LMFDB - Embedded newform 140.3.x.a.103.41

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			103.41
Character	$\chi$	$=$	140.103
Dual form			140.3.x.a.87.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.96631 - 0.365565i) q^{2} +(0.389805 - 1.45477i) q^{3} +(3.73272 - 1.43763i) q^{4} +(-3.73805 - 3.32069i) q^{5} +(0.234662 - 3.00303i) q^{6} +(-5.02867 - 4.86954i) q^{7} +(6.81413 - 4.19137i) q^{8} +(5.82981 + 3.36584i) q^{9} +O(q^{10})$	\(q+(1.96631 - 0.365565i) q^{2} +(0.389805 - 1.45477i) q^{3} +(3.73272 - 1.43763i) q^{4} +(-3.73805 - 3.32069i) q^{5} +(0.234662 - 3.00303i) q^{6} +(-5.02867 - 4.86954i) q^{7} +(6.81413 - 4.19137i) q^{8} +(5.82981 + 3.36584i) q^{9} +(-8.56408 - 5.16299i) q^{10} +(8.96422 - 5.17549i) q^{11} +(-0.636386 - 5.99066i) q^{12} +(-2.72924 + 2.72924i) q^{13} +(-11.6681 - 7.73670i) q^{14} +(-6.28796 + 4.14359i) q^{15} +(11.8665 - 10.7325i) q^{16} +(-8.39248 + 31.3211i) q^{17} +(12.6936 + 4.48710i) q^{18} +(16.5359 + 9.54701i) q^{19} +(-18.7270 - 7.02129i) q^{20} +(-9.04428 + 5.41740i) q^{21} +(15.7344 - 13.4536i) q^{22} +(-2.49054 - 9.29482i) q^{23} +(-3.44131 - 11.5468i) q^{24} +(2.94606 + 24.8258i) q^{25} +(-4.36881 + 6.36424i) q^{26} +(16.7537 - 16.7537i) q^{27} +(-25.7712 - 10.9473i) q^{28} +4.14768i q^{29} +(-10.8493 + 10.4462i) q^{30} +(-13.7219 - 23.7671i) q^{31} +(19.4096 - 25.4414i) 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} +(36.0047 + 12.7274i) q^{38} +(2.90655 + 5.03430i) q^{39} +(-39.3898 - 6.96005i) q^{40} -42.9640i q^{41} +(-15.8034 + 13.9586i) q^{42} +(-51.7850 + 51.7850i) q^{43} +(26.0205 - 32.2059i) q^{44} +(-10.6152 - 31.9407i) q^{45} +(-8.29503 - 17.3660i) q^{46} +(9.58506 + 35.7719i) q^{47} +(-10.9878 - 21.4466i) q^{48} +(1.57512 + 48.9747i) q^{49} +(14.8683 + 47.7382i) q^{50} +(42.2937 + 24.4183i) q^{51} +(-6.26387 + 14.1111i) q^{52} +(7.62542 - 28.4585i) q^{53} +(26.8184 - 39.0676i) q^{54} +(-50.6949 - 10.4211i) q^{55} +(-54.6761 - 12.1047i) q^{56} +(20.3345 - 20.3345i) q^{57} +(1.51625 + 8.15561i) q^{58} +(-5.94136 + 3.43025i) q^{59} +(-17.5143 + 24.5066i) q^{60} +(44.2972 + 25.5750i) q^{61} +(-35.6700 - 41.7172i) q^{62} +(-12.9261 - 45.3143i) q^{63} +(28.8648 - 57.1211i) q^{64} +(19.2650 - 1.13909i) q^{65} +(-13.4386 - 28.1343i) q^{66} +(17.7208 - 66.1349i) q^{67} +(13.7013 + 128.978i) q^{68} -14.4927 q^{69} +(17.9246 + 67.6662i) q^{70} -71.0505i q^{71} +(53.8326 - 1.49960i) q^{72} +(-75.1765 - 20.1435i) q^{73} +(32.8982 + 68.8739i) q^{74} +(37.2643 + 5.39138i) q^{75} +(75.4491 + 11.8639i) q^{76} +(-70.2804 - 17.6258i) q^{77} +(7.55554 + 8.83643i) q^{78} +(-66.7677 + 115.645i) q^{79} +(-79.9968 + 0.713968i) q^{80} +(12.4504 + 21.5647i) q^{81} +(-15.7062 - 84.4804i) q^{82} +(-3.23971 - 3.23971i) q^{83} +(-25.9716 + 33.2240i) q^{84} +(135.379 - 89.2113i) q^{85} +(-82.8944 + 120.756i) q^{86} +(6.03393 + 1.61679i) q^{87} +(39.3910 - 72.8389i) q^{88} +(16.9269 - 29.3183i) q^{89} +(-32.5492 - 58.9246i) q^{90} +(27.0146 - 0.434309i) q^{91} +(-22.6590 - 31.1145i) q^{92} +(-39.9246 + 10.6978i) q^{93} +(31.9241 + 66.8346i) q^{94} +(-30.1094 - 90.5978i) q^{95} +(-29.4455 - 38.1538i) q^{96} +(-108.302 - 108.302i) q^{97} +(21.0006 + 95.7234i) 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 $

$2$	1.96631	−	0.365565i	0.983153	−	0.182783i
$2$	1.96631	−	0.365565i	0.983153	−	0.182783i
$3$	0.389805	−	1.45477i	0.129935	−	0.484924i	−0.870032	−	0.492995i	$-0.835902\pi$
$3$	0.389805	−	1.45477i	0.129935	−	0.484924i	0.999967	+	0.00807035i	$0.00256890\pi$
$4$	3.73272	−	1.43763i	0.933181	−	0.359407i
$5$	−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
$8$	6.81413	−	4.19137i	0.851767	−	0.523921i
$9$	5.82981	+	3.36584i	0.647757	+	0.373983i
$10$	−8.56408	−	5.16299i	−0.856408	−	0.516299i
$11$	8.96422	−	5.17549i	0.814929	−	0.470499i	−0.0337356	−	0.999431i	$-0.510740\pi$
$11$	8.96422	−	5.17549i	0.814929	−	0.470499i	0.848665	+	0.528931i	$0.177407\pi$
$12$	−0.636386	−	5.99066i	−0.0530322	−	0.499222i
$13$	−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	$0.297429\pi$
$14$	−11.6681	−	7.73670i	−0.833432	−	0.552622i
$15$	−6.28796	+	4.14359i	−0.419197	+	0.276240i
$16$	11.8665	−	10.7325i	0.741653	−	0.670783i
$17$	−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	$0.680566\pi$
$18$	12.6936	+	4.48710i	0.705202	+	0.249284i
$19$	16.5359	+	9.54701i	0.870311	+	0.502474i	0.867452	−	0.497521i	$-0.165756\pi$
$19$	16.5359	+	9.54701i	0.870311	+	0.502474i	0.00285961	+	0.999996i	$0.499090\pi$
$20$	−18.7270	−	7.02129i	−0.936351	−	0.351064i
$21$	−9.04428	+	5.41740i	−0.430680	+	0.257972i
$22$	15.7344	−	13.4536i	0.715201	−	0.611528i
$23$	−2.49054	−	9.29482i	−0.108284	−	0.404122i	0.890413	−	0.455154i	$-0.150416\pi$
$23$	−2.49054	−	9.29482i	−0.108284	−	0.404122i	−0.998697	+	0.0510315i	$0.983749\pi$
$24$	−3.44131	−	11.5468i	−0.143388	−	0.481118i
$25$	2.94606	+	24.8258i	0.117843	+	0.993032i
$26$	−4.36881	+	6.36424i	−0.168031	+	0.244778i
$27$	16.7537	−	16.7537i	0.620509	−	0.620509i
$28$	−25.7712	−	10.9473i	−0.920401	−	0.390975i
$29$			4.14768i			0.143023i	0.997440	+	0.0715117i	$0.0227823\pi$
$29$			4.14768i			0.143023i	−0.997440	+	0.0715117i	$0.977218\pi$
$30$	−10.8493	+	10.4462i	−0.361643	+	0.348208i
$31$	−13.7219	−	23.7671i	−0.442643	−	0.766681i	0.555241	−	0.831689i	$-0.312626\pi$
$31$	−13.7219	−	23.7671i	−0.442643	−	0.766681i	−0.997885	+	0.0650083i	$0.979293\pi$
$32$	19.4096	−	25.4414i	0.606551	−	0.795044i
$33$	−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	$0.744188\pi$
$38$	36.0047	+	12.7274i	0.947493	+	0.334932i
$39$	2.90655	+	5.03430i	0.0745270	+	0.129085i
$40$	−39.3898	−	6.96005i	−0.984745	−	0.174001i
$41$		−	42.9640i		−	1.04790i	−0.851748	−	0.523951i	$-0.824457\pi$
$41$		−	42.9640i		−	1.04790i	0.851748	−	0.523951i	$-0.175543\pi$
$42$	−15.8034	+	13.9586i	−0.376272	+	0.332347i
$43$	−51.7850	+	51.7850i	−1.20430	+	1.20430i	−0.231457	+	0.972845i	$0.574349\pi$
$43$	−51.7850	+	51.7850i	−1.20430	+	1.20430i	−0.972845	+	0.231457i	$0.925651\pi$
$44$	26.0205	−	32.2059i	0.591375	−	0.731952i
$45$	−10.6152	−	31.9407i	−0.235894	−	0.709793i
$46$	−8.29503	−	17.3660i	−0.180327	−	0.377522i
$47$	9.58506	+	35.7719i	0.203937	+	0.761105i	0.989771	+	0.142667i	$0.0455677\pi$
$47$	9.58506	+	35.7719i	0.203937	+	0.761105i	−0.785833	+	0.618438i	$0.787766\pi$
$48$	−10.9878	−	21.4466i	−0.228912	−	0.446804i
$49$	1.57512	+	48.9747i	0.0321453	+	0.999483i
$50$	14.8683	+	47.7382i	0.297366	+	0.954763i
$51$	42.2937	+	24.4183i	0.829289	+	0.478790i
$52$	−6.26387	+	14.1111i	−0.120459	+	0.271368i
$53$	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	$-0.00632055\pi$
$54$	26.8184	−	39.0676i	0.496637	−	0.723474i
$55$	−50.6949	−	10.4211i	−0.921726	−	0.189475i
$56$	−54.6761	−	12.1047i	−0.976359	−	0.216155i
$57$	20.3345	−	20.3345i	0.356746	−	0.356746i
$58$	1.51625	+	8.15561i	0.0261422	+	0.140614i
$59$	−5.94136	+	3.43025i	−0.100701	+	0.0581398i	−0.549505	−	0.835491i	$-0.685184\pi$
$59$	−5.94136	+	3.43025i	−0.100701	+	0.0581398i	0.448804	+	0.893630i	$0.351850\pi$
$60$	−17.5143	+	24.5066i	−0.291904	+	0.408444i
$61$	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	$0.528956\pi$
$62$	−35.6700	−	41.7172i	−0.575322	−	0.672857i
$63$	−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
$66$	−13.4386	−	28.1343i	−0.203615	−	0.426277i
$67$	17.7208	−	66.1349i	0.264490	−	0.987088i	−0.698073	−	0.716027i	$-0.745959\pi$
$67$	17.7208	−	66.1349i	0.264490	−	0.987088i	0.962562	−	0.271061i	$-0.0873746\pi$
$68$	13.7013	+	128.978i	0.201490	+	1.89674i
$69$	−14.4927			−0.210039
$70$	17.9246	+	67.6662i	0.256066	+	0.966659i
$71$		−	71.0505i		−	1.00071i	−0.865820	−	0.500356i	$-0.833203\pi$
$71$		−	71.0505i		−	1.00071i	0.865820	−	0.500356i	$-0.166797\pi$
$72$	53.8326	−	1.49960i	0.747675	−	0.0208278i
$73$	−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	$0.762296\pi$
$74$	32.8982	+	68.8739i	0.444571	+	0.930729i
$75$	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
$78$	7.55554	+	8.83643i	0.0968659	+	0.113288i
$79$	−66.7677	+	115.645i	−0.845161	+	1.46386i	0.0403208	+	0.999187i	$0.487162\pi$
$79$	−66.7677	+	115.645i	−0.845161	+	1.46386i	−0.885482	+	0.464675i	$0.846171\pi$
$80$	−79.9968	+	0.713968i	−0.999960	+	0.00892459i
$81$	12.4504	+	21.5647i	0.153709	+	0.266231i
$82$	−15.7062	−	84.4804i	−0.191538	−	1.03025i
$83$	−3.23971	−	3.23971i	−0.0390327	−	0.0390327i	0.687321	−	0.726354i	$-0.258787\pi$
$83$	−3.23971	−	3.23971i	−0.0390327	−	0.0390327i	−0.726354	+	0.687321i	$0.758787\pi$
$84$	−25.9716	+	33.2240i	−0.309186	+	0.395524i
$85$	135.379	−	89.2113i	1.59270	−	1.04954i
$86$	−82.8944	+	120.756i	−0.963888	+	1.40414i
$87$	6.03393	+	1.61679i	0.0693555	+	0.0185838i
$88$	39.3910	−	72.8389i	0.447625	−	0.827714i
$89$	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	$0.105756\pi$
$90$	−32.5492	−	58.9246i	−0.361658	−	0.654718i
$91$	27.0146	−	0.434309i	0.296864	−	0.00477263i
$92$	−22.6590	−	31.1145i	−0.246293	−	0.338201i
$93$	−39.9246	+	10.6978i	−0.429297	+	0.115030i
$94$	31.9241	+	66.8346i	0.339619	+	0.711007i
$95$	−30.1094	−	90.5978i	−0.316942	−	0.953662i
$96$	−29.4455	−	38.1538i	−0.306724	−	0.397436i
$97$	−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	$-0.539659\pi$
$98$	21.0006	+	95.7234i	0.214292	+	0.976770i
$99$	69.6796			0.703835
$100$	46.6871	+	88.4325i	0.466871	+	0.884325i
$101$	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	$0.177080\pi$
$102$	92.0889	+	32.5527i	0.902832	+	0.319144i
$103$	94.6821	−	25.3700i	0.919243	−	0.246310i	0.231981	−	0.972720i	$-0.425479\pi$
$103$	94.6821	−	25.3700i	0.919243	−	0.246310i	0.687262	+	0.726410i	$0.258812\pi$
$104$	−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	−0.490968	−	0.871178i	$-0.663357\pi$
$107$	−51.4210	+	13.7782i	−0.480570	+	0.128768i	0.0103978	+	0.999946i	$0.496690\pi$
$108$	38.4514	−	86.6227i	0.356032	−	0.802062i
$109$	−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	$0.405248\pi$
$110$	−103.491	−	1.95879i	−0.940830	−	0.0178072i
$111$	57.4782			0.517822
$112$	−111.935	−	3.81380i	−0.999420	−	0.0340518i
$113$	−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	$0.926570\pi$
$114$	32.5503	−	47.4175i	0.285529	−	0.415943i
$115$	−21.5554	+	43.0148i	−0.187438	+	0.374042i
$116$	5.96282	+	15.4821i	0.0514036	+	0.133467i
$117$	−25.0972	+	6.72476i	−0.214506	+	0.0574766i
$118$	−10.4286	+	8.91687i	−0.0883776	+	0.0755667i
$119$	194.723	−	116.636i	1.63633	−	0.980137i
$120$	−25.4796	+	54.5902i	−0.212330	+	0.454918i
$121$	−6.92852	+	12.0005i	−0.0572605	+	0.0991781i
$122$	96.4511	+	34.0947i	0.790583	+	0.279465i
$123$	−62.5029	−	16.7476i	−0.508153	−	0.136159i
$124$	−85.3885	−	68.9890i	−0.688617	−	0.556363i
$125$	71.4262	−	102.583i	0.571410	−	0.820665i
$126$	−41.9820	−	84.3764i	−0.333191	−	0.669654i
$127$	−103.692	−	103.692i	−0.816476	−	0.816476i	0.169119	−	0.985596i	$-0.445908\pi$
$127$	−103.692	−	103.692i	−0.816476	−	0.816476i	−0.985596	+	0.169119i	$0.945908\pi$
$128$	35.8756	−	122.870i	0.280278	−	0.959919i
$129$	55.1494	+	95.5215i	0.427514	+	0.740477i
$130$	37.4645	−	9.28241i	0.288188	−	0.0714031i
$131$	−19.9882	+	34.6205i	−0.152581	+	0.264279i	−0.932176	−	0.362006i	$-0.882092\pi$
$131$	−19.9882	+	34.6205i	−0.152581	+	0.264279i	0.779594	+	0.626285i	$0.215425\pi$
$132$	−36.7093	−	50.4080i	−0.278101	−	0.381879i
$133$	−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
$136$	74.0911	+	248.602i	0.544788	+	1.82796i
$137$	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	$0.428633\pi$
$138$	−28.4970	+	5.29802i	−0.206500	+	0.0383914i
$139$			45.8622i			0.329944i	0.986298	+	0.164972i	$0.0527534\pi$
$139$			45.8622i			0.329944i	−0.986298	+	0.164972i	$0.947247\pi$
$140$	59.9817	+	126.500i	0.428440	+	0.903570i
$141$	55.7763			0.395577
$142$	−25.9736	−	139.707i	−0.182913	−	0.983852i
$143$	−10.3403	+	38.5907i	−0.0723101	+	0.269865i
$144$	105.303	−	22.6280i	0.731273	−	0.157139i
$145$	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
$148$	89.8660	+	123.401i	0.607203	+	0.833789i
$149$	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	$0.529359\pi$
$150$	75.2439	−	3.02144i	0.501626	−	0.0201429i
$151$	−190.770	+	110.141i	−1.26338	+	0.729412i	−0.973727	−	0.227720i	$-0.926873\pi$
$151$	−190.770	+	110.141i	−1.26338	+	0.729412i	−0.289652	+	0.957132i	$0.593540\pi$
$152$	152.693	−	4.25353i	1.00456	−	0.0279837i
$153$	−154.349	+	154.349i	−1.00881	+	1.00881i
$154$	−144.636	−	8.96557i	−0.939196	−	0.0582180i
$155$	−27.6298	+	134.409i	−0.178257	+	0.867155i
$156$	18.0868	+	14.6131i	0.115941	+	0.0936737i
$157$	−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	$0.814121\pi$
$158$	−89.0099	+	251.802i	−0.563354	+	1.59368i
$159$	−38.4281	−	22.1865i	−0.241686	−	0.139538i
$160$	−157.037	+	30.6479i	−0.981483	+	0.191550i
$161$	−32.7374	+	58.8684i	−0.203338	+	0.365642i
$162$	32.3647	+	37.8515i	0.199782	+	0.233651i
$163$	53.4872	+	199.617i	0.328142	+	1.22464i	0.911115	+	0.412152i	$0.135223\pi$
$163$	53.4872	+	199.617i	0.328142	+	1.22464i	−0.582973	+	0.812491i	$0.698111\pi$
$164$	−61.7662	−	160.373i	−0.376623	−	0.977883i
$165$	−34.9215	+	69.6874i	−0.211645	+	0.422348i
$166$	−7.55460	−	5.18594i	−0.0455096	−	0.0312406i
$167$	−8.07187	+	8.07187i	−0.0483345	+	0.0483345i	−0.730861	−	0.682526i	$-0.760881\pi$
$167$	−8.07187	+	8.07187i	−0.0483345	+	0.0483345i	0.682526	+	0.730861i	$0.260881\pi$
$168$	−38.9226	+	74.8229i	−0.231682	+	0.445374i
$169$			154.102i			0.911849i
$170$	233.585	−	224.907i	1.37403	−	1.32298i
$171$	64.2675	+	111.315i	0.375833	+	0.650963i
$172$	−118.852	+	267.747i	−0.690998	+	1.55667i
$173$	−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
$178$	22.5658	−	63.8366i	0.126774	−	0.358633i
$179$	−111.945	−	193.895i	−0.625393	−	1.08321i	−0.988465	−	0.151452i	$-0.951605\pi$
$179$	−111.945	−	193.895i	−0.625393	−	1.08321i	0.363071	−	0.931761i	$-0.381728\pi$
$180$	−85.5425	−	103.965i	−0.475236	−	0.577584i
$181$			106.329i			0.587451i	0.955890	+	0.293725i	$0.0948951\pi$
$181$			106.329i			0.587451i	−0.955890	+	0.293725i	$0.905105\pi$
$182$	52.9602	−	10.7296i	0.290990	−	0.0589538i
$183$	54.4730	−	54.4730i	0.297667	−	0.297667i
$184$	−55.9289	−	52.8973i	−0.303961	−	0.287486i
$185$	85.4893	−	170.598i	0.462104	−	0.922149i
$186$	−74.5933	+	35.6302i	−0.401039	+	0.191560i
$187$	86.8704	+	324.205i	0.464548	+	1.73372i
$188$	87.2051	+	119.747i	0.463857	+	0.636952i
$189$	−165.832	+	2.66605i	−0.877419	+	0.0141061i
$190$	−92.3238	−	167.136i	−0.485915	−	0.879664i
$191$	−131.793	−	76.0905i	−0.690014	−	0.398380i	0.113603	−	0.993526i	$-0.463761\pi$
$191$	−131.793	−	76.0905i	−0.690014	−	0.398380i	−0.803617	+	0.595146i	$0.797094\pi$
$192$	−71.8466	−	64.2579i	−0.374201	−	0.334676i
$193$	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	$-0.0217924\pi$
$194$	−252.547	−	173.364i	−1.30179	−	0.893630i
$195$	5.85248	−	28.4702i	0.0300127	−	0.146001i
$196$	76.2868	+	180.545i	0.389219	+	0.921145i
$197$	−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	$0.380087\pi$
$198$	137.012	−	25.4725i	0.691977	−	0.128649i
$199$	−92.6809	+	53.5093i	−0.465733	+	0.268891i	−0.714452	−	0.699685i	$-0.753324\pi$
$199$	−92.6809	+	53.5093i	−0.465733	+	0.268891i	0.248719	+	0.968576i	$0.419990\pi$
$200$	124.129	+	156.818i	0.620645	+	0.784092i
$201$	−89.3036	−	51.5595i	−0.444297	−	0.256515i
$202$	144.749	−	123.767i	0.716579	−	0.612706i
$203$	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
$206$	176.900	−	84.4976i	0.858736	−	0.410183i
$207$	16.7655	−	62.5698i	0.0809929	−	0.302270i
$208$	−3.09475	+	61.6781i	−0.0148786	+	0.296529i
$209$	197.642			0.945656
$210$	105.426	+	0.300397i	0.502028	+	0.00143046i
$211$		−	100.172i		−	0.474748i	−0.971418	−	0.237374i	$-0.923713\pi$
$211$		−	100.172i		−	0.474748i	0.971418	−	0.237374i	$-0.0762867\pi$
$212$	−12.4491	−	117.190i	−0.0587220	−	0.552783i
$213$	−103.362	−	27.6958i	−0.485269	−	0.130027i
$214$	−96.0727	+	45.8900i	−0.448938	+	0.214439i
$215$	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
$218$	−74.2323	+	63.4718i	−0.340515	+	0.291155i
$219$	−58.6084	+	101.513i	−0.267618	+	0.463528i
$220$	−204.212	+	33.9813i	−0.928235	+	0.154460i
$221$	−62.5778	−	108.388i	−0.283158	−	0.490444i
$222$	113.020	−	21.0121i	0.509098	−	0.0946489i
$223$	−218.632	−	218.632i	−0.980412	−	0.980412i	0.0193998	−	0.999812i	$-0.493824\pi$
$223$	−218.632	−	218.632i	−0.980412	−	0.980412i	−0.999812	+	0.0193998i	$0.993824\pi$
$224$	−221.493	+	33.4205i	−0.988807	+	0.149199i
$225$	−66.3848	+	154.646i	−0.295044	+	0.687315i
$226$	−196.273	−	134.734i	−0.868465	−	0.596168i
$227$	98.3908	+	26.3637i	0.433440	+	0.116140i	0.468940	−	0.883230i	$-0.344636\pi$
$227$	98.3908	+	26.3637i	0.433440	+	0.116140i	−0.0355007	+	0.999370i	$0.511303\pi$
$228$	46.6697	−	105.137i	0.204692	−	0.461126i
$229$	−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	$0.235850\pi$
$230$	−26.6598	+	92.4602i	−0.115912	+	0.402001i
$231$	−53.0372	+	95.3714i	−0.229598	+	0.412863i
$232$	17.3845	+	28.2628i	0.0749330	+	0.121823i
$233$	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	$0.141427\pi$
$234$	−46.8904	+	22.3976i	−0.200386	+	0.0957162i
$235$	82.9580	−	165.546i	0.353013	−	0.704452i
$236$	−17.2460	+	21.3456i	−0.0730764	+	0.0904475i
$237$	142.211	+	142.211i	0.600046	+	0.600046i
$238$	340.246	−	300.527i	1.42961	−	1.26272i
$239$	−295.712			−1.23729			−0.618645	−	0.785671i	$-0.712318\pi$
$239$	−295.712			−1.23729			−0.618645	+	0.785671i	$0.712318\pi$
$240$	−30.1445	+	116.655i	−0.125602	+	0.486065i
$241$	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	$0.236035\pi$
$242$	−9.23661	+	26.1296i	−0.0381678	+	0.107973i
$243$	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
$248$	−193.120	−	104.438i	−0.778710	−	0.421123i
$249$	−5.97590	+	3.45019i	−0.0239996	+	0.0138562i
$250$	102.945	−	227.821i	0.411780	−	0.911283i
$251$	230.270			0.917412			0.458706	−	0.888588i	$-0.348313\pi$
$251$	230.270			0.917412			0.458706	+	0.888588i	$0.348313\pi$
$252$	−113.395	−	150.563i	−0.449979	−	0.597471i
$253$	−70.4310	−	70.4310i	−0.278383	−	0.278383i
$254$	−241.798	−	165.985i	−0.951959	−	0.653484i
$255$	−77.0106	−	231.721i	−0.302002	−	0.908710i
$256$	25.6255	−	254.714i	0.100100	−	0.994977i
$257$	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	$0.256035\pi$
$258$	143.360	+	167.664i	0.555658	+	0.649860i
$259$	129.837	−	233.473i	0.501302	−	0.901441i
$260$	70.2733	−	31.9478i	0.270282	−	0.122876i
$261$	−13.9604	+	24.1802i	−0.0534883	+	0.0926444i
$262$	−26.6468	+	75.3816i	−0.101705	+	0.287716i
$263$	262.922	+	70.4497i	0.999704	+	0.267870i	0.721321	−	0.692601i	$-0.243535\pi$
$263$	262.922	+	70.4497i	0.999704	+	0.267870i	0.278382	+	0.960470i	$0.410202\pi$
$264$	−90.6092	−	85.6979i	−0.343217	−	0.324613i
$265$	−123.006	+	81.0575i	−0.464173	+	0.305877i
$266$	−119.079	−	239.329i	−0.447667	−	0.899731i
$267$	−36.0532	−	36.0532i	−0.135031	−	0.135031i
$268$	−28.9305	−	272.339i	−0.107950	−	1.01619i
$269$	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	$0.735351\pi$
$270$	−229.980	+	56.9811i	−0.851777	+	0.211041i
$271$	4.61358	−	7.99095i	0.0170243	−	0.0294869i	−0.857388	−	0.514671i	$-0.827914\pi$
$271$	4.61358	−	7.99095i	0.0170243	−	0.0294869i	0.874412	+	0.485184i	$0.161247\pi$
$272$	236.566	+	461.744i	0.869729	+	1.69759i
$273$	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
$276$	−54.0971	+	20.8351i	−0.196004	+	0.0754894i
$277$	−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	$0.681786\pi$
$278$	16.7656	+	90.1792i	0.0603081	+	0.324386i
$279$		−	184.744i		−	0.662164i
$280$	164.186	+	226.810i	0.586380	+	0.810036i
$281$	−104.482			−0.371822			−0.185911	−	0.982567i	$-0.559524\pi$
$281$	−104.482			−0.371822			−0.185911	+	0.982567i	$0.559524\pi$
$282$	109.673	−	20.3899i	0.388913	−	0.0723046i
$283$	−27.1980	+	101.504i	−0.0961060	+	0.358673i	−0.997185	−	0.0749828i	$-0.976110\pi$
$283$	−27.1980	+	101.504i	−0.0961060	+	0.358673i	0.901079	+	0.433655i	$0.142776\pi$
$284$	−102.144	−	265.212i	−0.359662	−	0.933845i
$285$	−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
$288$	198.786	−	82.9888i	0.690231	−	0.288156i
$289$	−660.299	−	381.224i	−2.28477	−	1.31911i
$290$	21.4144	−	35.5211i	0.0738428	−	0.122486i
$291$	−199.772	+	115.339i	−0.686503	+	0.396353i
$292$	−309.572	+	32.8858i	−1.06018	+	0.112622i
$293$	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	$0.217954\pi$
$294$	147.442	+	6.76236i	0.501503	+	0.0230012i
$295$	33.5999	+	6.90697i	0.113898	+	0.0234134i
$296$	221.815	+	209.792i	0.749375	+	0.708757i
$297$	63.4753	−	236.893i	0.213722	−	0.797620i
$298$	234.947	+	83.0518i	0.788411	+	0.278697i
$299$	32.1651	+	18.5705i	0.107575	+	0.0621087i
$300$	146.848	−	33.4477i	0.489494	−	0.111492i
$301$	512.579	−	8.24065i	1.70292	−	0.0273776i
$302$	−334.849	+	286.310i	−1.10877	+	0.948048i
$303$	−37.1188	−	138.529i	−0.122504	−	0.457192i
$304$	298.686	−	64.1830i	0.982521	−	0.211128i
$305$	−80.6586	−	242.698i	−0.264454	−	0.795730i
$306$	−247.072	+	359.921i	−0.807426	+	1.17621i
$307$	129.652	−	129.652i	0.422320	−	0.422320i	−0.463682	−	0.886002i	$-0.653472\pi$
$307$	129.652	−	129.652i	0.422320	−	0.422320i	0.886002	+	0.463682i	$0.153472\pi$
$308$	−287.677	+	35.2449i	−0.934015	+	0.114432i
$309$		−	147.630i		−	0.477768i
$310$	−5.19339	+	274.390i	−0.0167529	+	0.885128i
$311$	−211.858	−	366.949i	−0.681216	−	1.17990i	−0.974610	−	0.223909i	$-0.928118\pi$
$311$	−211.858	−	366.949i	−0.681216	−	1.17990i	0.293395	−	0.955991i	$-0.405215\pi$
$312$	40.9062	+	22.1219i	0.131110	+	0.0709036i
$313$	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	$-0.305269\pi$
$318$	−83.6721	−	29.5775i	−0.263120	−	0.0930109i
$319$	21.4663	+	37.1807i	0.0672924	+	0.116554i
$320$	−297.580	+	117.671i	−0.929936	+	0.367721i
$321$			80.1767i			0.249772i
$322$	−42.8515	+	127.721i	−0.133079	+	0.396649i
$323$	−437.801	+	437.801i	−1.35542	+	1.35542i
$324$	77.4760	+	62.5962i	0.239123	+	0.193198i
$325$	−75.7961	−	59.7151i	−0.233219	−	0.183739i
$326$	178.145	+	372.955i	0.546458	+	1.14403i
$327$	19.0358	+	71.0426i	0.0582135	+	0.217256i
$328$	−180.078	−	292.762i	−0.549019	−	0.892569i
$329$	125.993	−	226.560i	0.382957	−	0.688633i
$330$	−43.1911	+	149.793i	−0.130882	+	0.453918i
$331$	230.336	+	132.985i	0.695879	+	0.401766i	0.805811	−	0.592173i	$-0.201730\pi$
$331$	230.336	+	132.985i	0.695879	+	0.401766i	−0.109932	+	0.993939i	$0.535063\pi$
$332$	−16.7505	−	7.43546i	−0.0504532	−	0.0223960i
$333$	−66.4924	+	248.153i	−0.199677	+	0.745205i
$334$	−12.9210	+	18.8226i	−0.0386856	+	0.0563550i
$335$	−285.855	+	188.371i	−0.853298	+	0.562300i
$336$	−49.1811	+	161.353i	−0.146372	+	0.480219i
$337$	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	$0.206720\pi$
$338$	56.3345	+	303.013i	0.166670	+	0.896487i
$339$	−155.258	+	89.6380i	−0.457987	+	0.264419i
$340$	377.081	−	527.626i	1.10906	−	1.55184i
$341$	−246.013	−	142.036i	−0.721446	−	0.416527i
$342$	167.062	+	195.385i	0.488487	+	0.571300i
$343$	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
$346$	−9.96460	−	20.8613i	−0.0287994	−	0.0602929i
$347$	63.0751	−	235.400i	0.181773	−	0.678385i	−0.813526	−	0.581529i	$-0.802455\pi$
$347$	63.0751	−	235.400i	0.181773	−	0.678385i	0.995298	−	0.0968561i	$-0.0308786\pi$
$348$	24.8473	−	2.63952i	0.0714004	−	0.00758484i
$349$	201.731			0.578027			0.289013	−	0.957325i	$-0.406673\pi$
$349$	201.731			0.578027			0.289013	+	0.957325i	$0.406673\pi$
$350$	157.695	−	312.462i	0.450557	−	0.892747i
$351$			91.4499i			0.260541i
$352$	42.3204	−	328.517i	0.120228	−	0.933287i
$353$	−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	$0.596908\pi$
$354$	8.90691	+	18.6470i	0.0251608	+	0.0526752i
$355$	−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
$358$	−291.000	−	340.334i	−0.812850	−	0.950653i
$359$	−9.46267	+	16.3898i	−0.0263584	+	0.0456541i	−0.878904	−	0.476999i	$-0.841724\pi$
$359$	−9.46267	+	16.3898i	−0.0263584	+	0.0456541i	0.852545	+	0.522653i	$0.175058\pi$
$360$	−206.209	−	173.156i	−0.572802	−	0.480988i
$361$	1.79097	+	3.10206i	0.00496115	+	0.00859296i
$362$	38.8701	+	209.075i	0.107376	+	0.577554i
$363$	14.7573	+	14.7573i	0.0406537	+	0.0406537i
$364$	100.214	−	40.4581i	0.275312	−	0.111149i
$365$	214.124	+	324.935i	0.586640	+	0.890234i
$366$	87.1973	−	127.024i	0.238244	−	0.347061i
$367$	97.9045	+	26.2334i	0.266770	+	0.0714807i	0.389724	−	0.920932i	$-0.372570\pi$
$367$	97.9045	+	26.2334i	0.266770	+	0.0714807i	−0.122955	+	0.992412i	$0.539237\pi$
$368$	−129.311	−	83.5667i	−0.351388	−	0.227084i
$369$	144.610	−	250.472i	0.391897	−	0.678786i
$370$	105.734	−	366.699i	0.285766	−	0.991079i
$371$	−176.925	+	105.976i	−0.476888	+	0.285650i
$372$	−133.648	+	97.3286i	−0.359269	+	0.261636i
$373$	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	$0.212184\pi$
$374$	289.332	+	605.729i	0.773615	+	1.61960i
$375$	−121.393	−	143.896i	−0.323714	−	0.383724i
$376$	215.247	+	203.580i	0.572466	+	0.541437i
$377$	−11.3200	−	11.3200i	−0.0300265	−	0.0300265i
$378$	−325.102	+	65.8648i	−0.860059	+	0.174245i
$379$	677.446			1.78746			0.893728	−	0.448610i	$-0.148081\pi$
$379$	677.446			1.78746			0.893728	+	0.448610i	$0.148081\pi$
$380$	−242.636	−	294.891i	−0.638516	−	0.776028i
$381$	−191.269	+	110.429i	−0.502018	+	0.289840i
$382$	−286.961	−	101.438i	−0.751207	−	0.265546i
$383$	−457.505	+	122.588i	−1.19453	+	0.320074i	−0.800675	−	0.599099i	$-0.795526\pi$
$383$	−457.505	+	122.588i	−1.19453	+	0.320074i	−0.393856	+	0.919172i	$0.628859\pi$
$384$	−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
$388$	−559.962	−	248.565i	−1.44320	−	0.640630i
$389$	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	$0.278872\pi$
$390$	1.10005	−	58.1206i	0.00282065	−	0.149027i
$391$	312.026			0.798021
$392$	216.004	+	327.118i	0.551031	+	0.834485i
$393$	42.5735	+	42.5735i	0.108330	+	0.108330i
$394$	−177.226	+	258.173i	−0.449812	+	0.655262i
$395$	633.602	−	210.572i	1.60406	−	0.533095i
$396$	260.095	−	100.173i	0.656805	−	0.252963i
$397$	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	$0.210377\pi$
$398$	−162.678	+	139.097i	−0.408738	+	0.349489i
$399$	−201.275	+	3.23587i	−0.504450	+	0.00810995i
$400$	301.403	+	262.976i	0.753508	+	0.657439i
$401$	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	$0.110349\pi$
$402$	−194.447	−	68.7354i	−0.483698	−	0.170984i
$403$	102.317	+	27.4157i	0.253887	+	0.0680289i
$404$	239.376	−	296.278i	0.592515	−	0.733362i
$405$	25.0695	−	121.954i	0.0619000	−	0.301121i
$406$	32.0894	−	48.3953i	0.0790378	−	0.119200i
$407$	279.331	+	279.331i	0.686317	+	0.686317i
$408$	390.541	−	10.8792i	0.957209	−	0.0266647i
$409$	−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	$0.919431\pi$
$410$	−221.823	+	367.947i	−0.541031	+	0.897433i
$411$	96.3782	−	166.932i	0.234497	−	0.406160i
$412$	316.949	−	230.817i	0.769295	−	0.560235i
$413$	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
$416$	16.4621	+	122.409i	0.0395725	+	0.294253i
$417$	66.7191	+	17.8773i	0.159998	+	0.0428713i
$418$	388.625	−	72.2511i	0.929725	−	0.172850i
$419$			210.999i			0.503579i	0.967782	+	0.251789i	$0.0810190\pi$
$419$			210.999i			0.503579i	−0.967782	+	0.251789i	$0.918981\pi$
$420$	207.410	−	37.9494i	0.493832	−	0.0903558i
$421$	−582.411			−1.38340			−0.691700	−	0.722185i	$-0.743138\pi$
$421$	−582.411			−1.38340			−0.691700	+	0.722185i	$0.743138\pi$
$422$	−36.6194	−	196.969i	−0.0867758	−	0.466750i
$423$	−64.5236	+	240.806i	−0.152538	+	0.569280i
$424$	−67.3193	−	225.881i	−0.158772	−	0.532737i
$425$	−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
$428$	−172.133	+	125.355i	−0.402179	+	0.292885i
$429$	52.1099	+	30.0857i	0.121468	+	0.0701298i
$430$	710.857	−	176.126i	1.65315	−	0.409595i
$431$	265.980	−	153.564i	0.617123	−	0.356296i	−0.158625	−	0.987339i	$-0.550706\pi$
$431$	265.980	−	153.564i	0.617123	−	0.356296i	0.775748	+	0.631043i	$0.217373\pi$
$432$	18.9974	−	378.617i	0.0439756	−	0.876429i
$433$	−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	$0.281748\pi$
$434$	−23.7707	+	383.479i	−0.0547712	+	0.883591i
$435$	−17.1863	−	26.0804i	−0.0395087	−	0.0599550i
$436$	−122.760	+	151.942i	−0.281560	+	0.348490i
$437$	47.5544	−	177.476i	0.108820	−	0.406122i
$438$	−78.1326	+	221.030i	−0.178385	+	0.504636i
$439$	−162.117	−	93.5984i	−0.369288	−	0.213208i	0.303860	−	0.952717i	$-0.401725\pi$
$439$	−162.117	−	93.5984i	−0.369288	−	0.213208i	−0.673147	+	0.739509i	$0.735058\pi$
$440$	−389.121	+	141.470i	−0.884365	+	0.321524i
$441$	−155.658	+	290.815i	−0.352967	+	0.659444i
$442$	−162.670	−	190.248i	−0.368032	−	0.430425i
$443$	−143.110	−	534.094i	−0.323047	−	1.20563i	−0.916260	−	0.400583i	$-0.868808\pi$
$443$	−143.110	−	534.094i	−0.323047	−	1.20563i	0.593213	−	0.805045i	$-0.297859\pi$
$444$	214.550	−	82.6323i	0.483222	−	0.186109i
$445$	−160.631	+	53.3842i	−0.360967	+	0.119965i
$446$	−509.822	−	349.973i	−1.14310	−	0.784693i
$447$	132.692	−	132.692i	0.296849	−	0.296849i
$448$	−423.305	+	146.685i	−0.944878	+	0.327422i
$449$			318.872i			0.710182i	0.934832	+	0.355091i	$0.115550\pi$
$449$			318.872i			0.710182i	−0.934832	+	0.355091i	$0.884450\pi$
$450$	−73.9997	+	328.349i	−0.164444	+	0.729665i
$451$	−222.360	−	385.139i	−0.493038	−	0.853966i
$452$	−435.187	−	193.178i	−0.962803	−	0.427384i
$453$	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	$0.906028\pi$
$458$	−65.8315	+	186.232i	−0.143737	+	0.406620i
$459$	384.141	+	665.352i	0.836908	+	1.44957i
$460$	−18.6212	+	191.551i	−0.0404808	+	0.416415i
$461$			31.0353i			0.0673218i	0.999433	+	0.0336609i	$0.0107166\pi$
$461$			31.0353i			0.0673218i	−0.999433	+	0.0336609i	$0.989283\pi$
$462$	−69.4228	+	206.918i	−0.150266	+	0.447874i
$463$	356.134	−	356.134i	0.769189	−	0.769189i	−0.208775	−	0.977964i	$-0.566948\pi$
$463$	356.134	−	356.134i	0.769189	−	0.769189i	0.977964	+	0.208775i	$0.0669476\pi$
$464$	44.5151	+	49.2182i	0.0959377	+	0.106074i
$465$	184.764	+	92.5884i	0.397343	+	0.199115i
$466$	639.901	−	305.655i	1.37318	−	0.655911i
$467$	−228.694	−	853.497i	−0.489708	−	1.82762i	−0.557851	−	0.829941i	$-0.688374\pi$
$467$	−228.694	−	853.497i	−0.489708	−	1.82762i	0.0681423	−	0.997676i	$-0.478293\pi$
$468$	−84.0130	+	61.1820i	−0.179515	+	0.130731i
$469$	−411.159	+	246.279i	−0.876671	+	0.525115i
$470$	102.603	−	355.841i	0.218304	−	0.757109i
$471$	306.540	+	176.981i	0.650828	+	0.375756i
$472$	−26.1078	+	48.2766i	−0.0553131	+	0.102281i
$473$	−196.199	+	732.225i	−0.414797	+	1.54804i
$474$	331.618	+	227.643i	0.699615	+	0.480259i
$475$	−188.296	+	438.644i	−0.396414	+	0.923460i
$476$	559.166	−	715.310i	1.17472	−	1.50275i
$477$	140.241	−	140.241i	0.294007	−	0.294007i
$478$	−581.461	+	108.102i	−1.21644	+	0.226155i
$479$	−630.243	+	363.871i	−1.31575	+	0.759648i	−0.983042	−	0.183383i	$-0.941295\pi$
$479$	−630.243	+	363.871i	−1.31575	+	0.759648i	−0.332707	+	0.943030i	$0.607962\pi$
$480$	−16.6281	+	240.400i	−0.0346420	+	0.500834i
$481$	−127.567	−	73.6510i	−0.265213	−	0.153121i
$482$	220.490	−	188.528i	0.457447	−	0.391138i
$483$	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
$486$	452.514	−	216.147i	0.931099	−	0.444748i
$487$	−104.569	+	390.256i	−0.214720	+	0.801346i	0.771545	+	0.636175i	$0.219484\pi$
$487$	−104.569	+	390.256i	−0.214720	+	0.801346i	−0.986265	+	0.165171i	$0.947182\pi$
$488$	409.041	−	11.3945i	0.838199	−	0.0233495i
$489$	311.247			0.636496
$490$	239.366	−	427.556i	0.488502	−	0.872563i
$491$		−	468.769i		−	0.954724i	−0.878707	−	0.477362i	$-0.841593\pi$
$491$		−	468.769i		−	0.954724i	0.878707	−	0.477362i	$-0.158407\pi$
$492$	−257.383	+	27.3417i	−0.523136	+	0.0555726i
$493$	−129.910	−	34.8093i	−0.263509	−	0.0706071i
$494$	−133.002	+	63.5294i	−0.269234	+	0.128602i
$495$	−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
$498$	−10.4892	+	8.96872i	−0.0210626	+	0.0180095i
$499$	304.759	−	527.858i	0.610740	−	1.05783i	−0.380376	−	0.924832i	$-0.624206\pi$
$499$	304.759	−	527.858i	0.610740	−	1.05783i	0.991116	−	0.133000i	$-0.0424611\pi$
$500$	119.138	−	485.599i	0.238276	−	0.971197i
$501$	8.59628	+	14.8892i	0.0171582	+	0.0297189i
$502$	452.782	−	84.1789i	0.901956	−	0.167687i
$503$	195.469	+	195.469i	0.388606	+	0.388606i	0.874190	−	0.485584i	$-0.161393\pi$
$503$	195.469	+	195.469i	0.388606	+	0.388606i	−0.485584	+	0.874190i	$0.661393\pi$
$504$	−278.009	−	254.599i	−0.551605	−	0.505157i
$505$	−466.368	−	95.8691i	−0.923501	−	0.189840i
$506$	−164.236	−	112.742i	−0.324577	−	0.222810i
$507$	224.184	+	60.0700i	0.442178	+	0.118481i
$508$	−536.127	−	237.984i	−1.05537	−	0.468473i
$509$	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	$-0.0998774\pi$
$510$	−236.136	−	427.482i	−0.463011	−	0.838201i
$511$	279.949	+	467.370i	0.547845	+	0.914619i
$512$	−42.7271	−	510.214i	−0.0834514	−	0.996512i
$513$	436.987	−	117.090i	0.851826	−	0.228246i
$514$	448.493	−	214.227i	0.872554	−	0.416783i
$515$	−438.172	−	219.575i	−0.850820	−	0.426360i
$516$	343.182	+	277.271i	0.665081	+	0.537347i
$517$	271.060	+	271.060i	0.524294	+	0.524294i
$518$	169.950	−	506.544i	0.328089	−	0.977884i
$519$	−17.4097			−0.0335447
$520$	126.500	−	88.5086i	0.243269	−	0.170209i
$521$	−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	$0.506299\pi$
$522$	−18.6111	+	52.6491i	−0.0356534	+	0.100860i
$523$	−167.971	+	45.0076i	−0.321168	+	0.0860566i	−0.415801	−	0.909456i	$-0.636499\pi$
$523$	−167.971	+	45.0076i	−0.321168	+	0.0860566i	0.0946334	+	0.995512i	$0.469832\pi$
$524$	−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
$528$	−209.494	−	135.385i	−0.396768	−	0.256410i
$529$	377.937	−	218.202i	0.714436	−	0.412480i
$530$	−212.235	+	204.351i	−0.400444	+	0.385567i
$531$	−46.1827			−0.0869730
$532$	−321.637	−	427.062i	−0.604581	−	0.802748i
$533$	117.259	+	117.259i	0.219998	+	0.219998i
$534$	−84.0715	−	57.7119i	−0.157437	−	0.108075i
$535$	237.968	+	119.249i	0.444799	+	0.222896i
$536$	−156.444	−	524.927i	−0.291873	−	0.979341i
$537$	−325.710	+	87.2738i	−0.606537	+	0.162521i
$538$	211.864	+	247.782i	0.393800	+	0.460561i
$539$	267.588	+	430.868i	0.496452	+	0.799383i
$540$	−431.380	+	196.115i	−0.798853	+	0.363176i
$541$	−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	$0.322676\pi$
$542$	6.15049	−	17.3992i	0.0113478	−	0.0321019i
$543$	154.684	+	41.4474i	0.284869	+	0.0763304i
$544$	633.959	+	821.449i	1.16537	+	1.51002i
$545$	239.170	+	49.1650i	0.438844	+	0.0902110i
$546$	5.03506	−	81.2276i	0.00922172	−	0.148768i
$547$	−326.968	−	326.968i	−0.597749	−	0.597749i	0.341964	−	0.939713i	$-0.388908\pi$
$547$	−326.968	−	326.968i	−0.597749	−	0.597749i	−0.939713	+	0.341964i	$0.888908\pi$
$548$	509.074	−	54.0788i	0.928967	−	0.0986839i
$549$	172.163	+	298.195i	0.313593	+	0.543160i
$550$	380.352	+	350.985i	0.691548	+	0.638154i
$551$	−39.5979	+	68.5856i	−0.0718656	+	0.124475i
$552$	−98.7550	+	60.7442i	−0.178904	+	0.110044i
$553$	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
$556$	65.9328	+	171.191i	0.118584	+	0.307897i
$557$	−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	$0.670727\pi$
$558$	−67.5359	−	363.263i	−0.121032	−	0.651009i
$559$		−	282.667i		−	0.505666i
$560$	405.755	+	385.958i	0.724562	+	0.689210i
$561$	505.507			0.901082
$562$	−205.444	+	38.1950i	−0.365559	+	0.0679627i
$563$	−116.617	+	435.219i	−0.207134	+	0.773036i	0.781654	+	0.623712i	$0.214376\pi$
$563$	−116.617	+	435.219i	−0.207134	+	0.773036i	−0.988788	+	0.149324i	$0.952290\pi$
$564$	208.198	−	80.1856i	0.369145	−	0.142173i
$565$	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
$568$	−297.799	−	484.147i	−0.524294	−	0.852372i
$569$	−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	$0.766234\pi$
$570$	−279.133	+	69.1597i	−0.489708	+	0.121333i
$571$	−760.051	+	438.816i	−1.33109	+	0.768504i	−0.985466	−	0.169870i	$-0.945665\pi$
$571$	−760.051	+	438.816i	−1.33109	+	0.768504i	−0.345621	+	0.938374i	$0.612332\pi$
$572$	16.8814	+	158.914i	0.0295129	+	0.277821i
$573$	−162.068	+	162.068i	−0.282841	+	0.282841i
$574$	−332.400	+	501.306i	−0.579094	+	0.873356i
$575$	223.414	−	89.2128i	0.388546	−	0.155153i
$576$	360.537	−	235.851i	0.625933	−	0.409463i
$577$	−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	$0.980401\pi$
$578$	−1437.71	−	508.221i	−2.48739	−	0.879275i
$579$	−163.269	−	94.2635i	−0.281985	−	0.162804i
$580$	29.1220	−	77.6737i	0.0502104	−	0.133920i
$581$	0.515542	+	32.0674i	0.000887335	+	0.0551934i
$582$	−350.650	+	299.821i	−0.602491	+	0.515156i
$583$	−78.9306	−	294.573i	−0.135387	−	0.505271i
$584$	−596.692	+	177.832i	−1.02173	+	0.304507i
$585$	116.145	+	58.2023i	0.198539	+	0.0994911i
$586$	66.6644	−	97.1131i	0.113762	−	0.165722i
$587$	−765.163	+	765.163i	−1.30351	+	1.30351i	−0.377509	+	0.926006i	$0.623219\pi$
$587$	−765.163	+	765.163i	−1.30351	+	1.30351i	−0.926006	+	0.377509i	$0.876781\pi$
$588$	292.388	−	40.6028i	0.497259	−	0.0690524i
$589$		−	524.015i		−	0.889668i
$590$	68.5926	+	1.29826i	0.116259	+	0.00220043i
$591$	117.908	+	204.222i	0.199506	+	0.345554i
$592$	512.849	+	331.427i	0.866299	+	0.559844i
$593$	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
$598$	70.0351	+	24.7569i	0.117116	+	0.0413995i
$599$	393.897	+	682.249i	0.657591	+	1.13898i	0.981238	+	0.192803i	$0.0617577\pi$
$599$	393.897	+	682.249i	0.657591	+	1.13898i	−0.323647	+	0.946178i	$0.604909\pi$
$600$	276.521	−	119.451i	0.460869	−	0.199085i
$601$		−	1030.28i		−	1.71428i	−0.515080	−	0.857142i	$-0.672238\pi$
$601$		−	1030.28i		−	1.71428i	0.515080	−	0.857142i	$-0.327762\pi$
$602$	1004.88	−	203.585i	1.66923	−	0.338181i
$603$	325.909	−	325.909i	0.540479	−	0.540479i
$604$	−553.750	+	685.383i	−0.916805	+	1.13474i
$605$	65.7492	−	21.8512i	0.108676	−	0.0361177i
$606$	−123.628	−	258.822i	−0.204007	−	0.427098i
$607$	−21.4888	−	80.1971i	−0.0354016	−	0.132120i	0.945963	−	0.324273i	$-0.105120\pi$
$607$	−21.4888	−	80.1971i	−0.0354016	−	0.132120i	−0.981365	+	0.192153i	$0.938453\pi$
$608$	563.846	−	235.393i	0.927378	−	0.387159i
$609$	−22.4697	−	37.5128i	−0.0368960	−	0.0615973i
$610$	−247.321	−	447.732i	−0.405445	−	0.733987i
$611$	−123.790	−	71.4703i	−0.202602	−	0.116973i
$612$	−354.245	+	798.037i	−0.578832	+	1.30398i
$613$	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	$-0.255124\pi$
$614$	207.540	−	302.333i	0.338013	−	0.492398i
$615$	178.025	+	270.156i	0.289472	+	0.439278i
$616$	−552.776	+	174.467i	−0.897364	+	0.283226i
$617$	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	$0.0896367\pi$
$618$	−53.9685	−	290.286i	−0.0873277	−	0.469719i
$619$	678.334	−	391.636i	1.09585	−	0.632692i	0.160725	−	0.986999i	$-0.448617\pi$
$619$	678.334	−	391.636i	1.09585	−	0.632692i	0.935129	+	0.354308i	$0.115283\pi$
$620$	90.0956	+	541.433i	0.145316	+	0.873279i
$621$	−197.449	−	113.997i	−0.317953	−	0.183570i
$622$	−550.722	−	644.086i	−0.885405	−	1.03551i
$623$	−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
$626$	391.086	+	818.756i	0.624738	+	1.30792i
$627$	77.0419	−	287.524i	0.122874	−	0.458571i
$628$	99.3058	+	934.821i	0.158130	+	1.48857i
$629$	−1237.50			−1.96741
$630$	−123.257	+	454.812i	−0.195645	+	0.721925i
$631$			865.154i			1.37108i	0.728033	+	0.685542i	$0.240435\pi$
$631$			865.154i			1.37108i	−0.728033	+	0.685542i	$0.759565\pi$
$632$	29.7473	+	1067.87i	0.0470685	+	1.68967i
$633$	−145.727	−	39.0475i	−0.230217	−	0.0616864i
$634$	−350.923	−	734.672i	−0.553506	−	1.15879i
$635$	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
$638$	55.8013	+	65.2613i	0.0874628	+	0.102290i
$639$	239.145	−	414.211i	0.374249	−	0.648218i
$640$	−542.116	+	340.161i	−0.847057	+	0.531502i
$641$	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	$0.677771\pi$
$642$	29.3098	+	157.652i	0.0456540	+	0.245564i
$643$	−726.677	−	726.677i	−1.13013	−	1.13013i	−0.990154	−	0.139981i	$-0.955296\pi$
$643$	−726.677	−	726.677i	−1.13013	−	1.13013i	−0.139981	−	0.990154i	$-0.544704\pi$
$644$	−37.5689	+	266.804i	−0.0583367	+	0.414291i
$645$	111.046	−	540.198i	0.172164	−	0.837516i
$646$	−700.806	+	1020.90i	−1.08484	+	1.58033i
$647$	665.627	+	178.354i	1.02879	+	0.275664i	0.733461	−	0.679732i	$-0.237904\pi$
$647$	665.627	+	178.354i	1.02879	+	0.275664i	0.295330	+	0.955395i	$0.404570\pi$
$648$	175.225	+	94.7607i	0.270408	+	0.146236i
$649$	−35.5064	+	61.4989i	−0.0547094	+	0.0947595i
$650$	−170.868	−	89.7097i	−0.262874	−	0.138015i
$651$	252.861	+	140.619i	0.388420	+	0.216005i
$652$	486.627	+	668.220i	0.746361	+	1.02488i
$653$	−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	$0.459857\pi$
$654$	63.4010	+	132.733i	0.0969434	+	0.202955i
$655$	189.681	−	63.0389i	0.289589	−	0.0962425i
$656$	−461.113	−	509.831i	−0.702916	−	0.777181i
$657$	−370.465	−	370.465i	−0.563874	−	0.563874i
$658$	164.918	−	491.546i	0.250635	−	0.747030i
$659$	−480.601			−0.729288			−0.364644	−	0.931147i	$-0.618809\pi$
$659$	−480.601			−0.729288			−0.364644	+	0.931147i	$0.618809\pi$
$660$	−30.1678	+	310.328i	−0.0457087	+	0.470194i
$661$	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	$0.00396574\pi$
$662$	501.526	+	177.286i	0.757592	+	0.267803i
$663$	−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
$668$	−18.5257	+	41.7344i	−0.0277331	+	0.0624766i
$669$	−403.284	+	232.836i	−0.602815	+	0.348036i
$670$	−493.216	+	474.893i	−0.736144	+	0.708795i
$671$	529.453			0.789050
$672$	−37.7198	+	335.249i	−0.0561307	+	0.498883i
$673$	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	$0.735072\pi$
$674$	103.411	−	150.644i	0.153429	−	0.223507i
$675$	465.283	+	366.567i	0.689308	+	0.543063i
$676$	221.542	+	575.222i	0.327725	+	0.850920i
$677$	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	$0.112123\pi$
$678$	−272.516	+	233.013i	−0.401940	+	0.343676i
$679$	17.2344	+	1072.00i	0.0253820	+	1.57879i
$680$	548.575	−	1175.32i	0.806728	−	1.72842i
$681$	76.7065	−	132.860i	0.112638	−	0.195095i
$682$	−535.661	−	189.352i	−0.785426	−	0.277642i
$683$	982.574	+	263.280i	1.43862	+	0.385476i	0.892048	−	0.451940i	$-0.149268\pi$
$683$	982.574	+	263.280i	1.43862	+	0.385476i	0.546567	+	0.837416i	$0.315934\pi$
$684$	399.922	+	323.114i	0.584681	+	0.472389i
$685$	−352.114	−	534.338i	−0.514035	−	0.780055i
$686$	360.524	−	583.625i	0.525545	−	0.850766i
$687$	105.179	+	105.179i	0.153099	+	0.153099i
$688$	−58.7202	+	1170.29i	−0.0853491	+	1.70100i
$689$	56.8583	+	98.4815i	0.0825230	+	0.142934i
$690$	124.116	+	74.8255i	0.179879	+	0.108443i
$691$	515.676	−	893.177i	0.746275	−	1.29259i	−0.203322	−	0.979112i	$-0.565174\pi$
$691$	515.676	−	893.177i	0.746275	−	1.29259i	0.949597	−	0.313474i	$-0.101493\pi$
$692$	−27.2196	−	37.3771i	−0.0393348	−	0.0540131i
$693$	−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
$696$	47.8925	−	14.2734i	0.0688111	−	0.0205078i
$697$	1345.68	+	360.574i	1.93068	+	0.517323i
$698$	396.666	−	73.7460i	0.568289	−	0.105653i
$699$		−	534.025i		−	0.763984i
$700$	195.852	−	672.043i	0.279788	−	0.960062i
$701$	291.683			0.416095			0.208048	−	0.978119i	$-0.433289\pi$
$701$	291.683			0.416095			0.208048	+	0.978119i	$0.433289\pi$
$702$	33.4309	+	179.819i	0.0476224	+	0.256152i
$703$	−188.602	+	703.872i	−0.268281	+	1.00124i
$704$	−36.8795	−	661.436i	−0.0523856	−	0.939540i
$705$	−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
$708$	24.3304	+	33.4097i	0.0343650	+	0.0471888i
$709$	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	$0.613267\pi$
$710$	−366.833	+	608.482i	−0.516666	+	0.857018i
$711$	−778.486	+	449.459i	−1.09492	+	0.632151i
$712$	−7.54152	−	270.726i	−0.0105920	−	0.380233i
$713$	−186.736	+	186.736i	−0.261902	+	0.261902i
$714$	−304.568	−	612.128i	−0.426566	−	0.857322i
$715$	166.800	−	109.917i	0.233287	−	0.153730i
$716$	−696.610	−	562.821i	−0.972919	−	0.786063i
$717$	−115.270	+	430.194i	−0.160767	+	0.599991i
$718$	−12.6150	+	35.6867i	−0.0175696	+	0.0497029i
$719$	−1099.60	−	634.855i	−1.52935	−	0.882969i	−0.999389	−	0.0349445i	$-0.988875\pi$
$719$	−1099.60	−	634.855i	−1.52935	−	0.882969i	−0.529957	−	0.848024i	$-0.677792\pi$
$720$	−468.770	−	265.095i	−0.651069	−	0.368187i
$721$	−599.665	−	333.481i	−0.831713	−	0.462526i
$722$	4.65561	+	5.44488i	0.00644821	+	0.00754139i
$723$	−56.5414	−	211.016i	−0.0782039	−	0.291861i
$724$	152.861	+	396.895i	0.211134	+	0.548198i
$725$	−102.969	+	12.2193i	−0.142027	+	0.0168542i
$726$	34.4121	+	23.6226i	0.0473996	+	0.0325380i
$727$	−361.549	+	361.549i	−0.497317	+	0.497317i	−0.910602	−	0.413285i	$-0.864381\pi$
$727$	−361.549	+	361.549i	−0.497317	+	0.497317i	0.413285	+	0.910602i	$0.364381\pi$
$728$	182.261	−	116.188i	0.250358	−	0.159598i
$729$		−	153.535i		−	0.210610i
$730$	539.818	+	560.646i	0.739476	+	0.768008i
$731$	−1187.36	−	2056.57i	−1.62430	−	2.81337i
$732$	125.021	−	281.645i	0.170794	−	0.384761i
$733$	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
$738$	192.784	−	545.370i	0.261225	−	0.738983i
$739$	55.5469	+	96.2101i	0.0751650	+	0.130190i	0.901158	−	0.433491i	$-0.142718\pi$
$739$	55.5469	+	96.2101i	0.0751650	+	0.130190i	−0.825993	+	0.563680i	$0.809385\pi$
$740$	73.8520	−	759.696i	0.0998000	−	1.02662i
$741$			110.996i			0.149792i
$742$	−309.148	+	273.059i	−0.416642	+	0.368004i
$743$	57.1447	−	57.1447i	0.0769108	−	0.0769108i	−0.667605	−	0.744516i	$-0.732680\pi$
$743$	57.1447	−	57.1447i	0.0769108	−	0.0769108i	0.744516	+	0.667605i	$0.232680\pi$
$744$	−227.213	+	240.235i	−0.305394	+	0.322896i
$745$	−196.477	−	591.190i	−0.263728	−	0.793544i
$746$	806.595	−	385.277i	1.08123	−	0.516457i
$747$	−7.98255	−	29.7913i	−0.0106862	−	0.0398813i
$748$	790.349	+	1085.28i	1.05662	+	1.45091i
$749$	325.673	+	181.111i	0.434811	+	0.241803i
$750$	−291.299	−	238.567i	−0.388399	−	0.318090i
$751$	58.0140	+	33.4944i	0.0772490	+	0.0445997i	0.538127	−	0.842864i	$-0.319132\pi$
$751$	58.0140	+	33.4944i	0.0772490	+	0.0445997i	−0.460878	+	0.887464i	$0.652465\pi$
$752$	497.664	+	321.614i	0.661787	+	0.427678i
$753$	89.7606	−	334.991i	0.119204	−	0.444875i
$754$	−26.3968	−	18.1204i	−0.0350090	−	0.0240324i
$755$	1078.85	+	221.775i	1.42895	+	0.293741i
$756$	−615.173	+	248.356i	−0.813720	+	0.328514i
$757$	−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	$0.377902\pi$
$758$	1332.07	−	247.651i	1.75734	−	0.326716i
$759$	−129.915	+	75.0067i	−0.171167	+	0.0988231i
$760$	−584.899	−	491.146i	−0.769604	−	0.646245i
$761$	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	$0.643841\pi$
$762$	−335.724	+	287.059i	−0.440583	+	0.376718i
$763$	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
$766$	−854.782	+	408.294i	−1.11590	+	0.533021i
$767$	6.85343	−	25.5774i	0.00893537	−	0.0333473i
$768$	−360.562	−	136.568i	−0.469482	−	0.177823i
$769$	102.995			0.133933			0.0669666	−	0.997755i	$-0.478668\pi$
$769$	102.995			0.133933			0.0669666	+	0.997755i	$0.478668\pi$
$770$	510.886	+	513.806i	0.663488	+	0.667280i
$771$		−	374.286i		−	0.485456i
$772$	−52.8922	−	497.904i	−0.0685132	−	0.644953i
$773$	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	$0.578924\pi$
$774$	−889.705	+	424.975i	−1.14949	+	0.549064i
$775$	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
$778$	201.356	−	172.169i	0.258813	−	0.221296i
$779$	410.178	−	710.449i	0.526544	−	0.912002i
$780$	−19.0839	−	114.685i	−0.0244665	−	0.147032i
$781$	−367.721	−	636.912i	−0.470834	−	0.815509i
$782$	613.539	−	114.066i	0.784577	−	0.145864i
$783$	69.4891	+	69.4891i	0.0887473	+	0.0887473i
$784$	544.313	+	564.251i	0.694277	+	0.719708i
$785$	981.213	−	646.593i	1.24995	−	0.823685i
$786$	99.2760	+	68.1492i	0.126305	+	0.0867038i
$787$	−460.602	−	123.418i	−0.585263	−	0.156821i	−0.0459759	−	0.998943i	$-0.514640\pi$
$787$	−460.602	−	123.418i	−0.585263	−	0.156821i	−0.539288	+	0.842122i	$0.681306\pi$
$788$	−254.102	+	572.435i	−0.322464	+	0.726441i
$789$	204.977	−	355.030i	0.259793	−	0.449975i
$790$	1168.88	−	645.673i	1.47959	−	0.817308i
$791$	13.3941	+	833.130i	0.0169331	+	1.05326i
$792$	474.806	−	292.053i	0.599503	−	0.368754i
$793$	−190.698	+	51.0973i	−0.240476	+	0.0644355i
$794$	864.991	−	413.171i	1.08941	−	0.520366i
$795$	69.9720	+	210.542i	0.0880150	+	0.264833i
$796$	−269.026	+	332.976i	−0.337972	+	0.418312i
$797$	−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	$0.895735\pi$
$798$	−394.586	+	79.9421i	−0.494469	+	0.100178i
$799$	−1200.86			−1.50295
$800$	688.786	+	406.908i	0.860982	+	0.508635i
$801$	197.361	−	113.947i	0.246394	−	0.142256i
$802$	94.0894	−	266.171i	0.117318	−	0.331884i
$803$	−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
$808$	362.377	−	670.082i	0.448487	−	0.829309i
$809$	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	$0.280113\pi$
$810$	4.71215	−	248.964i	0.00581747	−	0.307363i
$811$	524.159			0.646312			0.323156	−	0.946346i	$-0.395256\pi$
$811$	524.159			0.646312			0.323156	+	0.946346i	$0.395256\pi$
$812$	45.4059	−	106.891i	0.0559185	−	0.131639i
$813$	−9.82662	−	9.82662i	−0.0120869	−	0.0120869i
$814$	651.364	+	447.136i	0.800201	+	0.549308i
$815$	462.927	−	923.792i	0.568009	−	1.13349i
$816$	763.947	−	164.160i	0.936209	−	0.201177i
$817$	−1350.70	+	361.920i	−1.65325	+	0.442987i
$818$	−284.082	−	332.242i	−0.347288	−	0.406164i
$819$	158.952	+	88.3950i	0.194080	+	0.107930i
$820$	−301.663	+	804.588i	−0.367881	+	0.981205i
$821$	−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	$0.324339\pi$
$822$	128.485	−	363.472i	0.156307	−	0.442180i
$823$	937.391	+	251.173i	1.13899	+	0.305192i	0.778546	−	0.627588i	$-0.215958\pi$
$823$	937.391	+	251.173i	1.13899	+	0.305192i	0.360447	+	0.932780i	$0.382624\pi$
$824$	538.841	−	569.722i	0.653933	−	0.691410i
$825$	361.948	−	144.532i	0.438725	−	0.175190i
$826$	95.8629	+	5.94226i	0.116057	+	0.00719402i
$827$	999.090	+	999.090i	1.20809	+	1.20809i	0.971645	+	0.236444i	$0.0759820\pi$
$827$	999.090	+	999.090i	1.20809	+	1.20809i	0.236444	+	0.971645i	$0.424018\pi$
$828$	−27.3710	−	257.658i	−0.0330567	−	0.311182i
$829$	−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	$0.854238\pi$
$830$	11.0186	+	44.4718i	0.0132754	+	0.0535805i
$831$	−126.988	+	219.950i	−0.152814	+	0.264681i
$832$	77.1182	+	234.676i	0.0926902	+	0.282063i
$833$	−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
$836$	737.743	−	284.136i	0.882468	−	0.339875i
$837$	−628.082	−	168.294i	−0.750396	−	0.201068i
$838$	77.1341	+	414.890i	0.0920454	+	0.495095i
$839$		−	1200.44i		−	1.43080i	−0.698713	−	0.715402i	$-0.746244\pi$
$839$		−	1200.44i		−	1.43080i	0.698713	−	0.715402i	$-0.253756\pi$
$840$	393.958	−	150.442i	0.468998	−	0.179098i
$841$	823.797			0.979544
$842$	−1145.20	+	212.909i	−1.36009	+	0.252862i
$843$	−40.7277	+	151.998i	−0.0483128	+	0.180306i
$844$	−144.010	−	373.914i	−0.170628	−	0.443026i
$845$	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
$848$	−214.945	−	419.541i	−0.253472	−	0.494742i
$849$	137.064	+	79.1338i	0.161441	+	0.0932083i
$850$	−1620.00	+	65.0514i	−1.90588	+	0.0765310i
$851$	318.039	−	183.620i	0.373723	−	0.215769i
$852$	−425.639	+	45.2155i	−0.499577	+	0.0530699i
$853$	−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	$0.277221\pi$
$854$	−318.996	−	641.124i	−0.373531	−	0.750731i
$855$	129.406	−	629.512i	0.151352	−	0.736272i
$856$	−292.640	+	309.411i	−0.341869	+	0.361462i
$857$	−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	$0.102636\pi$
$858$	113.462	+	40.1081i	0.132241	+	0.0467460i
$859$	−492.269	−	284.212i	−0.573072	−	0.330863i	0.185303	−	0.982681i	$-0.440673\pi$
$859$	−492.269	−	284.212i	−0.573072	−	0.330863i	−0.758375	+	0.651818i	$0.774007\pi$
$860$	1333.38	−	606.182i	1.55044	−	0.704863i
$861$	232.753	+	388.579i	0.270329	+	0.451311i
$862$	466.861	−	399.187i	0.541602	−	0.463093i
$863$	69.2023	+	258.266i	0.0801880	+	0.299266i	0.994360	−	0.106062i	$-0.0338241\pi$
$863$	69.2023	+	258.266i	0.0801880	+	0.299266i	−0.914171	+	0.405328i	$0.867157\pi$
$864$	−101.055	−	751.423i	−0.116961	−	0.869702i
$865$	−25.8940	+	51.6726i	−0.0299352	+	0.0597371i
$866$	−97.6055	+	142.186i	−0.112708	+	0.164187i
$867$	−811.982	+	811.982i	−0.936543	+	0.936543i
$868$	93.4460	+	762.726i	0.107657	+	0.878717i
$869$			1382.22i			1.59059i
$870$	−43.3276	−	44.9994i	−0.0498019	−	0.0517234i
$871$	132.134	+	228.862i	0.151704	+	0.262758i
$872$	−185.840	+	343.641i	−0.213119	+	0.394084i
$873$	−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	$0.748332\pi$
$878$	−352.989	−	124.779i	−0.402037	−	0.142117i
$879$	−44.3516	−	76.8192i	−0.0504569	−	0.0873939i
$880$	−713.414	+	420.423i	−0.810698	+	0.477754i
$881$			1385.67i			1.57284i	0.617692	+	0.786420i	$0.288068\pi$
$881$			1385.67i			1.57284i	−0.617692	+	0.786420i	$0.711932\pi$
$882$	−199.760	+	628.734i	−0.226486	+	0.712851i
$883$	−50.6144	+	50.6144i	−0.0573210	+	0.0573210i	−0.735186	−	0.677865i	$-0.762905\pi$
$883$	−50.6144	+	50.6144i	−0.0573210	+	0.0573210i	0.677865	+	0.735186i	$0.262905\pi$
$884$	−389.407	−	314.619i	−0.440506	−	0.355904i
$885$	23.1455	−	46.1878i	0.0261531	−	0.0521896i
$886$	−476.644	−	997.876i	−0.537973	−	1.12627i
$887$	252.563	+	942.577i	0.284738	+	1.06266i	0.949030	+	0.315185i	$0.102066\pi$
$887$	252.563	+	942.577i	0.284738	+	1.06266i	−0.664292	+	0.747473i	$0.731267\pi$
$888$	391.664	−	240.913i	0.441063	−	0.271298i
$889$	16.5008	+	1026.37i	0.0185611	+	1.15452i
$890$	−296.333	+	163.691i	−0.332959	+	0.183922i
$891$	223.216	+	128.874i	0.250523	+	0.144640i
$892$	−1130.40	−	501.781i	−1.26727	−	0.562535i
$893$	−183.017	+	683.030i	−0.204947	+	0.764872i
$894$	212.405	−	309.420i	0.237589	−	0.346107i
$895$	−225.407	+	1096.53i	−0.251852	+	1.22517i
$896$	−778.725	+	443.174i	−0.869113	+	0.494613i
$897$	39.5540	−	39.5540i	0.0440959	−	0.0440959i
$898$	116.568	+	627.000i	0.129809	+	0.698218i
$899$	98.5783	−	56.9142i	0.109653	−	0.0633084i
$900$	−25.4731	+	672.687i	−0.0283034	+	0.747430i
$901$	827.355	+	477.674i	0.918263	+	0.530160i
$902$	−578.021	−	676.014i	−0.640822	−	0.749461i
$903$	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
$906$	285.991	+	598.734i	0.315663	+	0.660855i
$907$	160.432	−	598.741i	0.176882	−	0.660133i	−0.819341	−	0.573306i	$-0.805661\pi$
$907$	160.432	−	598.741i	0.176882	−	0.660133i	0.996223	−	0.0868271i	$-0.0276728\pi$
$908$	405.167	−	43.0408i	0.446219	−	0.0474017i
$909$	641.018			0.705191
$910$	−233.598	−	135.757i	−0.256701	−	0.149183i
$911$			671.186i			0.736757i	0.929676	+	0.368379i	$0.120087\pi$
$911$			671.186i			0.736757i	−0.929676	+	0.368379i	$0.879913\pi$
$912$	23.0578	−	459.540i	0.0252827	−	0.503881i
$913$	−45.8086	−	12.2744i	−0.0501737	−	0.0134440i
$914$	26.3284	+	55.1197i	0.0288057	+	0.0603060i
$915$	−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
$918$	998.568	+	1167.86i	1.08777	+	1.27218i
$919$	−409.427	+	709.149i	−0.445514	+	0.771653i	−0.998088	−	0.0618111i	$-0.980312\pi$
$919$	−409.427	+	709.149i	−0.445514	+	0.771653i	0.552574	+	0.833464i	$0.313646\pi$
$920$	33.4095	+	383.455i	0.0363147	+	0.416799i
$921$	−138.076	−	239.154i	−0.149919	−	0.259668i
$922$	11.3454	+	61.0250i	0.0123053	+	0.0661876i
$923$	193.914	+	193.914i	0.210091	+	0.210091i
$924$	−60.8645	+	432.243i	−0.0658707	+	0.467795i
$925$	−886.065	+	353.820i	−0.957908	+	0.382508i
$926$	570.079	−	830.460i	0.615636	−	0.896825i
$927$	637.370	+	170.783i	0.687562	+	0.184232i
$928$	105.523	+	80.5050i	0.113710	+	0.0867510i
$929$	−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	$0.715235\pi$
$930$	397.150	+	114.514i	0.427043	+	0.123133i
$931$	−441.516	+	824.879i	−0.474238	+	0.886014i
$932$	1146.51	−	834.936i	1.23016	−	0.895854i
$933$	−616.411	+	165.167i	−0.660676	+	0.177028i
$934$	−761.691	−	1594.63i	−0.815515	−	1.70732i
$935$	751.857	−	1500.36i	0.804125	−	1.60467i
$936$	−142.829	+	151.015i	−0.152595	+	0.161341i
$937$	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	$0.394342\pi$
$938$	−718.434	+	634.565i	−0.765921	+	0.676509i
$939$	683.287			0.727675
$940$	71.6653	−	737.201i	0.0762396	−	0.784257i
$941$	−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	$0.558309\pi$
$942$	667.450	+	235.938i	0.708545	+	0.250465i
$943$	−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	−0.467332	−	0.884082i	$-0.654785\pi$
$947$	−407.222	+	109.115i	−0.430013	+	0.115222i	0.0373192	+	0.999303i	$0.488118\pi$
$948$	735.280	+	326.388i	0.775612	+	0.344291i
$949$	260.151	−	150.198i	0.274132	−	0.158270i
$950$	−209.896	+	931.342i	−0.220943	+	0.980360i
$951$	−613.115			−0.644706
$952$	838.000	−	1610.93i	0.880252	−	1.69215i
$953$	−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	$-0.517728\pi$
$954$	224.490	−	327.025i	0.235315	−	0.342794i
$955$	239.975	+	722.073i	0.251283	+	0.756097i
$956$	−1103.81	+	425.124i	−1.15461	+	0.444690i
$957$	62.4571	−	16.7353i	0.0652635	−	0.0174873i
$958$	−1106.23	+	945.878i	−1.15473	+	0.987346i
$959$	−460.360	−	768.564i	−0.480042	−	0.801422i
$960$	55.1860	+	478.779i	0.0574854	+	0.498728i
$961$	103.916	−	179.988i	0.108133	−	0.187293i
$962$	−277.761	−	98.1863i	−0.288733	−	0.102065i
$963$	−346.150	−	92.7507i	−0.359450	−	0.0963143i
$964$	364.631	−	451.308i	0.378248	−	0.468162i
$965$	−522.613	+	344.388i	−0.541568	+	0.356879i
$966$	169.101	+	112.126i	0.175053	+	0.116072i
$967$	605.438	+	605.438i	0.626099	+	0.626099i	0.947084	−	0.320985i	$-0.104014\pi$
$967$	605.438	+	605.438i	0.626099	+	0.626099i	−0.320985	+	0.947084i	$0.604014\pi$
$968$	3.08689	+	110.813i	0.00318894	+	0.114477i
$969$	466.244	+	807.558i	0.481160	+	0.833393i
$970$	368.347	+	1486.68i	0.379739	+	1.53266i
$971$	166.320	−	288.075i	0.171287	−	0.296678i	−0.767583	−	0.640950i	$-0.778541\pi$
$971$	166.320	−	288.075i	0.171287	−	0.296678i	0.938870	+	0.344271i	$0.111874\pi$
$972$	810.765	−	590.435i	0.834121	−	0.607444i
$973$	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
$976$	800.135	−	171.936i	0.819810	−	0.176164i
$977$	−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	$0.736665\pi$
$978$	612.006	−	113.781i	0.625773	−	0.116341i
$979$		−	350.421i		−	0.357937i
$980$	314.368	−	928.209i	0.320784	−	0.947153i
$981$	−328.736			−0.335103
$982$	−171.366	−	921.744i	−0.174507	−	0.938640i
$983$	48.5391	−	181.151i	0.0493786	−	0.184283i	−0.936832	−	0.349780i	$-0.886256\pi$
$983$	48.5391	−	181.151i	0.0493786	−	0.184283i	0.986210	+	0.165497i	$0.0529228\pi$
$984$	−496.098	+	147.852i	−0.504165	+	0.150256i
$985$	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
$988$	−238.298	+	173.539i	−0.241192	+	0.175647i
$989$	610.305	+	352.360i	0.617093	+	0.356279i
$990$	−596.742	−	359.755i	−0.602770	−	0.363389i
$991$	−1559.36	+	900.300i	−1.57353	+	0.908476i	−0.577795	+	0.816182i	$0.696087\pi$
$991$	−1559.36	+	900.300i	−1.57353	+	0.908476i	−0.995732	+	0.0922937i	$0.970580\pi$
$992$	−871.007	−	112.205i	−0.878031	−	0.113110i
$993$	283.248	−	283.248i	0.285245	−	0.285245i
$994$	−549.697	+	829.021i	−0.553015	+	0.834025i
$995$	524.134	+	107.744i	0.526767	+	0.108285i
$996$	−17.3463	+	21.4697i	−0.0174160	+	0.0215560i
$997$	−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	$0.909935\pi$
$998$	406.283	−	1149.34i	0.407097	−	1.15164i
$999$	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.103.41	yes	176
4.3	odd	2	inner	140.3.x.a.103.4	yes	176
5.2	odd	4	inner	140.3.x.a.47.26	yes	176
7.3	odd	6	inner	140.3.x.a.3.19	✓	176
20.7	even	4	inner	140.3.x.a.47.19	yes	176
28.3	even	6	inner	140.3.x.a.3.26	yes	176
35.17	even	12	inner	140.3.x.a.87.4	yes	176
140.87	odd	12	inner	140.3.x.a.87.41	yes	176

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

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

\(f(q)\)	\(=\)	\(q+(1.96631 - 0.365565i) q^{2} +(0.389805 - 1.45477i) q^{3} +(3.73272 - 1.43763i) q^{4} +(-3.73805 - 3.32069i) q^{5} +(0.234662 - 3.00303i) q^{6} +(-5.02867 - 4.86954i) q^{7} +(6.81413 - 4.19137i) q^{8} +(5.82981 + 3.36584i) q^{9} +O(q^{10})\)	\(q+(1.96631 - 0.365565i) q^{2} +(0.389805 - 1.45477i) q^{3} +(3.73272 - 1.43763i) q^{4} +(-3.73805 - 3.32069i) q^{5} +(0.234662 - 3.00303i) q^{6} +(-5.02867 - 4.86954i) q^{7} +(6.81413 - 4.19137i) q^{8} +(5.82981 + 3.36584i) q^{9} +(-8.56408 - 5.16299i) q^{10} +(8.96422 - 5.17549i) q^{11} +(-0.636386 - 5.99066i) q^{12} +(-2.72924 + 2.72924i) q^{13} +(-11.6681 - 7.73670i) q^{14} +(-6.28796 + 4.14359i) q^{15} +(11.8665 - 10.7325i) q^{16} +(-8.39248 + 31.3211i) q^{17} +(12.6936 + 4.48710i) q^{18} +(16.5359 + 9.54701i) q^{19} +(-18.7270 - 7.02129i) q^{20} +(-9.04428 + 5.41740i) q^{21} +(15.7344 - 13.4536i) q^{22} +(-2.49054 - 9.29482i) q^{23} +(-3.44131 - 11.5468i) q^{24} +(2.94606 + 24.8258i) q^{25} +(-4.36881 + 6.36424i) q^{26} +(16.7537 - 16.7537i) q^{27} +(-25.7712 - 10.9473i) q^{28} +4.14768i q^{29} +(-10.8493 + 10.4462i) q^{30} +(-13.7219 - 23.7671i) q^{31} +(19.4096 - 25.4414i) 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} +(36.0047 + 12.7274i) q^{38} +(2.90655 + 5.03430i) q^{39} +(-39.3898 - 6.96005i) q^{40} -42.9640i q^{41} +(-15.8034 + 13.9586i) q^{42} +(-51.7850 + 51.7850i) q^{43} +(26.0205 - 32.2059i) q^{44} +(-10.6152 - 31.9407i) q^{45} +(-8.29503 - 17.3660i) q^{46} +(9.58506 + 35.7719i) q^{47} +(-10.9878 - 21.4466i) q^{48} +(1.57512 + 48.9747i) q^{49} +(14.8683 + 47.7382i) q^{50} +(42.2937 + 24.4183i) q^{51} +(-6.26387 + 14.1111i) q^{52} +(7.62542 - 28.4585i) q^{53} +(26.8184 - 39.0676i) q^{54} +(-50.6949 - 10.4211i) q^{55} +(-54.6761 - 12.1047i) q^{56} +(20.3345 - 20.3345i) q^{57} +(1.51625 + 8.15561i) q^{58} +(-5.94136 + 3.43025i) q^{59} +(-17.5143 + 24.5066i) q^{60} +(44.2972 + 25.5750i) q^{61} +(-35.6700 - 41.7172i) q^{62} +(-12.9261 - 45.3143i) q^{63} +(28.8648 - 57.1211i) q^{64} +(19.2650 - 1.13909i) q^{65} +(-13.4386 - 28.1343i) q^{66} +(17.7208 - 66.1349i) q^{67} +(13.7013 + 128.978i) q^{68} -14.4927 q^{69} +(17.9246 + 67.6662i) q^{70} -71.0505i q^{71} +(53.8326 - 1.49960i) q^{72} +(-75.1765 - 20.1435i) q^{73} +(32.8982 + 68.8739i) q^{74} +(37.2643 + 5.39138i) q^{75} +(75.4491 + 11.8639i) q^{76} +(-70.2804 - 17.6258i) q^{77} +(7.55554 + 8.83643i) q^{78} +(-66.7677 + 115.645i) q^{79} +(-79.9968 + 0.713968i) q^{80} +(12.4504 + 21.5647i) q^{81} +(-15.7062 - 84.4804i) q^{82} +(-3.23971 - 3.23971i) q^{83} +(-25.9716 + 33.2240i) q^{84} +(135.379 - 89.2113i) q^{85} +(-82.8944 + 120.756i) q^{86} +(6.03393 + 1.61679i) q^{87} +(39.3910 - 72.8389i) q^{88} +(16.9269 - 29.3183i) q^{89} +(-32.5492 - 58.9246i) q^{90} +(27.0146 - 0.434309i) q^{91} +(-22.6590 - 31.1145i) q^{92} +(-39.9246 + 10.6978i) q^{93} +(31.9241 + 66.8346i) q^{94} +(-30.1094 - 90.5978i) q^{95} +(-29.4455 - 38.1538i) q^{96} +(-108.302 - 108.302i) q^{97} +(21.0006 + 95.7234i) 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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