LMFDB - Embedded newform 230.3.i.a.19.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(19,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 15]))

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

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

chi := DirichletCharacter("230.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.i (of order $22$, degree $10$, 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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.19
Character	$\chi$	$=$	230.19
Dual form			230.3.i.a.109.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28641 - 0.587486i) q^{2} +(0.00972304 + 0.0331137i) q^{3} +(1.30972 - 1.51150i) q^{4} +(1.88998 + 4.62904i) q^{5} +(0.0319617 + 0.0368857i) q^{6} +(-0.869641 - 6.04849i) q^{7} +(0.796860 - 2.71386i) q^{8} +(7.57028 - 4.86512i) q^{9} +O(q^{10})$	\(q+(1.28641 - 0.587486i) q^{2} +(0.00972304 + 0.0331137i) q^{3} +(1.30972 - 1.51150i) q^{4} +(1.88998 + 4.62904i) q^{5} +(0.0319617 + 0.0368857i) q^{6} +(-0.869641 - 6.04849i) q^{7} +(0.796860 - 2.71386i) q^{8} +(7.57028 - 4.86512i) q^{9} +(5.15079 + 4.84452i) q^{10} +(-0.789357 - 0.360487i) q^{11} +(0.0627857 + 0.0286733i) q^{12} +(12.0743 + 1.73602i) q^{13} +(-4.67212 - 7.26996i) q^{14} +(-0.134908 + 0.107592i) q^{15} +(-0.569259 - 3.95929i) q^{16} +(19.6346 + 22.6595i) q^{17} +(6.88032 - 10.7060i) q^{18} +(-7.05521 - 6.11337i) q^{19} +(9.47213 + 3.20605i) q^{20} +(0.191832 - 0.0876067i) q^{21} -1.22722 q^{22} +(20.5841 - 10.2614i) q^{23} +0.0976136 q^{24} +(-17.8560 + 17.4975i) q^{25} +(16.5524 - 4.86022i) q^{26} +(0.469447 + 0.406778i) q^{27} +(-10.2813 - 6.60737i) q^{28} +(-13.1874 - 15.2191i) q^{29} +(-0.110339 + 0.217665i) q^{30} +(-43.4091 - 12.7460i) q^{31} +(-3.05833 - 4.75885i) q^{32} +(0.00426210 - 0.0296435i) q^{33} +(38.5703 + 17.6145i) q^{34} +(26.3551 - 15.4571i) q^{35} +(2.56133 - 17.8144i) q^{36} +(11.9429 - 7.67524i) q^{37} +(-12.6674 - 3.71949i) q^{38} +(0.0599128 + 0.416703i) q^{39} +(14.0686 - 1.44043i) q^{40} +(-45.5878 - 29.2975i) q^{41} +(0.195308 - 0.225397i) q^{42} +(-61.6500 + 18.1021i) q^{43} +(-1.57871 + 0.720974i) q^{44} +(36.8285 + 25.8481i) q^{45} +(20.4513 - 25.2932i) q^{46} +58.7319i q^{47} +(0.125571 - 0.0573466i) q^{48} +(11.1872 - 3.28487i) q^{49} +(-12.6906 + 32.9992i) q^{50} +(-0.559431 + 0.870491i) q^{51} +(18.4379 - 15.9765i) q^{52} +(0.467135 + 3.24899i) q^{53} +(0.842880 + 0.247492i) q^{54} +(0.176843 - 4.33528i) q^{55} +(-17.1077 - 2.45972i) q^{56} +(0.133838 - 0.293064i) q^{57} +(-25.9055 - 11.8307i) q^{58} +(-15.7619 + 109.627i) q^{59} +(-0.0140661 + 0.344829i) q^{60} +(-26.5531 + 90.4315i) q^{61} +(-63.3301 + 9.10550i) q^{62} +(-36.0101 - 41.5578i) q^{63} +(-6.73003 - 4.32513i) q^{64} +(14.7840 + 59.1733i) q^{65} +(-0.0119323 - 0.0406378i) q^{66} +(-16.7830 - 36.7496i) q^{67} +59.9656 q^{68} +(0.539931 + 0.581843i) q^{69} +(24.8227 - 35.3675i) q^{70} +(-31.2064 - 68.3326i) q^{71} +(-7.17079 - 24.4215i) q^{72} +(-66.0949 - 57.2715i) q^{73} +(10.8544 - 16.8898i) q^{74} +(-0.753022 - 0.421147i) q^{75} +(-18.4807 + 2.65713i) q^{76} +(-1.49394 + 5.08791i) q^{77} +(0.321879 + 0.500854i) q^{78} +(66.1445 + 9.51014i) q^{79} +(17.2518 - 10.1181i) q^{80} +(33.6353 - 73.6509i) q^{81} +(-75.8566 - 10.9065i) q^{82} +(25.0249 - 16.0825i) q^{83} +(0.118829 - 0.404694i) q^{84} +(-67.7827 + 133.715i) q^{85} +(-68.6727 + 59.5052i) q^{86} +(0.375739 - 0.584661i) q^{87} +(-1.60732 + 1.85494i) q^{88} +(4.94644 + 16.8460i) q^{89} +(62.5621 + 11.6152i) q^{90} -74.5408i q^{91} +(11.4494 - 44.5523i) q^{92} -1.56136i q^{93} +(34.5042 + 75.5536i) q^{94} +(14.9649 - 44.2130i) q^{95} +(0.127847 - 0.147543i) q^{96} +(112.999 + 72.6201i) q^{97} +(12.4616 - 10.7980i) q^{98} +(-7.72947 + 1.11133i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 48 q^{4} - 8 q^{6} + 96 q^{9}+O(q^{10}) $ 240 * q + 48 * q^4 - 8 * q^6 + 96 * q^9	$ 240 q + 48 q^{4} - 8 q^{6} + 96 q^{9} + 154 q^{15} - 96 q^{16} + 44 q^{20} + 16 q^{24} - 84 q^{25} + 32 q^{26} - 100 q^{29} - 352 q^{30} + 124 q^{31} + 28 q^{35} - 192 q^{36} + 72 q^{39} + 116 q^{41} - 148 q^{46} - 188 q^{49} + 144 q^{50} + 324 q^{54} + 796 q^{55} - 264 q^{56} + 400 q^{59} + 176 q^{60} - 616 q^{61} + 192 q^{64} + 462 q^{65} - 176 q^{66} + 120 q^{69} - 504 q^{70} + 464 q^{71} - 528 q^{74} - 934 q^{75} - 968 q^{79} - 264 q^{80} + 664 q^{81} - 352 q^{84} - 1196 q^{85} + 396 q^{86} + 376 q^{94} + 126 q^{95} - 32 q^{96} - 3300 q^{99}+O(q^{100}) $ 240 * q + 48 * q^4 - 8 * q^6 + 96 * q^9 + 154 * q^15 - 96 * q^16 + 44 * q^20 + 16 * q^24 - 84 * q^25 + 32 * q^26 - 100 * q^29 - 352 * q^30 + 124 * q^31 + 28 * q^35 - 192 * q^36 + 72 * q^39 + 116 * q^41 - 148 * q^46 - 188 * q^49 + 144 * q^50 + 324 * q^54 + 796 * q^55 - 264 * q^56 + 400 * q^59 + 176 * q^60 - 616 * q^61 + 192 * q^64 + 462 * q^65 - 176 * q^66 + 120 * q^69 - 504 * q^70 + 464 * q^71 - 528 * q^74 - 934 * q^75 - 968 * q^79 - 264 * q^80 + 664 * q^81 - 352 * q^84 - 1196 * q^85 + 396 * q^86 + 376 * q^94 + 126 * q^95 - 32 * q^96 - 3300 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	1.28641	−	0.587486i	0.643207	−	0.293743i
$2$	1.28641	−	0.587486i	0.643207	−	0.293743i
$3$	0.00972304	+	0.0331137i	0.00324101	+	0.0110379i	0.961098	−	0.276209i	$-0.0890782\pi$
$3$	0.00972304	+	0.0331137i	0.00324101	+	0.0110379i	−0.957857	+	0.287247i	$0.907260\pi$
$4$	1.30972	−	1.51150i	0.327430	−	0.377875i
$5$	1.88998	+	4.62904i	0.377995	+	0.925807i
$5$	1.88998	+	4.62904i	0.377995	+	0.925807i
$6$	0.0319617	+	0.0368857i	0.00532694	+	0.00614762i
$7$	−0.869641	−	6.04849i	−0.124234	−	0.864070i	−0.952675	−	0.303992i	$-0.901680\pi$
$7$	−0.869641	−	6.04849i	−0.124234	−	0.864070i	0.828440	−	0.560078i	$-0.189229\pi$
$8$	0.796860	−	2.71386i	0.0996075	−	0.339232i
$9$	7.57028	−	4.86512i	0.841142	−	0.540569i
$10$	5.15079	+	4.84452i	0.515079	+	0.484452i
$11$	−0.789357	−	0.360487i	−0.0717597	−	0.0327716i	0.379212	−	0.925310i	$-0.376195\pi$
$11$	−0.789357	−	0.360487i	−0.0717597	−	0.0327716i	−0.450972	+	0.892538i	$0.648922\pi$
$12$	0.0627857	+	0.0286733i	0.00523214	+	0.00238944i
$13$	12.0743	+	1.73602i	0.928790	+	0.133540i	0.590074	−	0.807349i	$-0.299098\pi$
$13$	12.0743	+	1.73602i	0.928790	+	0.133540i	0.338716	+	0.940889i	$0.390008\pi$
$14$	−4.67212	−	7.26996i	−0.333723	−	0.519283i
$15$	−0.134908	+	0.107592i	−0.00899387	+	0.00717282i
$16$	−0.569259	−	3.95929i	−0.0355787	−	0.247455i
$17$	19.6346	+	22.6595i	1.15497	+	1.33291i	0.933850	+	0.357665i	$0.116427\pi$
$17$	19.6346	+	22.6595i	1.15497	+	1.33291i	0.221124	+	0.975246i	$0.429027\pi$
$18$	6.88032	−	10.7060i	0.382240	−	0.594777i
$19$	−7.05521	−	6.11337i	−0.371327	−	0.321756i	0.449129	−	0.893467i	$-0.351735\pi$
$19$	−7.05521	−	6.11337i	−0.371327	−	0.321756i	−0.820455	+	0.571711i	$0.806280\pi$
$20$	9.47213	+	3.20605i	0.473606	+	0.160303i
$21$	0.191832	−	0.0876067i	0.00913485	−	0.00417175i
$22$	−1.22722			−0.0557828
$23$	20.5841	−	10.2614i	0.894960	−	0.446146i
$23$	20.5841	−	10.2614i	0.894960	−	0.446146i
$24$	0.0976136			0.00406723
$25$	−17.8560	+	17.4975i	−0.714239	+	0.699902i
$26$	16.5524	−	4.86022i	0.636631	−	0.186932i
$27$	0.469447	+	0.406778i	0.0173869	+	0.0150659i
$28$	−10.2813	−	6.60737i	−0.367188	−	0.235978i
$29$	−13.1874	−	15.2191i	−0.454740	−	0.524797i	0.481365	−	0.876521i	$-0.340141\pi$
$29$	−13.1874	−	15.2191i	−0.454740	−	0.524797i	−0.936104	+	0.351723i	$0.885596\pi$
$30$	−0.110339	+	0.217665i	−0.00367795	+	0.00725549i
$31$	−43.4091	−	12.7460i	−1.40029	−	0.411163i	−0.507508	−	0.861647i	$-0.669433\pi$
$31$	−43.4091	−	12.7460i	−1.40029	−	0.411163i	−0.892784	+	0.450484i	$0.851251\pi$
$32$	−3.05833	−	4.75885i	−0.0955727	−	0.148714i
$33$	0.00426210	−	0.0296435i	0.000129154	−	0.000898289i
$34$	38.5703	+	17.6145i	1.13442	+	0.518072i
$35$	26.3551	−	15.4571i	0.753002	−	0.441631i
$36$	2.56133	−	17.8144i	0.0711480	−	0.494845i
$37$	11.9429	−	7.67524i	0.322781	−	0.207439i	−0.369208	−	0.929347i	$-0.620371\pi$
$37$	11.9429	−	7.67524i	0.322781	−	0.207439i	0.691989	+	0.721908i	$0.256735\pi$
$38$	−12.6674	−	3.71949i	−0.333354	−	0.0978814i
$39$	0.0599128	+	0.416703i	0.00153623	+	0.0106847i
$40$	14.0686	−	1.44043i	0.351715	−	0.0360108i
$41$	−45.5878	−	29.2975i	−1.11190	−	0.714573i	−0.150191	−	0.988657i	$-0.547989\pi$
$41$	−45.5878	−	29.2975i	−1.11190	−	0.714573i	−0.961706	+	0.274084i	$0.911625\pi$
$42$	0.195308	−	0.225397i	0.00465018	−	0.00536659i
$43$	−61.6500	+	18.1021i	−1.43372	+	0.420978i	−0.904123	−	0.427271i	$-0.859475\pi$
$43$	−61.6500	+	18.1021i	−1.43372	+	0.420978i	−0.529597	+	0.848250i	$0.677657\pi$
$44$	−1.57871	+	0.720974i	−0.0358799	+	0.0163858i
$45$	36.8285	+	25.8481i	0.818411	+	0.574403i
$46$	20.4513	−	25.2932i	0.444592	−	0.549852i
$47$			58.7319i			1.24962i	0.780779	+	0.624808i	$0.214823\pi$
$47$			58.7319i			1.24962i	−0.780779	+	0.624808i	$0.785177\pi$
$48$	0.125571	−	0.0573466i	0.00261607	−	0.00119472i
$49$	11.1872	−	3.28487i	0.228311	−	0.0670382i
$50$	−12.6906	+	32.9992i	−0.253812	+	0.659984i
$51$	−0.559431	+	0.870491i	−0.0109692	+	0.0170685i
$52$	18.4379	−	15.9765i	0.354575	−	0.307241i
$53$	0.467135	+	3.24899i	0.00881386	+	0.0613018i	0.993754	−	0.111596i	$-0.0355962\pi$
$53$	0.467135	+	3.24899i	0.00881386	+	0.0613018i	−0.984940	+	0.172897i	$0.944687\pi$
$54$	0.842880	+	0.247492i	0.0156089	+	0.00458318i
$55$	0.176843	−	4.33528i	0.00321532	−	0.0788232i
$56$	−17.1077	−	2.45972i	−0.305495	−	0.0439235i
$57$	0.133838	−	0.293064i	0.00234803	−	0.00514148i
$58$	−25.9055	−	11.8307i	−0.446647	−	0.203977i
$59$	−15.7619	+	109.627i	−0.267151	+	1.85808i	0.207942	+	0.978141i	$0.433323\pi$
$59$	−15.7619	+	109.627i	−0.267151	+	1.85808i	−0.475093	+	0.879936i	$0.657586\pi$
$60$	−0.0140661	+	0.344829i	−0.000234435	+	0.00574716i
$61$	−26.5531	+	90.4315i	−0.435296	+	1.48248i	0.391604	+	0.920134i	$0.371920\pi$
$61$	−26.5531	+	90.4315i	−0.435296	+	1.48248i	−0.826900	+	0.562349i	$0.809898\pi$
$62$	−63.3301	+	9.10550i	−1.02145	+	0.146863i
$63$	−36.0101	−	41.5578i	−0.571588	−	0.659648i
$64$	−6.73003	−	4.32513i	−0.105157	−	0.0675801i
$65$	14.7840	+	59.1733i	0.227446	+	0.910358i
$66$	−0.0119323	−	0.0406378i	−0.000180793	−	0.000615724i
$67$	−16.7830	−	36.7496i	−0.250493	−	0.548502i	0.742058	−	0.670336i	$-0.233850\pi$
$67$	−16.7830	−	36.7496i	−0.250493	−	0.548502i	−0.992551	+	0.121834i	$0.961123\pi$
$68$	59.9656			0.881847
$69$	0.539931	+	0.581843i	0.00782509	+	0.00843250i
$70$	24.8227	−	35.3675i	0.354610	−	0.505249i
$71$	−31.2064	−	68.3326i	−0.439527	−	0.962431i	−0.991685	−	0.128691i	$-0.958922\pi$
$71$	−31.2064	−	68.3326i	−0.439527	−	0.962431i	0.552157	−	0.833740i	$-0.313805\pi$
$72$	−7.17079	−	24.4215i	−0.0995943	−	0.339187i
$73$	−66.0949	−	57.2715i	−0.905409	−	0.784542i	0.0716675	−	0.997429i	$-0.477168\pi$
$73$	−66.0949	−	57.2715i	−0.905409	−	0.784542i	−0.977077	+	0.212887i	$0.931713\pi$
$74$	10.8544	−	16.8898i	0.146681	−	0.228241i
$75$	−0.753022	−	0.421147i	−0.0100403	−	0.00561529i
$76$	−18.4807	+	2.65713i	−0.243167	+	0.0349622i
$77$	−1.49394	+	5.08791i	−0.0194019	+	0.0660767i
$78$	0.321879	+	0.500854i	0.00412666	+	0.00642121i
$79$	66.1445	+	9.51014i	0.837272	+	0.120381i	0.547595	−	0.836743i	$-0.315543\pi$
$79$	66.1445	+	9.51014i	0.837272	+	0.120381i	0.289676	+	0.957125i	$0.406452\pi$
$80$	17.2518	−	10.1181i	0.215647	−	0.126476i
$81$	33.6353	−	73.6509i	0.415250	−	0.909271i
$82$	−75.8566	−	10.9065i	−0.925081	−	0.133007i
$83$	25.0249	−	16.0825i	0.301504	−	0.193765i	−0.381137	−	0.924519i	$-0.624467\pi$
$83$	25.0249	−	16.0825i	0.301504	−	0.193765i	0.682642	+	0.730753i	$0.260831\pi$
$84$	0.118829	−	0.404694i	0.00141463	−	0.00481779i
$85$	−67.7827	+	133.715i	−0.797444	+	1.57312i
$86$	−68.6727	+	59.5052i	−0.798519	+	0.691921i
$87$	0.375739	−	0.584661i	0.00431884	−	0.00672024i
$88$	−1.60732	+	1.85494i	−0.0182650	+	0.0210789i
$89$	4.94644	+	16.8460i	0.0555780	+	0.189281i	0.982603	−	0.185718i	$-0.0594611\pi$
$89$	4.94644	+	16.8460i	0.0555780	+	0.189281i	−0.927025	+	0.374999i	$0.877643\pi$
$90$	62.5621	+	11.6152i	0.695134	+	0.129058i
$91$		−	74.5408i		−	0.819129i
$92$	11.4494	−	44.5523i	0.124450	−	0.484265i
$93$		−	1.56136i		−	0.0167888i
$94$	34.5042	+	75.5536i	0.367065	+	0.803761i
$95$	14.9649	−	44.2130i	0.157525	−	0.465400i
$96$	0.127847	−	0.147543i	0.00133174	−	0.00153690i
$97$	112.999	+	72.6201i	1.16494	+	0.748661i	0.972558	−	0.232660i	$-0.0747429\pi$
$97$	112.999	+	72.6201i	1.16494	+	0.748661i	0.192380	+	0.981320i	$0.438379\pi$
$98$	12.4616	−	10.7980i	0.127159	−	0.110184i
$99$	−7.72947	+	1.11133i	−0.0780754	+	0.0112256i
$100$	3.06117	+	49.9062i	0.0306117	+	0.499062i
$101$	−32.5067	+	20.8908i	−0.321848	+	0.206839i	−0.691581	−	0.722299i	$-0.743086\pi$
$101$	−32.5067	+	20.8908i	−0.321848	+	0.206839i	0.369733	+	0.929138i	$0.379449\pi$
$102$	−0.208258	+	1.44847i	−0.00204175	+	0.0142007i
$103$	2.77210	−	6.07006i	0.0269136	−	0.0589326i	−0.895698	−	0.444663i	$-0.853323\pi$
$103$	2.77210	−	6.07006i	0.0269136	−	0.0589326i	0.922611	+	0.385731i	$0.126051\pi$
$104$	14.3328	−	31.3845i	0.137815	−	0.301774i
$105$	0.768093	+	0.722422i	0.00731517	+	0.00688021i
$106$	2.50967	+	3.90512i	0.0236761	+	0.0368407i
$107$	−77.3002	−	22.6974i	−0.722431	−	0.212125i	−0.100210	−	0.994966i	$-0.531951\pi$
$107$	−77.3002	−	22.6974i	−0.722431	−	0.212125i	−0.622221	+	0.782841i	$0.713770\pi$
$108$	1.22969	−	0.176803i	0.0113860	−	0.00163706i
$109$	−147.615	+	127.909i	−1.35426	+	1.17348i	−0.386305	+	0.922371i	$0.626249\pi$
$109$	−147.615	+	127.909i	−1.35426	+	1.17348i	−0.967960	+	0.251106i	$0.919206\pi$
$110$	−2.31942	−	5.68085i	−0.0210856	−	0.0516441i
$111$	0.370277	+	0.320847i	0.00333583	+	0.00289051i
$112$	−23.4526	+	6.88632i	−0.209399	+	0.0614850i
$113$	−22.1292	−	48.4561i	−0.195833	−	0.428815i	0.786086	−	0.618118i	$-0.212105\pi$
$113$	−22.1292	−	48.4561i	−0.195833	−	0.428815i	−0.981919	+	0.189303i	$0.939377\pi$
$114$		−	0.455630i		−	0.00399675i
$115$	86.4037	+	75.8908i	0.751336	+	0.659920i
$116$	−40.2756			−0.347203
$117$	99.8515	−	45.6007i	0.853432	−	0.389749i
$118$	44.1277	+	150.285i	0.373963	+	1.27360i
$119$	119.981	−	138.465i	1.00824	−	1.16357i
$120$	0.184487	+	0.451857i	0.00153740	+	0.00376547i
$121$	−78.7450	−	90.8766i	−0.650785	−	0.751046i
$122$	18.9689	+	131.932i	0.155483	+	1.08141i
$123$	0.526895	−	1.79444i	0.00428370	−	0.0145889i
$124$	−76.1194	+	48.9190i	−0.613866	+	0.394508i
$125$	−114.744	−	49.5860i	−0.917953	−	0.396688i
$126$	−70.7385	−	32.3052i	−0.561416	−	0.256390i
$127$	50.9674	+	23.2760i	0.401318	+	0.183276i	0.605841	−	0.795586i	$-0.292837\pi$
$127$	50.9674	+	23.2760i	0.401318	+	0.183276i	−0.204522	+	0.978862i	$0.565564\pi$
$128$	−11.1986	−	1.61011i	−0.0874887	−	0.0125790i
$129$	−1.19885	−	1.86545i	−0.00929342	−	0.0144608i
$130$	53.7818	+	67.4359i	0.413706	+	0.518738i
$131$	−24.3466	−	169.335i	−0.185852	−	1.29263i	−0.842608	−	0.538527i	$-0.818981\pi$
$131$	−24.3466	−	169.335i	−0.185852	−	1.29263i	0.656756	−	0.754103i	$-0.271928\pi$
$132$	−0.0392240	−	0.0452669i	−0.000297152	−	0.000342931i
$133$	−30.8412	+	47.9898i	−0.231888	+	0.360825i
$134$	−43.1798	−	37.4155i	−0.322237	−	0.279220i
$135$	−0.995748	+	2.94189i	−0.00737591	+	0.0217918i
$136$	77.1406	−	35.2289i	0.567210	−	0.259036i
$137$	22.8318			0.166655			0.0833276	−	0.996522i	$-0.473445\pi$
$137$	22.8318			0.166655			0.0833276	+	0.996522i	$0.473445\pi$
$138$	1.03640	+	0.431289i	0.00751014	+	0.00312528i
$139$	206.211			1.48353			0.741767	−	0.670658i	$-0.233988\pi$
$139$	206.211			1.48353			0.741767	+	0.670658i	$0.233988\pi$
$140$	11.1544	−	60.0802i	0.0796743	−	0.429144i
$141$	−1.94483	+	0.571053i	−0.0137931	+	0.00405002i
$142$	−80.2888	−	69.5707i	−0.565414	−	0.489934i
$143$	−8.90510	−	5.72296i	−0.0622734	−	0.0400207i
$144$	−23.5719	−	27.2034i	−0.163694	−	0.188912i
$145$	45.5259	−	89.8090i	0.313972	−	0.619372i
$146$	−118.672	−	34.8451i	−0.812819	−	0.238665i
$147$	0.217548	+	0.338511i	0.00147992	+	0.00230280i
$148$	4.04076	−	28.1041i	0.0273025	−	0.189893i
$149$	122.948	+	56.1483i	0.825153	+	0.376835i	0.782804	−	0.622268i	$-0.213789\pi$
$149$	122.948	+	56.1483i	0.825153	+	0.376835i	0.0423486	+	0.999103i	$0.486516\pi$
$150$	−1.21612	−	0.0993798i	−0.00810744	−	0.000662532i
$151$	5.15663	−	35.8652i	0.0341499	−	0.237518i	−0.965596	−	0.260046i	$-0.916262\pi$
$151$	5.15663	−	35.8652i	0.0341499	−	0.237518i	0.999746	+	0.0225280i	$0.00717149\pi$
$152$	−22.2128	+	14.2753i	−0.146137	+	0.0939166i
$153$	258.880	+	76.0141i	1.69203	+	0.496824i
$154$	1.06724	+	7.42283i	0.00693014	+	0.0482002i
$155$	−23.0402	−	225.032i	−0.148646	−	1.45182i
$156$	0.708315	+	0.455206i	0.00454048	+	0.00291799i
$157$	15.9489	−	18.4060i	0.101585	−	0.117236i	−0.702680	−	0.711506i	$-0.748014\pi$
$157$	15.9489	−	18.4060i	0.101585	−	0.117236i	0.804266	+	0.594270i	$0.202559\pi$
$158$	90.6762	−	26.6249i	0.573900	−	0.168512i
$159$	−0.103044	+	0.0470587i	−0.000648076	+	0.000295966i
$160$	16.2487	−	23.1512i	0.101555	−	0.144695i
$161$	−79.9664	−	115.579i	−0.496686	−	0.717881i
$162$		−	114.506i		−	0.706826i
$163$	−72.4088	+	33.0680i	−0.444226	+	0.202871i	−0.624953	−	0.780662i	$-0.714882\pi$
$163$	−72.4088	+	33.0680i	−0.444226	+	0.202871i	0.180728	+	0.983533i	$0.442155\pi$
$164$	−103.990	+	30.5343i	−0.634088	+	0.186185i
$165$	0.145276	−	0.0362962i	0.000880462	−	0.000219977i
$166$	22.7441	−	35.3905i	0.137013	−	0.213196i
$167$	20.1775	−	17.4839i	0.120823	−	0.104694i	−0.592353	−	0.805678i	$-0.701801\pi$
$167$	20.1775	−	17.4839i	0.120823	−	0.104694i	0.713177	+	0.700984i	$0.247256\pi$
$168$	−0.0848888	−	0.590414i	−0.000505290	−	0.00351437i
$169$	−19.3801	−	5.69051i	−0.114675	−	0.0336716i
$170$	−8.64104	+	211.834i	−0.0508297	+	1.24608i
$171$	−83.1522	−	11.9555i	−0.486270	−	0.0699151i
$172$	−53.3830	+	116.893i	−0.310366	+	0.679608i
$173$	101.792	+	46.4870i	0.588395	+	0.268711i	0.687286	−	0.726387i	$-0.258802\pi$
$173$	101.792	+	46.4870i	0.588395	+	0.268711i	−0.0988904	+	0.995098i	$0.531529\pi$
$174$	0.139876	−	0.972857i	0.000803883	−	0.00559113i
$175$	121.362	+	92.7850i	0.693497	+	0.530200i
$176$	−0.977923	+	3.33050i	−0.00555638	+	0.0189233i
$177$	−3.78339	+	0.543969i	−0.0213751	+	0.00307327i
$178$	16.2600	+	18.7650i	0.0913482	+	0.105421i
$179$	−86.6806	−	55.7062i	−0.484249	−	0.311208i	0.275640	−	0.961261i	$-0.411110\pi$
$179$	−86.6806	−	55.7062i	−0.484249	−	0.311208i	−0.759889	+	0.650053i	$0.774747\pi$
$180$	87.3045	−	21.8124i	0.485025	−	0.121180i
$181$	55.2311	+	188.100i	0.305144	+	1.03923i	0.959188	+	0.282769i	$0.0912530\pi$
$181$	55.2311	+	188.100i	0.305144	+	1.03923i	−0.654044	+	0.756457i	$0.726929\pi$
$182$	−43.7916	−	95.8903i	−0.240613	−	0.526870i
$183$	−3.25269			−0.0177743
$184$	−11.4452	−	64.0391i	−0.0622022	−	0.348039i
$185$	58.1008	+	40.7781i	0.314058	+	0.220422i
$186$	−0.917278	−	2.00856i	−0.00493160	−	0.0107987i
$187$	−7.33022	−	24.9644i	−0.0391990	−	0.133500i
$188$	88.7732	+	76.9225i	0.472198	+	0.409162i
$189$	2.05214	−	3.19320i	0.0108579	−	0.0168952i
$190$	−6.72348	−	65.6678i	−0.0353867	−	0.345620i
$191$	204.057	−	29.3389i	1.06836	−	0.153607i	0.414369	−	0.910109i	$-0.364002\pi$
$191$	204.057	−	29.3389i	1.06836	−	0.153607i	0.653991	+	0.756502i	$0.273093\pi$
$192$	0.0777844	−	0.264909i	0.000405127	−	0.00137974i
$193$	126.116	+	196.241i	0.653453	+	1.01679i	0.996981	+	0.0776503i	$0.0247418\pi$
$193$	126.116	+	196.241i	0.653453	+	1.01679i	−0.343528	+	0.939143i	$0.611622\pi$
$194$	188.027	+	27.0342i	0.969210	+	0.139351i
$195$	−1.81570	+	1.06490i	−0.00931127	+	0.00546101i
$196$	9.68709	−	21.2118i	0.0494239	−	0.108223i
$197$	244.276	+	35.1216i	1.23998	+	0.178282i	0.730928	−	0.682454i	$-0.239087\pi$
$197$	244.276	+	35.1216i	1.23998	+	0.178282i	0.509051	+	0.860736i	$0.329996\pi$
$198$	−9.29040	+	5.97058i	−0.0469212	+	0.0301544i
$199$	66.1612	−	225.324i	0.332468	−	1.13228i	−0.608434	−	0.793605i	$-0.708202\pi$
$199$	66.1612	−	225.324i	0.332468	−	1.13228i	0.940902	−	0.338678i	$-0.109980\pi$
$200$	33.2571	+	62.4016i	0.166286	+	0.312008i
$201$	1.05373	−	0.913065i	0.00524245	−	0.00454261i
$202$	−29.5440	+	45.9714i	−0.146258	+	0.227581i
$203$	−80.5843	+	92.9993i	−0.396967	+	0.458125i
$204$	0.583048	+	1.98568i	0.00285808	+	0.00973372i
$205$	49.4593	−	266.399i	0.241265	−	1.29951i
$206$		−	9.43717i		−	0.0458115i
$207$	105.905	−	177.825i	0.511616	−	0.859060i
$208$		−	48.7937i		−	0.234585i
$209$	3.36528	+	7.36895i	0.0161018	+	0.0352581i
$210$	1.41250	+	0.478091i	0.00672618	+	0.00227662i
$211$	−57.4827	+	66.3385i	−0.272430	+	0.314401i	−0.875434	−	0.483337i	$-0.839425\pi$
$211$	−57.4827	+	66.3385i	−0.272430	+	0.314401i	0.603005	+	0.797738i	$0.293970\pi$
$212$	5.52267	+	3.54920i	0.0260503	+	0.0167415i
$213$	1.95932	−	1.69776i	0.00919868	−	0.00797071i
$214$	−112.774	+	16.2145i	−0.526983	+	0.0757687i
$215$	−200.312	−	251.167i	−0.931684	−	1.16822i
$216$	1.47802	−	0.949867i	0.00684269	−	0.00439753i
$217$	−39.3440	+	273.644i	−0.181309	+	1.26103i
$218$	−114.749	+	251.265i	−0.526372	+	1.15259i
$219$	1.25383	−	2.74550i	0.00572523	−	0.0125365i
$220$	−6.32115	−	5.94530i	−0.0287325	−	0.0270241i
$221$	197.736	+	307.683i	0.894731	+	1.39223i
$222$	0.664822	+	0.195209i	0.00299469	+	0.000879321i
$223$	−408.838	+	58.7820i	−1.83335	+	0.263596i	−0.970368	−	0.241633i	$-0.922317\pi$
$223$	−408.838	+	58.7820i	−1.83335	+	0.263596i	−0.862985	+	0.505230i	$0.831408\pi$
$224$	−26.1242	+	22.6367i	−0.116626	+	0.101057i
$225$	−50.0470	+	219.333i	−0.222431	+	0.974813i
$226$	−56.9345	−	49.3340i	−0.251923	−	0.218292i
$227$	306.892	−	90.1115i	1.35195	−	0.396967i	0.476029	−	0.879430i	$-0.342076\pi$
$227$	306.892	−	90.1115i	1.35195	−	0.396967i	0.875917	+	0.482463i	$0.160258\pi$
$228$	−0.267676	−	0.586129i	−0.00117402	−	0.00257074i
$229$		−	52.1414i		−	0.227692i	−0.993498	−	0.113846i	$-0.963683\pi$
$229$		−	52.1414i		−	0.227692i	0.993498	−	0.113846i	$-0.0363170\pi$
$230$	155.736	+	46.8660i	0.677111	+	0.203765i
$231$	−0.183005			−0.000792229
$232$	−51.8111	+	23.6613i	−0.223324	+	0.101988i
$233$	−117.127	−	398.896i	−0.502689	−	1.71200i	−0.684807	−	0.728725i	$-0.740113\pi$
$233$	−117.127	−	398.896i	−0.502689	−	1.71200i	0.182117	−	0.983277i	$-0.441705\pi$
$234$	101.661	−	117.323i	0.434447	−	0.501379i
$235$	−271.872	+	111.002i	−1.15690	+	0.472349i
$236$	145.057	+	167.404i	0.614647	+	0.709340i
$237$	0.328210	+	2.28275i	0.00138485	+	0.00963186i
$238$	72.9985	−	248.610i	0.306716	−	1.04458i
$239$	−233.886	+	150.309i	−0.978602	+	0.628910i	−0.929086	−	0.369864i	$-0.879404\pi$
$239$	−233.886	+	150.309i	−0.978602	+	0.628910i	−0.0495164	+	0.998773i	$0.515768\pi$
$240$	0.502787	+	0.472891i	0.00209494	+	0.00197038i
$241$	−164.597	−	75.1689i	−0.682975	−	0.311904i	0.0435430	−	0.999052i	$-0.486135\pi$
$241$	−164.597	−	75.1689i	−0.682975	−	0.311904i	−0.726518	+	0.687147i	$0.758863\pi$
$242$	−154.687	−	70.6434i	−0.639204	−	0.291915i
$243$	8.29950	+	1.19329i	0.0341543	+	0.00491065i
$244$	101.910	+	158.575i	0.417664	+	0.649898i
$245$	36.3494	+	45.5778i	0.148365	+	0.186032i
$246$	−0.376402	−	2.61793i	−0.00153009	−	0.0106420i
$247$	−74.5736	−	86.0625i	−0.301917	−	0.348431i
$248$	−69.1819	+	107.649i	−0.278959	+	0.434069i
$249$	0.775868	+	0.672294i	0.00311594	+	0.00269998i
$250$	−176.740	+	3.62241i	−0.706958	+	0.0144896i
$251$	62.6190	−	28.5972i	0.249478	−	0.113933i	−0.286751	−	0.958005i	$-0.592575\pi$
$251$	62.6190	−	28.5972i	0.249478	−	0.113933i	0.536230	+	0.844072i	$0.319848\pi$
$252$	−109.978			−0.436420
$253$	−19.9473	+	0.679574i	−0.0788430	+	0.00268606i
$254$	79.2395			0.311967
$255$	−5.08685	−	0.944417i	−0.0199484	−	0.00370360i
$256$	−15.3519	+	4.50772i	−0.0599683	+	0.0176083i
$257$	−318.770	−	276.216i	−1.24035	−	1.07477i	−0.994421	−	0.105483i	$-0.966361\pi$
$257$	−318.770	−	276.216i	−1.24035	−	1.07477i	−0.245930	−	0.969288i	$-0.579093\pi$
$258$	−2.63814	−	1.69543i	−0.0102254	−	0.00657144i
$259$	−56.8096	−	65.5618i	−0.219342	−	0.253134i
$260$	108.803	+	55.1545i	0.418474	+	0.212133i
$261$	−173.876	−	51.0545i	−0.666190	−	0.195611i
$262$	−130.801	−	203.531i	−0.499242	−	0.776836i
$263$	−12.7624	+	88.7647i	−0.0485264	+	0.337508i	0.951067	+	0.308985i	$0.0999894\pi$
$263$	−12.7624	+	88.7647i	−0.0485264	+	0.337508i	−0.999593	+	0.0285228i	$0.990920\pi$
$264$	−0.0770520	−	0.0351885i	−0.000291863	−	0.000133290i
$265$	−14.1568	+	8.30291i	−0.0534220	+	0.0313317i
$266$	−11.4812	+	79.8534i	−0.0431624	+	0.300201i
$267$	−0.509739	+	0.327590i	−0.00190914	+	0.00122693i
$268$	−77.5281	−	22.7643i	−0.289284	−	0.0849414i
$269$	−49.6147	−	345.078i	−0.184441	−	1.28282i	−0.846105	−	0.533017i	$-0.821058\pi$
$269$	−49.6147	−	345.078i	−0.184441	−	1.28282i	0.661663	−	0.749801i	$-0.269851\pi$
$270$	0.447375	+	4.36948i	0.00165694	+	0.0161833i
$271$	242.847	+	156.068i	0.896114	+	0.575898i	0.905635	−	0.424057i	$-0.139394\pi$
$271$	242.847	+	156.068i	0.896114	+	0.575898i	−0.00952138	+	0.999955i	$0.503031\pi$
$272$	78.5382	−	90.6379i	0.288743	−	0.333228i
$273$	2.46832	−	0.724763i	0.00904145	−	0.00265481i
$274$	29.3711	−	13.4133i	0.107194	−	0.0489538i
$275$	20.4024	−	7.37496i	0.0741905	−	0.0268180i
$276$	1.58661	−	0.0540536i	0.00574860	−	0.000195846i
$277$			279.737i			1.00988i	0.863154	+	0.504941i	$0.168486\pi$
$277$			279.737i			1.00988i	−0.863154	+	0.504941i	$0.831514\pi$
$278$	265.273	−	121.146i	0.954219	−	0.435777i
$279$	−390.630	+	114.699i	−1.40011	+	0.411108i
$280$	−20.9470	−	83.8410i	−0.0748109	−	0.299432i
$281$	−117.982	+	183.583i	−0.419864	+	0.653320i	−0.985174	−	0.171558i	$-0.945120\pi$
$281$	−117.982	+	183.583i	−0.419864	+	0.653320i	0.565311	+	0.824878i	$0.308756\pi$
$282$	−2.16637	+	1.87717i	−0.00768216	+	0.00665663i
$283$	31.4531	+	218.761i	0.111142	+	0.773007i	0.966813	+	0.255487i	$0.0822357\pi$
$283$	31.4531	+	218.761i	0.111142	+	0.773007i	−0.855671	+	0.517520i	$0.826855\pi$
$284$	−144.156	−	42.3281i	−0.507593	−	0.149043i
$285$	1.60956	+	0.0656563i	0.00564757	+	0.000230373i
$286$	−14.8178	−	2.13048i	−0.0518105	−	0.00744922i
$287$	−137.560	+	301.215i	−0.479305	+	1.04953i
$288$	−46.3048	−	21.1467i	−0.160780	−	0.0734260i
$289$	−86.8075	+	603.759i	−0.300372	+	2.08913i
$290$	5.80371	−	142.277i	0.0200128	−	0.490612i
$291$	−1.30602	+	4.44790i	−0.00448804	+	0.0152849i
$292$	−173.132	+	24.8926i	−0.592917	+	0.0852486i
$293$	−11.8223	−	13.6437i	−0.0403491	−	0.0465654i	0.735216	−	0.677833i	$-0.237081\pi$
$293$	−11.8223	−	13.6437i	−0.0403491	−	0.0465654i	−0.775565	+	0.631267i	$0.782535\pi$
$294$	0.478727	+	0.307659i	0.00162832	+	0.00104646i
$295$	−537.255	+	134.229i	−1.82120	+	0.455014i
$296$	−11.3127	−	38.5274i	−0.0382185	−	0.130160i
$297$	−0.223923	−	0.490323i	−0.000753950	−	0.00165092i
$298$	191.148			0.641436
$299$	266.352	−	88.1641i	0.890808	−	0.294863i
$300$	−1.62281	+	0.586607i	−0.00540938	+	0.00195536i
$301$	163.103	+	357.147i	0.541872	+	1.18653i
$302$	−14.4367	−	49.1669i	−0.0478036	−	0.162804i
$303$	−1.00783	−	0.873293i	−0.00332618	−	0.00288216i
$304$	−20.1883	+	31.4137i	−0.0664090	+	0.103334i
$305$	−468.795	+	47.9982i	−1.53703	+	0.157371i
$306$	377.684	−	54.3028i	1.23426	−	0.177460i
$307$	−85.9053	+	292.567i	−0.279822	+	0.952986i	0.692904	+	0.721030i	$0.256331\pi$
$307$	−85.9053	+	292.567i	−0.279822	+	0.952986i	−0.972726	+	0.231956i	$0.925487\pi$
$308$	5.73372	+	8.92184i	0.0186160	+	0.0289670i
$309$	0.227955	+	0.0327750i	0.000737718	+	0.000106068i
$310$	−161.842	−	275.948i	−0.522072	−	0.890156i
$311$	10.0007	−	21.8984i	0.0321565	−	0.0704128i	−0.892872	−	0.450310i	$-0.851313\pi$
$311$	10.0007	−	21.8984i	0.0321565	−	0.0704128i	0.925029	+	0.379897i	$0.124041\pi$
$312$	1.17861	+	0.169459i	0.00377760	+	0.000543138i
$313$	143.810	−	92.4212i	0.459457	−	0.295275i	−0.290363	−	0.956916i	$-0.593776\pi$
$313$	143.810	−	92.4212i	0.459457	−	0.295275i	0.749821	+	0.661641i	$0.230140\pi$
$314$	9.70361	−	33.0475i	0.0309032	−	0.105247i
$315$	124.315	−	245.235i	0.394649	−	0.778525i
$316$	101.005	−	87.5217i	0.319637	−	0.276967i
$317$	−64.7724	+	100.788i	−0.204329	+	0.317943i	−0.928261	−	0.371929i	$-0.878697\pi$
$317$	−64.7724	+	100.788i	−0.204329	+	0.317943i	0.723932	+	0.689871i	$0.242333\pi$
$318$	−0.104911	+	0.121074i	−0.000329909	+	0.000380735i
$319$	4.92330	+	16.7672i	0.0154336	+	0.0525618i
$320$	7.30157	−	39.3279i	0.0228174	−	0.122900i
$321$		−	2.78038i		−	0.00866161i
$322$	−170.771	−	101.703i	−0.530344	−	0.315848i
$323$		−	279.901i		−	0.866566i
$324$	−67.2705	−	147.302i	−0.207625	−	0.454635i
$325$	−245.974	+	180.272i	−0.756843	+	0.554682i
$326$	−73.7207	+	85.0783i	−0.226137	+	0.260976i
$327$	−5.67080	−	3.64440i	−0.0173419	−	0.0111450i
$328$	−115.836	+	100.373i	−0.353159	+	0.306014i
$329$	355.239	−	51.0757i	1.07975	−	0.155245i
$330$	0.165562	−	0.132040i	0.000501703	−	0.000400120i
$331$	−140.504	+	90.2964i	−0.424483	+	0.272799i	−0.735393	−	0.677641i	$-0.763003\pi$
$331$	−140.504	+	90.2964i	−0.424483	+	0.272799i	0.310910	+	0.950439i	$0.399366\pi$
$332$	8.46691	−	58.8887i	0.0255027	−	0.177376i
$333$	53.0702	−	116.207i	0.159370	−	0.348971i
$334$	15.6851	−	34.3455i	0.0469613	−	0.102831i
$335$	138.396	−	147.145i	0.413122	−	0.439239i
$336$	−0.456062	−	0.709646i	−0.00135733	−	0.00211204i
$337$	187.980	+	55.1960i	0.557805	+	0.163786i	0.548470	−	0.836170i	$-0.315210\pi$
$337$	187.980	+	55.1960i	0.557805	+	0.163786i	0.00933470	+	0.999956i	$0.497029\pi$
$338$	−28.2739	+	4.06517i	−0.0836506	+	0.0120271i
$339$	1.38940	−	1.20392i	0.00409851	−	0.00355138i
$340$	113.334	+	277.583i	0.333334	+	0.816420i
$341$	29.6705	+	25.7096i	0.0870101	+	0.0753947i
$342$	−113.992	+	33.4710i	−0.333309	+	0.0978685i
$343$	−153.982	−	337.174i	−0.448928	−	0.983016i
$344$			181.734i			0.528296i
$345$	−1.67291	+	3.59903i	−0.00484903	+	0.0104320i
$346$	158.258			0.457392
$347$	437.868	−	199.968i	1.26187	−	0.576276i	0.331691	−	0.943388i	$-0.392381\pi$
$347$	437.868	−	199.968i	1.26187	−	0.576276i	0.930177	+	0.367112i	$0.119653\pi$
$348$	−0.391601	−	1.33367i	−0.00112529	−	0.00383239i
$349$	−165.998	+	191.571i	−0.475638	+	0.548915i	−0.941971	−	0.335694i	$-0.891029\pi$
$349$	−165.998	+	191.571i	−0.475638	+	0.548915i	0.466334	+	0.884609i	$0.345575\pi$
$350$	210.632	+	48.0616i	0.601805	+	0.137319i
$351$	4.96206	+	5.72652i	0.0141369	+	0.0163149i
$352$	0.698607	+	4.85892i	0.00198468	+	0.0138037i
$353$	−88.2043	+	300.396i	−0.249870	+	0.850981i	0.735056	+	0.678006i	$0.237156\pi$
$353$	−88.2043	+	300.396i	−0.249870	+	0.850981i	−0.984926	+	0.172974i	$0.944662\pi$
$354$	−4.54743	+	2.92246i	−0.0128458	+	0.00825552i
$355$	257.335	−	273.603i	0.724886	−	0.770712i
$356$	31.9412	+	14.5871i	0.0897226	+	0.0409749i
$357$	5.75166	+	2.62669i	0.0161111	+	0.00735769i
$358$	−144.234	−	20.7377i	−0.402887	−	0.0579265i
$359$	208.372	+	324.234i	0.580425	+	0.903158i	0.999990	−	0.00456690i	$-0.00145370\pi$
$359$	208.372	+	324.234i	0.580425	+	0.903158i	−0.419565	+	0.907725i	$0.637817\pi$
$360$	99.4953	−	79.3499i	0.276376	−	0.220416i
$361$	−38.9730	−	271.063i	−0.107959	−	0.750868i
$362$	181.556	+	209.527i	0.501536	+	0.578803i
$363$	2.24361	−	3.49113i	0.00618076	−	0.00961744i
$364$	−112.668	−	97.6276i	−0.309528	−	0.268208i
$365$	140.194	−	414.198i	0.384094	−	1.13479i
$366$	−4.18431	+	1.91091i	−0.0114325	+	0.00522107i
$367$	654.177			1.78250			0.891249	−	0.453514i	$-0.149830\pi$
$367$	654.177			1.78250			0.891249	+	0.453514i	$0.149830\pi$
$368$	−52.3453	−	75.6569i	−0.142243	−	0.205589i
$369$	−487.648			−1.32154
$370$	98.6982	+	18.3242i	0.266752	+	0.0495248i
$371$	19.2453	−	5.65092i	0.0518740	−	0.0152316i
$372$	−2.36000	−	2.04495i	−0.00634408	−	0.00549718i
$373$	−121.316	−	77.9652i	−0.325245	−	0.209022i	0.367821	−	0.929897i	$-0.380104\pi$
$373$	−121.316	−	77.9652i	−0.325245	−	0.209022i	−0.693065	+	0.720875i	$0.743740\pi$
$374$	−24.0959	−	27.8082i	−0.0644276	−	0.0743535i
$375$	0.526311	−	4.28173i	0.00140350	−	0.0114179i
$376$	159.390	+	46.8011i	0.423910	+	0.124471i
$377$	−132.808	−	206.653i	−0.352276	−	0.548152i
$378$	0.763948	−	5.31338i	0.00202103	−	0.0140566i
$379$	−461.018	−	210.540i	−1.21641	−	0.555514i	−0.299301	−	0.954159i	$-0.596753\pi$
$379$	−461.018	−	210.540i	−1.21641	−	0.555514i	−0.917105	+	0.398645i	$0.869481\pi$
$380$	−47.2281	−	80.5260i	−0.124284	−	0.211911i
$381$	−0.275196	+	1.91403i	−0.000722300	+	0.00502371i
$382$	245.265	−	157.622i	0.642056	−	0.412624i
$383$	−155.583	−	45.6833i	−0.406222	−	0.119278i	0.0722369	−	0.997388i	$-0.476986\pi$
$383$	−155.583	−	45.6833i	−0.406222	−	0.119278i	−0.478459	+	0.878110i	$0.658804\pi$
$384$	−0.0555674	−	0.386480i	−0.000144707	−	0.00100646i
$385$	−26.3756	+	2.70050i	−0.0685082	+	0.00701430i
$386$	277.527	+	178.356i	0.718981	+	0.462061i
$387$	−378.639	+	436.972i	−0.978395	+	1.12913i
$388$	257.762	−	75.6859i	0.664336	−	0.195067i
$389$	449.155	−	205.122i	1.15464	−	0.527306i	0.256296	−	0.966598i	$-0.417498\pi$
$389$	449.155	−	205.122i	1.15464	−	0.527306i	0.898344	+	0.439292i	$0.144771\pi$
$390$	−1.71013	+	2.43659i	−0.00438494	+	0.00624768i
$391$	636.676	+	264.948i	1.62833	+	0.677615i
$392$		−	32.9781i		−	0.0841279i
$393$	5.37056	−	2.45265i	0.0136656	−	0.00624085i
$394$	334.873	−	98.3277i	0.849932	−	0.249563i
$395$	80.9887	+	324.159i	0.205035	+	0.820656i
$396$	−8.44368	+	13.1386i	−0.0213224	+	0.0331783i
$397$	199.715	−	173.054i	0.503061	−	0.435905i	−0.365996	−	0.930616i	$-0.619272\pi$
$397$	199.715	−	173.054i	0.503061	−	0.435905i	0.869057	+	0.494712i	$0.164726\pi$
$398$	−47.2641	−	328.729i	−0.118754	−	0.825953i
$399$	−1.88899	−	0.554656i	−0.00473430	−	0.00139012i
$400$	79.4425	+	60.7363i	0.198606	+	0.151841i
$401$	377.428	+	54.2659i	0.941217	+	0.135327i	0.595809	−	0.803126i	$-0.296832\pi$
$401$	377.428	+	54.2659i	0.941217	+	0.135327i	0.345408	+	0.938453i	$0.387741\pi$
$402$	0.819124	−	1.79363i	0.00203762	−	0.00446177i
$403$	−502.005	−	229.258i	−1.24567	−	0.568879i
$404$	−10.9983	+	76.4949i	−0.0272235	+	0.189344i
$405$	404.503	+	16.5003i	0.998772	+	0.0407415i
$406$	−49.0291	+	166.978i	−0.120761	+	0.411275i
$407$	−12.1940	+	1.75324i	−0.0299608	+	0.00430771i
$408$	1.91660	+	2.21187i	0.00469755	+	0.00542126i
$409$	−558.396	−	358.860i	−1.36527	−	0.877407i	−0.366675	−	0.930349i	$-0.619504\pi$
$409$	−558.396	−	358.860i	−1.36527	−	0.877407i	−0.998598	+	0.0529420i	$0.983140\pi$
$410$	−92.8805	−	371.756i	−0.226538	−	0.906722i
$411$	0.221994	+	0.756043i	0.000540132	+	0.00183952i
$412$	−5.54420	−	12.1401i	−0.0134568	−	0.0294663i
$413$	676.782			1.63870
$414$	31.7671	−	290.975i	0.0767322	−	0.702837i
$415$	121.743	+	85.4455i	0.293356	+	0.205893i
$416$	−28.6656	−	62.7689i	−0.0689077	−	0.150887i
$417$	2.00500	+	6.82840i	0.00480815	+	0.0163751i
$418$	8.65830	+	7.50246i	0.0207136	+	0.0179485i
$419$	94.6408	−	147.264i	0.225873	−	0.351465i	−0.709758	−	0.704446i	$-0.751196\pi$
$419$	94.6408	−	147.264i	0.225873	−	0.351465i	0.935631	+	0.352981i	$0.114832\pi$
$420$	2.09793	−	0.214799i	0.00499507	−	0.000511426i
$421$	267.384	−	38.4441i	0.635118	−	0.0913161i	0.182767	−	0.983156i	$-0.441495\pi$
$421$	267.384	−	38.4441i	0.635118	−	0.0913161i	0.452351	+	0.891840i	$0.350586\pi$
$422$	−34.9736	+	119.109i	−0.0828757	+	0.282249i
$423$	285.738	+	444.617i	0.675504	+	1.05110i
$424$	9.18954	+	1.32126i	0.0216735	+	0.00311617i
$425$	−747.080	−	61.0506i	−1.75783	−	0.143649i
$426$	1.52309	−	3.33509i	0.00357532	−	0.00782886i
$427$	570.065	+	81.9630i	1.33505	+	0.191951i
$428$	−135.549	+	87.1119i	−0.316703	+	0.203532i
$429$	0.102923	−	0.350525i	0.000239915	−	0.000817074i
$430$	−405.242	−	205.425i	−0.942422	−	0.477732i
$431$	−100.221	+	86.8416i	−0.232530	+	0.201489i	−0.763330	−	0.646008i	$-0.776437\pi$
$431$	−100.221	+	86.8416i	−0.232530	+	0.201489i	0.530800	+	0.847497i	$0.321892\pi$
$432$	1.34331	−	2.09024i	0.00310953	−	0.00483852i
$433$	149.884	−	172.976i	0.346153	−	0.399482i	−0.555800	−	0.831316i	$-0.687588\pi$
$433$	149.884	−	172.976i	0.346153	−	0.399482i	0.901953	+	0.431834i	$0.142133\pi$
$434$	110.149	+	375.133i	0.253799	+	0.864362i
$435$	3.41655	+	0.634313i	0.00785415	+	0.00145819i
$436$			390.645i			0.895974i
$437$	−207.957	−	53.4422i	−0.475873	−	0.122293i
$438$		−	4.26845i		−	0.00974532i
$439$	−200.772	−	439.629i	−0.457339	−	1.00143i	−0.988086	−	0.153902i	$-0.950816\pi$
$439$	−200.772	−	439.629i	−0.457339	−	1.00143i	0.530747	−	0.847530i	$-0.321911\pi$
$440$	−11.6244	−	3.93453i	−0.0264191	−	0.00894212i
$441$	68.7092	−	79.2947i	0.155803	−	0.179807i
$442$	435.129	+	279.640i	0.984455	+	0.632671i
$443$	36.9542	−	32.0210i	0.0834181	−	0.0722822i	−0.612154	−	0.790739i	$-0.709697\pi$
$443$	36.9542	−	32.0210i	0.0834181	−	0.0722822i	0.695572	+	0.718457i	$0.255151\pi$
$444$	0.969919	−	0.139453i	0.00218450	−	0.000314084i
$445$	−68.6323	+	54.7359i	−0.154230	+	0.123002i
$446$	−491.401	+	315.804i	−1.10180	+	0.708081i
$447$	−0.663850	+	4.61718i	−0.00148512	+	0.0103293i
$448$	−20.3078	+	44.4678i	−0.0453298	+	0.0992585i
$449$	295.991	−	648.131i	0.659224	−	1.44350i	−0.224020	−	0.974585i	$-0.571918\pi$
$449$	295.991	−	648.131i	0.659224	−	1.44350i	0.883244	−	0.468914i	$-0.155355\pi$
$450$	64.4737	+	311.555i	0.143275	+	0.692344i
$451$	25.4237	+	39.5600i	0.0563718	+	0.0877162i
$452$	−102.224	−	30.0158i	−0.226160	−	0.0664066i
$453$	1.23776	−	0.177964i	0.00273237	−	0.000392856i
$454$	341.850	−	296.215i	0.752975	−	0.652456i
$455$	345.052	−	140.880i	0.758356	−	0.309627i
$456$	−0.688684	−	0.596748i	−0.00151027	−	0.00130866i
$457$	−300.101	+	88.1175i	−0.656675	+	0.192817i	−0.593061	−	0.805157i	$-0.702081\pi$
$457$	−300.101	+	88.1175i	−0.656675	+	0.192817i	−0.0636139	+	0.997975i	$0.520263\pi$
$458$	−30.6323	−	67.0755i	−0.0668829	−	0.146453i
$459$			18.6244i			0.0405759i
$460$	227.874	−	31.2033i	0.495377	−	0.0678332i
$461$	399.052			0.865623			0.432811	−	0.901485i	$-0.357522\pi$
$461$	399.052			0.865623			0.432811	+	0.901485i	$0.357522\pi$
$462$	−0.235420	+	0.107513i	−0.000509567	+	0.000232712i
$463$	149.008	+	507.475i	0.321831	+	1.09606i	0.948502	+	0.316773i	$0.102599\pi$
$463$	149.008	+	507.475i	0.321831	+	1.09606i	−0.626670	+	0.779285i	$0.715583\pi$
$464$	−52.7498	+	60.8765i	−0.113685	+	0.131199i
$465$	7.22761	−	2.95094i	0.0155432	−	0.00634611i
$466$	−385.019	−	444.336i	−0.826221	−	0.953510i
$467$	−22.1729	−	154.216i	−0.0474795	−	0.330227i	−0.999693	−	0.0247929i	$-0.992107\pi$
$467$	−22.1729	−	154.216i	−0.0474795	−	0.330227i	0.952213	−	0.305435i	$-0.0988017\pi$
$468$	61.8523	−	210.650i	0.132163	−	0.450106i
$469$	−207.685	+	133.471i	−0.442824	+	0.284586i
$470$	−284.528	+	302.516i	−0.605379	+	0.643650i
$471$	0.764561	+	0.349163i	0.00162327	+	0.000741324i
$472$	284.951	+	130.133i	0.603709	+	0.275705i
$473$	55.1894	+	7.93504i	0.116679	+	0.0167760i
$474$	1.76330	+	2.74375i	0.00372004	+	0.00578849i
$475$	232.947	−	14.2886i	0.490414	−	0.0300813i
$476$	−52.1485	−	362.701i	−0.109556	−	0.761977i
$477$	19.3431	+	22.3231i	0.0405516	+	0.0467990i
$478$	−212.570	+	330.765i	−0.444706	+	0.691976i
$479$	307.106	+	266.109i	0.641140	+	0.555551i	0.913599	−	0.406616i	$-0.133291\pi$
$479$	307.106	+	266.109i	0.641140	+	0.555551i	−0.272459	+	0.962167i	$0.587837\pi$
$480$	0.924608	+	0.312954i	0.00192627	+	0.000651988i
$481$	157.526	−	71.9398i	0.327497	−	0.149563i
$482$	−255.901			−0.530914
$483$	3.04972	−	3.77176i	0.00631412	−	0.00780903i
$484$	−240.494			−0.496888
$485$	−122.595	+	660.327i	−0.252774	+	1.36150i
$486$	11.3776	−	3.34077i	0.0234108	−	0.00687402i
$487$	30.3963	+	26.3385i	0.0624153	+	0.0540832i	0.685510	−	0.728063i	$-0.259579\pi$
$487$	30.3963	+	26.3385i	0.0624153	+	0.0540832i	−0.623095	+	0.782147i	$0.714125\pi$
$488$	224.259	+	144.122i	0.459547	+	0.295333i
$489$	−1.79904	−	2.07620i	−0.00367901	−	0.00424581i
$490$	73.5367	+	37.2772i	0.150075	+	0.0760759i
$491$	−212.265	−	62.3267i	−0.432312	−	0.126938i	0.0583344	−	0.998297i	$-0.481421\pi$
$491$	−212.265	−	62.3267i	−0.432312	−	0.126938i	−0.490646	+	0.871359i	$0.663239\pi$
$492$	−2.02221	−	3.14662i	−0.00411018	−	0.00639556i
$493$	85.9279	−	597.642i	0.174296	−	1.21225i
$494$	−146.493	−	66.9011i	−0.296544	−	0.135427i
$495$	−19.7529	−	33.6796i	−0.0399049	−	0.0680396i
$496$	−25.7542	+	179.125i	−0.0519239	+	0.361138i
$497$	−386.170	+	248.177i	−0.777003	+	0.499349i
$498$	1.39305	+	0.409037i	0.00279729	+	0.000821359i
$499$	26.2310	+	182.441i	0.0525671	+	0.365612i	0.999078	+	0.0429395i	$0.0136723\pi$
$499$	26.2310	+	182.441i	0.0525671	+	0.365612i	−0.946511	+	0.322673i	$0.895419\pi$
$500$	−225.232	+	108.492i	−0.450464	+	0.216984i
$501$	0.775143	+	0.498154i	0.00154719	+	0.000994320i
$502$	63.7536	−	73.5756i	0.126999	−	0.146565i
$503$	−312.774	+	91.8387i	−0.621817	+	0.182582i	−0.577440	−	0.816433i	$-0.695948\pi$
$503$	−312.774	+	91.8387i	−0.621817	+	0.182582i	−0.0443766	+	0.999015i	$0.514130\pi$
$504$	−141.477	+	64.6103i	−0.280708	+	0.128195i
$505$	−158.141	−	110.992i	−0.313151	−	0.219785i
$506$	−25.2612	+	12.5930i	−0.0499234	+	0.0248873i
$507$		−	0.697075i		−	0.00137490i
$508$	101.935	−	46.5521i	0.200659	−	0.0916380i
$509$	216.556	−	63.5867i	0.425455	−	0.124925i	−0.0619938	−	0.998077i	$-0.519746\pi$
$509$	216.556	−	63.5867i	0.425455	−	0.124925i	0.487448	+	0.873152i	$0.337928\pi$
$510$	−7.09862	+	1.77354i	−0.0139189	+	0.00347752i
$511$	−288.927	+	449.580i	−0.565415	+	0.879804i
$512$	−17.1007	+	14.8178i	−0.0333997	+	0.0289410i
$513$	−0.825261	−	5.73981i	−0.00160870	−	0.0111887i
$514$	−572.343	−	168.055i	−1.11351	−	0.326956i
$515$	33.3377	+	1.35990i	0.0647335	+	0.00264058i
$516$	−4.38978	−	0.631156i	−0.00850733	−	0.00122317i
$517$	21.1721	−	46.3605i	0.0409519	−	0.0896721i
$518$	−111.597	−	50.9648i	−0.215439	−	0.0983876i
$519$	−0.549623	+	3.82271i	−0.00105900	+	0.00736554i
$520$	172.369	+	7.03118i	0.331478	+	0.0135215i
$521$	108.427	−	369.269i	0.208114	−	0.708770i	−0.787592	−	0.616197i	$-0.788673\pi$
$521$	108.427	−	369.269i	0.208114	−	0.708770i	0.995706	−	0.0925734i	$-0.0295093\pi$
$522$	−253.670	+	36.4722i	−0.485957	+	0.0698701i
$523$	115.107	+	132.841i	0.220091	+	0.253998i	0.855048	−	0.518549i	$-0.173528\pi$
$523$	115.107	+	132.841i	0.220091	+	0.253998i	−0.634957	+	0.772547i	$0.718982\pi$
$524$	−287.836	−	184.981i	−0.549306	−	0.353018i
$525$	−1.89244	+	4.92089i	−0.00360465	+	0.00937313i
$526$	35.7302	+	121.686i	0.0679281	+	0.231342i
$527$	−563.499	−	1233.89i	−1.06926	−	2.34135i
$528$	−0.119793			−0.000226881
$529$	318.409	−	422.441i	0.601908	−	0.798566i
$530$	−13.3337	+	18.9979i	−0.0251580	+	0.0358451i
$531$	414.024	+	906.587i	0.779707	+	1.70732i
$532$	32.1432	+	109.470i	0.0604195	+	0.205770i
$533$	−499.578	−	432.887i	−0.937295	−	0.812171i
$534$	−0.463282	+	0.720880i	−0.000867569	+	0.00134996i
$535$	−41.0285	−	400.723i	−0.0766888	−	0.749015i
$536$	−113.107	+	16.2623i	−0.211020	+	0.0303402i
$537$	1.00184	−	3.41194i	0.00186562	−	0.00635371i
$538$	−266.553	−	414.765i	−0.495453	−	0.770939i
$539$	−10.0149	−	1.43992i	−0.0185805	−	0.00267147i
$540$	3.14251	+	5.35813i	0.00581947	+	0.00992246i
$541$	89.9297	−	196.919i	0.166229	−	0.363990i	−0.808125	−	0.589010i	$-0.799518\pi$
$541$	89.9297	−	196.919i	0.166229	−	0.363990i	0.974354	+	0.225021i	$0.0722449\pi$
$542$	404.089	+	58.0993i	0.745553	+	0.107194i
$543$	−5.69166	+	3.65781i	−0.0104819	+	0.00673629i
$544$	47.7842	−	162.738i	0.0878386	−	0.299151i
$545$	−871.084	−	441.570i	−1.59832	−	0.810219i
$546$	2.74949	−	2.38245i	0.00503569	−	0.00436345i
$547$	90.9899	−	141.583i	0.166344	−	0.258836i	−0.748067	−	0.663623i	$-0.769018\pi$
$547$	90.9899	−	141.583i	0.166344	−	0.258836i	0.914411	+	0.404787i	$0.132654\pi$
$548$	29.9032	−	34.5102i	0.0545680	−	0.0629748i
$549$	238.946	+	813.776i	0.435239	+	1.48229i
$550$	21.9132	−	21.4734i	0.0398422	−	0.0390425i
$551$			187.994i			0.341187i
$552$	2.00929	−	1.00165i	0.00364001	−	0.00181458i
$553$		−	408.344i		−	0.738416i
$554$	164.342	+	359.858i	0.296646	+	0.649563i
$555$	−0.785396	+	2.32042i	−0.00141513	+	0.00418093i
$556$	270.079	−	311.688i	0.485754	−	0.560590i
$557$	−299.455	−	192.448i	−0.537621	−	0.345508i	0.243487	−	0.969904i	$-0.421709\pi$
$557$	−299.455	−	192.448i	−0.537621	−	0.345508i	−0.781108	+	0.624396i	$0.785345\pi$
$558$	−435.127	+	377.040i	−0.779798	+	0.675699i
$559$	−775.804	+	111.544i	−1.38784	+	0.199542i
$560$	−76.2019	−	95.5482i	−0.136075	−	0.170622i
$561$	0.755391	−	0.485461i	0.00134651	−	0.000865349i
$562$	−43.9209	+	305.476i	−0.0781510	+	0.543552i
$563$	−393.910	+	862.542i	−0.699662	+	1.53205i	0.140719	+	0.990050i	$0.455059\pi$
$563$	−393.910	+	862.542i	−0.699662	+	1.53205i	−0.840381	+	0.541997i	$0.817669\pi$
$564$	−1.68404	+	3.68753i	−0.00298588	+	0.00653817i
$565$	182.481	−	194.018i	0.322976	−	0.343394i
$566$	168.981	+	262.939i	0.298552	+	0.464557i
$567$	−474.727	−	139.393i	−0.837262	−	0.245842i
$568$	−210.312	+	30.2383i	−0.370268	+	0.0532364i
$569$	−100.516	+	87.0973i	−0.176653	+	0.153071i	−0.738700	−	0.674035i	$-0.764560\pi$
$569$	−100.516	+	87.0973i	−0.176653	+	0.153071i	0.562046	+	0.827106i	$0.310014\pi$
$570$	2.10913	−	0.861130i	0.00370022	−	0.00151075i
$571$	−648.995	−	562.357i	−1.13659	−	0.984864i	−0.136610	−	0.990625i	$-0.543621\pi$
$571$	−648.995	−	562.357i	−1.13659	−	0.984864i	−0.999983	+	0.00576109i	$0.998166\pi$
$572$	−20.3134	+	5.96456i	−0.0355130	+	0.0104276i
$573$	2.95557	+	6.47180i	0.00515807	+	0.0112946i
$574$			468.302i			0.815858i
$575$	−188.000	+	543.398i	−0.326957	+	0.945039i
$576$	−71.9905			−0.124983
$577$	−365.105	+	166.738i	−0.632764	+	0.288974i	−0.705860	−	0.708351i	$-0.749439\pi$
$577$	−365.105	+	166.738i	−0.632764	+	0.288974i	0.0730959	+	0.997325i	$0.476712\pi$
$578$	243.030	+	827.683i	0.420466	+	1.43198i
$579$	−5.27202	+	6.08424i	−0.00910539	+	0.0105082i
$580$	−76.1199	−	186.437i	−0.131241	−	0.321443i
$581$	−119.037	−	137.377i	−0.204884	−	0.236448i
$582$	0.932993	+	6.48911i	0.00160308	+	0.0111497i
$583$	0.802485	−	2.73301i	0.00137647	−	0.00468784i
$584$	−208.095	+	133.735i	−0.356327	+	0.228998i
$585$	399.804	+	376.032i	0.683426	+	0.642790i
$586$	−23.2238	−	10.6060i	−0.0396311	−	0.0180989i
$587$	−175.362	−	80.0852i	−0.298743	−	0.136431i	0.260404	−	0.965500i	$-0.416144\pi$
$587$	−175.362	−	80.0852i	−0.298743	−	0.136431i	−0.559147	+	0.829068i	$0.688871\pi$
$588$	0.796587	+	0.114532i	0.00135474	+	0.000194782i
$589$	228.339	+	355.302i	0.387672	+	0.603229i
$590$	−612.275	+	488.304i	−1.03775	+	0.827633i
$591$	1.21210	+	8.43036i	0.00205093	+	0.0142646i
$592$	−37.1871	−	42.9162i	−0.0628160	−	0.0724936i
$593$	504.014	−	784.260i	0.849938	−	1.32253i	−0.0950654	−	0.995471i	$-0.530306\pi$
$593$	504.014	−	784.260i	0.849938	−	1.32253i	0.945004	−	0.327059i	$-0.106058\pi$
$594$	−0.576116	−	0.499207i	−0.000969892	−	0.000840416i
$595$	867.720	+	293.699i	1.45835	+	0.493612i
$596$	245.895	−	112.297i	0.412576	−	0.188417i
$597$	8.10460			0.0135755
$598$	290.843	−	269.893i	0.486360	−	0.451326i
$599$	583.085			0.973431			0.486716	−	0.873560i	$-0.338195\pi$
$599$	583.085			0.973431			0.486716	+	0.873560i	$0.338195\pi$
$600$	−1.74299	+	1.70800i	−0.00290498	+	0.00284666i
$601$	−294.726	+	86.5394i	−0.490393	+	0.143992i	−0.517574	−	0.855638i	$-0.673165\pi$
$601$	−294.726	+	86.5394i	−0.490393	+	0.143992i	0.0271817	+	0.999631i	$0.491347\pi$
$602$	419.637	+	363.618i	0.697071	+	0.604016i
$603$	−305.844	−	196.554i	−0.507203	−	0.325960i
$604$	−47.4564	−	54.7676i	−0.0785702	−	0.0906748i
$605$	271.845	−	536.268i	0.449330	−	0.886394i
$606$	−1.80954	−	0.531328i	−0.00298604	−	0.000876780i
$607$	587.064	+	913.489i	0.967157	+	1.50492i	0.859753	+	0.510709i	$0.170617\pi$
$607$	587.064	+	913.489i	0.967157	+	1.50492i	0.107403	+	0.994216i	$0.465746\pi$
$608$	−7.51549	+	52.2714i	−0.0123610	+	0.0859726i
$609$	−3.86307	−	1.76421i	−0.00634330	−	0.00289689i
$610$	−574.867	+	337.156i	−0.942404	+	0.552715i
$611$	−101.960	+	709.145i	−0.166873	+	1.16063i
$612$	453.956	−	291.740i	0.741759	−	0.476699i
$613$	570.361	+	167.473i	0.930441	+	0.273202i	0.711622	−	0.702563i	$-0.247961\pi$
$613$	570.361	+	167.473i	0.930441	+	0.273202i	0.218820	+	0.975765i	$0.429779\pi$
$614$	61.3689	+	426.830i	0.0999493	+	0.695163i
$615$	9.30234	−	0.952432i	0.0151258	−	0.00154867i
$616$	12.6174	+	8.10870i	0.0204828	+	0.0131635i
$617$	−423.170	+	488.364i	−0.685851	+	0.791514i	−0.986768	−	0.162136i	$-0.948162\pi$
$617$	−423.170	+	488.364i	−0.685851	+	0.791514i	0.300918	+	0.953650i	$0.402707\pi$
$618$	0.312499	−	0.0917581i	0.000505662	−	0.000148476i
$619$	938.360	−	428.534i	1.51593	−	0.692301i	0.528292	−	0.849063i	$-0.322833\pi$
$619$	938.360	−	428.534i	1.51593	−	0.692301i	0.987636	+	0.156762i	$0.0501055\pi$
$620$	−370.312	−	259.904i	−0.597277	−	0.419200i
$621$	13.8372	+	3.55600i	0.0222822	+	0.00572624i
$622$		−	34.0456i		−	0.0547357i
$623$	97.5914	−	44.5685i	0.156648	−	0.0715385i
$624$	1.61574	−	0.474424i	0.00258932	−	0.000760294i
$625$	12.6717	−	624.872i	0.0202747	−	0.999794i
$626$	130.703	−	203.378i	0.208791	−	0.324885i
$627$	−0.211292	+	0.183085i	−0.000336989	+	0.000292002i
$628$	−6.93205	−	48.2135i	−0.0110383	−	0.0767730i
$629$	408.411	+	119.920i	0.649302	+	0.190652i
$630$	15.8478	−	388.507i	0.0251552	−	0.616678i
$631$	−647.807	−	93.1406i	−1.02664	−	0.147608i	−0.391636	−	0.920120i	$-0.628091\pi$
$631$	−647.807	−	93.1406i	−1.02664	−	0.147608i	−0.635000	+	0.772512i	$0.719000\pi$
$632$	78.5170	−	171.928i	0.124236	−	0.272038i
$633$	−2.75562	−	1.25845i	−0.00435327	−	0.00198807i
$634$	−24.1127	+	167.708i	−0.0380327	+	0.264523i
$635$	−11.4184	+	279.921i	−0.0179818	+	0.440821i
$636$	−0.0638299	+	0.217385i	−0.000100362	+	0.000341800i
$637$	140.780	−	20.2412i	0.221005	−	0.0317758i
$638$	16.1839	+	18.6772i	0.0253666	+	0.0292747i
$639$	−568.688	−	365.474i	−0.889966	−	0.571946i
$640$	−13.7117	−	54.8816i	−0.0214246	−	0.0857525i
$641$	−26.0047	−	88.5640i	−0.0405690	−	0.138165i	0.936718	−	0.350084i	$-0.113847\pi$
$641$	−26.0047	−	88.5640i	−0.0405690	−	0.138165i	−0.977287	+	0.211919i	$0.932029\pi$
$642$	−1.63343	−	3.57672i	−0.00254429	−	0.00557121i
$643$	−415.065			−0.645513			−0.322757	−	0.946482i	$-0.604610\pi$
$643$	−415.065			−0.645513			−0.322757	+	0.946482i	$0.604610\pi$
$644$	−279.431	−	30.5069i	−0.433899	−	0.0473710i
$645$	6.36943	−	9.07518i	0.00987508	−	0.0140700i
$646$	−164.438	−	360.068i	−0.254547	−	0.557381i
$647$	−95.8985	−	326.600i	−0.148220	−	0.504792i	0.851591	−	0.524206i	$-0.175638\pi$
$647$	−95.8985	−	326.600i	−0.148220	−	0.504792i	−0.999812	+	0.0194146i	$0.993820\pi$
$648$	−173.075	−	149.971i	−0.267092	−	0.231436i
$649$	51.9607	−	80.8525i	0.0800628	−	0.124580i
$650$	−210.517	+	376.410i	−0.323873	+	0.579093i
$651$	−9.44388	+	1.35783i	−0.0145067	+	0.00208575i
$652$	−44.8531	+	152.756i	−0.0687931	+	0.234288i
$653$	680.604	+	1059.04i	1.04227	+	1.62181i	0.745061	+	0.666996i	$0.232420\pi$
$653$	680.604	+	1059.04i	1.04227	+	1.62181i	0.297211	+	0.954812i	$0.403943\pi$
$654$	−9.43603	−	1.35670i	−0.0144282	−	0.00207446i
$655$	737.842	−	432.740i	1.12648	−	0.660672i
$656$	−90.0459	+	197.173i	−0.137265	+	0.300568i
$657$	−778.990	−	112.002i	−1.18568	−	0.170475i
$658$	426.978	−	274.402i	0.648903	−	0.417025i
$659$	−359.332	+	1223.77i	−0.545268	+	1.85701i	−0.0307598	+	0.999527i	$0.509793\pi$
$659$	−359.332	+	1223.77i	−0.545268	+	1.85701i	−0.514508	+	0.857485i	$0.672026\pi$
$660$	0.135410	−	0.267123i	0.000205166	−	0.000404732i
$661$	288.576	−	250.052i	0.436574	−	0.378294i	−0.408663	−	0.912686i	$-0.634005\pi$
$661$	288.576	−	250.052i	0.436574	−	0.378294i	0.845237	+	0.534392i	$0.179459\pi$
$662$	−127.698	+	198.703i	−0.192898	+	0.300155i
$663$	−8.26590	+	9.53936i	−0.0124674	+	0.0143882i
$664$	−23.7043	−	80.7294i	−0.0356992	−	0.121580i
$665$	−280.436	−	52.0653i	−0.421708	−	0.0782937i
$666$		−	180.669i		−	0.271275i
$667$	−427.620	−	177.951i	−0.641110	−	0.266793i
$668$		−	53.3973i		−	0.0799361i
$669$	−5.92163	−	12.9666i	−0.00885147	−	0.0193820i
$670$	91.5889	−	270.595i	0.136700	−	0.403873i
$671$	53.5592	−	61.8107i	0.0798200	−	0.0921172i
$672$	−1.00359	−	0.644969i	−0.00149344	−	0.000959776i
$673$	−67.3740	+	58.3799i	−0.100110	+	0.0867457i	−0.703478	−	0.710717i	$-0.748371\pi$
$673$	−67.3740	+	58.3799i	−0.100110	+	0.0867457i	0.603368	+	0.797463i	$0.293825\pi$
$674$	274.247	−	39.4308i	0.406895	−	0.0585027i
$675$	−15.5001	+	0.950752i	−0.0229631	+	0.00140852i
$676$	−33.9837	+	21.8400i	−0.0502718	+	0.0323077i
$677$	38.5826	−	268.348i	0.0569906	−	0.396378i	−0.941282	−	0.337622i	$-0.890377\pi$
$677$	38.5826	−	268.348i	0.0569906	−	0.396378i	0.998272	−	0.0587561i	$-0.0187134\pi$
$678$	1.08005	−	2.36499i	0.00159300	−	0.00348818i
$679$	340.973	−	746.627i	0.502169	−	1.09960i
$680$	308.870	+	290.505i	0.454220	+	0.427213i
$681$	5.96784	+	9.28614i	0.00876335	+	0.0136360i
$682$	53.2725	+	15.6422i	0.0781122	+	0.0229358i
$683$	440.111	−	63.2785i	0.644380	−	0.0926478i	0.187625	−	0.982241i	$-0.439921\pi$
$683$	440.111	−	63.2785i	0.644380	−	0.0926478i	0.456754	+	0.889593i	$0.349012\pi$
$684$	−126.977	+	110.026i	−0.185639	+	0.160857i
$685$	43.1515	+	105.689i	0.0629949	+	0.154291i
$686$	−396.170	−	343.283i	−0.577508	−	0.500413i
$687$	1.72659	−	0.506974i	0.00251324	−	0.000737953i
$688$	106.766	+	233.785i	0.155183	+	0.339804i
$689$			40.0402i			0.0581135i
$690$	−0.0376817	+	5.61265i	−5.46112e−5	+	0.00813428i
$691$	787.585			1.13978			0.569888	−	0.821722i	$-0.306987\pi$
$691$	787.585			1.13978			0.569888	+	0.821722i	$0.306987\pi$
$692$	203.585	−	92.9741i	0.294198	−	0.134356i
$693$	13.4437	+	45.7851i	0.0193993	+	0.0660680i
$694$	445.802	−	514.483i	0.642365	−	0.741329i
$695$	389.734	+	954.559i	0.560769	+	1.37347i
$696$	−1.28727	−	1.48559i	−0.00184953	−	0.00213447i
$697$	−231.230	−	1608.24i	−0.331750	−	2.30737i
$698$	−100.996	+	343.961i	−0.144694	+	0.492781i
$699$	12.0701	−	7.75698i	0.0172677	−	0.0110972i
$700$	299.195	−	61.9160i	0.427421	−	0.0884514i
$701$	−957.196	−	437.137i	−1.36547	−	0.623590i	−0.408230	−	0.912879i	$-0.633854\pi$
$701$	−957.196	−	437.137i	−1.36547	−	0.623590i	−0.957242	+	0.289289i	$0.906581\pi$
$702$	9.74751	+	4.45154i	0.0138853	+	0.00634122i
$703$	−131.181	−	18.8610i	−0.186602	−	0.0268293i
$704$	3.75324	+	5.84016i	0.00533131	+	0.00829568i
$705$	−6.31911	−	7.92341i	−0.00896327	−	0.0112389i
$706$	63.0112	+	438.252i	0.0892510	+	0.620754i
$707$	154.627	+	178.449i	0.218708	+	0.252403i
$708$	−4.13298	+	6.43104i	−0.00583754	+	0.00908338i
$709$	329.221	+	285.272i	0.464346	+	0.402358i	0.855366	−	0.518024i	$-0.173332\pi$
$709$	329.221	+	285.272i	0.464346	+	0.402358i	−0.391020	+	0.920382i	$0.627878\pi$
$710$	170.301	−	503.147i	0.239861	−	0.708658i
$711$	547.000	−	249.807i	0.769339	−	0.351345i
$712$	49.6593			0.0697463
$713$	−1024.33	+	183.070i	−1.43664	+	0.256760i
$714$	8.94216			0.0125240
$715$	9.66136	−	52.0383i	0.0135124	−	0.0727808i
$716$	−197.727	+	58.0580i	−0.276155	+	0.0810866i
$717$	−7.25138	−	6.28335i	−0.0101135	−	0.00876339i
$718$	458.536	+	294.683i	0.638629	+	0.410422i
$719$	34.0127	+	39.2528i	0.0473056	+	0.0545936i	0.778909	−	0.627137i	$-0.215773\pi$
$719$	34.0127	+	39.2528i	0.0473056	+	0.0545936i	−0.731604	+	0.681730i	$0.761228\pi$
$720$	81.3752	−	160.529i	0.113021	−	0.222957i
$721$	−39.1254	−	11.4883i	−0.0542654	−	0.0159338i
$722$	−209.381	−	325.804i	−0.290002	−	0.451251i
$723$	0.888734	−	6.18128i	0.00122923	−	0.00854949i
$724$	356.650	+	162.877i	0.492611	+	0.224968i
$725$	501.772	+	41.0043i	0.692099	+	0.0565577i
$726$	0.835227	−	5.80913i	0.00115045	−	0.00800156i
$727$	883.641	−	567.882i	1.21546	−	0.781130i	0.233898	−	0.972261i	$-0.424852\pi$
$727$	883.641	−	567.882i	1.21546	−	0.781130i	0.981565	+	0.191131i	$0.0612154\pi$
$728$	−202.293	−	59.3986i	−0.277875	−	0.0815914i
$729$	−103.665	−	721.007i	−0.142202	−	0.989036i
$730$	−62.9872	−	615.192i	−0.0862838	−	0.842728i
$731$	−1620.65	−	1041.53i	−2.21704	−	1.42480i
$732$	−4.26012	+	4.91644i	−0.00581984	+	0.00671645i
$733$	106.223	−	31.1900i	0.144916	−	0.0425512i	−0.208470	−	0.978029i	$-0.566848\pi$
$733$	106.223	−	31.1900i	0.144916	−	0.0425512i	0.353386	+	0.935478i	$0.385030\pi$
$734$	841.542	−	384.319i	1.14652	−	0.523596i
$735$	−1.15582	+	1.64682i	−0.00157255	+	0.00224057i
$736$	−111.785	−	66.5740i	−0.151882	−	0.0904538i
$737$			35.0586i			0.0475694i
$738$	−627.317	+	286.486i	−0.850024	+	0.388193i
$739$	−488.070	+	143.310i	−0.660446	+	0.193924i	−0.594744	−	0.803915i	$-0.702747\pi$
$739$	−488.070	+	143.310i	−0.660446	+	0.193924i	−0.0657016	+	0.997839i	$0.520929\pi$
$740$	137.732	−	34.4113i	0.186124	−	0.0465018i
$741$	2.12476	−	3.30619i	0.00286742	−	0.00446180i
$742$	21.4375	−	18.5757i	0.0288916	−	0.0250347i
$743$	174.755	+	1215.45i	0.235202	+	1.63586i	0.675036	+	0.737785i	$0.264128\pi$
$743$	174.755	+	1215.45i	0.235202	+	1.63586i	−0.439834	+	0.898079i	$0.644963\pi$
$744$	−4.23731	−	1.24419i	−0.00569531	−	0.00167229i
$745$	−27.5444	+	675.249i	−0.0369724	+	0.906374i
$746$	−201.866	−	29.0240i	−0.270598	−	0.0389062i
$747$	111.202	−	243.498i	0.148865	−	0.325968i
$748$	−47.3343	−	21.6168i	−0.0632811	−	0.0288995i
$749$	−70.0614	+	487.288i	−0.0935399	+	0.650584i
$750$	−1.83840	−	5.81727i	−0.00245120	−	0.00775636i
$751$	169.329	−	576.681i	0.225471	−	0.767884i	−0.766591	−	0.642136i	$-0.778049\pi$
$751$	169.329	−	576.681i	0.225471	−	0.767884i	0.992062	−	0.125749i	$-0.0401333\pi$
$752$	232.536	−	33.4337i	0.309224	−	0.0444597i
$753$	1.55580	+	1.79549i	0.00206614	+	0.00238445i
$754$	−292.252	−	187.819i	−0.387602	−	0.249097i
$755$	175.767	−	43.9141i	0.232804	−	0.0581643i
$756$	−2.13878	−	7.28401i	−0.00282907	−	0.00963494i
$757$	503.636	+	1102.81i	0.665306	+	1.45682i	0.877494	+	0.479587i	$0.159214\pi$
$757$	503.636	+	1102.81i	0.665306	+	1.45682i	−0.212188	+	0.977229i	$0.568059\pi$
$758$	−716.749			−0.945579
$759$	−0.216451	−	0.653920i	−0.000285180	−	0.000861554i
$760$	−108.063	−	75.8440i	−0.142188	−	0.0997947i
$761$	−272.945	−	597.667i	−0.358667	−	0.785371i	−0.999838	−	0.0179732i	$-0.994279\pi$
$761$	−272.945	−	597.667i	−0.358667	−	0.785371i	0.641172	−	0.767397i	$-0.278449\pi$
$762$	0.770450	+	2.62391i	0.00101109	+	0.00344345i
$763$	902.028	+	781.611i	1.18221	+	1.02439i
$764$	222.912	−	346.857i	0.291769	−	0.454002i
$765$	137.406	+	1342.03i	0.179615	+	1.75429i
$766$	−226.982	+	32.6351i	−0.296322	+	0.0426046i
$767$	−380.627	+	1296.30i	−0.496254	+	1.69009i
$768$	−0.298534	−	0.464528i	−0.000388716	−	0.000604855i
$769$	−1441.92	−	207.317i	−1.87506	−	0.269593i	−0.891888	−	0.452256i	$-0.850619\pi$
$769$	−1441.92	−	207.317i	−1.87506	−	0.269593i	−0.983176	+	0.182663i	$0.941528\pi$
$770$	−32.3435	+	18.9693i	−0.0420045	+	0.0246354i
$771$	6.04710	−	13.2413i	0.00784320	−	0.0171742i
$772$	461.796	+	66.3962i	0.598181	+	0.0860054i
$773$	612.818	−	393.834i	0.792779	−	0.509488i	−0.0804730	−	0.996757i	$-0.525643\pi$
$773$	612.818	−	393.834i	0.792779	−	0.509488i	0.873252	+	0.487269i	$0.162007\pi$
$774$	−230.371	+	784.572i	−0.297637	+	1.01366i
$775$	998.136	−	531.959i	1.28792	−	0.686399i
$776$	287.125	−	248.795i	0.370006	−	0.320612i
$777$	1.61863	−	2.51864i	0.00208318	−	0.00324149i
$778$	457.293	−	527.744i	0.587780	−	0.678334i
$779$	142.525	+	485.395i	0.182959	+	0.623100i
$780$	−0.768468	+	4.13914i	−0.000985215	+	0.00530659i
$781$			65.1883i			0.0834678i
$782$	974.682	−	33.2060i	1.24640	−	0.0424629i
$783$		−	12.5089i		−	0.0159757i
$784$	−19.3742	−	42.4235i	−0.0247120	−	0.0541117i
$785$	115.345	+	39.0411i	0.146936	+	0.0497339i
$786$	5.46787	−	6.31026i	0.00695658	−	0.00802832i
$787$	−1013.31	−	651.215i	−1.28756	−	0.827465i	−0.295761	−	0.955262i	$-0.595573\pi$
$787$	−1013.31	−	651.215i	−1.28756	−	0.827465i	−0.991800	+	0.127797i	$0.959209\pi$
$788$	373.020	−	323.223i	0.473375	−	0.410182i
$789$	−3.06341	+	0.440452i	−0.00388265	+	0.000558241i
$790$	294.624	+	369.423i	0.372942	+	0.467624i
$791$	−273.842	+	175.987i	−0.346197	+	0.222487i
$792$	−3.14332	+	21.8622i	−0.00396883	+	0.0276038i
$793$	−477.600	+	1045.80i	−0.602269	+	1.31879i
$794$	155.250	−	339.949i	0.195528	−	0.428147i
$795$	−0.412587	−	0.388055i	−0.000518978	−	0.000488120i
$796$	−253.925	−	395.115i	−0.319001	−	0.496375i
$797$	179.262	+	52.6362i	0.224921	+	0.0660429i	0.392251	−	0.919858i	$-0.371696\pi$
$797$	179.262	+	52.6362i	0.224921	+	0.0660429i	−0.167330	+	0.985901i	$0.553515\pi$
$798$	−2.75587	+	0.396234i	−0.00345347	+	0.000496534i
$799$	−1330.84	+	1153.18i	−1.66563	+	1.44327i
$800$	137.878	+	31.4607i	0.172347	+	0.0393258i
$801$	119.404	+	103.464i	0.149069	+	0.129169i
$802$	517.409	−	151.925i	0.645148	−	0.189433i
$803$	31.5268	+	69.0340i	0.0392613	+	0.0859702i
$804$		−	2.78858i		−	0.00346838i
$805$	383.884	−	588.609i	0.476875	−	0.731191i
$806$	−780.472			−0.968328
$807$	10.9444	−	4.99814i	0.0135618	−	0.00619348i
$808$	30.7913	+	104.865i	0.0381080	+	0.129784i
$809$	535.442	−	617.933i	0.661857	−	0.763824i	−0.321222	−	0.947004i	$-0.604094\pi$
$809$	535.442	−	617.933i	0.661857	−	0.763824i	0.983079	+	0.183180i	$0.0586391\pi$
$810$	530.052	−	216.413i	0.654385	−	0.267177i
$811$	−523.049	−	603.631i	−0.644944	−	0.744305i	0.335297	−	0.942112i	$-0.391163\pi$
$811$	−523.049	−	603.631i	−0.644944	−	0.744305i	−0.980241	+	0.197808i	$0.936618\pi$
$812$	35.0253	+	243.606i	0.0431346	+	0.300008i
$813$	−2.80678	+	9.55901i	−0.00345237	+	0.0117577i
$814$	−14.6566	+	9.41922i	−0.0180056	+	0.0115715i
$815$	−289.924	−	272.685i	−0.355735	−	0.334583i
$816$	3.76498	+	1.71941i	0.00461395	+	0.00210712i
$817$	545.618	+	249.175i	0.667831	+	0.304988i
$818$	−929.154	−	133.592i	−1.13588	−	0.163316i
$819$	−362.650	−	564.294i	−0.442796	−	0.689004i
$820$	−337.884	−	423.666i	−0.412054	−	0.516666i
$821$	−139.526	−	970.424i	−0.169946	−	1.18200i	−0.878991	−	0.476839i	$-0.841783\pi$
$821$	−139.526	−	970.424i	−0.169946	−	1.18200i	0.709045	−	0.705164i	$-0.249126\pi$
$822$	0.729741	+	0.842166i	0.000887763	+	0.00102453i
$823$	306.425	−	476.807i	0.372327	−	0.579352i	−0.603644	−	0.797254i	$-0.706285\pi$
$823$	306.425	−	476.807i	0.372327	−	0.579352i	0.975971	+	0.217902i	$0.0699214\pi$
$824$	−14.2643	−	12.3601i	−0.0173110	−	0.0150001i
$825$	0.442585	+	0.603890i	0.000536467	+	0.000731988i
$826$	870.621	−	397.599i	1.05402	−	0.481355i
$827$	−177.704			−0.214878			−0.107439	−	0.994212i	$-0.534265\pi$
$827$	−177.704			−0.214878			−0.107439	+	0.994212i	$0.534265\pi$
$828$	−130.078	−	392.976i	−0.157099	−	0.474609i
$829$	552.542			0.666516			0.333258	−	0.942836i	$-0.391852\pi$
$829$	552.542			0.666516			0.333258	+	0.942836i	$0.391852\pi$
$830$	206.810	+	38.3960i	0.249168	+	0.0462603i
$831$	−9.26313	+	2.71990i	−0.0111470	+	0.00327304i
$832$	−73.7517	−	63.9062i	−0.0886438	−	0.0768103i
$833$	294.090	+	189.000i	0.353049	+	0.226891i
$834$	6.59085	+	7.60625i	0.00790270	+	0.00912020i
$835$	119.069	+	60.3583i	0.142597	+	0.0722853i
$836$	15.5457	+	4.56464i	0.0185954	+	0.00546010i
$837$	−15.1934	−	23.6415i	−0.0181523	−	0.0282455i
$838$	35.2318	−	245.042i	0.0420427	−	0.292413i
$839$	1211.37	+	553.212i	1.44382	+	0.659371i	0.974650	−	0.223737i	$-0.0718255\pi$
$839$	1211.37	+	553.212i	1.44382	+	0.659371i	0.469171	+	0.883107i	$0.344553\pi$
$840$	2.57261	−	1.50882i	0.00306263	−	0.00179622i
$841$	61.9738	−	431.037i	0.0736906	−	0.512529i
$842$	321.382	−	206.540i	0.381689	−	0.245296i
$843$	−7.22625	−	2.12182i	−0.00857206	−	0.00251698i
$844$	24.9843	+	173.770i	0.0296023	+	0.205889i
$845$	−10.2863	−	100.466i	−0.0121732	−	0.118895i
$846$	628.784	+	404.095i	0.743243	+	0.477653i
$847$	−481.186	+	555.318i	−0.568106	+	0.655630i
$848$	12.5978	−	3.69904i	0.0148559	−	0.00436208i
$849$	−6.93816	+	3.16855i	−0.00817215	+	0.00373210i
$850$	−996.920	+	360.362i	−1.17285	+	0.423955i
$851$	167.075	−	280.538i	0.196328	−	0.329657i
$852$		−	5.18510i		−	0.00608580i
$853$	1251.99	−	571.764i	1.46775	−	0.670297i	0.488425	−	0.872606i	$-0.337572\pi$
$853$	1251.99	−	571.764i	1.46775	−	0.670297i	0.979322	+	0.202309i	$0.0648444\pi$
$854$	781.492	−	229.467i	0.915096	−	0.268696i
$855$	−101.813	−	407.510i	−0.119080	−	0.476620i
$856$	−123.195	+	191.695i	−0.143919	+	0.223943i
$857$	−167.050	+	144.750i	−0.194925	+	0.168903i	−0.746855	−	0.664987i	$-0.768437\pi$
$857$	−167.050	+	144.750i	−0.194925	+	0.168903i	0.551930	+	0.833890i	$0.313892\pi$
$858$	−0.0735262	−	0.511386i	−8.56949e−5	−	0.000596021i
$859$	381.999	+	112.165i	0.444702	+	0.130576i	0.496414	−	0.868086i	$-0.334650\pi$
$859$	381.999	+	112.165i	0.444702	+	0.130576i	−0.0517123	+	0.998662i	$0.516468\pi$
$860$	−641.993	−	26.1879i	−0.746503	−	0.0304510i
$861$	−11.3118	−	1.62640i	−0.0131380	−	0.00188896i
$862$	−77.9070	+	170.592i	−0.0903793	+	0.197903i
$863$	−593.585	−	271.081i	−0.687815	−	0.314115i	0.0406735	−	0.999172i	$-0.487050\pi$
$863$	−593.585	−	271.081i	−0.687815	−	0.314115i	−0.728489	+	0.685058i	$0.759777\pi$
$864$	0.500074	−	3.47809i	0.000578789	−	0.00402557i
$865$	−22.8049	+	559.060i	−0.0263641	+	0.646312i
$866$	91.1926	−	310.573i	0.105303	−	0.358630i
$867$	−20.8367	+	2.99587i	−0.0240331	+	0.00345544i
$868$	362.082	+	417.865i	0.417146	+	0.481412i
$869$	−48.7833	−	31.3511i	−0.0561373	−	0.0360772i
$870$	4.76775	−	1.19119i	0.00548018	−	0.00136918i
$871$	−138.844	−	472.861i	−0.159408	−	0.542894i
$872$	229.498	+	502.531i	0.263186	+	0.576297i
$873$	1208.74			1.38458
$874$	−298.915	+	53.4227i	−0.342008	+	0.0611244i
$875$	−200.134	+	737.151i	−0.228725	+	0.842458i
$876$	−2.50765	−	5.49099i	−0.00286262	−	0.00626826i
$877$	−154.194	−	525.137i	−0.175820	−	0.598788i	−0.999497	−	0.0317278i	$-0.989899\pi$
$877$	−154.194	−	525.137i	−0.175820	−	0.598788i	0.823677	−	0.567060i	$-0.191919\pi$
$878$	−516.551	−	447.594i	−0.588327	−	0.509788i
$879$	0.336843	−	0.524137i	0.000383211	−	0.000596288i
$880$	−17.2653	+	1.76773i	−0.0196196	+	0.00200878i
$881$	−1469.08	+	211.222i	−1.66752	+	0.239753i	−0.910460	−	0.413598i	$-0.864272\pi$
$881$	−1469.08	+	211.222i	−1.66752	+	0.239753i	−0.757056	+	0.653350i	$0.773363\pi$
$882$	41.8040	−	142.371i	0.0473969	−	0.161419i
$883$	240.219	+	373.788i	0.272049	+	0.423316i	0.950216	−	0.311591i	$-0.100862\pi$
$883$	240.219	+	373.788i	0.272049	+	0.423316i	−0.678168	+	0.734907i	$0.737226\pi$
$884$	724.041	+	104.101i	0.819051	+	0.117762i
$885$	−9.66857	−	16.4854i	−0.0109249	−	0.0186275i
$886$	28.7265	−	62.9023i	0.0324227	−	0.0709958i
$887$	369.141	+	53.0744i	0.416168	+	0.0598359i	0.347218	−	0.937784i	$-0.387126\pi$
$887$	369.141	+	53.0744i	0.416168	+	0.0598359i	0.0689493	+	0.997620i	$0.478035\pi$
$888$	1.16579	−	0.749208i	0.00131283	−	0.000843702i
$889$	96.4615	−	328.518i	0.108506	−	0.369536i
$890$	−56.1330	+	110.733i	−0.0630708	+	0.124420i
$891$	−53.1004	+	46.0118i	−0.0595965	+	0.0516406i
$892$	−446.615	+	694.946i	−0.500689	+	0.779087i
$893$	359.050	−	414.366i	0.402072	−	0.464016i
$894$	1.85854	+	6.32961i	0.00207890	+	0.00708010i
$895$	94.0419	−	506.531i	0.105075	−	0.565956i
$896$			69.1345i			0.0771590i
$897$	5.50918	+	7.96265i	0.00614179	+	0.00887698i
$898$		−	1007.66i		−	1.12211i
$899$	378.471	+	828.736i	0.420991	+	0.921842i
$900$	265.974	+	362.911i	0.295526	+	0.403234i
$901$	−64.4486	+	74.3776i	−0.0715300	+	0.0825500i
$902$	55.9463	+	35.9545i	0.0620247	+	0.0398608i
$903$	−10.2406	+	8.87350i	−0.0113406	+	0.00982669i
$904$	−149.137	+	21.4426i	−0.164974	+	0.0237197i
$905$	−766.336	+	611.171i	−0.846780	+	0.675327i
$906$	1.48773	−	0.956104i	0.00164208	−	0.00105530i
$907$	45.1902	−	314.305i	0.0498238	−	0.346532i	−0.949627	−	0.313384i	$-0.898537\pi$
$907$	45.1902	−	314.305i	0.0498238	−	0.346532i	0.999450	−	0.0331486i	$-0.0105535\pi$
$908$	265.739	−	581.887i	0.292664	−	0.640845i
$909$	−144.448	+	316.298i	−0.158909	+	0.347963i
$910$	361.115	−	383.943i	0.396829	−	0.421916i
$911$	265.923	+	413.784i	0.291902	+	0.454209i	0.955970	−	0.293463i	$-0.0948078\pi$
$911$	265.923	+	413.784i	0.291902	+	0.454209i	−0.664068	+	0.747672i	$0.731171\pi$
$912$	−1.23651	−	0.363073i	−0.00135583	−	0.000398107i
$913$	−25.5511	+	3.67369i	−0.0279859	+	0.00402376i
$914$	−334.286	+	289.660i	−0.365739	+	0.316915i
$915$	−6.14751	−	15.0568i	−0.00671859	−	0.0164556i
$916$	−78.8118	−	68.2908i	−0.0860390	−	0.0745532i
$917$	−1003.05	+	294.521i	−1.09383	+	0.321178i
$918$	10.9415	+	23.9586i	0.0119189	+	0.0260987i
$919$			923.853i			1.00528i	0.864496	+	0.502640i	$0.167638\pi$
$919$			923.853i			1.00528i	−0.864496	+	0.502640i	$0.832362\pi$
$920$	274.808	−	174.013i	0.298705	−	0.189144i
$921$	−10.5232			−0.0114259
$922$	513.346	−	234.437i	0.556774	−	0.254270i
$923$	−258.168	−	879.241i	−0.279706	−	0.952591i
$924$	−0.239686	+	0.276612i	−0.000259400	+	0.000299363i
$925$	−78.9544	+	346.021i	−0.0853561	+	0.374076i
$926$	489.820	+	565.282i	0.528963	+	0.610456i
$927$	−8.54599	−	59.4386i	−0.00921897	−	0.0641194i
$928$	−32.0940	+	109.302i	−0.0345841	+	0.117782i
$929$	1333.59	−	857.046i	1.43551	−	0.922547i	0.435764	−	0.900061i	$-0.356478\pi$
$929$	1333.59	−	857.046i	1.43551	−	0.922547i	0.999747	−	0.0224858i	$-0.00715806\pi$
$930$	7.56406	−	8.04224i	0.00813340	−	0.00864757i
$931$	−99.0100	−	45.2163i	−0.106348	−	0.0485675i
$932$	−756.335	−	345.406i	−0.811518	−	0.370608i
$933$	0.822372	+	0.118239i	0.000881428	+	0.000126730i
$934$	−119.123	−	185.360i	−0.127541	−	0.198458i
$935$	101.707	−	81.1140i	0.108778	−	0.0867530i
$936$	−44.1860	−	307.320i	−0.0472072	−	0.328333i
$937$	−131.237	−	151.456i	−0.140061	−	0.161639i	0.681385	−	0.731925i	$-0.261378\pi$
$937$	−131.237	−	151.456i	−0.140061	−	0.161639i	−0.821446	+	0.570286i	$0.806832\pi$
$938$	−188.756	+	293.710i	−0.201233	+	0.313124i
$939$	4.45867	+	3.86346i	0.00474832	+	0.00411444i
$940$	−188.298	+	556.316i	−0.200317	+	0.591826i
$941$	−1203.48	+	549.609i	−1.27893	+	0.584069i	−0.934907	−	0.354892i	$-0.884518\pi$
$941$	−1203.48	+	549.609i	−1.27893	+	0.584069i	−0.344025	+	0.938961i	$0.611790\pi$
$942$	1.18867			0.00126186
$943$	−1239.01	−	135.269i	−1.31391	−	0.143446i
$944$	443.015			0.469296
$945$	18.6599	+	3.46438i	0.0197460	+	0.00366601i
$946$	75.6581	−	22.2152i	0.0799769	−	0.0234833i
$947$	97.0542	+	84.0979i	0.102486	+	0.0888046i	0.704597	−	0.709608i	$-0.251128\pi$
$947$	97.0542	+	84.0979i	0.102486	+	0.0888046i	−0.602111	+	0.798413i	$0.705673\pi$
$948$	3.88024	+	2.49368i	0.00409308	+	0.00263046i
$949$	−698.623	−	806.254i	−0.736168	−	0.849583i
$950$	291.271	−	155.234i	0.306602	−	0.163404i
$951$	−3.96724	−	1.16489i	−0.00417165	−	0.00122491i
$952$	−280.166	−	435.947i	−0.294292	−	0.457928i
$953$	76.9571	−	535.248i	0.0807525	−	0.561646i	−0.908773	−	0.417290i	$-0.862980\pi$
$953$	76.9571	−	535.248i	0.0807525	−	0.561646i	0.989526	−	0.144356i	$-0.0461110\pi$
$954$	37.9977	+	17.3530i	0.0398299	+	0.0181897i
$955$	521.474	+	889.136i	0.546046	+	0.931033i
$956$	−79.1330	+	550.382i	−0.0827751	+	0.575713i
$957$	−0.507355	+	0.326057i	−0.000530151	+	0.000340707i
$958$	551.401	+	161.906i	0.575575	+	0.169004i
$959$	−19.8554	−	138.098i	−0.0207043	−	0.144002i
$960$	1.37329	−	0.140606i	0.00143051	−	0.000146464i
$961$	913.440	+	587.032i	0.950510	+	0.610855i
$962$	160.380	−	185.089i	0.166716	−	0.192400i
$963$	−695.609	+	204.249i	−0.722336	+	0.212097i
$964$	−329.194	+	150.338i	−0.341488	+	0.155952i
$965$	−670.050	+	954.689i	−0.694352	+	0.989315i
$966$	1.70735	−	6.64371i	0.00176744	−	0.00687755i
$967$		−	852.303i		−	0.881389i	−0.897657	−	0.440694i	$-0.854732\pi$
$967$		−	852.303i		−	0.881389i	0.897657	−	0.440694i	$-0.145268\pi$
$968$	−309.375	+	141.287i	−0.319602	+	0.145957i
$969$	9.26854	−	2.72149i	0.00956505	−	0.00280855i
$970$	230.224	+	921.477i	0.237344	+	0.949976i
$971$	−77.7145	+	120.926i	−0.0800355	+	0.124538i	−0.878964	−	0.476889i	$-0.841764\pi$
$971$	−77.7145	+	120.926i	−0.0800355	+	0.124538i	0.798928	+	0.601427i	$0.205401\pi$
$972$	12.6737	−	10.9818i	0.0130388	−	0.0112982i
$973$	−179.330	−	1247.27i	−0.184306	−	1.28188i
$974$	54.5757	+	16.0249i	0.0560325	+	0.0164526i
$975$	−8.36107	−	6.39230i	−0.00857546	−	0.00655621i
$976$	373.160	+	53.6523i	0.382336	+	0.0549716i
$977$	66.6445	−	145.931i	0.0682134	−	0.149366i	−0.872454	−	0.488696i	$-0.837473\pi$
$977$	66.6445	−	145.931i	0.0682134	−	0.149366i	0.940668	+	0.339329i	$0.110200\pi$
$978$	−3.53404	−	1.61394i	−0.00361354	−	0.00165025i
$979$	2.16827	−	15.0807i	0.00221478	−	0.0154042i
$980$	116.498	+	4.75215i	0.118876	+	0.00484913i
$981$	−495.193	+	1686.47i	−0.504783	+	1.71913i
$982$	−309.677	+	44.5248i	−0.315353	+	0.0453409i
$983$	665.695	+	768.253i	0.677207	+	0.781539i	0.985486	−	0.169757i	$-0.0542984\pi$
$983$	665.695	+	768.253i	0.677207	+	0.781539i	−0.308279	+	0.951296i	$0.599753\pi$
$984$	−4.44999	−	2.85983i	−0.00452234	−	0.00290633i
$985$	299.097	+	1197.14i	0.303652	+	1.21537i
$986$	−240.567	−	819.296i	−0.243983	−	0.830929i
$987$	5.14531	+	11.2667i	0.00521308	+	0.0114151i
$988$	−227.754			−0.230520
$989$	−1083.26	+	1005.23i	−1.09530	+	1.01641i
$990$	−45.1967	−	31.7214i	−0.0456532	−	0.0320418i
$991$	−345.439	−	756.406i	−0.348576	−	0.763276i	−0.999990	−	0.00455253i	$-0.998551\pi$
$991$	−345.439	−	756.406i	−0.348576	−	0.763276i	0.651413	−	0.758723i	$-0.274176\pi$
$992$	72.1025	+	245.559i	0.0726840	+	0.247539i
$993$	−4.35617	−	3.77464i	−0.00438688	−	0.00380125i
$994$	−350.975	+	546.127i	−0.353093	+	0.549424i
$995$	1168.08	−	119.595i	1.17395	−	0.120196i
$996$	2.03234	−	0.292207i	0.00204050	−	0.000293380i
$997$	−12.5448	+	42.7237i	−0.0125826	+	0.0428523i	−0.965545	−	0.260236i	$-0.916200\pi$
$997$	−12.5448	+	42.7237i	−0.0125826	+	0.0428523i	0.952962	+	0.303088i	$0.0980178\pi$
$998$	140.925	+	219.284i	0.141208	+	0.219723i
$999$	8.72869	+	1.25500i	0.00873743	+	0.00125625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.i.a.19.19	yes	240
5.4	even	2	inner	230.3.i.a.19.6	✓	240
23.17	odd	22	inner	230.3.i.a.109.6	yes	240
115.109	odd	22	inner	230.3.i.a.109.19	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.i.a.19.6	✓	240	5.4	even	2	inner
230.3.i.a.19.19	yes	240	1.1	even	1	trivial
230.3.i.a.109.6	yes	240	23.17	odd	22	inner
230.3.i.a.109.19	yes	240	115.109	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.i (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28641 - 0.587486i) q^{2} +(0.00972304 + 0.0331137i) q^{3} +(1.30972 - 1.51150i) q^{4} +(1.88998 + 4.62904i) q^{5} +(0.0319617 + 0.0368857i) q^{6} +(-0.869641 - 6.04849i) q^{7} +(0.796860 - 2.71386i) q^{8} +(7.57028 - 4.86512i) q^{9} +O(q^{10})\)	\(q+(1.28641 - 0.587486i) q^{2} +(0.00972304 + 0.0331137i) q^{3} +(1.30972 - 1.51150i) q^{4} +(1.88998 + 4.62904i) q^{5} +(0.0319617 + 0.0368857i) q^{6} +(-0.869641 - 6.04849i) q^{7} +(0.796860 - 2.71386i) q^{8} +(7.57028 - 4.86512i) q^{9} +(5.15079 + 4.84452i) q^{10} +(-0.789357 - 0.360487i) q^{11} +(0.0627857 + 0.0286733i) q^{12} +(12.0743 + 1.73602i) q^{13} +(-4.67212 - 7.26996i) q^{14} +(-0.134908 + 0.107592i) q^{15} +(-0.569259 - 3.95929i) q^{16} +(19.6346 + 22.6595i) q^{17} +(6.88032 - 10.7060i) q^{18} +(-7.05521 - 6.11337i) q^{19} +(9.47213 + 3.20605i) q^{20} +(0.191832 - 0.0876067i) q^{21} -1.22722 q^{22} +(20.5841 - 10.2614i) q^{23} +0.0976136 q^{24} +(-17.8560 + 17.4975i) q^{25} +(16.5524 - 4.86022i) q^{26} +(0.469447 + 0.406778i) q^{27} +(-10.2813 - 6.60737i) q^{28} +(-13.1874 - 15.2191i) q^{29} +(-0.110339 + 0.217665i) q^{30} +(-43.4091 - 12.7460i) q^{31} +(-3.05833 - 4.75885i) q^{32} +(0.00426210 - 0.0296435i) q^{33} +(38.5703 + 17.6145i) q^{34} +(26.3551 - 15.4571i) q^{35} +(2.56133 - 17.8144i) q^{36} +(11.9429 - 7.67524i) q^{37} +(-12.6674 - 3.71949i) q^{38} +(0.0599128 + 0.416703i) q^{39} +(14.0686 - 1.44043i) q^{40} +(-45.5878 - 29.2975i) q^{41} +(0.195308 - 0.225397i) q^{42} +(-61.6500 + 18.1021i) q^{43} +(-1.57871 + 0.720974i) q^{44} +(36.8285 + 25.8481i) q^{45} +(20.4513 - 25.2932i) q^{46} +58.7319i q^{47} +(0.125571 - 0.0573466i) q^{48} +(11.1872 - 3.28487i) q^{49} +(-12.6906 + 32.9992i) q^{50} +(-0.559431 + 0.870491i) q^{51} +(18.4379 - 15.9765i) q^{52} +(0.467135 + 3.24899i) q^{53} +(0.842880 + 0.247492i) q^{54} +(0.176843 - 4.33528i) q^{55} +(-17.1077 - 2.45972i) q^{56} +(0.133838 - 0.293064i) q^{57} +(-25.9055 - 11.8307i) q^{58} +(-15.7619 + 109.627i) q^{59} +(-0.0140661 + 0.344829i) q^{60} +(-26.5531 + 90.4315i) q^{61} +(-63.3301 + 9.10550i) q^{62} +(-36.0101 - 41.5578i) q^{63} +(-6.73003 - 4.32513i) q^{64} +(14.7840 + 59.1733i) q^{65} +(-0.0119323 - 0.0406378i) q^{66} +(-16.7830 - 36.7496i) q^{67} +59.9656 q^{68} +(0.539931 + 0.581843i) q^{69} +(24.8227 - 35.3675i) q^{70} +(-31.2064 - 68.3326i) q^{71} +(-7.17079 - 24.4215i) q^{72} +(-66.0949 - 57.2715i) q^{73} +(10.8544 - 16.8898i) q^{74} +(-0.753022 - 0.421147i) q^{75} +(-18.4807 + 2.65713i) q^{76} +(-1.49394 + 5.08791i) q^{77} +(0.321879 + 0.500854i) q^{78} +(66.1445 + 9.51014i) q^{79} +(17.2518 - 10.1181i) q^{80} +(33.6353 - 73.6509i) q^{81} +(-75.8566 - 10.9065i) q^{82} +(25.0249 - 16.0825i) q^{83} +(0.118829 - 0.404694i) q^{84} +(-67.7827 + 133.715i) q^{85} +(-68.6727 + 59.5052i) q^{86} +(0.375739 - 0.584661i) q^{87} +(-1.60732 + 1.85494i) q^{88} +(4.94644 + 16.8460i) q^{89} +(62.5621 + 11.6152i) q^{90} -74.5408i q^{91} +(11.4494 - 44.5523i) q^{92} -1.56136i q^{93} +(34.5042 + 75.5536i) q^{94} +(14.9649 - 44.2130i) q^{95} +(0.127847 - 0.147543i) q^{96} +(112.999 + 72.6201i) q^{97} +(12.4616 - 10.7980i) q^{98} +(-7.72947 + 1.11133i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 48 q^{4} - 8 q^{6} + 96 q^{9}+O(q^{10}) \) 240 * q + 48 * q^4 - 8 * q^6 + 96 * q^9	\( 240 q + 48 q^{4} - 8 q^{6} + 96 q^{9} + 154 q^{15} - 96 q^{16} + 44 q^{20} + 16 q^{24} - 84 q^{25} + 32 q^{26} - 100 q^{29} - 352 q^{30} + 124 q^{31} + 28 q^{35} - 192 q^{36} + 72 q^{39} + 116 q^{41} - 148 q^{46} - 188 q^{49} + 144 q^{50} + 324 q^{54} + 796 q^{55} - 264 q^{56} + 400 q^{59} + 176 q^{60} - 616 q^{61} + 192 q^{64} + 462 q^{65} - 176 q^{66} + 120 q^{69} - 504 q^{70} + 464 q^{71} - 528 q^{74} - 934 q^{75} - 968 q^{79} - 264 q^{80} + 664 q^{81} - 352 q^{84} - 1196 q^{85} + 396 q^{86} + 376 q^{94} + 126 q^{95} - 32 q^{96} - 3300 q^{99}+O(q^{100}) \) 240 * q + 48 * q^4 - 8 * q^6 + 96 * q^9 + 154 * q^15 - 96 * q^16 + 44 * q^20 + 16 * q^24 - 84 * q^25 + 32 * q^26 - 100 * q^29 - 352 * q^30 + 124 * q^31 + 28 * q^35 - 192 * q^36 + 72 * q^39 + 116 * q^41 - 148 * q^46 - 188 * q^49 + 144 * q^50 + 324 * q^54 + 796 * q^55 - 264 * q^56 + 400 * q^59 + 176 * q^60 - 616 * q^61 + 192 * q^64 + 462 * q^65 - 176 * q^66 + 120 * q^69 - 504 * q^70 + 464 * q^71 - 528 * q^74 - 934 * q^75 - 968 * q^79 - 264 * q^80 + 664 * q^81 - 352 * q^84 - 1196 * q^85 + 396 * q^86 + 376 * q^94 + 126 * q^95 - 32 * q^96 - 3300 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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