LMFDB - Embedded newform 14.10.c.b.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,10,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, 10, names="a")

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

chi := DirichletCharacter("14.9");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
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:	$7.21050170629$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4038x^{4} - 137923x^{3} + 16368349x^{2} - 286546260x + 5038160400 $ x^6 - x^5 + 4038x^4 - 137923x^3 + 16368349x^2 - 286546260x + 5038160400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.2
Root			$26.1296 + 45.2579i$ of defining polynomial
Character	$\chi$	$=$	14.9
Dual form			14.10.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)

$f(q)$	$=$	$q+(8.00000 - 13.8564i) q^{2} +(38.4345 + 66.5705i) q^{3} +(-128.000 - 221.703i) q^{4} +(546.130 - 945.925i) q^{5} +1229.90 q^{6} +(6111.84 - 1731.76i) q^{7} -4096.00 q^{8} +(6887.08 - 11928.8i) q^{9} +O(q^{10})$	\(q+(8.00000 - 13.8564i) q^{2} +(38.4345 + 66.5705i) q^{3} +(-128.000 - 221.703i) q^{4} +(546.130 - 945.925i) q^{5} +1229.90 q^{6} +(6111.84 - 1731.76i) q^{7} -4096.00 q^{8} +(6887.08 - 11928.8i) q^{9} +(-8738.08 - 15134.8i) q^{10} +(-27030.4 - 46818.1i) q^{11} +(9839.23 - 17042.0i) q^{12} +37802.6 q^{13} +(24898.8 - 98542.3i) q^{14} +83960.9 q^{15} +(-32768.0 + 56755.8i) q^{16} +(176735. + 306114. i) q^{17} +(-110193. - 190860. i) q^{18} +(-25105.3 + 43483.7i) q^{19} -279618. q^{20} +(350190. + 340309. i) q^{21} -864974. q^{22} +(-1.22926e6 + 2.12914e6i) q^{23} +(-157428. - 272673. i) q^{24} +(380047. + 658261. i) q^{25} +(302421. - 523808. i) q^{26} +2.57182e6 q^{27} +(-1.16625e6 - 1.13335e6i) q^{28} +1.40865e6 q^{29} +(671687. - 1.16340e6i) q^{30} +(-2.89162e6 - 5.00843e6i) q^{31} +(524288. + 908093. i) q^{32} +(2.07780e6 - 3.59886e6i) q^{33} +5.65552e6 q^{34} +(1.69974e6 - 6.72711e6i) q^{35} -3.52619e6 q^{36} +(-2.72938e6 + 4.72743e6i) q^{37} +(401685. + 695739. i) q^{38} +(1.45292e6 + 2.51653e6i) q^{39} +(-2.23695e6 + 3.87451e6i) q^{40} -1.73066e7 q^{41} +(7.51697e6 - 2.12990e6i) q^{42} +1.43644e6 q^{43} +(-6.91979e6 + 1.19854e7i) q^{44} +(-7.52248e6 - 1.30293e7i) q^{45} +(1.96682e7 + 3.40663e7i) q^{46} +(-1.52194e7 + 2.63607e7i) q^{47} -5.03768e6 q^{48} +(3.43556e7 - 2.11685e7i) q^{49} +1.21615e7 q^{50} +(-1.35854e7 + 2.35307e7i) q^{51} +(-4.83873e6 - 8.38092e6i) q^{52} +(2.15398e6 + 3.73080e6i) q^{53} +(2.05745e7 - 3.56361e7i) q^{54} -5.90485e7 q^{55} +(-2.50341e7 + 7.09329e6i) q^{56} -3.85964e6 q^{57} +(1.12692e7 - 1.95189e7i) q^{58} +(3.30728e7 + 5.72837e7i) q^{59} +(-1.07470e7 - 1.86143e7i) q^{60} +(1.00462e8 - 1.74006e8i) q^{61} -9.25317e7 q^{62} +(2.14350e7 - 8.48336e7i) q^{63} +1.67772e7 q^{64} +(2.06451e7 - 3.57584e7i) q^{65} +(-3.32448e7 - 5.75817e7i) q^{66} +(1.36301e8 + 2.36080e8i) q^{67} +(4.52441e7 - 7.83651e7i) q^{68} -1.88984e8 q^{69} +(-7.96156e7 - 7.73692e7i) q^{70} +1.43433e8 q^{71} +(-2.82095e7 + 4.88603e7i) q^{72} +(1.84016e8 + 3.18725e8i) q^{73} +(4.36701e7 + 7.56389e7i) q^{74} +(-2.92138e7 + 5.05998e7i) q^{75} +1.28539e7 q^{76} +(-2.46283e8 - 2.39334e8i) q^{77} +4.64935e7 q^{78} +(-2.31998e8 + 4.01832e8i) q^{79} +(3.57912e7 + 6.19921e7i) q^{80} +(-3.67120e7 - 6.35870e7i) q^{81} +(-1.38453e8 + 2.39808e8i) q^{82} -7.47626e8 q^{83} +(3.06231e7 - 1.21197e8i) q^{84} +3.86081e8 q^{85} +(1.14915e7 - 1.99038e7i) q^{86} +(5.41409e7 + 9.37748e7i) q^{87} +(1.10717e8 + 1.91767e8i) q^{88} +(5.63943e8 - 9.76778e8i) q^{89} -2.40719e8 q^{90} +(2.31043e8 - 6.54650e7i) q^{91} +6.29382e8 q^{92} +(2.22276e8 - 3.84992e8i) q^{93} +(2.43510e8 + 4.21771e8i) q^{94} +(2.74215e7 + 4.74955e7i) q^{95} +(-4.03015e7 + 6.98042e7i) q^{96} -1.27313e8 q^{97} +(-1.84743e7 - 6.45393e8i) q^{98} -7.44643e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 48 q^{2} + 71 q^{3} - 768 q^{4} - 1085 q^{5} + 2272 q^{6} - 6796 q^{7} - 24576 q^{8} - 9106 q^{9}+O(q^{10}) $ 6 * q + 48 * q^2 + 71 * q^3 - 768 * q^4 - 1085 * q^5 + 2272 * q^6 - 6796 * q^7 - 24576 * q^8 - 9106 * q^9	\( 6 q + 48 q^{2} + 71 q^{3} - 768 q^{4} - 1085 q^{5} + 2272 q^{6} - 6796 q^{7} - 24576 q^{8} - 9106 q^{9} + 17360 q^{10} + 2555 q^{11} + 18176 q^{12} + 36140 q^{13} + 43504 q^{14} - 706146 q^{15} - 196608 q^{16} + 20759 q^{17} + 145696 q^{18} + 1220649 q^{19} + 555520 q^{20} + 1951577 q^{21} + 81760 q^{22} - 1960903 q^{23} - 290816 q^{24} - 863572 q^{25} + 289120 q^{26} + 5777318 q^{27} + 2435840 q^{28} - 5212292 q^{29} - 5649168 q^{30} - 9377989 q^{31} + 3145728 q^{32} - 10778103 q^{33} + 664288 q^{34} + 20361719 q^{35} + 4662272 q^{36} - 25814913 q^{37} - 19530384 q^{38} + 37990822 q^{39} + 4444160 q^{40} + 418500 q^{41} - 2053952 q^{42} + 5888616 q^{43} + 654080 q^{44} - 37350558 q^{45} + 31374448 q^{46} + 48391269 q^{47} - 9306112 q^{48} + 108466086 q^{49} - 27634304 q^{50} - 75441987 q^{51} - 4625920 q^{52} + 102186411 q^{53} + 46218544 q^{54} - 456557402 q^{55} + 27836416 q^{56} + 86169178 q^{57} - 41698336 q^{58} + 144220135 q^{59} + 90386688 q^{60} + 280936871 q^{61} - 300095648 q^{62} + 33751838 q^{63} + 100663296 q^{64} - 186819738 q^{65} + 172449648 q^{66} + 170710399 q^{67} + 5314304 q^{68} - 1807308342 q^{69} - 347247824 q^{70} + 939517376 q^{71} + 37298176 q^{72} + 613838539 q^{73} + 413038608 q^{74} + 902254676 q^{75} - 624972288 q^{76} - 729499715 q^{77} + 1215706304 q^{78} + 197445809 q^{79} - 71106560 q^{80} + 887872901 q^{81} + 3348000 q^{82} - 2148362872 q^{83} - 532466944 q^{84} + 822545038 q^{85} + 47108928 q^{86} + 753428670 q^{87} - 10465280 q^{88} + 805730427 q^{89} - 1195217856 q^{90} + 17178248 q^{91} + 1003982336 q^{92} - 1721516327 q^{93} - 774260304 q^{94} + 1799421743 q^{95} - 74448896 q^{96} - 4525836188 q^{97} - 597954960 q^{98} - 2607425268 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 + 71 * q^3 - 768 * q^4 - 1085 * q^5 + 2272 * q^6 - 6796 * q^7 - 24576 * q^8 - 9106 * q^9 + 17360 * q^10 + 2555 * q^11 + 18176 * q^12 + 36140 * q^13 + 43504 * q^14 - 706146 * q^15 - 196608 * q^16 + 20759 * q^17 + 145696 * q^18 + 1220649 * q^19 + 555520 * q^20 + 1951577 * q^21 + 81760 * q^22 - 1960903 * q^23 - 290816 * q^24 - 863572 * q^25 + 289120 * q^26 + 5777318 * q^27 + 2435840 * q^28 - 5212292 * q^29 - 5649168 * q^30 - 9377989 * q^31 + 3145728 * q^32 - 10778103 * q^33 + 664288 * q^34 + 20361719 * q^35 + 4662272 * q^36 - 25814913 * q^37 - 19530384 * q^38 + 37990822 * q^39 + 4444160 * q^40 + 418500 * q^41 - 2053952 * q^42 + 5888616 * q^43 + 654080 * q^44 - 37350558 * q^45 + 31374448 * q^46 + 48391269 * q^47 - 9306112 * q^48 + 108466086 * q^49 - 27634304 * q^50 - 75441987 * q^51 - 4625920 * q^52 + 102186411 * q^53 + 46218544 * q^54 - 456557402 * q^55 + 27836416 * q^56 + 86169178 * q^57 - 41698336 * q^58 + 144220135 * q^59 + 90386688 * q^60 + 280936871 * q^61 - 300095648 * q^62 + 33751838 * q^63 + 100663296 * q^64 - 186819738 * q^65 + 172449648 * q^66 + 170710399 * q^67 + 5314304 * q^68 - 1807308342 * q^69 - 347247824 * q^70 + 939517376 * q^71 + 37298176 * q^72 + 613838539 * q^73 + 413038608 * q^74 + 902254676 * q^75 - 624972288 * q^76 - 729499715 * q^77 + 1215706304 * q^78 + 197445809 * q^79 - 71106560 * q^80 + 887872901 * q^81 + 3348000 * q^82 - 2148362872 * q^83 - 532466944 * q^84 + 822545038 * q^85 + 47108928 * q^86 + 753428670 * q^87 - 10465280 * q^88 + 805730427 * q^89 - 1195217856 * q^90 + 17178248 * q^91 + 1003982336 * q^92 - 1721516327 * q^93 - 774260304 * q^94 + 1799421743 * q^95 - 74448896 * q^96 - 4525836188 * q^97 - 597954960 * q^98 - 2607425268 * 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 $

$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$3$	38.4345	+	66.5705i	0.273953	+	0.474500i	0.969870	−	0.243622i	$-0.0783355\pi$
$3$	38.4345	+	66.5705i	0.273953	+	0.474500i	−0.695918	+	0.718121i	$0.745002\pi$
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	546.130	−	945.925i	0.390779	−	0.676849i	−0.601774	−	0.798667i	$-0.705539\pi$
$5$	546.130	−	945.925i	0.390779	−	0.676849i	0.992552	+	0.121818i	$0.0388725\pi$
$6$	1229.90			0.387427
$7$	6111.84	−	1731.76i	0.962124	−	0.272613i
$7$	6111.84	−	1731.76i	0.962124	−	0.272613i
$8$	−4096.00			−0.353553
$9$	6887.08	−	11928.8i	0.349900	−	0.606045i
$10$	−8738.08	−	15134.8i	−0.276322	−	0.478604i
$11$	−27030.4	−	46818.1i	−0.556655	−	0.964154i	−0.997773	−	0.0667050i	$-0.978751\pi$
$11$	−27030.4	−	46818.1i	−0.556655	−	0.964154i	0.441118	−	0.897449i	$-0.354582\pi$
$12$	9839.23	−	17042.0i	0.136976	−	0.237250i
$13$	37802.6			0.367093			0.183547	−	0.983011i	$-0.441242\pi$
$13$	37802.6			0.367093			0.183547	+	0.983011i	$0.441242\pi$
$14$	24898.8	−	98542.3i	0.173221	−	0.685561i
$15$	83960.9			0.428219
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	176735.	+	306114.i	0.513218	+	0.888920i	0.999882	+	0.0153311i	$0.00488024\pi$
$17$	176735.	+	306114.i	0.513218	+	0.888920i	−0.486664	+	0.873589i	$0.661786\pi$
$18$	−110193.	−	190860.i	−0.247417	−	0.428538i
$19$	−25105.3	+	43483.7i	−0.0441952	+	0.0765483i	−0.887277	−	0.461237i	$-0.847406\pi$
$19$	−25105.3	+	43483.7i	−0.0441952	+	0.0765483i	0.843082	+	0.537786i	$0.180739\pi$
$20$	−279618.			−0.390779
$21$	350190.	+	340309.i	0.392931	+	0.381844i
$22$	−864974.			−0.787228
$23$	−1.22926e6	+	2.12914e6i	−0.915944	+	1.58646i	−0.110432	+	0.993884i	$0.535223\pi$
$23$	−1.22926e6	+	2.12914e6i	−0.915944	+	1.58646i	−0.805513	+	0.592579i	$0.798110\pi$
$24$	−157428.	−	272673.i	−0.0968569	−	0.167761i
$25$	380047.	+	658261.i	0.194584	+	0.337029i
$26$	302421.	−	523808.i	0.129787	−	0.224798i
$27$	2.57182e6			0.931329
$28$	−1.16625e6	−	1.13335e6i	−0.358576	−	0.348459i
$29$	1.40865e6			0.369840			0.184920	−	0.982754i	$-0.440797\pi$
$29$	1.40865e6			0.369840			0.184920	+	0.982754i	$0.440797\pi$
$30$	671687.	−	1.16340e6i	0.151398	−	0.262230i
$31$	−2.89162e6	−	5.00843e6i	−0.562358	−	0.974033i	−0.997290	−	0.0735696i	$-0.976561\pi$
$31$	−2.89162e6	−	5.00843e6i	−0.562358	−	0.974033i	0.434932	−	0.900463i	$-0.356772\pi$
$32$	524288.	+	908093.i	0.0883883	+	0.153093i
$33$	2.07780e6	−	3.59886e6i	0.304994	−	0.528265i
$34$	5.65552e6			0.725800
$35$	1.69974e6	−	6.72711e6i	0.191460	−	0.757743i
$36$	−3.52619e6			−0.349900
$37$	−2.72938e6	+	4.72743e6i	−0.239418	+	0.414684i	−0.960547	−	0.278116i	$-0.910290\pi$
$37$	−2.72938e6	+	4.72743e6i	−0.239418	+	0.414684i	0.721129	+	0.692800i	$0.243623\pi$
$38$	401685.	+	695739.i	0.0312507	+	0.0541278i
$39$	1.45292e6	+	2.51653e6i	0.100566	+	0.174186i
$40$	−2.23695e6	+	3.87451e6i	−0.138161	+	0.239302i
$41$	−1.73066e7			−0.956501			−0.478251	−	0.878223i	$-0.658729\pi$
$41$	−1.73066e7			−0.956501			−0.478251	+	0.878223i	$0.658729\pi$
$42$	7.51697e6	−	2.12990e6i	0.372753	−	0.105618i
$43$	1.43644e6			0.0640735			0.0320367	−	0.999487i	$-0.489801\pi$
$43$	1.43644e6			0.0640735			0.0320367	+	0.999487i	$0.489801\pi$
$44$	−6.91979e6	+	1.19854e7i	−0.278327	+	0.482077i
$45$	−7.52248e6	−	1.30293e7i	−0.273467	−	0.473659i
$46$	1.96682e7	+	3.40663e7i	0.647671	+	1.12180i
$47$	−1.52194e7	+	2.63607e7i	−0.454942	+	0.787982i	−0.998685	−	0.0512695i	$-0.983673\pi$
$47$	−1.52194e7	+	2.63607e7i	−0.454942	+	0.787982i	0.543743	+	0.839252i	$0.317007\pi$
$48$	−5.03768e6			−0.136976
$49$	3.43556e7	−	2.11685e7i	0.851364	−	0.524575i
$50$	1.21615e7			0.275183
$51$	−1.35854e7	+	2.35307e7i	−0.281195	+	0.487044i
$52$	−4.83873e6	−	8.38092e6i	−0.0917733	−	0.158956i
$53$	2.15398e6	+	3.73080e6i	0.0374973	+	0.0649473i	0.884165	−	0.467175i	$-0.154728\pi$
$53$	2.15398e6	+	3.73080e6i	0.0374973	+	0.0649473i	−0.846668	+	0.532122i	$0.821395\pi$
$54$	2.05745e7	−	3.56361e7i	0.329275	−	0.570320i
$55$	−5.90485e7			−0.870115
$56$	−2.50341e7	+	7.09329e6i	−0.340162	+	0.0963833i
$57$	−3.85964e6			−0.0484295
$58$	1.12692e7	−	1.95189e7i	0.130758	−	0.226480i
$59$	3.30728e7	+	5.72837e7i	0.355334	+	0.615456i	0.987175	−	0.159642i	$-0.0510338\pi$
$59$	3.30728e7	+	5.72837e7i	0.355334	+	0.615456i	−0.631841	+	0.775098i	$0.717700\pi$
$60$	−1.07470e7	−	1.86143e7i	−0.107055	−	0.185424i
$61$	1.00462e8	−	1.74006e8i	0.929008	−	1.60909i	0.144022	−	0.989574i	$-0.453996\pi$
$61$	1.00462e8	−	1.74006e8i	0.929008	−	1.60909i	0.784986	−	0.619514i	$-0.212670\pi$
$62$	−9.25317e7			−0.795295
$63$	2.14350e7	−	8.48336e7i	0.171431	−	0.678477i
$64$	1.67772e7			0.125000
$65$	2.06451e7	−	3.57584e7i	0.143452	−	0.248466i
$66$	−3.32448e7	−	5.75817e7i	−0.215663	−	0.373540i
$67$	1.36301e8	+	2.36080e8i	0.826347	+	1.43127i	0.900886	+	0.434057i	$0.142918\pi$
$67$	1.36301e8	+	2.36080e8i	0.826347	+	1.43127i	−0.0745386	+	0.997218i	$0.523748\pi$
$68$	4.52441e7	−	7.83651e7i	0.256609	−	0.444460i
$69$	−1.88984e8			−1.00370
$70$	−7.96156e7	−	7.73692e7i	−0.396330	−	0.385147i
$71$	1.43433e8			0.669866			0.334933	−	0.942242i	$-0.391286\pi$
$71$	1.43433e8			0.669866			0.334933	+	0.942242i	$0.391286\pi$
$72$	−2.82095e7	+	4.88603e7i	−0.123708	+	0.214269i
$73$	1.84016e8	+	3.18725e8i	0.758407	+	1.31360i	0.943663	+	0.330909i	$0.107355\pi$
$73$	1.84016e8	+	3.18725e8i	0.758407	+	1.31360i	−0.185256	+	0.982690i	$0.559311\pi$
$74$	4.36701e7	+	7.56389e7i	0.169294	+	0.293226i
$75$	−2.92138e7	+	5.05998e7i	−0.106614	+	0.184660i
$76$	1.28539e7			0.0441952
$77$	−2.46283e8	−	2.39334e8i	−0.798412	−	0.775884i
$78$	4.64935e7			0.142222
$79$	−2.31998e8	+	4.01832e8i	−0.670134	+	1.16071i	0.307731	+	0.951473i	$0.400430\pi$
$79$	−2.31998e8	+	4.01832e8i	−0.670134	+	1.16071i	−0.977866	+	0.209233i	$0.932903\pi$
$80$	3.57912e7	+	6.19921e7i	0.0976947	+	0.169212i
$81$	−3.67120e7	−	6.35870e7i	−0.0947600	−	0.164129i
$82$	−1.38453e8	+	2.39808e8i	−0.338174	+	0.585735i
$83$	−7.47626e8			−1.72915			−0.864576	−	0.502503i	$-0.832413\pi$
$83$	−7.47626e8			−1.72915			−0.864576	+	0.502503i	$0.832413\pi$
$84$	3.06231e7	−	1.21197e8i	0.0671107	−	0.265605i
$85$	3.86081e8			0.802219
$86$	1.14915e7	−	1.99038e7i	0.0226534	−	0.0392368i
$87$	5.41409e7	+	9.37748e7i	0.101319	+	0.175489i
$88$	1.10717e8	+	1.91767e8i	0.196807	+	0.340880i
$89$	5.63943e8	−	9.76778e8i	0.952753	−	1.65022i	0.213325	−	0.976981i	$-0.431571\pi$
$89$	5.63943e8	−	9.76778e8i	0.952753	−	1.65022i	0.739428	−	0.673235i	$-0.235096\pi$
$90$	−2.40719e8			−0.386741
$91$	2.31043e8	−	6.54650e7i	0.353189	−	0.100074i
$92$	6.29382e8			0.915944
$93$	2.22276e8	−	3.84992e8i	0.308119	−	0.533678i
$94$	2.43510e8	+	4.21771e8i	0.321692	+	0.557188i
$95$	2.74215e7	+	4.74955e7i	0.0345410	+	0.0598269i
$96$	−4.03015e7	+	6.98042e7i	−0.0484284	+	0.0838805i
$97$	−1.27313e8			−0.146016			−0.0730079	−	0.997331i	$-0.523260\pi$
$97$	−1.27313e8			−0.146016			−0.0730079	+	0.997331i	$0.523260\pi$
$98$	−1.84743e7	−	6.45393e8i	−0.0202325	−	0.706817i
$99$	−7.44643e8			−0.779094
$100$	9.72920e7	−	1.68515e8i	0.0972920	−	0.168515i
$101$	−7.52725e8	−	1.30376e9i	−0.719764	−	1.24667i	−0.961093	−	0.276225i	$-0.910917\pi$
$101$	−7.52725e8	−	1.30376e9i	−0.719764	−	1.24667i	0.241329	−	0.970443i	$-0.422417\pi$
$102$	2.17367e8	+	3.76490e8i	0.198835	+	0.344392i
$103$	2.97478e8	−	5.15246e8i	0.260428	−	0.451074i	−0.705928	−	0.708284i	$-0.749470\pi$
$103$	2.97478e8	−	5.15246e8i	0.260428	−	0.451074i	0.966356	+	0.257210i	$0.0828032\pi$
$104$	−1.54839e8			−0.129787
$105$	5.13155e8	−	1.45400e8i	0.412000	−	0.116738i
$106$	6.89274e7			0.0530292
$107$	−6.77457e8	+	1.17339e9i	−0.499637	+	0.865397i	−1.00000		0.000418881i	$-0.999867\pi$
$107$	−6.77457e8	+	1.17339e9i	−0.499637	+	0.865397i	0.500363	+	0.865816i	$0.333200\pi$
$108$	−3.29193e8	−	5.70178e8i	−0.232832	−	0.403277i
$109$	9.68920e8	+	1.67822e9i	0.657459	+	1.13875i	0.981271	+	0.192631i	$0.0617021\pi$
$109$	9.68920e8	+	1.67822e9i	0.657459	+	1.13875i	−0.323812	+	0.946121i	$0.604965\pi$
$110$	−4.72388e8	+	8.18200e8i	−0.307632	+	0.532834i
$111$	−4.19610e8			−0.262357
$112$	−1.01985e8	+	4.03629e8i	−0.0612430	+	0.242383i
$113$	−1.98306e9			−1.14415			−0.572074	−	0.820202i	$-0.693861\pi$
$113$	−1.98306e9			−1.14415			−0.572074	+	0.820202i	$0.693861\pi$
$114$	−3.08771e7	+	5.34808e7i	−0.0171224	+	0.0296569i
$115$	1.34267e9	+	2.32558e9i	0.715863	+	1.23991i
$116$	−1.80308e8	−	3.12302e8i	−0.0924599	−	0.160145i
$117$	2.60349e8	−	4.50938e8i	0.128446	−	0.222475i
$118$	1.05833e9			0.502518
$119$	1.61029e9	+	1.56486e9i	0.736111	+	0.715341i
$120$	−3.43904e8			−0.151398
$121$	−2.82314e8	+	4.88982e8i	−0.119729	+	0.207376i
$122$	−1.60740e9	−	2.78410e9i	−0.656908	−	1.13780i
$123$	−6.65172e8	−	1.15211e9i	−0.262036	−	0.453860i
$124$	−7.40254e8	+	1.28216e9i	−0.281179	+	0.487016i
$125$	2.96354e9			1.08571
$126$	−1.00401e9	−	9.75680e8i	−0.354871	−	0.344858i
$127$	3.90286e7			0.0133127			0.00665635	−	0.999978i	$-0.497881\pi$
$127$	3.90286e7			0.0133127			0.00665635	+	0.999978i	$0.497881\pi$
$128$	1.34218e8	−	2.32472e8i	0.0441942	−	0.0765466i
$129$	5.52087e7	+	9.56243e7i	0.0175531	+	0.0304029i
$130$	−3.30322e8	−	5.72134e8i	−0.101436	−	0.175692i
$131$	−7.96889e8	+	1.38025e9i	−0.236416	+	0.409485i	−0.959683	−	0.281083i	$-0.909306\pi$
$131$	−7.96889e8	+	1.38025e9i	−0.236416	+	0.409485i	0.723267	+	0.690568i	$0.242640\pi$
$132$	−1.06383e9			−0.304994
$133$	−7.81364e7	+	3.09242e8i	−0.0216532	+	0.0856971i
$134$	4.36163e9			1.16863
$135$	1.40455e9	−	2.43275e9i	0.363944	−	0.630369i
$136$	−7.23906e8	−	1.25384e9i	−0.181450	−	0.314281i
$137$	−2.81817e9	−	4.88122e9i	−0.683479	−	1.18382i	−0.973912	−	0.226925i	$-0.927133\pi$
$137$	−2.81817e9	−	4.88122e9i	−0.683479	−	1.18382i	0.290433	−	0.956895i	$-0.406201\pi$
$138$	−1.51187e9	+	2.61864e9i	−0.354862	+	0.614639i
$139$	2.40520e9			0.546493			0.273246	−	0.961944i	$-0.411903\pi$
$139$	2.40520e9			0.546493			0.273246	+	0.961944i	$0.411903\pi$
$140$	−1.70898e9	+	4.84232e8i	−0.375977	+	0.106531i
$141$	−2.33979e9			−0.498530
$142$	1.14747e9	−	1.98747e9i	0.236833	−	0.410208i
$143$	−1.02182e9	−	1.76984e9i	−0.204344	−	0.353934i
$144$	4.51352e8	+	7.81764e8i	0.0874750	+	0.151511i
$145$	7.69308e8	−	1.33248e9i	0.144525	−	0.250325i
$146$	5.88851e9			1.07255
$147$	2.72964e9	+	1.47347e9i	0.482144	+	0.260263i
$148$	1.39744e9			0.239418
$149$	−2.41463e9	+	4.18227e9i	−0.401341	+	0.695143i	−0.993888	−	0.110393i	$-0.964789\pi$
$149$	−2.41463e9	+	4.18227e9i	−0.401341	+	0.695143i	0.592547	+	0.805536i	$0.298122\pi$
$150$	4.67421e8	+	8.09597e8i	0.0753872	+	0.130574i
$151$	−5.33310e9	−	9.23721e9i	−0.834802	−	1.44592i	−0.894191	−	0.447685i	$-0.852248\pi$
$151$	−5.33310e9	−	9.23721e9i	−0.834802	−	1.44592i	0.0593887	−	0.998235i	$-0.481085\pi$
$152$	1.02831e8	−	1.78109e8i	0.0156253	−	0.0270639i
$153$	4.86875e9			0.718300
$154$	−5.28658e9	+	1.49793e9i	−0.757411	+	0.214609i
$155$	−6.31679e9			−0.879030
$156$	3.71948e8	−	6.44233e8i	0.0502830	−	0.0870928i
$157$	4.95301e9	+	8.57886e9i	0.650610	+	1.12689i	0.982975	+	0.183738i	$0.0588199\pi$
$157$	4.95301e9	+	8.57886e9i	0.650610	+	1.12689i	−0.332365	+	0.943151i	$0.607847\pi$
$158$	3.71196e9	+	6.42931e9i	0.473857	+	0.820744i
$159$	−1.65574e8	+	2.86783e8i	−0.0205450	+	0.0355850i
$160$	1.14532e9			0.138161
$161$	−3.82589e9	+	1.51418e10i	−0.448762	+	1.77607i
$162$	−1.17478e9			−0.134011
$163$	6.21440e9	−	1.07637e10i	0.689533	−	1.19431i	−0.282457	−	0.959280i	$-0.591149\pi$
$163$	6.21440e9	−	1.07637e10i	0.689533	−	1.19431i	0.971989	−	0.235025i	$-0.0755173\pi$
$164$	2.21525e9	+	3.83693e9i	0.239125	+	0.414177i
$165$	−2.26950e9	−	3.93089e9i	−0.238370	−	0.412869i
$166$	−5.98101e9	+	1.03594e10i	−0.611347	+	1.05888i
$167$	−5.48234e9			−0.545434			−0.272717	−	0.962094i	$-0.587922\pi$
$167$	−5.48234e9			−0.545434			−0.272717	+	0.962094i	$0.587922\pi$
$168$	−1.43438e9	−	1.39391e9i	−0.138922	−	0.135002i
$169$	−9.17547e9			−0.865243
$170$	3.08865e9	−	5.34969e9i	0.283627	−	0.491257i
$171$	3.45805e8	+	5.98952e8i	0.0309278	+	0.0535685i
$172$	−1.83864e8	−	3.18462e8i	−0.0160184	−	0.0277446i
$173$	2.29883e9	−	3.98170e9i	0.195119	−	0.337956i	−0.751820	−	0.659368i	$-0.770824\pi$
$173$	2.29883e9	−	3.98170e9i	0.195119	−	0.337956i	0.946940	+	0.321412i	$0.104157\pi$
$174$	1.73251e9			0.143286
$175$	3.46274e9	+	3.36504e9i	0.279093	+	0.271218i
$176$	3.54293e9			0.278327
$177$	−2.54227e9	+	4.40334e9i	−0.194689	+	0.337212i
$178$	−9.02309e9	−	1.56285e10i	−0.673698	−	1.16688i
$179$	−1.28201e9	−	2.22051e9i	−0.0933370	−	0.161664i	0.815576	−	0.578650i	$-0.196420\pi$
$179$	−1.28201e9	−	2.22051e9i	−0.0933370	−	0.161664i	−0.908913	+	0.416985i	$0.863087\pi$
$180$	−1.92576e9	+	3.33551e9i	−0.136733	+	0.236829i
$181$	−3.58323e9			−0.248154			−0.124077	−	0.992273i	$-0.539597\pi$
$181$	−3.58323e9			−0.248154			−0.124077	+	0.992273i	$0.539597\pi$
$182$	9.41237e8	−	3.72515e9i	0.0635884	−	0.251665i
$183$	1.54449e10			1.01802
$184$	5.03506e9	−	8.72097e9i	0.323835	−	0.560899i
$185$	2.98120e9	+	5.16358e9i	0.187119	+	0.324099i
$186$	−3.55641e9	−	6.15988e9i	−0.217873	−	0.377367i
$187$	9.55444e9	−	1.65488e10i	0.571371	−	0.989643i
$188$	7.79231e9			0.454942
$189$	1.57185e10	−	4.45377e9i	0.896054	−	0.253892i
$190$	8.77489e8			0.0488484
$191$	3.48694e8	−	6.03956e8i	0.0189581	−	0.0328364i	−0.856391	−	0.516328i	$-0.827298\pi$
$191$	3.48694e8	−	6.03956e8i	0.0189581	−	0.0328364i	0.875349	+	0.483492i	$0.160632\pi$
$192$	6.44824e8	+	1.11687e9i	0.0342441	+	0.0593125i
$193$	2.85429e8	+	4.94378e8i	0.0148078	+	0.0256479i	0.873334	−	0.487121i	$-0.161953\pi$
$193$	2.85429e8	+	4.94378e8i	0.0148078	+	0.0256479i	−0.858527	+	0.512769i	$0.828620\pi$
$194$	−1.01850e9	+	1.76410e9i	−0.0516244	+	0.0894161i
$195$	3.17394e9			0.157196
$196$	−9.09063e9	−	4.90716e9i	−0.439989	−	0.237508i
$197$	−4.88945e9			−0.231293			−0.115646	−	0.993290i	$-0.536894\pi$
$197$	−4.88945e9			−0.231293			−0.115646	+	0.993290i	$0.536894\pi$
$198$	−5.95714e9	+	1.03181e10i	−0.275451	+	0.477096i
$199$	−5.09120e9	−	8.81822e9i	−0.230134	−	0.398604i	0.727713	−	0.685882i	$-0.240583\pi$
$199$	−5.09120e9	−	8.81822e9i	−0.230134	−	0.398604i	−0.957847	+	0.287277i	$0.907250\pi$
$200$	−1.55667e9	−	2.69624e9i	−0.0687959	−	0.119158i
$201$	−1.04773e10	+	1.81472e10i	−0.452760	+	0.784203i
$202$	−2.40872e10			−1.01790
$203$	8.60948e9	−	2.43945e9i	0.355832	−	0.100823i
$204$	6.95574e9			0.281195
$205$	−9.45167e9	+	1.63708e10i	−0.373780	+	0.647406i
$206$	−4.75964e9	−	8.24394e9i	−0.184150	−	0.318957i
$207$	1.69321e10	+	2.93272e10i	0.640978	+	1.11021i
$208$	−1.23871e9	+	2.14552e9i	−0.0458866	+	0.0794780i
$209$	2.71443e9			0.0984058
$210$	2.09052e9	−	8.27369e9i	0.0741767	−	0.293571i
$211$	−2.89906e10			−1.00690			−0.503450	−	0.864025i	$-0.667936\pi$
$211$	−2.89906e10			−1.00690			−0.503450	+	0.864025i	$0.667936\pi$
$212$	5.51419e8	−	9.55086e8i	0.0187487	−	0.0324736i
$213$	5.51279e9	+	9.54844e9i	0.183512	+	0.317851i
$214$	1.08393e10	+	1.87742e10i	0.353297	+	0.611928i
$215$	7.84481e8	−	1.35876e9i	0.0250386	−	0.0433680i
$216$	−1.05342e10			−0.329275
$217$	−2.63465e10	−	2.56031e10i	−0.806592	−	0.783834i
$218$	3.10054e10			0.929788
$219$	−1.41451e10	+	2.45000e10i	−0.415535	+	0.719728i
$220$	7.55821e9	+	1.30912e10i	0.217529	+	0.376771i
$221$	6.68103e9	+	1.15719e10i	0.188399	+	0.326316i
$222$	−3.35688e9	+	5.81428e9i	−0.0927571	+	0.160660i
$223$	−9.01973e9			−0.244243			−0.122121	−	0.992515i	$-0.538970\pi$
$223$	−9.01973e9			−0.244243			−0.122121	+	0.992515i	$0.538970\pi$
$224$	4.77697e9	+	4.64218e9i	0.126776	+	0.123199i
$225$	1.04697e10			0.272340
$226$	−1.58645e10	+	2.74780e10i	−0.404517	+	0.700644i
$227$	−6.63153e9	−	1.14861e10i	−0.165767	−	0.287116i	0.771161	−	0.636641i	$-0.219677\pi$
$227$	−6.63153e9	−	1.14861e10i	−0.165767	−	0.287116i	−0.936927	+	0.349524i	$0.886343\pi$
$228$	4.94034e8	+	8.55692e8i	0.0121074	+	0.0209706i
$229$	3.83833e10	−	6.64819e10i	0.922323	−	1.59751i	0.126512	−	0.991965i	$-0.459622\pi$
$229$	3.83833e10	−	6.64819e10i	0.922323	−	1.59751i	0.795811	−	0.605545i	$-0.207045\pi$
$230$	4.29655e10			1.01238
$231$	6.46683e9	−	2.55939e10i	0.149430	−	0.591402i
$232$	−5.76985e9			−0.130758
$233$	1.14694e9	−	1.98657e9i	0.0254942	−	0.0441572i	−0.852997	−	0.521916i	$-0.825217\pi$
$233$	1.14694e9	−	1.98657e9i	0.0254942	−	0.0441572i	0.878491	+	0.477759i	$0.158551\pi$
$234$	−4.16559e9	−	7.21501e9i	−0.0908249	−	0.157313i
$235$	1.66235e10	+	2.87927e10i	0.355563	+	0.615853i
$236$	8.46663e9	−	1.46646e10i	0.177667	−	0.307728i
$237$	−3.56669e10			−0.734340
$238$	3.45656e10	−	9.79400e9i	0.698310	−	0.197863i
$239$	−4.06748e10			−0.806372			−0.403186	−	0.915118i	$-0.632097\pi$
$239$	−4.06748e10			−0.806372			−0.403186	+	0.915118i	$0.632097\pi$
$240$	−2.75123e9	+	4.76527e9i	−0.0535274	+	0.0927122i
$241$	−4.71851e9	−	8.17271e9i	−0.0901008	−	0.156059i	0.817453	−	0.575996i	$-0.195386\pi$
$241$	−4.71851e9	−	8.17271e9i	−0.0901008	−	0.156059i	−0.907553	+	0.419937i	$0.862052\pi$
$242$	4.51702e9	+	7.82372e9i	0.0846610	+	0.146637i
$243$	2.81326e10	−	4.87270e10i	0.517584	−	0.896482i
$244$	−5.14367e10			−0.929008
$245$	−1.26117e9	−	4.40586e10i	−0.0223628	−	0.781237i
$246$	−2.12855e10			−0.370575
$247$	−9.49046e8	+	1.64380e9i	−0.0162237	+	0.0281003i
$248$	1.18441e10	+	2.05145e10i	0.198824	+	0.344373i
$249$	−2.87346e10	−	4.97698e10i	−0.473705	−	0.820482i
$250$	2.37083e10	−	4.10640e10i	0.383858	−	0.664862i
$251$	−7.60552e10			−1.20948			−0.604738	−	0.796425i	$-0.706722\pi$
$251$	−7.60552e10			−1.20948			−0.604738	+	0.796425i	$0.706722\pi$
$252$	−2.15515e10	+	6.10651e9i	−0.336647	+	0.0953873i
$253$	1.32910e11			2.03946
$254$	3.12229e8	−	5.40796e8i	0.00470675	−	0.00815233i
$255$	1.48388e10	+	2.57016e10i	0.219770	+	0.380653i
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	−4.51105e10	+	7.81337e10i	−0.645028	+	1.11722i	0.339266	+	0.940690i	$0.389821\pi$
$257$	−4.51105e10	+	7.81337e10i	−0.645028	+	1.11722i	−0.984295	+	0.176532i	$0.943512\pi$
$258$	1.76668e9			0.0248238
$259$	−8.49478e9	+	3.36200e10i	−0.117301	+	0.464246i
$260$	−1.05703e10			−0.143452
$261$	9.70152e9	−	1.68035e10i	0.129407	−	0.224139i
$262$	1.27502e10	+	2.20840e10i	0.167172	+	0.289550i
$263$	4.67841e10	+	8.10324e10i	0.602972	+	1.04438i	0.992368	+	0.123308i	$0.0393503\pi$
$263$	4.67841e10	+	8.10324e10i	0.602972	+	1.04438i	−0.389396	+	0.921070i	$0.627316\pi$
$264$	−8.51067e9	+	1.47409e10i	−0.107832	+	0.186770i
$265$	4.70541e9			0.0586126
$266$	3.65989e9	+	3.55663e9i	0.0448230	+	0.0435583i
$267$	8.66995e10			1.04404
$268$	3.48931e10	−	6.04365e10i	0.413173	−	0.715637i
$269$	−7.42816e9	−	1.28660e10i	−0.0864960	−	0.149815i	0.819532	−	0.573034i	$-0.194234\pi$
$269$	−7.42816e9	−	1.28660e10i	−0.0864960	−	0.149815i	−0.906028	+	0.423218i	$0.860900\pi$
$270$	−2.24727e10	−	3.89239e10i	−0.257347	−	0.445738i
$271$	−5.85924e10	+	1.01485e11i	−0.659902	+	1.14298i	0.320739	+	0.947168i	$0.396069\pi$
$271$	−5.85924e10	+	1.01485e11i	−0.659902	+	1.14298i	−0.980641	+	0.195816i	$0.937264\pi$
$272$	−2.31650e10			−0.256609
$273$	1.32381e10	+	1.28645e10i	0.144242	+	0.140172i
$274$	−9.01815e10			−0.966585
$275$	2.05457e10	−	3.55861e10i	0.216632	−	0.375218i
$276$	2.41900e10	+	4.18983e10i	0.250925	+	0.434615i
$277$	1.43612e10	+	2.48743e10i	0.146565	+	0.253859i	0.929956	−	0.367671i	$-0.119845\pi$
$277$	1.43612e10	+	2.48743e10i	0.146565	+	0.253859i	−0.783390	+	0.621530i	$0.786511\pi$
$278$	1.92416e10	−	3.33274e10i	0.193214	−	0.334657i
$279$	−7.96592e10			−0.787076
$280$	−6.96215e9	+	2.75542e10i	−0.0676912	+	0.267903i
$281$	−7.39690e10			−0.707736			−0.353868	−	0.935295i	$-0.615134\pi$
$281$	−7.39690e10			−0.707736			−0.353868	+	0.935295i	$0.615134\pi$
$282$	−1.87183e10	+	3.24211e10i	−0.176257	+	0.305286i
$283$	3.63744e10	+	6.30023e10i	0.337098	+	0.583872i	0.983886	−	0.178799i	$-0.0572212\pi$
$283$	3.63744e10	+	6.30023e10i	0.337098	+	0.583872i	−0.646787	+	0.762671i	$0.723888\pi$
$284$	−1.83595e10	−	3.17996e10i	−0.167467	−	0.290061i
$285$	−2.10786e9	+	3.65093e9i	−0.0189252	+	0.0327794i
$286$	−3.26982e10			−0.288986
$287$	−1.05775e11	+	2.99710e10i	−0.920273	+	0.260755i
$288$	1.44433e10			0.123708
$289$	−3.17652e9	+	5.50189e9i	−0.0267862	+	0.0463950i
$290$	−1.23089e10	−	2.13197e10i	−0.102195	−	0.177007i
$291$	−4.89321e9	−	8.47529e9i	−0.0400014	−	0.0692845i
$292$	4.71081e10	−	8.15935e10i	0.379204	−	0.656800i
$293$	2.43926e11			1.93354			0.966771	−	0.255644i	$-0.0822876\pi$
$293$	2.43926e11			1.93354			0.966771	+	0.255644i	$0.0822876\pi$
$294$	4.22541e10	−	2.60352e10i	0.329842	−	0.203235i
$295$	7.22481e10			0.555428
$296$	1.11796e10	−	1.93636e10i	0.0846471	−	0.146613i
$297$	−6.95173e10	−	1.20408e11i	−0.518429	−	0.897945i
$298$	3.86342e10	+	6.69163e10i	0.283791	+	0.491540i
$299$	−4.64692e10	+	8.04871e10i	−0.336237	+	0.582379i
$300$	1.49575e10			0.106614
$301$	8.77927e9	−	2.48756e9i	0.0616466	−	0.0174673i
$302$	−1.70659e11			−1.18059
$303$	5.78612e10	−	1.00219e11i	0.394362	−	0.683056i
$304$	−1.64530e9	−	2.84975e9i	−0.0110488	−	0.0191371i
$305$	−1.09731e11	−	1.90060e11i	−0.726073	−	1.25759i
$306$	3.89500e10	−	6.74634e10i	0.253958	−	0.439867i
$307$	1.41661e11			0.910182			0.455091	−	0.890445i	$-0.349607\pi$
$307$	1.41661e11			0.910182			0.455091	+	0.890445i	$0.349607\pi$
$308$	−2.15368e10	+	8.52364e10i	−0.136365	+	0.539693i
$309$	4.57336e10			0.285379
$310$	−5.05343e10	+	8.75280e10i	−0.310784	+	0.538294i
$311$	−6.45871e10	−	1.11868e11i	−0.391493	−	0.678086i	0.601154	−	0.799133i	$-0.294708\pi$
$311$	−6.45871e10	−	1.11868e11i	−0.391493	−	0.678086i	−0.992647	+	0.121048i	$0.961375\pi$
$312$	−5.95117e9	−	1.03077e10i	−0.0355555	−	0.0615839i
$313$	−2.22325e10	+	3.85078e10i	−0.130930	+	0.226777i	−0.924035	−	0.382307i	$-0.875130\pi$
$313$	−2.22325e10	+	3.85078e10i	−0.130930	+	0.226777i	0.793106	+	0.609084i	$0.208463\pi$
$314$	1.58496e11			0.920101
$315$	−6.85399e10	−	6.66060e10i	−0.392235	−	0.381168i
$316$	1.18783e11			0.670134
$317$	1.24213e11	−	2.15143e11i	0.690877	−	1.19663i	−0.280674	−	0.959803i	$-0.590558\pi$
$317$	1.24213e11	−	2.15143e11i	0.690877	−	1.19663i	0.971551	−	0.236830i	$-0.0761085\pi$
$318$	2.64919e9	+	4.58853e9i	0.0145275	+	0.0251624i
$319$	−3.80765e10	−	6.59505e10i	−0.205873	−	0.356583i
$320$	9.16254e9	−	1.58700e10i	0.0488473	−	0.0846061i
$321$	−1.04151e11			−0.547508
$322$	1.79204e11	+	1.74147e11i	0.928956	+	0.902745i
$323$	−1.77480e10			−0.0907271
$324$	−9.39826e9	+	1.62783e10i	−0.0473800	+	0.0820646i
$325$	1.43668e10	+	2.48839e10i	0.0714305	+	0.123721i
$326$	−9.94303e10	−	1.72218e11i	−0.487573	−	0.844501i
$327$	−7.44799e10	+	1.29003e11i	−0.360225	+	0.623928i
$328$	7.08880e10			0.338174
$329$	−4.73679e10	+	1.87469e11i	−0.222896	+	0.882159i
$330$	−7.26239e10			−0.337106
$331$	−1.81110e11	+	3.13691e11i	−0.829307	+	1.43640i	0.0692754	+	0.997598i	$0.477931\pi$
$331$	−1.81110e11	+	3.13691e11i	−0.829307	+	1.43640i	−0.898583	+	0.438805i	$0.855402\pi$
$332$	9.56961e10	+	1.65751e11i	0.432288	+	0.748744i
$333$	3.75950e10	+	6.51164e10i	0.167545	+	0.290196i
$334$	−4.38587e10	+	7.59656e10i	−0.192840	+	0.334009i
$335$	2.97752e11			1.29167
$336$	−3.07895e10	+	8.72406e9i	−0.131788	+	0.0373415i
$337$	−4.33951e11			−1.83276			−0.916380	−	0.400309i	$-0.868903\pi$
$337$	−4.33951e11			−1.83276			−0.916380	+	0.400309i	$0.868903\pi$
$338$	−7.34037e10	+	1.27139e11i	−0.305909	+	0.529851i
$339$	−7.62177e10	−	1.32013e11i	−0.313442	−	0.542898i
$340$	−4.94183e10	−	8.55951e10i	−0.200555	−	0.347371i
$341$	−1.56323e11	+	2.70760e11i	−0.626079	+	1.08440i
$342$	1.10658e10			0.0437385
$343$	1.73317e11	−	1.88874e11i	0.676112	−	0.736799i
$344$	−5.88364e9			−0.0226534
$345$	−1.03210e11	+	1.78765e11i	−0.392225	+	0.679354i
$346$	−3.67813e10	−	6.37071e10i	−0.137970	−	0.238971i
$347$	−9.64888e10	−	1.67124e11i	−0.357268	−	0.618807i	0.630235	−	0.776404i	$-0.282958\pi$
$347$	−9.64888e10	−	1.67124e11i	−0.357268	−	0.618807i	−0.987503	+	0.157597i	$0.949625\pi$
$348$	1.38601e10	−	2.40064e10i	0.0506593	−	0.0877444i
$349$	2.85795e11			1.03119			0.515596	−	0.856832i	$-0.327570\pi$
$349$	2.85795e11			1.03119			0.515596	+	0.856832i	$0.327570\pi$
$350$	7.43292e10	−	2.10608e10i	0.264761	−	0.0750186i
$351$	9.72213e10			0.341884
$352$	2.83435e10	−	4.90923e10i	0.0984036	−	0.170440i
$353$	−2.08069e10	−	3.60386e10i	−0.0713217	−	0.123533i	0.828159	−	0.560493i	$-0.189388\pi$
$353$	−2.08069e10	−	3.60386e10i	−0.0713217	−	0.123533i	−0.899481	+	0.436960i	$0.856055\pi$
$354$	4.06763e10	+	7.04535e10i	0.137666	+	0.238445i
$355$	7.83333e10	−	1.35677e11i	0.261769	−	0.453398i
$356$	−2.88739e11			−0.952753
$357$	−4.22825e10	+	1.67342e11i	−0.137770	+	0.545254i
$358$	−4.10244e10			−0.131998
$359$	2.05388e11	−	3.55742e11i	0.652604	−	1.13034i	−0.329885	−	0.944021i	$-0.607010\pi$
$359$	2.05388e11	−	3.55742e11i	0.652604	−	1.13034i	0.982489	−	0.186322i	$-0.0596566\pi$
$360$	3.08121e10	+	5.33681e10i	0.0966852	+	0.167464i
$361$	1.60083e11	+	2.77272e11i	0.496094	+	0.859259i
$362$	−2.86658e10	+	4.96507e10i	−0.0877356	+	0.151962i
$363$	−4.34024e10			−0.131200
$364$	−4.40873e10	−	4.28434e10i	−0.131631	−	0.127917i
$365$	4.01986e11			1.18548
$366$	1.23559e11	−	2.14011e11i	0.359923	−	0.623405i
$367$	−9.15209e10	−	1.58519e11i	−0.263344	−	0.456125i	0.703785	−	0.710413i	$-0.251492\pi$
$367$	−9.15209e10	−	1.58519e11i	−0.263344	−	0.456125i	−0.967128	+	0.254289i	$0.918159\pi$
$368$	−8.05609e10	−	1.39536e11i	−0.228986	−	0.396616i
$369$	−1.19192e11	+	2.06447e11i	−0.334680	+	0.579682i
$370$	9.53983e10			0.264626
$371$	1.96256e10	+	1.90719e10i	0.0537826	+	0.0522651i
$372$	−1.13805e11			−0.308119
$373$	1.42882e11	−	2.47479e11i	0.382198	−	0.661987i	−0.609178	−	0.793034i	$-0.708501\pi$
$373$	1.42882e11	−	2.47479e11i	0.382198	−	0.661987i	0.991376	+	0.131047i	$0.0418338\pi$
$374$	−1.52871e11	−	2.64780e11i	−0.404020	−	0.699783i
$375$	1.13902e11	+	1.97284e11i	0.297434	+	0.515171i
$376$	6.23385e10	−	1.07973e11i	0.160846	−	0.278594i
$377$	5.32508e10			0.135766
$378$	6.40351e10	−	2.53433e11i	0.161326	−	0.638483i
$379$	4.76362e10			0.118593			0.0592967	−	0.998240i	$-0.481114\pi$
$379$	4.76362e10			0.118593			0.0592967	+	0.998240i	$0.481114\pi$
$380$	7.01991e9	−	1.21588e10i	0.0172705	−	0.0299134i
$381$	1.50004e9	+	2.59815e9i	0.00364705	+	0.00631687i
$382$	−5.57910e9	−	9.66329e9i	−0.0134054	−	0.0232188i
$383$	2.04495e11	−	3.54196e11i	0.485611	−	0.841104i	−0.514252	−	0.857639i	$-0.671930\pi$
$383$	2.04495e11	−	3.54196e11i	0.485611	−	0.841104i	0.999863	+	0.0165355i	$0.00526366\pi$
$384$	2.06344e10			0.0484284
$385$	−3.60895e11	+	1.02258e11i	−0.837158	+	0.237205i
$386$	9.13374e9			0.0209414
$387$	9.89286e9	−	1.71349e10i	0.0224193	−	0.0388314i
$388$	1.62961e10	+	2.82256e10i	0.0365040	+	0.0632267i
$389$	5.61626e10	+	9.72765e10i	0.124358	+	0.215394i	0.921482	−	0.388421i	$-0.126980\pi$
$389$	5.61626e10	+	9.72765e10i	0.124358	+	0.215394i	−0.797124	+	0.603816i	$0.793646\pi$
$390$	2.53915e10	−	4.39793e10i	0.0555773	−	0.0962627i
$391$	−8.69014e11			−1.88032
$392$	−1.40721e11	+	8.67061e10i	−0.301003	+	0.185465i
$393$	−1.22512e11			−0.259067
$394$	−3.91156e10	+	6.77501e10i	−0.0817743	+	0.141637i
$395$	2.53402e11	+	4.38905e11i	0.523748	+	0.907159i
$396$	9.53143e10	+	1.65089e11i	0.194773	+	0.337358i
$397$	1.92843e11	−	3.34013e11i	0.389624	−	0.674848i	−0.602775	−	0.797911i	$-0.705938\pi$
$397$	1.92843e11	−	3.34013e11i	0.389624	−	0.674848i	0.992399	+	0.123063i	$0.0392717\pi$
$398$	−1.62918e11			−0.325459
$399$	−2.35895e10	+	6.68397e9i	−0.0465952	+	0.0132025i
$400$	−4.98135e10			−0.0972920
$401$	−9.03426e10	+	1.56478e11i	−0.174479	+	0.302206i	−0.939981	−	0.341227i	$-0.889157\pi$
$401$	−9.03426e10	+	1.56478e11i	−0.174479	+	0.302206i	0.765502	+	0.643434i	$0.222491\pi$
$402$	1.67637e11	+	2.90356e11i	0.320149	+	0.554515i
$403$	−1.09311e11	−	1.89331e11i	−0.206438	−	0.357561i
$404$	−1.92698e11	+	3.33762e11i	−0.359882	+	0.623334i
$405$	−8.01980e10			−0.148121
$406$	3.50738e10	−	1.38812e11i	0.0640642	−	0.253548i
$407$	2.95106e11			0.533093
$408$	5.56459e10	−	9.63816e10i	0.0994174	−	0.172196i
$409$	1.24009e11	+	2.14789e11i	0.219127	+	0.379540i	0.954541	−	0.298078i	$-0.0963456\pi$
$409$	1.24009e11	+	2.14789e11i	0.219127	+	0.379540i	−0.735414	+	0.677618i	$0.763012\pi$
$410$	1.51227e11	+	2.61932e11i	0.264303	+	0.457785i
$411$	2.16630e11	−	3.75214e11i	0.374482	−	0.648621i
$412$	−1.52309e11			−0.260428
$413$	3.01337e11	+	2.92835e11i	0.509657	+	0.495277i
$414$	5.41826e11			0.906480
$415$	−4.08301e11	+	7.07198e11i	−0.675715	+	1.17037i
$416$	1.98194e10	+	3.43283e10i	0.0324468	+	0.0561994i
$417$	9.24426e10	+	1.60115e11i	0.149713	+	0.259311i
$418$	2.17154e10	−	3.76123e10i	0.0347917	−	0.0602610i
$419$	−2.26007e11			−0.358227			−0.179113	−	0.983828i	$-0.557323\pi$
$419$	−2.26007e11			−0.358227			−0.179113	+	0.983828i	$0.557323\pi$
$420$	−9.79195e10	−	9.51566e10i	−0.153549	−	0.149217i
$421$	−3.76981e11			−0.584858			−0.292429	−	0.956287i	$-0.594464\pi$
$421$	−3.76981e11			−0.584858			−0.292429	+	0.956287i	$0.594464\pi$
$422$	−2.31925e11	+	4.01705e11i	−0.355993	+	0.616597i
$423$	2.09634e11	+	3.63096e11i	0.318368	+	0.551430i
$424$	−8.82271e9	−	1.52814e10i	−0.0132573	−	0.0229623i
$425$	−1.34335e11	+	2.32675e11i	−0.199728	+	0.345939i
$426$	1.76409e11			0.259525
$427$	3.12674e11	−	1.23747e12i	0.455162	−	1.80140i
$428$	3.46858e11			0.499637
$429$	7.85462e10	−	1.36046e11i	0.111961	−	0.193922i
$430$	−1.25517e10	−	2.17402e10i	−0.0177049	−	0.0306658i
$431$	7.15512e10	+	1.23930e11i	0.0998779	+	0.172994i	0.911634	−	0.411003i	$-0.134821\pi$
$431$	7.15512e10	+	1.23930e11i	0.0998779	+	0.172994i	−0.811756	+	0.583997i	$0.801488\pi$
$432$	−8.42733e10	+	1.45966e11i	−0.116416	+	0.201639i
$433$	−1.36985e12			−1.87275			−0.936373	−	0.351007i	$-0.885839\pi$
$433$	−1.36985e12			−1.87275			−0.936373	+	0.351007i	$0.885839\pi$
$434$	−5.65539e11	+	1.60243e11i	−0.765172	+	0.216808i
$435$	1.18272e11			0.158373
$436$	2.48044e11	−	4.29624e11i	0.328730	−	0.569376i
$437$	−6.17220e10	−	1.06906e11i	−0.0809606	−	0.140228i
$438$	2.26322e11	+	3.92001e11i	0.293828	+	0.508924i
$439$	5.27776e11	−	9.14136e11i	0.678203	−	1.17468i	−0.297319	−	0.954778i	$-0.596092\pi$
$439$	5.27776e11	−	9.14136e11i	0.678203	−	1.17468i	0.975522	−	0.219904i	$-0.0705743\pi$
$440$	2.41863e11			0.307632
$441$	−1.59042e10	−	5.55610e11i	−0.0200234	−	0.699513i
$442$	2.13793e11			0.266436
$443$	−3.68388e11	+	6.38067e11i	−0.454453	+	0.787136i	−0.998657	−	0.0518173i	$-0.983499\pi$
$443$	−3.68388e11	+	6.38067e11i	−0.454453	+	0.787136i	0.544203	+	0.838953i	$0.316832\pi$
$444$	5.37101e10	+	9.30285e10i	0.0655892	+	0.113604i
$445$	−6.15972e11	−	1.06690e12i	−0.744631	−	1.28974i
$446$	−7.21578e10	+	1.24981e11i	−0.0863528	+	0.149567i
$447$	−3.71221e11			−0.439793
$448$	1.02540e11	−	2.90541e10i	0.120265	−	0.0340766i
$449$	−1.37800e11			−0.160007			−0.0800036	−	0.996795i	$-0.525493\pi$
$449$	−1.37800e11			−0.160007			−0.0800036	+	0.996795i	$0.525493\pi$
$450$	8.37573e10	−	1.45072e11i	0.0962867	−	0.166773i
$451$	4.67806e11	+	8.10264e11i	0.532441	+	0.922215i
$452$	2.53831e11	+	4.39649e11i	0.286037	+	0.495430i
$453$	4.09950e11	−	7.10054e11i	0.457393	−	0.792227i
$454$	−2.12209e11			−0.234429
$455$	6.42547e10	−	2.54302e11i	0.0702835	−	0.278162i
$456$	1.58091e10			0.0171224
$457$	4.08741e11	−	7.07960e11i	0.438354	−	0.759252i	−0.559209	−	0.829027i	$-0.688895\pi$
$457$	4.08741e11	−	7.07960e11i	0.438354	−	0.759252i	0.997563	+	0.0697754i	$0.0222283\pi$
$458$	−6.14133e11	−	1.06371e12i	−0.652181	−	1.12961i
$459$	4.54530e11	+	7.87269e11i	0.477975	+	0.827877i
$460$	3.43724e11	−	5.95348e11i	0.357932	−	0.619956i
$461$	1.54090e12			1.58899			0.794495	−	0.607270i	$-0.207735\pi$
$461$	1.54090e12			1.58899			0.794495	+	0.607270i	$0.207735\pi$
$462$	−3.02905e11	−	2.94358e11i	−0.309327	−	0.300599i
$463$	−7.47957e11			−0.756419			−0.378209	−	0.925720i	$-0.623460\pi$
$463$	−7.47957e11			−0.756419			−0.378209	+	0.925720i	$0.623460\pi$
$464$	−4.61588e10	+	7.99494e10i	−0.0462300	+	0.0800727i
$465$	−2.42783e11	−	4.20512e11i	−0.240813	−	0.417100i
$466$	−1.83511e10	−	3.17851e10i	−0.0180271	−	0.0312238i
$467$	−1.20537e11	+	2.08776e11i	−0.117272	+	0.203121i	−0.918686	−	0.394989i	$-0.870748\pi$
$467$	−1.20537e11	+	2.08776e11i	−0.117272	+	0.203121i	0.801414	+	0.598110i	$0.204082\pi$
$468$	−1.33299e11			−0.128446
$469$	1.24188e12	+	1.20684e12i	1.18523	+	1.15179i
$470$	5.31951e11			0.502842
$471$	−3.80733e11	+	6.59448e11i	−0.356472	+	0.617428i
$472$	−1.35466e11	−	2.34634e11i	−0.125630	−	0.217597i
$473$	−3.88275e10	−	6.72512e10i	−0.0356668	−	0.0617767i
$474$	−2.85335e11	+	4.94214e11i	−0.259628	+	0.449690i
$475$	−3.81648e10			−0.0343987
$476$	1.40815e11	−	5.57307e11i	0.125724	−	0.497581i
$477$	5.93386e10			0.0524813
$478$	−3.25399e11	+	5.63607e11i	−0.285095	+	0.493800i
$479$	−2.09044e11	−	3.62075e11i	−0.181438	−	0.314259i	0.760933	−	0.648831i	$-0.224742\pi$
$479$	−2.09044e11	−	3.62075e11i	−0.181438	−	0.314259i	−0.942370	+	0.334571i	$0.891408\pi$
$480$	4.40197e10	+	7.62443e10i	0.0378496	+	0.0655574i
$481$	−1.03178e11	+	1.78709e11i	−0.0878887	+	0.152228i
$482$	−1.50992e11			−0.127422
$483$	−1.15504e12	+	3.27275e11i	−0.965685	+	0.273622i
$484$	1.44545e11			0.119729
$485$	−6.95294e10	+	1.20428e11i	−0.0570599	+	0.0988306i
$486$	−4.50121e11	−	7.79632e11i	−0.365987	−	0.633908i
$487$	8.57863e11	+	1.48586e12i	0.691095	+	1.19701i	0.971480	+	0.237123i	$0.0762046\pi$
$487$	8.57863e11	+	1.48586e12i	0.691095	+	1.19701i	−0.280385	+	0.959888i	$0.590462\pi$
$488$	−4.11494e11	+	7.12728e11i	−0.328454	+	0.568899i
$489$	9.55388e11			0.755597
$490$	−6.20583e11	−	3.34993e11i	−0.486315	−	0.262515i
$491$	3.34731e11			0.259914			0.129957	−	0.991520i	$-0.458516\pi$
$491$	3.34731e11			0.259914			0.129957	+	0.991520i	$0.458516\pi$
$492$	−1.70284e11	+	2.94941e11i	−0.131018	+	0.226930i
$493$	2.48958e11	+	4.31209e11i	0.189809	+	0.328758i
$494$	1.51847e10	+	2.63007e10i	0.0114719	+	0.0198699i
$495$	−4.06672e11	+	7.04376e11i	−0.304453	+	0.527328i
$496$	3.79010e11			0.281179
$497$	8.76643e11	−	2.48392e11i	0.644494	−	0.182614i
$498$	−9.19508e11			−0.669921
$499$	−3.55022e11	+	6.14916e11i	−0.256332	+	0.443980i	−0.965256	−	0.261304i	$-0.915847\pi$
$499$	−3.55022e11	+	6.14916e11i	−0.256332	+	0.443980i	0.708924	+	0.705285i	$0.249181\pi$
$500$	−3.79333e11	−	6.57024e11i	−0.271429	−	0.470128i
$501$	−2.10711e11	−	3.64962e11i	−0.149423	−	0.258808i
$502$	−6.08441e11	+	1.05385e12i	−0.427614	+	0.740649i
$503$	−2.16835e12			−1.51033			−0.755167	−	0.655532i	$-0.772444\pi$
$503$	−2.16835e12			−1.51033			−0.755167	+	0.655532i	$0.772444\pi$
$504$	−8.77977e10	+	3.47478e11i	−0.0606102	+	0.239878i
$505$	−1.64434e12			−1.12507
$506$	1.06328e12	−	1.84165e12i	0.721058	−	1.24891i
$507$	−3.52654e11	−	6.10815e11i	−0.237035	−	0.410557i
$508$	−4.99566e9	−	8.65273e9i	−0.00332817	−	0.00576457i
$509$	−3.84948e11	+	6.66750e11i	−0.254198	+	0.440284i	−0.964677	−	0.263434i	$-0.915145\pi$
$509$	−3.84948e11	+	6.66750e11i	−0.254198	+	0.440284i	0.710479	+	0.703718i	$0.248478\pi$
$510$	4.74842e11			0.310802
$511$	1.67663e12	+	1.62932e12i	1.08779	+	1.05709i
$512$	−6.87195e10			−0.0441942
$513$	−6.45663e10	+	1.11832e11i	−0.0411602	+	0.0712916i
$514$	7.21768e11	+	1.25014e12i	0.456104	+	0.789995i
$515$	−3.24923e11	−	5.62783e11i	−0.203539	−	0.352540i
$516$	1.41334e10	−	2.44798e10i	0.00877655	−	0.0152014i
$517$	1.64554e12			1.01298
$518$	3.97893e11	+	3.86667e11i	0.242819	+	0.235968i
$519$	3.53418e11			0.213814
$520$	−8.45624e10	+	1.46466e11i	−0.0507180	+	0.0878461i
$521$	−1.16046e11	−	2.00998e11i	−0.0690021	−	0.119515i	0.829460	−	0.558566i	$-0.188648\pi$
$521$	−1.16046e11	−	2.00998e11i	−0.0690021	−	0.119515i	−0.898462	+	0.439051i	$0.855315\pi$
$522$	−1.55224e11	−	2.68856e11i	−0.0915045	−	0.158490i
$523$	1.04130e12	−	1.80358e12i	0.608580	−	1.05409i	−0.382895	−	0.923792i	$-0.625073\pi$
$523$	1.04130e12	−	1.80358e12i	0.608580	−	1.05409i	0.991475	−	0.130299i	$-0.0415938\pi$
$524$	4.08007e11			0.236416
$525$	−9.09235e10	+	3.59849e11i	−0.0522347	+	0.206730i
$526$	1.49709e12			0.852731
$527$	1.02210e12	−	1.77033e12i	0.577225	−	0.999783i
$528$	1.36171e11	+	2.35855e11i	0.0762485	+	0.132066i
$529$	−2.12159e12	−	3.67471e12i	−1.17791	−	2.04020i
$530$	3.76433e10	−	6.52001e10i	0.0207227	−	0.0358928i
$531$	9.11100e11			0.497325
$532$	7.85612e10	−	2.22599e10i	0.0425212	−	0.0120482i
$533$	−6.54236e11			−0.351125
$534$	6.93596e11	−	1.20134e12i	0.369123	−	0.639339i
$535$	7.39959e11	+	1.28165e12i	0.390495	+	0.676357i
$536$	−5.58289e11	−	9.66985e11i	−0.292158	−	0.506032i
$537$	9.85470e10	−	1.70688e11i	0.0511398	−	0.0885768i
$538$	−2.37701e11			−0.122324
$539$	−1.91971e12	−	1.03627e12i	−0.979687	−	0.528839i
$540$	−7.19128e11			−0.363944
$541$	4.19871e11	−	7.27238e11i	0.210731	−	0.364996i	−0.741213	−	0.671270i	$-0.765749\pi$
$541$	4.19871e11	−	7.27238e11i	0.210731	−	0.364996i	0.951943	+	0.306274i	$0.0990823\pi$
$542$	9.37478e11	+	1.62376e12i	0.466621	+	0.808212i
$543$	−1.37719e11	−	2.38537e11i	−0.0679823	−	0.117749i
$544$	−1.85320e11	+	3.20984e11i	−0.0907250	+	0.157140i
$545$	2.11662e12			1.02768
$546$	2.84161e11	−	8.05156e10i	0.136835	−	0.0387715i
$547$	−7.58235e11			−0.362127			−0.181064	−	0.983471i	$-0.557954\pi$
$547$	−7.58235e11			−0.362127			−0.181064	+	0.983471i	$0.557954\pi$
$548$	−7.21452e11	+	1.24959e12i	−0.341739	+	0.591910i
$549$	−1.38379e12	−	2.39679e12i	−0.650120	−	1.12604i
$550$	−3.28731e11	−	5.69378e11i	−0.153182	−	0.265319i
$551$	−3.53647e10	+	6.12535e10i	−0.0163451	+	0.0283106i
$552$	7.74079e11			0.354862
$553$	−7.22057e11	+	2.85770e12i	−0.328328	+	1.29943i
$554$	4.59558e11			0.207275
$555$	−2.29161e11	+	3.96919e11i	−0.102523	+	0.177576i
$556$	−3.07866e11	−	5.33239e11i	−0.136623	−	0.236638i
$557$	−7.98622e11	−	1.38325e12i	−0.351555	−	0.608911i	0.634967	−	0.772539i	$-0.281014\pi$
$557$	−7.98622e11	−	1.38325e12i	−0.351555	−	0.608911i	−0.986522	+	0.163628i	$0.947680\pi$
$558$	−6.37273e11	+	1.10379e12i	−0.278274	+	0.481984i
$559$	5.43010e10			0.0235209
$560$	3.26105e11	+	3.16904e11i	0.140124	+	0.136170i
$561$	1.46888e12			0.626114
$562$	−5.91752e11	+	1.02494e12i	−0.250222	+	0.433398i
$563$	−1.30480e11	−	2.25999e11i	−0.0547340	−	0.0948021i	0.837360	−	0.546652i	$-0.184098\pi$
$563$	−1.30480e11	−	2.25999e11i	−0.0547340	−	0.0948021i	−0.892094	+	0.451849i	$0.850764\pi$
$564$	2.99493e11	+	5.18738e11i	0.124632	+	0.215870i
$565$	−1.08301e12	+	1.87582e12i	−0.447108	+	0.774415i
$566$	1.16398e12			0.476729
$567$	−3.34495e11	−	3.25057e11i	−0.135915	−	0.132080i
$568$	−5.87504e11			−0.236833
$569$	7.66696e11	−	1.32796e12i	0.306632	−	0.531103i	−0.670991	−	0.741465i	$-0.734131\pi$
$569$	7.66696e11	−	1.32796e12i	0.306632	−	0.531103i	0.977623	+	0.210363i	$0.0674645\pi$
$570$	3.37258e10	+	5.84149e10i	0.0133821	+	0.0231786i
$571$	1.38056e12	+	2.39120e12i	0.543492	+	0.941355i	0.998700	+	0.0509702i	$0.0162313\pi$
$571$	1.38056e12	+	2.39120e12i	0.543492	+	0.941355i	−0.455209	+	0.890385i	$0.650435\pi$
$572$	−2.61586e11	+	4.53080e11i	−0.102172	+	0.176967i
$573$	5.36075e10			0.0207745
$574$	−4.30914e11	+	1.70544e12i	−0.165686	+	0.655740i
$575$	−1.86871e12			−0.712913
$576$	1.15546e11	−	2.00132e11i	0.0437375	−	0.0757556i
$577$	2.00235e12	+	3.46817e12i	0.752054	+	1.30260i	0.946826	+	0.321747i	$0.104270\pi$
$577$	2.00235e12	+	3.46817e12i	0.752054	+	1.30260i	−0.194771	+	0.980849i	$0.562396\pi$
$578$	5.08243e10	+	8.80302e10i	0.0189407	+	0.0328063i
$579$	−2.19407e10	+	3.80023e10i	−0.00811327	+	0.0140526i
$580$	−3.93886e11			−0.144525
$581$	−4.56937e12	+	1.29471e12i	−1.66366	+	0.471389i
$582$	−1.56583e11			−0.0565705
$583$	1.16446e11	−	2.01690e11i	0.0417461	−	0.0723064i
$584$	−7.53729e11	−	1.30550e12i	−0.268137	−	0.464428i
$585$	−2.84369e11	−	4.92542e11i	−0.100388	−	0.173877i
$586$	1.95141e12	−	3.37994e12i	0.683610	−	1.18405i
$587$	−1.31451e12			−0.456976			−0.228488	−	0.973547i	$-0.573378\pi$
$587$	−1.31451e12			−0.456976			−0.228488	+	0.973547i	$0.573378\pi$
$588$	−2.27216e10	−	7.93771e11i	−0.00783863	−	0.273840i
$589$	2.90380e11			0.0994140
$590$	5.77985e11	−	1.00110e12i	0.196373	−	0.340129i
$591$	−1.87923e11	−	3.25493e11i	−0.0633632	−	0.109748i
$592$	−1.78873e11	−	3.09817e11i	−0.0598545	−	0.103671i
$593$	−2.09286e12	+	3.62495e12i	−0.695016	+	1.20380i	0.275159	+	0.961399i	$0.411269\pi$
$593$	−2.09286e12	+	3.62495e12i	−0.695016	+	1.20380i	−0.970175	+	0.242404i	$0.922064\pi$
$594$	−2.22455e12			−0.733169
$595$	2.35966e12	−	6.68599e11i	0.771834	−	0.218695i
$596$	1.23629e12			0.401341
$597$	3.91355e11	−	6.77847e11i	0.126092	−	0.218397i
$598$	7.43508e11	+	1.28779e12i	0.237755	+	0.411804i
$599$	9.72836e11	+	1.68500e12i	0.308758	+	0.534785i	0.978091	−	0.208178i	$-0.0667532\pi$
$599$	9.72836e11	+	1.68500e12i	0.308758	+	0.534785i	−0.669333	+	0.742963i	$0.733420\pi$
$600$	1.19660e11	−	2.07257e11i	0.0376936	−	0.0652872i
$601$	4.58168e12			1.43248			0.716242	−	0.697852i	$-0.245861\pi$
$601$	4.58168e12			1.43248			0.716242	+	0.697852i	$0.245861\pi$
$602$	3.57655e10	−	1.41550e11i	0.0110989	−	0.0439263i
$603$	3.75486e12			1.15656
$604$	−1.36527e12	+	2.36472e12i	−0.417401	+	0.722960i
$605$	3.08360e11	+	5.34096e11i	0.0935749	+	0.162076i
$606$	−9.25779e11	−	1.60350e12i	−0.278856	−	0.482993i
$607$	1.86944e12	−	3.23796e12i	0.558936	−	0.968106i	−0.438650	−	0.898658i	$-0.644543\pi$
$607$	1.86944e12	−	3.23796e12i	0.558936	−	0.968106i	0.997586	−	0.0694474i	$-0.0221236\pi$
$608$	−5.26497e10			−0.0156253
$609$	4.93296e11	+	4.79378e11i	0.145322	+	0.141221i
$610$	−3.51139e12			−1.02682
$611$	−5.75331e11	+	9.96502e11i	−0.167006	+	0.289263i
$612$	−6.23200e11	−	1.07941e12i	−0.179575	−	0.311033i
$613$	−5.61986e11	−	9.73387e11i	−0.160751	−	0.278428i	0.774387	−	0.632712i	$-0.218058\pi$
$613$	−5.61986e11	−	9.73387e11i	−0.160751	−	0.278428i	−0.935138	+	0.354283i	$0.884725\pi$
$614$	1.13329e12	−	1.96291e12i	0.321798	−	0.557370i
$615$	−1.45308e12			−0.409592
$616$	1.00878e12	+	9.80314e11i	0.282281	+	0.274317i
$617$	8.34463e11			0.231805			0.115903	−	0.993261i	$-0.463024\pi$
$617$	8.34463e11			0.231805			0.115903	+	0.993261i	$0.463024\pi$
$618$	3.65869e11	−	6.33703e11i	0.100897	−	0.174758i
$619$	−1.23873e12	−	2.14554e12i	−0.339132	−	0.587394i	0.645138	−	0.764066i	$-0.276800\pi$
$619$	−1.23873e12	−	2.14554e12i	−0.339132	−	0.587394i	−0.984270	+	0.176673i	$0.943467\pi$
$620$	8.08549e11	+	1.40045e12i	0.219758	+	0.380631i
$621$	−3.16144e12	+	5.47577e12i	−0.853046	+	1.47752i
$622$	−2.06679e12			−0.553655
$623$	1.75519e12	−	6.94653e12i	0.466796	−	1.84745i
$624$	−1.90437e11			−0.0502830
$625$	8.76198e11	−	1.51762e12i	0.229690	−	0.397835i
$626$	3.55719e11	+	6.16124e11i	0.0925813	+	0.160355i
$627$	1.04328e11	+	1.80701e11i	0.0269585	+	0.0466935i
$628$	1.26797e12	−	2.19619e12i	0.325305	−	0.563445i
$629$	−1.92951e12			−0.491495
$630$	−1.47124e12	+	4.16868e11i	−0.372092	+	0.105431i
$631$	1.00841e12			0.253223			0.126612	−	0.991952i	$-0.459590\pi$
$631$	1.00841e12			0.253223			0.126612	+	0.991952i	$0.459590\pi$
$632$	9.50263e11	−	1.64590e12i	0.236928	−	0.410372i
$633$	−1.11424e12	−	1.92992e12i	−0.275843	−	0.477773i
$634$	−1.98741e12	−	3.44229e12i	−0.488524	−	0.846148i
$635$	2.13147e10	−	3.69181e10i	0.00520232	−	0.00901068i
$636$	8.47740e10			0.0205450
$637$	1.29873e12	−	8.00223e11i	0.312530	−	0.192568i
$638$	−1.21845e12			−0.291148
$639$	9.87838e11	−	1.71099e12i	0.234386	−	0.405969i
$640$	−1.46601e11	−	2.53920e11i	−0.0345403	−	0.0598255i
$641$	3.49112e12	+	6.04681e12i	0.816778	+	1.41470i	0.908044	+	0.418875i	$0.137575\pi$
$641$	3.49112e12	+	6.04681e12i	0.816778	+	1.41470i	−0.0912655	+	0.995827i	$0.529091\pi$
$642$	−8.33207e11	+	1.44316e12i	−0.193573	+	0.335279i
$643$	−5.09779e12			−1.17607			−0.588034	−	0.808836i	$-0.700098\pi$
$643$	−5.09779e12			−1.17607			−0.588034	+	0.808836i	$0.700098\pi$
$644$	3.84668e12	−	1.08994e12i	0.881252	−	0.249698i
$645$	1.20604e11			0.0274375
$646$	−1.41984e11	+	2.45923e11i	−0.0320769	+	0.0555588i
$647$	−1.10368e12	−	1.91163e12i	−0.247613	−	0.428879i	0.715250	−	0.698869i	$-0.246313\pi$
$647$	−1.10368e12	−	1.91163e12i	−0.247613	−	0.428879i	−0.962863	+	0.269990i	$0.912980\pi$
$648$	1.50372e11	+	2.60452e11i	0.0335027	+	0.0580284i
$649$	1.78794e12	−	3.09681e12i	0.395597	−	0.685193i
$650$	4.59736e11			0.101018
$651$	6.91798e11	−	2.73794e12i	0.150961	−	0.597461i
$652$	−3.18177e12			−0.689533
$653$	−4.10454e12	+	7.10928e12i	−0.883397	+	1.53009i	−0.0358561	+	0.999357i	$0.511416\pi$
$653$	−4.10454e12	+	7.10928e12i	−0.883397	+	1.53009i	−0.847540	+	0.530731i	$0.821918\pi$
$654$	1.19168e12	+	2.06405e12i	0.254718	+	0.441184i
$655$	8.70410e11	+	1.50759e12i	0.184773	+	0.320036i
$656$	5.67104e11	−	9.82253e11i	0.119563	−	0.207089i
$657$	5.06933e12			1.06147
$658$	2.21870e12	+	2.15610e12i	0.461404	+	0.448386i
$659$	5.75171e12			1.18799			0.593994	−	0.804469i	$-0.297550\pi$
$659$	5.75171e12			1.18799			0.593994	+	0.804469i	$0.297550\pi$
$660$	−5.80991e11	+	1.00631e12i	−0.119185	+	0.206435i
$661$	−1.70202e12	−	2.94798e12i	−0.346783	−	0.600646i	0.638893	−	0.769296i	$-0.279393\pi$
$661$	−1.70202e12	−	2.94798e12i	−0.346783	−	0.600646i	−0.985676	+	0.168650i	$0.946059\pi$
$662$	2.89775e12	+	5.01906e12i	0.586409	+	1.01569i
$663$	−5.13564e11	+	8.89519e11i	−0.103225	+	0.178790i
$664$	3.06228e12			0.611347
$665$	2.49847e11	+	2.42797e11i	0.0495423	+	0.0481445i
$666$	1.20304e12			0.236944
$667$	−1.73161e12	+	2.99923e12i	−0.338753	+	0.586737i
$668$	7.01740e11	+	1.21545e12i	0.136358	+	0.236180i
$669$	−3.46669e11	−	6.00448e11i	−0.0669109	−	0.115893i
$670$	2.38202e12	−	4.12577e12i	0.456676	−	0.790986i
$671$	−1.08622e13			−2.06855
$672$	−1.25432e11	+	4.96425e11i	−0.0237272	+	0.0939056i
$673$	−7.13050e12			−1.33984			−0.669918	−	0.742435i	$-0.733671\pi$
$673$	−7.13050e12			−1.33984			−0.669918	+	0.742435i	$0.733671\pi$
$674$	−3.47160e12	+	6.01300e12i	−0.647979	+	1.12233i
$675$	9.77411e11	+	1.69293e12i	0.181222	+	0.313885i
$676$	1.17446e12	+	2.03422e12i	0.216311	+	0.374661i
$677$	6.50974e11	−	1.12752e12i	0.119101	−	0.206289i	−0.800311	−	0.599585i	$-0.795332\pi$
$677$	6.50974e11	−	1.12752e12i	0.119101	−	0.206289i	0.919412	+	0.393297i	$0.128666\pi$
$678$	−2.43897e12			−0.443274
$679$	−7.78117e11	+	2.20476e11i	−0.140485	+	0.0398058i
$680$	−1.58139e12			−0.283627
$681$	5.09759e11	−	8.82928e11i	0.0908244	−	0.157312i
$682$	2.50117e12	+	4.33216e12i	0.442704	+	0.766786i
$683$	2.31279e12	+	4.00587e12i	0.406671	+	0.704374i	0.994514	−	0.104600i	$-0.0333563\pi$
$683$	2.31279e12	+	4.00587e12i	0.406671	+	0.704374i	−0.587844	+	0.808975i	$0.700023\pi$
$684$	8.85261e10	−	1.53332e11i	0.0154639	−	0.0267842i
$685$	−6.15635e12			−1.06836
$686$	−1.23058e12	−	3.91255e12i	−0.212154	−	0.674530i
$687$	5.90097e12			1.01069
$688$	−4.70692e10	+	8.15262e10i	−0.00800919	+	0.0138723i
$689$	8.14260e10	+	1.41034e11i	0.0137650	+	0.0238417i
$690$	1.65136e12	+	2.86024e12i	0.277345	+	0.480376i
$691$	1.46317e12	−	2.53428e12i	0.244142	−	0.422866i	−0.717748	−	0.696303i	$-0.754827\pi$
$691$	1.46317e12	−	2.53428e12i	0.244142	−	0.422866i	0.961890	+	0.273437i	$0.0881604\pi$
$692$	−1.17700e12			−0.195119
$693$	−4.55114e12	+	1.28954e12i	−0.749585	+	0.212391i
$694$	−3.08764e12			−0.505254
$695$	1.31355e12	−	2.27514e12i	0.213558	−	0.369893i
$696$	−2.21761e11	−	3.84102e11i	−0.0358215	−	0.0620447i
$697$	−3.05869e12	−	5.29780e12i	−0.490894	−	0.850253i
$698$	2.28636e12	−	3.96009e12i	0.364582	−	0.631474i
$699$	1.76329e11			0.0279368
$700$	3.02806e11	−	1.19842e12i	0.0476677	−	0.188655i
$701$	5.32710e12			0.833220			0.416610	−	0.909085i	$-0.363218\pi$
$701$	5.32710e12			0.833220			0.416610	+	0.909085i	$0.363218\pi$
$702$	7.77770e11	−	1.34714e12i	0.120874	−	0.209361i
$703$	−1.37044e11	−	2.37367e11i	−0.0211622	−	0.0366541i
$704$	−4.53495e11	−	7.85477e11i	−0.0695818	−	0.120519i
$705$	−1.27783e12	+	2.21327e12i	−0.194815	+	0.337429i
$706$	−6.65821e11			−0.100864
$707$	−6.85833e12	−	6.66482e12i	−1.03236	−	1.00323i
$708$	1.30164e12			0.194689
$709$	−1.57111e12	+	2.72124e12i	−0.233506	+	0.404444i	−0.958837	−	0.283956i	$-0.908353\pi$
$709$	−1.57111e12	+	2.72124e12i	−0.233506	+	0.404444i	0.725332	+	0.688400i	$0.241686\pi$
$710$	−1.25333e12	−	2.17084e12i	−0.185099	−	0.320601i
$711$	3.19557e12	+	5.53490e12i	0.468960	+	0.812263i
$712$	−2.30991e12	+	4.00088e12i	−0.336849	+	0.583440i
$713$	1.42182e13			2.06036
$714$	1.98050e12	+	1.92462e12i	0.285190	+	0.277143i
$715$	−2.23218e12			−0.319413
$716$	−3.28195e11	+	5.68451e11i	−0.0466685	+	0.0808322i
$717$	−1.56332e12	−	2.70774e12i	−0.220908	−	0.382623i
$718$	−3.28620e12	−	5.69187e12i	−0.461460	−	0.799273i
$719$	−7.96174e11	+	1.37901e12i	−0.111104	+	0.192437i	−0.916216	−	0.400686i	$-0.868772\pi$
$719$	−7.96174e11	+	1.37901e12i	−0.111104	+	0.192437i	0.805112	+	0.593123i	$0.202105\pi$
$720$	9.85987e11			0.136733
$721$	9.25853e11	−	3.66426e12i	0.127595	−	0.504985i
$722$	5.12267e12			0.701582
$723$	3.62707e11	−	6.28228e11i	0.0493667	−	0.0855056i
$724$	4.58653e11	+	7.94410e11i	0.0620384	+	0.107454i
$725$	5.35355e11	+	9.27262e11i	0.0719649	+	0.124647i
$726$	−3.47219e11	+	6.01401e11i	−0.0463862	+	0.0803432i
$727$	6.30493e11			0.0837096			0.0418548	−	0.999124i	$-0.486673\pi$
$727$	6.30493e11			0.0837096			0.0418548	+	0.999124i	$0.486673\pi$
$728$	−9.46353e11	+	2.68145e11i	−0.124871	+	0.0353816i
$729$	2.87984e12			0.377654
$730$	3.21589e12	−	5.57008e12i	0.419129	−	0.725954i
$731$	2.53868e11	+	4.39713e11i	0.0328837	+	0.0569562i
$732$	−1.97694e12	−	3.42417e12i	−0.254504	−	0.440814i
$733$	5.97049e12	−	1.03412e13i	0.763910	−	1.32313i	−0.176911	−	0.984227i	$-0.556610\pi$
$733$	5.97049e12	−	1.03412e13i	0.763910	−	1.32313i	0.940821	−	0.338904i	$-0.110056\pi$
$734$	−2.92867e12			−0.372424
$735$	2.88453e12	−	1.77732e12i	0.364571	−	0.224633i
$736$	−2.57795e12			−0.323835
$737$	7.36855e12	−	1.27627e13i	0.919980	−	1.59345i
$738$	1.90708e12	+	3.30315e12i	0.236654	+	0.409897i
$739$	2.68231e11	+	4.64590e11i	0.0330833	+	0.0573020i	0.882093	−	0.471075i	$-0.156134\pi$
$739$	2.68231e11	+	4.64590e11i	0.0330833	+	0.0573020i	−0.849010	+	0.528377i	$0.822801\pi$
$740$	7.63186e11	−	1.32188e12i	0.0935595	−	0.162050i
$741$	−1.45904e11			−0.0177781
$742$	4.21273e11	−	1.19366e11i	0.0510207	−	0.0144565i
$743$	7.16300e12			0.862274			0.431137	−	0.902286i	$-0.358112\pi$
$743$	7.16300e12			0.862274			0.431137	+	0.902286i	$0.358112\pi$
$744$	−9.10440e11	+	1.57693e12i	−0.108936	+	0.188684i
$745$	2.63741e12	+	4.56812e12i	0.313671	+	0.543294i
$746$	−2.28612e12	−	3.95967e12i	−0.270255	−	0.468095i
$747$	−5.14896e12	+	8.91826e12i	−0.605030	+	1.04794i
$748$	−4.89187e12			−0.571371
$749$	−2.10848e12	+	8.34477e12i	−0.244794	+	0.968827i
$750$	3.64487e12			0.420636
$751$	−6.44748e12	+	1.11674e13i	−0.739623	+	1.28106i	0.213042	+	0.977043i	$0.431663\pi$
$751$	−6.44748e12	+	1.11674e13i	−0.739623	+	1.28106i	−0.952665	+	0.304021i	$0.901671\pi$
$752$	−9.97415e11	−	1.72757e12i	−0.113735	−	0.196996i
$753$	−2.92314e12	−	5.06303e12i	−0.331339	−	0.573896i
$754$	4.26006e11	−	7.37864e11i	0.0480004	−	0.0831391i
$755$	−1.16503e13			−1.30489
$756$	−2.99939e12	−	2.91476e12i	−0.333952	−	0.324530i
$757$	−1.53380e13			−1.69761			−0.848804	−	0.528708i	$-0.822677\pi$
$757$	−1.53380e13			−1.69761			−0.848804	+	0.528708i	$0.822677\pi$
$758$	3.81090e11	−	6.60067e11i	0.0419291	−	0.0726234i
$759$	5.10832e12	+	8.84787e12i	0.558715	+	0.967723i
$760$	−1.12319e11	−	1.94542e11i	−0.0122121	−	0.0211520i
$761$	−4.27674e12	+	7.40753e12i	−0.462256	+	0.800650i	−0.999073	−	0.0430484i	$-0.986293\pi$
$761$	−4.27674e12	+	7.40753e12i	−0.462256	+	0.800650i	0.536817	+	0.843698i	$0.319626\pi$
$762$	4.80014e10			0.00515770
$763$	8.82816e12	+	8.57907e12i	0.942996	+	0.916389i
$764$	−1.78531e11			−0.0189581
$765$	2.65897e12	−	4.60547e12i	0.280696	−	0.486181i
$766$	−3.27193e12	−	5.66714e12i	−0.343379	−	0.594750i
$767$	1.25024e12	+	2.16547e12i	0.130441	+	0.225930i
$768$	1.65075e11	−	2.85918e11i	0.0171220	−	0.0296562i
$769$	5.63703e12			0.581275			0.290638	−	0.956833i	$-0.406133\pi$
$769$	5.63703e12			0.581275			0.290638	+	0.956833i	$0.406133\pi$
$770$	−1.47023e12	+	5.81877e12i	−0.150723	+	0.596517i
$771$	−6.93520e12			−0.706829
$772$	7.30699e10	−	1.26561e11i	0.00740390	−	0.0128239i
$773$	1.24471e12	+	2.15590e12i	0.125390	+	0.217181i	0.921885	−	0.387463i	$-0.126649\pi$
$773$	1.24471e12	+	2.15590e12i	0.125390	+	0.217181i	−0.796496	+	0.604644i	$0.793315\pi$
$774$	−1.58286e11	−	2.74159e11i	−0.0158528	−	0.0274579i
$775$	2.19790e12	−	3.80687e12i	0.218852	−	0.379063i
$776$	5.21474e11			0.0516244
$777$	−2.56459e12	+	7.26664e11i	−0.252420	+	0.0715219i
$778$	1.79720e12			0.175869
$779$	4.34489e11	−	7.52557e11i	0.0422727	−	0.0732185i
$780$	−4.06264e11	−	7.03670e11i	−0.0392991	−	0.0680680i
$781$	−3.87707e12	−	6.71528e12i	−0.372884	−	0.645854i
$782$	−6.95211e12	+	1.20414e13i	−0.664793	+	1.15145i
$783$	3.62280e12			0.344443
$784$	7.56706e10	+	2.64353e12i	0.00715327	+	0.249898i
$785$	1.08199e13			1.01698
$786$	−9.80097e11	+	1.69758e12i	−0.0915941	+	0.158646i
$787$	6.87537e12	+	1.19085e13i	0.638866	+	1.10655i	0.985682	+	0.168615i	$0.0539294\pi$
$787$	6.87537e12	+	1.19085e13i	0.638866	+	1.10655i	−0.346816	+	0.937933i	$0.612737\pi$
$788$	6.25849e11	+	1.08400e12i	0.0578231	+	0.100153i
$789$	−3.59624e12	+	6.22888e12i	−0.330372	+	0.572220i
$790$	8.10886e12			0.740692
$791$	−1.21201e13	+	3.43418e12i	−1.10081	+	0.311910i
$792$	3.05006e12			0.275451
$793$	3.79774e12	−	6.57787e12i	0.341032	−	0.590685i
$794$	−3.08548e12	−	5.34421e12i	−0.275506	−	0.477190i
$795$	1.80850e11	+	3.13242e11i	0.0160571	+	0.0278117i
$796$	−1.30335e12	+	2.25746e12i	−0.115067	+	0.199302i
$797$	1.44214e12			0.126603			0.0633016	−	0.997994i	$-0.479837\pi$
$797$	1.44214e12			0.126603			0.0633016	+	0.997994i	$0.479837\pi$
$798$	−9.61003e10	+	3.80338e11i	−0.00838903	+	0.0332014i
$799$	−1.07592e13			−0.933938
$800$	−3.98508e11	+	6.90236e11i	−0.0343979	+	0.0595790i
$801$	−7.76785e12	−	1.34543e13i	−0.666737	−	1.15482i
$802$	1.44548e12	+	2.50365e12i	0.123375	+	0.213692i
$803$	9.94805e12	−	1.72305e13i	0.844342	−	1.46244i
$804$	5.36439e12			0.452760
$805$	1.22335e13	+	1.18884e13i	1.02676	+	0.997794i
$806$	−3.49794e12			−0.291947
$807$	5.70995e11	−	9.88992e11i	0.0473916	−	0.0820847i
$808$	3.08316e12	+	5.34019e12i	0.254475	+	0.440764i
$809$	−1.35494e11	−	2.34683e11i	−0.0111212	−	0.0192625i	0.860411	−	0.509600i	$-0.170207\pi$
$809$	−1.35494e11	−	2.34683e11i	−0.0111212	−	0.0192625i	−0.871532	+	0.490338i	$0.836873\pi$
$810$	−6.41584e11	+	1.11126e12i	−0.0523686	+	0.0907051i
$811$	1.23287e13			1.00075			0.500373	−	0.865810i	$-0.333196\pi$
$811$	1.23287e13			1.00075			0.500373	+	0.865810i	$0.333196\pi$
$812$	−1.64285e12	−	1.59649e12i	−0.132616	−	0.128874i
$813$	−9.00787e12			−0.723127
$814$	2.36085e12	−	4.08910e12i	0.188477	−	0.326451i
$815$	−6.78773e12	−	1.17567e13i	−0.538909	−	0.933418i
$816$	−8.90335e11	−	1.54210e12i	−0.0702987	−	0.121761i
$817$	−3.60622e10	+	6.24616e10i	−0.00283174	+	0.00490471i
$818$	3.96827e12			0.309893
$819$	8.10297e11	−	3.20693e12i	0.0629313	−	0.249064i
$820$	4.83926e12			0.373780
$821$	4.37808e12	−	7.58306e12i	0.336310	−	0.582506i	−0.647426	−	0.762129i	$-0.724154\pi$
$821$	4.37808e12	−	7.58306e12i	0.336310	−	0.582506i	0.983736	+	0.179623i	$0.0574877\pi$
$822$	−3.46608e12	−	6.00343e12i	−0.264798	−	0.458644i
$823$	−6.64063e12	−	1.15019e13i	−0.504557	−	0.873918i	−0.999986	−	0.00526950i	$-0.998323\pi$
$823$	−6.64063e12	−	1.15019e13i	−0.504557	−	0.873918i	0.495430	−	0.868648i	$-0.335011\pi$
$824$	−1.21847e12	+	2.11045e12i	−0.0920750	+	0.159479i
$825$	3.15865e12			0.237388
$826$	6.46834e12	−	1.83277e12i	0.483485	−	0.136993i
$827$	−1.28106e13			−0.952345			−0.476173	−	0.879352i	$-0.657976\pi$
$827$	−1.28106e13			−0.952345			−0.476173	+	0.879352i	$0.657976\pi$
$828$	4.33461e12	−	7.50776e12i	0.320489	−	0.555103i
$829$	−7.12962e12	−	1.23489e13i	−0.524289	−	0.908095i	−0.999600	−	0.0282773i	$-0.990998\pi$
$829$	−7.12962e12	−	1.23489e13i	−0.524289	−	0.908095i	0.475311	−	0.879818i	$-0.342335\pi$
$830$	6.53281e12	+	1.13152e13i	0.477803	+	0.827579i
$831$	−1.10393e12	+	1.91206e12i	−0.0803040	+	0.139091i
$832$	6.34222e11			0.0458866
$833$	1.25518e13	+	6.77552e12i	0.903241	+	0.487573i
$834$	2.95816e12			0.211726
$835$	−2.99407e12	+	5.18588e12i	−0.213144	+	0.369176i
$836$	−3.47447e11	−	6.01796e11i	−0.0246014	−	0.0426109i
$837$	−7.43671e12	−	1.28808e13i	−0.523741	−	0.907145i
$838$	−1.80805e12	+	3.13164e12i	−0.126652	+	0.219368i
$839$	5.62810e12			0.392133			0.196066	−	0.980591i	$-0.437183\pi$
$839$	5.62810e12			0.392133			0.196066	+	0.980591i	$0.437183\pi$
$840$	−2.10188e12	+	5.95559e11i	−0.145664	+	0.0412732i
$841$	−1.25228e13			−0.863219
$842$	−3.01585e12	+	5.22361e12i	−0.206779	+	0.358151i
$843$	−2.84296e12	−	4.92415e12i	−0.193886	−	0.335820i
$844$	3.71080e12	+	6.42729e12i	0.251725	+	0.436000i
$845$	−5.01099e12	+	8.67930e12i	−0.338118	+	0.585638i
$846$	6.70828e12			0.450241
$847$	−8.78659e11	+	3.47748e12i	−0.0586604	+	0.232161i
$848$	−2.82327e11			−0.0187487
$849$	−2.79606e12	+	4.84292e12i	−0.184698	+	0.319906i
$850$	2.14936e12	+	3.72280e12i	0.141229	+	0.244616i
$851$	−6.71025e12	−	1.16225e13i	−0.438587	−	0.759655i
$852$	1.41127e12	−	2.44440e12i	0.0917558	−	0.158926i
$853$	1.54422e13			0.998709			0.499354	−	0.866398i	$-0.333571\pi$
$853$	1.54422e13			0.998709			0.499354	+	0.866398i	$0.333571\pi$
$854$	−1.46456e13	−	1.42323e13i	−0.942205	−	0.915620i
$855$	7.55417e11			0.0483437
$856$	2.77486e12	−	4.80621e12i	0.176648	−	0.305964i
$857$	8.04165e12	+	1.39286e13i	0.509251	+	0.882048i	0.999943	+	0.0107150i	$0.00341077\pi$
$857$	8.04165e12	+	1.39286e13i	0.509251	+	0.882048i	−0.490692	+	0.871333i	$0.663256\pi$
$858$	−1.25674e12	−	2.17674e12i	−0.0791685	−	0.137124i
$859$	1.51461e12	−	2.62338e12i	0.0949141	−	0.164396i	−0.814659	−	0.579941i	$-0.803076\pi$
$859$	1.51461e12	−	2.62338e12i	0.0949141	−	0.164396i	0.909573	+	0.415545i	$0.136409\pi$
$860$	−4.01654e11			−0.0250386
$861$	−6.06061e12	−	5.88961e12i	−0.375839	−	0.365235i
$862$	2.28964e12			0.141249
$863$	−6.78181e12	+	1.17464e13i	−0.416195	+	0.720871i	−0.995553	−	0.0942019i	$-0.969970\pi$
$863$	−6.78181e12	+	1.17464e13i	−0.416195	+	0.720871i	0.579358	+	0.815073i	$0.303303\pi$
$864$	1.34837e12	+	2.33545e12i	0.0823186	+	0.142580i
$865$	−2.51092e12	−	4.34904e12i	−0.152497	−	0.264132i
$866$	−1.09588e13	+	1.89813e13i	−0.662116	+	1.14682i
$867$	−4.88351e11			−0.0293526
$868$	−2.30393e12	+	9.11828e12i	−0.137762	+	0.545223i
$869$	2.50840e13			1.49213
$870$	9.46175e11	−	1.63882e12i	0.0559931	−	0.0969830i
$871$	5.15253e12	+	8.92444e12i	0.303346	+	0.525411i
$872$	−3.96870e12	−	6.87399e12i	−0.232447	−	0.402610i
$873$	−8.76815e11	+	1.51869e12i	−0.0510909	+	0.0884921i
$874$	−1.97511e12			−0.114496
$875$	1.81127e13	−	5.13214e12i	1.04459	−	0.295980i
$876$	7.24229e12			0.415535
$877$	−1.04192e13	+	1.80465e13i	−0.594751	+	1.03014i	0.398831	+	0.917024i	$0.369416\pi$
$877$	−1.04192e13	+	1.80465e13i	−0.594751	+	1.03014i	−0.993582	+	0.113114i	$0.963917\pi$
$878$	−8.44442e12	−	1.46262e13i	−0.479562	−	0.830626i
$879$	9.37516e12	+	1.62383e13i	0.529699	+	0.917465i
$880$	1.93490e12	−	3.35135e12i	0.108764	−	0.188385i
$881$	−1.45413e13			−0.813225			−0.406612	−	0.913601i	$-0.633290\pi$
$881$	−1.45413e13			−0.813225			−0.406612	+	0.913601i	$0.633290\pi$
$882$	−7.82599e12	−	4.22450e12i	−0.435442	−	0.235054i
$883$	6.56890e12			0.363638			0.181819	−	0.983332i	$-0.441802\pi$
$883$	6.56890e12			0.363638			0.181819	+	0.983332i	$0.441802\pi$
$884$	1.71034e12	−	2.96240e12i	0.0941995	−	0.163158i
$885$	2.77682e12	+	4.80959e12i	0.152161	+	0.263550i
$886$	5.89421e12	+	1.02091e13i	0.321347	+	0.556589i
$887$	−6.13102e11	+	1.06192e12i	−0.0332565	+	0.0576020i	−0.882175	−	0.470922i	$-0.843921\pi$
$887$	−6.13102e11	+	1.06192e12i	−0.0332565	+	0.0576020i	0.848918	+	0.528524i	$0.177254\pi$
$888$	1.71872e12			0.0927571
$889$	2.38537e11	−	6.75881e10i	0.0128085	−	0.00362921i
$890$	−1.97111e13			−1.05307
$891$	−1.98468e12	+	3.43757e12i	−0.105497	+	0.182727i
$892$	1.15453e12	+	1.99970e12i	0.0610607	+	0.105760i
$893$	−7.64174e11	−	1.32359e12i	−0.0402124	−	0.0696500i
$894$	−2.96977e12	+	5.14379e12i	−0.155490	+	0.269317i
$895$	−2.80058e12			−0.145896
$896$	4.17732e11	−	1.65326e12i	0.0216527	−	0.0856952i
$897$	−7.14409e12			−0.368452
$898$	−1.10240e12	+	1.90941e12i	−0.0565711	+	0.0979840i
$899$	−4.07329e12	−	7.05514e12i	−0.207982	−	0.360236i
$900$	−1.34012e12	−	2.32115e12i	−0.0680850	−	0.117927i
$901$	−7.61367e11	+	1.31873e12i	−0.0384886	+	0.0666643i
$902$	1.49698e13			0.752985
$903$	5.03025e11	+	4.88832e11i	0.0251765	+	0.0244661i
$904$	8.12260e12			0.404517
$905$	−1.95691e12	+	3.38946e12i	−0.0969732	+	0.167962i
$906$	−6.55920e12	−	1.13609e13i	−0.323425	−	0.560189i
$907$	6.95770e12	+	1.20511e13i	0.341376	+	0.591280i	0.984688	−	0.174323i	$-0.0557737\pi$
$907$	6.95770e12	+	1.20511e13i	0.341376	+	0.591280i	−0.643313	+	0.765604i	$0.722440\pi$
$908$	−1.69767e12	+	2.94045e12i	−0.0828833	+	0.143558i
$909$	−2.07363e13			−1.00738
$910$	−3.00967e12	−	2.92475e12i	−0.145490	−	0.141385i
$911$	5.99228e11			0.0288243			0.0144122	−	0.999896i	$-0.495412\pi$
$911$	5.99228e11			0.0288243			0.0144122	+	0.999896i	$0.495412\pi$
$912$	1.26473e11	−	2.19057e11i	0.00605369	−	0.0104853i
$913$	2.02086e13	+	3.50024e13i	0.962540	+	1.66717i
$914$	−6.53985e12	−	1.13274e13i	−0.309963	−	0.536872i
$915$	8.43491e12	−	1.46097e13i	0.397819	−	0.689043i
$916$	−1.96523e13			−0.922323
$917$	−2.48020e12	+	9.81591e12i	−0.115831	+	0.458425i
$918$	1.45450e13			0.675959
$919$	2.60385e12	−	4.51000e12i	0.120419	−	0.208572i	−0.799514	−	0.600648i	$-0.794909\pi$
$919$	2.60385e12	−	4.51000e12i	0.120419	−	0.208572i	0.919933	+	0.392075i	$0.128243\pi$
$920$	−5.49959e12	−	9.52557e12i	−0.253096	−	0.438375i
$921$	5.44467e12	+	9.43045e12i	0.249347	+	0.431881i
$922$	1.23272e13	−	2.13514e13i	0.561793	−	0.973054i
$923$	5.42215e12			0.245903
$924$	−6.50199e12	+	1.84231e12i	−0.293442	+	0.0831453i
$925$	−4.14918e12			−0.186348
$926$	−5.98366e12	+	1.03640e13i	−0.267434	+	0.463210i
$927$	−4.09751e12	−	7.09709e12i	−0.182247	−	0.315661i
$928$	7.38541e11	+	1.27919e12i	0.0326895	+	0.0566199i
$929$	1.01430e13	−	1.75682e13i	0.446783	−	0.773850i	−0.551392	−	0.834246i	$-0.685903\pi$
$929$	1.01430e13	−	1.75682e13i	0.446783	−	0.773850i	0.998174	+	0.0603962i	$0.0192364\pi$
$930$	−7.76904e12			−0.340560
$931$	5.79753e10	+	2.02535e12i	0.00252912	+	0.0883541i
$932$	−5.87236e11			−0.0254942
$933$	4.96474e12	−	8.59919e12i	0.214501	−	0.371527i
$934$	1.92859e12	+	3.34042e12i	0.0829238	+	0.143628i
$935$	−1.04359e13	−	1.80756e13i	−0.446559	−	0.773463i
$936$	−1.06639e12	+	1.84704e12i	−0.0454125	+	0.0786567i
$937$	−3.47244e13			−1.47166			−0.735828	−	0.677169i	$-0.763207\pi$
$937$	−3.47244e13			−1.47166			−0.735828	+	0.677169i	$0.763207\pi$
$938$	2.66576e13	−	7.55330e12i	1.12437	−	0.318584i
$939$	−3.41797e12			−0.143474
$940$	4.25561e12	−	7.37094e12i	0.177782	−	0.307927i
$941$	2.32792e12	+	4.03208e12i	0.0967866	+	0.167639i	0.910353	−	0.413833i	$-0.135810\pi$
$941$	2.32792e12	+	4.03208e12i	0.0967866	+	0.167639i	−0.813566	+	0.581472i	$0.802477\pi$
$942$	6.09172e12	+	1.05512e13i	0.252064	+	0.436588i
$943$	2.12744e13	−	3.68483e13i	0.876102	−	1.51745i
$944$	−4.33492e12			−0.177667
$945$	4.37143e12	−	1.73009e13i	0.178312	−	0.705708i
$946$	−1.24248e12			−0.0504405
$947$	1.98170e13	−	3.43240e13i	0.800687	−	1.38683i	−0.118478	−	0.992957i	$-0.537802\pi$
$947$	1.98170e13	−	3.43240e13i	0.800687	−	1.38683i	0.919165	−	0.393873i	$-0.128865\pi$
$948$	4.56536e12	+	7.90743e12i	0.183585	+	0.317979i
$949$	6.95627e12	+	1.20486e13i	0.278406	+	0.482213i
$950$	−3.05319e11	+	5.28827e11i	−0.0121618	+	0.0210648i
$951$	1.90963e13			0.757070
$952$	−6.59575e12	−	6.40965e12i	−0.260254	−	0.252911i
$953$	−3.33592e13			−1.31008			−0.655040	−	0.755594i	$-0.727348\pi$
$953$	−3.33592e13			−1.31008			−0.655040	+	0.755594i	$0.727348\pi$
$954$	4.74709e11	−	8.22219e11i	0.0185549	−	0.0321381i
$955$	−3.80864e11	−	6.59676e11i	−0.0148168	−	0.0256635i
$956$	5.20638e12	+	9.01771e12i	0.201593	+	0.349169i
$957$	2.92690e12	−	5.06955e12i	0.112799	−	0.195373i
$958$	−6.68941e12			−0.256592
$959$	−2.56773e13	−	2.49528e13i	−0.980316	−	0.952656i
$960$	1.40863e12			0.0535274
$961$	−3.50307e12	+	6.06750e12i	−0.132493	+	0.229485i
$962$	1.65084e12	+	2.85934e12i	0.0621467	+	0.107641i
$963$	9.33140e12	+	1.61625e13i	0.349646	+	0.605605i
$964$	−1.20794e12	+	2.09221e12i	−0.0450504	+	0.0780296i
$965$	6.23526e11			0.0231463
$966$	−4.70547e12	+	1.86229e13i	−0.173863	+	0.688099i
$967$	3.72454e13			1.36979			0.684893	−	0.728643i	$-0.259849\pi$
$967$	3.72454e13			1.36979			0.684893	+	0.728643i	$0.259849\pi$
$968$	1.15636e12	−	2.00287e12i	0.0423305	−	0.0733186i
$969$	−6.82133e11	−	1.18149e12i	−0.0248549	−	0.0430500i
$970$	1.11247e12	+	1.92686e12i	0.0403474	+	0.0698838i
$971$	−1.23678e13	+	2.14217e13i	−0.446485	+	0.773334i	−0.998154	−	0.0607287i	$-0.980658\pi$
$971$	−1.23678e13	+	2.14217e13i	−0.446485	+	0.773334i	0.551670	+	0.834063i	$0.313991\pi$
$972$	−1.44039e13			−0.517584
$973$	1.47002e13	−	4.16523e12i	0.525794	−	0.148981i
$974$	2.74516e13			0.977356
$975$	−1.10436e12	+	1.91280e12i	−0.0391371	+	0.0677875i
$976$	6.58390e12	+	1.14037e13i	0.232252	+	0.402272i
$977$	1.96826e13	+	3.40912e13i	0.691125	+	1.19706i	0.971470	+	0.237164i	$0.0762178\pi$
$977$	1.96826e13	+	3.40912e13i	0.691125	+	1.19706i	−0.280345	+	0.959899i	$0.590449\pi$
$978$	7.64311e12	−	1.32383e13i	0.267144	−	0.462707i
$979$	−6.09745e13			−2.12142
$980$	−9.60647e12	+	5.91910e12i	−0.332695	+	0.204993i
$981$	2.66921e13			0.920180
$982$	2.67785e12	−	4.63817e12i	0.0918935	−	0.159164i
$983$	1.85175e13	+	3.20732e13i	0.632544	+	1.09560i	0.987030	+	0.160537i	$0.0513227\pi$
$983$	1.85175e13	+	3.20732e13i	0.632544	+	1.09560i	−0.354486	+	0.935062i	$0.615344\pi$
$984$	2.72454e12	+	4.71905e12i	0.0926437	+	0.160464i
$985$	−2.67027e12	+	4.62505e12i	−0.0903842	+	0.156550i
$986$	7.96667e12			0.268430
$987$	−1.43004e13	+	4.05196e12i	−0.479647	+	0.135906i
$988$	4.85911e11			0.0162237
$989$	−1.76576e12	+	3.05838e12i	−0.0586878	+	0.101650i
$990$	6.50675e12	+	1.12700e13i	0.215281	+	0.372878i
$991$	−1.41148e13	−	2.44476e13i	−0.464883	−	0.805201i	0.534313	−	0.845287i	$-0.320570\pi$
$991$	−1.41148e13	−	2.44476e13i	−0.464883	−	0.805201i	−0.999196	+	0.0400853i	$0.987237\pi$
$992$	3.03208e12	−	5.25172e12i	0.0994118	−	0.172186i
$993$	−2.78434e13			−0.908763
$994$	3.57132e12	−	1.41343e13i	0.116035	−	0.459234i
$995$	−1.11218e13			−0.359726
$996$	−7.35606e12	+	1.27411e13i	−0.236853	+	0.410241i
$997$	−1.72255e13	−	2.98354e13i	−0.552132	−	0.956321i	−0.998120	−	0.0612823i	$-0.980481\pi$
$997$	−1.72255e13	−	2.98354e13i	−0.552132	−	0.956321i	0.445988	−	0.895039i	$-0.352852\pi$
$998$	5.68035e12	+	9.83866e12i	0.181254	+	0.313941i
$999$	−7.01948e12	+	1.21581e13i	−0.222977	+	0.386207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.10.c.b.9.2	✓	6
3.2	odd	2		126.10.g.e.37.1		6
4.3	odd	2		112.10.i.a.65.2		6
7.2	even	3		98.10.a.g.1.2		3
7.3	odd	6		98.10.c.l.67.2		6
7.4	even	3	inner	14.10.c.b.11.2	yes	6
7.5	odd	6		98.10.a.h.1.2		3
7.6	odd	2		98.10.c.l.79.2		6
21.11	odd	6		126.10.g.e.109.1		6
28.11	odd	6		112.10.i.a.81.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.c.b.9.2	✓	6	1.1	even	1	trivial
14.10.c.b.11.2	yes	6	7.4	even	3	inner
98.10.a.g.1.2		3	7.2	even	3
98.10.a.h.1.2		3	7.5	odd	6
98.10.c.l.67.2		6	7.3	odd	6
98.10.c.l.79.2		6	7.6	odd	2
112.10.i.a.65.2		6	4.3	odd	2
112.10.i.a.81.2		6	28.11	odd	6
126.10.g.e.37.1		6	3.2	odd	2
126.10.g.e.109.1		6	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 - 13.8564i) q^{2} +(38.4345 + 66.5705i) q^{3} +(-128.000 - 221.703i) q^{4} +(546.130 - 945.925i) q^{5} +1229.90 q^{6} +(6111.84 - 1731.76i) q^{7} -4096.00 q^{8} +(6887.08 - 11928.8i) q^{9} +O(q^{10})\)	\(q+(8.00000 - 13.8564i) q^{2} +(38.4345 + 66.5705i) q^{3} +(-128.000 - 221.703i) q^{4} +(546.130 - 945.925i) q^{5} +1229.90 q^{6} +(6111.84 - 1731.76i) q^{7} -4096.00 q^{8} +(6887.08 - 11928.8i) q^{9} +(-8738.08 - 15134.8i) q^{10} +(-27030.4 - 46818.1i) q^{11} +(9839.23 - 17042.0i) q^{12} +37802.6 q^{13} +(24898.8 - 98542.3i) q^{14} +83960.9 q^{15} +(-32768.0 + 56755.8i) q^{16} +(176735. + 306114. i) q^{17} +(-110193. - 190860. i) q^{18} +(-25105.3 + 43483.7i) q^{19} -279618. q^{20} +(350190. + 340309. i) q^{21} -864974. q^{22} +(-1.22926e6 + 2.12914e6i) q^{23} +(-157428. - 272673. i) q^{24} +(380047. + 658261. i) q^{25} +(302421. - 523808. i) q^{26} +2.57182e6 q^{27} +(-1.16625e6 - 1.13335e6i) q^{28} +1.40865e6 q^{29} +(671687. - 1.16340e6i) q^{30} +(-2.89162e6 - 5.00843e6i) q^{31} +(524288. + 908093. i) q^{32} +(2.07780e6 - 3.59886e6i) q^{33} +5.65552e6 q^{34} +(1.69974e6 - 6.72711e6i) q^{35} -3.52619e6 q^{36} +(-2.72938e6 + 4.72743e6i) q^{37} +(401685. + 695739. i) q^{38} +(1.45292e6 + 2.51653e6i) q^{39} +(-2.23695e6 + 3.87451e6i) q^{40} -1.73066e7 q^{41} +(7.51697e6 - 2.12990e6i) q^{42} +1.43644e6 q^{43} +(-6.91979e6 + 1.19854e7i) q^{44} +(-7.52248e6 - 1.30293e7i) q^{45} +(1.96682e7 + 3.40663e7i) q^{46} +(-1.52194e7 + 2.63607e7i) q^{47} -5.03768e6 q^{48} +(3.43556e7 - 2.11685e7i) q^{49} +1.21615e7 q^{50} +(-1.35854e7 + 2.35307e7i) q^{51} +(-4.83873e6 - 8.38092e6i) q^{52} +(2.15398e6 + 3.73080e6i) q^{53} +(2.05745e7 - 3.56361e7i) q^{54} -5.90485e7 q^{55} +(-2.50341e7 + 7.09329e6i) q^{56} -3.85964e6 q^{57} +(1.12692e7 - 1.95189e7i) q^{58} +(3.30728e7 + 5.72837e7i) q^{59} +(-1.07470e7 - 1.86143e7i) q^{60} +(1.00462e8 - 1.74006e8i) q^{61} -9.25317e7 q^{62} +(2.14350e7 - 8.48336e7i) q^{63} +1.67772e7 q^{64} +(2.06451e7 - 3.57584e7i) q^{65} +(-3.32448e7 - 5.75817e7i) q^{66} +(1.36301e8 + 2.36080e8i) q^{67} +(4.52441e7 - 7.83651e7i) q^{68} -1.88984e8 q^{69} +(-7.96156e7 - 7.73692e7i) q^{70} +1.43433e8 q^{71} +(-2.82095e7 + 4.88603e7i) q^{72} +(1.84016e8 + 3.18725e8i) q^{73} +(4.36701e7 + 7.56389e7i) q^{74} +(-2.92138e7 + 5.05998e7i) q^{75} +1.28539e7 q^{76} +(-2.46283e8 - 2.39334e8i) q^{77} +4.64935e7 q^{78} +(-2.31998e8 + 4.01832e8i) q^{79} +(3.57912e7 + 6.19921e7i) q^{80} +(-3.67120e7 - 6.35870e7i) q^{81} +(-1.38453e8 + 2.39808e8i) q^{82} -7.47626e8 q^{83} +(3.06231e7 - 1.21197e8i) q^{84} +3.86081e8 q^{85} +(1.14915e7 - 1.99038e7i) q^{86} +(5.41409e7 + 9.37748e7i) q^{87} +(1.10717e8 + 1.91767e8i) q^{88} +(5.63943e8 - 9.76778e8i) q^{89} -2.40719e8 q^{90} +(2.31043e8 - 6.54650e7i) q^{91} +6.29382e8 q^{92} +(2.22276e8 - 3.84992e8i) q^{93} +(2.43510e8 + 4.21771e8i) q^{94} +(2.74215e7 + 4.74955e7i) q^{95} +(-4.03015e7 + 6.98042e7i) q^{96} -1.27313e8 q^{97} +(-1.84743e7 - 6.45393e8i) q^{98} -7.44643e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 48 q^{2} + 71 q^{3} - 768 q^{4} - 1085 q^{5} + 2272 q^{6} - 6796 q^{7} - 24576 q^{8} - 9106 q^{9}+O(q^{10}) \) 6 * q + 48 * q^2 + 71 * q^3 - 768 * q^4 - 1085 * q^5 + 2272 * q^6 - 6796 * q^7 - 24576 * q^8 - 9106 * q^9	\( 6 q + 48 q^{2} + 71 q^{3} - 768 q^{4} - 1085 q^{5} + 2272 q^{6} - 6796 q^{7} - 24576 q^{8} - 9106 q^{9} + 17360 q^{10} + 2555 q^{11} + 18176 q^{12} + 36140 q^{13} + 43504 q^{14} - 706146 q^{15} - 196608 q^{16} + 20759 q^{17} + 145696 q^{18} + 1220649 q^{19} + 555520 q^{20} + 1951577 q^{21} + 81760 q^{22} - 1960903 q^{23} - 290816 q^{24} - 863572 q^{25} + 289120 q^{26} + 5777318 q^{27} + 2435840 q^{28} - 5212292 q^{29} - 5649168 q^{30} - 9377989 q^{31} + 3145728 q^{32} - 10778103 q^{33} + 664288 q^{34} + 20361719 q^{35} + 4662272 q^{36} - 25814913 q^{37} - 19530384 q^{38} + 37990822 q^{39} + 4444160 q^{40} + 418500 q^{41} - 2053952 q^{42} + 5888616 q^{43} + 654080 q^{44} - 37350558 q^{45} + 31374448 q^{46} + 48391269 q^{47} - 9306112 q^{48} + 108466086 q^{49} - 27634304 q^{50} - 75441987 q^{51} - 4625920 q^{52} + 102186411 q^{53} + 46218544 q^{54} - 456557402 q^{55} + 27836416 q^{56} + 86169178 q^{57} - 41698336 q^{58} + 144220135 q^{59} + 90386688 q^{60} + 280936871 q^{61} - 300095648 q^{62} + 33751838 q^{63} + 100663296 q^{64} - 186819738 q^{65} + 172449648 q^{66} + 170710399 q^{67} + 5314304 q^{68} - 1807308342 q^{69} - 347247824 q^{70} + 939517376 q^{71} + 37298176 q^{72} + 613838539 q^{73} + 413038608 q^{74} + 902254676 q^{75} - 624972288 q^{76} - 729499715 q^{77} + 1215706304 q^{78} + 197445809 q^{79} - 71106560 q^{80} + 887872901 q^{81} + 3348000 q^{82} - 2148362872 q^{83} - 532466944 q^{84} + 822545038 q^{85} + 47108928 q^{86} + 753428670 q^{87} - 10465280 q^{88} + 805730427 q^{89} - 1195217856 q^{90} + 17178248 q^{91} + 1003982336 q^{92} - 1721516327 q^{93} - 774260304 q^{94} + 1799421743 q^{95} - 74448896 q^{96} - 4525836188 q^{97} - 597954960 q^{98} - 2607425268 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 + 71 * q^3 - 768 * q^4 - 1085 * q^5 + 2272 * q^6 - 6796 * q^7 - 24576 * q^8 - 9106 * q^9 + 17360 * q^10 + 2555 * q^11 + 18176 * q^12 + 36140 * q^13 + 43504 * q^14 - 706146 * q^15 - 196608 * q^16 + 20759 * q^17 + 145696 * q^18 + 1220649 * q^19 + 555520 * q^20 + 1951577 * q^21 + 81760 * q^22 - 1960903 * q^23 - 290816 * q^24 - 863572 * q^25 + 289120 * q^26 + 5777318 * q^27 + 2435840 * q^28 - 5212292 * q^29 - 5649168 * q^30 - 9377989 * q^31 + 3145728 * q^32 - 10778103 * q^33 + 664288 * q^34 + 20361719 * q^35 + 4662272 * q^36 - 25814913 * q^37 - 19530384 * q^38 + 37990822 * q^39 + 4444160 * q^40 + 418500 * q^41 - 2053952 * q^42 + 5888616 * q^43 + 654080 * q^44 - 37350558 * q^45 + 31374448 * q^46 + 48391269 * q^47 - 9306112 * q^48 + 108466086 * q^49 - 27634304 * q^50 - 75441987 * q^51 - 4625920 * q^52 + 102186411 * q^53 + 46218544 * q^54 - 456557402 * q^55 + 27836416 * q^56 + 86169178 * q^57 - 41698336 * q^58 + 144220135 * q^59 + 90386688 * q^60 + 280936871 * q^61 - 300095648 * q^62 + 33751838 * q^63 + 100663296 * q^64 - 186819738 * q^65 + 172449648 * q^66 + 170710399 * q^67 + 5314304 * q^68 - 1807308342 * q^69 - 347247824 * q^70 + 939517376 * q^71 + 37298176 * q^72 + 613838539 * q^73 + 413038608 * q^74 + 902254676 * q^75 - 624972288 * q^76 - 729499715 * q^77 + 1215706304 * q^78 + 197445809 * q^79 - 71106560 * q^80 + 887872901 * q^81 + 3348000 * q^82 - 2148362872 * q^83 - 532466944 * q^84 + 822545038 * q^85 + 47108928 * q^86 + 753428670 * q^87 - 10465280 * q^88 + 805730427 * q^89 - 1195217856 * q^90 + 17178248 * q^91 + 1003982336 * q^92 - 1721516327 * q^93 - 774260304 * q^94 + 1799421743 * q^95 - 74448896 * q^96 - 4525836188 * q^97 - 597954960 * q^98 - 2607425268 * q^99

Introduction

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