LMFDB - Embedded newform 14.12.c.b.11.1

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			11.1
Root			$-178.705 + 309.527i$ of defining polynomial
Character	$\chi$	$=$	14.11
Dual form			14.12.c.b.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16.0000 + 27.7128i) q^{2} +(-390.910 + 677.077i) q^{3} +(-512.000 + 886.810i) q^{4} +(4992.28 + 8646.88i) q^{5} -25018.3 q^{6} +(24330.9 + 37220.1i) q^{7} -32768.0 q^{8} +(-217048. - 375939. i) q^{9} +O(q^{10})$	\(q+(16.0000 + 27.7128i) q^{2} +(-390.910 + 677.077i) q^{3} +(-512.000 + 886.810i) q^{4} +(4992.28 + 8646.88i) q^{5} -25018.3 q^{6} +(24330.9 + 37220.1i) q^{7} -32768.0 q^{8} +(-217048. - 375939. i) q^{9} +(-159753. + 276700. i) q^{10} +(79178.4 - 137141. i) q^{11} +(-400292. - 693327. i) q^{12} +1.79763e6 q^{13} +(-642178. + 1.26980e6i) q^{14} -7.80614e6 q^{15} +(-524288. - 908093. i) q^{16} +(1.39628e6 - 2.41842e6i) q^{17} +(6.94555e6 - 1.20300e7i) q^{18} +(374482. + 648622. i) q^{19} -1.02242e7 q^{20} +(-3.47121e7 + 1.92417e6i) q^{21} +5.06742e6 q^{22} +(1.66245e7 + 2.87945e7i) q^{23} +(1.28094e7 - 2.21865e7i) q^{24} +(-2.54317e7 + 4.40490e7i) q^{25} +(2.87621e7 + 4.98174e7i) q^{26} +2.00889e8 q^{27} +(-4.54646e7 + 2.52021e6i) q^{28} +9.28902e7 q^{29} +(-1.24898e8 - 2.16330e8i) q^{30} +(-1.41494e7 + 2.45075e7i) q^{31} +(1.67772e7 - 2.90590e7i) q^{32} +(6.19033e7 + 1.07220e8i) q^{33} +8.93618e7 q^{34} +(-2.00371e8 + 3.96200e8i) q^{35} +4.44515e8 q^{36} +(-3.28309e8 - 5.68647e8i) q^{37} +(-1.19834e7 + 2.07559e7i) q^{38} +(-7.02712e8 + 1.21713e9i) q^{39} +(-1.63587e8 - 2.83341e8i) q^{40} -5.18887e8 q^{41} +(-6.08717e8 - 9.31182e8i) q^{42} +4.47337e7 q^{43} +(8.10787e7 + 1.40432e8i) q^{44} +(2.16713e9 - 3.75359e9i) q^{45} +(-5.31985e8 + 9.21425e8i) q^{46} +(-3.99885e8 - 6.92620e8i) q^{47} +8.19799e8 q^{48} +(-7.93341e8 + 1.81120e9i) q^{49} -1.62763e9 q^{50} +(1.09164e9 + 1.89077e9i) q^{51} +(-9.20386e8 + 1.59416e9i) q^{52} +(5.54293e8 - 9.60064e8i) q^{53} +(3.21422e9 + 5.56720e9i) q^{54} +1.58112e9 q^{55} +(-7.97275e8 - 1.21963e9i) q^{56} -5.85556e8 q^{57} +(1.48624e9 + 2.57425e9i) q^{58} +(-2.10667e9 + 3.64887e9i) q^{59} +(3.99674e9 - 6.92256e9i) q^{60} +(-3.73122e9 - 6.46267e9i) q^{61} -9.05561e8 q^{62} +(8.71149e9 - 1.72255e10i) q^{63} +1.07374e9 q^{64} +(8.97427e9 + 1.55439e10i) q^{65} +(-1.98091e9 + 3.43103e9i) q^{66} +(-5.49559e9 + 9.51864e9i) q^{67} +(1.42979e9 + 2.47647e9i) q^{68} -2.59948e10 q^{69} +(-1.41857e10 + 7.86350e8i) q^{70} +1.63957e10 q^{71} +(7.11225e9 + 1.23188e10i) q^{72} +(3.74721e9 - 6.49036e9i) q^{73} +(1.05059e10 - 1.81967e10i) q^{74} +(-1.98830e10 - 3.44384e10i) q^{75} -7.66939e8 q^{76} +(7.03088e9 - 3.89739e8i) q^{77} -4.49736e10 q^{78} +(-7.98611e9 - 1.38323e10i) q^{79} +(5.23479e9 - 9.06692e9i) q^{80} +(-4.00801e10 + 6.94207e10i) q^{81} +(-8.30219e9 - 1.43798e10i) q^{82} +6.04748e10 q^{83} +(1.60662e10 - 3.17682e10i) q^{84} +2.78825e10 q^{85} +(7.15740e8 + 1.23970e9i) q^{86} +(-3.63118e10 + 6.28938e10i) q^{87} +(-2.59452e9 + 4.49384e9i) q^{88} +(-1.08709e10 - 1.88289e10i) q^{89} +1.38697e11 q^{90} +(4.37379e10 + 6.69079e10i) q^{91} -3.40471e10 q^{92} +(-1.10623e10 - 1.91604e10i) q^{93} +(1.27963e10 - 2.21639e10i) q^{94} +(-3.73904e9 + 6.47621e9i) q^{95} +(1.31168e10 + 2.27189e10i) q^{96} +9.95342e10 q^{97} +(-6.28868e10 + 6.99343e9i) q^{98} -6.87422e10 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 $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

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

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
$3$	−390.910	+	677.077i	−0.928775	+	1.60869i	−0.143400	+	0.989665i	$0.545803\pi$
$3$	−390.910	+	677.077i	−0.928775	+	1.60869i	−0.785375	+	0.619020i	$0.787530\pi$
$4$	−512.000	+	886.810i	−0.250000	+	0.433013i
$5$	4992.28	+	8646.88i	0.714437	+	1.23744i	0.963176	+	0.268871i	$0.0866505\pi$
$5$	4992.28	+	8646.88i	0.714437	+	1.23744i	−0.248739	+	0.968571i	$0.580016\pi$
$6$	−25018.3			−1.31349
$7$	24330.9	+	37220.1i	0.547166	+	0.837024i
$7$	24330.9	+	37220.1i	0.547166	+	0.837024i
$8$	−32768.0			−0.353553
$9$	−217048.	−	375939.i	−1.22525	−	2.12219i
$10$	−159753.	+	276700.i	−0.505183	+	0.875003i
$11$	79178.4	−	137141.i	0.148234	−	0.256748i	−0.782341	−	0.622850i	$-0.785975\pi$
$11$	79178.4	−	137141.i	0.148234	−	0.256748i	0.930575	+	0.366102i	$0.119308\pi$
$12$	−400292.	−	693327.i	−0.464387	−	0.804343i
$13$	1.79763e6			1.34280			0.671401	−	0.741095i	$-0.265693\pi$
$13$	1.79763e6			1.34280			0.671401	+	0.741095i	$0.265693\pi$
$14$	−642178.	+	1.26980e6i	−0.319118	+	0.631002i
$15$	−7.80614e6			−2.65420
$16$	−524288.	−	908093.i	−0.125000	−	0.216506i
$17$	1.39628e6	−	2.41842e6i	0.238508	−	0.413108i	−0.721778	−	0.692124i	$-0.756675\pi$
$17$	1.39628e6	−	2.41842e6i	0.238508	−	0.413108i	0.960286	+	0.279016i	$0.0900084\pi$
$18$	6.94555e6	−	1.20300e7i	0.866379	−	1.50061i
$19$	374482.	+	648622.i	0.0346965	+	0.0600962i	0.882852	−	0.469651i	$-0.155620\pi$
$19$	374482.	+	648622.i	0.0346965	+	0.0600962i	−0.848156	+	0.529747i	$0.822287\pi$
$20$	−1.02242e7			−0.714437
$21$	−3.47121e7	+	1.92417e6i	−1.85470	+	0.102811i
$22$	5.06742e6			0.209634
$23$	1.66245e7	+	2.87945e7i	0.538575	+	0.932840i	0.998981	+	0.0451313i	$0.0143706\pi$
$23$	1.66245e7	+	2.87945e7i	0.538575	+	0.932840i	−0.460406	+	0.887709i	$0.652296\pi$
$24$	1.28094e7	−	2.21865e7i	0.328371	−	0.568756i
$25$	−2.54317e7	+	4.40490e7i	−0.520841	+	0.902123i
$26$	2.87621e7	+	4.98174e7i	0.474752	+	0.822294i
$27$	2.00889e8			2.69436
$28$	−4.54646e7	+	2.52021e6i	−0.499234	+	0.0276737i
$29$	9.28902e7			0.840971			0.420485	−	0.907299i	$-0.361860\pi$
$29$	9.28902e7			0.840971			0.420485	+	0.907299i	$0.361860\pi$
$30$	−1.24898e8	−	2.16330e8i	−0.938403	−	1.62536i
$31$	−1.41494e7	+	2.45075e7i	−0.0887663	+	0.153748i	−0.906990	−	0.421152i	$-0.861626\pi$
$31$	−1.41494e7	+	2.45075e7i	−0.0887663	+	0.153748i	0.818224	+	0.574900i	$0.194959\pi$
$32$	1.67772e7	−	2.90590e7i	0.0883883	−	0.153093i
$33$	6.19033e7	+	1.07220e8i	0.275351	+	0.476923i
$34$	8.93618e7			0.337301
$35$	−2.00371e8	+	3.96200e8i	−0.644853	+	1.27509i
$36$	4.44515e8			1.22525
$37$	−3.28309e8	−	5.68647e8i	−0.778346	−	1.34814i	−0.932894	−	0.360150i	$-0.882725\pi$
$37$	−3.28309e8	−	5.68647e8i	−0.778346	−	1.34814i	0.154548	−	0.987985i	$-0.450608\pi$
$38$	−1.19834e7	+	2.07559e7i	−0.0245342	+	0.0424944i
$39$	−7.02712e8	+	1.21713e9i	−1.24716	+	2.16014i
$40$	−1.63587e8	−	2.83341e8i	−0.252592	−	0.437502i
$41$	−5.18887e8			−0.699458			−0.349729	−	0.936851i	$-0.613726\pi$
$41$	−5.18887e8			−0.699458			−0.349729	+	0.936851i	$0.613726\pi$
$42$	−6.08717e8	−	9.31182e8i	−0.718695	−	1.09942i
$43$	4.47337e7			0.0464043			0.0232022	−	0.999731i	$-0.492614\pi$
$43$	4.47337e7			0.0464043			0.0232022	+	0.999731i	$0.492614\pi$
$44$	8.10787e7	+	1.40432e8i	0.0741169	+	0.128374i
$45$	2.16713e9	−	3.75359e9i	1.75072	−	3.03234i
$46$	−5.31985e8	+	9.21425e8i	−0.380830	+	0.659617i
$47$	−3.99885e8	−	6.92620e8i	−0.254329	−	0.440511i	0.710384	−	0.703815i	$-0.248521\pi$
$47$	−3.99885e8	−	6.92620e8i	−0.254329	−	0.440511i	−0.964713	+	0.263303i	$0.915188\pi$
$48$	8.19799e8			0.464387
$49$	−7.93341e8	+	1.81120e9i	−0.401219	+	0.915982i
$50$	−1.62763e9			−0.736580
$51$	1.09164e9	+	1.89077e9i	0.443040	+	0.767368i
$52$	−9.20386e8	+	1.59416e9i	−0.335700	+	0.581450i
$53$	5.54293e8	−	9.60064e8i	0.182063	−	0.315343i	−0.760520	−	0.649315i	$-0.775056\pi$
$53$	5.54293e8	−	9.60064e8i	0.182063	−	0.315343i	0.942583	+	0.333972i	$0.108389\pi$
$54$	3.21422e9	+	5.56720e9i	0.952599	+	1.64995i
$55$	1.58112e9			0.423615
$56$	−7.97275e8	−	1.21963e9i	−0.193452	−	0.295933i
$57$	−5.85556e8			−0.128901
$58$	1.48624e9	+	2.57425e9i	0.297328	+	0.514987i
$59$	−2.10667e9	+	3.64887e9i	−0.383629	+	0.664465i	−0.991578	−	0.129511i	$-0.958659\pi$
$59$	−2.10667e9	+	3.64887e9i	−0.383629	+	0.664465i	0.607949	+	0.793976i	$0.291993\pi$
$60$	3.99674e9	−	6.92256e9i	0.663551	−	1.14930i
$61$	−3.73122e9	−	6.46267e9i	−0.565636	−	0.979711i	−0.996990	−	0.0775280i	$-0.975297\pi$
$61$	−3.73122e9	−	6.46267e9i	−0.565636	−	0.979711i	0.431354	−	0.902183i	$-0.358036\pi$
$62$	−9.05561e8			−0.125535
$63$	8.71149e9	−	1.72255e10i	1.10591	−	2.18675i
$64$	1.07374e9			0.125000
$65$	8.97427e9	+	1.55439e10i	0.959347	+	1.66164i
$66$	−1.98091e9	+	3.43103e9i	−0.194703	+	0.337235i
$67$	−5.49559e9	+	9.51864e9i	−0.497282	+	0.861318i	−0.999995	−	0.00313534i	$-0.999002\pi$
$67$	−5.49559e9	+	9.51864e9i	−0.497282	+	0.861318i	0.502713	+	0.864453i	$0.332335\pi$
$68$	1.42979e9	+	2.47647e9i	0.119254	+	0.206554i
$69$	−2.59948e10			−2.00086
$70$	−1.41857e10	+	7.86350e8i	−1.00882	+	0.0559212i
$71$	1.63957e10			1.07847			0.539237	−	0.842154i	$-0.318713\pi$
$71$	1.63957e10			1.07847			0.539237	+	0.842154i	$0.318713\pi$
$72$	7.11225e9	+	1.23188e10i	0.433190	+	0.750306i
$73$	3.74721e9	−	6.49036e9i	0.211560	−	0.366432i	−0.740643	−	0.671898i	$-0.765479\pi$
$73$	3.74721e9	−	6.49036e9i	0.211560	−	0.366432i	0.952203	+	0.305467i	$0.0988124\pi$
$74$	1.05059e10	−	1.81967e10i	0.550374	−	0.953276i
$75$	−1.98830e10	−	3.44384e10i	−0.967488	−	1.67574i
$76$	−7.66939e8			−0.0346965
$77$	7.03088e9	−	3.89739e8i	0.296013	−	0.0164087i
$78$	−4.49736e10			−1.76375
$79$	−7.98611e9	−	1.38323e10i	−0.292002	−	0.505763i	0.682281	−	0.731090i	$-0.260988\pi$
$79$	−7.98611e9	−	1.38323e10i	−0.292002	−	0.505763i	−0.974283	+	0.225327i	$0.927655\pi$
$80$	5.23479e9	−	9.06692e9i	0.178609	−	0.309360i
$81$	−4.00801e10	+	6.94207e10i	−1.27721	+	2.21219i
$82$	−8.30219e9	−	1.43798e10i	−0.247296	−	0.428329i
$83$	6.04748e10			1.68517			0.842587	−	0.538560i	$-0.181032\pi$
$83$	6.04748e10			1.68517			0.842587	+	0.538560i	$0.181032\pi$
$84$	1.60662e10	−	3.17682e10i	0.419157	−	0.828812i
$85$	2.78825e10			0.681596
$86$	7.15740e8	+	1.23970e9i	0.0164064	+	0.0284167i
$87$	−3.63118e10	+	6.28938e10i	−0.781073	+	1.35286i
$88$	−2.59452e9	+	4.49384e9i	−0.0524085	+	0.0907742i
$89$	−1.08709e10	−	1.88289e10i	−0.206357	−	0.357420i	0.744207	−	0.667949i	$-0.232827\pi$
$89$	−1.08709e10	−	1.88289e10i	−0.206357	−	0.357420i	−0.950564	+	0.310528i	$0.899494\pi$
$90$	1.38697e11			2.47589
$91$	4.37379e10	+	6.69079e10i	0.734735	+	1.12396i
$92$	−3.40471e10			−0.538575
$93$	−1.10623e10	−	1.91604e10i	−0.164888	−	0.285594i
$94$	1.27963e10	−	2.21639e10i	0.179838	−	0.311489i
$95$	−3.73904e9	+	6.47621e9i	−0.0495770	+	0.0858699i
$96$	1.31168e10	+	2.27189e10i	0.164186	+	0.284378i
$97$	9.95342e10			1.17687			0.588434	−	0.808545i	$-0.299745\pi$
$97$	9.95342e10			1.17687			0.588434	+	0.808545i	$0.299745\pi$
$98$	−6.28868e10	+	6.99343e9i	−0.702775	+	0.0781532i
$99$	−6.87422e10			−0.726491
$100$	−2.60420e10	−	4.51061e10i	−0.260420	−	0.451061i
$101$	6.53712e10	−	1.13226e11i	0.618897	−	1.07196i	−0.370790	−	0.928717i	$-0.620913\pi$
$101$	6.53712e10	−	1.13226e11i	0.618897	−	1.07196i	0.989687	−	0.143245i	$-0.0457537\pi$
$102$	−3.49325e10	+	6.05048e10i	−0.313277	+	0.542611i
$103$	6.41218e10	+	1.11062e11i	0.545006	+	0.943978i	0.998607	+	0.0527728i	$0.0168059\pi$
$103$	6.41218e10	+	1.11062e11i	0.545006	+	0.943978i	−0.453601	+	0.891205i	$0.649861\pi$
$104$	−5.89047e10			−0.474752
$105$	−1.89930e11	−	2.90545e11i	−1.45229	−	2.22163i
$106$	3.54748e10			0.257476
$107$	−5.93975e10	−	1.02879e11i	−0.409409	−	0.709117i	0.585415	−	0.810734i	$-0.300932\pi$
$107$	−5.93975e10	−	1.02879e11i	−0.409409	−	0.709117i	−0.994824	+	0.101617i	$0.967598\pi$
$108$	−1.02855e11	+	1.78150e11i	−0.673589	+	1.16669i
$109$	−1.22410e11	+	2.12020e11i	−0.762028	+	1.31987i	0.179775	+	0.983708i	$0.442463\pi$
$109$	−1.22410e11	+	2.12020e11i	−0.762028	+	1.31987i	−0.941803	+	0.336164i	$0.890870\pi$
$110$	2.52980e10	+	4.38174e10i	0.149770	+	0.259410i
$111$	5.13357e11			2.89163
$112$	2.10429e10	−	4.16088e10i	0.112825	−	0.223093i
$113$	−2.65326e11			−1.35472			−0.677358	−	0.735653i	$-0.736875\pi$
$113$	−2.65326e11			−1.35472			−0.677358	+	0.735653i	$0.736875\pi$
$114$	−9.36889e9	−	1.62274e10i	−0.0455734	−	0.0789355i
$115$	−1.65989e11	+	2.87501e11i	−0.769556	+	1.33291i
$116$	−4.75598e10	+	8.23760e10i	−0.210243	+	0.364151i
$117$	−3.90173e11	−	6.75799e11i	−1.64526	−	2.84967i
$118$	−1.34827e11			−0.542533
$119$	1.23987e11	−	6.87288e9i	0.476285	−	0.0264016i
$120$	2.55792e11			0.938403
$121$	1.30117e11	+	2.25370e11i	0.456054	+	0.789908i
$122$	1.19399e11	−	2.06805e11i	0.399965	−	0.692760i
$123$	2.02838e11	−	3.51326e11i	0.649639	−	1.12521i
$124$	−1.44890e10	−	2.50956e10i	−0.0443832	−	0.0768739i
$125$	−2.03210e10			−0.0595579
$126$	6.16751e11	−	3.41880e10i	1.73010	−	0.0959038i
$127$	−2.24538e11			−0.603073			−0.301536	−	0.953455i	$-0.597499\pi$
$127$	−2.24538e11			−0.603073			−0.301536	+	0.953455i	$0.597499\pi$
$128$	1.71799e10	+	2.97564e10i	0.0441942	+	0.0765466i
$129$	−1.74869e10	+	3.02882e10i	−0.0430992	+	0.0746500i
$130$	−2.87177e11	+	4.97405e11i	−0.678361	+	1.17496i
$131$	−9.59825e9	−	1.66247e10i	−0.0217370	−	0.0376496i	0.854952	−	0.518707i	$-0.173586\pi$
$131$	−9.59825e9	−	1.66247e10i	−0.0217370	−	0.0376496i	−0.876689	+	0.481057i	$0.840253\pi$
$132$	−1.26778e11			−0.275351
$133$	−1.50303e10	+	2.97198e10i	−0.0313172	+	0.0619244i
$134$	−3.51718e11			−0.703263
$135$	1.00289e12	+	1.73706e12i	1.92495	+	3.33411i
$136$	−4.57532e10	+	7.92469e10i	−0.0843253	+	0.146056i
$137$	6.08474e10	−	1.05391e11i	0.107716	−	0.186569i	−0.807129	−	0.590375i	$-0.798980\pi$
$137$	6.08474e10	−	1.05391e11i	0.107716	−	0.186569i	0.914844	+	0.403806i	$0.132313\pi$
$138$	−4.15917e11	−	7.20390e11i	−0.707411	−	1.22527i
$139$	−1.46631e11			−0.239687			−0.119843	−	0.992793i	$-0.538239\pi$
$139$	−1.46631e11			−0.239687			−0.119843	+	0.992793i	$0.538239\pi$
$140$	−2.48764e11	−	3.80545e11i	−0.390916	−	0.598001i
$141$	6.25276e11			0.944859
$142$	2.62332e11	+	4.54372e11i	0.381298	+	0.660428i
$143$	1.42333e11	−	2.46529e11i	0.199048	−	0.344762i
$144$	−2.27592e11	+	3.94201e11i	−0.306311	+	0.530547i
$145$	4.63734e11	+	8.03211e11i	0.600821	+	1.04065i
$146$	2.39822e11			0.299190
$147$	−9.16194e11	−	1.24517e12i	−1.10088	−	1.49618i
$148$	6.72376e11			0.778346
$149$	−6.05258e11	−	1.04834e12i	−0.675174	−	1.16944i	−0.976418	−	0.215889i	$-0.930735\pi$
$149$	−6.05258e11	−	1.04834e12i	−0.675174	−	1.16944i	0.301243	−	0.953547i	$-0.402598\pi$
$150$	6.36257e11	−	1.10203e12i	0.684117	−	1.18493i
$151$	3.28533e11	−	5.69037e11i	0.340570	−	0.589885i	−0.643969	−	0.765052i	$-0.722713\pi$
$151$	3.28533e11	−	5.69037e11i	0.340570	−	0.589885i	0.984539	+	0.175167i	$0.0560466\pi$
$152$	−1.22710e10	−	2.12540e10i	−0.0122671	−	0.0212472i
$153$	−1.21224e12			−1.16892
$154$	1.23295e11	+	1.88610e11i	0.114705	+	0.175469i
$155$	−2.82551e11			−0.253672
$156$	−7.19577e11	−	1.24634e12i	−0.623580	−	1.08007i
$157$	−9.53281e11	+	1.65113e12i	−0.797578	+	1.38145i	0.123612	+	0.992331i	$0.460552\pi$
$157$	−9.53281e11	+	1.65113e12i	−0.797578	+	1.38145i	−0.921189	+	0.389114i	$0.872781\pi$
$158$	2.55556e11	−	4.42635e11i	0.206477	−	0.357628i
$159$	4.33358e11	+	7.50598e11i	0.338192	+	0.585765i
$160$	3.35026e11			0.252592
$161$	−6.67245e11	+	1.31936e12i	−0.486119	+	0.961219i
$162$	−2.56513e12			−1.80624
$163$	−5.12933e11	−	8.88426e11i	−0.349164	−	0.604769i	0.636938	−	0.770915i	$-0.280201\pi$
$163$	−5.12933e11	−	8.88426e11i	−0.349164	−	0.604769i	−0.986101	+	0.166146i	$0.946868\pi$
$164$	2.65670e11	−	4.60154e11i	0.174864	−	0.302874i
$165$	−6.18078e11	+	1.07054e12i	−0.393443	+	0.681463i
$166$	9.67596e11	+	1.67593e12i	0.595799	+	1.03195i
$167$	2.39071e12			1.42425			0.712126	−	0.702051i	$-0.247732\pi$
$167$	2.39071e12			1.42425			0.712126	+	0.702051i	$0.247732\pi$
$168$	1.13744e12	−	6.30513e10i	0.655736	−	0.0363491i
$169$	1.43931e12			0.803115
$170$	4.46119e11	+	7.72701e11i	0.240980	+	0.417390i
$171$	1.62562e11	−	2.81565e11i	0.0850235	−	0.147265i
$172$	−2.29037e10	+	3.96703e10i	−0.0116011	+	0.0200937i
$173$	−1.43391e12	−	2.48361e12i	−0.703507	−	1.21851i	−0.967228	−	0.253911i	$-0.918283\pi$
$173$	−1.43391e12	−	2.48361e12i	−0.703507	−	1.21851i	0.263721	−	0.964599i	$-0.415050\pi$
$174$	−2.32395e12			−1.10460
$175$	−2.25828e12	+	1.25182e11i	−1.04008	+	0.0576545i
$176$	−1.66049e11			−0.0741169
$177$	−1.64704e12	−	2.85276e12i	−0.712610	−	1.23428i
$178$	3.47867e11	−	6.02524e11i	0.145916	−	0.252734i
$179$	1.36744e11	−	2.36847e11i	0.0556180	−	0.0963332i	−0.836876	−	0.547393i	$-0.815620\pi$
$179$	1.36744e11	−	2.36847e11i	0.0556180	−	0.0963332i	0.892494	+	0.451059i	$0.148954\pi$
$180$	2.21915e12	+	3.84367e12i	0.875361	+	1.51617i
$181$	2.88576e12			1.10415			0.552074	−	0.833795i	$-0.313836\pi$
$181$	2.88576e12			1.10415			0.552074	+	0.833795i	$0.313836\pi$
$182$	−1.15440e12	+	2.28263e12i	−0.428512	+	0.847310i
$183$	5.83430e12			2.10139
$184$	−5.44753e11	−	9.43540e11i	−0.190415	−	0.329809i
$185$	3.27802e12	−	5.67769e12i	1.11216	−	1.92632i
$186$	3.53993e11	−	6.13134e11i	0.116593	−	0.201946i
$187$	−2.21110e11	−	3.82974e11i	−0.0707098	−	0.122473i
$188$	8.18964e11			0.254329
$189$	4.88781e12	+	7.47710e12i	1.47426	+	2.25524i
$190$	−2.39299e11			−0.0701125
$191$	1.62685e12	+	2.81779e12i	0.463089	+	0.802094i	0.999113	−	0.0421086i	$-0.0134076\pi$
$191$	1.62685e12	+	2.81779e12i	0.463089	+	0.802094i	−0.536024	+	0.844203i	$0.680074\pi$
$192$	−4.19737e11	+	7.27006e11i	−0.116097	+	0.201086i
$193$	−4.75159e11	+	8.23000e11i	−0.127724	+	0.221225i	−0.922795	−	0.385292i	$-0.874101\pi$
$193$	−4.75159e11	+	8.23000e11i	−0.127724	+	0.221225i	0.795070	+	0.606517i	$0.207434\pi$
$194$	1.59255e12	+	2.75837e12i	0.416086	+	0.720682i
$195$	−1.40325e13			−3.56407
$196$	−1.20000e12	−	1.63088e12i	−0.296327	−	0.402728i
$197$	1.00428e10			0.00241152			0.00120576	−	0.999999i	$-0.499616\pi$
$197$	1.00428e10			0.00241152			0.00120576	+	0.999999i	$0.499616\pi$
$198$	−1.09988e12	−	1.90504e12i	−0.256853	−	0.444883i
$199$	−3.15890e12	+	5.47138e12i	−0.717537	+	1.24281i	0.244436	+	0.969665i	$0.421397\pi$
$199$	−3.15890e12	+	5.47138e12i	−0.717537	+	1.24281i	−0.961973	+	0.273145i	$0.911936\pi$
$200$	8.33345e11	−	1.44340e12i	0.184145	−	0.318949i
$201$	−4.29657e12	−	7.44187e12i	−0.923726	−	1.59994i
$202$	4.18375e12			0.875253
$203$	2.26010e12	+	3.45738e12i	0.460151	+	0.703913i
$204$	−2.23568e12			−0.443040
$205$	−2.59043e12	−	4.48676e12i	−0.499719	−	0.865538i
$206$	−2.05190e12	+	3.55399e12i	−0.385377	+	0.667493i
$207$	7.21666e12	−	1.24996e13i	1.31977	−	2.28592i
$208$	−9.42475e11	−	1.63242e12i	−0.167850	−	0.290725i
$209$	1.18604e11			0.0205728
$210$	5.01294e12	−	9.91223e12i	0.847005	−	1.67481i
$211$	−5.42132e12			−0.892383			−0.446191	−	0.894938i	$-0.647220\pi$
$211$	−5.42132e12			−0.892383			−0.446191	+	0.894938i	$0.647220\pi$
$212$	5.67596e11	+	9.83106e11i	0.0910316	+	0.157671i
$213$	−6.40927e12	+	1.11012e13i	−1.00166	+	1.73493i
$214$	1.90072e12	−	3.29214e12i	0.289496	−	0.501421i
$215$	2.23323e11	+	3.86807e11i	0.0331530	+	0.0574227i
$216$	−6.58273e12			−0.952599
$217$	−1.25644e12	+	6.96474e10i	−0.177261	+	0.00982598i
$218$	−7.83424e12			−1.07767
$219$	2.92965e12	+	5.07430e12i	0.392982	+	0.680665i
$220$	−8.09535e11	+	1.40216e12i	−0.105904	+	0.183431i
$221$	2.50999e12	−	4.34743e12i	0.320269	−	0.554722i
$222$	8.21372e12	+	1.42266e13i	1.02235	+	1.77076i
$223$	−9.98983e12			−1.21306			−0.606528	−	0.795062i	$-0.707438\pi$
$223$	−9.98983e12			−1.21306			−0.606528	+	0.795062i	$0.707438\pi$
$224$	1.48978e12	−	8.25823e10i	0.176506	−	0.00978414i
$225$	2.20796e13			2.55263
$226$	−4.24522e12	−	7.35293e12i	−0.478965	−	0.829591i
$227$	1.20640e12	−	2.08955e12i	0.132846	−	0.230096i	−0.791926	−	0.610616i	$-0.790922\pi$
$227$	1.20640e12	−	2.08955e12i	0.132846	−	0.230096i	0.924773	+	0.380520i	$0.124255\pi$
$228$	2.99805e11	−	5.19277e11i	0.0322253	−	0.0558158i
$229$	7.44079e12	+	1.28878e13i	0.780771	+	1.35234i	0.931493	+	0.363759i	$0.118507\pi$
$229$	7.44079e12	+	1.28878e13i	0.780771	+	1.35234i	−0.150722	+	0.988576i	$0.548160\pi$
$230$	−1.06233e13			−1.08832
$231$	−2.48456e12	+	4.91280e12i	−0.248533	+	0.491432i
$232$	−3.04383e12			−0.297328
$233$	7.96979e12	+	1.38041e13i	0.760308	+	1.31689i	0.942692	+	0.333664i	$0.108285\pi$
$233$	7.96979e12	+	1.38041e13i	0.760308	+	1.31689i	−0.182384	+	0.983227i	$0.558381\pi$
$234$	1.24855e13	−	2.16256e13i	1.16337	−	2.01502i
$235$	3.99267e12	−	6.91551e12i	0.363405	−	0.629435i
$236$	−2.15723e12	−	3.73644e12i	−0.191814	−	0.332232i
$237$	1.24874e13			1.08482
$238$	2.17425e12	+	3.32605e12i	0.184560	+	0.282329i
$239$	−1.48885e13			−1.23499			−0.617494	−	0.786576i	$-0.711852\pi$
$239$	−1.48885e13			−1.23499			−0.617494	+	0.786576i	$0.711852\pi$
$240$	4.09267e12	+	7.08870e12i	0.331776	+	0.574652i
$241$	8.18935e12	−	1.41844e13i	0.648867	−	1.12387i	−0.334526	−	0.942386i	$-0.608576\pi$
$241$	8.18935e12	−	1.41844e13i	0.648867	−	1.12387i	0.983394	−	0.181485i	$-0.0580903\pi$
$242$	−4.16376e12	+	7.21184e12i	−0.322479	+	0.558549i
$243$	−1.35420e13	−	2.34555e13i	−1.02529	−	1.77586i
$244$	7.64155e12			0.565636
$245$	−1.96218e13	+	2.18207e12i	−1.42012	+	0.157927i
$246$	1.29817e13			0.918728
$247$	6.73180e11	+	1.16598e12i	0.0465906	+	0.0806972i
$248$	4.63647e11	−	8.03060e11i	0.0313836	−	0.0543581i
$249$	−2.36402e13	+	4.09461e13i	−1.56515	+	2.71091i
$250$	−3.25136e11	−	5.63152e11i	−0.0210569	−	0.0364716i
$251$	1.36880e13			0.867232			0.433616	−	0.901098i	$-0.357238\pi$
$251$	1.36880e13			0.867232			0.433616	+	0.901098i	$0.357238\pi$
$252$	1.08155e13	+	1.65449e13i	0.670412	+	1.02556i
$253$	5.26522e12			0.319340
$254$	−3.59261e12	−	6.22259e12i	−0.213218	−	0.369305i
$255$	−1.08995e13	+	1.88786e13i	−0.633049	+	1.09647i
$256$	−5.49756e11	+	9.52205e11i	−0.0312500	+	0.0541266i
$257$	1.27360e13	+	2.20593e13i	0.708597	+	1.22733i	0.965378	+	0.260857i	$0.0840050\pi$
$257$	1.27360e13	+	2.20593e13i	0.708597	+	1.22733i	−0.256780	+	0.966470i	$0.582662\pi$
$258$	−1.11916e12			−0.0609514
$259$	1.31770e13	−	2.60554e13i	0.702537	−	1.38915i
$260$	−1.83793e13			−0.959347
$261$	−2.01617e13	−	3.49211e13i	−1.03040	−	1.78470i
$262$	3.07144e11	−	5.31989e11i	0.0153704	−	0.0266223i
$263$	1.52870e13	−	2.64778e13i	0.749144	−	1.29756i	−0.199089	−	0.979981i	$-0.563798\pi$
$263$	1.52870e13	−	2.64778e13i	0.749144	−	1.29756i	0.948233	−	0.317574i	$-0.102868\pi$
$264$	−2.02845e12	−	3.51338e12i	−0.0973515	−	0.168618i
$265$	1.10688e13			0.520291
$266$	−1.06410e12	+	5.89859e10i	−0.0489931	+	0.00271581i
$267$	1.69981e13			0.766635
$268$	−5.62748e12	−	9.74709e12i	−0.248641	−	0.430659i
$269$	9.40859e12	−	1.62961e13i	0.407274	−	0.705419i	−0.587309	−	0.809363i	$-0.699813\pi$
$269$	9.40859e12	−	1.62961e13i	0.407274	−	0.705419i	0.994583	+	0.103943i	$0.0331460\pi$
$270$	−3.20926e13	+	5.55860e13i	−1.36114	+	2.35757i
$271$	−1.96569e13	−	3.40468e13i	−0.816930	−	1.41496i	−0.907934	−	0.419114i	$-0.862341\pi$
$271$	−1.96569e13	−	3.40468e13i	−0.816930	−	1.41496i	0.0910034	−	0.995851i	$-0.470993\pi$
$272$	−2.92821e12			−0.119254
$273$	−6.23994e13	+	3.45895e12i	−2.49050	+	0.138054i
$274$	3.89423e12			0.152333
$275$	4.02728e12	+	6.97545e12i	0.154412	+	0.267450i
$276$	1.33093e13	−	2.30525e13i	0.500215	−	0.866398i
$277$	1.91126e13	−	3.31040e13i	0.704176	−	1.21967i	−0.262813	−	0.964847i	$-0.584650\pi$
$277$	1.91126e13	−	3.31040e13i	0.704176	−	1.21967i	0.966988	−	0.254821i	$-0.0820165\pi$
$278$	−2.34610e12	−	4.06356e12i	−0.0847421	−	0.146778i
$279$	1.22844e13			0.435042
$280$	6.56576e12	−	1.29827e13i	0.227990	−	0.450811i
$281$	2.43790e13			0.830103			0.415051	−	0.909798i	$-0.363764\pi$
$281$	2.43790e13			0.830103			0.415051	+	0.909798i	$0.363764\pi$
$282$	1.00044e13	+	1.73282e13i	0.334058	+	0.578605i
$283$	−2.21500e13	+	3.83649e13i	−0.725350	+	1.25634i	0.233480	+	0.972362i	$0.424989\pi$
$283$	−2.21500e13	+	3.83649e13i	−0.725350	+	1.25634i	−0.958830	+	0.283981i	$0.908345\pi$
$284$	−8.39462e12	+	1.45399e13i	−0.269619	+	0.466993i
$285$	−2.92326e12	−	5.06323e12i	−0.0920917	−	0.159508i
$286$	9.10934e12			0.281497
$287$	−1.26250e13	−	1.93130e13i	−0.382719	−	0.585463i
$288$	−1.45659e13			−0.433190
$289$	1.32368e13	+	2.29267e13i	0.386228	+	0.668966i
$290$	−1.48395e13	+	2.57028e13i	−0.424845	+	0.735852i
$291$	−3.89090e13	+	6.73923e13i	−1.09305	+	1.89321i
$292$	3.83715e12	+	6.64613e12i	0.105780	+	0.183216i
$293$	3.62215e13			0.979930			0.489965	−	0.871742i	$-0.337010\pi$
$293$	3.62215e13			0.979930			0.489965	+	0.871742i	$0.337010\pi$
$294$	1.98480e13	−	4.53130e13i	0.526995	−	1.20313i
$295$	−4.20684e13			−1.09632
$296$	1.07580e13	+	1.86334e13i	0.275187	+	0.476638i
$297$	1.59061e13	−	2.75501e13i	0.399395	−	0.691772i
$298$	1.93683e13	−	3.35468e13i	0.477420	−	0.826916i
$299$	2.98848e13	+	5.17619e13i	0.723200	+	1.25262i
$300$	4.07204e13			0.967488
$301$	1.08841e12	+	1.66499e12i	0.0253909	+	0.0388416i
$302$	2.10261e13			0.481639
$303$	5.11085e13	+	8.85226e13i	1.14963	+	1.99122i
$304$	3.92673e11	−	6.80129e11i	0.00867413	−	0.0150240i
$305$	3.72546e13	−	6.45269e13i	0.808223	−	1.39988i
$306$	−1.93958e13	−	3.35946e13i	−0.413277	−	0.715816i
$307$	−1.51099e13			−0.316229			−0.158115	−	0.987421i	$-0.550542\pi$
$307$	−1.51099e13			−0.316229			−0.158115	+	0.987421i	$0.550542\pi$
$308$	−3.25419e12	+	6.43460e12i	−0.0668981	+	0.132280i
$309$	−1.00264e14			−2.02475
$310$	−4.52081e12	−	7.83028e12i	−0.0896865	−	0.155342i
$311$	−2.68576e13	+	4.65186e13i	−0.523461	+	0.906661i	0.476166	+	0.879355i	$0.342026\pi$
$311$	−2.68576e13	+	4.65186e13i	−0.523461	+	0.906661i	−0.999627	+	0.0273057i	$0.991307\pi$
$312$	2.30265e13	−	3.98830e13i	0.440938	−	0.763726i
$313$	−2.70143e13	−	4.67901e13i	−0.508275	−	0.880359i	−0.999954	−	0.00958212i	$-0.996950\pi$
$313$	−2.70143e13	−	4.67901e13i	−0.508275	−	0.880359i	0.491679	−	0.870777i	$-0.336383\pi$
$314$	−6.10100e13			−1.12795
$315$	1.92437e14	−	1.06673e13i	3.49608	−	0.193796i
$316$	1.63556e13			0.292002
$317$	−1.72833e13	−	2.99356e13i	−0.303251	−	0.525245i	0.673620	−	0.739078i	$-0.264739\pi$
$317$	−1.72833e13	−	2.99356e13i	−0.303251	−	0.525245i	−0.976870	+	0.213833i	$0.931405\pi$
$318$	−1.38675e13	+	2.40191e13i	−0.239138	+	0.414198i
$319$	7.35490e12	−	1.27391e13i	0.124660	−	0.215918i
$320$	5.36042e12	+	9.28452e12i	0.0893046	+	0.154680i
$321$	9.28763e13			1.52099
$322$	−4.72392e13	+	2.61858e12i	−0.760493	+	0.0421560i
$323$	2.09152e12			0.0331016
$324$	−4.10420e13	−	7.10868e13i	−0.638603	−	1.10609i
$325$	−4.57167e13	+	7.91837e13i	−0.699386	+	1.21137i
$326$	1.64139e13	−	2.84296e13i	0.246896	−	0.427636i
$327$	−9.57027e13	−	1.65762e14i	−1.41551	−	2.45173i
$328$	1.70029e13			0.247296
$329$	1.60498e13	−	3.17358e13i	0.229558	−	0.453913i
$330$	−3.95570e13			−0.556412
$331$	6.42548e13	+	1.11293e14i	0.888897	+	1.53961i	0.841181	+	0.540754i	$0.181861\pi$
$331$	6.42548e13	+	1.11293e14i	0.888897	+	1.53961i	0.0477161	+	0.998861i	$0.484806\pi$
$332$	−3.09631e13	+	5.36296e13i	−0.421294	+	0.729702i
$333$	−1.42518e14	+	2.46848e14i	−1.90733	+	3.30359i
$334$	3.82514e13	+	6.62534e13i	0.503549	+	0.872173i
$335$	−1.09742e14			−1.42111
$336$	1.99464e13	+	3.05130e13i	0.254097	+	0.388703i
$337$	−1.03299e14			−1.29459			−0.647293	−	0.762241i	$-0.724099\pi$
$337$	−1.03299e14			−1.29459			−0.647293	+	0.762241i	$0.724099\pi$
$338$	2.30290e13	+	3.98873e13i	0.283944	+	0.491805i
$339$	1.03719e14	−	1.79646e14i	1.25823	−	2.17931i
$340$	−1.42758e13	+	2.47264e13i	−0.170399	+	0.295140i
$341$	2.24065e12	+	3.88092e12i	0.0263163	+	0.0455812i
$342$	1.04039e13			0.120241
$343$	−8.67156e13	+	1.45398e13i	−0.986233	+	0.165364i
$344$	−1.46583e12			−0.0164064
$345$	−1.29773e14	−	2.24774e14i	−1.42949	−	2.47595i
$346$	4.58851e13	−	7.94754e13i	0.497455	−	0.861617i
$347$	6.83703e12	−	1.18421e13i	0.0729551	−	0.126362i	−0.827240	−	0.561849i	$-0.810090\pi$
$347$	6.83703e12	−	1.18421e13i	0.0729551	−	0.126362i	0.900195	+	0.435487i	$0.143424\pi$
$348$	−3.71832e13	−	6.44033e13i	−0.390536	−	0.676429i
$349$	3.25361e13			0.336376			0.168188	−	0.985755i	$-0.446208\pi$
$349$	3.25361e13			0.336376			0.168188	+	0.985755i	$0.446208\pi$
$350$	−3.96017e13	−	6.05804e13i	−0.403032	−	0.616535i
$351$	3.61124e14			3.61799
$352$	−2.65679e12	−	4.60169e12i	−0.0262043	−	0.0453871i
$353$	−9.46425e12	+	1.63926e13i	−0.0919021	+	0.159179i	−0.908311	−	0.418294i	$-0.862628\pi$
$353$	−9.46425e12	+	1.63926e13i	−0.0919021	+	0.159179i	0.816409	+	0.577474i	$0.195961\pi$
$354$	5.27054e13	−	9.12883e13i	0.503891	−	0.872765i
$355$	8.18521e13	+	1.41772e14i	0.770503	+	1.33455i
$356$	2.22635e13			0.206357
$357$	−4.38142e13	+	8.66352e13i	−0.399889	+	0.790713i
$358$	8.75159e12			0.0786558
$359$	−7.36621e13	−	1.27586e14i	−0.651965	−	1.12924i	−0.982645	−	0.185494i	$-0.940611\pi$
$359$	−7.36621e13	−	1.27586e14i	−0.651965	−	1.12924i	0.330680	−	0.943743i	$-0.392722\pi$
$360$	−7.10127e13	+	1.22998e14i	−0.618973	+	1.07209i
$361$	5.79647e13	−	1.00398e14i	0.497592	−	0.861855i
$362$	4.61721e13	+	7.99724e13i	0.390375	+	0.676150i
$363$	−2.03457e14			−1.69428
$364$	−8.17284e13	+	4.53041e12i	−0.670371	+	0.0371603i
$365$	7.48286e13			0.604584
$366$	9.33488e13	+	1.61685e14i	0.742955	+	1.28684i
$367$	−2.11924e12	+	3.67063e12i	−0.0166156	+	0.0287791i	−0.874214	−	0.485541i	$-0.838622\pi$
$367$	−2.11924e12	+	3.67063e12i	−0.0166156	+	0.0287791i	0.857598	+	0.514321i	$0.171956\pi$
$368$	1.74321e13	−	3.01933e13i	0.134644	−	0.233210i
$369$	1.12624e14	+	1.95070e14i	0.857007	+	1.48438i
$370$	2.09793e14			1.57283
$371$	4.92201e13	−	2.72839e12i	0.363568	−	0.0201535i
$372$	2.26556e13			0.164888
$373$	−3.52994e13	−	6.11403e13i	−0.253144	−	0.438459i	0.711246	−	0.702944i	$-0.248131\pi$
$373$	−3.52994e13	−	6.11403e13i	−0.253144	−	0.438459i	−0.964390	+	0.264485i	$0.914798\pi$
$374$	7.07553e12	−	1.22552e13i	0.0499994	−	0.0866015i
$375$	7.94368e12	−	1.37589e13i	0.0553159	−	0.0958100i
$376$	1.31034e13	+	2.26958e13i	0.0899190	+	0.155744i
$377$	1.66982e14			1.12926
$378$	−1.29007e14	+	2.55088e14i	−0.859818	+	1.70015i
$379$	−2.89337e14			−1.90059			−0.950294	−	0.311354i	$-0.899218\pi$
$379$	−2.89337e14			−1.90059			−0.950294	+	0.311354i	$0.899218\pi$
$380$	−3.82878e12	−	6.63163e12i	−0.0247885	−	0.0429349i
$381$	8.77743e13	−	1.52030e14i	0.560119	−	0.970154i
$382$	−5.20593e13	+	9.01694e13i	−0.327454	+	0.567166i
$383$	5.67291e13	+	9.82577e13i	0.351733	+	0.609219i	0.986553	−	0.163441i	$-0.0522593\pi$
$383$	5.67291e13	+	9.82577e13i	0.351733	+	0.609219i	−0.634821	+	0.772660i	$0.718926\pi$
$384$	−2.68632e13			−0.164186
$385$	3.84702e13	+	5.88495e13i	0.231788	+	0.354576i
$386$	−3.04102e13			−0.180630
$387$	−9.70939e12	−	1.68172e13i	−0.0568567	−	0.0984787i
$388$	−5.09615e13	+	8.82680e13i	−0.294217	+	0.509599i
$389$	6.63469e13	−	1.14916e14i	0.377657	−	0.654122i	−0.613063	−	0.790034i	$-0.710063\pi$
$389$	6.63469e13	−	1.14916e14i	0.377657	−	0.654122i	0.990721	+	0.135912i	$0.0433964\pi$
$390$	−2.24521e14	−	3.88881e14i	−1.26009	−	2.18254i
$391$	9.28499e13			0.513818
$392$	2.59962e13	−	5.93493e13i	0.141852	−	0.323849i
$393$	1.50082e13			0.0807552
$394$	1.60685e11	+	2.78315e11i	0.000852603	+	0.00147675i
$395$	7.97378e13	−	1.38110e14i	0.417235	−	0.722671i
$396$	3.51960e13	−	6.09613e13i	0.181623	−	0.314580i
$397$	7.36118e13	+	1.27499e14i	0.374627	+	0.648874i	0.990271	−	0.139151i	$-0.0444373\pi$
$397$	7.36118e13	+	1.27499e14i	0.374627	+	0.648874i	−0.615644	+	0.788025i	$0.711104\pi$
$398$	−2.02170e14			−1.01475
$399$	−1.42471e13	−	2.17944e13i	−0.0705303	−	0.107893i
$400$	5.33341e13			0.260420
$401$	−5.51572e13	−	9.55351e13i	−0.265649	−	0.460118i	0.702084	−	0.712094i	$-0.252253\pi$
$401$	−5.51572e13	−	9.55351e13i	−0.265649	−	0.460118i	−0.967733	+	0.251976i	$0.918920\pi$
$402$	1.37490e14	−	2.38140e14i	0.653173	−	1.13133i
$403$	−2.54353e13	+	4.40553e13i	−0.119196	+	0.206453i
$404$	6.69401e13	+	1.15944e14i	0.309449	+	0.535981i
$405$	−8.00364e14			−3.64993
$406$	−5.96521e13	+	1.17952e14i	−0.268369	+	0.530654i
$407$	−1.03980e14			−0.461509
$408$	−3.57708e13	−	6.19569e13i	−0.156638	−	0.271306i
$409$	5.62078e13	−	9.73547e13i	0.242839	−	0.420609i	−0.718683	−	0.695338i	$-0.755255\pi$
$409$	5.62078e13	−	9.73547e13i	0.242839	−	0.420609i	0.961522	+	0.274729i	$0.0885880\pi$
$410$	8.28938e13	−	1.43576e14i	0.353354	−	0.612028i
$411$	4.75718e13	+	8.23967e13i	0.200087	+	0.346561i
$412$	−1.31322e14			−0.545006
$413$	−1.87068e14	+	1.03697e13i	−0.766082	+	0.0424658i
$414$	4.61866e14			1.86644
$415$	3.01907e14	+	5.22918e14i	1.20395	+	2.08530i
$416$	3.01592e13	−	5.22373e13i	0.118688	−	0.205574i
$417$	5.73196e13	−	9.92804e13i	0.222615	−	0.385581i
$418$	1.89766e12	+	3.28684e12i	0.00727358	+	0.0125982i
$419$	−1.89825e14			−0.718085			−0.359043	−	0.933321i	$-0.616897\pi$
$419$	−1.89825e14			−0.718085			−0.359043	+	0.933321i	$0.616897\pi$
$420$	3.54903e14	−	1.96731e13i	1.32507	−	0.0734518i
$421$	1.99203e14			0.734082			0.367041	−	0.930205i	$-0.380371\pi$
$421$	1.99203e14			0.734082			0.367041	+	0.930205i	$0.380371\pi$
$422$	−8.67410e13	−	1.50240e14i	−0.315505	−	0.546471i
$423$	−1.73589e14	+	3.00664e14i	−0.623232	+	1.07947i
$424$	−1.81631e13	+	3.14594e13i	−0.0643691	+	0.111491i
$425$	7.10194e13	+	1.23009e14i	0.248449	+	0.430327i
$426$	−4.10193e14			−1.41656
$427$	1.49757e14	−	2.96119e14i	0.510545	−	1.00952i
$428$	1.21646e14			0.409409
$429$	1.11279e14	+	1.92741e14i	0.369742	+	0.640412i
$430$	−7.14635e12	+	1.23778e13i	−0.0234427	+	0.0406039i
$431$	3.43729e13	−	5.95356e13i	0.111325	−	0.192820i	−0.804980	−	0.593302i	$-0.797824\pi$
$431$	3.43729e13	−	5.95356e13i	0.111325	−	0.192820i	0.916305	+	0.400482i	$0.131157\pi$
$432$	−1.05324e14	−	1.82426e14i	−0.336795	−	0.583345i
$433$	−2.77431e13			−0.0875935			−0.0437968	−	0.999040i	$-0.513945\pi$
$433$	−2.77431e13			−0.0875935			−0.0437968	+	0.999040i	$0.513945\pi$
$434$	−2.20331e13	−	3.37050e13i	−0.0686882	−	0.105075i
$435$	−7.25114e14			−2.23211
$436$	−1.25348e14	−	2.17109e14i	−0.381014	−	0.659936i
$437$	−1.24512e13	+	2.15661e13i	−0.0373734	+	0.0647326i
$438$	−9.37488e13	+	1.62378e14i	−0.277880	+	0.481303i
$439$	−4.16339e13	−	7.21121e13i	−0.121869	−	0.211083i	0.798636	−	0.601815i	$-0.205555\pi$
$439$	−4.16339e13	−	7.21121e13i	−0.121869	−	0.211083i	−0.920505	+	0.390732i	$0.872222\pi$
$440$	−5.18103e13			−0.149770
$441$	8.53093e14	−	9.48695e13i	2.43548	−	0.270841i
$442$	1.60639e14			0.452928
$443$	−2.69384e14	−	4.66587e14i	−0.750155	−	1.29931i	−0.947747	−	0.319023i	$-0.896645\pi$
$443$	−2.69384e14	−	4.66587e14i	−0.750155	−	1.29931i	0.197592	−	0.980284i	$-0.436688\pi$
$444$	−2.62839e14	+	4.55250e14i	−0.722908	+	1.25211i
$445$	1.08541e14	−	1.87998e14i	0.294858	−	0.510709i
$446$	−1.59837e14	−	2.76846e14i	−0.428880	−	0.742843i
$447$	9.46407e14			2.50834
$448$	2.61251e13	+	3.99647e13i	0.0683957	+	0.104628i
$449$	1.14100e14			0.295074			0.147537	−	0.989057i	$-0.452865\pi$
$449$	1.14100e14			0.295074			0.147537	+	0.989057i	$0.452865\pi$
$450$	3.53274e14	+	6.11889e14i	0.902491	+	1.56316i
$451$	−4.10846e13	+	7.11607e13i	−0.103683	+	0.179585i
$452$	1.35847e14	−	2.35294e14i	0.338679	−	0.586609i
$453$	2.56854e14	+	4.44885e14i	0.632626	+	1.09574i
$454$	7.72096e13			0.187873
$455$	−3.60193e14	+	7.12220e14i	−0.865909	+	1.71219i
$456$	1.91875e13			0.0455734
$457$	2.27653e14	+	3.94307e14i	0.534237	+	0.925326i	0.999200	+	0.0399959i	$0.0127345\pi$
$457$	2.27653e14	+	3.94307e14i	0.534237	+	0.925326i	−0.464962	+	0.885330i	$0.653932\pi$
$458$	−2.38105e14	+	4.12410e14i	−0.552089	+	0.956245i
$459$	2.80497e14	−	4.85835e14i	0.642626	−	1.11306i
$460$	−1.69972e14	−	2.94401e14i	−0.384778	−	0.666455i
$461$	−1.77822e14			−0.397768			−0.198884	−	0.980023i	$-0.563732\pi$
$461$	−1.77822e14			−0.397768			−0.198884	+	0.980023i	$0.563732\pi$
$462$	−1.75900e14	+	9.75059e12i	−0.388809	+	0.0215526i
$463$	−4.30595e13			−0.0940531			−0.0470266	−	0.998894i	$-0.514975\pi$
$463$	−4.30595e13			−0.0940531			−0.0470266	+	0.998894i	$0.514975\pi$
$464$	−4.87012e13	−	8.43530e13i	−0.105121	−	0.182076i
$465$	1.10452e14	−	1.91309e14i	0.235604	−	0.408078i
$466$	−2.55033e14	+	4.41731e14i	−0.537619	+	0.931183i
$467$	2.86216e14	+	4.95741e14i	0.596281	+	1.03279i	0.993365	+	0.115007i	$0.0366890\pi$
$467$	2.86216e14	+	4.95741e14i	0.596281	+	1.03279i	−0.397083	+	0.917783i	$0.629978\pi$
$468$	7.99074e14			1.64526
$469$	−4.87997e14	+	2.70509e13i	−0.993040	+	0.0550466i
$470$	2.55531e14			0.513932
$471$	−7.45295e14	−	1.29089e15i	−1.48154	−	2.56610i
$472$	6.90315e13	−	1.19566e14i	0.135633	−	0.234924i
$473$	3.54195e12	−	6.13483e12i	0.00687869	−	0.0119142i
$474$	1.99799e14	+	3.46061e14i	0.383541	+	0.664312i
$475$	−3.80948e13			−0.0722855
$476$	−5.73862e13	+	1.13472e14i	−0.107639	+	0.212838i
$477$	−4.81234e14			−0.892288
$478$	−2.38216e14	−	4.12602e14i	−0.436634	−	0.756272i
$479$	7.88521e13	−	1.36576e14i	0.142879	−	0.247474i	−0.785701	−	0.618607i	$-0.787697\pi$
$479$	7.88521e13	−	1.36576e14i	0.142879	−	0.247474i	0.928580	+	0.371133i	$0.121031\pi$
$480$	−1.30965e14	+	2.26839e14i	−0.234601	+	0.406340i
$481$	−5.90177e14	−	1.02222e15i	−1.04516	−	1.81028i
$482$	5.24119e14			0.917637
$483$	−6.32478e14	−	9.67529e14i	−1.09480	−	1.67477i
$484$	−2.66480e14			−0.456054
$485$	4.96903e14	+	8.60661e14i	0.840799	+	1.45631i
$486$	4.33344e14	−	7.50575e14i	0.724993	−	1.25572i
$487$	−1.43196e14	+	2.48022e14i	−0.236876	+	0.410281i	−0.959816	−	0.280629i	$-0.909457\pi$
$487$	−1.43196e14	+	2.48022e14i	−0.236876	+	0.410281i	0.722940	+	0.690910i	$0.242790\pi$
$488$	1.22265e14	+	2.11769e14i	0.199983	+	0.346380i
$489$	8.02044e14			1.29718
$490$	−3.74420e14	−	5.08862e14i	−0.598798	−	0.813807i
$491$	−4.94798e14			−0.782491			−0.391246	−	0.920286i	$-0.627956\pi$
$491$	−4.94798e14			−0.782491			−0.391246	+	0.920286i	$0.627956\pi$
$492$	2.07706e14	+	3.59758e14i	0.324819	+	0.562604i
$493$	1.29701e14	−	2.24648e14i	0.200578	−	0.347412i
$494$	−2.15418e13	+	3.73114e13i	−0.0329445	+	0.0570615i
$495$	−3.43181e14	−	5.94406e14i	−0.519032	−	0.898990i
$496$	2.96734e13			0.0443832
$497$	3.98923e14	+	6.10251e14i	0.590105	+	0.902710i
$498$	−1.51297e15			−2.21345
$499$	−5.17660e14	−	8.96614e14i	−0.749017	−	1.29734i	−0.948294	−	0.317393i	$-0.897193\pi$
$499$	−5.17660e14	−	8.96614e14i	−0.749017	−	1.29734i	0.199277	−	0.979943i	$-0.436141\pi$
$500$	1.04043e13	−	1.80208e13i	0.0148895	−	0.0257893i
$501$	−9.34555e14	+	1.61870e15i	−1.32281	+	2.29117i
$502$	2.19008e14	+	3.79333e14i	0.306613	+	0.531069i
$503$	4.63983e14			0.642508			0.321254	−	0.946993i	$-0.395896\pi$
$503$	4.63983e14			0.642508			0.321254	+	0.946993i	$0.395896\pi$
$504$	−2.85458e14	+	5.64445e14i	−0.390998	+	0.773132i
$505$	1.30541e15			1.76865
$506$	8.42435e13	+	1.45914e14i	0.112904	+	0.195555i
$507$	−5.62642e14	+	9.74524e14i	−0.745913	+	1.29196i
$508$	1.14964e14	−	1.99123e14i	0.150768	−	0.261138i
$509$	−3.91489e14	−	6.78079e14i	−0.507892	−	0.879695i	−0.999958	−	0.00913743i	$-0.997091\pi$
$509$	−3.91489e14	−	6.78079e14i	−0.507892	−	0.879695i	0.492066	−	0.870558i	$-0.336242\pi$
$510$	−6.97571e14			−0.895266
$511$	3.32745e14	−	1.84449e13i	0.422470	−	0.0234186i
$512$	−3.51844e13			−0.0441942
$513$	7.52293e13	+	1.30301e14i	0.0934849	+	0.161921i
$514$	−4.07551e14	+	7.05898e14i	−0.501054	+	0.867851i
$515$	−6.40228e14	+	1.10891e15i	−0.778745	+	1.34883i
$516$	−1.79066e13	−	3.10151e13i	−0.0215496	−	0.0373250i
$517$	−1.26649e14			−0.150801
$518$	9.32901e14	−	5.17130e13i	1.09906	−	0.0609236i
$519$	2.24212e15			2.61360
$520$	−2.94069e14	−	5.09342e14i	−0.339180	−	0.587478i
$521$	7.30719e13	−	1.26564e14i	0.0833956	−	0.144445i	−0.821311	−	0.570481i	$-0.806757\pi$
$521$	7.30719e13	−	1.26564e14i	0.0833956	−	0.144445i	0.904706	+	0.426036i	$0.140090\pi$
$522$	6.45174e14	−	1.11747e15i	0.728600	−	1.26197i
$523$	−6.08353e13	−	1.05370e14i	−0.0679824	−	0.117749i	0.830031	−	0.557718i	$-0.188323\pi$
$523$	−6.08353e13	−	1.05370e14i	−0.0679824	−	0.117749i	−0.898013	+	0.439969i	$0.854990\pi$
$524$	1.96572e13			0.0217370
$525$	7.98028e14	−	1.57797e15i	0.873257	−	1.72672i
$526$	9.78367e14			1.05945
$527$	3.95130e13	+	6.84384e13i	0.0423430	+	0.0733401i
$528$	6.49104e13	−	1.12428e14i	0.0688379	−	0.119231i
$529$	−7.63456e13	+	1.32235e14i	−0.0801268	+	0.138784i
$530$	1.77100e14	+	3.06746e14i	0.183951	+	0.318612i
$531$	1.82900e15			1.88016
$532$	−1.86603e13	−	2.85455e13i	−0.0189848	−	0.0290418i
$533$	−9.32766e14			−0.939233
$534$	2.71970e14	+	4.71066e14i	0.271047	+	0.469466i
$535$	5.93058e14	−	1.02721e15i	0.584994	−	1.01324i
$536$	1.80080e14	−	3.11907e14i	0.175816	−	0.304522i
$537$	1.06909e14	+	1.85172e14i	0.103313	+	0.178944i
$538$	6.02150e14			0.575973
$539$	1.85574e14	+	2.52207e14i	0.175703	+	0.238792i
$540$	−2.05393e15			−1.92495
$541$	2.27463e14	+	3.93977e14i	0.211021	+	0.365499i	0.952034	−	0.305991i	$-0.0989878\pi$
$541$	2.27463e14	+	3.93977e14i	0.211021	+	0.365499i	−0.741013	+	0.671490i	$0.765655\pi$
$542$	6.29022e14	−	1.08950e15i	0.577657	−	1.00053i
$543$	−1.12807e15	+	1.95388e15i	−1.02551	+	1.77623i
$544$	−4.68513e13	−	8.11489e13i	−0.0421626	−	0.0730278i
$545$	−2.44442e15			−2.17769
$546$	−1.09425e15	−	1.67392e15i	−0.965064	−	1.47630i
$547$	−6.58812e14			−0.575217			−0.287608	−	0.957748i	$-0.592860\pi$
$547$	−6.58812e14			−0.575217			−0.287608	+	0.957748i	$0.592860\pi$
$548$	6.23077e13	+	1.07920e14i	0.0538578	+	0.0932845i
$549$	−1.61971e15	+	2.80543e15i	−1.38609	+	2.40077i
$550$	−1.28873e14	+	2.23215e14i	−0.109186	+	0.189116i
$551$	3.47857e13	+	6.02506e13i	0.0291788	+	0.0505391i
$552$	8.51798e14			0.707411
$553$	3.20532e14	−	6.33797e14i	0.263562	−	0.521149i
$554$	1.22321e15			0.995855
$555$	2.56282e15	+	4.43894e15i	2.06589	+	3.57823i
$556$	7.50751e13	−	1.30034e14i	0.0599217	−	0.103787i
$557$	1.12454e15	−	1.94777e15i	0.888735	−	1.53933i	0.0473637	−	0.998878i	$-0.484918\pi$
$557$	1.12454e15	−	1.94777e15i	0.888735	−	1.53933i	0.841372	−	0.540457i	$-0.181749\pi$
$558$	1.96551e14	+	3.40436e14i	0.153811	+	0.266408i
$559$	8.04147e13			0.0623118
$560$	4.64838e14	−	2.57671e13i	0.356671	−	0.0197711i
$561$	3.45737e14			0.262694
$562$	3.90065e14	+	6.75612e14i	0.293486	+	0.508332i
$563$	1.20750e15	−	2.09145e15i	0.899684	−	1.55830i	0.0717849	−	0.997420i	$-0.477130\pi$
$563$	1.20750e15	−	2.09145e15i	0.899684	−	1.55830i	0.827899	−	0.560878i	$-0.189536\pi$
$564$	−3.20141e14	+	5.54501e14i	−0.236215	+	0.409136i
$565$	−1.32458e15	−	2.29424e15i	−0.967860	−	1.67638i
$566$	−1.41760e15			−1.02580
$567$	−3.55903e15	+	1.97286e14i	−2.55050	+	0.141380i
$568$	−5.37256e14			−0.381298
$569$	2.92094e14	+	5.05922e14i	0.205308	+	0.355603i	0.950231	−	0.311547i	$-0.100847\pi$
$569$	2.92094e14	+	5.05922e14i	0.205308	+	0.355603i	−0.744923	+	0.667150i	$0.767514\pi$
$570$	9.35443e13	−	1.62023e14i	0.0651187	−	0.112789i
$571$	4.51312e14	−	7.81696e14i	0.311156	−	0.538938i	−0.667457	−	0.744649i	$-0.732617\pi$
$571$	4.51312e14	−	7.81696e14i	0.311156	−	0.538938i	0.978613	+	0.205710i	$0.0659504\pi$
$572$	1.45749e14	+	2.52445e14i	0.0995242	+	0.172381i
$573$	−2.54382e15			−1.72042
$574$	3.33218e14	−	6.58882e14i	0.223210	−	0.441359i
$575$	−1.69116e15			−1.12205
$576$	−2.33054e14	−	4.03661e14i	−0.153156	−	0.265273i
$577$	2.46431e14	−	4.26832e14i	0.160409	−	0.277837i	−0.774606	−	0.632444i	$-0.782052\pi$
$577$	2.46431e14	−	4.26832e14i	0.160409	−	0.277837i	0.935015	+	0.354607i	$0.115385\pi$
$578$	−4.23576e14	+	7.33656e14i	−0.273104	+	0.473031i
$579$	−3.71489e14	−	6.43439e14i	−0.237254	−	0.410937i
$580$	−9.49727e14			−0.600821
$581$	1.47141e15	+	2.25088e15i	0.922070	+	1.41053i
$582$	−2.49017e15			−1.54580
$583$	−8.77761e13	−	1.52033e14i	−0.0539758	−	0.0934889i
$584$	−1.22789e14	+	2.12676e14i	−0.0747976	+	0.129553i
$585$	3.89570e15	−	6.74756e15i	2.35087	−	4.07183i
$586$	5.79545e14	+	1.00380e15i	0.346458	+	0.600082i
$587$	4.72586e14			0.279880			0.139940	−	0.990160i	$-0.455309\pi$
$587$	4.72586e14			0.279880			0.139940	+	0.990160i	$0.455309\pi$
$588$	1.57332e15	−	1.74963e14i	0.923084	−	0.102653i
$589$	−2.11948e13			−0.0123195
$590$	−6.73095e14	−	1.16584e15i	−0.387606	−	0.671353i
$591$	−3.92585e12	+	6.79976e12i	−0.00223976	+	0.00387938i
$592$	−3.44257e14	+	5.96270e14i	−0.194587	+	0.337034i
$593$	1.03063e14	+	1.78510e14i	0.0577167	+	0.0999682i	0.893440	−	0.449182i	$-0.148285\pi$
$593$	1.03063e14	+	1.78510e14i	0.0577167	+	0.0999682i	−0.835723	+	0.549151i	$0.814951\pi$
$594$	1.01799e15			0.564829
$595$	6.78405e14	+	1.03779e15i	0.372946	+	0.570512i
$596$	1.23957e15			0.675174
$597$	−2.46970e15	−	4.27764e15i	−1.33286	−	2.30858i
$598$	−9.56312e14	+	1.65638e15i	−0.511379	+	0.885735i
$599$	−1.15771e15	+	2.00522e15i	−0.613414	+	1.06246i	0.377246	+	0.926113i	$0.376871\pi$
$599$	−1.15771e15	+	2.00522e15i	−0.613414	+	1.06246i	−0.990660	+	0.136352i	$0.956462\pi$
$600$	6.51527e14	+	1.12848e15i	0.342059	+	0.592463i
$601$	1.95172e15			1.01533			0.507665	−	0.861554i	$-0.330509\pi$
$601$	1.95172e15			1.01533			0.507665	+	0.861554i	$0.330509\pi$
$602$	−2.87270e13	+	5.68028e13i	−0.0148085	+	0.0292812i
$603$	4.77124e15			2.43717
$604$	3.36418e14	+	5.82694e14i	0.170285	+	0.294942i
$605$	−1.29917e15	+	2.25022e15i	−0.651643	+	1.12868i
$606$	−1.63547e15	+	2.83272e15i	−0.812913	+	1.40801i
$607$	−3.33270e14	−	5.77241e14i	−0.164157	−	0.284328i	0.772199	−	0.635381i	$-0.219157\pi$
$607$	−3.33270e14	−	5.77241e14i	−0.164157	−	0.284328i	−0.936356	+	0.351053i	$0.885824\pi$
$608$	2.51311e13			0.0122671
$609$	−3.22441e15	+	1.78737e14i	−1.55975	+	0.0864608i
$610$	2.38430e15			1.14300
$611$	−7.18844e14	−	1.24507e15i	−0.341514	−	0.591519i
$612$	6.20667e14	−	1.07503e15i	0.292231	−	0.506158i
$613$	−1.04774e15	+	1.81474e15i	−0.488902	+	0.846803i	−0.999918	−	0.0127677i	$-0.995936\pi$
$613$	−1.04774e15	+	1.81474e15i	−0.488902	+	0.846803i	0.511016	+	0.859571i	$0.329269\pi$
$614$	−2.41759e14	−	4.18739e14i	−0.111804	−	0.193650i
$615$	4.05050e15			1.85650
$616$	−2.30388e14	+	1.27710e13i	−0.104656	+	0.00580136i
$617$	−2.06813e15			−0.931128			−0.465564	−	0.885014i	$-0.654148\pi$
$617$	−2.06813e15			−0.931128			−0.465564	+	0.885014i	$0.654148\pi$
$618$	−1.60422e15	−	2.77859e15i	−0.715857	−	1.23990i
$619$	−1.23313e15	+	2.13584e15i	−0.545394	+	0.944650i	0.453188	+	0.891415i	$0.350287\pi$
$619$	−1.23313e15	+	2.13584e15i	−0.545394	+	0.944650i	−0.998582	+	0.0532349i	$0.983047\pi$
$620$	1.44666e14	−	2.50569e14i	0.0634180	−	0.109843i
$621$	3.33968e15	+	5.78450e15i	1.45111	+	2.51340i
$622$	−1.71888e15			−0.740286
$623$	4.36314e14	−	8.62737e14i	0.186258	−	0.368294i
$624$	1.47369e15			0.623580
$625$	1.14033e15	+	1.97512e15i	0.478290	+	0.828423i
$626$	8.64456e14	−	1.49728e15i	0.359405	−	0.622508i
$627$	−4.63634e13	+	8.03037e13i	−0.0191075	+	0.0330951i
$628$	−9.76160e14	−	1.69076e15i	−0.398789	−	0.690723i
$629$	−1.83364e15			−0.742567
$630$	3.37461e15	+	5.16230e15i	1.35472	+	2.07238i
$631$	1.15579e14			0.0459958			0.0229979	−	0.999736i	$-0.492679\pi$
$631$	1.15579e14			0.0459958			0.0229979	+	0.999736i	$0.492679\pi$
$632$	2.61689e14	+	4.53258e14i	0.103238	+	0.178814i
$633$	2.11925e15	−	3.67065e15i	0.828823	−	1.43556i
$634$	5.53067e14	−	9.57940e14i	0.214431	−	0.371405i
$635$	−1.12096e15	−	1.94156e15i	−0.430858	−	0.746267i
$636$	−8.87517e14			−0.338192
$637$	−1.42613e15	+	3.25586e15i	−0.538757	+	1.22998i
$638$	4.70714e14			0.176296
$639$	−3.55867e15	−	6.16380e15i	−1.32140	−	2.28873i
$640$	−1.71533e14	+	2.97105e14i	−0.0631479	+	0.109375i
$641$	−2.24626e14	+	3.89063e14i	−0.0819861	+	0.142004i	−0.904103	−	0.427315i	$-0.859460\pi$
$641$	−2.24626e14	+	3.89063e14i	−0.0819861	+	0.142004i	0.822117	+	0.569319i	$0.192793\pi$
$642$	1.48602e15	+	2.57386e15i	0.537753	+	0.931415i
$643$	4.10162e14			0.147162			0.0735809	−	0.997289i	$-0.476557\pi$
$643$	4.10162e14			0.147162			0.0735809	+	0.997289i	$0.476557\pi$
$644$	−8.28396e14	−	1.26723e15i	−0.294690	−	0.450801i
$645$	−3.49198e14			−0.123167
$646$	3.34644e13	+	5.79620e13i	0.0117032	+	0.0202705i
$647$	2.10384e15	−	3.64396e15i	0.729524	−	1.26357i	−0.227560	−	0.973764i	$-0.573075\pi$
$647$	2.10384e15	−	3.64396e15i	0.729524	−	1.26357i	0.957084	−	0.289809i	$-0.0935918\pi$
$648$	1.31334e15	−	2.27478e15i	0.451561	−	0.782126i
$649$	3.33606e14	+	5.77823e14i	0.113733	+	0.196992i
$650$	−2.92587e15			−0.989081
$651$	4.43998e14	−	8.77930e14i	0.148828	−	0.294282i
$652$	1.05049e15			0.349164
$653$	5.69350e14	+	9.86142e14i	0.187653	+	0.325025i	0.944467	−	0.328605i	$-0.106578\pi$
$653$	5.69350e14	+	9.86142e14i	0.187653	+	0.325025i	−0.756814	+	0.653630i	$0.773245\pi$
$654$	3.06249e15	−	5.30438e15i	1.00091	−	1.73363i
$655$	9.58343e13	−	1.65990e14i	0.0310595	−	0.0537966i
$656$	2.72046e14	+	4.71198e14i	0.0874322	+	0.151437i
$657$	−3.25331e15			−1.03685
$658$	1.13629e15	−	6.29871e13i	0.359125	−	0.0199072i
$659$	4.18339e15			1.31117			0.655584	−	0.755122i	$-0.272423\pi$
$659$	4.18339e15			1.31117			0.655584	+	0.755122i	$0.272423\pi$
$660$	−6.32912e14	−	1.09624e15i	−0.196721	−	0.340731i
$661$	−2.81203e15	+	4.87057e15i	−0.866785	+	1.50132i	−0.00152075	+	0.999999i	$0.500484\pi$
$661$	−2.81203e15	+	4.87057e15i	−0.866785	+	1.50132i	−0.865264	+	0.501316i	$0.832849\pi$
$662$	−2.05615e15	+	3.56136e15i	−0.628545	+	1.08867i
$663$	1.96236e15	+	3.39891e15i	0.594915	+	1.03042i
$664$	−1.98164e15			−0.595799
$665$	−3.32019e14	+	1.84046e13i	−0.0990020	+	0.00548792i
$666$	−9.12114e15			−2.69737
$667$	1.54426e15	+	2.67473e15i	0.452926	+	0.784491i
$668$	−1.22405e15	+	2.12011e15i	−0.356063	+	0.616719i
$669$	3.90513e15	−	6.76388e15i	1.12666	−	1.95143i
$670$	−1.75587e15	−	3.04126e15i	−0.502437	−	0.870247i
$671$	−1.18173e15			−0.335386
$672$	−5.26457e14	+	1.04098e15i	−0.148194	+	0.293029i
$673$	5.05272e14			0.141072			0.0705362	−	0.997509i	$-0.477529\pi$
$673$	5.05272e14			0.141072			0.0705362	+	0.997509i	$0.477529\pi$
$674$	−1.65278e15	−	2.86270e15i	−0.457706	−	0.792769i
$675$	−5.10894e15	+	8.84895e15i	−1.40333	+	2.43064i
$676$	−7.36927e14	+	1.27639e15i	−0.200779	+	0.347759i
$677$	−7.63868e14	−	1.32306e15i	−0.206434	−	0.357553i	0.744155	−	0.668007i	$-0.232852\pi$
$677$	−7.63868e14	−	1.32306e15i	−0.206434	−	0.357553i	−0.950589	+	0.310454i	$0.899519\pi$
$678$	6.63800e15			1.77940
$679$	2.42176e15	+	3.70467e15i	0.643942	+	0.985067i
$680$	−9.13652e14			−0.240980
$681$	9.43188e14	+	1.63365e15i	0.246768	+	0.427415i
$682$	−7.17009e13	+	1.24190e14i	−0.0186085	+	0.0322308i
$683$	3.40746e15	−	5.90190e15i	0.877238	−	1.51942i	0.0228783	−	0.999738i	$-0.492717\pi$
$683$	3.40746e15	−	5.90190e15i	0.877238	−	1.51942i	0.854360	−	0.519682i	$-0.173950\pi$
$684$	1.66463e14	+	2.88322e14i	0.0425118	+	0.0736325i
$685$	1.21507e15			0.307824
$686$	−1.79039e15	−	2.17049e15i	−0.449950	−	0.545477i
$687$	−1.16347e16			−2.90064
$688$	−2.34534e13	−	4.06224e13i	−0.00580054	−	0.0100468i
$689$	9.96414e14	−	1.72584e15i	0.244475	−	0.423443i
$690$	4.15275e15	−	7.19278e15i	1.01080	−	1.75076i
$691$	−2.80338e15	−	4.85560e15i	−0.676944	−	1.17250i	−0.975897	−	0.218234i	$-0.929971\pi$
$691$	−2.80338e15	−	4.85560e15i	−0.676944	−	1.17250i	0.298953	−	0.954268i	$-0.403363\pi$
$692$	2.93665e15			0.703507
$693$	−1.67256e15	−	2.55859e15i	−0.397511	−	0.608090i
$694$	4.37570e14			0.103174
$695$	−7.32023e14	−	1.26790e15i	−0.171241	−	0.296599i
$696$	1.18986e15	−	2.06090e15i	0.276151	−	0.478307i
$697$	−7.24511e14	+	1.25489e15i	−0.166826	+	0.288952i
$698$	5.20578e14	+	9.01667e14i	0.118927	+	0.205988i
$699$	−1.24619e16			−2.82462
$700$	1.04523e15	−	2.06676e15i	0.235056	−	0.464784i
$701$	7.51596e15			1.67701			0.838504	−	0.544895i	$-0.183430\pi$
$701$	7.51596e15			1.67701			0.838504	+	0.544895i	$0.183430\pi$
$702$	5.77798e15	+	1.00078e16i	1.27915	+	2.21555i
$703$	2.45891e14	−	4.25896e14i	0.0540119	−	0.0935513i
$704$	8.50172e13	−	1.47254e14i	0.0185292	−	0.0320935i
$705$	3.12156e15	+	5.40669e15i	0.675042	+	1.16921i
$706$	−6.05712e14			−0.129969
$707$	5.80483e15	−	3.21776e14i	1.23590	−	0.0685088i
$708$	3.37314e15			0.712610
$709$	−1.35794e15	−	2.35201e15i	−0.284659	−	0.493044i	0.687868	−	0.725836i	$-0.258547\pi$
$709$	−1.35794e15	−	2.35201e15i	−0.284659	−	0.493044i	−0.972526	+	0.232793i	$0.925214\pi$
$710$	−2.61927e15	+	4.53671e15i	−0.544828	+	0.943669i
$711$	−3.46675e15	+	6.00458e15i	−0.715549	+	1.23937i
$712$	3.56216e14	+	6.16984e14i	0.0729581	+	0.126367i
$713$	−9.40908e14			−0.191229
$714$	−3.10193e15	+	1.71948e14i	−0.625593	+	0.0346782i
$715$	2.84227e15			0.568830
$716$	1.40026e14	+	2.42531e14i	0.0278090	+	0.0481666i
$717$	5.82007e15	−	1.00807e16i	1.14703	−	1.98671i
$718$	2.35719e15	−	4.08277e15i	0.461009	−	0.798491i
$719$	3.07684e15	+	5.32925e15i	0.597168	+	1.03433i	0.993237	+	0.116104i	$0.0370407\pi$
$719$	3.07684e15	+	5.32925e15i	0.597168	+	1.03433i	−0.396069	+	0.918221i	$0.629626\pi$
$720$	−4.54481e15			−0.875361
$721$	−2.57360e15	+	5.08886e15i	−0.491924	+	0.972696i
$722$	3.70974e15			0.703702
$723$	6.40261e15	+	1.10896e16i	1.20530	+	2.08765i
$724$	−1.47751e15	+	2.55912e15i	−0.276037	+	0.478110i
$725$	−2.36235e15	+	4.09172e15i	−0.438012	+	0.758659i
$726$	−3.25531e15	−	5.63837e15i	−0.599020	−	1.03753i
$727$	3.95637e15			0.722533			0.361266	−	0.932463i	$-0.382345\pi$
$727$	3.95637e15			0.722533			0.361266	+	0.932463i	$0.382345\pi$
$728$	−1.43320e15	−	2.19244e15i	−0.259768	−	0.397379i
$729$	6.97473e15			1.25466
$730$	1.19726e15	+	2.07371e15i	0.213753	+	0.370231i
$731$	6.24607e13	−	1.08185e14i	0.0110678	−	0.0191700i
$732$	−2.98716e15	+	5.17391e15i	−0.525349	+	0.909931i
$733$	−1.81738e15	−	3.14779e15i	−0.317229	−	0.549457i	0.662680	−	0.748903i	$-0.269419\pi$
$733$	−1.81738e15	−	3.14779e15i	−0.317229	−	0.549457i	−0.979909	+	0.199446i	$0.936086\pi$
$734$	−1.35631e14			−0.0234980
$735$	6.19293e15	−	1.41385e16i	1.06492	−	2.43120i
$736$	1.11565e15			0.190415
$737$	8.70264e14	+	1.50734e15i	0.147428	+	0.255353i
$738$	−3.60396e15	+	6.24224e15i	−0.605996	+	1.04962i
$739$	−2.53693e15	+	4.39409e15i	−0.423413	+	0.733373i	−0.996271	−	0.0862819i	$-0.972501\pi$
$739$	−2.53693e15	+	4.39409e15i	−0.423413	+	0.733373i	0.572858	+	0.819655i	$0.305835\pi$
$740$	3.35669e15	+	5.81396e15i	0.556080	+	0.963158i
$741$	−1.05261e15			−0.173089
$742$	8.63133e14	+	1.32037e15i	0.140882	+	0.215514i
$743$	1.73028e15			0.280335			0.140168	−	0.990128i	$-0.455236\pi$
$743$	1.73028e15			0.280335			0.140168	+	0.990128i	$0.455236\pi$
$744$	3.62489e14	+	6.27849e14i	0.0582967	+	0.100973i
$745$	6.04324e15	−	1.04672e16i	0.964739	−	1.67098i
$746$	1.12958e15	−	1.95649e15i	0.179000	−	0.310037i
$747$	−1.31260e16	−	2.27348e16i	−2.06475	−	3.57625i
$748$	4.52834e14			0.0707098
$749$	2.38399e15	−	4.71393e15i	0.369533	−	0.730689i
$750$	5.08396e14			0.0782285
$751$	−4.99394e14	−	8.64975e14i	−0.0762822	−	0.132125i	0.825361	−	0.564605i	$-0.190972\pi$
$751$	−4.99394e14	−	8.64975e14i	−0.0762822	−	0.132125i	−0.901643	+	0.432481i	$0.857638\pi$
$752$	−4.19309e14	+	7.26265e14i	−0.0635823	+	0.110128i
$753$	−5.35079e15	+	9.26784e15i	−0.805463	+	1.39510i
$754$	2.67171e15	+	4.62755e15i	0.399253	+	0.691526i
$755$	6.56053e15			0.973264
$756$	−9.13332e15	+	5.06282e14i	−1.34511	+	0.0745629i
$757$	−1.72753e15			−0.252579			−0.126290	−	0.991993i	$-0.540307\pi$
$757$	−1.72753e15			−0.252579			−0.126290	+	0.991993i	$0.540307\pi$
$758$	−4.62939e15	−	8.01834e15i	−0.671959	−	1.16387i
$759$	−2.05823e15	+	3.56496e15i	−0.296595	+	0.513718i
$760$	1.22521e14	−	2.12212e14i	0.0175281	−	0.0303596i
$761$	7.75708e14	+	1.34357e15i	0.110175	+	0.190829i	0.915841	−	0.401542i	$-0.131526\pi$
$761$	7.75708e14	+	1.34357e15i	0.110175	+	0.190829i	−0.805666	+	0.592370i	$0.798192\pi$
$762$	5.61756e15			0.792128
$763$	−1.08698e16	+	6.02537e14i	−1.52172	+	0.0843527i
$764$	−3.33180e15			−0.463089
$765$	−6.05184e15	−	1.04821e16i	−0.835122	−	1.44647i
$766$	−1.81533e15	+	3.14425e15i	−0.248712	+	0.430783i
$767$	−3.78702e15	+	6.55931e15i	−0.515137	+	0.892244i
$768$	−4.29811e14	−	7.44454e14i	−0.0580484	−	0.100543i
$769$	2.36048e15			0.316524			0.158262	−	0.987397i	$-0.449411\pi$
$769$	2.36048e15			0.316524			0.158262	+	0.987397i	$0.449411\pi$
$770$	−1.01536e15	+	2.00771e15i	−0.135183	+	0.267302i
$771$	−1.99145e16			−2.63251
$772$	−4.86563e14	−	8.42752e14i	−0.0638622	−	0.110613i
$773$	−6.38424e13	+	1.10578e14i	−0.00831997	+	0.0144106i	−0.870155	−	0.492777i	$-0.835982\pi$
$773$	−6.38424e13	+	1.10578e14i	−0.00831997	+	0.0144106i	0.861835	+	0.507188i	$0.169315\pi$
$774$	3.10700e14	−	5.38149e14i	0.0402038	−	0.0696349i
$775$	−7.19685e14	−	1.24653e15i	−0.0924663	−	0.160156i
$776$	−3.26154e15			−0.416086
$777$	1.24904e16	+	1.91072e16i	1.58220	+	2.42037i
$778$	4.24620e15			0.534088
$779$	−1.94314e14	−	3.36561e14i	−0.0242688	−	0.0420347i
$780$	7.18466e15	−	1.24442e16i	0.891017	−	1.54329i
$781$	1.29819e15	−	2.24853e15i	0.159866	−	0.276897i
$782$	1.48560e15	+	2.57313e15i	0.181662	+	0.314648i
$783$	1.86606e16			2.26588
$784$	2.06067e15	−	2.29161e14i	0.248468	−	0.0276313i
$785$	−1.90362e16			−2.27928
$786$	2.40132e14	+	4.15920e14i	0.0285513	+	0.0494522i
$787$	3.90777e15	−	6.76846e15i	0.461390	−	0.799151i	−0.537641	−	0.843174i	$-0.680684\pi$
$787$	3.90777e15	−	6.76846e15i	0.461390	−	0.799151i	0.999031	+	0.0440233i	$0.0140176\pi$
$788$	−5.14193e12	+	8.90608e12i	−0.000602881	+	0.00104422i
$789$	1.19517e16	+	2.07009e16i	1.39157	+	2.41027i
$790$	5.10322e15			0.590059
$791$	−6.45562e15	−	9.87545e15i	−0.741255	−	1.13393i
$792$	2.25255e15			0.256853
$793$	−6.70736e15	−	1.16175e16i	−0.759537	−	1.31556i
$794$	−2.35558e15	+	4.07998e15i	−0.264902	+	0.458823i
$795$	−4.32689e15	+	7.49439e15i	−0.483233	+	0.836984i
$796$	−3.23472e15	−	5.60269e15i	−0.358768	−	0.621405i
$797$	6.95757e15			0.766368			0.383184	−	0.923672i	$-0.374828\pi$
$797$	6.95757e15			0.766368			0.383184	+	0.923672i	$0.374828\pi$
$798$	3.76031e14	−	7.43538e14i	0.0411347	−	0.0813368i
$799$	−2.23340e15			−0.242638
$800$	8.53346e14	+	1.47804e15i	0.0920725	+	0.159474i
$801$	−4.71900e15	+	8.17355e15i	−0.505675	+	0.875855i
$802$	1.76503e15	−	3.05712e15i	0.187842	−	0.325352i
$803$	−5.93397e14	−	1.02779e15i	−0.0627205	−	0.108635i
$804$	8.79937e15			0.923726
$805$	−1.47395e16	+	8.17044e14i	−1.53675	+	0.0851860i
$806$	−1.62786e15			−0.168568
$807$	7.35583e15	+	1.27407e16i	0.756532	+	1.31035i
$808$	−2.14208e15	+	3.71020e15i	−0.218813	+	0.378996i
$809$	−3.61624e15	+	6.26351e15i	−0.366894	+	0.635478i	−0.989078	−	0.147392i	$-0.952912\pi$
$809$	−3.61624e15	+	6.26351e15i	−0.366894	+	0.635478i	0.622185	+	0.782871i	$0.286245\pi$
$810$	−1.28058e16	−	2.21803e16i	−1.29045	−	2.23512i
$811$	4.95682e15			0.496122			0.248061	−	0.968744i	$-0.420207\pi$
$811$	4.95682e15			0.496122			0.248061	+	0.968744i	$0.420207\pi$
$812$	−4.22321e15	+	2.34103e14i	−0.419841	+	0.0232728i
$813$	3.07364e16			3.03498
$814$	−1.66368e15	−	2.88157e15i	−0.163168	−	0.282615i
$815$	5.12141e15	−	8.87055e15i	0.498911	−	0.864139i
$816$	1.14467e15	−	1.98262e15i	0.110760	−	0.191842i
$817$	1.67520e13	+	2.90153e13i	0.00161007	+	0.00278872i
$818$	3.59730e15			0.343426
$819$	1.56600e16	−	3.09651e16i	1.48502	−	2.93637i
$820$	5.30520e15			0.499719
$821$	−3.69548e14	−	6.40076e14i	−0.0345767	−	0.0598886i	0.848219	−	0.529645i	$-0.177675\pi$
$821$	−3.69548e14	−	6.40076e14i	−0.0345767	−	0.0598886i	−0.882796	+	0.469757i	$0.844342\pi$
$822$	−1.52230e15	+	2.63670e15i	−0.141483	+	0.245056i
$823$	8.05747e15	−	1.39560e16i	0.743875	−	1.28843i	−0.206844	−	0.978374i	$-0.566319\pi$
$823$	8.05747e15	−	1.39560e16i	0.743875	−	1.28843i	0.950719	−	0.310055i	$-0.100347\pi$
$824$	−2.10114e15	−	3.63929e15i	−0.192689	−	0.333747i
$825$	−6.29722e15			−0.573657
$826$	−3.28047e15	−	5.01828e15i	−0.296856	−	0.454113i
$827$	−1.78503e16			−1.60459			−0.802296	−	0.596926i	$-0.796389\pi$
$827$	−1.78503e16			−1.60459			−0.802296	+	0.596926i	$0.796389\pi$
$828$	7.38986e15	+	1.27996e16i	0.659887	+	1.14296i
$829$	−6.49860e15	+	1.12559e16i	−0.576461	+	0.998460i	0.419420	+	0.907792i	$0.362233\pi$
$829$	−6.49860e15	+	1.12559e16i	−0.576461	+	0.998460i	−0.995881	+	0.0906676i	$0.971100\pi$
$830$	−9.66103e15	+	1.67334e16i	−0.851322	+	1.47453i
$831$	1.49426e16	+	2.58814e16i	1.30804	+	2.26559i
$832$	1.93019e15			0.167850
$833$	3.27252e15	+	4.44757e15i	0.282706	+	0.384216i
$834$	3.66845e15			0.314825
$835$	1.19351e16	+	2.06722e16i	1.01754	+	1.76243i
$836$	−6.07250e13	+	1.05179e14i	−0.00514320	+	0.00890828i
$837$	−2.84245e15	+	4.92328e15i	−0.239168	+	0.414252i
$838$	−3.03720e15	−	5.26058e15i	−0.253882	−	0.439736i
$839$	−3.83501e15			−0.318475			−0.159238	−	0.987240i	$-0.550904\pi$
$839$	−3.83501e15			−0.318475			−0.159238	+	0.987240i	$0.550904\pi$
$840$	6.22364e15	+	9.52058e15i	0.513462	+	0.785466i
$841$	−3.57192e15			−0.292768
$842$	3.18725e15	+	5.52048e15i	0.259537	+	0.449532i
$843$	−9.53002e15	+	1.65065e16i	−0.770979	+	1.33537i
$844$	2.77571e15	−	4.80768e15i	0.223096	−	0.386413i
$845$	7.18544e15	+	1.24456e16i	0.573775	+	0.993808i
$846$	−1.11097e16			−0.881383
$847$	−5.22241e15	+	1.03264e16i	−0.411635	+	0.813938i
$848$	−1.16244e15			−0.0910316
$849$	−1.73173e16	−	2.99945e16i	−1.34737	−	2.33372i
$850$	−2.27262e15	+	3.93629e15i	−0.175680	+	0.304287i
$851$	1.09160e16	−	1.89070e16i	0.838396	−	1.45215i
$852$	−6.56309e15	−	1.13676e16i	−0.500830	−	0.867463i
$853$	−8.88285e15			−0.673492			−0.336746	−	0.941596i	$-0.609326\pi$
$853$	−8.88285e15			−0.673492			−0.336746	+	0.941596i	$0.609326\pi$
$854$	1.06024e16	−	5.87717e14i	0.798704	−	0.0442741i
$855$	3.24621e15			0.242976
$856$	1.94634e15	+	3.37115e15i	0.144748	+	0.250711i
$857$	−4.30831e15	+	7.46222e15i	−0.318356	+	0.551409i	−0.980145	−	0.198281i	$-0.936464\pi$
$857$	−4.30831e15	+	7.46222e15i	−0.318356	+	0.551409i	0.661789	+	0.749690i	$0.269797\pi$
$858$	−3.56094e15	+	6.16772e15i	−0.261447	+	0.452840i
$859$	−4.98251e15	−	8.62996e15i	−0.363484	−	0.629573i	0.625047	−	0.780587i	$-0.285080\pi$
$859$	−4.98251e15	−	8.62996e15i	−0.363484	−	0.629573i	−0.988532	+	0.151014i	$0.951746\pi$
$860$	−4.57366e14			−0.0331530
$861$	1.80116e16	−	9.98429e14i	1.29729	−	0.0719117i
$862$	2.19986e15			0.157437
$863$	1.52755e15	+	2.64580e15i	0.108627	+	0.188147i	0.915214	−	0.402968i	$-0.132021\pi$
$863$	1.52755e15	+	2.64580e15i	0.108627	+	0.188147i	−0.806587	+	0.591115i	$0.798688\pi$
$864$	3.37036e15	−	5.83763e15i	0.238150	−	0.412488i
$865$	1.43170e16	−	2.47977e16i	1.00522	−	1.74110i
$866$	−4.43890e14	−	7.68840e14i	−0.0309690	−	0.0536398i
$867$	−2.06976e16			−1.43487
$868$	5.81532e14	−	1.14988e15i	0.0400604	−	0.0792126i
$869$	−2.52931e15			−0.173138
$870$	−1.16018e16	−	2.00950e16i	−0.789170	−	1.36688i
$871$	−9.87903e15	+	1.71110e16i	−0.667751	+	1.15658i
$872$	4.01113e15	−	6.94748e15i	0.269418	−	0.466645i
$873$	−2.16038e16	−	3.74188e16i	−1.44195	−	2.49753i
$874$	−7.96876e14			−0.0528540
$875$	−4.94428e14	−	7.56348e14i	−0.0325881	−	0.0498514i
$876$	−5.99992e15			−0.392982
$877$	−2.06631e15	−	3.57895e15i	−0.134492	−	0.232948i	0.790911	−	0.611931i	$-0.209607\pi$
$877$	−2.06631e15	−	3.57895e15i	−0.134492	−	0.232948i	−0.925403	+	0.378983i	$0.876274\pi$
$878$	1.33229e15	−	2.30759e15i	0.0861743	−	0.149258i
$879$	−1.41594e16	+	2.45248e16i	−0.910134	+	1.57640i
$880$	−8.28964e14	−	1.43581e15i	−0.0529518	−	0.0917153i
$881$	2.04897e16			1.30067			0.650336	−	0.759647i	$-0.274628\pi$
$881$	2.04897e16			1.30067			0.650336	+	0.759647i	$0.274628\pi$
$882$	1.62786e16	+	2.21237e16i	1.02693	+	1.39566i
$883$	1.67624e16			1.05088			0.525438	−	0.850832i	$-0.323902\pi$
$883$	1.67624e16			1.05088			0.525438	+	0.850832i	$0.323902\pi$
$884$	2.57023e15	+	4.45177e15i	0.160134	+	0.277361i
$885$	1.64450e16	−	2.84836e16i	1.01823	−	1.76363i
$886$	8.62028e15	−	1.49308e16i	0.530440	−	0.918749i
$887$	−9.84570e15	−	1.70533e16i	−0.602097	−	1.04286i	−0.992503	−	0.122220i	$-0.960999\pi$
$887$	−9.84570e15	−	1.70533e16i	−0.602097	−	1.04286i	0.390406	−	0.920643i	$-0.372335\pi$
$888$	−1.68217e16			−1.02235
$889$	−5.46322e15	−	8.35733e15i	−0.329981	−	0.504787i
$890$	6.94660e15			0.416992
$891$	6.34695e15	+	1.09932e16i	0.378650	+	0.655841i
$892$	5.11479e15	−	8.85908e15i	0.303264	−	0.525269i
$893$	2.99499e14	−	5.18748e14i	0.0176487	−	0.0305684i
$894$	1.51425e16	+	2.62276e16i	0.886832	+	1.53604i
$895$	2.73065e15			0.158942
$896$	−6.89534e14	+	1.36344e15i	−0.0398898	+	0.0788753i
$897$	−4.67291e16			−2.68676
$898$	1.82560e15	+	3.16204e15i	0.104325	+	0.180695i
$899$	−1.31434e15	+	2.27650e15i	−0.0746499	+	0.129297i
$900$	−1.13048e16	+	1.95804e16i	−0.638158	+	1.10532i
$901$	−1.54790e15	−	2.68103e15i	−0.0868471	−	0.150424i
$902$	−2.62942e15			−0.146630
$903$	−1.55280e15	+	8.60755e13i	−0.0860662	+	0.00477086i
$904$	8.69420e15			0.478965
$905$	1.44065e16	+	2.49528e16i	0.788845	+	1.36632i
$906$	−8.21934e15	+	1.42363e16i	−0.447334	+	0.774805i
$907$	7.98542e15	−	1.38311e16i	0.431974	−	0.748201i	−0.565069	−	0.825043i	$-0.691151\pi$
$907$	7.98542e15	−	1.38311e16i	0.431974	−	0.748201i	0.997043	+	0.0768426i	$0.0244839\pi$
$908$	1.23535e15	+	2.13969e15i	0.0664231	+	0.115048i
$909$	−5.67549e16			−3.03320
$910$	−2.55007e16	+	1.41357e15i	−1.35464	+	0.0750911i
$911$	−7.80377e15			−0.412053			−0.206027	−	0.978546i	$-0.566053\pi$
$911$	−7.80377e15			−0.412053			−0.206027	+	0.978546i	$0.566053\pi$
$912$	3.07000e14	+	5.31739e14i	0.0161126	+	0.0279079i
$913$	4.78830e15	−	8.29357e15i	0.249800	−	0.432666i
$914$	−7.28490e15	+	1.26178e16i	−0.377763	+	0.654304i
$915$	2.91265e16	+	5.04485e16i	1.50131	+	2.60035i
$916$	−1.52387e16			−0.780771
$917$	3.85237e14	−	7.61740e14i	0.0196199	−	0.0387950i
$918$	1.79518e16			0.908810
$919$	4.34918e15	+	7.53299e15i	0.218863	+	0.379081i	0.954461	−	0.298337i	$-0.0964320\pi$
$919$	4.34918e15	+	7.53299e15i	0.218863	+	0.379081i	−0.735598	+	0.677418i	$0.763099\pi$
$920$	5.43912e15	−	9.42083e15i	0.272079	−	0.471255i
$921$	5.90664e15	−	1.02306e16i	0.293706	−	0.508713i
$922$	−2.84515e15	−	4.92794e15i	−0.140632	−	0.243582i
$923$	2.94735e16			1.44818
$924$	−3.08462e15	−	4.71869e15i	−0.150663	−	0.230476i
$925$	3.33978e16			1.62158
$926$	−6.88952e14	−	1.19330e15i	−0.0332528	−	0.0575956i
$927$	2.78351e16	−	4.82118e16i	1.33553	−	2.31321i
$928$	1.55844e15	−	2.69930e15i	0.0743320	−	0.128747i
$929$	2.05086e16	+	3.55220e16i	0.972412	+	1.68427i	0.688222	+	0.725500i	$0.258391\pi$
$929$	2.05086e16	+	3.55220e16i	0.972412	+	1.68427i	0.284190	+	0.958768i	$0.408275\pi$
$930$	7.06893e15			0.333194
$931$	−1.47187e15	+	1.63682e14i	−0.0689679	+	0.00766969i
$932$	−1.63221e16			−0.760308
$933$	−2.09978e16	−	3.63693e16i	−0.972355	−	1.68417i
$934$	−9.15891e15	+	1.58637e16i	−0.421635	+	0.730292i
$935$	2.20769e15	−	3.82383e15i	0.101035	−	0.174999i
$936$	1.27852e16	+	2.21446e16i	0.581687	+	1.00751i
$937$	−7.62475e15			−0.344872			−0.172436	−	0.985021i	$-0.555164\pi$
$937$	−7.62475e15			−0.344872			−0.172436	+	0.985021i	$0.555164\pi$
$938$	−8.55761e15	−	1.30910e16i	−0.384802	−	0.588648i
$939$	4.22406e16			1.88829
$940$	4.08850e15	+	7.08148e15i	0.181702	+	0.314718i
$941$	1.36567e16	−	2.36540e16i	0.603395	−	1.04511i	−0.388908	−	0.921277i	$-0.627148\pi$
$941$	1.36567e16	−	2.36540e16i	0.603395	−	1.04511i	0.992303	−	0.123834i	$-0.0395190\pi$
$942$	2.38494e16	−	4.13085e16i	1.04761	−	1.81451i
$943$	−8.62626e15	−	1.49411e16i	−0.376711	−	0.652482i
$944$	4.41802e15			0.191814
$945$	−4.02523e16	+	7.95921e16i	−1.73746	+	3.43554i
$946$	2.26685e14			0.00972793
$947$	−1.29620e16	−	2.24508e16i	−0.553027	−	0.957871i	−0.998054	−	0.0623538i	$-0.980139\pi$
$947$	−1.29620e16	−	2.24508e16i	−0.553027	−	0.957871i	0.445027	−	0.895517i	$-0.353194\pi$
$948$	−6.39356e15	+	1.10740e16i	−0.271204	+	0.469740i
$949$	6.73610e15	−	1.16673e16i	0.284082	−	0.492045i
$950$	−6.09517e14	−	1.05571e15i	−0.0255568	−	0.0442656i
$951$	2.70249e16			1.12661
$952$	−4.06279e15	+	2.25211e14i	−0.168392	+	0.00933438i
$953$	−3.31043e16			−1.36419			−0.682093	−	0.731265i	$-0.738930\pi$
$953$	−3.31043e16			−1.36419			−0.682093	+	0.731265i	$0.738930\pi$
$954$	−7.69974e15	−	1.33363e16i	−0.315472	−	0.546413i
$955$	−1.62434e16	+	2.81344e16i	−0.661697	+	1.14609i
$956$	7.62291e15	−	1.32033e16i	0.308747	−	0.534765i
$957$	5.75022e15	+	9.95966e15i	0.231563	+	0.401078i
$958$	5.04654e15			0.202061
$959$	5.40313e15	−	2.99508e14i	0.215101	−	0.0119236i
$960$	−8.38178e15			−0.331776
$961$	1.23038e16	+	2.13109e16i	0.484241	+	0.838730i
$962$	1.88857e16	−	3.27109e16i	0.739043	−	1.28006i
$963$	−2.57843e16	+	4.46596e16i	−1.00325	+	1.73768i
$964$	8.38590e15	+	1.45248e16i	0.324434	+	0.561936i
$965$	−9.48851e15			−0.365004
$966$	1.66933e16	−	3.30082e16i	0.638511	−	1.26255i
$967$	1.03306e16			0.392897			0.196449	−	0.980514i	$-0.437059\pi$
$967$	1.03306e16			0.392897			0.196449	+	0.980514i	$0.437059\pi$
$968$	−4.26369e15	−	7.38492e15i	−0.161239	−	0.279275i
$969$	−8.17599e14	+	1.41612e15i	−0.0307439	+	0.0532501i
$970$	−1.59009e16	+	2.75412e16i	−0.594534	+	1.02976i
$971$	−4.84130e14	−	8.38537e14i	−0.0179993	−	0.0311757i	0.856885	−	0.515507i	$-0.172396\pi$
$971$	−4.84130e14	−	8.38537e14i	−0.0179993	−	0.0311757i	−0.874885	+	0.484331i	$0.839063\pi$
$972$	2.77340e16			1.02529
$973$	−3.56766e15	−	5.45762e15i	−0.131149	−	0.200624i
$974$	−9.16453e15			−0.334993
$975$	−3.57423e16	−	6.19075e16i	−1.29914	−	2.25018i
$976$	−3.91247e15	+	6.77660e15i	−0.141409	+	0.244928i
$977$	−7.09083e15	+	1.22817e16i	−0.254846	+	0.441406i	−0.964854	−	0.262788i	$-0.915358\pi$
$977$	−7.09083e15	+	1.22817e16i	−0.254846	+	0.441406i	0.710008	+	0.704194i	$0.248691\pi$
$978$	1.28327e16	+	2.22269e16i	0.458621	+	0.794355i
$979$	−3.44295e15			−0.122356
$980$	8.11127e15	−	1.85180e16i	0.286646	−	0.654412i
$981$	1.06276e17			3.73469
$982$	−7.91676e15	−	1.37122e16i	−0.276652	−	0.479176i
$983$	−2.43090e16	+	4.21044e16i	−0.844738	+	1.46313i	0.0411098	+	0.999155i	$0.486911\pi$
$983$	−2.43090e16	+	4.21044e16i	−0.844738	+	1.46313i	−0.885848	+	0.463975i	$0.846423\pi$
$984$	−6.64661e15	+	1.15123e16i	−0.229682	+	0.397821i
$985$	5.01366e13	+	8.68392e13i	0.00172288	+	0.00298412i
$986$	8.30084e15			0.283660
$987$	1.52135e16	+	2.32728e16i	0.516994	+	0.790870i
$988$	−1.37867e15			−0.0465906
$989$	7.43678e14	+	1.28809e15i	0.0249922	+	0.0432878i
$990$	1.09818e16	−	1.90210e16i	0.367011	−	0.635682i
$991$	−1.72625e16	+	2.98995e16i	−0.573718	+	0.993709i	0.422461	+	0.906381i	$0.361166\pi$
$991$	−1.72625e16	+	2.98995e16i	−0.573718	+	0.993709i	−0.996180	+	0.0873282i	$0.972167\pi$
$992$	4.74775e14	+	8.22334e14i	0.0156918	+	0.0271790i
$993$	−1.00471e17			−3.30234
$994$	−1.05290e16	+	2.08193e16i	−0.344161	+	0.680520i
$995$	−6.30805e16			−2.05054
$996$	−2.42076e16	−	4.19288e16i	−0.782574	−	1.35546i
$997$	−1.72913e16	+	2.99493e16i	−0.555909	+	0.962862i	0.441924	+	0.897053i	$0.354296\pi$
$997$	−1.72913e16	+	2.99493e16i	−0.555909	+	0.962862i	−0.997832	+	0.0658092i	$0.979037\pi$
$998$	1.65651e16	−	2.86916e16i	0.529635	−	0.917355i
$999$	−6.59536e16	−	1.14235e17i	−2.09714	−	3.63236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.12.c.b.11.1	yes	8
3.2	odd	2		126.12.g.c.109.1		8
4.3	odd	2		112.12.i.b.81.4		8
7.2	even	3	inner	14.12.c.b.9.1	✓	8
7.3	odd	6		98.12.a.h.1.1		4
7.4	even	3		98.12.a.i.1.4		4
7.5	odd	6		98.12.c.n.79.4		8
7.6	odd	2		98.12.c.n.67.4		8
21.2	odd	6		126.12.g.c.37.1		8
28.23	odd	6		112.12.i.b.65.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.12.c.b.9.1	✓	8	7.2	even	3	inner
14.12.c.b.11.1	yes	8	1.1	even	1	trivial
98.12.a.h.1.1		4	7.3	odd	6
98.12.a.i.1.4		4	7.4	even	3
98.12.c.n.67.4		8	7.6	odd	2
98.12.c.n.79.4		8	7.5	odd	6
112.12.i.b.65.4		8	28.23	odd	6
112.12.i.b.81.4		8	4.3	odd	2
126.12.g.c.37.1		8	21.2	odd	6
126.12.g.c.109.1		8	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(16.0000 + 27.7128i) q^{2} +(-390.910 + 677.077i) q^{3} +(-512.000 + 886.810i) q^{4} +(4992.28 + 8646.88i) q^{5} -25018.3 q^{6} +(24330.9 + 37220.1i) q^{7} -32768.0 q^{8} +(-217048. - 375939. i) q^{9} +O(q^{10})\)	\(q+(16.0000 + 27.7128i) q^{2} +(-390.910 + 677.077i) q^{3} +(-512.000 + 886.810i) q^{4} +(4992.28 + 8646.88i) q^{5} -25018.3 q^{6} +(24330.9 + 37220.1i) q^{7} -32768.0 q^{8} +(-217048. - 375939. i) q^{9} +(-159753. + 276700. i) q^{10} +(79178.4 - 137141. i) q^{11} +(-400292. - 693327. i) q^{12} +1.79763e6 q^{13} +(-642178. + 1.26980e6i) q^{14} -7.80614e6 q^{15} +(-524288. - 908093. i) q^{16} +(1.39628e6 - 2.41842e6i) q^{17} +(6.94555e6 - 1.20300e7i) q^{18} +(374482. + 648622. i) q^{19} -1.02242e7 q^{20} +(-3.47121e7 + 1.92417e6i) q^{21} +5.06742e6 q^{22} +(1.66245e7 + 2.87945e7i) q^{23} +(1.28094e7 - 2.21865e7i) q^{24} +(-2.54317e7 + 4.40490e7i) q^{25} +(2.87621e7 + 4.98174e7i) q^{26} +2.00889e8 q^{27} +(-4.54646e7 + 2.52021e6i) q^{28} +9.28902e7 q^{29} +(-1.24898e8 - 2.16330e8i) q^{30} +(-1.41494e7 + 2.45075e7i) q^{31} +(1.67772e7 - 2.90590e7i) q^{32} +(6.19033e7 + 1.07220e8i) q^{33} +8.93618e7 q^{34} +(-2.00371e8 + 3.96200e8i) q^{35} +4.44515e8 q^{36} +(-3.28309e8 - 5.68647e8i) q^{37} +(-1.19834e7 + 2.07559e7i) q^{38} +(-7.02712e8 + 1.21713e9i) q^{39} +(-1.63587e8 - 2.83341e8i) q^{40} -5.18887e8 q^{41} +(-6.08717e8 - 9.31182e8i) q^{42} +4.47337e7 q^{43} +(8.10787e7 + 1.40432e8i) q^{44} +(2.16713e9 - 3.75359e9i) q^{45} +(-5.31985e8 + 9.21425e8i) q^{46} +(-3.99885e8 - 6.92620e8i) q^{47} +8.19799e8 q^{48} +(-7.93341e8 + 1.81120e9i) q^{49} -1.62763e9 q^{50} +(1.09164e9 + 1.89077e9i) q^{51} +(-9.20386e8 + 1.59416e9i) q^{52} +(5.54293e8 - 9.60064e8i) q^{53} +(3.21422e9 + 5.56720e9i) q^{54} +1.58112e9 q^{55} +(-7.97275e8 - 1.21963e9i) q^{56} -5.85556e8 q^{57} +(1.48624e9 + 2.57425e9i) q^{58} +(-2.10667e9 + 3.64887e9i) q^{59} +(3.99674e9 - 6.92256e9i) q^{60} +(-3.73122e9 - 6.46267e9i) q^{61} -9.05561e8 q^{62} +(8.71149e9 - 1.72255e10i) q^{63} +1.07374e9 q^{64} +(8.97427e9 + 1.55439e10i) q^{65} +(-1.98091e9 + 3.43103e9i) q^{66} +(-5.49559e9 + 9.51864e9i) q^{67} +(1.42979e9 + 2.47647e9i) q^{68} -2.59948e10 q^{69} +(-1.41857e10 + 7.86350e8i) q^{70} +1.63957e10 q^{71} +(7.11225e9 + 1.23188e10i) q^{72} +(3.74721e9 - 6.49036e9i) q^{73} +(1.05059e10 - 1.81967e10i) q^{74} +(-1.98830e10 - 3.44384e10i) q^{75} -7.66939e8 q^{76} +(7.03088e9 - 3.89739e8i) q^{77} -4.49736e10 q^{78} +(-7.98611e9 - 1.38323e10i) q^{79} +(5.23479e9 - 9.06692e9i) q^{80} +(-4.00801e10 + 6.94207e10i) q^{81} +(-8.30219e9 - 1.43798e10i) q^{82} +6.04748e10 q^{83} +(1.60662e10 - 3.17682e10i) q^{84} +2.78825e10 q^{85} +(7.15740e8 + 1.23970e9i) q^{86} +(-3.63118e10 + 6.28938e10i) q^{87} +(-2.59452e9 + 4.49384e9i) q^{88} +(-1.08709e10 - 1.88289e10i) q^{89} +1.38697e11 q^{90} +(4.37379e10 + 6.69079e10i) q^{91} -3.40471e10 q^{92} +(-1.10623e10 - 1.91604e10i) q^{93} +(1.27963e10 - 2.21639e10i) q^{94} +(-3.73904e9 + 6.47621e9i) q^{95} +(1.31168e10 + 2.27189e10i) q^{96} +9.95342e10 q^{97} +(-6.28868e10 + 6.99343e9i) q^{98} -6.87422e10 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

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