LMFDB - Embedded newform 140.3.x.a.103.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,3,Mod(3,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("140.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	140.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.81472370104$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.4
Character	$\chi$	$=$	140.103
Dual form			140.3.x.a.87.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88565 + 0.666564i) q^{2} +(-0.389805 + 1.45477i) q^{3} +(3.11138 - 2.51382i) q^{4} +(-3.73805 - 3.32069i) q^{5} +(-0.234662 - 3.00303i) q^{6} +(5.02867 + 4.86954i) q^{7} +(-4.19137 + 6.81413i) q^{8} +(5.82981 + 3.36584i) q^{9} +O(q^{10})$	\(q+(-1.88565 + 0.666564i) q^{2} +(-0.389805 + 1.45477i) q^{3} +(3.11138 - 2.51382i) q^{4} +(-3.73805 - 3.32069i) q^{5} +(-0.234662 - 3.00303i) q^{6} +(5.02867 + 4.86954i) q^{7} +(-4.19137 + 6.81413i) q^{8} +(5.82981 + 3.36584i) q^{9} +(9.26213 + 3.77002i) q^{10} +(-8.96422 + 5.17549i) q^{11} +(2.44420 + 5.50626i) q^{12} +(-2.72924 + 2.72924i) q^{13} +(-12.7282 - 5.83034i) q^{14} +(6.28796 - 4.14359i) q^{15} +(3.36142 - 15.6429i) q^{16} +(-8.39248 + 31.3211i) q^{17} +(-13.2366 - 2.46087i) q^{18} +(-16.5359 - 9.54701i) q^{19} +(-19.9781 - 0.935145i) q^{20} +(-9.04428 + 5.41740i) q^{21} +(13.4536 - 15.7344i) q^{22} +(2.49054 + 9.29482i) q^{23} +(-8.27920 - 8.75368i) q^{24} +(2.94606 + 24.8258i) q^{25} +(3.32719 - 6.96562i) q^{26} +(-16.7537 + 16.7537i) q^{27} +(27.8873 + 2.50983i) q^{28} +4.14768i q^{29} +(-9.09494 + 12.0047i) q^{30} +(13.7219 + 23.7671i) q^{31} +(4.08854 + 31.7377i) q^{32} +(-4.03487 - 15.0583i) q^{33} +(-5.05225 - 64.6550i) q^{34} +(-2.62721 - 34.9013i) q^{35} +(26.5999 - 4.18267i) q^{36} +(9.87753 + 36.8634i) q^{37} +(37.5447 + 6.98012i) q^{38} +(-2.90655 - 5.03430i) q^{39} +(38.2952 - 11.5533i) q^{40} -42.9640i q^{41} +(13.4433 - 16.2439i) q^{42} +(51.7850 - 51.7850i) q^{43} +(-14.8809 + 38.6374i) q^{44} +(-10.6152 - 31.9407i) q^{45} +(-10.8919 - 15.8667i) q^{46} +(-9.58506 - 35.7719i) q^{47} +(21.4466 + 10.9878i) q^{48} +(1.57512 + 48.9747i) q^{49} +(-22.1033 - 44.8491i) q^{50} +(-42.2937 - 24.4183i) q^{51} +(-1.63089 + 15.3525i) q^{52} +(7.62542 - 28.4585i) q^{53} +(20.4243 - 42.7592i) q^{54} +(50.6949 + 10.4211i) q^{55} +(-54.2587 + 13.8560i) q^{56} +(20.3345 - 20.3345i) q^{57} +(-2.76469 - 7.82109i) q^{58} +(5.94136 - 3.43025i) q^{59} +(9.14800 - 28.6991i) q^{60} +(44.2972 + 25.5750i) q^{61} +(-41.7172 - 35.6700i) q^{62} +(12.9261 + 45.3143i) q^{63} +(-28.8648 - 57.1211i) q^{64} +(19.2650 - 1.13909i) q^{65} +(17.6457 + 25.7053i) q^{66} +(-17.7208 + 66.1349i) q^{67} +(52.6235 + 118.549i) q^{68} -14.4927 q^{69} +(28.2180 + 64.0605i) q^{70} +71.0505i q^{71} +(-47.3702 + 25.6176i) q^{72} +(-75.1765 - 20.1435i) q^{73} +(-43.1975 - 62.9277i) q^{74} +(-37.2643 - 5.39138i) q^{75} +(-75.4491 + 11.8639i) q^{76} +(-70.2804 - 17.6258i) q^{77} +(8.83643 + 7.55554i) q^{78} +(66.7677 - 115.645i) q^{79} +(-64.5104 + 47.3118i) q^{80} +(12.4504 + 21.5647i) q^{81} +(28.6383 + 81.0153i) q^{82} +(3.23971 + 3.23971i) q^{83} +(-14.5218 + 39.5913i) q^{84} +(135.379 - 89.2113i) q^{85} +(-63.1306 + 132.167i) q^{86} +(-6.03393 - 1.61679i) q^{87} +(2.30586 - 82.7758i) q^{88} +(16.9269 - 29.3183i) q^{89} +(41.3072 + 53.1534i) q^{90} +(-27.0146 + 0.434309i) q^{91} +(31.1145 + 22.6590i) q^{92} +(-39.9246 + 10.6978i) q^{93} +(41.9184 + 61.0644i) q^{94} +(30.1094 + 90.5978i) q^{95} +(-47.7649 - 6.42364i) q^{96} +(-108.302 - 108.302i) q^{97} +(-35.6149 - 91.2994i) q^{98} -69.6796 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.88565	+	0.666564i	−0.942827	+	0.333282i
$2$	−1.88565	+	0.666564i	−0.942827	+	0.333282i
$3$	−0.389805	+	1.45477i	−0.129935	+	0.484924i	−0.999967	−	0.00807035i	$-0.997431\pi$
$3$	−0.389805	+	1.45477i	−0.129935	+	0.484924i	0.870032	+	0.492995i	$0.164098\pi$
$4$	3.11138	−	2.51382i	0.777846	−	0.628455i
$5$	−3.73805	−	3.32069i	−0.747610	−	0.664138i
$5$	−3.73805	−	3.32069i	−0.747610	−	0.664138i
$6$	−0.234662	−	3.00303i	−0.0391103	−	0.500505i
$7$	5.02867	+	4.86954i	0.718382	+	0.695649i
$7$	5.02867	+	4.86954i	0.718382	+	0.695649i
$8$	−4.19137	+	6.81413i	−0.523921	+	0.851767i
$9$	5.82981	+	3.36584i	0.647757	+	0.373983i
$10$	9.26213	+	3.77002i	0.926213	+	0.377002i
$11$	−8.96422	+	5.17549i	−0.814929	+	0.470499i	−0.848665	−	0.528931i	$-0.822593\pi$
$11$	−8.96422	+	5.17549i	−0.814929	+	0.470499i	0.0337356	+	0.999431i	$0.489260\pi$
$12$	2.44420	+	5.50626i	0.203684	+	0.458855i
$13$	−2.72924	+	2.72924i	−0.209942	+	0.209942i	−0.804243	−	0.594301i	$-0.797429\pi$
$13$	−2.72924	+	2.72924i	−0.209942	+	0.209942i	0.594301	+	0.804243i	$0.297429\pi$
$14$	−12.7282	−	5.83034i	−0.909157	−	0.416453i
$15$	6.28796	−	4.14359i	0.419197	−	0.276240i
$16$	3.36142	−	15.6429i	0.210089	−	0.977682i
$17$	−8.39248	+	31.3211i	−0.493675	+	1.84242i	0.0436522	+	0.999047i	$0.486101\pi$
$17$	−8.39248	+	31.3211i	−0.493675	+	1.84242i	−0.537327	+	0.843374i	$0.680566\pi$
$18$	−13.2366	−	2.46087i	−0.735365	−	0.136715i
$19$	−16.5359	−	9.54701i	−0.870311	−	0.502474i	−0.00285961	−	0.999996i	$-0.500910\pi$
$19$	−16.5359	−	9.54701i	−0.870311	−	0.502474i	−0.867452	+	0.497521i	$0.834244\pi$
$20$	−19.9781	−	0.935145i	−0.998906	−	0.0467573i
$21$	−9.04428	+	5.41740i	−0.430680	+	0.257972i
$22$	13.4536	−	15.7344i	0.611528	−	0.715201i
$23$	2.49054	+	9.29482i	0.108284	+	0.404122i	0.998697	−	0.0510315i	$-0.0162509\pi$
$23$	2.49054	+	9.29482i	0.108284	+	0.404122i	−0.890413	+	0.455154i	$0.849584\pi$
$24$	−8.27920	−	8.75368i	−0.344967	−	0.364737i
$25$	2.94606	+	24.8258i	0.117843	+	0.993032i
$26$	3.32719	−	6.96562i	0.127969	−	0.267908i
$27$	−16.7537	+	16.7537i	−0.620509	+	0.620509i
$28$	27.8873	+	2.50983i	0.995975	+	0.0896369i
$29$			4.14768i			0.143023i	0.997440	+	0.0715117i	$0.0227823\pi$
$29$			4.14768i			0.143023i	−0.997440	+	0.0715117i	$0.977218\pi$
$30$	−9.09494	+	12.0047i	−0.303165	+	0.400157i
$31$	13.7219	+	23.7671i	0.442643	+	0.766681i	0.997885	−	0.0650083i	$-0.0207074\pi$
$31$	13.7219	+	23.7671i	0.442643	+	0.766681i	−0.555241	+	0.831689i	$0.687374\pi$
$32$	4.08854	+	31.7377i	0.127767	+	0.991804i
$33$	−4.03487	−	15.0583i	−0.122269	−	0.456313i
$34$	−5.05225	−	64.6550i	−0.148596	−	1.90162i
$35$	−2.62721	−	34.9013i	−0.0750633	−	0.997179i
$36$	26.5999	−	4.18267i	0.738886	−	0.116185i
$37$	9.87753	+	36.8634i	0.266960	+	0.996309i	0.961040	+	0.276411i	$0.0891450\pi$
$37$	9.87753	+	36.8634i	0.266960	+	0.996309i	−0.694079	+	0.719898i	$0.744188\pi$
$38$	37.5447	+	6.98012i	0.988019	+	0.183687i
$39$	−2.90655	−	5.03430i	−0.0745270	−	0.129085i
$40$	38.2952	−	11.5533i	0.957379	−	0.288834i
$41$		−	42.9640i		−	1.04790i	−0.851748	−	0.523951i	$-0.824457\pi$
$41$		−	42.9640i		−	1.04790i	0.851748	−	0.523951i	$-0.175543\pi$
$42$	13.4433	−	16.2439i	0.320079	−	0.386761i
$43$	51.7850	−	51.7850i	1.20430	−	1.20430i	0.231457	−	0.972845i	$-0.425651\pi$
$43$	51.7850	−	51.7850i	1.20430	−	1.20430i	0.972845	−	0.231457i	$-0.0743494\pi$
$44$	−14.8809	+	38.6374i	−0.338201	+	0.878122i
$45$	−10.6152	−	31.9407i	−0.235894	−	0.709793i
$46$	−10.8919	−	15.8667i	−0.236780	−	0.344928i
$47$	−9.58506	−	35.7719i	−0.203937	−	0.761105i	−0.989771	−	0.142667i	$-0.954432\pi$
$47$	−9.58506	−	35.7719i	−0.203937	−	0.761105i	0.785833	−	0.618438i	$-0.212234\pi$
$48$	21.4466	+	10.9878i	0.446804	+	0.228912i
$49$	1.57512	+	48.9747i	0.0321453	+	0.999483i
$50$	−22.1033	−	44.8491i	−0.442065	−	0.896983i
$51$	−42.2937	−	24.4183i	−0.829289	−	0.478790i
$52$	−1.63089	+	15.3525i	−0.0313634	+	0.295241i
$53$	7.62542	−	28.4585i	0.143876	−	0.536952i	−0.855927	−	0.517097i	$-0.827013\pi$
$53$	7.62542	−	28.4585i	0.143876	−	0.536952i	0.999803	−	0.0198553i	$-0.00632055\pi$
$54$	20.4243	−	42.7592i	0.378228	−	0.791837i
$55$	50.6949	+	10.4211i	0.921726	+	0.189475i
$56$	−54.2587	+	13.8560i	−0.968906	+	0.247428i
$57$	20.3345	−	20.3345i	0.356746	−	0.356746i
$58$	−2.76469	−	7.82109i	−0.0476671	−	0.134846i
$59$	5.94136	−	3.43025i	0.100701	−	0.0581398i	−0.448804	−	0.893630i	$-0.648150\pi$
$59$	5.94136	−	3.43025i	0.100701	−	0.0581398i	0.549505	+	0.835491i	$0.314816\pi$
$60$	9.14800	−	28.6991i	0.152467	−	0.478318i
$61$	44.2972	+	25.5750i	0.726183	+	0.419262i	0.817024	−	0.576603i	$-0.195622\pi$
$61$	44.2972	+	25.5750i	0.726183	+	0.419262i	−0.0908411	+	0.995865i	$0.528956\pi$
$62$	−41.7172	−	35.6700i	−0.672857	−	0.575322i
$63$	12.9261	+	45.3143i	0.205176	+	0.719274i
$64$	−28.8648	−	57.1211i	−0.451013	−	0.892517i
$65$	19.2650	−	1.13909i	0.296385	−	0.0175244i
$66$	17.6457	+	25.7053i	0.267359	+	0.389474i
$67$	−17.7208	+	66.1349i	−0.264490	+	0.987088i	0.698073	+	0.716027i	$0.254041\pi$
$67$	−17.7208	+	66.1349i	−0.264490	+	0.987088i	−0.962562	+	0.271061i	$0.912625\pi$
$68$	52.6235	+	118.549i	0.773875	+	1.74337i
$69$	−14.4927			−0.210039
$70$	28.2180	+	64.0605i	0.403114	+	0.915150i
$71$			71.0505i			1.00071i	0.865820	+	0.500356i	$0.166797\pi$
$71$			71.0505i			1.00071i	−0.865820	+	0.500356i	$0.833203\pi$
$72$	−47.3702	+	25.6176i	−0.657920	+	0.355800i
$73$	−75.1765	−	20.1435i	−1.02982	−	0.275938i	−0.295929	−	0.955210i	$-0.595629\pi$
$73$	−75.1765	−	20.1435i	−1.02982	−	0.275938i	−0.733887	+	0.679272i	$0.762296\pi$
$74$	−43.1975	−	62.9277i	−0.583749	−	0.850374i
$75$	−37.2643	−	5.39138i	−0.496857	−	0.0718850i
$76$	−75.4491	+	11.8639i	−0.992751	+	0.156104i
$77$	−70.2804	−	17.6258i	−0.912733	−	0.228906i
$78$	8.83643	+	7.55554i	0.113288	+	0.0968659i
$79$	66.7677	−	115.645i	0.845161	−	1.46386i	−0.0403208	−	0.999187i	$-0.512838\pi$
$79$	66.7677	−	115.645i	0.845161	−	1.46386i	0.885482	−	0.464675i	$-0.153829\pi$
$80$	−64.5104	+	47.3118i	−0.806380	+	0.591398i
$81$	12.4504	+	21.5647i	0.153709	+	0.266231i
$82$	28.6383	+	81.0153i	0.349247	+	0.987991i
$83$	3.23971	+	3.23971i	0.0390327	+	0.0390327i	0.726354	−	0.687321i	$-0.241213\pi$
$83$	3.23971	+	3.23971i	0.0390327	+	0.0390327i	−0.687321	+	0.726354i	$0.741213\pi$
$84$	−14.5218	+	39.5913i	−0.172879	+	0.471325i
$85$	135.379	−	89.2113i	1.59270	−	1.04954i
$86$	−63.1306	+	132.167i	−0.734076	+	1.53682i
$87$	−6.03393	−	1.61679i	−0.0693555	−	0.0185838i
$88$	2.30586	−	82.7758i	0.0262030	−	0.940634i
$89$	16.9269	−	29.3183i	0.190190	−	0.329419i	−0.755123	−	0.655583i	$-0.772423\pi$
$89$	16.9269	−	29.3183i	0.190190	−	0.329419i	0.945313	+	0.326164i	$0.105756\pi$
$90$	41.3072	+	53.1534i	0.458969	+	0.590593i
$91$	−27.0146	+	0.434309i	−0.296864	+	0.00477263i
$92$	31.1145	+	22.6590i	0.338201	+	0.246293i
$93$	−39.9246	+	10.6978i	−0.429297	+	0.115030i
$94$	41.9184	+	61.0644i	0.445941	+	0.649622i
$95$	30.1094	+	90.5978i	0.316942	+	0.953662i
$96$	−47.7649	−	6.42364i	−0.497551	−	0.0669129i
$97$	−108.302	−	108.302i	−1.11652	−	1.11652i	−0.992248	−	0.124272i	$-0.960341\pi$
$97$	−108.302	−	108.302i	−1.11652	−	1.11652i	−0.124272	−	0.992248i	$-0.539659\pi$
$98$	−35.6149	−	91.2994i	−0.363417	−	0.931626i
$99$	−69.6796			−0.703835
$100$	71.5739	+	69.8367i	0.715739	+	0.698367i
$101$	82.4664	−	47.6120i	0.816499	−	0.471406i	−0.0327087	−	0.999465i	$-0.510413\pi$
$101$	82.4664	−	47.6120i	0.816499	−	0.471406i	0.849208	+	0.528059i	$0.177080\pi$
$102$	96.0277	+	17.8530i	0.941448	+	0.175029i
$103$	−94.6821	+	25.3700i	−0.919243	+	0.246310i	−0.687262	−	0.726410i	$-0.741188\pi$
$103$	−94.6821	+	25.3700i	−0.919243	+	0.246310i	−0.231981	+	0.972720i	$0.574521\pi$
$104$	−7.15815	−	30.0367i	−0.0688283	−	0.288814i
$105$	51.7975	+	9.78269i	0.493310	+	0.0931685i
$106$	4.59049	+	58.7456i	0.0433065	+	0.554204i
$107$	51.4210	−	13.7782i	0.480570	−	0.128768i	−0.0103978	−	0.999946i	$-0.503310\pi$
$107$	51.4210	−	13.7782i	0.480570	−	0.128768i	0.490968	+	0.871178i	$0.336643\pi$
$108$	−10.0114	+	94.2432i	−0.0926984	+	0.872622i
$109$	−42.2916	+	24.4171i	−0.387997	+	0.224010i	−0.681292	−	0.732012i	$-0.738581\pi$
$109$	−42.2916	+	24.4171i	−0.387997	+	0.224010i	0.293295	+	0.956022i	$0.405248\pi$
$110$	−102.539	+	14.1408i	−0.932177	+	0.128553i
$111$	−57.4782			−0.517822
$112$	93.0773	−	62.2946i	0.831047	−	0.556201i
$113$	−84.1697	−	84.1697i	−0.744865	−	0.744865i	0.228645	−	0.973510i	$-0.426570\pi$
$113$	−84.1697	−	84.1697i	−0.744865	−	0.744865i	−0.973510	+	0.228645i	$0.926570\pi$
$114$	−24.7896	+	51.8981i	−0.217453	+	0.455247i
$115$	21.5554	−	43.0148i	0.187438	−	0.374042i
$116$	10.4265	+	12.9050i	0.0898838	+	0.111250i
$117$	−25.0972	+	6.72476i	−0.214506	+	0.0574766i
$118$	−8.91687	+	10.4286i	−0.0755667	+	0.0883776i
$119$	−194.723	+	116.636i	−1.63633	+	0.980137i
$120$	1.87984	+	60.2143i	0.0156653	+	0.501786i
$121$	−6.92852	+	12.0005i	−0.0572605	+	0.0991781i
$122$	−100.577	−	18.6987i	−0.824398	−	0.153268i
$123$	62.5029	+	16.7476i	0.508153	+	0.136159i
$124$	102.440	+	39.4541i	0.826133	+	0.318178i
$125$	71.4262	−	102.583i	0.571410	−	0.820665i
$126$	−54.5790	−	76.8309i	−0.433167	−	0.609769i
$127$	103.692	+	103.692i	0.816476	+	0.816476i	0.985596	−	0.169119i	$-0.0540923\pi$
$127$	103.692	+	103.692i	0.816476	+	0.816476i	−0.169119	+	0.985596i	$0.554092\pi$
$128$	92.5040	+	88.4704i	0.722687	+	0.691175i
$129$	55.1494	+	95.5215i	0.427514	+	0.740477i
$130$	−35.5678	+	14.9893i	−0.273599	+	0.115302i
$131$	19.9882	−	34.6205i	0.152581	−	0.264279i	−0.779594	−	0.626285i	$-0.784575\pi$
$131$	19.9882	−	34.6205i	0.152581	−	0.264279i	0.932176	+	0.362006i	$0.117908\pi$
$132$	−50.4080	−	36.7093i	−0.381879	−	0.278101i
$133$	−36.6641	−	128.531i	−0.275670	−	0.966400i
$134$	−10.6679	−	136.520i	−0.0796111	−	1.01880i
$135$	118.260	−	6.99240i	0.876002	−	0.0517956i
$136$	−178.250	−	188.466i	−1.31067	−	1.38578i
$137$	123.624	+	33.1248i	0.902362	+	0.241787i	0.680030	−	0.733184i	$-0.261967\pi$
$137$	123.624	+	33.1248i	0.902362	+	0.241787i	0.222332	+	0.974971i	$0.428633\pi$
$138$	27.3282	−	9.66030i	0.198030	−	0.0700022i
$139$		−	45.8622i		−	0.329944i	−0.986298	−	0.164972i	$-0.947247\pi$
$139$		−	45.8622i		−	0.329944i	0.986298	−	0.164972i	$-0.0527534\pi$
$140$	−95.9097	−	101.987i	−0.685070	−	0.728478i
$141$	55.7763			0.395577
$142$	−47.3597	−	133.977i	−0.333519	−	0.943498i
$143$	10.3403	−	38.5907i	0.0723101	−	0.269865i
$144$	72.2481	−	79.8813i	0.501723	−	0.554731i
$145$	13.7731	−	15.5042i	0.0949872	−	0.106926i
$146$	155.184	−	12.1263i	1.06290	−	0.0830571i
$147$	−71.8610	−	16.7991i	−0.488850	−	0.114280i
$148$	123.401	+	89.8660i	0.833789	+	0.607203i
$149$	107.904	+	62.2984i	0.724188	+	0.418110i	0.816292	−	0.577639i	$-0.196026\pi$
$149$	107.904	+	62.2984i	0.724188	+	0.418110i	−0.0921040	+	0.995749i	$0.529359\pi$
$150$	73.8613	−	14.6728i	0.492409	−	0.0978186i
$151$	190.770	−	110.141i	1.26338	−	0.729412i	0.289652	−	0.957132i	$-0.406460\pi$
$151$	190.770	−	110.141i	1.26338	−	0.729412i	0.973727	+	0.227720i	$0.0731270\pi$
$152$	134.363	−	72.6628i	0.883966	−	0.478045i
$153$	−154.349	+	154.349i	−1.00881	+	1.00881i
$154$	144.273	−	13.6103i	0.936839	−	0.0883787i
$155$	27.6298	−	134.409i	0.178257	−	0.867155i
$156$	−21.6987	−	8.35708i	−0.139094	−	0.0535710i
$157$	−60.8277	+	227.012i	−0.387438	+	1.44594i	0.446851	+	0.894609i	$0.352545\pi$
$157$	−60.8277	+	227.012i	−0.387438	+	1.44594i	−0.834288	+	0.551328i	$0.814121\pi$
$158$	−48.8159	+	262.572i	−0.308962	+	1.66185i
$159$	38.4281	+	22.1865i	0.241686	+	0.139538i
$160$	90.1079	−	132.214i	0.563175	−	0.826338i
$161$	−32.7374	+	58.8684i	−0.203338	+	0.365642i
$162$	−37.8515	−	32.3647i	−0.233651	−	0.199782i
$163$	−53.4872	−	199.617i	−0.328142	−	1.22464i	−0.911115	−	0.412152i	$-0.864777\pi$
$163$	−53.4872	−	199.617i	−0.328142	−	1.22464i	0.582973	−	0.812491i	$-0.301889\pi$
$164$	−108.004	−	133.678i	−0.658560	−	0.815107i
$165$	−34.9215	+	69.6874i	−0.211645	+	0.422348i
$166$	−8.26846	−	3.94950i	−0.0498100	−	0.0237922i
$167$	8.07187	−	8.07187i	0.0483345	−	0.0483345i	−0.682526	−	0.730861i	$-0.739119\pi$
$167$	8.07187	−	8.07187i	0.0483345	−	0.0483345i	0.730861	+	0.682526i	$0.239119\pi$
$168$	0.993015	−	84.3353i	0.00591081	−	0.501996i
$169$			154.102i			0.911849i
$170$	−195.813	+	258.461i	−1.15184	+	1.52036i
$171$	−64.2675	−	111.315i	−0.375833	−	0.650963i
$172$	30.9448	−	291.301i	0.179912	−	1.69361i
$173$	−2.99182	−	11.1656i	−0.0172938	−	0.0645412i	0.956740	−	0.290945i	$-0.0939697\pi$
$173$	−2.99182	−	11.1656i	−0.0172938	−	0.0645412i	−0.974033	+	0.226404i	$0.927303\pi$
$174$	12.4556	−	0.973302i	0.0715839	−	0.00559369i
$175$	−106.076	+	139.187i	−0.606146	+	0.795354i
$176$	50.8273	+	157.624i	0.288792	+	0.895588i
$177$	2.67425	+	9.98045i	0.0151088	+	0.0563867i
$178$	−12.3758	+	66.5670i	−0.0695269	+	0.373972i
$179$	111.945	+	193.895i	0.625393	+	1.08321i	0.988465	+	0.151452i	$0.0483948\pi$
$179$	111.945	+	193.895i	0.625393	+	1.08321i	−0.363071	+	0.931761i	$0.618272\pi$
$180$	−113.321	−	72.6950i	−0.629562	−	0.403861i
$181$			106.329i			0.587451i	0.955890	+	0.293725i	$0.0948951\pi$
$181$			106.329i			0.587451i	−0.955890	+	0.293725i	$0.905105\pi$
$182$	50.6507	−	18.8259i	0.278301	−	0.103439i
$183$	−54.4730	+	54.4730i	−0.297667	+	0.297667i
$184$	−73.7749	−	21.9872i	−0.400951	−	0.119495i
$185$	85.4893	−	170.598i	0.462104	−	0.922149i
$186$	68.1533	−	46.7846i	0.366416	−	0.251530i
$187$	−86.8704	−	324.205i	−0.464548	−	1.73372i
$188$	−119.747	−	87.2051i	−0.636952	−	0.463857i
$189$	−165.832	+	2.66605i	−0.877419	+	0.0141061i
$190$	−117.165	−	150.766i	−0.616660	−	0.793507i
$191$	131.793	+	76.0905i	0.690014	+	0.398380i	0.803617	−	0.595146i	$-0.202906\pi$
$191$	131.793	+	76.0905i	0.690014	+	0.398380i	−0.113603	+	0.993526i	$0.536239\pi$
$192$	94.3499	−	19.7256i	0.491406	−	0.102738i
$193$	32.3980	−	120.911i	0.167865	−	0.626482i	−0.829792	−	0.558073i	$-0.811541\pi$
$193$	32.3980	−	120.911i	0.167865	−	0.626482i	0.997657	−	0.0684092i	$-0.0217924\pi$
$194$	276.412	+	132.030i	1.42480	+	0.680569i
$195$	−5.85248	+	28.4702i	−0.0300127	+	0.146001i
$196$	128.014	+	148.419i	0.653134	+	0.757242i
$197$	−110.715	+	110.715i	−0.562005	+	0.562005i	−0.929877	−	0.367872i	$-0.880087\pi$
$197$	−110.715	+	110.715i	−0.562005	+	0.562005i	0.367872	+	0.929877i	$0.380087\pi$
$198$	131.392	−	46.4460i	0.663594	−	0.234576i
$199$	92.6809	−	53.5093i	0.465733	−	0.268891i	−0.248719	−	0.968576i	$-0.580010\pi$
$199$	92.6809	−	53.5093i	0.465733	−	0.268891i	0.714452	+	0.699685i	$0.246676\pi$
$200$	−181.514	−	83.9793i	−0.907572	−	0.419897i
$201$	−89.3036	−	51.5595i	−0.444297	−	0.256515i
$202$	−123.767	+	144.749i	−0.612706	+	0.716579i
$203$	−20.1973	+	20.8573i	−0.0994941	+	0.102745i
$204$	−192.975	+	30.3441i	−0.945957	+	0.148746i
$205$	−142.670	+	160.602i	−0.695952	+	0.783423i
$206$	161.627	−	110.951i	0.784597	−	0.538596i
$207$	−16.7655	+	62.5698i	−0.0809929	+	0.302270i
$208$	33.5192	+	51.8674i	0.161150	+	0.249362i
$209$	197.642			0.945656
$210$	−104.193	+	16.0796i	−0.496157	+	0.0765695i
$211$			100.172i			0.474748i	0.971418	+	0.237374i	$0.0762867\pi$
$211$			100.172i			0.474748i	−0.971418	+	0.237374i	$0.923713\pi$
$212$	−47.8138	−	107.714i	−0.225537	−	0.508085i
$213$	−103.362	−	27.6958i	−0.485269	−	0.130027i
$214$	−87.7782	+	60.2564i	−0.410179	+	0.281572i
$215$	−365.537	+	21.6132i	−1.70017	+	0.100526i
$216$	−43.9411	−	184.383i	−0.203431	−	0.853627i
$217$	−46.7317	+	186.337i	−0.215354	+	0.858694i
$218$	63.4718	−	74.2323i	0.291155	−	0.340515i
$219$	58.6084	−	101.513i	0.267618	−	0.463528i
$220$	183.928	−	95.0138i	0.836037	−	0.431881i
$221$	−62.5778	−	108.388i	−0.283158	−	0.490444i
$222$	108.384	−	38.3129i	0.488217	−	0.172581i
$223$	218.632	+	218.632i	0.980412	+	0.980412i	0.999812	−	0.0193998i	$-0.00617555\pi$
$223$	218.632	+	218.632i	0.980412	+	0.980412i	−0.0193998	+	0.999812i	$0.506176\pi$
$224$	−133.988	+	179.508i	−0.598162	+	0.801375i
$225$	−66.3848	+	154.646i	−0.295044	+	0.687315i
$226$	214.820	+	102.610i	0.950529	+	0.454029i
$227$	−98.3908	−	26.3637i	−0.433440	−	0.116140i	0.0355007	−	0.999370i	$-0.488697\pi$
$227$	−98.3908	−	26.3637i	−0.433440	−	0.116140i	−0.468940	+	0.883230i	$0.655364\pi$
$228$	12.1512	−	114.386i	0.0532946	−	0.501692i
$229$	−49.3812	+	85.5308i	−0.215639	+	0.373497i	−0.953470	−	0.301488i	$-0.902517\pi$
$229$	−49.3812	+	85.5308i	−0.215639	+	0.373497i	0.737831	+	0.674985i	$0.235850\pi$
$230$	−11.9739	+	95.4791i	−0.0520606	+	0.415127i
$231$	53.0372	−	95.3714i	0.229598	−	0.412863i
$232$	−28.2628	−	17.3845i	−0.121823	−	0.0749330i
$233$	342.495	−	91.7712i	1.46993	−	0.393868i	0.567026	−	0.823700i	$-0.308094\pi$
$233$	342.495	−	91.7712i	1.46993	−	0.393868i	0.902909	+	0.429832i	$0.141427\pi$
$234$	42.8421	−	29.4094i	0.183086	−	0.125681i
$235$	−82.9580	+	165.546i	−0.353013	+	0.704452i
$236$	9.86283	−	25.6083i	0.0417916	−	0.108510i
$237$	142.211	+	142.211i	0.600046	+	0.600046i
$238$	289.434	−	349.731i	1.21611	−	1.46946i
$239$	295.712			1.23729			0.618645	−	0.785671i	$-0.287682\pi$
$239$	295.712			1.23729			0.618645	+	0.785671i	$0.287682\pi$
$240$	−43.6815	−	112.290i	−0.182006	−	0.467877i
$241$	125.617	−	72.5253i	0.521234	−	0.300935i	−0.216205	−	0.976348i	$-0.569368\pi$
$241$	125.617	−	72.5253i	0.521234	−	0.300935i	0.737439	+	0.675413i	$0.236035\pi$
$242$	5.06565	−	27.2472i	0.0209325	−	0.112592i
$243$	−242.199	+	64.8971i	−0.996705	+	0.267066i
$244$	202.116	−	31.7815i	0.828346	−	0.130252i
$245$	156.742	−	188.300i	0.639762	−	0.768573i
$246$	−129.022	+	10.0820i	−0.524480	+	0.0409838i
$247$	71.1866	−	19.0744i	0.288205	−	0.0772242i
$248$	−219.466	−	6.11360i	−0.884944	−	0.0246516i
$249$	−5.97590	+	3.45019i	−0.0239996	+	0.0138562i
$250$	−66.3069	+	241.046i	−0.265228	+	0.964186i
$251$	−230.270			−0.917412			−0.458706	−	0.888588i	$-0.651687\pi$
$251$	−230.270			−0.917412			−0.458706	+	0.888588i	$0.651687\pi$
$252$	154.130	+	108.496i	0.611627	+	0.430540i
$253$	−70.4310	−	70.4310i	−0.278383	−	0.278383i
$254$	−264.646	−	126.410i	−1.04191	−	0.497679i
$255$	77.0106	+	231.721i	0.302002	+	0.908710i
$256$	−233.402	−	105.165i	−0.911726	−	0.410800i
$257$	240.047	−	64.3204i	0.934035	−	0.250274i	0.240461	−	0.970659i	$-0.422701\pi$
$257$	240.047	−	64.3204i	0.934035	−	0.250274i	0.693575	+	0.720385i	$0.256035\pi$
$258$	−167.664	−	143.360i	−0.649860	−	0.555658i
$259$	−129.837	+	233.473i	−0.501302	+	0.901441i
$260$	57.0773	−	51.9729i	0.219528	−	0.199896i
$261$	−13.9604	+	24.1802i	−0.0534883	+	0.0926444i
$262$	−14.6140	+	78.6058i	−0.0557785	+	0.300022i
$263$	−262.922	−	70.4497i	−0.999704	−	0.267870i	−0.278382	−	0.960470i	$-0.589798\pi$
$263$	−262.922	−	70.4497i	−0.999704	−	0.267870i	−0.721321	+	0.692601i	$0.756465\pi$
$264$	119.521	+	35.6209i	0.452732	+	0.134928i
$265$	−123.006	+	81.0575i	−0.464173	+	0.305877i
$266$	154.810	+	217.926i	0.581993	+	0.819272i
$267$	36.0532	+	36.0532i	0.135031	+	0.135031i
$268$	111.115	+	250.318i	0.414609	+	0.934023i
$269$	81.5025	+	141.166i	0.302983	+	0.524782i	0.976810	−	0.214107i	$-0.0686841\pi$
$269$	81.5025	+	141.166i	0.302983	+	0.524782i	−0.673827	+	0.738889i	$0.735351\pi$
$270$	−218.337	+	92.0133i	−0.808656	+	0.340790i
$271$	−4.61358	+	7.99095i	−0.0170243	+	0.0294869i	−0.874412	−	0.485184i	$-0.838753\pi$
$271$	−4.61358	+	7.99095i	−0.0170243	+	0.0294869i	0.857388	+	0.514671i	$0.172086\pi$
$272$	461.744	+	236.566i	1.69759	+	0.869729i
$273$	9.89861	−	39.4694i	0.0362587	−	0.144577i
$274$	−255.191	+	19.9411i	−0.931355	+	0.0727777i
$275$	−154.895	−	207.297i	−0.563254	−	0.753806i
$276$	−45.0923	+	36.4320i	−0.163378	+	0.132000i
$277$	−162.887	−	43.6454i	−0.588039	−	0.157564i	−0.0474820	−	0.998872i	$-0.515120\pi$
$277$	−162.887	−	43.6454i	−0.588039	−	0.157564i	−0.540557	+	0.841308i	$0.681786\pi$
$278$	30.5701	+	86.4803i	0.109964	+	0.311080i
$279$			184.744i			0.662164i
$280$	248.833	+	128.382i	0.888691	+	0.458507i
$281$	−104.482			−0.371822			−0.185911	−	0.982567i	$-0.559524\pi$
$281$	−104.482			−0.371822			−0.185911	+	0.982567i	$0.559524\pi$
$282$	−105.175	+	37.1785i	−0.372961	+	0.131839i
$283$	27.1980	−	101.504i	0.0961060	−	0.358673i	−0.901079	−	0.433655i	$-0.857224\pi$
$283$	27.1980	−	101.504i	0.0961060	−	0.358673i	0.997185	+	0.0749828i	$0.0238902\pi$
$284$	178.608	+	221.065i	0.628902	+	0.778399i
$285$	−143.536	+	8.48689i	−0.503635	+	0.0297786i
$286$	6.22486	+	79.6612i	0.0217653	+	0.278536i
$287$	209.215	−	216.052i	0.728972	−	0.752794i
$288$	−82.9888	+	198.786i	−0.288156	+	0.690231i
$289$	−660.299	−	381.224i	−2.28477	−	1.31911i
$290$	−15.6368	+	38.4163i	−0.0539201	+	0.132470i
$291$	199.772	−	115.339i	0.686503	−	0.396353i
$292$	−284.540	+	126.306i	−0.974453	+	0.432555i
$293$	41.6460	−	41.6460i	0.142136	−	0.142136i	−0.632458	−	0.774595i	$-0.717954\pi$
$293$	41.6460	−	41.6460i	0.142136	−	0.142136i	0.774595	+	0.632458i	$0.217954\pi$
$294$	146.703	−	16.2226i	0.498989	−	0.0551790i
$295$	−33.5999	−	6.90697i	−0.113898	−	0.0234134i
$296$	−292.593	−	87.2016i	−0.988489	−	0.294600i
$297$	63.4753	−	236.893i	0.213722	−	0.797620i
$298$	−244.996	−	45.5483i	−0.822133	−	0.152847i
$299$	−32.1651	−	18.5705i	−0.107575	−	0.0621087i
$300$	−129.496	+	76.9011i	−0.431655	+	0.256337i
$301$	512.579	−	8.24065i	1.70292	−	0.0273776i
$302$	−286.310	+	334.849i	−0.948048	+	1.10877i
$303$	37.1188	+	138.529i	0.122504	+	0.457192i
$304$	−204.927	+	226.578i	−0.674103	+	0.745324i
$305$	−80.6586	−	242.698i	−0.264454	−	0.795730i
$306$	188.165	−	393.932i	0.614918	−	1.28736i
$307$	−129.652	+	129.652i	−0.422320	+	0.422320i	−0.886002	−	0.463682i	$-0.846528\pi$
$307$	−129.652	+	129.652i	−0.422320	+	0.422320i	0.463682	+	0.886002i	$0.346528\pi$
$308$	−262.977	+	121.832i	−0.853823	+	0.395558i
$309$		−	147.630i		−	0.477768i
$310$	37.4920	+	271.866i	0.120942	+	0.876987i
$311$	211.858	+	366.949i	0.681216	+	1.17990i	0.974610	+	0.223909i	$0.0718817\pi$
$311$	211.858	+	366.949i	0.681216	+	1.17990i	−0.293395	+	0.955991i	$0.594785\pi$
$312$	46.4868	+	1.29497i	0.148996	+	0.00415054i
$313$	117.422	+	438.223i	0.375149	+	1.40007i	0.853127	+	0.521703i	$0.174703\pi$
$313$	117.422	+	438.223i	0.375149	+	1.40007i	−0.477978	+	0.878372i	$0.658630\pi$
$314$	−36.6182	−	468.612i	−0.116618	−	1.49239i
$315$	102.156	−	212.311i	0.324305	−	0.674002i
$316$	−82.9709	−	527.658i	−0.262566	−	1.66980i
$317$	−105.363	−	393.219i	−0.332375	−	1.24044i	−0.906688	−	0.421803i	$-0.861397\pi$
$317$	−105.363	−	393.219i	−0.332375	−	1.24044i	0.574313	−	0.818636i	$-0.305269\pi$
$318$	−87.2509	−	16.2212i	−0.274374	−	0.0510102i
$319$	−21.4663	−	37.1807i	−0.0672924	−	0.116554i
$320$	−81.7832	+	309.373i	−0.255573	+	0.966790i
$321$			80.1767i			0.249772i
$322$	22.4918	−	132.827i	0.0698504	−	0.412506i
$323$	437.801	−	437.801i	1.35542	−	1.35542i
$324$	92.9479	+	35.7981i	0.286876	+	0.110488i
$325$	−75.7961	−	59.7151i	−0.233219	−	0.183739i
$326$	233.916	+	340.756i	0.717533	+	1.04526i
$327$	−19.0358	−	71.0426i	−0.0582135	−	0.217256i
$328$	292.762	+	180.078i	0.892569	+	0.549019i
$329$	125.993	−	226.560i	0.382957	−	0.688633i
$330$	19.3987	−	154.684i	0.0587840	−	0.468739i
$331$	−230.336	−	132.985i	−0.695879	−	0.401766i	0.109932	−	0.993939i	$-0.464937\pi$
$331$	−230.336	−	132.985i	−0.695879	−	0.401766i	−0.805811	+	0.592173i	$0.798270\pi$
$332$	18.2241	+	1.93594i	0.0548917	+	0.00583113i
$333$	−66.4924	+	248.153i	−0.199677	+	0.745205i
$334$	−9.84033	+	20.6012i	−0.0294621	+	0.0616802i
$335$	285.855	−	188.371i	0.853298	−	0.562300i
$336$	54.3424	+	159.689i	0.161733	+	0.475265i
$337$	64.6022	−	64.6022i	0.191698	−	0.191698i	−0.604732	−	0.796429i	$-0.706720\pi$
$337$	64.6022	−	64.6022i	0.191698	−	0.191698i	0.796429	+	0.604732i	$0.206720\pi$
$338$	−102.719	−	290.584i	−0.303903	−	0.859716i
$339$	155.258	−	89.6380i	0.457987	−	0.264419i
$340$	196.956	−	617.890i	0.579282	−	1.81732i
$341$	−246.013	−	142.036i	−0.721446	−	0.416527i
$342$	195.385	+	167.062i	0.571300	+	0.488487i
$343$	−230.563	+	253.948i	−0.672197	+	0.740373i
$344$	135.820	+	569.920i	0.394825	+	1.65674i
$345$	54.1744	+	48.1256i	0.157027	+	0.139495i
$346$	13.0841	+	19.0603i	0.0378155	+	0.0550875i
$347$	−63.0751	+	235.400i	−0.181773	+	0.678385i	0.813526	+	0.581529i	$0.197545\pi$
$347$	−63.0751	+	235.400i	−0.181773	+	0.678385i	−0.995298	+	0.0968561i	$0.969121\pi$
$348$	−22.8382	+	10.1378i	−0.0656269	+	0.0291315i
$349$	201.731			0.578027			0.289013	−	0.957325i	$-0.406673\pi$
$349$	201.731			0.578027			0.289013	+	0.957325i	$0.406673\pi$
$350$	107.245	−	333.164i	0.306414	−	0.951898i
$351$		−	91.4499i		−	0.260541i
$352$	−200.909	−	263.344i	−0.570764	−	0.748136i
$353$	−29.0741	−	7.79038i	−0.0823629	−	0.0220691i	0.217402	−	0.976082i	$-0.430242\pi$
$353$	−29.0741	−	7.79038i	−0.0823629	−	0.0220691i	−0.299765	+	0.954013i	$0.596908\pi$
$354$	−11.6953	−	17.0371i	−0.0330377	−	0.0481275i
$355$	235.937	−	265.590i	0.664610	−	0.748142i
$356$	−21.0347	−	133.772i	−0.0590863	−	0.375763i
$357$	−93.7754	−	328.743i	−0.262676	−	0.920848i
$358$	−340.334	−	291.000i	−0.950653	−	0.812850i
$359$	9.46267	−	16.3898i	0.0263584	−	0.0456541i	−0.852545	−	0.522653i	$-0.824942\pi$
$359$	9.46267	−	16.3898i	0.0263584	−	0.0456541i	0.878904	+	0.476999i	$0.158276\pi$
$360$	262.140	+	61.5417i	0.728168	+	0.170949i
$361$	1.79097	+	3.10206i	0.00496115	+	0.00859296i
$362$	−70.8749	−	200.499i	−0.195787	−	0.553864i
$363$	−14.7573	−	14.7573i	−0.0406537	−	0.0406537i
$364$	−82.9610	+	69.2612i	−0.227915	+	0.190278i
$365$	214.124	+	324.935i	0.586640	+	0.890234i
$366$	66.4075	−	139.027i	0.181441	−	0.379856i
$367$	−97.9045	−	26.2334i	−0.266770	−	0.0714807i	0.122955	−	0.992412i	$-0.460763\pi$
$367$	−97.9045	−	26.2334i	−0.266770	−	0.0714807i	−0.389724	+	0.920932i	$0.627430\pi$
$368$	153.770	−	7.71553i	0.417853	−	0.0209661i
$369$	144.610	−	250.472i	0.391897	−	0.678786i
$370$	−47.4889	+	378.672i	−0.128348	+	1.02344i
$371$	176.925	−	105.976i	0.476888	−	0.285650i
$372$	−97.3286	+	133.648i	−0.261636	+	0.359269i
$373$	431.714	−	115.677i	1.15741	−	0.310127i	0.371480	−	0.928441i	$-0.378851\pi$
$373$	431.714	−	115.677i	1.15741	−	0.310127i	0.785931	+	0.618314i	$0.212184\pi$
$374$	379.911	+	553.434i	1.01580	+	1.47977i
$375$	121.393	+	143.896i	0.323714	+	0.383724i
$376$	283.929	+	84.6196i	0.755131	+	0.225052i
$377$	−11.3200	−	11.3200i	−0.0300265	−	0.0300265i
$378$	310.925	−	115.565i	0.822553	−	0.305728i
$379$	−677.446			−1.78746			−0.893728	−	0.448610i	$-0.851919\pi$
$379$	−677.446			−1.78746			−0.893728	+	0.448610i	$0.851919\pi$
$380$	321.429	+	206.195i	0.845865	+	0.542618i
$381$	−191.269	+	110.429i	−0.502018	+	0.289840i
$382$	−299.235	−	55.6321i	−0.783337	−	0.145634i
$383$	457.505	−	122.588i	1.19453	−	0.320074i	0.393856	−	0.919172i	$-0.371141\pi$
$383$	457.505	−	122.588i	1.19453	−	0.320074i	0.800675	+	0.599099i	$0.204474\pi$
$384$	−164.763	+	100.086i	−0.429070	+	0.260641i
$385$	204.182	+	299.265i	0.530343	+	0.777313i
$386$	19.5035	+	249.592i	0.0505273	+	0.646611i
$387$	476.197	−	127.597i	1.23048	−	0.329707i
$388$	−609.223	−	64.7176i	−1.57016	−	0.166798i
$389$	114.717	−	66.2318i	0.294902	−	0.170262i	−0.345248	−	0.938511i	$-0.612205\pi$
$389$	114.717	−	66.2318i	0.294902	−	0.170262i	0.640150	+	0.768250i	$0.278872\pi$
$390$	−7.94147	−	57.5860i	−0.0203627	−	0.147656i
$391$	−312.026			−0.798021
$392$	−340.322	−	194.538i	−0.868168	−	0.496270i
$393$	42.5735	+	42.5735i	0.108330	+	0.108330i
$394$	134.972	−	282.569i	0.342567	−	0.717180i
$395$	−633.602	+	210.572i	−1.60406	+	0.533095i
$396$	−216.800	+	175.162i	−0.547475	+	0.442328i
$397$	462.970	−	124.052i	1.16617	−	0.312475i	0.376743	−	0.926318i	$-0.377044\pi$
$397$	462.970	−	124.052i	1.16617	−	0.312475i	0.789428	+	0.613843i	$0.210377\pi$
$398$	−139.097	+	162.678i	−0.349489	+	0.408738i
$399$	201.275	−	3.23587i	0.504450	−	0.00810995i
$400$	398.251	+	37.3649i	0.995628	+	0.0934122i
$401$	70.5779	−	122.244i	0.176005	−	0.304849i	−0.764504	−	0.644619i	$-0.777016\pi$
$401$	70.5779	−	122.244i	0.176005	−	0.304849i	0.940509	+	0.339770i	$0.110349\pi$
$402$	202.763	+	37.6967i	0.504387	+	0.0937729i
$403$	−102.317	−	27.4157i	−0.253887	−	0.0680289i
$404$	136.897	−	355.445i	0.338853	−	0.879814i
$405$	25.0695	−	121.954i	0.0619000	−	0.301121i
$406$	24.1824	−	52.7925i	0.0595625	−	0.130031i
$407$	−279.331	−	279.331i	−0.686317	−	0.686317i
$408$	343.658	−	185.849i	0.842299	−	0.455512i
$409$	−109.284	−	189.285i	−0.267198	−	0.462800i	0.700939	−	0.713221i	$-0.252764\pi$
$409$	−109.284	−	189.285i	−0.267198	−	0.462800i	−0.968137	+	0.250421i	$0.919431\pi$
$410$	161.975	−	397.938i	0.395061	−	0.970581i
$411$	−96.3782	+	166.932i	−0.234497	+	0.406160i
$412$	−230.817	+	316.949i	−0.560235	+	0.769295i
$413$	46.5809	+	11.6821i	0.112787	+	0.0282860i
$414$	−10.0928	−	129.160i	−0.0243788	−	0.311981i
$415$	−1.35214	−	22.8683i	−0.00325817	−	0.0551043i
$416$	−97.7785	−	75.4613i	−0.235044	−	0.181397i
$417$	66.7191	+	17.8773i	0.159998	+	0.0428713i
$418$	−372.685	+	131.741i	−0.891590	+	0.315170i
$419$		−	210.999i		−	0.503579i	−0.967782	−	0.251789i	$-0.918981\pi$
$419$		−	210.999i		−	0.503579i	0.967782	−	0.251789i	$-0.0810190\pi$
$420$	185.754	−	99.7719i	0.442271	−	0.237552i
$421$	−582.411			−1.38340			−0.691700	−	0.722185i	$-0.743138\pi$
$421$	−582.411			−1.38340			−0.691700	+	0.722185i	$0.743138\pi$
$422$	−66.7710	−	188.890i	−0.158225	−	0.447606i
$423$	64.5236	−	240.806i	0.152538	−	0.569280i
$424$	161.959	+	171.241i	0.381978	+	0.403869i
$425$	−802.298	−	116.076i	−1.88776	−	0.273120i
$426$	213.367	−	16.6728i	0.500861	−	0.0391381i
$427$	98.2176	+	344.315i	0.230018	+	0.806359i
$428$	125.355	−	172.133i	0.292885	−	0.402179i
$429$	52.1099	+	30.0857i	0.121468	+	0.0701298i
$430$	674.870	−	284.409i	1.56946	−	0.661416i
$431$	−265.980	+	153.564i	−0.617123	+	0.356296i	−0.775748	−	0.631043i	$-0.782627\pi$
$431$	−265.980	+	153.564i	−0.617123	+	0.356296i	0.158625	+	0.987339i	$0.449294\pi$
$432$	205.761	+	318.394i	0.476299	+	0.737022i
$433$	−60.9752	+	60.9752i	−0.140820	+	0.140820i	−0.774003	−	0.633182i	$-0.781748\pi$
$433$	−60.9752	+	60.9752i	−0.140820	+	0.140820i	0.633182	+	0.774003i	$0.281748\pi$
$434$	−36.0855	−	382.516i	−0.0831462	−	0.881374i
$435$	17.1863	+	26.0804i	0.0395087	+	0.0599550i
$436$	−70.2053	+	182.284i	−0.161021	+	0.418084i
$437$	47.5544	−	177.476i	0.108820	−	0.406122i
$438$	−42.8504	+	230.484i	−0.0978320	+	0.526220i
$439$	162.117	+	93.5984i	0.369288	+	0.213208i	0.673147	−	0.739509i	$-0.264942\pi$
$439$	162.117	+	93.5984i	0.369288	+	0.213208i	−0.303860	+	0.952717i	$0.598275\pi$
$440$	−283.492	+	301.763i	−0.644300	+	0.685825i
$441$	−155.658	+	290.815i	−0.352967	+	0.659444i
$442$	190.248	+	162.670i	0.430425	+	0.368032i
$443$	143.110	+	534.094i	0.323047	+	1.20563i	0.916260	+	0.400583i	$0.131192\pi$
$443$	143.110	+	534.094i	0.323047	+	1.20563i	−0.593213	+	0.805045i	$0.702141\pi$
$444$	−178.837	+	144.490i	−0.402786	+	0.325428i
$445$	−160.631	+	53.3842i	−0.360967	+	0.119965i
$446$	−557.996	−	266.532i	−1.25111	−	0.597605i
$447$	−132.692	+	132.692i	−0.296849	+	0.296849i
$448$	133.002	−	427.802i	0.296879	−	0.954915i
$449$			318.872i			0.710182i	0.934832	+	0.355091i	$0.115550\pi$
$449$			318.872i			0.710182i	−0.934832	+	0.355091i	$0.884450\pi$
$450$	22.0974	−	335.858i	0.0491053	−	0.746352i
$451$	222.360	+	385.139i	0.493038	+	0.853966i
$452$	−473.472	−	50.2968i	−1.04750	−	0.111276i
$453$	85.8672	+	320.461i	0.189552	+	0.707419i
$454$	203.104	−	15.8709i	0.447366	−	0.0349580i
$455$	102.424	+	88.0836i	0.225108	+	0.193590i
$456$	53.3326	+	223.792i	0.116957	+	0.490771i
$457$	7.90497	+	29.5017i	0.0172975	+	0.0645552i	0.974035	−	0.226397i	$-0.0726946\pi$
$457$	7.90497	+	29.5017i	0.0172975	+	0.0645552i	−0.956738	+	0.290952i	$0.906028\pi$
$458$	36.1041	−	194.197i	0.0788300	−	0.424011i
$459$	−384.141	−	665.352i	−0.836908	−	1.44957i
$460$	−41.0643	−	188.022i	−0.0892702	−	0.408744i
$461$			31.0353i			0.0673218i	0.999433	+	0.0336609i	$0.0107166\pi$
$461$			31.0353i			0.0673218i	−0.999433	+	0.0336609i	$0.989283\pi$
$462$	−36.4385	+	215.190i	−0.0788713	+	0.465780i
$463$	−356.134	+	356.134i	−0.769189	+	0.769189i	−0.977964	−	0.208775i	$-0.933052\pi$
$463$	−356.134	+	356.134i	−0.769189	+	0.769189i	0.208775	+	0.977964i	$0.433052\pi$
$464$	64.8818	+	13.9421i	0.139831	+	0.0300476i
$465$	184.764	+	92.5884i	0.397343	+	0.199115i
$466$	−584.655	+	401.344i	−1.25463	+	0.861252i
$467$	228.694	+	853.497i	0.489708	+	1.82762i	0.557851	+	0.829941i	$0.311626\pi$
$467$	228.694	+	853.497i	0.489708	+	1.82762i	−0.0681423	+	0.997676i	$0.521707\pi$
$468$	−61.1820	+	84.0130i	−0.130731	+	0.179515i
$469$	−411.159	+	246.279i	−0.876671	+	0.525115i
$470$	46.0828	−	367.460i	0.0980484	−	0.781830i
$471$	−306.540	−	176.981i	−0.650828	−	0.375756i
$472$	−1.52829	+	54.8626i	−0.00323791	+	0.116234i
$473$	−196.199	+	732.225i	−0.414797	+	1.54804i
$474$	−362.953	−	173.368i	−0.765724	−	0.365755i
$475$	188.296	−	438.644i	0.396414	−	0.923460i
$476$	−312.654	+	852.398i	−0.656837	+	1.79075i
$477$	140.241	−	140.241i	0.294007	−	0.294007i
$478$	−557.611	+	197.111i	−1.16655	+	0.412366i
$479$	630.243	−	363.871i	1.31575	−	0.759648i	0.332707	−	0.943030i	$-0.392038\pi$
$479$	630.243	−	363.871i	1.31575	−	0.759648i	0.983042	+	0.183383i	$0.0587047\pi$
$480$	157.217	+	182.624i	0.327535	+	0.380467i
$481$	−127.567	−	73.6510i	−0.265213	−	0.153121i
$482$	−188.528	+	220.490i	−0.391138	+	0.457447i
$483$	−72.8789	−	70.5727i	−0.150888	−	0.146113i
$484$	8.60993	+	54.7554i	0.0177891	+	0.113131i
$485$	45.2015	+	764.479i	0.0931990	+	1.57624i
$486$	413.446	−	283.815i	0.850712	−	0.583981i
$487$	104.569	−	390.256i	0.214720	−	0.801346i	−0.771545	−	0.636175i	$-0.780516\pi$
$487$	104.569	−	390.256i	0.214720	−	0.801346i	0.986265	−	0.165171i	$-0.0528176\pi$
$488$	−359.937	+	194.653i	−0.737576	+	0.398878i
$489$	311.247			0.636496
$490$	−170.046	+	459.548i	−0.347033	+	0.937853i
$491$			468.769i			0.954724i	0.878707	+	0.477362i	$0.158407\pi$
$491$			468.769i			0.954724i	−0.878707	+	0.477362i	$0.841593\pi$
$492$	236.571	−	105.013i	0.480835	−	0.213441i
$493$	−129.910	−	34.8093i	−0.263509	−	0.0706071i
$494$	−121.519	+	83.4181i	−0.245990	+	0.168863i
$495$	260.466	+	231.384i	0.526194	+	0.467443i
$496$	417.912	−	134.760i	0.842565	−	0.271694i
$497$	−345.983	+	357.290i	−0.696144	+	0.718893i
$498$	8.96872	−	10.4892i	0.0180095	−	0.0210626i
$499$	−304.759	+	527.858i	−0.610740	+	1.05783i	0.380376	+	0.924832i	$0.375794\pi$
$499$	−304.759	+	527.858i	−0.610740	+	1.05783i	−0.991116	+	0.133000i	$0.957539\pi$
$500$	−35.6411	−	498.728i	−0.0712822	−	0.997456i
$501$	8.59628	+	14.8892i	0.0171582	+	0.0297189i
$502$	434.210	−	153.490i	0.864961	−	0.305757i
$503$	−195.469	−	195.469i	−0.388606	−	0.388606i	0.485584	−	0.874190i	$-0.338607\pi$
$503$	−195.469	−	195.469i	−0.388606	−	0.388606i	−0.874190	+	0.485584i	$0.838607\pi$
$504$	−362.955	−	101.849i	−0.720150	−	0.202081i
$505$	−466.368	−	95.8691i	−0.923501	−	0.189840i
$506$	179.755	+	85.8617i	0.355248	+	0.169687i
$507$	−224.184	−	60.0700i	−0.442178	−	0.118481i
$508$	583.291	+	61.9629i	1.14821	+	0.121974i
$509$	378.130	−	654.940i	0.742887	−	1.28672i	−0.208288	−	0.978067i	$-0.566789\pi$
$509$	378.130	−	654.940i	0.742887	−	1.28672i	0.951175	−	0.308651i	$-0.0998774\pi$
$510$	−299.672	−	385.613i	−0.587593	−	0.756105i
$511$	−279.949	−	467.370i	−0.547845	−	0.914619i
$512$	510.214	+	42.7271i	0.996512	+	0.0834514i
$513$	436.987	−	117.090i	0.851826	−	0.228246i
$514$	−409.772	+	281.293i	−0.797222	+	0.547263i
$515$	438.172	+	219.575i	0.850820	+	0.426360i
$516$	411.715	+	158.568i	0.797897	+	0.307303i
$517$	271.060	+	271.060i	0.524294	+	0.524294i
$518$	89.2031	−	526.795i	0.172207	−	1.01698i
$519$	17.4097			0.0335447
$520$	−72.9849	+	136.049i	−0.140355	+	0.261632i
$521$	−466.575	+	269.377i	−0.895538	+	0.517039i	−0.875750	−	0.482765i	$-0.839632\pi$
$521$	−466.575	+	269.377i	−0.895538	+	0.517039i	−0.0197880	+	0.999804i	$0.506299\pi$
$522$	10.2069	−	54.9010i	0.0195535	−	0.105174i
$523$	167.971	−	45.0076i	0.321168	−	0.0860566i	−0.0946334	−	0.995512i	$-0.530168\pi$
$523$	167.971	−	45.0076i	0.321168	−	0.0860566i	0.415801	+	0.909456i	$0.363501\pi$
$524$	−24.8389	−	157.964i	−0.0474025	−	0.301459i
$525$	−161.136	−	208.572i	−0.306927	−	0.397279i
$526$	542.739	−	42.4106i	1.03182	−	0.0806285i
$527$	−859.574	+	230.322i	−1.63107	+	0.437044i
$528$	−249.119	+	12.4998i	−0.471817	+	0.0236738i
$529$	377.937	−	218.202i	0.714436	−	0.412480i
$530$	177.916	−	234.838i	0.335691	−	0.443090i
$531$	46.1827			0.0869730
$532$	−437.180	−	307.743i	−0.821768	−	0.578464i
$533$	117.259	+	117.259i	0.219998	+	0.219998i
$534$	−92.0157	−	43.9521i	−0.172314	−	0.0823073i
$535$	−237.968	−	119.249i	−0.444799	−	0.222896i
$536$	−376.378	−	397.948i	−0.702197	−	0.742440i
$537$	−325.710	+	87.2738i	−0.606537	+	0.162521i
$538$	−247.782	−	211.864i	−0.460561	−	0.393800i
$539$	−267.588	−	430.868i	−0.496452	−	0.799383i
$540$	350.375	−	319.041i	0.648843	−	0.590817i
$541$	−254.665	+	441.092i	−0.470729	+	0.815327i	−0.999440	−	0.0334752i	$-0.989343\pi$
$541$	−254.665	+	441.092i	−0.470729	+	0.815327i	0.528710	+	0.848802i	$0.322676\pi$
$542$	3.37313	−	18.1434i	0.00622348	−	0.0334749i
$543$	−154.684	−	41.4474i	−0.284869	−	0.0763304i
$544$	−1028.38	−	138.300i	−1.89040	−	0.254229i
$545$	239.170	+	49.1650i	0.438844	+	0.0902110i
$546$	7.64354	+	81.0237i	0.0139992	+	0.148395i
$547$	326.968	+	326.968i	0.597749	+	0.597749i	0.939713	−	0.341964i	$-0.111092\pi$
$547$	326.968	+	326.968i	0.597749	+	0.597749i	−0.341964	+	0.939713i	$0.611092\pi$
$548$	467.910	−	207.703i	0.853851	−	0.379021i
$549$	172.163	+	298.195i	0.313593	+	0.543160i
$550$	430.255	+	287.642i	0.782282	+	0.522986i
$551$	39.5979	−	68.5856i	0.0718656	−	0.124475i
$552$	60.7442	−	98.7550i	0.110044	−	0.178904i
$553$	898.891	−	256.413i	1.62548	−	0.463677i
$554$	336.240	−	26.2744i	0.606932	−	0.0474267i
$555$	214.857	+	190.867i	0.387129	+	0.343905i
$556$	−115.289	−	142.695i	−0.207355	−	0.256646i
$557$	−291.734	−	78.1700i	−0.523760	−	0.140341i	−0.0127547	−	0.999919i	$-0.504060\pi$
$557$	−291.734	−	78.1700i	−0.523760	−	0.140341i	−0.511005	+	0.859578i	$0.670727\pi$
$558$	−123.144	−	348.363i	−0.220687	−	0.624306i
$559$			282.667i			0.505666i
$560$	−554.789	−	76.2204i	−0.990694	−	0.136108i
$561$	505.507			0.901082
$562$	197.017	−	69.6441i	0.350564	−	0.123922i
$563$	116.617	−	435.219i	0.207134	−	0.773036i	−0.781654	−	0.623712i	$-0.785624\pi$
$563$	116.617	−	435.219i	0.207134	−	0.773036i	0.988788	−	0.149324i	$-0.0477097\pi$
$564$	173.542	−	140.212i	0.307698	−	0.248602i
$565$	35.1294	+	594.132i	0.0621759	+	1.05156i
$566$	16.3731	+	209.531i	0.0289278	+	0.370197i
$567$	−42.4014	+	169.070i	−0.0747820	+	0.298183i
$568$	−484.147	−	297.799i	−0.852372	−	0.524294i
$569$	−303.274	−	175.095i	−0.532994	−	0.307724i	0.209241	−	0.977864i	$-0.432901\pi$
$569$	−303.274	−	175.095i	−0.532994	−	0.307724i	−0.742235	+	0.670140i	$0.766234\pi$
$570$	265.002	−	111.679i	0.464916	−	0.195929i
$571$	760.051	−	438.816i	1.33109	−	0.768504i	0.345621	−	0.938374i	$-0.387668\pi$
$571$	760.051	−	438.816i	1.33109	−	0.768504i	0.985466	+	0.169870i	$0.0543349\pi$
$572$	−64.8372	−	146.064i	−0.113352	−	0.255357i
$573$	−162.068	+	162.068i	−0.282841	+	0.282841i
$574$	−250.495	+	546.855i	−0.436402	+	0.952709i
$575$	−223.414	+	89.2128i	−0.388546	+	0.155153i
$576$	23.9843	−	430.160i	0.0416394	−	0.746805i
$577$	−94.9089	+	354.205i	−0.164487	+	0.613873i	0.833618	+	0.552341i	$0.186265\pi$
$577$	−94.9089	+	354.205i	−0.164487	+	0.613873i	−0.998105	+	0.0615321i	$0.980401\pi$
$578$	1499.21	+	278.725i	2.59378	+	0.482223i
$579$	163.269	+	94.2635i	0.281985	+	0.162804i
$580$	3.87868	−	82.8628i	0.00668738	−	0.142867i
$581$	0.515542	+	32.0674i	0.000887335	+	0.0551934i
$582$	−299.821	+	350.650i	−0.515156	+	0.602491i
$583$	78.9306	+	294.573i	0.135387	+	0.505271i
$584$	452.353	−	427.834i	0.774577	−	0.732593i
$585$	116.145	+	58.2023i	0.198539	+	0.0994911i
$586$	−50.7702	+	106.290i	−0.0866385	+	0.181382i
$587$	765.163	−	765.163i	1.30351	−	1.30351i	0.377509	−	0.926006i	$-0.376781\pi$
$587$	765.163	−	765.163i	1.30351	−	1.30351i	0.926006	−	0.377509i	$-0.123219\pi$
$588$	−265.817	+	128.377i	−0.452070	+	0.218328i
$589$		−	524.015i		−	0.889668i
$590$	67.9617	−	9.37234i	0.115189	−	0.0158853i
$591$	−117.908	−	204.222i	−0.199506	−	0.345554i
$592$	609.854	−	30.5999i	1.03016	−	0.0516891i
$593$	119.161	+	444.714i	0.200946	+	0.749939i	0.990647	+	0.136448i	$0.0435687\pi$
$593$	119.161	+	444.714i	0.200946	+	0.749939i	−0.789702	+	0.613491i	$0.789765\pi$
$594$	38.2120	+	489.009i	0.0643300	+	0.823247i
$595$	1115.20	+	210.621i	1.87428	+	0.353984i
$596$	492.338	−	77.4170i	0.826070	−	0.129894i
$597$	41.7164	+	155.688i	0.0698767	+	0.260784i
$598$	73.0306	+	13.5775i	0.122125	+	0.0227048i
$599$	−393.897	−	682.249i	−0.657591	−	1.13898i	−0.981238	−	0.192803i	$-0.938242\pi$
$599$	−393.897	−	682.249i	−0.657591	−	1.13898i	0.323647	−	0.946178i	$-0.395091\pi$
$600$	192.926	−	231.327i	0.321543	−	0.385544i
$601$		−	1030.28i		−	1.71428i	−0.515080	−	0.857142i	$-0.672238\pi$
$601$		−	1030.28i		−	1.71428i	0.515080	−	0.857142i	$-0.327762\pi$
$602$	−961.054	+	357.206i	−1.59644	+	0.593366i
$603$	−325.909	+	325.909i	−0.540479	+	0.540479i
$604$	316.684	−	822.254i	0.524311	−	1.36135i
$605$	65.7492	−	21.8512i	0.108676	−	0.0361177i
$606$	−162.332	−	236.476i	−0.267874	−	0.390225i
$607$	21.4888	+	80.1971i	0.0354016	+	0.132120i	0.981365	−	0.192153i	$-0.0615469\pi$
$607$	21.4888	+	80.1971i	0.0354016	+	0.132120i	−0.945963	+	0.324273i	$0.894880\pi$
$608$	235.393	−	563.846i	0.387159	−	0.927378i
$609$	−22.4697	−	37.5128i	−0.0368960	−	0.0615973i
$610$	313.868	+	403.880i	0.514537	+	0.662098i
$611$	123.790	+	71.4703i	0.202602	+	0.116973i
$612$	−92.2332	+	868.243i	−0.150708	+	1.41870i
$613$	277.319	−	1034.97i	0.452396	−	1.68837i	−0.243236	−	0.969967i	$-0.578209\pi$
$613$	277.319	−	1034.97i	0.452396	−	1.68837i	0.695632	−	0.718398i	$-0.255124\pi$
$614$	158.058	−	330.901i	0.257423	−	0.538927i
$615$	−178.025	−	270.156i	−0.289472	−	0.439278i
$616$	414.676	−	405.024i	0.673175	−	0.657506i
$617$	421.236	−	421.236i	0.682717	−	0.682717i	−0.277895	−	0.960611i	$-0.589637\pi$
$617$	421.236	−	421.236i	0.682717	−	0.682717i	0.960611	+	0.277895i	$0.0896367\pi$
$618$	98.4051	+	278.380i	0.159231	+	0.450452i
$619$	−678.334	+	391.636i	−1.09585	+	0.632692i	−0.935129	−	0.354308i	$-0.884717\pi$
$619$	−678.334	+	391.636i	−1.09585	+	0.632692i	−0.160725	+	0.986999i	$0.551383\pi$
$620$	−251.913	−	487.654i	−0.406311	−	0.786539i
$621$	−197.449	−	113.997i	−0.317953	−	0.183570i
$622$	−644.086	−	550.722i	−1.03551	−	0.885405i
$623$	227.886	−	65.0057i	0.365789	−	0.104343i
$624$	−88.5212	+	28.5446i	−0.141861	+	0.0457445i
$625$	−607.641	+	146.277i	−0.972226	+	0.234043i
$626$	−513.521	−	748.069i	−0.820320	−	1.19500i
$627$	−77.0419	+	287.524i	−0.122874	+	0.458571i
$628$	381.409	+	859.232i	0.607339	+	1.36820i
$629$	−1237.50			−1.96741
$630$	−51.1123	+	468.438i	−0.0811306	+	0.743552i
$631$		−	865.154i		−	1.37108i	−0.728033	−	0.685542i	$-0.759565\pi$
$631$		−	865.154i		−	1.37108i	0.728033	−	0.685542i	$-0.240435\pi$
$632$	508.173	+	939.675i	0.804070	+	1.48683i
$633$	−145.727	−	39.0475i	−0.230217	−	0.0616864i
$634$	460.783	+	671.244i	0.726788	+	1.05874i
$635$	−43.2775	−	731.938i	−0.0681535	−	1.15266i
$636$	175.338	−	27.5707i	0.275688	−	0.0433502i
$637$	−137.963	−	129.365i	−0.216582	−	0.203084i
$638$	65.2613	+	55.8013i	0.102290	+	0.0874628i
$639$	−239.145	+	414.211i	−0.374249	+	0.648218i
$640$	−52.0020	−	637.884i	−0.0812531	−	0.996694i
$641$	300.943	+	521.248i	0.469489	+	0.813179i	0.999392	−	0.0348796i	$-0.0111048\pi$
$641$	300.943	+	521.248i	0.469489	+	0.813179i	−0.529902	+	0.848059i	$0.677771\pi$
$642$	−53.4430	−	151.186i	−0.0832445	−	0.235492i
$643$	726.677	+	726.677i	1.13013	+	1.13013i	0.990154	+	0.139981i	$0.0447040\pi$
$643$	726.677	+	726.677i	1.13013	+	1.13013i	0.139981	+	0.990154i	$0.455296\pi$
$644$	46.1259	+	265.458i	0.0716241	+	0.412202i
$645$	111.046	−	540.198i	0.172164	−	0.837516i
$646$	−533.718	+	1117.36i	−0.826190	+	1.72966i
$647$	−665.627	−	178.354i	−1.02879	−	0.275664i	−0.295330	−	0.955395i	$-0.595430\pi$
$647$	−665.627	−	178.354i	−1.02879	−	0.275664i	−0.733461	+	0.679732i	$0.762096\pi$
$648$	−199.129	−	5.54709i	−0.307298	−	0.00856032i
$649$	−35.5064	+	61.4989i	−0.0547094	+	0.0947595i
$650$	182.729	+	62.0790i	0.281122	+	0.0955062i
$651$	−252.861	−	140.619i	−0.388420	−	0.216005i
$652$	−668.220	−	486.627i	−1.02488	−	0.746361i
$653$	−170.643	+	45.7236i	−0.261321	+	0.0700209i	−0.387101	−	0.922037i	$-0.626523\pi$
$653$	−170.643	+	45.7236i	−0.261321	+	0.0700209i	0.125779	+	0.992058i	$0.459857\pi$
$654$	83.2494	+	121.273i	0.127293	+	0.185433i
$655$	−189.681	+	63.0389i	−0.289589	+	0.0962425i
$656$	−672.082	−	144.420i	−1.02452	−	0.220152i
$657$	−370.465	−	370.465i	−0.563874	−	0.563874i
$658$	−86.5618	+	511.197i	−0.131553	+	0.776894i
$659$	480.601			0.729288			0.364644	−	0.931147i	$-0.381191\pi$
$659$	480.601			0.729288			0.364644	+	0.931147i	$0.381191\pi$
$660$	66.5274	+	304.611i	0.100799	+	0.461531i
$661$	984.291	−	568.281i	1.48909	−	0.859729i	0.489172	−	0.872187i	$-0.337299\pi$
$661$	984.291	−	568.281i	1.48909	−	0.859729i	0.999922	+	0.0124584i	$0.00396574\pi$
$662$	522.977	+	97.2291i	0.789995	+	0.146872i
$663$	182.073	−	48.7863i	0.274620	−	0.0735842i
$664$	−35.6547	+	8.49700i	−0.0536968	+	0.0127967i
$665$	−289.759	+	602.206i	−0.435728	+	0.905573i
$666$	−40.0283	−	512.253i	−0.0601026	−	0.769148i
$667$	−38.5519	+	10.3300i	−0.0577990	+	0.0154872i
$668$	4.82346	−	45.4059i	0.00722074	−	0.0679729i
$669$	−403.284	+	232.836i	−0.602815	+	0.348036i
$670$	−413.462	+	545.742i	−0.617108	+	0.814541i
$671$	−529.453			−0.789050
$672$	−208.914	−	264.896i	−0.310884	−	0.394190i
$673$	44.6202	+	44.6202i	0.0663004	+	0.0663004i	0.739479	−	0.673179i	$-0.235072\pi$
$673$	44.6202	+	44.6202i	0.0663004	+	0.0663004i	−0.673179	+	0.739479i	$0.735072\pi$
$674$	−78.7558	+	164.879i	−0.116848	+	0.244627i
$675$	−465.283	−	366.567i	−0.689308	−	0.543063i
$676$	387.386	+	479.472i	0.573056	+	0.709278i
$677$	1068.95	−	286.424i	1.57895	−	0.423078i	0.640349	−	0.768084i	$-0.278790\pi$
$677$	1068.95	−	286.424i	1.57895	−	0.423078i	0.938601	+	0.345005i	$0.112123\pi$
$678$	−233.013	+	272.516i	−0.343676	+	0.401940i
$679$	−17.2344	−	1072.00i	−0.0253820	−	1.57879i
$680$	40.4728	+	1296.41i	0.0595188	+	1.90649i
$681$	76.7065	−	132.860i	0.112638	−	0.195095i
$682$	558.572	+	103.847i	0.819020	+	0.152268i
$683$	−982.574	−	263.280i	−1.43862	−	0.385476i	−0.546567	−	0.837416i	$-0.684066\pi$
$683$	−982.574	−	263.280i	−1.43862	−	0.385476i	−0.892048	+	0.451940i	$0.850732\pi$
$684$	−479.786	−	184.786i	−0.701441	−	0.270154i
$685$	−352.114	−	534.338i	−0.514035	−	0.780055i
$686$	265.490	−	632.543i	0.387012	−	0.922075i
$687$	−105.179	−	105.179i	−0.153099	−	0.153099i
$688$	−635.998	−	984.140i	−0.924415	−	1.43044i
$689$	56.8583	+	98.4815i	0.0825230	+	0.142934i
$690$	−134.233	−	54.6376i	−0.194541	−	0.0791850i
$691$	−515.676	+	893.177i	−0.746275	+	1.29259i	0.203322	+	0.979112i	$0.434826\pi$
$691$	−515.676	+	893.177i	−0.746275	+	1.29259i	−0.949597	+	0.313474i	$0.898507\pi$
$692$	−37.3771	−	27.2196i	−0.0540131	−	0.0393348i
$693$	−350.396	−	339.308i	−0.505622	−	0.489622i
$694$	−37.9711	−	485.926i	−0.0547134	−	0.700181i
$695$	−152.294	+	171.435i	−0.219128	+	0.246670i
$696$	36.3074	−	34.3394i	0.0521659	−	0.0493383i
$697$	1345.68	+	360.574i	1.93068	+	0.517323i
$698$	−380.395	+	134.467i	−0.544979	+	0.192646i
$699$			534.025i			0.763984i
$700$	19.8491	+	699.719i	0.0283558	+	0.999598i
$701$	291.683			0.416095			0.208048	−	0.978119i	$-0.433289\pi$
$701$	291.683			0.416095			0.208048	+	0.978119i	$0.433289\pi$
$702$	60.9573	+	172.443i	0.0868337	+	0.245645i
$703$	188.602	−	703.872i	0.268281	−	1.00124i
$704$	554.381	+	362.657i	0.787472	+	0.515137i
$705$	−208.495	−	185.216i	−0.295737	−	0.262717i
$706$	60.0165	−	4.68979i	0.0850092	−	0.00664277i
$707$	646.545	+	162.148i	0.914491	+	0.229347i
$708$	33.4097	+	24.3304i	0.0471888	+	0.0343650i
$709$	205.049	+	118.385i	0.289209	+	0.166975i	0.637585	−	0.770380i	$-0.279934\pi$
$709$	205.049	+	118.385i	0.289209	+	0.166975i	−0.348376	+	0.937355i	$0.613267\pi$
$710$	−267.862	+	658.079i	−0.377270	+	0.926871i
$711$	778.486	−	449.459i	1.09492	−	0.632151i
$712$	128.832	+	238.226i	0.180943	+	0.334587i
$713$	−186.736	+	186.736i	−0.261902	+	0.261902i
$714$	395.956	+	557.388i	0.554561	+	0.780655i
$715$	−166.800	+	109.917i	−0.233287	+	0.153730i
$716$	835.723	+	321.872i	1.16721	+	0.449541i
$717$	−115.270	+	430.194i	−0.160767	+	0.599991i
$718$	−6.91845	+	37.2130i	−0.00963573	+	0.0518287i
$719$	1099.60	+	634.855i	1.52935	+	0.882969i	0.999389	+	0.0349445i	$0.0111255\pi$
$719$	1099.60	+	634.855i	1.52935	+	0.882969i	0.529957	+	0.848024i	$0.322208\pi$
$720$	−535.328	+	58.6871i	−0.743511	+	0.0815098i
$721$	−599.665	−	333.481i	−0.831713	−	0.462526i
$722$	−5.44488	−	4.65561i	−0.00754139	−	0.00644821i
$723$	56.5414	+	211.016i	0.0782039	+	0.291861i
$724$	267.291	+	330.829i	0.369186	+	0.456946i
$725$	−102.969	+	12.2193i	−0.142027	+	0.0168542i
$726$	37.6638	+	17.9905i	0.0518786	+	0.0247803i
$727$	361.549	−	361.549i	0.497317	−	0.497317i	−0.413285	−	0.910602i	$-0.635619\pi$
$727$	361.549	−	361.549i	0.497317	−	0.497317i	0.910602	+	0.413285i	$0.135619\pi$
$728$	110.269	−	185.901i	0.151468	−	0.255359i
$729$		−	153.535i		−	0.210610i
$730$	−620.353	−	469.988i	−0.849799	−	0.643820i
$731$	1187.36	+	2056.57i	1.62430	+	2.81337i
$732$	−32.5511	+	306.422i	−0.0444687	+	0.418609i
$733$	116.041	+	433.072i	0.158310	+	0.590821i	0.998799	+	0.0489925i	$0.0156011\pi$
$733$	116.041	+	433.072i	0.158310	+	0.590821i	−0.840489	+	0.541828i	$0.817732\pi$
$734$	202.100	−	15.7925i	0.275341	−	0.0215156i
$735$	212.836	+	301.424i	0.289572	+	0.410101i
$736$	−284.814	+	117.046i	−0.386975	+	0.159030i
$737$	−183.428	−	684.562i	−0.248884	−	0.928849i
$738$	−105.729	+	568.696i	−0.143264	+	0.770591i
$739$	−55.5469	−	96.2101i	−0.0751650	−	0.130190i	0.825993	−	0.563680i	$-0.190615\pi$
$739$	−55.5469	−	96.2101i	−0.0751650	−	0.130190i	−0.901158	+	0.433491i	$0.857282\pi$
$740$	−162.862	−	745.699i	−0.220084	−	1.00770i
$741$			110.996i			0.149792i
$742$	−262.980	+	317.766i	−0.354421	+	0.428256i
$743$	−57.1447	+	57.1447i	−0.0769108	+	0.0769108i	−0.744516	−	0.667605i	$-0.767320\pi$
$743$	−57.1447	+	57.1447i	−0.0769108	+	0.0769108i	0.667605	+	0.744516i	$0.267320\pi$
$744$	94.4429	−	316.890i	0.126939	−	0.425928i
$745$	−196.477	−	591.190i	−0.263728	−	0.793544i
$746$	−736.957	+	505.893i	−0.987878	+	0.678141i
$747$	7.98255	+	29.7913i	0.0106862	+	0.0398813i
$748$	−1085.28	−	790.349i	−1.45091	−	1.05662i
$749$	325.673	+	181.111i	0.434811	+	0.241803i
$750$	−324.821	−	190.423i	−0.433095	−	0.253897i
$751$	−58.0140	−	33.4944i	−0.0772490	−	0.0445997i	0.460878	−	0.887464i	$-0.347535\pi$
$751$	−58.0140	−	33.4944i	−0.0772490	−	0.0445997i	−0.538127	+	0.842864i	$0.680868\pi$
$752$	−591.797	+	29.6939i	−0.786964	+	0.0394866i
$753$	89.7606	−	334.991i	0.119204	−	0.444875i
$754$	28.8911	+	13.8001i	0.0383172	+	0.0183025i
$755$	−1078.85	−	221.775i	−1.42895	−	0.293741i
$756$	−509.265	+	425.167i	−0.673631	+	0.562390i
$757$	−418.684	+	418.684i	−0.553083	+	0.553083i	−0.927329	−	0.374246i	$-0.877902\pi$
$757$	−418.684	+	418.684i	−0.553083	+	0.553083i	0.374246	+	0.927329i	$0.377902\pi$
$758$	1277.43	−	451.561i	1.68526	−	0.595727i
$759$	129.915	−	75.0067i	0.171167	−	0.0988231i
$760$	−743.546	−	174.559i	−0.978350	−	0.229683i
$761$	94.4364	+	54.5229i	0.124095	+	0.0716463i	0.560763	−	0.827977i	$-0.310508\pi$
$761$	94.4364	+	54.5229i	0.124095	+	0.0716463i	−0.436668	+	0.899623i	$0.643841\pi$
$762$	287.059	−	335.724i	0.376718	−	0.440583i
$763$	−331.571	−	83.1553i	−0.434562	−	0.108985i
$764$	601.336	−	94.5562i	0.787088	−	0.123765i
$765$	1089.51	−	64.4196i	1.42419	−	0.0842086i
$766$	−780.984	+	536.116i	−1.01956	+	0.699890i
$767$	−6.85343	+	25.5774i	−0.00893537	+	0.0333473i
$768$	243.972	−	298.553i	0.317672	−	0.388741i
$769$	102.995			0.133933			0.0669666	−	0.997755i	$-0.478668\pi$
$769$	102.995			0.133933			0.0669666	+	0.997755i	$0.478668\pi$
$770$	−584.497	−	428.210i	−0.759087	−	0.556117i
$771$			374.286i			0.485456i
$772$	−203.146	−	457.643i	−0.263142	−	0.592802i
$773$	20.6876	+	5.54323i	0.0267628	+	0.00717106i	0.272176	−	0.962248i	$-0.412257\pi$
$773$	20.6876	+	5.54323i	0.0267628	+	0.00717106i	−0.245413	+	0.969419i	$0.578924\pi$
$774$	−812.892	+	558.019i	−1.05025	+	0.720955i
$775$	−549.612	+	410.678i	−0.709177	+	0.529907i
$776$	1191.92	−	284.052i	1.53598	−	0.366046i
$777$	−289.039	−	279.893i	−0.371994	−	0.360222i
$778$	−172.169	+	201.356i	−0.221296	+	0.258813i
$779$	−410.178	+	710.449i	−0.526544	+	0.912002i
$780$	53.3597	+	103.294i	0.0684098	+	0.132428i
$781$	−367.721	−	636.912i	−0.470834	−	0.815509i
$782$	588.373	−	207.986i	0.752396	−	0.265966i
$783$	−69.4891	−	69.4891i	−0.0887473	−	0.0887473i
$784$	771.401	+	139.985i	0.983930	+	0.178552i
$785$	981.213	−	646.593i	1.24995	−	0.823685i
$786$	−108.657	−	51.9009i	−0.138240	−	0.0660317i
$787$	460.602	+	123.418i	0.585263	+	0.156821i	0.539288	−	0.842122i	$-0.318694\pi$
$787$	460.602	+	123.418i	0.585263	+	0.156821i	0.0459759	+	0.998943i	$0.485360\pi$
$788$	−66.1593	+	622.794i	−0.0839585	+	0.790348i
$789$	204.977	−	355.030i	0.259793	−	0.449975i
$790$	1054.39	−	819.404i	1.33468	−	1.03722i
$791$	−13.3941	−	833.130i	−0.0169331	−	1.05326i
$792$	292.053	−	474.806i	0.368754	−	0.599503i
$793$	−190.698	+	51.0973i	−0.240476	+	0.0644355i
$794$	−790.312	+	542.519i	−0.995355	+	0.683273i
$795$	−69.9720	−	210.542i	−0.0880150	−	0.264833i
$796$	153.853	−	399.471i	0.193283	−	0.501848i
$797$	−498.204	−	498.204i	−0.625099	−	0.625099i	0.321732	−	0.946831i	$-0.395735\pi$
$797$	−498.204	−	498.204i	−0.625099	−	0.625099i	−0.946831	+	0.321732i	$0.895735\pi$
$798$	−377.379	+	140.265i	−0.472906	+	0.175770i
$799$	1200.86			1.50295
$800$	−775.870	+	195.003i	−0.969837	+	0.243753i
$801$	197.361	−	113.947i	0.246394	−	0.142256i
$802$	−51.6017	+	277.556i	−0.0643412	+	0.346079i
$803$	778.151	−	208.505i	0.969055	−	0.259658i
$804$	−407.469	+	64.0719i	−0.506802	+	0.0796915i
$805$	317.858	−	111.342i	0.394854	−	0.138314i
$806$	211.208	−	16.5042i	0.262045	−	0.0204766i
$807$	−237.135	+	63.5402i	−0.293848	+	0.0787363i
$808$	−21.2128	+	761.497i	−0.0262535	+	0.942446i
$809$	233.193	−	134.634i	0.288248	−	0.166420i	−0.348903	−	0.937159i	$-0.613446\pi$
$809$	233.193	−	134.634i	0.288248	−	0.166420i	0.637152	+	0.770739i	$0.280113\pi$
$810$	34.0178	+	246.674i	0.0419973	+	0.304535i
$811$	−524.159			−0.646312			−0.323156	−	0.946346i	$-0.604744\pi$
$811$	−524.159			−0.646312			−0.323156	+	0.946346i	$0.604744\pi$
$812$	−10.4100	+	115.667i	−0.0128202	+	0.142448i
$813$	−9.82662	−	9.82662i	−0.0120869	−	0.0120869i
$814$	712.913	+	340.529i	0.875815	+	0.418341i
$815$	−462.927	+	923.792i	−0.568009	+	1.13349i
$816$	−524.140	+	579.517i	−0.642329	+	0.710193i
$817$	−1350.70	+	361.920i	−1.65325	+	0.442987i
$818$	332.242	+	284.082i	0.406164	+	0.347288i
$819$	−158.952	−	88.3950i	−0.194080	−	0.107930i
$820$	−40.1776	+	858.340i	−0.0489971	+	1.04676i
$821$	−390.249	+	675.931i	−0.475334	+	0.823302i	−0.999601	−	0.0282516i	$-0.991006\pi$
$821$	−390.249	+	675.931i	−0.475334	+	0.823302i	0.524267	+	0.851554i	$0.324339\pi$
$822$	70.4651	−	379.018i	0.0857239	−	0.461093i
$823$	−937.391	−	251.173i	−1.13899	−	0.305192i	−0.360447	−	0.932780i	$-0.617376\pi$
$823$	−937.391	−	251.173i	−1.13899	−	0.305192i	−0.778546	+	0.627588i	$0.784042\pi$
$824$	223.973	−	751.511i	0.271812	−	0.912028i
$825$	361.948	−	144.532i	0.438725	−	0.175190i
$826$	−95.6223	+	9.02073i	−0.115766	+	0.0109210i
$827$	−999.090	−	999.090i	−1.20809	−	1.20809i	−0.971645	−	0.236444i	$-0.924018\pi$
$827$	−999.090	−	999.090i	−1.20809	−	1.20809i	−0.236444	−	0.971645i	$-0.575982\pi$
$828$	105.125	+	236.824i	0.126963	+	0.286020i
$829$	−54.4034	−	94.2295i	−0.0656254	−	0.113666i	0.831346	−	0.555755i	$-0.187571\pi$
$829$	−54.4034	−	94.2295i	−0.0656254	−	0.113666i	−0.896971	+	0.442089i	$0.854238\pi$
$830$	17.7929	+	42.2204i	0.0214372	+	0.0508680i
$831$	126.988	−	219.950i	0.152814	−	0.264681i
$832$	234.676	+	77.1182i	0.282063	+	0.0926902i
$833$	−1547.16	−	361.684i	−1.85734	−	0.434195i
$834$	−137.726	+	10.7621i	−0.165139	+	0.0129042i
$835$	−56.9772	+	3.36891i	−0.0682362	+	0.00403462i
$836$	614.940	−	496.837i	0.735575	−	0.594302i
$837$	−628.082	−	168.294i	−0.750396	−	0.201068i
$838$	140.645	+	397.872i	0.167834	+	0.474787i
$839$			1200.44i			1.43080i	0.698713	+	0.715402i	$0.253756\pi$
$839$			1200.44i			1.43080i	−0.698713	+	0.715402i	$0.746244\pi$
$840$	−283.763	+	311.952i	−0.337813	+	0.371372i
$841$	823.797			0.979544
$842$	1098.23	−	388.215i	1.30431	−	0.461062i
$843$	40.7277	−	151.998i	0.0483128	−	0.180306i
$844$	251.814	+	311.673i	0.298358	+	0.369281i
$845$	511.726	−	576.043i	0.605593	−	0.681708i
$846$	38.8431	+	497.085i	0.0459138	+	0.587571i
$847$	−93.2784	+	26.6081i	−0.110128	+	0.0314145i
$848$	−419.541	−	214.945i	−0.494742	−	0.253472i
$849$	137.064	+	79.1338i	0.161441	+	0.0932083i
$850$	1590.23	−	315.904i	1.87086	−	0.371652i
$851$	−318.039	+	183.620i	−0.373723	+	0.215769i
$852$	−391.222	+	173.662i	−0.459181	+	0.203828i
$853$	−103.037	+	103.037i	−0.120794	+	0.120794i	−0.764920	−	0.644126i	$-0.777221\pi$
$853$	−103.037	+	103.037i	−0.120794	+	0.120794i	0.644126	+	0.764920i	$0.277221\pi$
$854$	−414.713	−	583.791i	−0.485612	−	0.683596i
$855$	−129.406	+	629.512i	−0.151352	+	0.736272i
$856$	−121.638	+	408.139i	−0.142100	+	0.476798i
$857$	−26.8852	+	100.337i	−0.0313713	+	0.117079i	−0.979836	−	0.199804i	$-0.935970\pi$
$857$	−26.8852	+	100.337i	−0.0313713	+	0.117079i	0.948465	+	0.316883i	$0.102636\pi$
$858$	−118.315	−	21.9966i	−0.137897	−	0.0256370i
$859$	492.269	+	284.212i	0.573072	+	0.330863i	0.758375	−	0.651818i	$-0.225993\pi$
$859$	492.269	+	284.212i	0.573072	+	0.330863i	−0.185303	+	0.982681i	$0.559327\pi$
$860$	−1082.99	+	986.141i	−1.25930	+	1.14668i
$861$	232.753	+	388.579i	0.270329	+	0.451311i
$862$	399.187	−	466.861i	0.463093	−	0.541602i
$863$	−69.2023	−	258.266i	−0.0801880	−	0.299266i	0.914171	−	0.405328i	$-0.132843\pi$
$863$	−69.2023	−	258.266i	−0.0801880	−	0.299266i	−0.994360	+	0.106062i	$0.966176\pi$
$864$	−600.224	−	463.227i	−0.694704	−	0.536143i
$865$	−25.8940	+	51.6726i	−0.0299352	+	0.0597371i
$866$	74.3342	−	155.622i	0.0858363	−	0.179702i
$867$	811.982	−	811.982i	0.936543	−	0.936543i
$868$	323.016	+	697.240i	0.372139	+	0.803272i
$869$			1382.22i			1.59059i
$870$	−49.7917	−	37.7229i	−0.0572318	−	0.0433596i
$871$	−132.134	−	228.862i	−0.151704	−	0.262758i
$872$	10.8787	−	390.522i	0.0124755	−	0.447846i
$873$	−266.854	−	995.912i	−0.305675	−	1.14079i
$874$	28.6277	+	366.356i	0.0327548	+	0.419171i
$875$	858.712	−	168.044i	0.981385	−	0.192050i
$876$	−72.8315	−	463.176i	−0.0831410	−	0.528740i
$877$	229.041	+	854.793i	0.261164	+	0.974679i	0.964556	+	0.263877i	$0.0850012\pi$
$877$	229.041	+	854.793i	0.261164	+	0.974679i	−0.703392	+	0.710802i	$0.748332\pi$
$878$	−368.086	−	68.4327i	−0.419233	−	0.0779416i
$879$	44.3516	+	76.8192i	0.0504569	+	0.0873939i
$880$	333.423	−	757.987i	0.378890	−	0.861349i
$881$			1385.67i			1.57284i	0.617692	+	0.786420i	$0.288068\pi$
$881$			1385.67i			1.57284i	−0.617692	+	0.786420i	$0.711932\pi$
$882$	99.6712	−	652.133i	0.113006	−	0.739379i
$883$	50.6144	−	50.6144i	0.0573210	−	0.0573210i	−0.677865	−	0.735186i	$-0.737095\pi$
$883$	50.6144	−	50.6144i	0.0573210	−	0.0573210i	0.735186	+	0.677865i	$0.237095\pi$
$884$	−467.172	−	179.927i	−0.528475	−	0.203538i
$885$	23.1455	−	46.1878i	0.0261531	−	0.0521896i
$886$	−625.864	−	911.724i	−0.706392	−	1.02903i
$887$	−252.563	−	942.577i	−0.284738	−	1.06266i	−0.949030	−	0.315185i	$-0.897934\pi$
$887$	−252.563	−	942.577i	−0.284738	−	1.06266i	0.664292	−	0.747473i	$-0.268733\pi$
$888$	240.913	−	391.664i	0.271298	−	0.441063i
$889$	16.5008	+	1026.37i	0.0185611	+	1.15452i
$890$	267.310	−	207.735i	0.300348	−	0.233410i
$891$	−223.216	−	128.874i	−0.250523	−	0.144640i
$892$	1229.85	+	130.646i	1.37875	+	0.146465i
$893$	−183.017	+	683.030i	−0.204947	+	0.764872i
$894$	161.763	−	338.658i	0.180943	−	0.378812i
$895$	225.407	−	1096.53i	0.251852	−	1.22517i
$896$	34.3619	+	895.341i	0.0383503	+	0.999264i
$897$	39.5540	−	39.5540i	0.0440959	−	0.0440959i
$898$	−212.549	−	601.282i	−0.236691	−	0.669579i
$899$	−98.5783	+	56.9142i	−0.109653	+	0.0633084i
$900$	182.203	+	648.042i	0.202448	+	0.720047i
$901$	827.355	+	477.674i	0.918263	+	0.530160i
$902$	−676.014	−	578.021i	−0.749461	−	0.640822i
$903$	−187.818	+	748.898i	−0.207993	+	0.829345i
$904$	926.330	−	220.757i	1.02470	−	0.244200i
$905$	353.084	−	397.462i	0.390148	−	0.439184i
$906$	−375.524	−	547.042i	−0.414485	−	0.603800i
$907$	−160.432	+	598.741i	−0.176882	+	0.660133i	0.819341	+	0.573306i	$0.194339\pi$
$907$	−160.432	+	598.741i	−0.176882	+	0.660133i	−0.996223	+	0.0868271i	$0.972327\pi$
$908$	−372.405	+	165.309i	−0.410138	+	0.182058i
$909$	641.018			0.705191
$910$	−251.850	−	97.8229i	−0.276758	−	0.107498i
$911$		−	671.186i		−	0.736757i	−0.929676	−	0.368379i	$-0.879913\pi$
$911$		−	671.186i		−	0.736757i	0.929676	−	0.368379i	$-0.120087\pi$
$912$	−249.738	−	386.444i	−0.273836	−	0.423733i
$913$	−45.8086	−	12.2744i	−0.0501737	−	0.0134440i
$914$	−34.5708	−	50.3609i	−0.0378237	−	0.0550995i
$915$	384.511	−	22.7351i	0.420231	−	0.0248471i
$916$	61.3651	+	390.255i	0.0669924	+	0.426042i
$917$	269.100	−	76.7621i	0.293457	−	0.0837100i
$918$	1167.86	+	998.568i	1.27218	+	1.08777i
$919$	409.427	−	709.149i	0.445514	−	0.771653i	−0.552574	−	0.833464i	$-0.686354\pi$
$919$	409.427	−	709.149i	0.445514	−	0.771653i	0.998088	+	0.0618111i	$0.0196876\pi$
$920$	202.762	+	327.173i	0.220393	+	0.355622i
$921$	−138.076	−	239.154i	−0.149919	−	0.259668i
$922$	−20.6870	−	58.5219i	−0.0224371	−	0.0634728i
$923$	−193.914	−	193.914i	−0.210091	−	0.210091i
$924$	−74.7276	−	430.063i	−0.0808741	−	0.465436i
$925$	−886.065	+	353.820i	−0.957908	+	0.382508i
$926$	434.160	−	908.933i	0.468855	−	0.981569i
$927$	−637.370	−	170.783i	−0.687562	−	0.184232i
$928$	−131.638	+	16.9579i	−0.141851	+	0.0182737i
$929$	−918.207	+	1590.38i	−0.988382	+	1.71193i	−0.362563	+	0.931959i	$0.618098\pi$
$929$	−918.207	+	1590.38i	−0.988382	+	1.71193i	−0.625819	+	0.779969i	$0.715235\pi$
$930$	−410.118	−	51.4324i	−0.440987	−	0.0553037i
$931$	441.516	−	824.879i	0.474238	−	0.886014i
$932$	834.936	−	1146.51i	0.895854	−	1.23016i
$933$	−616.411	+	165.167i	−0.660676	+	0.177028i
$934$	−1000.15	−	1456.96i	−1.07082	−	1.55992i
$935$	−751.857	+	1500.36i	−0.804125	+	1.60467i
$936$	59.3681	−	199.201i	0.0634274	−	0.212822i
$937$	1191.20	+	1191.20i	1.27129	+	1.27129i	0.945413	+	0.325873i	$0.105658\pi$
$937$	1191.20	+	1191.20i	1.27129	+	1.27129i	0.325873	+	0.945413i	$0.394342\pi$
$938$	611.143	−	738.461i	0.651538	−	0.787271i
$939$	−683.287			−0.727675
$940$	158.040	+	723.620i	0.168127	+	0.769808i
$941$	−1058.41	+	611.076i	−1.12478	+	0.649390i	−0.942616	−	0.333879i	$-0.891642\pi$
$941$	−1058.41	+	611.076i	−1.12478	+	0.649390i	−0.182160	+	0.983269i	$0.558309\pi$
$942$	695.998	+	129.396i	0.738851	+	0.137363i
$943$	399.343	−	107.004i	0.423481	−	0.113471i
$944$	−33.6877	−	104.471i	−0.0356861	−	0.110668i
$945$	628.742	+	540.711i	0.665336	+	0.572181i
$946$	−118.111	−	1511.50i	−0.124854	−	1.59778i
$947$	407.222	−	109.115i	0.430013	−	0.115222i	−0.0373192	−	0.999303i	$-0.511882\pi$
$947$	407.222	−	109.115i	0.430013	−	0.115222i	0.467332	+	0.884082i	$0.345215\pi$
$948$	799.965	+	84.9801i	0.843845	+	0.0896414i
$949$	260.151	−	150.198i	0.274132	−	0.158270i
$950$	−62.6779	+	952.642i	−0.0659768	+	1.00278i
$951$	613.115			0.644706
$952$	21.3795	−	1815.73i	0.0224575	−	1.90728i
$953$	−1004.57	−	1004.57i	−1.05412	−	1.05412i	−0.998449	−	0.0556659i	$-0.982272\pi$
$953$	−1004.57	−	1004.57i	−1.05412	−	1.05412i	−0.0556659	−	0.998449i	$-0.517728\pi$
$954$	−170.967	+	357.927i	−0.179211	+	0.375185i
$955$	−239.975	−	722.073i	−0.251283	−	0.756097i
$956$	920.074	−	743.367i	0.962420	−	0.777580i
$957$	62.4571	−	16.7353i	0.0652635	−	0.0174873i
$958$	−945.878	+	1106.23i	−0.987346	+	1.15473i
$959$	460.360	+	768.564i	0.480042	+	0.801422i
$960$	−418.188	−	239.571i	−0.435612	−	0.249553i
$961$	103.916	−	179.988i	0.108133	−	0.187293i
$962$	289.641	+	53.8485i	0.301082	+	0.0559756i
$963$	346.150	+	92.7507i	0.359450	+	0.0963143i
$964$	208.529	−	541.434i	0.216316	−	0.561653i
$965$	−522.613	+	344.388i	−0.541568	+	0.356879i
$966$	184.466	+	84.4972i	0.190958	+	0.0874712i
$967$	−605.438	−	605.438i	−0.626099	−	0.626099i	0.320985	−	0.947084i	$-0.395986\pi$
$967$	−605.438	−	605.438i	−0.626099	−	0.626099i	−0.947084	+	0.320985i	$0.895986\pi$
$968$	−52.7333	−	97.5106i	−0.0544766	−	0.100734i
$969$	466.244	+	807.558i	0.481160	+	0.833393i
$970$	−594.809	−	1411.41i	−0.613205	−	1.45506i
$971$	−166.320	+	288.075i	−0.171287	+	0.296678i	−0.938870	−	0.344271i	$-0.888126\pi$
$971$	−166.320	+	288.075i	−0.171287	+	0.296678i	0.767583	+	0.640950i	$0.221459\pi$
$972$	−590.435	+	810.765i	−0.607444	+	0.834121i
$973$	223.328	−	230.626i	0.229525	−	0.237026i
$974$	62.9501	+	805.589i	0.0646305	+	0.827093i
$975$	116.418	−	86.9889i	0.119403	−	0.0892193i
$976$	548.969	−	606.969i	0.562468	−	0.621894i
$977$	−874.423	−	234.301i	−0.895008	−	0.239817i	−0.218137	−	0.975918i	$-0.569998\pi$
$977$	−874.423	−	234.301i	−0.895008	−	0.239817i	−0.676871	+	0.736101i	$0.736665\pi$
$978$	−586.904	+	207.466i	−0.600106	+	0.212133i
$979$			350.421i			0.357937i
$980$	14.3304	−	979.895i	0.0146229	−	0.999893i
$981$	−328.736			−0.335103
$982$	−312.465	−	883.937i	−0.318192	−	0.900139i
$983$	−48.5391	+	181.151i	−0.0493786	+	0.184283i	−0.986210	−	0.165497i	$-0.947077\pi$
$983$	−48.5391	+	181.151i	−0.0493786	+	0.184283i	0.936832	+	0.349780i	$0.113744\pi$
$984$	−376.093	+	355.708i	−0.382208	+	0.361491i
$985$	781.508	−	46.2084i	0.793410	−	0.0469121i
$986$	268.168	−	20.9551i	0.271976	−	0.0212527i
$987$	280.481	+	271.605i	0.284175	+	0.275183i
$988$	173.539	−	238.298i	0.175647	−	0.241192i
$989$	610.305	+	352.360i	0.617093	+	0.356279i
$990$	−645.381	−	262.693i	−0.651900	−	0.265347i
$991$	1559.36	−	900.300i	1.57353	−	0.908476i	0.577795	−	0.816182i	$-0.303913\pi$
$991$	1559.36	−	900.300i	1.57353	−	0.908476i	0.995732	−	0.0922937i	$-0.0294199\pi$
$992$	−698.212	+	532.676i	−0.703842	+	0.536972i
$993$	283.248	−	283.248i	0.285245	−	0.285245i
$994$	414.248	−	904.345i	0.416749	−	0.909804i
$995$	−524.134	−	107.744i	−0.526767	−	0.108285i
$996$	−9.92018	+	25.7572i	−0.00996002	+	0.0258607i
$997$	−267.436	+	998.085i	−0.268241	+	1.00109i	0.691996	+	0.721901i	$0.256732\pi$
$997$	−267.436	+	998.085i	−0.268241	+	1.00109i	−0.960237	+	0.279187i	$0.909935\pi$
$998$	222.819	−	1198.50i	0.223265	−	1.20090i
$999$	−783.086	−	452.115i	−0.783870	−	0.452567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.3.x.a.103.4	yes	176
4.3	odd	2	inner	140.3.x.a.103.41	yes	176
5.2	odd	4	inner	140.3.x.a.47.19	yes	176
7.3	odd	6	inner	140.3.x.a.3.26	yes	176
20.7	even	4	inner	140.3.x.a.47.26	yes	176
28.3	even	6	inner	140.3.x.a.3.19	✓	176
35.17	even	12	inner	140.3.x.a.87.41	yes	176
140.87	odd	12	inner	140.3.x.a.87.4	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.3.x.a.3.19	✓	176	28.3	even	6	inner
140.3.x.a.3.26	yes	176	7.3	odd	6	inner
140.3.x.a.47.19	yes	176	5.2	odd	4	inner
140.3.x.a.47.26	yes	176	20.7	even	4	inner
140.3.x.a.87.4	yes	176	140.87	odd	12	inner
140.3.x.a.87.41	yes	176	35.17	even	12	inner
140.3.x.a.103.4	yes	176	1.1	even	1	trivial
140.3.x.a.103.41	yes	176	4.3	odd	2	inner

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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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	140.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88565 + 0.666564i) q^{2} +(-0.389805 + 1.45477i) q^{3} +(3.11138 - 2.51382i) q^{4} +(-3.73805 - 3.32069i) q^{5} +(-0.234662 - 3.00303i) q^{6} +(5.02867 + 4.86954i) q^{7} +(-4.19137 + 6.81413i) q^{8} +(5.82981 + 3.36584i) q^{9} +O(q^{10})\)	\(q+(-1.88565 + 0.666564i) q^{2} +(-0.389805 + 1.45477i) q^{3} +(3.11138 - 2.51382i) q^{4} +(-3.73805 - 3.32069i) q^{5} +(-0.234662 - 3.00303i) q^{6} +(5.02867 + 4.86954i) q^{7} +(-4.19137 + 6.81413i) q^{8} +(5.82981 + 3.36584i) q^{9} +(9.26213 + 3.77002i) q^{10} +(-8.96422 + 5.17549i) q^{11} +(2.44420 + 5.50626i) q^{12} +(-2.72924 + 2.72924i) q^{13} +(-12.7282 - 5.83034i) q^{14} +(6.28796 - 4.14359i) q^{15} +(3.36142 - 15.6429i) q^{16} +(-8.39248 + 31.3211i) q^{17} +(-13.2366 - 2.46087i) q^{18} +(-16.5359 - 9.54701i) q^{19} +(-19.9781 - 0.935145i) q^{20} +(-9.04428 + 5.41740i) q^{21} +(13.4536 - 15.7344i) q^{22} +(2.49054 + 9.29482i) q^{23} +(-8.27920 - 8.75368i) q^{24} +(2.94606 + 24.8258i) q^{25} +(3.32719 - 6.96562i) q^{26} +(-16.7537 + 16.7537i) q^{27} +(27.8873 + 2.50983i) q^{28} +4.14768i q^{29} +(-9.09494 + 12.0047i) q^{30} +(13.7219 + 23.7671i) q^{31} +(4.08854 + 31.7377i) q^{32} +(-4.03487 - 15.0583i) q^{33} +(-5.05225 - 64.6550i) q^{34} +(-2.62721 - 34.9013i) q^{35} +(26.5999 - 4.18267i) q^{36} +(9.87753 + 36.8634i) q^{37} +(37.5447 + 6.98012i) q^{38} +(-2.90655 - 5.03430i) q^{39} +(38.2952 - 11.5533i) q^{40} -42.9640i q^{41} +(13.4433 - 16.2439i) q^{42} +(51.7850 - 51.7850i) q^{43} +(-14.8809 + 38.6374i) q^{44} +(-10.6152 - 31.9407i) q^{45} +(-10.8919 - 15.8667i) q^{46} +(-9.58506 - 35.7719i) q^{47} +(21.4466 + 10.9878i) q^{48} +(1.57512 + 48.9747i) q^{49} +(-22.1033 - 44.8491i) q^{50} +(-42.2937 - 24.4183i) q^{51} +(-1.63089 + 15.3525i) q^{52} +(7.62542 - 28.4585i) q^{53} +(20.4243 - 42.7592i) q^{54} +(50.6949 + 10.4211i) q^{55} +(-54.2587 + 13.8560i) q^{56} +(20.3345 - 20.3345i) q^{57} +(-2.76469 - 7.82109i) q^{58} +(5.94136 - 3.43025i) q^{59} +(9.14800 - 28.6991i) q^{60} +(44.2972 + 25.5750i) q^{61} +(-41.7172 - 35.6700i) q^{62} +(12.9261 + 45.3143i) q^{63} +(-28.8648 - 57.1211i) q^{64} +(19.2650 - 1.13909i) q^{65} +(17.6457 + 25.7053i) q^{66} +(-17.7208 + 66.1349i) q^{67} +(52.6235 + 118.549i) q^{68} -14.4927 q^{69} +(28.2180 + 64.0605i) q^{70} +71.0505i q^{71} +(-47.3702 + 25.6176i) q^{72} +(-75.1765 - 20.1435i) q^{73} +(-43.1975 - 62.9277i) q^{74} +(-37.2643 - 5.39138i) q^{75} +(-75.4491 + 11.8639i) q^{76} +(-70.2804 - 17.6258i) q^{77} +(8.83643 + 7.55554i) q^{78} +(66.7677 - 115.645i) q^{79} +(-64.5104 + 47.3118i) q^{80} +(12.4504 + 21.5647i) q^{81} +(28.6383 + 81.0153i) q^{82} +(3.23971 + 3.23971i) q^{83} +(-14.5218 + 39.5913i) q^{84} +(135.379 - 89.2113i) q^{85} +(-63.1306 + 132.167i) q^{86} +(-6.03393 - 1.61679i) q^{87} +(2.30586 - 82.7758i) q^{88} +(16.9269 - 29.3183i) q^{89} +(41.3072 + 53.1534i) q^{90} +(-27.0146 + 0.434309i) q^{91} +(31.1145 + 22.6590i) q^{92} +(-39.9246 + 10.6978i) q^{93} +(41.9184 + 61.0644i) q^{94} +(30.1094 + 90.5978i) q^{95} +(-47.7649 - 6.42364i) q^{96} +(-108.302 - 108.302i) q^{97} +(-35.6149 - 91.2994i) q^{98} -69.6796 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

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