LMFDB - Embedded newform 72.3.j.a.29.5

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			29.5
Character	$\chi$	$=$	72.29
Dual form			72.3.j.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55605 + 1.25647i) q^{2} +(-2.97841 - 0.359265i) q^{3} +(0.842586 - 3.91025i) q^{4} +(0.661853 + 1.14636i) q^{5} +(5.08596 - 3.18324i) q^{6} +(4.89334 - 8.47551i) q^{7} +(3.60199 + 7.14323i) q^{8} +(8.74186 + 2.14008i) q^{9} +O(q^{10})$	\(q+(-1.55605 + 1.25647i) q^{2} +(-2.97841 - 0.359265i) q^{3} +(0.842586 - 3.91025i) q^{4} +(0.661853 + 1.14636i) q^{5} +(5.08596 - 3.18324i) 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} +(-3.91438 + 11.3436i) q^{12} +(1.13377 - 0.654580i) q^{13} +(3.03491 + 19.3366i) q^{14} +(-1.55942 - 3.65212i) q^{15} +(-14.5801 - 6.58944i) q^{16} +0.636905i q^{17} +(-16.2917 + 7.65378i) q^{18} -22.9776i q^{19} +(5.04023 - 1.62210i) q^{20} +(-17.6193 + 23.4856i) q^{21} +(4.22761 + 26.9358i) q^{22} +(-22.3745 + 12.9179i) q^{23} +(-8.16189 - 22.5695i) 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} +(7.01531 + 3.72352i) q^{30} +(18.7759 + 32.5209i) q^{31} +(30.9668 - 8.06590i) q^{32} +(-24.5436 + 32.7152i) q^{33} +(-0.800250 - 0.991057i) q^{34} +12.9547 q^{35} +(15.7340 - 32.3796i) q^{36} +51.3250i q^{37} +(28.8705 + 35.7543i) q^{38} +(-3.61198 + 1.54228i) q^{39} +(-5.80474 + 8.85696i) q^{40} +(31.8097 - 18.3654i) q^{41} +(-2.09224 - 58.6828i) 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} +(41.0582 + 24.8642i) q^{48} +(-23.3896 - 40.5119i) q^{49} +(7.20929 + 45.9333i) q^{50} +(0.228818 - 1.89697i) q^{51} +(-1.60427 - 4.98484i) q^{52} +9.23648 q^{53} +(51.2731 - 16.9431i) q^{54} +18.0458 q^{55} +(78.1683 + 4.42552i) q^{56} +(-8.25503 + 68.4366i) q^{57} +(4.12049 + 26.2533i) q^{58} +(-14.5822 - 25.2571i) q^{59} +(-15.5947 + 3.02050i) 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} +(-2.91447 - 81.7448i) q^{66} +(-24.3260 + 14.0446i) q^{67} +(2.49046 + 0.536647i) q^{68} +(71.2815 - 30.4366i) q^{69} +(-20.1582 + 16.2771i) q^{70} +83.8624i q^{71} +(16.2010 + 70.1536i) q^{72} -88.8409 q^{73} +(-64.4882 - 79.8644i) q^{74} +(-41.8539 + 55.7888i) q^{75} +(-89.8480 - 19.3606i) q^{76} +(-66.7099 - 115.545i) q^{77} +(3.68260 - 6.93821i) 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} +(76.9886 + 88.6846i) q^{84} +(-0.730125 + 0.421538i) q^{85} +(-129.375 + 20.3055i) q^{86} +(-23.9217 + 31.8863i) q^{87} +(108.888 + 6.16472i) q^{88} -23.0693i q^{89} +(-19.5567 - 13.6105i) q^{90} -12.8123i q^{91} +(31.6599 + 98.3745i) q^{92} +(-44.2389 - 103.606i) q^{93} +(173.350 - 27.2075i) q^{94} +(26.3406 - 15.2078i) q^{95} +(-95.1296 + 12.8983i) 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 $

$2$	−1.55605	+	1.25647i	−0.778025	+	0.628233i
$2$	−1.55605	+	1.25647i	−0.778025	+	0.628233i
$3$	−2.97841	−	0.359265i	−0.992803	−	0.119755i
$3$	−2.97841	−	0.359265i	−0.992803	−	0.119755i
$4$	0.842586	−	3.91025i	0.210646	−	0.977562i
$5$	0.661853	+	1.14636i	0.132371	+	0.229273i	0.924590	−	0.380964i	$-0.124408\pi$
$5$	0.661853	+	1.14636i	0.132371	+	0.229273i	−0.792219	+	0.610236i	$0.791074\pi$
$6$	5.08596	−	3.18324i	0.847660	−	0.530540i
$7$	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	$-0.620599\pi$
$11$	6.81639	−	11.8063i	0.619672	−	1.07330i	0.989545	−	0.144222i	$-0.0460678\pi$
$12$	−3.91438	+	11.3436i	−0.326198	+	0.945301i
$13$	1.13377	−	0.654580i	0.0872127	−	0.0503523i	−0.455759	−	0.890103i	$-0.650632\pi$
$13$	1.13377	−	0.654580i	0.0872127	−	0.0503523i	0.542972	+	0.839751i	$0.317299\pi$
$14$	3.03491	+	19.3366i	0.216779	+	1.38119i
$15$	−1.55942	−	3.65212i	−0.103961	−	0.243475i
$16$	−14.5801	−	6.58944i	−0.911256	−	0.411840i
$17$			0.636905i			0.0374650i	0.999825	+	0.0187325i	$0.00596309\pi$
$17$			0.636905i			0.0374650i	−0.999825	+	0.0187325i	$0.994037\pi$
$18$	−16.2917	+	7.65378i	−0.905095	+	0.425210i
$19$		−	22.9776i		−	1.20935i	−0.796474	−	0.604673i	$-0.793304\pi$
$19$		−	22.9776i		−	1.20935i	0.796474	−	0.604673i	$-0.206696\pi$
$20$	5.04023	−	1.62210i	0.252012	−	0.0811051i
$21$	−17.6193	+	23.4856i	−0.839016	+	1.11836i
$22$	4.22761	+	26.9358i	0.192164	+	1.22436i
$23$	−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	$0.523166\pi$
$24$	−8.16189	−	22.5695i	−0.340079	−	0.940397i
$25$	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	−0.728447	−	0.685102i	$-0.759758\pi$
$29$	6.64367	−	11.5072i	0.229092	−	0.396799i	0.957539	+	0.288303i	$0.0930910\pi$
$30$	7.01531	+	3.72352i	0.233844	+	0.124117i
$31$	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	$0.626236\pi$
$32$	30.9668	−	8.06590i	0.967712	−	0.252059i
$33$	−24.5436	+	32.7152i	−0.743746	+	0.991371i
$34$	−0.800250	−	0.991057i	−0.0235368	−	0.0291487i
$35$	12.9547			0.370134
$36$	15.7340	−	32.3796i	0.437055	−	0.899435i
$37$			51.3250i			1.38716i	0.720378	+	0.693582i	$0.243968\pi$
$37$			51.3250i			1.38716i	−0.720378	+	0.693582i	$0.756032\pi$
$38$	28.8705	+	35.7543i	0.759751	+	0.940901i
$39$	−3.61198	+	1.54228i	−0.0926150	+	0.0395458i
$40$	−5.80474	+	8.85696i	−0.145119	+	0.221424i
$41$	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	$0.185493\pi$
$42$	−2.09224	−	58.6828i	−0.0498152	−	1.39721i
$43$	56.7067	+	32.7396i	1.31876	+	0.761387i	0.983529	−	0.180749i	$-0.0578523\pi$
$43$	56.7067	+	32.7396i	1.31876	+	0.761387i	0.335231	+	0.942136i	$0.391186\pi$
$44$	−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	$-0.716472\pi$
$48$	41.0582	+	24.8642i	0.855378	+	0.518004i
$49$	−23.3896	−	40.5119i	−0.477338	−	0.826774i
$50$	7.20929	+	45.9333i	0.144186	+	0.918666i
$51$	0.228818	−	1.89697i	0.00448662	−	0.0371954i
$52$	−1.60427	−	4.98484i	−0.0308514	−	0.0958624i
$53$	9.23648			0.174273			0.0871366	−	0.996196i	$-0.472228\pi$
$53$	9.23648			0.174273			0.0871366	+	0.996196i	$0.472228\pi$
$54$	51.2731	−	16.9431i	0.949502	−	0.313760i
$55$	18.0458			0.328106
$56$	78.1683	+	4.42552i	1.39586	+	0.0790271i
$57$	−8.25503	+	68.4366i	−0.144825	+	1.20064i
$58$	4.12049	+	26.2533i	0.0710429	+	0.452643i
$59$	−14.5822	−	25.2571i	−0.247156	−	0.428087i	0.715579	−	0.698531i	$-0.246163\pi$
$59$	−14.5822	−	25.2571i	−0.247156	−	0.428087i	−0.962736	+	0.270444i	$0.912829\pi$
$60$	−15.5947	+	3.02050i	−0.259911	+	0.0503417i
$61$	7.53730	+	4.35166i	0.123562	+	0.0713387i	0.560507	−	0.828150i	$-0.310606\pi$
$61$	7.53730	+	4.35166i	0.123562	+	0.0713387i	−0.436945	+	0.899488i	$0.643940\pi$
$62$	−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
$66$	−2.91447	−	81.7448i	−0.0441587	−	1.23856i
$67$	−24.3260	+	14.0446i	−0.363075	+	0.209621i	−0.670429	−	0.741974i	$-0.733890\pi$
$67$	−24.3260	+	14.0446i	−0.363075	+	0.209621i	0.307354	+	0.951595i	$0.400557\pi$
$68$	2.49046	+	0.536647i	0.0366244	+	0.00789187i
$69$	71.2815	−	30.4366i	1.03307	−	0.441109i
$70$	−20.1582	+	16.2771i	−0.287974	+	0.232530i
$71$			83.8624i			1.18116i	0.806979	+	0.590580i	$0.201101\pi$
$71$			83.8624i			1.18116i	−0.806979	+	0.590580i	$0.798899\pi$
$72$	16.2010	+	70.1536i	0.225014	+	0.974355i
$73$	−88.8409			−1.21700			−0.608500	−	0.793554i	$-0.708228\pi$
$73$	−88.8409			−1.21700			−0.608500	+	0.793554i	$0.708228\pi$
$74$	−64.4882	−	79.8644i	−0.871462	−	1.07925i
$75$	−41.8539	+	55.7888i	−0.558052	+	0.743851i
$76$	−89.8480	−	19.3606i	−1.18221	−	0.254744i
$77$	−66.7099	−	115.545i	−0.866362	−	1.50058i
$78$	3.68260	−	6.93821i	0.0472129	−	0.0889514i
$79$	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	$0.452589\pi$
$83$	−64.9258	+	112.455i	−0.782239	+	1.35488i	−0.930635	+	0.365950i	$0.880744\pi$
$84$	76.9886	+	88.6846i	0.916531	+	1.05577i
$85$	−0.730125	+	0.421538i	−0.00858970	+	0.00495927i
$86$	−129.375	+	20.3055i	−1.50436	+	0.236111i
$87$	−23.9217	+	31.8863i	−0.274962	+	0.366509i
$88$	108.888	+	6.16472i	1.23736	+	0.0700537i
$89$		−	23.0693i		−	0.259206i	−0.991566	−	0.129603i	$-0.958630\pi$
$89$		−	23.0693i		−	0.259206i	0.991566	−	0.129603i	$-0.0413703\pi$
$90$	−19.5567	−	13.6105i	−0.217297	−	0.151228i
$91$		−	12.8123i		−	0.140795i
$92$	31.6599	+	98.3745i	0.344129	+	1.06929i
$93$	−44.2389	−	103.606i	−0.475687	−	1.11404i
$94$	173.350	−	27.2075i	1.84415	−	0.289441i
$95$	26.3406	−	15.2078i	0.277270	−	0.160082i
$96$	−95.1296	+	12.8983i	−0.990933	+	0.134357i
$97$	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	−0.934098	−	0.357017i	$-0.883794\pi$
$101$	−15.9442	+	27.6161i	−0.157863	+	0.273427i	0.776235	+	0.630444i	$0.217127\pi$
$102$	2.02742	+	3.23928i	0.0198767	+	0.0317576i
$103$	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	$0.531513\pi$
$104$	8.75962	+	5.74095i	0.0842271	+	0.0552014i
$105$	−38.5844	−	4.65417i	−0.367470	−	0.0443254i
$106$	−14.3724	+	11.6053i	−0.135589	+	0.109484i
$107$	80.7131			0.754328			0.377164	−	0.926146i	$-0.376899\pi$
$107$	80.7131			0.754328			0.377164	+	0.926146i	$0.376899\pi$
$108$	−58.4952	+	90.7872i	−0.541622	+	0.840622i
$109$		−	71.8978i		−	0.659613i	−0.944049	−	0.329806i	$-0.893017\pi$
$109$		−	71.8978i		−	0.659613i	0.944049	−	0.329806i	$-0.106983\pi$
$110$	−28.0802	+	22.6739i	−0.255274	+	0.206127i
$111$	18.4393	−	152.867i	0.166120	−	1.37718i
$112$	−127.194	+	91.3295i	−1.13566	+	0.815442i
$113$	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	$0.0446043\pi$
$114$	−73.1431	−	116.863i	−0.641606	−	1.02511i
$115$	−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
$120$	20.4709	−	24.2942i	0.170591	−	0.202452i
$121$	−32.4265	−	56.1643i	−0.267987	−	0.464168i
$122$	−17.1961	+	2.69896i	−0.140952	+	0.0221226i
$123$	−101.341	+	43.2715i	−0.823907	+	0.351801i
$124$	142.985	−	46.0170i	1.15311	−	0.371105i
$125$	63.8659			0.510927
$126$	−14.8511	+	175.533i	−0.117866	+	1.39312i
$127$	26.3523			0.207498			0.103749	−	0.994604i	$-0.466916\pi$
$127$	26.3523			0.207498			0.103749	+	0.994604i	$0.466916\pi$
$128$	−5.44750	−	127.884i	−0.0425586	−	0.999094i
$129$	−157.134	−	117.885i	−1.21809	−	0.913835i
$130$	−3.42397	+	0.537396i	−0.0263382	+	0.00413382i
$131$	41.9643	+	72.6843i	0.320338	+	0.554842i	0.980558	−	0.196230i	$-0.0628701\pi$
$131$	41.9643	+	72.6843i	0.320338	+	0.554842i	−0.660219	+	0.751073i	$0.729537\pi$
$132$	107.245	+	123.537i	0.812459	+	0.935887i
$133$	−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	$0.580017\pi$
$138$	−72.6751	+	136.924i	−0.526631	+	0.992200i
$139$	−16.1347	+	9.31538i	−0.116077	+	0.0670171i	−0.556914	−	0.830570i	$-0.688015\pi$
$139$	−16.1347	+	9.31538i	−0.116077	+	0.0670171i	0.440837	+	0.897587i	$0.354682\pi$
$140$	10.9154	−	50.6561i	0.0779674	−	0.361829i
$141$	210.544	+	157.954i	1.49322	+	1.12024i
$142$	−105.370	−	130.494i	−0.742044	−	0.918972i
$143$		−	17.8475i		−	0.124808i
$144$	−113.355	−	88.8065i	−0.787189	−	0.616712i
$145$	17.5885			0.121300
$146$	138.241	−	111.626i	0.946856	−	0.764559i
$147$	55.1092	+	129.064i	0.374893	+	0.877988i
$148$	200.694	+	43.2458i	1.35604	+	0.292201i
$149$	63.9386	+	110.745i	0.429118	+	0.743255i	0.996795	−	0.0799967i	$-0.0254910\pi$
$149$	63.9386	+	110.745i	0.429118	+	0.743255i	−0.567677	+	0.823252i	$0.692158\pi$
$150$	−4.97001	−	139.398i	−0.0331334	−	0.929322i
$151$	−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
$156$	2.98731	+	15.4233i	0.0191494	+	0.0988671i
$157$	67.9800	−	39.2483i	0.432994	−	0.249989i	−0.267627	−	0.963522i	$-0.586240\pi$
$157$	67.9800	−	39.2483i	0.432994	−	0.249989i	0.700621	+	0.713533i	$0.252906\pi$
$158$	13.6463	+	86.9461i	0.0863690	+	0.550292i
$159$	−27.5100	−	3.31834i	−0.173019	−	0.0208701i
$160$	29.7419	+	30.1607i	0.185887	+	0.188505i
$161$			252.848i			1.57048i
$162$	−158.799	+	32.0428i	−0.980243	+	0.197795i
$163$		−	222.413i		−	1.36450i	−0.731121	−	0.682248i	$-0.761002\pi$
$163$		−	222.413i		−	1.36450i	0.731121	−	0.682248i	$-0.238998\pi$
$164$	−45.0107	−	139.858i	−0.274456	−	0.852795i
$165$	−53.7478	−	6.48323i	−0.325744	−	0.0392923i
$166$	−40.2678	−	256.563i	−0.242577	−	1.54556i
$167$	−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	$0.391438\pi$
$168$	−231.227	−	41.2641i	−1.37635	−	0.245620i
$169$	−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	$0.358221\pi$
$173$	−97.9378	+	169.633i	−0.566115	+	0.980539i	−0.996945	+	0.0781062i	$0.975113\pi$
$174$	−2.84062	−	79.6734i	−0.0163254	−	0.457893i
$175$	−113.759	−	197.037i	−0.650054	−	1.12593i
$176$	−177.181	+	127.221i	−1.00671	+	0.722849i
$177$	34.3578	+	80.4650i	0.194112	+	0.454605i
$178$	28.9858	+	35.8970i	0.162842	+	0.201669i
$179$	−14.6878			−0.0820548			−0.0410274	−	0.999158i	$-0.513063\pi$
$179$	−14.6878			−0.0820548			−0.0410274	+	0.999158i	$0.513063\pi$
$180$	47.5324	−	3.39369i	0.264069	−	0.0188538i
$181$			239.158i			1.32132i	0.750687	+	0.660658i	$0.229723\pi$
$181$			239.158i			1.32132i	−0.750687	+	0.660658i	$0.770277\pi$
$182$	16.0982	+	19.9366i	0.0884519	+	0.109542i
$183$	−20.8858	−	15.6689i	−0.114130	−	0.0856225i
$184$	−172.869	−	113.296i	−0.939503	−	0.615739i
$185$	−58.8372	+	33.9696i	−0.318039	+	0.183620i
$186$	199.015	+	105.632i	1.06998	+	0.567912i
$187$	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	$0.625020\pi$
$192$	131.820	−	139.597i	0.686563	−	0.727070i
$193$	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	$0.818376\pi$
$194$	0.846806	+	5.39534i	0.00436498	+	0.0278110i
$195$	−4.15862	−	3.11988i	−0.0213263	−	0.0159994i
$196$	−178.119	+	57.3243i	−0.908773	+	0.292471i
$197$	87.1848			0.442563			0.221281	−	0.975210i	$-0.428976\pi$
$197$	87.1848			0.442563			0.221281	+	0.975210i	$0.428976\pi$
$198$	−20.6875	+	244.517i	−0.104483	+	1.23493i
$199$	−168.666			−0.847569			−0.423784	−	0.905763i	$-0.639299\pi$
$199$	−168.666			−0.847569			−0.423784	+	0.905763i	$0.639299\pi$
$200$	185.685	+	10.5126i	0.928425	+	0.0525631i
$201$	77.4986	−	33.0912i	0.385565	−	0.164633i
$202$	−9.88878	−	63.0054i	−0.0489544	−	0.311908i
$203$	−65.0195	−	112.617i	−0.320293	−	0.554764i
$204$	−7.22481	−	2.49309i	−0.0354157	−	0.0122210i
$205$	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
$210$	65.8871	−	41.2379i	0.313748	−	0.196371i
$211$	−171.873	+	99.2311i	−0.814566	+	0.470290i	−0.848539	−	0.529133i	$-0.822517\pi$
$211$	−171.873	+	99.2311i	−0.814566	+	0.470290i	0.0339732	+	0.999423i	$0.489184\pi$
$212$	7.78253	−	36.1169i	0.0367100	−	0.170363i
$213$	30.1288	−	249.777i	0.141450	−	1.17266i
$214$	−125.594	+	101.413i	−0.586886	+	0.473894i
$215$			86.6753i			0.403141i
$216$	−23.0496	−	214.767i	−0.106711	−	0.994290i
$217$	367.508			1.69359
$218$	90.3371	+	111.877i	0.414390	+	0.513195i
$219$	264.605	+	31.9174i	1.20824	+	0.145742i
$220$	15.2051	−	70.5636i	0.0691143	−	0.320744i
$221$	0.416905	+	0.722101i	0.00188645	+	0.00326743i
$222$	163.380	+	261.037i	0.735945	+	1.17584i
$223$	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	$-0.608595\pi$
$227$	147.283	−	255.102i	0.648824	−	1.12380i	0.983404	−	0.181428i	$-0.0580721\pi$
$228$	260.649	+	89.9430i	1.14320	+	0.394487i
$229$	194.465	−	112.274i	0.849190	−	0.490280i	−0.0111873	−	0.999937i	$-0.503561\pi$
$229$	194.465	−	112.274i	0.849190	−	0.490280i	0.860378	+	0.509657i	$0.170228\pi$
$230$	67.5711	−	10.6054i	0.293787	−	0.0461103i
$231$	157.178	+	368.107i	0.680425	+	1.59354i
$232$	106.129	+	6.00851i	0.457452	+	0.0258988i
$233$		−	231.203i		−	0.992286i	−0.868241	−	0.496143i	$-0.834749\pi$
$233$		−	231.203i		−	0.992286i	0.868241	−	0.496143i	$-0.165251\pi$
$234$	−13.4610	+	19.3418i	−0.0575255	+	0.0826573i
$235$		−	116.137i		−	0.494198i
$236$	−111.048	+	35.7388i	−0.470544	+	0.151436i
$237$	−79.2243	+	105.601i	−0.334280	+	0.445576i
$238$	−12.3156	+	1.93295i	−0.0517463	+	0.00812165i
$239$	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	$0.0132379\pi$
$240$	−1.32891	+	63.5240i	−0.00553711	+	0.264683i
$241$	−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
$246$	103.322	−	194.664i	0.420007	−	0.791315i
$247$	−15.0406	−	26.0512i	−0.0608933	−	0.105470i
$248$	−164.673	+	251.261i	−0.664005	+	1.01315i
$249$	233.777	−	311.611i	0.938863	−	1.25145i
$250$	−99.3786	+	80.2454i	−0.397514	+	0.320981i
$251$	−143.980			−0.573624			−0.286812	−	0.957987i	$-0.592596\pi$
$251$	−143.980			−0.573624			−0.286812	+	0.957987i	$0.592596\pi$
$252$	−197.442	−	291.798i	−0.783501	−	1.15793i
$253$			352.215i			1.39215i
$254$	−41.0054	+	33.1107i	−0.161439	+	0.130357i
$255$	2.32606	−	0.993204i	0.00912179	−	0.00389492i
$256$	169.159	+	192.149i	0.660776	+	0.750584i
$257$	−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	$0.424982\pi$
$258$	392.626	−	13.9984i	1.52181	−	0.0542575i
$259$	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	$0.629366\pi$
$264$	−322.098	−	57.4807i	−1.22007	−	0.217730i
$265$	6.11319	+	10.5884i	0.0230687	+	0.0399561i
$266$	444.309	−	69.7349i	1.67033	−	0.262161i
$267$	−8.28800	+	68.7099i	−0.0310412	+	0.257341i
$268$	34.4213	+	106.955i	0.128438	+	0.399085i
$269$	−413.485			−1.53712			−0.768560	−	0.639778i	$-0.779026\pi$
$269$	−413.485			−1.53712			−0.768560	+	0.639778i	$0.779026\pi$
$270$	53.3582	+	47.5638i	0.197623	+	0.176162i
$271$	−122.547			−0.452203			−0.226101	−	0.974104i	$-0.572598\pi$
$271$	−122.547			−0.452203			−0.226101	+	0.974104i	$0.572598\pi$
$272$	4.19685	−	9.28614i	0.0154296	−	0.0341402i
$273$	−4.60302	+	38.1604i	−0.0168609	+	0.139782i
$274$	−145.557	+	22.8454i	−0.531231	+	0.0833775i
$275$	−158.466	−	274.472i	−0.576241	−	0.998078i
$276$	−58.9537	−	304.374i	−0.213600	−	1.10280i
$277$	−342.883	−	197.964i	−1.23785	−	0.714671i	−0.269192	−	0.963086i	$-0.586757\pi$
$277$	−342.883	−	197.964i	−1.23785	−	0.714671i	−0.968653	+	0.248416i	$0.920090\pi$
$278$	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	$0.600136\pi$
$282$	−526.081	+	18.7565i	−1.86554	+	0.0665126i
$283$	−244.975	+	141.437i	−0.865637	+	0.499776i	−0.865896	−	0.500224i	$-0.833251\pi$
$283$	−244.975	+	141.437i	−0.865637	+	0.499776i	0.000258855		1.00000i	$0.499918\pi$
$284$	327.923	+	70.6612i	1.15466	+	0.248807i
$285$	−83.9169	+	35.8317i	−0.294445	+	0.125725i
$286$	22.4248	+	27.7716i	0.0784083	+	0.0971035i
$287$		−	359.472i		−	1.25252i
$288$	287.969	−	4.23965i	0.999892	−	0.0147210i
$289$	288.594			0.998596
$290$	−27.3687	+	22.0994i	−0.0943747	+	0.0762048i
$291$	−4.91617	+	6.55298i	−0.0168941	+	0.0225188i
$292$	−74.8561	+	347.390i	−0.256357	+	1.18969i
$293$	22.4604	+	38.9026i	0.0766567	+	0.132773i	0.901805	−	0.432142i	$-0.142242\pi$
$293$	22.4604	+	38.9026i	0.0766567	+	0.132773i	−0.825149	+	0.564915i	$0.808909\pi$
$294$	−247.918	−	131.587i	−0.843257	−	0.447577i
$295$	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
$300$	182.883	+	210.666i	0.609609	+	0.702220i
$301$	554.970	−	320.412i	1.84376	−	1.06449i
$302$	−58.1036	−	370.201i	−0.192396	−	1.22583i
$303$	57.4098	−	76.5240i	0.189471	−	0.252554i
$304$	−151.409	+	335.015i	−0.498057	+	1.10202i
$305$			11.5206i			0.0377726i
$306$	−4.87473	−	10.3763i	−0.0159305	−	0.0339094i
$307$			349.592i			1.13874i	0.822082	+	0.569369i	$0.192812\pi$
$307$			349.592i			1.13874i	−0.822082	+	0.569369i	$0.807188\pi$
$308$	−508.018	+	163.496i	−1.64941	+	0.530830i
$309$	−197.147	−	461.713i	−0.638017	−	1.49422i
$310$	−15.4147	−	98.2130i	−0.0497247	−	0.316816i
$311$	−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	$0.376947\pi$
$312$	−24.0272	−	20.2459i	−0.0770103	−	0.0648908i
$313$	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	$-0.482650\pi$
$317$	282.757	−	489.750i	0.891979	−	1.54495i	0.837500	−	0.546437i	$-0.184016\pi$
$318$	46.9764	−	29.4019i	0.147724	−	0.0924588i
$319$	−90.5718	−	156.875i	−0.283924	−	0.491771i
$320$	−84.1759	−	9.56193i	−0.263050	−	0.0298810i
$321$	−240.397	−	28.9974i	−0.748900	−	0.0903345i
$322$	−317.694	−	393.444i	−0.986629	−	1.22187i
$323$	14.6345			0.0453082
$324$	206.839	−	249.386i	0.638393	−	0.769711i
$325$		−	30.4351i		−	0.0936464i
$326$	279.454	+	346.086i	0.857222	+	1.06161i
$327$	−25.8303	+	214.141i	−0.0789919	+	0.654866i
$328$	245.766	+	161.072i	0.749288	+	0.491074i
$329$	−743.607	+	429.322i	−2.26020	+	1.30493i
$330$	91.7803	−	57.4441i	0.278122	−	0.174073i
$331$	14.1913	+	8.19333i	0.0428739	+	0.0247533i	0.521284	−	0.853383i	$-0.325453\pi$
$331$	14.1913	+	8.19333i	0.0428739	+	0.0247533i	−0.478410	+	0.878137i	$0.658787\pi$
$332$	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
$336$	411.648	−	226.320i	1.22514	−	0.673572i
$337$	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	$0.782457\pi$
$338$	−51.8765	−	330.526i	−0.153481	−	0.977887i
$339$	−491.161	+	209.721i	−1.44885	+	0.618646i
$340$	1.03313	+	3.21015i	0.00303860	+	0.00944162i
$341$	511.937			1.50128
$342$	175.865	+	374.344i	0.514226	+	1.09457i
$343$	21.7349			0.0633670
$344$	−29.6096	+	522.996i	−0.0860744	+	1.52034i
$345$	82.0692	+	61.5700i	0.237882	+	0.178464i
$346$	−60.7423	−	387.013i	−0.175556	−	1.11854i
$347$	272.055	+	471.212i	0.784019	+	1.35796i	0.929583	+	0.368612i	$0.120167\pi$
$347$	272.055	+	471.212i	0.784019	+	1.35796i	−0.145564	+	0.989349i	$0.546500\pi$
$348$	104.527	+	120.407i	0.300365	+	0.345996i
$349$	280.435	+	161.909i	0.803540	+	0.463924i	0.844707	−	0.535228i	$-0.179774\pi$
$349$	280.435	+	161.909i	0.803540	+	0.463924i	−0.0411675	+	0.999152i	$0.513108\pi$
$350$	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	$0.739435\pi$
$354$	−154.564	−	82.0382i	−0.436622	−	0.231746i
$355$	−96.1367	+	55.5046i	−0.270808	+	0.156351i
$356$	−90.2068	−	19.4379i	−0.253390	−	0.0546008i
$357$	−14.9581	−	11.2218i	−0.0418994	−	0.0314337i
$358$	22.8550	−	18.4547i	0.0638407	−	0.0515496i
$359$		−	7.98509i		−	0.0222426i	−0.999938	−	0.0111213i	$-0.996460\pi$
$359$		−	7.98509i		−	0.0222426i	0.999938	−	0.0111213i	$-0.00354009\pi$
$360$	−69.6988	+	65.0036i	−0.193608	+	0.180566i
$361$	−166.969			−0.462517
$362$	−300.494	−	372.142i	−0.830095	−	1.02802i
$363$	76.4015	+	178.930i	0.210472	+	0.492920i
$364$	−50.0994	−	10.7955i	−0.137636	−	0.0296579i
$365$	−58.7997	−	101.844i	−0.161095	−	0.279025i
$366$	52.1868	−	1.86063i	0.142587	−	0.00508369i
$367$	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
$372$	−442.401	+	85.6879i	−1.18925	+	0.230344i
$373$	−382.669	+	220.934i	−1.02592	+	0.592317i	−0.915814	−	0.401603i	$-0.868453\pi$
$373$	−382.669	+	220.934i	−1.02592	+	0.592317i	−0.110109	+	0.993920i	$0.535120\pi$
$374$	−17.1556	+	2.69259i	−0.0458705	+	0.00719944i
$375$	−190.219	−	22.9448i	−0.507250	−	0.0611861i
$376$	39.6740	−	700.765i	0.105516	−	1.86374i
$377$		−	17.3952i		−	0.0461412i
$378$	107.296	−	517.474i	0.283851	−	1.36898i
$379$		−	158.494i		−	0.418190i	−0.977895	−	0.209095i	$-0.932948\pi$
$379$		−	158.494i		−	0.418190i	0.977895	−	0.209095i	$-0.0670518\pi$
$380$	−37.2719	−	115.812i	−0.0980841	−	0.304769i
$381$	−78.4879	−	9.46744i	−0.206005	−	0.0248489i
$382$	−98.4691	+	15.4549i	−0.257773	+	0.0404577i
$383$	−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	$0.461340\pi$
$384$	−29.7193	+	382.848i	−0.0773941	+	0.997001i
$385$	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	−0.999858	−	0.0168663i	$-0.994631\pi$
$389$	−188.790	+	326.994i	−0.485322	+	0.840603i	0.514535	+	0.857469i	$0.327964\pi$
$390$	10.3911	−	0.370476i	0.0266437	−	0.000949937i
$391$	−8.22751	−	14.2505i	−0.0210422	−	0.0364462i
$392$	205.137	−	313.000i	0.523308	−	0.798471i
$393$	−98.8740	−	231.560i	−0.251588	−	0.589211i
$394$	−135.664	+	109.545i	−0.344325	+	0.278032i
$395$	58.2500			0.147468
$396$	−275.036	−	406.473i	−0.694535	−	1.02645i
$397$		−	652.144i		−	1.64268i	−0.570438	−	0.821340i	$-0.693227\pi$
$397$		−	652.144i		−	1.64268i	0.570438	−	0.821340i	$-0.306773\pi$
$398$	262.453	−	211.923i	0.659430	−	0.532471i
$399$	539.641	+	404.849i	1.35248	+	1.01466i
$400$	−302.144	+	216.949i	−0.755360	+	0.542372i
$401$	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	$0.266980\pi$
$402$	−79.0138	+	148.866i	−0.196552	+	0.370313i
$403$	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
$408$	14.3747	−	5.19835i	0.0352320	−	0.0127411i
$409$	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	$0.753392\pi$
$410$	−96.0654	+	15.0776i	−0.234306	+	0.0367746i
$411$	−176.788	−	132.630i	−0.430142	−	0.322701i
$412$	637.202	−	205.071i	1.54661	−	0.497746i
$413$	−285.423			−0.691097
$414$	265.648	−	381.705i	0.641662	−	0.921993i
$415$	−171.885			−0.414182
$416$	29.8293	−	29.4151i	0.0717050	−	0.0707093i
$417$	51.4025	−	21.9484i	0.123267	−	0.0526340i
$418$	618.920	−	97.1403i	1.48067	−	0.232393i
$419$	−7.70600	−	13.3472i	−0.0183914	−	0.0318548i	0.856683	−	0.515843i	$-0.172521\pi$
$419$	−7.70600	−	13.3472i	−0.0183914	−	0.0318548i	−0.875075	+	0.483988i	$0.839188\pi$
$420$	−50.7096	+	146.953i	−0.120737	+	0.349888i
$421$	−86.3264	−	49.8406i	−0.205051	−	0.118386i	0.393958	−	0.919128i	$-0.371105\pi$
$421$	−86.3264	−	49.8406i	−0.205051	−	0.118386i	−0.599009	+	0.800742i	$0.704439\pi$
$422$	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
$426$	266.954	+	426.521i	0.626652	+	1.00122i
$427$	73.7651	−	42.5883i	0.172752	−	0.0997384i
$428$	68.0077	−	315.608i	0.158897	−	0.737403i
$429$	−6.41198	+	53.1572i	−0.0149463	+	0.123909i
$430$	−108.905	−	134.871i	−0.253266	−	0.313654i
$431$			269.164i			0.624509i	0.949998	+	0.312255i	$0.101084\pi$
$431$			269.164i			0.624509i	−0.949998	+	0.312255i	$0.898916\pi$
$432$	305.713	+	305.227i	0.707670	+	0.706543i
$433$	−302.385			−0.698350			−0.349175	−	0.937058i	$-0.613538\pi$
$433$	−302.385			−0.698350			−0.349175	+	0.937058i	$0.613538\pi$
$434$	−571.862	+	461.762i	−1.31765	+	1.06397i
$435$	−52.3859	−	6.31894i	−0.120427	−	0.0145263i
$436$	−281.138	−	60.5800i	−0.644812	−	0.138945i
$437$	296.823	+	514.112i	0.679229	+	1.17646i
$438$	−451.842	+	282.802i	−1.03160	+	0.645666i
$439$	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	−0.845674	−	0.533701i	$-0.820801\pi$
$443$	17.4371	−	30.2020i	0.0393614	−	0.0681760i	0.885035	+	0.465525i	$0.154134\pi$
$444$	−582.212	−	200.906i	−1.31129	−	0.452491i
$445$	26.4458	−	15.2685i	0.0594288	−	0.0343113i
$446$	88.7208	+	565.276i	0.198926	+	1.26744i
$447$	−150.649	−	352.815i	−0.337022	−	0.789295i
$448$	249.949	+	574.314i	0.557922	+	1.28195i
$449$		−	196.732i		−	0.438155i	−0.975707	−	0.219077i	$-0.929695\pi$
$449$		−	196.732i		−	0.438155i	0.975707	−	0.219077i	$-0.0703047\pi$
$450$	−35.2782	+	416.971i	−0.0783959	+	0.926602i
$451$		−	500.742i		−	1.11029i
$452$	−218.151	−	677.843i	−0.482634	−	1.49965i
$453$	337.323	−	449.632i	0.744642	−	0.992566i
$454$	91.3468	+	582.007i	0.201204	+	1.28195i
$455$	14.6876	−	8.47988i	0.0322804	−	0.0186371i
$456$	−518.593	+	187.540i	−1.13726	+	0.411273i
$457$	−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	−0.899192	−	0.437555i	$-0.855845\pi$
$461$	−32.5753	+	56.4220i	−0.0706622	+	0.122390i	0.828530	+	0.559945i	$0.189178\pi$
$462$	−707.091	−	375.304i	−1.53050	−	0.812345i
$463$	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	$0.582301\pi$
$464$	−172.691	+	123.998i	−0.372179	+	0.267236i
$465$	89.4906	−	119.286i	0.192453	−	0.256529i
$466$	290.498	+	359.763i	0.623387	+	0.772023i
$467$	−23.0928			−0.0494492			−0.0247246	−	0.999694i	$-0.507871\pi$
$467$	−23.0928			−0.0494492			−0.0247246	+	0.999694i	$0.507871\pi$
$468$	−3.35640	−	47.0101i	−0.00717179	−	0.100449i
$469$			274.901i			0.586143i
$470$	145.922	+	180.714i	0.310472	+	0.384499i
$471$	−216.573	+	92.4746i	−0.459815	+	0.196337i
$472$	127.892	−	195.140i	0.270959	−	0.413432i
$473$	773.070	−	446.332i	1.63440	−	0.943620i
$474$	−9.40762	−	263.864i	−0.0198473	−	0.556674i
$475$	−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	$0.772798\pi$
$480$	−77.7479	−	100.516i	−0.161975	−	0.209409i
$481$	33.5963	+	58.1905i	0.0698468	+	0.120978i
$482$	−46.8639	−	298.589i	−0.0972280	−	0.619479i
$483$	90.8393	−	753.084i	0.188073	−	1.55918i
$484$	−246.939	+	79.4724i	−0.510204	+	0.164199i
$485$	3.61464			0.00745286
$486$	484.482	−	38.3855i	0.996876	−	0.0789824i
$487$	−14.6465			−0.0300750			−0.0150375	−	0.999887i	$-0.504787\pi$
$487$	−14.6465			−0.0300750			−0.0150375	+	0.999887i	$0.504787\pi$
$488$	−3.93563	+	69.5152i	−0.00806481	+	0.142449i
$489$	−79.9052	+	662.437i	−0.163405	+	1.35468i
$490$	19.2024	+	122.346i	0.0391885	+	0.249686i
$491$	−127.655	−	221.104i	−0.259989	−	0.450314i	0.706250	−	0.707963i	$-0.250386\pi$
$491$	−127.655	−	221.104i	−0.259989	−	0.450314i	−0.966239	+	0.257649i	$0.917052\pi$
$492$	83.8142	+	432.727i	0.170354	+	0.879526i
$493$	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
$498$	27.7602	+	778.615i	0.0557434	+	1.56348i
$499$	229.726	−	132.632i	0.460372	−	0.265796i	−0.251829	−	0.967772i	$-0.581032\pi$
$499$	229.726	−	132.632i	0.460372	−	0.265796i	0.712201	+	0.701976i	$0.247699\pi$
$500$	53.8125	−	249.732i	0.107625	−	0.499463i
$501$	167.281	−	71.4275i	0.333894	−	0.142570i
$502$	224.040	−	180.906i	0.446294	−	0.360370i
$503$		−	740.126i		−	1.47142i	−0.677295	−	0.735711i	$-0.736848\pi$
$503$		−	740.126i		−	1.47142i	0.677295	−	0.735711i	$-0.263152\pi$
$504$	673.865	+	205.973i	1.33703	+	0.408677i
$505$	−42.2108			−0.0835858
$506$	−442.546	−	548.065i	−0.874598	−	1.08313i
$507$	301.171	−	401.444i	0.594027	−	0.791803i
$508$	22.2040	−	103.044i	0.0437087	−	0.202842i
$509$	−313.529	−	543.047i	−0.615970	−	1.06689i	−0.990214	−	0.139560i	$-0.955431\pi$
$509$	−313.529	−	543.047i	−0.615970	−	1.06689i	0.374244	−	0.927330i	$-0.377902\pi$
$510$	−2.37153	+	4.46809i	−0.00465006	+	0.00876095i
$511$	−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
$516$	−593.357	+	515.104i	−1.14992	+	0.998263i
$517$	−1035.84	+	598.043i	−2.00356	+	1.15676i
$518$	−992.454	+	155.767i	−1.91593	+	0.300709i
$519$	352.642	−	470.052i	0.679465	−	0.905688i
$520$	−0.783633	+	13.8414i	−0.00150699	+	0.0266180i
$521$			44.2824i			0.0849950i	0.999097	+	0.0424975i	$0.0135315\pi$
$521$			44.2824i			0.0849950i	−0.999097	+	0.0424975i	$0.986469\pi$
$522$	−20.1633	+	238.321i	−0.0386271	+	0.456553i
$523$			114.110i			0.218184i	0.994032	+	0.109092i	$0.0347943\pi$
$523$			114.110i			0.218184i	−0.994032	+	0.109092i	$0.965206\pi$
$524$	319.572	−	102.848i	0.609871	−	0.196275i
$525$	268.034	+	627.727i	0.510540	+	1.19567i
$526$	−121.508	+	19.0709i	−0.231004	+	0.0362564i
$527$	−20.7127	+	11.9585i	−0.0393031	+	0.0226916i
$528$	573.424	−	315.263i	1.08603	−	0.597088i
$529$	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
$534$	−73.4352	−	117.330i	−0.137519	−	0.219719i
$535$	53.4202	+	92.5266i	0.0998509	+	0.172947i
$536$	−187.946	−	123.178i	−0.350646	−	0.229809i
$537$	43.7463	+	5.27682i	0.0814643	+	0.00982647i
$538$	643.404	−	519.530i	1.19592	−	0.965670i
$539$	−637.730			−1.18317
$540$	−142.790	−	6.96892i	−0.264427	−	0.0129054i
$541$			212.795i			0.393337i	0.980470	+	0.196668i	$0.0630123\pi$
$541$			212.795i			0.393337i	−0.980470	+	0.196668i	$0.936988\pi$
$542$	190.689	−	153.976i	0.351825	−	0.284089i
$543$	85.9212	−	712.312i	0.158234	−	1.31181i
$544$	5.13721	+	19.7229i	0.00944341	+	0.0362553i
$545$	82.4210	−	47.5858i	0.151231	−	0.0873133i
$546$	−40.7847	−	65.1630i	−0.0746972	−	0.119346i
$547$	−385.456	−	222.543i	−0.704672	−	0.406843i	0.104413	−	0.994534i	$-0.466704\pi$
$547$	−385.456	−	222.543i	−0.704672	−	0.406843i	−0.809085	+	0.587691i	$0.800037\pi$
$548$	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
$552$	474.170	+	399.548i	0.859004	+	0.723818i
$553$	−215.333	−	372.967i	−0.389390	−	0.674443i
$554$	782.278	−	122.780i	1.41205	−	0.221624i
$555$	187.445	−	80.0374i	0.337739	−	0.144212i
$556$	22.8306	+	70.9397i	0.0410622	+	0.127589i
$557$	−853.934			−1.53310			−0.766548	−	0.642187i	$-0.778027\pi$
$557$	−853.934			−1.53310			−0.766548	+	0.642187i	$0.778027\pi$
$558$	−554.800	−	386.114i	−0.994265	−	0.691960i
$559$	85.7228			0.153350
$560$	−188.881	−	85.3642i	−0.337287	−	0.152436i
$561$	−20.8365	−	15.6320i	−0.0371417	−	0.0278645i
$562$	−230.402	+	36.1619i	−0.409968	+	0.0643451i
$563$	400.378	+	693.475i	0.711151	+	1.23175i	0.964425	+	0.264355i	$0.0851590\pi$
$563$	400.378	+	693.475i	0.711151	+	1.23175i	−0.253275	+	0.967394i	$0.581508\pi$
$564$	795.042	−	690.189i	1.40965	−	1.22374i
$565$	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	$0.417969\pi$
$570$	85.5575	−	161.195i	0.150101	−	0.282798i
$571$	390.209	−	225.288i	0.683379	−	0.394549i	−0.117748	−	0.993044i	$-0.537567\pi$
$571$	390.209	−	225.288i	0.683379	−	0.394549i	0.801127	+	0.598494i	$0.204234\pi$
$572$	−69.7881	−	15.0380i	−0.122007	−	0.0262903i
$573$	−119.597	−	89.7239i	−0.208720	−	0.156586i
$574$	451.664	+	559.357i	0.786872	+	0.974489i
$575$			600.628i			1.04457i
$576$	−442.767	+	368.420i	−0.768693	+	0.639618i
$577$	−985.430			−1.70785			−0.853925	−	0.520395i	$-0.825785\pi$
$577$	−985.430			−1.70785			−0.853925	+	0.520395i	$0.825785\pi$
$578$	−449.067	+	362.609i	−0.776933	+	0.627351i
$579$	−21.3603	−	50.0252i	−0.0368917	−	0.0863993i
$580$	14.8199	−	68.7756i	0.0255515	−	0.118579i
$581$	635.408	+	1100.56i	1.09365	+	1.89425i
$582$	−0.583779	−	16.3738i	−0.00100306	−	0.0281336i
$583$	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	−0.740951	−	0.671559i	$-0.765625\pi$
$587$	123.922	−	214.640i	0.211111	−	0.365655i	0.952063	+	0.305903i	$0.0989585\pi$
$588$	551.107	−	106.743i	0.937257	−	0.181536i
$589$	747.251	−	431.425i	1.26868	−	0.732471i
$590$	11.9717	+	76.2765i	0.0202910	+	0.129282i
$591$	−259.672	−	31.3224i	−0.439378	−	0.0529991i
$592$	338.203	−	748.324i	0.571289	−	1.26406i
$593$		−	355.619i		−	0.599694i	−0.953987	−	0.299847i	$-0.903064\pi$
$593$		−	355.619i		−	0.599694i	0.953987	−	0.299847i	$-0.0969357\pi$
$594$	149.462	−	720.839i	0.251620	−	1.21353i
$595$			8.25091i			0.0138671i
$596$	486.914	−	156.704i	0.816970	−	0.262926i
$597$	502.357	+	60.5958i	0.841469	+	0.101501i
$598$	−10.4888	−	66.8285i	−0.0175398	−	0.111753i
$599$	−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	$0.962777\pi$
$600$	−549.270	−	98.0210i	−0.915449	−	0.163368i
$601$	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
$606$	6.81722	+	191.209i	0.0112495	+	0.315526i
$607$	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	$0.760467\pi$
$608$	−185.335	−	711.541i	−0.304827	−	1.17030i
$609$	153.195	+	358.779i	0.251552	+	0.589128i
$610$	−14.4753	−	17.9267i	−0.0237300	−	0.0293880i
$611$	−114.860			−0.187987
$612$	20.6228	+	10.0211i	0.0336973	+	0.0163743i
$613$		−	73.3264i		−	0.119619i	−0.998210	−	0.0598094i	$-0.980951\pi$
$613$		−	73.3264i		−	0.119619i	0.998210	−	0.0598094i	$-0.0190493\pi$
$614$	−439.251	−	543.983i	−0.715392	−	0.885966i
$615$	−116.677	−	87.5337i	−0.189719	−	0.142331i
$616$	585.075	−	892.715i	0.949797	−	1.44921i
$617$	−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	$0.349504\pi$
$618$	886.897	+	470.740i	1.43511	+	0.761715i
$619$	945.035	+	545.616i	1.52671	+	0.881448i	0.999497	+	0.0317160i	$0.0100972\pi$
$619$	945.035	+	545.616i	1.52671	+	0.881448i	0.527215	+	0.849732i	$0.323236\pi$
$620$	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
$624$	62.8259	+	1.31430i	0.100683	+	0.00210625i
$625$	−248.328	−	430.116i	−0.397324	−	0.688186i
$626$	30.4499	+	194.008i	0.0486420	+	0.309918i
$627$	751.717	+	563.953i	1.19891	+	0.899446i
$628$	−96.1916	−	298.889i	−0.153171	−	0.475938i
$629$	−32.6892			−0.0519701
$630$	−211.054	+	99.1524i	−0.335006	+	0.157385i
$631$	196.018			0.310646			0.155323	−	0.987864i	$-0.450358\pi$
$631$	196.018			0.310646			0.155323	+	0.987864i	$0.450358\pi$
$632$	351.479	+	19.8991i	0.556138	+	0.0314859i
$633$	547.560	−	233.803i	0.865023	−	0.369357i
$634$	175.370	+	1117.35i	0.276608	+	1.76238i
$635$	17.4413	+	30.2093i	0.0274667	+	0.0475737i
$636$	−36.1551	+	104.775i	−0.0568476	+	0.164741i
$637$	−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	$0.759116\pi$
$642$	410.504	−	256.929i	0.639414	−	0.400201i
$643$	−209.243	+	120.807i	−0.325417	+	0.187880i	−0.653805	−	0.756663i	$-0.726828\pi$
$643$	−209.243	+	120.807i	−0.325417	+	0.187880i	0.328387	+	0.944543i	$0.393495\pi$
$644$	988.697	+	213.046i	1.53524	+	0.330816i
$645$	31.1394	−	258.155i	0.0482781	−	0.400240i
$646$	−22.7721	+	18.3878i	−0.0352509	+	0.0284641i
$647$		−	17.7113i		−	0.0273745i	−0.999906	−	0.0136872i	$-0.995643\pi$
$647$		−	17.7113i		−	0.0273745i	0.999906	−	0.0136872i	$-0.00435692\pi$
$648$	−8.50694	+	647.944i	−0.0131280	+	0.999914i
$649$	−397.593			−0.612623
$650$	38.2406	+	47.3585i	0.0588317	+	0.0728592i
$651$	−1094.59	−	132.033i	−1.68140	−	0.202815i
$652$	−869.690	−	187.402i	−1.33388	−	0.287426i
$653$	−572.158	−	991.007i	−0.876200	−	1.51762i	−0.855479	−	0.517837i	$-0.826737\pi$
$653$	−572.158	−	991.007i	−0.876200	−	1.51762i	−0.0207205	−	0.999785i	$-0.506596\pi$
$654$	−228.868	−	365.669i	−0.349951	−	0.559127i
$655$	−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	−0.891200	−	0.453611i	$-0.850136\pi$
$659$	−34.7697	+	60.2229i	−0.0527613	+	0.0913853i	0.838438	+	0.544996i	$0.183469\pi$
$660$	−70.6382	+	204.705i	−0.107028	+	0.310159i
$661$	−817.965	+	472.253i	−1.23747	+	0.714452i	−0.968576	−	0.248719i	$-0.919990\pi$
$661$	−817.965	+	472.253i	−1.23747	+	0.714452i	−0.268891	+	0.963171i	$0.586657\pi$
$662$	−32.3770	+	5.08161i	−0.0489078	+	0.00767615i
$663$	−0.982289	−	2.30049i	−0.00148158	−	0.00346982i
$664$	−1037.15	−	58.7187i	−1.56198	−	0.0884318i
$665$		−	297.667i		−	0.447620i
$666$	−392.831	−	836.172i	−0.589836	−	1.25551i
$667$			343.290i			0.514678i
$668$	74.2984	+	230.862i	0.111225	+	0.345602i
$669$	−515.073	+	686.563i	−0.769915	+	1.02625i
$670$	73.4646	−	11.5304i	0.109649	−	0.0172095i
$671$	102.754	−	59.3253i	0.153136	−	0.0884132i
$672$	−356.182	+	869.388i	−0.530033	+	1.29373i
$673$	−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	−0.753739	−	0.657174i	$-0.771752\pi$
$677$	130.160	−	225.444i	0.192260	−	0.333004i	0.945999	+	0.324170i	$0.105085\pi$
$678$	500.763	−	943.464i	0.738589	−	1.39154i
$679$	−13.3622	−	23.1440i	−0.0196793	−	0.0340855i
$680$	−5.64104	−	3.69707i	−0.00829565	−	0.00543687i
$681$	−530.318	+	706.884i	−0.778735	+	1.03801i
$682$	−796.600	+	643.231i	−1.16803	+	0.943155i
$683$	1054.30			1.54363			0.771816	−	0.635846i	$-0.219349\pi$
$683$	1054.30			1.54363			0.771816	+	0.635846i	$0.219349\pi$
$684$	−744.005	−	361.529i	−1.08773	−	0.528551i
$685$			97.5170i			0.142361i
$686$	−33.8206	+	27.3091i	−0.0493011	+	0.0398092i
$687$	−619.531	+	264.534i	−0.901792	+	0.385057i
$688$	−611.053	−	851.012i	−0.888159	−	1.23694i
$689$	10.4720	−	6.04601i	0.0151988	−	0.00877505i
$690$	−205.064	+	7.31123i	−0.297195	+	0.0105960i
$691$	−520.398	−	300.452i	−0.753109	−	0.434808i	0.0737072	−	0.997280i	$-0.476517\pi$
$691$	−520.398	−	300.452i	−0.753109	−	0.434808i	−0.826816	+	0.562472i	$0.809850\pi$
$692$	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
$696$	−313.936	−	56.0242i	−0.451058	−	0.0804945i
$697$	11.6970	+	20.2598i	0.0167819	+	0.0290671i
$698$	−639.805	+	100.418i	−0.916627	+	0.143866i
$699$	−83.0629	+	688.616i	−0.118831	+	0.985145i
$700$	−866.316	+	278.807i	−1.23759	+	0.398296i
$701$	759.963			1.08411			0.542056	−	0.840342i	$-0.317646\pi$
$701$	759.963			1.08411			0.542056	+	0.840342i	$0.317646\pi$
$702$	47.0411	−	52.7718i	0.0670101	−	0.0751735i
$703$	1179.32			1.67756
$704$	348.177	+	800.016i	0.494570	+	1.13639i
$705$	−41.7238	+	345.902i	−0.0591827	+	0.490642i
$706$	316.123	−	49.6159i	0.447766	−	0.0702774i
$707$	156.041	+	270.270i	0.220708	+	0.382277i
$708$	343.588	−	66.5490i	0.485293	−	0.0939957i
$709$	−336.476	−	194.264i	−0.474578	−	0.273998i	0.243576	−	0.969882i	$-0.421679\pi$
$709$	−336.476	−	194.264i	−0.474578	−	0.273998i	−0.718154	+	0.695884i	$0.755013\pi$
$710$	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
$714$	37.3754	−	1.33256i	0.0523465	−	0.00186633i
$715$	20.4597	−	11.8124i	0.0286150	−	0.0165209i
$716$	−12.3757	+	57.4330i	−0.0172846	+	0.0802137i
$717$	−1113.72	+	475.547i	−1.55330	+	0.663246i
$718$	10.0330	+	12.4252i	0.0139735	+	0.0173053i
$719$			994.711i			1.38346i	0.722154	+	0.691732i	$0.243152\pi$
$719$			994.711i			1.38346i	−0.722154	+	0.691732i	$0.756848\pi$
$720$	26.7800	−	188.723i	0.0371944	−	0.262115i
$721$	1637.77			2.27153
$722$	259.812	−	209.790i	0.359850	−	0.290568i
$723$	272.071	−	362.655i	0.376308	−	0.501597i
$724$	935.169	+	201.511i	1.29167	+	0.278331i
$725$	−154.451	−	267.517i	−0.213036	−	0.368988i
$726$	−343.704	−	182.428i	−0.473422	−	0.251279i
$727$	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
$732$	−78.8674	+	68.4661i	−0.107742	+	0.0935330i
$733$	978.173	−	564.749i	1.33448	−	0.770462i	0.348497	−	0.937310i	$-0.386692\pi$
$733$	978.173	−	564.749i	1.33448	−	0.770462i	0.985983	+	0.166848i	$0.0533589\pi$
$734$	64.1938	+	409.005i	0.0874575	+	0.557227i
$735$	−111.480	+	148.597i	−0.151674	+	0.202172i
$736$	−588.672	+	580.498i	−0.799827	+	0.788720i
$737$			382.935i			0.519586i
$738$	−377.671	+	542.668i	−0.511749	+	0.735322i
$739$			227.082i			0.307282i	0.988127	+	0.153641i	$0.0491000\pi$
$739$			227.082i			0.307282i	−0.988127	+	0.153641i	$0.950900\pi$
$740$	83.2544	+	258.690i	0.112506	+	0.349581i
$741$	35.4379	+	82.9946i	0.0478245	+	0.112004i
$742$	28.0319	+	178.603i	0.0377788	+	0.240704i
$743$	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	$0.275285\pi$
$744$	580.734	−	689.196i	0.780556	−	0.926339i
$745$	−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
$750$	324.820	−	203.300i	0.433093	−	0.271067i
$751$	−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	$0.884158\pi$
$752$	818.753	+	1140.28i	1.08877	+	1.51632i
$753$	428.831	+	51.7268i	0.569496	+	0.0686944i
$754$	21.8565	+	27.0679i	0.0289874	+	0.0358990i
$755$	−248.018			−0.328501
$756$	483.231	+	940.029i	0.639195	+	1.24343i
$757$		−	716.991i		−	0.947148i	−0.880754	−	0.473574i	$-0.842964\pi$
$757$		−	716.991i		−	0.947148i	0.880754	−	0.473574i	$-0.157036\pi$
$758$	199.142	+	246.625i	0.262721	+	0.325363i
$759$	126.539	−	1049.04i	0.166717	−	1.38214i
$760$	203.511	+	133.379i	0.267778	+	0.175499i
$761$	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	$0.216188\pi$
$762$	134.027	−	83.8855i	0.175888	−	0.110086i
$763$	−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
$768$	−434.791	−	633.072i	−0.566134	−	0.824313i
$769$	−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	$-0.367689\pi$
$770$	54.7675	+	348.945i	0.0711266	+	0.453176i
$771$	402.694	−	171.947i	0.522301	−	0.223018i
$772$	69.0390	−	22.2189i	0.0894288	−	0.0287809i
$773$	984.863			1.27408			0.637040	−	0.770831i	$-0.280159\pi$
$773$	984.863			1.27408			0.637040	+	0.770831i	$0.280159\pi$
$774$	−1174.43	−	99.3637i	−1.51735	−	0.128377i
$775$	872.999			1.12645
$776$	21.8106	+	1.23482i	0.0281065	+	0.00159126i
$777$	−1205.40	−	904.313i	−1.55135	−	1.16385i
$778$	−117.090	−	746.029i	−0.150502	−	0.958906i
$779$	−421.991	−	730.911i	−0.541709	−	0.938268i
$780$	−15.7035	+	13.6325i	−0.0201327	+	0.0174775i
$781$	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
$786$	444.800	+	236.087i	0.565904	+	0.300366i
$787$	1007.34	−	581.590i	1.27998	−	0.738997i	0.303135	−	0.952948i	$-0.401967\pi$
$787$	1007.34	−	581.590i	1.27998	−	0.738997i	0.976844	+	0.213951i	$0.0686333\pi$
$788$	73.4607	−	340.914i	0.0932242	−	0.432633i
$789$	−147.579	−	110.717i	−0.187046	−	0.140326i
$790$	−90.6399	+	73.1891i	−0.114734	+	0.0926445i
$791$		−	1742.23i		−	2.20257i
$792$	938.690	+	286.920i	1.18521	+	0.362272i
$793$	11.3940			0.0143683
$794$	819.397	+	1014.77i	1.03199	+	1.27805i
$795$	−14.4036	−	33.7327i	−0.0181177	−	0.0424311i
$796$	−142.116	+	659.527i	−0.178537	+	0.828551i
$797$	−417.748	−	723.560i	−0.524150	−	0.907855i	−0.999605	−	0.0281145i	$-0.991050\pi$
$797$	−417.748	−	723.560i	−0.524150	−	0.907855i	0.475455	−	0.879740i	$-0.342284\pi$
$798$	−1348.39	+	48.0745i	−1.68971	+	0.0602438i
$799$	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
$804$	−64.0956	−	330.921i	−0.0797209	−	0.411594i
$805$	−289.855	+	167.348i	−0.360069	+	0.207886i
$806$	−97.1337	+	15.2453i	−0.120513	+	0.0189147i
$807$	1231.53	+	148.551i	1.52606	+	0.184078i
$808$	−254.699	−	14.4199i	−0.315221	−	0.0178464i
$809$			1227.66i			1.51750i	0.651380	+	0.758752i	$0.274190\pi$
$809$			1227.66i			1.51750i	−0.651380	+	0.758752i	$0.725810\pi$
$810$	−141.835	−	160.834i	−0.175104	−	0.198561i
$811$			1196.45i			1.47528i	0.675195	+	0.737639i	$0.264060\pi$
$811$			1196.45i			1.47528i	−0.675195	+	0.737639i	$0.735940\pi$
$812$	−495.145	+	159.353i	−0.609785	+	0.196247i
$813$	364.995	+	44.0268i	0.448949	+	0.0541535i
$814$	−1382.48	+	216.983i	−1.69838	+	0.266563i
$815$	254.966	−	147.205i	0.312842	−	0.180619i
$816$	−15.8361	+	26.1502i	−0.0194070	+	0.0320468i
$817$	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	−0.937134	−	0.348970i	$-0.886531\pi$
$821$	−136.573	+	236.552i	−0.166350	+	0.288126i	0.770784	+	0.637096i	$0.219865\pi$
$822$	441.737	−	15.7494i	0.537393	−	0.0191598i
$823$	−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	$-0.401562\pi$
$824$	−733.854	+	1119.72i	−0.890600	+	1.35889i
$825$	373.369	+	874.420i	0.452569	+	1.05990i
$826$	444.133	−	358.624i	0.537691	−	0.434170i
$827$	720.992			0.871816			0.435908	−	0.899991i	$-0.356427\pi$
$827$	720.992			0.871816			0.435908	+	0.899991i	$0.356427\pi$
$828$	66.2375	+	927.730i	0.0799970	+	1.12045i
$829$		−	635.956i		−	0.767137i	−0.923513	−	0.383568i	$-0.874695\pi$
$829$		−	635.956i		−	0.767137i	0.923513	−	0.383568i	$-0.125305\pi$
$830$	267.462	−	215.968i	0.322244	−	0.260203i
$831$	950.126	+	712.803i	1.14335	+	0.857766i
$832$	−9.45685	+	83.2508i	−0.0113664	+	0.100061i
$833$	25.8023	−	14.8969i	0.0309751	−	0.0178835i
$834$	−52.4074	+	98.7382i	−0.0628386	+	0.118391i
$835$	−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	$0.838960\pi$
$840$	−105.735	−	292.381i	−0.125875	−	0.348073i
$841$	332.223	+	575.428i	0.395034	+	0.684218i
$842$	196.951	−	30.9118i	0.233909	−	0.0367123i
$843$	−279.838	−	209.940i	−0.331955	−	0.249039i
$844$	243.200	+	755.678i	0.288152	+	0.895354i
$845$	−221.438			−0.262056
$846$	1573.62	+	133.138i	1.86008	+	0.157373i
$847$	−634.695			−0.749345
$848$	−134.669	−	60.8632i	−0.158808	−	0.0717727i
$849$	780.450	−	333.245i	0.919258	−	0.392515i
$850$	−29.2552	+	4.59164i	−0.0344178	+	0.00540192i
$851$	−663.014	−	1148.37i	−0.779100	−	1.34944i
$852$	−951.302	−	328.269i	−1.11655	−	0.385293i
$853$	62.5316	+	36.1027i	0.0733079	+	0.0423243i	0.536206	−	0.844087i	$-0.319857\pi$
$853$	62.5316	+	36.1027i	0.0733079	+	0.0423243i	−0.462898	+	0.886412i	$0.653190\pi$
$854$	−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	$0.881750\pi$
$858$	−56.8128	−	90.7716i	−0.0662154	−	0.105794i
$859$	930.598	−	537.281i	1.08335	−	0.625472i	0.151552	−	0.988449i	$-0.451573\pi$
$859$	930.598	−	537.281i	1.08335	−	0.625472i	0.931798	+	0.362977i	$0.118240\pi$
$860$	338.922	+	73.0314i	0.394095	+	0.0849202i
$861$	−129.146	+	1070.66i	−0.149995	+	1.24350i
$862$	−338.195	−	418.832i	−0.392337	−	0.485884i
$863$			1519.81i			1.76107i	0.473979	+	0.880536i	$0.342817\pi$
$863$			1519.81i			1.76107i	−0.473979	+	0.880536i	$0.657183\pi$
$864$	−859.212	−	90.8296i	−0.994459	−	0.105127i
$865$	−259.282			−0.299748
$866$	470.527	−	379.937i	0.543334	−	0.438726i
$867$	−859.552	−	103.682i	−0.991410	−	0.119587i
$868$	309.657	−	1437.05i	0.356748	−	1.65559i
$869$	−299.957	−	519.541i	−0.345175	−	0.597860i
$870$	89.4546	−	55.9885i	0.102821	−	0.0643546i
$871$	−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
$876$	347.757	−	1007.78i	0.396983	−	1.15043i
$877$	−1336.39	+	771.565i	−1.52382	+	0.879778i	−0.524217	+	0.851585i	$0.675642\pi$
$877$	−1336.39	+	771.565i	−1.52382	+	0.879778i	−0.999602	+	0.0281931i	$0.991025\pi$
$878$	63.5344	+	404.803i	0.0723626	+	0.461051i
$879$	−52.9200	−	123.937i	−0.0602047	−	0.140998i
$880$	−263.110	−	118.912i	−0.298988	−	0.135127i
$881$			16.6706i			0.0189223i	0.999955	+	0.00946117i	$0.00301163\pi$
$881$			16.6706i			0.0189223i	−0.999955	+	0.00946117i	$0.996988\pi$
$882$	691.125	+	480.990i	0.783589	+	0.545340i
$883$			828.778i			0.938594i	0.883040	+	0.469297i	$0.155493\pi$
$883$			828.778i			0.938594i	−0.883040	+	0.469297i	$0.844507\pi$
$884$	3.17487	−	1.02177i	0.00359149	−	0.00115585i
$885$	−69.5023	+	92.6426i	−0.0785337	+	0.104681i
$886$	10.8147	+	68.9049i	0.0122062	+	0.0777708i
$887$	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	$0.265367\pi$
$888$	1158.38	−	418.910i	1.30448	−	0.471745i
$889$	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
$894$	677.717	+	359.713i	0.758073	+	0.402363i
$895$	−9.72118	−	16.8376i	−0.0108616	−	0.0188129i
$896$	−1110.54	−	579.610i	−1.23944	−	0.646886i
$897$	60.8933	−	81.1673i	0.0678855	−	0.0904875i
$898$	247.187	+	306.124i	0.275263	+	0.340896i
$899$	498.965			0.555022
$900$	−469.015	−	693.153i	−0.521128	−	0.770170i
$901$			5.88276i			0.00652915i
$902$	629.166	+	779.180i	0.697523	+	0.863836i
$903$	−1768.04	+	754.938i	−1.95797	+	0.836033i
$904$	1191.14	+	780.659i	1.31763	+	0.863561i
$905$	−274.162	+	158.288i	−0.302942	+	0.174904i
$906$	40.0560	+	1123.49i	0.0442119	+	1.24005i
$907$	−196.054	−	113.192i	−0.216156	−	0.124798i	0.388013	−	0.921654i	$-0.373162\pi$
$907$	−196.054	−	113.192i	−0.216156	−	0.124798i	−0.604169	+	0.796856i	$0.706495\pi$
$908$	−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	$0.738614\pi$
$912$	571.318	−	943.417i	0.626446	−	1.03445i
$913$	885.120	+	1533.07i	0.969464	+	1.67916i
$914$	−55.8831	−	356.053i	−0.0611412	−	0.389555i
$915$	4.13896	−	34.3132i	0.00452346	−	0.0375008i
$916$	−275.167	−	855.006i	−0.300401	−	0.933412i
$917$	821.383			0.895728
$918$	10.7911	+	32.6561i	0.0117550	+	0.0355731i
$919$	−504.252			−0.548696			−0.274348	−	0.961630i	$-0.588462\pi$
$919$	−504.252			−0.548696			−0.274348	+	0.961630i	$0.588462\pi$
$920$	15.4648	−	273.156i	0.0168095	−	0.296908i
$921$	125.596	−	1041.23i	0.136369	−	1.13054i
$922$	−20.2036	−	128.725i	−0.0219128	−	0.139615i
$923$	54.8946	+	95.0802i	0.0594741	+	0.103012i
$924$	1571.83	−	304.444i	1.70111	−	0.329485i
$925$	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	$0.689974\pi$
$930$	10.6267	+	298.057i	0.0114266	+	0.320491i
$931$	−930.865	+	537.435i	−0.999855	+	0.577267i
$932$	−904.060	−	194.808i	−0.970021	−	0.209021i
$933$	234.397	−	100.086i	0.251230	−	0.107273i
$934$	35.9336	−	29.0153i	0.0384728	−	0.0310656i
$935$			11.4935i			0.0122925i
$936$	64.2893	+	68.9328i	0.0686851	+	0.0736462i
$937$	−602.591			−0.643107			−0.321554	−	0.946891i	$-0.604205\pi$
$937$	−602.591			−0.643107			−0.321554	+	0.946891i	$0.604205\pi$
$938$	−345.404	−	427.760i	−0.368234	−	0.456034i
$939$	−176.778	+	235.635i	−0.188262	+	0.250943i
$940$	−454.123	−	97.8551i	−0.483110	−	0.104101i
$941$	417.475	+	723.088i	0.443651	+	0.768425i	0.997957	−	0.0638872i	$-0.0203498\pi$
$941$	417.475	+	723.088i	0.443651	+	0.768425i	−0.554307	+	0.832313i	$0.687016\pi$
$942$	220.807	−	416.012i	0.234402	−	0.441626i
$943$	−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	$-0.552172\pi$
$947$	731.873	−	1267.64i	0.772833	−	1.33859i	0.936004	−	0.351989i	$-0.114494\pi$
$948$	346.175	+	398.765i	0.365163	+	0.420638i
$949$	−100.725	+	58.1535i	−0.106138	+	0.0612787i
$950$	1055.44	−	165.652i	1.11098	−	0.174371i
$951$	−1018.12	+	1357.09i	−1.07058	+	1.42701i
$952$	−2.81864	+	49.7858i	−0.00296075	+	0.0522960i
$953$		−	335.327i		−	0.351864i	−0.984402	−	0.175932i	$-0.943706\pi$
$953$		−	335.327i		−	0.351864i	0.984402	−	0.175932i	$-0.0562939\pi$
$954$	−150.478	+	70.6940i	−0.157734	+	0.0741027i
$955$			65.9699i			0.0690785i
$956$	−494.661	−	1537.02i	−0.517428	−	1.60777i
$957$	213.400	+	499.777i	0.222989	+	0.522233i
$958$	619.481	−	97.2284i	0.646640	−	0.101491i
$959$	624.388	−	360.491i	0.651082	−	0.375903i
$960$	247.275	+	58.7208i	0.257578	+	0.0611675i
$961$	−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
$966$	804.874	+	1285.97i	0.833203	+	1.33123i
$967$	−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	$0.980499\pi$
$968$	284.394	−	433.933i	0.293796	−	0.448278i
$969$	−43.5877	−	5.25767i	−0.0449821	−	0.00542588i
$970$	−5.62456	+	4.54167i	−0.00579852	+	0.00468214i
$971$	−1837.35			−1.89223			−0.946114	−	0.323835i	$-0.895028\pi$
$971$	−1837.35			−1.89223			−0.946114	+	0.323835i	$0.895028\pi$
$972$	−705.648	+	668.465i	−0.725975	+	0.687721i
$973$			182.333i			0.187393i
$974$	22.7907	−	18.4028i	0.0233991	−	0.0188941i
$975$	−10.9343	+	90.6481i	−0.0112146	+	0.0929724i
$976$	−81.2195	−	113.114i	−0.0832167	−	0.115896i
$977$	−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	$0.575970\pi$
$978$	−707.993	−	1131.18i	−0.723919	−	1.15663i
$979$	−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	$0.359018\pi$
$984$	−674.125	−	568.035i	−0.685087	−	0.577271i
$985$	57.7036	+	99.9455i	0.0585823	+	0.101468i
$986$	−16.7209	+	2.62436i	−0.0169583	+	0.00266162i
$987$	2369.01	−	1011.54i	2.40021	−	1.02487i
$988$	−114.540	+	36.8623i	−0.115931	+	0.0373101i
$989$	−1691.71			−1.71053
$990$	−293.997	+	138.119i	−0.296967	+	0.139514i
$991$	−1031.59			−1.04096			−0.520478	−	0.853875i	$-0.674246\pi$
$991$	−1031.59			−1.04096			−0.520478	+	0.853875i	$0.674246\pi$
$992$	843.741	+	855.622i	0.850545	+	0.862522i
$993$	−39.3239	−	29.5015i	−0.0396011	−	0.0297095i
$994$	−1621.62	+	254.515i	−1.63141	+	0.256051i
$995$	−111.632	−	193.353i	−0.112193	−	0.194324i
$996$	−1021.50	−	1176.68i	−1.02560	−	1.18141i
$997$	768.361	+	443.613i	0.770673	+	0.444948i	0.833114	−	0.553101i	$-0.186555\pi$
$997$	768.361	+	443.613i	0.770673	+	0.444948i	−0.0624419	+	0.998049i	$0.519889\pi$
$998$	−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.29.5	yes	44
3.2	odd	2		216.3.j.a.197.18		44
4.3	odd	2		288.3.n.a.209.21		44
8.3	odd	2		288.3.n.a.209.2		44
8.5	even	2	inner	72.3.j.a.29.13	yes	44
9.2	odd	6		648.3.h.a.485.7		44
9.4	even	3		216.3.j.a.125.10		44
9.5	odd	6	inner	72.3.j.a.5.13	yes	44
9.7	even	3		648.3.h.a.485.38		44
12.11	even	2		864.3.n.a.305.10		44
24.5	odd	2		216.3.j.a.197.10		44
24.11	even	2		864.3.n.a.305.13		44
36.7	odd	6		2592.3.h.a.1457.19		44
36.11	even	6		2592.3.h.a.1457.26		44
36.23	even	6		288.3.n.a.113.2		44
36.31	odd	6		864.3.n.a.17.13		44
72.5	odd	6	inner	72.3.j.a.5.5	✓	44
72.11	even	6		2592.3.h.a.1457.20		44
72.13	even	6		216.3.j.a.125.18		44
72.29	odd	6		648.3.h.a.485.37		44
72.43	odd	6		2592.3.h.a.1457.25		44
72.59	even	6		288.3.n.a.113.21		44
72.61	even	6		648.3.h.a.485.8		44
72.67	odd	6		864.3.n.a.17.10		44

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

\(f(q)\)	\(=\)	\(q+(-1.55605 + 1.25647i) q^{2} +(-2.97841 - 0.359265i) q^{3} +(0.842586 - 3.91025i) q^{4} +(0.661853 + 1.14636i) q^{5} +(5.08596 - 3.18324i) q^{6} +(4.89334 - 8.47551i) q^{7} +(3.60199 + 7.14323i) q^{8} +(8.74186 + 2.14008i) q^{9} +O(q^{10})\)	\(q+(-1.55605 + 1.25647i) q^{2} +(-2.97841 - 0.359265i) q^{3} +(0.842586 - 3.91025i) q^{4} +(0.661853 + 1.14636i) q^{5} +(5.08596 - 3.18324i) 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} +(-3.91438 + 11.3436i) q^{12} +(1.13377 - 0.654580i) q^{13} +(3.03491 + 19.3366i) q^{14} +(-1.55942 - 3.65212i) q^{15} +(-14.5801 - 6.58944i) q^{16} +0.636905i q^{17} +(-16.2917 + 7.65378i) q^{18} -22.9776i q^{19} +(5.04023 - 1.62210i) q^{20} +(-17.6193 + 23.4856i) q^{21} +(4.22761 + 26.9358i) q^{22} +(-22.3745 + 12.9179i) q^{23} +(-8.16189 - 22.5695i) 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} +(7.01531 + 3.72352i) q^{30} +(18.7759 + 32.5209i) q^{31} +(30.9668 - 8.06590i) q^{32} +(-24.5436 + 32.7152i) q^{33} +(-0.800250 - 0.991057i) q^{34} +12.9547 q^{35} +(15.7340 - 32.3796i) q^{36} +51.3250i q^{37} +(28.8705 + 35.7543i) q^{38} +(-3.61198 + 1.54228i) q^{39} +(-5.80474 + 8.85696i) q^{40} +(31.8097 - 18.3654i) q^{41} +(-2.09224 - 58.6828i) 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} +(41.0582 + 24.8642i) q^{48} +(-23.3896 - 40.5119i) q^{49} +(7.20929 + 45.9333i) q^{50} +(0.228818 - 1.89697i) q^{51} +(-1.60427 - 4.98484i) q^{52} +9.23648 q^{53} +(51.2731 - 16.9431i) q^{54} +18.0458 q^{55} +(78.1683 + 4.42552i) q^{56} +(-8.25503 + 68.4366i) q^{57} +(4.12049 + 26.2533i) q^{58} +(-14.5822 - 25.2571i) q^{59} +(-15.5947 + 3.02050i) 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} +(-2.91447 - 81.7448i) q^{66} +(-24.3260 + 14.0446i) q^{67} +(2.49046 + 0.536647i) q^{68} +(71.2815 - 30.4366i) q^{69} +(-20.1582 + 16.2771i) q^{70} +83.8624i q^{71} +(16.2010 + 70.1536i) q^{72} -88.8409 q^{73} +(-64.4882 - 79.8644i) q^{74} +(-41.8539 + 55.7888i) q^{75} +(-89.8480 - 19.3606i) q^{76} +(-66.7099 - 115.545i) q^{77} +(3.68260 - 6.93821i) 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} +(76.9886 + 88.6846i) q^{84} +(-0.730125 + 0.421538i) q^{85} +(-129.375 + 20.3055i) q^{86} +(-23.9217 + 31.8863i) q^{87} +(108.888 + 6.16472i) q^{88} -23.0693i q^{89} +(-19.5567 - 13.6105i) q^{90} -12.8123i q^{91} +(31.6599 + 98.3745i) q^{92} +(-44.2389 - 103.606i) q^{93} +(173.350 - 27.2075i) q^{94} +(26.3406 - 15.2078i) q^{95} +(-95.1296 + 12.8983i) 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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