LMFDB - Embedded newform 100.9.j.b.11.84

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(11,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [464] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			11.84
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.84

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(10.4569 + 12.1100i) q^{2} +(-89.5931 - 29.1106i) q^{3} +(-37.3057 + 253.267i) q^{4} +(-624.689 + 19.7078i) q^{5} +(-584.338 - 1389.38i) q^{6} +1003.88i q^{7} +(-3457.18 + 2196.62i) q^{8} +(1871.54 + 1359.75i) q^{9} +(-6770.99 - 7358.92i) q^{10} +(-5707.24 - 7855.34i) q^{11} +(10715.1 - 21605.0i) q^{12} +(-31703.7 - 23034.1i) q^{13} +(-12157.0 + 10497.5i) q^{14} +(56541.6 + 16419.4i) q^{15} +(-62752.6 - 18896.6i) q^{16} +(17422.3 + 53620.2i) q^{17} +(3103.88 + 36883.2i) q^{18} +(-168174. + 54643.0i) q^{19} +(18313.1 - 158949. i) q^{20} +(29223.4 - 89940.4i) q^{21} +(35448.3 - 151257. i) q^{22} +(-48326.1 - 66515.1i) q^{23} +(373684. - 96161.7i) q^{24} +(389848. - 24622.5i) q^{25} +(-52579.5 - 624799. i) q^{26} +(235199. + 323724. i) q^{27} +(-254249. - 37450.3i) q^{28} +(-157167. + 483712. i) q^{29} +(392411. + 856416. i) q^{30} +(753344. - 244776. i) q^{31} +(-427360. - 957536. i) q^{32} +(282656. + 869925. i) q^{33} +(-467159. + 771686. i) q^{34} +(-19784.2 - 627111. i) q^{35} +(-414200. + 423273. i) q^{36} +(3.00094e6 + 2.18031e6i) q^{37} +(-2.42031e6 - 1.46519e6i) q^{38} +(2.16990e6 + 2.98661e6i) q^{39} +(2.11637e6 - 1.44034e6i) q^{40} +(2.51995e6 + 1.83085e6i) q^{41} +(1.39477e6 - 586603. i) q^{42} -5.08373e6i q^{43} +(2.20241e6 - 1.15241e6i) q^{44} +(-1.19593e6 - 812539. i) q^{45} +(300159. - 1.28077e6i) q^{46} +(-4.55608e6 - 1.48036e6i) q^{47} +(5.07211e6 + 3.51977e6i) q^{48} +4.75703e6 q^{49} +(4.37479e6 + 4.46360e6i) q^{50} -5.31117e6i q^{51} +(7.01651e6 - 7.17021e6i) q^{52} +(1.79340e6 - 5.51951e6i) q^{53} +(-1.46085e6 + 6.23342e6i) q^{54} +(3.72006e6 + 4.79467e6i) q^{55} +(-2.20514e6 - 3.47058e6i) q^{56} +1.66579e7 q^{57} +(-7.50125e6 + 3.15483e6i) q^{58} +(-1.32908e6 + 1.82932e6i) q^{59} +(-6.26781e6 + 1.37076e7i) q^{60} +(-1.41872e7 + 1.03076e7i) q^{61} +(1.08419e7 + 6.56342e6i) q^{62} +(-1.36502e6 + 1.87879e6i) q^{63} +(7.12693e6 - 1.51882e7i) q^{64} +(2.02589e7 + 1.37643e7i) q^{65} +(-7.57911e6 + 1.25197e7i) q^{66} +(-2.79483e7 + 9.08096e6i) q^{67} +(-1.42302e7 + 2.41215e6i) q^{68} +(2.39339e6 + 7.36610e6i) q^{69} +(7.38745e6 - 6.79723e6i) q^{70} +(-7.40334e6 - 2.40549e6i) q^{71} +(-9.45710e6 - 589844. i) q^{72} +(7.52022e6 - 5.46376e6i) q^{73} +(4.97696e6 + 5.91408e7i) q^{74} +(-3.56445e7 - 9.14270e6i) q^{75} +(-7.56543e6 - 4.46314e7i) q^{76} +(7.88579e6 - 5.72936e6i) q^{77} +(-1.34775e7 + 5.75083e7i) q^{78} +(2.50843e7 + 8.15037e6i) q^{79} +(3.95733e7 + 1.05678e7i) q^{80} +(-1.63387e7 - 5.02852e7i) q^{81} +(4.17924e6 + 4.96617e7i) q^{82} +(-3.74353e7 + 1.21635e7i) q^{83} +(2.16888e7 + 1.07566e7i) q^{84} +(-1.19402e7 - 3.31526e7i) q^{85} +(6.15642e7 - 5.31602e7i) q^{86} +(2.81622e7 - 3.87620e7i) q^{87} +(3.69861e7 + 1.46207e7i) q^{88} +(3.63526e7 - 2.64117e7i) q^{89} +(-2.66585e6 - 2.29794e7i) q^{90} +(2.31234e7 - 3.18266e7i) q^{91} +(1.86489e7 - 9.75801e6i) q^{92} -7.46200e7 q^{93} +(-2.97153e7 - 7.06542e7i) q^{94} +(1.03979e8 - 3.74492e7i) q^{95} +(1.04141e7 + 9.82293e7i) q^{96} +(-1.64337e7 + 5.05777e7i) q^{97} +(4.97439e7 + 5.76078e7i) q^{98} -2.24620e7i 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 $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	10.4569	+	12.1100i	0.653557	+	0.756877i
$2$	10.4569	+	12.1100i	0.653557	+	0.756877i
$3$	−89.5931	−	29.1106i	−1.10609	−	0.359390i	−0.301645	−	0.953420i	$-0.597536\pi$
$3$	−89.5931	−	29.1106i	−1.10609	−	0.359390i	−0.804442	+	0.594031i	$0.797536\pi$
$4$	−37.3057	+	253.267i	−0.145725	+	0.989325i
$5$	−624.689	+	19.7078i	−0.999503	+	0.0315325i
$5$	−624.689	+	19.7078i	−0.999503	+	0.0315325i
$6$	−584.338	−	1389.38i	−0.450878	−	1.07205i
$7$			1003.88i			0.418108i	0.977904	+	0.209054i	$0.0670384\pi$
$7$			1003.88i			0.418108i	−0.977904	+	0.209054i	$0.932962\pi$
$8$	−3457.18	+	2196.62i	−0.844037	+	0.536284i
$9$	1871.54	+	1359.75i	0.285252	+	0.207248i
$10$	−6770.99	−	7358.92i	−0.677099	−	0.735892i
$11$	−5707.24	−	7855.34i	−0.389812	−	0.536530i	0.568339	−	0.822795i	$-0.307586\pi$
$11$	−5707.24	−	7855.34i	−0.389812	−	0.536530i	−0.958151	+	0.286265i	$0.907586\pi$
$12$	10715.1	−	21605.0i	0.516738	−	1.04191i
$13$	−31703.7	−	23034.1i	−1.11004	−	0.806488i	−0.127366	−	0.991856i	$-0.540652\pi$
$13$	−31703.7	−	23034.1i	−1.11004	−	0.806488i	−0.982669	+	0.185368i	$0.940652\pi$
$14$	−12157.0	+	10497.5i	−0.316456	+	0.273257i
$15$	56541.6	+	16419.4i	1.11687	+	0.324333i
$16$	−62752.6	−	18896.6i	−0.957528	−	0.288340i
$17$	17422.3	+	53620.2i	0.208597	+	0.641996i	0.999546	+	0.0301145i	$0.00958719\pi$
$17$	17422.3	+	53620.2i	0.208597	+	0.641996i	−0.790949	+	0.611882i	$0.790413\pi$
$18$	3103.88	+	36883.2i	0.0295675	+	0.351349i
$19$	−168174.	+	54643.0i	−1.29046	+	0.419295i	−0.872252	−	0.489057i	$-0.837341\pi$
$19$	−168174.	+	54643.0i	−1.29046	+	0.419295i	−0.418206	+	0.908352i	$0.637341\pi$
$20$	18313.1	−	158949.i	0.114457	−	0.993428i
$21$	29223.4	−	89940.4i	0.150264	−	0.462464i
$22$	35448.3	−	151257.i	0.151323	−	0.645693i
$23$	−48326.1	−	66515.1i	−0.172691	−	0.237689i	0.713895	−	0.700253i	$-0.246930\pi$
$23$	−48326.1	−	66515.1i	−0.172691	−	0.237689i	−0.886586	+	0.462564i	$0.846930\pi$
$24$	373684.	−	96161.7i	1.12631	−	0.289839i
$25$	389848.	−	24622.5i	0.998011	−	0.0630335i
$26$	−52579.5	−	624799.i	−0.115060	−	1.36725i
$27$	235199.	+	323724.i	0.442569	+	0.609143i
$28$	−254249.	−	37450.3i	−0.413644	−	0.0609289i
$29$	−157167.	+	483712.i	−0.222214	+	0.683903i	0.776349	+	0.630303i	$0.217069\pi$
$29$	−157167.	+	483712.i	−0.222214	+	0.683903i	−0.998563	+	0.0535997i	$0.982931\pi$
$30$	392411.	+	856416.i	0.484458	+	1.05730i
$31$	753344.	−	244776.i	0.815730	−	0.265047i	0.128707	−	0.991683i	$-0.458917\pi$
$31$	753344.	−	244776.i	0.815730	−	0.265047i	0.687023	+	0.726636i	$0.258917\pi$
$32$	−427360.	−	957536.i	−0.407562	−	0.913178i
$33$	282656.	+	869925.i	0.238343	+	0.733544i
$34$	−467159.	+	771686.i	−0.349582	+	0.577464i
$35$	−19784.2	−	627111.i	−0.0131840	−	0.417900i
$36$	−414200.	+	423273.i	−0.246604	+	0.252006i
$37$	3.00094e6	+	2.18031e6i	1.60122	+	1.16335i	0.885129	+	0.465345i	$0.154070\pi$
$37$	3.00094e6	+	2.18031e6i	1.60122	+	1.16335i	0.716089	+	0.698009i	$0.245930\pi$
$38$	−2.42031e6	−	1.46519e6i	−1.16074	−	0.702685i
$39$	2.16990e6	+	2.98661e6i	0.937953	+	1.29098i
$40$	2.11637e6	−	1.44034e6i	0.826707	−	0.562632i
$41$	2.51995e6	+	1.83085e6i	0.891776	+	0.647913i	0.936341	−	0.351093i	$-0.114190\pi$
$41$	2.51995e6	+	1.83085e6i	0.891776	+	0.647913i	−0.0445643	+	0.999007i	$0.514190\pi$
$42$	1.39477e6	−	586603.i	0.448234	−	0.188516i
$43$		−	5.08373e6i		−	1.48699i	−0.668740	−	0.743496i	$-0.733166\pi$
$43$		−	5.08373e6i		−	1.48699i	0.668740	−	0.743496i	$-0.266834\pi$
$44$	2.20241e6	−	1.15241e6i	0.587608	−	0.307465i
$45$	−1.19593e6	−	812539.i	−0.291645	−	0.198150i
$46$	300159.	−	1.28077e6i	0.0670377	−	0.286049i
$47$	−4.55608e6	−	1.48036e6i	−0.933683	−	0.303372i	−0.197615	−	0.980280i	$-0.563320\pi$
$47$	−4.55608e6	−	1.48036e6i	−0.933683	−	0.303372i	−0.736068	+	0.676908i	$0.763320\pi$
$48$	5.07211e6	+	3.51977e6i	0.955484	+	0.663055i
$49$	4.75703e6			0.825186
$50$	4.37479e6	+	4.46360e6i	0.699966	+	0.714176i
$51$		−	5.31117e6i		−	0.785072i
$52$	7.01651e6	−	7.17021e6i	0.959639	−	0.980660i
$53$	1.79340e6	−	5.51951e6i	0.227286	−	0.699515i	−0.770765	−	0.637119i	$-0.780126\pi$
$53$	1.79340e6	−	5.51951e6i	0.227286	−	0.699515i	0.998051	−	0.0623956i	$-0.0198741\pi$
$54$	−1.46085e6	+	6.23342e6i	−0.171803	+	0.733080i
$55$	3.72006e6	+	4.79467e6i	0.406536	+	0.523971i
$56$	−2.20514e6	−	3.47058e6i	−0.224225	−	0.352898i
$57$	1.66579e7			1.57805
$58$	−7.50125e6	+	3.15483e6i	−0.662860	+	0.278782i
$59$	−1.32908e6	+	1.82932e6i	−0.109684	+	0.150967i	−0.860330	−	0.509738i	$-0.829742\pi$
$59$	−1.32908e6	+	1.82932e6i	−0.109684	+	0.150967i	0.750646	+	0.660705i	$0.229742\pi$
$60$	−6.26781e6	+	1.37076e7i	−0.483628	+	1.05768i
$61$	−1.41872e7	+	1.03076e7i	−1.02465	+	0.744454i	−0.967232	−	0.253896i	$-0.918288\pi$
$61$	−1.41872e7	+	1.03076e7i	−1.02465	+	0.744454i	−0.0574216	+	0.998350i	$0.518288\pi$
$62$	1.08419e7	+	6.56342e6i	0.733735	+	0.444184i
$63$	−1.36502e6	+	1.87879e6i	−0.0866519	+	0.119266i
$64$	7.12693e6	−	1.51882e7i	0.424798	−	0.905288i
$65$	2.02589e7	+	1.37643e7i	1.13491	+	0.771085i
$66$	−7.57911e6	+	1.25197e7i	−0.399432	+	0.659809i
$67$	−2.79483e7	+	9.08096e6i	−1.38694	+	0.450643i	−0.904943	−	0.425532i	$-0.860087\pi$
$67$	−2.79483e7	+	9.08096e6i	−1.38694	+	0.450643i	−0.481993	+	0.876175i	$0.660087\pi$
$68$	−1.42302e7	+	2.41215e6i	−0.665541	+	0.112815i
$69$	2.39339e6	+	7.36610e6i	0.105589	+	0.324968i
$70$	7.38745e6	−	6.79723e6i	0.307682	−	0.283100i
$71$	−7.40334e6	−	2.40549e6i	−0.291336	−	0.0946608i	0.159703	−	0.987165i	$-0.448946\pi$
$71$	−7.40334e6	−	2.40549e6i	−0.291336	−	0.0946608i	−0.451039	+	0.892504i	$0.648946\pi$
$72$	−9.45710e6	−	589844.i	−0.351907	−	0.0219486i
$73$	7.52022e6	−	5.46376e6i	0.264813	−	0.192398i	−0.447453	−	0.894307i	$-0.647669\pi$
$73$	7.52022e6	−	5.46376e6i	0.264813	−	0.192398i	0.712266	+	0.701910i	$0.247669\pi$
$74$	4.97696e6	+	5.91408e7i	0.165973	+	1.97224i
$75$	−3.56445e7	−	9.14270e6i	−1.12654	−	0.288954i
$76$	−7.56543e6	−	4.46314e7i	−0.226767	−	1.33778i
$77$	7.88579e6	−	5.72936e6i	0.224327	−	0.162983i
$78$	−1.34775e7	+	5.75083e7i	−0.364108	+	1.55365i
$79$	2.50843e7	+	8.15037e6i	0.644010	+	0.209252i	0.612771	−	0.790260i	$-0.290055\pi$
$79$	2.50843e7	+	8.15037e6i	0.644010	+	0.209252i	0.0312391	+	0.999512i	$0.490055\pi$
$80$	3.95733e7	+	1.05678e7i	0.966144	+	0.258003i
$81$	−1.63387e7	−	5.02852e7i	−0.379556	−	1.16815i
$82$	4.17924e6	+	4.96617e7i	0.0924362	+	1.09841i
$83$	−3.74353e7	+	1.21635e7i	−0.788803	+	0.256298i	−0.675594	−	0.737274i	$-0.736113\pi$
$83$	−3.74353e7	+	1.21635e7i	−0.788803	+	0.256298i	−0.113209	+	0.993571i	$0.536113\pi$
$84$	2.16888e7	+	1.07566e7i	0.435630	+	0.216052i
$85$	−1.19402e7	−	3.31526e7i	−0.228737	−	0.635099i
$86$	6.15642e7	−	5.31602e7i	1.12547	−	0.971835i
$87$	2.81622e7	−	3.87620e7i	0.491575	−	0.676596i
$88$	3.69861e7	+	1.46207e7i	0.616748	+	0.243801i
$89$	3.63526e7	−	2.64117e7i	0.579397	−	0.420956i	−0.259110	−	0.965848i	$-0.583429\pi$
$89$	3.63526e7	−	2.64117e7i	0.579397	−	0.420956i	0.838507	+	0.544892i	$0.183429\pi$
$90$	−2.66585e6	−	2.29794e7i	−0.0406317	−	0.350242i
$91$	2.31234e7	−	3.18266e7i	0.337199	−	0.464114i
$92$	1.86489e7	−	9.75801e6i	0.260317	−	0.136210i
$93$	−7.46200e7			−0.997525
$94$	−2.97153e7	−	7.06542e7i	−0.380600	−	0.904955i
$95$	1.03979e8	−	3.74492e7i	1.27660	−	0.459778i
$96$	1.04141e7	+	9.82293e7i	0.122613	+	1.15653i
$97$	−1.64337e7	+	5.05777e7i	−0.185630	+	0.571310i	−0.999959	−	0.00909375i	$-0.997105\pi$
$97$	−1.64337e7	+	5.05777e7i	−0.185630	+	0.571310i	0.814329	+	0.580404i	$0.197105\pi$
$98$	4.97439e7	+	5.76078e7i	0.539306	+	0.624564i
$99$		−	2.24620e7i		−	0.233834i
$100$	−8.30750e6	+	9.96543e7i	−0.0830750	+	0.996543i
$101$	9.52737e7			0.915562			0.457781	−	0.889065i	$-0.348644\pi$
$101$	9.52737e7			0.915562			0.457781	+	0.889065i	$0.348644\pi$
$102$	6.43184e7	−	5.55385e7i	0.594203	−	0.513090i
$103$	5.96443e7	+	1.93796e7i	0.529932	+	0.172185i	0.561748	−	0.827308i	$-0.310129\pi$
$103$	5.96443e7	+	1.93796e7i	0.529932	+	0.172185i	−0.0318159	+	0.999494i	$0.510129\pi$
$104$	1.60203e8	+	9.99190e6i	1.36942	+	0.0854112i
$105$	−1.64830e7	+	5.67607e7i	−0.135606	+	0.466972i
$106$	8.55948e7	−	3.59989e7i	0.677991	−	0.285145i
$107$		−	1.61542e8i		−	1.23239i	−0.787592	−	0.616197i	$-0.788672\pi$
$107$		−	1.61542e8i		−	1.23239i	0.787592	−	0.616197i	$-0.211328\pi$
$108$	−9.07629e7	+	4.74915e7i	−0.667134	+	0.349077i
$109$	−1.08044e8	−	7.84986e7i	−0.765411	−	0.556104i	0.135154	−	0.990825i	$-0.456847\pi$
$109$	−1.08044e8	−	7.84986e7i	−0.765411	−	0.556104i	−0.900565	+	0.434721i	$0.856847\pi$
$110$	−1.91632e7	+	9.51875e7i	−0.130887	+	0.650143i
$111$	−2.05394e8	−	2.82700e8i	−1.35299	−	1.86223i
$112$	1.89699e7	−	6.29958e7i	0.120557	−	0.400350i
$113$	6.92801e7	+	5.03349e7i	0.424908	+	0.308714i	0.779610	−	0.626266i	$-0.215418\pi$
$113$	6.92801e7	+	5.03349e7i	0.424908	+	0.308714i	−0.354702	+	0.934980i	$0.615418\pi$
$114$	1.74190e8	+	2.01728e8i	1.03135	+	1.19439i
$115$	3.14996e7	+	4.05989e7i	0.180100	+	0.232125i
$116$	−1.16645e8	−	5.78506e7i	−0.644220	−	0.319504i
$117$	−2.80141e7	−	8.62185e7i	−0.149497	−	0.460105i
$118$	−3.60511e7	+	3.03386e6i	−0.185948	+	0.0156483i
$119$	−5.38280e7	+	1.74898e7i	−0.268424	+	0.0872161i
$120$	−2.31541e8	+	6.74357e7i	−1.11662	+	0.325211i
$121$	3.71068e7	−	1.14203e8i	0.173106	−	0.532765i
$122$	−2.73180e8	−	6.40216e7i	−1.23313	−	0.288993i
$123$	−1.72473e8	−	2.37388e8i	−0.753529	−	1.03714i
$124$	3.38898e7	+	1.99929e8i	0.143345	+	0.845647i
$125$	−2.43049e8	+	2.30644e7i	−0.995528	+	0.0944719i
$126$	−3.70262e7	+	3.11591e6i	−0.146902	+	0.0123624i
$127$	−2.68232e8	−	3.69189e8i	−1.03109	−	1.41917i	−0.904128	−	0.427262i	$-0.859478\pi$
$127$	−2.68232e8	−	3.69189e8i	−1.03109	−	1.41917i	−0.126959	−	0.991908i	$-0.540522\pi$
$128$	2.58455e8	−	7.25146e7i	0.962822	−	0.270138i
$129$	−1.47990e8	+	4.55467e8i	−0.534410	+	1.64474i
$130$	4.51593e7	+	3.89269e8i	0.158115	+	1.36294i
$131$	−4.46212e7	+	1.44983e7i	−0.151515	+	0.0492302i	−0.383793	−	0.923419i	$-0.625382\pi$
$131$	−4.46212e7	+	1.44983e7i	−0.151515	+	0.0492302i	0.232278	+	0.972650i	$0.425382\pi$
$132$	−2.30868e8	+	3.91342e7i	−0.760446	+	0.128902i
$133$	−5.48548e7	−	1.68826e8i	−0.175311	−	0.539550i
$134$	−4.02224e8	−	2.43496e8i	−1.24752	−	0.755219i
$135$	−1.53306e8	−	1.97592e8i	−0.461556	−	0.594885i
$136$	−1.78015e8	−	1.47104e8i	−0.520356	−	0.430001i
$137$	1.38804e7	+	1.00847e7i	0.0394021	+	0.0286273i	0.607312	−	0.794463i	$-0.292248\pi$
$137$	1.38804e7	+	1.00847e7i	0.0394021	+	0.0286273i	−0.567910	+	0.823091i	$0.692248\pi$
$138$	−6.41762e7	+	1.06011e8i	−0.176953	+	0.292303i
$139$	2.39410e8	+	3.29520e8i	0.641333	+	0.882719i	0.998686	−	0.0512503i	$-0.0163206\pi$
$139$	2.39410e8	+	3.29520e8i	0.641333	+	0.882719i	−0.357353	+	0.933969i	$0.616321\pi$
$140$	1.59565e8	+	1.83841e7i	0.415360	+	0.0478554i
$141$	3.65099e8	+	2.65260e8i	0.923707	+	0.671112i
$142$	−4.82855e7	−	1.14809e8i	−0.118758	−	0.282372i
$143$			3.80504e8i			0.909946i
$144$	−9.17491e7	−	1.20694e8i	−0.213379	−	0.280695i
$145$	8.86479e7	−	3.05267e8i	0.200538	−	0.690570i
$146$	1.44805e8	+	3.39360e7i	0.318692	+	0.0746877i
$147$	−4.26197e8	−	1.38480e8i	−0.912728	−	0.296563i
$148$	−6.64154e8	+	6.78702e8i	−1.38427	+	1.41460i
$149$	3.38643e8			0.687064			0.343532	−	0.939141i	$-0.388377\pi$
$149$	3.38643e8			0.687064			0.343532	+	0.939141i	$0.388377\pi$
$150$	−2.62013e8	−	5.27260e8i	−0.517557	−	1.04150i
$151$		−	6.20556e8i		−	1.19364i	−0.802375	−	0.596820i	$-0.796431\pi$
$151$		−	6.20556e8i		−	1.19364i	0.802375	−	0.596820i	$-0.203569\pi$
$152$	4.61377e8	−	5.58325e8i	0.864333	−	1.04595i
$153$	−4.03038e7	+	1.24042e8i	−0.0735495	+	0.226362i
$154$	1.51844e8	+	3.55857e7i	0.269969	+	0.0632692i
$155$	−4.65782e8	+	1.67756e8i	−0.806967	+	0.290637i
$156$	−8.37360e8	+	4.38147e8i	−1.41388	+	0.739812i
$157$	−1.05089e9			−1.72966			−0.864829	−	0.502066i	$-0.832573\pi$
$157$	−1.05089e9			−1.72966			−0.864829	+	0.502066i	$0.832573\pi$
$158$	1.63603e8	+	3.88999e8i	0.262520	+	0.624195i
$159$	−3.21352e8	+	4.42303e8i	−0.502797	+	0.692040i
$160$	2.85838e8	+	5.89740e8i	0.436154	+	0.899872i
$161$	6.67730e7	−	4.85134e7i	0.0993796	−	0.0722035i
$162$	4.38104e8	−	7.23690e8i	0.636087	−	1.05073i
$163$	4.45868e8	−	6.13684e8i	0.631620	−	0.869350i	−0.366514	−	0.930412i	$-0.619449\pi$
$163$	4.45868e8	−	6.13684e8i	0.631620	−	0.869350i	0.998134	+	0.0610626i	$0.0194489\pi$
$164$	−5.57702e8	+	5.69919e8i	−0.770951	+	0.787839i
$165$	−1.93716e8	−	5.37862e8i	−0.261355	−	0.725663i
$166$	−5.38757e8	−	3.26150e8i	−0.709514	−	0.429522i
$167$	9.50587e8	−	3.08864e8i	1.22215	−	0.397102i	0.374288	−	0.927312i	$-0.377887\pi$
$167$	9.50587e8	−	3.08864e8i	1.22215	−	0.397102i	0.847866	+	0.530211i	$0.177887\pi$
$168$	9.65345e7	+	3.75133e8i	0.121184	+	0.470921i
$169$	2.22482e8	+	6.84728e8i	0.272739	+	0.839404i
$170$	2.76621e8	−	4.91270e8i	0.331199	−	0.588200i
$171$	−3.89045e8	−	1.26408e8i	−0.455004	−	0.147840i
$172$	1.28754e9	+	1.89652e8i	1.47112	+	0.216693i
$173$	1.11005e9	−	8.06496e8i	1.23924	−	0.900364i	0.241696	−	0.970352i	$-0.422296\pi$
$173$	1.11005e9	−	8.06496e8i	1.23924	−	0.900364i	0.997548	+	0.0699884i	$0.0222962\pi$
$174$	7.63899e8	−	6.42854e7i	0.833372	−	0.0701319i
$175$	2.47179e7	+	3.91359e8i	0.0263548	+	0.417276i
$176$	2.09704e8	+	6.00790e8i	0.218553	+	0.626141i
$177$	1.72328e8	−	1.25204e8i	0.175576	−	0.127563i
$178$	6.99984e8	+	1.64046e8i	0.697281	+	0.163413i
$179$	1.93794e8	+	6.29675e7i	0.188768	+	0.0613344i	0.401875	−	0.915694i	$-0.368358\pi$
$179$	1.93794e8	+	6.29675e7i	0.188768	+	0.0613344i	−0.213108	+	0.977029i	$0.568358\pi$
$180$	2.50404e8	−	2.72577e8i	0.238535	−	0.259657i
$181$	4.70011e8	+	1.44654e9i	0.437919	+	1.34778i	0.890066	+	0.455832i	$0.150658\pi$
$181$	4.70011e8	+	1.44654e9i	0.437919	+	1.34778i	−0.452147	+	0.891944i	$0.649342\pi$
$182$	6.27221e8	−	5.27833e7i	0.571656	−	0.0481073i
$183$	1.57113e9	−	5.10492e8i	1.40091	−	0.455182i
$184$	3.13180e8	+	1.23801e8i	0.273227	+	0.108007i
$185$	−1.91763e9	−	1.30288e9i	−1.63711	−	1.11228i
$186$	−7.80295e8	−	9.03651e8i	−0.651940	−	0.755003i
$187$	3.21772e8	−	4.42881e8i	0.263137	−	0.362176i
$188$	5.44894e8	−	1.09868e9i	0.436195	−	0.879507i
$189$	−3.24979e8	+	2.36111e8i	−0.254688	+	0.185041i
$190$	1.54082e9	+	8.67591e8i	1.18232	+	0.665734i
$191$	−9.79271e8	+	1.34785e9i	−0.735817	+	1.01276i	0.263032	+	0.964787i	$0.415278\pi$
$191$	−9.79271e8	+	1.34785e9i	−0.735817	+	1.01276i	−0.998848	+	0.0479775i	$0.984722\pi$
$192$	−1.08066e9	+	1.15329e9i	−0.795215	+	0.848660i
$193$	−3.31133e8			−0.238656			−0.119328	−	0.992855i	$-0.538074\pi$
$193$	−3.31133e8			−0.238656			−0.119328	+	0.992855i	$0.538074\pi$
$194$	−7.84343e8	+	3.29874e8i	−0.553731	+	0.232885i
$195$	−1.41437e9	−	1.82294e9i	−0.978195	−	1.26076i
$196$	−1.77465e8	+	1.20480e9i	−0.120251	+	0.816377i
$197$	−8.12668e6	+	2.50113e7i	−0.00539570	+	0.0166063i	−0.953718	−	0.300702i	$-0.902779\pi$
$197$	−8.12668e6	+	2.50113e7i	−0.00539570	+	0.0166063i	0.948322	+	0.317308i	$0.102779\pi$
$198$	2.72016e8	−	2.34883e8i	0.176984	−	0.152824i
$199$		−	1.67210e9i		−	1.06623i	−0.846044	−	0.533114i	$-0.821022\pi$
$199$		−	1.67210e9i		−	1.06623i	0.846044	−	0.533114i	$-0.178978\pi$
$200$	−1.29369e9	+	9.41473e8i	−0.808555	+	0.588421i
$201$	2.76833e9			1.69603
$202$	9.96269e8	+	1.15377e9i	0.598372	+	0.692968i
$203$	−4.85587e8	−	1.57777e8i	−0.285945	−	0.0929092i
$204$	1.34515e9	+	1.98137e8i	0.776691	+	0.114405i
$205$	−1.61027e9	−	1.09405e9i	−0.911763	−	0.619471i
$206$	3.89008e8	+	9.24946e8i	0.216018	+	0.513626i
$207$		−	1.90197e8i		−	0.103591i
$208$	1.55422e9	+	2.04454e9i	0.830348	+	1.09230i
$209$	1.38905e9	+	1.00920e9i	0.728001	+	0.528923i
$210$	−8.59736e8	+	3.93932e8i	−0.442067	+	0.202556i
$211$	4.01150e8	+	5.52136e8i	0.202385	+	0.278558i	0.898130	−	0.439730i	$-0.144926\pi$
$211$	4.01150e8	+	5.52136e8i	0.202385	+	0.278558i	−0.695746	+	0.718288i	$0.744926\pi$
$212$	1.33101e9	+	6.60118e8i	0.658926	+	0.326797i
$213$	5.93263e8	+	4.31031e8i	0.288223	+	0.209406i
$214$	1.95628e9	−	1.68923e9i	0.932771	−	0.805441i
$215$	1.00189e8	+	3.17575e9i	0.0468885	+	1.48625i
$216$	−1.52422e9	−	6.02527e8i	−0.700219	−	0.276797i
$217$	2.45725e8	+	7.56264e8i	0.110818	+	0.341063i
$218$	−1.79187e8	−	2.12927e9i	−0.0793380	−	0.942768i
$219$	−8.32813e8	+	2.70597e8i	−0.362052	+	0.117638i
$220$	−1.35311e9	+	7.63301e8i	−0.577621	+	0.325840i
$221$	6.82742e8	−	2.10127e9i	0.286212	−	0.880870i
$222$	1.27572e9	−	5.44349e9i	0.525224	−	2.24112i
$223$	−1.79170e8	−	2.46606e8i	−0.0724511	−	0.0997204i	0.771254	−	0.636528i	$-0.219630\pi$
$223$	−1.79170e8	−	2.46606e8i	−0.0724511	−	0.0997204i	−0.843705	+	0.536808i	$0.819630\pi$
$224$	9.61248e8	−	4.29016e8i	0.381806	−	0.170405i
$225$	7.63097e8	+	4.84015e8i	0.297748	+	0.188855i
$226$	1.14899e8	+	1.36533e9i	0.0440434	+	0.523365i
$227$	−1.10519e8	−	1.52116e8i	−0.0416229	−	0.0572890i	0.787698	−	0.616061i	$-0.211273\pi$
$227$	−1.10519e8	−	1.52116e8i	−0.0416229	−	0.0572890i	−0.829321	+	0.558772i	$0.811273\pi$
$228$	−6.21435e8	+	4.21890e9i	−0.229962	+	1.56120i
$229$	8.27338e8	−	2.54629e9i	0.300844	−	0.925902i	−0.680352	−	0.732886i	$-0.738173\pi$
$229$	8.27338e8	−	2.54629e9i	0.300844	−	0.925902i	0.981196	−	0.193016i	$-0.0618271\pi$
$230$	−1.62265e8	+	8.06001e8i	−0.0579846	+	0.288021i
$231$	−8.73297e8	+	2.83751e8i	−0.306700	+	0.0996529i
$232$	−5.19176e8	−	2.01751e9i	−0.179210	−	0.696409i
$233$	2.66030e8	+	8.18756e8i	0.0902624	+	0.277799i	0.985990	−	0.166804i	$-0.0533447\pi$
$233$	2.66030e8	+	8.18756e8i	0.0902624	+	0.277799i	−0.895728	+	0.444603i	$0.853345\pi$
$234$	7.51167e8	−	1.24083e9i	0.250538	−	0.413856i
$235$	2.87531e9	+	8.34974e8i	0.942785	+	0.273780i
$236$	−4.13724e8	−	4.04855e8i	−0.133371	−	0.130512i
$237$	−2.01011e9	−	1.46043e9i	−0.637129	−	0.462901i
$238$	−7.74677e8	−	4.68970e8i	−0.241442	−	0.146163i
$239$	1.16336e9	+	1.60123e9i	0.356553	+	0.490753i	0.949184	−	0.314721i	$-0.101911\pi$
$239$	1.16336e9	+	1.60123e9i	0.356553	+	0.490753i	−0.592631	+	0.805474i	$0.701911\pi$
$240$	−3.23786e9	−	2.09880e9i	−0.975916	−	0.632596i
$241$	4.14469e9	+	3.01130e9i	1.22864	+	0.892659i	0.996787	−	0.0800926i	$-0.0255216\pi$
$241$	4.14469e9	+	3.01130e9i	1.22864	+	0.892659i	0.231852	+	0.972751i	$0.425522\pi$
$242$	1.77102e9	−	7.44846e8i	0.516372	−	0.217173i
$243$			2.35549e9i			0.675548i
$244$	−2.08131e9	−	3.97768e9i	−0.587189	−	1.12220i
$245$	−2.97167e9	+	9.37506e7i	−0.824776	+	0.0260201i
$246$	1.07125e9	−	4.57100e9i	0.292516	−	1.24816i
$247$	6.59039e9	+	2.14135e9i	1.77061	+	0.575306i
$248$	−2.06676e9	+	2.50105e9i	−0.546366	+	0.661173i
$249$	3.70803e9			0.964596
$250$	−2.82085e9	−	2.70214e9i	−0.722138	−	0.691749i
$251$			4.44916e9i			1.12094i	0.828174	+	0.560470i	$0.189380\pi$
$251$			4.44916e9i			1.12094i	−0.828174	+	0.560470i	$0.810620\pi$
$252$	−4.24914e8	−	4.15806e8i	−0.105366	−	0.103107i
$253$	−2.46690e8	+	7.59235e8i	−0.0602102	+	0.185308i
$254$	1.66602e9	−	7.10888e9i	0.400262	−	1.70791i
$255$	1.04671e8	+	3.31783e9i	0.0247552	+	0.784682i
$256$	3.58080e9	+	2.37162e9i	0.833720	+	0.552187i
$257$	−7.19531e9			−1.64937			−0.824683	−	0.565595i	$-0.808647\pi$
$257$	−7.19531e9			−1.64937			−0.824683	+	0.565595i	$0.808647\pi$
$258$	−7.06325e9	+	2.97062e9i	−1.59414	+	0.670452i
$259$	−2.18876e9	+	3.01257e9i	−0.486407	+	0.669482i
$260$	−4.24183e9	+	4.61743e9i	−0.928239	+	1.01043i
$261$	−9.51873e8	+	6.91576e8i	−0.205124	+	0.149032i
$262$	−6.42175e8	−	3.88756e8i	−0.136285	−	0.0825035i
$263$	−3.83074e8	+	5.27257e8i	−0.0800682	+	0.110204i	−0.847172	−	0.531318i	$-0.821697\pi$
$263$	−3.83074e8	+	5.27257e8i	−0.0800682	+	0.110204i	0.767104	+	0.641523i	$0.221697\pi$
$264$	−2.88809e9	−	2.38660e9i	−0.594558	−	0.491319i
$265$	−1.01154e9	+	3.48332e9i	−0.205116	+	0.706334i
$266$	1.47087e9	−	2.42969e9i	0.293798	−	0.485316i
$267$	−4.02581e9	+	1.30806e9i	−0.792151	+	0.257385i
$268$	−1.25728e9	−	7.41717e9i	−0.243720	−	1.43780i
$269$	2.10331e9	+	6.47333e9i	0.401693	+	1.23628i	0.923625	+	0.383297i	$0.125211\pi$
$269$	2.10331e9	+	6.47333e9i	0.401693	+	1.23628i	−0.521932	+	0.852987i	$0.674789\pi$
$270$	7.89729e8	−	3.92274e9i	0.148601	−	0.738133i
$271$	5.09936e9	+	1.65688e9i	0.945450	+	0.307195i	0.740865	−	0.671654i	$-0.234416\pi$
$271$	5.09936e9	+	1.65688e9i	0.945450	+	0.307195i	0.204585	+	0.978849i	$0.434416\pi$
$272$	−8.00501e7	−	3.69403e9i	−0.0146247	−	0.674876i
$273$	−2.99819e9	+	2.17831e9i	−0.539769	+	0.392165i
$274$	2.30201e7	+	2.73546e8i	0.00408418	+	0.0485321i
$275$	−2.41837e9	−	2.92186e9i	−0.422856	−	0.510892i
$276$	−1.95488e9	+	3.31370e8i	−0.336886	+	0.0571053i
$277$	4.00657e9	−	2.91094e9i	0.680540	−	0.494441i	−0.192997	−	0.981199i	$-0.561821\pi$
$277$	4.00657e9	−	2.91094e9i	0.680540	−	0.494441i	0.873537	+	0.486758i	$0.161821\pi$
$278$	−1.48700e9	+	6.34503e9i	−0.248962	+	1.06232i
$279$	1.74275e9	+	5.66253e8i	0.287619	+	0.0934532i
$280$	1.44592e9	+	2.12457e9i	0.235241	+	0.345653i
$281$	5.37211e8	+	1.65336e9i	0.0861627	+	0.265182i	0.984850	−	0.173408i	$-0.0554781\pi$
$281$	5.37211e8	+	1.65336e9i	0.0861627	+	0.265182i	−0.898687	+	0.438590i	$0.855478\pi$
$282$	6.05504e8	+	7.19516e9i	0.0957460	+	1.13774i
$283$	8.47409e8	−	2.75340e8i	0.132114	−	0.0429263i	−0.242214	−	0.970223i	$-0.577874\pi$
$283$	8.47409e8	−	2.75340e8i	0.132114	−	0.0429263i	0.374327	+	0.927297i	$0.377874\pi$
$284$	8.85418e8	−	1.78528e9i	0.136105	−	0.274431i
$285$	−1.04060e10	+	3.28290e8i	−1.57727	+	0.0497598i
$286$	−4.60792e9	+	3.97890e9i	−0.688717	+	0.594702i
$287$	−1.83795e9	+	2.52971e9i	−0.270898	+	0.372858i
$288$	5.02192e8	−	2.37317e9i	0.0729962	−	0.344952i
$289$	3.07192e9	−	2.23188e9i	0.440371	−	0.319948i
$290$	4.62378e9	−	2.11862e9i	0.653740	−	0.299545i
$291$	2.94469e9	−	4.05302e9i	0.410646	−	0.565206i
$292$	1.10324e9	+	2.10845e9i	0.151754	+	0.290023i
$293$	9.59899e8			0.130243			0.0651216	−	0.997877i	$-0.479256\pi$
$293$	9.59899e8			0.130243			0.0651216	+	0.997877i	$0.479256\pi$
$294$	−2.77971e9	−	6.60934e9i	−0.372058	−	0.884644i
$295$	7.94208e8	−	1.16895e9i	0.104869	−	0.154350i
$296$	−1.51641e10	−	9.45792e8i	−1.97538	−	0.123205i
$297$	1.20062e9	−	3.69514e9i	0.154305	−	0.474903i
$298$	3.54116e9	+	4.10098e9i	0.449036	+	0.520023i
$299$			3.22193e9i			0.403117i
$300$	3.64529e9	−	8.68650e9i	0.450036	−	1.07241i
$301$	5.10344e9			0.621723
$302$	7.51496e9	−	6.48911e9i	0.903439	−	0.780112i
$303$	−8.53587e9	−	2.77347e9i	−1.01269	−	0.329043i
$304$	1.15859e10	−	2.51068e8i	1.35655	−	0.0293966i
$305$	8.65944e9	−	6.71864e9i	1.00067	−	0.776394i
$306$	−1.92361e9	+	8.09020e8i	−0.219397	+	0.0922727i
$307$		−	4.42477e9i		−	0.498124i	−0.968488	−	0.249062i	$-0.919878\pi$
$307$		−	4.42477e9i		−	0.498124i	0.968488	−	0.249062i	$-0.0801222\pi$
$308$	1.15687e9	+	2.21095e9i	0.128553	+	0.245683i
$309$	−4.77957e9	−	3.47256e9i	−0.524270	−	0.380904i
$310$	−6.90217e9	−	3.88642e9i	−0.747376	−	0.420827i
$311$	4.43203e9	+	6.10017e9i	0.473763	+	0.652079i	0.977291	−	0.211900i	$-0.0679651\pi$
$311$	4.43203e9	+	6.10017e9i	0.473763	+	0.652079i	−0.503528	+	0.863979i	$0.667965\pi$
$312$	−1.40622e10	−	5.55879e9i	−1.48400	−	0.586627i
$313$	−1.35424e10	−	9.83916e9i	−1.41098	−	1.02513i	−0.993180	−	0.116593i	$-0.962803\pi$
$313$	−1.35424e10	−	9.83916e9i	−1.41098	−	1.02513i	−0.417796	−	0.908541i	$-0.637197\pi$
$314$	−1.09891e10	−	1.27264e10i	−1.13043	−	1.30914i
$315$	8.15689e8	−	1.20056e9i	0.0828480	−	0.121939i
$316$	−3.00001e9	+	6.04897e9i	−0.300867	+	0.606642i
$317$	−3.82478e8	−	1.17715e9i	−0.0378765	−	0.116572i	0.930331	−	0.366722i	$-0.119520\pi$
$317$	−3.82478e8	−	1.17715e9i	−0.0378765	−	0.116572i	−0.968207	+	0.250150i	$0.919520\pi$
$318$	−8.71665e9	+	7.33544e8i	−0.852396	+	0.0717328i
$319$	4.69671e9	−	1.52605e9i	0.453556	−	0.147369i
$320$	−4.15279e9	+	9.62837e9i	−0.396041	+	0.918233i
$321$	−4.70257e9	+	1.44730e10i	−0.442910	+	1.36314i
$322$	1.28574e9	+	3.01322e8i	0.119599	+	0.0280290i
$323$	−5.85993e9	−	8.06551e9i	−0.538372	−	0.741006i
$324$	1.33451e10	−	2.26212e9i	1.21100	−	0.205275i
$325$	−1.29268e10	−	8.19918e9i	−1.15866	−	0.734915i
$326$	1.20941e10	−	1.01777e9i	1.07079	−	0.0901117i
$327$	7.39486e9	+	1.01782e10i	0.646754	+	0.890181i
$328$	−1.27336e10	−	7.94199e8i	−1.10016	−	0.0686174i
$329$	1.48610e9	−	4.57374e9i	0.126842	−	0.390380i
$330$	4.48785e9	−	7.97029e9i	0.378428	−	0.672076i
$331$	7.93604e9	−	2.57858e9i	0.661138	−	0.214817i	0.0408189	−	0.999167i	$-0.487003\pi$
$331$	7.93604e9	−	2.57858e9i	0.661138	−	0.214817i	0.620319	+	0.784350i	$0.287003\pi$
$332$	−1.68405e9	−	9.93489e9i	−0.138613	−	0.817732i
$333$	2.65170e9	+	8.16108e9i	0.215649	+	0.663698i
$334$	1.36806e10	+	8.28187e9i	1.09931	+	0.665491i
$335$	1.72801e10	−	6.22358e9i	1.37204	−	0.494153i
$336$	−3.53341e9	+	5.09177e9i	−0.277228	+	0.399495i
$337$	−1.13030e10	−	8.21210e9i	−0.876342	−	0.636700i	0.0559389	−	0.998434i	$-0.482185\pi$
$337$	−1.13030e10	−	8.21210e9i	−0.876342	−	0.636700i	−0.932281	+	0.361734i	$0.882185\pi$
$338$	−5.96560e9	+	9.85440e9i	−0.457075	+	0.755029i
$339$	−4.74174e9	−	6.52645e9i	−0.359037	−	0.494172i
$340$	8.84190e9	−	1.78729e9i	0.661653	−	0.133745i
$341$	−6.22231e9	−	4.52078e9i	−0.460187	−	0.334345i
$342$	−2.53740e9	−	6.03319e9i	−0.185475	−	0.441004i
$343$			1.05626e10i			0.763124i
$344$	1.11670e10	+	1.75754e10i	0.797451	+	1.25508i
$345$	−1.64029e9	−	4.55435e9i	−0.115783	−	0.321477i
$346$	2.13744e10	+	5.00924e9i	1.49138	+	0.349516i
$347$	−2.20934e10	−	7.17857e9i	−1.52386	−	0.495131i	−0.576988	−	0.816753i	$-0.695772\pi$
$347$	−2.20934e10	−	7.17857e9i	−1.52386	−	0.495131i	−0.946868	+	0.321622i	$0.895772\pi$
$348$	8.76653e9	+	8.57862e9i	0.597738	+	0.584925i
$349$	6.66195e9			0.449055			0.224528	−	0.974468i	$-0.427916\pi$
$349$	6.66195e9			0.449055			0.224528	+	0.974468i	$0.427916\pi$
$350$	−4.48090e9	+	4.39175e9i	−0.298602	+	0.292661i
$351$		−	1.56809e10i		−	1.03310i
$352$	−5.08273e9	+	8.82194e9i	−0.331075	+	0.574637i
$353$	−6.71286e9	+	2.06601e10i	−0.432324	+	1.33056i	0.463481	+	0.886107i	$0.346600\pi$
$353$	−6.71286e9	+	2.06601e10i	−0.432324	+	1.33056i	−0.895804	+	0.444448i	$0.853400\pi$
$354$	3.31825e9	+	7.77656e8i	0.211298	+	0.0495193i
$355$	4.67219e9	+	1.35678e9i	0.294176	+	0.0854272i
$356$	5.33307e9	+	1.01922e10i	0.332030	+	0.634556i
$357$	5.33176e9			0.328245
$358$	1.26395e9	+	3.00530e9i	0.0769480	+	0.182960i
$359$	−1.18619e10	+	1.63265e10i	−0.714127	+	0.982911i	0.285572	+	0.958357i	$0.407817\pi$
$359$	−1.18619e10	+	1.63265e10i	−0.714127	+	0.982911i	−0.999699	+	0.0245538i	$0.992183\pi$
$360$	5.91938e9	+	1.82090e8i	0.352424	+	0.0108412i
$361$	1.15566e10	−	8.39635e9i	0.680457	−	0.494381i
$362$	−1.26028e10	+	2.08182e10i	−0.733895	+	1.21230i
$363$	−6.64902e9	+	9.15159e9i	−0.382940	+	0.527072i
$364$	7.19800e9	+	7.04371e9i	0.410021	+	0.401232i
$365$	−4.59012e9	+	3.56136e9i	−0.258614	+	0.200652i
$366$	2.26113e10	+	1.36883e10i	1.26009	+	0.762826i
$367$	1.23852e10	−	4.02421e9i	0.682716	−	0.221828i	0.0529317	−	0.998598i	$-0.483143\pi$
$367$	1.23852e10	−	4.02421e9i	0.682716	−	0.221828i	0.629784	+	0.776770i	$0.283143\pi$
$368$	1.77567e9	+	5.08720e9i	0.0968215	+	0.277388i
$369$	2.22668e9	+	6.85301e9i	0.120102	+	0.369637i
$370$	−4.27459e9	−	3.68466e10i	−0.228080	−	1.96603i
$371$	5.54090e9	+	1.80035e9i	0.292472	+	0.0950300i
$372$	2.78375e9	−	1.88988e10i	0.145365	−	0.986876i
$373$	1.08155e10	−	7.85791e9i	0.558741	−	0.405949i	−0.272257	−	0.962225i	$-0.587770\pi$
$373$	1.08155e10	−	7.85791e9i	0.558741	−	0.405949i	0.830998	+	0.556276i	$0.187770\pi$
$374$	8.72804e9	−	7.34502e8i	0.446098	−	0.0375411i
$375$	2.24469e10	+	5.00887e9i	1.13509	+	0.253288i
$376$	1.90030e10	−	4.89011e9i	0.950757	−	0.244662i
$377$	1.61247e10	−	1.17152e10i	0.798225	−	0.579944i
$378$	−6.25759e9	−	1.46651e9i	−0.306506	−	0.0718320i
$379$	−1.73162e10	−	5.62636e9i	−0.839256	−	0.272691i	−0.142317	−	0.989821i	$-0.545455\pi$
$379$	−1.73162e10	−	5.62636e9i	−0.839256	−	0.272691i	−0.696939	+	0.717130i	$0.745455\pi$
$380$	5.60563e9	+	2.77317e10i	0.268838	+	1.32997i
$381$	1.32844e10	+	4.08852e10i	0.630438	+	1.94029i
$382$	−2.65627e10	+	2.23536e9i	−1.24744	+	0.104977i
$383$	−3.09369e10	+	1.00520e10i	−1.43774	+	0.467151i	−0.921193	−	0.389106i	$-0.872784\pi$
$383$	−3.09369e10	+	1.00520e10i	−1.43774	+	0.467151i	−0.516550	+	0.856257i	$0.672784\pi$
$384$	−2.52668e10	−	1.02698e9i	−1.16205	−	0.0472319i
$385$	−4.81325e9	+	3.73448e9i	−0.219076	+	0.169976i
$386$	−3.46263e9	−	4.01003e9i	−0.155976	−	0.180634i
$387$	6.91262e9	−	9.51441e9i	0.308176	−	0.424168i
$388$	−1.21966e10	−	6.04895e9i	−0.538160	−	0.266903i
$389$	3.29299e10	−	2.39250e10i	1.43811	−	1.04485i	0.449676	−	0.893192i	$-0.351539\pi$
$389$	3.29299e10	−	2.39250e10i	1.43811	−	1.04485i	0.988433	−	0.151656i	$-0.0484605\pi$
$390$	7.28588e9	−	3.61904e10i	0.314937	−	1.56435i
$391$	2.72460e9	−	3.75010e9i	0.116573	−	0.160448i
$392$	−1.64459e10	+	1.04494e10i	−0.696488	+	0.442534i
$393$	4.41980e9			0.185282
$394$	−3.87868e8	+	1.63127e8i	−0.0160953	+	0.00676927i
$395$	−1.58305e10	−	4.59709e9i	−0.650288	−	0.188840i
$396$	5.68889e9	+	8.37961e8i	0.231338	+	0.0340756i
$397$	3.31320e9	−	1.01970e10i	0.133378	−	0.410496i	−0.861956	−	0.506983i	$-0.830761\pi$
$397$	3.31320e9	−	1.01970e10i	0.133378	−	0.410496i	0.995334	+	0.0964868i	$0.0307606\pi$
$398$	2.02492e10	−	1.74850e10i	0.807003	−	0.696841i
$399$			1.67225e10i			0.659795i
$400$	−2.49293e10	−	5.82170e9i	−0.973799	−	0.227410i
$401$	7.60740e9			0.294211			0.147105	−	0.989121i	$-0.453004\pi$
$401$	7.60740e9			0.294211			0.147105	+	0.989121i	$0.453004\pi$
$402$	2.89482e10	+	3.35246e10i	1.10845	+	1.28369i
$403$	−2.95220e10	−	9.59229e9i	−1.11925	−	0.363665i
$404$	−3.55425e9	+	2.41297e10i	−0.133421	+	0.905788i
$405$	1.11976e10	+	3.10906e10i	0.416203	+	1.15561i
$406$	−3.16706e9	−	7.53033e9i	−0.116561	−	0.277147i
$407$		−	3.60170e10i		−	1.31259i
$408$	1.16666e10	+	1.83617e10i	0.421022	+	0.662630i
$409$	−2.23996e10	−	1.62743e10i	−0.800474	−	0.581579i	0.110579	−	0.993867i	$-0.464730\pi$
$409$	−2.23996e10	−	1.62743e10i	−0.800474	−	0.581579i	−0.911053	+	0.412289i	$0.864730\pi$
$410$	−3.58945e9	−	3.09407e10i	−0.127026	−	1.09495i
$411$	−9.50015e8	−	1.30758e9i	−0.0332938	−	0.0458250i
$412$	−7.13330e9	+	1.43830e10i	−0.247572	+	0.499183i
$413$	−1.83641e9	−	1.33423e9i	−0.0631203	−	0.0458596i
$414$	2.30329e9	−	1.98888e9i	0.0784058	−	0.0677028i
$415$	2.31457e10	−	8.33614e9i	0.780329	−	0.281043i
$416$	−8.50710e9	+	4.02013e10i	−0.284059	+	1.34235i
$417$	−1.18570e10	−	3.64921e10i	−0.392130	−	1.20685i
$418$	2.30369e9	+	2.73745e10i	0.0754602	+	0.896689i
$419$	1.03758e10	−	3.37129e9i	0.336639	−	0.109381i	−0.135819	−	0.990734i	$-0.543367\pi$
$419$	1.03758e10	−	3.37129e9i	0.336639	−	0.109381i	0.472458	+	0.881353i	$0.343367\pi$
$420$	−1.37607e10	−	6.29211e9i	−0.442226	−	0.202208i
$421$	−4.15191e8	+	1.27783e9i	−0.0132166	+	0.0406764i	−0.957447	−	0.288608i	$-0.906808\pi$
$421$	−4.15191e8	+	1.27783e9i	−0.0132166	+	0.0406764i	0.944231	+	0.329285i	$0.106808\pi$
$422$	−2.49159e9	+	1.06316e10i	−0.0785645	+	0.335234i
$423$	−6.51395e9	−	8.96569e9i	−0.203462	−	0.280041i
$424$	5.92418e9	+	2.30213e10i	0.183301	+	0.712307i
$425$	8.11229e9	+	2.04747e10i	0.248650	+	0.627571i
$426$	9.83906e8	+	1.16917e10i	0.0298755	+	0.355008i
$427$	−1.03475e10	−	1.42422e10i	−0.311262	−	0.428415i
$428$	4.09132e10	+	6.02643e9i	1.21924	+	0.179591i
$429$	1.10767e10	−	3.40906e10i	0.327025	−	1.00648i
$430$	−3.74108e10	+	3.44219e10i	−1.09427	+	1.00684i
$431$	−2.29339e10	+	7.45168e9i	−0.664614	+	0.215946i	−0.621847	−	0.783139i	$-0.713617\pi$
$431$	−2.29339e10	+	7.45168e9i	−0.664614	+	0.215946i	−0.0427669	+	0.999085i	$0.513617\pi$
$432$	−8.64206e9	−	2.47590e10i	−0.248132	−	0.710882i
$433$	1.92146e10	+	5.91365e10i	0.546613	+	1.68230i	0.717124	+	0.696946i	$0.245458\pi$
$433$	1.92146e10	+	5.91365e10i	0.546613	+	1.68230i	−0.170511	+	0.985356i	$0.554542\pi$
$434$	−6.58886e9	+	1.08839e10i	−0.185717	+	0.306780i
$435$	−1.68287e10	+	2.47692e10i	−0.469996	+	0.691760i
$436$	2.39118e10	−	2.44356e10i	0.661707	−	0.676202i
$437$	1.17618e10	+	8.54542e9i	0.322513	+	0.234319i
$438$	−1.19856e10	−	7.25578e9i	−0.325659	−	0.197146i
$439$	−3.93167e10	−	5.41148e10i	−1.05857	−	1.45699i	−0.881137	−	0.472861i	$-0.843221\pi$
$439$	−3.93167e10	−	5.41148e10i	−1.05857	−	1.45699i	−0.177431	−	0.984133i	$-0.556779\pi$
$440$	−2.33930e10	−	8.40445e9i	−0.624129	−	0.224232i
$441$	8.90297e9	+	6.46839e9i	0.235386	+	0.171018i
$442$	3.25858e10	−	1.37047e10i	0.853766	−	0.359072i
$443$		−	6.38592e10i		−	1.65809i	−0.559180	−	0.829046i	$-0.688884\pi$
$443$		−	6.38592e10i		−	1.65809i	0.559180	−	0.829046i	$-0.311116\pi$
$444$	7.92610e10	−	4.14731e10i	2.03952	−	1.06717i
$445$	−2.21886e10	+	1.72156e10i	−0.565835	+	0.439017i
$446$	1.11284e9	−	4.74849e9i	0.0281251	−	0.120010i
$447$	−3.03401e10	−	9.85809e9i	−0.759953	−	0.246924i
$448$	1.52471e10	+	7.15455e9i	0.378508	+	0.177611i
$449$	3.49473e10			0.859860			0.429930	−	0.902862i	$-0.358538\pi$
$449$	3.49473e10			0.859860			0.429930	+	0.902862i	$0.358538\pi$
$450$	2.11820e9	+	1.43024e10i	0.0516555	+	0.348787i
$451$		−	3.02441e10i		−	0.731029i
$452$	−1.53327e10	+	1.56686e10i	−0.367338	+	0.375385i
$453$	−1.80647e10	+	5.55976e10i	−0.428982	+	1.32027i
$454$	6.86444e8	−	2.92905e9i	0.0161578	−	0.0689451i
$455$	−1.38177e10	+	2.03375e10i	−0.322396	+	0.474516i
$456$	−5.75893e10	+	3.65911e10i	−1.33193	+	0.846284i
$457$	3.70953e10			0.850461			0.425231	−	0.905085i	$-0.360193\pi$
$457$	3.70953e10			0.850461			0.425231	+	0.905085i	$0.360193\pi$
$458$	3.94870e10	−	1.66072e10i	0.897413	−	0.377428i
$459$	−1.32604e10	+	1.82514e10i	−0.298749	+	0.411193i
$460$	−1.14575e10	+	6.46326e9i	−0.255893	+	0.144351i
$461$	−1.55537e10	+	1.13004e10i	−0.344373	+	0.250202i	−0.746505	−	0.665380i	$-0.768269\pi$
$461$	−1.55537e10	+	1.13004e10i	−0.344373	+	0.250202i	0.402132	+	0.915582i	$0.368269\pi$
$462$	−1.25682e10	−	7.60849e9i	−0.275871	−	0.167005i
$463$	4.39226e10	−	6.04543e10i	0.955794	−	1.31554i	0.00688863	−	0.999976i	$-0.497807\pi$
$463$	4.39226e10	−	6.04543e10i	0.955794	−	1.31554i	0.948905	−	0.315561i	$-0.102193\pi$
$464$	1.90032e10	−	2.73842e10i	0.409972	−	0.590783i
$465$	4.66143e10	−	1.47060e9i	0.997029	−	0.0314544i
$466$	−7.13331e9	+	1.17833e10i	−0.151268	+	0.249875i
$467$	7.39534e10	−	2.40289e10i	1.55486	−	0.505204i	0.599429	−	0.800428i	$-0.295394\pi$
$467$	7.39534e10	−	2.40289e10i	1.55486	−	0.505204i	0.955428	+	0.295224i	$0.0953944\pi$
$468$	2.28814e10	−	3.87860e9i	0.476979	−	0.0808523i
$469$	−9.11616e9	−	2.80567e10i	−0.188417	−	0.579889i
$470$	1.99553e10	+	4.35513e10i	0.408946	+	0.892503i
$471$	9.41529e10	+	3.05921e10i	1.91315	+	0.621621i
$472$	5.76537e8	−	9.24375e9i	0.0116161	−	0.186243i
$473$	−3.99344e10	+	2.90141e10i	−0.797816	+	0.579647i
$474$	−3.33371e9	−	3.96142e10i	−0.0660410	−	0.784761i
$475$	−6.42168e10	+	2.54433e10i	−1.26146	+	0.499804i
$476$	−2.42150e9	−	1.42853e10i	−0.0471689	−	0.278268i
$477$	1.08616e10	−	7.89140e9i	0.209807	−	0.152434i
$478$	−7.22578e9	+	3.08323e10i	−0.138412	+	0.590602i
$479$	9.57533e10	+	3.11121e10i	1.81891	+	0.591001i	0.999850	+	0.0172960i	$0.00550577\pi$
$479$	9.57533e10	+	3.11121e10i	1.81891	+	0.591001i	0.819062	+	0.573705i	$0.194494\pi$
$480$	−8.44143e9	−	6.11576e10i	−0.159020	−	1.15209i
$481$	−4.49195e10	−	1.38248e11i	−0.839179	−	2.58273i
$482$	6.87383e9	+	8.16813e10i	0.127353	+	1.51333i
$483$	−7.39465e9	+	2.40267e9i	−0.135872	+	0.0441474i
$484$	2.75396e10	+	1.36584e10i	0.501852	+	0.248895i
$485$	9.26917e9	−	3.19192e10i	0.167523	−	0.576879i
$486$	−2.85250e10	+	2.46312e10i	−0.511306	+	0.441509i
$487$	−3.48331e9	+	4.79436e9i	−0.0619264	+	0.0852344i	−0.838857	−	0.544352i	$-0.816776\pi$
$487$	−3.48331e9	+	4.79436e9i	−0.0619264	+	0.0852344i	0.776931	+	0.629586i	$0.216776\pi$
$488$	2.64057e10	−	6.67990e10i	0.465606	−	1.17785i
$489$	−5.78114e10	+	4.20024e10i	−1.01106	+	0.734580i
$490$	−3.22098e10	−	3.50066e10i	−0.558732	−	0.607248i
$491$	3.95001e9	−	5.43673e9i	0.0679630	−	0.0935431i	−0.773682	−	0.633574i	$-0.781587\pi$
$491$	3.95001e9	−	5.43673e9i	0.0679630	−	0.0935431i	0.841645	+	0.540031i	$0.181587\pi$
$492$	6.65569e10	−	3.48258e10i	1.13588	−	0.594347i
$493$	−2.86749e10			−0.485416
$494$	4.29834e10	+	1.02202e11i	0.721760	+	1.71613i
$495$	4.42676e8	+	1.40318e10i	0.00737336	+	0.233718i
$496$	−5.18997e10	+	1.12467e9i	−0.857508	+	0.0185823i
$497$	2.41481e9	−	7.43203e9i	0.0395784	−	0.121810i
$498$	3.87745e10	+	4.49043e10i	0.630419	+	0.730080i
$499$			6.45355e10i			1.04087i	0.853901	+	0.520435i	$0.174230\pi$
$499$			6.45355e10i			1.04087i	−0.853901	+	0.520435i	$0.825770\pi$
$500$	3.22564e9	−	6.24167e10i	0.0516103	−	0.998667i
$501$	−9.41573e10			−1.49452
$502$	−5.38794e10	+	4.65245e10i	−0.848414	+	0.732599i
$503$	−1.14209e10	−	3.71088e9i	−0.178414	−	0.0579703i	0.218448	−	0.975849i	$-0.429901\pi$
$503$	−1.14209e10	−	3.71088e9i	−0.178414	−	0.0579703i	−0.396862	+	0.917878i	$0.629901\pi$
$504$	5.92130e8	−	9.49376e9i	0.00917688	−	0.147135i
$505$	−5.95165e10	+	1.87763e9i	−0.915106	+	0.0288699i
$506$	−1.17740e10	+	4.95183e9i	−0.179606	+	0.0755377i
$507$		−	6.78235e10i		−	1.02647i
$508$	1.03510e11	−	5.41614e10i	1.55428	−	0.813271i
$509$	−3.99727e10	−	2.90418e10i	−0.595514	−	0.432666i	0.248770	−	0.968563i	$-0.419974\pi$
$509$	−3.99727e10	−	2.90418e10i	−0.595514	−	0.432666i	−0.844284	+	0.535896i	$0.819974\pi$
$510$	−3.90845e10	+	3.59619e10i	−0.577728	+	0.531571i
$511$	5.48494e9	+	7.54937e9i	0.0804430	+	0.110720i
$512$	8.72370e9	+	6.81635e10i	0.126947	+	0.991910i
$513$	−5.72436e10	−	4.15899e10i	−0.826527	−	0.600507i
$514$	−7.52408e10	−	8.71355e10i	−1.07796	−	1.24837i
$515$	−3.76411e10	−	1.09308e10i	−0.535098	−	0.155390i
$516$	−1.09834e11	−	5.44726e10i	−1.54931	−	0.768386i
$517$	1.43739e10	+	4.42383e10i	0.201193	+	0.619207i
$518$	−5.93701e10	+	4.99625e9i	−0.824610	+	0.0693945i
$519$	−1.22930e11	+	3.99424e10i	−1.69429	+	0.550510i
$520$	−1.00274e11	−	3.08460e9i	−1.37143	−	0.0421876i
$521$	−1.85368e10	+	5.70505e10i	−0.251585	+	0.774299i	0.742898	+	0.669404i	$0.233451\pi$
$521$	−1.85368e10	+	5.70505e10i	−0.251585	+	0.774299i	−0.994483	+	0.104895i	$0.966549\pi$
$522$	−1.83287e10	−	4.29546e9i	−0.246859	−	0.0578532i
$523$	3.75049e10	+	5.16210e10i	0.501281	+	0.689953i	0.982419	−	0.186691i	$-0.0597764\pi$
$523$	3.75049e10	+	5.16210e10i	0.501281	+	0.689953i	−0.481138	+	0.876645i	$0.659776\pi$
$524$	−2.00732e9	−	1.18419e10i	−0.0266251	−	0.157072i
$525$	9.17814e9	−	3.57827e10i	0.120814	−	0.471016i
$526$	−1.03909e10	+	8.74437e8i	−0.135740	+	0.0114231i
$527$	2.62499e10	+	3.61299e10i	0.340318	+	0.468408i
$528$	−1.29872e9	−	5.99313e10i	−0.0167101	−	0.771112i
$529$	2.21106e10	−	6.80493e10i	0.282343	−	0.868963i
$530$	−5.27607e10	+	2.41750e10i	−0.668663	+	0.306382i
$531$	−4.97484e9	+	1.61642e9i	−0.0625750	+	0.0203318i
$532$	4.48044e10	−	7.59476e9i	0.559338	−	0.0948129i
$533$	−3.77197e10	−	1.16089e11i	−0.467369	−	1.43841i
$534$	−5.79382e10	−	3.50743e10i	−0.712525	−	0.431345i
$535$	3.18363e9	+	1.00913e11i	0.0388604	+	1.23178i
$536$	7.66749e10	−	9.27864e10i	0.928954	−	1.12415i
$537$	−1.55296e10	−	1.12829e10i	−0.186751	−	0.135682i
$538$	−5.63980e10	+	9.31622e10i	−0.673186	+	1.11201i
$539$	−2.71495e10	−	3.73681e10i	−0.321667	−	0.442737i
$540$	5.57627e10	−	3.14561e10i	0.655795	−	0.369939i
$541$	1.92757e10	+	1.40046e10i	0.225020	+	0.163486i	0.694583	−	0.719412i	$-0.255589\pi$
$541$	1.92757e10	+	1.40046e10i	0.225020	+	0.163486i	−0.469564	+	0.882899i	$0.655589\pi$
$542$	3.32587e10	+	7.90793e10i	0.385397	+	0.916359i
$543$		−	1.43283e11i		−	1.64814i
$544$	4.38977e10	−	3.95975e10i	0.501240	−	0.452140i
$545$	6.90410e10	+	4.69079e10i	0.782566	+	0.531692i
$546$	−5.77312e10	−	1.35297e10i	−0.649591	−	0.152236i
$547$	−9.13061e9	−	2.96671e9i	−0.101988	−	0.0331380i	0.257578	−	0.966257i	$-0.417075\pi$
$547$	−9.13061e9	−	2.96671e9i	−0.101988	−	0.0331380i	−0.359567	+	0.933119i	$0.617075\pi$
$548$	−3.07194e9	+	3.13923e9i	−0.0340636	+	0.0348097i
$549$	−4.05677e10			−0.446571
$550$	1.00951e10	−	5.98403e10i	0.110322	−	0.653947i
$551$		−	8.99357e10i		−	0.975722i
$552$	−2.44549e10	−	2.02085e10i	−0.263396	−	0.217660i
$553$	−8.18196e9	+	2.51815e10i	−0.0874897	+	0.269266i
$554$	7.71480e10	+	1.80802e10i	0.819003	+	0.191939i
$555$	1.33879e11	+	1.72552e11i	1.41104	+	1.81864i
$556$	−9.23880e10	+	4.83418e10i	−0.966755	+	0.505852i
$557$	1.32413e11			1.37566			0.687830	−	0.725872i	$-0.258563\pi$
$557$	1.32413e11			1.37566			0.687830	+	0.725872i	$0.258563\pi$
$558$	1.13664e10	+	2.70260e10i	0.117243	+	0.278769i
$559$	−1.17099e11	+	1.61173e11i	−1.19924	+	1.65061i
$560$	−1.06088e10	+	3.97267e10i	−0.107873	+	0.403952i
$561$	−4.17210e10	+	3.03121e10i	−0.421215	+	0.306030i
$562$	−1.44047e10	+	2.37947e10i	−0.144398	+	0.238526i
$563$	−9.15251e10	+	1.25973e11i	−0.910975	+	1.25385i	0.0558573	+	0.998439i	$0.482211\pi$
$563$	−9.15251e10	+	1.25973e11i	−0.910975	+	1.25385i	−0.966833	+	0.255411i	$0.917789\pi$
$564$	−8.08019e10	+	8.25719e10i	−0.798556	+	0.816048i
$565$	−4.42705e10	−	3.00783e10i	−0.434431	−	0.295162i
$566$	1.21957e10	+	7.38294e9i	0.118834	+	0.0719389i
$567$	5.04802e10	−	1.64020e10i	0.488414	−	0.158695i
$568$	3.08786e10	−	7.94612e9i	0.296663	−	0.0763417i
$569$	2.37300e10	+	7.30335e10i	0.226386	+	0.696744i	0.998148	+	0.0608326i	$0.0193756\pi$
$569$	2.37300e10	+	7.30335e10i	0.226386	+	0.696744i	−0.771762	+	0.635911i	$0.780624\pi$
$570$	−1.12790e11	−	1.22584e11i	−1.06850	−	1.16128i
$571$	3.32576e10	+	1.08061e10i	0.312858	+	0.101654i	0.461237	−	0.887277i	$-0.347406\pi$
$571$	3.32576e10	+	1.08061e10i	0.312858	+	0.101654i	−0.148380	+	0.988930i	$0.547406\pi$
$572$	−9.63693e10	−	1.41950e10i	−0.900232	−	0.132602i
$573$	1.26973e11	−	9.22511e10i	1.17785	−	0.855762i
$574$	−4.98542e10	+	4.19544e9i	−0.459255	+	0.0386483i
$575$	−2.04776e10	−	2.47409e10i	−0.187330	−	0.226331i
$576$	3.39905e10	−	1.87345e10i	0.308794	−	0.170197i
$577$	−3.71397e10	+	2.69836e10i	−0.335070	+	0.243443i	−0.742579	−	0.669759i	$-0.766398\pi$
$577$	−3.71397e10	+	2.69836e10i	−0.335070	+	0.243443i	0.407509	+	0.913201i	$0.366398\pi$
$578$	5.91509e10	+	1.38624e10i	0.529969	+	0.124202i
$579$	2.96672e10	+	9.63946e9i	0.263975	+	0.0857706i
$580$	7.40070e10	+	3.38398e10i	0.653975	+	0.299031i
$581$	−1.22106e10	−	3.75804e10i	−0.107160	−	0.329804i
$582$	7.98746e10	−	6.72179e9i	0.696172	−	0.0585859i
$583$	−5.35929e10	+	1.74134e10i	−0.463909	+	0.150733i
$584$	−1.39969e10	+	3.54082e10i	−0.120332	+	0.304406i
$585$	1.91993e10	+	5.33076e10i	0.163931	+	0.455162i
$586$	1.00376e10	+	1.16244e10i	0.0851214	+	0.0985781i
$587$	8.10078e10	−	1.11498e11i	0.682299	−	0.939104i	−0.317660	−	0.948205i	$-0.602897\pi$
$587$	8.10078e10	−	1.11498e11i	0.682299	−	0.939104i	0.999959	+	0.00910114i	$0.00289702\pi$
$588$	5.09720e10	−	1.02776e11i	0.426405	−	0.859768i
$589$	−1.13317e11	+	8.23300e10i	−0.941533	+	0.684064i
$590$	2.24610e10	−	2.60571e9i	0.185362	−	0.0215039i
$591$	1.45619e9	−	2.00427e9i	0.0119362	−	0.0164288i
$592$	−1.47116e11	−	1.93528e11i	−1.19777	−	1.57564i
$593$	2.40972e11			1.94871			0.974356	−	0.225010i	$-0.0722416\pi$
$593$	2.40972e11			1.94871			0.974356	+	0.225010i	$0.0722416\pi$
$594$	5.73030e10	−	2.41002e10i	0.460290	−	0.193586i
$595$	3.32811e10	−	1.19865e10i	0.265540	−	0.0956368i
$596$	−1.26333e10	+	8.57672e10i	−0.100123	+	0.679729i
$597$	−4.86758e10	+	1.49809e11i	−0.383191	+	1.17934i
$598$	−3.90176e10	+	3.36914e10i	−0.305110	+	0.263460i
$599$			1.17364e11i			0.911650i	0.890070	+	0.455825i	$0.150656\pi$
$599$			1.17364e11i			0.911650i	−0.890070	+	0.455825i	$0.849344\pi$
$600$	1.43312e11	−	4.66895e10i	1.10581	−	0.360259i
$601$	2.29067e10			0.175576			0.0877879	−	0.996139i	$-0.472020\pi$
$601$	2.29067e10			0.175576			0.0877879	+	0.996139i	$0.472020\pi$
$602$	5.33662e10	+	6.18028e10i	0.406332	+	0.470568i
$603$	−6.46543e10	−	2.10074e10i	−0.489022	−	0.158893i
$604$	1.57167e11	+	2.31503e10i	1.18090	+	0.173944i
$605$	−2.09295e10	+	7.20726e10i	−0.156220	+	0.537959i
$606$	−5.56720e10	−	1.32372e11i	−0.412807	−	0.981532i
$607$		−	2.00204e11i		−	1.47475i	−0.675485	−	0.737374i	$-0.736066\pi$
$607$		−	2.00204e11i		−	1.47475i	0.675485	−	0.737374i	$-0.263934\pi$
$608$	1.24193e11	+	1.37680e11i	0.908833	+	1.00753i
$609$	3.89122e10	+	2.82714e10i	0.282890	+	0.205531i
$610$	1.71914e11	+	3.46098e10i	1.24163	+	0.249966i
$611$	1.10346e11	+	1.51878e11i	0.791756	+	1.08976i
$612$	−2.99123e10	−	1.48351e10i	−0.213228	−	0.105751i
$613$	2.34318e10	+	1.70242e10i	0.165945	+	0.120566i	0.667658	−	0.744468i	$-0.267297\pi$
$613$	2.34318e10	+	1.70242e10i	0.165945	+	0.120566i	−0.501713	+	0.865034i	$0.667297\pi$
$614$	5.35841e10	−	4.62695e10i	0.377018	−	0.325552i
$615$	1.12420e11	+	1.44895e11i	0.785858	+	1.01287i
$616$	−1.46773e10	+	3.71295e10i	−0.101935	+	0.257867i
$617$	5.36645e10	+	1.65162e11i	0.370294	+	1.13965i	0.946599	+	0.322413i	$0.104494\pi$
$617$	5.36645e10	+	1.65162e11i	0.370294	+	1.13965i	−0.576305	+	0.817234i	$0.695506\pi$
$618$	−7.92675e9	−	9.41930e10i	−0.0543427	−	0.645750i
$619$	1.14501e11	−	3.72035e10i	0.779911	−	0.253408i	0.108109	−	0.994139i	$-0.465520\pi$
$619$	1.14501e11	−	3.72035e10i	0.779911	−	0.253408i	0.671802	+	0.740731i	$0.265520\pi$
$620$	−2.51107e10	−	1.24226e11i	−0.169939	−	0.840706i
$621$	1.01663e10	−	3.12886e10i	0.0683590	−	0.210387i
$622$	−2.75278e10	+	1.17461e11i	−0.183912	+	0.784751i
$623$	2.65141e10	+	3.64936e10i	0.176005	+	0.242250i
$624$	−7.97299e10	−	2.28421e11i	−0.525875	−	1.50660i
$625$	1.51375e11	−	1.91981e10i	0.992054	−	0.125816i
$626$	−2.24597e10	−	2.66887e11i	−0.146253	−	1.73792i
$627$	−9.50706e10	−	1.30853e11i	−0.615143	−	0.846671i
$628$	3.92044e10	−	2.66157e11i	0.252055	−	1.71119i
$629$	−6.46255e10	+	1.98897e11i	−0.412859	+	1.27065i
$630$	2.30685e10	−	2.67618e9i	0.146439	−	0.0169884i
$631$	2.46690e11	−	8.01545e10i	1.55609	−	0.505604i	0.600330	−	0.799753i	$-0.295036\pi$
$631$	2.46690e11	−	8.01545e10i	1.55609	−	0.505604i	0.955760	+	0.294148i	$0.0950360\pi$
$632$	−1.04624e11	+	2.69233e10i	−0.655787	+	0.168757i
$633$	−1.98673e10	−	6.11453e10i	−0.123744	−	0.380845i
$634$	1.02557e10	−	1.69412e10i	0.0634761	−	0.104854i
$635$	1.74837e11	+	2.25342e11i	1.07532	+	1.38595i
$636$	−1.00033e11	−	9.78884e10i	−0.611383	−	0.598277i
$637$	−1.50816e11	−	1.09574e11i	−0.915986	−	0.665503i
$638$	6.75937e10	+	4.09195e10i	0.407965	+	0.246972i
$639$	−1.05848e10	−	1.45687e10i	−0.0634860	−	0.0873809i
$640$	−1.60025e11	+	5.03927e10i	−0.953825	+	0.300364i
$641$	1.61845e11	+	1.17587e11i	0.958666	+	0.696512i	0.952841	−	0.303471i	$-0.0981456\pi$
$641$	1.61845e11	+	1.17587e11i	0.958666	+	0.696512i	0.00582561	+	0.999983i	$0.498146\pi$
$642$	−2.24443e11	+	9.43950e10i	−1.32119	+	0.555660i
$643$			8.39525e10i			0.491122i	0.969381	+	0.245561i	$0.0789722\pi$
$643$			8.39525e10i			0.491122i	−0.969381	+	0.245561i	$0.921028\pi$
$644$	9.79584e9	+	1.87212e10i	0.0569506	+	0.108841i
$645$	8.34717e10	−	2.87442e11i	0.482281	−	1.66078i
$646$	3.63967e10	−	1.55304e11i	0.208993	−	0.891771i
$647$	−7.78021e10	−	2.52794e10i	−0.443991	−	0.144261i	0.0784853	−	0.996915i	$-0.474992\pi$
$647$	−7.78021e10	−	2.52794e10i	−0.443991	−	0.144261i	−0.522476	+	0.852654i	$0.674992\pi$
$648$	1.66943e11	+	1.37955e11i	0.946823	+	0.782416i
$649$	2.19552e10			0.123754
$650$	−3.58821e10	−	2.42282e11i	−0.201013	−	1.35728i
$651$		−	7.49093e10i		−	0.417073i
$652$	1.38793e11	+	1.35818e11i	0.768027	+	0.751564i
$653$	5.51775e10	−	1.69819e11i	0.303465	−	0.933970i	−0.676780	−	0.736185i	$-0.736625\pi$
$653$	5.51775e10	−	1.69819e11i	0.303465	−	0.933970i	0.980245	−	0.197785i	$-0.0633748\pi$
$654$	−4.59303e10	+	1.95984e11i	−0.251066	+	1.07130i
$655$	2.75886e10	−	9.93631e9i	0.149887	−	0.0539834i
$656$	−1.23536e11	−	1.62509e11i	−0.667082	−	0.877530i
$657$	2.15037e10			0.115412
$658$	7.09281e10	−	2.98305e10i	0.378368	−	0.159132i
$659$	−1.81245e11	+	2.49462e11i	−0.961000	+	1.32270i	−0.0145359	+	0.999894i	$0.504627\pi$
$659$	−1.81245e11	+	2.49462e11i	−0.961000	+	1.32270i	−0.946464	+	0.322809i	$0.895373\pi$
$660$	1.43450e11	−	2.89966e10i	0.756003	−	0.152817i
$661$	2.83241e11	−	2.05786e11i	1.48371	−	1.07798i	0.507376	−	0.861725i	$-0.330616\pi$
$661$	2.83241e11	−	2.05786e11i	1.48371	−	1.07798i	0.976337	−	0.216256i	$-0.0693844\pi$
$662$	1.14213e11	+	6.91417e10i	0.594681	+	0.360005i
$663$	−1.22338e11	+	1.68384e11i	−0.633151	+	0.871458i
$664$	1.02702e11	−	1.24282e11i	0.528331	−	0.639347i
$665$	3.75944e10	+	1.04383e11i	0.192237	+	0.533754i
$666$	−7.11024e10	+	1.17452e11i	−0.361399	+	0.596984i
$667$	3.97694e10	−	1.29219e10i	0.200931	−	0.0652863i
$668$	4.27629e10	+	2.52275e11i	0.214764	+	1.26698i
$669$	8.87353e9	+	2.73099e10i	0.0442988	+	0.136338i
$670$	2.56064e11	+	1.44183e11i	1.27072	+	0.715506i
$671$	1.61939e11	+	5.26172e10i	0.798844	+	0.259560i
$672$	−9.86101e10	+	1.04544e10i	−0.483553	+	0.0512652i
$673$	1.09536e11	−	7.95826e10i	0.533945	−	0.387934i	−0.287886	−	0.957665i	$-0.592953\pi$
$673$	1.09536e11	−	7.95826e10i	0.533945	−	0.387934i	0.821831	+	0.569731i	$0.192953\pi$
$674$	−1.87456e10	−	2.22753e11i	−0.0908365	−	1.07940i
$675$	9.96628e10	+	1.20412e11i	0.480085	+	0.580035i
$676$	−1.81719e11	+	3.08030e10i	−0.870189	+	0.147505i
$677$	−2.24537e11	+	1.63136e11i	−1.06889	+	0.776596i	−0.975713	−	0.219053i	$-0.929703\pi$
$677$	−2.24537e11	+	1.63136e11i	−1.06889	+	0.776596i	−0.0931798	+	0.995649i	$0.529703\pi$
$678$	2.94515e10	−	1.25669e11i	0.139376	−	0.594716i
$679$	−5.07737e10	−	1.64974e10i	−0.238869	−	0.0776133i
$680$	1.14103e11	+	8.83862e10i	0.533657	+	0.413379i
$681$	5.47354e9	+	1.68458e10i	0.0254495	+	0.0783255i
$682$	−1.03195e10	−	1.22626e11i	−0.0477003	−	0.566819i
$683$	1.29596e11	−	4.21083e10i	0.595537	−	0.193502i	0.00428806	−	0.999991i	$-0.498635\pi$
$683$	1.29596e11	−	4.21083e10i	0.595537	−	0.193502i	0.591249	+	0.806489i	$0.298635\pi$
$684$	4.65287e10	−	9.38166e10i	0.212567	−	0.428603i
$685$	−8.86967e9	−	6.02624e9i	−0.0402851	−	0.0273706i
$686$	−1.27914e11	+	1.10452e11i	−0.577591	+	0.498745i
$687$	−1.48248e11	+	2.04045e11i	−0.665520	+	0.916009i
$688$	−9.60654e10	+	3.19017e11i	−0.428759	+	1.42384i
$689$	−1.83994e11	+	1.33680e11i	−0.816446	+	0.593183i
$690$	3.80009e10	−	6.74885e10i	0.167648	−	0.297737i
$691$	5.64002e10	−	7.76283e10i	0.247382	−	0.340493i	−0.667210	−	0.744870i	$-0.732512\pi$
$691$	5.64002e10	−	7.76283e10i	0.247382	−	0.340493i	0.914592	+	0.404377i	$0.132512\pi$
$692$	1.62848e11	+	3.11225e11i	0.710163	+	1.35722i
$693$	2.25491e10			0.0977678
$694$	−1.44096e11	−	3.42617e11i	−0.621174	−	1.47697i
$695$	−1.56051e11	−	2.01129e11i	−0.668848	−	0.862057i
$696$	−1.22164e10	+	1.95869e11i	−0.0520604	+	0.834696i
$697$	−5.42673e10	+	1.67017e11i	−0.229936	+	0.707670i
$698$	6.96635e10	+	8.06764e10i	0.293483	+	0.339880i
$699$		−	8.10992e10i		−	0.339710i
$700$	−1.00041e11	−	8.33971e9i	−0.416662	−	0.0347343i
$701$	5.83193e10			0.241513			0.120756	−	0.992682i	$-0.461468\pi$
$701$	5.83193e10			0.241513			0.120756	+	0.992682i	$0.461468\pi$
$702$	1.89896e11	−	1.63973e11i	0.781928	−	0.675188i
$703$	−6.23819e11	−	2.02691e11i	−2.55409	−	0.829876i
$704$	−1.59984e11	+	3.06983e10i	−0.651306	+	0.124975i
$705$	−2.33301e11	−	1.58510e11i	−0.944409	−	0.641652i
$706$	−3.20390e11	+	1.34748e11i	−1.28961	+	0.542378i
$707$			9.56430e10i			0.382803i
$708$	2.52812e10	+	4.83160e10i	0.100616	+	0.192290i
$709$	−1.37678e11	−	1.00029e11i	−0.544853	−	0.395859i	0.281031	−	0.959699i	$-0.409324\pi$
$709$	−1.37678e11	−	1.00029e11i	−0.544853	−	0.395859i	−0.825884	+	0.563840i	$0.809324\pi$
$710$	3.24261e10	+	7.07681e10i	0.127603	+	0.278487i
$711$	3.58637e10	+	4.93621e10i	0.140338	+	0.193159i
$712$	−6.76609e10	+	1.71163e11i	−0.263280	+	0.666024i
$713$	−5.26875e10	−	3.82797e10i	−0.203868	−	0.148119i
$714$	5.57537e10	+	6.45677e10i	0.214527	+	0.248441i
$715$	−7.49890e9	−	2.37697e11i	−0.0286928	−	0.909493i
$716$	−2.31772e10	+	4.67326e10i	−0.0881879	+	0.177815i
$717$	−5.76166e10	−	1.77326e11i	−0.218007	−	0.670957i
$718$	−3.21753e11	+	2.70769e10i	−1.21067	+	0.101883i
$719$	−3.74234e11	+	1.21596e11i	−1.40032	+	0.454992i	−0.909295	−	0.416153i	$-0.863378\pi$
$719$	−3.74234e11	+	1.21596e11i	−1.40032	+	0.454992i	−0.491027	+	0.871145i	$0.663378\pi$
$720$	5.96933e10	+	7.35879e10i	0.222124	+	0.273827i
$721$	−1.94547e10	+	5.98755e10i	−0.0719920	+	0.221569i
$722$	2.22526e11	+	5.21507e10i	0.818903	+	0.191916i
$723$	−2.83675e11	−	3.90446e11i	−1.03817	−	1.42892i
$724$	−3.83897e11	+	6.50740e10i	−1.39720	+	0.236839i
$725$	−4.93613e10	+	1.92444e11i	−0.178663	+	0.696550i
$726$	−1.80354e11	+	1.51776e10i	−0.649203	+	0.0546332i
$727$	−1.95211e11	−	2.68685e11i	−0.698822	−	0.961846i	−0.999966	−	0.00826711i	$-0.997368\pi$
$727$	−1.95211e11	−	2.68685e11i	−0.698822	−	0.961846i	0.301144	−	0.953579i	$-0.402632\pi$
$728$	−1.00306e10	+	1.60824e11i	−0.0357111	+	0.572564i
$729$	−3.86284e10	+	1.18886e11i	−0.136772	+	0.420940i
$730$	−9.11267e10	−	1.83457e10i	−0.320888	−	0.0646015i
$731$	2.72591e11	−	8.85701e10i	0.954644	−	0.310183i
$732$	7.06787e10	+	4.16961e11i	0.246175	+	1.45228i
$733$	−1.63257e11	−	5.02455e11i	−0.565532	−	1.74053i	−0.666365	−	0.745625i	$-0.732151\pi$
$733$	−1.63257e11	−	5.02455e11i	−0.565532	−	1.74053i	0.100833	−	0.994903i	$-0.467849\pi$
$734$	1.78245e11	+	1.07905e11i	0.614090	+	0.371755i
$735$	2.68970e11	+	7.81075e10i	0.921626	+	0.267635i
$736$	−4.30380e10	+	7.46998e10i	−0.146670	+	0.254571i
$737$	2.30842e11	+	1.67716e11i	0.782428	+	0.568467i
$738$	−5.97060e10	+	9.86265e10i	−0.201276	+	0.332482i
$739$	7.30799e10	+	1.00586e11i	0.245030	+	0.337255i	0.913763	−	0.406248i	$-0.133163\pi$
$739$	7.30799e10	+	1.00586e11i	0.245030	+	0.337255i	−0.668733	+	0.743503i	$0.733163\pi$
$740$	4.01514e11	−	4.37067e11i	1.33898	−	1.45754i
$741$	−5.28118e11	−	3.83700e11i	−1.75169	−	1.27268i
$742$	3.61385e10	+	8.59266e10i	0.119221	+	0.283473i
$743$		−	1.56884e11i		−	0.514781i	−0.966308	−	0.257390i	$-0.917137\pi$
$743$		−	1.56884e11i		−	0.514781i	0.966308	−	0.257390i	$-0.0828626\pi$
$744$	2.57975e11	−	1.63912e11i	0.841948	−	0.534957i
$745$	−2.11547e11	+	6.67390e9i	−0.686722	+	0.0216648i
$746$	2.08256e11	+	4.88063e10i	0.672423	+	0.157587i
$747$	−8.66009e10	−	2.81383e10i	−0.278125	−	0.0903682i
$748$	1.00163e11	+	9.80162e10i	0.319965	+	0.313106i
$749$	1.62168e11			0.515274
$750$	1.74068e11	+	3.24210e11i	0.550141	+	1.02466i
$751$		−	3.04106e11i		−	0.956016i	−0.878355	−	0.478008i	$-0.841359\pi$
$751$		−	3.04106e11i		−	0.956016i	0.878355	−	0.478008i	$-0.158641\pi$
$752$	2.57932e11	+	1.78991e11i	0.806554	+	0.559705i
$753$	1.29517e11	−	3.98614e11i	0.402855	−	1.23986i
$754$	3.10486e11	+	7.27647e10i	0.960632	+	0.225131i
$755$	1.22298e10	+	3.87655e11i	0.0376384	+	1.19305i
$756$	−4.76756e10	−	9.11147e10i	−0.145952	−	0.278934i
$757$	−6.11599e11			−1.86244			−0.931221	−	0.364454i	$-0.881256\pi$
$757$	−6.11599e11			−1.86244			−0.931221	+	0.364454i	$0.881256\pi$
$758$	−1.12938e11	−	2.68534e11i	−0.342109	−	0.813433i
$759$	4.42035e10	−	6.08409e10i	0.133196	−	0.183328i
$760$	−2.77214e11	+	3.57872e11i	−0.830922	+	1.07269i
$761$	−2.66910e11	+	1.93921e11i	−0.795840	+	0.578212i	−0.909691	−	0.415286i	$-0.863681\pi$
$761$	−2.66910e11	+	1.93921e11i	−0.795840	+	0.578212i	0.113851	+	0.993498i	$0.463681\pi$
$762$	−3.56207e11	+	5.88408e11i	−1.05653	+	1.74525i
$763$	7.88029e10	−	1.08463e11i	0.232511	−	0.320024i
$764$	−3.04834e11	−	2.98300e11i	−0.894726	−	0.875547i
$765$	2.27327e10	−	7.82821e10i	0.0663752	−	0.228569i
$766$	−4.45234e11	−	2.69533e11i	−1.29322	−	0.782884i
$767$	8.42733e10	−	2.73821e10i	0.243505	−	0.0791197i
$768$	−2.51776e11	−	3.16720e11i	−0.723718	−	0.910398i
$769$	6.46439e10	+	1.98954e11i	0.184851	+	0.568914i	0.999946	−	0.0104144i	$-0.00331505\pi$
$769$	6.46439e10	+	1.98954e11i	0.184851	+	0.568914i	−0.815095	+	0.579328i	$0.803315\pi$
$770$	−9.55565e10	−	1.92375e10i	−0.271830	−	0.0547250i
$771$	6.44651e11	+	2.09460e11i	1.82434	+	0.592765i
$772$	1.23532e10	−	8.38651e10i	0.0347783	−	0.236109i
$773$	−4.07651e11	+	2.96176e11i	−1.14175	+	0.829529i	−0.987362	−	0.158482i	$-0.949340\pi$
$773$	−4.07651e11	+	2.96176e11i	−1.14175	+	0.829529i	−0.154386	+	0.988011i	$0.549340\pi$
$774$	1.87504e11	−	1.57793e10i	0.522454	−	0.0439667i
$775$	2.87663e11	−	1.13975e11i	0.797401	−	0.315938i
$776$	−5.42858e10	−	2.10955e11i	−0.149706	−	0.581758i
$777$	2.83796e11	−	2.06190e11i	0.778614	−	0.565696i
$778$	6.34077e11	+	1.48601e11i	1.73071	+	0.405604i
$779$	−5.23832e11	−	1.70203e11i	−1.42247	−	0.462188i
$780$	5.14455e11	−	2.90208e11i	1.38985	−	0.784027i
$781$	2.33567e10	+	7.18844e10i	0.0627779	+	0.193210i
$782$	7.39047e10	−	6.21940e9i	0.197627	−	0.0166311i
$783$	−1.93555e11	+	6.28897e10i	−0.514940	+	0.167314i
$784$	−2.98516e11	−	8.98919e10i	−0.790139	−	0.237934i
$785$	6.56482e11	−	2.07108e10i	1.72880	−	0.0545404i
$786$	4.62175e10	+	5.35240e10i	0.121092	+	0.140236i
$787$	3.08126e11	−	4.24099e11i	0.803211	−	1.10552i	−0.189125	−	0.981953i	$-0.560565\pi$
$787$	3.08126e11	−	4.24099e11i	0.803211	−	1.10552i	0.992336	−	0.123572i	$-0.0394350\pi$
$788$	−6.03138e9	−	2.99129e9i	−0.0156427	−	0.00775806i
$789$	4.96696e10	−	3.60871e10i	0.128169	−	0.0931201i
$790$	−1.09867e11	−	2.39779e11i	−0.282072	−	0.615606i
$791$	−5.05301e10	+	6.95487e10i	−0.129076	+	0.177657i
$792$	4.93405e10	+	7.76551e10i	0.125402	+	0.197365i
$793$	6.87213e11			1.73779
$794$	1.58132e11	−	6.65060e10i	0.397866	−	0.167332i
$795$	1.92028e11	−	2.82635e11i	0.480725	−	0.707551i
$796$	4.23488e11	+	6.23789e10i	1.05485	+	0.155377i
$797$	6.91162e10	−	2.12718e11i	0.171296	−	0.527194i	−0.828149	−	0.560508i	$-0.810606\pi$
$797$	6.91162e10	−	2.12718e11i	0.171296	−	0.527194i	0.999445	+	0.0333137i	$0.0106060\pi$
$798$	−2.02510e11	+	1.74866e11i	−0.499384	+	0.431214i
$799$		−	2.70089e11i		−	0.662704i
$800$	−1.90182e11	−	3.62771e11i	−0.464312	−	0.885672i
$801$	1.03949e11			0.252516
$802$	7.95499e10	+	9.21258e10i	0.192284	+	0.222681i
$803$	−8.58393e10	−	2.78909e10i	−0.206454	−	0.0670811i
$804$	−1.03275e11	+	7.01127e11i	−0.247155	+	1.67793i
$805$	−4.07563e10	+	3.16217e10i	−0.0970534	+	0.0753013i
$806$	−1.92546e11	−	4.57818e11i	−0.456242	−	1.08481i
$807$		−	6.41194e11i		−	1.51180i
$808$	−3.29378e11	+	2.09280e11i	−0.772768	+	0.491001i
$809$	−1.53577e11	−	1.11580e11i	−0.358535	−	0.260491i	0.393906	−	0.919151i	$-0.371124\pi$
$809$	−1.53577e11	−	1.11580e11i	−0.358535	−	0.260491i	−0.752441	+	0.658660i	$0.771124\pi$
$810$	−2.59416e11	+	4.60716e11i	−0.602639	+	1.07027i
$811$	−1.85619e11	−	2.55482e11i	−0.429080	−	0.590578i	0.538662	−	0.842522i	$-0.318930\pi$
$811$	−1.85619e11	−	2.55482e11i	−0.429080	−	0.590578i	−0.967742	+	0.251944i	$0.918930\pi$
$812$	5.80748e10	−	1.17097e11i	0.133587	−	0.269353i
$813$	−4.08635e11	−	2.96891e11i	−0.935348	−	0.679570i
$814$	4.36167e11	−	3.76626e11i	0.993470	−	0.857854i
$815$	−2.66434e11	+	3.92149e11i	−0.603893	+	0.888834i
$816$	−1.00363e11	+	3.33290e11i	−0.226367	+	0.751728i
$817$	2.77790e11	+	8.54951e11i	0.623489	+	1.91890i
$818$	−3.71490e10	−	4.41439e11i	−0.0829724	−	0.985956i
$819$	8.65527e10	−	2.81227e10i	0.192373	−	0.0625059i
$820$	3.37159e11	−	3.67013e11i	0.745726	−	0.811757i
$821$	−4.37000e10	+	1.34495e11i	−0.0961854	+	0.296028i	−0.987561	−	0.157238i	$-0.949741\pi$
$821$	−4.37000e10	+	1.34495e11i	−0.0961854	+	0.296028i	0.891375	+	0.453266i	$0.149741\pi$
$822$	5.90065e9	−	2.51780e10i	0.0129245	−	0.0551485i
$823$	−1.00318e11	−	1.38076e11i	−0.218665	−	0.300967i	0.685565	−	0.728011i	$-0.259555\pi$
$823$	−1.00318e11	−	1.38076e11i	−0.218665	−	0.300967i	−0.904231	+	0.427044i	$0.859555\pi$
$824$	−2.48771e11	+	6.40172e10i	−0.539623	+	0.138863i
$825$	1.31613e11	+	3.32179e11i	0.284107	+	0.717061i
$826$	−3.04562e9	−	3.61909e10i	−0.00654267	−	0.0777461i
$827$	3.98455e11	+	5.48427e11i	0.851839	+	1.17246i	0.983454	+	0.181155i	$0.0579837\pi$
$827$	3.98455e11	+	5.48427e11i	0.851839	+	1.17246i	−0.131615	+	0.991301i	$0.542016\pi$
$828$	4.81707e10	+	7.09544e9i	0.102485	+	0.0150959i
$829$	4.78856e10	−	1.47377e11i	0.101388	−	0.312041i	−0.887478	−	0.460851i	$-0.847544\pi$
$829$	4.78856e10	−	1.47377e11i	0.101388	−	0.312041i	0.988866	+	0.148810i	$0.0475443\pi$
$830$	3.42984e11	+	1.93125e11i	0.722705	+	0.406935i
$831$	−4.43700e11	+	1.44167e11i	−0.930434	+	0.302316i
$832$	−5.75797e11	+	3.17361e11i	−1.20164	+	0.662308i
$833$	8.28782e10	+	2.55073e11i	0.172132	+	0.529766i
$834$	3.17933e11	−	5.25183e11i	0.657160	−	1.08554i
$835$	−5.87734e11	+	2.11678e11i	−1.20902	+	0.435442i
$836$	−3.07417e11	+	3.14151e11i	−0.629365	+	0.643152i
$837$	2.56426e11	+	1.86304e11i	0.522468	+	0.379595i
$838$	1.49325e11	+	9.03976e10i	0.302801	+	0.183308i
$839$	−4.39605e11	−	6.05064e11i	−0.887186	−	1.22111i	−0.974378	−	0.224916i	$-0.927789\pi$
$839$	−4.39605e11	−	6.05064e11i	−0.887186	−	1.22111i	0.0871920	−	0.996192i	$-0.472211\pi$
$840$	−6.76971e10	−	2.32439e11i	−0.135973	−	0.466865i
$841$	1.95433e11	+	1.41990e11i	0.390672	+	0.283840i
$842$	−1.98161e10	+	8.33414e9i	−0.0394249	+	0.0165811i
$843$		−	1.63769e11i		−	0.324280i
$844$	−1.54803e11	+	8.10004e10i	−0.305077	+	0.159631i
$845$	−1.52476e11	−	4.23357e11i	−0.299072	−	0.830387i
$846$	4.04589e10	−	1.72638e11i	0.0789828	−	0.337019i
$847$	1.14646e11	+	3.72506e10i	0.222753	+	0.0723769i
$848$	−2.16840e11	+	3.12474e11i	−0.419331	+	0.604269i
$849$	−8.39373e10			−0.161556
$850$	−1.63120e11	+	3.12343e11i	−0.312487	+	0.598351i
$851$		−	3.04974e11i		−	0.581493i
$852$	−1.31298e11	+	1.34174e11i	−0.249172	+	0.254630i
$853$	−2.74643e11	+	8.45265e11i	−0.518767	+	1.59660i	0.257554	+	0.966264i	$0.417084\pi$
$853$	−2.74643e11	+	8.45265e11i	−0.518767	+	1.59660i	−0.776321	+	0.630338i	$0.782916\pi$
$854$	6.42698e10	−	2.74238e11i	0.120830	−	0.515581i
$855$	2.45523e11	+	7.12987e10i	0.459440	+	0.133419i
$856$	3.54846e11	+	5.58479e11i	0.660914	+	1.04019i
$857$	−5.24907e10			−0.0973104			−0.0486552	−	0.998816i	$-0.515494\pi$
$857$	−5.24907e10			−0.0973104			−0.0486552	+	0.998816i	$0.515494\pi$
$858$	5.28666e11	−	2.22343e11i	0.975511	−	0.410275i
$859$	−2.23321e11	+	3.07375e11i	−0.410164	+	0.564542i	−0.963258	−	0.268576i	$-0.913447\pi$
$859$	−2.23321e11	+	3.07375e11i	−0.410164	+	0.564542i	0.553094	+	0.833119i	$0.313447\pi$
$860$	−8.08052e11	−	9.30992e10i	−1.47722	−	0.170197i
$861$	2.38309e11	−	1.73141e11i	0.433638	−	0.315056i
$862$	−3.30058e11	−	1.99809e11i	−0.597808	−	0.361898i
$863$	−3.46166e11	+	4.76457e11i	−0.624082	+	0.858975i	−0.997642	−	0.0686313i	$-0.978137\pi$
$863$	−3.46166e11	+	4.76457e11i	−0.624082	+	0.858975i	0.373561	+	0.927606i	$0.378137\pi$
$864$	2.09463e11	−	3.63558e11i	0.375882	−	0.652407i
$865$	−6.77540e11	+	5.25686e11i	−1.21024	+	0.938992i
$866$	−5.15219e11	+	8.51075e11i	−0.916052	+	1.51320i
$867$	−3.40194e11	+	1.10536e11i	−0.602074	+	0.195626i
$868$	−2.00704e11	+	3.40211e10i	−0.353571	+	0.0599336i
$869$	−7.91379e10	−	2.43561e11i	−0.138773	−	0.427100i
$870$	−4.75933e11	+	5.52132e10i	−0.830746	+	0.0963753i
$871$	1.09524e12	+	3.55864e11i	1.90299	+	0.618318i
$872$	5.45959e11	+	3.40517e10i	0.944266	+	0.0588943i
$873$	−9.95294e10	+	7.23124e10i	−0.171354	+	0.124496i
$874$	1.95065e10	+	2.31794e11i	0.0334298	+	0.397243i
$875$	−2.31538e10	−	2.43991e11i	−0.0394994	−	0.416238i
$876$	−3.74647e10	−	2.21019e11i	−0.0636218	−	0.375330i
$877$	4.66757e11	−	3.39119e11i	0.789028	−	0.573263i	−0.118647	−	0.992937i	$-0.537856\pi$
$877$	4.66757e11	−	3.39119e11i	0.789028	−	0.573263i	0.907675	+	0.419674i	$0.137856\pi$
$878$	2.44200e11	−	1.04200e12i	0.410930	−	1.75344i
$879$	−8.60003e10	−	2.79432e10i	−0.144060	−	0.0468081i
$880$	−1.42840e11	−	3.71174e11i	−0.238188	−	0.618938i
$881$	−2.41037e10	−	7.41837e10i	−0.0400111	−	0.123142i	0.929056	−	0.369940i	$-0.120622\pi$
$881$	−2.41037e10	−	7.41837e10i	−0.0400111	−	0.123142i	−0.969067	+	0.246798i	$0.920622\pi$
$882$	1.47653e10	+	1.75455e11i	0.0243987	+	0.289928i
$883$	9.03067e11	−	2.93424e11i	1.48552	−	0.482673i	0.549760	−	0.835323i	$-0.314719\pi$
$883$	9.03067e11	−	2.93424e11i	1.48552	−	0.482673i	0.935755	+	0.352650i	$0.114719\pi$
$884$	5.06711e11	+	2.51306e11i	0.829758	+	0.411522i
$885$	−1.05184e11	+	8.16098e10i	−0.171466	+	0.133036i
$886$	7.73337e11	−	6.67771e11i	1.25497	−	1.08366i
$887$	2.83347e11	−	3.89994e11i	0.457746	−	0.630033i	−0.516294	−	0.856412i	$-0.672689\pi$
$887$	2.83347e11	−	3.89994e11i	0.457746	−	0.630033i	0.974039	+	0.226379i	$0.0726887\pi$
$888$	1.33107e12	+	5.26172e11i	2.14066	+	0.846206i
$889$	3.70620e11	−	2.69272e11i	0.593366	−	0.431105i
$890$	−4.40505e11	−	8.86828e10i	−0.702087	−	0.141345i
$891$	−3.01759e11	+	4.15335e11i	−0.478794	+	0.659004i
$892$	6.91412e10	−	3.61780e10i	0.109214	−	0.0571459i
$893$	8.47104e11			1.33208
$894$	−1.97882e11	−	4.70505e11i	−0.309782	−	0.736570i
$895$	−1.22302e11	−	3.55158e10i	−0.190608	−	0.0553516i
$896$	7.27957e10	+	2.59457e11i	0.112947	+	0.402563i
$897$	9.37921e10	−	2.88662e11i	0.144876	−	0.445882i
$898$	3.65441e11	+	4.23213e11i	0.561968	+	0.650808i
$899$			4.02872e11i			0.616778i
$900$	−1.51053e11	+	1.75211e11i	−0.230229	+	0.267049i
$901$	3.27202e11			0.496497
$902$	3.66257e11	−	3.16260e11i	0.553299	−	0.477769i
$903$	−4.57233e11	−	1.48564e11i	−0.687680	−	0.223441i
$904$	−3.50080e11	−	2.18347e10i	−0.524196	−	0.0326944i
$905$	−3.22119e11	−	8.94378e11i	−0.480200	−	1.33330i
$906$	−8.62190e11	+	3.62615e11i	−1.27965	+	0.538186i
$907$		−	3.52972e11i		−	0.521568i	−0.965397	−	0.260784i	$-0.916019\pi$
$907$		−	3.52972e11i		−	0.521568i	0.965397	−	0.260784i	$-0.0839811\pi$
$908$	4.26490e10	−	2.23160e10i	0.0627430	−	0.0328301i
$909$	1.78308e11	+	1.29549e11i	0.261166	+	0.189748i
$910$	−3.90778e11	+	4.53343e10i	−0.569855	+	0.0661091i
$911$	−1.17576e11	−	1.61830e11i	−0.170705	−	0.234955i	0.715090	−	0.699033i	$-0.246386\pi$
$911$	−1.17576e11	−	1.61830e11i	−0.170705	−	0.234955i	−0.885795	+	0.464078i	$0.846386\pi$
$912$	−1.04533e12	−	3.14778e11i	−1.51103	−	0.455015i
$913$	3.09200e11	+	2.24647e11i	0.444996	+	0.323309i
$914$	3.87903e11	+	4.49226e11i	0.555825	+	0.643694i
$915$	−9.71410e11	+	3.49863e11i	−1.38586	+	0.499129i
$916$	6.14026e11	+	3.04529e11i	0.872178	+	0.432560i
$917$	−1.45545e10	−	4.47941e10i	−0.0205835	−	0.0633496i
$918$	−3.59688e11	+	3.02693e10i	−0.506472	+	0.0426218i
$919$	4.66750e11	−	1.51656e11i	0.654368	−	0.212617i	0.0370290	−	0.999314i	$-0.488211\pi$
$919$	4.66750e11	−	1.51656e11i	0.654368	−	0.212617i	0.617339	+	0.786697i	$0.288211\pi$
$920$	−1.98080e11	−	7.11648e10i	−0.276497	−	0.0993376i
$921$	−1.28808e11	+	3.96429e11i	−0.179021	+	0.550969i
$922$	−2.99492e11	−	7.01880e10i	−0.414439	−	0.0971269i
$923$	1.79305e11	+	2.46792e11i	0.247050	+	0.340036i
$924$	−3.92859e10	−	2.31763e11i	−0.0538951	−	0.317948i
$925$	1.22360e12	+	7.76100e11i	1.67136	+	1.06011i
$926$	1.19140e12	−	1.00261e11i	1.62037	−	0.136361i
$927$	8.52752e10	+	1.17371e11i	0.115479	+	0.158944i
$928$	5.30338e11	−	5.62253e10i	0.715091	−	0.0758124i
$929$	3.30230e11	−	1.01634e12i	0.443357	−	1.36451i	−0.440919	−	0.897547i	$-0.645347\pi$
$929$	3.30230e11	−	1.01634e12i	0.443357	−	1.36451i	0.884276	−	0.466965i	$-0.154653\pi$
$930$	5.05251e11	+	5.49123e11i	0.675422	+	0.734071i
$931$	−8.00008e11	+	2.59939e11i	−1.06487	+	0.345997i
$932$	−2.17289e11	+	3.68324e10i	−0.287987	+	0.0488165i
$933$	−2.19500e11	−	6.75552e11i	−0.289673	−	0.891522i
$934$	1.06432e12	+	6.44309e11i	1.39857	+	0.846656i
$935$	−1.92279e11	+	2.83004e11i	−0.251585	+	0.370294i
$936$	2.86239e11	+	2.36536e11i	0.372928	+	0.308173i
$937$	−7.32663e11	−	5.32311e11i	−0.950486	−	0.690568i	0.000435789	−	1.00000i	$-0.499861\pi$
$937$	−7.32663e11	−	5.32311e11i	−0.950486	−	0.690568i	−0.950922	+	0.309431i	$0.899861\pi$
$938$	2.44440e11	−	4.03783e11i	0.315763	−	0.521599i
$939$	9.26886e11	+	1.27575e12i	1.19224	+	1.64098i
$940$	−3.18737e11	+	6.97072e11i	−0.408245	+	0.892824i
$941$	−3.72200e11	−	2.70419e11i	−0.474698	−	0.344888i	0.324571	−	0.945861i	$-0.394780\pi$
$941$	−3.72200e11	−	2.70419e11i	−0.474698	−	0.344888i	−0.799269	+	0.600973i	$0.794780\pi$
$942$	6.14077e11	+	1.46009e12i	0.779865	+	1.85429i
$943$		−	2.56092e11i		−	0.323854i
$944$	1.17971e11	−	8.96792e10i	0.148555	−	0.112929i
$945$	1.98357e11	−	1.53900e11i	0.248726	−	0.192980i
$946$	−7.68952e11	−	1.80210e11i	−0.960141	−	0.225016i
$947$	−7.92284e10	−	2.57429e10i	−0.0985102	−	0.0320079i	0.259347	−	0.965784i	$-0.416493\pi$
$947$	−7.92284e10	−	2.57429e10i	−0.0985102	−	0.0320079i	−0.357857	+	0.933776i	$0.616493\pi$
$948$	4.44869e11	−	4.54614e11i	0.550806	−	0.562871i
$949$	−3.64272e11			−0.449118
$950$	−9.79629e11	−	5.11609e11i	−1.20273	−	0.628122i
$951$			1.16598e11i			0.142551i
$952$	1.47675e11	−	1.78705e11i	0.179787	−	0.217565i
$953$	−4.17464e11	+	1.28482e12i	−0.506113	+	1.55766i	0.292778	+	0.956180i	$0.405420\pi$
$953$	−4.17464e11	+	1.28482e12i	−0.506113	+	1.55766i	−0.798891	+	0.601476i	$0.794580\pi$
$954$	2.09144e11	+	4.90143e10i	0.252494	+	0.0591738i
$955$	5.85177e11	−	8.61287e11i	0.703516	−	1.03546i
$956$	−4.48940e11	+	2.34907e11i	−0.537473	+	0.281231i
$957$	−4.65217e11			−0.554636
$958$	6.24516e11	+	1.48491e12i	0.741449	+	1.76295i
$959$	−1.01238e10	+	1.39342e10i	−0.0119693	+	0.0164743i
$960$	6.52349e11	−	7.41746e11i	0.768059	−	0.873313i
$961$	−1.82391e11	+	1.32515e11i	−0.213851	+	0.155372i
$962$	1.20447e12	−	1.98962e12i	1.40636	−	2.32312i
$963$	2.19657e11	−	3.02332e11i	0.255411	−	0.351543i
$964$	−9.17284e11	+	9.37377e11i	−1.06217	+	1.08544i
$965$	2.06855e11	−	6.52589e9i	0.238538	−	0.00752542i
$966$	−1.06422e11	−	6.44249e10i	−0.122214	−	0.0739853i
$967$	4.21734e11	−	1.37030e11i	0.482317	−	0.156714i	−0.0577592	−	0.998331i	$-0.518396\pi$
$967$	4.21734e11	−	1.37030e11i	0.482317	−	0.156714i	0.540076	+	0.841616i	$0.318396\pi$
$968$	1.22576e11	+	4.76329e11i	0.139606	+	0.542507i
$969$	2.90218e11	+	8.93200e11i	0.329177	+	1.01310i
$970$	4.83470e11	−	2.21527e11i	0.546113	−	0.250230i
$971$	−9.32307e11	−	3.02925e11i	−1.04877	−	0.340767i	−0.266587	−	0.963811i	$-0.585896\pi$
$971$	−9.32307e11	−	3.02925e11i	−1.04877	−	0.340767i	−0.782187	+	0.623044i	$0.785896\pi$
$972$	−5.96568e11	−	8.78732e10i	−0.668336	−	0.0984445i
$973$	−3.30797e11	+	2.40338e11i	−0.369072	+	0.268146i
$974$	−9.44845e10	+	7.95128e9i	−0.104984	+	0.00883489i
$975$	9.19469e11	+	1.11090e12i	1.01746	+	1.22929i
$976$	1.08506e12	−	3.78738e11i	1.19579	−	0.417388i
$977$	8.35998e11	−	6.07388e11i	0.917544	−	0.666635i	−0.0253677	−	0.999678i	$-0.508076\pi$
$977$	8.35998e11	−	6.07388e11i	0.917544	−	0.666635i	0.942911	+	0.333044i	$0.108076\pi$
$978$	−1.11318e12	−	2.60882e11i	−1.21677	−	0.285160i
$979$	−4.14946e11	−	1.34824e11i	−0.451711	−	0.146770i
$980$	8.71163e10	−	7.56123e11i	0.0944485	−	0.819763i
$981$	−9.54700e10	−	2.93826e11i	−0.103084	−	0.317260i
$982$	1.07144e11	−	9.01663e9i	0.115218	−	0.00969612i
$983$	7.97924e11	−	2.59261e11i	0.854570	−	0.277667i	0.151211	−	0.988502i	$-0.451683\pi$
$983$	7.97924e11	−	2.59261e11i	0.854570	−	0.277667i	0.703359	+	0.710835i	$0.251683\pi$
$984$	1.11772e12	+	4.41837e11i	1.19221	+	0.471282i
$985$	4.58373e9	−	1.57845e10i	0.00486938	−	0.0167682i
$986$	−2.99851e11	−	3.47254e11i	−0.317247	−	0.367400i
$987$	−2.66288e11	+	3.66514e11i	−0.280597	+	0.386209i
$988$	−7.88192e11	+	1.58924e12i	−0.827188	+	1.66787i
$989$	−3.38145e11	+	2.45677e11i	−0.353442	+	0.256791i
$990$	−1.65296e11	+	1.52090e11i	−0.172077	+	0.158329i
$991$	5.12520e11	−	7.05423e11i	0.531393	−	0.731400i	−0.455949	−	0.890006i	$-0.650700\pi$
$991$	5.12520e11	−	7.05423e11i	0.531393	−	0.731400i	0.987342	+	0.158606i	$0.0507000\pi$
$992$	−5.56331e11	−	6.16747e11i	−0.574496	−	0.636884i
$993$	−7.86078e11			−0.808479
$994$	1.15254e11	−	4.84727e10i	0.118062	−	0.0496537i
$995$	3.29534e10	+	1.04454e12i	0.0336208	+	1.06570i
$996$	−1.38331e11	+	9.39122e11i	−0.140566	+	0.954299i
$997$	4.70386e11	−	1.44770e12i	0.476074	−	1.46520i	−0.368431	−	0.929655i	$-0.620105\pi$
$997$	4.70386e11	−	1.44770e12i	0.476074	−	1.46520i	0.844504	−	0.535549i	$-0.179895\pi$
$998$	−7.81527e11	+	6.74842e11i	−0.787811	+	0.680268i
$999$			1.48428e12i			1.49024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.84	yes	464
4.3	odd	2	inner	100.9.j.b.11.39	✓	464
25.16	even	5	inner	100.9.j.b.91.39	yes	464
100.91	odd	10	inner	100.9.j.b.91.84	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.39	✓	464	4.3	odd	2	inner
100.9.j.b.11.84	yes	464	1.1	even	1	trivial
100.9.j.b.91.39	yes	464	25.16	even	5	inner
100.9.j.b.91.84	yes	464	100.91	odd	10	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 $\F_{q}$
Belyi maps

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+(10.4569 + 12.1100i) q^{2} +(-89.5931 - 29.1106i) q^{3} +(-37.3057 + 253.267i) q^{4} +(-624.689 + 19.7078i) q^{5} +(-584.338 - 1389.38i) q^{6} +1003.88i q^{7} +(-3457.18 + 2196.62i) q^{8} +(1871.54 + 1359.75i) q^{9} +(-6770.99 - 7358.92i) q^{10} +(-5707.24 - 7855.34i) q^{11} +(10715.1 - 21605.0i) q^{12} +(-31703.7 - 23034.1i) q^{13} +(-12157.0 + 10497.5i) q^{14} +(56541.6 + 16419.4i) q^{15} +(-62752.6 - 18896.6i) q^{16} +(17422.3 + 53620.2i) q^{17} +(3103.88 + 36883.2i) q^{18} +(-168174. + 54643.0i) q^{19} +(18313.1 - 158949. i) q^{20} +(29223.4 - 89940.4i) q^{21} +(35448.3 - 151257. i) q^{22} +(-48326.1 - 66515.1i) q^{23} +(373684. - 96161.7i) q^{24} +(389848. - 24622.5i) q^{25} +(-52579.5 - 624799. i) q^{26} +(235199. + 323724. i) q^{27} +(-254249. - 37450.3i) q^{28} +(-157167. + 483712. i) q^{29} +(392411. + 856416. i) q^{30} +(753344. - 244776. i) q^{31} +(-427360. - 957536. i) q^{32} +(282656. + 869925. i) q^{33} +(-467159. + 771686. i) q^{34} +(-19784.2 - 627111. i) q^{35} +(-414200. + 423273. i) q^{36} +(3.00094e6 + 2.18031e6i) q^{37} +(-2.42031e6 - 1.46519e6i) q^{38} +(2.16990e6 + 2.98661e6i) q^{39} +(2.11637e6 - 1.44034e6i) q^{40} +(2.51995e6 + 1.83085e6i) q^{41} +(1.39477e6 - 586603. i) q^{42} -5.08373e6i q^{43} +(2.20241e6 - 1.15241e6i) q^{44} +(-1.19593e6 - 812539. i) q^{45} +(300159. - 1.28077e6i) q^{46} +(-4.55608e6 - 1.48036e6i) q^{47} +(5.07211e6 + 3.51977e6i) q^{48} +4.75703e6 q^{49} +(4.37479e6 + 4.46360e6i) q^{50} -5.31117e6i q^{51} +(7.01651e6 - 7.17021e6i) q^{52} +(1.79340e6 - 5.51951e6i) q^{53} +(-1.46085e6 + 6.23342e6i) q^{54} +(3.72006e6 + 4.79467e6i) q^{55} +(-2.20514e6 - 3.47058e6i) q^{56} +1.66579e7 q^{57} +(-7.50125e6 + 3.15483e6i) q^{58} +(-1.32908e6 + 1.82932e6i) q^{59} +(-6.26781e6 + 1.37076e7i) q^{60} +(-1.41872e7 + 1.03076e7i) q^{61} +(1.08419e7 + 6.56342e6i) q^{62} +(-1.36502e6 + 1.87879e6i) q^{63} +(7.12693e6 - 1.51882e7i) q^{64} +(2.02589e7 + 1.37643e7i) q^{65} +(-7.57911e6 + 1.25197e7i) q^{66} +(-2.79483e7 + 9.08096e6i) q^{67} +(-1.42302e7 + 2.41215e6i) q^{68} +(2.39339e6 + 7.36610e6i) q^{69} +(7.38745e6 - 6.79723e6i) q^{70} +(-7.40334e6 - 2.40549e6i) q^{71} +(-9.45710e6 - 589844. i) q^{72} +(7.52022e6 - 5.46376e6i) q^{73} +(4.97696e6 + 5.91408e7i) q^{74} +(-3.56445e7 - 9.14270e6i) q^{75} +(-7.56543e6 - 4.46314e7i) q^{76} +(7.88579e6 - 5.72936e6i) q^{77} +(-1.34775e7 + 5.75083e7i) q^{78} +(2.50843e7 + 8.15037e6i) q^{79} +(3.95733e7 + 1.05678e7i) q^{80} +(-1.63387e7 - 5.02852e7i) q^{81} +(4.17924e6 + 4.96617e7i) q^{82} +(-3.74353e7 + 1.21635e7i) q^{83} +(2.16888e7 + 1.07566e7i) q^{84} +(-1.19402e7 - 3.31526e7i) q^{85} +(6.15642e7 - 5.31602e7i) q^{86} +(2.81622e7 - 3.87620e7i) q^{87} +(3.69861e7 + 1.46207e7i) q^{88} +(3.63526e7 - 2.64117e7i) q^{89} +(-2.66585e6 - 2.29794e7i) q^{90} +(2.31234e7 - 3.18266e7i) q^{91} +(1.86489e7 - 9.75801e6i) q^{92} -7.46200e7 q^{93} +(-2.97153e7 - 7.06542e7i) q^{94} +(1.03979e8 - 3.74492e7i) q^{95} +(1.04141e7 + 9.82293e7i) q^{96} +(-1.64337e7 + 5.05777e7i) q^{97} +(4.97439e7 + 5.76078e7i) q^{98} -2.24620e7i 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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