LMFDB - Embedded newform 180.3.v.a.23.14

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			23.14
Character	$\chi$	$=$	180.23
Dual form			180.3.v.a.47.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61680 + 1.17726i) q^{2} +(-0.319431 + 2.98295i) q^{3} +(1.22810 - 3.80680i) q^{4} +(2.64586 - 4.24257i) q^{5} +(-2.99525 - 5.19889i) q^{6} +(-1.90052 + 7.09282i) q^{7} +(2.49601 + 7.60065i) q^{8} +(-8.79593 - 1.90569i) q^{9} +O(q^{10})$	\(q+(-1.61680 + 1.17726i) q^{2} +(-0.319431 + 2.98295i) q^{3} +(1.22810 - 3.80680i) q^{4} +(2.64586 - 4.24257i) q^{5} +(-2.99525 - 5.19889i) q^{6} +(-1.90052 + 7.09282i) q^{7} +(2.49601 + 7.60065i) q^{8} +(-8.79593 - 1.90569i) q^{9} +(0.716781 + 9.97428i) q^{10} +(6.90992 + 11.9683i) q^{11} +(10.9632 + 4.87938i) q^{12} +(-8.20800 + 2.19933i) q^{13} +(-5.27736 - 13.7051i) q^{14} +(11.8102 + 9.24767i) q^{15} +(-12.9835 - 9.35031i) q^{16} +(19.5704 + 19.5704i) q^{17} +(16.4648 - 7.27399i) q^{18} -27.8736 q^{19} +(-12.9012 - 15.2826i) q^{20} +(-20.5504 - 7.93481i) q^{21} +(-25.2618 - 11.2156i) q^{22} +(-23.4697 + 6.28869i) q^{23} +(-23.4696 + 5.01757i) q^{24} +(-10.9988 - 22.4505i) q^{25} +(10.6815 - 13.2188i) q^{26} +(8.49426 - 25.6290i) q^{27} +(24.6670 + 15.9456i) q^{28} +(1.37932 + 2.38905i) q^{29} +(-29.9817 - 1.04797i) q^{30} +(1.95683 + 1.12978i) q^{31} +(31.9996 - 0.167407i) q^{32} +(-37.9081 + 16.7888i) 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} +(45.0662 - 32.8146i) q^{38} +(-3.93858 - 25.1865i) q^{39} +(38.8504 + 9.52081i) q^{40} +(28.6563 + 16.5447i) q^{41} +(42.5673 - 11.3642i) q^{42} +(61.2432 + 16.4101i) q^{43} +(54.0472 - 11.6063i) q^{44} +(-31.3578 + 32.2752i) q^{45} +(30.5425 - 37.7976i) q^{46} +(-35.3239 - 9.46501i) q^{47} +(32.0388 - 35.7424i) q^{48} +(-4.26096 - 2.46006i) q^{49} +(44.2131 + 23.3496i) q^{50} +(-64.6289 + 52.1261i) q^{51} +(-1.70787 + 33.9472i) 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} +(8.90370 - 83.1455i) q^{57} +(-5.04263 - 2.23880i) q^{58} +(-7.02941 - 4.05843i) q^{59} +(49.7082 - 33.6020i) q^{60} +(20.9812 + 36.3405i) q^{61} +(-4.49386 + 0.477078i) q^{62} +(30.2335 - 58.7662i) q^{63} +(-51.5399 + 37.9426i) q^{64} +(-12.3864 + 40.6421i) q^{65} +(41.5250 - 71.7721i) q^{66} +(44.8365 - 12.0139i) q^{67} +(98.5353 - 50.4663i) q^{68} +(-11.2619 - 72.0177i) q^{69} +(-72.1081 - 13.8723i) q^{70} -3.29546 q^{71} +(-7.47019 - 71.6114i) q^{72} +(-9.77104 - 9.77104i) q^{73} +(17.2829 - 109.864i) q^{74} +(70.4821 - 25.6375i) q^{75} +(-34.2317 + 106.109i) q^{76} +(-98.0216 + 26.2648i) q^{77} +(36.0191 + 36.0849i) q^{78} +(5.14562 + 8.91247i) q^{79} +(-74.0220 + 30.3439i) q^{80} +(73.7367 + 33.5246i) q^{81} +(-65.8092 + 6.98645i) q^{82} +(-8.78320 + 32.7794i) q^{83} +(-55.4443 + 68.4867i) q^{84} +(134.810 - 31.2483i) q^{85} +(-118.337 + 45.5675i) q^{86} +(-7.56701 + 3.35130i) q^{87} +(-73.7199 + 82.3929i) q^{88} +100.456 q^{89} +(12.7031 - 89.0990i) q^{90} -62.3977i q^{91} +(-4.88345 + 97.0678i) q^{92} +(-3.99514 + 5.47624i) q^{93} +(68.2546 - 26.2824i) q^{94} +(-73.7498 + 118.256i) q^{95} +(-9.72228 + 95.5064i) q^{96} +(-7.80472 - 2.09127i) q^{97} +(9.78527 - 1.03883i) 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 $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.61680	+	1.17726i	−0.808402	+	0.588631i
$2$	−1.61680	+	1.17726i	−0.808402	+	0.588631i
$3$	−0.319431	+	2.98295i	−0.106477	+	0.994315i
$3$	−0.319431	+	2.98295i	−0.106477	+	0.994315i
$4$	1.22810	−	3.80680i	0.307026	−	0.951701i
$5$	2.64586	−	4.24257i	0.529173	−	0.848514i
$5$	2.64586	−	4.24257i	0.529173	−	0.848514i
$6$	−2.99525	−	5.19889i	−0.499209	−	0.866482i
$7$	−1.90052	+	7.09282i	−0.271502	+	1.01326i	0.686647	+	0.726991i	$0.259082\pi$
$7$	−1.90052	+	7.09282i	−0.271502	+	1.01326i	−0.958149	+	0.286269i	$0.907585\pi$
$8$	2.49601	+	7.60065i	0.312001	+	0.950082i
$9$	−8.79593	−	1.90569i	−0.977325	−	0.211743i
$10$	0.716781	+	9.97428i	0.0716781	+	0.997428i
$11$	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	$0.617136\pi$
$12$	10.9632	+	4.87938i	0.913600	+	0.406615i
$13$	−8.20800	+	2.19933i	−0.631384	+	0.169179i	−0.560298	−	0.828291i	$-0.689313\pi$
$13$	−8.20800	+	2.19933i	−0.631384	+	0.169179i	−0.0710866	+	0.997470i	$0.522647\pi$
$14$	−5.27736	−	13.7051i	−0.376954	−	0.978936i
$15$	11.8102	+	9.24767i	0.787346	+	0.616512i
$16$	−12.9835	−	9.35031i	−0.811470	−	0.584394i
$17$	19.5704	+	19.5704i	1.15120	+	1.15120i	0.986312	+	0.164890i	$0.0527268\pi$
$17$	19.5704	+	19.5704i	1.15120	+	1.15120i	0.164890	+	0.986312i	$0.447273\pi$
$18$	16.4648	−	7.27399i	0.914710	−	0.404111i
$19$	−27.8736			−1.46703			−0.733516	−	0.679672i	$-0.762122\pi$
$19$	−27.8736			−1.46703			−0.733516	+	0.679672i	$0.762122\pi$
$20$	−12.9012	−	15.2826i	−0.645062	−	0.764130i
$21$	−20.5504	−	7.93481i	−0.978592	−	0.377848i
$22$	−25.2618	−	11.2156i	−1.14827	−	0.509802i
$23$	−23.4697	+	6.28869i	−1.02042	+	0.273421i	−0.729978	−	0.683471i	$-0.760470\pi$
$23$	−23.4697	+	6.28869i	−1.02042	+	0.273421i	−0.290444	+	0.956892i	$0.593803\pi$
$24$	−23.4696	+	5.01757i	−0.977902	+	0.209065i
$25$	−10.9988	−	22.4505i	−0.439953	−	0.898021i
$26$	10.6815	−	13.2188i	0.410828	−	0.508417i
$27$	8.49426	−	25.6290i	0.314602	−	0.949224i
$28$	24.6670	+	15.9456i	0.880963	+	0.569487i
$29$	1.37932	+	2.38905i	0.0475627	+	0.0823811i	0.888827	−	0.458244i	$-0.151521\pi$
$29$	1.37932	+	2.38905i	0.0475627	+	0.0823811i	−0.841264	+	0.540625i	$0.818188\pi$
$30$	−29.9817	−	1.04797i	−0.999390	−	0.0349325i
$31$	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	$0.655063\pi$
$32$	31.9996	−	0.167407i	0.999986	−	0.00523148i
$33$	−37.9081	+	16.7888i	−1.14873	+	0.508753i
$34$	−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	$0.979353\pi$
$38$	45.0662	−	32.8146i	1.18595	−	0.863542i
$39$	−3.93858	−	25.1865i	−0.100989	−	0.645809i
$40$	38.8504	+	9.52081i	0.971260	+	0.238020i
$41$	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	$0.534450\pi$
$42$	42.5673	−	11.3642i	1.01351	−	0.270577i
$43$	61.2432	+	16.4101i	1.42426	+	0.381629i	0.886993	−	0.461783i	$-0.152790\pi$
$43$	61.2432	+	16.4101i	1.42426	+	0.381629i	0.537267	+	0.843412i	$0.319457\pi$
$44$	54.0472	−	11.6063i	1.22834	−	0.263780i
$45$	−31.3578	+	32.2752i	−0.696841	+	0.717226i
$46$	30.5425	−	37.7976i	0.663967	−	0.821687i
$47$	−35.3239	−	9.46501i	−0.751572	−	0.201383i	−0.137357	−	0.990522i	$-0.543861\pi$
$47$	−35.3239	−	9.46501i	−0.751572	−	0.201383i	−0.614215	+	0.789138i	$0.710527\pi$
$48$	32.0388	−	35.7424i	0.667475	−	0.744632i
$49$	−4.26096	−	2.46006i	−0.0869583	−	0.0502054i
$50$	44.2131	+	23.3496i	0.884262	+	0.466992i
$51$	−64.6289	+	52.1261i	−1.26723	+	1.02208i
$52$	−1.70787	+	33.9472i	−0.0328437	+	0.652832i
$53$	31.2552	−	31.2552i	0.589721	−	0.589721i	−0.347835	−	0.937556i	$-0.613083\pi$
$53$	31.2552	−	31.2552i	0.589721	−	0.589721i	0.937556	+	0.347835i	$0.113083\pi$
$54$	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
$57$	8.90370	−	83.1455i	0.156205	−	1.45869i
$58$	−5.04263	−	2.23880i	−0.0869419	−	0.0386001i
$59$	−7.02941	−	4.05843i	−0.119143	−	0.0687870i	0.439244	−	0.898368i	$-0.355246\pi$
$59$	−7.02941	−	4.05843i	−0.119143	−	0.0687870i	−0.558387	+	0.829581i	$0.688580\pi$
$60$	49.7082	−	33.6020i	0.828471	−	0.560033i
$61$	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	$0.721567\pi$
$62$	−4.49386	+	0.477078i	−0.0724816	+	0.00769481i
$63$	30.2335	−	58.7662i	0.479897	−	0.932797i
$64$	−51.5399	+	37.9426i	−0.805311	+	0.592852i
$65$	−12.3864	+	40.6421i	−0.190561	+	0.625264i
$66$	41.5250	−	71.7721i	0.629167	−	1.08746i
$67$	44.8365	−	12.0139i	0.669202	−	0.179312i	0.0918066	−	0.995777i	$-0.470736\pi$
$67$	44.8365	−	12.0139i	0.669202	−	0.179312i	0.577395	+	0.816465i	$0.304069\pi$
$68$	98.5353	−	50.4663i	1.44905	−	0.742151i
$69$	−11.2619	−	72.0177i	−0.163215	−	1.04373i
$70$	−72.1081	−	13.8723i	−1.03012	−	0.198175i
$71$	−3.29546			−0.0464149			−0.0232075	−	0.999731i	$-0.507388\pi$
$71$	−3.29546			−0.0464149			−0.0232075	+	0.999731i	$0.507388\pi$
$72$	−7.47019	−	71.6114i	−0.103753	−	0.994603i
$73$	−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
$75$	70.4821	−	25.6375i	0.939761	−	0.341833i
$76$	−34.2317	+	106.109i	−0.450417	+	1.39618i
$77$	−98.0216	+	26.2648i	−1.27301	+	0.341102i
$78$	36.0191	+	36.0849i	0.461783	+	0.462627i
$79$	5.14562	+	8.91247i	0.0651344	+	0.112816i	0.896754	−	0.442530i	$-0.145919\pi$
$79$	5.14562	+	8.91247i	0.0651344	+	0.112816i	−0.831619	+	0.555346i	$0.812586\pi$
$80$	−74.0220	+	30.3439i	−0.925274	+	0.379298i
$81$	73.7367	+	33.5246i	0.910330	+	0.413884i
$82$	−65.8092	+	6.98645i	−0.802551	+	0.0852006i
$83$	−8.78320	+	32.7794i	−0.105822	+	0.394932i	−0.998437	−	0.0558870i	$-0.982201\pi$
$83$	−8.78320	+	32.7794i	−0.105822	+	0.394932i	0.892615	+	0.450819i	$0.148868\pi$
$84$	−55.4443	+	68.4867i	−0.660051	+	0.815318i
$85$	134.810	−	31.2483i	1.58600	−	0.367626i
$86$	−118.337	+	45.5675i	−1.37601	+	0.529854i
$87$	−7.56701	+	3.35130i	−0.0869771	+	0.0385207i
$88$	−73.7199	+	82.3929i	−0.837726	+	0.936283i
$89$	100.456			1.12872			0.564359	−	0.825529i	$-0.309123\pi$
$89$	100.456			1.12872			0.564359	+	0.825529i	$0.309123\pi$
$90$	12.7031	−	89.0990i	0.141146	−	0.989989i
$91$		−	62.3977i		−	0.685690i
$92$	−4.88345	+	97.0678i	−0.0530809	+	1.05508i
$93$	−3.99514	+	5.47624i	−0.0429585	+	0.0588843i
$94$	68.2546	−	26.2824i	0.726113	−	0.279601i
$95$	−73.7498	+	118.256i	−0.776314	+	1.24480i
$96$	−9.72228	+	95.5064i	−0.101274	+	0.994859i
$97$	−7.80472	−	2.09127i	−0.0804610	−	0.0215595i	0.218364	−	0.975867i	$-0.429928\pi$
$97$	−7.80472	−	2.09127i	−0.0804610	−	0.0215595i	−0.298825	+	0.954308i	$0.596595\pi$
$98$	9.78527	−	1.03883i	0.0998497	−	0.0106003i
$99$	−37.9712	−	118.441i	−0.383547	−	1.19637i
$100$	−98.9724	+	14.2987i	−0.989724	+	0.142987i
$101$	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	$0.0734394\pi$
$102$	43.1261	−	160.363i	0.422805	−	1.57219i
$103$	14.1725	+	52.8927i	0.137598	+	0.513521i	0.999974	+	0.00725290i	$0.00230869\pi$
$103$	14.1725	+	52.8927i	0.137598	+	0.513521i	−0.862376	+	0.506268i	$0.831025\pi$
$104$	−37.2035	−	56.8966i	−0.357726	−	0.547083i
$105$	−88.0376	+	66.1922i	−0.838453	+	0.630402i
$106$	−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	$0.109063\pi$
$108$	−87.1329	−	63.8111i	−0.806786	−	0.590844i
$109$		−	186.892i		−	1.71461i	−0.514812	−	0.857303i	$-0.672138\pi$
$109$		−	186.892i		−	1.71461i	0.514812	−	0.857303i	$-0.327862\pi$
$110$	−114.422	+	77.5001i	−1.04020	+	0.704546i
$111$	−104.731	−	129.851i	−0.943520	−	1.16983i
$112$	90.9955	−	74.3194i	0.812460	−	0.663566i
$113$	45.6052	+	170.201i	0.403586	+	1.50620i	0.806649	+	0.591030i	$0.201279\pi$
$113$	45.6052	+	170.201i	0.403586	+	1.50620i	−0.403064	+	0.915172i	$0.632055\pi$
$114$	83.4886	+	144.912i	0.732356	+	1.27116i
$115$	−35.4174	+	116.211i	−0.307978	+	1.01053i
$116$	10.7886	−	2.31679i	0.0930051	−	0.0199724i
$117$	76.3882	−	3.70322i	0.652891	−	0.0316514i
$118$	16.1430	−	1.71378i	0.136805	−	0.0145235i
$119$	−176.004	+	101.616i	−1.47902	+	0.853913i
$120$	−40.8101	+	112.847i	−0.340084	+	0.940395i
$121$	−34.9939	+	60.6111i	−0.289205	+	0.500919i
$122$	−76.7048	−	34.0551i	−0.628728	−	0.279140i
$123$	−58.5058	+	80.1954i	−0.475657	+	0.651995i
$124$	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	$-0.477930\pi$
$127$	−117.896	−	117.896i	−0.928318	−	0.928318i	−0.997597	+	0.0692793i	$0.977930\pi$
$128$	38.6615	−	122.022i	0.302043	−	0.953294i
$129$	−68.5133	+	177.443i	−0.531111	+	1.37553i
$130$	−27.8200	−	80.2924i	−0.214000	−	0.617634i
$131$	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	$0.0373249\pi$
$132$	17.3567	+	164.927i	0.131491	+	1.24945i
$133$	52.9743	−	197.703i	0.398303	−	1.48649i
$134$	−58.3483	+	72.2085i	−0.435435	+	0.538869i
$135$	−86.2584	−	103.848i	−0.638951	−	0.769248i
$136$	−99.9002	+	197.596i	−0.734560	+	1.45291i
$137$	−5.48770	+	20.4804i	−0.0400562	+	0.149492i	−0.983058	−	0.183297i	$-0.941323\pi$
$137$	−5.48770	+	20.4804i	−0.0400562	+	0.149492i	0.943001	+	0.332789i	$0.107990\pi$
$138$	102.992	+	103.180i	0.746319	+	0.747683i
$139$	−17.4393	+	30.2057i	−0.125462	+	0.217307i	−0.921914	−	0.387396i	$-0.873375\pi$
$139$	−17.4393	+	30.2057i	−0.125462	+	0.217307i	0.796451	+	0.604703i	$0.206708\pi$
$140$	132.916	−	62.4614i	0.949399	−	0.446153i
$141$	39.5171	−	102.346i	0.280263	−	0.725857i
$142$	5.32811	−	3.87962i	0.0375219	−	0.0273213i
$143$	−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
$147$	8.69932	−	11.9244i	0.0591791	−	0.0811182i
$148$	101.396	+	197.975i	0.685107	+	1.33767i
$149$	42.0868	−	72.8964i	0.282461	−	0.489238i	−0.689529	−	0.724258i	$-0.742182\pi$
$149$	42.0868	−	72.8964i	0.282461	−	0.489238i	0.971990	+	0.235020i	$0.0755157\pi$
$150$	−83.7736	+	124.427i	−0.558490	+	0.829511i
$151$	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	$0.226294\pi$
$152$	−69.5727	−	211.858i	−0.457715	−	1.39380i
$153$	−134.845	−	209.435i	−0.881339	−	1.36886i
$154$	127.561	−	157.862i	0.828319	−	1.02508i
$155$	9.97068	−	5.31276i	0.0643269	−	0.0342759i
$156$	−100.717	−	15.9383i	−0.645623	−	0.102169i
$157$	7.34004	+	27.3934i	0.0467518	+	0.174480i	0.985354	−	0.170521i	$-0.0545451\pi$
$157$	7.34004	+	27.3934i	0.0467518	+	0.174480i	−0.938602	+	0.345001i	$0.887878\pi$
$158$	−18.8118	−	8.35197i	−0.119062	−	0.0528606i
$159$	83.2488	+	103.217i	0.523577	+	0.649161i
$160$	83.9562	−	136.203i	0.524726	−	0.851271i
$161$		−	178.418i		−	1.10819i
$162$	−158.685	+	32.6047i	−0.979537	+	0.201264i
$163$	159.023	−	159.023i	0.975603	−	0.975603i	−0.0241065	−	0.999709i	$-0.507674\pi$
$163$	159.023	−	159.023i	0.975603	−	0.975603i	0.999709	+	0.0241065i	$0.00767408\pi$
$164$	98.1756	−	88.7704i	0.598632	−	0.541283i
$165$	−29.0718	+	205.249i	−0.176193	+	1.24393i
$166$	−24.3892	−	63.3379i	−0.146923	−	0.381554i
$167$	34.3782	+	128.301i	0.205857	+	0.768271i	0.989186	+	0.146663i	$0.0468534\pi$
$167$	34.3782	+	128.301i	0.205857	+	0.768271i	−0.783329	+	0.621607i	$0.786480\pi$
$168$	9.01573	−	176.002i	0.0536651	−	1.04763i
$169$	−83.8241	+	48.3959i	−0.496001	+	0.286366i
$170$	−181.173	+	209.229i	−1.06572	+	1.23076i
$171$	245.174	+	53.1185i	1.43377	+	0.310634i
$172$	137.683	−	212.987i	0.800482	−	1.23830i
$173$	−32.0405	−	8.58522i	−0.185205	−	0.0496256i	0.165024	−	0.986289i	$-0.447230\pi$
$173$	−32.0405	−	8.58522i	−0.185205	−	0.0496256i	−0.350229	+	0.936664i	$0.613896\pi$
$174$	8.28900	−	14.3267i	0.0476379	−	0.0823376i
$175$	180.141	−	35.3451i	1.02938	−	0.201972i
$176$	22.1925	−	220.001i	0.126094	−	1.25000i
$177$	14.3515	−	19.6720i	0.0810819	−	0.111141i
$178$	−162.418	+	118.263i	−0.912458	+	0.664399i
$179$			36.8511i			0.205872i	0.994688	+	0.102936i	$0.0328237\pi$
$179$			36.8511i			0.205872i	−0.994688	+	0.102936i	$0.967176\pi$
$180$	84.3545	+	159.010i	0.468636	+	0.883391i
$181$	221.518			1.22386			0.611929	−	0.790913i	$-0.290394\pi$
$181$	221.518			1.22386			0.611929	+	0.790913i	$0.290394\pi$
$182$	73.4585	+	100.885i	0.403618	+	0.554312i
$183$	−115.104	+	50.9775i	−0.628982	+	0.278566i
$184$	−106.379	−	162.689i	−0.578145	−	0.884177i
$185$	62.7833	+	270.857i	0.339369	+	1.46409i
$186$	0.0123799	−	13.5573i	6.65585e−5	−	0.0728889i
$187$	−98.9952	+	369.455i	−0.529386	+	1.97570i
$188$	−79.4129	+	122.847i	−0.422409	+	0.653442i
$189$	165.639	+	108.957i	0.876396	+	0.576491i
$190$	−19.9793	−	278.019i	−0.105154	−	1.46326i
$191$	−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	$0.924214\pi$
$192$	−96.7171	−	165.861i	−0.503735	−	0.863858i
$193$	−67.0896	+	17.9766i	−0.347615	+	0.0931431i	−0.428402	−	0.903588i	$-0.640923\pi$
$193$	−67.0896	+	17.9766i	−0.347615	+	0.0931431i	0.0807872	+	0.996731i	$0.474257\pi$
$194$	15.0807	−	5.80704i	0.0777354	−	0.0299332i
$195$	−117.277	−	49.9304i	−0.601419	−	0.256053i
$196$	−14.5979	+	13.1994i	−0.0744790	+	0.0673439i
$197$	152.887	+	152.887i	0.776078	+	0.776078i	0.979161	−	0.203083i	$-0.0650963\pi$
$197$	152.887	+	152.887i	0.776078	+	0.776078i	−0.203083	+	0.979161i	$0.565096\pi$
$198$	200.828	+	146.793i	1.01428	+	0.741380i
$199$	−26.6313			−0.133826			−0.0669129	−	0.997759i	$-0.521315\pi$
$199$	−26.6313			−0.133826			−0.0669129	+	0.997759i	$0.521315\pi$
$200$	143.186	−	139.635i	0.715928	−	0.698174i
$201$	21.5147	+	137.583i	0.107038	+	0.684490i
$202$	−119.466	+	269.083i	−0.591418	+	1.33209i
$203$	−19.5665	+	5.24284i	−0.0963869	+	0.0258268i
$204$	119.063	+	310.046i	0.583641	+	1.51983i
$205$	146.013	−	77.8014i	0.712259	−	0.379519i
$206$	−85.1828	−	68.8322i	−0.413509	−	0.334137i
$207$	218.422	−	10.5889i	1.05518	−	0.0511539i
$208$	127.133	+	48.1923i	0.611217	+	0.231694i
$209$	−192.604	−	333.601i	−0.921552	−	1.59617i
$210$	64.4138	−	210.663i	0.306732	−	1.00316i
$211$	−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	$0.702031\pi$
$212$	−80.5979	−	157.367i	−0.380179	−	0.742298i
$213$	1.05267	−	9.83018i	0.00494212	−	0.0461511i
$214$	−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
$218$	220.021	+	302.168i	1.00927	+	1.38609i
$219$	32.2677	−	26.0253i	0.147341	−	0.118837i
$220$	93.7607	−	260.008i	0.426185	−	1.18185i
$221$	−203.676	−	117.592i	−0.921610	−	0.532092i
$222$	322.198	+	86.6481i	1.45134	+	0.390307i
$223$	−23.9227	−	6.41007i	−0.107277	−	0.0287447i	0.204781	−	0.978808i	$-0.434352\pi$
$223$	−23.9227	−	6.41007i	−0.107277	−	0.0287447i	−0.312058	+	0.950063i	$0.601018\pi$
$224$	−59.6283	+	227.285i	−0.266198	+	1.01467i
$225$	53.9610	+	218.434i	0.239827	+	0.970816i
$226$	−274.106	−	221.492i	−1.21286	−	0.980053i
$227$	62.9973	+	16.8801i	0.277521	+	0.0743616i	0.394895	−	0.918726i	$-0.370781\pi$
$227$	62.9973	+	16.8801i	0.277521	+	0.0743616i	−0.117374	+	0.993088i	$0.537448\pi$
$228$	−305.584	−	136.006i	−1.34028	−	0.596518i
$229$	−153.672	−	88.7223i	−0.671055	−	0.387434i	0.125421	−	0.992104i	$-0.459972\pi$
$229$	−153.672	−	88.7223i	−0.671055	−	0.387434i	−0.796476	+	0.604670i	$0.793305\pi$
$230$	−79.5478	−	229.586i	−0.345860	−	0.998199i
$231$	−47.0354	−	300.783i	−0.203616	−	1.30209i
$232$	−14.7156	+	16.4468i	−0.0634291	+	0.0708914i
$233$	−292.500	+	292.500i	−1.25536	+	1.25536i	−0.302082	+	0.953282i	$0.597682\pi$
$233$	−292.500	+	292.500i	−1.25536	+	1.25536i	−0.953282	+	0.302082i	$0.902318\pi$
$234$	−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
$237$	−28.2291	+	12.5022i	−0.119110	+	0.0527518i
$238$	164.935	−	371.495i	0.693003	−	1.56090i
$239$	153.767	+	88.7775i	0.643377	+	0.371454i	0.785914	−	0.618335i	$-0.212193\pi$
$239$	153.767	+	88.7775i	0.643377	+	0.371454i	−0.142537	+	0.989789i	$0.545526\pi$
$240$	−66.8692	−	230.496i	−0.278622	−	0.960401i
$241$	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	$0.828594\pi$
$242$	−14.7771	−	139.193i	−0.0610622	−	0.575179i
$243$	−123.556	+	209.244i	−0.508461	+	0.861085i
$244$	164.108	−	35.2414i	0.672575	−	0.144432i
$245$	−21.7109	+	11.5684i	−0.0886160	+	0.0472180i
$246$	0.181294	−	198.537i	0.000736968	−	0.807061i
$247$	228.787	−	61.3032i	0.926262	−	0.248191i
$248$	−3.70279	+	17.6931i	−0.0149306	+	0.0713433i
$249$	−94.9734	−	36.6705i	−0.381419	−	0.147271i
$250$	216.044	−	125.797i	0.864176	−	0.503189i
$251$	7.10374			0.0283017			0.0141509	−	0.999900i	$-0.495495\pi$
$251$	7.10374			0.0283017			0.0141509	+	0.999900i	$0.495495\pi$
$252$	−186.581	−	187.264i	−0.740402	−	0.743112i
$253$	−237.439	−	237.439i	−0.938493	−	0.938493i
$254$	329.410	+	51.8202i	1.29689	+	0.204017i
$255$	50.1495	+	412.111i	0.196665	+	1.61612i
$256$	81.1435	+	242.800i	0.316967	+	0.948437i
$257$	−476.241	+	127.609i	−1.85308	+	0.496531i	−0.999694	−	0.0247487i	$-0.992121\pi$
$257$	−476.241	+	127.609i	−1.85308	+	0.496531i	−0.853386	+	0.521280i	$0.825455\pi$
$258$	−98.1247	−	367.549i	−0.380328	−	1.42461i
$259$	−204.164	−	353.623i	−0.788279	−	1.36534i
$260$	139.505	+	97.0655i	0.536557	+	0.373329i
$261$	−7.57960	−	23.6425i	−0.0290406	−	0.0905842i
$262$	21.8645	+	205.953i	0.0834521	+	0.786081i
$263$	−85.1934	+	317.946i	−0.323929	+	1.20892i	0.591455	+	0.806338i	$0.298554\pi$
$263$	−85.1934	+	317.946i	−0.323929	+	1.20892i	−0.915384	+	0.402582i	$0.868113\pi$
$264$	−222.225	−	246.221i	−0.841762	−	0.932657i
$265$	−49.9055	−	215.300i	−0.188323	−	0.812451i
$266$	147.099	+	382.011i	0.553004	+	1.43613i
$267$	−32.0887	+	299.655i	−0.120183	+	1.12230i
$268$	9.32933	−	185.438i	0.0348109	−	0.691934i
$269$	467.847			1.73921			0.869604	−	0.493750i	$-0.164374\pi$
$269$	467.847			1.73921			0.869604	+	0.493750i	$0.164374\pi$
$270$	261.720	+	66.3537i	0.969332	+	0.245755i
$271$			258.025i			0.952122i	0.879412	+	0.476061i	$0.157936\pi$
$271$			258.025i			0.952122i	−0.879412	+	0.476061i	$0.842064\pi$
$272$	−71.1035	−	437.082i	−0.261410	−	1.60692i
$273$	186.129	+	19.9318i	0.681792	+	0.0730101i
$274$	−15.2383	−	39.5732i	−0.0556141	−	0.144428i
$275$	192.694	−	286.769i	0.700706	−	1.04279i
$276$	−287.988	−	45.5735i	−1.04343	−	0.165121i
$277$	−26.9794	−	7.22910i	−0.0973985	−	0.0260978i	0.209791	−	0.977746i	$-0.432722\pi$
$277$	−26.9794	−	7.22910i	−0.0973985	−	0.0260978i	−0.307189	+	0.951648i	$0.599388\pi$
$278$	−7.36418	−	69.3673i	−0.0264899	−	0.249523i
$279$	−15.0592	−	13.6666i	−0.0539755	−	0.0489841i
$280$	−141.365	+	257.465i	−0.504876	+	0.919517i
$281$	−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	$0.389587\pi$
$282$	56.5965	+	211.995i	0.200697	+	0.751756i
$283$	26.0781	+	97.3247i	0.0921487	+	0.343903i	0.996572	−	0.0827333i	$-0.0263650\pi$
$283$	26.0781	+	97.3247i	0.0921487	+	0.343903i	−0.904423	+	0.426637i	$0.859698\pi$
$284$	−4.04717	+	12.5452i	−0.0142506	+	0.0441731i
$285$	−329.193	−	257.766i	−1.15506	−	0.904443i
$286$	232.016	+	36.4989i	0.811245	+	0.127619i
$287$	−171.811	+	171.811i	−0.598644	+	0.598644i
$288$	−281.785	−	59.5087i	−0.978420	−	0.206628i
$289$			477.003i			1.65053i
$290$	−22.8404	+	15.4701i	−0.0787600	+	0.0533453i
$291$	8.73121	−	22.6130i	0.0300042	−	0.0777080i
$292$	−49.1963	+	25.1966i	−0.168480	+	0.0862897i
$293$	−71.5100	−	266.879i	−0.244061	−	0.910849i	−0.973853	−	0.227180i	$-0.927050\pi$
$293$	−71.5100	−	266.879i	−0.244061	−	0.910849i	0.729792	−	0.683670i	$-0.239617\pi$
$294$	−0.0269569	+	29.5208i	−9.16901e−5	+	0.100411i
$295$	−35.8171	+	19.0847i	−0.121414	+	0.0646940i
$296$	−397.006	−	200.717i	−1.34124	−	0.678099i
$297$	365.431	−	75.4324i	1.23041	−	0.253981i
$298$	17.7722	+	167.406i	0.0596383	+	0.561766i
$299$	178.808	−	103.235i	0.598022	−	0.345268i
$300$	−11.0375	−	299.797i	−0.0367918	−	0.999323i
$301$	−232.787	+	403.199i	−0.773380	+	1.33953i
$302$	−80.8734	+	182.157i	−0.267793	+	0.603170i
$303$	178.831	+	403.788i	0.590201	+	1.33263i
$304$	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	$-0.445198\pi$
$307$	−249.868	−	249.868i	−0.813901	−	0.813901i	−0.985216	+	0.171315i	$0.945198\pi$
$308$	−20.3958	+	405.405i	−0.0662201	+	1.31625i
$309$	−162.303	+	25.3804i	−0.525253	+	0.0821371i
$310$	−9.86610	+	20.3278i	−0.0318261	+	0.0655736i
$311$	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	$0.0278877\pi$
$312$	181.603	−	92.8016i	0.582062	−	0.297441i
$313$	−52.2726	+	195.084i	−0.167005	+	0.623272i	0.830771	+	0.556615i	$0.187900\pi$
$313$	−52.2726	+	195.084i	−0.167005	+	0.623272i	−0.997776	+	0.0666572i	$0.978767\pi$
$314$	−44.1166	−	35.6486i	−0.140499	−	0.113530i
$315$	−169.326	−	283.755i	−0.537543	−	0.900810i
$316$	40.2474	−	8.64292i	0.127365	−	0.0273510i
$317$	73.7587	−	275.271i	0.232677	−	0.868363i	−0.746505	−	0.665380i	$-0.768270\pi$
$317$	73.7587	−	275.271i	0.232677	−	0.868363i	0.979182	−	0.202983i	$-0.0650637\pi$
$318$	−256.110	−	68.8751i	−0.805377	−	0.216589i
$319$	−19.0620	+	33.0163i	−0.0597554	+	0.103499i
$320$	24.6065	+	319.053i	0.0768952	+	0.997039i
$321$	172.681	+	214.100i	0.537947	+	0.666977i
$322$	210.045	+	288.467i	0.652314	+	0.895861i
$323$	−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
$327$	557.489	+	59.6991i	1.70486	+	0.182566i
$328$	−54.2245	+	259.103i	−0.165319	+	0.789947i
$329$	134.267	−	232.558i	0.408107	−	0.706863i
$330$	−194.628	−	366.072i	−0.589783	−	1.10931i
$331$	−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	$0.428966\pi$
$332$	113.998	+	73.6924i	0.343367	+	0.221965i
$333$	420.793	−	270.928i	1.26364	−	0.813596i
$334$	−206.627	−	166.966i	−0.618644	−	0.499897i
$335$	67.6614	−	222.009i	0.201974	−	0.662714i
$336$	192.624	+	295.174i	0.573286	+	0.878496i
$337$	116.143	+	433.451i	0.344638	+	1.28621i	0.893035	+	0.449987i	$0.148571\pi$
$337$	116.143	+	433.451i	0.344638	+	1.28621i	−0.548397	+	0.836218i	$0.684762\pi$
$338$	78.5524	−	176.930i	0.232404	−	0.523460i
$339$	−522.268	+	81.6703i	−1.54061	+	0.240915i
$340$	46.6043	−	551.570i	0.137071	−	1.62226i
$341$			31.2267i			0.0915739i
$342$	−458.933	+	202.753i	−1.34191	+	0.592844i
$343$	−228.876	+	228.876i	−0.667278	+	0.667278i
$344$	28.1361	+	506.448i	0.0817911	+	1.47223i
$345$	−335.337	−	142.770i	−0.971993	−	0.413825i
$346$	61.9102	−	23.8395i	0.178931	−	0.0689002i
$347$	133.150	+	496.922i	0.383717	+	1.43205i	0.840179	+	0.542310i	$0.182450\pi$
$347$	133.150	+	496.922i	0.383717	+	1.43205i	−0.456461	+	0.889743i	$0.650883\pi$
$348$	3.46466	+	32.9219i	0.00995591	+	0.0946030i
$349$	−377.599	+	218.007i	−1.08195	+	0.624662i	−0.931421	−	0.363944i	$-0.881430\pi$
$349$	−377.599	+	218.007i	−1.08195	+	0.624662i	−0.150525	+	0.988606i	$0.548096\pi$
$350$	−249.642	+	269.219i	−0.713263	+	0.769198i
$351$	−13.3543	+	229.045i	−0.0380463	+	0.652549i
$352$	223.118	+	381.824i	0.633858	+	1.08473i
$353$	−257.842	−	69.0885i	−0.730430	−	0.195718i	−0.125609	−	0.992080i	$-0.540088\pi$
$353$	−257.842	−	69.0885i	−0.730430	−	0.195718i	−0.604821	+	0.796362i	$0.706755\pi$
$354$	−0.0444715	+	48.7012i	−0.000125626	+	0.137574i
$355$	−8.71934	+	13.9812i	−0.0245615	+	0.0393837i
$356$	123.370	−	382.416i	0.346546	−	1.07420i
$357$	−246.893	−	557.468i	−0.691577	−	1.56154i
$358$	−43.3834	−	59.5810i	−0.121183	−	0.166427i
$359$			301.913i			0.840983i	0.907297	+	0.420491i	$0.138142\pi$
$359$			301.913i			0.840983i	−0.907297	+	0.420491i	$0.861858\pi$
$360$	−323.582	−	157.781i	−0.898838	−	0.438281i
$361$	415.939			1.15219
$362$	−358.151	+	260.785i	−0.989369	+	0.720401i
$363$	−169.622	−	123.746i	−0.467277	−	0.340898i
$364$	−237.536	−	76.6310i	−0.652571	−	0.210525i
$365$	−67.3072	+	15.6015i	−0.184403	+	0.0427438i
$366$	126.086	−	217.928i	0.344498	−	0.595432i
$367$	138.389	−	516.474i	0.377081	−	1.40729i	−0.473199	−	0.880956i	$-0.656901\pi$
$367$	138.389	−	516.474i	0.377081	−	1.40729i	0.850280	−	0.526331i	$-0.176433\pi$
$368$	363.521	+	137.800i	0.987828	+	0.374456i
$369$	−220.530	−	200.137i	−0.597642	−	0.542375i
$370$	−420.378	−	364.009i	−1.13616	−	0.983809i
$371$	162.287	+	281.089i	0.437431	+	0.757652i
$372$	15.9405	+	21.9341i	0.0428509	+	0.0589627i
$373$	502.535	−	134.654i	1.34728	−	0.361003i	0.488150	−	0.872760i	$-0.337672\pi$
$373$	502.535	−	134.654i	1.34728	−	0.361003i	0.859130	+	0.511757i	$0.171005\pi$
$374$	−274.890	−	713.880i	−0.735000	−	1.90877i
$375$	77.7171	−	366.858i	0.207245	−	0.978289i
$376$	−16.2284	−	292.109i	−0.0431606	−	0.776887i
$377$	−16.5758	−	16.5758i	−0.0439675	−	0.0439675i
$378$	−396.076	+	18.8388i	−1.04782	+	0.0498381i
$379$	273.266			0.721017			0.360509	−	0.932756i	$-0.382603\pi$
$379$	273.266			0.721017			0.360509	+	0.932756i	$0.382603\pi$
$380$	359.604	+	425.982i	0.946327	+	1.12100i
$381$	389.338	−	314.019i	1.02189	−	0.824196i
$382$	196.666	+	87.3149i	0.514833	+	0.228573i
$383$	219.236	−	58.7442i	0.572419	−	0.153379i	0.0390132	−	0.999239i	$-0.487579\pi$
$383$	219.236	−	58.7442i	0.572419	−	0.153379i	0.533406	+	0.845859i	$0.320912\pi$
$384$	351.634	+	154.303i	0.915714	+	0.401830i
$385$	−147.921	+	485.357i	−0.384212	+	1.26067i
$386$	87.3075	−	108.047i	0.226185	−	0.279914i
$387$	−507.418	−	261.052i	−1.31116	−	0.674553i
$388$	−17.5461	+	27.1427i	−0.0452218	+	0.0699555i
$389$	45.3539	+	78.5553i	0.116591	+	0.201942i	0.918415	−	0.395619i	$-0.129470\pi$
$389$	45.3539	+	78.5553i	0.116591	+	0.201942i	−0.801824	+	0.597561i	$0.796137\pi$
$390$	248.394	−	57.3378i	0.636909	−	0.147020i
$391$	−582.385	−	336.240i	−1.48947	−	0.859949i
$392$	8.06273	−	38.5264i	0.0205682	−	0.0982816i
$393$	250.976	+	183.097i	0.638615	+	0.465896i
$394$	−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	$0.989209\pi$
$398$	43.0576	−	31.3521i	0.108185	−	0.0787741i
$399$	572.815	+	221.172i	1.43563	+	0.554315i
$400$	−67.1160	+	394.329i	−0.167790	+	0.985823i
$401$	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	$0.665907\pi$
$402$	−196.756	−	197.115i	−0.489442	−	0.490337i
$403$	−18.5464	−	4.96950i	−0.0460209	−	0.0123313i
$404$	−123.628	−	575.698i	−0.306010	−	1.42499i
$405$	337.328	−	224.132i	0.832908	−	0.553411i
$406$	25.4630	−	31.5116i	0.0627169	−	0.0776148i
$407$	−742.302	−	198.899i	−1.82384	−	0.488696i
$408$	−557.507	−	361.115i	−1.36644	−	0.885086i
$409$	−299.641	−	172.998i	−0.732619	−	0.422978i	0.0867603	−	0.996229i	$-0.472349\pi$
$409$	−299.641	−	172.998i	−0.732619	−	0.422978i	−0.819380	+	0.573251i	$0.805682\pi$
$410$	−144.482	+	297.685i	−0.352394	+	0.726062i
$411$	−59.3389	−	22.9116i	−0.144377	−	0.0557460i
$412$	218.757	+	11.0056i	0.530964	+	0.0267126i
$413$	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
$417$	−84.5313	−	61.6690i	−0.202713	−	0.147887i
$418$	704.139	+	312.620i	1.68454	+	0.747896i
$419$	622.189	+	359.221i	1.48494	+	0.857329i	0.999853	−	0.0171385i	$-0.00545561\pi$
$419$	622.189	+	359.221i	1.48494	+	0.857329i	0.485084	+	0.874467i	$0.338789\pi$
$420$	143.862	+	416.433i	0.342527	+	0.991507i
$421$	−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	$0.898185\pi$
$422$	93.0528	−	9.87869i	0.220504	−	0.0234092i
$423$	292.669	+	150.570i	0.691889	+	0.355957i
$424$	315.573	+	159.547i	0.744277	+	0.376290i
$425$	224.115	−	654.618i	0.527329	−	1.54028i
$426$	9.87074	+	17.1327i	0.0231707	+	0.0402177i
$427$	−297.632	+	79.7502i	−0.697030	+	0.186769i
$428$	−167.182	−	326.423i	−0.390613	−	0.762671i
$429$	274.225	−	221.175i	0.639220	−	0.515560i
$430$	−119.781	+	622.619i	−0.278559	+	1.44795i
$431$	209.773			0.486713			0.243356	−	0.969937i	$-0.421752\pi$
$431$	209.773			0.486713			0.243356	+	0.969937i	$0.421752\pi$
$432$	−349.925	+	253.331i	−0.810011	+	0.586415i
$433$	−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
$435$	−5.80315	+	40.9706i	−0.0133406	+	0.0941854i
$436$	−711.461	−	229.523i	−1.63179	−	0.526429i
$437$	654.186	−	175.289i	1.49699	−	0.401118i
$438$	−21.5318	+	80.0653i	−0.0491594	+	0.182798i
$439$	−379.156	−	656.718i	−0.863682	−	1.49594i	−0.868350	−	0.495952i	$-0.834819\pi$
$439$	−379.156	−	656.718i	−0.863682	−	1.49594i	0.00466802	−	0.999989i	$-0.498514\pi$
$440$	154.505	+	530.762i	0.351147	+	1.20628i
$441$	32.7909	+	29.7586i	0.0743559	+	0.0674799i
$442$	467.741	−	49.6564i	1.05824	−	0.112345i
$443$	192.624	−	718.882i	0.434817	−	1.62276i	−0.306688	−	0.951810i	$-0.599221\pi$
$443$	192.624	−	718.882i	0.434817	−	1.62276i	0.741505	−	0.670948i	$-0.234113\pi$
$444$	−622.938	+	239.219i	−1.40301	+	0.538781i
$445$	265.793	−	426.192i	0.597287	−	0.957734i
$446$	46.2246	−	17.7995i	0.103643	−	0.0399091i
$447$	204.002	+	148.828i	0.456381	+	0.332948i
$448$	−171.167	−	437.674i	−0.382070	−	0.976951i
$449$	754.075			1.67945			0.839727	−	0.543008i	$-0.182715\pi$
$449$	754.075			1.67945			0.839727	+	0.543008i	$0.182715\pi$
$450$	−344.398	−	289.638i	−0.765329	−	0.643639i
$451$			457.291i			1.01395i
$452$	703.929	+	35.4144i	1.55737	+	0.0783505i
$453$	121.061	+	273.347i	0.267242	+	0.603414i
$454$	−121.727	+	46.8726i	−0.268120	+	0.103244i
$455$	−264.727	−	165.096i	−0.581817	−	0.362848i
$456$	654.184	−	139.858i	1.43461	−	0.306706i
$457$	111.322	+	29.8287i	0.243593	+	0.0652706i	0.378550	−	0.925581i	$-0.376423\pi$
$457$	111.322	+	29.8287i	0.243593	+	0.0652706i	−0.134957	+	0.990852i	$0.543089\pi$
$458$	352.906	−	37.4653i	0.770538	−	0.0818020i
$459$	667.807	−	335.335i	1.45492	−	0.730577i
$460$	398.896	+	277.546i	0.867165	+	0.603362i
$461$	−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	$0.499717\pi$
$462$	430.148	+	430.934i	0.931055	+	0.932757i
$463$	−180.939	−	675.274i	−0.390797	−	1.45847i	−0.828823	−	0.559512i	$-0.810989\pi$
$463$	−180.939	−	675.274i	−0.390797	−	1.45847i	0.438026	−	0.898963i	$-0.355678\pi$
$464$	4.42994	−	43.9153i	0.00954729	−	0.0946451i
$465$	12.6627	+	31.4390i	0.0272317	+	0.0676109i
$466$	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	$-0.0144422\pi$
$468$	79.7153	−	295.343i	0.170332	−	0.631074i
$469$			340.850i			0.726760i
$470$	69.0871	−	359.115i	0.146994	−	0.764074i
$471$	−84.0576	+	13.1446i	−0.178466	+	0.0279079i
$472$	13.3013	−	63.5580i	0.0281807	−	0.134657i
$473$	226.784	+	846.370i	0.479459	+	1.78937i
$474$	30.9225	−	53.4466i	0.0652374	−	0.112757i
$475$	306.577	+	625.777i	0.645425	+	1.31743i
$476$	170.680	+	794.806i	0.358572	+	1.66976i
$477$	−334.482	+	215.356i	−0.701219	+	0.451480i
$478$	−353.126	+	37.4886i	−0.738757	+	0.0784280i
$479$	−34.4778	+	19.9058i	−0.0719787	+	0.0415569i	−0.535557	−	0.844499i	$-0.679898\pi$
$479$	−34.4778	+	19.9058i	−0.0719787	+	0.0415569i	0.463579	+	0.886056i	$0.346565\pi$
$480$	379.469	+	293.944i	0.790560	+	0.612384i
$481$	236.264	−	409.221i	0.491193	−	0.850772i
$482$	−13.1173	−	5.82377i	−0.0272144	−	0.0120825i
$483$	532.212	+	56.9923i	1.10189	+	0.117997i
$484$	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	$-0.237570\pi$
$487$	26.8873	+	26.8873i	0.0552100	+	0.0552100i	−0.678963	+	0.734173i	$0.737570\pi$
$488$	−223.842	+	250.177i	−0.458694	+	0.512658i
$489$	423.561	+	525.155i	0.866178	+	1.07394i
$490$	21.4832	−	44.2633i	0.0438433	−	0.0903333i
$491$	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	$0.152330\pi$
$492$	233.437	+	321.208i	0.474465	+	0.652863i
$493$	−19.7609	+	73.7486i	−0.0400829	+	0.149591i
$494$	−297.733	+	368.457i	−0.602698	+	0.745865i
$495$	−602.960	−	152.282i	−1.21810	−	0.307641i
$496$	−14.8428	−	32.9655i	−0.0299250	−	0.0664627i
$497$	6.26308	−	23.3741i	0.0126018	−	0.0470304i
$498$	196.724	−	52.5196i	0.395028	−	0.105461i
$499$	−448.438	+	776.718i	−0.898674	+	1.55655i	−0.0694839	+	0.997583i	$0.522135\pi$
$499$	−448.438	+	776.718i	−0.898674	+	1.55655i	−0.829190	+	0.558966i	$0.811198\pi$
$500$	−201.204	+	457.730i	−0.402408	+	0.915460i
$501$	−393.697	+	61.5649i	−0.785822	+	0.122884i
$502$	−11.4853	+	8.36297i	−0.0228792	+	0.0166593i
$503$	−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
$507$	−117.586	−	265.502i	−0.231925	−	0.523672i
$508$	−593.598	+	304.019i	−1.16850	+	0.598463i
$509$	−131.338	+	227.484i	−0.258031	+	0.446922i	−0.965714	−	0.259607i	$-0.916407\pi$
$509$	−131.338	+	227.484i	−0.258031	+	0.446922i	0.707684	+	0.706530i	$0.249740\pi$
$510$	−566.245	−	607.264i	−1.11028	−	1.19071i
$511$	87.8743	−	50.7343i	0.171965	−	0.0992843i
$512$	−417.032	−	297.032i	−0.814516	−	0.580141i
$513$	−236.766	+	714.374i	−0.461532	+	1.39254i
$514$	619.760	−	766.979i	1.20576	−	1.49218i
$515$	261.899	+	79.8187i	0.508543	+	0.154988i
$516$	591.350	+	478.735i	1.14603	+	0.927782i
$517$	−130.805	−	488.170i	−0.253007	−	0.944236i
$518$	746.400	+	331.383i	1.44093	+	0.639736i
$519$	35.8440	−	92.8326i	0.0690635	−	0.178868i
$520$	−339.823	+	7.29793i	−0.653507	+	0.0140345i
$521$		−	262.661i		−	0.504148i	−0.967708	−	0.252074i	$-0.918887\pi$
$521$		−	262.661i		−	0.504148i	0.967708	−	0.252074i	$-0.0811126\pi$
$522$	40.0881	+	29.3020i	0.0767972	+	0.0561342i
$523$	603.390	−	603.390i	1.15371	−	1.15371i	0.167906	−	0.985803i	$-0.446300\pi$
$523$	603.390	−	603.390i	1.15371	−	1.15371i	0.985803	−	0.167906i	$-0.0537004\pi$
$524$	−277.812	−	307.246i	−0.530175	−	0.586347i
$525$	47.8898	+	548.641i	0.0912187	+	1.04503i
$526$	−236.565	−	614.351i	−0.449743	−	1.16797i
$527$	16.1858	+	60.4063i	0.0307131	+	0.114623i
$528$	649.161	+	136.474i	1.22947	+	0.258474i
$529$	53.1523	−	30.6875i	0.100477	−	0.0580104i
$530$	334.152	+	289.345i	0.630475	+	0.545934i
$531$	54.0961	+	49.0936i	0.101876	+	0.0924549i
$532$	−687.558	−	444.462i	−1.29240	−	0.835456i
$533$	−271.599	−	72.7746i	−0.509566	−	0.136538i
$534$	−300.891	−	522.260i	−0.563467	−	0.978014i
$535$	−103.518	−	446.591i	−0.193491	−	0.834749i
$536$	203.226	+	310.800i	0.379153	+	0.579851i
$537$	−109.925	−	11.7714i	−0.204702	−	0.0219206i
$538$	−756.416	+	550.779i	−1.40598	+	1.02375i
$539$		−	67.9954i		−	0.126151i
$540$	−501.265	+	200.832i	−0.928268	+	0.371911i
$541$	−509.824			−0.942374			−0.471187	−	0.882033i	$-0.656174\pi$
$541$	−509.824			−0.942374			−0.471187	+	0.882033i	$0.656174\pi$
$542$	−303.763	−	417.176i	−0.560449	−	0.769697i
$543$	−70.7598	+	660.777i	−0.130313	+	1.21690i
$544$	629.521	+	622.969i	1.15721	+	1.14516i
$545$	−792.903	−	494.491i	−1.45487	−	0.907323i
$546$	−324.399	+	186.897i	−0.594137	+	0.342302i
$547$	164.746	−	614.842i	0.301182	−	1.12402i	−0.635001	−	0.772511i	$-0.719000\pi$
$547$	164.746	−	614.842i	0.301182	−	1.12402i	0.936183	−	0.351514i	$-0.114333\pi$
$548$	71.2254	+	46.0427i	0.129973	+	0.0840195i
$549$	−115.295	−	359.632i	−0.210010	−	0.655068i
$550$	26.0533	+	690.500i	0.0473697	+	1.25545i
$551$	−38.4466	−	66.5915i	−0.0697761	−	0.120856i
$552$	519.272	−	265.354i	0.940710	−	0.480714i
$553$	−72.9940	+	19.5587i	−0.131996	+	0.0353683i
$554$	52.1309	−	20.0738i	0.0940991	−	0.0362343i
$555$	−828.006	+	100.759i	−1.49190	+	0.181548i
$556$	93.5700	+	103.484i	0.168291	+	0.186122i
$557$	−3.60960	−	3.60960i	−0.00648043	−	0.00648043i	0.703859	−	0.710340i	$-0.251459\pi$
$557$	−3.60960	−	3.60960i	−0.00648043	−	0.00648043i	−0.710340	+	0.703859i	$0.751459\pi$
$558$	40.4368	+	4.36756i	0.0724674	+	0.00782717i
$559$	−538.775			−0.963819
$560$	−74.5437	−	582.694i	−0.133114	−	1.04052i
$561$	−1070.44	−	413.313i	−1.90810	−	0.736743i
$562$	80.1856	−	180.608i	0.142679	−	0.321367i
$563$	−511.673	+	137.102i	−0.908833	+	0.243521i	−0.682806	−	0.730600i	$-0.739240\pi$
$563$	−511.673	+	137.102i	−0.908833	+	0.243521i	−0.226027	+	0.974121i	$0.572574\pi$
$564$	−341.079	−	276.125i	−0.604751	−	0.489584i
$565$	842.754	+	256.845i	1.49160	+	0.454593i
$566$	−156.740	−	126.654i	−0.276926	−	0.223771i
$567$	−377.922	+	459.287i	−0.666529	+	0.810031i
$568$	−8.22549	−	25.0477i	−0.0144815	−	0.0440980i
$569$	291.032	+	504.082i	0.511479	+	0.885908i	0.999911	+	0.0133061i	$0.00423559\pi$
$569$	291.032	+	504.082i	0.511479	+	0.885908i	−0.488432	+	0.872602i	$0.662431\pi$
$570$	835.698	+	29.2108i	1.46614	+	0.0512471i
$571$	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	$0.374208\pi$
$572$	−418.093	+	214.132i	−0.730932	+	0.374357i
$573$	295.119	−	130.703i	0.515041	−	0.228103i
$574$	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	$0.114553\pi$
$578$	−561.558	−	771.220i	−0.971554	−	1.33429i
$579$	−32.1928	−	205.867i	−0.0556006	−	0.355556i
$580$	18.7160	−	51.9013i	0.0322689	−	0.0894850i
$581$	−215.806	−	124.595i	−0.371438	−	0.214450i
$582$	12.5048	+	46.8398i	0.0214860	+	0.0804807i
$583$	590.044	+	158.102i	1.01208	+	0.271187i
$584$	49.8777	−	98.6549i	0.0854071	−	0.168930i
$585$	186.402	−	333.881i	0.318635	−	0.570736i
$586$	429.804	+	347.304i	0.733454	+	0.592670i
$587$	−984.077	−	263.683i	−1.67645	−	0.449204i	−0.709613	−	0.704592i	$-0.751130\pi$
$587$	−984.077	−	263.683i	−1.67645	−	0.449204i	−0.966839	+	0.255388i	$0.917797\pi$
$588$	−34.7101	−	47.7610i	−0.0590308	−	0.0812262i
$589$	−54.5440	−	31.4910i	−0.0926045	−	0.0534652i
$590$	35.4414	−	73.0223i	0.0600702	−	0.123767i
$591$	−504.892	+	407.218i	−0.854301	+	0.689032i
$592$	878.177	−	142.860i	1.48341	−	0.241317i
$593$	−238.904	+	238.904i	−0.402873	+	0.402873i	−0.879244	−	0.476371i	$-0.841952\pi$
$593$	−238.904	+	238.904i	−0.402873	+	0.402873i	0.476371	+	0.879244i	$0.341952\pi$
$594$	−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
$597$	8.50687	−	79.4398i	0.0142494	−	0.133065i
$598$	−167.563	+	377.415i	−0.280206	+	0.631129i
$599$	−653.086	−	377.059i	−1.09029	−	0.629482i	−0.156639	−	0.987656i	$-0.550066\pi$
$599$	−653.086	−	377.059i	−1.09029	−	0.629482i	−0.933655	+	0.358174i	$0.883399\pi$
$600$	370.785	+	471.718i	0.617975	+	0.786197i
$601$	−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	$0.880637\pi$
$602$	−98.3005	−	925.946i	−0.163290	−	1.53812i
$603$	−417.274	+	20.2290i	−0.691996	+	0.0335472i
$604$	−83.6907	−	389.722i	−0.138561	−	0.645235i
$605$	164.558	+	308.833i	0.271997	+	0.510467i
$606$	−764.499	−	442.315i	−1.26155	−	0.729893i
$607$	235.568	−	63.1201i	0.388085	−	0.103987i	−0.0595003	−	0.998228i	$-0.518951\pi$
$607$	235.568	−	63.1201i	0.388085	−	0.103987i	0.447585	+	0.894241i	$0.352284\pi$
$608$	−891.944	+	4.66625i	−1.46701	+	0.00767476i
$609$	−9.38894	−	60.0406i	−0.0154170	−	0.0985889i
$610$	−347.431	+	235.321i	−0.569560	+	0.385771i
$611$	310.755			0.508601
$612$	−962.883	+	256.120i	−1.57334	+	0.418496i
$613$	−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
$615$	185.436	+	460.401i	0.301523	+	0.748620i
$616$	−444.292	−	679.471i	−0.721254	−	1.10304i
$617$	381.152	−	102.129i	0.617750	−	0.165526i	0.0636454	−	0.997973i	$-0.479727\pi$
$617$	381.152	−	102.129i	0.617750	−	0.165526i	0.554105	+	0.832447i	$0.313061\pi$
$618$	232.533	−	232.108i	0.376267	−	0.375580i
$619$	334.588	+	579.524i	0.540530	+	0.936226i	0.998874	+	0.0474504i	$0.0151096\pi$
$619$	334.588	+	579.524i	0.540530	+	0.936226i	−0.458344	+	0.888775i	$0.651557\pi$
$620$	−7.97962	−	44.4810i	−0.0128704	−	0.0717436i
$621$	−38.1848	+	654.924i	−0.0614892	+	1.05463i
$622$	55.4604	+	522.412i	0.0891647	+	0.839891i
$623$	−190.918	+	712.517i	−0.306450	+	1.14369i
$624$	−184.365	+	363.837i	−0.295457	+	0.583072i
$625$	−383.052	+	493.858i	−0.612883	+	0.790173i
$626$	−145.151	−	376.951i	−0.231870	−	0.602159i
$627$	1056.64	−	467.966i	1.68522	−	0.746357i
$628$	113.296	+	5.69986i	0.180407	+	0.00907622i
$629$	−1539.04			−2.44680
$630$	607.821	+	259.435i	0.964795	+	0.411802i
$631$			606.850i			0.961728i	0.876795	+	0.480864i	$0.159677\pi$
$631$			606.850i			0.961728i	−0.876795	+	0.480864i	$0.840323\pi$
$632$	−54.8971	+	61.3557i	−0.0868626	+	0.0970817i
$633$	82.7260	−	113.395i	0.130689	−	0.179138i
$634$	204.813	+	531.893i	0.323049	+	0.838947i
$635$	−812.122	+	188.246i	−1.27893	+	0.296451i
$636$	495.163	−	190.151i	0.778559	−	0.298980i
$637$	40.3844	+	10.8210i	0.0633978	+	0.0169874i
$638$	−8.04941	−	75.8218i	−0.0126166	−	0.118843i
$639$	28.9866	+	6.28013i	0.0453625	+	0.00982805i
$640$	−415.392	−	486.877i	−0.649051	−	0.760745i
$641$	−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	$0.429032\pi$
$642$	−531.242	−	142.866i	−0.827480	−	0.222533i
$643$	99.1452	+	370.015i	0.154192	+	0.575451i	0.999173	+	0.0406555i	$0.0129446\pi$
$643$	99.1452	+	370.015i	0.154192	+	0.575451i	−0.844982	+	0.534795i	$0.820389\pi$
$644$	−679.204	−	219.116i	−1.05466	−	0.340243i
$645$	571.538	+	760.163i	0.886106	+	1.17855i
$646$	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	$0.245866\pi$
$648$	−70.7619	+	644.125i	−0.109200	+	0.994020i
$649$		−	112.174i		−	0.172841i
$650$	−414.254	−	94.4143i	−0.637314	−	0.145253i
$651$	−31.2492	−	38.7445i	−0.0480018	−	0.0595154i
$652$	−410.073	−	800.668i	−0.628947	−	1.22802i
$653$	162.097	+	604.956i	0.248235	+	0.926426i	0.971730	+	0.236096i	$0.0758679\pi$
$653$	162.097	+	604.956i	0.248235	+	0.926426i	−0.723495	+	0.690330i	$0.757465\pi$
$654$	−971.631	+	559.789i	−1.48567	+	0.855947i
$655$	−243.484	−	456.955i	−0.371731	−	0.697642i
$656$	−217.362	−	482.755i	−0.331344	−	0.735907i
$657$	67.3248	+	104.566i	0.102473	+	0.159157i
$658$	56.6978	+	534.068i	0.0861669	+	0.811654i
$659$	579.013	−	334.293i	0.878623	−	0.507273i	0.00841895	−	0.999965i	$-0.497320\pi$
$659$	579.013	−	334.293i	0.878623	−	0.507273i	0.870204	+	0.492691i	$0.163987\pi$
$660$	745.639	+	362.738i	1.12976	+	0.549602i
$661$	−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	$0.995159\pi$
$662$	158.995	−	358.116i	0.240174	−	0.540961i
$663$	415.832	−	569.991i	0.627197	−	0.859715i
$664$	−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
$668$	530.638	+	26.6962i	0.794368	+	0.0399644i
$669$	26.7625	−	69.3125i	0.0400038	−	0.103606i
$670$	151.968	+	438.601i	0.226818	+	0.654628i
$671$	−289.957	+	502.220i	−0.432126	+	0.748464i
$672$	−658.933	−	250.470i	−0.980555	−	0.372723i
$673$	316.784	−	1182.25i	0.470705	−	1.75669i	−0.166543	−	0.986034i	$-0.553260\pi$
$673$	316.784	−	1182.25i	0.470705	−	1.75669i	0.637247	−	0.770659i	$-0.280073\pi$
$674$	−698.066	−	564.074i	−1.03571	−	0.836906i
$675$	−668.812	+	91.1884i	−0.990833	+	0.135094i
$676$	81.2888	+	378.537i	0.120250	+	0.559966i
$677$	80.3686	−	299.940i	0.118713	−	0.443042i	−0.880825	−	0.473442i	$-0.843011\pi$
$677$	80.3686	−	299.940i	0.118713	−	0.443042i	0.999538	+	0.0303997i	$0.00967802\pi$
$678$	748.256	−	746.891i	1.10362	−	1.10161i
$679$	29.6660	−	51.3830i	0.0436907	−	0.0756746i
$680$	573.993	+	946.645i	0.844107	+	1.39213i
$681$	−70.4756	+	182.525i	−0.103488	+	0.268026i
$682$	−36.7620	−	50.4874i	−0.0539032	−	0.0740284i
$683$	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
$687$	313.741	−	430.053i	0.456683	−	0.625987i
$688$	−641.713	−	785.703i	−0.932722	−	1.14201i
$689$	−187.802	+	325.283i	−0.272572	+	0.472109i
$690$	710.252	−	163.950i	1.02935	−	0.237609i
$691$	−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	$0.397753\pi$
$692$	−72.0313	+	111.428i	−0.104092	+	0.161024i
$693$	912.244	−	44.2246i	1.31637	−	0.0638161i
$694$	−800.286	−	646.673i	−1.15315	−	0.931806i
$695$	82.0079	+	153.908i	0.117997	+	0.221450i
$696$	−44.3593	−	49.1493i	−0.0637347	−	0.0706169i
$697$	237.029	+	884.605i	0.340070	+	1.26916i
$698$	353.852	−	797.008i	0.506951	−	1.14184i
$699$	−779.077	−	965.944i	−1.11456	−	1.38189i
$700$	86.6803	−	729.169i	0.123829	−	1.04167i
$701$		−	114.693i		−	0.163613i	−0.996648	−	0.0818063i	$-0.973931\pi$
$701$		−	114.693i		−	0.163613i	0.996648	−	0.0818063i	$-0.0260689\pi$
$702$	−248.055	−	386.042i	−0.353354	−	0.549917i
$703$	1096.00	−	1096.00i	1.55904	−	1.55904i
$704$	−810.245	−	354.666i	−1.15092	−	0.503788i
$705$	−329.652	−	438.447i	−0.467592	−	0.621911i
$706$	498.214	−	191.845i	0.705686	−	0.271735i
$707$	279.767	+	1044.10i	0.395710	+	1.47681i
$708$	−57.2622	−	78.7926i	−0.0808788	−	0.111289i
$709$	866.555	−	500.306i	1.22222	−	0.705650i	0.256830	−	0.966457i	$-0.417322\pi$
$709$	866.555	−	500.306i	1.22222	−	0.705650i	0.965391	+	0.260807i	$0.0839885\pi$
$710$	−2.36212	−	32.8698i	−0.00332693	−	0.0462955i
$711$	−28.2761	−	88.1994i	−0.0397695	−	0.124050i
$712$	250.739	+	763.531i	0.352161	+	1.07238i
$713$	−53.0311	−	14.2096i	−0.0743775	−	0.0199294i
$714$	1055.46	+	610.658i	1.47824	+	0.855264i
$715$	−572.007	+	132.589i	−0.800010	+	0.185439i
$716$	140.285	+	45.2570i	0.195929	+	0.0632081i
$717$	−313.936	+	430.321i	−0.437847	+	0.600168i
$718$	−355.431	−	488.134i	−0.495029	−	0.679852i
$719$			1173.00i			1.63143i	0.578452	+	0.815716i	$0.303657\pi$
$719$			1173.00i			1.63143i	−0.578452	+	0.815716i	$0.696343\pi$
$720$	708.918	−	125.840i	0.984608	−	0.174777i
$721$	−402.094			−0.557689
$722$	−672.491	+	489.669i	−0.931428	+	0.678212i
$723$	−19.6840	+	8.71769i	−0.0272254	+	0.0120577i
$724$	272.048	−	843.277i	0.375756	−	1.16475i
$725$	38.4646	−	57.2432i	0.0530546	−	0.0789561i
$726$	419.926	+	0.383456i	0.578411	+	0.000528176i
$727$	−126.975	+	473.878i	−0.174656	+	0.651827i	0.821954	+	0.569555i	$0.192884\pi$
$727$	−126.975	+	473.878i	−0.174656	+	0.651827i	−0.996610	+	0.0822720i	$0.973782\pi$
$728$	474.264	−	155.745i	0.651461	−	0.213936i
$729$	−584.695	−	435.399i	−0.802051	−	0.597256i
$730$	90.4554	−	104.463i	0.123911	−	0.143100i
$731$	877.403	+	1519.71i	1.20028	+	2.07894i
$732$	52.7019	+	500.783i	0.0719971	+	0.684130i
$733$	−114.671	+	30.7259i	−0.156440	+	0.0419181i	−0.336189	−	0.941794i	$-0.609138\pi$
$733$	−114.671	+	30.7259i	−0.156440	+	0.0419181i	0.179749	+	0.983713i	$0.442471\pi$
$734$	384.278	+	997.957i	0.523540	+	1.35961i
$735$	−27.5728	−	68.4578i	−0.0375140	−	0.0931398i
$736$	−749.968	+	205.164i	−1.01898	+	0.278756i
$737$	453.603	+	453.603i	0.615472	+	0.615472i
$738$	592.167	+	63.9596i	0.802394	+	0.0866661i
$739$	820.074			1.10971			0.554854	−	0.831948i	$-0.312774\pi$
$739$	820.074			1.10971			0.554854	+	0.831948i	$0.312774\pi$
$740$	1108.20	+	93.6364i	1.49757	+	0.126536i
$741$	109.783	+	702.040i	0.148155	+	0.947423i
$742$	−593.301	−	263.411i	−0.799598	−	0.355002i
$743$	728.676	−	195.248i	0.980722	−	0.262784i	0.267373	−	0.963593i	$-0.413844\pi$
$743$	728.676	−	195.248i	0.980722	−	0.262784i	0.713348	+	0.700810i	$0.247178\pi$
$744$	−51.5949	−	16.6969i	−0.0693480	−	0.0224421i
$745$	−197.912	−	371.430i	−0.265654	−	0.498564i
$746$	−653.978	+	809.325i	−0.876646	+	1.08489i
$747$	139.724	−	271.587i	0.187046	−	0.363570i
$748$	1284.87	+	830.585i	1.71774	+	1.11041i
$749$	336.628	+	583.056i	0.449436	+	0.778446i
$750$	306.236	+	684.631i	0.408314	+	0.912842i
$751$	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	$0.593559\pi$
$752$	370.128	+	453.178i	0.492191	+	0.602631i
$753$	−2.26915	+	21.1901i	−0.00301348	+	0.0281409i
$754$	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	$-0.0249673\pi$
$758$	−441.817	+	321.705i	−0.582872	+	0.424414i
$759$	784.112	−	632.422i	1.03309	−	0.833230i
$760$	−1082.90	−	265.379i	−1.42487	−	0.349184i
$761$	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	$0.599343\pi$
$762$	−259.801	+	966.060i	−0.340946	+	1.26780i
$763$	1325.59	+	355.191i	1.73734	+	0.465520i
$764$	−420.763	+	90.3566i	−0.550737	+	0.118268i
$765$	−1245.32	+	17.9520i	−1.62788	+	0.0234667i
$766$	−285.305	+	353.077i	−0.372461	+	0.460936i
$767$	66.6232	+	17.8516i	0.0868621	+	0.0232746i
$768$	−750.178	+	164.489i	−0.976795	+	0.214178i
$769$	888.690	+	513.085i	1.15564	+	0.667211i	0.950256	−	0.311469i	$-0.100821\pi$
$769$	888.690	+	513.085i	1.15564	+	0.667211i	0.205388	+	0.978681i	$0.434154\pi$
$770$	−332.233	−	958.869i	−0.431471	−	1.24528i
$771$	−228.523	−	1461.36i	−0.296398	−	1.89541i
$772$	−13.9596	+	277.474i	−0.0180824	+	0.359423i
$773$	420.414	−	420.414i	0.543873	−	0.543873i	−0.380789	−	0.924662i	$-0.624348\pi$
$773$	420.414	−	420.414i	0.543873	−	0.543873i	0.924662	+	0.380789i	$0.124348\pi$
$774$	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
$777$	1120.05	−	496.053i	1.44151	−	0.638420i
$778$	−165.809	−	73.6150i	−0.213122	−	0.0946208i
$779$	−798.756	−	461.162i	−1.02536	−	0.591992i
$780$	−334.103	+	385.129i	−0.428338	+	0.493756i
$781$	−22.7713	−	39.4411i	−0.0291567	−	0.0505008i
$782$	1337.44	−	141.986i	1.71029	−	0.181568i
$783$	72.9454	−	15.0574i	0.0931614	−	0.0192304i
$784$	32.3199	+	71.7816i	0.0412243	+	0.0915581i
$785$	135.639	+	41.3385i	0.172789	+	0.0526606i
$786$	−621.332	−	0.567369i	−0.790498	−	0.000721844i
$787$	−944.882	+	253.180i	−1.20061	+	0.321703i	−0.803072	−	0.595882i	$-0.796803\pi$
$787$	−944.882	+	253.180i	−1.20061	+	0.321703i	−0.397540	+	0.917585i	$0.630136\pi$
$788$	769.774	−	394.251i	0.976870	−	0.500318i
$789$	−921.202	−	355.689i	−1.16756	−	0.450810i
$790$	−85.2072	+	57.7121i	−0.107857	+	0.0730533i
$791$	−1293.88			−1.63575
$792$	805.450	−	584.235i	1.01698	−	0.737670i
$793$	−252.138	−	252.138i	−0.317955	−	0.317955i
$794$	180.312	−	1146.21i	0.227093	−	1.44358i
$795$	658.168	−	80.0919i	0.827885	−	0.100745i
$796$	−32.7061	+	101.380i	−0.0410880	+	0.127362i
$797$	−244.550	+	65.5269i	−0.306838	+	0.0822170i	−0.408952	−	0.912556i	$-0.634106\pi$
$797$	−244.550	+	65.5269i	−0.306838	+	0.0822170i	0.102115	+	0.994773i	$0.467439\pi$
$798$	−1186.51	+	316.762i	−1.48685	+	0.396945i
$799$	−506.069	−	876.538i	−0.633378	−	1.09704i
$800$	−355.716	−	716.566i	−0.444645	−	0.895707i
$801$	−883.604	−	191.438i	−1.10313	−	0.238999i
$802$	−3.80500	+	0.403948i	−0.00474439	+	0.000503675i
$803$	49.4259	−	184.460i	0.0615516	−	0.229714i
$804$	550.172	+	87.0636i	0.684294	+	0.108288i
$805$	−756.952	−	472.070i	−0.940314	−	0.586423i
$806$	35.8363	−	13.7993i	0.0444620	−	0.0171207i
$807$	−149.445	+	1395.56i	−0.185186	+	1.72932i
$808$	877.630	+	785.247i	1.08618	+	0.971841i
$809$	627.119			0.775177			0.387589	−	0.921832i	$-0.373308\pi$
$809$	627.119			0.775177			0.387589	+	0.921832i	$0.373308\pi$
$810$	−281.531	+	759.500i	−0.347569	+	0.937654i
$811$		−	1145.58i		−	1.41255i	−0.707937	−	0.706276i	$-0.750374\pi$
$811$		−	1145.58i		−	1.41255i	0.707937	−	0.706276i	$-0.249626\pi$
$812$	−4.07130	+	80.9247i	−0.00501391	+	0.0996610i
$813$	−769.675	−	82.4212i	−0.946710	−	0.101379i
$814$	1434.31	−	552.304i	1.76205	−	0.678506i
$815$	−253.914	−	1095.42i	−0.311551	−	1.34408i
$816$	1326.51	−	72.4802i	1.62562	−	0.0888237i
$817$	−1707.07	−	457.408i	−2.08944	−	0.559863i
$818$	688.125	−	73.0529i	0.841229	−	0.0893067i
$819$	−118.911	+	548.846i	−0.145190	+	0.670142i
$820$	−116.856	−	651.391i	−0.142507	−	0.794380i
$821$	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	$-0.0108287\pi$
$822$	122.912	−	32.8140i	0.149528	−	0.0399197i
$823$	74.1653	+	276.789i	0.0901158	+	0.336317i	0.996234	−	0.0867084i	$-0.0276348\pi$
$823$	74.1653	+	276.789i	0.0901158	+	0.336317i	−0.906118	+	0.423025i	$0.860968\pi$
$824$	−366.644	+	239.741i	−0.444956	+	0.290948i
$825$	793.863	+	666.399i	0.962258	+	0.807757i
$826$	−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	$0.237345\pi$
$828$	227.936	−	844.495i	0.275284	−	1.01992i
$829$			1466.67i			1.76920i	0.466347	+	0.884602i	$0.345570\pi$
$829$			1466.67i			1.76920i	−0.466347	+	0.884602i	$0.654430\pi$
$830$	−333.246	−	64.1105i	−0.401501	−	0.0772415i
$831$	30.1821	−	78.1688i	0.0363202	−	0.0940660i
$832$	339.591	−	424.786i	0.408163	−	0.510560i
$833$	−35.2442	−	131.533i	−0.0423100	−	0.157903i
$834$	209.271	+	0.191096i	0.250925	+	0.000229132i
$835$	635.287	+	193.615i	0.760823	+	0.231875i
$836$	−1506.49	+	323.511i	−1.80202	+	0.386975i
$837$	45.5770	−	40.5551i	0.0544528	−	0.0484529i
$838$	−1428.85	+	151.690i	−1.70508	+	0.181015i
$839$	−1074.43	+	620.325i	−1.28061	+	0.739363i	−0.976961	−	0.213420i	$-0.931540\pi$
$839$	−1074.43	+	620.325i	−1.28061	+	0.739363i	−0.303653	+	0.952783i	$0.598206\pi$
$840$	−722.847	−	503.927i	−0.860532	−	0.599913i
$841$	416.695	−	721.737i	0.495476	−	0.858189i
$842$	311.413	+	138.260i	0.369849	+	0.164204i
$843$	−120.031	−	271.022i	−0.142386	−	0.321497i
$844$	−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
$848$	−698.049	+	113.557i	−0.823171	+	0.133911i
$849$	−298.644	+	46.7009i	−0.351760	+	0.0550070i
$850$	408.308	+	1322.23i	0.480362	+	1.55556i
$851$	675.566	−	1170.12i	0.793850	−	1.37499i
$852$	−36.1288	−	16.0798i	−0.0424047	−	0.0188730i
$853$	−296.836	+	1107.81i	−0.347991	+	1.29872i	0.541088	+	0.840966i	$0.318012\pi$
$853$	−296.836	+	1107.81i	−0.347991	+	1.29872i	−0.889079	+	0.457754i	$0.848654\pi$
$854$	387.325	−	479.331i	0.453542	−	0.561278i
$855$	874.057	−	899.625i	1.02229	−	1.05219i
$856$	654.586	+	330.944i	0.764704	+	0.386617i
$857$	−231.031	+	862.219i	−0.269581	+	1.00609i	0.689805	+	0.723995i	$0.257696\pi$
$857$	−231.031	+	862.219i	−0.269581	+	1.00609i	−0.959386	+	0.282095i	$0.908971\pi$
$858$	−182.987	+	680.432i	−0.213272	+	0.793044i
$859$	380.496	−	659.038i	0.442952	−	0.767216i	−0.554955	−	0.831880i	$-0.687264\pi$
$859$	380.496	−	659.038i	0.442952	−	0.767216i	0.997907	+	0.0646648i	$0.0205978\pi$
$860$	−539.324	−	1147.67i	−0.627121	−	1.33449i
$861$	−457.621	−	567.384i	−0.531499	−	0.658983i
$862$	−339.162	+	246.958i	−0.393459	+	0.286494i
$863$	−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
$867$	−1422.87	−	152.370i	−1.64115	−	0.175743i
$868$	30.2541	+	59.0711i	0.0348550	+	0.0680543i
$869$	−71.1116	+	123.169i	−0.0818315	+	0.141736i
$870$	−38.8507	−	73.0733i	−0.0446559	−	0.0839923i
$871$	−341.596	+	197.220i	−0.392188	+	0.226430i
$872$	1420.50	−	466.484i	1.62902	−	0.534958i
$873$	64.6644	+	33.2680i	0.0740715	+	0.0381077i
$874$	−851.329	+	1053.56i	−0.974061	+	1.20544i
$875$	326.675	−	857.780i	0.373342	−	0.980319i
$876$	−59.4452	−	154.798i	−0.0678598	−	0.176711i
$877$	−268.154	−	1000.76i	−0.305763	−	1.14112i	−0.932287	−	0.361720i	$-0.882190\pi$
$877$	−268.154	−	1000.76i	−0.305763	−	1.14112i	0.626524	−	0.779402i	$-0.284477\pi$
$878$	1386.15	+	615.417i	1.57876	+	0.700931i
$879$	818.927	−	128.061i	0.931658	−	0.145689i
$880$	−874.651	−	676.245i	−0.993921	−	0.768461i
$881$			482.103i			0.547223i	0.961840	+	0.273611i	$0.0882182\pi$
$881$			482.103i			0.547223i	−0.961840	+	0.273611i	$0.911782\pi$
$882$	−88.0502	−	9.51026i	−0.0998302	−	0.0107826i
$883$	−702.762	+	702.762i	−0.795880	+	0.795880i	−0.982443	−	0.186563i	$-0.940265\pi$
$883$	−702.762	+	702.762i	−0.795880	+	0.795880i	0.186563	+	0.982443i	$0.440265\pi$
$884$	−697.786	+	630.938i	−0.789351	+	0.713731i
$885$	−45.4876	−	112.937i	−0.0513984	−	0.127612i
$886$	534.878	+	1389.06i	0.603700	+	1.56779i
$887$	−127.139	−	474.487i	−0.143335	−	0.534935i	−0.999824	−	0.0187688i	$-0.994025\pi$
$887$	−127.139	−	474.487i	−0.143335	−	0.534935i	0.856488	−	0.516166i	$-0.172641\pi$
$888$	725.545	−	1120.13i	0.817055	−	1.26141i
$889$	1060.28	−	612.154i	1.19267	−	0.688588i
$890$	72.0049	+	1001.98i	0.0809044	+	1.12582i
$891$	108.281	+	1114.16i	0.121527	+	1.25046i
$892$	−53.7814	+	83.1968i	−0.0602931	+	0.0932699i
$893$	984.605	+	263.824i	1.10258	+	0.295436i
$894$	−505.041	−	0.461178i	−0.564923	−	0.000515859i
$895$	156.343	+	97.5030i	0.174685	+	0.108942i
$896$	792.001	+	506.124i	0.883930	+	0.564870i
$897$	250.828	+	566.352i	0.279630	+	0.631385i
$898$	−1219.19	+	887.745i	−1.35767	+	0.988580i
$899$			6.23330i			0.00693359i
$900$	897.804	+	62.8401i	0.997559	+	0.0698223i
$901$	1223.36			1.35778
$902$	−538.352	−	739.350i	−0.596843	−	0.819678i
$903$	−1128.36	−	823.186i	−1.24957	−	0.911613i
$904$	−1179.81	+	771.451i	−1.30510	+	0.853376i
$905$	586.107	−	939.807i	0.647632	−	1.03846i
$906$	−517.532	−	299.428i	−0.571227	−	0.330494i
$907$	−130.194	+	485.891i	−0.143544	+	0.535712i	0.856272	+	0.516525i	$0.172775\pi$
$907$	−130.194	+	485.891i	−0.143544	+	0.535712i	−0.999816	+	0.0191873i	$0.993892\pi$
$908$	141.626	−	219.088i	0.155976	−	0.241286i
$909$	−1261.60	+	404.460i	−1.38790	+	0.444951i
$910$	622.372	−	44.7255i	0.683926	−	0.0491489i
$911$	−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	$0.926599\pi$
$912$	−893.037	+	996.269i	−0.979208	+	1.09240i
$913$	−453.005	+	121.382i	−0.496172	+	0.132949i
$914$	−215.102	+	82.8283i	−0.235342	+	0.0906218i
$915$	−88.2732	+	623.215i	−0.0964735	+	0.681110i
$916$	−526.473	+	476.037i	−0.574753	+	0.519691i
$917$	537.691	+	537.691i	0.586359	+	0.586359i
$918$	−684.936	+	1328.36i	−0.746118	+	1.44701i
$919$	12.3908			0.0134830			0.00674148	−	0.999977i	$-0.497854\pi$
$919$	12.3908			0.0134830			0.00674148	+	0.999977i	$0.497854\pi$
$920$	−971.681	+	20.8675i	−1.05618	+	0.0226821i
$921$	825.157	−	665.526i	0.895936	−	0.722613i
$922$	373.553	−	841.381i	0.405155	−	0.912561i
$923$	27.0491	−	7.24779i	0.0293057	−	0.00785243i
$924$	−1202.79	−	190.338i	−1.30172	−	0.205994i
$925$	1315.24	+	450.287i	1.42189	+	0.486797i
$926$	1087.52	+	878.772i	1.17442	+	0.948997i
$927$	−23.8637	−	492.248i	−0.0257429	−	0.531012i
$928$	44.5376	+	76.2177i	0.0479931	+	0.0821311i
$929$	11.6687	+	20.2108i	0.0125605	+	0.0217554i	0.872237	−	0.489083i	$-0.162668\pi$
$929$	11.6687	+	20.2108i	0.0125605	+	0.0217554i	−0.859677	+	0.510838i	$0.829335\pi$
$930$	−57.4852	−	35.9234i	−0.0618120	−	0.0386273i
$931$	118.768	+	68.5709i	0.127571	+	0.0736530i
$932$	754.269	+	1472.71i	0.809302	+	1.58016i
$933$	636.614	+	464.436i	0.682330	+	0.497788i
$934$	−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	$0.217564\pi$
$938$	−401.270	−	551.088i	−0.427794	−	0.587514i
$939$	−565.228	−	218.242i	−0.601947	−	0.232420i
$940$	311.072	+	661.951i	0.330928	+	0.704204i
$941$	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	$0.604335\pi$
$942$	120.430	−	120.210i	0.127845	−	0.127612i
$943$	−776.601	−	208.090i	−0.823543	−	0.220668i
$944$	53.3189	+	118.420i	0.0564819	+	0.125445i
$945$	900.514	−	414.450i	0.952925	−	0.438571i
$946$	−1363.07	−	1101.43i	−1.44087	−	1.16430i
$947$	1517.00	+	406.478i	1.60190	+	0.429227i	0.945615	−	0.325288i	$-0.105461\pi$
$947$	1517.00	+	406.478i	1.60190	+	0.429227i	0.656282	+	0.754515i	$0.272128\pi$
$948$	12.9251	+	122.817i	0.0136341	+	0.129553i
$949$	101.690	+	58.7110i	0.107155	+	0.0618662i
$950$	−1232.38	−	650.837i	−1.29724	−	0.685092i
$951$	797.558	+	307.948i	0.838652	+	0.323815i
$952$	−1211.65	−	1084.11i	−1.27274	−	1.13877i
$953$	435.647	−	435.647i	0.457133	−	0.457133i	−0.440581	−	0.897713i	$-0.645227\pi$
$953$	435.647	−	435.647i	0.457133	−	0.457133i	0.897713	+	0.440581i	$0.145227\pi$
$954$	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
$957$	−92.3968	−	67.4072i	−0.0965484	−	0.0704359i
$958$	32.3095	−	72.7732i	0.0337260	−	0.0759636i
$959$	−134.834	−	77.8467i	−0.140599	−	0.0811748i
$960$	−959.576	−	28.5155i	−0.999559	−	0.0297037i
$961$	−477.947	−	827.829i	−0.497344	−	0.861424i
$962$	99.7686	+	939.775i	0.103710	+	0.976897i
$963$	−693.807	+	446.708i	−0.720464	+	0.463871i
$964$	28.0642	−	6.02665i	0.0291123	−	0.00625171i
$965$	−101.243	+	332.196i	−0.104915	+	0.344245i
$966$	−927.577	+	534.408i	−0.960225	+	0.553218i
$967$	1481.00	−	396.834i	1.53154	−	0.410376i	0.608022	−	0.793920i	$-0.291963\pi$
$967$	1481.00	−	396.834i	1.53154	−	0.410376i	0.923523	+	0.383544i	$0.125297\pi$
$968$	−548.029	−	114.690i	−0.566146	−	0.118482i
$969$	1801.44	−	1452.94i	1.85907	−	1.49943i
$970$	15.2646	−	79.3454i	0.0157367	−	0.0817994i
$971$	−1052.92			−1.08436			−0.542181	−	0.840261i	$-0.682401\pi$
$971$	−1052.92			−1.08436			−0.542181	+	0.840261i	$0.682401\pi$
$972$	644.810	+	727.326i	0.663385	+	0.748278i
$973$	−181.100	−	181.100i	−0.186126	−	0.186126i
$974$	−75.1249	−	11.8180i	−0.0771303	−	0.0121335i
$975$	−522.131	+	365.445i	−0.535519	+	0.374816i
$976$	67.3851	−	668.008i	0.0690421	−	0.684435i
$977$	1139.21	−	305.250i	1.16603	−	0.312436i	0.376657	−	0.926353i	$-0.377073\pi$
$977$	1139.21	−	305.250i	1.16603	−	0.312436i	0.789371	+	0.613916i	$0.210407\pi$
$978$	−1303.06	−	350.429i	−1.33237	−	0.358312i
$979$	694.142	+	1202.29i	0.709032	+	1.22808i
$980$	17.3754	+	96.8564i	0.0177300	+	0.0988331i
$981$	−356.158	+	1643.89i	−0.363056	+	1.67573i
$982$	9.33533	+	87.9346i	0.00950645	+	0.0895465i
$983$	−223.128	+	832.727i	−0.226987	+	0.847128i	0.754611	+	0.656172i	$0.227825\pi$
$983$	−223.128	+	832.727i	−0.226987	+	0.847128i	−0.981599	+	0.190956i	$0.938841\pi$
$984$	−755.568	−	244.514i	−0.767854	−	0.248490i
$985$	1053.15	−	244.116i	1.06919	−	0.247834i
$986$	−54.8720	−	142.501i	−0.0556512	−	0.144524i
$987$	650.818	+	474.798i	0.659390	+	0.481052i
$988$	47.6046	−	946.233i	0.0481828	−	0.957725i
$989$	−1540.56			−1.55769
$990$	1154.14	−	463.631i	1.16580	−	0.468314i
$991$		−	1028.85i		−	1.03819i	−0.854717	−	0.519094i	$-0.826269\pi$
$991$		−	1028.85i		−	1.03819i	0.854717	−	0.519094i	$-0.173731\pi$
$992$	62.8069	+	35.8248i	0.0633134	+	0.0361137i
$993$	−238.002	−	537.392i	−0.239680	−	0.541181i
$994$	17.3913	+	45.1646i	0.0174963	+	0.0454373i
$995$	−70.4629	+	112.985i	−0.0708169	+	0.113553i
$996$	−256.235	+	316.510i	−0.257264	+	0.317781i
$997$	−1897.61	−	508.463i	−1.90332	−	0.509993i	−0.995978	−	0.0895988i	$-0.971442\pi$
$997$	−1897.61	−	508.463i	−1.90332	−	0.509993i	−0.907342	−	0.420394i	$-0.861892\pi$
$998$	−189.365	−	1783.73i	−0.189744	−	1.78730i
$999$	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.23.14	✓	272
4.3	odd	2	inner	180.3.v.a.23.44	yes	272
5.2	odd	4	inner	180.3.v.a.167.21	yes	272
9.2	odd	6	inner	180.3.v.a.83.9	yes	272
20.7	even	4	inner	180.3.v.a.167.9	yes	272
36.11	even	6	inner	180.3.v.a.83.21	yes	272
45.2	even	12	inner	180.3.v.a.47.44	yes	272
180.47	odd	12	inner	180.3.v.a.47.14	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.v.a.23.14	✓	272	1.1	even	1	trivial
180.3.v.a.23.44	yes	272	4.3	odd	2	inner
180.3.v.a.47.14	yes	272	180.47	odd	12	inner
180.3.v.a.47.44	yes	272	45.2	even	12	inner
180.3.v.a.83.9	yes	272	9.2	odd	6	inner
180.3.v.a.83.21	yes	272	36.11	even	6	inner
180.3.v.a.167.9	yes	272	20.7	even	4	inner
180.3.v.a.167.21	yes	272	5.2	odd	4	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)

\(f(q)\)	\(=\)	\(q+(-1.61680 + 1.17726i) q^{2} +(-0.319431 + 2.98295i) q^{3} +(1.22810 - 3.80680i) q^{4} +(2.64586 - 4.24257i) q^{5} +(-2.99525 - 5.19889i) q^{6} +(-1.90052 + 7.09282i) q^{7} +(2.49601 + 7.60065i) q^{8} +(-8.79593 - 1.90569i) q^{9} +O(q^{10})\)	\(q+(-1.61680 + 1.17726i) q^{2} +(-0.319431 + 2.98295i) q^{3} +(1.22810 - 3.80680i) q^{4} +(2.64586 - 4.24257i) q^{5} +(-2.99525 - 5.19889i) q^{6} +(-1.90052 + 7.09282i) q^{7} +(2.49601 + 7.60065i) q^{8} +(-8.79593 - 1.90569i) q^{9} +(0.716781 + 9.97428i) q^{10} +(6.90992 + 11.9683i) q^{11} +(10.9632 + 4.87938i) q^{12} +(-8.20800 + 2.19933i) q^{13} +(-5.27736 - 13.7051i) q^{14} +(11.8102 + 9.24767i) q^{15} +(-12.9835 - 9.35031i) q^{16} +(19.5704 + 19.5704i) q^{17} +(16.4648 - 7.27399i) q^{18} -27.8736 q^{19} +(-12.9012 - 15.2826i) q^{20} +(-20.5504 - 7.93481i) q^{21} +(-25.2618 - 11.2156i) q^{22} +(-23.4697 + 6.28869i) q^{23} +(-23.4696 + 5.01757i) q^{24} +(-10.9988 - 22.4505i) q^{25} +(10.6815 - 13.2188i) q^{26} +(8.49426 - 25.6290i) q^{27} +(24.6670 + 15.9456i) q^{28} +(1.37932 + 2.38905i) q^{29} +(-29.9817 - 1.04797i) q^{30} +(1.95683 + 1.12978i) q^{31} +(31.9996 - 0.167407i) q^{32} +(-37.9081 + 16.7888i) 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} +(45.0662 - 32.8146i) q^{38} +(-3.93858 - 25.1865i) q^{39} +(38.8504 + 9.52081i) q^{40} +(28.6563 + 16.5447i) q^{41} +(42.5673 - 11.3642i) q^{42} +(61.2432 + 16.4101i) q^{43} +(54.0472 - 11.6063i) q^{44} +(-31.3578 + 32.2752i) q^{45} +(30.5425 - 37.7976i) q^{46} +(-35.3239 - 9.46501i) q^{47} +(32.0388 - 35.7424i) q^{48} +(-4.26096 - 2.46006i) q^{49} +(44.2131 + 23.3496i) q^{50} +(-64.6289 + 52.1261i) q^{51} +(-1.70787 + 33.9472i) 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} +(8.90370 - 83.1455i) q^{57} +(-5.04263 - 2.23880i) q^{58} +(-7.02941 - 4.05843i) q^{59} +(49.7082 - 33.6020i) q^{60} +(20.9812 + 36.3405i) q^{61} +(-4.49386 + 0.477078i) q^{62} +(30.2335 - 58.7662i) q^{63} +(-51.5399 + 37.9426i) q^{64} +(-12.3864 + 40.6421i) q^{65} +(41.5250 - 71.7721i) q^{66} +(44.8365 - 12.0139i) q^{67} +(98.5353 - 50.4663i) q^{68} +(-11.2619 - 72.0177i) q^{69} +(-72.1081 - 13.8723i) q^{70} -3.29546 q^{71} +(-7.47019 - 71.6114i) q^{72} +(-9.77104 - 9.77104i) q^{73} +(17.2829 - 109.864i) q^{74} +(70.4821 - 25.6375i) q^{75} +(-34.2317 + 106.109i) q^{76} +(-98.0216 + 26.2648i) q^{77} +(36.0191 + 36.0849i) q^{78} +(5.14562 + 8.91247i) q^{79} +(-74.0220 + 30.3439i) q^{80} +(73.7367 + 33.5246i) q^{81} +(-65.8092 + 6.98645i) q^{82} +(-8.78320 + 32.7794i) q^{83} +(-55.4443 + 68.4867i) q^{84} +(134.810 - 31.2483i) q^{85} +(-118.337 + 45.5675i) q^{86} +(-7.56701 + 3.35130i) q^{87} +(-73.7199 + 82.3929i) q^{88} +100.456 q^{89} +(12.7031 - 89.0990i) q^{90} -62.3977i q^{91} +(-4.88345 + 97.0678i) q^{92} +(-3.99514 + 5.47624i) q^{93} +(68.2546 - 26.2824i) q^{94} +(-73.7498 + 118.256i) q^{95} +(-9.72228 + 95.5064i) q^{96} +(-7.80472 - 2.09127i) q^{97} +(9.78527 - 1.03883i) 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

Introduction

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