LMFDB - Embedded newform 72.3.j.a.29.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(5,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("72.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.j (of order $6$, degree $2$, 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:	$1.96185790339$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.13
Character	$\chi$	$=$	72.29
Dual form			72.3.j.a.5.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.310106 - 1.97581i) q^{2} +(2.97841 + 0.359265i) q^{3} +(-3.80767 - 1.22542i) q^{4} +(-0.661853 - 1.14636i) q^{5} +(1.63346 - 5.77337i) q^{6} +(4.89334 - 8.47551i) q^{7} +(-3.60199 + 7.14323i) q^{8} +(8.74186 + 2.14008i) q^{9} +O(q^{10})$	\(q+(0.310106 - 1.97581i) q^{2} +(2.97841 + 0.359265i) q^{3} +(-3.80767 - 1.22542i) q^{4} +(-0.661853 - 1.14636i) q^{5} +(1.63346 - 5.77337i) q^{6} +(4.89334 - 8.47551i) q^{7} +(-3.60199 + 7.14323i) q^{8} +(8.74186 + 2.14008i) q^{9} +(-2.47024 + 0.952203i) q^{10} +(-6.81639 + 11.8063i) q^{11} +(-10.9005 - 5.01778i) q^{12} +(-1.13377 + 0.654580i) q^{13} +(-15.2286 - 12.2966i) q^{14} +(-1.55942 - 3.65212i) q^{15} +(12.9967 + 9.33202i) q^{16} +0.636905i q^{17} +(6.93929 - 16.6086i) q^{18} +22.9776i q^{19} +(1.11534 + 5.17602i) q^{20} +(17.6193 - 23.4856i) q^{21} +(21.2133 + 17.1291i) q^{22} +(-22.3745 + 12.9179i) q^{23} +(-13.2945 + 19.9814i) q^{24} +(11.6239 - 20.1332i) q^{25} +(0.941739 + 2.44310i) q^{26} +(25.2680 + 9.51467i) q^{27} +(-29.0183 + 26.2755i) q^{28} +(-6.64367 + 11.5072i) q^{29} +(-7.69949 + 1.94858i) q^{30} +(18.7759 + 32.5209i) q^{31} +(22.4687 - 22.7851i) q^{32} +(-24.5436 + 32.7152i) q^{33} +(1.25841 + 0.197508i) q^{34} -12.9547 q^{35} +(-30.6636 - 18.8612i) q^{36} -51.3250i q^{37} +(45.3994 + 7.12549i) q^{38} +(-3.61198 + 1.54228i) q^{39} +(10.5727 - 0.598578i) q^{40} +(31.8097 - 18.3654i) q^{41} +(-40.9392 - 42.0955i) q^{42} +(-56.7067 - 32.7396i) q^{43} +(40.4223 - 36.6017i) q^{44} +(-3.33252 - 11.4378i) q^{45} +(18.5849 + 48.2138i) q^{46} +(-75.9815 - 43.8680i) q^{47} +(35.3568 + 32.4638i) q^{48} +(-23.3896 - 40.5119i) q^{49} +(-36.1748 - 29.2101i) q^{50} +(-0.228818 + 1.89697i) q^{51} +(5.11914 - 1.10308i) q^{52} -9.23648 q^{53} +(26.6350 - 46.9742i) q^{54} +18.0458 q^{55} +(42.9168 + 65.4830i) q^{56} +(-8.25503 + 68.4366i) q^{57} +(20.6758 + 16.6951i) q^{58} +(14.5822 + 25.2571i) q^{59} +(1.46237 + 15.8170i) q^{60} +(-7.53730 - 4.35166i) q^{61} +(70.0777 - 27.0128i) q^{62} +(60.9151 - 63.6196i) q^{63} +(-38.0513 - 51.4596i) q^{64} +(1.50077 + 0.866471i) q^{65} +(57.0280 + 58.6388i) q^{66} +(24.3260 - 14.0446i) q^{67} +(0.780479 - 2.42512i) q^{68} +(-71.2815 + 30.4366i) q^{69} +(-4.01733 + 25.5960i) q^{70} +83.8624i q^{71} +(-46.7751 + 54.7365i) q^{72} -88.8409 q^{73} +(-101.409 - 15.9162i) q^{74} +(41.8539 - 55.7888i) q^{75} +(28.1573 - 87.4910i) q^{76} +(66.7099 + 115.545i) q^{77} +(1.92717 + 7.61488i) q^{78} +(22.0026 - 38.1096i) q^{79} +(2.09599 - 21.0753i) q^{80} +(71.8401 + 37.4165i) q^{81} +(-26.4221 - 68.5453i) q^{82} +(64.9258 - 112.455i) q^{83} +(-95.8683 + 67.8341i) q^{84} +(0.730125 - 0.421538i) q^{85} +(-82.2725 + 101.889i) q^{86} +(-23.9217 + 31.8863i) q^{87} +(-59.7828 - 91.2174i) q^{88} -23.0693i q^{89} +(-23.6323 + 3.03751i) q^{90} +12.8123i q^{91} +(101.025 - 21.7690i) q^{92} +(44.2389 + 103.606i) q^{93} +(-110.237 + 136.522i) q^{94} +(26.3406 - 15.2078i) q^{95} +(75.1068 - 59.7911i) q^{96} +(1.36535 - 2.36485i) q^{97} +(-87.2972 + 33.6504i) q^{98} +(-84.8544 + 88.6218i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.310106	−	1.97581i	0.155053	−	0.987906i
$2$	0.310106	−	1.97581i	0.155053	−	0.987906i
$3$	2.97841	+	0.359265i	0.992803	+	0.119755i
$3$	2.97841	+	0.359265i	0.992803	+	0.119755i
$4$	−3.80767	−	1.22542i	−0.951917	−	0.306356i
$5$	−0.661853	−	1.14636i	−0.132371	−	0.229273i	0.792219	−	0.610236i	$-0.208926\pi$
$5$	−0.661853	−	1.14636i	−0.132371	−	0.229273i	−0.924590	+	0.380964i	$0.875592\pi$
$6$	1.63346	−	5.77337i	0.272244	−	0.962228i
$7$	4.89334	−	8.47551i	0.699049	−	1.21079i	−0.269748	−	0.962931i	$-0.586940\pi$
$7$	4.89334	−	8.47551i	0.699049	−	1.21079i	0.968797	−	0.247857i	$-0.0797263\pi$
$8$	−3.60199	+	7.14323i	−0.450249	+	0.892903i
$9$	8.74186	+	2.14008i	0.971318	+	0.237786i
$10$	−2.47024	+	0.952203i	−0.247024	+	0.0952203i
$11$	−6.81639	+	11.8063i	−0.619672	+	1.07330i	0.369873	+	0.929082i	$0.379401\pi$
$11$	−6.81639	+	11.8063i	−0.619672	+	1.07330i	−0.989545	+	0.144222i	$0.953932\pi$
$12$	−10.9005	−	5.01778i	−0.908379	−	0.418148i
$13$	−1.13377	+	0.654580i	−0.0872127	+	0.0503523i	−0.542972	−	0.839751i	$-0.682701\pi$
$13$	−1.13377	+	0.654580i	−0.0872127	+	0.0503523i	0.455759	+	0.890103i	$0.349368\pi$
$14$	−15.2286	−	12.2966i	−1.08776	−	0.878331i
$15$	−1.55942	−	3.65212i	−0.103961	−	0.243475i
$16$	12.9967	+	9.33202i	0.812292	+	0.583251i
$17$			0.636905i			0.0374650i	0.999825	+	0.0187325i	$0.00596309\pi$
$17$			0.636905i			0.0374650i	−0.999825	+	0.0187325i	$0.994037\pi$
$18$	6.93929	−	16.6086i	0.385516	−	0.922701i
$19$			22.9776i			1.20935i	0.796474	+	0.604673i	$0.206696\pi$
$19$			22.9776i			1.20935i	−0.796474	+	0.604673i	$0.793304\pi$
$20$	1.11534	+	5.17602i	0.0557668	+	0.258801i
$21$	17.6193	−	23.4856i	0.839016	−	1.11836i
$22$	21.2133	+	17.1291i	0.964241	+	0.778597i
$23$	−22.3745	+	12.9179i	−0.972806	+	0.561650i	−0.900090	−	0.435703i	$-0.856500\pi$
$23$	−22.3745	+	12.9179i	−0.972806	+	0.561650i	−0.0727153	+	0.997353i	$0.523166\pi$
$24$	−13.2945	+	19.9814i	−0.553938	+	0.832558i
$25$	11.6239	−	20.1332i	0.464956	−	0.805327i
$26$	0.941739	+	2.44310i	0.0362207	+	0.0939652i
$27$	25.2680	+	9.51467i	0.935851	+	0.352395i
$28$	−29.0183	+	26.2755i	−1.03637	+	0.938412i
$29$	−6.64367	+	11.5072i	−0.229092	+	0.396799i	−0.957539	−	0.288303i	$-0.906909\pi$
$29$	−6.64367	+	11.5072i	−0.229092	+	0.396799i	0.728447	+	0.685102i	$0.240242\pi$
$30$	−7.69949	+	1.94858i	−0.256650	+	0.0649527i
$31$	18.7759	+	32.5209i	0.605676	+	1.04906i	0.991944	+	0.126675i	$0.0404304\pi$
$31$	18.7759	+	32.5209i	0.605676	+	1.04906i	−0.386269	+	0.922386i	$0.626236\pi$
$32$	22.4687	−	22.7851i	0.702146	−	0.712033i
$33$	−24.5436	+	32.7152i	−0.743746	+	0.991371i
$34$	1.25841	+	0.197508i	0.0370119	+	0.00580907i
$35$	−12.9547			−0.370134
$36$	−30.6636	−	18.8612i	−0.851766	−	0.523922i
$37$		−	51.3250i		−	1.38716i	−0.720378	−	0.693582i	$-0.756032\pi$
$37$		−	51.3250i		−	1.38716i	0.720378	−	0.693582i	$-0.243968\pi$
$38$	45.3994	+	7.12549i	1.19472	+	0.187513i
$39$	−3.61198	+	1.54228i	−0.0926150	+	0.0395458i
$40$	10.5727	−	0.598578i	0.264318	−	0.0149644i
$41$	31.8097	−	18.3654i	0.775848	−	0.447936i	−0.0591091	−	0.998252i	$-0.518826\pi$
$41$	31.8097	−	18.3654i	0.775848	−	0.447936i	0.834957	+	0.550316i	$0.185493\pi$
$42$	−40.9392	−	42.0955i	−0.974742	−	1.00227i
$43$	−56.7067	−	32.7396i	−1.31876	−	0.761387i	−0.335231	−	0.942136i	$-0.608814\pi$
$43$	−56.7067	−	32.7396i	−1.31876	−	0.761387i	−0.983529	+	0.180749i	$0.942148\pi$
$44$	40.4223	−	36.6017i	0.918690	−	0.831856i
$45$	−3.33252	−	11.4378i	−0.0740560	−	0.254172i
$46$	18.5849	+	48.2138i	0.404021	+	1.04813i
$47$	−75.9815	−	43.8680i	−1.61663	−	0.933361i	−0.987784	−	0.155830i	$-0.950195\pi$
$47$	−75.9815	−	43.8680i	−1.61663	−	0.933361i	−0.628845	−	0.777531i	$-0.716472\pi$
$48$	35.3568	+	32.4638i	0.736599	+	0.676330i
$49$	−23.3896	−	40.5119i	−0.477338	−	0.826774i
$50$	−36.1748	−	29.2101i	−0.723495	−	0.584201i
$51$	−0.228818	+	1.89697i	−0.00448662	+	0.0371954i
$52$	5.11914	−	1.10308i	0.0984450	−	0.0212131i
$53$	−9.23648			−0.174273			−0.0871366	−	0.996196i	$-0.527772\pi$
$53$	−9.23648			−0.174273			−0.0871366	+	0.996196i	$0.527772\pi$
$54$	26.6350	−	46.9742i	0.493240	−	0.869893i
$55$	18.0458			0.328106
$56$	42.9168	+	65.4830i	0.766371	+	1.16934i
$57$	−8.25503	+	68.4366i	−0.144825	+	1.20064i
$58$	20.6758	+	16.6951i	0.356479	+	0.287846i
$59$	14.5822	+	25.2571i	0.247156	+	0.428087i	0.962736	−	0.270444i	$-0.0871706\pi$
$59$	14.5822	+	25.2571i	0.247156	+	0.428087i	−0.715579	+	0.698531i	$0.753837\pi$
$60$	1.46237	+	15.8170i	0.0243728	+	0.263617i
$61$	−7.53730	−	4.35166i	−0.123562	−	0.0713387i	0.436945	−	0.899488i	$-0.356060\pi$
$61$	−7.53730	−	4.35166i	−0.123562	−	0.0713387i	−0.560507	+	0.828150i	$0.689394\pi$
$62$	70.0777	−	27.0128i	1.13029	−	0.435690i
$63$	60.9151	−	63.6196i	0.966907	−	1.00984i
$64$	−38.0513	−	51.4596i	−0.594552	−	0.804057i
$65$	1.50077	+	0.866471i	0.0230888	+	0.0133303i
$66$	57.0280	+	58.6388i	0.864061	+	0.888467i
$67$	24.3260	−	14.0446i	0.363075	−	0.209621i	−0.307354	−	0.951595i	$-0.599443\pi$
$67$	24.3260	−	14.0446i	0.363075	−	0.209621i	0.670429	+	0.741974i	$0.266110\pi$
$68$	0.780479	−	2.42512i	0.0114776	−	0.0356636i
$69$	−71.2815	+	30.4366i	−1.03307	+	0.441109i
$70$	−4.01733	+	25.5960i	−0.0573905	+	0.365658i
$71$			83.8624i			1.18116i	0.806979	+	0.590580i	$0.201101\pi$
$71$			83.8624i			1.18116i	−0.806979	+	0.590580i	$0.798899\pi$
$72$	−46.7751	+	54.7365i	−0.649655	+	0.760230i
$73$	−88.8409			−1.21700			−0.608500	−	0.793554i	$-0.708228\pi$
$73$	−88.8409			−1.21700			−0.608500	+	0.793554i	$0.708228\pi$
$74$	−101.409	−	15.9162i	−1.37039	−	0.215084i
$75$	41.8539	−	55.7888i	0.558052	−	0.743851i
$76$	28.1573	−	87.4910i	0.370490	−	1.15120i
$77$	66.7099	+	115.545i	0.866362	+	1.50058i
$78$	1.92717	+	7.61488i	0.0247072	+	0.0976266i
$79$	22.0026	−	38.1096i	0.278514	−	0.482401i	−0.692502	−	0.721416i	$-0.743491\pi$
$79$	22.0026	−	38.1096i	0.278514	−	0.482401i	0.971016	+	0.239016i	$0.0768248\pi$
$80$	2.09599	−	21.0753i	0.0261999	−	0.263442i
$81$	71.8401	+	37.4165i	0.886915	+	0.461932i
$82$	−26.4221	−	68.5453i	−0.322221	−	0.835918i
$83$	64.9258	−	112.455i	0.782239	−	1.35488i	−0.148396	−	0.988928i	$-0.547411\pi$
$83$	64.9258	−	112.455i	0.782239	−	1.35488i	0.930635	−	0.365950i	$-0.119256\pi$
$84$	−95.8683	+	67.8341i	−1.14129	+	0.807548i
$85$	0.730125	−	0.421538i	0.00858970	−	0.00495927i
$86$	−82.2725	+	101.889i	−0.956657	+	1.18476i
$87$	−23.9217	+	31.8863i	−0.274962	+	0.366509i
$88$	−59.7828	−	91.2174i	−0.679350	−	1.03656i
$89$		−	23.0693i		−	0.259206i	−0.991566	−	0.129603i	$-0.958630\pi$
$89$		−	23.0693i		−	0.259206i	0.991566	−	0.129603i	$-0.0413703\pi$
$90$	−23.6323	+	3.03751i	−0.262581	+	0.0337501i
$91$			12.8123i			0.140795i
$92$	101.025	−	21.7690i	1.09810	−	0.236619i
$93$	44.2389	+	103.606i	0.475687	+	1.11404i
$94$	−110.237	+	136.522i	−1.17274	+	1.45236i
$95$	26.3406	−	15.2078i	0.277270	−	0.160082i
$96$	75.1068	−	59.7911i	0.782362	−	0.622824i
$97$	1.36535	−	2.36485i	0.0140757	−	0.0243799i	−0.858902	−	0.512140i	$-0.828853\pi$
$97$	1.36535	−	2.36485i	0.0140757	−	0.0243799i	0.872977	+	0.487761i	$0.162186\pi$
$98$	−87.2972	+	33.6504i	−0.890788	+	0.343371i
$99$	−84.8544	+	88.6218i	−0.857115	+	0.895169i
$100$	−68.9316	+	62.4163i	−0.689316	+	0.624163i
$101$	15.9442	−	27.6161i	0.157863	−	0.273427i	−0.776235	−	0.630444i	$-0.782873\pi$
$101$	15.9442	−	27.6161i	0.157863	−	0.273427i	0.934098	+	0.357017i	$0.116206\pi$
$102$	3.67709	+	1.04036i	0.0360499	+	0.0101996i
$103$	83.6736	+	144.927i	0.812365	+	1.40706i	0.911205	+	0.411954i	$0.135153\pi$
$103$	83.6736	+	144.927i	0.812365	+	1.40706i	−0.0988399	+	0.995103i	$0.531513\pi$
$104$	−0.591999	−	10.4565i	−0.00569230	−	0.100544i
$105$	−38.5844	−	4.65417i	−0.367470	−	0.0443254i
$106$	−2.86429	+	18.2495i	−0.0270216	+	0.172166i
$107$	−80.7131			−0.754328			−0.377164	−	0.926146i	$-0.623101\pi$
$107$	−80.7131			−0.754328			−0.377164	+	0.926146i	$0.623101\pi$
$108$	−84.5526	−	67.1927i	−0.782894	−	0.622155i
$109$			71.8978i			0.659613i	0.944049	+	0.329806i	$0.106983\pi$
$109$			71.8978i			0.659613i	−0.944049	+	0.329806i	$0.893017\pi$
$110$	5.59612	−	35.6551i	0.0508738	−	0.324138i
$111$	18.4393	−	152.867i	0.166120	−	1.37718i
$112$	142.691	−	64.4888i	1.27402	−	0.575793i
$113$	154.170	−	89.0103i	1.36434	−	0.787702i	0.374141	−	0.927372i	$-0.377938\pi$
$113$	154.170	−	89.0103i	1.36434	−	0.787702i	0.990198	+	0.139670i	$0.0446043\pi$
$114$	132.658	+	37.5330i	1.16367	+	0.329237i
$115$	29.6173	+	17.0996i	0.257542	+	0.148692i
$116$	39.3981	−	35.6742i	0.339638	−	0.307536i
$117$	−11.3121	+	3.29590i	−0.0966843	+	0.0281701i
$118$	54.4254	−	20.9793i	0.461232	−	0.177791i
$119$	5.39810	+	3.11659i	0.0453622	+	0.0261899i
$120$	31.7049	+	2.01560i	0.264208	+	0.0167966i
$121$	−32.4265	−	56.1643i	−0.267987	−	0.464168i
$122$	−10.9354	+	13.5428i	−0.0896346	+	0.111007i
$123$	101.341	−	43.2715i	0.823907	−	0.351801i
$124$	−31.6407	−	146.837i	−0.255167	−	1.18417i
$125$	−63.8659			−0.510927
$126$	−106.810	−	140.086i	−0.847700	−	1.11179i
$127$	26.3523			0.207498			0.103749	−	0.994604i	$-0.466916\pi$
$127$	26.3523			0.207498			0.103749	+	0.994604i	$0.466916\pi$
$128$	−113.475	+	59.2243i	−0.886520	+	0.462690i
$129$	−157.134	−	117.885i	−1.21809	−	0.913835i
$130$	2.17738	−	2.69655i	0.0167491	−	0.0207427i
$131$	−41.9643	−	72.6843i	−0.320338	−	0.554842i	0.660219	−	0.751073i	$-0.270463\pi$
$131$	−41.9643	−	72.6843i	−0.320338	−	0.554842i	−0.980558	+	0.196230i	$0.937130\pi$
$132$	133.544	−	94.4924i	1.01170	−	0.715852i
$133$	194.747	+	112.437i	1.46426	+	0.845392i
$134$	−20.2059	−	52.4190i	−0.150790	−	0.391187i
$135$	−5.81643	−	35.2636i	−0.0430847	−	0.261212i
$136$	−4.54956	−	2.29413i	−0.0334526	−	0.0168686i
$137$	63.7998	+	36.8348i	0.465692	+	0.268867i	0.714435	−	0.699702i	$-0.246684\pi$
$137$	63.7998	+	36.8348i	0.465692	+	0.268867i	−0.248743	+	0.968570i	$0.580017\pi$
$138$	38.0321	+	150.277i	0.275595	+	1.08897i
$139$	16.1347	−	9.31538i	0.116077	−	0.0670171i	−0.440837	−	0.897587i	$-0.645318\pi$
$139$	16.1347	−	9.31538i	0.116077	−	0.0670171i	0.556914	+	0.830570i	$0.311985\pi$
$140$	49.3272	+	15.8750i	0.352337	+	0.113393i
$141$	−210.544	−	157.954i	−1.49322	−	1.12024i
$142$	165.696	+	26.0063i	1.16688	+	0.183143i
$143$		−	17.8475i		−	0.124808i
$144$	93.6438	+	109.393i	0.650304	+	0.759674i
$145$	17.5885			0.121300
$146$	−27.5501	+	175.533i	−0.188700	+	1.20228i
$147$	−55.1092	−	129.064i	−0.374893	−	0.877988i
$148$	−62.8949	+	195.429i	−0.424966	+	1.32046i
$149$	−63.9386	−	110.745i	−0.429118	−	0.743255i	0.567677	−	0.823252i	$-0.307842\pi$
$149$	−63.9386	−	110.745i	−0.429118	−	0.743255i	−0.996795	+	0.0799967i	$0.974509\pi$
$150$	−97.2491	−	99.9959i	−0.648327	−	0.666639i
$151$	−93.6833	+	162.264i	−0.620419	+	1.07460i	0.368989	+	0.929434i	$0.379704\pi$
$151$	−93.6833	+	162.264i	−0.620419	+	1.07460i	−0.989408	+	0.145163i	$0.953629\pi$
$152$	−164.134	−	82.7650i	−1.07983	−	0.544506i
$153$	−1.36303	+	5.56774i	−0.00890867	+	0.0363904i
$154$	248.982	−	95.9750i	1.61677	−	0.623214i
$155$	24.8538	−	43.0481i	0.160347	−	0.277730i
$156$	15.6432	−	1.44630i	0.100277	−	0.00927112i
$157$	−67.9800	+	39.2483i	−0.432994	+	0.249989i	−0.700621	−	0.713533i	$-0.747094\pi$
$157$	−67.9800	+	39.2483i	−0.432994	+	0.249989i	0.267627	+	0.963522i	$0.413760\pi$
$158$	−68.4744	−	55.2911i	−0.433382	−	0.349944i
$159$	−27.5100	−	3.31834i	−0.173019	−	0.0208701i
$160$	−40.9909	−	10.6769i	−0.256193	−	0.0667305i
$161$			252.848i			1.57048i
$162$	96.2060	−	130.340i	0.593864	−	0.804565i
$163$			222.413i			1.36450i	0.731121	+	0.682248i	$0.238998\pi$
$163$			222.413i			1.36450i	−0.731121	+	0.682248i	$0.761002\pi$
$164$	−143.626	+	30.9488i	−0.875770	+	0.188712i
$165$	53.7478	+	6.48323i	0.325744	+	0.0392923i
$166$	−202.056	−	163.154i	−1.21720	−	0.982857i
$167$	−52.5078	+	30.3154i	−0.314418	+	0.181529i	−0.648902	−	0.760872i	$-0.724771\pi$
$167$	−52.5078	+	30.3154i	−0.314418	+	0.181529i	0.334484	+	0.942401i	$0.391438\pi$
$168$	104.298	+	210.454i	0.620821	+	1.25270i
$169$	−83.6431	+	144.874i	−0.494929	+	0.857243i
$170$	−0.606463	−	1.57331i	−0.00356743	−	0.00925477i
$171$	−49.1738	+	200.867i	−0.287566	+	1.17466i
$172$	175.800	+	194.151i	1.02210	+	1.12879i
$173$	97.9378	−	169.633i	0.566115	−	0.980539i	−0.430831	−	0.902433i	$-0.641779\pi$
$173$	97.9378	−	169.633i	0.566115	−	0.980539i	0.996945	−	0.0781062i	$-0.0248873\pi$
$174$	55.5830	+	57.1529i	0.319442	+	0.328465i
$175$	−113.759	−	197.037i	−0.650054	−	1.12593i
$176$	−198.767	+	89.8325i	−1.12936	+	0.510412i
$177$	34.3578	+	80.4650i	0.194112	+	0.454605i
$178$	−45.5807	−	7.15395i	−0.256071	−	0.0401907i
$179$	14.6878			0.0820548			0.0410274	−	0.999158i	$-0.486937\pi$
$179$	14.6878			0.0820548			0.0410274	+	0.999158i	$0.486937\pi$
$180$	−1.32697	+	47.6350i	−0.00737207	+	0.264639i
$181$		−	239.158i		−	1.32132i	−0.750687	−	0.660658i	$-0.770277\pi$
$181$		−	239.158i		−	1.32132i	0.750687	−	0.660658i	$-0.229723\pi$
$182$	25.3147	+	3.97318i	0.139092	+	0.0218307i
$183$	−20.8858	−	15.6689i	−0.114130	−	0.0856225i
$184$	−11.6829	−	206.357i	−0.0634942	−	1.12150i
$185$	−58.8372	+	33.9696i	−0.318039	+	0.183620i
$186$	218.425	−	55.2788i	1.17433	−	0.297198i
$187$	−7.51952	−	4.34140i	−0.0402113	−	0.0232160i
$188$	235.556	+	260.144i	1.25296	+	1.38375i
$189$	204.287	−	167.601i	1.08088	−	0.886776i
$190$	−21.8793	−	56.7602i	−0.115154	−	0.298738i
$191$	43.1603	+	24.9186i	0.225970	+	0.130464i	0.608712	−	0.793391i	$-0.291687\pi$
$191$	43.1603	+	24.9186i	0.225970	+	0.130464i	−0.382741	+	0.923856i	$0.625020\pi$
$192$	−94.8449	−	166.938i	−0.493984	−	0.869471i
$193$	9.06578	+	15.7024i	0.0469730	+	0.0813596i	0.888556	−	0.458768i	$-0.151709\pi$
$193$	9.06578	+	15.7024i	0.0469730	+	0.0813596i	−0.841583	+	0.540128i	$0.818376\pi$
$194$	−4.24910	−	3.43103i	−0.0219026	−	0.0176857i
$195$	4.15862	+	3.11988i	0.0213263	+	0.0159994i
$196$	39.4154	+	182.918i	0.201099	+	0.933256i
$197$	−87.1848			−0.442563			−0.221281	−	0.975210i	$-0.571024\pi$
$197$	−87.1848			−0.442563			−0.221281	+	0.975210i	$0.571024\pi$
$198$	148.786	+	195.139i	0.751445	+	0.985548i
$199$	−168.666			−0.847569			−0.423784	−	0.905763i	$-0.639299\pi$
$199$	−168.666			−0.847569			−0.423784	+	0.905763i	$0.639299\pi$
$200$	101.947	+	155.552i	0.509734	+	0.777758i
$201$	77.4986	−	33.0912i	0.385565	−	0.164633i
$202$	−49.6199	−	40.0666i	−0.245643	−	0.198350i
$203$	65.0195	+	112.617i	0.320293	+	0.554764i
$204$	3.19585	−	6.94262i	0.0156659	−	0.0340324i
$205$	−42.1068	−	24.3104i	−0.205399	−	0.118587i
$206$	312.296	−	120.381i	1.51600	−	0.584371i
$207$	−223.240	+	65.0436i	−1.07846	+	0.314220i
$208$	−20.8437	−	2.07296i	−0.100210	−	0.00996614i
$209$	−271.281	−	156.624i	−1.29800	−	0.749398i
$210$	−21.1610	+	74.7922i	−0.100767	+	0.356153i
$211$	171.873	−	99.2311i	0.814566	−	0.470290i	−0.0339732	−	0.999423i	$-0.510816\pi$
$211$	171.873	−	99.2311i	0.814566	−	0.470290i	0.848539	+	0.529133i	$0.177483\pi$
$212$	35.1694	+	11.3186i	0.165894	+	0.0533896i
$213$	−30.1288	+	249.777i	−0.141450	+	1.17266i
$214$	−25.0296	+	159.474i	−0.116961	+	0.745205i
$215$			86.6753i			0.403141i
$216$	−158.980	+	146.223i	−0.736021	+	0.676959i
$217$	367.508			1.69359
$218$	142.056	+	22.2960i	0.651635	+	0.102275i
$219$	−264.605	−	31.9174i	−1.20824	−	0.145742i
$220$	−68.7125	−	22.1138i	−0.312329	−	0.100517i
$221$	−0.416905	−	0.722101i	−0.00188645	−	0.00326743i
$222$	−296.318	−	83.8376i	−1.33477	−	0.377647i
$223$	143.049	−	247.768i	0.641476	−	1.11107i	−0.343628	−	0.939106i	$-0.611656\pi$
$223$	143.049	−	247.768i	0.641476	−	1.11107i	0.985104	−	0.171962i	$-0.0550108\pi$
$224$	−83.1684	−	301.929i	−0.371287	−	1.34790i
$225$	144.701	−	151.125i	0.643116	−	0.671668i
$226$	−128.058	−	332.214i	−0.566630	−	1.46997i
$227$	−147.283	+	255.102i	−0.648824	+	1.12380i	0.334580	+	0.942367i	$0.391405\pi$
$227$	−147.283	+	255.102i	−0.648824	+	1.12380i	−0.983404	+	0.181428i	$0.941928\pi$
$228$	115.296	−	250.468i	0.505686	−	1.09854i
$229$	−194.465	+	112.274i	−0.849190	+	0.490280i	−0.860378	−	0.509657i	$-0.829772\pi$
$229$	−194.465	+	112.274i	−0.849190	+	0.490280i	0.0111873	+	0.999937i	$0.496439\pi$
$230$	42.9700	−	53.2156i	0.186826	−	0.231372i
$231$	157.178	+	368.107i	0.680425	+	1.59354i
$232$	−58.2679	−	88.9060i	−0.251155	−	0.383215i
$233$		−	231.203i		−	0.992286i	−0.868241	−	0.496143i	$-0.834749\pi$
$233$		−	231.203i		−	0.992286i	0.868241	−	0.496143i	$-0.165251\pi$
$234$	3.00413	+	23.3726i	0.0128382	+	0.0998829i
$235$			116.137i			0.494198i
$236$	−24.5735	−	114.040i	−0.104125	−	0.483221i
$237$	79.2243	−	105.601i	0.334280	−	0.445576i
$238$	7.83179	−	9.69916i	0.0329067	−	0.0407528i
$239$	349.585	−	201.833i	1.46270	−	0.844489i	0.463562	−	0.886065i	$-0.346571\pi$
$239$	349.585	−	201.833i	1.46270	−	0.844489i	0.999135	+	0.0415760i	$0.0132379\pi$
$240$	13.8143	−	62.0180i	0.0575598	−	0.258408i
$241$	−75.5610	+	130.876i	−0.313531	+	0.543052i	−0.979124	−	0.203263i	$-0.934845\pi$
$241$	−75.5610	+	130.876i	−0.313531	+	0.543052i	0.665593	+	0.746315i	$0.268179\pi$
$242$	−121.026	+	46.6517i	−0.500107	+	0.192776i
$243$	200.527	+	137.251i	0.825214	+	0.564820i
$244$	23.3669	+	25.8061i	0.0957660	+	0.105763i
$245$	−30.9609	+	53.6259i	−0.126371	+	0.218881i
$246$	−54.0700	−	213.649i	−0.219797	−	0.868490i
$247$	−15.0406	−	26.0512i	−0.0608933	−	0.105470i
$248$	−299.935	+	16.9809i	−1.20941	+	0.0684713i
$249$	233.777	−	311.611i	0.938863	−	1.25145i
$250$	−19.8052	+	126.187i	−0.0792209	+	0.504748i
$251$	143.980			0.573624			0.286812	−	0.957987i	$-0.407404\pi$
$251$	143.980			0.573624			0.286812	+	0.957987i	$0.407404\pi$
$252$	−309.906	+	167.596i	−1.22978	+	0.665062i
$253$		−	352.215i		−	1.39215i
$254$	8.17200	−	52.0671i	0.0321732	−	0.204989i
$255$	2.32606	−	0.993204i	0.00912179	−	0.00389492i
$256$	81.8270	+	242.570i	0.319637	+	0.947540i
$257$	−126.401	+	72.9779i	−0.491834	+	0.283961i	−0.725335	−	0.688396i	$-0.758315\pi$
$257$	−126.401	+	72.9779i	−0.491834	+	0.283961i	0.233501	+	0.972357i	$0.424982\pi$
$258$	−281.646	+	273.910i	−1.09165	+	1.06167i
$259$	−435.006	−	251.151i	−1.67956	−	0.969695i
$260$	−4.65265	−	5.13832i	−0.0178948	−	0.0197628i
$261$	−82.7043	+	86.3761i	−0.316875	+	0.330943i
$262$	−156.624	+	60.3737i	−0.597802	+	0.230434i
$263$	53.2587	+	30.7489i	0.202505	+	0.116916i	0.597823	−	0.801628i	$-0.296032\pi$
$263$	53.2587	+	30.7489i	0.202505	+	0.116916i	−0.395319	+	0.918544i	$0.629366\pi$
$264$	−145.286	−	293.161i	−0.550328	−	1.11046i
$265$	6.11319	+	10.5884i	0.0230687	+	0.0399561i
$266$	282.547	−	349.916i	1.06221	−	1.31547i
$267$	8.28800	−	68.7099i	0.0310412	−	0.257341i
$268$	−109.836	+	23.6676i	−0.409836	+	0.0883120i
$269$	413.485			1.53712			0.768560	−	0.639778i	$-0.220974\pi$
$269$	413.485			1.53712			0.768560	+	0.639778i	$0.220974\pi$
$270$	−71.4780	+	0.556704i	−0.264733	+	0.00206187i
$271$	−122.547			−0.452203			−0.226101	−	0.974104i	$-0.572598\pi$
$271$	−122.547			−0.452203			−0.226101	+	0.974104i	$0.572598\pi$
$272$	−5.94361	+	8.27765i	−0.0218515	+	0.0304325i
$273$	−4.60302	+	38.1604i	−0.0168609	+	0.139782i
$274$	92.5634	−	114.634i	0.337823	−	0.418371i
$275$	158.466	+	274.472i	0.576241	+	0.998078i
$276$	308.714	−	28.5422i	1.11853	−	0.103414i
$277$	342.883	+	197.964i	1.23785	+	0.714671i	0.968653	−	0.248416i	$-0.0799100\pi$
$277$	342.883	+	197.964i	1.23785	+	0.714671i	0.269192	+	0.963086i	$0.413243\pi$
$278$	−13.4020	−	34.7679i	−0.0482085	−	0.125064i
$279$	94.5394	+	324.475i	0.338851	+	1.16299i
$280$	46.6627	−	92.5383i	0.166652	−	0.330494i
$281$	100.988	+	58.3057i	0.359389	+	0.207494i	0.668813	−	0.743431i	$-0.266803\pi$
$281$	100.988	+	58.3057i	0.359389	+	0.207494i	−0.309424	+	0.950924i	$0.600136\pi$
$282$	−377.379	+	367.013i	−1.33822	+	1.30146i
$283$	244.975	−	141.437i	0.865637	−	0.499776i	−0.000258855	−	1.00000i	$-0.500082\pi$
$283$	244.975	−	141.437i	0.865637	−	0.499776i	0.865896	+	0.500224i	$0.166749\pi$
$284$	102.767	−	319.320i	0.361855	−	1.12437i
$285$	83.9169	−	35.8317i	0.294445	−	0.125725i
$286$	−35.2633	−	5.53462i	−0.123298	−	0.0193518i
$287$		−	359.472i		−	1.25252i
$288$	245.180	−	151.099i	0.851318	−	0.524650i
$289$	288.594			0.998596
$290$	5.45432	−	34.7517i	0.0188080	−	0.119833i
$291$	4.91617	−	6.55298i	0.0168941	−	0.0225188i
$292$	338.277	+	108.868i	1.15848	+	0.372835i
$293$	−22.4604	−	38.9026i	−0.0766567	−	0.132773i	0.825149	−	0.564915i	$-0.191091\pi$
$293$	−22.4604	−	38.9026i	−0.0766567	−	0.132773i	−0.901805	+	0.432142i	$0.857758\pi$
$294$	−272.096	+	68.8619i	−0.925498	+	0.234224i
$295$	19.3026	−	33.4330i	0.0654325	−	0.113332i
$296$	366.626	+	184.872i	1.23860	+	0.624569i
$297$	−284.570	+	233.467i	−0.958148	+	0.786083i
$298$	−238.639	+	91.9880i	−0.800802	+	0.308685i
$299$	16.9116	−	29.2918i	0.0565607	−	0.0979660i
$300$	−227.731	+	161.137i	−0.759102	+	0.537122i
$301$	−554.970	+	320.412i	−1.84376	+	1.06449i
$302$	291.552	+	235.420i	0.965403	+	0.779535i
$303$	57.4098	−	76.5240i	0.189471	−	0.252554i
$304$	−214.427	+	298.632i	−0.705352	+	0.982342i
$305$			11.5206i			0.0377726i
$306$	10.5781	+	4.41967i	0.0345690	+	0.0144434i
$307$		−	349.592i		−	1.13874i	−0.822082	−	0.569369i	$-0.807188\pi$
$307$		−	349.592i		−	1.13874i	0.822082	−	0.569369i	$-0.192812\pi$
$308$	−112.418	−	521.705i	−0.364992	−	1.69385i
$309$	197.147	+	461.713i	0.638017	+	1.49422i
$310$	−77.3476	−	62.4560i	−0.249509	−	0.201471i
$311$	−73.5749	+	42.4785i	−0.236575	+	0.136587i	−0.613602	−	0.789616i	$-0.710280\pi$
$311$	−73.5749	+	42.4785i	−0.236575	+	0.136587i	0.377026	+	0.926203i	$0.376947\pi$
$312$	1.99345	−	31.3565i	0.00638925	−	0.100502i
$313$	49.0959	−	85.0365i	0.156856	−	0.271682i	−0.776877	−	0.629652i	$-0.783198\pi$
$313$	49.0959	−	85.0365i	0.156856	−	0.271682i	0.933733	+	0.357970i	$0.116531\pi$
$314$	56.4662	+	146.487i	0.179829	+	0.466519i
$315$	−113.248	−	27.7240i	−0.359518	−	0.0880128i
$316$	−130.479	+	118.146i	−0.412909	+	0.373881i
$317$	−282.757	+	489.750i	−0.891979	+	1.54495i	−0.0544784	+	0.998515i	$0.517350\pi$
$317$	−282.757	+	489.750i	−0.891979	+	1.54495i	−0.837500	+	0.546437i	$0.815984\pi$
$318$	−15.0875	+	53.3256i	−0.0474448	+	0.167691i
$319$	−90.5718	−	156.875i	−0.283924	−	0.491771i
$320$	−33.8071	+	77.6794i	−0.105647	+	0.242748i
$321$	−240.397	−	28.9974i	−0.748900	−	0.0903345i
$322$	499.579	+	78.4096i	1.55149	+	0.243508i
$323$	−14.6345			−0.0453082
$324$	−227.692	−	230.504i	−0.702754	−	0.711433i
$325$			30.4351i			0.0936464i
$326$	439.446	+	68.9717i	1.34799	+	0.211570i
$327$	−25.8303	+	214.141i	−0.0789919	+	0.654866i
$328$	16.6096	+	293.376i	0.0506389	+	0.894439i
$329$	−743.607	+	429.322i	−2.26020	+	1.30493i
$330$	29.4772	−	104.185i	0.0893248	−	0.315713i
$331$	−14.1913	−	8.19333i	−0.0428739	−	0.0247533i	0.478410	−	0.878137i	$-0.341213\pi$
$331$	−14.1913	−	8.19333i	−0.0428739	−	0.0247533i	−0.521284	+	0.853383i	$0.674547\pi$
$332$	−385.021	+	348.629i	−1.15970	+	1.05009i
$333$	109.840	−	448.676i	0.329848	−	1.34738i
$334$	43.6145	+	113.147i	0.130582	+	0.338762i
$335$	−32.2005	−	18.5910i	−0.0961210	−	0.0554955i
$336$	448.160	−	140.810i	1.33381	−	0.419078i
$337$	53.6341	+	92.8971i	0.159152	+	0.275659i	0.934563	−	0.355798i	$-0.115791\pi$
$337$	53.6341	+	92.8971i	0.159152	+	0.275659i	−0.775411	+	0.631457i	$0.782457\pi$
$338$	260.306	+	210.189i	0.770135	+	0.621862i
$339$	491.161	−	209.721i	1.44885	−	0.618646i
$340$	−3.29664	+	0.710364i	−0.00969599	+	0.00208930i
$341$	−511.937			−1.50128
$342$	381.626	+	159.448i	1.11586	+	0.466223i
$343$	21.7349			0.0633670
$344$	438.123	−	287.141i	1.27361	−	0.834712i
$345$	82.0692	+	61.5700i	0.237882	+	0.178464i
$346$	−304.792	−	246.111i	−0.880903	−	0.711304i
$347$	−272.055	−	471.212i	−0.784019	−	1.35796i	−0.929583	−	0.368612i	$-0.879833\pi$
$347$	−272.055	−	471.212i	−0.784019	−	1.35796i	0.145564	−	0.989349i	$-0.453500\pi$
$348$	130.160	−	92.0980i	0.374023	−	0.264650i
$349$	−280.435	−	161.909i	−0.803540	−	0.463924i	0.0411675	−	0.999152i	$-0.486892\pi$
$349$	−280.435	−	161.909i	−0.803540	−	0.463924i	−0.844707	+	0.535228i	$0.820226\pi$
$350$	−424.586	+	163.665i	−1.21310	+	0.467614i
$351$	−34.8761	+	5.75251i	−0.0993620	+	0.0163889i
$352$	115.853	+	420.585i	0.329128	+	1.19484i
$353$	−138.561	−	79.9981i	−0.392524	−	0.226624i	0.290729	−	0.956805i	$-0.406102\pi$
$353$	−138.561	−	79.9981i	−0.392524	−	0.226624i	−0.683253	+	0.730182i	$0.739435\pi$
$354$	169.638	−	42.9319i	0.479204	−	0.121277i
$355$	96.1367	−	55.5046i	0.270808	−	0.156351i
$356$	−28.2697	+	87.8404i	−0.0794093	+	0.246743i
$357$	14.9581	+	11.2218i	0.0418994	+	0.0314337i
$358$	4.55478	−	29.0204i	0.0127229	−	0.0810625i
$359$		−	7.98509i		−	0.0222426i	−0.999938	−	0.0111213i	$-0.996460\pi$
$359$		−	7.98509i		−	0.0222426i	0.999938	−	0.0111213i	$-0.00354009\pi$
$360$	93.7062	+	17.3937i	0.260295	+	0.0483160i
$361$	−166.969			−0.462517
$362$	−472.532	−	74.1645i	−1.30534	−	0.204874i
$363$	−76.4015	−	178.930i	−0.210472	−	0.492920i
$364$	15.7005	−	48.7851i	0.0431333	−	0.134025i
$365$	58.7997	+	101.844i	0.161095	+	0.279025i
$366$	−37.4356	+	36.4073i	−0.102283	+	0.0994735i
$367$	103.503	−	179.272i	0.282024	−	0.488480i	−0.689859	−	0.723944i	$-0.742327\pi$
$367$	103.503	−	179.272i	0.282024	−	0.488480i	0.971883	+	0.235464i	$0.0756608\pi$
$368$	−411.345	−	40.9092i	−1.11779	−	0.111166i
$369$	317.380	−	92.4721i	0.860107	−	0.250602i
$370$	48.8719	+	126.785i	0.132086	+	0.342663i
$371$	−45.1972	+	78.2839i	−0.121825	+	0.211008i
$372$	−41.4855	−	448.709i	−0.111520	−	1.20621i
$373$	382.669	−	220.934i	1.02592	−	0.592317i	0.110109	−	0.993920i	$-0.464880\pi$
$373$	382.669	−	220.934i	1.02592	−	0.592317i	0.915814	+	0.401603i	$0.131547\pi$
$374$	−10.9096	+	13.5109i	−0.0291702	+	0.0361253i
$375$	−190.219	−	22.9448i	−0.507250	−	0.0611861i
$376$	587.043	−	384.741i	1.56129	−	1.02325i
$377$		−	17.3952i		−	0.0461412i
$378$	−267.797	−	455.606i	−0.708457	−	1.20531i
$379$			158.494i			0.418190i	0.977895	+	0.209095i	$0.0670518\pi$
$379$			158.494i			0.418190i	−0.977895	+	0.209095i	$0.932948\pi$
$380$	−118.932	+	25.6277i	−0.312980	+	0.0674414i
$381$	78.4879	+	9.46744i	0.206005	+	0.0248489i
$382$	62.6189	−	77.5493i	0.163924	−	0.203009i
$383$	−259.641	+	149.904i	−0.677913	+	0.391393i	−0.799068	−	0.601240i	$-0.794673\pi$
$383$	−259.641	+	149.904i	−0.677913	+	0.391393i	0.121155	+	0.992634i	$0.461340\pi$
$384$	−359.251	+	135.627i	−0.935550	+	0.353195i
$385$	88.3043	−	152.948i	0.229362	−	0.397266i
$386$	33.8364	−	13.0429i	0.0876589	−	0.0337898i
$387$	−425.657	−	407.562i	−1.09989	−	1.05313i
$388$	−8.09674	+	7.33144i	−0.0208679	+	0.0188955i
$389$	188.790	−	326.994i	0.485322	−	0.840603i	−0.514535	−	0.857469i	$-0.672036\pi$
$389$	188.790	−	326.994i	0.485322	−	0.840603i	0.999858	+	0.0168663i	$0.00536896\pi$
$390$	7.45391	−	7.24916i	0.0191126	−	0.0185876i
$391$	−8.22751	−	14.2505i	−0.0210422	−	0.0364462i
$392$	373.635	−	21.1534i	0.953150	−	0.0539629i
$393$	−98.8740	−	231.560i	−0.251588	−	0.589211i
$394$	−27.0366	+	172.261i	−0.0686207	+	0.437210i
$395$	−58.2500			−0.147468
$396$	431.697	−	233.460i	1.09014	−	0.589544i
$397$			652.144i			1.64268i	0.570438	+	0.821340i	$0.306773\pi$
$397$			652.144i			1.64268i	−0.570438	+	0.821340i	$0.693227\pi$
$398$	−52.3044	+	333.253i	−0.131418	+	0.837318i
$399$	539.641	+	404.849i	1.35248	+	1.01466i
$400$	338.955	−	153.190i	0.847388	−	0.382975i
$401$	143.736	−	82.9859i	0.358443	−	0.206947i	−0.309954	−	0.950751i	$-0.600314\pi$
$401$	143.736	−	82.9859i	0.358443	−	0.206947i	0.668398	+	0.743804i	$0.266980\pi$
$402$	−41.3492	−	163.385i	−0.102859	−	0.406429i
$403$	−42.5750	−	24.5807i	−0.105645	−	0.0609943i
$404$	−94.5516	+	85.6146i	−0.234039	+	0.211917i
$405$	−4.65474	−	107.119i	−0.0114932	−	0.264492i
$406$	242.673	−	93.5430i	0.597717	−	0.230402i
$407$	605.961	+	349.852i	1.48885	+	0.859587i
$408$	−12.7263	−	8.46735i	−0.0311918	−	0.0207533i
$409$	101.641	+	176.047i	0.248511	+	0.430433i	0.963113	−	0.269098i	$-0.0867256\pi$
$409$	101.641	+	176.047i	0.248511	+	0.430433i	−0.714602	+	0.699531i	$0.753392\pi$
$410$	−61.0903	+	75.6563i	−0.149001	+	0.184527i
$411$	176.788	+	132.630i	0.430142	+	0.322701i
$412$	−141.004	−	654.369i	−0.342244	−	1.58827i
$413$	285.423			0.691097
$414$	59.2857	+	461.252i	0.143202	+	1.11413i
$415$	−171.885			−0.414182
$416$	−10.5595	+	40.5404i	−0.0253835	+	0.0974530i
$417$	51.4025	−	21.9484i	0.123267	−	0.0526340i
$418$	−393.586	+	487.430i	−0.941593	+	1.16610i
$419$	7.70600	+	13.3472i	0.0183914	+	0.0318548i	0.875075	−	0.483988i	$-0.160812\pi$
$419$	7.70600	+	13.3472i	0.0183914	+	0.0318548i	−0.856683	+	0.515843i	$0.827479\pi$
$420$	141.213	+	65.0038i	0.336222	+	0.154771i
$421$	86.3264	+	49.8406i	0.205051	+	0.118386i	0.599009	−	0.800742i	$-0.295561\pi$
$421$	86.3264	+	49.8406i	0.205051	+	0.118386i	−0.393958	+	0.919128i	$0.628895\pi$
$422$	−142.763	−	370.362i	−0.338301	−	0.877634i
$423$	−570.339	−	546.094i	−1.34832	−	1.29100i
$424$	33.2697	−	65.9783i	0.0784663	−	0.155609i
$425$	12.8229	+	7.40332i	0.0301716	+	0.0174196i
$426$	484.168	+	136.986i	1.13655	+	0.321564i
$427$	−73.7651	+	42.5883i	−0.172752	+	0.0997384i
$428$	307.329	+	98.9078i	0.718058	+	0.231093i
$429$	6.41198	−	53.1572i	0.0149463	−	0.123909i
$430$	171.254	+	26.8786i	0.398265	+	0.0625083i
$431$			269.164i			0.624509i	0.949998	+	0.312255i	$0.101084\pi$
$431$			269.164i			0.624509i	−0.949998	+	0.312255i	$0.898916\pi$
$432$	239.609	+	359.460i	0.554650	+	0.832084i
$433$	−302.385			−0.698350			−0.349175	−	0.937058i	$-0.613538\pi$
$433$	−302.385			−0.698350			−0.349175	+	0.937058i	$0.613538\pi$
$434$	113.967	−	726.127i	0.262596	−	1.67310i
$435$	52.3859	+	6.31894i	0.120427	+	0.0145263i
$436$	88.1052	−	273.763i	0.202076	−	0.627896i
$437$	−296.823	−	514.112i	−0.679229	−	1.17646i
$438$	−145.118	+	512.912i	−0.331321	+	1.17103i
$439$	102.440	−	177.431i	0.233348	−	0.404170i	−0.725443	−	0.688282i	$-0.758365\pi$
$439$	102.440	−	177.431i	0.233348	−	0.404170i	0.958791	+	0.284112i	$0.0916986\pi$
$440$	−65.0008	+	128.905i	−0.147729	+	0.292967i
$441$	−117.770	−	404.205i	−0.267051	−	0.916564i
$442$	−1.55602	+	0.599798i	−0.00352041	+	0.00135701i
$443$	−17.4371	+	30.2020i	−0.0393614	+	0.0681760i	−0.885035	−	0.465525i	$-0.845866\pi$
$443$	−17.4371	+	30.2020i	−0.0393614	+	0.0681760i	0.845674	+	0.533701i	$0.179199\pi$
$444$	−257.538	+	559.471i	−0.580040	+	1.26007i
$445$	−26.4458	+	15.2685i	−0.0594288	+	0.0343113i
$446$	−445.183	−	359.473i	−0.998168	−	0.805992i
$447$	−150.649	−	352.815i	−0.337022	−	0.789295i
$448$	−622.345	+	70.6951i	−1.38916	+	0.157802i
$449$		−	196.732i		−	0.438155i	−0.975707	−	0.219077i	$-0.929695\pi$
$449$		−	196.732i		−	0.438155i	0.975707	−	0.219077i	$-0.0703047\pi$
$450$	−253.723	−	332.767i	−0.563828	−	0.739482i
$451$			500.742i			1.11029i
$452$	−696.105	+	149.998i	−1.54005	+	0.331853i
$453$	−337.323	+	449.632i	−0.744642	+	0.992566i
$454$	458.360	+	370.112i	1.00960	+	0.815225i
$455$	14.6876	−	8.47988i	0.0322804	−	0.0186371i
$456$	−459.124	−	305.476i	−1.00685	−	0.669903i
$457$	−90.1031	+	156.063i	−0.197162	+	0.341495i	−0.947607	−	0.319438i	$-0.896506\pi$
$457$	−90.1031	+	156.063i	−0.197162	+	0.341495i	0.750445	+	0.660933i	$0.229839\pi$
$458$	161.528	+	419.042i	0.352681	+	0.914940i
$459$	−6.05994	+	16.0933i	−0.0132025	+	0.0350617i
$460$	−91.8187	−	101.403i	−0.199606	−	0.220442i
$461$	32.5753	−	56.4220i	0.0706622	−	0.122390i	−0.828530	−	0.559945i	$-0.810822\pi$
$461$	32.5753	−	56.4220i	0.0706622	−	0.122390i	0.899192	+	0.437555i	$0.144155\pi$
$462$	776.052	−	196.402i	1.67977	−	0.425113i
$463$	328.450	+	568.892i	0.709396	+	1.22871i	0.965082	+	0.261949i	$0.0843654\pi$
$463$	328.450	+	568.892i	0.709396	+	1.22871i	−0.255686	+	0.966760i	$0.582301\pi$
$464$	−193.731	+	87.5562i	−0.417523	+	0.188699i
$465$	89.4906	−	119.286i	0.192453	−	0.256529i
$466$	−456.813	−	71.6974i	−0.980285	−	0.153857i
$467$	23.0928			0.0494492			0.0247246	−	0.999694i	$-0.492129\pi$
$467$	23.0928			0.0494492			0.0247246	+	0.999694i	$0.492129\pi$
$468$	47.1115	+	1.31239i	0.100665	+	0.00280425i
$469$		−	274.901i		−	0.586143i
$470$	229.464	+	36.0147i	0.488222	+	0.0766270i
$471$	−216.573	+	92.4746i	−0.459815	+	0.196337i
$472$	−232.942	+	13.1881i	−0.493522	+	0.0279409i
$473$	773.070	−	446.332i	1.63440	−	0.943620i
$474$	−184.081	−	189.280i	−0.388356	−	0.399325i
$475$	462.612	+	267.089i	0.973919	+	0.562293i
$476$	−16.7350	−	18.4819i	−0.0351576	−	0.0388276i
$477$	−80.7440	−	19.7668i	−0.169275	−	0.0414398i
$478$	−290.375	−	753.303i	−0.607480	−	1.57595i
$479$	−271.527	−	156.766i	−0.566863	−	0.327278i	0.189033	−	0.981971i	$-0.439465\pi$
$479$	−271.527	−	156.766i	−0.566863	−	0.327278i	−0.755895	+	0.654693i	$0.772798\pi$
$480$	−118.252	−	46.5267i	−0.246358	−	0.0969307i
$481$	33.5963	+	58.1905i	0.0698468	+	0.120978i
$482$	235.154	+	189.880i	0.487870	+	0.393941i
$483$	−90.8393	+	753.084i	−0.188073	+	1.55918i
$484$	54.6442	+	253.591i	0.112901	+	0.523949i
$485$	−3.61464			−0.00745286
$486$	333.367	−	353.641i	0.685941	−	0.727657i
$487$	−14.6465			−0.0300750			−0.0150375	−	0.999887i	$-0.504787\pi$
$487$	−14.6465			−0.0300750			−0.0150375	+	0.999887i	$0.504787\pi$
$488$	58.2342	−	38.1660i	0.119332	−	0.0782090i
$489$	−79.9052	+	662.437i	−0.163405	+	1.35468i
$490$	96.3535	+	77.8027i	0.196640	+	0.158781i
$491$	127.655	+	221.104i	0.259989	+	0.450314i	0.966239	−	0.257649i	$-0.0829477\pi$
$491$	127.655	+	221.104i	0.259989	+	0.450314i	−0.706250	+	0.707963i	$0.749614\pi$
$492$	−438.897	+	40.5783i	−0.892067	+	0.0824763i
$493$	−7.32898	−	4.23139i	−0.0148661	−	0.00858294i
$494$	−56.1364	+	21.6389i	−0.113636	+	0.0438034i
$495$	157.754	+	38.6194i	0.318695	+	0.0780190i
$496$	−59.4606	+	597.881i	−0.119880	+	1.20540i
$497$	710.777	+	410.367i	1.43013	+	0.825688i
$498$	−543.189	−	558.532i	−1.09074	−	1.12155i
$499$	−229.726	+	132.632i	−0.460372	+	0.265796i	−0.712201	−	0.701976i	$-0.752301\pi$
$499$	−229.726	+	132.632i	−0.460372	+	0.265796i	0.251829	+	0.967772i	$0.418968\pi$
$500$	243.180	+	78.2628i	0.486360	+	0.156526i
$501$	−167.281	+	71.4275i	−0.333894	+	0.142570i
$502$	44.6490	−	284.477i	0.0889423	−	0.566687i
$503$		−	740.126i		−	1.47142i	−0.677295	−	0.735711i	$-0.736848\pi$
$503$		−	740.126i		−	1.47142i	0.677295	−	0.735711i	$-0.263152\pi$
$504$	235.034	+	664.288i	0.466336	+	1.31803i
$505$	−42.2108			−0.0835858
$506$	−695.911	−	109.224i	−1.37532	−	0.215858i
$507$	−301.171	+	401.444i	−0.594027	+	0.791803i
$508$	−100.341	−	32.2927i	−0.197521	−	0.0635683i
$509$	313.529	+	543.047i	0.615970	+	1.06689i	0.990214	+	0.139560i	$0.0445689\pi$
$509$	313.529	+	543.047i	0.615970	+	1.06689i	−0.374244	+	0.927330i	$0.622098\pi$
$510$	−1.24106	−	4.90385i	−0.00243345	−	0.00961539i
$511$	−434.729	+	752.973i	−0.850742	+	1.47353i
$512$	504.648	−	86.4522i	0.985641	−	0.168852i
$513$	−218.624	+	580.597i	−0.426168	+	1.13177i
$514$	104.993	+	272.376i	0.204266	+	0.529915i
$515$	110.759	−	191.841i	0.215066	−	0.372506i
$516$	453.854	+	641.421i	0.879562	+	1.24306i
$517$	1035.84	−	598.043i	2.00356	−	1.15676i
$518$	−631.125	+	781.607i	−1.21839	+	1.50889i
$519$	352.642	−	470.052i	0.679465	−	0.905688i
$520$	−11.5952	+	7.59933i	−0.0222984	+	0.0146141i
$521$			44.2824i			0.0849950i	0.999097	+	0.0424975i	$0.0135315\pi$
$521$			44.2824i			0.0849950i	−0.999097	+	0.0424975i	$0.986469\pi$
$522$	145.016	+	190.194i	0.277808	+	0.364356i
$523$		−	114.110i		−	0.218184i	−0.994032	−	0.109092i	$-0.965206\pi$
$523$		−	114.110i		−	0.218184i	0.994032	−	0.109092i	$-0.0347943\pi$
$524$	70.7171	+	328.182i	0.134956	+	0.626301i
$525$	−268.034	−	627.727i	−0.510540	−	1.19567i
$526$	77.2700	−	95.6937i	0.146901	−	0.181927i
$527$	−20.7127	+	11.9585i	−0.0393031	+	0.0226916i
$528$	−624.285	+	196.148i	−1.18236	+	0.371492i
$529$	69.2465	−	119.938i	0.130901	−	0.226727i
$530$	22.8164	−	8.79500i	0.0430497	−	0.0165943i
$531$	73.4234	+	252.001i	0.138274	+	0.474579i
$532$	−603.748	−	666.770i	−1.13486	−	1.25333i
$533$	−24.0432	+	41.6440i	−0.0451092	+	0.0781314i
$534$	−133.188	−	37.6829i	−0.249415	−	0.0705673i
$535$	53.4202	+	92.5266i	0.0998509	+	0.172947i
$536$	12.7019	+	224.355i	0.0236976	+	0.418573i
$537$	43.7463	+	5.27682i	0.0814643	+	0.00982647i
$538$	128.224	−	816.969i	0.238335	−	1.51853i
$539$	637.730			1.18317
$540$	−21.0658	+	141.400i	−0.0390108	+	0.261851i
$541$		−	212.795i		−	0.393337i	−0.980470	−	0.196668i	$-0.936988\pi$
$541$		−	212.795i		−	0.393337i	0.980470	−	0.196668i	$-0.0630123\pi$
$542$	−38.0026	+	242.130i	−0.0701155	+	0.446734i
$543$	85.9212	−	712.312i	0.158234	−	1.31181i
$544$	14.5119	+	14.3104i	0.0266763	+	0.0263059i
$545$	82.4210	−	47.5858i	0.151231	−	0.0873133i
$546$	73.9703	+	20.9285i	0.135477	+	0.0383305i
$547$	385.456	+	222.543i	0.704672	+	0.406843i	0.809085	−	0.587691i	$-0.199963\pi$
$547$	385.456	+	222.543i	0.704672	+	0.406843i	−0.104413	+	0.994534i	$0.533296\pi$
$548$	−197.790	−	218.437i	−0.360931	−	0.398607i
$549$	−56.5771	−	54.1720i	−0.103055	−	0.0986739i
$550$	591.446	−	227.984i	1.07536	−	0.414517i
$551$	−264.407	−	152.655i	−0.479867	−	0.277052i
$552$	39.3401	−	618.812i	0.0712683	−	1.12104i
$553$	−215.333	−	372.967i	−0.389390	−	0.674443i
$554$	497.469	−	616.083i	0.897959	−	1.11206i
$555$	−187.445	+	80.0374i	−0.337739	+	0.144212i
$556$	−72.8509	+	15.6980i	−0.131027	+	0.0282338i
$557$	853.934			1.53310			0.766548	−	0.642187i	$-0.221973\pi$
$557$	853.934			1.53310			0.766548	+	0.642187i	$0.221973\pi$
$558$	670.419	−	86.1704i	1.20147	−	0.154427i
$559$	85.7228			0.153350
$560$	−168.368	−	120.893i	−0.300657	−	0.215881i
$561$	−20.8365	−	15.6320i	−0.0371417	−	0.0278645i
$562$	146.518	−	181.453i	0.260709	−	0.322870i
$563$	−400.378	−	693.475i	−0.711151	−	1.23175i	−0.964425	−	0.264355i	$-0.914841\pi$
$563$	−400.378	−	693.475i	−0.711151	−	1.23175i	0.253275	−	0.967394i	$-0.418492\pi$
$564$	608.121	+	859.443i	1.07823	+	1.52384i
$565$	−204.076	−	117.823i	−0.361197	−	0.208537i
$566$	−203.484	−	527.886i	−0.359512	−	0.932660i
$567$	668.662	−	425.791i	1.17930	−	0.750953i
$568$	−599.048	−	302.071i	−1.05466	−	0.531816i
$569$	694.024	+	400.695i	1.21973	+	0.704209i	0.964859	−	0.262767i	$-0.0846352\pi$
$569$	694.024	+	400.695i	1.21973	+	0.704209i	0.254866	+	0.966976i	$0.417969\pi$
$570$	−44.7736	−	176.916i	−0.0785502	−	0.310378i
$571$	−390.209	+	225.288i	−0.683379	+	0.394549i	−0.801127	−	0.598494i	$-0.795766\pi$
$571$	−390.209	+	225.288i	−0.683379	+	0.394549i	0.117748	+	0.993044i	$0.462433\pi$
$572$	−21.8707	+	67.9573i	−0.0382356	+	0.118807i
$573$	119.597	+	89.7239i	0.208720	+	0.156586i
$574$	−710.249	−	111.475i	−1.23737	−	0.194207i
$575$			600.628i			1.04457i
$576$	−222.512	−	531.286i	−0.386305	−	0.922371i
$577$	−985.430			−1.70785			−0.853925	−	0.520395i	$-0.825785\pi$
$577$	−985.430			−1.70785			−0.853925	+	0.520395i	$0.825785\pi$
$578$	89.4949	−	570.208i	0.154836	−	0.986519i
$579$	21.3603	+	50.0252i	0.0368917	+	0.0863993i
$580$	−66.9713	−	21.5534i	−0.115468	−	0.0371611i
$581$	−635.408	−	1100.56i	−1.09365	−	1.89425i
$582$	−11.4229	−	11.7456i	−0.0196270	−	0.0201814i
$583$	62.9595	−	109.049i	0.107992	−	0.187048i
$584$	320.004	−	634.611i	0.547952	−	1.08666i
$585$	11.2652	+	10.7863i	0.0192568	+	0.0184382i
$586$	−83.8293	+	32.3136i	−0.143053	+	0.0551427i
$587$	−123.922	+	214.640i	−0.211111	+	0.365655i	−0.952063	−	0.305903i	$-0.901042\pi$
$587$	−123.922	+	214.640i	−0.211111	+	0.365655i	0.740951	+	0.671559i	$0.234375\pi$
$588$	51.6793	+	558.966i	0.0878900	+	0.950622i
$589$	−747.251	+	431.425i	−1.26868	+	0.732471i
$590$	−60.0716	−	48.5061i	−0.101816	−	0.0822137i
$591$	−259.672	−	31.3224i	−0.439378	−	0.0529991i
$592$	478.966	−	667.055i	0.809064	−	1.12678i
$593$		−	355.619i		−	0.599694i	−0.953987	−	0.299847i	$-0.903064\pi$
$593$		−	355.619i		−	0.599694i	0.953987	−	0.299847i	$-0.0969357\pi$
$594$	373.039	+	634.656i	0.628013	+	1.06845i
$595$		−	8.25091i		−	0.0138671i
$596$	107.748	+	500.032i	0.180785	+	0.838980i
$597$	−502.357	−	60.5958i	−0.841469	−	0.101501i
$598$	−52.6307	−	42.4978i	−0.0880113	−	0.0710666i
$599$	−952.887	+	550.150i	−1.59080	+	0.918447i	−0.597626	+	0.801775i	$0.703889\pi$
$599$	−952.887	+	550.150i	−1.59080	+	0.918447i	−0.993171	+	0.116672i	$0.962777\pi$
$600$	247.755	+	499.923i	0.412925	+	0.833204i
$601$	330.403	−	572.275i	0.549756	−	0.952205i	−0.448535	−	0.893765i	$-0.648054\pi$
$601$	330.403	−	572.275i	0.549756	−	0.952205i	0.998291	−	0.0584399i	$-0.0186126\pi$
$602$	460.975	+	1195.88i	0.765739	+	1.98651i
$603$	242.711	−	70.7167i	0.402506	−	0.117275i
$604$	555.557	−	503.046i	0.919797	−	0.832858i
$605$	−42.9231	+	74.3451i	−0.0709473	+	0.122884i
$606$	−133.394	−	137.162i	−0.220122	−	0.226339i
$607$	137.743	+	238.577i	0.226924	+	0.393043i	0.956895	−	0.290435i	$-0.0937999\pi$
$607$	137.743	+	238.577i	0.226924	+	0.393043i	−0.729971	+	0.683478i	$0.760467\pi$
$608$	523.545	+	516.275i	0.861094	+	0.849137i
$609$	153.195	+	358.779i	0.251552	+	0.589128i
$610$	22.7626	+	3.57262i	0.0373158	+	0.00585676i
$611$	114.860			0.187987
$612$	12.0128	−	19.5298i	0.0196287	−	0.0319114i
$613$			73.3264i			0.119619i	0.998210	+	0.0598094i	$0.0190493\pi$
$613$			73.3264i			0.119619i	−0.998210	+	0.0598094i	$0.980951\pi$
$614$	−690.729	−	108.411i	−1.12497	−	0.176565i
$615$	−116.677	−	87.5337i	−0.189719	−	0.142331i
$616$	−1065.65	+	60.3322i	−1.72995	+	0.0979418i
$617$	−54.2660	+	31.3305i	−0.0879513	+	0.0507787i	−0.543331	−	0.839519i	$-0.682837\pi$
$617$	−54.2660	+	31.3305i	−0.0879513	+	0.0507787i	0.455379	+	0.890298i	$0.349504\pi$
$618$	973.394	−	246.346i	1.57507	−	0.398618i
$619$	−945.035	−	545.616i	−1.52671	−	0.881448i	−0.999497	−	0.0317160i	$-0.989903\pi$
$619$	−945.035	−	545.616i	−1.52671	−	0.881448i	−0.527215	−	0.849732i	$-0.676764\pi$
$620$	−147.387	+	133.456i	−0.237721	+	0.215252i
$621$	−688.269	+	113.524i	−1.10832	+	0.182809i
$622$	61.1135	+	158.543i	0.0982532	+	0.254892i
$623$	−195.524	−	112.886i	−0.313843	−	0.181198i
$624$	−61.3364	−	13.6625i	−0.0982955	−	0.0218951i
$625$	−248.328	−	430.116i	−0.397324	−	0.688186i
$626$	−152.791	−	123.375i	−0.244076	−	0.197084i
$627$	−751.717	−	563.953i	−1.19891	−	0.899446i
$628$	306.941	−	66.1401i	0.488760	−	0.105319i
$629$	32.6892			0.0519701
$630$	−89.8964	+	215.160i	−0.142693	+	0.341523i
$631$	196.018			0.310646			0.155323	−	0.987864i	$-0.450358\pi$
$631$	196.018			0.310646			0.155323	+	0.987864i	$0.450358\pi$
$632$	192.973	+	294.440i	0.305336	+	0.465886i
$633$	547.560	−	233.803i	0.865023	−	0.369357i
$634$	879.969	+	710.550i	1.38796	+	1.12074i
$635$	−17.4413	−	30.2093i	−0.0274667	−	0.0475737i
$636$	100.683	+	46.3466i	0.158306	+	0.0728720i
$637$	53.0365	+	30.6207i	0.0832599	+	0.0480701i
$638$	−338.042	+	130.305i	−0.529847	+	0.204240i
$639$	−179.472	+	733.113i	−0.280864	+	1.14728i
$640$	142.996	+	90.8853i	0.223431	+	0.142008i
$641$	−317.942	−	183.564i	−0.496009	−	0.286371i	0.231055	−	0.972941i	$-0.425782\pi$
$641$	−317.942	−	183.564i	−0.496009	−	0.286371i	−0.727064	+	0.686570i	$0.759116\pi$
$642$	−131.842	+	465.987i	−0.205361	+	0.725836i
$643$	209.243	−	120.807i	0.325417	−	0.187880i	−0.328387	−	0.944543i	$-0.606505\pi$
$643$	209.243	−	120.807i	0.325417	−	0.187880i	0.653805	+	0.756663i	$0.273172\pi$
$644$	309.845	−	962.760i	0.481127	−	1.49497i
$645$	−31.1394	+	258.155i	−0.0482781	+	0.400240i
$646$	−4.53826	+	28.9151i	−0.00702517	+	0.0447602i
$647$		−	17.7113i		−	0.0273745i	−0.999906	−	0.0136872i	$-0.995643\pi$
$647$		−	17.7113i		−	0.0273745i	0.999906	−	0.0136872i	$-0.00435692\pi$
$648$	−526.042	+	378.397i	−0.811793	+	0.583945i
$649$	−397.593			−0.612623
$650$	60.1340	+	9.43811i	0.0925138	+	0.0145202i
$651$	1094.59	+	132.033i	1.68140	+	0.202815i
$652$	272.550	−	846.875i	0.418022	−	1.29889i
$653$	572.158	+	991.007i	0.876200	+	1.51762i	0.855479	+	0.517837i	$0.173263\pi$
$653$	572.158	+	991.007i	0.876200	+	1.51762i	0.0207205	+	0.999785i	$0.493404\pi$
$654$	415.092	+	117.442i	0.634698	+	0.179576i
$655$	−55.5484	+	96.2127i	−0.0848068	+	0.146890i
$656$	584.807	+	58.1604i	0.891474	+	0.0886591i
$657$	−776.635	−	190.126i	−1.18209	−	0.289386i
$658$	617.662	+	1602.36i	0.938696	+	2.43520i
$659$	34.7697	−	60.2229i	0.0527613	−	0.0913853i	−0.838438	−	0.544996i	$-0.816531\pi$
$659$	34.7697	−	60.2229i	0.0527613	−	0.0913853i	0.891200	+	0.453611i	$0.149864\pi$
$660$	−196.709	−	90.5499i	−0.298044	−	0.137197i
$661$	817.965	−	472.253i	1.23747	−	0.714452i	0.268891	−	0.963171i	$-0.413343\pi$
$661$	817.965	−	472.253i	1.23747	−	0.714452i	0.968576	+	0.248719i	$0.0800096\pi$
$662$	−20.5893	+	25.4985i	−0.0311017	+	0.0385173i
$663$	−0.982289	−	2.30049i	−0.00148158	−	0.00346982i
$664$	569.428	+	868.841i	0.857572	+	1.30850i
$665$		−	297.667i		−	0.447620i
$666$	−852.438	−	356.160i	−1.27994	−	0.534774i
$667$		−	343.290i		−	0.514678i
$668$	237.081	−	51.0866i	0.354912	−	0.0764770i
$669$	515.073	−	686.563i	0.769915	−	1.02625i
$670$	−46.7179	+	57.8570i	−0.0697282	+	0.0863537i
$671$	102.754	−	59.3253i	0.153136	−	0.0884132i
$672$	−139.237	−	929.147i	−0.207198	−	1.38266i
$673$	−491.029	+	850.487i	−0.729612	+	1.26373i	0.227435	+	0.973793i	$0.426966\pi$
$673$	−491.029	+	850.487i	−0.729612	+	1.26373i	−0.957047	+	0.289932i	$0.906367\pi$
$674$	200.179	−	77.1630i	0.297002	−	0.114485i
$675$	485.273	−	398.128i	0.718923	−	0.589819i
$676$	496.017	−	449.134i	0.733753	−	0.664399i
$677$	−130.160	+	225.444i	−0.192260	+	0.333004i	−0.945999	−	0.324170i	$-0.894915\pi$
$677$	−130.160	+	225.444i	−0.192260	+	0.333004i	0.753739	+	0.657174i	$0.228248\pi$
$678$	−262.058	−	1035.48i	−0.386516	−	1.52725i
$679$	−13.3622	−	23.1440i	−0.0196793	−	0.0340855i
$680$	0.381237	+	6.73382i	0.000560643	+	0.00990268i
$681$	−530.318	+	706.884i	−0.778735	+	1.03801i
$682$	−158.755	+	1011.49i	−0.232778	+	1.48313i
$683$	−1054.30			−1.54363			−0.771816	−	0.635846i	$-0.780651\pi$
$683$	−1054.30			−1.54363			−0.771816	+	0.635846i	$0.780651\pi$
$684$	433.384	−	704.575i	0.633602	−	1.03008i
$685$		−	97.5170i		−	0.142361i
$686$	6.74012	−	42.9440i	0.00982525	−	0.0626006i
$687$	−619.531	+	264.534i	−0.901792	+	0.385057i
$688$	−431.472	−	954.694i	−0.627139	−	1.38764i
$689$	10.4720	−	6.04601i	0.0151988	−	0.00877505i
$690$	147.101	−	143.060i	0.213190	−	0.207334i
$691$	520.398	+	300.452i	0.753109	+	0.434808i	0.826816	−	0.562472i	$-0.190150\pi$
$691$	520.398	+	300.452i	0.753109	+	0.434808i	−0.0737072	+	0.997280i	$0.523483\pi$
$692$	−580.787	+	525.892i	−0.839288	+	0.759959i
$693$	335.893	+	1152.84i	0.484695	+	1.66355i
$694$	−1015.39	+	391.403i	−1.46310	+	0.563981i
$695$	−21.3576	−	12.3308i	−0.0307304	−	0.0177422i
$696$	−141.605	−	285.732i	−0.203455	−	0.410535i
$697$	11.6970	+	20.2598i	0.0167819	+	0.0290671i
$698$	−406.868	+	503.879i	−0.582905	+	0.721889i
$699$	83.0629	−	688.616i	0.118831	−	0.985145i
$700$	191.704	+	889.655i	0.273863	+	1.27094i
$701$	−759.963			−1.08411			−0.542056	−	0.840342i	$-0.682354\pi$
$701$	−759.963			−1.08411			−0.542056	+	0.840342i	$0.682354\pi$
$702$	0.550586	+	70.6924i	0.000784310	+	0.100701i
$703$	1179.32			1.67756
$704$	866.923	−	98.4779i	1.23143	−	0.139883i
$705$	−41.7238	+	345.902i	−0.0591827	+	0.490642i
$706$	−201.030	+	248.962i	−0.284745	+	0.352638i
$707$	−156.041	−	270.270i	−0.220708	−	0.382277i
$708$	−32.2194	−	348.487i	−0.0455077	−	0.492213i
$709$	336.476	+	194.264i	0.474578	+	0.273998i	0.718154	−	0.695884i	$-0.244987\pi$
$709$	336.476	+	194.264i	0.474578	+	0.273998i	−0.243576	+	0.969882i	$0.578321\pi$
$710$	−79.8540	−	207.160i	−0.112470	−	0.291775i
$711$	273.901	−	286.062i	0.385234	−	0.402337i
$712$	164.789	+	83.0955i	0.231446	+	0.116707i
$713$	−840.206	−	485.093i	−1.17841	−	0.680355i
$714$	26.8109	−	26.0744i	0.0375502	−	0.0365187i
$715$	−20.4597	+	11.8124i	−0.0286150	+	0.0165209i
$716$	−55.9263	−	17.9988i	−0.0781094	−	0.0251380i
$717$	1113.72	−	475.547i	1.55330	−	0.663246i
$718$	−15.7770	−	2.47623i	−0.0219736	−	0.00344878i
$719$			994.711i			1.38346i	0.722154	+	0.691732i	$0.243152\pi$
$719$			994.711i			1.38346i	−0.722154	+	0.691732i	$0.756848\pi$
$720$	63.4257	−	179.752i	0.0880912	−	0.249656i
$721$	1637.77			2.27153
$722$	−51.7780	+	329.899i	−0.0717147	+	0.456923i
$723$	−272.071	+	362.655i	−0.376308	+	0.501597i
$724$	−293.070	+	910.636i	−0.404793	+	1.25778i
$725$	154.451	+	267.517i	0.213036	+	0.368988i
$726$	−377.225	+	95.4677i	−0.519593	+	0.131498i
$727$	27.0039	−	46.7721i	0.0371443	−	0.0643357i	−0.846856	−	0.531823i	$-0.821507\pi$
$727$	27.0039	−	46.7721i	0.0371443	−	0.0643357i	0.884000	+	0.467487i	$0.154841\pi$
$728$	−91.5213	−	46.1499i	−0.125716	−	0.0633927i
$729$	547.942	+	480.833i	0.751635	+	0.659579i
$730$	219.459	−	84.5946i	0.300628	−	0.115883i
$731$	20.8520	−	36.1168i	0.0285254	−	0.0494074i
$732$	60.3250	+	85.2559i	0.0824112	+	0.116470i
$733$	−978.173	+	564.749i	−1.33448	+	0.770462i	−0.985983	−	0.166848i	$-0.946641\pi$
$733$	−978.173	+	564.749i	−1.33448	+	0.770462i	−0.348497	+	0.937310i	$0.613308\pi$
$734$	−322.111	−	260.096i	−0.438844	−	0.354354i
$735$	−111.480	+	148.597i	−0.151674	+	0.202172i
$736$	−208.390	+	800.054i	−0.283138	+	1.08703i
$737$			382.935i			0.519586i
$738$	−84.2861	−	655.759i	−0.114209	−	0.888562i
$739$		−	227.082i		−	0.307282i	−0.988127	−	0.153641i	$-0.950900\pi$
$739$		−	227.082i		−	0.307282i	0.988127	−	0.153641i	$-0.0491000\pi$
$740$	265.660	−	57.2447i	0.358999	−	0.0773577i
$741$	−35.4379	−	82.9946i	−0.0478245	−	0.112004i
$742$	140.658	+	113.578i	0.189567	+	0.153070i
$743$	233.389	−	134.747i	0.314116	−	0.181355i	−0.334651	−	0.942342i	$-0.608618\pi$
$743$	233.389	−	134.747i	0.314116	−	0.181355i	0.648767	+	0.760987i	$0.275285\pi$
$744$	−899.429	−	57.1800i	−1.20891	−	0.0768548i
$745$	−84.6360	+	146.594i	−0.113605	+	0.196770i
$746$	−317.856	−	824.595i	−0.426081	−	1.10536i
$747$	808.234	−	844.118i	1.08197	−	1.13001i
$748$	23.3118	+	25.7452i	0.0311655	+	0.0344187i
$749$	−394.957	+	684.085i	−0.527312	+	0.913331i
$750$	−104.323	+	368.722i	−0.139097	+	0.491629i
$751$	−119.404	−	206.813i	−0.158993	−	0.275384i	0.775513	−	0.631332i	$-0.217491\pi$
$751$	−119.404	−	206.813i	−0.158993	−	0.275384i	−0.934506	+	0.355948i	$0.884158\pi$
$752$	−578.131	−	1279.20i	−0.768791	−	1.70106i
$753$	428.831	+	51.7268i	0.569496	+	0.0686944i
$754$	−34.3697	−	5.39438i	−0.0455832	−	0.00715434i
$755$	248.018			0.328501
$756$	−983.237	+	387.830i	−1.30058	+	0.513003i
$757$			716.991i			0.947148i	0.880754	+	0.473574i	$0.157036\pi$
$757$			716.991i			0.947148i	−0.880754	+	0.473574i	$0.842964\pi$
$758$	313.155	+	49.1500i	0.413133	+	0.0648417i
$759$	126.539	−	1049.04i	0.166717	−	1.38214i
$760$	13.7539	+	242.935i	0.0180972	+	0.319652i
$761$	474.212	−	273.787i	0.623144	−	0.359772i	−0.154948	−	0.987923i	$-0.549521\pi$
$761$	474.212	−	273.787i	0.623144	−	0.359772i	0.778092	+	0.628150i	$0.216188\pi$
$762$	43.0455	−	152.141i	0.0564901	−	0.199661i
$763$	609.371	+	351.820i	0.798651	+	0.461101i
$764$	−133.804	−	147.772i	−0.175137	−	0.193418i
$765$	7.28477	−	2.12250i	0.00952258	−	0.00277451i
$766$	215.665	+	559.487i	0.281547	+	0.730401i
$767$	−33.0656	−	19.0904i	−0.0431103	−	0.0248898i
$768$	156.567	+	751.871i	0.203864	+	0.978999i
$769$	−454.002	−	786.355i	−0.590380	−	1.02257i	−0.994181	−	0.107721i	$-0.965645\pi$
$769$	−454.002	−	786.355i	−0.590380	−	1.02257i	0.403801	−	0.914847i	$-0.367689\pi$
$770$	−274.812	−	221.903i	−0.356899	−	0.288185i
$771$	−402.694	+	171.947i	−0.522301	+	0.223018i
$772$	−15.2774	−	70.8990i	−0.0197894	−	0.0918380i
$773$	−984.863			−1.27408			−0.637040	−	0.770831i	$-0.719841\pi$
$773$	−984.863			−1.27408			−0.637040	+	0.770831i	$0.719841\pi$
$774$	−937.264	+	714.630i	−1.21094	+	0.923294i
$775$	872.999			1.12645
$776$	11.9747	+	18.2712i	0.0154313	+	0.0235453i
$777$	−1205.40	−	904.313i	−1.55135	−	1.16385i
$778$	−587.535	−	474.417i	−0.755186	−	0.609791i
$779$	421.991	+	730.911i	0.541709	+	0.938268i
$780$	−12.0115	−	16.9755i	−0.0153993	−	0.0217635i
$781$	−990.108	−	571.639i	−1.26774	−	0.731932i
$782$	−30.7076	+	11.8369i	−0.0392681	+	0.0151366i
$783$	−277.359	+	227.551i	−0.354226	+	0.290614i
$784$	74.0713	−	744.792i	0.0944787	−	0.949990i
$785$	89.9856	+	51.9532i	0.114631	+	0.0661824i
$786$	−488.181	+	123.548i	−0.621095	+	0.157186i
$787$	−1007.34	+	581.590i	−1.27998	+	0.738997i	−0.976844	−	0.213951i	$-0.931367\pi$
$787$	−1007.34	+	581.590i	−1.27998	+	0.738997i	−0.303135	+	0.952948i	$0.598033\pi$
$788$	331.971	+	106.838i	0.421283	+	0.135582i
$789$	147.579	+	110.717i	0.187046	+	0.140326i
$790$	−18.0637	+	115.091i	−0.0228654	+	0.145685i
$791$		−	1742.23i		−	2.20257i
$792$	−327.400	−	925.349i	−0.413384	−	1.16837i
$793$	11.3940			0.0143683
$794$	1288.51	+	202.234i	1.62281	+	0.254703i
$795$	14.4036	+	33.7327i	0.0181177	+	0.0424311i
$796$	642.225	+	206.688i	0.806815	+	0.259658i
$797$	417.748	+	723.560i	0.524150	+	0.907855i	0.999605	+	0.0281145i	$0.00895029\pi$
$797$	417.748	+	723.560i	0.524150	+	0.907855i	−0.475455	+	0.879740i	$0.657716\pi$
$798$	967.253	−	940.683i	1.21210	−	1.17880i
$799$	27.9397	−	48.3930i	0.0349684	−	0.0605670i
$800$	−197.563	−	717.217i	−0.246953	−	0.896521i
$801$	49.3701	−	201.669i	0.0616356	−	0.251771i
$802$	−119.391	−	309.730i	−0.148867	−	0.386196i
$803$	605.575	−	1048.89i	0.754141	−	1.30621i
$804$	−335.640	+	31.0317i	−0.417463	+	0.0385966i
$805$	289.855	−	167.348i	0.360069	−	0.207886i
$806$	−61.7696	+	76.4976i	−0.0766372	+	0.0949102i
$807$	1231.53	+	148.551i	1.52606	+	0.184078i
$808$	139.837	+	213.366i	0.173066	+	0.264067i
$809$			1227.66i			1.51750i	0.651380	+	0.758752i	$0.274190\pi$
$809$			1227.66i			1.51750i	−0.651380	+	0.758752i	$0.725810\pi$
$810$	−213.091	−	24.0214i	−0.263075	−	0.0296561i
$811$		−	1196.45i		−	1.47528i	−0.675195	−	0.737639i	$-0.735940\pi$
$811$		−	1196.45i		−	1.47528i	0.675195	−	0.737639i	$-0.264060\pi$
$812$	−109.569	−	508.485i	−0.134937	−	0.626213i
$813$	−364.995	−	44.0268i	−0.448949	−	0.0541535i
$814$	879.154	−	1088.77i	1.08004	−	1.33756i
$815$	254.966	−	147.205i	0.312842	−	0.180619i
$816$	−20.6764	+	22.5189i	−0.0253387	+	0.0275967i
$817$	752.277	−	1302.98i	0.920780	−	1.59484i
$818$	379.356	−	146.230i	0.463760	−	0.178765i
$819$	−27.4194	+	112.004i	−0.0334791	+	0.136756i
$820$	130.538	+	144.164i	0.159193	+	0.175810i
$821$	136.573	−	236.552i	0.166350	−	0.288126i	−0.770784	−	0.637096i	$-0.780135\pi$
$821$	136.573	−	236.552i	0.166350	−	0.288126i	0.937134	+	0.348970i	$0.113469\pi$
$822$	316.876	−	308.171i	0.385493	−	0.374904i
$823$	−553.690	−	959.019i	−0.672770	−	1.16527i	−0.977115	−	0.212710i	$-0.931771\pi$
$823$	−553.690	−	959.019i	−0.672770	−	1.16527i	0.304345	−	0.952562i	$-0.401562\pi$
$824$	−1336.64	+	75.6741i	−1.62213	+	0.0918375i
$825$	373.369	+	874.420i	0.452569	+	1.05990i
$826$	88.5115	−	563.942i	0.107157	−	0.682739i
$827$	−720.992			−0.871816			−0.435908	−	0.899991i	$-0.643573\pi$
$827$	−720.992			−0.871816			−0.435908	+	0.899991i	$0.643573\pi$
$828$	929.731	+	25.8996i	1.12286	+	0.0312798i
$829$			635.956i			0.767137i	0.923513	+	0.383568i	$0.125305\pi$
$829$			635.956i			0.767137i	−0.923513	+	0.383568i	$0.874695\pi$
$830$	−53.3028	+	339.613i	−0.0642202	+	0.409173i
$831$	950.126	+	712.803i	1.14335	+	0.857766i
$832$	76.8257	+	33.4355i	0.0923386	+	0.0401869i
$833$	25.8023	−	14.8969i	0.0309751	−	0.0178835i
$834$	−27.4257	−	108.368i	−0.0328845	−	0.129938i
$835$	69.5049	+	40.1287i	0.0832394	+	0.0480583i
$836$	841.017	+	928.807i	1.00600	+	1.11101i
$837$	165.005	+	1000.38i	0.197138	+	1.19520i
$838$	28.7612	−	11.0866i	0.0343212	−	0.0132298i
$839$	−748.725	−	432.277i	−0.892402	−	0.515228i	−0.0176745	−	0.999844i	$-0.505626\pi$
$839$	−748.725	−	432.277i	−0.892402	−	0.515228i	−0.874727	+	0.484615i	$0.838960\pi$
$840$	172.226	−	258.853i	0.205031	−	0.308158i
$841$	332.223	+	575.428i	0.395034	+	0.684218i
$842$	125.246	−	155.109i	0.148748	−	0.184215i
$843$	279.838	+	209.940i	0.331955	+	0.249039i
$844$	−776.037	+	167.221i	−0.919475	+	0.198130i
$845$	221.438			0.262056
$846$	−1255.84	+	957.536i	−1.48445	+	1.13184i
$847$	−634.695			−0.749345
$848$	−120.043	−	86.1950i	−0.141561	−	0.101645i
$849$	780.450	−	333.245i	0.919258	−	0.392515i
$850$	18.6041	−	23.0399i	0.0218871	−	0.0271058i
$851$	663.014	+	1148.37i	0.779100	+	1.34944i
$852$	420.803	−	914.146i	0.493900	−	1.07294i
$853$	−62.5316	−	36.1027i	−0.0733079	−	0.0423243i	0.462898	−	0.886412i	$-0.346810\pi$
$853$	−62.5316	−	36.1027i	−0.0733079	−	0.0423243i	−0.536206	+	0.844087i	$0.680143\pi$
$854$	61.2715	+	158.953i	0.0717465	+	0.186128i
$855$	262.812	−	76.5732i	0.307382	−	0.0895593i
$856$	290.728	−	576.552i	0.339635	−	0.673542i
$857$	−928.395	−	536.009i	−1.08331	−	0.625448i	−0.151521	−	0.988454i	$-0.548417\pi$
$857$	−928.395	−	536.009i	−1.08331	−	0.625448i	−0.931787	+	0.363006i	$0.881750\pi$
$858$	−103.040	−	29.1532i	−0.120093	−	0.0339781i
$859$	−930.598	+	537.281i	−1.08335	+	0.625472i	−0.931798	−	0.362977i	$-0.881760\pi$
$859$	−930.598	+	537.281i	−1.08335	+	0.625472i	−0.151552	+	0.988449i	$0.548427\pi$
$860$	106.214	−	330.031i	0.123505	−	0.383757i
$861$	129.146	−	1070.66i	0.149995	−	1.24350i
$862$	531.817	+	83.4693i	0.616957	+	0.0968322i
$863$			1519.81i			1.76107i	0.473979	+	0.880536i	$0.342817\pi$
$863$			1519.81i			1.76107i	−0.473979	+	0.880536i	$0.657183\pi$
$864$	784.530	−	361.951i	0.908021	−	0.418925i
$865$	−259.282			−0.299748
$866$	−93.7717	+	597.457i	−0.108281	+	0.689904i
$867$	859.552	+	103.682i	0.991410	+	0.119587i
$868$	−1399.35	−	450.354i	−1.61215	−	0.518840i
$869$	299.957	+	519.541i	0.345175	+	0.597860i
$870$	28.7302	−	101.545i	0.0330233	−	0.116719i
$871$	−18.3867	+	31.8466i	−0.0211098	+	0.0365633i
$872$	−513.582	−	258.975i	−0.588970	−	0.296990i
$873$	16.9966	−	17.7512i	0.0194692	−	0.0203336i
$874$	−1107.84	+	427.037i	−1.26755	+	0.488601i
$875$	−312.518	+	541.297i	−0.357163	+	0.618625i
$876$	968.415	+	445.784i	1.10550	+	0.508886i
$877$	1336.39	−	771.565i	1.52382	−	0.879778i	0.524217	−	0.851585i	$-0.324358\pi$
$877$	1336.39	−	771.565i	1.52382	−	0.879778i	0.999602	−	0.0281931i	$-0.00897534\pi$
$878$	−318.803	−	257.424i	−0.363101	−	0.293194i
$879$	−52.9200	−	123.937i	−0.0602047	−	0.140998i
$880$	234.535	+	168.404i	0.266518	+	0.191368i
$881$			16.6706i			0.0189223i	0.999955	+	0.00946117i	$0.00301163\pi$
$881$			16.6706i			0.0189223i	−0.999955	+	0.00946117i	$0.996988\pi$
$882$	−835.154	+	107.344i	−0.946887	+	0.121705i
$883$		−	828.778i		−	0.938594i	−0.883040	−	0.469297i	$-0.844507\pi$
$883$		−	828.778i		−	0.938594i	0.883040	−	0.469297i	$-0.155493\pi$
$884$	0.702557	+	3.26041i	0.000794747	+	0.00368824i
$885$	69.5023	−	92.6426i	0.0785337	−	0.104681i
$886$	54.2660	+	43.8183i	0.0612484	+	0.0494563i
$887$	325.556	−	187.960i	0.367031	−	0.211905i	−0.305130	−	0.952311i	$-0.598700\pi$
$887$	325.556	−	187.960i	0.367031	−	0.211905i	0.672160	+	0.740406i	$0.265367\pi$
$888$	1025.55	+	682.342i	1.15489	+	0.768403i
$889$	128.951	−	223.349i	0.145051	−	0.251236i
$890$	21.9667	+	56.9869i	0.0246817	+	0.0640302i
$891$	−931.443	+	593.124i	−1.04539	+	0.665683i
$892$	−848.304	+	768.123i	−0.951014	+	0.861125i
$893$	1007.98	−	1745.87i	1.12876	−	1.95506i
$894$	−743.813	+	188.243i	−0.832006	+	0.210563i
$895$	−9.72118	−	16.8376i	−0.0108616	−	0.0188129i
$896$	−53.3130	+	1251.56i	−0.0595011	+	1.39683i
$897$	60.8933	−	81.1673i	0.0678855	−	0.0904875i
$898$	−388.705	−	61.0077i	−0.432856	−	0.0679373i
$899$	−498.965			−0.555022
$900$	−736.166	+	398.115i	−0.817962	+	0.442350i
$901$		−	5.88276i		−	0.00652915i
$902$	989.373	+	155.283i	1.09687	+	0.172155i
$903$	−1768.04	+	754.938i	−1.95797	+	0.836033i
$904$	80.5006	+	1421.89i	0.0890493	+	1.57288i
$905$	−274.162	+	158.288i	−0.302942	+	0.174904i
$906$	783.783	+	805.921i	0.865102	+	0.889537i
$907$	196.054	+	113.192i	0.216156	+	0.124798i	0.604169	−	0.796856i	$-0.293505\pi$
$907$	196.054	+	113.192i	0.216156	+	0.124798i	−0.388013	+	0.921654i	$0.626838\pi$
$908$	873.412	−	790.858i	0.961908	−	0.870989i
$909$	198.482	−	207.294i	0.218352	−	0.228047i
$910$	−12.1999	−	31.6496i	−0.0134065	−	0.0347797i
$911$	−353.621	−	204.163i	−0.388168	−	0.224109i	0.293198	−	0.956052i	$-0.405280\pi$
$911$	−353.621	−	204.163i	−0.388168	−	0.224109i	−0.681366	+	0.731943i	$0.738614\pi$
$912$	−745.940	+	812.412i	−0.817916	+	0.890803i
$913$	885.120	+	1533.07i	0.969464	+	1.67916i
$914$	280.410	+	226.423i	0.306794	+	0.247727i
$915$	−4.13896	+	34.3132i	−0.00452346	+	0.0375008i
$916$	878.040	−	189.201i	0.958559	−	0.206552i
$917$	−821.383			−0.895728
$918$	29.9181	+	16.9639i	0.0325906	+	0.0184792i
$919$	−504.252			−0.548696			−0.274348	−	0.961630i	$-0.588462\pi$
$919$	−504.252			−0.548696			−0.274348	+	0.961630i	$0.588462\pi$
$920$	−228.827	+	149.971i	−0.248725	+	0.163012i
$921$	125.596	−	1041.23i	0.136369	−	1.13054i
$922$	−101.377	−	81.8594i	−0.109954	−	0.0887846i
$923$	−54.8946	−	95.0802i	−0.0594741	−	0.103012i
$924$	−147.396	−	1594.24i	−0.159519	−	1.72537i
$925$	−1033.34	−	596.597i	−1.11712	−	0.644970i
$926$	1225.88	−	472.539i	1.32384	−	0.510301i
$927$	421.308	+	1446.00i	0.454485	+	1.55987i
$928$	112.917	+	409.927i	0.121678	+	0.441732i
$929$	−117.715	−	67.9630i	−0.126712	−	0.0731572i	0.435304	−	0.900283i	$-0.356641\pi$
$929$	−117.715	−	67.9630i	−0.126712	−	0.0731572i	−0.562016	+	0.827126i	$0.689974\pi$
$930$	−207.935	−	213.808i	−0.223586	−	0.229901i
$931$	930.865	−	537.435i	0.999855	−	0.577267i
$932$	−283.321	+	880.343i	−0.303993	+	0.944574i
$933$	−234.397	+	100.086i	−0.251230	+	0.107273i
$934$	7.16122	−	45.6270i	0.00766726	−	0.0488512i
$935$			11.4935i			0.0122925i
$936$	17.2026	−	92.6764i	0.0183788	−	0.0990132i
$937$	−602.591			−0.643107			−0.321554	−	0.946891i	$-0.604205\pi$
$937$	−602.591			−0.643107			−0.321554	+	0.946891i	$0.604205\pi$
$938$	−543.152	−	85.2485i	−0.579054	−	0.0908833i
$939$	176.778	−	235.635i	0.188262	−	0.250943i
$940$	142.317	−	442.210i	0.151401	−	0.470436i
$941$	−417.475	−	723.088i	−0.443651	−	0.768425i	0.554307	−	0.832313i	$-0.312984\pi$
$941$	−417.475	−	723.088i	−0.443651	−	0.768425i	−0.997957	+	0.0638872i	$0.979650\pi$
$942$	115.552	+	456.584i	0.122667	+	0.484697i
$943$	−474.486	+	821.833i	−0.503166	+	0.871509i
$944$	−46.1797	+	464.340i	−0.0489192	+	0.491886i
$945$	−327.339	−	123.260i	−0.346390	−	0.130433i
$946$	−642.135	−	1665.85i	−0.678790	−	1.76094i
$947$	−731.873	+	1267.64i	−0.772833	+	1.33859i	0.163171	+	0.986598i	$0.447828\pi$
$947$	−731.873	+	1267.64i	−0.772833	+	1.33859i	−0.936004	+	0.351989i	$0.885506\pi$
$948$	−431.066	+	305.012i	−0.454711	+	0.321742i
$949$	100.725	−	58.1535i	0.106138	−	0.0612787i
$950$	671.176	−	831.208i	0.706502	−	0.874956i
$951$	−1018.12	+	1357.09i	−1.07058	+	1.42701i
$952$	−41.7064	+	27.3339i	−0.0438093	+	0.0287121i
$953$		−	335.327i		−	0.351864i	−0.984402	−	0.175932i	$-0.943706\pi$
$953$		−	335.327i		−	0.351864i	0.984402	−	0.175932i	$-0.0562939\pi$
$954$	−64.0947	+	153.405i	−0.0671852	+	0.160802i
$955$		−	65.9699i		−	0.0690785i
$956$	−1578.43	+	340.123i	−1.65108	+	0.355777i
$957$	−213.400	−	499.777i	−0.222989	−	0.522233i
$958$	−393.943	+	487.872i	−0.411214	+	0.509261i
$959$	624.388	−	360.491i	0.651082	−	0.375903i
$960$	−128.599	+	219.215i	−0.133957	+	0.228349i
$961$	−224.572	+	388.970i	−0.233686	+	0.404756i
$962$	125.392	−	48.3348i	0.130345	−	0.0502440i
$963$	−705.583	−	172.732i	−0.732692	−	0.179369i
$964$	448.089	−	405.736i	0.464823	−	0.420888i
$965$	12.0004	−	20.7854i	0.0124357	−	0.0215392i
$966$	1459.78	+	413.017i	1.51116	+	0.427554i
$967$	−431.319	−	747.066i	−0.446038	−	0.772561i	0.552086	−	0.833787i	$-0.313832\pi$
$967$	−431.319	−	747.066i	−0.446038	−	0.772561i	−0.998124	+	0.0612266i	$0.980499\pi$
$968$	517.994	−	29.3264i	0.535118	−	0.0302959i
$969$	−43.5877	−	5.25767i	−0.0449821	−	0.00542588i
$970$	−1.12092	+	7.14185i	−0.00115559	+	0.00736273i
$971$	1837.35			1.89223			0.946114	−	0.323835i	$-0.104972\pi$
$971$	1837.35			1.89223			0.946114	+	0.323835i	$0.104972\pi$
$972$	−595.349	−	768.338i	−0.612499	−	0.790471i
$973$		−	182.333i		−	0.187393i
$974$	−4.54197	+	28.9387i	−0.00466322	+	0.0297112i
$975$	−10.9343	+	90.6481i	−0.0112146	+	0.0929724i
$976$	−57.3500	−	126.895i	−0.0587603	−	0.130016i
$977$	−1168.58	+	674.680i	−1.19609	+	0.690563i	−0.959681	−	0.281091i	$-0.909304\pi$
$977$	−1168.58	+	674.680i	−1.19609	+	0.690563i	−0.236409	+	0.971654i	$0.575970\pi$
$978$	1284.07	+	363.304i	1.31296	+	0.371476i
$979$	272.364	+	157.250i	0.278207	+	0.160623i
$980$	183.603	−	166.249i	0.187350	−	0.169642i
$981$	−153.867	+	628.520i	−0.156847	+	0.640693i
$982$	476.447	−	183.656i	0.485180	−	0.187022i
$983$	1401.08	+	808.916i	1.42531	+	0.822906i	0.996746	−	0.0806035i	$-0.0256848\pi$
$983$	1401.08	+	808.916i	1.42531	+	0.822906i	0.428568	+	0.903509i	$0.359018\pi$
$984$	−55.9296	+	879.762i	−0.0568390	+	0.894067i
$985$	57.7036	+	99.9455i	0.0585823	+	0.101468i
$986$	−10.6332	+	13.1685i	−0.0107842	+	0.0133555i
$987$	−2369.01	+	1011.54i	−2.40021	+	1.02487i
$988$	25.3461	+	117.625i	0.0256539	+	0.119054i
$989$	1691.71			1.71053
$990$	125.225	−	299.716i	0.126490	−	0.302743i
$991$	−1031.59			−1.04096			−0.520478	−	0.853875i	$-0.674246\pi$
$991$	−1031.59			−1.04096			−0.520478	+	0.853875i	$0.674246\pi$
$992$	1162.86	+	302.890i	1.17224	+	0.305332i
$993$	−39.3239	−	29.5015i	−0.0396011	−	0.0297095i
$994$	1031.22	−	1277.10i	1.03745	−	1.28481i
$995$	111.632	+	193.353i	0.112193	+	0.194324i
$996$	−1272.00	+	900.036i	−1.27711	+	0.903650i
$997$	−768.361	−	443.613i	−0.770673	−	0.444948i	0.0624419	−	0.998049i	$-0.480111\pi$
$997$	−768.361	−	443.613i	−0.770673	−	0.444948i	−0.833114	+	0.553101i	$0.813445\pi$
$998$	190.817	+	495.025i	0.191199	+	0.496017i
$999$	488.341	−	1296.88i	0.488830	−	1.29818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.j.a.29.13	yes	44
3.2	odd	2		216.3.j.a.197.10		44
4.3	odd	2		288.3.n.a.209.2		44
8.3	odd	2		288.3.n.a.209.21		44
8.5	even	2	inner	72.3.j.a.29.5	yes	44
9.2	odd	6		648.3.h.a.485.37		44
9.4	even	3		216.3.j.a.125.18		44
9.5	odd	6	inner	72.3.j.a.5.5	✓	44
9.7	even	3		648.3.h.a.485.8		44
12.11	even	2		864.3.n.a.305.13		44
24.5	odd	2		216.3.j.a.197.18		44
24.11	even	2		864.3.n.a.305.10		44
36.7	odd	6		2592.3.h.a.1457.25		44
36.11	even	6		2592.3.h.a.1457.20		44
36.23	even	6		288.3.n.a.113.21		44
36.31	odd	6		864.3.n.a.17.10		44
72.5	odd	6	inner	72.3.j.a.5.13	yes	44
72.11	even	6		2592.3.h.a.1457.26		44
72.13	even	6		216.3.j.a.125.10		44
72.29	odd	6		648.3.h.a.485.7		44
72.43	odd	6		2592.3.h.a.1457.19		44
72.59	even	6		288.3.n.a.113.2		44
72.61	even	6		648.3.h.a.485.38		44
72.67	odd	6		864.3.n.a.17.13		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.5	✓	44	9.5	odd	6	inner
72.3.j.a.5.13	yes	44	72.5	odd	6	inner
72.3.j.a.29.5	yes	44	8.5	even	2	inner
72.3.j.a.29.13	yes	44	1.1	even	1	trivial
216.3.j.a.125.10		44	72.13	even	6
216.3.j.a.125.18		44	9.4	even	3
216.3.j.a.197.10		44	3.2	odd	2
216.3.j.a.197.18		44	24.5	odd	2
288.3.n.a.113.2		44	72.59	even	6
288.3.n.a.113.21		44	36.23	even	6
288.3.n.a.209.2		44	4.3	odd	2
288.3.n.a.209.21		44	8.3	odd	2
648.3.h.a.485.7		44	72.29	odd	6
648.3.h.a.485.8		44	9.7	even	3
648.3.h.a.485.37		44	9.2	odd	6
648.3.h.a.485.38		44	72.61	even	6
864.3.n.a.17.10		44	36.31	odd	6
864.3.n.a.17.13		44	72.67	odd	6
864.3.n.a.305.10		44	24.11	even	2
864.3.n.a.305.13		44	12.11	even	2
2592.3.h.a.1457.19		44	72.43	odd	6
2592.3.h.a.1457.20		44	36.11	even	6
2592.3.h.a.1457.25		44	36.7	odd	6
2592.3.h.a.1457.26		44	72.11	even	6

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.310106 - 1.97581i) q^{2} +(2.97841 + 0.359265i) q^{3} +(-3.80767 - 1.22542i) q^{4} +(-0.661853 - 1.14636i) q^{5} +(1.63346 - 5.77337i) q^{6} +(4.89334 - 8.47551i) q^{7} +(-3.60199 + 7.14323i) q^{8} +(8.74186 + 2.14008i) q^{9} +O(q^{10})\)	\(q+(0.310106 - 1.97581i) q^{2} +(2.97841 + 0.359265i) q^{3} +(-3.80767 - 1.22542i) q^{4} +(-0.661853 - 1.14636i) q^{5} +(1.63346 - 5.77337i) q^{6} +(4.89334 - 8.47551i) q^{7} +(-3.60199 + 7.14323i) q^{8} +(8.74186 + 2.14008i) q^{9} +(-2.47024 + 0.952203i) q^{10} +(-6.81639 + 11.8063i) q^{11} +(-10.9005 - 5.01778i) q^{12} +(-1.13377 + 0.654580i) q^{13} +(-15.2286 - 12.2966i) q^{14} +(-1.55942 - 3.65212i) q^{15} +(12.9967 + 9.33202i) q^{16} +0.636905i q^{17} +(6.93929 - 16.6086i) q^{18} +22.9776i q^{19} +(1.11534 + 5.17602i) q^{20} +(17.6193 - 23.4856i) q^{21} +(21.2133 + 17.1291i) q^{22} +(-22.3745 + 12.9179i) q^{23} +(-13.2945 + 19.9814i) q^{24} +(11.6239 - 20.1332i) q^{25} +(0.941739 + 2.44310i) q^{26} +(25.2680 + 9.51467i) q^{27} +(-29.0183 + 26.2755i) q^{28} +(-6.64367 + 11.5072i) q^{29} +(-7.69949 + 1.94858i) q^{30} +(18.7759 + 32.5209i) q^{31} +(22.4687 - 22.7851i) q^{32} +(-24.5436 + 32.7152i) q^{33} +(1.25841 + 0.197508i) q^{34} -12.9547 q^{35} +(-30.6636 - 18.8612i) q^{36} -51.3250i q^{37} +(45.3994 + 7.12549i) q^{38} +(-3.61198 + 1.54228i) q^{39} +(10.5727 - 0.598578i) q^{40} +(31.8097 - 18.3654i) q^{41} +(-40.9392 - 42.0955i) q^{42} +(-56.7067 - 32.7396i) q^{43} +(40.4223 - 36.6017i) q^{44} +(-3.33252 - 11.4378i) q^{45} +(18.5849 + 48.2138i) q^{46} +(-75.9815 - 43.8680i) q^{47} +(35.3568 + 32.4638i) q^{48} +(-23.3896 - 40.5119i) q^{49} +(-36.1748 - 29.2101i) q^{50} +(-0.228818 + 1.89697i) q^{51} +(5.11914 - 1.10308i) q^{52} -9.23648 q^{53} +(26.6350 - 46.9742i) q^{54} +18.0458 q^{55} +(42.9168 + 65.4830i) q^{56} +(-8.25503 + 68.4366i) q^{57} +(20.6758 + 16.6951i) q^{58} +(14.5822 + 25.2571i) q^{59} +(1.46237 + 15.8170i) q^{60} +(-7.53730 - 4.35166i) q^{61} +(70.0777 - 27.0128i) q^{62} +(60.9151 - 63.6196i) q^{63} +(-38.0513 - 51.4596i) q^{64} +(1.50077 + 0.866471i) q^{65} +(57.0280 + 58.6388i) q^{66} +(24.3260 - 14.0446i) q^{67} +(0.780479 - 2.42512i) q^{68} +(-71.2815 + 30.4366i) q^{69} +(-4.01733 + 25.5960i) q^{70} +83.8624i q^{71} +(-46.7751 + 54.7365i) q^{72} -88.8409 q^{73} +(-101.409 - 15.9162i) q^{74} +(41.8539 - 55.7888i) q^{75} +(28.1573 - 87.4910i) q^{76} +(66.7099 + 115.545i) q^{77} +(1.92717 + 7.61488i) q^{78} +(22.0026 - 38.1096i) q^{79} +(2.09599 - 21.0753i) q^{80} +(71.8401 + 37.4165i) q^{81} +(-26.4221 - 68.5453i) q^{82} +(64.9258 - 112.455i) q^{83} +(-95.8683 + 67.8341i) q^{84} +(0.730125 - 0.421538i) q^{85} +(-82.2725 + 101.889i) q^{86} +(-23.9217 + 31.8863i) q^{87} +(-59.7828 - 91.2174i) q^{88} -23.0693i q^{89} +(-23.6323 + 3.03751i) q^{90} +12.8123i q^{91} +(101.025 - 21.7690i) q^{92} +(44.2389 + 103.606i) q^{93} +(-110.237 + 136.522i) q^{94} +(26.3406 - 15.2078i) q^{95} +(75.1068 - 59.7911i) q^{96} +(1.36535 - 2.36485i) q^{97} +(-87.2972 + 33.6504i) q^{98} +(-84.8544 + 88.6218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

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