LMFDB - Embedded newform 13.10.c.a.3.1

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			3.1
Root			$20.5607 - 35.6122i$ of defining polynomial
Character	$\chi$	$=$	13.3
Dual form			13.10.c.a.9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-19.5607 - 33.8802i) q^{2} +(-36.0748 - 62.4834i) q^{3} +(-509.244 + 882.037i) q^{4} -1007.31 q^{5} +(-1411.30 + 2444.44i) q^{6} +(190.054 - 329.184i) q^{7} +19814.6 q^{8} +(7238.71 - 12537.8i) q^{9} +(19703.7 + 34127.8i) q^{10} +(31169.2 + 53986.6i) q^{11} +73483.6 q^{12} +(-84829.8 - 58381.6i) q^{13} -14870.4 q^{14} +(36338.5 + 62940.2i) q^{15} +(-126855. - 219718. i) q^{16} +(-208585. + 361280. i) q^{17} -566378. q^{18} +(-118612. + 205442. i) q^{19} +(512967. - 888485. i) q^{20} -27424.7 q^{21} +(1.21938e6 - 2.11203e6i) q^{22} +(586199. + 1.01533e6i) q^{23} +(-714807. - 1.23808e6i) q^{24} -938451. q^{25} +(-318645. + 4.01603e6i) q^{26} -2.46466e6 q^{27} +(193568. + 335270. i) q^{28} +(2.97533e6 + 5.15343e6i) q^{29} +(1.42162e6 - 2.46231e6i) q^{30} -5.96360e6 q^{31} +(109798. - 190176. i) q^{32} +(2.24884e6 - 3.89511e6i) q^{33} +1.63203e7 q^{34} +(-191444. + 331590. i) q^{35} +(7.37255e6 + 1.27696e7i) q^{36} +(-8.42902e6 - 1.45995e7i) q^{37} +9.28057e6 q^{38} +(-587661. + 7.40656e6i) q^{39} -1.99594e7 q^{40} +(-6.53603e6 - 1.13207e7i) q^{41} +(536448. + 929155. i) q^{42} +(9.45149e6 - 1.63705e7i) q^{43} -6.34909e7 q^{44} +(-7.29163e6 + 1.26295e7i) q^{45} +(2.29330e7 - 3.97211e7i) q^{46} -4.10521e7 q^{47} +(-9.15251e6 + 1.58526e7i) q^{48} +(2.01046e7 + 3.48221e7i) q^{49} +(1.83568e7 + 3.17949e7i) q^{50} +3.00987e7 q^{51} +(9.46938e7 - 4.50925e7i) q^{52} -9.90131e6 q^{53} +(4.82106e7 + 8.35032e7i) q^{54} +(-3.13970e7 - 5.43812e7i) q^{55} +(3.76585e6 - 6.52264e6i) q^{56} +1.71157e7 q^{57} +(1.16399e8 - 2.01610e8i) q^{58} +(-4.79303e7 + 8.30178e7i) q^{59} -7.40208e7 q^{60} +(-1.00980e8 + 1.74903e8i) q^{61} +(1.16652e8 + 2.02048e8i) q^{62} +(-2.75150e6 - 4.76574e6i) q^{63} -1.38490e8 q^{64} +(8.54499e7 + 5.88083e7i) q^{65} -1.75956e8 q^{66} +(2.73151e6 + 4.73111e6i) q^{67} +(-2.12442e8 - 3.67960e8i) q^{68} +(4.22941e7 - 7.32554e7i) q^{69} +1.49791e7 q^{70} +(1.64680e8 - 2.85234e8i) q^{71} +(1.43432e8 - 2.48432e8i) q^{72} +1.75959e8 q^{73} +(-3.29755e8 + 5.71153e8i) q^{74} +(3.38545e7 + 5.86377e7i) q^{75} +(-1.20805e8 - 2.09241e8i) q^{76} +2.36954e7 q^{77} +(2.62431e8 - 1.24968e8i) q^{78} -2.17413e7 q^{79} +(1.27782e8 + 2.21325e8i) q^{80} +(-5.35673e7 - 9.27813e7i) q^{81} +(-2.55699e8 + 4.42884e8i) q^{82} -1.59466e7 q^{83} +(1.39659e7 - 2.41896e7i) q^{84} +(2.10110e8 - 3.63921e8i) q^{85} -7.39512e8 q^{86} +(2.14669e8 - 3.71818e8i) q^{87} +(6.17604e8 + 1.06972e9i) q^{88} +(-2.38369e8 - 4.12867e8i) q^{89} +5.70518e8 q^{90} +(-3.53406e7 + 1.68289e7i) q^{91} -1.19407e9 q^{92} +(2.15136e8 + 3.72626e8i) q^{93} +(8.03010e8 + 1.39085e9i) q^{94} +(1.19479e8 - 2.06944e8i) q^{95} -1.58438e7 q^{96} +(-3.12816e8 + 5.41812e8i) q^{97} +(7.86520e8 - 1.36229e9i) q^{98} +9.02499e8 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 $

$2$	−19.5607	−	33.8802i	−0.864470	−	1.49731i	−0.867572	−	0.497311i	$-0.834321\pi$
$2$	−19.5607	−	33.8802i	−0.864470	−	1.49731i	0.00310184	−	0.999995i	$-0.499013\pi$
$3$	−36.0748	−	62.4834i	−0.257133	−	0.445368i	0.708339	−	0.705872i	$-0.249445\pi$
$3$	−36.0748	−	62.4834i	−0.257133	−	0.445368i	−0.965473	+	0.260504i	$0.916111\pi$
$4$	−509.244	+	882.037i	−0.994618	+	1.72273i
$5$	−1007.31			−0.720772			−0.360386	−	0.932803i	$-0.617355\pi$
$5$	−1007.31			−0.720772			−0.360386	+	0.932803i	$0.617355\pi$
$6$	−1411.30	+	2444.44i	−0.444568	+	0.770015i
$7$	190.054	−	329.184i	0.0299183	−	0.0518200i	−0.850679	−	0.525686i	$-0.823809\pi$
$7$	190.054	−	329.184i	0.0299183	−	0.0518200i	0.880597	+	0.473866i	$0.157142\pi$
$8$	19814.6			1.71033
$9$	7238.71	−	12537.8i	0.367765	−	0.636987i
$10$	19703.7	+	34127.8i	0.623086	+	1.07922i
$11$	31169.2	+	53986.6i	0.641886	+	1.11178i	0.985011	+	0.172490i	$0.0551812\pi$
$11$	31169.2	+	53986.6i	0.641886	+	1.11178i	−0.343125	+	0.939290i	$0.611485\pi$
$12$	73483.6			1.02300
$13$	−84829.8	−	58381.6i	−0.823765	−	0.566932i
$13$	−84829.8	−	58381.6i	−0.823765	−	0.566932i
$14$	−14870.4			−0.103454
$15$	36338.5	+	62940.2i	0.185335	+	0.321009i
$16$	−126855.	−	219718.i	−0.483912	−	0.838159i
$17$	−208585.	+	361280.i	−0.605708	+	1.04912i	0.386231	+	0.922402i	$0.373777\pi$
$17$	−208585.	+	361280.i	−0.605708	+	1.04912i	−0.991939	+	0.126715i	$0.959557\pi$
$18$	−566378.			−1.27169
$19$	−118612.	+	205442.i	−0.208804	+	0.361659i	−0.951338	−	0.308149i	$-0.900290\pi$
$19$	−118612.	+	205442.i	−0.208804	+	0.361659i	0.742534	+	0.669808i	$0.233624\pi$
$20$	512967.	−	888485.i	0.716893	−	1.24170i
$21$	−27424.7			−0.0307720
$22$	1.21938e6	−	2.11203e6i	1.10978	−	1.92220i
$23$	586199.	+	1.01533e6i	0.436787	+	0.756537i	0.997440	−	0.0715137i	$-0.0227830\pi$
$23$	586199.	+	1.01533e6i	0.436787	+	0.756537i	−0.560653	+	0.828051i	$0.689450\pi$
$24$	−714807.	−	1.23808e6i	−0.439783	−	0.761727i
$25$	−938451.			−0.480487
$26$	−318645.	+	4.01603e6i	−0.136750	+	1.72352i
$27$	−2.46466e6			−0.892525
$28$	193568.	+	335270.i	0.0595146	+	0.103082i
$29$	2.97533e6	+	5.15343e6i	0.781168	+	1.35302i	0.931262	+	0.364351i	$0.118709\pi$
$29$	2.97533e6	+	5.15343e6i	0.781168	+	1.35302i	−0.150093	+	0.988672i	$0.547957\pi$
$30$	1.42162e6	−	2.46231e6i	0.320433	−	0.555006i
$31$	−5.96360e6			−1.15979			−0.579897	−	0.814689i	$-0.696907\pi$
$31$	−5.96360e6			−1.15979			−0.579897	+	0.814689i	$0.696907\pi$
$32$	109798.	−	190176.i	0.0185106	−	0.0320613i
$33$	2.24884e6	−	3.89511e6i	0.330101	−	0.571751i
$34$	1.63203e7			2.09447
$35$	−191444.	+	331590.i	−0.0215643	+	0.0373504i
$36$	7.37255e6	+	1.27696e7i	0.731571	+	1.26712i
$37$	−8.42902e6	−	1.45995e7i	−0.739383	−	1.28065i	−0.952774	−	0.303681i	$-0.901784\pi$
$37$	−8.42902e6	−	1.45995e7i	−0.739383	−	1.28065i	0.213391	−	0.976967i	$-0.431549\pi$
$38$	9.28057e6			0.722019
$39$	−587661.	+	7.40656e6i	−0.0406758	+	0.512656i
$40$	−1.99594e7			−1.23276
$41$	−6.53603e6	−	1.13207e7i	−0.361232	−	0.625673i	0.626932	−	0.779074i	$-0.284311\pi$
$41$	−6.53603e6	−	1.13207e7i	−0.361232	−	0.625673i	−0.988164	+	0.153402i	$0.950977\pi$
$42$	536448.	+	929155.i	0.0266015	+	0.0460751i
$43$	9.45149e6	−	1.63705e7i	0.421592	−	0.730219i	−0.574503	−	0.818502i	$-0.694805\pi$
$43$	9.45149e6	−	1.63705e7i	0.421592	−	0.730219i	0.996095	+	0.0882834i	$0.0281381\pi$
$44$	−6.34909e7			−2.55373
$45$	−7.29163e6	+	1.26295e7i	−0.265075	+	0.459123i
$46$	2.29330e7	−	3.97211e7i	0.755179	−	1.30801i
$47$	−4.10521e7			−1.22714			−0.613572	−	0.789639i	$-0.710268\pi$
$47$	−4.10521e7			−1.22714			−0.613572	+	0.789639i	$0.710268\pi$
$48$	−9.15251e6	+	1.58526e7i	−0.248860	+	0.431038i
$49$	2.01046e7	+	3.48221e7i	0.498210	+	0.862925i
$50$	1.83568e7	+	3.17949e7i	0.415367	+	0.719436i
$51$	3.00987e7			0.622991
$52$	9.46938e7	−	4.50925e7i	1.79600	−	0.855243i
$53$	−9.90131e6			−0.172366			−0.0861829	−	0.996279i	$-0.527467\pi$
$53$	−9.90131e6			−0.172366			−0.0861829	+	0.996279i	$0.527467\pi$
$54$	4.82106e7	+	8.35032e7i	0.771562	+	1.33638i
$55$	−3.13970e7	−	5.43812e7i	−0.462654	−	0.801340i
$56$	3.76585e6	−	6.52264e6i	0.0511702	−	0.0886293i
$57$	1.71157e7			0.214762
$58$	1.16399e8	−	2.01610e8i	1.35059	−	2.33930i
$59$	−4.79303e7	+	8.30178e7i	−0.514963	+	0.891943i	0.484886	+	0.874577i	$0.338861\pi$
$59$	−4.79303e7	+	8.30178e7i	−0.514963	+	0.891943i	−0.999849	+	0.0173653i	$0.994472\pi$
$60$	−7.40208e7			−0.737349
$61$	−1.00980e8	+	1.74903e8i	−0.933797	+	1.61738i	−0.157032	+	0.987594i	$0.550193\pi$
$61$	−1.00980e8	+	1.74903e8i	−0.933797	+	1.61738i	−0.776765	+	0.629790i	$0.783141\pi$
$62$	1.16652e8	+	2.02048e8i	1.00261	+	1.73657i
$63$	−2.75150e6	−	4.76574e6i	−0.0220058	−	0.0381152i
$64$	−1.38490e8			−1.03183
$65$	8.54499e7	+	5.88083e7i	0.593747	+	0.408629i
$66$	−1.75956e8			−1.14145
$67$	2.73151e6	+	4.73111e6i	0.0165602	+	0.0286831i	0.874187	−	0.485590i	$-0.161395\pi$
$67$	2.73151e6	+	4.73111e6i	0.0165602	+	0.0286831i	−0.857627	+	0.514273i	$0.828062\pi$
$68$	−2.12442e8	−	3.67960e8i	−1.20490	−	2.08694i
$69$	4.22941e7	−	7.32554e7i	0.224625	−	0.389062i
$70$	1.49791e7			0.0745668
$71$	1.64680e8	−	2.85234e8i	0.769091	−	1.33211i	−0.168965	−	0.985622i	$-0.554042\pi$
$71$	1.64680e8	−	2.85234e8i	0.769091	−	1.33211i	0.938056	−	0.346483i	$-0.112624\pi$
$72$	1.43432e8	−	2.48432e8i	0.628999	−	1.08946i
$73$	1.75959e8			0.725201			0.362601	−	0.931945i	$-0.381889\pi$
$73$	1.75959e8			0.725201			0.362601	+	0.931945i	$0.381889\pi$
$74$	−3.29755e8	+	5.71153e8i	−1.27835	+	2.21416i
$75$	3.38545e7	+	5.86377e7i	0.123549	+	0.213994i
$76$	−1.20805e8	−	2.09241e8i	−0.415360	−	0.719425i
$77$	2.36954e7			0.0768166
$78$	2.62431e8	−	1.24968e8i	0.802766	−	0.382272i
$79$	−2.17413e7			−0.0628006			−0.0314003	−	0.999507i	$-0.509997\pi$
$79$	−2.17413e7			−0.0628006			−0.0314003	+	0.999507i	$0.509997\pi$
$80$	1.27782e8	+	2.21325e8i	0.348790	+	0.604122i
$81$	−5.35673e7	−	9.27813e7i	−0.138267	−	0.239485i
$82$	−2.55699e8	+	4.42884e8i	−0.624549	+	1.08175i
$83$	−1.59466e7			−0.0368823			−0.0184411	−	0.999830i	$-0.505870\pi$
$83$	−1.59466e7			−0.0368823			−0.0184411	+	0.999830i	$0.505870\pi$
$84$	1.39659e7	−	2.41896e7i	0.0306064	−	0.0530118i
$85$	2.10110e8	−	3.63921e8i	0.436578	−	0.756174i
$86$	−7.39512e8			−1.45782
$87$	2.14669e8	−	3.71818e8i	0.401729	−	0.695815i
$88$	6.17604e8	+	1.06972e9i	1.09784	+	1.90151i
$89$	−2.38369e8	−	4.12867e8i	−0.402712	−	0.697518i	0.591340	−	0.806422i	$-0.298599\pi$
$89$	−2.38369e8	−	4.12867e8i	−0.402712	−	0.697518i	−0.994052	+	0.108904i	$0.965266\pi$
$90$	5.70518e8			0.916597
$91$	−3.53406e7	+	1.68289e7i	−0.0540241	+	0.0257259i
$92$	−1.19407e9			−1.73774
$93$	2.15136e8	+	3.72626e8i	0.298222	+	0.516536i
$94$	8.03010e8	+	1.39085e9i	1.06083	+	1.83741i
$95$	1.19479e8	−	2.06944e8i	0.150500	−	0.260674i
$96$	−1.58438e7			−0.0190388
$97$	−3.12816e8	+	5.41812e8i	−0.358770	+	0.621407i	−0.987756	−	0.156010i	$-0.950137\pi$
$97$	−3.12816e8	+	5.41812e8i	−0.358770	+	0.621407i	0.628986	+	0.777417i	$0.283470\pi$
$98$	7.86520e8	−	1.36229e9i	0.861375	−	1.49195i
$99$	9.02499e8			0.944252
$100$	4.77901e8	−	8.27749e8i	0.477901	−	0.827749i
$101$	1.65242e8	+	2.86208e8i	0.158006	+	0.273675i	0.934150	−	0.356882i	$-0.116160\pi$
$101$	1.65242e8	+	2.86208e8i	0.158006	+	0.273675i	−0.776143	+	0.630557i	$0.782827\pi$
$102$	−5.88752e8	−	1.01975e9i	−0.538557	−	0.932809i
$103$	−3.53086e8			−0.309110			−0.154555	−	0.987984i	$-0.549394\pi$
$103$	−3.53086e8			−0.309110			−0.154555	+	0.987984i	$0.549394\pi$
$104$	−1.68087e9	−	1.15681e9i	−1.40891	−	0.969640i
$105$	2.76252e7			0.0221796
$106$	1.93677e8	+	3.35458e8i	0.149005	+	0.258084i
$107$	2.01274e8	+	3.48617e8i	0.148444	+	0.257112i	0.930652	−	0.365905i	$-0.119240\pi$
$107$	2.01274e8	+	3.48617e8i	0.148444	+	0.257112i	−0.782209	+	0.623016i	$0.785907\pi$
$108$	1.25512e9	−	2.17392e9i	0.887722	−	1.53758i
$109$	−1.03344e9			−0.701240			−0.350620	−	0.936518i	$-0.614029\pi$
$109$	−1.03344e9			−0.701240			−0.350620	+	0.936518i	$0.614029\pi$
$110$	−1.22830e9	+	2.12747e9i	−0.799901	+	1.38547i
$111$	−6.08151e8	+	1.05335e9i	−0.380240	+	0.658595i
$112$	−9.64371e7			−0.0579112
$113$	−5.05104e8	+	8.74866e8i	−0.291426	+	0.504764i	−0.974147	−	0.225915i	$-0.927463\pi$
$113$	−5.05104e8	+	8.74866e8i	−0.291426	+	0.504764i	0.682721	+	0.730679i	$0.260796\pi$
$114$	−3.34795e8	−	5.79882e8i	−0.185655	−	0.321564i
$115$	−5.90484e8	−	1.02275e9i	−0.314824	−	0.545291i
$116$	−6.06069e9			−3.10786
$117$	−1.34604e9	+	6.40973e8i	−0.664080	+	0.316230i
$118$	3.75021e9			1.78068
$119$	7.92851e7	+	1.37326e8i	0.0362435	+	0.0627756i
$120$	7.20033e8	+	1.24713e9i	0.316984	+	0.549032i
$121$	−7.64059e8	+	1.32339e9i	−0.324036	+	0.561246i
$122$	7.90100e9			3.22896
$123$	−4.71572e8	+	8.16787e8i	−0.185770	+	0.321763i
$124$	3.03693e9	−	5.26012e9i	1.15355	−	1.99801i
$125$	2.91271e9			1.06709
$126$	−1.07643e8	+	1.86443e8i	−0.0380467	+	0.0658988i
$127$	−1.37009e9	−	2.37307e9i	−0.467341	−	0.809458i	0.531963	−	0.846768i	$-0.321455\pi$
$127$	−1.37009e9	−	2.37307e9i	−0.467341	−	0.809458i	−0.999304	+	0.0373094i	$0.988121\pi$
$128$	2.65275e9	+	4.59469e9i	0.873476	+	1.51291i
$129$	−1.36384e9			−0.433622
$130$	3.20975e8	−	4.04539e9i	0.0985656	−	1.24227i
$131$	−9.23197e8			−0.273888			−0.136944	−	0.990579i	$-0.543728\pi$
$131$	−9.23197e8			−0.273888			−0.136944	+	0.990579i	$0.543728\pi$
$132$	2.29042e9	+	3.96713e9i	0.656648	+	1.13735i
$133$	4.50856e7	+	7.80905e7i	0.0124941	+	0.0216404i
$134$	1.06861e8	−	1.85088e8i	0.0286316	−	0.0495914i
$135$	2.48268e9			0.643308
$136$	−4.13303e9	+	7.15861e9i	−1.03596	+	1.79434i
$137$	−3.13731e9	+	5.43398e9i	−0.760878	+	1.31788i	0.181521	+	0.983387i	$0.441898\pi$
$137$	−3.13731e9	+	5.43398e9i	−0.760878	+	1.31788i	−0.942399	+	0.334492i	$0.891435\pi$
$138$	−3.30921e9			−0.776727
$139$	2.97106e9	−	5.14602e9i	0.675063	−	1.16924i	−0.301387	−	0.953502i	$-0.597450\pi$
$139$	2.97106e9	−	5.14602e9i	0.675063	−	1.16924i	0.976450	−	0.215742i	$-0.0692171\pi$
$140$	−1.94983e8	−	3.37721e8i	−0.0428965	−	0.0742988i
$141$	1.48095e9	+	2.56508e9i	0.315540	+	0.546531i
$142$	−1.28850e10			−2.65943
$143$	5.07747e8	−	6.39937e9i	0.101540	−	1.27975i
$144$	−3.67305e9			−0.711862
$145$	−2.99708e9	−	5.19110e9i	−0.563045	−	0.975222i
$146$	−3.44189e9	−	5.96152e9i	−0.626915	−	1.08585i
$147$	1.45054e9	−	2.51240e9i	0.256213	−	0.443774i
$148$	1.71697e10			2.94161
$149$	−1.38943e9	+	2.40656e9i	−0.230939	+	0.399998i	−0.958085	−	0.286485i	$-0.907513\pi$
$149$	−1.38943e9	+	2.40656e9i	−0.230939	+	0.399998i	0.727146	+	0.686483i	$0.240846\pi$
$150$	1.32444e9	−	2.29399e9i	0.213609	−	0.369982i
$151$	−9.37019e9			−1.46674			−0.733369	−	0.679831i	$-0.762053\pi$
$151$	−9.37019e9			−1.46674			−0.733369	+	0.679831i	$0.762053\pi$
$152$	−2.35025e9	+	4.07076e9i	−0.357123	+	0.618556i
$153$	3.01978e9	+	5.23041e9i	0.445516	+	0.771656i
$154$	−4.63498e8	−	8.02803e8i	−0.0664057	−	0.115018i
$155$	6.00720e9			0.835948
$156$	−6.23360e9	−	4.29009e9i	−0.842710	−	0.579970i
$157$	7.24646e9			0.951869			0.475935	−	0.879481i	$-0.342110\pi$
$157$	7.24646e9			0.951869			0.475935	+	0.879481i	$0.342110\pi$
$158$	4.25276e8	+	7.36599e8i	0.0542892	+	0.0940317i
$159$	3.57188e8	+	6.18668e8i	0.0443210	+	0.0767663i
$160$	−1.10601e8	+	1.91567e8i	−0.0133420	+	0.0231089i
$161$	4.45639e8			0.0522717
$162$	−2.09563e9	+	3.62974e9i	−0.239055	+	0.414055i
$163$	5.35351e9	−	9.27254e9i	0.594010	−	1.02886i	−0.399675	−	0.916657i	$-0.630877\pi$
$163$	5.35351e9	−	9.27254e9i	0.594010	−	1.02886i	0.993686	−	0.112199i	$-0.0357895\pi$
$164$	1.33137e10			1.43715
$165$	−2.26528e9	+	3.92359e9i	−0.237928	+	0.412103i
$166$	3.11928e8	+	5.40275e8i	0.0318836	+	0.0552241i
$167$	−6.25073e9	−	1.08266e10i	−0.621881	−	1.07713i	−0.989135	−	0.147008i	$-0.953036\pi$
$167$	−6.25073e9	−	1.08266e10i	−0.621881	−	1.07713i	0.367255	−	0.930120i	$-0.380298\pi$
$168$	−5.43409e8			−0.0526302
$169$	3.78769e9	+	9.90499e9i	0.357177	+	0.934037i
$170$	−1.64396e10			−1.50963
$171$	1.71720e9	+	2.97428e9i	0.153581	+	0.266011i
$172$	9.62624e9	+	1.66731e10i	0.838646	+	1.45258i
$173$	−1.10127e9	+	1.90746e9i	−0.0934731	+	0.161900i	−0.908970	−	0.416861i	$-0.863130\pi$
$173$	−1.10127e9	+	1.90746e9i	−0.0934731	+	0.161900i	0.815497	+	0.578761i	$0.196464\pi$
$174$	−1.67964e10			−1.38913
$175$	−1.78357e8	+	3.08923e8i	−0.0143754	+	0.0248988i
$176$	7.90790e9	−	1.36969e10i	0.621232	−	1.07601i
$177$	6.91631e9			0.529657
$178$	−9.32534e9	+	1.61520e10i	−0.696265	+	1.20597i
$179$	8.86004e9	+	1.53460e10i	0.645055	+	1.11727i	0.984289	+	0.176566i	$0.0564990\pi$
$179$	8.86004e9	+	1.53460e10i	0.645055	+	1.11727i	−0.339234	+	0.940702i	$0.610168\pi$
$180$	−7.42644e9	−	1.28630e10i	−0.527296	−	0.913304i
$181$	−1.21707e10			−0.842874			−0.421437	−	0.906858i	$-0.638474\pi$
$181$	−1.21707e10			−0.842874			−0.421437	+	0.906858i	$0.638474\pi$
$182$	1.26145e9	+	8.68158e8i	0.0852217	+	0.0586513i
$183$	1.45714e10			0.960442
$184$	1.16153e10	+	2.01183e10i	0.747050	+	1.29393i
$185$	8.49064e9	+	1.47062e10i	0.532927	+	0.923056i
$186$	8.41643e9	−	1.45777e10i	0.515608	−	0.893060i
$187$	−2.60057e10			−1.55518
$188$	2.09056e10	−	3.62095e10i	1.22054	−	2.11404i
$189$	−4.68420e8	+	8.11328e8i	−0.0267028	+	0.0462507i
$190$	−9.34841e9			−0.520411
$191$	1.67304e10	−	2.89780e10i	0.909614	−	1.57550i	0.0950137	−	0.995476i	$-0.469710\pi$
$191$	1.67304e10	−	2.89780e10i	0.909614	−	1.57550i	0.814601	−	0.580022i	$-0.196956\pi$
$192$	4.99600e9	+	8.65333e9i	0.265318	+	0.459545i
$193$	−9.27040e9	−	1.60568e10i	−0.480939	−	0.833012i	0.518821	−	0.854883i	$-0.326371\pi$
$193$	−9.27040e9	−	1.60568e10i	−0.480939	−	0.833012i	−0.999761	+	0.0218712i	$0.993038\pi$
$194$	2.44756e10			1.24058
$195$	5.91957e8	−	7.46070e9i	0.0293180	−	0.369508i
$196$	−4.09525e10			−1.98211
$197$	6.64676e9	+	1.15125e10i	0.314421	+	0.544594i	0.979314	−	0.202345i	$-0.0648562\pi$
$197$	6.64676e9	+	1.15125e10i	0.314421	+	0.544594i	−0.664893	+	0.746939i	$0.731523\pi$
$198$	−1.76535e10	−	3.05768e10i	−0.816278	−	1.41384i
$199$	−1.20064e10	+	2.07957e10i	−0.542718	+	0.940014i	0.456029	+	0.889965i	$0.349271\pi$
$199$	−1.20064e10	+	2.07957e10i	−0.542718	+	0.940014i	−0.998747	+	0.0500496i	$0.984062\pi$
$200$	−1.85950e10			−0.821791
$201$	1.97077e8	−	3.41348e8i	0.00851637	−	0.0147508i
$202$	6.46451e9	−	1.11969e10i	0.273183	−	0.473168i
$203$	2.26190e9			0.0934849
$204$	−1.53276e10	+	2.65482e10i	−0.619638	+	1.07324i
$205$	6.58381e9	+	1.14035e10i	0.260366	+	0.450968i
$206$	6.90663e9	+	1.19626e10i	0.267217	+	0.462833i
$207$	1.69733e10			0.642540
$208$	−2.06647e9	+	2.60446e10i	−0.0765497	+	0.964791i
$209$	−1.47882e10			−0.536113
$210$	−5.40369e8	−	9.35947e8i	−0.0191736	−	0.0332097i
$211$	−1.67609e10	−	2.90308e10i	−0.582139	−	1.00830i	−0.995225	−	0.0976030i	$-0.968882\pi$
$211$	−1.67609e10	−	2.90308e10i	−0.582139	−	1.00830i	0.413086	−	0.910692i	$-0.364451\pi$
$212$	5.04218e9	−	8.73332e9i	0.171438	−	0.296940i
$213$	−2.37632e10			−0.791037
$214$	7.87415e9	−	1.36384e10i	0.256650	−	0.444531i
$215$	−9.52058e9	+	1.64901e10i	−0.303872	+	0.526322i
$216$	−4.88363e10			−1.52651
$217$	−1.13341e9	+	1.96312e9i	−0.0346991	+	0.0601006i
$218$	2.02149e10	+	3.50132e10i	0.606201	+	1.04997i
$219$	−6.34769e9	−	1.09945e10i	−0.186474	−	0.322982i
$220$	6.39550e10			1.84066
$221$	3.87863e10	−	1.84698e10i	1.09374	−	0.520831i
$222$	4.75835e10			1.31482
$223$	−1.41346e10	−	2.44818e10i	−0.382747	−	0.662937i	0.608707	−	0.793395i	$-0.291689\pi$
$223$	−1.41346e10	−	2.44818e10i	−0.382747	−	0.662937i	−0.991454	+	0.130458i	$0.958355\pi$
$224$	−4.17354e7	−	7.22878e7i	−0.00110761	−	0.00191844i
$225$	−6.79318e9	+	1.17661e10i	−0.176706	+	0.306064i
$226$	3.95208e10			1.00772
$227$	1.77304e10	−	3.07099e10i	0.443202	−	0.767649i	−0.554723	−	0.832035i	$-0.687176\pi$
$227$	1.77304e10	−	3.07099e10i	0.443202	−	0.767649i	0.997925	+	0.0643866i	$0.0205091\pi$
$228$	−8.71606e9	+	1.50967e10i	−0.213606	+	0.369976i
$229$	1.62143e10			0.389618			0.194809	−	0.980841i	$-0.437591\pi$
$229$	1.62143e10			0.389618			0.194809	+	0.980841i	$0.437591\pi$
$230$	−2.31006e10	+	4.00114e10i	−0.544312	+	0.942776i
$231$	−8.54806e8	−	1.48057e9i	−0.0197521	−	0.0342117i
$232$	5.89550e10	+	1.02113e11i	1.33606	+	2.31412i
$233$	−7.69258e10			−1.70990			−0.854949	−	0.518712i	$-0.826412\pi$
$233$	−7.69258e10			−1.70990			−0.854949	+	0.518712i	$0.826412\pi$
$234$	4.80457e10	+	3.30660e10i	1.04757	+	0.720959i
$235$	4.13522e10			0.884492
$236$	−4.88165e10	−	8.45527e10i	−1.02438	−	1.77428i
$237$	7.84314e8	+	1.35847e9i	0.0161481	+	0.0279694i
$238$	3.10175e9	−	5.37239e9i	0.0626629	−	0.108535i
$239$	1.87454e10			0.371624			0.185812	−	0.982585i	$-0.440508\pi$
$239$	1.87454e10			0.371624			0.185812	+	0.982585i	$0.440508\pi$
$240$	9.21941e9	−	1.59685e10i	0.179371	−	0.310680i
$241$	−3.00260e10	+	5.20066e10i	−0.573351	+	0.993074i	0.422867	+	0.906192i	$0.361024\pi$
$241$	−3.00260e10	+	5.20066e10i	−0.573351	+	0.993074i	−0.996219	+	0.0868820i	$0.972310\pi$
$242$	5.97822e10			1.12048
$243$	−2.81208e10	+	4.87067e10i	−0.517369	+	0.896109i
$244$	−1.02847e11	−	1.78137e11i	−1.85754	−	3.21736i
$245$	−2.02515e10	−	3.50767e10i	−0.359096	−	0.621972i
$246$	3.68972e10			0.642370
$247$	2.20559e10	−	1.05029e10i	0.377041	−	0.179544i
$248$	−1.18166e11			−1.98363
$249$	5.75272e8	+	9.96400e8i	0.00948367	+	0.0164262i
$250$	−5.69748e10	−	9.86833e10i	−0.922471	−	1.59777i
$251$	−3.56277e10	+	6.17091e10i	−0.566574	+	0.981335i	0.430327	+	0.902673i	$0.358398\pi$
$251$	−3.56277e10	+	6.17091e10i	−0.566574	+	0.981335i	−0.996901	+	0.0786620i	$0.974935\pi$
$252$	5.60474e9			0.0875494
$253$	−3.65427e10	+	6.32937e10i	−0.560735	+	0.971222i
$254$	−5.36001e10	+	9.28381e10i	−0.808005	+	1.39951i
$255$	−3.03187e10			−0.449035
$256$	6.83259e10	−	1.18344e11i	0.994273	−	1.72213i
$257$	−3.89341e9	−	6.74358e9i	−0.0556712	−	0.0964254i	0.836847	−	0.547437i	$-0.184397\pi$
$257$	−3.89341e9	−	6.74358e9i	−0.0556712	−	0.0964254i	−0.892518	+	0.451012i	$0.851063\pi$
$258$	2.66778e10	+	4.62073e10i	0.374853	+	0.649265i
$259$	−6.40789e9			−0.0884843
$260$	−9.53860e10	+	4.54222e10i	−1.29451	+	0.616436i
$261$	8.61503e10			1.14914
$262$	1.80584e10	+	3.12781e10i	0.236768	+	0.410095i
$263$	6.45119e10	+	1.11738e11i	0.831455	+	1.44012i	0.896884	+	0.442265i	$0.145825\pi$
$263$	6.45119e10	+	1.11738e11i	0.831455	+	1.44012i	−0.0654292	+	0.997857i	$0.520842\pi$
$264$	4.45599e10	−	7.71800e10i	0.564581	−	0.977883i
$265$	9.97369e9			0.124237
$266$	1.76381e9	−	3.05502e9i	0.0216016	−	0.0374150i
$267$	−1.71982e10	+	2.97882e10i	−0.207102	+	0.358710i
$268$	−5.56402e9			−0.0658844
$269$	7.57471e10	−	1.31198e11i	0.882025	−	1.52771i	0.0329385	−	0.999457i	$-0.489513\pi$
$269$	7.57471e10	−	1.31198e11i	0.882025	−	1.52771i	0.849086	−	0.528254i	$-0.177153\pi$
$270$	−4.85630e10	−	8.41136e10i	−0.556120	−	0.963229i
$271$	−4.54320e10	−	7.86906e10i	−0.511682	−	0.886260i	−0.999908	−	0.0135426i	$-0.995689\pi$
$271$	−4.54320e10	−	7.86906e10i	−0.511682	−	0.886260i	0.488226	−	0.872717i	$-0.337644\pi$
$272$	1.05840e11			1.17244
$273$	2.32643e9	+	1.60110e9i	0.0253489	+	0.0174456i
$274$	2.45472e11			2.63102
$275$	−2.92507e10	−	5.06638e10i	−0.308418	−	0.534196i
$276$	4.30760e10	+	7.46098e10i	0.446832	+	0.773936i
$277$	3.76870e10	−	6.52759e10i	0.384621	−	0.666183i	−0.607095	−	0.794629i	$-0.707665\pi$
$277$	3.76870e10	−	6.52759e10i	0.384621	−	0.666183i	0.991717	+	0.128446i	$0.0409988\pi$
$278$	−2.32464e11			−2.33429
$279$	−4.31688e10	+	7.47706e10i	−0.426532	+	0.738775i
$280$	−3.79338e9	+	6.57032e9i	−0.0368820	+	0.0638816i
$281$	1.00023e11			0.957019			0.478509	−	0.878082i	$-0.341177\pi$
$281$	1.00023e11			0.957019			0.478509	+	0.878082i	$0.341177\pi$
$282$	5.79369e10	−	1.00350e11i	0.545550	−	0.944920i
$283$	5.44231e10	+	9.42636e10i	0.504364	+	0.873585i	0.999987	+	0.00504677i	$0.00160644\pi$
$283$	5.44231e10	+	9.42636e10i	0.504364	+	0.873585i	−0.495623	+	0.868538i	$0.665060\pi$
$284$	1.67725e11	+	2.90508e11i	1.52990	+	2.64987i
$285$	−1.72408e10			−0.154794
$286$	−2.26744e11	+	1.07974e11i	−2.00396	+	0.954270i
$287$	−4.96881e9			−0.0432298
$288$	−1.58960e9	−	2.75327e9i	−0.0136151	−	0.0235821i
$289$	−2.77216e10	−	4.80152e10i	−0.233764	−	0.404891i
$290$	−1.17250e11	+	2.03083e11i	−0.973471	+	1.68610i
$291$	4.51391e10			0.369007
$292$	−8.96061e10	+	1.55202e11i	−0.721298	+	1.24933i
$293$	−2.73056e10	+	4.72946e10i	−0.216445	+	0.374893i	−0.953718	−	0.300701i	$-0.902779\pi$
$293$	−2.73056e10	+	4.72946e10i	−0.216445	+	0.374893i	0.737274	+	0.675594i	$0.236113\pi$
$294$	−1.13494e11			−0.885954
$295$	4.82807e10	−	8.36246e10i	0.371171	−	0.642888i
$296$	−1.67017e11	−	2.89283e11i	−1.26459	−	2.19033i
$297$	−7.68215e10	−	1.33059e11i	−0.572900	−	0.992291i
$298$	1.08713e11			0.798559
$299$	9.54921e9	−	1.20353e11i	0.0690951	−	0.870837i
$300$	−6.89608e10			−0.491537
$301$	−3.59260e9	−	6.22256e9i	−0.0252266	−	0.0436938i
$302$	1.83288e11	+	3.17464e11i	1.26795	+	2.19616i
$303$	1.19222e10	−	2.06498e10i	0.0812574	−	0.140742i
$304$	6.01860e10			0.404170
$305$	1.01719e11	−	1.76182e11i	0.673055	−	1.16577i
$306$	1.18138e11	−	2.04621e11i	0.770271	−	1.33415i
$307$	1.14486e11			0.735577			0.367789	−	0.929909i	$-0.380115\pi$
$307$	1.14486e11			0.735577			0.367789	+	0.929909i	$0.380115\pi$
$308$	−1.20667e10	+	2.09002e10i	−0.0764031	+	0.132334i
$309$	1.27375e10	+	2.20620e10i	0.0794826	+	0.137668i
$310$	−1.17505e11	−	2.03525e11i	−0.722652	−	1.25167i
$311$	−7.56404e10			−0.458492			−0.229246	−	0.973368i	$-0.573626\pi$
$311$	−7.56404e10			−0.458492			−0.229246	+	0.973368i	$0.573626\pi$
$312$	−1.16442e10	+	1.46758e11i	−0.0695690	+	0.876810i
$313$	1.70325e11			1.00306			0.501532	−	0.865139i	$-0.332770\pi$
$313$	1.70325e11			1.00306			0.501532	+	0.865139i	$0.332770\pi$
$314$	−1.41746e11	−	2.45511e11i	−0.822863	−	1.42524i
$315$	2.77161e9	+	4.80058e9i	0.0158612	+	0.0274724i
$316$	1.10716e10	−	1.91766e10i	0.0624626	−	0.108188i
$317$	−4.97165e9			−0.0276525			−0.0138262	−	0.999904i	$-0.504401\pi$
$317$	−4.97165e9			−0.0276525			−0.0138262	+	0.999904i	$0.504401\pi$
$318$	1.39737e10	−	2.42032e10i	0.0766284	−	0.132724i
$319$	−1.85477e11	+	3.21256e11i	−1.00284	+	1.73697i
$320$	1.39502e11			0.743715
$321$	1.45219e10	−	2.51526e10i	0.0763396	−	0.132224i
$322$	−8.71702e9	−	1.50983e10i	−0.0451873	−	0.0782668i
$323$	−4.94815e10	−	8.57045e10i	−0.252948	−	0.438119i
$324$	1.09115e11			0.550090
$325$	7.96086e10	+	5.47883e10i	0.395808	+	0.272403i
$326$	−4.18874e11			−2.05402
$327$	3.72812e10	+	6.45730e10i	0.180312	+	0.312310i
$328$	−1.29509e11	−	2.24316e11i	−0.617826	−	1.07011i
$329$	−7.80214e9	+	1.35137e10i	−0.0367141	+	0.0635906i
$330$	1.77242e11			0.822725
$331$	−1.00040e11	+	1.73274e11i	−0.458085	+	0.793426i	−0.998860	−	0.0477411i	$-0.984798\pi$
$331$	−1.00040e11	+	1.73274e11i	−0.458085	+	0.793426i	0.540775	+	0.841167i	$0.318131\pi$
$332$	8.12073e9	−	1.40655e10i	0.0366838	−	0.0635381i
$333$	−2.44061e11			−1.08768
$334$	−2.44538e11	+	4.23552e11i	−1.07519	+	1.86229i
$335$	−2.75148e9	−	4.76570e9i	−0.0119361	−	0.0206740i
$336$	3.47895e9	+	6.02572e9i	0.0148909	+	0.0257918i
$337$	−8.30132e10			−0.350601			−0.175300	−	0.984515i	$-0.556090\pi$
$337$	−8.30132e10			−0.350601			−0.175300	+	0.984515i	$0.556090\pi$
$338$	2.61493e11	−	3.22076e11i	1.08977	−	1.34225i
$339$	7.28862e10			0.299741
$340$	2.13995e11	+	3.70649e11i	0.868456	+	1.50421i
$341$	−1.85881e11	−	3.21955e11i	−0.744456	−	1.28944i
$342$	6.71794e10	−	1.16358e11i	0.265533	−	0.459917i
$343$	3.06226e10			0.119459
$344$	1.87277e11	−	3.24374e11i	0.721061	−	1.24891i
$345$	−4.26032e10	+	7.37910e10i	−0.161904	+	0.280425i
$346$	8.61666e10			0.323219
$347$	−9.09370e10	+	1.57507e11i	−0.336712	+	0.583201i	−0.983812	−	0.179203i	$-0.942648\pi$
$347$	−9.09370e10	+	1.57507e11i	−0.336712	+	0.583201i	0.647101	+	0.762405i	$0.275981\pi$
$348$	2.18638e11	+	3.78693e11i	0.799134	+	1.38414i
$349$	1.03338e11	+	1.78986e11i	0.372859	+	0.645810i	0.990004	−	0.141039i	$-0.0450442\pi$
$349$	1.03338e11	+	1.78986e11i	0.372859	+	0.645810i	−0.617145	+	0.786849i	$0.711711\pi$
$350$	1.39552e10			0.0497083
$351$	2.09077e11	+	1.43891e11i	0.735231	+	0.506001i
$352$	1.36893e10			0.0475269
$353$	7.67530e10	+	1.32940e11i	0.263093	+	0.455690i	0.967062	−	0.254540i	$-0.0819241\pi$
$353$	7.67530e10	+	1.32940e11i	0.263093	+	0.455690i	−0.703969	+	0.710230i	$0.748591\pi$
$354$	−1.35288e11	−	2.34326e11i	−0.457873	−	0.793059i
$355$	−1.65884e11	+	2.87319e11i	−0.554340	+	0.960145i
$356$	4.85552e11			1.60218
$357$	5.72039e9	−	9.90801e9i	0.0186388	−	0.0322834i
$358$	3.46618e11	−	6.00359e11i	1.11526	−	1.93169i
$359$	−3.19621e11			−1.01557			−0.507786	−	0.861483i	$-0.669536\pi$
$359$	−3.19621e11			−1.01557			−0.507786	+	0.861483i	$0.669536\pi$
$360$	−1.44481e11	+	2.50248e11i	−0.453365	+	0.785252i
$361$	1.33206e11	+	2.30720e11i	0.412802	+	0.714994i
$362$	2.38068e11	+	4.12346e11i	0.728640	+	1.26204i
$363$	1.10253e11			0.333282
$364$	3.15324e9	−	3.97417e10i	0.00941457	−	0.118656i
$365$	−1.77245e11			−0.522705
$366$	−2.85027e11	−	4.93681e11i	−0.830273	−	1.43808i
$367$	−9.86548e10	−	1.70875e11i	−0.283871	−	0.491679i	0.688464	−	0.725271i	$-0.258285\pi$
$367$	−9.86548e10	−	1.70875e11i	−0.283871	−	0.491679i	−0.972335	+	0.233592i	$0.924952\pi$
$368$	1.48724e11	−	2.57597e11i	0.422733	−	0.732194i
$369$	−1.89250e11			−0.531394
$370$	3.32166e11	−	5.75328e11i	0.921398	−	1.59591i
$371$	−1.88179e9	+	3.25935e9i	−0.00515689	+	0.00893200i
$372$	−4.38227e11			−1.18647
$373$	1.71292e11	−	2.96687e11i	0.458192	−	0.793612i	−0.540673	−	0.841233i	$-0.681830\pi$
$373$	1.71292e11	−	2.96687e11i	0.458192	−	0.793612i	0.998865	+	0.0476205i	$0.0151638\pi$
$374$	5.08690e11	+	8.81078e11i	1.34441	+	2.32858i
$375$	−1.05076e11	−	1.81996e11i	−0.274386	−	0.475250i
$376$	−8.13431e11			−2.09882
$377$	4.84683e10	−	6.10869e11i	0.123573	−	1.55744i
$378$	3.66506e10			0.0923353
$379$	2.35895e11	+	4.08583e11i	0.587277	+	1.01719i	0.994587	+	0.103904i	$0.0331333\pi$
$379$	2.35895e11	+	4.08583e11i	0.587277	+	1.01719i	−0.407311	+	0.913290i	$0.633533\pi$
$380$	1.21688e11	+	2.10770e11i	0.299380	+	0.518541i
$381$	−9.88519e10	+	1.71216e11i	−0.240338	+	0.416278i
$382$	−1.30904e12			−3.14534
$383$	1.29397e11	−	2.24123e11i	0.307277	−	0.532220i	−0.670488	−	0.741920i	$-0.733915\pi$
$383$	1.29397e11	−	2.24123e11i	0.307277	−	0.532220i	0.977766	+	0.209700i	$0.0672487\pi$
$384$	1.91395e11	−	3.31506e11i	0.449200	−	0.778037i
$385$	−2.38686e10			−0.0553673
$386$	−3.62671e11	+	6.28165e11i	−0.831516	+	1.44023i
$387$	−1.36833e11	−	2.37002e11i	−0.310093	−	0.537097i
$388$	−3.18599e11	−	5.51830e11i	−0.713677	−	1.23613i
$389$	−1.06537e11			−0.235899			−0.117949	−	0.993020i	$-0.537632\pi$
$389$	−1.06537e11			−0.235899			−0.117949	+	0.993020i	$0.537632\pi$
$390$	−2.64349e11	+	1.25881e11i	−0.578612	+	0.275531i
$391$	−4.89090e11			−1.05826
$392$	3.98363e11	+	6.89986e11i	0.852103	+	1.47589i
$393$	3.33042e10	+	5.76845e10i	0.0704258	+	0.121981i
$394$	2.60031e11	−	4.50387e11i	0.543616	−	0.941571i
$395$	2.19002e10			0.0452649
$396$	−4.59592e11	+	7.96037e11i	−0.939170	+	1.62669i
$397$	2.23577e11	−	3.87247e11i	0.451721	−	0.782403i	−0.546772	−	0.837281i	$-0.684144\pi$
$397$	2.23577e11	−	3.87247e11i	0.451721	−	0.782403i	0.998493	+	0.0548781i	$0.0174770\pi$
$398$	9.39416e11			1.87665
$399$	3.25291e9	−	5.63420e9i	0.00642531	−	0.0111290i
$400$	1.19047e11	+	2.06195e11i	0.232513	+	0.402725i
$401$	−8.75737e10	−	1.51682e11i	−0.169131	−	0.292944i	0.768983	−	0.639269i	$-0.220763\pi$
$401$	−8.75737e10	−	1.51682e11i	−0.169131	−	0.292944i	−0.938115	+	0.346325i	$0.887430\pi$
$402$	−1.54199e10			−0.0294486
$403$	5.05891e11	+	3.48165e11i	0.955398	+	0.657524i
$404$	−3.36594e11			−0.628624
$405$	5.39589e10	+	9.34596e10i	0.0996588	+	0.172614i
$406$	−4.42445e10	−	7.66336e10i	−0.0808149	−	0.139976i
$407$	5.25451e11	−	9.10108e11i	0.949199	−	1.64406i
$408$	5.96393e11			1.06552
$409$	1.28371e11	−	2.22344e11i	0.226835	−	0.392890i	−0.730033	−	0.683412i	$-0.760495\pi$
$409$	1.28371e11	−	2.22344e11i	0.226835	−	0.392890i	0.956869	+	0.290521i	$0.0938287\pi$
$410$	2.57568e11	−	4.46121e11i	0.450158	−	0.779696i
$411$	4.52712e11			0.782588
$412$	1.79807e11	−	3.11435e11i	0.307447	−	0.532513i
$413$	1.82187e10	+	3.15558e10i	0.0308137	+	0.0533708i
$414$	−3.32010e11	−	5.75059e11i	−0.555456	−	0.962079i
$415$	1.60632e10			0.0265837
$416$	−2.04170e10	+	9.72242e9i	−0.0334250	+	0.0159168i
$417$	−4.28722e11			−0.694326
$418$	2.89268e11	+	5.01026e11i	0.463454	+	0.802726i
$419$	5.78724e11	+	1.00238e12i	0.917294	+	1.58880i	0.803508	+	0.595294i	$0.202964\pi$
$419$	5.78724e11	+	1.00238e12i	0.917294	+	1.58880i	0.113786	+	0.993505i	$0.463702\pi$
$420$	−1.40680e10	+	2.43665e10i	−0.0220602	+	0.0382094i
$421$	4.28980e11			0.665529			0.332765	−	0.943010i	$-0.392019\pi$
$421$	4.28980e11			0.665529			0.332765	+	0.943010i	$0.392019\pi$
$422$	−6.55712e11	+	1.13573e12i	−1.00648	+	1.74328i
$423$	−2.97165e11	+	5.14704e11i	−0.451300	+	0.781675i
$424$	−1.96190e11			−0.294802
$425$	1.95747e11	−	3.39044e11i	0.291035	−	0.504087i
$426$	4.64825e11	+	8.05101e11i	0.683828	+	1.18442i
$427$	3.83835e10	+	6.64822e10i	0.0558752	+	0.0967788i
$428$	−4.09991e11			−0.590579
$429$	−4.18172e11	+	1.99130e11i	−0.596069	+	0.283844i
$430$	7.44918e11			1.05075
$431$	−4.68105e11	−	8.10782e11i	−0.653425	−	1.13176i	−0.982286	−	0.187387i	$-0.939998\pi$
$431$	−4.68105e11	−	8.10782e11i	−0.653425	−	1.13176i	0.328862	−	0.944378i	$-0.393335\pi$
$432$	3.12654e11	+	5.41532e11i	0.431903	+	0.748079i
$433$	−3.28378e11	+	5.68768e11i	−0.448930	+	0.777570i	−0.998317	−	0.0579981i	$-0.981528\pi$
$433$	−3.28378e11	+	5.68768e11i	−0.448930	+	0.777570i	0.549386	+	0.835569i	$0.314862\pi$
$434$	8.86813e10			0.119985
$435$	−2.16239e11	+	3.74536e11i	−0.289555	+	0.501524i
$436$	5.26274e11	−	9.11534e11i	0.697466	−	1.20805i
$437$	−2.78122e11			−0.364811
$438$	−2.48331e11	+	4.30122e11i	−0.322402	+	0.558416i
$439$	−2.48368e11	−	4.30185e11i	−0.319157	−	0.552797i	0.661155	−	0.750249i	$-0.270066\pi$
$439$	−2.48368e11	−	4.30185e11i	−0.319157	−	0.552797i	−0.980312	+	0.197453i	$0.936733\pi$
$440$	−6.22119e11	−	1.07754e12i	−0.791291	−	1.37056i
$441$	5.82125e11			0.732896
$442$	−1.38445e12	−	9.52805e11i	−1.72535	−	1.18742i
$443$	−1.55746e11			−0.192132			−0.0960662	−	0.995375i	$-0.530626\pi$
$443$	−1.55746e11			−0.192132			−0.0960662	+	0.995375i	$0.530626\pi$
$444$	−6.19395e11	−	1.07282e12i	−0.756387	−	1.31010i
$445$	2.40112e11	+	4.15885e11i	0.290264	+	0.502752i
$446$	−5.52966e11	+	9.57766e11i	−0.661747	+	1.14618i
$447$	2.00493e11			0.237528
$448$	−2.63206e10	+	4.55887e10i	−0.0308706	+	0.0534695i
$449$	1.08106e10	−	1.87245e10i	0.0125528	−	0.0217421i	−0.859681	−	0.510832i	$-0.829338\pi$
$449$	1.08106e10	−	1.87245e10i	0.0125528	−	0.0217421i	0.872234	+	0.489090i	$0.162671\pi$
$450$	5.31518e11			0.611029
$451$	4.07445e11	−	7.05715e11i	0.463740	−	0.803221i
$452$	−5.14443e11	−	8.91041e11i	−0.579715	−	1.00410i
$453$	3.38028e11	+	5.85482e11i	0.377147	+	0.653238i
$454$	−1.38728e12			−1.53254
$455$	3.55989e10	−	1.69520e10i	0.0389391	−	0.0185425i
$456$	3.39140e11			0.367313
$457$	7.93463e11	+	1.37432e12i	0.850950	+	1.47389i	0.880352	+	0.474320i	$0.157306\pi$
$457$	7.93463e11	+	1.37432e12i	0.850950	+	1.47389i	−0.0294026	+	0.999568i	$0.509360\pi$
$458$	−3.17164e11	−	5.49344e11i	−0.336813	−	0.583378i
$459$	5.14092e11	−	8.90434e11i	0.540610	−	0.936363i
$460$	1.20280e12			1.25252
$461$	−2.98722e11	+	5.17402e11i	−0.308045	+	0.533549i	−0.977935	−	0.208911i	$-0.933008\pi$
$461$	−2.98722e11	+	5.17402e11i	−0.308045	+	0.533549i	0.669890	+	0.742460i	$0.266341\pi$
$462$	−3.34413e10	+	5.79219e10i	−0.0341502	+	0.0591499i
$463$	−1.53221e12			−1.54955			−0.774773	−	0.632240i	$-0.782136\pi$
$463$	−1.53221e12			−1.54955			−0.774773	+	0.632240i	$0.782136\pi$
$464$	7.54869e11	−	1.30747e12i	0.756033	−	1.30949i
$465$	−2.16709e11	−	3.75350e11i	−0.214950	−	0.372305i
$466$	1.50472e12	+	2.60626e12i	1.47816	+	2.56024i
$467$	3.65472e11			0.355573			0.177786	−	0.984069i	$-0.443106\pi$
$467$	3.65472e11			0.355573			0.177786	+	0.984069i	$0.443106\pi$
$468$	1.20099e11	−	1.51367e12i	0.115727	−	1.45856i
$469$	2.07654e9			0.00198181
$470$	−8.08880e11	−	1.40102e12i	−0.764617	−	1.32436i
$471$	−2.61415e11	−	4.52783e11i	−0.244757	−	0.423932i
$472$	−9.49719e11	+	1.64496e12i	−0.880757	+	1.52552i
$473$	1.17838e12			1.08246
$474$	3.06835e10	−	5.31454e10i	0.0279192	−	0.0483574i
$475$	1.11312e11	−	1.92798e11i	0.100328	−	0.173772i
$476$	−1.61502e11			−0.144194
$477$	−7.16727e10	+	1.24141e11i	−0.0633901	+	0.109795i
$478$	−3.66673e11	−	6.35097e11i	−0.321258	−	0.556435i
$479$	1.18756e11	+	2.05691e11i	0.103073	+	0.178528i	0.912949	−	0.408073i	$-0.133799\pi$
$479$	1.18756e11	+	2.05691e11i	0.103073	+	0.178528i	−0.809876	+	0.586601i	$0.800466\pi$
$480$	1.59597e10			0.0137226
$481$	−1.37309e11	+	1.73057e12i	−0.116962	+	1.47413i
$482$	2.34932e12			1.98258
$483$	−1.60763e10	−	2.78451e10i	−0.0134408	−	0.0232802i
$484$	−7.78186e11	−	1.34786e12i	−0.644583	−	1.11645i
$485$	3.15102e11	−	5.45773e11i	0.258591	−	0.447893i
$486$	2.20026e12			1.78900
$487$	7.27900e11	−	1.26076e12i	0.586397	−	1.01567i	−0.408303	−	0.912846i	$-0.633879\pi$
$487$	7.27900e11	−	1.26076e12i	0.586397	−	1.01567i	0.994700	−	0.102822i	$-0.0327874\pi$
$488$	−2.00088e12	+	3.46563e12i	−1.59710	+	2.76626i
$489$	−7.72507e11			−0.610960
$490$	−7.92269e11	+	1.37225e12i	−0.620855	+	1.07535i
$491$	−8.26511e11	−	1.43156e12i	−0.641774	−	1.11158i	−0.985037	−	0.172345i	$-0.944866\pi$
$491$	−8.26511e11	−	1.43156e12i	−0.641774	−	1.11158i	0.343263	−	0.939239i	$-0.388468\pi$
$492$	−4.80291e11	−	8.31888e11i	−0.369540	−	0.640062i
$493$	−2.48244e12			−1.89264
$494$	−7.87269e11	−	5.41814e11i	−0.594774	−	0.409335i
$495$	−9.09096e11			−0.680591
$496$	7.56510e11	+	1.31031e12i	0.561238	+	0.972093i
$497$	−6.25963e10	−	1.08420e11i	−0.0460198	−	0.0797087i
$498$	2.25055e10	−	3.89806e10i	0.0163967	−	0.0283999i
$499$	7.48158e11			0.540183			0.270092	−	0.962835i	$-0.412946\pi$
$499$	7.48158e11			0.540183			0.270092	+	0.962835i	$0.412946\pi$
$500$	−1.48328e12	+	2.56912e12i	−1.06135	+	1.83831i
$501$	−4.50988e11	+	7.81135e11i	−0.319813	+	0.553932i
$502$	2.78762e12			1.95915
$503$	−1.88001e11	+	3.25627e11i	−0.130949	+	0.226811i	−0.924043	−	0.382289i	$-0.875136\pi$
$503$	−1.88001e11	+	3.25627e11i	−0.130949	+	0.226811i	0.793093	+	0.609100i	$0.208469\pi$
$504$	−5.45198e10	−	9.44311e10i	−0.0376372	−	0.0651895i
$505$	−1.66450e11	−	2.88300e11i	−0.113887	−	0.197257i
$506$	2.85920e12			1.93896
$507$	4.82258e11	−	5.93988e11i	0.324148	−	0.399247i
$508$	2.79085e12			1.85930
$509$	1.28548e12	+	2.22652e12i	0.848860	+	1.47027i	0.882226	+	0.470826i	$0.156044\pi$
$509$	1.28548e12	+	2.22652e12i	0.848860	+	1.47027i	−0.0333655	+	0.999443i	$0.510623\pi$
$510$	5.93056e11	+	1.02720e12i	0.388177	+	0.672343i
$511$	3.34418e10	−	5.79229e10i	0.0216968	−	0.0375800i
$512$	−2.62961e12			−1.69113
$513$	2.92339e11	−	5.06346e11i	0.186363	−	0.322790i
$514$	−1.52316e11	+	2.63819e11i	−0.0962522	+	0.166714i
$515$	3.55667e11			0.222798
$516$	6.94530e11	−	1.20296e12i	0.431288	−	0.747012i
$517$	−1.27956e12	−	2.21626e12i	−0.787687	−	1.36431i
$518$	1.25343e11	+	2.17100e11i	0.0764920	+	0.132488i
$519$	1.58913e11			0.0961402
$520$	1.69315e12	+	1.16526e12i	1.01550	+	0.698890i
$521$	−2.17185e12			−1.29140			−0.645700	−	0.763591i	$-0.723434\pi$
$521$	−2.17185e12			−1.29140			−0.645700	+	0.763591i	$0.723434\pi$
$522$	−1.68516e12	−	2.91879e12i	−0.993402	−	1.72062i
$523$	1.01365e11	+	1.75570e11i	0.0592423	+	0.102611i	0.894125	−	0.447817i	$-0.147798\pi$
$523$	1.01365e11	+	1.75570e11i	0.0592423	+	0.102611i	−0.834883	+	0.550427i	$0.814465\pi$
$524$	4.70133e11	−	8.14294e11i	0.272414	−	0.471835i
$525$	2.57368e10			0.0147855
$526$	2.52380e12	−	4.37135e12i	1.43754	−	2.48989i
$527$	1.24392e12	−	2.15453e12i	0.702497	−	1.21676i
$528$	−1.14110e12			−0.638958
$529$	2.13318e11	−	3.69477e11i	0.118434	−	0.205134i
$530$	−1.95093e11	−	3.37910e11i	−0.107399	−	0.186020i
$531$	6.93908e11	+	1.20188e12i	0.378771	+	0.656050i
$532$	−9.18383e10			−0.0497075
$533$	−1.06472e11	+	1.34192e12i	−0.0571431	+	0.720201i
$534$	1.34564e12			0.716133
$535$	−2.02746e11	−	3.51166e11i	−0.106994	−	0.185319i
$536$	5.41237e10	+	9.37450e10i	0.0283234	+	0.0490576i
$537$	6.39249e11	−	1.10721e12i	0.331731	−	0.574574i
$538$	−5.92667e12			−3.04994
$539$	−1.25328e12	+	2.17075e12i	−0.639588	+	1.10780i
$540$	−1.26429e12	+	2.18982e12i	−0.639845	+	1.10824i
$541$	6.36853e11			0.319633			0.159816	−	0.987147i	$-0.448910\pi$
$541$	6.36853e11			0.319633			0.159816	+	0.987147i	$0.448910\pi$
$542$	−1.77737e12	+	3.07849e12i	−0.884668	+	1.53229i
$543$	4.39057e11	+	7.60469e11i	0.216731	+	0.375389i
$544$	4.58046e10	+	7.93359e10i	0.0224241	+	0.0388396i
$545$	1.04100e12			0.505435
$546$	8.73876e9	−	1.10139e11i	0.00420807	−	0.0530363i
$547$	−3.23579e12			−1.54539			−0.772695	−	0.634778i	$-0.781092\pi$
$547$	−3.23579e12			−1.54539			−0.772695	+	0.634778i	$0.781092\pi$
$548$	−3.19531e12	−	5.53445e12i	−1.51356	−	2.62157i
$549$	1.46194e12	+	2.53215e12i	0.686835	+	1.18963i
$550$	−1.14433e12	+	1.98204e12i	−0.533236	+	0.923593i
$551$	−1.41164e12			−0.652444
$552$	8.38039e11	−	1.45153e12i	0.384183	−	0.665425i
$553$	−4.13203e9	+	7.15689e9i	−0.00187889	+	0.00325433i
$554$	−2.94874e12			−1.32997
$555$	6.12596e11	−	1.06105e12i	0.274067	−	0.474697i
$556$	3.02599e12	+	5.24117e12i	1.34286	+	2.32590i
$557$	−8.06014e11	−	1.39606e12i	−0.354809	−	0.614547i	0.632277	−	0.774743i	$-0.282121\pi$
$557$	−8.06014e11	−	1.39606e12i	−0.354809	−	0.614547i	−0.987085	+	0.160196i	$0.948787\pi$
$558$	3.37766e12			1.47490
$559$	−1.75750e12	+	8.36910e11i	−0.761277	+	0.362515i
$560$	9.71420e10			0.0417408
$561$	9.38151e11	+	1.62492e12i	0.399889	+	0.692629i
$562$	−1.95652e12	−	3.38879e12i	−0.827314	−	1.43295i
$563$	5.96428e11	−	1.03304e12i	0.250190	−	0.433342i	−0.713388	−	0.700769i	$-0.752840\pi$
$563$	5.96428e11	−	1.03304e12i	0.250190	−	0.433342i	0.963578	+	0.267427i	$0.0861736\pi$
$564$	−3.01666e12			−1.25537
$565$	5.08797e11	−	8.81262e11i	0.210052	−	0.363820i
$566$	2.12911e12	−	3.68773e12i	0.872016	−	1.51038i
$567$	−4.07228e10			−0.0165468
$568$	3.26306e12	−	5.65179e12i	1.31540	−	2.27834i
$569$	1.24731e12	+	2.16041e12i	0.498851	+	0.864035i	0.999999	−	0.00132616i	$-0.000422131\pi$
$569$	1.24731e12	+	2.16041e12i	0.498851	+	0.864035i	−0.501148	+	0.865362i	$0.667089\pi$
$570$	3.37242e11	+	5.84121e11i	0.133815	+	0.231775i
$571$	4.82125e12			1.89801			0.949003	−	0.315267i	$-0.102094\pi$
$571$	4.82125e12			1.89801			0.949003	+	0.315267i	$0.102094\pi$
$572$	5.38592e12	+	3.70670e12i	2.10367	+	1.44779i
$573$	−2.41419e12			−0.935569
$574$	9.71935e10	+	1.68344e11i	0.0373709	+	0.0647283i
$575$	−5.50119e11	−	9.52834e11i	−0.209871	−	0.363506i
$576$	−1.00249e12	+	1.73636e12i	−0.379471	+	0.657263i
$577$	−1.39254e12			−0.523018			−0.261509	−	0.965201i	$-0.584220\pi$
$577$	−1.39254e12			−0.523018			−0.261509	+	0.965201i	$0.584220\pi$
$578$	−1.08451e12	+	1.87842e12i	−0.404164	+	0.700033i
$579$	−6.68856e11	+	1.15849e12i	−0.247331	+	0.428390i
$580$	6.10499e12			2.24006
$581$	−3.03073e9	+	5.24938e9i	−0.00110345	+	0.00191124i
$582$	−8.82953e11	−	1.52932e12i	−0.318995	−	0.552516i
$583$	−3.08615e11	−	5.34538e11i	−0.110639	−	0.191633i
$584$	3.48655e12			1.24033
$585$	1.35588e12	−	6.45659e11i	0.478651	−	0.227930i
$586$	2.13647e12			0.748440
$587$	2.56964e12	+	4.45074e12i	0.893306	+	1.54725i	0.835887	+	0.548901i	$0.184954\pi$
$587$	2.56964e12	+	4.45074e12i	0.893306	+	1.54725i	0.0574191	+	0.998350i	$0.481713\pi$
$588$	1.47736e12	+	2.55886e12i	0.509668	+	0.882770i
$589$	7.07357e11	−	1.22518e12i	0.242170	−	0.419450i
$590$	−3.77762e12			−1.28347
$591$	4.79562e11	−	8.30625e11i	0.161697	−	0.280067i
$592$	−2.13852e12	+	3.70402e12i	−0.715591	+	1.23944i
$593$	−2.50959e12			−0.833406			−0.416703	−	0.909043i	$-0.636814\pi$
$593$	−2.50959e12			−0.833406			−0.416703	+	0.909043i	$0.636814\pi$
$594$	−3.00537e12	+	5.20545e12i	−0.990510	+	1.71561i
$595$	−7.98647e10	−	1.38330e11i	−0.0261233	−	0.0452469i
$596$	−1.41511e12	−	2.45105e12i	−0.459392	−	0.795690i
$597$	1.73251e12			0.558203
$598$	−4.26438e12	+	2.03067e12i	−1.36364	+	0.649357i
$599$	−7.59345e11			−0.241001			−0.120500	−	0.992713i	$-0.538450\pi$
$599$	−7.59345e11			−0.241001			−0.120500	+	0.992713i	$0.538450\pi$
$600$	6.70812e11	+	1.16188e12i	0.211310	+	0.366000i
$601$	−1.60204e12	−	2.77482e12i	−0.500886	−	0.867561i	−0.999999	−	0.00102381i	$-0.999674\pi$
$601$	−1.60204e12	−	2.77482e12i	−0.500886	−	0.867561i	0.499113	−	0.866537i	$-0.333659\pi$
$602$	−1.40548e11	+	2.43436e11i	−0.0436154	+	0.0755440i
$603$	7.90905e10			0.0243611
$604$	4.77172e12	−	8.26486e12i	1.45884	−	2.52679i
$605$	7.69645e11	−	1.33306e12i	0.233556	−	0.404531i
$606$	−9.32824e11			−0.280978
$607$	1.78675e12	−	3.09474e12i	0.534213	−	0.925283i	−0.464989	−	0.885317i	$-0.653942\pi$
$607$	1.78675e12	−	3.09474e12i	0.534213	−	0.925283i	0.999201	−	0.0399665i	$-0.0127251\pi$
$608$	2.60469e10	+	4.51145e10i	0.00773018	+	0.0133891i
$609$	−8.15977e10	−	1.41331e11i	−0.0240381	−	0.0416352i
$610$	−7.95875e12			−2.32734
$611$	3.48244e12	+	2.39669e12i	1.01088	+	0.695707i
$612$	−6.15122e12			−1.77247
$613$	−1.71549e11	−	2.97131e11i	−0.0490699	−	0.0849916i	0.840447	−	0.541893i	$-0.182292\pi$
$613$	−1.71549e11	−	2.97131e11i	−0.0490699	−	0.0849916i	−0.889517	+	0.456902i	$0.848959\pi$
$614$	−2.23942e12	−	3.87879e12i	−0.635885	−	1.10138i
$615$	4.75019e11	−	8.22758e11i	0.133898	−	0.231918i
$616$	4.69513e11			0.131382
$617$	5.08703e8	−	8.81099e8i	0.000141313	−	0.000244761i	−0.865955	−	0.500122i	$-0.833288\pi$
$617$	5.08703e8	−	8.81099e8i	0.000141313	−	0.000244761i	0.866096	+	0.499878i	$0.166622\pi$
$618$	4.98311e11	−	8.63099e11i	0.137421	−	0.238020i
$619$	−4.19411e10			−0.0114824			−0.00574118	−	0.999984i	$-0.501827\pi$
$619$	−4.19411e10			−0.0114824			−0.00574118	+	0.999984i	$0.501827\pi$
$620$	−3.05913e12	+	5.29857e12i	−0.831449	+	1.44011i
$621$	−1.44478e12	−	2.50244e12i	−0.389844	−	0.675229i
$622$	1.47958e12	+	2.56271e12i	0.396353	+	0.686504i
$623$	−1.81212e11			−0.0481939
$624$	1.70191e12	−	8.10436e11i	0.449371	−	0.213987i
$625$	−1.10109e12			−0.288645
$626$	−3.33168e12	−	5.77064e12i	−0.867119	−	1.50189i
$627$	5.33481e11	+	9.24016e11i	0.137853	+	0.238768i
$628$	−3.69022e12	+	6.39164e12i	−0.946746	+	1.63981i
$629$	7.03267e12			1.79140
$630$	1.08430e11	−	1.87806e11i	0.0274230	−	0.0474981i
$631$	−2.55256e12	+	4.42116e12i	−0.640979	+	1.11021i	0.344236	+	0.938883i	$0.388138\pi$
$631$	−2.55256e12	+	4.42116e12i	−0.640979	+	1.11021i	−0.985215	+	0.171324i	$0.945195\pi$
$632$	−4.30795e11			−0.107410
$633$	−1.20930e12	+	2.09456e12i	−0.299375	+	0.518533i
$634$	9.72491e10	+	1.68440e11i	0.0239047	+	0.0414042i
$635$	1.38011e12	+	2.39042e12i	0.336847	+	0.583435i
$636$	−7.27584e11			−0.176330
$637$	3.27504e11	−	4.12769e12i	0.0788115	−	0.993298i
$638$	1.45123e13			3.46771
$639$	−2.38414e12	−	4.12945e12i	−0.565689	−	0.979803i
$640$	−2.67214e12	−	4.62828e12i	−0.629578	−	1.09046i
$641$	1.48797e12	−	2.57724e12i	0.348124	−	0.602968i	−0.637793	−	0.770208i	$-0.720152\pi$
$641$	1.48797e12	−	2.57724e12i	0.348124	−	0.602968i	0.985916	+	0.167240i	$0.0534856\pi$
$642$	−1.13623e12			−0.263973
$643$	2.02163e12	−	3.50156e12i	0.466392	−	0.807815i	−0.532871	−	0.846197i	$-0.678887\pi$
$643$	2.02163e12	−	3.50156e12i	0.466392	−	0.807815i	0.999263	+	0.0383816i	$0.0122202\pi$
$644$	−2.26939e11	+	3.93070e11i	−0.0519904	+	0.0900500i
$645$	1.37381e12			0.312543
$646$	−1.93579e12	+	3.35288e12i	−0.437332	+	0.757482i
$647$	−2.05756e12	−	3.56381e12i	−0.461620	−	0.799549i	0.537422	−	0.843313i	$-0.319398\pi$
$647$	−2.05756e12	−	3.56381e12i	−0.461620	−	0.799549i	−0.999042	+	0.0437646i	$0.986065\pi$
$648$	−1.06141e12	−	1.83842e12i	−0.236482	−	0.409598i
$649$	−5.97579e12			−1.32219
$650$	2.99033e11	−	3.76885e12i	0.0657066	−	0.828131i
$651$	1.63550e11			0.0356892
$652$	5.45248e12	+	9.44398e12i	1.18163	+	2.04664i
$653$	1.30425e12	+	2.25903e12i	0.280706	+	0.486197i	0.971559	−	0.236798i	$-0.0760980\pi$
$653$	1.30425e12	+	2.25903e12i	0.280706	+	0.486197i	−0.690853	+	0.722996i	$0.742765\pi$
$654$	1.45850e12	−	2.52619e12i	0.311749	−	0.539966i
$655$	9.29945e11			0.197411
$656$	−1.65825e12	+	2.87217e12i	−0.349609	+	0.605540i
$657$	1.27372e12	−	2.20614e12i	0.266704	−	0.461944i
$658$	6.10463e11			0.126953
$659$	1.13035e12	−	1.95782e12i	0.233468	−	0.404378i	−0.725358	−	0.688371i	$-0.758326\pi$
$659$	1.13035e12	−	1.95782e12i	0.233468	−	0.404378i	0.958826	+	0.283993i	$0.0916593\pi$
$660$	−2.30717e12	−	3.99613e12i	−0.473294	−	0.819769i
$661$	1.43406e12	+	2.48387e12i	0.292188	+	0.506084i	0.974327	−	0.225138i	$-0.0722834\pi$
$661$	1.43406e12	+	2.48387e12i	0.292188	+	0.506084i	−0.682139	+	0.731223i	$0.738950\pi$
$662$	7.82739e12			1.58400
$663$	−2.55327e12	−	1.75721e12i	−0.513198	−	0.353193i
$664$	−3.15976e11			−0.0630808
$665$	−4.54152e10	−	7.86614e10i	−0.00900541	−	0.0155978i
$666$	4.77401e12	+	8.26883e12i	0.940263	+	1.62858i
$667$	−3.48827e12	+	6.04187e12i	−0.682409	+	1.18197i
$668$	1.27326e13			2.47413
$669$	−1.01981e12	+	1.76636e12i	−0.196834	+	0.340927i
$670$	−1.07642e11	+	1.86441e11i	−0.0206369	+	0.0357441i
$671$	−1.25899e13			−2.39757
$672$	−3.01119e9	+	5.21554e9i	−0.000569609	+	0.000986591i
$673$	2.66570e12	+	4.61713e12i	0.500892	+	0.867570i	0.999999	+	0.00102978i	$0.000327788\pi$
$673$	2.66570e12	+	4.61713e12i	0.500892	+	0.867570i	−0.499108	+	0.866540i	$0.666339\pi$
$674$	1.62380e12	+	2.81250e12i	0.303084	+	0.524957i
$675$	2.31297e12			0.428847
$676$	−1.06654e13	−	1.70318e12i	−1.96435	−	0.313690i
$677$	−1.49701e12			−0.273889			−0.136945	−	0.990579i	$-0.543728\pi$
$677$	−1.49701e12			−0.273889			−0.136945	+	0.990579i	$0.543728\pi$
$678$	−1.42571e12	−	2.46940e12i	−0.259117	−	0.448805i
$679$	1.18904e11	+	2.05948e11i	0.0214675	+	0.0371829i
$680$	4.16324e12	−	7.21094e12i	0.746692	−	1.29331i
$681$	−2.55848e12			−0.455848
$682$	−7.27192e12	+	1.25953e13i	−1.28712	+	2.22936i
$683$	−3.61464e12	+	6.26075e12i	−0.635583	+	1.10086i	0.350808	+	0.936447i	$0.385907\pi$
$683$	−3.61464e12	+	6.26075e12i	−0.635583	+	1.10086i	−0.986391	+	0.164415i	$0.947426\pi$
$684$	−3.49790e12			−0.611019
$685$	3.16024e12	−	5.47370e12i	0.548420	−	0.949891i
$686$	−5.99001e11	−	1.03750e12i	−0.103269	−	0.178867i
$687$	−5.84929e11	−	1.01313e12i	−0.100184	−	0.173524i
$688$	−4.79586e12			−0.816053
$689$	8.39926e11	+	5.78054e11i	0.141989	+	0.0977196i
$690$	3.33340e12			0.559844
$691$	4.01707e12	+	6.95777e12i	0.670283	+	1.16096i	0.977824	+	0.209429i	$0.0671605\pi$
$691$	4.01707e12	+	6.95777e12i	0.670283	+	1.16096i	−0.307541	+	0.951535i	$0.599506\pi$
$692$	−1.12163e12	−	1.94272e12i	−0.185940	−	0.322057i
$693$	1.71524e11	−	2.97088e11i	0.0282504	−	0.0489312i
$694$	7.11518e12			1.16431
$695$	−2.99278e12	+	5.18364e12i	−0.486567	+	0.842759i
$696$	4.25358e12	−	7.36742e12i	0.687089	−	1.19007i
$697$	5.45327e12			0.875205
$698$	4.04272e12	−	7.00220e12i	0.644651	−	1.11657i
$699$	2.77508e12	+	4.80659e12i	0.439672	+	0.761534i
$700$	−1.81654e11	−	3.14635e11i	−0.0285960	−	0.0495297i
$701$	−5.45440e12			−0.853132			−0.426566	−	0.904456i	$-0.640277\pi$
$701$	−5.45440e12			−0.853132			−0.426566	+	0.904456i	$0.640277\pi$
$702$	7.85353e11	−	9.89817e12i	0.122053	−	1.53829i
$703$	3.99914e12			0.617544
$704$	−4.31662e12	−	7.47660e12i	−0.662318	−	1.14717i
$705$	−1.49178e12	−	2.58383e12i	−0.227432	−	0.393924i
$706$	3.00269e12	−	5.20081e12i	0.454872	−	0.787861i
$707$	1.25620e11			0.0189091
$708$	−3.52209e12	+	6.10044e12i	−0.526807	+	0.912456i
$709$	−3.33094e11	+	5.76935e11i	−0.0495060	+	0.0857470i	−0.889717	−	0.456513i	$-0.849098\pi$
$709$	−3.33094e11	+	5.76935e11i	−0.0495060	+	0.0857470i	0.840210	+	0.542260i	$0.182431\pi$
$710$	1.29792e13			1.91684
$711$	−1.57379e11	+	2.72589e11i	−0.0230958	+	0.0400032i
$712$	−4.72318e12	−	8.18079e12i	−0.688771	−	1.19299i
$713$	−3.49586e12	−	6.05501e12i	−0.506583	−	0.877428i
$714$	−4.47580e11			−0.0644509
$715$	−5.11459e11	+	6.44615e12i	−0.0731869	+	0.922409i
$716$	−1.80477e13			−2.56633
$717$	−6.76237e11	−	1.17128e12i	−0.0955570	−	0.165510i
$718$	6.25202e12	+	1.08288e13i	0.877931	+	1.52062i
$719$	−6.64847e11	+	1.15155e12i	−0.0927773	+	0.160695i	−0.908679	−	0.417496i	$-0.862908\pi$
$719$	−6.64847e11	+	1.15155e12i	−0.0927773	+	0.160695i	0.815902	+	0.578191i	$0.196241\pi$
$720$	3.69990e12			0.513091
$721$	−6.71056e10	+	1.16230e11i	−0.00924805	+	0.0160181i
$722$	5.21122e12	−	9.02609e12i	0.713710	−	1.23618i
$723$	4.33273e12			0.589711
$724$	6.19787e12	−	1.07350e13i	0.838338	−	1.45204i
$725$	−2.79221e12	−	4.83624e12i	−0.375341	−	0.650110i
$726$	−2.15663e12	−	3.73540e12i	−0.288112	−	0.499025i
$727$	−1.06853e13			−1.41868			−0.709338	−	0.704868i	$-0.751006\pi$
$727$	−1.06853e13			−1.41868			−0.709338	+	0.704868i	$0.751006\pi$
$728$	−7.00258e11	+	3.33458e11i	−0.0923989	+	0.0439997i
$729$	1.94909e12			0.255598
$730$	3.46705e12	+	6.00510e12i	0.451863	+	0.782650i
$731$	3.94288e12	+	6.82927e12i	0.510723	+	0.884598i
$732$	−7.42040e12	+	1.28525e13i	−0.955273	+	1.65458i
$733$	−8.01109e11			−0.102500			−0.0512500	−	0.998686i	$-0.516321\pi$
$733$	−8.01109e11			−0.102500			−0.0512500	+	0.998686i	$0.516321\pi$
$734$	−3.85952e12	+	6.68488e12i	−0.490796	+	0.850083i
$735$	−1.46114e12	+	2.53077e12i	−0.184671	+	0.319860i
$736$	2.57455e11			0.0323408
$737$	−1.70278e11	+	2.94930e11i	−0.0212596	+	0.0368226i
$738$	3.70186e12	+	6.41181e12i	0.459374	+	0.795660i
$739$	−4.20810e12	−	7.28864e12i	−0.519022	−	0.898972i	−0.999756	−	0.0221057i	$-0.992963\pi$
$739$	−4.20810e12	−	7.28864e12i	−0.519022	−	0.898972i	0.480734	−	0.876867i	$-0.340370\pi$
$740$	−1.72952e13			−2.12023
$741$	−1.45192e12	−	9.99239e11i	−0.176913	−	0.121755i
$742$	1.47237e11			0.0178319
$743$	−7.56591e11	−	1.31045e12i	−0.0910775	−	0.157751i	0.816887	−	0.576797i	$-0.195698\pi$
$743$	−7.56591e11	−	1.31045e12i	−0.0910775	−	0.157751i	−0.907965	+	0.419046i	$0.862364\pi$
$744$	4.26283e12	+	7.38344e12i	0.510058	+	0.883447i
$745$	1.39958e12	−	2.42415e12i	0.166454	−	0.288308i
$746$	−1.34024e13			−1.58437
$747$	−1.15433e11	+	1.99936e11i	−0.0135640	+	0.0234935i
$748$	1.32433e13	−	2.29380e13i	1.54681	−	2.67916i
$749$	1.53012e11			0.0177647
$750$	−4.11071e12	+	7.11996e12i	−0.474397	+	0.821679i
$751$	−3.93516e12	−	6.81590e12i	−0.451422	−	0.781886i	0.547053	−	0.837098i	$-0.315750\pi$
$751$	−3.93516e12	−	6.81590e12i	−0.451422	−	0.781886i	−0.998475	+	0.0552123i	$0.982416\pi$
$752$	5.20765e12	+	9.01991e12i	0.593829	+	1.02854i
$753$	5.14106e12			0.582741
$754$	−2.16444e13	+	1.03069e13i	−2.43879	+	1.16134i
$755$	9.43869e12			1.05718
$756$	−4.77081e11	−	8.26328e11i	−0.0531183	−	0.0920035i
$757$	−7.99179e11	−	1.38422e12i	−0.0884531	−	0.153205i	0.818404	−	0.574643i	$-0.194859\pi$
$757$	−7.99179e11	−	1.38422e12i	−0.0884531	−	0.153205i	−0.906857	+	0.421438i	$0.861526\pi$
$758$	9.22857e12	−	1.59844e13i	1.01537	−	1.75867i
$759$	5.27308e12			0.576735
$760$	2.36743e12	−	4.10051e12i	0.257405	−	0.445838i
$761$	5.70048e11	−	9.87353e11i	0.0616142	−	0.106719i	−0.833573	−	0.552409i	$-0.813708\pi$
$761$	5.70048e11	−	9.87353e11i	0.0616142	−	0.106719i	0.895187	+	0.445691i	$0.147042\pi$
$762$	7.73446e12			0.831060
$763$	−1.96410e11	+	3.40193e11i	−0.0209799	+	0.0363383i
$764$	1.70398e13	+	2.95137e13i	1.80944	+	3.13404i
$765$	−3.04185e12	−	5.26864e12i	−0.321116	−	0.556189i
$766$	−1.01244e13			−1.06253
$767$	8.91263e12	−	4.24413e12i	0.929879	−	0.442802i
$768$	−9.85939e12			−1.02264
$769$	−1.64916e12	−	2.85643e12i	−0.170057	−	0.294548i	0.768383	−	0.639991i	$-0.221062\pi$
$769$	−1.64916e12	−	2.85643e12i	−0.170057	−	0.294548i	−0.938440	+	0.345443i	$0.887729\pi$
$770$	4.66887e11	+	8.08671e11i	0.0478634	+	0.0829018i
$771$	−2.80908e11	+	4.86547e11i	−0.0286299	+	0.0495884i
$772$	1.88836e13			1.91340
$773$	−2.85189e12	+	4.93962e12i	−0.287293	+	0.497606i	−0.973163	−	0.230118i	$-0.926089\pi$
$773$	−2.85189e12	+	4.93962e12i	−0.287293	+	0.497606i	0.685870	+	0.727725i	$0.259422\pi$
$774$	−5.35312e12	+	9.27187e12i	−0.536133	+	0.928610i
$775$	5.59655e12			0.557266
$776$	−6.19831e12	+	1.07358e13i	−0.613614	+	1.06281i
$777$	2.31164e11	+	4.00387e11i	0.0227523	+	0.0394081i
$778$	2.08394e12	+	3.60948e12i	0.203928	+	0.353213i
$779$	3.10101e12			0.301707
$780$	6.27917e12	+	4.32145e12i	0.607402	+	0.418026i
$781$	2.05317e13			1.97468
$782$	9.56695e12	+	1.65704e13i	0.914836	+	1.58454i
$783$	−7.33319e12	−	1.27015e13i	−0.697213	−	1.20761i
$784$	5.10071e12	−	8.83469e12i	0.482179	−	0.835158i
$785$	−7.29943e12			−0.686081
$786$	1.30291e12	−	2.25670e12i	0.121762	−	0.210898i
$787$	8.49468e11	−	1.47132e12i	0.0789333	−	0.136717i	−0.823857	−	0.566798i	$-0.808182\pi$
$787$	8.49468e11	−	1.47132e12i	0.0789333	−	0.136717i	0.902790	+	0.430082i	$0.141515\pi$
$788$	−1.35393e13			−1.25092
$789$	4.65451e12	−	8.06185e12i	0.427590	−	0.740607i
$790$	−4.28385e11	−	7.41984e11i	−0.0391302	−	0.0677755i
$791$	1.91995e11	+	3.32545e11i	0.0174379	+	0.0302034i
$792$	1.78826e13			1.61498
$793$	1.87773e13	−	8.94160e12i	1.68618	−	0.802945i
$794$	−1.74933e13			−1.56200
$795$	−3.59799e11	−	6.23190e11i	−0.0319454	−	0.0553310i
$796$	−1.22284e13	−	2.11802e13i	−1.07959	−	1.86991i
$797$	−9.39351e12	+	1.62700e13i	−0.824642	+	1.42832i	0.0775511	+	0.996988i	$0.475290\pi$
$797$	−9.39351e12	+	1.62700e13i	−0.824642	+	1.42832i	−0.902193	+	0.431333i	$0.858043\pi$
$798$	−2.54517e11			−0.0222180
$799$	8.56287e12	−	1.48313e13i	0.743291	−	1.28742i
$800$	−1.03040e11	+	1.78471e11i	−0.00889412	+	0.0154051i
$801$	−6.90194e12			−0.592413
$802$	−3.42601e12	+	5.93403e12i	−0.292418	+	0.506483i
$803$	5.48450e12	+	9.49942e12i	0.465497	+	0.806264i
$804$	2.00721e11	+	3.47659e11i	0.0169411	+	0.0293428i
$805$	−4.48897e11			−0.0376760
$806$	1.90027e12	−	2.39500e13i	0.158602	−	1.99893i
$807$	−1.09303e13			−0.907192
$808$	3.27420e12	+	5.67108e12i	0.270243	+	0.468074i
$809$	1.87088e12	+	3.24046e12i	0.153560	+	0.265973i	0.932534	−	0.361083i	$-0.117593\pi$
$809$	1.87088e12	+	3.24046e12i	0.153560	+	0.265973i	−0.778974	+	0.627056i	$0.784260\pi$
$810$	2.11095e12	−	3.65627e12i	0.172304	−	0.298439i
$811$	−1.00987e13			−0.819731			−0.409865	−	0.912146i	$-0.634424\pi$
$811$	−1.00987e13			−0.819731			−0.409865	+	0.912146i	$0.634424\pi$
$812$	−1.15186e12	+	1.99508e12i	−0.0929818	+	0.161049i
$813$	−3.27791e12	+	5.67750e12i	−0.263141	+	0.455774i
$814$	−4.11128e13			−3.28222
$815$	−5.39264e12	+	9.34033e12i	−0.428146	+	0.741571i
$816$	−3.81815e12	−	6.61324e12i	−0.301473	−	0.522166i
$817$	2.24213e12	+	3.88348e12i	0.176060	+	0.304945i
$818$	−1.00441e13			−0.784370
$819$	−4.48221e10	+	5.64913e11i	−0.00348108	+	0.0438737i
$820$	−1.34111e13			−1.03586
$821$	−6.28365e12	−	1.08836e13i	−0.482689	−	0.836043i	0.517113	−	0.855917i	$-0.327007\pi$
$821$	−6.28365e12	−	1.08836e13i	−0.482689	−	0.836043i	−0.999802	+	0.0198744i	$0.993673\pi$
$822$	−8.85537e12	−	1.53379e13i	−0.676524	−	1.17177i
$823$	−2.20563e12	+	3.82026e12i	−0.167584	+	0.290264i	−0.937570	−	0.347797i	$-0.886930\pi$
$823$	−2.20563e12	+	3.82026e12i	−0.167584	+	0.290264i	0.769986	+	0.638061i	$0.220263\pi$
$824$	−6.99626e12			−0.528680
$825$	−2.11043e12	+	3.65537e12i	−0.158609	+	0.274719i
$826$	7.12744e11	−	1.23451e12i	0.0532750	−	0.0922750i
$827$	2.07294e13			1.54103			0.770516	−	0.637420i	$-0.219998\pi$
$827$	2.07294e13			1.54103			0.770516	+	0.637420i	$0.219998\pi$
$828$	−8.64356e12	+	1.49711e13i	−0.639081	+	1.10692i
$829$	9.11723e12	+	1.57915e13i	0.670451	+	1.16126i	0.977776	+	0.209651i	$0.0672329\pi$
$829$	9.11723e12	+	1.57915e13i	0.670451	+	1.16126i	−0.307325	+	0.951605i	$0.599434\pi$
$830$	−3.14208e11	−	5.44224e11i	−0.0229808	−	0.0398040i
$831$	−5.43821e12			−0.395596
$832$	1.17481e13	+	8.08526e12i	0.849986	+	0.584977i
$833$	−1.67741e13			−1.20708
$834$	8.38611e12	+	1.45252e13i	0.600224	+	1.03962i
$835$	6.29643e12	+	1.09057e13i	0.448234	+	0.776365i
$836$	7.53080e12	−	1.30437e13i	0.533228	−	0.923577i
$837$	1.46983e13			1.03515
$838$	2.26405e13	−	3.92146e13i	1.58595	−	2.74694i
$839$	−7.74314e12	+	1.34115e13i	−0.539496	+	0.934435i	0.459435	+	0.888211i	$0.348052\pi$
$839$	−7.74314e12	+	1.34115e13i	−0.539496	+	0.934435i	−0.998931	+	0.0462232i	$0.985281\pi$
$840$	5.47382e11			0.0379344
$841$	−1.04516e13	+	1.81028e13i	−0.720448	+	1.24785i
$842$	−8.39115e12	−	1.45339e13i	−0.575330	−	0.996501i
$843$	−3.60830e12	−	6.24977e12i	−0.246082	−	0.426226i
$844$	3.41416e13			2.31602
$845$	−3.81537e12	−	9.97740e12i	−0.257444	−	0.673228i
$846$	2.32510e13			1.56054
$847$	2.90426e11	+	5.03032e11i	0.0193892	+	0.0335831i
$848$	1.25603e12	+	2.17550e12i	0.0834098	+	0.144470i
$849$	3.92661e12	−	6.80108e12i	0.259378	−	0.449256i
$850$	−1.53158e13			−1.00636
$851$	9.88216e12	−	1.71164e13i	0.645906	−	1.11874i
$852$	1.21013e13	−	2.09600e13i	0.786779	−	1.36274i
$853$	−1.90934e13			−1.23485			−0.617423	−	0.786631i	$-0.711823\pi$
$853$	−1.90934e13			−1.23485			−0.617423	+	0.786631i	$0.711823\pi$
$854$	1.50162e12	−	2.60088e12i	0.0966050	−	0.167325i
$855$	−1.72975e12	−	2.99602e12i	−0.110697	−	0.191733i
$856$	3.98817e12	+	6.90771e12i	0.253888	+	0.439746i
$857$	2.74745e12			0.173987			0.0869934	−	0.996209i	$-0.472274\pi$
$857$	2.74745e12			0.173987			0.0869934	+	0.996209i	$0.472274\pi$
$858$	1.49263e13	+	1.02726e13i	0.940286	+	0.647124i
$859$	2.86786e13			1.79717			0.898585	−	0.438800i	$-0.144596\pi$
$859$	2.86786e13			1.79717			0.898585	+	0.438800i	$0.144596\pi$
$860$	−9.69661e12	−	1.67950e13i	−0.604473	−	1.04698i
$861$	1.79249e11	+	3.10468e11i	0.0111158	+	0.0192532i
$862$	−1.83129e13	+	3.17190e13i	−1.12973	+	1.95675i
$863$	−8.55263e12			−0.524869			−0.262435	−	0.964950i	$-0.584525\pi$
$863$	−8.55263e12			−0.524869			−0.262435	+	0.964950i	$0.584525\pi$
$864$	−2.70616e11	+	4.68721e11i	−0.0165212	+	0.0286156i
$865$	1.10932e12	−	1.92140e12i	0.0673728	−	0.116693i
$866$	2.56933e13			1.55235
$867$	−2.00010e12	+	3.46428e12i	−0.120217	+	0.208222i
$868$	−1.15437e12	−	1.99942e12i	−0.0690247	−	0.119554i
$869$	−6.77658e11	−	1.17374e12i	−0.0403108	−	0.0698204i
$870$	1.69191e13			1.00125
$871$	4.44964e10	−	5.60809e11i	0.00261965	−	0.0330167i
$872$	−2.04772e13			−1.19935
$873$	4.52876e12	+	7.84405e12i	0.263886	+	0.457063i
$874$	5.44026e12	+	9.42281e12i	0.315368	+	0.546234i
$875$	5.53574e11	−	9.58819e11i	0.0319257	−	0.0552968i
$876$	1.29301e13			0.741880
$877$	−1.55075e13	+	2.68598e13i	−0.885207	+	1.53322i	−0.0397298	+	0.999210i	$0.512650\pi$
$877$	−1.55075e13	+	2.68598e13i	−0.885207	+	1.53322i	−0.845477	+	0.534012i	$0.820684\pi$
$878$	−9.71651e12	+	1.68295e13i	−0.551804	+	0.955753i
$879$	3.94017e12			0.222621
$880$	−7.96570e12	+	1.37970e13i	−0.447767	+	0.775555i
$881$	9.67042e12	+	1.67497e13i	0.540822	+	0.936730i	0.998857	+	0.0477965i	$0.0152199\pi$
$881$	9.67042e12	+	1.67497e13i	0.540822	+	0.936730i	−0.458036	+	0.888934i	$0.651447\pi$
$882$	−1.13868e13	−	1.97225e13i	−0.633567	−	1.09737i
$883$	−2.02565e13			−1.12135			−0.560675	−	0.828036i	$-0.689458\pi$
$883$	−2.02565e13			−1.12135			−0.560675	+	0.828036i	$0.689458\pi$
$884$	−3.46068e12	+	4.36166e13i	−0.190602	+	2.40224i
$885$	−6.96687e12			−0.381762
$886$	3.04651e12	+	5.27671e12i	0.166093	+	0.287681i
$887$	−9.35870e12	−	1.62098e13i	−0.507644	−	0.879266i	−0.999961	−	0.00884940i	$-0.997183\pi$
$887$	−9.35870e12	−	1.62098e13i	−0.507644	−	0.879266i	0.492317	−	0.870416i	$-0.336150\pi$
$888$	−1.20502e13	+	2.08716e13i	−0.650336	+	1.12641i
$889$	−1.04157e12			−0.0559282
$890$	9.39351e12	−	1.62700e13i	0.501849	−	0.869228i
$891$	3.33930e12	−	5.78383e12i	0.177503	−	0.307444i
$892$	2.87919e13			1.52275
$893$	4.86929e12	−	8.43385e12i	0.256232	−	0.443807i
$894$	−3.92179e12	−	6.79274e12i	−0.205336	−	0.355653i
$895$	−8.92481e12	−	1.54582e13i	−0.464938	−	0.805296i
$896$	2.01667e12			0.104532
$897$	−7.86456e12	+	3.74505e12i	−0.405610	+	0.193149i
$898$	−8.45851e11			−0.0434061
$899$	−1.77437e13	−	3.07330e13i	−0.905995	−	1.56923i
$900$	−6.91878e12	−	1.19837e13i	−0.351510	−	0.608834i
$901$	2.06527e12	−	3.57714e12i	0.104403	−	0.180832i
$902$	−3.18797e13			−1.60356
$903$	−2.59205e11	+	4.48956e11i	−0.0129732	+	0.0224703i
$904$	−1.00084e13	+	1.73351e13i	−0.498434	+	0.863314i
$905$	1.22597e13			0.607521
$906$	1.32242e13	−	2.29049e13i	0.652065	−	1.12941i
$907$	3.47024e11	+	6.01063e11i	0.0170266	+	0.0294909i	0.874413	−	0.485182i	$-0.161247\pi$
$907$	3.47024e11	+	6.01063e11i	0.0170266	+	0.0294909i	−0.857387	+	0.514673i	$0.827913\pi$
$908$	1.80582e13	+	3.12777e13i	0.881633	+	1.52703i
$909$	4.78456e12			0.232437
$910$	−1.27068e12	−	8.74505e11i	−0.0614255	−	0.0422742i
$911$	1.72255e13			0.828587			0.414293	−	0.910143i	$-0.364029\pi$
$911$	1.72255e13			0.828587			0.414293	+	0.910143i	$0.364029\pi$
$912$	−2.17120e12	−	3.76063e12i	−0.103926	−	0.180005i
$913$	−4.97043e11	−	8.60904e11i	−0.0236742	−	0.0410049i
$914$	3.10414e13	−	5.37653e13i	1.47124	−	2.54826i
$915$	−1.46779e13			−0.692260
$916$	−8.25705e12	+	1.43016e13i	−0.387521	+	0.671206i
$917$	−1.75458e11	+	3.03902e11i	−0.00819427	+	0.0141929i
$918$	−4.02241e13			−1.86936
$919$	1.65859e13	−	2.87276e13i	0.767041	−	1.32855i	−0.172120	−	0.985076i	$-0.555062\pi$
$919$	1.65859e13	−	2.87276e13i	0.767041	−	1.32855i	0.939161	−	0.343478i	$-0.111605\pi$
$920$	−1.17002e13	−	2.02653e13i	−0.538453	−	0.932628i
$921$	−4.13005e12	−	7.15346e12i	−0.189142	−	0.327603i
$922$	2.33729e13			1.06518
$923$	−3.06222e13	+	1.45821e13i	−1.38876	+	0.661320i
$924$	1.74122e12			0.0785832
$925$	7.91022e12	+	1.37009e13i	0.355264	+	0.615335i
$926$	2.99712e13	+	5.19116e13i	1.33954	+	2.32014i
$927$	−2.55589e12	+	4.42693e12i	−0.113680	+	0.196899i
$928$	1.30675e12			0.0578397
$929$	1.05551e13	−	1.82820e13i	0.464934	−	0.805290i	−0.534264	−	0.845318i	$-0.679411\pi$
$929$	1.05551e13	−	1.82820e13i	0.464934	−	0.805290i	0.999199	+	0.0400275i	$0.0127446\pi$
$930$	−8.47796e12	+	1.46843e13i	−0.371636	+	0.643693i
$931$	−9.53859e12			−0.416112
$932$	3.91740e13	−	6.78514e13i	1.70070	−	2.94569i
$933$	2.72871e12	+	4.72627e12i	0.117894	+	0.204198i
$934$	−7.14890e12	−	1.23823e13i	−0.307382	−	0.532401i
$935$	2.61958e13			1.12093
$936$	−2.66711e13	+	1.27006e13i	−1.13580	+	0.540858i
$937$	−5.73180e12			−0.242920			−0.121460	−	0.992596i	$-0.538758\pi$
$937$	−5.73180e12			−0.242920			−0.121460	+	0.992596i	$0.538758\pi$
$938$	−4.06187e10	−	7.03536e10i	−0.00171322	−	0.00296738i
$939$	−6.14444e12	−	1.06425e13i	−0.257921	−	0.446733i
$940$	−2.10584e13	+	3.64742e13i	−0.879731	+	1.52374i
$941$	−2.02770e13			−0.843044			−0.421522	−	0.906818i	$-0.638504\pi$
$941$	−2.02770e13			−0.843044			−0.421522	+	0.906818i	$0.638504\pi$
$942$	−1.02269e13	+	1.77135e13i	−0.423171	+	0.732954i
$943$	7.66283e12	−	1.32724e13i	0.315563	−	0.546571i
$944$	2.43207e13			0.996787
$945$	4.71844e11	−	8.17259e11i	0.0192467	−	0.0333362i
$946$	−2.30500e13	−	3.99237e13i	−0.935751	−	1.62077i
$947$	1.94064e13	+	3.36128e13i	0.784096	+	1.35809i	0.929538	+	0.368727i	$0.120206\pi$
$947$	1.94064e13	+	3.36128e13i	0.784096	+	1.35809i	−0.145442	+	0.989367i	$0.546460\pi$
$948$	−1.59763e12			−0.0642449
$949$	−1.49266e13	−	1.02728e13i	−0.597396	−	0.411140i
$950$	−8.70936e12			−0.346921
$951$	1.79351e11	+	3.10646e11i	0.00711037	+	0.0123155i
$952$	1.57100e12	+	2.72105e12i	0.0619883	+	0.107367i
$953$	−1.64511e13	+	2.84941e13i	−0.646066	+	1.11902i	0.337989	+	0.941150i	$0.390253\pi$
$953$	−1.64511e13	+	2.84941e13i	−0.646066	+	1.11902i	−0.984054	+	0.177868i	$0.943080\pi$
$954$	5.60788e12			0.219195
$955$	−1.68527e13	+	2.91898e13i	−0.655625	+	1.13558i
$956$	−9.54598e12	+	1.65341e13i	−0.369624	+	0.640207i
$957$	2.67642e13			1.03146
$958$	4.64590e12	−	8.04693e12i	0.178207	−	0.308663i
$959$	1.19252e12	+	2.06550e12i	0.0455283	+	0.0788574i
$960$	−5.03252e12	−	8.71658e12i	−0.191234	−	0.331227i
$961$	9.12496e12			0.345124
$962$	6.13179e13	−	2.91992e13i	2.30834	−	1.09921i
$963$	5.82787e12			0.218369
$964$	−3.05811e13	−	5.29681e13i	−1.14053	−	1.97546i
$965$	9.33816e12	+	1.61742e13i	0.346648	+	0.600412i
$966$	−6.28930e11	+	1.08934e12i	−0.0232384	+	0.0402500i
$967$	−1.49312e13			−0.549130			−0.274565	−	0.961569i	$-0.588534\pi$
$967$	−1.49312e13			−0.549130			−0.274565	+	0.961569i	$0.588534\pi$
$968$	−1.51395e13	+	2.62224e13i	−0.554208	+	0.959916i
$969$	−3.57007e12	+	6.18355e12i	−0.130083	+	0.225310i
$970$	−2.46545e13			−0.894178
$971$	6.92253e12	−	1.19902e13i	0.249907	−	0.432851i	−0.713593	−	0.700561i	$-0.752933\pi$
$971$	6.92253e12	−	1.19902e13i	0.249907	−	0.432851i	0.963500	+	0.267709i	$0.0862667\pi$
$972$	−2.86408e13	−	4.96073e13i	−1.02917	−	1.78257i
$973$	−1.12933e12	−	1.95605e12i	−0.0403935	−	0.0699636i
$974$	−5.69530e13			−2.02769
$975$	5.51491e11	−	6.95070e12i	0.0195442	−	0.246324i
$976$	5.12392e13			1.80750
$977$	1.90974e11	+	3.30776e11i	0.00670576	+	0.0116147i	0.869359	−	0.494181i	$-0.164532\pi$
$977$	1.90974e11	+	3.30776e11i	0.00670576	+	0.0116147i	−0.862653	+	0.505796i	$0.831199\pi$
$978$	1.51108e13	+	2.61727e13i	0.528157	+	0.914794i
$979$	1.48595e13	−	2.57375e13i	0.516991	−	0.895454i
$980$	4.12519e13			1.42865
$981$	−7.48079e12	+	1.29571e13i	−0.257891	+	0.446681i
$982$	−3.23343e13	+	5.60047e13i	−1.10959	+	1.92186i
$983$	−2.84763e12			−0.0972733			−0.0486366	−	0.998817i	$-0.515488\pi$
$983$	−2.84763e12			−0.0972733			−0.0486366	+	0.998817i	$0.515488\pi$
$984$	−9.34400e12	+	1.61843e13i	−0.317728	+	0.550320i
$985$	−6.69535e12	−	1.15967e13i	−0.226626	−	0.392528i
$986$	4.85584e13	+	8.41056e13i	1.63613	+	2.83386i
$987$	1.12584e12			0.0377617
$988$	−1.96792e12	+	2.48027e13i	−0.0657055	+	0.828117i
$989$	2.21618e13			0.736584
$990$	1.77826e13	+	3.08003e13i	0.588351	+	1.01905i
$991$	−2.53534e12	−	4.39134e12i	−0.0835035	−	0.144632i	0.821249	−	0.570570i	$-0.193278\pi$
$991$	−2.53534e12	−	4.39134e12i	−0.0835035	−	0.144632i	−0.904753	+	0.425938i	$0.859944\pi$
$992$	−6.54794e11	+	1.13414e12i	−0.0214685	+	0.0371846i
$993$	1.44356e13			0.471156
$994$	−2.44886e12	+	4.24155e12i	−0.0795655	+	0.137812i
$995$	1.20942e13	−	2.09477e13i	0.391176	−	0.677537i
$996$	−1.17182e12			−0.0377305
$997$	−2.76685e13	+	4.79233e13i	−0.886866	+	1.53610i	−0.0433055	+	0.999062i	$0.513789\pi$
$997$	−2.76685e13	+	4.79233e13i	−0.886866	+	1.53610i	−0.843560	+	0.537035i	$0.819544\pi$
$998$	−1.46345e13	−	2.53477e13i	−0.466972	−	0.808820i
$999$	2.07747e13	+	3.59828e13i	0.659918	+	1.14301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.10.c.a.3.1	✓	18
13.3	even	3		169.10.a.c.1.9		9
13.9	even	3	inner	13.10.c.a.9.1	yes	18
13.10	even	6		169.10.a.d.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.c.a.3.1	✓	18	1.1	even	1	trivial
13.10.c.a.9.1	yes	18	13.9	even	3	inner
169.10.a.c.1.9		9	13.3	even	3
169.10.a.d.1.1		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+(-19.5607 - 33.8802i) q^{2} +(-36.0748 - 62.4834i) q^{3} +(-509.244 + 882.037i) q^{4} -1007.31 q^{5} +(-1411.30 + 2444.44i) q^{6} +(190.054 - 329.184i) q^{7} +19814.6 q^{8} +(7238.71 - 12537.8i) q^{9} +(19703.7 + 34127.8i) q^{10} +(31169.2 + 53986.6i) q^{11} +73483.6 q^{12} +(-84829.8 - 58381.6i) q^{13} -14870.4 q^{14} +(36338.5 + 62940.2i) q^{15} +(-126855. - 219718. i) q^{16} +(-208585. + 361280. i) q^{17} -566378. q^{18} +(-118612. + 205442. i) q^{19} +(512967. - 888485. i) q^{20} -27424.7 q^{21} +(1.21938e6 - 2.11203e6i) q^{22} +(586199. + 1.01533e6i) q^{23} +(-714807. - 1.23808e6i) q^{24} -938451. q^{25} +(-318645. + 4.01603e6i) q^{26} -2.46466e6 q^{27} +(193568. + 335270. i) q^{28} +(2.97533e6 + 5.15343e6i) q^{29} +(1.42162e6 - 2.46231e6i) q^{30} -5.96360e6 q^{31} +(109798. - 190176. i) q^{32} +(2.24884e6 - 3.89511e6i) q^{33} +1.63203e7 q^{34} +(-191444. + 331590. i) q^{35} +(7.37255e6 + 1.27696e7i) q^{36} +(-8.42902e6 - 1.45995e7i) q^{37} +9.28057e6 q^{38} +(-587661. + 7.40656e6i) q^{39} -1.99594e7 q^{40} +(-6.53603e6 - 1.13207e7i) q^{41} +(536448. + 929155. i) q^{42} +(9.45149e6 - 1.63705e7i) q^{43} -6.34909e7 q^{44} +(-7.29163e6 + 1.26295e7i) q^{45} +(2.29330e7 - 3.97211e7i) q^{46} -4.10521e7 q^{47} +(-9.15251e6 + 1.58526e7i) q^{48} +(2.01046e7 + 3.48221e7i) q^{49} +(1.83568e7 + 3.17949e7i) q^{50} +3.00987e7 q^{51} +(9.46938e7 - 4.50925e7i) q^{52} -9.90131e6 q^{53} +(4.82106e7 + 8.35032e7i) q^{54} +(-3.13970e7 - 5.43812e7i) q^{55} +(3.76585e6 - 6.52264e6i) q^{56} +1.71157e7 q^{57} +(1.16399e8 - 2.01610e8i) q^{58} +(-4.79303e7 + 8.30178e7i) q^{59} -7.40208e7 q^{60} +(-1.00980e8 + 1.74903e8i) q^{61} +(1.16652e8 + 2.02048e8i) q^{62} +(-2.75150e6 - 4.76574e6i) q^{63} -1.38490e8 q^{64} +(8.54499e7 + 5.88083e7i) q^{65} -1.75956e8 q^{66} +(2.73151e6 + 4.73111e6i) q^{67} +(-2.12442e8 - 3.67960e8i) q^{68} +(4.22941e7 - 7.32554e7i) q^{69} +1.49791e7 q^{70} +(1.64680e8 - 2.85234e8i) q^{71} +(1.43432e8 - 2.48432e8i) q^{72} +1.75959e8 q^{73} +(-3.29755e8 + 5.71153e8i) q^{74} +(3.38545e7 + 5.86377e7i) q^{75} +(-1.20805e8 - 2.09241e8i) q^{76} +2.36954e7 q^{77} +(2.62431e8 - 1.24968e8i) q^{78} -2.17413e7 q^{79} +(1.27782e8 + 2.21325e8i) q^{80} +(-5.35673e7 - 9.27813e7i) q^{81} +(-2.55699e8 + 4.42884e8i) q^{82} -1.59466e7 q^{83} +(1.39659e7 - 2.41896e7i) q^{84} +(2.10110e8 - 3.63921e8i) q^{85} -7.39512e8 q^{86} +(2.14669e8 - 3.71818e8i) q^{87} +(6.17604e8 + 1.06972e9i) q^{88} +(-2.38369e8 - 4.12867e8i) q^{89} +5.70518e8 q^{90} +(-3.53406e7 + 1.68289e7i) q^{91} -1.19407e9 q^{92} +(2.15136e8 + 3.72626e8i) q^{93} +(8.03010e8 + 1.39085e9i) q^{94} +(1.19479e8 - 2.06944e8i) q^{95} -1.58438e7 q^{96} +(-3.12816e8 + 5.41812e8i) q^{97} +(7.86520e8 - 1.36229e9i) q^{98} +9.02499e8 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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