LMFDB - Embedded newform 100.9.j.b.11.17

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			11.17
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-14.5364 + 6.68529i) q^{2} +(-78.1238 - 25.3840i) q^{3} +(166.614 - 194.360i) q^{4} +(-624.998 - 1.49949i) q^{5} +(1305.34 - 153.289i) q^{6} +3856.33i q^{7} +(-1122.61 + 3939.16i) q^{8} +(151.027 + 109.727i) q^{9} +(9095.25 - 4156.50i) q^{10} +(-7608.90 - 10472.7i) q^{11} +(-17950.1 + 10954.8i) q^{12} +(38872.9 + 28242.8i) q^{13} +(-25780.7 - 56057.2i) q^{14} +(48789.2 + 15982.1i) q^{15} +(-10015.8 - 64766.1i) q^{16} +(-32234.1 - 99206.5i) q^{17} +(-2928.94 - 585.381i) q^{18} +(122026. - 39648.6i) q^{19} +(-104425. + 121225. i) q^{20} +(97889.0 - 301271. i) q^{21} +(180619. + 101368. i) q^{22} +(12181.6 + 16766.5i) q^{23} +(187694. - 279246. i) q^{24} +(390621. + 1874.36i) q^{25} +(-753883. - 150672. i) q^{26} +(307773. + 423613. i) q^{27} +(749518. + 642518. i) q^{28} +(-261306. + 804217. i) q^{29} +(-816064. + 93848.2i) q^{30} +(1.17576e6 - 382028. i) q^{31} +(578574. + 874508. i) q^{32} +(328596. + 1.01132e6i) q^{33} +(1.13179e6 + 1.22661e6i) q^{34} +(5782.53 - 2.41020e6i) q^{35} +(46489.7 - 11071.5i) q^{36} +(-783538. - 569274. i) q^{37} +(-1.50876e6 + 1.39213e6i) q^{38} +(-2.31998e6 - 3.19318e6i) q^{39} +(707535. - 2.46028e6i) q^{40} +(-19301.7 - 14023.5i) q^{41} +(591134. + 5.03382e6i) q^{42} -2.10977e6i q^{43} +(-3.30323e6 - 266037. i) q^{44} +(-94226.8 - 68805.8i) q^{45} +(-289166. - 162287. i) q^{46} +(3.86810e6 + 1.25682e6i) q^{47} +(-861553. + 5.31402e6i) q^{48} -9.10650e6 q^{49} +(-5.69075e6 + 2.58417e6i) q^{50} +8.56862e6i q^{51} +(1.19660e7 - 2.84970e6i) q^{52} +(1.07615e6 - 3.31206e6i) q^{53} +(-7.30588e6 - 4.10025e6i) q^{54} +(4.73984e6 + 6.55686e6i) q^{55} +(-1.51907e7 - 4.32915e6i) q^{56} -1.05396e7 q^{57} +(-1.57798e6 - 1.34373e7i) q^{58} +(-9.22247e6 + 1.26936e7i) q^{59} +(1.12352e7 - 6.81984e6i) q^{60} +(-1.68110e7 + 1.22139e7i) q^{61} +(-1.45374e7 + 1.34136e7i) q^{62} +(-423145. + 582409. i) q^{63} +(-1.42567e7 - 8.84426e6i) q^{64} +(-2.42531e7 - 1.77100e7i) q^{65} +(-1.15375e7 - 1.25041e7i) q^{66} +(1.95220e7 - 6.34307e6i) q^{67} +(-2.46524e7 - 1.02641e7i) q^{68} +(-526072. - 1.61908e6i) q^{69} +(1.60288e7 + 3.50743e7i) q^{70} +(4.99450e6 + 1.62281e6i) q^{71} +(-601776. + 471737. i) q^{72} +(-3.51723e7 + 2.55542e7i) q^{73} +(1.51956e7 + 3.03701e6i) q^{74} +(-3.04692e7 - 1.00619e7i) q^{75} +(1.26251e7 - 3.03230e7i) q^{76} +(4.03864e7 - 2.93424e7i) q^{77} +(5.50716e7 + 3.09076e7i) q^{78} +(3.39918e7 + 1.10446e7i) q^{79} +(6.16271e6 + 4.04937e7i) q^{80} +(-1.36699e7 - 4.20716e7i) q^{81} +(374328. + 74813.7i) q^{82} +(-4.40773e7 + 1.43216e7i) q^{83} +(-4.22455e7 - 6.92217e7i) q^{84} +(1.99975e7 + 6.20522e7i) q^{85} +(1.41044e7 + 3.06684e7i) q^{86} +(4.08285e7 - 5.61955e7i) q^{87} +(4.97956e7 - 1.82159e7i) q^{88} +(-1.11535e7 + 8.10348e6i) q^{89} +(1.82970e6 + 370254. i) q^{90} +(-1.08914e8 + 1.49907e8i) q^{91} +(5.28837e6 + 425916. i) q^{92} -1.01552e8 q^{93} +(-6.46304e7 + 7.58972e6i) q^{94} +(-7.63255e7 + 2.45974e7i) q^{95} +(-2.30019e7 - 8.30064e7i) q^{96} +(-2.89920e7 + 8.92281e7i) q^{97} +(1.32376e8 - 6.08796e7i) q^{98} -2.41657e6i 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 $

$2$	−14.5364	+	6.68529i	−0.908525	+	0.417831i
$2$	−14.5364	+	6.68529i	−0.908525	+	0.417831i
$3$	−78.1238	−	25.3840i	−0.964492	−	0.313382i	−0.215901	−	0.976415i	$-0.569269\pi$
$3$	−78.1238	−	25.3840i	−0.964492	−	0.313382i	−0.748590	+	0.663033i	$0.769269\pi$
$4$	166.614	−	194.360i	0.650835	−	0.759219i
$5$	−624.998	−	1.49949i	−0.999997	−	0.00239918i
$5$	−624.998	−	1.49949i	−0.999997	−	0.00239918i
$6$	1305.34	−	153.289i	1.00721	−	0.118279i
$7$			3856.33i			1.60614i	0.595887	+	0.803068i	$0.296800\pi$
$7$			3856.33i			1.60614i	−0.595887	+	0.803068i	$0.703200\pi$
$8$	−1122.61	+	3939.16i	−0.274074	+	0.961709i
$9$	151.027	+	109.727i	0.0230188	+	0.0167242i
$10$	9095.25	−	4156.50i	0.909525	−	0.415650i
$11$	−7608.90	−	10472.7i	−0.519698	−	0.715303i	0.465819	−	0.884880i	$-0.345760\pi$
$11$	−7608.90	−	10472.7i	−0.519698	−	0.715303i	−0.985517	+	0.169577i	$0.945760\pi$
$12$	−17950.1	+	10954.8i	−0.865651	+	0.528301i
$13$	38872.9	+	28242.8i	1.36105	+	0.988859i	0.998378	+	0.0569416i	$0.0181349\pi$
$13$	38872.9	+	28242.8i	1.36105	+	0.988859i	0.362670	+	0.931918i	$0.381865\pi$
$14$	−25780.7	−	56057.2i	−0.671093	−	1.45921i
$15$	48789.2	+	15982.1i	0.963737	+	0.315695i
$16$	−10015.8	−	64766.1i	−0.152828	−	0.988253i
$17$	−32234.1	−	99206.5i	−0.385941	−	1.18780i	−0.935796	−	0.352543i	$-0.885317\pi$
$17$	−32234.1	−	99206.5i	−0.385941	−	1.18780i	0.549855	−	0.835260i	$-0.314683\pi$
$18$	−2928.94	−	585.381i	−0.0279010	−	0.00557634i
$19$	122026.	−	39648.6i	0.936349	−	0.304238i	0.199193	−	0.979960i	$-0.436168\pi$
$19$	122026.	−	39648.6i	0.936349	−	0.304238i	0.737157	+	0.675722i	$0.236168\pi$
$20$	−104425.	+	121225.i	−0.652654	+	0.757656i
$21$	97889.0	−	301271.i	0.503335	−	1.54911i
$22$	180619.	+	101368.i	0.771034	+	0.432724i
$23$	12181.6	+	16766.5i	0.0435304	+	0.0599145i	0.830227	−	0.557425i	$-0.188211\pi$
$23$	12181.6	+	16766.5i	0.0435304	+	0.0599145i	−0.786697	+	0.617339i	$0.788211\pi$
$24$	187694.	−	279246.i	0.565725	−	0.841670i
$25$	390621.	+	1874.36i	0.999988	+	0.00479835i
$26$	−753883.	−	150672.i	−1.64972	−	0.329715i
$27$	307773.	+	423613.i	0.579128	+	0.797102i
$28$	749518.	+	642518.i	1.21941	+	1.04533i
$29$	−261306.	+	804217.i	−0.369452	+	1.13705i	0.577695	+	0.816253i	$0.303952\pi$
$29$	−261306.	+	804217.i	−0.369452	+	1.13705i	−0.947146	+	0.320802i	$0.896048\pi$
$30$	−816064.	+	93848.2i	−1.00749	+	0.115862i
$31$	1.17576e6	−	382028.i	1.27313	−	0.413665i	0.406974	−	0.913440i	$-0.366584\pi$
$31$	1.17576e6	−	382028.i	1.27313	−	0.413665i	0.866155	+	0.499775i	$0.166584\pi$
$32$	578574.	+	874508.i	0.551771	+	0.833996i
$33$	328596.	+	1.01132e6i	0.277081	+	0.852768i
$34$	1.13179e6	+	1.22661e6i	0.846937	+	0.917890i
$35$	5782.53	−	2.41020e6i	0.00385341	−	1.60613i
$36$	46489.7	−	11071.5i	0.0276788	−	0.00659168i
$37$	−783538.	−	569274.i	−0.418074	−	0.303749i	0.358788	−	0.933419i	$-0.383190\pi$
$37$	−783538.	−	569274.i	−0.418074	−	0.303749i	−0.776862	+	0.629670i	$0.783190\pi$
$38$	−1.50876e6	+	1.39213e6i	−0.723576	+	0.667644i
$39$	−2.31998e6	−	3.19318e6i	−1.00283	−	1.38027i
$40$	707535.	−	2.46028e6i	0.276381	−	0.961048i
$41$	−19301.7	−	14023.5i	−0.00683062	−	0.00496273i	0.584365	−	0.811491i	$-0.301344\pi$
$41$	−19301.7	−	14023.5i	−0.00683062	−	0.00496273i	−0.591195	+	0.806528i	$0.701344\pi$
$42$	591134.	+	5.03382e6i	0.189972	+	1.61771i
$43$		−	2.10977e6i		−	0.617107i	−0.951207	−	0.308553i	$-0.900155\pi$
$43$		−	2.10977e6i		−	0.617107i	0.951207	−	0.308553i	$-0.0998449\pi$
$44$	−3.30323e6	−	266037.i	−0.881309	−	0.0709792i
$45$	−94226.8	−	68805.8i	−0.0229786	−	0.0167793i
$46$	−289166.	−	162287.i	−0.0645826	−	0.0362454i
$47$	3.86810e6	+	1.25682e6i	0.792695	+	0.257562i	0.677251	−	0.735752i	$-0.263171\pi$
$47$	3.86810e6	+	1.25682e6i	0.792695	+	0.257562i	0.115444	+	0.993314i	$0.463171\pi$
$48$	−861553.	+	5.31402e6i	−0.162299	+	1.00106i
$49$	−9.10650e6			−1.57967
$50$	−5.69075e6	+	2.58417e6i	−0.910519	+	0.413467i
$51$			8.56862e6i			1.26657i
$52$	1.19660e7	−	2.84970e6i	1.63658	−	0.389750i
$53$	1.07615e6	−	3.31206e6i	0.136386	−	0.419754i	−0.859417	−	0.511276i	$-0.829173\pi$
$53$	1.07615e6	−	3.31206e6i	0.136386	−	0.419754i	0.995803	+	0.0915216i	$0.0291731\pi$
$54$	−7.30588e6	−	4.10025e6i	−0.859206	−	0.482209i
$55$	4.73984e6	+	6.55686e6i	0.517980	+	0.716547i
$56$	−1.51907e7	−	4.32915e6i	−1.54463	−	0.440201i
$57$	−1.05396e7			−0.998444
$58$	−1.57798e6	−	1.34373e7i	−0.139441	−	1.18741i
$59$	−9.22247e6	+	1.26936e7i	−0.761096	+	1.04756i	0.236026	+	0.971747i	$0.424155\pi$
$59$	−9.22247e6	+	1.26936e7i	−0.761096	+	1.04756i	−0.997122	+	0.0758120i	$0.975845\pi$
$60$	1.12352e7	−	6.81984e6i	0.866916	−	0.526222i
$61$	−1.68110e7	+	1.22139e7i	−1.21416	+	0.882138i	−0.995602	−	0.0936864i	$-0.970135\pi$
$61$	−1.68110e7	+	1.22139e7i	−1.21416	+	0.882138i	−0.218557	+	0.975824i	$0.570135\pi$
$62$	−1.45374e7	+	1.34136e7i	−0.983827	+	0.907777i
$63$	−423145.	+	582409.i	−0.0268613	+	0.0369714i
$64$	−1.42567e7	−	8.84426e6i	−0.849767	−	0.527159i
$65$	−2.42531e7	−	1.77100e7i	−1.35867	−	0.992122i
$66$	−1.15375e7	−	1.25041e7i	−0.608048	−	0.658988i
$67$	1.95220e7	−	6.34307e6i	0.968779	−	0.314775i	0.218456	−	0.975847i	$-0.429898\pi$
$67$	1.95220e7	−	6.34307e6i	0.968779	−	0.314775i	0.750323	+	0.661072i	$0.229898\pi$
$68$	−2.46524e7	−	1.02641e7i	−1.15299	−	0.480050i
$69$	−526072.	−	1.61908e6i	−0.0232086	−	0.0714287i
$70$	1.60288e7	+	3.50743e7i	0.667590	+	1.46082i
$71$	4.99450e6	+	1.62281e6i	0.196544	+	0.0638609i	0.405635	−	0.914035i	$-0.367051\pi$
$71$	4.99450e6	+	1.62281e6i	0.196544	+	0.0638609i	−0.209091	+	0.977896i	$0.567051\pi$
$72$	−601776.	+	471737.i	−0.0223926	+	0.0175537i
$73$	−3.51723e7	+	2.55542e7i	−1.23854	+	0.899850i	−0.997500	−	0.0706652i	$-0.977488\pi$
$73$	−3.51723e7	+	2.55542e7i	−1.23854	+	0.899850i	−0.241038	+	0.970516i	$0.577488\pi$
$74$	1.51956e7	+	3.03701e6i	0.506746	+	0.101279i
$75$	−3.04692e7	−	1.00619e7i	−0.962977	−	0.318007i
$76$	1.26251e7	−	3.03230e7i	0.378425	−	0.908903i
$77$	4.03864e7	−	2.93424e7i	1.14887	−	0.834705i
$78$	5.50716e7	+	3.09076e7i	1.48782	+	0.835001i
$79$	3.39918e7	+	1.10446e7i	0.872703	+	0.283558i	0.710924	−	0.703269i	$-0.248277\pi$
$79$	3.39918e7	+	1.10446e7i	0.872703	+	0.283558i	0.161779	+	0.986827i	$0.448277\pi$
$80$	6.16271e6	+	4.04937e7i	0.150457	+	0.988617i
$81$	−1.36699e7	−	4.20716e7i	−0.317559	−	0.977347i
$82$	374328.	+	74813.7i	0.00827937	+	0.00165472i
$83$	−4.40773e7	+	1.43216e7i	−0.928759	+	0.301772i	−0.734055	−	0.679090i	$-0.762375\pi$
$83$	−4.40773e7	+	1.43216e7i	−0.928759	+	0.301772i	−0.194704	+	0.980862i	$0.562375\pi$
$84$	−4.22455e7	−	6.92217e7i	−0.848523	−	1.39035i
$85$	1.99975e7	+	6.20522e7i	0.383090	+	1.18873i
$86$	1.41044e7	+	3.06684e7i	0.257846	+	0.560657i
$87$	4.08285e7	−	5.61955e7i	0.712666	−	0.980900i
$88$	4.97956e7	−	1.82159e7i	0.830348	−	0.303752i
$89$	−1.11535e7	+	8.10348e6i	−0.177767	+	0.129155i	−0.673110	−	0.739542i	$-0.735042\pi$
$89$	−1.11535e7	+	8.10348e6i	−0.177767	+	0.129155i	0.495344	+	0.868697i	$0.335042\pi$
$90$	1.82970e6	+	370254.i	0.0278876	+	0.00564326i
$91$	−1.08914e8	+	1.49907e8i	−1.58824	+	2.18603i
$92$	5.28837e6	+	425916.i	0.0738194	+	0.00594529i
$93$	−1.01552e8			−1.35756
$94$	−6.46304e7	+	7.58972e6i	−0.827801	+	0.0972108i
$95$	−7.63255e7	+	2.45974e7i	−0.937077	+	0.301991i
$96$	−2.30019e7	−	8.30064e7i	−0.270819	−	0.977297i
$97$	−2.89920e7	+	8.92281e7i	−0.327484	+	1.00789i	0.642822	+	0.766015i	$0.277763\pi$
$97$	−2.89920e7	+	8.92281e7i	−0.327484	+	1.00789i	−0.970307	+	0.241878i	$0.922237\pi$
$98$	1.32376e8	−	6.08796e7i	1.43517	−	0.660036i
$99$		−	2.41657e6i		−	0.0251569i
$100$	6.54470e7	−	7.56088e7i	0.654470	−	0.756088i
$101$	7.28254e7			0.699838			0.349919	−	0.936780i	$-0.386209\pi$
$101$	7.28254e7			0.699838			0.349919	+	0.936780i	$0.386209\pi$
$102$	−5.72837e7	−	1.24557e8i	−0.529213	−	1.15071i
$103$	4.79850e7	+	1.55913e7i	0.426341	+	0.138526i	0.514325	−	0.857595i	$-0.328043\pi$
$103$	4.79850e7	+	1.55913e7i	0.426341	+	0.138526i	−0.0879844	+	0.996122i	$0.528043\pi$
$104$	−1.54892e8	+	1.21421e8i	−1.32402	+	1.03791i
$105$	−6.16322e7	+	1.88147e8i	−0.507050	+	1.54789i
$106$	6.49870e6	+	5.53399e7i	0.0514758	+	0.438344i
$107$		−	1.33956e8i		−	1.02194i	−0.859598	−	0.510971i	$-0.829286\pi$
$107$		−	1.33956e8i		−	1.02194i	0.859598	−	0.510971i	$-0.170714\pi$
$108$	1.33613e8	+	1.07609e7i	0.982092	+	0.0790960i
$109$	−8.78560e7	−	6.38311e7i	−0.622394	−	0.452196i	0.231363	−	0.972867i	$-0.425681\pi$
$109$	−8.78560e7	−	6.38311e7i	−0.622394	−	0.452196i	−0.853757	+	0.520672i	$0.825681\pi$
$110$	−1.12735e8	−	6.36258e7i	−0.769993	−	0.434573i
$111$	4.67626e7	+	6.43632e7i	0.308040	+	0.423980i
$112$	2.49760e8	−	3.86241e7i	1.58727	−	0.245463i
$113$	2.68031e7	+	1.94736e7i	0.164388	+	0.119435i	0.666938	−	0.745113i	$-0.267605\pi$
$113$	2.68031e7	+	1.94736e7i	0.164388	+	0.119435i	−0.502550	+	0.864548i	$0.667605\pi$
$114$	1.53207e8	−	7.04602e7i	0.907111	−	0.417181i
$115$	−7.58834e6	−	1.04973e7i	−0.0433866	−	0.0600188i
$116$	1.12771e8	+	1.84781e8i	0.622822	+	1.02053i
$117$	2.77183e6	+	8.53083e6i	0.0147919	+	0.0455248i
$118$	4.92008e7	−	2.46175e8i	0.253772	−	1.26974i
$119$	3.82573e8	−	1.24306e8i	1.90777	−	0.619873i
$120$	−1.17727e8	+	1.74247e8i	−0.567743	+	0.840310i
$121$	1.44574e7	−	4.44954e7i	0.0674449	−	0.207574i
$122$	1.62718e8	−	2.89933e8i	0.734509	−	1.30876i
$123$	1.15195e6	+	1.58552e6i	0.00503284	+	0.00692711i
$124$	1.21647e8	−	2.92172e8i	0.514534	−	1.23581i
$125$	−2.44134e8	−	1.75720e6i	−0.999974	−	0.00719749i
$126$	2.25743e6	−	1.12950e7i	0.00895635	−	0.0448129i
$127$	2.12069e8	+	2.91888e8i	0.815196	+	1.12202i	0.990501	+	0.137507i	$0.0439091\pi$
$127$	2.12069e8	+	2.91888e8i	0.815196	+	1.12202i	−0.175304	+	0.984514i	$0.556091\pi$
$128$	2.66368e8	+	3.32533e7i	0.992297	+	0.123878i
$129$	−5.35542e7	+	1.64823e8i	−0.193390	+	0.595195i
$130$	4.70950e8	+	9.53002e7i	1.64893	+	0.333672i
$131$	−8.90014e7	+	2.89183e7i	−0.302212	+	0.0981946i	−0.456198	−	0.889878i	$-0.650789\pi$
$131$	−8.90014e7	+	2.89183e7i	−0.302212	+	0.0981946i	0.153986	+	0.988073i	$0.450789\pi$
$132$	2.51308e8	+	1.04633e8i	0.827772	+	0.344646i
$133$	1.52898e8	+	4.70573e8i	0.488648	+	1.50390i
$134$	−2.41374e8	+	2.22716e8i	−0.748637	+	0.690767i
$135$	−1.91722e8	−	2.65219e8i	−0.577214	−	0.798489i
$136$	4.26976e8	−	1.56054e7i	1.24810	−	0.0456162i
$137$	2.25200e8	+	1.63617e8i	0.639272	+	0.464458i	0.859600	−	0.510968i	$-0.170713\pi$
$137$	2.25200e8	+	1.63617e8i	0.639272	+	0.464458i	−0.220328	+	0.975426i	$0.570713\pi$
$138$	1.84712e7	+	2.00187e7i	0.0509307	+	0.0551975i
$139$	2.99170e7	+	4.11772e7i	0.0801416	+	0.110306i	0.847206	−	0.531265i	$-0.178283\pi$
$139$	2.99170e7	+	4.11772e7i	0.0801416	+	0.110306i	−0.767064	+	0.641571i	$0.778283\pi$
$140$	−4.67484e8	−	4.02696e8i	−1.21690	−	1.04825i
$141$	−2.70288e8	−	1.96375e8i	−0.683832	−	0.496833i
$142$	−8.34510e7	+	9.79987e6i	−0.205248	+	0.0241028i
$143$		−	6.22002e8i		−	1.48747i
$144$	5.59396e6	−	1.08804e7i	0.0130098	−	0.0253043i
$145$	1.64522e8	−	5.02243e8i	0.372178	−	1.13617i
$146$	3.40441e8	−	6.06603e8i	0.749257	−	1.33504i
$147$	7.11435e8	+	2.31159e8i	1.52358	+	0.495042i
$148$	−2.41192e8	+	5.74398e7i	−0.502709	+	0.119720i
$149$	−9.48883e8			−1.92516			−0.962581	−	0.270993i	$-0.912648\pi$
$149$	−9.48883e8			−1.92516			−0.962581	+	0.270993i	$0.912648\pi$
$150$	5.10179e8	−	5.74313e7i	1.00776	−	0.113444i
$151$		−	1.00003e9i		−	1.92356i	−0.273832	−	0.961778i	$-0.588291\pi$
$151$		−	1.00003e9i		−	1.92356i	0.273832	−	0.961778i	$-0.411709\pi$
$152$	1.91949e7	+	5.25189e8i	0.0359594	+	0.983879i
$153$	6.01744e6	−	1.85198e7i	0.0109811	−	0.0337964i
$154$	−3.90910e8	+	6.96528e8i	−0.695014	+	1.23839i
$155$	−7.35421e8	+	2.37004e8i	−1.27412	+	0.410609i
$156$	−1.00717e9	−	8.11157e7i	−1.70061	−	0.136964i
$157$	−5.51253e8			−0.907304			−0.453652	−	0.891179i	$-0.649879\pi$
$157$	−5.51253e8			−0.907304			−0.453652	+	0.891179i	$0.649879\pi$
$158$	−5.67955e8	+	6.66965e7i	−0.911351	+	0.107022i
$159$	−1.68147e8	+	2.31434e8i	−0.263087	+	0.362108i
$160$	−3.60296e8	−	5.47433e8i	−0.549768	−	0.835317i
$161$	−6.46573e7	+	4.69763e7i	−0.0962308	+	0.0699158i
$162$	4.79972e8	+	5.20182e8i	0.696876	+	0.755258i
$163$	−3.13513e8	+	4.31514e8i	−0.444126	+	0.611286i	−0.971123	−	0.238581i	$-0.923318\pi$
$163$	−3.13513e8	+	4.31514e8i	−0.444126	+	0.611286i	0.526997	+	0.849867i	$0.323318\pi$
$164$	−5.94154e6	+	1.41497e6i	−0.00821341	+	0.00195602i
$165$	−2.03856e8	−	6.32563e8i	−0.275034	−	0.853430i
$166$	5.44982e8	−	5.02854e8i	0.717711	−	0.662232i
$167$	−7.10908e8	+	2.30988e8i	−0.914002	+	0.296977i	−0.728004	−	0.685573i	$-0.759552\pi$
$167$	−7.10908e8	+	2.30988e8i	−0.914002	+	0.296977i	−0.185998	+	0.982550i	$0.559552\pi$
$168$	1.07687e9	+	7.23810e8i	1.35184	+	0.908631i
$169$	4.61371e8	+	1.41995e9i	0.565592	+	1.74071i
$170$	−7.05529e8	−	7.68326e8i	−0.844733	−	0.919920i
$171$	2.27797e7	+	7.40157e6i	0.0266418	+	0.00865644i
$172$	−4.10054e8	−	3.51516e8i	−0.468520	−	0.401635i
$173$	5.22343e8	−	3.79504e8i	0.583138	−	0.423675i	−0.256716	−	0.966487i	$-0.582640\pi$
$173$	5.22343e8	−	3.79504e8i	0.583138	−	0.423675i	0.839854	+	0.542812i	$0.182640\pi$
$174$	−2.17815e8	+	1.08983e9i	−0.237624	+	1.18895i
$175$	−7.22814e6	+	1.50636e9i	−0.00770680	+	1.60612i
$176$	−6.02070e8	+	5.97691e8i	−0.627475	+	0.622911i
$177$	1.04271e9	−	7.57573e8i	1.06236	−	0.771848i
$178$	1.07957e8	−	1.92360e8i	0.107540	−	0.191617i
$179$	−627020.	−	203731.i	−0.000610758	−	0.000198447i	0.308712	−	0.951156i	$-0.400102\pi$
$179$	−627020.	−	203731.i	−0.000610758	−	0.000198447i	−0.309322	+	0.950957i	$0.600102\pi$
$180$	−2.90726e7	+	6.84995e6i	−0.0276945	+	0.00652525i
$181$	1.67006e8	+	5.13992e8i	0.155603	+	0.478897i	0.998222	−	0.0596140i	$-0.0189870\pi$
$181$	1.67006e8	+	5.13992e8i	0.155603	+	0.478897i	−0.842618	+	0.538511i	$0.818987\pi$
$182$	5.81041e8	−	2.90722e9i	0.529568	−	2.64968i
$183$	1.62338e9	−	5.27469e8i	1.44749	−	0.470319i
$184$	−7.97212e7	+	2.91630e7i	−0.0695508	+	0.0254426i
$185$	4.88856e8	+	3.56970e8i	0.417344	+	0.304751i
$186$	1.47621e9	−	6.78907e8i	1.23337	−	0.567229i
$187$	−7.93698e8	+	1.09243e9i	−0.649066	+	0.893363i
$188$	8.88754e8	−	5.42401e8i	0.711460	−	0.434199i
$189$	−1.63359e9	+	1.18687e9i	−1.28025	+	0.930159i
$190$	9.45057e8	−	8.67815e8i	0.725176	−	0.665906i
$191$	1.41377e9	−	1.94589e9i	1.06230	−	1.46212i	0.184655	−	0.982803i	$-0.440883\pi$
$191$	1.41377e9	−	1.94589e9i	1.06230	−	1.46212i	0.877640	−	0.479320i	$-0.159117\pi$
$192$	8.89287e8	+	1.05284e9i	0.654391	+	0.774742i
$193$	−1.12323e9			−0.809544			−0.404772	−	0.914418i	$-0.632649\pi$
$193$	−1.12323e9			−0.809544			−0.404772	+	0.914418i	$0.632649\pi$
$194$	−1.75077e8	−	1.49087e9i	−0.123601	−	1.05253i
$195$	1.44520e9	+	1.99921e9i	0.999514	+	1.38268i
$196$	−1.51727e9	+	1.76994e9i	−1.02811	+	1.19932i
$197$	−2.79134e8	+	8.59088e8i	−0.185331	+	0.570391i	−0.999954	−	0.00960040i	$-0.996944\pi$
$197$	−2.79134e8	+	8.59088e8i	−0.185331	+	0.570391i	0.814623	+	0.579991i	$0.196944\pi$
$198$	1.61554e7	+	3.51282e7i	0.0105113	+	0.0228557i
$199$			1.94279e9i			1.23883i	0.785062	+	0.619417i	$0.212631\pi$
$199$			1.94279e9i			1.23883i	−0.785062	+	0.619417i	$0.787369\pi$
$200$	−4.45897e8	+	1.53661e9i	−0.278686	+	0.960382i
$201$	−1.68614e9			−1.03302
$202$	−1.05862e9	+	4.86859e8i	−0.635820	+	0.292414i
$203$	−3.10133e9	−	1.00768e9i	−1.82626	−	0.593389i
$204$	1.66540e9	+	1.42765e9i	0.961607	+	0.824330i
$205$	1.20425e7	+	8.79361e6i	0.00681869	+	0.00497911i
$206$	−8.01761e8	+	9.41529e7i	−0.445222	+	0.0522835i
$207$			3.86884e6i			0.00210717i
$208$	1.43984e9	−	2.80052e9i	0.769236	−	1.49618i
$209$	−1.34371e9	−	9.76265e8i	−0.704241	−	0.511661i
$210$	−3.61910e8	−	3.14701e9i	−0.186090	−	1.61816i
$211$	−1.56755e9	−	2.15755e9i	−0.790845	−	1.08850i	−0.994002	−	0.109358i	$-0.965120\pi$
$211$	−1.56755e9	−	2.15755e9i	−0.790845	−	1.08850i	0.203158	−	0.979146i	$-0.434880\pi$
$212$	−4.64431e8	−	7.60997e8i	−0.229921	−	0.376738i
$213$	−3.48996e8	−	2.53561e8i	−0.169552	−	0.123187i
$214$	8.95533e8	+	1.94723e9i	0.426999	+	0.928459i
$215$	−3.16357e6	+	1.31860e9i	−0.00148055	+	0.617105i
$216$	−2.01418e9	+	7.36814e8i	−0.925304	+	0.338488i
$217$	1.47323e9	+	4.53413e9i	0.664402	+	2.04482i
$218$	1.70384e9	+	3.40531e8i	0.754401	+	0.150776i
$219$	3.39646e9	−	1.10358e9i	1.47656	−	0.479762i
$220$	2.06411e9	+	1.71226e8i	0.881136	+	0.0730934i
$221$	1.54884e9	−	4.76682e9i	0.649286	−	1.99830i
$222$	−1.11005e9	−	6.22987e8i	−0.457014	−	0.256488i
$223$	−4.12703e8	−	5.68036e8i	−0.166885	−	0.229698i	0.717381	−	0.696681i	$-0.245341\pi$
$223$	−4.12703e8	−	5.68036e8i	−0.166885	−	0.229698i	−0.884266	+	0.466983i	$0.845341\pi$
$224$	−3.37239e9	+	2.23117e9i	−1.33951	+	0.886219i
$225$	5.87884e7	+	4.31448e7i	0.0229383	+	0.0168344i
$226$	−5.19807e8	−	1.03889e8i	−0.199255	−	0.0398233i
$227$	−1.00635e9	−	1.38513e9i	−0.379007	−	0.521659i	0.576314	−	0.817228i	$-0.304491\pi$
$227$	−1.00635e9	−	1.38513e9i	−0.379007	−	0.521659i	−0.955321	+	0.295570i	$0.904491\pi$
$228$	−1.75604e9	+	2.04847e9i	−0.649822	+	0.758038i
$229$	1.61164e9	−	4.96013e9i	0.586040	−	1.80365i	−0.00901205	−	0.999959i	$-0.502869\pi$
$229$	1.61164e9	−	4.96013e9i	0.586040	−	1.80365i	0.595052	−	0.803687i	$-0.297131\pi$
$230$	1.80485e8	+	1.01863e8i	0.0644954	+	0.0364003i
$231$	−3.89997e9	+	1.26718e9i	−1.36966	+	0.445030i
$232$	−2.87459e9	−	1.93215e9i	−0.992258	−	0.666942i
$233$	6.75327e8	+	2.07844e9i	0.229134	+	0.705203i	0.997846	+	0.0656069i	$0.0208983\pi$
$233$	6.75327e8	+	2.07844e9i	0.229134	+	0.705203i	−0.768711	+	0.639596i	$0.779102\pi$
$234$	−9.73235e7	−	1.05477e8i	−0.0324604	−	0.0351799i
$235$	−2.41567e9	−	7.91311e8i	−0.792075	−	0.259463i
$236$	9.30549e8	+	3.90742e9i	0.299979	+	1.25963i
$237$	−2.37522e9	−	1.72570e9i	−0.752852	−	0.546979i
$238$	−4.73022e9	+	4.36457e9i	−1.47426	+	1.36030i
$239$	1.13271e9	+	1.55905e9i	0.347159	+	0.477823i	0.946515	−	0.322659i	$-0.104577\pi$
$239$	1.13271e9	+	1.55905e9i	0.347159	+	0.477823i	−0.599356	+	0.800482i	$0.704577\pi$
$240$	5.46437e8	−	3.31996e9i	0.164701	−	1.00066i
$241$	−5.00984e9	−	3.63986e9i	−1.48510	−	1.07899i	−0.975869	−	0.218359i	$-0.929930\pi$
$241$	−5.00984e9	−	3.63986e9i	−1.48510	−	1.07899i	−0.509232	−	0.860629i	$-0.670070\pi$
$242$	8.73058e7	+	7.43454e8i	0.0254555	+	0.216767i
$243$			1.98358e8i			0.0568886i
$244$	−4.27047e8	+	5.30241e9i	−0.120480	+	1.49594i
$245$	5.69155e9	+	1.36551e7i	1.57967	+	0.00378992i
$246$	−2.73449e7	−	1.53467e7i	−0.00746682	−	0.00419058i
$247$	5.86329e9	+	1.90510e9i	1.57526	+	0.511835i
$248$	1.84950e8	+	5.06038e9i	0.0488930	+	1.33775i
$249$	3.80703e9			0.990350
$250$	3.56058e9	−	1.60657e9i	0.911509	−	0.411281i
$251$			8.43395e8i			0.212489i	0.994340	+	0.106244i	$0.0338826\pi$
$251$			8.43395e8i			0.212489i	−0.994340	+	0.106244i	$0.966117\pi$
$252$	4.26953e7	+	1.79280e8i	0.0105871	+	0.0444559i
$253$	8.29031e7	−	2.55150e8i	0.0202343	−	0.0622749i
$254$	−5.03408e9	−	2.82526e9i	−1.20944	−	0.678770i
$255$	1.28486e7	−	5.35537e9i	0.00303874	−	1.26657i
$256$	−4.09434e9	+	1.29736e9i	−0.953287	+	0.302066i
$257$	6.05433e9			1.38782			0.693911	−	0.720061i	$-0.255886\pi$
$257$	6.05433e9			1.38782			0.693911	+	0.720061i	$0.255886\pi$
$258$	−3.23404e8	−	2.75396e9i	−0.0729906	−	0.621554i
$259$	2.19531e9	−	3.02158e9i	0.487862	−	0.671484i
$260$	−7.48302e9	+	1.76312e9i	−1.63751	+	0.385822i
$261$	−1.27709e8	+	9.27858e7i	−0.0275206	+	0.0199949i
$262$	1.10043e9	−	1.01537e9i	0.233538	−	0.215486i
$263$	−3.73218e9	+	5.13691e9i	−0.780082	+	1.07369i	0.215191	+	0.976572i	$0.430962\pi$
$263$	−3.73218e9	+	5.13691e9i	−0.780082	+	1.07369i	−0.995273	+	0.0971182i	$0.969038\pi$
$264$	−4.35261e9	+	1.59082e8i	−0.896055	+	0.0327495i
$265$	−6.77561e8	+	2.06842e9i	−0.137393	+	0.419426i
$266$	−5.36851e9	−	5.81826e9i	−1.07233	−	1.16216i
$267$	1.07705e9	−	3.49955e8i	0.211929	−	0.0688600i
$268$	2.01979e9	−	4.85114e9i	0.391531	−	0.940382i
$269$	1.13672e9	+	3.49845e9i	0.217092	+	0.668139i	0.998998	+	0.0447439i	$0.0142472\pi$
$269$	1.13672e9	+	3.49845e9i	0.217092	+	0.668139i	−0.781907	+	0.623395i	$0.785753\pi$
$270$	4.56001e9	+	2.57360e9i	0.858047	+	0.484269i
$271$	2.54495e9	+	8.26904e8i	0.471848	+	0.153313i	0.535282	−	0.844673i	$-0.320205\pi$
$271$	2.54495e9	+	8.26904e8i	0.471848	+	0.153313i	−0.0634343	+	0.997986i	$0.520205\pi$
$272$	−6.10237e9	+	3.08131e9i	−1.11487	+	0.562937i
$273$	1.23140e10	−	8.94663e9i	2.21691	−	1.61068i
$274$	−4.36742e9	−	8.72878e8i	−0.774859	−	0.154864i
$275$	−2.95256e9	−	4.10513e9i	−0.516260	−	0.717788i
$276$	−4.02336e8	−	1.67514e8i	−0.0693350	−	0.0288679i
$277$	−3.71899e9	+	2.70201e9i	−0.631693	+	0.458952i	−0.856986	−	0.515339i	$-0.827666\pi$
$277$	−3.71899e9	+	2.70201e9i	−0.631693	+	0.458952i	0.225293	+	0.974291i	$0.427666\pi$
$278$	−7.10166e8	−	3.98564e8i	−0.118900	−	0.0667296i
$279$	2.19490e8	+	7.13166e7i	0.0362241	+	0.0117699i
$280$	9.48767e9	+	2.72849e9i	1.54357	+	0.443905i
$281$	−4.72382e8	−	1.45384e9i	−0.0757650	−	0.233181i	0.906001	−	0.423277i	$-0.139120\pi$
$281$	−4.72382e8	−	1.45384e9i	−0.0757650	−	0.233181i	−0.981766	+	0.190096i	$0.939120\pi$
$282$	5.24184e9	+	1.04764e9i	0.828871	+	0.165659i
$283$	−3.79053e9	+	1.23162e9i	−0.590955	+	0.192013i	−0.589202	−	0.807986i	$-0.700558\pi$
$283$	−3.79053e9	+	1.23162e9i	−0.590955	+	0.192013i	−0.00175264	+	0.999998i	$0.500558\pi$
$284$	1.14756e9	−	7.00349e8i	0.176402	−	0.107657i
$285$	6.58722e9	+	1.58040e7i	0.998441	+	0.00239545i
$286$	4.15827e9	+	9.04167e9i	0.621510	+	1.35140i
$287$	5.40793e7	−	7.44338e7i	0.00797083	−	0.0109709i
$288$	−8.57735e6	+	1.95559e8i	−0.00124676	+	0.0284255i
$289$	−3.15938e9	+	2.29542e9i	−0.452908	+	0.329057i
$290$	9.66086e8	+	8.40067e9i	0.136592	+	1.18774i
$291$	4.52993e9	−	6.23491e9i	0.631712	−	0.869477i
$292$	−8.93474e8	+	1.10938e10i	−0.122900	+	1.52598i
$293$	−6.08704e9			−0.825915			−0.412958	−	0.910750i	$-0.635504\pi$
$293$	−6.08704e9			−0.825915			−0.412958	+	0.910750i	$0.635504\pi$
$294$	−1.18871e10	+	1.39593e9i	−1.59106	+	0.186842i
$295$	5.78306e9	−	7.91968e9i	0.763607	−	1.04573i
$296$	3.12207e9	−	2.44741e9i	0.406701	−	0.318816i
$297$	2.09458e9	−	6.44645e9i	0.269197	−	0.828504i
$298$	1.37933e10	−	6.34356e9i	1.74906	−	0.804392i
$299$			9.95806e8i			0.124592i
$300$	−7.03222e9	+	4.24554e9i	−0.868176	+	0.524141i
$301$	8.13596e9			0.991158
$302$	6.68549e9	+	1.45368e10i	0.803721	+	1.74760i
$303$	−5.68940e9	−	1.84860e9i	−0.674988	−	0.219317i
$304$	−3.79007e9	−	7.50604e9i	−0.443765	−	0.878854i
$305$	1.05252e10	−	7.60848e9i	1.21627	−	0.879222i
$306$	3.63382e7	+	3.09439e8i	0.00414456	+	0.0352931i
$307$		−	5.19946e9i		−	0.585336i	−0.956214	−	0.292668i	$-0.905457\pi$
$307$		−	5.19946e9i		−	0.585336i	0.956214	−	0.292668i	$-0.0945430\pi$
$308$	1.02593e9	−	1.27384e10i	0.114002	−	1.41550i
$309$	−3.35300e9	−	2.43610e9i	−0.367790	−	0.267215i
$310$	9.10594e9	−	8.36169e9i	0.986002	−	0.905414i
$311$	5.42529e9	+	7.46727e9i	0.579938	+	0.798216i	0.993689	−	0.112174i	$-0.0357814\pi$
$311$	5.42529e9	+	7.46727e9i	0.579938	+	0.798216i	−0.413751	+	0.910390i	$0.635781\pi$
$312$	1.51829e10	−	5.55409e9i	1.60227	−	0.586131i
$313$	−1.24228e9	−	9.02569e8i	−0.129432	−	0.0940379i	0.521186	−	0.853443i	$-0.325490\pi$
$313$	−1.24228e9	−	9.02569e8i	−0.129432	−	0.0940379i	−0.650618	+	0.759405i	$0.725490\pi$
$314$	8.01324e9	−	3.68529e9i	0.824308	−	0.379099i
$315$	2.65338e8	−	3.63370e8i	0.0269499	−	0.0369068i
$316$	7.81014e9	−	4.76647e9i	0.783268	−	0.478023i
$317$	1.32940e9	+	4.09148e9i	0.131650	+	0.405176i	0.995054	−	0.0993370i	$-0.0316722\pi$
$317$	1.32940e9	+	4.09148e9i	0.131650	+	0.405176i	−0.863404	+	0.504513i	$0.831672\pi$
$318$	8.97042e8	−	4.48833e9i	0.0877211	−	0.438910i
$319$	1.04106e10	−	3.38261e9i	1.00534	−	0.326655i
$320$	8.89716e9	+	5.54903e9i	0.848499	+	0.529196i
$321$	−3.40033e9	+	1.04651e10i	−0.320259	+	0.985654i
$322$	6.25834e8	−	1.11512e9i	0.0582151	−	0.103728i
$323$	−7.86680e9	−	1.08277e10i	−0.722750	−	0.994780i
$324$	−1.04546e10	−	4.35282e9i	−0.948699	−	0.394994i
$325$	1.51316e10	+	1.11051e10i	1.35629	+	0.995379i
$326$	1.67256e9	−	8.36859e9i	0.148085	−	0.740938i
$327$	5.24336e9	+	7.21686e9i	0.458584	+	0.631186i
$328$	7.69090e7	−	6.02895e7i	0.00664480	−	0.00520891i
$329$	−4.84672e9	+	1.49167e10i	−0.413680	+	1.27318i
$330$	7.19219e9	+	7.83235e9i	0.606465	+	0.660444i
$331$	−2.19328e10	+	7.12640e9i	−1.82718	+	0.593688i	−0.827713	+	0.561151i	$0.810359\pi$
$331$	−2.19328e10	+	7.12640e9i	−1.82718	+	0.593688i	−0.999471	+	0.0325367i	$0.989641\pi$
$332$	−4.56034e9	+	1.09531e10i	−0.375357	+	0.901536i
$333$	−5.58702e7	−	1.71951e8i	−0.00454364	−	0.0139839i
$334$	8.78981e9	−	8.11036e9i	0.706308	−	0.651710i
$335$	−1.22107e10	+	3.93514e9i	−0.969531	+	0.312450i
$336$	−2.04926e10	−	3.32243e9i	−1.60783	−	0.260675i
$337$	7.37076e9	+	5.35517e9i	0.571469	+	0.415196i	0.835638	−	0.549280i	$-0.185098\pi$
$337$	7.37076e9	+	5.35517e9i	0.571469	+	0.415196i	−0.264170	+	0.964476i	$0.585098\pi$
$338$	−1.61995e10	−	1.75566e10i	−1.24118	−	1.34516i
$339$	−1.59964e9	−	2.20172e9i	−0.121122	−	0.166711i
$340$	1.53923e10	+	6.45203e9i	1.15183	+	0.482815i
$341$	−1.29471e10	−	9.40664e9i	−0.957538	−	0.695692i
$342$	−3.80616e8	+	4.46968e7i	−0.0278217	+	0.00326717i
$343$		−	1.28867e10i		−	0.931034i
$344$	8.31070e9	+	2.36844e9i	0.593477	+	0.169133i
$345$	3.26366e8	+	1.01271e9i	0.0230372	+	0.0714842i
$346$	−5.05589e9	+	9.00864e9i	−0.352771	+	0.628572i
$347$	2.28853e10	+	7.43587e9i	1.57848	+	0.512878i	0.961663	−	0.274233i	$-0.0884238\pi$
$347$	2.28853e10	+	7.43587e9i	1.57848	+	0.512878i	0.616812	+	0.787110i	$0.288424\pi$
$348$	−4.11960e9	−	1.72984e10i	−0.280891	−	1.17947i
$349$	1.42992e10			0.963853			0.481926	−	0.876212i	$-0.339937\pi$
$349$	1.42992e10			0.963853			0.481926	+	0.876212i	$0.339937\pi$
$350$	−9.96541e9	−	2.19454e10i	−0.664084	−	1.46242i
$351$			2.51594e10i			1.65757i
$352$	4.75619e9	−	1.27133e10i	0.309805	−	0.828109i
$353$	7.91035e9	−	2.43456e10i	0.509444	−	1.56791i	−0.283724	−	0.958906i	$-0.591570\pi$
$353$	7.91035e9	−	2.43456e10i	0.509444	−	1.56791i	0.793168	−	0.609003i	$-0.208430\pi$
$354$	−1.00927e10	+	1.79832e10i	−0.642676	+	1.14513i
$355$	−3.11912e9	−	1.02174e9i	−0.196390	−	0.0643322i
$356$	−2.83329e8	+	3.51794e9i	−0.0176397	+	0.219022i
$357$	−3.30435e10			−2.03429
$358$	1.04766e7	−	1.23030e6i	0.000637806	−	7.48992e-5i
$359$	−1.57349e10	+	2.16572e10i	−0.947294	+	1.30384i	0.00542468	+	0.999985i	$0.498273\pi$
$359$	−1.57349e10	+	2.16572e10i	−0.947294	+	1.30384i	−0.952719	+	0.303853i	$0.901727\pi$
$360$	3.76817e8	−	2.93932e8i	0.0224347	−	0.0175000i
$361$	−4.21668e8	+	3.06360e8i	−0.0248280	+	0.0180386i
$362$	−5.86386e9	−	6.35511e9i	−0.341467	−	0.370074i
$363$	−2.25894e9	+	3.10916e9i	−0.130100	+	0.179067i
$364$	1.09894e10	+	4.61450e10i	0.625992	+	2.62857i
$365$	2.20209e10	−	1.59186e10i	1.24069	−	0.896876i
$366$	−2.00718e10	+	1.85203e10i	−1.11857	+	1.03210i
$367$	−1.93673e10	+	6.29280e9i	−1.06759	+	0.346881i	−0.789548	−	0.613689i	$-0.789685\pi$
$367$	−1.93673e10	+	6.29280e9i	−1.06759	+	0.346881i	−0.278041	+	0.960569i	$0.589685\pi$
$368$	9.63895e8	−	9.56884e8i	0.0525580	−	0.0521757i
$369$	−1.37631e6	−	4.23584e6i	−7.42353e−5	−	0.000228473i
$370$	−9.49266e9	−	1.92091e9i	−0.506502	−	0.102494i
$371$	1.27724e10	+	4.15001e9i	0.674182	+	0.219055i
$372$	−1.69200e10	+	1.97377e10i	−0.883546	+	1.03068i
$373$	−1.16792e10	+	8.48546e9i	−0.603364	+	0.438369i	−0.847071	−	0.531479i	$-0.821636\pi$
$373$	−1.16792e10	+	8.48546e9i	−0.603364	+	0.438369i	0.243707	+	0.969849i	$0.421636\pi$
$374$	4.23428e9	−	2.11861e10i	0.216418	−	1.08284i
$375$	1.90281e10	+	6.33438e9i	0.962211	+	0.320316i
$376$	−9.29318e9	+	1.38261e10i	−0.464957	+	0.691750i
$377$	−3.28711e10	+	2.38822e10i	−1.62723	+	1.18225i
$378$	1.58119e10	−	2.81739e10i	0.774493	−	1.38000i
$379$	−1.15893e10	−	3.76560e9i	−0.561696	−	0.182506i	0.0143881	−	0.999896i	$-0.495420\pi$
$379$	−1.15893e10	−	3.76560e9i	−0.561696	−	0.182506i	−0.576084	+	0.817390i	$0.695420\pi$
$380$	−7.93612e9	+	1.89329e10i	−0.380605	+	0.907993i
$381$	−9.15837e9	−	2.81866e10i	−0.434628	−	1.33765i
$382$	−7.54229e9	+	3.77376e10i	−0.354201	+	1.77224i
$383$	1.17764e10	−	3.82640e9i	0.547292	−	0.177826i	−0.0223034	−	0.999751i	$-0.507100\pi$
$383$	1.17764e10	−	3.82640e9i	0.547292	−	0.177826i	0.569595	+	0.821925i	$0.307100\pi$
$384$	−1.99656e10	−	9.35935e9i	−0.918241	−	0.430448i
$385$	−2.52854e10	+	1.82784e10i	−1.15087	+	0.831947i
$386$	1.63277e10	−	7.50914e9i	0.735490	−	0.338252i
$387$	2.31499e8	−	3.18631e8i	0.0103206	−	0.0142051i
$388$	1.25119e10	+	2.05015e10i	0.552074	+	0.904604i
$389$	−1.59650e10	+	1.15993e10i	−0.697222	+	0.506561i	−0.879026	−	0.476774i	$-0.841806\pi$
$389$	−1.59650e10	+	1.15993e10i	−0.697222	+	0.506561i	0.181805	+	0.983335i	$0.441806\pi$
$390$	−3.43733e10	−	1.93998e10i	−1.48581	−	0.838568i
$391$	1.27069e9	−	1.74895e9i	0.0543664	−	0.0748290i
$392$	1.02230e10	−	3.58720e10i	0.432948	−	1.51919i
$393$	7.68719e9			0.322253
$394$	−1.68564e9	−	1.43541e10i	−0.0699489	−	0.595651i
$395$	−2.12283e10	−	6.95384e9i	−0.872020	−	0.285651i
$396$	−4.69684e8	−	4.02633e8i	−0.0190996	−	0.0163730i
$397$	−4.95167e9	+	1.52397e10i	−0.199338	+	0.613498i	0.800561	+	0.599251i	$0.204535\pi$
$397$	−4.95167e9	+	1.52397e10i	−0.199338	+	0.613498i	−0.999899	+	0.0142467i	$0.995465\pi$
$398$	−1.29881e10	−	2.82411e10i	−0.517623	−	1.12551i
$399$		−	4.06441e10i		−	1.60364i
$400$	−3.79096e9	−	2.53178e10i	−0.148085	−	0.988975i
$401$	−3.85050e10			−1.48915			−0.744577	−	0.667537i	$-0.767349\pi$
$401$	−3.85050e10			−1.48915			−0.744577	+	0.667537i	$0.767349\pi$
$402$	2.45105e10	−	1.12724e10i	0.938528	−	0.431629i
$403$	5.64948e10	+	1.83563e10i	2.14185	+	0.695928i
$404$	1.21337e10	−	1.41544e10i	0.455479	−	0.531331i
$405$	8.48057e9	+	2.63152e10i	0.315213	+	0.978106i
$406$	5.18188e10	−	6.08522e9i	1.90714	−	0.223961i
$407$			1.25373e10i			0.456907i
$408$	−3.37532e10	−	9.61920e9i	−1.21807	−	0.347135i
$409$	−1.17409e10	−	8.53025e9i	−0.419573	−	0.304838i	0.357893	−	0.933763i	$-0.383495\pi$
$409$	−1.17409e10	−	8.53025e9i	−0.419573	−	0.304838i	−0.777466	+	0.628925i	$0.783495\pi$
$410$	−2.33842e8	−	4.73197e7i	−0.00827538	−	0.00167458i
$411$	−1.34402e10	−	1.84989e10i	−0.471019	−	0.648302i
$412$	1.10253e10	−	6.72865e9i	0.382649	−	0.233528i
$413$	−4.89509e10	−	3.55649e10i	−1.68252	−	1.22242i
$414$	−2.58644e7	−	5.62390e7i	−0.000880441	−	0.00191442i
$415$	2.75697e10	−	8.88488e9i	0.929480	−	0.299543i
$416$	−2.20773e9	+	5.03352e10i	−0.0737180	+	1.68073i
$417$	−1.29199e9	−	3.97633e9i	−0.0427282	−	0.131504i
$418$	2.60594e10	+	5.20825e9i	0.853608	+	0.170603i
$419$	−3.32082e10	+	1.07900e10i	−1.07743	+	0.350079i	−0.793378	−	0.608730i	$-0.791679\pi$
$419$	−3.32082e10	+	1.07900e10i	−1.07743	+	0.350079i	−0.284054	+	0.958808i	$0.591679\pi$
$420$	2.62996e10	+	4.33268e10i	0.845185	+	1.39238i
$421$	9.27474e9	−	2.85447e10i	0.295239	−	0.908652i	−0.687902	−	0.725803i	$-0.741468\pi$
$421$	9.27474e9	−	2.85447e10i	0.295239	−	0.908652i	0.983141	−	0.182848i	$-0.0585318\pi$
$422$	3.72103e10	+	2.08834e10i	1.17331	+	0.658494i
$423$	4.46278e8	+	6.14249e8i	0.0139394	+	0.0191859i
$424$	1.18386e10	+	7.95729e9i	0.366301	+	0.246208i
$425$	−1.24054e10	−	3.88125e10i	−0.380237	−	1.18964i
$426$	6.76827e9	+	1.35272e9i	0.205513	+	0.0410741i
$427$	−4.71010e10	−	6.48290e10i	−1.41683	−	1.95010i
$428$	−2.60357e10	−	2.23189e10i	−0.775878	−	0.665115i
$429$	−1.57889e10	+	4.85932e10i	−0.466147	+	1.43465i
$430$	−8.76924e9	−	1.91888e10i	−0.256500	−	0.561274i
$431$	4.81881e9	−	1.56573e9i	0.139647	−	0.0453740i	−0.238360	−	0.971177i	$-0.576610\pi$
$431$	4.81881e9	−	1.56573e9i	0.139647	−	0.0453740i	0.378006	+	0.925803i	$0.376610\pi$
$432$	2.43532e10	−	2.41760e10i	0.699231	−	0.694145i
$433$	1.12629e10	+	3.46636e10i	0.320404	+	0.986102i	0.973473	+	0.228803i	$0.0734813\pi$
$433$	1.12629e10	+	3.46636e10i	0.320404	+	0.986102i	−0.653069	+	0.757299i	$0.726519\pi$
$434$	−5.17274e10	−	5.60609e10i	−1.45801	−	1.58016i
$435$	−2.56020e10	+	3.50609e10i	−0.715017	+	0.979188i
$436$	−2.70442e10	+	6.44057e9i	−0.748391	+	0.178229i
$437$	2.15124e9	+	1.56297e9i	0.0589880	+	0.0428573i
$438$	−4.19946e10	+	3.87484e10i	−1.14103	+	1.05283i
$439$	3.74964e10	+	5.16093e10i	1.00956	+	1.38954i	0.919273	+	0.393621i	$0.128778\pi$
$439$	3.74964e10	+	5.16093e10i	1.00956	+	1.38954i	0.0902851	+	0.995916i	$0.471222\pi$
$440$	−3.11495e10	+	1.13102e10i	−0.831075	+	0.301759i
$441$	−1.37532e9	−	9.99231e8i	−0.0363622	−	0.0264187i
$442$	9.35314e9	+	7.96469e10i	0.245058	+	2.08679i
$443$			3.50607e10i			0.910344i	0.890403	+	0.455172i	$0.150422\pi$
$443$			3.50607e10i			0.910344i	−0.890403	+	0.455172i	$0.849578\pi$
$444$	2.03009e10	+	1.63500e9i	0.522377	+	0.0420714i
$445$	6.98305e9	−	5.04793e9i	0.178076	−	0.128728i
$446$	9.79670e9	+	5.49816e9i	0.247594	+	0.138956i
$447$	7.41303e10	+	2.40864e10i	1.85680	+	0.603312i
$448$	3.41064e10	−	5.49787e10i	0.846689	−	1.36484i
$449$	−1.31680e10			−0.323992			−0.161996	−	0.986791i	$-0.551793\pi$
$449$	−1.31680e10			−0.323992			−0.161996	+	0.986791i	$0.551793\pi$
$450$	−1.14301e9	−	2.34152e8i	−0.0278740	−	0.00571015i
$451$			3.08845e8i			0.00746508i
$452$	8.25065e9	−	1.96489e9i	0.197667	−	0.0470743i
$453$	−2.53847e10	+	7.81261e10i	−0.602808	+	1.85525i
$454$	2.38888e10	+	1.34070e10i	0.562303	+	0.315579i
$455$	6.82956e10	−	9.35282e10i	1.59348	−	2.18221i
$456$	1.18318e10	−	4.15171e10i	0.273648	−	0.960212i
$457$	−1.40284e10			−0.321621			−0.160811	−	0.986985i	$-0.551411\pi$
$457$	−1.40284e10			−0.321621			−0.160811	+	0.986985i	$0.551411\pi$
$458$	9.73244e9	+	8.28768e10i	0.221187	+	1.88352i
$459$	3.21043e10	−	4.41878e10i	0.723291	−	0.995524i
$460$	−3.30458e9	−	2.74127e8i	−0.0738049	−	0.00612238i
$461$	−1.61691e10	+	1.17475e10i	−0.357999	+	0.260102i	−0.752217	−	0.658915i	$-0.771016\pi$
$461$	−1.61691e10	+	1.17475e10i	−0.357999	+	0.260102i	0.394218	+	0.919017i	$0.371016\pi$
$462$	4.82200e10	−	4.44926e10i	1.05842	−	0.976607i
$463$	−1.21615e10	+	1.67389e10i	−0.264646	+	0.364253i	−0.920573	−	0.390571i	$-0.872278\pi$
$463$	−1.21615e10	+	1.67389e10i	−0.264646	+	0.364253i	0.655927	+	0.754824i	$0.272278\pi$
$464$	5.47032e10	+	8.86894e9i	1.18016	+	0.191337i
$465$	6.34700e10	+	1.52277e8i	1.35755	+	0.00325703i
$466$	−2.37118e10	−	2.56983e10i	−0.502830	−	0.544955i
$467$	−6.02584e10	+	1.95791e10i	−1.26692	+	0.411648i	−0.863956	−	0.503566i	$-0.832021\pi$
$467$	−6.02584e10	+	1.95791e10i	−1.26692	+	0.411648i	−0.402967	+	0.915215i	$0.632021\pi$
$468$	2.11988e9	+	8.82618e8i	0.0441904	+	0.0183988i
$469$	2.44610e10	+	7.52832e10i	0.505572	+	1.55599i
$470$	4.04053e10	−	4.64665e9i	0.828031	−	0.0952244i
$471$	4.30660e10	+	1.39930e10i	0.875087	+	0.284333i
$472$	−3.96491e10	−	5.05788e10i	−0.798849	−	1.01906i
$473$	−2.20950e10	+	1.60530e10i	−0.441418	+	0.320709i
$474$	4.60639e10	+	9.20638e9i	0.912530	+	0.182379i
$475$	4.77402e10	−	1.52589e10i	0.937798	−	0.299742i
$476$	3.95819e10	−	9.50680e10i	0.771025	−	1.85185i
$477$	5.25951e8	−	3.82126e8i	0.0101595	−	0.00738130i
$478$	−2.68883e10	−	1.50904e10i	−0.515052	−	0.289061i
$479$	−8.39320e10	−	2.72712e10i	−1.59436	−	0.518038i	−0.628653	−	0.777686i	$-0.716394\pi$
$479$	−8.39320e10	−	2.72712e10i	−1.59436	−	0.518038i	−0.965703	+	0.259648i	$0.916394\pi$
$480$	1.42517e10	+	5.19133e10i	0.268473	+	0.977944i
$481$	−1.43805e10	−	4.42586e10i	−0.268654	−	0.826833i
$482$	9.71586e10	+	1.94182e10i	1.80009	+	0.359767i
$483$	6.24372e9	−	2.02871e9i	0.114724	−	0.0372762i
$484$	−6.23932e9	−	1.02235e10i	−0.113699	−	0.186302i
$485$	1.82537e10	−	5.57239e10i	0.329902	−	1.00710i
$486$	−1.32608e9	−	2.88341e9i	−0.0237698	−	0.0516847i
$487$	−4.82525e10	+	6.64139e10i	−0.857836	+	1.18071i	0.124245	+	0.992252i	$0.460349\pi$
$487$	−4.82525e10	+	6.64139e10i	−0.857836	+	1.18071i	−0.982081	+	0.188458i	$0.939651\pi$
$488$	−2.92404e10	−	7.99328e10i	−0.515590	−	1.40944i
$489$	3.54464e10	−	2.57533e10i	0.619922	−	0.450400i
$490$	−8.28259e10	+	3.78512e10i	−1.43675	+	0.656591i
$491$	−6.08277e10	+	8.37221e10i	−1.04659	+	1.44050i	−0.154856	+	0.987937i	$0.549491\pi$
$491$	−6.08277e10	+	8.37221e10i	−1.04659	+	1.44050i	−0.891731	+	0.452566i	$0.850509\pi$
$492$	5.00093e8	+	4.02767e7i	0.00853475	+	0.000687374i
$493$	8.82065e10			1.49318
$494$	−9.79673e10	+	1.15045e10i	−1.64503	+	0.193180i
$495$	−3.62361e6	+	1.51035e9i	−6.03561e−5	+	0.0251569i
$496$	−3.65186e10	−	7.23232e10i	−0.603375	−	1.19495i
$497$	−6.25810e9	+	1.92605e10i	−0.102569	+	0.315676i
$498$	−5.53405e10	+	2.54511e10i	−0.899758	+	0.413799i
$499$			8.03299e10i			1.29561i	0.761805	+	0.647806i	$0.224313\pi$
$499$			8.03299e10i			1.29561i	−0.761805	+	0.647806i	$0.775687\pi$
$500$	−4.10176e10	+	4.71572e10i	−0.656282	+	0.754515i
$501$	6.14022e10			0.974615
$502$	−5.63835e9	−	1.22599e10i	−0.0887844	−	0.193051i
$503$	3.48292e10	+	1.13167e10i	0.544091	+	0.176786i	0.568151	−	0.822925i	$-0.307659\pi$
$503$	3.48292e10	+	1.13167e10i	0.544091	+	0.176786i	−0.0240595	+	0.999711i	$0.507659\pi$
$504$	−1.81917e9	−	2.32065e9i	−0.0281937	−	0.0359656i
$505$	−4.55158e10	−	1.09201e8i	−0.699836	−	0.00167904i
$506$	5.00637e8	+	4.26319e9i	0.00763697	+	0.0650328i
$507$		−	1.22644e11i		−	1.85615i
$508$	9.20650e10	+	7.41476e9i	1.38242	+	0.111338i
$509$	6.42537e10	+	4.66830e10i	0.957253	+	0.695485i	0.952511	−	0.304504i	$-0.0984906\pi$
$509$	6.42537e10	+	4.66830e10i	0.957253	+	0.695485i	0.00474203	+	0.999989i	$0.498491\pi$
$510$	3.56155e10	+	7.79337e10i	0.526451	+	1.15198i
$511$	−9.85454e10	−	1.35636e11i	−1.44528	−	1.98926i
$512$	5.08437e10	−	4.62308e10i	0.739872	−	0.672747i
$513$	5.43519e10	+	3.94890e10i	0.784775	+	0.570173i
$514$	−8.80082e10	+	4.04750e10i	−1.26087	+	0.579875i
$515$	−2.99672e10	−	9.81647e9i	−0.426007	−	0.139549i
$516$	2.31122e10	+	3.78706e10i	0.326018	+	0.534199i
$517$	−1.62696e10	−	5.00726e10i	−0.227727	−	0.700871i
$518$	−1.17117e10	+	5.85992e10i	−0.162668	+	0.813904i
$519$	−5.04408e10	+	1.63892e10i	−0.695204	+	0.225885i
$520$	9.69892e10	−	7.56556e10i	1.32651	−	1.03473i
$521$	1.55495e10	−	4.78565e10i	0.211041	−	0.649517i	−0.788370	−	0.615201i	$-0.789075\pi$
$521$	1.55495e10	−	4.78565e10i	0.211041	−	0.649517i	0.999411	−	0.0343156i	$-0.0109251\pi$
$522$	1.23612e9	−	2.20254e9i	0.0166487	−	0.0296648i
$523$	2.83003e10	+	3.89521e10i	0.378255	+	0.520623i	0.955121	−	0.296215i	$-0.0957246\pi$
$523$	2.83003e10	+	3.89521e10i	0.378255	+	0.520623i	−0.576866	+	0.816839i	$0.695725\pi$
$524$	−9.20829e9	+	2.21165e10i	−0.122139	+	0.293354i
$525$	3.88022e10	−	1.17499e11i	0.510762	−	1.54667i
$526$	1.99108e10	−	9.96229e10i	0.260103	−	1.30142i
$527$	−7.57993e10	−	1.04329e11i	−0.982704	−	1.35258i
$528$	6.22078e10	−	3.14110e10i	0.800404	−	0.404153i
$529$	2.40667e10	−	7.40697e10i	0.307322	−	0.945840i
$530$	−3.97870e9	−	3.45971e10i	−0.0504240	−	0.438466i
$531$	−2.78568e9	+	9.05121e8i	−0.0350391	+	0.0113849i
$532$	1.16936e11	+	4.86865e10i	1.45982	+	0.607802i
$533$	−3.54250e8	−	1.09027e9i	−0.00438935	−	0.0135090i
$534$	−1.33169e10	+	1.22875e10i	−0.163771	+	0.151112i
$535$	−2.00865e8	+	8.37221e10i	−0.00245182	+	1.02194i
$536$	3.07085e9	+	8.40209e10i	0.0372048	+	1.01795i
$537$	4.38137e7	+	3.18325e7i	0.000526881	+	0.000382802i
$538$	−3.99119e10	−	4.32556e10i	−0.476402	−	0.516313i
$539$	6.92904e10	+	9.53701e10i	0.820953	+	1.12994i
$540$	−8.34914e10	−	6.92591e9i	−0.981899	−	0.0814520i
$541$	−6.48733e10	−	4.71332e10i	−0.757315	−	0.550222i	0.140771	−	0.990042i	$-0.455042\pi$
$541$	−6.48733e10	−	4.71332e10i	−0.757315	−	0.550222i	−0.898086	+	0.439821i	$0.855042\pi$
$542$	−4.25225e10	+	4.99353e9i	−0.492744	+	0.0578642i
$543$		−	4.43943e10i		−	0.510656i
$544$	6.81070e10	−	8.55873e10i	0.777672	−	0.977268i
$545$	5.48141e10	+	4.00261e10i	0.621307	+	0.453687i
$546$	−1.19190e11	+	2.12374e11i	−1.34113	+	2.38963i
$547$	2.85956e10	+	9.29129e9i	0.319411	+	0.103783i	0.464335	−	0.885660i	$-0.346294\pi$
$547$	2.85956e10	+	9.29129e9i	0.319411	+	0.103783i	−0.144923	+	0.989443i	$0.546294\pi$
$548$	6.93220e10	−	1.65090e10i	0.768686	−	0.183062i
$549$	−3.87912e9			−0.0427015
$550$	7.03636e10	+	3.99351e10i	0.768949	+	0.436419i
$551$			1.08496e11i			1.17708i
$552$	6.96840e9	−	2.54685e8i	0.0750545	−	0.00274313i
$553$	−4.25917e10	+	1.31084e11i	−0.455433	+	1.40168i
$554$	3.59970e10	−	6.41400e10i	0.382145	−	0.680910i
$555$	−2.91300e10	−	4.02970e10i	−0.307022	−	0.424718i
$556$	1.29878e10	+	1.04601e9i	0.135905	+	0.0109456i
$557$	−5.53831e9			−0.0575382			−0.0287691	−	0.999586i	$-0.509159\pi$
$557$	−5.53831e9			−0.0575382			−0.0287691	+	0.999586i	$0.509159\pi$
$558$	−3.66737e9	+	4.30668e8i	−0.0378284	+	0.00444228i
$559$	5.95857e10	−	8.20127e10i	0.610232	−	0.839912i
$560$	−1.56157e11	+	2.37655e10i	−1.58785	+	0.241654i
$561$	8.97370e10	−	6.51977e10i	0.905983	−	0.658235i
$562$	1.65861e10	+	1.79756e10i	0.166264	+	0.180193i
$563$	2.16888e10	−	2.98521e10i	0.215875	−	0.297127i	−0.687322	−	0.726353i	$-0.741214\pi$
$563$	2.16888e10	−	2.98521e10i	0.215875	−	0.297127i	0.903197	+	0.429226i	$0.141214\pi$
$564$	−8.32012e10	+	1.98143e10i	−0.822267	+	0.195822i
$565$	−1.67227e10	−	1.22111e10i	−0.164101	−	0.119829i
$566$	4.68669e10	−	4.32441e10i	0.456668	−	0.421368i
$567$	1.62242e11	−	5.27156e10i	1.56975	−	0.510043i
$568$	−1.19994e10	+	1.78523e10i	−0.115283	+	0.171515i
$569$	1.23160e10	+	3.79048e10i	0.117495	+	0.361614i	0.992459	−	0.122575i	$-0.0391151\pi$
$569$	1.23160e10	+	3.79048e10i	0.117495	+	0.361614i	−0.874964	+	0.484188i	$0.839115\pi$
$570$	−9.58600e10	+	4.38077e10i	−0.908110	+	0.415003i
$571$	−2.84311e10	−	9.23783e9i	−0.267454	−	0.0869012i	0.172220	−	0.985059i	$-0.444906\pi$
$571$	−2.84311e10	−	9.23783e9i	−0.267454	−	0.0869012i	−0.439674	+	0.898157i	$0.644906\pi$
$572$	−1.20892e11	−	1.03634e11i	−1.12932	−	0.968096i
$573$	−1.59843e11	+	1.16133e11i	−1.48278	+	1.07730i
$574$	−2.88507e8	+	1.44353e9i	−0.00265771	+	0.0132978i
$575$	4.72696e9	+	6.57218e9i	0.0432424	+	0.0601227i
$576$	−1.18269e9	−	2.90007e9i	−0.0107443	−	0.0263462i
$577$	−7.67538e10	+	5.57649e10i	−0.692463	+	0.503104i	−0.877469	−	0.479634i	$-0.840770\pi$
$577$	−7.67538e10	+	5.57649e10i	−0.692463	+	0.503104i	0.185006	+	0.982737i	$0.440770\pi$
$578$	3.05804e10	−	5.44886e10i	0.273988	−	0.488196i
$579$	8.77512e10	+	2.85121e10i	0.780798	+	0.253697i
$580$	−7.02044e10	−	1.15657e11i	−0.620372	−	1.02202i
$581$	−5.52288e10	−	1.69977e11i	−0.484687	−	1.49171i
$582$	−2.41666e10	+	1.20917e11i	−0.210632	+	1.05389i
$583$	−4.28747e10	+	1.39308e10i	−0.371131	+	0.120588i
$584$	−6.11772e10	−	1.67237e11i	−0.525943	−	1.43774i
$585$	−1.71960e9	−	5.33591e9i	−0.0146826	−	0.0455601i
$586$	8.84836e10	−	4.06936e10i	0.750365	−	0.345093i
$587$	1.23108e10	−	1.69444e10i	0.103689	−	0.142716i	−0.754019	−	0.656852i	$-0.771887\pi$
$587$	1.23108e10	−	1.69444e10i	0.103689	−	0.142716i	0.857709	+	0.514136i	$0.171887\pi$
$588$	1.63463e11	−	9.97603e10i	1.36745	−	0.834543i
$589$	1.28327e11	−	9.32347e10i	1.06624	−	0.774669i
$590$	−3.11195e10	+	1.53785e11i	−0.256818	+	1.26913i
$591$	4.36141e10	−	6.00297e10i	0.357501	−	0.492058i
$592$	−2.90219e10	+	5.64485e10i	−0.236287	+	0.459584i
$593$	−9.16511e10			−0.741172			−0.370586	−	0.928798i	$-0.620843\pi$
$593$	−9.16511e10			−0.741172			−0.370586	+	0.928798i	$0.620843\pi$
$594$	1.26488e10	+	1.07711e11i	0.101602	+	0.865195i
$595$	−2.39294e11	+	7.71171e10i	−1.90925	+	0.615294i
$596$	−1.58097e11	+	1.84425e11i	−1.25296	+	1.46162i
$597$	4.93157e10	−	1.51778e11i	0.388229	−	1.19485i
$598$	−6.65726e9	−	1.44754e10i	−0.0520584	−	0.113195i
$599$		−	1.50463e11i		−	1.16875i	−0.811482	−	0.584377i	$-0.801339\pi$
$599$		−	1.50463e11i		−	1.16875i	0.811482	−	0.584377i	$-0.198661\pi$
$600$	7.38405e10	−	1.08727e11i	0.569757	−	0.838946i
$601$	2.42713e11			1.86035			0.930175	−	0.367117i	$-0.119655\pi$
$601$	2.42713e11			1.86035			0.930175	+	0.367117i	$0.119655\pi$
$602$	−1.18268e11	+	5.43913e10i	−0.900491	+	0.414136i
$603$	3.64434e9	+	1.18412e9i	0.0275645	+	0.00895625i
$604$	−1.94366e11	−	1.66618e11i	−1.46040	−	1.25192i
$605$	−9.10258e9	+	2.77878e10i	−0.0679427	+	0.207412i
$606$	9.50618e10	−	1.11634e10i	0.704881	−	0.0827760i
$607$			1.78077e11i			1.31176i	0.754866	+	0.655879i	$0.227702\pi$
$607$			1.78077e11i			1.31176i	−0.754866	+	0.655879i	$0.772298\pi$
$608$	1.05274e11	+	8.37730e10i	0.770384	+	0.613042i
$609$	2.16709e11	+	1.57448e11i	1.57546	+	1.14464i
$610$	−1.02133e11	+	1.80964e11i	−0.737647	+	1.30699i
$611$	1.14868e11	+	1.58102e11i	0.824203	+	1.13442i
$612$	−2.59692e9	−	4.25520e9i	−0.0185120	−	0.0303329i
$613$	−4.81201e9	−	3.49613e9i	−0.0340789	−	0.0247597i	0.570615	−	0.821217i	$-0.306705\pi$
$613$	−4.81201e9	−	3.49613e9i	−0.0340789	−	0.0247597i	−0.604694	+	0.796458i	$0.706705\pi$
$614$	3.47599e10	+	7.55815e10i	0.244571	+	0.531792i
$615$	−7.17589e8	−	9.92677e8i	−0.00501621	−	0.00693917i
$616$	7.02464e10	+	1.92028e11i	0.487867	+	1.33365i
$617$	−3.16948e10	−	9.75466e10i	−0.218699	−	0.673087i	−0.998870	−	0.0475210i	$-0.984868\pi$
$617$	−3.16948e10	−	9.75466e10i	−0.218699	−	0.673087i	0.780171	−	0.625566i	$-0.215132\pi$
$618$	6.50266e10	+	1.29963e10i	0.445797	+	0.0890976i
$619$	1.14141e11	−	3.70866e10i	0.777460	−	0.252612i	0.106705	−	0.994291i	$-0.465970\pi$
$619$	1.14141e11	−	3.70866e10i	0.777460	−	0.252612i	0.670755	+	0.741679i	$0.265970\pi$
$620$	−7.64672e10	+	1.82425e11i	−0.517498	+	1.23457i
$621$	−3.35335e9	+	1.03206e10i	−0.0225482	+	0.0693963i
$622$	−1.28785e11	−	7.22776e10i	−0.860408	−	0.482883i
$623$	−3.12497e10	−	4.30115e10i	−0.207441	−	0.285517i
$624$	−1.83574e11	+	1.82239e11i	−1.21080	+	1.20199i
$625$	1.52581e11	+	1.46432e9i	0.999954	+	0.00959659i
$626$	2.40922e10	+	4.81510e9i	0.156884	+	0.0313551i
$627$	8.01945e10	+	1.10378e11i	0.518889	+	0.714190i
$628$	−9.18464e10	+	1.07142e11i	−0.590505	+	0.688842i
$629$	−3.12190e10	+	9.60821e10i	−0.199442	+	0.613819i
$630$	−1.42782e9	+	7.05595e9i	−0.00906384	+	0.0447913i
$631$	−1.17899e11	+	3.83077e10i	−0.743692	+	0.241640i	−0.656265	−	0.754531i	$-0.727864\pi$
$631$	−1.17899e11	+	3.83077e10i	−0.743692	+	0.241640i	−0.0874271	+	0.996171i	$0.527864\pi$
$632$	−8.16660e10	+	1.21500e11i	−0.511886	+	0.761570i
$633$	6.76958e10	+	2.08346e11i	0.421645	+	1.29769i
$634$	−4.66775e10	−	5.05879e10i	−0.288902	−	0.313105i
$635$	−1.32105e11	−	1.82747e11i	−0.812502	−	1.12397i
$636$	1.69660e10	+	7.12411e10i	0.103693	+	0.435414i
$637$	−3.53996e11	−	2.57193e11i	−2.15001	−	1.56207i
$638$	−1.28719e11	+	1.18769e11i	−0.776891	+	0.716837i
$639$	5.76236e8	+	7.93120e8i	0.00345618	+	0.00475703i
$640$	−1.66430e11	−	2.11827e10i	−0.991997	−	0.126259i
$641$	−5.08263e10	−	3.69274e10i	−0.301062	−	0.218734i	0.426990	−	0.904256i	$-0.359574\pi$
$641$	−5.08263e10	−	3.69274e10i	−0.301062	−	0.218734i	−0.728052	+	0.685522i	$0.759574\pi$
$642$	−2.05340e10	−	1.74858e11i	−0.120874	−	1.02931i
$643$		−	2.40176e11i		−	1.40503i	−0.711670	−	0.702514i	$-0.752061\pi$
$643$		−	2.40176e11i		−	1.40503i	0.711670	−	0.702514i	$-0.247939\pi$
$644$	−1.64247e9	+	2.03937e10i	−0.00954894	+	0.118564i
$645$	3.37185e10	−	1.02934e11i	0.194818	−	0.594729i
$646$	1.86742e11	+	1.04804e11i	1.07229	+	0.601795i
$647$	−4.43103e10	−	1.43973e10i	−0.252865	−	0.0821607i	0.179842	−	0.983696i	$-0.442441\pi$
$647$	−4.43103e10	−	1.43973e10i	−0.252865	−	0.0821607i	−0.432706	+	0.901535i	$0.642441\pi$
$648$	1.81073e11	−	6.61794e9i	1.02696	−	0.0375339i
$649$	2.03110e11			1.14486
$650$	−2.94200e11	−	6.02686e10i	−1.64812	−	0.337627i
$651$		−	3.91620e11i		−	2.18042i
$652$	3.16335e10	+	1.32831e11i	0.175048	+	0.735035i
$653$	−2.36346e9	+	7.27397e9i	−0.0129986	+	0.0400054i	−0.957345	−	0.288946i	$-0.906695\pi$
$653$	−2.36346e9	+	7.27397e9i	−0.0129986	+	0.0400054i	0.944347	+	0.328951i	$0.106695\pi$
$654$	−1.24466e11	−	6.98538e10i	−0.680364	−	0.381838i
$655$	5.56691e10	−	1.79404e10i	0.302447	−	0.0974693i
$656$	−7.14927e8	+	1.39055e9i	−0.00386052	+	0.00750882i
$657$	−8.11594e9			−0.0435589
$658$	−2.92685e10	−	2.49237e11i	−0.156134	−	1.32956i
$659$	8.75185e10	−	1.20459e11i	0.464043	−	0.638701i	−0.511298	−	0.859404i	$-0.670835\pi$
$659$	8.75185e10	−	1.20459e11i	0.464043	−	0.638701i	0.975341	+	0.220703i	$0.0708351\pi$
$660$	−1.56910e11	−	6.57722e10i	−0.826942	−	0.346631i
$661$	−3.27962e10	+	2.38279e10i	−0.171798	+	0.124819i	−0.670362	−	0.742035i	$-0.733861\pi$
$661$	−3.27962e10	+	2.38279e10i	−0.171798	+	0.124819i	0.498564	+	0.866853i	$0.333861\pi$
$662$	2.71182e11	−	2.50219e11i	1.41198	−	1.30283i
$663$	−2.42002e11	+	3.33087e11i	−1.25246	+	1.72387i
$664$	−6.93346e9	−	1.89705e11i	−0.0356679	−	0.975903i
$665$	−9.48556e10	−	2.94336e11i	−0.485039	−	1.50507i
$666$	1.96169e9	+	2.12604e9i	0.00997090	+	0.0108062i
$667$	−1.66671e10	+	5.41546e9i	−0.0842084	+	0.0273610i
$668$	−7.35521e10	+	1.76658e11i	−0.369394	+	0.887212i
$669$	1.78229e10	+	5.48532e10i	0.0889762	+	0.273840i
$670$	1.51192e11	−	1.38835e11i	0.750292	−	0.688969i
$671$	2.55827e11	+	8.31232e10i	1.26199	+	0.410046i
$672$	3.20100e11	−	8.87030e10i	1.56967	−	0.434972i
$673$	−1.60132e11	+	1.16343e11i	−0.780582	+	0.567126i	−0.905154	−	0.425085i	$-0.860244\pi$
$673$	−1.60132e11	+	1.16343e11i	−0.780582	+	0.567126i	0.124572	+	0.992211i	$0.460244\pi$
$674$	−1.42945e11	−	2.85692e10i	−0.692675	−	0.138439i
$675$	1.19428e11	+	1.66049e11i	0.575297	+	0.799871i
$676$	3.52853e11	+	1.46911e11i	1.68969	+	0.703508i
$677$	−6.47752e10	+	4.70619e10i	−0.308357	+	0.224035i	−0.731191	−	0.682173i	$-0.761035\pi$
$677$	−6.47752e10	+	4.70619e10i	−0.308357	+	0.224035i	0.422834	+	0.906207i	$0.361035\pi$
$678$	3.79722e10	+	2.13110e10i	0.179699	+	0.100852i
$679$	−3.44093e11	−	1.11803e11i	−1.61881	−	0.525984i
$680$	−2.66883e11	+	9.11309e9i	−1.24820	+	0.0426216i
$681$	4.34602e10	+	1.33757e11i	0.202071	+	0.621910i
$682$	2.51091e11	+	5.01833e10i	1.16063	+	0.231965i
$683$	2.48980e11	−	8.08984e10i	1.14415	−	0.371755i	0.325210	−	0.945642i	$-0.394565\pi$
$683$	2.48980e11	−	8.08984e10i	1.14415	−	0.371755i	0.818935	+	0.573886i	$0.194565\pi$
$684$	5.23398e9	−	3.19426e9i	0.0239115	−	0.0145931i
$685$	−1.40504e11	−	1.02598e11i	−0.638156	−	0.465990i
$686$	8.61515e10	+	1.87326e11i	0.389015	+	0.845868i
$687$	−2.51816e11	+	3.46595e11i	−1.13046	+	1.55595i
$688$	−1.36641e11	+	2.11309e10i	−0.609858	+	0.0943114i
$689$	1.35375e11	−	9.83558e10i	0.600706	−	0.436439i
$690$	−1.15145e10	−	1.25393e10i	−0.0507981	−	0.0553195i
$691$	1.40308e11	−	1.93117e11i	0.615417	−	0.847050i	−0.381592	−	0.924331i	$-0.624624\pi$
$691$	1.40308e11	−	1.93117e11i	0.615417	−	0.847050i	0.997009	+	0.0772814i	$0.0246240\pi$
$692$	1.32690e10	−	1.64753e11i	0.0578645	−	0.718472i
$693$	9.31908e9			0.0404055
$694$	−3.82380e11	+	4.49039e10i	−1.64838	+	0.193574i
$695$	−1.86363e10	−	2.57805e10i	−0.0798768	−	0.110497i
$696$	1.75529e11	+	2.23915e11i	0.748017	+	0.954216i
$697$	−7.69049e8	+	2.36689e9i	−0.00325854	+	0.0100287i
$698$	−2.07859e11	+	9.55945e10i	−0.875684	+	0.402727i
$699$		−	1.79518e11i		−	0.751969i
$700$	2.91573e11	+	2.52386e11i	1.21438	+	1.05117i
$701$	1.26058e11			0.522035			0.261017	−	0.965334i	$-0.415942\pi$
$701$	1.26058e11			0.522035			0.261017	+	0.965334i	$0.415942\pi$
$702$	−1.68198e11	−	3.65727e11i	−0.692584	−	1.50594i
$703$	−1.18183e11	−	3.84000e10i	−0.483875	−	0.157221i
$704$	1.58542e10	+	2.16602e11i	0.0645436	+	0.881804i
$705$	1.68635e11	+	1.23140e11i	0.682638	+	0.498473i
$706$	4.77692e10	+	4.06780e11i	0.192278	+	1.63735i
$707$			2.80839e11i			1.12404i
$708$	2.64877e10	−	3.28883e11i	0.105417	−	1.30891i
$709$	−2.98596e11	−	2.16942e11i	−1.18168	−	0.858538i	−0.189317	−	0.981916i	$-0.560627\pi$
$709$	−2.98596e11	−	2.16942e11i	−1.18168	−	0.858538i	−0.992360	+	0.123378i	$0.960627\pi$
$710$	5.21714e10	−	5.99977e9i	0.205305	−	0.0236103i
$711$	3.92177e9	+	5.39786e9i	0.0153463	+	0.0211224i
$712$	−1.93999e10	−	5.30323e10i	−0.0754882	−	0.206358i
$713$	2.07279e10	+	1.50597e10i	0.0802043	+	0.0582719i
$714$	4.80333e11	−	2.20905e11i	1.84820	−	0.849989i
$715$	−9.32686e8	+	3.88750e11i	−0.00356871	+	1.48746i
$716$	−1.44067e8	+	8.79233e7i	−0.000548168	+	0.000334543i
$717$	−4.89171e10	−	1.50551e11i	−0.185091	−	0.569650i
$718$	8.39435e10	−	4.20009e11i	0.315856	−	1.58038i
$719$	1.00119e11	−	3.25307e10i	0.374629	−	0.121724i	−0.115649	−	0.993290i	$-0.536895\pi$
$719$	1.00119e11	−	3.25307e10i	0.374629	−	0.121724i	0.490279	+	0.871566i	$0.336895\pi$
$720$	−3.51253e9	+	6.79185e9i	−0.0130704	+	0.0252731i
$721$	−6.01251e10	+	1.85046e11i	−0.222492	+	0.684761i
$722$	4.08143e9	−	7.27234e9i	0.0150198	−	0.0267624i
$723$	2.98994e11	+	4.11530e11i	1.09423	+	1.50608i
$724$	1.27725e11	+	5.31788e10i	0.464860	+	0.193546i
$725$	−1.03579e11	+	3.13654e11i	−0.374903	+	1.13527i
$726$	1.20512e10	−	6.02977e10i	0.0433793	−	0.217047i
$727$	2.50887e11	+	3.45316e11i	0.898131	+	1.23617i	0.971060	+	0.238834i	$0.0767652\pi$
$727$	2.50887e11	+	3.45316e11i	0.898131	+	1.23617i	−0.0729294	+	0.997337i	$0.523235\pi$
$728$	−4.68239e11	−	5.97315e11i	−1.66703	−	2.12656i
$729$	−8.46530e10	+	2.60535e11i	−0.299731	+	0.922478i
$730$	−2.13685e11	+	3.78615e11i	−0.752458	+	1.33323i
$731$	−2.09302e11	+	6.80065e10i	−0.733001	+	0.238167i
$732$	1.67959e11	−	4.03404e11i	0.585003	−	1.40506i
$733$	1.05740e11	+	3.25434e11i	0.366289	+	1.12732i	0.949170	+	0.314763i	$0.101925\pi$
$733$	1.05740e11	+	3.25434e11i	0.366289	+	1.12732i	−0.582882	+	0.812557i	$0.698075\pi$
$734$	2.39461e11	−	2.20951e11i	0.824993	−	0.761221i
$735$	−4.44299e11	−	1.45541e11i	−1.52239	−	0.498696i
$736$	−7.61451e9	+	2.03536e10i	−0.0259496	+	0.0693633i
$737$	−2.14970e11	−	1.56185e11i	−0.728632	−	0.529382i
$738$	4.83244e7	+	5.23729e7i	0.000162908	+	0.000176555i
$739$	7.51422e10	+	1.03424e11i	0.251945	+	0.346773i	0.916191	−	0.400741i	$-0.131247\pi$
$739$	7.51422e10	+	1.03424e11i	0.251945	+	0.346773i	−0.664246	+	0.747514i	$0.731247\pi$
$740$	1.50831e11	−	3.55381e10i	0.502995	−	0.118513i
$741$	−4.09704e11	−	2.97667e11i	−1.35893	−	0.987321i
$742$	−2.13409e11	+	2.50612e10i	−0.704039	+	0.0826772i
$743$		−	3.98250e11i		−	1.30677i	−0.757024	−	0.653387i	$-0.773348\pi$
$743$		−	3.98250e11i		−	1.30677i	0.757024	−	0.653387i	$-0.226652\pi$
$744$	1.14003e11	−	4.00031e11i	0.372071	−	1.30557i
$745$	5.93050e11	+	1.42284e9i	1.92516	+	0.00461882i
$746$	1.13046e11	−	2.01427e11i	0.365007	−	0.650374i
$747$	−8.22832e9	−	2.67354e9i	−0.0264258	−	0.00858627i
$748$	8.00842e10	+	3.36277e11i	0.255824	+	1.07422i
$749$	5.16578e11			1.64138
$750$	−3.18947e11	+	3.51294e10i	−1.00803	+	0.111026i
$751$		−	3.63920e11i		−	1.14405i	−0.820235	−	0.572026i	$-0.806157\pi$
$751$		−	3.63920e11i		−	1.14405i	0.820235	−	0.572026i	$-0.193843\pi$
$752$	4.26575e10	−	2.63110e11i	0.133390	−	0.822746i
$753$	2.14087e10	−	6.58893e10i	0.0665903	−	0.204944i
$754$	3.18167e11	−	5.66914e11i	0.984396	−	1.75401i
$755$	−1.49953e9	+	6.25016e11i	−0.00461496	+	1.92355i
$756$	−4.14977e10	+	5.15254e11i	−0.127039	+	1.57737i
$757$	−4.94057e11			−1.50450			−0.752252	−	0.658876i	$-0.771032\pi$
$757$	−4.94057e11			−1.50450			−0.752252	+	0.658876i	$0.771032\pi$
$758$	1.93641e11	−	2.27398e10i	0.586571	−	0.0688826i
$759$	−1.29534e10	+	1.78289e10i	−0.0390317	+	0.0537225i
$760$	−1.12093e10	−	3.28271e11i	−0.0335988	−	0.983962i
$761$	−1.90413e10	+	1.38343e10i	−0.0567750	+	0.0412495i	−0.615811	−	0.787894i	$-0.711171\pi$
$761$	−1.90413e10	+	1.38343e10i	−0.0567750	+	0.0412495i	0.559036	+	0.829144i	$0.311171\pi$
$762$	3.21565e11	+	3.48505e11i	0.953782	+	1.03369i
$763$	2.46154e11	−	3.38802e11i	0.726288	−	0.999649i
$764$	−1.42650e11	−	5.98992e11i	−0.418694	−	1.75812i
$765$	−3.78866e9	+	1.15658e10i	−0.0110622	+	0.0337699i
$766$	−1.45606e11	+	1.34351e11i	−0.422927	+	0.390235i
$767$	−7.17008e11	+	2.32970e11i	−2.07178	+	0.673161i
$768$	3.52797e11	+	2.57554e9i	1.01410	+	0.00740328i
$769$	1.02929e11	+	3.16783e11i	0.294329	+	0.905850i	0.983446	+	0.181201i	$0.0579984\pi$
$769$	1.02929e11	+	3.16783e11i	0.294329	+	0.905850i	−0.689117	+	0.724650i	$0.742002\pi$
$770$	2.45362e11	−	4.34743e11i	0.697983	−	1.23671i
$771$	−4.72988e11	−	1.53683e11i	−1.33854	−	0.434919i
$772$	−1.87146e11	+	2.18312e11i	−0.526879	+	0.614621i
$773$	−3.74319e11	+	2.71959e11i	−1.04839	+	0.761702i	−0.971906	−	0.235369i	$-0.924370\pi$
$773$	−3.74319e11	+	2.71959e11i	−1.04839	+	0.761702i	−0.0764865	+	0.997071i	$0.524370\pi$
$774$	−1.23502e9	+	6.17938e9i	−0.00344120	+	0.0172179i
$775$	4.59992e11	−	1.47024e11i	1.27510	−	0.407551i
$776$	−3.18937e11	−	2.14372e11i	−0.879544	−	0.591182i
$777$	−2.48206e11	+	1.80332e11i	−0.680970	+	0.494754i
$778$	1.54529e11	−	2.75342e11i	0.421786	−	0.751544i
$779$	−2.91132e9	−	9.45946e8i	−0.00790570	−	0.00256872i
$780$	6.29357e11	+	5.22074e10i	1.70027	+	0.141044i
$781$	−2.10073e10	−	6.46539e10i	−0.0564634	−	0.173776i
$782$	−6.77895e9	+	3.39183e10i	−0.0181274	+	0.0907000i
$783$	−4.21099e11	+	1.36823e11i	−1.12031	+	0.364010i
$784$	9.12085e10	+	5.89793e11i	0.241419	+	1.56112i
$785$	3.44532e11	+	8.26598e8i	0.907301	+	0.00217679i
$786$	−1.11744e11	+	5.13911e10i	−0.292775	+	0.134647i
$787$	3.63388e11	−	5.00160e11i	0.947265	−	1.30380i	−0.00546702	−	0.999985i	$-0.501740\pi$
$787$	3.63388e11	−	5.00160e11i	0.947265	−	1.30380i	0.952732	−	0.303813i	$-0.0982598\pi$
$788$	1.20465e11	+	1.97388e11i	0.312432	+	0.511937i
$789$	4.21968e11	−	3.06577e11i	1.08886	−	0.791101i
$790$	3.55071e11	−	4.08335e10i	0.911606	−	0.104836i
$791$	−7.50966e10	+	1.03362e11i	−0.191829	+	0.264030i
$792$	9.51923e9	+	2.71286e9i	0.0241936	+	0.00689487i
$793$	−9.98450e11			−2.52484
$794$	−2.99022e10	−	2.54633e11i	−0.0752353	−	0.640668i
$795$	1.05438e11	−	1.44394e11i	0.263955	−	0.361476i
$796$	3.77601e11	+	3.23695e11i	0.940547	+	0.806276i
$797$	−6.25210e10	+	1.92420e11i	−0.154950	+	0.476888i	−0.998156	−	0.0607033i	$-0.980666\pi$
$797$	−6.25210e10	+	1.92420e11i	−0.154950	+	0.476888i	0.843206	+	0.537591i	$0.180666\pi$
$798$	2.71718e11	+	5.90819e11i	0.670049	+	1.45694i
$799$		−	4.24253e11i		−	1.04097i
$800$	2.24364e11	+	3.42685e11i	0.547763	+	0.836634i
$801$	−2.57364e9			−0.00625199
$802$	5.59724e11	−	2.57417e11i	1.35293	−	0.622214i
$803$	5.35245e11	+	1.73912e11i	1.28733	+	0.418279i
$804$	−2.80935e11	+	3.27719e11i	−0.672328	+	0.784292i
$805$	4.04812e10	−	2.92631e10i	0.0963983	−	0.0696847i
$806$	−9.43947e11	+	1.10850e11i	−2.23670	+	0.262661i
$807$		−	3.02167e11i		−	0.712447i
$808$	−8.17544e10	+	2.86871e11i	−0.191808	+	0.673040i
$809$	4.71490e11	+	3.42558e11i	1.10072	+	0.799724i	0.981178	−	0.193105i	$-0.0618558\pi$
$809$	4.71490e11	+	3.42558e11i	1.10072	+	0.799724i	0.119547	+	0.992829i	$0.461856\pi$
$810$	−2.99201e11	−	3.25833e11i	−0.695062	−	0.756928i
$811$	7.72685e10	+	1.06351e11i	0.178615	+	0.245843i	0.888932	−	0.458039i	$-0.151448\pi$
$811$	7.72685e10	+	1.06351e11i	0.178615	+	0.245843i	−0.710316	+	0.703882i	$0.751448\pi$
$812$	−7.12577e11	+	4.34881e11i	−1.63911	+	1.00034i
$813$	−1.77831e11	−	1.29202e11i	−0.407048	−	0.295738i
$814$	−8.38158e10	−	1.82248e11i	−0.190910	−	0.415111i
$815$	1.96592e11	−	2.69226e11i	0.445591	−	0.610219i
$816$	5.54956e11	−	8.58212e10i	1.25169	−	0.193568i
$817$	−8.36494e10	−	2.57446e11i	−0.187748	−	0.577828i
$818$	2.27697e11	+	4.55079e10i	0.508563	+	0.101642i
$819$	−3.28977e10	+	1.06891e10i	−0.0731190	+	0.0237578i
$820$	3.71557e9	−	8.75446e8i	0.00821808	−	0.00193631i
$821$	2.74153e10	−	8.43757e10i	0.0603421	−	0.185714i	−0.916342	−	0.400398i	$-0.868872\pi$
$821$	2.74153e10	−	8.43757e10i	0.0603421	−	0.185714i	0.976684	+	0.214684i	$0.0688720\pi$
$822$	3.19043e11	+	1.79055e11i	0.698813	+	0.392192i
$823$	−6.17207e10	−	8.49512e10i	−0.134534	−	0.185170i	0.736435	−	0.676508i	$-0.236508\pi$
$823$	−6.17207e10	−	8.49512e10i	−0.134534	−	0.185170i	−0.870969	+	0.491339i	$0.836508\pi$
$824$	−1.15285e11	+	1.71518e11i	−0.250071	+	0.372049i
$825$	1.26461e11	+	3.95656e11i	0.272986	+	0.854087i
$826$	9.49332e11	+	1.89735e11i	2.03938	+	0.407593i
$827$	−1.01826e11	−	1.40151e11i	−0.217688	−	0.299622i	0.686181	−	0.727431i	$-0.259286\pi$
$827$	−1.01826e11	−	1.40151e11i	−0.217688	−	0.299622i	−0.903869	+	0.427809i	$0.859286\pi$
$828$	7.51949e8	+	6.44602e8i	0.00159981	+	0.00137142i
$829$	2.38876e10	−	7.35185e10i	0.0505772	−	0.155661i	−0.922578	−	0.385811i	$-0.873922\pi$
$829$	2.38876e10	−	7.35185e10i	0.0505772	−	0.155661i	0.973155	+	0.230150i	$0.0739218\pi$
$830$	−3.41367e11	+	3.13466e11i	−0.719298	+	0.660508i
$831$	3.59130e11	−	1.16688e11i	0.753090	−	0.244694i
$832$	−3.04413e11	−	7.46452e11i	−0.635287	−	1.55779i
$833$	2.93540e11	+	9.03424e11i	0.609660	+	1.87634i
$834$	4.53638e10	+	4.91642e10i	0.0937659	+	0.101621i
$835$	4.44662e11	−	1.43301e11i	0.914712	−	0.294784i
$836$	−4.13628e11	+	9.85052e10i	−0.846808	+	0.201667i
$837$	5.23699e11	+	3.80489e11i	1.06704	+	0.775248i
$838$	4.10594e11	−	3.78855e11i	0.832599	−	0.768239i
$839$	3.42884e9	+	4.71939e9i	0.00691989	+	0.00952441i	0.812463	−	0.583013i	$-0.198126\pi$
$839$	3.42884e9	+	4.71939e9i	0.00691989	+	0.00952441i	−0.805543	+	0.592537i	$0.798126\pi$
$840$	−6.71953e11	−	4.53995e11i	−1.34965	−	0.911872i
$841$	−1.73777e11	−	1.26256e11i	−0.347382	−	0.252388i
$842$	5.60085e10	+	4.76942e11i	0.111431	+	0.948893i
$843$			1.25571e11i			0.248644i
$844$	−6.80516e11	−	5.48076e10i	−1.34112	−	0.108012i
$845$	−2.86227e11	−	8.88160e11i	−0.561414	−	1.74206i
$846$	−1.05937e10	−	5.94547e9i	−0.0206808	−	0.0116066i
$847$	1.71589e11	+	5.57526e10i	0.333392	+	0.108326i
$848$	−2.25288e11	−	3.65256e10i	−0.435667	−	0.0706339i
$849$	3.27394e11			0.630145
$850$	4.39802e11	+	4.81260e11i	0.842523	+	0.921944i
$851$		−	2.00719e10i		−	0.0382710i
$852$	−1.07430e11	+	2.55843e10i	−0.203876	+	0.0485529i
$853$	8.43186e10	−	2.59506e11i	0.159267	−	0.490175i	−0.839301	−	0.543667i	$-0.817035\pi$
$853$	8.43186e10	−	2.59506e11i	0.159267	−	0.490175i	0.998568	+	0.0534925i	$0.0170353\pi$
$854$	1.11808e12	+	6.27496e11i	2.10204	+	1.17972i
$855$	−1.42262e10	−	4.66013e9i	−0.0266209	−	0.00872034i
$856$	5.27673e11	+	1.50380e11i	0.982810	+	0.280088i
$857$	7.70884e10			0.142911			0.0714555	−	0.997444i	$-0.477236\pi$
$857$	7.70884e10			0.142911			0.0714555	+	0.997444i	$0.477236\pi$
$858$	−9.53463e10	−	8.11924e11i	−0.175936	−	1.49819i
$859$	−1.18741e11	+	1.63433e11i	−0.218087	+	0.300171i	−0.904017	−	0.427497i	$-0.859396\pi$
$859$	−1.18741e11	+	1.63433e11i	−0.218087	+	0.300171i	0.685930	+	0.727667i	$0.259396\pi$
$860$	2.55756e11	+	2.20312e11i	0.467555	+	0.402758i
$861$	−6.11431e9	+	4.44230e9i	−0.0111259	+	0.00808343i
$862$	−5.95808e10	+	5.49752e10i	−0.107914	+	0.0995721i
$863$	−4.33592e11	+	5.96788e11i	−0.781696	+	1.07591i	0.213396	+	0.976966i	$0.431547\pi$
$863$	−4.33592e11	+	5.96788e11i	−0.781696	+	1.07591i	−0.995093	+	0.0989471i	$0.968453\pi$
$864$	−1.92383e11	+	5.14241e11i	−0.345233	+	0.922808i
$865$	−3.27033e11	+	2.36406e11i	−0.584153	+	0.422274i
$866$	−3.95458e11	−	4.28588e11i	−0.703119	−	0.762024i
$867$	3.05090e11	−	9.91297e10i	0.539947	−	0.175439i
$868$	1.12671e12	+	4.69111e11i	1.98488	+	0.826412i
$869$	−1.42973e11	−	4.40025e11i	−0.250712	−	0.771611i
$870$	1.37768e11	−	6.80816e11i	0.240476	−	1.18837i
$871$	9.38022e11	+	3.04782e11i	1.62982	+	0.529561i
$872$	3.50069e11	−	2.74421e11i	0.605462	−	0.474626i
$873$	−1.41693e10	+	1.02946e10i	−0.0243945	+	0.0177236i
$874$	−4.17202e10	−	8.33825e9i	−0.0714991	−	0.0142899i
$875$	6.77635e9	−	9.41463e11i	0.0115602	−	1.60609i
$876$	3.51405e11	−	8.44008e11i	0.596750	−	1.43328i
$877$	−3.65985e11	+	2.65904e11i	−0.618679	+	0.449496i	−0.852460	−	0.522793i	$-0.824890\pi$
$877$	−3.65985e11	+	2.65904e11i	−0.618679	+	0.449496i	0.233781	+	0.972289i	$0.424890\pi$
$878$	−8.90086e11	−	4.99539e11i	−1.49780	−	0.840605i
$879$	4.75543e11	+	1.54513e11i	0.796589	+	0.258827i
$880$	3.77189e11	−	3.72653e11i	0.628968	−	0.621404i
$881$	−3.60492e11	−	1.10948e12i	−0.598401	−	1.84169i	−0.537011	−	0.843575i	$-0.680447\pi$
$881$	−3.60492e11	−	1.10948e12i	−0.598401	−	1.84169i	−0.0613903	−	0.998114i	$-0.519553\pi$
$882$	2.66724e10	+	5.33078e9i	0.0440745	+	0.00880879i
$883$	−7.96844e11	+	2.58910e11i	−1.31078	+	0.425899i	−0.879320	−	0.476232i	$-0.842002\pi$
$883$	−7.96844e11	+	2.58910e11i	−1.31078	+	0.425899i	−0.431462	+	0.902131i	$0.642002\pi$
$884$	−6.68424e11	−	1.09525e12i	−1.09457	−	1.79351i
$885$	−6.52828e11	+	4.71918e11i	−1.06421	+	0.769297i
$886$	−2.34391e11	−	5.09656e11i	−0.380370	−	0.827070i
$887$	4.61006e11	−	6.34521e11i	0.744753	−	1.02507i	−0.253578	−	0.967315i	$-0.581607\pi$
$887$	4.61006e11	−	6.34521e11i	0.744753	−	1.02507i	0.998331	−	0.0577501i	$-0.0183927\pi$
$888$	−3.06033e11	+	1.11951e11i	−0.492171	+	0.180042i
$889$	−1.12562e12	+	8.17809e11i	−1.80212	+	1.30932i
$890$	−6.77615e10	+	1.20063e11i	−0.108000	+	0.191358i
$891$	−3.36592e11	+	4.63279e11i	−0.534064	+	0.735076i
$892$	−1.79166e11	−	1.44297e10i	−0.283006	−	0.0227928i
$893$	5.21840e11			0.820600
$894$	−1.23861e12	+	1.45454e11i	−1.93903	+	0.227706i
$895$	3.91581e8	+	1.28272e8i	0.000610280	+	0.000199912i
$896$	−1.28236e11	+	1.02720e12i	−0.198966	+	1.59376i
$897$	2.52775e10	−	7.77962e10i	0.0390449	−	0.120168i
$898$	1.91415e11	−	8.80319e10i	0.294355	−	0.135374i
$899$			1.04539e12i			1.60045i
$900$	1.81806e10	−	4.23761e9i	0.0277101	−	0.00645879i
$901$	−3.63267e11			−0.551222
$902$	−2.06472e9	−	4.48950e9i	−0.00311914	−	0.00678221i
$903$	−6.35612e11	−	2.06523e11i	−0.955964	−	0.310611i
$904$	−1.06799e11	+	8.37204e10i	−0.159916	+	0.125360i
$905$	−1.03608e11	−	3.21495e11i	−0.154454	−	0.479269i
$906$	−1.53294e11	−	1.30538e12i	−0.227516	−	1.93742i
$907$			3.48260e11i			0.514605i	0.966331	+	0.257303i	$0.0828337\pi$
$907$			3.48260e11i			0.514605i	−0.966331	+	0.257303i	$0.917166\pi$
$908$	−4.36886e11	−	3.51861e10i	−0.642724	−	0.0517640i
$909$	1.09986e10	+	7.99093e9i	0.0161095	+	0.0117042i
$910$	−3.67509e11	+	1.81614e12i	−0.535923	+	2.64840i
$911$	5.62317e11	+	7.73963e11i	0.816409	+	1.12369i	0.990303	+	0.138926i	$0.0443650\pi$
$911$	5.62317e11	+	7.73963e11i	0.816409	+	1.12369i	−0.173894	+	0.984764i	$0.555635\pi$
$912$	1.05562e11	+	6.82608e11i	0.152590	+	0.986715i
$913$	4.85366e11	+	3.52639e11i	0.698532	+	0.507513i
$914$	2.03923e11	−	9.37842e10i	0.292201	−	0.134383i
$915$	−1.01540e12	+	3.27233e11i	−1.44862	+	0.466845i
$916$	−6.95530e11	−	1.13967e12i	−0.987948	−	1.61881i
$917$	−1.11519e11	−	3.43219e11i	−0.157714	−	0.485394i
$918$	−1.71273e11	+	8.56958e11i	−0.241167	+	1.20667i
$919$	4.15580e11	−	1.35030e11i	0.582630	−	0.189308i	−0.00284856	−	0.999996i	$-0.500907\pi$
$919$	4.15580e11	−	1.35030e11i	0.582630	−	0.189308i	0.585478	+	0.810688i	$0.300907\pi$
$920$	4.98693e10	−	1.81073e10i	0.0696117	−	0.0252756i
$921$	−1.31983e11	+	4.06202e11i	−0.183434	+	0.564552i
$922$	1.56505e11	−	2.78862e11i	0.216573	−	0.385892i
$923$	1.48318e11	+	2.04142e11i	0.204356	+	0.281272i
$924$	−4.03499e11	+	9.69127e11i	−0.553548	+	1.32951i
$925$	−3.04999e11	−	2.23839e11i	−0.416612	−	0.305751i
$926$	6.48803e10	−	3.24627e11i	0.0882408	−	0.441510i
$927$	5.53622e9	+	7.61996e9i	0.00749712	+	0.0103189i
$928$	−8.54479e11	+	2.36785e11i	−1.15215	+	0.319273i
$929$	1.20687e11	−	3.71435e11i	0.162030	−	0.498678i	−0.836775	−	0.547547i	$-0.815562\pi$
$929$	1.20687e11	−	3.71435e11i	0.162030	−	0.498678i	0.998805	+	0.0488689i	$0.0155616\pi$
$930$	−9.23644e11	+	4.22102e11i	−1.23473	+	0.564269i
$931$	−1.11123e12	+	3.61060e11i	−1.47913	+	0.480597i
$932$	5.16485e11	+	2.15040e11i	0.684532	+	0.285007i
$933$	−2.34296e11	−	7.21088e11i	−0.309199	−	0.951615i
$934$	7.45048e11	−	6.87456e11i	0.979032	−	0.903352i
$935$	4.97698e11	−	6.81578e11i	0.651208	−	0.891803i
$936$	−3.67160e10	+	1.34192e9i	−0.0478356	+	0.00174832i
$937$	2.03520e10	+	1.47866e10i	0.0264027	+	0.0191827i	0.600908	−	0.799318i	$-0.294806\pi$
$937$	2.03520e10	+	1.47866e10i	0.0264027	+	0.0191827i	−0.574506	+	0.818501i	$0.694806\pi$
$938$	−8.58866e11	−	9.30818e11i	−1.10947	−	1.20241i
$939$	7.41408e10	+	1.02046e11i	0.0953664	+	0.131261i
$940$	−5.56283e11	+	3.37667e11i	−0.712499	+	0.432491i
$941$	3.99531e11	+	2.90276e11i	0.509556	+	0.370214i	0.812655	−	0.582745i	$-0.198021\pi$
$941$	3.99531e11	+	2.90276e11i	0.509556	+	0.370214i	−0.303099	+	0.952959i	$0.598021\pi$
$942$	−7.19572e11	+	8.45012e10i	−0.913841	+	0.107315i
$943$		−	4.94451e8i		−	0.000625283i
$944$	9.14489e11	+	4.70168e11i	1.15157	+	0.592059i
$945$	1.02277e12	−	7.39344e11i	1.28248	−	0.927085i
$946$	2.13863e11	−	3.81064e11i	0.267037	−	0.475810i
$947$	−1.09961e12	−	3.57286e11i	−1.36723	−	0.444239i	−0.468778	−	0.883316i	$-0.655305\pi$
$947$	−1.09961e12	−	3.57286e11i	−1.36723	−	0.444239i	−0.898449	+	0.439077i	$0.855305\pi$
$948$	−7.31150e11	+	1.74123e11i	−0.905260	+	0.215587i
$949$	−2.08897e12			−2.57553
$950$	−5.91960e11	+	5.40966e11i	−0.726772	+	0.664164i
$951$		−	3.53388e11i		−	0.432045i
$952$	6.01795e10	+	1.64656e12i	0.0732658	+	2.00461i
$953$	9.75477e10	−	3.00221e11i	0.118262	−	0.363973i	−0.874351	−	0.485293i	$-0.838713\pi$
$953$	9.75477e10	−	3.00221e11i	0.118262	−	0.363973i	0.992613	+	0.121320i	$0.0387128\pi$
$954$	−5.09081e9	+	9.07087e9i	−0.00614601	+	0.0109510i
$955$	−8.86521e11	+	1.21406e12i	−1.06580	+	1.45957i
$956$	4.91742e11	+	3.96041e10i	0.588716	+	0.0474142i
$957$	−8.99181e11			−1.07201
$958$	1.40238e12	−	1.64686e11i	1.66496	−	0.195521i
$959$	−6.30962e11	+	8.68445e11i	−0.745983	+	1.02676i
$960$	−5.54224e11	−	6.59356e11i	−0.652530	−	0.776310i
$961$	5.46466e11	−	3.97031e11i	0.640721	−	0.465511i
$962$	5.04923e11	+	5.47223e11i	0.589555	+	0.638946i
$963$	1.46986e10	−	2.02309e10i	0.0170911	−	0.0235239i
$964$	−1.54215e12	+	3.67263e11i	−1.78574	+	0.425274i
$965$	7.02018e11	+	1.68427e9i	0.809541	+	0.00194224i
$966$	−7.71987e10	+	7.12312e10i	−0.0886547	+	0.0818016i
$967$	−6.65503e11	+	2.16235e11i	−0.761104	+	0.247298i	−0.663752	−	0.747952i	$-0.731037\pi$
$967$	−6.65503e11	+	2.16235e11i	−0.761104	+	0.247298i	−0.0973515	+	0.995250i	$0.531037\pi$
$968$	1.59044e11	+	1.06901e11i	0.181141	+	0.121753i
$969$	3.39734e11	+	1.04559e12i	0.385340	+	1.18595i
$970$	1.07187e11	+	9.32056e11i	0.121076	+	1.05282i
$971$	−1.19622e12	−	3.88675e11i	−1.34566	−	0.437230i	−0.454427	−	0.890784i	$-0.650156\pi$
$971$	−1.19622e12	−	3.88675e11i	−1.34566	−	0.437230i	−0.891229	+	0.453554i	$0.850156\pi$
$972$	3.85529e10	+	3.30492e10i	0.0431909	+	0.0370251i
$973$	−1.58793e11	+	1.15370e11i	−0.177166	+	0.128718i
$974$	2.57421e11	−	1.28800e12i	0.286028	−	1.43113i
$975$	−9.00248e11	−	1.25167e12i	−0.996194	−	1.38507i
$976$	9.59425e11	+	9.66455e11i	1.05733	+	1.06508i
$977$	−4.48920e11	+	3.26160e11i	−0.492709	+	0.357974i	−0.806225	−	0.591609i	$-0.798493\pi$
$977$	−4.48920e11	+	3.26160e11i	−0.492709	+	0.357974i	0.313516	+	0.949583i	$0.398493\pi$
$978$	−3.43095e11	+	6.11330e11i	−0.375024	+	0.668222i
$979$	1.69731e11	+	5.51490e10i	0.184770	+	0.0600354i
$980$	9.50944e11	−	1.10394e12i	1.03098	−	1.19685i
$981$	−6.26457e9	−	1.92804e10i	−0.00676419	−	0.0208180i
$982$	3.24508e11	−	1.62367e12i	0.348963	−	1.74603i
$983$	1.25240e12	−	4.06929e11i	1.34131	−	0.435817i	0.451548	−	0.892247i	$-0.350872\pi$
$983$	1.25240e12	−	4.06929e11i	1.34131	−	0.435817i	0.889759	+	0.456430i	$0.150872\pi$
$984$	−7.53882e9	+	2.75779e9i	−0.00804124	+	0.00294158i
$985$	1.75747e11	−	5.36510e11i	0.186699	−	0.569945i
$986$	−1.28221e12	+	5.89687e11i	−1.35659	+	0.623898i
$987$	7.57289e11	−	1.04232e12i	0.797982	−	1.09833i
$988$	1.34718e12	−	8.22175e11i	1.41383	−	0.862852i
$989$	3.53735e10	−	2.57003e10i	0.0369736	−	0.0268629i
$990$	−1.00445e10	−	2.19793e10i	−0.0104565	−	0.0228809i
$991$	−9.52346e11	+	1.31079e12i	−0.987416	+	1.35906i	−0.0546796	+	0.998504i	$0.517414\pi$
$991$	−9.52346e11	+	1.31079e12i	−0.987416	+	1.35906i	−0.932737	+	0.360558i	$0.882586\pi$
$992$	1.01435e12	+	8.07181e11i	1.04747	+	0.833536i
$993$	1.89437e12			1.94836
$994$	−3.77916e10	−	3.21815e11i	−0.0387123	−	0.329656i
$995$	2.91319e9	−	1.21424e12i	0.00297219	−	1.23883i
$996$	6.34303e11	−	7.39935e11i	0.644555	−	0.751893i
$997$	−1.89401e10	+	5.82915e10i	−0.0191691	+	0.0589963i	−0.960183	−	0.279370i	$-0.909874\pi$
$997$	−1.89401e10	+	5.82915e10i	−0.0191691	+	0.0589963i	0.941014	+	0.338366i	$0.109874\pi$
$998$	−5.37029e11	−	1.16771e12i	−0.541347	−	1.17710i
$999$		−	5.07123e11i		−	0.509157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.17	✓	464
4.3	odd	2	inner	100.9.j.b.11.29	yes	464
25.16	even	5	inner	100.9.j.b.91.29	yes	464
100.91	odd	10	inner	100.9.j.b.91.17	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.17	✓	464	1.1	even	1	trivial
100.9.j.b.11.29	yes	464	4.3	odd	2	inner
100.9.j.b.91.17	yes	464	100.91	odd	10	inner
100.9.j.b.91.29	yes	464	25.16	even	5	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+(-14.5364 + 6.68529i) q^{2} +(-78.1238 - 25.3840i) q^{3} +(166.614 - 194.360i) q^{4} +(-624.998 - 1.49949i) q^{5} +(1305.34 - 153.289i) q^{6} +3856.33i q^{7} +(-1122.61 + 3939.16i) q^{8} +(151.027 + 109.727i) q^{9} +(9095.25 - 4156.50i) q^{10} +(-7608.90 - 10472.7i) q^{11} +(-17950.1 + 10954.8i) q^{12} +(38872.9 + 28242.8i) q^{13} +(-25780.7 - 56057.2i) q^{14} +(48789.2 + 15982.1i) q^{15} +(-10015.8 - 64766.1i) q^{16} +(-32234.1 - 99206.5i) q^{17} +(-2928.94 - 585.381i) q^{18} +(122026. - 39648.6i) q^{19} +(-104425. + 121225. i) q^{20} +(97889.0 - 301271. i) q^{21} +(180619. + 101368. i) q^{22} +(12181.6 + 16766.5i) q^{23} +(187694. - 279246. i) q^{24} +(390621. + 1874.36i) q^{25} +(-753883. - 150672. i) q^{26} +(307773. + 423613. i) q^{27} +(749518. + 642518. i) q^{28} +(-261306. + 804217. i) q^{29} +(-816064. + 93848.2i) q^{30} +(1.17576e6 - 382028. i) q^{31} +(578574. + 874508. i) q^{32} +(328596. + 1.01132e6i) q^{33} +(1.13179e6 + 1.22661e6i) q^{34} +(5782.53 - 2.41020e6i) q^{35} +(46489.7 - 11071.5i) q^{36} +(-783538. - 569274. i) q^{37} +(-1.50876e6 + 1.39213e6i) q^{38} +(-2.31998e6 - 3.19318e6i) q^{39} +(707535. - 2.46028e6i) q^{40} +(-19301.7 - 14023.5i) q^{41} +(591134. + 5.03382e6i) q^{42} -2.10977e6i q^{43} +(-3.30323e6 - 266037. i) q^{44} +(-94226.8 - 68805.8i) q^{45} +(-289166. - 162287. i) q^{46} +(3.86810e6 + 1.25682e6i) q^{47} +(-861553. + 5.31402e6i) q^{48} -9.10650e6 q^{49} +(-5.69075e6 + 2.58417e6i) q^{50} +8.56862e6i q^{51} +(1.19660e7 - 2.84970e6i) q^{52} +(1.07615e6 - 3.31206e6i) q^{53} +(-7.30588e6 - 4.10025e6i) q^{54} +(4.73984e6 + 6.55686e6i) q^{55} +(-1.51907e7 - 4.32915e6i) q^{56} -1.05396e7 q^{57} +(-1.57798e6 - 1.34373e7i) q^{58} +(-9.22247e6 + 1.26936e7i) q^{59} +(1.12352e7 - 6.81984e6i) q^{60} +(-1.68110e7 + 1.22139e7i) q^{61} +(-1.45374e7 + 1.34136e7i) q^{62} +(-423145. + 582409. i) q^{63} +(-1.42567e7 - 8.84426e6i) q^{64} +(-2.42531e7 - 1.77100e7i) q^{65} +(-1.15375e7 - 1.25041e7i) q^{66} +(1.95220e7 - 6.34307e6i) q^{67} +(-2.46524e7 - 1.02641e7i) q^{68} +(-526072. - 1.61908e6i) q^{69} +(1.60288e7 + 3.50743e7i) q^{70} +(4.99450e6 + 1.62281e6i) q^{71} +(-601776. + 471737. i) q^{72} +(-3.51723e7 + 2.55542e7i) q^{73} +(1.51956e7 + 3.03701e6i) q^{74} +(-3.04692e7 - 1.00619e7i) q^{75} +(1.26251e7 - 3.03230e7i) q^{76} +(4.03864e7 - 2.93424e7i) q^{77} +(5.50716e7 + 3.09076e7i) q^{78} +(3.39918e7 + 1.10446e7i) q^{79} +(6.16271e6 + 4.04937e7i) q^{80} +(-1.36699e7 - 4.20716e7i) q^{81} +(374328. + 74813.7i) q^{82} +(-4.40773e7 + 1.43216e7i) q^{83} +(-4.22455e7 - 6.92217e7i) q^{84} +(1.99975e7 + 6.20522e7i) q^{85} +(1.41044e7 + 3.06684e7i) q^{86} +(4.08285e7 - 5.61955e7i) q^{87} +(4.97956e7 - 1.82159e7i) q^{88} +(-1.11535e7 + 8.10348e6i) q^{89} +(1.82970e6 + 370254. i) q^{90} +(-1.08914e8 + 1.49907e8i) q^{91} +(5.28837e6 + 425916. i) q^{92} -1.01552e8 q^{93} +(-6.46304e7 + 7.58972e6i) q^{94} +(-7.63255e7 + 2.45974e7i) q^{95} +(-2.30019e7 - 8.30064e7i) q^{96} +(-2.89920e7 + 8.92281e7i) q^{97} +(1.32376e8 - 6.08796e7i) q^{98} -2.41657e6i 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

Related objects

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