LMFDB - Embedded newform 100.9.j.b.91.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,9,Mod(11,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("100.11");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.j (of order $10$, 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:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			91.15
Character	$\chi$	$=$	100.91
Dual form			100.9.j.b.11.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-14.9394 + 5.72837i) q^{2} +(-148.141 + 48.1341i) q^{3} +(190.372 - 171.157i) q^{4} +(-603.811 - 161.359i) q^{5} +(1937.42 - 1567.70i) q^{6} -2832.14i q^{7} +(-1863.59 + 3647.50i) q^{8} +(14321.0 - 10404.8i) q^{9} +(9944.91 - 1048.25i) q^{10} +(9819.91 - 13516.0i) q^{11} +(-19963.5 + 34518.8i) q^{12} +(-30680.3 + 22290.6i) q^{13} +(16223.5 + 42310.5i) q^{14} +(97216.4 - 5159.98i) q^{15} +(6946.74 - 65166.8i) q^{16} +(-2696.77 + 8299.81i) q^{17} +(-154345. + 237478. i) q^{18} +(-85818.9 - 27884.2i) q^{19} +(-142566. + 72628.3i) q^{20} +(136323. + 419558. i) q^{21} +(-69279.4 + 258172. i) q^{22} +(164536. - 226464. i) q^{23} +(100506. - 630048. i) q^{24} +(338552. + 194861. i) q^{25} +(330657. - 508756. i) q^{26} +(-1.02001e6 + 1.40392e6i) q^{27} +(-484740. - 539160. i) q^{28} +(169918. + 522954. i) q^{29} +(-1.42280e6 + 633978. i) q^{30} +(1.00917e6 + 327900. i) q^{31} +(269519. + 1.01335e6i) q^{32} +(-804159. + 2.47495e6i) q^{33} +(-7256.17 - 139442. i) q^{34} +(-456991. + 1.71008e6i) q^{35} +(945461. - 4.43193e6i) q^{36} +(-242445. + 176147. i) q^{37} +(1.44181e6 - 75027.8i) q^{38} +(3.47209e6 - 4.77893e6i) q^{39} +(1.71381e6 - 1.90169e6i) q^{40} +(897684. - 652206. i) q^{41} +(-4.43996e6 - 5.48704e6i) q^{42} -2.64599e6i q^{43} +(-443913. - 4.25380e6i) q^{44} +(-1.03261e7 + 3.97174e6i) q^{45} +(-1.16080e6 + 4.32576e6i) q^{46} +(8.28897e6 - 2.69325e6i) q^{47} +(2.10764e6 + 9.98828e6i) q^{48} -2.25623e6 q^{49} +(-6.17399e6 - 971755. i) q^{50} -1.35935e6i q^{51} +(-2.02549e6 + 9.49464e6i) q^{52} +(-3.37059e6 - 1.03736e7i) q^{53} +(7.19616e6 - 2.68168e7i) q^{54} +(-8.11029e6 + 6.57656e6i) q^{55} +(1.03302e7 + 5.27796e6i) q^{56} +1.40555e7 q^{57} +(-5.53415e6 - 6.83927e6i) q^{58} +(-5.53162e6 - 7.61362e6i) q^{59} +(1.76241e7 - 1.76216e7i) q^{60} +(9.37962e6 + 6.81469e6i) q^{61} +(-1.69548e7 + 882278. i) q^{62} +(-2.94680e7 - 4.05592e7i) q^{63} +(-9.83127e6 - 1.35949e7i) q^{64} +(2.21219e7 - 8.50876e6i) q^{65} +(-2.16374e6 - 4.15807e7i) q^{66} +(3.05075e7 + 9.91248e6i) q^{67} +(907179. + 2.04162e6i) q^{68} +(-1.34739e7 + 4.14685e7i) q^{69} +(-2.96879e6 - 2.81654e7i) q^{70} +(-1.48358e7 + 4.82046e6i) q^{71} +(1.12631e7 + 7.16264e7i) q^{72} +(2.26474e7 + 1.64543e7i) q^{73} +(2.61295e6 - 4.02034e6i) q^{74} +(-5.95330e7 - 1.25711e7i) q^{75} +(-2.11101e7 + 9.38011e6i) q^{76} +(-3.82791e7 - 2.78114e7i) q^{77} +(-2.44956e7 + 9.12838e7i) q^{78} +(5.24907e6 - 1.70553e6i) q^{79} +(-1.47098e7 + 3.82275e7i) q^{80} +(4.76396e7 - 1.46620e8i) q^{81} +(-9.67480e6 + 1.48858e7i) q^{82} +(-1.16854e7 - 3.79683e6i) q^{83} +(9.77621e7 + 5.65394e7i) q^{84} +(2.96759e6 - 4.57637e6i) q^{85} +(1.51572e7 + 3.95296e7i) q^{86} +(-5.03439e7 - 6.92924e7i) q^{87} +(3.09991e7 + 6.10063e7i) q^{88} +(-6.20573e7 - 4.50872e7i) q^{89} +(1.31515e8 - 1.18487e8i) q^{90} +(6.31301e7 + 8.68911e7i) q^{91} +(-7.43790e6 - 7.12738e7i) q^{92} -1.65284e8 q^{93} +(-1.08404e8 + 8.77178e7i) q^{94} +(4.73190e7 + 3.06845e7i) q^{95} +(-8.87034e7 - 1.37146e8i) q^{96} +(2.85197e7 + 8.77746e7i) q^{97} +(3.37067e7 - 1.29245e7i) q^{98} -2.95737e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) $ 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−14.9394	+	5.72837i	−0.933713	+	0.358023i
$2$	−14.9394	+	5.72837i	−0.933713	+	0.358023i
$3$	−148.141	+	48.1341i	−1.82891	+	0.594248i	−0.829549	+	0.558435i	$0.811402\pi$
$3$	−148.141	+	48.1341i	−1.82891	+	0.594248i	−0.999358	+	0.0358133i	$0.988598\pi$
$4$	190.372	−	171.157i	0.743639	−	0.668581i
$5$	−603.811	−	161.359i	−0.966098	−	0.258174i
$5$	−603.811	−	161.359i	−0.966098	−	0.258174i
$6$	1937.42	−	1567.70i	1.49492	−	1.20965i
$7$		−	2832.14i		−	1.17957i	−0.807561	−	0.589784i	$-0.799213\pi$
$7$		−	2832.14i		−	1.17957i	0.807561	−	0.589784i	$-0.200787\pi$
$8$	−1863.59	+	3647.50i	−0.454978	+	0.890503i
$9$	14321.0	−	10404.8i	2.18275	−	1.58586i
$10$	9944.91	−	1048.25i	0.994491	−	0.104825i
$11$	9819.91	−	13516.0i	0.670713	−	0.923158i	−0.329063	−	0.944308i	$-0.606733\pi$
$11$	9819.91	−	13516.0i	0.670713	−	0.923158i	0.999776	+	0.0211503i	$0.00673285\pi$
$12$	−19963.5	+	34518.8i	−0.962744	+	1.66468i
$13$	−30680.3	+	22290.6i	−1.07420	+	0.780455i	−0.976663	−	0.214777i	$-0.931098\pi$
$13$	−30680.3	+	22290.6i	−1.07420	+	0.780455i	−0.0975407	+	0.995232i	$0.531098\pi$
$14$	16223.5	+	42310.5i	0.422312	+	1.10138i
$15$	97216.4	−	5159.98i	1.92032	−	0.101925i
$16$	6946.74	−	65166.8i	0.105999	−	0.994366i
$17$	−2696.77	+	8299.81i	−0.0322885	+	0.0993739i	−0.965902	−	0.258908i	$-0.916637\pi$
$17$	−2696.77	+	8299.81i	−0.0322885	+	0.0993739i	0.933613	+	0.358282i	$0.116637\pi$
$18$	−154345.	+	237478.i	−1.47029	+	2.26222i
$19$	−85818.9	−	27884.2i	−0.658519	−	0.213966i	−0.0393523	−	0.999225i	$-0.512529\pi$
$19$	−85818.9	−	27884.2i	−0.658519	−	0.213966i	−0.619167	+	0.785260i	$0.712529\pi$
$20$	−142566.	+	72628.3i	−0.891039	+	0.453927i
$21$	136323.	+	419558.i	0.700956	+	2.15732i
$22$	−69279.4	+	258172.i	−0.295742	+	1.10209i
$23$	164536.	−	226464.i	0.587962	−	0.809260i	−0.406578	−	0.913616i	$-0.633278\pi$
$23$	164536.	−	226464.i	0.587962	−	0.809260i	0.994540	+	0.104356i	$0.0332782\pi$
$24$	100506.	−	630048.i	0.302934	−	1.89902i
$25$	338552.	+	194861.i	0.866692	+	0.498843i
$26$	330657.	−	508756.i	0.723577	−	1.11331i
$27$	−1.02001e6	+	1.40392e6i	−1.91933	+	2.64173i
$28$	−484740.	−	539160.i	−0.788637	−	0.877173i
$29$	169918.	+	522954.i	0.240241	+	0.739387i	0.996383	+	0.0849787i	$0.0270822\pi$
$29$	169918.	+	522954.i	0.240241	+	0.739387i	−0.756141	+	0.654408i	$0.772918\pi$
$30$	−1.42280e6	+	633978.i	−1.75654	+	0.782689i
$31$	1.00917e6	+	327900.i	1.09275	+	0.355055i	0.799307	−	0.600923i	$-0.205200\pi$
$31$	1.00917e6	+	327900.i	1.09275	+	0.355055i	0.293439	+	0.955978i	$0.405200\pi$
$32$	269519.	+	1.01335e6i	0.257033	+	0.966403i
$33$	−804159.	+	2.47495e6i	−0.678088	+	2.08694i
$34$	−7256.17	−	139442.i	−0.00542990	−	0.104347i
$35$	−456991.	+	1.71008e6i	−0.304534	+	1.13958i
$36$	945461.	−	4.43193e6i	0.562903	−	2.63866i
$37$	−242445.	+	176147.i	−0.129362	+	0.0939869i	−0.650585	−	0.759434i	$-0.725476\pi$
$37$	−242445.	+	176147.i	−0.129362	+	0.0939869i	0.521223	+	0.853421i	$0.325476\pi$
$38$	1.44181e6	−	75027.8i	0.691472	−	0.0359822i
$39$	3.47209e6	−	4.77893e6i	1.50084	−	2.06572i
$40$	1.71381e6	−	1.90169e6i	0.669459	−	0.742849i
$41$	897684.	−	652206.i	0.317679	−	0.230807i	−0.417506	−	0.908674i	$-0.637096\pi$
$41$	897684.	−	652206.i	0.317679	−	0.230807i	0.735184	+	0.677867i	$0.237096\pi$
$42$	−4.43996e6	−	5.48704e6i	−1.42686	−	1.76336i
$43$		−	2.64599e6i		−	0.773953i	−0.922089	−	0.386977i	$-0.873519\pi$
$43$		−	2.64599e6i		−	0.773953i	0.922089	−	0.386977i	$-0.126481\pi$
$44$	−443913.	−	4.25380e6i	−0.118437	−	1.13492i
$45$	−1.03261e7	+	3.97174e6i	−2.51818	+	0.968569i
$46$	−1.16080e6	+	4.32576e6i	−0.259254	+	0.966120i
$47$	8.28897e6	−	2.69325e6i	1.69867	−	0.551932i	0.710287	−	0.703912i	$-0.248565\pi$
$47$	8.28897e6	−	2.69325e6i	1.69867	−	0.551932i	0.988383	+	0.151981i	$0.0485651\pi$
$48$	2.10764e6	+	9.98828e6i	0.397038	+	1.88159i
$49$	−2.25623e6			−0.391380
$50$	−6.17399e6	−	971755.i	−0.987839	−	0.155481i
$51$		−	1.35935e6i		−	0.200933i
$52$	−2.02549e6	+	9.49464e6i	−0.277023	+	1.29857i
$53$	−3.37059e6	−	1.03736e7i	−0.427172	−	1.31470i	−0.900899	−	0.434029i	$-0.857092\pi$
$53$	−3.37059e6	−	1.03736e7i	−0.427172	−	1.31470i	0.473727	−	0.880672i	$-0.342908\pi$
$54$	7.19616e6	−	2.68168e7i	0.846303	−	3.15378i
$55$	−8.11029e6	+	6.57656e6i	−0.886310	+	0.718700i
$56$	1.03302e7	+	5.27796e6i	1.05041	+	0.536678i
$57$	1.40555e7			1.33152
$58$	−5.53415e6	−	6.83927e6i	−0.489034	−	0.604363i
$59$	−5.53162e6	−	7.61362e6i	−0.456503	−	0.628323i	0.517276	−	0.855819i	$-0.326946\pi$
$59$	−5.53162e6	−	7.61362e6i	−0.456503	−	0.628323i	−0.973779	+	0.227496i	$0.926946\pi$
$60$	1.76241e7	−	1.76216e7i	1.35988	−	1.35969i
$61$	9.37962e6	+	6.81469e6i	0.677432	+	0.492183i	0.872505	−	0.488606i	$-0.162494\pi$
$61$	9.37962e6	+	6.81469e6i	0.677432	+	0.492183i	−0.195073	+	0.980789i	$0.562494\pi$
$62$	−1.69548e7	+	882278.i	−1.14743	+	0.0597088i
$63$	−2.94680e7	−	4.05592e7i	−1.87063	−	2.57471i
$64$	−9.83127e6	−	1.35949e7i	−0.585989	−	0.810319i
$65$	2.21219e7	−	8.50876e6i	1.23928	−	0.476664i
$66$	−2.16374e6	−	4.15807e7i	−0.114033	−	2.19137i
$67$	3.05075e7	+	9.91248e6i	1.51393	+	0.491907i	0.944046	−	0.329815i	$-0.106986\pi$
$67$	3.05075e7	+	9.91248e6i	1.51393	+	0.491907i	0.569888	+	0.821722i	$0.306986\pi$
$68$	907179.	+	2.04162e6i	0.0424285	+	0.0954858i
$69$	−1.34739e7	+	4.14685e7i	−0.594426	+	1.82946i
$70$	−2.96879e6	−	2.81654e7i	−0.123648	−	1.17307i
$71$	−1.48358e7	+	4.82046e6i	−0.583820	+	0.189695i	−0.586011	−	0.810303i	$-0.699302\pi$
$71$	−1.48358e7	+	4.82046e6i	−0.583820	+	0.189695i	0.00219130	+	0.999998i	$0.499302\pi$
$72$	1.12631e7	+	7.16264e7i	0.419110	+	2.66528i
$73$	2.26474e7	+	1.64543e7i	0.797492	+	0.579412i	0.910177	−	0.414219i	$-0.135945\pi$
$73$	2.26474e7	+	1.64543e7i	0.797492	+	0.579412i	−0.112685	+	0.993631i	$0.535945\pi$
$74$	2.61295e6	−	4.02034e6i	0.0871374	−	0.134071i
$75$	−5.95330e7	−	1.25711e7i	−1.88154	−	0.397308i
$76$	−2.11101e7	+	9.38011e6i	−0.632754	+	0.281160i
$77$	−3.82791e7	−	2.78114e7i	−1.08893	−	0.791152i
$78$	−2.44956e7	+	9.12838e7i	−0.661773	+	2.46613i
$79$	5.24907e6	−	1.70553e6i	0.134764	−	0.0437875i	−0.240858	−	0.970560i	$-0.577429\pi$
$79$	5.24907e6	−	1.70553e6i	0.134764	−	0.0437875i	0.375622	+	0.926773i	$0.377429\pi$
$80$	−1.47098e7	+	3.82275e7i	−0.359125	+	0.933289i
$81$	4.76396e7	−	1.46620e8i	1.10670	−	3.40606i
$82$	−9.67480e6	+	1.48858e7i	−0.213987	+	0.329244i
$83$	−1.16854e7	−	3.79683e6i	−0.246225	−	0.0800035i	0.183304	−	0.983056i	$-0.441321\pi$
$83$	−1.16854e7	−	3.79683e6i	−0.246225	−	0.0800035i	−0.429530	+	0.903053i	$0.641321\pi$
$84$	9.77621e7	+	5.65394e7i	1.96360	+	1.13562i
$85$	2.96759e6	−	4.57637e6i	0.0568497	−	0.0876689i
$86$	1.51572e7	+	3.95296e7i	0.277093	+	0.722650i
$87$	−5.03439e7	−	6.92924e7i	−0.878758	−	1.20951i
$88$	3.09991e7	+	6.10063e7i	0.516914	+	1.01729i
$89$	−6.20573e7	−	4.50872e7i	−0.989083	−	0.718611i	−0.0293628	−	0.999569i	$-0.509348\pi$
$89$	−6.20573e7	−	4.50872e7i	−0.989083	−	0.718611i	−0.959720	+	0.280958i	$0.909348\pi$
$90$	1.31515e8	−	1.18487e8i	2.00449	−	1.80593i
$91$	6.31301e7	+	8.68911e7i	0.920599	+	1.26710i
$92$	−7.43790e6	−	7.12738e7i	−0.103824	−	0.994897i
$93$	−1.65284e8			−2.20952
$94$	−1.08404e8	+	8.77178e7i	−1.38847	+	1.12351i
$95$	4.73190e7	+	3.06845e7i	0.580954	+	0.376725i
$96$	−8.87034e7	−	1.37146e8i	−1.04437	−	1.61472i
$97$	2.85197e7	+	8.77746e7i	0.322150	+	0.991475i	0.972711	+	0.232021i	$0.0745338\pi$
$97$	2.85197e7	+	8.77746e7i	0.322150	+	0.991475i	−0.650561	+	0.759454i	$0.725466\pi$
$98$	3.37067e7	−	1.29245e7i	0.365436	−	0.140123i
$99$		−	2.95737e8i		−	3.07868i
$100$	9.78024e7	−	2.08495e7i	0.978024	−	0.208495i
$101$	1.42373e8			1.36818			0.684088	−	0.729400i	$-0.260201\pi$
$101$	1.42373e8			1.36818			0.684088	+	0.729400i	$0.260201\pi$
$102$	7.78687e6	+	2.03079e7i	0.0719386	+	0.187614i
$103$	1.70194e7	−	5.52995e6i	0.151215	−	0.0491329i	−0.232431	−	0.972613i	$-0.574668\pi$
$103$	1.70194e7	−	5.52995e6i	0.151215	−	0.0491329i	0.383647	+	0.923480i	$0.374668\pi$
$104$	−2.41292e7	−	1.53447e8i	−0.206257	−	1.31167i
$105$	−1.46138e7	−	2.75331e8i	−0.120228	−	2.26515i
$106$	1.09779e8	+	1.35668e8i	0.869549	+	1.07462i
$107$		−	1.64807e8i		−	1.25731i	−0.777685	−	0.628654i	$-0.783606\pi$
$107$		−	1.64807e8i		−	1.25731i	0.777685	−	0.628654i	$-0.216394\pi$
$108$	4.61100e7	+	4.41849e8i	0.338922	+	3.24772i
$109$	2.10510e6	−	1.52945e6i	0.0149131	−	0.0108350i	−0.580304	−	0.814400i	$-0.697066\pi$
$109$	2.10510e6	−	1.52945e6i	0.0149131	−	0.0108350i	0.595217	+	0.803565i	$0.297066\pi$
$110$	8.34901e7	−	1.44709e8i	0.570248	−	0.988379i
$111$	2.74375e7	−	3.77645e7i	0.180739	−	0.248766i
$112$	−1.84562e8	−	1.96742e7i	−1.17292	−	0.125033i
$113$	−9.20741e7	+	6.68958e7i	−0.564708	+	0.410284i	−0.833179	−	0.553003i	$-0.813482\pi$
$113$	−9.20741e7	+	6.68958e7i	−0.564708	+	0.410284i	0.268471	+	0.963288i	$0.413482\pi$
$114$	−2.09981e8	+	8.05151e7i	−1.24326	+	0.476714i
$115$	−1.35891e8	+	1.10192e8i	−0.776959	+	0.630028i
$116$	1.21855e8	+	7.04731e7i	0.672993	+	0.389216i
$117$	−2.07444e8	+	6.38448e8i	−1.10703	+	3.40708i
$118$	1.26253e8	+	8.20558e7i	0.651197	+	0.423235i
$119$	2.35062e7	+	7.63764e6i	0.117218	+	0.0380865i
$120$	−1.62351e8	+	3.64213e8i	−0.782941	+	1.75643i
$121$	−2.00097e7	−	6.15835e7i	−0.0933467	−	0.287292i
$122$	−1.79163e8	−	4.80776e7i	−0.808740	−	0.217022i
$123$	−1.01591e8	+	1.39828e8i	−0.443848	+	0.610905i
$124$	2.48240e8	−	1.10304e8i	1.04999	−	0.466556i
$125$	−1.72979e8	−	1.72287e8i	−0.708522	−	0.705689i
$126$	6.72573e8	+	4.37127e8i	2.66844	+	1.73431i
$127$	−1.65093e8	+	2.27232e8i	−0.634621	+	0.873481i	−0.998314	−	0.0580375i	$-0.981516\pi$
$127$	−1.65093e8	+	2.27232e8i	−0.634621	+	0.873481i	0.363693	+	0.931519i	$0.381516\pi$
$128$	2.24750e8	+	1.46782e8i	0.837258	+	0.546807i
$129$	1.27362e8	+	3.91981e8i	0.459920	+	1.41549i
$130$	−2.81747e8	+	2.53838e8i	−0.986475	+	0.888758i
$131$	1.17996e8	+	3.83393e7i	0.400666	+	0.130184i	0.502417	−	0.864626i	$-0.332444\pi$
$131$	1.17996e8	+	3.83393e7i	0.400666	+	0.130184i	−0.101750	+	0.994810i	$0.532444\pi$
$132$	2.70515e8	+	6.08797e8i	0.891035	+	2.00529i
$133$	−7.89721e7	+	2.43051e8i	−0.252387	+	0.776768i
$134$	−5.12546e8	+	2.66714e7i	−1.58969	+	0.0827231i
$135$	8.42430e8	−	6.83118e8i	2.53629	−	2.05665i
$136$	−2.52479e7	−	2.53039e7i	−0.0738021	−	0.0739660i
$137$	2.72017e8	−	1.97632e8i	0.772173	−	0.561016i	−0.130447	−	0.991455i	$-0.541641\pi$
$137$	2.72017e8	−	1.97632e8i	0.772173	−	0.561016i	0.902620	+	0.430439i	$0.141641\pi$
$138$	−3.62542e7	−	6.96698e8i	−0.0999635	−	1.92100i
$139$	1.75546e8	−	2.41618e8i	0.470253	−	0.647248i	−0.506342	−	0.862333i	$-0.669003\pi$
$139$	1.75546e8	−	2.41618e8i	0.470253	−	0.647248i	0.976595	+	0.215085i	$0.0690027\pi$
$140$	2.05694e8	+	4.03768e8i	0.535437	+	1.05104i
$141$	−1.09830e9	+	7.97964e8i	−2.77873	+	2.01886i
$142$	1.94025e8	−	1.57000e8i	0.477205	−	0.386141i
$143$			6.33565e8i			1.51512i
$144$	−5.78566e8	−	1.00554e9i	−1.34556	−	2.33856i
$145$	−1.82152e7	−	3.43184e8i	−0.0412062	−	0.776345i
$146$	−4.32594e8	−	1.16085e8i	−0.952071	−	0.255484i
$147$	3.34241e8	−	1.08601e8i	0.715798	−	0.232577i
$148$	−1.60060e7	+	7.50294e7i	−0.0333607	+	0.156381i
$149$	−4.42170e8			−0.897107			−0.448553	−	0.893756i	$-0.648061\pi$
$149$	−4.42170e8			−0.897107			−0.448553	+	0.893756i	$0.648061\pi$
$150$	9.61399e8	−	1.53222e8i	1.89906	−	0.302661i
$151$		−	6.47139e8i		−	1.24477i	−0.782711	−	0.622386i	$-0.786164\pi$
$151$		−	6.47139e8i		−	1.24477i	0.782711	−	0.622386i	$-0.213836\pi$
$152$	2.61639e8	−	2.61059e8i	0.490149	−	0.489063i
$153$	4.77377e7	+	1.46921e8i	0.0871155	+	0.268114i
$154$	7.31181e8	+	1.96209e8i	1.30000	+	0.348848i
$155$	−5.56441e8	−	3.60829e8i	−0.964034	−	0.625136i
$156$	−1.56957e8	−	1.50404e9i	−0.265023	−	2.53958i
$157$	2.12221e8			0.349294			0.174647	−	0.984631i	$-0.444122\pi$
$157$	2.12221e8			0.349294			0.174647	+	0.984631i	$0.444122\pi$
$158$	−6.86481e7	+	5.55481e7i	−0.110154	+	0.0891335i
$159$	9.98649e8	+	1.37452e9i	1.56252	+	2.15062i
$160$	773796.	−	6.55360e8i	0.00118072	−	0.999999i
$161$	−6.41378e8	−	4.65989e8i	−0.954577	−	0.693541i
$162$	1.28183e8	+	2.46331e9i	0.186111	+	3.57650i
$163$	−4.58259e8	−	6.30739e8i	−0.649173	−	0.893510i	0.349890	−	0.936791i	$-0.386219\pi$
$163$	−4.58259e8	−	6.30739e8i	−0.649173	−	0.893510i	−0.999063	+	0.0432809i	$0.986219\pi$
$164$	5.92642e7	−	2.77806e8i	0.0819252	−	0.384031i
$165$	8.84914e8	−	1.36464e9i	1.19389	−	1.84112i
$166$	1.96323e8	−	1.02161e7i	0.258547	−	0.0134540i
$167$	2.29074e8	+	7.44307e7i	0.294517	+	0.0956943i	0.452549	−	0.891740i	$-0.350515\pi$
$167$	2.29074e8	+	7.44307e7i	0.294517	+	0.0956943i	−0.158032	+	0.987434i	$0.550515\pi$
$168$	−1.78439e9	−	2.84648e8i	−2.24002	−	0.357331i
$169$	1.92339e8	−	5.91958e8i	0.235787	−	0.725679i
$170$	−1.81189e7	+	8.53677e7i	−0.0216938	+	0.102211i
$171$	−1.51915e9	+	4.93601e8i	−1.77670	+	0.577286i
$172$	−4.52880e8	−	5.03722e8i	−0.517451	−	0.575542i
$173$	−1.05883e9	−	7.69287e8i	−1.18207	−	0.858824i	−0.189666	−	0.981849i	$-0.560741\pi$
$173$	−1.05883e9	−	7.69287e8i	−1.18207	−	0.858824i	−0.992404	+	0.123024i	$0.960741\pi$
$174$	1.14904e9	+	7.46799e8i	1.25354	+	0.814717i
$175$	5.51873e8	−	9.58826e8i	0.588419	−	1.02232i
$176$	−8.12575e8	−	7.33824e8i	−0.846862	−	0.764788i
$177$	1.18594e9	+	8.61633e8i	1.20828	+	0.877868i
$178$	1.18538e9	+	3.18090e8i	1.18080	+	0.316862i
$179$	1.40365e9	−	4.56074e8i	1.36725	−	0.444246i	0.468791	−	0.883309i	$-0.344690\pi$
$179$	1.40365e9	−	4.56074e8i	1.36725	−	0.444246i	0.898456	+	0.439063i	$0.144690\pi$
$180$	−1.28601e9	+	2.52349e9i	−1.22505	+	2.40388i
$181$	2.02415e8	−	6.22969e8i	0.188594	−	0.580433i	−0.811398	−	0.584495i	$-0.801293\pi$
$181$	2.02415e8	−	6.22969e8i	0.188594	−	0.580433i	0.999992	+	0.00406146i	$0.00129281\pi$
$182$	−1.44087e9	−	9.36469e8i	−1.31322	−	0.853508i
$183$	−1.71753e9	−	5.58059e8i	−1.53144	−	0.497595i
$184$	5.19400e8	+	1.02218e9i	0.453138	+	0.891777i
$185$	1.74814e8	−	6.72387e7i	0.149241	−	0.0574027i
$186$	2.46924e9	−	9.46805e8i	2.06306	−	0.791059i
$187$	8.56977e7	+	1.17953e8i	0.0700814	+	0.0964588i
$188$	1.11702e9	−	1.93143e9i	0.894187	−	1.54614i
$189$	3.97611e9	+	2.88882e9i	3.11610	+	2.26398i
$190$	−8.82690e8	−	1.87347e8i	−0.677320	−	0.143758i
$191$	−4.37448e8	−	6.02096e8i	−0.328695	−	0.452410i	0.612402	−	0.790546i	$-0.290203\pi$
$191$	−4.37448e8	−	6.02096e8i	−0.328695	−	0.452410i	−0.941097	+	0.338137i	$0.890203\pi$
$192$	2.11080e9	+	1.54075e9i	1.55325	+	1.13377i
$193$	−1.30428e9			−0.940032			−0.470016	−	0.882658i	$-0.655752\pi$
$193$	−1.30428e9			−0.940032			−0.470016	+	0.882658i	$0.655752\pi$
$194$	−9.28872e8	−	1.14793e9i	−0.655766	−	0.810416i
$195$	−2.86761e9	+	2.32532e9i	−1.98327	+	1.60821i
$196$	−4.29522e8	+	3.86169e8i	−0.291046	+	0.261669i
$197$	−3.73776e8	−	1.15036e9i	−0.248168	−	0.763784i	−0.995099	−	0.0988819i	$-0.968473\pi$
$197$	−3.73776e8	−	1.15036e9i	−0.248168	−	0.763784i	0.746931	−	0.664902i	$-0.231527\pi$
$198$	1.69409e9	+	4.41814e9i	1.10224	+	2.87461i
$199$		−	2.18491e9i		−	1.39323i	−0.717447	−	0.696613i	$-0.754689\pi$
$199$		−	2.18491e9i		−	1.39323i	0.717447	−	0.696613i	$-0.245311\pi$
$200$	−1.34168e9	+	8.71726e8i	−0.838547	+	0.544829i
$201$	−4.99655e9			−3.06116
$202$	−2.12697e9	+	8.15564e8i	−1.27748	+	0.489838i
$203$	1.48108e9	−	4.81232e8i	0.872157	−	0.283381i
$204$	−2.32662e8	−	2.58782e8i	−0.134340	−	0.149422i
$205$	−6.47271e8	+	2.48960e8i	−0.366497	+	0.140966i
$206$	−2.22583e8	+	1.80108e8i	−0.123601	+	0.100015i
$207$		−	4.95517e9i		−	2.69884i
$208$	1.23948e9	+	2.15419e9i	0.662193	+	1.15088i
$209$	−1.21962e9	+	8.86103e8i	−0.639202	+	0.464407i
$210$	1.79552e9	+	4.02956e9i	0.923234	+	2.07196i
$211$	−1.02549e9	+	1.41147e9i	−0.517372	+	0.712101i	−0.985141	−	0.171750i	$-0.945058\pi$
$211$	−1.02549e9	+	1.41147e9i	−0.517372	+	0.712101i	0.467769	+	0.883851i	$0.345058\pi$
$212$	−2.41718e9	−	1.39794e9i	−1.19665	−	0.692064i
$213$	1.96578e9	−	1.42822e9i	0.955026	−	0.693867i
$214$	9.44077e8	+	2.46212e9i	0.450145	+	1.17396i
$215$	−4.26954e8	+	1.59768e9i	−0.199815	+	0.747715i
$216$	−3.21993e9	−	6.33683e9i	−1.47921	−	2.91110i
$217$	9.28660e8	−	2.85812e9i	0.418811	−	1.28897i
$218$	−2.26878e7	+	3.49078e7i	−0.0100454	+	0.0154560i
$219$	−4.14703e9	−	1.34745e9i	−1.80285	−	0.585782i
$220$	−4.18348e8	+	2.64012e9i	−0.178586	+	1.12702i
$221$	−1.02270e8	−	3.14753e8i	−0.0428724	−	0.131948i
$222$	−1.93571e8	+	7.21351e8i	−0.0796946	+	0.296985i
$223$	1.01684e8	−	1.39957e8i	0.0411183	−	0.0565945i	−0.787963	−	0.615723i	$-0.788864\pi$
$223$	1.01684e8	−	1.39957e8i	0.0411183	−	0.0565945i	0.829081	+	0.559128i	$0.188864\pi$
$224$	2.86994e9	−	7.63316e8i	1.13994	−	0.303188i
$225$	6.87591e9	−	7.31971e8i	2.68287	−	0.285604i
$226$	9.92329e8	−	1.52682e9i	0.380384	−	0.585266i
$227$	9.92415e8	−	1.36594e9i	0.373758	−	0.514433i	−0.580160	−	0.814503i	$-0.697010\pi$
$227$	9.92415e8	−	1.36594e9i	0.373758	−	0.514433i	0.953917	+	0.300069i	$0.0970099\pi$
$228$	2.67577e9	−	2.40570e9i	0.990170	−	0.890228i
$229$	1.00533e9	+	3.09408e9i	0.365566	+	1.12510i	0.949626	+	0.313386i	$0.101463\pi$
$229$	1.00533e9	+	3.09408e9i	0.365566	+	1.12510i	−0.584060	+	0.811710i	$0.698537\pi$
$230$	1.39890e9	−	2.42464e9i	0.499892	−	0.866434i
$231$	7.00940e9	+	2.27749e9i	2.46169	+	0.799850i
$232$	−2.22413e9	−	3.54797e8i	−0.767731	−	0.122470i
$233$	7.67949e8	−	2.36350e9i	0.260561	−	0.801923i	−0.732122	−	0.681173i	$-0.761470\pi$
$233$	7.67949e8	−	2.36350e9i	0.260561	−	0.801923i	0.992683	−	0.120750i	$-0.0385299\pi$
$234$	−5.58169e8	−	1.07264e10i	−0.186167	−	3.57758i
$235$	−5.43956e9	+	2.88717e8i	−1.78358	+	0.0946674i
$236$	−2.35619e9	−	5.02644e8i	−0.759559	−	0.162036i
$237$	−6.95511e8	+	5.05318e8i	−0.220450	+	0.160166i
$238$	−3.94920e8	+	2.05505e7i	−0.123084	+	0.00640494i
$239$	−3.36331e8	+	4.62920e8i	−0.103080	+	0.141878i	−0.857441	−	0.514582i	$-0.827947\pi$
$239$	−3.36331e8	+	4.62920e8i	−0.103080	+	0.141878i	0.754361	+	0.656460i	$0.227947\pi$
$240$	3.39078e8	−	6.37112e9i	0.102201	−	1.92031i
$241$	−2.53516e9	+	1.84190e9i	−0.751514	+	0.546007i	−0.896296	−	0.443457i	$-0.853752\pi$
$241$	−2.53516e9	+	1.84190e9i	−0.751514	+	0.546007i	0.144782	+	0.989464i	$0.453752\pi$
$242$	6.51706e8	+	8.05398e8i	0.190016	+	0.234828i
$243$			1.26279e10i			3.62166i
$244$	2.95199e9	−	3.08061e8i	0.832829	−	0.0869114i
$245$	1.36234e9	+	3.64062e8i	0.378112	+	0.101044i
$246$	7.16723e8	−	2.67090e9i	0.195709	−	0.729317i
$247$	3.25451e9	−	1.05745e9i	0.874374	−	0.284101i
$248$	−3.07670e9	+	3.06989e9i	−0.813353	+	0.811551i
$249$	1.91386e9			0.497865
$250$	3.57113e9	+	1.58298e9i	0.914208	+	0.405244i
$251$			5.74400e9i			1.44717i	0.690236	+	0.723584i	$0.257507\pi$
$251$			5.74400e9i			1.44717i	−0.690236	+	0.723584i	$0.742493\pi$
$252$	−1.25519e10	−	2.67768e9i	−3.11248	−	0.663983i
$253$	−1.44515e9	−	4.44772e9i	−0.352721	−	1.08556i
$254$	1.16473e9	−	4.34042e9i	0.279828	−	1.04279i
$255$	−2.19344e8	+	8.20793e8i	−0.0518757	+	0.194121i
$256$	−4.19845e9	−	9.05394e8i	−0.977528	−	0.210803i
$257$	−4.10372e8			−0.0940688			−0.0470344	−	0.998893i	$-0.514977\pi$
$257$	−4.10372e8			−0.0940688			−0.0470344	+	0.998893i	$0.514977\pi$
$258$	−4.14813e9	−	5.12639e9i	−0.936211	−	1.15700i
$259$	4.98872e8	+	6.86639e8i	0.110864	+	0.152591i
$260$	2.75506e9	−	5.40614e9i	0.602888	−	1.18303i
$261$	7.87467e9	+	5.72128e9i	1.69695	+	1.23291i
$262$	−1.98241e9	+	1.03159e8i	−0.420716	+	0.0218929i
$263$	−6.19848e8	−	8.53148e8i	−0.129557	−	0.178321i	0.739310	−	0.673365i	$-0.235152\pi$
$263$	−6.19848e8	−	8.53148e8i	−0.129557	−	0.178321i	−0.868868	+	0.495044i	$0.835152\pi$
$264$	−7.52874e9	−	7.54545e9i	−1.54991	−	1.55335i
$265$	3.61328e8	+	6.80758e9i	0.0732686	+	1.38041i
$266$	−2.12489e8	−	4.08342e9i	−0.0424435	−	0.815638i
$267$	1.13635e10	+	3.69222e9i	2.23597	+	0.726512i
$268$	7.50434e9	−	3.33450e9i	1.45470	−	0.646386i
$269$	−8.77805e8	+	2.70161e9i	−0.167644	+	0.515956i	−0.999221	−	0.0394532i	$-0.987438\pi$
$269$	−8.77805e8	+	2.70161e9i	−0.167644	+	0.515956i	0.831577	+	0.555409i	$0.187438\pi$
$270$	−8.67225e9	+	1.50311e10i	−1.63184	+	2.82837i
$271$	−7.19313e9	+	2.33719e9i	−1.33365	+	0.433328i	−0.887160	−	0.461462i	$-0.847325\pi$
$271$	−7.19313e9	+	2.33719e9i	−1.33365	+	0.433328i	−0.446487	+	0.894790i	$0.647325\pi$
$272$	5.22138e8	+	2.33397e8i	0.0953915	+	0.0426402i
$273$	−1.35346e10	−	9.83346e9i	−2.43666	−	1.77034i
$274$	−2.93167e9	+	4.51072e9i	−0.520131	+	0.800284i
$275$	5.95827e9	−	2.66233e9i	1.04181	−	0.465513i
$276$	4.53256e9	+	1.02006e10i	0.781101	+	1.75788i
$277$	3.34122e9	+	2.42754e9i	0.567526	+	0.412332i	0.834206	−	0.551453i	$-0.185927\pi$
$277$	3.34122e9	+	2.42754e9i	0.567526	+	0.412332i	−0.266680	+	0.963785i	$0.585927\pi$
$278$	−1.23848e9	+	4.61523e9i	−0.207352	+	0.772705i
$279$	1.78642e10	−	5.80442e9i	2.94826	−	0.957948i
$280$	−5.38587e9	−	4.85376e9i	−0.876241	−	0.789672i
$281$	2.95777e9	−	9.10307e9i	0.474393	−	1.46003i	−0.372381	−	0.928080i	$-0.621458\pi$
$281$	2.95777e9	−	9.10307e9i	0.474393	−	1.46003i	0.846774	−	0.531953i	$-0.178542\pi$
$282$	1.18370e10	−	1.82126e10i	1.87173	−	2.87989i
$283$	−2.09256e9	−	6.79915e8i	−0.326237	−	0.106001i	0.141320	−	0.989964i	$-0.454865\pi$
$283$	−2.09256e9	−	6.79915e8i	−0.326237	−	0.106001i	−0.467556	+	0.883963i	$0.654865\pi$
$284$	−1.99927e9	+	3.45693e9i	−0.307325	+	0.531395i
$285$	−8.48688e9	−	2.26798e9i	−1.28638	−	0.343764i
$286$	−3.62929e9	−	9.46509e9i	−0.542448	−	1.41469i
$287$	−1.84714e9	−	2.54237e9i	−0.272253	−	0.374724i
$288$	1.44035e10	+	1.17079e10i	2.09362	+	1.70180i
$289$	5.58189e9	+	4.05548e9i	0.800184	+	0.581368i
$290$	2.23801e9	+	5.02262e9i	0.316424	+	0.710130i
$291$	−8.44990e9	−	1.16303e10i	−1.17836	−	1.62188i
$292$	7.12768e9	−	7.43821e8i	0.980430	−	0.102315i
$293$	7.87014e9			1.06785			0.533927	−	0.845530i	$-0.320716\pi$
$293$	7.87014e9			1.06785			0.533927	+	0.845530i	$0.320716\pi$
$294$	−4.37125e9	+	3.53709e9i	−0.585082	+	0.473432i
$295$	2.11153e9	+	5.48977e9i	0.278810	+	0.724879i
$296$	−1.90676e8	−	1.21258e9i	−0.0248387	−	0.157959i
$297$	8.95896e9	+	2.75728e10i	1.15141	+	3.54369i
$298$	6.60576e9	−	2.53291e9i	0.837640	−	0.321185i
$299$			1.06156e10i			1.32819i
$300$	−1.34850e10	+	7.79629e9i	−1.66482	+	0.962506i
$301$	−7.49383e9			−0.912931
$302$	3.70705e9	+	9.66787e9i	0.445656	+	1.16226i
$303$	−2.10913e10	+	6.85299e9i	−2.50227	+	0.813035i
$304$	−2.41329e9	+	5.39883e9i	−0.282563	+	0.632129i
$305$	−4.56391e9	−	5.62827e9i	−0.527397	−	0.650393i
$306$	−1.55479e9	−	1.92146e9i	−0.177332	−	0.219152i
$307$			2.70284e9i			0.304275i	0.988359	+	0.152138i	$0.0486157\pi$
$307$			2.70284e9i			0.304275i	−0.988359	+	0.152138i	$0.951384\pi$
$308$	−1.20474e10	+	1.25722e9i	−1.33872	+	0.139704i
$309$	−2.25511e9	+	1.63843e9i	−0.247362	+	0.179719i
$310$	1.03799e10	+	2.20307e9i	1.12394	+	0.238552i
$311$	−7.15255e9	+	9.84464e9i	−0.764574	+	1.05235i	0.232246	+	0.972657i	$0.425392\pi$
$311$	−7.15255e9	+	9.84464e9i	−0.764574	+	1.05235i	−0.996820	+	0.0796882i	$0.974608\pi$
$312$	1.09606e10	+	2.15704e10i	1.15668	+	2.27636i
$313$	−3.26392e8	+	2.37138e8i	−0.0340065	+	0.0247072i	−0.604659	−	0.796485i	$-0.706690\pi$
$313$	−3.26392e8	+	2.37138e8i	−0.0340065	+	0.0247072i	0.570652	+	0.821192i	$0.306690\pi$
$314$	−3.17046e9	+	1.21568e9i	−0.326140	+	0.125055i
$315$	1.12485e10	+	2.92451e10i	1.14249	+	2.97037i
$316$	7.07362e8	−	1.22310e9i	0.0709403	−	0.122663i
$317$	1.19381e9	−	3.67418e9i	0.118222	−	0.363851i	−0.874383	−	0.485236i	$-0.838734\pi$
$317$	1.19381e9	−	3.67418e9i	0.118222	−	0.363851i	0.992605	+	0.121385i	$0.0387336\pi$
$318$	−2.27930e10	−	1.48139e10i	−2.22891	−	1.44864i
$319$	8.73681e9	+	2.83876e9i	0.843704	+	0.274136i
$320$	3.74258e9	+	9.79511e9i	0.356920	+	0.934135i
$321$	7.93285e9	+	2.44148e10i	0.747153	+	2.29950i
$322$	1.22512e10	+	3.28754e9i	1.13960	+	0.305808i
$323$	4.62868e8	−	6.37083e8i	0.0425252	−	0.0585310i
$324$	−1.60257e10	−	3.60661e10i	−1.45424	−	3.27280i
$325$	−1.47304e10	+	1.56812e9i	−1.32033	+	0.140555i
$326$	1.04592e10	+	6.79779e9i	0.926038	+	0.601863i
$327$	−2.38235e8	+	3.27902e8i	−0.0208360	+	0.0286783i
$328$	7.06003e8	+	4.48975e9i	0.0609974	+	0.387906i
$329$	−7.62767e9	−	2.34755e10i	−0.651041	−	2.00370i
$330$	−5.40293e9	+	2.54561e10i	−0.455589	+	2.14652i
$331$	4.11639e9	+	1.33750e9i	0.342929	+	0.111424i	0.475418	−	0.879760i	$-0.342297\pi$
$331$	4.11639e9	+	1.33750e9i	0.342929	+	0.111424i	−0.132489	+	0.991185i	$0.542297\pi$
$332$	−2.87443e9	+	1.27723e9i	−0.236592	+	0.105128i
$333$	−1.63929e9	+	5.04521e9i	−0.133315	+	0.410300i
$334$	−3.84860e9	+	2.00270e8i	−0.309255	+	0.0160927i
$335$	−1.68213e10	−	1.09079e10i	−1.33561	−	0.866089i
$336$	2.82882e10	−	5.96914e9i	2.21947	−	0.468333i
$337$	1.22949e10	−	8.93280e9i	0.953250	−	0.692577i	0.00167683	−	0.999999i	$-0.499466\pi$
$337$	1.22949e10	−	8.93280e9i	0.953250	−	0.692577i	0.951573	+	0.307422i	$0.0994662\pi$
$338$	5.17524e8	+	9.94529e9i	0.0396519	+	0.761993i
$339$	1.04200e10	−	1.43419e10i	0.788988	−	1.08595i
$340$	−2.18332e8	−	1.37913e9i	−0.0163381	−	0.103203i
$341$	1.43419e10	−	1.04200e10i	1.06069	−	0.770637i
$342$	1.98676e10	−	1.60763e10i	1.45225	−	1.17512i
$343$		−	9.93678e9i		−	0.717909i
$344$	9.65125e9	+	4.93105e9i	0.689208	+	0.352132i
$345$	1.48270e10	−	2.28650e10i	1.04659	−	1.61397i
$346$	2.02251e10	+	5.42731e9i	1.41119	+	0.378687i
$347$	−2.42845e10	+	7.89052e9i	−1.67499	+	0.544236i	−0.983929	−	0.178562i	$-0.942855\pi$
$347$	−2.42845e10	+	7.89052e9i	−1.67499	+	0.544236i	−0.691059	+	0.722799i	$0.742855\pi$
$348$	−2.14439e10	−	4.57461e9i	−1.46213	−	0.311916i
$349$	−1.10314e10			−0.743579			−0.371789	−	0.928317i	$-0.621256\pi$
$349$	−1.10314e10			−0.743579			−0.371789	+	0.928317i	$0.621256\pi$
$350$	−2.75215e9	+	1.74856e10i	−0.183400	+	1.16522i
$351$		−	6.58095e10i		−	4.33571i
$352$	1.63430e10	+	6.30817e9i	1.06454	+	0.410897i
$353$	−1.12038e9	−	3.44817e9i	−0.0721549	−	0.222070i	0.908475	−	0.417939i	$-0.137247\pi$
$353$	−1.12038e9	−	3.44817e9i	−0.0721549	−	0.222070i	−0.980630	+	0.195869i	$0.937247\pi$
$354$	−2.26529e10	−	6.07881e9i	−1.44249	−	0.387084i
$355$	9.73587e9	−	5.16753e8i	0.613002	−	0.0325364i
$356$	−1.95309e10	+	2.03819e9i	−1.21597	+	0.126895i
$357$	−3.84988e9			−0.237014
$358$	−1.83572e10	+	1.48541e10i	−1.11757	+	0.904304i
$359$	−1.03635e10	−	1.42641e10i	−0.623917	−	0.858748i	0.373713	−	0.927544i	$-0.378084\pi$
$359$	−1.03635e10	−	1.42641e10i	−0.623917	−	0.858748i	−0.997631	+	0.0687957i	$0.978084\pi$
$360$	4.75676e9	−	4.50662e10i	0.283205	−	2.68313i
$361$	−7.15265e9	−	5.19670e9i	−0.421151	−	0.305984i
$362$	5.44636e8	+	1.04663e10i	0.0317155	+	0.609479i
$363$	5.92853e9	+	8.15993e9i	0.341445	+	0.469959i
$364$	2.68902e10	+	5.73646e9i	1.53175	+	0.326767i
$365$	−1.10197e10	−	1.35896e10i	−0.620866	−	0.765660i
$366$	2.88556e10	−	1.50156e9i	1.60807	−	0.0836795i
$367$	2.84096e10	+	9.23083e9i	1.56603	+	0.508834i	0.958411	−	0.285393i	$-0.0921241\pi$
$367$	2.84096e10	+	9.23083e9i	1.56603	+	0.508834i	0.607621	+	0.794227i	$0.292124\pi$
$368$	−1.36149e10	−	1.22955e10i	−0.742377	−	0.670430i
$369$	6.06967e9	−	1.86805e10i	0.327386	−	1.00759i
$370$	−2.22645e9	+	2.00590e9i	−0.118797	+	0.107029i
$371$	−2.93796e10	+	9.54600e9i	−1.55078	+	0.503878i
$372$	−3.14653e10	+	2.82894e10i	−1.64309	+	1.47724i
$373$	7.05629e9	+	5.12669e9i	0.364537	+	0.264851i	0.754942	−	0.655792i	$-0.227665\pi$
$373$	7.05629e9	+	5.12669e9i	0.364537	+	0.264851i	−0.390405	+	0.920643i	$0.627665\pi$
$374$	−1.95595e9	−	1.27124e9i	−0.0999704	−	0.0649741i
$375$	3.39182e10	+	1.71967e10i	1.71517	+	0.869602i
$376$	−5.62363e9	+	3.52531e10i	−0.281362	+	1.76379i
$377$	−1.68701e10	−	1.22568e10i	−0.835126	−	0.606755i
$378$	−7.59490e10	−	2.03806e10i	−3.72010	−	0.998272i
$379$	−1.50505e10	+	4.89020e9i	−0.729447	+	0.237012i	−0.650114	−	0.759836i	$-0.725279\pi$
$379$	−1.50505e10	+	4.89020e9i	−0.729447	+	0.237012i	−0.0793329	+	0.996848i	$0.525279\pi$
$380$	1.42601e10	−	2.25752e9i	0.683891	−	0.108267i
$381$	1.35196e10	−	4.16090e10i	0.641599	−	1.97464i
$382$	9.98424e9	+	6.48909e9i	0.468880	+	0.304741i
$383$	9.21798e9	+	2.99510e9i	0.428391	+	0.139193i	0.515274	−	0.857026i	$-0.327690\pi$
$383$	9.21798e9	+	2.99510e9i	0.428391	+	0.139193i	−0.0868821	+	0.996219i	$0.527690\pi$
$384$	−4.03600e10	−	1.09264e10i	−1.85621	−	0.502521i
$385$	1.86257e10	+	2.29695e10i	0.847756	+	1.04546i
$386$	1.94852e10	−	7.47141e9i	0.877720	−	0.336553i
$387$	−2.75312e10	−	3.78934e10i	−1.22738	−	1.68935i
$388$	2.04525e10	+	1.18285e10i	0.902444	+	0.521917i
$389$	3.02849e10	+	2.20033e10i	1.32260	+	0.960925i	0.999896	+	0.0144246i	$0.00459165\pi$
$389$	3.02849e10	+	2.20033e10i	1.32260	+	0.960925i	0.322703	+	0.946500i	$0.395408\pi$
$390$	2.95202e10	−	5.11656e10i	1.27603	−	2.21167i
$391$	1.43589e9	+	1.97634e9i	0.0614349	+	0.0845579i
$392$	4.20469e9	−	8.22959e9i	0.178069	−	0.348525i
$393$	−1.93256e10			−0.810143
$394$	1.21737e10	+	1.50446e10i	0.505170	+	0.624305i
$395$	−3.44465e9	+	1.82832e8i	−0.141500	+	0.00751043i
$396$	−5.06174e10	−	5.63000e10i	−2.05835	−	2.28943i
$397$	−4.86773e9	−	1.49813e10i	−0.195959	−	0.603098i	−0.999964	−	0.00847659i	$-0.997302\pi$
$397$	−4.86773e9	−	1.49813e10i	−0.195959	−	0.603098i	0.804006	−	0.594622i	$-0.202698\pi$
$398$	1.25160e10	+	3.26413e10i	0.498807	+	1.30087i
$399$		−	3.98072e10i		−	1.57062i
$400$	1.50503e10	−	2.07087e10i	0.587901	−	0.808933i
$401$	3.22030e10			1.24543			0.622715	−	0.782449i	$-0.286030\pi$
$401$	3.22030e10			1.24543			0.622715	+	0.782449i	$0.286030\pi$
$402$	7.46455e10	−	2.86221e10i	2.85824	−	1.09596i
$403$	−3.82709e10	+	1.24350e10i	−1.45094	+	0.471438i
$404$	2.71038e10	−	2.43681e10i	1.01743	−	0.914736i
$405$	−5.24237e10	+	8.08436e10i	−1.94853	+	3.00487i
$406$	−1.93698e10	+	1.56735e10i	−0.712887	+	0.576849i
$407$			5.00662e9i			0.182460i
$408$	4.95824e9	+	2.53328e9i	0.178931	+	0.0914202i
$409$	−3.03932e10	+	2.20820e10i	−1.08614	+	0.789123i	−0.978742	−	0.205093i	$-0.934250\pi$
$409$	−3.03932e10	+	2.20820e10i	−1.08614	+	0.789123i	−0.107393	+	0.994217i	$0.534250\pi$
$410$	8.24371e9	−	7.42712e9i	0.291734	−	0.262836i
$411$	−3.07842e10	+	4.23708e10i	−1.07885	+	1.48491i
$412$	2.29353e9	−	3.96574e9i	0.0796005	−	0.137637i
$413$	−2.15628e10	+	1.56663e10i	−0.741150	+	0.538477i
$414$	2.83850e10	+	7.40273e10i	0.966247	+	2.51994i
$415$	6.44315e9	+	4.17812e9i	0.217223	+	0.140860i
$416$	−3.08570e10	−	2.50821e10i	−1.03034	−	0.837511i
$417$	−1.43756e10	+	4.42434e10i	−0.475424	+	1.46320i
$418$	1.31444e10	−	2.02243e10i	0.430562	−	0.662472i
$419$	−1.08007e10	−	3.50936e9i	−0.350426	−	0.113860i	0.128515	−	0.991708i	$-0.458979\pi$
$419$	−1.08007e10	−	3.50936e9i	−0.350426	−	0.113860i	−0.478941	+	0.877847i	$0.658979\pi$
$420$	−4.99067e10	−	4.99139e10i	−1.60384	−	1.60407i
$421$	1.39250e10	+	4.28568e10i	0.443269	+	1.36424i	0.884371	+	0.466785i	$0.154588\pi$
$421$	1.39250e10	+	4.28568e10i	0.443269	+	1.36424i	−0.441102	+	0.897457i	$0.645412\pi$
$422$	7.23484e9	−	2.69609e10i	0.228128	−	0.850129i
$423$	9.06839e10	−	1.24816e11i	2.83249	−	3.89859i
$424$	4.41192e10	+	7.03795e9i	1.36510	+	0.217762i
$425$	−2.53030e9	+	2.28442e9i	−0.0775562	+	0.0700197i
$426$	−2.11861e10	+	3.25974e10i	−0.643300	+	0.989794i
$427$	1.93002e10	−	2.65644e10i	0.580563	−	0.799077i
$428$	−2.82079e10	−	3.13747e10i	−0.840612	−	0.934984i
$429$	−3.04961e10	−	9.38573e10i	−0.900357	−	2.77102i
$430$	−2.77366e9	−	2.63142e10i	−0.0811295	−	0.769690i
$431$	1.24581e9	+	4.04790e8i	0.0361031	+	0.0117306i	0.327013	−	0.945020i	$-0.393958\pi$
$431$	1.24581e9	+	4.04790e8i	0.0361031	+	0.0117306i	−0.290910	+	0.956750i	$0.593958\pi$
$432$	8.44035e10	+	7.62235e10i	2.42340	+	2.18854i
$433$	1.29726e10	−	3.99254e10i	0.369041	−	1.13579i	−0.578371	−	0.815774i	$-0.696312\pi$
$433$	1.29726e10	−	3.99254e10i	0.369041	−	1.13579i	0.947412	−	0.320016i	$-0.103688\pi$
$434$	2.49874e9	+	4.80184e10i	0.0704306	+	1.35347i
$435$	1.92173e10	+	4.99630e10i	0.536704	+	1.39538i
$436$	1.38977e8	−	6.51466e8i	0.00384589	−	0.0180279i
$437$	−2.04350e10	+	1.48469e10i	−0.560338	+	0.407109i
$438$	6.96728e10	−	3.62557e9i	1.89307	−	0.0985099i
$439$	−3.08128e10	+	4.24101e10i	−0.829607	+	1.14186i	0.158389	+	0.987377i	$0.449370\pi$
$439$	−3.08128e10	+	4.24101e10i	−0.829607	+	1.14186i	−0.987996	+	0.154480i	$0.950630\pi$
$440$	−8.87371e9	−	4.18383e10i	−0.236752	−	1.11625i
$441$	−3.23115e10	+	2.34757e10i	−0.854286	+	0.620675i
$442$	3.33087e9	+	4.11639e9i	0.0872707	+	0.107852i
$443$		−	5.60897e9i		−	0.145636i	−0.997345	−	0.0728179i	$-0.976801\pi$
$443$		−	5.60897e9i		−	0.145636i	0.997345	−	0.0728179i	$-0.0231992\pi$
$444$	−1.24032e9	−	1.18854e10i	−0.0319156	−	0.305831i
$445$	3.01957e10	+	3.72377e10i	0.770025	+	0.949604i
$446$	−7.17383e8	+	2.67335e9i	−0.0181306	+	0.0675643i
$447$	6.55037e10	−	2.12834e10i	1.64072	−	0.533104i
$448$	−3.85027e10	+	2.78436e10i	−0.955826	+	0.691214i
$449$	−3.60445e10			−0.886856			−0.443428	−	0.896310i	$-0.646238\pi$
$449$	−3.60445e10			−0.886856			−0.443428	+	0.896310i	$0.646238\pi$
$450$	−9.85290e10	+	5.03229e10i	−2.40278	+	1.22720i
$451$		−	1.85377e10i		−	0.448073i
$452$	−6.07864e9	+	2.84942e10i	−0.145631	+	0.682657i
$453$	3.11494e10	+	9.58681e10i	0.739703	+	2.27657i
$454$	−7.00148e9	+	2.60913e10i	−0.164803	+	0.614147i
$455$	−2.40980e10	−	6.26524e10i	−0.562258	−	1.46181i
$456$	−2.61937e10	+	5.12675e10i	−0.605812	+	1.18572i
$457$	−4.06847e10			−0.932753			−0.466377	−	0.884586i	$-0.654441\pi$
$457$	−4.06847e10			−0.932753			−0.466377	+	0.884586i	$0.654441\pi$
$458$	−3.27430e10	−	4.04648e10i	−0.744144	−	0.919636i
$459$	−8.90157e9	−	1.22520e10i	−0.200547	−	0.276029i
$460$	−7.00956e9	+	4.42361e10i	−0.156552	+	0.987974i
$461$	2.03390e10	+	1.47771e10i	0.450325	+	0.327180i	0.789724	−	0.613462i	$-0.210224\pi$
$461$	2.03390e10	+	1.47771e10i	0.450325	+	0.327180i	−0.339399	+	0.940642i	$0.610224\pi$
$462$	−1.17763e11	+	6.12802e9i	−2.58487	+	0.134509i
$463$	−8.23039e9	−	1.13282e10i	−0.179100	−	0.246510i	0.710023	−	0.704179i	$-0.248685\pi$
$463$	−8.23039e9	−	1.13282e10i	−0.179100	−	0.246510i	−0.889123	+	0.457668i	$0.848685\pi$
$464$	3.52596e10	−	7.44019e9i	0.760687	−	0.160514i
$465$	9.98002e10	+	2.66700e10i	2.13461	+	0.570441i
$466$	2.06631e9	+	3.97084e10i	0.0438180	+	0.842052i
$467$	−2.23624e10	−	7.26598e9i	−0.470165	−	0.152766i	0.0643455	−	0.997928i	$-0.479504\pi$
$467$	−2.23624e10	−	7.26598e9i	−0.470165	−	0.152766i	−0.534511	+	0.845162i	$0.679504\pi$
$468$	6.97832e10	+	1.57048e11i	1.45468	+	3.27378i
$469$	2.80735e10	−	8.64015e10i	0.580238	−	1.78579i
$470$	7.96099e10	−	3.54730e10i	1.63146	−	0.726954i
$471$	−3.14388e10	+	1.02151e10i	−0.638826	+	0.207567i
$472$	3.80793e10	−	5.98789e9i	0.767222	−	0.120644i
$473$	−3.57631e10	−	2.59834e10i	−0.714481	−	0.519101i
$474$	7.49587e9	−	1.15333e10i	0.148494	−	0.228476i
$475$	−2.36206e10	−	2.61630e10i	−0.463998	−	0.513940i
$476$	5.78215e9	−	2.56926e9i	0.112632	−	0.0500473i
$477$	−1.56206e11	−	1.13491e11i	−3.01735	−	2.19223i
$478$	2.37281e9	−	8.84238e9i	0.0454519	−	0.169378i
$479$	−3.39261e10	+	1.10232e10i	−0.644453	+	0.209396i	−0.612967	−	0.790109i	$-0.710024\pi$
$479$	−3.39261e10	+	1.10232e10i	−0.644453	+	0.209396i	−0.0314865	+	0.999504i	$0.510024\pi$
$480$	3.14305e10	+	9.71232e10i	0.592088	+	1.82961i
$481$	3.51189e9	−	1.08085e10i	0.0656085	−	0.201922i
$482$	2.73227e10	−	4.20392e10i	0.506215	−	0.778873i
$483$	1.17445e11	+	3.81601e10i	2.15797	+	0.701166i
$484$	−1.43497e10	−	8.29896e9i	−0.261494	−	0.151232i
$485$	−3.05731e9	−	5.76012e10i	−0.0552552	−	1.04103i
$486$	−7.23374e10	−	1.88654e11i	−1.29664	−	3.38159i
$487$	−1.01471e10	−	1.39663e10i	−0.180396	−	0.248293i	0.709237	−	0.704970i	$-0.249040\pi$
$487$	−1.01471e10	−	1.39663e10i	−0.180396	−	0.248293i	−0.889633	+	0.456677i	$0.849040\pi$
$488$	−4.23363e10	+	2.15123e10i	−0.746507	+	0.379322i
$489$	9.82472e10	+	7.13808e10i	1.71824	+	1.24838i
$490$	−2.24380e10	+	2.36509e9i	−0.389224	+	0.0410263i
$491$	−2.91310e10	−	4.00954e10i	−0.501222	−	0.689873i	0.481186	−	0.876618i	$-0.340206\pi$
$491$	−2.91310e10	−	4.00954e10i	−0.501222	−	0.689873i	−0.982408	+	0.186746i	$0.940206\pi$
$492$	4.59246e9	+	4.40073e10i	0.0783763	+	0.751041i
$493$	−4.79865e9			−0.0812328
$494$	−4.25629e10	+	3.44407e10i	−0.714700	+	0.578315i
$495$	−4.77198e10	+	1.78570e11i	−0.794837	+	2.97431i
$496$	2.83787e10	−	6.34868e10i	0.468884	−	1.04895i
$497$	1.36522e10	+	4.20172e10i	0.223758	+	0.688655i
$498$	−2.85919e10	+	1.09633e10i	−0.464863	+	0.178247i
$499$			1.25011e10i			0.201626i	0.994905	+	0.100813i	$0.0321444\pi$
$499$			1.25011e10i			0.201626i	−0.994905	+	0.100813i	$0.967856\pi$
$500$	−6.24184e10	−	3.19214e9i	−0.998695	−	0.0510742i
$501$	−3.75180e10			−0.595510
$502$	−3.29037e10	−	8.58119e10i	−0.518119	−	1.35124i
$503$	3.77668e10	−	1.22712e10i	0.589981	−	0.191697i	0.00121418	−	0.999999i	$-0.499614\pi$
$503$	3.77668e10	−	1.22712e10i	0.589981	−	0.191697i	0.588767	+	0.808303i	$0.299614\pi$
$504$	2.02856e11	−	3.18987e10i	3.14388	−	0.494368i
$505$	−8.59664e10	−	2.29731e10i	−1.32179	−	0.353227i
$506$	4.70678e10	+	5.81679e10i	0.717996	+	0.887322i
$507$			9.69516e10i			1.46731i
$508$	7.46311e9	+	7.15153e10i	0.112064	+	1.07385i
$509$	9.54682e10	−	6.93617e10i	1.42229	−	1.03335i	0.430900	−	0.902400i	$-0.358196\pi$
$509$	9.54682e10	−	6.93617e10i	1.42229	−	1.03335i	0.991389	−	0.130953i	$-0.0418037\pi$
$510$	−1.42494e9	−	1.35186e10i	−0.0210628	−	0.199826i
$511$	4.66008e10	−	6.41406e10i	0.683455	−	0.940696i
$512$	6.79088e10	−	1.05242e10i	0.988203	−	0.153148i
$513$	1.26684e11	−	9.20410e10i	1.82916	−	1.32896i
$514$	6.13072e9	−	2.35076e9i	0.0878332	−	0.0336788i
$515$	−1.11688e10	+	5.92811e8i	−0.158774	+	0.00842728i
$516$	9.13364e10	+	5.28232e10i	1.28838	+	0.745119i
$517$	4.49951e10	−	1.38481e11i	0.629801	−	1.93833i
$518$	−1.13862e10	−	7.40025e9i	−0.158146	−	0.102784i
$519$	1.93886e11	+	6.29974e10i	2.67225	+	0.868267i
$520$	−1.01905e10	+	9.65465e10i	−0.139375	+	1.32045i
$521$	−1.78256e10	−	5.48615e10i	−0.241932	−	0.744589i	−0.996126	−	0.0879376i	$-0.971972\pi$
$521$	−1.78256e10	−	5.48615e10i	−0.241932	−	0.744589i	0.754194	−	0.656651i	$-0.228028\pi$
$522$	−1.50416e11	−	4.03636e10i	−2.02588	−	0.543635i
$523$	−3.38056e10	+	4.65294e10i	−0.451837	+	0.621901i	−0.972791	−	0.231684i	$-0.925576\pi$
$523$	−3.38056e10	+	4.65294e10i	−0.451837	+	0.621901i	0.520954	+	0.853585i	$0.325576\pi$
$524$	2.90252e10	−	1.28971e10i	0.384990	−	0.171068i
$525$	−3.56031e10	+	1.68606e11i	−0.468652	+	2.21940i
$526$	1.41473e10	+	9.19481e9i	0.184812	+	0.120116i
$527$	−5.44302e9	+	7.49167e9i	−0.0705663	+	0.0971262i
$528$	1.55698e11	+	6.95972e10i	2.00331	+	0.895481i
$529$	−1.45282e7	−	4.47131e7i	−0.000185519	−	0.000570969i
$530$	−4.43944e10	−	9.96315e10i	−0.562632	−	1.26268i
$531$	−1.58437e11	−	5.14793e10i	−1.99287	−	0.647522i
$532$	2.65658e10	+	5.97867e10i	0.331647	+	0.746376i
$533$	−1.30032e10	+	4.00198e10i	−0.161117	+	0.495868i
$534$	−1.90914e11	+	9.93462e9i	−2.34787	+	0.122176i
$535$	−2.65931e10	+	9.95126e10i	−0.324604	+	1.21468i
$536$	−9.30092e10	+	9.28031e10i	−1.12685	+	1.12436i
$537$	−1.85986e11	+	1.35127e11i	−2.23658	+	1.62497i
$538$	−2.36190e9	−	4.53888e10i	−0.0281924	−	0.541775i
$539$	−2.21560e10	+	3.04951e10i	−0.262504	+	0.361305i
$540$	4.34545e10	−	2.74234e11i	0.511046	−	3.22512i
$541$	4.88647e10	−	3.55023e10i	0.570435	−	0.414446i	−0.264828	−	0.964296i	$-0.585315\pi$
$541$	4.88647e10	−	3.55023e10i	0.570435	−	0.414446i	0.835263	+	0.549850i	$0.185315\pi$
$542$	9.40729e10	−	7.61211e10i	1.09010	−	0.882080i
$543$			1.02031e11i			1.17363i
$544$	−9.13741e9	−	4.95808e8i	−0.104334	−	0.00566133i
$545$	−1.51788e9	+	5.83821e8i	−0.0172048	+	0.00661750i
$546$	2.58529e11	+	6.93750e10i	2.90896	+	0.780607i
$547$	5.21163e10	−	1.69336e10i	0.582136	−	0.189147i	−0.00312128	−	0.999995i	$-0.500994\pi$
$547$	5.21163e10	−	1.69336e10i	0.582136	−	0.189147i	0.585257	+	0.810848i	$0.300994\pi$
$548$	1.79583e10	−	8.41812e10i	0.199133	−	0.933454i
$549$	2.05232e11			2.25920
$550$	−7.37623e10	+	7.39048e10i	−0.806090	+	0.807648i
$551$		−	4.96174e10i		−	0.538304i
$552$	−1.26146e11	−	1.26426e11i	−1.35868	−	1.36170i
$553$	−4.83029e9	−	1.48661e10i	−0.0516503	−	0.158963i
$554$	−6.38216e10	−	1.71262e10i	−0.677530	−	0.181812i
$555$	−2.26607e10	+	1.83753e10i	−0.238837	+	0.193671i
$556$	−7.93562e9	−	7.60432e10i	−0.0830390	−	0.795722i
$557$	−8.74131e10			−0.908146			−0.454073	−	0.890964i	$-0.650030\pi$
$557$	−8.74131e10			−0.908146			−0.454073	+	0.890964i	$0.650030\pi$
$558$	−2.33630e11	+	1.89047e11i	−2.40986	+	1.94999i
$559$	5.89807e10	+	8.11800e10i	0.604036	+	0.831384i
$560$	1.08266e11	+	4.16601e10i	1.10088	+	0.423612i
$561$	−1.83729e10	−	1.33487e10i	−0.185493	−	0.134768i
$562$	7.95843e9	+	1.52938e11i	0.0797778	+	1.53310i
$563$	−7.85969e10	−	1.08179e11i	−0.782297	−	1.07674i	−0.995025	−	0.0996280i	$-0.968235\pi$
$563$	−7.85969e10	−	1.08179e11i	−0.782297	−	1.07674i	0.212728	−	0.977112i	$-0.431765\pi$
$564$	−7.25089e10	+	3.39892e11i	−0.716597	+	3.35911i
$565$	6.63897e10	−	2.55355e10i	0.651488	−	0.250582i
$566$	3.51564e10	−	1.82944e9i	0.342562	−	0.0178259i
$567$	−4.15248e11	−	1.34922e11i	−4.01768	−	1.30542i
$568$	1.00653e10	−	6.30971e10i	0.0967019	−	0.606200i
$569$	1.04761e9	−	3.22422e9i	0.00999428	−	0.0307592i	−0.945935	−	0.324356i	$-0.894852\pi$
$569$	1.04761e9	−	3.22422e9i	0.00999428	−	0.0307592i	0.955929	+	0.293597i	$0.0948524\pi$
$570$	1.39781e11	−	1.47337e10i	1.32418	−	0.139576i
$571$	5.23550e10	−	1.70112e10i	0.492508	−	0.160026i	−0.0522243	−	0.998635i	$-0.516631\pi$
$571$	5.23550e10	−	1.70112e10i	0.492508	−	0.160026i	0.544733	+	0.838610i	$0.316631\pi$
$572$	1.08439e11	+	1.20613e11i	1.01298	+	1.12670i
$573$	9.37855e10	+	6.81392e10i	0.869996	+	0.632089i
$574$	4.21588e10	+	2.74004e10i	0.388365	+	0.252412i
$575$	9.98328e10	−	4.46082e10i	0.913276	−	0.408078i
$576$	−2.82247e11	−	9.24002e10i	−2.56412	−	0.839427i
$577$	9.59958e10	+	6.97450e10i	0.866062	+	0.629231i	0.929527	−	0.368753i	$-0.120215\pi$
$577$	9.59958e10	+	6.97450e10i	0.866062	+	0.629231i	−0.0634654	+	0.997984i	$0.520215\pi$
$578$	−1.06621e11	−	2.86114e10i	−0.955285	−	0.256346i
$579$	1.93218e11	−	6.27805e10i	1.71923	−	0.558612i
$580$	−6.22059e10	−	6.22148e10i	−0.549692	−	0.549771i
$581$	−1.07532e10	+	3.30948e10i	−0.0943695	+	0.290440i
$582$	1.92859e11	+	1.25345e11i	1.68092	+	1.09249i
$583$	−1.73308e11	−	5.63113e10i	−1.50019	−	0.487440i
$584$	−1.02222e11	+	5.19422e10i	−0.878809	+	0.446549i
$585$	2.28277e11	−	3.52030e11i	1.94912	−	3.00577i
$586$	−1.17575e11	+	4.50831e10i	−0.997070	+	0.382316i
$587$	2.83699e9	+	3.90478e9i	0.0238949	+	0.0328885i	0.820797	−	0.571220i	$-0.193530\pi$
$587$	2.83699e9	+	3.90478e9i	0.0238949	+	0.0328885i	−0.796902	+	0.604108i	$0.793530\pi$
$588$	4.50421e10	−	7.78822e10i	0.376799	−	0.651522i
$589$	−7.74629e10	−	5.62801e10i	−0.643624	−	0.467620i
$590$	−6.29924e10	−	6.99182e10i	−0.519852	−	0.577009i
$591$	1.10743e11	+	1.52425e11i	0.907754	+	1.24942i
$592$	9.79470e9	+	1.70230e10i	0.0797452	+	0.138596i
$593$	−1.60441e11			−1.29747			−0.648733	−	0.761016i	$-0.724701\pi$
$593$	−1.60441e11			−1.29747			−0.648733	+	0.761016i	$0.724701\pi$
$594$	−2.91789e11	−	3.60602e11i	−2.34381	−	2.89656i
$595$	−1.29609e10	−	8.40463e9i	−0.103411	−	0.0670580i
$596$	−8.41766e10	+	7.56804e10i	−0.667124	+	0.599789i
$597$	1.05169e11	+	3.23676e11i	0.827922	+	2.54808i
$598$	−6.08100e10	−	1.58591e11i	−0.475521	−	1.24015i
$599$			2.08054e11i			1.61610i	0.589112	+	0.808052i	$0.299478\pi$
$599$			2.08054e11i			1.61610i	−0.589112	+	0.808052i	$0.700522\pi$
$600$	1.56798e11	−	1.93719e11i	1.20986	−	1.49475i
$601$	−2.35120e11			−1.80215			−0.901077	−	0.433660i	$-0.857222\pi$
$601$	−2.35120e11			−1.80215			−0.901077	+	0.433660i	$0.857222\pi$
$602$	1.11953e11	−	4.29274e10i	0.852415	−	0.326850i
$603$	5.40037e11	−	1.75469e11i	4.08464	−	1.32718i
$604$	−1.10762e11	−	1.23197e11i	−0.832230	−	0.925661i
$605$	2.14504e9	+	4.04136e10i	0.0160108	+	0.301652i
$606$	2.75835e11	−	2.23198e11i	2.04531	−	1.65501i
$607$			3.44421e10i			0.253708i	0.991921	+	0.126854i	$0.0404880\pi$
$607$			3.44421e10i			0.253708i	−0.991921	+	0.126854i	$0.959512\pi$
$608$	5.12659e9	−	9.44796e10i	0.0375158	−	0.691391i
$609$	−1.96246e11	+	1.42581e11i	−1.42670	+	1.03656i
$610$	1.00423e11	+	5.79393e10i	0.725293	+	0.418460i
$611$	−1.94274e11	+	2.67396e11i	−1.39396	+	1.91862i
$612$	3.42345e10	+	1.97991e10i	0.244038	+	0.141136i
$613$	−2.67742e10	+	1.94526e10i	−0.189616	+	0.137764i	−0.678543	−	0.734561i	$-0.737388\pi$
$613$	−2.67742e10	+	1.94526e10i	−0.189616	+	0.137764i	0.488927	+	0.872325i	$0.337388\pi$
$614$	−1.54828e10	−	4.03788e10i	−0.108937	−	0.284106i
$615$	8.39043e10	−	6.80371e10i	0.586521	−	0.475604i
$616$	1.72779e11	−	8.77939e10i	1.19996	−	0.609735i
$617$	2.20309e10	−	6.78040e10i	0.152017	−	0.467859i	−0.845830	−	0.533453i	$-0.820894\pi$
$617$	2.20309e10	−	6.78040e10i	0.152017	−	0.467859i	0.997846	+	0.0655939i	$0.0208942\pi$
$618$	2.43044e10	−	3.73952e10i	0.166622	−	0.256367i
$619$	1.35960e11	+	4.41760e10i	0.926079	+	0.300901i	0.732958	−	0.680274i	$-0.238139\pi$
$619$	1.35960e11	+	4.41760e10i	0.926079	+	0.300901i	0.193121	+	0.981175i	$0.438139\pi$
$620$	−1.67689e11	+	2.65470e10i	−1.13485	+	0.179659i
$621$	1.50110e11	+	4.61992e11i	1.00935	+	3.10647i
$622$	5.04611e10	−	1.88045e11i	0.337129	−	1.25632i
$623$	−1.27693e11	+	1.75755e11i	−0.847650	+	1.16669i
$624$	−2.87308e11	−	2.59463e11i	−1.89500	−	1.71134i
$625$	7.66466e10	+	1.31941e11i	0.502311	+	0.864687i
$626$	3.51769e9	−	5.41239e9i	0.0229066	−	0.0352445i
$627$	1.38024e11	−	1.89974e11i	0.893067	−	1.22920i
$628$	4.04010e10	−	3.63231e10i	0.259748	−	0.233531i
$629$	−8.08164e8	−	2.48727e9i	−0.00516294	−	0.0158899i
$630$	−3.35573e11	−	3.72468e11i	−2.13022	−	2.36443i
$631$	−1.17576e11	−	3.82026e10i	−0.741651	−	0.240977i	−0.0862661	−	0.996272i	$-0.527494\pi$
$631$	−1.17576e11	−	3.82026e10i	−0.741651	−	0.240977i	−0.655385	+	0.755295i	$0.727494\pi$
$632$	−3.56122e9	+	2.23244e10i	−0.0223218	+	0.139930i
$633$	8.39782e10	−	2.58458e11i	0.523060	−	1.60981i
$634$	3.21218e9	+	6.17287e10i	0.0198812	+	0.382059i
$635$	1.36351e11	−	1.10566e11i	0.838617	−	0.680026i
$636$	4.25373e11	+	9.07446e10i	2.59981	+	0.554616i
$637$	6.92218e10	−	5.02926e10i	0.420422	−	0.305454i
$638$	−1.46784e11	+	7.63822e9i	−0.885924	+	0.0461009i
$639$	−1.62309e11	+	2.23399e11i	−0.973505	+	1.33991i
$640$	−1.12022e11	−	1.24894e11i	−0.667703	−	0.744428i
$641$	5.57041e10	−	4.04714e10i	0.329955	−	0.239726i	−0.410456	−	0.911880i	$-0.634631\pi$
$641$	5.57041e10	−	4.04714e10i	0.329955	−	0.239726i	0.740412	+	0.672154i	$0.234631\pi$
$642$	−2.58369e11	−	3.19301e11i	−1.52090	−	1.87957i
$643$		−	2.49649e11i		−	1.46045i	−0.683209	−	0.730223i	$-0.739416\pi$
$643$		−	2.49649e11i		−	1.46045i	0.683209	−	0.730223i	$-0.260584\pi$
$644$	−2.01857e11	+	2.10652e10i	−1.17355	+	0.122468i
$645$	−1.36533e10	−	2.57234e11i	−0.0788856	−	1.48624i
$646$	−3.26553e9	+	1.21691e10i	−0.0187509	+	0.0698761i
$647$	−1.45229e11	+	4.71877e10i	−0.828774	+	0.269285i	−0.692529	−	0.721390i	$-0.743503\pi$
$647$	−1.45229e11	+	4.71877e10i	−0.828774	+	0.269285i	−0.136245	+	0.990675i	$0.543503\pi$
$648$	4.46014e11	+	4.47005e11i	2.52958	+	2.53520i
$649$	−1.57225e11			−0.886224
$650$	2.11081e11	−	1.07808e11i	1.18249	−	0.603946i
$651$			4.68107e11i			2.60628i
$652$	−1.95195e11	−	4.16408e10i	−1.08013	−	0.230424i
$653$	2.25296e10	+	6.93390e10i	0.123908	+	0.381351i	0.993701	−	0.112067i	$-0.0357473\pi$
$653$	2.25296e10	+	6.93390e10i	0.123908	+	0.381351i	−0.869792	+	0.493418i	$0.835747\pi$
$654$	1.68074e9	−	6.26335e9i	0.00918735	−	0.0342370i
$655$	−6.50611e10	−	4.21894e10i	−0.353473	−	0.229213i
$656$	−3.62662e10	−	6.30299e10i	−0.195833	−	0.340354i
$657$	4.95538e11			2.65960
$658$	2.48429e11	+	3.07017e11i	1.32525	+	1.63779i
$659$	−1.73480e11	−	2.38775e11i	−0.919830	−	1.26604i	−0.963696	−	0.267000i	$-0.913967\pi$
$659$	−1.73480e11	−	2.38775e11i	−0.919830	−	1.26604i	0.0438660	−	0.999037i	$-0.486033\pi$
$660$	−6.51051e10	−	4.11248e11i	−0.343115	−	2.16735i
$661$	−2.55966e10	−	1.85970e10i	−0.134084	−	0.0974177i	0.518722	−	0.854943i	$-0.326408\pi$
$661$	−2.55966e10	−	1.85970e10i	−0.134084	−	0.0974177i	−0.652806	+	0.757526i	$0.726408\pi$
$662$	−6.91581e10	+	3.59879e9i	−0.360090	+	0.0187380i
$663$	3.03007e10	+	4.17054e10i	0.156819	+	0.215843i
$664$	3.56258e10	−	3.55469e10i	0.183271	−	0.182865i
$665$	8.69027e10	−	1.34014e11i	0.444372	−	0.685274i
$666$	−4.41081e9	−	8.47628e10i	−0.0224193	−	0.430832i
$667$	1.46388e11	+	4.75643e10i	0.739609	+	0.240314i
$668$	5.63485e10	−	2.50381e10i	0.282994	−	0.125746i
$669$	−8.32700e9	+	2.56279e10i	−0.0415704	+	0.127941i
$670$	3.13785e11	+	6.65993e10i	1.55716	+	0.330499i
$671$	1.84214e11	−	5.98548e10i	0.908725	−	0.295263i
$672$	−3.88416e11	+	2.51221e11i	−1.90467	+	1.23191i
$673$	−2.31400e11	−	1.68122e11i	−1.12799	−	0.819530i	−0.142586	−	0.989782i	$-0.545542\pi$
$673$	−2.31400e11	−	1.68122e11i	−1.12799	−	0.819530i	−0.985401	+	0.170252i	$0.945542\pi$
$674$	−1.32509e11	+	2.03881e11i	−0.642104	+	0.987953i
$675$	−6.18896e11	+	2.76541e11i	−2.98128	+	1.33212i
$676$	−6.47018e10	−	1.45612e11i	−0.309834	−	0.697286i
$677$	−2.11395e11	−	1.53588e11i	−1.00633	−	0.731142i	−0.0428943	−	0.999080i	$-0.513658\pi$
$677$	−2.11395e11	−	1.53588e11i	−1.00633	−	0.731142i	−0.963436	+	0.267938i	$0.913658\pi$
$678$	−7.35132e10	+	2.73950e11i	−0.347894	+	1.29644i
$679$	2.48590e11	−	8.07718e10i	1.16951	−	0.379997i
$680$	1.11619e10	+	1.93528e10i	0.0522040	+	0.0905122i
$681$	−8.12695e10	+	2.50122e11i	−0.377867	+	1.16296i
$682$	−1.54570e11	+	2.37824e11i	−0.714475	+	1.09930i
$683$	1.92345e11	+	6.24965e10i	0.883888	+	0.287192i	0.715571	−	0.698540i	$-0.246167\pi$
$683$	1.92345e11	+	6.24965e10i	0.883888	+	0.287192i	0.168317	+	0.985733i	$0.446167\pi$
$684$	−2.04719e11	+	3.53980e11i	−0.935265	+	1.61716i
$685$	−1.96137e11	+	7.54402e10i	−0.890835	+	0.342642i
$686$	5.69215e10	+	1.48450e11i	0.257028	+	0.670320i
$687$	−2.97861e11	−	4.09971e11i	−1.33717	−	1.84046i
$688$	−1.72431e11	−	1.83810e10i	−0.769593	−	0.0820382i
$689$	3.34645e11	+	2.43134e11i	1.48493	+	1.07887i
$690$	−9.05277e10	+	4.26524e11i	−0.399379	+	1.88169i
$691$	−6.41177e10	−	8.82504e10i	−0.281233	−	0.387083i	0.644909	−	0.764259i	$-0.276895\pi$
$691$	−6.41177e10	−	8.82504e10i	−0.281233	−	0.387083i	−0.926142	+	0.377176i	$0.876895\pi$
$692$	−3.33241e11	+	3.47759e10i	−1.45323	+	0.151654i
$693$	−8.37570e11			−3.63152
$694$	3.17596e11	−	2.56990e11i	1.36911	−	1.10784i
$695$	−1.44984e11	+	1.17566e11i	−0.621414	+	0.503898i
$696$	3.46564e11	−	5.44965e10i	1.47689	−	0.232237i
$697$	2.99233e9	+	9.20946e9i	0.0126788	+	0.0390214i
$698$	1.64802e11	−	6.31916e10i	0.694289	−	0.266218i
$699$			3.87097e11i			1.62148i
$700$	−5.90486e10	−	2.76990e11i	−0.245933	−	1.15364i
$701$	4.39219e11			1.81890			0.909450	−	0.415813i	$-0.136503\pi$
$701$	4.39219e11			1.81890			0.909450	+	0.415813i	$0.136503\pi$
$702$	3.76981e11	+	9.83155e11i	1.55228	+	4.04831i
$703$	2.57181e10	−	8.35630e9i	0.105297	−	0.0342131i
$704$	−2.80290e11	−	6.21680e8i	−1.14108	−	0.00253091i
$705$	7.91927e11	−	3.04599e11i	3.20574	−	1.23302i
$706$	3.64902e10	+	4.50957e10i	0.146878	+	0.181517i
$707$		−	4.03220e11i		−	1.61386i
$708$	3.73243e11	−	3.89504e10i	1.48545	−	0.155017i
$709$	−1.42897e11	+	1.03821e11i	−0.565509	+	0.410866i	−0.833471	−	0.552563i	$-0.813650\pi$
$709$	−1.42897e11	+	1.03821e11i	−0.565509	+	0.410866i	0.267962	+	0.963429i	$0.413650\pi$
$710$	−1.42488e11	+	6.34906e10i	−0.560719	+	0.249848i
$711$	5.74264e10	−	7.90407e10i	0.224716	−	0.309294i
$712$	2.80105e11	−	1.42330e11i	1.08994	−	0.553828i
$713$	2.40303e11	−	1.74590e11i	0.929824	−	0.675557i
$714$	5.75149e10	−	2.20535e10i	0.221303	−	0.0848565i
$715$	1.02231e11	−	3.82554e11i	0.391165	−	1.46376i
$716$	1.89155e11	−	3.27068e11i	0.719725	−	1.24447i
$717$	2.75424e10	−	8.47667e10i	0.104214	−	0.320737i
$718$	2.36534e11	+	1.53731e11i	0.890011	+	0.578448i
$719$	−3.11277e11	−	1.01140e11i	−1.16475	−	0.378449i	−0.338068	−	0.941122i	$-0.609773\pi$
$719$	−3.11277e11	−	1.01140e11i	−1.16475	−	0.378449i	−0.826680	+	0.562672i	$0.809773\pi$
$720$	1.87093e11	+	7.00511e11i	0.696188	+	2.60666i
$721$	−1.56616e10	−	4.82015e10i	−0.0579556	−	0.178369i
$722$	1.36625e11	+	3.66627e10i	0.502783	+	0.134920i
$723$	2.86904e11	−	3.94889e11i	1.04999	−	1.44518i
$724$	−6.80913e10	−	1.53240e11i	−0.247821	−	0.557723i
$725$	−4.43771e10	+	2.10157e11i	−0.160623	+	0.760664i
$726$	−1.35312e11	−	8.79436e10i	−0.487068	−	0.316561i
$727$	−4.88887e10	+	6.72895e10i	−0.175013	+	0.240885i	−0.887508	−	0.460793i	$-0.847565\pi$
$727$	−4.88887e10	+	6.72895e10i	−0.175013	+	0.240885i	0.712495	+	0.701677i	$0.247565\pi$
$728$	−4.34584e11	+	6.83373e10i	−1.54721	+	0.243295i
$729$	−2.95271e11	−	9.08749e11i	−1.04547	−	3.21761i
$730$	2.42474e11	+	1.39896e11i	0.853835	+	0.492623i
$731$	2.19612e10	+	7.13564e9i	0.0769108	+	0.0249898i
$732$	−4.22484e11	+	1.87728e11i	−1.47152	+	0.653860i
$733$	−1.39796e11	+	4.30249e11i	−0.484261	+	1.49040i	0.348787	+	0.937202i	$0.386594\pi$
$733$	−1.39796e11	+	4.30249e11i	−0.484261	+	1.49040i	−0.833048	+	0.553201i	$0.813406\pi$
$734$	−4.77300e11	+	2.48373e10i	−1.64440	+	0.0855697i
$735$	−2.19342e11	+	1.16421e10i	−0.751576	+	0.0398916i
$736$	2.73832e11	+	1.05695e11i	0.933196	+	0.360201i
$737$	4.33557e11	−	3.14998e11i	1.46952	−	1.06767i
$738$	1.63316e10	+	3.13845e11i	0.0550559	+	1.05801i
$739$	2.11975e11	−	2.91759e11i	0.710734	−	0.978241i	−0.289047	−	0.957315i	$-0.593338\pi$
$739$	2.11975e11	−	2.91759e11i	0.710734	−	0.978241i	0.999781	−	0.0209264i	$-0.00666157\pi$
$740$	2.17713e10	−	4.27209e10i	0.0726033	−	0.142467i
$741$	−4.31228e11	+	3.13305e11i	−1.43032	+	1.03919i
$742$	3.84230e11	−	3.10908e11i	1.26758	−	1.02569i
$743$		−	3.75296e11i		−	1.23146i	−0.787959	−	0.615728i	$-0.788862\pi$
$743$		−	3.75296e11i		−	1.23146i	0.787959	−	0.615728i	$-0.211138\pi$
$744$	3.08021e11	−	6.02872e11i	1.00528	−	1.96758i
$745$	2.66987e11	+	7.13480e10i	0.866693	+	0.231610i
$746$	−1.34784e11	−	3.61688e10i	−0.435195	−	0.116783i
$747$	−2.06853e11	+	6.72107e10i	−0.664324	+	0.215852i
$748$	3.65028e10	+	7.78713e9i	0.116606	+	0.0248755i
$749$	−4.66758e11			−1.48308
$750$	−6.05228e11	−	6.26128e10i	−1.91282	−	0.197887i
$751$			5.43742e11i			1.70936i	0.519156	+	0.854679i	$0.326246\pi$
$751$			5.43742e11i			1.70936i	−0.519156	+	0.854679i	$0.673754\pi$
$752$	−1.17929e11	−	5.58875e11i	−0.368765	−	1.74760i
$753$	−2.76482e11	−	8.50924e11i	−0.859977	−	2.64674i
$754$	3.22241e11	+	8.64719e10i	0.997000	+	0.267540i
$755$	−1.04422e11	+	3.90750e11i	−0.321368	+	1.20257i
$756$	1.25138e12	−	1.30590e11i	3.83091	−	0.399781i
$757$	−1.17410e11			−0.357537			−0.178768	−	0.983891i	$-0.557211\pi$
$757$	−1.17410e11			−0.357537			−0.178768	+	0.983891i	$0.557211\pi$
$758$	1.96833e11	−	1.59271e11i	0.596239	−	0.482460i
$759$	4.28173e11	+	5.89330e11i	1.29019	+	1.77579i
$760$	−2.00105e11	+	1.15413e11i	−0.599796	+	0.345939i
$761$	2.25188e10	+	1.63608e10i	0.0671438	+	0.0487828i	0.620851	−	0.783929i	$-0.286787\pi$
$761$	2.25188e10	+	1.63608e10i	0.0671438	+	0.0487828i	−0.553707	+	0.832712i	$0.686787\pi$
$762$	3.63770e10	+	6.99059e11i	0.107896	+	2.07345i
$763$	−4.33161e9	−	5.96195e9i	−0.0127806	−	0.0175910i
$764$	−1.86330e11	−	3.97498e10i	−0.546903	−	0.116671i
$765$	−5.11748e9	−	9.64157e10i	−0.0149421	−	0.281515i
$766$	−1.54868e11	+	8.05889e9i	−0.449829	+	0.0234078i
$767$	3.39424e11	+	1.10285e11i	0.980756	+	0.318667i
$768$	6.65545e11	−	6.79623e10i	1.91308	−	0.195354i
$769$	−1.19926e11	+	3.69093e11i	−0.342931	+	1.05543i	0.619751	+	0.784798i	$0.287233\pi$
$769$	−1.19926e11	+	3.69093e11i	−0.342931	+	1.05543i	−0.962682	+	0.270634i	$0.912767\pi$
$770$	−4.09835e11	−	2.36456e11i	−1.16586	−	0.672647i
$771$	6.07931e10	−	1.97529e10i	0.172043	−	0.0559002i
$772$	−2.48299e11	+	2.23237e11i	−0.699045	+	0.628488i
$773$	3.29073e11	+	2.39085e11i	0.921667	+	0.669630i	0.943938	−	0.330122i	$-0.107090\pi$
$773$	3.29073e11	+	2.39085e11i	0.921667	+	0.669630i	−0.0222712	+	0.999752i	$0.507090\pi$
$774$	6.28366e11	+	4.08396e11i	1.75085	+	1.13794i
$775$	2.77762e11	+	3.07659e11i	0.769958	+	0.852832i
$776$	−3.73307e11	−	5.95504e10i	−1.02948	−	0.164224i
$777$	−1.06954e11	−	7.77069e10i	−0.293437	−	0.213194i
$778$	−5.78482e11	−	1.55233e11i	−1.57896	−	0.423707i
$779$	−9.52245e10	+	3.09403e10i	−0.258582	+	0.0840185i
$780$	−1.47918e11	+	9.33486e11i	−0.399617	+	2.52191i
$781$	−8.05336e10	+	2.47857e11i	−0.216458	+	0.666188i
$782$	−3.27726e10	−	2.13000e10i	−0.0876362	−	0.0569577i
$783$	−9.07507e11	−	2.94867e11i	−2.41436	−	0.784475i
$784$	−1.56734e10	+	1.47031e11i	−0.0414858	+	0.389175i
$785$	−1.28142e11	−	3.42438e10i	−0.337452	−	0.0901786i
$786$	2.88712e11	−	1.10704e11i	0.756441	−	0.290050i
$787$	−2.11214e11	−	2.90711e11i	−0.550583	−	0.757813i	0.439508	−	0.898239i	$-0.355153\pi$
$787$	−2.11214e11	−	2.90711e11i	−0.550583	−	0.757813i	−0.990091	+	0.140426i	$0.955153\pi$
$788$	−2.68049e11	−	1.55022e11i	−0.695199	−	0.402059i
$789$	1.32891e11	+	9.65508e10i	0.342915	+	0.249142i
$790$	5.04137e10	−	2.24636e10i	0.129432	−	0.0576728i
$791$	1.89458e11	+	2.60767e11i	0.483958	+	0.666111i
$792$	1.07870e12	+	5.51133e11i	2.74158	+	1.40073i
$793$	−4.39673e11			−1.11183
$794$	1.58539e11	+	1.95928e11i	0.398892	+	0.492963i
$795$	−3.81204e11	−	9.91093e11i	−0.954310	−	2.48111i
$796$	−3.73963e11	−	4.15945e11i	−0.931485	−	1.03606i
$797$	−2.26805e10	−	6.98034e10i	−0.0562108	−	0.172999i	0.919009	−	0.394236i	$-0.128991\pi$
$797$	−2.26805e10	−	6.98034e10i	−0.0562108	−	0.172999i	−0.975220	+	0.221237i	$0.928991\pi$
$798$	2.28030e11	+	5.94696e11i	0.562317	+	1.46650i
$799$			7.60599e10i			0.186625i
$800$	−1.06215e11	+	3.95589e11i	−0.259315	+	0.965793i
$801$	−1.35785e12			−3.29854
$802$	−4.81094e11	+	1.84471e11i	−1.16287	+	0.445892i
$803$	4.44790e11	−	1.44521e11i	1.06978	−	0.347592i
$804$	−9.51201e11	+	8.55193e11i	−2.27640	+	2.04663i
$805$	3.12080e11	+	3.84861e11i	0.743161	+	0.916475i
$806$	5.00512e11	−	4.05000e11i	1.18597	−	0.959655i
$807$		−	4.42472e11i		−	1.04326i
$808$	−2.65325e11	+	5.19305e11i	−0.622490	+	1.21836i
$809$	1.28065e11	−	9.30445e10i	0.298975	−	0.217218i	−0.428176	−	0.903695i	$-0.640844\pi$
$809$	1.28065e11	−	9.30445e10i	0.298975	−	0.217218i	0.727152	+	0.686477i	$0.240844\pi$
$810$	3.20078e11	−	1.50806e12i	0.743559	−	3.50330i
$811$	4.81854e11	−	6.63215e11i	1.11386	−	1.53310i	0.298265	−	0.954483i	$-0.403592\pi$
$811$	4.81854e11	−	6.63215e11i	1.11386	−	1.53310i	0.815599	−	0.578618i	$-0.196408\pi$
$812$	1.99590e11	−	3.45110e11i	0.459107	−	0.793841i
$813$	9.53103e11	−	6.92470e11i	2.18161	−	1.58503i
$814$	−2.86797e10	−	7.47959e10i	−0.0653247	−	0.170365i
$815$	1.74927e11	+	4.54792e11i	0.396484	+	1.03082i
$816$	−8.85846e10	−	9.44307e9i	−0.199801	−	0.0212987i
$817$	−7.37815e10	+	2.27076e11i	−0.165600	+	0.509663i
$818$	3.27563e11	−	5.03995e11i	0.731614	−	1.12568i
$819$	1.80818e12	+	5.87512e11i	4.01888	+	1.30581i
$820$	−8.06109e10	+	1.58180e11i	−0.178295	+	0.349861i
$821$	1.03464e11	+	3.18430e11i	0.227729	+	0.700877i	0.998003	+	0.0631644i	$0.0201193\pi$
$821$	1.03464e11	+	3.18430e11i	0.227729	+	0.700877i	−0.770274	+	0.637713i	$0.779881\pi$
$822$	2.17182e11	−	8.09338e11i	0.475704	−	1.77273i
$823$	6.06127e10	−	8.34262e10i	0.132119	−	0.181846i	−0.737832	−	0.674984i	$-0.764150\pi$
$823$	6.06127e10	−	8.34262e10i	0.132119	−	0.181846i	0.869951	+	0.493138i	$0.164150\pi$
$824$	−1.15468e10	+	7.23839e10i	−0.0250468	+	0.157012i
$825$	−7.54519e11	+	6.81198e11i	−1.62875	+	1.47047i
$826$	2.32394e11	−	3.57565e11i	0.499234	−	0.768131i
$827$	2.39182e11	−	3.29206e11i	0.511337	−	0.703795i	−0.472807	−	0.881166i	$-0.656759\pi$
$827$	2.39182e11	−	3.29206e11i	0.511337	−	0.703795i	0.984144	+	0.177371i	$0.0567592\pi$
$828$	−8.48111e11	−	9.43324e11i	−1.80439	−	2.00696i
$829$	1.31511e11	+	4.04748e11i	0.278447	+	0.856973i	0.988287	+	0.152609i	$0.0487676\pi$
$829$	1.31511e11	+	4.04748e11i	0.278447	+	0.856973i	−0.709839	+	0.704364i	$0.751232\pi$
$830$	−1.20191e11	−	2.55099e10i	−0.253255	−	0.0537522i
$831$	−6.11820e11	−	1.98792e11i	−1.28298	−	0.416865i
$832$	6.04665e11	+	1.97951e11i	1.26189	+	0.413109i
$833$	6.08453e9	−	1.87263e10i	0.0126371	−	0.0388930i
$834$	−3.86802e10	−	7.43319e11i	−0.0799511	−	1.53642i
$835$	−1.26307e11	−	8.19052e10i	−0.259826	−	0.168487i
$836$	−8.05178e10	+	3.77434e11i	−0.164842	+	0.772709i
$837$	−1.48972e12	+	1.08234e12i	−3.03530	+	2.20527i
$838$	1.81459e11	−	9.44261e9i	0.367962	−	0.0191477i
$839$	4.41253e11	−	6.07332e11i	0.890512	−	1.22568i	−0.0828854	−	0.996559i	$-0.526414\pi$
$839$	4.41253e11	−	6.07332e11i	0.890512	−	1.22568i	0.973397	−	0.229125i	$-0.0735865\pi$
$840$	1.03150e12	+	4.59800e11i	2.07182	+	0.923532i
$841$	1.60099e11	−	1.16319e11i	0.320040	−	0.232522i
$842$	−4.53531e11	−	5.60487e11i	−0.902315	−	1.11511i
$843$			1.49091e12i			2.95217i
$844$	4.63578e10	+	4.44224e11i	0.0913593	+	0.875452i
$845$	−2.11654e11	+	3.26396e11i	−0.415145	+	0.640203i
$846$	−6.39774e11	+	2.38414e12i	−1.24895	+	4.65426i
$847$	−1.74413e11	+	5.66703e10i	−0.338880	+	0.110109i
$848$	−6.99430e11	+	1.47588e11i	−1.35257	+	0.285409i
$849$	3.42722e11			0.659647
$850$	2.47152e10	−	4.86224e10i	0.0473466	−	0.0931452i
$851$			8.38875e10i			0.159948i
$852$	1.29779e11	−	6.08348e11i	0.246289	−	1.15450i
$853$	−7.89236e10	−	2.42902e11i	−0.149077	−	0.458812i	0.848436	−	0.529299i	$-0.177545\pi$
$853$	−7.89236e10	−	2.42902e11i	−0.149077	−	0.458812i	−0.997513	+	0.0704864i	$0.977545\pi$
$854$	−1.36162e11	+	5.07415e11i	−0.255992	+	0.953963i
$855$	9.96925e11	−	5.29140e10i	1.86551	−	0.0990162i
$856$	6.01135e11	+	3.07134e11i	1.11964	+	0.572048i
$857$	−3.09345e11			−0.573483			−0.286741	−	0.958008i	$-0.592572\pi$
$857$	−3.09345e11			−0.573483			−0.286741	+	0.958008i	$0.592572\pi$
$858$	9.93242e11	+	1.22748e12i	1.83276	+	2.26498i
$859$	−4.61731e11	−	6.35518e11i	−0.848040	−	1.16723i	−0.984291	−	0.176552i	$-0.943505\pi$
$859$	−4.61731e11	−	6.35518e11i	−0.848040	−	1.16723i	0.136251	−	0.990674i	$-0.456495\pi$
$860$	1.92174e11	+	3.77229e11i	0.351318	+	0.689623i
$861$	3.96013e11	+	2.87720e11i	0.720604	+	0.523549i
$862$	−2.09305e10	+	1.08916e9i	−0.0379097	+	0.00197271i
$863$	4.89991e11	+	6.74415e11i	0.883375	+	1.21586i	0.975475	+	0.220112i	$0.0706423\pi$
$863$	4.89991e11	+	6.74415e11i	0.883375	+	1.21586i	−0.0920993	+	0.995750i	$0.529358\pi$
$864$	−1.69757e12	−	6.55240e11i	−3.04631	−	1.17583i
$865$	5.15204e11	+	6.35357e11i	0.920270	+	1.13489i
$866$	3.49051e10	+	6.70774e11i	0.0620608	+	1.19263i
$867$	−1.02212e12	−	3.32106e11i	−1.80894	−	0.587760i
$868$	−3.12396e11	−	7.03052e11i	−0.550335	−	1.23854i
$869$	2.84936e10	−	8.76943e10i	0.0499653	−	0.153777i
$870$	−5.73301e11	−	6.36333e11i	−1.00070	−	1.11073i
$871$	−1.15693e12	+	3.75911e11i	−2.01018	+	0.653149i
$872$	1.65560e9	+	1.05286e10i	0.00286346	+	0.0182098i
$873$	1.32171e12	+	9.60280e11i	2.27552	+	1.65326i
$874$	2.20239e11	−	3.38864e11i	0.377440	−	0.580737i
$875$	−4.87942e11	+	4.89901e11i	−0.832408	+	0.835749i
$876$	−1.02010e12	+	4.53275e11i	−1.73231	+	0.769742i
$877$	7.59289e11	+	5.51656e11i	1.28354	+	0.932545i	0.999654	−	0.0263132i	$-0.00837672\pi$
$877$	7.59289e11	+	5.51656e11i	1.28354	+	0.932545i	0.283885	+	0.958858i	$0.408377\pi$
$878$	2.17384e11	−	8.10089e11i	0.365804	−	1.36318i
$879$	−1.16589e12	+	3.78822e11i	−1.95301	+	0.634570i
$880$	3.72233e11	+	5.74208e11i	0.620703	+	0.957499i
$881$	9.29559e10	−	2.86089e11i	0.154303	−	0.474895i	−0.843787	−	0.536678i	$-0.819679\pi$
$881$	9.29559e10	−	2.86089e11i	0.154303	−	0.474895i	0.998090	+	0.0617836i	$0.0196788\pi$
$882$	3.48238e11	−	5.35805e11i	0.575442	−	0.885386i
$883$	4.16818e11	+	1.35432e11i	0.685651	+	0.222782i	0.631068	−	0.775728i	$-0.282617\pi$
$883$	4.16818e11	+	1.35432e11i	0.685651	+	0.222782i	0.0545835	+	0.998509i	$0.482617\pi$
$884$	−7.33414e10	−	4.24160e10i	−0.120099	−	0.0694578i
$885$	−5.77050e11	−	7.11625e11i	−0.940676	−	1.16005i
$886$	3.21302e10	+	8.37946e10i	0.0521409	+	0.135982i
$887$	3.50023e11	+	4.81766e11i	0.565461	+	0.778290i	0.992008	−	0.126175i	$-0.0402701\pi$
$887$	3.50023e11	+	4.81766e11i	0.565461	+	0.778290i	−0.426547	+	0.904465i	$0.640270\pi$
$888$	8.66136e10	+	1.70456e11i	0.139295	+	0.274132i
$889$	6.43552e11	+	4.67568e11i	1.03033	+	0.748579i
$890$	−6.64416e11	−	3.83337e11i	−1.05896	−	0.610971i
$891$	−1.51389e12	−	2.08369e12i	−2.40205	−	3.30614i
$892$	−4.59668e9	−	4.40478e10i	−0.00726081	−	0.0695768i
$893$	−7.86449e11			−1.23670
$894$	−8.56667e11	+	6.93191e11i	−1.34110	+	1.08518i
$895$	−9.21132e11	+	4.88912e10i	−1.43559	+	0.0761971i
$896$	4.15709e11	−	6.36523e11i	0.644996	−	0.987603i
$897$	−5.10972e11	−	1.57261e12i	−0.789273	−	2.42913i
$898$	5.38483e11	−	2.06476e11i	0.828069	−	0.317515i
$899$			5.83468e11i			0.893261i
$900$	1.18370e12	−	1.31620e12i	1.80414	−	2.00610i
$901$	9.51888e10			0.144440
$902$	1.06190e11	+	2.76942e11i	0.160420	+	0.418372i
$903$	1.11015e12	−	3.60709e11i	1.66967	−	0.542507i
$904$	−7.24137e10	−	4.60507e11i	−0.108429	−	0.689544i
$905$	−2.22742e11	+	3.43494e11i	−0.332053	+	0.512065i
$906$	−1.01452e12	−	1.25378e12i	−1.50573	−	1.86083i
$907$		−	3.88946e11i		−	0.574725i	−0.957822	−	0.287362i	$-0.907222\pi$
$907$		−	3.88946e11i		−	0.574725i	0.957822	−	0.287362i	$-0.0927784\pi$
$908$	−4.48625e10	−	4.29895e11i	−0.0659994	−	0.632440i
$909$	2.03893e12	−	1.48137e12i	2.98639	−	2.16974i
$910$	7.18906e11	+	7.97948e11i	1.04835	+	1.16361i
$911$	7.42148e11	−	1.02148e12i	1.07750	−	1.48305i	0.215255	−	0.976558i	$-0.430942\pi$
$911$	7.42148e11	−	1.02148e12i	1.07750	−	1.48305i	0.862244	−	0.506493i	$-0.169058\pi$
$912$	9.76401e10	−	9.15953e11i	0.141140	−	1.32402i
$913$	−1.66068e11	+	1.20655e11i	−0.239003	+	0.173645i
$914$	6.07806e11	−	2.33057e11i	0.870924	−	0.333947i
$915$	9.47016e11	+	6.14101e11i	1.35105	+	0.876103i
$916$	7.20959e11	+	4.16957e11i	1.02407	+	0.592255i
$917$	1.08582e11	−	3.34182e11i	0.153561	−	0.472613i
$918$	2.03168e11	+	1.32046e11i	0.286078	+	0.185931i
$919$	−6.52938e11	−	2.12152e11i	−0.915397	−	0.297431i	−0.186820	−	0.982394i	$-0.559818\pi$
$919$	−6.52938e11	−	2.12152e11i	−0.915397	−	0.297431i	−0.728577	+	0.684964i	$0.759818\pi$
$920$	−1.48682e11	−	7.01014e11i	−0.207542	−	0.978533i
$921$	−1.30099e11	−	4.00403e11i	−0.180815	−	0.556491i
$922$	−3.88501e11	−	1.04253e11i	−0.537612	−	0.144266i
$923$	3.47718e11	−	4.78593e11i	0.479093	−	0.659416i
$924$	1.72420e12	−	7.66136e11i	2.36537	−	1.05104i
$925$	−1.16404e11	+	1.23917e10i	−0.159002	+	0.0169264i
$926$	1.87849e11	+	1.22089e11i	0.255485	+	0.166048i
$927$	1.86198e11	−	2.56279e11i	0.252148	−	0.347052i
$928$	−4.84138e11	+	3.13132e11i	−0.652795	+	0.422217i
$929$	−2.56476e11	−	7.89353e11i	−0.344338	−	1.05976i	−0.961937	−	0.273270i	$-0.911895\pi$
$929$	−2.56476e11	−	7.89353e11i	−0.344338	−	1.05976i	0.617600	−	0.786493i	$-0.288105\pi$
$930$	−1.64373e12	+	1.73258e11i	−2.19735	+	0.231612i
$931$	1.93627e11	+	6.29132e10i	0.257731	+	0.0837419i
$932$	−2.58334e11	−	5.81384e11i	−0.342387	−	0.770547i
$933$	5.85726e11	−	1.80268e12i	0.772980	−	2.37899i
$934$	3.75703e11	−	1.95505e10i	0.493693	−	0.0256903i
$935$	−3.27126e10	−	8.50494e10i	−0.0428024	−	0.111282i
$936$	−1.94215e12	−	1.94646e12i	−2.53034	−	2.53596i
$937$	2.86243e11	−	2.07968e11i	0.371345	−	0.269798i	−0.386424	−	0.922321i	$-0.626290\pi$
$937$	2.86243e11	−	2.07968e11i	0.371345	−	0.269798i	0.757768	+	0.652524i	$0.226290\pi$
$938$	7.55372e10	+	1.45160e12i	0.0975774	+	1.87515i
$939$	3.69378e10	−	5.08405e10i	0.0475126	−	0.0653954i
$940$	−9.86121e11	+	9.85980e11i	−1.26305	+	1.26286i
$941$	1.13304e12	−	8.23204e11i	1.44507	−	1.04990i	0.458114	−	0.888893i	$-0.348525\pi$
$941$	1.13304e12	−	8.23204e11i	1.44507	−	1.04990i	0.986953	−	0.161009i	$-0.0514749\pi$
$942$	4.11161e11	−	3.32700e11i	0.522166	−	0.422522i
$943$		−	3.10604e11i		−	0.392790i
$944$	−5.34582e11	+	3.07588e11i	−0.673172	+	0.387330i
$945$	−1.93469e12	−	2.38588e12i	−2.42596	−	2.99172i
$946$	6.83122e11	+	1.83313e11i	0.852970	+	0.228891i
$947$	−7.54446e11	+	2.45134e11i	−0.938054	+	0.304792i	−0.737852	−	0.674962i	$-0.764160\pi$
$947$	−7.54446e11	+	2.45134e11i	−0.938054	+	0.304792i	−0.200202	+	0.979755i	$0.564160\pi$
$948$	−4.59169e10	+	2.15240e11i	−0.0568512	+	0.266495i
$949$	−1.06160e12			−1.30887
$950$	5.02748e11	+	2.55552e11i	0.617243	+	0.313751i
$951$			6.01762e11i			0.735703i
$952$	−7.16643e10	+	7.15055e10i	−0.0872479	+	0.0870546i
$953$	4.65598e11	+	1.43296e12i	0.564469	+	1.73726i	0.669525	+	0.742790i	$0.266498\pi$
$953$	4.65598e11	+	1.43296e12i	0.564469	+	1.73726i	−0.105056	+	0.994466i	$0.533502\pi$
$954$	2.98374e12	+	8.00674e11i	3.60220	+	0.966635i
$955$	1.66983e11	+	4.34138e11i	0.200751	+	0.521933i
$956$	1.52040e10	+	1.45692e11i	0.0182023	+	0.174423i
$957$	−1.43092e12			−1.70596
$958$	4.43690e11	−	3.59022e11i	0.526766	−	0.426244i
$959$	−5.59723e11	−	7.70392e11i	−0.661757	−	0.910830i
$960$	−1.02591e12	−	1.27092e12i	−1.20788	−	1.49635i
$961$	2.20909e11	+	1.60500e11i	0.259012	+	0.188183i
$962$	9.44939e9	+	1.81590e11i	0.0110333	+	0.212027i
$963$	−1.71480e12	−	2.36021e12i	−1.99392	−	2.74439i
$964$	−1.67369e11	+	7.84555e11i	−0.193806	+	0.908480i
$965$	7.87541e11	+	2.10458e11i	0.908164	+	0.242692i
$966$	−1.97315e12	+	1.02677e11i	−2.26596	+	0.117914i
$967$	6.78039e11	+	2.20308e11i	0.775441	+	0.251956i	0.669893	−	0.742458i	$-0.266340\pi$
$967$	6.78039e11	+	2.20308e11i	0.775441	+	0.251956i	0.105549	+	0.994414i	$0.466340\pi$
$968$	2.61916e11	+	4.17812e10i	0.298305	+	0.0475860i
$969$	−3.79045e10	+	1.16658e11i	−0.0429928	+	0.132318i
$970$	3.75635e11	+	8.43014e11i	0.424306	+	0.952243i
$971$	−6.64295e11	+	2.15843e11i	−0.747281	+	0.242806i	−0.657811	−	0.753183i	$-0.728517\pi$
$971$	−6.64295e11	+	2.15843e11i	−0.747281	+	0.242806i	−0.0894703	+	0.995989i	$0.528517\pi$
$972$	2.16136e12	+	2.40400e12i	2.42137	+	2.69321i
$973$	−6.84298e11	−	4.97171e11i	−0.763473	−	0.554696i
$974$	2.31596e11	+	1.50522e11i	0.257332	+	0.167249i
$975$	2.10671e12	−	9.41339e11i	2.33123	−	1.04166i
$976$	5.09249e11	−	5.63900e11i	0.561217	−	0.621445i
$977$	6.24751e11	+	4.53908e11i	0.685691	+	0.498184i	0.875241	−	0.483687i	$-0.160703\pi$
$977$	6.24751e11	+	4.53908e11i	0.685691	+	0.498184i	−0.189550	+	0.981871i	$0.560703\pi$
$978$	−1.87665e12	−	5.03590e11i	−2.05129	−	0.550455i
$979$	−1.21879e12	+	3.96010e11i	−1.32678	+	0.431098i
$980$	3.21662e11	−	1.63866e11i	0.348735	−	0.177658i
$981$	1.42336e10	−	4.38066e10i	0.0153688	−	0.0473002i
$982$	6.64882e11	+	4.32129e11i	0.714988	+	0.464694i
$983$	−7.77379e11	−	2.52586e11i	−0.832566	−	0.270517i	−0.138440	−	0.990371i	$-0.544209\pi$
$983$	−7.77379e11	−	2.52586e11i	−0.832566	−	0.270517i	−0.694126	+	0.719854i	$0.744209\pi$
$984$	−3.20698e11	−	6.31135e11i	−0.342071	−	0.673196i
$985$	4.00688e10	+	7.54915e11i	0.0425659	+	0.801961i
$986$	7.16890e10	−	2.74884e10i	0.0758481	−	0.0290832i
$987$	2.25995e12	+	3.11055e12i	2.38139	+	3.27770i
$988$	4.38576e11	−	7.58340e11i	0.460274	−	0.795859i
$989$	−5.99222e11	−	4.35361e11i	−0.626329	−	0.455055i
$990$	−3.10006e11	−	2.94108e12i	−0.322722	−	3.06172i
$991$	3.30804e11	+	4.55313e11i	0.342986	+	0.472079i	0.945311	−	0.326172i	$-0.105759\pi$
$991$	3.30804e11	+	4.55313e11i	0.342986	+	0.472079i	−0.602325	+	0.798251i	$0.705759\pi$
$992$	−6.02853e10	+	1.11102e12i	−0.0622537	+	1.14729i
$993$	−6.74187e11			−0.693400
$994$	−4.44646e11	−	5.49507e11i	−0.455479	−	0.562896i
$995$	−3.52555e11	+	1.31928e12i	−0.359695	+	1.34599i
$996$	3.64344e11	−	3.27569e11i	0.370232	−	0.332863i
$997$	−4.14964e10	−	1.27713e11i	−0.0419981	−	0.129257i	0.927859	−	0.372931i	$-0.121647\pi$
$997$	−4.14964e10	−	1.27713e11i	−0.0419981	−	0.129257i	−0.969857	+	0.243674i	$0.921647\pi$
$998$	−7.16110e10	−	1.86759e11i	−0.0721868	−	0.188261i
$999$		−	5.20046e11i		−	0.522131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.91.15	yes	464
4.3	odd	2	inner	100.9.j.b.91.60	yes	464
25.11	even	5	inner	100.9.j.b.11.60	yes	464
100.11	odd	10	inner	100.9.j.b.11.15	✓	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.15	✓	464	100.11	odd	10	inner
100.9.j.b.11.60	yes	464	25.11	even	5	inner
100.9.j.b.91.15	yes	464	1.1	even	1	trivial
100.9.j.b.91.60	yes	464	4.3	odd	2	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.9394 + 5.72837i) q^{2} +(-148.141 + 48.1341i) q^{3} +(190.372 - 171.157i) q^{4} +(-603.811 - 161.359i) q^{5} +(1937.42 - 1567.70i) q^{6} -2832.14i q^{7} +(-1863.59 + 3647.50i) q^{8} +(14321.0 - 10404.8i) q^{9} +(9944.91 - 1048.25i) q^{10} +(9819.91 - 13516.0i) q^{11} +(-19963.5 + 34518.8i) q^{12} +(-30680.3 + 22290.6i) q^{13} +(16223.5 + 42310.5i) q^{14} +(97216.4 - 5159.98i) q^{15} +(6946.74 - 65166.8i) q^{16} +(-2696.77 + 8299.81i) q^{17} +(-154345. + 237478. i) q^{18} +(-85818.9 - 27884.2i) q^{19} +(-142566. + 72628.3i) q^{20} +(136323. + 419558. i) q^{21} +(-69279.4 + 258172. i) q^{22} +(164536. - 226464. i) q^{23} +(100506. - 630048. i) q^{24} +(338552. + 194861. i) q^{25} +(330657. - 508756. i) q^{26} +(-1.02001e6 + 1.40392e6i) q^{27} +(-484740. - 539160. i) q^{28} +(169918. + 522954. i) q^{29} +(-1.42280e6 + 633978. i) q^{30} +(1.00917e6 + 327900. i) q^{31} +(269519. + 1.01335e6i) q^{32} +(-804159. + 2.47495e6i) q^{33} +(-7256.17 - 139442. i) q^{34} +(-456991. + 1.71008e6i) q^{35} +(945461. - 4.43193e6i) q^{36} +(-242445. + 176147. i) q^{37} +(1.44181e6 - 75027.8i) q^{38} +(3.47209e6 - 4.77893e6i) q^{39} +(1.71381e6 - 1.90169e6i) q^{40} +(897684. - 652206. i) q^{41} +(-4.43996e6 - 5.48704e6i) q^{42} -2.64599e6i q^{43} +(-443913. - 4.25380e6i) q^{44} +(-1.03261e7 + 3.97174e6i) q^{45} +(-1.16080e6 + 4.32576e6i) q^{46} +(8.28897e6 - 2.69325e6i) q^{47} +(2.10764e6 + 9.98828e6i) q^{48} -2.25623e6 q^{49} +(-6.17399e6 - 971755. i) q^{50} -1.35935e6i q^{51} +(-2.02549e6 + 9.49464e6i) q^{52} +(-3.37059e6 - 1.03736e7i) q^{53} +(7.19616e6 - 2.68168e7i) q^{54} +(-8.11029e6 + 6.57656e6i) q^{55} +(1.03302e7 + 5.27796e6i) q^{56} +1.40555e7 q^{57} +(-5.53415e6 - 6.83927e6i) q^{58} +(-5.53162e6 - 7.61362e6i) q^{59} +(1.76241e7 - 1.76216e7i) q^{60} +(9.37962e6 + 6.81469e6i) q^{61} +(-1.69548e7 + 882278. i) q^{62} +(-2.94680e7 - 4.05592e7i) q^{63} +(-9.83127e6 - 1.35949e7i) q^{64} +(2.21219e7 - 8.50876e6i) q^{65} +(-2.16374e6 - 4.15807e7i) q^{66} +(3.05075e7 + 9.91248e6i) q^{67} +(907179. + 2.04162e6i) q^{68} +(-1.34739e7 + 4.14685e7i) q^{69} +(-2.96879e6 - 2.81654e7i) q^{70} +(-1.48358e7 + 4.82046e6i) q^{71} +(1.12631e7 + 7.16264e7i) q^{72} +(2.26474e7 + 1.64543e7i) q^{73} +(2.61295e6 - 4.02034e6i) q^{74} +(-5.95330e7 - 1.25711e7i) q^{75} +(-2.11101e7 + 9.38011e6i) q^{76} +(-3.82791e7 - 2.78114e7i) q^{77} +(-2.44956e7 + 9.12838e7i) q^{78} +(5.24907e6 - 1.70553e6i) q^{79} +(-1.47098e7 + 3.82275e7i) q^{80} +(4.76396e7 - 1.46620e8i) q^{81} +(-9.67480e6 + 1.48858e7i) q^{82} +(-1.16854e7 - 3.79683e6i) q^{83} +(9.77621e7 + 5.65394e7i) q^{84} +(2.96759e6 - 4.57637e6i) q^{85} +(1.51572e7 + 3.95296e7i) q^{86} +(-5.03439e7 - 6.92924e7i) q^{87} +(3.09991e7 + 6.10063e7i) q^{88} +(-6.20573e7 - 4.50872e7i) q^{89} +(1.31515e8 - 1.18487e8i) q^{90} +(6.31301e7 + 8.68911e7i) q^{91} +(-7.43790e6 - 7.12738e7i) q^{92} -1.65284e8 q^{93} +(-1.08404e8 + 8.77178e7i) q^{94} +(4.73190e7 + 3.06845e7i) q^{95} +(-8.87034e7 - 1.37146e8i) q^{96} +(2.85197e7 + 8.77746e7i) q^{97} +(3.37067e7 - 1.29245e7i) q^{98} -2.95737e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) \) 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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