714	+	0.940710i
$553$	19.5587	+	72.9940i	0.0353683	+	0.131996i
$554$	−52.1309	+	20.0738i	−0.0940991	+	0.0362343i
$555$	819.237	−	156.831i	1.47610	−	0.282578i
$556$	93.5700	+	103.484i	0.168291	+	0.186122i
$557$	3.60960	−	3.60960i	0.00648043	−	0.00648043i	−0.703859	−	0.710340i	$-0.748541\pi$
$557$	3.60960	−	3.60960i	0.00648043	−	0.00648043i	0.710340	+	0.703859i	$0.248541\pi$
$558$	4.36756	−	40.4368i	0.00782717	−	0.0724674i
$559$	538.775			0.963819
$560$	−576.276	+	113.995i	−1.02906	+	0.203562i
$561$	−1070.44	−	413.313i	−1.90810	−	0.736743i
$562$	180.608	+	80.1856i	0.321367	+	0.142679i
$563$	137.102	+	511.673i	0.243521	+	0.908833i	0.974121	+	0.226027i	$0.0725737\pi$
$563$	137.102	+	511.673i	0.243521	+	0.908833i	−0.730600	+	0.682806i	$0.760760\pi$
$564$	341.079	+	276.125i	0.604751	+	0.489584i
$565$	−198.943	+	858.269i	−0.352111	+	1.51906i
$566$	−156.740	−	126.654i	−0.276926	−	0.223771i
$567$	−459.287	−	377.922i	−0.810031	−	0.666529i
$568$	−25.0477	+	8.22549i	−0.0440980	+	0.0144815i
$569$	−291.032	−	504.082i	−0.511479	−	0.885908i	−0.999911	−	0.0133061i	$-0.995764\pi$
$569$	−291.032	−	504.082i	−0.511479	−	0.885908i	0.488432	−	0.872602i	$-0.337569\pi$
$570$	835.750	−	27.6845i	1.46623	−	0.0485694i
$571$	786.123	+	453.868i	1.37675	+	0.794866i	0.991767	−	0.128058i	$-0.0408745\pi$
$571$	786.123	+	453.868i	1.37675	+	0.794866i	0.384982	+	0.922924i	$0.374208\pi$
$572$	−214.132	−	418.093i	−0.374357	−	0.730932i
$573$	−130.703	−	295.119i	−0.228103	−	0.515041i
$574$	−75.5178	+	480.051i	−0.131564	+	0.836326i
$575$	399.323	−	457.739i	0.694476	−	0.796068i
$576$	525.648	−	235.521i	0.912583	−	0.408890i
$577$	336.841	+	336.841i	0.583780	+	0.583780i	0.935940	−	0.352160i	$-0.114553\pi$
$577$	336.841	+	336.841i	0.583780	+	0.583780i	−0.352160	+	0.935940i	$0.614553\pi$
$578$	−771.220	+	561.558i	−1.33429	+	0.971554i
$579$	32.1928	+	205.867i	0.0556006	+	0.355556i
$580$	−15.1434	+	53.0539i	−0.0261092	+	0.0914722i
$581$	−215.806	−	124.595i	−0.371438	−	0.214450i
$582$	−46.8398	+	12.5048i	−0.0804807	+	0.0214860i
$583$	158.102	−	590.044i	0.271187	−	1.01208i
$584$	−49.8777	+	98.6549i	−0.0854071	+	0.168930i
$585$	−345.783	−	163.266i	−0.591082	−	0.279087i
$586$	429.804	+	347.304i	0.733454	+	0.592670i
$587$	263.683	−	984.077i	0.449204	−	1.67645i	−0.255388	−	0.966839i	$-0.582203\pi$
$587$	263.683	−	984.077i	0.449204	−	1.67645i	0.704592	−	0.709613i	$-0.251130\pi$
$588$	−47.7610	+	34.7101i	−0.0812262	+	0.0590308i
$589$	54.5440	+	31.4910i	0.0926045	+	0.0534652i
$590$	75.2633	+	30.3938i	0.127565	+	0.0515149i
$591$	−504.892	+	407.218i	−0.854301	+	0.689032i
$592$	142.860	+	878.177i	0.241317	+	1.48341i
$593$	238.904	+	238.904i	0.402873	+	0.402873i	0.879244	−	0.476371i	$-0.158048\pi$
$593$	238.904	+	238.904i	0.402873	+	0.402873i	−0.476371	+	0.879244i	$0.658048\pi$
$594$	502.027	−	552.168i	0.845163	−	0.929576i
$595$	34.5695	+	1015.57i	0.0581000	+	1.70684i
$596$	−225.815	−	249.740i	−0.378885	−	0.419028i
$597$	79.4398	+	8.50687i	0.133065	+	0.0142494i
$598$	377.415	+	167.563i	0.631129	+	0.280206i
$599$	653.086	+	377.059i	1.09029	+	0.629482i	0.933655	−	0.358174i	$-0.116601\pi$
$599$	653.086	+	377.059i	1.09029	+	0.629482i	0.156639	+	0.987656i	$0.449934\pi$
$600$	−431.362	−	417.046i	−0.718936	−	0.695076i
$601$	−88.9861	−	154.128i	−0.148063	−	0.256453i	0.782448	−	0.622716i	$-0.213971\pi$
$601$	−88.9861	−	154.128i	−0.148063	−	0.256453i	−0.930512	+	0.366262i	$0.880637\pi$
$602$	925.946	−	98.3005i	1.53812	−	0.163290i
$603$	20.2290	+	417.274i	0.0335472	+	0.691996i
$604$	83.6907	+	389.722i	0.138561	+	0.645235i
$605$	−185.178	−	296.928i	−0.306079	−	0.490790i
$606$	−764.499	−	442.315i	−1.26155	−	0.729893i
$607$	63.1201	+	235.568i	0.103987	+	0.388085i	0.998228	−	0.0595003i	$-0.0189507\pi$
$607$	63.1201	+	235.568i	0.103987	+	0.388085i	−0.894241	+	0.447585i	$0.852284\pi$
$608$	4.66625	+	891.944i	0.00767476	+	1.46701i
$609$	9.38894	+	60.0406i	0.0154170	+	0.0985889i
$610$	258.401	+	330.625i	0.423609	+	0.542009i
$611$	310.755			0.508601
$612$	−256.120	−	962.883i	−0.418496	−	1.57334i
$613$	−301.993	+	301.993i	−0.492648	+	0.492648i	−0.909139	−	0.416492i	$-0.863259\pi$
$613$	−301.993	+	301.993i	−0.492648	+	0.492648i	0.416492	+	0.909139i	$0.363259\pi$
$614$	−698.147	−	109.827i	−1.13705	−	0.178871i
$615$	−446.726	+	216.315i	−0.726383	+	0.351731i
$616$	−444.292	−	679.471i	−0.721254	−	1.10304i
$617$	102.129	+	381.152i	0.165526	+	0.617750i	0.997973	+	0.0636454i	$0.0202727\pi$
$617$	102.129	+	381.152i	0.165526	+	0.617750i	−0.832447	+	0.554105i	$0.813061\pi$
$618$	−232.108	−	232.533i	−0.375580	−	0.376267i
$619$	−334.588	−	579.524i	−0.540530	−	0.936226i	−0.998874	−	0.0474504i	$-0.984890\pi$
$619$	−334.588	−	579.524i	−0.540530	−	0.936226i	0.458344	−	0.888775i	$-0.348443\pi$
$620$	−10.9859	−	43.8355i	−0.0177192	−	0.0707024i
$621$	−38.1848	+	654.924i	−0.0614892	+	1.05463i
$622$	−522.412	+	55.4604i	−0.839891	+	0.0891647i
$623$	712.517	+	190.918i	1.14369	+	0.306450i
$624$	184.365	−	363.837i	0.295457	−	0.583072i
$625$	−236.168	+	578.662i	−0.377869	+	0.925859i
$626$	−145.151	−	376.951i	−0.231870	−	0.602159i
$627$	467.966	+	1056.64i	0.746357	+	1.68522i
$628$	5.69986	−	113.296i	0.00907622	−	0.180407i
$629$	1539.04			2.44680
$630$	−624.056	−	217.503i	−0.990565	−	0.345242i
$631$			606.850i			0.961728i	0.876795	+	0.480864i	$0.159677\pi$
$631$			606.850i			0.961728i	−0.876795	+	0.480864i	$0.840323\pi$
$632$	−61.3557	−	54.8971i	−0.0970817	−	0.0868626i
$633$	−113.395	−	82.7260i	−0.179138	−	0.130689i
$634$	−204.813	−	531.893i	−0.323049	−	0.838947i
$635$	243.035	+	797.441i	0.382732	+	1.25581i
$636$	495.163	−	190.151i	0.778559	−	0.298980i
$637$	−10.8210	+	40.3844i	−0.0169874	+	0.0633978i
$638$	−75.8218	+	8.04941i	−0.118843	+	0.0126166i
$639$	−28.9866	−	6.28013i	−0.0453625	−	0.00982805i
$640$	457.503	−	447.539i	0.714849	−	0.699279i
$641$	−328.784	+	189.823i	−0.512923	+	0.296136i	−0.734034	−	0.679112i	$-0.762365\pi$
$641$	−328.784	+	189.823i	−0.512923	+	0.296136i	0.221111	+	0.975249i	$0.429032\pi$
$642$	142.866	−	531.242i	0.222533	−	0.827480i
$643$	370.015	−	99.1452i	0.575451	−	0.154192i	0.0406555	−	0.999173i	$-0.487055\pi$
$643$	370.015	−	99.1452i	0.575451	−	0.154192i	0.534795	+	0.844982i	$0.320389\pi$
$644$	679.204	+	219.116i	1.05466	+	0.340243i
$645$	621.907	+	719.538i	0.964197	+	1.11556i
$646$	1524.16	+	239.769i	2.35938	+	0.371159i
$647$	11.8829	+	11.8829i	0.0183662	+	0.0183662i	0.716230	−	0.697864i	$-0.245866\pi$
$647$	11.8829	+	11.8829i	0.0183662	+	0.0183662i	−0.697864	+	0.716230i	$0.745866\pi$
$648$	644.125	+	70.7619i	0.994020	+	0.109200i
$649$			112.174i			0.172841i
$650$	−423.234	−	37.3327i	−0.651129	−	0.0574349i
$651$	−31.2492	−	38.7445i	−0.0480018	−	0.0595154i
$652$	800.668	−	410.073i	1.22802	−	0.628947i
$653$	604.956	−	162.097i	0.926426	−	0.248235i	0.236096	−	0.971730i	$-0.424132\pi$
$653$	604.956	−	162.097i	0.926426	−	0.248235i	0.690330	+	0.723495i	$0.257465\pi$
$654$	971.631	−	559.789i	1.48567	−	0.855947i
$655$	273.993	+	439.341i	0.418310	+	0.670749i
$656$	−217.362	−	482.755i	−0.331344	−	0.735907i
$657$	−104.566	+	67.3248i	−0.159157	+	0.102473i
$658$	534.068	−	56.6978i	0.811654	−	0.0861669i
$659$	−579.013	+	334.293i	−0.878623	+	0.507273i	−0.870204	−	0.492691i	$-0.836013\pi$
$659$	−579.013	+	334.293i	−0.878623	+	0.507273i	−0.00841895	+	0.999965i	$0.502680\pi$
$660$	311.194	−	768.579i	0.471506	−	1.16451i
$661$	−339.168	+	587.456i	−0.513114	+	0.888739i	0.486771	+	0.873530i	$0.338175\pi$
$661$	−339.168	+	587.456i	−0.513114	+	0.888739i	−0.999884	+	0.0152092i	$0.995159\pi$
$662$	358.116	+	158.995i	0.540961	+	0.240174i
$663$	−569.991	−	415.832i	−0.859715	−	0.627197i
$664$	271.067	−	15.0594i	0.408234	−	0.0226798i
$665$	698.605	−	747.842i	1.05053	−	1.12457i
$666$	−361.386	+	933.421i	−0.542622	+	1.40153i
$667$	47.3962	−	47.3962i	0.0710588	−	0.0710588i
$668$	26.6962	−	530.638i	0.0399644	−	0.794368i
$669$	−26.7625	+	69.3125i	−0.0400038	+	0.103606i
$670$	181.441	+	427.251i	0.270808	+	0.637689i
$671$	−289.957	+	502.220i	−0.432126	+	0.748464i
$672$	250.470	−	658.933i	0.372723	−	0.980555i
$673$	−1182.25	−	316.784i	−1.75669	−	0.470705i	−0.770659	−	0.637247i	$-0.780073\pi$
$673$	−1182.25	−	316.784i	−1.75669	−	0.470705i	−0.986034	+	0.166543i	$0.946740\pi$
$674$	698.066	+	564.074i	1.03571	+	0.836906i
$675$	−181.093	−	650.254i	−0.268287	−	0.963339i
$676$	81.2888	+	378.537i	0.120250	+	0.559966i
$677$	299.940	+	80.3686i	0.443042	+	0.118713i	0.473442	−	0.880825i	$-0.343011\pi$
$677$	299.940	+	80.3686i	0.443042	+	0.118713i	−0.0303997	+	0.999538i	$0.509678\pi$
$678$	−746.891	−	748.256i	−1.10161	−	1.10362i
$679$	−29.6660	+	51.3830i	−0.0436907	+	0.0756746i
$680$	−637.036	−	905.422i	−0.936818	−	1.33150i
$681$	−70.4756	+	182.525i	−0.103488	+	0.268026i
$682$	50.4874	−	36.7620i	0.0740284	−	0.0539032i
$683$	229.464	−	229.464i	0.335965	−	0.335965i	−0.518881	−	0.854846i	$-0.673651\pi$
$683$	229.464	−	229.464i	0.335965	−	0.335965i	0.854846	+	0.518881i	$0.173651\pi$
$684$	−503.311	+	868.096i	−0.735835	+	1.26915i
$685$	72.3698	−	77.4703i	0.105649	−	0.113095i
$686$	100.600	−	639.495i	0.146648	−	0.932209i
$687$	430.053	+	313.741i	0.625987	+	0.456683i
$688$	−785.703	+	641.713i	−1.14201	+	0.932722i
$689$	187.802	−	325.283i	0.272572	−	0.472109i
$690$	211.868	+	697.459i	0.307055	+	1.01081i
$691$	−240.568	+	138.892i	−0.348145	+	0.201002i	−0.663868	−	0.747850i	$-0.731086\pi$
$691$	−240.568	+	138.892i	−0.348145	+	0.201002i	0.315723	+	0.948851i	$0.397753\pi$
$692$	−111.428	−	72.0313i	−0.161024	−	0.104092i
$693$	−44.2246	−	912.244i	−0.0638161	−	1.31637i
$694$	800.286	+	646.673i	1.15315	+	0.931806i
$695$	92.2839	+	147.975i	0.132783	+	0.212913i
$696$	−44.3593	−	49.1493i	−0.0637347	−	0.0706169i
$697$	−884.605	+	237.029i	−1.26916	+	0.340070i
$698$	−797.008	−	353.852i	−1.14184	−	0.506951i
$699$	779.077	+	965.944i	1.11456	+	1.38189i
$700$	−734.187	+	13.0593i	−1.04884	+	0.0186562i
$701$		−	114.693i		−	0.163613i	−0.996648	−	0.0818063i	$-0.973931\pi$
$701$		−	114.693i		−	0.163613i	0.996648	−	0.0818063i	$-0.0260689\pi$
$702$	386.042	−	248.055i	0.549917	−	0.353354i
$703$	−1096.00	−	1096.00i	−1.55904	−	1.55904i
$704$	810.245	+	354.666i	1.15092	+	0.503788i
$705$	358.704	+	415.016i	0.508800	+	0.588675i
$706$	498.214	−	191.845i	0.705686	−	0.271735i
$707$	−1044.10	+	279.767i	−1.47681	+	0.395710i
$708$	−78.7926	+	57.2622i	−0.111289	+	0.0808788i
$709$	−866.555	+	500.306i	−1.22222	+	0.705650i	−0.965391	−	0.260807i	$-0.916011\pi$
$709$	−866.555	+	500.306i	−1.22222	+	0.705650i	−0.256830	+	0.966457i	$0.582678\pi$
$710$	−32.6331	+	4.59182i	−0.0459621	+	0.00646735i
$711$	−28.2761	−	88.1994i	−0.0397695	−	0.124050i
$712$	−763.531	+	250.739i	−1.07238	+	0.352161i
$713$	−14.2096	+	53.0311i	−0.0199294	+	0.0743775i
$714$	−1055.46	−	610.658i	−1.47824	−	0.855264i
$715$	−171.179	−	561.667i	−0.239411	−	0.785549i
$716$	140.285	+	45.2570i	0.195929	+	0.0632081i
$717$	−430.321	−	313.936i	−0.600168	−	0.437847i
$718$	−488.134	+	355.431i	−0.679852	+	0.495029i
$719$		−	1173.00i		−	1.63143i	−0.578452	−	0.815716i	$-0.696343\pi$
$719$		−	1173.00i		−	1.63143i	0.578452	−	0.815716i	$-0.303657\pi$
$720$	698.720	−	173.755i	0.970444	−	0.241326i
$721$	−402.094			−0.557689
$722$	−489.669	−	672.491i	−0.678212	−	0.931428i
$723$	8.71769	+	19.6840i	0.0120577	+	0.0272254i
$724$	−272.048	+	843.277i	−0.375756	+	1.16475i
$725$	−30.3418	+	61.9329i	−0.0418507	+	0.0854247i
$726$	419.926	+	0.383456i	0.578411	+	0.000528176i
$727$	−473.878	−	126.975i	−0.651827	−	0.174656i	−0.0822720	−	0.996610i	$-0.526218\pi$
$727$	−473.878	−	126.975i	−0.651827	−	0.174656i	−0.569555	+	0.821954i	$0.692884\pi$
$728$	−155.745	−	474.264i	−0.213936	−	0.651461i
$729$	584.695	+	435.399i	0.802051	+	0.597256i
$730$	−83.1425	+	110.372i	−0.113894	+	0.151194i
$731$	877.403	+	1519.71i	1.20028	+	2.07894i
$732$	−500.783	+	52.7019i	−0.684130	+	0.0719971i
$733$	30.7259	+	114.671i	0.0419181	+	0.156440i	0.983713	−	0.179749i	$-0.0575285\pi$
$733$	30.7259	+	114.671i	0.0419181	+	0.156440i	−0.941794	+	0.336189i	$0.890862\pi$
$734$	−384.278	−	997.957i	−0.523540	−	1.35961i
$735$	−66.4243	+	32.1642i	−0.0903733	+	0.0437608i
$736$	−749.968	+	205.164i	−1.01898	+	0.278756i
$737$	−453.603	+	453.603i	−0.615472	+	0.615472i
$738$	63.9596	−	592.167i	0.0866661	−	0.802394i
$739$	−820.074			−1.10971			−0.554854	−	0.831948i	$-0.687226\pi$
$739$	−820.074			−1.10971			−0.554854	+	0.831948i	$0.687226\pi$
$740$	−18.0615	+	1112.01i	−0.0244074	+	1.50271i
$741$	109.783	+	702.040i	0.148155	+	0.947423i
$742$	263.411	−	593.301i	0.355002	−	0.799598i
$743$	−195.248	−	728.676i	−0.262784	−	0.980722i	−0.963593	−	0.267373i	$-0.913844\pi$
$743$	−195.248	−	728.676i	−0.262784	−	0.980722i	0.700810	−	0.713348i	$-0.252822\pi$
$744$	51.5949	+	16.6969i	0.0693480	+	0.0224421i
$745$	−222.712	−	357.112i	−0.298942	−	0.479345i
$746$	−653.978	+	809.325i	−0.876646	+	1.08489i
$747$	271.587	+	139.724i	0.363570	+	0.187046i
$748$	830.585	−	1284.87i	1.11041	−	1.71774i
$749$	−336.628	−	583.056i	−0.449436	−	0.778446i
$750$	−438.680	−	608.325i	−0.584907	−	0.811101i
$751$	296.136	+	170.974i	0.394322	+	0.227662i	0.684031	−	0.729453i	$-0.260225\pi$
$751$	296.136	+	170.974i	0.394322	+	0.227662i	−0.289709	+	0.957115i	$0.593559\pi$
$752$	−453.178	+	370.128i	−0.602631	+	0.492191i
$753$	21.1901	+	2.26915i	0.0281409	+	0.00301348i
$754$	−46.3137	−	7.28571i	−0.0614241	−	0.00966275i
$755$	16.9507	+	497.970i	0.0224512	+	0.659562i
$756$	618.199	−	496.744i	0.817723	−	0.657069i
$757$	813.988	+	813.988i	1.07528	+	1.07528i	0.996925	+	0.0783566i	$0.0249673\pi$
$757$	813.988	+	813.988i	1.07528	+	1.07528i	0.0783566	+	0.996925i	$0.475033\pi$
$758$	321.705	+	441.817i	0.424414	+	0.582872i
$759$	−784.112	+	632.422i	−1.03309	+	0.833230i
$760$	−191.128	+	1098.44i	−0.251484	+	1.44532i
$761$	276.705	+	159.756i	0.363607	+	0.209929i	0.670662	−	0.741763i	$-0.266010\pi$
$761$	276.705	+	159.756i	0.363607	+	0.209929i	−0.307055	+	0.951692i	$0.599343\pi$
$762$	−966.060	−	259.801i	−1.26780	−	0.340946i
$763$	355.191	−	1325.59i	0.465520	−	1.73734i
$764$	420.763	−	90.3566i	0.550737	−	0.118268i
$765$	−102.593	−	1241.22i	−0.134108	−	1.62251i
$766$	−285.305	+	353.077i	−0.372461	+	0.460936i
$767$	−17.8516	+	66.6232i	−0.0232746	+	0.0868621i
$768$	164.489	+	750.178i	0.214178	+	0.976795i
$769$	−888.690	−	513.085i	−1.15564	−	0.667211i	−0.205388	−	0.978681i	$-0.565846\pi$
$769$	−888.690	−	513.085i	−1.15564	−	0.667211i	−0.950256	+	0.311469i	$0.899179\pi$
$770$	−396.667	−	934.058i	−0.515152	−	1.21306i
$771$	−228.523	−	1461.36i	−0.296398	−	1.89541i
$772$	−277.474	−	13.9596i	−0.359423	−	0.0180824i
$773$	−420.414	−	420.414i	−0.543873	−	0.543873i	0.380789	−	0.924662i	$-0.375652\pi$
$773$	−420.414	−	420.414i	−0.543873	−	0.543873i	−0.924662	+	0.380789i	$0.875652\pi$
$774$	−1127.72	+	175.294i	−1.45701	+	0.226478i
$775$	−3.84126	−	56.3582i	−0.00495647	−	0.0727202i
$776$	−3.58562	−	64.5408i	−0.00462064	−	0.0831711i
$777$	496.053	+	1120.05i	0.638420	+	1.44151i
$778$	−73.6150	+	165.809i	−0.0946208	+	0.213122i
$779$	798.756	+	461.162i	1.02536	+	0.591992i
$780$	307.141	−	406.957i	0.393771	−	0.521740i
$781$	−22.7713	−	39.4411i	−0.0291567	−	0.0505008i
$782$	141.986	+	1337.44i	0.181568	+	1.71029i
$783$	−15.0574	−	72.9454i	−0.0192304	−	0.0931614i
$784$	−32.3199	−	71.7816i	−0.0412243	−	0.0915581i
$785$	32.0193	−	138.136i	0.0407890	−	0.175970i
$786$	−621.332	−	0.567369i	−0.790498	−	0.000721844i
$787$	−253.180	−	944.882i	−0.321703	−	1.20061i	−0.917585	−	0.397540i	$-0.869864\pi$
$787$	−253.180	−	944.882i	−0.321703	−	1.20061i	0.595882	−	0.803072i	$-0.296803\pi$
$788$	−394.251	−	769.774i	−0.500318	−	0.976870i
$789$	921.202	+	355.689i	1.16756	+	0.450810i
$790$	−63.3727	−	81.0855i	−0.0802186	−	0.102640i
$791$	−1293.88			−1.63575
$792$	584.235	+	805.450i	0.737670	+	1.01698i
$793$	−252.138	+	252.138i	−0.317955	+	0.317955i
$794$	−180.312	+	1146.21i	−0.227093	+	1.44358i
$795$	651.199	−	124.662i	0.819118	−	0.156808i
$796$	−32.7061	+	101.380i	−0.0410880	+	0.127362i
$797$	−65.5269	−	244.550i	−0.0822170	−	0.306838i	0.912556	−	0.408952i	$-0.134106\pi$
$797$	−65.5269	−	244.550i	−0.0822170	−	0.306838i	−0.994773	+	0.102115i	$0.967439\pi$
$798$	316.762	+	1186.51i	0.396945	+	1.48685i
$799$	506.069	+	876.538i	0.633378	+	1.09704i
$800$	661.673	−	449.654i	0.827092	−	0.562067i
$801$	−883.604	−	191.438i	−1.10313	−	0.238999i
$802$	−0.403948	−	3.80500i	−0.000503675	−	0.00474439i
$803$	−184.460	−	49.4259i	−0.229714	−	0.0615516i
$804$	−550.172	−	87.0636i	−0.684294	−	0.108288i
$805$	787.301	+	419.505i	0.978014	+	0.521124i
$806$	35.8363	−	13.7993i	0.0444620	−	0.0171207i
$807$	−1395.56	−	149.445i	−1.72932	−	0.185186i
$808$	785.247	−	877.630i	0.971841	−	1.08618i
$809$	−627.119			−0.775177			−0.387589	−	0.921832i	$-0.626692\pi$
$809$	−627.119			−0.775177			−0.387589	+	0.921832i	$0.626692\pi$
$810$	776.886	+	229.233i	0.959119	+	0.283004i
$811$		−	1145.58i		−	1.41255i	−0.707937	−	0.706276i	$-0.750374\pi$
$811$		−	1145.58i		−	1.41255i	0.707937	−	0.706276i	$-0.249626\pi$
$812$	−80.9247	−	4.07130i	−0.0996610	−	0.00501391i
$813$	−82.4212	+	769.675i	−0.101379	+	0.946710i
$814$	−1434.31	+	552.304i	−1.76205	+	0.678506i
$815$	1075.62	−	327.815i	1.31978	−	0.402227i
$816$	1326.51	−	72.4802i	1.62562	−	0.0888237i
$817$	457.408	−	1707.07i	0.559863	−	2.08944i
$818$	−73.0529	−	688.125i	−0.0893067	−	0.841229i
$819$	118.911	−	548.846i	0.145190	−	0.670142i
$820$	−160.880	−	641.937i	−0.196195	−	0.782850i
$821$	1254.97	−	724.558i	1.52859	−	0.882531i	0.529167	−	0.848518i	$-0.322505\pi$
$821$	1254.97	−	724.558i	1.52859	−	0.882531i	0.999421	−	0.0340128i	$-0.0108287\pi$
$822$	32.8140	+	122.912i	0.0399197	+	0.149528i
$823$	276.789	−	74.1653i	0.336317	−	0.0901158i	−0.0867084	−	0.996234i	$-0.527635\pi$
$823$	276.789	−	74.1653i	0.336317	−	0.0901158i	0.423025	+	0.906118i	$0.360968\pi$
$824$	366.644	−	239.741i	0.444956	−	0.290948i
$825$	552.520	−	876.942i	0.669722	−	1.06296i
$826$	−18.5245	+	117.757i	−0.0224268	+	0.142563i
$827$	46.4859	+	46.4859i	0.0562103	+	0.0562103i	0.734653	−	0.678443i	$-0.237345\pi$
$827$	46.4859	+	46.4859i	0.0562103	+	0.0562103i	−0.678443	+	0.734653i	$0.737345\pi$
$828$	−844.495	−	227.936i	−1.01992	−	0.275284i
$829$		−	1466.67i		−	1.76920i	−0.466347	−	0.884602i	$-0.654430\pi$
$829$		−	1466.67i		−	1.76920i	0.466347	−	0.884602i	$-0.345570\pi$
$830$	336.834	+	41.3012i	0.405824	+	0.0497605i
$831$	30.1821	−	78.1688i	0.0363202	−	0.0940660i
$832$	424.786	+	339.591i	0.510560	+	0.408163i
$833$	−131.533	+	35.2442i	−0.157903	+	0.0423100i
$834$	−209.271	−	0.191096i	−0.250925	−	0.000229132i
$835$	149.968	−	646.982i	0.179602	−	0.774829i
$836$	−1506.49	+	323.511i	−1.80202	+	0.386975i
$837$	40.5551	+	45.5770i	0.0484529	+	0.0544528i
$838$	151.690	+	1428.85i	0.181015	+	1.70508i
$839$	1074.43	−	620.325i	1.28061	−	0.739363i	0.303653	−	0.952783i	$-0.401794\pi$
$839$	1074.43	−	620.325i	1.28061	−	0.739363i	0.976961	+	0.213420i	$0.0684603\pi$
$840$	453.607	−	755.441i	0.540008	−	0.899334i
$841$	416.695	−	721.737i	0.495476	−	0.858189i
$842$	−138.260	+	311.413i	−0.164204	+	0.369849i
$843$	−271.022	+	120.031i	−0.321497	+	0.142386i
$844$	138.818	−	125.520i	0.164477	−	0.148720i
$845$	16.4642	+	483.679i	0.0194843	+	0.572401i
$846$	−650.449	+	101.106i	−0.768852	+	0.119511i
$847$	363.398	−	363.398i	0.429041	−	0.429041i
$848$	113.557	+	698.049i	0.133911	+	0.823171i
$849$	298.644	−	46.7009i	0.351760	−	0.0550070i
$850$	−583.940	−	1254.60i	−0.686988	−	1.47600i
$851$	675.566	−	1170.12i	0.793850	−	1.37499i
$852$	16.0798	−	36.1288i	0.0188730	−	0.0424047i
$853$	1107.81	+	296.836i	1.29872	+	0.347991i	0.840966	−	0.541088i	$-0.181988\pi$
$853$	1107.81	+	296.836i	1.29872	+	0.347991i	0.457754	+	0.889079i	$0.348654\pi$
$854$	−387.325	+	479.331i	−0.453542	+	0.561278i
$855$	−810.859	+	956.979i	−0.948373	+	1.11927i
$856$	654.586	+	330.944i	0.764704	+	0.386617i
$857$	−862.219	−	231.031i	−1.00609	−	0.269581i	−0.282095	−	0.959386i	$-0.591029\pi$
$857$	−862.219	−	231.031i	−1.00609	−	0.269581i	−0.723995	+	0.689805i	$0.757696\pi$
$858$	680.432	+	182.987i	0.793044	+	0.213272i
$859$	−380.496	+	659.038i	−0.442952	+	0.767216i	−0.997907	−	0.0646648i	$-0.979402\pi$
$859$	−380.496	+	659.038i	−0.442952	+	0.767216i	0.554955	+	0.831880i	$0.312736\pi$
$860$	−1108.33	+	616.118i	−1.28876	+	0.716416i
$861$	−457.621	−	567.384i	−0.531499	−	0.658983i
$862$	−246.958	−	339.162i	−0.286494	−	0.393459i
$863$	−969.734	+	969.734i	−1.12368	+	1.12368i	−0.132493	+	0.991184i	$0.542298\pi$
$863$	−969.734	+	969.734i	−1.12368	+	1.12368i	−0.991184	+	0.132493i	$0.957702\pi$
$864$	−267.522	+	821.540i	−0.309632	+	0.950856i
$865$	−121.198	−	113.219i	−0.140113	−	0.130889i
$866$	110.772	+	17.4257i	0.127912	+	0.0201221i
$867$	152.370	−	1422.87i	0.175743	−	1.64115i
$868$	59.0711	−	30.2541i	0.0680543	−	0.0348550i
$869$	71.1116	−	123.169i	0.0818315	−	0.141736i
$870$	−43.7297	−	70.2623i	−0.0502641	−	0.0807612i
$871$	−341.596	+	197.220i	−0.392188	+	0.226430i
$872$	466.484	+	1420.50i	0.534958	+	1.62902i
$873$	33.2680	−	64.6644i	0.0381077	−	0.0740715i
$874$	851.329	−	1053.56i	0.974061	−	1.20544i
$875$	−906.196	−	145.981i	−1.03565	−	0.166836i
$876$	−59.4452	−	154.798i	−0.0678598	−	0.176711i
$877$	1000.76	−	268.154i	1.14112	−	0.305763i	0.361720	−	0.932287i	$-0.382190\pi$
$877$	1000.76	−	268.154i	1.14112	−	0.305763i	0.779402	+	0.626524i	$0.215523\pi$
$878$	615.417	−	1386.15i	0.700931	−	1.57876i
$879$	−818.927	+	128.061i	−0.931658	+	0.145689i
$880$	918.611	+	615.203i	1.04388	+	0.699095i
$881$			482.103i			0.547223i	0.961840	+	0.273611i	$0.0882182\pi$
$881$			482.103i			0.547223i	−0.961840	+	0.273611i	$0.911782\pi$
$882$	9.51026	−	88.0502i	0.0107826	−	0.0998302i
$883$	702.762	+	702.762i	0.795880	+	0.795880i	0.982443	−	0.186563i	$-0.0597349\pi$
$883$	702.762	+	702.762i	0.795880	+	0.795880i	−0.186563	+	0.982443i	$0.559735\pi$
$884$	697.786	−	630.938i	0.789351	−	0.713731i
$885$	−109.582	+	53.0620i	−0.123821	+	0.0599571i
$886$	534.878	+	1389.06i	0.603700	+	1.56779i
$887$	474.487	−	127.139i	0.534935	−	0.143335i	0.0187688	−	0.999824i	$-0.494025\pi$
$887$	474.487	−	127.139i	0.534935	−	0.143335i	0.516166	+	0.856488i	$0.327359\pi$
$888$	−1120.13	−	725.545i	−1.26141	−	0.817055i
$889$	−1060.28	+	612.154i	−1.19267	+	0.688588i
$890$	−994.760	+	139.973i	−1.11771	+	0.157273i
$891$	108.281	+	1114.16i	0.121527	+	1.25046i
$892$	−83.1968	−	53.7814i	−0.0932699	−	0.0602931i
$893$	263.824	−	984.605i	0.295436	−	1.10258i
$894$	505.041	+	0.461178i	0.564923	+	0.000515859i
$895$	162.612	+	86.6459i	0.181689	+	0.0968111i
$896$	792.001	+	506.124i	0.883930	+	0.564870i
$897$	−566.352	+	250.828i	−0.631385	+	0.279630i
$898$	887.745	+	1219.19i	0.988580	+	1.35767i
$899$		−	6.23330i		−	0.00693359i
$900$	898.027	−	59.5603i	0.997808	−	0.0661781i
$901$	1223.36			1.35778
$902$	739.350	−	538.352i	0.819678	−	0.596843i
$903$	−823.186	+	1128.36i	−0.911613	+	1.24957i
$904$	1179.81	−	771.451i	1.30510	−	0.853376i
$905$	−520.843	+	977.487i	−0.575517	+	1.08010i
$906$	−517.532	−	299.428i	−0.571227	−	0.330494i
$907$	−485.891	−	130.194i	−0.535712	−	0.143544i	−0.0191873	−	0.999816i	$-0.506108\pi$
$907$	−485.891	−	130.194i	−0.535712	−	0.143544i	−0.516525	+	0.856272i	$0.672775\pi$
$908$	−219.088	−	141.626i	−0.241286	−	0.155976i
$909$	1261.60	−	404.460i	1.38790	−	0.444951i
$910$	−86.9435	−	617.891i	−0.0955423	−	0.679001i
$911$	−263.122	−	455.740i	−0.288827	−	0.500264i	0.684703	−	0.728822i	$-0.259932\pi$
$911$	−263.122	−	455.740i	−0.288827	−	0.500264i	−0.973530	+	0.228559i	$0.926599\pi$
$912$	−996.269	−	893.037i	−1.09240	−	0.979208i
$913$	121.382	+	453.005i	0.132949	+	0.496172i
$914$	215.102	−	82.8283i	0.235342	−	0.0906218i
$915$	−627.776	−	45.6901i	−0.686093	−	0.0499345i
$916$	−526.473	+	476.037i	−0.574753	+	0.519691i
$917$	−537.691	+	537.691i	−0.586359	+	0.586359i
$918$	1328.36	+	684.936i	1.44701	+	0.746118i
$919$	−12.3908			−0.0134830			−0.00674148	−	0.999977i	$-0.502146\pi$
$919$	−12.3908			−0.0134830			−0.00674148	+	0.999977i	$0.502146\pi$
$920$	−968.013	+	86.8938i	−1.05219	+	0.0944498i
$921$	825.157	−	665.526i	0.895936	−	0.722613i
$922$	841.381	+	373.553i	0.912561	+	0.405155i
$923$	−7.24779	−	27.0491i	−0.00785243	−	0.0293057i
$924$	1202.79	+	190.338i	1.30172	+	0.205994i
$925$	−267.663	+	1364.18i	−0.289365	+	1.47479i
$926$	1087.52	+	878.772i	1.17442	+	0.948997i
$927$	492.248	−	23.8637i	0.531012	−	0.0257429i
$928$	76.2177	−	44.5376i	0.0821311	−	0.0479931i
$929$	−11.6687	−	20.2108i	−0.0125605	−	0.0217554i	0.859677	−	0.510838i	$-0.170665\pi$
$929$	−11.6687	−	20.2108i	−0.0125605	−	0.0217554i	−0.872237	+	0.489083i	$0.837332\pi$
$930$	59.7949	+	31.9312i	0.0642956	+	0.0343346i
$931$	118.768	+	68.5709i	0.127571	+	0.0736530i
$932$	−1472.71	+	754.269i	−1.58016	+	0.809302i
$933$	464.436	−	636.614i	0.497788	−	0.682330i
$934$	214.364	−	1362.67i	0.229512	−	1.45896i
$935$	1305.51	−	1397.52i	1.39627	−	1.49468i
$936$	218.812	+	571.357i	0.233774	+	0.610424i
$937$	134.796	+	134.796i	0.143859	+	0.143859i	0.775368	−	0.631509i	$-0.217564\pi$
$937$	134.796	+	134.796i	0.143859	+	0.143859i	−0.631509	+	0.775368i	$0.717564\pi$
$938$	−551.088	+	401.270i	−0.587514	+	0.427794i
$939$	565.228	+	218.242i	0.601947	+	0.232420i
$940$	−639.266	+	355.365i	−0.680070	+	0.378048i
$941$	317.122	+	183.090i	0.337005	+	0.194570i	0.658947	−	0.752189i	$-0.271002\pi$
$941$	317.122	+	183.090i	0.337005	+	0.194570i	−0.321942	+	0.946760i	$0.604335\pi$
$942$	120.210	+	120.430i	0.127612	+	0.127845i
$943$	−208.090	+	776.601i	−0.220668	+	0.823543i
$944$	−53.3189	−	118.420i	−0.0564819	−	0.125445i
$945$	870.247	−	474.726i	0.920896	−	0.502355i
$946$	−1363.07	−	1101.43i	−1.44087	−	1.16430i
$947$	−406.478	+	1517.00i	−0.429227	+	1.60190i	0.325288	+	0.945615i	$0.394539\pi$
$947$	−406.478	+	1517.00i	−0.429227	+	1.60190i	−0.754515	+	0.656282i	$0.772128\pi$
$948$	122.817	−	12.9251i	0.129553	−	0.0136341i
$949$	−101.690	−	58.7110i	−0.107155	−	0.0618662i
$950$	−477.602	+	1309.29i	−0.502739	+	1.37820i
$951$	797.558	+	307.948i	0.838652	+	0.323815i
$952$	1084.11	−	1211.65i	1.13877	−	1.27274i
$953$	−435.647	−	435.647i	−0.457133	−	0.457133i	0.440581	−	0.897713i	$-0.354773\pi$
$953$	−435.647	−	435.647i	−0.457133	−	0.457133i	−0.897713	+	0.440581i	$0.854773\pi$
$954$	−287.260	+	741.961i	−0.301111	+	0.777737i
$955$	537.633	−	18.3008i	0.562966	−	0.0191631i
$956$	526.801	−	476.333i	0.551047	−	0.498257i
$957$	67.4072	−	92.3968i	0.0704359	−	0.0965484i
$958$	−72.7732	−	32.3095i	−0.0759636	−	0.0337260i
$959$	134.834	+	77.8467i	0.140599	+	0.0811748i
$960$	36.8020	+	959.294i	0.0383354	+	0.999265i
$961$	−477.947	−	827.829i	−0.497344	−	0.861424i
$962$	−939.775	+	99.7686i	−0.976897	+	0.103710i
$963$	446.708	+	693.807i	0.463871	+	0.720464i
$964$	−28.0642	+	6.02665i	−0.0291123	+	0.00625171i
$965$	−338.312	−	78.4192i	−0.350582	−	0.0812634i
$966$	−927.577	+	534.408i	−0.960225	+	0.553218i
$967$	396.834	+	1481.00i	0.410376	+	1.53154i	0.793920	+	0.608022i	$0.208037\pi$
$967$	396.834	+	1481.00i	0.410376	+	1.53154i	−0.383544	+	0.923523i	$0.625297\pi$
$968$	−114.690	+	548.029i	−0.118482	+	0.566146i
$969$	−1801.44	+	1452.94i	−1.85907	+	1.49943i
$970$	9.83377	−	80.1998i	0.0101379	−	0.0826802i
$971$	−1052.92			−1.08436			−0.542181	−	0.840261i	$-0.682401\pi$
$971$	−1052.92			−1.08436			−0.542181	+	0.840261i	$0.682401\pi$
$972$	−727.326	+	644.810i	−0.748278	+	0.663385i
$973$	−181.100	+	181.100i	−0.186126	+	0.186126i
$974$	75.1249	+	11.8180i	0.0771303	+	0.0121335i
$975$	467.717	−	432.912i	0.479710	−	0.444012i
$976$	67.3851	−	668.008i	0.0690421	−	0.684435i
$977$	305.250	+	1139.21i	0.312436	+	1.16603i	0.926353	+	0.376657i	$0.122927\pi$
$977$	305.250	+	1139.21i	0.312436	+	1.16603i	−0.613916	+	0.789371i	$0.710407\pi$
$978$	−350.429	+	1303.06i	−0.358312	+	1.33237i
$979$	−694.142	−	1202.29i	−0.709032	−	1.22808i
$980$	−23.9215	−	95.4507i	−0.0244097	−	0.0973987i
$981$	−356.158	+	1643.89i	−0.363056	+	1.67573i
$982$	−87.9346	+	9.33533i	−0.0895465	+	0.00950645i
$983$	832.727	+	223.128i	0.847128	+	0.226987i	0.656172	−	0.754611i	$-0.272175\pi$
$983$	832.727	+	223.128i	0.847128	+	0.226987i	0.190956	+	0.981599i	$0.438841\pi$
$984$	755.568	+	244.514i	0.767854	+	0.248490i
$985$	−315.166	−	1034.12i	−0.319966	−	1.04986i
$986$	−54.8720	−	142.501i	−0.0556512	−	0.144524i
$987$	−474.798	+	650.818i	−0.481052	+	0.659390i
$988$	−946.233	−	47.6046i	−0.957725	−	0.0481828i
$989$	1540.56			1.55769
$990$	541.040	+	1119.94i	0.546505	+	1.13126i
$991$		−	1028.85i		−	1.03819i	−0.854717	−	0.519094i	$-0.826269\pi$
$991$		−	1028.85i		−	1.03819i	0.854717	−	0.519094i	$-0.173731\pi$
$992$	−35.8248	+	62.8069i	−0.0361137	+	0.0633134i
$993$	−537.392	+	238.002i	−0.541181	+	0.239680i
$994$	−17.3913	−	45.1646i	−0.0174963	−	0.0454373i
$995$	−62.6167	+	117.515i	−0.0629314	+	0.118106i
$996$	−256.235	+	316.510i	−0.257264	+	0.317781i
$997$	508.463	−	1897.61i	0.509993	−	1.90332i	0.0895988	−	0.995978i	$-0.471442\pi$
$997$	508.463	−	1897.61i	0.509993	−	1.90332i	0.420394	−	0.907342i	$-0.361892\pi$
$998$	−1783.73	+	189.365i	−1.78730	+	0.189744i
$999$	−673.748	−	1341.75i	−0.674422	−	1.34309i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.3.v.a.167.21	yes	272
4.3	odd	2	inner	180.3.v.a.167.9	yes	272
5.3	odd	4	inner	180.3.v.a.23.14	✓	272
9.2	odd	6	inner	180.3.v.a.47.44	yes	272
20.3	even	4	inner	180.3.v.a.23.44	yes	272
36.11	even	6	inner	180.3.v.a.47.14	yes	272
45.38	even	12	inner	180.3.v.a.83.9	yes	272
180.83	odd	12	inner	180.3.v.a.83.21	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.v.a.23.14	✓	272	5.3	odd	4	inner
180.3.v.a.23.44	yes	272	20.3	even	4	inner
180.3.v.a.47.14	yes	272	36.11	even	6	inner
180.3.v.a.47.44	yes	272	9.2	odd	6	inner
180.3.v.a.83.9	yes	272	45.38	even	12	inner
180.3.v.a.83.21	yes	272	180.83	odd	12	inner
180.3.v.a.167.9	yes	272	4.3	odd	2	inner
180.3.v.a.167.21	yes	272	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17726 - 1.61680i) q^{2} +(2.98295 + 0.319431i) q^{3} +(-1.22810 + 3.80680i) q^{4} +(-2.35124 + 4.41267i) q^{5} +(-2.99525 - 5.19889i) q^{6} +(-7.09282 - 1.90052i) q^{7} +(7.60065 - 2.49601i) q^{8} +(8.79593 + 1.90569i) q^{9} +O(q^{10})\)	\(q+(-1.17726 - 1.61680i) q^{2} +(2.98295 + 0.319431i) q^{3} +(-1.22810 + 3.80680i) q^{4} +(-2.35124 + 4.41267i) q^{5} +(-2.99525 - 5.19889i) q^{6} +(-7.09282 - 1.90052i) q^{7} +(7.60065 - 2.49601i) q^{8} +(8.79593 + 1.90569i) q^{9} +(9.90245 - 1.39338i) q^{10} +(6.90992 + 11.9683i) q^{11} +(-4.87938 + 10.9632i) q^{12} +(2.19933 + 8.20800i) q^{13} +(5.27736 + 13.7051i) q^{14} +(-8.42317 + 12.4117i) q^{15} +(-12.9835 - 9.35031i) q^{16} +(-19.5704 + 19.5704i) q^{17} +(-7.27399 - 16.4648i) q^{18} +27.8736 q^{19} +(-13.9106 - 14.3699i) q^{20} +(-20.5504 - 7.93481i) q^{21} +(11.2156 - 25.2618i) q^{22} +(6.28869 + 23.4697i) q^{23} +(23.4696 - 5.01757i) q^{24} +(-13.9433 - 20.7505i) q^{25} +(10.6815 - 13.2188i) q^{26} +(25.6290 + 8.49426i) q^{27} +(15.9456 - 24.6670i) q^{28} +(-1.37932 - 2.38905i) q^{29} +(29.9836 - 0.993217i) q^{30} +(1.95683 + 1.12978i) q^{31} +(0.167407 + 31.9996i) q^{32} +(16.7888 + 37.9081i) q^{33} +(54.6811 + 8.60199i) q^{34} +(25.0633 - 26.8297i) q^{35} +(-18.0569 + 31.1440i) q^{36} +(-39.3205 - 39.3205i) q^{37} +(-32.8146 - 45.0662i) q^{38} +(3.93858 + 25.1865i) q^{39} +(-6.85693 + 39.4079i) q^{40} +(28.6563 + 16.5447i) q^{41} +(11.3642 + 42.5673i) q^{42} +(16.4101 - 61.2432i) q^{43} +(-54.0472 + 11.6063i) q^{44} +(-29.0905 + 34.3328i) q^{45} +(30.5425 - 37.7976i) q^{46} +(9.46501 - 35.3239i) q^{47} +(-35.7424 - 32.0388i) q^{48} +(4.26096 + 2.46006i) q^{49} +(-17.1346 + 46.9724i) q^{50} +(-64.6289 + 52.1261i) q^{51} +(-33.9472 - 1.70787i) q^{52} +(-31.2552 - 31.2552i) q^{53} +(-16.4386 - 51.4371i) q^{54} +(-69.0592 + 2.35074i) q^{55} +(-58.6538 + 3.25856i) q^{56} +(83.1455 + 8.90370i) q^{57} +(-2.23880 + 5.04263i) q^{58} +(7.02941 + 4.05843i) q^{59} +(-36.9044 - 47.3082i) q^{60} +(20.9812 + 36.3405i) q^{61} +(-0.477078 - 4.49386i) q^{62} +(-58.7662 - 30.2335i) q^{63} +(51.5399 - 37.9426i) q^{64} +(-41.3903 - 9.59409i) q^{65} +(41.5250 - 71.7721i) q^{66} +(12.0139 + 44.8365i) q^{67} +(-50.4663 - 98.5353i) q^{68} +(11.2619 + 72.0177i) q^{69} +(-72.8845 - 8.93680i) q^{70} -3.29546 q^{71} +(71.6114 - 7.47019i) q^{72} +(-9.77104 + 9.77104i) q^{73} +(-17.2829 + 109.864i) q^{74} +(-34.9638 - 66.3516i) q^{75} +(-34.2317 + 106.109i) q^{76} +(-26.2648 - 98.0216i) q^{77} +(36.0849 - 36.0191i) q^{78} +(-5.14562 - 8.91247i) q^{79} +(71.7872 - 35.3071i) q^{80} +(73.7367 + 33.5246i) q^{81} +(-6.98645 - 65.8092i) q^{82} +(32.7794 + 8.78320i) q^{83} +(55.4443 - 68.4867i) q^{84} +(-40.3430 - 132.373i) q^{85} +(-118.337 + 45.5675i) q^{86} +(-3.35130 - 7.56701i) q^{87} +(82.3929 + 73.7199i) q^{88} -100.456 q^{89} +(89.7566 + 6.61496i) q^{90} -62.3977i q^{91} +(-97.0678 - 4.88345i) q^{92} +(5.47624 + 3.99514i) q^{93} +(-68.2546 + 26.2824i) q^{94} +(-65.5376 + 122.997i) q^{95} +(-9.72228 + 95.5064i) q^{96} +(2.09127 - 7.80472i) q^{97} +(-1.03883 - 9.78527i) q^{98} +(37.9712 + 118.441i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 6 q^{2} - 12 q^{5} - 8 q^{6}+O(q^{10}) \) 272 * q - 6 * q^2 - 12 * q^5 - 8 * q^6	\( 272 q - 6 q^{2} - 12 q^{5} - 8 q^{6} - 8 q^{10} + 14 q^{12} - 4 q^{13} - 4 q^{16} - 24 q^{18} - 6 q^{20} + 14 q^{22} - 4 q^{25} + 56 q^{28} - 74 q^{30} - 186 q^{32} + 28 q^{33} - 184 q^{36} - 16 q^{37} - 30 q^{38} - 2 q^{40} - 24 q^{41} + 178 q^{42} + 92 q^{45} + 152 q^{46} - 202 q^{48} - 6 q^{50} - 66 q^{52} - 264 q^{56} - 48 q^{57} + 14 q^{58} - 382 q^{60} - 8 q^{61} - 300 q^{65} - 84 q^{66} - 102 q^{68} + 98 q^{70} + 210 q^{72} - 16 q^{73} + 88 q^{76} - 12 q^{77} - 510 q^{78} - 96 q^{81} - 24 q^{82} - 4 q^{85} - 336 q^{86} - 106 q^{88} + 66 q^{90} + 336 q^{92} + 628 q^{93} - 140 q^{96} - 4 q^{97}+O(q^{100}) \) 272 * q - 6 * q^2 - 12 * q^5 - 8 * q^6 - 8 * q^10 + 14 * q^12 - 4 * q^13 - 4 * q^16 - 24 * q^18 - 6 * q^20 + 14 * q^22 - 4 * q^25 + 56 * q^28 - 74 * q^30 - 186 * q^32 + 28 * q^33 - 184 * q^36 - 16 * q^37 - 30 * q^38 - 2 * q^40 - 24 * q^41 + 178 * q^42 + 92 * q^45 + 152 * q^46 - 202 * q^48 - 6 * q^50 - 66 * q^52 - 264 * q^56 - 48 * q^57 + 14 * q^58 - 382 * q^60 - 8 * q^61 - 300 * q^65 - 84 * q^66 - 102 * q^68 + 98 * q^70 + 210 * q^72 - 16 * q^73 + 88 * q^76 - 12 * q^77 - 510 * q^78 - 96 * q^81 - 24 * q^82 - 4 * q^85 - 336 * q^86 - 106 * q^88 + 66 * q^90 + 336 * q^92 + 628 * q^93 - 140 * q^96 - 4 * q^97

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