LMFDB - Embedded newform 100.9.j.b.11.29

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			11.29
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.29

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-10.8501 + 11.7591i) q^{2} +(78.1238 + 25.3840i) q^{3} +(-20.5513 - 255.174i) q^{4} +(-624.998 - 1.49949i) q^{5} +(-1146.14 + 643.245i) q^{6} -3856.33i q^{7} +(3223.59 + 2526.99i) q^{8} +(151.027 + 109.727i) q^{9} +(6798.92 - 7333.13i) q^{10} +(7608.90 + 10472.7i) q^{11} +(4871.78 - 20456.8i) q^{12} +(38872.9 + 28242.8i) q^{13} +(45346.9 + 41841.5i) q^{14} +(-48789.2 - 15982.1i) q^{15} +(-64691.3 + 10488.3i) q^{16} +(-32234.1 - 99206.5i) q^{17} +(-2928.94 + 585.381i) q^{18} +(-122026. + 39648.6i) q^{19} +(12461.9 + 159514. i) q^{20} +(97889.0 - 301271. i) q^{21} +(-205707. - 24156.7i) 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} +(-984035. + 79252.5i) q^{28} +(-261306. + 804217. i) q^{29} +(717301. - 400308. i) q^{30} +(-1.17576e6 + 382028. i) q^{31} +(578574. - 874508. i) q^{32} +(328596. + 1.01132e6i) q^{33} +(1.51632e6 + 697355. i) q^{34} +(-5782.53 + 2.41020e6i) q^{35} +(24895.7 - 40793.0i) q^{36} +(-783538. - 569274. i) q^{37} +(857761. - 1.86510e6i) q^{38} +(2.31998e6 + 3.19318e6i) q^{39} +(-2.01095e6 - 1.58420e6i) q^{40} +(-19301.7 - 14023.5i) q^{41} +(2.48057e6 + 4.41991e6i) q^{42} +2.10977e6i q^{43} +(2.51600e6 - 2.15682e6i) q^{44} +(-94226.8 - 68805.8i) q^{45} +(329330. + 38674.1i) q^{46} +(-3.86810e6 - 1.25682e6i) q^{47} +(-5.32017e6 - 822737. i) q^{48} -9.10650e6 q^{49} +(-4.26031e6 + 4.57300e6i) q^{50} -8.56862e6i q^{51} +(6.40794e6 - 1.04998e7i) q^{52} +(1.07615e6 - 3.31206e6i) q^{53} +(8.32065e6 + 977115. i) q^{54} +(-4.73984e6 - 6.55686e6i) q^{55} +(9.74493e6 - 1.24312e7i) q^{56} -1.05396e7 q^{57} +(-6.62165e6 - 1.17985e7i) q^{58} +(9.22247e6 - 1.26936e7i) q^{59} +(-3.07553e6 + 1.27782e7i) q^{60} +(-1.68110e7 + 1.22139e7i) q^{61} +(8.26482e6 - 1.79709e7i) q^{62} +(423145. - 582409. i) q^{63} +(4.00582e6 + 1.62920e7i) q^{64} +(-2.42531e7 - 1.77100e7i) q^{65} +(-1.54574e7 - 7.10887e6i) q^{66} +(-1.95220e7 + 6.34307e6i) q^{67} +(-2.46524e7 + 1.02641e7i) q^{68} +(-526072. - 1.61908e6i) q^{69} +(-2.82790e7 - 2.62189e7i) q^{70} +(-4.99450e6 - 1.62281e6i) q^{71} +(209567. + 735358. 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} +(-6.27209e7 - 7.36548e6i) q^{78} +(-3.39918e7 - 1.10446e7i) q^{79} +(4.04477e7 - 6.45816e6i) q^{80} +(-1.36699e7 - 4.20716e7i) q^{81} +(374328. - 74813.7i) q^{82} +(4.40773e7 - 1.43216e7i) q^{83} +(-7.88883e7 - 1.87872e7i) q^{84} +(1.99975e7 + 6.20522e7i) q^{85} +(-2.48089e7 - 2.28911e7i) q^{86} +(-4.08285e7 + 5.61955e7i) q^{87} +(-1.93662e6 + 5.29874e7i) q^{88} +(-1.11535e7 + 8.10348e6i) q^{89} +(1.83146e6 - 361470. i) q^{90} +(1.08914e8 - 1.49907e8i) q^{91} +(-4.02803e6 + 3.45300e6i) q^{92} -1.01552e8 q^{93} +(5.67483e7 - 3.18486e7i) q^{94} +(7.63255e7 - 2.45974e7i) q^{95} +(6.73989e7 - 5.36334e7i) q^{96} +(-2.89920e7 + 8.92281e7i) q^{97} +(9.88063e7 - 1.07084e8i) 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 $

$2$	−10.8501	+	11.7591i	−0.678130	+	0.734942i
$2$	−10.8501	+	11.7591i	−0.678130	+	0.734942i
$3$	78.1238	+	25.3840i	0.964492	+	0.313382i	0.748590	−	0.663033i	$-0.230731\pi$
$3$	78.1238	+	25.3840i	0.964492	+	0.313382i	0.215901	+	0.976415i	$0.430731\pi$
$4$	−20.5513	−	255.174i	−0.0802784	−	0.996772i
$5$	−624.998	−	1.49949i	−0.999997	−	0.00239918i
$5$	−624.998	−	1.49949i	−0.999997	−	0.00239918i
$6$	−1146.14	+	643.245i	−0.884369	+	0.496331i
$7$		−	3856.33i		−	1.60614i	−0.595887	−	0.803068i	$-0.703200\pi$
$7$		−	3856.33i		−	1.60614i	0.595887	−	0.803068i	$-0.296800\pi$
$8$	3223.59	+	2526.99i	0.787009	+	0.616942i
$9$	151.027	+	109.727i	0.0230188	+	0.0167242i
$10$	6798.92	−	7333.13i	0.679892	−	0.733313i
$11$	7608.90	+	10472.7i	0.519698	+	0.715303i	0.985517	−	0.169577i	$-0.0542403\pi$
$11$	7608.90	+	10472.7i	0.519698	+	0.715303i	−0.465819	+	0.884880i	$0.654240\pi$
$12$	4871.78	−	20456.8i	0.234943	−	0.986537i
$13$	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	$0.381865\pi$
$14$	45346.9	+	41841.5i	1.18042	+	1.08917i
$15$	−48789.2	−	15982.1i	−0.963737	−	0.315695i
$16$	−64691.3	+	10488.3i	−0.987111	+	0.160039i
$17$	−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	−0.737157	−	0.675722i	$-0.763832\pi$
$19$	−122026.	+	39648.6i	−0.936349	+	0.304238i	−0.199193	+	0.979960i	$0.563832\pi$
$20$	12461.9	+	159514.i	0.0778867	+	0.996962i
$21$	97889.0	−	301271.i	0.503335	−	1.54911i
$22$	−205707.	−	24156.7i	−0.878129	−	0.103121i
$23$	−12181.6	−	16766.5i	−0.0435304	−	0.0599145i	0.786697	−	0.617339i	$-0.211789\pi$
$23$	−12181.6	−	16766.5i	−0.0435304	−	0.0599145i	−0.830227	+	0.557425i	$0.811789\pi$
$24$	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
$28$	−984035.	+	79252.5i	−1.60095	+	0.128938i
$29$	−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	$0.896048\pi$
$30$	717301.	−	400308.i	0.885557	−	0.494208i
$31$	−1.17576e6	+	382028.i	−1.27313	+	0.413665i	−0.866155	−	0.499775i	$-0.833416\pi$
$31$	−1.17576e6	+	382028.i	−1.27313	+	0.413665i	−0.406974	+	0.913440i	$0.633416\pi$
$32$	578574.	−	874508.i	0.551771	−	0.833996i
$33$	328596.	+	1.01132e6i	0.277081	+	0.852768i
$34$	1.51632e6	+	697355.i	1.13468	+	0.521841i
$35$	−5782.53	+	2.41020e6i	−0.00385341	+	1.60613i
$36$	24895.7	−	40793.0i	0.0148223	−	0.0242871i
$37$	−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	$0.783190\pi$
$38$	857761.	−	1.86510e6i	0.411369	−	0.894475i
$39$	2.31998e6	+	3.19318e6i	1.00283	+	1.38027i
$40$	−2.01095e6	−	1.58420e6i	−0.785526	−	0.618828i
$41$	−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	$0.701344\pi$
$42$	2.48057e6	+	4.41991e6i	0.797175	+	1.42042i
$43$			2.10977e6i			0.617107i	0.951207	+	0.308553i	$0.0998449\pi$
$43$			2.10977e6i			0.617107i	−0.951207	+	0.308553i	$0.900155\pi$
$44$	2.51600e6	−	2.15682e6i	0.671273	−	0.575444i
$45$	−94226.8	−	68805.8i	−0.0229786	−	0.0167793i
$46$	329330.	+	38674.1i	0.0735530	+	0.00863751i
$47$	−3.86810e6	−	1.25682e6i	−0.792695	−	0.257562i	−0.115444	−	0.993314i	$-0.536829\pi$
$47$	−3.86810e6	−	1.25682e6i	−0.792695	−	0.257562i	−0.677251	+	0.735752i	$0.736829\pi$
$48$	−5.32017e6	−	822737.i	−1.00221	−	0.154987i
$49$	−9.10650e6			−1.57967
$50$	−4.26031e6	+	4.57300e6i	−0.681649	+	0.731679i
$51$		−	8.56862e6i		−	1.26657i
$52$	6.40794e6	−	1.04998e7i	0.876405	−	1.43604i
$53$	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	$0.0291731\pi$
$54$	8.32065e6	+	977115.i	0.978548	+	0.114913i
$55$	−4.73984e6	−	6.55686e6i	−0.517980	−	0.716547i
$56$	9.74493e6	−	1.24312e7i	0.990892	−	1.26404i
$57$	−1.05396e7			−0.998444
$58$	−6.62165e6	−	1.17985e7i	−0.585133	−	1.04260i
$59$	9.22247e6	−	1.26936e7i	0.761096	−	1.04756i	−0.236026	−	0.971747i	$-0.575845\pi$
$59$	9.22247e6	−	1.26936e7i	0.761096	−	1.04756i	0.997122	−	0.0758120i	$-0.0241549\pi$
$60$	−3.07553e6	+	1.27782e7i	−0.237309	+	0.985970i
$61$	−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	$0.570135\pi$
$62$	8.26482e6	−	1.79709e7i	0.559328	−	1.21619i
$63$	423145.	−	582409.i	0.0268613	−	0.0369714i
$64$	4.00582e6	+	1.62920e7i	0.238766	+	0.971077i
$65$	−2.42531e7	−	1.77100e7i	−1.35867	−	0.992122i
$66$	−1.54574e7	−	7.10887e6i	−0.814631	−	0.374649i
$67$	−1.95220e7	+	6.34307e6i	−0.968779	+	0.314775i	−0.750323	−	0.661072i	$-0.770102\pi$
$67$	−1.95220e7	+	6.34307e6i	−0.968779	+	0.314775i	−0.218456	+	0.975847i	$0.570102\pi$
$68$	−2.46524e7	+	1.02641e7i	−1.15299	+	0.480050i
$69$	−526072.	−	1.61908e6i	−0.0232086	−	0.0714287i
$70$	−2.82790e7	−	2.62189e7i	−1.17780	−	1.09200i
$71$	−4.99450e6	−	1.62281e6i	−0.196544	−	0.0638609i	0.209091	−	0.977896i	$-0.432949\pi$
$71$	−4.99450e6	−	1.62281e6i	−0.196544	−	0.0638609i	−0.405635	+	0.914035i	$0.632949\pi$
$72$	209567.	+	735358.i	0.00779819	+	0.0273633i
$73$	−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
$78$	−6.27209e7	−	7.36548e6i	−1.69447	−	0.198986i
$79$	−3.39918e7	−	1.10446e7i	−0.872703	−	0.283558i	−0.161779	−	0.986827i	$-0.551723\pi$
$79$	−3.39918e7	−	1.10446e7i	−0.872703	−	0.283558i	−0.710924	+	0.703269i	$0.751723\pi$
$80$	4.04477e7	−	6.45816e6i	0.987492	−	0.157670i
$81$	−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	0.194704	−	0.980862i	$-0.437625\pi$
$83$	4.40773e7	−	1.43216e7i	0.928759	−	0.301772i	0.734055	+	0.679090i	$0.237625\pi$
$84$	−7.88883e7	−	1.87872e7i	−1.58451	−	0.377351i
$85$	1.99975e7	+	6.20522e7i	0.383090	+	1.18873i
$86$	−2.48089e7	−	2.28911e7i	−0.453538	−	0.418479i
$87$	−4.08285e7	+	5.61955e7i	−0.712666	+	0.980900i
$88$	−1.93662e6	+	5.29874e7i	−0.0322933	+	0.883573i
$89$	−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	$0.335042\pi$
$90$	1.83146e6	−	361470.i	0.0279143	−	0.00550938i
$91$	1.08914e8	−	1.49907e8i	1.58824	−	2.18603i
$92$	−4.02803e6	+	3.45300e6i	−0.0562266	+	0.0481998i
$93$	−1.01552e8			−1.35756
$94$	5.67483e7	−	3.18486e7i	0.726844	−	0.407924i
$95$	7.63255e7	−	2.45974e7i	0.937077	−	0.301991i
$96$	6.73989e7	−	5.36334e7i	0.793538	−	0.631467i
$97$	−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	$0.922237\pi$
$98$	9.88063e7	−	1.07084e8i	1.07122	−	1.16097i
$99$			2.41657e6i			0.0251569i
$100$	−7.54946e6	−	9.97146e7i	−0.0754946	−	0.997146i
$101$	7.28254e7			0.699838			0.349919	−	0.936780i	$-0.386209\pi$
$101$	7.28254e7			0.699838			0.349919	+	0.936780i	$0.386209\pi$
$102$	1.00759e8	+	9.29703e7i	0.930857	+	0.858902i
$103$	−4.79850e7	−	1.55913e7i	−0.426341	−	0.138526i	0.0879844	−	0.996122i	$-0.471957\pi$
$103$	−4.79850e7	−	1.55913e7i	−0.426341	−	0.138526i	−0.514325	+	0.857595i	$0.671957\pi$
$104$	5.39408e7	+	1.89275e8i	0.461088	+	1.61793i
$105$	−6.16322e7	+	1.88147e8i	−0.507050	+	1.54789i
$106$	2.72704e7	+	4.85907e7i	0.216007	+	0.384884i
$107$			1.33956e8i			1.02194i	0.859598	+	0.510971i	$0.170714\pi$
$107$			1.33956e8i			1.02194i	−0.859598	+	0.510971i	$0.829286\pi$
$108$	−1.01770e8	+	8.72412e7i	−0.748038	+	0.641249i
$109$	−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	$0.825681\pi$
$110$	1.28530e8	+	1.54063e7i	0.877879	+	0.105227i
$111$	−4.67626e7	−	6.43632e7i	−0.308040	−	0.423980i
$112$	4.04463e7	+	2.49471e8i	0.257044	+	1.58543i
$113$	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	$0.667605\pi$
$114$	1.14355e8	−	1.23936e8i	0.677075	−	0.733798i
$115$	7.58834e6	+	1.04973e7i	0.0433866	+	0.0600188i
$116$	2.10585e8	+	5.01508e7i	1.16304	+	0.276978i
$117$	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
$120$	−1.16890e8	−	1.74810e8i	−0.563704	−	0.843025i
$121$	1.44574e7	−	4.44954e7i	0.0674449	−	0.207574i
$122$	3.87768e7	−	3.30205e8i	0.175038	−	1.49054i
$123$	−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	$-0.956091\pi$
$127$	−2.12069e8	−	2.91888e8i	−0.815196	−	1.12202i	0.175304	−	0.984514i	$-0.443909\pi$
$128$	−2.35042e8	−	1.29665e8i	−0.875599	−	0.483038i
$129$	−5.35542e7	+	1.64823e8i	−0.193390	+	0.595195i
$130$	4.71402e8	−	9.30393e7i	1.65051	−	0.325756i
$131$	8.90014e7	−	2.89183e7i	0.302212	−	0.0981946i	−0.153986	−	0.988073i	$-0.549211\pi$
$131$	8.90014e7	−	2.89183e7i	0.302212	−	0.0981946i	0.456198	+	0.889878i	$0.349211\pi$
$132$	2.51308e8	−	1.04633e8i	0.827772	−	0.344646i
$133$	1.52898e8	+	4.70573e8i	0.488648	+	1.50390i
$134$	1.37226e8	−	2.98383e8i	0.425617	−	0.925454i
$135$	1.91722e8	+	2.65219e8i	0.577214	+	0.798489i
$136$	1.46785e8	−	4.01256e8i	0.429067	−	1.17291i
$137$	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	$0.570713\pi$
$138$	2.47468e7	+	1.13811e7i	0.0682344	+	0.0313810i
$139$	−2.99170e7	−	4.11772e7i	−0.0801416	−	0.110306i	0.767064	−	0.641571i	$-0.221717\pi$
$139$	−2.99170e7	−	4.11772e7i	−0.0801416	−	0.110306i	−0.847206	+	0.531265i	$0.821717\pi$
$140$	6.15139e8	−	4.80571e7i	1.60126	−	0.125097i
$141$	−2.70288e8	−	1.96375e8i	−0.683832	−	0.496833i
$142$	7.32735e7	−	4.11230e7i	0.180216	−	0.101142i
$143$			6.22002e8i			1.48747i
$144$	−1.09210e7	−	5.51438e6i	−0.0253986	−	0.0128247i
$145$	1.64522e8	−	5.02243e8i	0.372178	−	1.13617i
$146$	8.11293e7	−	6.90858e8i	0.178553	−	1.52047i
$147$	−7.11435e8	−	2.31159e8i	−1.52358	−	0.495042i
$148$	−1.29161e8	+	2.11638e8i	−0.269206	+	0.441109i
$149$	−9.48883e8			−1.92516			−0.962581	−	0.270993i	$-0.912648\pi$
$149$	−9.48883e8			−1.92516			−0.962581	+	0.270993i	$0.912648\pi$
$150$	−4.48912e8	+	2.49116e8i	−0.886740	+	0.492082i
$151$			1.00003e9i			1.92356i	0.273832	+	0.961778i	$0.411709\pi$
$151$			1.00003e9i			1.92356i	−0.273832	+	0.961778i	$0.588291\pi$
$152$	−4.93553e8	−	1.80548e8i	−0.924612	−	0.338235i
$153$	6.01744e6	−	1.85198e7i	0.0109811	−	0.0337964i
$154$	−9.31562e7	+	7.93274e8i	−0.165626	+	1.41039i
$155$	7.35421e8	−	2.37004e8i	1.27412	−	0.410609i
$156$	7.67138e8	−	6.57623e8i	1.29531	−	1.11040i
$157$	−5.51253e8			−0.907304			−0.453652	−	0.891179i	$-0.649879\pi$
$157$	−5.51253e8			−0.907304			−0.453652	+	0.891179i	$0.649879\pi$
$158$	4.98689e8	−	2.79877e8i	0.800205	−	0.449096i
$159$	1.68147e8	−	2.31434e8i	0.263087	−	0.362108i
$160$	−3.62919e8	+	5.45698e8i	−0.553770	+	0.832670i
$161$	−6.46573e7	+	4.69763e7i	−0.0962308	+	0.0699158i
$162$	6.43042e8	+	2.95735e8i	0.933639	+	0.429381i
$163$	3.13513e8	−	4.31514e8i	0.444126	−	0.611286i	−0.526997	−	0.849867i	$-0.676682\pi$
$163$	3.13513e8	−	4.31514e8i	0.444126	−	0.611286i	0.971123	+	0.238581i	$0.0766821\pi$
$164$	−3.18176e6	+	5.21349e6i	−0.00439837	+	0.00720697i
$165$	−2.03856e8	−	6.32563e8i	−0.275034	−	0.853430i
$166$	−3.09834e8	+	6.73699e8i	−0.408035	+	0.887225i
$167$	7.10908e8	−	2.30988e8i	0.914002	−	0.296977i	0.185998	−	0.982550i	$-0.440448\pi$
$167$	7.10908e8	−	2.30988e8i	0.914002	−	0.296977i	0.728004	+	0.685573i	$0.240448\pi$
$168$	1.07687e9	−	7.23810e8i	1.35184	−	0.908631i
$169$	4.61371e8	+	1.41995e9i	0.565592	+	1.74071i
$170$	−9.46651e8	−	4.38120e8i	−1.13343	−	0.524562i
$171$	−2.27797e7	−	7.40157e6i	−0.0266418	−	0.00865644i
$172$	5.38357e8	−	4.33584e7i	0.615115	−	0.0495404i
$173$	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
$178$	2.57269e7	−	2.19078e8i	0.0256276	−	0.218232i
$179$	627020.	+	203731.i	0.000610758	+	0.000198447i	0.309322	−	0.950957i	$-0.399898\pi$
$179$	627020.	+	203731.i	0.000610758	+	0.000198447i	−0.308712	+	0.951156i	$0.599898\pi$
$180$	−1.56209e7	+	2.54582e7i	−0.0148805	+	0.0242515i
$181$	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
$184$	3.10046e6	−	8.48312e7i	0.00270492	−	0.0740090i
$185$	4.88856e8	+	3.56970e8i	0.417344	+	0.304751i
$186$	1.10185e9	−	1.19416e9i	0.920601	−	0.997725i
$187$	7.93698e8	−	1.09243e9i	0.649066	−	0.893363i
$188$	−2.41214e8	+	1.01287e9i	−0.193095	+	0.810813i
$189$	−1.63359e9	+	1.18687e9i	−1.28025	+	0.930159i
$190$	−5.38896e8	+	1.16440e9i	−0.413514	+	0.893486i
$191$	−1.41377e9	+	1.94589e9i	−1.06230	+	1.46212i	−0.184655	+	0.982803i	$0.559117\pi$
$191$	−1.41377e9	+	1.94589e9i	−1.06230	+	1.46212i	−0.877640	+	0.479320i	$0.840883\pi$
$192$	−1.00605e8	+	1.37447e9i	−0.0740309	+	1.01142i
$193$	−1.12323e9			−0.809544			−0.404772	−	0.914418i	$-0.632649\pi$
$193$	−1.12323e9			−0.809544			−0.404772	+	0.914418i	$0.632649\pi$
$194$	−7.34673e8	−	1.30905e9i	−0.518666	−	0.924165i
$195$	−1.44520e9	−	1.99921e9i	−0.999514	−	1.38268i
$196$	1.87150e8	+	2.32374e9i	0.126814	+	1.57457i
$197$	−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	$0.196944\pi$
$198$	−2.84166e7	−	2.62199e7i	−0.0184889	−	0.0170597i
$199$		−	1.94279e9i		−	1.23883i	−0.785062	−	0.619417i	$-0.787369\pi$
$199$		−	1.94279e9i		−	1.23883i	0.785062	−	0.619417i	$-0.212631\pi$
$200$	1.25446e9	+	9.93138e8i	0.784039	+	0.620711i
$201$	−1.68614e9			−1.03302
$202$	−7.90162e8	+	8.56359e8i	−0.474581	+	0.514340i
$203$	3.10133e9	+	1.00768e9i	1.82626	+	0.593389i
$204$	−2.18649e9	+	1.76096e8i	−1.26249	+	0.101678i
$205$	1.20425e7	+	8.79361e6i	0.00681869	+	0.00497911i
$206$	7.03980e8	−	3.95092e8i	0.390923	−	0.219396i
$207$		−	3.86884e6i		−	0.00210717i
$208$	−2.81096e9	−	1.41935e9i	−1.50176	−	0.758293i
$209$	−1.34371e9	−	9.76265e8i	−0.704241	−	0.511661i
$210$	−1.54372e9	−	2.76615e9i	−0.793765	−	1.42233i
$211$	1.56755e9	+	2.15755e9i	0.790845	+	1.08850i	0.994002	+	0.109358i	$0.0348796\pi$
$211$	1.56755e9	+	2.15755e9i	0.790845	+	1.08850i	−0.203158	+	0.979146i	$0.565120\pi$
$212$	−8.67268e8	−	2.06539e8i	−0.429348	−	0.102249i
$213$	−3.48996e8	−	2.53561e8i	−0.169552	−	0.123187i
$214$	−1.57519e9	−	1.45343e9i	−0.751068	−	0.693010i
$215$	3.16357e6	−	1.31860e9i	0.00148055	−	0.617105i
$216$	7.83343e7	−	2.14329e9i	0.0359863	−	0.984614i
$217$	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
$220$	−1.57573e9	+	1.34424e9i	−0.672652	+	0.573832i
$221$	1.54884e9	−	4.76682e9i	0.649286	−	1.99830i
$222$	1.26423e9	+	1.48462e8i	0.520492	+	0.0611227i
$223$	4.12703e8	+	5.68036e8i	0.166885	+	0.229698i	0.884266	−	0.466983i	$-0.154659\pi$
$223$	4.12703e8	+	5.68036e8i	0.166885	+	0.229698i	−0.717381	+	0.696681i	$0.754659\pi$
$224$	−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	0.955321	−	0.295570i	$-0.0955094\pi$
$227$	1.00635e9	+	1.38513e9i	0.379007	+	0.521659i	−0.576314	+	0.817228i	$0.695509\pi$
$228$	2.16602e8	+	2.68942e9i	0.0801535	+	0.995222i
$229$	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	$-0.297131\pi$
$230$	−2.05773e8	−	2.46651e7i	−0.0735320	−	0.00881396i
$231$	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	$0.779102\pi$
$234$	−1.30389e8	−	5.99660e7i	−0.0434889	−	0.0200005i
$235$	2.41567e9	+	7.91311e8i	0.792075	+	0.259463i
$236$	−3.42862e9	−	2.09246e9i	−1.10528	−	0.674543i
$237$	−2.37522e9	−	1.72570e9i	−0.752852	−	0.546979i
$238$	2.68923e9	−	5.84743e9i	0.838148	−	1.82246i
$239$	−1.13271e9	−	1.55905e9i	−0.347159	−	0.477823i	0.599356	−	0.800482i	$-0.295423\pi$
$239$	−1.13271e9	−	1.55905e9i	−0.347159	−	0.477823i	−0.946515	+	0.322659i	$0.895423\pi$
$240$	3.32386e9	+	5.22186e8i	1.00184	+	0.157391i
$241$	−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	$-0.670070\pi$
$242$	3.66360e8	+	6.52784e8i	0.106818	+	0.190330i
$243$		−	1.98358e8i		−	0.0568886i
$244$	3.46217e9	+	4.03873e9i	0.976761	+	1.13942i
$245$	5.69155e9	+	1.36551e7i	1.57967	+	0.00378992i
$246$	3.11430e7	+	3.65721e6i	0.00850395	+	0.000998640i
$247$	−5.86329e9	−	1.90510e9i	−1.57526	−	0.511835i
$248$	−4.75555e9	−	1.73964e9i	−1.25717	−	0.459889i
$249$	3.80703e9			0.990350
$250$	2.66954e9	−	2.85173e9i	0.683403	−	0.730042i
$251$		−	8.43395e8i		−	0.212489i	−0.994340	−	0.106244i	$-0.966117\pi$
$251$		−	8.43395e8i		−	0.212489i	0.994340	−	0.106244i	$-0.0338826\pi$
$252$	−1.57312e8	−	9.60062e7i	−0.0390084	−	0.0238066i
$253$	8.29031e7	−	2.55150e8i	0.0202343	−	0.0622749i
$254$	5.73330e9	+	6.73276e8i	1.37743	+	0.161755i
$255$	−1.28486e7	+	5.35537e9i	−0.00303874	+	1.26657i
$256$	4.07496e9	−	1.35700e9i	0.948775	−	0.315952i
$257$	6.05433e9			1.38782			0.693911	−	0.720061i	$-0.255886\pi$
$257$	6.05433e9			1.38782			0.693911	+	0.720061i	$0.255886\pi$
$258$	−1.35710e9	−	2.41809e9i	−0.306289	−	0.545750i
$259$	−2.19531e9	+	3.02158e9i	−0.487862	+	0.671484i
$260$	−4.02069e9	+	6.55273e9i	−0.879848	+	1.43393i
$261$	−1.27709e8	+	9.27858e7i	−0.0275206	+	0.0199949i
$262$	−6.25621e8	+	1.36034e9i	−0.132772	+	0.288697i
$263$	3.73218e9	−	5.13691e9i	0.780082	−	1.07369i	−0.215191	−	0.976572i	$-0.569038\pi$
$263$	3.73218e9	−	5.13691e9i	0.780082	−	1.07369i	0.995273	−	0.0971182i	$-0.0309625\pi$
$264$	−1.49633e9	+	4.09042e9i	−0.308043	+	0.842078i
$265$	−6.77561e8	+	2.06842e9i	−0.137393	+	0.419426i
$266$	−7.19246e9	−	3.30781e9i	−1.43665	−	0.660715i
$267$	−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	$0.785753\pi$
$270$	−5.19892e9	−	6.23172e8i	−0.978269	−	0.117261i
$271$	−2.54495e9	−	8.26904e8i	−0.471848	−	0.153313i	0.0634343	−	0.997986i	$-0.479795\pi$
$271$	−2.54495e9	−	8.26904e8i	−0.471848	−	0.153313i	−0.535282	+	0.844673i	$0.679795\pi$
$272$	3.12577e9	+	6.07971e9i	0.571060	+	1.11073i
$273$	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	$0.427666\pi$
$278$	8.08807e8	+	9.49802e7i	0.135415	+	0.0159021i
$279$	−2.19490e8	−	7.13166e7i	−0.0362241	−	0.0117699i
$280$	−6.10920e9	+	7.75488e9i	−0.993922	+	1.26166i
$281$	−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	0.00175264	−	0.999998i	$-0.499442\pi$
$283$	3.79053e9	−	1.23162e9i	0.590955	−	0.192013i	0.589202	+	0.807986i	$0.299442\pi$
$284$	−3.11456e8	+	1.30782e9i	−0.0478765	+	0.201036i
$285$	6.58722e9	+	1.58040e7i	0.998441	+	0.00239545i
$286$	−7.31417e9	−	6.74878e9i	−1.09320	−	1.00870i
$287$	−5.40793e7	+	7.44338e7i	−0.00797083	+	0.0109709i
$288$	1.83337e8	−	6.85887e7i	0.0266490	−	0.00996971i
$289$	−3.15938e9	+	2.29542e9i	−0.452908	+	0.329057i
$290$	4.12083e9	+	7.38400e9i	0.582630	+	1.04400i
$291$	−4.52993e9	+	6.23491e9i	−0.631712	+	0.869477i
$292$	7.24359e9	+	8.44988e9i	0.996374	+	1.16230i
$293$	−6.08704e9			−0.825915			−0.412958	−	0.910750i	$-0.635504\pi$
$293$	−6.08704e9			−0.825915			−0.412958	+	0.910750i	$0.635504\pi$
$294$	1.04373e10	−	5.85771e9i	1.39701	−	0.784041i
$295$	−5.78306e9	+	7.91968e9i	−0.763607	+	1.04573i
$296$	−1.08725e9	−	3.81510e9i	−0.141633	−	0.496980i
$297$	2.09458e9	−	6.44645e9i	0.269197	−	0.828504i
$298$	1.02955e10	−	1.11580e10i	1.30551	−	1.41488i
$299$		−	9.95806e8i		−	0.124592i
$300$	1.94136e9	−	7.98172e9i	0.239674	−	0.985398i
$301$	8.13596e9			0.991158
$302$	−1.17594e10	−	1.08504e10i	−1.41370	−	1.30442i
$303$	5.68940e9	+	1.84860e9i	0.674988	+	0.219317i
$304$	7.47817e9	−	3.84477e9i	0.875591	−	0.450169i
$305$	1.05252e10	−	7.60848e9i	1.21627	−	0.879222i
$306$	1.52485e8	+	2.71701e8i	0.0173917	+	0.0309888i
$307$			5.19946e9i			0.585336i	0.956214	+	0.292668i	$0.0945430\pi$
$307$			5.19946e9i			0.585336i	−0.956214	+	0.292668i	$0.905457\pi$
$308$	−8.31741e9	−	9.70252e9i	−0.924241	−	1.07816i
$309$	−3.35300e9	−	2.43610e9i	−0.367790	−	0.267215i
$310$	−5.19244e9	+	1.12194e10i	−0.562244	+	1.21485i
$311$	−5.42529e9	−	7.46727e9i	−0.579938	−	0.798216i	0.413751	−	0.910390i	$-0.364219\pi$
$311$	−5.42529e9	−	7.46727e9i	−0.579938	−	0.798216i	−0.993689	+	0.112174i	$0.964219\pi$
$312$	−5.90483e8	+	1.61561e10i	−0.0623144	+	1.70498i
$313$	−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	$0.725490\pi$
$314$	5.98115e9	−	6.48222e9i	0.615270	−	0.666815i
$315$	−2.65338e8	+	3.63370e8i	−0.0269499	+	0.0369068i
$316$	−2.11972e9	+	8.90081e9i	−0.212584	+	0.892650i
$317$	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
$320$	−2.47920e9	−	1.01885e10i	−0.236435	−	0.971647i
$321$	−3.40033e9	+	1.04651e10i	−0.320259	+	0.985654i
$322$	1.49140e8	−	1.27001e9i	0.0138730	−	0.118136i
$323$	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
$328$	−2.67834e7	−	9.39813e7i	−0.00231404	−	0.00811981i
$329$	−4.84672e9	+	1.49167e10i	−0.413680	+	1.27318i
$330$	9.65020e9	+	4.46621e9i	0.813730	+	0.376603i
$331$	2.19328e10	−	7.12640e9i	1.82718	−	0.593688i	0.827713	−	0.561151i	$-0.189641\pi$
$331$	2.19328e10	−	7.12640e9i	1.82718	−	0.593688i	0.999471	−	0.0325367i	$-0.0103586\pi$
$332$	−4.56034e9	−	1.09531e10i	−0.375357	−	0.901536i
$333$	−5.58702e7	−	1.71951e8i	−0.00454364	−	0.0139839i
$334$	−4.99721e9	+	1.08658e10i	−0.401552	+	0.873128i
$335$	1.22107e10	−	3.93514e9i	0.969531	−	0.312450i
$336$	−3.17275e9	+	2.05163e10i	−0.248931	+	1.60969i
$337$	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	$0.585098\pi$
$338$	−2.17032e10	−	9.98132e9i	−1.66287	−	0.764753i
$339$	1.59964e9	+	2.20172e9i	0.121122	+	0.166711i
$340$	1.54231e10	−	6.37809e9i	1.15413	−	0.477282i
$341$	−1.29471e10	−	9.40664e9i	−0.957538	−	0.695692i
$342$	3.34197e8	−	1.87560e8i	0.0244286	−	0.0137100i
$343$			1.28867e10i			0.931034i
$344$	−5.33136e9	+	6.80102e9i	−0.380719	+	0.485669i
$345$	3.26366e8	+	1.01271e9i	0.0230372	+	0.0714842i
$346$	−1.20485e9	+	1.02599e10i	−0.0840675	+	0.715879i
$347$	−2.28853e10	−	7.43587e9i	−1.57848	−	0.512878i	−0.616812	−	0.787110i	$-0.711576\pi$
$347$	−2.28853e10	−	7.43587e9i	−1.57848	−	0.512878i	−0.961663	+	0.274233i	$0.911576\pi$
$348$	1.51787e10	+	9.26346e9i	1.03495	+	0.631621i
$349$	1.42992e10			0.963853			0.481926	−	0.876212i	$-0.339937\pi$
$349$	1.42992e10			0.963853			0.481926	+	0.876212i	$0.339937\pi$
$350$	1.76350e10	+	1.64292e10i	1.17518	+	1.09482i
$351$		−	2.51594e10i		−	1.65757i
$352$	1.35608e10	−	5.94786e8i	0.883313	−	0.0387427i
$353$	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	$-0.208430\pi$
$354$	−2.40514e9	+	2.04810e10i	−0.153154	+	1.30418i
$355$	3.11912e9	+	1.02174e9i	0.196390	+	0.0643322i
$356$	2.29701e9	+	2.67954e9i	0.143009	+	0.166825i
$357$	−3.30435e10			−2.03429
$358$	−9.19891e6	+	5.16267e6i	−0.000560021	+	0.000314298i
$359$	1.57349e10	−	2.16572e10i	0.947294	−	1.30384i	−0.00542468	−	0.999985i	$-0.501727\pi$
$359$	1.57349e10	−	2.16572e10i	0.947294	−	1.30384i	0.952719	−	0.303853i	$-0.0982733\pi$
$360$	−1.29877e8	−	4.59912e8i	−0.00773252	−	0.0273820i
$361$	−4.21668e8	+	3.06360e8i	−0.0248280	+	0.0180386i
$362$	−7.85610e9	−	3.61302e9i	−0.457481	−	0.210396i
$363$	2.25894e9	−	3.10916e9i	0.130100	−	0.179067i
$364$	−4.04906e10	−	2.47111e10i	−2.30647	−	1.40763i
$365$	2.20209e10	−	1.59186e10i	1.24069	−	0.896876i
$366$	1.14113e10	−	2.48125e10i	0.635932	−	1.38276i
$367$	1.93673e10	−	6.29280e9i	1.06759	−	0.346881i	0.278041	−	0.960569i	$-0.410315\pi$
$367$	1.93673e10	−	6.29280e9i	1.06759	−	0.346881i	0.789548	+	0.613689i	$0.210315\pi$
$368$	9.63895e8	+	9.56884e8i	0.0525580	+	0.0521757i
$369$	−1.37631e6	−	4.23584e6i	−7.42353e−5	−	0.000228473i
$370$	−9.50177e9	+	1.87534e9i	−0.506988	+	0.100063i
$371$	−1.27724e10	−	4.15001e9i	−0.674182	−	0.219055i
$372$	2.08703e9	+	2.59135e10i	0.108983	+	1.35318i
$373$	−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
$378$	3.76808e9	−	3.20872e10i	0.184567	−	1.57168i
$379$	1.15893e10	+	3.76560e9i	0.561696	+	0.182506i	0.576084	−	0.817390i	$-0.304580\pi$
$379$	1.15893e10	+	3.76560e9i	0.561696	+	0.182506i	−0.0143881	+	0.999896i	$0.504580\pi$
$380$	−7.84518e9	−	1.89707e10i	−0.376243	−	0.909809i
$381$	−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	−0.569595	−	0.821925i	$-0.692900\pi$
$383$	−1.17764e10	+	3.82640e9i	−0.547292	+	0.177826i	0.0223034	+	0.999751i	$0.492900\pi$
$384$	−1.50710e10	−	1.60962e10i	−0.693133	−	0.740284i
$385$	−2.52854e10	+	1.82784e10i	−1.15087	+	0.831947i
$386$	1.21872e10	−	1.32082e10i	0.548976	−	0.594967i
$387$	−2.31499e8	+	3.18631e8i	−0.0103206	+	0.0142051i
$388$	2.33645e10	+	5.56424e9i	1.03093	+	0.245515i
$389$	−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	$0.441806\pi$
$390$	3.91894e10	+	4.69746e9i	1.69399	+	0.203051i
$391$	−1.27069e9	+	1.74895e9i	−0.0543664	+	0.0748290i
$392$	−2.93556e10	−	2.30121e10i	−1.24322	−	0.974566i
$393$	7.68719e9			0.322253
$394$	−7.07344e9	−	1.26035e10i	−0.293525	−	0.523007i
$395$	2.12283e10	+	6.95384e9i	0.872020	+	0.285651i
$396$	6.16644e8	−	4.96635e7i	0.0250757	−	0.00201956i
$397$	−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	$0.995465\pi$
$398$	2.28454e10	+	2.10794e10i	0.910471	+	0.840091i
$399$			4.06441e10i			1.60364i
$400$	−2.52894e10	+	3.97569e9i	−0.987867	+	0.155300i
$401$	−3.85050e10			−1.48915			−0.744577	−	0.667537i	$-0.767349\pi$
$401$	−3.85050e10			−1.48915			−0.744577	+	0.667537i	$0.767349\pi$
$402$	1.82948e10	−	1.98275e10i	0.700525	−	0.759212i
$403$	−5.64948e10	−	1.83563e10i	−2.14185	−	0.695928i
$404$	−1.49665e9	−	1.85831e10i	−0.0561819	−	0.697579i
$405$	8.48057e9	+	2.63152e10i	0.315213	+	0.978106i
$406$	−4.54991e10	+	2.55353e10i	−1.67455	+	0.939803i
$407$		−	1.25373e10i		−	0.456907i
$408$	2.16528e10	−	2.76217e10i	0.781402	−	0.996804i
$409$	−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	$0.783495\pi$
$410$	−2.34067e8	+	4.61971e7i	−0.00828332	+	0.00163486i
$411$	1.34402e10	+	1.84989e10i	0.471019	+	0.648302i
$412$	−2.99233e9	+	1.25649e10i	−0.103853	+	0.436085i
$413$	−4.89509e10	−	3.55649e10i	−1.68252	−	1.22242i
$414$	4.54940e7	+	4.19773e7i	0.00154865	+	0.00142894i
$415$	−2.75697e10	+	8.88488e9i	−0.929480	+	0.299543i
$416$	4.71894e10	−	1.76541e10i	1.57569	−	0.589485i
$417$	−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	0.284054	−	0.958808i	$-0.408321\pi$
$419$	3.32082e10	−	1.07900e10i	1.07743	−	0.350079i	0.793378	+	0.608730i	$0.208321\pi$
$420$	4.92769e10	+	1.18603e10i	1.58360	+	0.381151i
$421$	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	$-0.0585318\pi$
$422$	−4.23788e10	−	4.97665e9i	−1.33628	−	0.156923i
$423$	−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
$428$	3.41820e10	−	2.75296e9i	1.01864	−	0.0820398i
$429$	−1.57889e10	+	4.85932e10i	−0.466147	+	1.43465i
$430$	1.54712e10	+	1.43441e10i	0.452532	+	0.419566i
$431$	−4.81881e9	+	1.56573e9i	−0.139647	+	0.0453740i	−0.378006	−	0.925803i	$-0.623390\pi$
$431$	−4.81881e9	+	1.56573e9i	−0.139647	+	0.0453740i	0.238360	+	0.971177i	$0.423390\pi$
$432$	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	$0.726519\pi$
$434$	−6.93017e10	−	3.18719e10i	−1.95337	−	0.898357i
$435$	2.56020e10	−	3.50609e10i	0.715017	−	0.979188i
$436$	−1.44825e10	+	2.37303e10i	−0.400771	+	0.656687i
$437$	2.15124e9	+	1.56297e9i	0.0589880	+	0.0428573i
$438$	2.38749e10	−	5.19131e10i	0.648701	−	1.41052i
$439$	−3.74964e10	−	5.16093e10i	−1.00956	−	1.38954i	−0.919273	−	0.393621i	$-0.871222\pi$
$439$	−3.74964e10	−	5.16093e10i	−1.00956	−	1.38954i	−0.0902851	−	0.995916i	$-0.528778\pi$
$440$	1.28984e9	−	3.31142e10i	0.0344131	−	0.883493i
$441$	−1.37532e9	−	9.99231e8i	−0.0363622	−	0.0264187i
$442$	3.92484e10	+	6.99333e10i	1.02833	+	1.83229i
$443$		−	3.50607e10i		−	0.910344i	−0.890403	−	0.455172i	$-0.849578\pi$
$443$		−	3.50607e10i		−	0.910344i	0.890403	−	0.455172i	$-0.150422\pi$
$444$	−1.54628e10	+	1.32553e10i	−0.397883	+	0.341082i
$445$	6.98305e9	−	5.04793e9i	0.178076	−	0.128728i
$446$	−1.11574e10	−	1.31025e9i	−0.281984	−	0.0331142i
$447$	−7.41303e10	−	2.40864e10i	−1.85680	−	0.603312i
$448$	6.28273e10	−	1.54478e10i	1.55968	−	0.383490i
$449$	−1.31680e10			−0.323992			−0.161996	−	0.986791i	$-0.551793\pi$
$449$	−1.31680e10			−0.323992			−0.161996	+	0.986791i	$0.551793\pi$
$450$	−1.14520e9	+	2.23172e8i	−0.0279275	+	0.00544239i
$451$		−	3.08845e8i		−	0.00746508i
$452$	4.41831e9	−	7.23965e9i	0.105853	−	0.173446i
$453$	−2.53847e10	+	7.81261e10i	−0.602808	+	1.85525i
$454$	−2.72068e10	−	3.19497e9i	−0.640405	−	0.0752044i
$455$	−6.82956e10	+	9.35282e10i	−1.59348	+	2.18221i
$456$	−3.39753e10	−	2.66334e10i	−0.785784	−	0.615982i
$457$	−1.40284e10			−0.321621			−0.160811	−	0.986985i	$-0.551411\pi$
$457$	−1.40284e10			−0.321621			−0.160811	+	0.986985i	$0.551411\pi$
$458$	4.08400e10	+	7.27693e10i	0.928163	+	1.65381i
$459$	−3.21043e10	+	4.41878e10i	−0.723291	+	0.995524i
$460$	2.52269e9	−	2.15208e9i	0.0563420	−	0.0480647i
$461$	−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	$0.371016\pi$
$462$	−2.74142e10	+	5.96089e10i	−0.601738	+	1.30841i
$463$	1.21615e10	−	1.67389e10i	0.264646	−	0.364253i	−0.655927	−	0.754824i	$-0.727722\pi$
$463$	1.21615e10	−	1.67389e10i	0.264646	−	0.364253i	0.920573	+	0.390571i	$0.127722\pi$
$464$	8.46936e9	−	5.47665e10i	0.182717	−	1.18153i
$465$	6.34700e10	+	1.52277e8i	1.35755	+	0.00325703i
$466$	−3.17679e10	−	1.46101e10i	−0.673666	−	0.309819i
$467$	6.02584e10	−	1.95791e10i	1.26692	−	0.411648i	0.402967	−	0.915215i	$-0.367979\pi$
$467$	6.02584e10	−	1.95791e10i	1.26692	−	0.411648i	0.863956	+	0.503566i	$0.167979\pi$
$468$	2.11988e9	−	8.82618e8i	0.0441904	−	0.0183988i
$469$	2.44610e10	+	7.52832e10i	0.505572	+	1.55599i
$470$	−3.55153e10	+	1.98202e10i	−0.727820	+	0.406179i
$471$	−4.30660e10	−	1.39930e10i	−0.875087	−	0.284333i
$472$	6.18062e10	−	1.76140e10i	1.24527	−	0.354886i
$473$	−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
$478$	3.06230e10	+	3.59613e9i	0.586591	+	0.0688849i
$479$	8.39320e10	+	2.72712e10i	1.59436	+	0.518038i	0.965703	−	0.259648i	$-0.0836064\pi$
$479$	8.39320e10	+	2.72712e10i	1.59436	+	0.518038i	0.628653	+	0.777686i	$0.283606\pi$
$480$	−4.22046e10	+	3.34197e10i	−0.795051	+	0.629561i
$481$	−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
$484$	−1.16512e10	−	2.77472e9i	−0.212319	−	0.0505635i
$485$	1.82537e10	−	5.57239e10i	0.329902	−	1.00710i
$486$	2.33251e9	+	2.15220e9i	0.0418098	+	0.0385779i
$487$	4.82525e10	−	6.64139e10i	0.857836	−	1.18071i	−0.124245	−	0.992252i	$-0.539651\pi$
$487$	4.82525e10	−	6.64139e10i	0.857836	−	1.18071i	0.982081	−	0.188458i	$-0.0603490\pi$
$488$	−8.50564e10	−	3.10869e9i	−1.49978	−	0.0548149i
$489$	3.54464e10	−	2.57533e10i	0.619922	−	0.450400i
$490$	−6.19144e10	+	6.67791e10i	−1.07401	+	1.15839i
$491$	6.08277e10	−	8.37221e10i	1.04659	−	1.44050i	0.154856	−	0.987937i	$-0.450509\pi$
$491$	6.08277e10	−	8.37221e10i	1.04659	−	1.44050i	0.891731	−	0.452566i	$-0.149491\pi$
$492$	−3.80910e8	+	3.26532e8i	−0.00650073	+	0.00557270i
$493$	8.82065e10			1.49318
$494$	8.60194e10	−	4.82763e10i	1.44440	−	0.810637i
$495$	3.62361e6	−	1.51035e9i	6.03561e−5	−	0.0251569i
$496$	7.20547e10	−	3.70456e10i	1.19052	−	0.612083i
$497$	−6.25810e9	+	1.92605e10i	−0.102569	+	0.315676i
$498$	−4.13066e10	+	4.47671e10i	−0.671587	+	0.727850i
$499$		−	8.03299e10i		−	1.29561i	−0.761805	−	0.647806i	$-0.775687\pi$
$499$		−	8.03299e10i		−	1.29561i	0.761805	−	0.647806i	$-0.224313\pi$
$500$	4.56888e9	+	6.23328e10i	0.0731021	+	0.997324i
$501$	6.14022e10			0.974615
$502$	9.91754e9	+	9.15091e9i	0.156167	+	0.144095i
$503$	−3.48292e10	−	1.13167e10i	−0.544091	−	0.176786i	0.0240595	−	0.999711i	$-0.492341\pi$
$503$	−3.48292e10	−	1.13167e10i	−0.544091	−	0.176786i	−0.568151	+	0.822925i	$0.692341\pi$
$504$	2.83579e9	−	8.08162e8i	0.0439492	−	0.0125250i
$505$	−4.55158e10	−	1.09201e8i	−0.699836	−	0.00167904i
$506$	2.10081e9	+	3.74326e9i	0.0320469	+	0.0571015i
$507$			1.22644e11i			1.85615i
$508$	−7.01238e10	+	6.01131e10i	−1.05296	+	0.902639i
$509$	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	$0.498491\pi$
$510$	−6.28348e10	−	5.82573e10i	−0.928794	−	0.861132i
$511$	9.85454e10	+	1.35636e11i	1.44528	+	1.98926i
$512$	−2.82566e10	+	6.26413e10i	−0.411187	+	0.911551i
$513$	5.43519e10	+	3.94890e10i	0.784775	+	0.570173i
$514$	−6.56900e10	+	7.11933e10i	−0.941125	+	1.01997i
$515$	2.99672e10	+	9.81647e9i	0.426007	+	0.139549i
$516$	4.31591e10	+	1.02783e10i	0.608799	+	0.144985i
$517$	−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
$520$	−3.34291e10	−	1.18377e11i	−0.457205	−	1.61903i
$521$	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	$-0.0109251\pi$
$522$	2.94576e8	−	2.50847e9i	0.00396748	−	0.0337852i
$523$	−2.83003e10	−	3.89521e10i	−0.378255	−	0.520623i	0.576866	−	0.816839i	$-0.304275\pi$
$523$	−2.83003e10	−	3.89521e10i	−0.378255	−	0.520623i	−0.955121	+	0.296215i	$0.904275\pi$
$524$	−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
$528$	−3.18643e10	−	6.19769e10i	−0.409985	−	0.797432i
$529$	2.40667e10	−	7.40697e10i	0.307322	−	0.945840i
$530$	−1.69711e10	−	3.04100e10i	−0.215083	−	0.385401i
$531$	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
$534$	7.57095e9	−	1.64622e10i	0.0931076	−	0.202452i
$535$	2.00865e8	−	8.37221e10i	0.00245182	−	1.02194i
$536$	−7.89597e10	−	2.88844e10i	−0.956635	−	0.349949i
$537$	4.38137e7	+	3.18325e7i	0.000526881	+	0.000382802i
$538$	−5.34720e10	−	2.45918e10i	−0.638260	−	0.293536i
$539$	−6.92904e10	−	9.53701e10i	−0.820953	−	1.12994i
$540$	6.37367e10	−	5.43730e10i	0.749574	−	0.639453i
$541$	−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	$0.855042\pi$
$542$	3.73365e10	−	2.09542e10i	0.432650	−	0.242815i
$543$			4.43943e10i			0.510656i
$544$	−1.05407e11	−	2.92092e10i	−1.20357	−	0.333522i
$545$	5.48141e10	+	4.00261e10i	0.621307	+	0.453687i
$546$	−2.84037e10	+	2.41873e11i	−0.319599	+	2.72155i
$547$	−2.85956e10	−	9.29129e9i	−0.319411	−	0.103783i	0.144923	−	0.989443i	$-0.453706\pi$
$547$	−2.85956e10	−	9.29129e9i	−0.319411	−	0.103783i	−0.464335	+	0.885660i	$0.653706\pi$
$548$	3.71227e10	−	6.08276e10i	0.411639	−	0.674494i
$549$	−3.87912e9			−0.0427015
$550$	−8.03080e10	−	9.82167e9i	−0.877624	−	0.107333i
$551$		−	1.08496e11i		−	1.17708i
$552$	2.39557e9	−	6.54864e9i	0.0258020	−	0.0705334i
$553$	−4.25917e10	+	1.31084e11i	−0.455433	+	1.40168i
$554$	8.57832e9	−	7.30489e10i	0.0910674	−	0.775487i
$555$	2.91300e10	+	4.02970e10i	0.307022	+	0.424718i
$556$	−9.89250e9	+	8.48027e9i	−0.103516	+	0.0887381i
$557$	−5.53831e9			−0.0575382			−0.0287691	−	0.999586i	$-0.509159\pi$
$557$	−5.53831e9			−0.0575382			−0.0287691	+	0.999586i	$0.509159\pi$
$558$	3.22010e9	−	1.80721e9i	0.0332149	−	0.0186411i
$559$	−5.95857e10	+	8.20127e10i	−0.610232	+	0.839912i
$560$	−2.49048e10	−	1.55980e11i	−0.253239	−	1.58605i
$561$	8.97370e10	−	6.51977e10i	0.905983	−	0.658235i
$562$	2.22212e10	+	1.02196e10i	0.222753	+	0.102444i
$563$	−2.16888e10	+	2.98521e10i	−0.215875	+	0.297127i	−0.903197	−	0.429226i	$-0.858786\pi$
$563$	−2.16888e10	+	2.98521e10i	−0.215875	+	0.297127i	0.687322	+	0.726353i	$0.258786\pi$
$564$	−4.45551e10	+	7.30061e10i	−0.440333	+	0.721510i
$565$	−1.67227e10	−	1.22111e10i	−0.164101	−	0.119829i
$566$	−2.66449e10	+	5.79363e10i	−0.259626	+	0.564527i
$567$	−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	$0.839115\pi$
$570$	−7.16577e10	+	7.72880e10i	−0.678834	+	0.732172i
$571$	2.84311e10	+	9.23783e9i	0.267454	+	0.0869012i	0.439674	−	0.898157i	$-0.355094\pi$
$571$	2.84311e10	+	9.23783e9i	0.267454	+	0.0869012i	−0.172220	+	0.985059i	$0.555094\pi$
$572$	1.58719e11	−	1.27829e10i	1.48267	−	0.119412i
$573$	−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	$0.440770\pi$
$578$	7.28750e9	−	6.20569e10i	0.0652931	−	0.556005i
$579$	−8.77512e10	−	2.85121e10i	−0.780798	−	0.253697i
$580$	−1.31540e11	−	3.16599e10i	−1.16238	−	0.279768i
$581$	−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
$584$	−1.77956e11	−	6.50405e9i	−1.52990	−	0.0559155i
$585$	−1.71960e9	−	5.33591e9i	−0.0146826	−	0.0455601i
$586$	6.60449e10	−	7.15779e10i	0.560078	−	0.607000i
$587$	−1.23108e10	+	1.69444e10i	−0.103689	+	0.142716i	−0.857709	−	0.514136i	$-0.828113\pi$
$587$	−1.23108e10	+	1.69444e10i	−0.103689	+	0.142716i	0.754019	+	0.656852i	$0.228113\pi$
$588$	−4.43649e10	+	1.86290e11i	−0.371133	+	1.55841i
$589$	1.28327e11	−	9.32347e10i	1.06624	−	0.774669i
$590$	−3.03813e10	−	1.53933e11i	−0.250725	−	1.27035i
$591$	−4.36141e10	+	6.00297e10i	−0.357501	+	0.492058i
$592$	5.66588e10	+	2.86091e10i	0.461297	+	0.232926i
$593$	−9.16511e10			−0.741172			−0.370586	−	0.928798i	$-0.620843\pi$
$593$	−9.16511e10			−0.741172			−0.370586	+	0.928798i	$0.620843\pi$
$594$	5.30778e10	+	9.45748e10i	0.426351	+	0.759678i
$595$	2.39294e11	−	7.71171e10i	1.90925	−	0.615294i
$596$	1.95007e10	+	2.42130e11i	0.154549	+	1.91895i
$597$	4.93157e10	−	1.51778e11i	0.388229	−	1.19485i
$598$	1.17097e10	+	1.08046e10i	0.0915678	+	0.0844896i
$599$			1.50463e11i			1.16875i	0.811482	+	0.584377i	$0.198661\pi$
$599$			1.50463e11i			1.16875i	−0.811482	+	0.584377i	$0.801339\pi$
$600$	7.27937e10	+	1.09431e11i	0.561680	+	0.844375i
$601$	2.42713e11			1.86035			0.930175	−	0.367117i	$-0.119655\pi$
$601$	2.42713e11			1.86035			0.930175	+	0.367117i	$0.119655\pi$
$602$	−8.82759e10	+	9.56713e10i	−0.672134	+	0.728443i
$603$	−3.64434e9	−	1.18412e9i	−0.0275645	−	0.00895625i
$604$	2.55181e11	−	2.05519e10i	1.91735	−	0.154420i
$605$	−9.10258e9	+	2.77878e10i	−0.0679427	+	0.207412i
$606$	−8.34683e10	+	4.68446e10i	−0.618915	+	0.347351i
$607$		−	1.78077e11i		−	1.31176i	−0.754866	−	0.655879i	$-0.772298\pi$
$607$		−	1.78077e11i		−	1.31176i	0.754866	−	0.655879i	$-0.227702\pi$
$608$	−3.59280e10	+	1.29652e11i	−0.262917	+	0.948781i
$609$	2.16709e11	+	1.57448e11i	1.57546	+	1.14464i
$610$	−2.47306e10	+	2.06319e11i	−0.178614	+	1.49012i
$611$	−1.14868e11	−	1.58102e11i	−0.824203	−	1.13442i
$612$	−4.84943e9	−	1.15489e9i	−0.0345688	−	0.00823254i
$613$	−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	$0.706705\pi$
$614$	−6.11408e10	−	5.64146e10i	−0.430188	−	0.396934i
$615$	7.17589e8	+	9.92677e8i	0.00501621	+	0.00693917i
$616$	2.04337e11	+	7.46824e9i	1.41914	+	0.0518675i
$617$	−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	−0.670755	−	0.741679i	$-0.734030\pi$
$619$	−1.14141e11	+	3.70866e10i	−0.777460	+	0.252612i	−0.106705	+	0.994291i	$0.534030\pi$
$620$	−7.55910e10	−	1.82790e11i	−0.511568	−	1.23704i
$621$	−3.35335e9	+	1.03206e10i	−0.0225482	+	0.0693963i
$622$	1.46673e11	+	1.72242e10i	0.979916	+	0.115074i
$623$	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
$628$	1.13290e10	+	1.40665e11i	0.0728369	+	0.904375i
$629$	−3.12190e10	+	9.60821e10i	−0.199442	+	0.613819i
$630$	−1.39395e9	−	7.06272e9i	−0.00884881	−	0.0448342i
$631$	1.17899e11	−	3.83077e10i	0.743692	−	0.241640i	0.0874271	−	0.996171i	$-0.472136\pi$
$631$	1.17899e11	−	3.83077e10i	0.743692	−	0.241640i	0.656265	+	0.754531i	$0.272136\pi$
$632$	−8.16660e10	−	1.21500e11i	−0.511886	−	0.761570i
$633$	6.76958e10	+	2.08346e11i	0.421645	+	1.29769i
$634$	−6.25361e10	−	2.87604e10i	−0.387056	−	0.178007i
$635$	1.32105e11	+	1.82747e11i	0.812502	+	1.12397i
$636$	−6.25115e10	−	3.81503e10i	−0.382060	−	0.233169i
$637$	−3.53996e11	−	2.57193e11i	−2.15001	−	1.56207i
$638$	7.31797e10	−	1.59121e11i	0.441680	−	0.960382i
$639$	−5.76236e8	−	7.93120e8i	−0.00345618	−	0.00475703i
$640$	1.46706e11	+	8.13926e10i	0.874438	+	0.485137i
$641$	−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	$0.759574\pi$
$642$	−8.61663e10	−	1.53532e11i	−0.507221	−	0.903773i
$643$			2.40176e11i			1.40503i	0.711670	+	0.702514i	$0.247939\pi$
$643$			2.40176e11i			1.40503i	−0.711670	+	0.702514i	$0.752061\pi$
$644$	1.33159e10	+	1.55334e10i	0.0774154	+	0.0903075i
$645$	3.37185e10	−	1.02934e11i	0.194818	−	0.594729i
$646$	−2.12679e11	−	2.49755e10i	−1.22122	−	0.143412i
$647$	4.43103e10	+	1.43973e10i	0.252865	+	0.0821607i	0.432706	−	0.901535i	$-0.357559\pi$
$647$	4.43103e10	+	1.43973e10i	0.252865	+	0.0821607i	−0.179842	+	0.983696i	$0.557559\pi$
$648$	6.22485e10	−	1.70165e11i	0.353044	−	0.965096i
$649$	2.03110e11			1.14486
$650$	−2.94765e11	+	5.74425e10i	−1.65128	+	0.321796i
$651$			3.91620e11i			2.18042i
$652$	−1.16554e11	−	7.11322e10i	−0.644967	−	0.393619i
$653$	−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	$0.106695\pi$
$654$	1.41754e11	+	1.66466e10i	0.774864	+	0.0909943i
$655$	−5.56691e10	+	1.79404e10i	−0.302447	+	0.0974693i
$656$	1.39573e9	+	7.04757e8i	0.00753681	+	0.00380561i
$657$	−8.11594e9			−0.0435589
$658$	−1.22819e11	−	2.18840e11i	−0.655181	−	1.16741i
$659$	−8.75185e10	+	1.20459e11i	−0.464043	+	0.638701i	−0.975341	−	0.220703i	$-0.929165\pi$
$659$	−8.75185e10	+	1.20459e11i	−0.464043	+	0.638701i	0.511298	+	0.859404i	$0.329165\pi$
$660$	−1.57224e11	+	6.50186e10i	−0.828596	+	0.342659i
$661$	−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	$0.333861\pi$
$662$	−1.54173e11	+	3.35231e11i	−0.802743	+	1.74547i
$663$	2.42002e11	−	3.33087e11i	1.25246	−	1.72387i
$664$	1.78278e11	+	6.52162e10i	0.917117	+	0.335493i
$665$	−9.48556e10	−	2.94336e11i	−0.485039	−	1.50507i
$666$	2.62818e9	+	1.20870e9i	0.0133585	+	0.00614358i
$667$	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
$670$	−8.62137e10	+	1.86283e11i	−0.427836	+	0.924431i
$671$	−2.55827e11	−	8.31232e10i	−1.26199	−	0.410046i
$672$	−2.06828e11	−	2.59912e11i	−1.01422	−	1.27453i
$673$	−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	$0.361035\pi$
$678$	−4.32464e10	−	5.07854e9i	−0.204659	−	0.0240337i
$679$	3.44093e11	+	1.11803e11i	1.61881	+	0.525984i
$680$	−9.23418e10	+	2.50564e11i	−0.431879	+	1.17188i
$681$	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	−0.818935	−	0.573886i	$-0.805435\pi$
$683$	−2.48980e11	+	8.08984e10i	−1.14415	+	0.371755i	−0.325210	+	0.945642i	$0.605435\pi$
$684$	−1.42054e9	+	5.96489e9i	−0.00648974	+	0.0272507i
$685$	−1.40504e11	−	1.02598e11i	−0.638156	−	0.465990i
$686$	−1.51536e11	−	1.39822e11i	−0.684256	−	0.631363i
$687$	2.51816e11	−	3.46595e11i	1.13046	−	1.55595i
$688$	−2.21278e10	−	1.36483e11i	−0.0987609	−	0.609153i
$689$	1.35375e11	−	9.83558e10i	0.600706	−	0.436439i
$690$	−1.54497e10	−	7.15026e9i	−0.0681589	−	0.0315446i
$691$	−1.40308e11	+	1.93117e11i	−0.615417	+	0.847050i	−0.997009	−	0.0772814i	$-0.975376\pi$
$691$	−1.40308e11	+	1.93117e11i	−0.615417	+	0.847050i	0.381592	+	0.924331i	$0.375376\pi$
$692$	−1.07574e11	−	1.25489e11i	−0.469121	−	0.547244i
$693$	9.31908e9			0.0404055
$694$	3.35746e11	−	1.88429e11i	1.44735	−	0.812289i
$695$	1.86363e10	+	2.57805e10i	0.0798768	+	0.110497i
$696$	−2.73620e11	+	7.79781e10i	−1.16603	+	0.332304i
$697$	−7.69049e8	+	2.36689e9i	−0.00325854	+	0.0100287i
$698$	−1.55148e11	+	1.68146e11i	−0.653618	+	0.708376i
$699$			1.79518e11i			0.751969i
$700$	−3.84533e11	+	2.91132e10i	−1.60155	+	0.121255i
$701$	1.26058e11			0.522035			0.261017	−	0.965334i	$-0.415942\pi$
$701$	1.26058e11			0.522035			0.261017	+	0.965334i	$0.415942\pi$
$702$	2.95851e11	+	2.72982e11i	1.21822	+	1.12405i
$703$	1.18183e11	+	3.84000e10i	0.483875	+	0.157221i
$704$	−1.40142e11	+	1.65916e11i	−0.570528	+	0.675456i
$705$	1.68635e11	+	1.23140e11i	0.682638	+	0.498473i
$706$	2.00453e11	+	3.57170e11i	0.806852	+	1.43766i
$707$		−	2.80839e11i		−	1.12404i
$708$	−2.14742e11	−	2.50503e11i	−0.854641	−	0.996966i
$709$	−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	$0.960627\pi$
$710$	−4.58575e10	+	2.55919e10i	−0.180458	+	0.100709i
$711$	−3.92177e9	−	5.39786e9i	−0.0153463	−	0.0211224i
$712$	−5.64317e10	−	2.06250e9i	−0.219585	−	0.00802552i
$713$	2.07279e10	+	1.50597e10i	0.0802043	+	0.0582719i
$714$	3.58524e11	−	3.88560e11i	1.37951	−	1.49508i
$715$	9.32686e8	−	3.88750e11i	0.00356871	−	1.48746i
$716$	3.91008e7	−	1.64186e8i	0.000148776	−	0.000624718i
$717$	−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	−0.490279	−	0.871566i	$-0.663105\pi$
$719$	−1.00119e11	+	3.25307e10i	−0.374629	+	0.121724i	0.115649	+	0.993290i	$0.463105\pi$
$720$	6.81731e9	+	3.46286e9i	0.0253678	+	0.0128856i
$721$	−6.01251e10	+	1.85046e11i	−0.222492	+	0.684761i
$722$	9.72629e8	−	8.28245e9i	0.00357930	−	0.0304796i
$723$	−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	$-0.923235\pi$
$727$	−2.50887e11	−	3.45316e11i	−0.898131	−	1.23617i	0.0729294	−	0.997337i	$-0.476765\pi$
$728$	7.29906e11	−	2.08014e11i	2.59861	−	0.740570i
$729$	−8.46530e10	+	2.60535e11i	−0.299731	+	0.922478i
$730$	−5.17416e10	+	4.31664e11i	−0.182200	+	1.52004i
$731$	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	$0.698075\pi$
$734$	−1.36139e11	+	2.96018e11i	−0.469027	+	1.01985i
$735$	4.44299e11	+	1.45541e11i	1.52239	+	0.498696i
$736$	−2.17104e10	+	9.52233e8i	−0.0739873	+	0.00324513i
$737$	−2.14970e11	−	1.56185e11i	−0.728632	−	0.529382i
$738$	6.47426e7	+	2.97751e7i	0.000218255	+	0.000100376i
$739$	−7.51422e10	−	1.03424e11i	−0.251945	−	0.346773i	0.664246	−	0.747514i	$-0.268753\pi$
$739$	−7.51422e10	−	1.03424e11i	−0.251945	−	0.346773i	−0.916191	+	0.400741i	$0.868753\pi$
$740$	8.10428e10	−	1.32080e11i	0.270264	−	0.440462i
$741$	−4.09704e11	−	2.97667e11i	−1.35893	−	0.987321i
$742$	1.87382e11	−	1.05164e11i	0.618176	−	0.346937i
$743$			3.98250e11i			1.30677i	0.757024	+	0.653387i	$0.226652\pi$
$743$			3.98250e11i			1.30677i	−0.757024	+	0.653387i	$0.773348\pi$
$744$	−3.27363e11	−	2.56622e11i	−1.06841	−	0.837534i
$745$	5.93050e11	+	1.42284e9i	1.92516	+	0.00461882i
$746$	2.69396e10	−	2.29405e11i	0.0869834	−	0.740709i
$747$	8.22832e9	+	2.67354e9i	0.0264258	+	0.00858627i
$748$	−2.95071e11	−	1.80080e11i	−0.942585	−	0.575253i
$749$	5.16578e11			1.64138
$750$	2.80943e11	−	1.55024e11i	0.887918	−	0.489953i
$751$			3.63920e11i			1.14405i	0.820235	+	0.572026i	$0.193843\pi$
$751$			3.63920e11i			1.14405i	−0.820235	+	0.572026i	$0.806157\pi$
$752$	2.63414e11	+	4.07357e10i	0.823698	+	0.127381i
$753$	2.14087e10	−	6.58893e10i	0.0665903	−	0.204944i
$754$	7.58212e10	−	6.45657e11i	0.234588	−	1.99764i
$755$	1.49953e9	−	6.25016e11i	0.00461496	−	1.92355i
$756$	3.36431e11	+	3.92458e11i	1.02993	+	1.20145i
$757$	−4.94057e11			−1.50450			−0.752252	−	0.658876i	$-0.771032\pi$
$757$	−4.94057e11			−1.50450			−0.752252	+	0.658876i	$0.771032\pi$
$758$	−1.70025e11	+	9.54226e10i	−0.515034	+	0.289051i
$759$	1.29534e10	−	1.78289e10i	0.0390317	−	0.0537225i
$760$	3.08199e11	+	1.13582e11i	0.923798	+	0.340452i
$761$	−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	$0.311171\pi$
$762$	4.30817e11	+	1.98133e11i	1.27783	+	0.587674i
$763$	−2.46154e11	+	3.38802e11i	−0.726288	+	0.999649i
$764$	5.25594e11	+	3.20766e11i	1.54268	+	0.941490i
$765$	−3.78866e9	+	1.15658e10i	−0.0110622	+	0.0337699i
$766$	8.27805e10	−	1.79997e11i	0.240444	−	0.522817i
$767$	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	$0.742002\pi$
$770$	5.94120e10	−	4.95655e11i	0.169010	−	1.40999i
$771$	4.72988e11	+	1.53683e11i	1.33854	+	0.434919i
$772$	2.30838e10	+	2.86619e11i	0.0649889	+	0.806931i
$773$	−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
$778$	3.68253e10	−	3.13587e11i	0.100514	−	0.855932i
$779$	2.91132e9	+	9.45946e8i	0.00790570	+	0.00256872i
$780$	−4.80446e11	+	4.09863e11i	−1.29797	+	1.10729i
$781$	−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
$784$	5.89111e11	−	9.55116e10i	1.55931	−	0.252809i
$785$	3.44532e11	+	8.26598e8i	0.907301	+	0.00217679i
$786$	−8.34067e10	+	9.03942e10i	−0.218530	+	0.236837i
$787$	−3.63388e11	+	5.00160e11i	−0.947265	+	1.30380i	0.00546702	+	0.999985i	$0.498260\pi$
$787$	−3.63388e11	+	5.00160e11i	−0.947265	+	1.30380i	−0.952732	+	0.303813i	$0.901740\pi$
$788$	2.24953e11	+	5.35725e10i	0.583428	+	0.138943i
$789$	4.21968e11	−	3.06577e11i	1.08886	−	0.791101i
$790$	−3.12099e11	+	1.74175e11i	−0.801280	+	0.447175i
$791$	7.50966e10	−	1.03362e11i	0.191829	−	0.264030i
$792$	−6.10664e9	+	7.79001e9i	−0.0155204	+	0.0197987i
$793$	−9.98450e11			−2.52484
$794$	−1.25478e11	−	2.23579e11i	−0.315708	−	0.562533i
$795$	−1.05438e11	+	1.44394e11i	−0.263955	+	0.361476i
$796$	−4.95749e11	+	3.99268e10i	−1.23484	+	0.0994516i
$797$	−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	$0.180666\pi$
$798$	−4.77937e11	−	4.40992e11i	−1.17858	−	1.08748i
$799$			4.24253e11i			1.04097i
$800$	2.27642e11	−	3.40516e11i	0.555766	−	0.831339i
$801$	−2.57364e9			−0.00625199
$802$	4.17782e11	−	4.52783e11i	1.00984	−	1.09444i
$803$	−5.35245e11	−	1.73912e11i	−1.28733	−	0.418279i
$804$	3.46524e10	+	4.30260e11i	0.0829295	+	1.02969i
$805$	4.04812e10	−	2.92631e10i	0.0963983	−	0.0696847i
$806$	8.28826e11	−	4.65159e11i	1.96392	−	1.10220i
$807$			3.02167e11i			0.712447i
$808$	2.34759e11	+	1.84029e11i	0.550779	+	0.431759i
$809$	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	$0.461856\pi$
$810$	−4.01457e11	−	1.85798e11i	−0.932607	−	0.431620i
$811$	−7.72685e10	−	1.06351e11i	−0.178615	−	0.245843i	0.710316	−	0.703882i	$-0.248552\pi$
$811$	−7.72685e10	−	1.06351e11i	−0.178615	−	0.245843i	−0.888932	+	0.458039i	$0.848552\pi$
$812$	1.93398e11	−	8.12087e11i	0.444865	−	1.86801i
$813$	−1.77831e11	−	1.29202e11i	−0.407048	−	0.295738i
$814$	1.47427e11	+	1.36031e11i	0.335800	+	0.309843i
$815$	−1.96592e11	+	2.69226e11i	−0.445591	+	0.610219i
$816$	8.98702e10	+	5.54315e11i	0.202701	+	1.25025i
$817$	−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
$820$	1.99641e9	−	3.25365e9i	0.00441564	−	0.00719640i
$821$	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	$0.0688720\pi$
$822$	−3.63357e11	−	4.26699e10i	−0.795877	−	0.0934619i
$823$	6.17207e10	+	8.49512e10i	0.134534	+	0.185170i	0.870969	−	0.491339i	$-0.163492\pi$
$823$	6.17207e10	+	8.49512e10i	0.134534	+	0.185170i	−0.736435	+	0.676508i	$0.763492\pi$
$824$	−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	0.903869	−	0.427809i	$-0.140714\pi$
$827$	1.01826e11	+	1.40151e11i	0.217688	+	0.299622i	−0.686181	+	0.727431i	$0.740714\pi$
$828$	−9.87227e8	+	7.95096e7i	−0.00210037	+	0.000169160i
$829$	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	$0.0739218\pi$
$830$	1.94656e11	−	4.20596e11i	0.410162	−	0.886243i
$831$	−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
$834$	6.07761e10	+	2.79509e10i	0.125623	+	0.0577740i
$835$	−4.44662e11	+	1.43301e11i	−0.914712	+	0.294784i
$836$	−2.21502e11	+	3.62944e11i	−0.453474	+	0.743043i
$837$	5.23699e11	+	3.80489e11i	1.06704	+	0.775248i
$838$	−2.33432e11	+	5.07570e11i	−0.473352	+	1.02925i
$839$	−3.42884e9	−	4.71939e9i	−0.00691989	−	0.00952441i	0.805543	−	0.592537i	$-0.201874\pi$
$839$	−3.42884e9	−	4.71939e9i	−0.00691989	−	0.00952441i	−0.812463	+	0.583013i	$0.801874\pi$
$840$	−6.74124e11	+	4.50765e11i	−1.35401	+	0.905385i
$841$	−1.73777e11	−	1.26256e11i	−0.347382	−	0.252388i
$842$	2.35028e11	+	4.18775e11i	0.467596	+	0.833168i
$843$		−	1.25571e11i		−	0.248644i
$844$	5.18334e11	−	4.44338e11i	1.02150	−	0.875676i
$845$	−2.86227e11	−	8.88160e11i	−0.561414	−	1.74206i
$846$	1.20652e10	+	1.41684e9i	0.0235533	+	0.00276592i
$847$	−1.71589e11	−	5.57526e10i	−0.333392	−	0.108326i
$848$	−3.48799e10	+	2.25549e11i	−0.0674516	+	0.436171i
$849$	3.27394e11			0.630145
$850$	5.90998e11	+	2.75243e11i	1.13217	+	0.527280i
$851$			2.00719e10i			0.0382710i
$852$	−5.75297e10	+	9.42657e10i	−0.109178	+	0.178894i
$853$	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	$0.0170353\pi$
$854$	−1.27338e12	−	1.49536e11i	−2.39401	−	0.281135i
$855$	1.42262e10	+	4.66013e9i	0.0266209	+	0.00872034i
$856$	−3.38505e11	+	4.31818e11i	−0.630479	+	0.804277i
$857$	7.70884e10			0.142911			0.0714555	−	0.997444i	$-0.477236\pi$
$857$	7.70884e10			0.142911			0.0714555	+	0.997444i	$0.477236\pi$
$858$	−4.00100e11	−	7.12903e11i	−0.738277	−	1.31547i
$859$	1.18741e11	−	1.63433e11i	0.218087	−	0.300171i	−0.685930	−	0.727667i	$-0.740604\pi$
$859$	1.18741e11	−	1.63433e11i	0.218087	−	0.300171i	0.904017	+	0.427497i	$0.140604\pi$
$860$	−3.36537e11	+	2.62916e10i	−0.615232	+	0.0480644i
$861$	−6.11431e9	+	4.44230e9i	−0.0111259	+	0.00808343i
$862$	3.38730e10	−	7.36530e10i	0.0613515	−	0.133402i
$863$	4.33592e11	−	5.96788e11i	0.781696	−	1.07591i	−0.213396	−	0.976966i	$-0.568453\pi$
$863$	4.33592e11	−	5.96788e11i	0.781696	−	1.07591i	0.995093	−	0.0989471i	$-0.0315475\pi$
$864$	−5.48522e11	+	2.40585e10i	−0.984326	+	0.0431731i
$865$	−3.27033e11	+	2.36406e11i	−0.584153	+	0.422274i
$866$	−5.29815e11	−	2.43662e11i	−0.942003	−	0.433228i
$867$	−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
$870$	1.34500e11	+	6.81469e11i	0.234771	+	1.18951i
$871$	−9.38022e11	−	3.04782e11i	−1.62982	−	0.529561i
$872$	−1.21911e11	−	4.27777e11i	−0.210851	−	0.739863i
$873$	−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	$0.424890\pi$
$878$	1.01372e12	+	1.19043e11i	1.70584	+	0.200321i
$879$	−4.75543e11	−	1.54513e11i	−0.796589	−	0.258827i
$880$	3.75397e11	+	3.74459e11i	0.625979	+	0.624415i
$881$	−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	0.431462	−	0.902131i	$-0.357998\pi$
$883$	7.96844e11	−	2.58910e11i	1.31078	−	0.425899i	0.879320	+	0.476232i	$0.157998\pi$
$884$	−1.24820e12	−	2.97258e11i	−2.04397	−	0.486770i
$885$	−6.52828e11	+	4.71918e11i	−1.06421	+	0.769297i
$886$	4.12281e11	+	3.80412e11i	0.669050	+	0.617332i
$887$	−4.61006e11	+	6.34521e11i	−0.744753	+	1.02507i	0.253578	+	0.967315i	$0.418393\pi$
$887$	−4.61006e11	+	6.34521e11i	−0.744753	+	1.02507i	−0.998331	+	0.0577501i	$0.981607\pi$
$888$	1.19020e10	−	3.25649e11i	0.0191412	−	0.523719i
$889$	−1.12562e12	+	8.17809e11i	−1.80212	+	1.30932i
$890$	−1.64078e10	+	1.36885e11i	−0.0261511	+	0.218170i
$891$	3.36592e11	−	4.63279e11i	0.534064	−	0.735076i
$892$	1.36466e11	−	1.16985e11i	0.215559	−	0.184786i
$893$	5.21840e11			0.820600
$894$	1.08755e12	−	6.10364e11i	1.70255	−	0.955518i
$895$	−3.91581e8	−	1.28272e8i	−0.000610280	−	0.000199912i
$896$	−5.00030e11	+	9.06400e11i	−0.775825	+	1.40633i
$897$	2.52775e10	−	7.77962e10i	0.0390449	−	0.120168i
$898$	1.42874e11	−	1.54843e11i	0.219709	−	0.238115i
$899$		−	1.04539e12i		−	1.60045i
$900$	9.80124e9	−	1.58879e10i	0.0149386	−	0.0242157i
$901$	−3.63267e11			−0.551222
$902$	3.63173e9	+	3.35100e9i	0.00548640	+	0.00506230i
$903$	6.35612e11	+	2.06523e11i	0.955964	+	0.310611i
$904$	3.71925e10	+	1.30506e11i	0.0556906	+	0.195415i
$905$	−1.03608e11	−	3.21495e11i	−0.154454	−	0.479269i
$906$	−6.43263e11	−	1.14617e12i	−0.954720	−	1.70113i
$907$		−	3.48260e11i		−	0.514605i	−0.966331	−	0.257303i	$-0.917166\pi$
$907$		−	3.48260e11i		−	0.514605i	0.966331	−	0.257303i	$-0.0828337\pi$
$908$	3.32766e11	−	2.85261e11i	0.489549	−	0.419662i
$909$	1.09986e10	+	7.99093e9i	0.0161095	+	0.0117042i
$910$	−3.58790e11	−	1.81788e12i	−0.523209	−	2.65094i
$911$	−5.62317e11	−	7.73963e11i	−0.816409	−	1.12369i	−0.990303	−	0.138926i	$-0.955635\pi$
$911$	−5.62317e11	−	7.73963e11i	−0.816409	−	1.12369i	0.173894	−	0.984764i	$-0.444365\pi$
$912$	6.81819e11	−	1.10542e11i	0.985575	−	0.159790i
$913$	4.85366e11	+	3.52639e11i	0.698532	+	0.507513i
$914$	1.52210e11	−	1.64961e11i	0.218101	−	0.236373i
$915$	1.01540e12	−	3.27233e11i	1.44862	−	0.466845i
$916$	−1.29882e12	−	3.09312e11i	−1.84487	−	0.439355i
$917$	−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	−0.585478	−	0.810688i	$-0.699093\pi$
$919$	−4.15580e11	+	1.35030e11i	−0.582630	+	0.189308i	0.00284856	+	0.999996i	$0.499093\pi$
$920$	−2.06499e9	+	5.30147e10i	−0.00288248	+	0.0740023i
$921$	−1.31983e11	+	4.06202e11i	−0.183434	+	0.564552i
$922$	3.72960e10	−	3.17595e11i	0.0516106	−	0.439491i
$923$	−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
$928$	5.52110e11	+	6.93813e11i	0.744446	+	0.935515i
$929$	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	$0.0155616\pi$
$930$	−6.90446e11	+	7.44696e11i	−0.922992	+	0.995514i
$931$	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
$934$	−4.23577e11	+	9.21018e11i	−0.556602	+	1.21027i
$935$	−4.97698e11	+	6.81578e11i	−0.651208	+	0.891803i
$936$	−1.26221e10	+	3.45043e10i	−0.0164448	+	0.0449541i
$937$	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	$0.694806\pi$
$938$	−1.15066e12	−	5.29191e11i	−1.48641	−	0.683599i
$939$	−7.41408e10	−	1.02046e11i	−0.0953664	−	0.131261i
$940$	1.52277e11	−	6.32678e11i	0.195039	−	0.810348i
$941$	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	$0.598021\pi$
$942$	6.31815e11	−	3.54591e11i	0.802391	−	0.450323i
$943$			4.94451e8i			0.000625283i
$944$	−4.63479e11	+	9.17896e11i	−0.583636	+	1.15586i
$945$	1.02277e12	−	7.39344e11i	1.28248	−	0.927085i
$946$	5.09650e10	−	4.33993e11i	0.0636366	−	0.541899i
$947$	1.09961e12	+	3.57286e11i	1.36723	+	0.444239i	0.898449	−	0.439077i	$-0.144695\pi$
$947$	1.09961e12	+	3.57286e11i	1.36723	+	0.444239i	0.468778	+	0.883316i	$0.344695\pi$
$948$	−3.91539e11	+	6.41558e11i	−0.484776	+	0.794333i
$949$	−2.08897e12			−2.57553
$950$	3.38555e11	−	7.26940e11i	0.415657	−	0.892491i
$951$			3.53388e11i			0.432045i
$952$	−1.54738e12	−	5.66050e11i	−1.88386	−	0.689139i
$953$	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	$0.0387128\pi$
$954$	−1.21317e9	+	1.03308e10i	−0.00146463	+	0.0124721i
$955$	8.86521e11	−	1.21406e12i	1.06580	−	1.45957i
$956$	−3.74549e11	+	3.21079e11i	−0.448412	+	0.384397i
$957$	−8.99181e11			−1.07201
$958$	−1.23135e12	+	6.91067e11i	−1.46191	+	0.820462i
$959$	6.30962e11	−	8.68445e11i	0.745983	−	1.02676i
$960$	6.49387e10	−	8.58894e11i	0.0764573	−	1.01124i
$961$	5.46466e11	−	3.97031e11i	0.640721	−	0.465511i
$962$	6.76470e11	+	3.11109e11i	0.789857	+	0.363255i
$963$	−1.46986e10	+	2.02309e10i	−0.0170911	+	0.0235239i
$964$	−8.25839e11	+	1.35318e12i	−0.956285	+	1.56693i
$965$	7.02018e11	+	1.68427e9i	0.809541	+	0.00194224i
$966$	4.38892e10	−	9.54320e10i	0.0504022	−	0.109594i
$967$	6.65503e11	−	2.16235e11i	0.761104	−	0.247298i	0.0973515	−	0.995250i	$-0.468963\pi$
$967$	6.65503e11	−	2.16235e11i	0.761104	−	0.247298i	0.663752	+	0.747952i	$0.268963\pi$
$968$	1.59044e11	−	1.06901e11i	0.181141	−	0.121753i
$969$	3.39734e11	+	1.04559e12i	0.385340	+	1.18595i
$970$	4.57207e11	+	8.19256e11i	0.516447	+	0.925407i
$971$	1.19622e12	+	3.88675e11i	1.34566	+	0.437230i	0.891229	−	0.453554i	$-0.149844\pi$
$971$	1.19622e12	+	3.88675e11i	1.34566	+	0.437230i	0.454427	+	0.890784i	$0.349844\pi$
$972$	−5.06158e10	+	4.07651e9i	−0.0567050	+	0.00456692i
$973$	−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	$0.398493\pi$
$978$	−8.17616e10	+	6.96243e11i	−0.0893704	+	0.761036i
$979$	−1.69731e11	−	5.51490e10i	−0.184770	−	0.0600354i
$980$	−1.13484e11	−	1.45261e12i	−0.123036	−	1.57487i
$981$	−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	−0.889759	−	0.456430i	$-0.849128\pi$
$983$	−1.25240e12	+	4.06929e11i	−1.34131	+	0.435817i	−0.451548	+	0.892247i	$0.649128\pi$
$984$	2.93194e8	−	8.02205e9i	0.000312734	−	0.00855667i
$985$	1.75747e11	−	5.36510e11i	0.186699	−	0.569945i
$986$	−9.57049e11	+	1.03723e12i	−1.01257	+	1.09740i
$987$	−7.57289e11	+	1.04232e12i	−0.797982	+	1.09833i
$988$	−3.65633e11	+	1.53531e12i	−0.383723	+	1.61127i
$989$	3.53735e10	−	2.57003e10i	0.0369736	−	0.0268629i
$990$	1.77210e10	+	1.64300e10i	0.0184479	+	0.0171040i
$991$	9.52346e11	−	1.31079e12i	0.987416	−	1.35906i	0.0546796	−	0.998504i	$-0.482586\pi$
$991$	9.52346e11	−	1.31079e12i	0.987416	−	1.35906i	0.932737	−	0.360558i	$-0.117414\pi$
$992$	−3.46178e11	+	1.24924e12i	−0.357481	+	1.29003i
$993$	1.89437e12			1.94836
$994$	−1.58584e11	−	2.82567e11i	−0.162448	−	0.289452i
$995$	−2.91319e9	+	1.21424e12i	−0.00297219	+	1.23883i
$996$	−7.82393e10	−	9.71454e11i	−0.0795037	−	0.987154i
$997$	−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	$0.109874\pi$
$998$	9.44605e11	+	8.71586e11i	0.952199	+	0.878594i
$999$			5.07123e11i			0.509157i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.17	✓	464	4.3	odd	2	inner
100.9.j.b.11.29	yes	464	1.1	even	1	trivial
100.9.j.b.91.17	yes	464	25.16	even	5	inner
100.9.j.b.91.29	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+(-10.8501 + 11.7591i) q^{2} +(78.1238 + 25.3840i) q^{3} +(-20.5513 - 255.174i) q^{4} +(-624.998 - 1.49949i) q^{5} +(-1146.14 + 643.245i) q^{6} -3856.33i q^{7} +(3223.59 + 2526.99i) q^{8} +(151.027 + 109.727i) q^{9} +(6798.92 - 7333.13i) q^{10} +(7608.90 + 10472.7i) q^{11} +(4871.78 - 20456.8i) q^{12} +(38872.9 + 28242.8i) q^{13} +(45346.9 + 41841.5i) q^{14} +(-48789.2 - 15982.1i) q^{15} +(-64691.3 + 10488.3i) q^{16} +(-32234.1 - 99206.5i) q^{17} +(-2928.94 + 585.381i) q^{18} +(-122026. + 39648.6i) q^{19} +(12461.9 + 159514. i) q^{20} +(97889.0 - 301271. i) q^{21} +(-205707. - 24156.7i) 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} +(-984035. + 79252.5i) q^{28} +(-261306. + 804217. i) q^{29} +(717301. - 400308. i) q^{30} +(-1.17576e6 + 382028. i) q^{31} +(578574. - 874508. i) q^{32} +(328596. + 1.01132e6i) q^{33} +(1.51632e6 + 697355. i) q^{34} +(-5782.53 + 2.41020e6i) q^{35} +(24895.7 - 40793.0i) q^{36} +(-783538. - 569274. i) q^{37} +(857761. - 1.86510e6i) q^{38} +(2.31998e6 + 3.19318e6i) q^{39} +(-2.01095e6 - 1.58420e6i) q^{40} +(-19301.7 - 14023.5i) q^{41} +(2.48057e6 + 4.41991e6i) q^{42} +2.10977e6i q^{43} +(2.51600e6 - 2.15682e6i) q^{44} +(-94226.8 - 68805.8i) q^{45} +(329330. + 38674.1i) q^{46} +(-3.86810e6 - 1.25682e6i) q^{47} +(-5.32017e6 - 822737. i) q^{48} -9.10650e6 q^{49} +(-4.26031e6 + 4.57300e6i) q^{50} -8.56862e6i q^{51} +(6.40794e6 - 1.04998e7i) q^{52} +(1.07615e6 - 3.31206e6i) q^{53} +(8.32065e6 + 977115. i) q^{54} +(-4.73984e6 - 6.55686e6i) q^{55} +(9.74493e6 - 1.24312e7i) q^{56} -1.05396e7 q^{57} +(-6.62165e6 - 1.17985e7i) q^{58} +(9.22247e6 - 1.26936e7i) q^{59} +(-3.07553e6 + 1.27782e7i) q^{60} +(-1.68110e7 + 1.22139e7i) q^{61} +(8.26482e6 - 1.79709e7i) q^{62} +(423145. - 582409. i) q^{63} +(4.00582e6 + 1.62920e7i) q^{64} +(-2.42531e7 - 1.77100e7i) q^{65} +(-1.54574e7 - 7.10887e6i) q^{66} +(-1.95220e7 + 6.34307e6i) q^{67} +(-2.46524e7 + 1.02641e7i) q^{68} +(-526072. - 1.61908e6i) q^{69} +(-2.82790e7 - 2.62189e7i) q^{70} +(-4.99450e6 - 1.62281e6i) q^{71} +(209567. + 735358. 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} +(-6.27209e7 - 7.36548e6i) q^{78} +(-3.39918e7 - 1.10446e7i) q^{79} +(4.04477e7 - 6.45816e6i) q^{80} +(-1.36699e7 - 4.20716e7i) q^{81} +(374328. - 74813.7i) q^{82} +(4.40773e7 - 1.43216e7i) q^{83} +(-7.88883e7 - 1.87872e7i) q^{84} +(1.99975e7 + 6.20522e7i) q^{85} +(-2.48089e7 - 2.28911e7i) q^{86} +(-4.08285e7 + 5.61955e7i) q^{87} +(-1.93662e6 + 5.29874e7i) q^{88} +(-1.11535e7 + 8.10348e6i) q^{89} +(1.83146e6 - 361470. i) q^{90} +(1.08914e8 - 1.49907e8i) q^{91} +(-4.02803e6 + 3.45300e6i) q^{92} -1.01552e8 q^{93} +(5.67483e7 - 3.18486e7i) q^{94} +(7.63255e7 - 2.45974e7i) q^{95} +(6.73989e7 - 5.36334e7i) q^{96} +(-2.89920e7 + 8.92281e7i) q^{97} +(9.88063e7 - 1.07084e8i) 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

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