LMFDB - Embedded newform 13.10.c.a.3.7

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)

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);

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")

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			3.7
Root			$-13.4651 + 23.3223i$ of defining polynomial
Character	$\chi$	$=$	13.3
Dual form			13.10.c.a.9.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(14.4651 + 25.0544i) q^{2} +(-95.3768 - 165.198i) q^{3} +(-162.481 + 281.425i) q^{4} +1752.49 q^{5} +(2759.28 - 4779.21i) q^{6} +(2202.24 - 3814.40i) q^{7} +5411.06 q^{8} +(-8351.99 + 14466.1i) q^{9} +(25350.1 + 43907.6i) q^{10} +(5879.88 + 10184.3i) q^{11} +61987.7 q^{12} +(-21586.3 - 100690. i) q^{13} +127423. q^{14} +(-167147. - 289508. i) q^{15} +(161462. + 279661. i) q^{16} +(196644. - 340597. i) q^{17} -483251. q^{18} +(-414131. + 717296. i) q^{19} +(-284747. + 493196. i) q^{20} -840172. q^{21} +(-170107. + 294634. i) q^{22} +(-204505. - 354213. i) q^{23} +(-516090. - 893895. i) q^{24} +1.11811e6 q^{25} +(2.21048e6 - 1.99733e6i) q^{26} -568260. q^{27} +(715645. + 1.23953e6i) q^{28} +(3.19758e6 + 5.53837e6i) q^{29} +(4.83562e6 - 8.37554e6i) q^{30} -6.65635e6 q^{31} +(-3.28591e6 + 5.69137e6i) q^{32} +(1.12161e6 - 1.94268e6i) q^{33} +1.13779e7 q^{34} +(3.85942e6 - 6.68470e6i) q^{35} +(-2.71408e6 - 4.70092e6i) q^{36} +(1.12941e7 + 1.95619e7i) q^{37} -2.39619e7 q^{38} +(-1.45749e7 + 1.31695e7i) q^{39} +9.48286e6 q^{40} +(-7.10477e6 - 1.23058e7i) q^{41} +(-1.21532e7 - 2.10500e7i) q^{42} +(1.50153e6 - 2.60073e6i) q^{43} -3.82148e6 q^{44} +(-1.46368e7 + 2.53517e7i) q^{45} +(5.91640e6 - 1.02475e7i) q^{46} +2.19063e6 q^{47} +(3.07995e7 - 5.33463e7i) q^{48} +(1.04771e7 + 1.81468e7i) q^{49} +(1.61736e7 + 2.80135e7i) q^{50} -7.50210e7 q^{51} +(3.18442e7 + 1.02853e7i) q^{52} -4.09094e6 q^{53} +(-8.21997e6 - 1.42374e7i) q^{54} +(1.03045e7 + 1.78478e7i) q^{55} +(1.19165e7 - 2.06399e7i) q^{56} +1.57994e8 q^{57} +(-9.25069e7 + 1.60227e8i) q^{58} +(-3.37467e7 + 5.84510e7i) q^{59} +1.08633e8 q^{60} +(6.92596e7 - 1.19961e8i) q^{61} +(-9.62851e7 - 1.66771e8i) q^{62} +(3.67862e7 + 6.37156e7i) q^{63} -2.47877e7 q^{64} +(-3.78299e7 - 1.76459e8i) q^{65} +6.48970e7 q^{66} +(-1.18839e8 - 2.05835e8i) q^{67} +(6.39017e7 + 1.10681e8i) q^{68} +(-3.90101e7 + 6.75675e7i) q^{69} +2.23308e8 q^{70} +(-1.06739e8 + 1.84877e8i) q^{71} +(-4.51931e7 + 7.82768e7i) q^{72} -3.17978e8 q^{73} +(-3.26741e8 + 5.65933e8i) q^{74} +(-1.06642e8 - 1.84709e8i) q^{75} +(-1.34577e8 - 2.33094e8i) q^{76} +5.17957e7 q^{77} +(-5.40783e8 - 1.74667e8i) q^{78} +3.54613e8 q^{79} +(2.82961e8 + 4.90103e8i) q^{80} +(2.18591e8 + 3.78611e8i) q^{81} +(2.05543e8 - 3.56011e8i) q^{82} +2.35429e8 q^{83} +(1.36512e8 - 2.36446e8i) q^{84} +(3.44617e8 - 5.96894e8i) q^{85} +8.68796e7 q^{86} +(6.09950e8 - 1.05646e9i) q^{87} +(3.18164e7 + 5.51077e7i) q^{88} +(6.81965e7 + 1.18120e8i) q^{89} -8.46894e8 q^{90} +(-4.31611e8 - 1.39406e8i) q^{91} +1.32913e8 q^{92} +(6.34862e8 + 1.09961e9i) q^{93} +(3.16878e7 + 5.48849e7i) q^{94} +(-7.25762e8 + 1.25706e9i) q^{95} +1.25360e9 q^{96} +(4.83370e7 - 8.37222e7i) q^{97} +(-3.03105e8 + 5.24992e8i) q^{98} -1.96435e8 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 $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	14.4651	+	25.0544i	0.639275	+	1.10726i	0.985592	+	0.169140i	$0.0540989\pi$
$2$	14.4651	+	25.0544i	0.639275	+	1.10726i	−0.346317	+	0.938118i	$0.612568\pi$
$3$	−95.3768	−	165.198i	−0.679825	−	1.17749i	−0.975033	−	0.222059i	$-0.928722\pi$
$3$	−95.3768	−	165.198i	−0.679825	−	1.17749i	0.295208	−	0.955433i	$-0.404611\pi$
$4$	−162.481	+	281.425i	−0.317346	+	0.549659i
$5$	1752.49			1.25398			0.626991	−	0.779026i	$-0.284286\pi$
$5$	1752.49			1.25398			0.626991	+	0.779026i	$0.284286\pi$
$6$	2759.28	−	4779.21i	0.869191	−	1.50548i
$7$	2202.24	−	3814.40i	0.346676	−	0.600461i	−0.638981	−	0.769223i	$-0.720644\pi$
$7$	2202.24	−	3814.40i	0.346676	−	0.600461i	0.985657	+	0.168762i	$0.0539770\pi$
$8$	5411.06			0.467065
$9$	−8351.99	+	14466.1i	−0.424325	+	0.734952i
$10$	25350.1	+	43907.6i	0.801640	+	1.38848i
$11$	5879.88	+	10184.3i	0.121088	+	0.209731i	0.920197	−	0.391455i	$-0.128028\pi$
$11$	5879.88	+	10184.3i	0.121088	+	0.209731i	−0.799109	+	0.601186i	$0.794695\pi$
$12$	61987.7			0.862959
$13$	−21586.3	−	100690.i	−0.209621	−	0.977783i
$13$	−21586.3	−	100690.i	−0.209621	−	0.977783i
$14$	127423.			0.886486
$15$	−167147.	−	289508.i	−0.852489	−	1.47655i
$16$	161462.	+	279661.i	0.615929	+	1.06682i
$17$	196644.	−	340597.i	0.571031	−	0.989055i	−0.425429	−	0.904992i	$-0.639877\pi$
$17$	196644.	−	340597.i	0.571031	−	0.989055i	0.996460	−	0.0840635i	$-0.0267899\pi$
$18$	−483251.			−1.08504
$19$	−414131.	+	717296.i	−0.729032	+	1.26272i	0.228261	+	0.973600i	$0.426696\pi$
$19$	−414131.	+	717296.i	−0.729032	+	1.26272i	−0.957293	+	0.289120i	$0.906637\pi$
$20$	−284747.	+	493196.i	−0.397946	+	0.689263i
$21$	−840172.			−0.942717
$22$	−170107.	+	294634.i	−0.154817	+	0.268151i
$23$	−204505.	−	354213.i	−0.152380	−	0.263931i	0.779722	−	0.626126i	$-0.215361\pi$
$23$	−204505.	−	354213.i	−0.152380	−	0.263931i	−0.932102	+	0.362196i	$0.882027\pi$
$24$	−516090.	−	893895.i	−0.317523	−	0.549966i
$25$	1.11811e6			0.572472
$26$	2.21048e6	−	1.99733e6i	0.948652	−	0.857176i
$27$	−568260.			−0.205783
$28$	715645.	+	1.23953e6i	0.220032	+	0.381107i
$29$	3.19758e6	+	5.53837e6i	0.839519	+	1.45409i	0.890298	+	0.455379i	$0.150496\pi$
$29$	3.19758e6	+	5.53837e6i	0.839519	+	1.45409i	−0.0507791	+	0.998710i	$0.516170\pi$
$30$	4.83562e6	−	8.37554e6i	1.08995	−	1.88785i
$31$	−6.65635e6			−1.29452			−0.647260	−	0.762269i	$-0.724085\pi$
$31$	−6.65635e6			−1.29452			−0.647260	+	0.762269i	$0.724085\pi$
$32$	−3.28591e6	+	5.69137e6i	−0.553964	+	0.959493i
$33$	1.12161e6	−	1.94268e6i	0.164638	−	0.285161i
$34$	1.13779e7			1.46018
$35$	3.85942e6	−	6.68470e6i	0.434726	−	0.752967i
$36$	−2.71408e6	−	4.70092e6i	−0.269315	−	0.466468i
$37$	1.12941e7	+	1.95619e7i	0.990703	+	1.71595i	0.613167	+	0.789953i	$0.289895\pi$
$37$	1.12941e7	+	1.95619e7i	0.990703	+	1.71595i	0.377536	+	0.925995i	$0.376772\pi$
$38$	−2.39619e7			−1.86421
$39$	−1.45749e7	+	1.31695e7i	−1.00883	+	0.911548i
$40$	9.48286e6			0.585692
$41$	−7.10477e6	−	1.23058e7i	−0.392665	−	0.680116i	0.600135	−	0.799899i	$-0.295114\pi$
$41$	−7.10477e6	−	1.23058e7i	−0.392665	−	0.680116i	−0.992800	+	0.119782i	$0.961780\pi$
$42$	−1.21532e7	−	2.10500e7i	−0.602655	−	1.04383i
$43$	1.50153e6	−	2.60073e6i	0.0669772	−	0.116008i	−0.830592	−	0.556881i	$-0.811998\pi$
$43$	1.50153e6	−	2.60073e6i	0.0669772	−	0.116008i	0.897569	+	0.440873i	$0.145331\pi$
$44$	−3.82148e6			−0.153707
$45$	−1.46368e7	+	2.53517e7i	−0.532096	+	0.921617i
$46$	5.91640e6	−	1.02475e7i	0.194826	−	0.337449i
$47$	2.19063e6			0.0654831			0.0327416	−	0.999464i	$-0.489576\pi$
$47$	2.19063e6			0.0654831			0.0327416	+	0.999464i	$0.489576\pi$
$48$	3.07995e7	−	5.33463e7i	0.837448	−	1.45050i
$49$	1.04771e7	+	1.81468e7i	0.259631	+	0.449695i
$50$	1.61736e7	+	2.80135e7i	0.365967	+	0.633874i
$51$	−7.50210e7			−1.55281
$52$	3.18442e7	+	1.02853e7i	0.603969	+	0.195075i
$53$	−4.09094e6			−0.0712167			−0.0356083	−	0.999366i	$-0.511337\pi$
$53$	−4.09094e6			−0.0712167			−0.0356083	+	0.999366i	$0.511337\pi$
$54$	−8.21997e6	−	1.42374e7i	−0.131552	−	0.227855i
$55$	1.03045e7	+	1.78478e7i	0.151842	+	0.262999i
$56$	1.19165e7	−	2.06399e7i	0.161920	−	0.280454i
$57$	1.57994e8			1.98246
$58$	−9.25069e7	+	1.60227e8i	−1.07337	+	1.85913i
$59$	−3.37467e7	+	5.84510e7i	−0.362575	+	0.627998i	−0.988384	−	0.151979i	$-0.951436\pi$
$59$	−3.37467e7	+	5.84510e7i	−0.362575	+	0.627998i	0.625809	+	0.779976i	$0.284769\pi$
$60$	1.08633e8			1.08213
$61$	6.92596e7	−	1.19961e8i	0.640466	−	1.10932i	−0.344863	−	0.938653i	$-0.612075\pi$
$61$	6.92596e7	−	1.19961e8i	0.640466	−	1.10932i	0.985329	−	0.170666i	$-0.0545920\pi$
$62$	−9.62851e7	−	1.66771e8i	−0.827554	−	1.43337i
$63$	3.67862e7	+	6.37156e7i	0.294207	+	0.509581i
$64$	−2.47877e7			−0.184683
$65$	−3.78299e7	−	1.76459e8i	−0.262860	−	1.22612i
$66$	6.48970e7			0.420995
$67$	−1.18839e8	−	2.05835e8i	−0.720479	−	1.24791i	−0.960808	−	0.277215i	$-0.910589\pi$
$67$	−1.18839e8	−	2.05835e8i	−0.720479	−	1.24791i	0.240329	−	0.970692i	$-0.422745\pi$
$68$	6.39017e7	+	1.10681e8i	0.362429	+	0.627745i
$69$	−3.90101e7	+	6.75675e7i	−0.207184	+	0.358853i
$70$	2.23308e8			1.11164
$71$	−1.06739e8	+	1.84877e8i	−0.498494	+	0.863416i	−0.999998	−	0.00173856i	$-0.999447\pi$
$71$	−1.06739e8	+	1.84877e8i	−0.498494	+	0.863416i	0.501505	+	0.865155i	$0.332780\pi$
$72$	−4.51931e7	+	7.82768e7i	−0.198188	+	0.343271i
$73$	−3.17978e8			−1.31052			−0.655260	−	0.755403i	$-0.727441\pi$
$73$	−3.17978e8			−1.31052			−0.655260	+	0.755403i	$0.727441\pi$
$74$	−3.26741e8	+	5.65933e8i	−1.26666	+	2.19393i
$75$	−1.06642e8	−	1.84709e8i	−0.389181	−	0.674081i
$76$	−1.34577e8	−	2.33094e8i	−0.462710	−	0.801438i
$77$	5.17957e7			0.167913
$78$	−5.40783e8	−	1.74667e8i	−1.65424	−	0.534300i
$79$	3.54613e8			1.02431			0.512157	−	0.858892i	$-0.328847\pi$
$79$	3.54613e8			1.02431			0.512157	+	0.858892i	$0.328847\pi$
$80$	2.82961e8	+	4.90103e8i	0.772364	+	1.33777i
$81$	2.18591e8	+	3.78611e8i	0.564222	+	0.977261i
$82$	2.05543e8	−	3.56011e8i	0.502043	−	0.869563i
$83$	2.35429e8			0.544513			0.272257	−	0.962225i	$-0.412230\pi$
$83$	2.35429e8			0.544513			0.272257	+	0.962225i	$0.412230\pi$
$84$	1.36512e8	−	2.36446e8i	0.299167	−	0.518173i
$85$	3.44617e8	−	5.96894e8i	0.716063	−	1.24026i
$86$	8.68796e7			0.171267
$87$	6.09950e8	−	1.05646e9i	1.14145	−	1.97705i
$88$	3.18164e7	+	5.51077e7i	0.0565561	+	0.0979580i
$89$	6.81965e7	+	1.18120e8i	0.115215	+	0.199557i	0.917865	−	0.396892i	$-0.129911\pi$
$89$	6.81965e7	+	1.18120e8i	0.115215	+	0.199557i	−0.802651	+	0.596449i	$0.796578\pi$
$90$	−8.46894e8			−1.36062
$91$	−4.31611e8	−	1.39406e8i	−0.659790	−	0.213105i
$92$	1.32913e8			0.193429
$93$	6.34862e8	+	1.09961e9i	0.880047	+	1.52429i
$94$	3.16878e7	+	5.48849e7i	0.0418617	+	0.0725066i
$95$	−7.25762e8	+	1.25706e9i	−0.914193	+	1.58343i
$96$	1.25360e9			1.50639
$97$	4.83370e7	−	8.37222e7i	0.0554379	−	0.0960213i	−0.836975	−	0.547242i	$-0.815678\pi$
$97$	4.83370e7	−	8.37222e7i	0.0554379	−	0.0960213i	0.892413	+	0.451220i	$0.149011\pi$
$98$	−3.03105e8	+	5.24992e8i	−0.331952	+	0.574957i
$99$	−1.96435e8			−0.205523
$100$	−1.81672e8	+	3.14664e8i	−0.181672	+	0.314664i
$101$	2.08512e8	+	3.61154e8i	0.199382	+	0.345339i	0.948328	−	0.317291i	$-0.102773\pi$
$101$	2.08512e8	+	3.61154e8i	0.199382	+	0.345339i	−0.748946	+	0.662631i	$0.769440\pi$
$102$	−1.08519e9	−	1.87960e9i	−0.992671	−	1.71936i
$103$	1.57656e8			0.138021			0.0690103	−	0.997616i	$-0.478016\pi$
$103$	1.57656e8			0.138021			0.0690103	+	0.997616i	$0.478016\pi$
$104$	−1.16805e8	−	5.44842e8i	−0.0979065	−	0.456689i
$105$	−1.47240e9			−1.18215
$106$	−5.91761e7	−	1.02496e8i	−0.0455271	−	0.0788552i
$107$	−1.08579e8	−	1.88064e8i	−0.0800790	−	0.138701i	0.823205	−	0.567745i	$-0.192184\pi$
$107$	−1.08579e8	−	1.88064e8i	−0.0800790	−	0.138701i	−0.903284	+	0.429044i	$0.858851\pi$
$108$	9.23315e7	−	1.59923e8i	0.0653045	−	0.113111i
$109$	−1.94632e9			−1.32067			−0.660336	−	0.750971i	$-0.729586\pi$
$109$	−1.94632e9			−1.32067			−0.660336	+	0.750971i	$0.729586\pi$
$110$	−2.98111e8	+	5.16343e8i	−0.194138	+	0.336257i
$111$	2.15439e9	−	3.73151e9i	1.34701	−	2.33309i
$112$	1.42231e9			0.854112
$113$	−1.19846e9	+	2.07579e9i	−0.691466	+	1.19765i	0.279892	+	0.960031i	$0.409701\pi$
$113$	−1.19846e9	+	2.07579e9i	−0.691466	+	1.19765i	−0.971358	+	0.237622i	$0.923632\pi$
$114$	2.28541e9	+	3.95844e9i	1.26734	+	2.19509i
$115$	−3.58394e8	−	6.20757e8i	−0.191082	−	0.330964i
$116$	−2.07818e9			−1.06567
$117$	1.63688e9	+	5.28694e8i	0.807571	+	0.260836i
$118$	−1.95260e9			−0.927140
$119$	−8.66114e8	−	1.50015e9i	−0.395926	−	0.685764i
$120$	−9.04445e8	−	1.56654e9i	−0.398168	−	0.689648i
$121$	1.10983e9	−	1.92228e9i	0.470675	−	0.815234i
$122$	4.00740e9			1.63774
$123$	−1.35526e9	+	2.34738e9i	−0.533888	+	0.924721i
$124$	1.08153e9	−	1.87327e9i	0.410810	−	0.711544i
$125$	−1.46336e9			−0.536113
$126$	−1.06424e9	+	1.84331e9i	−0.376158	+	0.651525i
$127$	1.88207e9	+	3.25983e9i	0.641975	+	1.11193i	0.984991	+	0.172604i	$0.0552181\pi$
$127$	1.88207e9	+	3.25983e9i	0.641975	+	1.11193i	−0.343016	+	0.939330i	$0.611449\pi$
$128$	1.32383e9	+	2.29294e9i	0.435900	+	0.755002i
$129$	−5.72846e8			−0.182131
$130$	3.87386e9	−	3.50031e9i	1.18959	−	1.07488i
$131$	−2.62771e9			−0.779572			−0.389786	−	0.920905i	$-0.627451\pi$
$131$	−2.62771e9			−0.779572			−0.389786	+	0.920905i	$0.627451\pi$
$132$	3.64480e8	+	6.31299e8i	0.104494	+	0.180989i
$133$	1.82403e9	+	3.15932e9i	0.505476	+	0.875510i
$134$	3.43804e9	−	5.95486e9i	0.921169	−	1.59551i
$135$	−9.95873e8			−0.258049
$136$	1.06405e9	−	1.84299e9i	0.266709	−	0.461954i
$137$	2.19468e8	−	3.80129e8i	0.0532265	−	0.0921910i	−0.838185	−	0.545387i	$-0.816383\pi$
$137$	2.19468e8	−	3.80129e8i	0.0532265	−	0.0921910i	0.891411	+	0.453196i	$0.149716\pi$
$138$	−2.25715e9			−0.529791
$139$	−1.08190e9	+	1.87390e9i	−0.245821	+	0.425775i	−0.962362	−	0.271770i	$-0.912391\pi$
$139$	−1.08190e9	+	1.87390e9i	−0.245821	+	0.425775i	0.716541	+	0.697545i	$0.245724\pi$
$140$	1.25416e9	+	2.17227e9i	0.275917	+	0.477902i
$141$	−2.08936e8	−	3.61887e8i	−0.0445171	−	0.0771058i
$142$	−6.17597e9			−1.27470
$143$	8.98530e8	−	8.11888e8i	0.179689	−	0.162362i
$144$	−5.39412e9			−1.04542
$145$	5.60374e9	+	9.70596e9i	1.05274	+	1.82340i
$146$	−4.59959e9	−	7.96673e9i	−0.837783	−	1.45108i
$147$	1.99854e9	−	3.46157e9i	0.353008	−	0.611428i
$148$	−7.34030e9			−1.25758
$149$	3.09827e9	−	5.36637e9i	0.514969	−	0.891953i	−0.484880	−	0.874581i	$-0.661137\pi$
$149$	3.09827e9	−	5.36637e9i	0.514969	−	0.891953i	0.999849	−	0.0173723i	$-0.00553006\pi$
$150$	3.08518e9	−	5.34368e9i	0.497588	−	0.861847i
$151$	−3.94967e8			−0.0618250			−0.0309125	−	0.999522i	$-0.509841\pi$
$151$	−3.94967e8			−0.0618250			−0.0309125	+	0.999522i	$0.509841\pi$
$152$	−2.24089e9	+	3.88134e9i	−0.340506	+	0.589773i
$153$	3.28473e9	+	5.68932e9i	0.484606	+	0.839362i
$154$	7.49233e8	+	1.29771e9i	0.107343	+	0.185923i
$155$	−1.16652e10			−1.62331
$156$	−1.33809e9	−	6.24156e9i	−0.180894	−	0.843786i
$157$	3.68266e9			0.483741			0.241871	−	0.970309i	$-0.422239\pi$
$157$	3.68266e9			0.483741			0.241871	+	0.970309i	$0.422239\pi$
$158$	5.12953e9	+	8.88461e9i	0.654818	+	1.13418i
$159$	3.90181e8	+	6.75813e8i	0.0484149	+	0.0838571i
$160$	−5.75854e9	+	9.97409e9i	−0.694661	+	1.20319i
$161$	−1.80148e9			−0.211307
$162$	−6.32390e9	+	1.09533e10i	−0.721386	+	1.24948i
$163$	5.12029e9	−	8.86861e9i	0.568134	−	0.984037i	−0.428617	−	0.903486i	$-0.640999\pi$
$163$	5.12029e9	−	8.86861e9i	0.568134	−	0.984037i	0.996751	−	0.0805503i	$-0.0256678\pi$
$164$	4.61756e9			0.498443
$165$	1.96561e9	−	3.40454e9i	0.206453	−	0.357586i
$166$	3.40551e9	+	5.89852e9i	0.348094	+	0.602916i
$167$	−4.89907e9	−	8.48544e9i	−0.487404	−	0.844209i	0.512491	−	0.858693i	$-0.328723\pi$
$167$	−4.89907e9	−	8.48544e9i	−0.487404	−	0.844209i	−0.999895	+	0.0144835i	$0.995390\pi$
$168$	−4.54622e9			−0.440310
$169$	−9.67256e9	+	4.34707e9i	−0.912118	+	0.409927i
$170$	1.99397e10			1.83105
$171$	−6.91763e9	−	1.19817e10i	−0.618693	−	1.07161i
$172$	4.87941e8	+	8.45139e8i	0.0425099	+	0.0736292i
$173$	5.43809e9	−	9.41905e9i	0.461572	−	0.799465i	−0.537468	−	0.843284i	$-0.680619\pi$
$173$	5.43809e9	−	9.41905e9i	0.461572	−	0.799465i	0.999039	+	0.0438188i	$0.0139524\pi$
$174$	3.52921e10			2.91881
$175$	2.46235e9	−	4.26491e9i	0.198462	−	0.343747i
$176$	−1.89876e9	+	3.28874e9i	−0.149163	+	0.258359i
$177$	1.28746e10			0.985949
$178$	−1.97295e9	+	3.41724e9i	−0.147308	+	0.255144i
$179$	−9.38237e9	−	1.62507e10i	−0.683084	−	1.18314i	−0.974035	−	0.226398i	$-0.927305\pi$
$179$	−9.38237e9	−	1.62507e10i	−0.683084	−	1.18314i	0.290951	−	0.956738i	$-0.406028\pi$
$180$	−4.75641e9	−	8.23834e9i	−0.337717	−	0.584943i
$181$	2.13567e10			1.47904			0.739520	−	0.673135i	$-0.235053\pi$
$181$	2.13567e10			1.47904			0.739520	+	0.673135i	$0.235053\pi$
$182$	−2.75060e9	−	1.28303e10i	−0.185826	−	0.866791i
$183$	−2.64231e10			−1.74162
$184$	−1.10659e9	−	1.91667e9i	−0.0711716	−	0.123273i
$185$	1.97928e10	+	3.42822e10i	1.24232	+	2.15177i
$186$	−1.83667e10	+	3.18121e10i	−1.12518	+	1.94888i
$187$	4.62497e9			0.276580
$188$	−3.55936e8	+	6.16500e8i	−0.0207808	+	0.0359934i
$189$	−1.25145e9	+	2.16757e9i	−0.0713402	+	0.123565i
$190$	−4.19930e10			−2.33768
$191$	7.86148e9	−	1.36165e10i	0.427419	−	0.740312i	−0.569224	−	0.822183i	$-0.692756\pi$
$191$	7.86148e9	−	1.36165e10i	0.427419	−	0.740312i	0.996643	+	0.0818708i	$0.0260895\pi$
$192$	2.36418e9	+	4.09487e9i	0.125552	+	0.217463i
$193$	−9.35737e9	−	1.62074e10i	−0.485452	−	0.840827i	0.514409	−	0.857545i	$-0.328011\pi$
$193$	−9.35737e9	−	1.62074e10i	−0.485452	−	0.840827i	−0.999860	+	0.0167184i	$0.994678\pi$
$194$	2.79681e9			0.141760
$195$	−2.55425e10	+	2.30795e10i	−1.26505	+	1.14307i
$196$	−6.80929e9			−0.329572
$197$	2.61952e9	+	4.53715e9i	0.123915	+	0.214627i	0.921308	−	0.388833i	$-0.127122\pi$
$197$	2.61952e9	+	4.53715e9i	0.123915	+	0.214627i	−0.797393	+	0.603460i	$0.793788\pi$
$198$	−2.84146e9	−	4.92155e9i	−0.131386	−	0.227567i
$199$	7.89636e9	−	1.36769e10i	0.356934	−	0.618228i	−0.630513	−	0.776179i	$-0.717155\pi$
$199$	7.89636e9	−	1.36769e10i	0.356934	−	0.618228i	0.987447	+	0.157951i	$0.0504887\pi$
$200$	6.05016e9			0.267382
$201$	−2.26689e10	+	3.92637e10i	−0.979600	+	1.69672i
$202$	−6.03232e9	+	1.04483e10i	−0.254919	+	0.441533i
$203$	2.81674e10			1.16416
$204$	1.21895e10	−	2.11128e10i	0.492776	−	0.853514i
$205$	−1.24511e10	−	2.15659e10i	−0.492396	−	0.852854i
$206$	2.28052e9	+	3.94998e9i	0.0882331	+	0.152824i
$207$	6.83210e9			0.258635
$208$	2.46737e10	−	2.22945e10i	0.914007	−	0.825872i
$209$	−9.74017e9			−0.353109
$210$	−2.12984e10	−	3.68899e10i	−0.755719	−	1.30894i
$211$	−8.79448e9	−	1.52325e10i	−0.305449	−	0.529054i	0.671912	−	0.740631i	$-0.265473\pi$
$211$	−8.79448e9	−	1.52325e10i	−0.305449	−	0.529054i	−0.977361	+	0.211577i	$0.932140\pi$
$212$	6.64700e8	−	1.15129e9i	0.0226003	−	0.0391449i
$213$	4.07216e10			1.35555
$214$	3.14122e9	−	5.44075e9i	0.102385	−	0.177336i
$215$	2.63143e9	−	4.55777e9i	0.0839882	−	0.145472i
$216$	−3.07489e9			−0.0961143
$217$	−1.46589e10	+	2.53900e10i	−0.448779	+	0.777308i
$218$	−2.81538e10	−	4.87638e10i	−0.844273	−	1.46232i
$219$	3.03277e10	+	5.25291e10i	0.890925	+	1.54313i
$220$	−6.69712e9			−0.192746
$221$	−3.85396e10	−	1.24479e10i	−1.08678	−	0.351018i
$222$	1.24654e11			3.44444
$223$	2.69075e10	+	4.66052e10i	0.728622	+	1.26201i	0.957466	+	0.288547i	$0.0931722\pi$
$223$	2.69075e10	+	4.66052e10i	0.728622	+	1.26201i	−0.228844	+	0.973463i	$0.573494\pi$
$224$	1.44728e10	+	2.50676e10i	0.384092	+	0.665267i
$225$	−9.33844e9	+	1.61746e10i	−0.242914	+	0.420740i
$226$	−6.93436e10			−1.76815
$227$	−1.56186e9	+	2.70522e9i	−0.0390414	+	0.0676218i	−0.884886	−	0.465808i	$-0.845764\pi$
$227$	−1.56186e9	+	2.70522e9i	−0.0390414	+	0.0676218i	0.845844	+	0.533430i	$0.179097\pi$
$228$	−2.56710e10	+	4.44635e10i	−0.629124	+	1.08968i
$229$	1.35357e10			0.325254			0.162627	−	0.986688i	$-0.448003\pi$
$229$	1.35357e10			0.325254			0.162627	+	0.986688i	$0.448003\pi$
$230$	1.03684e10	−	1.79587e10i	0.244308	−	0.423155i
$231$	−4.94011e9	−	8.55652e9i	−0.114152	−	0.197717i
$232$	1.73023e10	+	2.99685e10i	0.392110	+	0.679155i
$233$	−2.30046e9			−0.0511343			−0.0255672	−	0.999673i	$-0.508139\pi$
$233$	−2.30046e9			−0.0511343			−0.0255672	+	0.999673i	$0.508139\pi$
$234$	1.04316e10	+	4.86587e10i	0.227447	+	1.06094i
$235$	3.83907e9			0.0821147
$236$	−1.09664e10	−	1.89944e10i	−0.230123	−	0.398585i
$237$	−3.38219e10	−	5.85812e10i	−0.696354	−	1.20612i
$238$	2.50569e10	−	4.33999e10i	0.506211	−	0.876783i
$239$	−9.74915e10			−1.93275			−0.966376	−	0.257132i	$-0.917223\pi$
$239$	−9.74915e10			−1.93275			−0.966376	+	0.257132i	$0.917223\pi$
$240$	5.39759e10	−	9.34890e10i	1.05015	−	1.81891i
$241$	−9.57507e9	+	1.65845e10i	−0.182837	+	0.316684i	−0.942846	−	0.333230i	$-0.891862\pi$
$241$	−9.57507e9	+	1.65845e10i	−0.182837	+	0.316684i	0.760008	+	0.649913i	$0.225195\pi$
$242$	6.42153e10			1.20356
$243$	3.61045e10	−	6.25349e10i	0.664253	−	1.15052i
$244$	2.25068e10	+	3.89828e10i	0.406498	+	0.704075i
$245$	1.83610e10	+	3.18022e10i	0.325573	+	0.563909i
$246$	−7.84162e10			−1.36520
$247$	8.11643e10	+	2.62152e10i	1.38749	+	0.448143i
$248$	−3.60180e10			−0.604626
$249$	−2.24545e10	−	3.88923e10i	−0.370174	−	0.641160i
$250$	−2.11677e10	−	3.66636e10i	−0.342723	−	0.593615i
$251$	1.10818e10	−	1.91943e10i	0.176230	−	0.305240i	−0.764356	−	0.644794i	$-0.776943\pi$
$251$	1.10818e10	−	1.91943e10i	0.176230	−	0.305240i	0.940586	+	0.339555i	$0.110276\pi$
$252$	−2.39082e10			−0.373461
$253$	2.40493e9	−	4.16547e9i	0.0369029	−	0.0639177i
$254$	−5.44487e10	+	9.43080e10i	−0.820798	+	1.42166i
$255$	−1.31474e11			−1.94719
$256$	−4.46445e10	+	7.73265e10i	−0.649662	+	1.12525i
$257$	−1.85266e9	−	3.20890e9i	−0.0264909	−	0.0458836i	0.852476	−	0.522766i	$-0.175100\pi$
$257$	−1.85266e9	−	3.20890e9i	−0.0264909	−	0.0458836i	−0.878967	+	0.476883i	$0.841767\pi$
$258$	−8.28631e9	−	1.43523e10i	−0.116432	−	0.201666i
$259$	9.94893e10			1.37381
$260$	5.58067e10	+	1.80249e10i	0.757367	+	0.244621i
$261$	−1.06825e11			−1.42491
$262$	−3.80102e10	−	6.58356e10i	−0.498361	−	0.863187i
$263$	1.53575e10	+	2.65999e10i	0.197933	+	0.342830i	0.947858	−	0.318693i	$-0.103244\pi$
$263$	1.53575e10	+	2.65999e10i	0.197933	+	0.342830i	−0.749925	+	0.661523i	$0.769910\pi$
$264$	6.06910e9	−	1.05120e10i	0.0768965	−	0.133189i
$265$	−7.16935e9			−0.0893045
$266$	−5.27698e10	+	9.14000e10i	−0.646277	+	1.11938i
$267$	1.30087e10	−	2.25318e10i	0.156652	−	0.271328i
$268$	7.72362e10			0.914564
$269$	1.37521e10	−	2.38193e10i	0.160134	−	0.277360i	−0.774783	−	0.632228i	$-0.782141\pi$
$269$	1.37521e10	−	2.38193e10i	0.160134	−	0.277360i	0.934917	+	0.354868i	$0.115474\pi$
$270$	−1.44054e10	−	2.49510e10i	−0.164964	−	0.285726i
$271$	1.97112e10	+	3.41407e10i	0.221999	+	0.384513i	0.955415	−	0.295267i	$-0.0954086\pi$
$271$	1.97112e10	+	3.41407e10i	0.221999	+	0.384513i	−0.733416	+	0.679780i	$0.762075\pi$
$272$	1.27002e11			1.40686
$273$	1.81362e10	+	8.45971e10i	0.197613	+	0.921772i
$274$	1.26985e10			0.136106
$275$	6.57435e9	+	1.13871e10i	0.0693196	+	0.120065i
$276$	−1.26768e10	−	2.19569e10i	−0.131498	−	0.227761i
$277$	1.82901e10	−	3.16793e10i	0.186662	−	0.323308i	−0.757473	−	0.652866i	$-0.773566\pi$
$277$	1.82901e10	−	3.16793e10i	0.186662	−	0.323308i	0.944135	+	0.329558i	$0.106900\pi$
$278$	−6.25993e10			−0.628590
$279$	5.55938e10	−	9.62912e10i	0.549297	−	0.951410i
$280$	2.08835e10	−	3.61714e10i	0.203045	−	0.351685i
$281$	−4.30831e10			−0.412220			−0.206110	−	0.978529i	$-0.566080\pi$
$281$	−4.30831e10			−0.412220			−0.206110	+	0.978529i	$0.566080\pi$
$282$	6.04457e9	−	1.04695e10i	0.0569173	−	0.0985837i
$283$	5.40586e9	+	9.36323e9i	0.0500986	+	0.0867734i	0.889987	−	0.455985i	$-0.150713\pi$
$283$	5.40586e9	+	9.36323e9i	0.0500986	+	0.0867734i	−0.839889	+	0.542759i	$0.817380\pi$
$284$	−3.46860e10	−	6.00780e10i	−0.316390	−	0.548003i
$285$	2.76884e11			2.48597
$286$	3.33387e10	+	1.07680e10i	0.294647	+	0.0951676i
$287$	−6.25857e10			−0.544511
$288$	−5.48878e10	−	9.50685e10i	−0.470121	−	0.814274i
$289$	−1.80436e10	−	3.12524e10i	−0.152154	−	0.263538i
$290$	−1.62118e11	+	2.80796e11i	−1.34598	+	2.33131i
$291$	−1.84409e10			−0.150752
$292$	5.16653e10	−	8.94870e10i	0.415888	−	0.720339i
$293$	6.36245e10	−	1.10201e11i	0.504336	−	0.873535i	−0.495652	−	0.868521i	$-0.665071\pi$
$293$	6.36245e10	−	1.10201e11i	0.504336	−	0.873535i	0.999987	−	0.00501379i	$-0.00159595\pi$
$294$	1.15637e11			0.902677
$295$	−5.91409e10	+	1.02435e11i	−0.454662	+	0.787498i
$296$	6.11131e10	+	1.05851e11i	0.462723	+	0.801460i
$297$	−3.34130e9	−	5.78731e9i	−0.0249179	−	0.0431591i
$298$	1.79268e11			1.31683
$299$	−3.12513e10	+	2.82379e10i	−0.226125	+	0.204320i
$300$	6.93090e10			0.494020
$301$	−6.61348e9	−	1.14549e10i	−0.0464388	−	0.0804343i
$302$	−5.71325e9	−	9.89564e9i	−0.0395232	−	0.0684562i
$303$	3.97745e10	−	6.88914e10i	0.271089	−	0.469541i
$304$	−2.67466e11			−1.79613
$305$	1.21377e11	−	2.10231e11i	0.803133	−	1.39107i
$306$	−9.50283e10	+	1.64594e11i	−0.619593	+	1.07317i
$307$	−7.15413e10			−0.459657			−0.229829	−	0.973231i	$-0.573817\pi$
$307$	−7.15413e10			−0.459657			−0.229829	+	0.973231i	$0.573817\pi$
$308$	−8.41582e9	+	1.45766e10i	−0.0532866	+	0.0922951i
$309$	−1.50368e10	−	2.60444e10i	−0.0938298	−	0.162518i
$310$	−1.68739e11	−	2.92265e11i	−1.03774	−	1.79742i
$311$	−3.03968e11			−1.84250			−0.921248	−	0.388975i	$-0.872829\pi$
$311$	−3.03968e11			−1.84250			−0.921248	+	0.388975i	$0.872829\pi$
$312$	−7.88660e10	+	7.12612e10i	−0.471188	+	0.425753i
$313$	−1.70381e11			−1.00339			−0.501696	−	0.865044i	$-0.667290\pi$
$313$	−1.70381e11			−1.00339			−0.501696	+	0.865044i	$0.667290\pi$
$314$	5.32702e10	+	9.22667e10i	0.309244	+	0.535626i
$315$	6.44676e10	+	1.11661e11i	0.368930	+	0.639005i
$316$	−5.76179e10	+	9.97971e10i	−0.325061	+	0.563023i
$317$	1.74558e11			0.970896			0.485448	−	0.874266i	$-0.338657\pi$
$317$	1.74558e11			0.970896			0.485448	+	0.874266i	$0.338657\pi$
$318$	−1.12881e10	+	1.95515e10i	−0.0619009	+	0.107216i
$319$	−3.76028e10	+	6.51299e10i	−0.203311	+	0.352146i
$320$	−4.34404e10			−0.231589
$321$	−2.07118e10	+	3.58739e10i	−0.108879	+	0.188585i
$322$	−2.60587e10	−	4.51349e10i	−0.135083	−	0.233971i
$323$	1.62873e11	+	2.82104e11i	0.832600	+	1.44211i
$324$	−1.42068e11			−0.716213
$325$	−2.41359e10	−	1.12583e11i	−0.120002	−	0.559753i
$326$	2.96263e11			1.45278
$327$	1.85634e11	+	3.21527e11i	0.897826	+	1.55508i
$328$	−3.84444e10	−	6.65876e10i	−0.183400	−	0.317659i
$329$	4.82430e9	−	8.35594e9i	0.0227014	−	0.0393200i
$330$	1.13732e11			0.527920
$331$	3.99954e10	−	6.92741e10i	0.183140	−	0.317209i	−0.759808	−	0.650148i	$-0.774707\pi$
$331$	3.99954e10	−	6.92741e10i	0.183140	−	0.317209i	0.942948	+	0.332939i	$0.108040\pi$
$332$	−3.82527e10	+	6.62557e10i	−0.172799	+	0.299296i
$333$	−3.77312e11			−1.68152
$334$	1.41732e11	−	2.45486e11i	0.623171	−	1.07936i
$335$	−2.08264e11	−	3.60724e11i	−0.903468	−	1.56485i
$336$	−1.35656e11	−	2.34963e11i	−0.580647	−	1.00571i
$337$	−4.00263e10			−0.169048			−0.0845241	−	0.996421i	$-0.526937\pi$
$337$	−4.00263e10			−0.169048			−0.0845241	+	0.996421i	$0.526937\pi$
$338$	−2.48828e11	−	1.79459e11i	−1.03699	−	0.747894i
$339$	4.57221e11			1.88030
$340$	1.11987e11	+	1.93968e11i	0.454479	+	0.787181i
$341$	−3.91386e10	−	6.77900e10i	−0.156751	−	0.271501i
$342$	2.00129e11	−	3.46634e11i	0.791030	−	1.37010i
$343$	2.70029e11			1.05338
$344$	8.12490e9	−	1.40727e10i	0.0312827	−	0.0541833i
$345$	−6.83650e10	+	1.18412e11i	−0.259805	+	0.449996i
$346$	3.14651e11			1.18029
$347$	1.73006e9	−	2.99655e9i	0.00640587	−	0.0110953i	−0.862805	−	0.505537i	$-0.831294\pi$
$347$	1.73006e9	−	2.99655e9i	0.00640587	−	0.0110953i	0.869211	+	0.494442i	$0.164628\pi$
$348$	1.98211e11	+	3.43311e11i	0.724470	+	1.25482i
$349$	−1.54694e10	−	2.67938e10i	−0.0558160	−	0.0966761i	0.836767	−	0.547559i	$-0.184443\pi$
$349$	−1.54694e10	−	2.67938e10i	−0.0558160	−	0.0966761i	−0.892583	+	0.450882i	$0.851109\pi$
$350$	1.42473e11			0.507488
$351$	1.22667e10	+	5.72183e10i	0.0431364	+	0.201211i
$352$	−7.72832e10			−0.268314
$353$	−4.93521e10	−	8.54804e10i	−0.169169	−	0.293009i	0.768959	−	0.639298i	$-0.220775\pi$
$353$	−4.93521e10	−	8.54804e10i	−0.169169	−	0.293009i	−0.938128	+	0.346289i	$0.887442\pi$
$354$	1.86233e11	+	3.22565e11i	0.630293	+	1.09170i
$355$	−1.87059e11	+	3.23996e11i	−0.625102	+	1.08271i
$356$	−4.43226e10			−0.146251
$357$	−1.65214e11	+	2.86160e11i	−0.538321	+	0.932399i
$358$	2.71435e11	−	4.70139e11i	0.873357	−	1.51270i
$359$	3.74150e11			1.18883			0.594416	−	0.804158i	$-0.297383\pi$
$359$	3.74150e11			1.18883			0.594416	+	0.804158i	$0.297383\pi$
$360$	−7.92007e10	+	1.37180e11i	−0.248524	+	0.430456i
$361$	−1.81665e11	−	3.14653e11i	−0.562975	−	0.975102i
$362$	3.08927e11	+	5.35078e11i	0.945514	+	1.63768i
$363$	−4.23408e11			−1.27991
$364$	1.09361e11	−	9.88155e10i	0.326517	−	0.295032i
$365$	−5.57254e11			−1.64337
$366$	−3.82214e11	−	6.62013e11i	−1.11337	−	1.92842i
$367$	1.64797e9	+	2.85436e9i	0.00474188	+	0.00821318i	0.868387	−	0.495888i	$-0.165157\pi$
$367$	1.64797e9	+	2.85436e9i	0.00474188	+	0.00821318i	−0.863645	+	0.504101i	$0.831824\pi$
$368$	6.60397e10	−	1.14384e11i	0.187711	−	0.325125i
$369$	2.37356e11			0.666471
$370$	−5.72612e11	+	9.91794e11i	−1.58837	+	2.75115i
$371$	−9.00924e9	+	1.56045e10i	−0.0246891	+	0.0427628i
$372$	−4.12612e11			−1.11712
$373$	−2.17085e11	+	3.76003e11i	−0.580685	+	1.00578i	0.414713	+	0.909952i	$0.363882\pi$
$373$	−2.17085e11	+	3.76003e11i	−0.580685	+	1.00578i	−0.995398	+	0.0958237i	$0.969452\pi$
$374$	6.69009e10	+	1.15876e11i	0.176811	+	0.306246i
$375$	1.39571e11	+	2.41743e11i	0.364463	+	0.631268i
$376$	1.18537e10			0.0305849
$377$	4.88636e11	−	4.41518e11i	1.24580	−	1.12567i
$378$	−7.24094e10			−0.182424
$379$	−1.42055e11	−	2.46046e11i	−0.353654	−	0.612547i	0.633232	−	0.773962i	$-0.281728\pi$
$379$	−1.42055e11	−	2.46046e11i	−0.353654	−	0.612547i	−0.986887	+	0.161414i	$0.948394\pi$
$380$	−2.35845e11	−	4.08496e11i	−0.580231	−	1.00499i
$381$	3.59011e11	−	6.21826e11i	0.872862	−	1.51184i
$382$	4.54870e11			1.09295
$383$	−1.45647e11	+	2.52268e11i	−0.345866	+	0.599057i	−0.985511	−	0.169613i	$-0.945748\pi$
$383$	−1.45647e11	+	2.52268e11i	−0.345866	+	0.599057i	0.639645	+	0.768671i	$0.279081\pi$
$384$	2.52525e11	−	4.37387e11i	0.592672	−	1.02654i
$385$	9.07717e10			0.210561
$386$	2.70711e11	−	4.68886e11i	0.620674	−	1.07504i
$387$	2.50816e10	+	4.34426e10i	0.0568402	+	0.0984501i
$388$	1.57077e10	+	2.72065e10i	0.0351860	+	0.0609439i
$389$	−5.54986e11			−1.22888			−0.614439	−	0.788964i	$-0.710618\pi$
$389$	−5.54986e11			−1.22888			−0.614439	+	0.788964i	$0.710618\pi$
$390$	−9.47719e11	−	3.06103e11i	−2.07438	−	0.670003i
$391$	−1.60859e11			−0.348056
$392$	5.66921e10	+	9.81935e10i	0.121265	+	0.210037i
$393$	2.50622e11	+	4.34091e11i	0.529973	+	0.917940i
$394$	−7.57836e10	+	1.31261e11i	−0.158432	+	0.274412i
$395$	6.21457e11			1.28447
$396$	3.19169e10	−	5.52817e10i	0.0652218	−	0.112967i
$397$	−2.03224e11	+	3.51994e11i	−0.410599	+	0.711178i	−0.994955	−	0.100319i	$-0.968014\pi$
$397$	−2.03224e11	+	3.51994e11i	−0.410599	+	0.711178i	0.584356	+	0.811497i	$0.301347\pi$
$398$	4.56888e11			0.912717
$399$	3.47941e11	−	6.02652e11i	0.687271	−	1.19039i
$400$	1.80532e11	+	3.12691e11i	0.352602	+	0.610725i
$401$	−4.48663e11	−	7.77107e11i	−0.866504	−	1.50083i	−0.865546	−	0.500829i	$-0.833029\pi$
$401$	−4.48663e11	−	7.77107e11i	−0.866504	−	1.50083i	−0.000957193	−	1.00000i	$-0.500305\pi$
$402$	−1.31164e12			−2.50494
$403$	1.43686e11	+	6.70230e11i	0.271358	+	1.26576i
$404$	−1.35517e11			−0.253092
$405$	3.83079e11	+	6.63513e11i	0.707524	+	1.22547i
$406$	4.07445e11	+	7.05716e11i	0.744221	+	1.28903i
$407$	−1.32816e11	+	2.30044e11i	−0.239925	+	0.415562i
$408$	−4.05944e11			−0.725262
$409$	−5.15557e11	+	8.92971e11i	−0.911007	+	1.57791i	−0.0983621	+	0.995151i	$0.531360\pi$
$409$	−5.15557e11	+	8.92971e11i	−0.911007	+	1.57791i	−0.812645	+	0.582759i	$0.801973\pi$
$410$	3.60213e11	−	6.23907e11i	0.629553	−	1.09042i
$411$	−8.37285e10			−0.144739
$412$	−2.56161e10	+	4.43685e10i	−0.0438002	+	0.0758642i
$413$	1.48637e11	+	2.57447e11i	0.251392	+	0.435423i
$414$	9.88273e10	+	1.71174e11i	0.165339	+	0.286376i
$415$	4.12588e11			0.682810
$416$	6.43996e11	+	2.08004e11i	1.05430	+	0.340527i
$417$	4.12752e11			0.668463
$418$	−1.40893e11	−	2.44034e11i	−0.225734	−	0.390982i
$419$	−5.23880e11	−	9.07387e11i	−0.830365	−	1.43823i	−0.897749	−	0.440507i	$-0.854799\pi$
$419$	−5.23880e11	−	9.07387e11i	−0.830365	−	1.43823i	0.0673841	−	0.997727i	$-0.478535\pi$
$420$	2.39236e11	−	4.14369e11i	0.375150	−	0.649779i
$421$	5.38008e11			0.834678			0.417339	−	0.908751i	$-0.362963\pi$
$421$	5.38008e11			0.834678			0.417339	+	0.908751i	$0.362963\pi$
$422$	2.54427e11	−	4.40680e11i	0.390532	−	0.676422i
$423$	−1.82961e10	+	3.16898e10i	−0.0277861	+	0.0481270i
$424$	−2.21363e10			−0.0332629
$425$	2.19869e11	−	3.80825e11i	0.326899	−	0.566206i
$426$	5.89044e11	+	1.02025e12i	0.866572	+	1.50095i
$427$	−3.05053e11	−	5.28367e11i	−0.444068	−	0.769149i
$428$	7.05681e10			0.101651
$429$	−2.19821e11	−	7.09997e10i	−0.313337	−	0.101204i
$430$	1.52256e11			0.214766
$431$	4.61700e11	+	7.99688e11i	0.644484	+	1.11628i	0.984420	+	0.175831i	$0.0562612\pi$
$431$	4.61700e11	+	7.99688e11i	0.644484	+	1.11628i	−0.339936	+	0.940448i	$0.610405\pi$
$432$	−9.17525e10	−	1.58920e11i	−0.126748	−	0.219534i
$433$	4.28660e11	−	7.42461e11i	0.586027	−	1.01503i	−0.408720	−	0.912660i	$-0.634025\pi$
$433$	4.28660e11	−	7.42461e11i	0.586027	−	1.01503i	0.994747	−	0.102368i	$-0.0326420\pi$
$434$	−8.48173e11			−1.14757
$435$	1.06893e12	−	1.85145e12i	1.43136	−	2.47919i
$436$	3.16240e11	−	5.47744e11i	0.419109	−	0.725919i
$437$	3.38768e11			0.444361
$438$	−8.77390e11	+	1.51968e12i	−1.13909	+	1.97297i
$439$	−1.01773e11	−	1.76276e11i	−0.130780	−	0.226518i	0.793197	−	0.608965i	$-0.208415\pi$
$439$	−1.01773e11	−	1.76276e11i	−0.130780	−	0.226518i	−0.923978	+	0.382447i	$0.875082\pi$
$440$	5.57581e10	+	9.65758e10i	0.0709203	+	0.122838i
$441$	−3.50017e11			−0.440672
$442$	−2.45608e11	−	1.14565e12i	−0.306085	−	1.42774i
$443$	−7.19629e11			−0.887752			−0.443876	−	0.896088i	$-0.646397\pi$
$443$	−7.19629e11			−0.887752			−0.443876	+	0.896088i	$0.646397\pi$
$444$	7.00095e11	+	1.21260e12i	0.854936	+	1.48079i
$445$	1.19514e11	+	2.07004e11i	0.144477	+	0.250242i
$446$	−7.78443e11	+	1.34830e12i	−0.931580	+	1.61354i
$447$	−1.18201e12			−1.40036
$448$	−5.45886e10	+	9.45502e10i	−0.0640252	+	0.110895i
$449$	2.61565e11	−	4.53044e11i	0.303719	−	0.526056i	−0.673257	−	0.739409i	$-0.735105\pi$
$449$	2.61565e11	−	4.53044e11i	0.303719	−	0.526056i	0.976975	+	0.213353i	$0.0684384\pi$
$450$	−5.40327e11			−0.621156
$451$	8.35504e10	−	1.44714e11i	0.0950942	−	0.164708i
$452$	−3.89454e11	−	6.74554e11i	−0.438867	−	0.760141i
$453$	3.76707e10	+	6.52475e10i	0.0420302	+	0.0727985i
$454$	−9.03702e10			−0.0998329
$455$	−7.56395e11	−	2.44307e11i	−0.827366	−	0.267230i
$456$	8.54916e11			0.925938
$457$	−1.94437e11	−	3.36775e11i	−0.208524	−	0.361174i	0.742726	−	0.669596i	$-0.233533\pi$
$457$	−1.94437e11	−	3.36775e11i	−0.208524	−	0.361174i	−0.951250	+	0.308422i	$0.900199\pi$
$458$	1.95797e11	+	3.39130e11i	0.207927	+	0.360140i
$459$	−1.11745e11	+	1.93548e11i	−0.117509	+	0.203531i
$460$	2.32929e11			0.242557
$461$	−2.84024e11	+	4.91944e11i	−0.292888	+	0.507296i	−0.974491	−	0.224425i	$-0.927950\pi$
$461$	−2.84024e11	+	4.91944e11i	−0.292888	+	0.507296i	0.681604	+	0.731722i	$0.261283\pi$
$462$	1.42919e11	−	2.47543e11i	0.145949	−	0.252791i
$463$	−1.07126e12			−1.08338			−0.541688	−	0.840580i	$-0.682214\pi$
$463$	−1.07126e12			−1.08338			−0.541688	+	0.840580i	$0.682214\pi$
$464$	−1.03258e12	+	1.78847e12i	−1.03417	+	1.79123i
$465$	1.11259e12	+	1.92707e12i	1.10356	+	1.91143i
$466$	−3.32765e10	−	5.76365e10i	−0.0326889	−	0.0566189i
$467$	5.87702e11			0.571783			0.285892	−	0.958262i	$-0.407710\pi$
$467$	5.87702e11			0.571783			0.285892	+	0.958262i	$0.407710\pi$
$468$	−4.14750e11	+	3.74757e11i	−0.399650	+	0.361113i
$469$	−1.04685e12			−0.999092
$470$	5.55327e10	+	9.61855e10i	0.0524939	+	0.0909221i
$471$	−3.51240e11	−	6.08366e11i	−0.328859	−	0.569601i
$472$	−1.82606e11	+	3.16282e11i	−0.169346	+	0.293316i
$473$	3.53154e10			0.0324406
$474$	9.78477e11	−	1.69477e12i	0.890324	−	1.54209i
$475$	−4.63044e11	+	8.02016e11i	−0.417350	+	0.722872i
$476$	5.62908e11			0.502581
$477$	3.41675e10	−	5.91798e10i	0.0302190	−	0.0523409i
$478$	−1.41023e12	−	2.44259e12i	−1.23556	−	2.14005i
$479$	−9.29936e11	−	1.61070e12i	−0.807129	−	1.39799i	−0.914844	−	0.403807i	$-0.867687\pi$
$479$	−9.29936e11	−	1.61070e12i	−0.807129	−	1.39799i	0.107715	−	0.994182i	$-0.465647\pi$
$480$	2.19693e12			1.88899
$481$	1.72590e12	−	1.55948e12i	1.47015	−	1.32839i
$482$	−5.54019e11			−0.467534
$483$	1.71819e11	+	2.97600e11i	0.143652	+	0.248812i
$484$	3.60652e11	+	6.24667e11i	0.298734	+	0.517422i
$485$	8.47103e10	−	1.46723e11i	0.0695182	−	0.120409i
$486$	2.08903e12			1.69856
$487$	−3.23318e10	+	5.60004e10i	−0.0260465	+	0.0451139i	−0.878755	−	0.477273i	$-0.841625\pi$
$487$	−3.23318e10	+	5.60004e10i	−0.0260465	+	0.0451139i	0.852708	+	0.522387i	$0.174958\pi$
$488$	3.74768e11	−	6.49118e11i	0.299139	−	0.518125i
$489$	−1.95343e12			−1.54493
$490$	−5.31189e11	+	9.20046e11i	−0.416262	+	0.720987i
$491$	9.50880e11	+	1.64697e12i	0.738345	+	1.27885i	0.953240	+	0.302213i	$0.0977255\pi$
$491$	9.50880e11	+	1.64697e12i	0.738345	+	1.27885i	−0.214896	+	0.976637i	$0.568941\pi$
$492$	−4.40408e11	−	7.62810e11i	−0.338854	−	0.586912i
$493$	2.51514e12			1.91757
$494$	5.17249e11	+	2.41273e12i	0.390776	+	1.82279i
$495$	−3.44251e11			−0.257722
$496$	−1.07475e12	−	1.86152e12i	−0.797332	−	1.38102i
$497$	4.70129e11	+	8.14288e11i	0.345632	+	0.598652i
$498$	6.49614e11	−	1.12516e12i	0.473286	−	0.819755i
$499$	−1.60030e11			−0.115545			−0.0577723	−	0.998330i	$-0.518400\pi$
$499$	−1.60030e11			−0.115545			−0.0577723	+	0.998330i	$0.518400\pi$
$500$	2.37768e11	−	4.11826e11i	0.170133	−	0.294679i
$501$	−9.34516e11	+	1.61863e12i	−0.662700	+	1.14783i
$502$	6.41202e11			0.450638
$503$	7.16678e11	−	1.24132e12i	0.499193	−	0.864627i	−0.500807	−	0.865559i	$-0.666963\pi$
$503$	7.16678e11	−	1.24132e12i	0.499193	−	0.864627i	1.00000		0.000932081i	$0.000296691\pi$
$504$	1.99052e11	+	3.44769e11i	0.137414	+	0.238008i
$505$	3.65416e11	+	6.32919e11i	0.250021	+	0.433049i
$506$	1.39151e11			0.0943645
$507$	1.64066e12	+	1.18327e12i	1.10277	+	0.795334i
$508$	−1.22320e12			−0.814912
$509$	6.02420e11	+	1.04342e12i	0.397804	+	0.689017i	0.993455	−	0.114227i	$-0.0364391\pi$
$509$	6.02420e11	+	1.04342e12i	0.397804	+	0.689017i	−0.595651	+	0.803244i	$0.703106\pi$
$510$	−1.90179e12	−	3.29400e12i	−1.24479	−	2.15604i
$511$	−7.00264e11	+	1.21289e12i	−0.454326	+	0.786916i
$512$	−1.22755e12			−0.789451
$513$	2.35334e11	−	4.07611e11i	0.150023	−	0.259847i
$514$	5.35981e10	−	9.28346e10i	0.0338700	−	0.0586645i
$515$	2.76292e11			0.173075
$516$	9.30766e10	−	1.61213e11i	0.0577986	−	0.100110i
$517$	1.28807e10	+	2.23100e10i	0.00792923	+	0.0137338i
$518$	1.43913e12	+	2.49264e12i	0.878244	+	1.52116i
$519$	−2.07467e12			−1.25515
$520$	−2.04700e11	−	9.54831e11i	−0.122773	−	0.572679i
$521$	1.96441e12			1.16805			0.584025	−	0.811736i	$-0.301477\pi$
$521$	1.96441e12			1.16805			0.584025	+	0.811736i	$0.301477\pi$
$522$	−1.54523e12	−	2.67642e12i	−0.910913	−	1.57775i
$523$	5.14852e11	+	8.91750e11i	0.300902	+	0.521178i	0.976341	−	0.216239i	$-0.0693790\pi$
$523$	5.14852e11	+	8.91750e11i	0.300902	+	0.521178i	−0.675439	+	0.737416i	$0.736046\pi$
$524$	4.26953e11	−	7.39504e11i	0.247394	−	0.428499i
$525$	−9.39404e11			−0.539679
$526$	−4.44296e11	+	7.69543e11i	−0.253068	+	0.438326i
$527$	−1.30893e12	+	2.26713e12i	−0.739211	+	1.28035i
$528$	7.24390e11			0.405620
$529$	8.16932e11	−	1.41497e12i	0.453560	−	0.785590i
$530$	−1.03706e11	−	1.79624e11i	−0.0570902	−	0.0988830i
$531$	−5.63704e11	−	9.76364e11i	−0.307699	−	0.532950i
$532$	−1.18548e12			−0.641643
$533$	−1.08571e12	+	9.81019e11i	−0.582695	+	0.526508i
$534$	7.52693e11			0.400574
$535$	−1.90284e11	−	3.29581e11i	−0.100418	−	0.173928i
$536$	−6.43044e11	−	1.11379e12i	−0.336511	−	0.582854i
$537$	−1.78972e12	+	3.09989e12i	−0.928755	+	1.60865i
$538$	7.95704e11			0.409479
$539$	−1.23208e11	+	2.13402e11i	−0.0628766	+	0.108905i
$540$	1.61810e11	−	2.80264e11i	0.0818907	−	0.141839i
$541$	2.77786e12			1.39419			0.697096	−	0.716978i	$-0.254475\pi$
$541$	2.77786e12			1.39419			0.697096	+	0.716978i	$0.254475\pi$
$542$	−5.70250e11	+	9.87702e11i	−0.283837	+	0.491619i
$543$	−2.03693e12	−	3.52807e12i	−1.00549	−	1.74156i
$544$	1.29231e12	+	2.23834e12i	0.632661	+	1.09580i
$545$	−3.41091e12			−1.65610
$546$	−1.85718e12	+	1.67810e12i	−0.894310	+	0.808074i
$547$	1.15904e12			0.553548			0.276774	−	0.960935i	$-0.410735\pi$
$547$	1.15904e12			0.553548			0.276774	+	0.960935i	$0.410735\pi$
$548$	7.13186e10	+	1.23528e11i	0.0337824	+	0.0585128i
$549$	1.15691e12	+	2.00383e12i	0.543531	+	0.941424i
$550$	−1.90198e11	+	3.29433e11i	−0.0886286	+	0.153509i
$551$	−5.29687e12			−2.44814
$552$	−2.11086e11	+	3.65612e11i	−0.0967685	+	0.167608i
$553$	7.80944e11	−	1.35263e12i	0.355105	−	0.615060i
$554$	1.05827e12			0.477314
$555$	3.77555e12	−	6.53945e12i	1.68913	−	2.92565i
$556$	−3.51576e11	−	6.08947e11i	−0.156021	−	0.270236i
$557$	−8.51888e11	−	1.47551e12i	−0.375002	−	0.649523i	0.615325	−	0.788273i	$-0.289025\pi$
$557$	−8.51888e11	−	1.47551e12i	−0.375002	−	0.649523i	−0.990327	+	0.138750i	$0.955691\pi$
$558$	3.21669e12			1.40461
$559$	−2.94281e11	−	9.50495e10i	−0.127470	−	0.0411715i
$560$	2.49260e12			1.07104
$561$	−4.41115e11	−	7.64033e11i	−0.188026	−	0.325671i
$562$	−6.23204e11	−	1.07942e12i	−0.263522	−	0.456433i
$563$	1.88395e12	−	3.26310e12i	0.790281	−	1.36881i	−0.135511	−	0.990776i	$-0.543268\pi$
$563$	1.88395e12	−	3.26310e12i	0.790281	−	1.36881i	0.925793	−	0.378032i	$-0.123399\pi$
$564$	1.35792e11			0.0565092
$565$	−2.10029e12	+	3.63782e12i	−0.867086	+	1.50184i
$566$	−1.56393e11	+	2.70881e11i	−0.0640536	+	0.110944i
$567$	1.92556e12			0.782409
$568$	−5.77570e11	+	1.00038e12i	−0.232829	+	0.403272i
$569$	−8.24016e11	−	1.42724e12i	−0.329557	−	0.570809i	0.652867	−	0.757472i	$-0.273566\pi$
$569$	−8.24016e11	−	1.42724e12i	−0.329557	−	0.570809i	−0.982424	+	0.186663i	$0.940233\pi$
$570$	4.00516e12	+	6.93715e12i	1.58922	+	2.75261i
$571$	4.20757e12			1.65641			0.828207	−	0.560422i	$-0.189361\pi$
$571$	4.20757e12			1.65641			0.828207	+	0.560422i	$0.189361\pi$
$572$	8.24917e10	+	3.84786e11i	0.0322202	+	0.150292i
$573$	−2.99921e12			−1.16228
$574$	−9.05311e11	−	1.56805e12i	−0.348092	−	0.602914i
$575$	−2.28659e11	−	3.96049e11i	−0.0872335	−	0.151093i
$576$	2.07027e11	−	3.58581e11i	0.0783656	−	0.135733i
$577$	3.41509e11			0.128266			0.0641329	−	0.997941i	$-0.479572\pi$
$577$	3.41509e11			0.128266			0.0641329	+	0.997941i	$0.479572\pi$
$578$	5.22006e11	−	9.04140e11i	0.194536	−	0.336946i
$579$	−1.78495e12	+	3.09163e12i	−0.660045	+	1.14323i
$580$	−3.64200e12			−1.33633
$581$	5.18471e11	−	8.98019e11i	0.188770	−	0.326959i
$582$	−2.66751e11	−	4.62026e11i	−0.0963723	−	0.166922i
$583$	−2.40543e10	−	4.16632e10i	−0.00862350	−	0.0149363i
$584$	−1.72060e12			−0.612099
$585$	2.86862e12	+	9.26534e11i	1.01268	+	0.327084i
$586$	3.68135e12			1.28964
$587$	2.00284e12	+	3.46902e12i	0.696264	+	1.20597i	0.969753	+	0.244090i	$0.0784892\pi$
$587$	2.00284e12	+	3.46902e12i	0.696264	+	1.20597i	−0.273488	+	0.961875i	$0.588177\pi$
$588$	6.49449e11	+	1.12488e12i	0.224051	+	0.388068i
$589$	2.75660e12	−	4.77458e12i	0.943746	−	1.63462i
$590$	−3.42193e12			−1.16262
$591$	4.99684e11	−	8.65478e11i	0.168481	−	0.291818i
$592$	−3.64714e12	+	6.31702e12i	−1.22041	+	2.11380i
$593$	−2.43385e12			−0.808255			−0.404128	−	0.914703i	$-0.632425\pi$
$593$	−2.43385e12			−0.808255			−0.404128	+	0.914703i	$0.632425\pi$
$594$	9.66649e10	−	1.67429e11i	0.0318588	−	0.0551811i
$595$	−1.51786e12	−	2.62901e12i	−0.496484	−	0.859936i
$596$	1.00682e12	+	1.74386e12i	0.326847	+	0.566115i
$597$	−3.01252e12			−0.970611
$598$	−1.15954e12	−	3.74518e11i	−0.370791	−	0.119761i
$599$	4.30183e12			1.36532			0.682658	−	0.730738i	$-0.260824\pi$
$599$	4.30183e12			1.36532			0.682658	+	0.730738i	$0.260824\pi$
$600$	−5.77045e11	−	9.99472e11i	−0.181773	−	0.314840i
$601$	2.98862e12	+	5.17645e12i	0.934407	+	1.61844i	0.775688	+	0.631116i	$0.217403\pi$
$601$	2.98862e12	+	5.17645e12i	0.934407	+	1.61844i	0.158719	+	0.987324i	$0.449264\pi$
$602$	1.91330e11	−	3.31393e11i	0.0593743	−	0.102839i
$603$	3.97016e12			1.22287
$604$	6.41746e10	−	1.11154e11i	0.0196199	−	0.0339827i
$605$	1.94497e12	−	3.36878e12i	0.590219	−	1.02229i
$606$	2.30137e12			0.693203
$607$	−1.09301e12	+	1.89315e12i	−0.326796	+	0.566027i	−0.981874	−	0.189534i	$-0.939302\pi$
$607$	−1.09301e12	+	1.89315e12i	−0.326796	+	0.566027i	0.655079	+	0.755561i	$0.272636\pi$
$608$	−2.72160e12	−	4.71395e12i	−0.807715	−	1.39900i
$609$	−2.68652e12	−	4.65318e12i	−0.791428	−	1.37079i
$610$	7.02295e12			2.05369
$611$	−4.72877e10	−	2.20575e11i	−0.0137266	−	0.0640283i
$612$	−2.13483e12			−0.615150
$613$	−1.25110e12	−	2.16696e12i	−0.357864	−	0.619839i	0.629739	−	0.776806i	$-0.283162\pi$
$613$	−1.25110e12	−	2.16696e12i	−0.357864	−	0.619839i	−0.987604	+	0.156967i	$0.949828\pi$
$614$	−1.03486e12	−	1.79242e12i	−0.293848	−	0.508959i
$615$	−2.37509e12	+	4.11377e12i	−0.669486	+	1.15958i
$616$	2.80270e11			0.0784266
$617$	−7.42062e11	+	1.28529e12i	−0.206137	+	0.357040i	−0.950495	−	0.310741i	$-0.899423\pi$
$617$	−7.42062e11	+	1.28529e12i	−0.206137	+	0.357040i	0.744357	+	0.667782i	$0.232756\pi$
$618$	4.35018e11	−	7.53473e11i	0.119966	−	0.207788i
$619$	−3.37694e12			−0.924519			−0.462259	−	0.886745i	$-0.652961\pi$
$619$	−3.37694e12			−0.924519			−0.462259	+	0.886745i	$0.652961\pi$
$620$	1.89538e12	−	3.28289e12i	0.515149	−	0.892264i
$621$	1.16212e11	+	2.01285e11i	0.0313574	+	0.0543125i
$622$	−4.39695e12	−	7.61574e12i	−1.17786	−	2.04012i
$623$	6.00741e11			0.159768
$624$	−6.03630e12	−	1.94966e12i	−1.59382	−	0.514787i
$625$	−4.74834e12			−1.24475
$626$	−2.46458e12	−	4.26878e12i	−0.641444	−	1.11101i
$627$	9.28987e11	+	1.60905e12i	0.240052	+	0.415782i
$628$	−5.98362e11	+	1.03639e12i	−0.153513	+	0.265893i
$629$	8.88365e12			2.26289
$630$	−1.86507e12	+	3.23039e12i	−0.471696	+	0.817001i
$631$	−2.80721e12	+	4.86222e12i	−0.704924	+	1.22096i	0.261795	+	0.965123i	$0.415685\pi$
$631$	−2.80721e12	+	4.86222e12i	−0.704924	+	1.22096i	−0.966719	+	0.255840i	$0.917648\pi$
$632$	1.91883e12			0.478421
$633$	−1.67758e12	+	2.90565e12i	−0.415304	+	0.719328i
$634$	2.52500e12	+	4.37344e12i	0.620670	+	1.07503i
$635$	3.29831e12	+	5.71284e12i	0.805026	+	1.39435i
$636$	−2.53588e11			−0.0614571
$637$	1.60105e12	−	1.44666e12i	0.385280	−	0.348128i
$638$	−2.17572e12			−0.519888
$639$	−1.78296e12	−	3.08818e12i	−0.423046	−	0.732738i
$640$	2.32000e12	+	4.01836e12i	0.546612	+	0.946759i
$641$	−2.42178e12	+	4.19465e12i	−0.566596	+	0.981373i	0.430303	+	0.902684i	$0.358407\pi$
$641$	−2.42178e12	+	4.19465e12i	−0.566596	+	0.981373i	−0.996899	+	0.0786886i	$0.974927\pi$
$642$	−1.19840e12			−0.278416
$643$	1.76937e12	−	3.06464e12i	0.408196	−	0.707017i	−0.586491	−	0.809955i	$-0.699491\pi$
$643$	1.76937e12	−	3.06464e12i	0.408196	−	0.707017i	0.994688	+	0.102939i	$0.0328246\pi$
$644$	2.92706e11	−	5.06982e11i	0.0670572	−	0.116147i
$645$	−1.00391e12			−0.228389
$646$	−4.71195e12	+	8.16134e12i	−1.06452	+	1.84381i
$647$	−4.34747e11	−	7.53003e11i	−0.0975365	−	0.168938i	0.813128	−	0.582085i	$-0.197763\pi$
$647$	−4.34747e11	−	7.53003e11i	−0.0975365	−	0.168938i	−0.910664	+	0.413147i	$0.864430\pi$
$648$	1.18281e12	+	2.04869e12i	0.263528	+	0.456445i
$649$	−7.93707e11			−0.175614
$650$	2.47156e12	−	2.23324e12i	0.543077	−	0.490709i
$651$	5.59248e12			1.22037
$652$	1.66390e12	+	2.88196e12i	0.360590	+	0.624560i
$653$	−4.60119e12	−	7.96949e12i	−0.990286	−	1.71523i	−0.615559	−	0.788090i	$-0.711070\pi$
$653$	−4.60119e12	−	7.96949e12i	−0.990286	−	1.71523i	−0.374727	−	0.927135i	$-0.622263\pi$
$654$	−5.37044e12	+	9.30187e12i	−1.14792	+	1.98825i
$655$	−4.60504e12			−0.977570
$656$	2.29430e12	−	3.97385e12i	0.483708	−	0.837807i
$657$	2.65575e12	−	4.59989e12i	0.556086	−	0.963170i
$658$	2.79137e11			0.0580498
$659$	−4.06451e10	+	7.03993e10i	−0.00839506	+	0.0145407i	−0.870192	−	0.492712i	$-0.836006\pi$
$659$	−4.06451e10	+	7.03993e10i	−0.00839506	+	0.0145407i	0.861797	+	0.507253i	$0.169339\pi$
$660$	6.38750e11	+	1.10635e12i	0.131034	+	0.226957i
$661$	−3.89985e12	−	6.75473e12i	−0.794586	−	1.37626i	−0.923102	−	0.384556i	$-0.874355\pi$
$661$	−3.89985e12	−	6.75473e12i	−0.794586	−	1.37626i	0.128516	−	0.991707i	$-0.458979\pi$
$662$	2.31416e12			0.468309
$663$	1.61943e12	+	7.55389e12i	0.325500	+	1.51831i
$664$	1.27392e12			0.254323
$665$	3.19661e12	+	5.53669e12i	0.633858	+	1.09787i
$666$	−5.45788e12	−	9.45332e12i	−1.07495	−	1.86188i
$667$	1.30784e12	−	2.26525e12i	0.255852	−	0.443149i
$668$	3.18402e12			0.618703
$669$	5.13271e12	−	8.89012e12i	0.990671	−	1.71589i
$670$	6.02514e12	−	1.04359e13i	1.15513	−	2.00074i
$671$	1.62895e12			0.310211
$672$	2.76073e12	−	4.78173e12i	0.522231	−	0.904530i
$673$	3.20947e12	+	5.55897e12i	0.603067	+	1.04454i	0.992354	+	0.123426i	$0.0393883\pi$
$673$	3.20947e12	+	5.55897e12i	0.603067	+	1.04454i	−0.389287	+	0.921117i	$0.627278\pi$
$674$	−5.78986e11	−	1.00283e12i	−0.108068	−	0.187180i
$675$	−6.35377e11			−0.117805
$676$	3.48232e11	−	3.42842e12i	0.0641370	−	0.631443i
$677$	9.04416e11			0.165470			0.0827350	−	0.996572i	$-0.473635\pi$
$677$	9.04416e11			0.165470			0.0827350	+	0.996572i	$0.473635\pi$
$678$	6.61378e12	+	1.14554e13i	1.20203	+	2.08198i
$679$	−2.12900e11	−	3.68753e11i	−0.0384380	−	0.0665766i
$680$	1.86474e12	−	3.22983e12i	0.334448	−	0.579282i
$681$	5.95861e11			0.106165
$682$	1.13229e12	−	1.96118e12i	0.200414	−	0.347127i
$683$	−4.10660e12	+	7.11284e12i	−0.722087	+	1.25069i	0.238075	+	0.971247i	$0.423484\pi$
$683$	−4.10660e12	+	7.11284e12i	−0.722087	+	1.25069i	−0.960162	+	0.279444i	$0.909850\pi$
$684$	4.49594e12			0.785358
$685$	3.84616e11	−	6.66174e11i	0.0667451	−	0.115606i
$686$	3.90601e12	+	6.76541e12i	0.673402	+	1.16637i
$687$	−1.29100e12	−	2.23607e12i	−0.221116	−	0.382984i
$688$	9.69763e11			0.165013
$689$	8.83084e10	+	4.11918e11i	0.0149285	+	0.0696345i
$690$	−3.95564e12			−0.664348
$691$	−1.77746e12	−	3.07865e12i	−0.296584	−	0.513699i	0.678768	−	0.734353i	$-0.262514\pi$
$691$	−1.77746e12	−	3.07865e12i	−0.296584	−	0.513699i	−0.975352	+	0.220654i	$0.929181\pi$
$692$	1.76717e12	+	3.06083e12i	0.292956	+	0.507414i
$693$	−4.32597e11	+	7.49280e11i	−0.0712499	+	0.123408i
$694$	1.00102e11			0.0163804
$695$	−1.89602e12	+	3.28400e12i	−0.308256	+	0.533915i
$696$	3.30048e12	−	5.71660e12i	0.533133	−	0.923413i
$697$	−5.58843e12			−0.896897
$698$	4.47534e11	−	7.75151e11i	0.0713635	−	0.123605i
$699$	2.19410e11	+	3.80030e11i	0.0347624	+	0.0602103i
$700$	8.00169e11	+	1.38593e12i	0.125962	+	0.218173i
$701$	−1.10497e13			−1.72830			−0.864151	−	0.503233i	$-0.832144\pi$
$701$	−1.10497e13			−1.72830			−0.864151	+	0.503233i	$0.832144\pi$
$702$	−1.25613e12	+	1.13500e12i	−0.195217	+	0.176393i
$703$	−1.87089e13			−2.88902
$704$	−1.45749e11	−	2.52445e11i	−0.0223629	−	0.0387337i
$705$	−3.66158e11	−	6.34205e11i	−0.0558236	−	0.0966894i
$706$	1.42777e12	−	2.47297e12i	0.216291	−	0.374626i
$707$	1.83678e12			0.276483
$708$	−2.09188e12	+	3.62324e12i	−0.312887	+	0.541936i
$709$	−7.79505e11	+	1.35014e12i	−0.115854	+	0.200665i	−0.918121	−	0.396301i	$-0.870294\pi$
$709$	−7.79505e11	+	1.35014e12i	−0.115854	+	0.200665i	0.802267	+	0.596966i	$0.203627\pi$
$710$	−1.08233e13			−1.59845
$711$	−2.96172e12	+	5.12986e12i	−0.434642	+	0.752821i
$712$	3.69016e11	+	6.39154e11i	0.0538127	+	0.0932064i
$713$	1.36126e12	+	2.35777e12i	0.197259	+	0.341663i
$714$	−9.55941e12			−1.37654
$715$	1.57467e12	−	1.42283e12i	0.225326	−	0.203599i
$716$	6.09783e12			0.867095
$717$	9.29843e12	+	1.61054e13i	1.31393	+	2.27580i
$718$	5.41213e12	+	9.37409e12i	0.759991	+	1.31634i
$719$	3.98902e12	−	6.90919e12i	0.556655	−	0.964155i	−0.441118	−	0.897449i	$-0.645418\pi$
$719$	3.98902e12	−	6.90919e12i	0.556655	−	0.964155i	0.997773	−	0.0667056i	$-0.0212488\pi$
$720$	−9.45316e12			−1.31093
$721$	3.47197e11	−	6.01363e11i	0.0478484	−	0.0828759i
$722$	5.25563e12	−	9.10302e12i	0.719793	−	1.24672i
$723$	3.65296e12			0.497190
$724$	−3.47005e12	+	6.01031e12i	−0.469367	+	0.812968i
$725$	3.57524e12	+	6.19250e12i	0.480601	+	0.832425i
$726$	−6.12465e12	−	1.06082e13i	−0.818214	−	1.41719i
$727$	1.40953e13			1.87141			0.935705	−	0.352783i	$-0.114765\pi$
$727$	1.40953e13			1.87141			0.935705	+	0.352783i	$0.114765\pi$
$728$	−2.33547e12	−	7.54332e11i	−0.308165	−	0.0995340i
$729$	−5.16908e12			−0.677860
$730$	−8.06076e12	−	1.39616e13i	−1.05057	−	1.81963i
$731$	−5.90534e11	−	1.02284e12i	−0.0764922	−	0.132488i
$732$	4.29325e12	−	7.43612e12i	0.552695	−	0.957297i
$733$	1.52669e12			0.195336			0.0976682	−	0.995219i	$-0.468862\pi$
$733$	1.52669e12			0.195336			0.0976682	+	0.995219i	$0.468862\pi$
$734$	−4.76761e10	+	8.25775e10i	−0.00606274	+	0.0105010i
$735$	3.50243e12	−	6.06638e12i	0.442666	−	0.766720i
$736$	2.68795e12			0.337653
$737$	1.39752e12	−	2.42057e12i	0.174483	−	0.302213i
$738$	3.43339e12	+	5.94680e12i	0.426058	+	0.737955i
$739$	4.65333e12	+	8.05980e12i	0.573936	+	0.994087i	0.996156	+	0.0875932i	$0.0279176\pi$
$739$	4.65333e12	+	8.05980e12i	0.573936	+	0.994087i	−0.422220	+	0.906493i	$0.638749\pi$
$740$	−1.28638e13			−1.57699
$741$	−3.41051e12	−	1.59085e13i	−0.415564	−	1.93841i
$742$	−5.21280e11			−0.0631326
$743$	−3.05527e12	−	5.29188e12i	−0.367789	−	0.637030i	0.621430	−	0.783470i	$-0.286552\pi$
$743$	−3.05527e12	−	5.29188e12i	−0.367789	−	0.637030i	−0.989220	+	0.146440i	$0.953219\pi$
$744$	3.43528e12	+	5.95008e12i	0.411040	+	0.711942i
$745$	5.42970e12	−	9.40452e12i	0.645763	−	1.11849i
$746$	−1.25607e13			−1.48487
$747$	−1.96630e12	+	3.40573e12i	−0.231050	+	0.400191i
$748$	−7.51470e11	+	1.30158e12i	−0.0877716	+	0.152025i
$749$	−9.56468e11			−0.111046
$750$	−4.03782e12	+	6.99371e12i	−0.465984	+	0.807108i
$751$	2.86590e12	+	4.96389e12i	0.328762	+	0.569433i	0.982267	−	0.187490i	$-0.0600352\pi$
$751$	2.86590e12	+	4.96389e12i	0.328762	+	0.569433i	−0.653504	+	0.756923i	$0.726702\pi$
$752$	3.53704e11	+	6.12634e11i	0.0403330	+	0.0698587i
$753$	−4.22781e12			−0.479223
$754$	1.81302e13	+	5.85584e12i	2.04282	+	0.659809i
$755$	−6.92177e11			−0.0775275
$756$	−4.06673e11	−	7.04378e11i	−0.0452790	−	0.0784255i
$757$	−3.51216e12	−	6.08324e12i	−0.388725	−	0.673292i	0.603553	−	0.797323i	$-0.293751\pi$
$757$	−3.51216e12	−	6.08324e12i	−0.388725	−	0.673292i	−0.992278	+	0.124031i	$0.960418\pi$
$758$	4.10968e12	−	7.11818e12i	0.452165	−	0.783173i
$759$	−9.17500e11			−0.100350
$760$	−3.92715e12	+	6.80202e12i	−0.426988	+	0.739565i
$761$	1.82722e12	−	3.16484e12i	0.197497	−	0.342074i	−0.750219	−	0.661189i	$-0.770052\pi$
$761$	1.82722e12	−	3.16484e12i	0.197497	−	0.342074i	0.947716	+	0.319115i	$0.103386\pi$
$762$	2.07726e13			2.23200
$763$	−4.28627e12	+	7.42403e12i	−0.457845	+	0.793011i
$764$	2.55468e12	+	4.42484e12i	0.271279	+	0.469870i
$765$	5.75647e12	+	9.97050e12i	0.607687	+	1.05254i
$766$	−8.42724e12			−0.884414
$767$	6.61392e12	+	2.13622e12i	0.690048	+	0.222878i
$768$	1.70322e13			1.76663
$769$	3.05877e12	+	5.29795e12i	0.315413	+	0.546310i	0.979525	−	0.201322i	$-0.0645238\pi$
$769$	3.05877e12	+	5.29795e12i	0.315413	+	0.546310i	−0.664113	+	0.747633i	$0.731190\pi$
$770$	1.31303e12	+	2.27423e12i	0.134606	+	0.233145i
$771$	−3.53402e11	+	6.12110e11i	−0.0360184	+	0.0623857i
$772$	6.08158e12			0.616224
$773$	−4.39859e12	+	7.61858e12i	−0.443104	+	0.767478i	−0.997918	−	0.0644960i	$-0.979456\pi$
$773$	−4.39859e12	+	7.61858e12i	−0.443104	+	0.767478i	0.554814	+	0.831974i	$0.312789\pi$
$774$	−7.25618e11	+	1.25681e12i	−0.0726731	+	0.125873i
$775$	−7.44253e12			−0.741076
$776$	2.61555e11	−	4.53026e11i	0.0258931	−	0.0448482i
$777$	−9.48898e12	−	1.64354e13i	−0.933952	−	1.61765i
$778$	−8.02796e12	−	1.39048e13i	−0.785592	−	1.36068i
$779$	1.17692e13			1.14506
$780$	−2.34499e12	−	1.09383e13i	−0.226838	−	1.05809i
$781$	−2.51045e12			−0.241447
$782$	−2.32684e12	−	4.03021e12i	−0.222504	−	0.385387i
$783$	−1.81706e12	−	3.14724e12i	−0.172759	−	0.299227i
$784$	−3.38330e12	+	5.86004e12i	−0.319829	+	0.553960i
$785$	6.45384e12			0.606603
$786$	−7.25058e12	+	1.25584e13i	−0.677597	+	1.17363i
$787$	3.32096e12	−	5.75207e12i	0.308587	−	0.534488i	−0.669467	−	0.742842i	$-0.733477\pi$
$787$	3.32096e12	−	5.75207e12i	0.308587	−	0.534488i	0.978053	+	0.208354i	$0.0668107\pi$
$788$	−1.70249e12			−0.157296
$789$	2.92949e12	−	5.07403e12i	0.269120	−	0.466130i
$790$	8.98947e12	+	1.55702e13i	0.821130	+	1.42224i
$791$	5.27860e12	+	9.14280e12i	0.479429	+	0.830396i
$792$	−1.06292e12			−0.0959926
$793$	−1.35740e13	−	4.38425e12i	−1.21893	−	0.393700i
$794$	−1.17587e13			−1.04994
$795$	6.83790e11	+	1.18436e12i	0.0607115	+	0.105155i
$796$	2.56602e12	+	4.44447e12i	0.226543	+	0.392384i
$797$	−1.87944e12	+	3.25528e12i	−0.164993	+	0.285776i	−0.936653	−	0.350259i	$-0.886093\pi$
$797$	−1.87944e12	+	3.25528e12i	−0.164993	+	0.285776i	0.771660	+	0.636036i	$0.219427\pi$
$798$	2.01321e13			1.75742
$799$	4.30774e11	−	7.46123e11i	0.0373929	−	0.0647664i
$800$	−3.67401e12	+	6.36358e12i	−0.317129	+	0.549283i
$801$	−2.27831e12			−0.195554
$802$	1.29799e13	−	2.24819e13i	1.10787	−	1.91888i
$803$	−1.86967e12	−	3.23837e12i	−0.158688	−	0.274856i
$804$	−7.36654e12	−	1.27592e13i	−0.621744	−	1.07689i
$805$	−3.15708e12			−0.264975
$806$	−1.47137e13	+	1.32949e13i	−1.22805	+	1.10963i
$807$	−5.24652e12			−0.435452
$808$	1.12827e12	+	1.95423e12i	0.0931243	+	0.161296i
$809$	2.02491e10	+	3.50725e10i	0.00166203	+	0.00287871i	0.866855	−	0.498560i	$-0.166138\pi$
$809$	2.02491e10	+	3.50725e10i	0.00166203	+	0.00287871i	−0.865193	+	0.501439i	$0.832804\pi$
$810$	−1.10826e13	+	1.91956e13i	−0.904605	+	1.56682i
$811$	1.87983e13			1.52589			0.762947	−	0.646462i	$-0.223752\pi$
$811$	1.87983e13			1.52589			0.762947	+	0.646462i	$0.223752\pi$
$812$	−4.57666e12	+	7.92701e12i	−0.369442	+	0.639893i
$813$	3.75998e12	−	6.51247e12i	0.301841	−	0.522803i
$814$	−7.68480e12			−0.613512
$815$	8.97328e12	−	1.55422e13i	0.712430	−	1.23396i
$816$	−1.21131e13	−	2.09804e13i	−0.956419	−	1.65657i
$817$	1.24366e12	+	2.15409e12i	0.0976571	+	0.169147i
$818$	−2.98304e13			−2.32954
$819$	5.62146e12	−	5.07940e12i	0.436588	−	0.394489i
$820$	8.09225e12			0.625038
$821$	1.31650e12	+	2.28024e12i	0.101129	+	0.175160i	0.912150	−	0.409856i	$-0.134421\pi$
$821$	1.31650e12	+	2.28024e12i	0.101129	+	0.175160i	−0.811021	+	0.585017i	$0.801088\pi$
$822$	−1.21115e12	−	2.09777e12i	−0.0925280	−	0.160263i
$823$	−1.35036e12	+	2.33890e12i	−0.102601	+	0.177710i	−0.912756	−	0.408506i	$-0.866050\pi$
$823$	−1.35036e12	+	2.33890e12i	−0.102601	+	0.177710i	0.810155	+	0.586216i	$0.199383\pi$
$824$	8.53088e11			0.0644646
$825$	1.25408e12	−	2.17213e12i	0.0942504	−	0.163246i
$826$	−4.30011e12	+	7.44801e12i	−0.321417	+	0.556711i
$827$	3.18882e12			0.237059			0.118529	−	0.992951i	$-0.462182\pi$
$827$	3.18882e12			0.237059			0.118529	+	0.992951i	$0.462182\pi$
$828$	−1.11009e12	+	1.92273e12i	−0.0820768	+	0.142161i
$829$	−4.62393e12	−	8.00888e12i	−0.340029	−	0.588947i	0.644409	−	0.764681i	$-0.277103\pi$
$829$	−4.62393e12	−	8.00888e12i	−0.340029	−	0.588947i	−0.984438	+	0.175734i	$0.943770\pi$
$830$	5.96814e12	+	1.03371e13i	0.436503	+	0.756046i
$831$	−6.97779e12			−0.507590
$832$	5.35076e11	+	2.49588e12i	0.0387134	+	0.180580i
$833$	8.24099e12			0.593031
$834$	5.97052e12	+	1.03412e13i	0.427332	+	0.740160i
$835$	−8.58559e12	−	1.48707e13i	−0.611197	−	1.05862i
$836$	1.58259e12	−	2.74113e12i	0.112057	−	0.194089i
$837$	3.78254e12			0.266391
$838$	1.51560e13	−	2.62510e13i	1.06166	−	1.83886i
$839$	−8.71844e12	+	1.51008e13i	−0.607449	+	1.05213i	0.384210	+	0.923246i	$0.374474\pi$
$839$	−8.71844e12	+	1.51008e13i	−0.607449	+	1.05213i	−0.991659	+	0.128887i	$0.958859\pi$
$840$	−7.96723e12			−0.552142
$841$	−1.31955e13	+	2.28552e13i	−0.909583	+	1.57544i
$842$	7.78236e12	+	1.34794e13i	0.533589	+	0.924203i
$843$	4.10913e12	+	7.11723e12i	0.280238	+	0.485386i
$844$	5.71574e12			0.387732
$845$	−1.69511e13	+	7.61821e12i	−1.14378	+	0.514041i
$846$	−1.05863e12			−0.0710519
$847$	−4.88822e12	−	8.46664e12i	−0.326344	−	0.565244i
$848$	−6.60532e11	−	1.14408e12i	−0.0438644	−	0.0759754i
$849$	1.03119e12	−	1.78607e12i	0.0681166	−	0.117981i
$850$	1.27218e13			0.835915
$851$	4.61940e12	−	8.00104e12i	0.301927	−	0.522954i
$852$	−6.61649e12	+	1.14601e13i	−0.430179	+	0.745092i
$853$	3.80648e12			0.246180			0.123090	−	0.992396i	$-0.460720\pi$
$853$	3.80648e12			0.246180			0.123090	+	0.992396i	$0.460720\pi$
$854$	8.82527e12	−	1.52858e13i	0.567764	−	0.983396i
$855$	−1.21231e13	−	2.09978e13i	−0.775830	−	1.34378i
$856$	−5.87528e11	−	1.01763e12i	−0.0374021	−	0.0647824i
$857$	−7.81590e12			−0.494955			−0.247477	−	0.968894i	$-0.579602\pi$
$857$	−7.81590e12			−0.494955			−0.247477	+	0.968894i	$0.579602\pi$
$858$	−1.40089e12	−	6.53449e12i	−0.0882492	−	0.411642i
$859$	2.03800e13			1.27713			0.638564	−	0.769569i	$-0.279529\pi$
$859$	2.03800e13			1.27713			0.638564	+	0.769569i	$0.279529\pi$
$860$	8.55114e11	+	1.48110e12i	0.0533066	+	0.0923298i
$861$	5.96923e12	+	1.03390e13i	0.370172	+	0.641157i
$862$	−1.33571e13	+	2.31352e13i	−0.824006	+	1.42722i
$863$	−7.82400e12			−0.480153			−0.240077	−	0.970754i	$-0.577173\pi$
$863$	−7.82400e12			−0.480153			−0.240077	+	0.970754i	$0.577173\pi$
$864$	1.86725e12	−	3.23418e12i	0.113997	−	0.197448i
$865$	9.53022e12	−	1.65068e13i	0.578803	−	1.00252i
$866$	2.48025e13			1.49853
$867$	−3.44188e12	+	5.96151e12i	−0.206876	+	0.358319i
$868$	−4.76359e12	−	8.25077e12i	−0.284836	−	0.493351i
$869$	2.08508e12	+	3.61147e12i	0.124032	+	0.214830i
$870$	6.18491e13			3.66013
$871$	−1.81603e13	+	1.64091e13i	−1.06915	+	0.966059i
$872$	−1.05317e13			−0.616840
$873$	8.07420e11	+	1.39849e12i	0.0470474	+	0.0814885i
$874$	4.90033e12	+	8.48762e12i	0.284069	+	0.492022i
$875$	−3.22267e12	+	5.58183e12i	−0.185857	+	0.321914i
$876$	−1.97107e13			−1.13092
$877$	−8.26117e12	+	1.43088e13i	−0.471567	+	0.816778i	−0.999471	−	0.0325263i	$-0.989645\pi$
$877$	−8.26117e12	+	1.43088e13i	−0.471567	+	0.816778i	0.527904	+	0.849304i	$0.322978\pi$
$878$	2.94432e12	−	5.09971e12i	0.167209	−	0.289615i
$879$	−2.42732e13			−1.37144
$880$	−3.32756e12	+	5.76350e12i	−0.187048	+	0.323977i
$881$	8.39658e12	+	1.45433e13i	0.469581	+	0.813339i	0.999395	−	0.0347754i	$-0.0110716\pi$
$881$	8.39658e12	+	1.45433e13i	0.469581	+	0.813339i	−0.529814	+	0.848114i	$0.677738\pi$
$882$	−5.06305e12	−	8.76946e12i	−0.281711	−	0.487938i
$883$	2.45649e13			1.35985			0.679927	−	0.733279i	$-0.262011\pi$
$883$	2.45649e13			1.35985			0.679927	+	0.733279i	$0.262011\pi$
$884$	9.76510e12	−	8.82348e12i	0.537826	−	0.485965i
$885$	2.25627e13			1.23636
$886$	−1.04095e13	−	1.80298e13i	−0.567518	−	0.982970i
$887$	1.67423e13	+	2.89986e13i	0.908155	+	1.57297i	0.816625	+	0.577168i	$0.195842\pi$
$887$	1.67423e13	+	2.89986e13i	0.908155	+	1.57297i	0.0915294	+	0.995802i	$0.470824\pi$
$888$	1.16575e13	−	2.01915e13i	0.629142	−	1.08971i
$889$	1.65791e13			0.890230
$890$	−3.45758e12	+	5.98870e12i	−0.184721	+	0.319946i
$891$	−2.57058e12	+	4.45237e12i	−0.136641	+	0.236669i
$892$	−1.74879e13			−0.924900
$893$	−9.07209e11	+	1.57133e12i	−0.0477393	+	0.0826869i
$894$	−1.70980e13	−	2.96146e13i	−0.895214	−	1.55056i
$895$	−1.64425e13	−	2.84793e13i	−0.856575	−	1.48363i
$896$	1.16616e13			0.604465
$897$	7.64548e12	+	2.46940e12i	0.394311	+	0.127358i
$898$	1.51343e13			0.776639
$899$	−2.12842e13	−	3.68653e13i	−1.08677	−	1.88235i
$900$	−3.03464e12	−	5.25615e12i	−0.154176	−	0.267040i
$901$	−8.04458e11	+	1.39336e12i	−0.0406670	+	0.0704373i
$902$	4.83428e12			0.243166
$903$	−1.26155e12	+	2.18506e12i	−0.0631405	+	0.109363i
$904$	−6.48495e12	+	1.12323e13i	−0.322960	+	0.559383i
$905$	3.74274e13			1.85469
$906$	−1.08982e12	+	1.88763e12i	−0.0537377	+	0.0930765i
$907$	−1.35031e13	−	2.33880e13i	−0.662521	−	1.14752i	−0.979951	−	0.199238i	$-0.936153\pi$
$907$	−1.35031e13	−	2.33880e13i	−0.662521	−	1.14752i	0.317430	−	0.948282i	$-0.397180\pi$
$908$	−5.07545e11	−	8.79094e11i	−0.0247793	−	0.0429190i
$909$	−6.96596e12			−0.338410
$910$	−4.82040e12	−	2.24849e13i	−0.233022	−	1.08694i
$911$	−1.25461e13			−0.603496			−0.301748	−	0.953388i	$-0.597570\pi$
$911$	−1.25461e13			−0.603496			−0.301748	+	0.953388i	$0.597570\pi$
$912$	2.55101e13	+	4.41847e13i	1.22105	+	2.11493i
$913$	1.38429e12	+	2.39767e12i	0.0659341	+	0.114201i
$914$	5.62512e12	−	9.74299e12i	0.266608	−	0.461779i
$915$	−4.63063e13			−2.18396
$916$	−2.19930e12	+	3.80930e12i	−0.103218	+	0.178779i
$917$	−5.78685e12	+	1.00231e13i	−0.270259	+	0.468102i
$918$	−6.46562e12			−0.300482
$919$	1.39126e11	−	2.40973e11i	0.00643409	−	0.0111442i	−0.862790	−	0.505562i	$-0.831285\pi$
$919$	1.39126e11	−	2.40973e11i	0.00643409	−	0.0111442i	0.869225	+	0.494418i	$0.164619\pi$
$920$	−1.93929e12	−	3.35895e12i	−0.0892480	−	0.154582i
$921$	6.82338e12	+	1.18184e13i	0.312487	+	0.541243i
$922$	−1.64338e13			−0.748943
$923$	2.09194e13	+	6.75674e12i	0.948728	+	0.306429i
$924$	3.21070e12			0.144902
$925$	1.26280e13	+	2.18724e13i	0.567150	+	0.982332i
$926$	−1.54959e13	−	2.68397e13i	−0.692575	−	1.19958i
$927$	−1.31674e12	+	2.28067e12i	−0.0585655	+	0.101439i
$928$	−4.20279e13			−1.86025
$929$	4.01224e12	−	6.94941e12i	0.176732	−	0.306110i	−0.764027	−	0.645184i	$-0.776781\pi$
$929$	4.01224e12	−	6.94941e12i	0.176732	−	0.306110i	0.940759	+	0.339075i	$0.110114\pi$
$930$	−3.21876e13	+	5.57506e13i	−1.41096	+	2.44386i
$931$	−1.73555e13			−0.757118
$932$	3.73781e11	−	6.47407e11i	0.0162273	−	0.0281064i
$933$	2.89915e13	+	5.02148e13i	1.25258	+	2.16952i
$934$	8.50120e12	+	1.47245e13i	0.365527	+	0.633111i
$935$	8.10523e12			0.346827
$936$	8.85727e12	+	2.86080e12i	0.377188	+	0.121828i
$937$	−3.78935e13			−1.60597			−0.802984	−	0.596000i	$-0.796756\pi$
$937$	−3.78935e13			−1.60597			−0.802984	+	0.596000i	$0.796756\pi$
$938$	−1.51428e13	−	2.62281e13i	−0.638695	−	1.10625i
$939$	1.62504e13	+	2.81465e13i	0.682131	+	1.18149i
$940$	−6.23776e11	+	1.08041e12i	−0.0260587	+	0.0451351i
$941$	−3.79617e13			−1.57831			−0.789154	−	0.614195i	$-0.789481\pi$
$941$	−3.79617e13			−1.57831			−0.789154	+	0.614195i	$0.789481\pi$
$942$	1.01615e13	−	1.76002e13i	0.420463	−	0.728264i
$943$	−2.90592e12	+	5.03321e12i	−0.119669	+	0.207273i
$944$	−2.17953e13			−0.893281
$945$	−2.19315e12	+	3.79865e12i	−0.0894593	+	0.154948i
$946$	5.10842e11	+	8.84804e11i	0.0207385	+	0.0359201i
$947$	−1.06385e12	−	1.84263e12i	−0.0429837	−	0.0744499i	0.843733	−	0.536763i	$-0.180353\pi$
$947$	−1.06385e12	−	1.84263e12i	−0.0429837	−	0.0744499i	−0.886717	+	0.462313i	$0.847020\pi$
$948$	2.19816e13			0.883940
$949$	6.86397e12	+	3.20173e13i	0.274712	+	1.28140i
$950$	−2.67920e13			−1.06721
$951$	−1.66488e13	−	2.88365e13i	−0.660039	−	1.14322i
$952$	−4.68660e12	−	8.11743e12i	−0.184923	−	0.320297i
$953$	1.18484e13	−	2.05220e13i	0.465309	−	0.805939i	−0.533906	−	0.845544i	$-0.679276\pi$
$953$	1.18484e13	−	2.05220e13i	0.465309	−	0.805939i	0.999215	+	0.0396045i	$0.0126098\pi$
$954$	1.97695e12			0.0772731
$955$	1.37772e13	−	2.38628e13i	0.535976	−	0.928338i
$956$	1.58405e13	−	2.74366e13i	0.613351	−	1.06235i
$957$	1.43457e13			0.552865
$958$	2.69033e13	−	4.65979e13i	1.03196	−	1.78740i
$959$	−9.66642e11	−	1.67427e12i	−0.0369047	−	0.0639208i
$960$	4.14320e12	+	7.17624e12i	0.157440	+	0.272695i
$961$	1.78674e13			0.675782
$962$	6.40371e13	+	2.06833e13i	2.41070	+	0.778630i
$963$	3.62740e12			0.135918
$964$	−3.11153e12	−	5.38933e12i	−0.116045	−	0.200996i
$965$	−1.63987e13	−	2.84034e13i	−0.608748	−	1.05438i
$966$	−4.97079e12	+	8.60966e12i	−0.183666	+	0.318118i
$967$	1.20447e12			0.0442974			0.0221487	−	0.999755i	$-0.492949\pi$
$967$	1.20447e12			0.0442974			0.0221487	+	0.999755i	$0.492949\pi$
$968$	6.00535e12	−	1.04016e13i	0.219836	−	0.380767i
$969$	3.10685e13	−	5.38123e13i	1.13205	−	1.96076i
$970$	4.90139e12			0.177765
$971$	−9.83058e12	+	1.70271e13i	−0.354889	+	0.614686i	−0.987099	−	0.160111i	$-0.948815\pi$
$971$	−9.83058e12	+	1.70271e13i	−0.354889	+	0.614686i	0.632210	+	0.774797i	$0.282148\pi$
$972$	1.17326e13	+	2.03215e13i	0.421595	+	0.730225i
$973$	4.76520e12	+	8.25357e12i	0.170441	+	0.295212i
$974$	−1.87074e12			−0.0666037
$975$	−1.62964e13	+	1.47250e13i	−0.577525	+	0.521836i
$976$	4.47312e13			1.57793
$977$	−4.85269e12	−	8.40510e12i	−0.170395	−	0.295133i	0.768163	−	0.640254i	$-0.221171\pi$
$977$	−4.85269e12	−	8.40510e12i	−0.170395	−	0.295133i	−0.938558	+	0.345122i	$0.887838\pi$
$978$	−2.82567e13	−	4.89420e13i	−0.987634	−	1.71063i
$979$	−8.01975e11	+	1.38906e12i	−0.0279022	+	0.0483281i
$980$	−1.19332e13			−0.413277
$981$	1.62556e13	−	2.81556e13i	0.560394	−	0.970630i
$982$	−2.75092e13	+	4.76474e13i	−0.944011	+	1.63507i
$983$	3.17118e13			1.08325			0.541626	−	0.840619i	$-0.317809\pi$
$983$	3.17118e13			1.08325			0.541626	+	0.840619i	$0.317809\pi$
$984$	−7.33340e12	+	1.27018e13i	−0.249361	+	0.431905i
$985$	4.59070e12	+	7.95132e12i	0.155387	+	0.269139i
$986$	3.63818e13	+	6.30151e13i	1.22585	+	2.12324i
$987$	−1.84051e12			−0.0617320
$988$	−2.05653e13	+	1.85822e13i	−0.686639	+	0.620428i
$989$	−1.22829e12			−0.0408241
$990$	−4.97964e12	−	8.62499e12i	−0.164755	−	0.285365i
$991$	−1.91798e12	−	3.32204e12i	−0.0631704	−	0.109414i	0.832711	−	0.553709i	$-0.186788\pi$
$991$	−1.91798e12	−	3.32204e12i	−0.0631704	−	0.109414i	−0.895881	+	0.444294i	$0.853454\pi$
$992$	2.18722e13	−	3.78838e13i	0.717117	−	1.24208i
$993$	−1.52586e13			−0.498014
$994$	−1.36010e13	+	2.35576e13i	−0.441907	+	0.765406i
$995$	1.38383e13	−	2.39687e13i	0.447589	−	0.775247i
$996$	1.45937e13			0.469892
$997$	9.69323e12	−	1.67892e13i	0.310699	−	0.538147i	−0.667815	−	0.744328i	$-0.732770\pi$
$997$	9.69323e12	−	1.67892e13i	0.310699	−	0.538147i	0.978514	+	0.206180i	$0.0661034\pi$
$998$	−2.31486e12	−	4.00945e12i	−0.0738648	−	0.127938i
$999$	−6.41798e12	−	1.11163e13i	−0.203870	−	0.353114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.10.c.a.3.7	✓	18
13.3	even	3		169.10.a.c.1.3		9
13.9	even	3	inner	13.10.c.a.9.7	yes	18
13.10	even	6		169.10.a.d.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.c.a.3.7	✓	18	1.1	even	1	trivial
13.10.c.a.9.7	yes	18	13.9	even	3	inner
169.10.a.c.1.3		9	13.3	even	3
169.10.a.d.1.7		9	13.10	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+(14.4651 + 25.0544i) q^{2} +(-95.3768 - 165.198i) q^{3} +(-162.481 + 281.425i) q^{4} +1752.49 q^{5} +(2759.28 - 4779.21i) q^{6} +(2202.24 - 3814.40i) q^{7} +5411.06 q^{8} +(-8351.99 + 14466.1i) q^{9} +(25350.1 + 43907.6i) q^{10} +(5879.88 + 10184.3i) q^{11} +61987.7 q^{12} +(-21586.3 - 100690. i) q^{13} +127423. q^{14} +(-167147. - 289508. i) q^{15} +(161462. + 279661. i) q^{16} +(196644. - 340597. i) q^{17} -483251. q^{18} +(-414131. + 717296. i) q^{19} +(-284747. + 493196. i) q^{20} -840172. q^{21} +(-170107. + 294634. i) q^{22} +(-204505. - 354213. i) q^{23} +(-516090. - 893895. i) q^{24} +1.11811e6 q^{25} +(2.21048e6 - 1.99733e6i) q^{26} -568260. q^{27} +(715645. + 1.23953e6i) q^{28} +(3.19758e6 + 5.53837e6i) q^{29} +(4.83562e6 - 8.37554e6i) q^{30} -6.65635e6 q^{31} +(-3.28591e6 + 5.69137e6i) q^{32} +(1.12161e6 - 1.94268e6i) q^{33} +1.13779e7 q^{34} +(3.85942e6 - 6.68470e6i) q^{35} +(-2.71408e6 - 4.70092e6i) q^{36} +(1.12941e7 + 1.95619e7i) q^{37} -2.39619e7 q^{38} +(-1.45749e7 + 1.31695e7i) q^{39} +9.48286e6 q^{40} +(-7.10477e6 - 1.23058e7i) q^{41} +(-1.21532e7 - 2.10500e7i) q^{42} +(1.50153e6 - 2.60073e6i) q^{43} -3.82148e6 q^{44} +(-1.46368e7 + 2.53517e7i) q^{45} +(5.91640e6 - 1.02475e7i) q^{46} +2.19063e6 q^{47} +(3.07995e7 - 5.33463e7i) q^{48} +(1.04771e7 + 1.81468e7i) q^{49} +(1.61736e7 + 2.80135e7i) q^{50} -7.50210e7 q^{51} +(3.18442e7 + 1.02853e7i) q^{52} -4.09094e6 q^{53} +(-8.21997e6 - 1.42374e7i) q^{54} +(1.03045e7 + 1.78478e7i) q^{55} +(1.19165e7 - 2.06399e7i) q^{56} +1.57994e8 q^{57} +(-9.25069e7 + 1.60227e8i) q^{58} +(-3.37467e7 + 5.84510e7i) q^{59} +1.08633e8 q^{60} +(6.92596e7 - 1.19961e8i) q^{61} +(-9.62851e7 - 1.66771e8i) q^{62} +(3.67862e7 + 6.37156e7i) q^{63} -2.47877e7 q^{64} +(-3.78299e7 - 1.76459e8i) q^{65} +6.48970e7 q^{66} +(-1.18839e8 - 2.05835e8i) q^{67} +(6.39017e7 + 1.10681e8i) q^{68} +(-3.90101e7 + 6.75675e7i) q^{69} +2.23308e8 q^{70} +(-1.06739e8 + 1.84877e8i) q^{71} +(-4.51931e7 + 7.82768e7i) q^{72} -3.17978e8 q^{73} +(-3.26741e8 + 5.65933e8i) q^{74} +(-1.06642e8 - 1.84709e8i) q^{75} +(-1.34577e8 - 2.33094e8i) q^{76} +5.17957e7 q^{77} +(-5.40783e8 - 1.74667e8i) q^{78} +3.54613e8 q^{79} +(2.82961e8 + 4.90103e8i) q^{80} +(2.18591e8 + 3.78611e8i) q^{81} +(2.05543e8 - 3.56011e8i) q^{82} +2.35429e8 q^{83} +(1.36512e8 - 2.36446e8i) q^{84} +(3.44617e8 - 5.96894e8i) q^{85} +8.68796e7 q^{86} +(6.09950e8 - 1.05646e9i) q^{87} +(3.18164e7 + 5.51077e7i) q^{88} +(6.81965e7 + 1.18120e8i) q^{89} -8.46894e8 q^{90} +(-4.31611e8 - 1.39406e8i) q^{91} +1.32913e8 q^{92} +(6.34862e8 + 1.09961e9i) q^{93} +(3.16878e7 + 5.48849e7i) q^{94} +(-7.25762e8 + 1.25706e9i) q^{95} +1.25360e9 q^{96} +(4.83370e7 - 8.37222e7i) q^{97} +(-3.03105e8 + 5.24992e8i) q^{98} -1.96435e8 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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