LMFDB - Embedded newform 180.3.v.a.83.21

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			83.21
Character	$\chi$	$=$	180.83
Dual form			180.3.v.a.167.21

$q$-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 $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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	−0.726991	−	0.686647i	$-0.759082\pi$
$7$	−7.09282	+	1.90052i	−1.01326	+	0.271502i	−0.286269	+	0.958149i	$0.592415\pi$
$8$	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	−0.359744	−	0.933051i	$-0.617136\pi$
$11$	6.90992	−	11.9683i	0.628174	−	1.08803i	0.987918	−	0.154978i	$-0.0495308\pi$
$12$	−4.87938	−	10.9632i	−0.406615	−	0.913600i
$13$	2.19933	−	8.20800i	0.169179	−	0.631384i	−0.828291	−	0.560298i	$-0.810687\pi$
$13$	2.19933	−	8.20800i	0.169179	−	0.631384i	0.997470	−	0.0710866i	$-0.0226467\pi$
$14$	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	−0.986312	−	0.164890i	$-0.947273\pi$
$17$	−19.5704	−	19.5704i	−1.15120	−	1.15120i	−0.164890	−	0.986312i	$-0.552727\pi$
$18$	−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	−0.683471	−	0.729978i	$-0.739530\pi$
$23$	6.28869	−	23.4697i	0.273421	−	1.02042i	0.956892	−	0.290444i	$-0.0938031\pi$
$24$	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	−0.888827	−	0.458244i	$-0.848479\pi$
$29$	−1.37932	+	2.38905i	−0.0475627	+	0.0823811i	0.841264	+	0.540625i	$0.181812\pi$
$30$	29.9836	+	0.993217i	0.999452	+	0.0331072i
$31$	1.95683	−	1.12978i	0.0631236	−	0.0364445i	−0.468106	−	0.883672i	$-0.655063\pi$
$31$	1.95683	−	1.12978i	0.0631236	−	0.0364445i	0.531230	+	0.847228i	$0.321730\pi$
$32$	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	−0.0648192	+	0.997897i	$0.520647\pi$
$37$	−39.3205	+	39.3205i	−1.06272	+	1.06272i	−0.997897	+	0.0648192i	$0.979353\pi$
$38$	−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	−0.108015	−	0.994149i	$-0.534450\pi$
$41$	28.6563	−	16.5447i	0.698935	−	0.403530i	0.806951	+	0.590619i	$0.201116\pi$
$42$	11.3642	−	42.5673i	0.270577	−	1.01351i
$43$	16.4101	+	61.2432i	0.381629	+	1.42426i	0.843412	+	0.537267i	$0.180543\pi$
$43$	16.4101	+	61.2432i	0.381629	+	1.42426i	−0.461783	+	0.886993i	$0.652790\pi$
$44$	−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	0.990522	+	0.137357i	$0.0438607\pi$
$47$	9.46501	+	35.3239i	0.201383	+	0.751572i	−0.789138	+	0.614215i	$0.789473\pi$
$48$	−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	−0.937556	−	0.347835i	$-0.886917\pi$
$53$	−31.2552	+	31.2552i	−0.589721	+	0.589721i	0.347835	+	0.937556i	$0.386917\pi$
$54$	−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	−0.439244	−	0.898368i	$-0.644754\pi$
$59$	7.02941	−	4.05843i	0.119143	−	0.0687870i	0.558387	+	0.829581i	$0.311420\pi$
$60$	−36.9044	+	47.3082i	−0.615073	+	0.788470i
$61$	20.9812	−	36.3405i	0.343954	−	0.595746i	−0.641209	−	0.767366i	$-0.721567\pi$
$61$	20.9812	−	36.3405i	0.343954	−	0.595746i	0.985163	+	0.171620i	$0.0549002\pi$
$62$	−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	−0.816465	−	0.577395i	$-0.804069\pi$
$67$	12.0139	−	44.8365i	0.179312	−	0.669202i	0.995777	−	0.0918066i	$-0.0292641\pi$
$68$	−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	0.637008	−	0.770858i	$-0.280172\pi$
$73$	−9.77104	−	9.77104i	−0.133850	−	0.133850i	−0.770858	+	0.637008i	$0.780172\pi$
$74$	−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	−0.896754	−	0.442530i	$-0.854081\pi$
$79$	−5.14562	+	8.91247i	−0.0651344	+	0.112816i	0.831619	+	0.555346i	$0.187414\pi$
$80$	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	−0.0558870	−	0.998437i	$-0.517799\pi$
$83$	32.7794	−	8.78320i	0.394932	−	0.105822i	0.450819	+	0.892615i	$0.351132\pi$
$84$	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	0.975867	−	0.218364i	$-0.0700720\pi$
$97$	2.09127	+	7.80472i	0.0215595	+	0.0804610i	−0.954308	+	0.298825i	$0.903405\pi$
$98$	−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	0.973503	−	0.228675i	$-0.0734394\pi$
$101$	127.484	+	73.6028i	1.26222	+	0.728741i	0.288713	+	0.957416i	$0.406773\pi$
$102$	160.363	−	43.1261i	1.57219	−	0.422805i
$103$	52.8927	+	14.1725i	0.513521	+	0.137598i	0.506268	−	0.862376i	$-0.331025\pi$
$103$	52.8927	+	14.1725i	0.513521	+	0.137598i	0.00725290	+	0.999974i	$0.497691\pi$
$104$	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	−0.335967	−	0.941874i	$-0.609063\pi$
$107$	64.8320	−	64.8320i	0.605906	−	0.605906i	0.941874	+	0.335967i	$0.109063\pi$
$108$	−63.8111	−	87.1329i	−0.590844	−	0.806786i
$109$		−	186.892i		−	1.71461i	−0.514812	−	0.857303i	$-0.672138\pi$
$109$		−	186.892i		−	1.71461i	0.514812	−	0.857303i	$-0.327862\pi$
$110$	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	0.915172	−	0.403064i	$-0.132055\pi$
$113$	170.201	+	45.6052i	1.50620	+	0.403586i	0.591030	+	0.806649i	$0.298721\pi$
$114$	−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	0.997597	−	0.0692793i	$-0.0220700\pi$
$127$	117.896	+	117.896i	0.928318	+	0.928318i	−0.0692793	+	0.997597i	$0.522070\pi$
$128$	−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	0.993133	−	0.116991i	$-0.0373249\pi$
$131$	51.7777	+	89.6815i	0.395249	+	0.684592i	−0.597884	+	0.801583i	$0.703992\pi$
$132$	−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	−0.332789	−	0.943001i	$-0.607990\pi$
$137$	−20.4804	+	5.48770i	−0.149492	+	0.0400562i	0.183297	+	0.983058i	$0.441323\pi$
$138$	103.180	+	102.992i	0.747683	+	0.746319i
$139$	17.4393	+	30.2057i	0.125462	+	0.217307i	0.921914	−	0.387396i	$-0.126625\pi$
$139$	17.4393	+	30.2057i	0.125462	+	0.217307i	−0.796451	+	0.604703i	$0.793292\pi$
$140$	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	0.689529	−	0.724258i	$-0.257818\pi$
$149$	−42.0868	−	72.8964i	−0.282461	−	0.489238i	−0.971990	+	0.235020i	$0.924484\pi$
$150$	−66.1159	−	134.643i	−0.440772	−	0.897619i
$151$	86.3008	+	49.8258i	0.571529	+	0.329972i	0.757760	−	0.652534i	$-0.226294\pi$
$151$	86.3008	+	49.8258i	0.571529	+	0.329972i	−0.186231	+	0.982506i	$0.559627\pi$
$152$	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	0.170521	−	0.985354i	$-0.445455\pi$
$157$	−27.3934	−	7.34004i	−0.174480	−	0.0467518i	−0.345001	+	0.938602i	$0.612122\pi$
$158$	−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	−0.999709	−	0.0241065i	$-0.992326\pi$
$163$	−159.023	+	159.023i	−0.975603	+	0.975603i	0.0241065	+	0.999709i	$0.492326\pi$
$164$	−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	−0.146663	−	0.989186i	$-0.546853\pi$
$167$	−128.301	−	34.3782i	−0.768271	−	0.205857i	−0.621607	+	0.783329i	$0.713520\pi$
$168$	−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	0.936664	−	0.350229i	$-0.113896\pi$
$173$	−8.58522	−	32.0405i	−0.0496256	−	0.185205i	−0.986289	+	0.165024i	$0.947230\pi$
$174$	−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	$0.0328237\pi$
$179$			36.8511i			0.205872i	−0.994688	+	0.102936i	$0.967176\pi$
$180$	−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	−0.971790	−	0.235846i	$-0.924214\pi$
$191$	−53.7944	+	93.1747i	−0.281646	+	0.487826i	0.690144	+	0.723672i	$0.257547\pi$
$192$	165.861	+	96.7171i	0.863858	+	0.503735i
$193$	17.9766	−	67.0896i	0.0931431	−	0.347615i	−0.903588	−	0.428402i	$-0.859077\pi$
$193$	17.9766	−	67.0896i	0.0931431	−	0.347615i	0.996731	+	0.0807872i	$0.0257434\pi$
$194$	−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	0.203083	−	0.979161i	$-0.434904\pi$
$197$	−152.887	−	152.887i	−0.776078	−	0.776078i	−0.979161	+	0.203083i	$0.934904\pi$
$198$	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	−0.592935	−	0.805250i	$-0.702031\pi$
$211$	−40.5195	+	23.3939i	−0.192035	+	0.110872i	0.400900	+	0.916122i	$0.368698\pi$
$212$	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	0.950063	−	0.312058i	$-0.101018\pi$
$223$	−6.41007	−	23.9227i	−0.0287447	−	0.107277i	−0.978808	+	0.204781i	$0.934352\pi$
$224$	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	0.918726	−	0.394895i	$-0.129219\pi$
$227$	−16.8801	−	62.9973i	−0.0743616	−	0.277521i	−0.993088	+	0.117374i	$0.962552\pi$
$228$	−136.006	−	305.584i	−0.596518	−	1.34028i
$229$	153.672	−	88.7223i	0.671055	−	0.387434i	−0.125421	−	0.992104i	$-0.540028\pi$
$229$	153.672	−	88.7223i	0.671055	−	0.387434i	0.796476	+	0.604670i	$0.206695\pi$
$230$	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	0.302082	−	0.953282i	$-0.402318\pi$
$233$	292.500	−	292.500i	1.25536	−	1.25536i	0.953282	−	0.302082i	$-0.0976816\pi$
$234$	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	−0.785914	−	0.618335i	$-0.787807\pi$
$239$	−153.767	+	88.7775i	−0.643377	+	0.371454i	0.142537	+	0.989789i	$0.454474\pi$
$240$	225.416	+	82.3882i	0.939232	+	0.343284i
$241$	3.58801	−	6.21461i	0.0148880	−	0.0257868i	−0.858485	−	0.512838i	$-0.828594\pi$
$241$	3.58801	−	6.21461i	0.0148880	−	0.0257868i	0.873373	+	0.487051i	$0.161927\pi$
$242$	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	0.0247487	+	0.999694i	$0.492121\pi$
$257$	−127.609	+	476.241i	−0.496531	+	1.85308i	−0.521280	+	0.853386i	$0.674545\pi$
$258$	−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	0.402582	−	0.915384i	$-0.368113\pi$
$263$	317.946	−	85.1934i	1.20892	−	0.323929i	0.806338	+	0.591455i	$0.201446\pi$
$264$	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	$-0.842064\pi$
$271$		−	258.025i		−	0.952122i	0.879412	−	0.476061i	$-0.157936\pi$
$272$	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	0.977746	−	0.209791i	$-0.0672782\pi$
$277$	7.22910	+	26.9794i	0.0260978	+	0.0973985i	−0.951648	+	0.307189i	$0.900612\pi$
$278$	−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	0.339958	−	0.940441i	$-0.389587\pi$
$281$	−85.5669	−	49.4021i	−0.304509	−	0.175808i	−0.644467	+	0.764633i	$0.722920\pi$
$282$	−211.995	−	56.5965i	−0.751756	−	0.200697i
$283$	97.3247	+	26.0781i	0.343903	+	0.0921487i	0.426637	−	0.904423i	$-0.359698\pi$
$283$	97.3247	+	26.0781i	0.343903	+	0.0921487i	−0.0827333	+	0.996572i	$0.526365\pi$
$284$	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	−0.227180	−	0.973853i	$-0.572950\pi$
$293$	−266.879	−	71.5100i	−0.910849	−	0.244061i	−0.683670	+	0.729792i	$0.739617\pi$
$294$	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	0.985216	−	0.171315i	$-0.0548016\pi$
$307$	249.868	+	249.868i	0.813901	+	0.813901i	−0.171315	+	0.985216i	$0.554802\pi$
$308$	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	0.996165	−	0.0874997i	$-0.0278877\pi$
$311$	131.337	+	227.482i	0.422305	+	0.731454i	−0.573859	+	0.818954i	$0.694554\pi$
$312$	92.8016	−	181.603i	0.297441	−	0.582062i
$313$	195.084	−	52.2726i	0.623272	−	0.167005i	0.0666572	−	0.997776i	$-0.478767\pi$
$313$	195.084	−	52.2726i	0.623272	−	0.167005i	0.556615	+	0.830771i	$0.312100\pi$
$314$	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	0.202983	−	0.979182i	$-0.434936\pi$
$317$	275.271	−	73.7587i	0.868363	−	0.232677i	0.665380	+	0.746505i	$0.268270\pi$
$318$	−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	0.221311	−	0.975203i	$-0.428966\pi$
$331$	−169.665	−	97.9562i	−0.512584	−	0.295940i	−0.733895	+	0.679263i	$0.762300\pi$
$332$	−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	−0.449987	−	0.893035i	$-0.648571\pi$
$337$	−433.451	−	116.143i	−1.28621	−	0.344638i	−0.836218	+	0.548397i	$0.815238\pi$
$338$	−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	−0.542310	−	0.840179i	$-0.682450\pi$
$347$	−496.922	−	133.150i	−1.43205	−	0.383717i	−0.889743	+	0.456461i	$0.849117\pi$
$348$	32.9219	+	3.46466i	0.0946030	+	0.00995591i
$349$	377.599	+	218.007i	1.08195	+	0.624662i	0.931421	−	0.363944i	$-0.118570\pi$
$349$	377.599	+	218.007i	1.08195	+	0.624662i	0.150525	+	0.988606i	$0.451904\pi$
$350$	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	−0.992080	−	0.125609i	$-0.959912\pi$
$353$	−69.0885	−	257.842i	−0.195718	−	0.730430i	0.796362	−	0.604821i	$-0.206755\pi$
$354$	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	$0.138142\pi$
$359$			301.913i			0.840983i	−0.907297	+	0.420491i	$0.861858\pi$
$360$	−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	0.526331	−	0.850280i	$-0.323567\pi$
$367$	516.474	−	138.389i	1.40729	−	0.377081i	0.880956	+	0.473199i	$0.156901\pi$
$368$	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	0.511757	+	0.859130i	$0.328995\pi$
$373$	−134.654	+	502.535i	−0.361003	+	1.34728i	−0.872760	+	0.488150i	$0.837672\pi$
$374$	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	0.845859	+	0.533406i	$0.179088\pi$
$383$	−58.7442	+	219.236i	−0.153379	+	0.572419i	−0.999239	+	0.0390132i	$0.987579\pi$
$384$	−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	−0.918415	−	0.395619i	$-0.870530\pi$
$389$	−45.3539	+	78.5553i	−0.116591	+	0.201942i	0.801824	+	0.597561i	$0.203863\pi$
$390$	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	−0.0338954	+	0.999425i	$0.510791\pi$
$397$	−410.228	+	410.228i	−1.03332	+	1.03332i	−0.999425	+	0.0338954i	$0.989209\pi$
$398$	−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	−0.497933	−	0.867216i	$-0.665907\pi$
$401$	1.65687	−	0.956596i	0.00413185	−	0.00238553i	0.502065	+	0.864830i	$0.332574\pi$
$402$	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	−0.0867603	−	0.996229i	$-0.527651\pi$
$409$	299.641	−	172.998i	0.732619	−	0.422978i	0.819380	+	0.573251i	$0.194318\pi$
$410$	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	−0.999853	−	0.0171385i	$-0.994544\pi$
$419$	−622.189	+	359.221i	−1.48494	+	0.857329i	−0.485084	+	0.874467i	$0.661211\pi$
$420$	171.846	−	405.686i	0.409157	−	0.965920i
$421$	−85.1812	+	147.538i	−0.202331	+	0.350447i	−0.949279	−	0.314435i	$-0.898185\pi$
$421$	−85.1812	+	147.538i	−0.202331	+	0.350447i	0.746948	+	0.664882i	$0.231518\pi$
$422$	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	0.659844	−	0.751403i	$-0.270623\pi$
$433$	−39.6453	−	39.6453i	−0.0915595	−	0.0915595i	−0.751403	+	0.659844i	$0.770623\pi$
$434$	−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	−0.00466802	−	0.999989i	$-0.501486\pi$
$439$	379.156	−	656.718i	0.863682	−	1.49594i	0.868350	−	0.495952i	$-0.165181\pi$
$440$	−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	−0.951810	−	0.306688i	$-0.900779\pi$
$443$	−718.882	+	192.624i	−1.62276	+	0.434817i	−0.670948	+	0.741505i	$0.734113\pi$
$444$	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	0.925581	−	0.378550i	$-0.123577\pi$
$457$	−29.8287	−	111.322i	−0.0652706	−	0.243593i	−0.990852	+	0.134957i	$0.956911\pi$
$458$	−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	0.000890032	−	1.00000i	$-0.499717\pi$
$461$	−398.622	−	230.145i	−0.864690	−	0.499229i	−0.865580	+	0.500771i	$0.833050\pi$
$462$	−430.934	−	430.148i	−0.932757	−	0.931055i
$463$	−675.274	−	180.939i	−1.45847	−	0.390797i	−0.559512	−	0.828823i	$-0.689011\pi$
$463$	−675.274	−	180.939i	−1.45847	−	0.390797i	−0.898963	+	0.438026i	$0.855678\pi$
$464$	−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	0.0453559	−	0.998971i	$-0.485558\pi$
$467$	487.701	−	487.701i	1.04433	−	1.04433i	0.998971	−	0.0453559i	$-0.0144422\pi$
$468$	−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	0.535557	−	0.844499i	$-0.320102\pi$
$479$	34.4778	+	19.9058i	0.0719787	+	0.0415569i	−0.463579	+	0.886056i	$0.653435\pi$
$480$	−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	0.678963	−	0.734173i	$-0.262430\pi$
$487$	−26.8873	−	26.8873i	−0.0552100	−	0.0552100i	−0.734173	+	0.678963i	$0.762430\pi$
$488$	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	0.887660	−	0.460500i	$-0.152330\pi$
$491$	22.1072	+	38.2908i	0.0450248	+	0.0779853i	−0.842635	+	0.538486i	$0.818997\pi$
$492$	−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	0.829190	+	0.558966i	$0.188802\pi$
$499$	448.438	+	776.718i	0.898674	+	1.55655i	0.0694839	+	0.997583i	$0.477865\pi$
$500$	−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	0.560553	−	0.828118i	$-0.310589\pi$
$503$	−134.585	−	134.585i	−0.267565	−	0.267565i	−0.828118	+	0.560553i	$0.810589\pi$
$504$	−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	0.965714	−	0.259607i	$-0.0835931\pi$
$509$	131.338	+	227.484i	0.258031	+	0.446922i	−0.707684	+	0.706530i	$0.750260\pi$
$510$	−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	$0.0811126\pi$
$521$			262.661i			0.504148i	−0.967708	+	0.252074i	$0.918887\pi$
$522$	−29.3020	−	40.0881i	−0.0561342	−	0.0767972i
$523$	−603.390	+	603.390i	−1.15371	+	1.15371i	−0.167906	+	0.985803i	$0.553700\pi$
$523$	−603.390	+	603.390i	−1.15371	+	1.15371i	−0.985803	+	0.167906i	$0.946300\pi$
$524$	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	0.351514	−	0.936183i	$-0.385667\pi$
$547$	614.842	−	164.746i	1.12402	−	0.301182i	0.772511	+	0.635001i	$0.219000\pi$
$548$	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	0.710340	−	0.703859i	$-0.248541\pi$
$557$	3.60960	+	3.60960i	0.00648043	+	0.00648043i	−0.703859	+	0.710340i	$0.748541\pi$
$558$	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	−0.730600	−	0.682806i	$-0.760760\pi$
$563$	137.102	−	511.673i	0.243521	−	0.908833i	0.974121	−	0.226027i	$-0.0725737\pi$
$564$	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	0.488432	+	0.872602i	$0.337569\pi$
$569$	−291.032	+	504.082i	−0.511479	+	0.885908i	−0.999911	+	0.0133061i	$0.995764\pi$
$570$	835.750	+	27.6845i	1.46623	+	0.0485694i
$571$	786.123	−	453.868i	1.37675	−	0.794866i	0.384982	−	0.922924i	$-0.374208\pi$
$571$	786.123	−	453.868i	1.37675	−	0.794866i	0.991767	+	0.128058i	$0.0408745\pi$
$572$	−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	−0.352160	−	0.935940i	$-0.614553\pi$
$577$	336.841	−	336.841i	0.583780	−	0.583780i	0.935940	+	0.352160i	$0.114553\pi$
$578$	−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	0.704592	+	0.709613i	$0.251130\pi$
$587$	263.683	+	984.077i	0.449204	+	1.67645i	−0.255388	+	0.966839i	$0.582203\pi$
$588$	−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	−0.476371	−	0.879244i	$-0.658048\pi$
$593$	238.904	−	238.904i	0.402873	−	0.402873i	0.879244	+	0.476371i	$0.158048\pi$
$594$	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	0.156639	−	0.987656i	$-0.449934\pi$
$599$	653.086	−	377.059i	1.09029	−	0.629482i	0.933655	+	0.358174i	$0.116601\pi$
$600$	−431.362	+	417.046i	−0.718936	+	0.695076i
$601$	−88.9861	+	154.128i	−0.148063	+	0.256453i	−0.930512	−	0.366262i	$-0.880637\pi$
$601$	−88.9861	+	154.128i	−0.148063	+	0.256453i	0.782448	+	0.622716i	$0.213971\pi$
$602$	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	−0.894241	−	0.447585i	$-0.852284\pi$
$607$	63.1201	−	235.568i	0.103987	−	0.388085i	0.998228	+	0.0595003i	$0.0189507\pi$
$608$	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	0.416492	−	0.909139i	$-0.363259\pi$
$613$	−301.993	−	301.993i	−0.492648	−	0.492648i	−0.909139	+	0.416492i	$0.863259\pi$
$614$	−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	−0.832447	−	0.554105i	$-0.813061\pi$
$617$	102.129	−	381.152i	0.165526	−	0.617750i	0.997973	−	0.0636454i	$-0.0202727\pi$
$618$	−232.108	+	232.533i	−0.375580	+	0.376267i
$619$	−334.588	+	579.524i	−0.540530	+	0.936226i	0.458344	+	0.888775i	$0.348443\pi$
$619$	−334.588	+	579.524i	−0.540530	+	0.936226i	−0.998874	+	0.0474504i	$0.984890\pi$
$620$	−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	$-0.840323\pi$
$631$		−	606.850i		−	0.961728i	0.876795	−	0.480864i	$-0.159677\pi$
$632$	−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	0.221111	−	0.975249i	$-0.429032\pi$
$641$	−328.784	−	189.823i	−0.512923	−	0.296136i	−0.734034	+	0.679112i	$0.762365\pi$
$642$	142.866	+	531.242i	0.222533	+	0.827480i
$643$	370.015	+	99.1452i	0.575451	+	0.154192i	0.534795	−	0.844982i	$-0.320389\pi$
$643$	370.015	+	99.1452i	0.575451	+	0.154192i	0.0406555	+	0.999173i	$0.487055\pi$
$644$	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	−0.697864	−	0.716230i	$-0.745866\pi$
$647$	11.8829	−	11.8829i	0.0183662	−	0.0183662i	0.716230	+	0.697864i	$0.245866\pi$
$648$	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	0.690330	−	0.723495i	$-0.257465\pi$
$653$	604.956	+	162.097i	0.926426	+	0.248235i	0.236096	+	0.971730i	$0.424132\pi$
$654$	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	−0.00841895	−	0.999965i	$-0.502680\pi$
$659$	−579.013	−	334.293i	−0.878623	−	0.507273i	−0.870204	+	0.492691i	$0.836013\pi$
$660$	311.194	+	768.579i	0.471506	+	1.16451i
$661$	−339.168	−	587.456i	−0.513114	−	0.888739i	−0.999884	−	0.0152092i	$-0.995159\pi$
$661$	−339.168	−	587.456i	−0.513114	−	0.888739i	0.486771	−	0.873530i	$-0.338175\pi$
$662$	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	−0.986034	−	0.166543i	$-0.946740\pi$
$673$	−1182.25	+	316.784i	−1.75669	+	0.470705i	−0.770659	+	0.637247i	$0.780073\pi$
$674$	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	−0.0303997	−	0.999538i	$-0.509678\pi$
$677$	299.940	−	80.3686i	0.443042	−	0.118713i	0.473442	+	0.880825i	$0.343011\pi$
$678$	−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	0.854846	−	0.518881i	$-0.173651\pi$
$683$	229.464	+	229.464i	0.335965	+	0.335965i	−0.518881	+	0.854846i	$0.673651\pi$
$684$	−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	0.315723	−	0.948851i	$-0.397753\pi$
$691$	−240.568	−	138.892i	−0.348145	−	0.201002i	−0.663868	+	0.747850i	$0.731086\pi$
$692$	−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	$0.0260689\pi$
$701$			114.693i			0.163613i	−0.996648	+	0.0818063i	$0.973931\pi$
$702$	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	−0.256830	−	0.966457i	$-0.582678\pi$
$709$	−866.555	−	500.306i	−1.22222	−	0.705650i	−0.965391	+	0.260807i	$0.916011\pi$
$710$	−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	$0.303657\pi$
$719$			1173.00i			1.63143i	−0.578452	+	0.815716i	$0.696343\pi$
$720$	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	−0.569555	−	0.821954i	$-0.692884\pi$
$727$	−473.878	+	126.975i	−0.651827	+	0.174656i	−0.0822720	+	0.996610i	$0.526218\pi$
$728$	−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	−0.941794	−	0.336189i	$-0.890862\pi$
$733$	30.7259	−	114.671i	0.0419181	−	0.156440i	0.983713	+	0.179749i	$0.0575285\pi$
$734$	−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	0.700810	+	0.713348i	$0.252822\pi$
$743$	−195.248	+	728.676i	−0.262784	+	0.980722i	−0.963593	+	0.267373i	$0.913844\pi$
$744$	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	−0.289709	−	0.957115i	$-0.593559\pi$
$751$	296.136	−	170.974i	0.394322	−	0.227662i	0.684031	+	0.729453i	$0.260225\pi$
$752$	−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	0.0783566	−	0.996925i	$-0.475033\pi$
$757$	813.988	−	813.988i	1.07528	−	1.07528i	0.996925	−	0.0783566i	$-0.0249673\pi$
$758$	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	−0.307055	−	0.951692i	$-0.599343\pi$
$761$	276.705	−	159.756i	0.363607	−	0.209929i	0.670662	+	0.741763i	$0.266010\pi$
$762$	−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	−0.950256	−	0.311469i	$-0.899179\pi$
$769$	−888.690	+	513.085i	−1.15564	+	0.667211i	−0.205388	+	0.978681i	$0.565846\pi$
$770$	−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	−0.924662	−	0.380789i	$-0.875652\pi$
$773$	−420.414	+	420.414i	−0.543873	+	0.543873i	0.380789	+	0.924662i	$0.375652\pi$
$774$	−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	0.595882	+	0.803072i	$0.296803\pi$
$787$	−253.180	+	944.882i	−0.321703	+	1.20061i	−0.917585	+	0.397540i	$0.869864\pi$
$788$	−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	−0.994773	−	0.102115i	$-0.967439\pi$
$797$	−65.5269	+	244.550i	−0.0822170	+	0.306838i	0.912556	+	0.408952i	$0.134106\pi$
$798$	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	$0.249626\pi$
$811$			1145.58i			1.41255i	−0.707937	+	0.706276i	$0.750374\pi$
$812$	−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	0.999421	+	0.0340128i	$0.0108287\pi$
$821$	1254.97	+	724.558i	1.52859	+	0.882531i	0.529167	+	0.848518i	$0.322505\pi$
$822$	32.8140	−	122.912i	0.0399197	−	0.149528i
$823$	276.789	+	74.1653i	0.336317	+	0.0901158i	0.423025	−	0.906118i	$-0.360968\pi$
$823$	276.789	+	74.1653i	0.336317	+	0.0901158i	−0.0867084	+	0.996234i	$0.527635\pi$
$824$	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	−0.678443	−	0.734653i	$-0.737345\pi$
$827$	46.4859	−	46.4859i	0.0562103	−	0.0562103i	0.734653	+	0.678443i	$0.237345\pi$
$828$	−844.495	+	227.936i	−1.01992	+	0.275284i
$829$			1466.67i			1.76920i	0.466347	+	0.884602i	$0.345570\pi$
$829$			1466.67i			1.76920i	−0.466347	+	0.884602i	$0.654430\pi$
$830$	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	0.976961	−	0.213420i	$-0.0684603\pi$
$839$	1074.43	+	620.325i	1.28061	+	0.739363i	0.303653	+	0.952783i	$0.401794\pi$
$840$	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	0.457754	−	0.889079i	$-0.348654\pi$
$853$	1107.81	−	296.836i	1.29872	−	0.347991i	0.840966	+	0.541088i	$0.181988\pi$
$854$	−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	−0.723995	−	0.689805i	$-0.757696\pi$
$857$	−862.219	+	231.031i	−1.00609	+	0.269581i	−0.282095	+	0.959386i	$0.591029\pi$
$858$	680.432	−	182.987i	0.793044	−	0.213272i
$859$	−380.496	−	659.038i	−0.442952	−	0.767216i	0.554955	−	0.831880i	$-0.312736\pi$
$859$	−380.496	−	659.038i	−0.442952	−	0.767216i	−0.997907	+	0.0646648i	$0.979402\pi$
$860$	−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	−0.991184	−	0.132493i	$-0.957702\pi$
$863$	−969.734	−	969.734i	−1.12368	−	1.12368i	−0.132493	−	0.991184i	$-0.542298\pi$
$864$	−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	0.779402	−	0.626524i	$-0.215523\pi$
$877$	1000.76	+	268.154i	1.14112	+	0.305763i	0.361720	+	0.932287i	$0.382190\pi$
$878$	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	$-0.911782\pi$
$881$		−	482.103i		−	0.547223i	0.961840	−	0.273611i	$-0.0882182\pi$
$882$	9.51026	+	88.0502i	0.0107826	+	0.0998302i
$883$	702.762	−	702.762i	0.795880	−	0.795880i	−0.186563	−	0.982443i	$-0.559735\pi$
$883$	702.762	−	702.762i	0.795880	−	0.795880i	0.982443	+	0.186563i	$0.0597349\pi$
$884$	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	0.516166	−	0.856488i	$-0.327359\pi$
$887$	474.487	+	127.139i	0.534935	+	0.143335i	0.0187688	+	0.999824i	$0.494025\pi$
$888$	−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	−0.516525	−	0.856272i	$-0.672775\pi$
$907$	−485.891	+	130.194i	−0.535712	+	0.143544i	−0.0191873	+	0.999816i	$0.506108\pi$
$908$	−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	−0.973530	−	0.228559i	$-0.926599\pi$
$911$	−263.122	+	455.740i	−0.288827	+	0.500264i	0.684703	+	0.728822i	$0.259932\pi$
$912$	−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	−0.872237	−	0.489083i	$-0.837332\pi$
$929$	−11.6687	+	20.2108i	−0.0125605	+	0.0217554i	0.859677	+	0.510838i	$0.170665\pi$
$930$	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	−0.631509	−	0.775368i	$-0.717564\pi$
$937$	134.796	−	134.796i	0.143859	−	0.143859i	0.775368	+	0.631509i	$0.217564\pi$
$938$	−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	−0.321942	−	0.946760i	$-0.604335\pi$
$941$	317.122	−	183.090i	0.337005	−	0.194570i	0.658947	+	0.752189i	$0.271002\pi$
$942$	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	−0.754515	−	0.656282i	$-0.772128\pi$
$947$	−406.478	−	1517.00i	−0.429227	−	1.60190i	0.325288	−	0.945615i	$-0.394539\pi$
$948$	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	−0.897713	−	0.440581i	$-0.854773\pi$
$953$	−435.647	+	435.647i	−0.457133	+	0.457133i	0.440581	+	0.897713i	$0.354773\pi$
$954$	−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	−0.383544	−	0.923523i	$-0.625297\pi$
$967$	396.834	−	1481.00i	0.410376	−	1.53154i	0.793920	−	0.608022i	$-0.208037\pi$
$968$	−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	−0.613916	−	0.789371i	$-0.710407\pi$
$977$	305.250	−	1139.21i	0.312436	−	1.16603i	0.926353	−	0.376657i	$-0.122927\pi$
$978$	−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	0.190956	−	0.981599i	$-0.438841\pi$
$983$	832.727	−	223.128i	0.847128	−	0.226987i	0.656172	+	0.754611i	$0.272175\pi$
$984$	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	$0.173731\pi$
$991$			1028.85i			1.03819i	−0.854717	+	0.519094i	$0.826269\pi$
$992$	−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	0.420394	+	0.907342i	$0.361892\pi$
$997$	508.463	+	1897.61i	0.509993	+	1.90332i	0.0895988	+	0.995978i	$0.471442\pi$
$998$	−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.83.21	yes	272
4.3	odd	2	inner	180.3.v.a.83.9	yes	272
5.2	odd	4	inner	180.3.v.a.47.14	yes	272
9.5	odd	6	inner	180.3.v.a.23.44	yes	272
20.7	even	4	inner	180.3.v.a.47.44	yes	272
36.23	even	6	inner	180.3.v.a.23.14	✓	272
45.32	even	12	inner	180.3.v.a.167.9	yes	272
180.167	odd	12	inner	180.3.v.a.167.21	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.v.a.23.14	✓	272	36.23	even	6	inner
180.3.v.a.23.44	yes	272	9.5	odd	6	inner
180.3.v.a.47.14	yes	272	5.2	odd	4	inner
180.3.v.a.47.44	yes	272	20.7	even	4	inner
180.3.v.a.83.9	yes	272	4.3	odd	2	inner
180.3.v.a.83.21	yes	272	1.1	even	1	trivial
180.3.v.a.167.9	yes	272	45.32	even	12	inner
180.3.v.a.167.21	yes	272	180.167	odd	12	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 $\F_{q}$

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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