LMFDB - Embedded newform 7.14.c.a.2.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,14,Mod(2,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("7.2");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	7.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:	$7.50616502663$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 12266 x^{14} - 55087 x^{13} + 107030285 x^{12} - 640627660 x^{11} + \cdots + 12\!\cdots\!76 $ x^16 - x^15 + 12266x^14 - 55087x^13 + 107030285x^12 - 640627660x^11 + 438282746176x^10 - 5859940491984x^9 + 1300952456341392x^8 - 14674000482091008x^7 + 1878469861868220672x^6 - 14476511842718976000x^5 + 1885010114115081494784x^4 - 9244597941717380241408x^3 + 656480392494410296000512x^2 + 3883492623114966780739584x + 127864623964939499445682176
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{34}\cdot 3^{7}\cdot 7^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2.6
Root			$-18.3288 + 31.7465i$ of defining polynomial
Character	$\chi$	$=$	7.2
Dual form			7.14.c.a.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(36.6577 - 63.4930i) q^{2} +(306.948 + 531.649i) q^{3} +(1408.43 + 2439.47i) q^{4} +(-16706.4 + 28936.3i) q^{5} +45008.0 q^{6} +(-98806.7 + 295172. i) q^{7} +807118. q^{8} +(608728. - 1.05435e6i) q^{9} +O(q^{10})$	\(q+(36.6577 - 63.4930i) q^{2} +(306.948 + 531.649i) q^{3} +(1408.43 + 2439.47i) q^{4} +(-16706.4 + 28936.3i) q^{5} +45008.0 q^{6} +(-98806.7 + 295172. i) q^{7} +807118. q^{8} +(608728. - 1.05435e6i) q^{9} +(1.22484e6 + 2.12148e6i) q^{10} +(3.83866e6 + 6.64876e6i) q^{11} +(-864628. + 1.49758e6i) q^{12} -1.65980e6 q^{13} +(1.51193e7 + 1.70938e7i) q^{14} -2.05120e7 q^{15} +(1.80492e7 - 3.12622e7i) q^{16} +(-7.20703e7 - 1.24829e8i) q^{17} +(-4.46291e7 - 7.72998e7i) q^{18} +(-3.66670e7 + 6.35091e7i) q^{19} -9.41190e7 q^{20} +(-1.87256e8 + 3.80718e7i) q^{21} +5.62866e8 q^{22} +(-1.39288e8 + 2.41254e8i) q^{23} +(2.47743e8 + 4.29104e8i) q^{24} +(5.21446e7 + 9.03171e7i) q^{25} +(-6.08444e7 + 1.05386e8i) q^{26} +1.72614e9 q^{27} +(-8.59224e8 + 1.74692e8i) q^{28} +2.55113e9 q^{29} +(-7.51921e8 + 1.30236e9i) q^{30} +(-3.23131e9 - 5.59679e9i) q^{31} +(1.98267e9 + 3.43409e9i) q^{32} +(-2.35654e9 + 4.08164e9i) q^{33} -1.05677e10 q^{34} +(-6.89048e9 - 7.79035e9i) q^{35} +3.42940e9 q^{36} +(1.39483e10 - 2.41592e10i) q^{37} +(2.68825e9 + 4.65619e9i) q^{38} +(-5.09472e8 - 8.82431e8i) q^{39} +(-1.34840e10 + 2.33550e10i) q^{40} +1.89636e10 q^{41} +(-4.44709e9 + 1.32851e10i) q^{42} +2.29633e10 q^{43} +(-1.08130e10 + 1.87286e10i) q^{44} +(2.03393e10 + 3.52287e10i) q^{45} +(1.02120e10 + 1.76876e10i) q^{46} +(-4.03227e8 + 6.98410e8i) q^{47} +2.21607e10 q^{48} +(-7.73635e10 - 5.83298e10i) q^{49} +7.64600e9 q^{50} +(4.42436e10 - 7.66322e10i) q^{51} +(-2.33771e9 - 4.04903e9i) q^{52} +(-8.35551e10 - 1.44722e11i) q^{53} +(6.32762e10 - 1.09598e11i) q^{54} -2.56521e11 q^{55} +(-7.97487e10 + 2.38238e11i) q^{56} -4.50194e10 q^{57} +(9.35185e10 - 1.61979e11i) q^{58} +(2.79246e11 + 4.83668e11i) q^{59} +(-2.88896e10 - 5.00383e10i) q^{60} +(1.53033e11 - 2.65060e11i) q^{61} -4.73809e11 q^{62} +(2.51067e11 + 2.83856e11i) q^{63} +5.86439e11 q^{64} +(2.77293e10 - 4.80285e10i) q^{65} +(1.72770e11 + 2.99247e11i) q^{66} +(5.57499e10 + 9.65616e10i) q^{67} +(2.03012e11 - 3.51627e11i) q^{68} -1.71017e11 q^{69} +(-7.47221e11 + 1.51920e11i) q^{70} -5.44977e11 q^{71} +(4.91315e11 - 8.50983e11i) q^{72} +(1.04445e12 + 1.80904e12i) q^{73} +(-1.02263e12 - 1.77124e12i) q^{74} +(-3.20113e10 + 5.54453e10i) q^{75} -2.06571e11 q^{76} +(-2.34181e12 + 4.76122e11i) q^{77} -7.47042e10 q^{78} +(1.10489e12 - 1.91373e12i) q^{79} +(6.03075e11 + 1.04456e12i) q^{80} +(-4.40674e11 - 7.63270e11i) q^{81} +(6.95161e11 - 1.20405e12i) q^{82} -3.23594e12 q^{83} +(-3.56612e11 - 4.03184e11i) q^{84} +4.81614e12 q^{85} +(8.41781e11 - 1.45801e12i) q^{86} +(7.83064e11 + 1.35631e12i) q^{87} +(3.09826e12 + 5.36634e12i) q^{88} +(-3.56386e12 + 6.17278e12i) q^{89} +2.98236e12 q^{90} +(1.63999e11 - 4.89926e11i) q^{91} -7.84709e11 q^{92} +(1.98368e12 - 3.43584e12i) q^{93} +(2.95628e10 + 5.12042e10i) q^{94} +(-1.22515e12 - 2.12202e12i) q^{95} +(-1.21715e12 + 2.10817e12i) q^{96} -6.18110e12 q^{97} +(-6.53950e12 + 2.77380e12i) q^{98} +9.34680e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 728 q^{3} - 32588 q^{4} + 46928 q^{5} - 30212 q^{6} + 257992 q^{7} - 1093248 q^{8} - 2910808 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 728 * q^3 - 32588 * q^4 + 46928 * q^5 - 30212 * q^6 + 257992 * q^7 - 1093248 * q^8 - 2910808 * q^9	\( 16 q - 2 q^{2} + 728 q^{3} - 32588 q^{4} + 46928 q^{5} - 30212 q^{6} + 257992 q^{7} - 1093248 q^{8} - 2910808 q^{9} + 879018 q^{10} + 3746000 q^{11} + 13786276 q^{12} - 63556528 q^{13} - 45497410 q^{14} + 179729504 q^{15} - 158020976 q^{16} + 108548496 q^{17} + 358872748 q^{18} + 617001728 q^{19} - 1844979416 q^{20} + 400815352 q^{21} + 977603772 q^{22} - 274288968 q^{23} - 690136272 q^{24} + 342571888 q^{25} - 1890370748 q^{26} + 1818768224 q^{27} - 2830532012 q^{28} - 1243557136 q^{29} + 8470546342 q^{30} + 1983953552 q^{31} - 18584336224 q^{32} - 3534705832 q^{33} + 35123983356 q^{34} - 15057013664 q^{35} + 2810399728 q^{36} + 3822948680 q^{37} + 48271561702 q^{38} + 5559167432 q^{39} + 20095902624 q^{40} - 186830117264 q^{41} - 160102538512 q^{42} + 147613206080 q^{43} + 146754773860 q^{44} + 167965018760 q^{45} + 33234006318 q^{46} + 136146541776 q^{47} - 918554738528 q^{48} - 279115649456 q^{49} + 446501048144 q^{50} + 374908120992 q^{51} + 920059547960 q^{52} - 365779470792 q^{53} + 142841959918 q^{54} - 335157159792 q^{55} - 2232488591424 q^{56} + 1368890666384 q^{57} + 1968765302052 q^{58} + 1211924963928 q^{59} - 1696452613604 q^{60} - 155263824184 q^{61} - 3267358992324 q^{62} - 4123328121080 q^{63} + 3671045348608 q^{64} + 2491203210104 q^{65} + 6785854381222 q^{66} - 1812819047992 q^{67} + 2300642770860 q^{68} - 9833331511584 q^{69} - 10764563120010 q^{70} + 6413635527072 q^{71} + 9182131417728 q^{72} + 7135229075576 q^{73} - 1240472589270 q^{74} + 3092701132528 q^{75} - 24098923346008 q^{76} - 8899938075392 q^{77} + 16977900019528 q^{78} + 7912090175960 q^{79} + 18767635478704 q^{80} - 2029193868592 q^{81} + 2118830761068 q^{82} - 16937841300576 q^{83} - 32302920082804 q^{84} + 9546866646768 q^{85} + 17052910238024 q^{86} + 16147535411672 q^{87} - 15433836932304 q^{88} + 3654589406888 q^{89} - 6354662390216 q^{90} - 14961004874704 q^{91} + 2966525661672 q^{92} + 10829807426472 q^{93} + 7135101410430 q^{94} - 16751540432680 q^{95} - 4043645970784 q^{96} + 20623672673744 q^{97} + 1374873929086 q^{98} + 1803523183088 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 728 * q^3 - 32588 * q^4 + 46928 * q^5 - 30212 * q^6 + 257992 * q^7 - 1093248 * q^8 - 2910808 * q^9 + 879018 * q^10 + 3746000 * q^11 + 13786276 * q^12 - 63556528 * q^13 - 45497410 * q^14 + 179729504 * q^15 - 158020976 * q^16 + 108548496 * q^17 + 358872748 * q^18 + 617001728 * q^19 - 1844979416 * q^20 + 400815352 * q^21 + 977603772 * q^22 - 274288968 * q^23 - 690136272 * q^24 + 342571888 * q^25 - 1890370748 * q^26 + 1818768224 * q^27 - 2830532012 * q^28 - 1243557136 * q^29 + 8470546342 * q^30 + 1983953552 * q^31 - 18584336224 * q^32 - 3534705832 * q^33 + 35123983356 * q^34 - 15057013664 * q^35 + 2810399728 * q^36 + 3822948680 * q^37 + 48271561702 * q^38 + 5559167432 * q^39 + 20095902624 * q^40 - 186830117264 * q^41 - 160102538512 * q^42 + 147613206080 * q^43 + 146754773860 * q^44 + 167965018760 * q^45 + 33234006318 * q^46 + 136146541776 * q^47 - 918554738528 * q^48 - 279115649456 * q^49 + 446501048144 * q^50 + 374908120992 * q^51 + 920059547960 * q^52 - 365779470792 * q^53 + 142841959918 * q^54 - 335157159792 * q^55 - 2232488591424 * q^56 + 1368890666384 * q^57 + 1968765302052 * q^58 + 1211924963928 * q^59 - 1696452613604 * q^60 - 155263824184 * q^61 - 3267358992324 * q^62 - 4123328121080 * q^63 + 3671045348608 * q^64 + 2491203210104 * q^65 + 6785854381222 * q^66 - 1812819047992 * q^67 + 2300642770860 * q^68 - 9833331511584 * q^69 - 10764563120010 * q^70 + 6413635527072 * q^71 + 9182131417728 * q^72 + 7135229075576 * q^73 - 1240472589270 * q^74 + 3092701132528 * q^75 - 24098923346008 * q^76 - 8899938075392 * q^77 + 16977900019528 * q^78 + 7912090175960 * q^79 + 18767635478704 * q^80 - 2029193868592 * q^81 + 2118830761068 * q^82 - 16937841300576 * q^83 - 32302920082804 * q^84 + 9546866646768 * q^85 + 17052910238024 * q^86 + 16147535411672 * q^87 - 15433836932304 * q^88 + 3654589406888 * q^89 - 6354662390216 * q^90 - 14961004874704 * q^91 + 2966525661672 * q^92 + 10829807426472 * q^93 + 7135101410430 * q^94 - 16751540432680 * q^95 - 4043645970784 * q^96 + 20623672673744 * q^97 + 1374873929086 * q^98 + 1803523183088 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

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

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 $

$2$	36.6577	−	63.4930i	0.405014	−	0.701505i	−0.589309	−	0.807908i	$-0.700600\pi$
$2$	36.6577	−	63.4930i	0.405014	−	0.701505i	0.994323	+	0.106403i	$0.0339333\pi$
$3$	306.948	+	531.649i	0.243095	+	0.421053i	0.961594	−	0.274475i	$-0.0885039\pi$
$3$	306.948	+	531.649i	0.243095	+	0.421053i	−0.718499	+	0.695528i	$0.755171\pi$
$4$	1408.43	+	2439.47i	0.171927	+	0.297787i
$5$	−16706.4	+	28936.3i	−0.478165	+	0.828206i	−0.999687	−	0.0250322i	$-0.992031\pi$
$5$	−16706.4	+	28936.3i	−0.478165	+	0.828206i	0.521522	+	0.853238i	$0.325365\pi$
$6$	45008.0			0.393828
$7$	−98806.7	+	295172.i	−0.317431	+	0.948281i
$7$	−98806.7	+	295172.i	−0.317431	+	0.948281i
$8$	807118.			1.08856
$9$	608728.	−	1.05435e6i	0.381809	−	0.661313i
$10$	1.22484e6	+	2.12148e6i	0.387327	+	0.670870i
$11$	3.83866e6	+	6.64876e6i	0.653322	+	1.13159i	0.982312	+	0.187254i	$0.0599587\pi$
$11$	3.83866e6	+	6.64876e6i	0.653322	+	1.13159i	−0.328989	+	0.944334i	$0.606708\pi$
$12$	−864628.	+	1.49758e6i	−0.0835894	+	0.144781i
$13$	−1.65980e6			−0.0953726			−0.0476863	−	0.998862i	$-0.515185\pi$
$13$	−1.65980e6			−0.0953726			−0.0476863	+	0.998862i	$0.515185\pi$
$14$	1.51193e7	+	1.70938e7i	0.536660	+	0.606746i
$15$	−2.05120e7			−0.464958
$16$	1.80492e7	−	3.12622e7i	0.268955	−	0.465843i
$17$	−7.20703e7	−	1.24829e8i	−0.724167	−	1.25429i	−0.959316	−	0.282334i	$-0.908891\pi$
$17$	−7.20703e7	−	1.24829e8i	−0.724167	−	1.25429i	0.235150	−	0.971959i	$-0.424442\pi$
$18$	−4.46291e7	−	7.72998e7i	−0.309276	−	0.535682i
$19$	−3.66670e7	+	6.35091e7i	−0.178804	+	0.309697i	−0.941471	−	0.337094i	$-0.890556\pi$
$19$	−3.66670e7	+	6.35091e7i	−0.178804	+	0.309697i	0.762667	+	0.646791i	$0.223889\pi$
$20$	−9.41190e7			−0.328838
$21$	−1.87256e8	+	3.80718e7i	−0.476443	+	0.0968674i
$22$	5.62866e8			1.05842
$23$	−1.39288e8	+	2.41254e8i	−0.196193	+	0.339816i	−0.947291	−	0.320375i	$-0.896191\pi$
$23$	−1.39288e8	+	2.41254e8i	−0.196193	+	0.339816i	0.751098	+	0.660191i	$0.229525\pi$
$24$	2.47743e8	+	4.29104e8i	0.264624	+	0.458342i
$25$	5.21446e7	+	9.03171e7i	0.0427169	+	0.0739878i
$26$	−6.08444e7	+	1.05386e8i	−0.0386273	+	0.0669044i
$27$	1.72614e9			0.857454
$28$	−8.59224e8	+	1.74692e8i	−0.336961	+	0.0685088i
$29$	2.55113e9			0.796426			0.398213	−	0.917293i	$-0.369630\pi$
$29$	2.55113e9			0.796426			0.398213	+	0.917293i	$0.369630\pi$
$30$	−7.51921e8	+	1.30236e9i	−0.188315	+	0.326170i
$31$	−3.23131e9	−	5.59679e9i	−0.653924	−	1.13263i	−0.982162	−	0.188034i	$-0.939788\pi$
$31$	−3.23131e9	−	5.59679e9i	−0.653924	−	1.13263i	0.328239	−	0.944595i	$-0.393545\pi$
$32$	1.98267e9	+	3.43409e9i	0.326419	+	0.565375i
$33$	−2.35654e9	+	4.08164e9i	−0.317639	+	0.550167i
$34$	−1.05677e10			−1.17319
$35$	−6.89048e9	−	7.79035e9i	−0.633588	−	0.716333i
$36$	3.42940e9			0.262574
$37$	1.39483e10	−	2.41592e10i	0.893740	−	1.54800i	0.0583830	−	0.998294i	$-0.481406\pi$
$37$	1.39483e10	−	2.41592e10i	0.893740	−	1.54800i	0.835357	−	0.549708i	$-0.185261\pi$
$38$	2.68825e9	+	4.65619e9i	0.144836	+	0.250863i
$39$	−5.09472e8	−	8.82431e8i	−0.0231846	−	0.0401570i
$40$	−1.34840e10	+	2.33550e10i	−0.520511	+	0.901552i
$41$	1.89636e10			0.623484			0.311742	−	0.950167i	$-0.399088\pi$
$41$	1.89636e10			0.623484			0.311742	+	0.950167i	$0.399088\pi$
$42$	−4.44709e9	+	1.32851e10i	−0.125013	+	0.373460i
$43$	2.29633e10			0.553973			0.276987	−	0.960874i	$-0.410664\pi$
$43$	2.29633e10			0.553973			0.276987	+	0.960874i	$0.410664\pi$
$44$	−1.08130e10	+	1.87286e10i	−0.224648	+	0.389102i
$45$	2.03393e10	+	3.52287e10i	0.365136	+	0.632434i
$46$	1.02120e10	+	1.76876e10i	0.158922	+	0.275260i
$47$	−4.03227e8	+	6.98410e8i	−0.00545650	+	0.00945093i	−0.868741	−	0.495267i	$-0.835070\pi$
$47$	−4.03227e8	+	6.98410e8i	−0.00545650	+	0.00945093i	0.863284	+	0.504718i	$0.168404\pi$
$48$	2.21607e10			0.261526
$49$	−7.73635e10	−	5.83298e10i	−0.798475	−	0.602027i
$50$	7.64600e9			0.0692037
$51$	4.42436e10	−	7.66322e10i	0.352083	−	0.609825i
$52$	−2.33771e9	−	4.04903e9i	−0.0163972	−	0.0284007i
$53$	−8.35551e10	−	1.44722e11i	−0.517821	−	0.896892i	−0.999786	−	0.0207016i	$-0.993410\pi$
$53$	−8.35551e10	−	1.44722e11i	−0.517821	−	0.896892i	0.481965	−	0.876191i	$-0.339923\pi$
$54$	6.32762e10	−	1.09598e11i	0.347281	−	0.601508i
$55$	−2.56521e11			−1.24958
$56$	−7.97487e10	+	2.38238e11i	−0.345542	+	1.03226i
$57$	−4.50194e10			−0.173865
$58$	9.35185e10	−	1.61979e11i	0.322564	−	0.558697i
$59$	2.79246e11	+	4.83668e11i	0.861884	+	1.49283i	0.870108	+	0.492860i	$0.164049\pi$
$59$	2.79246e11	+	4.83668e11i	0.861884	+	1.49283i	−0.00822473	+	0.999966i	$0.502618\pi$
$60$	−2.88896e10	−	5.00383e10i	−0.0799390	−	0.138458i
$61$	1.53033e11	−	2.65060e11i	0.380312	−	0.658720i	−0.610794	−	0.791789i	$-0.709150\pi$
$61$	1.53033e11	−	2.65060e11i	0.380312	−	0.658720i	0.991107	+	0.133069i	$0.0424832\pi$
$62$	−4.73809e11			−1.05939
$63$	2.51067e11	+	2.83856e11i	0.505913	+	0.571984i
$64$	5.86439e11			1.06673
$65$	2.77293e10	−	4.80285e10i	0.0456038	−	0.0789882i
$66$	1.72770e11	+	2.99247e11i	0.257296	+	0.445651i
$67$	5.57499e10	+	9.65616e10i	0.0752935	+	0.130412i	0.901214	−	0.433375i	$-0.142677\pi$
$67$	5.57499e10	+	9.65616e10i	0.0752935	+	0.130412i	−0.825920	+	0.563787i	$0.809344\pi$
$68$	2.03012e11	−	3.51627e11i	0.249008	−	0.431295i
$69$	−1.71017e11			−0.190774
$70$	−7.47221e11	+	1.51920e11i	−0.759123	+	0.154340i
$71$	−5.44977e11			−0.504892			−0.252446	−	0.967611i	$-0.581235\pi$
$71$	−5.44977e11			−0.504892			−0.252446	+	0.967611i	$0.581235\pi$
$72$	4.91315e11	−	8.50983e11i	0.415622	−	0.719879i
$73$	1.04445e12	+	1.80904e12i	0.807773	+	1.39910i	0.914403	+	0.404805i	$0.132661\pi$
$73$	1.04445e12	+	1.80904e12i	0.807773	+	1.39910i	−0.106630	+	0.994299i	$0.534006\pi$
$74$	−1.02263e12	−	1.77124e12i	−0.723954	−	1.25393i
$75$	−3.20113e10	+	5.54453e10i	−0.0207685	+	0.0359721i
$76$	−2.06571e11			−0.122965
$77$	−2.34181e12	+	4.76122e11i	−1.28045	+	0.260333i
$78$	−7.47042e10			−0.0375604
$79$	1.10489e12	−	1.91373e12i	0.511380	−	0.885736i	−0.488533	−	0.872545i	$-0.662468\pi$
$79$	1.10489e12	−	1.91373e12i	0.511380	−	0.885736i	0.999913	−	0.0131907i	$-0.00419886\pi$
$80$	6.03075e11	+	1.04456e12i	0.257209	+	0.445500i
$81$	−4.40674e11	−	7.63270e11i	−0.173366	−	0.300280i
$82$	6.95161e11	−	1.20405e12i	0.252520	−	0.437377i
$83$	−3.23594e12			−1.08641			−0.543203	−	0.839601i	$-0.682789\pi$
$83$	−3.23594e12			−1.08641			−0.543203	+	0.839601i	$0.682789\pi$
$84$	−3.56612e11	−	4.03184e11i	−0.110759	−	0.125224i
$85$	4.81614e12			1.38508
$86$	8.41781e11	−	1.45801e12i	0.224367	−	0.388615i
$87$	7.83064e11	+	1.35631e12i	0.193607	+	0.335338i
$88$	3.09826e12	+	5.36634e12i	0.711180	+	1.23180i
$89$	−3.56386e12	+	6.17278e12i	−0.760125	+	1.31658i	0.182660	+	0.983176i	$0.441529\pi$
$89$	−3.56386e12	+	6.17278e12i	−0.760125	+	1.31658i	−0.942786	+	0.333400i	$0.891804\pi$
$90$	2.98236e12			0.591540
$91$	1.63999e11	−	4.89926e11i	0.0302742	−	0.0904401i
$92$	−7.84709e11			−0.134924
$93$	1.98368e12	−	3.43584e12i	0.317931	−	0.550673i
$94$	2.95628e10	+	5.12042e10i	0.00441992	+	0.00765552i
$95$	−1.22515e12	−	2.12202e12i	−0.170995	−	0.296173i
$96$	−1.21715e12	+	2.10817e12i	−0.158702	+	0.274880i
$97$	−6.18110e12			−0.753442			−0.376721	−	0.926327i	$-0.622948\pi$
$97$	−6.18110e12			−0.753442			−0.376721	+	0.926327i	$0.622948\pi$
$98$	−6.53950e12	+	2.77380e12i	−0.745719	+	0.316305i
$99$	9.34680e12			0.997779
$100$	−1.46884e11	+	2.54410e11i	−0.0146884	+	0.0254410i
$101$	−5.06765e12	−	8.77743e12i	−0.475027	−	0.822770i	0.524564	−	0.851371i	$-0.324228\pi$
$101$	−5.06765e12	−	8.77743e12i	−0.475027	−	0.822770i	−0.999591	+	0.0286005i	$0.990895\pi$
$102$	−3.24374e12	−	5.61832e12i	−0.285197	−	0.493976i
$103$	1.07907e13	−	1.86901e13i	0.890450	−	1.54230i	0.0511134	−	0.998693i	$-0.483723\pi$
$103$	1.07907e13	−	1.86901e13i	0.890450	−	1.54230i	0.839337	−	0.543612i	$-0.182944\pi$
$104$	−1.33965e12			−0.103819
$105$	2.02672e12	−	6.05455e12i	0.147592	−	0.440911i
$106$	−1.22517e13			−0.838899
$107$	−9.62459e12	+	1.66703e13i	−0.619995	+	1.07386i	0.369492	+	0.929234i	$0.379532\pi$
$107$	−9.62459e12	+	1.66703e13i	−0.619995	+	1.07386i	−0.989486	+	0.144628i	$0.953801\pi$
$108$	2.43114e12	+	4.21086e12i	0.147420	+	0.255339i
$109$	1.27499e12	+	2.20835e12i	0.0728174	+	0.126124i	0.900135	−	0.435611i	$-0.143468\pi$
$109$	1.27499e12	+	2.20835e12i	0.0728174	+	0.126124i	−0.827318	+	0.561734i	$0.810134\pi$
$110$	−9.40346e12	+	1.62873e13i	−0.506099	+	0.876588i
$111$	1.71256e13			0.869055
$112$	7.44433e12	+	8.41654e12i	0.356376	+	0.402918i
$113$	−6.19242e12			−0.279802			−0.139901	−	0.990166i	$-0.544678\pi$
$113$	−6.19242e12			−0.279802			−0.139901	+	0.990166i	$0.544678\pi$
$114$	−1.65031e12	+	2.85842e12i	−0.0704179	+	0.121967i
$115$	−4.65400e12	−	8.06097e12i	−0.187625	−	0.324976i
$116$	3.59308e12	+	6.22341e12i	0.136927	+	0.237165i
$117$	−1.01037e12	+	1.75000e12i	−0.0364142	+	0.0630712i
$118$	4.09460e13			1.39630
$119$	4.39671e13	−	8.93913e12i	1.41930	−	0.288563i
$120$	−1.65556e13			−0.506135
$121$	−1.22093e13	+	2.11471e13i	−0.353660	+	0.612557i
$122$	−1.12196e13	−	1.94330e13i	−0.308064	−	0.533582i
$123$	5.82083e12	+	1.00820e13i	0.151566	+	0.262520i
$124$	9.10213e12	−	1.57653e13i	0.224855	−	0.389460i
$125$	−4.42717e13			−1.03803
$126$	2.72264e13	−	5.53550e12i	0.606151	−	0.123239i
$127$	−6.38184e13			−1.34965			−0.674826	−	0.737977i	$-0.735781\pi$
$127$	−6.38184e13			−1.34965			−0.674826	+	0.737977i	$0.735781\pi$
$128$	5.25546e12	−	9.10273e12i	0.105620	−	0.182939i
$129$	7.04853e12	+	1.22084e13i	0.134668	+	0.233252i
$130$	−2.03298e12	−	3.52123e12i	−0.0369404	−	0.0639826i
$131$	6.77485e12	−	1.17344e13i	0.117121	−	0.202860i	−0.801504	−	0.597989i	$-0.795967\pi$
$131$	6.77485e12	−	1.17344e13i	0.117121	−	0.202860i	0.918626	+	0.395129i	$0.129300\pi$
$132$	−1.32761e13			−0.218443
$133$	−1.51231e13	−	1.70982e13i	−0.236922	−	0.267864i
$134$	8.17465e12			0.121980
$135$	−2.88375e13	+	4.99481e13i	−0.410005	+	0.710149i
$136$	−5.81693e13	−	1.00752e14i	−0.788299	−	1.36537i
$137$	1.79947e13	+	3.11677e13i	0.232520	+	0.402737i	0.958549	−	0.284927i	$-0.0919694\pi$
$137$	1.79947e13	+	3.11677e13i	0.232520	+	0.402737i	−0.726029	+	0.687664i	$0.758636\pi$
$138$	−6.26907e12	+	1.08584e13i	−0.0772662	+	0.133829i
$139$	9.66596e13			1.13671			0.568354	−	0.822784i	$-0.307581\pi$
$139$	9.66596e13			1.13671			0.568354	+	0.822784i	$0.307581\pi$
$140$	9.29959e12	−	2.77813e13i	0.104383	−	0.311831i
$141$	−4.95079e11			−0.00530579
$142$	−1.99776e13	+	3.46022e13i	−0.204488	+	0.354184i
$143$	−6.37141e12	−	1.10356e13i	−0.0623091	−	0.107922i
$144$	−2.19741e13	−	3.80603e13i	−0.205379	−	0.355727i
$145$	−4.26202e13	+	7.38203e13i	−0.380823	+	0.659605i
$146$	1.53149e14			1.30864
$147$	7.26445e12	−	5.90344e13i	0.0593800	−	0.482551i
$148$	7.85809e13			0.614633
$149$	−2.03549e13	+	3.52558e13i	−0.152391	+	0.263949i	−0.932106	−	0.362186i	$-0.882031\pi$
$149$	−2.03549e13	+	3.52558e13i	−0.152391	+	0.263949i	0.779715	+	0.626135i	$0.215364\pi$
$150$	2.34692e12	+	4.06499e12i	0.0168231	+	0.0291384i
$151$	9.11964e13	+	1.57957e14i	0.626077	+	1.08440i	0.988332	+	0.152317i	$0.0486736\pi$
$151$	9.11964e13	+	1.57957e14i	0.626077	+	1.08440i	−0.362255	+	0.932079i	$0.617993\pi$
$152$	−2.95946e13	+	5.12593e13i	−0.194639	+	0.337124i
$153$	−1.75485e14			−1.10597
$154$	−5.56149e13	+	1.66142e14i	−0.335975	+	1.00368i
$155$	2.15934e14			1.25073
$156$	1.43511e12	−	2.48568e12i	0.00797214	−	0.0138082i
$157$	−1.69388e13	−	2.93389e13i	−0.0902685	−	0.156350i	0.817356	−	0.576134i	$-0.195439\pi$
$157$	−1.69388e13	−	2.93389e13i	−0.0902685	−	0.156350i	−0.907624	+	0.419784i	$0.862106\pi$
$158$	−8.10056e13	−	1.40306e14i	−0.414232	−	0.717471i
$159$	5.12941e13	−	8.88439e13i	0.251760	−	0.436060i
$160$	−1.32493e14			−0.624329
$161$	−5.74487e13	−	6.49514e13i	−0.259963	−	0.293914i
$162$	−6.46164e13			−0.280863
$163$	1.85621e14	−	3.21505e14i	0.775190	−	1.34267i	−0.159497	−	0.987198i	$-0.550987\pi$
$163$	1.85621e14	−	3.21505e14i	0.775190	−	1.34267i	0.934688	−	0.355470i	$-0.115679\pi$
$164$	2.67089e13	+	4.62611e13i	0.107194	+	0.185665i
$165$	−7.87385e13	−	1.36379e14i	−0.303768	−	0.526141i
$166$	−1.18622e14	+	2.05459e14i	−0.440010	+	0.762119i
$167$	−8.60842e13			−0.307091			−0.153545	−	0.988142i	$-0.549069\pi$
$167$	−8.60842e13			−0.307091			−0.153545	+	0.988142i	$0.549069\pi$
$168$	−1.51138e14	+	3.07284e13i	−0.518637	+	0.105446i
$169$	−3.00120e14			−0.990904
$170$	1.76549e14	−	3.05791e14i	0.560978	−	0.971643i
$171$	4.46404e13	+	7.73195e13i	0.136538	+	0.236491i
$172$	3.23421e13	+	5.60182e13i	0.0952432	+	0.164966i
$173$	1.58098e14	−	2.73834e14i	0.448360	−	0.776582i	−0.549920	−	0.835218i	$-0.685342\pi$
$173$	1.58098e14	−	2.73834e14i	0.448360	−	0.776582i	0.998279	+	0.0586355i	$0.0186750\pi$
$174$	1.14821e14			0.313655
$175$	−3.18113e13	+	6.46767e12i	−0.0837209	+	0.0170216i
$176$	2.77140e14			0.702856
$177$	−1.71428e14	+	2.96922e14i	−0.419040	+	0.725798i
$178$	2.61286e14	+	4.52560e14i	0.615723	+	1.06646i
$179$	1.32736e14	+	2.29905e14i	0.301608	+	0.522401i	0.976500	−	0.215516i	$-0.0691432\pi$
$179$	1.32736e14	+	2.29905e14i	0.301608	+	0.522401i	−0.674892	+	0.737916i	$0.735810\pi$
$180$	−5.72929e13	+	9.92342e13i	−0.125554	+	0.217465i
$181$	−4.32173e14			−0.913580			−0.456790	−	0.889575i	$-0.651001\pi$
$181$	−4.32173e14			−0.913580			−0.456790	+	0.889575i	$0.651001\pi$
$182$	−2.50950e13	−	2.83723e13i	−0.0511827	−	0.0578670i
$183$	1.87892e14			0.369808
$184$	−1.12422e14	+	1.94721e14i	−0.213568	+	0.369910i
$185$	4.66053e14	+	8.07227e14i	0.854710	+	1.48040i
$186$	−1.45435e14	−	2.51900e14i	−0.257533	−	0.446061i
$187$	5.53307e14	−	9.58356e14i	0.946228	−	1.63892i
$188$	−2.27167e12			−0.00375248
$189$	−1.70554e14	+	5.09507e14i	−0.272182	+	0.813108i
$190$	−1.79644e14			−0.277022
$191$	3.11568e14	−	5.39651e14i	0.464339	−	0.804259i	−0.534832	−	0.844958i	$-0.679625\pi$
$191$	3.11568e14	−	5.39651e14i	0.464339	−	0.804259i	0.999171	+	0.0406989i	$0.0129584\pi$
$192$	1.80006e14	+	3.11780e14i	0.259316	+	0.449149i
$193$	−5.57667e14	−	9.65907e14i	−0.776698	−	1.34528i	−0.933835	−	0.357704i	$-0.883560\pi$
$193$	−5.57667e14	−	9.65907e14i	−0.776698	−	1.34528i	0.157137	−	0.987577i	$-0.449774\pi$
$194$	−2.26585e14	+	3.92457e14i	−0.305154	+	0.528543i
$195$	3.40457e13			0.0443443
$196$	3.33329e13	−	2.70879e14i	0.0419961	−	0.341280i
$197$	−2.76621e14			−0.337174			−0.168587	−	0.985687i	$-0.553920\pi$
$197$	−2.76621e14			−0.337174			−0.168587	+	0.985687i	$0.553920\pi$
$198$	3.42632e14	−	5.93456e14i	0.404114	−	0.699946i
$199$	2.05316e13	+	3.55618e13i	0.0234357	+	0.0405918i	0.877505	−	0.479567i	$-0.159206\pi$
$199$	2.05316e13	+	3.55618e13i	0.0234357	+	0.0405918i	−0.854070	+	0.520159i	$0.825873\pi$
$200$	4.20869e13	+	7.28966e13i	0.0464999	+	0.0805401i
$201$	−3.42246e13	+	5.92787e13i	−0.0366070	+	0.0634052i
$202$	−7.43074e14			−0.769570
$203$	−2.52069e14	+	7.53021e14i	−0.252810	+	0.755236i
$204$	2.49256e14			0.242131
$205$	−3.16813e14	+	5.48736e14i	−0.298128	+	0.516373i
$206$	−7.91128e14	−	1.37027e15i	−0.721289	−	1.24931i
$207$	1.69577e14	+	2.93716e14i	0.149817	+	0.259490i
$208$	−2.99581e13	+	5.18890e13i	−0.0256509	+	0.0444287i
$209$	−5.63009e14			−0.467266
$210$	−3.10126e14	−	3.50628e14i	−0.249525	−	0.282112i
$211$	3.31210e14			0.258385			0.129193	−	0.991620i	$-0.458761\pi$
$211$	3.31210e14			0.258385			0.129193	+	0.991620i	$0.458761\pi$
$212$	2.35363e14	−	4.07660e14i	0.178055	−	0.308401i
$213$	−1.67279e14	−	2.89736e14i	−0.122737	−	0.212587i
$214$	7.05631e14	+	1.22219e15i	0.502213	+	0.869858i
$215$	−3.83634e14	+	6.64473e14i	−0.264891	+	0.458804i
$216$	1.39320e15			0.933391
$217$	1.97129e15	−	4.00790e14i	1.28163	−	0.260572i
$218$	1.86953e14			0.117968
$219$	−6.41183e14	+	1.11056e15i	−0.392731	+	0.680231i
$220$	−3.61291e14	−	6.25775e14i	−0.214837	−	0.372109i
$221$	1.19622e14	+	2.07192e14i	0.0690657	+	0.119625i
$222$	6.27786e14	−	1.08736e15i	0.351979	−	0.609646i
$223$	2.00688e15			1.09280			0.546399	−	0.837525i	$-0.315998\pi$
$223$	2.00688e15			1.09280			0.546399	+	0.837525i	$0.315998\pi$
$224$	−1.20955e15	+	2.45917e14i	−0.639750	+	0.130070i
$225$	1.26967e14			0.0652388
$226$	−2.27000e14	+	3.93175e14i	−0.113324	+	0.196282i
$227$	1.29431e14	+	2.24180e14i	0.0627869	+	0.108750i	0.895710	−	0.444638i	$-0.146668\pi$
$227$	1.29431e14	+	2.24180e14i	0.0627869	+	0.108750i	−0.832923	+	0.553389i	$0.813334\pi$
$228$	−6.34066e13	−	1.09823e14i	−0.0298922	−	0.0517748i
$229$	−1.60244e15	+	2.77551e15i	−0.734262	+	1.27178i	0.220785	+	0.975323i	$0.429138\pi$
$229$	−1.60244e15	+	2.77551e15i	−0.734262	+	1.27178i	−0.955046	+	0.296456i	$0.904195\pi$
$230$	−6.82420e14			−0.303963
$231$	−9.71943e14	−	1.09888e15i	−0.420885	−	0.475851i
$232$	2.05906e15			0.866958
$233$	−4.71377e14	+	8.16449e14i	−0.192999	+	0.334284i	−0.946243	−	0.323458i	$-0.895155\pi$
$233$	−4.71377e14	+	8.16449e14i	−0.192999	+	0.334284i	0.753244	+	0.657741i	$0.228488\pi$
$234$	7.40753e13	+	1.28302e14i	0.0294965	+	0.0510894i
$235$	−1.34729e13	−	2.33358e13i	−0.00521821	−	0.00903820i
$236$	−7.86596e14	+	1.36242e15i	−0.296363	+	0.513315i
$237$	1.35658e15			0.497256
$238$	1.04416e15	−	3.11929e15i	0.372407	−	1.11251i
$239$	−5.48811e15			−1.90474			−0.952371	−	0.304941i	$-0.901363\pi$
$239$	−5.48811e15			−1.90474			−0.952371	+	0.304941i	$0.901363\pi$
$240$	−3.70225e14	+	6.41249e14i	−0.125053	+	0.216598i
$241$	−2.04565e15	−	3.54316e15i	−0.672542	−	1.16488i	−0.977181	−	0.212409i	$-0.931869\pi$
$241$	−2.04565e15	−	3.54316e15i	−0.672542	−	1.16488i	0.304638	−	0.952468i	$-0.401464\pi$
$242$	8.95130e14	+	1.55041e15i	0.286475	+	0.496188i
$243$	1.64654e15	−	2.85189e15i	0.513016	−	0.888570i
$244$	8.62143e14			0.261544
$245$	2.98032e15	−	1.26413e15i	0.880405	−	0.373434i
$246$	8.53513e14			0.245545
$247$	6.08598e13	−	1.05412e14i	0.0170530	−	0.0295367i
$248$	−2.60805e15	−	4.51727e15i	−0.711835	−	1.23293i
$249$	−9.93263e14	−	1.72038e15i	−0.264100	−	0.457435i
$250$	−1.62290e15	+	2.81094e15i	−0.420418	+	0.728185i
$251$	−6.86741e14			−0.173346			−0.0866730	−	0.996237i	$-0.527624\pi$
$251$	−6.86741e14			−0.173346			−0.0866730	+	0.996237i	$0.527624\pi$
$252$	−3.38847e14	+	1.01226e15i	−0.0833490	+	0.248994i
$253$	−2.13872e15			−0.512709
$254$	−2.33944e15	+	4.05202e15i	−0.546628	+	0.946788i
$255$	1.47830e15	+	2.56050e15i	0.336707	+	0.583194i
$256$	2.01675e15	+	3.49311e15i	0.447808	+	0.775626i
$257$	2.45375e15	−	4.25001e15i	0.531207	−	0.920078i	−0.468129	−	0.883660i	$-0.655072\pi$
$257$	2.45375e15	−	4.25001e15i	0.531207	−	0.920078i	0.999337	−	0.0364182i	$-0.0115948\pi$
$258$	1.03353e15			0.218170
$259$	5.75293e15	+	6.50424e15i	1.18424	+	1.33890i
$260$	1.56219e14			0.0313622
$261$	1.55294e15	−	2.68978e15i	0.304083	−	0.526687i
$262$	−4.96700e14	−	8.60310e14i	−0.0948716	−	0.164322i
$263$	−1.31144e15	−	2.27149e15i	−0.244364	−	0.423251i	0.717589	−	0.696467i	$-0.245246\pi$
$263$	−1.31144e15	−	2.27149e15i	−0.244364	−	0.423251i	−0.961953	+	0.273216i	$0.911912\pi$
$264$	−1.90200e15	+	3.29437e15i	−0.345769	+	0.598890i
$265$	5.58361e15			0.990415
$266$	−1.63999e15	+	3.33433e14i	−0.283865	+	0.0577136i
$267$	−4.37567e15			−0.739131
$268$	−1.57039e14	+	2.72000e14i	−0.0258900	+	0.0448429i
$269$	5.02151e15	+	8.69750e15i	0.808061	+	1.39960i	0.914205	+	0.405252i	$0.132816\pi$
$269$	5.02151e15	+	8.69750e15i	0.808061	+	1.39960i	−0.106144	+	0.994351i	$0.533850\pi$
$270$	2.11423e15	+	3.66196e15i	0.332115	+	0.575240i
$271$	1.95051e15	−	3.37838e15i	0.299122	−	0.518094i	−0.676813	−	0.736155i	$-0.736640\pi$
$271$	1.95051e15	−	3.37838e15i	0.299122	−	0.518094i	0.975935	+	0.218060i	$0.0699730\pi$
$272$	−5.20326e15			−0.779072
$273$	3.10808e14	−	6.31915e13i	0.0454396	−	0.00923850i
$274$	2.63858e15			0.376696
$275$	−4.00331e14	+	6.93394e14i	−0.0558158	+	0.0966757i
$276$	−2.40865e14	−	4.17190e14i	−0.0327993	−	0.0568100i
$277$	−5.36454e15	−	9.29166e15i	−0.713533	−	1.23588i	−0.963523	−	0.267627i	$-0.913761\pi$
$277$	−5.36454e15	−	9.29166e15i	−0.713533	−	1.23588i	0.249990	−	0.968249i	$-0.419573\pi$
$278$	3.54332e15	−	6.13720e15i	0.460382	−	0.797406i
$279$	−7.86794e15			−0.998697
$280$	−5.56143e15	−	6.28774e15i	−0.689698	−	0.779771i
$281$	8.28465e15			1.00388			0.501941	−	0.864902i	$-0.332619\pi$
$281$	8.28465e15			1.00388			0.501941	+	0.864902i	$0.332619\pi$
$282$	−1.81484e13	+	3.14340e13i	−0.00214892	+	0.00372204i
$283$	−4.67742e15	−	8.10152e15i	−0.541245	−	0.937465i	−0.998833	−	0.0483000i	$-0.984620\pi$
$283$	−4.67742e15	−	8.10152e15i	−0.541245	−	0.937465i	0.457587	−	0.889165i	$-0.348714\pi$
$284$	−7.67561e14	−	1.32945e15i	−0.0868048	−	0.150350i
$285$	7.52112e14	−	1.30270e15i	0.0831363	−	0.143996i
$286$	−9.34244e14			−0.100944
$287$	−1.87373e15	+	5.59751e15i	−0.197913	+	0.591238i
$288$	4.82762e15			0.498520
$289$	−5.43597e15	+	9.41538e15i	−0.548835	+	0.950609i
$290$	3.12471e15	+	5.41216e15i	0.308477	+	0.534298i
$291$	−1.89728e15	−	3.28618e15i	−0.183158	−	0.317239i
$292$	−2.94207e15	+	5.09581e15i	−0.277756	+	0.481088i
$293$	2.23985e15			0.206814			0.103407	−	0.994639i	$-0.467026\pi$
$293$	2.23985e15			0.206814			0.103407	+	0.994639i	$0.467026\pi$
$294$	−3.48197e15	−	2.62531e15i	−0.314462	−	0.237095i
$295$	−1.86608e16			−1.64849
$296$	1.12580e16	−	1.94993e16i	0.972889	−	1.68509i
$297$	6.62606e15	+	1.14767e16i	0.560194	+	0.970285i
$298$	1.49233e15	+	2.58479e15i	0.123441	+	0.213806i
$299$	2.31190e14	−	4.00433e14i	0.0187114	−	0.0324091i
$300$	−1.80343e14			−0.0142827
$301$	−2.26892e15	+	6.77811e15i	−0.175848	+	0.525323i
$302$	1.33722e16			1.01428
$303$	3.11101e15	−	5.38843e15i	0.230953	−	0.400023i
$304$	1.32362e15	+	2.29258e15i	0.0961802	+	0.166589i
$305$	5.11325e15	+	8.85641e15i	0.363704	+	0.629954i
$306$	−6.43287e15	+	1.11421e16i	−0.447935	+	0.775847i
$307$	−8.90343e15			−0.606957			−0.303478	−	0.952838i	$-0.598148\pi$
$307$	−8.90343e15			−0.606957			−0.303478	+	0.952838i	$0.598148\pi$
$308$	−4.45976e15	−	5.04219e15i	−0.297668	−	0.336542i
$309$	1.32488e16			0.865856
$310$	7.91563e15	−	1.37103e16i	0.506564	−	0.877395i
$311$	9.06969e15	+	1.57092e16i	0.568394	+	0.984488i	0.996725	+	0.0808657i	$0.0257685\pi$
$311$	9.06969e15	+	1.57092e16i	0.568394	+	0.984488i	−0.428331	+	0.903622i	$0.640898\pi$
$312$	−4.11204e14	−	7.12226e14i	−0.0252379	−	0.0437132i
$313$	5.50124e15	−	9.52842e15i	0.330691	−	0.572773i	−0.651957	−	0.758256i	$-0.726052\pi$
$313$	5.50124e15	−	9.52842e15i	0.330691	−	0.572773i	0.982647	+	0.185483i	$0.0593850\pi$
$314$	−2.48376e15			−0.146240
$315$	−1.24082e16	+	2.52275e15i	−0.715630	+	0.145498i
$316$	6.22465e15			0.351681
$317$	7.72730e15	−	1.33841e16i	0.427703	−	0.740804i	−0.568965	−	0.822361i	$-0.692656\pi$
$317$	7.72730e15	−	1.33841e16i	0.427703	−	0.740804i	0.996669	+	0.0815577i	$0.0259895\pi$
$318$	−3.76064e15	−	6.51363e15i	−0.203932	−	0.353221i
$319$	9.79293e15	+	1.69618e16i	0.520323	+	0.901226i
$320$	−9.79728e15	+	1.69694e16i	−0.510071	+	0.883469i
$321$	−1.18170e16			−0.602871
$322$	−6.22989e15	+	1.26662e15i	−0.311471	+	0.0633264i
$323$	1.05704e16			0.517935
$324$	1.24132e15	−	2.15002e15i	0.0596129	−	0.103253i
$325$	−8.65496e13	−	1.49908e14i	−0.00407402	−	0.00705641i
$326$	−1.36089e16	−	2.35713e16i	−0.627926	−	1.08760i
$327$	−7.82712e14	+	1.35570e15i	−0.0354031	+	0.0613200i
$328$	1.53059e16			0.678700
$329$	−1.66309e14	−	1.88029e14i	−0.00723008	−	0.00817431i
$330$	−1.15455e16			−0.492120
$331$	−1.03366e16	+	1.79035e16i	−0.432011	+	0.748264i	−0.997046	−	0.0768020i	$-0.975529\pi$
$331$	−1.03366e16	+	1.79035e16i	−0.432011	+	0.748264i	0.565036	+	0.825066i	$0.308862\pi$
$332$	−4.55759e15	−	7.89397e15i	−0.186783	−	0.323518i
$333$	−1.69815e16	−	2.94128e16i	−0.682477	−	1.18208i
$334$	−3.15565e15	+	5.46574e15i	−0.124376	+	0.215426i
$335$	−3.72552e15			−0.144011
$336$	−2.18962e15	+	6.54121e15i	−0.0830165	+	0.248001i
$337$	−2.57774e16			−0.958615			−0.479307	−	0.877647i	$-0.659112\pi$
$337$	−2.57774e16			−0.958615			−0.479307	+	0.877647i	$0.659112\pi$
$338$	−1.10017e16	+	1.90555e16i	−0.401330	+	0.695124i
$339$	−1.90075e15	−	3.29219e15i	−0.0680185	−	0.117811i
$340$	6.78319e15	+	1.17488e16i	0.238134	+	0.412460i
$341$	2.48078e16	−	4.29683e16i	0.854446	−	1.47994i
$342$	6.54566e15			0.221199
$343$	2.48613e16	−	1.70721e16i	0.824352	−	0.566078i
$344$	1.85341e16			0.603033
$345$	2.85707e15	−	4.94859e15i	0.0912214	−	0.158000i
$346$	−1.15910e16	−	2.00762e16i	−0.363184	−	0.629053i
$347$	−5.28908e14	−	9.16096e14i	−0.0162644	−	0.0281708i	0.857779	−	0.514019i	$-0.171844\pi$
$347$	−5.28908e14	−	9.16096e14i	−0.0162644	−	0.0281708i	−0.874043	+	0.485848i	$0.838511\pi$
$348$	−2.20578e15	+	3.82052e15i	−0.0665728	+	0.115307i
$349$	1.24687e16			0.369364			0.184682	−	0.982798i	$-0.440874\pi$
$349$	1.24687e16			0.369364			0.184682	+	0.982798i	$0.440874\pi$
$350$	−7.55476e14	+	2.25688e15i	−0.0219674	+	0.0656246i
$351$	−2.86504e15			−0.0817777
$352$	−1.52216e16	+	2.63646e16i	−0.426514	+	0.738744i
$353$	1.67634e16	+	2.90350e16i	0.461133	+	0.798705i	0.999018	−	0.0443131i	$-0.0141099\pi$
$353$	1.67634e16	+	2.90350e16i	0.461133	+	0.798705i	−0.537885	+	0.843018i	$0.680777\pi$
$354$	1.25683e16	+	2.17689e16i	0.339434	+	0.587916i
$355$	9.10460e15	−	1.57696e16i	0.241422	−	0.418155i
$356$	−2.00778e16			−0.522745
$357$	1.82481e16	+	2.06312e16i	0.466524	+	0.527451i
$358$	1.94631e16			0.488622
$359$	−3.85065e15	+	6.66952e15i	−0.0949335	+	0.164430i	−0.909581	−	0.415527i	$-0.863597\pi$
$359$	−3.85065e15	+	6.66952e15i	−0.0949335	+	0.164430i	0.814647	+	0.579957i	$0.196931\pi$
$360$	1.64162e16	+	2.84337e16i	0.397472	+	0.688442i
$361$	1.83376e16	+	3.17616e16i	0.436058	+	0.755275i
$362$	−1.58424e16	+	2.74399e16i	−0.370013	+	0.640881i
$363$	−1.49905e16			−0.343892
$364$	1.42614e15	−	2.89954e14i	0.0321368	−	0.00653387i
$365$	−6.97960e16			−1.54499
$366$	6.88769e15	−	1.19298e16i	0.149778	−	0.259422i
$367$	−2.60943e16	−	4.51966e16i	−0.557462	−	0.965553i	−0.997707	−	0.0676753i	$-0.978442\pi$
$367$	−2.60943e16	−	4.51966e16i	−0.557462	−	0.965553i	0.440245	−	0.897878i	$-0.354892\pi$
$368$	5.02809e15	+	8.70890e15i	0.105534	+	0.182790i
$369$	1.15437e16	−	1.99942e16i	0.238052	−	0.412318i
$370$	6.83376e16			1.38468
$371$	5.09735e16	−	1.03636e16i	1.01488	−	0.206339i
$372$	1.11755e16			0.218644
$373$	−2.60858e16	+	4.51818e16i	−0.501529	+	0.868674i	0.498470	+	0.866907i	$0.333896\pi$
$373$	−2.60858e16	+	4.51818e16i	−0.501529	+	0.868674i	−0.999998	+	0.00176631i	$0.999438\pi$
$374$	−4.05659e16	−	7.02622e16i	−0.766471	−	1.32757i
$375$	−1.35891e16	−	2.35370e16i	−0.252341	−	0.437067i
$376$	−3.25452e14	+	5.63700e14i	−0.00593972	+	0.0102879i
$377$	−4.23436e15			−0.0759573
$378$	2.60980e16	+	2.95063e16i	0.460162	+	0.520257i
$379$	−3.04480e16			−0.527721			−0.263860	−	0.964561i	$-0.584996\pi$
$379$	−3.04480e16			−0.527721			−0.263860	+	0.964561i	$0.584996\pi$
$380$	3.45106e15	−	5.97741e15i	0.0587976	−	0.101840i
$381$	−1.95889e16	−	3.39290e16i	−0.328094	−	0.568276i
$382$	−2.28427e16	−	3.95647e16i	−0.376128	−	0.651473i
$383$	−1.74359e16	+	3.01998e16i	−0.282262	+	0.488891i	−0.971941	−	0.235223i	$-0.924418\pi$
$383$	−1.74359e16	+	3.01998e16i	−0.282262	+	0.488891i	0.689680	+	0.724114i	$0.257751\pi$
$384$	6.45261e15			0.102703
$385$	2.53460e16	−	7.57176e16i	0.396656	−	1.18496i
$386$	−8.17711e16			−1.25829
$387$	1.39784e16	−	2.42113e16i	0.211512	−	0.366350i
$388$	−8.70564e15	−	1.50786e16i	−0.129537	−	0.224365i
$389$	1.23731e16	+	2.14308e16i	0.181053	+	0.313593i	0.942239	−	0.334940i	$-0.108716\pi$
$389$	1.23731e16	+	2.14308e16i	0.181053	+	0.313593i	−0.761186	+	0.648533i	$0.775383\pi$
$390$	1.24804e15	−	2.16166e15i	0.0179601	−	0.0311077i
$391$	4.01542e16			0.568305
$392$	−6.24415e16	−	4.70791e16i	−0.869188	−	0.655343i
$393$	8.31810e15			0.113887
$394$	−1.01403e16	+	1.75635e16i	−0.136560	+	0.236529i
$395$	3.69175e16	+	6.39430e16i	0.489048	+	0.847056i
$396$	1.31643e16	+	2.28012e16i	0.171545	+	0.297125i
$397$	−3.69816e16	+	6.40541e16i	−0.474076	+	0.821123i	−0.999559	−	0.0296805i	$-0.990551\pi$
$397$	−3.69816e16	+	6.40541e16i	−0.474076	+	0.821123i	0.525484	+	0.850804i	$0.323884\pi$
$398$	3.01056e15			0.0379671
$399$	4.44822e15	−	1.32884e16i	0.0551902	−	0.164873i
$400$	3.76468e15			0.0459556
$401$	−7.05205e16	+	1.22145e17i	−0.846987	+	1.46703i	0.0368966	+	0.999319i	$0.488253\pi$
$401$	−7.05205e16	+	1.22145e17i	−0.846987	+	1.46703i	−0.883884	+	0.467706i	$0.845081\pi$
$402$	2.50919e15	+	4.34604e15i	0.0296527	+	0.0513600i
$403$	5.36332e15	+	9.28954e15i	0.0623664	+	0.108022i
$404$	1.42749e16	−	2.47248e16i	0.163340	−	0.282913i
$405$	2.94483e16			0.331591
$406$	3.85713e16	+	4.36086e16i	0.427410	+	0.483229i
$407$	2.14172e17			2.33560
$408$	3.57099e16	−	6.18513e16i	0.383263	−	0.663831i
$409$	−3.12983e16	−	5.42103e16i	−0.330613	−	0.572638i	0.652019	−	0.758202i	$-0.273922\pi$
$409$	−3.12983e16	−	5.42103e16i	−0.330613	−	0.572638i	−0.982632	+	0.185564i	$0.940589\pi$
$410$	2.32273e16	+	4.02308e16i	0.241492	+	0.418277i
$411$	−1.10469e16	+	1.91337e16i	−0.113049	+	0.195807i
$412$	6.07920e16			0.612371
$413$	−1.70356e17	+	3.46358e16i	−1.68921	+	0.343439i
$414$	2.48652e16			0.242711
$415$	5.40608e16	−	9.36361e16i	0.519481	−	0.899768i
$416$	−3.29084e15	−	5.69989e15i	−0.0311315	−	0.0539213i
$417$	2.96694e16	+	5.13890e16i	0.276328	+	0.478614i
$418$	−2.06386e16	+	3.57471e16i	−0.189249	+	0.327789i
$419$	−8.72271e16			−0.787517			−0.393759	−	0.919214i	$-0.628825\pi$
$419$	−8.72271e16			−0.787517			−0.393759	+	0.919214i	$0.628825\pi$
$420$	1.76244e16	−	3.58328e15i	0.156673	−	0.0318537i
$421$	−1.16026e16			−0.101560			−0.0507800	−	0.998710i	$-0.516171\pi$
$421$	−1.16026e16			−0.101560			−0.0507800	+	0.998710i	$0.516171\pi$
$422$	1.21414e16	−	2.10295e16i	0.104650	−	0.181258i
$423$	4.90911e14	+	8.50283e14i	0.00416668	+	0.00721691i
$424$	−6.74388e16	−	1.16807e17i	−0.563679	−	0.976321i
$425$	7.51616e15	−	1.30184e16i	0.0618682	−	0.107159i
$426$	−2.45283e16			−0.198841
$427$	6.31177e16	+	7.13606e16i	0.503929	+	0.569741i
$428$	−5.42222e16			−0.426376
$429$	3.91138e15	−	6.77471e15i	0.0302941	−	0.0524709i
$430$	2.81262e16	+	4.87161e16i	0.214569	+	0.371644i
$431$	2.63188e16	+	4.55856e16i	0.197772	+	0.342551i	0.947806	−	0.318849i	$-0.103296\pi$
$431$	2.63188e16	+	4.55856e16i	0.197772	+	0.342551i	−0.750034	+	0.661400i	$0.769963\pi$
$432$	3.11555e16	−	5.39629e16i	0.230616	−	0.399439i
$433$	−1.03188e17			−0.752417			−0.376208	−	0.926535i	$-0.622772\pi$
$433$	−1.03188e17			−0.752417			−0.376208	+	0.926535i	$0.622772\pi$
$434$	4.68155e16	−	1.39855e17i	0.336284	−	1.00460i
$435$	−5.23287e16			−0.370305
$436$	−3.59147e15	+	6.22061e15i	−0.0250386	+	0.0433682i
$437$	−1.02145e16	−	1.76921e16i	−0.0701600	−	0.121521i
$438$	4.70086e16	+	8.14213e16i	0.318123	+	0.551006i
$439$	1.10814e16	−	1.91936e16i	0.0738885	−	0.127979i	−0.826714	−	0.562623i	$-0.809792\pi$
$439$	1.10814e16	−	1.91936e16i	0.0738885	−	0.127979i	0.900602	+	0.434644i	$0.143126\pi$
$440$	−2.07043e17			−1.36025
$441$	−1.08593e17	+	4.60610e16i	−0.702994	+	0.298183i
$442$	1.75403e16			0.111890
$443$	4.13822e16	−	7.16760e16i	0.260129	−	0.450557i	−0.706147	−	0.708065i	$-0.749568\pi$
$443$	4.13822e16	−	7.16760e16i	0.260129	−	0.450557i	0.966276	+	0.257508i	$0.0829015\pi$
$444$	2.41202e16	+	4.17775e16i	0.149414	+	0.258793i
$445$	−1.19078e17	−	2.06250e17i	−0.726930	−	1.25908i
$446$	7.35675e16	−	1.27423e17i	0.442598	−	0.766603i
$447$	−2.49916e16			−0.148182
$448$	−5.79441e16	+	1.73100e17i	−0.338612	+	1.01156i
$449$	1.43486e17			0.826434			0.413217	−	0.910633i	$-0.364405\pi$
$449$	1.43486e17			0.826434			0.413217	+	0.910633i	$0.364405\pi$
$450$	4.65433e15	−	8.06154e15i	0.0264226	−	0.0457653i
$451$	7.27948e16	+	1.26084e17i	0.407336	+	0.705527i
$452$	−8.72158e15	−	1.51062e16i	−0.0481056	−	0.0833213i
$453$	−5.59850e16	+	9.69689e16i	−0.304392	+	0.527223i
$454$	1.89785e16			0.101718
$455$	1.14368e16	+	1.29304e16i	0.0604270	+	0.0683185i
$456$	−3.63360e16			−0.189263
$457$	7.50121e16	−	1.29925e17i	0.385191	−	0.667171i	−0.606605	−	0.795004i	$-0.707469\pi$
$457$	7.50121e16	−	1.29925e17i	0.385191	−	0.667171i	0.991796	+	0.127833i	$0.0408022\pi$
$458$	1.17483e17	+	2.03487e17i	0.594773	+	1.03018i
$459$	−1.24403e17	−	2.15473e17i	−0.620940	−	1.07550i
$460$	1.31097e16	−	2.27066e16i	0.0645157	−	0.111745i
$461$	2.24646e17			1.09004			0.545020	−	0.838423i	$-0.316522\pi$
$461$	2.24646e17			1.09004			0.545020	+	0.838423i	$0.316522\pi$
$462$	−1.05400e17	+	2.14293e16i	−0.504276	+	0.102526i
$463$	2.70037e16			0.127393			0.0636966	−	0.997969i	$-0.479711\pi$
$463$	2.70037e16			0.127393			0.0636966	+	0.997969i	$0.479711\pi$
$464$	4.60460e16	−	7.97539e16i	0.214203	−	0.371010i
$465$	6.62804e16	+	1.14801e17i	0.304047	+	0.526625i
$466$	3.45592e16	+	5.98582e16i	0.156335	+	0.270779i
$467$	5.63259e16	−	9.75593e16i	0.251274	−	0.435220i	−0.712602	−	0.701568i	$-0.752484\pi$
$467$	5.63259e16	−	9.75593e16i	0.251274	−	0.435220i	0.963877	+	0.266348i	$0.0858170\pi$
$468$	−5.69211e15			−0.0250424
$469$	−3.40107e16	+	6.91485e15i	−0.147568	+	0.0300026i
$470$	−1.97555e15			−0.00845379
$471$	1.03987e16	−	1.80110e16i	0.0438877	−	0.0760157i
$472$	2.25384e17	+	3.90377e17i	0.938212	+	1.62503i
$473$	8.81483e16	+	1.52677e17i	0.361923	+	0.626869i
$474$	4.97289e16	−	8.61331e16i	0.201396	−	0.348827i
$475$	−7.64794e15			−0.0305518
$476$	8.37313e16	+	9.46664e16i	0.329946	+	0.373036i
$477$	−2.03449e17			−0.790836
$478$	−2.01181e17	+	3.48456e17i	−0.771447	+	1.33619i
$479$	−5.49755e16	−	9.52203e16i	−0.207964	−	0.360204i	0.743109	−	0.669170i	$-0.233350\pi$
$479$	−5.49755e16	−	9.52203e16i	−0.207964	−	0.360204i	−0.951073	+	0.308966i	$0.900017\pi$
$480$	−4.06684e16	−	7.04398e16i	−0.151771	−	0.262876i
$481$	−2.31514e16	+	4.00995e16i	−0.0852383	+	0.147637i
$482$	−2.99955e17			−1.08956
$483$	1.68976e16	−	5.04793e16i	0.0605576	−	0.180908i
$484$	−6.87837e16			−0.243215
$485$	1.03264e17	−	1.78858e17i	0.360269	−	0.624005i
$486$	−1.20717e17	−	2.09087e17i	−0.415558	−	0.719767i
$487$	4.44682e16	+	7.70212e16i	0.151047	+	0.261621i	0.931613	−	0.363453i	$-0.118402\pi$
$487$	4.44682e16	+	7.70212e16i	0.151047	+	0.261621i	−0.780566	+	0.625074i	$0.785069\pi$
$488$	1.23516e17	−	2.13935e17i	0.413993	−	0.717056i
$489$	2.27904e17			0.753780
$490$	2.89878e16	−	2.35569e17i	0.0946109	−	0.768854i
$491$	−4.78607e16			−0.154152			−0.0770760	−	0.997025i	$-0.524558\pi$
$491$	−4.78607e16			−0.154152			−0.0770760	+	0.997025i	$0.524558\pi$
$492$	−1.63964e16	+	2.83995e16i	−0.0521167	+	0.0902687i
$493$	−1.83861e17	−	3.18456e17i	−0.576745	−	0.998952i
$494$	−4.46196e15	−	7.72834e15i	−0.0138134	−	0.0239255i
$495$	−1.56151e17	+	2.70462e17i	−0.477103	+	0.826366i
$496$	−2.33290e17			−0.703503
$497$	5.38473e16	−	1.60862e17i	0.160268	−	0.478780i
$498$	−1.45643e17			−0.427857
$499$	1.77579e17	−	3.07576e17i	0.514917	−	0.891863i	−0.484933	−	0.874551i	$-0.661156\pi$
$499$	1.77579e17	−	3.07576e17i	0.514917	−	0.891863i	0.999850	−	0.0173117i	$-0.00551075\pi$
$500$	−6.23535e16	−	1.07999e17i	−0.178466	−	0.309112i
$501$	−2.64234e16	−	4.57666e16i	−0.0746522	−	0.129301i
$502$	−2.51743e16	+	4.36032e16i	−0.0702076	+	0.121603i
$503$	−5.24075e16			−0.144279			−0.0721393	−	0.997395i	$-0.522983\pi$
$503$	−5.24075e16			−0.144279			−0.0721393	+	0.997395i	$0.522983\pi$
$504$	2.02641e17	+	2.29105e17i	0.550717	+	0.622639i
$505$	3.38649e17			0.908564
$506$	−7.84005e16	+	1.35794e17i	−0.207654	+	0.359667i
$507$	−9.21212e16	−	1.59559e17i	−0.240884	−	0.417223i
$508$	−8.98837e16	−	1.55683e17i	−0.232042	−	0.401909i
$509$	−1.03470e17	+	1.79215e17i	−0.263723	+	0.456781i	−0.967228	−	0.253909i	$-0.918284\pi$
$509$	−1.03470e17	+	1.79215e17i	−0.263723	+	0.456781i	0.703506	+	0.710690i	$0.251617\pi$
$510$	2.16765e17			0.545484
$511$	−6.37176e17	+	1.29547e17i	−1.58316	+	0.321878i
$512$	3.81823e17			0.936714
$513$	−6.32923e16	+	1.09625e17i	−0.153316	+	0.265551i
$514$	−1.79897e17	−	3.11591e17i	−0.430293	−	0.745289i
$515$	3.60549e17	+	6.24489e17i	0.851564	+	1.47495i
$516$	−1.98547e16	+	3.43893e16i	−0.0463063	+	0.0802049i
$517$	−6.19142e15			−0.0142594
$518$	6.23863e17	−	1.26840e17i	1.41888	−	0.288478i
$519$	1.94111e17			0.435976
$520$	2.23808e16	−	3.87647e16i	0.0496425	−	0.0859834i
$521$	5.84860e16	+	1.01301e17i	0.128117	+	0.221905i	0.922947	−	0.384927i	$-0.125773\pi$
$521$	5.84860e16	+	1.01301e17i	0.128117	+	0.221905i	−0.794830	+	0.606832i	$0.792440\pi$
$522$	−1.13855e17	−	1.97202e17i	−0.246316	−	0.426632i
$523$	−3.18180e17	+	5.51103e17i	−0.679847	+	1.17753i	0.295179	+	0.955442i	$0.404621\pi$
$523$	−3.18180e17	+	5.51103e17i	−0.679847	+	1.17753i	−0.975027	+	0.222088i	$0.928713\pi$
$524$	3.81676e16			0.0805455
$525$	−1.32029e16	−	1.49272e16i	−0.0275191	−	0.0311131i
$526$	−1.92298e17			−0.395883
$527$	−4.65762e17	+	8.06724e17i	−0.947099	+	1.64042i
$528$	8.50674e16	+	1.47341e17i	0.170861	+	0.295940i
$529$	2.13216e17	+	3.69301e17i	0.423017	+	0.732687i
$530$	2.04682e17	−	3.54520e17i	0.401132	−	0.694781i
$531$	6.79939e17			1.31630
$532$	2.04106e16	−	6.09740e16i	0.0390329	−	0.116605i
$533$	−3.14757e16			−0.0594633
$534$	−1.60402e17	+	2.77824e17i	−0.299359	+	0.518504i
$535$	−3.21584e17	−	5.57001e17i	−0.592919	−	1.02697i
$536$	4.49968e16	+	7.79367e16i	0.0819615	+	0.141962i
$537$	−8.14859e16	+	1.41138e17i	−0.146639	+	0.253986i
$538$	7.36307e17			1.30910
$539$	9.08486e16	−	7.38280e17i	0.159585	−	1.29686i
$540$	−1.62462e17			−0.281964
$541$	1.90949e17	−	3.30734e17i	0.327443	−	0.567148i	−0.654561	−	0.756009i	$-0.727146\pi$
$541$	1.90949e17	−	3.30734e17i	0.327443	−	0.567148i	0.982004	+	0.188862i	$0.0604797\pi$
$542$	−1.43002e17	−	2.47687e17i	−0.242297	−	0.419671i
$543$	−1.32654e17	−	2.29764e17i	−0.222087	−	0.384666i
$544$	2.85783e17	−	4.94991e17i	0.472764	−	0.818851i
$545$	−8.52021e16			−0.139275
$546$	7.38127e15	−	2.20506e16i	0.0119228	−	0.0356178i
$547$	−5.55447e17			−0.886595			−0.443297	−	0.896375i	$-0.646191\pi$
$547$	−5.55447e17			−0.886595			−0.443297	+	0.896375i	$0.646191\pi$
$548$	−5.06885e16	+	8.77951e16i	−0.0799532	+	0.138483i
$549$	−1.86310e17	−	3.22699e17i	−0.290414	−	0.503011i
$550$	2.93504e16	+	5.08364e16i	0.0452123	+	0.0783100i
$551$	−9.35422e16	+	1.62020e17i	−0.142404	+	0.246651i
$552$	−1.38031e17			−0.207669
$553$	4.55708e17	+	5.15222e17i	0.677599	+	0.766092i
$554$	−7.86607e17			−1.15596
$555$	−2.86108e17	+	4.95553e17i	−0.415552	+	0.719756i
$556$	1.36138e17	+	2.35798e17i	0.195431	+	0.338497i
$557$	−3.16725e17	−	5.48583e17i	−0.449390	−	0.778366i	0.548956	−	0.835851i	$-0.315025\pi$
$557$	−3.16725e17	−	5.48583e17i	−0.449390	−	0.778366i	−0.998346	+	0.0574848i	$0.981692\pi$
$558$	−2.88420e17	+	4.99559e17i	−0.404486	+	0.700591i
$559$	−3.81144e16			−0.0528339
$560$	−3.67911e17	+	7.48015e16i	−0.504105	+	0.102492i
$561$	6.79346e17			0.920094
$562$	3.03696e17	−	5.26017e17i	0.406587	−	0.704229i
$563$	−3.86876e17	−	6.70088e17i	−0.511996	−	0.886803i	−0.999903	−	0.0139078i	$-0.995573\pi$
$563$	−3.86876e17	−	6.70088e17i	−0.511996	−	0.886803i	0.487907	−	0.872896i	$-0.337760\pi$
$564$	−6.97283e14	−	1.20773e15i	−0.000912211	−	0.00158000i
$565$	1.03453e17	−	1.79186e17i	0.133791	−	0.231733i
$566$	−6.85853e17			−0.876848
$567$	2.68837e17	−	5.46583e16i	0.339781	−	0.0690823i
$568$	−4.39861e17			−0.549606
$569$	−2.29097e17	+	3.96808e17i	−0.283002	+	0.490174i	−0.972123	−	0.234473i	$-0.924664\pi$
$569$	−2.29097e17	+	3.96808e17i	−0.283002	+	0.490174i	0.689121	+	0.724647i	$0.257997\pi$
$570$	−5.51413e16	−	9.55076e16i	−0.0673427	−	0.116641i
$571$	1.36522e17	+	2.36464e17i	0.164842	+	0.285515i	0.936599	−	0.350402i	$-0.113955\pi$
$571$	1.36522e17	+	2.36464e17i	0.164842	+	0.285515i	−0.771757	+	0.635918i	$0.780622\pi$
$572$	1.79474e16	−	3.10857e16i	0.0214253	−	0.0371097i
$573$	3.82540e17			0.451515
$574$	2.86716e17	+	3.24160e17i	0.334599	+	0.378297i
$575$	−2.90525e16			−0.0335230
$576$	3.56982e17	−	6.18310e17i	0.407286	−	0.705441i
$577$	8.47674e17	+	1.46821e18i	0.956282	+	1.65633i	0.731407	+	0.681942i	$0.238864\pi$
$577$	8.47674e17	+	1.46821e18i	0.956282	+	1.65633i	0.224876	+	0.974388i	$0.427802\pi$
$578$	3.98540e17	+	6.90292e17i	0.444571	+	0.770020i
$579$	3.42349e17	−	5.92966e17i	0.377623	−	0.654062i
$580$	−2.40110e17			−0.261896
$581$	3.19732e17	−	9.55156e17i	0.344859	−	1.03022i
$582$	−2.78199e17			−0.296726
$583$	6.41479e17	−	1.11107e18i	0.676608	−	1.17192i
$584$	8.42995e17	+	1.46011e18i	0.879309	+	1.52301i
$585$	−3.37591e16	−	5.84725e16i	−0.0348240	−	0.0603169i
$586$	8.21076e16	−	1.42215e17i	0.0837624	−	0.145081i
$587$	−1.65931e18			−1.67409			−0.837047	−	0.547131i	$-0.815720\pi$
$587$	−1.65931e18			−1.67409			−0.837047	+	0.547131i	$0.815720\pi$
$588$	1.54244e17	−	6.54244e16i	0.153906	−	0.0652811i
$589$	4.73929e17			0.467696
$590$	−6.84060e17	+	1.18483e18i	−0.667661	+	1.15642i
$591$	−8.49081e16	−	1.47065e17i	−0.0819654	−	0.141968i
$592$	−5.03514e17	−	8.72111e17i	−0.480751	−	0.832685i
$593$	3.95735e17	−	6.85433e17i	0.373722	−	0.647305i	−0.616413	−	0.787423i	$-0.711415\pi$
$593$	3.95735e17	−	6.85433e17i	0.373722	−	0.647305i	0.990135	+	0.140118i	$0.0447481\pi$
$594$	9.71584e17			0.907546
$595$	−4.75867e17	+	1.42159e18i	−0.439668	+	1.31345i
$596$	−1.14674e17			−0.104801
$597$	−1.26043e16	+	2.18312e16i	−0.0113942	+	0.0197353i
$598$	−1.69498e16	−	2.93579e16i	−0.0151568	−	0.0262523i
$599$	4.34308e17	+	7.52243e17i	0.384170	+	0.665402i	0.991654	−	0.128930i	$-0.0411543\pi$
$599$	4.34308e17	+	7.52243e17i	0.384170	+	0.665402i	−0.607484	+	0.794332i	$0.707821\pi$
$600$	−2.58369e16	+	4.47509e16i	−0.0226078	+	0.0391578i
$601$	6.24840e17			0.540860			0.270430	−	0.962740i	$-0.412834\pi$
$601$	6.24840e17			0.540860			0.270430	+	0.962740i	$0.412834\pi$
$602$	3.47189e17	+	3.92530e17i	0.297295	+	0.336121i
$603$	1.35746e17			0.114991
$604$	−2.56887e17	+	4.44942e17i	−0.215279	+	0.372875i
$605$	−4.07947e17	−	7.06585e17i	−0.338216	−	0.585807i
$606$	−2.28085e17	−	3.95054e17i	−0.187079	−	0.324030i
$607$	3.82513e16	−	6.62532e16i	0.0310399	−	0.0537626i	−0.850088	−	0.526640i	$-0.823451\pi$
$607$	3.82513e16	−	6.62532e16i	0.0310399	−	0.0537626i	0.881128	+	0.472878i	$0.156785\pi$
$608$	−2.90794e17			−0.233460
$609$	−4.77715e17	+	9.71261e16i	−0.379452	+	0.0771478i
$610$	7.49759e17			0.589221
$611$	6.69277e14	−	1.15922e15i	0.000520401	−	0.000901360i
$612$	−2.47158e17	−	4.28090e17i	−0.190147	−	0.329345i
$613$	−1.01907e18	−	1.76507e18i	−0.775728	−	1.34360i	−0.934385	−	0.356266i	$-0.884050\pi$
$613$	−1.01907e18	−	1.76507e18i	−0.775728	−	1.34360i	0.158657	−	0.987334i	$-0.449284\pi$
$614$	−3.26379e17	+	5.65305e17i	−0.245826	+	0.425783i
$615$	−3.88980e17			−0.289894
$616$	−1.89012e18	+	3.84287e17i	−1.39384	+	0.283388i
$617$	7.64014e17			0.557503			0.278752	−	0.960363i	$-0.410079\pi$
$617$	7.64014e17			0.557503			0.278752	+	0.960363i	$0.410079\pi$
$618$	4.85670e17	−	8.41205e17i	0.350684	−	0.607402i
$619$	9.53268e17	+	1.65111e18i	0.681124	+	1.17974i	0.974638	+	0.223786i	$0.0718417\pi$
$619$	9.53268e17	+	1.65111e18i	0.681124	+	1.17974i	−0.293515	+	0.955955i	$0.594825\pi$
$620$	3.04127e17	+	5.26764e17i	0.215035	+	0.372452i
$621$	−2.40430e17	+	4.16438e17i	−0.168226	+	0.291377i
$622$	1.32989e18			0.920831
$623$	−1.46990e18	−	1.66186e18i	−1.00720	−	1.13873i
$624$	−3.67823e16			−0.0249425
$625$	6.75967e17	−	1.17081e18i	0.453634	−	0.785717i
$626$	−4.03325e17	−	6.98579e17i	−0.267869	−	0.463962i
$627$	−1.72814e17	−	2.99323e17i	−0.113590	−	0.196744i
$628$	4.77143e16	−	8.26436e16i	0.0310392	−	0.0537615i
$629$	−4.02104e18			−2.58887
$630$	−2.94677e17	+	8.80309e17i	−0.187773	+	0.560947i
$631$	5.36643e17			0.338450			0.169225	−	0.985577i	$-0.445873\pi$
$631$	5.36643e17			0.338450			0.169225	+	0.985577i	$0.445873\pi$
$632$	8.91779e17	−	1.54461e18i	0.556668	−	0.964177i
$633$	1.01664e17	+	1.76087e17i	0.0628121	+	0.108794i
$634$	−5.66530e17	−	9.81258e17i	−0.346452	−	0.600072i
$635$	1.06618e18	−	1.84667e18i	0.645356	−	1.11779i
$636$	2.88976e17			0.173137
$637$	1.28408e17	+	9.68158e16i	0.0761527	+	0.0574169i
$638$	1.43594e18			0.842952
$639$	−3.31742e17	+	5.74595e17i	−0.192773	+	0.333892i
$640$	1.75600e17	+	3.04148e17i	0.101008	+	0.174950i
$641$	1.24072e18	+	2.14899e18i	0.706475	+	1.22365i	0.966157	+	0.257956i	$0.0830490\pi$
$641$	1.24072e18	+	2.14899e18i	0.706475	+	1.22365i	−0.259682	+	0.965694i	$0.583618\pi$
$642$	−4.33183e17	+	7.50296e17i	−0.244171	+	0.422917i
$643$	1.72636e17			0.0963294			0.0481647	−	0.998839i	$-0.484663\pi$
$643$	1.72636e17			0.0963294			0.0481647	+	0.998839i	$0.484663\pi$
$644$	7.75345e16	−	2.31624e17i	0.0428289	−	0.127946i
$645$	−4.71022e17			−0.257575
$646$	3.87487e17	−	6.71146e17i	0.209771	−	0.363334i
$647$	1.26356e18	+	2.18854e18i	0.677199	+	1.17294i	0.975821	+	0.218572i	$0.0701399\pi$
$647$	1.26356e18	+	2.18854e18i	0.677199	+	1.17294i	−0.298621	+	0.954372i	$0.596527\pi$
$648$	−3.55676e17	−	6.16049e17i	−0.188720	−	0.326872i
$649$	−2.14386e18	+	3.71328e18i	−1.12618	+	1.95059i
$650$	−1.26908e16			−0.00660014
$651$	8.18162e17	+	9.25011e17i	0.421272	+	0.476289i
$652$	1.04574e18			0.533106
$653$	3.79320e17	−	6.57001e17i	0.191456	−	0.331612i	−0.754277	−	0.656557i	$-0.772012\pi$
$653$	3.79320e17	−	6.57001e17i	0.191456	−	0.331612i	0.945733	+	0.324945i	$0.105346\pi$
$654$	5.73848e16	+	9.93934e16i	0.0286775	+	0.0496709i
$655$	2.26367e17	+	3.92078e17i	0.112007	+	0.194001i
$656$	3.42278e17	−	5.92843e17i	0.167689	−	0.290446i
$657$	2.54314e18			1.23366
$658$	−1.80350e16	+	3.66677e15i	−0.00866260	+	0.00176123i
$659$	7.02591e17			0.334155			0.167077	−	0.985944i	$-0.446567\pi$
$659$	7.02591e17			0.334155			0.167077	+	0.985944i	$0.446567\pi$
$660$	2.21795e17	−	3.84160e17i	0.104452	−	0.180916i
$661$	−7.77490e17	−	1.34665e18i	−0.362564	−	0.627980i	0.625818	−	0.779969i	$-0.284765\pi$
$661$	−7.77490e17	−	1.34665e18i	−0.362564	−	0.627980i	−0.988382	+	0.151989i	$0.951432\pi$
$662$	7.57829e17	+	1.31260e18i	0.349941	+	0.606115i
$663$	−7.34356e16	+	1.27194e17i	−0.0335791	+	0.0581606i
$664$	−2.61178e18			−1.18262
$665$	7.47411e17	−	1.51959e17i	0.335134	−	0.0681374i
$666$	−2.49001e18			−1.10565
$667$	−3.55342e17	+	6.15470e17i	−0.156253	+	0.270638i
$668$	−1.21243e17	−	2.10000e17i	−0.0527973	−	0.0914475i
$669$	6.16007e17	+	1.06696e18i	0.265654	+	0.460126i
$670$	−1.36569e17	+	2.36544e17i	−0.0583264	+	0.101024i
$671$	2.34976e18			0.993866
$672$	−5.02009e17	−	5.67570e17i	−0.210286	−	0.237749i
$673$	−2.46710e18			−1.02350			−0.511751	−	0.859134i	$-0.671003\pi$
$673$	−2.46710e18			−1.02350			−0.511751	+	0.859134i	$0.671003\pi$
$674$	−9.44938e17	+	1.63668e18i	−0.388252	+	0.672473i
$675$	9.00088e16	+	1.55900e17i	0.0366278	+	0.0634411i
$676$	−4.22698e17	−	7.32134e17i	−0.170364	−	0.295078i
$677$	9.32830e17	−	1.61571e18i	0.372371	−	0.644966i	−0.617559	−	0.786525i	$-0.711878\pi$
$677$	9.32830e17	−	1.61571e18i	0.372371	−	0.644966i	0.989930	+	0.141559i	$0.0452115\pi$
$678$	−2.78708e17			−0.110194
$679$	6.10734e17	−	1.82449e18i	0.239166	−	0.714475i
$680$	3.88720e18			1.50775
$681$	−7.94569e16	+	1.37623e17i	−0.0305264	+	0.0528732i
$682$	−1.81879e18	−	3.15024e18i	−0.692125	−	1.19880i
$683$	−8.64872e17	−	1.49800e18i	−0.326000	−	0.564648i	0.655714	−	0.755009i	$-0.272368\pi$
$683$	−8.64872e17	−	1.49800e18i	−0.326000	−	0.564648i	−0.981714	+	0.190361i	$0.939034\pi$
$684$	−1.25746e17	+	2.17798e17i	−0.0469492	+	0.0813184i
$685$	−1.20251e18			−0.444732
$686$	−1.72601e17	−	2.20434e18i	−0.0632320	−	0.807556i
$687$	−1.96746e18			−0.713982
$688$	4.14470e17	−	7.17883e17i	0.148994	−	0.258065i
$689$	1.38685e17	+	2.40209e17i	0.0493860	+	0.0855390i
$690$	−2.09467e17	−	3.62808e17i	−0.0738919	−	0.127985i
$691$	1.81501e18	−	3.14369e18i	0.634267	−	1.09858i	−0.352403	−	0.935848i	$-0.614635\pi$
$691$	1.81501e18	−	3.14369e18i	0.634267	−	1.09858i	0.986670	−	0.162735i	$-0.0520314\pi$
$692$	8.90679e17			0.308341
$693$	−9.23526e17	+	2.75891e18i	−0.316726	+	0.946175i
$694$	−7.75542e16			−0.0263493
$695$	−1.61483e18	+	2.79697e18i	−0.543533	+	0.941428i
$696$	6.32025e17	+	1.09470e18i	0.210753	+	0.365035i
$697$	−1.36671e18	−	2.36721e18i	−0.451506	−	0.782032i
$698$	4.57073e17	−	7.91673e17i	0.149598	−	0.259111i
$699$	−5.78752e17			−0.187668
$700$	−6.05816e16	−	6.84934e16i	−0.0194627	−	0.0220045i
$701$	−5.53631e18			−1.76219			−0.881096	−	0.472938i	$-0.843194\pi$
$701$	−5.53631e18			−1.76219			−0.881096	+	0.472938i	$0.843194\pi$
$702$	−1.05026e17	+	1.81910e17i	−0.0331211	+	0.0573674i
$703$	1.02289e18	+	1.77169e18i	0.319608	+	0.553578i
$704$	2.25114e18	+	3.89909e18i	0.696916	+	1.20709i
$705$	8.27098e15	−	1.43258e16i	0.00253704	−	0.00439429i
$706$	2.45803e18			0.747061
$707$	3.09157e18	−	6.28558e17i	0.931006	−	0.189286i
$708$	−9.65775e17			−0.288177
$709$	−2.12955e18	+	3.68848e18i	−0.629632	+	1.09055i	0.357994	+	0.933724i	$0.383461\pi$
$709$	−2.12955e18	+	3.68848e18i	−0.629632	+	1.09055i	−0.987626	+	0.156830i	$0.949873\pi$
$710$	−6.67507e17	−	1.15616e18i	−0.195558	−	0.338717i
$711$	−1.34516e18	−	2.32988e18i	−0.390499	−	0.676365i
$712$	−2.87645e18	+	4.98217e18i	−0.827442	+	1.43317i
$713$	1.80033e18			0.513180
$714$	1.97887e18	−	4.02332e17i	0.558958	−	0.113644i
$715$	4.25773e17			0.119176
$716$	−3.73898e17	+	6.47610e17i	−0.103709	+	0.179630i
$717$	−1.68456e18	−	2.91775e18i	−0.463034	−	0.801998i
$718$	2.82312e17	+	4.88978e17i	0.0768988	+	0.133193i
$719$	2.25554e18	−	3.90670e18i	0.608852	−	1.05456i	−0.382578	−	0.923923i	$-0.624964\pi$
$719$	2.25554e18	−	3.90670e18i	0.608852	−	1.05456i	0.991430	−	0.130640i	$-0.0417031\pi$
$720$	1.46843e18			0.392820
$721$	4.45060e18	+	5.03183e18i	1.17988	+	1.33397i
$722$	2.68885e18			0.706439
$723$	1.25581e18	−	2.17513e18i	0.326984	−	0.566352i
$724$	−6.08684e17	−	1.05427e18i	−0.157069	−	0.272052i
$725$	1.33028e17	+	2.30411e17i	0.0340208	+	0.0589258i
$726$	−5.49516e17	+	9.51790e17i	−0.139281	+	0.241242i
$727$	3.03689e18			0.762877			0.381439	−	0.924394i	$-0.375429\pi$
$727$	3.03689e18			0.762877			0.381439	+	0.924394i	$0.375429\pi$
$728$	1.32367e17	−	3.95428e17i	0.0329553	−	0.0984495i
$729$	6.16451e17			0.152114
$730$	−2.55856e18	+	4.43155e18i	−0.625744	+	1.08382i
$731$	−1.65497e18	−	2.86649e18i	−0.401169	−	0.694845i
$732$	2.64633e17	+	4.58357e17i	0.0635802	+	0.110124i
$733$	1.33169e18	−	2.30655e18i	0.317122	−	0.549272i	−0.662764	−	0.748828i	$-0.730617\pi$
$733$	1.33169e18	−	2.30655e18i	0.317122	−	0.549272i	0.979886	+	0.199556i	$0.0639501\pi$
$734$	−3.82622e18			−0.903120
$735$	1.58688e18	+	1.19646e18i	0.371258	+	0.279918i
$736$	−1.10465e18			−0.256164
$737$	−4.28010e17	+	7.41335e17i	−0.0983819	+	0.170402i
$738$	−8.46328e17	−	1.46588e18i	−0.192829	−	0.333989i
$739$	1.52870e18	+	2.64779e18i	0.345250	+	0.597991i	0.985399	−	0.170260i	$-0.0544607\pi$
$739$	1.52870e18	+	2.64779e18i	0.345250	+	0.597991i	−0.640149	+	0.768251i	$0.721127\pi$
$740$	−1.31280e18	+	2.27384e18i	−0.293896	+	0.509043i
$741$	7.47232e16			0.0165820
$742$	1.21055e18	−	3.61637e18i	0.266292	−	0.795512i
$743$	2.63430e18			0.574430			0.287215	−	0.957866i	$-0.407271\pi$
$743$	2.63430e18			0.574430			0.287215	+	0.957866i	$0.407271\pi$
$744$	1.60107e18	−	2.77313e18i	0.346087	−	0.599441i
$745$	−6.80115e17	−	1.17799e18i	−0.145736	−	0.252422i
$746$	1.91249e18	+	3.31252e18i	0.406252	+	0.703650i
$747$	−1.96980e18	+	3.41180e18i	−0.414800	+	0.718455i
$748$	3.11718e18			0.650730
$749$	−3.96962e18	−	4.48804e18i	−0.821518	−	0.928806i
$750$	−1.99258e18			−0.408806
$751$	8.59364e16	−	1.48846e17i	0.0174790	−	0.0302746i	−0.857154	−	0.515061i	$-0.827769\pi$
$751$	8.59364e16	−	1.48846e17i	0.0174790	−	0.0302746i	0.874633	+	0.484786i	$0.161103\pi$
$752$	1.45559e16	+	2.52116e16i	0.00293510	+	0.00508374i
$753$	−2.10794e17	−	3.65105e17i	−0.0421396	−	0.0729879i
$754$	−1.55222e17	+	2.68852e17i	−0.0307638	+	0.0532844i
$755$	−6.09425e18			−1.19747
$756$	−1.48314e18	+	3.01543e17i	−0.288929	+	0.0587432i
$757$	−6.06550e18			−1.17150			−0.585752	−	0.810490i	$-0.699201\pi$
$757$	−6.06550e18			−1.17150			−0.585752	+	0.810490i	$0.699201\pi$
$758$	−1.11615e18	+	1.93323e18i	−0.213734	+	0.370198i
$759$	−6.56475e17	−	1.13705e18i	−0.124637	−	0.215878i
$760$	−9.88838e17	−	1.71272e18i	−0.186139	−	0.322402i
$761$	6.76766e17	−	1.17219e18i	0.126310	−	0.218776i	−0.795934	−	0.605383i	$-0.793020\pi$
$761$	6.76766e17	−	1.17219e18i	0.126310	−	0.218776i	0.922244	+	0.386608i	$0.126353\pi$
$762$	−2.87234e18			−0.531531
$763$	−7.77821e17	+	1.58142e17i	−0.142715	+	0.0290160i
$764$	1.75528e18			0.319331
$765$	2.93172e18	−	5.07788e18i	0.528838	−	0.915975i
$766$	1.27832e18	+	2.21411e18i	0.228640	+	0.396016i
$767$	−4.63492e17	−	8.02792e17i	−0.0822001	−	0.142375i
$768$	−1.23807e18	+	2.14441e18i	−0.217720	+	0.377102i
$769$	7.96119e18			1.38821			0.694107	−	0.719871i	$-0.255799\pi$
$769$	7.96119e18			1.38821			0.694107	+	0.719871i	$0.255799\pi$
$770$	−3.87841e18	−	4.38492e18i	−0.670601	−	0.758180i
$771$	3.01269e18			0.516536
$772$	1.57087e18	−	2.72082e18i	0.267071	−	0.462581i
$773$	2.40227e18	+	4.16086e18i	0.405001	+	0.701482i	0.994322	−	0.106417i	$-0.0339380\pi$
$773$	2.40227e18	+	4.16086e18i	0.405001	+	0.701482i	−0.589321	+	0.807899i	$0.700605\pi$
$774$	−1.02483e18	−	1.77506e18i	−0.171331	−	0.296754i
$775$	3.36990e17	−	5.83684e17i	0.0558671	−	0.0967647i
$776$	−4.98888e18			−0.820166
$777$	−1.69213e18	+	5.05500e18i	−0.275865	+	0.824109i
$778$	1.81428e18			0.293316
$779$	−6.95338e17	+	1.20436e18i	−0.111481	+	0.193091i
$780$	4.79510e16	+	8.30536e16i	0.00762400	+	0.0132051i
$781$	−2.09198e18	−	3.62342e18i	−0.329857	−	0.571330i
$782$	1.47196e18	−	2.54951e18i	0.230172	−	0.398669i
$783$	4.40360e18			0.682899
$784$	−3.21987e18	+	1.36574e18i	−0.495204	+	0.210046i
$785$	1.13195e18			0.172653
$786$	3.04922e17	−	5.28141e17i	0.0461257	−	0.0798920i
$787$	−1.36282e18	−	2.36047e18i	−0.204457	−	0.354130i	0.745502	−	0.666503i	$-0.232210\pi$
$787$	−1.36282e18	−	2.36047e18i	−0.204457	−	0.354130i	−0.949960	+	0.312373i	$0.898876\pi$
$788$	−3.89601e17	−	6.74808e17i	−0.0579695	−	0.100406i
$789$	8.05089e17	−	1.39445e18i	0.118807	−	0.205780i
$790$	5.41324e18			0.792285
$791$	6.11852e17	−	1.82783e18i	0.0888177	−	0.265331i
$792$	7.54397e18			1.08614
$793$	−2.54004e17	+	4.39947e17i	−0.0362714	+	0.0628239i
$794$	2.71132e18	+	4.69615e18i	0.384015	+	0.665133i
$795$	1.71388e18	+	2.96852e18i	0.240765	+	0.417017i
$796$	−5.78346e16	+	1.00172e17i	−0.00805847	+	0.0139577i
$797$	−7.30364e18			−1.00939			−0.504697	−	0.863297i	$-0.668396\pi$
$797$	−7.30364e18			−1.00939			−0.504697	+	0.863297i	$0.668396\pi$
$798$	−6.80662e17	−	7.69554e17i	−0.0933066	−	0.105492i
$799$	1.16243e17			0.0158057
$800$	−2.06771e17	+	3.58138e17i	−0.0278872	+	0.0483021i
$801$	4.33884e18	+	7.51509e18i	0.580446	+	1.00536i
$802$	5.17024e18	+	8.95511e18i	0.686084	+	1.18833i
$803$	−8.01859e18	+	1.38886e19i	−1.05547	+	1.82813i
$804$	−1.92812e17			−0.0251750
$805$	2.83922e18	−	5.77252e17i	0.367727	−	0.0747639i
$806$	7.86427e17			0.101037
$807$	−3.08268e18	+	5.33936e18i	−0.392871	+	0.680473i
$808$	−4.09020e18	−	7.08443e18i	−0.517095	−	0.895635i
$809$	3.59842e17	+	6.23264e17i	0.0451280	+	0.0781640i	0.887707	−	0.460409i	$-0.152297\pi$
$809$	3.59842e17	+	6.23264e17i	0.0451280	+	0.0781640i	−0.842579	+	0.538573i	$0.818964\pi$
$810$	1.07951e18	−	1.86976e18i	0.134299	−	0.232613i
$811$	−4.66111e18			−0.575246			−0.287623	−	0.957744i	$-0.592865\pi$
$811$	−4.66111e18			−0.575246			−0.287623	+	0.957744i	$0.592865\pi$
$812$	−2.19199e18	+	4.45663e17i	−0.268364	+	0.0545622i
$813$	2.39482e18			0.290860
$814$	7.85104e18	−	1.35984e19i	0.945951	−	1.63843i
$815$	6.20212e18	+	1.07424e19i	0.741337	+	1.28403i
$816$	−1.59713e18	−	2.76631e18i	−0.189389	−	0.328031i
$817$	−8.41994e17	+	1.45838e18i	−0.0990526	+	0.171564i
$818$	−4.58929e18			−0.535611
$819$	−4.16721e17	−	4.71143e17i	−0.0482503	−	0.0545516i
$820$	−1.78483e18			−0.205026
$821$	5.23845e18	−	9.07326e18i	0.596997	−	1.03403i	−0.396265	−	0.918136i	$-0.629694\pi$
$821$	5.23845e18	−	9.07326e18i	0.596997	−	1.03403i	0.993262	−	0.115893i	$-0.0369729\pi$
$822$	8.09905e17	+	1.40280e18i	0.0915730	+	0.158609i
$823$	−5.02571e18	−	8.70478e18i	−0.563765	−	0.976470i	−0.997163	−	0.0752676i	$-0.976019\pi$
$823$	−5.02571e18	−	8.70478e18i	−0.563765	−	0.976470i	0.433398	−	0.901203i	$-0.357314\pi$
$824$	8.70941e18	−	1.50851e19i	0.969308	−	1.67889i
$825$	−4.91523e17			−0.0542742
$826$	−4.04574e18	+	1.20861e19i	−0.443228	+	1.32409i
$827$	−4.42607e18			−0.481096			−0.240548	−	0.970637i	$-0.577327\pi$
$827$	−4.42607e18			−0.481096			−0.240548	+	0.970637i	$0.577327\pi$
$828$	−4.77674e17	+	8.27356e17i	−0.0515151	+	0.0892268i
$829$	−1.16079e18	−	2.01054e18i	−0.124208	−	0.215134i	0.797215	−	0.603695i	$-0.206306\pi$
$829$	−1.16079e18	−	2.01054e18i	−0.124208	−	0.215134i	−0.921423	+	0.388561i	$0.872972\pi$
$830$	−3.96349e18	−	6.86496e18i	−0.420794	−	0.728837i
$831$	3.29327e18	−	5.70411e18i	0.346913	−	0.600871i
$832$	−9.73371e17			−0.101737
$833$	−1.70567e18	+	1.38611e19i	−0.176890	+	1.43749i
$834$	4.35045e18			0.447667
$835$	1.43816e18	−	2.49096e18i	0.146840	−	0.254334i
$836$	−7.92958e17	−	1.37344e18i	−0.0803358	−	0.139146i
$837$	−5.57768e18	−	9.66082e18i	−0.560710	−	0.971178i
$838$	−3.19754e18	+	5.53830e18i	−0.318955	+	0.552447i
$839$	−1.99842e19			−1.97804			−0.989019	−	0.147790i	$-0.952784\pi$
$839$	−1.99842e19			−1.97804			−0.989019	+	0.147790i	$0.952784\pi$
$840$	1.63580e18	−	4.88674e18i	0.160663	−	0.479958i
$841$	−3.75237e18			−0.365705
$842$	−4.25325e17	+	7.36685e17i	−0.0411332	+	0.0712448i
$843$	2.54295e18	+	4.40453e18i	0.244039	+	0.422688i
$844$	4.66486e17	+	8.07977e17i	0.0444234	+	0.0769437i
$845$	5.01392e18	−	8.68437e18i	0.473815	−	0.820672i
$846$	7.19827e16			0.00675026
$847$	−5.03567e18	−	5.69332e18i	−0.468614	−	0.529814i
$848$	−6.03242e18			−0.557081
$849$	2.87145e18	−	4.97349e18i	0.263148	−	0.455786i
$850$	−5.51050e17	−	9.54446e17i	−0.0501150	−	0.0868017i
$851$	3.88567e18	+	6.73018e18i	0.350691	+	0.607414i
$852$	4.71202e17	−	8.16146e17i	0.0422036	−	0.0730989i
$853$	1.70725e19			1.51750			0.758751	−	0.651381i	$-0.225810\pi$
$853$	1.70725e19			1.51750			0.758751	+	0.651381i	$0.225810\pi$
$854$	6.84465e18	−	1.39161e18i	0.603775	−	0.122756i
$855$	−2.98312e18			−0.261151
$856$	−7.76819e18	+	1.34549e19i	−0.674901	+	1.16896i
$857$	4.02740e18	+	6.97566e18i	0.347256	+	0.601465i	0.985761	−	0.168153i	$-0.0537802\pi$
$857$	4.02740e18	+	6.97566e18i	0.347256	+	0.601465i	−0.638505	+	0.769618i	$0.720447\pi$
$858$	−2.86764e17	−	4.96690e17i	−0.0245390	−	0.0425029i
$859$	7.27641e18	−	1.26031e19i	0.617962	−	1.07034i	−0.371895	−	0.928275i	$-0.621292\pi$
$859$	7.27641e18	−	1.26031e19i	0.617962	−	1.07034i	0.989857	−	0.142067i	$-0.0453748\pi$
$860$	−2.16128e18			−0.182168
$861$	−3.55105e18	+	7.21977e17i	−0.297055	+	0.0603953i
$862$	3.85915e18			0.320402
$863$	−4.79383e18	+	8.30316e18i	−0.395014	+	0.684185i	−0.993103	−	0.117245i	$-0.962594\pi$
$863$	−4.79383e18	+	8.30316e18i	−0.395014	+	0.684185i	0.598089	+	0.801430i	$0.295927\pi$
$864$	3.42236e18	+	5.92771e18i	0.279890	+	0.484783i
$865$	5.28249e18	+	9.14955e18i	0.428780	+	0.742668i
$866$	−3.78264e18	+	6.55172e18i	−0.304739	+	0.527824i
$867$	−6.67424e18			−0.533676
$868$	3.75413e18	+	4.24441e18i	0.297942	+	0.336852i
$869$	1.69652e19			1.33638
$870$	−1.91825e18	+	3.32250e18i	−0.149979	+	0.259771i
$871$	−9.25336e16	−	1.60273e17i	−0.00718094	−	0.0124378i
$872$	1.02907e18	+	1.78240e18i	0.0792662	+	0.137293i
$873$	−3.76261e18	+	6.51703e18i	−0.287671	+	0.498261i
$874$	−1.49777e18			−0.113663
$875$	4.37434e18	−	1.30677e19i	0.329503	−	0.984347i
$876$	−3.61225e18			−0.270085
$877$	−3.72550e18	+	6.45275e18i	−0.276495	+	0.478903i	−0.970511	−	0.241056i	$-0.922506\pi$
$877$	−3.72550e18	+	6.45275e18i	−0.276495	+	0.478903i	0.694016	+	0.719959i	$0.255839\pi$
$878$	−8.12440e17	−	1.40719e18i	−0.0598517	−	0.103666i
$879$	6.87516e17	+	1.19081e18i	0.0502754	+	0.0870795i
$880$	−4.63001e18	+	8.01940e18i	−0.336081	+	0.582110i
$881$	2.11522e19			1.52409			0.762047	−	0.647521i	$-0.224194\pi$
$881$	2.11522e19			1.52409			0.762047	+	0.647521i	$0.224194\pi$
$882$	−1.05622e18	+	8.58339e18i	−0.0755458	+	0.613922i
$883$	−3.79552e18			−0.269480			−0.134740	−	0.990881i	$-0.543020\pi$
$883$	−3.79552e18			−0.269480			−0.134740	+	0.990881i	$0.543020\pi$
$884$	−3.36959e17	+	5.83630e17i	−0.0237486	+	0.0411337i
$885$	−5.72788e18	−	9.92098e18i	−0.400740	−	0.694102i
$886$	−3.03395e18	−	5.25495e18i	−0.210712	−	0.364964i
$887$	4.45590e18	−	7.71784e18i	0.307207	−	0.532099i	−0.670543	−	0.741871i	$-0.733939\pi$
$887$	4.45590e18	−	7.71784e18i	0.307207	−	0.532099i	0.977750	+	0.209772i	$0.0672721\pi$
$888$	1.38224e19			0.946019
$889$	6.30569e18	−	1.88374e19i	0.428421	−	1.27985i
$890$	−1.74606e19			−1.17767
$891$	3.38320e18	−	5.85987e18i	0.226528	−	0.392359i
$892$	2.82655e18	+	4.89572e18i	0.187882	+	0.325421i
$893$	−2.95703e16	−	5.12172e16i	−0.00195129	−	0.00337972i
$894$	−9.16135e17	+	1.58679e18i	−0.0600158	+	0.103950i
$895$	−8.87014e18			−0.576874
$896$	2.16759e18	+	2.45067e18i	0.139951	+	0.158228i
$897$	2.83853e17			0.0181946
$898$	5.25986e18	−	9.11035e18i	0.334717	−	0.579748i
$899$	−8.24348e18	−	1.42781e19i	−0.520802	−	0.902055i
$900$	1.78825e17	+	3.09733e17i	0.0112163	+	0.0194273i
$901$	−1.20437e19	+	2.08603e19i	−0.749977	+	1.29900i
$902$	1.06740e19			0.659907
$903$	−4.30002e18	+	8.74253e17i	−0.263937	+	0.0536620i
$904$	−4.99802e18			−0.304581
$905$	7.22005e18	−	1.25055e19i	0.436842	−	0.756632i
$906$	4.10456e18	+	7.10931e18i	0.246566	+	0.427065i
$907$	6.65852e18	+	1.15329e19i	0.397128	+	0.687846i	0.993370	−	0.114959i	$-0.0366736\pi$
$907$	6.65852e18	+	1.15329e19i	0.397128	+	0.687846i	−0.596242	+	0.802804i	$0.703340\pi$
$908$	−3.64588e17	+	6.31484e17i	−0.0215896	+	0.0373942i
$909$	−1.23393e19			−0.725479
$910$	1.24024e18	−	2.52158e17i	0.0723996	−	0.0147198i
$911$	1.45717e19			0.844582			0.422291	−	0.906460i	$-0.361226\pi$
$911$	1.45717e19			0.844582			0.422291	+	0.906460i	$0.361226\pi$
$912$	−8.12566e17	+	1.40741e18i	−0.0467619	+	0.0809940i
$913$	−1.24217e19	−	2.15150e19i	−0.709774	−	1.22936i
$914$	−5.49954e18	−	9.52549e18i	−0.312016	−	0.540427i
$915$	−3.13900e18	+	5.43691e18i	−0.176829	+	0.306277i
$916$	−9.02769e18			−0.504959
$917$	2.79426e18	+	3.15918e18i	0.155191	+	0.175458i
$918$	−1.82414e19			−1.00596
$919$	−1.42218e19	+	2.46328e19i	−0.778759	+	1.34885i	0.153898	+	0.988087i	$0.450817\pi$
$919$	−1.42218e19	+	2.46328e19i	−0.778759	+	1.34885i	−0.932657	+	0.360764i	$0.882516\pi$
$920$	−3.75633e18	−	6.50616e18i	−0.204241	−	0.353756i
$921$	−2.73289e18	−	4.73350e18i	−0.147548	−	0.255561i
$922$	8.23500e18	−	1.42634e19i	0.441482	−	0.764669i
$923$	9.04552e17			0.0481529
$924$	1.31176e18	−	3.91872e18i	0.0693406	−	0.207146i
$925$	2.90932e18			0.152711
$926$	9.89892e17	−	1.71454e18i	0.0515961	−	0.0893670i
$927$	−1.31373e19	−	2.27544e19i	−0.679965	−	1.17773i
$928$	5.05805e18	+	8.76080e18i	0.259969	+	0.450279i
$929$	−7.87355e18	+	1.36374e19i	−0.401854	+	0.696032i	−0.993950	−	0.109836i	$-0.964968\pi$
$929$	−7.87355e18	+	1.36374e19i	−0.401854	+	0.696032i	0.592095	+	0.805868i	$0.298301\pi$
$930$	9.71874e18			0.492573
$931$	6.54116e18	−	2.77451e18i	0.329217	−	0.139641i
$932$	−2.65560e18			−0.132727
$933$	−5.56784e18	+	9.64378e18i	−0.276348	+	0.478648i
$934$	−4.12955e18	−	7.15260e18i	−0.203539	−	0.352541i
$935$	1.84875e19	+	3.20214e19i	0.904906	+	1.56734i
$936$	−8.15485e17	+	1.41246e18i	−0.0396390	+	0.0686568i
$937$	7.92472e18			0.382540			0.191270	−	0.981537i	$-0.438739\pi$
$937$	7.92472e18			0.382540			0.191270	+	0.981537i	$0.438739\pi$
$938$	−8.07709e17	+	2.41292e18i	−0.0387201	+	0.115671i
$939$	6.75437e18			0.321557
$940$	3.79514e16	−	6.57337e16i	0.00179431	−	0.00310783i
$941$	−9.14819e18	−	1.58451e19i	−0.429539	−	0.743983i	0.567293	−	0.823516i	$-0.307991\pi$
$941$	−9.14819e18	−	1.58451e19i	−0.429539	−	0.743983i	−0.996832	+	0.0795326i	$0.974657\pi$
$942$	−7.62383e17	−	1.32049e18i	−0.0355502	−	0.0615748i
$943$	−2.64140e18	+	4.57504e18i	−0.122323	+	0.211870i
$944$	2.01607e19			0.927231
$945$	−1.18939e19	−	1.34472e19i	−0.543273	−	0.614223i
$946$	1.29252e19			0.586336
$947$	6.04025e18	−	1.04620e19i	0.272132	−	0.471347i	−0.697275	−	0.716803i	$-0.745605\pi$
$947$	6.04025e18	−	1.04620e19i	0.272132	−	0.471347i	0.969408	+	0.245457i	$0.0789379\pi$
$948$	1.91064e18	+	3.30933e18i	0.0854919	+	0.148076i
$949$	−1.73358e18	−	3.00265e18i	−0.0770394	−	0.133436i
$950$	−2.80356e17	+	4.85591e17i	−0.0123739	+	0.0214322i
$951$	9.48751e18			0.415890
$952$	3.54867e19	−	7.21494e18i	1.54499	−	0.314118i
$953$	1.09257e19			0.472437			0.236218	−	0.971700i	$-0.424092\pi$
$953$	1.09257e19			0.472437			0.236218	+	0.971700i	$0.424092\pi$
$954$	−7.45797e18	+	1.29176e19i	−0.320300	+	0.554775i
$955$	1.04103e19	+	1.80312e19i	0.444062	+	0.769137i
$956$	−7.72961e18	−	1.33881e19i	−0.327477	−	0.567207i
$957$	−6.01183e18	+	1.04128e19i	−0.252976	+	0.438167i
$958$	−8.06109e18			−0.336913
$959$	−1.09778e19	+	2.23194e18i	−0.455717	+	0.0926536i
$960$	−1.20290e19			−0.495983
$961$	−8.67390e18	+	1.50236e19i	−0.355232	+	0.615280i
$962$	1.69736e18	+	2.93991e18i	0.0690454	+	0.119590i
$963$	1.17175e19	+	2.02953e19i	0.473440	+	0.820021i
$964$	5.76229e18	−	9.98058e18i	0.231257	−	0.400549i
$965$	3.72664e19			1.48556
$966$	−2.58565e18	−	2.92333e18i	−0.102381	−	0.115751i
$967$	−8.83677e18			−0.347553			−0.173777	−	0.984785i	$-0.555597\pi$
$967$	−8.83677e18			−0.347553			−0.173777	+	0.984785i	$0.555597\pi$
$968$	−9.85435e18	+	1.70682e19i	−0.384980	+	0.666805i
$969$	3.24456e18	+	5.61975e18i	0.125907	+	0.218078i
$970$	−7.57083e18	−	1.31131e19i	−0.291828	−	0.505461i
$971$	−2.17490e16	+	3.76704e16i	−0.000832751	+	0.00144237i	−0.866441	−	0.499279i	$-0.833598\pi$
$971$	−2.17490e16	+	3.76704e16i	−0.000832751	+	0.00144237i	0.865609	+	0.500721i	$0.166932\pi$
$972$	9.27613e18			0.352806
$973$	−9.55061e18	+	2.85312e19i	−0.360826	+	1.07792i
$974$	6.52040e18			0.244704
$975$	5.31324e16	−	9.20280e16i	0.00198075	−	0.00343076i
$976$	−5.52425e18	−	9.56828e18i	−0.204574	−	0.354332i
$977$	−1.35956e19	−	2.35484e19i	−0.500133	−	0.866255i	−1.00000		0.000153229i	$-0.999951\pi$
$977$	−1.35956e19	−	2.35484e19i	−0.500133	−	0.866255i	0.499867	−	0.866102i	$-0.333382\pi$
$978$	8.35444e18	−	1.44703e19i	0.305291	−	0.528780i
$979$	−5.47218e19			−1.98643
$980$	7.28138e18	+	5.48995e18i	0.262569	+	0.197970i
$981$	3.10449e18			0.111210
$982$	−1.75446e18	+	3.03882e18i	−0.0624337	+	0.108138i
$983$	4.21635e18	+	7.30293e18i	0.149052	+	0.258166i	0.930877	−	0.365332i	$-0.119044\pi$
$983$	4.21635e18	+	7.30293e18i	0.149052	+	0.258166i	−0.781825	+	0.623498i	$0.785711\pi$
$984$	4.69810e18	+	8.13735e18i	0.164989	+	0.285769i
$985$	4.62133e18	−	8.00439e18i	0.161225	−	0.279250i
$986$	−2.69596e19			−0.934360
$987$	4.89171e16	−	1.46133e17i	0.00168422	−	0.00503138i
$988$	3.42867e17			0.0117275
$989$	−3.19851e18	+	5.53998e18i	−0.108686	+	0.188249i
$990$	1.14483e19	+	1.98290e19i	0.386466	+	0.669380i
$991$	−7.13798e18	−	1.23633e19i	−0.239385	−	0.414627i	0.721153	−	0.692776i	$-0.243612\pi$
$991$	−7.13798e18	−	1.23633e19i	−0.239385	−	0.414627i	−0.960538	+	0.278149i	$0.910279\pi$
$992$	1.28132e19	−	2.21932e19i	0.426906	−	0.739424i
$993$	−1.26911e19			−0.420079
$994$	−8.23967e18	−	9.31574e18i	−0.270956	−	0.306342i
$995$	−1.37204e18			−0.0448245
$996$	2.79788e18	−	4.84607e18i	0.0908121	−	0.157291i
$997$	1.49732e19	+	2.59343e19i	0.482830	+	0.836287i	0.999806	−	0.0197135i	$-0.00627540\pi$
$997$	1.49732e19	+	2.59343e19i	0.482830	+	0.836287i	−0.516975	+	0.856000i	$0.672942\pi$
$998$	−1.30193e19	−	2.25500e19i	−0.417098	−	0.722434i
$999$	2.40767e19	−	4.17021e19i	0.766341	−	1.32734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.14.c.a.2.6	✓	16
3.2	odd	2		63.14.e.c.37.3		16
7.2	even	3		49.14.a.e.1.3		8
7.3	odd	6		49.14.c.g.18.6		16
7.4	even	3	inner	7.14.c.a.4.6	yes	16
7.5	odd	6		49.14.a.f.1.3		8
7.6	odd	2		49.14.c.g.30.6		16
21.11	odd	6		63.14.e.c.46.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.14.c.a.2.6	✓	16	1.1	even	1	trivial
7.14.c.a.4.6	yes	16	7.4	even	3	inner
49.14.a.e.1.3		8	7.2	even	3
49.14.a.f.1.3		8	7.5	odd	6
49.14.c.g.18.6		16	7.3	odd	6
49.14.c.g.30.6		16	7.6	odd	2
63.14.e.c.37.3		16	3.2	odd	2
63.14.e.c.46.3		16	21.11	odd	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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(36.6577 - 63.4930i) q^{2} +(306.948 + 531.649i) q^{3} +(1408.43 + 2439.47i) q^{4} +(-16706.4 + 28936.3i) q^{5} +45008.0 q^{6} +(-98806.7 + 295172. i) q^{7} +807118. q^{8} +(608728. - 1.05435e6i) q^{9} +O(q^{10})\)	\(q+(36.6577 - 63.4930i) q^{2} +(306.948 + 531.649i) q^{3} +(1408.43 + 2439.47i) q^{4} +(-16706.4 + 28936.3i) q^{5} +45008.0 q^{6} +(-98806.7 + 295172. i) q^{7} +807118. q^{8} +(608728. - 1.05435e6i) q^{9} +(1.22484e6 + 2.12148e6i) q^{10} +(3.83866e6 + 6.64876e6i) q^{11} +(-864628. + 1.49758e6i) q^{12} -1.65980e6 q^{13} +(1.51193e7 + 1.70938e7i) q^{14} -2.05120e7 q^{15} +(1.80492e7 - 3.12622e7i) q^{16} +(-7.20703e7 - 1.24829e8i) q^{17} +(-4.46291e7 - 7.72998e7i) q^{18} +(-3.66670e7 + 6.35091e7i) q^{19} -9.41190e7 q^{20} +(-1.87256e8 + 3.80718e7i) q^{21} +5.62866e8 q^{22} +(-1.39288e8 + 2.41254e8i) q^{23} +(2.47743e8 + 4.29104e8i) q^{24} +(5.21446e7 + 9.03171e7i) q^{25} +(-6.08444e7 + 1.05386e8i) q^{26} +1.72614e9 q^{27} +(-8.59224e8 + 1.74692e8i) q^{28} +2.55113e9 q^{29} +(-7.51921e8 + 1.30236e9i) q^{30} +(-3.23131e9 - 5.59679e9i) q^{31} +(1.98267e9 + 3.43409e9i) q^{32} +(-2.35654e9 + 4.08164e9i) q^{33} -1.05677e10 q^{34} +(-6.89048e9 - 7.79035e9i) q^{35} +3.42940e9 q^{36} +(1.39483e10 - 2.41592e10i) q^{37} +(2.68825e9 + 4.65619e9i) q^{38} +(-5.09472e8 - 8.82431e8i) q^{39} +(-1.34840e10 + 2.33550e10i) q^{40} +1.89636e10 q^{41} +(-4.44709e9 + 1.32851e10i) q^{42} +2.29633e10 q^{43} +(-1.08130e10 + 1.87286e10i) q^{44} +(2.03393e10 + 3.52287e10i) q^{45} +(1.02120e10 + 1.76876e10i) q^{46} +(-4.03227e8 + 6.98410e8i) q^{47} +2.21607e10 q^{48} +(-7.73635e10 - 5.83298e10i) q^{49} +7.64600e9 q^{50} +(4.42436e10 - 7.66322e10i) q^{51} +(-2.33771e9 - 4.04903e9i) q^{52} +(-8.35551e10 - 1.44722e11i) q^{53} +(6.32762e10 - 1.09598e11i) q^{54} -2.56521e11 q^{55} +(-7.97487e10 + 2.38238e11i) q^{56} -4.50194e10 q^{57} +(9.35185e10 - 1.61979e11i) q^{58} +(2.79246e11 + 4.83668e11i) q^{59} +(-2.88896e10 - 5.00383e10i) q^{60} +(1.53033e11 - 2.65060e11i) q^{61} -4.73809e11 q^{62} +(2.51067e11 + 2.83856e11i) q^{63} +5.86439e11 q^{64} +(2.77293e10 - 4.80285e10i) q^{65} +(1.72770e11 + 2.99247e11i) q^{66} +(5.57499e10 + 9.65616e10i) q^{67} +(2.03012e11 - 3.51627e11i) q^{68} -1.71017e11 q^{69} +(-7.47221e11 + 1.51920e11i) q^{70} -5.44977e11 q^{71} +(4.91315e11 - 8.50983e11i) q^{72} +(1.04445e12 + 1.80904e12i) q^{73} +(-1.02263e12 - 1.77124e12i) q^{74} +(-3.20113e10 + 5.54453e10i) q^{75} -2.06571e11 q^{76} +(-2.34181e12 + 4.76122e11i) q^{77} -7.47042e10 q^{78} +(1.10489e12 - 1.91373e12i) q^{79} +(6.03075e11 + 1.04456e12i) q^{80} +(-4.40674e11 - 7.63270e11i) q^{81} +(6.95161e11 - 1.20405e12i) q^{82} -3.23594e12 q^{83} +(-3.56612e11 - 4.03184e11i) q^{84} +4.81614e12 q^{85} +(8.41781e11 - 1.45801e12i) q^{86} +(7.83064e11 + 1.35631e12i) q^{87} +(3.09826e12 + 5.36634e12i) q^{88} +(-3.56386e12 + 6.17278e12i) q^{89} +2.98236e12 q^{90} +(1.63999e11 - 4.89926e11i) q^{91} -7.84709e11 q^{92} +(1.98368e12 - 3.43584e12i) q^{93} +(2.95628e10 + 5.12042e10i) q^{94} +(-1.22515e12 - 2.12202e12i) q^{95} +(-1.21715e12 + 2.10817e12i) q^{96} -6.18110e12 q^{97} +(-6.53950e12 + 2.77380e12i) q^{98} +9.34680e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 728 q^{3} - 32588 q^{4} + 46928 q^{5} - 30212 q^{6} + 257992 q^{7} - 1093248 q^{8} - 2910808 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 728 * q^3 - 32588 * q^4 + 46928 * q^5 - 30212 * q^6 + 257992 * q^7 - 1093248 * q^8 - 2910808 * q^9	\( 16 q - 2 q^{2} + 728 q^{3} - 32588 q^{4} + 46928 q^{5} - 30212 q^{6} + 257992 q^{7} - 1093248 q^{8} - 2910808 q^{9} + 879018 q^{10} + 3746000 q^{11} + 13786276 q^{12} - 63556528 q^{13} - 45497410 q^{14} + 179729504 q^{15} - 158020976 q^{16} + 108548496 q^{17} + 358872748 q^{18} + 617001728 q^{19} - 1844979416 q^{20} + 400815352 q^{21} + 977603772 q^{22} - 274288968 q^{23} - 690136272 q^{24} + 342571888 q^{25} - 1890370748 q^{26} + 1818768224 q^{27} - 2830532012 q^{28} - 1243557136 q^{29} + 8470546342 q^{30} + 1983953552 q^{31} - 18584336224 q^{32} - 3534705832 q^{33} + 35123983356 q^{34} - 15057013664 q^{35} + 2810399728 q^{36} + 3822948680 q^{37} + 48271561702 q^{38} + 5559167432 q^{39} + 20095902624 q^{40} - 186830117264 q^{41} - 160102538512 q^{42} + 147613206080 q^{43} + 146754773860 q^{44} + 167965018760 q^{45} + 33234006318 q^{46} + 136146541776 q^{47} - 918554738528 q^{48} - 279115649456 q^{49} + 446501048144 q^{50} + 374908120992 q^{51} + 920059547960 q^{52} - 365779470792 q^{53} + 142841959918 q^{54} - 335157159792 q^{55} - 2232488591424 q^{56} + 1368890666384 q^{57} + 1968765302052 q^{58} + 1211924963928 q^{59} - 1696452613604 q^{60} - 155263824184 q^{61} - 3267358992324 q^{62} - 4123328121080 q^{63} + 3671045348608 q^{64} + 2491203210104 q^{65} + 6785854381222 q^{66} - 1812819047992 q^{67} + 2300642770860 q^{68} - 9833331511584 q^{69} - 10764563120010 q^{70} + 6413635527072 q^{71} + 9182131417728 q^{72} + 7135229075576 q^{73} - 1240472589270 q^{74} + 3092701132528 q^{75} - 24098923346008 q^{76} - 8899938075392 q^{77} + 16977900019528 q^{78} + 7912090175960 q^{79} + 18767635478704 q^{80} - 2029193868592 q^{81} + 2118830761068 q^{82} - 16937841300576 q^{83} - 32302920082804 q^{84} + 9546866646768 q^{85} + 17052910238024 q^{86} + 16147535411672 q^{87} - 15433836932304 q^{88} + 3654589406888 q^{89} - 6354662390216 q^{90} - 14961004874704 q^{91} + 2966525661672 q^{92} + 10829807426472 q^{93} + 7135101410430 q^{94} - 16751540432680 q^{95} - 4043645970784 q^{96} + 20623672673744 q^{97} + 1374873929086 q^{98} + 1803523183088 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 728 * q^3 - 32588 * q^4 + 46928 * q^5 - 30212 * q^6 + 257992 * q^7 - 1093248 * q^8 - 2910808 * q^9 + 879018 * q^10 + 3746000 * q^11 + 13786276 * q^12 - 63556528 * q^13 - 45497410 * q^14 + 179729504 * q^15 - 158020976 * q^16 + 108548496 * q^17 + 358872748 * q^18 + 617001728 * q^19 - 1844979416 * q^20 + 400815352 * q^21 + 977603772 * q^22 - 274288968 * q^23 - 690136272 * q^24 + 342571888 * q^25 - 1890370748 * q^26 + 1818768224 * q^27 - 2830532012 * q^28 - 1243557136 * q^29 + 8470546342 * q^30 + 1983953552 * q^31 - 18584336224 * q^32 - 3534705832 * q^33 + 35123983356 * q^34 - 15057013664 * q^35 + 2810399728 * q^36 + 3822948680 * q^37 + 48271561702 * q^38 + 5559167432 * q^39 + 20095902624 * q^40 - 186830117264 * q^41 - 160102538512 * q^42 + 147613206080 * q^43 + 146754773860 * q^44 + 167965018760 * q^45 + 33234006318 * q^46 + 136146541776 * q^47 - 918554738528 * q^48 - 279115649456 * q^49 + 446501048144 * q^50 + 374908120992 * q^51 + 920059547960 * q^52 - 365779470792 * q^53 + 142841959918 * q^54 - 335157159792 * q^55 - 2232488591424 * q^56 + 1368890666384 * q^57 + 1968765302052 * q^58 + 1211924963928 * q^59 - 1696452613604 * q^60 - 155263824184 * q^61 - 3267358992324 * q^62 - 4123328121080 * q^63 + 3671045348608 * q^64 + 2491203210104 * q^65 + 6785854381222 * q^66 - 1812819047992 * q^67 + 2300642770860 * q^68 - 9833331511584 * q^69 - 10764563120010 * q^70 + 6413635527072 * q^71 + 9182131417728 * q^72 + 7135229075576 * q^73 - 1240472589270 * q^74 + 3092701132528 * q^75 - 24098923346008 * q^76 - 8899938075392 * q^77 + 16977900019528 * q^78 + 7912090175960 * q^79 + 18767635478704 * q^80 - 2029193868592 * q^81 + 2118830761068 * q^82 - 16937841300576 * q^83 - 32302920082804 * q^84 + 9546866646768 * q^85 + 17052910238024 * q^86 + 16147535411672 * q^87 - 15433836932304 * q^88 + 3654589406888 * q^89 - 6354662390216 * q^90 - 14961004874704 * q^91 + 2966525661672 * q^92 + 10829807426472 * q^93 + 7135101410430 * q^94 - 16751540432680 * q^95 - 4043645970784 * q^96 + 20623672673744 * q^97 + 1374873929086 * q^98 + 1803523183088 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more