LMFDB - Embedded newform 13.10.c.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,10,Mod(3,13)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("13.3");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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			3.8
Root			$-16.2753 + 28.1897i$ of defining polynomial
Character	$\chi$	$=$	13.3
Dual form			13.10.c.a.9.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(17.2753 + 29.9218i) q^{2} +(-28.8997 - 50.0557i) q^{3} +(-340.875 + 590.413i) q^{4} -2017.22 q^{5} +(998.503 - 1729.46i) q^{6} +(-5878.83 + 10182.4i) q^{7} -5865.01 q^{8} +(8171.12 - 14152.8i) q^{9} +(-34848.1 - 60358.7i) q^{10} +(-1019.13 - 1765.19i) q^{11} +39404.7 q^{12} +(43384.4 + 93393.2i) q^{13} -406235. q^{14} +(58296.8 + 100973. i) q^{15} +(73208.1 + 126800. i) q^{16} +(82491.5 - 142879. i) q^{17} +564636. q^{18} +(-279239. + 483656. i) q^{19} +(687619. - 1.19099e6i) q^{20} +679585. q^{21} +(35211.8 - 60988.7i) q^{22} +(143180. + 247996. i) q^{23} +(169497. + 293577. i) q^{24} +2.11603e6 q^{25} +(-2.04501e6 + 2.91154e6i) q^{26} -2.08223e6 q^{27} +(-4.00790e6 - 6.94188e6i) q^{28} +(868857. + 1.50490e6i) q^{29} +(-2.01420e6 + 3.48869e6i) q^{30} -3.33293e6 q^{31} +(-4.03083e6 + 6.98161e6i) q^{32} +(-58905.3 + 102027. i) q^{33} +5.70028e6 q^{34} +(1.18589e7 - 2.05402e7i) q^{35} +(5.57067e6 + 9.64868e6i) q^{36} +(-8.01209e6 - 1.38773e7i) q^{37} -1.92958e7 q^{38} +(3.42107e6 - 4.87067e6i) q^{39} +1.18310e7 q^{40} +(1.41678e7 + 2.45393e7i) q^{41} +(1.17401e7 + 2.03344e7i) q^{42} +(8.28411e6 - 1.43485e7i) q^{43} +1.38959e6 q^{44} +(-1.64829e7 + 2.85492e7i) q^{45} +(-4.94698e6 + 8.56842e6i) q^{46} +2.16117e7 q^{47} +(4.23138e6 - 7.32897e6i) q^{48} +(-4.89445e7 - 8.47743e7i) q^{49} +(3.65552e7 + 6.33155e7i) q^{50} -9.53590e6 q^{51} +(-6.99293e7 - 6.22072e6i) q^{52} +7.19649e7 q^{53} +(-3.59713e7 - 6.23042e7i) q^{54} +(2.05581e6 + 3.56077e6i) q^{55} +(3.44794e7 - 5.97200e7i) q^{56} +3.22796e7 q^{57} +(-3.00196e7 + 5.19955e7i) q^{58} +(-9.09421e6 + 1.57516e7i) q^{59} -7.94878e7 q^{60} +(-4.77195e7 + 8.26527e7i) q^{61} +(-5.75775e7 - 9.97272e7i) q^{62} +(9.60732e7 + 1.66404e8i) q^{63} -2.03571e8 q^{64} +(-8.75156e7 - 1.88394e8i) q^{65} -4.07044e6 q^{66} +(4.24441e7 + 7.35153e7i) q^{67} +(5.62386e7 + 9.74082e7i) q^{68} +(8.27572e6 - 1.43340e7i) q^{69} +8.19464e8 q^{70} +(-1.81561e8 + 3.14472e8i) q^{71} +(-4.79237e7 + 8.30062e7i) q^{72} -3.37404e7 q^{73} +(2.76823e8 - 4.79472e8i) q^{74} +(-6.11526e7 - 1.05919e8i) q^{75} +(-1.90371e8 - 3.29733e8i) q^{76} +2.39653e7 q^{77} +(2.04839e8 + 1.82219e7i) q^{78} +3.19686e8 q^{79} +(-1.47677e8 - 2.55783e8i) q^{80} +(-1.00656e8 - 1.74342e8i) q^{81} +(-4.89507e8 + 8.47851e8i) q^{82} -1.88466e8 q^{83} +(-2.31654e8 + 4.01236e8i) q^{84} +(-1.66403e8 + 2.88219e8i) q^{85} +5.72443e8 q^{86} +(5.02193e7 - 8.69825e7i) q^{87} +(5.97723e6 + 1.03529e7i) q^{88} +(-1.25885e8 - 2.18039e8i) q^{89} -1.13899e9 q^{90} +(-1.20602e9 - 1.07284e8i) q^{91} -1.95227e8 q^{92} +(9.63205e7 + 1.66832e8i) q^{93} +(3.73349e8 + 6.46659e8i) q^{94} +(5.63285e8 - 9.75638e8i) q^{95} +4.65959e8 q^{96} +(1.09677e8 - 1.89966e8i) q^{97} +(1.69107e9 - 2.92901e9i) q^{98} -3.33099e7 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 $

$2$	17.2753	+	29.9218i	0.763470	+	1.32237i	0.941052	+	0.338262i	$0.109839\pi$
$2$	17.2753	+	29.9218i	0.763470	+	1.32237i	−0.177582	+	0.984106i	$0.556828\pi$
$3$	−28.8997	−	50.0557i	−0.205990	−	0.356786i	0.744457	−	0.667670i	$-0.232708\pi$
$3$	−28.8997	−	50.0557i	−0.205990	−	0.356786i	−0.950448	+	0.310884i	$0.899375\pi$
$4$	−340.875	+	590.413i	−0.665772	+	1.15315i
$5$	−2017.22			−1.44340			−0.721701	−	0.692205i	$-0.756639\pi$
$5$	−2017.22			−1.44340			−0.721701	+	0.692205i	$0.756639\pi$
$6$	998.503	−	1729.46i	0.314535	−	0.544790i
$7$	−5878.83	+	10182.4i	−0.925443	+	1.60291i	−0.134596	+	0.990901i	$0.542974\pi$
$7$	−5878.83	+	10182.4i	−0.925443	+	1.60291i	−0.790847	+	0.612014i	$0.790360\pi$
$8$	−5865.01			−0.506248
$9$	8171.12	−	14152.8i	0.415136	−	0.719036i
$10$	−34848.1	−	60358.7i	−1.10199	−	1.90871i
$11$	−1019.13	−	1765.19i	−0.0209877	−	0.0363517i	0.855341	−	0.518066i	$-0.173348\pi$
$11$	−1019.13	−	1765.19i	−0.0209877	−	0.0363517i	−0.876328	+	0.481714i	$0.840014\pi$
$12$	39404.7			0.548571
$13$	43384.4	+	93393.2i	0.421297	+	0.906923i
$13$	43384.4	+	93393.2i	0.421297	+	0.906923i
$14$	−406235.			−2.82619
$15$	58296.8	+	100973.i	0.297327	+	0.514985i
$16$	73208.1	+	126800.i	0.279267	+	0.483705i
$17$	82491.5	−	142879.i	0.239546	−	0.414906i	−0.721038	−	0.692895i	$-0.756335\pi$
$17$	82491.5	−	142879.i	0.239546	−	0.414906i	0.960584	+	0.277990i	$0.0896681\pi$
$18$	564636.			1.26777
$19$	−279239.	+	483656.i	−0.491569	+	0.851423i	−0.999953	−	0.00970791i	$-0.996910\pi$
$19$	−279239.	+	483656.i	−0.491569	+	0.851423i	0.508384	+	0.861131i	$0.330243\pi$
$20$	687619.	−	1.19099e6i	0.960977	−	1.66446i
$21$	679585.			0.762530
$22$	35211.8	−	60988.7i	0.0320469	−	0.0555069i
$23$	143180.	+	247996.i	0.106686	+	0.184786i	0.914426	−	0.404753i	$-0.132643\pi$
$23$	143180.	+	247996.i	0.106686	+	0.184786i	−0.807740	+	0.589539i	$0.799309\pi$
$24$	169497.	+	293577.i	0.104282	+	0.180622i
$25$	2.11603e6			1.08341
$26$	−2.04501e6	+	2.91154e6i	−0.877638	+	1.24952i
$27$	−2.08223e6			−0.754037
$28$	−4.00790e6	−	6.94188e6i	−1.23227	−	2.13435i
$29$	868857.	+	1.50490e6i	0.228117	+	0.395110i	0.957250	−	0.289262i	$-0.0934098\pi$
$29$	868857.	+	1.50490e6i	0.228117	+	0.395110i	−0.729133	+	0.684372i	$0.760077\pi$
$30$	−2.01420e6	+	3.48869e6i	−0.454000	+	0.786351i
$31$	−3.33293e6			−0.648184			−0.324092	−	0.946026i	$-0.605059\pi$
$31$	−3.33293e6			−0.648184			−0.324092	+	0.946026i	$0.605059\pi$
$32$	−4.03083e6	+	6.98161e6i	−0.679548	+	1.17701i
$33$	−58905.3	+	102027.i	−0.00864652	+	0.0149762i
$34$	5.70028e6			0.731545
$35$	1.18589e7	−	2.05402e7i	1.33579	−	2.31365i
$36$	5.57067e6	+	9.64868e6i	0.552772	+	0.957429i
$37$	−8.01209e6	−	1.38773e7i	−0.702810	−	1.21730i	−0.967476	−	0.252963i	$-0.918595\pi$
$37$	−8.01209e6	−	1.38773e7i	−0.702810	−	1.21730i	0.264666	−	0.964340i	$-0.414738\pi$
$38$	−1.92958e7			−1.50119
$39$	3.42107e6	−	4.87067e6i	0.236794	−	0.337130i
$40$	1.18310e7			0.730720
$41$	1.41678e7	+	2.45393e7i	0.783023	+	1.35624i	0.930173	+	0.367122i	$0.119657\pi$
$41$	1.41678e7	+	2.45393e7i	0.783023	+	1.35624i	−0.147149	+	0.989114i	$0.547010\pi$
$42$	1.17401e7	+	2.03344e7i	0.582168	+	1.00834i
$43$	8.28411e6	−	1.43485e7i	0.369520	−	0.640027i	−0.619971	−	0.784625i	$-0.712856\pi$
$43$	8.28411e6	−	1.43485e7i	0.369520	−	0.640027i	0.989490	+	0.144598i	$0.0461889\pi$
$44$	1.38959e6			0.0558921
$45$	−1.64829e7	+	2.85492e7i	−0.599208	+	1.03786i
$46$	−4.94698e6	+	8.56842e6i	−0.162903	+	0.282157i
$47$	2.16117e7			0.646023			0.323011	−	0.946395i	$-0.395305\pi$
$47$	2.16117e7			0.646023			0.323011	+	0.946395i	$0.395305\pi$
$48$	4.23138e6	−	7.32897e6i	0.115053	−	0.199277i
$49$	−4.89445e7	−	8.47743e7i	−1.21289	−	2.10079i
$50$	3.65552e7	+	6.33155e7i	0.827150	+	1.43267i
$51$	−9.53590e6			−0.197377
$52$	−6.99293e7	−	6.22072e6i	−1.32631	−	0.117985i
$53$	7.19649e7			1.25279			0.626397	−	0.779504i	$-0.284529\pi$
$53$	7.19649e7			1.25279			0.626397	+	0.779504i	$0.284529\pi$
$54$	−3.59713e7	−	6.23042e7i	−0.575684	−	0.997115i
$55$	2.05581e6	+	3.56077e6i	0.0302937	+	0.0524702i
$56$	3.44794e7	−	5.97200e7i	0.468504	−	0.811473i
$57$	3.22796e7			0.405034
$58$	−3.00196e7	+	5.19955e7i	−0.348321	+	0.603309i
$59$	−9.09421e6	+	1.57516e7i	−0.0977082	+	0.169236i	−0.910736	−	0.412990i	$-0.864485\pi$
$59$	−9.09421e6	+	1.57516e7i	−0.0977082	+	0.169236i	0.813027	+	0.582225i	$0.197818\pi$
$60$	−7.94878e7			−0.791808
$61$	−4.77195e7	+	8.26527e7i	−0.441278	+	0.764315i	−0.997785	−	0.0665276i	$-0.978808\pi$
$61$	−4.77195e7	+	8.26527e7i	−0.441278	+	0.764315i	0.556507	+	0.830843i	$0.312141\pi$
$62$	−5.75775e7	−	9.97272e7i	−0.494869	−	0.857138i
$63$	9.60732e7	+	1.66404e8i	0.768369	+	1.33085i
$64$	−2.03571e8			−1.51672
$65$	−8.75156e7	−	1.88394e8i	−0.608101	−	1.30905i
$66$	−4.07044e6			−0.0264054
$67$	4.24441e7	+	7.35153e7i	0.257324	+	0.445698i	0.965524	−	0.260313i	$-0.0838259\pi$
$67$	4.24441e7	+	7.35153e7i	0.257324	+	0.445698i	−0.708200	+	0.706012i	$0.750493\pi$
$68$	5.62386e7	+	9.74082e7i	0.318966	+	0.552466i
$69$	8.27572e6	−	1.43340e7i	0.0439526	−	0.0761282i
$70$	8.19464e8			4.07933
$71$	−1.81561e8	+	3.14472e8i	−0.847929	+	1.46866i	0.0351244	+	0.999383i	$0.488817\pi$
$71$	−1.81561e8	+	3.14472e8i	−0.847929	+	1.46866i	−0.883053	+	0.469273i	$0.844516\pi$
$72$	−4.79237e7	+	8.30062e7i	−0.210162	+	0.364011i
$73$	−3.37404e7			−0.139058			−0.0695292	−	0.997580i	$-0.522150\pi$
$73$	−3.37404e7			−0.139058			−0.0695292	+	0.997580i	$0.522150\pi$
$74$	2.76823e8	−	4.79472e8i	1.07315	−	1.85875i
$75$	−6.11526e7	−	1.05919e8i	−0.223172	−	0.386545i
$76$	−1.90371e8	−	3.29733e8i	−0.654546	−	1.13371i
$77$	2.39653e7			0.0776916
$78$	2.04839e8	+	1.82219e7i	0.626595	+	0.0557403i
$79$	3.19686e8			0.923426			0.461713	−	0.887029i	$-0.347235\pi$
$79$	3.19686e8			0.923426			0.461713	+	0.887029i	$0.347235\pi$
$80$	−1.47677e8	−	2.55783e8i	−0.403094	−	0.698180i
$81$	−1.00656e8	−	1.74342e8i	−0.259812	−	0.450007i
$82$	−4.89507e8	+	8.47851e8i	−1.19563	+	2.07089i
$83$	−1.88466e8			−0.435895			−0.217947	−	0.975961i	$-0.569936\pi$
$83$	−1.88466e8			−0.435895			−0.217947	+	0.975961i	$0.569936\pi$
$84$	−2.31654e8	+	4.01236e8i	−0.507671	+	0.879312i
$85$	−1.66403e8	+	2.88219e8i	−0.345761	+	0.598876i
$86$	5.72443e8			1.12847
$87$	5.02193e7	−	8.69825e7i	0.0939798	−	0.162778i
$88$	5.97723e6	+	1.03529e7i	0.0106250	+	0.0184030i
$89$	−1.25885e8	−	2.18039e8i	−0.212676	−	0.368366i	0.739875	−	0.672745i	$-0.234885\pi$
$89$	−1.25885e8	−	2.18039e8i	−0.212676	−	0.368366i	−0.952551	+	0.304378i	$0.901551\pi$
$90$	−1.13899e9			−1.82991
$91$	−1.20602e9	−	1.07284e8i	−1.84361	−	0.164002i
$92$	−1.95227e8			−0.284115
$93$	9.63205e7	+	1.66832e8i	0.133520	+	0.231263i
$94$	3.73349e8	+	6.46659e8i	0.493219	+	0.854280i
$95$	5.63285e8	−	9.75638e8i	0.709532	−	1.22895i
$96$	4.65959e8			0.559921
$97$	1.09677e8	−	1.89966e8i	0.125789	−	0.217873i	−0.796252	−	0.604965i	$-0.793187\pi$
$97$	1.09677e8	−	1.89966e8i	0.125789	−	0.217873i	0.922041	+	0.387092i	$0.126520\pi$
$98$	1.69107e9	−	2.92901e9i	1.85201	−	3.20777i
$99$	−3.33099e7			−0.0348510
$100$	−7.21303e8	+	1.24933e9i	−0.721303	+	1.24933i
$101$	7.48187e8	+	1.29590e9i	0.715425	+	1.23915i	0.962795	+	0.270231i	$0.0871002\pi$
$101$	7.48187e8	+	1.29590e9i	0.715425	+	1.23915i	−0.247370	+	0.968921i	$0.579566\pi$
$102$	−1.64736e8	−	2.85331e8i	−0.150691	−	0.261005i
$103$	6.84849e8			0.599552			0.299776	−	0.954010i	$-0.403088\pi$
$103$	6.84849e8			0.599552			0.299776	+	0.954010i	$0.403088\pi$
$104$	−2.54450e8	−	5.47752e8i	−0.213281	−	0.459128i
$105$	−1.37087e9			−1.10064
$106$	1.24322e9	+	2.15332e9i	0.956470	+	1.65665i
$107$	7.17900e8	+	1.24344e9i	0.529465	+	0.917060i	0.999409	+	0.0343638i	$0.0109405\pi$
$107$	7.17900e8	+	1.24344e9i	0.529465	+	0.917060i	−0.469945	+	0.882696i	$0.655726\pi$
$108$	7.09782e8	−	1.22938e9i	0.502017	−	0.869519i
$109$	−2.89584e8			−0.196497			−0.0982484	−	0.995162i	$-0.531324\pi$
$109$	−2.89584e8			−0.196497			−0.0982484	+	0.995162i	$0.531324\pi$
$110$	−7.10298e7	+	1.23027e8i	−0.0462566	+	0.0801188i
$111$	−4.63093e8	+	8.02101e8i	−0.289544	+	0.501505i
$112$	−1.72151e9			−1.03378
$113$	8.58735e8	−	1.48737e9i	0.495457	−	0.858157i	−0.504529	−	0.863395i	$-0.668334\pi$
$113$	8.58735e8	−	1.48737e9i	0.495457	−	0.858157i	0.999986	+	0.00523743i	$0.00166713\pi$
$114$	5.57642e8	+	9.65864e8i	0.309231	+	0.535604i
$115$	−2.88826e8	−	5.00260e8i	−0.153991	−	0.266720i
$116$	−1.18469e9			−0.607496
$117$	1.67627e9	+	1.49117e8i	0.827006	+	0.0735683i
$118$	−6.28423e8			−0.298389
$119$	9.69907e8	+	1.67993e9i	0.443372	+	0.767944i
$120$	−3.41911e8	−	5.92208e8i	−0.150521	−	0.260710i
$121$	1.17690e9	−	2.03844e9i	0.499119	−	0.864500i
$122$	−3.29749e9			−1.34761
$123$	8.18888e8	−	1.41836e9i	0.322591	−	0.558743i
$124$	1.13611e9	−	1.96781e9i	0.431543	−	0.747454i
$125$	−3.28619e8			−0.120392
$126$	−3.31940e9	+	5.74937e9i	−1.17325	+	2.03213i
$127$	1.57537e9	+	2.72862e9i	0.537360	+	0.930735i	0.999045	+	0.0436912i	$0.0139118\pi$
$127$	1.57537e9	+	2.72862e9i	0.537360	+	0.930735i	−0.461685	+	0.887044i	$0.652755\pi$
$128$	−1.45298e9	−	2.51663e9i	−0.478424	−	0.828656i
$129$	−9.57631e8			−0.304470
$130$	4.12523e9	−	5.87320e9i	1.26678	−	1.80356i
$131$	−4.05727e9			−1.20369			−0.601843	−	0.798615i	$-0.705567\pi$
$131$	−4.05727e9			−1.20369			−0.601843	+	0.798615i	$0.705567\pi$
$132$	−4.01587e7	−	6.95569e7i	−0.0115132	−	0.0199415i
$133$	−3.28319e9	−	5.68666e9i	−0.909838	−	1.57589i
$134$	−1.46647e9	+	2.54000e9i	−0.392918	+	0.680555i
$135$	4.20031e9			1.08838
$136$	−4.83813e8	+	8.37989e8i	−0.121270	+	0.210045i
$137$	2.88168e9	−	4.99121e9i	0.698880	−	1.21050i	−0.269975	−	0.962867i	$-0.587015\pi$
$137$	2.88168e9	−	4.99121e9i	0.698880	−	1.21050i	0.968855	−	0.247628i	$-0.0796512\pi$
$138$	5.71864e8			0.134226
$139$	−3.28557e9	+	5.69078e9i	−0.746525	+	1.29302i	0.202953	+	0.979188i	$0.434946\pi$
$139$	−3.28557e9	+	5.69078e9i	−0.746525	+	1.29302i	−0.949479	+	0.313832i	$0.898387\pi$
$140$	8.08479e9	+	1.40033e10i	1.77866	+	3.08073i
$141$	−6.24570e8	−	1.08179e9i	−0.133074	−	0.230492i
$142$	−1.25461e10			−2.58947
$143$	1.20643e8	−	1.71762e8i	0.0241262	−	0.0343491i
$144$	2.39277e9			0.463735
$145$	−1.75267e9	−	3.03572e9i	−0.329264	−	0.570302i
$146$	−5.82877e8	−	1.00957e9i	−0.106167	−	0.183886i
$147$	−2.82896e9	+	4.89990e9i	−0.499687	+	0.865484i
$148$	1.09245e10			1.87165
$149$	1.08094e9	−	1.87225e9i	0.179666	−	0.311190i	−0.762100	−	0.647459i	$-0.775832\pi$
$149$	1.08094e9	−	1.87225e9i	0.179666	−	0.311190i	0.941766	+	0.336269i	$0.109165\pi$
$150$	2.11287e9	−	3.65959e9i	0.340770	−	0.590231i
$151$	7.18335e9			1.12443			0.562213	−	0.826992i	$-0.309950\pi$
$151$	7.18335e9			1.12443			0.562213	+	0.826992i	$0.309950\pi$
$152$	1.63774e9	−	2.83664e9i	0.248856	−	0.431031i
$153$	−1.34810e9	−	2.33497e9i	−0.198888	−	0.344485i
$154$	4.14009e8	+	7.17084e8i	0.0593152	+	0.102737i
$155$	6.72323e9			0.935590
$156$	1.70955e9	+	3.68013e9i	0.231111	+	0.497511i
$157$	−8.25511e9			−1.08436			−0.542181	−	0.840262i	$-0.682401\pi$
$157$	−8.25511e9			−1.08436			−0.542181	+	0.840262i	$0.682401\pi$
$158$	5.52269e9	+	9.56558e9i	0.705008	+	1.22111i
$159$	−2.07976e9	−	3.60225e9i	−0.258064	−	0.446979i
$160$	8.13106e9	−	1.40834e10i	0.980861	−	1.69890i
$161$	−3.36693e9			−0.394928
$162$	3.47775e9	−	6.02363e9i	0.396717	−	0.687133i
$163$	2.29565e9	−	3.97619e9i	0.254719	−	0.441187i	−0.710100	−	0.704101i	$-0.751350\pi$
$163$	2.29565e9	−	3.97619e9i	0.254719	−	0.441187i	0.964819	+	0.262914i	$0.0846836\pi$
$164$	−1.93178e10			−2.08526
$165$	1.18825e8	−	2.05810e8i	0.0124804	−	0.0216167i
$166$	−3.25582e9	−	5.63924e9i	−0.332793	−	0.576414i
$167$	3.53892e9	+	6.12959e9i	0.352085	+	0.609828i	0.986615	−	0.163070i	$-0.0521396\pi$
$167$	3.53892e9	+	6.12959e9i	0.352085	+	0.609828i	−0.634530	+	0.772898i	$0.718806\pi$
$168$	−3.98577e9			−0.386029
$169$	−6.84009e9	+	8.10362e9i	−0.645018	+	0.764168i
$170$	−1.14987e10			−1.05591
$171$	4.56339e9	+	7.90402e9i	0.408136	+	0.706912i
$172$	5.64770e9	+	9.78210e9i	0.492032	+	0.852224i
$173$	−2.26796e9	+	3.92823e9i	−0.192499	+	0.333418i	−0.946078	−	0.323940i	$-0.894993\pi$
$173$	−2.26796e9	+	3.92823e9i	−0.192499	+	0.333418i	0.753579	+	0.657358i	$0.228326\pi$
$174$	3.47023e9			0.287003
$175$	−1.24398e10	+	2.15464e10i	−1.00263	+	1.73661i
$176$	1.49218e8	−	2.58453e8i	0.0117223	−	0.0203037i
$177$	1.05128e9			0.0805078
$178$	4.34942e9	−	7.53341e9i	0.324744	−	0.562473i
$179$	−2.43781e9	−	4.22241e9i	−0.177485	−	0.307413i	0.763534	−	0.645768i	$-0.223463\pi$
$179$	−2.43781e9	−	4.22241e9i	−0.177485	−	0.307413i	−0.941018	+	0.338356i	$0.890129\pi$
$180$	−1.12372e10	−	1.94635e10i	−0.797872	−	1.38195i
$181$	−1.12856e10			−0.781576			−0.390788	−	0.920481i	$-0.627797\pi$
$181$	−1.12856e10			−0.781576			−0.390788	+	0.920481i	$0.627797\pi$
$182$	−1.76243e10	−	3.79396e10i	−1.19067	−	2.56314i
$183$	5.51631e9			0.363596
$184$	−8.39754e8	−	1.45450e9i	−0.0540097	−	0.0935475i
$185$	1.61621e10	+	2.79936e10i	1.01444	+	1.75706i
$186$	−3.32794e9	+	5.76416e9i	−0.203877	+	0.353125i
$187$	−3.36280e8			−0.0201101
$188$	−7.36688e9	+	1.27598e10i	−0.430104	+	0.744962i
$189$	1.22411e10	−	2.12022e10i	0.697818	−	1.20866i
$190$	3.89238e10			2.16682
$191$	1.68274e9	−	2.91460e9i	0.0914888	−	0.158463i	−0.816649	−	0.577135i	$-0.804171\pi$
$191$	1.68274e9	−	2.91460e9i	0.0914888	−	0.158463i	0.908138	+	0.418671i	$0.137504\pi$
$192$	5.88314e9	+	1.01899e10i	0.312430	+	0.541145i
$193$	−2.16724e9	−	3.75377e9i	−0.112434	−	0.194742i	0.804317	−	0.594201i	$-0.202532\pi$
$193$	−2.16724e9	−	3.75377e9i	−0.112434	−	0.194742i	−0.916751	+	0.399458i	$0.869198\pi$
$194$	7.57884e9			0.384145
$195$	−6.90103e9	+	9.82518e9i	−0.341789	+	0.486614i
$196$	6.67359e10			3.23003
$197$	−3.04660e9	−	5.27687e9i	−0.144118	−	0.249619i	0.784926	−	0.619590i	$-0.212701\pi$
$197$	−3.04660e9	−	5.27687e9i	−0.144118	−	0.249619i	−0.929043	+	0.369971i	$0.879368\pi$
$198$	−5.75440e8	−	9.96691e8i	−0.0266077	−	0.0460858i
$199$	1.19360e10	−	2.06737e10i	0.539533	−	0.934499i	−0.459396	−	0.888232i	$-0.651934\pi$
$199$	1.19360e10	−	2.06737e10i	0.539533	−	0.934499i	0.998929	−	0.0462676i	$-0.0147327\pi$
$200$	−1.24105e10			−0.548474
$201$	2.45324e9	−	4.24913e9i	0.106013	−	0.183619i
$202$	−2.58504e10	+	4.47742e10i	−1.09241	+	1.89211i
$203$	−2.04315e10			−0.844437
$204$	3.25055e9	−	5.63013e9i	0.131408	−	0.227605i
$205$	−2.85795e10	−	4.95011e10i	−1.13022	−	1.95759i
$206$	1.18310e10	+	2.04919e10i	0.457740	+	0.792829i
$207$	4.67977e9			0.177157
$208$	−8.66619e9	+	1.23383e10i	−0.321028	+	0.457057i
$209$	1.13833e9			0.0412676
$210$	−2.36822e10	−	4.10188e10i	−0.840303	−	1.45545i
$211$	1.81489e10	+	3.14349e10i	0.630347	+	1.09179i	0.987481	+	0.157740i	$0.0504208\pi$
$211$	1.81489e10	+	3.14349e10i	0.630347	+	1.09179i	−0.357133	+	0.934053i	$0.616246\pi$
$212$	−2.45311e10	+	4.24891e10i	−0.834075	+	1.44466i
$213$	2.09882e10			0.698661
$214$	−2.48039e10	+	4.29617e10i	−0.808460	+	1.40029i
$215$	−1.67108e10	+	2.89440e10i	−0.533365	+	0.923816i
$216$	1.22123e10			0.381730
$217$	1.95937e10	−	3.39373e10i	0.599857	−	1.03898i
$218$	−5.00267e9	−	8.66487e9i	−0.150019	−	0.259841i
$219$	9.75086e8	+	1.68890e9i	0.0286447	+	0.0496141i
$220$	−2.80311e9			−0.0806747
$221$	1.69228e10	+	1.50541e9i	0.477208	+	0.0424511i
$222$	−3.20004e10			−0.884233
$223$	1.02182e10	+	1.76984e10i	0.276695	+	0.479249i	0.970561	−	0.240854i	$-0.0774276\pi$
$223$	1.02182e10	+	1.76984e10i	0.276695	+	0.479249i	−0.693867	+	0.720104i	$0.744094\pi$
$224$	−4.73932e10	−	8.20874e10i	−1.25777	−	2.17851i
$225$	1.72904e10	−	2.99478e10i	0.449762	−	0.779010i
$226$	5.93398e10			1.51307
$227$	3.74735e10	−	6.49060e10i	0.936716	−	1.62244i	0.165172	−	0.986265i	$-0.447182\pi$
$227$	3.74735e10	−	6.49060e10i	0.936716	−	1.62244i	0.771544	−	0.636176i	$-0.219485\pi$
$228$	−1.10033e10	+	1.90583e10i	−0.269660	+	0.467066i
$229$	−7.40057e10			−1.77830			−0.889151	−	0.457614i	$-0.848704\pi$
$229$	−7.40057e10			−1.77830			−0.889151	+	0.457614i	$0.848704\pi$
$230$	9.97912e9	−	1.72843e10i	0.235135	−	0.407266i
$231$	−6.92588e8	−	1.19960e9i	−0.0160037	−	0.0277193i
$232$	−5.09585e9	−	8.82628e9i	−0.115484	−	0.200024i
$233$	−3.44528e10			−0.765814			−0.382907	−	0.923787i	$-0.625077\pi$
$233$	−3.44528e10			−0.765814			−0.382907	+	0.923787i	$0.625077\pi$
$234$	2.44964e10	+	5.27332e10i	0.534110	+	1.14977i
$235$	−4.35954e10			−0.932470
$236$	−6.19998e9	−	1.07387e10i	−0.130103	−	0.225345i
$237$	−9.23882e9	−	1.60021e10i	−0.190217	−	0.329465i
$238$	−3.35110e10	+	5.80427e10i	−0.677003	+	1.17260i
$239$	3.10527e10			0.615614			0.307807	−	0.951449i	$-0.400405\pi$
$239$	3.10527e10			0.615614			0.307807	+	0.951449i	$0.400405\pi$
$240$	−8.53561e9	+	1.47841e10i	−0.166067	+	0.287637i
$241$	3.83324e10	−	6.63937e10i	0.731964	−	1.26780i	−0.224079	−	0.974571i	$-0.571937\pi$
$241$	3.83324e10	−	6.63937e10i	0.731964	−	1.26780i	0.956043	−	0.293228i	$-0.0947294\pi$
$242$	8.13252e10			1.52425
$243$	−2.63102e10	+	4.55706e10i	−0.484056	+	0.838409i
$244$	−3.25328e10	−	5.63485e10i	−0.587581	−	1.01772i
$245$	9.87315e10	+	1.71008e11i	1.75069	+	3.03228i
$246$	5.65863e10			0.985153
$247$	−5.72848e10	−	5.09590e9i	−0.979271	−	0.0871134i
$248$	1.95477e10			0.328142
$249$	5.44660e9	+	9.43379e9i	0.0897901	+	0.155521i
$250$	−5.67701e9	−	9.83287e9i	−0.0919157	−	0.159203i
$251$	1.66676e10	−	2.88692e10i	0.265058	−	0.459095i	−0.702520	−	0.711664i	$-0.747942\pi$
$251$	1.66676e10	−	2.88692e10i	0.265058	−	0.459095i	0.967579	+	0.252569i	$0.0812754\pi$
$252$	−1.30996e11			−2.04624
$253$	2.91840e8	−	5.05482e8i	0.00447819	−	0.00775645i
$254$	−5.44301e10	+	9.42757e10i	−0.820517	+	1.42118i
$255$	1.92360e10			0.284894
$256$	−1.91290e9	+	3.31324e9i	−0.0278363	+	0.0482140i
$257$	−2.63494e9	−	4.56385e9i	−0.0376766	−	0.0652578i	0.846572	−	0.532274i	$-0.178662\pi$
$257$	−2.63494e9	−	4.56385e9i	−0.0376766	−	0.0652578i	−0.884249	+	0.467016i	$0.845329\pi$
$258$	−1.65434e10	−	2.86540e10i	−0.232454	−	0.402622i
$259$	1.88407e11			2.60164
$260$	1.41062e11	+	1.25485e10i	1.91439	+	0.170299i
$261$	2.83981e10			0.378798
$262$	−7.00907e10	−	1.21401e11i	−0.918977	−	1.59172i
$263$	−2.00875e10	−	3.47927e10i	−0.258896	−	0.448422i	0.707050	−	0.707163i	$-0.250026\pi$
$263$	−2.00875e10	−	3.47927e10i	−0.258896	−	0.448422i	−0.965947	+	0.258742i	$0.916692\pi$
$264$	3.45480e8	−	5.98389e8i	0.00437729	−	0.00758168i
$265$	−1.45169e11			−1.80828
$266$	1.13437e11	−	1.96478e11i	1.38927	−	2.40628i
$267$	−7.27607e9	+	1.26025e10i	−0.0876186	+	0.151760i
$268$	−5.78726e10			−0.685277
$269$	−3.93111e10	+	6.80888e10i	−0.457752	+	0.792849i	−0.998842	−	0.0481153i	$-0.984679\pi$
$269$	−3.93111e10	+	6.80888e10i	−0.457752	+	0.792849i	0.541090	+	0.840965i	$0.318012\pi$
$270$	7.25619e10	+	1.25681e11i	0.830944	+	1.43924i
$271$	−5.15625e10	−	8.93088e10i	−0.580727	−	1.00585i	−0.995393	−	0.0958748i	$-0.969435\pi$
$271$	−5.15625e10	−	8.93088e10i	−0.580727	−	1.00585i	0.414667	−	0.909973i	$-0.363898\pi$
$272$	2.41562e10			0.267589
$273$	2.94834e10	+	6.34686e10i	0.321251	+	0.691555i
$274$	1.99128e11			2.13430
$275$	−2.15652e9	−	3.73521e9i	−0.0227382	−	0.0393838i
$276$	5.64198e9	+	9.77220e9i	0.0585249	+	0.101368i
$277$	−1.73792e10	+	3.01017e10i	−0.177366	+	0.307207i	−0.940978	−	0.338469i	$-0.890091\pi$
$277$	−1.73792e10	+	3.01017e10i	−0.177366	+	0.307207i	0.763611	+	0.645676i	$0.223424\pi$
$278$	−2.27038e11			−2.27980
$279$	−2.72338e10	+	4.71703e10i	−0.269085	+	0.466068i
$280$	−6.95523e10	+	1.20468e11i	−0.676239	+	1.17128i
$281$	6.53013e10			0.624803			0.312401	−	0.949950i	$-0.398867\pi$
$281$	6.53013e10			0.624803			0.312401	+	0.949950i	$0.398867\pi$
$282$	2.15793e10	−	3.73765e10i	0.203197	−	0.351947i
$283$	−1.55036e10	−	2.68531e10i	−0.143679	−	0.248860i	0.785200	−	0.619242i	$-0.212560\pi$
$283$	−1.55036e10	−	2.68531e10i	−0.143679	−	0.248860i	−0.928879	+	0.370382i	$0.879227\pi$
$284$	−1.23779e11	−	2.14392e11i	−1.12905	−	1.95558i
$285$	−6.51149e10			−0.584627
$286$	7.22357e9	+	6.42590e8i	0.0638417	+	0.00567919i
$287$	−3.33160e11			−2.89857
$288$	6.58729e10	+	1.14095e11i	0.564209	+	0.977239i
$289$	4.56842e10	+	7.91274e10i	0.385235	+	0.667247i
$290$	6.05560e10	−	1.04886e11i	0.502767	−	0.870817i
$291$	−1.26785e10			−0.103645
$292$	1.15013e10	−	1.99208e10i	0.0925812	−	0.160355i
$293$	2.51615e10	−	4.35810e10i	0.199449	−	0.345456i	−0.748901	−	0.662682i	$-0.769418\pi$
$293$	2.51615e10	−	4.35810e10i	0.199449	−	0.345456i	0.948350	+	0.317226i	$0.102751\pi$
$294$	−1.95485e11			−1.52598
$295$	1.83450e10	−	3.17744e10i	0.141032	−	0.244275i
$296$	4.69910e10	+	8.13907e10i	0.355796	+	0.616257i
$297$	2.12208e9	+	3.67555e9i	0.0158255	+	0.0274105i
$298$	7.46947e10			0.548677
$299$	−1.69493e10	+	2.41312e10i	−0.122640	+	0.174606i
$300$	8.33817e10			0.594326
$301$	9.74017e10	+	1.68705e11i	0.683939	+	1.18462i
$302$	1.24095e11	+	2.14939e11i	0.858466	+	1.48691i
$303$	4.32447e10	−	7.49020e10i	0.294741	−	0.510507i
$304$	−8.17702e10			−0.549116
$305$	9.62606e10	−	1.66728e11i	0.636941	−	1.10321i
$306$	4.65776e10	−	8.06749e10i	0.303690	−	0.526007i
$307$	1.73065e10			0.111196			0.0555978	−	0.998453i	$-0.482294\pi$
$307$	1.73065e10			0.111196			0.0555978	+	0.998453i	$0.482294\pi$
$308$	−8.16917e9	+	1.41494e10i	−0.0517249	+	0.0895902i
$309$	−1.97919e10	−	3.42806e10i	−0.123502	−	0.213912i
$310$	1.16146e11	+	2.01171e11i	0.714295	+	1.23719i
$311$	2.49868e11			1.51457			0.757284	−	0.653086i	$-0.226526\pi$
$311$	2.49868e11			1.51457			0.757284	+	0.653086i	$0.226526\pi$
$312$	−2.00646e10	+	2.85665e10i	−0.119877	+	0.170672i
$313$	−1.10603e11			−0.651353			−0.325677	−	0.945481i	$-0.605592\pi$
$313$	−1.10603e11			−0.651353			−0.325677	+	0.945481i	$0.605592\pi$
$314$	−1.42610e11	−	2.47008e11i	−0.827878	−	1.43393i
$315$	−1.93800e11	−	3.35672e11i	−1.10907	−	1.92096i
$316$	−1.08973e11	+	1.88747e11i	−0.614791	+	1.06485i
$317$	1.24522e11			0.692596			0.346298	−	0.938125i	$-0.387439\pi$
$317$	1.24522e11			0.692596			0.346298	+	0.938125i	$0.387439\pi$
$318$	7.18572e10	−	1.24460e11i	0.394047	−	0.682510i
$319$	1.77097e9	−	3.06740e9i	0.00957529	−	0.0165849i
$320$	4.10647e11			2.18924
$321$	4.14941e10	−	7.18699e10i	0.218129	−	0.377811i
$322$	−5.81649e10	−	1.00745e11i	−0.301515	−	0.522240i
$323$	4.60697e10	+	7.97950e10i	0.235507	+	0.407910i
$324$	1.37245e11			0.691901
$325$	9.18028e10	+	1.97623e11i	0.456437	+	0.982568i
$326$	1.58633e11			0.777882
$327$	8.36888e9	+	1.44953e10i	0.0404764	+	0.0701073i
$328$	−8.30942e10	−	1.43923e11i	−0.396404	−	0.686592i
$329$	−1.27051e11	+	2.20059e11i	−0.597857	+	1.03552i
$330$	8.21095e9			0.0381137
$331$	−1.85043e11	+	3.20504e11i	−0.847319	+	1.46760i	0.0362736	+	0.999342i	$0.488451\pi$
$331$	−1.85043e11	+	3.20504e11i	−0.847319	+	1.46760i	−0.883592	+	0.468257i	$0.844882\pi$
$332$	6.42434e10	−	1.11273e11i	0.290207	−	0.502653i
$333$	−2.61871e11			−1.16705
$334$	−1.22272e11	+	2.11782e11i	−0.537612	+	0.931171i
$335$	−8.56188e10	−	1.48296e11i	−0.371422	−	0.643322i
$336$	4.97511e10	+	8.61715e10i	0.212949	+	0.368839i
$337$	−1.34350e11			−0.567418			−0.283709	−	0.958910i	$-0.591565\pi$
$337$	−1.34350e11			−0.567418			−0.283709	+	0.958910i	$0.591565\pi$
$338$	−3.60640e11	−	6.46749e10i	−1.50296	−	0.269532i
$339$	−9.92686e10			−0.408238
$340$	−1.13445e11	−	1.96493e11i	−0.460396	−	0.797430i
$341$	3.39670e9	+	5.88326e9i	0.0136039	+	0.0235626i
$342$	−1.57668e11	+	2.73089e11i	−0.623199	+	1.07941i
$343$	6.76481e11			2.63895
$344$	−4.85863e10	+	8.41540e10i	−0.187069	+	0.324013i
$345$	−1.66939e10	+	2.89147e10i	−0.0634413	+	0.109884i
$346$	−1.56719e11			−0.587869
$347$	2.53469e10	−	4.39021e10i	0.0938518	−	0.162556i	−0.815277	−	0.579071i	$-0.803415\pi$
$347$	2.53469e10	−	4.39021e10i	0.0938518	−	0.162556i	0.909129	+	0.416515i	$0.136749\pi$
$348$	3.42371e10	+	5.93004e10i	0.125138	+	0.216746i
$349$	7.73213e9	+	1.33924e10i	0.0278987	+	0.0483220i	0.879638	−	0.475644i	$-0.157785\pi$
$349$	7.73213e9	+	1.33924e10i	0.0278987	+	0.0483220i	−0.851739	+	0.523966i	$0.824452\pi$
$350$	−8.59607e11			−3.06192
$351$	−9.03364e10	−	1.94467e11i	−0.317673	−	0.683853i
$352$	1.64319e10			0.0570485
$353$	1.41601e11	+	2.45259e11i	0.485376	+	0.840697i	0.999859	−	0.0168043i	$-0.00534924\pi$
$353$	1.41601e11	+	2.45259e11i	0.485376	+	0.840697i	−0.514482	+	0.857501i	$0.672016\pi$
$354$	1.81612e10	+	3.14561e10i	0.0614653	+	0.106461i
$355$	3.66247e11	−	6.34359e11i	1.22390	−	2.11986i
$356$	1.71645e11			0.566376
$357$	5.60599e10	−	9.70987e10i	0.182661	−	0.316378i
$358$	8.42280e10	−	1.45887e11i	0.271008	−	0.469400i
$359$	1.07991e11			0.343133			0.171567	−	0.985173i	$-0.445117\pi$
$359$	1.07991e11			0.343133			0.171567	+	0.985173i	$0.445117\pi$
$360$	9.66724e10	−	1.67441e11i	0.303348	−	0.525414i
$361$	5.39520e9	+	9.34475e9i	0.0167196	+	0.0289591i
$362$	−1.94963e11	−	3.37685e11i	−0.596710	−	1.03353i
$363$	−1.36048e11			−0.411255
$364$	4.74444e11	−	6.75480e11i	1.41654	−	2.01677i
$365$	6.80616e10			0.200717
$366$	9.52962e10	+	1.65058e11i	0.277595	+	0.480808i
$367$	7.98421e10	+	1.38291e11i	0.229739	+	0.397920i	0.957731	−	0.287666i	$-0.0928794\pi$
$367$	7.98421e10	+	1.38291e11i	0.229739	+	0.397920i	−0.727992	+	0.685586i	$0.759546\pi$
$368$	−2.09639e10	+	3.63106e10i	−0.0595878	+	0.103209i
$369$	4.63067e11			1.30024
$370$	−5.58412e11	+	9.67198e11i	−1.54898	+	2.68292i
$371$	−4.23070e11	+	7.32778e11i	−1.15939	+	2.00812i
$372$	−1.31333e11			−0.355575
$373$	1.60463e11	−	2.77930e11i	0.429225	−	0.743440i	−0.567579	−	0.823319i	$-0.692120\pi$
$373$	1.60463e11	−	2.77930e11i	0.429225	−	0.743440i	0.996805	+	0.0798786i	$0.0254533\pi$
$374$	−5.80935e9	−	1.00621e10i	−0.0153534	−	0.0265929i
$375$	9.49698e9	+	1.64493e10i	0.0247996	+	0.0429542i
$376$	−1.26753e11			−0.327048
$377$	−1.02853e11	+	1.46435e11i	−0.262229	+	0.373343i
$378$	8.45877e11			2.13105
$379$	−2.85129e11	−	4.93858e11i	−0.709848	−	1.22949i	−0.964913	−	0.262569i	$-0.915430\pi$
$379$	−2.85129e11	−	4.93858e11i	−0.709848	−	1.22949i	0.255065	−	0.966924i	$-0.417903\pi$
$380$	3.84020e11	+	6.65142e11i	0.944773	+	1.63639i
$381$	9.10552e10	−	1.57712e11i	0.221382	−	0.383445i
$382$	1.16280e11			0.279396
$383$	5.14786e10	−	8.91635e10i	0.122245	−	0.211735i	−0.798408	−	0.602117i	$-0.794324\pi$
$383$	5.14786e10	−	8.91635e10i	0.122245	−	0.211735i	0.920653	+	0.390382i	$0.127657\pi$
$384$	−8.39810e10	+	1.45459e11i	−0.197102	+	0.341390i
$385$	−4.83431e10			−0.112140
$386$	7.48797e10	−	1.29695e11i	0.171681	−	0.297360i
$387$	−1.35381e11	−	2.34487e11i	−0.306802	−	0.531396i
$388$	7.47724e10	+	1.29510e11i	0.167494	+	0.290108i
$389$	−4.17081e11			−0.923522			−0.461761	−	0.887004i	$-0.652782\pi$
$389$	−4.17081e11			−0.923522			−0.461761	+	0.887004i	$0.652782\pi$
$390$	−4.13205e11	−	3.67576e10i	−0.904429	−	0.0804556i
$391$	4.72446e10			0.102225
$392$	2.87060e11	+	4.97202e11i	0.614023	+	1.06352i
$393$	1.17254e11	+	2.03089e11i	0.247948	+	0.429458i
$394$	1.05262e11	−	1.82320e11i	0.220059	−	0.381154i
$395$	−6.44876e11			−1.33287
$396$	1.13545e10	−	1.96666e10i	0.0232028	−	0.0401884i
$397$	3.74311e11	−	6.48326e11i	0.756268	−	1.30989i	−0.188474	−	0.982078i	$-0.560354\pi$
$397$	3.74311e11	−	6.48326e11i	0.756268	−	1.30989i	0.944742	−	0.327816i	$-0.106313\pi$
$398$	8.24791e11			1.64767
$399$	−1.89766e11	+	3.28685e11i	−0.374836	+	0.649235i
$400$	1.54911e11	+	2.68313e11i	0.302560	+	0.524050i
$401$	1.52549e11	+	2.64222e11i	0.294618	+	0.510293i	0.974896	−	0.222661i	$-0.0714742\pi$
$401$	1.52549e11	+	2.64222e11i	0.294618	+	0.510293i	−0.680278	+	0.732954i	$0.738141\pi$
$402$	1.69522e11			0.323750
$403$	−1.44597e11	−	3.11273e11i	−0.273078	−	0.587853i
$404$	−1.02015e12			−1.90524
$405$	2.03045e11	+	3.51685e11i	0.375012	+	0.649541i
$406$	−3.52960e11	−	6.11345e11i	−0.644702	−	1.11666i
$407$	−1.63308e10	+	2.82858e10i	−0.0295007	+	0.0510967i
$408$	5.59281e10			0.0999216
$409$	7.51958e8	−	1.30243e9i	0.00132874	−	0.00230144i	−0.865360	−	0.501150i	$-0.832910\pi$
$409$	7.51958e8	−	1.30243e9i	0.00132874	−	0.00230144i	0.866689	+	0.498849i	$0.166244\pi$
$410$	9.87441e11	−	1.71030e12i	1.72577	−	2.98913i
$411$	−3.33118e11			−0.575850
$412$	−2.33448e11	+	4.04344e11i	−0.399165	+	0.691374i
$413$	−1.06927e11	−	1.85202e11i	−0.180847	−	0.313236i
$414$	8.08447e10	+	1.40027e11i	0.135254	+	0.234267i
$415$	3.80177e11			0.629171
$416$	−8.26910e11	−	7.35597e10i	−1.35375	−	0.120426i
$417$	3.79808e11			0.615108
$418$	1.96650e10	+	3.40608e10i	0.0315066	+	0.0545710i
$419$	4.08775e11	+	7.08020e11i	0.647920	+	1.12223i	0.983619	+	0.180261i	$0.0576944\pi$
$419$	4.08775e11	+	7.08020e11i	0.647920	+	1.12223i	−0.335698	+	0.941970i	$0.608972\pi$
$420$	4.67295e11	−	8.09379e11i	0.732773	−	1.26920i
$421$	−6.33187e11			−0.982342			−0.491171	−	0.871063i	$-0.663431\pi$
$421$	−6.33187e11			−0.982342			−0.491171	+	0.871063i	$0.663431\pi$
$422$	−6.27058e11	+	1.08610e12i	−0.962502	+	1.66710i
$423$	1.76591e11	−	3.05865e11i	0.268187	−	0.464514i
$424$	−4.22075e11			−0.634225
$425$	1.74555e11	−	3.02338e11i	0.259526	−	0.449513i
$426$	3.62578e11	+	6.28003e11i	0.533406	+	0.923887i
$427$	−5.61070e11	−	9.71802e11i	−0.816755	−	1.41466i
$428$	−9.78858e11			−1.41001
$429$	−1.20842e10	−	1.07498e9i	−0.0172250	−	0.00153229i
$430$	−1.15474e12			−1.62883
$431$	3.39161e11	+	5.87444e11i	0.473433	+	0.820010i	0.999538	−	0.0304102i	$-0.00968135\pi$
$431$	3.39161e11	+	5.87444e11i	0.473433	+	0.820010i	−0.526105	+	0.850420i	$0.676348\pi$
$432$	−1.52436e11	−	2.64028e11i	−0.210578	−	0.364731i
$433$	−3.31827e11	+	5.74742e11i	−0.453646	+	0.785737i	−0.998609	−	0.0527225i	$-0.983210\pi$
$433$	−3.31827e11	+	5.74742e11i	−0.453646	+	0.785737i	0.544964	+	0.838460i	$0.316543\pi$
$434$	1.35395e12			1.83189
$435$	−1.01303e11	+	1.75462e11i	−0.135651	+	0.234954i
$436$	9.87121e10	−	1.70974e11i	0.130822	−	0.226590i
$437$	−1.59926e11			−0.209774
$438$	−3.36899e10	+	5.83526e10i	−0.0437387	+	0.0757577i
$439$	5.05986e11	+	8.76393e11i	0.650202	+	1.12618i	0.983074	+	0.183210i	$0.0586490\pi$
$439$	5.05986e11	+	8.76393e11i	0.650202	+	1.12618i	−0.332872	+	0.942972i	$0.608018\pi$
$440$	−1.20574e10	−	2.08840e10i	−0.0153361	−	0.0265629i
$441$	−1.59972e12			−2.01406
$442$	2.47303e11	+	5.32367e11i	0.308198	+	0.663454i
$443$	−4.30167e11			−0.530665			−0.265333	−	0.964157i	$-0.585482\pi$
$443$	−4.30167e11			−0.530665			−0.265333	+	0.964157i	$0.585482\pi$
$444$	−3.15714e11	−	5.46833e11i	−0.385541	−	0.667777i
$445$	2.53937e11	+	4.39832e11i	0.306978	+	0.531701i
$446$	−3.53045e11	+	6.11491e11i	−0.422496	+	0.731785i
$447$	−1.24956e11			−0.148038
$448$	1.19676e12	−	2.07285e12i	1.40364	−	2.43118i
$449$	−4.63677e11	+	8.03112e11i	−0.538403	+	0.932541i	0.460588	+	0.887614i	$0.347639\pi$
$449$	−4.63677e11	+	8.03112e11i	−0.538403	+	0.932541i	−0.998990	+	0.0449264i	$0.985695\pi$
$450$	1.19479e12			1.37352
$451$	2.88778e10	−	5.00178e10i	0.0328677	−	0.0569285i
$452$	5.85443e11	+	1.01402e12i	0.659724	+	1.14267i
$453$	−2.07596e11	−	3.59568e11i	−0.231621	−	0.401179i
$454$	2.58947e12			2.86062
$455$	2.43280e12	+	2.16415e11i	2.66106	+	0.236721i
$456$	−1.89320e11			−0.205048
$457$	6.11168e11	+	1.05857e12i	0.655447	+	1.13527i	0.981781	+	0.190013i	$0.0608531\pi$
$457$	6.11168e11	+	1.05857e12i	0.655447	+	1.13527i	−0.326334	+	0.945254i	$0.605814\pi$
$458$	−1.27847e12	−	2.21438e12i	−1.35768	−	2.35157i
$459$	−1.71767e11	+	2.97508e11i	−0.180627	+	0.312854i
$460$	3.93814e11			0.410092
$461$	6.39485e11	−	1.10762e12i	0.659441	−	1.14219i	−0.321319	−	0.946971i	$-0.604126\pi$
$461$	6.39485e11	−	1.10762e12i	0.659441	−	1.14219i	0.980760	−	0.195215i	$-0.0625405\pi$
$462$	2.39294e10	−	4.14469e10i	0.0244367	−	0.0423257i
$463$	−5.58191e11			−0.564505			−0.282253	−	0.959340i	$-0.591082\pi$
$463$	−5.58191e11			−0.564505			−0.282253	+	0.959340i	$0.591082\pi$
$464$	−1.27215e11	+	2.20343e11i	−0.127411	+	0.220682i
$465$	−1.94299e11	−	3.36536e11i	−0.192723	−	0.333805i
$466$	−5.95185e11	−	1.03089e12i	−0.584676	−	1.01269i
$467$	7.34179e11			0.714292			0.357146	−	0.934049i	$-0.383750\pi$
$467$	7.34179e11			0.714292			0.357146	+	0.934049i	$0.383750\pi$
$468$	−6.59441e11	+	9.38865e11i	−0.635433	+	0.904683i
$469$	−9.98086e11			−0.952555
$470$	−7.53125e11	−	1.30445e12i	−0.711913	−	1.23307i
$471$	2.38570e11	+	4.13215e11i	0.223368	+	0.386885i
$472$	5.33376e10	−	9.23834e10i	0.0494646	−	0.0856752i
$473$	−3.37705e10			−0.0310215
$474$	3.19208e11	−	5.52884e11i	0.290450	−	0.503073i
$475$	−5.90878e11	+	1.02343e12i	−0.532570	+	0.922439i
$476$	−1.32247e12			−1.18074
$477$	5.88034e11	−	1.01851e12i	0.520080	−	0.900804i
$478$	5.36446e11	+	9.29151e11i	0.470002	+	0.814068i
$479$	1.63859e11	+	2.83812e11i	0.142220	+	0.246332i	0.928332	−	0.371752i	$-0.121243\pi$
$479$	1.63859e11	+	2.83812e11i	0.142220	+	0.246332i	−0.786112	+	0.618083i	$0.787909\pi$
$480$	−9.39939e11			−0.808191
$481$	9.48450e11	−	1.35033e12i	0.807908	−	1.15024i
$482$	2.64882e12			2.23533
$483$	9.73031e10	+	1.68534e11i	0.0813513	+	0.140905i
$484$	8.02350e11	+	1.38971e12i	0.664599	+	1.15112i
$485$	−2.21242e11	+	3.83203e11i	−0.181564	+	0.314478i
$486$	−1.81807e12			−1.47825
$487$	−6.76471e11	+	1.17168e12i	−0.544965	+	0.943907i	0.453644	+	0.891183i	$0.350124\pi$
$487$	−6.76471e11	+	1.17168e12i	−0.544965	+	0.943907i	−0.998609	+	0.0527241i	$0.983210\pi$
$488$	2.79875e11	−	4.84759e11i	0.223396	−	0.386933i
$489$	−2.65374e11			−0.209879
$490$	−3.41124e12	+	5.90845e12i	−2.67319	+	4.63011i
$491$	9.17875e10	+	1.58981e11i	0.0712717	+	0.123446i	0.899459	−	0.437005i	$-0.143961\pi$
$491$	9.17875e10	+	1.58981e11i	0.0712717	+	0.123446i	−0.828187	+	0.560452i	$0.810628\pi$
$492$	5.58278e11	+	9.66966e11i	0.429544	+	0.743992i
$493$	2.86693e11			0.218578
$494$	−8.37136e11	−	1.80210e12i	−0.632448	−	1.36147i
$495$	6.71932e10			0.0503039
$496$	−2.43998e11	−	4.22616e11i	−0.181016	−	0.313530i
$497$	−2.13473e12	−	3.69746e12i	−1.56942	−	2.71831i
$498$	−1.88184e11	+	3.25944e11i	−0.137104	+	0.237471i
$499$	7.18255e10			0.0518593			0.0259296	−	0.999664i	$-0.491745\pi$
$499$	7.18255e10			0.0518593			0.0259296	+	0.999664i	$0.491745\pi$
$500$	1.12018e11	−	1.94021e11i	0.0801537	−	0.138830i
$501$	2.04547e11	−	3.54286e11i	0.145052	−	0.251238i
$502$	1.15176e12			0.809456
$503$	6.86219e11	−	1.18857e12i	0.477977	−	0.827880i	−0.521705	−	0.853126i	$-0.674704\pi$
$503$	6.86219e11	−	1.18857e12i	0.477977	−	0.827880i	0.999681	+	0.0252464i	$0.00803704\pi$
$504$	−5.63470e11	−	9.75959e11i	−0.388986	−	0.673743i
$505$	−1.50925e12	−	2.61411e12i	−1.03265	−	1.78859i
$506$	2.01666e10			0.0136759
$507$	6.03308e11	+	1.08194e11i	0.405512	+	0.0727220i
$508$	−2.14802e12			−1.43104
$509$	3.93102e11	+	6.80873e11i	0.259583	+	0.449610i	0.966130	−	0.258055i	$-0.0830817\pi$
$509$	3.93102e11	+	6.80873e11i	0.259583	+	0.449610i	−0.706548	+	0.707666i	$0.749748\pi$
$510$	3.32308e11	+	5.75574e11i	0.217508	+	0.376735i
$511$	1.98354e11	−	3.43559e11i	0.128691	−	0.222899i
$512$	−1.62003e12			−1.04186
$513$	5.81441e11	−	1.00708e12i	0.370661	−	0.642004i
$514$	9.10391e10	−	1.57684e11i	0.0575299	−	0.0996447i
$515$	−1.38149e12			−0.865395
$516$	3.26433e11	−	5.65398e11i	0.202708	−	0.351100i
$517$	−2.20252e10	−	3.81488e10i	−0.0135585	−	0.0234840i
$518$	3.25479e12	+	5.63747e12i	1.98628	+	3.44033i
$519$	2.62173e11			0.158612
$520$	5.13280e11	+	1.10493e12i	0.307850	+	0.662706i
$521$	1.98928e12			1.18284			0.591419	−	0.806364i	$-0.298568\pi$
$521$	1.98928e12			1.18284			0.591419	+	0.806364i	$0.298568\pi$
$522$	4.90588e11	+	8.49723e11i	0.289201	+	0.500911i
$523$	1.25851e12	+	2.17980e12i	0.735526	+	1.27397i	0.954492	+	0.298235i	$0.0963980\pi$
$523$	1.25851e12	+	2.17980e12i	0.735526	+	1.27397i	−0.218967	+	0.975732i	$0.570269\pi$
$524$	1.38302e12	−	2.39547e12i	0.801380	−	1.38803i
$525$	1.43802e12			0.826131
$526$	6.94039e11	−	1.20211e12i	0.395319	−	0.684713i
$527$	−2.74938e11	+	4.76207e11i	−0.155270	+	0.268935i
$528$	−1.72494e10			−0.00965875
$529$	8.59575e11	−	1.48883e12i	0.477236	−	0.826597i
$530$	−2.50784e12	−	4.34371e12i	−1.38057	−	2.39122i
$531$	1.48620e11	+	2.57417e11i	0.0811243	+	0.140511i
$532$	4.47664e12			2.42298
$533$	−1.67715e12	+	2.38780e12i	−0.900116	+	1.28152i
$534$	−5.02787e11			−0.267577
$535$	−1.44816e12	−	2.50828e12i	−0.764230	−	1.32369i
$536$	−2.48935e11	−	4.31168e11i	−0.130270	−	0.225634i
$537$	−1.40904e11	+	2.44052e11i	−0.0731203	+	0.126648i
$538$	−2.71645e12			−1.39792
$539$	−9.97620e10	+	1.72793e11i	−0.0509115	+	0.0881813i
$540$	−1.43178e12	+	2.47992e12i	−0.724612	+	1.25506i
$541$	1.35907e12			0.682112			0.341056	−	0.940043i	$-0.389216\pi$
$541$	1.35907e12			0.682112			0.341056	+	0.940043i	$0.389216\pi$
$542$	1.78152e12	−	3.08568e12i	0.886735	−	1.53587i
$543$	3.26150e11	+	5.64909e11i	0.160997	+	0.278855i
$544$	6.65019e11	+	1.15185e12i	0.325566	+	0.563897i
$545$	5.84153e11			0.283624
$546$	−1.38976e12	+	1.97864e12i	−0.669225	+	0.952794i
$547$	−7.08728e11			−0.338483			−0.169241	−	0.985575i	$-0.554132\pi$
$547$	−7.08728e11			−0.338483			−0.169241	+	0.985575i	$0.554132\pi$
$548$	1.96458e12	+	3.40276e12i	0.930590	+	1.61183i
$549$	7.79844e11	+	1.35073e12i	0.366380	+	0.634590i
$550$	7.45093e10	−	1.29054e11i	0.0347199	−	0.0601367i
$551$	−9.70475e11			−0.448541
$552$	−4.85372e10	+	8.40689e10i	−0.0222510	+	0.0385398i
$553$	−1.87938e12	+	3.25518e12i	−0.854578	+	1.48017i
$554$	−1.20093e12			−0.541655
$555$	9.34159e11	−	1.61801e12i	0.417929	−	0.723874i
$556$	−2.23994e12	−	3.87969e12i	−0.994032	−	1.72171i
$557$	−1.33342e12	−	2.30955e12i	−0.586974	−	1.01667i	−0.994626	−	0.103531i	$-0.966986\pi$
$557$	−1.33342e12	−	2.30955e12i	−0.586974	−	1.01667i	0.407653	−	0.913137i	$-0.366347\pi$
$558$	−1.88189e12			−0.821752
$559$	1.69945e12	+	1.51179e11i	0.736133	+	0.0654844i
$560$	3.47266e12			1.49216
$561$	9.71837e9	+	1.68327e10i	0.00414248	+	0.00717499i
$562$	1.12810e12	+	1.95393e12i	0.477018	+	0.826220i
$563$	−4.68765e11	+	8.11925e11i	−0.196638	+	0.340587i	−0.947436	−	0.319945i	$-0.896336\pi$
$563$	−4.68765e11	+	8.11925e11i	−0.196638	+	0.340587i	0.750798	+	0.660532i	$0.229669\pi$
$564$	8.51601e11			0.354389
$565$	−1.73225e12	+	3.00035e12i	−0.715144	+	1.23867i
$566$	5.35661e11	−	9.27792e11i	0.219390	−	0.379994i
$567$	2.36697e12			0.961763
$568$	1.06486e12	−	1.84438e12i	0.429263	−	0.743505i
$569$	2.33285e12	+	4.04062e12i	0.933000	+	1.61600i	0.778161	+	0.628064i	$0.216153\pi$
$569$	2.33285e12	+	4.04062e12i	0.933000	+	1.61600i	0.154839	+	0.987940i	$0.450514\pi$
$570$	−1.12488e12	−	1.94836e12i	−0.446345	−	0.773092i
$571$	−2.94538e12			−1.15952			−0.579761	−	0.814786i	$-0.696854\pi$
$571$	−2.94538e12			−1.15952			−0.579761	+	0.814786i	$0.696854\pi$
$572$	6.02866e10	+	1.29778e11i	0.0235472	+	0.0506898i
$573$	−1.94523e11			−0.0753833
$574$	−5.75546e12	−	9.96874e12i	−2.21297	−	3.83298i
$575$	3.02974e11	+	5.24767e11i	0.115585	+	0.200199i
$576$	−1.66340e12	+	2.88110e12i	−0.629646	+	1.09058i
$577$	6.34946e11			0.238477			0.119238	−	0.992866i	$-0.461955\pi$
$577$	6.34946e11			0.238477			0.119238	+	0.992866i	$0.461955\pi$
$578$	−1.57842e12	+	2.73391e12i	−0.588231	+	1.01885i
$579$	−1.25265e11	+	2.16965e11i	−0.0463208	+	0.0802301i
$580$	2.38977e12			0.876860
$581$	1.10796e12	−	1.91904e12i	0.403396	−	0.698702i
$582$	−2.19026e11	−	3.79364e11i	−0.0791301	−	0.137057i
$583$	−7.33420e10	−	1.27032e11i	−0.0262932	−	0.0455412i
$584$	1.97888e11			0.0703981
$585$	−3.38141e12	−	3.00801e11i	−1.19370	−	0.106189i
$586$	1.73870e12			0.609094
$587$	−2.64973e11	−	4.58947e11i	−0.0921151	−	0.159548i	0.816286	−	0.577648i	$-0.196029\pi$
$587$	−2.64973e11	−	4.58947e11i	−0.0921151	−	0.159548i	−0.908401	+	0.418100i	$0.862696\pi$
$588$	−1.92864e12	−	3.34051e12i	−0.665356	−	1.15243i
$589$	9.30683e11	−	1.61199e12i	0.318627	−	0.551879i
$590$	1.26766e12			0.430695
$591$	−1.76091e11	+	3.04999e11i	−0.0593738	+	0.102838i
$592$	1.17310e12	−	2.03187e12i	0.392543	−	0.679905i
$593$	1.34558e12			0.446853			0.223426	−	0.974721i	$-0.428276\pi$
$593$	1.34558e12			0.446853			0.223426	+	0.974721i	$0.428276\pi$
$594$	−7.33192e10	+	1.26993e11i	−0.0241646	+	0.0418543i
$595$	−1.95651e12	−	3.38878e12i	−0.639965	−	1.10845i
$596$	7.36934e11	+	1.27641e12i	0.239233	+	0.414363i
$597$	−1.37978e12			−0.444555
$598$	−1.01485e12	−	9.02787e10i	−0.324525	−	0.0288689i
$599$	2.18020e12			0.691951			0.345976	−	0.938243i	$-0.387548\pi$
$599$	2.18020e12			0.691951			0.345976	+	0.938243i	$0.387548\pi$
$600$	3.58660e11	+	6.21218e11i	0.112980	+	0.195688i
$601$	−1.54971e11	−	2.68417e11i	−0.0484523	−	0.0839219i	0.840782	−	0.541374i	$-0.182096\pi$
$601$	−1.54971e11	−	2.68417e11i	−0.0484523	−	0.0839219i	−0.889234	+	0.457452i	$0.848762\pi$
$602$	−3.36530e12	+	5.82887e12i	−1.04433	+	1.80884i
$603$	1.38726e12			0.427298
$604$	−2.44863e12	+	4.24115e12i	−0.748612	+	1.29663i
$605$	−2.37405e12	+	4.11198e12i	−0.720429	+	1.24782i
$606$	2.98827e12			0.900105
$607$	8.15592e11	−	1.41265e12i	0.243851	−	0.422361i	−0.717957	−	0.696087i	$-0.754923\pi$
$607$	8.15592e11	−	1.41265e12i	0.243851	−	0.422361i	0.961808	+	0.273726i	$0.0882560\pi$
$608$	−2.25113e12	−	3.89907e12i	−0.668090	−	1.15717i
$609$	5.90462e11	+	1.02271e12i	0.173946	+	0.301283i
$610$	6.65174e12			1.94514
$611$	9.37609e11	+	2.01838e12i	0.272167	+	0.585893i
$612$	1.83813e12			0.529657
$613$	5.34948e11	+	9.26557e11i	0.153017	+	0.265033i	0.932335	−	0.361595i	$-0.117768\pi$
$613$	5.34948e11	+	9.26557e11i	0.153017	+	0.265033i	−0.779318	+	0.626628i	$0.784434\pi$
$614$	2.98977e11	+	5.17843e11i	0.0848945	+	0.147042i
$615$	−1.65187e12	+	2.86113e12i	−0.465628	+	0.806491i
$616$	−1.40557e11			−0.0393313
$617$	−4.14961e11	+	7.18734e11i	−0.115272	+	0.199657i	−0.917888	−	0.396838i	$-0.870107\pi$
$617$	−4.14961e11	+	7.18734e11i	−0.115272	+	0.199657i	0.802616	+	0.596496i	$0.203441\pi$
$618$	6.83824e11	−	1.18442e12i	0.188580	−	0.326630i
$619$	−6.58527e12			−1.80287			−0.901437	−	0.432910i	$-0.857487\pi$
$619$	−6.58527e12			−1.80287			−0.901437	+	0.432910i	$0.857487\pi$
$620$	−2.29179e12	+	3.96949e12i	−0.622890	+	1.07888i
$621$	−2.98135e11	−	5.16385e11i	−0.0804453	−	0.139335i
$622$	4.31655e12	+	7.47649e12i	1.15633	+	2.00282i
$623$	2.96023e12			0.787280
$624$	8.68052e11	+	7.72196e10i	0.229200	+	0.0203890i
$625$	−3.46998e12			−0.909634
$626$	−1.91070e12	−	3.30943e12i	−0.497288	−	0.861329i
$627$	−3.28973e10	−	5.69798e10i	−0.00850073	−	0.0147237i
$628$	2.81396e12	−	4.87393e12i	0.721938	−	1.25043i
$629$	−2.64372e12			−0.673421
$630$	6.69594e12	−	1.15977e13i	1.69348	−	2.93319i
$631$	−3.59582e12	+	6.22815e12i	−0.902955	+	1.56396i	−0.0793164	+	0.996849i	$0.525274\pi$
$631$	−3.59582e12	+	6.22815e12i	−0.902955	+	1.56396i	−0.823639	+	0.567115i	$0.808060\pi$
$632$	−1.87496e12			−0.467483
$633$	1.04900e12	−	1.81691e12i	0.259691	−	0.449798i
$634$	2.15116e12	+	3.72592e12i	0.528776	+	0.915867i
$635$	−3.17786e12	−	5.50421e12i	−0.775627	−	1.34342i
$636$	2.83576e12			0.687246
$637$	5.79392e12	−	8.24896e12i	1.39426	−	1.98505i
$638$	1.22376e11			0.0292418
$639$	2.96711e12	+	5.13918e12i	0.704011	+	1.21938i
$640$	2.93096e12	+	5.07658e12i	0.690559	+	1.19608i
$641$	4.12776e12	−	7.14948e12i	0.965724	−	1.67268i	0.258066	−	0.966127i	$-0.416915\pi$
$641$	4.12776e12	−	7.14948e12i	0.965724	−	1.67268i	0.707658	−	0.706555i	$-0.249752\pi$
$642$	2.86730e12			0.666140
$643$	1.16767e12	−	2.02246e12i	0.269383	−	0.466585i	−0.699320	−	0.714809i	$-0.746514\pi$
$643$	1.16767e12	−	2.02246e12i	0.269383	−	0.466585i	0.968703	+	0.248224i	$0.0798470\pi$
$644$	1.14770e12	−	1.98788e12i	0.262932	−	0.455412i
$645$	1.93175e12			0.439473
$646$	−1.59174e12	+	2.75697e12i	−0.359605	+	0.622854i
$647$	−3.61361e12	−	6.25896e12i	−0.810723	−	1.40421i	−0.912359	−	0.409391i	$-0.865741\pi$
$647$	−3.61361e12	−	6.25896e12i	−0.810723	−	1.40421i	0.101636	−	0.994822i	$-0.467592\pi$
$648$	5.90350e11	+	1.02252e12i	0.131529	+	0.227815i
$649$	3.70729e10			0.00820267
$650$	−4.32731e12	+	6.16091e12i	−0.950841	+	1.35374i
$651$	−2.26501e12			−0.494260
$652$	1.56506e12	+	2.71077e12i	0.339170	+	0.587460i
$653$	−1.48931e12	−	2.57957e12i	−0.320536	−	0.555184i	0.660063	−	0.751210i	$-0.270530\pi$
$653$	−1.48931e12	−	2.57957e12i	−0.320536	−	0.555184i	−0.980599	+	0.196026i	$0.937196\pi$
$654$	−2.89151e11	+	5.00824e11i	−0.0618051	+	0.107050i
$655$	8.18438e12			1.73740
$656$	−2.07440e12	+	3.59296e12i	−0.437345	+	0.757504i
$657$	−2.75697e11	+	4.77521e11i	−0.0577281	+	0.0999881i
$658$	−8.77942e12			−1.82578
$659$	−8.92033e11	+	1.54505e12i	−0.184245	+	0.319122i	−0.943322	−	0.331879i	$-0.892317\pi$
$659$	−8.92033e11	+	1.54505e12i	−0.184245	+	0.319122i	0.759077	+	0.651001i	$0.225651\pi$
$660$	8.10088e10	+	1.40311e11i	0.0166182	+	0.0287836i
$661$	1.19570e12	+	2.07102e12i	0.243622	+	0.421965i	0.961743	−	0.273952i	$-0.0883311\pi$
$661$	1.19570e12	+	2.07102e12i	0.243622	+	0.421965i	−0.718121	+	0.695918i	$0.754998\pi$
$662$	−1.27867e13			−2.58761
$663$	−4.13709e11	−	8.90589e11i	−0.0831542	−	0.179005i
$664$	1.10535e12			0.220671
$665$	6.62291e12	+	1.14712e13i	1.31326	+	2.27464i
$666$	−4.52391e12	−	7.83565e12i	−0.891005	−	1.54327i
$667$	−2.48806e11	+	4.30945e11i	−0.0486738	+	0.0843055i
$668$	−4.82533e12			−0.937633
$669$	5.90603e11	−	1.02295e12i	0.113993	−	0.197442i
$670$	2.95819e12	−	5.12374e12i	0.567139	−	0.982314i
$671$	1.94531e11			0.0370456
$672$	−2.73929e12	+	4.74459e12i	−0.518175	+	0.897506i
$673$	4.24513e11	+	7.35279e11i	0.0797671	+	0.138161i	0.903149	−	0.429326i	$-0.141249\pi$
$673$	4.24513e11	+	7.35279e11i	0.0797671	+	0.138161i	−0.823382	+	0.567487i	$0.807916\pi$
$674$	−2.32094e12	−	4.01999e12i	−0.433207	−	0.750336i
$675$	−4.40607e12			−0.816930
$676$	−2.45287e12	−	6.80080e12i	−0.451766	−	1.25256i
$677$	−7.32191e12			−1.33960			−0.669801	−	0.742541i	$-0.733620\pi$
$677$	−7.32191e12			−1.33960			−0.669801	+	0.742541i	$0.733620\pi$
$678$	−1.71490e12	−	2.97029e12i	−0.311677	−	0.539841i
$679$	1.28955e12	+	2.23356e12i	0.232821	+	0.403258i
$680$	9.75955e11	−	1.69040e12i	0.175041	−	0.303180i
$681$	−4.33189e12			−0.771818
$682$	−1.17358e11	+	2.03271e11i	−0.0207723	+	0.0359787i
$683$	5.09863e12	−	8.83109e12i	0.896521	−	1.55282i	0.0646111	−	0.997911i	$-0.479419\pi$
$683$	5.09863e12	−	8.83109e12i	0.896521	−	1.55282i	0.831910	−	0.554910i	$-0.187247\pi$
$684$	−6.22219e12			−1.08690
$685$	−5.81296e12	+	1.00683e13i	−1.00876	+	1.74723i
$686$	1.16864e13	+	2.02415e13i	2.01476	+	3.48967i
$687$	2.13874e12	+	3.70440e12i	0.366313	+	0.634473i
$688$	2.42586e12			0.412779
$689$	3.12216e12	+	6.72104e12i	0.527798	+	1.13619i
$690$	−1.15357e12			−0.193742
$691$	−2.55690e12	−	4.42868e12i	−0.426641	−	0.738964i	0.569931	−	0.821692i	$-0.306970\pi$
$691$	−2.55690e12	−	4.42868e12i	−0.426641	−	0.738964i	−0.996572	+	0.0827287i	$0.973637\pi$
$692$	−1.54619e12	−	2.67807e12i	−0.256321	−	0.443961i
$693$	1.95823e11	−	3.39176e11i	0.0322526	−	0.0558631i
$694$	1.75151e12			0.286612
$695$	6.62771e12	−	1.14795e13i	1.07754	−	1.86635i
$696$	−2.94537e11	+	5.10153e11i	−0.0475771	+	0.0824060i
$697$	4.67489e12			0.750281
$698$	−2.67150e11	+	4.62718e11i	−0.0425997	+	0.0737848i
$699$	9.95675e11	+	1.72456e12i	0.157750	+	0.273232i
$700$	−8.48084e12	−	1.46892e13i	−1.33505	−	2.31237i
$701$	3.05596e12			0.477988			0.238994	−	0.971021i	$-0.423182\pi$
$701$	3.05596e12			0.477988			0.238994	+	0.971021i	$0.423182\pi$
$702$	4.25819e12	−	6.06250e12i	0.661772	−	0.942183i
$703$	8.94914e12			1.38192
$704$	2.07466e11	+	3.59342e11i	0.0318325	+	0.0551355i
$705$	1.25989e12	+	2.18220e12i	0.192080	+	0.332692i
$706$	−4.89240e12	+	8.47388e12i	−0.741140	+	1.28369i
$707$	−1.75939e13			−2.64834
$708$	−3.58355e11	+	6.20689e11i	−0.0535998	+	0.0928377i
$709$	8.17177e11	−	1.41539e12i	0.121453	−	0.210363i	−0.798888	−	0.601480i	$-0.794578\pi$
$709$	8.17177e11	−	1.41539e12i	0.121453	−	0.210363i	0.920341	+	0.391117i	$0.127911\pi$
$710$	2.53082e13			3.73765
$711$	2.61219e12	−	4.52445e12i	0.383347	−	0.663977i
$712$	7.38317e11	+	1.27880e12i	0.107667	+	0.186485i
$713$	−4.77210e11	−	8.26552e11i	−0.0691523	−	0.119775i
$714$	3.87382e12			0.557824
$715$	−2.43362e11	+	3.46481e11i	−0.0348237	+	0.0495795i
$716$	3.32396e12			0.472658
$717$	−8.97411e11	−	1.55436e12i	−0.126811	−	0.219642i
$718$	1.86558e12	+	3.23128e12i	0.261972	+	0.453749i
$719$	1.42598e12	−	2.46986e12i	0.198990	−	0.344661i	−0.749211	−	0.662331i	$-0.769567\pi$
$719$	1.42598e12	−	2.46986e12i	0.198990	−	0.344661i	0.948201	+	0.317670i	$0.102900\pi$
$720$	−4.82673e12			−0.669356
$721$	−4.02611e12	+	6.97342e12i	−0.554851	+	0.961031i
$722$	−1.86408e11	+	3.22868e11i	−0.0255298	+	0.0442188i
$723$	−4.43118e12			−0.603110
$724$	3.84699e12	−	6.66317e12i	0.520352	−	0.901276i
$725$	1.83853e12	+	3.18443e12i	0.247144	+	0.428066i
$726$	−2.35027e12	−	4.07079e12i	−0.313981	−	0.543831i
$727$	7.77894e12			1.03280			0.516400	−	0.856348i	$-0.327272\pi$
$727$	7.77894e12			1.03280			0.516400	+	0.856348i	$0.327272\pi$
$728$	7.07331e12	+	6.29223e11i	0.933322	+	0.0830259i
$729$	−9.21017e11			−0.120780
$730$	1.17579e12	+	2.03653e12i	0.153241	+	0.265422i
$731$	−1.36674e12	−	2.36726e12i	−0.177034	−	0.306632i
$732$	−1.88038e12	+	3.25691e12i	−0.242072	+	0.419281i
$733$	1.47426e13			1.88628			0.943139	−	0.332397i	$-0.107858\pi$
$733$	1.47426e13			1.88628			0.943139	+	0.332397i	$0.107858\pi$
$734$	−2.75860e12	+	4.77804e12i	−0.350798	+	0.607599i
$735$	5.70661e12	−	9.88414e12i	0.721249	−	1.24924i
$736$	−2.30854e12			−0.289993
$737$	8.65125e10	−	1.49844e11i	0.0108013	−	0.0187084i
$738$	7.99964e12	+	1.38558e13i	0.992697	+	1.71940i
$739$	−1.49877e12	−	2.59594e12i	−0.184856	−	0.320180i	0.758672	−	0.651473i	$-0.225849\pi$
$739$	−1.49877e12	−	2.59594e12i	−0.184856	−	0.320180i	−0.943528	+	0.331293i	$0.892515\pi$
$740$	−2.20371e13			−2.70154
$741$	1.40043e12	+	3.01470e12i	0.170640	+	0.367335i
$742$	−2.92347e13			−3.54063
$743$	−1.13143e11	−	1.95970e11i	−0.0136201	−	0.0235907i	0.859135	−	0.511749i	$-0.171002\pi$
$743$	−1.13143e11	−	1.95970e11i	−0.0136201	−	0.0235907i	−0.872755	+	0.488158i	$0.837669\pi$
$744$	−5.64920e11	−	9.78471e11i	−0.0675941	−	0.117076i
$745$	−2.18050e12	+	3.77673e12i	−0.259330	+	0.449172i
$746$	1.10882e13			1.31080
$747$	−1.53998e12	+	2.66732e12i	−0.180956	+	0.313424i
$748$	1.14629e11	−	1.98544e11i	0.0133887	−	0.0231899i
$749$	−1.68816e13			−1.95996
$750$	−3.28127e11	+	5.68333e11i	−0.0378675	+	0.0655885i
$751$	2.23667e12	+	3.87402e12i	0.256579	+	0.444409i	0.965323	−	0.261057i	$-0.0840711\pi$
$751$	2.23667e12	+	3.87402e12i	0.256579	+	0.444409i	−0.708744	+	0.705466i	$0.750738\pi$
$752$	1.58215e12	+	2.74036e12i	0.180413	+	0.312484i
$753$	−1.92675e12			−0.218398
$754$	−6.15841e12	−	5.47836e11i	−0.693901	−	0.0617276i
$755$	−1.44904e13			−1.62300
$756$	8.34538e12	+	1.44546e13i	0.929176	+	1.60938i
$757$	3.44790e12	+	5.97195e12i	0.381614	+	0.660974i	0.991293	−	0.131674i	$-0.0420352\pi$
$757$	3.44790e12	+	5.97195e12i	0.381614	+	0.660974i	−0.609680	+	0.792648i	$0.708702\pi$
$758$	9.85141e12	−	1.70631e13i	1.08389	−	1.87736i
$759$	−3.37363e10			−0.00368986
$760$	−3.30367e12	+	5.72212e12i	−0.359199	+	0.622151i
$761$	8.67200e12	−	1.50203e13i	0.937321	−	1.62349i	0.166878	−	0.985978i	$-0.446631\pi$
$761$	8.67200e12	−	1.50203e13i	0.937321	−	1.62349i	0.770443	−	0.637509i	$-0.220035\pi$
$762$	6.29204e12			0.676074
$763$	1.70242e12	−	2.94867e12i	0.181847	−	0.314967i
$764$	1.14721e12	+	1.98703e12i	0.121821	+	0.211001i
$765$	2.71940e12	+	4.71014e12i	0.287076	+	0.497230i
$766$	3.55724e12			0.373322
$767$	−1.86564e12	−	1.65963e11i	−0.194648	−	0.0173153i
$768$	2.21129e11			0.0229361
$769$	−5.40819e12	−	9.36726e12i	−0.557678	−	0.965927i	−0.997690	−	0.0679347i	$-0.978359\pi$
$769$	−5.40819e12	−	9.36726e12i	−0.557678	−	0.965927i	0.440012	−	0.897992i	$-0.354974\pi$
$770$	−8.35144e11	−	1.44651e12i	−0.0856157	−	0.148291i
$771$	−1.52298e11	+	2.63787e11i	−0.0155220	+	0.0268850i
$772$	2.95504e12			0.299423
$773$	−1.64694e12	+	2.85258e12i	−0.165909	+	0.287362i	−0.936978	−	0.349389i	$-0.886389\pi$
$773$	−1.64694e12	+	2.85258e12i	−0.165909	+	0.287362i	0.771069	+	0.636752i	$0.219722\pi$
$774$	4.67750e12	−	8.10167e12i	0.468468	−	0.811410i
$775$	−7.05259e12			−0.702248
$776$	−6.43257e11	+	1.11415e12i	−0.0636805	+	0.110298i
$777$	−5.44489e12	−	9.43083e12i	−0.535913	−	0.928229i
$778$	−7.20522e12	−	1.24798e13i	−0.705082	−	1.22124i
$779$	−1.58248e13			−1.53964
$780$	−3.44853e12	−	7.42362e12i	−0.333586	−	0.718109i
$781$	7.40139e11			0.0711842
$782$	8.16167e11	+	1.41364e12i	0.0780457	+	0.135179i
$783$	−1.80916e12	−	3.13356e12i	−0.172009	−	0.297928i
$784$	7.16627e12	−	1.24123e13i	0.677440	−	1.17336i
$785$	1.66523e13			1.56517
$786$	−4.05120e12	+	7.01688e12i	−0.378601	+	0.655756i
$787$	−5.39166e12	+	9.33863e12i	−0.500998	+	0.867754i	0.499001	+	0.866601i	$0.333700\pi$
$787$	−5.39166e12	+	9.33863e12i	−0.500998	+	0.867754i	−0.999999	+	0.00115307i	$0.999633\pi$
$788$	4.15405e12			0.383799
$789$	−1.16105e12	+	2.01099e12i	−0.106660	+	0.184741i
$790$	−1.11405e13	−	1.92958e13i	−1.01761	−	1.76255i
$791$	1.00967e13	+	1.74880e13i	0.917035	+	1.58835i
$792$	1.95363e11			0.0176432
$793$	−9.78948e12	−	8.70846e11i	−0.879084	−	0.0782010i
$794$	2.58654e13			2.30955
$795$	4.19533e12	+	7.26652e12i	0.372489	+	0.645170i
$796$	8.13735e12	+	1.40943e13i	0.718413	+	1.24433i
$797$	4.13509e11	−	7.16219e11i	0.0363013	−	0.0628758i	−0.847304	−	0.531108i	$-0.821776\pi$
$797$	4.13509e11	−	7.16219e11i	0.0363013	−	0.0628758i	0.883605	+	0.468233i	$0.155109\pi$
$798$	−1.31131e13			−1.14470
$799$	1.78278e12	−	3.08786e12i	0.154752	−	0.268039i
$800$	−8.52938e12	+	1.47733e13i	−0.736228	+	1.27518i
$801$	−4.11449e12			−0.353158
$802$	−5.27067e12	+	9.12907e12i	−0.449864	+	0.779187i
$803$	3.43860e10	+	5.95583e10i	0.00291851	+	0.00505501i
$804$	1.67250e12	+	2.89685e12i	0.141160	+	0.244497i
$805$	6.79182e12			0.570039
$806$	6.81588e12	−	9.70395e12i	0.568871	−	0.809918i
$807$	4.54431e12			0.377170
$808$	−4.38812e12	−	7.60045e12i	−0.362183	−	0.627319i
$809$	9.32513e11	+	1.61516e12i	0.0765397	+	0.132571i	0.901755	−	0.432248i	$-0.142279\pi$
$809$	9.32513e11	+	1.61516e12i	0.0765397	+	0.132571i	−0.825215	+	0.564819i	$0.808946\pi$
$810$	−7.01536e12	+	1.21510e13i	−0.572621	+	0.991809i
$811$	9.37569e12			0.761044			0.380522	−	0.924772i	$-0.375744\pi$
$811$	9.37569e12			0.761044			0.380522	+	0.924772i	$0.375744\pi$
$812$	6.96458e12	−	1.20630e13i	0.562202	−	0.973763i
$813$	−2.98027e12	+	5.16199e12i	−0.239248	+	0.414390i
$814$	−1.12848e12			−0.0900916
$815$	−4.63082e12	+	8.02082e12i	−0.367662	+	0.636810i
$816$	−6.98106e11	−	1.20915e12i	−0.0551208	−	0.0954720i
$817$	4.62649e12	+	8.01331e12i	0.363289	+	0.629235i
$818$	5.19613e10			0.00405780
$819$	−1.13729e13	+	1.61919e13i	−0.883271	+	1.25754i
$820$	3.89682e13			3.00987
$821$	−7.95351e12	−	1.37759e13i	−0.610962	−	1.05822i	−0.991079	−	0.133279i	$-0.957449\pi$
$821$	−7.95351e12	−	1.37759e13i	−0.610962	−	1.05822i	0.380116	−	0.924939i	$-0.375884\pi$
$822$	−5.75473e12	−	9.96748e12i	−0.439644	−	0.761486i
$823$	−7.15307e11	+	1.23895e12i	−0.0543492	+	0.0941356i	−0.891920	−	0.452193i	$-0.850642\pi$
$823$	−7.15307e11	+	1.23895e12i	−0.0543492	+	0.0941356i	0.837571	+	0.546329i	$0.183975\pi$
$824$	−4.01664e12			−0.303522
$825$	−1.24645e11	+	2.15892e11i	−0.00936772	+	0.0162254i
$826$	3.69439e12	−	6.39887e12i	0.276142	−	0.478292i
$827$	1.83657e13			1.36532			0.682658	−	0.730738i	$-0.260824\pi$
$827$	1.83657e13			1.36532			0.682658	+	0.730738i	$0.260824\pi$
$828$	−1.59522e12	+	2.76300e12i	−0.117946	+	0.204289i
$829$	−1.76688e12	−	3.06033e12i	−0.129931	−	0.225047i	0.793719	−	0.608285i	$-0.208142\pi$
$829$	−1.76688e12	−	3.06033e12i	−0.129931	−	0.225047i	−0.923650	+	0.383238i	$0.874809\pi$
$830$	6.56768e12	+	1.13756e13i	0.480353	+	0.831996i
$831$	2.00901e12			0.146143
$832$	−8.83181e12	−	1.90122e13i	−0.638991	−	1.37555i
$833$	−1.61500e13			−1.16217
$834$	6.56131e12	+	1.13645e13i	0.469617	+	0.813400i
$835$	−7.13877e12	−	1.23647e13i	−0.508199	−	0.880227i
$836$	−3.88028e11	+	6.72084e11i	−0.0274748	+	0.0475878i
$837$	6.93994e12			0.488755
$838$	−1.41235e13	+	2.44626e13i	−0.989335	+	1.71358i
$839$	−6.00258e12	+	1.03968e13i	−0.418224	+	0.724385i	−0.995761	−	0.0919793i	$-0.970681\pi$
$839$	−6.00258e12	+	1.03968e13i	−0.418224	+	0.724385i	0.577537	+	0.816365i	$0.304014\pi$
$840$	8.04015e12			0.557195
$841$	5.74375e12	−	9.94846e12i	0.395925	−	0.685763i
$842$	−1.09385e13	−	1.89461e13i	−0.749988	−	1.29902i
$843$	−1.88718e12	−	3.26870e12i	−0.128703	−	0.222921i
$844$	−2.47461e13			−1.67867
$845$	1.37979e13	−	1.63467e13i	0.931020	−	1.10300i
$846$	1.22027e13			0.819011
$847$	1.38375e13	+	2.39673e13i	0.923812	+	1.60009i
$848$	5.26842e12	+	9.12517e12i	0.349864	+	0.605982i
$849$	−8.96099e11	+	1.55209e12i	−0.0591931	+	0.102526i
$850$	1.20620e13			0.792562
$851$	2.29435e12	−	3.97392e12i	0.149960	−	0.259739i
$852$	−7.15435e12	+	1.23917e13i	−0.465149	+	0.805662i
$853$	−4.08408e12			−0.264134			−0.132067	−	0.991241i	$-0.542161\pi$
$853$	−4.08408e12			−0.264134			−0.132067	+	0.991241i	$0.542161\pi$
$854$	1.93854e13	−	3.35764e13i	1.24714	−	2.16010i
$855$	−9.20534e12	−	1.59441e13i	−0.589104	−	1.02036i
$856$	−4.21049e12	−	7.29278e12i	−0.268041	−	0.464260i
$857$	−9.43183e12			−0.597286			−0.298643	−	0.954365i	$-0.596534\pi$
$857$	−9.43183e12			−0.597286			−0.298643	+	0.954365i	$0.596534\pi$
$858$	−1.76593e11	−	3.80151e11i	−0.0111245	−	0.0239477i
$859$	1.99583e12			0.125071			0.0625353	−	0.998043i	$-0.480081\pi$
$859$	1.99583e12			0.125071			0.0625353	+	0.998043i	$0.480081\pi$
$860$	−1.13926e13	−	1.97326e13i	−0.710200	−	1.23010i
$861$	9.62821e12	+	1.66766e13i	0.597079	+	1.03417i
$862$	−1.17183e13	+	2.02966e13i	−0.722903	+	1.25211i
$863$	1.89496e13			1.16292			0.581461	−	0.813575i	$-0.302481\pi$
$863$	1.89496e13			1.16292			0.581461	+	0.813575i	$0.302481\pi$
$864$	8.39314e12	−	1.45373e13i	0.512404	−	0.887510i
$865$	4.57497e12	−	7.92408e12i	0.277853	−	0.481256i
$866$	−2.29297e13			−1.38538
$867$	2.64052e12	−	4.57351e12i	0.158710	−	0.274893i
$868$	1.33580e13	+	2.31368e13i	0.798737	+	1.38345i
$869$	−3.25803e11	−	5.64308e11i	−0.0193806	−	0.0335681i
$870$	−7.00019e12			−0.414260
$871$	−5.02442e12	+	7.15341e12i	−0.295804	+	0.421145i
$872$	1.69841e12			0.0994762
$873$	−1.79237e12	−	3.10447e12i	−0.104439	−	0.180894i
$874$	−2.76278e12	−	4.78527e12i	−0.160156	−	0.277399i
$875$	1.93190e12	−	3.34614e12i	0.111416	−	0.192978i
$876$	−1.32953e12			−0.0762834
$877$	−1.39331e13	+	2.41328e13i	−0.795333	+	1.37756i	0.127295	+	0.991865i	$0.459371\pi$
$877$	−1.39331e13	+	2.41328e13i	−0.795333	+	1.37756i	−0.922628	+	0.385692i	$0.873963\pi$
$878$	−1.74822e13	+	3.02800e13i	−0.992819	+	1.71961i
$879$	−2.90864e12			−0.164339
$880$	−3.01005e11	+	5.21355e11i	−0.0169200	+	0.0293064i
$881$	−4.74573e12	−	8.21985e12i	−0.265407	−	0.459698i	0.702263	−	0.711917i	$-0.252173\pi$
$881$	−4.74573e12	−	8.21985e12i	−0.265407	−	0.459698i	−0.967670	+	0.252219i	$0.918840\pi$
$882$	−2.76358e13	−	4.78666e13i	−1.53767	−	2.66332i
$883$	2.56505e13			1.41995			0.709974	−	0.704228i	$-0.248707\pi$
$883$	2.56505e13			1.41995			0.709974	+	0.704228i	$0.248707\pi$
$884$	−6.65738e12	+	9.47830e12i	−0.366664	+	0.522030i
$885$	−2.12065e12			−0.116205
$886$	−7.43129e12	−	1.28714e13i	−0.405147	−	0.701735i
$887$	−7.95184e12	−	1.37730e13i	−0.431332	−	0.747089i	0.565657	−	0.824641i	$-0.308623\pi$
$887$	−7.95184e12	−	1.37730e13i	−0.431332	−	0.747089i	−0.996988	+	0.0775524i	$0.975289\pi$
$888$	2.71604e12	−	4.70433e12i	0.146581	−	0.253886i
$889$	−3.70453e13			−1.98919
$890$	−8.77371e12	+	1.51965e13i	−0.468736	+	0.811875i
$891$	−2.05165e11	+	3.55356e11i	−0.0109057	+	0.0188892i
$892$	−1.39325e13			−0.736863
$893$	−6.03481e12	+	1.04526e13i	−0.317565	+	0.550038i
$894$	−2.15865e12	−	3.73889e12i	−0.113022	−	0.195760i
$895$	4.91758e12	+	8.51751e12i	0.256182	+	0.443720i
$896$	3.41672e13			1.77102
$897$	1.69773e12	+	1.51026e11i	0.0875595	+	0.00778906i
$898$	−3.20407e13			−1.64422
$899$	−2.89584e12	−	5.01574e12i	−0.147862	−	0.256104i
$900$	1.17877e13	+	2.04169e13i	0.598878	+	1.03729i
$901$	5.93650e12	−	1.02823e13i	0.300102	−	0.519792i
$902$	1.99549e12			0.100374
$903$	5.62975e12	−	9.75102e12i	0.281770	−	0.488040i
$904$	−5.03649e12	+	8.72345e12i	−0.250824	+	0.434441i
$905$	2.27655e13			1.12813
$906$	7.17260e12	−	1.24233e13i	0.353671	−	0.612577i
$907$	−1.67760e12	−	2.90569e12i	−0.0823106	−	0.142566i	0.821931	−	0.569586i	$-0.192897\pi$
$907$	−1.67760e12	−	2.90569e12i	−0.0823106	−	0.142566i	−0.904242	+	0.427020i	$0.859563\pi$
$908$	2.55476e13	+	4.42497e13i	1.24728	+	2.16035i
$909$	2.44541e13			1.18799
$910$	3.55519e13	+	7.65324e13i	1.71861	+	3.69964i
$911$	−1.30744e13			−0.628912			−0.314456	−	0.949272i	$-0.601822\pi$
$911$	−1.30744e13			−0.628912			−0.314456	+	0.949272i	$0.601822\pi$
$912$	2.36313e12	+	4.09306e12i	0.113113	+	0.195917i
$913$	1.92072e11	+	3.32679e11i	0.00914842	+	0.0158455i
$914$	−2.11163e13	+	3.65745e13i	−1.00083	+	1.73349i
$915$	−1.11276e13			−0.524815
$916$	2.52267e13	−	4.36940e13i	1.18394	−	2.05065i
$917$	2.38520e13	−	4.13129e13i	1.11394	−	1.92940i
$918$	−1.18693e13			−0.551612
$919$	1.38181e12	−	2.39336e12i	0.0639040	−	0.110685i	−0.832303	−	0.554320i	$-0.812978\pi$
$919$	1.38181e12	−	2.39336e12i	0.0639040	−	0.110685i	0.896207	+	0.443636i	$0.146312\pi$
$920$	1.69396e12	+	2.93403e12i	0.0779577	+	0.135027i
$921$	−5.00153e11	−	8.66291e11i	−0.0229052	−	0.0396730i
$922$	4.41893e13			2.01385
$923$	−3.72465e13	−	3.31335e12i	−1.68919	−	0.150266i
$924$	9.44345e11			0.0426194
$925$	−1.69538e13	−	2.93649e13i	−0.761430	−	1.31884i
$926$	−9.64294e12	−	1.67021e13i	−0.430983	−	0.746484i
$927$	5.59598e12	−	9.69252e12i	0.248896	−	0.431100i
$928$	−1.40089e13			−0.620065
$929$	1.66130e13	−	2.87745e13i	0.731774	−	1.26747i	−0.224350	−	0.974509i	$-0.572026\pi$
$929$	1.66130e13	−	2.87745e13i	0.731774	−	1.26747i	0.956124	−	0.292961i	$-0.0946406\pi$
$930$	6.71317e12	−	1.16276e13i	0.294276	−	0.509701i
$931$	5.46688e13			2.38488
$932$	1.17441e13	−	2.03414e13i	0.509858	−	0.883100i
$933$	−7.22110e12	−	1.25073e13i	−0.311986	−	0.540376i
$934$	1.26832e13	+	2.19679e13i	0.545340	+	0.944557i
$935$	6.78349e11			0.0290269
$936$	−9.83136e12	−	8.74572e11i	−0.418670	−	0.0372438i
$937$	2.58379e13			1.09504			0.547519	−	0.836793i	$-0.315572\pi$
$937$	2.58379e13			1.09504			0.547519	+	0.836793i	$0.315572\pi$
$938$	−1.72423e13	−	2.98645e13i	−0.727247	−	1.25963i
$939$	3.19638e12	+	5.53630e12i	0.134173	+	0.232394i
$940$	1.48606e13	−	2.57393e13i	0.620813	−	1.07528i
$941$	−3.11794e13			−1.29633			−0.648164	−	0.761501i	$-0.724463\pi$
$941$	−3.11794e13			−1.29633			−0.648164	+	0.761501i	$0.724463\pi$
$942$	−8.24275e12	+	1.42769e13i	−0.341070	+	0.590750i
$943$	−4.05710e12	+	7.02710e12i	−0.167076	+	0.289383i
$944$	−2.66308e12			−0.109147
$945$	−2.46929e13	+	4.27694e13i	−1.00723	+	1.74458i
$946$	−5.83397e11	−	1.01047e12i	−0.0236839	−	0.0410218i
$947$	8.33195e12	+	1.44314e13i	0.336645	+	0.583086i	0.983799	−	0.179273i	$-0.0573745\pi$
$947$	8.33195e12	+	1.44314e13i	0.336645	+	0.583086i	−0.647155	+	0.762359i	$0.724041\pi$
$948$	1.25971e13			0.506564
$949$	−1.46381e12	−	3.15112e12i	−0.0585849	−	0.126115i
$950$	−4.08305e13			−1.62641
$951$	−3.59865e12	−	6.23304e12i	−0.142668	−	0.247108i
$952$	−5.68851e12	−	9.85279e12i	−0.224457	−	0.388770i
$953$	−3.34004e12	+	5.78512e12i	−0.131170	+	0.227193i	−0.924128	−	0.382084i	$-0.875207\pi$
$953$	−3.34004e12	+	5.78512e12i	−0.131170	+	0.227193i	0.792958	+	0.609276i	$0.208540\pi$
$954$	4.06340e13			1.58826
$955$	−3.39446e12	+	5.87937e12i	−0.132055	+	0.228726i
$956$	−1.05851e13	+	1.83339e13i	−0.409858	+	0.709896i
$957$	−2.04721e11			−0.00788967
$958$	−5.66143e12	+	9.80589e12i	−0.217161	+	0.376134i
$959$	3.38818e13	+	5.86849e13i	1.29355	+	2.24049i
$960$	−1.18676e13	−	2.05552e13i	−0.450963	−	0.781090i
$961$	−1.53312e13			−0.579857
$962$	5.67892e13	+	5.05182e12i	2.13785	+	0.190178i
$963$	2.34642e13			0.879199
$964$	2.61332e13	+	4.52640e13i	0.974643	+	1.68813i
$965$	4.37179e12	+	7.57217e12i	0.162288	+	0.281091i
$966$	−3.36189e12	+	5.82297e12i	−0.124219	+	0.215153i
$967$	−4.90746e13			−1.80484			−0.902418	−	0.430862i	$-0.858210\pi$
$967$	−4.90746e13			−1.80484			−0.902418	+	0.430862i	$0.858210\pi$
$968$	−6.90251e12	+	1.19555e13i	−0.252678	+	0.437651i
$969$	2.66279e12	−	4.61209e12i	0.0970243	−	0.168051i
$970$	−1.52881e13			−0.554475
$971$	−1.20152e13	+	2.08110e13i	−0.433757	+	0.751289i	−0.997193	−	0.0748707i	$-0.976146\pi$
$971$	−1.20152e13	+	2.08110e13i	−0.433757	+	0.751289i	0.563437	+	0.826159i	$0.309479\pi$
$972$	−1.79370e13	−	3.10678e13i	−0.644542	−	1.11638i
$973$	−3.86307e13	−	6.69103e13i	−1.38173	−	2.39323i
$974$	−4.67451e13			−1.66426
$975$	7.23909e12	−	1.03065e13i	0.256545	−	0.365250i
$976$	−1.39738e13			−0.492937
$977$	2.27303e13	+	3.93701e13i	0.798141	+	1.38242i	0.920825	+	0.389976i	$0.127517\pi$
$977$	2.27303e13	+	3.93701e13i	0.798141	+	1.38242i	−0.122684	+	0.992446i	$0.539150\pi$
$978$	−4.58443e12	−	7.94047e12i	−0.160236	−	0.277537i
$979$	−2.56588e11	+	4.44423e11i	−0.00892717	+	0.0154623i
$980$	−1.34621e14			−4.66223
$981$	−2.36623e12	+	4.09842e12i	−0.0815729	+	0.141288i
$982$	−3.17132e12	+	5.49289e12i	−0.108828	+	0.188495i
$983$	−1.29574e13			−0.442617			−0.221308	−	0.975204i	$-0.571033\pi$
$983$	−1.29574e13			−0.442617			−0.221308	+	0.975204i	$0.571033\pi$
$984$	−4.80279e12	+	8.31867e12i	−0.163311	+	0.282863i
$985$	6.14565e12	+	1.06446e13i	0.208020	+	0.360301i
$986$	4.95273e12	+	8.57837e12i	0.166878	+	0.289041i
$987$	1.46870e13			0.492611
$988$	2.25357e13	−	3.20846e13i	0.752426	−	1.07125i
$989$	4.74448e12			0.157691
$990$	1.16079e12	+	2.01054e12i	0.0384055	+	0.0665203i
$991$	−2.34970e13	−	4.06981e13i	−0.773895	−	1.34042i	−0.935414	−	0.353555i	$-0.884973\pi$
$991$	−2.34970e13	−	4.06981e13i	−0.773895	−	1.34042i	0.161519	−	0.986870i	$-0.448361\pi$
$992$	1.34345e13	−	2.32692e13i	0.440472	−	0.762920i
$993$	2.13907e13			0.698158
$994$	7.37564e13	−	1.27750e14i	2.39641	−	4.15070i
$995$	−2.40774e13	+	4.17033e13i	−0.778764	+	1.34886i
$996$	−7.42645e12			−0.239119
$997$	−2.97596e12	+	5.15452e12i	−0.0953892	+	0.165219i	−0.909771	−	0.415111i	$-0.863743\pi$
$997$	−2.97596e12	+	5.15452e12i	−0.0953892	+	0.165219i	0.814382	+	0.580329i	$0.197076\pi$
$998$	1.24081e12	+	2.14915e12i	0.0395930	+	0.0685771i
$999$	1.66830e13	+	2.88959e13i	0.529945	+	0.917891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.10.c.a.3.8	✓	18
13.3	even	3		169.10.a.c.1.2		9
13.9	even	3	inner	13.10.c.a.9.8	yes	18
13.10	even	6		169.10.a.d.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.c.a.3.8	✓	18	1.1	even	1	trivial
13.10.c.a.9.8	yes	18	13.9	even	3	inner
169.10.a.c.1.2		9	13.3	even	3
169.10.a.d.1.8		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(17.2753 + 29.9218i) q^{2} +(-28.8997 - 50.0557i) q^{3} +(-340.875 + 590.413i) q^{4} -2017.22 q^{5} +(998.503 - 1729.46i) q^{6} +(-5878.83 + 10182.4i) q^{7} -5865.01 q^{8} +(8171.12 - 14152.8i) q^{9} +(-34848.1 - 60358.7i) q^{10} +(-1019.13 - 1765.19i) q^{11} +39404.7 q^{12} +(43384.4 + 93393.2i) q^{13} -406235. q^{14} +(58296.8 + 100973. i) q^{15} +(73208.1 + 126800. i) q^{16} +(82491.5 - 142879. i) q^{17} +564636. q^{18} +(-279239. + 483656. i) q^{19} +(687619. - 1.19099e6i) q^{20} +679585. q^{21} +(35211.8 - 60988.7i) q^{22} +(143180. + 247996. i) q^{23} +(169497. + 293577. i) q^{24} +2.11603e6 q^{25} +(-2.04501e6 + 2.91154e6i) q^{26} -2.08223e6 q^{27} +(-4.00790e6 - 6.94188e6i) q^{28} +(868857. + 1.50490e6i) q^{29} +(-2.01420e6 + 3.48869e6i) q^{30} -3.33293e6 q^{31} +(-4.03083e6 + 6.98161e6i) q^{32} +(-58905.3 + 102027. i) q^{33} +5.70028e6 q^{34} +(1.18589e7 - 2.05402e7i) q^{35} +(5.57067e6 + 9.64868e6i) q^{36} +(-8.01209e6 - 1.38773e7i) q^{37} -1.92958e7 q^{38} +(3.42107e6 - 4.87067e6i) q^{39} +1.18310e7 q^{40} +(1.41678e7 + 2.45393e7i) q^{41} +(1.17401e7 + 2.03344e7i) q^{42} +(8.28411e6 - 1.43485e7i) q^{43} +1.38959e6 q^{44} +(-1.64829e7 + 2.85492e7i) q^{45} +(-4.94698e6 + 8.56842e6i) q^{46} +2.16117e7 q^{47} +(4.23138e6 - 7.32897e6i) q^{48} +(-4.89445e7 - 8.47743e7i) q^{49} +(3.65552e7 + 6.33155e7i) q^{50} -9.53590e6 q^{51} +(-6.99293e7 - 6.22072e6i) q^{52} +7.19649e7 q^{53} +(-3.59713e7 - 6.23042e7i) q^{54} +(2.05581e6 + 3.56077e6i) q^{55} +(3.44794e7 - 5.97200e7i) q^{56} +3.22796e7 q^{57} +(-3.00196e7 + 5.19955e7i) q^{58} +(-9.09421e6 + 1.57516e7i) q^{59} -7.94878e7 q^{60} +(-4.77195e7 + 8.26527e7i) q^{61} +(-5.75775e7 - 9.97272e7i) q^{62} +(9.60732e7 + 1.66404e8i) q^{63} -2.03571e8 q^{64} +(-8.75156e7 - 1.88394e8i) q^{65} -4.07044e6 q^{66} +(4.24441e7 + 7.35153e7i) q^{67} +(5.62386e7 + 9.74082e7i) q^{68} +(8.27572e6 - 1.43340e7i) q^{69} +8.19464e8 q^{70} +(-1.81561e8 + 3.14472e8i) q^{71} +(-4.79237e7 + 8.30062e7i) q^{72} -3.37404e7 q^{73} +(2.76823e8 - 4.79472e8i) q^{74} +(-6.11526e7 - 1.05919e8i) q^{75} +(-1.90371e8 - 3.29733e8i) q^{76} +2.39653e7 q^{77} +(2.04839e8 + 1.82219e7i) q^{78} +3.19686e8 q^{79} +(-1.47677e8 - 2.55783e8i) q^{80} +(-1.00656e8 - 1.74342e8i) q^{81} +(-4.89507e8 + 8.47851e8i) q^{82} -1.88466e8 q^{83} +(-2.31654e8 + 4.01236e8i) q^{84} +(-1.66403e8 + 2.88219e8i) q^{85} +5.72443e8 q^{86} +(5.02193e7 - 8.69825e7i) q^{87} +(5.97723e6 + 1.03529e7i) q^{88} +(-1.25885e8 - 2.18039e8i) q^{89} -1.13899e9 q^{90} +(-1.20602e9 - 1.07284e8i) q^{91} -1.95227e8 q^{92} +(9.63205e7 + 1.66832e8i) q^{93} +(3.73349e8 + 6.46659e8i) q^{94} +(5.63285e8 - 9.75638e8i) q^{95} +4.65959e8 q^{96} +(1.09677e8 - 1.89966e8i) q^{97} +(1.69107e9 - 2.92901e9i) q^{98} -3.33099e7 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

Properties

Related objects

Downloads

Learn more