LMFDB - Embedded newform 13.10.c.a.9.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,10,Mod(3,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.3"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	13.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.69546587013$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 3193 x^{16} + 896 x^{15} + 6827472 x^{14} + 3327136 x^{13} + 8054385232 x^{12} + \cdots + 15\!\cdots\!00 $ x^18 - 3x^17 + 3193x^16 + 896x^15 + 6827472x^14 + 3327136x^13 + 8054385232x^12 + 694281600x^11 + 6899832636736x^10 - 1285276575488x^9 + 3495304064394496x^8 - 764853454571520x^7 + 1234658135287256064x^6 + 1254918535240499200x^5 + 146439647836867215360x^4 + 1052079877442940928000x^3 + 12856821885420326502400x^2 + 44600611845158952960000*x + 152210992401321984000000
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{3}\cdot 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.6
Root			$-3.59372 - 6.22451i$ of defining polynomial
Character	$\chi$	$=$	13.9
Dual form			13.10.c.a.3.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.59372 - 7.95656i) q^{2} +(74.2673 - 128.635i) q^{3} +(213.795 + 370.305i) q^{4} +1229.19 q^{5} +(-682.327 - 1181.82i) q^{6} +(-4166.53 - 7216.65i) q^{7} +8632.44 q^{8} +(-1189.76 - 2060.73i) q^{9} +(5646.55 - 9780.12i) q^{10} +(37589.4 - 65106.8i) q^{11} +63512.0 q^{12} +(-100375. + 23007.0i) q^{13} -76559.6 q^{14} +(91288.5 - 158116. i) q^{15} +(-69808.2 + 120911. i) q^{16} +(106339. + 184184. i) q^{17} -21861.8 q^{18} +(223907. + 387819. i) q^{19} +(262795. + 455174. i) q^{20} -1.23775e6 q^{21} +(-345351. - 598165. i) q^{22} +(-919629. + 1.59284e6i) q^{23} +(641108. - 1.11043e6i) q^{24} -442219. q^{25} +(-278039. + 904329. i) q^{26} +2.57016e6 q^{27} +(1.78157e6 - 3.08577e6i) q^{28} +(607245. - 1.05178e6i) q^{29} +(-838708. - 1.45269e6i) q^{30} +3.80320e6 q^{31} +(2.85126e6 + 4.93853e6i) q^{32} +(-5.58333e6 - 9.67061e6i) q^{33} +1.95396e6 q^{34} +(-5.12146e6 - 8.87062e6i) q^{35} +(508732. - 881149. i) q^{36} +(-8.49682e6 + 1.47169e7i) q^{37} +4.11427e6 q^{38} +(-4.49509e6 + 1.46204e7i) q^{39} +1.06109e7 q^{40} +(-3.85227e6 + 6.67232e6i) q^{41} +(-5.68587e6 + 9.84822e6i) q^{42} +(-1.30776e7 - 2.26511e7i) q^{43} +3.21458e7 q^{44} +(-1.46244e6 - 2.53303e6i) q^{45} +(8.44904e6 + 1.46342e7i) q^{46} -3.99265e7 q^{47} +(1.03689e7 + 1.79595e7i) q^{48} +(-1.45432e7 + 2.51896e7i) q^{49} +(-2.03143e6 + 3.51855e6i) q^{50} +3.15899e7 q^{51} +(-2.99794e7 - 3.22506e7i) q^{52} -2.84536e7 q^{53} +(1.18066e7 - 2.04497e7i) q^{54} +(4.62045e7 - 8.00285e7i) q^{55} +(-3.59673e7 - 6.22973e7i) q^{56} +6.65159e7 q^{57} +(-5.57903e6 - 9.66316e6i) q^{58} +(3.16858e7 + 5.48813e7i) q^{59} +7.80683e7 q^{60} +(6.00392e6 + 1.03991e7i) q^{61} +(1.74708e7 - 3.02604e7i) q^{62} +(-9.91437e6 + 1.71722e7i) q^{63} -1.90920e7 q^{64} +(-1.23380e8 + 2.82800e7i) q^{65} -1.02593e8 q^{66} +(3.54777e7 - 6.14492e7i) q^{67} +(-4.54694e7 + 7.87553e7i) q^{68} +(1.36597e8 + 2.36592e8i) q^{69} -9.41062e7 q^{70} +(-8.26051e7 - 1.43076e8i) q^{71} +(-1.02706e7 - 1.77891e7i) q^{72} +1.28511e8 q^{73} +(7.80641e7 + 1.35211e8i) q^{74} +(-3.28424e7 + 5.68848e7i) q^{75} +(-9.57407e7 + 1.65828e8i) q^{76} -6.26470e8 q^{77} +(9.56789e7 + 1.02928e8i) q^{78} +6.32753e8 q^{79} +(-8.58075e7 + 1.48623e8i) q^{80} +(2.14297e8 - 3.71174e8i) q^{81} +(3.53925e7 + 6.13016e7i) q^{82} -1.34044e8 q^{83} +(-2.64625e8 - 4.58344e8i) q^{84} +(1.30710e8 + 2.26397e8i) q^{85} -2.40299e8 q^{86} +(-9.01969e7 - 1.56226e8i) q^{87} +(3.24488e8 - 5.62030e8i) q^{88} +(4.02822e8 - 6.97708e8i) q^{89} -2.68722e7 q^{90} +(5.84250e8 + 6.28513e8i) q^{91} -7.86450e8 q^{92} +(2.82453e8 - 4.89223e8i) q^{93} +(-1.83411e8 + 3.17678e8i) q^{94} +(2.75224e8 + 4.76703e8i) q^{95} +8.47023e8 q^{96} +(-3.87434e7 - 6.71055e7i) q^{97} +(1.33615e8 + 2.31428e8i) q^{98} -1.78890e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 15 q^{2} + 161 q^{3} - 1793 q^{4} - 2280 q^{5} + 2118 q^{6} - 1939 q^{7} - 14478 q^{8} - 33654 q^{9} + 46923 q^{10} - 5433 q^{11} + 8712 q^{12} - 212524 q^{13} - 9900 q^{14} - 347428 q^{15} + 400127 q^{16}+ \cdots + 2262149268 q^{99}+O(q^{100}) $ 18 * q + 15 * q^2 + 161 * q^3 - 1793 * q^4 - 2280 * q^5 + 2118 * q^6 - 1939 * q^7 - 14478 * q^8 - 33654 * q^9 + 46923 * q^10 - 5433 * q^11 + 8712 * q^12 - 212524 * q^13 - 9900 * q^14 - 347428 * q^15 + 400127 * q^16 + 248589 * q^17 - 38738 * q^18 - 311001 * q^19 + 927069 * q^20 + 1553030 * q^21 + 1857242 * q^22 + 591609 * q^23 - 4492800 * q^24 + 7008998 * q^25 - 3801525 * q^26 - 11603482 * q^27 + 2697168 * q^28 + 11014155 * q^29 - 6597836 * q^30 - 23148076 * q^31 - 11868417 * q^32 + 14131427 * q^33 + 21859862 * q^34 + 21112794 * q^35 + 10792871 * q^36 - 29215749 * q^37 + 14572188 * q^38 - 71569875 * q^39 + 27322222 * q^40 + 3328377 * q^41 + 39828306 * q^42 + 6074381 * q^43 + 31824624 * q^44 + 32857342 * q^45 + 36693338 * q^46 - 45575052 * q^47 - 30270064 * q^48 + 10293266 * q^49 - 49601730 * q^50 - 136587494 * q^51 - 35278230 * q^52 - 29480016 * q^53 + 152965386 * q^54 - 18710998 * q^55 - 7665444 * q^56 + 523363230 * q^57 - 163479359 * q^58 - 32715855 * q^59 - 188638416 * q^60 - 220502845 * q^61 - 59980476 * q^62 + 166572574 * q^63 - 924604030 * q^64 + 128091756 * q^65 - 48128076 * q^66 + 112659045 * q^67 - 238942419 * q^68 + 86003951 * q^69 + 2040150992 * q^70 - 236450709 * q^71 + 995206683 * q^72 - 211881220 * q^73 - 455580507 * q^74 + 968954813 * q^75 - 365789708 * q^76 - 2399230890 * q^77 - 441111970 * q^78 - 817519096 * q^79 + 580424625 * q^80 + 176914851 * q^81 + 941792217 * q^82 + 2225691456 * q^83 - 1819004068 * q^84 + 1812284636 * q^85 + 291320076 * q^86 + 69564799 * q^87 + 3178375740 * q^88 - 1154379039 * q^89 - 10225809510 * q^90 - 1658338903 * q^91 - 4545506592 * q^92 + 3136878060 * q^93 + 2755131560 * q^94 + 1779441012 * q^95 + 5906965568 * q^96 - 3616470111 * q^97 + 8263323501 * q^98 + 2262149268 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	4.59372	−	7.95656i	0.203016	−	0.351634i	−0.746483	−	0.665405i	$-0.768259\pi$
$2$	4.59372	−	7.95656i	0.203016	−	0.351634i	0.949499	+	0.313771i	$0.101592\pi$
$3$	74.2673	−	128.635i	0.529361	−	0.916880i	−0.470053	−	0.882638i	$-0.655765\pi$
$3$	74.2673	−	128.635i	0.529361	−	0.916880i	0.999414	−	0.0342418i	$-0.0109016\pi$
$4$	213.795	+	370.305i	0.417569	+	0.723251i
$5$	1229.19			0.879536			0.439768	−	0.898111i	$-0.355061\pi$
$5$	1229.19			0.879536			0.439768	+	0.898111i	$0.355061\pi$
$6$	−682.327	−	1181.82i	−0.214937	−	0.372282i
$7$	−4166.53	−	7216.65i	−0.655894	−	1.13604i	−0.981669	−	0.190594i	$-0.938958\pi$
$7$	−4166.53	−	7216.65i	−0.655894	−	1.13604i	0.325775	−	0.945447i	$-0.394375\pi$
$8$	8632.44			0.745124
$9$	−1189.76	−	2060.73i	−0.0604462	−	0.104696i
$10$	5646.55	−	9780.12i	0.178560	−	0.309274i
$11$	37589.4	−	65106.8i	0.774103	−	1.34078i	−0.161195	−	0.986923i	$-0.551535\pi$
$11$	37589.4	−	65106.8i	0.774103	−	1.34078i	0.935298	−	0.353862i	$-0.115132\pi$
$12$	63512.0			0.884180
$13$	−100375.	+	23007.0i	−0.974723	+	0.223416i
$13$	−100375.	+	23007.0i	−0.974723	+	0.223416i
$14$	−76559.6			−0.532627
$15$	91288.5	−	158116.i	0.465592	−	0.806429i
$16$	−69808.2	+	120911.i	−0.266297	+	0.461240i
$17$	106339.	+	184184.i	0.308795	+	0.534849i	0.978099	−	0.208140i	$-0.0667409\pi$
$17$	106339.	+	184184.i	0.308795	+	0.534849i	−0.669304	+	0.742989i	$0.733408\pi$
$18$	−21861.8			−0.0490861
$19$	223907.	+	387819.i	0.394164	+	0.682712i	0.992994	−	0.118164i	$-0.0377009\pi$
$19$	223907.	+	387819.i	0.394164	+	0.682712i	−0.598830	+	0.800876i	$0.704368\pi$
$20$	262795.	+	455174.i	0.367267	+	0.636125i
$21$	−1.23775e6			−1.38882
$22$	−345351.	−	598165.i	−0.314310	−	0.544401i
$23$	−919629.	+	1.59284e6i	−0.685231	+	1.18686i	0.288133	+	0.957590i	$0.406966\pi$
$23$	−919629.	+	1.59284e6i	−0.685231	+	1.18686i	−0.973364	+	0.229265i	$0.926368\pi$
$24$	641108.	−	1.11043e6i	0.394440	−	0.683189i
$25$	−442219.			−0.226416
$26$	−278039.	+	904329.i	−0.119323	+	0.388102i
$27$	2.57016e6			0.930731
$28$	1.78157e6	−	3.08577e6i	0.547762	−	0.948752i
$29$	607245.	−	1.05178e6i	0.159431	−	0.276143i	−0.775233	−	0.631676i	$-0.782367\pi$
$29$	607245.	−	1.05178e6i	0.159431	−	0.276143i	0.934664	+	0.355533i	$0.115701\pi$
$30$	−838708.	−	1.45269e6i	−0.189045	−	0.327436i
$31$	3.80320e6			0.739641			0.369821	−	0.929103i	$-0.379419\pi$
$31$	3.80320e6			0.739641			0.369821	+	0.929103i	$0.379419\pi$
$32$	2.85126e6	+	4.93853e6i	0.480687	+	0.832574i
$33$	−5.58333e6	−	9.67061e6i	−0.819559	−	1.41952i
$34$	1.95396e6			0.250761
$35$	−5.12146e6	−	8.87062e6i	−0.576882	−	0.999190i
$36$	508732.	−	881149.i	0.0504810	−	0.0874356i
$37$	−8.49682e6	+	1.47169e7i	−0.745331	+	1.29095i	0.204710	+	0.978823i	$0.434375\pi$
$37$	−8.49682e6	+	1.47169e7i	−0.745331	+	1.29095i	−0.950040	+	0.312128i	$0.898958\pi$
$38$	4.11427e6			0.320086
$39$	−4.49509e6	+	1.46204e7i	−0.311134	+	1.01197i
$40$	1.06109e7			0.655363
$41$	−3.85227e6	+	6.67232e6i	−0.212907	+	0.368765i	−0.952623	−	0.304154i	$-0.901626\pi$
$41$	−3.85227e6	+	6.67232e6i	−0.212907	+	0.368765i	0.739716	+	0.672919i	$0.234960\pi$
$42$	−5.68587e6	+	9.84822e6i	−0.281952	+	0.488355i
$43$	−1.30776e7	−	2.26511e7i	−0.583338	−	1.01037i	−0.995080	−	0.0990702i	$-0.968413\pi$
$43$	−1.30776e7	−	2.26511e7i	−0.583338	−	1.01037i	0.411743	−	0.911300i	$-0.364920\pi$
$44$	3.21458e7			1.29297
$45$	−1.46244e6	−	2.53303e6i	−0.0531646	−	0.0920838i
$46$	8.44904e6	+	1.46342e7i	0.278225	+	0.481901i
$47$	−3.99265e7			−1.19350			−0.596748	−	0.802429i	$-0.703541\pi$
$47$	−3.99265e7			−1.19350			−0.596748	+	0.802429i	$0.703541\pi$
$48$	1.03689e7	+	1.79595e7i	0.281935	+	0.488326i
$49$	−1.45432e7	+	2.51896e7i	−0.360394	+	0.624221i
$50$	−2.03143e6	+	3.51855e6i	−0.0459661	+	0.0796156i
$51$	3.15899e7			0.653857
$52$	−2.99794e7	−	3.22506e7i	−0.568601	−	0.611678i
$53$	−2.84536e7			−0.495331			−0.247665	−	0.968846i	$-0.579663\pi$
$53$	−2.84536e7			−0.495331			−0.247665	+	0.968846i	$0.579663\pi$
$54$	1.18066e7	−	2.04497e7i	0.188953	−	0.327276i
$55$	4.62045e7	−	8.00285e7i	0.680851	−	1.17927i
$56$	−3.59673e7	−	6.22973e7i	−0.488722	−	0.846492i
$57$	6.65159e7			0.834620
$58$	−5.57903e6	−	9.66316e6i	−0.0647340	−	0.112123i
$59$	3.16858e7	+	5.48813e7i	0.340432	+	0.589645i	0.984513	−	0.175312i	$-0.0560935\pi$
$59$	3.16858e7	+	5.48813e7i	0.340432	+	0.589645i	−0.644081	+	0.764957i	$0.722760\pi$
$60$	7.80683e7			0.777668
$61$	6.00392e6	+	1.03991e7i	0.0555201	+	0.0961637i	0.892450	−	0.451147i	$-0.148985\pi$
$61$	6.00392e6	+	1.03991e7i	0.0555201	+	0.0961637i	−0.836930	+	0.547311i	$0.815652\pi$
$62$	1.74708e7	−	3.02604e7i	0.150159	−	0.260083i
$63$	−9.91437e6	+	1.71722e7i	−0.0792926	+	0.137339i
$64$	−1.90920e7			−0.142246
$65$	−1.23380e8	+	2.82800e7i	−0.857304	+	0.196503i
$66$	−1.02593e8			−0.665534
$67$	3.54777e7	−	6.14492e7i	0.215089	−	0.372546i	−0.738211	−	0.674570i	$-0.764329\pi$
$67$	3.54777e7	−	6.14492e7i	0.215089	−	0.372546i	0.953300	+	0.302024i	$0.0976624\pi$
$68$	−4.54694e7	+	7.87553e7i	−0.257887	+	0.446673i
$69$	1.36597e8	+	2.36592e8i	0.725469	+	1.25655i
$70$	−9.41062e7			−0.468465
$71$	−8.26051e7	−	1.43076e8i	−0.385784	−	0.668198i	0.606094	−	0.795393i	$-0.292736\pi$
$71$	−8.26051e7	−	1.43076e8i	−0.385784	−	0.668198i	−0.991878	+	0.127196i	$0.959402\pi$
$72$	−1.02706e7	−	1.77891e7i	−0.0450399	−	0.0780114i
$73$	1.28511e8			0.529647			0.264823	−	0.964297i	$-0.414686\pi$
$73$	1.28511e8			0.529647			0.264823	+	0.964297i	$0.414686\pi$
$74$	7.80641e7	+	1.35211e8i	0.302628	+	0.524166i
$75$	−3.28424e7	+	5.68848e7i	−0.119856	+	0.207597i
$76$	−9.57407e7	+	1.65828e8i	−0.329182	+	0.570159i
$77$	−6.26470e8			−2.03092
$78$	9.56789e7	+	1.02928e8i	0.292678	+	0.314852i
$79$	6.32753e8			1.82773			0.913865	−	0.406018i	$-0.133083\pi$
$79$	6.32753e8			1.82773			0.913865	+	0.406018i	$0.133083\pi$
$80$	−8.58075e7	+	1.48623e8i	−0.234218	+	0.405678i
$81$	2.14297e8	−	3.71174e8i	0.553139	−	0.958064i
$82$	3.53925e7	+	6.13016e7i	0.0864468	+	0.149730i
$83$	−1.34044e8			−0.310025			−0.155013	−	0.987912i	$-0.549542\pi$
$83$	−1.34044e8			−0.310025			−0.155013	+	0.987912i	$0.549542\pi$
$84$	−2.64625e8	−	4.58344e8i	−0.579928	−	1.00446i
$85$	1.30710e8	+	2.26397e8i	0.271597	+	0.470419i
$86$	−2.40299e8			−0.473707
$87$	−9.01969e7	−	1.56226e8i	−0.168793	−	0.292358i
$88$	3.24488e8	−	5.62030e8i	0.576802	−	0.999051i
$89$	4.02822e8	−	6.97708e8i	0.680547	−	1.17874i	−0.294268	−	0.955723i	$-0.595076\pi$
$89$	4.02822e8	−	6.97708e8i	0.680547	−	1.17874i	0.974814	−	0.223018i	$-0.0715910\pi$
$90$	−2.68722e7			−0.0431730
$91$	5.84250e8	+	6.28513e8i	0.893125	+	0.960789i
$92$	−7.86450e8			−1.14453
$93$	2.82453e8	−	4.89223e8i	0.391537	−	0.678163i
$94$	−1.83411e8	+	3.17678e8i	−0.242298	+	0.419673i
$95$	2.75224e8	+	4.76703e8i	0.346681	+	0.600470i
$96$	8.47023e8			1.01783
$97$	−3.87434e7	−	6.71055e7i	−0.0444349	−	0.0769636i	0.842953	−	0.537988i	$-0.180815\pi$
$97$	−3.87434e7	−	6.71055e7i	−0.0444349	−	0.0769636i	−0.887387	+	0.461024i	$0.847482\pi$
$98$	1.33615e8	+	2.31428e8i	0.146331	+	0.253453i
$99$	−1.78890e8			−0.187166
$100$	−9.45445e7	−	1.63756e8i	−0.0945445	−	0.163756i
$101$	1.04566e8	−	1.81113e8i	0.0999867	−	0.173182i	−0.811692	−	0.584085i	$-0.801453\pi$
$101$	1.04566e8	−	1.81113e8i	0.0999867	−	0.173182i	0.911679	+	0.410903i	$0.134787\pi$
$102$	1.45115e8	−	2.51347e8i	0.132743	−	0.229918i
$103$	−1.84658e9			−1.61659			−0.808297	−	0.588775i	$-0.799610\pi$
$103$	−1.84658e9			−1.61659			−0.808297	+	0.588775i	$0.799610\pi$
$104$	−8.66483e8	+	1.98607e8i	−0.726290	+	0.166473i
$105$	−1.52143e9			−1.22152
$106$	−1.30708e8	+	2.26393e8i	−0.100560	+	0.174175i
$107$	−8.10406e8	+	1.40366e9i	−0.597689	+	1.03523i	0.395472	+	0.918478i	$0.370581\pi$
$107$	−8.10406e8	+	1.40366e9i	−0.597689	+	1.03523i	−0.993161	+	0.116750i	$0.962752\pi$
$108$	5.49489e8	+	9.51744e8i	0.388644	+	0.673152i
$109$	2.30586e9			1.56464			0.782319	−	0.622878i	$-0.214037\pi$
$109$	2.30586e9			1.56464			0.782319	+	0.622878i	$0.214037\pi$
$110$	−4.24501e8	−	7.35258e8i	−0.276447	−	0.478820i
$111$	1.26207e9	+	2.18597e9i	0.789098	+	1.36676i
$112$	1.16343e9			0.698651
$113$	−9.61033e8	−	1.66456e9i	−0.554479	−	0.960386i	−0.997944	−	0.0640945i	$-0.979584\pi$
$113$	−9.61033e8	−	1.66456e9i	−0.554479	−	0.960386i	0.443464	−	0.896292i	$-0.353749\pi$
$114$	3.05556e8	−	5.29238e8i	0.169441	−	0.293481i
$115$	−1.13040e9	+	1.95791e9i	−0.602686	+	1.04388i
$116$	5.19305e8			0.266294
$117$	1.66834e8	+	1.79473e8i	0.0823091	+	0.0885449i
$118$	5.82222e8			0.276452
$119$	8.86126e8	−	1.53482e9i	0.405074	−	0.701609i
$120$	7.88043e8	−	1.36493e9i	0.346924	−	0.600890i
$121$	−1.64695e9	−	2.85261e9i	−0.698469	−	1.20978i
$122$	1.10321e8			0.0450858
$123$	5.72195e8	+	9.91071e8i	0.225409	+	0.390420i
$124$	8.13106e8	+	1.40834e9i	0.308852	+	0.534947i
$125$	−2.94433e9			−1.07868
$126$	9.10878e7	+	1.57769e8i	0.0321953	+	0.0557639i
$127$	2.45126e9	−	4.24570e9i	0.836126	−	1.44821i	−0.0569842	−	0.998375i	$-0.518148\pi$
$127$	2.45126e9	−	4.24570e9i	0.836126	−	1.44821i	0.893110	−	0.449838i	$-0.148518\pi$
$128$	−1.54755e9	+	2.68044e9i	−0.509565	+	0.882593i
$129$	−3.88495e9			−1.23518
$130$	−3.41762e8	+	1.11159e9i	−0.104949	+	0.341350i
$131$	−8.92924e8			−0.264907			−0.132454	−	0.991189i	$-0.542286\pi$
$131$	−8.92924e8			−0.264907			−0.132454	+	0.991189i	$0.542286\pi$
$132$	2.38738e9	−	4.13506e9i	0.684446	−	1.18549i
$133$	1.86583e9	−	3.23172e9i	0.517060	−	0.895574i
$134$	−3.25949e8	−	5.64561e8i	−0.0873331	−	0.151265i
$135$	3.15922e9			0.818611
$136$	9.17961e8	+	1.58996e9i	0.230091	+	0.398529i
$137$	2.36741e9	+	4.10048e9i	0.574158	+	0.994471i	0.996133	+	0.0878633i	$0.0280039\pi$
$137$	2.36741e9	+	4.10048e9i	0.574158	+	0.994471i	−0.421974	+	0.906608i	$0.638663\pi$
$138$	2.50995e9			0.589127
$139$	−1.31446e9	−	2.27672e9i	−0.298664	−	0.517301i	0.677167	−	0.735830i	$-0.263208\pi$
$139$	−1.31446e9	−	2.27672e9i	−0.298664	−	0.517301i	−0.975830	+	0.218529i	$0.929874\pi$
$140$	2.18989e9	−	3.79300e9i	0.481777	−	0.834462i
$141$	−2.96523e9	+	5.13593e9i	−0.631790	+	1.09429i
$142$	−1.51786e9			−0.313281
$143$	−2.27513e9	+	7.39992e9i	−0.454982	+	1.47984i
$144$	3.32221e8			0.0643867
$145$	7.46419e8	−	1.29284e9i	0.140225	−	0.242877i
$146$	5.90342e8	−	1.02250e9i	0.107527	−	0.186242i
$147$	2.16017e9	+	3.74152e9i	0.381557	+	0.660876i
$148$	−7.26633e9			−1.24491
$149$	−2.72279e9	−	4.71602e9i	−0.452560	−	0.783858i	0.545984	−	0.837796i	$-0.316156\pi$
$149$	−2.72279e9	−	4.71602e9i	−0.452560	−	0.783858i	−0.998544	+	0.0539381i	$0.982823\pi$
$150$	3.01738e8	+	5.22626e8i	0.0486653	+	0.0842908i
$151$	−3.29037e9			−0.515049			−0.257524	−	0.966272i	$-0.582907\pi$
$151$	−3.29037e9			−0.515049			−0.257524	+	0.966272i	$0.582907\pi$
$152$	1.93287e9	+	3.34782e9i	0.293701	+	0.508705i
$153$	2.53035e8	−	4.38270e8i	0.0373310	−	0.0646592i
$154$	−2.87783e9	+	4.98455e9i	−0.412308	+	0.714139i
$155$	4.67485e9			0.650541
$156$	−6.37503e9	+	1.46122e9i	−0.861830	+	0.197540i
$157$	−8.34748e9			−1.09650			−0.548248	−	0.836316i	$-0.684705\pi$
$157$	−8.34748e9			−1.09650			−0.548248	+	0.836316i	$0.684705\pi$
$158$	2.90669e9	−	5.03453e9i	0.371058	−	0.642691i
$159$	−2.11317e9	+	3.66012e9i	−0.262209	+	0.454159i
$160$	3.50474e9	+	6.07039e9i	0.422782	+	0.732279i
$161$	1.53267e10			1.79776
$162$	−1.96884e9	−	3.41014e9i	−0.224592	−	0.389004i
$163$	4.96669e9	+	8.60256e9i	0.551090	+	0.954517i	0.998196	+	0.0600355i	$0.0191214\pi$
$163$	4.96669e9	+	8.60256e9i	0.551090	+	0.954517i	−0.447106	+	0.894481i	$0.647545\pi$
$164$	−3.29439e9			−0.355613
$165$	−6.86297e9	−	1.18870e10i	−0.720832	−	1.24852i
$166$	−6.15763e8	+	1.06653e9i	−0.0629400	+	0.109015i
$167$	8.63684e9	−	1.49594e10i	0.859272	−	1.48830i	−0.0133516	−	0.999911i	$-0.504250\pi$
$167$	8.63684e9	−	1.49594e10i	0.859272	−	1.48830i	0.872624	−	0.488393i	$-0.162417\pi$
$168$	−1.06848e10			−1.03484
$169$	9.54585e9	−	4.61867e9i	0.900170	−	0.435538i
$170$	2.40179e9			0.220554
$171$	5.32793e8	−	9.22825e8i	0.0476515	−	0.0825347i
$172$	5.59186e9	−	9.68539e9i	0.487168	−	0.843799i
$173$	7.91384e7	+	1.37072e8i	0.00671707	+	0.0116343i	0.869364	−	0.494172i	$-0.164529\pi$
$173$	7.91384e7	+	1.37072e8i	0.00671707	+	0.0116343i	−0.862647	+	0.505806i	$0.831195\pi$
$174$	−1.65736e9			−0.137071
$175$	1.84252e9	+	3.19134e9i	0.148505	+	0.257218i
$176$	5.24810e9	+	9.08998e9i	0.412283	+	0.714095i
$177$	9.41286e9			0.720845
$178$	−3.70090e9	−	6.41015e9i	−0.276323	−	0.478606i
$179$	3.94718e9	−	6.83671e9i	0.287374	−	0.497747i	−0.685808	−	0.727783i	$-0.740551\pi$
$179$	3.94718e9	−	6.83671e9i	0.287374	−	0.497747i	0.973182	+	0.230036i	$0.0738843\pi$
$180$	6.25328e8	−	1.08310e9i	0.0443998	−	0.0769028i
$181$	−2.63730e10			−1.82644			−0.913221	−	0.407464i	$-0.866413\pi$
$181$	−2.63730e10			−1.82644			−0.913221	+	0.407464i	$0.866413\pi$
$182$	7.68468e9	−	1.76141e9i	0.519164	−	0.118998i
$183$	1.78358e9			0.117561
$184$	−7.93864e9	+	1.37501e10i	−0.510582	+	0.884354i
$185$	−1.04442e10	+	1.80899e10i	−0.655545	+	1.13544i
$186$	−2.59502e9	−	4.49471e9i	−0.158976	−	0.275355i
$187$	1.59888e10			0.956157
$188$	−8.53610e9	−	1.47850e10i	−0.498367	−	0.863197i
$189$	−1.07087e10	−	1.85480e10i	−0.610461	−	1.05735i
$190$	5.05722e9			0.281527
$191$	1.78801e10	+	3.09692e10i	0.972119	+	1.68376i	0.689133	+	0.724635i	$0.257991\pi$
$191$	1.78801e10	+	3.09692e10i	0.972119	+	1.68376i	0.282985	+	0.959124i	$0.408675\pi$
$192$	−1.41791e9	+	2.45589e9i	−0.0752997	+	0.130423i
$193$	5.60742e9	−	9.71234e9i	0.290908	−	0.503867i	−0.683117	−	0.730309i	$-0.739376\pi$
$193$	5.60742e9	−	9.71234e9i	0.290908	−	0.503867i	0.974025	+	0.226442i	$0.0727094\pi$
$194$	−7.11905e8			−0.0360840
$195$	−5.52532e9	+	1.79712e10i	−0.273654	+	0.890066i
$196$	−1.24371e10			−0.601958
$197$	−9.11393e8	+	1.57858e9i	−0.0431129	+	0.0746738i	−0.886777	−	0.462198i	$-0.847061\pi$
$197$	−9.11393e8	+	1.57858e9i	−0.0431129	+	0.0746738i	0.843664	+	0.536872i	$0.180394\pi$
$198$	−8.21771e8	+	1.42335e9i	−0.0379977	+	0.0658140i
$199$	5.42587e9	+	9.39789e9i	0.245262	+	0.424807i	0.962205	−	0.272325i	$-0.0877926\pi$
$199$	5.42587e9	+	9.39789e9i	0.245262	+	0.424807i	−0.716943	+	0.697132i	$0.754459\pi$
$200$	−3.81743e9			−0.168708
$201$	−5.26967e9	−	9.12733e9i	−0.227720	−	0.394422i
$202$	−9.60690e8	−	1.66396e9i	−0.0405978	−	0.0703174i
$203$	−1.01204e10			−0.418279
$204$	6.75378e9	+	1.16979e10i	0.273030	+	0.472903i
$205$	−4.73516e9	+	8.20155e9i	−0.187259	+	0.324342i
$206$	−8.48268e9	+	1.46924e10i	−0.328194	+	0.568449i
$207$	4.37656e9			0.165679
$208$	4.22520e9	−	1.37426e10i	0.156517	−	0.509077i
$209$	3.36662e10			1.22049
$210$	−6.98901e9	+	1.21053e10i	−0.247987	+	0.429526i
$211$	−1.36718e10	+	2.36802e10i	−0.474847	+	0.822460i	−0.999585	−	0.0288041i	$-0.990830\pi$
$211$	−1.36718e10	+	2.36802e10i	−0.474847	+	0.822460i	0.524738	+	0.851264i	$0.324163\pi$
$212$	−6.08324e9	−	1.05365e10i	−0.206835	−	0.358249i
$213$	−2.45394e10			−0.816876
$214$	7.44556e9	+	1.28961e10i	0.242681	+	0.420335i
$215$	−1.60748e10	−	2.78424e10i	−0.513066	−	0.888657i
$216$	2.21868e10			0.693510
$217$	−1.58461e10	−	2.74463e10i	−0.485126	−	0.840264i
$218$	1.05925e10	−	1.83467e10i	0.317646	−	0.550180i
$219$	9.54414e9	−	1.65309e10i	0.280374	−	0.485622i
$220$	3.95132e10			1.13721
$221$	−1.49113e10	−	1.60410e10i	−0.420484	−	0.452340i
$222$	2.31904e10			0.640797
$223$	1.60911e10	−	2.78707e10i	0.435727	−	0.754702i	−0.561628	−	0.827390i	$-0.689825\pi$
$223$	1.60911e10	−	2.78707e10i	0.435727	−	0.754702i	0.997355	+	0.0726886i	$0.0231579\pi$
$224$	2.37598e10	−	4.11531e10i	0.630560	−	1.09216i
$225$	5.26136e8	+	9.11295e8i	0.0136860	+	0.0237049i
$226$	−1.76589e10			−0.450272
$227$	−2.03143e9	−	3.51854e9i	−0.0507791	−	0.0879520i	0.839519	−	0.543331i	$-0.182837\pi$
$227$	−2.03143e9	−	3.51854e9i	−0.0507791	−	0.0879520i	−0.890298	+	0.455379i	$0.849504\pi$
$228$	1.42208e10	+	2.46312e10i	0.348512	+	0.603640i
$229$	−2.36623e10			−0.568587			−0.284293	−	0.958737i	$-0.591759\pi$
$229$	−2.36623e10			−0.568587			−0.284293	+	0.958737i	$0.591759\pi$
$230$	1.03855e10	+	1.79881e10i	0.244709	+	0.423849i
$231$	−4.65262e10	+	8.05858e10i	−1.07509	+	1.86211i
$232$	5.24200e9	−	9.07942e9i	0.118796	−	0.205761i
$233$	5.04339e10			1.12104			0.560519	−	0.828141i	$-0.310602\pi$
$233$	5.04339e10			1.12104			0.560519	+	0.828141i	$0.310602\pi$
$234$	2.19438e9	−	5.02974e8i	0.0478454	−	0.0109667i
$235$	−4.90772e10			−1.04972
$236$	−1.35485e10	+	2.34668e10i	−0.284308	+	0.492435i
$237$	4.69928e10	−	8.13940e10i	0.967529	−	1.67581i
$238$	−8.14124e9	−	1.41010e10i	−0.164473	−	0.284875i
$239$	−2.75780e10			−0.546728			−0.273364	−	0.961911i	$-0.588136\pi$
$239$	−2.75780e10			−0.546728			−0.273364	+	0.961911i	$0.588136\pi$
$240$	1.27454e10	+	2.20757e10i	0.247972	+	0.429500i
$241$	−9.46965e9	−	1.64019e10i	−0.180824	−	0.313197i	0.761337	−	0.648356i	$-0.224543\pi$
$241$	−9.46965e9	−	1.64019e10i	−0.180824	−	0.313197i	−0.942162	+	0.335159i	$0.891210\pi$
$242$	−3.02626e10			−0.567201
$243$	−6.53629e9	−	1.13212e10i	−0.120255	−	0.208288i
$244$	−2.56722e9	+	4.44656e9i	−0.0463670	+	0.0803100i
$245$	−1.78763e10	+	3.09627e10i	−0.316979	+	0.549025i
$246$	1.05140e10			0.183046
$247$	−3.13973e10	−	3.37759e10i	−0.536730	−	0.577392i
$248$	3.28309e10			0.551125
$249$	−9.95512e9	+	1.72428e10i	−0.164115	+	0.284256i
$250$	−1.35254e10	+	2.34267e10i	−0.218988	+	0.379299i
$251$	9.29923e9	+	1.61067e10i	0.147882	+	0.256139i	0.930444	−	0.366433i	$-0.119421\pi$
$251$	9.29923e9	+	1.61067e10i	0.147882	+	0.256139i	−0.782563	+	0.622572i	$0.786088\pi$
$252$	−8.47859e9			−0.132441
$253$	6.91366e10	+	1.19748e11i	1.06088	+	1.83750i
$254$	−2.25208e10	−	3.90071e10i	−0.339494	−	0.588020i
$255$	3.88300e10			0.575091
$256$	9.33048e9	+	1.61609e10i	0.135776	+	0.235172i
$257$	−4.02289e10	+	6.96785e10i	−0.575226	+	0.996321i	0.420791	+	0.907158i	$0.361753\pi$
$257$	−4.02289e10	+	6.96785e10i	−0.575226	+	0.996321i	−0.996017	+	0.0891636i	$0.971581\pi$
$258$	−1.78464e10	+	3.09108e10i	−0.250762	+	0.434332i
$259$	1.41609e11			1.95543
$260$	−3.68503e10	−	3.96421e10i	−0.500105	−	0.537993i
$261$	−2.88991e9			−0.0385480
$262$	−4.10185e9	+	7.10460e9i	−0.0537803	+	0.0931503i
$263$	−5.90696e10	+	1.02312e11i	−0.761313	+	1.31863i	0.180861	+	0.983509i	$0.442112\pi$
$263$	−5.90696e10	+	1.02312e11i	−0.761313	+	1.31863i	−0.942174	+	0.335124i	$0.891222\pi$
$264$	−4.81977e10	−	8.34809e10i	−0.610673	−	1.05772i
$265$	−3.49748e10			−0.435661
$266$	−1.71422e10	−	2.96912e10i	−0.209942	−	0.363631i
$267$	−5.98330e10	−	1.03634e11i	−0.720510	−	1.24796i
$268$	3.03399e10			0.359259
$269$	−4.62528e9	−	8.01123e9i	−0.0538584	−	0.0932854i	0.837839	−	0.545917i	$-0.183819\pi$
$269$	−4.62528e9	−	8.01123e9i	−0.0538584	−	0.0932854i	−0.891698	+	0.452632i	$0.850485\pi$
$270$	1.45126e10	−	2.51365e10i	0.166191	−	0.287851i
$271$	1.57007e9	−	2.71945e9i	0.0176831	−	0.0306280i	−0.857048	−	0.515236i	$-0.827704\pi$
$271$	1.57007e9	−	2.71945e9i	0.0176831	−	0.0306280i	0.874732	+	0.484608i	$0.161038\pi$
$272$	−2.96932e10			−0.328925
$273$	1.24239e11	−	2.84769e10i	1.35371	−	0.310285i
$274$	4.35010e10			0.466253
$275$	−1.66228e10	+	2.87915e10i	−0.175269	+	0.303576i
$276$	−5.84075e10	+	1.01165e11i	−0.605867	+	1.04939i
$277$	−3.15863e10	−	5.47092e10i	−0.322359	−	0.558343i	0.658615	−	0.752480i	$-0.271143\pi$
$277$	−3.15863e10	−	5.47092e10i	−0.322359	−	0.558343i	−0.980974	+	0.194137i	$0.937809\pi$
$278$	−2.41531e10			−0.242534
$279$	−4.52490e9	−	7.83736e9i	−0.0447085	−	0.0774375i
$280$	−4.42107e10	−	7.65751e10i	−0.429849	−	0.744520i
$281$	−8.75717e10			−0.837886			−0.418943	−	0.908012i	$-0.637599\pi$
$281$	−8.75717e10			−0.837886			−0.418943	+	0.908012i	$0.637599\pi$
$282$	2.72429e10	+	4.71861e10i	0.256527	+	0.444317i
$283$	9.97036e10	−	1.72692e11i	0.924000	−	1.60041i	0.130838	−	0.991404i	$-0.458233\pi$
$283$	9.97036e10	−	1.72692e11i	0.924000	−	1.60041i	0.793162	−	0.609011i	$-0.208434\pi$
$284$	3.53212e10	−	6.11781e10i	0.322183	−	0.558038i
$285$	8.17607e10			0.734079
$286$	4.84266e10	+	5.20954e10i	0.427993	+	0.460418i
$287$	6.42024e10			0.558577
$288$	6.78466e9	−	1.17514e10i	0.0581114	−	0.100652i
$289$	3.66782e10	−	6.35284e10i	0.309291	−	0.535708i
$290$	−6.85768e9	−	1.18779e10i	−0.0569359	−	0.0986159i
$291$	−1.15095e10			−0.0940885
$292$	2.74750e10	+	4.75881e10i	0.221164	+	0.383067i
$293$	5.09646e10	+	8.82733e10i	0.403984	+	0.699722i	0.994203	−	0.107522i	$-0.0342916\pi$
$293$	5.09646e10	+	8.82733e10i	0.403984	+	0.699722i	−0.590218	+	0.807244i	$0.700958\pi$
$294$	3.96928e10			0.309848
$295$	3.89478e10	+	6.74595e10i	0.299422	+	0.518614i
$296$	−7.33483e10	+	1.27043e11i	−0.555364	+	0.961918i
$297$	9.66110e10	−	1.67335e11i	0.720481	−	1.24791i
$298$	−5.00310e10			−0.367508
$299$	5.56613e10	−	1.81040e11i	0.402748	−	1.30995i
$300$	−2.80863e10			−0.200193
$301$	−1.08976e11	+	1.88753e11i	−0.765215	+	1.32539i
$302$	−1.51150e10	+	2.61800e10i	−0.104563	+	0.181108i
$303$	−1.55316e10	−	2.69015e10i	−0.105858	−	0.183352i
$304$	−6.25223e10			−0.419859
$305$	7.37995e9	+	1.27824e10i	0.0488319	+	0.0845794i
$306$	−2.32475e9	−	4.02658e9i	−0.0151576	−	0.0262537i
$307$	4.72074e10			0.303311			0.151655	−	0.988433i	$-0.451540\pi$
$307$	4.72074e10			0.303311			0.151655	+	0.988433i	$0.451540\pi$
$308$	−1.33936e11	−	2.31985e11i	−0.848048	−	1.46886i
$309$	−1.37141e11	+	2.37535e11i	−0.855762	+	1.48222i
$310$	2.14750e10	−	3.71957e10i	0.132070	−	0.228752i
$311$	−1.93470e11			−1.17271			−0.586356	−	0.810053i	$-0.699438\pi$
$311$	−1.93470e11			−1.17271			−0.586356	+	0.810053i	$0.699438\pi$
$312$	−3.88036e10	+	1.26210e11i	−0.231834	+	0.754045i
$313$	−1.51502e11			−0.892216			−0.446108	−	0.894979i	$-0.647190\pi$
$313$	−1.51502e11			−0.892216			−0.446108	+	0.894979i	$0.647190\pi$
$314$	−3.83460e10	+	6.64172e10i	−0.222606	+	0.385565i
$315$	−1.21866e10	+	2.11079e10i	−0.0697407	+	0.120794i
$316$	1.35280e11	+	2.34311e11i	0.763204	+	1.32191i
$317$	−1.67360e10			−0.0930862			−0.0465431	−	0.998916i	$-0.514820\pi$
$317$	−1.67360e10			−0.0930862			−0.0465431	+	0.998916i	$0.514820\pi$
$318$	1.94146e10	+	3.36271e10i	0.106465	+	0.184403i
$319$	−4.56520e10	−	7.90715e10i	−0.246832	−	0.427525i
$320$	−2.34677e10			−0.125111
$321$	1.20373e11	+	2.08493e11i	0.632787	+	1.09602i
$322$	7.04064e10	−	1.21947e11i	0.364973	−	0.632152i
$323$	−4.76200e10	+	8.24802e10i	−0.243432	+	0.421637i
$324$	1.83263e11			0.923895
$325$	4.43879e10	−	1.01741e10i	0.220693	−	0.0505851i
$326$	9.12624e10			0.447520
$327$	1.71250e11	−	2.96614e11i	0.828259	−	1.43459i
$328$	−3.32545e10	+	5.75984e10i	−0.158642	+	0.274776i
$329$	1.66355e11	+	2.88135e11i	0.782807	+	1.35586i
$330$	−1.26106e11			−0.585361
$331$	−6.80397e10	−	1.17848e11i	−0.311556	−	0.539631i	0.667143	−	0.744930i	$-0.267517\pi$
$331$	−6.80397e10	−	1.17848e11i	−0.311556	−	0.539631i	−0.978699	+	0.205298i	$0.934184\pi$
$332$	−2.86581e10	−	4.96373e10i	−0.129457	−	0.224226i
$333$	4.04368e10			0.180210
$334$	−7.93505e10	−	1.37439e11i	−0.348892	−	0.604298i
$335$	4.36088e10	−	7.55327e10i	0.189179	−	0.327667i
$336$	8.64051e10	−	1.49658e11i	0.369839	−	0.640580i
$337$	1.77982e10			0.0751694			0.0375847	−	0.999293i	$-0.488034\pi$
$337$	1.77982e10			0.0751694			0.0375847	+	0.999293i	$0.488034\pi$
$338$	7.10230e9	−	9.71690e10i	0.0295988	−	0.404951i
$339$	−2.85493e11			−1.17408
$340$	−5.58905e10	+	9.68052e10i	−0.226821	+	0.392865i
$341$	1.42960e11	−	2.47614e11i	0.572558	−	0.991700i
$342$	−4.89501e9	−	8.47840e9i	−0.0193480	−	0.0335117i
$343$	−9.38905e10			−0.366267
$344$	−1.12892e11	−	1.95534e11i	−0.434659	−	0.752851i
$345$	1.67903e11	+	2.90817e11i	0.638077	+	1.10518i
$346$	1.45416e9			0.00545468
$347$	3.53872e10	+	6.12925e10i	0.131028	+	0.226947i	0.924073	−	0.382216i	$-0.124839\pi$
$347$	3.53872e10	+	6.12925e10i	0.131028	+	0.226947i	−0.793045	+	0.609163i	$0.791506\pi$
$348$	3.85674e10	−	6.68006e10i	0.140966	−	0.244160i
$349$	−9.22353e10	+	1.59756e11i	−0.332799	+	0.576426i	−0.983060	−	0.183286i	$-0.941327\pi$
$349$	−9.22353e10	+	1.59756e11i	−0.332799	+	0.576426i	0.650260	+	0.759712i	$0.274660\pi$
$350$	3.38561e10			0.120596
$351$	−2.57981e11	+	5.91318e10i	−0.907205	+	0.207941i
$352$	4.28709e11			1.48840
$353$	9.62329e10	−	1.66680e11i	0.329866	−	0.571345i	−0.652619	−	0.757686i	$-0.726330\pi$
$353$	9.62329e10	−	1.66680e11i	0.329866	−	0.571345i	0.982485	+	0.186342i	$0.0596631\pi$
$354$	4.32401e10	−	7.48940e10i	0.146343	−	0.253473i
$355$	−1.01537e11	−	1.75868e11i	−0.339311	−	0.587704i
$356$	3.44486e11			1.13670
$357$	−1.31620e11	−	2.27973e11i	−0.428861	−	0.742809i
$358$	−3.62645e10	−	6.28119e10i	−0.116683	−	0.202101i
$359$	3.62698e10			0.115245			0.0576223	−	0.998338i	$-0.481648\pi$
$359$	3.62698e10			0.115245			0.0576223	+	0.998338i	$0.481648\pi$
$360$	−1.26245e10	−	2.18662e10i	−0.0396142	−	0.0686139i
$361$	6.10749e10	−	1.05785e11i	0.189269	−	0.327824i
$362$	−1.21150e11	+	2.09838e11i	−0.370797	+	0.642238i
$363$	−4.89259e11			−1.47897
$364$	−1.07831e11	+	3.50724e11i	−0.321950	+	1.04715i
$365$	1.57964e11			0.465843
$366$	8.19326e9	−	1.41912e10i	0.0238667	−	0.0413383i
$367$	1.45279e11	−	2.51630e11i	0.418027	−	0.724044i	−0.577714	−	0.816239i	$-0.696055\pi$
$367$	1.45279e11	−	2.51630e11i	0.418027	−	0.724044i	0.995741	+	0.0921954i	$0.0293884\pi$
$368$	−1.28395e11	−	2.22387e11i	−0.364951	−	0.632113i
$369$	1.83331e10			0.0514776
$370$	9.59555e10	+	1.66200e11i	0.266172	+	0.461023i
$371$	1.18553e11	+	2.05339e11i	0.324885	+	0.562716i
$372$	2.41549e11			0.653976
$373$	2.58734e11	+	4.48141e11i	0.692093	+	1.19874i	0.971151	+	0.238466i	$0.0766445\pi$
$373$	2.58734e11	+	4.48141e11i	0.692093	+	1.19874i	−0.279058	+	0.960274i	$0.590022\pi$
$374$	7.34482e10	−	1.27216e11i	0.194115	−	0.336217i
$375$	−2.18668e11	+	3.78743e11i	−0.571010	+	0.989018i
$376$	−3.44663e11			−0.889302
$377$	−3.67540e10	+	1.19543e11i	−0.0937063	+	0.304782i
$378$	−1.96771e11			−0.495732
$379$	7.13873e10	−	1.23646e11i	0.177723	−	0.307826i	−0.763377	−	0.645953i	$-0.776460\pi$
$379$	7.13873e10	−	1.23646e11i	0.177723	−	0.307826i	0.941100	+	0.338127i	$0.109793\pi$
$380$	−1.17683e11	+	2.03834e11i	−0.289527	+	0.501475i
$381$	−3.64096e11	−	6.30633e11i	−0.885225	−	1.53325i
$382$	3.28544e11			0.789422
$383$	1.64293e11	+	2.84563e11i	0.390143	+	0.675748i	0.992468	−	0.122503i	$-0.0390922\pi$
$383$	1.64293e11	+	2.84563e11i	0.390143	+	0.675748i	−0.602325	+	0.798251i	$0.705759\pi$
$384$	2.29865e11	+	3.98137e11i	0.539488	+	0.934421i
$385$	−7.70050e11			−1.78626
$386$	−5.15178e10	−	8.92315e10i	−0.118118	−	0.204586i
$387$	−3.11185e10	+	5.38988e10i	−0.0705211	+	0.122146i
$388$	1.65663e10	−	2.86937e10i	0.0371093	−	0.0642752i
$389$	2.42006e11			0.535861			0.267930	−	0.963438i	$-0.413660\pi$
$389$	2.42006e11			0.535861			0.267930	+	0.963438i	$0.413660\pi$
$390$	1.17607e11	+	1.26517e11i	0.257421	+	0.276923i
$391$	−3.91168e11			−0.846385
$392$	−1.25543e11	+	2.17447e11i	−0.268538	+	0.465122i
$393$	−6.63151e10	+	1.14861e11i	−0.140232	+	0.242888i
$394$	8.37337e9	+	1.45031e10i	0.0175052	+	0.0303199i
$395$	7.77773e11			1.60755
$396$	−3.82459e10	−	6.62438e10i	−0.0781549	−	0.135368i
$397$	−2.61446e10	−	4.52838e10i	−0.0528233	−	0.0914926i	0.838405	−	0.545048i	$-0.183489\pi$
$397$	−2.61446e10	−	4.52838e10i	−0.0528233	−	0.0914926i	−0.891228	+	0.453556i	$0.850155\pi$
$398$	9.96998e10			0.199168
$399$	−2.77141e11	−	4.80022e11i	−0.547422	−	0.948163i
$400$	3.08706e10	−	5.34694e10i	0.0602941	−	0.104432i
$401$	−1.25365e11	+	2.17138e11i	−0.242117	+	0.419359i	−0.961317	−	0.275444i	$-0.911175\pi$
$401$	−1.25365e11	+	2.17138e11i	−0.242117	+	0.419359i	0.719200	+	0.694803i	$0.244508\pi$
$402$	−9.68295e10			−0.184923
$403$	−3.81747e11	+	8.75002e10i	−0.720946	+	0.165248i
$404$	8.94225e10			0.167006
$405$	2.63412e11	−	4.56243e11i	0.486505	−	0.842652i
$406$	−4.64904e10	+	8.05238e10i	−0.0849173	+	0.147081i
$407$	6.38781e11	+	1.10640e12i	1.15392	+	1.99866i
$408$	2.72698e11			0.487204
$409$	−3.72424e11	−	6.45057e11i	−0.658086	−	1.13984i	−0.981111	−	0.193448i	$-0.938033\pi$
$409$	−3.72424e11	−	6.45057e11i	−0.658086	−	1.13984i	0.323025	−	0.946391i	$-0.395300\pi$
$410$	4.35041e10	+	7.53512e10i	0.0760331	+	0.131693i
$411$	7.03286e11			1.21575
$412$	−3.94791e11	−	6.83798e11i	−0.675040	−	1.16920i
$413$	2.64039e11	−	4.57330e11i	0.446574	−	0.773489i
$414$	2.01047e10	−	3.48224e10i	0.0336354	−	0.0582581i
$415$	−1.64766e11			−0.272679
$416$	−3.99817e11	−	4.30107e11i	−0.654548	−	0.704136i
$417$	−3.90487e11			−0.632404
$418$	1.54653e11	−	2.67867e11i	0.247779	−	0.429166i
$419$	6.13494e10	−	1.06260e11i	0.0972405	−	0.168425i	−0.813301	−	0.581843i	$-0.802332\pi$
$419$	6.13494e10	−	1.06260e11i	0.0972405	−	0.168425i	0.910541	+	0.413418i	$0.135665\pi$
$420$	−3.25274e11	−	5.63391e11i	−0.510068	−	0.883463i
$421$	9.85222e11			1.52850			0.764249	−	0.644922i	$-0.223110\pi$
$421$	9.85222e11			1.52850			0.764249	+	0.644922i	$0.223110\pi$
$422$	1.25609e11	+	2.17561e11i	0.192803	+	0.333945i
$423$	4.75031e10	+	8.22777e10i	0.0721423	+	0.124954i
$424$	−2.45624e11			−0.369083
$425$	−4.70250e10	−	8.14497e10i	−0.0699163	−	0.121099i
$426$	−1.12727e11	+	1.95249e11i	−0.165839	+	0.287241i
$427$	5.00310e10	−	8.66563e10i	0.0728306	−	0.126146i
$428$	−6.93044e11			−0.998307
$429$	7.82919e11	+	8.42233e11i	1.11599	+	1.20053i
$430$	−2.95373e11			−0.416642
$431$	5.82686e11	−	1.00924e12i	0.813367	−	1.40879i	−0.0971271	−	0.995272i	$-0.530965\pi$
$431$	5.82686e11	−	1.00924e12i	0.813367	−	1.40879i	0.910494	−	0.413521i	$-0.135701\pi$
$432$	−1.79419e11	+	3.10762e11i	−0.247851	+	0.429291i
$433$	3.95376e11	+	6.84812e11i	0.540524	+	0.936215i	0.998874	+	0.0474433i	$0.0151073\pi$
$433$	3.95376e11	+	6.84812e11i	0.540524	+	0.936215i	−0.458350	+	0.888772i	$0.651559\pi$
$434$	−2.91171e11			−0.393953
$435$	−1.10869e11	−	1.92031e11i	−0.148460	−	0.257140i
$436$	4.92983e11	+	8.53871e11i	0.653345	+	1.13163i
$437$	−8.23646e11			−1.08037
$438$	−8.76862e10	−	1.51877e11i	−0.113841	−	0.197178i
$439$	−1.09635e11	+	1.89893e11i	−0.140883	+	0.244017i	−0.927829	−	0.373005i	$-0.878327\pi$
$439$	−1.09635e11	+	1.89893e11i	−0.140883	+	0.244017i	0.786946	+	0.617021i	$0.211661\pi$
$440$	3.98857e11	−	6.90841e11i	0.507318	−	0.878701i
$441$	6.92118e10			0.0871378
$442$	−1.96129e11	+	4.49548e10i	−0.244423	+	0.0560242i
$443$	3.60046e11			0.444162			0.222081	−	0.975028i	$-0.428715\pi$
$443$	3.60046e11			0.444162			0.222081	+	0.975028i	$0.428715\pi$
$444$	−5.39651e11	+	9.34702e11i	−0.659006	+	1.14143i
$445$	4.95144e11	−	8.57615e11i	0.598565	−	1.03675i
$446$	−1.47836e11	−	2.56060e11i	−0.176919	−	0.306433i
$447$	−8.08858e11			−0.958271
$448$	7.95475e10	+	1.37780e11i	0.0932986	+	0.161598i
$449$	−3.46614e11	−	6.00354e11i	−0.402474	−	0.697106i	0.591550	−	0.806269i	$-0.298516\pi$
$449$	−3.46614e11	−	6.00354e11i	−0.402474	−	0.697106i	−0.994024	+	0.109163i	$0.965183\pi$
$450$	9.66770e9			0.0111139
$451$	2.89609e11	+	5.01617e11i	0.329623	+	0.570924i
$452$	4.10929e11	−	7.11750e11i	0.463067	−	0.802056i
$453$	−2.44367e11	+	4.23256e11i	−0.272647	+	0.472238i
$454$	−3.73273e10			−0.0412358
$455$	7.18154e11	+	7.72561e11i	0.785536	+	0.845048i
$456$	5.74195e11			0.621896
$457$	−4.33791e11	+	7.51348e11i	−0.465219	+	0.805783i	−0.999211	−	0.0397060i	$-0.987358\pi$
$457$	−4.33791e11	+	7.51348e11i	−0.465219	+	0.805783i	0.533992	+	0.845489i	$0.320691\pi$
$458$	−1.08698e11	+	1.88270e11i	−0.115432	+	0.199934i
$459$	2.73308e11	+	4.73383e11i	0.287405	+	0.497800i
$460$	−9.66695e11			−1.00665
$461$	2.10599e11	+	3.64767e11i	0.217171	+	0.376151i	0.953942	−	0.299991i	$-0.0969838\pi$
$461$	2.10599e11	+	3.64767e11i	0.217171	+	0.376151i	−0.736771	+	0.676142i	$0.763650\pi$
$462$	4.27457e11	+	7.40378e11i	0.436520	+	0.756074i
$463$	3.14438e10			0.0317995			0.0158998	−	0.999874i	$-0.494939\pi$
$463$	3.14438e10			0.0317995			0.0158998	+	0.999874i	$0.494939\pi$
$464$	8.47814e10	+	1.46846e11i	0.0849121	+	0.147072i
$465$	3.47188e11	−	6.01348e11i	0.344371	−	0.596468i
$466$	2.31679e11	−	4.01280e11i	0.227589	−	0.394195i
$467$	−1.59083e12			−1.54774			−0.773870	−	0.633344i	$-0.781682\pi$
$467$	−1.59083e12			−1.54774			−0.773870	+	0.633344i	$0.781682\pi$
$468$	−3.07914e10	+	1.00150e11i	−0.0296704	+	0.0965038i
$469$	−5.91276e11			−0.564303
$470$	−2.25447e11	+	3.90486e11i	−0.213110	+	0.369118i
$471$	−6.19945e11	+	1.07378e12i	−0.580442	+	1.00536i
$472$	2.73525e11	+	4.73760e11i	0.253664	+	0.439359i
$473$	−1.96632e12			−1.80625
$474$	−4.31744e11	−	7.47803e11i	−0.392847	−	0.680431i
$475$	−9.90161e10	−	1.71501e11i	−0.0892452	−	0.154577i
$476$	7.57799e11			0.676586
$477$	3.38530e10	+	5.86351e10i	0.0299409	+	0.0518591i
$478$	−1.26686e11	+	2.19426e11i	−0.110994	+	0.192248i
$479$	−2.86767e11	+	4.96694e11i	−0.248896	+	0.431101i	−0.963220	−	0.268714i	$-0.913401\pi$
$479$	−2.86767e11	+	4.96694e11i	−0.248896	+	0.431101i	0.714323	+	0.699816i	$0.246735\pi$
$480$	1.04115e12			0.895216
$481$	5.14278e11	−	1.67270e12i	0.438071	−	1.42484i
$482$	−1.74004e11			−0.146841
$483$	1.13827e12	−	1.97154e12i	0.951662	−	1.64833i
$484$	7.04223e11	−	1.21975e12i	0.583319	−	1.01034i
$485$	−4.76229e10	−	8.24853e10i	−0.0390821	−	0.0676922i
$486$	−1.20104e11			−0.0976545
$487$	1.41600e11	+	2.45258e11i	0.114073	+	0.197580i	0.917409	−	0.397946i	$-0.130277\pi$
$487$	1.41600e11	+	2.45258e11i	0.114073	+	0.197580i	−0.803336	+	0.595526i	$0.796944\pi$
$488$	5.18284e10	+	8.97695e10i	0.0413694	+	0.0716539i
$489$	1.47545e12			1.16690
$490$	1.64238e11	+	2.84468e11i	0.128704	+	0.222921i
$491$	7.81748e11	−	1.35403e12i	0.607016	−	1.05138i	−0.384713	−	0.923036i	$-0.625700\pi$
$491$	7.81748e11	−	1.35403e12i	0.607016	−	1.05138i	0.991729	−	0.128347i	$-0.0409671\pi$
$492$	−2.44665e11	+	4.23773e11i	−0.188248	+	0.326054i
$493$	2.58294e11			0.196926
$494$	−4.12971e11	+	9.46571e10i	−0.311995	+	0.0715125i
$495$	−2.19890e11			−0.164620
$496$	−2.65495e11	+	4.59850e11i	−0.196965	+	0.341153i
$497$	−6.88354e11	+	1.19226e12i	−0.506067	+	0.876534i
$498$	9.14621e10	+	1.58417e11i	0.0666360	+	0.115417i
$499$	2.35052e12			1.69712			0.848559	−	0.529100i	$-0.177470\pi$
$499$	2.35052e12			1.69712			0.848559	+	0.529100i	$0.177470\pi$
$500$	−6.29485e11	−	1.09030e12i	−0.450422	−	0.780155i
$501$	−1.28287e12	−	2.22200e12i	−0.909731	−	1.57570i
$502$	1.70872e11			0.120089
$503$	1.05484e12	+	1.82703e12i	0.734732	+	1.27259i	0.954841	+	0.297118i	$0.0960255\pi$
$503$	1.05484e12	+	1.82703e12i	0.734732	+	1.27259i	−0.220109	+	0.975475i	$0.570641\pi$
$504$	−8.55852e10	+	1.48238e11i	−0.0590828	+	0.102334i
$505$	1.28531e11	−	2.22622e11i	0.0879419	−	0.152320i
$506$	1.27038e12			0.861500
$507$	1.14824e11	−	1.57094e12i	0.0771785	−	1.05591i
$508$	2.09627e12			1.39656
$509$	−6.51983e11	+	1.12927e12i	−0.430533	+	0.745704i	−0.996919	−	0.0784354i	$-0.975008\pi$
$509$	−6.51983e11	+	1.12927e12i	−0.430533	+	0.745704i	0.566387	+	0.824140i	$0.308341\pi$
$510$	1.78374e11	−	3.08953e11i	0.116752	−	0.202221i
$511$	−5.35444e11	−	9.27416e11i	−0.347392	−	0.601701i
$512$	−1.41324e12			−0.908872
$513$	5.75478e11	+	9.96758e11i	0.366860	+	0.635421i
$514$	3.69601e11	+	6.40167e11i	0.233560	+	0.404538i
$515$	−2.26980e12			−1.42185
$516$	−8.30585e11	−	1.43862e12i	−0.515775	−	0.893349i
$517$	−1.50081e12	+	2.59949e12i	−0.923888	+	1.60022i
$518$	6.50513e11	−	1.12672e12i	0.396983	−	0.687595i
$519$	2.35096e10			0.0142230
$520$	−1.06507e12	+	2.44125e11i	−0.638798	+	0.146419i
$521$	−2.93717e12			−1.74646			−0.873230	−	0.487308i	$-0.837979\pi$
$521$	−2.93717e12			−1.74646			−0.873230	+	0.487308i	$0.837979\pi$
$522$	−1.32754e10	+	2.29937e10i	−0.00782585	+	0.0135548i
$523$	−7.46413e10	+	1.29283e11i	−0.0436236	+	0.0755583i	−0.887013	−	0.461745i	$-0.847224\pi$
$523$	−7.46413e10	+	1.29283e11i	−0.0436236	+	0.0755583i	0.843389	+	0.537303i	$0.180557\pi$
$524$	−1.90903e11	−	3.30654e11i	−0.110617	−	0.191594i
$525$	5.47357e11			0.314451
$526$	5.42699e11	+	9.39982e11i	0.309117	+	0.535406i
$527$	4.04427e11	+	7.00487e11i	0.228398	+	0.395597i
$528$	1.55905e12			0.872986
$529$	−7.90857e11	−	1.36980e12i	−0.439084	−	0.760516i
$530$	−1.60665e11	+	2.78279e11i	−0.0884461	+	0.153193i
$531$	7.53971e10	−	1.30592e11i	0.0411556	−	0.0712836i
$532$	1.59563e12			0.863633
$533$	2.33162e11	−	7.58365e11i	0.125137	−	0.407011i
$534$	−1.09942e12			−0.585099
$535$	−9.96142e11	+	1.72537e12i	−0.525689	+	0.910521i
$536$	3.06259e11	−	5.30456e11i	0.160268	−	0.277593i
$537$	−5.86292e11	−	1.01549e12i	−0.304249	−	0.526975i
$538$	−8.49891e10			−0.0437364
$539$	1.09334e12	+	1.89372e12i	0.557964	+	0.966422i
$540$	6.75426e11	+	1.16987e12i	0.341827	+	0.592061i
$541$	−6.48443e11			−0.325450			−0.162725	−	0.986671i	$-0.552028\pi$
$541$	−6.48443e11			−0.325450			−0.162725	+	0.986671i	$0.552028\pi$
$542$	−1.44250e10	−	2.49848e10i	−0.00717989	−	0.0124359i
$543$	−1.95865e12	+	3.39248e12i	−0.966847	+	1.67463i
$544$	−6.06399e11	+	1.05031e12i	−0.296868	+	0.514190i
$545$	2.83434e12			1.37616
$546$	3.44142e11	−	1.11933e12i	0.165719	−	0.539004i
$547$	1.75877e12			0.839972			0.419986	−	0.907531i	$-0.362035\pi$
$547$	1.75877e12			0.839972			0.419986	+	0.907531i	$0.362035\pi$
$548$	−1.01228e12	+	1.75333e12i	−0.479502	+	0.830521i
$549$	1.42865e10	−	2.47449e10i	0.00671196	−	0.0116255i
$550$	1.52721e11	+	2.64520e11i	0.0711649	+	0.123261i
$551$	5.43866e11			0.251368
$552$	1.17916e12	+	2.04237e12i	0.540565	+	0.936286i
$553$	−2.63639e12	−	4.56635e12i	−1.19880	−	2.07638i
$554$	−5.80396e11			−0.261776
$555$	1.55133e12	+	2.68697e12i	0.694040	+	1.20211i
$556$	5.62053e11	−	9.73505e11i	0.249426	−	0.432018i
$557$	8.45808e11	−	1.46498e12i	0.372326	−	0.644888i	−0.617597	−	0.786495i	$-0.711894\pi$
$557$	8.45808e11	−	1.46498e12i	0.372326	−	0.644888i	0.989923	+	0.141607i	$0.0452269\pi$
$558$	−8.31446e10			−0.0363061
$559$	1.83380e12	+	1.97273e12i	0.794326	+	0.854504i
$560$	1.43008e12			0.614489
$561$	1.18745e12	−	2.05672e12i	0.506152	−	0.876681i
$562$	−4.02280e11	+	6.96769e11i	−0.170104	+	0.294629i
$563$	−2.14156e12	−	3.70929e12i	−0.898344	−	1.55598i	−0.829610	−	0.558343i	$-0.811437\pi$
$563$	−2.14156e12	−	3.70929e12i	−0.898344	−	1.55598i	−0.0687337	−	0.997635i	$-0.521896\pi$
$564$	−2.53581e12			−1.05526
$565$	−1.18129e12	−	2.04606e12i	−0.487685	−	0.844695i
$566$	−9.16021e11	−	1.58660e12i	−0.375173	−	0.649819i
$567$	−3.57151e12			−1.45120
$568$	−7.13083e11	−	1.23510e12i	−0.287457	−	0.497890i
$569$	−1.05360e12	+	1.82490e12i	−0.421378	+	0.729849i	−0.996075	−	0.0885180i	$-0.971787\pi$
$569$	−1.05360e12	+	1.82490e12i	−0.421378	+	0.729849i	0.574696	+	0.818367i	$0.305120\pi$
$570$	3.75586e11	−	6.50534e11i	0.149030	−	0.258127i
$571$	1.29222e12			0.508713			0.254356	−	0.967111i	$-0.418136\pi$
$571$	1.29222e12			0.508713			0.254356	+	0.967111i	$0.418136\pi$
$572$	−3.22664e12	+	7.39578e11i	−1.26028	+	0.288870i
$573$	5.31162e12			2.05841
$574$	2.94928e11	−	5.10830e11i	0.113400	−	0.196414i
$575$	4.06678e11	−	7.04386e11i	0.155148	−	0.268723i
$576$	2.27150e10	+	3.93435e10i	0.00859826	+	0.0148926i
$577$	1.67362e12			0.628589			0.314295	−	0.949326i	$-0.398232\pi$
$577$	1.67362e12			0.628589			0.314295	+	0.949326i	$0.398232\pi$
$578$	−3.36978e11	−	5.83664e11i	−0.125582	−	0.217514i
$579$	−8.32896e11	−	1.44262e12i	−0.307990	−	0.533455i
$580$	6.38324e11			0.234215
$581$	5.58501e11	+	9.67351e11i	0.203344	+	0.352202i
$582$	−5.28713e10	+	9.15757e10i	−0.0191015	+	0.0330847i
$583$	−1.06955e12	+	1.85252e12i	−0.383437	+	0.664132i
$584$	1.10936e12			0.394652
$585$	2.05070e11	+	2.20607e11i	0.0723938	+	0.0778784i
$586$	9.36470e11			0.328061
$587$	1.74453e11	−	3.02162e11i	0.0606467	−	0.105043i	−0.834108	−	0.551601i	$-0.814017\pi$
$587$	1.74453e11	−	3.02162e11i	0.0606467	−	0.105043i	0.894755	+	0.446558i	$0.147350\pi$
$588$	−9.23668e11	+	1.59984e12i	−0.318653	+	0.551923i
$589$	8.51563e11	+	1.47495e12i	0.291540	+	0.504962i
$590$	7.15661e11			0.243149
$591$	1.35373e11	+	2.34474e11i	0.0456446	+	0.0790588i
$592$	−1.18630e12	−	2.05473e12i	−0.396959	−	0.687553i
$593$	3.90032e12			1.29525			0.647626	−	0.761958i	$-0.275762\pi$
$593$	3.90032e12			1.29525			0.647626	+	0.761958i	$0.275762\pi$
$594$	−8.87608e11	−	1.53738e12i	−0.292538	−	0.506691i
$595$	1.08922e12	−	1.88658e12i	0.356277	−	0.617090i
$596$	1.16424e12	−	2.01653e12i	0.377951	−	0.654630i
$597$	1.61186e12			0.519329
$598$	−1.18476e12	−	1.27452e12i	−0.378857	−	0.407560i
$599$	−8.07785e11			−0.256375			−0.128187	−	0.991750i	$-0.540916\pi$
$599$	−8.07785e11			−0.256375			−0.128187	+	0.991750i	$0.540916\pi$
$600$	−2.83510e11	+	4.91054e11i	−0.0893076	+	0.154685i
$601$	−9.50416e10	+	1.64617e11i	−0.0297152	+	0.0514682i	−0.880501	−	0.474045i	$-0.842793\pi$
$601$	−9.50416e10	+	1.64617e11i	−0.0297152	+	0.0514682i	0.850785	+	0.525513i	$0.176127\pi$
$602$	1.00122e12	+	1.73416e12i	0.310701	+	0.538151i
$603$	−1.68840e11			−0.0520054
$604$	−7.03466e11	−	1.21844e12i	−0.215068	−	0.372510i
$605$	−2.02442e12	−	3.50640e12i	−0.614329	−	1.06405i
$606$	−2.85391e11			−0.0859635
$607$	3.71393e11	+	6.43272e11i	0.111041	+	0.192329i	0.916190	−	0.400743i	$-0.131248\pi$
$607$	3.71393e11	+	6.43272e11i	0.111041	+	0.192329i	−0.805149	+	0.593073i	$0.797915\pi$
$608$	−1.27684e12	+	2.21155e12i	−0.378939	+	0.656342i
$609$	−7.51617e11	+	1.30184e12i	−0.221421	+	0.383512i
$610$	1.35606e11			0.0396546
$611$	4.00763e12	−	9.18590e11i	1.16333	−	0.266647i
$612$	2.16391e11			0.0623531
$613$	−9.21930e11	+	1.59683e12i	−0.263709	+	0.456758i	−0.967225	−	0.253922i	$-0.918279\pi$
$613$	−9.21930e11	+	1.59683e12i	−0.263709	+	0.456758i	0.703515	+	0.710680i	$0.251613\pi$
$614$	2.16858e11	−	3.75609e11i	0.0615768	−	0.106654i
$615$	7.03336e11	+	1.21821e12i	0.198255	+	0.343388i
$616$	−5.40797e12			−1.51328
$617$	2.55042e12	+	4.41745e12i	0.708480	+	1.22712i	0.965421	+	0.260696i	$0.0839521\pi$
$617$	2.55042e12	+	4.41745e12i	0.708480	+	1.22712i	−0.256941	+	0.966427i	$0.582715\pi$
$618$	1.25997e12	+	2.18234e12i	0.347466	+	0.601829i
$619$	−1.32741e12			−0.363409			−0.181705	−	0.983353i	$-0.558161\pi$
$619$	−1.32741e12			−0.363409			−0.181705	+	0.983353i	$0.558161\pi$
$620$	9.99461e11	+	1.73112e12i	0.271646	+	0.470505i
$621$	−2.36360e12	+	4.09387e12i	−0.637766	+	1.10464i
$622$	−8.88747e11	+	1.53935e12i	−0.238079	+	0.412365i
$623$	−6.71348e12			−1.78547
$624$	−1.45398e12	−	1.56413e12i	−0.383908	−	0.412993i
$625$	−2.75543e12			−0.722319
$626$	−6.95960e11	+	1.20544e12i	−0.181134	+	0.313733i
$627$	2.50030e12	−	4.33064e12i	0.646082	−	1.11905i
$628$	−1.78465e12	−	3.09111e12i	−0.457863	−	0.793042i
$629$	−3.61416e12			−0.920618
$630$	1.11964e11	+	1.93927e11i	0.0283169	+	0.0490464i
$631$	2.59515e12	+	4.49493e12i	0.651674	+	1.12873i	0.982717	+	0.185117i	$0.0592663\pi$
$631$	2.59515e12	+	4.49493e12i	0.651674	+	1.12873i	−0.331042	+	0.943616i	$0.607400\pi$
$632$	5.46220e12			1.36189
$633$	2.03073e12	+	3.51733e12i	0.502732	+	0.870757i
$634$	−7.68806e10	+	1.33161e11i	−0.0188980	+	0.0327322i
$635$	3.01306e12	−	5.21877e12i	0.735403	−	1.27376i
$636$	−1.80714e12			−0.437961
$637$	8.80239e11	−	2.86300e12i	0.211823	−	0.688960i
$638$	−8.38850e11			−0.200443
$639$	−1.96561e11	+	3.40454e11i	−0.0466384	+	0.0807800i
$640$	−1.90223e12	+	3.29476e12i	−0.448181	+	0.776272i
$641$	2.95207e12	+	5.11313e12i	0.690661	+	1.19626i	0.971622	+	0.236541i	$0.0760137\pi$
$641$	2.95207e12	+	5.11313e12i	0.690661	+	1.19626i	−0.280960	+	0.959719i	$0.590653\pi$
$642$	2.21185e12			0.513863
$643$	−2.52883e12	−	4.38007e12i	−0.583406	−	1.01049i	−0.995072	−	0.0991539i	$-0.968386\pi$
$643$	−2.52883e12	−	4.38007e12i	−0.583406	−	1.01049i	0.411666	−	0.911335i	$-0.364947\pi$
$644$	3.27677e12	+	5.67553e12i	0.750688	+	1.30023i
$645$	−4.77534e12			−1.08639
$646$	4.37506e11	+	7.57782e11i	0.0988411	+	0.171198i
$647$	2.50348e12	−	4.33615e12i	0.561662	−	0.972827i	−0.435690	−	0.900097i	$-0.643496\pi$
$647$	2.50348e12	−	4.33615e12i	0.561662	−	0.972827i	0.997352	−	0.0727298i	$-0.0231711\pi$
$648$	1.84991e12	−	3.20413e12i	0.412157	−	0.713877i
$649$	4.76420e12			1.05412
$650$	1.22954e11	−	3.99912e11i	0.0270168	−	0.0878727i
$651$	−4.70740e12			−1.02723
$652$	−2.12371e12	+	3.67838e12i	−0.460237	+	0.797153i
$653$	1.85211e11	−	3.20794e11i	0.0398618	−	0.0690426i	−0.845406	−	0.534124i	$-0.820642\pi$
$653$	1.85211e11	−	3.20794e11i	0.0398618	−	0.0690426i	0.885268	+	0.465081i	$0.153975\pi$
$654$	−1.57335e12	−	2.72512e12i	−0.336299	−	0.582487i
$655$	−1.09757e12			−0.232995
$656$	−5.37840e11	−	9.31566e11i	−0.113393	−	0.196402i
$657$	−1.52897e11	−	2.64826e11i	−0.0320151	−	0.0554518i
$658$	3.05676e12			0.635688
$659$	−1.31557e12	−	2.27864e12i	−0.271726	−	0.470642i	0.697578	−	0.716509i	$-0.254261\pi$
$659$	−1.31557e12	−	2.27864e12i	−0.271726	−	0.470642i	−0.969304	+	0.245866i	$0.920928\pi$
$660$	2.93454e12	−	5.08278e12i	0.601995	−	1.04269i
$661$	−1.14571e12	+	1.98443e12i	−0.233436	+	0.404323i	−0.958817	−	0.284024i	$-0.908330\pi$
$661$	−1.14571e12	+	1.98443e12i	−0.233436	+	0.404323i	0.725381	+	0.688348i	$0.241664\pi$
$662$	−1.25022e12			−0.253003
$663$	−3.17084e12	+	7.26790e11i	−0.637329	+	0.146082i
$664$	−1.15713e12			−0.231007
$665$	2.29346e12	−	3.97239e12i	0.454773	−	0.787689i
$666$	1.85756e11	−	3.21738e11i	0.0365854	−	0.0633678i
$667$	1.11688e12	+	1.93449e12i	0.218494	+	0.378443i
$668$	7.38607e12			1.43522
$669$	−2.39009e12	−	4.13976e12i	−0.461314	−	0.799019i
$670$	−4.00654e11	−	6.93952e11i	−0.0768126	−	0.133043i
$671$	9.02735e11			0.171913
$672$	−3.52915e12	−	6.11266e12i	−0.667587	−	1.15630i
$673$	3.16406e11	−	5.48031e11i	0.0594534	−	0.102976i	−0.834767	−	0.550604i	$-0.814398\pi$
$673$	3.16406e11	−	5.48031e11i	0.0594534	−	0.102976i	0.894220	+	0.447627i	$0.147731\pi$
$674$	8.17599e10	−	1.41612e11i	0.0152606	−	0.0264321i
$675$	−1.13658e12			−0.210733
$676$	3.75117e12	+	2.54742e12i	0.690887	+	0.469182i
$677$	−4.59387e11			−0.0840484			−0.0420242	−	0.999117i	$-0.513381\pi$
$677$	−4.59387e11			−0.0840484			−0.0420242	+	0.999117i	$0.513381\pi$
$678$	−1.31148e12	+	2.27154e12i	−0.238357	+	0.412846i
$679$	−3.22851e11	+	5.59195e11i	−0.0582892	+	0.100960i
$680$	1.12835e12	+	1.95436e12i	0.202373	+	0.350521i
$681$	−6.03475e11			−0.107522
$682$	−1.31344e12	−	2.27494e12i	−0.232477	−	0.402661i
$683$	5.98622e11	+	1.03684e12i	0.105259	+	0.182314i	0.913844	−	0.406065i	$-0.133100\pi$
$683$	5.98622e11	+	1.03684e12i	0.105259	+	0.182314i	−0.808585	+	0.588379i	$0.799766\pi$
$684$	4.55635e11			0.0795911
$685$	2.91000e12	+	5.04027e12i	0.504993	+	0.874673i
$686$	−4.31307e11	+	7.47045e11i	−0.0743580	+	0.128792i
$687$	−1.75733e12	+	3.04379e12i	−0.300988	+	0.521326i
$688$	3.65170e12			0.621365
$689$	2.85603e12	−	6.54632e11i	0.482810	−	0.110665i
$690$	3.08520e12			0.518158
$691$	5.71951e12	−	9.90649e12i	0.954350	−	1.65298i	0.218503	−	0.975836i	$-0.429883\pi$
$691$	5.71951e12	−	9.90649e12i	0.954350	−	1.65298i	0.735848	−	0.677147i	$-0.236784\pi$
$692$	−3.38389e10	+	5.86106e10i	−0.00560968	+	0.00971626i
$693$	7.45351e11	+	1.29099e12i	0.122761	+	0.212629i
$694$	6.50236e11			0.106403
$695$	−1.61573e12	−	2.79852e12i	−0.262685	−	0.454985i
$696$	−7.78619e11	−	1.34861e12i	−0.125772	−	0.217843i
$697$	−1.63858e12			−0.262978
$698$	8.47406e11	+	1.46775e12i	0.135127	+	0.234047i
$699$	3.74559e12	−	6.48755e12i	0.593434	−	1.02786i
$700$	−7.87846e11	+	1.36459e12i	−0.124022	+	0.214813i
$701$	−7.96702e12			−1.24613			−0.623067	−	0.782169i	$-0.714114\pi$
$701$	−7.96702e12			−1.24613			−0.623067	+	0.782169i	$0.714114\pi$
$702$	−7.14606e11	+	2.32427e12i	−0.111058	+	0.361219i
$703$	−7.61000e12			−1.17513
$704$	−7.17657e11	+	1.24302e12i	−0.110113	+	0.190722i
$705$	−3.64483e12	+	6.31303e12i	−0.555682	+	0.962470i
$706$	−8.84135e11	−	1.53137e12i	−0.133936	−	0.231984i
$707$	−1.74270e12			−0.262323
$708$	2.01243e12	+	3.48563e12i	0.301003	+	0.521352i
$709$	1.66249e12	+	2.87953e12i	0.247088	+	0.427970i	0.962717	−	0.270512i	$-0.0871929\pi$
$709$	1.66249e12	+	2.87953e12i	0.247088	+	0.427970i	−0.715628	+	0.698481i	$0.753860\pi$
$710$	−1.86574e12			−0.275542
$711$	−7.52826e11	−	1.30393e12i	−0.110479	−	0.191356i
$712$	3.47733e12	−	6.02292e12i	0.507092	−	0.878308i
$713$	−3.49753e12	+	6.05790e12i	−0.506825	+	0.877847i
$714$	−2.41851e12			−0.348262
$715$	−2.79657e12	+	9.09591e12i	−0.400173	+	1.30157i
$716$	3.37555e12			0.479995
$717$	−2.04814e12	+	3.54748e12i	−0.289417	+	0.501285i
$718$	1.66613e11	−	2.88583e11i	0.0233965	−	0.0405239i
$719$	−7.38632e11	−	1.27935e12i	−0.103074	−	0.178529i	0.809876	−	0.586601i	$-0.199534\pi$
$719$	−7.38632e11	−	1.27935e12i	−0.103074	−	0.178529i	−0.912950	+	0.408072i	$0.866201\pi$
$720$	4.08362e11			0.0566304
$721$	7.69384e12	+	1.33261e13i	1.06031	+	1.83652i
$722$	−5.61122e11	−	9.71893e11i	−0.0768494	−	0.133107i
$723$	−2.81314e12			−0.382886
$724$	−5.63843e12	−	9.76604e12i	−0.762666	−	1.32098i
$725$	−2.68536e11	+	4.65117e11i	−0.0360978	+	0.0625232i
$726$	−2.24752e12	+	3.89282e12i	−0.300254	+	0.520056i
$727$	−5.16476e12			−0.685717			−0.342859	−	0.939387i	$-0.611395\pi$
$727$	−5.16476e12			−0.685717			−0.342859	+	0.939387i	$0.611395\pi$
$728$	5.04350e12	+	5.42560e12i	0.665489	+	0.715907i
$729$	6.49430e12			0.851644
$730$	7.25642e11	−	1.25685e12i	0.0945735	−	0.163806i
$731$	2.78131e12	−	4.81736e12i	0.360264	−	0.623995i
$732$	3.81321e11	+	6.60467e11i	0.0490898	+	0.0850259i
$733$	2.65026e12			0.339094			0.169547	−	0.985522i	$-0.445770\pi$
$733$	2.65026e12			0.339094			0.169547	+	0.985522i	$0.445770\pi$
$734$	−1.33474e12	−	2.31183e12i	−0.169732	−	0.293985i
$735$	2.65525e12	+	4.59904e12i	0.335593	+	0.581264i
$736$	−1.04884e13			−1.31753
$737$	−2.66717e12	−	4.61968e12i	−0.333002	−	0.576777i
$738$	8.42174e10	−	1.45869e11i	0.0104508	−	0.0181013i
$739$	−1.73033e12	+	2.99702e12i	−0.213417	+	0.369649i	−0.952782	−	0.303656i	$-0.901793\pi$
$739$	−1.73033e12	+	2.99702e12i	−0.213417	+	0.369649i	0.739365	+	0.673305i	$0.235126\pi$
$740$	−8.93169e12			−1.09494
$741$	−6.67655e12	+	1.53033e12i	−0.813524	+	0.186468i
$742$	2.17839e12			0.263827
$743$	3.72154e12	−	6.44590e12i	0.447995	−	0.775950i	−0.550260	−	0.834993i	$-0.685471\pi$
$743$	3.72154e12	−	6.44590e12i	0.447995	−	0.775950i	0.998255	+	0.0590428i	$0.0188048\pi$
$744$	2.43826e12	−	4.22319e12i	0.291744	−	0.505315i
$745$	−3.34683e12	−	5.79688e12i	−0.398043	−	0.689431i
$746$	4.75422e12			0.562023
$747$	1.59481e11	+	2.76229e11i	0.0187399	+	0.0324584i
$748$	3.41834e12	+	5.92073e12i	0.399262	+	0.691542i
$749$	1.35063e13			1.56808
$750$	2.00900e12	+	3.47968e12i	0.231848	+	0.401572i
$751$	−3.71424e12	+	6.43326e12i	−0.426080	+	0.737991i	−0.996521	−	0.0833472i	$-0.973439\pi$
$751$	−3.71424e12	+	6.43326e12i	−0.426080	+	0.737991i	0.570441	+	0.821339i	$0.306772\pi$
$752$	2.78720e12	−	4.82757e12i	0.317825	−	0.550489i
$753$	2.76251e12			0.313132
$754$	7.82316e11	+	8.41585e11i	0.0881478	+	0.0948259i
$755$	−4.04448e12			−0.453004
$756$	4.57893e12	−	7.93094e12i	0.509819	−	0.883033i
$757$	3.99089e12	−	6.91242e12i	0.441711	−	0.765066i	−0.556106	−	0.831112i	$-0.687705\pi$
$757$	3.99089e12	−	6.91242e12i	0.441711	−	0.765066i	0.997817	+	0.0660459i	$0.0210384\pi$
$758$	−6.55867e11	−	1.13599e12i	−0.0721613	−	0.124987i
$759$	2.05384e13			2.24635
$760$	2.37586e12	+	4.11511e12i	0.258321	+	0.447425i
$761$	5.70907e11	+	9.88840e11i	0.0617070	+	0.106880i	0.895229	−	0.445607i	$-0.147012\pi$
$761$	5.70907e11	+	9.88840e11i	0.0617070	+	0.106880i	−0.833522	+	0.552487i	$0.813679\pi$
$762$	−6.69023e12			−0.718859
$763$	−9.60745e12	−	1.66406e13i	−1.02624	−	1.77749i
$764$	−7.64536e12	+	1.32421e13i	−0.811854	+	1.40617i
$765$	3.11028e11	−	5.38717e11i	0.0328340	−	0.0568701i
$766$	3.01886e12			0.316821
$767$	−4.44312e12	−	4.77973e12i	−0.463563	−	0.498683i
$768$	2.77180e12			0.287499
$769$	7.16990e12	−	1.24186e13i	0.739340	−	1.28057i	−0.213452	−	0.976953i	$-0.568471\pi$
$769$	7.16990e12	−	1.24186e13i	0.739340	−	1.28057i	0.952793	−	0.303621i	$-0.0981958\pi$
$770$	−3.53740e12	+	6.12695e12i	−0.362640	+	0.628111i
$771$	5.97538e12	+	1.03497e13i	0.609005	+	1.05483i
$772$	4.79536e12			0.485896
$773$	−7.11868e12	−	1.23299e13i	−0.717119	−	1.24209i	−0.962136	−	0.272568i	$-0.912127\pi$
$773$	−7.11868e12	−	1.23299e13i	−0.717119	−	1.24209i	0.245017	−	0.969519i	$-0.421206\pi$
$774$	2.85899e11	+	4.95192e11i	0.0286338	+	0.0495952i
$775$	−1.68185e12			−0.167467
$776$	−3.34450e11	−	5.79284e11i	−0.0331095	−	0.0573474i
$777$	1.05169e13	−	1.82159e13i	1.03513	−	1.79290i
$778$	1.11171e12	−	1.92553e12i	0.108788	−	0.188427i
$779$	−3.45020e12			−0.335680
$780$	−7.83612e12	+	1.79612e12i	−0.758011	+	0.173744i
$781$	−1.24203e13			−1.19455
$782$	−1.79692e12	+	3.11235e12i	−0.171829	+	0.297617i
$783$	1.56072e12	−	2.70325e12i	0.148387	−	0.257014i
$784$	−2.03047e12	−	3.51688e12i	−0.191944	−	0.332457i
$785$	−1.02606e13			−0.964407
$786$	6.09266e11	+	1.05528e12i	0.0569384	+	0.0986202i
$787$	6.56039e12	+	1.13629e13i	0.609598	+	1.05585i	0.991307	+	0.131572i	$0.0420025\pi$
$787$	6.56039e12	+	1.13629e13i	0.609598	+	1.05585i	−0.381708	+	0.924283i	$0.624664\pi$
$788$	−7.79407e11			−0.0720105
$789$	8.77388e12	+	1.51968e13i	0.806019	+	1.39607i
$790$	3.57287e12	−	6.18839e12i	0.326359	−	0.565270i
$791$	−8.00835e12	+	1.38709e13i	−0.727359	+	1.25982i
$792$	−1.54426e12			−0.139462
$793$	−8.41896e11	−	9.05678e11i	−0.0756013	−	0.0813288i
$794$	−4.80405e11			−0.0428958
$795$	−2.59748e12	+	4.49898e12i	−0.230622	+	0.399449i
$796$	−2.32005e12	+	4.01845e12i	−0.204828	+	0.354772i
$797$	−9.97986e11	−	1.72856e12i	−0.0876117	−	0.151748i	0.818889	−	0.573951i	$-0.194590\pi$
$797$	−9.97986e11	−	1.72856e12i	−0.0876117	−	0.151748i	−0.906501	+	0.422203i	$0.861257\pi$
$798$	−5.09243e12			−0.444541
$799$	−4.24573e12	−	7.35382e12i	−0.368546	−	0.638340i
$800$	−1.26088e12	−	2.18392e12i	−0.108835	−	0.188508i
$801$	−1.91705e12			−0.164546
$802$	1.15178e12	+	1.99494e12i	0.0983071	+	0.170273i
$803$	4.83064e12	−	8.36691e12i	0.410001	−	0.710142i
$804$	2.25326e12	−	3.90276e12i	0.190178	−	0.329397i
$805$	1.88394e13			1.58119
$806$	−1.05744e12	+	3.43934e12i	−0.0882565	+	0.287057i
$807$	−1.37403e12			−0.114042
$808$	9.02656e11	−	1.56345e12i	0.0745025	−	0.129042i
$809$	−7.35588e12	+	1.27408e13i	−0.603763	+	1.04575i	0.388483	+	0.921456i	$0.372999\pi$
$809$	−7.35588e12	+	1.27408e13i	−0.603763	+	1.04575i	−0.992246	+	0.124292i	$0.960334\pi$
$810$	−2.42008e12	−	4.19170e12i	−0.197537	−	0.342143i
$811$	1.06958e13			0.868199			0.434100	−	0.900865i	$-0.357067\pi$
$811$	1.06958e13			0.868199			0.434100	+	0.900865i	$0.357067\pi$
$812$	−2.16370e12	−	3.74764e12i	−0.174661	−	0.302521i
$813$	−2.33210e11	−	4.03932e11i	−0.0187215	−	0.0324265i
$814$	1.17375e13			0.937059
$815$	6.10500e12	+	1.05742e13i	0.484704	+	0.839532i
$816$	−2.20524e12	+	3.81958e12i	−0.174120	+	0.301585i
$817$	5.85634e12	−	1.01435e13i	0.459861	−	0.796503i
$818$	−6.84325e12			−0.534407
$819$	6.00076e11	−	1.95176e12i	0.0466046	−	0.151583i
$820$	−4.04943e12			−0.312774
$821$	−8.16792e12	+	1.41473e13i	−0.627433	+	1.08675i	0.360632	+	0.932708i	$0.382561\pi$
$821$	−8.16792e12	+	1.41473e13i	−0.627433	+	1.08675i	−0.988065	+	0.154038i	$0.950772\pi$
$822$	3.23070e12	−	5.59573e12i	0.246816	−	0.427498i
$823$	5.52544e12	+	9.57034e12i	0.419824	+	0.727157i	0.995921	−	0.0902244i	$-0.0287584\pi$
$823$	5.52544e12	+	9.57034e12i	0.419824	+	0.727157i	−0.576097	+	0.817381i	$0.695425\pi$
$824$	−1.59405e13			−1.20456
$825$	2.46906e12	+	4.27653e12i	0.185562	+	0.321402i
$826$	−2.42585e12	−	4.20169e12i	−0.181323	−	0.314061i
$827$	1.02665e13			0.763215			0.381608	−	0.924324i	$-0.375371\pi$
$827$	1.02665e13			0.763215			0.381608	+	0.924324i	$0.375371\pi$
$828$	9.35689e11	+	1.62066e12i	0.0691823	+	0.119827i
$829$	−1.23741e13	+	2.14326e13i	−0.909952	+	1.57608i	−0.0958240	+	0.995398i	$0.530549\pi$
$829$	−1.23741e13	+	2.14326e13i	−0.909952	+	1.57608i	−0.814128	+	0.580685i	$0.802785\pi$
$830$	−7.56889e11	+	1.31097e12i	−0.0553580	+	0.0958829i
$831$	−9.38333e12			−0.682578
$832$	1.91636e12	−	4.39250e11i	0.138651	−	0.0317802i
$833$	−6.18601e12			−0.445152
$834$	−1.79379e12	+	3.10693e12i	−0.128388	+	0.222374i
$835$	1.06163e13	−	1.83880e13i	0.755761	−	1.30902i
$836$	7.19767e12	+	1.24667e13i	0.509640	+	0.882723i
$837$	9.77484e12			0.688407
$838$	−5.63644e11	−	9.76260e11i	−0.0394827	−	0.0683860i
$839$	1.99560e12	+	3.45649e12i	0.139042	+	0.240828i	0.927134	−	0.374729i	$-0.122264\pi$
$839$	1.99560e12	+	3.45649e12i	0.139042	+	0.240828i	−0.788092	+	0.615557i	$0.788931\pi$
$840$	−1.31336e13			−0.910181
$841$	6.51608e12	+	1.12862e13i	0.449163	+	0.777974i
$842$	4.52584e12	−	7.83898e12i	0.310309	−	0.537471i
$843$	−6.50371e12	+	1.12648e13i	−0.443544	+	0.768241i
$844$	−1.16919e13			−0.793127
$845$	1.17337e13	−	5.67721e12i	0.791732	−	0.383072i
$846$	8.72864e11			0.0585841
$847$	−1.37242e13	+	2.37710e13i	−0.916244	+	1.58698i
$848$	1.98629e12	−	3.44036e12i	0.131905	−	0.228467i
$849$	−1.48094e13	−	2.56507e13i	−0.978259	−	1.69439i
$850$	−8.64079e11			−0.0567764
$851$	−1.56278e13	−	2.70682e13i	−1.02145	−	1.76920i
$852$	−5.24642e12	−	9.08706e12i	−0.341102	−	0.590807i
$853$	−3.00925e11			−0.0194620			−0.00973099	−	0.999953i	$-0.503098\pi$
$853$	−3.00925e11			−0.0194620			−0.00973099	+	0.999953i	$0.503098\pi$
$854$	−4.59657e11	−	7.96150e11i	−0.0295715	−	0.0512194i
$855$	6.54903e11	−	1.13433e12i	0.0419112	−	0.0725923i
$856$	−6.99578e12	+	1.21170e13i	−0.445353	+	0.771374i
$857$	−7.65732e12			−0.484912			−0.242456	−	0.970162i	$-0.577953\pi$
$857$	−7.65732e12			−0.484912			−0.242456	+	0.970162i	$0.577953\pi$
$858$	1.02978e13	−	2.36036e12i	0.648711	−	0.148691i
$859$	1.94999e13			1.22198			0.610988	−	0.791640i	$-0.290773\pi$
$859$	1.94999e13			1.22198			0.610988	+	0.791640i	$0.290773\pi$
$860$	6.87345e12	−	1.19052e13i	0.428481	−	0.742152i
$861$	4.76814e12	−	8.25866e12i	0.295689	−	0.512148i
$862$	−5.35339e12	−	9.27235e12i	−0.330253	−	0.572014i
$863$	−1.52132e13			−0.933626			−0.466813	−	0.884356i	$-0.654598\pi$
$863$	−1.52132e13			−0.933626			−0.466813	+	0.884356i	$0.654598\pi$
$864$	7.32822e12	+	1.26928e13i	0.447390	+	0.774902i
$865$	9.72761e10	+	1.68487e11i	0.00590790	+	0.0102328i
$866$	7.26499e12			0.438940
$867$	−5.44797e12	−	9.43617e12i	−0.327453	−	0.567165i
$868$	6.77567e12	−	1.17358e13i	0.405148	−	0.701736i
$869$	2.37848e13	−	4.11965e13i	1.41485	−	2.45059i
$870$	−2.03721e12			−0.120559
$871$	−2.14732e12	+	6.98421e12i	−0.126420	+	0.411183i
$872$	1.99052e13			1.16585
$873$	−9.21909e10	+	1.59679e11i	−0.00537185	+	0.00930432i
$874$	−3.78360e12	+	6.55339e12i	−0.219333	+	0.379896i
$875$	1.22677e13	+	2.12482e13i	0.707498	+	1.22542i
$876$	8.16197e12			0.468303
$877$	1.54217e12	+	2.67112e12i	0.0880307	+	0.152474i	0.906679	−	0.421822i	$-0.138609\pi$
$877$	1.54217e12	+	2.67112e12i	0.0880307	+	0.152474i	−0.818648	+	0.574296i	$0.805276\pi$
$878$	1.00727e12	+	1.74463e12i	0.0572030	+	0.0990784i
$879$	1.51400e13			0.855415
$880$	6.45091e12	+	1.11733e13i	0.362618	+	0.628072i
$881$	−6.29558e12	+	1.09043e13i	−0.352082	+	0.609824i	−0.986614	−	0.163072i	$-0.947860\pi$
$881$	−6.29558e12	+	1.09043e13i	−0.352082	+	0.609824i	0.634532	+	0.772897i	$0.281193\pi$
$882$	3.17940e11	−	5.50688e11i	0.0176903	−	0.0306406i
$883$	1.13028e13			0.625696			0.312848	−	0.949803i	$-0.398717\pi$
$883$	1.13028e13			0.625696			0.312848	+	0.949803i	$0.398717\pi$
$884$	2.75208e12	−	8.95120e12i	0.151574	−	0.492999i
$885$	1.15702e13			0.634009
$886$	1.65395e12	−	2.86473e12i	0.0901719	−	0.156182i
$887$	−1.47392e13	+	2.55291e13i	−0.799501	+	1.38478i	0.120441	+	0.992721i	$0.461569\pi$
$887$	−1.47392e13	+	2.55291e13i	−0.799501	+	1.38478i	−0.919942	+	0.392056i	$0.871764\pi$
$888$	1.08948e13	+	1.88703e13i	0.587976	+	1.01840i
$889$	−4.08529e13			−2.19364
$890$	−4.54911e12	−	7.87929e12i	−0.243036	−	0.420951i
$891$	−1.61106e13	−	2.79044e13i	−0.856372	−	1.48328i
$892$	1.37608e13			0.727785
$893$	−8.93983e12	−	1.54842e13i	−0.470433	−	0.814814i
$894$	−3.71567e12	+	6.43573e12i	−0.194544	+	0.336960i
$895$	4.85182e12	−	8.40361e12i	0.252756	−	0.437786i
$896$	2.57917e13			1.33688
$897$	−1.91542e13	−	2.06053e13i	−0.987866	−	1.06271i
$898$	−6.36900e12			−0.326834
$899$	2.30947e12	−	4.00012e12i	0.117922	−	0.204247i
$900$	−2.24971e11	+	3.89661e11i	−0.0114297	+	0.0197968i
$901$	−3.02571e12	−	5.24069e12i	−0.152956	−	0.264927i
$902$	5.32153e12			0.267675
$903$	1.61868e13	+	2.80363e13i	0.810150	+	1.40322i
$904$	−8.29606e12	−	1.43692e13i	−0.413156	−	0.715607i
$905$	−3.24174e13			−1.60642
$906$	2.24511e12	+	3.88864e12i	0.110703	+	0.191743i
$907$	−7.93735e12	+	1.37479e13i	−0.389442	+	0.674533i	−0.992375	−	0.123259i	$-0.960665\pi$
$907$	−7.93735e12	+	1.37479e13i	−0.389442	+	0.674533i	0.602933	+	0.797792i	$0.293999\pi$
$908$	8.68620e11	−	1.50449e12i	0.0424076	−	0.0734521i
$909$	−4.97633e11			−0.0241753
$910$	9.44593e12	−	2.16510e12i	0.456624	−	0.104663i
$911$	−9.45057e12			−0.454596			−0.227298	−	0.973825i	$-0.572989\pi$
$911$	−9.45057e12			−0.454596			−0.227298	+	0.973825i	$0.572989\pi$
$912$	−4.64336e12	+	8.04254e12i	−0.222257	+	0.384961i
$913$	−5.03865e12	+	8.72720e12i	−0.239991	+	0.415677i
$914$	3.98543e12	+	6.90297e12i	0.188894	+	0.327173i
$915$	2.19236e12			0.103399
$916$	−5.05889e12	−	8.76225e12i	−0.237424	−	0.411231i
$917$	3.72040e12	+	6.44392e12i	0.173751	+	0.300946i
$918$	5.02200e12			0.233391
$919$	−7.55903e12	−	1.30926e13i	−0.349580	−	0.605490i	0.636595	−	0.771198i	$-0.280342\pi$
$919$	−7.55903e12	−	1.30926e13i	−0.349580	−	0.605490i	−0.986175	+	0.165708i	$0.947009\pi$
$920$	−9.75808e12	+	1.69015e13i	−0.449075	+	0.777822i
$921$	3.50597e12	−	6.07251e12i	0.160561	−	0.278100i
$922$	3.86973e12			0.176356
$923$	1.15833e13	+	1.24608e13i	0.525319	+	0.565117i
$924$	−3.97884e13			−1.79570
$925$	3.75746e12	−	6.50811e12i	0.168755	−	0.292292i
$926$	1.44444e11	−	2.50185e11i	0.00645581	−	0.0111818i
$927$	2.19699e12	+	3.80531e12i	0.0977170	+	0.169251i
$928$	6.92566e12			0.306546
$929$	1.66280e13	+	2.88005e13i	0.732435	+	1.26862i	0.955840	+	0.293889i	$0.0949497\pi$
$929$	1.66280e13	+	2.88005e13i	0.732435	+	1.26862i	−0.223404	+	0.974726i	$0.571717\pi$
$930$	−3.18977e12	−	5.52485e12i	−0.139826	−	0.242185i
$931$	−1.30253e13			−0.568217
$932$	1.07825e13	+	1.86759e13i	0.468111	+	0.810793i
$933$	−1.43685e13	+	2.48869e13i	−0.620788	+	1.07524i
$934$	−7.30783e12	+	1.26575e13i	−0.314216	+	0.544237i
$935$	1.96533e13			0.840974
$936$	1.44018e12	+	1.54929e12i	0.0613305	+	0.0659769i
$937$	3.60385e13			1.52735			0.763674	−	0.645602i	$-0.223393\pi$
$937$	3.60385e13			1.52735			0.763674	+	0.645602i	$0.223393\pi$
$938$	−2.71616e12	+	4.70452e12i	−0.114562	+	0.198428i
$939$	−1.12517e13	+	1.94885e13i	−0.472304	+	0.818055i
$940$	−1.04925e13	−	1.81735e13i	−0.438332	−	0.759213i
$941$	−1.35496e13			−0.563341			−0.281671	−	0.959511i	$-0.590889\pi$
$941$	−1.35496e13			−0.563341			−0.281671	+	0.959511i	$0.590889\pi$
$942$	5.69571e12	+	9.86525e12i	0.235678	+	0.408206i
$943$	−7.08531e12	−	1.22721e13i	−0.291781	−	0.505379i
$944$	−8.84771e12			−0.362624
$945$	−1.31630e13	−	2.27990e13i	−0.536922	−	0.929976i
$946$	−9.03271e12	+	1.56451e13i	−0.366698	+	0.635139i
$947$	1.69093e13	−	2.92878e13i	0.683205	−	1.18335i	−0.290792	−	0.956786i	$-0.593919\pi$
$947$	1.69093e13	−	2.92878e13i	0.683205	−	1.18335i	0.973997	−	0.226560i	$-0.0727480\pi$
$948$	4.01874e13			1.61604
$949$	−1.28993e13	+	2.95665e12i	−0.516259	+	0.118332i
$950$	−1.81941e12			−0.0724727
$951$	−1.24294e12	+	2.15283e12i	−0.0492762	+	0.0853489i
$952$	7.64943e12	−	1.32492e13i	0.301830	−	0.522786i
$953$	−9.21335e12	−	1.59580e13i	−0.361826	−	0.626701i	0.626436	−	0.779473i	$-0.284513\pi$
$953$	−9.21335e12	−	1.59580e13i	−0.361826	−	0.626701i	−0.988261	+	0.152772i	$0.951180\pi$
$954$	6.22045e11			0.0243139
$955$	2.19780e13	+	3.80670e13i	0.855013	+	1.48093i
$956$	−5.89604e12	−	1.02122e13i	−0.228297	−	0.395422i
$957$	−1.35618e13			−0.522653
$958$	2.63465e12	+	4.56335e12i	0.101060	+	0.175041i
$959$	1.97278e13	−	3.41696e13i	0.753174	−	1.30454i
$960$	−1.74288e12	+	3.01876e12i	−0.0662288	+	0.114712i
$961$	−1.19753e13			−0.452930
$962$	−1.09465e13	−	1.17758e13i	−0.412086	−	0.443305i
$963$	3.85676e12			0.144512
$964$	4.04914e12	−	7.01331e12i	0.151013	−	0.261563i
$965$	6.89258e12	−	1.19383e13i	0.255864	−	0.443169i
$966$	−1.04578e13	−	1.81134e13i	−0.386405	−	0.669273i
$967$	1.53512e13			0.564577			0.282288	−	0.959330i	$-0.408906\pi$
$967$	1.53512e13			0.564577			0.282288	+	0.959330i	$0.408906\pi$
$968$	−1.42172e13	−	2.46250e13i	−0.520446	−	0.901439i
$969$	7.07321e12	+	1.22512e13i	0.257727	+	0.446396i
$970$	−8.75066e11			−0.0317372
$971$	1.66858e13	+	2.89007e13i	0.602366	+	1.04333i	0.992462	+	0.122554i	$0.0391086\pi$
$971$	1.66858e13	+	2.89007e13i	0.602366	+	1.04333i	−0.390096	+	0.920774i	$0.627558\pi$
$972$	2.79486e12	−	4.84083e12i	0.100429	−	0.173949i
$973$	−1.09535e13	+	1.89721e13i	−0.391783	+	0.678589i
$974$	2.60188e12			0.0926342
$975$	1.98782e12	−	6.46543e12i	0.0704459	−	0.229127i
$976$	−1.67649e12			−0.0591394
$977$	−1.91344e13	+	3.31418e13i	−0.671877	+	1.16373i	0.305494	+	0.952194i	$0.401178\pi$
$977$	−1.91344e13	+	3.31418e13i	−0.671877	+	1.16373i	−0.977371	+	0.211531i	$0.932155\pi$
$978$	6.77781e12	−	1.17395e13i	0.236900	−	0.410322i
$979$	−3.02837e13	−	5.24529e13i	−1.05363	−	1.82493i
$980$	−1.52875e13			−0.529443
$981$	−2.74343e12	−	4.75176e12i	−0.0945765	−	0.163811i
$982$	−7.18227e12	−	1.24401e13i	−0.246468	−	0.426895i
$983$	1.14311e13			0.390478			0.195239	−	0.980756i	$-0.437452\pi$
$983$	1.14311e13			0.390478			0.195239	+	0.980756i	$0.437452\pi$
$984$	4.93944e12	+	8.55536e12i	0.167958	+	0.290911i
$985$	−1.12027e12	+	1.94037e12i	−0.0379194	+	0.0656783i
$986$	1.18653e12	−	2.05513e12i	0.0399791	−	0.0692459i
$987$	4.94190e13			1.65755
$988$	5.79479e12	−	1.88477e13i	0.193478	−	0.629292i
$989$	4.81061e13			1.59888
$990$	−1.01011e12	+	1.74956e12i	−0.0334203	+	0.0578857i
$991$	6.19304e12	−	1.07267e13i	0.203973	−	0.353292i	−0.745832	−	0.666134i	$-0.767948\pi$
$991$	6.19304e12	−	1.07267e13i	0.203973	−	0.353292i	0.949805	+	0.312843i	$0.101281\pi$
$992$	1.08439e13	+	1.87822e13i	0.355536	+	0.615807i
$993$	−2.02125e13			−0.659703
$994$	6.32421e12	+	1.09539e13i	0.205479	+	0.355900i
$995$	6.66942e12	+	1.15518e13i	0.215717	+	0.373633i
$996$	−8.51343e12			−0.274118
$997$	−1.73641e13	−	3.00756e13i	−0.556577	−	0.964019i	−0.997779	−	0.0666112i	$-0.978781\pi$
$997$	−1.73641e13	−	3.00756e13i	−0.556577	−	0.964019i	0.441202	−	0.897408i	$-0.354552\pi$
$998$	1.07977e13	−	1.87021e13i	0.344542	−	0.596764i
$999$	−2.18382e13	+	3.78249e13i	−0.693702	+	1.20153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.10.c.a.9.6	yes	18
13.3	even	3	inner	13.10.c.a.3.6	✓	18
13.4	even	6		169.10.a.d.1.6		9
13.9	even	3		169.10.a.c.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.c.a.3.6	✓	18	13.3	even	3	inner
13.10.c.a.9.6	yes	18	1.1	even	1	trivial
169.10.a.c.1.4		9	13.9	even	3
169.10.a.d.1.6		9	13.4	even	6

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	13.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.59372 - 7.95656i) q^{2} +(74.2673 - 128.635i) q^{3} +(213.795 + 370.305i) q^{4} +1229.19 q^{5} +(-682.327 - 1181.82i) q^{6} +(-4166.53 - 7216.65i) q^{7} +8632.44 q^{8} +(-1189.76 - 2060.73i) q^{9} +(5646.55 - 9780.12i) q^{10} +(37589.4 - 65106.8i) q^{11} +63512.0 q^{12} +(-100375. + 23007.0i) q^{13} -76559.6 q^{14} +(91288.5 - 158116. i) q^{15} +(-69808.2 + 120911. i) q^{16} +(106339. + 184184. i) q^{17} -21861.8 q^{18} +(223907. + 387819. i) q^{19} +(262795. + 455174. i) q^{20} -1.23775e6 q^{21} +(-345351. - 598165. i) q^{22} +(-919629. + 1.59284e6i) q^{23} +(641108. - 1.11043e6i) q^{24} -442219. q^{25} +(-278039. + 904329. i) q^{26} +2.57016e6 q^{27} +(1.78157e6 - 3.08577e6i) q^{28} +(607245. - 1.05178e6i) q^{29} +(-838708. - 1.45269e6i) q^{30} +3.80320e6 q^{31} +(2.85126e6 + 4.93853e6i) q^{32} +(-5.58333e6 - 9.67061e6i) q^{33} +1.95396e6 q^{34} +(-5.12146e6 - 8.87062e6i) q^{35} +(508732. - 881149. i) q^{36} +(-8.49682e6 + 1.47169e7i) q^{37} +4.11427e6 q^{38} +(-4.49509e6 + 1.46204e7i) q^{39} +1.06109e7 q^{40} +(-3.85227e6 + 6.67232e6i) q^{41} +(-5.68587e6 + 9.84822e6i) q^{42} +(-1.30776e7 - 2.26511e7i) q^{43} +3.21458e7 q^{44} +(-1.46244e6 - 2.53303e6i) q^{45} +(8.44904e6 + 1.46342e7i) q^{46} -3.99265e7 q^{47} +(1.03689e7 + 1.79595e7i) q^{48} +(-1.45432e7 + 2.51896e7i) q^{49} +(-2.03143e6 + 3.51855e6i) q^{50} +3.15899e7 q^{51} +(-2.99794e7 - 3.22506e7i) q^{52} -2.84536e7 q^{53} +(1.18066e7 - 2.04497e7i) q^{54} +(4.62045e7 - 8.00285e7i) q^{55} +(-3.59673e7 - 6.22973e7i) q^{56} +6.65159e7 q^{57} +(-5.57903e6 - 9.66316e6i) q^{58} +(3.16858e7 + 5.48813e7i) q^{59} +7.80683e7 q^{60} +(6.00392e6 + 1.03991e7i) q^{61} +(1.74708e7 - 3.02604e7i) q^{62} +(-9.91437e6 + 1.71722e7i) q^{63} -1.90920e7 q^{64} +(-1.23380e8 + 2.82800e7i) q^{65} -1.02593e8 q^{66} +(3.54777e7 - 6.14492e7i) q^{67} +(-4.54694e7 + 7.87553e7i) q^{68} +(1.36597e8 + 2.36592e8i) q^{69} -9.41062e7 q^{70} +(-8.26051e7 - 1.43076e8i) q^{71} +(-1.02706e7 - 1.77891e7i) q^{72} +1.28511e8 q^{73} +(7.80641e7 + 1.35211e8i) q^{74} +(-3.28424e7 + 5.68848e7i) q^{75} +(-9.57407e7 + 1.65828e8i) q^{76} -6.26470e8 q^{77} +(9.56789e7 + 1.02928e8i) q^{78} +6.32753e8 q^{79} +(-8.58075e7 + 1.48623e8i) q^{80} +(2.14297e8 - 3.71174e8i) q^{81} +(3.53925e7 + 6.13016e7i) q^{82} -1.34044e8 q^{83} +(-2.64625e8 - 4.58344e8i) q^{84} +(1.30710e8 + 2.26397e8i) q^{85} -2.40299e8 q^{86} +(-9.01969e7 - 1.56226e8i) q^{87} +(3.24488e8 - 5.62030e8i) q^{88} +(4.02822e8 - 6.97708e8i) q^{89} -2.68722e7 q^{90} +(5.84250e8 + 6.28513e8i) q^{91} -7.86450e8 q^{92} +(2.82453e8 - 4.89223e8i) q^{93} +(-1.83411e8 + 3.17678e8i) q^{94} +(2.75224e8 + 4.76703e8i) q^{95} +8.47023e8 q^{96} +(-3.87434e7 - 6.71055e7i) q^{97} +(1.33615e8 + 2.31428e8i) q^{98} -1.78890e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 15 q^{2} + 161 q^{3} - 1793 q^{4} - 2280 q^{5} + 2118 q^{6} - 1939 q^{7} - 14478 q^{8} - 33654 q^{9} + 46923 q^{10} - 5433 q^{11} + 8712 q^{12} - 212524 q^{13} - 9900 q^{14} - 347428 q^{15} + 400127 q^{16}+ \cdots + 2262149268 q^{99}+O(q^{100}) \) 18 * q + 15 * q^2 + 161 * q^3 - 1793 * q^4 - 2280 * q^5 + 2118 * q^6 - 1939 * q^7 - 14478 * q^8 - 33654 * q^9 + 46923 * q^10 - 5433 * q^11 + 8712 * q^12 - 212524 * q^13 - 9900 * q^14 - 347428 * q^15 + 400127 * q^16 + 248589 * q^17 - 38738 * q^18 - 311001 * q^19 + 927069 * q^20 + 1553030 * q^21 + 1857242 * q^22 + 591609 * q^23 - 4492800 * q^24 + 7008998 * q^25 - 3801525 * q^26 - 11603482 * q^27 + 2697168 * q^28 + 11014155 * q^29 - 6597836 * q^30 - 23148076 * q^31 - 11868417 * q^32 + 14131427 * q^33 + 21859862 * q^34 + 21112794 * q^35 + 10792871 * q^36 - 29215749 * q^37 + 14572188 * q^38 - 71569875 * q^39 + 27322222 * q^40 + 3328377 * q^41 + 39828306 * q^42 + 6074381 * q^43 + 31824624 * q^44 + 32857342 * q^45 + 36693338 * q^46 - 45575052 * q^47 - 30270064 * q^48 + 10293266 * q^49 - 49601730 * q^50 - 136587494 * q^51 - 35278230 * q^52 - 29480016 * q^53 + 152965386 * q^54 - 18710998 * q^55 - 7665444 * q^56 + 523363230 * q^57 - 163479359 * q^58 - 32715855 * q^59 - 188638416 * q^60 - 220502845 * q^61 - 59980476 * q^62 + 166572574 * q^63 - 924604030 * q^64 + 128091756 * q^65 - 48128076 * q^66 + 112659045 * q^67 - 238942419 * q^68 + 86003951 * q^69 + 2040150992 * q^70 - 236450709 * q^71 + 995206683 * q^72 - 211881220 * q^73 - 455580507 * q^74 + 968954813 * q^75 - 365789708 * q^76 - 2399230890 * q^77 - 441111970 * q^78 - 817519096 * q^79 + 580424625 * q^80 + 176914851 * q^81 + 941792217 * q^82 + 2225691456 * q^83 - 1819004068 * q^84 + 1812284636 * q^85 + 291320076 * q^86 + 69564799 * q^87 + 3178375740 * q^88 - 1154379039 * q^89 - 10225809510 * q^90 - 1658338903 * q^91 - 4545506592 * q^92 + 3136878060 * q^93 + 2755131560 * q^94 + 1779441012 * q^95 + 5906965568 * q^96 - 3616470111 * q^97 + 8263323501 * q^98 + 2262149268 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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