LMFDB - Embedded newform 14.12.c.b.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,12,Mod(9,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("14.9");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	14.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:	$10.7568045278$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 149344 x^{6} + 5578711 x^{5} + 20557200983 x^{4} + 408905884576 x^{3} + \cdots + 30\!\cdots\!24 $ x^8 - x^7 + 149344x^6 + 5578711x^5 + 20557200983x^4 + 408905884576x^3 + 267736482219682x^2 - 4732823471679688x + 3039499286293024324
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3\cdot 7^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.2
Root			$-62.4133 - 108.103i$ of defining polynomial
Character	$\chi$	$=$	14.9
Dual form			14.12.c.b.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16.0000 - 27.7128i) q^{2} +(-158.327 - 274.230i) q^{3} +(-512.000 - 886.810i) q^{4} +(-6009.47 + 10408.7i) q^{5} -10132.9 q^{6} +(34168.3 + 28457.9i) q^{7} -32768.0 q^{8} +(38438.9 - 66578.1i) q^{9} +O(q^{10})$	\(q+(16.0000 - 27.7128i) q^{2} +(-158.327 - 274.230i) q^{3} +(-512.000 - 886.810i) q^{4} +(-6009.47 + 10408.7i) q^{5} -10132.9 q^{6} +(34168.3 + 28457.9i) q^{7} -32768.0 q^{8} +(38438.9 - 66578.1i) q^{9} +(192303. + 333079. i) q^{10} +(187066. + 324007. i) q^{11} +(-162126. + 280811. i) q^{12} -625709. q^{13} +(1.33534e6 - 491573. i) q^{14} +3.80583e6 q^{15} +(-524288. + 908093. i) q^{16} +(3.56150e6 + 6.16869e6i) q^{17} +(-1.23004e6 - 2.13050e6i) q^{18} +(-9.63596e6 + 1.66900e7i) q^{19} +1.23074e7 q^{20} +(2.39426e6 - 1.38756e7i) q^{21} +1.19722e7 q^{22} +(-1.19610e7 + 2.07171e7i) q^{23} +(5.18805e6 + 8.98596e6i) q^{24} +(-4.78134e7 - 8.28152e7i) q^{25} +(-1.00113e7 + 1.73401e7i) q^{26} -8.04377e7 q^{27} +(7.74261e6 - 4.48713e7i) q^{28} +7.06535e7 q^{29} +(6.08934e7 - 1.05470e8i) q^{30} +(-7.36573e7 - 1.27578e8i) q^{31} +(1.67772e7 + 2.90590e7i) q^{32} +(5.92349e7 - 1.02598e8i) q^{33} +2.27936e8 q^{34} +(-5.01544e8 + 1.84631e8i) q^{35} -7.87228e7 q^{36} +(-2.68355e8 + 4.64805e8i) q^{37} +(3.08351e8 + 5.34079e8i) q^{38} +(9.90663e7 + 1.71588e8i) q^{39} +(1.96918e8 - 3.41072e8i) q^{40} +4.82553e8 q^{41} +(-3.46224e8 - 2.88361e8i) q^{42} +5.66805e8 q^{43} +(1.91555e8 - 3.31783e8i) q^{44} +(4.61994e8 + 8.00198e8i) q^{45} +(3.82753e8 + 6.62948e8i) q^{46} +(5.35695e8 - 9.27851e8i) q^{47} +3.32035e8 q^{48} +(3.57619e8 + 1.94472e9i) q^{49} -3.06005e9 q^{50} +(1.12776e9 - 1.95334e9i) q^{51} +(3.20363e8 + 5.54885e8i) q^{52} +(-2.88664e9 - 4.99981e9i) q^{53} +(-1.28700e9 + 2.22916e9i) q^{54} -4.49666e9 q^{55} +(-1.11963e9 - 9.32509e8i) q^{56} +6.10251e9 q^{57} +(1.13046e9 - 1.95801e9i) q^{58} +(1.69150e9 + 2.92976e9i) q^{59} +(-1.94859e9 - 3.37505e9i) q^{60} +(-2.55605e9 + 4.42721e9i) q^{61} -4.71407e9 q^{62} +(3.20807e9 - 1.18097e9i) q^{63} +1.07374e9 q^{64} +(3.76018e9 - 6.51282e9i) q^{65} +(-1.89552e9 - 3.28313e9i) q^{66} +(-1.24117e9 - 2.14977e9i) q^{67} +(3.64697e9 - 6.31674e9i) q^{68} +7.57500e9 q^{69} +(-2.90806e9 + 1.68533e10i) q^{70} -2.40523e9 q^{71} +(-1.25957e9 + 2.18163e9i) q^{72} +(9.20676e8 + 1.59466e9i) q^{73} +(8.58736e9 + 1.48737e10i) q^{74} +(-1.51403e10 + 2.62237e10i) q^{75} +1.97344e10 q^{76} +(-2.82886e9 + 1.63943e10i) q^{77} +6.34025e9 q^{78} +(1.37771e10 - 2.38626e10i) q^{79} +(-6.30138e9 - 1.09143e10i) q^{80} +(5.92610e9 + 1.02643e10i) q^{81} +(7.72085e9 - 1.33729e10i) q^{82} +3.20498e10 q^{83} +(-1.35309e10 + 4.98106e9i) q^{84} -8.56108e10 q^{85} +(9.06888e9 - 1.57078e10i) q^{86} +(-1.11863e10 - 1.93753e10i) q^{87} +(-6.12977e9 - 1.06171e10i) q^{88} +(-1.01067e10 + 1.75053e10i) q^{89} +2.95676e10 q^{90} +(-2.13794e10 - 1.78064e10i) q^{91} +2.44962e10 q^{92} +(-2.33238e10 + 4.03980e10i) q^{93} +(-1.71422e10 - 2.96912e10i) q^{94} +(-1.15814e11 - 2.00596e11i) q^{95} +(5.31256e9 - 9.20162e9i) q^{96} +1.43007e11 q^{97} +(5.96155e10 + 2.12049e10i) q^{98} +2.87624e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 128 q^{2} - 266 q^{3} - 4096 q^{4} + 3808 q^{5} - 17024 q^{6} + 110328 q^{7} - 262144 q^{8} - 503848 q^{9}+O(q^{10}) $ 8 * q + 128 * q^2 - 266 * q^3 - 4096 * q^4 + 3808 * q^5 - 17024 * q^6 + 110328 * q^7 - 262144 * q^8 - 503848 * q^9	\( 8 q + 128 q^{2} - 266 q^{3} - 4096 q^{4} + 3808 q^{5} - 17024 q^{6} + 110328 q^{7} - 262144 q^{8} - 503848 q^{9} - 121856 q^{10} + 920150 q^{11} - 272384 q^{12} + 997472 q^{13} + 1396800 q^{14} - 500444 q^{15} - 4194304 q^{16} + 1333724 q^{17} + 16123136 q^{18} - 21551726 q^{19} - 7798784 q^{20} - 90442480 q^{21} + 58889600 q^{22} + 72510158 q^{23} + 8716288 q^{24} - 77154744 q^{25} + 15959552 q^{26} + 156683212 q^{27} - 68278272 q^{28} + 213575104 q^{29} - 8007104 q^{30} - 194359774 q^{31} + 134217728 q^{32} - 164547124 q^{33} + 85358336 q^{34} - 981719074 q^{35} + 1031880704 q^{36} + 171517048 q^{37} + 689655232 q^{38} - 653125236 q^{39} - 124780544 q^{40} - 3312095136 q^{41} - 1152719104 q^{42} + 850279648 q^{43} + 942233600 q^{44} + 6784014272 q^{45} - 2320325056 q^{46} + 2223880974 q^{47} + 557842432 q^{48} - 4232044312 q^{49} - 4937903616 q^{50} + 6968362082 q^{51} - 510705664 q^{52} - 7185483360 q^{53} + 2506931392 q^{54} + 624915620 q^{55} - 3615227904 q^{56} + 4959469112 q^{57} + 3417201664 q^{58} + 6997401502 q^{59} + 256227328 q^{60} - 6476463280 q^{61} - 12439025536 q^{62} - 17252507684 q^{63} + 8589934592 q^{64} + 30625528248 q^{65} + 5265507968 q^{66} - 18660972186 q^{67} + 1365733376 q^{68} + 31319762096 q^{69} - 27279047488 q^{70} + 23224449248 q^{71} + 16510091264 q^{72} + 3731641452 q^{73} - 5488545536 q^{74} - 91204646176 q^{75} + 44137934848 q^{76} - 29345595440 q^{77} - 41800015104 q^{78} + 12221157926 q^{79} + 3992977408 q^{80} - 97333443028 q^{81} - 52993522176 q^{82} + 316739523968 q^{83} + 55726088192 q^{84} - 147794862544 q^{85} + 13604474368 q^{86} - 218122807364 q^{87} - 30151475200 q^{88} - 71204406084 q^{89} + 434176913408 q^{90} + 189816116528 q^{91} - 148500803584 q^{92} + 9838293624 q^{93} - 71164191168 q^{94} - 215091896614 q^{95} + 8925478912 q^{96} + 688251797184 q^{97} + 137152279424 q^{98} - 545487662552 q^{99}+O(q^{100}) \) 8 * q + 128 * q^2 - 266 * q^3 - 4096 * q^4 + 3808 * q^5 - 17024 * q^6 + 110328 * q^7 - 262144 * q^8 - 503848 * q^9 - 121856 * q^10 + 920150 * q^11 - 272384 * q^12 + 997472 * q^13 + 1396800 * q^14 - 500444 * q^15 - 4194304 * q^16 + 1333724 * q^17 + 16123136 * q^18 - 21551726 * q^19 - 7798784 * q^20 - 90442480 * q^21 + 58889600 * q^22 + 72510158 * q^23 + 8716288 * q^24 - 77154744 * q^25 + 15959552 * q^26 + 156683212 * q^27 - 68278272 * q^28 + 213575104 * q^29 - 8007104 * q^30 - 194359774 * q^31 + 134217728 * q^32 - 164547124 * q^33 + 85358336 * q^34 - 981719074 * q^35 + 1031880704 * q^36 + 171517048 * q^37 + 689655232 * q^38 - 653125236 * q^39 - 124780544 * q^40 - 3312095136 * q^41 - 1152719104 * q^42 + 850279648 * q^43 + 942233600 * q^44 + 6784014272 * q^45 - 2320325056 * q^46 + 2223880974 * q^47 + 557842432 * q^48 - 4232044312 * q^49 - 4937903616 * q^50 + 6968362082 * q^51 - 510705664 * q^52 - 7185483360 * q^53 + 2506931392 * q^54 + 624915620 * q^55 - 3615227904 * q^56 + 4959469112 * q^57 + 3417201664 * q^58 + 6997401502 * q^59 + 256227328 * q^60 - 6476463280 * q^61 - 12439025536 * q^62 - 17252507684 * q^63 + 8589934592 * q^64 + 30625528248 * q^65 + 5265507968 * q^66 - 18660972186 * q^67 + 1365733376 * q^68 + 31319762096 * q^69 - 27279047488 * q^70 + 23224449248 * q^71 + 16510091264 * q^72 + 3731641452 * q^73 - 5488545536 * q^74 - 91204646176 * q^75 + 44137934848 * q^76 - 29345595440 * q^77 - 41800015104 * q^78 + 12221157926 * q^79 + 3992977408 * q^80 - 97333443028 * q^81 - 52993522176 * q^82 + 316739523968 * q^83 + 55726088192 * q^84 - 147794862544 * q^85 + 13604474368 * q^86 - 218122807364 * q^87 - 30151475200 * q^88 - 71204406084 * q^89 + 434176913408 * q^90 + 189816116528 * q^91 - 148500803584 * q^92 + 9838293624 * q^93 - 71164191168 * q^94 - 215091896614 * q^95 + 8925478912 * q^96 + 688251797184 * q^97 + 137152279424 * q^98 - 545487662552 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

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

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 $

$2$	16.0000	−	27.7128i	0.353553	−	0.612372i
$2$	16.0000	−	27.7128i	0.353553	−	0.612372i
$3$	−158.327	−	274.230i	−0.376172	−	0.651550i	0.614329	−	0.789050i	$-0.289427\pi$
$3$	−158.327	−	274.230i	−0.376172	−	0.651550i	−0.990502	+	0.137500i	$0.956093\pi$
$4$	−512.000	−	886.810i	−0.250000	−	0.433013i
$5$	−6009.47	+	10408.7i	−0.860005	+	1.48957i	0.0119176	+	0.999929i	$0.496206\pi$
$5$	−6009.47	+	10408.7i	−0.860005	+	1.48957i	−0.871923	+	0.489644i	$0.837127\pi$
$6$	−10132.9			−0.531988
$7$	34168.3	+	28457.9i	0.768394	+	0.639977i
$7$	34168.3	+	28457.9i	0.768394	+	0.639977i
$8$	−32768.0			−0.353553
$9$	38438.9	−	66578.1i	0.216989	−	0.375835i
$10$	192303.	+	333079.i	0.608115	+	1.05329i
$11$	187066.	+	324007.i	0.350215	+	0.606590i	0.986287	−	0.165040i	$-0.0527753\pi$
$11$	187066.	+	324007.i	0.350215	+	0.606590i	−0.636072	+	0.771630i	$0.719442\pi$
$12$	−162126.	+	280811.i	−0.188086	+	0.325775i
$13$	−625709.			−0.467395			−0.233697	−	0.972309i	$-0.575082\pi$
$13$	−625709.			−0.467395			−0.233697	+	0.972309i	$0.575082\pi$
$14$	1.33534e6	−	491573.i	0.663572	−	0.244278i
$15$	3.80583e6			1.29404
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	3.56150e6	+	6.16869e6i	0.608364	+	1.05372i	0.991510	+	0.130030i	$0.0415072\pi$
$17$	3.56150e6	+	6.16869e6i	0.608364	+	1.05372i	−0.383146	+	0.923688i	$0.625159\pi$
$18$	−1.23004e6	−	2.13050e6i	−0.153434	−	0.265756i
$19$	−9.63596e6	+	1.66900e7i	−0.892792	+	1.54636i	−0.0562775	+	0.998415i	$0.517923\pi$
$19$	−9.63596e6	+	1.66900e7i	−0.892792	+	1.54636i	−0.836514	+	0.547945i	$0.815410\pi$
$20$	1.23074e7			0.860005
$21$	2.39426e6	−	1.38756e7i	0.127928	−	0.741389i
$22$	1.19722e7			0.495278
$23$	−1.19610e7	+	2.07171e7i	−0.387494	+	0.671160i	−0.992112	−	0.125356i	$-0.959993\pi$
$23$	−1.19610e7	+	2.07171e7i	−0.387494	+	0.671160i	0.604617	+	0.796516i	$0.293326\pi$
$24$	5.18805e6	+	8.98596e6i	0.132997	+	0.230358i
$25$	−4.78134e7	−	8.28152e7i	−0.979218	−	1.69605i
$26$	−1.00113e7	+	1.73401e7i	−0.165249	+	0.286220i
$27$	−8.04377e7			−1.07885
$28$	7.74261e6	−	4.48713e7i	0.0850194	−	0.492719i
$29$	7.06535e7			0.639654			0.319827	−	0.947476i	$-0.396375\pi$
$29$	7.06535e7			0.639654			0.319827	+	0.947476i	$0.396375\pi$
$30$	6.08934e7	−	1.05470e8i	0.457513	−	0.792435i
$31$	−7.36573e7	−	1.27578e8i	−0.462090	−	0.800363i	0.536975	−	0.843598i	$-0.319567\pi$
$31$	−7.36573e7	−	1.27578e8i	−0.462090	−	0.800363i	−0.999065	+	0.0432348i	$0.986234\pi$
$32$	1.67772e7	+	2.90590e7i	0.0883883	+	0.153093i
$33$	5.92349e7	−	1.02598e8i	0.263482	−	0.456365i
$34$	2.27936e8			0.860357
$35$	−5.01544e8	+	1.84631e8i	−1.61411	+	0.594196i
$36$	−7.87228e7			−0.216989
$37$	−2.68355e8	+	4.64805e8i	−0.636210	+	1.10195i	0.350048	+	0.936732i	$0.386165\pi$
$37$	−2.68355e8	+	4.64805e8i	−0.636210	+	1.10195i	−0.986257	+	0.165216i	$0.947168\pi$
$38$	3.08351e8	+	5.34079e8i	0.631299	+	1.09344i
$39$	9.90663e7	+	1.71588e8i	0.175821	+	0.304531i
$40$	1.96918e8	−	3.41072e8i	0.304058	−	0.526643i
$41$	4.82553e8			0.650480			0.325240	−	0.945632i	$-0.394555\pi$
$41$	4.82553e8			0.650480			0.325240	+	0.945632i	$0.394555\pi$
$42$	−3.46224e8	−	2.88361e8i	−0.408777	−	0.340460i
$43$	5.66805e8			0.587973			0.293986	−	0.955810i	$-0.405018\pi$
$43$	5.66805e8			0.587973			0.293986	+	0.955810i	$0.405018\pi$
$44$	1.91555e8	−	3.31783e8i	0.175107	−	0.303295i
$45$	4.61994e8	+	8.00198e8i	0.373223	+	0.646441i
$46$	3.82753e8	+	6.62948e8i	0.274000	+	0.474582i
$47$	5.35695e8	−	9.27851e8i	0.340706	−	0.590119i	−0.643858	−	0.765145i	$-0.722667\pi$
$47$	5.35695e8	−	9.27851e8i	0.340706	−	0.590119i	0.984564	+	0.175025i	$0.0560007\pi$
$48$	3.32035e8			0.188086
$49$	3.57619e8	+	1.94472e9i	0.180860	+	0.983509i
$50$	−3.06005e9			−1.38482
$51$	1.12776e9	−	1.95334e9i	0.457699	−	0.792759i
$52$	3.20363e8	+	5.54885e8i	0.116849	+	0.202388i
$53$	−2.88664e9	−	4.99981e9i	−0.948147	−	1.64224i	−0.749323	−	0.662204i	$-0.769621\pi$
$53$	−2.88664e9	−	4.99981e9i	−0.948147	−	1.64224i	−0.198824	−	0.980035i	$-0.563712\pi$
$54$	−1.28700e9	+	2.22916e9i	−0.381429	+	0.660655i
$55$	−4.49666e9			−1.20475
$56$	−1.11963e9	−	9.32509e8i	−0.271668	−	0.226266i
$57$	6.10251e9			1.34337
$58$	1.13046e9	−	1.95801e9i	0.226152	−	0.391706i
$59$	1.69150e9	+	2.92976e9i	0.308024	+	0.533514i	0.977930	−	0.208932i	$-0.0669988\pi$
$59$	1.69150e9	+	2.92976e9i	0.308024	+	0.533514i	−0.669906	+	0.742446i	$0.733665\pi$
$60$	−1.94859e9	−	3.37505e9i	−0.323510	−	0.560336i
$61$	−2.55605e9	+	4.42721e9i	−0.387485	+	0.671144i	−0.992111	−	0.125366i	$-0.959989\pi$
$61$	−2.55605e9	+	4.42721e9i	−0.387485	+	0.671144i	0.604626	+	0.796510i	$0.293323\pi$
$62$	−4.71407e9			−0.653494
$63$	3.20807e9	−	1.18097e9i	0.407259	−	0.149922i
$64$	1.07374e9			0.125000
$65$	3.76018e9	−	6.51282e9i	0.401962	−	0.696218i
$66$	−1.89552e9	−	3.28313e9i	−0.186310	−	0.322698i
$67$	−1.24117e9	−	2.14977e9i	−0.112310	−	0.194527i	0.804391	−	0.594100i	$-0.202492\pi$
$67$	−1.24117e9	−	2.14977e9i	−0.112310	−	0.194527i	−0.916701	+	0.399573i	$0.869158\pi$
$68$	3.64697e9	−	6.31674e9i	0.304182	−	0.526859i
$69$	7.57500e9			0.583059
$70$	−2.90806e9	+	1.68533e10i	−0.206806	+	1.19852i
$71$	−2.40523e9			−0.158210			−0.0791052	−	0.996866i	$-0.525206\pi$
$71$	−2.40523e9			−0.158210			−0.0791052	+	0.996866i	$0.525206\pi$
$72$	−1.25957e9	+	2.18163e9i	−0.0767171	+	0.132878i
$73$	9.20676e8	+	1.59466e9i	0.0519794	+	0.0900309i	0.890844	−	0.454309i	$-0.150114\pi$
$73$	9.20676e8	+	1.59466e9i	0.0519794	+	0.0900309i	−0.838865	+	0.544340i	$0.816780\pi$
$74$	8.58736e9	+	1.48737e10i	0.449868	+	0.779194i
$75$	−1.51403e10	+	2.62237e10i	−0.736709	+	1.27602i
$76$	1.97344e10			0.892792
$77$	−2.82886e9	+	1.63943e10i	−0.119100	+	0.690229i
$78$	6.34025e9			0.248648
$79$	1.37771e10	−	2.38626e10i	0.503742	−	0.872506i	−0.496249	−	0.868180i	$-0.665290\pi$
$79$	1.37771e10	−	2.38626e10i	0.503742	−	0.872506i	0.999991	−	0.00432604i	$-0.00137702\pi$
$80$	−6.30138e9	−	1.09143e10i	−0.215001	−	0.372393i
$81$	5.92610e9	+	1.02643e10i	0.188843	+	0.327086i
$82$	7.72085e9	−	1.33729e10i	0.229979	−	0.398336i
$83$	3.20498e10			0.893090			0.446545	−	0.894761i	$-0.352654\pi$
$83$	3.20498e10			0.893090			0.446545	+	0.894761i	$0.352654\pi$
$84$	−1.35309e10	+	4.98106e9i	−0.353013	+	0.129953i
$85$	−8.56108e10			−2.09278
$86$	9.06888e9	−	1.57078e10i	0.207880	−	0.360058i
$87$	−1.11863e10	−	1.93753e10i	−0.240620	−	0.416766i
$88$	−6.12977e9	−	1.06171e10i	−0.123820	−	0.214462i
$89$	−1.01067e10	+	1.75053e10i	−0.191851	+	0.332295i	−0.945864	−	0.324565i	$-0.894782\pi$
$89$	−1.01067e10	+	1.75053e10i	−0.191851	+	0.332295i	0.754013	+	0.656860i	$0.228116\pi$
$90$	2.95676e10			0.527817
$91$	−2.13794e10	−	1.78064e10i	−0.359143	−	0.299122i
$92$	2.44962e10			0.387494
$93$	−2.33238e10	+	4.03980e10i	−0.347651	+	0.602149i
$94$	−1.71422e10	−	2.96912e10i	−0.240915	−	0.417277i
$95$	−1.15814e11	−	2.00596e11i	−1.53561	−	2.65976i
$96$	5.31256e9	−	9.20162e9i	0.0664985	−	0.115179i
$97$	1.43007e11			1.69088			0.845439	−	0.534072i	$-0.179339\pi$
$97$	1.43007e11			1.69088			0.845439	+	0.534072i	$0.179339\pi$
$98$	5.96155e10	+	2.12049e10i	0.666217	+	0.236969i
$99$	2.87624e10			0.303970
$100$	−4.89609e10	+	8.48027e10i	−0.489609	+	0.848027i
$101$	−7.13461e8	−	1.23575e9i	−0.00675465	−	0.0116994i	0.862628	−	0.505838i	$-0.168817\pi$
$101$	−7.13461e8	−	1.23575e9i	−0.00675465	−	0.0116994i	−0.869383	+	0.494139i	$0.835483\pi$
$102$	−3.60883e10	−	6.25068e10i	−0.323642	−	0.560565i
$103$	−7.14015e10	+	1.23671e11i	−0.606880	+	1.05115i	0.384871	+	0.922970i	$0.374246\pi$
$103$	−7.14015e10	+	1.23671e11i	−0.606880	+	1.05115i	−0.991751	+	0.128177i	$0.959087\pi$
$104$	2.05032e10			0.165249
$105$	1.30039e11	+	1.08306e11i	0.994334	+	0.828156i
$106$	−1.84745e11			−1.34088
$107$	−1.84715e10	+	3.19935e10i	−0.127318	+	0.220522i	−0.922637	−	0.385670i	$-0.873970\pi$
$107$	−1.84715e10	+	3.19935e10i	−0.127318	+	0.220522i	0.795319	+	0.606192i	$0.207304\pi$
$108$	4.11841e10	+	7.13330e10i	0.269711	+	0.467154i
$109$	4.86415e10	+	8.42495e10i	0.302803	+	0.524471i	0.976770	−	0.214291i	$-0.0687441\pi$
$109$	4.86415e10	+	8.42495e10i	0.302803	+	0.524471i	−0.673966	+	0.738762i	$0.735411\pi$
$110$	−7.19466e10	+	1.24615e11i	−0.425942	+	0.737753i
$111$	1.69951e11			0.957298
$112$	−4.37565e10	+	1.61079e10i	−0.234608	+	0.0863652i
$113$	2.51526e11			1.28425			0.642127	−	0.766598i	$-0.278052\pi$
$113$	2.51526e11			1.28425			0.642127	+	0.766598i	$0.278052\pi$
$114$	9.76402e10	−	1.69118e11i	0.474955	−	0.822645i
$115$	−1.43759e11	−	2.48998e11i	−0.666494	−	1.15440i
$116$	−3.61746e10	−	6.26563e10i	−0.159913	−	0.276978i
$117$	−2.40515e10	+	4.16585e10i	−0.101419	+	0.175663i
$118$	1.08256e11			0.435612
$119$	−5.38579e10	+	3.12127e11i	−0.206891	+	1.19901i
$120$	−1.24710e11			−0.457513
$121$	7.26687e10	−	1.25866e11i	0.254699	−	0.441152i
$122$	8.17935e10	+	1.41671e11i	0.273993	+	0.474570i
$123$	−7.64009e10	−	1.32330e11i	−0.244692	−	0.423820i
$124$	−7.54251e10	+	1.30640e11i	−0.231045	+	0.400182i
$125$	5.62469e11			1.64852
$126$	1.86011e10	−	1.07800e11i	0.0521795	−	0.302399i
$127$	−4.50975e11			−1.21124			−0.605622	−	0.795752i	$-0.707076\pi$
$127$	−4.50975e11			−1.21124			−0.605622	+	0.795752i	$0.707076\pi$
$128$	1.71799e10	−	2.97564e10i	0.0441942	−	0.0765466i
$129$	−8.97403e10	−	1.55435e11i	−0.221179	−	0.383094i
$130$	−1.20326e11	−	2.08410e11i	−0.284230	−	0.492301i
$131$	5.58869e10	−	9.67990e10i	0.126566	−	0.219219i	−0.795778	−	0.605589i	$-0.792938\pi$
$131$	5.58869e10	−	9.67990e10i	0.126566	−	0.219219i	0.922344	+	0.386369i	$0.126271\pi$
$132$	−1.21313e11			−0.263482
$133$	−8.04206e11	+	2.96049e11i	−1.67565	+	0.616849i
$134$	−7.94348e10			−0.158831
$135$	4.83388e11	−	8.37253e11i	0.927813	−	1.60702i
$136$	−1.16703e11	−	2.02136e11i	−0.215089	−	0.372545i
$137$	3.08019e11	+	5.33504e11i	0.545273	+	0.944441i	0.998590	+	0.0530914i	$0.0169075\pi$
$137$	3.08019e11	+	5.33504e11i	0.545273	+	0.944441i	−0.453316	+	0.891350i	$0.649759\pi$
$138$	1.21200e11	−	2.09924e11i	0.206142	−	0.357049i
$139$	−7.99626e11			−1.30709			−0.653545	−	0.756888i	$-0.726719\pi$
$139$	−7.99626e11			−1.30709			−0.653545	+	0.756888i	$0.726719\pi$
$140$	4.20523e11	+	3.50243e11i	0.660823	+	0.550383i
$141$	−3.39259e11			−0.512656
$142$	−3.84836e10	+	6.66556e10i	−0.0559358	+	0.0968837i
$143$	−1.17049e11	−	2.02734e11i	−0.163688	−	0.283517i
$144$	4.03061e10	+	6.98122e10i	0.0542472	+	0.0939588i
$145$	−4.24590e11	+	7.35412e11i	−0.550105	+	0.952810i
$146$	5.89232e10			0.0735099
$147$	4.76679e11	−	4.05970e11i	0.572770	−	0.487808i
$148$	5.49591e11			0.636210
$149$	7.62790e10	−	1.32119e11i	0.0850904	−	0.147381i	−0.820339	−	0.571877i	$-0.806215\pi$
$149$	7.62790e10	−	1.32119e11i	0.0850904	−	0.147381i	0.905430	+	0.424496i	$0.139549\pi$
$150$	4.84488e11	+	8.39158e11i	0.520932	+	0.902281i
$151$	−7.92887e11	−	1.37332e12i	−0.821936	−	1.42363i	−0.904239	−	0.427027i	$-0.859561\pi$
$151$	−7.92887e11	−	1.37332e12i	−0.821936	−	1.42363i	0.0823028	−	0.996607i	$-0.473773\pi$
$152$	3.15751e11	−	5.46897e11i	0.315650	−	0.546721i
$153$	5.47600e11			0.528032
$154$	4.09070e11	+	3.40704e11i	0.380569	+	0.316967i
$155$	1.77057e12			1.58960
$156$	1.01444e11	−	1.75706e11i	0.0879105	−	0.152265i
$157$	8.01268e11	+	1.38784e12i	0.670393	+	1.16115i	0.977793	+	0.209574i	$0.0672079\pi$
$157$	8.01268e11	+	1.38784e12i	0.670393	+	1.16115i	−0.307400	+	0.951581i	$0.599459\pi$
$158$	−4.40866e11	−	7.63603e11i	−0.356199	−	0.616955i
$159$	−9.14065e11	+	1.58321e12i	−0.713334	+	1.23553i
$160$	−4.03289e11			−0.304058
$161$	−9.98254e11	+	3.67482e11i	−0.727275	+	0.267728i
$162$	3.79270e11			0.267065
$163$	−6.37573e11	+	1.10431e12i	−0.434008	+	0.751724i	−0.997214	−	0.0745923i	$-0.976234\pi$
$163$	−6.37573e11	+	1.10431e12i	−0.434008	+	0.751724i	0.563206	+	0.826317i	$0.309568\pi$
$164$	−2.47067e11	−	4.27933e11i	−0.162620	−	0.281666i
$165$	7.11941e11	+	1.23312e12i	0.453192	+	0.784952i
$166$	5.12796e11	−	8.88189e11i	0.315755	−	0.546904i
$167$	−8.99273e11			−0.535736			−0.267868	−	0.963456i	$-0.586319\pi$
$167$	−8.99273e11			−0.535736			−0.267868	+	0.963456i	$0.586319\pi$
$168$	−7.84551e10	+	4.54676e11i	−0.0452293	+	0.262120i
$169$	−1.40065e12			−0.781542
$170$	−1.36977e12	+	2.37252e12i	−0.739911	+	1.28156i
$171$	7.40791e11	+	1.28309e12i	0.387451	+	0.671085i
$172$	−2.90204e11	−	5.02649e11i	−0.146993	−	0.254600i
$173$	2.01703e12	−	3.49359e12i	0.989596	−	1.71403i	0.370202	−	0.928951i	$-0.379289\pi$
$173$	2.01703e12	−	3.49359e12i	0.989596	−	1.71403i	0.619395	−	0.785080i	$-0.287378\pi$
$174$	−7.15925e11			−0.340288
$175$	7.23047e11	−	4.19032e12i	0.333010	−	1.92992i
$176$	−3.92305e11			−0.175107
$177$	5.35618e11	−	9.27717e11i	0.231741	−	0.401386i
$178$	3.23414e11	+	5.60169e11i	0.135659	+	0.234968i
$179$	5.94728e11	+	1.03010e12i	0.241895	+	0.418975i	0.961254	−	0.275664i	$-0.0888977\pi$
$179$	5.94728e11	+	1.03010e12i	0.241895	+	0.418975i	−0.719359	+	0.694638i	$0.755564\pi$
$180$	4.73082e11	−	8.19403e11i	0.186611	−	0.323220i
$181$	1.14571e12			0.438372			0.219186	−	0.975683i	$-0.429660\pi$
$181$	1.14571e12			0.438372			0.219186	+	0.975683i	$0.429660\pi$
$182$	−8.35535e11	+	3.07581e11i	−0.310150	+	0.114174i
$183$	1.61876e12			0.583045
$184$	3.91939e11	−	6.78858e11i	0.137000	−	0.237291i
$185$	−3.22534e12	−	5.58646e12i	−1.09429	−	1.89536i
$186$	7.46362e11	+	1.29274e12i	0.245826	+	0.425784i
$187$	−1.33247e12	+	2.30790e12i	−0.426116	+	0.738054i
$188$	−1.09710e12			−0.340706
$189$	−2.74842e12	−	2.28909e12i	−0.828979	−	0.690436i
$190$	−7.41209e12			−2.17168
$191$	−5.67271e11	+	9.82541e11i	−0.161476	+	0.279684i	−0.935398	−	0.353596i	$-0.884959\pi$
$191$	−5.67271e11	+	9.82541e11i	−0.161476	+	0.279684i	0.773923	+	0.633280i	$0.218292\pi$
$192$	−1.70002e11	−	2.94452e11i	−0.0470216	−	0.0814437i
$193$	3.38313e12	+	5.85975e12i	0.909397	+	1.57512i	0.814904	+	0.579596i	$0.196789\pi$
$193$	3.38313e12	+	5.85975e12i	0.909397	+	1.57512i	0.0944924	+	0.995526i	$0.469877\pi$
$194$	2.28811e12	−	3.96312e12i	0.597816	−	1.03545i
$195$	−2.38134e12			−0.604828
$196$	1.54149e12	−	1.31284e12i	0.380657	−	0.324192i
$197$	7.83137e12			1.88050			0.940251	−	0.340483i	$-0.110591\pi$
$197$	7.83137e12			1.88050			0.940251	+	0.340483i	$0.110591\pi$
$198$	4.60198e11	−	7.97086e11i	0.107470	−	0.186143i
$199$	−8.07265e11	−	1.39822e12i	−0.183368	−	0.317603i	0.759657	−	0.650324i	$-0.225367\pi$
$199$	−8.07265e11	−	1.39822e12i	−0.183368	−	0.317603i	−0.943025	+	0.332721i	$0.892033\pi$
$200$	1.56675e12	+	2.71369e12i	0.346206	+	0.599646i
$201$	−3.93020e11	+	6.80731e11i	−0.0844960	+	0.146351i
$202$	−4.56615e10			−0.00955252
$203$	2.41411e12	+	2.01065e12i	0.491506	+	0.409363i
$204$	−2.30965e12			−0.457699
$205$	−2.89989e12	+	5.02275e12i	−0.559416	+	0.968937i
$206$	2.28485e12	+	3.95748e12i	0.429129	+	0.743273i
$207$	9.19537e11	+	1.59269e12i	0.168164	+	0.291268i
$208$	3.28052e11	−	5.68202e11i	0.0584243	−	0.101194i
$209$	−7.21023e12			−1.25067
$210$	5.08209e12	−	1.87085e12i	0.858690	−	0.316105i
$211$	8.54136e12			1.40596			0.702981	−	0.711209i	$-0.251852\pi$
$211$	8.54136e12			1.40596			0.702981	+	0.711209i	$0.251852\pi$
$212$	−2.95592e12	+	5.11981e12i	−0.474074	+	0.821120i
$213$	3.80811e11	+	6.59585e11i	0.0595144	+	0.103082i
$214$	5.91087e11	+	1.02379e12i	0.0900275	+	0.155932i
$215$	−3.40620e12	+	5.89971e12i	−0.505660	+	0.875828i
$216$	2.63578e12			0.381429
$217$	1.11387e12	−	6.45527e12i	0.157146	−	0.910722i
$218$	3.11305e12			0.428229
$219$	2.91535e11	−	5.04953e11i	0.0391064	−	0.0677343i
$220$	2.30229e12	+	3.98768e12i	0.301186	+	0.521670i
$221$	−2.22846e12	−	3.85981e12i	−0.284346	−	0.492502i
$222$	2.71921e12	−	4.70982e12i	0.338456	−	0.586223i
$223$	−4.63010e12			−0.562229			−0.281115	−	0.959674i	$-0.590704\pi$
$223$	−4.63010e12			−0.562229			−0.281115	+	0.959674i	$0.590704\pi$
$224$	−2.53710e11	+	1.47034e12i	−0.0300589	+	0.174202i
$225$	−7.35157e12			−0.849916
$226$	4.02441e12	−	6.97049e12i	0.454053	−	0.786442i
$227$	−4.35358e12	−	7.54061e12i	−0.479406	−	0.830356i	0.520315	−	0.853975i	$-0.325815\pi$
$227$	−4.35358e12	−	7.54061e12i	−0.479406	−	0.830356i	−0.999721	+	0.0236183i	$0.992481\pi$
$228$	−3.12449e12	−	5.41177e12i	−0.335844	−	0.581698i
$229$	1.11477e12	−	1.93085e12i	0.116975	−	0.202606i	−0.801593	−	0.597870i	$-0.796014\pi$
$229$	1.11477e12	−	1.93085e12i	0.116975	−	0.202606i	0.918567	+	0.395264i	$0.129347\pi$
$230$	−9.20057e12			−0.942566
$231$	4.94368e12	−	1.81989e12i	0.494521	−	0.182046i
$232$	−2.31517e12			−0.226152
$233$	1.22410e12	−	2.12021e12i	0.116778	−	0.202265i	−0.801711	−	0.597712i	$-0.796077\pi$
$233$	1.22410e12	−	2.12021e12i	0.116778	−	0.202265i	0.918489	+	0.395447i	$0.129410\pi$
$234$	7.69649e11	+	1.33307e12i	0.0717143	+	0.124213i
$235$	6.43848e12	+	1.11518e13i	0.586017	+	1.01501i
$236$	1.73209e12	−	3.00007e12i	0.154012	−	0.266757i
$237$	−8.72511e12			−0.757975
$238$	7.78818e12	+	6.48658e12i	0.661093	+	0.550608i
$239$	5.62092e12			0.466250			0.233125	−	0.972447i	$-0.425105\pi$
$239$	5.62092e12			0.466250			0.233125	+	0.972447i	$0.425105\pi$
$240$	−1.99535e12	+	3.45605e12i	−0.161755	+	0.280168i
$241$	−2.21149e12	−	3.83041e12i	−0.175223	−	0.303495i	0.765015	−	0.644012i	$-0.222731\pi$
$241$	−2.21149e12	−	3.83041e12i	−0.175223	−	0.303495i	−0.940238	+	0.340517i	$0.889398\pi$
$242$	−2.32540e12	−	4.02771e12i	−0.180100	−	0.311942i
$243$	−5.24813e12	+	9.09003e12i	−0.397347	+	0.688226i
$244$	5.23479e12			0.387485
$245$	−2.23911e13	−	7.96437e12i	−1.62055	−	0.576419i
$246$	−4.88966e12			−0.346047
$247$	6.02930e12	−	1.04431e13i	0.417286	−	0.722761i
$248$	2.41360e12	+	4.18048e12i	0.163373	+	0.282971i
$249$	−5.07433e12	−	8.78900e12i	−0.335956	−	0.581893i
$250$	8.99951e12	−	1.55876e13i	0.582839	−	1.00951i
$251$	9.24639e12			0.585823			0.292912	−	0.956140i	$-0.405376\pi$
$251$	9.24639e12			0.585823			0.292912	+	0.956140i	$0.405376\pi$
$252$	−2.68983e12	−	2.24029e12i	−0.166733	−	0.138868i
$253$	−8.94999e12			−0.542825
$254$	−7.21559e12	+	1.24978e13i	−0.428239	+	0.741733i
$255$	1.35545e13	+	2.34770e13i	0.787248	+	1.36355i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	5.95716e12	−	1.03181e13i	0.331441	−	0.574073i	−0.651353	−	0.758775i	$-0.725798\pi$
$257$	5.95716e12	−	1.03181e13i	0.331441	−	0.574073i	0.982795	+	0.184701i	$0.0591317\pi$
$258$	−5.74338e12			−0.312795
$259$	−2.23966e13	+	8.24475e12i	−1.19408	+	0.439571i
$260$	−7.70084e12			−0.401962
$261$	2.71584e12	−	4.70398e12i	0.138798	−	0.240404i
$262$	−1.78838e12	−	3.09757e12i	−0.0894959	−	0.155011i
$263$	1.14495e13	+	1.98311e13i	0.561086	+	0.971830i	0.997402	+	0.0720364i	$0.0229498\pi$
$263$	1.14495e13	+	1.98311e13i	0.561086	+	0.971830i	−0.436316	+	0.899794i	$0.643717\pi$
$264$	−1.94101e12	+	3.36193e12i	−0.0931550	+	0.161349i
$265$	6.93888e13			3.26165
$266$	−4.66296e12	+	2.70236e13i	−0.214691	+	1.24421i
$267$	6.40062e12			0.288676
$268$	−1.27096e12	+	2.20136e12i	−0.0561551	+	0.0972635i
$269$	3.05703e12	+	5.29494e12i	0.132331	+	0.229205i	0.924575	−	0.381000i	$-0.124420\pi$
$269$	3.05703e12	+	5.29494e12i	0.132331	+	0.229205i	−0.792243	+	0.610205i	$0.791087\pi$
$270$	−1.54684e13	−	2.67921e13i	−0.656063	−	1.13633i
$271$	−5.40943e11	+	9.36941e11i	−0.0224813	+	0.0389387i	−0.877047	−	0.480404i	$-0.840490\pi$
$271$	−5.40943e11	+	9.36941e11i	−0.0224813	+	0.0389387i	0.854566	+	0.519343i	$0.173823\pi$
$272$	−7.46900e12			−0.304182
$273$	−1.49811e12	+	8.68209e12i	−0.0597928	+	0.346521i
$274$	1.97132e13			0.771133
$275$	1.78885e13	−	3.09837e13i	0.685873	−	1.18797i
$276$	−3.87840e12	−	6.71758e12i	−0.145765	−	0.252472i
$277$	−5.14069e12	−	8.90394e12i	−0.189401	−	0.328053i	0.755649	−	0.654976i	$-0.227321\pi$
$277$	−5.14069e12	−	8.90394e12i	−0.189401	−	0.328053i	−0.945051	+	0.326924i	$0.893988\pi$
$278$	−1.27940e13	+	2.21599e13i	−0.462126	+	0.800426i
$279$	−1.13252e13			−0.401073
$280$	1.64346e13	−	6.04998e12i	0.570676	−	0.210080i
$281$	2.64698e13			0.901292			0.450646	−	0.892703i	$-0.351194\pi$
$281$	2.64698e13			0.901292			0.450646	+	0.892703i	$0.351194\pi$
$282$	−5.42814e12	+	9.40182e12i	−0.181251	+	0.313936i
$283$	−1.20657e13	−	2.08984e13i	−0.395118	−	0.684364i	0.597999	−	0.801497i	$-0.295963\pi$
$283$	−1.20657e13	−	2.08984e13i	−0.395118	−	0.684364i	−0.993116	+	0.117133i	$0.962630\pi$
$284$	1.23148e12	+	2.13298e12i	0.0395526	+	0.0685071i
$285$	−3.66729e13	+	6.35193e13i	−1.15531	+	2.00105i
$286$	−7.49111e12			−0.231490
$287$	1.64880e13	+	1.37325e13i	0.499825	+	0.416292i
$288$	2.57959e12			0.0767171
$289$	−8.23257e12	+	1.42592e13i	−0.240213	+	0.416062i
$290$	1.35869e13	+	2.35332e13i	0.388983	+	0.673739i
$291$	−2.26418e13	−	3.92167e13i	−0.636062	−	1.10169i
$292$	9.42772e11	−	1.63293e12i	0.0259897	−	0.0450154i
$293$	−2.33914e13			−0.632825			−0.316413	−	0.948622i	$-0.602478\pi$
$293$	−2.33914e13			−0.632825			−0.316413	+	0.948622i	$0.602478\pi$
$294$	−3.62372e12	−	1.97056e13i	−0.0962153	−	0.523215i
$295$	−4.06600e13			−1.05961
$296$	8.79346e12	−	1.52307e13i	0.224934	−	0.389597i
$297$	−1.50471e13	−	2.60624e13i	−0.377827	−	0.654416i
$298$	−2.44093e12	−	4.22781e12i	−0.0601680	−	0.104214i
$299$	7.48412e12	−	1.29629e13i	0.181113	−	0.313697i
$300$	3.10072e13			0.736709
$301$	1.93668e13	+	1.61301e13i	0.451795	+	0.376289i
$302$	−5.07448e13			−1.16239
$303$	−2.25920e11	+	3.91305e11i	−0.00508183	+	0.00880198i
$304$	−1.01040e13	−	1.75007e13i	−0.223198	−	0.386590i
$305$	−3.07210e13	−	5.32103e13i	−0.666478	−	1.15437i
$306$	8.76160e12	−	1.51755e13i	0.186688	−	0.323352i
$307$	3.45847e13			0.723807			0.361903	−	0.932216i	$-0.382127\pi$
$307$	3.45847e13			0.723807			0.361903	+	0.932216i	$0.382127\pi$
$308$	1.59870e13	−	5.88521e12i	0.328653	−	0.120985i
$309$	4.52191e13			0.913166
$310$	2.83290e13	−	4.90673e13i	0.562008	−	0.973427i
$311$	−3.75500e13	−	6.50385e13i	−0.731860	−	1.26762i	−0.956087	−	0.293082i	$-0.905319\pi$
$311$	−3.75500e13	−	6.50385e13i	−0.731860	−	1.26762i	0.224228	−	0.974537i	$-0.428014\pi$
$312$	−3.24621e12	−	5.62259e12i	−0.0621621	−	0.107668i
$313$	−1.89963e13	+	3.29025e13i	−0.357417	+	0.619064i	−0.987528	−	0.157440i	$-0.949676\pi$
$313$	−1.89963e13	+	3.29025e13i	−0.357417	+	0.619064i	0.630112	+	0.776505i	$0.283009\pi$
$314$	5.12811e13			0.948079
$315$	−6.98641e12	+	4.04888e13i	−0.126925	+	0.735575i
$316$	−2.82154e13			−0.503742
$317$	−3.61930e12	+	6.26882e12i	−0.0635037	+	0.109992i	−0.896029	−	0.443995i	$-0.853561\pi$
$317$	−3.61930e12	+	6.26882e12i	−0.0635037	+	0.109992i	0.832526	+	0.553987i	$0.186894\pi$
$318$	2.92501e13	+	5.06626e13i	0.504403	+	0.873652i
$319$	1.32168e13	+	2.28923e13i	0.224016	+	0.388007i
$320$	−6.45262e12	+	1.11763e13i	−0.107501	+	0.186197i
$321$	1.16981e13			0.191574
$322$	−5.78810e12	+	3.35442e13i	−0.0931812	+	0.540020i
$323$	−1.37274e14			−2.17257
$324$	6.06833e12	−	1.05107e13i	0.0944216	−	0.163543i
$325$	2.99172e13	+	5.18182e13i	0.457681	+	0.792727i
$326$	2.04023e13	+	3.53379e13i	0.306890	+	0.531549i
$327$	1.54025e13	−	2.66779e13i	0.227813	−	0.394583i
$328$	−1.58123e13			−0.229979
$329$	4.47085e13	−	1.64583e13i	0.639459	−	0.235401i
$330$	4.55642e13			0.640910
$331$	−8.29737e12	+	1.43715e13i	−0.114785	+	0.198814i	−0.917694	−	0.397288i	$-0.869951\pi$
$331$	−8.29737e12	+	1.43715e13i	−0.114785	+	0.198814i	0.802909	+	0.596102i	$0.203285\pi$
$332$	−1.64095e13	−	2.84221e13i	−0.223273	−	0.386720i
$333$	2.06305e13	+	3.57331e13i	0.276100	+	0.478220i
$334$	−1.43884e13	+	2.49214e13i	−0.189411	+	0.328070i
$335$	2.98351e13			0.386350
$336$	1.13451e13	+	9.44903e12i	0.144524	+	0.120371i
$337$	4.49127e13			0.562865			0.281433	−	0.959581i	$-0.409190\pi$
$337$	4.49127e13			0.562865			0.281433	+	0.959581i	$0.409190\pi$
$338$	−2.24104e13	+	3.88159e13i	−0.276317	+	0.478595i
$339$	−3.98232e13	−	6.89758e13i	−0.483101	−	0.836756i
$340$	4.38327e13	+	7.59205e13i	0.523196	+	0.906202i
$341$	2.75575e13	−	4.77310e13i	0.323661	−	0.560598i
$342$	4.74106e13			0.547939
$343$	−4.31234e13	+	7.66248e13i	−0.490451	+	0.871469i
$344$	−1.85731e13			−0.207880
$345$	−4.55217e13	+	7.88459e13i	−0.501434	+	0.868509i
$346$	−6.45449e13	−	1.11795e14i	−0.699750	−	1.21200i
$347$	6.08265e13	+	1.05355e14i	0.649054	+	1.12419i	0.983349	+	0.181726i	$0.0581684\pi$
$347$	6.08265e13	+	1.05355e14i	0.649054	+	1.12419i	−0.334295	+	0.942468i	$0.608498\pi$
$348$	−1.14548e13	+	1.98403e13i	−0.120310	+	0.208383i
$349$	−2.22919e13			−0.230466			−0.115233	−	0.993338i	$-0.536761\pi$
$349$	−2.22919e13			−0.230466			−0.115233	+	0.993338i	$0.536761\pi$
$350$	−1.04557e14	−	8.70828e13i	−1.06409	−	0.886254i
$351$	5.03306e13			0.504247
$352$	−6.27688e12	+	1.08719e13i	−0.0619098	+	0.107231i
$353$	8.78147e13	+	1.52099e14i	0.852719	+	1.47695i	0.878745	+	0.477292i	$0.158382\pi$
$353$	8.78147e13	+	1.52099e14i	0.852719	+	1.47695i	−0.0260253	+	0.999661i	$0.508285\pi$
$354$	−1.71398e13	−	2.96870e13i	−0.163865	−	0.283823i
$355$	1.44541e13	−	2.50353e13i	0.136062	−	0.235666i
$356$	2.06985e13			0.191851
$357$	9.41215e13	−	3.46485e13i	0.859041	−	0.316234i
$358$	3.80626e13			0.342091
$359$	8.08719e13	−	1.40074e14i	0.715778	−	1.23976i	−0.246881	−	0.969046i	$-0.579406\pi$
$359$	8.08719e13	−	1.40074e14i	0.715778	−	1.23976i	0.962659	−	0.270717i	$-0.0872609\pi$
$360$	−1.51386e13	−	2.62209e13i	−0.131954	−	0.228551i
$361$	−1.27458e14	−	2.20764e14i	−1.09415	−	1.89513i
$362$	1.83314e13	−	3.17509e13i	0.154988	−	0.268447i
$363$	−4.60216e13			−0.383244
$364$	−4.84462e12	+	2.80763e13i	−0.0397376	+	0.230294i
$365$	−2.21311e13			−0.178810
$366$	2.59002e13	−	4.48604e13i	0.206137	−	0.357041i
$367$	3.77419e12	+	6.53709e12i	0.0295911	+	0.0512532i	0.880442	−	0.474154i	$-0.157246\pi$
$367$	3.77419e12	+	6.53709e12i	0.0295911	+	0.0512532i	−0.850851	+	0.525408i	$0.823913\pi$
$368$	−1.25421e13	−	2.17235e13i	−0.0968736	−	0.167790i
$369$	1.85488e13	−	3.21275e13i	0.141147	−	0.244473i
$370$	−2.06422e14			−1.54756
$371$	4.36526e13	−	2.52983e14i	0.322444	−	1.86868i
$372$	4.77672e13			0.347651
$373$	−1.17613e14	+	2.03712e14i	−0.843445	+	1.46089i	0.0435200	+	0.999053i	$0.486143\pi$
$373$	−1.17613e14	+	2.03712e14i	−0.843445	+	1.46089i	−0.886965	+	0.461837i	$0.847191\pi$
$374$	4.26390e13	+	7.38528e13i	0.301309	+	0.521883i
$375$	−8.90538e13	−	1.54246e14i	−0.620127	−	1.07409i
$376$	−1.75536e13	+	3.04038e13i	−0.120458	+	0.208639i
$377$	−4.42085e13			−0.298971
$378$	−1.07412e14	+	3.95410e13i	−0.715892	+	0.263538i
$379$	5.99930e13			0.394080			0.197040	−	0.980395i	$-0.436867\pi$
$379$	5.99930e13			0.394080			0.197040	+	0.980395i	$0.436867\pi$
$380$	−1.18594e14	+	2.05410e14i	−0.767805	+	1.32988i
$381$	7.14013e13	+	1.23671e14i	0.455637	+	0.789186i
$382$	1.81527e13	+	3.14413e13i	0.114180	+	0.197766i
$383$	7.45203e12	−	1.29073e13i	0.0462042	−	0.0800280i	−0.841998	−	0.539480i	$-0.818621\pi$
$383$	7.45203e12	−	1.29073e13i	0.0462042	−	0.0800280i	0.888203	+	0.459452i	$0.151954\pi$
$384$	−1.08801e13			−0.0664985
$385$	−1.53643e14	−	1.27966e14i	−0.925720	−	0.771009i
$386$	2.16520e14			1.28608
$387$	2.17874e13	−	3.77368e13i	0.127583	−	0.220981i
$388$	−7.32195e13	−	1.26820e14i	−0.422720	−	0.732172i
$389$	1.66207e14	+	2.87879e14i	0.946078	+	1.63866i	0.753578	+	0.657359i	$0.228326\pi$
$389$	1.66207e14	+	2.87879e14i	0.946078	+	1.63866i	0.192501	+	0.981297i	$0.438340\pi$
$390$	−3.81015e13	+	6.59937e13i	−0.213839	+	0.370380i
$391$	−1.70397e14			−0.942951
$392$	−1.17185e13	−	6.37245e13i	−0.0639436	−	0.347723i
$393$	−3.53936e13			−0.190443
$394$	1.25302e14	−	2.17029e14i	0.664858	−	1.15157i
$395$	1.65586e14	+	2.86803e14i	0.866441	+	1.50072i
$396$	−1.47263e13	−	2.55068e13i	−0.0759926	−	0.131623i
$397$	7.83509e13	−	1.35708e14i	0.398746	−	0.690648i	−0.594826	−	0.803855i	$-0.702779\pi$
$397$	7.83509e13	−	1.35708e14i	0.398746	−	0.690648i	0.993571	+	0.113207i	$0.0361122\pi$
$398$	−5.16650e13			−0.259322
$399$	2.08513e14	+	1.73665e14i	1.03224	+	0.859728i
$400$	1.00272e14			0.489609
$401$	1.42128e14	−	2.46172e14i	0.684518	−	1.18562i	−0.289071	−	0.957308i	$-0.593346\pi$
$401$	1.42128e14	−	2.46172e14i	0.684518	−	1.18562i	0.973588	−	0.228311i	$-0.0733204\pi$
$402$	1.25766e13	+	2.17834e13i	0.0597477	+	0.103486i
$403$	4.60880e13	+	7.98268e13i	0.215978	+	0.374086i
$404$	−7.30584e11	+	1.26541e12i	−0.00337733	+	0.00584970i
$405$	−1.42451e14			−0.649625
$406$	9.43466e13	−	3.47314e13i	0.424457	−	0.156253i
$407$	−2.00800e14			−0.891240
$408$	−3.69544e13	+	6.40069e13i	−0.161821	+	0.280283i
$409$	−1.39877e13	−	2.42275e13i	−0.0604323	−	0.104672i	0.834226	−	0.551422i	$-0.185915\pi$
$409$	−1.39877e13	−	2.42275e13i	−0.0604323	−	0.104672i	−0.894659	+	0.446750i	$0.852581\pi$
$410$	9.27964e13	+	1.60728e14i	0.395567	+	0.685142i
$411$	9.75352e13	−	1.68936e14i	0.410234	−	0.710545i
$412$	1.46230e14			0.606880
$413$	−2.55793e13	+	1.48241e14i	−0.104752	+	0.607078i
$414$	5.88504e13			0.237820
$415$	−1.92602e14	+	3.33597e14i	−0.768062	+	1.33032i
$416$	−1.04977e13	−	1.81825e13i	−0.0413122	−	0.0715549i
$417$	1.26602e14	+	2.19281e14i	0.491691	+	0.851634i
$418$	−1.15364e14	+	1.99816e14i	−0.442180	+	0.765879i
$419$	−3.30060e14			−1.24858			−0.624288	−	0.781194i	$-0.714611\pi$
$419$	−3.30060e14			−1.24858			−0.624288	+	0.781194i	$0.714611\pi$
$420$	2.94671e13	−	1.70773e14i	0.110019	−	0.637598i
$421$	−2.84800e14			−1.04951			−0.524756	−	0.851252i	$-0.675844\pi$
$421$	−2.84800e14			−1.04951			−0.524756	+	0.851252i	$0.675844\pi$
$422$	1.36662e14	−	2.36705e14i	0.497083	−	0.860972i
$423$	−4.11830e13	−	7.13311e13i	−0.147858	−	0.256098i
$424$	9.45895e13	+	1.63834e14i	0.335221	+	0.580619i
$425$	3.40574e14	−	5.89892e14i	1.19144	−	2.06364i
$426$	2.43719e13			0.0841661
$427$	−2.13325e14	+	7.85302e13i	−0.727258	+	0.267722i
$428$	3.78295e13			0.127318
$429$	−3.70638e13	+	6.41964e13i	−0.123150	+	0.213302i
$430$	1.08998e14	+	1.88791e14i	0.357555	+	0.619304i
$431$	1.10769e14	+	1.91858e14i	0.358753	+	0.621378i	0.987753	−	0.156028i	$-0.0498689\pi$
$431$	1.10769e14	+	1.91858e14i	0.358753	+	0.621378i	−0.629000	+	0.777405i	$0.716536\pi$
$432$	4.21725e13	−	7.30450e13i	0.134856	−	0.233577i
$433$	−9.21086e13			−0.290815			−0.145407	−	0.989372i	$-0.546449\pi$
$433$	−9.21086e13			−0.290815			−0.145407	+	0.989372i	$0.546449\pi$
$434$	−1.61072e14	−	1.34153e14i	−0.502141	−	0.418221i
$435$	2.68896e14			0.827738
$436$	4.98088e13	−	8.62715e13i	0.151402	−	0.262235i
$437$	−2.30512e14	−	3.99259e14i	−0.691904	−	1.19841i
$438$	−9.32912e12	−	1.61585e13i	−0.0276524	−	0.0478954i
$439$	1.10254e14	−	1.90966e14i	0.322731	−	0.558986i	−0.658320	−	0.752738i	$-0.728732\pi$
$439$	1.10254e14	−	1.90966e14i	0.322731	−	0.558986i	0.981050	+	0.193752i	$0.0620658\pi$
$440$	1.47347e14			0.425942
$441$	1.43222e14	+	5.09432e13i	0.408882	+	0.145437i
$442$	−1.42621e14			−0.402126
$443$	−2.47563e14	+	4.28791e14i	−0.689389	+	1.19406i	0.282647	+	0.959224i	$0.408788\pi$
$443$	−2.47563e14	+	4.28791e14i	−0.689389	+	1.19406i	−0.972036	+	0.234833i	$0.924546\pi$
$444$	−8.70149e13	−	1.50714e14i	−0.239325	−	0.414522i
$445$	−1.21471e14	−	2.10395e14i	−0.329985	−	0.571551i
$446$	−7.40816e13	+	1.28313e14i	−0.198778	+	0.344294i
$447$	−4.83080e13			−0.128035
$448$	3.66879e13	+	3.05565e13i	0.0960493	+	0.0799971i
$449$	2.17377e13			0.0562158			0.0281079	−	0.999605i	$-0.491052\pi$
$449$	2.17377e13			0.0562158			0.0281079	+	0.999605i	$0.491052\pi$
$450$	−1.17625e14	+	2.03733e14i	−0.300491	+	0.520465i
$451$	9.02691e13	+	1.56351e14i	0.227807	+	0.394574i
$452$	−1.28781e14	−	2.23056e14i	−0.321064	−	0.556098i
$453$	−2.51070e14	+	4.34866e14i	−0.618379	+	1.07106i
$454$	−2.78629e14			−0.677983
$455$	3.13820e14	−	1.15525e14i	0.754429	−	0.277724i
$456$	−1.99967e14			−0.474955
$457$	3.48611e14	−	6.03813e14i	0.818093	−	1.41698i	−0.0889930	−	0.996032i	$-0.528365\pi$
$457$	3.48611e14	−	6.03813e14i	0.818093	−	1.41698i	0.907086	−	0.420946i	$-0.138302\pi$
$458$	−3.56728e13	−	6.17871e13i	−0.0827136	−	0.143264i
$459$	−2.86479e14	−	4.96196e14i	−0.656331	−	1.13680i
$460$	−1.47209e14	+	2.54974e14i	−0.333247	+	0.577201i
$461$	−2.66359e14			−0.595817			−0.297908	−	0.954594i	$-0.596289\pi$
$461$	−2.66359e14			−0.595817			−0.297908	+	0.954594i	$0.596289\pi$
$462$	2.86645e13	−	1.66122e14i	0.0633599	−	0.367194i
$463$	1.80648e14			0.394583			0.197291	−	0.980345i	$-0.436786\pi$
$463$	1.80648e14			0.394583			0.197291	+	0.980345i	$0.436786\pi$
$464$	−3.70428e13	+	6.41600e13i	−0.0799567	+	0.138489i
$465$	−2.80328e14	−	4.85542e14i	−0.597963	−	1.03570i
$466$	−3.91713e13	−	6.78466e13i	−0.0825743	−	0.143023i
$467$	−3.56563e14	+	6.17585e14i	−0.742837	+	1.28663i	0.208362	+	0.978052i	$0.433187\pi$
$467$	−3.56563e14	+	6.17585e14i	−0.742837	+	1.28663i	−0.951199	+	0.308579i	$0.900147\pi$
$468$	4.92576e13			0.101419
$469$	1.87693e13	−	1.08775e14i	0.0381942	−	0.221349i
$470$	4.12063e14			0.828753
$471$	2.53724e14	−	4.39463e14i	0.504367	−	0.873589i
$472$	−5.54270e13	−	9.60023e13i	−0.108903	−	0.188626i
$473$	1.06030e14	+	1.83649e14i	0.205917	+	0.356658i
$474$	−1.39602e14	+	2.41797e14i	−0.267985	+	0.464163i
$475$	1.84291e15			3.49695
$476$	3.04372e14	−	1.12047e14i	0.570909	−	0.210166i
$477$	−4.43837e14			−0.822949
$478$	8.99346e13	−	1.55771e14i	0.164844	−	0.285518i
$479$	1.92124e14	+	3.32769e14i	0.348126	+	0.602972i	0.985917	−	0.167238i	$-0.0534848\pi$
$479$	1.92124e14	+	3.32769e14i	0.348126	+	0.602972i	−0.637790	+	0.770210i	$0.720151\pi$
$480$	6.38513e13	+	1.10594e14i	0.114378	+	0.198109i
$481$	1.67912e14	−	2.90832e14i	0.297361	−	0.515044i
$482$	−1.41535e14			−0.247803
$483$	2.58825e14	+	2.15569e14i	0.448019	+	0.373144i
$484$	−1.48826e14			−0.254699
$485$	−8.59395e14	+	1.48852e15i	−1.45416	+	2.51869i
$486$	1.67940e14	+	2.90881e14i	0.280967	+	0.486649i
$487$	−9.35583e13	−	1.62048e14i	−0.154765	−	0.268061i	0.778208	−	0.628006i	$-0.216129\pi$
$487$	−9.35583e13	−	1.62048e14i	−0.154765	−	0.268061i	−0.932973	+	0.359945i	$0.882795\pi$
$488$	8.37566e13	−	1.45071e14i	0.136997	−	0.237285i
$489$	4.03779e14			0.653048
$490$	−5.78973e14	+	4.93090e14i	−0.925933	+	0.788584i
$491$	3.62679e14			0.573553			0.286777	−	0.957997i	$-0.407416\pi$
$491$	3.62679e14			0.573553			0.286777	+	0.957997i	$0.407416\pi$
$492$	−7.82346e13	+	1.35506e14i	−0.122346	+	0.211910i
$493$	2.51632e14	+	4.35840e14i	0.389142	+	0.674014i
$494$	−1.92938e14	−	3.34178e14i	−0.295066	−	0.511069i
$495$	−1.72847e14	+	2.99379e14i	−0.261416	+	0.452786i
$496$	1.54471e14			0.231045
$497$	−8.21825e13	−	6.84478e13i	−0.121568	−	0.101251i
$498$	−3.24757e14			−0.475114
$499$	−1.98331e13	+	3.43519e13i	−0.0286970	+	0.0497047i	−0.880017	−	0.474942i	$-0.842469\pi$
$499$	−1.98331e13	+	3.43519e13i	−0.0286970	+	0.0497047i	0.851320	+	0.524646i	$0.175802\pi$
$500$	−2.87984e14	−	4.98803e14i	−0.412129	−	0.713829i
$501$	1.42379e14	+	2.46607e14i	0.201529	+	0.349059i
$502$	1.47942e14	−	2.56243e14i	0.207120	−	0.358742i
$503$	−2.17027e14			−0.300531			−0.150265	−	0.988646i	$-0.548013\pi$
$503$	−2.17027e14			−0.300531			−0.150265	+	0.988646i	$0.548013\pi$
$504$	−1.05122e14	+	3.86980e13i	−0.143988	+	0.0530055i
$505$	1.71501e13			0.0232361
$506$	−1.43200e14	+	2.48029e14i	−0.191918	+	0.332411i
$507$	2.21760e14	+	3.84100e14i	0.293995	+	0.509214i
$508$	2.30899e14	+	3.99929e14i	0.302811	+	0.524484i
$509$	4.08850e13	−	7.08148e13i	0.0530415	−	0.0918706i	−0.838286	−	0.545231i	$-0.816442\pi$
$509$	4.08850e13	−	7.08148e13i	0.0530415	−	0.0918706i	0.891327	+	0.453361i	$0.149775\pi$
$510$	8.67486e14			1.11334
$511$	−1.39227e13	+	8.06872e13i	−0.0176770	+	0.102445i
$512$	−3.51844e13			−0.0441942
$513$	7.75095e14	−	1.34250e15i	0.963184	−	1.66828i
$514$	−1.90629e14	−	3.30179e14i	−0.234365	−	0.405931i
$515$	−8.58171e14	−	1.48640e15i	−1.04384	−	1.80798i
$516$	−9.18941e13	+	1.59165e14i	−0.110590	+	0.191547i
$517$	4.00840e14			0.477280
$518$	−1.29860e14	+	7.52589e14i	−0.152990	+	0.886634i
$519$	−1.27740e15			−1.48904
$520$	−1.23213e14	+	2.13412e14i	−0.142115	+	0.246150i
$521$	−4.50760e14	−	7.80740e14i	−0.514444	−	0.891044i	−0.999860	−	0.0167599i	$-0.994665\pi$
$521$	−4.50760e14	−	7.80740e14i	−0.514444	−	0.891044i	0.485415	−	0.874284i	$-0.338668\pi$
$522$	−8.69070e13	−	1.50527e14i	−0.0981447	−	0.169992i
$523$	−5.25079e14	+	9.09464e14i	−0.586767	+	1.01631i	0.407886	+	0.913033i	$0.366266\pi$
$523$	−5.25079e14	+	9.09464e14i	−0.586767	+	1.01631i	−0.994653	+	0.103277i	$0.967067\pi$
$524$	−1.14456e14			−0.126566
$525$	−1.26359e15	+	4.65159e14i	−1.38270	+	0.509008i
$526$	7.32768e14			0.793496
$527$	5.24661e14	−	9.08739e14i	0.562238	−	0.973824i
$528$	6.21123e13	+	1.07582e14i	0.0658705	+	0.114091i
$529$	1.90272e14	+	3.29561e14i	0.199696	+	0.345884i
$530$	1.11022e15	−	1.92296e15i	1.15317	−	1.99734i
$531$	2.60077e14			0.267351
$532$	6.74292e14	+	5.61601e14i	0.686016	+	0.571366i
$533$	−3.01938e14			−0.304031
$534$	1.02410e14	−	1.77379e14i	0.102062	−	0.176777i
$535$	−2.22007e14	−	3.84528e14i	−0.218989	−	0.379299i
$536$	4.06706e13	+	7.04436e13i	0.0397077	+	0.0687757i
$537$	1.88323e14	−	3.26184e14i	0.181989	−	0.315213i
$538$	1.95650e14			0.187145
$539$	−5.63205e14	+	4.79661e14i	−0.533246	+	0.454147i
$540$	−9.89979e14			−0.927813
$541$	8.68979e14	−	1.50512e15i	0.806166	−	1.39632i	−0.109336	−	0.994005i	$-0.534872\pi$
$541$	8.68979e14	−	1.50512e15i	0.806166	−	1.39632i	0.915501	−	0.402315i	$-0.131794\pi$
$542$	1.73102e13	+	2.99821e13i	0.0158967	+	0.0275338i
$543$	−1.81397e14	−	3.14188e14i	−0.164904	−	0.285621i
$544$	−1.19504e14	+	2.06987e14i	−0.107545	+	0.186273i
$545$	−1.16924e15			−1.04165
$546$	2.16635e14	+	1.80430e14i	0.191060	+	0.159129i
$547$	3.12142e14			0.272535			0.136268	−	0.990672i	$-0.456489\pi$
$547$	3.12142e14			0.272535			0.136268	+	0.990672i	$0.456489\pi$
$548$	3.15411e14	−	5.46308e14i	0.272637	−	0.472221i
$549$	1.96503e14	+	3.40354e14i	0.168160	+	0.291261i
$550$	−5.72431e14	−	9.91480e14i	−0.484985	−	0.840019i
$551$	−6.80814e14	+	1.17921e15i	−0.571077	+	0.989135i
$552$	−2.48218e14			−0.206142
$553$	1.14982e15	−	4.23277e14i	0.945456	−	0.348046i
$554$	−3.29004e14			−0.267854
$555$	−1.02131e15	+	1.76897e15i	−0.823281	+	1.42596i
$556$	4.09408e14	+	7.09116e14i	0.326772	+	0.565986i
$557$	5.34209e14	+	9.25277e14i	0.422190	+	0.731254i	0.996153	−	0.0876266i	$-0.0279282\pi$
$557$	5.34209e14	+	9.25277e14i	0.422190	+	0.731254i	−0.573964	+	0.818881i	$0.694595\pi$
$558$	−1.81204e14	+	3.13854e14i	−0.141801	+	0.245606i
$559$	−3.54655e14			−0.274815
$560$	9.52913e13	−	5.52248e14i	0.0731171	−	0.423741i
$561$	8.43860e14			0.641172
$562$	4.23516e14	−	7.33552e14i	0.318655	−	0.551926i
$563$	−3.17399e14	−	5.49751e14i	−0.236488	−	0.409609i	0.723216	−	0.690622i	$-0.242663\pi$
$563$	−3.17399e14	−	5.49751e14i	−0.236488	−	0.409609i	−0.959704	+	0.281013i	$0.909330\pi$
$564$	1.73701e14	+	3.00858e14i	0.128164	+	0.221987i
$565$	−1.51154e15	+	2.61806e15i	−1.10447	+	1.91299i
$566$	−7.72204e14			−0.558781
$567$	−8.96162e13	+	5.19359e14i	−0.0642214	+	0.372186i
$568$	7.88145e13			0.0559358
$569$	−3.27952e14	+	5.68030e14i	−0.230512	+	0.399258i	−0.957959	−	0.286906i	$-0.907373\pi$
$569$	−3.27952e14	+	5.68030e14i	−0.230512	+	0.399258i	0.727447	+	0.686164i	$0.240707\pi$
$570$	1.17353e15	+	2.03262e15i	0.816927	+	1.41496i
$571$	−8.48277e14	−	1.46926e15i	−0.584843	−	1.01298i	−0.994895	−	0.100916i	$-0.967823\pi$
$571$	−8.48277e14	−	1.46926e15i	−0.584843	−	1.01298i	0.410052	−	0.912062i	$-0.365511\pi$
$572$	−1.19858e14	+	2.07600e14i	−0.0818442	+	0.141758i
$573$	3.59256e14			0.242971
$574$	6.44373e14	−	2.37210e14i	0.431640	−	0.158898i
$575$	2.28759e15			1.51777
$576$	4.12734e13	−	7.14877e13i	0.0271236	−	0.0469794i
$577$	7.34164e14	+	1.27161e15i	0.477888	+	0.827726i	0.999679	−	0.0253472i	$-0.00806914\pi$
$577$	7.34164e14	+	1.27161e15i	0.477888	+	0.827726i	−0.521791	+	0.853074i	$0.674736\pi$
$578$	2.63442e14	+	4.56295e14i	0.169856	+	0.294200i
$579$	1.07128e15	−	1.85551e15i	0.684180	−	1.18503i
$580$	8.69561e14			0.550105
$581$	1.09509e15	+	9.12070e14i	0.686246	+	0.571557i
$582$	−1.44907e15			−0.899527
$583$	1.07998e15	−	1.87059e15i	0.664110	−	1.15027i
$584$	−3.01687e13	−	5.22537e13i	−0.0183775	−	0.0318307i
$585$	−2.89074e14	−	5.00691e14i	−0.174442	−	0.302143i
$586$	−3.74262e14	+	6.48241e14i	−0.223738	+	0.387525i
$587$	9.32618e14			0.552324			0.276162	−	0.961111i	$-0.410937\pi$
$587$	9.32618e14			0.552324			0.276162	+	0.961111i	$0.410937\pi$
$588$	−6.04078e14	−	2.14867e14i	−0.354420	−	0.126065i
$589$	2.83904e15			1.65020
$590$	−6.50560e14	+	1.12680e15i	−0.374629	+	0.648876i
$591$	−1.23991e15	−	2.14759e15i	−0.707393	−	1.22524i
$592$	−2.81391e14	−	4.87383e14i	−0.159052	−	0.275487i
$593$	2.42040e14	−	4.19225e14i	0.135546	−	0.234772i	−0.790260	−	0.612772i	$-0.790055\pi$
$593$	2.42040e14	−	4.19225e14i	0.135546	−	0.234772i	0.925806	+	0.378000i	$0.123388\pi$
$594$	−9.63017e14			−0.534329
$595$	−2.92518e15	−	2.43631e15i	−1.60808	−	1.33933i
$596$	−1.56219e14			−0.0850904
$597$	−2.55623e14	+	4.42752e14i	−0.137956	+	0.238947i
$598$	−2.39492e14	−	4.14812e14i	−0.128066	−	0.221817i
$599$	1.72211e15	+	2.98279e15i	0.912461	+	1.58043i	0.810576	+	0.585633i	$0.199154\pi$
$599$	1.72211e15	+	2.98279e15i	0.912461	+	1.58043i	0.101885	+	0.994796i	$0.467513\pi$
$600$	4.96116e14	−	8.59298e14i	0.260466	−	0.451140i
$601$	−1.43451e15			−0.746268			−0.373134	−	0.927778i	$-0.621717\pi$
$601$	−1.43451e15			−0.746268			−0.373134	+	0.927778i	$0.621717\pi$
$602$	7.56879e14	−	2.78626e14i	0.390163	−	0.143629i
$603$	−1.90837e14			−0.0974802
$604$	−8.11916e14	+	1.40628e15i	−0.410968	+	0.711817i
$605$	8.73401e14	+	1.51277e15i	0.438086	+	0.758786i
$606$	7.22943e12	+	1.25217e13i	0.00359339	+	0.00622394i
$607$	−5.74851e14	+	9.95671e14i	−0.283151	+	0.490431i	−0.972159	−	0.234322i	$-0.924713\pi$
$607$	−5.74851e14	+	9.95671e14i	−0.283151	+	0.490431i	0.689008	+	0.724753i	$0.258046\pi$
$608$	−6.46658e14			−0.315650
$609$	1.69163e14	−	9.80361e14i	0.0818295	−	0.474232i
$610$	−1.96614e15			−0.942542
$611$	−3.35189e14	+	5.80564e14i	−0.159244	+	0.275819i
$612$	−2.80371e14	−	4.85617e14i	−0.132008	−	0.228645i
$613$	1.03786e15	+	1.79763e15i	0.484293	+	0.838820i	0.999837	−	0.0180430i	$-0.00574358\pi$
$613$	1.03786e15	+	1.79763e15i	0.484293	+	0.838820i	−0.515544	+	0.856863i	$0.672410\pi$
$614$	5.53355e14	−	9.58439e14i	0.255904	−	0.443239i
$615$	1.83652e15			0.841747
$616$	9.26960e13	−	5.37208e14i	0.0421083	−	0.244033i
$617$	1.93418e14			0.0870822			0.0435411	−	0.999052i	$-0.486136\pi$
$617$	1.93418e14			0.0870822			0.0435411	+	0.999052i	$0.486136\pi$
$618$	7.23505e14	−	1.25315e15i	0.322853	−	0.559198i
$619$	−2.02998e15	−	3.51604e15i	−0.897830	−	1.55509i	−0.830262	−	0.557373i	$-0.811809\pi$
$619$	−2.02998e15	−	3.51604e15i	−0.897830	−	1.55509i	−0.0675677	−	0.997715i	$-0.521524\pi$
$620$	−9.06529e14	−	1.57016e15i	−0.397400	−	0.688317i
$621$	9.62118e14	−	1.66644e15i	0.418047	−	0.724078i
$622$	−2.40320e15			−1.03501
$623$	−8.43492e14	+	3.10510e14i	−0.360078	+	0.132554i
$624$	−2.07757e14			−0.0879105
$625$	−1.04550e15	+	1.81087e15i	−0.438516	+	0.759533i
$626$	6.07881e14	+	1.05288e15i	0.252732	+	0.437744i
$627$	1.14157e15	+	1.97726e15i	0.470469	+	0.814877i
$628$	8.20498e14	−	1.42114e15i	0.335197	−	0.580577i
$629$	−3.82298e15			−1.54819
$630$	1.01028e15	+	8.41434e14i	0.405571	+	0.337790i
$631$	−3.98410e15			−1.58551			−0.792754	−	0.609541i	$-0.791354\pi$
$631$	−3.98410e15			−1.58551			−0.792754	+	0.609541i	$0.791354\pi$
$632$	−4.51447e14	+	7.81929e14i	−0.178100	+	0.308478i
$633$	−1.35232e15	−	2.34229e15i	−0.528884	−	0.916054i
$634$	1.15818e14	+	2.00602e14i	0.0449039	+	0.0777758i
$635$	2.71012e15	−	4.69406e15i	1.04168	−	1.80424i
$636$	1.87200e15			0.713334
$637$	−2.23765e14	−	1.21683e15i	−0.0845330	−	0.459687i
$638$	8.45878e14			0.316807
$639$	−9.24542e13	+	1.60135e14i	−0.0343299	+	0.0594611i
$640$	2.06484e14	+	3.57640e14i	0.0760144	+	0.131661i
$641$	4.16479e14	+	7.21364e14i	0.152011	+	0.263290i	0.931967	−	0.362544i	$-0.118092\pi$
$641$	4.16479e14	+	7.21364e14i	0.152011	+	0.263290i	−0.779956	+	0.625835i	$0.784758\pi$
$642$	1.87169e14	−	3.24187e14i	0.0677318	−	0.117315i
$643$	3.12211e15			1.12018			0.560090	−	0.828432i	$-0.310767\pi$
$643$	3.12211e15			1.12018			0.560090	+	0.828432i	$0.310767\pi$
$644$	8.36993e14	+	6.97111e14i	0.297749	+	0.247987i
$645$	2.15717e15			0.760861
$646$	−2.19638e15	+	3.80424e15i	−0.768119	+	1.33042i
$647$	1.63841e15	+	2.83782e15i	0.568133	+	0.984036i	0.996751	+	0.0805495i	$0.0256675\pi$
$647$	1.63841e15	+	2.83782e15i	0.568133	+	0.984036i	−0.428617	+	0.903486i	$0.640999\pi$
$648$	−1.94186e14	−	3.36341e14i	−0.0667662	−	0.115642i
$649$	−6.32842e14	+	1.09611e15i	−0.215749	+	0.373689i
$650$	1.91470e15			0.647259
$651$	−1.94658e15	+	7.16585e14i	−0.652495	+	0.240200i
$652$	1.30575e15			0.434008
$653$	−8.72175e14	+	1.51065e15i	−0.287463	+	0.497900i	−0.973203	−	0.229946i	$-0.926145\pi$
$653$	−8.72175e14	+	1.51065e15i	−0.287463	+	0.497900i	0.685741	+	0.727846i	$0.259478\pi$
$654$	−4.92879e14	−	8.53692e14i	−0.161088	−	0.279012i
$655$	6.71702e14	+	1.16342e15i	0.217695	+	0.377060i
$656$	−2.52997e14	+	4.38203e14i	−0.0813100	+	0.140833i
$657$	1.41559e14			0.0451157
$658$	2.59230e14	−	1.50233e15i	0.0819299	−	0.474814i
$659$	−2.29700e15			−0.719931			−0.359965	−	0.932966i	$-0.617212\pi$
$659$	−2.29700e15			−0.719931			−0.359965	+	0.932966i	$0.617212\pi$
$660$	7.29028e14	−	1.26271e15i	0.226596	−	0.392476i
$661$	−5.25673e14	−	9.10492e14i	−0.162034	−	0.280652i	0.773564	−	0.633718i	$-0.218472\pi$
$661$	−5.25673e14	−	9.10492e14i	−0.162034	−	0.280652i	−0.935598	+	0.353067i	$0.885139\pi$
$662$	2.65516e14	+	4.59887e14i	0.0811655	+	0.140583i
$663$	−7.05649e14	+	1.22222e15i	−0.213926	+	0.370531i
$664$	−1.05021e15			−0.315755
$665$	1.75137e15	−	1.01498e16i	0.522227	−	3.02650i
$666$	1.32035e15			0.390465
$667$	−8.45089e14	+	1.46374e15i	−0.247862	+	0.429310i
$668$	4.60428e14	+	7.97484e14i	0.133934	+	0.231981i
$669$	7.33068e14	+	1.26971e15i	0.211495	+	0.366320i
$670$	4.77361e14	−	8.26813e14i	0.136595	−	0.236590i
$671$	−1.91260e15			−0.542812
$672$	4.43380e14	−	1.63219e14i	0.124809	−	0.0459453i
$673$	1.81381e15			0.506417			0.253208	−	0.967412i	$-0.418514\pi$
$673$	1.81381e15			0.506417			0.253208	+	0.967412i	$0.418514\pi$
$674$	7.18603e14	−	1.24466e15i	0.199003	−	0.344683i
$675$	3.84600e15	+	6.66147e15i	1.05642	+	1.82978i
$676$	7.17132e14	+	1.24211e15i	0.195386	+	0.338418i
$677$	−1.34262e15	+	2.32549e15i	−0.362840	+	0.628458i	−0.988427	−	0.151697i	$-0.951526\pi$
$677$	−1.34262e15	+	2.32549e15i	−0.362840	+	0.628458i	0.625587	+	0.780155i	$0.284860\pi$
$678$	−2.54869e15			−0.683208
$679$	4.88630e15	+	4.06968e15i	1.29926	+	1.08212i
$680$	2.80529e15			0.739911
$681$	−1.37857e15	+	2.38776e15i	−0.360679	+	0.624714i
$682$	−8.81840e14	−	1.52739e15i	−0.228863	−	0.396403i
$683$	−2.14946e15	−	3.72298e15i	−0.553371	−	0.958466i	−0.998028	−	0.0627655i	$-0.980008\pi$
$683$	−2.14946e15	−	3.72298e15i	−0.553371	−	0.958466i	0.444658	−	0.895701i	$-0.353325\pi$
$684$	7.58570e14	−	1.31388e15i	0.193726	−	0.335543i
$685$	−7.40412e15			−1.87575
$686$	1.43351e15	+	2.42107e15i	0.360263	+	0.608449i
$687$	−7.05994e14			−0.176011
$688$	−2.97169e14	+	5.14712e14i	−0.0734966	+	0.127300i
$689$	1.80620e15	+	3.12843e15i	0.443159	+	0.767574i
$690$	1.45669e15	+	2.52307e15i	0.354567	+	0.614128i
$691$	−3.40151e15	+	5.89158e15i	−0.821376	+	1.42267i	0.0832817	+	0.996526i	$0.473460\pi$
$691$	−3.40151e15	+	5.89158e15i	−0.821376	+	1.42267i	−0.904658	+	0.426139i	$0.859873\pi$
$692$	−4.13087e15			−0.989596
$693$	9.82762e14	+	8.18518e14i	0.233569	+	0.194534i
$694$	3.89290e15			0.917901
$695$	4.80533e15	−	8.32307e15i	1.12410	−	1.94700i
$696$	3.66554e14	+	6.34890e14i	0.0850720	+	0.147349i
$697$	1.71861e15	+	2.97672e15i	0.395728	+	0.685422i
$698$	−3.56670e14	+	6.17771e14i	−0.0814821	+	0.141131i
$699$	−7.75232e14			−0.175714
$700$	−4.08622e15	+	1.50424e15i	−0.918930	+	0.338281i
$701$	−3.11376e15			−0.694763			−0.347381	−	0.937724i	$-0.612929\pi$
$701$	−3.11376e15			−0.694763			−0.347381	+	0.937724i	$0.612929\pi$
$702$	8.05290e14	−	1.39480e15i	0.178278	−	0.308787i
$703$	−5.17172e15	−	8.95767e15i	−1.13601	−	1.96762i
$704$	2.00860e14	+	3.47900e14i	0.0437768	+	0.0758237i
$705$	2.03877e15	−	3.53125e15i	0.440887	−	0.763638i
$706$	5.62014e15			1.20593
$707$	1.07892e13	−	6.25272e13i	0.00229711	−	0.0133126i
$708$	−1.09695e15			−0.231741
$709$	7.68726e14	−	1.33147e15i	0.161145	−	0.279111i	−0.774135	−	0.633021i	$-0.781815\pi$
$709$	7.68726e14	−	1.33147e15i	0.161145	−	0.279111i	0.935280	+	0.353910i	$0.115148\pi$
$710$	−4.62532e14	−	8.01130e14i	−0.0962102	−	0.166641i
$711$	−1.05915e15	−	1.83450e15i	−0.218612	−	0.378648i
$712$	3.31176e14	−	5.73613e14i	0.0678295	−	0.117484i
$713$	3.52407e15			0.716229
$714$	5.45737e14	−	3.16275e15i	0.110064	−	0.637859i
$715$	2.81360e15			0.563092
$716$	6.09002e14	−	1.05482e15i	0.120948	−	0.209487i
$717$	−8.89940e14	−	1.54142e15i	−0.175390	−	0.303785i
$718$	−2.58790e15	−	4.48237e15i	−0.506131	−	0.876645i
$719$	−4.99680e14	+	8.65472e14i	−0.0969803	+	0.167975i	−0.910433	−	0.413656i	$-0.864252\pi$
$719$	−4.99680e14	+	8.65472e14i	−0.0969803	+	0.167975i	0.813453	+	0.581631i	$0.197585\pi$
$720$	−9.68873e14			−0.186611
$721$	−5.95909e15	+	2.19369e15i	−1.13903	+	0.419307i
$722$	−8.15733e15			−1.54737
$723$	−7.00275e14	+	1.21291e15i	−0.131828	+	0.228333i
$724$	−5.86604e14	−	1.01603e15i	−0.109593	−	0.189821i
$725$	−3.37818e15	−	5.85118e15i	−0.626360	−	1.08489i
$726$	−7.36345e14	+	1.27539e15i	−0.135497	+	0.234688i
$727$	−2.08683e15			−0.381108			−0.190554	−	0.981677i	$-0.561028\pi$
$727$	−2.08683e15			−0.381108			−0.190554	+	0.981677i	$0.561028\pi$
$728$	7.00560e14	+	5.83479e14i	0.126976	+	0.105755i
$729$	5.42326e15			0.975571
$730$	−3.54097e14	+	6.13315e14i	−0.0632189	+	0.109498i
$731$	2.01868e15	+	3.49645e15i	0.357702	+	0.619557i
$732$	−8.28806e14	−	1.43553e15i	−0.145761	−	0.252466i
$733$	4.40887e15	−	7.63638e15i	0.769583	−	1.33296i	−0.168207	−	0.985752i	$-0.553798\pi$
$733$	4.40887e15	−	7.63638e15i	0.769583	−	1.33296i	0.937790	−	0.347204i	$-0.112869\pi$
$734$	2.41548e14			0.0418481
$735$	1.36104e15	+	7.40128e15i	0.234040	+	1.27270i
$736$	−8.02691e14			−0.137000
$737$	4.64360e14	−	8.04295e14i	0.0786654	−	0.136252i
$738$	−5.93561e14	−	1.02808e15i	−0.0998058	−	0.172869i
$739$	1.07263e15	+	1.85784e15i	0.179021	+	0.310074i	0.941545	−	0.336886i	$-0.109374\pi$
$739$	1.07263e15	+	1.85784e15i	0.179021	+	0.310074i	−0.762524	+	0.646959i	$0.776040\pi$
$740$	−3.30275e15	+	5.72053e15i	−0.547143	+	0.947680i
$741$	−3.81840e15			−0.627886
$742$	−6.31243e15	−	5.25747e15i	−1.03033	−	0.858134i
$743$	1.27352e15			0.206332			0.103166	−	0.994664i	$-0.467103\pi$
$743$	1.27352e15			0.206332			0.103166	+	0.994664i	$0.467103\pi$
$744$	7.64275e14	−	1.32376e15i	0.122913	−	0.212892i
$745$	9.16792e14	+	1.58793e15i	0.146356	+	0.253497i
$746$	3.76362e15	+	6.51877e15i	0.596406	+	1.03300i
$747$	1.23196e15	−	2.13381e15i	0.193790	−	0.335655i
$748$	2.72889e15			0.426116
$749$	−1.54161e15	+	5.67504e14i	−0.238959	+	0.0879669i
$750$	−5.69945e15			−0.876992
$751$	2.64201e15	−	4.57610e15i	0.403566	−	0.698997i	−0.590587	−	0.806974i	$-0.701104\pi$
$751$	2.64201e15	−	4.57610e15i	0.403566	−	0.698997i	0.994153	+	0.107977i	$0.0344372\pi$
$752$	5.61717e14	+	9.72922e14i	0.0851764	+	0.147530i
$753$	−1.46395e15	−	2.53563e15i	−0.220371	−	0.381693i
$754$	−7.07336e14	+	1.22514e15i	−0.105702	+	0.183081i
$755$	1.90593e16			2.82748
$756$	−6.22798e14	+	3.60934e15i	−0.0917228	+	0.531567i
$757$	1.16812e15			0.170789			0.0853943	−	0.996347i	$-0.472785\pi$
$757$	1.16812e15			0.170789			0.0853943	+	0.996347i	$0.472785\pi$
$758$	9.59887e14	−	1.66257e15i	0.139328	−	0.241324i
$759$	1.41702e15	+	2.45435e15i	0.204196	+	0.353677i
$760$	3.79499e15	+	6.57312e15i	0.542920	+	0.940366i
$761$	2.88187e15	−	4.99155e15i	0.409316	−	0.708957i	−0.585497	−	0.810675i	$-0.699101\pi$
$761$	2.88187e15	−	4.99155e15i	0.409316	−	0.708957i	0.994813	+	0.101718i	$0.0324339\pi$
$762$	4.56968e15			0.644368
$763$	−7.35570e14	+	4.26290e15i	−0.102977	+	0.596788i
$764$	1.16177e15			0.161476
$765$	−3.29078e15	+	5.69980e15i	−0.454110	+	0.786542i
$766$	−2.38465e14	−	4.13033e14i	−0.0326713	−	0.0565883i
$767$	−1.05838e15	−	1.83318e15i	−0.143969	−	0.249362i
$768$	−1.74082e14	+	3.01519e14i	−0.0235108	+	0.0407219i
$769$	−6.97867e14			−0.0935788			−0.0467894	−	0.998905i	$-0.514899\pi$
$769$	−6.97867e14			−0.0935788			−0.0467894	+	0.998905i	$0.514899\pi$
$770$	−6.00458e15	+	2.21044e15i	−0.799436	+	0.294292i
$771$	−3.77271e15			−0.498717
$772$	3.46432e15	−	6.00039e15i	0.454698	−	0.787561i
$773$	7.91519e14	+	1.37095e15i	0.103151	+	0.178663i	0.912981	−	0.408001i	$-0.133774\pi$
$773$	7.91519e14	+	1.37095e15i	0.103151	+	0.178663i	−0.809830	+	0.586664i	$0.800441\pi$
$774$	−6.97196e14	−	1.20758e15i	−0.0902151	−	0.156257i
$775$	−7.04361e15	+	1.21999e16i	−0.904973	+	1.56746i
$776$	−4.68605e15			−0.597816
$777$	5.80693e15	+	4.83645e15i	0.735582	+	0.612648i
$778$	1.06373e16			1.33796
$779$	−4.64986e15	+	8.05379e15i	−0.580743	+	1.00588i
$780$	1.21925e15	+	2.11180e15i	0.151207	+	0.261898i
$781$	−4.49935e14	−	7.79311e14i	−0.0554076	−	0.0959688i
$782$	−2.72635e15	+	4.72217e15i	−0.333383	+	0.577437i
$783$	−5.68321e15			−0.690087
$784$	−1.95348e15	−	6.94841e14i	−0.235543	−	0.0837813i
$785$	−1.92608e16			−2.30617
$786$	−5.66297e14	+	9.80855e14i	−0.0673318	+	0.116622i
$787$	5.71998e15	+	9.90730e15i	0.675357	+	1.16975i	0.976364	+	0.216131i	$0.0693440\pi$
$787$	5.71998e15	+	9.90730e15i	0.675357	+	1.16975i	−0.301007	+	0.953622i	$0.597323\pi$
$788$	−4.00966e15	−	6.94494e15i	−0.470125	−	0.814281i
$789$	3.62552e15	−	6.27958e15i	0.422130	−	0.731151i
$790$	1.05975e16			1.22533
$791$	8.59421e15	+	7.15790e15i	0.986814	+	0.821893i
$792$	−9.42486e14			−0.107470
$793$	1.59934e15	−	2.77014e15i	0.181108	−	0.313689i
$794$	−2.50723e15	−	4.34265e15i	−0.281956	−	0.488362i
$795$	−1.09861e16	−	1.90285e16i	−1.22694	−	2.12512i
$796$	−8.26639e14	+	1.43178e15i	−0.0916841	+	0.158802i
$797$	8.30315e15			0.914581			0.457291	−	0.889317i	$-0.348820\pi$
$797$	8.30315e15			0.914581			0.457291	+	0.889317i	$0.348820\pi$
$798$	8.14894e15	−	2.99983e15i	0.891426	−	0.328156i
$799$	7.63150e15			0.829092
$800$	1.60435e15	−	2.77882e15i	0.173103	−	0.299823i
$801$	7.76979e14	+	1.34577e15i	0.0832588	+	0.144209i
$802$	−4.54809e15	−	7.87752e15i	−0.484027	−	0.838359i
$803$	−3.44454e14	+	5.96611e14i	−0.0364079	+	0.0630603i
$804$	8.04905e14			0.0844960
$805$	2.17396e15	−	1.25989e16i	0.226660	−	1.31358i
$806$	2.94963e15			0.305440
$807$	9.68020e14	−	1.67666e15i	0.0995588	−	0.172441i
$808$	2.33787e13	+	4.04931e13i	0.00238813	+	0.00413636i
$809$	−2.71897e15	−	4.70939e15i	−0.275859	−	0.477802i	0.694492	−	0.719500i	$-0.255629\pi$
$809$	−2.71897e15	−	4.70939e15i	−0.275859	−	0.477802i	−0.970351	+	0.241698i	$0.922296\pi$
$810$	−2.27921e15	+	3.94771e15i	−0.229677	+	0.397812i
$811$	1.07407e16			1.07502			0.537511	−	0.843257i	$-0.319365\pi$
$811$	1.07407e16			1.07502			0.537511	+	0.843257i	$0.319365\pi$
$812$	5.47042e14	−	3.17031e15i	0.0543830	−	0.315169i
$813$	3.42583e14			0.0338273
$814$	−3.21280e15	+	5.56473e15i	−0.315101	+	0.545771i
$815$	−7.66295e15	−	1.32726e16i	−0.746499	−	1.29297i
$816$	1.18254e15	+	2.04822e15i	0.114425	+	0.198190i
$817$	−5.46171e15	+	9.45996e15i	−0.524937	+	0.909218i
$818$	−8.95215e14			−0.0854642
$819$	−2.00732e15	+	7.38943e14i	−0.190351	+	0.0700728i
$820$	5.93897e15			0.559416
$821$	−4.49814e15	+	7.79100e15i	−0.420868	+	0.728964i	−0.996025	−	0.0890790i	$-0.971608\pi$
$821$	−4.49814e15	+	7.79100e15i	−0.420868	+	0.728964i	0.575157	+	0.818043i	$0.304941\pi$
$822$	−3.12113e15	−	5.40595e15i	−0.290079	−	0.502431i
$823$	−1.51454e15	−	2.62327e15i	−0.139824	−	0.242183i	0.787606	−	0.616180i	$-0.211320\pi$
$823$	−1.51454e15	−	2.62327e15i	−0.139824	−	0.242183i	−0.927430	+	0.373997i	$0.877987\pi$
$824$	2.33969e15	−	4.05245e15i	0.214565	−	0.371637i
$825$	−1.13289e16			−1.03203
$826$	3.69892e15	+	3.08074e15i	0.334722	+	0.278782i
$827$	−1.73797e16			−1.56229			−0.781146	−	0.624349i	$-0.785364\pi$
$827$	−1.73797e16			−1.56229			−0.781146	+	0.624349i	$0.785364\pi$
$828$	9.41606e14	−	1.63091e15i	0.0840819	−	0.145634i
$829$	−5.68518e15	−	9.84703e15i	−0.504307	−	0.873485i	−0.999988	−	0.00497994i	$-0.998415\pi$
$829$	−5.68518e15	−	9.84703e15i	−0.504307	−	0.873485i	0.495681	−	0.868505i	$-0.334919\pi$
$830$	6.16327e15	+	1.06751e16i	0.543102	+	0.940680i
$831$	−1.62782e15	+	2.81946e15i	−0.142495	+	0.246809i
$832$	−6.71850e14			−0.0584243
$833$	−1.07227e16	+	9.13215e15i	−0.926312	+	0.788907i
$834$	8.10253e15			0.695356
$835$	5.40415e15	−	9.36027e15i	0.460736	−	0.798018i
$836$	3.69164e15	+	6.39410e15i	0.312669	+	0.541558i
$837$	5.92483e15	+	1.02621e16i	0.498524	+	0.863468i
$838$	−5.28095e15	+	9.14688e15i	−0.441439	+	0.764594i
$839$	7.75755e14			0.0644219			0.0322109	−	0.999481i	$-0.489745\pi$
$839$	7.75755e14			0.0644219			0.0322109	+	0.999481i	$0.489745\pi$
$840$	−4.26111e15	−	3.54898e15i	−0.351550	−	0.292797i
$841$	−7.20859e15			−0.590843
$842$	−4.55679e15	+	7.89260e15i	−0.371059	+	0.642693i
$843$	−4.19087e15	−	7.25880e15i	−0.339041	−	0.587236i
$844$	−4.37318e15	−	7.57456e15i	−0.351490	−	0.608799i
$845$	8.41716e15	−	1.45789e16i	0.672130	−	1.16416i
$846$	−2.63571e15			−0.209103
$847$	6.06485e15	−	2.23262e15i	0.478037	−	0.175977i
$848$	6.05373e15			0.474074
$849$	−3.82064e15	+	6.61754e15i	−0.297265	+	0.514878i
$850$	−1.08984e16	−	1.88765e16i	−0.842476	−	1.45921i
$851$	−6.41961e15	−	1.11191e16i	−0.493055	−	0.853997i
$852$	3.89951e14	−	6.75415e14i	0.0297572	−	0.0515410i
$853$	1.32476e16			1.00443			0.502213	−	0.864744i	$-0.332519\pi$
$853$	1.32476e16			1.00443			0.502213	+	0.864744i	$0.332519\pi$
$854$	−1.23690e15	+	7.16832e15i	−0.0931790	+	0.540006i
$855$	−1.78070e16			−1.33284
$856$	6.05273e14	−	1.04836e15i	0.0450138	−	0.0779661i
$857$	1.01543e16	+	1.75878e16i	0.750339	+	1.29963i	0.947658	+	0.319286i	$0.103443\pi$
$857$	1.01543e16	+	1.75878e16i	0.750339	+	1.29963i	−0.197320	+	0.980339i	$0.563224\pi$
$858$	1.18604e15	+	2.05429e15i	0.0870803	+	0.150828i
$859$	−4.32609e15	+	7.49302e15i	−0.315598	+	0.546631i	−0.979564	−	0.201131i	$-0.935538\pi$
$859$	−4.32609e15	+	7.49302e15i	−0.315598	+	0.546631i	0.663967	+	0.747762i	$0.268872\pi$
$860$	6.97589e15			0.505660
$861$	1.15536e15	−	6.69572e15i	0.0832144	−	0.482258i
$862$	7.08924e15			0.507353
$863$	8.96775e15	−	1.55326e16i	0.637712	−	1.10455i	−0.348222	−	0.937412i	$-0.613214\pi$
$863$	8.96775e15	−	1.55326e16i	0.637712	−	1.10455i	0.985934	−	0.167137i	$-0.0534522\pi$
$864$	−1.34952e15	−	2.33744e15i	−0.0953574	−	0.165164i
$865$	2.42425e16	+	4.19893e16i	1.70212	+	2.94815i
$866$	−1.47374e15	+	2.55259e15i	−0.102819	+	0.178087i
$867$	5.21374e15			0.361447
$868$	−6.29489e15	+	2.31731e15i	−0.433641	+	0.159634i
$869$	1.03089e16			0.705671
$870$	4.30233e15	−	7.45185e15i	0.292650	−	0.506884i
$871$	7.76610e14	+	1.34513e15i	0.0524932	+	0.0909209i
$872$	−1.59388e15	−	2.76069e15i	−0.107057	−	0.185428i
$873$	5.49703e15	−	9.52113e15i	0.366901	−	0.635492i
$874$	−1.47528e16			−0.978500
$875$	1.92186e16	+	1.60067e16i	1.26671	+	1.05501i
$876$	−5.97063e14			−0.0391064
$877$	2.96085e15	−	5.12835e15i	0.192717	−	0.333795i	−0.753433	−	0.657525i	$-0.771604\pi$
$877$	2.96085e15	−	5.12835e15i	0.192717	−	0.333795i	0.946150	+	0.323730i	$0.104937\pi$
$878$	−3.52814e15	−	6.11091e15i	−0.228205	−	0.395263i
$879$	3.70348e15	+	6.41461e15i	0.238051	+	0.412317i
$880$	2.35755e15	−	4.08339e15i	0.150593	−	0.260835i
$881$	−1.75489e16			−1.11399			−0.556996	−	0.830515i	$-0.688046\pi$
$881$	−1.75489e16			−1.11399			−0.556996	+	0.830515i	$0.688046\pi$
$882$	3.70333e15	−	3.15400e15i	0.233623	−	0.198968i
$883$	1.15068e16			0.721392			0.360696	−	0.932684i	$-0.382539\pi$
$883$	1.15068e16			0.721392			0.360696	+	0.932684i	$0.382539\pi$
$884$	−2.28194e15	+	3.95244e15i	−0.142173	+	0.246251i
$885$	6.43756e15	+	1.11502e16i	0.398596	+	0.690389i
$886$	7.92200e15	+	1.37213e16i	0.487472	+	0.844326i
$887$	1.40939e15	−	2.44113e15i	0.0861886	−	0.149283i	−0.819708	−	0.572781i	$-0.805865\pi$
$887$	1.40939e15	−	2.44113e15i	0.0861886	−	0.149283i	0.905897	+	0.423498i	$0.139198\pi$
$888$	−5.56895e15			−0.338456
$889$	−1.54090e16	−	1.28338e16i	−0.930713	−	0.775168i
$890$	−7.77418e15			−0.466669
$891$	−2.21714e15	+	3.84020e15i	−0.132271	+	0.229101i
$892$	2.37061e15	+	4.10602e15i	0.140557	+	0.243452i
$893$	1.03239e16	+	1.78815e16i	0.608358	+	1.05371i
$894$	−7.72927e14	+	1.33875e15i	−0.0452671	+	0.0784049i
$895$	−1.42960e16			−0.832124
$896$	1.43381e15	−	5.27822e14i	0.0829466	−	0.0305347i
$897$	−4.73974e15			−0.272519
$898$	3.47803e14	−	6.02413e14i	0.0198753	−	0.0344250i
$899$	−5.20415e15	−	9.01385e15i	−0.295578	−	0.511955i
$900$	3.76400e15	+	6.51944e15i	0.212479	+	0.368025i
$901$	2.05615e16	−	3.56136e16i	1.15364	−	1.99816i
$902$	5.77722e15			0.322168
$903$	1.35708e15	−	7.86477e15i	0.0752181	−	0.435917i
$904$	−8.24200e15			−0.454053
$905$	−6.88512e15	+	1.19254e16i	−0.377002	+	0.652987i
$906$	8.03424e15	+	1.39157e16i	0.437260	+	0.757357i
$907$	−8.05870e15	−	1.39581e16i	−0.435938	−	0.755067i	0.561433	−	0.827522i	$-0.310250\pi$
$907$	−8.05870e15	−	1.39581e16i	−0.435938	−	0.755067i	−0.997372	+	0.0724547i	$0.976917\pi$
$908$	−4.45806e15	+	7.72159e15i	−0.239703	+	0.415178i
$909$	−1.09699e14			−0.00586273
$910$	1.81960e15	−	1.05452e16i	0.0966602	−	0.560182i
$911$	−3.29746e15			−0.174112			−0.0870560	−	0.996203i	$-0.527746\pi$
$911$	−3.29746e15			−0.174112			−0.0870560	+	0.996203i	$0.527746\pi$
$912$	−3.19947e15	+	5.54165e15i	−0.167922	+	0.290849i
$913$	5.99541e15	+	1.03844e16i	0.312773	+	0.541739i
$914$	−1.11556e16	−	1.93220e16i	−0.578479	−	1.00195i
$915$	−9.72790e15	+	1.68492e16i	−0.501421	+	0.868487i
$916$	−2.28306e15			−0.116975
$917$	4.66426e15	−	1.71703e15i	0.237548	−	0.0874474i
$918$	−1.83346e16			−0.928192
$919$	−3.65486e14	+	6.33041e14i	−0.0183923	+	0.0318564i	−0.875075	−	0.483987i	$-0.839188\pi$
$919$	−3.65486e14	+	6.33041e14i	−0.0183923	+	0.0318564i	0.856683	+	0.515844i	$0.172521\pi$
$920$	4.71069e15	+	8.15916e15i	0.235641	+	0.408143i
$921$	−5.47567e15	−	9.48415e15i	−0.272276	−	0.471596i
$922$	−4.26175e15	+	7.38157e15i	−0.210653	+	0.364862i
$923$	1.50497e15			0.0739467
$924$	−4.14506e15	−	3.45232e15i	−0.202458	−	0.168622i
$925$	5.13238e16			2.49195
$926$	2.89037e15	−	5.00627e15i	0.139506	−	0.241632i
$927$	5.48919e15	+	9.50756e15i	0.263372	+	0.456174i
$928$	1.18537e15	+	2.05312e15i	0.0565379	+	0.0979266i
$929$	−4.35522e13	+	7.54347e13i	−0.00206502	+	0.00357672i	−0.867056	−	0.498211i	$-0.833991\pi$
$929$	−4.35522e13	+	7.54347e13i	−0.00206502	+	0.00357672i	0.864991	+	0.501787i	$0.167324\pi$
$930$	−1.79410e16			−0.845648
$931$	−3.59033e16	−	1.27706e16i	−1.68233	−	0.598394i
$932$	−2.50696e15			−0.116778
$933$	−1.18903e16	+	2.05947e16i	−0.550611	+	0.953686i
$934$	1.14100e16	+	1.97627e16i	0.525265	+	0.909785i
$935$	−1.60148e16	−	2.77385e16i	−0.732924	−	1.26946i
$936$	7.88121e14	−	1.36507e15i	0.0358571	−	0.0621064i
$937$	−2.38126e16			−1.07706			−0.538530	−	0.842607i	$-0.681020\pi$
$937$	−2.38126e16			−1.07706			−0.538530	+	0.842607i	$0.681020\pi$
$938$	−2.71415e15	−	2.26055e15i	−0.122045	−	0.101648i
$939$	1.20305e16			0.537801
$940$	6.59301e15	−	1.14194e16i	0.293009	−	0.507506i
$941$	−1.76098e16	−	3.05011e16i	−0.778059	−	1.34764i	−0.933059	−	0.359723i	$-0.882871\pi$
$941$	−1.76098e16	−	3.05011e16i	−0.778059	−	1.34764i	0.155000	−	0.987914i	$-0.450462\pi$
$942$	−8.11917e15	−	1.40628e16i	−0.356641	−	0.617721i
$943$	−5.77183e15	+	9.99710e15i	−0.252057	+	0.436576i
$944$	−3.54733e15			−0.154012
$945$	4.03430e16	−	1.48513e16i	1.74138	−	0.641046i
$946$	6.78591e15			0.291210
$947$	−3.37685e15	+	5.84888e15i	−0.144075	+	0.249544i	−0.929027	−	0.370011i	$-0.879354\pi$
$947$	−3.37685e15	+	5.84888e15i	−0.144075	+	0.249544i	0.784953	+	0.619556i	$0.212687\pi$
$948$	4.46726e15	+	7.73751e15i	0.189494	+	0.328213i
$949$	−5.76075e14	−	9.97791e14i	−0.0242949	−	0.0420800i
$950$	2.94866e16	−	5.10722e16i	1.23636	−	2.14144i
$951$	2.29213e15			0.0955533
$952$	1.76482e15	−	1.02278e16i	0.0731470	−	0.423914i
$953$	2.08782e16			0.860363			0.430181	−	0.902742i	$-0.358450\pi$
$953$	2.08782e16			0.860363			0.430181	+	0.902742i	$0.358450\pi$
$954$	−7.10140e15	+	1.23000e16i	−0.290956	+	0.503951i
$955$	−6.81799e15	−	1.18091e16i	−0.277740	−	0.481059i
$956$	−2.87791e15	−	4.98468e15i	−0.116562	−	0.201892i
$957$	4.18516e15	−	7.24890e15i	0.168537	−	0.291915i
$958$	1.22959e16			0.492325
$959$	−4.65795e15	+	2.69945e16i	−0.185435	+	1.07467i
$960$	4.08648e15			0.161755
$961$	1.85344e15	−	3.21025e15i	0.0729456	−	0.126346i
$962$	−5.37319e15	−	9.30663e15i	−0.210266	−	0.364191i
$963$	1.42004e15	+	2.45959e15i	0.0552532	+	0.0957013i
$964$	−2.26457e15	+	3.92234e15i	−0.0876115	+	0.151748i
$965$	−8.13232e16			−3.12834
$966$	1.01152e16	−	3.72366e15i	0.386902	−	0.142428i
$967$	−1.65586e16			−0.629766			−0.314883	−	0.949130i	$-0.601965\pi$
$967$	−1.65586e16			−0.629766			−0.314883	+	0.949130i	$0.601965\pi$
$968$	−2.38121e15	+	4.12437e15i	−0.0900498	+	0.155971i
$969$	2.17341e16	+	3.76445e16i	0.817261	+	1.41554i
$970$	2.75007e16	+	4.76325e16i	1.02825	+	1.78098i
$971$	2.20252e16	−	3.81487e16i	0.818867	−	1.41832i	−0.0876514	−	0.996151i	$-0.527936\pi$
$971$	2.20252e16	−	3.81487e16i	0.818867	−	1.41832i	0.906518	−	0.422167i	$-0.138731\pi$
$972$	1.07482e16			0.397347
$973$	−2.73219e16	−	2.27557e16i	−1.00436	−	0.836507i
$974$	−5.98773e15			−0.218871
$975$	9.47339e15	−	1.64084e16i	0.344334	−	0.596404i
$976$	−2.68021e15	−	4.64226e15i	−0.0968713	−	0.167786i
$977$	8.24600e15	+	1.42825e16i	0.296362	+	0.513315i	0.975301	−	0.220880i	$-0.0708930\pi$
$977$	8.24600e15	+	1.42825e16i	0.296362	+	0.513315i	−0.678938	+	0.734195i	$0.737560\pi$
$978$	6.46046e15	−	1.11898e16i	0.230887	−	0.399908i
$979$	−7.56245e15			−0.268756
$980$	4.40136e15	+	2.39344e16i	0.155540	+	0.845823i
$981$	7.47889e15			0.262820
$982$	5.80286e15	−	1.00508e16i	0.202782	−	0.351228i
$983$	1.78403e16	+	3.09004e16i	0.619953	+	1.07379i	0.989494	+	0.144575i	$0.0461815\pi$
$983$	1.78403e16	+	3.09004e16i	0.619953	+	1.07379i	−0.369541	+	0.929214i	$0.620485\pi$
$984$	2.50351e15	+	4.33620e15i	0.0865119	+	0.149843i
$985$	−4.70624e16	+	8.15144e16i	−1.61724	+	2.80114i
$986$	1.61045e16			0.550330
$987$	−1.15919e16	−	9.65461e15i	−0.393922	−	0.328088i
$988$	−1.23480e16			−0.417286
$989$	−6.77958e15	+	1.17426e16i	−0.227836	+	0.394624i
$990$	5.53109e15	+	9.58013e15i	0.184849	+	0.320168i
$991$	1.46282e16	+	2.53368e16i	0.486168	+	0.842067i	0.999874	−	0.0158991i	$-0.00506105\pi$
$991$	1.46282e16	+	2.53368e16i	0.486168	+	0.842067i	−0.513706	+	0.857966i	$0.671728\pi$
$992$	2.47153e15	−	4.28081e15i	0.0816867	−	0.141486i
$993$	5.25478e15			0.172716
$994$	−3.21180e15	+	1.18234e15i	−0.104984	+	0.0386473i
$995$	1.94049e16			0.630791
$996$	−5.19612e15	+	8.99994e15i	−0.167978	+	0.290946i
$997$	−9.38310e15	−	1.62520e16i	−0.301664	−	0.522497i	0.674849	−	0.737956i	$-0.264209\pi$
$997$	−9.38310e15	−	1.62520e16i	−0.301664	−	0.522497i	−0.976513	+	0.215459i	$0.930875\pi$
$998$	6.34658e14	+	1.09926e15i	0.0202918	+	0.0351465i
$999$	2.15859e16	−	3.73878e16i	0.686372	−	1.18883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.12.c.b.9.2	✓	8
3.2	odd	2		126.12.g.c.37.4		8
4.3	odd	2		112.12.i.b.65.3		8
7.2	even	3		98.12.a.i.1.3		4
7.3	odd	6		98.12.c.n.67.3		8
7.4	even	3	inner	14.12.c.b.11.2	yes	8
7.5	odd	6		98.12.a.h.1.2		4
7.6	odd	2		98.12.c.n.79.3		8
21.11	odd	6		126.12.g.c.109.4		8
28.11	odd	6		112.12.i.b.81.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.12.c.b.9.2	✓	8	1.1	even	1	trivial
14.12.c.b.11.2	yes	8	7.4	even	3	inner
98.12.a.h.1.2		4	7.5	odd	6
98.12.a.i.1.3		4	7.2	even	3
98.12.c.n.67.3		8	7.3	odd	6
98.12.c.n.79.3		8	7.6	odd	2
112.12.i.b.65.3		8	4.3	odd	2
112.12.i.b.81.3		8	28.11	odd	6
126.12.g.c.37.4		8	3.2	odd	2
126.12.g.c.109.4		8	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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(16.0000 - 27.7128i) q^{2} +(-158.327 - 274.230i) q^{3} +(-512.000 - 886.810i) q^{4} +(-6009.47 + 10408.7i) q^{5} -10132.9 q^{6} +(34168.3 + 28457.9i) q^{7} -32768.0 q^{8} +(38438.9 - 66578.1i) q^{9} +O(q^{10})\)	\(q+(16.0000 - 27.7128i) q^{2} +(-158.327 - 274.230i) q^{3} +(-512.000 - 886.810i) q^{4} +(-6009.47 + 10408.7i) q^{5} -10132.9 q^{6} +(34168.3 + 28457.9i) q^{7} -32768.0 q^{8} +(38438.9 - 66578.1i) q^{9} +(192303. + 333079. i) q^{10} +(187066. + 324007. i) q^{11} +(-162126. + 280811. i) q^{12} -625709. q^{13} +(1.33534e6 - 491573. i) q^{14} +3.80583e6 q^{15} +(-524288. + 908093. i) q^{16} +(3.56150e6 + 6.16869e6i) q^{17} +(-1.23004e6 - 2.13050e6i) q^{18} +(-9.63596e6 + 1.66900e7i) q^{19} +1.23074e7 q^{20} +(2.39426e6 - 1.38756e7i) q^{21} +1.19722e7 q^{22} +(-1.19610e7 + 2.07171e7i) q^{23} +(5.18805e6 + 8.98596e6i) q^{24} +(-4.78134e7 - 8.28152e7i) q^{25} +(-1.00113e7 + 1.73401e7i) q^{26} -8.04377e7 q^{27} +(7.74261e6 - 4.48713e7i) q^{28} +7.06535e7 q^{29} +(6.08934e7 - 1.05470e8i) q^{30} +(-7.36573e7 - 1.27578e8i) q^{31} +(1.67772e7 + 2.90590e7i) q^{32} +(5.92349e7 - 1.02598e8i) q^{33} +2.27936e8 q^{34} +(-5.01544e8 + 1.84631e8i) q^{35} -7.87228e7 q^{36} +(-2.68355e8 + 4.64805e8i) q^{37} +(3.08351e8 + 5.34079e8i) q^{38} +(9.90663e7 + 1.71588e8i) q^{39} +(1.96918e8 - 3.41072e8i) q^{40} +4.82553e8 q^{41} +(-3.46224e8 - 2.88361e8i) q^{42} +5.66805e8 q^{43} +(1.91555e8 - 3.31783e8i) q^{44} +(4.61994e8 + 8.00198e8i) q^{45} +(3.82753e8 + 6.62948e8i) q^{46} +(5.35695e8 - 9.27851e8i) q^{47} +3.32035e8 q^{48} +(3.57619e8 + 1.94472e9i) q^{49} -3.06005e9 q^{50} +(1.12776e9 - 1.95334e9i) q^{51} +(3.20363e8 + 5.54885e8i) q^{52} +(-2.88664e9 - 4.99981e9i) q^{53} +(-1.28700e9 + 2.22916e9i) q^{54} -4.49666e9 q^{55} +(-1.11963e9 - 9.32509e8i) q^{56} +6.10251e9 q^{57} +(1.13046e9 - 1.95801e9i) q^{58} +(1.69150e9 + 2.92976e9i) q^{59} +(-1.94859e9 - 3.37505e9i) q^{60} +(-2.55605e9 + 4.42721e9i) q^{61} -4.71407e9 q^{62} +(3.20807e9 - 1.18097e9i) q^{63} +1.07374e9 q^{64} +(3.76018e9 - 6.51282e9i) q^{65} +(-1.89552e9 - 3.28313e9i) q^{66} +(-1.24117e9 - 2.14977e9i) q^{67} +(3.64697e9 - 6.31674e9i) q^{68} +7.57500e9 q^{69} +(-2.90806e9 + 1.68533e10i) q^{70} -2.40523e9 q^{71} +(-1.25957e9 + 2.18163e9i) q^{72} +(9.20676e8 + 1.59466e9i) q^{73} +(8.58736e9 + 1.48737e10i) q^{74} +(-1.51403e10 + 2.62237e10i) q^{75} +1.97344e10 q^{76} +(-2.82886e9 + 1.63943e10i) q^{77} +6.34025e9 q^{78} +(1.37771e10 - 2.38626e10i) q^{79} +(-6.30138e9 - 1.09143e10i) q^{80} +(5.92610e9 + 1.02643e10i) q^{81} +(7.72085e9 - 1.33729e10i) q^{82} +3.20498e10 q^{83} +(-1.35309e10 + 4.98106e9i) q^{84} -8.56108e10 q^{85} +(9.06888e9 - 1.57078e10i) q^{86} +(-1.11863e10 - 1.93753e10i) q^{87} +(-6.12977e9 - 1.06171e10i) q^{88} +(-1.01067e10 + 1.75053e10i) q^{89} +2.95676e10 q^{90} +(-2.13794e10 - 1.78064e10i) q^{91} +2.44962e10 q^{92} +(-2.33238e10 + 4.03980e10i) q^{93} +(-1.71422e10 - 2.96912e10i) q^{94} +(-1.15814e11 - 2.00596e11i) q^{95} +(5.31256e9 - 9.20162e9i) q^{96} +1.43007e11 q^{97} +(5.96155e10 + 2.12049e10i) q^{98} +2.87624e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 128 q^{2} - 266 q^{3} - 4096 q^{4} + 3808 q^{5} - 17024 q^{6} + 110328 q^{7} - 262144 q^{8} - 503848 q^{9}+O(q^{10}) \) 8 * q + 128 * q^2 - 266 * q^3 - 4096 * q^4 + 3808 * q^5 - 17024 * q^6 + 110328 * q^7 - 262144 * q^8 - 503848 * q^9	\( 8 q + 128 q^{2} - 266 q^{3} - 4096 q^{4} + 3808 q^{5} - 17024 q^{6} + 110328 q^{7} - 262144 q^{8} - 503848 q^{9} - 121856 q^{10} + 920150 q^{11} - 272384 q^{12} + 997472 q^{13} + 1396800 q^{14} - 500444 q^{15} - 4194304 q^{16} + 1333724 q^{17} + 16123136 q^{18} - 21551726 q^{19} - 7798784 q^{20} - 90442480 q^{21} + 58889600 q^{22} + 72510158 q^{23} + 8716288 q^{24} - 77154744 q^{25} + 15959552 q^{26} + 156683212 q^{27} - 68278272 q^{28} + 213575104 q^{29} - 8007104 q^{30} - 194359774 q^{31} + 134217728 q^{32} - 164547124 q^{33} + 85358336 q^{34} - 981719074 q^{35} + 1031880704 q^{36} + 171517048 q^{37} + 689655232 q^{38} - 653125236 q^{39} - 124780544 q^{40} - 3312095136 q^{41} - 1152719104 q^{42} + 850279648 q^{43} + 942233600 q^{44} + 6784014272 q^{45} - 2320325056 q^{46} + 2223880974 q^{47} + 557842432 q^{48} - 4232044312 q^{49} - 4937903616 q^{50} + 6968362082 q^{51} - 510705664 q^{52} - 7185483360 q^{53} + 2506931392 q^{54} + 624915620 q^{55} - 3615227904 q^{56} + 4959469112 q^{57} + 3417201664 q^{58} + 6997401502 q^{59} + 256227328 q^{60} - 6476463280 q^{61} - 12439025536 q^{62} - 17252507684 q^{63} + 8589934592 q^{64} + 30625528248 q^{65} + 5265507968 q^{66} - 18660972186 q^{67} + 1365733376 q^{68} + 31319762096 q^{69} - 27279047488 q^{70} + 23224449248 q^{71} + 16510091264 q^{72} + 3731641452 q^{73} - 5488545536 q^{74} - 91204646176 q^{75} + 44137934848 q^{76} - 29345595440 q^{77} - 41800015104 q^{78} + 12221157926 q^{79} + 3992977408 q^{80} - 97333443028 q^{81} - 52993522176 q^{82} + 316739523968 q^{83} + 55726088192 q^{84} - 147794862544 q^{85} + 13604474368 q^{86} - 218122807364 q^{87} - 30151475200 q^{88} - 71204406084 q^{89} + 434176913408 q^{90} + 189816116528 q^{91} - 148500803584 q^{92} + 9838293624 q^{93} - 71164191168 q^{94} - 215091896614 q^{95} + 8925478912 q^{96} + 688251797184 q^{97} + 137152279424 q^{98} - 545487662552 q^{99}+O(q^{100}) \) 8 * q + 128 * q^2 - 266 * q^3 - 4096 * q^4 + 3808 * q^5 - 17024 * q^6 + 110328 * q^7 - 262144 * q^8 - 503848 * q^9 - 121856 * q^10 + 920150 * q^11 - 272384 * q^12 + 997472 * q^13 + 1396800 * q^14 - 500444 * q^15 - 4194304 * q^16 + 1333724 * q^17 + 16123136 * q^18 - 21551726 * q^19 - 7798784 * q^20 - 90442480 * q^21 + 58889600 * q^22 + 72510158 * q^23 + 8716288 * q^24 - 77154744 * q^25 + 15959552 * q^26 + 156683212 * q^27 - 68278272 * q^28 + 213575104 * q^29 - 8007104 * q^30 - 194359774 * q^31 + 134217728 * q^32 - 164547124 * q^33 + 85358336 * q^34 - 981719074 * q^35 + 1031880704 * q^36 + 171517048 * q^37 + 689655232 * q^38 - 653125236 * q^39 - 124780544 * q^40 - 3312095136 * q^41 - 1152719104 * q^42 + 850279648 * q^43 + 942233600 * q^44 + 6784014272 * q^45 - 2320325056 * q^46 + 2223880974 * q^47 + 557842432 * q^48 - 4232044312 * q^49 - 4937903616 * q^50 + 6968362082 * q^51 - 510705664 * q^52 - 7185483360 * q^53 + 2506931392 * q^54 + 624915620 * q^55 - 3615227904 * q^56 + 4959469112 * q^57 + 3417201664 * q^58 + 6997401502 * q^59 + 256227328 * q^60 - 6476463280 * q^61 - 12439025536 * q^62 - 17252507684 * q^63 + 8589934592 * q^64 + 30625528248 * q^65 + 5265507968 * q^66 - 18660972186 * q^67 + 1365733376 * q^68 + 31319762096 * q^69 - 27279047488 * q^70 + 23224449248 * q^71 + 16510091264 * q^72 + 3731641452 * q^73 - 5488545536 * q^74 - 91204646176 * q^75 + 44137934848 * q^76 - 29345595440 * q^77 - 41800015104 * q^78 + 12221157926 * q^79 + 3992977408 * q^80 - 97333443028 * q^81 - 52993522176 * q^82 + 316739523968 * q^83 + 55726088192 * q^84 - 147794862544 * q^85 + 13604474368 * q^86 - 218122807364 * q^87 - 30151475200 * q^88 - 71204406084 * q^89 + 434176913408 * q^90 + 189816116528 * q^91 - 148500803584 * q^92 + 9838293624 * q^93 - 71164191168 * q^94 - 215091896614 * q^95 + 8925478912 * q^96 + 688251797184 * q^97 + 137152279424 * q^98 - 545487662552 * q^99

Introduction

L-functions

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